Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(37,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.9924270768.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 25x^{4} + 12x^{3} + 582x^{2} - 144x + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 46.2 | ||
Root | \(0.124036 + 0.214837i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 63.46 |
Dual form | 63.4.e.c.37.2 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.124036 | + | 0.214837i | 0.0438533 | + | 0.0759562i | 0.887119 | − | 0.461541i | \(-0.152703\pi\) |
−0.843266 | + | 0.537497i | \(0.819370\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.96923 | − | 6.87491i | 0.496154 | − | 0.859364i | ||||
\(5\) | −6.21730 | − | 10.7687i | −0.556092 | − | 0.963180i | −0.997818 | − | 0.0660299i | \(-0.978967\pi\) |
0.441725 | − | 0.897150i | \(-0.354367\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.4385 | + | 1.73873i | −0.995583 | + | 0.0938826i | ||||
\(8\) | 3.95388 | 0.174739 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.54234 | − | 2.67141i | 0.0487730 | − | 0.0844773i | ||||
\(11\) | 30.1558 | − | 52.2313i | 0.826573 | − | 1.43167i | −0.0741379 | − | 0.997248i | \(-0.523621\pi\) |
0.900711 | − | 0.434419i | \(-0.143046\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 36.4269 | 0.777154 | 0.388577 | − | 0.921416i | \(-0.372967\pi\) | ||||
0.388577 | + | 0.921416i | \(0.372967\pi\) | |||||||
\(14\) | −2.66058 | − | 3.74559i | −0.0507906 | − | 0.0715037i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −31.2634 | − | 54.1498i | −0.488491 | − | 0.846091i | ||||
\(17\) | −24.3731 | + | 42.2154i | −0.347726 | + | 0.602279i | −0.985845 | − | 0.167659i | \(-0.946379\pi\) |
0.638119 | + | 0.769937i | \(0.279713\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.2750 | + | 43.7776i | 0.305183 | + | 0.528593i | 0.977302 | − | 0.211851i | \(-0.0679490\pi\) |
−0.672119 | + | 0.740443i | \(0.734616\pi\) | |||||||
\(20\) | −98.7116 | −1.10363 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 14.9616 | 0.144992 | ||||||||
\(23\) | 69.3962 | + | 120.198i | 0.629135 | + | 1.08969i | 0.987726 | + | 0.156199i | \(0.0499241\pi\) |
−0.358590 | + | 0.933495i | \(0.616743\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −14.8097 | + | 25.6511i | −0.118478 | + | 0.205209i | ||||
\(26\) | 4.51824 | + | 7.82583i | 0.0340808 | + | 0.0590297i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −61.2329 | + | 133.664i | −0.413283 | + | 0.902148i | ||||
\(29\) | 61.1345 | 0.391462 | 0.195731 | − | 0.980658i | \(-0.437292\pi\) | ||||
0.195731 | + | 0.980658i | \(0.437292\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.584676 | − | 1.01269i | 0.00338745 | − | 0.00586724i | −0.864327 | − | 0.502931i | \(-0.832255\pi\) |
0.867714 | + | 0.497064i | \(0.165588\pi\) | |||||||
\(32\) | 23.5711 | − | 40.8264i | 0.130213 | − | 0.225536i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −12.0925 | −0.0609957 | ||||||||
\(35\) | 133.361 | + | 187.748i | 0.644062 | + | 0.906719i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −34.7634 | − | 60.2120i | −0.154461 | − | 0.267535i | 0.778401 | − | 0.627767i | \(-0.216031\pi\) |
−0.932863 | + | 0.360232i | \(0.882698\pi\) | |||||||
\(38\) | −6.27001 | + | 10.8600i | −0.0267666 | + | 0.0463611i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −24.5825 | − | 42.5781i | −0.0971708 | − | 0.168305i | ||||
\(41\) | −308.115 | −1.17365 | −0.586823 | − | 0.809715i | \(-0.699622\pi\) | ||||
−0.586823 | + | 0.809715i | \(0.699622\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 174.443 | 0.618657 | 0.309329 | − | 0.950955i | \(-0.399896\pi\) | ||||
0.309329 | + | 0.950955i | \(0.399896\pi\) | |||||||
\(44\) | −239.390 | − | 414.636i | −0.820215 | − | 1.42065i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −17.2153 | + | 29.8177i | −0.0551794 | + | 0.0955734i | ||||
\(47\) | 194.681 | + | 337.197i | 0.604194 | + | 1.04649i | 0.992178 | + | 0.124829i | \(0.0398382\pi\) |
−0.387984 | + | 0.921666i | \(0.626828\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 336.954 | − | 64.1190i | 0.982372 | − | 0.186936i | ||||
\(50\) | −7.34774 | −0.0207825 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 144.587 | − | 250.432i | 0.385588 | − | 0.667858i | ||||
\(53\) | 157.467 | − | 272.742i | 0.408110 | − | 0.706867i | −0.586568 | − | 0.809900i | \(-0.699521\pi\) |
0.994678 | + | 0.103033i | \(0.0328547\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −749.950 | −1.83860 | ||||||||
\(56\) | −72.9035 | + | 6.87474i | −0.173967 | + | 0.0164049i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.58287 | + | 13.1339i | 0.0171669 | + | 0.0297339i | ||||
\(59\) | 422.263 | − | 731.381i | 0.931762 | − | 1.61386i | 0.151455 | − | 0.988464i | \(-0.451604\pi\) |
0.780308 | − | 0.625396i | \(-0.215062\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 169.269 | + | 293.182i | 0.355290 | + | 0.615380i | 0.987167 | − | 0.159688i | \(-0.0510489\pi\) |
−0.631878 | + | 0.775068i | \(0.717716\pi\) | |||||||
\(62\) | 0.290084 | 0.000594204 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −488.520 | −0.954141 | ||||||||
\(65\) | −226.477 | − | 392.270i | −0.432169 | − | 0.748539i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 485.775 | − | 841.387i | 0.885774 | − | 1.53421i | 0.0409498 | − | 0.999161i | \(-0.486962\pi\) |
0.844824 | − | 0.535044i | \(-0.179705\pi\) | |||||||
\(68\) | 193.485 | + | 335.125i | 0.345051 | + | 0.597646i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −23.7935 | + | 51.9384i | −0.0406266 | + | 0.0886832i | ||||
\(71\) | 98.4698 | 0.164595 | 0.0822973 | − | 0.996608i | \(-0.473774\pi\) | ||||
0.0822973 | + | 0.996608i | \(0.473774\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −355.117 | + | 615.082i | −0.569361 | + | 0.986162i | 0.427268 | + | 0.904125i | \(0.359476\pi\) |
−0.996629 | + | 0.0820374i | \(0.973857\pi\) | |||||||
\(74\) | 8.62383 | − | 14.9369i | 0.0135473 | − | 0.0234646i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 401.289 | 0.605671 | ||||||||
\(77\) | −465.210 | + | 1015.50i | −0.688514 | + | 1.50294i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 243.442 | + | 421.654i | 0.346701 | + | 0.600504i | 0.985661 | − | 0.168736i | \(-0.0539686\pi\) |
−0.638960 | + | 0.769240i | \(0.720635\pi\) | |||||||
\(80\) | −388.748 | + | 673.332i | −0.543292 | + | 0.941010i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −38.2174 | − | 66.1944i | −0.0514683 | − | 0.0891458i | ||||
\(83\) | −605.688 | −0.800999 | −0.400499 | − | 0.916297i | \(-0.631163\pi\) | ||||
−0.400499 | + | 0.916297i | \(0.631163\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 606.139 | 0.773470 | ||||||||
\(86\) | 21.6372 | + | 37.4767i | 0.0271302 | + | 0.0469908i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 119.232 | − | 206.517i | 0.144434 | − | 0.250168i | ||||
\(89\) | 109.034 | + | 188.853i | 0.129861 | + | 0.224925i | 0.923622 | − | 0.383303i | \(-0.125214\pi\) |
−0.793762 | + | 0.608229i | \(0.791880\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −671.656 | + | 63.3365i | −0.773722 | + | 0.0729612i | ||||
\(92\) | 1101.80 | 1.24859 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −48.2949 | + | 83.6491i | −0.0529919 | + | 0.0917846i | ||||
\(95\) | 314.284 | − | 544.357i | 0.339420 | − | 0.587893i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −782.288 | −0.818859 | −0.409429 | − | 0.912342i | \(-0.634272\pi\) | ||||
−0.409429 | + | 0.912342i | \(0.634272\pi\) | |||||||
\(98\) | 55.5695 | + | 64.4369i | 0.0572792 | + | 0.0664195i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 117.566 | + | 203.631i | 0.117566 | + | 0.203631i | ||||
\(101\) | −155.823 | + | 269.893i | −0.153514 | + | 0.265895i | −0.932517 | − | 0.361126i | \(-0.882392\pi\) |
0.779003 | + | 0.627021i | \(0.215726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 74.6289 | + | 129.261i | 0.0713922 | + | 0.123655i | 0.899512 | − | 0.436897i | \(-0.143922\pi\) |
−0.828119 | + | 0.560552i | \(0.810589\pi\) | |||||||
\(104\) | 144.028 | 0.135799 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 78.1265 | 0.0715879 | ||||||||
\(107\) | 425.760 | + | 737.437i | 0.384670 | + | 0.666269i | 0.991723 | − | 0.128393i | \(-0.0409818\pi\) |
−0.607053 | + | 0.794661i | \(0.707648\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −680.939 | + | 1179.42i | −0.598369 | + | 1.03640i | 0.394694 | + | 0.918813i | \(0.370851\pi\) |
−0.993062 | + | 0.117592i | \(0.962483\pi\) | |||||||
\(110\) | −93.0208 | − | 161.117i | −0.0806289 | − | 0.139653i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 670.601 | + | 944.081i | 0.565767 | + | 0.796493i | ||||
\(113\) | −1048.55 | −0.872917 | −0.436459 | − | 0.899724i | \(-0.643767\pi\) | ||||
−0.436459 | + | 0.899724i | \(0.643767\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 862.914 | − | 1494.61i | 0.699715 | − | 1.21194i | ||||
\(116\) | 242.657 | − | 420.294i | 0.194225 | − | 0.336408i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 209.503 | 0.163444 | ||||||||
\(119\) | 376.001 | − | 820.765i | 0.289646 | − | 0.632264i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1153.24 | − | 1997.47i | −0.866446 | − | 1.50073i | ||||
\(122\) | −41.9909 | + | 72.7303i | −0.0311613 | + | 0.0539729i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.64143 | − | 8.03919i | −0.00336139 | − | 0.00582210i | ||||
\(125\) | −1186.02 | −0.848647 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 488.408 | 0.341254 | 0.170627 | − | 0.985336i | \(-0.445421\pi\) | ||||
0.170627 | + | 0.985336i | \(0.445421\pi\) | |||||||
\(128\) | −249.163 | − | 431.563i | −0.172056 | − | 0.298009i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 56.1826 | − | 97.3111i | 0.0379041 | − | 0.0656519i | ||||
\(131\) | −927.114 | − | 1605.81i | −0.618338 | − | 1.07099i | −0.989789 | − | 0.142541i | \(-0.954473\pi\) |
0.371451 | − | 0.928453i | \(-0.378861\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −542.149 | − | 763.244i | −0.353461 | − | 0.497607i | ||||
\(134\) | 241.014 | 0.155377 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −96.3683 | + | 166.915i | −0.0607611 | + | 0.105241i | ||||
\(137\) | −255.558 | + | 442.639i | −0.159370 | + | 0.276038i | −0.934642 | − | 0.355591i | \(-0.884280\pi\) |
0.775271 | + | 0.631628i | \(0.217613\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2266.10 | 1.38279 | 0.691397 | − | 0.722475i | \(-0.256995\pi\) | ||||
0.691397 | + | 0.722475i | \(0.256995\pi\) | |||||||
\(140\) | 1820.09 | − | 171.633i | 1.09875 | − | 0.103612i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.2138 | + | 21.1549i | 0.00721802 | + | 0.0125020i | ||||
\(143\) | 1098.48 | − | 1902.62i | 0.642375 | − | 1.11263i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −380.091 | − | 658.338i | −0.217689 | − | 0.377048i | ||||
\(146\) | −176.189 | −0.0998735 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −551.936 | −0.306546 | ||||||||
\(149\) | 753.950 | + | 1305.88i | 0.414537 | + | 0.717999i | 0.995380 | − | 0.0960168i | \(-0.0306102\pi\) |
−0.580843 | + | 0.814016i | \(0.697277\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −795.913 | + | 1378.56i | −0.428943 | + | 0.742952i | −0.996780 | − | 0.0801897i | \(-0.974447\pi\) |
0.567836 | + | 0.823142i | \(0.307781\pi\) | |||||||
\(152\) | 99.9344 | + | 173.091i | 0.0533273 | + | 0.0923656i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −275.869 | + | 26.0142i | −0.144352 | + | 0.0136122i | ||||
\(155\) | −14.5404 | −0.00753494 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −582.080 | + | 1008.19i | −0.295892 | + | 0.512500i | −0.975192 | − | 0.221361i | \(-0.928950\pi\) |
0.679300 | + | 0.733861i | \(0.262283\pi\) | |||||||
\(158\) | −60.3911 | + | 104.601i | −0.0304080 | + | 0.0526682i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −586.195 | −0.289642 | ||||||||
\(161\) | −1488.55 | − | 2095.60i | −0.728660 | − | 1.02582i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 577.940 | + | 1001.02i | 0.277716 | + | 0.481019i | 0.970817 | − | 0.239822i | \(-0.0770892\pi\) |
−0.693101 | + | 0.720841i | \(0.743756\pi\) | |||||||
\(164\) | −1222.98 | + | 2118.26i | −0.582309 | + | 1.00859i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −75.1271 | − | 130.124i | −0.0351265 | − | 0.0608408i | ||||
\(167\) | 2890.61 | 1.33941 | 0.669707 | − | 0.742626i | \(-0.266420\pi\) | ||||
0.669707 | + | 0.742626i | \(0.266420\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −870.082 | −0.396032 | ||||||||
\(170\) | 75.1830 | + | 130.221i | 0.0339193 | + | 0.0587499i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 692.403 | − | 1199.28i | 0.306949 | − | 0.531651i | ||||
\(173\) | 947.468 | + | 1641.06i | 0.416385 | + | 0.721200i | 0.995573 | − | 0.0939940i | \(-0.0299635\pi\) |
−0.579188 | + | 0.815194i | \(0.696630\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 228.467 | − | 498.718i | 0.0986887 | − | 0.215426i | ||||
\(176\) | −3771.09 | −1.61509 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −27.0483 | + | 46.8491i | −0.0113897 | + | 0.0197275i | ||||
\(179\) | −2144.25 | + | 3713.94i | −0.895355 | + | 1.55080i | −0.0619893 | + | 0.998077i | \(0.519744\pi\) |
−0.833365 | + | 0.552723i | \(0.813589\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 383.732 | 0.157583 | 0.0787917 | − | 0.996891i | \(-0.474894\pi\) | ||||
0.0787917 | + | 0.996891i | \(0.474894\pi\) | |||||||
\(182\) | −96.9165 | − | 136.440i | −0.0394721 | − | 0.0555694i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 274.385 | + | 475.248i | 0.109934 | + | 0.190412i | ||||
\(185\) | −432.269 | + | 748.712i | −0.171790 | + | 0.297548i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1469.98 | + | 2546.07i | 0.574841 | + | 0.995655i | ||||
\(188\) | 3090.93 | 1.19909 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 155.930 | 0.0595388 | ||||||||
\(191\) | 192.655 | + | 333.689i | 0.0729845 | + | 0.126413i | 0.900208 | − | 0.435460i | \(-0.143414\pi\) |
−0.827224 | + | 0.561873i | \(0.810081\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −315.112 | + | 545.790i | −0.117525 | + | 0.203559i | −0.918786 | − | 0.394756i | \(-0.870829\pi\) |
0.801262 | + | 0.598314i | \(0.204163\pi\) | |||||||
\(194\) | −97.0318 | − | 168.064i | −0.0359097 | − | 0.0621974i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 896.634 | − | 2571.03i | 0.326762 | − | 0.936964i | ||||
\(197\) | 1250.23 | 0.452158 | 0.226079 | − | 0.974109i | \(-0.427409\pi\) | ||||
0.226079 | + | 0.974109i | \(0.427409\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 546.122 | − | 945.912i | 0.194541 | − | 0.336954i | −0.752209 | − | 0.658924i | \(-0.771012\pi\) |
0.946750 | + | 0.321970i | \(0.104345\pi\) | |||||||
\(200\) | −58.5558 | + | 101.422i | −0.0207026 | + | 0.0358580i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −77.3105 | −0.0269285 | ||||||||
\(203\) | −1127.23 | + | 106.296i | −0.389733 | + | 0.0367514i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1915.65 | + | 3318.00i | 0.652656 | + | 1.13043i | ||||
\(206\) | −18.5133 | + | 32.0660i | −0.00626158 | + | 0.0108454i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1138.83 | − | 1972.51i | −0.379633 | − | 0.657543i | ||||
\(209\) | 3048.75 | 1.00902 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3620.05 | −1.18111 | −0.590556 | − | 0.806997i | \(-0.701091\pi\) | ||||
−0.590556 | + | 0.806997i | \(0.701091\pi\) | |||||||
\(212\) | −1250.05 | − | 2165.15i | −0.404970 | − | 0.701429i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −105.619 | + | 182.937i | −0.0337382 | + | 0.0584362i | ||||
\(215\) | −1084.56 | − | 1878.52i | −0.344030 | − | 0.595878i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.01974 | + | 19.6890i | −0.00282166 | + | 0.00615935i | ||||
\(218\) | −337.844 | −0.104962 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2976.72 | + | 5155.84i | −0.912230 | + | 1.58003i | ||||
\(221\) | −887.835 | + | 1537.78i | −0.270236 | + | 0.468063i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −183.844 | −0.0552069 | −0.0276034 | − | 0.999619i | \(-0.508788\pi\) | ||||
−0.0276034 | + | 0.999619i | \(0.508788\pi\) | |||||||
\(224\) | −363.629 | + | 793.759i | −0.108464 | + | 0.236765i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −130.058 | − | 225.268i | −0.0382803 | − | 0.0663035i | ||||
\(227\) | 1139.76 | − | 1974.12i | 0.333253 | − | 0.577211i | −0.649895 | − | 0.760024i | \(-0.725187\pi\) |
0.983148 | + | 0.182813i | \(0.0585203\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2706.34 | − | 4687.51i | −0.780960 | − | 1.35266i | −0.931383 | − | 0.364040i | \(-0.881397\pi\) |
0.150424 | − | 0.988622i | \(-0.451936\pi\) | |||||||
\(230\) | 428.130 | 0.122739 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 241.719 | 0.0684035 | ||||||||
\(233\) | 569.184 | + | 985.856i | 0.160036 | + | 0.277191i | 0.934882 | − | 0.354960i | \(-0.115506\pi\) |
−0.774845 | + | 0.632151i | \(0.782172\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2420.78 | − | 4192.91i | 0.671975 | − | 1.16390i | ||||
\(236\) | −3352.12 | − | 5806.04i | −0.924595 | − | 1.60145i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 222.968 | − | 21.0257i | 0.0607263 | − | 0.00572644i | ||||
\(239\) | 6226.36 | 1.68515 | 0.842573 | − | 0.538583i | \(-0.181040\pi\) | ||||
0.842573 | + | 0.538583i | \(0.181040\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1598.10 | − | 2767.99i | 0.427147 | − | 0.739841i | −0.569471 | − | 0.822012i | \(-0.692852\pi\) |
0.996618 | + | 0.0821704i | \(0.0261852\pi\) | |||||||
\(242\) | 286.086 | − | 495.516i | 0.0759931 | − | 0.131624i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2687.47 | 0.705113 | ||||||||
\(245\) | −2785.42 | − | 3229.90i | −0.726343 | − | 0.842248i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 920.689 | + | 1594.68i | 0.237174 | + | 0.410798i | ||||
\(248\) | 2.31174 | − | 4.00406i | 0.000591919 | − | 0.00102523i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −147.109 | − | 254.801i | −0.0372160 | − | 0.0644600i | ||||
\(251\) | −239.608 | −0.0602546 | −0.0301273 | − | 0.999546i | \(-0.509591\pi\) | ||||
−0.0301273 | + | 0.999546i | \(0.509591\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8370.78 | 2.08010 | ||||||||
\(254\) | 60.5802 | + | 104.928i | 0.0149651 | + | 0.0259203i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1892.27 | + | 3277.51i | −0.461980 | + | 0.800173i | ||||
\(257\) | 349.559 | + | 605.453i | 0.0848439 | + | 0.146954i | 0.905325 | − | 0.424720i | \(-0.139628\pi\) |
−0.820481 | + | 0.571674i | \(0.806294\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 745.676 | + | 1049.77i | 0.178896 | + | 0.251852i | ||||
\(260\) | −3595.76 | −0.857690 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 229.991 | − | 398.356i | 0.0542324 | − | 0.0939333i | ||||
\(263\) | −459.520 | + | 795.912i | −0.107738 | + | 0.186609i | −0.914854 | − | 0.403785i | \(-0.867694\pi\) |
0.807115 | + | 0.590394i | \(0.201028\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3916.09 | −0.907787 | ||||||||
\(266\) | 96.7268 | − | 211.143i | 0.0222959 | − | 0.0486693i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3856.30 | − | 6679.32i | −0.878960 | − | 1.52240i | ||||
\(269\) | −1389.59 | + | 2406.84i | −0.314961 | + | 0.545529i | −0.979429 | − | 0.201788i | \(-0.935325\pi\) |
0.664468 | + | 0.747317i | \(0.268658\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1113.49 | − | 1928.62i | −0.249593 | − | 0.432308i | 0.713820 | − | 0.700329i | \(-0.246964\pi\) |
−0.963413 | + | 0.268021i | \(0.913630\pi\) | |||||||
\(272\) | 3047.94 | 0.679443 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −126.793 | −0.0279557 | ||||||||
\(275\) | 893.195 | + | 1547.06i | 0.195861 | + | 0.339241i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3653.85 | + | 6328.65i | −0.792557 | + | 1.37275i | 0.131821 | + | 0.991273i | \(0.457917\pi\) |
−0.924379 | + | 0.381476i | \(0.875416\pi\) | |||||||
\(278\) | 281.078 | + | 486.842i | 0.0606402 | + | 0.105032i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 527.295 | + | 742.333i | 0.112543 | + | 0.158439i | ||||
\(281\) | −2730.61 | −0.579696 | −0.289848 | − | 0.957073i | \(-0.593605\pi\) | ||||
−0.289848 | + | 0.957073i | \(0.593605\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 884.926 | − | 1532.74i | 0.185878 | − | 0.321950i | −0.757994 | − | 0.652261i | \(-0.773821\pi\) |
0.943872 | + | 0.330312i | \(0.107154\pi\) | |||||||
\(284\) | 390.849 | − | 676.971i | 0.0816642 | − | 0.141447i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 545.004 | 0.112681 | ||||||||
\(287\) | 5681.17 | − | 535.729i | 1.16846 | − | 0.110185i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1268.41 | + | 2196.95i | 0.258174 | + | 0.447170i | ||||
\(290\) | 94.2900 | − | 163.315i | 0.0190928 | − | 0.0330696i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2819.09 | + | 4882.80i | 0.564981 | + | 0.978576i | ||||
\(293\) | −8228.81 | −1.64072 | −0.820362 | − | 0.571844i | \(-0.806228\pi\) | ||||
−0.820362 | + | 0.571844i | \(0.806228\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10501.4 | −2.07258 | ||||||||
\(296\) | −137.451 | − | 238.071i | −0.0269904 | − | 0.0467487i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −187.034 | + | 323.952i | −0.0363577 | + | 0.0629733i | ||||
\(299\) | 2527.89 | + | 4378.43i | 0.488935 | + | 0.846860i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3216.45 | + | 303.309i | −0.615925 | + | 0.0580811i | ||||
\(302\) | −394.887 | −0.0752424 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1580.36 | − | 2737.27i | 0.298158 | − | 0.516425i | ||||
\(305\) | 2104.79 | − | 3645.61i | 0.395148 | − | 0.684416i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6019.62 | 1.11908 | 0.559541 | − | 0.828803i | \(-0.310977\pi\) | ||||
0.559541 | + | 0.828803i | \(0.310977\pi\) | |||||||
\(308\) | 5134.93 | + | 7229.02i | 0.949967 | + | 1.33738i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.80354 | − | 3.12382i | −0.000330432 | − | 0.000572326i | ||||
\(311\) | 596.857 | − | 1033.79i | 0.108825 | − | 0.188491i | −0.806469 | − | 0.591276i | \(-0.798624\pi\) |
0.915295 | + | 0.402785i | \(0.131958\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4423.02 | + | 7660.89i | 0.798734 | + | 1.38345i | 0.920441 | + | 0.390882i | \(0.127830\pi\) |
−0.121707 | + | 0.992566i | \(0.538837\pi\) | |||||||
\(314\) | −288.795 | −0.0519034 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3865.11 | 0.688068 | ||||||||
\(317\) | 3040.72 | + | 5266.68i | 0.538750 | + | 0.933142i | 0.998972 | + | 0.0453380i | \(0.0144365\pi\) |
−0.460222 | + | 0.887804i | \(0.652230\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1843.56 | − | 3193.13i | 0.323572 | − | 0.560442i | ||||
\(320\) | 3037.28 | + | 5260.72i | 0.530590 | + | 0.919009i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 265.578 | − | 579.725i | 0.0459630 | − | 0.100332i | ||||
\(323\) | −2464.12 | −0.424480 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −539.471 | + | 934.391i | −0.0920753 | + | 0.159479i | ||||
\(326\) | −143.371 | + | 248.325i | −0.0243576 | + | 0.0421885i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1218.25 | −0.205082 | ||||||||
\(329\) | −4175.91 | − | 5878.90i | −0.699773 | − | 0.985149i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1526.65 | − | 2644.23i | −0.253511 | − | 0.439094i | 0.710979 | − | 0.703213i | \(-0.248252\pi\) |
−0.964490 | + | 0.264119i | \(0.914919\pi\) | |||||||
\(332\) | −2404.12 | + | 4164.05i | −0.397419 | + | 0.688349i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 358.539 | + | 621.009i | 0.0587377 | + | 0.101737i | ||||
\(335\) | −12080.8 | −1.97029 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3865.80 | 0.624877 | 0.312438 | − | 0.949938i | \(-0.398854\pi\) | ||||
0.312438 | + | 0.949938i | \(0.398854\pi\) | |||||||
\(338\) | −107.921 | − | 186.925i | −0.0173673 | − | 0.0300811i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2405.90 | − | 4167.15i | 0.383760 | − | 0.664692i | ||||
\(341\) | −35.2627 | − | 61.0768i | −0.00559995 | − | 0.00969940i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6101.42 | + | 1768.13i | −0.960483 | + | 0.278338i | ||||
\(344\) | 689.726 | 0.108103 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −235.040 | + | 407.101i | −0.0365198 | + | 0.0632541i | ||||
\(347\) | −49.7965 | + | 86.2501i | −0.00770380 | + | 0.0133434i | −0.869852 | − | 0.493313i | \(-0.835786\pi\) |
0.862148 | + | 0.506657i | \(0.169119\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3607.34 | −0.553285 | −0.276643 | − | 0.960973i | \(-0.589222\pi\) | ||||
−0.276643 | + | 0.960973i | \(0.589222\pi\) | |||||||
\(350\) | 135.481 | − | 12.7757i | 0.0206907 | − | 0.00195112i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1421.61 | − | 2462.30i | −0.215262 | − | 0.372844i | ||||
\(353\) | 3565.37 | − | 6175.40i | 0.537579 | − | 0.931114i | −0.461455 | − | 0.887164i | \(-0.652672\pi\) |
0.999034 | − | 0.0439501i | \(-0.0139942\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −612.216 | − | 1060.39i | −0.0915298 | − | 0.158534i | ||||
\(356\) | 1731.13 | 0.257724 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1063.85 | −0.157057 | ||||||||
\(359\) | −3250.14 | − | 5629.41i | −0.477816 | − | 0.827602i | 0.521860 | − | 0.853031i | \(-0.325238\pi\) |
−0.999677 | + | 0.0254289i | \(0.991905\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2151.85 | − | 3727.11i | 0.313727 | − | 0.543390i | ||||
\(362\) | 47.5966 | + | 82.4398i | 0.00691056 | + | 0.0119694i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2230.52 | + | 4868.97i | −0.321185 | + | 0.701108i | ||||
\(365\) | 8831.49 | 1.26647 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −412.443 | + | 714.372i | −0.0586631 | + | 0.101607i | −0.893866 | − | 0.448335i | \(-0.852017\pi\) |
0.835202 | + | 0.549943i | \(0.185350\pi\) | |||||||
\(368\) | 4339.12 | − | 7515.58i | 0.614654 | − | 1.06461i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −214.468 | −0.0301342 | ||||||||
\(371\) | −2429.23 | + | 5302.73i | −0.339945 | + | 0.742059i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −666.925 | − | 1155.15i | −0.0925793 | − | 0.160352i | 0.816016 | − | 0.578029i | \(-0.196178\pi\) |
−0.908596 | + | 0.417677i | \(0.862845\pi\) | |||||||
\(374\) | −364.660 | + | 631.610i | −0.0504174 | + | 0.0873255i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 769.746 | + | 1333.24i | 0.105576 | + | 0.182863i | ||||
\(377\) | 2226.94 | 0.304226 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1338.29 | −0.181380 | −0.0906902 | − | 0.995879i | \(-0.528907\pi\) | ||||
−0.0906902 | + | 0.995879i | \(0.528907\pi\) | |||||||
\(380\) | −2494.93 | − | 4321.35i | −0.336809 | − | 0.583370i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −47.7924 | + | 82.7788i | −0.00640123 | + | 0.0110873i | ||||
\(383\) | 176.688 | + | 306.032i | 0.0235727 | + | 0.0408290i | 0.877571 | − | 0.479447i | \(-0.159163\pi\) |
−0.853998 | + | 0.520276i | \(0.825829\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13827.9 | − | 1303.96i | 1.83048 | − | 0.172613i | ||||
\(386\) | −156.341 | −0.0206154 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3105.08 | + | 5378.16i | −0.406280 | + | 0.703697i | ||||
\(389\) | 5868.59 | − | 10164.7i | 0.764908 | − | 1.32486i | −0.175387 | − | 0.984500i | \(-0.556118\pi\) |
0.940295 | − | 0.340360i | \(-0.110549\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6765.59 | −0.875066 | ||||||||
\(392\) | 1332.28 | − | 253.519i | 0.171658 | − | 0.0326649i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 155.073 | + | 268.595i | 0.0198286 | + | 0.0343442i | ||||
\(395\) | 3027.11 | − | 5243.10i | 0.385595 | − | 0.667871i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6640.71 | − | 11502.1i | −0.839516 | − | 1.45408i | −0.890300 | − | 0.455374i | \(-0.849505\pi\) |
0.0507841 | − | 0.998710i | \(-0.483828\pi\) | |||||||
\(398\) | 270.955 | 0.0341250 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1852.01 | 0.231501 | ||||||||
\(401\) | −3741.18 | − | 6479.91i | −0.465899 | − | 0.806961i | 0.533343 | − | 0.845899i | \(-0.320936\pi\) |
−0.999242 | + | 0.0389385i | \(0.987602\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.2979 | − | 36.8891i | 0.00263257 | − | 0.00455975i | ||||
\(404\) | 1236.99 | + | 2142.54i | 0.152333 | + | 0.263849i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −162.653 | − | 228.985i | −0.0198826 | − | 0.0279909i | ||||
\(407\) | −4193.27 | −0.510694 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6898.30 | − | 11948.2i | 0.833983 | − | 1.44450i | −0.0608735 | − | 0.998145i | \(-0.519389\pi\) |
0.894856 | − | 0.446355i | \(-0.147278\pi\) | |||||||
\(410\) | −475.218 | + | 823.102i | −0.0572423 | + | 0.0991466i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1184.88 | 0.141686 | ||||||||
\(413\) | −6514.21 | + | 14219.7i | −0.776134 | + | 1.69421i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3765.75 | + | 6522.46i | 0.445429 | + | 0.771506i | ||||
\(416\) | 858.622 | − | 1487.18i | 0.101196 | − | 0.175276i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 378.154 | + | 654.982i | 0.0442491 | + | 0.0766417i | ||||
\(419\) | −9497.56 | −1.10737 | −0.553683 | − | 0.832728i | \(-0.686778\pi\) | ||||
−0.553683 | + | 0.832728i | \(0.686778\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 624.367 | 0.0722797 | 0.0361399 | − | 0.999347i | \(-0.488494\pi\) | ||||
0.0361399 | + | 0.999347i | \(0.488494\pi\) | |||||||
\(422\) | −449.016 | − | 777.719i | −0.0517957 | − | 0.0897127i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 622.608 | − | 1078.39i | 0.0713126 | − | 0.123517i | ||||
\(425\) | −721.915 | − | 1250.39i | −0.0823954 | − | 0.142713i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3630.82 | − | 5111.52i | −0.411494 | − | 0.579306i | ||||
\(428\) | 6759.75 | 0.763423 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 269.050 | − | 466.007i | 0.0301738 | − | 0.0522625i | ||||
\(431\) | −6698.64 | + | 11602.4i | −0.748636 | + | 1.29668i | 0.199840 | + | 0.979829i | \(0.435958\pi\) |
−0.948476 | + | 0.316848i | \(0.897376\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14057.3 | −1.56016 | −0.780079 | − | 0.625681i | \(-0.784821\pi\) | ||||
−0.780079 | + | 0.625681i | \(0.784821\pi\) | |||||||
\(434\) | −5.34870 | + | 0.504377i | −0.000591580 | + | 5.57854e-5i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5405.61 | + | 9362.79i | 0.593766 | + | 1.02843i | ||||
\(437\) | −3507.98 | + | 6075.99i | −0.384003 | + | 0.665112i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8184.42 | + | 14175.8i | 0.889798 | + | 1.54117i | 0.840114 | + | 0.542409i | \(0.182488\pi\) |
0.0496832 | + | 0.998765i | \(0.484179\pi\) | |||||||
\(440\) | −2965.22 | −0.321275 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −440.494 | −0.0474031 | ||||||||
\(443\) | −589.354 | − | 1020.79i | −0.0632078 | − | 0.109479i | 0.832690 | − | 0.553740i | \(-0.186800\pi\) |
−0.895898 | + | 0.444261i | \(0.853466\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1355.80 | − | 2348.31i | 0.144429 | − | 0.250159i | ||||
\(446\) | −22.8033 | − | 39.4965i | −0.00242101 | − | 0.00419331i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9007.56 | − | 849.404i | 0.949926 | − | 0.0895772i | ||||
\(449\) | 12400.9 | 1.30342 | 0.651709 | − | 0.758469i | \(-0.274052\pi\) | ||||
0.651709 | + | 0.758469i | \(0.274052\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9291.45 | + | 16093.3i | −0.970105 | + | 1.68027i | ||||
\(452\) | −4161.95 | + | 7208.71i | −0.433101 | + | 0.750153i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 565.484 | 0.0584570 | ||||||||
\(455\) | 4857.94 | + | 6839.07i | 0.500535 | + | 0.704660i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4962.79 | − | 8595.81i | −0.507986 | − | 0.879858i | −0.999957 | − | 0.00924618i | \(-0.997057\pi\) |
0.491971 | − | 0.870611i | \(-0.336277\pi\) | |||||||
\(458\) | 671.366 | − | 1162.84i | 0.0684954 | − | 0.118637i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6850.21 | − | 11864.9i | −0.694332 | − | 1.20262i | ||||
\(461\) | 16010.3 | 1.61751 | 0.808755 | − | 0.588146i | \(-0.200142\pi\) | ||||
0.808755 | + | 0.588146i | \(0.200142\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17372.4 | 1.74377 | 0.871883 | − | 0.489714i | \(-0.162899\pi\) | ||||
0.871883 | + | 0.489714i | \(0.162899\pi\) | |||||||
\(464\) | −1911.27 | − | 3310.42i | −0.191225 | − | 0.331212i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −141.199 | + | 244.563i | −0.0140363 | + | 0.0243115i | ||||
\(467\) | 1054.03 | + | 1825.64i | 0.104443 | + | 0.180900i | 0.913510 | − | 0.406815i | \(-0.133361\pi\) |
−0.809068 | + | 0.587716i | \(0.800027\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7494.00 | + | 16358.5i | −0.737826 | + | 1.61059i | ||||
\(470\) | 1201.05 | 0.117873 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1669.58 | − | 2891.80i | 0.162815 | − | 0.282004i | ||||
\(473\) | 5260.45 | − | 9111.37i | 0.511365 | − | 0.885711i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1497.26 | −0.144629 | ||||||||
\(476\) | −4150.25 | − | 5842.77i | −0.399635 | − | 0.562612i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 772.293 | + | 1337.65i | 0.0738992 | + | 0.127997i | ||||
\(479\) | −1225.02 | + | 2121.80i | −0.116853 | + | 0.202395i | −0.918519 | − | 0.395377i | \(-0.870614\pi\) |
0.801666 | + | 0.597772i | \(0.203947\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1266.32 | − | 2193.34i | −0.120040 | − | 0.207916i | ||||
\(482\) | 792.887 | 0.0749274 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18309.9 | −1.71956 | ||||||||
\(485\) | 4863.72 | + | 8424.21i | 0.455361 | + | 0.788709i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −322.618 | + | 558.791i | −0.0300189 | + | 0.0519943i | −0.880645 | − | 0.473778i | \(-0.842890\pi\) |
0.850626 | + | 0.525772i | \(0.176223\pi\) | |||||||
\(488\) | 669.270 | + | 1159.21i | 0.0620828 | + | 0.107531i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 348.408 | − | 999.034i | 0.0321214 | − | 0.0921056i | ||||
\(491\) | −11766.1 | −1.08146 | −0.540731 | − | 0.841196i | \(-0.681852\pi\) | ||||
−0.540731 | + | 0.841196i | \(0.681852\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1490.03 | + | 2580.81i | −0.136121 | + | 0.235769i | ||||
\(494\) | −228.397 | + | 395.595i | −0.0208018 | + | 0.0360297i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −73.1159 | −0.00661896 | ||||||||
\(497\) | −1815.63 | + | 171.212i | −0.163868 | + | 0.0154526i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.0104 | + | 38.1232i | 0.00197459 | + | 0.00342010i | 0.867011 | − | 0.498289i | \(-0.166038\pi\) |
−0.865036 | + | 0.501709i | \(0.832705\pi\) | |||||||
\(500\) | −4707.59 | + | 8153.78i | −0.421059 | + | 0.729296i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −29.7200 | − | 51.4765i | −0.00264236 | − | 0.00457671i | ||||
\(503\) | −8290.27 | −0.734880 | −0.367440 | − | 0.930047i | \(-0.619766\pi\) | ||||
−0.367440 | + | 0.930047i | \(0.619766\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3875.19 | 0.341473 | ||||||||
\(506\) | 1038.28 | + | 1798.35i | 0.0912195 | + | 0.157997i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1938.60 | − | 3357.76i | 0.169314 | − | 0.293261i | ||||
\(509\) | 3457.52 | + | 5988.60i | 0.301084 | + | 0.521493i | 0.976382 | − | 0.216052i | \(-0.0693181\pi\) |
−0.675298 | + | 0.737545i | \(0.735985\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5478.36 | − | 11958.6i | 0.474263 | − | 1.03526i | ||||
\(512\) | −4925.45 | −0.425148 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −86.7157 | + | 150.196i | −0.00744137 | + | 0.0128888i | ||||
\(515\) | 927.980 | − | 1607.31i | 0.0794014 | − | 0.137527i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23483.0 | 1.99764 | ||||||||
\(518\) | −133.039 | + | 290.408i | −0.0112845 | + | 0.0246328i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −895.464 | − | 1550.99i | −0.0755167 | − | 0.130799i | ||||
\(521\) | 6699.64 | − | 11604.1i | 0.563371 | − | 0.975788i | −0.433828 | − | 0.900996i | \(-0.642837\pi\) |
0.997199 | − | 0.0747919i | \(-0.0238293\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4968.50 | + | 8605.69i | 0.415406 | + | 0.719504i | 0.995471 | − | 0.0950662i | \(-0.0303063\pi\) |
−0.580065 | + | 0.814570i | \(0.696973\pi\) | |||||||
\(524\) | −14719.7 | −1.22716 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −227.988 | −0.0188988 | ||||||||
\(527\) | 28.5007 | + | 49.3647i | 0.00235581 | + | 0.00408038i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3548.17 | + | 6145.60i | −0.291622 | + | 0.505104i | ||||
\(530\) | −485.736 | − | 841.320i | −0.0398095 | − | 0.0689521i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7399.15 | + | 697.733i | −0.602996 | + | 0.0568620i | ||||
\(533\) | −11223.7 | −0.912104 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5294.15 | − | 9169.74i | 0.427825 | − | 0.741014i | ||||
\(536\) | 1920.70 | − | 3326.75i | 0.154779 | − | 0.268085i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −689.435 | −0.0552484 | ||||||||
\(539\) | 6812.07 | − | 19533.1i | 0.544373 | − | 1.56095i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4643.08 | − | 8042.06i | −0.368987 | − | 0.639103i | 0.620421 | − | 0.784269i | \(-0.286962\pi\) |
−0.989407 | + | 0.145166i | \(0.953628\pi\) | |||||||
\(542\) | 276.226 | − | 478.437i | 0.0218910 | − | 0.0379163i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1149.00 | + | 1990.13i | 0.0905570 | + | 0.156849i | ||||
\(545\) | 16934.4 | 1.33099 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16821.6 | −1.31488 | −0.657438 | − | 0.753508i | \(-0.728360\pi\) | ||||
−0.657438 | + | 0.753508i | \(0.728360\pi\) | |||||||
\(548\) | 2028.73 | + | 3513.87i | 0.158144 | + | 0.273914i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −221.577 | + | 383.782i | −0.0171783 | + | 0.0297537i | ||||
\(551\) | 1545.17 | + | 2676.32i | 0.119467 | + | 0.206924i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5221.84 | − | 7351.37i | −0.401546 | − | 0.565302i | ||||
\(554\) | −1812.83 | −0.139025 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8994.69 | − | 15579.3i | 0.686079 | − | 1.18832i | ||||
\(557\) | 902.972 | − | 1563.99i | 0.0686897 | − | 0.118974i | −0.829635 | − | 0.558306i | \(-0.811451\pi\) |
0.898325 | + | 0.439332i | \(0.144785\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6354.40 | 0.480792 | ||||||||
\(560\) | 5997.18 | − | 13091.1i | 0.452548 | − | 0.987859i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −338.694 | − | 586.635i | −0.0254216 | − | 0.0440315i | ||||
\(563\) | 6107.45 | − | 10578.4i | 0.457190 | − | 0.791877i | −0.541621 | − | 0.840623i | \(-0.682189\pi\) |
0.998811 | + | 0.0487460i | \(0.0155225\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6519.17 | + | 11291.5i | 0.485423 | + | 0.840776i | ||||
\(566\) | 439.050 | 0.0326054 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 389.338 | 0.0287610 | ||||||||
\(569\) | 2141.89 | + | 3709.86i | 0.157808 | + | 0.273331i | 0.934078 | − | 0.357070i | \(-0.116224\pi\) |
−0.776270 | + | 0.630400i | \(0.782891\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3179.97 | + | 5507.87i | −0.233060 | + | 0.403673i | −0.958707 | − | 0.284395i | \(-0.908207\pi\) |
0.725647 | + | 0.688067i | \(0.241541\pi\) | |||||||
\(572\) | −8720.25 | − | 15103.9i | −0.637433 | − | 1.10407i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 819.764 | + | 1154.07i | 0.0596103 | + | 0.0839201i | ||||
\(575\) | −4110.95 | −0.298153 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7234.36 | + | 12530.3i | −0.521959 | + | 0.904059i | 0.477715 | + | 0.878515i | \(0.341465\pi\) |
−0.999674 | + | 0.0255444i | \(0.991868\pi\) | |||||||
\(578\) | −314.656 | + | 545.001i | −0.0226436 | + | 0.0392198i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6034.68 | −0.432028 | ||||||||
\(581\) | 11168.0 | − | 1053.13i | 0.797461 | − | 0.0751998i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9497.10 | − | 16449.5i | −0.674665 | − | 1.16855i | ||||
\(584\) | −1404.09 | + | 2431.96i | −0.0994894 | + | 0.172321i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1020.67 | − | 1767.85i | −0.0719513 | − | 0.124623i | ||||
\(587\) | 11132.6 | 0.782777 | 0.391388 | − | 0.920226i | \(-0.371995\pi\) | ||||
0.391388 | + | 0.920226i | \(0.371995\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 59.1108 | 0.00413517 | ||||||||
\(590\) | −1302.55 | − | 2256.07i | −0.0908897 | − | 0.157426i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2173.65 | + | 3764.87i | −0.150906 | + | 0.261377i | ||||
\(593\) | −9887.81 | − | 17126.2i | −0.684728 | − | 1.18598i | −0.973522 | − | 0.228592i | \(-0.926588\pi\) |
0.288794 | − | 0.957391i | \(-0.406746\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11176.3 | + | 1053.91i | −0.770054 | + | 0.0726154i | ||||
\(596\) | 11970.4 | 0.822696 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −627.098 | + | 1086.17i | −0.0428829 | + | 0.0742753i | ||||
\(599\) | −11945.5 | + | 20690.2i | −0.814825 | + | 1.41132i | 0.0946282 | + | 0.995513i | \(0.469834\pi\) |
−0.909453 | + | 0.415806i | \(0.863500\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19395.5 | 1.31641 | 0.658204 | − | 0.752840i | \(-0.271317\pi\) | ||||
0.658204 | + | 0.752840i | \(0.271317\pi\) | |||||||
\(602\) | −464.118 | − | 653.391i | −0.0314220 | − | 0.0442362i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6318.32 | + | 10943.7i | 0.425644 | + | 0.737237i | ||||
\(605\) | −14340.1 | + | 24837.8i | −0.963648 | + | 1.66909i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7298.36 | − | 12641.1i | −0.488025 | − | 0.845285i | 0.511880 | − | 0.859057i | \(-0.328949\pi\) |
−0.999905 | + | 0.0137724i | \(0.995616\pi\) | |||||||
\(608\) | 2383.04 | 0.158956 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1044.28 | 0.0693142 | ||||||||
\(611\) | 7091.62 | + | 12283.0i | 0.469552 | + | 0.813288i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −989.898 | + | 1714.55i | −0.0652229 | + | 0.112969i | −0.896793 | − | 0.442451i | \(-0.854109\pi\) |
0.831570 | + | 0.555420i | \(0.187442\pi\) | |||||||
\(614\) | 746.650 | + | 1293.24i | 0.0490755 | + | 0.0850012i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1839.39 | + | 4015.16i | −0.120310 | + | 0.262622i | ||||
\(617\) | −16262.4 | −1.06110 | −0.530551 | − | 0.847653i | \(-0.678015\pi\) | ||||
−0.530551 | + | 0.847653i | \(0.678015\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6010.49 | − | 10410.5i | 0.390278 | − | 0.675981i | −0.602208 | − | 0.798339i | \(-0.705712\pi\) |
0.992486 | + | 0.122358i | \(0.0390457\pi\) | |||||||
\(620\) | −57.7143 | + | 99.9642i | −0.00373849 | + | 0.00647526i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 296.127 | 0.0190894 | ||||||||
\(623\) | −2338.79 | − | 3292.58i | −0.150404 | − | 0.211740i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9225.06 | + | 15978.3i | 0.590404 | + | 1.02261i | ||||
\(626\) | −1097.23 | + | 1900.45i | −0.0700543 | + | 0.121338i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4620.82 | + | 8003.49i | 0.293616 | + | 0.508557i | ||||
\(629\) | 3389.16 | 0.214841 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25347.6 | 1.59916 | 0.799582 | − | 0.600557i | \(-0.205055\pi\) | ||||
0.799582 | + | 0.600557i | \(0.205055\pi\) | |||||||
\(632\) | 962.542 | + | 1667.17i | 0.0605821 | + | 0.104931i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −754.317 | + | 1306.51i | −0.0472519 | + | 0.0818428i | ||||
\(635\) | −3036.58 | − | 5259.51i | −0.189769 | − | 0.328689i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12274.2 | − | 2335.66i | 0.763454 | − | 0.145278i | ||||
\(638\) | 914.669 | 0.0567588 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3098.24 | + | 5366.31i | −0.191358 | + | 0.331441i | ||||
\(641\) | −2555.80 | + | 4426.78i | −0.157485 | + | 0.272772i | −0.933961 | − | 0.357374i | \(-0.883672\pi\) |
0.776476 | + | 0.630147i | \(0.217005\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10931.3 | −0.670435 | −0.335217 | − | 0.942141i | \(-0.608810\pi\) | ||||
−0.335217 | + | 0.942141i | \(0.608810\pi\) | |||||||
\(644\) | −20315.5 | + | 1915.73i | −1.24308 | + | 0.117221i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −305.639 | − | 529.382i | −0.0186149 | − | 0.0322419i | ||||
\(647\) | −9203.06 | + | 15940.2i | −0.559211 | + | 0.968582i | 0.438352 | + | 0.898804i | \(0.355563\pi\) |
−0.997563 | + | 0.0697783i | \(0.977771\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25467.3 | − | 44110.7i | −1.54034 | − | 2.66795i | ||||
\(650\) | −267.655 | −0.0161512 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9175.91 | 0.551160 | ||||||||
\(653\) | 9960.71 | + | 17252.5i | 0.596926 | + | 1.03391i | 0.993272 | + | 0.115805i | \(0.0369447\pi\) |
−0.396346 | + | 0.918101i | \(0.629722\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11528.3 | + | 19967.6i | −0.687707 | + | 1.19114i | ||||
\(656\) | 9632.74 | + | 16684.4i | 0.573316 | + | 0.993012i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 745.040 | − | 1626.33i | 0.0441408 | − | 0.0963542i | ||||
\(659\) | 18858.8 | 1.11477 | 0.557385 | − | 0.830254i | \(-0.311805\pi\) | ||||
0.557385 | + | 0.830254i | \(0.311805\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12916.0 | + | 22371.2i | −0.760023 | + | 1.31640i | 0.182815 | + | 0.983147i | \(0.441479\pi\) |
−0.942838 | + | 0.333251i | \(0.891854\pi\) | |||||||
\(662\) | 378.718 | − | 655.960i | 0.0222346 | − | 0.0385115i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2394.82 | −0.139965 | ||||||||
\(665\) | −4848.43 | + | 10583.6i | −0.282728 | + | 0.617162i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4242.50 | + | 7348.22i | 0.246282 | + | 0.426573i | ||||
\(668\) | 11473.5 | − | 19872.7i | 0.664555 | − | 1.15104i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1498.46 | − | 2595.41i | −0.0864037 | − | 0.149656i | ||||
\(671\) | 20417.7 | 1.17469 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16275.0 | −0.932178 | −0.466089 | − | 0.884738i | \(-0.654337\pi\) | ||||
−0.466089 | + | 0.884738i | \(0.654337\pi\) | |||||||
\(674\) | 479.498 | + | 830.515i | 0.0274029 | + | 0.0474633i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3453.55 | + | 5981.73i | −0.196493 | + | 0.340335i | ||||
\(677\) | −13135.9 | − | 22752.0i | −0.745720 | − | 1.29163i | −0.949857 | − | 0.312683i | \(-0.898772\pi\) |
0.204137 | − | 0.978942i | \(-0.434561\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14424.2 | − | 1360.19i | 0.815242 | − | 0.0768766i | ||||
\(680\) | 2396.60 | 0.135155 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.74769 | − | 15.1514i | 0.000491153 | − | 0.000850702i | ||||
\(683\) | −4036.14 | + | 6990.81i | −0.226118 | + | 0.391648i | −0.956654 | − | 0.291226i | \(-0.905937\pi\) |
0.730536 | + | 0.682874i | \(0.239270\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6355.51 | 0.354499 | ||||||||
\(686\) | −1136.65 | − | 1091.50i | −0.0632619 | − | 0.0607486i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5453.67 | − | 9446.04i | −0.302208 | − | 0.523440i | ||||
\(689\) | 5736.05 | − | 9935.13i | 0.317164 | − | 0.549344i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12242.6 | + | 21204.9i | 0.673997 | + | 1.16740i | 0.976761 | + | 0.214332i | \(0.0687575\pi\) |
−0.302763 | + | 0.953066i | \(0.597909\pi\) | |||||||
\(692\) | 15042.9 | 0.826364 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −24.7062 | −0.00135135 | ||||||||
\(695\) | −14089.1 | − | 24403.0i | −0.768962 | − | 1.33188i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7509.71 | − | 13007.2i | 0.408107 | − | 0.706862i | ||||
\(698\) | −447.440 | − | 774.989i | −0.0242634 | − | 0.0420254i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2521.80 | − | 3550.22i | −0.136164 | − | 0.191694i | ||||
\(701\) | −778.448 | −0.0419423 | −0.0209712 | − | 0.999780i | \(-0.506676\pi\) | ||||
−0.0209712 | + | 0.999780i | \(0.506676\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1757.29 | − | 3043.72i | 0.0942780 | − | 0.163294i | ||||
\(704\) | −14731.7 | + | 25516.0i | −0.788667 | + | 1.36601i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1768.93 | 0.0942985 | ||||||||
\(707\) | 2403.86 | − | 5247.35i | 0.127873 | − | 0.279133i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12086.0 | + | 20933.6i | 0.640197 | + | 1.10885i | 0.985389 | + | 0.170322i | \(0.0544806\pi\) |
−0.345192 | + | 0.938532i | \(0.612186\pi\) | |||||||
\(710\) | 151.874 | − | 263.053i | 0.00802777 | − | 0.0139045i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 431.109 | + | 746.703i | 0.0226917 | + | 0.0393032i | ||||
\(713\) | 162.297 | 0.00852466 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −27318.3 | −1.42888 | ||||||||
\(716\) | 17022.0 | + | 29483.0i | 0.888467 | + | 1.53887i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 806.269 | − | 1396.50i | 0.0419077 | − | 0.0725862i | ||||
\(719\) | −40.9418 | − | 70.9132i | −0.00212360 | − | 0.00367819i | 0.864962 | − | 0.501838i | \(-0.167343\pi\) |
−0.867085 | + | 0.498160i | \(0.834009\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1600.79 | − | 2253.61i | −0.0826860 | − | 0.116406i | ||||
\(722\) | 1067.63 | 0.0550318 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1523.12 | − | 2638.13i | 0.0781856 | − | 0.135421i | ||||
\(725\) | −905.382 | + | 1568.17i | −0.0463794 | + | 0.0803315i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32542.9 | −1.66018 | −0.830088 | − | 0.557632i | \(-0.811710\pi\) | ||||
−0.830088 | + | 0.557632i | \(0.811710\pi\) | |||||||
\(728\) | −2655.65 | + | 250.425i | −0.135199 | + | 0.0127491i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1095.42 | + | 1897.33i | 0.0555389 | + | 0.0961962i | ||||
\(731\) | −4251.70 | + | 7364.16i | −0.215123 | + | 0.372604i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2534.47 | + | 4389.83i | 0.127712 | + | 0.221203i | 0.922790 | − | 0.385304i | \(-0.125903\pi\) |
−0.795078 | + | 0.606507i | \(0.792570\pi\) | |||||||
\(734\) | −204.631 | −0.0102903 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6542.98 | 0.327687 | ||||||||
\(737\) | −29297.8 | − | 50745.3i | −1.46431 | − | 2.53627i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19214.2 | − | 33280.0i | 0.956437 | − | 1.65660i | 0.225392 | − | 0.974268i | \(-0.427634\pi\) |
0.731045 | − | 0.682329i | \(-0.239033\pi\) | |||||||
\(740\) | 3431.55 | + | 5943.62i | 0.170468 | + | 0.295259i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1440.53 | + | 135.841i | −0.0712717 | + | 0.00672086i | ||||
\(743\) | −21592.9 | −1.06617 | −0.533086 | − | 0.846061i | \(-0.678968\pi\) | ||||
−0.533086 | + | 0.846061i | \(0.678968\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9375.07 | − | 16238.1i | 0.461042 | − | 0.798548i | ||||
\(746\) | 165.445 | − | 286.560i | 0.00811982 | − | 0.0140639i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 23338.7 | 1.14084 | ||||||||
\(749\) | −9132.55 | − | 12856.9i | −0.445522 | − | 0.627212i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4056.30 | − | 7025.72i | −0.197093 | − | 0.341374i | 0.750492 | − | 0.660880i | \(-0.229817\pi\) |
−0.947585 | + | 0.319505i | \(0.896483\pi\) | |||||||
\(752\) | 12172.8 | − | 21083.9i | 0.590287 | − | 1.02241i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 276.220 | + | 478.428i | 0.0133413 | + | 0.0231078i | ||||
\(755\) | 19793.7 | 0.954129 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3108.01 | 0.149224 | 0.0746120 | − | 0.997213i | \(-0.476228\pi\) | ||||
0.0746120 | + | 0.997213i | \(0.476228\pi\) | |||||||
\(758\) | −165.996 | − | 287.513i | −0.00795414 | − | 0.0137770i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1242.64 | − | 2152.32i | 0.0593098 | − | 0.102728i | ||||
\(761\) | −3605.96 | − | 6245.71i | −0.171769 | − | 0.297512i | 0.767269 | − | 0.641325i | \(-0.221615\pi\) |
−0.939038 | + | 0.343812i | \(0.888282\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10504.8 | − | 22930.7i | 0.498425 | − | 1.08800i | ||||
\(764\) | 3058.77 | 0.144846 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −43.8313 | + | 75.9181i | −0.00206748 | + | 0.00358098i | ||||
\(767\) | 15381.7 | − | 26641.9i | 0.724123 | − | 1.25422i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7533.07 | −0.353250 | −0.176625 | − | 0.984278i | \(-0.556518\pi\) | ||||
−0.176625 | + | 0.984278i | \(0.556518\pi\) | |||||||
\(770\) | 1995.30 | + | 2809.01i | 0.0933838 | + | 0.131467i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2501.50 | + | 4332.73i | 0.116621 | + | 0.201993i | ||||
\(773\) | −12416.3 | + | 21505.7i | −0.577728 | + | 1.00065i | 0.418012 | + | 0.908442i | \(0.362727\pi\) |
−0.995739 | + | 0.0922122i | \(0.970606\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.3178 | + | 29.9952i | 0.000802674 | + | 0.00139027i | ||||
\(776\) | −3093.08 | −0.143086 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2911.66 | 0.134175 | ||||||||
\(779\) | −7787.61 | − | 13488.5i | −0.358177 | − | 0.620381i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2969.43 | − | 5143.20i | 0.136049 | − | 0.235644i | ||||
\(782\) | −839.177 | − | 1453.50i | −0.0383746 | − | 0.0664667i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −14006.4 | − | 16241.4i | −0.638045 | − | 0.739860i | ||||
\(785\) | 14475.9 | 0.658173 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18156.6 | + | 31448.1i | −0.822378 | + | 1.42440i | 0.0815287 | + | 0.996671i | \(0.474020\pi\) |
−0.903907 | + | 0.427730i | \(0.859314\pi\) | |||||||
\(788\) | 4962.45 | − | 8595.21i | 0.224340 | − | 0.388568i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1501.88 | 0.0676386 | ||||||||
\(791\) | 19333.7 | − | 1823.15i | 0.869062 | − | 0.0819517i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6165.94 | + | 10679.7i | 0.276115 | + | 0.478245i | ||||
\(794\) | 1647.37 | − | 2853.34i | 0.0736311 | − | 0.127533i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4335.37 | − | 7509.08i | −0.193044 | − | 0.334362i | ||||
\(797\) | −31665.7 | −1.40735 | −0.703675 | − | 0.710522i | \(-0.748459\pi\) | ||||
−0.703675 | + | 0.710522i | \(0.748459\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18979.9 | −0.840375 | ||||||||
\(800\) | 698.162 | + | 1209.25i | 0.0308547 | + | 0.0534419i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 928.081 | − | 1607.48i | 0.0408625 | − | 0.0707759i | ||||
\(803\) | 21417.7 | + | 37096.5i | 0.941237 | + | 1.63027i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13312.1 | + | 29058.7i | −0.582844 | + | 1.27228i | ||||
\(806\) | 10.5668 | 0.000461788 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −616.105 | + | 1067.13i | −0.0268249 | + | 0.0464621i | ||||
\(809\) | 6192.30 | − | 10725.4i | 0.269110 | − | 0.466111i | −0.699523 | − | 0.714610i | \(-0.746604\pi\) |
0.968632 | + | 0.248499i | \(0.0799373\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16742.4 | 0.724914 | 0.362457 | − | 0.932000i | \(-0.381938\pi\) | ||||
0.362457 | + | 0.932000i | \(0.381938\pi\) | |||||||
\(812\) | −3743.44 | + | 8171.49i | −0.161784 | + | 0.353156i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −520.116 | − | 900.868i | −0.0223957 | − | 0.0387904i | ||||
\(815\) | 7186.45 | − | 12447.3i | 0.308872 | − | 0.534982i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4409.04 | + | 7636.67i | 0.188804 | + | 0.327018i | ||||
\(818\) | 3422.55 | 0.146292 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 30414.6 | 1.29527 | ||||||||
\(821\) | 13228.2 | + | 22911.9i | 0.562322 | + | 0.973970i | 0.997293 | + | 0.0735259i | \(0.0234252\pi\) |
−0.434971 | + | 0.900444i | \(0.643241\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11549.3 | + | 20003.9i | −0.489164 | + | 0.847257i | −0.999922 | − | 0.0124673i | \(-0.996031\pi\) |
0.510758 | + | 0.859724i | \(0.329365\pi\) | |||||||
\(824\) | 295.074 | + | 511.083i | 0.0124750 | + | 0.0216073i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3862.92 | + | 364.270i | −0.162722 | + | 0.0153445i | ||||
\(827\) | −20647.6 | −0.868183 | −0.434092 | − | 0.900869i | \(-0.642931\pi\) | ||||
−0.434092 | + | 0.900869i | \(0.642931\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11684.3 | − | 20237.7i | 0.489519 | − | 0.847871i | −0.510409 | − | 0.859932i | \(-0.670506\pi\) |
0.999927 | + | 0.0120609i | \(0.00383919\pi\) | |||||||
\(830\) | −934.176 | + | 1618.04i | −0.0390671 | + | 0.0676662i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −17795.3 | −0.741514 | ||||||||
\(833\) | −5505.78 | + | 15787.4i | −0.229009 | + | 0.656664i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17971.8 | − | 31128.0i | −0.744838 | − | 1.29010i | ||||
\(836\) | 12101.2 | − | 20959.8i | 0.500631 | − | 0.867119i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1178.04 | − | 2040.42i | −0.0485617 | − | 0.0841113i | ||||
\(839\) | −16735.5 | −0.688645 | −0.344322 | − | 0.938851i | \(-0.611891\pi\) | ||||
−0.344322 | + | 0.938851i | \(0.611891\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20651.6 | −0.846758 | ||||||||
\(842\) | 77.4439 | + | 134.137i | 0.00316971 | + | 0.00549009i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14368.8 | + | 24887.5i | −0.586013 | + | 1.01500i | ||||
\(845\) | 5409.56 | + | 9369.63i | 0.220230 | + | 0.381450i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24737.0 | + | 34825.1i | 1.00351 | + | 1.41276i | ||||
\(848\) | −19691.9 | −0.797432 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 179.087 | − | 310.188i | 0.00722662 | − | 0.0125169i | ||||
\(851\) | 4824.90 | − | 8356.97i | 0.194354 | − | 0.336631i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10294.5 | −0.413219 | −0.206609 | − | 0.978424i | \(-0.566243\pi\) | ||||
−0.206609 | + | 0.978424i | \(0.566243\pi\) | |||||||
\(854\) | 647.789 | − | 1414.05i | 0.0259565 | − | 0.0566600i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1683.40 | + | 2915.74i | 0.0672168 | + | 0.116423i | ||||
\(857\) | −16394.3 | + | 28395.7i | −0.653463 | + | 1.13183i | 0.328813 | + | 0.944395i | \(0.393351\pi\) |
−0.982277 | + | 0.187437i | \(0.939982\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2454.88 | + | 4251.98i | 0.0975081 | + | 0.168889i | 0.910653 | − | 0.413173i | \(-0.135579\pi\) |
−0.813145 | + | 0.582062i | \(0.802246\pi\) | |||||||
\(860\) | −17219.5 | −0.682768 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3323.49 | −0.131321 | ||||||||
\(863\) | 8897.48 | + | 15410.9i | 0.350954 | + | 0.607871i | 0.986417 | − | 0.164261i | \(-0.0525239\pi\) |
−0.635463 | + | 0.772132i | \(0.719191\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11781.4 | − | 20406.0i | 0.463097 | − | 0.802108i | ||||
\(866\) | −1743.60 | − | 3020.01i | −0.0684181 | − | 0.118504i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 99.5588 | + | 140.160i | 0.00389314 | + | 0.00548081i | ||||
\(869\) | 29364.7 | 1.14629 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17695.3 | − | 30649.1i | 0.688383 | − | 1.19231i | ||||
\(872\) | −2692.36 | + | 4663.30i | −0.104558 | + | 0.181100i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1740.46 | −0.0673592 | ||||||||
\(875\) | 21868.4 | − | 2062.17i | 0.844899 | − | 0.0796732i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17336.1 | − | 30027.0i | −0.667501 | − | 1.15615i | −0.978601 | − | 0.205769i | \(-0.934030\pi\) |
0.311099 | − | 0.950377i | \(-0.399303\pi\) | |||||||
\(878\) | −2030.33 | + | 3516.63i | −0.0780412 | + | 0.135171i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 23446.0 | + | 40609.7i | 0.898141 | + | 1.55563i | ||||
\(881\) | −40848.2 | −1.56210 | −0.781051 | − | 0.624467i | \(-0.785316\pi\) | ||||
−0.781051 | + | 0.624467i | \(0.785316\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30035.1 | 1.14469 | 0.572345 | − | 0.820013i | \(-0.306034\pi\) | ||||
0.572345 | + | 0.820013i | \(0.306034\pi\) | |||||||
\(884\) | 7048.04 | + | 12207.6i | 0.268158 | + | 0.464463i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 146.202 | − | 253.230i | 0.00554375 | − | 0.00960205i | ||||
\(887\) | 16605.4 | + | 28761.3i | 0.628583 | + | 1.08874i | 0.987836 | + | 0.155498i | \(0.0496983\pi\) |
−0.359253 | + | 0.933240i | \(0.616968\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9005.49 | + | 849.210i | −0.339746 | + | 0.0320378i | ||||
\(890\) | 672.671 | 0.0253348 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −729.721 | + | 1263.91i | −0.0273911 | + | 0.0474428i | ||||
\(893\) | −9841.11 | + | 17045.3i | −0.368780 | + | 0.638745i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 53325.7 | 1.99160 | ||||||||
\(896\) | 5344.55 | + | 7524.13i | 0.199273 | + | 0.280540i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1538.16 | + | 2664.17i | 0.0571592 | + | 0.0990027i | ||||
\(899\) | 35.7439 | − | 61.9102i | 0.00132606 | − | 0.00229680i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7675.93 | + | 13295.1i | 0.283820 | + | 0.491591i | ||||
\(902\) | −4609.90 | −0.170169 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4145.86 | −0.152532 | ||||||||
\(905\) | −2385.78 | − | 4132.29i | −0.0876310 | − | 0.151781i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1248.92 | + | 2163.18i | −0.0457217 | + | 0.0791923i | −0.887981 | − | 0.459881i | \(-0.847892\pi\) |
0.842259 | + | 0.539073i | \(0.181225\pi\) | |||||||
\(908\) | −9047.93 | − | 15671.5i | −0.330690 | − | 0.572771i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −866.723 | + | 1891.95i | −0.0315732 | + | 0.0689205i | ||||
\(911\) | 1895.00 | 0.0689180 | 0.0344590 | − | 0.999406i | \(-0.489029\pi\) | ||||
0.0344590 | + | 0.999406i | \(0.489029\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18265.0 | + | 31635.9i | −0.662084 | + | 1.14676i | ||||
\(914\) | 1231.13 | − | 2132.38i | 0.0445538 | − | 0.0771694i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −42968.3 | −1.54990 | ||||||||
\(917\) | 19886.6 | + | 27996.6i | 0.716155 | + | 1.00821i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3135.36 | − | 5430.59i | −0.112542 | − | 0.194928i | 0.804253 | − | 0.594287i | \(-0.202566\pi\) |
−0.916794 | + | 0.399360i | \(0.869233\pi\) | |||||||
\(920\) | 3411.86 | − | 5909.52i | 0.122267 | − | 0.211773i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1985.85 | + | 3439.59i | 0.0709332 | + | 0.122860i | ||||
\(923\) | 3586.95 | 0.127915 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2059.34 | 0.0732008 | ||||||||
\(926\) | 2154.80 | + | 3732.23i | 0.0764700 | + | 0.132450i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1441.01 | − | 2495.90i | 0.0509735 | − | 0.0882887i | ||||
\(929\) | −15776.3 | − | 27325.3i | −0.557161 | − | 0.965032i | −0.997732 | − | 0.0673138i | \(-0.978557\pi\) |
0.440570 | − | 0.897718i | \(-0.354776\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11323.5 | + | 13130.4i | 0.398616 | + | 0.462225i | ||||
\(932\) | 9036.89 | 0.317611 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −261.476 | + | 452.889i | −0.00916033 | + | 0.0158662i | ||||
\(935\) | 18278.6 | − | 31659.4i | 0.639330 | − | 1.10735i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22030.2 | −0.768084 | −0.384042 | − | 0.923316i | \(-0.625468\pi\) | ||||
−0.384042 | + | 0.923316i | \(0.625468\pi\) | |||||||
\(938\) | −4443.93 | + | 419.059i | −0.154690 | + | 0.0145872i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −19217.3 | − | 33285.3i | −0.666806 | − | 1.15494i | ||||
\(941\) | −16269.3 | + | 28179.3i | −0.563618 | + | 0.976214i | 0.433559 | + | 0.901125i | \(0.357258\pi\) |
−0.997177 | + | 0.0750892i | \(0.976076\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21382.0 | − | 37034.8i | −0.738383 | − | 1.27892i | ||||
\(944\) | −52805.6 | −1.82063 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2609.94 | 0.0897003 | ||||||||
\(947\) | −20355.5 | − | 35256.8i | −0.698485 | − | 1.20981i | −0.968992 | − | 0.247093i | \(-0.920525\pi\) |
0.270507 | − | 0.962718i | \(-0.412809\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12935.8 | + | 22405.5i | −0.442481 | + | 0.766400i | ||||
\(950\) | −185.714 | − | 321.666i | −0.00634248 | − | 0.0109855i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1486.66 | − | 3245.21i | 0.0506124 | − | 0.110481i | ||||
\(953\) | 52516.4 | 1.78507 | 0.892536 | − | 0.450976i | \(-0.148924\pi\) | ||||
0.892536 | + | 0.450976i | \(0.148924\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2395.59 | − | 4149.29i | 0.0811723 | − | 0.140595i | ||||
\(956\) | 24713.9 | − | 42805.7i | 0.836091 | − | 1.44815i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −607.786 | −0.0204976 | ||||||||
\(959\) | 3942.46 | − | 8605.92i | 0.132751 | − | 0.289781i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14894.8 | + | 25798.6i | 0.499977 | + | 0.865986i | ||||
\(962\) | 314.139 | − | 544.105i | 0.0105283 | − | 0.0182356i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12686.4 | − | 21973.6i | −0.423862 | − | 0.734150i | ||||
\(965\) | 7836.58 | 0.261418 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14721.6 | 0.489570 | 0.244785 | − | 0.969577i | \(-0.421283\pi\) | ||||
0.244785 | + | 0.969577i | \(0.421283\pi\) | |||||||
\(968\) | −4559.78 | − | 7897.77i | −0.151402 | − | 0.262235i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1206.55 | + | 2089.81i | −0.0399382 | + | 0.0691750i | ||||
\(971\) | 6886.25 | + | 11927.3i | 0.227590 | + | 0.394198i | 0.957093 | − | 0.289779i | \(-0.0935819\pi\) |
−0.729503 | + | 0.683978i | \(0.760249\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −41783.5 | + | 3940.14i | −1.37669 | + | 0.129820i | ||||
\(974\) | −160.065 | −0.00526572 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10583.8 | − | 18331.8i | 0.347111 | − | 0.601215i | ||||
\(977\) | 12391.0 | − | 21461.9i | 0.405757 | − | 0.702791i | −0.588653 | − | 0.808386i | \(-0.700341\pi\) |
0.994409 | + | 0.105595i | \(0.0336748\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13152.0 | 0.429358 | ||||||||
\(980\) | −33261.2 | + | 6329.29i | −1.08417 | + | 0.206308i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1459.42 | − | 2527.79i | −0.0474257 | − | 0.0821437i | ||||
\(983\) | 21402.4 | − | 37070.0i | 0.694435 | − | 1.20280i | −0.275936 | − | 0.961176i | \(-0.588988\pi\) |
0.970371 | − | 0.241620i | \(-0.0776788\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7773.05 | − | 13463.3i | −0.251442 | − | 0.435510i | ||||
\(986\) | −739.271 | −0.0238775 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14617.7 | 0.470700 | ||||||||
\(989\) | 12105.7 | + | 20967.6i | 0.389219 | + | 0.674147i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −224.931 | + | 389.592i | −0.00721006 | + | 0.0124882i | −0.869608 | − | 0.493743i | \(-0.835628\pi\) |
0.862398 | + | 0.506231i | \(0.168962\pi\) | |||||||
\(992\) | −27.5630 | − | 47.7404i | −0.000882182 | − | 0.00152798i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −261.986 | − | 368.827i | −0.00835986 | − | 0.0117691i | ||||
\(995\) | −13581.6 | −0.432730 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10736.9 | − | 18596.8i | 0.341063 | − | 0.590739i | −0.643567 | − | 0.765390i | \(-0.722546\pi\) |
0.984630 | + | 0.174651i | \(0.0558796\pi\) | |||||||
\(998\) | −5.46017 | + | 9.45729i | −0.000173185 | + | 0.000299965i | ||||
\(999\) | 0 | 0 |
(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 | 63.4.e.c.46.2 | 6 | ||
3.2 | odd | 2 | 21.4.e.b.4.2 | ✓ | 6 | ||
7.2 | even | 3 | inner | 63.4.e.c.37.2 | 6 | ||
7.3 | odd | 6 | 441.4.a.t.1.2 | 3 | |||
7.4 | even | 3 | 441.4.a.s.1.2 | 3 | |||
7.5 | odd | 6 | 441.4.e.w.226.2 | 6 | |||
7.6 | odd | 2 | 441.4.e.w.361.2 | 6 | |||
12.11 | even | 2 | 336.4.q.k.193.3 | 6 | |||
21.2 | odd | 6 | 21.4.e.b.16.2 | yes | 6 | ||
21.5 | even | 6 | 147.4.e.n.79.2 | 6 | |||
21.11 | odd | 6 | 147.4.a.l.1.2 | 3 | |||
21.17 | even | 6 | 147.4.a.m.1.2 | 3 | |||
21.20 | even | 2 | 147.4.e.n.67.2 | 6 | |||
84.11 | even | 6 | 2352.4.a.ci.1.1 | 3 | |||
84.23 | even | 6 | 336.4.q.k.289.3 | 6 | |||
84.59 | odd | 6 | 2352.4.a.cg.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.e.b.4.2 | ✓ | 6 | 3.2 | odd | 2 | ||
21.4.e.b.16.2 | yes | 6 | 21.2 | odd | 6 | ||
63.4.e.c.37.2 | 6 | 7.2 | even | 3 | inner | ||
63.4.e.c.46.2 | 6 | 1.1 | even | 1 | trivial | ||
147.4.a.l.1.2 | 3 | 21.11 | odd | 6 | |||
147.4.a.m.1.2 | 3 | 21.17 | even | 6 | |||
147.4.e.n.67.2 | 6 | 21.20 | even | 2 | |||
147.4.e.n.79.2 | 6 | 21.5 | even | 6 | |||
336.4.q.k.193.3 | 6 | 12.11 | even | 2 | |||
336.4.q.k.289.3 | 6 | 84.23 | even | 6 | |||
441.4.a.s.1.2 | 3 | 7.4 | even | 3 | |||
441.4.a.t.1.2 | 3 | 7.3 | odd | 6 | |||
441.4.e.w.226.2 | 6 | 7.5 | odd | 6 | |||
441.4.e.w.361.2 | 6 | 7.6 | odd | 2 | |||
2352.4.a.cg.1.3 | 3 | 84.59 | odd | 6 | |||
2352.4.a.ci.1.1 | 3 | 84.11 | even | 6 |