LMFDB - Embedded newform 912.2.bn.o.449.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(65,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("912.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bn (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - x^{15} - 6 x^{14} + 5 x^{13} + 21 x^{12} - 4 x^{11} - 94 x^{10} - 6 x^{9} + 364 x^{8} + \cdots + 6561 $ x^16 - x^15 - 6x^14 + 5x^13 + 21x^12 - 4x^11 - 94x^10 - 6x^9 + 364x^8 - 18x^7 - 846x^6 - 108x^5 + 1701x^4 + 1215x^3 - 4374x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			449.5
Root			$0.956703 - 1.44386i$ of defining polynomial
Character	$\chi$	$=$	912.449
Dual form			912.2.bn.o.65.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.956703 + 1.44386i) q^{3} +(-1.67415 + 0.966572i) q^{5} +1.30064 q^{7} +(-1.16944 + 2.76268i) q^{9} +O(q^{10})$	\(q+(0.956703 + 1.44386i) q^{3} +(-1.67415 + 0.966572i) q^{5} +1.30064 q^{7} +(-1.16944 + 2.76268i) q^{9} +0.793801i q^{11} +(5.90939 + 3.41179i) q^{13} +(-2.99726 - 1.49251i) q^{15} +(-3.61147 + 2.08509i) q^{17} +(-0.402708 - 4.34026i) q^{19} +(1.24433 + 1.87794i) q^{21} +(-3.32751 - 1.92114i) q^{23} +(-0.631475 + 1.09375i) q^{25} +(-5.10772 + 0.954566i) q^{27} +(-0.449563 + 0.778667i) q^{29} +5.18115i q^{31} +(-1.14613 + 0.759432i) q^{33} +(-2.17747 + 1.25716i) q^{35} +1.51885i q^{37} +(0.727402 + 11.7964i) q^{39} +(4.52140 + 7.83130i) q^{41} +(-3.92424 - 6.79699i) q^{43} +(-0.712514 - 5.75550i) q^{45} +(6.48235 + 3.74258i) q^{47} -5.30833 q^{49} +(-6.46567 - 3.21964i) q^{51} +(-4.22330 + 7.31497i) q^{53} +(-0.767266 - 1.32894i) q^{55} +(5.88143 - 4.73379i) q^{57} +(-4.84305 - 8.38842i) q^{59} +(1.28870 - 2.23210i) q^{61} +(-1.52102 + 3.59326i) q^{63} -13.1910 q^{65} +(11.5355 + 6.66003i) q^{67} +(-0.409592 - 6.64240i) q^{69} +(4.99871 + 8.65802i) q^{71} +(-3.83888 - 6.64913i) q^{73} +(-2.18335 + 0.134632i) q^{75} +1.03245i q^{77} +(1.00467 - 0.580044i) q^{79} +(-6.26483 - 6.46157i) q^{81} -12.7552i q^{83} +(4.03077 - 6.98150i) q^{85} +(-1.55438 + 0.0958481i) q^{87} +(1.30989 - 2.26880i) q^{89} +(7.68599 + 4.43751i) q^{91} +(-7.48084 + 4.95683i) q^{93} +(4.86937 + 6.87700i) q^{95} +(-2.72744 + 1.57469i) q^{97} +(-2.19302 - 0.928302i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{3} - 3 q^{5} + 13 q^{9}+O(q^{10}) $ 16 * q + q^3 - 3 * q^5 + 13 * q^9	$ 16 q + q^{3} - 3 q^{5} + 13 q^{9} - 3 q^{13} - 15 q^{15} + 3 q^{17} - 11 q^{19} - 6 q^{21} - 3 q^{23} + 11 q^{25} + 4 q^{27} - 5 q^{29} + q^{33} + 24 q^{35} + 9 q^{39} - 6 q^{41} - 13 q^{43} + 33 q^{45} + 27 q^{47} + 8 q^{49} - 15 q^{51} + 7 q^{53} + 12 q^{55} + 23 q^{57} - 10 q^{59} - q^{61} + 8 q^{63} + 30 q^{65} + 24 q^{67} + 41 q^{69} + 27 q^{71} + 2 q^{73} + 21 q^{75} + 21 q^{79} - 7 q^{81} - 5 q^{85} + 23 q^{87} - 25 q^{89} + 78 q^{91} - 56 q^{93} + 13 q^{95} - 60 q^{97} + 35 q^{99}+O(q^{100}) $ 16 * q + q^3 - 3 * q^5 + 13 * q^9 - 3 * q^13 - 15 * q^15 + 3 * q^17 - 11 * q^19 - 6 * q^21 - 3 * q^23 + 11 * q^25 + 4 * q^27 - 5 * q^29 + q^33 + 24 * q^35 + 9 * q^39 - 6 * q^41 - 13 * q^43 + 33 * q^45 + 27 * q^47 + 8 * q^49 - 15 * q^51 + 7 * q^53 + 12 * q^55 + 23 * q^57 - 10 * q^59 - q^61 + 8 * q^63 + 30 * q^65 + 24 * q^67 + 41 * q^69 + 27 * q^71 + 2 * q^73 + 21 * q^75 + 21 * q^79 - 7 * q^81 - 5 * q^85 + 23 * q^87 - 25 * q^89 + 78 * q^91 - 56 * q^93 + 13 * q^95 - 60 * q^97 + 35 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

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			0
$2$		0			0
$3$	0.956703	+	1.44386i	0.552353	+	0.833610i
$3$	0.956703	+	1.44386i	0.552353	+	0.833610i
$4$		0			0
$5$	−1.67415	+	0.966572i	−0.748704	+	0.432264i	−0.825225	−	0.564804i	$-0.808952\pi$
$5$	−1.67415	+	0.966572i	−0.748704	+	0.432264i	0.0765216	+	0.997068i	$0.475619\pi$
$6$		0			0
$7$	1.30064			0.491596			0.245798	−	0.969321i	$-0.420950\pi$
$7$	1.30064			0.491596			0.245798	+	0.969321i	$0.420950\pi$
$8$		0			0
$9$	−1.16944	+	2.76268i	−0.389813	+	0.920894i
$10$		0			0
$11$			0.793801i			0.239340i	0.992814	+	0.119670i	$0.0381837\pi$
$11$			0.793801i			0.239340i	−0.992814	+	0.119670i	$0.961816\pi$
$12$		0			0
$13$	5.90939	+	3.41179i	1.63897	+	0.946259i	0.981189	+	0.193050i	$0.0618379\pi$
$13$	5.90939	+	3.41179i	1.63897	+	0.946259i	0.657781	+	0.753210i	$0.271495\pi$
$14$		0			0
$15$	−2.99726	−	1.49251i	−0.773889	−	0.385365i
$16$		0			0
$17$	−3.61147	+	2.08509i	−0.875911	+	0.505708i	−0.869308	−	0.494271i	$-0.835435\pi$
$17$	−3.61147	+	2.08509i	−0.875911	+	0.505708i	−0.00660316	+	0.999978i	$0.502102\pi$
$18$		0			0
$19$	−0.402708	−	4.34026i	−0.0923876	−	0.995723i
$19$	−0.402708	−	4.34026i	−0.0923876	−	0.995723i
$20$		0			0
$21$	1.24433	+	1.87794i	0.271534	+	0.409800i
$22$		0			0
$23$	−3.32751	−	1.92114i	−0.693834	−	0.400585i	0.111213	−	0.993797i	$-0.464526\pi$
$23$	−3.32751	−	1.92114i	−0.693834	−	0.400585i	−0.805047	+	0.593211i	$0.797860\pi$
$24$		0			0
$25$	−0.631475	+	1.09375i	−0.126295	+	0.218750i
$26$		0			0
$27$	−5.10772	+	0.954566i	−0.982981	+	0.183706i
$28$		0			0
$29$	−0.449563	+	0.778667i	−0.0834818	+	0.144595i	−0.904743	−	0.425957i	$-0.859937\pi$
$29$	−0.449563	+	0.778667i	−0.0834818	+	0.144595i	0.821261	+	0.570552i	$0.193271\pi$
$30$		0			0
$31$			5.18115i			0.930563i	0.885163	+	0.465281i	$0.154047\pi$
$31$			5.18115i			0.930563i	−0.885163	+	0.465281i	$0.845953\pi$
$32$		0			0
$33$	−1.14613	+	0.759432i	−0.199516	+	0.132200i
$34$		0			0
$35$	−2.17747	+	1.25716i	−0.368060	+	0.212499i
$36$		0			0
$37$			1.51885i			0.249697i	0.992176	+	0.124849i	$0.0398445\pi$
$37$			1.51885i			0.249697i	−0.992176	+	0.124849i	$0.960156\pi$
$38$		0			0
$39$	0.727402	+	11.7964i	0.116478	+	1.88893i
$40$		0			0
$41$	4.52140	+	7.83130i	0.706124	+	1.22304i	0.966284	+	0.257477i	$0.0828913\pi$
$41$	4.52140	+	7.83130i	0.706124	+	1.22304i	−0.260160	+	0.965565i	$0.583775\pi$
$42$		0			0
$43$	−3.92424	−	6.79699i	−0.598442	−	1.03653i	−0.993051	−	0.117682i	$-0.962454\pi$
$43$	−3.92424	−	6.79699i	−0.598442	−	1.03653i	0.394610	−	0.918849i	$-0.370880\pi$
$44$		0			0
$45$	−0.712514	−	5.75550i	−0.106215	−	0.857979i
$46$		0			0
$47$	6.48235	+	3.74258i	0.945547	+	0.545912i	0.891695	−	0.452637i	$-0.149517\pi$
$47$	6.48235	+	3.74258i	0.945547	+	0.545912i	0.0538524	+	0.998549i	$0.482850\pi$
$48$		0			0
$49$	−5.30833			−0.758333
$50$		0			0
$51$	−6.46567	−	3.21964i	−0.905375	−	0.450840i
$52$		0			0
$53$	−4.22330	+	7.31497i	−0.580115	+	1.00479i	0.415351	+	0.909661i	$0.363659\pi$
$53$	−4.22330	+	7.31497i	−0.580115	+	1.00479i	−0.995465	+	0.0951266i	$0.969674\pi$
$54$		0			0
$55$	−0.767266	−	1.32894i	−0.103458	−	0.179195i
$56$		0			0
$57$	5.88143	−	4.73379i	0.779015	−	0.627006i
$58$		0			0
$59$	−4.84305	−	8.38842i	−0.630512	−	1.09208i	−0.987447	−	0.157950i	$-0.949512\pi$
$59$	−4.84305	−	8.38842i	−0.630512	−	1.09208i	0.356935	−	0.934129i	$-0.383822\pi$
$60$		0			0
$61$	1.28870	−	2.23210i	0.165002	−	0.285791i	−0.771654	−	0.636042i	$-0.780570\pi$
$61$	1.28870	−	2.23210i	0.165002	−	0.285791i	0.936656	+	0.350251i	$0.113904\pi$
$62$		0			0
$63$	−1.52102	+	3.59326i	−0.191630	+	0.452708i
$64$		0			0
$65$	−13.1910			−1.63614
$66$		0			0
$67$	11.5355	+	6.66003i	1.40929	+	0.813652i	0.995320	−	0.0966390i	$-0.0308092\pi$
$67$	11.5355	+	6.66003i	1.40929	+	0.813652i	0.413968	+	0.910291i	$0.364143\pi$
$68$		0			0
$69$	−0.409592	−	6.64240i	−0.0493091	−	0.799651i
$70$		0			0
$71$	4.99871	+	8.65802i	0.593238	+	1.02752i	0.993793	+	0.111245i	$0.0354839\pi$
$71$	4.99871	+	8.65802i	0.593238	+	1.02752i	−0.400555	+	0.916273i	$0.631183\pi$
$72$		0			0
$73$	−3.83888	−	6.64913i	−0.449307	−	0.778222i	0.549034	−	0.835800i	$-0.314996\pi$
$73$	−3.83888	−	6.64913i	−0.449307	−	0.778222i	−0.998341	+	0.0575779i	$0.981662\pi$
$74$		0			0
$75$	−2.18335	+	0.134632i	−0.252111	+	0.0155460i
$76$		0			0
$77$			1.03245i			0.117659i
$78$		0			0
$79$	1.00467	−	0.580044i	0.113034	−	0.0652600i	−0.442417	−	0.896809i	$-0.645879\pi$
$79$	1.00467	−	0.580044i	0.113034	−	0.0652600i	0.555451	+	0.831549i	$0.312546\pi$
$80$		0			0
$81$	−6.26483	−	6.46157i	−0.696092	−	0.717953i
$82$		0			0
$83$		−	12.7552i		−	1.40007i	−0.714110	−	0.700033i	$-0.753168\pi$
$83$		−	12.7552i		−	1.40007i	0.714110	−	0.700033i	$-0.246832\pi$
$84$		0			0
$85$	4.03077	−	6.98150i	0.437199	−	0.757250i
$86$		0			0
$87$	−1.55438	+	0.0958481i	−0.166647	+	0.0102760i
$88$		0			0
$89$	1.30989	−	2.26880i	0.138848	−	0.240492i	−0.788213	−	0.615403i	$-0.788993\pi$
$89$	1.30989	−	2.26880i	0.138848	−	0.240492i	0.927061	+	0.374911i	$0.122327\pi$
$90$		0			0
$91$	7.68599	+	4.43751i	0.805711	+	0.465177i
$92$		0			0
$93$	−7.48084	+	4.95683i	−0.775727	+	0.513999i
$94$		0			0
$95$	4.86937	+	6.87700i	0.499587	+	0.705566i
$96$		0			0
$97$	−2.72744	+	1.57469i	−0.276930	+	0.159885i	−0.632033	−	0.774942i	$-0.717779\pi$
$97$	−2.72744	+	1.57469i	−0.276930	+	0.159885i	0.355103	+	0.934827i	$0.384446\pi$
$98$		0			0
$99$	−2.19302	−	0.928302i	−0.220407	−	0.0932978i
$100$		0			0
$101$	8.52866	+	4.92402i	0.848633	+	0.489959i	0.860189	−	0.509975i	$-0.170345\pi$
$101$	8.52866	+	4.92402i	0.848633	+	0.489959i	−0.0115562	+	0.999933i	$0.503679\pi$
$102$		0			0
$103$		−	3.63796i		−	0.358458i	−0.983807	−	0.179229i	$-0.942640\pi$
$103$		−	3.63796i		−	0.358458i	0.983807	−	0.179229i	$-0.0573604\pi$
$104$		0			0
$105$	−3.89836	−	1.94122i	−0.380441	−	0.189444i
$106$		0			0
$107$	0.00580472			0.000561163			0.000280582	−	1.00000i	$-0.499911\pi$
$107$	0.00580472			0.000561163			0.000280582		1.00000i	$0.499911\pi$
$108$		0			0
$109$	11.0505	−	6.38000i	1.05844	−	0.611093i	0.133443	−	0.991056i	$-0.457397\pi$
$109$	11.0505	−	6.38000i	1.05844	−	0.611093i	0.925002	+	0.379963i	$0.124063\pi$
$110$		0			0
$111$	−2.19300	+	1.45309i	−0.208150	+	0.137921i
$112$		0			0
$113$	−0.492052			−0.0462884			−0.0231442	−	0.999732i	$-0.507368\pi$
$113$	−0.492052			−0.0462884			−0.0231442	+	0.999732i	$0.507368\pi$
$114$		0			0
$115$	7.42768			0.692635
$116$		0			0
$117$	−16.3363	+	12.3359i	−1.51030	+	1.14045i
$118$		0			0
$119$	−4.69723	+	2.71195i	−0.430594	+	0.248604i
$120$		0			0
$121$	10.3699			0.942716
$122$		0			0
$123$	−6.98162	+	14.0205i	−0.629512	+	1.26418i
$124$		0			0
$125$		−	12.1072i		−	1.08290i
$126$		0			0
$127$	11.1015	+	6.40947i	0.985101	+	0.568748i	0.903806	−	0.427942i	$-0.140761\pi$
$127$	11.1015	+	6.40947i	0.985101	+	0.568748i	0.0812945	+	0.996690i	$0.474095\pi$
$128$		0			0
$129$	6.05954	−	12.1687i	0.533512	−	1.07140i
$130$		0			0
$131$	8.84734	−	5.10801i	0.772996	−	0.446289i	−0.0609466	−	0.998141i	$-0.519412\pi$
$131$	8.84734	−	5.10801i	0.772996	−	0.446289i	0.833942	+	0.551852i	$0.186079\pi$
$132$		0			0
$133$	−0.523779	−	5.64511i	−0.0454174	−	0.489493i
$134$		0			0
$135$	7.62844	−	6.53507i	0.656552	−	0.562449i
$136$		0			0
$137$	5.48481	+	3.16666i	0.468599	+	0.270546i	0.715653	−	0.698456i	$-0.246129\pi$
$137$	5.48481	+	3.16666i	0.468599	+	0.270546i	−0.247054	+	0.969002i	$0.579462\pi$
$138$		0			0
$139$	−6.96498	+	12.0637i	−0.590762	+	1.02323i	0.403368	+	0.915038i	$0.367839\pi$
$139$	−6.96498	+	12.0637i	−0.590762	+	1.02323i	−0.994130	+	0.108192i	$0.965494\pi$
$140$		0			0
$141$	0.797929	+	12.9401i	0.0671977	+	1.08975i
$142$		0			0
$143$	−2.70828	+	4.69088i	−0.226478	+	0.392271i
$144$		0			0
$145$		−	1.73814i		−	0.144345i
$146$		0			0
$147$	−5.07850	−	7.66447i	−0.418868	−	0.632155i
$148$		0			0
$149$	16.6153	−	9.59285i	1.36118	−	0.785877i	0.371398	−	0.928474i	$-0.378879\pi$
$149$	16.6153	−	9.59285i	1.36118	−	0.785877i	0.989781	+	0.142597i	$0.0455452\pi$
$150$		0			0
$151$		−	6.07694i		−	0.494534i	−0.968947	−	0.247267i	$-0.920467\pi$
$151$		−	6.07694i		−	0.494534i	0.968947	−	0.247267i	$-0.0795325\pi$
$152$		0			0
$153$	−1.53703	−	12.4157i	−0.124262	−	1.00375i
$154$		0			0
$155$	−5.00796	−	8.67404i	−0.402249	−	0.696716i
$156$		0			0
$157$	−0.368262	−	0.637848i	−0.0293905	−	0.0509058i	0.850956	−	0.525237i	$-0.176023\pi$
$157$	−0.368262	−	0.637848i	−0.0293905	−	0.0509058i	−0.880347	+	0.474331i	$0.842690\pi$
$158$		0			0
$159$	−14.6022	+	0.900419i	−1.15803	+	0.0714078i
$160$		0			0
$161$	−4.32790	−	2.49871i	−0.341086	−	0.196926i
$162$		0			0
$163$	−0.849743			−0.0665570			−0.0332785	−	0.999446i	$-0.510595\pi$
$163$	−0.849743			−0.0665570			−0.0332785	+	0.999446i	$0.510595\pi$
$164$		0			0
$165$	1.18476	−	2.37923i	0.0922333	−	0.185223i
$166$		0			0
$167$	10.1917	−	17.6525i	0.788656	−	1.36599i	−0.138134	−	0.990414i	$-0.544111\pi$
$167$	10.1917	−	17.6525i	0.788656	−	1.36599i	0.926790	−	0.375579i	$-0.122556\pi$
$168$		0			0
$169$	16.7806	+	29.0648i	1.29081	+	2.23576i
$170$		0			0
$171$	12.4617	+	3.96311i	0.952969	+	0.303066i
$172$		0			0
$173$	7.51229	+	13.0117i	0.571149	+	0.989259i	0.996448	+	0.0842065i	$0.0268356\pi$
$173$	7.51229	+	13.0117i	0.571149	+	0.989259i	−0.425299	+	0.905053i	$0.639831\pi$
$174$		0			0
$175$	−0.821323	+	1.42257i	−0.0620862	+	0.107536i
$176$		0			0
$177$	7.47830	−	15.0179i	0.562103	−	1.12881i
$178$		0			0
$179$	2.49961			0.186829			0.0934147	−	0.995627i	$-0.470222\pi$
$179$	2.49961			0.186829			0.0934147	+	0.995627i	$0.470222\pi$
$180$		0			0
$181$	4.07510	+	2.35276i	0.302899	+	0.174879i	0.643745	−	0.765240i	$-0.277380\pi$
$181$	4.07510	+	2.35276i	0.302899	+	0.174879i	−0.340845	+	0.940119i	$0.610713\pi$
$182$		0			0
$183$	4.45574	−	0.274755i	0.329377	−	0.0203105i
$184$		0			0
$185$	−1.46808	−	2.54278i	−0.107935	−	0.186949i
$186$		0			0
$187$	−1.65514	−	2.86679i	−0.121036	−	0.209641i
$188$		0			0
$189$	−6.64331	+	1.24155i	−0.483230	+	0.0903093i
$190$		0			0
$191$			4.02439i			0.291195i	0.989344	+	0.145598i	$0.0465104\pi$
$191$			4.02439i			0.291195i	−0.989344	+	0.145598i	$0.953490\pi$
$192$		0			0
$193$	−18.3046	+	10.5682i	−1.31760	+	0.760714i	−0.983341	−	0.181768i	$-0.941818\pi$
$193$	−18.3046	+	10.5682i	−1.31760	+	0.760714i	−0.334255	+	0.942483i	$0.608485\pi$
$194$		0			0
$195$	−12.6198	−	19.0458i	−0.903725	−	1.36390i
$196$		0			0
$197$		−	18.7827i		−	1.33821i	−0.743166	−	0.669107i	$-0.766677\pi$
$197$		−	18.7827i		−	1.33821i	0.743166	−	0.669107i	$-0.233323\pi$
$198$		0			0
$199$	−4.92424	+	8.52904i	−0.349070	+	0.604608i	−0.986085	−	0.166244i	$-0.946836\pi$
$199$	−4.92424	+	8.52904i	−0.349070	+	0.604608i	0.637014	+	0.770852i	$0.280169\pi$
$200$		0			0
$201$	1.41994	+	23.0273i	0.100155	+	1.62422i
$202$		0			0
$203$	−0.584720	+	1.01277i	−0.0410393	+	0.0710822i
$204$		0			0
$205$	−15.1390	−	8.74052i	−1.05736	−	0.610465i
$206$		0			0
$207$	9.19881	−	6.94620i	0.639362	−	0.482794i
$208$		0			0
$209$	3.44530	−	0.319670i	0.238316	−	0.0221121i
$210$		0			0
$211$	11.2715	−	6.50760i	0.775961	−	0.448001i	−0.0590358	−	0.998256i	$-0.518803\pi$
$211$	11.2715	−	6.50760i	0.775961	−	0.448001i	0.834997	+	0.550254i	$0.185469\pi$
$212$		0			0
$213$	−7.71865	+	15.5006i	−0.528873	+	1.06208i
$214$		0			0
$215$	13.1396	+	7.58613i	0.896111	+	0.517370i
$216$		0			0
$217$			6.73882i			0.457461i
$218$		0			0
$219$	5.92772	−	11.9040i	0.400558	−	0.804400i
$220$		0			0
$221$	−28.4555			−1.91412
$222$		0			0
$223$	−2.91879	+	1.68516i	−0.195457	+	0.112847i	−0.594534	−	0.804070i	$-0.702664\pi$
$223$	−2.91879	+	1.68516i	−0.195457	+	0.112847i	0.399078	+	0.916917i	$0.369330\pi$
$224$		0			0
$225$	−2.28321	−	3.02364i	−0.152214	−	0.201576i
$226$		0			0
$227$	−24.8192			−1.64731			−0.823654	−	0.567093i	$-0.808068\pi$
$227$	−24.8192			−1.64731			−0.823654	+	0.567093i	$0.808068\pi$
$228$		0			0
$229$	21.9704			1.45185			0.725923	−	0.687776i	$-0.241413\pi$
$229$	21.9704			1.45185			0.725923	+	0.687776i	$0.241413\pi$
$230$		0			0
$231$	−1.49071	+	0.987748i	−0.0980814	+	0.0649891i
$232$		0			0
$233$	−3.00291	+	1.73373i	−0.196727	+	0.113581i	−0.595128	−	0.803631i	$-0.702899\pi$
$233$	−3.00291	+	1.73373i	−0.196727	+	0.113581i	0.398401	+	0.917211i	$0.369565\pi$
$234$		0			0
$235$	−14.4699			−0.943913
$236$		0			0
$237$	1.79867	+	0.895662i	0.116836	+	0.0581795i
$238$		0			0
$239$			7.14202i			0.461979i	0.972956	+	0.230990i	$0.0741963\pi$
$239$			7.14202i			0.461979i	−0.972956	+	0.230990i	$0.925804\pi$
$240$		0			0
$241$	23.4727	+	13.5520i	1.51201	+	0.872961i	0.999901	+	0.0140411i	$0.00446958\pi$
$241$	23.4727	+	13.5520i	1.51201	+	0.872961i	0.512111	+	0.858919i	$0.328864\pi$
$242$		0			0
$243$	3.33600	−	15.2273i	0.214004	−	0.976833i
$244$		0			0
$245$	8.88696	−	5.13089i	0.567767	−	0.327800i
$246$		0			0
$247$	12.4283	−	27.0222i	0.790792	−	1.71938i
$248$		0			0
$249$	18.4167	−	12.2030i	1.16711	−	0.773331i
$250$		0			0
$251$	−2.57079	−	1.48424i	−0.162267	−	0.0936847i	0.416668	−	0.909059i	$-0.363198\pi$
$251$	−2.57079	−	1.48424i	−0.162267	−	0.0936847i	−0.578934	+	0.815374i	$0.696531\pi$
$252$		0			0
$253$	1.52500	−	2.64138i	0.0958761	−	0.166062i
$254$		0			0
$255$	13.9365	−	0.859372i	0.872740	−	0.0538159i
$256$		0			0
$257$	9.45905	−	16.3836i	0.590039	−	1.02198i	−0.404187	−	0.914676i	$-0.632446\pi$
$257$	9.45905	−	16.3836i	0.590039	−	1.02198i	0.994226	−	0.107302i	$-0.0342212\pi$
$258$		0			0
$259$			1.97548i			0.122750i
$260$		0			0
$261$	−1.62547	−	2.15260i	−0.100614	−	0.133243i
$262$		0			0
$263$	11.7958	−	6.81028i	0.727357	−	0.419940i	−0.0900972	−	0.995933i	$-0.528718\pi$
$263$	11.7958	−	6.81028i	0.727357	−	0.419940i	0.817455	+	0.575993i	$0.195384\pi$
$264$		0			0
$265$		−	16.3285i		−	1.00305i
$266$		0			0
$267$	4.52900	−	0.279273i	0.277170	−	0.0170912i
$268$		0			0
$269$	−13.9198	−	24.1098i	−0.848705	−	1.47000i	−0.882364	−	0.470567i	$-0.844049\pi$
$269$	−13.9198	−	24.1098i	−0.848705	−	1.47000i	0.0336594	−	0.999433i	$-0.489284\pi$
$270$		0			0
$271$	−9.87820	−	17.1096i	−0.600058	−	1.03933i	−0.992812	−	0.119687i	$-0.961811\pi$
$271$	−9.87820	−	17.1096i	−0.600058	−	1.03933i	0.392754	−	0.919644i	$-0.371523\pi$
$272$		0			0
$273$	0.946089	+	15.3428i	0.0572599	+	0.928591i
$274$		0			0
$275$	−0.868218	−	0.501266i	−0.0523555	−	0.0302275i
$276$		0			0
$277$	−14.5784			−0.875930			−0.437965	−	0.898992i	$-0.644301\pi$
$277$	−14.5784			−0.875930			−0.437965	+	0.898992i	$0.644301\pi$
$278$		0			0
$279$	−14.3139	−	6.05904i	−0.856950	−	0.362745i
$280$		0			0
$281$	15.1048	−	26.1622i	0.901076	−	1.56071i	0.0749753	−	0.997185i	$-0.476112\pi$
$281$	15.1048	−	26.1622i	0.901076	−	1.56071i	0.826100	−	0.563523i	$-0.190554\pi$
$282$		0			0
$283$	−10.7570	−	18.6317i	−0.639438	−	1.10754i	−0.985556	−	0.169348i	$-0.945834\pi$
$283$	−10.7570	−	18.6317i	−0.639438	−	1.10754i	0.346118	−	0.938191i	$-0.387500\pi$
$284$		0			0
$285$	−5.27086	+	13.6099i	−0.312219	+	0.806182i
$286$		0			0
$287$	5.88072	+	10.1857i	0.347128	+	0.601243i
$288$		0			0
$289$	0.195166	−	0.338038i	0.0114804	−	0.0198846i
$290$		0			0
$291$	−4.88298	−	2.43152i	−0.286245	−	0.142538i
$292$		0			0
$293$	31.6245			1.84752			0.923762	−	0.382968i	$-0.125098\pi$
$293$	31.6245			1.84752			0.923762	+	0.382968i	$0.125098\pi$
$294$		0			0
$295$	16.2160	+	9.36233i	0.944134	+	0.545096i
$296$		0			0
$297$	−0.757736	−	4.05451i	−0.0439683	−	0.235267i
$298$		0			0
$299$	−13.1090	−	22.7055i	−0.758115	−	1.31309i
$300$		0			0
$301$	−5.10403	−	8.84044i	−0.294191	−	0.509555i
$302$		0			0
$303$	1.04982	+	17.0250i	0.0603103	+	0.978060i
$304$		0			0
$305$			4.98250i			0.285297i
$306$		0			0
$307$	24.3867	−	14.0797i	1.39182	−	0.803570i	0.398306	−	0.917253i	$-0.369598\pi$
$307$	24.3867	−	14.0797i	1.39182	−	0.803570i	0.993517	+	0.113683i	$0.0362648\pi$
$308$		0			0
$309$	5.25268	−	3.48044i	0.298815	−	0.197996i
$310$		0			0
$311$			6.92040i			0.392420i	0.980562	+	0.196210i	$0.0628634\pi$
$311$			6.92040i			0.392420i	−0.980562	+	0.196210i	$0.937137\pi$
$312$		0			0
$313$	−1.96545	+	3.40425i	−0.111094	+	0.192420i	−0.916211	−	0.400695i	$-0.868769\pi$
$313$	−1.96545	+	3.40425i	−0.111094	+	0.192420i	0.805118	+	0.593115i	$0.202102\pi$
$314$		0			0
$315$	−0.926725	−	7.48584i	−0.0522150	−	0.421779i
$316$		0			0
$317$	−14.9648	+	25.9197i	−0.840504	+	1.45580i	0.0489643	+	0.998801i	$0.484408\pi$
$317$	−14.9648	+	25.9197i	−0.840504	+	1.45580i	−0.889469	+	0.456996i	$0.848925\pi$
$318$		0			0
$319$	−0.618106	−	0.356864i	−0.0346073	−	0.0199805i
$320$		0			0
$321$	0.00555339	+	0.00838118i	0.000309960	+	0.000467792i
$322$		0			0
$323$	10.5042	+	14.8350i	0.584468	+	0.825444i
$324$		0			0
$325$	−7.46327	+	4.30892i	−0.413988	+	0.239016i
$326$		0			0
$327$	19.7838	+	9.85154i	1.09405	+	0.544792i
$328$		0			0
$329$	8.43120	+	4.86776i	0.464827	+	0.268368i
$330$		0			0
$331$			19.9269i			1.09528i	0.836713	+	0.547641i	$0.184474\pi$
$331$			19.9269i			1.09528i	−0.836713	+	0.547641i	$0.815526\pi$
$332$		0			0
$333$	−4.19609	−	1.77620i	−0.229945	−	0.0973351i
$334$		0			0
$335$	−25.7496			−1.40685
$336$		0			0
$337$	8.02237	−	4.63172i	0.437006	−	0.252306i	−0.265321	−	0.964160i	$-0.585478\pi$
$337$	8.02237	−	4.63172i	0.437006	−	0.252306i	0.702327	+	0.711854i	$0.252144\pi$
$338$		0			0
$339$	−0.470748	−	0.710452i	−0.0255675	−	0.0385865i
$340$		0			0
$341$	−4.11281			−0.222721
$342$		0			0
$343$	−16.0087			−0.864390
$344$		0			0
$345$	7.10608	+	10.7245i	0.382579	+	0.577388i
$346$		0			0
$347$	−0.406998	+	0.234980i	−0.0218488	+	0.0126144i	−0.510885	−	0.859649i	$-0.670682\pi$
$347$	−0.406998	+	0.234980i	−0.0218488	+	0.0126144i	0.489036	+	0.872264i	$0.337349\pi$
$348$		0			0
$349$	−0.754750			−0.0404008			−0.0202004	−	0.999796i	$-0.506430\pi$
$349$	−0.754750			−0.0404008			−0.0202004	+	0.999796i	$0.506430\pi$
$350$		0			0
$351$	−33.4403	−	11.7855i	−1.78491	−	0.629066i
$352$		0			0
$353$			16.6706i			0.887284i	0.896204	+	0.443642i	$0.146314\pi$
$353$			16.6706i			0.887284i	−0.896204	+	0.443642i	$0.853686\pi$
$354$		0			0
$355$	−16.7372	−	9.66323i	−0.888319	−	0.512871i
$356$		0			0
$357$	−8.40952	−	4.18760i	−0.445079	−	0.221631i
$358$		0			0
$359$	−27.4728	+	15.8614i	−1.44996	+	0.837134i	−0.998478	−	0.0551476i	$-0.982437\pi$
$359$	−27.4728	+	15.8614i	−1.44996	+	0.837134i	−0.451480	+	0.892281i	$0.649104\pi$
$360$		0			0
$361$	−18.6757	+	3.49571i	−0.982929	+	0.183985i
$362$		0			0
$363$	9.92090	+	14.9726i	0.520712	+	0.785858i
$364$		0			0
$365$	12.8537	+	7.42111i	0.672795	+	0.388438i
$366$		0			0
$367$	−16.6052	+	28.7611i	−0.866786	+	1.50132i	−0.00152368	+	0.999999i	$0.500485\pi$
$367$	−16.6052	+	28.7611i	−0.866786	+	1.50132i	−0.865263	+	0.501319i	$0.832848\pi$
$368$		0			0
$369$	−26.9229	+	3.33298i	−1.40155	+	0.173508i
$370$		0			0
$371$	−5.49299	+	9.51414i	−0.285182	+	0.493950i
$372$		0			0
$373$		−	33.8778i		−	1.75413i	−0.480375	−	0.877063i	$-0.659500\pi$
$373$		−	33.8778i		−	1.75413i	0.480375	−	0.877063i	$-0.340500\pi$
$374$		0			0
$375$	17.4810	−	11.5830i	0.902717	−	0.598143i
$376$		0			0
$377$	−5.31329	+	3.06763i	−0.273648	+	0.157991i
$378$		0			0
$379$		−	4.17484i		−	0.214447i	−0.994235	−	0.107224i	$-0.965804\pi$
$379$		−	4.17484i		−	0.214447i	0.994235	−	0.107224i	$-0.0341961\pi$
$380$		0			0
$381$	1.36652	+	22.1610i	0.0700087	+	1.13534i
$382$		0			0
$383$	6.20093	+	10.7403i	0.316853	+	0.548805i	0.979830	−	0.199835i	$-0.0640406\pi$
$383$	6.20093	+	10.7403i	0.316853	+	0.548805i	−0.662977	+	0.748640i	$0.730707\pi$
$384$		0			0
$385$	−0.997938	−	1.72848i	−0.0508596	−	0.0880914i
$386$		0			0
$387$	23.3671	−	2.89278i	1.18782	−	0.147048i
$388$		0			0
$389$	−16.7244	−	9.65581i	−0.847959	−	0.489569i	0.0120030	−	0.999928i	$-0.496179\pi$
$389$	−16.7244	−	9.65581i	−0.847959	−	0.489569i	−0.859962	+	0.510359i	$0.829513\pi$
$390$		0			0
$391$	16.0230			0.810316
$392$		0			0
$393$	15.8395	+	7.88743i	0.798998	+	0.397868i
$394$		0			0
$395$	−1.12131	+	1.94216i	−0.0564192	+	0.0977209i
$396$		0			0
$397$	6.12390	+	10.6069i	0.307350	+	0.532346i	0.977782	−	0.209626i	$-0.0672245\pi$
$397$	6.12390	+	10.6069i	0.307350	+	0.532346i	−0.670432	+	0.741971i	$0.733891\pi$
$398$		0			0
$399$	7.64963	−	6.15696i	0.382960	−	0.308233i
$400$		0			0
$401$	−2.29012	−	3.96660i	−0.114363	−	0.198083i	0.803162	−	0.595761i	$-0.203149\pi$
$401$	−2.29012	−	3.96660i	−0.114363	−	0.198083i	−0.917525	+	0.397678i	$0.869816\pi$
$402$		0			0
$403$	−17.6770	+	30.6175i	−0.880554	+	1.52516i
$404$		0			0
$405$	16.7339	+	4.76225i	0.831512	+	0.236638i
$406$		0			0
$407$	−1.20566			−0.0597625
$408$		0			0
$409$	−14.4669	−	8.35244i	−0.715340	−	0.413002i	0.0976951	−	0.995216i	$-0.468853\pi$
$409$	−14.4669	−	8.35244i	−0.715340	−	0.413002i	−0.813035	+	0.582215i	$0.802186\pi$
$410$		0			0
$411$	0.675140	+	10.9488i	0.0333022	+	0.540066i
$412$		0			0
$413$	−6.29907	−	10.9103i	−0.309957	−	0.536862i
$414$		0			0
$415$	12.3288	+	21.3542i	0.605199	+	1.04824i
$416$		0			0
$417$	−24.0816	+	1.48495i	−1.17928	+	0.0727184i
$418$		0			0
$419$			3.68172i			0.179864i	0.995948	+	0.0899319i	$0.0286650\pi$
$419$			3.68172i			0.179864i	−0.995948	+	0.0899319i	$0.971335\pi$
$420$		0			0
$421$	−12.0314	+	6.94636i	−0.586377	+	0.338545i	−0.763664	−	0.645614i	$-0.776601\pi$
$421$	−12.0314	+	6.94636i	−0.586377	+	0.338545i	0.177287	+	0.984159i	$0.443268\pi$
$422$		0			0
$423$	−17.9203	+	13.5319i	−0.871314	+	0.657945i
$424$		0			0
$425$		−	5.26672i		−	0.255474i
$426$		0			0
$427$	1.67614	−	2.90316i	0.0811141	−	0.140494i
$428$		0			0
$429$	−9.36397	+	0.577413i	−0.452097	+	0.0278777i
$430$		0			0
$431$	3.58081	−	6.20215i	0.172482	−	0.298747i	−0.766805	−	0.641880i	$-0.778155\pi$
$431$	3.58081	−	6.20215i	0.172482	−	0.298747i	0.939287	+	0.343133i	$0.111488\pi$
$432$		0			0
$433$	0.878402	+	0.507145i	0.0422133	+	0.0243719i	0.520958	−	0.853582i	$-0.325575\pi$
$433$	0.878402	+	0.507145i	0.0422133	+	0.0243719i	−0.478745	+	0.877954i	$0.658908\pi$
$434$		0			0
$435$	2.50963	−	1.66289i	0.120327	−	0.0797293i
$436$		0			0
$437$	−6.99822	+	15.2159i	−0.334770	+	0.727875i
$438$		0			0
$439$	−6.74514	+	3.89431i	−0.321928	+	0.185865i	−0.652252	−	0.758003i	$-0.726175\pi$
$439$	−6.74514	+	3.89431i	−0.321928	+	0.185865i	0.330324	+	0.943868i	$0.392842\pi$
$440$		0			0
$441$	6.20777	−	14.6652i	0.295608	−	0.698345i
$442$		0			0
$443$	34.9016	+	20.1504i	1.65822	+	0.957376i	0.973534	+	0.228542i	$0.0733958\pi$
$443$	34.9016	+	20.1504i	1.65822	+	0.957376i	0.684690	+	0.728834i	$0.259938\pi$
$444$		0			0
$445$			5.06442i			0.240077i
$446$		0			0
$447$	29.7466	+	14.8126i	1.40697	+	0.700612i
$448$		0			0
$449$	−19.7378			−0.931485			−0.465743	−	0.884920i	$-0.654213\pi$
$449$	−19.7378			−0.931485			−0.465743	+	0.884920i	$0.654213\pi$
$450$		0			0
$451$	−6.21649	+	3.58909i	−0.292723	+	0.169004i
$452$		0			0
$453$	8.77422	−	5.81383i	0.412249	−	0.273157i
$454$		0			0
$455$	−17.1567			−0.804318
$456$		0			0
$457$	−30.4745			−1.42554			−0.712768	−	0.701399i	$-0.752559\pi$
$457$	−30.4745			−1.42554			−0.712768	+	0.701399i	$0.752559\pi$
$458$		0			0
$459$	16.4560	−	14.0974i	0.768103	−	0.658012i
$460$		0			0
$461$	−9.40513	+	5.43005i	−0.438040	+	0.252903i	−0.702766	−	0.711421i	$-0.748052\pi$
$461$	−9.40513	+	5.43005i	−0.438040	+	0.252903i	0.264726	+	0.964324i	$0.414719\pi$
$462$		0			0
$463$	−13.0733			−0.607569			−0.303785	−	0.952741i	$-0.598250\pi$
$463$	−13.0733			−0.607569			−0.303785	+	0.952741i	$0.598250\pi$
$464$		0			0
$465$	7.73293	−	15.5293i	0.358606	−	0.720152i
$466$		0			0
$467$			13.8765i			0.642128i	0.947058	+	0.321064i	$0.104040\pi$
$467$			13.8765i			0.642128i	−0.947058	+	0.321064i	$0.895960\pi$
$468$		0			0
$469$	15.0036	+	8.66231i	0.692800	+	0.399988i
$470$		0			0
$471$	0.568643	−	1.14195i	0.0262017	−	0.0526182i
$472$		0			0
$473$	5.39546	−	3.11507i	0.248083	−	0.143231i
$474$		0			0
$475$	5.00145	+	2.30030i	0.229482	+	0.105545i
$476$		0			0
$477$	−15.2700	−	20.2220i	−0.699167	−	0.925903i
$478$		0			0
$479$	−0.698122	−	0.403061i	−0.0318980	−	0.0184163i	0.483966	−	0.875087i	$-0.339196\pi$
$479$	−0.698122	−	0.403061i	−0.0318980	−	0.0184163i	−0.515864	+	0.856670i	$0.672529\pi$
$480$		0			0
$481$	−5.18199	+	8.97546i	−0.236278	+	0.409246i
$482$		0			0
$483$	−0.532732	−	8.63938i	−0.0242401	−	0.393105i
$484$		0			0
$485$	3.04410	−	5.27254i	0.138226	−	0.239414i
$486$		0			0
$487$			29.8196i			1.35125i	0.737244	+	0.675627i	$0.236127\pi$
$487$			29.8196i			1.35125i	−0.737244	+	0.675627i	$0.763873\pi$
$488$		0			0
$489$	−0.812952	−	1.22691i	−0.0367630	−	0.0554826i
$490$		0			0
$491$	12.2737	−	7.08625i	0.553907	−	0.319798i	−0.196790	−	0.980446i	$-0.563052\pi$
$491$	12.2737	−	7.08625i	0.553907	−	0.319798i	0.750696	+	0.660648i	$0.229718\pi$
$492$		0			0
$493$		−	3.74951i		−	0.168870i
$494$		0			0
$495$	4.56872	−	0.565595i	0.205349	−	0.0254216i
$496$		0			0
$497$	6.50152	+	11.2610i	0.291633	+	0.505124i
$498$		0			0
$499$	2.94453	+	5.10007i	0.131815	+	0.228311i	0.924376	−	0.381482i	$-0.124586\pi$
$499$	2.94453	+	5.10007i	0.131815	+	0.228311i	−0.792561	+	0.609792i	$0.791253\pi$
$500$		0			0
$501$	35.2381	−	2.17289i	1.57432	−	0.0970778i
$502$		0			0
$503$	4.87723	+	2.81587i	0.217465	+	0.125554i	0.604776	−	0.796396i	$-0.293263\pi$
$503$	4.87723	+	2.81587i	0.217465	+	0.125554i	−0.387311	+	0.921949i	$0.626596\pi$
$504$		0			0
$505$	−19.0377			−0.847167
$506$		0			0
$507$	−25.9114	+	52.0351i	−1.15076	+	2.31096i
$508$		0			0
$509$	−6.33041	+	10.9646i	−0.280590	+	0.485997i	−0.971530	−	0.236915i	$-0.923864\pi$
$509$	−6.33041	+	10.9646i	−0.280590	+	0.485997i	0.690940	+	0.722912i	$0.257197\pi$
$510$		0			0
$511$	−4.99300	−	8.64813i	−0.220877	−	0.382571i
$512$		0			0
$513$	6.19998	+	21.7844i	0.273736	+	0.961805i
$514$		0			0
$515$	3.51635	+	6.09049i	0.154949	+	0.268379i
$516$		0			0
$517$	−2.97087	+	5.14569i	−0.130659	+	0.226307i
$518$		0			0
$519$	−11.5999	+	23.2950i	−0.509181	+	1.02254i
$520$		0			0
$521$	23.9375			1.04872			0.524360	−	0.851497i	$-0.324305\pi$
$521$	23.9375			1.04872			0.524360	+	0.851497i	$0.324305\pi$
$522$		0			0
$523$	0.938282	+	0.541717i	0.0410282	+	0.0236876i	0.520374	−	0.853939i	$-0.325793\pi$
$523$	0.938282	+	0.541717i	0.0410282	+	0.0236876i	−0.479346	+	0.877626i	$0.659126\pi$
$524$		0			0
$525$	−2.83975	+	0.175108i	−0.123937	+	0.00764235i
$526$		0			0
$527$	−10.8032	−	18.7116i	−0.470593	−	0.815090i
$528$		0			0
$529$	−4.11845	−	7.13337i	−0.179063	−	0.310146i
$530$		0			0
$531$	28.8382	−	3.57009i	1.25147	−	0.154928i
$532$		0			0
$533$			61.7042i			2.67271i
$534$		0			0
$535$	−0.00971798	+	0.00561068i	−0.000420145	+	0.000242571i
$536$		0			0
$537$	2.39138	+	3.60907i	0.103196	+	0.155743i
$538$		0			0
$539$		−	4.21376i		−	0.181500i
$540$		0			0
$541$	21.6976	−	37.5813i	0.932852	−	1.61575i	0.154432	−	0.988003i	$-0.450645\pi$
$541$	21.6976	−	37.5813i	0.932852	−	1.61575i	0.778420	−	0.627744i	$-0.216021\pi$
$542$		0			0
$543$	0.501614	+	8.13474i	0.0215263	+	0.349095i
$544$		0			0
$545$	−12.3335	+	21.3622i	−0.528308	+	0.915056i
$546$		0			0
$547$	0.823387	+	0.475382i	0.0352055	+	0.0203259i	0.517499	−	0.855684i	$-0.326863\pi$
$547$	0.823387	+	0.475382i	0.0352055	+	0.0203259i	−0.482294	+	0.876009i	$0.660196\pi$
$548$		0			0
$549$	4.65952	+	6.17058i	0.198864	+	0.263354i
$550$		0			0
$551$	3.56066	+	1.63765i	0.151689	+	0.0697660i
$552$		0			0
$553$	1.30671	−	0.754429i	0.0555669	−	0.0320816i
$554$		0			0
$555$	2.26690	−	4.55238i	0.0962245	−	0.193238i
$556$		0			0
$557$	15.4008	+	8.89166i	0.652553	+	0.376752i	0.789434	−	0.613836i	$-0.210374\pi$
$557$	15.4008	+	8.89166i	0.652553	+	0.376752i	−0.136881	+	0.990588i	$0.543708\pi$
$558$		0			0
$559$		−	53.5547i		−	2.26512i
$560$		0			0
$561$	2.55575	−	5.13246i	0.107904	−	0.216693i
$562$		0			0
$563$	−33.4123			−1.40816			−0.704080	−	0.710120i	$-0.748641\pi$
$563$	−33.4123			−1.40816			−0.704080	+	0.710120i	$0.748641\pi$
$564$		0			0
$565$	0.823770	−	0.475604i	0.0346563	−	0.0200088i
$566$		0			0
$567$	−8.14829	−	8.40419i	−0.342196	−	0.352943i
$568$		0			0
$569$	15.3812			0.644814			0.322407	−	0.946601i	$-0.395508\pi$
$569$	15.3812			0.644814			0.322407	+	0.946601i	$0.395508\pi$
$570$		0			0
$571$	25.8806			1.08307			0.541534	−	0.840679i	$-0.317844\pi$
$571$	25.8806			1.08307			0.541534	+	0.840679i	$0.317844\pi$
$572$		0			0
$573$	−5.81065	+	3.85015i	−0.242743	+	0.160842i
$574$		0			0
$575$	4.20248	−	2.42630i	0.175256	−	0.101184i
$576$		0			0
$577$	−21.2717			−0.885554			−0.442777	−	0.896632i	$-0.646007\pi$
$577$	−21.2717			−0.885554			−0.442777	+	0.896632i	$0.646007\pi$
$578$		0			0
$579$	−32.7710	−	16.3186i	−1.36192	−	0.678179i
$580$		0			0
$581$		−	16.5900i		−	0.688267i
$582$		0			0
$583$	−5.80663	−	3.35246i	−0.240486	−	0.138845i
$584$		0			0
$585$	15.4260	−	36.4424i	0.637787	−	1.50671i
$586$		0			0
$587$	−21.1678	+	12.2212i	−0.873688	+	0.504424i	−0.868572	−	0.495563i	$-0.834962\pi$
$587$	−21.1678	+	12.2212i	−0.873688	+	0.504424i	−0.00511624	+	0.999987i	$0.501629\pi$
$588$		0			0
$589$	22.4875	−	2.08649i	0.926583	−	0.0859725i
$590$		0			0
$591$	27.1195	−	17.9695i	1.11555	−	0.739166i
$592$		0			0
$593$	−30.2941	−	17.4903i	−1.24403	−	0.718240i	−0.274116	−	0.961697i	$-0.588385\pi$
$593$	−30.2941	−	17.4903i	−1.24403	−	0.718240i	−0.969912	+	0.243457i	$0.921719\pi$
$594$		0			0
$595$	5.24259	−	9.08043i	0.214925	−	0.372261i
$596$		0			0
$597$	−17.0257	+	1.04986i	−0.696817	+	0.0429680i
$598$		0			0
$599$	18.2634	−	31.6331i	0.746223	−	1.29250i	−0.203399	−	0.979096i	$-0.565199\pi$
$599$	18.2634	−	31.6331i	0.746223	−	1.29250i	0.949621	−	0.313399i	$-0.101468\pi$
$600$		0			0
$601$			29.5408i			1.20500i	0.798121	+	0.602498i	$0.205828\pi$
$601$			29.5408i			1.20500i	−0.798121	+	0.602498i	$0.794172\pi$
$602$		0			0
$603$	−31.8896	+	24.0805i	−1.29865	+	0.980632i
$604$		0			0
$605$	−17.3608	+	10.0232i	−0.705815	+	0.407503i
$606$		0			0
$607$		−	46.5886i		−	1.89097i	−0.325663	−	0.945486i	$-0.605587\pi$
$607$		−	46.5886i		−	1.89097i	0.325663	−	0.945486i	$-0.394413\pi$
$608$		0			0
$609$	−2.02169	+	0.124664i	−0.0819231	+	0.00505164i
$610$		0			0
$611$	25.5378	+	44.2328i	1.03315	+	1.78947i
$612$		0			0
$613$	8.82907	+	15.2924i	0.356603	+	0.617654i	0.987391	−	0.158301i	$-0.0506016\pi$
$613$	8.82907	+	15.2924i	0.356603	+	0.617654i	−0.630788	+	0.775955i	$0.717268\pi$
$614$		0			0
$615$	−1.86350	−	30.2207i	−0.0751437	−	1.21861i
$616$		0			0
$617$	24.6018	+	14.2038i	0.990431	+	0.571825i	0.905403	−	0.424553i	$-0.139569\pi$
$617$	24.6018	+	14.2038i	0.990431	+	0.571825i	0.0850277	+	0.996379i	$0.472902\pi$
$618$		0			0
$619$	−37.7034			−1.51543			−0.757713	−	0.652588i	$-0.773683\pi$
$619$	−37.7034			−1.51543			−0.757713	+	0.652588i	$0.773683\pi$
$620$		0			0
$621$	18.8298	+	6.63631i	0.755616	+	0.266306i
$622$		0			0
$623$	1.70370	−	2.95089i	0.0682573	−	0.118225i
$624$		0			0
$625$	8.54510	+	14.8005i	0.341804	+	0.592022i
$626$		0			0
$627$	3.75769	+	4.66869i	0.150068	+	0.186449i
$628$		0			0
$629$	−3.16693	−	5.48528i	−0.126274	−	0.218712i
$630$		0			0
$631$	−0.866898	+	1.50151i	−0.0345107	+	0.0597742i	−0.882765	−	0.469815i	$-0.844321\pi$
$631$	−0.866898	+	1.50151i	−0.0345107	+	0.0597742i	0.848254	+	0.529589i	$0.177654\pi$
$632$		0			0
$633$	20.1795	+	10.0486i	0.802063	+	0.399395i
$634$		0			0
$635$	−24.7809			−0.983398
$636$		0			0
$637$	−31.3690	−	18.1109i	−1.24289	−	0.717580i
$638$		0			0
$639$	−29.7650	+	3.68483i	−1.17749	+	0.145769i
$640$		0			0
$641$	−14.7315	−	25.5157i	−0.581858	−	1.00781i	−0.995259	−	0.0972589i	$-0.968993\pi$
$641$	−14.7315	−	25.5157i	−0.581858	−	1.00781i	0.413401	−	0.910549i	$-0.364341\pi$
$642$		0			0
$643$	−9.57102	−	16.5775i	−0.377444	−	0.653753i	0.613245	−	0.789892i	$-0.289864\pi$
$643$	−9.57102	−	16.5775i	−0.377444	−	0.653753i	−0.990690	+	0.136140i	$0.956530\pi$
$644$		0			0
$645$	1.61738	+	26.2293i	0.0636844	+	1.03278i
$646$		0			0
$647$			4.36953i			0.171784i	0.996304	+	0.0858920i	$0.0273740\pi$
$647$			4.36953i			0.171784i	−0.996304	+	0.0858920i	$0.972626\pi$
$648$		0			0
$649$	6.65873	−	3.84442i	0.261378	−	0.150907i
$650$		0			0
$651$	−9.72988	+	6.44705i	−0.381344	+	0.252680i
$652$		0			0
$653$		−	33.9531i		−	1.32869i	−0.747428	−	0.664343i	$-0.768711\pi$
$653$		−	33.9531i		−	1.32869i	0.747428	−	0.664343i	$-0.231289\pi$
$654$		0			0
$655$	−9.87453	+	17.1032i	−0.385830	+	0.668277i
$656$		0			0
$657$	22.8588	−	2.82985i	0.891805	−	0.110403i
$658$		0			0
$659$	20.6438	−	35.7561i	0.804169	−	1.39286i	−0.112682	−	0.993631i	$-0.535944\pi$
$659$	20.6438	−	35.7561i	0.804169	−	1.39286i	0.916851	−	0.399230i	$-0.130723\pi$
$660$		0			0
$661$	−2.79843	−	1.61568i	−0.108846	−	0.0628425i	0.444588	−	0.895735i	$-0.353350\pi$
$661$	−2.79843	−	1.61568i	−0.108846	−	0.0628425i	−0.553435	+	0.832892i	$0.686683\pi$
$662$		0			0
$663$	−27.2234	−	41.0856i	−1.05727	−	1.59563i
$664$		0			0
$665$	6.33330	+	8.94451i	0.245595	+	0.346853i
$666$		0			0
$667$	2.99185	−	1.72735i	0.115845	−	0.0668832i
$668$		0			0
$669$	−5.22555	−	2.60211i	−0.202031	−	0.100603i
$670$		0			0
$671$	1.77184	+	1.02297i	0.0684012	+	0.0394915i
$672$		0			0
$673$			32.5789i			1.25582i	0.778284	+	0.627912i	$0.216090\pi$
$673$			32.5789i			1.25582i	−0.778284	+	0.627912i	$0.783910\pi$
$674$		0			0
$675$	2.18134	−	6.18934i	0.0839600	−	0.238228i
$676$		0			0
$677$	33.5889			1.29093			0.645463	−	0.763792i	$-0.276665\pi$
$677$	33.5889			1.29093			0.645463	+	0.763792i	$0.276665\pi$
$678$		0			0
$679$	−3.54742	+	2.04810i	−0.136138	+	0.0785991i
$680$		0			0
$681$	−23.7446	−	35.8353i	−0.909895	−	1.37321i
$682$		0			0
$683$	6.37989			0.244120			0.122060	−	0.992523i	$-0.461050\pi$
$683$	6.37989			0.244120			0.122060	+	0.992523i	$0.461050\pi$
$684$		0			0
$685$	−12.2432			−0.467789
$686$		0			0
$687$	21.0192	+	31.7221i	0.801931	+	1.21027i
$688$		0			0
$689$	−49.9142	+	28.8180i	−1.90158	+	1.09788i
$690$		0			0
$691$	−36.5207			−1.38931			−0.694657	−	0.719341i	$-0.744444\pi$
$691$	−36.5207			−1.38931			−0.694657	+	0.719341i	$0.744444\pi$
$692$		0			0
$693$	−2.85233	−	1.20739i	−0.108351	−	0.0458648i
$694$		0			0
$695$		−	26.9286i		−	1.02146i
$696$		0			0
$697$	−32.6578	−	18.8550i	−1.23700	−	0.714185i
$698$		0			0
$699$	−5.37616	−	2.67711i	−0.203345	−	0.101257i
$700$		0			0
$701$	−2.61450	+	1.50948i	−0.0987485	+	0.0570124i	−0.548561	−	0.836111i	$-0.684824\pi$
$701$	−2.61450	+	1.50948i	−0.0987485	+	0.0570124i	0.449813	+	0.893123i	$0.351491\pi$
$702$		0			0
$703$	6.59219	−	0.611653i	0.248629	−	0.0230689i
$704$		0			0
$705$	−13.8434	−	20.8925i	−0.521373	−	0.786856i
$706$		0			0
$707$	11.0927	+	6.40439i	0.417185	+	0.240862i
$708$		0			0
$709$	13.3528	−	23.1277i	0.501474	−	0.868578i	−0.498525	−	0.866875i	$-0.666125\pi$
$709$	13.3528	−	23.1277i	0.501474	−	0.868578i	0.999999	−	0.00170254i	$-0.000541934\pi$
$710$		0			0
$711$	0.427583	+	3.45390i	0.0160356	+	0.129531i
$712$		0			0
$713$	9.95372	−	17.2403i	0.372770	−	0.645656i
$714$		0			0
$715$		−	10.4710i		−	0.391593i
$716$		0			0
$717$	−10.3121	+	6.83280i	−0.385111	+	0.255175i
$718$		0			0
$719$	11.8592	−	6.84690i	0.442273	−	0.255346i	−0.262289	−	0.964989i	$-0.584477\pi$
$719$	11.8592	−	6.84690i	0.442273	−	0.255346i	0.704561	+	0.709643i	$0.251144\pi$
$720$		0			0
$721$		−	4.73167i		−	0.176217i
$722$		0			0
$723$	2.88932	+	46.8565i	0.107455	+	1.74261i
$724$		0			0
$725$	−0.567777	−	0.983418i	−0.0210867	−	0.0365232i
$726$		0			0
$727$	1.88211	+	3.25992i	0.0698038	+	0.120904i	0.898815	−	0.438329i	$-0.144429\pi$
$727$	1.88211	+	3.25992i	0.0698038	+	0.120904i	−0.829011	+	0.559232i	$0.811096\pi$
$728$		0			0
$729$	25.1776	−	9.75132i	0.932504	−	0.361160i
$730$		0			0
$731$	28.3446	+	16.3648i	1.04836	+	0.605273i
$732$		0			0
$733$	13.7582			0.508172			0.254086	−	0.967182i	$-0.418225\pi$
$733$	13.7582			0.508172			0.254086	+	0.967182i	$0.418225\pi$
$734$		0			0
$735$	15.9104	+	7.92275i	0.586866	+	0.292235i
$736$		0			0
$737$	−5.28674	+	9.15690i	−0.194740	+	0.337299i
$738$		0			0
$739$	3.86210	+	6.68936i	0.142070	+	0.246072i	0.928276	−	0.371892i	$-0.121291\pi$
$739$	3.86210	+	6.68936i	0.142070	+	0.246072i	−0.786206	+	0.617964i	$0.787958\pi$
$740$		0			0
$741$	50.9063	−	7.90761i	1.87009	−	0.290493i
$742$		0			0
$743$	−14.0170	−	24.2781i	−0.514233	−	0.890678i	−0.999864	−	0.0165141i	$-0.994743\pi$
$743$	−14.0170	−	24.2781i	−0.514233	−	0.890678i	0.485630	−	0.874164i	$-0.338590\pi$
$744$		0			0
$745$	−18.5444	+	32.1198i	−0.679413	+	1.17678i
$746$		0			0
$747$	35.2386	+	14.9164i	1.28931	+	0.545764i
$748$		0			0
$749$	0.00754985			0.000275866
$750$		0			0
$751$	−35.9167	−	20.7365i	−1.31062	−	0.756686i	−0.328420	−	0.944532i	$-0.606516\pi$
$751$	−35.9167	−	20.7365i	−1.31062	−	0.756686i	−0.982199	+	0.187845i	$0.939850\pi$
$752$		0			0
$753$	−0.316445	−	5.13183i	−0.0115319	−	0.187014i
$754$		0			0
$755$	5.87380	+	10.1737i	0.213770	+	0.370260i
$756$		0			0
$757$	18.7352	+	32.4504i	0.680944	+	1.17943i	0.974693	+	0.223547i	$0.0717635\pi$
$757$	18.7352	+	32.4504i	0.680944	+	1.17943i	−0.293749	+	0.955882i	$0.594903\pi$
$758$		0			0
$759$	5.27275	−	0.325135i	0.191389	−	0.0118016i
$760$		0			0
$761$			37.5981i			1.36293i	0.731850	+	0.681466i	$0.238657\pi$
$761$			37.5981i			1.36293i	−0.731850	+	0.681466i	$0.761343\pi$
$762$		0			0
$763$	14.3727	−	8.29809i	0.520327	−	0.300411i
$764$		0			0
$765$	14.5739	+	19.3002i	0.526922	+	0.697800i
$766$		0			0
$767$		−	66.0939i		−	2.38651i
$768$		0			0
$769$	−2.77926	+	4.81383i	−0.100223	+	0.173591i	−0.911776	−	0.410687i	$-0.865289\pi$
$769$	−2.77926	+	4.81383i	−0.100223	+	0.173591i	0.811554	+	0.584278i	$0.198622\pi$
$770$		0			0
$771$	32.7050	−	2.01670i	1.17784	−	0.0726295i
$772$		0			0
$773$	−6.15991	+	10.6693i	−0.221556	+	0.383747i	−0.955281	−	0.295700i	$-0.904447\pi$
$773$	−6.15991	+	10.6693i	−0.221556	+	0.383747i	0.733724	+	0.679447i	$0.237780\pi$
$774$		0			0
$775$	−5.66687	−	3.27177i	−0.203560	−	0.117526i
$776$		0			0
$777$	−2.85230	+	1.88994i	−0.102326	+	0.0678014i
$778$		0			0
$779$	32.1690	−	22.7778i	1.15257	−	0.816098i
$780$		0			0
$781$	−6.87274	+	3.96798i	−0.245926	+	0.141986i
$782$		0			0
$783$	1.55295	−	4.40635i	0.0554981	−	0.157470i
$784$		0			0
$785$	1.23305	+	0.711903i	0.0440095	+	0.0254089i
$786$		0			0
$787$			42.0917i			1.50041i	0.661207	+	0.750203i	$0.270044\pi$
$787$			42.0917i			1.50041i	−0.661207	+	0.750203i	$0.729956\pi$
$788$		0			0
$789$	21.1181	+	10.5160i	0.751824	+	0.374378i
$790$		0			0
$791$	−0.639983			−0.0227552
$792$		0			0
$793$	15.2309	−	8.79356i	0.540865	−	0.312269i
$794$		0			0
$795$	23.5760	−	15.6215i	0.836154	−	0.554038i
$796$		0			0
$797$	−24.6078			−0.871653			−0.435827	−	0.900031i	$-0.643544\pi$
$797$	−24.6078			−0.871653			−0.435827	+	0.900031i	$0.643544\pi$
$798$		0			0
$799$	−31.2144			−1.10429
$800$		0			0
$801$	4.73614	+	6.27204i	0.167343	+	0.221612i
$802$		0			0
$803$	5.27809	−	3.04730i	0.186260	−	0.107537i
$804$		0			0
$805$	9.66074			0.340496
$806$		0			0
$807$	21.4940	−	43.1641i	0.756623	−	1.51945i
$808$		0			0
$809$		−	48.4308i		−	1.70274i	−0.524568	−	0.851368i	$-0.675773\pi$
$809$		−	48.4308i		−	1.70274i	0.524568	−	0.851368i	$-0.324227\pi$
$810$		0			0
$811$	−38.5693	−	22.2680i	−1.35435	−	0.781935i	−0.365496	−	0.930813i	$-0.619100\pi$
$811$	−38.5693	−	22.2680i	−1.35435	−	0.781935i	−0.988856	+	0.148878i	$0.952434\pi$
$812$		0			0
$813$	15.2532	−	30.6315i	0.534954	−	1.07429i
$814$		0			0
$815$	1.42260	−	0.821338i	0.0498315	−	0.0287702i
$816$		0			0
$817$	−27.9204	+	19.7694i	−0.976809	+	0.691645i
$818$		0			0
$819$	−21.2477	+	16.0446i	−0.742455	+	0.560642i
$820$		0			0
$821$	19.7131	+	11.3814i	0.687992	+	0.397212i	0.802859	−	0.596169i	$-0.203311\pi$
$821$	19.7131	+	11.3814i	0.687992	+	0.397212i	−0.114868	+	0.993381i	$0.536644\pi$
$822$		0			0
$823$	−3.16804	+	5.48721i	−0.110431	+	0.191272i	−0.915944	−	0.401306i	$-0.868556\pi$
$823$	−3.16804	+	5.48721i	−0.110431	+	0.191272i	0.805513	+	0.592578i	$0.201890\pi$
$824$		0			0
$825$	−0.106871	−	1.73314i	−0.00372078	−	0.0603403i
$826$		0			0
$827$	14.9335	−	25.8656i	0.519290	−	0.899436i	−0.480459	−	0.877017i	$-0.659530\pi$
$827$	14.9335	−	25.8656i	0.519290	−	0.899436i	0.999749	−	0.0224191i	$-0.00713683\pi$
$828$		0			0
$829$		−	35.7744i		−	1.24250i	−0.783613	−	0.621249i	$-0.786626\pi$
$829$		−	35.7744i		−	1.24250i	0.783613	−	0.621249i	$-0.213374\pi$
$830$		0			0
$831$	−13.9472	−	21.0491i	−0.483823	−	0.730185i
$832$		0			0
$833$	19.1709	−	11.0683i	0.664233	−	0.383495i
$834$		0			0
$835$			39.4040i			1.36363i
$836$		0			0
$837$	−4.94576	−	26.4639i	−0.170950	−	0.914726i
$838$		0			0
$839$	−26.7675	−	46.3627i	−0.924117	−	1.60062i	−0.792975	−	0.609255i	$-0.791469\pi$
$839$	−26.7675	−	46.3627i	−0.924117	−	1.60062i	−0.131143	−	0.991363i	$-0.541865\pi$
$840$		0			0
$841$	14.0958	+	24.4146i	0.486062	+	0.841883i
$842$		0			0
$843$	52.2253	−	3.22038i	1.79873	−	0.110916i
$844$		0			0
$845$	−56.1865	−	32.4393i	−1.93287	−	1.11595i
$846$		0			0
$847$	13.4875			0.463436
$848$		0			0
$849$	16.6102	−	33.3566i	0.570061	−	1.14479i
$850$		0			0
$851$	2.91792	−	5.05398i	0.100025	−	0.173248i
$852$		0			0
$853$	−0.409912	−	0.709988i	−0.0140351	−	0.0243095i	0.858923	−	0.512106i	$-0.171134\pi$
$853$	−0.409912	−	0.709988i	−0.0140351	−	0.0243095i	−0.872958	+	0.487796i	$0.837801\pi$
$854$		0			0
$855$	−24.6934	+	5.41028i	−0.844497	+	0.185028i
$856$		0			0
$857$	19.1530	+	33.1740i	0.654255	+	1.13320i	0.982080	+	0.188464i	$0.0603510\pi$
$857$	19.1530	+	33.1740i	0.654255	+	1.13320i	−0.327825	+	0.944738i	$0.606316\pi$
$858$		0			0
$859$	16.3273	−	28.2796i	0.557079	−	0.964889i	−0.440660	−	0.897674i	$-0.645255\pi$
$859$	16.3273	−	28.2796i	0.557079	−	0.964889i	0.997739	−	0.0672147i	$-0.0214112\pi$
$860$		0			0
$861$	−9.08058	+	18.2356i	−0.309465	+	0.621468i
$862$		0			0
$863$	−20.2375			−0.688892			−0.344446	−	0.938806i	$-0.611933\pi$
$863$	−20.2375			−0.688892			−0.344446	+	0.938806i	$0.611933\pi$
$864$		0			0
$865$	−25.1535	−	14.5224i	−0.855243	−	0.493775i
$866$		0			0
$867$	0.674794	−	0.0416099i	0.0229172	−	0.00141315i
$868$		0			0
$869$	0.460439	+	0.797504i	0.0156193	+	0.0270535i
$870$		0			0
$871$	45.4452	+	78.7134i	1.53985	+	2.66710i
$872$		0			0
$873$	−1.16079	−	9.37656i	−0.0392868	−	0.317348i
$874$		0			0
$875$		−	15.7471i		−	0.532349i
$876$		0			0
$877$	−1.51881	+	0.876883i	−0.0512864	+	0.0296102i	−0.525424	−	0.850841i	$-0.676093\pi$
$877$	−1.51881	+	0.876883i	−0.0512864	+	0.0296102i	0.474138	+	0.880451i	$0.342760\pi$
$878$		0			0
$879$	30.2553	+	45.6612i	1.02048	+	1.54011i
$880$		0			0
$881$		−	44.2106i		−	1.48949i	−0.667348	−	0.744746i	$-0.732571\pi$
$881$		−	44.2106i		−	1.48949i	0.667348	−	0.744746i	$-0.267429\pi$
$882$		0			0
$883$	8.11102	−	14.0487i	0.272958	−	0.472776i	−0.696660	−	0.717401i	$-0.745331\pi$
$883$	8.11102	−	14.0487i	0.272958	−	0.472776i	0.969618	+	0.244625i	$0.0786648\pi$
$884$		0			0
$885$	1.99607	+	32.3706i	0.0670973	+	1.08812i
$886$		0			0
$887$	−13.6974	+	23.7245i	−0.459913	+	0.796592i	−0.998956	−	0.0456862i	$-0.985453\pi$
$887$	−13.6974	+	23.7245i	−0.459913	+	0.796592i	0.539043	+	0.842278i	$0.318786\pi$
$888$		0			0
$889$	14.4391	+	8.33641i	0.484272	+	0.279594i
$890$		0			0
$891$	5.12920	−	4.97303i	0.171835	−	0.166603i
$892$		0			0
$893$	13.6333	−	29.6422i	0.456220	−	0.991939i
$894$		0			0
$895$	−4.18473	+	2.41605i	−0.139880	+	0.0807597i
$896$		0			0
$897$	20.2420	−	40.6500i	0.675862	−	1.35726i
$898$		0			0
$899$	−4.03439	−	2.32926i	−0.134555	−	0.0776851i
$900$		0			0
$901$		−	35.2238i		−	1.17347i
$902$		0			0
$903$	7.88128	−	15.8272i	0.262273	−	0.526695i
$904$		0			0
$905$	−9.09644			−0.302376
$906$		0			0
$907$	13.9353	−	8.04555i	0.462714	−	0.267148i	−0.250471	−	0.968124i	$-0.580585\pi$
$907$	13.9353	−	8.04555i	0.462714	−	0.267148i	0.713185	+	0.700976i	$0.247252\pi$
$908$		0			0
$909$	−23.5773	+	17.8036i	−0.782008	+	0.590509i
$910$		0			0
$911$	−34.6402			−1.14768			−0.573840	−	0.818967i	$-0.694547\pi$
$911$	−34.6402			−1.14768			−0.573840	+	0.818967i	$0.694547\pi$
$912$		0			0
$913$	10.1251			0.335092
$914$		0			0
$915$	−7.19401	+	4.76677i	−0.237827	+	0.157585i
$916$		0			0
$917$	11.5072	−	6.64369i	0.380002	−	0.219394i
$918$		0			0
$919$	6.69808			0.220949			0.110475	−	0.993879i	$-0.464763\pi$
$919$	6.69808			0.220949			0.110475	+	0.993879i	$0.464763\pi$
$920$		0			0
$921$	43.6599	+	21.7408i	1.43864	+	0.716385i
$922$		0			0
$923$			68.2181i			2.24543i
$924$		0			0
$925$	−1.66124	−	0.959115i	−0.0546211	−	0.0315355i
$926$		0			0
$927$	10.0505	+	4.25437i	0.330102	+	0.139732i
$928$		0			0
$929$	10.8891	−	6.28680i	0.357258	−	0.206263i	−0.310619	−	0.950534i	$-0.600536\pi$
$929$	10.8891	−	6.28680i	0.357258	−	0.206263i	0.667877	+	0.744271i	$0.267203\pi$
$930$		0			0
$931$	2.13771	+	23.0395i	0.0700606	+	0.755090i
$932$		0			0
$933$	−9.99206	+	6.62077i	−0.327125	+	0.216754i
$934$		0			0
$935$	5.54193	+	3.19963i	0.181240	+	0.104639i
$936$		0			0
$937$	19.1946	−	33.2459i	0.627059	−	1.08610i	−0.361080	−	0.932535i	$-0.617592\pi$
$937$	19.1946	−	33.2459i	0.627059	−	1.08610i	0.988139	−	0.153563i	$-0.0490747\pi$
$938$		0			0
$939$	−6.79560	+	0.419038i	−0.221766	+	0.0136748i
$940$		0			0
$941$	−8.21882	+	14.2354i	−0.267926	+	0.464061i	−0.968326	−	0.249689i	$-0.919672\pi$
$941$	−8.21882	+	14.2354i	−0.267926	+	0.464061i	0.700400	+	0.713750i	$0.253005\pi$
$942$		0			0
$943$		−	34.7450i		−	1.13145i
$944$		0			0
$945$	9.92187	−	8.49978i	0.322758	−	0.276498i
$946$		0			0
$947$	−1.67734	+	0.968410i	−0.0545061	+	0.0314691i	−0.527005	−	0.849862i	$-0.676685\pi$
$947$	−1.67734	+	0.968410i	−0.0545061	+	0.0314691i	0.472499	+	0.881331i	$0.343352\pi$
$948$		0			0
$949$		−	52.3897i		−	1.70064i
$950$		0			0
$951$	−51.7412	+	3.19053i	−1.67782	+	0.103460i
$952$		0			0
$953$	8.51948	+	14.7562i	0.275973	+	0.477999i	0.970380	−	0.241583i	$-0.0776666\pi$
$953$	8.51948	+	14.7562i	0.275973	+	0.477999i	−0.694407	+	0.719582i	$0.744333\pi$
$954$		0			0
$955$	−3.88987	−	6.73745i	−0.125873	−	0.218019i
$956$		0			0
$957$	−0.0760843	−	1.23387i	−0.00245946	−	0.0398853i
$958$		0			0
$959$	7.13377	+	4.11868i	0.230361	+	0.132999i
$960$		0			0
$961$	4.15564			0.134053
$962$		0			0
$963$	−0.00678826	+	0.0160366i	−0.000218749	+	0.000516772i
$964$		0			0
$965$	20.4298	−	35.3855i	0.657659	−	1.13910i
$966$		0			0
$967$	26.5406	+	45.9696i	0.853487	+	1.47828i	0.878042	+	0.478584i	$0.158850\pi$
$967$	26.5406	+	45.9696i	0.853487	+	1.47828i	−0.0245550	+	0.999698i	$0.507817\pi$
$968$		0			0
$969$	−11.3703	+	29.3593i	−0.365266	+	0.943155i
$970$		0			0
$971$	8.69902	+	15.0671i	0.279165	+	0.483527i	0.971177	−	0.238358i	$-0.0766091\pi$
$971$	8.69902	+	15.0671i	0.279165	+	0.483527i	−0.692013	+	0.721885i	$0.743276\pi$
$972$		0			0
$973$	−9.05893	+	15.6905i	−0.290416	+	0.503015i
$974$		0			0
$975$	−13.3616	−	6.65352i	−0.427913	−	0.213083i
$976$		0			0
$977$	29.5379			0.945001			0.472500	−	0.881330i	$-0.343352\pi$
$977$	29.5379			0.945001			0.472500	+	0.881330i	$0.343352\pi$
$978$		0			0
$979$	1.80098	+	1.03979i	0.0575594	+	0.0332320i
$980$		0			0
$981$	4.70305	+	37.9900i	0.150157	+	1.21293i
$982$		0			0
$983$	15.0373	+	26.0453i	0.479614	+	0.830716i	0.999727	−	0.0233820i	$-0.00744339\pi$
$983$	15.0373	+	26.0453i	0.479614	+	0.830716i	−0.520113	+	0.854098i	$0.674110\pi$
$984$		0			0
$985$	18.1549	+	31.4451i	0.578462	+	1.00193i
$986$		0			0
$987$	1.03782	+	16.8304i	0.0330341	+	0.535719i
$988$		0			0
$989$			30.1561i			0.958907i
$990$		0			0
$991$	18.5003	−	10.6812i	0.587682	−	0.339299i	−0.176498	−	0.984301i	$-0.556477\pi$
$991$	18.5003	−	10.6812i	0.587682	−	0.339299i	0.764181	+	0.645002i	$0.223144\pi$
$992$		0			0
$993$	−28.7716	+	19.0641i	−0.913039	+	0.604982i
$994$		0			0
$995$		−	19.0386i		−	0.603563i
$996$		0			0
$997$	−17.6952	+	30.6490i	−0.560413	+	0.970664i	0.437047	+	0.899439i	$0.356024\pi$
$997$	−17.6952	+	30.6490i	−0.560413	+	0.970664i	−0.997460	+	0.0712253i	$0.977309\pi$
$998$		0			0
$999$	−1.44984	−	7.75785i	−0.0458710	−	0.245448i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bn.o.449.5		16
3.2	odd	2		912.2.bn.n.449.3		16
4.3	odd	2		456.2.bf.c.449.4	yes	16
12.11	even	2		456.2.bf.d.449.6	yes	16
19.8	odd	6		912.2.bn.n.65.3		16
57.8	even	6	inner	912.2.bn.o.65.5		16
76.27	even	6		456.2.bf.d.65.6	yes	16
228.179	odd	6		456.2.bf.c.65.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bf.c.65.4	✓	16	228.179	odd	6
456.2.bf.c.449.4	yes	16	4.3	odd	2
456.2.bf.d.65.6	yes	16	76.27	even	6
456.2.bf.d.449.6	yes	16	12.11	even	2
912.2.bn.n.65.3		16	19.8	odd	6
912.2.bn.n.449.3		16	3.2	odd	2
912.2.bn.o.65.5		16	57.8	even	6	inner
912.2.bn.o.449.5		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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bn (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.956703 + 1.44386i) q^{3} +(-1.67415 + 0.966572i) q^{5} +1.30064 q^{7} +(-1.16944 + 2.76268i) q^{9} +O(q^{10})\)	\(q+(0.956703 + 1.44386i) q^{3} +(-1.67415 + 0.966572i) q^{5} +1.30064 q^{7} +(-1.16944 + 2.76268i) q^{9} +0.793801i q^{11} +(5.90939 + 3.41179i) q^{13} +(-2.99726 - 1.49251i) q^{15} +(-3.61147 + 2.08509i) q^{17} +(-0.402708 - 4.34026i) q^{19} +(1.24433 + 1.87794i) q^{21} +(-3.32751 - 1.92114i) q^{23} +(-0.631475 + 1.09375i) q^{25} +(-5.10772 + 0.954566i) q^{27} +(-0.449563 + 0.778667i) q^{29} +5.18115i q^{31} +(-1.14613 + 0.759432i) q^{33} +(-2.17747 + 1.25716i) q^{35} +1.51885i q^{37} +(0.727402 + 11.7964i) q^{39} +(4.52140 + 7.83130i) q^{41} +(-3.92424 - 6.79699i) q^{43} +(-0.712514 - 5.75550i) q^{45} +(6.48235 + 3.74258i) q^{47} -5.30833 q^{49} +(-6.46567 - 3.21964i) q^{51} +(-4.22330 + 7.31497i) q^{53} +(-0.767266 - 1.32894i) q^{55} +(5.88143 - 4.73379i) q^{57} +(-4.84305 - 8.38842i) q^{59} +(1.28870 - 2.23210i) q^{61} +(-1.52102 + 3.59326i) q^{63} -13.1910 q^{65} +(11.5355 + 6.66003i) q^{67} +(-0.409592 - 6.64240i) q^{69} +(4.99871 + 8.65802i) q^{71} +(-3.83888 - 6.64913i) q^{73} +(-2.18335 + 0.134632i) q^{75} +1.03245i q^{77} +(1.00467 - 0.580044i) q^{79} +(-6.26483 - 6.46157i) q^{81} -12.7552i q^{83} +(4.03077 - 6.98150i) q^{85} +(-1.55438 + 0.0958481i) q^{87} +(1.30989 - 2.26880i) q^{89} +(7.68599 + 4.43751i) q^{91} +(-7.48084 + 4.95683i) q^{93} +(4.86937 + 6.87700i) q^{95} +(-2.72744 + 1.57469i) q^{97} +(-2.19302 - 0.928302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{3} - 3 q^{5} + 13 q^{9}+O(q^{10}) \) 16 * q + q^3 - 3 * q^5 + 13 * q^9	\( 16 q + q^{3} - 3 q^{5} + 13 q^{9} - 3 q^{13} - 15 q^{15} + 3 q^{17} - 11 q^{19} - 6 q^{21} - 3 q^{23} + 11 q^{25} + 4 q^{27} - 5 q^{29} + q^{33} + 24 q^{35} + 9 q^{39} - 6 q^{41} - 13 q^{43} + 33 q^{45} + 27 q^{47} + 8 q^{49} - 15 q^{51} + 7 q^{53} + 12 q^{55} + 23 q^{57} - 10 q^{59} - q^{61} + 8 q^{63} + 30 q^{65} + 24 q^{67} + 41 q^{69} + 27 q^{71} + 2 q^{73} + 21 q^{75} + 21 q^{79} - 7 q^{81} - 5 q^{85} + 23 q^{87} - 25 q^{89} + 78 q^{91} - 56 q^{93} + 13 q^{95} - 60 q^{97} + 35 q^{99}+O(q^{100}) \) 16 * q + q^3 - 3 * q^5 + 13 * q^9 - 3 * q^13 - 15 * q^15 + 3 * q^17 - 11 * q^19 - 6 * q^21 - 3 * q^23 + 11 * q^25 + 4 * q^27 - 5 * q^29 + q^33 + 24 * q^35 + 9 * q^39 - 6 * q^41 - 13 * q^43 + 33 * q^45 + 27 * q^47 + 8 * q^49 - 15 * q^51 + 7 * q^53 + 12 * q^55 + 23 * q^57 - 10 * q^59 - q^61 + 8 * q^63 + 30 * q^65 + 24 * q^67 + 41 * q^69 + 27 * q^71 + 2 * q^73 + 21 * q^75 + 21 * q^79 - 7 * q^81 - 5 * q^85 + 23 * q^87 - 25 * q^89 + 78 * q^91 - 56 * q^93 + 13 * q^95 - 60 * q^97 + 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more