LMFDB - Embedded newform 396.2.c.a.287.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [396,2,Mod(287,396)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(396, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("396.287"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 396 = 2^{2} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	396.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,0,4,0,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$3.16207592004$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.5236158660608.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{8} - 4x^{7} + 3x^{6} + 8x^{5} + 6x^{4} - 16x^{3} - 16x^{2} + 32 $ x^10 - 2x^8 - 4x^7 + 3x^6 + 8x^5 + 6x^4 - 16x^3 - 16*x^2 + 32
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			287.8
Root			$-0.929398 - 1.06594i$ of defining polynomial
Character	$\chi$	$=$	396.287
Dual form			396.2.c.a.287.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.929398 + 1.06594i) q^{2} +(-0.272438 + 1.98136i) q^{4} +3.24506i q^{5} -1.06027i q^{7} +(-2.36520 + 1.55107i) q^{8} +(-3.45902 + 3.01595i) q^{10} -1.00000 q^{11} -0.185530 q^{13} +(1.13018 - 0.985414i) q^{14} +(-3.85155 - 1.07960i) q^{16} +1.21452i q^{17} -0.402364i q^{19} +(-6.42962 - 0.884078i) q^{20} +(-0.929398 - 1.06594i) q^{22} +8.43352 q^{23} -5.53039 q^{25} +(-0.172432 - 0.197764i) q^{26} +(2.10078 + 0.288859i) q^{28} +7.33643i q^{29} -8.06243i q^{31} +(-2.42885 - 5.10888i) q^{32} +(-1.29460 + 1.12877i) q^{34} +3.44064 q^{35} -0.871611 q^{37} +(0.428895 - 0.373957i) q^{38} +(-5.03330 - 7.67522i) q^{40} +6.18615i q^{41} +9.72091i q^{43} +(0.272438 - 1.98136i) q^{44} +(7.83809 + 8.98959i) q^{46} +4.14689 q^{47} +5.87583 q^{49} +(-5.13994 - 5.89504i) q^{50} +(0.0505456 - 0.367602i) q^{52} -11.7725i q^{53} -3.24506i q^{55} +(1.64455 + 2.50776i) q^{56} +(-7.82016 + 6.81846i) q^{58} +10.0298 q^{59} +4.64744 q^{61} +(8.59404 - 7.49321i) q^{62} +(3.18838 - 7.33718i) q^{64} -0.602057i q^{65} -2.66796i q^{67} +(-2.40640 - 0.330882i) q^{68} +(3.19772 + 3.66750i) q^{70} -9.80568 q^{71} +14.1185 q^{73} +(-0.810074 - 0.929081i) q^{74} +(0.797228 + 0.109620i) q^{76} +1.06027i q^{77} -13.5157i q^{79} +(3.50335 - 12.4985i) q^{80} +(-6.59404 + 5.74940i) q^{82} -17.7975 q^{83} -3.94119 q^{85} +(-10.3619 + 9.03459i) q^{86} +(2.36520 - 1.55107i) q^{88} -15.1445i q^{89} +0.196713i q^{91} +(-2.29761 + 16.7098i) q^{92} +(3.85412 + 4.42032i) q^{94} +1.30570 q^{95} +2.18496 q^{97} +(5.46098 + 6.26325i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4} - 12 q^{8} + 4 q^{10} - 10 q^{11} + 8 q^{13} + 8 q^{14} - 4 q^{16} - 24 q^{20} - 8 q^{23} - 10 q^{25} + 16 q^{26} + 16 q^{28} + 8 q^{34} + 16 q^{35} - 4 q^{37} + 32 q^{38} - 4 q^{44} + 20 q^{46}+ \cdots + 60 q^{98}+O(q^{100}) $ 10 * q + 4 * q^4 - 12 * q^8 + 4 * q^10 - 10 * q^11 + 8 * q^13 + 8 * q^14 - 4 * q^16 - 24 * q^20 - 8 * q^23 - 10 * q^25 + 16 * q^26 + 16 * q^28 + 8 * q^34 + 16 * q^35 - 4 * q^37 + 32 * q^38 - 4 * q^44 + 20 * q^46 - 34 * q^49 + 12 * q^50 - 20 * q^52 - 32 * q^56 - 28 * q^58 + 40 * q^59 + 20 * q^61 + 28 * q^62 - 8 * q^64 - 20 * q^68 - 36 * q^70 - 16 * q^71 + 24 * q^73 + 28 * q^74 - 12 * q^76 - 32 * q^80 - 8 * q^82 + 8 * q^83 - 36 * q^85 - 24 * q^86 + 12 * q^88 - 24 * q^92 - 20 * q^94 - 96 * q^95 + 24 * q^97 + 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	0.929398	+	1.06594i	0.657184	+	0.753730i
$2$	0.929398	+	1.06594i	0.657184	+	0.753730i
$3$		0			0
$3$		0			0
$4$	−0.272438	+	1.98136i	−0.136219	+	0.990679i
$5$			3.24506i			1.45123i	0.688099	+	0.725617i	$0.258445\pi$
$5$			3.24506i			1.45123i	−0.688099	+	0.725617i	$0.741555\pi$
$6$		0			0
$7$		−	1.06027i		−	0.400745i	−0.979720	−	0.200372i	$-0.935785\pi$
$7$		−	1.06027i		−	0.400745i	0.979720	−	0.200372i	$-0.0642152\pi$
$8$	−2.36520	+	1.55107i	−0.836226	+	0.548385i
$9$		0			0
$10$	−3.45902	+	3.01595i	−1.09384	+	0.953727i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$		0			0
$13$	−0.185530			−0.0514569			−0.0257284	−	0.999669i	$-0.508191\pi$
$13$	−0.185530			−0.0514569			−0.0257284	+	0.999669i	$0.508191\pi$
$14$	1.13018	−	0.985414i	0.302054	−	0.263363i
$15$		0			0
$16$	−3.85155	−	1.07960i	−0.962889	−	0.269899i
$17$			1.21452i			0.294565i	0.989094	+	0.147282i	$0.0470526\pi$
$17$			1.21452i			0.294565i	−0.989094	+	0.147282i	$0.952947\pi$
$18$		0			0
$19$		−	0.402364i		−	0.0923087i	−0.998934	−	0.0461544i	$-0.985303\pi$
$19$		−	0.402364i		−	0.0923087i	0.998934	−	0.0461544i	$-0.0146966\pi$
$20$	−6.42962	−	0.884078i	−1.43771	−	0.197686i
$21$		0			0
$22$	−0.929398	−	1.06594i	−0.198148	−	0.227258i
$23$	8.43352			1.75851			0.879255	−	0.476352i	$-0.158041\pi$
$23$	8.43352			1.75851			0.879255	+	0.476352i	$0.158041\pi$
$24$		0			0
$25$	−5.53039			−1.10608
$26$	−0.172432	−	0.197764i	−0.0338166	−	0.0387846i
$27$		0			0
$28$	2.10078	+	0.288859i	0.397009	+	0.0545891i
$29$			7.33643i			1.36234i	0.732125	+	0.681170i	$0.238529\pi$
$29$			7.33643i			1.36234i	−0.732125	+	0.681170i	$0.761471\pi$
$30$		0			0
$31$		−	8.06243i		−	1.44806i	−0.689771	−	0.724028i	$-0.742289\pi$
$31$		−	8.06243i		−	1.44806i	0.689771	−	0.724028i	$-0.257711\pi$
$32$	−2.42885	−	5.10888i	−0.429364	−	0.903132i
$33$		0			0
$34$	−1.29460	+	1.12877i	−0.222022	+	0.193583i
$35$	3.44064			0.581574
$36$		0			0
$37$	−0.871611			−0.143292			−0.0716460	−	0.997430i	$-0.522825\pi$
$37$	−0.871611			−0.143292			−0.0716460	+	0.997430i	$0.522825\pi$
$38$	0.428895	−	0.373957i	0.0695759	−	0.0606638i
$39$		0			0
$40$	−5.03330	−	7.67522i	−0.795835	−	1.21356i
$41$			6.18615i			0.966114i	0.875589	+	0.483057i	$0.160474\pi$
$41$			6.18615i			0.966114i	−0.875589	+	0.483057i	$0.839526\pi$
$42$		0			0
$43$			9.72091i			1.48242i	0.671271	+	0.741212i	$0.265749\pi$
$43$			9.72091i			1.48242i	−0.671271	+	0.741212i	$0.734251\pi$
$44$	0.272438	−	1.98136i	0.0410716	−	0.298701i
$45$		0			0
$46$	7.83809	+	8.98959i	1.15566	+	1.32544i
$47$	4.14689			0.604887			0.302443	−	0.953167i	$-0.402198\pi$
$47$	4.14689			0.604887			0.302443	+	0.953167i	$0.402198\pi$
$48$		0			0
$49$	5.87583			0.839404
$50$	−5.13994	−	5.89504i	−0.726897	−	0.833685i
$51$		0			0
$52$	0.0505456	−	0.367602i	0.00700941	−	0.0509772i
$53$		−	11.7725i		−	1.61708i	−0.588439	−	0.808542i	$-0.700257\pi$
$53$		−	11.7725i		−	1.61708i	0.588439	−	0.808542i	$-0.299743\pi$
$54$		0			0
$55$		−	3.24506i		−	0.437563i
$56$	1.64455	+	2.50776i	0.219763	+	0.335113i
$57$		0			0
$58$	−7.82016	+	6.81846i	−1.02684	+	0.895308i
$59$	10.0298			1.30577			0.652887	−	0.757455i	$-0.273558\pi$
$59$	10.0298			1.30577			0.652887	+	0.757455i	$0.273558\pi$
$60$		0			0
$61$	4.64744			0.595044			0.297522	−	0.954715i	$-0.403840\pi$
$61$	4.64744			0.595044			0.297522	+	0.954715i	$0.403840\pi$
$62$	8.59404	−	7.49321i	1.09144	−	0.951639i
$63$		0			0
$64$	3.18838	−	7.33718i	0.398547	−	0.917148i
$65$		−	0.602057i		−	0.0746760i
$66$		0			0
$67$		−	2.66796i		−	0.325943i	−0.986631	−	0.162972i	$-0.947892\pi$
$67$		−	2.66796i		−	0.325943i	0.986631	−	0.162972i	$-0.0521079\pi$
$68$	−2.40640	−	0.330882i	−0.291819	−	0.0401254i
$69$		0			0
$70$	3.19772	+	3.66750i	0.382201	+	0.438350i
$71$	−9.80568			−1.16372			−0.581860	−	0.813289i	$-0.697675\pi$
$71$	−9.80568			−1.16372			−0.581860	+	0.813289i	$0.697675\pi$
$72$		0			0
$73$	14.1185			1.65245			0.826223	−	0.563344i	$-0.190485\pi$
$73$	14.1185			1.65245			0.826223	+	0.563344i	$0.190485\pi$
$74$	−0.810074	−	0.929081i	−0.0941691	−	0.108004i
$75$		0			0
$76$	0.797228	+	0.109620i	0.0914483	+	0.0125742i
$77$			1.06027i			0.120829i
$78$		0			0
$79$		−	13.5157i		−	1.52064i	−0.649549	−	0.760320i	$-0.725042\pi$
$79$		−	13.5157i		−	1.52064i	0.649549	−	0.760320i	$-0.274958\pi$
$80$	3.50335	−	12.4985i	0.391686	−	1.39738i
$81$		0			0
$82$	−6.59404	+	5.74940i	−0.728190	+	0.634915i
$83$	−17.7975			−1.95352			−0.976762	−	0.214326i	$-0.931244\pi$
$83$	−17.7975			−1.95352			−0.976762	+	0.214326i	$0.931244\pi$
$84$		0			0
$85$	−3.94119			−0.427482
$86$	−10.3619	+	9.03459i	−1.11735	+	0.974225i
$87$		0			0
$88$	2.36520	−	1.55107i	0.252132	−	0.165344i
$89$		−	15.1445i		−	1.60532i	−0.596439	−	0.802659i	$-0.703418\pi$
$89$		−	15.1445i		−	1.60532i	0.596439	−	0.802659i	$-0.296582\pi$
$90$		0			0
$91$			0.196713i			0.0206211i
$92$	−2.29761	+	16.7098i	−0.239543	+	1.74212i
$93$		0			0
$94$	3.85412	+	4.42032i	0.397522	+	0.455922i
$95$	1.30570			0.133962
$96$		0			0
$97$	2.18496			0.221849			0.110925	−	0.993829i	$-0.464619\pi$
$97$	2.18496			0.221849			0.110925	+	0.993829i	$0.464619\pi$
$98$	5.46098	+	6.26325i	0.551642	+	0.632684i
$99$		0			0
$100$	1.50669	−	10.9577i	0.150669	−	1.09577i
$101$			3.04922i			0.303409i	0.988426	+	0.151704i	$0.0484762\pi$
$101$			3.04922i			0.303409i	−0.988426	+	0.151704i	$0.951524\pi$
$102$		0			0
$103$		−	4.00136i		−	0.394266i	−0.980377	−	0.197133i	$-0.936837\pi$
$103$		−	4.00136i		−	0.394266i	0.980377	−	0.197133i	$-0.0631631\pi$
$104$	0.438817	−	0.287770i	0.0430296	−	0.0282182i
$105$		0			0
$106$	12.5488	−	10.9414i	1.21884	−	1.06272i
$107$	−1.74744			−0.168931			−0.0844655	−	0.996426i	$-0.526918\pi$
$107$	−1.74744			−0.168931			−0.0844655	+	0.996426i	$0.526918\pi$
$108$		0			0
$109$	11.0227			1.05579			0.527893	−	0.849311i	$-0.322982\pi$
$109$	11.0227			1.05579			0.527893	+	0.849311i	$0.322982\pi$
$110$	3.45902	−	3.01595i	0.329805	−	0.287560i
$111$		0			0
$112$	−1.14466	+	4.08369i	−0.108161	+	0.385873i
$113$			7.51266i			0.706731i	0.935485	+	0.353366i	$0.114963\pi$
$113$			7.51266i			0.706731i	−0.935485	+	0.353366i	$0.885037\pi$
$114$		0			0
$115$			27.3672i			2.55201i
$116$	−14.5361	−	1.99872i	−1.34964	−	0.185577i
$117$		0			0
$118$	9.32172	+	10.6912i	0.858134	+	0.984202i
$119$	1.28772			0.118045
$120$		0			0
$121$	1.00000			0.0909091
$122$	4.31933	+	4.95388i	0.391053	+	0.448503i
$123$		0			0
$124$	15.9746	+	2.19652i	1.43456	+	0.197253i
$125$		−	1.72116i		−	0.153945i
$126$		0			0
$127$		−	3.84649i		−	0.341321i	−0.985330	−	0.170661i	$-0.945410\pi$
$127$		−	3.84649i		−	0.341321i	0.985330	−	0.170661i	$-0.0545901\pi$
$128$	10.7842	−	3.42056i	0.953201	−	0.302338i
$129$		0			0
$130$	0.641754	−	0.559550i	0.0562855	−	0.0490758i
$131$	−10.9313			−0.955072			−0.477536	−	0.878612i	$-0.658470\pi$
$131$	−10.9313			−0.955072			−0.477536	+	0.878612i	$0.658470\pi$
$132$		0			0
$133$	−0.426615			−0.0369923
$134$	2.84387	−	2.47960i	0.245673	−	0.214205i
$135$		0			0
$136$	−1.88381	−	2.87259i	−0.161535	−	0.246323i
$137$			1.35957i			0.116156i	0.998312	+	0.0580781i	$0.0184973\pi$
$137$			1.35957i			0.116156i	−0.998312	+	0.0580781i	$0.981503\pi$
$138$		0			0
$139$		−	4.00941i		−	0.340074i	−0.985438	−	0.170037i	$-0.945611\pi$
$139$		−	4.00941i		−	0.340074i	0.985438	−	0.170037i	$-0.0543887\pi$
$140$	−0.937362	+	6.81714i	−0.0792216	+	0.576153i
$141$		0			0
$142$	−9.11338	−	10.4522i	−0.764778	−	0.877131i
$143$	0.185530			0.0155148
$144$		0			0
$145$	−23.8071			−1.97707
$146$	13.1217	+	15.0494i	1.08596	+	1.24550i
$147$		0			0
$148$	0.237460	−	1.72697i	0.0195191	−	0.141956i
$149$		−	2.29913i		−	0.188352i	−0.995556	−	0.0941761i	$-0.969978\pi$
$149$		−	2.29913i		−	0.188352i	0.995556	−	0.0941761i	$-0.0300217\pi$
$150$		0			0
$151$			19.6564i			1.59961i	0.600257	+	0.799807i	$0.295065\pi$
$151$			19.6564i			1.59961i	−0.600257	+	0.799807i	$0.704935\pi$
$152$	0.624095	+	0.951674i	0.0506208	+	0.0771909i
$153$		0			0
$154$	−1.13018	+	0.985414i	−0.0910726	+	0.0794069i
$155$	26.1631			2.10147
$156$		0			0
$157$	−20.6103			−1.64488			−0.822439	−	0.568854i	$-0.807387\pi$
$157$	−20.6103			−1.64488			−0.822439	+	0.568854i	$0.807387\pi$
$158$	14.4069	−	12.5615i	1.14615	−	0.999339i
$159$		0			0
$160$	16.5786	−	7.88175i	1.31065	−	0.623107i
$161$		−	8.94181i		−	0.704714i
$162$		0			0
$163$			13.2602i			1.03862i	0.854586	+	0.519309i	$0.173811\pi$
$163$			13.2602i			1.03862i	−0.854586	+	0.519309i	$0.826189\pi$
$164$	−12.2570	−	1.68534i	−0.957109	−	0.131603i
$165$		0			0
$166$	−16.5409	−	18.9709i	−1.28382	−	1.47243i
$167$	−23.2511			−1.79922			−0.899612	−	0.436690i	$-0.856151\pi$
$167$	−23.2511			−1.79922			−0.899612	+	0.436690i	$0.856151\pi$
$168$		0			0
$169$	−12.9656			−0.997352
$170$	−3.66293	−	4.20106i	−0.280934	−	0.322206i
$171$		0			0
$172$	−19.2606	−	2.64835i	−1.46861	−	0.201935i
$173$		−	12.4685i		−	0.947964i	−0.880534	−	0.473982i	$-0.842816\pi$
$173$		−	12.4685i		−	0.947964i	0.880534	−	0.473982i	$-0.157184\pi$
$174$		0			0
$175$			5.86372i			0.443255i
$176$	3.85155	+	1.07960i	0.290322	+	0.0813776i
$177$		0			0
$178$	16.1431	−	14.0753i	1.20998	−	1.05499i
$179$	1.22250			0.0913738			0.0456869	−	0.998956i	$-0.485452\pi$
$179$	1.22250			0.0913738			0.0456869	+	0.998956i	$0.485452\pi$
$180$		0			0
$181$	8.33243			0.619344			0.309672	−	0.950843i	$-0.399781\pi$
$181$	8.33243			0.619344			0.309672	+	0.950843i	$0.399781\pi$
$182$	−0.209683	+	0.182824i	−0.0155427	+	0.0135518i
$183$		0			0
$184$	−19.9470	+	13.0810i	−1.47051	+	0.964341i
$185$		−	2.82843i		−	0.207950i
$186$		0			0
$187$		−	1.21452i		−	0.0888146i
$188$	−1.12977	+	8.21648i	−0.0823972	+	0.599248i
$189$		0			0
$190$	1.21351	+	1.39179i	0.0880373	+	0.100971i
$191$	−10.2540			−0.741954			−0.370977	−	0.928642i	$-0.620977\pi$
$191$	−10.2540			−0.741954			−0.370977	+	0.928642i	$0.620977\pi$
$192$		0			0
$193$	−11.0287			−0.793866			−0.396933	−	0.917848i	$-0.629926\pi$
$193$	−11.0287			−0.793866			−0.396933	+	0.917848i	$0.629926\pi$
$194$	2.03070	+	2.32903i	0.145796	+	0.167215i
$195$		0			0
$196$	−1.60080	+	11.6421i	−0.114343	+	0.831579i
$197$		−	1.19186i		−	0.0849167i	−0.999098	−	0.0424584i	$-0.986481\pi$
$197$		−	1.19186i		−	0.0849167i	0.999098	−	0.0424584i	$-0.0135190\pi$
$198$		0			0
$199$		−	9.47429i		−	0.671615i	−0.941931	−	0.335807i	$-0.890991\pi$
$199$		−	9.47429i		−	0.671615i	0.941931	−	0.335807i	$-0.109009\pi$
$200$	13.0805	−	8.57802i	0.924932	−	0.606557i
$201$		0			0
$202$	−3.25028	+	2.83394i	−0.228689	+	0.199395i
$203$	7.77860			0.545951
$204$		0			0
$205$	−20.0744			−1.40206
$206$	4.26520	−	3.71886i	0.297170	−	0.259105i
$207$		0			0
$208$	0.714581	+	0.200298i	0.0495473	+	0.0138882i
$209$			0.402364i			0.0278321i
$210$		0			0
$211$		−	8.97677i		−	0.617987i	−0.951064	−	0.308993i	$-0.900008\pi$
$211$		−	8.97677i		−	0.617987i	0.951064	−	0.308993i	$-0.0999921\pi$
$212$	23.3256	+	3.20729i	1.60201	+	0.220278i
$213$		0			0
$214$	−1.62406	−	1.86265i	−0.111019	−	0.127328i
$215$	−31.5449			−2.15134
$216$		0			0
$217$	−8.54837			−0.580301
$218$	10.2445	+	11.7495i	0.693845	+	0.795777i
$219$		0			0
$220$	6.42962	+	0.884078i	0.433485	+	0.0596045i
$221$		−	0.225331i		−	0.0151574i
$222$		0			0
$223$		−	21.2266i		−	1.42144i	−0.703476	−	0.710719i	$-0.748370\pi$
$223$		−	21.2266i		−	1.42144i	0.703476	−	0.710719i	$-0.251630\pi$
$224$	−5.41680	+	2.57524i	−0.361925	+	0.172065i
$225$		0			0
$226$	−8.00801	+	6.98225i	−0.532685	+	0.464452i
$227$	14.6713			0.973766			0.486883	−	0.873467i	$-0.338134\pi$
$227$	14.6713			0.973766			0.486883	+	0.873467i	$0.338134\pi$
$228$		0			0
$229$	19.7773			1.30692			0.653460	−	0.756961i	$-0.273317\pi$
$229$	19.7773			1.30692			0.653460	+	0.756961i	$0.273317\pi$
$230$	−29.1717	+	25.4351i	−1.92353	+	1.67714i
$231$		0			0
$232$	−11.3793	−	17.3521i	−0.747087	−	1.13922i
$233$			4.68721i			0.307069i	0.988143	+	0.153535i	$0.0490657\pi$
$233$			4.68721i			0.307069i	−0.988143	+	0.153535i	$0.950934\pi$
$234$		0			0
$235$			13.4569i			0.877832i
$236$	−2.73251	+	19.8727i	−0.177872	+	1.29360i
$237$		0			0
$238$	1.19681	+	1.37263i	0.0775774	+	0.0889743i
$239$	−14.6779			−0.949432			−0.474716	−	0.880139i	$-0.657449\pi$
$239$	−14.6779			−0.949432			−0.474716	+	0.880139i	$0.657449\pi$
$240$		0			0
$241$	−0.836312			−0.0538716			−0.0269358	−	0.999637i	$-0.508575\pi$
$241$	−0.836312			−0.0538716			−0.0269358	+	0.999637i	$0.508575\pi$
$242$	0.929398	+	1.06594i	0.0597440	+	0.0685209i
$243$		0			0
$244$	−1.26614	+	9.20825i	−0.0810565	+	0.589498i
$245$			19.0674i			1.21817i
$246$		0			0
$247$			0.0746509i			0.00474992i
$248$	12.5054	+	19.0693i	0.794093	+	1.21090i
$249$		0			0
$250$	1.83464	−	1.59964i	0.116033	−	0.101170i
$251$	15.4031			0.972238			0.486119	−	0.873893i	$-0.338412\pi$
$251$	15.4031			0.972238			0.486119	+	0.873893i	$0.338412\pi$
$252$		0			0
$253$	−8.43352			−0.530211
$254$	4.10011	−	3.57492i	0.257264	−	0.224311i
$255$		0			0
$256$	13.6689	+	8.31624i	0.854309	+	0.519765i
$257$		−	5.65841i		−	0.352962i	−0.984304	−	0.176481i	$-0.943529\pi$
$257$		−	5.65841i		−	0.352962i	0.984304	−	0.176481i	$-0.0564714\pi$
$258$		0			0
$259$			0.924144i			0.0574235i
$260$	1.19289	+	0.164023i	0.0739799	+	0.0101723i
$261$		0			0
$262$	−10.1595	−	11.6521i	−0.627658	−	0.719867i
$263$	−6.79434			−0.418957			−0.209478	−	0.977813i	$-0.567177\pi$
$263$	−6.79434			−0.418957			−0.209478	+	0.977813i	$0.567177\pi$
$264$		0			0
$265$	38.2026			2.34677
$266$	−0.396496	−	0.454745i	−0.0243107	−	0.0278822i
$267$		0			0
$268$	5.28618	+	0.726855i	0.322905	+	0.0443997i
$269$		−	13.5299i		−	0.824935i	−0.910972	−	0.412468i	$-0.864667\pi$
$269$		−	13.5299i		−	0.824935i	0.910972	−	0.412468i	$-0.135333\pi$
$270$		0			0
$271$		−	16.5604i		−	1.00597i	−0.864294	−	0.502987i	$-0.832234\pi$
$271$		−	16.5604i		−	1.00597i	0.864294	−	0.502987i	$-0.167766\pi$
$272$	1.31119	−	4.67779i	0.0795027	−	0.283633i
$273$		0			0
$274$	−1.44922	+	1.26359i	−0.0875505	+	0.0763360i
$275$	5.53039			0.333495
$276$		0			0
$277$	−15.1917			−0.912782			−0.456391	−	0.889779i	$-0.650858\pi$
$277$	−15.1917			−0.912782			−0.456391	+	0.889779i	$0.650858\pi$
$278$	4.27378	−	3.72634i	0.256324	−	0.223491i
$279$		0			0
$280$	−8.13781	+	5.33667i	−0.486327	+	0.318927i
$281$			21.4290i			1.27835i	0.769063	+	0.639173i	$0.220723\pi$
$281$			21.4290i			1.27835i	−0.769063	+	0.639173i	$0.779277\pi$
$282$		0			0
$283$			0.856388i			0.0509070i	0.999676	+	0.0254535i	$0.00810297\pi$
$283$			0.856388i			0.0509070i	−0.999676	+	0.0254535i	$0.991897\pi$
$284$	2.67144	−	19.4286i	0.158521	−	1.15287i
$285$		0			0
$286$	0.172432	+	0.197764i	0.0101961	+	0.0116940i
$287$	6.55900			0.387165
$288$		0			0
$289$	15.5249			0.913232
$290$	−22.1263	−	25.3769i	−1.29930	−	1.49018i
$291$		0			0
$292$	−3.84642	+	27.9738i	−0.225095	+	1.63704i
$293$		−	24.6999i		−	1.44298i	−0.692423	−	0.721492i	$-0.743457\pi$
$293$		−	24.6999i		−	1.44298i	0.692423	−	0.721492i	$-0.256543\pi$
$294$		0			0
$295$			32.5474i			1.89498i
$296$	2.06154	−	1.35193i	0.119824	−	0.0785792i
$297$		0			0
$298$	2.45073	−	2.13681i	0.141967	−	0.123782i
$299$	−1.56467			−0.0904874
$300$		0			0
$301$	10.3068			0.594074
$302$	−20.9524	+	18.2686i	−1.20568	+	1.05124i
$303$		0			0
$304$	−0.434391	+	1.54973i	−0.0249140	+	0.0888830i
$305$			15.0812i			0.863548i
$306$		0			0
$307$			12.2331i			0.698181i	0.937089	+	0.349090i	$0.113509\pi$
$307$			12.2331i			0.698181i	−0.937089	+	0.349090i	$0.886491\pi$
$308$	−2.10078	−	0.288859i	−0.119703	−	0.0164592i
$309$		0			0
$310$	24.3159	+	27.8881i	1.38105	+	1.58394i
$311$	−9.18118			−0.520617			−0.260308	−	0.965526i	$-0.583824\pi$
$311$	−9.18118			−0.520617			−0.260308	+	0.965526i	$0.583824\pi$
$312$		0			0
$313$	−19.7806			−1.11807			−0.559033	−	0.829145i	$-0.688828\pi$
$313$	−19.7806			−1.11807			−0.559033	+	0.829145i	$0.688828\pi$
$314$	−19.1551	−	21.9692i	−1.08099	−	1.23979i
$315$		0			0
$316$	26.7795	+	3.68221i	1.50647	+	0.207140i
$317$			8.50253i			0.477549i	0.971075	+	0.238775i	$0.0767458\pi$
$317$			8.50253i			0.477549i	−0.971075	+	0.238775i	$0.923254\pi$
$318$		0			0
$319$		−	7.33643i		−	0.410761i
$320$	23.8096	+	10.3465i	1.33100	+	0.578385i
$321$		0			0
$322$	9.53140	−	8.31051i	0.531164	−	0.463126i
$323$	0.488680			0.0271909
$324$		0			0
$325$	1.02606			0.0569154
$326$	−14.1345	+	12.3240i	−0.782839	+	0.682563i
$327$		0			0
$328$	−9.59514	−	14.6315i	−0.529803	−	0.807890i
$329$		−	4.39683i		−	0.242405i
$330$		0			0
$331$			24.0491i			1.32186i	0.750447	+	0.660930i	$0.229838\pi$
$331$			24.0491i			1.32186i	−0.750447	+	0.660930i	$0.770162\pi$
$332$	4.84871	−	35.2631i	0.266107	−	1.93531i
$333$		0			0
$334$	−21.6095	−	24.7842i	−1.18242	−	1.35613i
$335$	8.65768			0.473020
$336$		0			0
$337$	−3.97103			−0.216316			−0.108158	−	0.994134i	$-0.534495\pi$
$337$	−3.97103			−0.216316			−0.108158	+	0.994134i	$0.534495\pi$
$338$	−12.0502	−	13.8205i	−0.655444	−	0.751735i
$339$		0			0
$340$	1.07373	−	7.80891i	0.0582313	−	0.423497i
$341$			8.06243i			0.436605i
$342$		0			0
$343$		−	13.6519i		−	0.737131i
$344$	−15.0778	−	22.9919i	−0.812940	−	1.23964i
$345$		0			0
$346$	13.2906	−	11.5882i	0.714509	−	0.622987i
$347$	21.1839			1.13721			0.568605	−	0.822611i	$-0.307483\pi$
$347$	21.1839			1.13721			0.568605	+	0.822611i	$0.307483\pi$
$348$		0			0
$349$	21.3207			1.14127			0.570636	−	0.821203i	$-0.306697\pi$
$349$	21.3207			1.14127			0.570636	+	0.821203i	$0.306697\pi$
$350$	−6.25035	+	5.44973i	−0.334095	+	0.291300i
$351$		0			0
$352$	2.42885	+	5.10888i	0.129458	+	0.272304i
$353$		−	13.3234i		−	0.709134i	−0.935031	−	0.354567i	$-0.884628\pi$
$353$		−	13.3234i		−	0.709134i	0.935031	−	0.354567i	$-0.115372\pi$
$354$		0			0
$355$		−	31.8200i		−	1.68883i
$356$	30.0067	+	4.12595i	1.59035	+	0.218675i
$357$		0			0
$358$	1.13619	+	1.30310i	0.0600494	+	0.0688712i
$359$	32.4904			1.71478			0.857390	−	0.514668i	$-0.172085\pi$
$359$	32.4904			1.71478			0.857390	+	0.514668i	$0.172085\pi$
$360$		0			0
$361$	18.8381			0.991479
$362$	7.74414	+	8.88183i	0.407023	+	0.466819i
$363$		0			0
$364$	−0.389758	−	0.0535921i	−0.0204289	−	0.00280899i
$365$			45.8153i			2.39808i
$366$		0			0
$367$		−	12.6522i		−	0.660438i	−0.943904	−	0.330219i	$-0.892877\pi$
$367$		−	12.6522i		−	0.660438i	0.943904	−	0.330219i	$-0.107123\pi$
$368$	−32.4821	−	9.10479i	−1.69325	−	0.474620i
$369$		0			0
$370$	3.01492	−	2.62873i	0.156738	−	0.136661i
$371$	−12.4821			−0.648038
$372$		0			0
$373$	28.9497			1.49896			0.749478	−	0.662029i	$-0.230304\pi$
$373$	28.9497			1.49896			0.749478	+	0.662029i	$0.230304\pi$
$374$	1.29460	−	1.12877i	0.0669423	−	0.0583675i
$375$		0			0
$376$	−9.80825	+	6.43212i	−0.505822	+	0.331711i
$377$		−	1.36113i		−	0.0701018i
$378$		0			0
$379$		−	3.84009i		−	0.197252i	−0.995125	−	0.0986262i	$-0.968555\pi$
$379$		−	3.84009i		−	0.197252i	0.995125	−	0.0986262i	$-0.0314448\pi$
$380$	−0.355722	+	2.58705i	−0.0182481	+	0.132713i
$381$		0			0
$382$	−9.53006	−	10.9301i	−0.487600	−	0.559233i
$383$	−25.9426			−1.32561			−0.662803	−	0.748793i	$-0.730633\pi$
$383$	−25.9426			−1.32561			−0.662803	+	0.748793i	$0.730633\pi$
$384$		0			0
$385$	−3.44064			−0.175351
$386$	−10.2501	−	11.7559i	−0.521716	−	0.598361i
$387$		0			0
$388$	−0.595268	+	4.32919i	−0.0302201	+	0.219781i
$389$			16.2437i			0.823587i	0.911277	+	0.411794i	$0.135098\pi$
$389$			16.2437i			0.823587i	−0.911277	+	0.411794i	$0.864902\pi$
$390$		0			0
$391$			10.2427i			0.517995i
$392$	−13.8975	+	9.11380i	−0.701931	+	0.460317i
$393$		0			0
$394$	1.27045	−	1.10771i	0.0640043	−	0.0558059i
$395$	43.8593			2.20680
$396$		0			0
$397$	−5.79658			−0.290922			−0.145461	−	0.989364i	$-0.546467\pi$
$397$	−5.79658			−0.290922			−0.145461	+	0.989364i	$0.546467\pi$
$398$	10.0990	−	8.80539i	0.506216	−	0.441374i
$399$		0			0
$400$	21.3006	+	5.97059i	1.06503	+	0.298529i
$401$		−	27.4792i		−	1.37225i	−0.727485	−	0.686124i	$-0.759311\pi$
$401$		−	27.4792i		−	1.37225i	0.727485	−	0.686124i	$-0.240689\pi$
$402$		0			0
$403$			1.49583i			0.0745125i
$404$	−6.04160	−	0.830725i	−0.300581	−	0.0413301i
$405$		0			0
$406$	7.22942	+	8.29149i	0.358790	+	0.411500i
$407$	0.871611			0.0432042
$408$		0			0
$409$	5.93028			0.293233			0.146617	−	0.989193i	$-0.453162\pi$
$409$	5.93028			0.293233			0.146617	+	0.989193i	$0.453162\pi$
$410$	−18.6571	−	21.3980i	−0.921409	−	1.05677i
$411$		0			0
$412$	7.92813	+	1.09012i	0.390591	+	0.0537066i
$413$		−	10.6344i		−	0.523282i
$414$		0			0
$415$		−	57.7537i		−	2.83502i
$416$	0.450625	+	0.947854i	0.0220937	+	0.0464723i
$417$		0			0
$418$	−0.428895	+	0.373957i	−0.0209779	+	0.0182908i
$419$	17.3154			0.845911			0.422955	−	0.906150i	$-0.360993\pi$
$419$	17.3154			0.845911			0.422955	+	0.906150i	$0.360993\pi$
$420$		0			0
$421$	−27.7108			−1.35054			−0.675271	−	0.737570i	$-0.735973\pi$
$421$	−27.7108			−1.35054			−0.675271	+	0.737570i	$0.735973\pi$
$422$	9.56867	−	8.34300i	0.465795	−	0.406131i
$423$		0			0
$424$	18.2600	+	27.8445i	0.886785	+	1.35225i
$425$		−	6.71678i		−	0.325812i
$426$		0			0
$427$		−	4.92755i		−	0.238461i
$428$	0.476069	−	3.46230i	0.0230116	−	0.167356i
$429$		0			0
$430$	−29.3178	−	33.6248i	−1.41383	−	1.62153i
$431$	−5.24601			−0.252691			−0.126346	−	0.991986i	$-0.540325\pi$
$431$	−5.24601			−0.252691			−0.126346	+	0.991986i	$0.540325\pi$
$432$		0			0
$433$	32.5052			1.56210			0.781049	−	0.624470i	$-0.214685\pi$
$433$	32.5052			1.56210			0.781049	+	0.624470i	$0.214685\pi$
$434$	−7.94484	−	9.11201i	−0.381364	−	0.437391i
$435$		0			0
$436$	−3.00301	+	21.8399i	−0.143818	+	1.04594i
$437$		−	3.39335i		−	0.162326i
$438$		0			0
$439$		−	1.53039i		−	0.0730416i	−0.999333	−	0.0365208i	$-0.988372\pi$
$439$		−	1.53039i		−	0.0730416i	0.999333	−	0.0365208i	$-0.0116275\pi$
$440$	5.03330	+	7.67522i	0.239953	+	0.365902i
$441$		0			0
$442$	0.240188	−	0.209422i	0.0114246	−	0.00996118i
$443$	−9.06192			−0.430545			−0.215272	−	0.976554i	$-0.569064\pi$
$443$	−9.06192			−0.430545			−0.215272	+	0.976554i	$0.569064\pi$
$444$		0			0
$445$	49.1449			2.32969
$446$	22.6262	−	19.7280i	1.07138	−	0.934146i
$447$		0			0
$448$	−7.77940	−	3.38054i	−0.367542	−	0.159716i
$449$			12.3571i			0.583166i	0.956546	+	0.291583i	$0.0941820\pi$
$449$			12.3571i			0.583166i	−0.956546	+	0.291583i	$0.905818\pi$
$450$		0			0
$451$		−	6.18615i		−	0.291294i
$452$	−14.8853	−	2.04674i	−0.700144	−	0.0962704i
$453$		0			0
$454$	13.6354	+	15.6386i	0.639943	+	0.733957i
$455$	−0.638343			−0.0299260
$456$		0			0
$457$	−35.4290			−1.65730			−0.828649	−	0.559769i	$-0.810890\pi$
$457$	−35.4290			−1.65730			−0.828649	+	0.559769i	$0.810890\pi$
$458$	18.3810	+	21.0813i	0.858886	+	0.985065i
$459$		0			0
$460$	−54.2243	−	7.45589i	−2.52822	−	0.347632i
$461$		−	36.5837i		−	1.70387i	−0.523646	−	0.851936i	$-0.675428\pi$
$461$		−	36.5837i		−	1.70387i	0.523646	−	0.851936i	$-0.324572\pi$
$462$		0			0
$463$			30.3672i			1.41128i	0.708570	+	0.705641i	$0.249341\pi$
$463$			30.3672i			1.41128i	−0.708570	+	0.705641i	$0.750659\pi$
$464$	7.92037	−	28.2567i	0.367694	−	1.31178i
$465$		0			0
$466$	−4.99627	+	4.35628i	−0.231448	+	0.201801i
$467$	−11.8907			−0.550235			−0.275118	−	0.961411i	$-0.588717\pi$
$467$	−11.8907			−0.550235			−0.275118	+	0.961411i	$0.588717\pi$
$468$		0			0
$469$	−2.82876			−0.130620
$470$	−14.3442	+	12.5068i	−0.661649	+	0.576897i
$471$		0			0
$472$	−23.7226	+	15.5570i	−1.09192	+	0.716068i
$473$		−	9.72091i		−	0.446968i
$474$		0			0
$475$			2.22523i			0.102101i
$476$	−0.350825	+	2.55144i	−0.0160800	+	0.116945i
$477$		0			0
$478$	−13.6416	−	15.6457i	−0.623951	−	0.715616i
$479$	19.6734			0.898901			0.449451	−	0.893305i	$-0.351620\pi$
$479$	19.6734			0.898901			0.449451	+	0.893305i	$0.351620\pi$
$480$		0			0
$481$	0.161710			0.00737336
$482$	−0.777267	−	0.891455i	−0.0354035	−	0.0406047i
$483$		0			0
$484$	−0.272438	+	1.98136i	−0.0123836	+	0.0900617i
$485$			7.09033i			0.321955i
$486$		0			0
$487$		−	20.5609i		−	0.931704i	−0.884863	−	0.465852i	$-0.845748\pi$
$487$		−	20.5609i		−	0.931704i	0.884863	−	0.465852i	$-0.154252\pi$
$488$	−10.9922	+	7.20850i	−0.497591	+	0.326314i
$489$		0			0
$490$	−20.3246	+	17.7212i	−0.918172	+	0.800562i
$491$	11.2621			0.508251			0.254126	−	0.967171i	$-0.418212\pi$
$491$	11.2621			0.508251			0.254126	+	0.967171i	$0.418212\pi$
$492$		0			0
$493$	−8.91025			−0.401297
$494$	−0.0795730	+	0.0693804i	−0.00358016	+	0.00312157i
$495$		0			0
$496$	−8.70417	+	31.0529i	−0.390829	+	1.39432i
$497$			10.3967i			0.466355i
$498$		0			0
$499$		−	18.4254i		−	0.824835i	−0.910995	−	0.412418i	$-0.864684\pi$
$499$		−	18.4254i		−	0.824835i	0.910995	−	0.412418i	$-0.135316\pi$
$500$	3.41023	+	0.468909i	0.152510	+	0.0209703i
$501$		0			0
$502$	14.3156	+	16.4188i	0.638939	+	0.732805i
$503$	0.361391			0.0161136			0.00805682	−	0.999968i	$-0.497435\pi$
$503$	0.361391			0.0161136			0.00805682	+	0.999968i	$0.497435\pi$
$504$		0			0
$505$	−9.89490			−0.440317
$506$	−7.83809	−	8.98959i	−0.348446	−	0.399636i
$507$		0			0
$508$	7.62128	+	1.04793i	0.338140	+	0.0464945i
$509$		−	10.1060i		−	0.447942i	−0.974596	−	0.223971i	$-0.928098\pi$
$509$		−	10.1060i		−	0.447942i	0.974596	−	0.223971i	$-0.0719020\pi$
$510$		0			0
$511$		−	14.9694i		−	0.662209i
$512$	3.83931	+	22.2993i	0.169675	+	0.985500i
$513$		0			0
$514$	6.03150	−	5.25892i	0.266038	−	0.231961i
$515$	12.9847			0.572172
$516$		0			0
$517$	−4.14689			−0.182380
$518$	−0.985078	+	0.858898i	−0.0432819	+	0.0377378i
$519$		0			0
$520$	0.933831	+	1.42399i	0.0409512	+	0.0624460i
$521$			13.4234i			0.588089i	0.955792	+	0.294044i	$0.0950013\pi$
$521$			13.4234i			0.588089i	−0.955792	+	0.294044i	$0.904999\pi$
$522$		0			0
$523$			22.9205i			1.00224i	0.865377	+	0.501122i	$0.167079\pi$
$523$			22.9205i			1.00224i	−0.865377	+	0.501122i	$0.832921\pi$
$524$	2.97810	−	21.6588i	0.130099	−	0.946169i
$525$		0			0
$526$	−6.31465	−	7.24233i	−0.275332	−	0.315781i
$527$	9.79200			0.426546
$528$		0			0
$529$	48.1242			2.09236
$530$	35.5054	+	40.7215i	1.54226	+	1.76883i
$531$		0			0
$532$	0.116226	−	0.845278i	0.00503905	−	0.0366474i
$533$		−	1.14772i		−	0.0497132i
$534$		0			0
$535$		−	5.67053i		−	0.245158i
$536$	4.13819	+	6.31027i	0.178742	+	0.272562i
$537$		0			0
$538$	14.4221	−	12.5747i	0.621779	−	0.542134i
$539$	−5.87583			−0.253090
$540$		0			0
$541$	−23.8245			−1.02430			−0.512148	−	0.858897i	$-0.671150\pi$
$541$	−23.8245			−1.02430			−0.512148	+	0.858897i	$0.671150\pi$
$542$	17.6524	−	15.3912i	0.758233	−	0.661110i
$543$		0			0
$544$	6.20485	−	2.94989i	0.266031	−	0.126475i
$545$			35.7694i			1.53219i
$546$		0			0
$547$			27.6830i			1.18364i	0.806071	+	0.591819i	$0.201590\pi$
$547$			27.6830i			1.18364i	−0.806071	+	0.591819i	$0.798410\pi$
$548$	−2.69380	−	0.370400i	−0.115074	−	0.0158227i
$549$		0			0
$550$	5.13994	+	5.89504i	0.219168	+	0.251366i
$551$	2.95192			0.125756
$552$		0			0
$553$	−14.3303			−0.609388
$554$	−14.1192	−	16.1934i	−0.599866	−	0.687992i
$555$		0			0
$556$	7.94408	+	1.09232i	0.336904	+	0.0463246i
$557$			34.6170i			1.46677i	0.679813	+	0.733386i	$0.262061\pi$
$557$			34.6170i			1.46677i	−0.679813	+	0.733386i	$0.737939\pi$
$558$		0			0
$559$		−	1.80352i		−	0.0762809i
$560$	−13.2518	−	3.71450i	−0.559991	−	0.156966i
$561$		0			0
$562$	−22.8419	+	19.9161i	−0.963529	+	0.840108i
$563$	−30.1107			−1.26901			−0.634507	−	0.772917i	$-0.718797\pi$
$563$	−30.1107			−1.26901			−0.634507	+	0.772917i	$0.718797\pi$
$564$		0			0
$565$	−24.3790			−1.02563
$566$	−0.912855	+	0.795925i	−0.0383701	+	0.0334552i
$567$		0			0
$568$	23.1924	−	15.2093i	0.973132	−	0.638167i
$569$			14.3040i			0.599656i	0.953993	+	0.299828i	$0.0969293\pi$
$569$			14.3040i			0.599656i	−0.953993	+	0.299828i	$0.903071\pi$
$570$		0			0
$571$			27.2222i			1.13921i	0.821918	+	0.569607i	$0.192904\pi$
$571$			27.2222i			1.13921i	−0.821918	+	0.569607i	$0.807096\pi$
$572$	−0.0505456	+	0.367602i	−0.00211342	+	0.0153702i
$573$		0			0
$574$	6.09592	+	6.99147i	0.254439	+	0.291818i
$575$	−46.6407			−1.94505
$576$		0			0
$577$	−21.5696			−0.897956			−0.448978	−	0.893543i	$-0.648212\pi$
$577$	−21.5696			−0.897956			−0.448978	+	0.893543i	$0.648212\pi$
$578$	14.4288	+	16.5486i	0.600161	+	0.688331i
$579$		0			0
$580$	6.48597	−	47.1704i	0.269315	−	1.95865i
$581$			18.8701i			0.782865i
$582$		0			0
$583$			11.7725i			0.487569i
$584$	−33.3931	+	21.8987i	−1.38182	+	0.906177i
$585$		0			0
$586$	26.3285	−	22.9560i	1.08762	−	0.948305i
$587$	−22.8444			−0.942888			−0.471444	−	0.881896i	$-0.656267\pi$
$587$	−22.8444			−0.942888			−0.471444	+	0.881896i	$0.656267\pi$
$588$		0			0
$589$	−3.24404			−0.133668
$590$	−34.6935	+	30.2495i	−1.42831	+	1.24535i
$591$		0			0
$592$	3.35706	+	0.940987i	0.137974	+	0.0386743i
$593$			17.4178i			0.715265i	0.933862	+	0.357633i	$0.116416\pi$
$593$			17.4178i			0.715265i	−0.933862	+	0.357633i	$0.883584\pi$
$594$		0			0
$595$			4.17873i			0.171311i
$596$	4.55540	+	0.626372i	0.186597	+	0.0256572i
$597$		0			0
$598$	−1.45421	−	1.66784i	−0.0594669	−	0.0682031i
$599$	40.5099			1.65519			0.827596	−	0.561325i	$-0.189708\pi$
$599$	40.5099			1.65519			0.827596	+	0.561325i	$0.189708\pi$
$600$		0			0
$601$	30.5031			1.24425			0.622125	−	0.782918i	$-0.286270\pi$
$601$	30.5031			1.24425			0.622125	+	0.782918i	$0.286270\pi$
$602$	9.57912	+	10.9864i	0.390416	+	0.447772i
$603$		0			0
$604$	−38.9463	−	5.35515i	−1.58470	−	0.217898i
$605$			3.24506i			0.131930i
$606$		0			0
$607$		−	3.37637i		−	0.137043i	−0.997650	−	0.0685214i	$-0.978172\pi$
$607$		−	3.37637i		−	0.137043i	0.997650	−	0.0685214i	$-0.0218281\pi$
$608$	−2.05563	+	0.977282i	−0.0833669	+	0.0396340i
$609$		0			0
$610$	−16.0756	+	14.0165i	−0.650883	+	0.567510i
$611$	−0.769375			−0.0311256
$612$		0			0
$613$	−19.6548			−0.793849			−0.396924	−	0.917851i	$-0.629922\pi$
$613$	−19.6548			−0.793849			−0.396924	+	0.917851i	$0.629922\pi$
$614$	−13.0397	+	11.3694i	−0.526240	+	0.458833i
$615$		0			0
$616$	−1.64455	−	2.50776i	−0.0662609	−	0.101040i
$617$		−	14.8544i		−	0.598017i	−0.954251	−	0.299008i	$-0.903344\pi$
$617$		−	14.8544i		−	0.598017i	0.954251	−	0.299008i	$-0.0966558\pi$
$618$		0			0
$619$			12.1665i			0.489014i	0.969648	+	0.244507i	$0.0786260\pi$
$619$			12.1665i			0.489014i	−0.969648	+	0.244507i	$0.921374\pi$
$620$	−7.12782	+	51.8384i	−0.286260	+	2.08188i
$621$		0			0
$622$	−8.53297	−	9.78654i	−0.342141	−	0.392405i
$623$	−16.0573			−0.643323
$624$		0			0
$625$	−22.0667			−0.882669
$626$	−18.3841	−	21.0849i	−0.734775	−	0.842721i
$627$		0			0
$628$	5.61502	−	40.8363i	0.224064	−	1.62955i
$629$		−	1.05859i		−	0.0422087i
$630$		0			0
$631$			22.2468i			0.885630i	0.896613	+	0.442815i	$0.146020\pi$
$631$			22.2468i			0.885630i	−0.896613	+	0.442815i	$0.853980\pi$
$632$	20.9638	+	31.9675i	0.833896	+	1.27160i
$633$		0			0
$634$	−9.06315	+	7.90223i	−0.359944	+	0.313838i
$635$	12.4821			0.495337
$636$		0			0
$637$	−1.09014			−0.0431931
$638$	7.82016	−	6.81846i	0.309603	−	0.269945i
$639$		0			0
$640$	11.0999	+	34.9955i	0.438763	+	1.38332i
$641$			5.57524i			0.220209i	0.993920	+	0.110104i	$0.0351185\pi$
$641$			5.57524i			0.220209i	−0.993920	+	0.110104i	$0.964881\pi$
$642$		0			0
$643$		−	26.5625i		−	1.04752i	−0.851865	−	0.523762i	$-0.824528\pi$
$643$		−	26.5625i		−	1.04752i	0.851865	−	0.523762i	$-0.175472\pi$
$644$	17.7169	+	2.43609i	0.698145	+	0.0959955i
$645$		0			0
$646$	0.454178	+	0.520902i	0.0178694	+	0.0204946i
$647$	28.7081			1.12863			0.564316	−	0.825559i	$-0.309140\pi$
$647$	28.7081			1.12863			0.564316	+	0.825559i	$0.309140\pi$
$648$		0			0
$649$	−10.0298			−0.393706
$650$	0.953615	+	1.09371i	0.0374039	+	0.0428988i
$651$		0			0
$652$	−26.2732	−	3.61259i	−1.02894	−	0.141480i
$653$			4.97393i			0.194645i	0.995253	+	0.0973225i	$0.0310278\pi$
$653$			4.97393i			0.194645i	−0.995253	+	0.0973225i	$0.968972\pi$
$654$		0			0
$655$		−	35.4727i		−	1.38603i
$656$	6.67854	−	23.8263i	0.260753	−	0.930260i
$657$		0			0
$658$	4.68674	−	4.08641i	0.182708	−	0.159305i
$659$	−30.9216			−1.20454			−0.602268	−	0.798294i	$-0.705736\pi$
$659$	−30.9216			−1.20454			−0.602268	+	0.798294i	$0.705736\pi$
$660$		0			0
$661$	−34.9847			−1.36075			−0.680373	−	0.732866i	$-0.738182\pi$
$661$	−34.9847			−1.36075			−0.680373	+	0.732866i	$0.738182\pi$
$662$	−25.6348	+	22.3512i	−0.996327	+	0.868705i
$663$		0			0
$664$	42.0946	−	27.6051i	1.63359	−	1.07128i
$665$		−	1.38439i		−	0.0536844i
$666$		0			0
$667$			61.8719i			2.39569i
$668$	6.33449	−	46.0687i	0.245089	−	1.78245i
$669$		0			0
$670$	8.04643	+	9.22853i	0.310861	+	0.356529i
$671$	−4.64744			−0.179413
$672$		0			0
$673$	−28.8775			−1.11315			−0.556574	−	0.830798i	$-0.687884\pi$
$673$	−28.8775			−1.11315			−0.556574	+	0.830798i	$0.687884\pi$
$674$	−3.69067	−	4.23287i	−0.142159	−	0.163044i
$675$		0			0
$676$	3.53232	−	25.6894i	0.135858	−	0.988056i
$677$		−	27.9239i		−	1.07320i	−0.843836	−	0.536602i	$-0.819708\pi$
$677$		−	27.9239i		−	1.07320i	0.843836	−	0.536602i	$-0.180292\pi$
$678$		0			0
$679$		−	2.31665i		−	0.0889050i
$680$	9.32172	−	6.11305i	0.357472	−	0.234425i
$681$		0			0
$682$	−8.59404	+	7.49321i	−0.329083	+	0.286930i
$683$	−28.9339			−1.10712			−0.553562	−	0.832808i	$-0.686732\pi$
$683$	−28.9339			−1.10712			−0.553562	+	0.832808i	$0.686732\pi$
$684$		0			0
$685$	−4.41190			−0.168570
$686$	14.5520	−	12.6880i	0.555598	−	0.484431i
$687$		0			0
$688$	10.4946	−	37.4406i	0.400105	−	1.42741i
$689$			2.18417i			0.0832101i
$690$		0			0
$691$			37.6866i			1.43367i	0.697245	+	0.716833i	$0.254409\pi$
$691$			37.6866i			1.43367i	−0.697245	+	0.716833i	$0.745591\pi$
$692$	24.7046	+	3.39690i	0.939128	+	0.129131i
$693$		0			0
$694$	19.6882	+	22.5806i	0.747355	+	0.857149i
$695$	13.0108			0.493527
$696$		0			0
$697$	−7.51321			−0.284583
$698$	19.8154	+	22.7265i	0.750025	+	0.860212i
$699$		0			0
$700$	−11.6181	−	1.59750i	−0.439124	−	0.0603799i
$701$		−	18.7196i		−	0.707031i	−0.935429	−	0.353515i	$-0.884986\pi$
$701$		−	18.7196i		−	0.707031i	0.935429	−	0.353515i	$-0.115014\pi$
$702$		0			0
$703$			0.350705i			0.0132271i
$704$	−3.18838	+	7.33718i	−0.120166	+	0.276531i
$705$		0			0
$706$	14.2019	−	12.3828i	0.534496	−	0.466031i
$707$	3.23300			0.121590
$708$		0			0
$709$	40.3909			1.51691			0.758456	−	0.651725i	$-0.225954\pi$
$709$	40.3909			1.51691			0.758456	+	0.651725i	$0.225954\pi$
$710$	33.9181	−	29.5734i	1.27292	−	1.10987i
$711$		0			0
$712$	23.4902	+	35.8199i	0.880332	+	1.34241i
$713$		−	67.9947i		−	2.54642i
$714$		0			0
$715$			0.602057i			0.0225156i
$716$	−0.333055	+	2.42221i	−0.0124469	+	0.0905221i
$717$		0			0
$718$	30.1965	+	34.6327i	1.12693	+	1.29248i
$719$	13.1039			0.488693			0.244347	−	0.969688i	$-0.421427\pi$
$719$	13.1039			0.488693			0.244347	+	0.969688i	$0.421427\pi$
$720$		0			0
$721$	−4.24253			−0.158000
$722$	17.5081	+	20.0802i	0.651584	+	0.747308i
$723$		0			0
$724$	−2.27007	+	16.5095i	−0.0843666	+	0.613571i
$725$		−	40.5733i		−	1.50686i
$726$		0			0
$727$			6.43892i			0.238806i	0.992846	+	0.119403i	$0.0380981\pi$
$727$			6.43892i			0.238806i	−0.992846	+	0.119403i	$0.961902\pi$
$728$	−0.305115	−	0.465265i	−0.0113083	−	0.0172439i
$729$		0			0
$730$	−48.8362	+	42.5807i	−1.80751	+	1.57598i
$731$	−11.8062			−0.436670
$732$		0			0
$733$	−30.2045			−1.11563			−0.557814	−	0.829966i	$-0.688360\pi$
$733$	−30.2045			−1.11563			−0.557814	+	0.829966i	$0.688360\pi$
$734$	13.4864	−	11.7589i	0.497793	−	0.434029i
$735$		0			0
$736$	−20.4837	−	43.0859i	−0.755040	−	1.58817i
$737$			2.66796i			0.0982756i
$738$		0			0
$739$		−	49.5603i		−	1.82311i	−0.411183	−	0.911553i	$-0.634884\pi$
$739$		−	49.5603i		−	1.82311i	0.411183	−	0.911553i	$-0.365116\pi$
$740$	5.60413	+	0.770572i	0.206012	+	0.0283268i
$741$		0			0
$742$	−11.6008	−	13.3051i	−0.425880	−	0.488446i
$743$	20.1653			0.739792			0.369896	−	0.929073i	$-0.379393\pi$
$743$	20.1653			0.739792			0.369896	+	0.929073i	$0.379393\pi$
$744$		0			0
$745$	7.46081			0.273343
$746$	26.9058	+	30.8585i	0.985090	+	1.12981i
$747$		0			0
$748$	2.40640	+	0.330882i	0.0879867	+	0.0120983i
$749$			1.85276i			0.0676982i
$750$		0			0
$751$			4.30079i			0.156938i	0.996917	+	0.0784691i	$0.0250032\pi$
$751$			4.30079i			0.156938i	−0.996917	+	0.0784691i	$0.974997\pi$
$752$	−15.9720	−	4.47697i	−0.582439	−	0.163258i
$753$		0			0
$754$	1.45088	−	1.26503i	0.0528379	−	0.0460698i
$755$	−63.7861			−2.32141
$756$		0			0
$757$	28.5859			1.03897			0.519486	−	0.854479i	$-0.326124\pi$
$757$	28.5859			1.03897			0.519486	+	0.854479i	$0.326124\pi$
$758$	4.09329	−	3.56898i	0.148675	−	0.129631i
$759$		0			0
$760$	−3.08824	+	2.02522i	−0.112022	+	0.0734625i
$761$		−	23.6149i		−	0.856038i	−0.903770	−	0.428019i	$-0.859212\pi$
$761$		−	23.6149i		−	0.856038i	0.903770	−	0.428019i	$-0.140788\pi$
$762$		0			0
$763$		−	11.6871i		−	0.423100i
$764$	2.79359	−	20.3169i	0.101068	−	0.735038i
$765$		0			0
$766$	−24.1110	−	27.6532i	−0.871167	−	0.999150i
$767$	−1.86084			−0.0671911
$768$		0			0
$769$	−7.68353			−0.277075			−0.138538	−	0.990357i	$-0.544240\pi$
$769$	−7.68353			−0.277075			−0.138538	+	0.990357i	$0.544240\pi$
$770$	−3.19772	−	3.66750i	−0.115238	−	0.132168i
$771$		0			0
$772$	3.00465	−	21.8519i	0.108140	−	0.786466i
$773$		−	3.96538i		−	0.142625i	−0.997454	−	0.0713123i	$-0.977281\pi$
$773$		−	3.96538i		−	0.142625i	0.997454	−	0.0713123i	$-0.0227187\pi$
$774$		0			0
$775$			44.5884i			1.60166i
$776$	−5.16788	+	3.38903i	−0.185516	+	0.121659i
$777$		0			0
$778$	−17.3147	+	15.0968i	−0.620763	+	0.541248i
$779$	2.48909			0.0891808
$780$		0			0
$781$	9.80568			0.350875
$782$	−10.9180	+	9.51953i	−0.390428	+	0.340418i
$783$		0			0
$784$	−22.6311	−	6.34351i	−0.808252	−	0.226554i
$785$		−	66.8814i		−	2.38710i
$786$		0			0
$787$		−	18.0547i		−	0.643581i	−0.946811	−	0.321790i	$-0.895715\pi$
$787$		−	18.0547i		−	0.643581i	0.946811	−	0.321790i	$-0.104285\pi$
$788$	2.36151	+	0.324709i	0.0841252	+	0.0115673i
$789$		0			0
$790$	40.7628	+	46.7512i	1.45027	+	1.66333i
$791$	7.96545			0.283219
$792$		0			0
$793$	−0.862242			−0.0306191
$794$	−5.38733	−	6.17878i	−0.191189	−	0.219277i
$795$		0			0
$796$	18.7720	+	2.58116i	0.665354	+	0.0914868i
$797$			11.1711i			0.395700i	0.980232	+	0.197850i	$0.0633959\pi$
$797$			11.1711i			0.395700i	−0.980232	+	0.197850i	$0.936604\pi$
$798$		0			0
$799$			5.03649i			0.178178i
$800$	13.4325	+	28.2541i	0.474910	+	0.998935i
$801$		0			0
$802$	29.2911	−	25.5391i	1.03430	−	0.901818i
$803$	−14.1185			−0.498231
$804$		0			0
$805$	29.0167			1.02270
$806$	−1.59446	+	1.39022i	−0.0561623	+	0.0489684i
$807$		0			0
$808$	−4.72955	−	7.21203i	−0.166385	−	0.253718i
$809$			28.7742i			1.01165i	0.862637	+	0.505824i	$0.168811\pi$
$809$			28.7742i			1.01165i	−0.862637	+	0.505824i	$0.831189\pi$
$810$		0			0
$811$		−	12.0121i		−	0.421803i	−0.977507	−	0.210902i	$-0.932360\pi$
$811$		−	12.0121i		−	0.421803i	0.977507	−	0.210902i	$-0.0676400\pi$
$812$	−2.11919	+	15.4122i	−0.0743690	+	0.540862i
$813$		0			0
$814$	0.810074	+	0.929081i	0.0283931	+	0.0325643i
$815$	−43.0301			−1.50728
$816$		0			0
$817$	3.91135			0.136841
$818$	5.51159	+	6.32130i	0.192708	+	0.221019i
$819$		0			0
$820$	5.46904	−	39.7746i	0.190987	−	1.38899i
$821$			10.5039i			0.366590i	0.983058	+	0.183295i	$0.0586763\pi$
$821$			10.5039i			0.366590i	−0.983058	+	0.183295i	$0.941324\pi$
$822$		0			0
$823$		−	1.22919i		−	0.0428470i	−0.999770	−	0.0214235i	$-0.993180\pi$
$823$		−	1.22919i		−	0.0428470i	0.999770	−	0.0214235i	$-0.00681984\pi$
$824$	6.20639	+	9.46404i	0.216210	+	0.329695i
$825$		0			0
$826$	11.3355	−	9.88355i	0.394414	−	0.343893i
$827$	1.67808			0.0583525			0.0291763	−	0.999574i	$-0.490712\pi$
$827$	1.67808			0.0583525			0.0291763	+	0.999574i	$0.490712\pi$
$828$		0			0
$829$	30.1865			1.04842			0.524210	−	0.851589i	$-0.324361\pi$
$829$	30.1865			1.04842			0.524210	+	0.851589i	$0.324361\pi$
$830$	61.5618	−	53.6762i	2.13684	−	1.86313i
$831$		0			0
$832$	−0.591541	+	1.36127i	−0.0205080	+	0.0471936i
$833$			7.13631i			0.247259i
$834$		0			0
$835$		−	75.4511i		−	2.61109i
$836$	−0.797228	−	0.109620i	−0.0275727	−	0.00379127i
$837$		0			0
$838$	16.0929	+	18.4571i	0.555919	+	0.637589i
$839$	16.0148			0.552893			0.276446	−	0.961029i	$-0.410843\pi$
$839$	16.0148			0.552893			0.276446	+	0.961029i	$0.410843\pi$
$840$		0			0
$841$	−24.8232			−0.855971
$842$	−25.7544	−	29.5379i	−0.887554	−	1.01794i
$843$		0			0
$844$	17.7862	+	2.44562i	0.612226	+	0.0841816i
$845$		−	42.0740i		−	1.44739i
$846$		0			0
$847$		−	1.06027i		−	0.0364313i
$848$	−12.7096	+	45.3426i	−0.436449	+	1.55707i
$849$		0			0
$850$	7.15966	−	6.24256i	0.245574	−	0.214118i
$851$	−7.35075			−0.251980
$852$		0			0
$853$	6.74902			0.231082			0.115541	−	0.993303i	$-0.463140\pi$
$853$	6.74902			0.231082			0.115541	+	0.993303i	$0.463140\pi$
$854$	5.25245	−	4.57966i	0.179735	−	0.156713i
$855$		0			0
$856$	4.13304	−	2.71039i	0.141264	−	0.0926393i
$857$			18.2593i			0.623725i	0.950127	+	0.311862i	$0.100953\pi$
$857$			18.2593i			0.623725i	−0.950127	+	0.311862i	$0.899047\pi$
$858$		0			0
$859$			30.8970i			1.05419i	0.849806	+	0.527096i	$0.176719\pi$
$859$			30.8970i			1.05419i	−0.849806	+	0.527096i	$0.823281\pi$
$860$	8.59404	−	62.5017i	0.293054	−	2.13129i
$861$		0			0
$862$	−4.87563	−	5.59191i	−0.166065	−	0.190461i
$863$	−35.3480			−1.20326			−0.601630	−	0.798775i	$-0.705482\pi$
$863$	−35.3480			−1.20326			−0.601630	+	0.798775i	$0.705482\pi$
$864$		0			0
$865$	40.4611			1.37572
$866$	30.2102	+	34.6484i	1.02659	+	1.17740i
$867$		0			0
$868$	2.32890	−	16.9374i	0.0790481	−	0.574892i
$869$			13.5157i			0.458490i
$870$		0			0
$871$			0.494988i			0.0167720i
$872$	−26.0710	+	17.0970i	−0.882875	+	0.578977i
$873$		0			0
$874$	3.61709	−	3.15377i	0.122350	−	0.106678i
$875$	−1.82489			−0.0616927
$876$		0			0
$877$	−8.27638			−0.279474			−0.139737	−	0.990189i	$-0.544626\pi$
$877$	−8.27638			−0.279474			−0.139737	+	0.990189i	$0.544626\pi$
$878$	1.63130	−	1.42234i	0.0550537	−	0.0480018i
$879$		0			0
$880$	−3.50335	+	12.4985i	−0.118098	+	0.421325i
$881$		−	49.4332i		−	1.66545i	−0.553688	−	0.832724i	$-0.686780\pi$
$881$		−	49.4332i		−	1.66545i	0.553688	−	0.832724i	$-0.313220\pi$
$882$		0			0
$883$			29.4375i			0.990651i	0.868708	+	0.495325i	$0.164951\pi$
$883$			29.4375i			0.990651i	−0.868708	+	0.495325i	$0.835049\pi$
$884$	0.446461	+	0.0613887i	0.0150161	+	0.00206473i
$885$		0			0
$886$	−8.42213	−	9.65943i	−0.282947	−	0.324515i
$887$	−37.0377			−1.24360			−0.621802	−	0.783175i	$-0.713599\pi$
$887$	−37.0377			−1.24360			−0.621802	+	0.783175i	$0.713599\pi$
$888$		0			0
$889$	−4.07833			−0.136783
$890$	45.6751	+	52.3853i	1.53103	+	1.75596i
$891$		0			0
$892$	42.0575	+	5.78294i	1.40819	+	0.193627i
$893$		−	1.66856i		−	0.0558363i
$894$		0			0
$895$			3.96707i			0.132605i
$896$	−3.62672	−	11.4342i	−0.121160	−	0.381990i
$897$		0			0
$898$	−13.1718	+	11.4846i	−0.439550	+	0.383247i
$899$	59.1495			1.97275
$900$		0			0
$901$	14.2980			0.476336
$902$	6.59404	−	5.74940i	0.219557	−	0.191434i
$903$		0			0
$904$	−11.6526	−	17.7690i	−0.387561	−	0.590987i
$905$			27.0392i			0.898813i
$906$		0			0
$907$			25.0154i			0.830623i	0.909679	+	0.415311i	$0.136327\pi$
$907$			25.0154i			0.830623i	−0.909679	+	0.415311i	$0.863673\pi$
$908$	−3.99702	+	29.0690i	−0.132646	+	0.964689i
$909$		0			0
$910$	−0.593275	−	0.680433i	−0.0196669	−	0.0225561i
$911$	34.0603			1.12847			0.564233	−	0.825615i	$-0.309172\pi$
$911$	34.0603			1.12847			0.564233	+	0.825615i	$0.309172\pi$
$912$		0			0
$913$	17.7975			0.589010
$914$	−32.9276	−	37.7650i	−1.08915	−	1.24916i
$915$		0			0
$916$	−5.38809	+	39.1859i	−0.178027	+	1.29474i
$917$			11.5901i			0.382740i
$918$		0			0
$919$		−	27.2051i		−	0.897413i	−0.893679	−	0.448707i	$-0.851885\pi$
$919$		−	27.2051i		−	0.897413i	0.893679	−	0.448707i	$-0.148115\pi$
$920$	−42.4485	−	64.7291i	−1.39948	−	2.13406i
$921$		0			0
$922$	38.9959	−	34.0008i	1.28426	−	1.11976i
$923$	1.81925			0.0598814
$924$		0			0
$925$	4.82035			0.158492
$926$	−32.3694	+	28.2232i	−1.06373	+	0.927471i
$927$		0			0
$928$	37.4810	−	17.8191i	1.23037	−	0.584940i
$929$			12.7577i			0.418566i	0.977855	+	0.209283i	$0.0671130\pi$
$929$			12.7577i			0.418566i	−0.977855	+	0.209283i	$0.932887\pi$
$930$		0			0
$931$		−	2.36422i		−	0.0774843i
$932$	−9.28704	−	1.27698i	−0.304207	−	0.0418287i
$933$		0			0
$934$	−11.0512	−	12.6747i	−0.361606	−	0.414729i
$935$	3.94119			0.128891
$936$		0			0
$937$	−15.9382			−0.520679			−0.260340	−	0.965517i	$-0.583835\pi$
$937$	−15.9382			−0.520679			−0.260340	+	0.965517i	$0.583835\pi$
$938$	−2.62905	−	3.01528i	−0.0858414	−	0.0984523i
$939$		0			0
$940$	−26.6629	−	3.66618i	−0.869649	−	0.119578i
$941$		−	48.2168i		−	1.57182i	−0.618338	−	0.785912i	$-0.712194\pi$
$941$		−	48.2168i		−	1.57182i	0.618338	−	0.785912i	$-0.287806\pi$
$942$		0			0
$943$			52.1710i			1.69892i
$944$	−38.6305	−	10.8282i	−1.25732	−	0.352427i
$945$		0			0
$946$	10.3619	−	9.03459i	0.336893	−	0.293740i
$947$	−18.0381			−0.586161			−0.293081	−	0.956088i	$-0.594680\pi$
$947$	−18.0381			−0.586161			−0.293081	+	0.956088i	$0.594680\pi$
$948$		0			0
$949$	−2.61941			−0.0850297
$950$	−2.37196	+	2.06813i	−0.0769564	+	0.0670989i
$951$		0			0
$952$	−3.04572	+	1.99734i	−0.0987125	+	0.0647343i
$953$			18.0668i			0.585242i	0.956229	+	0.292621i	$0.0945274\pi$
$953$			18.0668i			0.585242i	−0.956229	+	0.292621i	$0.905473\pi$
$954$		0			0
$955$		−	33.2748i		−	1.07675i
$956$	3.99881	−	29.0821i	0.129331	−	0.940582i
$957$		0			0
$958$	18.2844	+	20.9706i	0.590743	+	0.677529i
$959$	1.44152			0.0465490
$960$		0			0
$961$	−34.0029			−1.09687
$962$	0.150293	+	0.172373i	0.00484565	+	0.00555752i
$963$		0			0
$964$	0.227843	−	1.65703i	0.00733834	−	0.0533694i
$965$		−	35.7889i		−	1.15209i
$966$		0			0
$967$			13.9092i			0.447289i	0.974671	+	0.223644i	$0.0717954\pi$
$967$			13.9092i			0.447289i	−0.974671	+	0.223644i	$0.928205\pi$
$968$	−2.36520	+	1.55107i	−0.0760205	+	0.0498532i
$969$		0			0
$970$	−7.55783	+	6.58974i	−0.242667	+	0.211584i
$971$	−12.4711			−0.400217			−0.200108	−	0.979774i	$-0.564129\pi$
$971$	−12.4711			−0.400217			−0.200108	+	0.979774i	$0.564129\pi$
$972$		0			0
$973$	−4.25106			−0.136283
$974$	21.9166	−	19.1093i	0.702254	−	0.612301i
$975$		0			0
$976$	−17.8999	−	5.01736i	−0.572961	−	0.160602i
$977$			32.2725i			1.03249i	0.856441	+	0.516245i	$0.172671\pi$
$977$			32.2725i			1.03249i	−0.856441	+	0.516245i	$0.827329\pi$
$978$		0			0
$979$			15.1445i			0.484021i
$980$	−37.7793	−	5.19469i	−1.20682	−	0.165938i
$981$		0			0
$982$	10.4670	+	12.0047i	0.334014	+	0.383084i
$983$	15.3727			0.490314			0.245157	−	0.969483i	$-0.421161\pi$
$983$	15.3727			0.490314			0.245157	+	0.969483i	$0.421161\pi$
$984$		0			0
$985$	3.86766			0.123234
$986$	−8.28117	−	9.49775i	−0.263726	−	0.302470i
$987$		0			0
$988$	−0.147910	−	0.0203378i	−0.00470564	−	0.000647030i
$989$			81.9814i			2.60686i
$990$		0			0
$991$		−	1.06000i		−	0.0336719i	−0.999858	−	0.0168359i	$-0.994641\pi$
$991$		−	1.06000i		−	0.0336719i	0.999858	−	0.0168359i	$-0.00535930\pi$
$992$	−41.1900	+	19.5824i	−1.30779	+	0.621743i
$993$		0			0
$994$	−11.0822	+	9.66265i	−0.351506	+	0.306481i
$995$	30.7446			0.974670
$996$		0			0
$997$	−13.8296			−0.437988			−0.218994	−	0.975726i	$-0.570277\pi$
$997$	−13.8296			−0.437988			−0.218994	+	0.975726i	$0.570277\pi$
$998$	19.6403	−	17.1246i	0.621704	−	0.542068i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.2.c.a.287.8	yes	10
3.2	odd	2		396.2.c.b.287.3	yes	10
4.3	odd	2		396.2.c.b.287.4	yes	10
8.3	odd	2		6336.2.d.g.3455.2		10
8.5	even	2		6336.2.d.h.3455.2		10
12.11	even	2	inner	396.2.c.a.287.7	✓	10
24.5	odd	2		6336.2.d.g.3455.9		10
24.11	even	2		6336.2.d.h.3455.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
396.2.c.a.287.7	✓	10	12.11	even	2	inner
396.2.c.a.287.8	yes	10	1.1	even	1	trivial
396.2.c.b.287.3	yes	10	3.2	odd	2
396.2.c.b.287.4	yes	10	4.3	odd	2
6336.2.d.g.3455.2		10	8.3	odd	2
6336.2.d.g.3455.9		10	24.5	odd	2
6336.2.d.h.3455.2		10	8.5	even	2
6336.2.d.h.3455.9		10	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	396.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.929398 + 1.06594i) q^{2} +(-0.272438 + 1.98136i) q^{4} +3.24506i q^{5} -1.06027i q^{7} +(-2.36520 + 1.55107i) q^{8} +(-3.45902 + 3.01595i) q^{10} -1.00000 q^{11} -0.185530 q^{13} +(1.13018 - 0.985414i) q^{14} +(-3.85155 - 1.07960i) q^{16} +1.21452i q^{17} -0.402364i q^{19} +(-6.42962 - 0.884078i) q^{20} +(-0.929398 - 1.06594i) q^{22} +8.43352 q^{23} -5.53039 q^{25} +(-0.172432 - 0.197764i) q^{26} +(2.10078 + 0.288859i) q^{28} +7.33643i q^{29} -8.06243i q^{31} +(-2.42885 - 5.10888i) q^{32} +(-1.29460 + 1.12877i) q^{34} +3.44064 q^{35} -0.871611 q^{37} +(0.428895 - 0.373957i) q^{38} +(-5.03330 - 7.67522i) q^{40} +6.18615i q^{41} +9.72091i q^{43} +(0.272438 - 1.98136i) q^{44} +(7.83809 + 8.98959i) q^{46} +4.14689 q^{47} +5.87583 q^{49} +(-5.13994 - 5.89504i) q^{50} +(0.0505456 - 0.367602i) q^{52} -11.7725i q^{53} -3.24506i q^{55} +(1.64455 + 2.50776i) q^{56} +(-7.82016 + 6.81846i) q^{58} +10.0298 q^{59} +4.64744 q^{61} +(8.59404 - 7.49321i) q^{62} +(3.18838 - 7.33718i) q^{64} -0.602057i q^{65} -2.66796i q^{67} +(-2.40640 - 0.330882i) q^{68} +(3.19772 + 3.66750i) q^{70} -9.80568 q^{71} +14.1185 q^{73} +(-0.810074 - 0.929081i) q^{74} +(0.797228 + 0.109620i) q^{76} +1.06027i q^{77} -13.5157i q^{79} +(3.50335 - 12.4985i) q^{80} +(-6.59404 + 5.74940i) q^{82} -17.7975 q^{83} -3.94119 q^{85} +(-10.3619 + 9.03459i) q^{86} +(2.36520 - 1.55107i) q^{88} -15.1445i q^{89} +0.196713i q^{91} +(-2.29761 + 16.7098i) q^{92} +(3.85412 + 4.42032i) q^{94} +1.30570 q^{95} +2.18496 q^{97} +(5.46098 + 6.26325i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4} - 12 q^{8} + 4 q^{10} - 10 q^{11} + 8 q^{13} + 8 q^{14} - 4 q^{16} - 24 q^{20} - 8 q^{23} - 10 q^{25} + 16 q^{26} + 16 q^{28} + 8 q^{34} + 16 q^{35} - 4 q^{37} + 32 q^{38} - 4 q^{44} + 20 q^{46}+ \cdots + 60 q^{98}+O(q^{100}) \) 10 * q + 4 * q^4 - 12 * q^8 + 4 * q^10 - 10 * q^11 + 8 * q^13 + 8 * q^14 - 4 * q^16 - 24 * q^20 - 8 * q^23 - 10 * q^25 + 16 * q^26 + 16 * q^28 + 8 * q^34 + 16 * q^35 - 4 * q^37 + 32 * q^38 - 4 * q^44 + 20 * q^46 - 34 * q^49 + 12 * q^50 - 20 * q^52 - 32 * q^56 - 28 * q^58 + 40 * q^59 + 20 * q^61 + 28 * q^62 - 8 * q^64 - 20 * q^68 - 36 * q^70 - 16 * q^71 + 24 * q^73 + 28 * q^74 - 12 * q^76 - 32 * q^80 - 8 * q^82 + 8 * q^83 - 36 * q^85 - 24 * q^86 + 12 * q^88 - 24 * q^92 - 20 * q^94 - 96 * q^95 + 24 * q^97 + 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more