Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,4,Mod(4,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.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: | \(1.23904011012\) |
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: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 16.2 | ||
Root | \(0.124036 - 0.214837i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.16 |
Dual form | 21.4.e.b.4.2 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.124036 | + | 0.214837i | −0.0438533 | + | 0.0759562i | −0.887119 | − | 0.461541i | \(-0.847297\pi\) |
0.843266 | + | 0.537497i | \(0.180630\pi\) | |||||||
\(3\) | 1.50000 | + | 2.59808i | 0.288675 | + | 0.500000i | ||||
\(4\) | 3.96923 | + | 6.87491i | 0.496154 | + | 0.859364i | ||||
\(5\) | 6.21730 | − | 10.7687i | 0.556092 | − | 0.963180i | −0.441725 | − | 0.897150i | \(-0.645633\pi\) |
0.997818 | − | 0.0660299i | \(-0.0210333\pi\) | |||||||
\(6\) | −0.744216 | −0.0506375 | ||||||||
\(7\) | −18.4385 | − | 1.73873i | −0.995583 | − | 0.0938826i | ||||
\(8\) | −3.95388 | −0.174739 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.54234 | + | 2.67141i | 0.0487730 | + | 0.0844773i | ||||
\(11\) | −30.1558 | − | 52.2313i | −0.826573 | − | 1.43167i | −0.900711 | − | 0.434419i | \(-0.856954\pi\) |
0.0741379 | − | 0.997248i | \(-0.476379\pi\) | |||||||
\(12\) | −11.9077 | + | 20.6247i | −0.286455 | + | 0.496154i | ||||
\(13\) | 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 | ||||
\(15\) | 37.3038 | 0.642120 | ||||||||
\(16\) | −31.2634 | + | 54.1498i | −0.488491 | + | 0.846091i | ||||
\(17\) | 24.3731 | + | 42.2154i | 0.347726 | + | 0.602279i | 0.985845 | − | 0.167659i | \(-0.0536207\pi\) |
−0.638119 | + | 0.769937i | \(0.720287\pi\) | |||||||
\(18\) | −1.11632 | − | 1.93353i | −0.0146178 | − | 0.0253187i | ||||
\(19\) | 25.2750 | − | 43.7776i | 0.305183 | − | 0.528593i | −0.672119 | − | 0.740443i | \(-0.734616\pi\) |
0.977302 | + | 0.211851i | \(0.0679490\pi\) | |||||||
\(20\) | 98.7116 | 1.10363 | ||||||||
\(21\) | −23.1403 | − | 50.5126i | −0.240459 | − | 0.524893i | ||||
\(22\) | 14.9616 | 0.144992 | ||||||||
\(23\) | −69.3962 | + | 120.198i | −0.629135 | + | 1.08969i | 0.358590 | + | 0.933495i | \(0.383257\pi\) |
−0.987726 | + | 0.156199i | \(0.950076\pi\) | |||||||
\(24\) | −5.93083 | − | 10.2725i | −0.0504427 | − | 0.0873693i | ||||
\(25\) | −14.8097 | − | 25.6511i | −0.118478 | − | 0.205209i | ||||
\(26\) | −4.51824 | + | 7.82583i | −0.0340808 | + | 0.0590297i | ||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −61.2329 | − | 133.664i | −0.413283 | − | 0.902148i | ||||
\(29\) | −61.1345 | −0.391462 | −0.195731 | − | 0.980658i | \(-0.562708\pi\) | ||||
−0.195731 | + | 0.980658i | \(0.562708\pi\) | |||||||
\(30\) | −4.62701 | + | 8.01422i | −0.0281591 | + | 0.0487730i | ||||
\(31\) | 0.584676 | + | 1.01269i | 0.00338745 | + | 0.00586724i | 0.867714 | − | 0.497064i | \(-0.165588\pi\) |
−0.864327 | + | 0.502931i | \(0.832255\pi\) | |||||||
\(32\) | −23.5711 | − | 40.8264i | −0.130213 | − | 0.225536i | ||||
\(33\) | 90.4673 | − | 156.694i | 0.477222 | − | 0.826573i | ||||
\(34\) | −12.0925 | −0.0609957 | ||||||||
\(35\) | −133.361 | + | 187.748i | −0.644062 | + | 0.906719i | ||||
\(36\) | −71.4461 | −0.330769 | ||||||||
\(37\) | −34.7634 | + | 60.2120i | −0.154461 | + | 0.267535i | −0.932863 | − | 0.360232i | \(-0.882698\pi\) |
0.778401 | + | 0.627767i | \(0.216031\pi\) | |||||||
\(38\) | 6.27001 | + | 10.8600i | 0.0267666 | + | 0.0463611i | ||||
\(39\) | 54.6403 | + | 94.6398i | 0.224345 | + | 0.388577i | ||||
\(40\) | −24.5825 | + | 42.5781i | −0.0971708 | + | 0.168305i | ||||
\(41\) | 308.115 | 1.17365 | 0.586823 | − | 0.809715i | \(-0.300378\pi\) | ||||
0.586823 | + | 0.809715i | \(0.300378\pi\) | |||||||
\(42\) | 13.7222 | + | 1.29399i | 0.0504138 | + | 0.00475398i | ||||
\(43\) | 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 | ||||
\(45\) | 55.9557 | + | 96.9181i | 0.185364 | + | 0.321060i | ||||
\(46\) | −17.2153 | − | 29.8177i | −0.0551794 | − | 0.0955734i | ||||
\(47\) | −194.681 | + | 337.197i | −0.604194 | + | 1.04649i | 0.387984 | + | 0.921666i | \(0.373172\pi\) |
−0.992178 | + | 0.124829i | \(0.960162\pi\) | |||||||
\(48\) | −187.581 | −0.564061 | ||||||||
\(49\) | 336.954 | + | 64.1190i | 0.982372 | + | 0.186936i | ||||
\(50\) | 7.34774 | 0.0207825 | ||||||||
\(51\) | −73.1192 | + | 126.646i | −0.200760 | + | 0.347726i | ||||
\(52\) | 144.587 | + | 250.432i | 0.385588 | + | 0.667858i | ||||
\(53\) | −157.467 | − | 272.742i | −0.408110 | − | 0.706867i | 0.586568 | − | 0.809900i | \(-0.300479\pi\) |
−0.994678 | + | 0.103033i | \(0.967145\pi\) | |||||||
\(54\) | 3.34897 | − | 5.80059i | 0.00843958 | − | 0.0146178i | ||||
\(55\) | −749.950 | −1.83860 | ||||||||
\(56\) | 72.9035 | + | 6.87474i | 0.173967 | + | 0.0164049i | ||||
\(57\) | 151.650 | 0.352395 | ||||||||
\(58\) | 7.58287 | − | 13.1339i | 0.0171669 | − | 0.0297339i | ||||
\(59\) | −422.263 | − | 731.381i | −0.931762 | − | 1.61386i | −0.780308 | − | 0.625396i | \(-0.784938\pi\) |
−0.151455 | − | 0.988464i | \(-0.548396\pi\) | |||||||
\(60\) | 148.067 | + | 256.460i | 0.318590 | + | 0.551815i | ||||
\(61\) | 169.269 | − | 293.182i | 0.355290 | − | 0.615380i | −0.631878 | − | 0.775068i | \(-0.717716\pi\) |
0.987167 | + | 0.159688i | \(0.0510489\pi\) | |||||||
\(62\) | −0.290084 | −0.000594204 | ||||||||
\(63\) | 96.5251 | − | 135.889i | 0.193032 | − | 0.271753i | ||||
\(64\) | −488.520 | −0.954141 | ||||||||
\(65\) | 226.477 | − | 392.270i | 0.432169 | − | 0.748539i | ||||
\(66\) | 22.4424 | + | 38.8714i | 0.0418556 | + | 0.0724960i | ||||
\(67\) | 485.775 | + | 841.387i | 0.885774 | + | 1.53421i | 0.844824 | + | 0.535044i | \(0.179705\pi\) |
0.0409498 | + | 0.999161i | \(0.486962\pi\) | |||||||
\(68\) | −193.485 | + | 335.125i | −0.345051 | + | 0.597646i | ||||
\(69\) | −416.377 | −0.726463 | ||||||||
\(70\) | −23.7935 | − | 51.9384i | −0.0406266 | − | 0.0886832i | ||||
\(71\) | −98.4698 | −0.164595 | −0.0822973 | − | 0.996608i | \(-0.526226\pi\) | ||||
−0.0822973 | + | 0.996608i | \(0.526226\pi\) | |||||||
\(72\) | 17.7925 | − | 30.8175i | 0.0291231 | − | 0.0504427i | ||||
\(73\) | −355.117 | − | 615.082i | −0.569361 | − | 0.986162i | −0.996629 | − | 0.0820374i | \(-0.973857\pi\) |
0.427268 | − | 0.904125i | \(-0.359476\pi\) | |||||||
\(74\) | −8.62383 | − | 14.9369i | −0.0135473 | − | 0.0234646i | ||||
\(75\) | 44.4291 | − | 76.9534i | 0.0684030 | − | 0.118478i | ||||
\(76\) | 401.289 | 0.605671 | ||||||||
\(77\) | 465.210 | + | 1015.50i | 0.688514 | + | 1.50294i | ||||
\(78\) | −27.1095 | −0.0393531 | ||||||||
\(79\) | 243.442 | − | 421.654i | 0.346701 | − | 0.600504i | −0.638960 | − | 0.769240i | \(-0.720635\pi\) |
0.985661 | + | 0.168736i | \(0.0539686\pi\) | |||||||
\(80\) | 388.748 | + | 673.332i | 0.543292 | + | 0.941010i | ||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −38.2174 | + | 66.1944i | −0.0514683 | + | 0.0891458i | ||||
\(83\) | 605.688 | 0.800999 | 0.400499 | − | 0.916297i | \(-0.368837\pi\) | ||||
0.400499 | + | 0.916297i | \(0.368837\pi\) | |||||||
\(84\) | 255.420 | − | 359.584i | 0.331770 | − | 0.467069i | ||||
\(85\) | 606.139 | 0.773470 | ||||||||
\(86\) | −21.6372 | + | 37.4767i | −0.0271302 | + | 0.0469908i | ||||
\(87\) | −91.7017 | − | 158.832i | −0.113005 | − | 0.195731i | ||||
\(88\) | 119.232 | + | 206.517i | 0.144434 | + | 0.250168i | ||||
\(89\) | −109.034 | + | 188.853i | −0.129861 | + | 0.224925i | −0.923622 | − | 0.383303i | \(-0.874786\pi\) |
0.793762 | + | 0.608229i | \(0.208120\pi\) | |||||||
\(90\) | −27.7621 | −0.0325153 | ||||||||
\(91\) | −671.656 | − | 63.3365i | −0.773722 | − | 0.0729612i | ||||
\(92\) | −1101.80 | −1.24859 | ||||||||
\(93\) | −1.75403 | + | 3.03807i | −0.00195575 | + | 0.00338745i | ||||
\(94\) | −48.2949 | − | 83.6491i | −0.0529919 | − | 0.0917846i | ||||
\(95\) | −314.284 | − | 544.357i | −0.339420 | − | 0.587893i | ||||
\(96\) | 70.7133 | − | 122.479i | 0.0751787 | − | 0.130213i | ||||
\(97\) | −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 | ||||
\(99\) | 542.804 | 0.551049 | ||||||||
\(100\) | 117.566 | − | 203.631i | 0.117566 | − | 0.203631i | ||||
\(101\) | 155.823 | + | 269.893i | 0.153514 | + | 0.265895i | 0.932517 | − | 0.361126i | \(-0.117608\pi\) |
−0.779003 | + | 0.627021i | \(0.784274\pi\) | |||||||
\(102\) | −18.1388 | − | 31.4174i | −0.0176079 | − | 0.0304979i | ||||
\(103\) | 74.6289 | − | 129.261i | 0.0713922 | − | 0.123655i | −0.828119 | − | 0.560552i | \(-0.810589\pi\) |
0.899512 | + | 0.436897i | \(0.143922\pi\) | |||||||
\(104\) | −144.028 | −0.135799 | ||||||||
\(105\) | −687.825 | − | 64.8613i | −0.639284 | − | 0.0602839i | ||||
\(106\) | 78.1265 | 0.0715879 | ||||||||
\(107\) | −425.760 | + | 737.437i | −0.384670 | + | 0.666269i | −0.991723 | − | 0.128393i | \(-0.959018\pi\) |
0.607053 | + | 0.794661i | \(0.292352\pi\) | |||||||
\(108\) | −107.169 | − | 185.623i | −0.0954848 | − | 0.165385i | ||||
\(109\) | −680.939 | − | 1179.42i | −0.598369 | − | 1.03640i | −0.993062 | − | 0.117592i | \(-0.962483\pi\) |
0.394694 | − | 0.918813i | \(-0.370851\pi\) | |||||||
\(110\) | 93.0208 | − | 161.117i | 0.0806289 | − | 0.139653i | ||||
\(111\) | −208.581 | −0.178357 | ||||||||
\(112\) | 670.601 | − | 944.081i | 0.565767 | − | 0.796493i | ||||
\(113\) | 1048.55 | 0.872917 | 0.436459 | − | 0.899724i | \(-0.356233\pi\) | ||||
0.436459 | + | 0.899724i | \(0.356233\pi\) | |||||||
\(114\) | −18.8100 | + | 32.5800i | −0.0154537 | + | 0.0267666i | ||||
\(115\) | 862.914 | + | 1494.61i | 0.699715 | + | 1.21194i | ||||
\(116\) | −242.657 | − | 420.294i | −0.194225 | − | 0.336408i | ||||
\(117\) | −163.921 | + | 283.920i | −0.129526 | + | 0.224345i | ||||
\(118\) | 209.503 | 0.163444 | ||||||||
\(119\) | −376.001 | − | 820.765i | −0.289646 | − | 0.632264i | ||||
\(120\) | −147.495 | −0.112203 | ||||||||
\(121\) | −1153.24 | + | 1997.47i | −0.866446 | + | 1.50073i | ||||
\(122\) | 41.9909 | + | 72.7303i | 0.0311613 | + | 0.0539729i | ||||
\(123\) | 462.173 | + | 800.507i | 0.338803 | + | 0.586823i | ||||
\(124\) | −4.64143 | + | 8.03919i | −0.00336139 | + | 0.00582210i | ||||
\(125\) | 1186.02 | 0.848647 | ||||||||
\(126\) | 17.2214 | + | 37.5923i | 0.0121762 | + | 0.0265793i | ||||
\(127\) | 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 | ||||
\(129\) | 261.664 | + | 453.215i | 0.178591 | + | 0.309329i | ||||
\(130\) | 56.1826 | + | 97.3111i | 0.0379041 | + | 0.0656519i | ||||
\(131\) | 927.114 | − | 1605.81i | 0.618338 | − | 1.07099i | −0.371451 | − | 0.928453i | \(-0.621139\pi\) |
0.989789 | − | 0.142541i | \(-0.0455272\pi\) | |||||||
\(132\) | 1436.34 | 0.947102 | ||||||||
\(133\) | −542.149 | + | 763.244i | −0.353461 | + | 0.497607i | ||||
\(134\) | −241.014 | −0.155377 | ||||||||
\(135\) | −167.867 | + | 290.754i | −0.107020 | + | 0.185364i | ||||
\(136\) | −96.3683 | − | 166.915i | −0.0607611 | − | 0.105241i | ||||
\(137\) | 255.558 | + | 442.639i | 0.159370 | + | 0.276038i | 0.934642 | − | 0.355591i | \(-0.115720\pi\) |
−0.775271 | + | 0.631628i | \(0.782387\pi\) | |||||||
\(138\) | 51.6458 | − | 89.4531i | 0.0318578 | − | 0.0551794i | ||||
\(139\) | 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 | ||||
\(141\) | −1168.09 | −0.697663 | ||||||||
\(142\) | 12.2138 | − | 21.1549i | 0.00721802 | − | 0.0125020i | ||||
\(143\) | −1098.48 | − | 1902.62i | −0.642375 | − | 1.11263i | ||||
\(144\) | −281.371 | − | 487.348i | −0.162830 | − | 0.282030i | ||||
\(145\) | −380.091 | + | 658.338i | −0.217689 | + | 0.377048i | ||||
\(146\) | 176.189 | 0.0998735 | ||||||||
\(147\) | 338.844 | + | 971.610i | 0.190118 | + | 0.545150i | ||||
\(148\) | −551.936 | −0.306546 | ||||||||
\(149\) | −753.950 | + | 1305.88i | −0.414537 | + | 0.717999i | −0.995380 | − | 0.0960168i | \(-0.969390\pi\) |
0.580843 | + | 0.814016i | \(0.302723\pi\) | |||||||
\(150\) | 11.0216 | + | 19.0900i | 0.00599940 | + | 0.0103913i | ||||
\(151\) | −795.913 | − | 1378.56i | −0.428943 | − | 0.742952i | 0.567836 | − | 0.823142i | \(-0.307781\pi\) |
−0.996780 | + | 0.0801897i | \(0.974447\pi\) | |||||||
\(152\) | −99.9344 | + | 173.091i | −0.0533273 | + | 0.0923656i | ||||
\(153\) | −438.715 | −0.231817 | ||||||||
\(154\) | −275.869 | − | 26.0142i | −0.144352 | − | 0.0136122i | ||||
\(155\) | 14.5404 | 0.00753494 | ||||||||
\(156\) | −433.760 | + | 751.295i | −0.222619 | + | 0.385588i | ||||
\(157\) | −582.080 | − | 1008.19i | −0.295892 | − | 0.512500i | 0.679300 | − | 0.733861i | \(-0.262283\pi\) |
−0.975192 | + | 0.221361i | \(0.928950\pi\) | |||||||
\(158\) | 60.3911 | + | 104.601i | 0.0304080 | + | 0.0526682i | ||||
\(159\) | 472.402 | − | 818.225i | 0.235622 | − | 0.408110i | ||||
\(160\) | −586.195 | −0.289642 | ||||||||
\(161\) | 1488.55 | − | 2095.60i | 0.728660 | − | 1.02582i | ||||
\(162\) | 20.0938 | 0.00974519 | ||||||||
\(163\) | 577.940 | − | 1001.02i | 0.277716 | − | 0.481019i | −0.693101 | − | 0.720841i | \(-0.743756\pi\) |
0.970817 | + | 0.239822i | \(0.0770892\pi\) | |||||||
\(164\) | 1222.98 | + | 2118.26i | 0.582309 | + | 1.00859i | ||||
\(165\) | −1124.92 | − | 1948.43i | −0.530759 | − | 0.919302i | ||||
\(166\) | −75.1271 | + | 130.124i | −0.0351265 | + | 0.0608408i | ||||
\(167\) | −2890.61 | −1.33941 | −0.669707 | − | 0.742626i | \(-0.733580\pi\) | ||||
−0.669707 | + | 0.742626i | \(0.733580\pi\) | |||||||
\(168\) | 91.4942 | + | 199.721i | 0.0420175 | + | 0.0917191i | ||||
\(169\) | −870.082 | −0.396032 | ||||||||
\(170\) | −75.1830 | + | 130.221i | −0.0339193 | + | 0.0587499i | ||||
\(171\) | 227.475 | + | 393.998i | 0.101728 | + | 0.176198i | ||||
\(172\) | 692.403 | + | 1199.28i | 0.306949 | + | 0.531651i | ||||
\(173\) | −947.468 | + | 1641.06i | −0.416385 | + | 0.721200i | −0.995573 | − | 0.0939940i | \(-0.970037\pi\) |
0.579188 | + | 0.815194i | \(0.303370\pi\) | |||||||
\(174\) | 45.4972 | 0.0198226 | ||||||||
\(175\) | 228.467 | + | 498.718i | 0.0986887 | + | 0.215426i | ||||
\(176\) | 3771.09 | 1.61509 | ||||||||
\(177\) | 1266.79 | − | 2194.14i | 0.537953 | − | 0.931762i | ||||
\(178\) | −27.0483 | − | 46.8491i | −0.0113897 | − | 0.0197275i | ||||
\(179\) | 2144.25 | + | 3713.94i | 0.895355 | + | 1.55080i | 0.833365 | + | 0.552723i | \(0.186411\pi\) |
0.0619893 | + | 0.998077i | \(0.480256\pi\) | |||||||
\(180\) | −444.202 | + | 769.381i | −0.183938 | + | 0.318590i | ||||
\(181\) | 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 | ||||
\(183\) | 1015.61 | 0.410253 | ||||||||
\(184\) | 274.385 | − | 475.248i | 0.109934 | − | 0.190412i | ||||
\(185\) | 432.269 | + | 748.712i | 0.171790 | + | 0.297548i | ||||
\(186\) | −0.435125 | − | 0.753659i | −0.000171532 | − | 0.000297102i | ||||
\(187\) | 1469.98 | − | 2546.07i | 0.574841 | − | 0.995655i | ||||
\(188\) | −3090.93 | −1.19909 | ||||||||
\(189\) | 497.838 | + | 46.9457i | 0.191600 | + | 0.0180677i | ||||
\(190\) | 155.930 | 0.0595388 | ||||||||
\(191\) | −192.655 | + | 333.689i | −0.0729845 | + | 0.126413i | −0.900208 | − | 0.435460i | \(-0.856586\pi\) |
0.827224 | + | 0.561873i | \(0.189919\pi\) | |||||||
\(192\) | −732.780 | − | 1269.21i | −0.275437 | − | 0.477070i | ||||
\(193\) | −315.112 | − | 545.790i | −0.117525 | − | 0.203559i | 0.801262 | − | 0.598314i | \(-0.204163\pi\) |
−0.918786 | + | 0.394756i | \(0.870829\pi\) | |||||||
\(194\) | 97.0318 | − | 168.064i | 0.0359097 | − | 0.0621974i | ||||
\(195\) | 1358.86 | 0.499026 | ||||||||
\(196\) | 896.634 | + | 2571.03i | 0.326762 | + | 0.936964i | ||||
\(197\) | −1250.23 | −0.452158 | −0.226079 | − | 0.974109i | \(-0.572591\pi\) | ||||
−0.226079 | + | 0.974109i | \(0.572591\pi\) | |||||||
\(198\) | −67.3272 | + | 116.614i | −0.0241653 | + | 0.0418556i | ||||
\(199\) | 546.122 | + | 945.912i | 0.194541 | + | 0.336954i | 0.946750 | − | 0.321970i | \(-0.104345\pi\) |
−0.752209 | + | 0.658924i | \(0.771012\pi\) | |||||||
\(200\) | 58.5558 | + | 101.422i | 0.0207026 | + | 0.0358580i | ||||
\(201\) | −1457.32 | + | 2524.16i | −0.511402 | + | 0.885774i | ||||
\(202\) | −77.3105 | −0.0269285 | ||||||||
\(203\) | 1127.23 | + | 106.296i | 0.389733 | + | 0.0367514i | ||||
\(204\) | −1160.91 | −0.398430 | ||||||||
\(205\) | 1915.65 | − | 3318.00i | 0.652656 | − | 1.13043i | ||||
\(206\) | 18.5133 | + | 32.0660i | 0.00626158 | + | 0.0108454i | ||||
\(207\) | −624.566 | − | 1081.78i | −0.209712 | − | 0.363231i | ||||
\(208\) | −1138.83 | + | 1972.51i | −0.379633 | + | 0.657543i | ||||
\(209\) | −3048.75 | −1.00902 | ||||||||
\(210\) | 99.2496 | − | 139.725i | 0.0326137 | − | 0.0459139i | ||||
\(211\) | −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 | ||||
\(213\) | −147.705 | − | 255.832i | −0.0475143 | − | 0.0822973i | ||||
\(214\) | −105.619 | − | 182.937i | −0.0337382 | − | 0.0584362i | ||||
\(215\) | 1084.56 | − | 1878.52i | 0.344030 | − | 0.595878i | ||||
\(216\) | 106.755 | 0.0336285 | ||||||||
\(217\) | −9.01974 | − | 19.6890i | −0.00282166 | − | 0.00615935i | ||||
\(218\) | 337.844 | 0.104962 | ||||||||
\(219\) | 1065.35 | − | 1845.24i | 0.328721 | − | 0.569361i | ||||
\(220\) | −2976.72 | − | 5155.84i | −0.912230 | − | 1.58003i | ||||
\(221\) | 887.835 | + | 1537.78i | 0.270236 | + | 0.468063i | ||||
\(222\) | 25.8715 | − | 44.8107i | 0.00782153 | − | 0.0135473i | ||||
\(223\) | −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 | ||||
\(225\) | 266.574 | 0.0789850 | ||||||||
\(226\) | −130.058 | + | 225.268i | −0.0382803 | + | 0.0663035i | ||||
\(227\) | −1139.76 | − | 1974.12i | −0.333253 | − | 0.577211i | 0.649895 | − | 0.760024i | \(-0.274813\pi\) |
−0.983148 | + | 0.182813i | \(0.941480\pi\) | |||||||
\(228\) | 601.933 | + | 1042.58i | 0.174842 | + | 0.302836i | ||||
\(229\) | −2706.34 | + | 4687.51i | −0.780960 | + | 1.35266i | 0.150424 | + | 0.988622i | \(0.451936\pi\) |
−0.931383 | + | 0.364040i | \(0.881397\pi\) | |||||||
\(230\) | −428.130 | −0.122739 | ||||||||
\(231\) | −1940.53 | + | 2731.90i | −0.552715 | + | 0.778120i | ||||
\(232\) | 241.719 | 0.0684035 | ||||||||
\(233\) | −569.184 | + | 985.856i | −0.160036 | + | 0.277191i | −0.934882 | − | 0.354960i | \(-0.884494\pi\) |
0.774845 | + | 0.632151i | \(0.217828\pi\) | |||||||
\(234\) | −40.6642 | − | 70.4325i | −0.0113603 | − | 0.0196766i | ||||
\(235\) | 2420.78 | + | 4192.91i | 0.671975 | + | 1.16390i | ||||
\(236\) | 3352.12 | − | 5806.04i | 0.924595 | − | 1.60145i | ||||
\(237\) | 1460.65 | 0.400336 | ||||||||
\(238\) | 222.968 | + | 21.0257i | 0.0607263 | + | 0.00572644i | ||||
\(239\) | −6226.36 | −1.68515 | −0.842573 | − | 0.538583i | \(-0.818960\pi\) | ||||
−0.842573 | + | 0.538583i | \(0.818960\pi\) | |||||||
\(240\) | −1166.24 | + | 2020.00i | −0.313670 | + | 0.543292i | ||||
\(241\) | 1598.10 | + | 2767.99i | 0.427147 | + | 0.739841i | 0.996618 | − | 0.0821704i | \(-0.0261852\pi\) |
−0.569471 | + | 0.822012i | \(0.692852\pi\) | |||||||
\(242\) | −286.086 | − | 495.516i | −0.0759931 | − | 0.131624i | ||||
\(243\) | 121.500 | − | 210.444i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 2687.47 | 0.705113 | ||||||||
\(245\) | 2785.42 | − | 3229.90i | 0.726343 | − | 0.842248i | ||||
\(246\) | −229.304 | −0.0594305 | ||||||||
\(247\) | 920.689 | − | 1594.68i | 0.237174 | − | 0.410798i | ||||
\(248\) | −2.31174 | − | 4.00406i | −0.000591919 | − | 0.00102523i | ||||
\(249\) | 908.532 | + | 1573.62i | 0.231228 | + | 0.400499i | ||||
\(250\) | −147.109 | + | 254.801i | −0.0372160 | + | 0.0644600i | ||||
\(251\) | 239.608 | 0.0602546 | 0.0301273 | − | 0.999546i | \(-0.490409\pi\) | ||||
0.0301273 | + | 0.999546i | \(0.490409\pi\) | |||||||
\(252\) | 1317.36 | + | 124.226i | 0.329308 | + | 0.0310535i | ||||
\(253\) | 8370.78 | 2.08010 | ||||||||
\(254\) | −60.5802 | + | 104.928i | −0.0149651 | + | 0.0259203i | ||||
\(255\) | 909.208 | + | 1574.79i | 0.223282 | + | 0.386735i | ||||
\(256\) | −1892.27 | − | 3277.51i | −0.461980 | − | 0.800173i | ||||
\(257\) | −349.559 | + | 605.453i | −0.0848439 | + | 0.146954i | −0.905325 | − | 0.424720i | \(-0.860372\pi\) |
0.820481 | + | 0.571674i | \(0.193706\pi\) | |||||||
\(258\) | −129.823 | −0.0313272 | ||||||||
\(259\) | 745.676 | − | 1049.77i | 0.178896 | − | 0.251852i | ||||
\(260\) | 3595.76 | 0.857690 | ||||||||
\(261\) | 275.105 | − | 476.496i | 0.0652436 | − | 0.113005i | ||||
\(262\) | 229.991 | + | 398.356i | 0.0542324 | + | 0.0939333i | ||||
\(263\) | 459.520 | + | 795.912i | 0.107738 | + | 0.186609i | 0.914854 | − | 0.403785i | \(-0.132306\pi\) |
−0.807115 | + | 0.590394i | \(0.798972\pi\) | |||||||
\(264\) | −357.697 | + | 619.550i | −0.0833892 | + | 0.144434i | ||||
\(265\) | −3916.09 | −0.907787 | ||||||||
\(266\) | −96.7268 | − | 211.143i | −0.0222959 | − | 0.0486693i | ||||
\(267\) | −654.206 | −0.149950 | ||||||||
\(268\) | −3856.30 | + | 6679.32i | −0.878960 | + | 1.52240i | ||||
\(269\) | 1389.59 | + | 2406.84i | 0.314961 | + | 0.545529i | 0.979429 | − | 0.201788i | \(-0.0646751\pi\) |
−0.664468 | + | 0.747317i | \(0.731342\pi\) | |||||||
\(270\) | −41.6431 | − | 72.1280i | −0.00938637 | − | 0.0162577i | ||||
\(271\) | −1113.49 | + | 1928.62i | −0.249593 | + | 0.432308i | −0.963413 | − | 0.268021i | \(-0.913630\pi\) |
0.713820 | + | 0.700329i | \(0.246964\pi\) | |||||||
\(272\) | −3047.94 | −0.679443 | ||||||||
\(273\) | −842.931 | − | 1840.02i | −0.186874 | − | 0.407923i | ||||
\(274\) | −126.793 | −0.0279557 | ||||||||
\(275\) | −893.195 | + | 1547.06i | −0.195861 | + | 0.339241i | ||||
\(276\) | −1652.70 | − | 2862.56i | −0.360437 | − | 0.624296i | ||||
\(277\) | −3653.85 | − | 6328.65i | −0.792557 | − | 1.37275i | −0.924379 | − | 0.381476i | \(-0.875416\pi\) |
0.131821 | − | 0.991273i | \(-0.457917\pi\) | |||||||
\(278\) | −281.078 | + | 486.842i | −0.0606402 | + | 0.105032i | ||||
\(279\) | −10.5242 | −0.00225830 | ||||||||
\(280\) | 527.295 | − | 742.333i | 0.112543 | − | 0.158439i | ||||
\(281\) | 2730.61 | 0.579696 | 0.289848 | − | 0.957073i | \(-0.406395\pi\) | ||||
0.289848 | + | 0.957073i | \(0.406395\pi\) | |||||||
\(282\) | 144.885 | − | 250.947i | 0.0305949 | − | 0.0529919i | ||||
\(283\) | 884.926 | + | 1532.74i | 0.185878 | + | 0.321950i | 0.943872 | − | 0.330312i | \(-0.107154\pi\) |
−0.757994 | + | 0.652261i | \(0.773821\pi\) | |||||||
\(284\) | −390.849 | − | 676.971i | −0.0816642 | − | 0.141447i | ||||
\(285\) | 942.853 | − | 1633.07i | 0.195964 | − | 0.339420i | ||||
\(286\) | 545.004 | 0.112681 | ||||||||
\(287\) | −5681.17 | − | 535.729i | −1.16846 | − | 0.110185i | ||||
\(288\) | 424.280 | 0.0868088 | ||||||||
\(289\) | 1268.41 | − | 2196.95i | 0.258174 | − | 0.447170i | ||||
\(290\) | −94.2900 | − | 163.315i | −0.0190928 | − | 0.0330696i | ||||
\(291\) | −1173.43 | − | 2032.44i | −0.236384 | − | 0.409429i | ||||
\(292\) | 2819.09 | − | 4882.80i | 0.564981 | − | 0.978576i | ||||
\(293\) | 8228.81 | 1.64072 | 0.820362 | − | 0.571844i | \(-0.193772\pi\) | ||||
0.820362 | + | 0.571844i | \(0.193772\pi\) | |||||||
\(294\) | −250.766 | − | 47.7184i | −0.0497448 | − | 0.00946596i | ||||
\(295\) | −10501.4 | −2.07258 | ||||||||
\(296\) | 137.451 | − | 238.071i | 0.0269904 | − | 0.0467487i | ||||
\(297\) | 814.206 | + | 1410.25i | 0.159074 | + | 0.275524i | ||||
\(298\) | −187.034 | − | 323.952i | −0.0363577 | − | 0.0629733i | ||||
\(299\) | −2527.89 | + | 4378.43i | −0.488935 | + | 0.846860i | ||||
\(300\) | 705.397 | 0.135754 | ||||||||
\(301\) | −3216.45 | − | 303.309i | −0.615925 | − | 0.0580811i | ||||
\(302\) | 394.887 | 0.0752424 | ||||||||
\(303\) | −467.468 | + | 809.679i | −0.0886316 | + | 0.153514i | ||||
\(304\) | 1580.36 | + | 2737.27i | 0.298158 | + | 0.516425i | ||||
\(305\) | −2104.79 | − | 3645.61i | −0.395148 | − | 0.684416i | ||||
\(306\) | 54.4165 | − | 94.2521i | 0.0101660 | − | 0.0176079i | ||||
\(307\) | 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 | ||||
\(309\) | 447.773 | 0.0824366 | ||||||||
\(310\) | −1.80354 | + | 3.12382i | −0.000330432 | + | 0.000572326i | ||||
\(311\) | −596.857 | − | 1033.79i | −0.108825 | − | 0.188491i | 0.806469 | − | 0.591276i | \(-0.201376\pi\) |
−0.915295 | + | 0.402785i | \(0.868042\pi\) | |||||||
\(312\) | −216.042 | − | 374.195i | −0.0392018 | − | 0.0678994i | ||||
\(313\) | 4423.02 | − | 7660.89i | 0.798734 | − | 1.38345i | −0.121707 | − | 0.992566i | \(-0.538837\pi\) |
0.920441 | − | 0.390882i | \(-0.127830\pi\) | |||||||
\(314\) | 288.795 | 0.0519034 | ||||||||
\(315\) | −863.223 | − | 1884.31i | −0.154403 | − | 0.337045i | ||||
\(316\) | 3865.11 | 0.688068 | ||||||||
\(317\) | −3040.72 | + | 5266.68i | −0.538750 | + | 0.933142i | 0.460222 | + | 0.887804i | \(0.347770\pi\) |
−0.998972 | + | 0.0453380i | \(0.985564\pi\) | |||||||
\(318\) | 117.190 | + | 202.979i | 0.0206656 | + | 0.0357940i | ||||
\(319\) | 1843.56 | + | 3193.13i | 0.323572 | + | 0.560442i | ||||
\(320\) | −3037.28 | + | 5260.72i | −0.530590 | + | 0.919009i | ||||
\(321\) | −2554.56 | −0.444179 | ||||||||
\(322\) | 265.578 | + | 579.725i | 0.0459630 | + | 0.100332i | ||||
\(323\) | 2464.12 | 0.424480 | ||||||||
\(324\) | 321.508 | − | 556.868i | 0.0551282 | − | 0.0954848i | ||||
\(325\) | −539.471 | − | 934.391i | −0.0920753 | − | 0.159479i | ||||
\(326\) | 143.371 | + | 248.325i | 0.0243576 | + | 0.0421885i | ||||
\(327\) | 2042.82 | − | 3538.26i | 0.345468 | − | 0.598369i | ||||
\(328\) | −1218.25 | −0.205082 | ||||||||
\(329\) | 4175.91 | − | 5878.90i | 0.699773 | − | 0.985149i | ||||
\(330\) | 558.125 | 0.0931023 | ||||||||
\(331\) | −1526.65 | + | 2644.23i | −0.253511 | + | 0.439094i | −0.964490 | − | 0.264119i | \(-0.914919\pi\) |
0.710979 | + | 0.703213i | \(0.248252\pi\) | |||||||
\(332\) | 2404.12 | + | 4164.05i | 0.397419 | + | 0.688349i | ||||
\(333\) | −312.871 | − | 541.908i | −0.0514871 | − | 0.0891783i | ||||
\(334\) | 358.539 | − | 621.009i | 0.0587377 | − | 0.101737i | ||||
\(335\) | 12080.8 | 1.97029 | ||||||||
\(336\) | 3458.70 | + | 326.152i | 0.561569 | + | 0.0529555i | ||||
\(337\) | 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 | ||||
\(339\) | 1572.83 | + | 2724.22i | 0.251989 | + | 0.436459i | ||||
\(340\) | 2405.90 | + | 4167.15i | 0.383760 | + | 0.664692i | ||||
\(341\) | 35.2627 | − | 61.0768i | 0.00559995 | − | 0.00969940i | ||||
\(342\) | −112.860 | −0.0178444 | ||||||||
\(343\) | −6101.42 | − | 1768.13i | −0.960483 | − | 0.278338i | ||||
\(344\) | −689.726 | −0.108103 | ||||||||
\(345\) | −2588.74 | + | 4483.83i | −0.403980 | + | 0.699715i | ||||
\(346\) | −235.040 | − | 407.101i | −0.0365198 | − | 0.0632541i | ||||
\(347\) | 49.7965 | + | 86.2501i | 0.00770380 | + | 0.0133434i | 0.869852 | − | 0.493313i | \(-0.164214\pi\) |
−0.862148 | + | 0.506657i | \(0.830881\pi\) | |||||||
\(348\) | 727.970 | − | 1260.88i | 0.112136 | − | 0.194225i | ||||
\(349\) | −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 | ||||
\(351\) | −983.526 | −0.149563 | ||||||||
\(352\) | −1421.61 | + | 2462.30i | −0.215262 | + | 0.372844i | ||||
\(353\) | −3565.37 | − | 6175.40i | −0.537579 | − | 0.931114i | −0.999034 | − | 0.0439501i | \(-0.986006\pi\) |
0.461455 | − | 0.887164i | \(-0.347328\pi\) | |||||||
\(354\) | 314.255 | + | 544.306i | 0.0471821 | + | 0.0817218i | ||||
\(355\) | −612.216 | + | 1060.39i | −0.0915298 | + | 0.158534i | ||||
\(356\) | −1731.13 | −0.257724 | ||||||||
\(357\) | 1568.41 | − | 2208.03i | 0.232518 | − | 0.327342i | ||||
\(358\) | −1063.85 | −0.157057 | ||||||||
\(359\) | 3250.14 | − | 5629.41i | 0.477816 | − | 0.827602i | −0.521860 | − | 0.853031i | \(-0.674762\pi\) |
0.999677 | + | 0.0254289i | \(0.00809514\pi\) | |||||||
\(360\) | −221.242 | − | 383.203i | −0.0323903 | − | 0.0561016i | ||||
\(361\) | 2151.85 | + | 3727.11i | 0.313727 | + | 0.543390i | ||||
\(362\) | −47.5966 | + | 82.4398i | −0.00691056 | + | 0.0119694i | ||||
\(363\) | −6919.44 | −1.00049 | ||||||||
\(364\) | −2230.52 | − | 4868.97i | −0.321185 | − | 0.701108i | ||||
\(365\) | −8831.49 | −1.26647 | ||||||||
\(366\) | −125.973 | + | 218.191i | −0.0179910 | + | 0.0311613i | ||||
\(367\) | −412.443 | − | 714.372i | −0.0586631 | − | 0.101607i | 0.835202 | − | 0.549943i | \(-0.185350\pi\) |
−0.893866 | + | 0.448335i | \(0.852017\pi\) | |||||||
\(368\) | −4339.12 | − | 7515.58i | −0.614654 | − | 1.06461i | ||||
\(369\) | −1386.52 | + | 2401.52i | −0.195608 | + | 0.338803i | ||||
\(370\) | −214.468 | −0.0301342 | ||||||||
\(371\) | 2429.23 | + | 5302.73i | 0.339945 | + | 0.742059i | ||||
\(372\) | −27.8486 | −0.00388140 | ||||||||
\(373\) | −666.925 | + | 1155.15i | −0.0925793 | + | 0.160352i | −0.908596 | − | 0.417677i | \(-0.862845\pi\) |
0.816016 | + | 0.578029i | \(0.196178\pi\) | |||||||
\(374\) | 364.660 | + | 631.610i | 0.0504174 | + | 0.0873255i | ||||
\(375\) | 1779.03 | + | 3081.37i | 0.244983 | + | 0.424324i | ||||
\(376\) | 769.746 | − | 1333.24i | 0.105576 | − | 0.182863i | ||||
\(377\) | −2226.94 | −0.304226 | ||||||||
\(378\) | −71.8355 | + | 101.131i | −0.00977466 | + | 0.0137609i | ||||
\(379\) | −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 | ||||
\(381\) | 732.612 | + | 1268.92i | 0.0985114 | + | 0.170627i | ||||
\(382\) | −47.7924 | − | 82.7788i | −0.00640123 | − | 0.0110873i | ||||
\(383\) | −176.688 | + | 306.032i | −0.0235727 | + | 0.0408290i | −0.877571 | − | 0.479447i | \(-0.840837\pi\) |
0.853998 | + | 0.520276i | \(0.174171\pi\) | |||||||
\(384\) | 1494.98 | 0.198673 | ||||||||
\(385\) | 13827.9 | + | 1303.96i | 1.83048 | + | 0.172613i | ||||
\(386\) | 156.341 | 0.0206154 | ||||||||
\(387\) | −784.992 | + | 1359.65i | −0.103110 | + | 0.178591i | ||||
\(388\) | −3105.08 | − | 5378.16i | −0.406280 | − | 0.703697i | ||||
\(389\) | −5868.59 | − | 10164.7i | −0.764908 | − | 1.32486i | −0.940295 | − | 0.340360i | \(-0.889451\pi\) |
0.175387 | − | 0.984500i | \(-0.443882\pi\) | |||||||
\(390\) | −168.548 | + | 291.933i | −0.0218840 | + | 0.0379041i | ||||
\(391\) | −6765.59 | −0.875066 | ||||||||
\(392\) | −1332.28 | − | 253.519i | −0.171658 | − | 0.0326649i | ||||
\(393\) | 5562.68 | 0.713996 | ||||||||
\(394\) | 155.073 | − | 268.595i | 0.0198286 | − | 0.0343442i | ||||
\(395\) | −3027.11 | − | 5243.10i | −0.385595 | − | 0.667871i | ||||
\(396\) | 2154.51 | + | 3731.73i | 0.273405 | + | 0.473551i | ||||
\(397\) | −6640.71 | + | 11502.1i | −0.839516 | + | 1.45408i | 0.0507841 | + | 0.998710i | \(0.483828\pi\) |
−0.890300 | + | 0.455374i | \(0.849505\pi\) | |||||||
\(398\) | −270.955 | −0.0341250 | ||||||||
\(399\) | −2796.19 | − | 263.678i | −0.350839 | − | 0.0330838i | ||||
\(400\) | 1852.01 | 0.231501 | ||||||||
\(401\) | 3741.18 | − | 6479.91i | 0.465899 | − | 0.806961i | −0.533343 | − | 0.845899i | \(-0.679064\pi\) |
0.999242 | + | 0.0389385i | \(0.0123976\pi\) | |||||||
\(402\) | −361.521 | − | 626.173i | −0.0448534 | − | 0.0776883i | ||||
\(403\) | 21.2979 | + | 36.8891i | 0.00263257 | + | 0.00455975i | ||||
\(404\) | −1236.99 | + | 2142.54i | −0.152333 | + | 0.263849i | ||||
\(405\) | −1007.20 | −0.123576 | ||||||||
\(406\) | −162.653 | + | 228.985i | −0.0198826 | + | 0.0279909i | ||||
\(407\) | 4193.27 | 0.510694 | ||||||||
\(408\) | 289.105 | − | 500.744i | 0.0350805 | − | 0.0607611i | ||||
\(409\) | 6898.30 | + | 11948.2i | 0.833983 | + | 1.44450i | 0.894856 | + | 0.446355i | \(0.147278\pi\) |
−0.0608735 | + | 0.998145i | \(0.519389\pi\) | |||||||
\(410\) | 475.218 | + | 823.102i | 0.0572423 | + | 0.0991466i | ||||
\(411\) | −766.673 | + | 1327.92i | −0.0920126 | + | 0.159370i | ||||
\(412\) | 1184.88 | 0.141686 | ||||||||
\(413\) | 6514.21 | + | 14219.7i | 0.776134 | + | 1.69421i | ||||
\(414\) | 309.875 | 0.0367862 | ||||||||
\(415\) | 3765.75 | − | 6522.46i | 0.445429 | − | 0.771506i | ||||
\(416\) | −858.622 | − | 1487.18i | −0.101196 | − | 0.175276i | ||||
\(417\) | 3399.16 | + | 5887.51i | 0.399179 | + | 0.691397i | ||||
\(418\) | 378.154 | − | 654.982i | 0.0442491 | − | 0.0766417i | ||||
\(419\) | 9497.56 | 1.10737 | 0.553683 | − | 0.832728i | \(-0.313222\pi\) | ||||
0.553683 | + | 0.832728i | \(0.313222\pi\) | |||||||
\(420\) | −2284.22 | − | 4986.18i | −0.265377 | − | 0.579288i | ||||
\(421\) | 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 | ||||
\(423\) | −1752.13 | − | 3034.77i | −0.201398 | − | 0.348832i | ||||
\(424\) | 622.608 | + | 1078.39i | 0.0713126 | + | 0.123517i | ||||
\(425\) | 721.915 | − | 1250.39i | 0.0823954 | − | 0.142713i | ||||
\(426\) | 73.2827 | 0.00833465 | ||||||||
\(427\) | −3630.82 | + | 5111.52i | −0.411494 | + | 0.579306i | ||||
\(428\) | −6759.75 | −0.763423 | ||||||||
\(429\) | 3295.44 | − | 5707.87i | 0.370875 | − | 0.642375i | ||||
\(430\) | 269.050 | + | 466.007i | 0.0301738 | + | 0.0522625i | ||||
\(431\) | 6698.64 | + | 11602.4i | 0.748636 | + | 1.29668i | 0.948476 | + | 0.316848i | \(0.102624\pi\) |
−0.199840 | + | 0.979829i | \(0.564042\pi\) | |||||||
\(432\) | 844.112 | − | 1462.05i | 0.0940101 | − | 0.162830i | ||||
\(433\) | −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 | ||||
\(435\) | −2280.55 | −0.251365 | ||||||||
\(436\) | 5405.61 | − | 9362.79i | 0.593766 | − | 1.02843i | ||||
\(437\) | 3507.98 | + | 6075.99i | 0.384003 | + | 0.665112i | ||||
\(438\) | 264.284 | + | 457.753i | 0.0288310 | + | 0.0499368i | ||||
\(439\) | 8184.42 | − | 14175.8i | 0.889798 | − | 1.54117i | 0.0496832 | − | 0.998765i | \(-0.484179\pi\) |
0.840114 | − | 0.542409i | \(-0.182488\pi\) | |||||||
\(440\) | 2965.22 | 0.321275 | ||||||||
\(441\) | −2016.05 | + | 2337.76i | −0.217692 | + | 0.252430i | ||||
\(442\) | −440.494 | −0.0474031 | ||||||||
\(443\) | 589.354 | − | 1020.79i | 0.0632078 | − | 0.109479i | −0.832690 | − | 0.553740i | \(-0.813200\pi\) |
0.895898 | + | 0.444261i | \(0.146534\pi\) | |||||||
\(444\) | −827.904 | − | 1433.97i | −0.0884923 | − | 0.153273i | ||||
\(445\) | 1355.80 | + | 2348.31i | 0.144429 | + | 0.250159i | ||||
\(446\) | 22.8033 | − | 39.4965i | 0.00242101 | − | 0.00419331i | ||||
\(447\) | −4523.70 | −0.478666 | ||||||||
\(448\) | 9007.56 | + | 849.404i | 0.949926 | + | 0.0895772i | ||||
\(449\) | −12400.9 | −1.30342 | −0.651709 | − | 0.758469i | \(-0.725948\pi\) | ||||
−0.651709 | + | 0.758469i | \(0.725948\pi\) | |||||||
\(450\) | −33.0648 | + | 57.2699i | −0.00346376 | + | 0.00599940i | ||||
\(451\) | −9291.45 | − | 16093.3i | −0.970105 | − | 1.68027i | ||||
\(452\) | 4161.95 | + | 7208.71i | 0.433101 | + | 0.750153i | ||||
\(453\) | 2387.74 | − | 4135.68i | 0.247651 | − | 0.428943i | ||||
\(454\) | 565.484 | 0.0584570 | ||||||||
\(455\) | −4857.94 | + | 6839.07i | −0.500535 | + | 0.704660i | ||||
\(456\) | −599.606 | −0.0615771 | ||||||||
\(457\) | −4962.79 | + | 8595.81i | −0.507986 | + | 0.879858i | 0.491971 | + | 0.870611i | \(0.336277\pi\) |
−0.999957 | + | 0.00924618i | \(0.997057\pi\) | |||||||
\(458\) | −671.366 | − | 1162.84i | −0.0684954 | − | 0.118637i | ||||
\(459\) | −658.073 | − | 1139.82i | −0.0669198 | − | 0.115909i | ||||
\(460\) | −6850.21 | + | 11864.9i | −0.694332 | + | 1.20262i | ||||
\(461\) | −16010.3 | −1.61751 | −0.808755 | − | 0.588146i | \(-0.799858\pi\) | ||||
−0.808755 | + | 0.588146i | \(0.799858\pi\) | |||||||
\(462\) | −346.216 | − | 755.749i | −0.0348646 | − | 0.0761053i | ||||
\(463\) | 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 | ||||
\(465\) | 21.8107 | + | 37.7772i | 0.00217515 | + | 0.00376747i | ||||
\(466\) | −141.199 | − | 244.563i | −0.0140363 | − | 0.0243115i | ||||
\(467\) | −1054.03 | + | 1825.64i | −0.104443 | + | 0.180900i | −0.913510 | − | 0.406815i | \(-0.866639\pi\) |
0.809068 | + | 0.587716i | \(0.199973\pi\) | |||||||
\(468\) | −2602.56 | −0.257059 | ||||||||
\(469\) | −7494.00 | − | 16358.5i | −0.737826 | − | 1.61059i | ||||
\(470\) | −1201.05 | −0.117873 | ||||||||
\(471\) | 1746.24 | − | 3024.58i | 0.170833 | − | 0.295892i | ||||
\(472\) | 1669.58 | + | 2891.80i | 0.162815 | + | 0.282004i | ||||
\(473\) | −5260.45 | − | 9111.37i | −0.511365 | − | 0.885711i | ||||
\(474\) | −181.173 | + | 313.802i | −0.0175561 | + | 0.0304080i | ||||
\(475\) | −1497.26 | −0.144629 | ||||||||
\(476\) | 4150.25 | − | 5842.77i | 0.399635 | − | 0.562612i | ||||
\(477\) | 2834.41 | 0.272073 | ||||||||
\(478\) | 772.293 | − | 1337.65i | 0.0738992 | − | 0.127997i | ||||
\(479\) | 1225.02 | + | 2121.80i | 0.116853 | + | 0.202395i | 0.918519 | − | 0.395377i | \(-0.129386\pi\) |
−0.801666 | + | 0.597772i | \(0.796053\pi\) | |||||||
\(480\) | −879.292 | − | 1522.98i | −0.0836126 | − | 0.144821i | ||||
\(481\) | −1266.32 | + | 2193.34i | −0.120040 | + | 0.207916i | ||||
\(482\) | −792.887 | −0.0749274 | ||||||||
\(483\) | 7677.35 | + | 723.967i | 0.723254 | + | 0.0682022i | ||||
\(484\) | −18309.9 | −1.71956 | ||||||||
\(485\) | −4863.72 | + | 8424.21i | −0.455361 | + | 0.788709i | ||||
\(486\) | 30.1407 | + | 52.2053i | 0.00281319 | + | 0.00487259i | ||||
\(487\) | −322.618 | − | 558.791i | −0.0300189 | − | 0.0519943i | 0.850626 | − | 0.525772i | \(-0.176223\pi\) |
−0.880645 | + | 0.473778i | \(0.842890\pi\) | |||||||
\(488\) | −669.270 | + | 1159.21i | −0.0620828 | + | 0.107531i | ||||
\(489\) | 3467.64 | 0.320679 | ||||||||
\(490\) | 348.408 | + | 999.034i | 0.0321214 | + | 0.0921056i | ||||
\(491\) | 11766.1 | 1.08146 | 0.540731 | − | 0.841196i | \(-0.318148\pi\) | ||||
0.540731 | + | 0.841196i | \(0.318148\pi\) | |||||||
\(492\) | −3668.94 | + | 6354.79i | −0.336196 | + | 0.582309i | ||||
\(493\) | −1490.03 | − | 2580.81i | −0.136121 | − | 0.235769i | ||||
\(494\) | 228.397 | + | 395.595i | 0.0208018 | + | 0.0360297i | ||||
\(495\) | 3374.77 | − | 5845.28i | 0.306434 | − | 0.530759i | ||||
\(496\) | −73.1159 | −0.00661896 | ||||||||
\(497\) | 1815.63 | + | 171.212i | 0.163868 | + | 0.0154526i | ||||
\(498\) | −450.763 | −0.0405606 | ||||||||
\(499\) | 22.0104 | − | 38.1232i | 0.00197459 | − | 0.00342010i | −0.865036 | − | 0.501709i | \(-0.832705\pi\) |
0.867011 | + | 0.498289i | \(0.166038\pi\) | |||||||
\(500\) | 4707.59 | + | 8153.78i | 0.421059 | + | 0.729296i | ||||
\(501\) | −4335.91 | − | 7510.02i | −0.386655 | − | 0.669707i | ||||
\(502\) | −29.7200 | + | 51.4765i | −0.00264236 | + | 0.00457671i | ||||
\(503\) | 8290.27 | 0.734880 | 0.367440 | − | 0.930047i | \(-0.380234\pi\) | ||||
0.367440 | + | 0.930047i | \(0.380234\pi\) | |||||||
\(504\) | −381.649 | + | 537.291i | −0.0337302 | + | 0.0474858i | ||||
\(505\) | 3875.19 | 0.341473 | ||||||||
\(506\) | −1038.28 | + | 1798.35i | −0.0912195 | + | 0.157997i | ||||
\(507\) | −1305.12 | − | 2260.54i | −0.114324 | − | 0.198016i | ||||
\(508\) | 1938.60 | + | 3357.76i | 0.169314 | + | 0.293261i | ||||
\(509\) | −3457.52 | + | 5988.60i | −0.301084 | + | 0.521493i | −0.976382 | − | 0.216052i | \(-0.930682\pi\) |
0.675298 | + | 0.737545i | \(0.264015\pi\) | |||||||
\(510\) | −451.098 | −0.0391666 | ||||||||
\(511\) | 5478.36 | + | 11958.6i | 0.474263 | + | 1.03526i | ||||
\(512\) | 4925.45 | 0.425148 | ||||||||
\(513\) | −682.425 | + | 1181.99i | −0.0587325 | + | 0.101728i | ||||
\(514\) | −86.7157 | − | 150.196i | −0.00744137 | − | 0.0128888i | ||||
\(515\) | −927.980 | − | 1607.31i | −0.0794014 | − | 0.137527i | ||||
\(516\) | −2077.21 | + | 3597.83i | −0.177217 | + | 0.306949i | ||||
\(517\) | 23483.0 | 1.99764 | ||||||||
\(518\) | 133.039 | + | 290.408i | 0.0112845 | + | 0.0246328i | ||||
\(519\) | −5684.81 | −0.480800 | ||||||||
\(520\) | −895.464 | + | 1550.99i | −0.0755167 | + | 0.130799i | ||||
\(521\) | −6699.64 | − | 11604.1i | −0.563371 | − | 0.975788i | −0.997199 | − | 0.0747919i | \(-0.976171\pi\) |
0.433828 | − | 0.900996i | \(-0.357163\pi\) | |||||||
\(522\) | 68.2458 | + | 118.205i | 0.00572230 | + | 0.00991131i | ||||
\(523\) | 4968.50 | − | 8605.69i | 0.415406 | − | 0.719504i | −0.580065 | − | 0.814570i | \(-0.696973\pi\) |
0.995471 | + | 0.0950662i | \(0.0303063\pi\) | |||||||
\(524\) | 14719.7 | 1.22716 | ||||||||
\(525\) | −953.005 | + | 1341.65i | −0.0792239 | + | 0.111532i | ||||
\(526\) | −227.988 | −0.0188988 | ||||||||
\(527\) | −28.5007 | + | 49.3647i | −0.00235581 | + | 0.00408038i | ||||
\(528\) | 5656.63 | + | 9797.58i | 0.466237 | + | 0.807547i | ||||
\(529\) | −3548.17 | − | 6145.60i | −0.291622 | − | 0.505104i | ||||
\(530\) | 485.736 | − | 841.320i | 0.0398095 | − | 0.0689521i | ||||
\(531\) | 7600.74 | 0.621175 | ||||||||
\(532\) | −7399.15 | − | 697.733i | −0.602996 | − | 0.0568620i | ||||
\(533\) | 11223.7 | 0.912104 | ||||||||
\(534\) | 81.1450 | − | 140.547i | 0.00657582 | − | 0.0113897i | ||||
\(535\) | 5294.15 | + | 9169.74i | 0.427825 | + | 0.741014i | ||||
\(536\) | −1920.70 | − | 3326.75i | −0.154779 | − | 0.268085i | ||||
\(537\) | −6432.74 | + | 11141.8i | −0.516933 | + | 0.895355i | ||||
\(538\) | −689.435 | −0.0552484 | ||||||||
\(539\) | −6812.07 | − | 19533.1i | −0.544373 | − | 1.56095i | ||||
\(540\) | −2665.21 | −0.212394 | ||||||||
\(541\) | −4643.08 | + | 8042.06i | −0.368987 | + | 0.639103i | −0.989407 | − | 0.145166i | \(-0.953628\pi\) |
0.620421 | + | 0.784269i | \(0.286962\pi\) | |||||||
\(542\) | −276.226 | − | 478.437i | −0.0218910 | − | 0.0379163i | ||||
\(543\) | 575.599 | + | 996.966i | 0.0454904 | + | 0.0787917i | ||||
\(544\) | 1149.00 | − | 1990.13i | 0.0905570 | − | 0.156849i | ||||
\(545\) | −16934.4 | −1.33099 | ||||||||
\(546\) | 499.857 | + | 47.1360i | 0.0391793 | + | 0.00369457i | ||||
\(547\) | −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 | ||||
\(549\) | 1523.42 | + | 2638.64i | 0.118430 | + | 0.205127i | ||||
\(550\) | −221.577 | − | 383.782i | −0.0171783 | − | 0.0297537i | ||||
\(551\) | −1545.17 | + | 2676.32i | −0.119467 | + | 0.206924i | ||||
\(552\) | 1646.31 | 0.126941 | ||||||||
\(553\) | −5221.84 | + | 7351.37i | −0.401546 | + | 0.565302i | ||||
\(554\) | 1812.83 | 0.139025 | ||||||||
\(555\) | −1296.81 | + | 2246.14i | −0.0991828 | + | 0.171790i | ||||
\(556\) | 8994.69 | + | 15579.3i | 0.686079 | + | 1.18832i | ||||
\(557\) | −902.972 | − | 1563.99i | −0.0686897 | − | 0.118974i | 0.829635 | − | 0.558306i | \(-0.188549\pi\) |
−0.898325 | + | 0.439332i | \(0.855215\pi\) | |||||||
\(558\) | 1.30538 | − | 2.26098i | 9.90340e−5 | − | 0.000171532i | ||||
\(559\) | 6354.40 | 0.480792 | ||||||||
\(560\) | −5997.18 | − | 13091.1i | −0.452548 | − | 0.987859i | ||||
\(561\) | 8819.86 | 0.663770 | ||||||||
\(562\) | −338.694 | + | 586.635i | −0.0254216 | + | 0.0440315i | ||||
\(563\) | −6107.45 | − | 10578.4i | −0.457190 | − | 0.791877i | 0.541621 | − | 0.840623i | \(-0.317811\pi\) |
−0.998811 | + | 0.0487460i | \(0.984478\pi\) | |||||||
\(564\) | −4636.40 | − | 8030.48i | −0.346148 | − | 0.599546i | ||||
\(565\) | 6519.17 | − | 11291.5i | 0.485423 | − | 0.840776i | ||||
\(566\) | −439.050 | −0.0326054 | ||||||||
\(567\) | 624.789 | + | 1363.84i | 0.0462763 | + | 0.101016i | ||||
\(568\) | 389.338 | 0.0287610 | ||||||||
\(569\) | −2141.89 | + | 3709.86i | −0.157808 | + | 0.273331i | −0.934078 | − | 0.357070i | \(-0.883776\pi\) |
0.776270 | + | 0.630400i | \(0.217109\pi\) | |||||||
\(570\) | 233.895 | + | 405.119i | 0.0171874 | + | 0.0297694i | ||||
\(571\) | −3179.97 | − | 5507.87i | −0.233060 | − | 0.403673i | 0.725647 | − | 0.688067i | \(-0.241541\pi\) |
−0.958707 | + | 0.284395i | \(0.908207\pi\) | |||||||
\(572\) | 8720.25 | − | 15103.9i | 0.637433 | − | 1.10407i | ||||
\(573\) | −1155.93 | −0.0842753 | ||||||||
\(574\) | 819.764 | − | 1154.07i | 0.0596103 | − | 0.0839201i | ||||
\(575\) | 4110.95 | 0.298153 | ||||||||
\(576\) | 2198.34 | − | 3807.64i | 0.159023 | − | 0.275437i | ||||
\(577\) | −7234.36 | − | 12530.3i | −0.521959 | − | 0.904059i | −0.999674 | − | 0.0255444i | \(-0.991868\pi\) |
0.477715 | − | 0.878515i | \(-0.341465\pi\) | |||||||
\(578\) | 314.656 | + | 545.001i | 0.0226436 | + | 0.0392198i | ||||
\(579\) | 945.335 | − | 1637.37i | 0.0678528 | − | 0.117525i | ||||
\(580\) | −6034.68 | −0.432028 | ||||||||
\(581\) | −11168.0 | − | 1053.13i | −0.797461 | − | 0.0751998i | ||||
\(582\) | 582.191 | 0.0414649 | ||||||||
\(583\) | −9497.10 | + | 16449.5i | −0.674665 | + | 1.16855i | ||||
\(584\) | 1404.09 | + | 2431.96i | 0.0994894 | + | 0.172321i | ||||
\(585\) | 2038.29 | + | 3530.43i | 0.144056 | + | 0.249513i | ||||
\(586\) | −1020.67 | + | 1767.85i | −0.0719513 | + | 0.124623i | ||||
\(587\) | −11132.6 | −0.782777 | −0.391388 | − | 0.920226i | \(-0.628005\pi\) | ||||
−0.391388 | + | 0.920226i | \(0.628005\pi\) | |||||||
\(588\) | −5334.78 | + | 6186.07i | −0.374154 | + | 0.433859i | ||||
\(589\) | 59.1108 | 0.00413517 | ||||||||
\(590\) | 1302.55 | − | 2256.07i | 0.0908897 | − | 0.157426i | ||||
\(591\) | −1875.34 | − | 3248.19i | −0.130527 | − | 0.226079i | ||||
\(592\) | −2173.65 | − | 3764.87i | −0.150906 | − | 0.261377i | ||||
\(593\) | 9887.81 | − | 17126.2i | 0.684728 | − | 1.18598i | −0.288794 | − | 0.957391i | \(-0.593254\pi\) |
0.973522 | − | 0.228592i | \(-0.0734123\pi\) | |||||||
\(594\) | −403.963 | −0.0279037 | ||||||||
\(595\) | −11176.3 | − | 1053.91i | −0.770054 | − | 0.0726154i | ||||
\(596\) | −11970.4 | −0.822696 | ||||||||
\(597\) | −1638.37 | + | 2837.73i | −0.112318 | + | 0.194541i | ||||
\(598\) | −627.098 | − | 1086.17i | −0.0428829 | − | 0.0742753i | ||||
\(599\) | 11945.5 | + | 20690.2i | 0.814825 | + | 1.41132i | 0.909453 | + | 0.415806i | \(0.136500\pi\) |
−0.0946282 | + | 0.995513i | \(0.530166\pi\) | |||||||
\(600\) | −175.667 | + | 304.265i | −0.0119527 | + | 0.0207026i | ||||
\(601\) | 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 | ||||
\(603\) | −8743.95 | −0.590516 | ||||||||
\(604\) | 6318.32 | − | 10943.7i | 0.425644 | − | 0.737237i | ||||
\(605\) | 14340.1 | + | 24837.8i | 0.963648 | + | 1.66909i | ||||
\(606\) | −115.966 | − | 200.859i | −0.00777358 | − | 0.0134642i | ||||
\(607\) | −7298.36 | + | 12641.1i | −0.488025 | + | 0.845285i | −0.999905 | − | 0.0137724i | \(-0.995616\pi\) |
0.511880 | + | 0.859057i | \(0.328949\pi\) | |||||||
\(608\) | −2383.04 | −0.158956 | ||||||||
\(609\) | 1414.67 | + | 3088.06i | 0.0941304 | + | 0.205475i | ||||
\(610\) | 1044.28 | 0.0693142 | ||||||||
\(611\) | −7091.62 | + | 12283.0i | −0.469552 | + | 0.813288i | ||||
\(612\) | −1741.36 | − | 3016.13i | −0.115017 | − | 0.199215i | ||||
\(613\) | −989.898 | − | 1714.55i | −0.0652229 | − | 0.112969i | 0.831570 | − | 0.555420i | \(-0.187442\pi\) |
−0.896793 | + | 0.442451i | \(0.854109\pi\) | |||||||
\(614\) | −746.650 | + | 1293.24i | −0.0490755 | + | 0.0850012i | ||||
\(615\) | 11493.9 | 0.753622 | ||||||||
\(616\) | −1839.39 | − | 4015.16i | −0.120310 | − | 0.262622i | ||||
\(617\) | 16262.4 | 1.06110 | 0.530551 | − | 0.847653i | \(-0.321985\pi\) | ||||
0.530551 | + | 0.847653i | \(0.321985\pi\) | |||||||
\(618\) | −55.5400 | + | 96.1981i | −0.00361512 | + | 0.00626158i | ||||
\(619\) | 6010.49 | + | 10410.5i | 0.390278 | + | 0.675981i | 0.992486 | − | 0.122358i | \(-0.0390457\pi\) |
−0.602208 | + | 0.798339i | \(0.705712\pi\) | |||||||
\(620\) | 57.7143 | + | 99.9642i | 0.00373849 | + | 0.00647526i | ||||
\(621\) | 1873.70 | − | 3245.34i | 0.121077 | − | 0.209712i | ||||
\(622\) | 296.127 | 0.0190894 | ||||||||
\(623\) | 2338.79 | − | 3292.58i | 0.150404 | − | 0.211740i | ||||
\(624\) | −6832.97 | −0.438362 | ||||||||
\(625\) | 9225.06 | − | 15978.3i | 0.590404 | − | 1.02261i | ||||
\(626\) | 1097.23 | + | 1900.45i | 0.0700543 | + | 0.121338i | ||||
\(627\) | −4573.12 | − | 7920.87i | −0.291280 | − | 0.504512i | ||||
\(628\) | 4620.82 | − | 8003.49i | 0.293616 | − | 0.508557i | ||||
\(629\) | −3389.16 | −0.214841 | ||||||||
\(630\) | 511.890 | + | 48.2708i | 0.0323717 | + | 0.00305262i | ||||
\(631\) | 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 | ||||
\(633\) | −5430.07 | − | 9405.16i | −0.340957 | − | 0.590556i | ||||
\(634\) | −754.317 | − | 1306.51i | −0.0472519 | − | 0.0818428i | ||||
\(635\) | 3036.58 | − | 5259.51i | 0.189769 | − | 0.328689i | ||||
\(636\) | 7500.29 | 0.467620 | ||||||||
\(637\) | 12274.2 | + | 2335.66i | 0.763454 | + | 0.145278i | ||||
\(638\) | −914.669 | −0.0567588 | ||||||||
\(639\) | 443.114 | − | 767.496i | 0.0274324 | − | 0.0475143i | ||||
\(640\) | −3098.24 | − | 5366.31i | −0.191358 | − | 0.331441i | ||||
\(641\) | 2555.80 | + | 4426.78i | 0.157485 | + | 0.272772i | 0.933961 | − | 0.357374i | \(-0.116328\pi\) |
−0.776476 | + | 0.630147i | \(0.782995\pi\) | |||||||
\(642\) | 316.857 | − | 548.812i | 0.0194787 | − | 0.0337382i | ||||
\(643\) | −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 | ||||
\(645\) | 6507.38 | 0.397252 | ||||||||
\(646\) | −305.639 | + | 529.382i | −0.0186149 | + | 0.0322419i | ||||
\(647\) | 9203.06 | + | 15940.2i | 0.559211 | + | 0.968582i | 0.997563 | + | 0.0697783i | \(0.0222292\pi\) |
−0.438352 | + | 0.898804i | \(0.644437\pi\) | |||||||
\(648\) | 160.132 | + | 277.357i | 0.00970770 | + | 0.0168142i | ||||
\(649\) | −25467.3 | + | 44110.7i | −1.54034 | + | 2.66795i | ||||
\(650\) | 267.655 | 0.0161512 | ||||||||
\(651\) | 37.6240 | − | 52.9675i | 0.00226513 | − | 0.00318888i | ||||
\(652\) | 9175.91 | 0.551160 | ||||||||
\(653\) | −9960.71 | + | 17252.5i | −0.596926 | + | 1.03391i | 0.396346 | + | 0.918101i | \(0.370278\pi\) |
−0.993272 | + | 0.115805i | \(0.963055\pi\) | |||||||
\(654\) | 506.766 | + | 877.744i | 0.0302999 | + | 0.0524809i | ||||
\(655\) | −11528.3 | − | 19967.6i | −0.687707 | − | 1.19114i | ||||
\(656\) | −9632.74 | + | 16684.4i | −0.573316 | + | 0.993012i | ||||
\(657\) | 6392.11 | 0.379574 | ||||||||
\(658\) | 745.040 | + | 1626.33i | 0.0441408 | + | 0.0963542i | ||||
\(659\) | −18858.8 | −1.11477 | −0.557385 | − | 0.830254i | \(-0.688195\pi\) | ||||
−0.557385 | + | 0.830254i | \(0.688195\pi\) | |||||||
\(660\) | 8930.17 | − | 15467.5i | 0.526676 | − | 0.912230i | ||||
\(661\) | −12916.0 | − | 22371.2i | −0.760023 | − | 1.31640i | −0.942838 | − | 0.333251i | \(-0.891854\pi\) |
0.182815 | − | 0.983147i | \(-0.441479\pi\) | |||||||
\(662\) | −378.718 | − | 655.960i | −0.0222346 | − | 0.0385115i | ||||
\(663\) | −2663.50 | + | 4613.33i | −0.156021 | + | 0.270236i | ||||
\(664\) | −2394.82 | −0.139965 | ||||||||
\(665\) | 4848.43 | + | 10583.6i | 0.282728 | + | 0.617162i | ||||
\(666\) | 155.229 | 0.00903153 | ||||||||
\(667\) | 4242.50 | − | 7348.22i | 0.246282 | − | 0.426573i | ||||
\(668\) | −11473.5 | − | 19872.7i | −0.664555 | − | 1.15104i | ||||
\(669\) | −275.767 | − | 477.642i | −0.0159369 | − | 0.0276034i | ||||
\(670\) | −1498.46 | + | 2595.41i | −0.0864037 | + | 0.149656i | ||||
\(671\) | −20417.7 | −1.17469 | ||||||||
\(672\) | −1516.80 | + | 2135.37i | −0.0870714 | + | 0.122580i | ||||
\(673\) | −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 | ||||
\(675\) | 399.862 | + | 692.581i | 0.0228010 | + | 0.0394925i | ||||
\(676\) | −3453.55 | − | 5981.73i | −0.196493 | − | 0.340335i | ||||
\(677\) | 13135.9 | − | 22752.0i | 0.745720 | − | 1.29163i | −0.204137 | − | 0.978942i | \(-0.565439\pi\) |
0.949857 | − | 0.312683i | \(-0.101228\pi\) | |||||||
\(678\) | −780.350 | −0.0442023 | ||||||||
\(679\) | 14424.2 | + | 1360.19i | 0.815242 | + | 0.0768766i | ||||
\(680\) | −2396.60 | −0.135155 | ||||||||
\(681\) | 3419.28 | − | 5922.36i | 0.192404 | − | 0.333253i | ||||
\(682\) | 8.74769 | + | 15.1514i | 0.000491153 | + | 0.000850702i | ||||
\(683\) | 4036.14 | + | 6990.81i | 0.226118 | + | 0.391648i | 0.956654 | − | 0.291226i | \(-0.0940631\pi\) |
−0.730536 | + | 0.682874i | \(0.760730\pi\) | |||||||
\(684\) | −1805.80 | + | 3127.74i | −0.100945 | + | 0.174842i | ||||
\(685\) | 6355.51 | 0.354499 | ||||||||
\(686\) | 1136.65 | − | 1091.50i | 0.0632619 | − | 0.0607486i | ||||
\(687\) | −16238.0 | −0.901774 | ||||||||
\(688\) | −5453.67 | + | 9446.04i | −0.302208 | + | 0.523440i | ||||
\(689\) | −5736.05 | − | 9935.13i | −0.317164 | − | 0.549344i | ||||
\(690\) | −642.194 | − | 1112.31i | −0.0354318 | − | 0.0613696i | ||||
\(691\) | 12242.6 | − | 21204.9i | 0.673997 | − | 1.16740i | −0.302763 | − | 0.953066i | \(-0.597909\pi\) |
0.976761 | − | 0.214332i | \(-0.0687575\pi\) | |||||||
\(692\) | −15042.9 | −0.826364 | ||||||||
\(693\) | −10008.5 | − | 943.789i | −0.548615 | − | 0.0517339i | ||||
\(694\) | −24.7062 | −0.00135135 | ||||||||
\(695\) | 14089.1 | − | 24403.0i | 0.768962 | − | 1.33188i | ||||
\(696\) | 362.578 | + | 628.003i | 0.0197464 | + | 0.0342017i | ||||
\(697\) | 7509.71 | + | 13007.2i | 0.408107 | + | 0.706862i | ||||
\(698\) | 447.440 | − | 774.989i | 0.0242634 | − | 0.0420254i | ||||
\(699\) | −3415.10 | −0.184794 | ||||||||
\(700\) | −2521.80 | + | 3550.22i | −0.136164 | + | 0.191694i | ||||
\(701\) | 778.448 | 0.0419423 | 0.0209712 | − | 0.999780i | \(-0.493324\pi\) | ||||
0.0209712 | + | 0.999780i | \(0.493324\pi\) | |||||||
\(702\) | 121.993 | − | 211.297i | 0.00655885 | − | 0.0113603i | ||||
\(703\) | 1757.29 | + | 3043.72i | 0.0942780 | + | 0.163294i | ||||
\(704\) | 14731.7 | + | 25516.0i | 0.788667 | + | 1.36601i | ||||
\(705\) | −7262.34 | + | 12578.7i | −0.387965 | + | 0.671975i | ||||
\(706\) | 1768.93 | 0.0942985 | ||||||||
\(707\) | −2403.86 | − | 5247.35i | −0.127873 | − | 0.279133i | ||||
\(708\) | 20112.7 | 1.06763 | ||||||||
\(709\) | 12086.0 | − | 20933.6i | 0.640197 | − | 1.10885i | −0.345192 | − | 0.938532i | \(-0.612186\pi\) |
0.985389 | − | 0.170322i | \(-0.0544806\pi\) | |||||||
\(710\) | −151.874 | − | 263.053i | −0.00802777 | − | 0.0139045i | ||||
\(711\) | 2190.98 | + | 3794.89i | 0.115567 | + | 0.200168i | ||||
\(712\) | 431.109 | − | 746.703i | 0.0226917 | − | 0.0393032i | ||||
\(713\) | −162.297 | −0.00852466 | ||||||||
\(714\) | 279.826 | + | 610.826i | 0.0146670 | + | 0.0320162i | ||||
\(715\) | −27318.3 | −1.42888 | ||||||||
\(716\) | −17022.0 | + | 29483.0i | −0.888467 | + | 1.53887i | ||||
\(717\) | −9339.54 | − | 16176.6i | −0.486460 | − | 0.842573i | ||||
\(718\) | 806.269 | + | 1396.50i | 0.0419077 | + | 0.0725862i | ||||
\(719\) | 40.9418 | − | 70.9132i | 0.00212360 | − | 0.00367819i | −0.864962 | − | 0.501838i | \(-0.832657\pi\) |
0.867085 | + | 0.498160i | \(0.165991\pi\) | |||||||
\(720\) | −6997.47 | −0.362195 | ||||||||
\(721\) | −1600.79 | + | 2253.61i | −0.0826860 | + | 0.116406i | ||||
\(722\) | −1067.63 | −0.0550318 | ||||||||
\(723\) | −4794.29 | + | 8303.96i | −0.246614 | + | 0.427147i | ||||
\(724\) | 1523.12 | + | 2638.13i | 0.0781856 | + | 0.135421i | ||||
\(725\) | 905.382 | + | 1568.17i | 0.0463794 | + | 0.0803315i | ||||
\(726\) | 858.259 | − | 1486.55i | 0.0438747 | − | 0.0759931i | ||||
\(727\) | −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 | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 1095.42 | − | 1897.33i | 0.0555389 | − | 0.0961962i | ||||
\(731\) | 4251.70 | + | 7364.16i | 0.215123 | + | 0.372604i | ||||
\(732\) | 4031.20 | + | 6982.25i | 0.203549 | + | 0.352557i | ||||
\(733\) | 2534.47 | − | 4389.83i | 0.127712 | − | 0.221203i | −0.795078 | − | 0.606507i | \(-0.792570\pi\) |
0.922790 | + | 0.385304i | \(0.125903\pi\) | |||||||
\(734\) | 204.631 | 0.0102903 | ||||||||
\(735\) | 12569.7 | + | 2391.88i | 0.630801 | + | 0.120035i | ||||
\(736\) | 6542.98 | 0.327687 | ||||||||
\(737\) | 29297.8 | − | 50745.3i | 1.46431 | − | 2.53627i | ||||
\(738\) | −343.956 | − | 595.750i | −0.0171561 | − | 0.0297153i | ||||
\(739\) | 19214.2 | + | 33280.0i | 0.956437 | + | 1.65660i | 0.731045 | + | 0.682329i | \(0.239033\pi\) |
0.225392 | + | 0.974268i | \(0.427634\pi\) | |||||||
\(740\) | −3431.55 | + | 5943.62i | −0.170468 | + | 0.295259i | ||||
\(741\) | 5524.14 | 0.273865 | ||||||||
\(742\) | −1440.53 | − | 135.841i | −0.0712717 | − | 0.00672086i | ||||
\(743\) | 21592.9 | 1.06617 | 0.533086 | − | 0.846061i | \(-0.321032\pi\) | ||||
0.533086 | + | 0.846061i | \(0.321032\pi\) | |||||||
\(744\) | 6.93523 | − | 12.0122i | 0.000341744 | − | 0.000591919i | ||||
\(745\) | 9375.07 | + | 16238.1i | 0.461042 | + | 0.798548i | ||||
\(746\) | −165.445 | − | 286.560i | −0.00811982 | − | 0.0140639i | ||||
\(747\) | −2725.60 | + | 4720.87i | −0.133500 | + | 0.231228i | ||||
\(748\) | 23338.7 | 1.14084 | ||||||||
\(749\) | 9132.55 | − | 12856.9i | 0.445522 | − | 0.627212i | ||||
\(750\) | −882.655 | −0.0429733 | ||||||||
\(751\) | −4056.30 | + | 7025.72i | −0.197093 | + | 0.341374i | −0.947585 | − | 0.319505i | \(-0.896483\pi\) |
0.750492 | + | 0.660880i | \(0.229817\pi\) | |||||||
\(752\) | −12172.8 | − | 21083.9i | −0.590287 | − | 1.02241i | ||||
\(753\) | 359.411 | + | 622.519i | 0.0173940 | + | 0.0301273i | ||||
\(754\) | 276.220 | − | 478.428i | 0.0133413 | − | 0.0231078i | ||||
\(755\) | −19793.7 | −0.954129 | ||||||||
\(756\) | 1653.29 | + | 3608.93i | 0.0795364 | + | 0.173618i | ||||
\(757\) | 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 | ||||
\(759\) | 12556.2 | + | 21747.9i | 0.600475 | + | 1.04005i | ||||
\(760\) | 1242.64 | + | 2152.32i | 0.0593098 | + | 0.102728i | ||||
\(761\) | 3605.96 | − | 6245.71i | 0.171769 | − | 0.297512i | −0.767269 | − | 0.641325i | \(-0.778385\pi\) |
0.939038 | + | 0.343812i | \(0.111718\pi\) | |||||||
\(762\) | −363.481 | −0.0172802 | ||||||||
\(763\) | 10504.8 | + | 22930.7i | 0.498425 | + | 1.08800i | ||||
\(764\) | −3058.77 | −0.144846 | ||||||||
\(765\) | −2727.62 | + | 4724.38i | −0.128912 | + | 0.223282i | ||||
\(766\) | −43.8313 | − | 75.9181i | −0.00206748 | − | 0.00358098i | ||||
\(767\) | −15381.7 | − | 26641.9i | −0.724123 | − | 1.25422i | ||||
\(768\) | 5676.81 | − | 9832.52i | 0.266724 | − | 0.461980i | ||||
\(769\) | −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 | ||||
\(771\) | −2097.35 | −0.0979693 | ||||||||
\(772\) | 2501.50 | − | 4332.73i | 0.116621 | − | 0.201993i | ||||
\(773\) | 12416.3 | + | 21505.7i | 0.577728 | + | 1.00065i | 0.995739 | + | 0.0922122i | \(0.0293938\pi\) |
−0.418012 | + | 0.908442i | \(0.637273\pi\) | |||||||
\(774\) | −194.734 | − | 337.290i | −0.00904339 | − | 0.0156636i | ||||
\(775\) | 17.3178 | − | 29.9952i | 0.000802674 | − | 0.00139027i | ||||
\(776\) | 3093.08 | 0.143086 | ||||||||
\(777\) | 3845.90 | + | 362.665i | 0.177569 | + | 0.0167446i | ||||
\(778\) | 2911.66 | 0.134175 | ||||||||
\(779\) | 7787.61 | − | 13488.5i | 0.358177 | − | 0.620381i | ||||
\(780\) | 5393.64 | + | 9342.05i | 0.247594 | + | 0.428845i | ||||
\(781\) | 2969.43 | + | 5143.20i | 0.136049 | + | 0.235644i | ||||
\(782\) | 839.177 | − | 1453.50i | 0.0383746 | − | 0.0664667i | ||||
\(783\) | 1650.63 | 0.0753368 | ||||||||
\(784\) | −14006.4 | + | 16241.4i | −0.638045 | + | 0.739860i | ||||
\(785\) | −14475.9 | −0.658173 | ||||||||
\(786\) | −689.973 | + | 1195.07i | −0.0313111 | + | 0.0542324i | ||||
\(787\) | −18156.6 | − | 31448.1i | −0.822378 | − | 1.42440i | −0.903907 | − | 0.427730i | \(-0.859314\pi\) |
0.0815287 | − | 0.996671i | \(-0.474020\pi\) | |||||||
\(788\) | −4962.45 | − | 8595.21i | −0.224340 | − | 0.388568i | ||||
\(789\) | −1378.56 | + | 2387.74i | −0.0622028 | + | 0.107738i | ||||
\(790\) | 1501.88 | 0.0676386 | ||||||||
\(791\) | −19333.7 | − | 1823.15i | −0.869062 | − | 0.0819517i | ||||
\(792\) | −2146.18 | −0.0962895 | ||||||||
\(793\) | 6165.94 | − | 10679.7i | 0.276115 | − | 0.478245i | ||||
\(794\) | −1647.37 | − | 2853.34i | −0.0736311 | − | 0.127533i | ||||
\(795\) | −5874.14 | − | 10174.3i | −0.262056 | − | 0.453893i | ||||
\(796\) | −4335.37 | + | 7509.08i | −0.193044 | + | 0.334362i | ||||
\(797\) | 31665.7 | 1.40735 | 0.703675 | − | 0.710522i | \(-0.251541\pi\) | ||||
0.703675 | + | 0.710522i | \(0.251541\pi\) | |||||||
\(798\) | 403.476 | − | 568.019i | 0.0178984 | − | 0.0251975i | ||||
\(799\) | −18979.9 | −0.840375 | ||||||||
\(800\) | −698.162 | + | 1209.25i | −0.0308547 | + | 0.0534419i | ||||
\(801\) | −981.308 | − | 1699.68i | −0.0432869 | − | 0.0749752i | ||||
\(802\) | 928.081 | + | 1607.48i | 0.0408625 | + | 0.0707759i | ||||
\(803\) | −21417.7 | + | 37096.5i | −0.941237 | + | 1.63027i | ||||
\(804\) | −23137.8 | −1.01494 | ||||||||
\(805\) | −13312.1 | − | 29058.7i | −0.582844 | − | 1.27228i | ||||
\(806\) | −10.5668 | −0.000461788 | ||||||||
\(807\) | −4168.76 | + | 7220.51i | −0.181843 | + | 0.314961i | ||||
\(808\) | −616.105 | − | 1067.13i | −0.0268249 | − | 0.0464621i | ||||
\(809\) | −6192.30 | − | 10725.4i | −0.269110 | − | 0.466111i | 0.699523 | − | 0.714610i | \(-0.253396\pi\) |
−0.968632 | + | 0.248499i | \(0.920063\pi\) | |||||||
\(810\) | 124.929 | − | 216.384i | 0.00541922 | − | 0.00938637i | ||||
\(811\) | 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 | ||||
\(813\) | −6680.94 | −0.288205 | ||||||||
\(814\) | −520.116 | + | 900.868i | −0.0223957 | + | 0.0387904i | ||||
\(815\) | −7186.45 | − | 12447.3i | −0.308872 | − | 0.534982i | ||||
\(816\) | −4571.91 | − | 7918.78i | −0.196138 | − | 0.339722i | ||||
\(817\) | 4409.04 | − | 7636.67i | 0.188804 | − | 0.327018i | ||||
\(818\) | −3422.55 | −0.146292 | ||||||||
\(819\) | 3516.11 | − | 4950.02i | 0.150016 | − | 0.211194i | ||||
\(820\) | 30414.6 | 1.29527 | ||||||||
\(821\) | −13228.2 | + | 22911.9i | −0.562322 | + | 0.973970i | 0.434971 | + | 0.900444i | \(0.356759\pi\) |
−0.997293 | + | 0.0735259i | \(0.976575\pi\) | |||||||
\(822\) | −190.190 | − | 329.419i | −0.00807012 | − | 0.0139779i | ||||
\(823\) | −11549.3 | − | 20003.9i | −0.489164 | − | 0.847257i | 0.510758 | − | 0.859724i | \(-0.329365\pi\) |
−0.999922 | + | 0.0124673i | \(0.996031\pi\) | |||||||
\(824\) | −295.074 | + | 511.083i | −0.0124750 | + | 0.0216073i | ||||
\(825\) | −5359.17 | −0.226160 | ||||||||
\(826\) | −3862.92 | − | 364.270i | −0.162722 | − | 0.0153445i | ||||
\(827\) | 20647.6 | 0.868183 | 0.434092 | − | 0.900869i | \(-0.357069\pi\) | ||||
0.434092 | + | 0.900869i | \(0.357069\pi\) | |||||||
\(828\) | 4958.09 | − | 8587.67i | 0.208099 | − | 0.360437i | ||||
\(829\) | 11684.3 | + | 20237.7i | 0.489519 | + | 0.847871i | 0.999927 | − | 0.0120609i | \(-0.00383919\pi\) |
−0.510409 | + | 0.859932i | \(0.670506\pi\) | |||||||
\(830\) | 934.176 | + | 1618.04i | 0.0390671 | + | 0.0676662i | ||||
\(831\) | 10961.5 | − | 18985.9i | 0.457583 | − | 0.792557i | ||||
\(832\) | −17795.3 | −0.741514 | ||||||||
\(833\) | 5505.78 | + | 15787.4i | 0.229009 | + | 0.656664i | ||||
\(834\) | −1686.47 | −0.0700212 | ||||||||
\(835\) | −17971.8 | + | 31128.0i | −0.744838 | + | 1.29010i | ||||
\(836\) | −12101.2 | − | 20959.8i | −0.500631 | − | 0.867119i | ||||
\(837\) | −15.7863 | − | 27.3426i | −0.000651915 | − | 0.00112915i | ||||
\(838\) | −1178.04 | + | 2040.42i | −0.0485617 | + | 0.0841113i | ||||
\(839\) | 16735.5 | 0.688645 | 0.344322 | − | 0.938851i | \(-0.388109\pi\) | ||||
0.344322 | + | 0.938851i | \(0.388109\pi\) | |||||||
\(840\) | 2719.58 | + | 256.454i | 0.111708 | + | 0.0105339i | ||||
\(841\) | −20651.6 | −0.846758 | ||||||||
\(842\) | −77.4439 | + | 134.137i | −0.00316971 | + | 0.00549009i | ||||
\(843\) | 4095.92 | + | 7094.34i | 0.167344 | + | 0.289848i | ||||
\(844\) | −14368.8 | − | 24887.5i | −0.586013 | − | 1.01500i | ||||
\(845\) | −5409.56 | + | 9369.63i | −0.220230 | + | 0.381450i | ||||
\(846\) | 869.307 | 0.0353279 | ||||||||
\(847\) | 24737.0 | − | 34825.1i | 1.00351 | − | 1.41276i | ||||
\(848\) | 19691.9 | 0.797432 | ||||||||
\(849\) | −2654.78 | + | 4598.21i | −0.107317 | + | 0.185878i | ||||
\(850\) | 179.087 | + | 310.188i | 0.00722662 | + | 0.0125169i | ||||
\(851\) | −4824.90 | − | 8356.97i | −0.194354 | − | 0.336631i | ||||
\(852\) | 1172.55 | − | 2030.91i | 0.0471488 | − | 0.0816642i | ||||
\(853\) | −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 | ||||
\(855\) | 5657.12 | 0.226280 | ||||||||
\(856\) | 1683.40 | − | 2915.74i | 0.0672168 | − | 0.116423i | ||||
\(857\) | 16394.3 | + | 28395.7i | 0.653463 | + | 1.13183i | 0.982277 | + | 0.187437i | \(0.0600180\pi\) |
−0.328813 | + | 0.944395i | \(0.606649\pi\) | |||||||
\(858\) | 817.507 | + | 1415.96i | 0.0325282 | + | 0.0563405i | ||||
\(859\) | 2454.88 | − | 4251.98i | 0.0975081 | − | 0.168889i | −0.813145 | − | 0.582062i | \(-0.802246\pi\) |
0.910653 | + | 0.413173i | \(0.135579\pi\) | |||||||
\(860\) | 17219.5 | 0.682768 | ||||||||
\(861\) | −7129.89 | − | 15563.7i | −0.282214 | − | 0.616039i | ||||
\(862\) | −3323.49 | −0.131321 | ||||||||
\(863\) | −8897.48 | + | 15410.9i | −0.350954 | + | 0.607871i | −0.986417 | − | 0.164261i | \(-0.947476\pi\) |
0.635463 | + | 0.772132i | \(0.280809\pi\) | |||||||
\(864\) | 636.420 | + | 1102.31i | 0.0250596 | + | 0.0434044i | ||||
\(865\) | 11781.4 | + | 20406.0i | 0.463097 | + | 0.802108i | ||||
\(866\) | 1743.60 | − | 3020.01i | 0.0684181 | − | 0.118504i | ||||
\(867\) | 7610.44 | 0.298113 | ||||||||
\(868\) | 99.5588 | − | 140.160i | 0.00389314 | − | 0.00548081i | ||||
\(869\) | −29364.7 | −1.14629 | ||||||||
\(870\) | 282.870 | − | 489.945i | 0.0110232 | − | 0.0190928i | ||||
\(871\) | 17695.3 | + | 30649.1i | 0.688383 | + | 1.19231i | ||||
\(872\) | 2692.36 | + | 4663.30i | 0.104558 | + | 0.181100i | ||||
\(873\) | 3520.30 | − | 6097.33i | 0.136476 | − | 0.236384i | ||||
\(874\) | −1740.46 | −0.0673592 | ||||||||
\(875\) | −21868.4 | − | 2062.17i | −0.844899 | − | 0.0796732i | ||||
\(876\) | 16914.5 | 0.652384 | ||||||||
\(877\) | −17336.1 | + | 30027.0i | −0.667501 | + | 1.15615i | 0.311099 | + | 0.950377i | \(0.399303\pi\) |
−0.978601 | + | 0.205769i | \(0.934030\pi\) | |||||||
\(878\) | 2030.33 | + | 3516.63i | 0.0780412 | + | 0.135171i | ||||
\(879\) | 12343.2 | + | 21379.1i | 0.473636 | + | 0.820362i | ||||
\(880\) | 23446.0 | − | 40609.7i | 0.898141 | − | 1.55563i | ||||
\(881\) | 40848.2 | 1.56210 | 0.781051 | − | 0.624467i | \(-0.214684\pi\) | ||||
0.781051 | + | 0.624467i | \(0.214684\pi\) | |||||||
\(882\) | −252.173 | − | 723.087i | −0.00962712 | − | 0.0276050i | ||||
\(883\) | 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 | ||||
\(885\) | −15752.0 | − | 27283.3i | −0.598304 | − | 1.03629i | ||||
\(886\) | 146.202 | + | 253.230i | 0.00554375 | + | 0.00960205i | ||||
\(887\) | −16605.4 | + | 28761.3i | −0.628583 | + | 1.08874i | 0.359253 | + | 0.933240i | \(0.383032\pi\) |
−0.987836 | + | 0.155498i | \(0.950302\pi\) | |||||||
\(888\) | 824.703 | 0.0311658 | ||||||||
\(889\) | −9005.49 | − | 849.210i | −0.339746 | − | 0.0320378i | ||||
\(890\) | −672.671 | −0.0253348 | ||||||||
\(891\) | −2442.62 | + | 4230.74i | −0.0918415 | + | 0.159074i | ||||
\(892\) | −729.721 | − | 1263.91i | −0.0273911 | − | 0.0474428i | ||||
\(893\) | 9841.11 | + | 17045.3i | 0.368780 | + | 0.638745i | ||||
\(894\) | 561.102 | − | 971.856i | 0.0209911 | − | 0.0363577i | ||||
\(895\) | 53325.7 | 1.99160 | ||||||||
\(896\) | −5344.55 | + | 7524.13i | −0.199273 | + | 0.280540i | ||||
\(897\) | −15167.3 | −0.564573 | ||||||||
\(898\) | 1538.16 | − | 2664.17i | 0.0571592 | − | 0.0990027i | ||||
\(899\) | −35.7439 | − | 61.9102i | −0.00132606 | − | 0.00229680i | ||||
\(900\) | 1058.10 | + | 1832.67i | 0.0391887 | + | 0.0678768i | ||||
\(901\) | 7675.93 | − | 13295.1i | 0.283820 | − | 0.491591i | ||||
\(902\) | 4609.90 | 0.170169 | ||||||||
\(903\) | −4036.66 | − | 8811.55i | −0.148762 | − | 0.324729i | ||||
\(904\) | −4145.86 | −0.152532 | ||||||||
\(905\) | 2385.78 | − | 4132.29i | 0.0876310 | − | 0.151781i | ||||
\(906\) | 592.331 | + | 1025.95i | 0.0217206 | + | 0.0376212i | ||||
\(907\) | −1248.92 | − | 2163.18i | −0.0457217 | − | 0.0791923i | 0.842259 | − | 0.539073i | \(-0.181225\pi\) |
−0.887981 | + | 0.459881i | \(0.847892\pi\) | |||||||
\(908\) | 9047.93 | − | 15671.5i | 0.330690 | − | 0.572771i | ||||
\(909\) | −2804.81 | −0.102343 | ||||||||
\(910\) | −866.723 | − | 1891.95i | −0.0315732 | − | 0.0689205i | ||||
\(911\) | −1895.00 | −0.0689180 | −0.0344590 | − | 0.999406i | \(-0.510971\pi\) | ||||
−0.0344590 | + | 0.999406i | \(0.510971\pi\) | |||||||
\(912\) | −4741.09 | + | 8211.82i | −0.172142 | + | 0.298158i | ||||
\(913\) | −18265.0 | − | 31635.9i | −0.662084 | − | 1.14676i | ||||
\(914\) | −1231.13 | − | 2132.38i | −0.0445538 | − | 0.0771694i | ||||
\(915\) | 6314.38 | − | 10936.8i | 0.228139 | − | 0.395148i | ||||
\(916\) | −42968.3 | −1.54990 | ||||||||
\(917\) | −19886.6 | + | 27996.6i | −0.716155 | + | 1.00821i | ||||
\(918\) | 326.499 | 0.0117386 | ||||||||
\(919\) | −3135.36 | + | 5430.59i | −0.112542 | + | 0.194928i | −0.916794 | − | 0.399360i | \(-0.869233\pi\) |
0.804253 | + | 0.594287i | \(0.202566\pi\) | |||||||
\(920\) | −3411.86 | − | 5909.52i | −0.122267 | − | 0.211773i | ||||
\(921\) | 9029.44 | + | 15639.4i | 0.323051 | + | 0.559541i | ||||
\(922\) | 1985.85 | − | 3439.59i | 0.0709332 | − | 0.122860i | ||||
\(923\) | −3586.95 | −0.127915 | ||||||||
\(924\) | −26483.9 | − | 2497.41i | −0.942919 | − | 0.0889164i | ||||
\(925\) | 2059.34 | 0.0732008 | ||||||||
\(926\) | −2154.80 | + | 3732.23i | −0.0764700 | + | 0.132450i | ||||
\(927\) | 671.660 | + | 1163.35i | 0.0237974 | + | 0.0412183i | ||||
\(928\) | 1441.01 | + | 2495.90i | 0.0509735 | + | 0.0882887i | ||||
\(929\) | 15776.3 | − | 27325.3i | 0.557161 | − | 0.965032i | −0.440570 | − | 0.897718i | \(-0.645224\pi\) |
0.997732 | − | 0.0673138i | \(-0.0214429\pi\) | |||||||
\(930\) | −10.8212 | −0.000381550 | ||||||||
\(931\) | 11323.5 | − | 13130.4i | 0.398616 | − | 0.462225i | ||||
\(932\) | −9036.89 | −0.317611 | ||||||||
\(933\) | 1790.57 | − | 3101.36i | 0.0628303 | − | 0.108825i | ||||
\(934\) | −261.476 | − | 452.889i | −0.00916033 | − | 0.0158662i | ||||
\(935\) | −18278.6 | − | 31659.4i | −0.639330 | − | 1.10735i | ||||
\(936\) | 648.125 | − | 1122.59i | 0.0226331 | − | 0.0392018i | ||||
\(937\) | −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 | ||||
\(939\) | 26538.1 | 0.922299 | ||||||||
\(940\) | −19217.3 | + | 33285.3i | −0.666806 | + | 1.15494i | ||||
\(941\) | 16269.3 | + | 28179.3i | 0.563618 | + | 0.976214i | 0.997177 | + | 0.0750892i | \(0.0239242\pi\) |
−0.433559 | + | 0.901125i | \(0.642742\pi\) | |||||||
\(942\) | 433.193 | + | 750.312i | 0.0149832 | + | 0.0259517i | ||||
\(943\) | −21382.0 | + | 37034.8i | −0.738383 | + | 1.27892i | ||||
\(944\) | 52805.6 | 1.82063 | ||||||||
\(945\) | 3600.76 | − | 5069.19i | 0.123950 | − | 0.174498i | ||||
\(946\) | 2609.94 | 0.0897003 | ||||||||
\(947\) | 20355.5 | − | 35256.8i | 0.698485 | − | 1.20981i | −0.270507 | − | 0.962718i | \(-0.587191\pi\) |
0.968992 | − | 0.247093i | \(-0.0794753\pi\) | |||||||
\(948\) | 5797.67 | + | 10041.9i | 0.198628 | + | 0.344034i | ||||
\(949\) | −12935.8 | − | 22405.5i | −0.442481 | − | 0.766400i | ||||
\(950\) | 185.714 | − | 321.666i | 0.00634248 | − | 0.0109855i | ||||
\(951\) | −18244.3 | −0.622095 | ||||||||
\(952\) | 1486.66 | + | 3245.21i | 0.0506124 | + | 0.110481i | ||||
\(953\) | −52516.4 | −1.78507 | −0.892536 | − | 0.450976i | \(-0.851076\pi\) | ||||
−0.892536 | + | 0.450976i | \(0.851076\pi\) | |||||||
\(954\) | −351.569 | + | 608.936i | −0.0119313 | + | 0.0206656i | ||||
\(955\) | 2395.59 | + | 4149.29i | 0.0811723 | + | 0.140595i | ||||
\(956\) | −24713.9 | − | 42805.7i | −0.836091 | − | 1.44815i | ||||
\(957\) | −5530.67 | + | 9579.40i | −0.186814 | + | 0.323572i | ||||
\(958\) | −607.786 | −0.0204976 | ||||||||
\(959\) | −3942.46 | − | 8605.92i | −0.132751 | − | 0.289781i | ||||
\(960\) | −18223.7 | −0.612673 | ||||||||
\(961\) | 14894.8 | − | 25798.6i | 0.499977 | − | 0.865986i | ||||
\(962\) | −314.139 | − | 544.105i | −0.0105283 | − | 0.0182356i | ||||
\(963\) | −3831.84 | − | 6636.93i | −0.128223 | − | 0.222090i | ||||
\(964\) | −12686.4 | + | 21973.6i | −0.423862 | + | 0.734150i | ||||
\(965\) | −7836.58 | −0.261418 | ||||||||
\(966\) | −1107.80 | + | 1559.58i | −0.0368975 | + | 0.0519447i | ||||
\(967\) | 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 | ||||
\(969\) | 3696.17 | + | 6401.96i | 0.122537 | + | 0.212240i | ||||
\(970\) | −1206.55 | − | 2089.81i | −0.0399382 | − | 0.0691750i | ||||
\(971\) | −6886.25 | + | 11927.3i | −0.227590 | + | 0.394198i | −0.957093 | − | 0.289779i | \(-0.906418\pi\) |
0.729503 | + | 0.683978i | \(0.239751\pi\) | |||||||
\(972\) | 1929.05 | 0.0636566 | ||||||||
\(973\) | −41783.5 | − | 3940.14i | −1.37669 | − | 0.129820i | ||||
\(974\) | 160.065 | 0.00526572 | ||||||||
\(975\) | 1618.41 | − | 2803.17i | 0.0531597 | − | 0.0920753i | ||||
\(976\) | 10583.8 | + | 18331.8i | 0.347111 | + | 0.601215i | ||||
\(977\) | −12391.0 | − | 21461.9i | −0.405757 | − | 0.702791i | 0.588653 | − | 0.808386i | \(-0.299659\pi\) |
−0.994409 | + | 0.105595i | \(0.966325\pi\) | |||||||
\(978\) | −430.112 | + | 744.976i | −0.0140628 | + | 0.0243576i | ||||
\(979\) | 13152.0 | 0.429358 | ||||||||
\(980\) | 33261.2 | + | 6329.29i | 1.08417 | + | 0.206308i | ||||
\(981\) | 12256.9 | 0.398912 | ||||||||
\(982\) | −1459.42 | + | 2527.79i | −0.0474257 | + | 0.0821437i | ||||
\(983\) | −21402.4 | − | 37070.0i | −0.694435 | − | 1.20280i | −0.970371 | − | 0.241620i | \(-0.922321\pi\) |
0.275936 | − | 0.961176i | \(-0.411012\pi\) | |||||||
\(984\) | −1827.38 | − | 3165.11i | −0.0592019 | − | 0.102541i | ||||
\(985\) | −7773.05 | + | 13463.3i | −0.251442 | + | 0.435510i | ||||
\(986\) | 739.271 | 0.0238775 | ||||||||
\(987\) | 21537.7 | + | 2030.98i | 0.694582 | + | 0.0654984i | ||||
\(988\) | 14617.7 | 0.470700 | ||||||||
\(989\) | −12105.7 | + | 20967.6i | −0.389219 | + | 0.674147i | ||||
\(990\) | 837.187 | + | 1450.05i | 0.0268763 | + | 0.0465511i | ||||
\(991\) | −224.931 | − | 389.592i | −0.00721006 | − | 0.0124882i | 0.862398 | − | 0.506231i | \(-0.168962\pi\) |
−0.869608 | + | 0.493743i | \(0.835628\pi\) | |||||||
\(992\) | 27.5630 | − | 47.7404i | 0.000882182 | − | 0.00152798i | ||||
\(993\) | −9159.89 | −0.292729 | ||||||||
\(994\) | −261.986 | + | 368.827i | −0.00835986 | + | 0.0117691i | ||||
\(995\) | 13581.6 | 0.432730 | ||||||||
\(996\) | −7212.35 | + | 12492.1i | −0.229450 | + | 0.397419i | ||||
\(997\) | 10736.9 | + | 18596.8i | 0.341063 | + | 0.590739i | 0.984630 | − | 0.174651i | \(-0.0558796\pi\) |
−0.643567 | + | 0.765390i | \(0.722546\pi\) | |||||||
\(998\) | 5.46017 | + | 9.45729i | 0.000173185 | + | 0.000299965i | ||||
\(999\) | 938.612 | − | 1625.72i | 0.0297261 | − | 0.0514871i |
(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 | 21.4.e.b.16.2 | yes | 6 | |
3.2 | odd | 2 | 63.4.e.c.37.2 | 6 | |||
4.3 | odd | 2 | 336.4.q.k.289.3 | 6 | |||
7.2 | even | 3 | 147.4.a.l.1.2 | 3 | |||
7.3 | odd | 6 | 147.4.e.n.67.2 | 6 | |||
7.4 | even | 3 | inner | 21.4.e.b.4.2 | ✓ | 6 | |
7.5 | odd | 6 | 147.4.a.m.1.2 | 3 | |||
7.6 | odd | 2 | 147.4.e.n.79.2 | 6 | |||
21.2 | odd | 6 | 441.4.a.s.1.2 | 3 | |||
21.5 | even | 6 | 441.4.a.t.1.2 | 3 | |||
21.11 | odd | 6 | 63.4.e.c.46.2 | 6 | |||
21.17 | even | 6 | 441.4.e.w.361.2 | 6 | |||
21.20 | even | 2 | 441.4.e.w.226.2 | 6 | |||
28.11 | odd | 6 | 336.4.q.k.193.3 | 6 | |||
28.19 | even | 6 | 2352.4.a.cg.1.3 | 3 | |||
28.23 | odd | 6 | 2352.4.a.ci.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.e.b.4.2 | ✓ | 6 | 7.4 | even | 3 | inner | |
21.4.e.b.16.2 | yes | 6 | 1.1 | even | 1 | trivial | |
63.4.e.c.37.2 | 6 | 3.2 | odd | 2 | |||
63.4.e.c.46.2 | 6 | 21.11 | odd | 6 | |||
147.4.a.l.1.2 | 3 | 7.2 | even | 3 | |||
147.4.a.m.1.2 | 3 | 7.5 | odd | 6 | |||
147.4.e.n.67.2 | 6 | 7.3 | odd | 6 | |||
147.4.e.n.79.2 | 6 | 7.6 | odd | 2 | |||
336.4.q.k.193.3 | 6 | 28.11 | odd | 6 | |||
336.4.q.k.289.3 | 6 | 4.3 | odd | 2 | |||
441.4.a.s.1.2 | 3 | 21.2 | odd | 6 | |||
441.4.a.t.1.2 | 3 | 21.5 | even | 6 | |||
441.4.e.w.226.2 | 6 | 21.20 | even | 2 | |||
441.4.e.w.361.2 | 6 | 21.17 | even | 6 | |||
2352.4.a.cg.1.3 | 3 | 28.19 | even | 6 | |||
2352.4.a.ci.1.1 | 3 | 28.23 | odd | 6 |