LMFDB - Embedded newform 200.3.u.a.97.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [200,3,Mod(17,200)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("200.17"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(200, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 0, 13])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	200.u (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.44960528721$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			97.4
Character	$\chi$	$=$	200.97
Dual form			200.3.u.a.33.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.304092 + 0.0481634i) q^{3} +(-1.19185 + 4.85587i) q^{5} +(-5.20977 - 5.20977i) q^{7} +(-8.46936 + 2.75186i) q^{9} +(0.00492385 - 0.0151541i) q^{11} +(-7.35975 - 3.74998i) q^{13} +(0.128557 - 1.53404i) q^{15} +(-16.3649 - 2.59194i) q^{17} +(-1.93234 - 2.65964i) q^{19} +(1.83517 + 1.33333i) q^{21} +(5.56670 + 10.9253i) q^{23} +(-22.1590 - 11.5750i) q^{25} +(4.91185 - 2.50271i) q^{27} +(-22.5752 + 31.0721i) q^{29} +(-19.1612 + 13.9214i) q^{31} +(-0.000767432 + 0.00484538i) q^{33} +(31.5073 - 19.0887i) q^{35} +(-7.24555 + 14.2202i) q^{37} +(2.41865 + 0.785868i) q^{39} +(12.8290 + 39.4837i) q^{41} +(46.2243 - 46.2243i) q^{43} +(-3.26846 - 44.4059i) q^{45} +(-4.56574 - 28.8270i) q^{47} +5.28342i q^{49} +5.10126 q^{51} +(38.5577 - 6.10694i) q^{53} +(0.0677177 + 0.0419710i) q^{55} +(0.715706 + 0.715706i) q^{57} +(44.3689 - 14.4163i) q^{59} +(-5.55183 + 17.0868i) q^{61} +(58.4600 + 29.7868i) q^{63} +(26.9812 - 31.2686i) q^{65} +(-82.3392 - 13.0412i) q^{67} +(-2.21899 - 3.05417i) q^{69} +(87.7801 + 63.7759i) q^{71} +(56.9118 + 111.696i) q^{73} +(7.29586 + 2.45260i) q^{75} +(-0.104601 + 0.0532970i) q^{77} +(-78.7669 + 108.413i) q^{79} +(63.4671 - 46.1115i) q^{81} +(20.4786 - 129.296i) q^{83} +(32.0906 - 76.3765i) q^{85} +(5.36840 - 10.5361i) q^{87} +(-65.2768 - 21.2097i) q^{89} +(18.8061 + 57.8792i) q^{91} +(5.15625 - 5.15625i) q^{93} +(15.2179 - 6.21329i) q^{95} +(-10.8430 - 68.4600i) q^{97} +0.141895i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 10 q^{5} - 4 q^{7} + 40 q^{9} - 16 q^{11} + 14 q^{13} - 10 q^{15} + 22 q^{17} + 50 q^{19} + 100 q^{21} - 48 q^{23} + 150 q^{25} - 210 q^{27} - 108 q^{31} - 140 q^{33} + 70 q^{35} + 236 q^{37} + 80 q^{39}+ \cdots + 386 q^{97}+O(q^{100}) $ 56 * q - 10 * q^5 - 4 * q^7 + 40 * q^9 - 16 * q^11 + 14 * q^13 - 10 * q^15 + 22 * q^17 + 50 * q^19 + 100 * q^21 - 48 * q^23 + 150 * q^25 - 210 * q^27 - 108 * q^31 - 140 * q^33 + 70 * q^35 + 236 * q^37 + 80 * q^39 + 104 * q^41 + 96 * q^43 + 20 * q^45 + 104 * q^47 - 200 * q^51 + 88 * q^53 - 140 * q^55 - 280 * q^57 + 200 * q^59 + 108 * q^61 - 654 * q^63 - 510 * q^65 - 282 * q^67 + 40 * q^69 + 470 * q^71 + 62 * q^73 + 350 * q^75 - 396 * q^77 - 560 * q^79 - 586 * q^81 - 468 * q^83 + 50 * q^85 - 280 * q^87 + 230 * q^89 - 62 * q^91 - 300 * q^93 - 360 * q^95 + 386 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$1$	$1$	$e\left(\frac{17}{20}\right)$

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			0
$2$		0			0
$3$	−0.304092	+	0.0481634i	−0.101364	+	0.0160545i	−0.206910	−	0.978360i	$-0.566341\pi$
$3$	−0.304092	+	0.0481634i	−0.101364	+	0.0160545i	0.105546	+	0.994414i	$0.466341\pi$
$4$		0			0
$5$	−1.19185	+	4.85587i	−0.238371	+	0.971174i
$5$	−1.19185	+	4.85587i	−0.238371	+	0.971174i
$6$		0			0
$7$	−5.20977	−	5.20977i	−0.744253	−	0.744253i	0.229140	−	0.973393i	$-0.426408\pi$
$7$	−5.20977	−	5.20977i	−0.744253	−	0.744253i	−0.973393	+	0.229140i	$0.926408\pi$
$8$		0			0
$9$	−8.46936	+	2.75186i	−0.941040	+	0.305762i
$10$		0			0
$11$	0.00492385	−	0.0151541i	0.000447623	−	0.00137764i	−0.950832	−	0.309706i	$-0.899769\pi$
$11$	0.00492385	−	0.0151541i	0.000447623	−	0.00137764i	0.951280	+	0.308328i	$0.0997695\pi$
$12$		0			0
$13$	−7.35975	−	3.74998i	−0.566135	−	0.288460i	0.147403	−	0.989076i	$-0.452908\pi$
$13$	−7.35975	−	3.74998i	−0.566135	−	0.288460i	−0.713538	+	0.700616i	$0.752908\pi$
$14$		0			0
$15$	0.128557	−	1.53404i	0.00857049	−	0.102269i
$16$		0			0
$17$	−16.3649	−	2.59194i	−0.962639	−	0.152467i	−0.344717	−	0.938707i	$-0.612025\pi$
$17$	−16.3649	−	2.59194i	−0.962639	−	0.152467i	−0.617922	+	0.786240i	$0.712025\pi$
$18$		0			0
$19$	−1.93234	−	2.65964i	−0.101702	−	0.139981i	0.755133	−	0.655572i	$-0.227572\pi$
$19$	−1.93234	−	2.65964i	−0.101702	−	0.139981i	−0.856835	+	0.515591i	$0.827572\pi$
$20$		0			0
$21$	1.83517	+	1.33333i	0.0873890	+	0.0634919i
$22$		0			0
$23$	5.56670	+	10.9253i	0.242030	+	0.475011i	0.979784	−	0.200059i	$-0.0641133\pi$
$23$	5.56670	+	10.9253i	0.242030	+	0.475011i	−0.737754	+	0.675070i	$0.764113\pi$
$24$		0			0
$25$	−22.1590	−	11.5750i	−0.886359	−	0.462999i
$26$		0			0
$27$	4.91185	−	2.50271i	0.181920	−	0.0926931i
$28$		0			0
$29$	−22.5752	+	31.0721i	−0.778455	+	1.07145i	0.216996	+	0.976173i	$0.430374\pi$
$29$	−22.5752	+	31.0721i	−0.778455	+	1.07145i	−0.995451	+	0.0952788i	$0.969626\pi$
$30$		0			0
$31$	−19.1612	+	13.9214i	−0.618102	+	0.449077i	−0.852258	−	0.523122i	$-0.824767\pi$
$31$	−19.1612	+	13.9214i	−0.618102	+	0.449077i	0.234156	+	0.972199i	$0.424767\pi$
$32$		0			0
$33$	−0.000767432		0.00484538i	−2.32555e−5		0.000146830i
$34$		0			0
$35$	31.5073	−	19.0887i	0.900207	−	0.545391i
$36$		0			0
$37$	−7.24555	+	14.2202i	−0.195826	+	0.384330i	−0.967950	−	0.251141i	$-0.919194\pi$
$37$	−7.24555	+	14.2202i	−0.195826	+	0.384330i	0.772125	+	0.635471i	$0.219194\pi$
$38$		0			0
$39$	2.41865	+	0.785868i	0.0620168	+	0.0201505i
$40$		0			0
$41$	12.8290	+	39.4837i	0.312903	+	0.963016i	0.976609	+	0.215023i	$0.0689825\pi$
$41$	12.8290	+	39.4837i	0.312903	+	0.963016i	−0.663706	+	0.747993i	$0.731017\pi$
$42$		0			0
$43$	46.2243	−	46.2243i	1.07498	−	1.07498i	0.0780332	−	0.996951i	$-0.475136\pi$
$43$	46.2243	−	46.2243i	1.07498	−	1.07498i	0.996951	−	0.0780332i	$-0.0248640\pi$
$44$		0			0
$45$	−3.26846	−	44.4059i	−0.0726324	−	0.986798i
$46$		0			0
$47$	−4.56574	−	28.8270i	−0.0971435	−	0.613340i	−0.987444	−	0.157967i	$-0.949506\pi$
$47$	−4.56574	−	28.8270i	−0.0971435	−	0.613340i	0.890301	−	0.455373i	$-0.150494\pi$
$48$		0			0
$49$			5.28342i			0.107825i
$50$		0			0
$51$	5.10126			0.100025
$52$		0			0
$53$	38.5577	−	6.10694i	0.727504	−	0.115225i	0.218313	−	0.975879i	$-0.429945\pi$
$53$	38.5577	−	6.10694i	0.727504	−	0.115225i	0.509191	+	0.860653i	$0.329945\pi$
$54$		0			0
$55$	0.0677177	+	0.0419710i	0.00123123	+	0.000763109i
$56$		0			0
$57$	0.715706	+	0.715706i	0.0125562	+	0.0125562i
$58$		0			0
$59$	44.3689	−	14.4163i	0.752015	−	0.244344i	0.0921669	−	0.995744i	$-0.470621\pi$
$59$	44.3689	−	14.4163i	0.752015	−	0.244344i	0.659848	+	0.751399i	$0.270621\pi$
$60$		0			0
$61$	−5.55183	+	17.0868i	−0.0910136	+	0.280111i	−0.986194	−	0.165592i	$-0.947046\pi$
$61$	−5.55183	+	17.0868i	−0.0910136	+	0.280111i	0.895181	+	0.445703i	$0.147046\pi$
$62$		0			0
$63$	58.4600	+	29.7868i	0.927936	+	0.472807i
$64$		0			0
$65$	26.9812	−	31.2686i	0.415095	−	0.481055i
$66$		0			0
$67$	−82.3392	−	13.0412i	−1.22894	−	0.194645i	−0.491997	−	0.870597i	$-0.663733\pi$
$67$	−82.3392	−	13.0412i	−1.22894	−	0.194645i	−0.736946	+	0.675952i	$0.763733\pi$
$68$		0			0
$69$	−2.21899	−	3.05417i	−0.0321592	−	0.0442634i
$70$		0			0
$71$	87.7801	+	63.7759i	1.23634	+	0.898253i	0.997349	−	0.0727693i	$-0.0231837\pi$
$71$	87.7801	+	63.7759i	1.23634	+	0.898253i	0.238990	+	0.971022i	$0.423184\pi$
$72$		0			0
$73$	56.9118	+	111.696i	0.779614	+	1.53008i	0.846542	+	0.532321i	$0.178680\pi$
$73$	56.9118	+	111.696i	0.779614	+	1.53008i	−0.0669283	+	0.997758i	$0.521320\pi$
$74$		0			0
$75$	7.29586	+	2.45260i	0.0972781	+	0.0327014i
$76$		0			0
$77$	−0.104601	+	0.0532970i	−0.00135846	+	0.000692169i
$78$		0			0
$79$	−78.7669	+	108.413i	−0.997049	+	1.37232i	−0.0699304	+	0.997552i	$0.522278\pi$
$79$	−78.7669	+	108.413i	−0.997049	+	1.37232i	−0.927119	+	0.374768i	$0.877722\pi$
$80$		0			0
$81$	63.4671	−	46.1115i	0.783544	−	0.569278i
$82$		0			0
$83$	20.4786	−	129.296i	0.246730	−	1.55779i	−0.483967	−	0.875086i	$-0.660804\pi$
$83$	20.4786	−	129.296i	0.246730	−	1.55779i	0.730696	−	0.682703i	$-0.239196\pi$
$84$		0			0
$85$	32.0906	−	76.3765i	0.377537	−	0.898547i
$86$		0			0
$87$	5.36840	−	10.5361i	0.0617057	−	0.121104i
$88$		0			0
$89$	−65.2768	−	21.2097i	−0.733447	−	0.238311i	−0.0816033	−	0.996665i	$-0.526004\pi$
$89$	−65.2768	−	21.2097i	−0.733447	−	0.238311i	−0.651843	+	0.758354i	$0.726004\pi$
$90$		0			0
$91$	18.8061	+	57.8792i	0.206660	+	0.636035i
$92$		0			0
$93$	5.15625	−	5.15625i	0.0554436	−	0.0554436i
$94$		0			0
$95$	15.2179	−	6.21329i	0.160189	−	0.0654031i
$96$		0			0
$97$	−10.8430	−	68.4600i	−0.111784	−	0.705774i	−0.978388	−	0.206778i	$-0.933702\pi$
$97$	−10.8430	−	68.4600i	−0.111784	−	0.705774i	0.866604	−	0.498996i	$-0.166298\pi$
$98$		0			0
$99$			0.141895i			0.00143328i
$100$		0			0
$101$	16.3060			0.161446			0.0807228	−	0.996737i	$-0.474277\pi$
$101$	16.3060			0.161446			0.0807228	+	0.996737i	$0.474277\pi$
$102$		0			0
$103$	−10.9428	+	1.73317i	−0.106241	+	0.0168269i	−0.209328	−	0.977845i	$-0.567128\pi$
$103$	−10.9428	+	1.73317i	−0.106241	+	0.0168269i	0.103088	+	0.994672i	$0.467128\pi$
$104$		0			0
$105$	−8.66173	+	7.32222i	−0.0824926	+	0.0697354i
$106$		0			0
$107$	−111.065	−	111.065i	−1.03799	−	1.03799i	−0.999249	−	0.0387372i	$-0.987666\pi$
$107$	−111.065	−	111.065i	−1.03799	−	1.03799i	−0.0387372	−	0.999249i	$-0.512334\pi$
$108$		0			0
$109$	−154.778	+	50.2905i	−1.41998	+	0.461381i	−0.915597	−	0.402097i	$-0.868281\pi$
$109$	−154.778	+	50.2905i	−1.41998	+	0.461381i	−0.504387	+	0.863478i	$0.668281\pi$
$110$		0			0
$111$	1.51842	−	4.67322i	0.0136795	−	0.0421011i
$112$		0			0
$113$	−50.6257	−	25.7951i	−0.448015	−	0.228275i	0.215401	−	0.976526i	$-0.430894\pi$
$113$	−50.6257	−	25.7951i	−0.448015	−	0.228275i	−0.663416	+	0.748250i	$0.730894\pi$
$114$		0			0
$115$	−59.6863	+	14.0099i	−0.519012	+	0.121825i
$116$		0			0
$117$	72.6518	+	11.5069i	0.620955	+	0.0983497i
$118$		0			0
$119$	71.7538	+	98.7606i	0.602973	+	0.829921i
$120$		0			0
$121$	97.8909	+	71.1219i	0.809015	+	0.587784i
$122$		0			0
$123$	−5.80287	−	11.3888i	−0.0471778	−	0.0925916i
$124$		0			0
$125$	82.6168	−	93.8055i	0.660934	−	0.750444i
$126$		0			0
$127$	−151.665	+	77.2771i	−1.19421	+	0.608481i	−0.934070	−	0.357090i	$-0.883769\pi$
$127$	−151.665	+	77.2771i	−1.19421	+	0.608481i	−0.260141	+	0.965571i	$0.583769\pi$
$128$		0			0
$129$	−11.8301	+	16.2828i	−0.0917064	+	0.126223i
$130$		0			0
$131$	−193.977	+	140.933i	−1.48074	+	1.07582i	−0.503428	+	0.864037i	$0.667928\pi$
$131$	−193.977	+	140.933i	−1.48074	+	1.07582i	−0.977316	+	0.211787i	$0.932072\pi$
$132$		0			0
$133$	−3.78905	+	23.9231i	−0.0284891	+	0.179873i
$134$		0			0
$135$	6.29865	+	26.8342i	0.0466567	+	0.198772i
$136$		0			0
$137$	−15.4651	+	30.3519i	−0.112884	+	0.221547i	−0.940536	−	0.339695i	$-0.889676\pi$
$137$	−15.4651	+	30.3519i	−0.112884	+	0.221547i	0.827652	+	0.561242i	$0.189676\pi$
$138$		0			0
$139$	−54.7441	−	17.7874i	−0.393843	−	0.127967i	0.105399	−	0.994430i	$-0.466388\pi$
$139$	−54.7441	−	17.7874i	−0.393843	−	0.127967i	−0.499242	+	0.866463i	$0.666388\pi$
$140$		0			0
$141$	2.77681	+	8.54615i	0.0196937	+	0.0606110i
$142$		0			0
$143$	−0.0930658	+	0.0930658i	−0.000650810	+	0.000650810i
$144$		0			0
$145$	−123.976	−	146.656i	−0.855005	−	1.01142i
$146$		0			0
$147$	−0.254467	−	1.60664i	−0.00173107	−	0.0109296i
$148$		0			0
$149$			73.2146i			0.491373i	0.969349	+	0.245687i	$0.0790134\pi$
$149$			73.2146i			0.491373i	−0.969349	+	0.245687i	$0.920987\pi$
$150$		0			0
$151$	−239.940			−1.58901			−0.794505	−	0.607258i	$-0.792269\pi$
$151$	−239.940			−1.58901			−0.794505	+	0.607258i	$0.792269\pi$
$152$		0			0
$153$	145.733	−	23.0818i	0.952500	−	0.150861i
$154$		0			0
$155$	−44.7632	−	109.636i	−0.288795	−	0.707331i
$156$		0			0
$157$	33.6220	+	33.6220i	0.214153	+	0.214153i	0.806029	−	0.591876i	$-0.201612\pi$
$157$	33.6220	+	33.6220i	0.214153	+	0.214153i	−0.591876	+	0.806029i	$0.701612\pi$
$158$		0			0
$159$	−11.4310	+	3.71415i	−0.0718929	+	0.0233594i
$160$		0			0
$161$	27.9169	−	85.9193i	0.173397	−	0.533660i
$162$		0			0
$163$	−4.54279	−	2.31467i	−0.0278699	−	0.0142004i	0.440000	−	0.897998i	$-0.354978\pi$
$163$	−4.54279	−	2.31467i	−0.0278699	−	0.0142004i	−0.467870	+	0.883797i	$0.654978\pi$
$164$		0			0
$165$	−0.0226139	−	0.00950153i	−0.000137054	−	5.75850e-5i
$166$		0			0
$167$	−76.5318	−	12.1214i	−0.458274	−	0.0725835i	−0.0769706	−	0.997033i	$-0.524525\pi$
$167$	−76.5318	−	12.1214i	−0.458274	−	0.0725835i	−0.381304	+	0.924450i	$0.624525\pi$
$168$		0			0
$169$	−59.2321	−	81.5260i	−0.350486	−	0.482402i
$170$		0			0
$171$	23.6846	+	17.2079i	0.138506	+	0.100631i
$172$		0			0
$173$	8.32806	+	16.3447i	0.0481391	+	0.0944783i	0.913823	−	0.406113i	$-0.133116\pi$
$173$	8.32806	+	16.3447i	0.0481391	+	0.0944783i	−0.865684	+	0.500591i	$0.833116\pi$
$174$		0			0
$175$	55.1403	+	175.746i	0.315087	+	1.00426i
$176$		0			0
$177$	−12.7979	+	6.52085i	−0.0723044	+	0.0368409i
$178$		0			0
$179$	176.529	−	242.971i	0.986193	−	1.35738i	0.0527675	−	0.998607i	$-0.483196\pi$
$179$	176.529	−	242.971i	0.986193	−	1.35738i	0.933425	−	0.358771i	$-0.116804\pi$
$180$		0			0
$181$	128.129	−	93.0908i	0.707892	−	0.514314i	−0.174601	−	0.984639i	$-0.555863\pi$
$181$	128.129	−	93.0908i	0.707892	−	0.514314i	0.882493	+	0.470325i	$0.155863\pi$
$182$		0			0
$183$	0.865309	−	5.46335i	0.00472847	−	0.0298544i
$184$		0			0
$185$	−60.4158	−	52.1318i	−0.326572	−	0.281794i
$186$		0			0
$187$	−0.119857	+	0.235232i	−0.000640944	+	0.00125792i
$188$		0			0
$189$	−38.6282	−	12.5511i	−0.204382	−	0.0664077i
$190$		0			0
$191$	38.7640	+	119.303i	0.202953	+	0.624625i	0.999791	+	0.0204322i	$0.00650422\pi$
$191$	38.7640	+	119.303i	0.202953	+	0.624625i	−0.796838	+	0.604193i	$0.793496\pi$
$192$		0			0
$193$	−181.855	+	181.855i	−0.942256	+	0.942256i	−0.998421	−	0.0561658i	$-0.982112\pi$
$193$	−181.855	+	181.855i	−0.942256	+	0.942256i	0.0561658	+	0.998421i	$0.482112\pi$
$194$		0			0
$195$	−6.69875	+	10.8080i	−0.0343526	+	0.0554258i
$196$		0			0
$197$	20.8407	+	131.583i	0.105790	+	0.667934i	0.982408	+	0.186747i	$0.0597943\pi$
$197$	20.8407	+	131.583i	0.105790	+	0.667934i	−0.876618	+	0.481187i	$0.840206\pi$
$198$		0			0
$199$			88.0843i			0.442635i	0.975202	+	0.221317i	$0.0710356\pi$
$199$			88.0843i			0.442635i	−0.975202	+	0.221317i	$0.928964\pi$
$200$		0			0
$201$	25.6668			0.127695
$202$		0			0
$203$	279.490	−	44.2669i	1.37680	−	0.218063i
$204$		0			0
$205$	−207.018	+	15.2374i	−1.00984	+	0.0743286i
$206$		0			0
$207$	−77.2111	−	77.2111i	−0.373001	−	0.373001i
$208$		0			0
$209$	−0.0498188	+	0.0161871i	−0.000238368	+	7.74503e-5i
$210$		0			0
$211$	68.7332	−	211.539i	0.325750	−	1.00255i	−0.645351	−	0.763886i	$-0.723289\pi$
$211$	68.7332	−	211.539i	0.325750	−	1.00255i	0.971101	−	0.238669i	$-0.0767110\pi$
$212$		0			0
$213$	−29.7649	−	15.1660i	−0.139741	−	0.0712017i
$214$		0			0
$215$	169.367	+	279.552i	0.787752	+	1.30024i
$216$		0			0
$217$	172.353	+	27.2980i	0.794251	+	0.125797i
$218$		0			0
$219$	−22.6861	−	31.2247i	−0.103589	−	0.142579i
$220$		0			0
$221$	110.722	+	80.4440i	0.501003	+	0.364000i
$222$		0			0
$223$	−40.4867	−	79.4597i	−0.181555	−	0.356321i	0.782235	−	0.622983i	$-0.214079\pi$
$223$	−40.4867	−	79.4597i	−0.181555	−	0.356321i	−0.963790	+	0.266662i	$0.914079\pi$
$224$		0			0
$225$	219.525	+	37.0541i	0.975666	+	0.164685i
$226$		0			0
$227$	334.709	−	170.543i	1.47449	−	0.751289i	0.482296	−	0.876008i	$-0.339803\pi$
$227$	334.709	−	170.543i	1.47449	−	0.751289i	0.992192	+	0.124719i	$0.0398029\pi$
$228$		0			0
$229$	60.1228	−	82.7519i	0.262545	−	0.361362i	−0.657310	−	0.753620i	$-0.728306\pi$
$229$	60.1228	−	82.7519i	0.262545	−	0.361362i	0.919855	+	0.392258i	$0.128306\pi$
$230$		0			0
$231$	0.0292414	−	0.0212452i	0.000126586	−	9.19704e-5i
$232$		0			0
$233$	−7.73105	+	48.8119i	−0.0331805	+	0.209493i	−0.998709	−	0.0508057i	$-0.983821\pi$
$233$	−7.73105	+	48.8119i	−0.0331805	+	0.209493i	0.965528	+	0.260299i	$0.0838211\pi$
$234$		0			0
$235$	145.422	+	12.1868i	0.618816	+	0.0518589i
$236$		0			0
$237$	18.7308	−	36.7613i	0.0790330	−	0.155111i
$238$		0			0
$239$	333.655	+	108.411i	1.39604	+	0.453602i	0.907910	−	0.419166i	$-0.137677\pi$
$239$	333.655	+	108.411i	1.39604	+	0.453602i	0.488135	+	0.872768i	$0.337677\pi$
$240$		0			0
$241$	−61.6285	−	189.673i	−0.255720	−	0.787025i	−0.993687	−	0.112188i	$-0.964214\pi$
$241$	−61.6285	−	189.673i	−0.255720	−	0.787025i	0.737967	−	0.674837i	$-0.235786\pi$
$242$		0			0
$243$	−52.1615	+	52.1615i	−0.214657	+	0.214657i
$244$		0			0
$245$	−25.6556	−	6.29705i	−0.104717	−	0.0257023i
$246$		0			0
$247$	4.24795	+	26.8205i	0.0171982	+	0.108585i
$248$		0			0
$249$			40.3043i			0.161865i
$250$		0			0
$251$	−159.329			−0.634776			−0.317388	−	0.948296i	$-0.602806\pi$
$251$	−159.329			−0.634776			−0.317388	+	0.948296i	$0.602806\pi$
$252$		0			0
$253$	0.192972	−	0.0305637i	0.000762734	−	0.000120805i
$254$		0			0
$255$	−6.07995	+	24.7711i	−0.0238429	+	0.0971414i
$256$		0			0
$257$	176.897	+	176.897i	0.688314	+	0.688314i	0.961859	−	0.273545i	$-0.0881964\pi$
$257$	176.897	+	176.897i	0.688314	+	0.688314i	−0.273545	+	0.961859i	$0.588196\pi$
$258$		0			0
$259$	111.832	−	36.3363i	0.431782	−	0.140295i
$260$		0			0
$261$	105.691	−	325.284i	0.404948	−	1.24630i
$262$		0			0
$263$	−398.342	−	202.966i	−1.51461	−	0.771732i	−0.518109	−	0.855314i	$-0.673364\pi$
$263$	−398.342	−	202.966i	−1.51461	−	0.771732i	−0.996501	+	0.0835821i	$0.973364\pi$
$264$		0			0
$265$	−16.3006	+	194.510i	−0.0615117	+	0.734000i
$266$		0			0
$267$	20.8717	+	3.30575i	0.0781711	+	0.0123811i
$268$		0			0
$269$	23.4782	+	32.3149i	0.0872794	+	0.120130i	0.850424	−	0.526098i	$-0.176346\pi$
$269$	23.4782	+	32.3149i	0.0872794	+	0.120130i	−0.763144	+	0.646228i	$0.776346\pi$
$270$		0			0
$271$	106.223	+	77.1756i	0.391967	+	0.284781i	0.766261	−	0.642529i	$-0.222115\pi$
$271$	106.223	+	77.1756i	0.391967	+	0.284781i	−0.374294	+	0.927310i	$0.622115\pi$
$272$		0			0
$273$	−8.50644	−	16.6948i	−0.0311591	−	0.0611532i
$274$		0			0
$275$	−0.284515	+	0.278805i	−0.00103460	+	0.00101384i
$276$		0			0
$277$	−162.600	+	82.8488i	−0.587003	+	0.299093i	−0.722154	−	0.691732i	$-0.756848\pi$
$277$	−162.600	+	82.8488i	−0.587003	+	0.299093i	0.135151	+	0.990825i	$0.456848\pi$
$278$		0			0
$279$	123.973	−	170.634i	0.444347	−	0.611592i
$280$		0			0
$281$	−152.477	+	110.781i	−0.542621	+	0.394237i	−0.825058	−	0.565049i	$-0.808857\pi$
$281$	−152.477	+	110.781i	−0.542621	+	0.394237i	0.282436	+	0.959286i	$0.408857\pi$
$282$		0			0
$283$	39.6693	−	250.462i	0.140174	−	0.885024i	−0.812926	−	0.582368i	$-0.802126\pi$
$283$	39.6693	−	250.462i	0.140174	−	0.885024i	0.953100	−	0.302657i	$-0.0978735\pi$
$284$		0			0
$285$	−4.32839	+	2.62236i	−0.0151873	+	0.00920126i
$286$		0			0
$287$	138.865	−	272.537i	0.483849	−	0.949606i
$288$		0			0
$289$	−13.7648	−	4.47244i	−0.0476289	−	0.0154756i
$290$		0			0
$291$	6.59454	+	20.2959i	0.0226617	+	0.0697454i
$292$		0			0
$293$	−371.385	+	371.385i	−1.26752	+	1.26752i	−0.320161	+	0.947363i	$0.603737\pi$
$293$	−371.385	+	371.385i	−1.26752	+	1.26752i	−0.947363	+	0.320161i	$0.896263\pi$
$294$		0			0
$295$	17.1226	+	232.632i	0.0580429	+	0.788582i
$296$		0			0
$297$	−0.0137410	−	0.0867575i	−4.62661e−5	−	0.000292113i
$298$		0			0
$299$		−	101.282i		−	0.338736i
$300$		0			0
$301$	−481.636			−1.60012
$302$		0			0
$303$	−4.95853	+	0.785354i	−0.0163648	+	0.00259193i
$304$		0			0
$305$	−76.3542	−	47.3239i	−0.250342	−	0.155160i
$306$		0			0
$307$	192.147	+	192.147i	0.625887	+	0.625887i	0.947031	−	0.321143i	$-0.104067\pi$
$307$	192.147	+	192.147i	0.625887	+	0.625887i	−0.321143	+	0.947031i	$0.604067\pi$
$308$		0			0
$309$	3.24414	−	1.05408i	0.0104988	−	0.00341127i
$310$		0			0
$311$	167.394	−	515.187i	0.538246	−	1.65655i	−0.198284	−	0.980145i	$-0.563537\pi$
$311$	167.394	−	515.187i	0.538246	−	1.65655i	0.736530	−	0.676405i	$-0.236463\pi$
$312$		0			0
$313$	−100.623	−	51.2702i	−0.321481	−	0.163803i	0.285801	−	0.958289i	$-0.407740\pi$
$313$	−100.623	−	51.2702i	−0.321481	−	0.163803i	−0.607282	+	0.794486i	$0.707740\pi$
$314$		0			0
$315$	−214.317	+	248.373i	−0.680371	+	0.788484i
$316$		0			0
$317$	371.223	+	58.7959i	1.17105	+	0.185476i	0.711507	−	0.702680i	$-0.248013\pi$
$317$	371.223	+	58.7959i	1.17105	+	0.185476i	0.459543	+	0.888156i	$0.348013\pi$
$318$		0			0
$319$	0.359711	+	0.495100i	0.00112762	+	0.00155204i
$320$		0			0
$321$	39.1231	+	28.4246i	0.121879	+	0.0885501i
$322$		0			0
$323$	24.7288	+	48.5331i	0.0765599	+	0.150257i
$324$		0			0
$325$	119.679	+	168.285i	0.368242	+	0.517799i
$326$		0			0
$327$	44.6447	−	22.7476i	0.136528	−	0.0695645i
$328$		0			0
$329$	−126.395	+	173.968i	−0.384181	+	0.528779i
$330$		0			0
$331$	−245.947	+	178.691i	−0.743044	+	0.539853i	−0.893663	−	0.448739i	$-0.851873\pi$
$331$	−245.947	+	178.691i	−0.743044	+	0.539853i	0.150619	+	0.988592i	$0.451873\pi$
$332$		0			0
$333$	22.2332	−	140.375i	0.0667662	−	0.421545i
$334$		0			0
$335$	161.463	−	384.285i	0.481978	−	1.14712i
$336$		0			0
$337$	−120.484	+	236.463i	−0.357519	+	0.701671i	−0.997788	−	0.0664804i	$-0.978823\pi$
$337$	−120.484	+	236.463i	−0.357519	+	0.701671i	0.640269	+	0.768151i	$0.278823\pi$
$338$		0			0
$339$	16.6373	+	5.40577i	0.0490775	+	0.0159462i
$340$		0			0
$341$	0.116619	+	0.358916i	0.000341991	+	0.00105254i
$342$		0			0
$343$	−227.753	+	227.753i	−0.664004	+	0.664004i
$344$		0			0
$345$	17.4754	−	7.13499i	0.0506533	−	0.0206811i
$346$		0			0
$347$	74.7456	+	471.925i	0.215405	+	1.36002i	0.824025	+	0.566553i	$0.191723\pi$
$347$	74.7456	+	471.925i	0.215405	+	1.36002i	−0.608620	+	0.793462i	$0.708277\pi$
$348$		0			0
$349$		−	668.360i		−	1.91507i	−0.288313	−	0.957536i	$-0.593094\pi$
$349$		−	668.360i		−	1.91507i	0.288313	−	0.957536i	$-0.406906\pi$
$350$		0			0
$351$	−45.5351			−0.129730
$352$		0			0
$353$	−407.821	+	64.5925i	−1.15530	+	0.182982i	−0.704540	−	0.709664i	$-0.748847\pi$
$353$	−407.821	+	64.5925i	−1.15530	+	0.182982i	−0.450759	+	0.892645i	$0.648847\pi$
$354$		0			0
$355$	−414.309	+	350.237i	−1.16707	+	0.986584i
$356$		0			0
$357$	−26.5764	−	26.5764i	−0.0744437	−	0.0744437i
$358$		0			0
$359$	208.215	−	67.6531i	0.579985	−	0.188449i	−0.00430872	−	0.999991i	$-0.501372\pi$
$359$	208.215	−	67.6531i	0.579985	−	0.188449i	0.584294	+	0.811542i	$0.301372\pi$
$360$		0			0
$361$	108.215	−	333.053i	0.299766	−	0.922584i
$362$		0			0
$363$	−33.1933	−	16.9128i	−0.0914416	−	0.0465918i
$364$		0			0
$365$	−610.211	+	143.232i	−1.67181	+	0.392415i
$366$		0			0
$367$	−434.943	−	68.8883i	−1.18513	−	0.187706i	−0.467413	−	0.884039i	$-0.654814\pi$
$367$	−434.943	−	68.8883i	−1.18513	−	0.187706i	−0.717719	+	0.696333i	$0.754814\pi$
$368$		0			0
$369$	−217.307	−	299.097i	−0.588908	−	0.810562i
$370$		0			0
$371$	−232.693	−	169.061i	−0.627204	−	0.455690i
$372$		0			0
$373$	202.184	+	396.808i	0.542047	+	1.06383i	0.985839	+	0.167697i	$0.0536331\pi$
$373$	202.184	+	396.808i	0.542047	+	1.06383i	−0.443791	+	0.896130i	$0.646367\pi$
$374$		0			0
$375$	−20.6051	+	32.5046i	−0.0549469	+	0.0866789i
$376$		0			0
$377$	282.668	−	144.026i	0.749781	−	0.382033i
$378$		0			0
$379$	13.1824	−	18.1441i	0.0347822	−	0.0478735i	−0.791272	−	0.611465i	$-0.790581\pi$
$379$	13.1824	−	18.1441i	0.0347822	−	0.0478735i	0.826054	+	0.563591i	$0.190581\pi$
$380$		0			0
$381$	42.3981	−	30.8040i	0.111281	−	0.0808505i
$382$		0			0
$383$	−10.8701	+	68.6309i	−0.0283814	+	0.179193i	−0.997807	−	0.0661930i	$-0.978915\pi$
$383$	−10.8701	+	68.6309i	−0.0283814	+	0.179193i	0.969425	+	0.245386i	$0.0789147\pi$
$384$		0			0
$385$	−0.134134	−	0.571453i	−0.000348400	−	0.00148429i
$386$		0			0
$387$	−264.287	+	518.693i	−0.682913	+	1.34029i
$388$		0			0
$389$	198.486	+	64.4919i	0.510246	+	0.165789i	0.552814	−	0.833305i	$-0.313554\pi$
$389$	198.486	+	64.4919i	0.510246	+	0.165789i	−0.0425683	+	0.999094i	$0.513554\pi$
$390$		0			0
$391$	−62.7806	−	193.219i	−0.160564	−	0.494166i
$392$		0			0
$393$	52.1992	−	52.1992i	0.132822	−	0.132822i
$394$		0			0
$395$	−432.562	−	511.694i	−1.09509	−	1.29543i
$396$		0			0
$397$	−63.3818	−	400.177i	−0.159652	−	1.00800i	−0.929244	−	0.369466i	$-0.879540\pi$
$397$	−63.3818	−	400.177i	−0.159652	−	1.00800i	0.769592	−	0.638536i	$-0.220460\pi$
$398$		0			0
$399$		−	7.45732i		−	0.0186900i
$400$		0			0
$401$	−769.970			−1.92012			−0.960062	−	0.279788i	$-0.909736\pi$
$401$	−769.970			−1.92012			−0.960062	+	0.279788i	$0.909736\pi$
$402$		0			0
$403$	193.226	−	30.6040i	0.479470	−	0.0759406i
$404$		0			0
$405$	148.268	+	363.146i	0.366094	+	0.896657i
$406$		0			0
$407$	0.179818	+	0.179818i	0.000441812	+	0.000441812i
$408$		0			0
$409$	527.294	−	171.328i	1.28923	−	0.418895i	0.417407	−	0.908720i	$-0.362939\pi$
$409$	527.294	−	171.328i	1.28923	−	0.418895i	0.871821	+	0.489824i	$0.162939\pi$
$410$		0			0
$411$	3.24095	−	9.97463i	0.00788553	−	0.0242692i
$412$		0			0
$413$	−306.257	−	156.046i	−0.741543	−	0.377835i
$414$		0			0
$415$	603.440	+	253.544i	1.45407	+	0.610948i
$416$		0			0
$417$	17.5040	+	2.77235i	0.0419759	+	0.00664833i
$418$		0			0
$419$	−145.995	−	200.945i	−0.348437	−	0.479583i	0.598445	−	0.801164i	$-0.295786\pi$
$419$	−145.995	−	200.945i	−0.348437	−	0.479583i	−0.946882	+	0.321581i	$0.895786\pi$
$420$		0			0
$421$	614.701	+	446.607i	1.46010	+	1.06082i	0.983337	+	0.181791i	$0.0581893\pi$
$421$	614.701	+	446.607i	1.46010	+	1.06082i	0.476761	+	0.879033i	$0.341811\pi$
$422$		0			0
$423$	117.997	+	231.582i	0.278952	+	0.547474i
$424$		0			0
$425$	332.627	+	246.857i	0.782652	+	0.580841i
$426$		0			0
$427$	117.942	−	60.0944i	0.276211	−	0.140736i
$428$		0			0
$429$	0.0238182	−	0.0327829i	5.55202e−5	−	7.64171e-5i
$430$		0			0
$431$	103.495	−	75.1934i	0.240127	−	0.174463i	−0.461213	−	0.887290i	$-0.652586\pi$
$431$	103.495	−	75.1934i	0.240127	−	0.174463i	0.701340	+	0.712827i	$0.252586\pi$
$432$		0			0
$433$	84.3368	−	532.482i	0.194773	−	1.22975i	−0.675567	−	0.737299i	$-0.736101\pi$
$433$	84.3368	−	532.482i	0.194773	−	1.22975i	0.870340	−	0.492451i	$-0.163899\pi$
$434$		0			0
$435$	44.7635	+	38.6257i	0.102905	+	0.0887947i
$436$		0			0
$437$	18.3005	−	35.9167i	0.0418775	−	0.0821892i
$438$		0			0
$439$	−212.729	−	69.1197i	−0.484576	−	0.157448i	0.0565333	−	0.998401i	$-0.481995\pi$
$439$	−212.729	−	69.1197i	−0.484576	−	0.157448i	−0.541109	+	0.840953i	$0.681995\pi$
$440$		0			0
$441$	−14.5392	−	44.7471i	−0.0329688	−	0.101467i
$442$		0			0
$443$	−247.036	+	247.036i	−0.557644	+	0.557644i	−0.928636	−	0.370992i	$-0.879018\pi$
$443$	−247.036	+	247.036i	−0.557644	+	0.557644i	0.370992	+	0.928636i	$0.379018\pi$
$444$		0			0
$445$	180.792	−	291.697i	0.406274	−	0.655498i
$446$		0			0
$447$	−3.52627	−	22.2640i	−0.00788874	−	0.0498076i
$448$		0			0
$449$			449.315i			1.00070i	0.865823	+	0.500350i	$0.166795\pi$
$449$			449.315i			1.00070i	−0.865823	+	0.500350i	$0.833205\pi$
$450$		0			0
$451$	0.661506			0.00146675
$452$		0			0
$453$	72.9640	−	11.5564i	0.161068	−	0.0255107i
$454$		0			0
$455$	−303.468	+	22.3365i	−0.666962	+	0.0490911i
$456$		0			0
$457$	387.513	+	387.513i	0.847951	+	0.847951i	0.989877	−	0.141927i	$-0.0453297\pi$
$457$	387.513	+	387.513i	0.847951	+	0.847951i	−0.141927	+	0.989877i	$0.545330\pi$
$458$		0			0
$459$	−86.8687	+	28.2253i	−0.189256	+	0.0614931i
$460$		0			0
$461$	99.5542	−	306.396i	0.215953	−	0.664634i	−0.783132	−	0.621856i	$-0.786379\pi$
$461$	99.5542	−	306.396i	0.215953	−	0.664634i	0.999085	−	0.0427785i	$-0.0136210\pi$
$462$		0			0
$463$	−507.902	−	258.789i	−1.09698	−	0.558939i	−0.190714	−	0.981646i	$-0.561080\pi$
$463$	−507.902	−	258.789i	−1.09698	−	0.558939i	−0.906267	+	0.422706i	$0.861080\pi$
$464$		0			0
$465$	18.8926	+	31.1836i	0.0406293	+	0.0670615i
$466$		0			0
$467$	512.366	+	81.1507i	1.09714	+	0.173770i	0.678659	−	0.734454i	$-0.262562\pi$
$467$	512.366	+	81.1507i	1.09714	+	0.173770i	0.418484	+	0.908224i	$0.362562\pi$
$468$		0			0
$469$	361.026	+	496.910i	0.769779	+	1.05951i
$470$		0			0
$471$	−11.8435	−	8.60484i	−0.0251455	−	0.0182693i
$472$		0			0
$473$	−0.472884	−	0.928088i	−0.000999755	−	0.00196213i
$474$		0			0
$475$	12.0334	+	81.3015i	0.0253336	+	0.171161i
$476$		0			0
$477$	−309.754	+	157.827i	−0.649379	+	0.330875i
$478$		0			0
$479$	−385.360	+	530.403i	−0.804510	+	1.10731i	0.187638	+	0.982238i	$0.439917\pi$
$479$	−385.360	+	530.403i	−0.804510	+	1.10731i	−0.992147	+	0.125074i	$0.960083\pi$
$480$		0			0
$481$	106.651	−	77.4864i	0.221727	−	0.161094i
$482$		0			0
$483$	−4.35113	+	27.4719i	−0.00900855	+	0.0568777i
$484$		0			0
$485$	345.356	+	28.9420i	0.712075	+	0.0596743i
$486$		0			0
$487$	337.237	−	661.865i	0.692479	−	1.35907i	−0.230065	−	0.973175i	$-0.573894\pi$
$487$	337.237	−	661.865i	0.692479	−	1.35907i	0.922544	−	0.385891i	$-0.126106\pi$
$488$		0			0
$489$	1.49291	+	0.485075i	0.00305298	+	0.000991973i
$490$		0			0
$491$	253.951	+	781.581i	0.517212	+	1.59182i	0.779221	+	0.626750i	$0.215615\pi$
$491$	253.951	+	781.581i	0.517212	+	1.59182i	−0.262009	+	0.965066i	$0.584385\pi$
$492$		0			0
$493$	449.977	−	449.977i	0.912732	−	0.912732i
$494$		0			0
$495$	−0.689023	−	0.169118i	−0.00139197	−	0.000341652i
$496$		0			0
$497$	−125.056	−	789.572i	−0.251622	−	1.58868i
$498$		0			0
$499$		−	214.512i		−	0.429883i	−0.976627	−	0.214941i	$-0.931044\pi$
$499$		−	214.512i		−	0.429883i	0.976627	−	0.214941i	$-0.0689561\pi$
$500$		0			0
$501$	23.8565			0.0476178
$502$		0			0
$503$	−267.349	+	42.3440i	−0.531510	+	0.0841829i	−0.416420	−	0.909172i	$-0.636715\pi$
$503$	−267.349	+	42.3440i	−0.531510	+	0.0841829i	−0.115089	+	0.993355i	$0.536715\pi$
$504$		0			0
$505$	−19.4344	+	79.1799i	−0.0384839	+	0.156792i
$506$		0			0
$507$	21.9386	+	21.9386i	0.0432714	+	0.0432714i
$508$		0			0
$509$	−29.0432	+	9.43670i	−0.0570593	+	0.0185397i	−0.337408	−	0.941359i	$-0.609550\pi$
$509$	−29.0432	+	9.43670i	−0.0570593	+	0.0185397i	0.280348	+	0.959898i	$0.409550\pi$
$510$		0			0
$511$	285.412	−	878.407i	0.558536	−	1.71900i
$512$		0			0
$513$	−16.1477	−	8.22765i	−0.0314769	−	0.0160383i
$514$		0			0
$515$	4.62615	−	55.2024i	0.00898282	−	0.107189i
$516$		0			0
$517$	−0.459327	−	0.0727502i	−0.000888446	−	0.000140716i
$518$		0			0
$519$	−3.31972	−	4.56920i	−0.00639637	−	0.00880385i
$520$		0			0
$521$	666.465	+	484.215i	1.27920	+	0.929395i	0.999529	−	0.0306998i	$-0.00977359\pi$
$521$	666.465	+	484.215i	1.27920	+	0.929395i	0.279674	+	0.960095i	$0.409774\pi$
$522$		0			0
$523$	389.695	+	764.820i	0.745115	+	1.46237i	0.881734	+	0.471746i	$0.156376\pi$
$523$	389.695	+	764.820i	0.745115	+	1.46237i	−0.136620	+	0.990624i	$0.543624\pi$
$524$		0			0
$525$	−25.2322	−	50.7872i	−0.0480614	−	0.0967376i
$526$		0			0
$527$	349.653	−	178.157i	0.663478	−	0.338059i
$528$		0			0
$529$	222.565	−	306.335i	0.420728	−	0.579083i
$530$		0			0
$531$	−336.104	+	244.194i	−0.632964	+	0.459876i
$532$		0			0
$533$	53.6446	−	338.698i	0.100646	−	0.635457i
$534$		0			0
$535$	671.688	−	406.943i	1.25549	−	0.760641i
$536$		0			0
$537$	−41.9786	+	82.3877i	−0.0781725	+	0.153422i
$538$		0			0
$539$	0.0800652	+	0.0260148i	0.000148544	+	4.82649e-5i
$540$		0			0
$541$	−78.9271	−	242.913i	−0.145891	−	0.449007i	0.851233	−	0.524787i	$-0.175855\pi$
$541$	−78.9271	−	242.913i	−0.145891	−	0.449007i	−0.997125	+	0.0757807i	$0.975855\pi$
$542$		0			0
$543$	−34.4793	+	34.4793i	−0.0634978	+	0.0634978i
$544$		0			0
$545$	−59.7313	−	811.522i	−0.109599	−	1.48903i
$546$		0			0
$547$	124.567	+	786.484i	0.227727	+	1.43781i	0.791139	+	0.611636i	$0.209488\pi$
$547$	124.567	+	786.484i	0.227727	+	1.43781i	−0.563412	+	0.826176i	$0.690512\pi$
$548$		0			0
$549$		−	159.992i		−	0.291424i
$550$		0			0
$551$	126.263			0.229153
$552$		0			0
$553$	975.166	−	154.451i	1.76341	−	0.279297i
$554$		0			0
$555$	20.8828	+	12.9430i	0.0376267	+	0.0233208i
$556$		0			0
$557$	−305.214	−	305.214i	−0.547960	−	0.547960i	0.377890	−	0.925850i	$-0.376650\pi$
$557$	−305.214	−	305.214i	−0.547960	−	0.547960i	−0.925850	+	0.377890i	$0.876650\pi$
$558$		0			0
$559$	−513.540	+	166.859i	−0.918676	+	0.298496i
$560$		0			0
$561$	0.0251179	−	0.0773048i	4.47734e−5	−	0.000137798i
$562$		0			0
$563$	23.8528	+	12.1536i	0.0423674	+	0.0215873i	0.475046	−	0.879961i	$-0.342431\pi$
$563$	23.8528	+	12.1536i	0.0423674	+	0.0215873i	−0.432678	+	0.901548i	$0.642431\pi$
$564$		0			0
$565$	185.596	−	215.088i	0.328489	−	0.380687i
$566$		0			0
$567$	−570.879	−	90.4184i	−1.00684	−	0.159468i
$568$		0			0
$569$	356.899	+	491.229i	0.627239	+	0.863320i	0.997855	−	0.0654660i	$-0.0208534\pi$
$569$	356.899	+	491.229i	0.627239	+	0.863320i	−0.370616	+	0.928786i	$0.620853\pi$
$570$		0			0
$571$	513.921	+	373.385i	0.900036	+	0.653915i	0.938475	−	0.345346i	$-0.112239\pi$
$571$	513.921	+	373.385i	0.900036	+	0.653915i	−0.0384389	+	0.999261i	$0.512239\pi$
$572$		0			0
$573$	−17.5339	−	34.4122i	−0.0306001	−	0.0600562i
$574$		0			0
$575$	3.10720	−	306.527i	0.00540383	−	0.533090i
$576$		0			0
$577$	−859.619	+	437.998i	−1.48981	+	0.759095i	−0.994004	−	0.109340i	$-0.965126\pi$
$577$	−859.619	+	437.998i	−1.48981	+	0.759095i	−0.495803	+	0.868435i	$0.665126\pi$
$578$		0			0
$579$	46.5420	−	64.0595i	0.0803834	−	0.110638i
$580$		0			0
$581$	−780.294	+	566.916i	−1.34302	+	0.975760i
$582$		0			0
$583$	0.0973076	−	0.614376i	0.000166908	−	0.00105382i
$584$		0			0
$585$	−142.466	+	339.073i	−0.243532	+	0.579612i
$586$		0			0
$587$	33.1929	−	65.1447i	0.0565467	−	0.110979i	−0.861004	−	0.508599i	$-0.830164\pi$
$587$	33.1929	−	65.1447i	0.0565467	−	0.110979i	0.917550	+	0.397620i	$0.130164\pi$
$588$		0			0
$589$	74.0517	+	24.0608i	0.125724	+	0.0408503i
$590$		0			0
$591$	−12.6750	−	39.0096i	−0.0214467	−	0.0660060i
$592$		0			0
$593$	−11.1016	+	11.1016i	−0.0187211	+	0.0187211i	−0.716405	−	0.697684i	$-0.754214\pi$
$593$	−11.1016	+	11.1016i	−0.0187211	+	0.0187211i	0.697684	+	0.716405i	$0.254214\pi$
$594$		0			0
$595$	−565.089	+	230.719i	−0.949729	+	0.387763i
$596$		0			0
$597$	−4.24244	−	26.7857i	−0.00710627	−	0.0448672i
$598$		0			0
$599$			460.985i			0.769592i	0.923002	+	0.384796i	$0.125728\pi$
$599$			460.985i			0.769592i	−0.923002	+	0.384796i	$0.874272\pi$
$600$		0			0
$601$	−685.715			−1.14096			−0.570478	−	0.821313i	$-0.693242\pi$
$601$	−685.715			−1.14096			−0.570478	+	0.821313i	$0.693242\pi$
$602$		0			0
$603$	733.247	−	116.135i	1.21600	−	0.192595i
$604$		0			0
$605$	−462.030	+	390.579i	−0.763686	+	0.645584i
$606$		0			0
$607$	−296.064	−	296.064i	−0.487749	−	0.487749i	0.419846	−	0.907595i	$-0.362084\pi$
$607$	−296.064	−	296.064i	−0.487749	−	0.487749i	−0.907595	+	0.419846i	$0.862084\pi$
$608$		0			0
$609$	−82.8586	+	26.9224i	−0.136057	+	0.0442076i
$610$		0			0
$611$	−74.4979	+	229.281i	−0.121928	+	0.375255i
$612$		0			0
$613$	289.170	+	147.339i	0.471729	+	0.240358i	0.673659	−	0.739042i	$-0.264721\pi$
$613$	289.170	+	147.339i	0.471729	+	0.240358i	−0.201930	+	0.979400i	$0.564721\pi$
$614$		0			0
$615$	62.2186	−	14.6042i	0.101168	−	0.0237467i
$616$		0			0
$617$	−139.099	−	22.0311i	−0.225444	−	0.0357068i	0.0426905	−	0.999088i	$-0.486407\pi$
$617$	−139.099	−	22.0311i	−0.225444	−	0.0357068i	−0.268134	+	0.963382i	$0.586407\pi$
$618$		0			0
$619$	−275.089	−	378.627i	−0.444409	−	0.611676i	0.526776	−	0.850004i	$-0.323401\pi$
$619$	−275.089	−	378.627i	−0.444409	−	0.611676i	−0.971185	+	0.238328i	$0.923401\pi$
$620$		0			0
$621$	54.6856	+	39.7314i	0.0880605	+	0.0639797i
$622$		0			0
$623$	229.579	+	450.575i	0.368506	+	0.723234i
$624$		0			0
$625$	357.040	+	512.979i	0.571264	+	0.820766i
$626$		0			0
$627$	0.0143699	−	0.00732182i	2.29185e−5	−	1.16775e-5i
$628$		0			0
$629$	155.430	−	213.931i	0.247107	−	0.340114i
$630$		0			0
$631$	742.298	−	539.311i	1.17638	−	0.854693i	0.184624	−	0.982809i	$-0.440893\pi$
$631$	742.298	−	539.311i	1.17638	−	0.854693i	0.991759	+	0.128116i	$0.0408931\pi$
$632$		0			0
$633$	−10.7128	+	67.6378i	−0.0169238	+	0.106853i
$634$		0			0
$635$	−194.485	−	828.568i	−0.306276	−	1.30483i
$636$		0			0
$637$	19.8127	−	38.8846i	0.0311032	−	0.0610434i
$638$		0			0
$639$	−918.943	−	298.583i	−1.43810	−	0.467266i
$640$		0			0
$641$	223.674	+	688.399i	0.348946	+	1.07394i	0.959437	+	0.281922i	$0.0909720\pi$
$641$	223.674	+	688.399i	0.348946	+	1.07394i	−0.610491	+	0.792023i	$0.709028\pi$
$642$		0			0
$643$	126.289	−	126.289i	0.196405	−	0.196405i	−0.602052	−	0.798457i	$-0.705650\pi$
$643$	126.289	−	126.289i	0.196405	−	0.196405i	0.798457	+	0.602052i	$0.205650\pi$
$644$		0			0
$645$	−64.9672	−	76.8522i	−0.100724	−	0.119151i
$646$		0			0
$647$	45.1994	+	285.378i	0.0698600	+	0.441079i	0.997682	+	0.0680545i	$0.0216792\pi$
$647$	45.1994	+	285.378i	0.0698600	+	0.441079i	−0.927822	+	0.373024i	$0.878321\pi$
$648$		0			0
$649$		−	0.743352i		−	0.00114538i
$650$		0			0
$651$	−53.7258			−0.0825281
$652$		0			0
$653$	−27.7696	+	4.39828i	−0.0425263	+	0.00673550i	−0.177661	−	0.984092i	$-0.556853\pi$
$653$	−27.7696	+	4.39828i	−0.0425263	+	0.00673550i	0.135135	+	0.990827i	$0.456853\pi$
$654$		0			0
$655$	−453.159	−	1109.90i	−0.691846	−	1.69451i
$656$		0			0
$657$	−789.378	−	789.378i	−1.20149	−	1.20149i
$658$		0			0
$659$	−251.811	+	81.8182i	−0.382110	+	0.124155i	−0.493773	−	0.869591i	$-0.664382\pi$
$659$	−251.811	+	81.8182i	−0.382110	+	0.124155i	0.111662	+	0.993746i	$0.464382\pi$
$660$		0			0
$661$	−189.648	+	583.677i	−0.286911	+	0.883021i	0.698908	+	0.715211i	$0.253670\pi$
$661$	−189.648	+	583.677i	−0.286911	+	0.883021i	−0.985819	+	0.167810i	$0.946330\pi$
$662$		0			0
$663$	−37.5440	−	19.1296i	−0.0566275	−	0.0288531i
$664$		0			0
$665$	−111.652	−	46.9120i	−0.167897	−	0.0705443i
$666$		0			0
$667$	−465.140	−	73.6709i	−0.697361	−	0.110451i
$668$		0			0
$669$	16.1387	+	22.2131i	0.0241237	+	0.0332034i
$670$		0			0
$671$	0.231598	+	0.168266i	0.000345153	+	0.000250768i
$672$		0			0
$673$	31.7428	+	62.2988i	0.0471662	+	0.0925689i	0.913387	−	0.407093i	$-0.133458\pi$
$673$	31.7428	+	62.2988i	0.0471662	+	0.0925689i	−0.866220	+	0.499662i	$0.833458\pi$
$674$		0			0
$675$	−137.810	−	1.39696i	−0.204164	−	0.00206956i
$676$		0			0
$677$	−480.023	+	244.584i	−0.709044	+	0.361276i	−0.771028	−	0.636801i	$-0.780257\pi$
$677$	−480.023	+	244.584i	−0.709044	+	0.361276i	0.0619841	+	0.998077i	$0.480257\pi$
$678$		0			0
$679$	−300.172	+	413.151i	−0.442079	+	0.608469i
$680$		0			0
$681$	−93.5683	+	67.9814i	−0.137398	+	0.0998258i
$682$		0			0
$683$	139.326	−	879.672i	0.203992	−	1.28795i	−0.646885	−	0.762587i	$-0.723929\pi$
$683$	139.326	−	879.672i	0.203992	−	1.28795i	0.850877	−	0.525365i	$-0.176071\pi$
$684$		0			0
$685$	−128.953	−	111.271i	−0.188252	−	0.162440i
$686$		0			0
$687$	−14.2972	+	28.0599i	−0.0208111	+	0.0408441i
$688$		0			0
$689$	−306.676	−	99.6451i	−0.445103	−	0.144623i
$690$		0			0
$691$	304.837	+	938.192i	0.441153	+	1.35773i	0.886648	+	0.462446i	$0.153028\pi$
$691$	304.837	+	938.192i	0.441153	+	1.35773i	−0.445494	+	0.895285i	$0.646972\pi$
$692$		0			0
$693$	0.739240	−	0.739240i	0.00106672	−	0.00106672i
$694$		0			0
$695$	151.620	−	244.630i	0.218159	−	0.351986i
$696$		0			0
$697$	−107.606	−	679.397i	−0.154384	−	0.974744i
$698$		0			0
$699$		−	15.2157i		−	0.0217678i
$700$		0			0
$701$	−817.348			−1.16597			−0.582987	−	0.812481i	$-0.698116\pi$
$701$	−817.348			−1.16597			−0.582987	+	0.812481i	$0.698116\pi$
$702$		0			0
$703$	51.8214	−	8.20770i	0.0737146	−	0.0116752i
$704$		0			0
$705$	−44.8086	+	3.29809i	−0.0635582	+	0.00467815i
$706$		0			0
$707$	−84.9506	−	84.9506i	−0.120156	−	0.120156i
$708$		0			0
$709$	−824.089	+	267.763i	−1.16233	+	0.377662i	−0.825773	−	0.564002i	$-0.809261\pi$
$709$	−824.089	+	267.763i	−1.16233	+	0.377662i	−0.336552	+	0.941665i	$0.609261\pi$
$710$		0			0
$711$	368.766	−	1134.95i	0.518659	−	1.59627i
$712$		0			0
$713$	−258.759	−	131.844i	−0.362916	−	0.184915i
$714$		0			0
$715$	−0.340995	−	0.562836i	−0.000476916	−	0.000787183i
$716$		0			0
$717$	−106.683	−	16.8969i	−0.148791	−	0.0235662i
$718$		0			0
$719$	702.075	+	966.323i	0.976460	+	1.34398i	0.938715	+	0.344694i	$0.112017\pi$
$719$	702.075	+	966.323i	0.976460	+	1.34398i	0.0377446	+	0.999287i	$0.487983\pi$
$720$		0			0
$721$	66.0388	+	47.9800i	0.0915933	+	0.0665464i
$722$		0			0
$723$	27.8760	+	54.7098i	0.0385561	+	0.0756706i
$724$		0			0
$725$	859.902	−	427.219i	1.18607	−	0.589267i
$726$		0			0
$727$	353.144	−	179.936i	0.485754	−	0.247504i	−0.193921	−	0.981017i	$-0.562121\pi$
$727$	353.144	−	179.936i	0.485754	−	0.247504i	0.679676	+	0.733513i	$0.262121\pi$
$728$		0			0
$729$	−401.654	+	552.829i	−0.550966	+	0.758339i
$730$		0			0
$731$	−876.265	+	636.644i	−1.19872	+	0.870922i
$732$		0			0
$733$	20.8879	−	131.881i	0.0284965	−	0.179920i	−0.969335	−	0.245744i	$-0.920968\pi$
$733$	20.8879	−	131.881i	0.0284965	−	0.179920i	0.997831	+	0.0658244i	$0.0209677\pi$
$734$		0			0
$735$	8.10495	+	0.679222i	0.0110271	+	0.000924112i
$736$		0			0
$737$	−0.603054	+	1.18356i	−0.000818255	+	0.00160592i
$738$		0			0
$739$	−164.642	−	53.4955i	−0.222791	−	0.0723891i	0.195495	−	0.980705i	$-0.437369\pi$
$739$	−164.642	−	53.4955i	−0.222791	−	0.0723891i	−0.418285	+	0.908316i	$0.637369\pi$
$740$		0			0
$741$	−2.58353	−	7.95130i	−0.00348655	−	0.0107305i
$742$		0			0
$743$	−587.217	+	587.217i	−0.790332	+	0.790332i	−0.981548	−	0.191216i	$-0.938757\pi$
$743$	−587.217	+	587.217i	−0.790332	+	0.790332i	0.191216	+	0.981548i	$0.438757\pi$
$744$		0			0
$745$	−355.521	−	87.2610i	−0.477209	−	0.117129i
$746$		0			0
$747$	182.366	+	1151.41i	0.244131	+	1.54138i
$748$		0			0
$749$			1157.24i			1.54505i
$750$		0			0
$751$	1229.55			1.63721			0.818607	−	0.574354i	$-0.194747\pi$
$751$	1229.55			1.63721			0.818607	+	0.574354i	$0.194747\pi$
$752$		0			0
$753$	48.4506	−	7.67382i	0.0643434	−	0.0101910i
$754$		0			0
$755$	285.974	−	1165.12i	0.378773	−	1.54321i
$756$		0			0
$757$	178.090	+	178.090i	0.235258	+	0.235258i	0.814883	−	0.579625i	$-0.196801\pi$
$757$	178.090	+	178.090i	0.235258	+	0.235258i	−0.579625	+	0.814883i	$0.696801\pi$
$758$		0			0
$759$	−0.0572091	+	0.0185884i	−7.53743e−5	+	2.44906e-5i
$760$		0			0
$761$	−254.019	+	781.791i	−0.333797	+	1.02732i	0.633515	+	0.773731i	$0.281612\pi$
$761$	−254.019	+	781.791i	−0.333797	+	1.02732i	−0.967312	+	0.253591i	$0.918388\pi$
$762$		0			0
$763$	1068.36	+	544.357i	1.40021	+	0.713443i
$764$		0			0
$765$	−61.6096	+	735.168i	−0.0805354	+	0.961004i
$766$		0			0
$767$	−380.605	−	60.2819i	−0.496225	−	0.0785944i
$768$		0			0
$769$	−577.219	−	794.474i	−0.750610	−	1.03313i	−0.997937	−	0.0641945i	$-0.979552\pi$
$769$	−577.219	−	794.474i	−0.750610	−	1.03313i	0.247327	−	0.968932i	$-0.420448\pi$
$770$		0			0
$771$	−62.3128	−	45.2729i	−0.0808207	−	0.0587197i
$772$		0			0
$773$	−425.185	−	834.473i	−0.550046	−	1.07953i	−0.983930	−	0.178556i	$-0.942857\pi$
$773$	−425.185	−	834.473i	−0.550046	−	1.07953i	0.433884	−	0.900969i	$-0.357143\pi$
$774$		0			0
$775$	585.731	−	86.6941i	0.755782	−	0.111863i
$776$		0			0
$777$	−32.2570	+	16.4358i	−0.0415148	+	0.0211529i
$778$		0			0
$779$	80.2221	−	110.416i	0.102981	−	0.141741i
$780$		0			0
$781$	1.39868	−	1.01620i	0.00179088	−	0.00130115i
$782$		0			0
$783$	−33.1215	+	209.121i	−0.0423007	+	0.267076i
$784$		0			0
$785$	−203.337	+	123.192i	−0.259028	+	0.156932i
$786$		0			0
$787$	142.203	−	279.088i	0.180689	−	0.354623i	−0.782841	−	0.622222i	$-0.786230\pi$
$787$	142.203	−	279.088i	0.180689	−	0.354623i	0.963530	+	0.267599i	$0.0862302\pi$
$788$		0			0
$789$	130.908	+	42.5347i	0.165917	+	0.0539096i
$790$		0			0
$791$	129.362	+	398.135i	0.163542	+	0.503331i
$792$		0			0
$793$	104.935	−	104.935i	0.132327	−	0.132327i
$794$		0			0
$795$	−4.41139	−	59.9340i	−0.00554891	−	0.0753887i
$796$		0			0
$797$	−177.193	−	1118.75i	−0.222325	−	1.40370i	−0.806096	−	0.591785i	$-0.798423\pi$
$797$	−177.193	−	1118.75i	−0.222325	−	1.40370i	0.583771	−	0.811918i	$-0.301577\pi$
$798$		0			0
$799$			483.584i			0.605236i
$800$		0			0
$801$	611.218			0.763069
$802$		0			0
$803$	1.97287	−	0.312472i	0.00245687	−	0.000389131i
$804$		0			0
$805$	383.940	+	237.964i	0.476944	+	0.295607i
$806$		0			0
$807$	−8.69591	−	8.69591i	−0.0107756	−	0.0107756i
$808$		0			0
$809$	599.534	−	194.800i	0.741080	−	0.240792i	0.0859416	−	0.996300i	$-0.472610\pi$
$809$	599.534	−	194.800i	0.741080	−	0.240792i	0.655139	+	0.755509i	$0.272610\pi$
$810$		0			0
$811$	325.384	−	1001.43i	0.401213	−	1.23481i	−0.522803	−	0.852454i	$-0.675114\pi$
$811$	325.384	−	1001.43i	0.401213	−	1.23481i	0.924016	−	0.382354i	$-0.124886\pi$
$812$		0			0
$813$	−36.0186	−	18.3524i	−0.0443033	−	0.0225737i
$814$		0			0
$815$	16.6541	−	19.3005i	0.0204344	−	0.0236815i
$816$		0			0
$817$	−212.261	−	33.6188i	−0.259805	−	0.0411491i
$818$		0			0
$819$	−318.551	−	438.448i	−0.388951	−	0.535345i
$820$		0			0
$821$	814.064	+	591.452i	0.991552	+	0.720405i	0.960260	−	0.279105i	$-0.0900379\pi$
$821$	814.064	+	591.452i	0.991552	+	0.720405i	0.0312917	+	0.999510i	$0.490038\pi$
$822$		0			0
$823$	−162.195	−	318.326i	−0.197078	−	0.386787i	0.771226	−	0.636561i	$-0.219644\pi$
$823$	−162.195	−	318.326i	−0.197078	−	0.386787i	−0.968304	+	0.249774i	$0.919644\pi$
$824$		0			0
$825$	0.0730906	−	0.0984856i	8.85947e−5	−	0.000119376i
$826$		0			0
$827$	687.457	−	350.277i	0.831266	−	0.423551i	0.0140628	−	0.999901i	$-0.495524\pi$
$827$	687.457	−	350.277i	0.831266	−	0.423551i	0.817203	+	0.576350i	$0.195524\pi$
$828$		0			0
$829$	−80.1869	+	110.368i	−0.0967272	+	0.133134i	−0.854637	−	0.519225i	$-0.826221\pi$
$829$	−80.1869	+	110.368i	−0.0967272	+	0.133134i	0.757910	+	0.652359i	$0.226221\pi$
$830$		0			0
$831$	45.4550	−	33.0250i	0.0546992	−	0.0397413i
$832$		0			0
$833$	13.6943	−	86.4624i	0.0164397	−	0.103796i
$834$		0			0
$835$	150.075	−	357.182i	0.179730	−	0.427762i
$836$		0			0
$837$	−59.2755	+	116.335i	−0.0708190	+	0.138990i
$838$		0			0
$839$	167.630	+	54.4663i	0.199798	+	0.0649182i	0.407206	−	0.913336i	$-0.366503\pi$
$839$	167.630	+	54.4663i	0.199798	+	0.0649182i	−0.207409	+	0.978254i	$0.566503\pi$
$840$		0			0
$841$	−195.952	−	603.078i	−0.232999	−	0.717097i
$842$		0			0
$843$	41.0313	−	41.0313i	0.0486730	−	0.0486730i
$844$		0			0
$845$	466.476	−	190.457i	0.552042	−	0.225392i
$846$		0			0
$847$	−139.460	−	880.517i	−0.164652	−	1.03957i
$848$		0			0
$849$			78.0740i			0.0919600i
$850$		0			0
$851$	−195.693			−0.229957
$852$		0			0
$853$	1497.82	−	237.231i	1.75594	−	0.278113i	0.806310	−	0.591493i	$-0.201461\pi$
$853$	1497.82	−	237.231i	1.75594	−	0.278113i	0.949628	+	0.313379i	$0.101461\pi$
$854$		0			0
$855$	−111.788	+	94.5002i	−0.130746	+	0.110526i
$856$		0			0
$857$	−20.1336	−	20.1336i	−0.0234931	−	0.0234931i	0.695263	−	0.718756i	$-0.255288\pi$
$857$	−20.1336	−	20.1336i	−0.0234931	−	0.0234931i	−0.718756	+	0.695263i	$0.755288\pi$
$858$		0			0
$859$	−561.717	+	182.513i	−0.653920	+	0.212472i	−0.617142	−	0.786852i	$-0.711710\pi$
$859$	−561.717	+	182.513i	−0.653920	+	0.212472i	−0.0367783	+	0.999323i	$0.511710\pi$
$860$		0			0
$861$	−29.1013	+	89.5645i	−0.0337994	+	0.104024i
$862$		0			0
$863$	−215.182	−	109.640i	−0.249341	−	0.127046i	0.324854	−	0.945764i	$-0.394685\pi$
$863$	−215.182	−	109.640i	−0.249341	−	0.127046i	−0.574195	+	0.818719i	$0.694685\pi$
$864$		0			0
$865$	−89.2938	+	20.9595i	−0.103230	+	0.0242306i
$866$		0			0
$867$	4.40116	+	0.697075i	0.00507631	+	0.000804009i
$868$		0			0
$869$	1.25506	+	1.72745i	0.00144426	+	0.00198786i
$870$		0			0
$871$	557.091	+	404.751i	0.639600	+	0.464696i
$872$		0			0
$873$	280.226	+	549.974i	0.320992	+	0.629982i
$874$		0			0
$875$	−919.119	+	58.2905i	−1.05042	+	0.0666177i
$876$		0			0
$877$	−853.531	+	434.896i	−0.973239	+	0.495890i	−0.866923	−	0.498442i	$-0.833906\pi$
$877$	−853.531	+	434.896i	−0.973239	+	0.495890i	−0.106316	+	0.994332i	$0.533906\pi$
$878$		0			0
$879$	95.0479	−	130.822i	0.108132	−	0.148831i
$880$		0			0
$881$	730.560	−	530.783i	0.829239	−	0.602477i	−0.0901049	−	0.995932i	$-0.528720\pi$
$881$	730.560	−	530.783i	0.829239	−	0.602477i	0.919344	+	0.393455i	$0.128720\pi$
$882$		0			0
$883$	−27.0756	+	170.949i	−0.0306632	+	0.193600i	−0.998265	−	0.0588815i	$-0.981247\pi$
$883$	−27.0756	+	170.949i	−0.0306632	+	0.193600i	0.967602	+	0.252481i	$0.0812466\pi$
$884$		0			0
$885$	−16.4112	−	69.9167i	−0.0185437	−	0.0790020i
$886$		0			0
$887$	−11.0071	+	21.6026i	−0.0124093	+	0.0243546i	−0.897128	−	0.441771i	$-0.854350\pi$
$887$	−11.0071	+	21.6026i	−0.0124093	+	0.0243546i	0.884719	+	0.466125i	$0.154350\pi$
$888$		0			0
$889$	1192.73	+	387.543i	1.34166	+	0.435931i
$890$		0			0
$891$	−0.386274	−	1.18883i	−0.000433529	−	0.00133426i
$892$		0			0
$893$	−67.8467	+	67.8467i	−0.0759761	+	0.0759761i
$894$		0			0
$895$	969.438	+	1146.79i	1.08317	+	1.28132i
$896$		0			0
$897$	4.87810	+	30.7991i	0.00543824	+	0.0343357i
$898$		0			0
$899$		−	909.655i		−	1.01185i
$900$		0			0
$901$	−646.821			−0.717892
$902$		0			0
$903$	146.462	−	23.1972i	0.162195	−	0.0256891i
$904$		0			0
$905$	299.327	+	733.126i	0.330748	+	0.810084i
$906$		0			0
$907$	438.721	+	438.721i	0.483706	+	0.483706i	0.906313	−	0.422607i	$-0.138885\pi$
$907$	438.721	+	438.721i	0.483706	+	0.483706i	−0.422607	+	0.906313i	$0.638885\pi$
$908$		0			0
$909$	−138.101	+	44.8719i	−0.151927	+	0.0493640i
$910$		0			0
$911$	−272.037	+	837.244i	−0.298614	+	0.919038i	0.683370	+	0.730072i	$0.260514\pi$
$911$	−272.037	+	837.244i	−0.298614	+	0.919038i	−0.981984	+	0.188966i	$0.939486\pi$
$912$		0			0
$913$	−1.85853	−	0.946970i	−0.00203563	−	0.00103721i
$914$		0			0
$915$	25.4980	+	10.7133i	0.0278667	+	0.0117086i
$916$		0			0
$917$	1744.81	+	276.350i	1.90273	+	0.301363i
$918$		0			0
$919$	112.533	+	154.888i	0.122451	+	0.168540i	0.865842	−	0.500318i	$-0.166784\pi$
$919$	112.533	+	154.888i	0.122451	+	0.168540i	−0.743391	+	0.668858i	$0.766784\pi$
$920$		0			0
$921$	−67.6850	−	49.1760i	−0.0734908	−	0.0533942i
$922$		0			0
$923$	−406.881	−	798.549i	−0.440824	−	0.865167i
$924$		0			0
$925$	325.152	−	231.238i	0.351516	−	0.249987i
$926$		0			0
$927$	87.9089	−	44.7918i	0.0948316	−	0.0483191i
$928$		0			0
$929$	684.405	−	942.002i	0.736711	−	1.01400i	−0.262090	−	0.965043i	$-0.584412\pi$
$929$	684.405	−	942.002i	0.736711	−	1.01400i	0.998801	−	0.0489527i	$-0.0155883\pi$
$930$		0			0
$931$	14.0520	−	10.2093i	0.0150934	−	0.0109660i
$932$		0			0
$933$	−26.0901	+	164.726i	−0.0279637	+	0.176556i
$934$		0			0
$935$	−0.999404	−	0.862370i	−0.00106888	−	0.000922321i
$936$		0			0
$937$	−357.510	+	701.653i	−0.381547	+	0.748829i	−0.999295	−	0.0375477i	$-0.988045\pi$
$937$	−357.510	+	701.653i	−0.381547	+	0.748829i	0.617747	+	0.786377i	$0.288045\pi$
$938$		0			0
$939$	33.0681	+	10.7445i	0.0352163	+	0.0114425i
$940$		0			0
$941$	−87.1483	−	268.215i	−0.0926124	−	0.285032i	0.894012	−	0.448044i	$-0.147879\pi$
$941$	−87.1483	−	268.215i	−0.0926124	−	0.285032i	−0.986624	+	0.163012i	$0.947879\pi$
$942$		0			0
$943$	−359.954	+	359.954i	−0.381711	+	0.381711i
$944$		0			0
$945$	106.985	−	172.614i	0.113212	−	0.182661i
$946$		0			0
$947$	158.446	+	1000.39i	0.167313	+	1.05638i	0.918250	+	0.396001i	$0.129602\pi$
$947$	158.446	+	1000.39i	0.167313	+	1.05638i	−0.750937	+	0.660374i	$0.770398\pi$
$948$		0			0
$949$		−	1035.47i		−	1.09112i
$950$		0			0
$951$	−115.718			−0.121680
$952$		0			0
$953$	455.212	−	72.0985i	0.477662	−	0.0756542i	0.0870388	−	0.996205i	$-0.472260\pi$
$953$	455.212	−	72.0985i	0.477662	−	0.0756542i	0.390623	+	0.920551i	$0.372260\pi$
$954$		0			0
$955$	−625.523	+	46.0410i	−0.654997	+	0.0482105i
$956$		0			0
$957$	−0.133231	−	0.133231i	−0.000139217	−	0.000139217i
$958$		0			0
$959$	238.696	−	77.5570i	0.248901	−	0.0808728i
$960$		0			0
$961$	−123.621	+	380.465i	−0.128638	+	0.395906i
$962$		0			0
$963$	1246.28	+	635.011i	1.29416	+	0.659409i
$964$		0			0
$965$	−666.321	−	1099.81i	−0.690488	−	1.13970i
$966$		0			0
$967$	−989.452	−	156.714i	−1.02322	−	0.162062i	−0.377797	−	0.925889i	$-0.623318\pi$
$967$	−989.452	−	156.714i	−1.02322	−	0.162062i	−0.645421	+	0.763827i	$0.723318\pi$
$968$		0			0
$969$	−9.85736	−	13.5675i	−0.0101727	−	0.0140015i
$970$		0			0
$971$	−373.712	−	271.518i	−0.384873	−	0.279627i	0.378478	−	0.925610i	$-0.376448\pi$
$971$	−373.712	−	271.518i	−0.384873	−	0.279627i	−0.763351	+	0.645983i	$0.776448\pi$
$972$		0			0
$973$	192.536	+	377.873i	0.197879	+	0.388358i
$974$		0			0
$975$	−44.4985	−	45.4099i	−0.0456395	−	0.0465742i
$976$		0			0
$977$	−22.3418	+	11.3837i	−0.0228677	+	0.0116517i	−0.465387	−	0.885107i	$-0.654085\pi$
$977$	−22.3418	+	11.3837i	−0.0228677	+	0.0116517i	0.442519	+	0.896759i	$0.354085\pi$
$978$		0			0
$979$	−0.642826	+	0.884774i	−0.000656615	+	0.000903753i
$980$		0			0
$981$	1172.48	−	851.856i	1.19519	−	0.868355i
$982$		0			0
$983$	−188.847	+	1192.33i	−0.192112	+	1.21295i	0.683505	+	0.729946i	$0.260455\pi$
$983$	−188.847	+	1192.33i	−0.192112	+	1.21295i	−0.875618	+	0.483005i	$0.839545\pi$
$984$		0			0
$985$	−663.789	−	55.6278i	−0.673897	−	0.0564749i
$986$		0			0
$987$	30.0569	−	58.9900i	0.0304528	−	0.0597670i
$988$		0			0
$989$	762.329	+	247.696i	0.770808	+	0.250451i
$990$		0			0
$991$	−310.612	−	955.967i	−0.313433	−	0.964648i	−0.976395	−	0.215995i	$-0.930701\pi$
$991$	−310.612	−	955.967i	−0.313433	−	0.964648i	0.662961	−	0.748654i	$-0.269299\pi$
$992$		0			0
$993$	66.1843	−	66.1843i	0.0666508	−	0.0666508i
$994$		0			0
$995$	−427.726	−	104.983i	−0.429875	−	0.105511i
$996$		0			0
$997$	59.5222	+	375.808i	0.0597013	+	0.376939i	0.999390	+	0.0349096i	$0.0111143\pi$
$997$	59.5222	+	375.808i	0.0597013	+	0.376939i	−0.939689	+	0.342030i	$0.888886\pi$
$998$		0			0
$999$			87.9810i			0.0880691i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.3.u.a.97.4	yes	56
4.3	odd	2		400.3.bg.e.97.4		56
25.8	odd	20	inner	200.3.u.a.33.4	✓	56
100.83	even	20		400.3.bg.e.33.4		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.3.u.a.33.4	✓	56	25.8	odd	20	inner
200.3.u.a.97.4	yes	56	1.1	even	1	trivial
400.3.bg.e.33.4		56	100.83	even	20
400.3.bg.e.97.4		56	4.3	odd	2

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

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	200.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.304092 + 0.0481634i) q^{3} +(-1.19185 + 4.85587i) q^{5} +(-5.20977 - 5.20977i) q^{7} +(-8.46936 + 2.75186i) q^{9} +(0.00492385 - 0.0151541i) q^{11} +(-7.35975 - 3.74998i) q^{13} +(0.128557 - 1.53404i) q^{15} +(-16.3649 - 2.59194i) q^{17} +(-1.93234 - 2.65964i) q^{19} +(1.83517 + 1.33333i) q^{21} +(5.56670 + 10.9253i) q^{23} +(-22.1590 - 11.5750i) q^{25} +(4.91185 - 2.50271i) q^{27} +(-22.5752 + 31.0721i) q^{29} +(-19.1612 + 13.9214i) q^{31} +(-0.000767432 + 0.00484538i) q^{33} +(31.5073 - 19.0887i) q^{35} +(-7.24555 + 14.2202i) q^{37} +(2.41865 + 0.785868i) q^{39} +(12.8290 + 39.4837i) q^{41} +(46.2243 - 46.2243i) q^{43} +(-3.26846 - 44.4059i) q^{45} +(-4.56574 - 28.8270i) q^{47} +5.28342i q^{49} +5.10126 q^{51} +(38.5577 - 6.10694i) q^{53} +(0.0677177 + 0.0419710i) q^{55} +(0.715706 + 0.715706i) q^{57} +(44.3689 - 14.4163i) q^{59} +(-5.55183 + 17.0868i) q^{61} +(58.4600 + 29.7868i) q^{63} +(26.9812 - 31.2686i) q^{65} +(-82.3392 - 13.0412i) q^{67} +(-2.21899 - 3.05417i) q^{69} +(87.7801 + 63.7759i) q^{71} +(56.9118 + 111.696i) q^{73} +(7.29586 + 2.45260i) q^{75} +(-0.104601 + 0.0532970i) q^{77} +(-78.7669 + 108.413i) q^{79} +(63.4671 - 46.1115i) q^{81} +(20.4786 - 129.296i) q^{83} +(32.0906 - 76.3765i) q^{85} +(5.36840 - 10.5361i) q^{87} +(-65.2768 - 21.2097i) q^{89} +(18.8061 + 57.8792i) q^{91} +(5.15625 - 5.15625i) q^{93} +(15.2179 - 6.21329i) q^{95} +(-10.8430 - 68.4600i) q^{97} +0.141895i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 10 q^{5} - 4 q^{7} + 40 q^{9} - 16 q^{11} + 14 q^{13} - 10 q^{15} + 22 q^{17} + 50 q^{19} + 100 q^{21} - 48 q^{23} + 150 q^{25} - 210 q^{27} - 108 q^{31} - 140 q^{33} + 70 q^{35} + 236 q^{37} + 80 q^{39}+ \cdots + 386 q^{97}+O(q^{100}) \) 56 * q - 10 * q^5 - 4 * q^7 + 40 * q^9 - 16 * q^11 + 14 * q^13 - 10 * q^15 + 22 * q^17 + 50 * q^19 + 100 * q^21 - 48 * q^23 + 150 * q^25 - 210 * q^27 - 108 * q^31 - 140 * q^33 + 70 * q^35 + 236 * q^37 + 80 * q^39 + 104 * q^41 + 96 * q^43 + 20 * q^45 + 104 * q^47 - 200 * q^51 + 88 * q^53 - 140 * q^55 - 280 * q^57 + 200 * q^59 + 108 * q^61 - 654 * q^63 - 510 * q^65 - 282 * q^67 + 40 * q^69 + 470 * q^71 + 62 * q^73 + 350 * q^75 - 396 * q^77 - 560 * q^79 - 586 * q^81 - 468 * q^83 + 50 * q^85 - 280 * q^87 + 230 * q^89 - 62 * q^91 - 300 * q^93 - 360 * q^95 + 386 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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