LMFDB - Embedded newform 200.2.q.a.169.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,2,Mod(9,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("200.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	200.q (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.59700804043$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			169.7
Character	$\chi$	$=$	200.169
Dual form			200.2.q.a.129.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.35643 + 1.86696i) q^{3} +(1.16787 - 1.90685i) q^{5} +4.74404i q^{7} +(-0.718596 + 2.21161i) q^{9} +(-1.69253 - 5.20907i) q^{11} +(-0.855610 - 0.278005i) q^{13} +(5.14414 - 0.406141i) q^{15} +(-0.419832 + 0.577849i) q^{17} +(4.33157 + 3.14707i) q^{19} +(-8.85692 + 6.43493i) q^{21} +(-2.89267 + 0.939884i) q^{23} +(-2.27217 - 4.45390i) q^{25} +(1.48052 - 0.481050i) q^{27} +(-0.515235 + 0.374340i) q^{29} +(-4.88535 - 3.54941i) q^{31} +(7.42933 - 10.2256i) q^{33} +(9.04617 + 5.54041i) q^{35} +(-1.61438 - 0.524543i) q^{37} +(-0.641548 - 1.97448i) q^{39} +(3.19882 - 9.84495i) q^{41} -8.11200i q^{43} +(3.37799 + 3.95312i) q^{45} +(-0.534394 - 0.735531i) q^{47} -15.5059 q^{49} -1.64829 q^{51} +(-0.605064 - 0.832800i) q^{53} +(-11.9096 - 2.85610i) q^{55} +12.3556i q^{57} +(-1.73043 + 5.32571i) q^{59} +(2.52925 + 7.78422i) q^{61} +(-10.4920 - 3.40904i) q^{63} +(-1.52935 + 1.30685i) q^{65} +(0.801238 - 1.10281i) q^{67} +(-5.67841 - 4.12561i) q^{69} +(-1.26639 + 0.920086i) q^{71} +(7.71383 - 2.50637i) q^{73} +(5.23323 - 10.2834i) q^{75} +(24.7120 - 8.02942i) q^{77} +(-9.83997 + 7.14916i) q^{79} +(8.55024 + 6.21211i) q^{81} +(-7.54215 + 10.3809i) q^{83} +(0.611564 + 1.47541i) q^{85} +(-1.39776 - 0.454158i) q^{87} +(1.23150 + 3.79018i) q^{89} +(1.31886 - 4.05904i) q^{91} -13.9353i q^{93} +(11.0597 - 4.58431i) q^{95} +(5.26145 + 7.24176i) q^{97} +12.7367 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{5} + 10 q^{9} + 6 q^{11} + 12 q^{15} - 6 q^{19} - 4 q^{21} - 30 q^{23} + 6 q^{25} - 2 q^{29} + 6 q^{31} + 8 q^{35} - 40 q^{37} - 12 q^{39} - 12 q^{45} - 20 q^{47} - 60 q^{49} - 60 q^{51} - 30 q^{53}+ \cdots + 92 q^{99}+O(q^{100}) $ 32 * q + 2 * q^5 + 10 * q^9 + 6 * q^11 + 12 * q^15 - 6 * q^19 - 4 * q^21 - 30 * q^23 + 6 * q^25 - 2 * q^29 + 6 * q^31 + 8 * q^35 - 40 * q^37 - 12 * q^39 - 12 * q^45 - 20 * q^47 - 60 * q^49 - 60 * q^51 - 30 * q^53 - 28 * q^55 - 30 * q^59 + 14 * q^61 - 20 * q^63 - 26 * q^65 - 4 * q^69 + 12 * q^71 + 40 * q^73 + 16 * q^75 + 16 * q^79 - 52 * q^81 + 30 * q^83 + 60 * q^85 + 110 * q^87 + 24 * q^89 - 4 * q^91 + 68 * q^95 + 30 * q^97 + 92 * q^99

Character values

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

$n$	$101$	$151$	$177$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{10}\right)$

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
$3$	1.35643	+	1.86696i	0.783132	+	1.07789i	0.994929	+	0.100576i	$0.0320684\pi$
$3$	1.35643	+	1.86696i	0.783132	+	1.07789i	−0.211797	+	0.977314i	$0.567932\pi$
$4$		0			0
$5$	1.16787	−	1.90685i	0.522286	−	0.852770i
$5$	1.16787	−	1.90685i	0.522286	−	0.852770i
$6$		0			0
$7$			4.74404i			1.79308i	0.442966	+	0.896538i	$0.353926\pi$
$7$			4.74404i			1.79308i	−0.442966	+	0.896538i	$0.646074\pi$
$8$		0			0
$9$	−0.718596	+	2.21161i	−0.239532	+	0.737203i
$10$		0			0
$11$	−1.69253	−	5.20907i	−0.510317	−	1.57059i	−0.791645	−	0.610982i	$-0.790775\pi$
$11$	−1.69253	−	5.20907i	−0.510317	−	1.57059i	0.281328	−	0.959612i	$-0.409225\pi$
$12$		0			0
$13$	−0.855610	−	0.278005i	−0.237304	−	0.0771046i	0.187951	−	0.982178i	$-0.439815\pi$
$13$	−0.855610	−	0.278005i	−0.237304	−	0.0771046i	−0.425254	+	0.905074i	$0.639815\pi$
$14$		0			0
$15$	5.14414	−	0.406141i	1.32821	−	0.104865i
$16$		0			0
$17$	−0.419832	+	0.577849i	−0.101824	+	0.140149i	−0.856889	−	0.515502i	$-0.827606\pi$
$17$	−0.419832	+	0.577849i	−0.101824	+	0.140149i	0.755064	+	0.655651i	$0.227606\pi$
$18$		0			0
$19$	4.33157	+	3.14707i	0.993731	+	0.721988i	0.960735	−	0.277467i	$-0.0894951\pi$
$19$	4.33157	+	3.14707i	0.993731	+	0.721988i	0.0329963	+	0.999455i	$0.489495\pi$
$20$		0			0
$21$	−8.85692	+	6.43493i	−1.93274	+	1.40422i
$22$		0			0
$23$	−2.89267	+	0.939884i	−0.603163	+	0.195979i	−0.594650	−	0.803984i	$-0.702710\pi$
$23$	−2.89267	+	0.939884i	−0.603163	+	0.195979i	−0.00851216	+	0.999964i	$0.502710\pi$
$24$		0			0
$25$	−2.27217	−	4.45390i	−0.454434	−	0.890780i
$26$		0			0
$27$	1.48052	−	0.481050i	0.284926	−	0.0925781i
$28$		0			0
$29$	−0.515235	+	0.374340i	−0.0956768	+	0.0695132i	−0.634595	−	0.772845i	$-0.718833\pi$
$29$	−0.515235	+	0.374340i	−0.0956768	+	0.0695132i	0.538918	+	0.842358i	$0.318833\pi$
$30$		0			0
$31$	−4.88535	−	3.54941i	−0.877434	−	0.637493i	0.0551370	−	0.998479i	$-0.482440\pi$
$31$	−4.88535	−	3.54941i	−0.877434	−	0.637493i	−0.932571	+	0.360985i	$0.882440\pi$
$32$		0			0
$33$	7.42933	−	10.2256i	1.29328	−	1.78005i
$34$		0			0
$35$	9.04617	+	5.54041i	1.52908	+	0.936500i
$36$		0			0
$37$	−1.61438	−	0.524543i	−0.265402	−	0.0862344i	0.173293	−	0.984870i	$-0.444559\pi$
$37$	−1.61438	−	0.524543i	−0.265402	−	0.0862344i	−0.438695	+	0.898636i	$0.644559\pi$
$38$		0			0
$39$	−0.641548	−	1.97448i	−0.102730	−	0.316170i
$40$		0			0
$41$	3.19882	−	9.84495i	0.499572	−	1.53752i	−0.310137	−	0.950692i	$-0.600375\pi$
$41$	3.19882	−	9.84495i	0.499572	−	1.53752i	0.809709	−	0.586832i	$-0.199625\pi$
$42$		0			0
$43$		−	8.11200i		−	1.23707i	−0.785758	−	0.618534i	$-0.787727\pi$
$43$		−	8.11200i		−	1.23707i	0.785758	−	0.618534i	$-0.212273\pi$
$44$		0			0
$45$	3.37799	+	3.95312i	0.503561	+	0.589297i
$46$		0			0
$47$	−0.534394	−	0.735531i	−0.0779494	−	0.107288i	0.768262	−	0.640136i	$-0.221122\pi$
$47$	−0.534394	−	0.735531i	−0.0779494	−	0.107288i	−0.846211	+	0.532848i	$0.821122\pi$
$48$		0			0
$49$	−15.5059			−2.21512
$50$		0			0
$51$	−1.64829			−0.230807
$52$		0			0
$53$	−0.605064	−	0.832800i	−0.0831120	−	0.114394i	0.765437	−	0.643511i	$-0.222523\pi$
$53$	−0.605064	−	0.832800i	−0.0831120	−	0.114394i	−0.848549	+	0.529118i	$0.822523\pi$
$54$		0			0
$55$	−11.9096	−	2.85610i	−1.60589	−	0.385117i
$56$		0			0
$57$			12.3556i			1.63654i
$58$		0			0
$59$	−1.73043	+	5.32571i	−0.225282	+	0.693348i	0.772980	+	0.634430i	$0.218765\pi$
$59$	−1.73043	+	5.32571i	−0.225282	+	0.693348i	−0.998263	+	0.0589180i	$0.981235\pi$
$60$		0			0
$61$	2.52925	+	7.78422i	0.323837	+	0.996667i	0.971963	+	0.235134i	$0.0755530\pi$
$61$	2.52925	+	7.78422i	0.323837	+	0.996667i	−0.648126	+	0.761533i	$0.724447\pi$
$62$		0			0
$63$	−10.4920	−	3.40904i	−1.32186	−	0.429499i
$64$		0			0
$65$	−1.52935	+	1.30685i	−0.189693	+	0.162095i
$66$		0			0
$67$	0.801238	−	1.10281i	0.0978868	−	0.134730i	−0.757264	−	0.653109i	$-0.773464\pi$
$67$	0.801238	−	1.10281i	0.0978868	−	0.134730i	0.855151	+	0.518379i	$0.173464\pi$
$68$		0			0
$69$	−5.67841	−	4.12561i	−0.683600	−	0.496665i
$70$		0			0
$71$	−1.26639	+	0.920086i	−0.150293	+	0.109194i	−0.660390	−	0.750922i	$-0.729609\pi$
$71$	−1.26639	+	0.920086i	−0.150293	+	0.109194i	0.510098	+	0.860116i	$0.329609\pi$
$72$		0			0
$73$	7.71383	−	2.50637i	0.902835	−	0.293349i	0.179429	−	0.983771i	$-0.442575\pi$
$73$	7.71383	−	2.50637i	0.902835	−	0.293349i	0.723407	+	0.690422i	$0.242575\pi$
$74$		0			0
$75$	5.23323	−	10.2834i	0.604281	−	1.18743i
$76$		0			0
$77$	24.7120	−	8.02942i	2.81619	−	0.915037i
$78$		0			0
$79$	−9.83997	+	7.14916i	−1.10708	+	0.804343i	−0.982202	−	0.187829i	$-0.939855\pi$
$79$	−9.83997	+	7.14916i	−1.10708	+	0.804343i	−0.124881	+	0.992172i	$0.539855\pi$
$80$		0			0
$81$	8.55024	+	6.21211i	0.950026	+	0.690235i
$82$		0			0
$83$	−7.54215	+	10.3809i	−0.827858	+	1.13945i	0.160459	+	0.987042i	$0.448702\pi$
$83$	−7.54215	+	10.3809i	−0.827858	+	1.13945i	−0.988318	+	0.152407i	$0.951298\pi$
$84$		0			0
$85$	0.611564	+	1.47541i	0.0663334	+	0.160030i
$86$		0			0
$87$	−1.39776	−	0.454158i	−0.149855	−	0.0486909i
$88$		0			0
$89$	1.23150	+	3.79018i	0.130539	+	0.401758i	0.994870	−	0.101166i	$-0.0322574\pi$
$89$	1.23150	+	3.79018i	0.130539	+	0.401758i	−0.864330	+	0.502924i	$0.832257\pi$
$90$		0			0
$91$	1.31886	−	4.05904i	0.138254	−	0.425503i
$92$		0			0
$93$		−	13.9353i		−	1.44502i
$94$		0			0
$95$	11.0597	−	4.58431i	1.13470	−	0.470340i
$96$		0			0
$97$	5.26145	+	7.24176i	0.534219	+	0.735290i	0.987766	−	0.155943i	$-0.0498415\pi$
$97$	5.26145	+	7.24176i	0.534219	+	0.735290i	−0.453547	+	0.891232i	$0.649842\pi$
$98$		0			0
$99$	12.7367			1.28008
$100$		0			0
$101$	4.17849			0.415775			0.207888	−	0.978153i	$-0.433341\pi$
$101$	4.17849			0.415775			0.207888	+	0.978153i	$0.433341\pi$
$102$		0			0
$103$	5.57874	+	7.67847i	0.549689	+	0.756583i	0.989970	−	0.141278i	$-0.0451210\pi$
$103$	5.57874	+	7.67847i	0.549689	+	0.756583i	−0.440281	+	0.897860i	$0.645121\pi$
$104$		0			0
$105$	1.92675	+	24.4040i	0.188031	+	2.38158i
$106$		0			0
$107$			5.22384i			0.505008i	0.967596	+	0.252504i	$0.0812540\pi$
$107$			5.22384i			0.505008i	−0.967596	+	0.252504i	$0.918746\pi$
$108$		0			0
$109$	0.593929	−	1.82793i	0.0568881	−	0.175084i	−0.918575	−	0.395247i	$-0.870659\pi$
$109$	0.593929	−	1.82793i	0.0568881	−	0.175084i	0.975463	+	0.220163i	$0.0706590\pi$
$110$		0			0
$111$	−1.21048	−	3.72548i	−0.114894	−	0.353607i
$112$		0			0
$113$	−2.82035	−	0.916388i	−0.265316	−	0.0862065i	0.173338	−	0.984862i	$-0.444545\pi$
$113$	−2.82035	−	0.916388i	−0.265316	−	0.0862065i	−0.438654	+	0.898656i	$0.644545\pi$
$114$		0			0
$115$	−1.58603	+	6.61355i	−0.147898	+	0.616716i
$116$		0			0
$117$	1.22968	−	1.69250i	0.113684	−	0.156472i
$118$		0			0
$119$	−2.74133	−	1.99170i	−0.251298	−	0.182578i
$120$		0			0
$121$	−15.3706	+	11.1674i	−1.39732	+	1.01522i
$122$		0			0
$123$	22.7191	−	7.38188i	2.04851	−	0.665601i
$124$		0			0
$125$	−11.1465	−	0.868878i	−0.996976	−	0.0777148i
$126$		0			0
$127$	−12.3430	+	4.01047i	−1.09526	+	0.355872i	−0.800277	−	0.599631i	$-0.795314\pi$
$127$	−12.3430	+	4.01047i	−1.09526	+	0.355872i	−0.294984	+	0.955502i	$0.595314\pi$
$128$		0			0
$129$	15.1448	−	11.0033i	1.33342	−	0.968789i
$130$		0			0
$131$	1.88372	+	1.36860i	0.164581	+	0.119575i	0.667027	−	0.745033i	$-0.267566\pi$
$131$	1.88372	+	1.36860i	0.164581	+	0.119575i	−0.502446	+	0.864609i	$0.667566\pi$
$132$		0			0
$133$	−14.9298	+	20.5491i	−1.29458	+	1.78184i
$134$		0			0
$135$	0.811760	−	3.38493i	0.0698652	−	0.291329i
$136$		0			0
$137$	−12.6064	−	4.09607i	−1.07704	−	0.349951i	−0.283813	−	0.958880i	$-0.591600\pi$
$137$	−12.6064	−	4.09607i	−1.07704	−	0.349951i	−0.793225	+	0.608929i	$0.791600\pi$
$138$		0			0
$139$	1.19232	+	3.66957i	0.101131	+	0.311249i	0.988803	−	0.149227i	$-0.0476786\pi$
$139$	1.19232	+	3.66957i	0.101131	+	0.311249i	−0.887672	+	0.460476i	$0.847679\pi$
$140$		0			0
$141$	0.648340	−	1.99538i	0.0546001	−	0.168042i
$142$		0			0
$143$			4.92746i			0.412055i
$144$		0			0
$145$	0.112085	+	1.41966i	0.00930815	+	0.117896i
$146$		0			0
$147$	−21.0326	−	28.9488i	−1.73474	−	2.38766i
$148$		0			0
$149$	21.2606			1.74173			0.870866	−	0.491520i	$-0.163558\pi$
$149$	21.2606			1.74173			0.870866	+	0.491520i	$0.163558\pi$
$150$		0			0
$151$	13.6617			1.11177			0.555886	−	0.831258i	$-0.312379\pi$
$151$	13.6617			1.11177			0.555886	+	0.831258i	$0.312379\pi$
$152$		0			0
$153$	−0.976287	−	1.34374i	−0.0789281	−	0.108635i
$154$		0			0
$155$	−12.4736	+	5.17039i	−1.00191	+	0.415296i
$156$		0			0
$157$		−	10.4154i		−	0.831241i	−0.909538	−	0.415621i	$-0.863564\pi$
$157$		−	10.4154i		−	0.831241i	0.909538	−	0.415621i	$-0.136436\pi$
$158$		0			0
$159$	0.734078	−	2.25926i	0.0582162	−	0.179171i
$160$		0			0
$161$	−4.45884	−	13.7229i	−0.351406	−	1.08152i
$162$		0			0
$163$	8.37076	+	2.71983i	0.655649	+	0.213033i	0.617903	−	0.786254i	$-0.287982\pi$
$163$	8.37076	+	2.71983i	0.655649	+	0.213033i	0.0377455	+	0.999287i	$0.487982\pi$
$164$		0			0
$165$	−10.8222	−	26.1088i	−0.842509	−	2.03257i
$166$		0			0
$167$	−9.01319	+	12.4056i	−0.697461	+	0.959973i	0.302515	+	0.953145i	$0.402174\pi$
$167$	−9.01319	+	12.4056i	−0.697461	+	0.959973i	−0.999977	+	0.00682879i	$0.997826\pi$
$168$		0			0
$169$	−9.86244	−	7.16548i	−0.758649	−	0.551191i
$170$		0			0
$171$	−10.0727	+	7.31828i	−0.770282	+	0.559643i
$172$		0			0
$173$	−0.415055	+	0.134860i	−0.0315561	+	0.0102532i	−0.324752	−	0.945799i	$-0.605281\pi$
$173$	−0.415055	+	0.134860i	−0.0315561	+	0.0102532i	0.293196	+	0.956052i	$0.405281\pi$
$174$		0			0
$175$	21.1295	−	10.7793i	1.59724	−	0.814835i
$176$		0			0
$177$	−12.2901	+	3.99328i	−0.923778	+	0.300154i
$178$		0			0
$179$	−2.55087	+	1.85331i	−0.190661	+	0.138523i	−0.679021	−	0.734119i	$-0.737595\pi$
$179$	−2.55087	+	1.85331i	−0.190661	+	0.138523i	0.488360	+	0.872642i	$0.337595\pi$
$180$		0			0
$181$	2.29432	+	1.66692i	0.170535	+	0.123901i	0.669779	−	0.742560i	$-0.266389\pi$
$181$	2.29432	+	1.66692i	0.170535	+	0.123901i	−0.499244	+	0.866462i	$0.666389\pi$
$182$		0			0
$183$	−11.1021	+	15.2807i	−0.820690	+	1.12958i
$184$		0			0
$185$	−2.88561	+	2.46578i	−0.212154	+	0.181288i
$186$		0			0
$187$	3.72063	+	1.20891i	0.272079	+	0.0884040i
$188$		0			0
$189$	2.28212	+	7.02364i	0.166000	+	0.510894i
$190$		0			0
$191$	3.96648	−	12.2076i	0.287004	−	0.883308i	−0.698787	−	0.715330i	$-0.746276\pi$
$191$	3.96648	−	12.2076i	0.287004	−	0.883308i	0.985791	−	0.167978i	$-0.0537237\pi$
$192$		0			0
$193$			12.6967i			0.913931i	0.889484	+	0.456965i	$0.151064\pi$
$193$			12.6967i			0.913931i	−0.889484	+	0.456965i	$0.848936\pi$
$194$		0			0
$195$	−4.51429	−	1.08260i	−0.323275	−	0.0775263i
$196$		0			0
$197$	14.6268	+	20.1321i	1.04212	+	1.43435i	0.895448	+	0.445167i	$0.146856\pi$
$197$	14.6268	+	20.1321i	1.04212	+	1.43435i	0.146670	+	0.989185i	$0.453144\pi$
$198$		0			0
$199$	9.23973			0.654987			0.327493	−	0.944853i	$-0.393796\pi$
$199$	9.23973			0.654987			0.327493	+	0.944853i	$0.393796\pi$
$200$		0			0
$201$	3.14572			0.221882
$202$		0			0
$203$	−1.77588	−	2.44429i	−0.124643	−	0.171556i
$204$		0			0
$205$	−15.0371	−	17.5973i	−1.05023	−	1.22905i
$206$		0			0
$207$		−	7.07285i		−	0.491597i
$208$		0			0
$209$	9.06201	−	27.8900i	0.626832	−	1.92919i
$210$		0			0
$211$	−3.65928	−	11.2621i	−0.251915	−	0.775314i	−0.994422	−	0.105476i	$-0.966363\pi$
$211$	−3.65928	−	11.2621i	−0.251915	−	0.775314i	0.742507	−	0.669838i	$-0.233637\pi$
$212$		0			0
$213$	−3.43552	−	1.11627i	−0.235398	−	0.0764855i
$214$		0			0
$215$	−15.4684	−	9.47375i	−1.05494	−	0.646104i
$216$		0			0
$217$	16.8385	−	23.1763i	1.14307	−	1.57331i
$218$		0			0
$219$	15.1425	+	11.0017i	1.02324	+	0.743425i
$220$		0			0
$221$	0.519857	−	0.377698i	0.0349693	−	0.0254067i
$222$		0			0
$223$	−16.5646	+	5.38218i	−1.10925	+	0.360417i	−0.805656	−	0.592384i	$-0.798187\pi$
$223$	−16.5646	+	5.38218i	−1.10925	+	0.360417i	−0.303595	+	0.952801i	$0.598187\pi$
$224$		0			0
$225$	11.4831	−	1.82460i	0.765538	−	0.121640i
$226$		0			0
$227$	11.6759	−	3.79373i	0.774957	−	0.251799i	0.105271	−	0.994444i	$-0.466429\pi$
$227$	11.6759	−	3.79373i	0.774957	−	0.251799i	0.669685	+	0.742645i	$0.266429\pi$
$228$		0			0
$229$	−2.90584	+	2.11121i	−0.192023	+	0.139513i	−0.679643	−	0.733543i	$-0.737865\pi$
$229$	−2.90584	+	2.11121i	−0.192023	+	0.139513i	0.487620	+	0.873056i	$0.337865\pi$
$230$		0			0
$231$	48.5106	+	35.2450i	3.19176	+	2.31895i
$232$		0			0
$233$	−6.77467	+	9.32454i	−0.443824	+	0.610871i	−0.971056	−	0.238850i	$-0.923230\pi$
$233$	−6.77467	+	9.32454i	−0.443824	+	0.610871i	0.527233	+	0.849721i	$0.323230\pi$
$234$		0			0
$235$	−2.02665	+	0.160008i	−0.132204	+	0.0104378i
$236$		0			0
$237$	−26.6944	−	8.67352i	−1.73399	−	0.563406i
$238$		0			0
$239$	−8.08015	−	24.8681i	−0.522661	−	1.60859i	−0.768894	−	0.639376i	$-0.779193\pi$
$239$	−8.08015	−	24.8681i	−0.522661	−	1.60859i	0.246233	−	0.969211i	$-0.420807\pi$
$240$		0			0
$241$	4.27552	−	13.1587i	0.275411	−	0.847627i	−0.713700	−	0.700452i	$-0.752982\pi$
$241$	4.27552	−	13.1587i	0.275411	−	0.847627i	0.989110	−	0.147175i	$-0.0470182\pi$
$242$		0			0
$243$			19.7191i			1.26498i
$244$		0			0
$245$	−18.1088	+	29.5674i	−1.15693	+	1.88899i
$246$		0			0
$247$	−2.83124	−	3.89686i	−0.180147	−	0.247952i
$248$		0			0
$249$	−29.6110			−1.87652
$250$		0			0
$251$	−21.1529			−1.33516			−0.667581	−	0.744537i	$-0.732670\pi$
$251$	−21.1529			−1.33516			−0.667581	+	0.744537i	$0.732670\pi$
$252$		0			0
$253$	9.79184	+	13.4773i	0.615608	+	0.847312i
$254$		0			0
$255$	−1.92498	+	3.14304i	−0.120547	+	0.196825i
$256$		0			0
$257$		−	10.6839i		−	0.666442i	−0.942849	−	0.333221i	$-0.891865\pi$
$257$		−	10.6839i		−	0.666442i	0.942849	−	0.333221i	$-0.108135\pi$
$258$		0			0
$259$	2.48845	−	7.65867i	0.154625	−	0.475887i
$260$		0			0
$261$	−0.457649	−	1.40850i	−0.0283278	−	0.0871839i
$262$		0			0
$263$	0.0758648	+	0.0246500i	0.00467802	+	0.00151998i	0.311355	−	0.950294i	$-0.399217\pi$
$263$	0.0758648	+	0.0246500i	0.00467802	+	0.00151998i	−0.306677	+	0.951814i	$0.599217\pi$
$264$		0			0
$265$	−2.29466	+	0.181168i	−0.140960	+	0.0111291i
$266$		0			0
$267$	−5.40567	+	7.44026i	−0.330821	+	0.455337i
$268$		0			0
$269$	2.92805	+	2.12735i	0.178526	+	0.129707i	0.673460	−	0.739224i	$-0.264808\pi$
$269$	2.92805	+	2.12735i	0.178526	+	0.129707i	−0.494933	+	0.868931i	$0.664808\pi$
$270$		0			0
$271$	−8.65029	+	6.28480i	−0.525468	+	0.381775i	−0.818660	−	0.574279i	$-0.805282\pi$
$271$	−8.65029	+	6.28480i	−0.525468	+	0.381775i	0.293192	+	0.956054i	$0.405282\pi$
$272$		0			0
$273$	9.36701	−	3.04353i	0.566917	−	0.184203i
$274$		0			0
$275$	−19.3550	+	19.3742i	−1.16715	+	1.16831i
$276$		0			0
$277$	−31.0990	+	10.1047i	−1.86856	+	0.607132i	−0.876493	+	0.481414i	$0.840123\pi$
$277$	−31.0990	+	10.1047i	−1.86856	+	0.607132i	−0.992066	+	0.125717i	$0.959877\pi$
$278$		0			0
$279$	11.3605	−	8.25389i	0.680136	−	0.494148i
$280$		0			0
$281$	13.1207	+	9.53275i	0.782715	+	0.568676i	0.905793	−	0.423721i	$-0.139276\pi$
$281$	13.1207	+	9.53275i	0.782715	+	0.568676i	−0.123077	+	0.992397i	$0.539276\pi$
$282$		0			0
$283$	18.9130	−	26.0315i	1.12426	−	1.54741i	0.325720	−	0.945466i	$-0.394393\pi$
$283$	18.9130	−	26.0315i	1.12426	−	1.54741i	0.798539	−	0.601943i	$-0.205607\pi$
$284$		0			0
$285$	23.5604	+	14.4298i	1.39560	+	0.854745i
$286$		0			0
$287$	46.7048	+	15.1753i	2.75690	+	0.895770i
$288$		0			0
$289$	5.09564	+	15.6828i	0.299743	+	0.922515i
$290$		0			0
$291$	−6.38331	+	19.6458i	−0.374197	+	1.15166i
$292$		0			0
$293$		−	24.6970i		−	1.44281i	−0.692513	−	0.721406i	$-0.743496\pi$
$293$		−	24.6970i		−	1.44281i	0.692513	−	0.721406i	$-0.256504\pi$
$294$		0			0
$295$	8.13442	+	9.51939i	0.473604	+	0.554240i
$296$		0			0
$297$	−5.01164	−	6.89794i	−0.290805	−	0.400259i
$298$		0			0
$299$	2.73629			0.158244
$300$		0			0
$301$	38.4836			2.21816
$302$		0			0
$303$	5.66781	+	7.80107i	0.325607	+	0.448160i
$304$		0			0
$305$	17.7972	+	4.26804i	1.01906	+	0.244387i
$306$		0			0
$307$		−	32.1625i		−	1.83561i	−0.397029	−	0.917806i	$-0.629959\pi$
$307$		−	32.1625i		−	1.83561i	0.397029	−	0.917806i	$-0.370041\pi$
$308$		0			0
$309$	−6.76826	+	20.8305i	−0.385033	+	1.18501i
$310$		0			0
$311$	−6.78533	−	20.8831i	−0.384761	−	1.18417i	−0.936654	−	0.350257i	$-0.886094\pi$
$311$	−6.78533	−	20.8831i	−0.384761	−	1.18417i	0.551893	−	0.833915i	$-0.313906\pi$
$312$		0			0
$313$	−5.18348	−	1.68422i	−0.292988	−	0.0951975i	0.158835	−	0.987305i	$-0.449226\pi$
$313$	−5.18348	−	1.68422i	−0.292988	−	0.0951975i	−0.451823	+	0.892108i	$0.649226\pi$
$314$		0			0
$315$	−18.7538	+	16.0253i	−1.05665	+	0.902923i
$316$		0			0
$317$	−0.0839194	+	0.115505i	−0.00471338	+	0.00648742i	−0.811367	−	0.584537i	$-0.801276\pi$
$317$	−0.0839194	+	0.115505i	−0.00471338	+	0.00648742i	0.806654	+	0.591024i	$0.201276\pi$
$318$		0			0
$319$	2.82202	+	2.05031i	0.158003	+	0.114796i
$320$		0			0
$321$	−9.75269	+	7.08575i	−0.544342	+	0.395488i
$322$		0			0
$323$	−3.63706	+	1.18175i	−0.202372	+	0.0657545i
$324$		0			0
$325$	0.705886	+	4.44248i	0.0391555	+	0.246424i
$326$		0			0
$327$	4.21828	−	1.37060i	0.233272	−	0.0757946i
$328$		0			0
$329$	3.48938	−	2.53519i	0.192376	−	0.139769i
$330$		0			0
$331$	18.8935	+	13.7269i	1.03848	+	0.754499i	0.969988	−	0.243153i	$-0.0781817\pi$
$331$	18.8935	+	13.7269i	1.03848	+	0.754499i	0.0684907	+	0.997652i	$0.478182\pi$
$332$		0			0
$333$	2.32017	−	3.19344i	0.127145	−	0.175000i
$334$		0			0
$335$	−1.16715	−	2.81578i	−0.0637684	−	0.153842i
$336$		0			0
$337$	15.4589	+	5.02291i	0.842101	+	0.273615i	0.698134	−	0.715967i	$-0.254014\pi$
$337$	15.4589	+	5.02291i	0.842101	+	0.273615i	0.143967	+	0.989582i	$0.454014\pi$
$338$		0			0
$339$	−2.11474	−	6.50849i	−0.114857	−	0.353493i
$340$		0			0
$341$	−10.2205	+	31.4556i	−0.553474	+	1.70342i
$342$		0			0
$343$		−	40.3522i		−	2.17881i
$344$		0			0
$345$	−14.4986	+	6.00972i	−0.780576	+	0.323553i
$346$		0			0
$347$	4.04280	+	5.56443i	0.217029	+	0.298714i	0.903625	−	0.428325i	$-0.140896\pi$
$347$	4.04280	+	5.56443i	0.217029	+	0.298714i	−0.686596	+	0.727039i	$0.740896\pi$
$348$		0			0
$349$	14.7392			0.788970			0.394485	−	0.918902i	$-0.370923\pi$
$349$	14.7392			0.788970			0.394485	+	0.918902i	$0.370923\pi$
$350$		0			0
$351$	−1.40048			−0.0747522
$352$		0			0
$353$	14.7400	+	20.2879i	0.784532	+	1.07982i	0.994767	+	0.102165i	$0.0325770\pi$
$353$	14.7400	+	20.2879i	0.784532	+	1.07982i	−0.210235	+	0.977651i	$0.567423\pi$
$354$		0			0
$355$	0.275492	+	3.48935i	0.0146216	+	0.185196i
$356$		0			0
$357$		−	7.81954i		−	0.413854i
$358$		0			0
$359$	−0.940477	+	2.89449i	−0.0496365	+	0.152765i	−0.972803	−	0.231636i	$-0.925592\pi$
$359$	−0.940477	+	2.89449i	−0.0496365	+	0.152765i	0.923166	+	0.384401i	$0.125592\pi$
$360$		0			0
$361$	2.98715	+	9.19349i	0.157218	+	0.483868i
$362$		0			0
$363$	−41.6980	−	13.5485i	−2.18858	−	0.711112i
$364$		0			0
$365$	4.22945	−	17.6362i	0.221379	−	0.923123i
$366$		0			0
$367$	2.47416	−	3.40539i	0.129150	−	0.177760i	−0.739545	−	0.673107i	$-0.764959\pi$
$367$	2.47416	−	3.40539i	0.129150	−	0.177760i	0.868695	+	0.495347i	$0.164959\pi$
$368$		0			0
$369$	19.4745	+	14.1491i	1.01380	+	0.736572i
$370$		0			0
$371$	3.95083	−	2.87045i	0.205117	−	0.149026i
$372$		0			0
$373$	17.0370	−	5.53566i	0.882143	−	0.286626i	0.167296	−	0.985907i	$-0.446496\pi$
$373$	17.0370	−	5.53566i	0.882143	−	0.286626i	0.714847	+	0.699281i	$0.246496\pi$
$374$		0			0
$375$	−13.4973	−	21.9887i	−0.696996	−	1.13549i
$376$		0			0
$377$	0.544909	−	0.177052i	0.0280642	−	0.00911862i
$378$		0			0
$379$	−12.0031	+	8.72079i	−0.616560	+	0.447957i	−0.851718	−	0.524000i	$-0.824439\pi$
$379$	−12.0031	+	8.72079i	−0.616560	+	0.447957i	0.235158	+	0.971957i	$0.424439\pi$
$380$		0			0
$381$	−24.2297	−	17.6039i	−1.24132	−	0.901875i
$382$		0			0
$383$	−6.35843	+	8.75163i	−0.324901	+	0.447187i	−0.939956	−	0.341297i	$-0.889134\pi$
$383$	−6.35843	+	8.75163i	−0.324901	+	0.447187i	0.615055	+	0.788484i	$0.289134\pi$
$384$		0			0
$385$	13.5494	−	56.4994i	0.690544	−	2.87948i
$386$		0			0
$387$	17.9406	+	5.82925i	0.911971	+	0.296317i
$388$		0			0
$389$	−7.11821	−	21.9076i	−0.360908	−	1.11076i	−0.952504	−	0.304526i	$-0.901502\pi$
$389$	−7.11821	−	21.9076i	−0.360908	−	1.11076i	0.591596	−	0.806234i	$-0.298498\pi$
$390$		0			0
$391$	0.671322	−	2.06612i	0.0339502	−	0.104488i
$392$		0			0
$393$			5.37323i			0.271044i
$394$		0			0
$395$	2.14060	+	27.1126i	0.107705	+	1.36418i
$396$		0			0
$397$	2.19656	+	3.02330i	0.110242	+	0.151735i	0.860573	−	0.509327i	$-0.170106\pi$
$397$	2.19656	+	3.02330i	0.110242	+	0.151735i	−0.750331	+	0.661063i	$0.770106\pi$
$398$		0			0
$399$	−58.6156			−2.93445
$400$		0			0
$401$	−21.9778			−1.09752			−0.548760	−	0.835980i	$-0.684900\pi$
$401$	−21.9778			−1.09752			−0.548760	+	0.835980i	$0.684900\pi$
$402$		0			0
$403$	3.19320	+	4.39506i	0.159065	+	0.218934i
$404$		0			0
$405$	21.8311	−	9.04911i	1.08480	−	0.449654i
$406$		0			0
$407$			9.29722i			0.460846i
$408$		0			0
$409$	−9.04832	+	27.8479i	−0.447410	+	1.37699i	0.432408	+	0.901678i	$0.357664\pi$
$409$	−9.04832	+	27.8479i	−0.447410	+	1.37699i	−0.879819	+	0.475310i	$0.842336\pi$
$410$		0			0
$411$	−9.45245	−	29.0917i	−0.466255	−	1.43499i
$412$		0			0
$413$	−25.2653	−	8.20920i	−1.24323	−	0.403949i
$414$		0			0
$415$	10.9866	+	26.5053i	0.539309	+	1.30109i
$416$		0			0
$417$	−5.23366	+	7.20351i	−0.256293	+	0.352757i
$418$		0			0
$419$	−32.9023	−	23.9049i	−1.60738	−	1.16783i	−0.871021	−	0.491247i	$-0.836541\pi$
$419$	−32.9023	−	23.9049i	−1.60738	−	1.16783i	−0.736363	−	0.676586i	$-0.763459\pi$
$420$		0			0
$421$	22.8307	−	16.5875i	1.11270	−	0.808425i	0.129615	−	0.991564i	$-0.458626\pi$
$421$	22.8307	−	16.5875i	1.11270	−	0.808425i	0.983087	+	0.183139i	$0.0586259\pi$
$422$		0			0
$423$	2.01072	−	0.653323i	0.0977646	−	0.0317656i
$424$		0			0
$425$	3.52761	+	0.556919i	0.171114	+	0.0270145i
$426$		0			0
$427$	−36.9286	+	11.9988i	−1.78710	+	0.580664i
$428$		0			0
$429$	−9.19937	+	6.68373i	−0.444150	+	0.322694i
$430$		0			0
$431$	−2.43193	−	1.76690i	−0.117142	−	0.0851086i	0.527672	−	0.849448i	$-0.323065\pi$
$431$	−2.43193	−	1.76690i	−0.117142	−	0.0851086i	−0.644814	+	0.764340i	$0.723065\pi$
$432$		0			0
$433$	−2.60850	+	3.59029i	−0.125357	+	0.172539i	−0.867082	−	0.498165i	$-0.834008\pi$
$433$	−2.60850	+	3.59029i	−0.125357	+	0.172539i	0.741726	+	0.670703i	$0.234008\pi$
$434$		0			0
$435$	−2.49841	+	2.13492i	−0.119789	+	0.102361i
$436$		0			0
$437$	−15.4877	−	5.03225i	−0.740876	−	0.240725i
$438$		0			0
$439$	−5.67846	−	17.4765i	−0.271018	−	0.834108i	−0.990246	−	0.139333i	$-0.955504\pi$
$439$	−5.67846	−	17.4765i	−0.271018	−	0.834108i	0.719227	−	0.694775i	$-0.244496\pi$
$440$		0			0
$441$	11.1425	−	34.2929i	0.530593	−	1.63300i
$442$		0			0
$443$		−	8.18925i		−	0.389083i	−0.980894	−	0.194541i	$-0.937678\pi$
$443$		−	8.18925i		−	0.389083i	0.980894	−	0.194541i	$-0.0623219\pi$
$444$		0			0
$445$	8.66555	+	2.07813i	0.410786	+	0.0985130i
$446$		0			0
$447$	28.8384	+	39.6926i	1.36401	+	1.87740i
$448$		0			0
$449$	21.4953			1.01442			0.507212	−	0.861821i	$-0.330676\pi$
$449$	21.4953			1.01442			0.507212	+	0.861821i	$0.330676\pi$
$450$		0			0
$451$	−56.6971			−2.66976
$452$		0			0
$453$	18.5311	+	25.5058i	0.870665	+	1.19837i
$454$		0			0
$455$	−6.19974	−	7.25530i	−0.290648	−	0.340134i
$456$		0			0
$457$			19.9426i			0.932875i	0.884554	+	0.466438i	$0.154463\pi$
$457$			19.9426i			0.932875i	−0.884554	+	0.466438i	$0.845537\pi$
$458$		0			0
$459$	−0.343595	+	1.05748i	−0.0160376	+	0.0493588i
$460$		0			0
$461$	−7.61758	−	23.4445i	−0.354786	−	1.09192i	−0.956134	−	0.292931i	$-0.905369\pi$
$461$	−7.61758	−	23.4445i	−0.354786	−	1.09192i	0.601348	−	0.798987i	$-0.294631\pi$
$462$		0			0
$463$	30.3515	+	9.86181i	1.41055	+	0.458317i	0.912588	−	0.408879i	$-0.134080\pi$
$463$	30.3515	+	9.86181i	1.41055	+	0.458317i	0.497966	+	0.867196i	$0.334080\pi$
$464$		0			0
$465$	−26.5725	−	16.2745i	−1.23227	−	0.754714i
$466$		0			0
$467$	−3.39194	+	4.66860i	−0.156960	+	0.216037i	−0.880253	−	0.474504i	$-0.842627\pi$
$467$	−3.39194	+	4.66860i	−0.156960	+	0.216037i	0.723293	+	0.690541i	$0.242627\pi$
$468$		0			0
$469$	5.23176	+	3.80110i	0.241580	+	0.175518i
$470$		0			0
$471$	19.4452	−	14.1277i	0.895986	−	0.650972i
$472$		0			0
$473$	−42.2560	+	13.7298i	−1.94293	+	0.631297i
$474$		0			0
$475$	4.17468	−	26.4431i	0.191548	−	1.21329i
$476$		0			0
$477$	2.27662	−	0.739720i	0.104239	−	0.0338695i
$478$		0			0
$479$	29.9435	−	21.7552i	1.36815	−	0.994021i	0.370273	−	0.928923i	$-0.379264\pi$
$479$	29.9435	−	21.7552i	1.36815	−	0.994021i	0.997879	−	0.0650976i	$-0.0207359\pi$
$480$		0			0
$481$	1.23545	+	0.897609i	0.0563318	+	0.0409275i
$482$		0			0
$483$	19.5720	−	26.9386i	0.890558	−	1.22575i
$484$		0			0
$485$	19.9537	−	1.57538i	0.906049	−	0.0715344i
$486$		0			0
$487$	1.68760	+	0.548334i	0.0764724	+	0.0248474i	0.347003	−	0.937864i	$-0.387199\pi$
$487$	1.68760	+	0.548334i	0.0764724	+	0.0248474i	−0.270531	+	0.962711i	$0.587199\pi$
$488$		0			0
$489$	6.27651	+	19.3171i	0.283834	+	0.873550i
$490$		0			0
$491$	2.09693	−	6.45370i	0.0946333	−	0.291251i	−0.892525	−	0.450999i	$-0.851068\pi$
$491$	2.09693	−	6.45370i	0.0946333	−	0.291251i	0.987158	+	0.159747i	$0.0510679\pi$
$492$		0			0
$493$		−	0.454888i		−	0.0204871i
$494$		0			0
$495$	14.8748	−	24.2870i	0.668570	−	1.09162i
$496$		0			0
$497$	−4.36492	−	6.00779i	−0.195793	−	0.269486i
$498$		0			0
$499$	31.3417			1.40305			0.701524	−	0.712645i	$-0.252503\pi$
$499$	31.3417			1.40305			0.701524	+	0.712645i	$0.252503\pi$
$500$		0			0
$501$	−35.3864			−1.58095
$502$		0			0
$503$	−15.8717	−	21.8455i	−0.707683	−	0.974042i	−0.999844	−	0.0176728i	$-0.994374\pi$
$503$	−15.8717	−	21.8455i	−0.707683	−	0.974042i	0.292161	−	0.956369i	$-0.405626\pi$
$504$		0			0
$505$	4.87992	−	7.96776i	0.217154	−	0.354561i
$506$		0			0
$507$		−	28.1322i		−	1.24940i
$508$		0			0
$509$	−2.55879	+	7.87516i	−0.113417	+	0.349060i	−0.991613	−	0.129239i	$-0.958747\pi$
$509$	−2.55879	+	7.87516i	−0.113417	+	0.349060i	0.878197	+	0.478299i	$0.158747\pi$
$510$		0			0
$511$	11.8903	+	36.5947i	0.525997	+	1.61885i
$512$		0			0
$513$	7.92688	+	2.57560i	0.349980	+	0.113715i
$514$		0			0
$515$	21.1569	−	1.67039i	0.932286	−	0.0736060i
$516$		0			0
$517$	−2.92695	+	4.02861i	−0.128727	+	0.177178i
$518$		0			0
$519$	−0.814769	−	0.591964i	−0.0357644	−	0.0259843i
$520$		0			0
$521$	−25.8273	+	18.7646i	−1.13151	+	0.822092i	−0.985914	−	0.167252i	$-0.946511\pi$
$521$	−25.8273	+	18.7646i	−1.13151	+	0.822092i	−0.145598	+	0.989344i	$0.546511\pi$
$522$		0			0
$523$	40.4318	−	13.1371i	1.76796	−	0.574445i	0.769985	−	0.638062i	$-0.220264\pi$
$523$	40.4318	−	13.1371i	1.76796	−	0.574445i	0.997974	+	0.0636177i	$0.0202638\pi$
$524$		0			0
$525$	48.7850	+	24.8266i	2.12915	+	1.08352i
$526$		0			0
$527$	4.10205	−	1.33284i	0.178688	−	0.0580592i
$528$		0			0
$529$	−11.1233	+	8.08152i	−0.483620	+	0.351370i
$530$		0			0
$531$	−10.5349	−	7.65406i	−0.457176	−	0.332158i
$532$		0			0
$533$	−5.47388	+	7.53415i	−0.237100	+	0.326340i
$534$		0			0
$535$	9.96109	+	6.10075i	0.430655	+	0.263759i
$536$		0			0
$537$	−6.92012	−	2.24848i	−0.298625	−	0.0970293i
$538$		0			0
$539$	26.2441	+	80.7712i	1.13042	+	3.47906i
$540$		0			0
$541$	6.21935	−	19.1412i	0.267391	−	0.822945i	−0.723742	−	0.690071i	$-0.757579\pi$
$541$	6.21935	−	19.1412i	0.267391	−	0.822945i	0.991133	−	0.132874i	$-0.0424206\pi$
$542$		0			0
$543$			6.54444i			0.280849i
$544$		0			0
$545$	−2.79195	−	3.26731i	−0.119594	−	0.139956i
$546$		0			0
$547$	2.86005	+	3.93652i	0.122287	+	0.168314i	0.865771	−	0.500440i	$-0.166828\pi$
$547$	2.86005	+	3.93652i	0.122287	+	0.168314i	−0.743484	+	0.668753i	$0.766828\pi$
$548$		0			0
$549$	−19.0332			−0.812316
$550$		0			0
$551$	−3.40986			−0.145265
$552$		0			0
$553$	−33.9159	−	46.6812i	−1.44225	−	1.98509i
$554$		0			0
$555$	−8.51763	−	2.04266i	−0.361553	−	0.0867061i
$556$		0			0
$557$			22.9342i			0.971754i	0.874027	+	0.485877i	$0.161500\pi$
$557$			22.9342i			0.971754i	−0.874027	+	0.485877i	$0.838500\pi$
$558$		0			0
$559$	−2.25517	+	6.94071i	−0.0953837	+	0.293561i
$560$		0			0
$561$	2.78978	+	8.58605i	0.117785	+	0.362504i
$562$		0			0
$563$	16.0201	+	5.20525i	0.675167	+	0.219375i	0.626478	−	0.779439i	$-0.284496\pi$
$563$	16.0201	+	5.20525i	0.675167	+	0.219375i	0.0486890	+	0.998814i	$0.484496\pi$
$564$		0			0
$565$	−5.04122	+	4.30777i	−0.212086	+	0.181229i
$566$		0			0
$567$	−29.4705	+	40.5626i	−1.23764	+	1.70347i
$568$		0			0
$569$	20.0653	+	14.5783i	0.841181	+	0.611153i	0.922700	−	0.385518i	$-0.125977\pi$
$569$	20.0653	+	14.5783i	0.841181	+	0.611153i	−0.0815196	+	0.996672i	$0.525977\pi$
$570$		0			0
$571$	−21.8426	+	15.8696i	−0.914085	+	0.664122i	−0.942045	−	0.335487i	$-0.891099\pi$
$571$	−21.8426	+	15.8696i	−0.914085	+	0.664122i	0.0279596	+	0.999609i	$0.491099\pi$
$572$		0			0
$573$	28.1712	−	9.15339i	1.17687	−	0.382388i
$574$		0			0
$575$	10.7588	+	10.7481i	0.448672	+	0.448226i
$576$		0			0
$577$	−11.7353	+	3.81304i	−0.488549	+	0.158739i	−0.542925	−	0.839781i	$-0.682683\pi$
$577$	−11.7353	+	3.81304i	−0.488549	+	0.158739i	0.0543759	+	0.998521i	$0.482683\pi$
$578$		0			0
$579$	−23.7043	+	17.2222i	−0.985116	+	0.715729i
$580$		0			0
$581$	−49.2473	−	35.7802i	−2.04312	−	1.48441i
$582$		0			0
$583$	−3.31402	+	4.56136i	−0.137253	+	0.188912i
$584$		0			0
$585$	−1.79125	−	4.32143i	−0.0740592	−	0.178669i
$586$		0			0
$587$	4.04083	+	1.31295i	0.166783	+	0.0541911i	0.391218	−	0.920298i	$-0.372054\pi$
$587$	4.04083	+	1.31295i	0.166783	+	0.0541911i	−0.224435	+	0.974489i	$0.572054\pi$
$588$		0			0
$589$	−9.99099	−	30.7491i	−0.411671	−	1.26699i
$590$		0			0
$591$	−17.7456	+	54.6154i	−0.729957	+	2.24658i
$592$		0			0
$593$		−	4.87578i		−	0.200224i	−0.994976	−	0.100112i	$-0.968080\pi$
$593$		−	4.87578i		−	0.200224i	0.994976	−	0.100112i	$-0.0319202\pi$
$594$		0			0
$595$	−6.99939	+	2.90128i	−0.286947	+	0.118941i
$596$		0			0
$597$	12.5330	+	17.2502i	0.512941	+	0.706003i
$598$		0			0
$599$	−3.33018			−0.136068			−0.0680338	−	0.997683i	$-0.521673\pi$
$599$	−3.33018			−0.136068			−0.0680338	+	0.997683i	$0.521673\pi$
$600$		0			0
$601$	21.2834			0.868169			0.434084	−	0.900872i	$-0.357072\pi$
$601$	21.2834			0.868169			0.434084	+	0.900872i	$0.357072\pi$
$602$		0			0
$603$	1.86322	+	2.56450i	0.0758761	+	0.104434i
$604$		0			0
$605$	3.34373	+	42.3514i	0.135942	+	1.72183i
$606$		0			0
$607$		−	5.70241i		−	0.231454i	−0.993281	−	0.115727i	$-0.963080\pi$
$607$		−	5.70241i		−	0.231454i	0.993281	−	0.115727i	$-0.0369198\pi$
$608$		0			0
$609$	2.15454	−	6.63100i	0.0873065	−	0.268702i
$610$		0			0
$611$	0.252752	+	0.777892i	0.0102253	+	0.0314701i
$612$		0			0
$613$	14.2319	+	4.62422i	0.574821	+	0.186771i	0.581979	−	0.813204i	$-0.302279\pi$
$613$	14.2319	+	4.62422i	0.574821	+	0.186771i	−0.00715828	+	0.999974i	$0.502279\pi$
$614$		0			0
$615$	12.4567	−	51.9430i	0.502304	−	2.09454i
$616$		0			0
$617$	8.61313	−	11.8550i	0.346752	−	0.477263i	−0.599647	−	0.800265i	$-0.704692\pi$
$617$	8.61313	−	11.8550i	0.346752	−	0.477263i	0.946398	+	0.323002i	$0.104692\pi$
$618$		0			0
$619$	0.994220	+	0.722343i	0.0399611	+	0.0290334i	0.607586	−	0.794254i	$-0.292138\pi$
$619$	0.994220	+	0.722343i	0.0399611	+	0.0290334i	−0.567625	+	0.823287i	$0.692138\pi$
$620$		0			0
$621$	−3.83052	+	2.78303i	−0.153713	+	0.111679i
$622$		0			0
$623$	−17.9807	+	5.84230i	−0.720383	+	0.234067i
$624$		0			0
$625$	−14.6745	+	20.2400i	−0.586980	+	0.809602i
$626$		0			0
$627$	64.3614	−	20.9123i	2.57035	−	0.835156i
$628$		0			0
$629$	0.980874	−	0.712647i	0.0391100	−	0.0284151i
$630$		0			0
$631$	5.95746	+	4.32835i	0.237163	+	0.172309i	0.700018	−	0.714125i	$-0.253175\pi$
$631$	5.95746	+	4.32835i	0.237163	+	0.172309i	−0.462855	+	0.886434i	$0.653175\pi$
$632$		0			0
$633$	16.0623	−	22.1079i	0.638420	−	0.878710i
$634$		0			0
$635$	−6.76757	+	28.2199i	−0.268563	+	1.11987i
$636$		0			0
$637$	13.2670	+	4.31070i	0.525657	+	0.170796i
$638$		0			0
$639$	−1.12485	−	3.46193i	−0.0444983	−	0.136952i
$640$		0			0
$641$	9.03936	−	27.8203i	0.357033	−	1.09884i	−0.597788	−	0.801654i	$-0.703953\pi$
$641$	9.03936	−	27.8203i	0.357033	−	1.09884i	0.954821	−	0.297181i	$-0.0960465\pi$
$642$		0			0
$643$		−	4.03921i		−	0.159291i	−0.996823	−	0.0796454i	$-0.974621\pi$
$643$		−	4.03921i		−	0.159291i	0.996823	−	0.0796454i	$-0.0253788\pi$
$644$		0			0
$645$	−3.29461	−	41.7293i	−0.129725	−	1.64309i
$646$		0			0
$647$	−10.2270	−	14.0763i	−0.402066	−	0.553397i	0.559195	−	0.829036i	$-0.311110\pi$
$647$	−10.2270	−	14.0763i	−0.402066	−	0.553397i	−0.961261	+	0.275639i	$0.911110\pi$
$648$		0			0
$649$	30.6708			1.20393
$650$		0			0
$651$	66.1094			2.59103
$652$		0			0
$653$	−14.8035	−	20.3753i	−0.579307	−	0.797347i	0.414313	−	0.910135i	$-0.364022\pi$
$653$	−14.8035	−	20.3753i	−0.579307	−	0.797347i	−0.993619	+	0.112788i	$0.964022\pi$
$654$		0			0
$655$	4.80966	−	1.99363i	0.187929	−	0.0778975i
$656$		0			0
$657$			18.8611i			0.735840i
$658$		0			0
$659$	6.41249	−	19.7356i	0.249795	−	0.768790i	−0.745016	−	0.667047i	$-0.767558\pi$
$659$	6.41249	−	19.7356i	0.249795	−	0.768790i	0.994811	−	0.101743i	$-0.0324419\pi$
$660$		0			0
$661$	−7.93078	−	24.4084i	−0.308472	−	0.949378i	−0.978359	−	0.206915i	$-0.933658\pi$
$661$	−7.93078	−	24.4084i	−0.308472	−	0.949378i	0.669887	−	0.742463i	$-0.266342\pi$
$662$		0			0
$663$	1.41029	+	0.458232i	0.0547712	+	0.0177963i
$664$		0			0
$665$	21.7481	+	52.4677i	0.843356	+	2.03461i
$666$		0			0
$667$	1.13857	−	1.56710i	0.0440855	−	0.0606785i
$668$		0			0
$669$	−32.5170	−	23.6250i	−1.25718	−	0.913395i
$670$		0			0
$671$	36.2677	−	26.3500i	1.40010	−	1.01723i
$672$		0			0
$673$	−24.7424	+	8.03928i	−0.953748	+	0.309892i	−0.744238	−	0.667915i	$-0.767187\pi$
$673$	−24.7424	+	8.03928i	−0.953748	+	0.309892i	−0.209511	+	0.977806i	$0.567187\pi$
$674$		0			0
$675$	−5.50654	−	5.50106i	−0.211947	−	0.211736i
$676$		0			0
$677$	−11.6504	+	3.78545i	−0.447762	+	0.145487i	−0.524214	−	0.851587i	$-0.675641\pi$
$677$	−11.6504	+	3.78545i	−0.447762	+	0.145487i	0.0764519	+	0.997073i	$0.475641\pi$
$678$		0			0
$679$	−34.3552	+	24.9605i	−1.31843	+	0.957896i
$680$		0			0
$681$	22.9202	+	16.6525i	0.878305	+	0.638126i
$682$		0			0
$683$	−19.2888	+	26.5488i	−0.738067	+	1.01586i	0.260660	+	0.965431i	$0.416060\pi$
$683$	−19.2888	+	26.5488i	−0.738067	+	1.01586i	−0.998728	+	0.0504316i	$0.983940\pi$
$684$		0			0
$685$	−22.5332	+	19.2549i	−0.860950	+	0.735691i
$686$		0			0
$687$	−7.88310	−	2.56137i	−0.300759	−	0.0977225i
$688$		0			0
$689$	0.286177	+	0.880762i	0.0109025	+	0.0335544i
$690$		0			0
$691$	−12.8444	+	39.5310i	−0.488624	+	1.50383i	0.338040	+	0.941132i	$0.390236\pi$
$691$	−12.8444	+	39.5310i	−0.488624	+	1.50383i	−0.826663	+	0.562697i	$0.809764\pi$
$692$		0			0
$693$			60.4232i			2.29529i
$694$		0			0
$695$	8.38980	+	2.01201i	0.318243	+	0.0763197i
$696$		0			0
$697$	4.34593	+	5.98166i	0.164614	+	0.226571i
$698$		0			0
$699$	−26.5979			−1.00602
$700$		0			0
$701$	39.2783			1.48352			0.741760	−	0.670666i	$-0.233991\pi$
$701$	39.2783			1.48352			0.741760	+	0.670666i	$0.233991\pi$
$702$		0			0
$703$	−5.34203	−	7.35267i	−0.201478	−	0.277311i
$704$		0			0
$705$	−3.04773	−	3.56663i	−0.114784	−	0.134327i
$706$		0			0
$707$			19.8229i			0.745517i
$708$		0			0
$709$	8.56055	−	26.3467i	0.321498	−	0.989470i	−0.651498	−	0.758650i	$-0.725859\pi$
$709$	8.56055	−	26.3467i	0.321498	−	0.989470i	0.972997	−	0.230820i	$-0.0741408\pi$
$710$		0			0
$711$	−8.74019	−	26.8995i	−0.327783	−	1.00881i
$712$		0			0
$713$	17.4677	+	5.67561i	0.654171	+	0.212553i
$714$		0			0
$715$	9.39594	+	5.75462i	0.351388	+	0.215211i
$716$		0			0
$717$	35.4677	−	48.8171i	1.32457	−	1.82311i
$718$		0			0
$719$	−32.7615	−	23.8026i	−1.22180	−	0.887687i	−0.225548	−	0.974232i	$-0.572417\pi$
$719$	−32.7615	−	23.8026i	−1.22180	−	0.887687i	−0.996248	+	0.0865450i	$0.972417\pi$
$720$		0			0
$721$	−36.4270	+	26.4657i	−1.35661	+	0.985635i
$722$		0			0
$723$	30.3662	−	9.86658i	1.12933	−	0.366942i
$724$		0			0
$725$	2.83798	+	1.44424i	0.105400	+	0.0536378i
$726$		0			0
$727$	28.3901	−	9.22452i	1.05293	−	0.342118i	0.269114	−	0.963108i	$-0.413269\pi$
$727$	28.3901	−	9.22452i	1.05293	−	0.342118i	0.783819	+	0.620990i	$0.213269\pi$
$728$		0			0
$729$	−11.1640	+	8.11111i	−0.413481	+	0.300412i
$730$		0			0
$731$	4.68751	+	3.40568i	0.173374	+	0.125963i
$732$		0			0
$733$	−4.81385	+	6.62569i	−0.177803	+	0.244725i	−0.888612	−	0.458660i	$-0.848329\pi$
$733$	−4.81385	+	6.62569i	−0.177803	+	0.244725i	0.710808	+	0.703386i	$0.248329\pi$
$734$		0			0
$735$	−79.7644	+	6.29756i	−2.94215	+	0.232289i
$736$		0			0
$737$	−7.10073	−	2.30717i	−0.261559	−	0.0849856i
$738$		0			0
$739$	−5.32564	−	16.3906i	−0.195907	−	0.602939i	−0.999965	−	0.00838832i	$-0.997330\pi$
$739$	−5.32564	−	16.3906i	−0.195907	−	0.602939i	0.804058	−	0.594551i	$-0.202670\pi$
$740$		0			0
$741$	3.43492	−	10.5716i	0.126185	−	0.388358i
$742$		0			0
$743$		−	33.0772i		−	1.21348i	−0.794899	−	0.606742i	$-0.792476\pi$
$743$		−	33.0772i		−	1.21348i	0.794899	−	0.606742i	$-0.207524\pi$
$744$		0			0
$745$	24.8295	−	40.5407i	0.909683	−	1.48530i
$746$		0			0
$747$	−17.5387	−	24.1399i	−0.641707	−	0.883234i
$748$		0			0
$749$	−24.7821			−0.905517
$750$		0			0
$751$	−8.95863			−0.326905			−0.163453	−	0.986551i	$-0.552263\pi$
$751$	−8.95863			−0.326905			−0.163453	+	0.986551i	$0.552263\pi$
$752$		0			0
$753$	−28.6924	−	39.4917i	−1.04561	−	1.43916i
$754$		0			0
$755$	15.9550	−	26.0508i	0.580663	−	0.948086i
$756$		0			0
$757$			41.5769i			1.51114i	0.655069	+	0.755569i	$0.272640\pi$
$757$			41.5769i			1.51114i	−0.655069	+	0.755569i	$0.727360\pi$
$758$		0			0
$759$	−11.8797	+	36.5619i	−0.431206	+	1.32711i
$760$		0			0
$761$	8.91224	+	27.4290i	0.323068	+	0.994302i	0.972305	+	0.233716i	$0.0750884\pi$
$761$	8.91224	+	27.4290i	0.323068	+	0.994302i	−0.649237	+	0.760586i	$0.724912\pi$
$762$		0			0
$763$	8.67175	+	2.81762i	0.313938	+	0.102005i
$764$		0			0
$765$	−3.70249	+	0.292320i	−0.133864	+	0.0105688i
$766$		0			0
$767$	2.96114	−	4.07566i	0.106921	−	0.147164i
$768$		0			0
$769$	−14.5312	−	10.5575i	−0.524009	−	0.380715i	0.294103	−	0.955774i	$-0.404979\pi$
$769$	−14.5312	−	10.5575i	−0.524009	−	0.380715i	−0.818112	+	0.575059i	$0.804979\pi$
$770$		0			0
$771$	19.9463	−	14.4919i	0.718350	−	0.521912i
$772$		0			0
$773$	11.2650	−	3.66022i	0.405174	−	0.131649i	−0.0993377	−	0.995054i	$-0.531672\pi$
$773$	11.2650	−	3.66022i	0.405174	−	0.131649i	0.504512	+	0.863405i	$0.331672\pi$
$774$		0			0
$775$	−4.70840	+	29.8237i	−0.169131	+	1.07130i
$776$		0			0
$777$	17.6738	−	5.74257i	0.634045	−	0.206014i
$778$		0			0
$779$	44.8387	−	32.5772i	1.60651	−	1.16720i
$780$		0			0
$781$	6.93619	+	5.03944i	0.248196	+	0.180325i
$782$		0			0
$783$	−0.582739	+	0.802072i	−0.0208254	+	0.0286637i
$784$		0			0
$785$	−19.8607	−	12.1638i	−0.708858	−	0.434146i
$786$		0			0
$787$	−26.5822	−	8.63708i	−0.947553	−	0.307879i	−0.205832	−	0.978587i	$-0.565990\pi$
$787$	−26.5822	−	8.63708i	−0.947553	−	0.307879i	−0.741721	+	0.670709i	$0.765990\pi$
$788$		0			0
$789$	0.0568844	+	0.175072i	0.00202514	+	0.00623274i
$790$		0			0
$791$	4.34738	−	13.3799i	0.154575	−	0.475733i
$792$		0			0
$793$		−	7.36340i		−	0.261482i
$794$		0			0
$795$	−3.45077	−	4.03830i	−0.122386	−	0.143224i
$796$		0			0
$797$	−9.76290	−	13.4375i	−0.345820	−	0.475980i	0.600310	−	0.799767i	$-0.295044\pi$
$797$	−9.76290	−	13.4375i	−0.345820	−	0.475980i	−0.946130	+	0.323787i	$0.895044\pi$
$798$		0			0
$799$	0.649381			0.0229735
$800$		0			0
$801$	−9.26735			−0.327446
$802$		0			0
$803$	−26.1118	−	35.9398i	−0.921464	−	1.26829i
$804$		0			0
$805$	−31.3749	−	7.52419i	−1.10582	−	0.265193i
$806$		0			0
$807$			8.35214i			0.294009i
$808$		0			0
$809$	5.56807	−	17.1368i	0.195763	−	0.602496i	−0.804204	−	0.594353i	$-0.797408\pi$
$809$	5.56807	−	17.1368i	0.195763	−	0.602496i	0.999967	−	0.00814278i	$-0.00259195\pi$
$810$		0			0
$811$	10.6951	+	32.9161i	0.375555	+	1.15584i	0.943103	+	0.332500i	$0.107892\pi$
$811$	10.6951	+	32.9161i	0.375555	+	1.15584i	−0.567548	+	0.823340i	$0.692108\pi$
$812$		0			0
$813$	−23.4669	−	7.62487i	−0.823021	−	0.267416i
$814$		0			0
$815$	14.9622	−	12.7854i	0.524105	−	0.447853i
$816$		0			0
$817$	25.5291	−	35.1377i	0.893149	−	1.22931i
$818$		0			0
$819$	8.02929	+	5.83362i	0.280566	+	0.203843i
$820$		0			0
$821$	5.74383	−	4.17314i	0.200461	−	0.145644i	−0.483026	−	0.875606i	$-0.660462\pi$
$821$	5.74383	−	4.17314i	0.200461	−	0.145644i	0.683487	+	0.729962i	$0.260462\pi$
$822$		0			0
$823$	−47.8938	+	15.5616i	−1.66947	+	0.542445i	−0.982824	−	0.184545i	$-0.940919\pi$
$823$	−47.8938	+	15.5616i	−1.66947	+	0.542445i	−0.686648	+	0.726990i	$0.740919\pi$
$824$		0			0
$825$	−62.4245	−	9.85522i	−2.17334	−	0.343115i
$826$		0			0
$827$	−13.7780	+	4.47675i	−0.479108	+	0.155672i	−0.538608	−	0.842557i	$-0.681050\pi$
$827$	−13.7780	+	4.47675i	−0.479108	+	0.155672i	0.0594995	+	0.998228i	$0.481050\pi$
$828$		0			0
$829$	−36.0753	+	26.2102i	−1.25295	+	0.910319i	−0.998389	−	0.0567386i	$-0.981930\pi$
$829$	−36.0753	+	26.2102i	−1.25295	+	0.910319i	−0.254558	+	0.967058i	$0.581930\pi$
$830$		0			0
$831$	−61.0485	−	44.3543i	−2.11775	−	1.53864i
$832$		0			0
$833$	6.50985	−	8.96005i	0.225553	−	0.310447i
$834$		0			0
$835$	13.1294	+	31.6749i	0.454362	+	1.09616i
$836$		0			0
$837$	−8.94030	−	2.90488i	−0.309022	−	0.100407i
$838$		0			0
$839$	9.49108	+	29.2105i	0.327668	+	1.00846i	0.970222	+	0.242219i	$0.0778751\pi$
$839$	9.49108	+	29.2105i	0.327668	+	1.00846i	−0.642553	+	0.766241i	$0.722125\pi$
$840$		0			0
$841$	−8.83616	+	27.1949i	−0.304695	+	0.937755i
$842$		0			0
$843$			37.4263i			1.28903i
$844$		0			0
$845$	−25.1815	+	10.4379i	−0.866271	+	0.359074i
$846$		0			0
$847$	−52.9784	−	72.9185i	−1.82036	−	2.50551i
$848$		0			0
$849$	74.2537			2.54838
$850$		0			0
$851$	5.16287			0.176981
$852$		0			0
$853$	9.07778	+	12.4945i	0.310817	+	0.427803i	0.935636	−	0.352967i	$-0.114827\pi$
$853$	9.07778	+	12.4945i	0.310817	+	0.427803i	−0.624819	+	0.780770i	$0.714827\pi$
$854$		0			0
$855$	2.19124	+	27.7540i	0.0749388	+	0.949168i
$856$		0			0
$857$		−	39.7161i		−	1.35668i	−0.734750	−	0.678338i	$-0.762701\pi$
$857$		−	39.7161i		−	1.35668i	0.734750	−	0.678338i	$-0.237299\pi$
$858$		0			0
$859$	10.5848	−	32.5767i	0.361149	−	1.11150i	−0.591209	−	0.806519i	$-0.701349\pi$
$859$	10.5848	−	32.5767i	0.361149	−	1.11150i	0.952358	−	0.304984i	$-0.0986510\pi$
$860$		0			0
$861$	35.0199	+	107.780i	1.19347	+	3.67314i
$862$		0			0
$863$	3.96924	+	1.28969i	0.135115	+	0.0439014i	0.375794	−	0.926703i	$-0.377370\pi$
$863$	3.96924	+	1.28969i	0.135115	+	0.0439014i	−0.240679	+	0.970605i	$0.577370\pi$
$864$		0			0
$865$	−0.227572	+	0.948947i	−0.00773769	+	0.0322652i
$866$		0			0
$867$	−22.3672	+	30.7858i	−0.759631	+	1.04554i
$868$		0			0
$869$	53.8949	+	39.1569i	1.82826	+	1.32831i
$870$		0			0
$871$	−0.992133	+	0.720827i	−0.0336171	+	0.0244243i
$872$		0			0
$873$	−19.7968	+	6.43237i	−0.670021	+	0.217703i
$874$		0			0
$875$	4.12199	−	52.8795i	0.139349	−	1.78765i
$876$		0			0
$877$	6.06523	−	1.97071i	0.204808	−	0.0665462i	−0.204816	−	0.978800i	$-0.565660\pi$
$877$	6.06523	−	1.97071i	0.204808	−	0.0665462i	0.409625	+	0.912254i	$0.365660\pi$
$878$		0			0
$879$	46.1082	−	33.4996i	1.55519	−	1.12991i
$880$		0			0
$881$	2.10044	+	1.52606i	0.0707655	+	0.0514141i	0.622606	−	0.782536i	$-0.286074\pi$
$881$	2.10044	+	1.52606i	0.0707655	+	0.0514141i	−0.551840	+	0.833950i	$0.686074\pi$
$882$		0			0
$883$	−1.59774	+	2.19910i	−0.0537683	+	0.0740057i	−0.835054	−	0.550167i	$-0.814564\pi$
$883$	−1.59774	+	2.19910i	−0.0537683	+	0.0740057i	0.781286	+	0.624173i	$0.214564\pi$
$884$		0			0
$885$	−6.73857	+	28.0990i	−0.226515	+	0.944536i
$886$		0			0
$887$	−24.3954	−	7.92654i	−0.819117	−	0.266147i	−0.130663	−	0.991427i	$-0.541710\pi$
$887$	−24.3954	−	7.92654i	−0.819117	−	0.266147i	−0.688454	+	0.725280i	$0.741710\pi$
$888$		0			0
$889$	−19.0258	−	58.5554i	−0.638105	−	1.96389i
$890$		0			0
$891$	17.8878	−	55.0530i	0.599264	−	1.84434i
$892$		0			0
$893$		−	4.86778i		−	0.162894i
$894$		0			0
$895$	0.554919	+	7.02856i	0.0185489	+	0.234939i
$896$		0			0
$897$	3.71157	+	5.10853i	0.123926	+	0.170569i
$898$		0			0
$899$	3.84579			0.128264
$900$		0			0
$901$	0.735257			0.0244950
$902$		0			0
$903$	52.2002	+	71.8474i	1.73711	+	2.39093i
$904$		0			0
$905$	5.85802	−	2.42818i	0.194727	−	0.0807155i
$906$		0			0
$907$			4.64330i			0.154178i	0.997024	+	0.0770892i	$0.0245626\pi$
$907$			4.64330i			0.154178i	−0.997024	+	0.0770892i	$0.975437\pi$
$908$		0			0
$909$	−3.00264	+	9.24119i	−0.0995914	+	0.306511i
$910$		0			0
$911$	12.1764	+	37.4752i	0.403423	+	1.24161i	0.922205	+	0.386702i	$0.126386\pi$
$911$	12.1764	+	37.4752i	0.403423	+	1.24161i	−0.518782	+	0.854907i	$0.673614\pi$
$912$		0			0
$913$	66.8400	+	21.7176i	2.21208	+	0.718749i
$914$		0			0
$915$	16.1723	+	39.0159i	0.534639	+	1.28983i
$916$		0			0
$917$	−6.49270	+	8.93643i	−0.214408	+	0.295107i
$918$		0			0
$919$	38.1655	+	27.7289i	1.25896	+	0.914691i	0.998706	−	0.0508479i	$-0.0161924\pi$
$919$	38.1655	+	27.7289i	1.25896	+	0.914691i	0.260258	+	0.965539i	$0.416192\pi$
$920$		0			0
$921$	60.0461	−	43.6261i	1.97859	−	1.43753i
$922$		0			0
$923$	1.33932	−	0.435172i	0.0440844	−	0.0143239i
$924$		0			0
$925$	1.33188	+	8.38214i	0.0437918	+	0.275603i
$926$		0			0
$927$	−20.9906	+	6.82027i	−0.689423	+	0.224007i
$928$		0			0
$929$	−12.3373	+	8.96357i	−0.404774	+	0.294085i	−0.771483	−	0.636251i	$-0.780484\pi$
$929$	−12.3373	+	8.96357i	−0.404774	+	0.294085i	0.366709	+	0.930336i	$0.380484\pi$
$930$		0			0
$931$	−67.1648	−	48.7981i	−2.20124	−	1.59929i
$932$		0			0
$933$	29.7841	−	40.9943i	0.975087	−	1.34209i
$934$		0			0
$935$	6.65041	−	5.68285i	0.217492	−	0.185849i
$936$		0			0
$937$	−24.5440	−	7.97482i	−0.801817	−	0.260526i	−0.120689	−	0.992690i	$-0.538510\pi$
$937$	−24.5440	−	7.97482i	−0.801817	−	0.260526i	−0.681128	+	0.732164i	$0.738510\pi$
$938$		0			0
$939$	−3.88664	−	11.9619i	−0.126836	−	0.390361i
$940$		0			0
$941$	−7.80115	+	24.0095i	−0.254310	+	0.782686i	0.739655	+	0.672987i	$0.234989\pi$
$941$	−7.80115	+	24.0095i	−0.254310	+	0.782686i	−0.993965	+	0.109700i	$0.965011\pi$
$942$		0			0
$943$			31.4847i			1.02528i
$944$		0			0
$945$	16.0582	+	3.85102i	0.522375	+	0.125274i
$946$		0			0
$947$	13.9453	+	19.1940i	0.453161	+	0.623722i	0.973073	−	0.230497i	$-0.0740354\pi$
$947$	13.9453	+	19.1940i	0.453161	+	0.623722i	−0.519912	+	0.854220i	$0.674035\pi$
$948$		0			0
$949$	−7.29681			−0.236865
$950$		0			0
$951$	−0.329474			−0.0106839
$952$		0			0
$953$	28.0510	+	38.6089i	0.908661	+	1.25066i	0.967622	+	0.252404i	$0.0812212\pi$
$953$	28.0510	+	38.6089i	0.908661	+	1.25066i	−0.0589610	+	0.998260i	$0.518779\pi$
$954$		0			0
$955$	−18.6457	−	21.8203i	−0.603360	−	0.706088i
$956$		0			0
$957$			8.04968i			0.260209i
$958$		0			0
$959$	19.4319	−	59.8052i	0.627489	−	1.93121i
$960$		0			0
$961$	1.68877	+	5.19749i	0.0544764	+	0.167661i
$962$		0			0
$963$	−11.5531	−	3.75383i	−0.372293	−	0.120965i
$964$		0			0
$965$	24.2108	+	14.8281i	0.779373	+	0.477334i
$966$		0			0
$967$	−22.2597	+	30.6379i	−0.715825	+	0.985248i	0.283827	+	0.958875i	$0.408396\pi$
$967$	−22.2597	+	30.6379i	−0.715825	+	0.985248i	−0.999652	+	0.0263728i	$0.991604\pi$
$968$		0			0
$969$	−7.13969	−	5.18729i	−0.229360	−	0.166640i
$970$		0			0
$971$	23.1067	−	16.7880i	0.741528	−	0.538752i	−0.151661	−	0.988433i	$-0.548462\pi$
$971$	23.1067	−	16.7880i	0.741528	−	0.538752i	0.893189	+	0.449681i	$0.148462\pi$
$972$		0			0
$973$	−17.4086	+	5.65639i	−0.558094	+	0.181336i
$974$		0			0
$975$	−7.33644	+	7.34375i	−0.234954	+	0.235188i
$976$		0			0
$977$	20.4567	−	6.64677i	0.654467	−	0.212649i	0.0370841	−	0.999312i	$-0.488193\pi$
$977$	20.4567	−	6.64677i	0.654467	−	0.212649i	0.617383	+	0.786663i	$0.288193\pi$
$978$		0			0
$979$	17.6590	−	12.8300i	0.564383	−	0.410048i
$980$		0			0
$981$	3.61587	+	2.62708i	0.115446	+	0.0838762i
$982$		0			0
$983$	−0.131193	+	0.180572i	−0.00418441	+	0.00575934i	−0.811104	−	0.584902i	$-0.801133\pi$
$983$	−0.131193	+	0.180572i	−0.00418441	+	0.00575934i	0.806920	+	0.590661i	$0.201133\pi$
$984$		0			0
$985$	55.4711	−	4.37956i	1.76746	−	0.139544i
$986$		0			0
$987$	9.46618	+	3.07575i	0.301312	+	0.0979021i
$988$		0			0
$989$	7.62434	+	23.4653i	0.242440	+	0.746154i
$990$		0			0
$991$	5.95183	−	18.3179i	0.189066	−	0.581886i	−0.810929	−	0.585145i	$-0.801038\pi$
$991$	5.95183	−	18.3179i	0.189066	−	0.581886i	0.999995	+	0.00325947i	$0.00103752\pi$
$992$		0			0
$993$			53.8928i			1.71024i
$994$		0			0
$995$	10.7908	−	17.6188i	0.342091	−	0.558553i
$996$		0			0
$997$	−27.1237	−	37.3325i	−0.859015	−	1.18233i	−0.981803	−	0.189900i	$-0.939184\pi$
$997$	−27.1237	−	37.3325i	−0.859015	−	1.18233i	0.122789	−	0.992433i	$-0.460816\pi$
$998$		0			0
$999$	−2.64245			−0.0836034

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.2.q.a.169.7	yes	32
4.3	odd	2		400.2.y.d.369.2		32
5.2	odd	4		1000.2.m.e.401.7		32
5.3	odd	4		1000.2.m.d.401.2		32
5.4	even	2		1000.2.q.c.849.2		32
25.2	odd	20		5000.2.a.q.1.4		16
25.3	odd	20		1000.2.m.d.601.2		32
25.4	even	10	inner	200.2.q.a.129.7	✓	32
25.21	even	5		1000.2.q.c.649.2		32
25.22	odd	20		1000.2.m.e.601.7		32
25.23	odd	20		5000.2.a.r.1.13		16
100.23	even	20		10000.2.a.bq.1.4		16
100.27	even	20		10000.2.a.br.1.13		16
100.79	odd	10		400.2.y.d.129.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.q.a.129.7	✓	32	25.4	even	10	inner
200.2.q.a.169.7	yes	32	1.1	even	1	trivial
400.2.y.d.129.2		32	100.79	odd	10
400.2.y.d.369.2		32	4.3	odd	2
1000.2.m.d.401.2		32	5.3	odd	4
1000.2.m.d.601.2		32	25.3	odd	20
1000.2.m.e.401.7		32	5.2	odd	4
1000.2.m.e.601.7		32	25.22	odd	20
1000.2.q.c.649.2		32	25.21	even	5
1000.2.q.c.849.2		32	5.4	even	2
5000.2.a.q.1.4		16	25.2	odd	20
5000.2.a.r.1.13		16	25.23	odd	20
10000.2.a.bq.1.4		16	100.23	even	20
10000.2.a.br.1.13		16	100.27	even	20

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	200.q (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35643 + 1.86696i) q^{3} +(1.16787 - 1.90685i) q^{5} +4.74404i q^{7} +(-0.718596 + 2.21161i) q^{9} +(-1.69253 - 5.20907i) q^{11} +(-0.855610 - 0.278005i) q^{13} +(5.14414 - 0.406141i) q^{15} +(-0.419832 + 0.577849i) q^{17} +(4.33157 + 3.14707i) q^{19} +(-8.85692 + 6.43493i) q^{21} +(-2.89267 + 0.939884i) q^{23} +(-2.27217 - 4.45390i) q^{25} +(1.48052 - 0.481050i) q^{27} +(-0.515235 + 0.374340i) q^{29} +(-4.88535 - 3.54941i) q^{31} +(7.42933 - 10.2256i) q^{33} +(9.04617 + 5.54041i) q^{35} +(-1.61438 - 0.524543i) q^{37} +(-0.641548 - 1.97448i) q^{39} +(3.19882 - 9.84495i) q^{41} -8.11200i q^{43} +(3.37799 + 3.95312i) q^{45} +(-0.534394 - 0.735531i) q^{47} -15.5059 q^{49} -1.64829 q^{51} +(-0.605064 - 0.832800i) q^{53} +(-11.9096 - 2.85610i) q^{55} +12.3556i q^{57} +(-1.73043 + 5.32571i) q^{59} +(2.52925 + 7.78422i) q^{61} +(-10.4920 - 3.40904i) q^{63} +(-1.52935 + 1.30685i) q^{65} +(0.801238 - 1.10281i) q^{67} +(-5.67841 - 4.12561i) q^{69} +(-1.26639 + 0.920086i) q^{71} +(7.71383 - 2.50637i) q^{73} +(5.23323 - 10.2834i) q^{75} +(24.7120 - 8.02942i) q^{77} +(-9.83997 + 7.14916i) q^{79} +(8.55024 + 6.21211i) q^{81} +(-7.54215 + 10.3809i) q^{83} +(0.611564 + 1.47541i) q^{85} +(-1.39776 - 0.454158i) q^{87} +(1.23150 + 3.79018i) q^{89} +(1.31886 - 4.05904i) q^{91} -13.9353i q^{93} +(11.0597 - 4.58431i) q^{95} +(5.26145 + 7.24176i) q^{97} +12.7367 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{5} + 10 q^{9} + 6 q^{11} + 12 q^{15} - 6 q^{19} - 4 q^{21} - 30 q^{23} + 6 q^{25} - 2 q^{29} + 6 q^{31} + 8 q^{35} - 40 q^{37} - 12 q^{39} - 12 q^{45} - 20 q^{47} - 60 q^{49} - 60 q^{51} - 30 q^{53}+ \cdots + 92 q^{99}+O(q^{100}) \) 32 * q + 2 * q^5 + 10 * q^9 + 6 * q^11 + 12 * q^15 - 6 * q^19 - 4 * q^21 - 30 * q^23 + 6 * q^25 - 2 * q^29 + 6 * q^31 + 8 * q^35 - 40 * q^37 - 12 * q^39 - 12 * q^45 - 20 * q^47 - 60 * q^49 - 60 * q^51 - 30 * q^53 - 28 * q^55 - 30 * q^59 + 14 * q^61 - 20 * q^63 - 26 * q^65 - 4 * q^69 + 12 * q^71 + 40 * q^73 + 16 * q^75 + 16 * q^79 - 52 * q^81 + 30 * q^83 + 60 * q^85 + 110 * q^87 + 24 * q^89 - 4 * q^91 + 68 * q^95 + 30 * q^97 + 92 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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