LMFDB - Embedded newform 135.3.l.a.127.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,3,Mod(37,135)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 3]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("135.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$N$	$=$	$135 = 3^{3} \cdot 5$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	135.l (of order $12$ , 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:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			127.6
Character	$\chi$	$=$	135.127
Dual form			135.3.l.a.118.6

$q$ -expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.725667 - 0.194442i) q^{2} +(-2.97532 + 1.71780i) q^{4} +(-4.81907 - 1.33289i) q^{5} +(-1.79727 + 0.481578i) q^{7} +(-3.94998 + 3.94998i) q^{8} +(-3.75621 - 0.0302083i) q^{10} +(-5.82294 + 10.0856i) q^{11} +(-19.8070 - 5.30726i) q^{13} +(-1.21058 + 0.698930i) q^{14} +(4.77288 - 8.26686i) q^{16} +(10.0254 + 10.0254i) q^{17} -10.8032i q^{19} +(16.6279 - 4.31241i) q^{20} +(-2.26444 + 8.45102i) q^{22} +(1.34569 + 0.360576i) q^{23} +(21.4468 + 12.8466i) q^{25} -15.4052 q^{26} +(4.52021 - 4.52021i) q^{28} +(-20.7968 - 12.0070i) q^{29} +(21.6233 + 37.4526i) q^{31} +(7.63926 - 28.5101i) q^{32} +(9.22442 + 5.32572i) q^{34} +(9.30307 + 0.0748176i) q^{35} +(-32.5443 - 32.5443i) q^{37} +(-2.10058 - 7.83949i) q^{38} +(24.3001 - 13.7703i) q^{40} +(20.5409 + 35.5778i) q^{41} +(2.14721 + 8.01349i) q^{43} -40.0106i q^{44} +1.04663 q^{46} +(-17.2577 + 4.62418i) q^{47} +(-39.4370 + 22.7689i) q^{49} +(18.0611 + 5.15220i) q^{50} +(68.0488 - 18.2336i) q^{52} +(51.3281 - 51.3281i) q^{53} +(41.5042 - 40.8419i) q^{55} +(5.19697 - 9.00141i) q^{56} +(-17.4262 - 4.66933i) q^{58} +(-24.3449 + 14.0555i) q^{59} +(-41.1002 + 71.1876i) q^{61} +(22.9736 + 22.9736i) q^{62} +16.0088i q^{64} +(88.3771 + 51.9766i) q^{65} +(8.65757 - 32.3105i) q^{67} +(-47.0502 - 12.6071i) q^{68} +(6.76548 - 1.75461i) q^{70} -99.6917 q^{71} +(-22.3583 + 22.3583i) q^{73} +(-29.9443 - 17.2883i) q^{74} +(18.5577 + 32.1428i) q^{76} +(5.60840 - 20.9308i) q^{77} +(-52.9926 - 30.5953i) q^{79} +(-34.0196 + 33.4768i) q^{80} +(21.8237 + 21.8237i) q^{82} +(-13.3760 - 49.9199i) q^{83} +(-34.9502 - 61.6757i) q^{85} +(3.11631 + 5.39761i) q^{86} +(-16.8375 - 62.8384i) q^{88} +113.914i q^{89} +38.1544 q^{91} +(-4.62324 + 1.23879i) q^{92} +(-11.6242 + 6.71123i) q^{94} +(-14.3995 + 52.0611i) q^{95} +(-29.5689 + 7.92297i) q^{97} +(-24.1909 + 24.1909i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$40 q + 2 q^{2} + 2 q^{5} - 2 q^{7} + 24 q^{8} - 8 q^{10} - 8 q^{11} - 2 q^{13} + 28 q^{16} - 28 q^{17} + 114 q^{20} + 14 q^{22} - 82 q^{23} - 8 q^{25} + 112 q^{26} - 88 q^{28} - 4 q^{31} + 14 q^{32} - 352 q^{35}+ \cdots + 1876 q^{98}+O(q^{100})$ 40 * q + 2 * q^2 + 2 * q^5 - 2 * q^7 + 24 * q^8 - 8 * q^10 - 8 * q^11 - 2 * q^13 + 28 * q^16 - 28 * q^17 + 114 * q^20 + 14 * q^22 - 82 * q^23 - 8 * q^25 + 112 * q^26 - 88 * q^28 - 4 * q^31 + 14 * q^32 - 352 * q^35 - 92 * q^37 - 330 * q^38 + 30 * q^40 + 28 * q^41 - 2 * q^43 - 136 * q^46 - 64 * q^47 + 458 * q^50 - 74 * q^52 + 608 * q^53 + 224 * q^55 + 192 * q^56 + 30 * q^58 + 92 * q^61 + 100 * q^62 + 326 * q^65 - 80 * q^67 - 626 * q^68 - 102 * q^70 - 248 * q^71 - 8 * q^73 - 96 * q^76 - 338 * q^77 - 1444 * q^80 + 104 * q^82 - 370 * q^83 - 98 * q^85 + 328 * q^86 - 210 * q^88 + 152 * q^91 - 388 * q^92 + 360 * q^95 + 292 * q^97 + 1876 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$ .

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	0.725667	−	0.194442i	0.362833	−	0.0972209i	−0.0727965	−	0.997347i	$-0.523192\pi$
$2$	0.725667	−	0.194442i	0.362833	−	0.0972209i	0.435630	+	0.900126i	$0.356526\pi$
$3$		0			0
$3$		0			0
$4$	−2.97532	+	1.71780i	−0.743829	+	0.429450i
$5$	−4.81907	−	1.33289i	−0.963813	−	0.266579i
$5$	−4.81907	−	1.33289i	−0.963813	−	0.266579i
$6$		0			0
$7$	−1.79727	+	0.481578i	−0.256753	+	0.0687969i	−0.384900	−	0.922958i	$-0.625764\pi$
$7$	−1.79727	+	0.481578i	−0.256753	+	0.0687969i	0.128146	+	0.991755i	$0.459097\pi$
$8$	−3.94998	+	3.94998i	−0.493747	+	0.493747i
$9$		0			0
$10$	−3.75621	−	0.0302083i	−0.375621	−	0.00302083i
$11$	−5.82294	+	10.0856i	−0.529358	+	0.916875i	0.470056	+	0.882637i	$0.344234\pi$
$11$	−5.82294	+	10.0856i	−0.529358	+	0.916875i	−0.999414	+	0.0342381i	$0.989100\pi$
$12$		0			0
$13$	−19.8070	−	5.30726i	−1.52361	−	0.408251i	−0.602684	−	0.797980i	$-0.705902\pi$
$13$	−19.8070	−	5.30726i	−1.52361	−	0.408251i	−0.920930	+	0.389729i	$0.872569\pi$
$14$	−1.21058	+	0.698930i	−0.0864702	+	0.0499236i
$15$		0			0
$16$	4.77288	−	8.26686i	0.298305	−	0.516679i
$17$	10.0254	+	10.0254i	0.589728	+	0.589728i	0.937558	−	0.347830i	$-0.113081\pi$
$17$	10.0254	+	10.0254i	0.589728	+	0.589728i	−0.347830	+	0.937558i	$0.613081\pi$
$18$		0			0
$19$		−	10.8032i		−	0.568587i	−0.958737	−	0.284294i	$-0.908241\pi$
$19$		−	10.8032i		−	0.568587i	0.958737	−	0.284294i	$-0.0917590\pi$
$20$	16.6279	−	4.31241i	0.831395	−	0.215621i
$21$		0			0
$22$	−2.26444	+	8.45102i	−0.102929	+	0.384137i
$23$	1.34569	+	0.360576i	0.0585081	+	0.0156772i	0.287954	−	0.957644i	$-0.407025\pi$
$23$	1.34569	+	0.360576i	0.0585081	+	0.0156772i	−0.229446	+	0.973321i	$0.573692\pi$
$24$		0			0
$25$	21.4468	+	12.8466i	0.857872	+	0.513864i
$26$	−15.4052			−0.592508
$27$		0			0
$28$	4.52021	−	4.52021i	0.161436	−	0.161436i
$29$	−20.7968	−	12.0070i	−0.717130	−	0.414035i	0.0965656	−	0.995327i	$-0.469214\pi$
$29$	−20.7968	−	12.0070i	−0.717130	−	0.414035i	−0.813695	+	0.581292i	$0.802548\pi$
$30$		0			0
$31$	21.6233	+	37.4526i	0.697524	+	1.20815i	0.969322	+	0.245793i	$0.0790484\pi$
$31$	21.6233	+	37.4526i	0.697524	+	1.20815i	−0.271798	+	0.962354i	$0.587618\pi$
$32$	7.63926	−	28.5101i	0.238727	−	0.890941i
$33$		0			0
$34$	9.22442	+	5.32572i	0.271307	+	0.156639i
$35$	9.30307	+	0.0748176i	0.265802	+	0.00213765i
$36$		0			0
$37$	−32.5443	−	32.5443i	−0.879576	−	0.879576i	0.113915	−	0.993491i	$-0.463661\pi$
$37$	−32.5443	−	32.5443i	−0.879576	−	0.879576i	−0.993491	+	0.113915i	$0.963661\pi$
$38$	−2.10058	−	7.83949i	−0.0552785	−	0.206302i
$39$		0			0
$40$	24.3001	−	13.7703i	0.607502	−	0.344257i
$41$	20.5409	+	35.5778i	0.500997	+	0.867752i	0.999999	+	0.00115173i	$0.000366608\pi$
$41$	20.5409	+	35.5778i	0.500997	+	0.867752i	−0.499002	+	0.866601i	$0.666300\pi$
$42$		0			0
$43$	2.14721	+	8.01349i	0.0499351	+	0.186360i	0.986388	−	0.164432i	$-0.0525791\pi$
$43$	2.14721	+	8.01349i	0.0499351	+	0.186360i	−0.936453	+	0.350792i	$0.885912\pi$
$44$		−	40.0106i		−	0.909331i
$45$		0			0
$46$	1.04663			0.0227528
$47$	−17.2577	+	4.62418i	−0.367185	+	0.0983868i	−0.437693	−	0.899124i	$-0.644204\pi$
$47$	−17.2577	+	4.62418i	−0.367185	+	0.0983868i	0.0705087	+	0.997511i	$0.477538\pi$
$48$		0			0
$49$	−39.4370	+	22.7689i	−0.804836	+	0.464672i
$50$	18.0611	+	5.15220i	0.361223	+	0.103044i
$51$		0			0
$52$	68.0488	−	18.2336i	1.30863	−	0.350647i
$53$	51.3281	−	51.3281i	0.968455	−	0.968455i	−0.0310621	−	0.999517i	$-0.509889\pi$
$53$	51.3281	−	51.3281i	0.968455	−	0.968455i	0.999517	+	0.0310621i	$0.00988897\pi$
$54$		0			0
$55$	41.5042	−	40.8419i	0.754621	−	0.742580i
$56$	5.19697	−	9.00141i	0.0928030	−	0.160739i
$57$		0			0
$58$	−17.4262	−	4.66933i	−0.300451	−	0.0805057i
$59$	−24.3449	+	14.0555i	−0.412625	+	0.238229i	−0.691917	−	0.721977i	$-0.743234\pi$
$59$	−24.3449	+	14.0555i	−0.412625	+	0.238229i	0.279292	+	0.960206i	$0.409900\pi$
$60$		0			0
$61$	−41.1002	+	71.1876i	−0.673774	+	1.16701i	0.303052	+	0.952974i	$0.401994\pi$
$61$	−41.1002	+	71.1876i	−0.673774	+	1.16701i	−0.976826	+	0.214036i	$0.931339\pi$
$62$	22.9736	+	22.9736i	0.370542	+	0.370542i
$63$		0			0
$64$			16.0088i			0.250137i
$65$	88.3771	+	51.9766i	1.35965	+	0.799640i
$66$		0			0
$67$	8.65757	−	32.3105i	0.129217	−	0.482246i	−0.870737	−	0.491748i	$-0.836358\pi$
$67$	8.65757	−	32.3105i	0.129217	−	0.482246i	0.999955	+	0.00950210i	$0.00302466\pi$
$68$	−47.0502	−	12.6071i	−0.691915	−	0.185398i
$69$		0			0
$70$	6.76548	−	1.75461i	0.0966497	−	0.0250659i
$71$	−99.6917			−1.40411			−0.702054	−	0.712123i	$-0.747734\pi$
$71$	−99.6917			−1.40411			−0.702054	+	0.712123i	$0.747734\pi$
$72$		0			0
$73$	−22.3583	+	22.3583i	−0.306278	+	0.306278i	−0.843464	−	0.537186i	$-0.819487\pi$
$73$	−22.3583	+	22.3583i	−0.306278	+	0.306278i	0.537186	+	0.843464i	$0.319487\pi$
$74$	−29.9443	−	17.2883i	−0.404653	−	0.233626i
$75$		0			0
$76$	18.5577	+	32.1428i	0.244180	+	0.422932i
$77$	5.60840	−	20.9308i	0.0728363	−	0.271829i
$78$		0			0
$79$	−52.9926	−	30.5953i	−0.670793	−	0.387282i	0.125584	−	0.992083i	$-0.459919\pi$
$79$	−52.9926	−	30.5953i	−0.670793	−	0.387282i	−0.796377	+	0.604801i	$0.793253\pi$
$80$	−34.0196	+	33.4768i	−0.425246	+	0.418460i
$81$		0			0
$82$	21.8237	+	21.8237i	0.266142	+	0.266142i
$83$	−13.3760	−	49.9199i	−0.161157	−	0.601444i	−0.998499	−	0.0547660i	$-0.982559\pi$
$83$	−13.3760	−	49.9199i	−0.161157	−	0.601444i	0.837343	−	0.546678i	$-0.184108\pi$
$84$		0			0
$85$	−34.9502	−	61.6757i	−0.411178	−	0.725596i
$86$	3.11631	+	5.39761i	0.0362362	+	0.0627630i
$87$		0			0
$88$	−16.8375	−	62.8384i	−0.191335	−	0.714073i
$89$			113.914i			1.27993i	0.768402	+	0.639967i	$0.221052\pi$
$89$			113.914i			1.27993i	−0.768402	+	0.639967i	$0.778948\pi$
$90$		0			0
$91$	38.1544			0.419279
$92$	−4.62324	+	1.23879i	−0.0502526	+	0.0134651i
$93$		0			0
$94$	−11.6242	+	6.71123i	−0.123662	+	0.0713960i
$95$	−14.3995	+	52.0611i	−0.151573	+	0.548012i
$96$		0			0
$97$	−29.5689	+	7.92297i	−0.304834	+	0.0816801i	−0.407994	−	0.912985i	$-0.633771\pi$
$97$	−29.5689	+	7.92297i	−0.304834	+	0.0816801i	0.103160	+	0.994665i	$0.467105\pi$
$98$	−24.1909	+	24.1909i	−0.246845	+	0.246845i
$99$		0			0
$100$	−85.8789	−	1.38141i	−0.858789	−	0.0138141i
$101$	−29.8920	+	51.7745i	−0.295961	+	0.512619i	−0.975208	−	0.221291i	$-0.928973\pi$
$101$	−29.8920	+	51.7745i	−0.295961	+	0.512619i	0.679247	+	0.733909i	$0.262306\pi$
$102$		0			0
$103$	−48.8939	−	13.1011i	−0.474698	−	0.127195i	0.0135348	−	0.999908i	$-0.495692\pi$
$103$	−48.8939	−	13.1011i	−0.474698	−	0.127195i	−0.488233	+	0.872713i	$0.662358\pi$
$104$	99.2006	−	57.2735i	0.953852	−	0.550707i
$105$		0			0
$106$	27.2668	−	47.2274i	0.257234	−	0.445542i
$107$	14.8359	+	14.8359i	0.138653	+	0.138653i	0.773027	−	0.634374i	$-0.218742\pi$
$107$	14.8359	+	14.8359i	0.138653	+	0.138653i	−0.634374	+	0.773027i	$0.718742\pi$
$108$		0			0
$109$			115.290i			1.05770i	0.848714	+	0.528852i	$0.177377\pi$
$109$			115.290i			1.05770i	−0.848714	+	0.528852i	$0.822623\pi$
$110$	22.1768	−	37.7078i	0.201607	−	0.342798i
$111$		0			0
$112$	−4.59703	+	17.1563i	−0.0410449	+	0.153182i
$113$	−101.212	−	27.1198i	−0.895686	−	0.239998i	−0.218523	−	0.975832i	$-0.570124\pi$
$113$	−101.212	−	27.1198i	−0.895686	−	0.239998i	−0.677163	+	0.735833i	$0.736791\pi$
$114$		0			0
$115$	−6.00434	−	3.53129i	−0.0522117	−	0.0307069i
$116$	82.5026			0.711229
$117$		0			0
$118$	−14.9333	+	14.9333i	−0.126553	+	0.126553i
$119$	−22.8463	−	13.1903i	−0.191986	−	0.110843i
$120$		0			0
$121$	−7.31319	−	12.6668i	−0.0604396	−	0.104684i
$122$	−15.9832	+	59.6501i	−0.131010	+	0.488935i
$123$		0			0
$124$	−128.672	−	74.2889i	−1.03768	−	0.599104i
$125$	−86.2304	−	90.4949i	−0.689843	−	0.723959i
$126$		0			0
$127$	56.0831	+	56.0831i	0.441599	+	0.441599i	0.892549	−	0.450950i	$-0.148915\pi$
$127$	56.0831	+	56.0831i	0.441599	+	0.441599i	−0.450950	+	0.892549i	$0.648915\pi$
$128$	33.6698	+	125.657i	0.263045	+	0.981699i
$129$		0			0
$130$	74.2387	+	20.5335i	0.571067	+	0.157950i
$131$	2.31731	+	4.01371i	0.0176894	+	0.0306390i	0.874735	−	0.484602i	$-0.161036\pi$
$131$	2.31731	+	4.01371i	0.0176894	+	0.0306390i	−0.857045	+	0.515241i	$0.827702\pi$
$132$		0			0
$133$	5.20256	+	19.4162i	0.0391170	+	0.145987i
$134$		−	25.1300i		−	0.187538i
$135$		0			0
$136$	−79.1999			−0.582352
$137$	−2.29751	+	0.615617i	−0.0167702	+	0.00449355i	−0.267194	−	0.963643i	$-0.586097\pi$
$137$	−2.29751	+	0.615617i	−0.0167702	+	0.00449355i	0.250424	+	0.968136i	$0.419430\pi$
$138$		0			0
$139$	221.925	−	128.128i	1.59658	−	0.921786i	0.604441	−	0.796650i	$-0.293397\pi$
$139$	221.925	−	128.128i	1.59658	−	0.921786i	0.992140	−	0.125136i	$-0.0399367\pi$
$140$	−27.8081	+	15.7582i	−0.198629	+	0.112559i
$141$		0			0
$142$	−72.3429	+	19.3842i	−0.509457	+	0.136509i
$143$	168.862	−	168.862i	1.18085	−	1.18085i
$144$		0			0
$145$	84.2169	+	85.5825i	0.580806	+	0.590224i
$146$	−11.8773	+	20.5721i	−0.0813513	+	0.140905i
$147$		0			0
$148$	152.734	+	40.9250i	1.03199	+	0.276520i
$149$	81.5954	−	47.1091i	0.547620	−	0.316168i	−0.200542	−	0.979685i	$-0.564270\pi$
$149$	81.5954	−	47.1091i	0.547620	−	0.316168i	0.748161	+	0.663517i	$0.230937\pi$
$150$		0			0
$151$	14.0475	−	24.3310i	0.0930299	−	0.161133i	−0.815755	−	0.578398i	$-0.803678\pi$
$151$	14.0475	−	24.3310i	0.0930299	−	0.161133i	0.908785	+	0.417265i	$0.137011\pi$
$152$	42.6722	+	42.6722i	0.280738	+	0.280738i
$153$		0			0
$154$		−	16.2793i		−	0.105710i
$155$	−54.2836	−	209.308i	−0.350217	−	1.35037i
$156$		0			0
$157$	9.98621	−	37.2690i	0.0636064	−	0.237382i	−0.926803	−	0.375549i	$-0.877454\pi$
$157$	9.98621	−	37.2690i	0.0636064	−	0.237382i	0.990409	+	0.138166i	$0.0441209\pi$
$158$	−44.4040	−	11.8980i	−0.281038	−	0.0753039i
$159$		0			0
$160$	−74.8150	+	127.210i	−0.467594	+	0.795061i
$161$	−2.59221			−0.0161007
$162$		0			0
$163$	140.797	−	140.797i	0.863787	−	0.863787i	−0.127989	−	0.991776i	$-0.540852\pi$
$163$	140.797	−	140.797i	0.863787	−	0.863787i	0.991776	+	0.127989i	$0.0408522\pi$
$164$	−122.231	−	70.5703i	−0.745313	−	0.430306i
$165$		0			0
$166$	−19.4130	−	33.6243i	−0.116946	−	0.202556i
$167$	73.2232	−	273.273i	0.438462	−	1.63636i	−0.294180	−	0.955750i	$-0.595047\pi$
$167$	73.2232	−	273.273i	0.438462	−	1.63636i	0.732642	−	0.680614i	$-0.238287\pi$
$168$		0			0
$169$	217.791	+	125.742i	1.28870	+	0.744033i
$170$	−37.3545	−	37.9602i	−0.219732	−	0.223295i
$171$		0			0
$172$	−20.1542	−	20.1542i	−0.117176	−	0.117176i
$173$	80.2289	+	299.418i	0.463751	+	1.73074i	0.660998	+	0.750387i	$0.270133\pi$
$173$	80.2289	+	299.418i	0.463751	+	1.73074i	−0.197248	+	0.980354i	$0.563200\pi$
$174$		0			0
$175$	−44.7324	−	12.7606i	−0.255614	−	0.0729175i
$176$	55.5843	+	96.2748i	0.315820	+	0.547016i
$177$		0			0
$178$	22.1497	+	82.6637i	0.124436	+	0.464403i
$179$			151.884i			0.848512i	0.905542	+	0.424256i	$0.139464\pi$
$179$			151.884i			0.848512i	−0.905542	+	0.424256i	$0.860536\pi$
$180$		0			0
$181$	48.0978			0.265734			0.132867	−	0.991134i	$-0.457582\pi$
$181$	48.0978			0.265734			0.132867	+	0.991134i	$0.457582\pi$
$182$	27.6874	−	7.41881i	0.152128	−	0.0407627i
$183$		0			0
$184$	−6.73969	+	3.89116i	−0.0366288	+	0.0211476i
$185$	113.455	+	200.211i	0.613271	+	1.08222i
$186$		0			0
$187$	−159.489	+	42.7350i	−0.852883	+	0.228529i
$188$	43.4036	−	43.4036i	0.230870	−	0.230870i
$189$		0			0
$190$	−0.326345	+	40.5789i	−0.00171761	+	0.213573i
$191$	181.698	−	314.711i	0.951300	−	1.64770i	0.208683	−	0.977983i	$-0.433082\pi$
$191$	181.698	−	314.711i	0.951300	−	1.64770i	0.742617	−	0.669717i	$-0.233584\pi$
$192$		0			0
$193$	11.5607	+	3.09769i	0.0599001	+	0.0160502i	0.288645	−	0.957436i	$-0.406795\pi$
$193$	11.5607	+	3.09769i	0.0599001	+	0.0160502i	−0.228745	+	0.973486i	$0.573462\pi$
$194$	−19.9166	+	11.4989i	−0.102663	+	0.0592725i
$195$		0			0
$196$	78.2250	−	135.490i	0.399107	−	0.691274i
$197$	−45.3414	−	45.3414i	−0.230159	−	0.230159i	0.582600	−	0.812759i	$-0.302036\pi$
$197$	−45.3414	−	45.3414i	−0.230159	−	0.230159i	−0.812759	+	0.582600i	$0.802036\pi$
$198$		0			0
$199$		−	17.0082i		−	0.0854685i	−0.999086	−	0.0427343i	$-0.986393\pi$
$199$		−	17.0082i		−	0.0854685i	0.999086	−	0.0427343i	$-0.0136069\pi$
$200$	−135.458	+	33.9705i	−0.677290	+	0.169853i
$201$		0			0
$202$	−11.6245	+	43.3833i	−0.0575471	+	0.214769i
$203$	43.1598	+	11.5646i	0.212610	+	0.0569686i
$204$		0			0
$205$	−51.5664	−	198.831i	−0.251543	−	0.969906i
$206$	−38.0281			−0.184602
$207$		0			0
$208$	−138.411	+	138.411i	−0.665436	+	0.665436i
$209$	108.957	+	62.9061i	0.521323	+	0.300986i
$210$		0			0
$211$	−148.887	−	257.879i	−0.705624	−	1.22218i	−0.966466	−	0.256795i	$-0.917333\pi$
$211$	−148.887	−	257.879i	−0.705624	−	1.22218i	0.260842	−	0.965382i	$-0.416000\pi$
$212$	−64.5460	+	240.889i	−0.304462	+	1.13627i
$213$		0			0
$214$	13.6506	+	7.88119i	0.0637879	+	0.0368280i
$215$	0.333589	−	41.4795i	0.00155157	−	0.192928i
$216$		0			0
$217$	−56.8993	−	56.8993i	−0.262209	−	0.262209i
$218$	22.4172	+	83.6620i	0.102831	+	0.383771i
$219$		0			0
$220$	−53.3298	+	192.814i	−0.242408	+	0.876425i
$221$	−145.365	−	251.779i	−0.657760	−	1.13927i
$222$		0			0
$223$	−8.27356	−	30.8773i	−0.0371012	−	0.138463i	0.944891	−	0.327385i	$-0.106167\pi$
$223$	−8.27356	−	30.8773i	−0.0371012	−	0.138463i	−0.981992	+	0.188922i	$0.939501\pi$
$224$			54.9194i			0.245176i
$225$		0			0
$226$	−78.7197			−0.348317
$227$	−377.838	+	101.241i	−1.66449	+	0.445997i	−0.963616	−	0.267292i	$-0.913871\pi$
$227$	−377.838	+	101.241i	−1.66449	+	0.445997i	−0.700870	+	0.713289i	$0.747205\pi$
$228$		0			0
$229$	−217.228	+	125.417i	−0.948594	+	0.547671i	−0.892644	−	0.450762i	$-0.851152\pi$
$229$	−217.228	+	125.417i	−0.948594	+	0.547671i	−0.0559502	+	0.998434i	$0.517819\pi$
$230$	−5.04378	−	1.39505i	−0.0219295	−	0.00606542i
$231$		0			0
$232$	129.574	−	34.7193i	0.558509	−	0.149652i
$233$	−239.086	+	239.086i	−1.02612	+	1.02612i	−0.0264709	+	0.999650i	$0.508427\pi$
$233$	−239.086	+	239.086i	−1.02612	+	1.02612i	−0.999650	+	0.0264709i	$0.991573\pi$
$234$		0			0
$235$	89.3294	+	0.718409i	0.380125	+	0.00305706i
$236$	48.2891	−	83.6392i	0.204615	−	0.354404i
$237$		0			0
$238$	−19.1436	−	5.12950i	−0.0804352	−	0.0215525i
$239$	−33.8483	+	19.5423i	−0.141625	+	0.0817672i	−0.569138	−	0.822242i	$-0.692723\pi$
$239$	−33.8483	+	19.5423i	−0.141625	+	0.0817672i	0.427513	+	0.904009i	$0.359390\pi$
$240$		0			0
$241$	−41.8525	+	72.4907i	−0.173662	+	0.300791i	−0.939697	−	0.342007i	$-0.888893\pi$
$241$	−41.8525	+	72.4907i	−0.173662	+	0.300791i	0.766036	+	0.642798i	$0.222227\pi$
$242$	−7.76989	−	7.76989i	−0.0321070	−	0.0321070i
$243$		0			0
$244$		−	282.408i		−	1.15741i
$245$	220.398	−	57.1598i	0.899583	−	0.233305i
$246$		0			0
$247$	−57.3352	+	213.978i	−0.232126	+	0.866307i
$248$	−233.348	−	62.5254i	−0.940920	−	0.252119i
$249$		0			0
$250$	−80.1705	−	48.9023i	−0.320682	−	0.195609i
$251$	116.674			0.464837			0.232418	−	0.972616i	$-0.425336\pi$
$251$	116.674			0.464837			0.232418	+	0.972616i	$0.425336\pi$
$252$		0			0
$253$	−11.4725	+	11.4725i	−0.0453458	+	0.0453458i
$254$	51.6025	+	29.7927i	0.203159	+	0.117294i
$255$		0			0
$256$	16.8485	+	29.1825i	0.0658146	+	0.113994i
$257$	1.23843	−	4.62189i	0.00481880	−	0.0179840i	−0.963475	−	0.267800i	$-0.913703\pi$
$257$	1.23843	−	4.62189i	0.00481880	−	0.0179840i	0.968293	+	0.249816i	$0.0803701\pi$
$258$		0			0
$259$	74.1637	+	42.8184i	0.286346	+	0.165322i
$260$	−352.235	−	2.83276i	−1.35475	−	0.0108952i
$261$		0			0
$262$	2.46203	+	2.46203i	0.00939706	+	0.00939706i
$263$	25.3145	+	94.4750i	0.0962529	+	0.359221i	0.997206	−	0.0746949i	$-0.0237983\pi$
$263$	25.3145	+	94.4750i	0.0962529	+	0.359221i	−0.900954	+	0.433916i	$0.857132\pi$
$264$		0			0
$265$	−315.769	+	178.939i	−1.19158	+	0.675241i
$266$	7.55065	+	13.0781i	0.0283859	+	0.0491658i
$267$		0			0
$268$	29.7440	+	111.006i	0.110985	+	0.414201i
$269$			212.871i			0.791340i	0.918393	+	0.395670i	$0.129488\pi$
$269$			212.871i			0.791340i	−0.918393	+	0.395670i	$0.870512\pi$
$270$		0			0
$271$	−180.243			−0.665102			−0.332551	−	0.943085i	$-0.607909\pi$
$271$	−180.243			−0.665102			−0.332551	+	0.943085i	$0.607909\pi$
$272$	130.728	−	35.0285i	0.480618	−	0.128781i
$273$		0			0
$274$	−1.54753	+	0.893465i	−0.00564791	+	0.00326082i
$275$	−254.449	+	141.499i	−0.925270	+	0.514543i
$276$		0			0
$277$	316.123	−	84.7048i	1.14124	−	0.305794i	0.361789	−	0.932260i	$-0.382166\pi$
$277$	316.123	−	84.7048i	1.14124	−	0.305794i	0.779448	+	0.626467i	$0.215499\pi$
$278$	136.130	−	136.130i	0.489676	−	0.489676i
$279$		0			0
$280$	−37.0424	+	36.4514i	−0.132294	+	0.130184i
$281$	15.6356	−	27.0816i	0.0556426	−	0.0963758i	−0.836862	−	0.547413i	$-0.815613\pi$
$281$	15.6356	−	27.0816i	0.0556426	−	0.0963758i	0.892505	+	0.451037i	$0.148946\pi$
$282$		0			0
$283$	195.826	+	52.4715i	0.691966	+	0.185412i	0.587629	−	0.809130i	$-0.300061\pi$
$283$	195.826	+	52.4715i	0.691966	+	0.185412i	0.104337	+	0.994542i	$0.466728\pi$
$284$	296.614	−	171.250i	1.04442	−	0.602995i
$285$		0			0
$286$	89.7036	−	155.371i	0.313649	−	0.543256i
$287$	−54.0511	−	54.0511i	−0.188331	−	0.188331i
$288$		0			0
$289$		−	87.9840i		−	0.304443i
$290$	77.7542	+	45.7291i	0.268118	+	0.157686i
$291$		0			0
$292$	28.1159	−	104.930i	0.0962875	−	0.359350i
$293$	37.6696	+	10.0935i	0.128565	+	0.0344490i	0.322528	−	0.946560i	$-0.395467\pi$
$293$	37.6696	+	10.0935i	0.128565	+	0.0344490i	−0.193963	+	0.981009i	$0.562134\pi$
$294$		0			0
$295$	136.054	−	35.2854i	0.461200	−	0.119611i
$296$	257.098			0.868576
$297$		0			0
$298$	50.0510	−	50.0510i	0.167957	−	0.167957i
$299$	−24.7403	−	14.2838i	−0.0827435	−	0.0477720i
$300$		0			0
$301$	−7.71824	−	13.3684i	−0.0256420	−	0.0444132i
$302$	5.46285	−	20.3876i	0.0180889	−	0.0675087i
$303$		0			0
$304$	−89.3082	−	51.5621i	−0.293777	−	0.169612i
$305$	292.950	−	288.276i	0.960492	−	0.945166i
$306$		0			0
$307$	−28.4359	−	28.4359i	−0.0926251	−	0.0926251i	0.659276	−	0.751901i	$-0.270863\pi$
$307$	−28.4359	−	28.4359i	−0.0926251	−	0.0926251i	−0.751901	+	0.659276i	$0.770863\pi$
$308$	19.2682	+	71.9100i	0.0625591	+	0.233474i
$309$		0			0
$310$	−80.0900	−	141.333i	−0.258355	−	0.455912i
$311$	215.953	+	374.041i	0.694381	+	1.20270i	0.970389	+	0.241548i	$0.0776553\pi$
$311$	215.953	+	374.041i	0.694381	+	1.20270i	−0.276007	+	0.961156i	$0.589011\pi$
$312$		0			0
$313$	53.6933	+	200.386i	0.171544	+	0.640211i	0.997115	+	0.0759119i	$0.0241868\pi$
$313$	53.6933	+	200.386i	0.171544	+	0.640211i	−0.825571	+	0.564299i	$0.809147\pi$
$314$		−	28.9866i		−	0.0923141i
$315$		0			0
$316$	210.226			0.665274
$317$	−342.998	+	91.9060i	−1.08201	+	0.289924i	−0.755420	−	0.655241i	$-0.772567\pi$
$317$	−342.998	+	91.9060i	−1.08201	+	0.289924i	−0.326593	+	0.945165i	$0.605900\pi$
$318$		0			0
$319$	242.196	−	139.832i	0.759237	−	0.438345i
$320$	21.3380	−	77.1474i	0.0666813	−	0.241086i
$321$		0			0
$322$	−1.88108	+	0.504034i	−0.00584187	+	0.00156532i
$323$	108.306	−	108.306i	0.335311	−	0.335311i
$324$		0			0
$325$	−356.616	−	368.276i	−1.09728	−	1.13316i
$326$	74.7950	−	129.549i	0.229432	−	0.397389i
$327$		0			0
$328$	−221.668	−	59.3957i	−0.675816	−	0.181084i
$329$	28.7899	−	16.6218i	0.0875072	−	0.0505223i
$330$		0			0
$331$	−187.451	+	324.675i	−0.566318	+	0.980891i	0.430608	+	0.902539i	$0.358299\pi$
$331$	−187.451	+	324.675i	−0.566318	+	0.980891i	−0.996926	+	0.0783519i	$0.975034\pi$
$332$	125.550	+	125.550i	0.378163	+	0.378163i
$333$		0			0
$334$		−	212.543i		−	0.636355i
$335$	−84.7879	+	144.167i	−0.253098	+	0.430349i
$336$		0			0
$337$	−38.4732	+	143.584i	−0.114164	+	0.426065i	−0.999223	−	0.0394135i	$-0.987451\pi$
$337$	−38.4732	+	143.584i	−0.114164	+	0.426065i	0.885059	+	0.465478i	$0.154118\pi$
$338$	182.493	+	48.8988i	0.539920	+	0.144671i
$339$		0			0
$340$	209.934	+	123.467i	0.617454	+	0.363139i
$341$	−503.643			−1.47696
$342$		0			0
$343$	124.383	−	124.383i	0.362633	−	0.362633i
$344$	−40.1345	−	23.1717i	−0.116670	−	0.0673595i
$345$		0			0
$346$	116.439	+	201.678i	0.336528	+	0.582884i
$347$	62.5014	−	233.258i	0.180119	−	0.672214i	−0.815504	−	0.578752i	$-0.803540\pi$
$347$	62.5014	−	233.258i	0.180119	−	0.672214i	0.995623	−	0.0934622i	$-0.0297934\pi$
$348$		0			0
$349$	331.191	+	191.213i	0.948971	+	0.547889i	0.892761	−	0.450530i	$-0.148765\pi$
$349$	331.191	+	191.213i	0.948971	+	0.547889i	0.0562101	+	0.998419i	$0.482098\pi$
$350$	−34.9420	−	0.562061i	−0.0998343	−	0.00160589i
$351$		0			0
$352$	243.059	+	243.059i	0.690509	+	0.690509i
$353$	−134.782	−	503.013i	−0.381819	−	1.42497i	−0.843121	−	0.537724i	$-0.819284\pi$
$353$	−134.782	−	503.013i	−0.381819	−	1.42497i	0.461302	−	0.887243i	$-0.347382\pi$
$354$		0			0
$355$	480.421	+	132.878i	1.35330	+	0.374305i
$356$	−195.682	−	338.931i	−0.549668	−	0.952052i
$357$		0			0
$358$	29.5325	+	110.217i	0.0824931	+	0.307868i
$359$		−	326.956i		−	0.910741i	−0.890302	−	0.455370i	$-0.849507\pi$
$359$		−	326.956i		−	0.910741i	0.890302	−	0.455370i	$-0.150493\pi$
$360$		0			0
$361$	244.292			0.676709
$362$	34.9030	−	9.35222i	0.0964170	−	0.0258349i
$363$		0			0
$364$	−113.521	+	65.5417i	−0.311872	+	0.180060i
$365$	137.547	−	77.9449i	0.376842	−	0.213548i
$366$		0			0
$367$	−505.039	+	135.325i	−1.37613	+	0.368733i	−0.869713	−	0.493557i	$-0.835696\pi$
$367$	−505.039	+	135.325i	−1.37613	+	0.368733i	−0.506415	+	0.862290i	$0.669030\pi$
$368$	9.40362	−	9.40362i	0.0255533	−	0.0255533i
$369$		0			0
$370$	121.260	+	123.226i	0.327730	+	0.333044i
$371$	−67.5322	+	116.969i	−0.182028	+	0.315281i
$372$		0			0
$373$	−23.4631	−	6.28693i	−0.0629039	−	0.0168550i	0.227230	−	0.973841i	$-0.427033\pi$
$373$	−23.4631	−	6.28693i	−0.0629039	−	0.0168550i	−0.290134	+	0.956986i	$0.593700\pi$
$374$	−107.426	+	62.0227i	−0.287237	+	0.165836i
$375$		0			0
$376$	49.9020	−	86.4328i	0.132718	−	0.229874i
$377$	348.197	+	348.197i	0.923598	+	0.923598i
$378$		0			0
$379$			364.939i			0.962900i	0.876474	+	0.481450i	$0.159890\pi$
$379$			364.939i			0.962900i	−0.876474	+	0.481450i	$0.840110\pi$
$380$	−46.5877	−	179.634i	−0.122599	−	0.472720i
$381$		0			0
$382$	70.6595	−	263.705i	0.184972	−	0.690327i
$383$	−3.24720	−	0.870084i	−0.00847832	−	0.00227176i	0.254577	−	0.967052i	$-0.418064\pi$
$383$	−3.24720	−	0.870084i	−0.00847832	−	0.00227176i	−0.263056	+	0.964781i	$0.584730\pi$
$384$		0			0
$385$	−54.9258	+	93.3916i	−0.142664	+	0.242576i
$386$	8.99155			0.0232942
$387$		0			0
$388$	74.3668	−	74.3668i	0.191667	−	0.191667i
$389$	−131.808	−	76.0995i	−0.338838	−	0.195628i	0.320920	−	0.947106i	$-0.396008\pi$
$389$	−131.808	−	76.0995i	−0.338838	−	0.195628i	−0.659758	+	0.751478i	$0.729341\pi$
$390$		0			0
$391$	9.87610	+	17.1059i	0.0252586	+	0.0437491i
$392$	65.8383	−	245.712i	0.167955	−	0.626816i
$393$		0			0
$394$	−41.7190	−	24.0865i	−0.105886	−	0.0611332i
$395$	214.595	+	218.074i	0.543278	+	0.552087i
$396$		0			0
$397$	−275.868	−	275.868i	−0.694882	−	0.694882i	0.268420	−	0.963302i	$-0.413498\pi$
$397$	−275.868	−	275.868i	−0.694882	−	0.694882i	−0.963302	+	0.268420i	$0.913498\pi$
$398$	−3.30711	−	12.3423i	−0.00830933	−	0.0310108i
$399$		0			0
$400$	208.564	−	115.982i	0.521410	−	0.289956i
$401$	337.489	+	584.548i	0.841618	+	1.45773i	0.888526	+	0.458826i	$0.151730\pi$
$401$	337.489	+	584.548i	0.841618	+	1.45773i	−0.0469080	+	0.998899i	$0.514937\pi$
$402$		0			0
$403$	−229.521	−	856.582i	−0.569530	−	2.12551i
$404$		−	205.394i		−	0.508401i
$405$		0			0
$406$	33.5683			0.0826805
$407$	517.733	−	138.726i	1.27207	−	0.340850i
$408$		0			0
$409$	−375.213	+	216.629i	−0.917390	+	0.529655i	−0.882802	−	0.469746i	$-0.844345\pi$
$409$	−375.213	+	216.629i	−0.917390	+	0.529655i	−0.0345887	+	0.999402i	$0.511012\pi$
$410$	−76.0810	−	134.258i	−0.185563	−	0.327459i
$411$		0			0
$412$	167.980	−	45.0101i	0.407718	−	0.109248i
$413$	36.9856	−	36.9856i	0.0895534	−	0.0895534i
$414$		0			0
$415$	−2.07808	+	258.396i	−0.00500743	+	0.622641i
$416$	−302.621	+	524.155i	−0.727455	+	1.25999i
$417$		0			0
$418$	91.2977	+	24.4631i	0.218416	+	0.0585243i
$419$	−432.869	+	249.917i	−1.03310	+	0.596461i	−0.917871	−	0.396878i	$-0.870093\pi$
$419$	−432.869	+	249.917i	−1.03310	+	0.596461i	−0.115229	+	0.993339i	$0.536760\pi$
$420$		0			0
$421$	15.0425	−	26.0544i	0.0357304	−	0.0618869i	−0.847607	−	0.530624i	$-0.821958\pi$
$421$	15.0425	−	26.0544i	0.0357304	−	0.0618869i	0.883338	+	0.468737i	$0.155291\pi$
$422$	−158.185	−	158.185i	−0.374845	−	0.374845i
$423$		0			0
$424$			405.490i			0.956344i
$425$	86.2201	+	343.804i	0.202871	+	0.808950i
$426$		0			0
$427$	39.5859	−	147.737i	0.0927071	−	0.345987i
$428$	−69.6265	−	18.6564i	−0.162679	−	0.0435896i
$429$		0			0
$430$	−7.82328	−	30.1652i	−0.0181937	−	0.0701516i
$431$	−515.749			−1.19663			−0.598316	−	0.801260i	$-0.704163\pi$
$431$	−515.749			−1.19663			−0.598316	+	0.801260i	$0.704163\pi$
$432$		0			0
$433$	−305.797	+	305.797i	−0.706229	+	0.706229i	−0.965740	−	0.259511i	$-0.916439\pi$
$433$	−305.797	+	305.797i	−0.706229	+	0.706229i	0.259511	+	0.965740i	$0.416439\pi$
$434$	−52.3535	−	30.2263i	−0.120630	−	0.0696458i
$435$		0			0
$436$	−198.045	−	343.024i	−0.454231	−	0.786752i
$437$	3.89535	−	14.5377i	0.00891385	−	0.0332669i
$438$		0			0
$439$	−437.591	−	252.643i	−0.996790	−	0.575497i	−0.0894929	−	0.995987i	$-0.528525\pi$
$439$	−437.591	−	252.643i	−0.996790	−	0.575497i	−0.907297	+	0.420491i	$0.861858\pi$
$440$	−2.61586	+	325.265i	−0.00594514	+	0.739239i
$441$		0			0
$442$	−154.443	−	154.443i	−0.349418	−	0.349418i
$443$	52.3076	+	195.215i	0.118076	+	0.440665i	0.999499	−	0.0316632i	$-0.0100804\pi$
$443$	52.3076	+	195.215i	0.118076	+	0.440665i	−0.881423	+	0.472328i	$0.843414\pi$
$444$		0			0
$445$	151.835	−	548.960i	0.341203	−	1.23362i
$446$	−12.0077	−	20.7979i	−0.0269231	−	0.0466321i
$447$		0			0
$448$	−7.70948	−	28.7722i	−0.0172087	−	0.0642236i
$449$			145.089i			0.323138i	0.986861	+	0.161569i	$0.0516554\pi$
$449$			145.089i			0.323138i	−0.986861	+	0.161569i	$0.948345\pi$
$450$		0			0
$451$	−478.433			−1.06083
$452$	347.726	−	93.1728i	0.769305	−	0.206135i
$453$		0			0
$454$	−254.499	+	146.935i	−0.560570	+	0.323645i
$455$	−183.869	−	50.8558i	−0.404107	−	0.111771i
$456$		0			0
$457$	−286.527	+	76.7746i	−0.626973	+	0.167997i	−0.558296	−	0.829642i	$-0.688545\pi$
$457$	−286.527	+	76.7746i	−0.626973	+	0.167997i	−0.0686775	+	0.997639i	$0.521878\pi$
$458$	−133.249	+	133.249i	−0.290936	+	0.290936i
$459$		0			0
$460$	23.9309	+	0.192458i	0.0520236	+	0.000418387i
$461$	−143.044	+	247.759i	−0.310291	+	0.537439i	−0.978425	−	0.206601i	$-0.933760\pi$
$461$	−143.044	+	247.759i	−0.310291	+	0.537439i	0.668135	+	0.744040i	$0.267093\pi$
$462$		0			0
$463$	−241.707	−	64.7653i	−0.522046	−	0.139882i	−0.0118333	−	0.999930i	$-0.503767\pi$
$463$	−241.707	−	64.7653i	−0.522046	−	0.139882i	−0.510213	+	0.860048i	$0.670433\pi$
$464$	−198.521	+	114.616i	−0.427846	+	0.247017i
$465$		0			0
$466$	−127.008	+	219.985i	−0.272550	+	0.472071i
$467$	71.3291	+	71.3291i	0.152739	+	0.152739i	0.779340	−	0.626601i	$-0.215554\pi$
$467$	71.3291	+	71.3291i	0.152739	+	0.152739i	−0.626601	+	0.779340i	$0.715554\pi$
$468$		0			0
$469$			62.2401i			0.132708i
$470$	64.9631	−	16.8480i	0.138219	−	0.0358469i
$471$		0			0
$472$	40.6427	−	151.681i	0.0861074	−	0.321357i
$473$	−93.3241	−	25.0061i	−0.197302	−	0.0528670i
$474$		0			0
$475$	138.784	−	231.693i	0.292176	−	0.487775i
$476$	90.6334			0.190406
$477$		0			0
$478$	−20.7628	+	20.7628i	−0.0434367	+	0.0434367i
$479$	169.803	+	98.0357i	0.354494	+	0.204667i	0.666663	−	0.745359i	$-0.267722\pi$
$479$	169.803	+	98.0357i	0.354494	+	0.204667i	−0.312169	+	0.950027i	$0.601055\pi$
$480$		0			0
$481$	471.883	+	817.325i	0.981046	+	1.69922i
$482$	−16.2758	+	60.7419i	−0.0337671	+	0.126021i
$483$		0			0
$484$	43.5181	+	25.1252i	0.0899135	+	0.0519116i
$485$	153.055	+	1.23091i	0.315577	+	0.00253795i
$486$		0			0
$487$	660.124	+	660.124i	1.35549	+	1.35549i	0.879391	+	0.476100i	$0.157950\pi$
$487$	660.124	+	660.124i	1.35549	+	1.35549i	0.476100	+	0.879391i	$0.342050\pi$
$488$	−118.845	−	443.534i	−0.243534	−	0.908882i
$489$		0			0
$490$	148.821	−	84.3335i	0.303717	−	0.172109i
$491$	−393.999	−	682.426i	−0.802442	−	1.38987i	−0.918004	−	0.396570i	$-0.870200\pi$
$491$	−393.999	−	682.426i	−0.802442	−	1.38987i	0.115562	−	0.993300i	$-0.463133\pi$
$492$		0			0
$493$	−88.1204	−	328.870i	−0.178743	−	0.667079i
$494$			166.425i			0.336892i
$495$		0			0
$496$	412.820			0.832299
$497$	179.173	−	48.0093i	0.360510	−	0.0965983i
$498$		0			0
$499$	144.756	−	83.5751i	0.290093	−	0.167485i	−0.347891	−	0.937535i	$-0.613102\pi$
$499$	144.756	−	83.5751i	0.290093	−	0.167485i	0.637984	+	0.770050i	$0.279769\pi$
$500$	412.015	+	121.124i	0.824030	+	0.242249i
$501$		0			0
$502$	84.6664	−	22.6863i	0.168658	−	0.0451918i
$503$	−249.990	+	249.990i	−0.496998	+	0.496998i	−0.910502	−	0.413504i	$-0.864305\pi$
$503$	−249.990	+	249.990i	−0.496998	+	0.496998i	0.413504	+	0.910502i	$0.364305\pi$
$504$		0			0
$505$	213.061	−	209.662i	0.421904	−	0.415172i
$506$	−6.09446	+	10.5559i	−0.0120444	+	0.0208615i
$507$		0			0
$508$	−263.204	−	70.5254i	−0.518119	−	0.138830i
$509$	−95.6645	+	55.2319i	−0.187946	+	0.108511i	−0.591021	−	0.806656i	$-0.701275\pi$
$509$	−95.6645	+	55.2319i	−0.187946	+	0.108511i	0.403075	+	0.915167i	$0.367941\pi$
$510$		0			0
$511$	29.4167	−	50.9513i	0.0575670	−	0.0997089i
$512$	−350.050	−	350.050i	−0.683691	−	0.683691i
$513$		0			0
$514$		−	3.59475i		−	0.00699368i
$515$	218.160	+	128.305i	0.423613	+	0.249136i
$516$		0			0
$517$	53.8526	−	200.981i	0.104164	−	0.388744i
$518$	62.1438	+	16.6514i	0.119969	+	0.0321455i
$519$		0			0
$520$	−554.394	+	143.781i	−1.06614	+	0.276502i
$521$	415.088			0.796715			0.398357	−	0.917230i	$-0.369580\pi$
$521$	415.088			0.796715			0.398357	+	0.917230i	$0.369580\pi$
$522$		0			0
$523$	−384.585	+	384.585i	−0.735344	+	0.735344i	−0.971673	−	0.236329i	$-0.924056\pi$
$523$	−384.585	+	384.585i	−0.735344	+	0.735344i	0.236329	+	0.971673i	$0.424056\pi$
$524$	−13.7895	−	7.96136i	−0.0263158	−	0.0151934i
$525$		0			0
$526$	36.7398	+	63.6352i	0.0698475	+	0.120979i
$527$	−158.695	+	592.257i	−0.301129	+	1.12383i
$528$		0			0
$529$	−456.447	−	263.530i	−0.862848	−	0.498166i
$530$	−194.350	+	191.248i	−0.366697	+	0.360846i
$531$		0			0
$532$	−48.8325	−	48.8325i	−0.0917904	−	0.0917904i
$533$	−218.032	−	813.705i	−0.409065	−	1.52665i
$534$		0			0
$535$	−51.7204	−	91.2697i	−0.0966737	−	0.170598i
$536$	93.4285	+	161.823i	0.174307	+	0.301908i
$537$		0			0
$538$	41.3909	+	154.473i	0.0769348	+	0.287125i
$539$		−	530.329i		−	0.983912i
$540$		0			0
$541$	251.489			0.464859			0.232430	−	0.972613i	$-0.425332\pi$
$541$	251.489			0.464859			0.232430	+	0.972613i	$0.425332\pi$
$542$	−130.796	+	35.0467i	−0.241321	+	0.0646618i
$543$		0			0
$544$	362.411	−	209.238i	0.666196	−	0.384628i
$545$	153.669	−	555.589i	0.281961	−	1.01943i
$546$		0			0
$547$	539.479	−	144.553i	0.986251	−	0.264265i	0.270576	−	0.962699i	$-0.412786\pi$
$547$	539.479	−	144.553i	0.986251	−	0.264265i	0.715675	+	0.698433i	$0.246119\pi$
$548$	5.77833	−	5.77833i	0.0105444	−	0.0105444i
$549$		0			0
$550$	−157.132	+	152.157i	−0.285694	+	0.276649i
$551$	−129.714	+	224.671i	−0.235415	+	0.407751i
$552$		0			0
$553$	109.976	+	29.4681i	0.198872	+	0.0532876i
$554$	212.930	−	122.935i	0.384349	−	0.221904i
$555$		0			0
$556$	−440.197	+	762.444i	−0.791722	+	1.37130i
$557$	−302.419	−	302.419i	−0.542943	−	0.542943i	0.381447	−	0.924391i	$-0.375426\pi$
$557$	−302.419	−	302.419i	−0.542943	−	0.542943i	−0.924391	+	0.381447i	$0.875426\pi$
$558$		0			0
$559$		−	170.119i		−	0.304327i
$560$	45.0209	−	76.5501i	0.0803945	−	0.136697i
$561$		0			0
$562$	6.08041	−	22.6924i	0.0108192	−	0.0403780i
$563$	874.123	+	234.221i	1.55262	+	0.416022i	0.930317	−	0.366756i	$-0.119532\pi$
$563$	874.123	+	234.221i	1.55262	+	0.416022i	0.622300	+	0.782779i	$0.286198\pi$
$564$		0			0
$565$	451.602	+	265.598i	0.799295	+	0.470084i
$566$	152.307			0.269094
$567$		0			0
$568$	393.780	−	393.780i	0.693274	−	0.693274i
$569$	−194.081	−	112.053i	−0.341092	−	0.196929i	0.319663	−	0.947531i	$-0.396430\pi$
$569$	−194.081	−	112.053i	−0.341092	−	0.196929i	−0.660755	+	0.750602i	$0.729764\pi$
$570$		0			0
$571$	−28.3061	−	49.0275i	−0.0495728	−	0.0858626i	0.840174	−	0.542317i	$-0.182453\pi$
$571$	−28.3061	−	49.0275i	−0.0495728	−	0.0858626i	−0.889747	+	0.456454i	$0.849119\pi$
$572$	−212.347	+	792.488i	−0.371235	+	1.38547i
$573$		0			0
$574$	−49.7329	−	28.7133i	−0.0866426	−	0.0500232i
$575$	24.2285	+	25.0207i	0.0421365	+	0.0435142i
$576$		0			0
$577$	−450.543	−	450.543i	−0.780838	−	0.780838i	0.199135	−	0.979972i	$-0.436187\pi$
$577$	−450.543	−	450.543i	−0.780838	−	0.780838i	−0.979972	+	0.199135i	$0.936187\pi$
$578$	−17.1078	−	63.8471i	−0.0295982	−	0.110462i
$579$		0			0
$580$	−397.586	−	109.967i	−0.685492	−	0.189599i
$581$	48.0806	+	83.2781i	0.0827550	+	0.143336i
$582$		0			0
$583$	218.796	+	816.557i	0.375293	+	1.40061i
$584$		−	176.630i		−	0.302448i
$585$		0			0
$586$	29.2982			0.0499969
$587$	−335.371	+	89.8623i	−0.571330	+	0.153087i	−0.532906	−	0.846174i	$-0.678900\pi$
$587$	−335.371	+	89.8623i	−0.571330	+	0.153087i	−0.0384234	+	0.999262i	$0.512234\pi$
$588$		0			0
$589$	404.606	−	233.599i	0.686937	−	0.396603i
$590$	91.8689	−	52.0600i	0.155710	−	0.0882373i
$591$		0			0
$592$	−424.369	+	113.709i	−0.716840	+	0.192077i
$593$	235.628	−	235.628i	0.397350	−	0.397350i	−0.479948	−	0.877297i	$-0.659344\pi$
$593$	235.628	−	235.628i	0.397350	−	0.397350i	0.877297	+	0.479948i	$0.159344\pi$
$594$		0			0
$595$	92.5167	+	94.0168i	0.155490	+	0.158011i
$596$	−161.848	+	280.329i	−0.271557	+	0.470351i
$597$		0			0
$598$	−20.7306	−	5.55474i	−0.0346665	−	0.00928887i
$599$	513.829	−	296.659i	0.857811	−	0.495258i	−0.00546746	−	0.999985i	$-0.501740\pi$
$599$	513.829	−	296.659i	0.857811	−	0.495258i	0.863279	+	0.504727i	$0.168407\pi$
$600$		0			0
$601$	269.249	−	466.354i	0.448002	−	0.775963i	−0.550254	−	0.834998i	$-0.685469\pi$
$601$	269.249	−	466.354i	0.448002	−	0.775963i	0.998256	+	0.0590349i	$0.0188023\pi$
$602$	−8.20024	−	8.20024i	−0.0136217	−	0.0136217i
$603$		0			0
$604$			96.5233i			0.159807i
$605$	18.3592	+	70.7899i	0.0303458	+	0.117008i
$606$		0			0
$607$	105.915	−	395.280i	0.174489	−	0.651203i	−0.822149	−	0.569273i	$-0.807225\pi$
$607$	105.915	−	395.280i	0.174489	−	0.651203i	0.996638	−	0.0819303i	$-0.0261085\pi$
$608$	−307.999	−	82.5281i	−0.506577	−	0.135737i
$609$		0			0
$610$	156.531	−	266.154i	0.256609	−	0.436318i
$611$	366.364			0.599614
$612$		0			0
$613$	−10.5026	+	10.5026i	−0.0171331	+	0.0171331i	−0.715621	−	0.698488i	$-0.753856\pi$
$613$	−10.5026	+	10.5026i	−0.0171331	+	0.0171331i	0.698488	+	0.715621i	$0.253856\pi$
$614$	−26.1641	−	15.1059i	−0.0426126	−	0.0246024i
$615$		0			0
$616$	60.5232	+	104.829i	0.0982520	+	0.170177i
$617$	113.048	−	421.900i	0.183222	−	0.683793i	−0.811782	−	0.583960i	$-0.801502\pi$
$617$	113.048	−	421.900i	0.183222	−	0.683793i	0.995004	−	0.0998331i	$-0.0318309\pi$
$618$		0			0
$619$	−8.91186	−	5.14527i	−0.0143972	−	0.00831222i	0.492784	−	0.870152i	$-0.335979\pi$
$619$	−8.91186	−	5.14527i	−0.0143972	−	0.00831222i	−0.507181	+	0.861839i	$0.669313\pi$
$620$	521.060	+	529.509i	0.840420	+	0.854047i
$621$		0			0
$622$	229.439	+	229.439i	0.368873	+	0.368873i
$623$	−54.8585	−	204.735i	−0.0880554	−	0.328627i
$624$		0			0
$625$	294.930	+	551.037i	0.471888	+	0.881659i
$626$	77.9268	+	134.973i	0.124484	+	0.215612i
$627$		0			0
$628$	34.3086	+	128.042i	0.0546316	+	0.203888i
$629$		−	652.537i		−	1.03742i
$630$		0			0
$631$	154.559			0.244943			0.122472	−	0.992472i	$-0.460918\pi$
$631$	154.559			0.244943			0.122472	+	0.992472i	$0.460918\pi$
$632$	330.170	−	88.4689i	0.522421	−	0.139982i
$633$		0			0
$634$	−231.032	+	133.386i	−0.364403	+	0.210388i
$635$	−195.515	−	345.021i	−0.307898	−	0.543340i
$636$		0			0
$637$	901.968	−	241.682i	1.41596	−	0.379406i
$638$	148.565	−	148.565i	0.232860	−	0.232860i
$639$		0			0
$640$	5.23092	−	650.430i	0.00817331	−	1.01630i
$641$	302.816	−	524.493i	0.472412	−	0.818242i	−0.527089	−	0.849810i	$-0.676717\pi$
$641$	302.816	−	524.493i	0.472412	−	0.818242i	0.999502	+	0.0315680i	$0.0100501\pi$
$642$		0			0
$643$	450.687	+	120.761i	0.700912	+	0.187809i	0.591639	−	0.806203i	$-0.298481\pi$
$643$	450.687	+	120.761i	0.700912	+	0.187809i	0.109273	+	0.994012i	$0.465148\pi$
$644$	7.71265	−	4.45290i	0.0119762	−	0.00691444i
$645$		0			0
$646$	57.5346	−	99.6529i	0.0890629	−	0.154261i
$647$	117.084	+	117.084i	0.180965	+	0.180965i	0.791776	−	0.610811i	$-0.209157\pi$
$647$	117.084	+	117.084i	0.180965	+	0.180965i	−0.610811	+	0.791776i	$0.709157\pi$
$648$		0			0
$649$		−	327.378i		−	0.504434i
$650$	−330.392	−	197.905i	−0.508296	−	0.304469i
$651$		0			0
$652$	−177.055	+	660.778i	−0.271557	+	1.01346i
$653$	−322.638	−	86.4506i	−0.494086	−	0.132390i	0.00316798	−	0.999995i	$-0.498992\pi$
$653$	−322.638	−	86.4506i	−0.494086	−	0.132390i	−0.497254	+	0.867605i	$0.665658\pi$
$654$		0			0
$655$	−5.81745	−	22.4310i	−0.00888160	−	0.0342459i
$656$	392.156			0.597799
$657$		0			0
$658$	17.6599	−	17.6599i	0.0268387	−	0.0268387i
$659$	1062.27	+	613.303i	1.61195	+	0.930657i	0.988919	+	0.148457i	$0.0474308\pi$
$659$	1062.27	+	613.303i	1.61195	+	0.930657i	0.623027	+	0.782200i	$0.285903\pi$
$660$		0			0
$661$	79.8777	+	138.352i	0.120844	+	0.209307i	0.920101	−	0.391682i	$-0.128107\pi$
$661$	79.8777	+	138.352i	0.120844	+	0.209307i	−0.799257	+	0.600989i	$0.794773\pi$
$662$	−72.8967	+	272.054i	−0.110116	+	0.410958i
$663$		0			0
$664$	250.017	+	144.347i	0.376532	+	0.217391i
$665$	0.808266	−	100.503i	0.00121544	−	0.151132i
$666$		0			0
$667$	−23.6565	−	23.6565i	−0.0354670	−	0.0354670i
$668$	251.566	+	938.856i	0.376595	+	1.40547i
$669$		0			0
$670$	−33.4957	+	121.103i	−0.0499935	+	0.180751i
$671$	−478.648	−	829.042i	−0.713335	−	1.23553i
$672$		0			0
$673$	12.3181	+	45.9717i	0.0183032	+	0.0683086i	0.974473	−	0.224503i	$-0.0720758\pi$
$673$	12.3181	+	45.9717i	0.0183032	+	0.0683086i	−0.956170	+	0.292811i	$0.905409\pi$
$674$			111.675i			0.165690i
$675$		0			0
$676$	−863.996			−1.27810
$677$	141.633	−	37.9504i	0.209206	−	0.0560567i	−0.152694	−	0.988274i	$-0.548795\pi$
$677$	141.633	−	37.9504i	0.209206	−	0.0560567i	0.361900	+	0.932217i	$0.382128\pi$
$678$		0			0
$679$	49.3279	−	28.4795i	0.0726479	−	0.0419433i
$680$	381.670	+	105.565i	0.561279	+	0.155243i
$681$		0			0
$682$	−365.477	+	97.9293i	−0.535890	+	0.143591i
$683$	−882.608	+	882.608i	−1.29225	+	1.29225i	−0.358860	+	0.933391i	$0.616835\pi$
$683$	−882.608	+	882.608i	−1.29225	+	1.29225i	−0.933391	+	0.358860i	$0.883165\pi$
$684$		0			0
$685$	11.8924	+	0.0956418i	0.0173612	+	0.000139623i
$686$	66.0754	−	114.446i	0.0963198	−	0.166831i
$687$		0			0
$688$	76.4948	+	20.4967i	0.111184	+	0.0297917i
$689$	−1289.07	+	744.243i	−1.87092	+	1.08018i
$690$		0			0
$691$	253.832	−	439.650i	0.367340	−	0.636252i	−0.621808	−	0.783169i	$-0.713602\pi$
$691$	253.832	−	439.650i	0.367340	−	0.636252i	0.989149	+	0.146917i	$0.0469351\pi$
$692$	−753.047	−	753.047i	−1.08822	−	1.08822i
$693$		0			0
$694$		−	181.421i		−	0.261413i
$695$	−1240.25	+	321.657i	−1.78453	+	0.462815i
$696$		0			0
$697$	−150.751	+	562.611i	−0.216286	+	0.807189i
$698$	277.514	+	74.3597i	0.397585	+	0.106532i
$699$		0			0
$700$	155.013	−	38.8746i	0.221447	−	0.0555352i
$701$	−194.042			−0.276807			−0.138403	−	0.990376i	$-0.544197\pi$
$701$	−194.042			−0.276807			−0.138403	+	0.990376i	$0.544197\pi$
$702$		0			0
$703$	−351.581	+	351.581i	−0.500115	+	0.500115i
$704$	−161.459	−	93.2182i	−0.229345	−	0.132412i
$705$		0			0
$706$	−195.614	−	338.813i	−0.277073	−	0.479905i
$707$	28.7907	−	107.448i	0.0407223	−	0.151978i
$708$		0			0
$709$	414.499	+	239.311i	0.584625	+	0.337534i	0.762969	−	0.646435i	$-0.223741\pi$
$709$	414.499	+	239.311i	0.584625	+	0.337534i	−0.178344	+	0.983968i	$0.557074\pi$
$710$	374.463	+	3.01152i	0.527412	+	0.00424158i
$711$		0			0
$712$	−449.958	−	449.958i	−0.631963	−	0.631963i
$713$	15.5936	+	58.1962i	0.0218705	+	0.0816216i
$714$		0			0
$715$	−1038.83	+	588.681i	−1.45291	+	0.823331i
$716$	−260.906	−	451.902i	−0.364393	−	0.631148i
$717$		0			0
$718$	−63.5739	−	237.261i	−0.0885430	−	0.330447i
$719$			443.536i			0.616879i	0.951244	+	0.308439i	$0.0998067\pi$
$719$			443.536i			0.616879i	−0.951244	+	0.308439i	$0.900193\pi$
$720$		0			0
$721$	94.1849			0.130631
$722$	177.274	−	47.5005i	0.245532	−	0.0657902i
$723$		0			0
$724$	−143.106	+	82.6224i	−0.197660	+	0.114119i
$725$	−291.774	−	524.680i	−0.402448	−	0.723696i
$726$		0			0
$727$	−280.010	+	75.0285i	−0.385158	+	0.103203i	−0.446202	−	0.894932i	$-0.647224\pi$
$727$	−280.010	+	75.0285i	−0.385158	+	0.103203i	0.0610438	+	0.998135i	$0.480557\pi$
$728$	−150.709	+	150.709i	−0.207018	+	0.207018i
$729$		0			0
$730$	84.6578	−	83.3070i	0.115970	−	0.114119i
$731$	−58.8116	+	101.865i	−0.0804536	+	0.139350i
$732$		0			0
$733$	−987.435	−	264.583i	−1.34712	−	0.360958i	−0.488046	−	0.872818i	$-0.662290\pi$
$733$	−987.435	−	264.583i	−1.34712	−	0.360958i	−0.859069	+	0.511859i	$0.828957\pi$
$734$	−340.177	+	196.401i	−0.463457	+	0.267577i
$735$		0			0
$736$	20.5601	−	35.6111i	0.0279349	−	0.0483847i
$737$	275.459	+	275.459i	0.373757	+	0.373757i
$738$		0			0
$739$			153.917i			0.208277i	0.994563	+	0.104138i	$0.0332085\pi$
$739$			153.917i			0.208277i	−0.994563	+	0.104138i	$0.966791\pi$
$740$	−681.488	−	400.799i	−0.920929	−	0.541620i
$741$		0			0
$742$	−26.2622	+	98.0117i	−0.0353938	+	0.132091i
$743$	1261.02	+	337.889i	1.69720	+	0.454763i	0.972231	−	0.234021i	$-0.0751886\pi$
$743$	1261.02	+	337.889i	1.69720	+	0.454763i	0.724966	+	0.688784i	$0.241855\pi$
$744$		0			0
$745$	−456.005	+	118.264i	−0.612087	+	0.158744i
$746$	−18.2489			−0.0244623
$747$		0			0
$748$	401.121	−	401.121i	0.536258	−	0.536258i
$749$	−33.8088	−	19.5195i	−0.0451385	−	0.0260607i
$750$		0			0
$751$	−728.908	−	1262.51i	−0.970583	−	1.68110i	−0.693801	−	0.720167i	$-0.744065\pi$
$751$	−728.908	−	1262.51i	−0.970583	−	1.68110i	−0.276783	−	0.960933i	$-0.589268\pi$
$752$	−44.1413	+	164.737i	−0.0586985	+	0.219066i
$753$		0			0
$754$	320.379	+	184.971i	0.424905	+	0.245319i
$755$	−100.127	+	98.5289i	−0.132618	+	0.130502i
$756$		0			0
$757$	−575.216	−	575.216i	−0.759863	−	0.759863i	0.216434	−	0.976297i	$-0.430557\pi$
$757$	−575.216	−	575.216i	−0.759863	−	0.759863i	−0.976297	+	0.216434i	$0.930557\pi$
$758$	70.9594	+	264.824i	0.0936140	+	0.349372i
$759$		0			0
$760$	−148.763	−	262.518i	−0.195740	−	0.345418i
$761$	506.722	+	877.668i	0.665863	+	1.15331i	0.979051	+	0.203618i	$0.0652699\pi$
$761$	506.722	+	877.668i	0.665863	+	1.15331i	−0.313187	+	0.949691i	$0.601397\pi$
$762$		0			0
$763$	−55.5211	−	207.207i	−0.0727668	−	0.271569i
$764$			1248.49i			1.63414i
$765$		0			0
$766$	−2.52556			−0.00329708
$767$	556.794	−	149.193i	0.725938	−	0.194515i
$768$		0			0
$769$	−486.081	+	280.639i	−0.632095	+	0.364940i	−0.781563	−	0.623827i	$-0.785577\pi$
$769$	−486.081	+	280.639i	−0.632095	+	0.364940i	0.149468	+	0.988767i	$0.452244\pi$
$770$	−21.6986	+	78.4511i	−0.0281800	+	0.101884i
$771$		0			0
$772$	−39.7180	+	10.6424i	−0.0514482	+	0.0137855i
$773$	−445.834	+	445.834i	−0.576758	+	0.576758i	−0.934008	−	0.357251i	$-0.883714\pi$
$773$	−445.834	+	445.834i	−0.576758	+	0.576758i	0.357251	+	0.934008i	$0.383714\pi$
$774$		0			0
$775$	−17.3888	+	1081.02i	−0.0224372	+	1.39487i
$776$	85.5009	−	148.092i	0.110182	−	0.190840i
$777$		0			0
$778$	−110.446	−	29.5938i	−0.141961	−	0.0380383i
$779$	384.353	−	221.906i	0.493393	−	0.284860i
$780$		0			0
$781$	580.499	−	1005.45i	0.743276	−	1.28739i
$782$	10.4929	+	10.4929i	0.0134180	+	0.0134180i
$783$		0			0
$784$			434.693i			0.554456i
$785$	−97.7999	+	166.291i	−0.124586	+	0.211836i
$786$		0			0
$787$	−362.598	+	1353.23i	−0.460734	+	1.71948i	0.209925	+	0.977717i	$0.432678\pi$
$787$	−362.598	+	1353.23i	−0.460734	+	1.71948i	−0.670659	+	0.741766i	$0.733989\pi$
$788$	212.793	+	57.0176i	0.270041	+	0.0723573i
$789$		0			0
$790$	198.127	+	116.523i	0.250794	+	0.147498i
$791$	194.967			0.246482
$792$		0			0
$793$	1191.88	−	1191.88i	1.50300	−	1.50300i
$794$	−253.828	−	146.548i	−0.319683	−	0.184569i
$795$		0			0
$796$	29.2167	+	50.6049i	0.0367045	+	0.0635740i
$797$	122.829	−	458.403i	0.154114	−	0.575160i	−0.845066	−	0.534662i	$-0.820439\pi$
$797$	122.829	−	458.403i	0.154114	−	0.575160i	0.999180	−	0.0404981i	$-0.0128945\pi$
$798$		0			0
$799$	−219.374	−	126.655i	−0.274560	−	0.158517i
$800$	530.095	−	513.312i	0.662619	−	0.641640i
$801$		0			0
$802$	358.565	+	358.565i	0.447088	+	0.447088i
$803$	−95.3064	−	355.688i	−0.118688	−	0.442949i
$804$		0			0
$805$	12.4920	+	3.45514i	0.0155181	+	0.00429210i
$806$	−333.111	−	576.965i	−0.413289	−	0.715837i
$807$		0			0
$808$	−86.4352	−	322.581i	−0.106974	−	0.399234i
$809$		−	806.321i		−	0.996689i	−0.866979	−	0.498344i	$-0.833941\pi$
$809$		−	806.321i		−	0.996689i	0.866979	−	0.498344i	$-0.166059\pi$
$810$		0			0
$811$	−928.637			−1.14505			−0.572526	−	0.819887i	$-0.694036\pi$
$811$	−928.637			−1.14505			−0.572526	+	0.819887i	$0.694036\pi$
$812$	−148.280	+	39.7315i	−0.182611	+	0.0489304i
$813$		0			0
$814$	348.727	−	201.338i	0.428412	−	0.247344i
$815$	−866.179	+	490.843i	−1.06280	+	0.602262i
$816$		0			0
$817$	86.5709	−	23.1966i	0.105962	−	0.0283924i
$818$	−230.158	+	230.158i	−0.281366	+	0.281366i
$819$		0			0
$820$	494.978	+	503.004i	0.603632	+	0.613419i
$821$	259.589	−	449.622i	0.316187	−	0.547652i	−0.663502	−	0.748174i	$-0.730931\pi$
$821$	259.589	−	449.622i	0.316187	−	0.547652i	0.979689	+	0.200523i	$0.0642640\pi$
$822$		0			0
$823$	1245.48	+	333.724i	1.51334	+	0.405497i	0.917542	−	0.397639i	$-0.130170\pi$
$823$	1245.48	+	333.724i	1.51334	+	0.405497i	0.595795	+	0.803136i	$0.296837\pi$
$824$	244.879	−	141.381i	0.297183	−	0.171579i
$825$		0			0
$826$	19.6477	−	34.0307i	0.0237865	−	0.0411994i
$827$	380.149	+	380.149i	0.459672	+	0.459672i	0.898548	−	0.438876i	$-0.144623\pi$
$827$	380.149	+	380.149i	0.459672	+	0.459672i	−0.438876	+	0.898548i	$0.644623\pi$
$828$		0			0
$829$		−	511.167i		−	0.616606i	−0.951288	−	0.308303i	$-0.900239\pi$
$829$		−	511.167i		−	0.616606i	0.951288	−	0.308303i	$-0.0997611\pi$
$830$	48.7350	+	187.913i	0.0587168	+	0.226402i
$831$		0			0
$832$	84.9628	−	317.086i	0.102119	−	0.381113i
$833$	−623.637	−	167.103i	−0.748664	−	0.200604i
$834$		0			0
$835$	−717.111	+	1219.32i	−0.858815	+	1.46026i
$836$	−432.240			−0.517034
$837$		0			0
$838$	−265.524	+	265.524i	−0.316855	+	0.316855i
$839$	889.044	+	513.290i	1.05965	+	0.611788i	0.925335	−	0.379151i	$-0.123784\pi$
$839$	889.044	+	513.290i	1.05965	+	0.611788i	0.134313	+	0.990939i	$0.457117\pi$
$840$		0			0
$841$	−132.163	−	228.913i	−0.157150	−	0.272192i
$842$	5.84978	−	21.8317i	0.00694749	−	0.0259284i
$843$		0			0
$844$	885.970	+	511.515i	1.04973	+	0.606061i
$845$	−881.948	−	896.249i	−1.04373	−	1.06065i
$846$		0			0
$847$	19.2439	+	19.2439i	0.0227200	+	0.0227200i
$848$	−179.340	−	669.305i	−0.211486	−	0.789275i
$849$		0			0
$850$	129.417	+	232.722i	0.152255	+	0.273791i
$851$	−32.0597	−	55.5291i	−0.0376730	−	0.0652516i
$852$		0			0
$853$	360.478	+	1345.32i	0.422600	+	1.57717i	0.769108	+	0.639119i	$0.220701\pi$
$853$	360.478	+	1345.32i	0.422600	+	1.57717i	−0.346508	+	0.938047i	$0.612633\pi$
$854$		−	114.905i		−	0.134549i
$855$		0			0
$856$	−117.203			−0.136919
$857$	−319.058	+	85.4914i	−0.372297	+	0.0997566i	−0.440116	−	0.897941i	$-0.645063\pi$
$857$	−319.058	+	85.4914i	−0.372297	+	0.0997566i	0.0678191	+	0.997698i	$0.478396\pi$
$858$		0			0
$859$	264.795	−	152.879i	0.308259	−	0.177974i	−0.337888	−	0.941186i	$-0.609713\pi$
$859$	264.795	−	152.879i	0.308259	−	0.177974i	0.646147	+	0.763213i	$0.276379\pi$
$860$	70.2610	+	123.988i	0.0816988	+	0.144172i
$861$		0			0
$862$	−374.262	+	100.283i	−0.434178	+	0.116338i
$863$	−386.017	+	386.017i	−0.447297	+	0.447297i	−0.894455	−	0.447158i	$-0.852436\pi$
$863$	−386.017	+	386.017i	−0.447297	+	0.447297i	0.447158	+	0.894455i	$0.352436\pi$
$864$		0			0
$865$	12.4643	−	1549.85i	0.0144096	−	1.79174i
$866$	−162.447	+	281.367i	−0.187583	+	0.324904i
$867$		0			0
$868$	267.035	+	71.5518i	0.307644	+	0.0824329i
$869$	617.145	−	356.309i	0.710179	−	0.410022i
$870$		0			0
$871$	−342.961	+	594.025i	−0.393755	+	0.682004i
$872$	−455.392	−	455.392i	−0.522238	−	0.522238i
$873$		0			0
$874$		−	11.3069i		−	0.0129370i
$875$	198.560	+	121.117i	0.226926	+	0.138420i
$876$		0			0
$877$	108.142	−	403.592i	0.123309	−	0.460196i	−0.876465	−	0.481466i	$-0.840104\pi$
$877$	108.142	−	403.592i	0.123309	−	0.460196i	0.999774	+	0.0212701i	$0.00677100\pi$
$878$	−366.669	−	98.2488i	−0.417619	−	0.111901i
$879$		0			0
$880$	−139.540	−	538.043i	−0.158569	−	0.611412i
$881$	1495.93			1.69799			0.848993	−	0.528403i	$-0.177209\pi$
$881$	1495.93			1.69799			0.848993	+	0.528403i	$0.177209\pi$
$882$		0			0
$883$	−158.383	+	158.383i	−0.179369	+	0.179369i	−0.791081	−	0.611712i	$-0.790481\pi$
$883$	−158.383	+	158.383i	−0.179369	+	0.179369i	0.611712	+	0.791081i	$0.290481\pi$
$884$	865.014	+	499.416i	0.978522	+	0.564950i
$885$		0			0
$886$	75.9157	+	131.490i	0.0856837	+	0.148408i
$887$	−355.206	+	1325.65i	−0.400458	+	1.49453i	0.411823	+	0.911264i	$0.364892\pi$
$887$	−355.206	+	1325.65i	−0.400458	+	1.49453i	−0.812281	+	0.583266i	$0.801775\pi$
$888$		0			0
$889$	−127.805	−	73.7883i	−0.143763	−	0.0830014i
$890$	3.44115	−	427.885i	0.00386647	−	0.480769i
$891$		0			0
$892$	77.6576	+	77.6576i	0.0870601	+	0.0870601i
$893$	49.9557	+	186.437i	0.0559415	+	0.208776i
$894$		0			0
$895$	202.445	−	731.937i	0.226195	−	0.817807i
$896$	−121.028	−	209.626i	−0.135076	−	0.233958i
$897$		0			0
$898$	28.2113	+	105.286i	0.0314157	+	0.117245i
$899$		−	1038.52i		−	1.15520i
$900$		0			0
$901$	1029.17			1.14225
$902$	−347.183	+	93.0274i	−0.384903	+	0.103135i
$903$		0			0
$904$	506.909	−	292.664i	0.560741	−	0.323744i
$905$	−231.786	−	64.1092i	−0.256118	−	0.0708389i
$906$		0			0
$907$	535.743	−	143.552i	0.590676	−	0.158271i	0.0489140	−	0.998803i	$-0.484424\pi$
$907$	535.743	−	143.552i	0.590676	−	0.158271i	0.541762	+	0.840532i	$0.317757\pi$
$908$	950.276	−	950.276i	1.04656	−	1.04656i
$909$		0			0
$910$	−143.316	−	1.15258i	−0.157490	−	0.00126657i
$911$	484.409	−	839.021i	0.531733	−	0.920989i	−0.467581	−	0.883950i	$-0.654874\pi$
$911$	484.409	−	839.021i	0.531733	−	0.920989i	0.999314	−	0.0370382i	$-0.0117923\pi$
$912$		0			0
$913$	581.361	+	155.775i	0.636759	+	0.170619i
$914$	−192.995	+	111.426i	−0.211154	+	0.121910i
$915$		0			0
$916$	430.882	−	746.309i	0.470395	−	0.814748i
$917$	−6.09776	−	6.09776i	−0.00664968	−	0.00664968i
$918$		0			0
$919$		−	600.903i		−	0.653866i	−0.945048	−	0.326933i	$-0.893985\pi$
$919$		−	600.903i		−	0.653866i	0.945048	−	0.326933i	$-0.106015\pi$
$920$	37.6655	−	9.76848i	0.0409408	−	0.0106179i
$921$		0			0
$922$	−55.6275	+	207.604i	−0.0603335	+	0.225168i
$923$	1974.59	+	529.090i	2.13932	+	0.573229i
$924$		0			0
$925$	−279.887	−	1116.05i	−0.302581	−	1.20655i
$926$	−187.992			−0.203015
$927$		0			0
$928$	−501.193	+	501.193i	−0.540079	+	0.540079i
$929$	−435.996	−	251.722i	−0.469318	−	0.270961i	0.246636	−	0.969108i	$-0.420675\pi$
$929$	−435.996	−	251.722i	−0.469318	−	0.270961i	−0.715954	+	0.698147i	$0.754008\pi$
$930$		0			0
$931$	245.976	+	426.044i	0.264207	+	0.457619i
$932$	300.655	−	1122.06i	0.322591	−	1.20393i
$933$		0			0
$934$	65.6305	+	37.8918i	0.0702682	+	0.0405694i
$935$	825.550	+	6.63928i	0.882941	+	0.00710083i
$936$		0			0
$937$	1181.10	+	1181.10i	1.26051	+	1.26051i	0.950847	+	0.309660i	$0.100215\pi$
$937$	1181.10	+	1181.10i	1.26051	+	1.26051i	0.309660	+	0.950847i	$0.399785\pi$
$938$	12.1021	+	45.1656i	0.0129020	+	0.0481509i
$939$		0			0
$940$	−267.017	+	151.313i	−0.284061	+	0.160971i
$941$	576.616	+	998.729i	0.612770	+	1.06135i	0.990771	+	0.135543i	$0.0432780\pi$
$941$	576.616	+	998.729i	0.612770	+	1.06135i	−0.378002	+	0.925805i	$0.623389\pi$
$942$		0			0
$943$	14.8131	+	55.2832i	0.0157085	+	0.0586248i
$944$			268.341i			0.284259i
$945$		0			0
$946$	−72.5844			−0.0767277
$947$	−1323.45	+	354.616i	−1.39751	+	0.374463i	−0.877451	−	0.479665i	$-0.840758\pi$
$947$	−1323.45	+	354.616i	−1.39751	+	0.374463i	−0.520063	+	0.854128i	$0.674091\pi$
$948$		0			0
$949$	561.512	−	324.189i	0.591688	−	0.341611i
$950$	55.6600	−	195.117i	0.0585894	−	0.205387i
$951$		0			0
$952$	142.344	−	38.1409i	0.149521	−	0.0400640i
$953$	−77.4456	+	77.4456i	−0.0812650	+	0.0812650i	−0.746571	−	0.665306i	$-0.768301\pi$
$953$	−77.4456	+	77.4456i	−0.0812650	+	0.0812650i	0.665306	+	0.746571i	$0.268301\pi$
$954$		0			0
$955$	−1295.09	+	1274.43i	−1.35612	+	1.33448i
$956$	67.1397	−	116.289i	0.0702298	−	0.121642i
$957$		0			0
$958$	142.282	+	38.1245i	0.148520	+	0.0397959i
$959$	3.83279	−	2.21286i	0.00399666	−	0.00230747i
$960$		0			0
$961$	−454.630	+	787.443i	−0.473080	+	0.819399i
$962$	501.352	+	501.352i	0.521156	+	0.521156i
$963$		0			0
$964$		−	287.577i		−	0.298316i
$965$	−51.5830	−	30.3372i	−0.0534539	−	0.0314375i
$966$		0			0
$967$	417.733	−	1559.00i	0.431989	−	1.61220i	−0.316183	−	0.948698i	$-0.602401\pi$
$967$	417.733	−	1559.00i	0.431989	−	1.61220i	0.748172	−	0.663505i	$-0.230932\pi$
$968$	78.9205	+	21.1467i	0.0815295	+	0.0218458i
$969$		0			0
$970$	111.306	−	28.8671i	0.114749	−	0.0297599i
$971$	−158.612			−0.163349			−0.0816745	−	0.996659i	$-0.526027\pi$
$971$	−158.612			−0.163349			−0.0816745	+	0.996659i	$0.526027\pi$
$972$		0			0
$973$	−337.156	+	337.156i	−0.346511	+	0.346511i
$974$	607.386	+	350.674i	0.623599	+	0.360035i
$975$		0			0
$976$	392.332	+	679.539i	0.401980	+	0.696249i
$977$	−2.86555	+	10.6944i	−0.00293301	+	0.0109461i	−0.967377	−	0.253342i	$-0.918470\pi$
$977$	−2.86555	+	10.6944i	−0.00293301	+	0.0109461i	0.964444	+	0.264288i	$0.0851369\pi$
$978$		0			0
$979$	−1148.89	−	663.315i	−1.17354	−	0.677543i
$980$	−557.565	+	548.668i	−0.568944	+	0.559865i
$981$		0			0
$982$	−418.604	−	418.604i	−0.426277	−	0.426277i
$983$	−295.182	−	1101.63i	−0.300287	−	1.12069i	−0.936927	−	0.349525i	$-0.886343\pi$
$983$	−295.182	−	1101.63i	−0.300287	−	1.12069i	0.636640	−	0.771161i	$-0.280324\pi$
$984$		0			0
$985$	158.068	+	278.938i	0.160475	+	0.283186i
$986$	−127.892	−	221.516i	−0.129708	−	0.224661i
$987$		0			0
$988$	−196.981	−	735.142i	−0.199373	−	0.744071i
$989$			11.5579i			0.0116864i
$990$		0			0
$991$	−95.8581			−0.0967287			−0.0483643	−	0.998830i	$-0.515401\pi$
$991$	−95.8581			−0.0967287			−0.0483643	+	0.998830i	$0.515401\pi$
$992$	1232.96	−	330.371i	1.24291	−	0.333036i
$993$		0			0
$994$	120.685	−	69.6776i	0.121414	−	0.0700982i
$995$	−22.6702	+	81.9638i	−0.0227841	+	0.0823757i
$996$		0			0
$997$	−850.093	+	227.782i	−0.852651	+	0.228467i	−0.658571	−	0.752518i	$-0.728839\pi$
$997$	−850.093	+	227.782i	−0.852651	+	0.228467i	−0.194080	+	0.980986i	$0.562172\pi$
$998$	88.7943	−	88.7943i	0.0889723	−	0.0889723i
$999$		0			0

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (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	135.3.l.a.127.6		40
3.2	odd	2		45.3.k.a.7.5	✓	40
5.3	odd	4	inner	135.3.l.a.73.5		40
9.2	odd	6		405.3.g.h.82.6		20
9.4	even	3	inner	135.3.l.a.37.5		40
9.5	odd	6		45.3.k.a.22.6	yes	40
9.7	even	3		405.3.g.g.82.5		20
15.2	even	4		225.3.o.b.43.5		40
15.8	even	4		45.3.k.a.43.6	yes	40
15.14	odd	2		225.3.o.b.7.6		40
45.13	odd	12	inner	135.3.l.a.118.6		40
45.14	odd	6		225.3.o.b.157.5		40
45.23	even	12		45.3.k.a.13.5	yes	40
45.32	even	12		225.3.o.b.193.6		40
45.38	even	12		405.3.g.h.163.6		20
45.43	odd	12		405.3.g.g.163.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.5	✓	40	3.2	odd	2
45.3.k.a.13.5	yes	40	45.23	even	12
45.3.k.a.22.6	yes	40	9.5	odd	6
45.3.k.a.43.6	yes	40	15.8	even	4
135.3.l.a.37.5		40	9.4	even	3	inner
135.3.l.a.73.5		40	5.3	odd	4	inner
135.3.l.a.118.6		40	45.13	odd	12	inner
135.3.l.a.127.6		40	1.1	even	1	trivial
225.3.o.b.7.6		40	15.14	odd	2
225.3.o.b.43.5		40	15.2	even	4
225.3.o.b.157.5		40	45.14	odd	6
225.3.o.b.193.6		40	45.32	even	12
405.3.g.g.82.5		20	9.7	even	3
405.3.g.g.163.5		20	45.43	odd	12
405.3.g.h.82.6		20	9.2	odd	6
405.3.g.h.163.6		20	45.38	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	135.3.l.a.127.6

Level	$135$
Weight	$3$
Character	135.127
Analytic conductor	$3.678$
Analytic rank	$0$
Dimension	$40$
Inner twists	$4$