Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.159390625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 323.2 | ||
Root | \(1.43801 + 1.04478i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.323 |
Dual form | 847.2.f.s.729.2 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.43801 | + | 1.04478i | 1.01683 | + | 0.738770i | 0.965631 | − | 0.259918i | \(-0.0836956\pi\) |
0.0511995 | + | 0.998688i | \(0.483696\pi\) | |||||||
\(3\) | 0.190983 | − | 0.587785i | 0.110264 | − | 0.339358i | −0.880666 | − | 0.473738i | \(-0.842904\pi\) |
0.990930 | + | 0.134380i | \(0.0429043\pi\) | |||||||
\(4\) | 0.358290 | + | 1.10270i | 0.179145 | + | 0.551351i | ||||
\(5\) | 2.24703 | − | 1.63256i | 1.00490 | − | 0.730105i | 0.0417693 | − | 0.999127i | \(-0.486701\pi\) |
0.963134 | + | 0.269022i | \(0.0867005\pi\) | |||||||
\(6\) | 0.888742 | − | 0.645709i | 0.362827 | − | 0.263610i | ||||
\(7\) | 0.309017 | + | 0.951057i | 0.116797 | + | 0.359466i | ||||
\(8\) | 0.461691 | − | 1.42094i | 0.163232 | − | 0.502378i | ||||
\(9\) | 2.11803 | + | 1.53884i | 0.706011 | + | 0.512947i | ||||
\(10\) | 4.93693 | 1.56120 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.716580 | 0.206859 | ||||||||
\(13\) | −3.47350 | − | 2.52364i | −0.963374 | − | 0.699932i | −0.00944228 | − | 0.999955i | \(-0.503006\pi\) |
−0.953932 | + | 0.300023i | \(0.903006\pi\) | |||||||
\(14\) | −0.549273 | + | 1.69049i | −0.146799 | + | 0.451802i | ||||
\(15\) | −0.530452 | − | 1.63256i | −0.136962 | − | 0.421526i | ||||
\(16\) | 4.02452 | − | 2.92398i | 1.00613 | − | 0.730996i | ||||
\(17\) | −2.22929 | + | 1.61968i | −0.540683 | + | 0.392829i | −0.824339 | − | 0.566097i | \(-0.808453\pi\) |
0.283656 | + | 0.958926i | \(0.408453\pi\) | |||||||
\(18\) | 1.43801 | + | 4.42575i | 0.338943 | + | 1.04316i | ||||
\(19\) | −0.599213 | + | 1.84419i | −0.137469 | + | 0.423086i | −0.995966 | − | 0.0897327i | \(-0.971399\pi\) |
0.858497 | + | 0.512819i | \(0.171399\pi\) | |||||||
\(20\) | 2.60532 | + | 1.89288i | 0.582568 | + | 0.423260i | ||||
\(21\) | 0.618034 | 0.134866 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.37009 | 0.911228 | 0.455614 | − | 0.890178i | \(-0.349420\pi\) | ||||
0.455614 | + | 0.890178i | \(0.349420\pi\) | |||||||
\(24\) | −0.747032 | − | 0.542750i | −0.152487 | − | 0.110788i | ||||
\(25\) | 0.838802 | − | 2.58157i | 0.167760 | − | 0.516313i | ||||
\(26\) | −2.35829 | − | 7.25807i | −0.462499 | − | 1.42342i | ||||
\(27\) | 2.80902 | − | 2.04087i | 0.540596 | − | 0.392766i | ||||
\(28\) | −0.938015 | + | 0.681508i | −0.177268 | + | 0.128793i | ||||
\(29\) | −2.66623 | − | 8.20580i | −0.495106 | − | 1.52378i | −0.816792 | − | 0.576933i | \(-0.804250\pi\) |
0.321686 | − | 0.946846i | \(-0.395750\pi\) | |||||||
\(30\) | 0.942871 | − | 2.90186i | 0.172144 | − | 0.529804i | ||||
\(31\) | 0.162279 | + | 0.117903i | 0.0291462 | + | 0.0211759i | 0.602263 | − | 0.798298i | \(-0.294266\pi\) |
−0.573117 | + | 0.819474i | \(0.694266\pi\) | |||||||
\(32\) | 5.85410 | 1.03487 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.89796 | −0.839993 | ||||||||
\(35\) | 2.24703 | + | 1.63256i | 0.379818 | + | 0.275954i | ||||
\(36\) | −0.938015 | + | 2.88691i | −0.156336 | + | 0.481152i | ||||
\(37\) | 0.319981 | + | 0.984800i | 0.0526045 | + | 0.161900i | 0.973907 | − | 0.226946i | \(-0.0728739\pi\) |
−0.921303 | + | 0.388846i | \(0.872874\pi\) | |||||||
\(38\) | −2.78845 | + | 2.02593i | −0.452346 | + | 0.328649i | ||||
\(39\) | −2.14674 | + | 1.55970i | −0.343753 | + | 0.249751i | ||||
\(40\) | −1.28234 | − | 3.94664i | −0.202756 | − | 0.624018i | ||||
\(41\) | −2.96847 | + | 9.13600i | −0.463597 | + | 1.42680i | 0.397142 | + | 0.917757i | \(0.370002\pi\) |
−0.860739 | + | 0.509047i | \(0.829998\pi\) | |||||||
\(42\) | 0.888742 | + | 0.645709i | 0.137136 | + | 0.0996351i | ||||
\(43\) | 4.70820 | 0.717994 | 0.358997 | − | 0.933339i | \(-0.383119\pi\) | ||||
0.358997 | + | 0.933339i | \(0.383119\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.27155 | 1.08398 | ||||||||
\(46\) | 6.28426 | + | 4.56578i | 0.926564 | + | 0.673188i | ||||
\(47\) | −4.03129 | + | 12.4070i | −0.588024 | + | 1.80975i | −0.00125473 | + | 0.999999i | \(0.500399\pi\) |
−0.586770 | + | 0.809754i | \(0.699601\pi\) | |||||||
\(48\) | −0.950059 | − | 2.92398i | −0.137129 | − | 0.422040i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 3.90337 | − | 2.83597i | 0.552021 | − | 0.401066i | ||||
\(51\) | 0.526264 | + | 1.61968i | 0.0736918 | + | 0.226800i | ||||
\(52\) | 1.53831 | − | 4.73443i | 0.213325 | − | 0.656547i | ||||
\(53\) | 3.15526 | + | 2.29243i | 0.433409 | + | 0.314890i | 0.783010 | − | 0.622009i | \(-0.213683\pi\) |
−0.349602 | + | 0.936898i | \(0.613683\pi\) | |||||||
\(54\) | 6.17167 | 0.839857 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.49406 | 0.199653 | ||||||||
\(57\) | 0.969548 | + | 0.704418i | 0.128420 | + | 0.0933024i | ||||
\(58\) | 4.73918 | − | 14.5857i | 0.622284 | − | 1.91519i | ||||
\(59\) | −2.64430 | − | 8.13831i | −0.344258 | − | 1.05952i | −0.961980 | − | 0.273121i | \(-0.911944\pi\) |
0.617721 | − | 0.786397i | \(-0.288056\pi\) | |||||||
\(60\) | 1.61018 | − | 1.16986i | 0.207873 | − | 0.151029i | ||||
\(61\) | −0.799801 | + | 0.581090i | −0.102404 | + | 0.0744009i | −0.637809 | − | 0.770195i | \(-0.720159\pi\) |
0.535405 | + | 0.844596i | \(0.320159\pi\) | |||||||
\(62\) | 0.110177 | + | 0.339091i | 0.0139925 | + | 0.0430646i | ||||
\(63\) | −0.809017 | + | 2.48990i | −0.101927 | + | 0.313698i | ||||
\(64\) | 0.369254 | + | 0.268279i | 0.0461567 | + | 0.0335348i | ||||
\(65\) | −11.9251 | −1.47912 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.41745 | −0.661846 | −0.330923 | − | 0.943658i | \(-0.607360\pi\) | ||||
−0.330923 | + | 0.943658i | \(0.607360\pi\) | |||||||
\(68\) | −2.58475 | − | 1.87793i | −0.313447 | − | 0.227733i | ||||
\(69\) | 0.834614 | − | 2.56868i | 0.100476 | − | 0.309232i | ||||
\(70\) | 1.52560 | + | 4.69530i | 0.182344 | + | 0.561196i | ||||
\(71\) | 1.63183 | − | 1.18559i | 0.193662 | − | 0.140704i | −0.486729 | − | 0.873553i | \(-0.661810\pi\) |
0.680391 | + | 0.732849i | \(0.261810\pi\) | |||||||
\(72\) | 3.16448 | − | 2.29913i | 0.372937 | − | 0.270955i | ||||
\(73\) | 3.08123 | + | 9.48306i | 0.360631 | + | 1.10991i | 0.952672 | + | 0.304000i | \(0.0983224\pi\) |
−0.592041 | + | 0.805908i | \(0.701678\pi\) | |||||||
\(74\) | −0.568761 | + | 1.75047i | −0.0661171 | + | 0.203488i | ||||
\(75\) | −1.35721 | − | 0.986070i | −0.156717 | − | 0.113862i | ||||
\(76\) | −2.24828 | −0.257896 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.71658 | −0.534047 | ||||||||
\(79\) | 5.09153 | + | 3.69921i | 0.572842 | + | 0.416194i | 0.836136 | − | 0.548522i | \(-0.184809\pi\) |
−0.263295 | + | 0.964715i | \(0.584809\pi\) | |||||||
\(80\) | 4.26963 | − | 13.1406i | 0.477359 | − | 1.46916i | ||||
\(81\) | 1.76393 | + | 5.42882i | 0.195992 | + | 0.603203i | ||||
\(82\) | −13.8138 | + | 10.0363i | −1.52548 | + | 1.10833i | ||||
\(83\) | −1.39269 | + | 1.01185i | −0.152868 | + | 0.111065i | −0.661590 | − | 0.749866i | \(-0.730118\pi\) |
0.508722 | + | 0.860931i | \(0.330118\pi\) | |||||||
\(84\) | 0.221435 | + | 0.681508i | 0.0241606 | + | 0.0743586i | ||||
\(85\) | −2.36507 | + | 7.27892i | −0.256527 | + | 0.789510i | ||||
\(86\) | 6.77047 | + | 4.91903i | 0.730078 | + | 0.530433i | ||||
\(87\) | −5.33245 | −0.571699 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.3035 | −1.62217 | −0.811086 | − | 0.584928i | \(-0.801123\pi\) | ||||
−0.811086 | + | 0.584928i | \(0.801123\pi\) | |||||||
\(90\) | 10.4566 | + | 7.59716i | 1.10222 | + | 0.800811i | ||||
\(91\) | 1.32676 | − | 4.08334i | 0.139082 | − | 0.428050i | ||||
\(92\) | 1.56576 | + | 4.81891i | 0.163242 | + | 0.502407i | ||||
\(93\) | 0.100294 | − | 0.0728678i | 0.0104000 | − | 0.00755604i | ||||
\(94\) | −18.7597 | + | 13.6297i | −1.93491 | + | 1.40580i | ||||
\(95\) | 1.66431 | + | 5.12221i | 0.170754 | + | 0.525527i | ||||
\(96\) | 1.11803 | − | 3.44095i | 0.114109 | − | 0.351191i | ||||
\(97\) | −9.39772 | − | 6.82784i | −0.954194 | − | 0.693262i | −0.00239864 | − | 0.999997i | \(-0.500764\pi\) |
−0.951795 | + | 0.306735i | \(0.900764\pi\) | |||||||
\(98\) | −1.77748 | −0.179553 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.14723 | 0.314723 | ||||||||
\(101\) | 2.76020 | + | 2.00540i | 0.274650 | + | 0.199545i | 0.716580 | − | 0.697505i | \(-0.245706\pi\) |
−0.441931 | + | 0.897049i | \(0.645706\pi\) | |||||||
\(102\) | −0.935427 | + | 2.87895i | −0.0926210 | + | 0.285058i | ||||
\(103\) | −5.61873 | − | 17.2927i | −0.553629 | − | 1.70390i | −0.699536 | − | 0.714598i | \(-0.746610\pi\) |
0.145906 | − | 0.989298i | \(-0.453390\pi\) | |||||||
\(104\) | −5.18962 | + | 3.77048i | −0.508884 | + | 0.369726i | ||||
\(105\) | 1.38874 | − | 1.00898i | 0.135527 | − | 0.0984664i | ||||
\(106\) | 2.14223 | + | 6.59310i | 0.208072 | + | 0.640379i | ||||
\(107\) | −1.00352 | + | 3.08852i | −0.0970140 | + | 0.298578i | −0.987773 | − | 0.155897i | \(-0.950173\pi\) |
0.890759 | + | 0.454475i | \(0.150173\pi\) | |||||||
\(108\) | 3.25692 | + | 2.36629i | 0.313397 | + | 0.227696i | ||||
\(109\) | −12.6912 | −1.21559 | −0.607796 | − | 0.794093i | \(-0.707946\pi\) | ||||
−0.607796 | + | 0.794093i | \(0.707946\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.639962 | 0.0607425 | ||||||||
\(112\) | 4.02452 | + | 2.92398i | 0.380281 | + | 0.276290i | ||||
\(113\) | −5.70076 | + | 17.5451i | −0.536282 | + | 1.65051i | 0.204579 | + | 0.978850i | \(0.434417\pi\) |
−0.740862 | + | 0.671658i | \(0.765583\pi\) | |||||||
\(114\) | 0.658263 | + | 2.02593i | 0.0616520 | + | 0.189745i | ||||
\(115\) | 9.81974 | − | 7.13446i | 0.915696 | − | 0.665292i | ||||
\(116\) | 8.09328 | − | 5.88011i | 0.751442 | − | 0.545955i | ||||
\(117\) | −3.47350 | − | 10.6903i | −0.321125 | − | 0.988320i | ||||
\(118\) | 4.70020 | − | 14.4657i | 0.432688 | − | 1.33168i | ||||
\(119\) | −2.22929 | − | 1.61968i | −0.204359 | − | 0.148475i | ||||
\(120\) | −2.56468 | −0.234122 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.75724 | −0.159093 | ||||||||
\(123\) | 4.80308 | + | 3.48964i | 0.433079 | + | 0.314650i | ||||
\(124\) | −0.0718686 | + | 0.221189i | −0.00645399 | + | 0.0198633i | ||||
\(125\) | 1.96169 | + | 6.03746i | 0.175459 | + | 0.540007i | ||||
\(126\) | −3.76477 | + | 2.73527i | −0.335393 | + | 0.243677i | ||||
\(127\) | 15.7834 | − | 11.4673i | 1.40055 | − | 1.01756i | 0.405933 | − | 0.913903i | \(-0.366947\pi\) |
0.994613 | − | 0.103653i | \(-0.0330532\pi\) | |||||||
\(128\) | −3.36733 | − | 10.3636i | −0.297633 | − | 0.916020i | ||||
\(129\) | 0.899187 | − | 2.76741i | 0.0791690 | − | 0.243657i | ||||
\(130\) | −17.1484 | − | 12.4591i | −1.50402 | − | 1.09273i | ||||
\(131\) | 6.89796 | 0.602677 | 0.301339 | − | 0.953517i | \(-0.402567\pi\) | ||||
0.301339 | + | 0.953517i | \(0.402567\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.93910 | −0.168141 | ||||||||
\(134\) | −7.79037 | − | 5.66003i | −0.672985 | − | 0.488952i | ||||
\(135\) | 2.98010 | − | 9.17180i | 0.256486 | − | 0.789383i | ||||
\(136\) | 1.27222 | + | 3.91548i | 0.109092 | + | 0.335749i | ||||
\(137\) | 2.11210 | − | 1.53453i | 0.180449 | − | 0.131104i | −0.493894 | − | 0.869522i | \(-0.664427\pi\) |
0.674343 | + | 0.738418i | \(0.264427\pi\) | |||||||
\(138\) | 3.88389 | − | 2.82181i | 0.330618 | − | 0.240208i | ||||
\(139\) | 0.309430 | + | 0.952327i | 0.0262455 | + | 0.0807753i | 0.963321 | − | 0.268351i | \(-0.0864786\pi\) |
−0.937076 | + | 0.349126i | \(0.886479\pi\) | |||||||
\(140\) | −0.995144 | + | 3.06274i | −0.0841051 | + | 0.258849i | ||||
\(141\) | 6.52277 | + | 4.73907i | 0.549316 | + | 0.399102i | ||||
\(142\) | 3.58527 | 0.300869 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 13.0236 | 1.08530 | ||||||||
\(145\) | −19.3876 | − | 14.0859i | −1.61005 | − | 1.16977i | ||||
\(146\) | −5.47684 | + | 16.8560i | −0.453267 | + | 1.39501i | ||||
\(147\) | 0.190983 | + | 0.587785i | 0.0157520 | + | 0.0484797i | ||||
\(148\) | −0.971296 | + | 0.705688i | −0.0798400 | + | 0.0580072i | ||||
\(149\) | −12.0501 | + | 8.75492i | −0.987184 | + | 0.717231i | −0.959303 | − | 0.282380i | \(-0.908876\pi\) |
−0.0278812 | + | 0.999611i | \(0.508876\pi\) | |||||||
\(150\) | −0.921462 | − | 2.83597i | −0.0752370 | − | 0.231556i | ||||
\(151\) | −4.88389 | + | 15.0311i | −0.397445 | + | 1.22321i | 0.529596 | + | 0.848250i | \(0.322344\pi\) |
−0.927041 | + | 0.374960i | \(0.877656\pi\) | |||||||
\(152\) | 2.34383 | + | 1.70289i | 0.190110 | + | 0.138123i | ||||
\(153\) | −7.21414 | −0.583229 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.557129 | 0.0447497 | ||||||||
\(156\) | −2.48904 | − | 1.80839i | −0.199282 | − | 0.144787i | ||||
\(157\) | 1.41877 | − | 4.36652i | 0.113230 | − | 0.348486i | −0.878344 | − | 0.478029i | \(-0.841351\pi\) |
0.991574 | + | 0.129544i | \(0.0413512\pi\) | |||||||
\(158\) | 3.45684 | + | 10.6390i | 0.275011 | + | 0.846397i | ||||
\(159\) | 1.95006 | − | 1.41680i | 0.154650 | − | 0.112360i | ||||
\(160\) | 13.1544 | − | 9.55720i | 1.03994 | − | 0.755563i | ||||
\(161\) | 1.35043 | + | 4.15621i | 0.106429 | + | 0.327555i | ||||
\(162\) | −3.13536 | + | 9.64965i | −0.246337 | + | 0.758148i | ||||
\(163\) | −6.50259 | − | 4.72441i | −0.509322 | − | 0.370044i | 0.303244 | − | 0.952913i | \(-0.401930\pi\) |
−0.812566 | + | 0.582869i | \(0.801930\pi\) | |||||||
\(164\) | −11.1379 | −0.869721 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.05987 | −0.237492 | ||||||||
\(167\) | −10.8464 | − | 7.88038i | −0.839321 | − | 0.609802i | 0.0828599 | − | 0.996561i | \(-0.473595\pi\) |
−0.922181 | + | 0.386759i | \(0.873595\pi\) | |||||||
\(168\) | 0.285341 | − | 0.878189i | 0.0220145 | − | 0.0677537i | ||||
\(169\) | 1.67918 | + | 5.16798i | 0.129168 | + | 0.397537i | ||||
\(170\) | −11.0059 | + | 7.99623i | −0.844112 | + | 0.613283i | ||||
\(171\) | −4.10707 | + | 2.98396i | −0.314075 | + | 0.228189i | ||||
\(172\) | 1.68690 | + | 5.19175i | 0.128625 | + | 0.395867i | ||||
\(173\) | 6.36021 | − | 19.5747i | 0.483558 | − | 1.48824i | −0.350501 | − | 0.936562i | \(-0.613989\pi\) |
0.834059 | − | 0.551676i | \(-0.186011\pi\) | |||||||
\(174\) | −7.66815 | − | 5.57123i | −0.581321 | − | 0.422354i | ||||
\(175\) | 2.71442 | 0.205191 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.28860 | −0.397515 | ||||||||
\(178\) | −22.0067 | − | 15.9888i | −1.64947 | − | 1.19841i | ||||
\(179\) | −1.14806 | + | 3.53336i | −0.0858100 | + | 0.264096i | −0.984750 | − | 0.173976i | \(-0.944338\pi\) |
0.898940 | + | 0.438072i | \(0.144338\pi\) | |||||||
\(180\) | 2.60532 | + | 8.01836i | 0.194189 | + | 0.597653i | ||||
\(181\) | −3.86049 | + | 2.80481i | −0.286948 | + | 0.208480i | −0.721942 | − | 0.691953i | \(-0.756750\pi\) |
0.434994 | + | 0.900433i | \(0.356750\pi\) | |||||||
\(182\) | 6.17408 | − | 4.48573i | 0.457653 | − | 0.332505i | ||||
\(183\) | 0.188807 | + | 0.581090i | 0.0139570 | + | 0.0429554i | ||||
\(184\) | 2.01763 | − | 6.20964i | 0.148742 | − | 0.457781i | ||||
\(185\) | 2.32676 | + | 1.69049i | 0.171067 | + | 0.124287i | ||||
\(186\) | 0.220355 | 0.0161572 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −15.1257 | −1.10315 | ||||||||
\(189\) | 2.80902 | + | 2.04087i | 0.204326 | + | 0.148451i | ||||
\(190\) | −2.95828 | + | 9.10464i | −0.214616 | + | 0.660520i | ||||
\(191\) | −0.256224 | − | 0.788577i | −0.0185397 | − | 0.0570594i | 0.941359 | − | 0.337408i | \(-0.109550\pi\) |
−0.959898 | + | 0.280348i | \(0.909550\pi\) | |||||||
\(192\) | 0.228211 | − | 0.165805i | 0.0164697 | − | 0.0119660i | ||||
\(193\) | −5.45118 | + | 3.96051i | −0.392384 | + | 0.285084i | −0.766432 | − | 0.642326i | \(-0.777970\pi\) |
0.374047 | + | 0.927410i | \(0.377970\pi\) | |||||||
\(194\) | −6.38047 | − | 19.6371i | −0.458091 | − | 1.40986i | ||||
\(195\) | −2.27748 | + | 7.00938i | −0.163094 | + | 0.501952i | ||||
\(196\) | −0.938015 | − | 0.681508i | −0.0670011 | − | 0.0486791i | ||||
\(197\) | 10.9216 | 0.778129 | 0.389065 | − | 0.921210i | \(-0.372798\pi\) | ||||
0.389065 | + | 0.921210i | \(0.372798\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.9746 | 1.48685 | 0.743424 | − | 0.668820i | \(-0.233200\pi\) | ||||
0.743424 | + | 0.668820i | \(0.233200\pi\) | |||||||
\(200\) | −3.28098 | − | 2.38377i | −0.232000 | − | 0.168558i | ||||
\(201\) | −1.03464 | + | 3.18429i | −0.0729779 | + | 0.224603i | ||||
\(202\) | 1.87400 | + | 5.76759i | 0.131854 | + | 0.405806i | ||||
\(203\) | 6.98027 | − | 5.07146i | 0.489919 | − | 0.355947i | ||||
\(204\) | −1.59747 | + | 1.16063i | −0.111845 | + | 0.0812601i | ||||
\(205\) | 8.24487 | + | 25.3751i | 0.575847 | + | 1.77227i | ||||
\(206\) | 9.98720 | − | 30.7374i | 0.695841 | − | 2.14158i | ||||
\(207\) | 9.25601 | + | 6.72488i | 0.643337 | + | 0.467412i | ||||
\(208\) | −21.3582 | −1.48093 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.05119 | 0.210552 | ||||||||
\(211\) | −4.87320 | − | 3.54059i | −0.335485 | − | 0.243744i | 0.407269 | − | 0.913308i | \(-0.366481\pi\) |
−0.742754 | + | 0.669564i | \(0.766481\pi\) | |||||||
\(212\) | −1.39737 | + | 4.30067i | −0.0959720 | + | 0.295371i | ||||
\(213\) | −0.385222 | − | 1.18559i | −0.0263950 | − | 0.0812354i | ||||
\(214\) | −4.66990 | + | 3.39288i | −0.319227 | + | 0.231932i | ||||
\(215\) | 10.5795 | − | 7.68645i | 0.721515 | − | 0.524211i | ||||
\(216\) | −1.60305 | − | 4.93369i | −0.109074 | − | 0.335695i | ||||
\(217\) | −0.0619850 | + | 0.190770i | −0.00420782 | + | 0.0129503i | ||||
\(218\) | −18.2501 | − | 13.2595i | −1.23605 | − | 0.898043i | ||||
\(219\) | 6.16247 | 0.416421 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.8309 | 0.795833 | ||||||||
\(222\) | 0.920275 | + | 0.668619i | 0.0617648 | + | 0.0448748i | ||||
\(223\) | −1.42923 | + | 4.39871i | −0.0957081 | + | 0.294559i | −0.987438 | − | 0.158010i | \(-0.949492\pi\) |
0.891729 | + | 0.452569i | \(0.149492\pi\) | |||||||
\(224\) | 1.80902 | + | 5.56758i | 0.120870 | + | 0.372000i | ||||
\(225\) | 5.74923 | − | 4.17706i | 0.383282 | − | 0.278471i | ||||
\(226\) | −26.5286 | + | 19.2741i | −1.76465 | + | 1.28210i | ||||
\(227\) | −5.34610 | − | 16.4536i | −0.354833 | − | 1.09206i | −0.956106 | − | 0.293020i | \(-0.905340\pi\) |
0.601273 | − | 0.799043i | \(-0.294660\pi\) | |||||||
\(228\) | −0.429384 | + | 1.32151i | −0.0284367 | + | 0.0875190i | ||||
\(229\) | 3.58081 | + | 2.60161i | 0.236626 | + | 0.171919i | 0.699779 | − | 0.714359i | \(-0.253282\pi\) |
−0.463153 | + | 0.886279i | \(0.653282\pi\) | |||||||
\(230\) | 21.5749 | 1.42260 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.8909 | −0.846330 | ||||||||
\(233\) | −8.52141 | − | 6.19117i | −0.558256 | − | 0.405597i | 0.272564 | − | 0.962138i | \(-0.412128\pi\) |
−0.830820 | + | 0.556541i | \(0.812128\pi\) | |||||||
\(234\) | 6.17408 | − | 19.0019i | 0.403612 | − | 1.24219i | ||||
\(235\) | 11.1969 | + | 34.4604i | 0.730402 | + | 2.24795i | ||||
\(236\) | 8.02672 | − | 5.83175i | 0.522495 | − | 0.379615i | ||||
\(237\) | 3.14674 | − | 2.28624i | 0.204403 | − | 0.148507i | ||||
\(238\) | −1.51355 | − | 4.65823i | −0.0981090 | − | 0.301949i | ||||
\(239\) | 3.01491 | − | 9.27894i | 0.195018 | − | 0.600205i | −0.804958 | − | 0.593332i | \(-0.797812\pi\) |
0.999976 | − | 0.00687311i | \(-0.00218780\pi\) | |||||||
\(240\) | −6.90840 | − | 5.01925i | −0.445935 | − | 0.323991i | ||||
\(241\) | −12.5501 | −0.808422 | −0.404211 | − | 0.914666i | \(-0.632454\pi\) | ||||
−0.404211 | + | 0.914666i | \(0.632454\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.9443 | 0.894525 | ||||||||
\(244\) | −0.927330 | − | 0.673744i | −0.0593662 | − | 0.0431321i | ||||
\(245\) | −0.858290 | + | 2.64154i | −0.0548341 | + | 0.168762i | ||||
\(246\) | 3.26100 | + | 10.0363i | 0.207914 | + | 0.639892i | ||||
\(247\) | 6.73544 | − | 4.89358i | 0.428566 | − | 0.311371i | ||||
\(248\) | 0.242455 | − | 0.176154i | 0.0153959 | − | 0.0111858i | ||||
\(249\) | 0.328769 | + | 1.01185i | 0.0208349 | + | 0.0641233i | ||||
\(250\) | −3.48688 | + | 10.7315i | −0.220529 | + | 0.678720i | ||||
\(251\) | 8.89206 | + | 6.46046i | 0.561262 | + | 0.407781i | 0.831921 | − | 0.554895i | \(-0.187241\pi\) |
−0.270659 | + | 0.962675i | \(0.587241\pi\) | |||||||
\(252\) | −3.03548 | −0.191217 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 34.6775 | 2.17586 | ||||||||
\(255\) | 3.82676 | + | 2.78030i | 0.239641 | + | 0.174109i | ||||
\(256\) | 6.26747 | − | 19.2893i | 0.391717 | − | 1.20558i | ||||
\(257\) | 1.64792 | + | 5.07179i | 0.102795 | + | 0.316370i | 0.989207 | − | 0.146528i | \(-0.0468098\pi\) |
−0.886412 | + | 0.462898i | \(0.846810\pi\) | |||||||
\(258\) | 4.18438 | − | 3.04013i | 0.260508 | − | 0.189270i | ||||
\(259\) | −0.837721 | + | 0.608640i | −0.0520535 | + | 0.0378190i | ||||
\(260\) | −4.27263 | − | 13.1498i | −0.264977 | − | 0.815516i | ||||
\(261\) | 6.98027 | − | 21.4831i | 0.432068 | − | 1.32977i | ||||
\(262\) | 9.91937 | + | 7.20684i | 0.612821 | + | 0.445240i | ||||
\(263\) | 8.18034 | 0.504421 | 0.252211 | − | 0.967672i | \(-0.418842\pi\) | ||||
0.252211 | + | 0.967672i | \(0.418842\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.8325 | 0.665436 | ||||||||
\(266\) | −2.78845 | − | 2.02593i | −0.170971 | − | 0.124218i | ||||
\(267\) | −2.92271 | + | 8.99519i | −0.178867 | + | 0.550497i | ||||
\(268\) | −1.94102 | − | 5.97383i | −0.118566 | − | 0.364910i | ||||
\(269\) | −10.3909 | + | 7.54946i | −0.633547 | + | 0.460299i | −0.857627 | − | 0.514272i | \(-0.828062\pi\) |
0.224080 | + | 0.974571i | \(0.428062\pi\) | |||||||
\(270\) | 13.8679 | − | 10.0756i | 0.843976 | − | 0.613184i | ||||
\(271\) | 6.81296 | + | 20.9681i | 0.413858 | + | 1.27372i | 0.913268 | + | 0.407359i | \(0.133550\pi\) |
−0.499410 | + | 0.866366i | \(0.666450\pi\) | |||||||
\(272\) | −4.23592 | + | 13.0368i | −0.256840 | + | 0.790473i | ||||
\(273\) | −2.14674 | − | 1.55970i | −0.129926 | − | 0.0943971i | ||||
\(274\) | 4.64047 | 0.280341 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.13152 | 0.188495 | ||||||||
\(277\) | 19.4787 | + | 14.1521i | 1.17036 | + | 0.850316i | 0.991052 | − | 0.133477i | \(-0.0426141\pi\) |
0.179308 | + | 0.983793i | \(0.442614\pi\) | |||||||
\(278\) | −0.550006 | + | 1.69275i | −0.0329872 | + | 0.101524i | ||||
\(279\) | 0.162279 | + | 0.499443i | 0.00971539 | + | 0.0299009i | ||||
\(280\) | 3.35721 | − | 2.43916i | 0.200632 | − | 0.145767i | ||||
\(281\) | 12.4927 | − | 9.07648i | 0.745252 | − | 0.541457i | −0.149099 | − | 0.988822i | \(-0.547637\pi\) |
0.894352 | + | 0.447365i | \(0.147637\pi\) | |||||||
\(282\) | 4.42856 | + | 13.6297i | 0.263717 | + | 0.811637i | ||||
\(283\) | 1.03747 | − | 3.19300i | 0.0616711 | − | 0.189804i | −0.915474 | − | 0.402377i | \(-0.868184\pi\) |
0.977145 | + | 0.212573i | \(0.0681842\pi\) | |||||||
\(284\) | 1.89202 | + | 1.37463i | 0.112271 | + | 0.0815695i | ||||
\(285\) | 3.32861 | 0.197170 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.60616 | −0.567034 | ||||||||
\(288\) | 12.3992 | + | 9.00854i | 0.730629 | + | 0.530833i | ||||
\(289\) | −2.90689 | + | 8.94650i | −0.170994 | + | 0.526265i | ||||
\(290\) | −13.1630 | − | 40.5115i | −0.772957 | − | 2.37892i | ||||
\(291\) | −5.80811 | + | 4.21984i | −0.340477 | + | 0.247371i | ||||
\(292\) | −9.35302 | + | 6.79537i | −0.547344 | + | 0.397669i | ||||
\(293\) | −2.11277 | − | 6.50242i | −0.123429 | − | 0.379876i | 0.870183 | − | 0.492730i | \(-0.164001\pi\) |
−0.993612 | + | 0.112854i | \(0.964001\pi\) | |||||||
\(294\) | −0.339469 | + | 1.04478i | −0.0197983 | + | 0.0609328i | ||||
\(295\) | −19.2281 | − | 13.9701i | −1.11951 | − | 0.813369i | ||||
\(296\) | 1.54707 | 0.0899218 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −26.4752 | −1.53367 | ||||||||
\(299\) | −15.1795 | − | 11.0286i | −0.877853 | − | 0.637798i | ||||
\(300\) | 0.601068 | − | 1.84990i | 0.0347027 | − | 0.106804i | ||||
\(301\) | 1.45492 | + | 4.47777i | 0.0838599 | + | 0.258094i | ||||
\(302\) | −22.7272 | + | 16.5123i | −1.30781 | + | 0.950176i | ||||
\(303\) | 1.70589 | − | 1.23940i | 0.0980011 | − | 0.0712019i | ||||
\(304\) | 2.98083 | + | 9.17406i | 0.170962 | + | 0.526168i | ||||
\(305\) | −0.848513 | + | 2.61145i | −0.0485857 | + | 0.149531i | ||||
\(306\) | −10.3740 | − | 7.53718i | −0.593044 | − | 0.430872i | ||||
\(307\) | 11.7970 | 0.673293 | 0.336646 | − | 0.941631i | \(-0.390707\pi\) | ||||
0.336646 | + | 0.941631i | \(0.390707\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.2375 | −0.639276 | ||||||||
\(310\) | 0.801160 | + | 0.582077i | 0.0455029 | + | 0.0330598i | ||||
\(311\) | 7.82242 | − | 24.0749i | 0.443569 | − | 1.36516i | −0.440477 | − | 0.897764i | \(-0.645191\pi\) |
0.884046 | − | 0.467400i | \(-0.154809\pi\) | |||||||
\(312\) | 1.22510 | + | 3.77048i | 0.0693579 | + | 0.213462i | ||||
\(313\) | 15.9007 | − | 11.5525i | 0.898760 | − | 0.652988i | −0.0393869 | − | 0.999224i | \(-0.512540\pi\) |
0.938147 | + | 0.346236i | \(0.112540\pi\) | |||||||
\(314\) | 6.60225 | − | 4.79682i | 0.372587 | − | 0.270700i | ||||
\(315\) | 2.24703 | + | 6.91565i | 0.126606 | + | 0.389653i | ||||
\(316\) | −2.25489 | + | 6.93983i | −0.126847 | + | 0.390396i | ||||
\(317\) | −2.92100 | − | 2.12223i | −0.164060 | − | 0.119197i | 0.502726 | − | 0.864446i | \(-0.332330\pi\) |
−0.666786 | + | 0.745249i | \(0.732330\pi\) | |||||||
\(318\) | 4.28446 | 0.240261 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.26771 | 0.0708670 | ||||||||
\(321\) | 1.62373 | + | 1.17971i | 0.0906278 | + | 0.0658449i | ||||
\(322\) | −2.40037 | + | 7.38759i | −0.133768 | + | 0.411694i | ||||
\(323\) | −1.65117 | − | 5.08177i | −0.0918734 | − | 0.282757i | ||||
\(324\) | −5.35438 | + | 3.89019i | −0.297466 | + | 0.216121i | ||||
\(325\) | −9.42852 | + | 6.85022i | −0.523000 | + | 0.379982i | ||||
\(326\) | −4.41486 | − | 13.5875i | −0.244516 | − | 0.752544i | ||||
\(327\) | −2.42379 | + | 7.45967i | −0.134036 | + | 0.412521i | ||||
\(328\) | 11.6112 | + | 8.43602i | 0.641121 | + | 0.465801i | ||||
\(329\) | −13.0455 | −0.719224 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.5335 | −1.45841 | −0.729205 | − | 0.684295i | \(-0.760110\pi\) | ||||
−0.729205 | + | 0.684295i | \(0.760110\pi\) | |||||||
\(332\) | −1.61475 | − | 1.17319i | −0.0886212 | − | 0.0643870i | ||||
\(333\) | −0.837721 | + | 2.57824i | −0.0459068 | + | 0.141287i | ||||
\(334\) | −7.36405 | − | 22.6642i | −0.402943 | − | 1.24013i | ||||
\(335\) | −12.1732 | + | 8.84433i | −0.665092 | + | 0.483217i | ||||
\(336\) | 2.48729 | − | 1.80712i | 0.135693 | − | 0.0985865i | ||||
\(337\) | 0.211979 | + | 0.652405i | 0.0115472 | + | 0.0355387i | 0.956664 | − | 0.291194i | \(-0.0940524\pi\) |
−0.945117 | + | 0.326732i | \(0.894052\pi\) | |||||||
\(338\) | −2.98471 | + | 9.18601i | −0.162347 | + | 0.499653i | ||||
\(339\) | 9.22402 | + | 6.70165i | 0.500980 | + | 0.363983i | ||||
\(340\) | −8.87387 | −0.481253 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −9.02361 | −0.487941 | ||||||||
\(343\) | −0.809017 | − | 0.587785i | −0.0436828 | − | 0.0317374i | ||||
\(344\) | 2.17374 | − | 6.69007i | 0.117200 | − | 0.360704i | ||||
\(345\) | −2.31813 | − | 7.13446i | −0.124804 | − | 0.384106i | ||||
\(346\) | 29.5973 | − | 21.5037i | 1.59116 | − | 1.15605i | ||||
\(347\) | 17.3983 | − | 12.6406i | 0.933989 | − | 0.678582i | −0.0129776 | − | 0.999916i | \(-0.504131\pi\) |
0.946966 | + | 0.321333i | \(0.104131\pi\) | |||||||
\(348\) | −1.91056 | − | 5.88011i | −0.102417 | − | 0.315207i | ||||
\(349\) | −6.00818 | + | 18.4913i | −0.321610 | + | 0.989815i | 0.651337 | + | 0.758788i | \(0.274208\pi\) |
−0.972947 | + | 0.231026i | \(0.925792\pi\) | |||||||
\(350\) | 3.90337 | + | 2.83597i | 0.208644 | + | 0.151589i | ||||
\(351\) | −14.9075 | −0.795705 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.9307 | −1.11403 | −0.557015 | − | 0.830502i | \(-0.688053\pi\) | ||||
−0.557015 | + | 0.830502i | \(0.688053\pi\) | |||||||
\(354\) | −7.60508 | − | 5.52542i | −0.404206 | − | 0.293672i | ||||
\(355\) | 1.73121 | − | 5.32812i | 0.0918832 | − | 0.282787i | ||||
\(356\) | −5.48310 | − | 16.8752i | −0.290604 | − | 0.894386i | ||||
\(357\) | −1.37778 | + | 1.00101i | −0.0729198 | + | 0.0529793i | ||||
\(358\) | −5.34251 | + | 3.88156i | −0.282360 | + | 0.205147i | ||||
\(359\) | −3.01949 | − | 9.29303i | −0.159362 | − | 0.490467i | 0.839214 | − | 0.543801i | \(-0.183015\pi\) |
−0.998577 | + | 0.0533336i | \(0.983015\pi\) | |||||||
\(360\) | 3.35721 | − | 10.3324i | 0.176940 | − | 0.544567i | ||||
\(361\) | 12.3293 | + | 8.95779i | 0.648913 | + | 0.471463i | ||||
\(362\) | −8.48185 | −0.445796 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.97807 | 0.260922 | ||||||||
\(365\) | 22.4053 | + | 16.2784i | 1.17275 | + | 0.852052i | ||||
\(366\) | −0.335602 | + | 1.03288i | −0.0175422 | + | 0.0539894i | ||||
\(367\) | 3.05917 | + | 9.41516i | 0.159687 | + | 0.491467i | 0.998606 | − | 0.0527902i | \(-0.0168114\pi\) |
−0.838918 | + | 0.544258i | \(0.816811\pi\) | |||||||
\(368\) | 17.5875 | − | 12.7781i | 0.916813 | − | 0.666103i | ||||
\(369\) | −20.3462 | + | 14.7824i | −1.05918 | + | 0.769539i | ||||
\(370\) | 1.57973 | + | 4.86189i | 0.0821260 | + | 0.252758i | ||||
\(371\) | −1.20520 | + | 3.70923i | −0.0625710 | + | 0.192574i | ||||
\(372\) | 0.116286 | + | 0.0844866i | 0.00602914 | + | 0.00438042i | ||||
\(373\) | 4.27475 | 0.221338 | 0.110669 | − | 0.993857i | \(-0.464701\pi\) | ||||
0.110669 | + | 0.993857i | \(0.464701\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.92338 | 0.202603 | ||||||||
\(376\) | 15.7684 | + | 11.4564i | 0.813195 | + | 0.590821i | ||||
\(377\) | −11.4474 | + | 35.2314i | −0.589570 | + | 1.81451i | ||||
\(378\) | 1.90715 | + | 5.86960i | 0.0980932 | + | 0.301900i | ||||
\(379\) | −3.49976 | + | 2.54272i | −0.179771 | + | 0.130611i | −0.674031 | − | 0.738703i | \(-0.735439\pi\) |
0.494261 | + | 0.869314i | \(0.335439\pi\) | |||||||
\(380\) | −5.05197 | + | 3.67047i | −0.259160 | + | 0.188291i | ||||
\(381\) | −3.72594 | − | 11.4673i | −0.190886 | − | 0.587486i | ||||
\(382\) | 0.455434 | − | 1.40168i | 0.0233020 | − | 0.0717163i | ||||
\(383\) | 1.06960 | + | 0.777111i | 0.0546541 | + | 0.0397085i | 0.614777 | − | 0.788701i | \(-0.289246\pi\) |
−0.560123 | + | 0.828410i | \(0.689246\pi\) | |||||||
\(384\) | −6.73467 | −0.343677 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.9767 | −0.609600 | ||||||||
\(387\) | 9.97214 | + | 7.24518i | 0.506912 | + | 0.368293i | ||||
\(388\) | 4.16197 | − | 12.8092i | 0.211292 | − | 0.650290i | ||||
\(389\) | −11.9000 | − | 36.6244i | −0.603353 | − | 1.85693i | −0.507737 | − | 0.861512i | \(-0.669518\pi\) |
−0.0956157 | − | 0.995418i | \(-0.530482\pi\) | |||||||
\(390\) | −10.5983 | + | 7.70012i | −0.536666 | + | 0.389911i | ||||
\(391\) | −9.74221 | + | 7.07813i | −0.492685 | + | 0.357957i | ||||
\(392\) | 0.461691 | + | 1.42094i | 0.0233189 | + | 0.0717683i | ||||
\(393\) | 1.31739 | − | 4.05452i | 0.0664537 | − | 0.204523i | ||||
\(394\) | 15.7054 | + | 11.4106i | 0.791225 | + | 0.574859i | ||||
\(395\) | 17.4800 | 0.879516 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.410109 | −0.0205828 | −0.0102914 | − | 0.999947i | \(-0.503276\pi\) | ||||
−0.0102914 | + | 0.999947i | \(0.503276\pi\) | |||||||
\(398\) | 30.1618 | + | 21.9138i | 1.51187 | + | 1.09844i | ||||
\(399\) | −0.370334 | + | 1.13977i | −0.0185399 | + | 0.0570600i | ||||
\(400\) | −4.17268 | − | 12.8422i | −0.208634 | − | 0.642110i | ||||
\(401\) | 1.26760 | − | 0.920966i | 0.0633010 | − | 0.0459908i | −0.555685 | − | 0.831393i | \(-0.687544\pi\) |
0.618986 | + | 0.785402i | \(0.287544\pi\) | |||||||
\(402\) | −4.81471 | + | 3.49809i | −0.240136 | + | 0.174469i | ||||
\(403\) | −0.266131 | − | 0.819068i | −0.0132569 | − | 0.0408007i | ||||
\(404\) | −1.22241 | + | 3.76219i | −0.0608171 | + | 0.187176i | ||||
\(405\) | 12.8265 | + | 9.31901i | 0.637355 | + | 0.463065i | ||||
\(406\) | 15.3363 | 0.761127 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.54443 | 0.125968 | ||||||||
\(409\) | −5.48394 | − | 3.98432i | −0.271163 | − | 0.197012i | 0.443891 | − | 0.896081i | \(-0.353598\pi\) |
−0.715054 | + | 0.699069i | \(0.753598\pi\) | |||||||
\(410\) | −14.6551 | + | 45.1038i | −0.723765 | + | 2.22752i | ||||
\(411\) | −0.498599 | − | 1.53453i | −0.0245941 | − | 0.0756927i | ||||
\(412\) | 17.0555 | − | 12.3916i | 0.840266 | − | 0.610489i | ||||
\(413\) | 6.92286 | − | 5.02975i | 0.340652 | − | 0.247498i | ||||
\(414\) | 6.28426 | + | 19.3410i | 0.308855 | + | 0.950557i | ||||
\(415\) | −1.47751 | + | 4.54731i | −0.0725282 | + | 0.223219i | ||||
\(416\) | −20.3342 | − | 14.7737i | −0.996966 | − | 0.724338i | ||||
\(417\) | 0.618859 | 0.0303057 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.7218 | 1.40315 | 0.701577 | − | 0.712594i | \(-0.252480\pi\) | ||||
0.701577 | + | 0.712594i | \(0.252480\pi\) | |||||||
\(420\) | 1.61018 | + | 1.16986i | 0.0785686 | + | 0.0570834i | ||||
\(421\) | 3.77791 | − | 11.6272i | 0.184124 | − | 0.566676i | −0.815808 | − | 0.578323i | \(-0.803707\pi\) |
0.999932 | + | 0.0116470i | \(0.00370742\pi\) | |||||||
\(422\) | −3.30860 | − | 10.1828i | −0.161060 | − | 0.495693i | ||||
\(423\) | −27.6309 | + | 20.0750i | −1.34346 | + | 0.976081i | ||||
\(424\) | 4.71416 | − | 3.42504i | 0.228940 | − | 0.166335i | ||||
\(425\) | 2.31136 | + | 7.11365i | 0.112118 | + | 0.345063i | ||||
\(426\) | 0.684726 | − | 2.10737i | 0.0331751 | − | 0.102102i | ||||
\(427\) | −0.799801 | − | 0.581090i | −0.0387051 | − | 0.0281209i | ||||
\(428\) | −3.76527 | −0.182001 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 23.2441 | 1.12093 | ||||||||
\(431\) | 2.98632 | + | 2.16969i | 0.143846 | + | 0.104510i | 0.657381 | − | 0.753559i | \(-0.271664\pi\) |
−0.513535 | + | 0.858069i | \(0.671664\pi\) | |||||||
\(432\) | 5.33747 | − | 16.4270i | 0.256799 | − | 0.790346i | ||||
\(433\) | 8.98463 | + | 27.6519i | 0.431774 | + | 1.32886i | 0.896357 | + | 0.443334i | \(0.146204\pi\) |
−0.464583 | + | 0.885530i | \(0.653796\pi\) | |||||||
\(434\) | −0.288448 | + | 0.209570i | −0.0138460 | + | 0.0100597i | ||||
\(435\) | −11.9822 | + | 8.70557i | −0.574502 | + | 0.417400i | ||||
\(436\) | −4.54711 | − | 13.9946i | −0.217767 | − | 0.670218i | ||||
\(437\) | −2.61862 | + | 8.05928i | −0.125266 | + | 0.385528i | ||||
\(438\) | 8.86172 | + | 6.43842i | 0.423429 | + | 0.307639i | ||||
\(439\) | 14.2017 | 0.677811 | 0.338905 | − | 0.940820i | \(-0.389943\pi\) | ||||
0.338905 | + | 0.940820i | \(0.389943\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.61803 | −0.124668 | ||||||||
\(442\) | 17.0130 | + | 12.3607i | 0.809227 | + | 0.587938i | ||||
\(443\) | 8.41626 | − | 25.9026i | 0.399869 | − | 1.23067i | −0.525236 | − | 0.850957i | \(-0.676023\pi\) |
0.925105 | − | 0.379712i | \(-0.123977\pi\) | |||||||
\(444\) | 0.229292 | + | 0.705688i | 0.0108817 | + | 0.0334905i | ||||
\(445\) | −34.3875 | + | 24.9840i | −1.63013 | + | 1.18436i | ||||
\(446\) | −6.65093 | + | 4.83218i | −0.314930 | + | 0.228810i | ||||
\(447\) | 2.84465 | + | 8.75492i | 0.134547 | + | 0.414093i | ||||
\(448\) | −0.141042 | + | 0.434084i | −0.00666363 | + | 0.0205085i | ||||
\(449\) | 33.9107 | + | 24.6376i | 1.60034 | + | 1.16272i | 0.886851 | + | 0.462056i | \(0.152888\pi\) |
0.713493 | + | 0.700662i | \(0.247112\pi\) | |||||||
\(450\) | 12.6316 | 0.595459 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −21.3896 | −1.00608 | ||||||||
\(453\) | 7.90229 | + | 5.74135i | 0.371282 | + | 0.269752i | ||||
\(454\) | 9.50260 | − | 29.2460i | 0.445979 | − | 1.37258i | ||||
\(455\) | −3.68505 | − | 11.3414i | −0.172758 | − | 0.531693i | ||||
\(456\) | 1.44857 | − | 1.05244i | 0.0678353 | − | 0.0492853i | ||||
\(457\) | 15.7740 | − | 11.4605i | 0.737875 | − | 0.536097i | −0.154170 | − | 0.988044i | \(-0.549270\pi\) |
0.892045 | + | 0.451947i | \(0.149270\pi\) | |||||||
\(458\) | 2.43115 | + | 7.48230i | 0.113600 | + | 0.349625i | ||||
\(459\) | −2.95657 | + | 9.09939i | −0.138001 | + | 0.424723i | ||||
\(460\) | 11.3855 | + | 8.27205i | 0.530852 | + | 0.385686i | ||||
\(461\) | −12.2251 | −0.569380 | −0.284690 | − | 0.958620i | \(-0.591891\pi\) | ||||
−0.284690 | + | 0.958620i | \(0.591891\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.8550 | 0.643894 | 0.321947 | − | 0.946758i | \(-0.395663\pi\) | ||||
0.321947 | + | 0.946758i | \(0.395663\pi\) | |||||||
\(464\) | −34.7239 | − | 25.2284i | −1.61202 | − | 1.17120i | ||||
\(465\) | 0.106402 | − | 0.327472i | 0.00493429 | − | 0.0151862i | ||||
\(466\) | −5.78551 | − | 17.8060i | −0.268009 | − | 0.824846i | ||||
\(467\) | 13.2846 | − | 9.65186i | 0.614740 | − | 0.446635i | −0.236340 | − | 0.971670i | \(-0.575948\pi\) |
0.851080 | + | 0.525035i | \(0.175948\pi\) | |||||||
\(468\) | 10.5437 | − | 7.66047i | 0.487384 | − | 0.354105i | ||||
\(469\) | −1.67408 | − | 5.15230i | −0.0773020 | − | 0.237911i | ||||
\(470\) | −19.9022 | + | 61.2528i | −0.918021 | + | 2.82538i | ||||
\(471\) | −2.29561 | − | 1.66786i | −0.105776 | − | 0.0768510i | ||||
\(472\) | −12.7849 | −0.588473 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 6.91367 | 0.317555 | ||||||||
\(475\) | 4.25827 | + | 3.09382i | 0.195383 | + | 0.141954i | ||||
\(476\) | 0.987288 | − | 3.03856i | 0.0452523 | − | 0.139272i | ||||
\(477\) | 3.15526 | + | 9.71090i | 0.144470 | + | 0.444632i | ||||
\(478\) | 14.0299 | − | 10.1933i | 0.641714 | − | 0.466233i | ||||
\(479\) | −20.0566 | + | 14.5720i | −0.916412 | + | 0.665812i | −0.942628 | − | 0.333844i | \(-0.891654\pi\) |
0.0262166 | + | 0.999656i | \(0.491654\pi\) | |||||||
\(480\) | −3.10532 | − | 9.55720i | −0.141738 | − | 0.436224i | ||||
\(481\) | 1.37383 | − | 4.22822i | 0.0626413 | − | 0.192790i | ||||
\(482\) | −18.0472 | − | 13.1121i | −0.822028 | − | 0.597238i | ||||
\(483\) | 2.70087 | 0.122894 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −32.2639 | −1.46503 | ||||||||
\(486\) | 20.0521 | + | 14.5687i | 0.909580 | + | 0.660849i | ||||
\(487\) | −4.42951 | + | 13.6326i | −0.200720 | + | 0.617753i | 0.799142 | + | 0.601142i | \(0.205288\pi\) |
−0.999862 | + | 0.0166105i | \(0.994712\pi\) | |||||||
\(488\) | 0.456432 | + | 1.40475i | 0.0206617 | + | 0.0635902i | ||||
\(489\) | −4.01882 | + | 2.91984i | −0.181737 | + | 0.132040i | ||||
\(490\) | −3.99406 | + | 2.90186i | −0.180433 | + | 0.131093i | ||||
\(491\) | 6.80435 | + | 20.9416i | 0.307076 | + | 0.945083i | 0.978894 | + | 0.204367i | \(0.0655135\pi\) |
−0.671818 | + | 0.740716i | \(0.734486\pi\) | |||||||
\(492\) | −2.12714 | + | 6.54667i | −0.0958990 | + | 0.295147i | ||||
\(493\) | 19.2345 | + | 13.9747i | 0.866280 | + | 0.629389i | ||||
\(494\) | 14.7984 | 0.665810 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.997839 | 0.0448043 | ||||||||
\(497\) | 1.63183 | + | 1.18559i | 0.0731974 | + | 0.0531810i | ||||
\(498\) | −0.584382 | + | 1.79854i | −0.0261868 | + | 0.0805947i | ||||
\(499\) | −7.82175 | − | 24.0729i | −0.350150 | − | 1.07765i | −0.958769 | − | 0.284187i | \(-0.908276\pi\) |
0.608619 | − | 0.793463i | \(-0.291724\pi\) | |||||||
\(500\) | −5.95467 | + | 4.32632i | −0.266301 | + | 0.193479i | ||||
\(501\) | −6.70345 | + | 4.87034i | −0.299488 | + | 0.217591i | ||||
\(502\) | 6.03716 | + | 18.5805i | 0.269452 | + | 0.829287i | ||||
\(503\) | 8.04107 | − | 24.7479i | 0.358534 | − | 1.10345i | −0.595399 | − | 0.803430i | \(-0.703006\pi\) |
0.953932 | − | 0.300022i | \(-0.0969942\pi\) | |||||||
\(504\) | 3.16448 | + | 2.29913i | 0.140957 | + | 0.102411i | ||||
\(505\) | 9.47619 | 0.421685 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.35836 | 0.149150 | ||||||||
\(508\) | 18.3000 | + | 13.2957i | 0.811932 | + | 0.589903i | ||||
\(509\) | 11.7819 | − | 36.2608i | 0.522222 | − | 1.60723i | −0.247523 | − | 0.968882i | \(-0.579617\pi\) |
0.769745 | − | 0.638351i | \(-0.220383\pi\) | |||||||
\(510\) | 2.59813 | + | 7.99623i | 0.115047 | + | 0.354079i | ||||
\(511\) | −8.06677 | + | 5.86085i | −0.356853 | + | 0.259269i | ||||
\(512\) | 11.5342 | − | 8.38006i | 0.509743 | − | 0.370350i | ||||
\(513\) | 2.08055 | + | 6.40328i | 0.0918585 | + | 0.282712i | ||||
\(514\) | −2.92916 | + | 9.01503i | −0.129200 | + | 0.397636i | ||||
\(515\) | −40.8568 | − | 29.6842i | −1.80037 | − | 1.30804i | ||||
\(516\) | 3.37380 | 0.148523 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.84055 | −0.0808691 | ||||||||
\(519\) | −10.2910 | − | 7.47688i | −0.451726 | − | 0.328198i | ||||
\(520\) | −5.50570 | + | 16.9448i | −0.241441 | + | 0.743078i | ||||
\(521\) | −8.04742 | − | 24.7674i | −0.352564 | − | 1.08508i | −0.957409 | − | 0.288736i | \(-0.906765\pi\) |
0.604845 | − | 0.796343i | \(-0.293235\pi\) | |||||||
\(522\) | 32.4828 | − | 23.6001i | 1.42173 | − | 1.03295i | ||||
\(523\) | 15.4708 | − | 11.2402i | 0.676492 | − | 0.491500i | −0.195700 | − | 0.980664i | \(-0.562698\pi\) |
0.872192 | + | 0.489164i | \(0.162698\pi\) | |||||||
\(524\) | 2.47147 | + | 7.60640i | 0.107967 | + | 0.332287i | ||||
\(525\) | 0.518408 | − | 1.59550i | 0.0226252 | − | 0.0696331i | ||||
\(526\) | 11.7635 | + | 8.54665i | 0.512911 | + | 0.372652i | ||||
\(527\) | −0.552731 | −0.0240773 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.90228 | −0.169664 | ||||||||
\(530\) | 15.5773 | + | 11.3176i | 0.676636 | + | 0.491605i | ||||
\(531\) | 6.92286 | − | 21.3064i | 0.300427 | − | 0.924618i | ||||
\(532\) | −0.694758 | − | 2.13825i | −0.0301216 | − | 0.0927047i | ||||
\(533\) | 33.3670 | − | 24.2425i | 1.44528 | − | 1.05006i | ||||
\(534\) | −13.6009 | + | 9.88163i | −0.588568 | + | 0.427620i | ||||
\(535\) | 2.78726 | + | 8.57831i | 0.120504 | + | 0.370873i | ||||
\(536\) | −2.50119 | + | 7.69786i | −0.108035 | + | 0.332497i | ||||
\(537\) | 1.85760 | + | 1.34962i | 0.0801613 | + | 0.0582406i | ||||
\(538\) | −22.8298 | −0.984265 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 11.1815 | 0.481176 | ||||||||
\(541\) | 8.80699 | + | 6.39865i | 0.378642 | + | 0.275100i | 0.760785 | − | 0.649003i | \(-0.224814\pi\) |
−0.382143 | + | 0.924103i | \(0.624814\pi\) | |||||||
\(542\) | −12.1099 | + | 37.2706i | −0.520166 | + | 1.60091i | ||||
\(543\) | 0.911338 | + | 2.80481i | 0.0391093 | + | 0.120366i | ||||
\(544\) | −13.0505 | + | 9.48174i | −0.559536 | + | 0.406526i | ||||
\(545\) | −28.5174 | + | 20.7191i | −1.22155 | + | 0.887510i | ||||
\(546\) | −1.45750 | − | 4.48573i | −0.0623754 | − | 0.191972i | ||||
\(547\) | 3.98912 | − | 12.2772i | 0.170562 | − | 0.524937i | −0.828841 | − | 0.559485i | \(-0.810999\pi\) |
0.999403 | + | 0.0345478i | \(0.0109991\pi\) | |||||||
\(548\) | 2.44887 | + | 1.77921i | 0.104611 | + | 0.0760041i | ||||
\(549\) | −2.58821 | −0.110462 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.7307 | 0.712751 | ||||||||
\(552\) | −3.26460 | − | 2.37187i | −0.138951 | − | 0.100954i | ||||
\(553\) | −1.94479 | + | 5.98545i | −0.0827009 | + | 0.254527i | ||||
\(554\) | 13.2248 | + | 40.7018i | 0.561869 | + | 1.72925i | ||||
\(555\) | 1.43801 | − | 1.04478i | 0.0610403 | − | 0.0443484i | ||||
\(556\) | −0.939268 | + | 0.682418i | −0.0398338 | + | 0.0289410i | ||||
\(557\) | 0.235664 | + | 0.725300i | 0.00998542 | + | 0.0307320i | 0.955925 | − | 0.293611i | \(-0.0948569\pi\) |
−0.945940 | + | 0.324343i | \(0.894857\pi\) | |||||||
\(558\) | −0.288448 | + | 0.887752i | −0.0122110 | + | 0.0375816i | ||||
\(559\) | −16.3539 | − | 11.8818i | −0.691697 | − | 0.502547i | ||||
\(560\) | 13.8168 | 0.583867 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.4476 | 1.15781 | ||||||||
\(563\) | −17.9829 | − | 13.0654i | −0.757890 | − | 0.550639i | 0.140373 | − | 0.990099i | \(-0.455170\pi\) |
−0.898262 | + | 0.439460i | \(0.855170\pi\) | |||||||
\(564\) | −2.88874 | + | 8.89063i | −0.121638 | + | 0.374363i | ||||
\(565\) | 15.8338 | + | 48.7313i | 0.666132 | + | 2.05014i | ||||
\(566\) | 4.82788 | − | 3.50766i | 0.202931 | − | 0.147438i | ||||
\(567\) | −4.61803 | + | 3.35520i | −0.193939 | + | 0.140905i | ||||
\(568\) | −0.931253 | − | 2.86610i | −0.0390745 | − | 0.120259i | ||||
\(569\) | 6.33891 | − | 19.5092i | 0.265741 | − | 0.817866i | −0.725781 | − | 0.687926i | \(-0.758521\pi\) |
0.991522 | − | 0.129940i | \(-0.0414786\pi\) | |||||||
\(570\) | 4.78659 | + | 3.47766i | 0.200488 | + | 0.145663i | ||||
\(571\) | 19.5654 | 0.818785 | 0.409393 | − | 0.912358i | \(-0.365741\pi\) | ||||
0.409393 | + | 0.912358i | \(0.365741\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.512448 | −0.0214078 | ||||||||
\(574\) | −13.8138 | − | 10.0363i | −0.576577 | − | 0.418908i | ||||
\(575\) | 3.66564 | − | 11.2817i | 0.152868 | − | 0.470479i | ||||
\(576\) | 0.369254 | + | 1.13645i | 0.0153856 | + | 0.0473519i | ||||
\(577\) | 15.8337 | − | 11.5039i | 0.659167 | − | 0.478913i | −0.207214 | − | 0.978296i | \(-0.566440\pi\) |
0.866382 | + | 0.499382i | \(0.166440\pi\) | |||||||
\(578\) | −13.5273 | + | 9.82814i | −0.562661 | + | 0.408797i | ||||
\(579\) | 1.28685 | + | 3.96051i | 0.0534796 | + | 0.164593i | ||||
\(580\) | 8.58620 | − | 26.4256i | 0.356522 | − | 1.09726i | ||||
\(581\) | −1.39269 | − | 1.01185i | −0.0577785 | − | 0.0419785i | ||||
\(582\) | −12.7609 | −0.528958 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 14.8974 | 0.616460 | ||||||||
\(585\) | −25.2577 | − | 18.3508i | −1.04428 | − | 0.758712i | ||||
\(586\) | 3.75541 | − | 11.5580i | 0.155134 | − | 0.477455i | ||||
\(587\) | 0.485367 | + | 1.49381i | 0.0200333 | + | 0.0616560i | 0.960573 | − | 0.278027i | \(-0.0896803\pi\) |
−0.940540 | + | 0.339683i | \(0.889680\pi\) | |||||||
\(588\) | −0.579725 | + | 0.421195i | −0.0239075 | + | 0.0173698i | ||||
\(589\) | −0.314674 | + | 0.228624i | −0.0129659 | + | 0.00942030i | ||||
\(590\) | −13.0547 | − | 40.1783i | −0.537455 | − | 1.65412i | ||||
\(591\) | 2.08583 | − | 6.41954i | 0.0857997 | − | 0.264064i | ||||
\(592\) | 4.16731 | + | 3.02773i | 0.171275 | + | 0.124439i | ||||
\(593\) | 30.1230 | 1.23700 | 0.618502 | − | 0.785783i | \(-0.287740\pi\) | ||||
0.618502 | + | 0.785783i | \(0.287740\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.65351 | −0.313763 | ||||||||
\(596\) | −13.9715 | − | 10.1509i | −0.572295 | − | 0.415797i | ||||
\(597\) | 4.00579 | − | 12.3285i | 0.163946 | − | 0.504574i | ||||
\(598\) | −10.3059 | − | 31.7184i | −0.421442 | − | 1.29706i | ||||
\(599\) | −4.67443 | + | 3.39617i | −0.190992 | + | 0.138764i | −0.679172 | − | 0.733979i | \(-0.737661\pi\) |
0.488180 | + | 0.872743i | \(0.337661\pi\) | |||||||
\(600\) | −2.02776 | + | 1.47325i | −0.0827829 | + | 0.0601453i | ||||
\(601\) | −14.0802 | − | 43.3345i | −0.574344 | − | 1.76765i | −0.638402 | − | 0.769703i | \(-0.720404\pi\) |
0.0640579 | − | 0.997946i | \(-0.479596\pi\) | |||||||
\(602\) | −2.58609 | + | 7.95916i | −0.105401 | + | 0.324391i | ||||
\(603\) | −11.4743 | − | 8.33659i | −0.467271 | − | 0.339492i | ||||
\(604\) | −18.3246 | −0.745619 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.74801 | 0.152252 | ||||||||
\(607\) | 28.0899 | + | 20.4085i | 1.14013 | + | 0.828356i | 0.987138 | − | 0.159870i | \(-0.0511076\pi\) |
0.152997 | + | 0.988227i | \(0.451108\pi\) | |||||||
\(608\) | −3.50786 | + | 10.7961i | −0.142262 | + | 0.437839i | ||||
\(609\) | −1.64782 | − | 5.07146i | −0.0667730 | − | 0.205506i | ||||
\(610\) | −3.94857 | + | 2.86880i | −0.159873 | + | 0.116154i | ||||
\(611\) | 45.3136 | − | 32.9223i | 1.83319 | − | 1.33189i | ||||
\(612\) | −2.58475 | − | 7.95505i | −0.104482 | − | 0.321564i | ||||
\(613\) | 7.46037 | − | 22.9607i | 0.301322 | − | 0.927372i | −0.679703 | − | 0.733488i | \(-0.737891\pi\) |
0.981024 | − | 0.193885i | \(-0.0621088\pi\) | |||||||
\(614\) | 16.9643 | + | 12.3253i | 0.684624 | + | 0.497409i | ||||
\(615\) | 16.4897 | 0.664931 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.4967 | −0.543358 | −0.271679 | − | 0.962388i | \(-0.587579\pi\) | ||||
−0.271679 | + | 0.962388i | \(0.587579\pi\) | |||||||
\(618\) | −16.1596 | − | 11.7407i | −0.650035 | − | 0.472278i | ||||
\(619\) | −13.4378 | + | 41.3573i | −0.540111 | + | 1.66229i | 0.192229 | + | 0.981350i | \(0.438428\pi\) |
−0.732339 | + | 0.680940i | \(0.761572\pi\) | |||||||
\(620\) | 0.199614 | + | 0.614348i | 0.00801668 | + | 0.0246728i | ||||
\(621\) | 12.2757 | − | 8.91879i | 0.492606 | − | 0.357899i | ||||
\(622\) | 36.4017 | − | 26.4474i | 1.45958 | − | 1.06044i | ||||
\(623\) | −4.72905 | − | 14.5545i | −0.189465 | − | 0.583115i | ||||
\(624\) | −4.07906 | + | 12.5540i | −0.163293 | + | 0.502564i | ||||
\(625\) | 25.2446 | + | 18.3413i | 1.00978 | + | 0.733651i | ||||
\(626\) | 34.9353 | 1.39629 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.32330 | 0.212423 | ||||||||
\(629\) | −2.30839 | − | 1.67714i | −0.0920414 | − | 0.0668720i | ||||
\(630\) | −3.99406 | + | 12.2925i | −0.159127 | + | 0.489744i | ||||
\(631\) | 1.98393 | + | 6.10589i | 0.0789788 | + | 0.243072i | 0.982748 | − | 0.184948i | \(-0.0592115\pi\) |
−0.903770 | + | 0.428019i | \(0.859212\pi\) | |||||||
\(632\) | 7.60707 | − | 5.52686i | 0.302593 | − | 0.219847i | ||||
\(633\) | −3.01180 | + | 2.18820i | −0.119708 | + | 0.0869733i | ||||
\(634\) | −1.98318 | − | 6.10361i | −0.0787622 | − | 0.242405i | ||||
\(635\) | 16.7446 | − | 51.5347i | 0.664490 | − | 2.04509i | ||||
\(636\) | 2.26100 | + | 1.64271i | 0.0896544 | + | 0.0651377i | ||||
\(637\) | 4.29348 | 0.170114 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.28070 | 0.208901 | ||||||||
\(640\) | −24.4857 | − | 17.7899i | −0.967883 | − | 0.703208i | ||||
\(641\) | −1.97647 | + | 6.08296i | −0.0780660 | + | 0.240262i | −0.982472 | − | 0.186411i | \(-0.940314\pi\) |
0.904406 | + | 0.426673i | \(0.140314\pi\) | |||||||
\(642\) | 1.10241 | + | 3.39288i | 0.0435088 | + | 0.133906i | ||||
\(643\) | −0.528013 | + | 0.383624i | −0.0208228 | + | 0.0151286i | −0.598148 | − | 0.801386i | \(-0.704097\pi\) |
0.577325 | + | 0.816514i | \(0.304097\pi\) | |||||||
\(644\) | −4.09921 | + | 2.97825i | −0.161532 | + | 0.117360i | ||||
\(645\) | −2.49748 | − | 7.68645i | −0.0983381 | − | 0.302653i | ||||
\(646\) | 2.93492 | − | 9.03276i | 0.115473 | − | 0.355389i | ||||
\(647\) | −14.5317 | − | 10.5579i | −0.571299 | − | 0.415073i | 0.264278 | − | 0.964447i | \(-0.414866\pi\) |
−0.835577 | + | 0.549373i | \(0.814866\pi\) | |||||||
\(648\) | 8.52842 | 0.335028 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −20.7153 | −0.812522 | ||||||||
\(651\) | 0.100294 | + | 0.0728678i | 0.00393083 | + | 0.00285591i | ||||
\(652\) | 2.87981 | − | 8.86313i | 0.112782 | − | 0.347107i | ||||
\(653\) | −5.22797 | − | 16.0900i | −0.204586 | − | 0.629652i | −0.999730 | − | 0.0232310i | \(-0.992605\pi\) |
0.795144 | − | 0.606421i | \(-0.207395\pi\) | |||||||
\(654\) | −11.2792 | + | 8.19479i | −0.441050 | + | 0.320442i | ||||
\(655\) | 15.4999 | − | 11.2614i | 0.605632 | − | 0.440018i | ||||
\(656\) | 14.7669 | + | 45.4477i | 0.576549 | + | 1.77444i | ||||
\(657\) | −8.06677 | + | 24.8270i | −0.314715 | + | 0.968592i | ||||
\(658\) | −18.7597 | − | 13.6297i | −0.731328 | − | 0.531341i | ||||
\(659\) | −23.6249 | −0.920297 | −0.460148 | − | 0.887842i | \(-0.652204\pi\) | ||||
−0.460148 | + | 0.887842i | \(0.652204\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.9819 | −0.816103 | −0.408051 | − | 0.912959i | \(-0.633792\pi\) | ||||
−0.408051 | + | 0.912959i | \(0.633792\pi\) | |||||||
\(662\) | −38.1555 | − | 27.7216i | −1.48296 | − | 1.07743i | ||||
\(663\) | 2.25950 | − | 6.95404i | 0.0877519 | − | 0.270072i | ||||
\(664\) | 0.794782 | + | 2.44609i | 0.0308435 | + | 0.0949266i | ||||
\(665\) | −4.35721 | + | 3.16570i | −0.168965 | + | 0.122760i | ||||
\(666\) | −3.89835 | + | 2.83231i | −0.151058 | + | 0.109750i | ||||
\(667\) | −11.6517 | − | 35.8601i | −0.451154 | − | 1.38851i | ||||
\(668\) | 4.80356 | − | 14.7838i | 0.185855 | − | 0.572004i | ||||
\(669\) | 2.31254 | + | 1.68016i | 0.0894078 | + | 0.0649586i | ||||
\(670\) | −26.7456 | −1.03327 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.61803 | 0.139569 | ||||||||
\(673\) | 9.78799 | + | 7.11139i | 0.377299 | + | 0.274124i | 0.760231 | − | 0.649653i | \(-0.225086\pi\) |
−0.382932 | + | 0.923777i | \(0.625086\pi\) | |||||||
\(674\) | −0.376790 | + | 1.15964i | −0.0145134 | + | 0.0446676i | ||||
\(675\) | −2.91243 | − | 8.96355i | −0.112100 | − | 0.345007i | ||||
\(676\) | −5.09711 | + | 3.70327i | −0.196043 | + | 0.142433i | ||||
\(677\) | −7.62893 | + | 5.54274i | −0.293204 | + | 0.213025i | −0.724656 | − | 0.689111i | \(-0.758001\pi\) |
0.431452 | + | 0.902136i | \(0.358001\pi\) | |||||||
\(678\) | 6.26255 | + | 19.2741i | 0.240512 | + | 0.740219i | ||||
\(679\) | 3.58961 | − | 11.0477i | 0.137757 | − | 0.423971i | ||||
\(680\) | 9.25098 | + | 6.72123i | 0.354759 | + | 0.257747i | ||||
\(681\) | −10.6922 | −0.409726 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.2986 | −0.585385 | −0.292692 | − | 0.956207i | \(-0.594551\pi\) | ||||
−0.292692 | + | 0.956207i | \(0.594551\pi\) | |||||||
\(684\) | −4.76194 | − | 3.45975i | −0.182077 | − | 0.132287i | ||||
\(685\) | 2.24073 | − | 6.89627i | 0.0856141 | − | 0.263493i | ||||
\(686\) | −0.549273 | − | 1.69049i | −0.0209713 | − | 0.0645431i | ||||
\(687\) | 2.21306 | − | 1.60788i | 0.0844335 | − | 0.0613445i | ||||
\(688\) | 18.9482 | − | 13.7667i | 0.722395 | − | 0.524851i | ||||
\(689\) | −5.17451 | − | 15.9255i | −0.197133 | − | 0.606713i | ||||
\(690\) | 4.12043 | − | 12.6814i | 0.156862 | − | 0.482772i | ||||
\(691\) | −18.4612 | − | 13.4128i | −0.702296 | − | 0.510248i | 0.178383 | − | 0.983961i | \(-0.442913\pi\) |
−0.880679 | + | 0.473713i | \(0.842913\pi\) | |||||||
\(692\) | 23.8639 | 0.907169 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 38.2256 | 1.45102 | ||||||||
\(695\) | 2.25003 | + | 1.63474i | 0.0853486 | + | 0.0620094i | ||||
\(696\) | −2.46195 | + | 7.57709i | −0.0933198 | + | 0.287209i | ||||
\(697\) | −8.17978 | − | 25.1748i | −0.309831 | − | 0.953562i | ||||
\(698\) | −27.9591 | + | 20.3135i | −1.05827 | + | 0.768877i | ||||
\(699\) | −5.26652 | + | 3.82635i | −0.199198 | + | 0.144726i | ||||
\(700\) | 0.972549 | + | 2.99320i | 0.0367589 | + | 0.113132i | ||||
\(701\) | 9.98872 | − | 30.7421i | 0.377269 | − | 1.16111i | −0.564667 | − | 0.825319i | \(-0.690995\pi\) |
0.941935 | − | 0.335794i | \(-0.109005\pi\) | |||||||
\(702\) | −21.4373 | − | 15.5751i | −0.809097 | − | 0.587843i | ||||
\(703\) | −2.00789 | −0.0757292 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 22.3937 | 0.843396 | ||||||||
\(706\) | −30.0987 | − | 21.8680i | −1.13278 | − | 0.823012i | ||||
\(707\) | −1.05430 | + | 3.24480i | −0.0396511 | + | 0.122033i | ||||
\(708\) | −1.89485 | − | 5.83175i | −0.0712128 | − | 0.219171i | ||||
\(709\) | −11.7791 | + | 8.55802i | −0.442373 | + | 0.321403i | −0.786577 | − | 0.617492i | \(-0.788149\pi\) |
0.344204 | + | 0.938895i | \(0.388149\pi\) | |||||||
\(710\) | 8.05622 | − | 5.85319i | 0.302345 | − | 0.219666i | ||||
\(711\) | 5.09153 | + | 15.6701i | 0.190947 | + | 0.587675i | ||||
\(712\) | −7.06551 | + | 21.7454i | −0.264791 | + | 0.814943i | ||||
\(713\) | 0.709174 | + | 0.515245i | 0.0265588 | + | 0.0192961i | ||||
\(714\) | −3.02710 | −0.113287 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.30759 | −0.160982 | ||||||||
\(717\) | −4.87823 | − | 3.54424i | −0.182181 | − | 0.132362i | ||||
\(718\) | 5.36709 | − | 16.5182i | 0.200298 | − | 0.616454i | ||||
\(719\) | 13.8626 | + | 42.6646i | 0.516986 | + | 1.59112i | 0.779639 | + | 0.626229i | \(0.215403\pi\) |
−0.262653 | + | 0.964890i | \(0.584597\pi\) | |||||||
\(720\) | 29.2645 | − | 21.2619i | 1.09062 | − | 0.792383i | ||||
\(721\) | 14.7100 | − | 10.6875i | 0.547830 | − | 0.398021i | ||||
\(722\) | 8.37087 | + | 25.7629i | 0.311531 | + | 0.958795i | ||||
\(723\) | −2.39685 | + | 7.37676i | −0.0891400 | + | 0.274345i | ||||
\(724\) | −4.47605 | − | 3.25204i | −0.166351 | − | 0.120861i | ||||
\(725\) | −23.4202 | −0.869806 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.3582 | 1.05175 | 0.525874 | − | 0.850562i | \(-0.323738\pi\) | ||||
0.525874 | + | 0.850562i | \(0.323738\pi\) | |||||||
\(728\) | −5.18962 | − | 3.77048i | −0.192340 | − | 0.139743i | ||||
\(729\) | −2.62868 | + | 8.09024i | −0.0973584 | + | 0.299638i | ||||
\(730\) | 15.2118 | + | 46.8172i | 0.563016 | + | 1.73278i | ||||
\(731\) | −10.4960 | + | 7.62576i | −0.388207 | + | 0.282049i | ||||
\(732\) | −0.573121 | + | 0.416397i | −0.0211832 | + | 0.0153905i | ||||
\(733\) | −1.93351 | − | 5.95072i | −0.0714157 | − | 0.219795i | 0.908978 | − | 0.416844i | \(-0.136864\pi\) |
−0.980394 | + | 0.197050i | \(0.936864\pi\) | |||||||
\(734\) | −5.43763 | + | 16.7353i | −0.200707 | + | 0.617711i | ||||
\(735\) | 1.38874 | + | 1.00898i | 0.0512245 | + | 0.0372168i | ||||
\(736\) | 25.5830 | 0.943001 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −44.7024 | −1.64552 | ||||||||
\(739\) | 7.56593 | + | 5.49697i | 0.278317 | + | 0.202209i | 0.718183 | − | 0.695854i | \(-0.244974\pi\) |
−0.439866 | + | 0.898064i | \(0.644974\pi\) | |||||||
\(740\) | −1.03045 | + | 3.17141i | −0.0378802 | + | 0.116583i | ||||
\(741\) | −1.59002 | − | 4.89358i | −0.0584109 | − | 0.179770i | ||||
\(742\) | −5.60843 | + | 4.07476i | −0.205892 | + | 0.149589i | ||||
\(743\) | 20.3926 | − | 14.8161i | 0.748130 | − | 0.543549i | −0.147116 | − | 0.989119i | \(-0.546999\pi\) |
0.895247 | + | 0.445571i | \(0.146999\pi\) | |||||||
\(744\) | −0.0572359 | − | 0.176154i | −0.00209837 | − | 0.00645812i | ||||
\(745\) | −12.7840 | + | 39.3452i | −0.468370 | + | 1.44150i | ||||
\(746\) | 6.14715 | + | 4.46617i | 0.225063 | + | 0.163518i | ||||
\(747\) | −4.50684 | −0.164897 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.24746 | −0.118660 | ||||||||
\(750\) | 5.64188 | + | 4.09907i | 0.206012 | + | 0.149677i | ||||
\(751\) | −10.7381 | + | 33.0485i | −0.391840 | + | 1.20596i | 0.539556 | + | 0.841950i | \(0.318592\pi\) |
−0.931396 | + | 0.364008i | \(0.881408\pi\) | |||||||
\(752\) | 20.0540 | + | 61.7198i | 0.731293 | + | 2.25069i | ||||
\(753\) | 5.49560 | − | 3.99278i | 0.200271 | − | 0.145505i | ||||
\(754\) | −53.2705 | + | 38.7033i | −1.94000 | + | 1.40949i | ||||
\(755\) | 13.5649 | + | 41.7485i | 0.493678 | + | 1.51938i | ||||
\(756\) | −1.24403 | + | 3.82873i | −0.0452450 | + | 0.139250i | ||||
\(757\) | −28.1505 | − | 20.4526i | −1.02315 | − | 0.743361i | −0.0562231 | − | 0.998418i | \(-0.517906\pi\) |
−0.966926 | + | 0.255057i | \(0.917906\pi\) | |||||||
\(758\) | −7.68929 | −0.279288 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.04674 | 0.291886 | ||||||||
\(761\) | −9.89060 | − | 7.18594i | −0.358534 | − | 0.260490i | 0.393906 | − | 0.919151i | \(-0.371123\pi\) |
−0.752440 | + | 0.658660i | \(0.771123\pi\) | |||||||
\(762\) | 6.62281 | − | 20.3829i | 0.239919 | − | 0.738395i | ||||
\(763\) | −3.92178 | − | 12.0700i | −0.141978 | − | 0.436964i | ||||
\(764\) | 0.777763 | − | 0.565078i | 0.0281385 | − | 0.0204438i | ||||
\(765\) | −16.2104 | + | 11.7775i | −0.586088 | + | 0.425818i | ||||
\(766\) | 0.726193 | + | 2.23499i | 0.0262384 | + | 0.0807536i | ||||
\(767\) | −11.3532 | + | 34.9417i | −0.409941 | + | 1.26167i | ||||
\(768\) | −10.1410 | − | 7.36785i | −0.365931 | − | 0.265864i | ||||
\(769\) | 2.61946 | 0.0944603 | 0.0472301 | − | 0.998884i | \(-0.484961\pi\) | ||||
0.0472301 | + | 0.998884i | \(0.484961\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.29585 | 0.118697 | ||||||||
\(772\) | −6.32037 | − | 4.59202i | −0.227475 | − | 0.165270i | ||||
\(773\) | −0.0657602 | + | 0.202389i | −0.00236523 | + | 0.00727943i | −0.952232 | − | 0.305375i | \(-0.901218\pi\) |
0.949867 | + | 0.312654i | \(0.101218\pi\) | |||||||
\(774\) | 6.77047 | + | 20.8374i | 0.243359 | + | 0.748983i | ||||
\(775\) | 0.440493 | − | 0.320037i | 0.0158230 | − | 0.0114961i | ||||
\(776\) | −14.0408 | + | 10.2012i | −0.504035 | + | 0.366203i | ||||
\(777\) | 0.197759 | + | 0.608640i | 0.00709457 | + | 0.0218348i | ||||
\(778\) | 21.1520 | − | 65.0993i | 0.758337 | − | 2.33392i | ||||
\(779\) | −15.0698 | − | 10.9488i | −0.539931 | − | 0.392283i | ||||
\(780\) | −8.54526 | −0.305969 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −21.4045 | −0.765425 | ||||||||
\(783\) | −24.2365 | − | 17.6088i | −0.866140 | − | 0.629288i | ||||
\(784\) | −1.53723 | + | 4.73110i | −0.0549010 | + | 0.168968i | ||||
\(785\) | −3.94060 | − | 12.1279i | −0.140646 | − | 0.432864i | ||||
\(786\) | 6.13051 | − | 4.45407i | 0.218668 | − | 0.158872i | ||||
\(787\) | 23.5728 | − | 17.1266i | 0.840278 | − | 0.610498i | −0.0821704 | − | 0.996618i | \(-0.526185\pi\) |
0.922448 | + | 0.386121i | \(0.126185\pi\) | |||||||
\(788\) | 3.91309 | + | 12.0432i | 0.139398 | + | 0.429023i | ||||
\(789\) | 1.56231 | − | 4.80828i | 0.0556196 | − | 0.171179i | ||||
\(790\) | 25.1365 | + | 18.2628i | 0.894318 | + | 0.649760i | ||||
\(791\) | −18.4480 | −0.655937 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.24457 | 0.150729 | ||||||||
\(794\) | −0.589743 | − | 0.428473i | −0.0209292 | − | 0.0152059i | ||||
\(795\) | 2.06883 | − | 6.36719i | 0.0733737 | − | 0.225821i | ||||
\(796\) | 7.51498 | + | 23.1287i | 0.266361 | + | 0.819776i | ||||
\(797\) | −26.0733 | + | 18.9434i | −0.923565 | + | 0.671009i | −0.944409 | − | 0.328774i | \(-0.893365\pi\) |
0.0208440 | + | 0.999783i | \(0.493365\pi\) | |||||||
\(798\) | −1.72336 | + | 1.25209i | −0.0610061 | + | 0.0443236i | ||||
\(799\) | −11.1085 | − | 34.1883i | −0.392989 | − | 1.20950i | ||||
\(800\) | 4.91043 | − | 15.1127i | 0.173610 | − | 0.534316i | ||||
\(801\) | −32.4134 | − | 23.5497i | −1.14527 | − | 0.832088i | ||||
\(802\) | 2.78503 | 0.0983430 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −3.88203 | −0.136909 | ||||||||
\(805\) | 9.81974 | + | 7.13446i | 0.346100 | + | 0.251457i | ||||
\(806\) | 0.473044 | − | 1.45588i | 0.0166623 | − | 0.0512812i | ||||
\(807\) | 2.45297 | + | 7.54946i | 0.0863486 | + | 0.265754i | ||||
\(808\) | 4.12391 | − | 2.99619i | 0.145079 | − | 0.105406i | ||||
\(809\) | −23.7415 | + | 17.2492i | −0.834706 | + | 0.606450i | −0.920887 | − | 0.389830i | \(-0.872534\pi\) |
0.0861807 | + | 0.996280i | \(0.472534\pi\) | |||||||
\(810\) | 8.70842 | + | 26.8018i | 0.305983 | + | 0.941718i | ||||
\(811\) | −0.321192 | + | 0.988526i | −0.0112786 | + | 0.0347118i | −0.956537 | − | 0.291610i | \(-0.905809\pi\) |
0.945259 | + | 0.326321i | \(0.105809\pi\) | |||||||
\(812\) | 8.09328 | + | 5.88011i | 0.284018 | + | 0.206351i | ||||
\(813\) | 13.6259 | 0.477882 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.3244 | −0.781990 | ||||||||
\(816\) | 6.85386 | + | 4.97962i | 0.239933 | + | 0.174322i | ||||
\(817\) | −2.82122 | + | 8.68282i | −0.0987020 | + | 0.303773i | ||||
\(818\) | −3.72326 | − | 11.4590i | −0.130181 | − | 0.400655i | ||||
\(819\) | 9.09373 | − | 6.60698i | 0.317761 | − | 0.230867i | ||||
\(820\) | −25.0271 | + | 18.1833i | −0.873986 | + | 0.634988i | ||||
\(821\) | −8.81698 | − | 27.1359i | −0.307715 | − | 0.947048i | −0.978650 | − | 0.205533i | \(-0.934107\pi\) |
0.670936 | − | 0.741516i | \(-0.265893\pi\) | |||||||
\(822\) | 0.886251 | − | 2.72760i | 0.0309116 | − | 0.0951360i | ||||
\(823\) | −21.5665 | − | 15.6690i | −0.751761 | − | 0.546186i | 0.144611 | − | 0.989489i | \(-0.453807\pi\) |
−0.896372 | + | 0.443302i | \(0.853807\pi\) | |||||||
\(824\) | −27.1659 | −0.946370 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.2102 | 0.529229 | ||||||||
\(827\) | 1.39122 | + | 1.01078i | 0.0483775 | + | 0.0351483i | 0.611711 | − | 0.791081i | \(-0.290481\pi\) |
−0.563334 | + | 0.826229i | \(0.690481\pi\) | |||||||
\(828\) | −4.09921 | + | 12.6161i | −0.142458 | + | 0.438439i | ||||
\(829\) | 8.64026 | + | 26.5920i | 0.300089 | + | 0.923578i | 0.981464 | + | 0.191644i | \(0.0613819\pi\) |
−0.681376 | + | 0.731934i | \(0.738618\pi\) | |||||||
\(830\) | −6.87562 | + | 4.99543i | −0.238656 | + | 0.173394i | ||||
\(831\) | 12.0385 | − | 8.74647i | 0.417610 | − | 0.303412i | ||||
\(832\) | −0.605562 | − | 1.86373i | −0.0209941 | − | 0.0646132i | ||||
\(833\) | 0.851514 | − | 2.62069i | 0.0295032 | − | 0.0908015i | ||||
\(834\) | 0.889929 | + | 0.646571i | 0.0308157 | + | 0.0223889i | ||||
\(835\) | −37.2375 | −1.28866 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.696468 | 0.0240735 | ||||||||
\(838\) | 41.3024 | + | 30.0080i | 1.42677 | + | 1.03661i | ||||
\(839\) | 11.0821 | − | 34.1072i | 0.382596 | − | 1.17751i | −0.555612 | − | 0.831441i | \(-0.687516\pi\) |
0.938209 | − | 0.346069i | \(-0.112484\pi\) | |||||||
\(840\) | −0.792530 | − | 2.43916i | −0.0273449 | − | 0.0841589i | ||||
\(841\) | −36.7649 | + | 26.7113i | −1.26776 | + | 0.921078i | ||||
\(842\) | 17.5806 | − | 12.7730i | 0.605866 | − | 0.440188i | ||||
\(843\) | −2.94913 | − | 9.07648i | −0.101573 | − | 0.312611i | ||||
\(844\) | 2.15820 | − | 6.64225i | 0.0742882 | − | 0.228636i | ||||
\(845\) | 12.2102 | + | 8.87125i | 0.420045 | + | 0.305180i | ||||
\(846\) | −60.7076 | −2.08717 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 19.4014 | 0.666248 | ||||||||
\(849\) | −1.67866 | − | 1.21962i | −0.0576115 | − | 0.0418572i | ||||
\(850\) | −4.10841 | + | 12.6444i | −0.140917 | + | 0.433699i | ||||
\(851\) | 1.39835 | + | 4.30367i | 0.0479347 | + | 0.147528i | ||||
\(852\) | 1.16933 | − | 0.849571i | 0.0400607 | − | 0.0291058i | ||||
\(853\) | −12.2507 | + | 8.90068i | −0.419457 | + | 0.304754i | −0.777419 | − | 0.628983i | \(-0.783472\pi\) |
0.357962 | + | 0.933736i | \(0.383472\pi\) | |||||||
\(854\) | −0.543016 | − | 1.67123i | −0.0185816 | − | 0.0571884i | ||||
\(855\) | −4.35721 | + | 13.4101i | −0.149013 | + | 0.458616i | ||||
\(856\) | 3.92528 | + | 2.85188i | 0.134163 | + | 0.0974753i | ||||
\(857\) | −25.3267 | −0.865142 | −0.432571 | − | 0.901600i | \(-0.642394\pi\) | ||||
−0.432571 | + | 0.901600i | \(0.642394\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.5291 | 1.41696 | 0.708478 | − | 0.705733i | \(-0.249382\pi\) | ||||
0.708478 | + | 0.705733i | \(0.249382\pi\) | |||||||
\(860\) | 12.2664 | + | 8.91205i | 0.418280 | + | 0.303898i | ||||
\(861\) | −1.83461 | + | 5.64636i | −0.0625235 | + | 0.192427i | ||||
\(862\) | 2.02753 | + | 6.24008i | 0.0690578 | + | 0.212538i | ||||
\(863\) | 19.4572 | − | 14.1365i | 0.662329 | − | 0.481210i | −0.205119 | − | 0.978737i | \(-0.565758\pi\) |
0.867449 | + | 0.497527i | \(0.165758\pi\) | |||||||
\(864\) | 16.4443 | − | 11.9475i | 0.559445 | − | 0.406461i | ||||
\(865\) | −17.6654 | − | 54.3685i | −0.600641 | − | 1.84858i | ||||
\(866\) | −15.9700 | + | 49.1507i | −0.542684 | + | 1.67021i | ||||
\(867\) | 4.70345 | + | 3.41726i | 0.159738 | + | 0.116056i | ||||
\(868\) | −0.232572 | −0.00789399 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −26.3260 | −0.892534 | ||||||||
\(871\) | 18.8175 | + | 13.6717i | 0.637606 | + | 0.463248i | ||||
\(872\) | −5.85939 | + | 18.0334i | −0.198424 | + | 0.610687i | ||||
\(873\) | −9.39772 | − | 28.9232i | −0.318065 | − | 0.978902i | ||||
\(874\) | −12.1858 | + | 8.85349i | −0.412190 | + | 0.299474i | ||||
\(875\) | −5.13577 | + | 3.73136i | −0.173621 | + | 0.126143i | ||||
\(876\) | 2.20795 | + | 6.79537i | 0.0745997 | + | 0.229594i | ||||
\(877\) | −10.4464 | + | 32.1506i | −0.352749 | + | 1.08565i | 0.604554 | + | 0.796564i | \(0.293351\pi\) |
−0.957303 | + | 0.289086i | \(0.906649\pi\) | |||||||
\(878\) | 20.4223 | + | 14.8376i | 0.689218 | + | 0.500746i | ||||
\(879\) | −4.22553 | −0.142524 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.8296 | −1.24082 | −0.620410 | − | 0.784278i | \(-0.713034\pi\) | ||||
−0.620410 | + | 0.784278i | \(0.713034\pi\) | |||||||
\(882\) | −3.76477 | − | 2.73527i | −0.126766 | − | 0.0921012i | ||||
\(883\) | 16.5047 | − | 50.7963i | 0.555428 | − | 1.70943i | −0.139384 | − | 0.990238i | \(-0.544512\pi\) |
0.694812 | − | 0.719192i | \(-0.255488\pi\) | |||||||
\(884\) | 4.23890 | + | 13.0460i | 0.142570 | + | 0.438784i | ||||
\(885\) | −11.8836 | + | 8.63397i | −0.399464 | + | 0.290228i | ||||
\(886\) | 39.1652 | − | 28.4552i | 1.31578 | − | 0.955970i | ||||
\(887\) | −3.54183 | − | 10.9006i | −0.118923 | − | 0.366007i | 0.873822 | − | 0.486246i | \(-0.161634\pi\) |
−0.992745 | + | 0.120239i | \(0.961634\pi\) | |||||||
\(888\) | 0.295465 | − | 0.909347i | 0.00991515 | − | 0.0305157i | ||||
\(889\) | 15.7834 | + | 11.4673i | 0.529357 | + | 0.384600i | ||||
\(890\) | −75.5525 | −2.53253 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.36254 | −0.179551 | ||||||||
\(893\) | −20.4653 | − | 14.8689i | −0.684846 | − | 0.497570i | ||||
\(894\) | −5.05631 | + | 15.5617i | −0.169108 | + | 0.520462i | ||||
\(895\) | 3.18872 | + | 9.81386i | 0.106587 | + | 0.328041i | ||||
\(896\) | 8.81579 | − | 6.40505i | 0.294515 | − | 0.213978i | ||||
\(897\) | −9.38145 | + | 6.81602i | −0.313237 | + | 0.227580i | ||||
\(898\) | 23.0233 | + | 70.8583i | 0.768296 | + | 2.36457i | ||||
\(899\) | 0.534812 | − | 1.64598i | 0.0178370 | − | 0.0548966i | ||||
\(900\) | 6.66595 | + | 4.84309i | 0.222198 | + | 0.161436i | ||||
\(901\) | −10.7470 | −0.358034 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.90983 | 0.0968331 | ||||||||
\(904\) | 22.2986 | + | 16.2009i | 0.741640 | + | 0.538833i | ||||
\(905\) | −4.09561 | + | 12.6050i | −0.136143 | + | 0.419004i | ||||
\(906\) | 5.36517 | + | 16.5123i | 0.178246 | + | 0.548585i | ||||
\(907\) | −46.1610 | + | 33.5380i | −1.53275 | + | 1.11361i | −0.578068 | + | 0.815989i | \(0.696193\pi\) |
−0.954684 | + | 0.297621i | \(0.903807\pi\) | |||||||
\(908\) | 16.2280 | − | 11.7903i | 0.538544 | − | 0.391275i | ||||
\(909\) | 2.76020 | + | 8.49501i | 0.0915499 | + | 0.281762i | ||||
\(910\) | 6.55011 | − | 20.1592i | 0.217134 | − | 0.668270i | ||||
\(911\) | −5.40072 | − | 3.92386i | −0.178934 | − | 0.130003i | 0.494713 | − | 0.869056i | \(-0.335273\pi\) |
−0.673647 | + | 0.739053i | \(0.735273\pi\) | |||||||
\(912\) | 5.96167 | 0.197410 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 34.6568 | 1.14635 | ||||||||
\(915\) | 1.37292 | + | 0.997487i | 0.0453874 | + | 0.0329759i | ||||
\(916\) | −1.58583 | + | 4.88069i | −0.0523974 | + | 0.161263i | ||||
\(917\) | 2.13159 | + | 6.56035i | 0.0703912 | + | 0.216642i | ||||
\(918\) | −13.7584 | + | 9.99610i | −0.454096 | + | 0.329920i | ||||
\(919\) | −23.5698 | + | 17.1245i | −0.777496 | + | 0.564884i | −0.904227 | − | 0.427053i | \(-0.859552\pi\) |
0.126730 | + | 0.991937i | \(0.459552\pi\) | |||||||
\(920\) | −5.60395 | − | 17.2472i | −0.184757 | − | 0.568622i | ||||
\(921\) | 2.25303 | − | 6.93413i | 0.0742400 | − | 0.228487i | ||||
\(922\) | −17.5799 | − | 12.7725i | −0.578962 | − | 0.420641i | ||||
\(923\) | −8.66015 | −0.285052 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.81073 | 0.0924161 | ||||||||
\(926\) | 19.9236 | + | 14.4754i | 0.654731 | + | 0.475690i | ||||
\(927\) | 14.7100 | − | 45.2728i | 0.483140 | − | 1.48695i | ||||
\(928\) | −15.6084 | − | 48.0376i | −0.512370 | − | 1.57691i | ||||
\(929\) | −1.89692 | + | 1.37819i | −0.0622358 | + | 0.0452169i | −0.618468 | − | 0.785810i | \(-0.712246\pi\) |
0.556232 | + | 0.831027i | \(0.312246\pi\) | |||||||
\(930\) | 0.495144 | − | 0.359743i | 0.0162364 | − | 0.0117965i | ||||
\(931\) | −0.599213 | − | 1.84419i | −0.0196384 | − | 0.0604409i | ||||
\(932\) | 3.77388 | − | 11.6148i | 0.123618 | − | 0.380456i | ||||
\(933\) | −12.6569 | − | 9.19581i | −0.414370 | − | 0.301057i | ||||
\(934\) | 29.1876 | 0.955047 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −16.7940 | −0.548928 | ||||||||
\(937\) | 7.10948 | + | 5.16534i | 0.232257 | + | 0.168744i | 0.697827 | − | 0.716267i | \(-0.254151\pi\) |
−0.465570 | + | 0.885011i | \(0.654151\pi\) | |||||||
\(938\) | 2.97566 | − | 9.15813i | 0.0971586 | − | 0.299023i | ||||
\(939\) | −3.75364 | − | 11.5525i | −0.122496 | − | 0.377003i | ||||
\(940\) | −33.9878 | + | 24.6936i | −1.10856 | + | 0.805416i | ||||
\(941\) | 7.19112 | − | 5.22465i | 0.234424 | − | 0.170319i | −0.464372 | − | 0.885640i | \(-0.653720\pi\) |
0.698795 | + | 0.715322i | \(0.253720\pi\) | |||||||
\(942\) | −1.55858 | − | 4.79682i | −0.0507813 | − | 0.156289i | ||||
\(943\) | −12.9725 | + | 39.9252i | −0.422442 | + | 1.30014i | ||||
\(944\) | −34.4383 | − | 25.0209i | −1.12087 | − | 0.814361i | ||||
\(945\) | 9.64380 | 0.313713 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.86275 | −0.255505 | −0.127752 | − | 0.991806i | \(-0.540776\pi\) | ||||
−0.127752 | + | 0.991806i | \(0.540776\pi\) | |||||||
\(948\) | 3.64849 | + | 2.65078i | 0.118497 | + | 0.0860933i | ||||
\(949\) | 13.2292 | − | 40.7153i | 0.429438 | − | 1.32167i | ||||
\(950\) | 2.89111 | + | 8.89791i | 0.0937999 | + | 0.288686i | ||||
\(951\) | −1.80528 | + | 1.31161i | −0.0585402 | + | 0.0425320i | ||||
\(952\) | −3.33070 | + | 2.41990i | −0.107949 | + | 0.0784294i | ||||
\(953\) | 5.39679 | + | 16.6096i | 0.174819 | + | 0.538039i | 0.999625 | − | 0.0273775i | \(-0.00871562\pi\) |
−0.824806 | + | 0.565416i | \(0.808716\pi\) | |||||||
\(954\) | −5.60843 | + | 17.2610i | −0.181580 | + | 0.558845i | ||||
\(955\) | −1.86315 | − | 1.35365i | −0.0602900 | − | 0.0438032i | ||||
\(956\) | 11.3121 | 0.365860 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −44.0663 | −1.42372 | ||||||||
\(959\) | 2.11210 | + | 1.53453i | 0.0682032 | + | 0.0495525i | ||||
\(960\) | 0.242111 | − | 0.745140i | 0.00781408 | − | 0.0240493i | ||||
\(961\) | −9.56709 | − | 29.4445i | −0.308616 | − | 0.949822i | ||||
\(962\) | 6.39314 | − | 4.64489i | 0.206123 | − | 0.149757i | ||||
\(963\) | −6.87823 | + | 4.99733i | −0.221648 | + | 0.161037i | ||||
\(964\) | −4.49657 | − | 13.8390i | −0.144825 | − | 0.445725i | ||||
\(965\) | −5.78318 | + | 17.7988i | −0.186167 | + | 0.572964i | ||||
\(966\) | 3.88389 | + | 2.82181i | 0.124962 | + | 0.0907902i | ||||
\(967\) | 45.6122 | 1.46679 | 0.733395 | − | 0.679802i | \(-0.237934\pi\) | ||||
0.733395 | + | 0.679802i | \(0.237934\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.30233 | −0.106086 | ||||||||
\(970\) | −46.3959 | − | 33.7086i | −1.48968 | − | 1.08232i | ||||
\(971\) | 0.736629 | − | 2.26711i | 0.0236396 | − | 0.0727551i | −0.938541 | − | 0.345168i | \(-0.887822\pi\) |
0.962180 | + | 0.272413i | \(0.0878218\pi\) | |||||||
\(972\) | 4.99609 | + | 15.3764i | 0.160250 | + | 0.493198i | ||||
\(973\) | −0.810097 | + | 0.588570i | −0.0259705 | + | 0.0188687i | ||||
\(974\) | −20.6128 | + | 14.9761i | −0.660476 | + | 0.479864i | ||||
\(975\) | 2.22577 | + | 6.85022i | 0.0712817 | + | 0.219383i | ||||
\(976\) | −1.51972 | + | 4.67721i | −0.0486450 | + | 0.149714i | ||||
\(977\) | 15.5867 | + | 11.3244i | 0.498662 | + | 0.362299i | 0.808506 | − | 0.588488i | \(-0.200277\pi\) |
−0.309844 | + | 0.950787i | \(0.600277\pi\) | |||||||
\(978\) | −8.82972 | −0.282343 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −3.22035 | −0.102870 | ||||||||
\(981\) | −26.8803 | − | 19.5297i | −0.858222 | − | 0.623535i | ||||
\(982\) | −12.0946 | + | 37.2234i | −0.385955 | + | 1.18785i | ||||
\(983\) | −5.01399 | − | 15.4315i | −0.159922 | − | 0.492188i | 0.838705 | − | 0.544587i | \(-0.183313\pi\) |
−0.998626 | + | 0.0523985i | \(0.983313\pi\) | |||||||
\(984\) | 7.17611 | − | 5.21375i | 0.228766 | − | 0.166208i | ||||
\(985\) | 24.5411 | − | 17.8302i | 0.781945 | − | 0.568116i | ||||
\(986\) | 13.0591 | + | 40.1917i | 0.415885 | + | 1.27996i | ||||
\(987\) | −2.49148 | + | 7.66797i | −0.0793045 | + | 0.244074i | ||||
\(988\) | 7.80941 | + | 5.67387i | 0.248450 | + | 0.180510i | ||||
\(989\) | 20.5753 | 0.654256 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.5214 | −1.60487 | −0.802433 | − | 0.596743i | \(-0.796461\pi\) | ||||
−0.802433 | + | 0.596743i | \(0.796461\pi\) | |||||||
\(992\) | 0.949997 | + | 0.690213i | 0.0301624 | + | 0.0219143i | ||||
\(993\) | −5.06744 | + | 15.5960i | −0.160810 | + | 0.494923i | ||||
\(994\) | 1.10791 | + | 3.40980i | 0.0351408 | + | 0.108152i | ||||
\(995\) | 47.1305 | − | 34.2423i | 1.49414 | − | 1.08556i | ||||
\(996\) | −0.997973 | + | 0.725070i | −0.0316220 | + | 0.0229747i | ||||
\(997\) | 13.9121 | + | 42.8172i | 0.440602 | + | 1.35603i | 0.887236 | + | 0.461316i | \(0.152623\pi\) |
−0.446634 | + | 0.894717i | \(0.647377\pi\) | |||||||
\(998\) | 13.9030 | − | 42.7892i | 0.440093 | − | 1.35447i | ||||
\(999\) | 2.90868 | + | 2.11328i | 0.0920266 | + | 0.0668612i |
(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 | 847.2.f.s.323.2 | 8 | ||
11.2 | odd | 10 | 77.2.f.a.71.2 | yes | 8 | ||
11.3 | even | 5 | inner | 847.2.f.s.729.2 | 8 | ||
11.4 | even | 5 | 847.2.f.q.372.1 | 8 | |||
11.5 | even | 5 | 847.2.a.k.1.2 | 4 | |||
11.6 | odd | 10 | 847.2.a.l.1.3 | 4 | |||
11.7 | odd | 10 | 77.2.f.a.64.2 | ✓ | 8 | ||
11.8 | odd | 10 | 847.2.f.p.729.1 | 8 | |||
11.9 | even | 5 | 847.2.f.q.148.1 | 8 | |||
11.10 | odd | 2 | 847.2.f.p.323.1 | 8 | |||
33.2 | even | 10 | 693.2.m.g.379.1 | 8 | |||
33.5 | odd | 10 | 7623.2.a.co.1.3 | 4 | |||
33.17 | even | 10 | 7623.2.a.ch.1.2 | 4 | |||
33.29 | even | 10 | 693.2.m.g.64.1 | 8 | |||
77.2 | odd | 30 | 539.2.q.c.214.2 | 16 | |||
77.6 | even | 10 | 5929.2.a.bi.1.3 | 4 | |||
77.13 | even | 10 | 539.2.f.d.148.2 | 8 | |||
77.18 | odd | 30 | 539.2.q.c.471.2 | 16 | |||
77.24 | even | 30 | 539.2.q.b.324.1 | 16 | |||
77.27 | odd | 10 | 5929.2.a.bb.1.2 | 4 | |||
77.40 | even | 30 | 539.2.q.b.361.1 | 16 | |||
77.46 | odd | 30 | 539.2.q.c.324.1 | 16 | |||
77.51 | odd | 30 | 539.2.q.c.361.1 | 16 | |||
77.62 | even | 10 | 539.2.f.d.295.2 | 8 | |||
77.68 | even | 30 | 539.2.q.b.214.2 | 16 | |||
77.73 | even | 30 | 539.2.q.b.471.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.a.64.2 | ✓ | 8 | 11.7 | odd | 10 | ||
77.2.f.a.71.2 | yes | 8 | 11.2 | odd | 10 | ||
539.2.f.d.148.2 | 8 | 77.13 | even | 10 | |||
539.2.f.d.295.2 | 8 | 77.62 | even | 10 | |||
539.2.q.b.214.2 | 16 | 77.68 | even | 30 | |||
539.2.q.b.324.1 | 16 | 77.24 | even | 30 | |||
539.2.q.b.361.1 | 16 | 77.40 | even | 30 | |||
539.2.q.b.471.2 | 16 | 77.73 | even | 30 | |||
539.2.q.c.214.2 | 16 | 77.2 | odd | 30 | |||
539.2.q.c.324.1 | 16 | 77.46 | odd | 30 | |||
539.2.q.c.361.1 | 16 | 77.51 | odd | 30 | |||
539.2.q.c.471.2 | 16 | 77.18 | odd | 30 | |||
693.2.m.g.64.1 | 8 | 33.29 | even | 10 | |||
693.2.m.g.379.1 | 8 | 33.2 | even | 10 | |||
847.2.a.k.1.2 | 4 | 11.5 | even | 5 | |||
847.2.a.l.1.3 | 4 | 11.6 | odd | 10 | |||
847.2.f.p.323.1 | 8 | 11.10 | odd | 2 | |||
847.2.f.p.729.1 | 8 | 11.8 | odd | 10 | |||
847.2.f.q.148.1 | 8 | 11.9 | even | 5 | |||
847.2.f.q.372.1 | 8 | 11.4 | even | 5 | |||
847.2.f.s.323.2 | 8 | 1.1 | even | 1 | trivial | ||
847.2.f.s.729.2 | 8 | 11.3 | even | 5 | inner | ||
5929.2.a.bb.1.2 | 4 | 77.27 | odd | 10 | |||
5929.2.a.bi.1.3 | 4 | 77.6 | even | 10 | |||
7623.2.a.ch.1.2 | 4 | 33.17 | even | 10 | |||
7623.2.a.co.1.3 | 4 | 33.5 | odd | 10 |