LMFDB - Embedded newform 351.2.i.b.242.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(161,351)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("351.161"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.i (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{14} + 184x^{12} + 600x^{10} + 894x^{8} + 600x^{6} + 184x^{4} + 24x^{2} + 1 $ x^16 + 24x^14 + 184x^12 + 600x^10 + 894x^8 + 600x^6 + 184x^4 + 24*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			242.8
Root			$3.60931i$ of defining polynomial
Character	$\chi$	$=$	351.242
Dual form			351.2.i.b.161.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.94318 - 1.94318i) q^{2} -5.55193i q^{4} +(0.426892 - 0.426892i) q^{5} +(-1.60020 + 1.60020i) q^{7} +(-6.90206 - 6.90206i) q^{8} -1.65906i q^{10} +(-1.16629 - 1.16629i) q^{11} +(3.11256 + 1.81988i) q^{13} +6.21895i q^{14} -15.7201 q^{16} +6.73139 q^{17} +(-1.61949 - 1.61949i) q^{19} +(-2.37008 - 2.37008i) q^{20} -4.53264 q^{22} +7.07274 q^{23} +4.63553i q^{25} +(9.58465 - 2.51191i) q^{26} +(8.88418 + 8.88418i) q^{28} +4.74015i q^{29} +(-3.99131 - 3.99131i) q^{31} +(-16.7429 + 16.7429i) q^{32} +(13.0803 - 13.0803i) q^{34} +1.36622i q^{35} +(-5.84461 + 5.84461i) q^{37} -6.29394 q^{38} -5.89287 q^{40} +(1.16629 - 1.16629i) q^{41} -2.02473i q^{43} +(-6.47517 + 6.47517i) q^{44} +(13.7436 - 13.7436i) q^{46} +(-5.13821 - 5.13821i) q^{47} +1.87875i q^{49} +(9.00768 + 9.00768i) q^{50} +(10.1039 - 17.2807i) q^{52} -0.512438i q^{53} -0.995761 q^{55} +22.0893 q^{56} +(9.21099 + 9.21099i) q^{58} +(4.62577 + 4.62577i) q^{59} -1.50693 q^{61} -15.5117 q^{62} +33.6290i q^{64} +(2.10562 - 0.551834i) q^{65} +(3.28398 + 3.28398i) q^{67} -37.3722i q^{68} +(2.65482 + 2.65482i) q^{70} +(7.49963 - 7.49963i) q^{71} +(-4.30752 + 4.30752i) q^{73} +22.7143i q^{74} +(-8.99131 + 8.99131i) q^{76} +3.73259 q^{77} -9.54324 q^{79} +(-6.71079 + 6.71079i) q^{80} -4.53264i q^{82} +(-1.71812 + 1.71812i) q^{83} +(2.87358 - 2.87358i) q^{85} +(-3.93442 - 3.93442i) q^{86} +16.0996i q^{88} +(-5.47955 - 5.47955i) q^{89} +(-7.89287 + 2.06854i) q^{91} -39.2674i q^{92} -19.9690 q^{94} -1.38270 q^{95} +(5.52721 + 5.52721i) q^{97} +(3.65075 + 3.65075i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7} + 16 q^{13} - 8 q^{16} - 32 q^{19} + 8 q^{22} + 40 q^{28} + 16 q^{31} + 24 q^{34} - 32 q^{37} - 72 q^{40} + 48 q^{46} + 48 q^{52} + 32 q^{55} + 56 q^{58} - 64 q^{61} - 32 q^{67} - 40 q^{70}+ \cdots + 64 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 + 16 * q^13 - 8 * q^16 - 32 * q^19 + 8 * q^22 + 40 * q^28 + 16 * q^31 + 24 * q^34 - 32 * q^37 - 72 * q^40 + 48 * q^46 + 48 * q^52 + 32 * q^55 + 56 * q^58 - 64 * q^61 - 32 * q^67 - 40 * q^70 - 56 * q^73 - 64 * q^76 - 16 * q^79 - 104 * q^91 - 64 * q^94 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	1.94318	−	1.94318i	1.37404	−	1.37404i	0.519675	−	0.854364i	$-0.326053\pi$
$2$	1.94318	−	1.94318i	1.37404	−	1.37404i	0.854364	−	0.519675i	$-0.173947\pi$
$3$		0			0
$3$		0			0
$4$		−	5.55193i		−	2.77597i
$5$	0.426892	−	0.426892i	0.190912	−	0.190912i	−0.605178	−	0.796090i	$-0.706898\pi$
$5$	0.426892	−	0.426892i	0.190912	−	0.190912i	0.796090	+	0.605178i	$0.206898\pi$
$6$		0			0
$7$	−1.60020	+	1.60020i	−0.604817	+	0.604817i	−0.941587	−	0.336770i	$-0.890666\pi$
$7$	−1.60020	+	1.60020i	−0.604817	+	0.604817i	0.336770	+	0.941587i	$0.390666\pi$
$8$	−6.90206	−	6.90206i	−2.44025	−	2.44025i
$9$		0			0
$10$		−	1.65906i		−	0.524641i
$11$	−1.16629	−	1.16629i	−0.351650	−	0.351650i	0.509073	−	0.860723i	$-0.329988\pi$
$11$	−1.16629	−	1.16629i	−0.351650	−	0.351650i	−0.860723	+	0.509073i	$0.829988\pi$
$12$		0			0
$13$	3.11256	+	1.81988i	0.863269	+	0.504745i
$13$	3.11256	+	1.81988i	0.863269	+	0.504745i
$14$			6.21895i			1.66208i
$15$		0			0
$16$	−15.7201			−3.93002
$17$	6.73139			1.63260			0.816301	−	0.577627i	$-0.196021\pi$
$17$	6.73139			1.63260			0.816301	+	0.577627i	$0.196021\pi$
$18$		0			0
$19$	−1.61949	−	1.61949i	−0.371537	−	0.371537i	0.496500	−	0.868037i	$-0.334618\pi$
$19$	−1.61949	−	1.61949i	−0.371537	−	0.371537i	−0.868037	+	0.496500i	$0.834618\pi$
$20$	−2.37008	−	2.37008i	−0.529965	−	0.529965i
$21$		0			0
$22$	−4.53264			−0.966362
$23$	7.07274			1.47477			0.737384	−	0.675474i	$-0.236061\pi$
$23$	7.07274			1.47477			0.737384	+	0.675474i	$0.236061\pi$
$24$		0			0
$25$			4.63553i			0.927105i
$26$	9.58465	−	2.51191i	1.87970	−	0.492626i
$27$		0			0
$28$	8.88418	+	8.88418i	1.67895	+	1.67895i
$29$			4.74015i			0.880224i	0.897943	+	0.440112i	$0.145061\pi$
$29$			4.74015i			0.880224i	−0.897943	+	0.440112i	$0.854939\pi$
$30$		0			0
$31$	−3.99131	−	3.99131i	−0.716860	−	0.716860i	0.251101	−	0.967961i	$-0.419207\pi$
$31$	−3.99131	−	3.99131i	−0.716860	−	0.716860i	−0.967961	+	0.251101i	$0.919207\pi$
$32$	−16.7429	+	16.7429i	−2.95976	+	2.95976i
$33$		0			0
$34$	13.0803	−	13.0803i	2.24326	−	2.24326i
$35$			1.36622i			0.230934i
$36$		0			0
$37$	−5.84461	+	5.84461i	−0.960848	+	0.960848i	−0.999262	−	0.0384139i	$-0.987769\pi$
$37$	−5.84461	+	5.84461i	−0.960848	+	0.960848i	0.0384139	+	0.999262i	$0.487769\pi$
$38$	−6.29394			−1.02101
$39$		0			0
$40$	−5.89287			−0.931745
$41$	1.16629	−	1.16629i	0.182144	−	0.182144i	−0.610145	−	0.792289i	$-0.708889\pi$
$41$	1.16629	−	1.16629i	0.182144	−	0.182144i	0.792289	+	0.610145i	$0.208889\pi$
$42$		0			0
$43$		−	2.02473i		−	0.308768i	−0.988011	−	0.154384i	$-0.950661\pi$
$43$		−	2.02473i		−	0.308768i	0.988011	−	0.154384i	$-0.0493393\pi$
$44$	−6.47517	+	6.47517i	−0.976169	+	0.976169i
$45$		0			0
$46$	13.7436	−	13.7436i	2.02639	−	2.02639i
$47$	−5.13821	−	5.13821i	−0.749484	−	0.749484i	0.224898	−	0.974382i	$-0.427795\pi$
$47$	−5.13821	−	5.13821i	−0.749484	−	0.749484i	−0.974382	+	0.224898i	$0.927795\pi$
$48$		0			0
$49$			1.87875i			0.268392i
$50$	9.00768	+	9.00768i	1.27388	+	1.27388i
$51$		0			0
$52$	10.1039	−	17.2807i	1.40115	−	2.39641i
$53$		−	0.512438i		−	0.0703887i	−0.999380	−	0.0351944i	$-0.988795\pi$
$53$		−	0.512438i		−	0.0703887i	0.999380	−	0.0351944i	$-0.0112050\pi$
$54$		0			0
$55$	−0.995761			−0.134268
$56$	22.0893			2.95181
$57$		0			0
$58$	9.21099	+	9.21099i	1.20946	+	1.20946i
$59$	4.62577	+	4.62577i	0.602224	+	0.602224i	0.940902	−	0.338678i	$-0.109980\pi$
$59$	4.62577	+	4.62577i	0.602224	+	0.602224i	−0.338678	+	0.940902i	$0.609980\pi$
$60$		0			0
$61$	−1.50693			−0.192943			−0.0964714	−	0.995336i	$-0.530756\pi$
$61$	−1.50693			−0.192943			−0.0964714	+	0.995336i	$0.530756\pi$
$62$	−15.5117			−1.96999
$63$		0			0
$64$			33.6290i			4.20363i
$65$	2.10562	−	0.551834i	0.261170	−	0.0684465i
$66$		0			0
$67$	3.28398	+	3.28398i	0.401203	+	0.401203i	0.878657	−	0.477454i	$-0.158440\pi$
$67$	3.28398	+	3.28398i	0.401203	+	0.401203i	−0.477454	+	0.878657i	$0.658440\pi$
$68$		−	37.3722i		−	4.53205i
$69$		0			0
$70$	2.65482	+	2.65482i	0.317312	+	0.317312i
$71$	7.49963	−	7.49963i	0.890042	−	0.890042i	−0.104484	−	0.994527i	$-0.533319\pi$
$71$	7.49963	−	7.49963i	0.890042	−	0.890042i	0.994527	+	0.104484i	$0.0333192\pi$
$72$		0			0
$73$	−4.30752	+	4.30752i	−0.504157	+	0.504157i	−0.912727	−	0.408570i	$-0.866028\pi$
$73$	−4.30752	+	4.30752i	−0.504157	+	0.504157i	0.408570	+	0.912727i	$0.366028\pi$
$74$			22.7143i			2.64049i
$75$		0			0
$76$	−8.99131	+	8.99131i	−1.03137	+	1.03137i
$77$	3.73259			0.425368
$78$		0			0
$79$	−9.54324			−1.07370			−0.536849	−	0.843678i	$-0.680386\pi$
$79$	−9.54324			−1.07370			−0.536849	+	0.843678i	$0.680386\pi$
$80$	−6.71079	+	6.71079i	−0.750289	+	0.750289i
$81$		0			0
$82$		−	4.53264i		−	0.500546i
$83$	−1.71812	+	1.71812i	−0.188589	+	0.188589i	−0.795086	−	0.606497i	$-0.792574\pi$
$83$	−1.71812	+	1.71812i	−0.188589	+	0.188589i	0.606497	+	0.795086i	$0.292574\pi$
$84$		0			0
$85$	2.87358	−	2.87358i	0.311683	−	0.311683i
$86$	−3.93442	−	3.93442i	−0.424259	−	0.424259i
$87$		0			0
$88$			16.0996i			1.71623i
$89$	−5.47955	−	5.47955i	−0.580831	−	0.580831i	0.354300	−	0.935132i	$-0.384719\pi$
$89$	−5.47955	−	5.47955i	−0.580831	−	0.580831i	−0.935132	+	0.354300i	$0.884719\pi$
$90$		0			0
$91$	−7.89287	+	2.06854i	−0.827398	+	0.216842i
$92$		−	39.2674i		−	4.09391i
$93$		0			0
$94$	−19.9690			−2.05964
$95$	−1.38270			−0.141862
$96$		0			0
$97$	5.52721	+	5.52721i	0.561203	+	0.561203i	0.929649	−	0.368446i	$-0.120110\pi$
$97$	5.52721	+	5.52721i	0.561203	+	0.561203i	−0.368446	+	0.929649i	$0.620110\pi$
$98$	3.65075	+	3.65075i	0.368782	+	0.368782i
$99$		0			0
$100$	25.7361			2.57361
$101$	−17.9742			−1.78850			−0.894248	−	0.447572i	$-0.852289\pi$
$101$	−17.9742			−1.78850			−0.894248	+	0.447572i	$0.852289\pi$
$102$		0			0
$103$		−	0.511171i		−	0.0503671i	−0.999683	−	0.0251836i	$-0.991983\pi$
$103$		−	0.511171i		−	0.0503671i	0.999683	−	0.0251836i	$-0.00801702\pi$
$104$	−8.92214	−	34.0440i	−0.874888	−	3.33829i
$105$		0			0
$106$	−0.995761	−	0.995761i	−0.0967169	−	0.0967169i
$107$			14.4291i			1.39492i	0.716625	+	0.697459i	$0.245686\pi$
$107$			14.4291i			1.39492i	−0.716625	+	0.697459i	$0.754314\pi$
$108$		0			0
$109$	2.50367	+	2.50367i	0.239808	+	0.239808i	0.816771	−	0.576962i	$-0.195762\pi$
$109$	2.50367	+	2.50367i	0.239808	+	0.239808i	−0.576962	+	0.816771i	$0.695762\pi$
$110$	−1.93495	+	1.93495i	−0.184490	+	0.184490i
$111$		0			0
$112$	25.1552	−	25.1552i	2.37695	−	2.37695i
$113$			2.50367i			0.235526i	0.993042	+	0.117763i	$0.0375723\pi$
$113$			2.50367i			0.235526i	−0.993042	+	0.117763i	$0.962428\pi$
$114$		0			0
$115$	3.01930	−	3.01930i	0.281551	−	0.281551i
$116$	26.3170			2.44347
$117$		0			0
$118$	17.9774			1.65496
$119$	−10.7715	+	10.7715i	−0.987425	+	0.987425i
$120$		0			0
$121$		−	8.27953i		−	0.752685i
$122$	−2.92825	+	2.92825i	−0.265111	+	0.265111i
$123$		0			0
$124$	−22.1595	+	22.1595i	−1.98998	+	1.98998i
$125$	4.11333	+	4.11333i	0.367907	+	0.367907i
$126$		0			0
$127$		−	10.5722i		−	0.938132i	−0.883163	−	0.469066i	$-0.844591\pi$
$127$		−	10.5722i		−	0.938132i	0.883163	−	0.469066i	$-0.155409\pi$
$128$	31.8615	+	31.8615i	2.81619	+	2.81619i
$129$		0			0
$130$	3.01930	−	5.16393i	0.264810	−	0.452906i
$131$		−	14.2416i		−	1.24429i	−0.782901	−	0.622146i	$-0.786261\pi$
$131$		−	14.2416i		−	1.24429i	0.782901	−	0.622146i	$-0.213739\pi$
$132$		0			0
$133$	5.18301			0.449424
$134$	12.7628			1.10254
$135$		0			0
$136$	−46.4605	−	46.4605i	−3.98395	−	3.98395i
$137$	−11.3466	−	11.3466i	−0.969406	−	0.969406i	0.0301401	−	0.999546i	$-0.490405\pi$
$137$	−11.3466	−	11.3466i	−0.969406	−	0.969406i	−0.999546	+	0.0301401i	$0.990405\pi$
$138$		0			0
$139$	3.84906			0.326473			0.163237	−	0.986587i	$-0.447807\pi$
$139$	3.84906			0.326473			0.163237	+	0.986587i	$0.447807\pi$
$140$	7.58517			0.641064
$141$		0			0
$142$		−	29.1463i		−	2.44591i
$143$	−1.50764	−	5.75266i	−0.126075	−	0.481062i
$144$		0			0
$145$	2.02353	+	2.02353i	0.168045	+	0.168045i
$146$			16.7406i			1.38546i
$147$		0			0
$148$	32.4489	+	32.4489i	2.66728	+	2.66728i
$149$	−0.114385	+	0.114385i	−0.00937082	+	0.00937082i	−0.711777	−	0.702406i	$-0.752109\pi$
$149$	−0.114385	+	0.114385i	−0.00937082	+	0.00937082i	0.702406	+	0.711777i	$0.252109\pi$
$150$		0			0
$151$	−10.9045	+	10.9045i	−0.887392	+	0.887392i	−0.994272	−	0.106880i	$-0.965914\pi$
$151$	−10.9045	+	10.9045i	−0.887392	+	0.887392i	0.106880	+	0.994272i	$0.465914\pi$
$152$			22.3557i			1.81328i
$153$		0			0
$154$	7.25311	−	7.25311i	0.584472	−	0.584472i
$155$	−3.40772			−0.273714
$156$		0			0
$157$	2.46410			0.196657			0.0983284	−	0.995154i	$-0.468650\pi$
$157$	2.46410			0.196657			0.0983284	+	0.995154i	$0.468650\pi$
$158$	−18.5443	+	18.5443i	−1.47530	+	1.47530i
$159$		0			0
$160$			14.2948i			1.13011i
$161$	−11.3178	+	11.3178i	−0.891965	+	0.891965i
$162$		0			0
$163$	−2.30426	+	2.30426i	−0.180483	+	0.180483i	−0.791566	−	0.611083i	$-0.790734\pi$
$163$	−2.30426	+	2.30426i	−0.180483	+	0.180483i	0.611083	+	0.791566i	$0.290734\pi$
$164$	−6.47517	−	6.47517i	−0.505626	−	0.505626i
$165$		0			0
$166$			6.67727i			0.518256i
$167$	−3.53447	−	3.53447i	−0.273505	−	0.273505i	0.557004	−	0.830510i	$-0.311951\pi$
$167$	−3.53447	−	3.53447i	−0.273505	−	0.273505i	−0.830510	+	0.557004i	$0.811951\pi$
$168$		0			0
$169$	6.37605	+	11.3290i	0.490466	+	0.871460i
$170$		−	11.1678i		−	0.856530i
$171$		0			0
$172$	−11.2412			−0.857130
$173$	1.13745			0.0864788			0.0432394	−	0.999065i	$-0.486232\pi$
$173$	1.13745			0.0864788			0.0432394	+	0.999065i	$0.486232\pi$
$174$		0			0
$175$	−7.41775	−	7.41775i	−0.560729	−	0.560729i
$176$	18.3342	+	18.3342i	1.38199	+	1.38199i
$177$		0			0
$178$	−21.2956			−1.59617
$179$	−16.0241			−1.19770			−0.598850	−	0.800861i	$-0.704375\pi$
$179$	−16.0241			−1.19770			−0.598850	+	0.800861i	$0.704375\pi$
$180$		0			0
$181$			17.2463i			1.28191i	0.767579	+	0.640955i	$0.221461\pi$
$181$			17.2463i			1.28191i	−0.767579	+	0.640955i	$0.778539\pi$
$182$	−11.3178	+	19.3569i	−0.838928	+	1.43483i
$183$		0			0
$184$	−48.8165	−	48.8165i	−3.59880	−	3.59880i
$185$			4.99004i			0.366875i
$186$		0			0
$187$	−7.85076	−	7.85076i	−0.574104	−	0.574104i
$188$	−28.5270	+	28.5270i	−2.08054	+	2.08054i
$189$		0			0
$190$	−2.68683	+	2.68683i	−0.194923	+	0.194923i
$191$			4.14892i			0.300206i	0.988670	+	0.150103i	$0.0479605\pi$
$191$			4.14892i			0.300206i	−0.988670	+	0.150103i	$0.952040\pi$
$192$		0			0
$193$	8.02762	−	8.02762i	0.577840	−	0.577840i	−0.356467	−	0.934308i	$-0.616019\pi$
$193$	8.02762	−	8.02762i	0.577840	−	0.577840i	0.934308	+	0.356467i	$0.116019\pi$
$194$	21.4808			1.54223
$195$		0			0
$196$	10.4307			0.745049
$197$	6.95835	−	6.95835i	0.495762	−	0.495762i	−0.414354	−	0.910116i	$-0.635992\pi$
$197$	6.95835	−	6.95835i	0.495762	−	0.495762i	0.910116	+	0.414354i	$0.135992\pi$
$198$		0			0
$199$			5.95717i			0.422293i	0.977454	+	0.211146i	$0.0677196\pi$
$199$			5.95717i			0.422293i	−0.977454	+	0.211146i	$0.932280\pi$
$200$	31.9947	−	31.9947i	2.26237	−	2.26237i
$201$		0			0
$202$	−34.9271	+	34.9271i	−2.45746	+	2.45746i
$203$	−7.58517	−	7.58517i	−0.532375	−	0.532375i
$204$		0			0
$205$		−	0.995761i		−	0.0695470i
$206$	−0.993299	−	0.993299i	−0.0692064	−	0.0692064i
$207$		0			0
$208$	−48.9297	−	28.6087i	−3.39267	−	1.98366i
$209$			3.77760i			0.261302i
$210$		0			0
$211$	13.9572			0.960851			0.480426	−	0.877035i	$-0.340482\pi$
$211$	13.9572			0.960851			0.480426	+	0.877035i	$0.340482\pi$
$212$	−2.84502			−0.195397
$213$		0			0
$214$	28.0385	+	28.0385i	1.91667	+	1.91667i
$215$	−0.864340	−	0.864340i	−0.0589475	−	0.0589475i
$216$		0			0
$217$	12.7737			0.867138
$218$	9.73019			0.659012
$219$		0			0
$220$			5.52840i			0.372725i
$221$	20.9519	+	12.2503i	1.40937	+	0.824047i
$222$		0			0
$223$	−8.32355	−	8.32355i	−0.557386	−	0.557386i	0.371176	−	0.928562i	$-0.378955\pi$
$223$	−8.32355	−	8.32355i	−0.557386	−	0.557386i	−0.928562	+	0.371176i	$0.878955\pi$
$224$		−	53.5839i		−	3.58023i
$225$		0			0
$226$	4.86510	+	4.86510i	0.323622	+	0.323622i
$227$	11.7447	−	11.7447i	0.779520	−	0.779520i	−0.200229	−	0.979749i	$-0.564169\pi$
$227$	11.7447	−	11.7447i	0.779520	−	0.779520i	0.979749	+	0.200229i	$0.0641686\pi$
$228$		0			0
$229$	3.63362	−	3.63362i	0.240116	−	0.240116i	−0.576782	−	0.816898i	$-0.695692\pi$
$229$	3.63362	−	3.63362i	0.240116	−	0.240116i	0.816898	+	0.576782i	$0.195692\pi$
$230$		−	11.7341i		−	0.773723i
$231$		0			0
$232$	32.7168	−	32.7168i	2.14797	−	2.14797i
$233$	3.77379			0.247229			0.123615	−	0.992330i	$-0.460551\pi$
$233$	3.77379			0.247229			0.123615	+	0.992330i	$0.460551\pi$
$234$		0			0
$235$	−4.38692			−0.286171
$236$	25.6820	−	25.6820i	1.67175	−	1.67175i
$237$		0			0
$238$			41.8622i			2.71352i
$239$	−18.7030	+	18.7030i	−1.20980	+	1.20980i	−0.238705	+	0.971092i	$0.576723\pi$
$239$	−18.7030	+	18.7030i	−1.20980	+	1.20980i	−0.971092	+	0.238705i	$0.923277\pi$
$240$		0			0
$241$	16.0618	−	16.0618i	1.03463	−	1.03463i	0.0352499	−	0.999379i	$-0.488777\pi$
$241$	16.0618	−	16.0618i	1.03463	−	1.03463i	0.999379	−	0.0352499i	$-0.0112227\pi$
$242$	−16.0887	−	16.0887i	−1.03422	−	1.03422i
$243$		0			0
$244$			8.36638i			0.535603i
$245$	0.802023	+	0.802023i	0.0512393	+	0.0512393i
$246$		0			0
$247$	−2.09348	−	7.98805i	−0.133205	−	0.508267i
$248$			55.0965i			3.49863i
$249$		0			0
$250$	15.9859			1.01104
$251$	15.8291			0.999127			0.499563	−	0.866277i	$-0.333494\pi$
$251$	15.8291			0.999127			0.499563	+	0.866277i	$0.333494\pi$
$252$		0			0
$253$	−8.24887	−	8.24887i	−0.518602	−	0.518602i
$254$	−20.5438	−	20.5438i	−1.28903	−	1.28903i
$255$		0			0
$256$	56.5676			3.53547
$257$	−13.3878			−0.835107			−0.417554	−	0.908652i	$-0.637112\pi$
$257$	−13.3878			−0.835107			−0.417554	+	0.908652i	$0.637112\pi$
$258$		0			0
$259$		−	18.7050i		−	1.16227i
$260$	−3.06374	−	11.6903i	−0.190005	−	0.725000i
$261$		0			0
$262$	−27.6740	−	27.6740i	−1.70971	−	1.70971i
$263$			4.87004i			0.300299i	0.988663	+	0.150150i	$0.0479756\pi$
$263$			4.87004i			0.300299i	−0.988663	+	0.150150i	$0.952024\pi$
$264$		0			0
$265$	−0.218756	−	0.218756i	−0.0134381	−	0.0134381i
$266$	10.0715	−	10.0715i	0.617526	−	0.617526i
$267$		0			0
$268$	18.2325	−	18.2325i	1.11372	−	1.11372i
$269$		−	25.3095i		−	1.54314i	−0.636142	−	0.771572i	$-0.719471\pi$
$269$		−	25.3095i		−	1.54314i	0.636142	−	0.771572i	$-0.280529\pi$
$270$		0			0
$271$	1.49752	−	1.49752i	0.0909680	−	0.0909680i	−0.660158	−	0.751126i	$-0.729511\pi$
$271$	1.49752	−	1.49752i	0.0909680	−	0.0909680i	0.751126	+	0.660158i	$0.229511\pi$
$272$	−105.818			−6.41616
$273$		0			0
$274$	−44.0971			−2.66400
$275$	5.40637	−	5.40637i	0.326017	−	0.326017i
$276$		0			0
$277$			23.8317i			1.43191i	0.698148	+	0.715953i	$0.254008\pi$
$277$			23.8317i			1.43191i	−0.698148	+	0.715953i	$0.745992\pi$
$278$	7.47944	−	7.47944i	0.448587	−	0.448587i
$279$		0			0
$280$	9.42975	−	9.42975i	0.563535	−	0.563535i
$281$	3.34690	+	3.34690i	0.199659	+	0.199659i	0.799854	−	0.600195i	$-0.204910\pi$
$281$	3.34690	+	3.34690i	0.199659	+	0.199659i	−0.600195	+	0.799854i	$0.704910\pi$
$282$		0			0
$283$		−	5.34357i		−	0.317642i	−0.987307	−	0.158821i	$-0.949231\pi$
$283$		−	5.34357i		−	0.317642i	0.987307	−	0.158821i	$-0.0507693\pi$
$284$	−41.6374	−	41.6374i	−2.47073	−	2.47073i
$285$		0			0
$286$	−14.1081	−	8.24887i	−0.834230	−	0.487766i
$287$			3.73259i			0.220328i
$288$		0			0
$289$	28.3116			1.66539
$290$	7.86420			0.461802
$291$		0			0
$292$	23.9151	+	23.9151i	1.39952	+	1.39952i
$293$	−10.1177	−	10.1177i	−0.591082	−	0.591082i	0.346842	−	0.937924i	$-0.387254\pi$
$293$	−10.1177	−	10.1177i	−0.591082	−	0.591082i	−0.937924	+	0.346842i	$0.887254\pi$
$294$		0			0
$295$	3.94941			0.229943
$296$	80.6797			4.68941
$297$		0			0
$298$			0.444544i			0.0257517i
$299$	22.0143	+	12.8715i	1.27312	+	0.744381i
$300$		0			0
$301$	3.23996	+	3.23996i	0.186748	+	0.186748i
$302$			42.3787i			2.43862i
$303$		0			0
$304$	25.4586	+	25.4586i	1.46015	+	1.46015i
$305$	−0.643297	+	0.643297i	−0.0368351	+	0.0368351i
$306$		0			0
$307$	−1.14598	+	1.14598i	−0.0654046	+	0.0654046i	−0.739052	−	0.673648i	$-0.764726\pi$
$307$	−1.14598	+	1.14598i	−0.0654046	+	0.0654046i	0.673648	+	0.739052i	$0.264726\pi$
$308$		−	20.7231i		−	1.18081i
$309$		0			0
$310$	−6.62182	+	6.62182i	−0.376094	+	0.376094i
$311$	13.2129			0.749235			0.374617	−	0.927180i	$-0.377774\pi$
$311$	13.2129			0.749235			0.374617	+	0.927180i	$0.377774\pi$
$312$		0			0
$313$	14.2614			0.806104			0.403052	−	0.915177i	$-0.367949\pi$
$313$	14.2614			0.806104			0.403052	+	0.915177i	$0.367949\pi$
$314$	4.78820	−	4.78820i	0.270214	−	0.270214i
$315$		0			0
$316$			52.9834i			2.98055i
$317$	10.6804	−	10.6804i	0.599870	−	0.599870i	−0.340408	−	0.940278i	$-0.610565\pi$
$317$	10.6804	−	10.6804i	0.599870	−	0.599870i	0.940278	+	0.340408i	$0.110565\pi$
$318$		0			0
$319$	5.52840	−	5.52840i	0.309531	−	0.309531i
$320$	14.3560	+	14.3560i	0.802522	+	0.802522i
$321$		0			0
$322$			43.9850i			2.45119i
$323$	−10.9014	−	10.9014i	−0.606572	−	0.606572i
$324$		0			0
$325$	−8.43611	+	14.4284i	−0.467951	+	0.800341i
$326$			8.95520i			0.495983i
$327$		0			0
$328$	−16.0996			−0.888953
$329$	16.4443			0.906602
$330$		0			0
$331$	−18.7676	−	18.7676i	−1.03156	−	1.03156i	−0.999485	−	0.0320776i	$-0.989788\pi$
$331$	−18.7676	−	18.7676i	−1.03156	−	1.03156i	−0.0320776	−	0.999485i	$-0.510212\pi$
$332$	9.53891	+	9.53891i	0.523516	+	0.523516i
$333$		0			0
$334$	−13.7362			−0.751614
$335$	2.80381			0.153189
$336$		0			0
$337$		−	13.0695i		−	0.711942i	−0.934497	−	0.355971i	$-0.884150\pi$
$337$		−	13.0695i		−	0.711942i	0.934497	−	0.355971i	$-0.115850\pi$
$338$	34.4042	+	9.62446i	1.87134	+	0.523502i
$339$		0			0
$340$	−15.9539	−	15.9539i	−0.865222	−	0.865222i
$341$			9.31005i			0.504168i
$342$		0			0
$343$	−14.2077	−	14.2077i	−0.767146	−	0.767146i
$344$	−13.9748	+	13.9748i	−0.753471	+	0.753471i
$345$		0			0
$346$	2.21028	−	2.21028i	0.118825	−	0.118825i
$347$			13.7080i			0.735885i	0.929848	+	0.367943i	$0.119938\pi$
$347$			13.7080i			0.735885i	−0.929848	+	0.367943i	$0.880062\pi$
$348$		0			0
$349$	−13.6226	+	13.6226i	−0.729201	+	0.729201i	−0.970461	−	0.241260i	$-0.922439\pi$
$349$	−13.6226	+	13.6226i	−0.729201	+	0.729201i	0.241260	+	0.970461i	$0.422439\pi$
$350$	−28.8281			−1.54093
$351$		0			0
$352$	39.0543			2.08160
$353$	16.0512	−	16.0512i	0.854317	−	0.854317i	−0.136344	−	0.990662i	$-0.543535\pi$
$353$	16.0512	−	16.0512i	0.854317	−	0.854317i	0.990662	+	0.136344i	$0.0435354\pi$
$354$		0			0
$355$		−	6.40306i		−	0.339839i
$356$	−30.4221	+	30.4221i	−1.61237	+	1.61237i
$357$		0			0
$358$	−31.1378	+	31.1378i	−1.64569	+	1.64569i
$359$	14.0435	+	14.0435i	0.741185	+	0.741185i	0.972806	−	0.231621i	$-0.0744029\pi$
$359$	14.0435	+	14.0435i	0.741185	+	0.741185i	−0.231621	+	0.972806i	$0.574403\pi$
$360$		0			0
$361$		−	13.7545i		−	0.723921i
$362$	33.5128	+	33.5128i	1.76139	+	1.76139i
$363$		0			0
$364$	11.4844	+	43.8207i	0.601945	+	2.29683i
$365$			3.67769i			0.192499i
$366$		0			0
$367$	−20.8336			−1.08751			−0.543753	−	0.839245i	$-0.682997\pi$
$367$	−20.8336			−1.08751			−0.543753	+	0.839245i	$0.682997\pi$
$368$	−111.184			−5.79587
$369$		0			0
$370$	9.69656	+	9.69656i	0.504100	+	0.504100i
$371$	0.820001	+	0.820001i	0.0425723	+	0.0425723i
$372$		0			0
$373$	−3.43357			−0.177783			−0.0888917	−	0.996041i	$-0.528333\pi$
$373$	−3.43357			−0.177783			−0.0888917	+	0.996041i	$0.528333\pi$
$374$	−30.5109			−1.57768
$375$		0			0
$376$			70.9284i			3.65785i
$377$	−8.62652	+	14.7540i	−0.444289	+	0.759870i
$378$		0			0
$379$	14.0653	+	14.0653i	0.722485	+	0.722485i	0.969111	−	0.246626i	$-0.0793219\pi$
$379$	14.0653	+	14.0653i	0.722485	+	0.722485i	−0.246626	+	0.969111i	$0.579322\pi$
$380$			7.67664i			0.393803i
$381$		0			0
$382$	8.06213	+	8.06213i	0.412494	+	0.412494i
$383$	19.8817	−	19.8817i	1.01591	−	1.01591i	0.0160340	−	0.999871i	$-0.494896\pi$
$383$	19.8817	−	19.8817i	1.01591	−	1.01591i	0.999871	−	0.0160340i	$-0.00510399\pi$
$384$		0			0
$385$	1.59341	−	1.59341i	0.0812078	−	0.0812078i
$386$		−	31.1983i		−	1.58795i
$387$		0			0
$388$	30.6867	−	30.6867i	1.55788	−	1.55788i
$389$	31.1571			1.57973			0.789863	−	0.613283i	$-0.210151\pi$
$389$	31.1571			1.57973			0.789863	+	0.613283i	$0.210151\pi$
$390$		0			0
$391$	47.6093			2.40771
$392$	12.9672	−	12.9672i	0.654944	−	0.654944i
$393$		0			0
$394$		−	27.0427i		−	1.36239i
$395$	−4.07393	+	4.07393i	−0.204982	+	0.204982i
$396$		0			0
$397$	−5.72025	+	5.72025i	−0.287091	+	0.287091i	−0.835929	−	0.548838i	$-0.815071\pi$
$397$	−5.72025	+	5.72025i	−0.287091	+	0.287091i	0.548838	+	0.835929i	$0.315071\pi$
$398$	11.5759	+	11.5759i	0.580247	+	0.580247i
$399$		0			0
$400$		−	72.8709i		−	3.64355i
$401$	−23.4537	−	23.4537i	−1.17122	−	1.17122i	−0.981919	−	0.189304i	$-0.939377\pi$
$401$	−23.4537	−	23.4537i	−1.17122	−	1.17122i	−0.189304	−	0.981919i	$-0.560623\pi$
$402$		0			0
$403$	−5.15947	−	19.6869i	−0.257012	−	0.980674i
$404$			99.7913i			4.96480i
$405$		0			0
$406$	−29.4788			−1.46301
$407$	13.6330			0.675764
$408$		0			0
$409$	0.765209	+	0.765209i	0.0378372	+	0.0378372i	0.725772	−	0.687935i	$-0.241483\pi$
$409$	0.765209	+	0.765209i	0.0378372	+	0.0378372i	−0.687935	+	0.725772i	$0.741483\pi$
$410$	−1.93495	−	1.93495i	−0.0955602	−	0.0955602i
$411$		0			0
$412$	−2.83798			−0.139817
$413$	−14.8043			−0.728470
$414$		0			0
$415$			1.46691i			0.0720077i
$416$	−82.5835	+	21.6432i	−4.04899	+	1.06115i
$417$		0			0
$418$	7.34057	+	7.34057i	0.359039	+	0.359039i
$419$			25.2592i			1.23399i	0.786966	+	0.616996i	$0.211651\pi$
$419$			25.2592i			1.23399i	−0.786966	+	0.616996i	$0.788349\pi$
$420$		0			0
$421$	26.4917	+	26.4917i	1.29113	+	1.29113i	0.934090	+	0.357037i	$0.116213\pi$
$421$	26.4917	+	26.4917i	1.29113	+	1.29113i	0.357037	+	0.934090i	$0.383787\pi$
$422$	27.1214	−	27.1214i	1.32025	−	1.32025i
$423$		0			0
$424$	−3.53688	+	3.53688i	−0.171766	+	0.171766i
$425$			31.2035i			1.51359i
$426$		0			0
$427$	2.41139	−	2.41139i	0.116695	−	0.116695i
$428$	80.1096			3.87224
$429$		0			0
$430$	−3.35915			−0.161992
$431$	6.69199	−	6.69199i	0.322342	−	0.322342i	−0.527323	−	0.849665i	$-0.676804\pi$
$431$	6.69199	−	6.69199i	0.322342	−	0.322342i	0.849665	+	0.527323i	$0.176804\pi$
$432$		0			0
$433$		−	40.5441i		−	1.94842i	−0.225636	−	0.974212i	$-0.572446\pi$
$433$		−	40.5441i		−	1.94842i	0.225636	−	0.974212i	$-0.427554\pi$
$434$	24.8217	−	24.8217i	1.19148	−	1.19148i
$435$		0			0
$436$	13.9002	−	13.9002i	0.665700	−	0.665700i
$437$	−11.4542	−	11.4542i	−0.547930	−	0.547930i
$438$		0			0
$439$		−	12.1128i		−	0.578111i	−0.957312	−	0.289056i	$-0.906659\pi$
$439$		−	12.1128i		−	0.578111i	0.957312	−	0.289056i	$-0.0933412\pi$
$440$	6.87280	+	6.87280i	0.327648	+	0.327648i
$441$		0			0
$442$	64.5180	−	16.9086i	3.06881	−	0.804262i
$443$		−	30.6985i		−	1.45853i	−0.684231	−	0.729265i	$-0.739862\pi$
$443$		−	30.6985i		−	1.45853i	0.684231	−	0.729265i	$-0.260138\pi$
$444$		0			0
$445$	−4.67836			−0.221775
$446$	−32.3484			−1.53174
$447$		0			0
$448$	−53.8130	−	53.8130i	−2.54242	−	2.54242i
$449$	22.8163	+	22.8163i	1.07677	+	1.07677i	0.996797	+	0.0799723i	$0.0254832\pi$
$449$	22.8163	+	22.8163i	1.07677	+	1.07677i	0.0799723	+	0.996797i	$0.474517\pi$
$450$		0			0
$451$	−2.72047			−0.128102
$452$	13.9002			0.653812
$453$		0			0
$454$		−	45.6441i		−	2.14218i
$455$	−2.48636	+	4.25245i	−0.116563	+	0.199358i
$456$		0			0
$457$	11.6442	+	11.6442i	0.544694	+	0.544694i	0.924901	−	0.380208i	$-0.124147\pi$
$457$	11.6442	+	11.6442i	0.544694	+	0.544694i	−0.380208	+	0.924901i	$0.624147\pi$
$458$		−	14.1216i		−	0.659858i
$459$		0			0
$460$	−16.7629	−	16.7629i	−0.781576	−	0.781576i
$461$	7.35821	−	7.35821i	0.342706	−	0.342706i	−0.514678	−	0.857384i	$-0.672088\pi$
$461$	7.35821	−	7.35821i	0.342706	−	0.342706i	0.857384	+	0.514678i	$0.172088\pi$
$462$		0			0
$463$	−21.8101	+	21.8101i	−1.01360	+	1.01360i	−0.0136951	+	0.999906i	$0.504359\pi$
$463$	−21.8101	+	21.8101i	−1.01360	+	1.01360i	−0.999906	+	0.0136951i	$0.995641\pi$
$464$		−	74.5157i		−	3.45930i
$465$		0			0
$466$	7.33318	−	7.33318i	0.339703	−	0.339703i
$467$	−2.69124			−0.124536			−0.0622678	−	0.998059i	$-0.519833\pi$
$467$	−2.69124			−0.124536			−0.0622678	+	0.998059i	$0.519833\pi$
$468$		0			0
$469$	−10.5100			−0.485308
$470$	−8.52460	+	8.52460i	−0.393210	+	0.393210i
$471$		0			0
$472$		−	63.8547i		−	2.93915i
$473$	−2.36142	+	2.36142i	−0.108578	+	0.108578i
$474$		0			0
$475$	7.50719	−	7.50719i	0.344454	−	0.344454i
$476$	59.8029	+	59.8029i	2.74106	+	2.74106i
$477$		0			0
$478$			72.6868i			3.32462i
$479$	−12.4608	−	12.4608i	−0.569350	−	0.569350i	0.362597	−	0.931946i	$-0.381890\pi$
$479$	−12.4608	−	12.4608i	−0.569350	−	0.569350i	−0.931946	+	0.362597i	$0.881890\pi$
$480$		0			0
$481$	−28.8282	+	7.55519i	−1.31445	+	0.344487i
$482$		−	62.4219i		−	2.84324i
$483$		0			0
$484$	−45.9674			−2.08943
$485$	4.71904			0.214281
$486$		0			0
$487$	8.26795	+	8.26795i	0.374657	+	0.374657i	0.869170	−	0.494513i	$-0.164654\pi$
$487$	8.26795	+	8.26795i	0.374657	+	0.374657i	−0.494513	+	0.869170i	$0.664654\pi$
$488$	10.4009	+	10.4009i	0.470828	+	0.470828i
$489$		0			0
$490$	3.11696			0.140810
$491$	−8.95140			−0.403971			−0.201985	−	0.979389i	$-0.564739\pi$
$491$	−8.95140			−0.403971			−0.201985	+	0.979389i	$0.564739\pi$
$492$		0			0
$493$			31.9078i			1.43706i
$494$	−19.5903	−	11.4542i	−0.881408	−	0.515350i
$495$		0			0
$496$	62.7437	+	62.7437i	2.81728	+	2.81728i
$497$			24.0017i			1.07663i
$498$		0			0
$499$	−12.8465	−	12.8465i	−0.575089	−	0.575089i	0.358457	−	0.933546i	$-0.383303\pi$
$499$	−12.8465	−	12.8465i	−0.575089	−	0.575089i	−0.933546	+	0.358457i	$0.883303\pi$
$500$	22.8369	−	22.8369i	1.02130	−	1.02130i
$501$		0			0
$502$	30.7590	−	30.7590i	1.37284	−	1.37284i
$503$		−	22.0270i		−	0.982135i	−0.871122	−	0.491067i	$-0.836607\pi$
$503$		−	22.0270i		−	0.982135i	0.871122	−	0.491067i	$-0.163393\pi$
$504$		0			0
$505$	−7.67303	+	7.67303i	−0.341445	+	0.341445i
$506$	−32.0582			−1.42516
$507$		0			0
$508$	−58.6962			−2.60422
$509$	−26.3902	+	26.3902i	−1.16972	+	1.16972i	−0.187451	+	0.982274i	$0.560023\pi$
$509$	−26.3902	+	26.3902i	−1.16972	+	1.16972i	−0.982274	+	0.187451i	$0.939977\pi$
$510$		0			0
$511$		−	13.7857i		−	0.609845i
$512$	46.1983	−	46.1983i	2.04169	−	2.04169i
$513$		0			0
$514$	−26.0149	+	26.0149i	−1.14747	+	1.14747i
$515$	−0.218215	−	0.218215i	−0.00961569	−	0.00961569i
$516$		0			0
$517$			11.9853i			0.527112i
$518$	−36.3473	−	36.3473i	−1.59701	−	1.59701i
$519$		0			0
$520$	−18.3419	−	10.7243i	−0.804346	−	0.470293i
$521$		−	35.6847i		−	1.56338i	−0.623669	−	0.781689i	$-0.714359\pi$
$521$		−	35.6847i		−	1.56338i	0.623669	−	0.781689i	$-0.285641\pi$
$522$		0			0
$523$	−9.07914			−0.397003			−0.198502	−	0.980101i	$-0.563607\pi$
$523$	−9.07914			−0.397003			−0.198502	+	0.980101i	$0.563607\pi$
$524$	−79.0683			−3.45411
$525$		0			0
$526$	9.46339	+	9.46339i	0.412623	+	0.412623i
$527$	−26.8670	−	26.8670i	−1.17035	−	1.17035i
$528$		0			0
$529$	27.0236			1.17494
$530$	−0.850165			−0.0369288
$531$		0			0
$532$		−	28.7757i		−	1.24758i
$533$	5.75266	−	1.50764i	0.249176	−	0.0653030i
$534$		0			0
$535$	6.15969	+	6.15969i	0.266306	+	0.266306i
$536$		−	45.3325i		−	1.95807i
$537$		0			0
$538$	−49.1809	−	49.1809i	−2.12034	−	2.12034i
$539$	2.19117	−	2.19117i	0.0943802	−	0.0943802i
$540$		0			0
$541$	2.25289	−	2.25289i	0.0968594	−	0.0968594i	−0.657017	−	0.753876i	$-0.728182\pi$
$541$	2.25289	−	2.25289i	0.0968594	−	0.0968594i	0.753876	+	0.657017i	$0.228182\pi$
$542$		−	5.81993i		−	0.249987i
$543$		0			0
$544$	−112.703	+	112.703i	−4.83211	+	4.83211i
$545$	2.13760			0.0915645
$546$		0			0
$547$	−16.0702			−0.687113			−0.343557	−	0.939132i	$-0.611632\pi$
$547$	−16.0702			−0.687113			−0.343557	+	0.939132i	$0.611632\pi$
$548$	−62.9956	+	62.9956i	−2.69104	+	2.69104i
$549$		0			0
$550$		−	21.0112i		−	0.895919i
$551$	7.67664	−	7.67664i	0.327036	−	0.327036i
$552$		0			0
$553$	15.2711	−	15.2711i	0.649391	−	0.649391i
$554$	46.3094	+	46.3094i	1.96750	+	1.96750i
$555$		0			0
$556$		−	21.3697i		−	0.906279i
$557$	14.4580	+	14.4580i	0.612604	+	0.612604i	0.943624	−	0.331020i	$-0.107393\pi$
$557$	14.4580	+	14.4580i	0.612604	+	0.612604i	−0.331020	+	0.943624i	$0.607393\pi$
$558$		0			0
$559$	3.68477	−	6.30209i	0.155849	−	0.266550i
$560$		−	21.4771i		−	0.907575i
$561$		0			0
$562$	13.0073			0.548680
$563$	−20.4441			−0.861614			−0.430807	−	0.902444i	$-0.641771\pi$
$563$	−20.4441			−0.861614			−0.430807	+	0.902444i	$0.641771\pi$
$564$		0			0
$565$	1.06880	+	1.06880i	0.0449647	+	0.0449647i
$566$	−10.3835	−	10.3835i	−0.436453	−	0.436453i
$567$		0			0
$568$	−103.526			−4.34385
$569$	28.4958			1.19461			0.597303	−	0.802015i	$-0.296239\pi$
$569$	28.4958			1.19461			0.597303	+	0.802015i	$0.296239\pi$
$570$		0			0
$571$			44.9174i			1.87974i	0.341537	+	0.939868i	$0.389052\pi$
$571$			44.9174i			1.87974i	−0.341537	+	0.939868i	$0.610948\pi$
$572$	−31.9384	+	8.37030i	−1.33541	+	0.349980i
$573$		0			0
$574$	7.25311	+	7.25311i	0.302739	+	0.302739i
$575$			32.7859i			1.36726i
$576$		0			0
$577$	5.69092	+	5.69092i	0.236916	+	0.236916i	0.815572	−	0.578656i	$-0.196423\pi$
$577$	5.69092	+	5.69092i	0.236916	+	0.236916i	−0.578656	+	0.815572i	$0.696423\pi$
$578$	55.0147	−	55.0147i	2.28831	−	2.28831i
$579$		0			0
$580$	11.2345	−	11.2345i	0.466488	−	0.466488i
$581$		−	5.49867i		−	0.228123i
$582$		0			0
$583$	−0.597651	+	0.597651i	−0.0247522	+	0.0247522i
$584$	59.4615			2.46054
$585$		0			0
$586$	−39.3211			−1.62434
$587$	−17.8319	+	17.8319i	−0.736002	+	0.736002i	−0.971802	−	0.235800i	$-0.924229\pi$
$587$	−17.8319	+	17.8319i	−0.736002	+	0.736002i	0.235800	+	0.971802i	$0.424229\pi$
$588$		0			0
$589$			12.9278i			0.532680i
$590$	7.67443	−	7.67443i	0.315951	−	0.315951i
$591$		0			0
$592$	91.8778	−	91.8778i	3.77616	−	3.77616i
$593$	−26.1382	−	26.1382i	−1.07337	−	1.07337i	−0.997086	−	0.0762808i	$-0.975695\pi$
$593$	−26.1382	−	26.1382i	−1.07337	−	1.07337i	−0.0762808	−	0.997086i	$-0.524305\pi$
$594$		0			0
$595$			9.19657i			0.377023i
$596$	0.635060	+	0.635060i	0.0260131	+	0.0260131i
$597$		0			0
$598$	67.7897	−	17.7661i	2.77213	−	0.726509i
$599$			31.8022i			1.29940i	0.760190	+	0.649701i	$0.225106\pi$
$599$			31.8022i			1.29940i	−0.760190	+	0.649701i	$0.774894\pi$
$600$		0			0
$601$	15.1081			0.616272			0.308136	−	0.951342i	$-0.400295\pi$
$601$	15.1081			0.616272			0.308136	+	0.951342i	$0.400295\pi$
$602$	12.5917			0.513199
$603$		0			0
$604$	60.5408	+	60.5408i	2.46337	+	2.46337i
$605$	−3.53447	−	3.53447i	−0.143697	−	0.143697i
$606$		0			0
$607$	6.24394			0.253434			0.126717	−	0.991939i	$-0.459556\pi$
$607$	6.24394			0.253434			0.126717	+	0.991939i	$0.459556\pi$
$608$	54.2300			2.19932
$609$		0			0
$610$			2.50009i			0.101226i
$611$	−6.64204	−	25.3439i	−0.268708	−	1.02530i
$612$		0			0
$613$	−13.8830	−	13.8830i	−0.560729	−	0.560729i	0.368786	−	0.929514i	$-0.379774\pi$
$613$	−13.8830	−	13.8830i	−0.560729	−	0.560729i	−0.929514	+	0.368786i	$0.879774\pi$
$614$			4.45370i			0.179737i
$615$		0			0
$616$	−25.7626	−	25.7626i	−1.03800	−	1.03800i
$617$	17.1721	−	17.1721i	0.691324	−	0.691324i	−0.271199	−	0.962523i	$-0.587420\pi$
$617$	17.1721	−	17.1721i	0.691324	−	0.691324i	0.962523	+	0.271199i	$0.0874202\pi$
$618$		0			0
$619$	−7.32775	+	7.32775i	−0.294527	+	0.294527i	−0.838866	−	0.544339i	$-0.816781\pi$
$619$	−7.32775	+	7.32775i	−0.294527	+	0.294527i	0.544339	+	0.838866i	$0.316781\pi$
$620$			18.9194i			0.759822i
$621$		0			0
$622$	25.6751	−	25.6751i	1.02948	−	1.02948i
$623$	17.5367			0.702594
$624$		0			0
$625$	−19.6657			−0.786629
$626$	27.7126	−	27.7126i	1.10762	−	1.10762i
$627$		0			0
$628$		−	13.6805i		−	0.545912i
$629$	−39.3423	+	39.3423i	−1.56868	+	1.56868i
$630$		0			0
$631$	17.1639	−	17.1639i	0.683285	−	0.683285i	−0.277454	−	0.960739i	$-0.589491\pi$
$631$	17.1639	−	17.1639i	0.683285	−	0.683285i	0.960739	+	0.277454i	$0.0894906\pi$
$632$	65.8680	+	65.8680i	2.62009	+	2.62009i
$633$		0			0
$634$		−	41.5079i		−	1.64849i
$635$	−4.51319	−	4.51319i	−0.179101	−	0.179101i
$636$		0			0
$637$	−3.41910	+	5.84771i	−0.135470	+	0.231695i
$638$		−	21.4854i		−	0.850615i
$639$		0			0
$640$	27.2029			1.07529
$641$	−19.1932			−0.758085			−0.379043	−	0.925379i	$-0.623747\pi$
$641$	−19.1932			−0.758085			−0.379043	+	0.925379i	$0.623747\pi$
$642$		0			0
$643$	−18.9358	−	18.9358i	−0.746753	−	0.746753i	0.227115	−	0.973868i	$-0.427071\pi$
$643$	−18.9358	−	18.9358i	−0.746753	−	0.746753i	−0.973868	+	0.227115i	$0.927071\pi$
$644$	62.8355	+	62.8355i	2.47606	+	2.47606i
$645$		0			0
$646$	−42.3670			−1.66691
$647$	−48.7650			−1.91715			−0.958574	−	0.284842i	$-0.908059\pi$
$647$	−48.7650			−1.91715			−0.958574	+	0.284842i	$0.908059\pi$
$648$		0			0
$649$		−	10.7900i		−	0.423544i
$650$	11.6440	+	44.4299i	0.456716	+	1.74268i
$651$		0			0
$652$	12.7931	+	12.7931i	0.501016	+	0.501016i
$653$			8.91019i			0.348683i	0.984685	+	0.174341i	$0.0557796\pi$
$653$			8.91019i			0.348683i	−0.984685	+	0.174341i	$0.944220\pi$
$654$		0			0
$655$	−6.07962	−	6.07962i	−0.237550	−	0.237550i
$656$	−18.3342	+	18.3342i	−0.715831	+	0.715831i
$657$		0			0
$658$	31.9543	−	31.9543i	1.24571	−	1.24571i
$659$			23.5920i			0.919014i	0.888174	+	0.459507i	$0.151974\pi$
$659$			23.5920i			0.919014i	−0.888174	+	0.459507i	$0.848026\pi$
$660$		0			0
$661$	−16.7726	+	16.7726i	−0.652377	+	0.652377i	−0.953565	−	0.301188i	$-0.902617\pi$
$661$	−16.7726	+	16.7726i	−0.652377	+	0.652377i	0.301188	+	0.953565i	$0.402617\pi$
$662$	−72.9380			−2.83482
$663$		0			0
$664$	23.7172			0.920406
$665$	2.21258	−	2.21258i	0.0858003	−	0.0858003i
$666$		0			0
$667$			33.5259i			1.29813i
$668$	−19.6231	+	19.6231i	−0.759241	+	0.759241i
$669$		0			0
$670$	5.44833	−	5.44833i	0.210487	−	0.210487i
$671$	1.75752	+	1.75752i	0.0678483	+	0.0678483i
$672$		0			0
$673$		−	28.9652i		−	1.11653i	−0.829664	−	0.558264i	$-0.811468\pi$
$673$		−	28.9652i		−	1.11653i	0.829664	−	0.558264i	$-0.188532\pi$
$674$	−25.3965	−	25.3965i	−0.978236	−	0.978236i
$675$		0			0
$676$	62.8978	−	35.3994i	2.41915	−	1.36152i
$677$			16.7241i			0.642761i	0.946950	+	0.321380i	$0.104147\pi$
$677$			16.7241i			0.642761i	−0.946950	+	0.321380i	$0.895853\pi$
$678$		0			0
$679$	−17.6892			−0.678850
$680$	−39.6672			−1.52117
$681$		0			0
$682$	18.0911	+	18.0911i	0.692746	+	0.692746i
$683$	4.91716	+	4.91716i	0.188150	+	0.188150i	0.794896	−	0.606746i	$-0.207525\pi$
$683$	4.91716	+	4.91716i	0.188150	+	0.188150i	−0.606746	+	0.794896i	$0.707525\pi$
$684$		0			0
$685$	−9.68755			−0.370142
$686$	−55.2165			−2.10818
$687$		0			0
$688$			31.8289i			1.21347i
$689$	0.932576	−	1.59499i	0.0355283	−	0.0607644i
$690$		0			0
$691$	18.8583	+	18.8583i	0.717404	+	0.717404i	0.968073	−	0.250669i	$-0.0806505\pi$
$691$	18.8583	+	18.8583i	0.717404	+	0.717404i	−0.250669	+	0.968073i	$0.580650\pi$
$692$		−	6.31505i		−	0.240062i
$693$		0			0
$694$	26.6372	+	26.6372i	1.01114	+	1.01114i
$695$	1.64314	−	1.64314i	0.0623277	−	0.0623277i
$696$		0			0
$697$	7.85076	−	7.85076i	0.297369	−	0.297369i
$698$			52.9424i			2.00390i
$699$		0			0
$700$	−41.1828	+	41.1828i	−1.55657	+	1.55657i
$701$	−39.2125			−1.48103			−0.740517	−	0.672037i	$-0.765419\pi$
$701$	−39.2125			−1.48103			−0.740517	+	0.672037i	$0.765419\pi$
$702$		0			0
$703$	18.9306			0.713981
$704$	39.2212	−	39.2212i	1.47820	−	1.47820i
$705$		0			0
$706$		−	62.3807i		−	2.34773i
$707$	28.7622	−	28.7622i	1.08171	−	1.08171i
$708$		0			0
$709$	6.90793	−	6.90793i	0.259433	−	0.259433i	−0.565391	−	0.824823i	$-0.691275\pi$
$709$	6.90793	−	6.90793i	0.259433	−	0.259433i	0.824823	+	0.565391i	$0.191275\pi$
$710$	−12.4423	−	12.4423i	−0.466953	−	0.466953i
$711$		0			0
$712$			75.6404i			2.83474i
$713$	−28.2295	−	28.2295i	−1.05720	−	1.05720i
$714$		0			0
$715$	−3.09937	−	1.81217i	−0.115910	−	0.0677712i
$716$			88.9649i			3.32477i
$717$		0			0
$718$	54.5780			2.03683
$719$	23.1518			0.863415			0.431708	−	0.902014i	$-0.357911\pi$
$719$	23.1518			0.863415			0.431708	+	0.902014i	$0.357911\pi$
$720$		0			0
$721$	0.817973	+	0.817973i	0.0304629	+	0.0304629i
$722$	−26.7275	−	26.7275i	−0.994696	−	0.994696i
$723$		0			0
$724$	95.7504			3.55854
$725$	−21.9731			−0.816061
$726$		0			0
$727$			20.1563i			0.747557i	0.927518	+	0.373778i	$0.121938\pi$
$727$			20.1563i			0.747557i	−0.927518	+	0.373778i	$0.878062\pi$
$728$	68.7543	+	40.1999i	2.54820	+	1.48991i
$729$		0			0
$730$	7.14643	+	7.14643i	0.264501	+	0.264501i
$731$		−	13.6292i		−	0.504095i
$732$		0			0
$733$	−7.58955	−	7.58955i	−0.280326	−	0.280326i	0.552913	−	0.833239i	$-0.313516\pi$
$733$	−7.58955	−	7.58955i	−0.280326	−	0.280326i	−0.833239	+	0.552913i	$0.813516\pi$
$734$	−40.4836	+	40.4836i	−1.49428	+	1.49428i
$735$		0			0
$736$	−118.418	+	118.418i	−4.36496	+	4.36496i
$737$		−	7.66016i		−	0.282166i
$738$		0			0
$739$	−27.5852	+	27.5852i	−1.01474	+	1.01474i	−0.0148481	+	0.999890i	$0.504726\pi$
$739$	−27.5852	+	27.5852i	−1.01474	+	1.01474i	−0.999890	+	0.0148481i	$0.995274\pi$
$740$	27.7044			1.01843
$741$		0			0
$742$	3.18683			0.116992
$743$	−5.54681	+	5.54681i	−0.203493	+	0.203493i	−0.801495	−	0.598002i	$-0.795962\pi$
$743$	−5.54681	+	5.54681i	−0.203493	+	0.203493i	0.598002	+	0.801495i	$0.295962\pi$
$744$		0			0
$745$			0.0976605i			0.00357800i
$746$	−6.67206	+	6.67206i	−0.244281	+	0.244281i
$747$		0			0
$748$	−43.5869	+	43.5869i	−1.59369	+	1.59369i
$749$	−23.0894	−	23.0894i	−0.843670	−	0.843670i
$750$		0			0
$751$			36.5949i			1.33537i	0.744445	+	0.667684i	$0.232714\pi$
$751$			36.5949i			1.33537i	−0.744445	+	0.667684i	$0.767286\pi$
$752$	80.7731	+	80.7731i	2.94549	+	2.94549i
$753$		0			0
$754$	11.9068	+	45.4327i	0.433622	+	1.65456i
$755$			9.31005i			0.338827i
$756$		0			0
$757$	−40.7089			−1.47959			−0.739794	−	0.672833i	$-0.765077\pi$
$757$	−40.7089			−1.47959			−0.739794	+	0.672833i	$0.765077\pi$
$758$	54.6629			1.98544
$759$		0			0
$760$	9.54346	+	9.54346i	0.346178	+	0.346178i
$761$	6.97072	+	6.97072i	0.252688	+	0.252688i	0.822072	−	0.569384i	$-0.192818\pi$
$761$	6.97072	+	6.97072i	0.252688	+	0.252688i	−0.569384	+	0.822072i	$0.692818\pi$
$762$		0			0
$763$	−8.01273			−0.290080
$764$	23.0345			0.833361
$765$		0			0
$766$		−	77.2675i		−	2.79179i
$767$	5.97962	+	22.8163i	0.215912	+	0.823850i
$768$		0			0
$769$	−13.4888	−	13.4888i	−0.486420	−	0.486420i	0.420755	−	0.907174i	$-0.361765\pi$
$769$	−13.4888	−	13.4888i	−0.486420	−	0.486420i	−0.907174	+	0.420755i	$0.861765\pi$
$770$		−	6.19259i		−	0.223165i
$771$		0			0
$772$	−44.5688	−	44.5688i	−1.60407	−	1.60407i
$773$	35.5292	−	35.5292i	1.27789	−	1.27789i	0.336051	−	0.941844i	$-0.390908\pi$
$773$	35.5292	−	35.5292i	1.27789	−	1.27789i	0.941844	−	0.336051i	$-0.109092\pi$
$774$		0			0
$775$	18.5018	−	18.5018i	0.664605	−	0.664605i
$776$		−	76.2982i		−	2.73895i
$777$		0			0
$778$	60.5440	−	60.5440i	2.17061	−	2.17061i
$779$	−3.77760			−0.135346
$780$		0			0
$781$	−17.4935			−0.625967
$782$	92.5137	−	92.5137i	3.30828	−	3.30828i
$783$		0			0
$784$		−	29.5341i		−	1.05479i
$785$	1.05191	−	1.05191i	0.0375441	−	0.0375441i
$786$		0			0
$787$	−13.7330	+	13.7330i	−0.489530	+	0.489530i	−0.908158	−	0.418628i	$-0.862511\pi$
$787$	−13.7330	+	13.7330i	−0.489530	+	0.489530i	0.418628	+	0.908158i	$0.362511\pi$
$788$	−38.6323	−	38.6323i	−1.37622	−	1.37622i
$789$		0			0
$790$			15.8328i			0.563306i
$791$	−4.00637	−	4.00637i	−0.142450	−	0.142450i
$792$		0			0
$793$	−4.69041	−	2.74244i	−0.166561	−	0.0973868i
$794$			22.2310i			0.788949i
$795$		0			0
$796$	33.0738			1.17227
$797$	5.03124			0.178216			0.0891079	−	0.996022i	$-0.471598\pi$
$797$	5.03124			0.178216			0.0891079	+	0.996022i	$0.471598\pi$
$798$		0			0
$799$	−34.5873	−	34.5873i	−1.22361	−	1.22361i
$800$	−77.6123	−	77.6123i	−2.74401	−	2.74401i
$801$		0			0
$802$	−91.1498			−3.21861
$803$	10.0476			0.354574
$804$		0			0
$805$			9.66293i			0.340573i
$806$	−48.2811	−	28.2295i	−1.70063	−	0.994340i
$807$		0			0
$808$	124.059	+	124.059i	4.36437	+	4.36437i
$809$			16.0030i			0.562636i	0.959615	+	0.281318i	$0.0907716\pi$
$809$			16.0030i			0.562636i	−0.959615	+	0.281318i	$0.909228\pi$
$810$		0			0
$811$	15.6191	+	15.6191i	0.548461	+	0.548461i	0.925996	−	0.377534i	$-0.123228\pi$
$811$	15.6191	+	15.6191i	0.548461	+	0.548461i	−0.377534	+	0.925996i	$0.623228\pi$
$812$	−42.1124	+	42.1124i	−1.47785	+	1.47785i
$813$		0			0
$814$	26.4915	−	26.4915i	0.928527	−	0.928527i
$815$			1.96734i			0.0689129i
$816$		0			0
$817$	−3.27903	+	3.27903i	−0.114719	+	0.114719i
$818$	2.97389			0.103979
$819$		0			0
$820$	−5.52840			−0.193060
$821$	−12.3130	+	12.3130i	−0.429725	+	0.429725i	−0.888535	−	0.458809i	$-0.848276\pi$
$821$	−12.3130	+	12.3130i	−0.429725	+	0.429725i	0.458809	+	0.888535i	$0.348276\pi$
$822$		0			0
$823$			37.3599i			1.30228i	0.758956	+	0.651142i	$0.225710\pi$
$823$			37.3599i			1.30228i	−0.758956	+	0.651142i	$0.774290\pi$
$824$	−3.52813	+	3.52813i	−0.122908	+	0.122908i
$825$		0			0
$826$	−28.7674	+	28.7674i	−1.00095	+	1.00095i
$827$	13.6004	+	13.6004i	0.472932	+	0.472932i	0.902862	−	0.429930i	$-0.141462\pi$
$827$	13.6004	+	13.6004i	0.472932	+	0.472932i	−0.429930	+	0.902862i	$0.641462\pi$
$828$		0			0
$829$		−	40.2785i		−	1.39893i	−0.714667	−	0.699465i	$-0.753422\pi$
$829$		−	40.2785i		−	1.39893i	0.714667	−	0.699465i	$-0.246578\pi$
$830$	2.85047	+	2.85047i	0.0989414	+	0.0989414i
$831$		0			0
$832$	−61.2008	+	104.672i	−2.12176	+	3.62886i
$833$			12.6466i			0.438178i
$834$		0			0
$835$	−3.01767			−0.104431
$836$	20.9730			0.725365
$837$		0			0
$838$	49.0833	+	49.0833i	1.69555	+	1.69555i
$839$	−27.2939	−	27.2939i	−0.942291	−	0.942291i	0.0561321	−	0.998423i	$-0.482123\pi$
$839$	−27.2939	−	27.2939i	−0.942291	−	0.942291i	−0.998423	+	0.0561321i	$0.982123\pi$
$840$		0			0
$841$	6.53094			0.225205
$842$	102.957			3.54812
$843$		0			0
$844$		−	77.4893i		−	2.66729i
$845$	7.55814	+	2.11437i	0.260008	+	0.0727365i
$846$		0			0
$847$	13.2489	+	13.2489i	0.455237	+	0.455237i
$848$			8.05557i			0.276629i
$849$		0			0
$850$	60.6342	+	60.6342i	2.07974	+	2.07974i
$851$	−41.3374	+	41.3374i	−1.41703	+	1.41703i
$852$		0			0
$853$	−35.9570	+	35.9570i	−1.23114	+	1.23114i	−0.267620	+	0.963524i	$0.586237\pi$
$853$	−35.9570	+	35.9570i	−1.23114	+	1.23114i	−0.963524	+	0.267620i	$0.913763\pi$
$854$		−	9.37153i		−	0.320687i
$855$		0			0
$856$	99.5908	−	99.5908i	3.40394	−	3.40394i
$857$	−15.0580			−0.514370			−0.257185	−	0.966362i	$-0.582795\pi$
$857$	−15.0580			−0.514370			−0.257185	+	0.966362i	$0.582795\pi$
$858$		0			0
$859$	25.9846			0.886582			0.443291	−	0.896378i	$-0.353811\pi$
$859$	25.9846			0.886582			0.443291	+	0.896378i	$0.353811\pi$
$860$	−4.79876	+	4.79876i	−0.163636	+	0.163636i
$861$		0			0
$862$		−	26.0076i		−	0.885821i
$863$	−23.5740	+	23.5740i	−0.802469	+	0.802469i	−0.983481	−	0.181012i	$-0.942063\pi$
$863$	−23.5740	+	23.5740i	−0.802469	+	0.802469i	0.181012	+	0.983481i	$0.442063\pi$
$864$		0			0
$865$	0.485569	−	0.485569i	0.0165098	−	0.0165098i
$866$	−78.7846	−	78.7846i	−2.67721	−	2.67721i
$867$		0			0
$868$		−	70.9190i		−	2.40715i
$869$	11.1302	+	11.1302i	0.377566	+	0.377566i
$870$		0			0
$871$	4.24513	+	16.1981i	0.143841	+	0.548850i
$872$		−	34.5610i		−	1.17038i
$873$		0			0
$874$	−44.5154			−1.50576
$875$	−13.1643			−0.445033
$876$		0			0
$877$	−28.7018	−	28.7018i	−0.969190	−	0.969190i	0.0303491	−	0.999539i	$-0.490338\pi$
$877$	−28.7018	−	28.7018i	−0.969190	−	0.969190i	−0.999539	+	0.0303491i	$0.990338\pi$
$878$	−23.5374	−	23.5374i	−0.794347	−	0.794347i
$879$		0			0
$880$	15.6535			0.527678
$881$	37.3137			1.25713			0.628565	−	0.777757i	$-0.283642\pi$
$881$	37.3137			1.25713			0.628565	+	0.777757i	$0.283642\pi$
$882$		0			0
$883$		−	14.9070i		−	0.501660i	−0.968031	−	0.250830i	$-0.919296\pi$
$883$		−	14.9070i		−	0.501660i	0.968031	−	0.250830i	$-0.0807036\pi$
$884$	68.0131	−	116.323i	2.28753	−	3.91238i
$885$		0			0
$886$	−59.6529	−	59.6529i	−2.00408	−	2.00408i
$887$		−	32.3657i		−	1.08673i	−0.839495	−	0.543367i	$-0.817149\pi$
$887$		−	32.3657i		−	1.08673i	0.839495	−	0.543367i	$-0.182851\pi$
$888$		0			0
$889$	16.9176	+	16.9176i	0.567398	+	0.567398i
$890$	−9.09091	+	9.09091i	−0.304728	+	0.304728i
$891$		0			0
$892$	−46.2118	+	46.2118i	−1.54729	+	1.54729i
$893$			16.6426i			0.556922i
$894$		0			0
$895$	−6.84058	+	6.84058i	−0.228655	+	0.228655i
$896$	−101.969			−3.40656
$897$		0			0
$898$	88.6727			2.95905
$899$	18.9194	−	18.9194i	0.630998	−	0.630998i
$900$		0			0
$901$		−	3.44942i		−	0.114917i
$902$	−5.28638	+	5.28638i	−0.176017	+	0.176017i
$903$		0			0
$904$	17.2805	−	17.2805i	0.574741	−	0.574741i
$905$	7.36232	+	7.36232i	0.244732	+	0.244732i
$906$		0			0
$907$		−	33.4143i		−	1.10950i	−0.832016	−	0.554752i	$-0.812813\pi$
$907$		−	33.4143i		−	1.10950i	0.832016	−	0.554752i	$-0.187187\pi$
$908$	−65.2055	−	65.2055i	−2.16392	−	2.16392i
$909$		0			0
$910$	3.43183	+	13.0948i	0.113764	+	0.434087i
$911$		−	7.69858i		−	0.255065i	−0.991834	−	0.127533i	$-0.959294\pi$
$911$		−	7.69858i		−	0.255065i	0.991834	−	0.127533i	$-0.0407058\pi$
$912$		0			0
$913$	4.00767			0.132634
$914$	45.2537			1.49686
$915$		0			0
$916$	−20.1736	−	20.1736i	−0.666554	−	0.666554i
$917$	22.7893	+	22.7893i	0.752569	+	0.752569i
$918$		0			0
$919$	34.8634			1.15004			0.575019	−	0.818140i	$-0.304995\pi$
$919$	34.8634			1.15004			0.575019	+	0.818140i	$0.304995\pi$
$920$	−41.6787			−1.37411
$921$		0			0
$922$		−	28.5967i		−	0.941783i
$923$	36.9915	−	9.69460i	1.21759	−	0.319102i
$924$		0			0
$925$	−27.0928	−	27.0928i	−0.890807	−	0.890807i
$926$			84.7621i			2.78546i
$927$		0			0
$928$	−79.3640	−	79.3640i	−2.60525	−	2.60525i
$929$	5.29791	−	5.29791i	0.173819	−	0.173819i	−0.614836	−	0.788655i	$-0.710778\pi$
$929$	5.29791	−	5.29791i	0.173819	−	0.173819i	0.788655	+	0.614836i	$0.210778\pi$
$930$		0			0
$931$	3.04261	−	3.04261i	0.0997177	−	0.0997177i
$932$		−	20.9519i		−	0.686301i
$933$		0			0
$934$	−5.22957	+	5.22957i	−0.171117	+	0.171117i
$935$	−6.70286			−0.219207
$936$		0			0
$937$	38.1244			1.24547			0.622734	−	0.782433i	$-0.286022\pi$
$937$	38.1244			1.24547			0.622734	+	0.782433i	$0.286022\pi$
$938$	−20.4229	+	20.4229i	−0.666833	+	0.666833i
$939$		0			0
$940$			24.3559i			0.794401i
$941$	28.7910	−	28.7910i	0.938560	−	0.938560i	−0.0596586	−	0.998219i	$-0.519001\pi$
$941$	28.7910	−	28.7910i	0.938560	−	0.938560i	0.998219	+	0.0596586i	$0.0190012\pi$
$942$		0			0
$943$	8.24887	−	8.24887i	0.268620	−	0.268620i
$944$	−72.7175	−	72.7175i	−2.36675	−	2.36675i
$945$		0			0
$946$			9.17736i			0.298382i
$947$	4.47941	+	4.47941i	0.145561	+	0.145561i	0.776132	−	0.630571i	$-0.217179\pi$
$947$	4.47941	+	4.47941i	0.145561	+	0.145561i	−0.630571	+	0.776132i	$0.717179\pi$
$948$		0			0
$949$	−21.2466	+	5.56823i	−0.689693	+	0.180752i
$950$		−	29.1757i		−	0.946586i
$951$		0			0
$952$	148.692			4.81913
$953$	27.9211			0.904452			0.452226	−	0.891903i	$-0.350630\pi$
$953$	27.9211			0.904452			0.452226	+	0.891903i	$0.350630\pi$
$954$		0			0
$955$	1.77114	+	1.77114i	0.0573128	+	0.0573128i
$956$	103.838	+	103.838i	3.35836	+	3.35836i
$957$		0			0
$958$	−48.4274			−1.56462
$959$	36.3136			1.17263
$960$		0			0
$961$			0.861065i			0.0277763i
$962$	−41.3374	+	70.6997i	−1.33277	+	2.27945i
$963$		0			0
$964$	−89.1738	−	89.1738i	−2.87209	−	2.87209i
$965$		−	6.85385i		−	0.220633i
$966$		0			0
$967$	4.80037	+	4.80037i	0.154370	+	0.154370i	0.780066	−	0.625697i	$-0.215185\pi$
$967$	4.80037	+	4.80037i	0.154370	+	0.154370i	−0.625697	+	0.780066i	$0.715185\pi$
$968$	−57.1458	+	57.1458i	−1.83674	+	1.83674i
$969$		0			0
$970$	9.16997	−	9.16997i	0.294430	−	0.294430i
$971$		−	51.5139i		−	1.65316i	−0.562820	−	0.826580i	$-0.690283\pi$
$971$		−	51.5139i		−	1.65316i	0.562820	−	0.826580i	$-0.309717\pi$
$972$		0			0
$973$	−6.15926	+	6.15926i	−0.197457	+	0.197457i
$974$	32.1323			1.02959
$975$		0			0
$976$	23.6891			0.758270
$977$	23.2538	−	23.2538i	0.743954	−	0.743954i	−0.229382	−	0.973336i	$-0.573671\pi$
$977$	23.2538	−	23.2538i	0.743954	−	0.743954i	0.973336	+	0.229382i	$0.0736705\pi$
$978$		0			0
$979$			12.7815i			0.408499i
$980$	4.45278	−	4.45278i	0.142239	−	0.142239i
$981$		0			0
$982$	−17.3942	+	17.3942i	−0.555072	+	0.555072i
$983$	1.95776	+	1.95776i	0.0624428	+	0.0624428i	0.737639	−	0.675196i	$-0.235941\pi$
$983$	1.95776	+	1.95776i	0.0624428	+	0.0624428i	−0.675196	+	0.737639i	$0.735941\pi$
$984$		0			0
$985$		−	5.94093i		−	0.189294i
$986$	62.0028	+	62.0028i	1.97457	+	1.97457i
$987$		0			0
$988$	−44.3491	+	11.6229i	−1.41093	+	0.369772i
$989$		−	14.3204i		−	0.455361i
$990$		0			0
$991$	43.5318			1.38283			0.691416	−	0.722457i	$-0.256987\pi$
$991$	43.5318			1.38283			0.691416	+	0.722457i	$0.256987\pi$
$992$	133.652			4.24347
$993$		0			0
$994$	46.6398	+	46.6398i	1.47933	+	1.47933i
$995$	2.54307	+	2.54307i	0.0806207	+	0.0806207i
$996$		0			0
$997$	40.2561			1.27492			0.637462	−	0.770481i	$-0.279984\pi$
$997$	40.2561			1.27492			0.637462	+	0.770481i	$0.279984\pi$
$998$	−49.9263			−1.58039
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.i.b.242.8	yes	16
3.2	odd	2	inner	351.2.i.b.242.1	yes	16
13.5	odd	4	inner	351.2.i.b.161.1	✓	16
39.5	even	4	inner	351.2.i.b.161.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
351.2.i.b.161.1	✓	16	13.5	odd	4	inner
351.2.i.b.161.8	yes	16	39.5	even	4	inner
351.2.i.b.242.1	yes	16	3.2	odd	2	inner
351.2.i.b.242.8	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.94318 - 1.94318i) q^{2} -5.55193i q^{4} +(0.426892 - 0.426892i) q^{5} +(-1.60020 + 1.60020i) q^{7} +(-6.90206 - 6.90206i) q^{8} -1.65906i q^{10} +(-1.16629 - 1.16629i) q^{11} +(3.11256 + 1.81988i) q^{13} +6.21895i q^{14} -15.7201 q^{16} +6.73139 q^{17} +(-1.61949 - 1.61949i) q^{19} +(-2.37008 - 2.37008i) q^{20} -4.53264 q^{22} +7.07274 q^{23} +4.63553i q^{25} +(9.58465 - 2.51191i) q^{26} +(8.88418 + 8.88418i) q^{28} +4.74015i q^{29} +(-3.99131 - 3.99131i) q^{31} +(-16.7429 + 16.7429i) q^{32} +(13.0803 - 13.0803i) q^{34} +1.36622i q^{35} +(-5.84461 + 5.84461i) q^{37} -6.29394 q^{38} -5.89287 q^{40} +(1.16629 - 1.16629i) q^{41} -2.02473i q^{43} +(-6.47517 + 6.47517i) q^{44} +(13.7436 - 13.7436i) q^{46} +(-5.13821 - 5.13821i) q^{47} +1.87875i q^{49} +(9.00768 + 9.00768i) q^{50} +(10.1039 - 17.2807i) q^{52} -0.512438i q^{53} -0.995761 q^{55} +22.0893 q^{56} +(9.21099 + 9.21099i) q^{58} +(4.62577 + 4.62577i) q^{59} -1.50693 q^{61} -15.5117 q^{62} +33.6290i q^{64} +(2.10562 - 0.551834i) q^{65} +(3.28398 + 3.28398i) q^{67} -37.3722i q^{68} +(2.65482 + 2.65482i) q^{70} +(7.49963 - 7.49963i) q^{71} +(-4.30752 + 4.30752i) q^{73} +22.7143i q^{74} +(-8.99131 + 8.99131i) q^{76} +3.73259 q^{77} -9.54324 q^{79} +(-6.71079 + 6.71079i) q^{80} -4.53264i q^{82} +(-1.71812 + 1.71812i) q^{83} +(2.87358 - 2.87358i) q^{85} +(-3.93442 - 3.93442i) q^{86} +16.0996i q^{88} +(-5.47955 - 5.47955i) q^{89} +(-7.89287 + 2.06854i) q^{91} -39.2674i q^{92} -19.9690 q^{94} -1.38270 q^{95} +(5.52721 + 5.52721i) q^{97} +(3.65075 + 3.65075i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} + 16 q^{13} - 8 q^{16} - 32 q^{19} + 8 q^{22} + 40 q^{28} + 16 q^{31} + 24 q^{34} - 32 q^{37} - 72 q^{40} + 48 q^{46} + 48 q^{52} + 32 q^{55} + 56 q^{58} - 64 q^{61} - 32 q^{67} - 40 q^{70}+ \cdots + 64 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 + 16 * q^13 - 8 * q^16 - 32 * q^19 + 8 * q^22 + 40 * q^28 + 16 * q^31 + 24 * q^34 - 32 * q^37 - 72 * q^40 + 48 * q^46 + 48 * q^52 + 32 * q^55 + 56 * q^58 - 64 * q^61 - 32 * q^67 - 40 * q^70 - 56 * q^73 - 64 * q^76 - 16 * q^79 - 104 * q^91 - 64 * q^94 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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