LMFDB - Embedded newform 896.2.z.a.159.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [896,2,Mod(31,896)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("896.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(896, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.z (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [56,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			159.11
Character	$\chi$	$=$	896.159
Dual form			896.2.z.a.479.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.67893 + 0.449868i) q^{3} +(-0.195879 - 0.731029i) q^{5} +(-2.52163 - 0.800849i) q^{7} +(0.0183525 + 0.0105958i) q^{9} +(-4.42364 - 1.18531i) q^{11} +(-2.89529 - 2.89529i) q^{13} -1.31547i q^{15} +(-2.28427 + 1.31882i) q^{17} +(-1.44161 - 5.38016i) q^{19} +(-3.87337 - 2.47897i) q^{21} +(-1.01143 + 1.75184i) q^{23} +(3.83409 - 2.21361i) q^{25} +(-3.66114 - 3.66114i) q^{27} +(0.209526 - 0.209526i) q^{29} +(3.33052 + 5.76864i) q^{31} +(-6.89376 - 3.98011i) q^{33} +(-0.0915096 + 2.00026i) q^{35} +(3.82183 - 1.02406i) q^{37} +(-3.55850 - 6.16350i) q^{39} +5.04472 q^{41} +(-3.79454 + 3.79454i) q^{43} +(0.00415099 - 0.0154917i) q^{45} +(-2.53993 + 4.39928i) q^{47} +(5.71728 + 4.03890i) q^{49} +(-4.42843 + 1.18659i) q^{51} +(2.87599 - 10.7333i) q^{53} +3.46599i q^{55} -9.68145i q^{57} +(-1.40190 + 5.23198i) q^{59} +(5.84791 - 1.56694i) q^{61} +(-0.0377926 - 0.0414163i) q^{63} +(-1.54942 + 2.68367i) q^{65} +(-2.47586 + 9.24005i) q^{67} +(-2.48621 + 2.48621i) q^{69} +7.25507 q^{71} +(-3.29633 - 5.70940i) q^{73} +(7.43301 - 1.99167i) q^{75} +(10.2056 + 6.53159i) q^{77} +(-13.0615 - 7.54108i) q^{79} +(-4.53156 - 7.84890i) q^{81} +(8.00548 - 8.00548i) q^{83} +(1.41154 + 1.41154i) q^{85} +(0.446039 - 0.257521i) q^{87} +(-3.92536 + 6.79892i) q^{89} +(4.98218 + 9.61956i) q^{91} +(2.99659 + 11.1834i) q^{93} +(-3.65067 + 2.10772i) q^{95} -8.79532i q^{97} +(-0.0686254 - 0.0686254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{3} + 6 q^{5} + 8 q^{7} + 2 q^{11} - 12 q^{17} - 6 q^{19} + 10 q^{21} + 12 q^{23} + 24 q^{29} - 12 q^{33} - 2 q^{35} - 6 q^{37} + 4 q^{39} - 12 q^{45} - 8 q^{49} - 34 q^{51} - 6 q^{53} + 42 q^{59}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q - 6 * q^3 + 6 * q^5 + 8 * q^7 + 2 * q^11 - 12 * q^17 - 6 * q^19 + 10 * q^21 + 12 * q^23 + 24 * q^29 - 12 * q^33 - 2 * q^35 - 6 * q^37 + 4 * q^39 - 12 * q^45 - 8 * q^49 - 34 * q^51 - 6 * q^53 + 42 * q^59 + 6 * q^61 - 4 * q^65 + 6 * q^67 + 80 * q^71 + 24 * q^75 - 10 * q^77 - 8 * q^81 + 28 * q^85 + 12 * q^87 + 16 * q^91 - 10 * q^93 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.67893	+	0.449868i	0.969331	+	0.259732i	0.708546	−	0.705665i	$-0.249352\pi$
$3$	1.67893	+	0.449868i	0.969331	+	0.259732i	0.260786	+	0.965397i	$0.416018\pi$
$4$		0			0
$5$	−0.195879	−	0.731029i	−0.0875996	−	0.326926i	0.908194	−	0.418549i	$-0.137461\pi$
$5$	−0.195879	−	0.731029i	−0.0875996	−	0.326926i	−0.995794	+	0.0916229i	$0.970795\pi$
$6$		0			0
$7$	−2.52163	−	0.800849i	−0.953088	−	0.302693i
$7$	−2.52163	−	0.800849i	−0.953088	−	0.302693i
$8$		0			0
$9$	0.0183525	+	0.0105958i	0.00611749	+	0.00353194i
$10$		0			0
$11$	−4.42364	−	1.18531i	−1.33378	−	0.357385i	−0.479656	−	0.877457i	$-0.659238\pi$
$11$	−4.42364	−	1.18531i	−1.33378	−	0.357385i	−0.854122	+	0.520072i	$0.825905\pi$
$12$		0			0
$13$	−2.89529	−	2.89529i	−0.803010	−	0.803010i	0.180555	−	0.983565i	$-0.442211\pi$
$13$	−2.89529	−	2.89529i	−0.803010	−	0.803010i	−0.983565	+	0.180555i	$0.942211\pi$
$14$		0			0
$15$		−	1.31547i		−	0.339652i
$16$		0			0
$17$	−2.28427	+	1.31882i	−0.554017	+	0.319862i	−0.750740	−	0.660597i	$-0.770303\pi$
$17$	−2.28427	+	1.31882i	−0.554017	+	0.319862i	0.196724	+	0.980459i	$0.436970\pi$
$18$		0			0
$19$	−1.44161	−	5.38016i	−0.330728	−	1.23429i	−0.908427	−	0.418043i	$-0.862716\pi$
$19$	−1.44161	−	5.38016i	−0.330728	−	1.23429i	0.577700	−	0.816249i	$-0.303951\pi$
$20$		0			0
$21$	−3.87337	−	2.47897i	−0.845240	−	0.540956i
$22$		0			0
$23$	−1.01143	+	1.75184i	−0.210897	+	0.365284i	−0.951995	−	0.306112i	$-0.900972\pi$
$23$	−1.01143	+	1.75184i	−0.210897	+	0.365284i	0.741099	+	0.671396i	$0.234305\pi$
$24$		0			0
$25$	3.83409	−	2.21361i	0.766818	−	0.442723i
$26$		0			0
$27$	−3.66114	−	3.66114i	−0.704587	−	0.704587i
$28$		0			0
$29$	0.209526	−	0.209526i	0.0389080	−	0.0389080i	−0.687385	−	0.726293i	$-0.741242\pi$
$29$	0.209526	−	0.209526i	0.0389080	−	0.0389080i	0.726293	+	0.687385i	$0.241242\pi$
$30$		0			0
$31$	3.33052	+	5.76864i	0.598180	+	1.03608i	0.993090	+	0.117358i	$0.0374424\pi$
$31$	3.33052	+	5.76864i	0.598180	+	1.03608i	−0.394910	+	0.918720i	$0.629224\pi$
$32$		0			0
$33$	−6.89376	−	3.98011i	−1.20005	−	0.692849i
$34$		0			0
$35$	−0.0915096	+	2.00026i	−0.0154679	+	0.338105i
$36$		0			0
$37$	3.82183	−	1.02406i	0.628305	−	0.168354i	0.0694046	−	0.997589i	$-0.477890\pi$
$37$	3.82183	−	1.02406i	0.628305	−	0.168354i	0.558900	+	0.829235i	$0.311223\pi$
$38$		0			0
$39$	−3.55850	−	6.16350i	−0.569815	−	0.986949i
$40$		0			0
$41$	5.04472			0.787853			0.393926	−	0.919142i	$-0.371117\pi$
$41$	5.04472			0.787853			0.393926	+	0.919142i	$0.371117\pi$
$42$		0			0
$43$	−3.79454	+	3.79454i	−0.578662	+	0.578662i	−0.934534	−	0.355873i	$-0.884184\pi$
$43$	−3.79454	+	3.79454i	−0.578662	+	0.578662i	0.355873	+	0.934534i	$0.384184\pi$
$44$		0			0
$45$	0.00415099	−	0.0154917i	0.000618792	−	0.00230936i
$46$		0			0
$47$	−2.53993	+	4.39928i	−0.370486	+	0.641701i	−0.989640	−	0.143568i	$-0.954142\pi$
$47$	−2.53993	+	4.39928i	−0.370486	+	0.641701i	0.619154	+	0.785270i	$0.287476\pi$
$48$		0			0
$49$	5.71728	+	4.03890i	0.816754	+	0.576985i
$50$		0			0
$51$	−4.42843	+	1.18659i	−0.620104	+	0.166156i
$52$		0			0
$53$	2.87599	−	10.7333i	0.395047	−	1.47434i	−0.426652	−	0.904416i	$-0.640307\pi$
$53$	2.87599	−	10.7333i	0.395047	−	1.47434i	0.821699	−	0.569921i	$-0.193026\pi$
$54$		0			0
$55$			3.46599i			0.467354i
$56$		0			0
$57$		−	9.68145i		−	1.28234i
$58$		0			0
$59$	−1.40190	+	5.23198i	−0.182512	+	0.681145i	0.812637	+	0.582770i	$0.198031\pi$
$59$	−1.40190	+	5.23198i	−0.182512	+	0.681145i	−0.995149	+	0.0983751i	$0.968635\pi$
$60$		0			0
$61$	5.84791	−	1.56694i	0.748748	−	0.200626i	0.135785	−	0.990738i	$-0.456644\pi$
$61$	5.84791	−	1.56694i	0.748748	−	0.200626i	0.612962	+	0.790112i	$0.289978\pi$
$62$		0			0
$63$	−0.0377926	−	0.0414163i	−0.00476142	−	0.00521796i
$64$		0			0
$65$	−1.54942	+	2.68367i	−0.192182	+	0.332868i
$66$		0			0
$67$	−2.47586	+	9.24005i	−0.302475	+	1.12885i	0.632622	+	0.774461i	$0.281979\pi$
$67$	−2.47586	+	9.24005i	−0.302475	+	1.12885i	−0.935097	+	0.354392i	$0.884688\pi$
$68$		0			0
$69$	−2.48621	+	2.48621i	−0.299305	+	0.299305i
$70$		0			0
$71$	7.25507			0.861018			0.430509	−	0.902586i	$-0.358334\pi$
$71$	7.25507			0.861018			0.430509	+	0.902586i	$0.358334\pi$
$72$		0			0
$73$	−3.29633	−	5.70940i	−0.385806	−	0.668235i	0.606075	−	0.795408i	$-0.292743\pi$
$73$	−3.29633	−	5.70940i	−0.385806	−	0.668235i	−0.991881	+	0.127172i	$0.959410\pi$
$74$		0			0
$75$	7.43301	−	1.99167i	0.858290	−	0.229978i
$76$		0			0
$77$	10.2056	+	6.53159i	1.16303	+	0.744344i
$78$		0			0
$79$	−13.0615	−	7.54108i	−1.46954	−	0.848437i	−0.470121	−	0.882602i	$-0.655790\pi$
$79$	−13.0615	−	7.54108i	−1.46954	−	0.848437i	−0.999416	+	0.0341648i	$0.989123\pi$
$80$		0			0
$81$	−4.53156	−	7.84890i	−0.503507	−	0.872100i
$82$		0			0
$83$	8.00548	−	8.00548i	0.878715	−	0.878715i	−0.114687	−	0.993402i	$-0.536586\pi$
$83$	8.00548	−	8.00548i	0.878715	−	0.878715i	0.993402	+	0.114687i	$0.0365864\pi$
$84$		0			0
$85$	1.41154	+	1.41154i	0.153103	+	0.153103i
$86$		0			0
$87$	0.446039	−	0.257521i	0.0478204	−	0.0276091i
$88$		0			0
$89$	−3.92536	+	6.79892i	−0.416087	+	0.720684i	−0.995542	−	0.0943203i	$-0.969932\pi$
$89$	−3.92536	+	6.79892i	−0.416087	+	0.720684i	0.579455	+	0.815004i	$0.303266\pi$
$90$		0			0
$91$	4.98218	+	9.61956i	0.522274	+	1.00840i
$92$		0			0
$93$	2.99659	+	11.1834i	0.310732	+	1.15967i
$94$		0			0
$95$	−3.65067	+	2.10772i	−0.374551	+	0.216247i
$96$		0			0
$97$		−	8.79532i		−	0.893029i	−0.894776	−	0.446514i	$-0.852665\pi$
$97$		−	8.79532i		−	0.893029i	0.894776	−	0.446514i	$-0.147335\pi$
$98$		0			0
$99$	−0.0686254	−	0.0686254i	−0.00689712	−	0.00689712i
$100$		0			0
$101$	−2.22819	−	0.597042i	−0.221713	−	0.0594079i	0.146252	−	0.989247i	$-0.453279\pi$
$101$	−2.22819	−	0.597042i	−0.221713	−	0.0594079i	−0.367966	+	0.929839i	$0.619946\pi$
$102$		0			0
$103$	−11.8007	−	6.81315i	−1.16276	−	0.671319i	−0.210795	−	0.977530i	$-0.567605\pi$
$103$	−11.8007	−	6.81315i	−1.16276	−	0.671319i	−0.951964	+	0.306211i	$0.900939\pi$
$104$		0			0
$105$	−1.05349	+	3.31713i	−0.102810	+	0.323719i
$106$		0			0
$107$	−1.22282	−	4.56363i	−0.118215	−	0.441183i	0.881293	−	0.472571i	$-0.156674\pi$
$107$	−1.22282	−	4.56363i	−0.118215	−	0.441183i	−0.999507	+	0.0313881i	$0.990007\pi$
$108$		0			0
$109$	−7.95931	−	2.13269i	−0.762364	−	0.204275i	−0.143368	−	0.989669i	$-0.545793\pi$
$109$	−7.95931	−	2.13269i	−0.762364	−	0.204275i	−0.618995	+	0.785395i	$0.712460\pi$
$110$		0			0
$111$	6.87728			0.652763
$112$		0			0
$113$	18.4851			1.73893			0.869467	−	0.493990i	$-0.164462\pi$
$113$	18.4851			1.73893			0.869467	+	0.493990i	$0.164462\pi$
$114$		0			0
$115$	1.47876	+	0.396233i	0.137895	+	0.0369490i
$116$		0			0
$117$	−0.0224578	−	0.0838137i	−0.00207623	−	0.00774858i
$118$		0			0
$119$	6.81627	−	1.49624i	0.624847	−	0.137160i
$120$		0			0
$121$	8.63736	+	4.98678i	0.785215	+	0.453344i
$122$		0			0
$123$	8.46974	+	2.26946i	0.763690	+	0.204630i
$124$		0			0
$125$	−5.04499	−	5.04499i	−0.451237	−	0.451237i
$126$		0			0
$127$		−	13.0667i		−	1.15948i	−0.814802	−	0.579739i	$-0.803154\pi$
$127$		−	13.0667i		−	1.15948i	0.814802	−	0.579739i	$-0.196846\pi$
$128$		0			0
$129$	−8.07781	+	4.66373i	−0.711212	+	0.410618i
$130$		0			0
$131$	−2.22382	−	8.29942i	−0.194296	−	0.725124i	−0.992448	−	0.122667i	$-0.960855\pi$
$131$	−2.22382	−	8.29942i	−0.194296	−	0.725124i	0.798152	−	0.602457i	$-0.205811\pi$
$132$		0			0
$133$	−0.673483	+	14.7213i	−0.0583984	+	1.27650i
$134$		0			0
$135$	−1.95926	+	3.39354i	−0.168626	+	0.292070i
$136$		0			0
$137$	−19.9938	+	11.5434i	−1.70818	+	0.986221i	−0.771376	+	0.636380i	$0.780431\pi$
$137$	−19.9938	+	11.5434i	−1.70818	+	0.986221i	−0.936809	+	0.349841i	$0.886236\pi$
$138$		0			0
$139$	−6.09369	−	6.09369i	−0.516860	−	0.516860i	0.399760	−	0.916620i	$-0.369093\pi$
$139$	−6.09369	−	6.09369i	−0.516860	−	0.516860i	−0.916620	+	0.399760i	$0.869093\pi$
$140$		0			0
$141$	−6.24346	+	6.24346i	−0.525794	+	0.525794i
$142$		0			0
$143$	9.37591	+	16.2396i	0.784053	+	1.35802i
$144$		0			0
$145$	−0.194211	−	0.112128i	−0.0161284	−	0.00931173i
$146$		0			0
$147$	7.78195	+	9.35305i	0.641844	+	0.771427i
$148$		0			0
$149$	−11.6694	+	3.12680i	−0.955992	+	0.256157i	−0.702903	−	0.711286i	$-0.748113\pi$
$149$	−11.6694	+	3.12680i	−0.955992	+	0.256157i	−0.253089	+	0.967443i	$0.581447\pi$
$150$		0			0
$151$	0.813682	+	1.40934i	0.0662165	+	0.114690i	0.897233	−	0.441557i	$-0.145574\pi$
$151$	0.813682	+	1.40934i	0.0662165	+	0.114690i	−0.831016	+	0.556248i	$0.812241\pi$
$152$		0			0
$153$	−0.0558960			−0.00451892
$154$		0			0
$155$	3.56466	−	3.56466i	0.286321	−	0.286321i
$156$		0			0
$157$	6.22579	−	23.2350i	0.496872	−	1.85435i	−0.0224085	−	0.999749i	$-0.507133\pi$
$157$	6.22579	−	23.2350i	0.496872	−	1.85435i	0.519281	−	0.854604i	$-0.326200\pi$
$158$		0			0
$159$	9.65717	−	16.7267i	0.765864	−	1.32651i
$160$		0			0
$161$	3.95341	−	3.60750i	0.311572	−	0.284311i
$162$		0			0
$163$	−8.80794	+	2.36008i	−0.689891	+	0.184856i	−0.586698	−	0.809806i	$-0.699573\pi$
$163$	−8.80794	+	2.36008i	−0.689891	+	0.184856i	−0.103193	+	0.994661i	$0.532906\pi$
$164$		0			0
$165$	−1.55924	+	5.81916i	−0.121387	+	0.453021i
$166$		0			0
$167$			3.18749i			0.246656i	0.992366	+	0.123328i	$0.0393566\pi$
$167$			3.18749i			0.246656i	−0.992366	+	0.123328i	$0.960643\pi$
$168$		0			0
$169$			3.76544i			0.289649i
$170$		0			0
$171$	0.0305500	−	0.114014i	0.00233622	−	0.00871888i
$172$		0			0
$173$	−18.6115	+	4.98693i	−1.41500	+	0.379149i	−0.883708	−	0.468038i	$-0.844961\pi$
$173$	−18.6115	+	4.98693i	−1.41500	+	0.379149i	−0.531295	+	0.847187i	$0.678294\pi$
$174$		0			0
$175$	−11.4409	+	2.51140i	−0.864854	+	0.189844i
$176$		0			0
$177$	−4.70740	+	8.15345i	−0.353830	+	0.612851i
$178$		0			0
$179$	1.88392	−	7.03090i	0.140811	−	0.525514i	−0.859095	−	0.511816i	$-0.828973\pi$
$179$	1.88392	−	7.03090i	0.140811	−	0.525514i	0.999906	−	0.0136980i	$-0.00436034\pi$
$180$		0			0
$181$	5.59617	−	5.59617i	0.415960	−	0.415960i	−0.467849	−	0.883809i	$-0.654971\pi$
$181$	5.59617	−	5.59617i	0.415960	−	0.415960i	0.883809	+	0.467849i	$0.154971\pi$
$182$		0			0
$183$	10.5231			0.777894
$184$		0			0
$185$	−1.49723	−	2.59328i	−0.110079	−	0.190662i
$186$		0			0
$187$	11.6680	−	3.12643i	0.853249	−	0.228627i
$188$		0			0
$189$	6.30004	+	12.1641i	0.458261	+	0.884807i
$190$		0			0
$191$	4.12735	+	2.38292i	0.298644	+	0.172422i	0.641834	−	0.766844i	$-0.278174\pi$
$191$	4.12735	+	2.38292i	0.298644	+	0.172422i	−0.343189	+	0.939266i	$0.611507\pi$
$192$		0			0
$193$	2.67050	+	4.62543i	0.192226	+	0.332946i	0.945988	−	0.324202i	$-0.105096\pi$
$193$	2.67050	+	4.62543i	0.192226	+	0.332946i	−0.753761	+	0.657148i	$0.771763\pi$
$194$		0			0
$195$	−3.80866	+	3.80866i	−0.272744	+	0.272744i
$196$		0			0
$197$	11.6754	+	11.6754i	0.831838	+	0.831838i	0.987768	−	0.155930i	$-0.0498374\pi$
$197$	11.6754	+	11.6754i	0.831838	+	0.831838i	−0.155930	+	0.987768i	$0.549837\pi$
$198$		0			0
$199$	9.02919	−	5.21301i	0.640062	−	0.369540i	−0.144576	−	0.989494i	$-0.546182\pi$
$199$	9.02919	−	5.21301i	0.640062	−	0.369540i	0.784639	+	0.619953i	$0.212849\pi$
$200$		0			0
$201$	−8.31361	+	14.3996i	−0.586397	+	1.01567i
$202$		0			0
$203$	−0.696147	+	0.360549i	−0.0488599	+	0.0253056i
$204$		0			0
$205$	−0.988153	−	3.68784i	−0.0690156	−	0.257570i
$206$		0			0
$207$	−0.0371243	+	0.0214337i	−0.00258032	+	0.00148975i
$208$		0			0
$209$			25.5086i			1.76447i
$210$		0			0
$211$	−0.716512	−	0.716512i	−0.0493267	−	0.0493267i	0.682013	−	0.731340i	$-0.261105\pi$
$211$	−0.716512	−	0.716512i	−0.0493267	−	0.0493267i	−0.731340	+	0.682013i	$0.761105\pi$
$212$		0			0
$213$	12.1808	+	3.26383i	0.834612	+	0.223634i
$214$		0			0
$215$	3.51719	+	2.03065i	0.239870	+	0.138489i
$216$		0			0
$217$	−3.77856	−	17.2136i	−0.256505	−	1.16854i
$218$		0			0
$219$	−2.96583	−	11.0686i	−0.200412	−	0.747947i
$220$		0			0
$221$	10.4320	+	2.79525i	0.701733	+	0.188029i
$222$		0			0
$223$	12.9181			0.865062			0.432531	−	0.901619i	$-0.357621\pi$
$223$	12.9181			0.865062			0.432531	+	0.901619i	$0.357621\pi$
$224$		0			0
$225$	0.0938201			0.00625467
$226$		0			0
$227$	15.0241	+	4.02569i	0.997184	+	0.267195i	0.720265	−	0.693699i	$-0.244020\pi$
$227$	15.0241	+	4.02569i	0.997184	+	0.267195i	0.276919	+	0.960893i	$0.410687\pi$
$228$		0			0
$229$	3.58406	+	13.3759i	0.236841	+	0.883903i	0.977310	+	0.211813i	$0.0679367\pi$
$229$	3.58406	+	13.3759i	0.236841	+	0.883903i	−0.740469	+	0.672090i	$0.765397\pi$
$230$		0			0
$231$	14.1961	+	15.5572i	0.934032	+	1.02359i
$232$		0			0
$233$	10.6523	+	6.15010i	0.697854	+	0.402906i	0.806548	−	0.591169i	$-0.201333\pi$
$233$	10.6523	+	6.15010i	0.697854	+	0.402906i	−0.108694	+	0.994075i	$0.534667\pi$
$234$		0			0
$235$	3.71352	+	0.995035i	0.242243	+	0.0649089i
$236$		0			0
$237$	−18.5369	−	18.5369i	−1.20410	−	1.20410i
$238$		0			0
$239$			7.20218i			0.465870i	0.972492	+	0.232935i	$0.0748329\pi$
$239$			7.20218i			0.465870i	−0.972492	+	0.232935i	$0.925167\pi$
$240$		0			0
$241$	20.7383	−	11.9733i	1.33587	−	0.771265i	0.349678	−	0.936870i	$-0.386291\pi$
$241$	20.7383	−	11.9733i	1.33587	−	0.771265i	0.986192	+	0.165605i	$0.0529577\pi$
$242$		0			0
$243$	−0.0569986	−	0.212722i	−0.00365646	−	0.0136461i
$244$		0			0
$245$	1.83266	−	4.97063i	0.117084	−	0.317562i
$246$		0			0
$247$	−11.4032	+	19.7510i	−0.725571	+	1.25673i
$248$		0			0
$249$	17.0421	−	9.83923i	1.08000	−	0.623536i
$250$		0			0
$251$	6.11266	+	6.11266i	0.385828	+	0.385828i	0.873196	−	0.487369i	$-0.162043\pi$
$251$	6.11266	+	6.11266i	0.385828	+	0.385828i	−0.487369	+	0.873196i	$0.662043\pi$
$252$		0			0
$253$	6.55066	−	6.55066i	0.411837	−	0.411837i
$254$		0			0
$255$	1.73487	+	3.00488i	0.108642	+	0.188173i
$256$		0			0
$257$	−19.7315	−	11.3920i	−1.23082	−	0.710613i	−0.263617	−	0.964627i	$-0.584915\pi$
$257$	−19.7315	−	11.3920i	−1.23082	−	0.710613i	−0.967200	+	0.254015i	$0.918249\pi$
$258$		0			0
$259$	−10.4574	−	0.478413i	−0.649790	−	0.0297272i
$260$		0			0
$261$	0.00606542	−	0.00162522i	0.000375440	−	0.000100599i
$262$		0			0
$263$	5.28788	+	9.15888i	0.326065	+	0.564761i	0.981727	−	0.190293i	$-0.0609439\pi$
$263$	5.28788	+	9.15888i	0.326065	+	0.564761i	−0.655662	+	0.755054i	$0.727611\pi$
$264$		0			0
$265$	−8.40973			−0.516605
$266$		0			0
$267$	−9.64903	+	9.64903i	−0.590511	+	0.590511i
$268$		0			0
$269$	−2.68103	+	10.0057i	−0.163465	+	0.610061i	0.834766	+	0.550605i	$0.185603\pi$
$269$	−2.68103	+	10.0057i	−0.163465	+	0.610061i	−0.998231	+	0.0594553i	$0.981064\pi$
$270$		0			0
$271$	12.3322	−	21.3601i	0.749131	−	1.29753i	−0.199109	−	0.979977i	$-0.563805\pi$
$271$	12.3322	−	21.3601i	0.749131	−	1.29753i	0.948240	−	0.317555i	$-0.102862\pi$
$272$		0			0
$273$	4.03720	+	18.3919i	0.244342	+	1.11313i
$274$		0			0
$275$	−19.5845	+	5.24764i	−1.18099	+	0.316445i
$276$		0			0
$277$	−2.77622	+	10.3610i	−0.166807	+	0.622531i	0.830996	+	0.556278i	$0.187771\pi$
$277$	−2.77622	+	10.3610i	−0.166807	+	0.622531i	−0.997803	+	0.0662529i	$0.978896\pi$
$278$		0			0
$279$			0.141158i			0.00845093i
$280$		0			0
$281$			6.46396i			0.385608i	0.981237	+	0.192804i	$0.0617581\pi$
$281$			6.46396i			0.385608i	−0.981237	+	0.192804i	$0.938242\pi$
$282$		0			0
$283$	5.09979	−	19.0327i	0.303151	−	1.13138i	−0.631374	−	0.775478i	$-0.717509\pi$
$283$	5.09979	−	19.0327i	0.303151	−	1.13138i	0.934525	−	0.355897i	$-0.115825\pi$
$284$		0			0
$285$	−7.07742	+	1.89639i	−0.419230	+	0.112332i
$286$		0			0
$287$	−12.7209	−	4.04006i	−0.750893	−	0.238477i
$288$		0			0
$289$	−5.02141	+	8.69734i	−0.295377	+	0.511608i
$290$		0			0
$291$	3.95673	−	14.7667i	0.231948	−	0.865641i
$292$		0			0
$293$	2.96394	−	2.96394i	0.173155	−	0.173155i	−0.615209	−	0.788364i	$-0.710928\pi$
$293$	2.96394	−	2.96394i	0.173155	−	0.173155i	0.788364	+	0.615209i	$0.210928\pi$
$294$		0			0
$295$	4.09933			0.238672
$296$		0			0
$297$	11.8560	+	20.5352i	0.687954	+	1.19157i
$298$		0			0
$299$	8.00046	−	2.14372i	0.462679	−	0.123974i
$300$		0			0
$301$	12.6073	−	6.52959i	0.726672	−	0.376359i
$302$		0			0
$303$	−3.47239	−	2.00479i	−0.199484	−	0.115172i
$304$		0			0
$305$	−2.29096	−	3.96806i	−0.131180	−	0.227210i
$306$		0			0
$307$	−8.60981	+	8.60981i	−0.491388	+	0.491388i	−0.908743	−	0.417356i	$-0.862957\pi$
$307$	−8.60981	+	8.60981i	−0.491388	+	0.491388i	0.417356	+	0.908743i	$0.362957\pi$
$308$		0			0
$309$	−16.7476	−	16.7476i	−0.952736	−	0.952736i
$310$		0			0
$311$	−4.98997	+	2.88096i	−0.282955	+	0.163364i	−0.634760	−	0.772709i	$-0.718901\pi$
$311$	−4.98997	+	2.88096i	−0.282955	+	0.163364i	0.351805	+	0.936073i	$0.385568\pi$
$312$		0			0
$313$	4.01618	−	6.95623i	0.227008	−	0.393190i	−0.729912	−	0.683541i	$-0.760439\pi$
$313$	4.01618	−	6.95623i	0.227008	−	0.393190i	0.956920	+	0.290352i	$0.0937723\pi$
$314$		0			0
$315$	−0.0228738	+	0.0357401i	−0.00128879	+	0.00201372i
$316$		0			0
$317$	2.41473	+	9.01190i	0.135625	+	0.506159i	0.999995	+	0.00330181i	$0.00105100\pi$
$317$	2.41473	+	9.01190i	0.135625	+	0.506159i	−0.864370	+	0.502857i	$0.832282\pi$
$318$		0			0
$319$	−1.17522	+	0.678515i	−0.0657998	+	0.0379895i
$320$		0			0
$321$		−	8.21213i		−	0.458356i
$322$		0			0
$323$	10.3885	+	10.3885i	0.578031	+	0.578031i
$324$		0			0
$325$	−17.5099	−	4.69176i	−0.971273	−	0.260252i
$326$		0			0
$327$	−12.4037	−	7.16128i	−0.685926	−	0.396020i
$328$		0			0
$329$	9.92793	−	9.05928i	0.547344	−	0.499454i
$330$		0			0
$331$	−1.32915	−	4.96046i	−0.0730568	−	0.272652i	0.919729	−	0.392554i	$-0.128408\pi$
$331$	−1.32915	−	4.96046i	−0.0730568	−	0.272652i	−0.992786	+	0.119903i	$0.961742\pi$
$332$		0			0
$333$	0.0809907	+	0.0217014i	0.00443827	+	0.00118923i
$334$		0			0
$335$	7.23972			0.395548
$336$		0			0
$337$	1.50446			0.0819532			0.0409766	−	0.999160i	$-0.486953\pi$
$337$	1.50446			0.0819532			0.0409766	+	0.999160i	$0.486953\pi$
$338$		0			0
$339$	31.0353	+	8.31587i	1.68560	+	0.451656i
$340$		0			0
$341$	−7.89541	−	29.4661i	−0.427561	−	1.59568i
$342$		0			0
$343$	−11.1823	−	14.7633i	−0.603790	−	0.797143i
$344$		0			0
$345$	2.30449	+	1.33050i	0.124070	+	0.0716316i
$346$		0			0
$347$	−8.39020	−	2.24815i	−0.450410	−	0.120687i	0.0264814	−	0.999649i	$-0.491570\pi$
$347$	−8.39020	−	2.24815i	−0.450410	−	0.120687i	−0.476891	+	0.878962i	$0.658236\pi$
$348$		0			0
$349$	15.6677	+	15.6677i	0.838672	+	0.838672i	0.988684	−	0.150012i	$-0.0479313\pi$
$349$	15.6677	+	15.6677i	0.838672	+	0.838672i	−0.150012	+	0.988684i	$0.547931\pi$
$350$		0			0
$351$			21.2002i			1.13158i
$352$		0			0
$353$	21.5439	−	12.4384i	1.14666	−	0.662027i	0.198592	−	0.980082i	$-0.436363\pi$
$353$	21.5439	−	12.4384i	1.14666	−	0.662027i	0.948072	+	0.318056i	$0.103030\pi$
$354$		0			0
$355$	−1.42111	−	5.30367i	−0.0754249	−	0.281490i
$356$		0			0
$357$	12.1172	+	0.554347i	0.641308	+	0.0293391i
$358$		0			0
$359$	4.32864	−	7.49742i	0.228457	−	0.395699i	−0.728894	−	0.684626i	$-0.759965\pi$
$359$	4.32864	−	7.49742i	0.228457	−	0.395699i	0.957351	+	0.288928i	$0.0932987\pi$
$360$		0			0
$361$	−10.4134	+	6.01216i	−0.548072	+	0.316429i
$362$		0			0
$363$	12.2581	+	12.2581i	0.643386	+	0.643386i
$364$		0			0
$365$	−3.52806	+	3.52806i	−0.184667	+	0.184667i
$366$		0			0
$367$	−11.9671	−	20.7276i	−0.624676	−	1.08197i	−0.988603	−	0.150543i	$-0.951898\pi$
$367$	−11.9671	−	20.7276i	−0.624676	−	1.08197i	0.363928	−	0.931427i	$-0.381436\pi$
$368$		0			0
$369$	0.0925831	+	0.0534529i	0.00481968	+	0.00278264i
$370$		0			0
$371$	−15.8480	+	24.7623i	−0.822786	+	1.28560i
$372$		0			0
$373$	2.28564	−	0.612436i	0.118346	−	0.0317107i	−0.199160	−	0.979967i	$-0.563821\pi$
$373$	2.28564	−	0.612436i	0.118346	−	0.0317107i	0.317506	+	0.948256i	$0.397155\pi$
$374$		0			0
$375$	−6.20061	−	10.7398i	−0.320198	−	0.554599i
$376$		0			0
$377$	−1.21328			−0.0624870
$378$		0			0
$379$	−5.34619	+	5.34619i	−0.274615	+	0.274615i	−0.830955	−	0.556340i	$-0.812205\pi$
$379$	−5.34619	+	5.34619i	−0.274615	+	0.274615i	0.556340	+	0.830955i	$0.312205\pi$
$380$		0			0
$381$	5.87828	−	21.9380i	0.301153	−	1.12392i
$382$		0			0
$383$	−12.5700	+	21.7718i	−0.642296	+	1.11249i	0.342623	+	0.939473i	$0.388685\pi$
$383$	−12.5700	+	21.7718i	−0.642296	+	1.11249i	−0.984919	+	0.173016i	$0.944649\pi$
$384$		0			0
$385$	2.77573	−	8.73996i	0.141464	−	0.445429i
$386$		0			0
$387$	−0.109845	+	0.0294330i	−0.00558375	+	0.00149616i
$388$		0			0
$389$	−1.62916	+	6.08010i	−0.0826016	+	0.308273i	−0.994849	−	0.101366i	$-0.967679\pi$
$389$	−1.62916	+	6.08010i	−0.0826016	+	0.308273i	0.912248	+	0.409639i	$0.134345\pi$
$390$		0			0
$391$		−	5.33557i		−	0.269831i
$392$		0			0
$393$		−	14.9346i		−	0.753350i
$394$		0			0
$395$	−2.95427	+	11.0255i	−0.148646	+	0.554753i
$396$		0			0
$397$	−17.4416	+	4.67347i	−0.875371	+	0.234555i	−0.668409	−	0.743794i	$-0.733024\pi$
$397$	−17.4416	+	4.67347i	−0.875371	+	0.234555i	−0.206962	+	0.978349i	$0.566358\pi$
$398$		0			0
$399$	−7.75338	+	24.4131i	−0.388154	+	1.22218i
$400$		0			0
$401$	−7.88832	+	13.6630i	−0.393924	+	0.682296i	−0.992963	−	0.118423i	$-0.962216\pi$
$401$	−7.88832	+	13.6630i	−0.393924	+	0.682296i	0.599039	+	0.800720i	$0.295549\pi$
$402$		0			0
$403$	7.05905	−	26.3447i	0.351636	−	1.31232i
$404$		0			0
$405$	−4.85014	+	4.85014i	−0.241005	+	0.241005i
$406$		0			0
$407$	−18.1202			−0.898186
$408$		0			0
$409$	−14.9850	−	25.9548i	−0.740963	−	1.28338i	−0.952057	−	0.305919i	$-0.901036\pi$
$409$	−14.9850	−	25.9548i	−0.740963	−	1.28338i	0.211095	−	0.977466i	$-0.432297\pi$
$410$		0			0
$411$	−38.7612	+	10.3860i	−1.91195	+	0.512305i
$412$		0			0
$413$	7.72511	−	12.0704i	0.380128	−	0.593946i
$414$		0			0
$415$	−7.42034	−	4.28413i	−0.364250	−	0.210300i
$416$		0			0
$417$	−7.48953	−	12.9722i	−0.366764	−	0.635253i
$418$		0			0
$419$	19.0681	−	19.0681i	0.931537	−	0.931537i	−0.0662653	−	0.997802i	$-0.521108\pi$
$419$	19.0681	−	19.0681i	0.931537	−	0.931537i	0.997802	+	0.0662653i	$0.0211084\pi$
$420$		0			0
$421$	−1.12116	−	1.12116i	−0.0546418	−	0.0546418i	0.679258	−	0.733900i	$-0.262302\pi$
$421$	−1.12116	−	1.12116i	−0.0546418	−	0.0546418i	−0.733900	+	0.679258i	$0.762302\pi$
$422$		0			0
$423$	−0.0932279	+	0.0538251i	−0.00453289	+	0.00261707i
$424$		0			0
$425$	−5.83873	+	10.1130i	−0.283220	+	0.490552i
$426$		0			0
$427$	−16.0012	−	0.732036i	−0.774351	−	0.0354257i
$428$		0			0
$429$	8.43585	+	31.4830i	0.407287	+	1.52001i
$430$		0			0
$431$	14.2383	−	8.22048i	0.685834	−	0.395966i	−0.116216	−	0.993224i	$-0.537076\pi$
$431$	14.2383	−	8.22048i	0.685834	−	0.395966i	0.802049	+	0.597258i	$0.203743\pi$
$432$		0			0
$433$		−	34.3709i		−	1.65176i	−0.563847	−	0.825879i	$-0.690679\pi$
$433$		−	34.3709i		−	1.65176i	0.563847	−	0.825879i	$-0.309321\pi$
$434$		0			0
$435$	−0.275625	−	0.275625i	−0.0132152	−	0.0132152i
$436$		0			0
$437$	10.8833	+	2.91616i	0.520617	+	0.139499i
$438$		0			0
$439$	−8.37299	−	4.83415i	−0.399621	−	0.230721i	0.286699	−	0.958021i	$-0.407442\pi$
$439$	−8.37299	−	4.83415i	−0.399621	−	0.230721i	−0.686321	+	0.727299i	$0.740775\pi$
$440$		0			0
$441$	0.0621309	+	0.134703i	0.00295861	+	0.00641443i
$442$		0			0
$443$	9.00239	+	33.5974i	0.427717	+	1.59626i	0.757918	+	0.652350i	$0.226217\pi$
$443$	9.00239	+	33.5974i	0.427717	+	1.59626i	−0.330202	+	0.943910i	$0.607117\pi$
$444$		0			0
$445$	5.73910	+	1.53779i	0.272060	+	0.0728982i
$446$		0			0
$447$	−20.9987			−0.993205
$448$		0			0
$449$	−35.5072			−1.67569			−0.837844	−	0.545910i	$-0.816184\pi$
$449$	−35.5072			−1.67569			−0.837844	+	0.545910i	$0.816184\pi$
$450$		0			0
$451$	−22.3160	−	5.97956i	−1.05082	−	0.281567i
$452$		0			0
$453$	0.732100	+	2.73223i	0.0343970	+	0.128372i
$454$		0			0
$455$	6.05628	−	5.52638i	0.283923	−	0.259081i
$456$		0			0
$457$	−26.0860	−	15.0607i	−1.22025	−	0.704512i	−0.255279	−	0.966867i	$-0.582167\pi$
$457$	−26.0860	−	15.0607i	−1.22025	−	0.704512i	−0.964971	+	0.262356i	$0.915501\pi$
$458$		0			0
$459$	13.1914	+	3.53464i	0.615724	+	0.164983i
$460$		0			0
$461$	2.37946	+	2.37946i	0.110822	+	0.110822i	0.760344	−	0.649521i	$-0.225031\pi$
$461$	2.37946	+	2.37946i	0.110822	+	0.110822i	−0.649521	+	0.760344i	$0.725031\pi$
$462$		0			0
$463$			1.23324i			0.0573136i	0.999589	+	0.0286568i	$0.00912299\pi$
$463$			1.23324i			0.0573136i	−0.999589	+	0.0286568i	$0.990877\pi$
$464$		0			0
$465$	7.58845	−	4.38120i	0.351906	−	0.203173i
$466$		0			0
$467$	−8.25258	−	30.7990i	−0.381884	−	1.42521i	−0.843021	−	0.537881i	$-0.819225\pi$
$467$	−8.25258	−	30.7990i	−0.381884	−	1.42521i	0.461137	−	0.887329i	$-0.347442\pi$
$468$		0			0
$469$	13.6431	−	21.3172i	0.629980	−	0.984339i
$470$		0			0
$471$	20.9054	−	36.2091i	0.963268	−	1.66843i
$472$		0			0
$473$	21.2834	−	12.2880i	0.978611	−	0.565001i
$474$		0			0
$475$	−17.4368	−	17.4368i	−0.800057	−	0.800057i
$476$		0			0
$477$	0.166510	−	0.166510i	0.00762396	−	0.00762396i
$478$		0			0
$479$	−6.64611	−	11.5114i	−0.303668	−	0.525969i	0.673296	−	0.739373i	$-0.264878\pi$
$479$	−6.64611	−	11.5114i	−0.303668	−	0.525969i	−0.976964	+	0.213404i	$0.931545\pi$
$480$		0			0
$481$	−14.0303	−	8.10037i	−0.639725	−	0.369345i
$482$		0			0
$483$	8.26040	−	4.27824i	0.375861	−	0.194667i
$484$		0			0
$485$	−6.42963	+	1.72281i	−0.291955	+	0.0782290i
$486$		0			0
$487$	−0.642044	−	1.11205i	−0.0290938	−	0.0503919i	0.851112	−	0.524984i	$-0.175929\pi$
$487$	−0.642044	−	1.11205i	−0.0290938	−	0.0503919i	−0.880206	+	0.474592i	$0.842595\pi$
$488$		0			0
$489$	−15.8497			−0.716746
$490$		0			0
$491$	7.08341	−	7.08341i	0.319670	−	0.319670i	−0.528970	−	0.848640i	$-0.677422\pi$
$491$	7.08341	−	7.08341i	0.319670	−	0.319670i	0.848640	+	0.528970i	$0.177422\pi$
$492$		0			0
$493$	−0.202286	+	0.754942i	−0.00911051	+	0.0340009i
$494$		0			0
$495$	−0.0367249	+	0.0636095i	−0.00165066	+	0.00285903i
$496$		0			0
$497$	−18.2946	−	5.81022i	−0.820627	−	0.260624i
$498$		0			0
$499$	−21.9365	+	5.87786i	−0.982011	+	0.263129i	−0.713891	−	0.700256i	$-0.753069\pi$
$499$	−21.9365	+	5.87786i	−0.982011	+	0.263129i	−0.268120	+	0.963386i	$0.586402\pi$
$500$		0			0
$501$	−1.43395	+	5.35158i	−0.0640642	+	0.239091i
$502$		0			0
$503$		−	36.0928i		−	1.60930i	−0.593751	−	0.804649i	$-0.702354\pi$
$503$		−	36.0928i		−	1.60930i	0.593751	−	0.804649i	$-0.297646\pi$
$504$		0			0
$505$			1.74582i			0.0776880i
$506$		0			0
$507$	−1.69395	+	6.32191i	−0.0752310	+	0.280766i
$508$		0			0
$509$	5.25856	−	1.40903i	0.233081	−	0.0624540i	−0.140388	−	0.990097i	$-0.544835\pi$
$509$	5.25856	−	1.40903i	0.233081	−	0.0624540i	0.373469	+	0.927643i	$0.378168\pi$
$510$		0			0
$511$	3.73976	+	17.0369i	0.165437	+	0.753668i
$512$		0			0
$513$	−14.4196	+	24.9755i	−0.636640	+	1.10269i
$514$		0			0
$515$	−2.66910	+	9.96122i	−0.117615	+	0.438944i
$516$		0			0
$517$	16.4502	−	16.4502i	0.723481	−	0.723481i
$518$		0			0
$519$	−33.4908			−1.47008
$520$		0			0
$521$	−2.57861	−	4.46629i	−0.112971	−	0.195672i	0.803996	−	0.594635i	$-0.202703\pi$
$521$	−2.57861	−	4.46629i	−0.112971	−	0.195672i	−0.916967	+	0.398963i	$0.869370\pi$
$522$		0			0
$523$	7.42474	−	1.98945i	0.324661	−	0.0869928i	−0.0928072	−	0.995684i	$-0.529584\pi$
$523$	7.42474	−	1.98945i	0.324661	−	0.0869928i	0.417469	+	0.908691i	$0.362917\pi$
$524$		0			0
$525$	−20.3384	−	0.930458i	−0.887639	−	0.0406085i
$526$		0			0
$527$	−15.2156	−	8.78475i	−0.662803	−	0.382670i
$528$		0			0
$529$	9.45404	+	16.3749i	0.411045	+	0.711951i
$530$		0			0
$531$	−0.0811654	+	0.0811654i	−0.00352228	+	0.00352228i
$532$		0			0
$533$	−14.6059	−	14.6059i	−0.632653	−	0.632653i
$534$		0			0
$535$	−3.09662	+	1.78784i	−0.133879	+	0.0772949i
$536$		0			0
$537$	6.32595	−	10.9569i	0.272985	−	0.472824i
$538$		0			0
$539$	−20.5039	−	24.6434i	−0.883163	−	1.06147i
$540$		0			0
$541$	2.02312	+	7.55039i	0.0869808	+	0.324617i	0.995682	−	0.0928305i	$-0.0295915\pi$
$541$	2.02312	+	7.55039i	0.0869808	+	0.324617i	−0.908701	+	0.417447i	$0.862925\pi$
$542$		0			0
$543$	11.9131	−	6.87805i	0.511241	−	0.295165i
$544$		0			0
$545$			6.23624i			0.267131i
$546$		0			0
$547$	3.45431	+	3.45431i	0.147696	+	0.147696i	0.777088	−	0.629392i	$-0.216696\pi$
$547$	3.45431	+	3.45431i	0.147696	+	0.147696i	−0.629392	+	0.777088i	$0.716696\pi$
$548$		0			0
$549$	0.123927	+	0.0332060i	0.00528906	+	0.00141720i
$550$		0			0
$551$	−1.42934	−	0.825229i	−0.0608918	−	0.0351559i
$552$		0			0
$553$	26.8971	+	29.4762i	1.14378	+	1.25345i
$554$		0			0
$555$	−1.34711	−	5.02749i	−0.0571817	−	0.213405i
$556$		0			0
$557$	−27.8991	−	7.47554i	−1.18212	−	0.316749i	−0.386354	−	0.922350i	$-0.626266\pi$
$557$	−27.8991	−	7.47554i	−1.18212	−	0.316749i	−0.795768	+	0.605602i	$0.792933\pi$
$558$		0			0
$559$	21.9726			0.929342
$560$		0			0
$561$	20.9963			0.886463
$562$		0			0
$563$	0.908166	+	0.243342i	0.0382746	+	0.0102557i	0.277906	−	0.960608i	$-0.410360\pi$
$563$	0.908166	+	0.243342i	0.0382746	+	0.0102557i	−0.239631	+	0.970864i	$0.577026\pi$
$564$		0			0
$565$	−3.62084	−	13.5132i	−0.152330	−	0.568503i
$566$		0			0
$567$	5.14116	+	23.4211i	0.215909	+	0.983596i
$568$		0			0
$569$	11.5141	+	6.64769i	0.482698	+	0.278686i	0.721540	−	0.692373i	$-0.243435\pi$
$569$	11.5141	+	6.64769i	0.482698	+	0.278686i	−0.238842	+	0.971058i	$0.576768\pi$
$570$		0			0
$571$	−7.90497	−	2.11813i	−0.330813	−	0.0886410i	0.0895898	−	0.995979i	$-0.471444\pi$
$571$	−7.90497	−	2.11813i	−0.330813	−	0.0886410i	−0.420402	+	0.907338i	$0.638111\pi$
$572$		0			0
$573$	5.85753	+	5.85753i	0.244702	+	0.244702i
$574$		0			0
$575$			8.95562i			0.373475i
$576$		0			0
$577$	23.0378	−	13.3009i	0.959077	−	0.553724i	0.0631883	−	0.998002i	$-0.479873\pi$
$577$	23.0378	−	13.3009i	0.959077	−	0.553724i	0.895889	+	0.444278i	$0.146540\pi$
$578$		0			0
$579$	2.40274	+	8.96716i	0.0998546	+	0.372662i
$580$		0			0
$581$	−26.5981	+	13.7757i	−1.10347	+	0.571513i
$582$		0			0
$583$	−25.4447	+	44.0715i	−1.05381	+	1.82525i
$584$		0			0
$585$	−0.0568713	+	0.0328347i	−0.00235134	+	0.00135755i
$586$		0			0
$587$	9.30074	+	9.30074i	0.383883	+	0.383883i	0.872499	−	0.488616i	$-0.162498\pi$
$587$	9.30074	+	9.30074i	0.383883	+	0.383883i	−0.488616	+	0.872499i	$0.662498\pi$
$588$		0			0
$589$	26.2349	−	26.2349i	1.08099	−	1.08099i
$590$		0			0
$591$	14.3498	+	24.8546i	0.590272	+	1.02238i
$592$		0			0
$593$	12.2162	+	7.05302i	0.501659	+	0.289633i	0.729398	−	0.684089i	$-0.239800\pi$
$593$	12.2162	+	7.05302i	0.501659	+	0.289633i	−0.227739	+	0.973722i	$0.573133\pi$
$594$		0			0
$595$	−2.42895	−	4.68981i	−0.0995774	−	0.192264i
$596$		0			0
$597$	17.5046	−	4.69033i	0.716414	−	0.191963i
$598$		0			0
$599$	14.7397	+	25.5299i	0.602247	+	1.04312i	0.992480	+	0.122406i	$0.0390610\pi$
$599$	14.7397	+	25.5299i	0.602247	+	1.04312i	−0.390233	+	0.920716i	$0.627606\pi$
$600$		0			0
$601$	23.6858			0.966164			0.483082	−	0.875575i	$-0.339517\pi$
$601$	23.6858			0.966164			0.483082	+	0.875575i	$0.339517\pi$
$602$		0			0
$603$	−0.143344	+	0.143344i	−0.00583742	+	0.00583742i
$604$		0			0
$605$	1.95361	−	7.29097i	0.0794255	−	0.296420i
$606$		0			0
$607$	−2.86300	+	4.95886i	−0.116206	+	0.201274i	−0.918261	−	0.395976i	$-0.870407\pi$
$607$	−2.86300	+	4.95886i	−0.116206	+	0.201274i	0.802055	+	0.597250i	$0.203740\pi$
$608$		0			0
$609$	−1.33098	+	0.292163i	−0.0539341	+	0.0118391i
$610$		0			0
$611$	20.0910	−	5.38338i	0.812796	−	0.217788i
$612$		0			0
$613$	0.582780	−	2.17496i	0.0235383	−	0.0878459i	−0.953158	−	0.302474i	$-0.902187\pi$
$613$	0.582780	−	2.17496i	0.0235383	−	0.0878459i	0.976696	+	0.214628i	$0.0688540\pi$
$614$		0			0
$615$		−	6.63616i		−	0.267596i
$616$		0			0
$617$		−	12.2572i		−	0.493457i	−0.969085	−	0.246729i	$-0.920644\pi$
$617$		−	12.2572i		−	0.493457i	0.969085	−	0.246729i	$-0.0793556\pi$
$618$		0			0
$619$	−1.93311	+	7.21445i	−0.0776981	+	0.289973i	−0.993832	−	0.110900i	$-0.964627\pi$
$619$	−1.93311	+	7.21445i	−0.0776981	+	0.289973i	0.916133	+	0.400873i	$0.131293\pi$
$620$		0			0
$621$	10.1167	−	2.71077i	0.405970	−	0.108779i
$622$		0			0
$623$	15.3432	−	14.0008i	0.614714	−	0.560929i
$624$		0			0
$625$	8.36824	−	14.4942i	0.334730	−	0.579769i
$626$		0			0
$627$	−11.4755	+	42.8272i	−0.458288	+	1.71036i
$628$		0			0
$629$	−7.37954	+	7.37954i	−0.294241	+	0.294241i
$630$		0			0
$631$	10.1046			0.402257			0.201129	−	0.979565i	$-0.435539\pi$
$631$	10.1046			0.402257			0.201129	+	0.979565i	$0.435539\pi$
$632$		0			0
$633$	−0.880639	−	1.52531i	−0.0350022	−	0.0606257i
$634$		0			0
$635$	−9.55211	+	2.55948i	−0.379064	+	0.101570i
$636$		0			0
$637$	−4.85941	−	28.2470i	−0.192537	−	1.11919i
$638$		0			0
$639$	0.133148	+	0.0768733i	0.00526727	+	0.00304106i
$640$		0			0
$641$	11.1392	+	19.2937i	0.439973	+	0.762056i	0.997687	−	0.0679772i	$-0.0216545\pi$
$641$	11.1392	+	19.2937i	0.439973	+	0.762056i	−0.557713	+	0.830034i	$0.688321\pi$
$642$		0			0
$643$	−2.94059	+	2.94059i	−0.115965	+	0.115965i	−0.762708	−	0.646743i	$-0.776131\pi$
$643$	−2.94059	+	2.94059i	−0.115965	+	0.115965i	0.646743	+	0.762708i	$0.276131\pi$
$644$		0			0
$645$	4.99159	+	4.99159i	0.196544	+	0.196544i
$646$		0			0
$647$	13.6596	−	7.88639i	0.537015	−	0.310046i	−0.206853	−	0.978372i	$-0.566322\pi$
$647$	13.6596	−	7.88639i	0.537015	−	0.310046i	0.743869	+	0.668326i	$0.232989\pi$
$648$		0			0
$649$	12.4030	−	21.4827i	0.486862	−	0.843269i
$650$		0			0
$651$	1.39993	−	30.6004i	0.0548677	−	1.19932i
$652$		0			0
$653$	−3.18397	−	11.8827i	−0.124598	−	0.465007i	0.875227	−	0.483713i	$-0.160712\pi$
$653$	−3.18397	−	11.8827i	−0.124598	−	0.465007i	−0.999825	+	0.0187058i	$0.994045\pi$
$654$		0			0
$655$	−5.63152	+	3.25136i	−0.220042	+	0.127041i
$656$		0			0
$657$		−	0.139709i		−	0.00545056i
$658$		0			0
$659$	22.1996	+	22.1996i	0.864775	+	0.864775i	0.991888	−	0.127114i	$-0.0405713\pi$
$659$	22.1996	+	22.1996i	0.864775	+	0.864775i	−0.127114	+	0.991888i	$0.540571\pi$
$660$		0			0
$661$	0.947777	+	0.253956i	0.0368642	+	0.00987774i	0.277204	−	0.960811i	$-0.410592\pi$
$661$	0.947777	+	0.253956i	0.0368642	+	0.00987774i	−0.240340	+	0.970689i	$0.577259\pi$
$662$		0			0
$663$	16.2571	+	9.38606i	0.631375	+	0.364524i
$664$		0			0
$665$	10.8936	−	2.39125i	0.422436	−	0.0927288i
$666$		0			0
$667$	0.155136	+	0.578976i	0.00600690	+	0.0224181i
$668$		0			0
$669$	21.6887	+	5.81146i	0.838532	+	0.224684i
$670$		0			0
$671$	−27.7264			−1.07036
$672$		0			0
$673$	−28.5560			−1.10075			−0.550376	−	0.834917i	$-0.685516\pi$
$673$	−28.5560			−1.10075			−0.550376	+	0.834917i	$0.685516\pi$
$674$		0			0
$675$	−22.1415	−	5.93280i	−0.852227	−	0.228354i
$676$		0			0
$677$	−1.91250	−	7.13755i	−0.0735033	−	0.274318i	0.919386	−	0.393356i	$-0.128686\pi$
$677$	−1.91250	−	7.13755i	−0.0735033	−	0.274318i	−0.992890	+	0.119037i	$0.962019\pi$
$678$		0			0
$679$	−7.04372	+	22.1786i	−0.270313	+	0.851135i
$680$		0			0
$681$	23.4134	+	13.5177i	0.897203	+	0.518001i
$682$		0			0
$683$	−1.90507	−	0.510463i	−0.0728956	−	0.0195323i	0.222187	−	0.975004i	$-0.428680\pi$
$683$	−1.90507	−	0.510463i	−0.0728956	−	0.0195323i	−0.295083	+	0.955472i	$0.595347\pi$
$684$		0			0
$685$	12.3549	+	12.3549i	0.472058	+	0.472058i
$686$		0			0
$687$			24.0695i			0.918310i
$688$		0			0
$689$	−39.4030	+	22.7493i	−1.50113	+	0.866680i
$690$		0			0
$691$	−0.0579544	−	0.216289i	−0.00220469	−	0.00822801i	0.964815	−	0.262931i	$-0.0846891\pi$
$691$	−0.0579544	−	0.216289i	−0.00220469	−	0.00822801i	−0.967019	+	0.254703i	$0.918022\pi$
$692$		0			0
$693$	0.118090	+	0.228007i	0.00448586	+	0.00866127i
$694$		0			0
$695$	−3.26104	+	5.64829i	−0.123698	+	0.214252i
$696$		0			0
$697$	−11.5235	+	6.65309i	−0.436484	+	0.252004i
$698$		0			0
$699$	15.1177	+	15.1177i	0.571804	+	0.571804i
$700$		0			0
$701$	−18.2761	+	18.2761i	−0.690279	+	0.690279i	−0.962293	−	0.272014i	$-0.912310\pi$
$701$	−18.2761	+	18.2761i	−0.690279	+	0.690279i	0.272014	+	0.962293i	$0.412310\pi$
$702$		0			0
$703$	−11.0192	−	19.0858i	−0.415596	−	0.719833i
$704$		0			0
$705$	5.78711	+	3.34119i	0.217955	+	0.125837i
$706$		0			0
$707$	5.14054	+	3.28997i	0.193330	+	0.123732i
$708$		0			0
$709$	1.66489	−	0.446105i	0.0625261	−	0.0167538i	−0.227420	−	0.973797i	$-0.573029\pi$
$709$	1.66489	−	0.446105i	0.0625261	−	0.0167538i	0.289946	+	0.957043i	$0.406362\pi$
$710$		0			0
$711$	−0.159808	−	0.276795i	−0.00599325	−	0.0103806i
$712$		0			0
$713$	−13.4743			−0.504617
$714$		0			0
$715$	10.0351	−	10.0351i	0.375290	−	0.375290i
$716$		0			0
$717$	−3.24003	+	12.0920i	−0.121001	+	0.451582i
$718$		0			0
$719$	25.5064	−	44.1784i	0.951229	−	1.64758i	0.208457	−	0.978031i	$-0.433156\pi$
$719$	25.5064	−	44.1784i	0.951229	−	1.64758i	0.742771	−	0.669545i	$-0.233511\pi$
$720$		0			0
$721$	24.3008	+	26.6309i	0.905009	+	0.991785i
$722$		0			0
$723$	40.2045	−	10.7728i	1.49522	−	0.400644i
$724$		0			0
$725$	0.339532	−	1.26715i	0.0126099	−	0.0470609i
$726$		0			0
$727$			31.5017i			1.16833i	0.811634	+	0.584166i	$0.198578\pi$
$727$			31.5017i			1.16833i	−0.811634	+	0.584166i	$0.801422\pi$
$728$		0			0
$729$			26.8066i			0.992837i
$730$		0			0
$731$	3.66342	−	13.6721i	0.135496	−	0.505680i
$732$		0			0
$733$	−40.3371	+	10.8083i	−1.48988	+	0.399213i	−0.909698	−	0.415271i	$-0.863687\pi$
$733$	−40.3371	+	10.8083i	−1.48988	+	0.399213i	−0.580186	+	0.814484i	$0.697020\pi$
$734$		0			0
$735$	5.31304	−	7.52090i	0.195974	−	0.277413i
$736$		0			0
$737$	21.9047	−	37.9400i	0.806869	−	1.39754i
$738$		0			0
$739$	4.66207	−	17.3991i	0.171497	−	0.640036i	−0.825625	−	0.564220i	$-0.809177\pi$
$739$	4.66207	−	17.3991i	0.171497	−	0.640036i	0.997122	−	0.0758162i	$-0.0241562\pi$
$740$		0			0
$741$	−28.0306	+	28.0306i	−1.02973	+	1.02973i
$742$		0			0
$743$	23.0128			0.844256			0.422128	−	0.906536i	$-0.361283\pi$
$743$	23.0128			0.844256			0.422128	+	0.906536i	$0.361283\pi$
$744$		0			0
$745$	4.57156	+	7.91818i	0.167489	+	0.290100i
$746$		0			0
$747$	0.231745	−	0.0620958i	0.00847910	−	0.00227197i
$748$		0			0
$749$	−0.571271	+	12.4871i	−0.0208738	+	0.456269i
$750$		0			0
$751$	0.399765	+	0.230804i	0.0145876	+	0.00842217i	0.507276	−	0.861784i	$-0.330652\pi$
$751$	0.399765	+	0.230804i	0.0145876	+	0.00842217i	−0.492688	+	0.870206i	$0.663986\pi$
$752$		0			0
$753$	7.51284	+	13.0126i	0.273783	+	0.474206i
$754$		0			0
$755$	0.870885	−	0.870885i	0.0316947	−	0.0316947i
$756$		0			0
$757$	5.23204	+	5.23204i	0.190162	+	0.190162i	0.795766	−	0.605604i	$-0.207069\pi$
$757$	5.23204	+	5.23204i	0.190162	+	0.190162i	−0.605604	+	0.795766i	$0.707069\pi$
$758$		0			0
$759$	13.9450	−	8.05117i	0.506173	−	0.292239i
$760$		0			0
$761$	−10.6052	+	18.3687i	−0.384437	+	0.665864i	−0.991691	−	0.128644i	$-0.958938\pi$
$761$	−10.6052	+	18.3687i	−0.384437	+	0.665864i	0.607254	+	0.794508i	$0.292271\pi$
$762$		0			0
$763$	18.3625	+	11.7521i	0.664767	+	0.425454i
$764$		0			0
$765$	0.0109488	+	0.0408616i	0.000395856	+	0.00147735i
$766$		0			0
$767$	19.2070	−	11.0892i	0.693525	−	0.400407i
$768$		0			0
$769$			10.8533i			0.391379i	0.980666	+	0.195689i	$0.0626944\pi$
$769$			10.8533i			0.391379i	−0.980666	+	0.195689i	$0.937306\pi$
$770$		0			0
$771$	−28.0029	−	28.0029i	−1.00850	−	1.00850i
$772$		0			0
$773$	46.9962	+	12.5926i	1.69034	+	0.452924i	0.970476	−	0.241196i	$-0.0775396\pi$
$773$	46.9962	+	12.5926i	1.69034	+	0.452924i	0.719859	+	0.694120i	$0.244206\pi$
$774$		0			0
$775$	25.5391	+	14.7450i	0.917390	+	0.529656i
$776$		0			0
$777$	−17.3420	−	5.50766i	−0.622140	−	0.197586i
$778$		0			0
$779$	−7.27251	−	27.1414i	−0.260565	−	0.972441i
$780$		0			0
$781$	−32.0938	−	8.59952i	−1.14841	−	0.307715i
$782$		0			0
$783$	−1.53421			−0.0548282
$784$		0			0
$785$	−18.2049			−0.649762
$786$		0			0
$787$	−12.9614	−	3.47299i	−0.462023	−	0.123799i	0.0202968	−	0.999794i	$-0.493539\pi$
$787$	−12.9614	−	3.47299i	−0.462023	−	0.123799i	−0.482319	+	0.875995i	$0.660206\pi$
$788$		0			0
$789$	4.75770	+	17.7560i	0.169379	+	0.632130i
$790$		0			0
$791$	−46.6127	−	14.8038i	−1.65736	−	0.526363i
$792$		0			0
$793$	−21.4682	−	12.3946i	−0.762356	−	0.440147i
$794$		0			0
$795$	−14.1194	−	3.78327i	−0.500762	−	0.134179i
$796$		0			0
$797$	−6.22856	−	6.22856i	−0.220627	−	0.220627i	0.588135	−	0.808762i	$-0.299862\pi$
$797$	−6.22856	−	6.22856i	−0.220627	−	0.220627i	−0.808762	+	0.588135i	$0.799862\pi$
$798$		0			0
$799$		−	13.3989i		−	0.474017i
$800$		0			0
$801$	−0.144080	+	0.0831847i	−0.00509082	+	0.00293919i
$802$		0			0
$803$	7.81434	+	29.1635i	0.275762	+	1.02916i
$804$		0			0
$805$	−3.41158	−	2.18342i	−0.120242	−	0.0769555i
$806$		0			0
$807$	−9.00253	+	15.5928i	−0.316904	+	0.548894i
$808$		0			0
$809$	−1.49336	+	0.862190i	−0.0525036	+	0.0303130i	−0.526022	−	0.850471i	$-0.676317\pi$
$809$	−1.49336	+	0.862190i	−0.0525036	+	0.0303130i	0.473518	+	0.880784i	$0.342984\pi$
$810$		0			0
$811$	29.5809	+	29.5809i	1.03872	+	1.03872i	0.999219	+	0.0395050i	$0.0125781\pi$
$811$	29.5809	+	29.5809i	1.03872	+	1.03872i	0.0395050	+	0.999219i	$0.487422\pi$
$812$		0			0
$813$	30.3142	−	30.3142i	1.06317	−	1.06317i
$814$		0			0
$815$	3.45058	+	5.97657i	0.120868	+	0.209350i
$816$		0			0
$817$	25.8854	+	14.9450i	0.905617	+	0.522858i
$818$		0			0
$819$	−0.0104917	+	0.229333i	−0.000366611	+	0.00801354i
$820$		0			0
$821$	−36.4661	+	9.77105i	−1.27267	+	0.341012i	−0.831055	−	0.556190i	$-0.812263\pi$
$821$	−36.4661	+	9.77105i	−1.27267	+	0.341012i	−0.441620	+	0.897202i	$0.645596\pi$
$822$		0			0
$823$	−18.3778	−	31.8313i	−0.640609	−	1.10957i	−0.985297	−	0.170850i	$-0.945349\pi$
$823$	−18.3778	−	31.8313i	−0.640609	−	1.10957i	0.344688	−	0.938717i	$-0.387985\pi$
$824$		0			0
$825$	−35.2417			−1.22696
$826$		0			0
$827$	25.1791	−	25.1791i	0.875565	−	0.875565i	−0.117507	−	0.993072i	$-0.537490\pi$
$827$	25.1791	−	25.1791i	0.875565	−	0.875565i	0.993072	+	0.117507i	$0.0374904\pi$
$828$		0			0
$829$	−6.08475	+	22.7086i	−0.211332	+	0.788702i	0.776094	+	0.630618i	$0.217198\pi$
$829$	−6.08475	+	22.7086i	−0.211332	+	0.788702i	−0.987426	+	0.158084i	$0.949468\pi$
$830$		0			0
$831$	−9.32215	+	16.1464i	−0.323382	+	0.560114i
$832$		0			0
$833$	−18.3864	−	1.68584i	−0.637051	−	0.0584110i
$834$		0			0
$835$	2.33015	−	0.624362i	0.0806382	−	0.0216069i
$836$		0			0
$837$	8.92628	−	33.3133i	0.308537	−	1.15148i
$838$		0			0
$839$		−	13.7267i		−	0.473899i	−0.971522	−	0.236949i	$-0.923852\pi$
$839$		−	13.7267i		−	0.473899i	0.971522	−	0.236949i	$-0.0761475\pi$
$840$		0			0
$841$			28.9122i			0.996972i
$842$		0			0
$843$	−2.90793	+	10.8525i	−0.100154	+	0.373782i
$844$		0			0
$845$	2.75264	−	0.737569i	0.0946938	−	0.0253731i
$846$		0			0
$847$	−17.7866	−	19.4921i	−0.611155	−	0.669755i
$848$		0			0
$849$	17.1244	−	29.6603i	0.587708	−	1.01794i
$850$		0			0
$851$	−2.07151	+	7.73099i	−0.0710106	+	0.265015i
$852$		0			0
$853$	−2.88131	+	2.88131i	−0.0986542	+	0.0986542i	−0.754711	−	0.656057i	$-0.772223\pi$
$853$	−2.88131	+	2.88131i	−0.0986542	+	0.0986542i	0.656057	+	0.754711i	$0.272223\pi$
$854$		0			0
$855$	−0.0893318			−0.00305508
$856$		0			0
$857$	−7.75242	−	13.4276i	−0.264817	−	0.458677i	0.702698	−	0.711488i	$-0.251978\pi$
$857$	−7.75242	−	13.4276i	−0.264817	−	0.458677i	−0.967516	+	0.252811i	$0.918645\pi$
$858$		0			0
$859$	23.6842	−	6.34616i	0.808094	−	0.216528i	0.168960	−	0.985623i	$-0.445959\pi$
$859$	23.6842	−	6.34616i	0.808094	−	0.216528i	0.639135	+	0.769095i	$0.279293\pi$
$860$		0			0
$861$	−19.5401	−	12.5057i	−0.665924	−	0.426194i
$862$		0			0
$863$	40.7734	+	23.5405i	1.38794	+	0.801329i	0.993083	−	0.117412i	$-0.0374598\pi$
$863$	40.7734	+	23.5405i	1.38794	+	0.801329i	0.394860	+	0.918741i	$0.370793\pi$
$864$		0			0
$865$	7.29118	+	12.6287i	0.247907	+	0.429388i
$866$		0			0
$867$	−12.3433	+	12.3433i	−0.419199	+	0.419199i
$868$		0			0
$869$	48.8410	+	48.8410i	1.65682	+	1.65682i
$870$		0			0
$871$	33.9210	−	19.5843i	1.14937	−	0.663589i
$872$		0			0
$873$	0.0931935	−	0.161416i	0.00315412	−	0.00546310i
$874$		0			0
$875$	8.68134	+	16.7619i	0.293483	+	0.566655i
$876$		0			0
$877$	−5.24273	−	19.5661i	−0.177034	−	0.660701i	−0.996196	−	0.0871389i	$-0.972228\pi$
$877$	−5.24273	−	19.5661i	−0.177034	−	0.660701i	0.819162	−	0.573563i	$-0.194439\pi$
$878$		0			0
$879$	6.30964	−	3.64287i	0.212819	−	0.122871i
$880$		0			0
$881$		−	29.7191i		−	1.00126i	−0.865660	−	0.500632i	$-0.833101\pi$
$881$		−	29.7191i		−	1.00126i	0.865660	−	0.500632i	$-0.166899\pi$
$882$		0			0
$883$	−10.1351	−	10.1351i	−0.341074	−	0.341074i	0.515697	−	0.856771i	$-0.327533\pi$
$883$	−10.1351	−	10.1351i	−0.341074	−	0.341074i	−0.856771	+	0.515697i	$0.827533\pi$
$884$		0			0
$885$	6.88249	+	1.84416i	0.231352	+	0.0619907i
$886$		0			0
$887$	29.8863	+	17.2549i	1.00348	+	0.579362i	0.909277	−	0.416191i	$-0.136635\pi$
$887$	29.8863	+	17.2549i	1.00348	+	0.579362i	0.0942069	+	0.995553i	$0.469968\pi$
$888$		0			0
$889$	−10.4644	+	32.9494i	−0.350966	+	1.10509i
$890$		0			0
$891$	10.7426	+	40.0920i	0.359891	+	1.34313i
$892$		0			0
$893$	27.3304	+	7.32316i	0.914577	+	0.245060i
$894$		0			0
$895$	−5.50881			−0.184139
$896$		0			0
$897$	14.3966			0.480689
$898$		0			0
$899$	1.90651	+	0.510848i	0.0635857	+	0.0170377i
$900$		0			0
$901$	7.58584	+	28.3107i	0.252721	+	0.943168i
$902$		0			0
$903$	24.1042	−	5.29111i	0.802138	−	0.176077i
$904$		0			0
$905$	−5.18714	−	2.99479i	−0.172426	−	0.0995503i
$906$		0			0
$907$	−8.06405	−	2.16076i	−0.267762	−	0.0717467i	0.122440	−	0.992476i	$-0.460928\pi$
$907$	−8.06405	−	2.16076i	−0.267762	−	0.0717467i	−0.390202	+	0.920729i	$0.627595\pi$
$908$		0			0
$909$	−0.0345667	−	0.0345667i	−0.00114650	−	0.00114650i
$910$		0			0
$911$			8.93090i			0.295894i	0.988995	+	0.147947i	$0.0472665\pi$
$911$			8.93090i			0.295894i	−0.988995	+	0.147947i	$0.952734\pi$
$912$		0			0
$913$	−44.9023	+	25.9244i	−1.48605	+	0.857972i
$914$		0			0
$915$	−2.06126	−	7.69273i	−0.0681432	−	0.254314i
$916$		0			0
$917$	−1.03891	+	22.7091i	−0.0343080	+	0.749919i
$918$		0			0
$919$	26.6631	−	46.1818i	0.879533	−	1.52340i	0.0276794	−	0.999617i	$-0.491188\pi$
$919$	26.6631	−	46.1818i	0.879533	−	1.52340i	0.851854	−	0.523779i	$-0.175478\pi$
$920$		0			0
$921$	−18.3286	+	10.5820i	−0.603946	+	0.348689i
$922$		0			0
$923$	−21.0055	−	21.0055i	−0.691406	−	0.691406i
$924$		0			0
$925$	12.3864	−	12.3864i	0.407262	−	0.407262i
$926$		0			0
$927$	−0.144382	−	0.250076i	−0.00474211	−	0.00821358i
$928$		0			0
$929$	33.5814	+	19.3882i	1.10177	+	0.636107i	0.936685	−	0.350173i	$-0.113877\pi$
$929$	33.5814	+	19.3882i	1.10177	+	0.636107i	0.165084	+	0.986280i	$0.447211\pi$
$930$		0			0
$931$	13.4878	−	36.5824i	0.442045	−	1.19894i
$932$		0			0
$933$	−9.67386	+	2.59210i	−0.316708	+	0.0848617i
$934$		0			0
$935$	−4.57103	−	7.91725i	−0.149489	−	0.258922i
$936$		0			0
$937$	−14.3493			−0.468771			−0.234385	−	0.972144i	$-0.575308\pi$
$937$	−14.3493			−0.468771			−0.234385	+	0.972144i	$0.575308\pi$
$938$		0			0
$939$	9.87228	−	9.87228i	0.322170	−	0.322170i
$940$		0			0
$941$	−8.50975	+	31.7588i	−0.277410	+	1.03531i	0.676799	+	0.736168i	$0.263367\pi$
$941$	−8.50975	+	31.7588i	−0.277410	+	1.03531i	−0.954209	+	0.299141i	$0.903300\pi$
$942$		0			0
$943$	−5.10236	+	8.83754i	−0.166156	+	0.287790i
$944$		0			0
$945$	7.65826	−	6.98820i	0.249123	−	0.227326i
$946$		0			0
$947$	−48.8089	+	13.0783i	−1.58608	+	0.424988i	−0.940800	−	0.338962i	$-0.889924\pi$
$947$	−48.8089	+	13.0783i	−1.58608	+	0.424988i	−0.645276	+	0.763950i	$0.723258\pi$
$948$		0			0
$949$	−6.98657	+	26.0742i	−0.226794	+	0.846405i
$950$		0			0
$951$			16.2167i			0.525861i
$952$		0			0
$953$			12.5441i			0.406345i	0.979143	+	0.203172i	$0.0651252\pi$
$953$			12.5441i			0.406345i	−0.979143	+	0.203172i	$0.934875\pi$
$954$		0			0
$955$	0.933528	−	3.48398i	0.0302083	−	0.112739i
$956$		0			0
$957$	−2.27836	+	0.610485i	−0.0736489	+	0.0197342i
$958$		0			0
$959$	59.6616	−	13.0963i	1.92657	−	0.422901i
$960$		0			0
$961$	−6.68477	+	11.5784i	−0.215638	+	0.373496i
$962$		0			0
$963$	0.0259135	−	0.0967106i	0.000835052	−	0.00311646i
$964$		0			0
$965$	2.85823	−	2.85823i	0.0920098	−	0.0920098i
$966$		0			0
$967$	19.7015			0.633559			0.316779	−	0.948499i	$-0.397399\pi$
$967$	19.7015			0.633559			0.316779	+	0.948499i	$0.397399\pi$
$968$		0			0
$969$	12.7681	+	22.1150i	0.410171	+	0.710437i
$970$		0			0
$971$	−19.1999	+	5.14459i	−0.616153	+	0.165098i	−0.553378	−	0.832930i	$-0.686662\pi$
$971$	−19.1999	+	5.14459i	−0.616153	+	0.165098i	−0.0627745	+	0.998028i	$0.519995\pi$
$972$		0			0
$973$	10.4859	+	20.2462i	0.336163	+	0.649063i
$974$		0			0
$975$	−27.2872	−	15.7543i	−0.873890	−	0.504541i
$976$		0			0
$977$	−22.0366	−	38.1686i	−0.705015	−	1.22112i	−0.966686	−	0.255965i	$-0.917607\pi$
$977$	−22.0366	−	38.1686i	−0.705015	−	1.22112i	0.261671	−	0.965157i	$-0.415726\pi$
$978$		0			0
$979$	25.4232	−	25.4232i	0.812530	−	0.812530i
$980$		0			0
$981$	−0.123475	−	0.123475i	−0.00394227	−	0.00394227i
$982$		0			0
$983$	−38.9733	+	22.5013i	−1.24306	+	0.717678i	−0.969715	−	0.244239i	$-0.921462\pi$
$983$	−38.9733	+	22.5013i	−1.24306	+	0.717678i	−0.273340	+	0.961917i	$0.588129\pi$
$984$		0			0
$985$	6.24810	−	10.8220i	0.199081	−	0.344818i
$986$		0			0
$987$	20.7438	−	10.7437i	0.660282	−	0.341974i
$988$		0			0
$989$	−2.80953	−	10.4853i	−0.0893379	−	0.333414i
$990$		0			0
$991$	−32.1531	+	18.5636i	−1.02138	+	0.589693i	−0.914503	−	0.404579i	$-0.867418\pi$
$991$	−32.1531	+	18.5636i	−1.02138	+	0.589693i	−0.106875	+	0.994272i	$0.534085\pi$
$992$		0			0
$993$		−	8.92622i		−	0.283265i
$994$		0			0
$995$	−5.57949	−	5.57949i	−0.176882	−	0.176882i
$996$		0			0
$997$	−55.7466	−	14.9373i	−1.76551	−	0.473067i	−0.777689	−	0.628649i	$-0.783608\pi$
$997$	−55.7466	−	14.9373i	−1.76551	−	0.473067i	−0.987823	+	0.155582i	$0.950275\pi$
$998$		0			0
$999$	−17.7415	−	10.2430i	−0.561316	−	0.324076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.z.a.159.11		56
4.3	odd	2		896.2.z.b.159.4		56
7.3	odd	6	inner	896.2.z.a.31.11		56
8.3	odd	2		112.2.v.a.75.5	yes	56
8.5	even	2		448.2.z.a.271.4		56
16.3	odd	4	inner	896.2.z.a.607.11		56
16.5	even	4		112.2.v.a.19.6	yes	56
16.11	odd	4		448.2.z.a.47.4		56
16.13	even	4		896.2.z.b.607.4		56
28.3	even	6		896.2.z.b.31.4		56
56.3	even	6		112.2.v.a.59.6	yes	56
56.11	odd	6		784.2.w.f.619.6		56
56.19	even	6		784.2.j.a.587.26		56
56.27	even	2		784.2.w.f.411.5		56
56.45	odd	6		448.2.z.a.143.4		56
56.51	odd	6		784.2.j.a.587.25		56
112.3	even	12	inner	896.2.z.a.479.11		56
112.5	odd	12		784.2.j.a.195.25		56
112.37	even	12		784.2.j.a.195.26		56
112.45	odd	12		896.2.z.b.479.4		56
112.53	even	12		784.2.w.f.227.5		56
112.59	even	12		448.2.z.a.367.4		56
112.69	odd	4		784.2.w.f.19.6		56
112.101	odd	12		112.2.v.a.3.5	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.5	✓	56	112.101	odd	12
112.2.v.a.19.6	yes	56	16.5	even	4
112.2.v.a.59.6	yes	56	56.3	even	6
112.2.v.a.75.5	yes	56	8.3	odd	2
448.2.z.a.47.4		56	16.11	odd	4
448.2.z.a.143.4		56	56.45	odd	6
448.2.z.a.271.4		56	8.5	even	2
448.2.z.a.367.4		56	112.59	even	12
784.2.j.a.195.25		56	112.5	odd	12
784.2.j.a.195.26		56	112.37	even	12
784.2.j.a.587.25		56	56.51	odd	6
784.2.j.a.587.26		56	56.19	even	6
784.2.w.f.19.6		56	112.69	odd	4
784.2.w.f.227.5		56	112.53	even	12
784.2.w.f.411.5		56	56.27	even	2
784.2.w.f.619.6		56	56.11	odd	6
896.2.z.a.31.11		56	7.3	odd	6	inner
896.2.z.a.159.11		56	1.1	even	1	trivial
896.2.z.a.479.11		56	112.3	even	12	inner
896.2.z.a.607.11		56	16.3	odd	4	inner
896.2.z.b.31.4		56	28.3	even	6
896.2.z.b.159.4		56	4.3	odd	2
896.2.z.b.479.4		56	112.45	odd	12
896.2.z.b.607.4		56	16.13	even	4

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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.z (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.67893 + 0.449868i) q^{3} +(-0.195879 - 0.731029i) q^{5} +(-2.52163 - 0.800849i) q^{7} +(0.0183525 + 0.0105958i) q^{9} +(-4.42364 - 1.18531i) q^{11} +(-2.89529 - 2.89529i) q^{13} -1.31547i q^{15} +(-2.28427 + 1.31882i) q^{17} +(-1.44161 - 5.38016i) q^{19} +(-3.87337 - 2.47897i) q^{21} +(-1.01143 + 1.75184i) q^{23} +(3.83409 - 2.21361i) q^{25} +(-3.66114 - 3.66114i) q^{27} +(0.209526 - 0.209526i) q^{29} +(3.33052 + 5.76864i) q^{31} +(-6.89376 - 3.98011i) q^{33} +(-0.0915096 + 2.00026i) q^{35} +(3.82183 - 1.02406i) q^{37} +(-3.55850 - 6.16350i) q^{39} +5.04472 q^{41} +(-3.79454 + 3.79454i) q^{43} +(0.00415099 - 0.0154917i) q^{45} +(-2.53993 + 4.39928i) q^{47} +(5.71728 + 4.03890i) q^{49} +(-4.42843 + 1.18659i) q^{51} +(2.87599 - 10.7333i) q^{53} +3.46599i q^{55} -9.68145i q^{57} +(-1.40190 + 5.23198i) q^{59} +(5.84791 - 1.56694i) q^{61} +(-0.0377926 - 0.0414163i) q^{63} +(-1.54942 + 2.68367i) q^{65} +(-2.47586 + 9.24005i) q^{67} +(-2.48621 + 2.48621i) q^{69} +7.25507 q^{71} +(-3.29633 - 5.70940i) q^{73} +(7.43301 - 1.99167i) q^{75} +(10.2056 + 6.53159i) q^{77} +(-13.0615 - 7.54108i) q^{79} +(-4.53156 - 7.84890i) q^{81} +(8.00548 - 8.00548i) q^{83} +(1.41154 + 1.41154i) q^{85} +(0.446039 - 0.257521i) q^{87} +(-3.92536 + 6.79892i) q^{89} +(4.98218 + 9.61956i) q^{91} +(2.99659 + 11.1834i) q^{93} +(-3.65067 + 2.10772i) q^{95} -8.79532i q^{97} +(-0.0686254 - 0.0686254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{3} + 6 q^{5} + 8 q^{7} + 2 q^{11} - 12 q^{17} - 6 q^{19} + 10 q^{21} + 12 q^{23} + 24 q^{29} - 12 q^{33} - 2 q^{35} - 6 q^{37} + 4 q^{39} - 12 q^{45} - 8 q^{49} - 34 q^{51} - 6 q^{53} + 42 q^{59}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q - 6 * q^3 + 6 * q^5 + 8 * q^7 + 2 * q^11 - 12 * q^17 - 6 * q^19 + 10 * q^21 + 12 * q^23 + 24 * q^29 - 12 * q^33 - 2 * q^35 - 6 * q^37 + 4 * q^39 - 12 * q^45 - 8 * q^49 - 34 * q^51 - 6 * q^53 + 42 * q^59 + 6 * q^61 - 4 * q^65 + 6 * q^67 + 80 * q^71 + 24 * q^75 - 10 * q^77 - 8 * q^81 + 28 * q^85 + 12 * q^87 + 16 * q^91 - 10 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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