LMFDB - Embedded newform 448.2.z.a.47.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [448,2,Mod(47,448)] 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("448.47"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(448, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.z (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.57729801055$
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			47.4
Character	$\chi$	$=$	448.47
Dual form			448.2.z.a.143.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.449868 + 1.67893i) q^{3} +(0.731029 - 0.195879i) q^{5} +(-2.52163 - 0.800849i) q^{7} +(-0.0183525 - 0.0105958i) q^{9} +(-1.18531 + 4.42364i) q^{11} +(-2.89529 + 2.89529i) q^{13} +1.31547i q^{15} +(-2.28427 + 1.31882i) q^{17} +(5.38016 - 1.44161i) q^{19} +(2.47897 - 3.87337i) q^{21} +(-1.01143 + 1.75184i) q^{23} +(-3.83409 + 2.21361i) q^{25} +(-3.66114 + 3.66114i) q^{27} +(-0.209526 - 0.209526i) q^{29} +(-3.33052 - 5.76864i) q^{31} +(-6.89376 - 3.98011i) q^{33} +(-2.00026 - 0.0915096i) q^{35} +(1.02406 + 3.82183i) q^{37} +(-3.55850 - 6.16350i) q^{39} -5.04472 q^{41} +(3.79454 + 3.79454i) q^{43} +(-0.0154917 - 0.00415099i) q^{45} +(2.53993 - 4.39928i) q^{47} +(5.71728 + 4.03890i) q^{49} +(-1.18659 - 4.42843i) q^{51} +(10.7333 + 2.87599i) q^{53} +3.46599i q^{55} +9.68145i q^{57} +(5.23198 + 1.40190i) q^{59} +(-1.56694 - 5.84791i) q^{61} +(0.0377926 + 0.0414163i) q^{63} +(-1.54942 + 2.68367i) q^{65} +(-9.24005 - 2.47586i) q^{67} +(-2.48621 - 2.48621i) q^{69} +7.25507 q^{71} +(3.29633 + 5.70940i) q^{73} +(-1.99167 - 7.43301i) q^{75} +(6.53159 - 10.2056i) q^{77} +(13.0615 + 7.54108i) q^{79} +(-4.53156 - 7.84890i) q^{81} +(8.00548 + 8.00548i) q^{83} +(-1.41154 + 1.41154i) q^{85} +(0.446039 - 0.257521i) q^{87} +(3.92536 - 6.79892i) q^{89} +(9.61956 - 4.98218i) q^{91} +(11.1834 - 2.99659i) q^{93} +(3.65067 - 2.10772i) q^{95} -8.79532i q^{97} +(0.0686254 - 0.0686254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.449868	+	1.67893i	−0.259732	+	0.969331i	0.705665	+	0.708546i	$0.250648\pi$
$3$	−0.449868	+	1.67893i	−0.259732	+	0.969331i	−0.965397	+	0.260786i	$0.916018\pi$
$4$		0			0
$5$	0.731029	−	0.195879i	0.326926	−	0.0875996i	−0.0916229	−	0.995794i	$-0.529205\pi$
$5$	0.731029	−	0.195879i	0.326926	−	0.0875996i	0.418549	+	0.908194i	$0.362539\pi$
$6$		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
$11$	−1.18531	+	4.42364i	−0.357385	+	1.33378i	0.520072	+	0.854122i	$0.325905\pi$
$11$	−1.18531	+	4.42364i	−0.357385	+	1.33378i	−0.877457	+	0.479656i	$0.840762\pi$
$12$		0			0
$13$	−2.89529	+	2.89529i	−0.803010	+	0.803010i	−0.983565	−	0.180555i	$-0.942211\pi$
$13$	−2.89529	+	2.89529i	−0.803010	+	0.803010i	0.180555	+	0.983565i	$0.442211\pi$
$14$		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
$19$	5.38016	−	1.44161i	1.23429	−	0.330728i	0.418043	−	0.908427i	$-0.362716\pi$
$19$	5.38016	−	1.44161i	1.23429	−	0.330728i	0.816249	+	0.577700i	$0.196049\pi$
$20$		0			0
$21$	2.47897	−	3.87337i	0.540956	−	0.845240i
$22$		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	$-0.258758\pi$
$29$	−0.209526	−	0.209526i	−0.0389080	−	0.0389080i	−0.726293	+	0.687385i	$0.758758\pi$
$30$		0			0
$31$	−3.33052	−	5.76864i	−0.598180	−	1.03608i	−0.993090	−	0.117358i	$-0.962558\pi$
$31$	−3.33052	−	5.76864i	−0.598180	−	1.03608i	0.394910	−	0.918720i	$-0.370776\pi$
$32$		0			0
$33$	−6.89376	−	3.98011i	−1.20005	−	0.692849i
$34$		0			0
$35$	−2.00026	−	0.0915096i	−0.338105	−	0.0154679i
$36$		0			0
$37$	1.02406	+	3.82183i	0.168354	+	0.628305i	0.997589	+	0.0694046i	$0.0221099\pi$
$37$	1.02406	+	3.82183i	0.168354	+	0.628305i	−0.829235	+	0.558900i	$0.811223\pi$
$38$		0			0
$39$	−3.55850	−	6.16350i	−0.569815	−	0.986949i
$40$		0			0
$41$	−5.04472			−0.787853			−0.393926	−	0.919142i	$-0.628883\pi$
$41$	−5.04472			−0.787853			−0.393926	+	0.919142i	$0.628883\pi$
$42$		0			0
$43$	3.79454	+	3.79454i	0.578662	+	0.578662i	0.934534	−	0.355873i	$-0.115816\pi$
$43$	3.79454	+	3.79454i	0.578662	+	0.578662i	−0.355873	+	0.934534i	$0.615816\pi$
$44$		0			0
$45$	−0.0154917	−	0.00415099i	−0.00230936	−	0.000618792i
$46$		0			0
$47$	2.53993	−	4.39928i	0.370486	−	0.641701i	−0.619154	−	0.785270i	$-0.712524\pi$
$47$	2.53993	−	4.39928i	0.370486	−	0.641701i	0.989640	+	0.143568i	$0.0458577\pi$
$48$		0			0
$49$	5.71728	+	4.03890i	0.816754	+	0.576985i
$50$		0			0
$51$	−1.18659	−	4.42843i	−0.166156	−	0.620104i
$52$		0			0
$53$	10.7333	+	2.87599i	1.47434	+	0.395047i	0.904416	−	0.426652i	$-0.140307\pi$
$53$	10.7333	+	2.87599i	1.47434	+	0.395047i	0.569921	+	0.821699i	$0.306974\pi$
$54$		0			0
$55$			3.46599i			0.467354i
$56$		0			0
$57$			9.68145i			1.28234i
$58$		0			0
$59$	5.23198	+	1.40190i	0.681145	+	0.182512i	0.582770	−	0.812637i	$-0.301969\pi$
$59$	5.23198	+	1.40190i	0.681145	+	0.182512i	0.0983751	+	0.995149i	$0.468635\pi$
$60$		0			0
$61$	−1.56694	−	5.84791i	−0.200626	−	0.748748i	−0.990738	−	0.135785i	$-0.956644\pi$
$61$	−1.56694	−	5.84791i	−0.200626	−	0.748748i	0.790112	−	0.612962i	$-0.210022\pi$
$62$		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
$67$	−9.24005	−	2.47586i	−1.12885	−	0.302475i	−0.354392	−	0.935097i	$-0.615312\pi$
$67$	−9.24005	−	2.47586i	−1.12885	−	0.302475i	−0.774461	+	0.632622i	$0.781979\pi$
$68$		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	0.991881	−	0.127172i	$-0.0405901\pi$
$73$	3.29633	+	5.70940i	0.385806	+	0.668235i	−0.606075	+	0.795408i	$0.707257\pi$
$74$		0			0
$75$	−1.99167	−	7.43301i	−0.229978	−	0.858290i
$76$		0			0
$77$	6.53159	−	10.2056i	0.744344	−	1.16303i
$78$		0			0
$79$	13.0615	+	7.54108i	1.46954	+	0.848437i	0.999416	−	0.0341648i	$-0.0108771\pi$
$79$	13.0615	+	7.54108i	1.46954	+	0.848437i	0.470121	+	0.882602i	$0.344210\pi$
$80$		0			0
$81$	−4.53156	−	7.84890i	−0.503507	−	0.872100i
$82$		0			0
$83$	8.00548	+	8.00548i	0.878715	+	0.878715i	0.993402	−	0.114687i	$-0.0365864\pi$
$83$	8.00548	+	8.00548i	0.878715	+	0.878715i	−0.114687	+	0.993402i	$0.536586\pi$
$84$		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	−0.579455	−	0.815004i	$-0.696734\pi$
$89$	3.92536	−	6.79892i	0.416087	−	0.720684i	0.995542	+	0.0943203i	$0.0300678\pi$
$90$		0			0
$91$	9.61956	−	4.98218i	1.00840	−	0.522274i
$92$		0			0
$93$	11.1834	−	2.99659i	1.15967	−	0.310732i
$94$		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
$101$	0.597042	−	2.22819i	0.0594079	−	0.221713i	−0.929839	−	0.367966i	$-0.880054\pi$
$101$	0.597042	−	2.22819i	0.0594079	−	0.221713i	0.989247	+	0.146252i	$0.0467211\pi$
$102$		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
$107$	−4.56363	+	1.22282i	−0.441183	+	0.118215i	−0.472571	−	0.881293i	$-0.656674\pi$
$107$	−4.56363	+	1.22282i	−0.441183	+	0.118215i	0.0313881	+	0.999507i	$0.490007\pi$
$108$		0			0
$109$	−2.13269	+	7.95931i	−0.204275	+	0.762364i	0.785395	+	0.618995i	$0.212460\pi$
$109$	−2.13269	+	7.95931i	−0.204275	+	0.762364i	−0.989669	+	0.143368i	$0.954207\pi$
$110$		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
$115$	−0.396233	+	1.47876i	−0.0369490	+	0.137895i
$116$		0			0
$117$	0.0838137	−	0.0224578i	0.00774858	−	0.00207623i
$118$		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
$123$	2.26946	−	8.46974i	0.204630	−	0.763690i
$124$		0			0
$125$	−5.04499	+	5.04499i	−0.451237	+	0.451237i
$126$		0			0
$127$			13.0667i			1.15948i	0.814802	+	0.579739i	$0.196846\pi$
$127$			13.0667i			1.15948i	−0.814802	+	0.579739i	$0.803154\pi$
$128$		0			0
$129$	−8.07781	+	4.66373i	−0.711212	+	0.410618i
$130$		0			0
$131$	8.29942	−	2.22382i	0.725124	−	0.194296i	0.122667	−	0.992448i	$-0.460855\pi$
$131$	8.29942	−	2.22382i	0.725124	−	0.194296i	0.602457	+	0.798152i	$0.294189\pi$
$132$		0			0
$133$	−14.7213	−	0.673483i	−1.27650	−	0.0583984i
$134$		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	$-0.219569\pi$
$137$	19.9938	−	11.5434i	1.70818	−	0.986221i	0.936809	−	0.349841i	$-0.113764\pi$
$138$		0			0
$139$	−6.09369	+	6.09369i	−0.516860	+	0.516860i	−0.916620	−	0.399760i	$-0.869093\pi$
$139$	−6.09369	+	6.09369i	−0.516860	+	0.516860i	0.399760	+	0.916620i	$0.369093\pi$
$140$		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
$147$	−9.35305	+	7.78195i	−0.771427	+	0.641844i
$148$		0			0
$149$	−3.12680	−	11.6694i	−0.256157	−	0.955992i	−0.967443	−	0.253089i	$-0.918553\pi$
$149$	−3.12680	−	11.6694i	−0.256157	−	0.955992i	0.711286	−	0.702903i	$-0.248113\pi$
$150$		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
$157$	−23.2350	−	6.22579i	−1.85435	−	0.496872i	−0.854604	−	0.519281i	$-0.826200\pi$
$157$	−23.2350	−	6.22579i	−1.85435	−	0.496872i	−0.999749	+	0.0224085i	$0.992867\pi$
$158$		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
$163$	−2.36008	−	8.80794i	−0.184856	−	0.689891i	−0.994661	−	0.103193i	$-0.967094\pi$
$163$	−2.36008	−	8.80794i	−0.184856	−	0.689891i	0.809806	−	0.586698i	$-0.199573\pi$
$164$		0			0
$165$	−5.81916	−	1.55924i	−0.453021	−	0.121387i
$166$		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
$171$	−0.114014	−	0.0305500i	−0.00871888	−	0.00233622i
$172$		0			0
$173$	4.98693	+	18.6115i	0.379149	+	1.41500i	0.847187	+	0.531295i	$0.178294\pi$
$173$	4.98693	+	18.6115i	0.379149	+	1.41500i	−0.468038	+	0.883708i	$0.655039\pi$
$174$		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
$179$	7.03090	+	1.88392i	0.525514	+	0.140811i	0.511816	−	0.859095i	$-0.328973\pi$
$179$	7.03090	+	1.88392i	0.525514	+	0.140811i	0.0136980	+	0.999906i	$0.495640\pi$
$180$		0			0
$181$	5.59617	+	5.59617i	0.415960	+	0.415960i	0.883809	−	0.467849i	$-0.154971\pi$
$181$	5.59617	+	5.59617i	0.415960	+	0.415960i	−0.467849	+	0.883809i	$0.654971\pi$
$182$		0			0
$183$	10.5231			0.777894
$184$		0			0
$185$	1.49723	+	2.59328i	0.110079	+	0.190662i
$186$		0			0
$187$	−3.12643	−	11.6680i	−0.228627	−	0.853249i
$188$		0			0
$189$	12.1641	−	6.30004i	0.884807	−	0.458261i
$190$		0			0
$191$	−4.12735	−	2.38292i	−0.298644	−	0.172422i	0.343189	−	0.939266i	$-0.388493\pi$
$191$	−4.12735	−	2.38292i	−0.298644	−	0.172422i	−0.641834	+	0.766844i	$0.721826\pi$
$192$		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	$-0.950163\pi$
$197$	−11.6754	+	11.6754i	−0.831838	+	0.831838i	0.155930	+	0.987768i	$0.450163\pi$
$198$		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
$203$	0.360549	+	0.696147i	0.0253056	+	0.0488599i
$204$		0			0
$205$	−3.68784	+	0.988153i	−0.257570	+	0.0690156i
$206$		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	$-0.738895\pi$
$211$	0.716512	−	0.716512i	0.0493267	−	0.0493267i	0.731340	+	0.682013i	$0.238895\pi$
$212$		0			0
$213$	−3.26383	+	12.1808i	−0.223634	+	0.834612i
$214$		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
$219$	−11.0686	+	2.96583i	−0.747947	+	0.200412i
$220$		0			0
$221$	2.79525	−	10.4320i	0.188029	−	0.701733i
$222$		0			0
$223$	−12.9181			−0.865062			−0.432531	−	0.901619i	$-0.642379\pi$
$223$	−12.9181			−0.865062			−0.432531	+	0.901619i	$0.642379\pi$
$224$		0			0
$225$	0.0938201			0.00625467
$226$		0			0
$227$	−4.02569	+	15.0241i	−0.267195	+	0.997184i	0.693699	+	0.720265i	$0.255980\pi$
$227$	−4.02569	+	15.0241i	−0.267195	+	0.997184i	−0.960893	+	0.276919i	$0.910687\pi$
$228$		0			0
$229$	−13.3759	+	3.58406i	−0.883903	+	0.236841i	−0.672090	−	0.740469i	$-0.734603\pi$
$229$	−13.3759	+	3.58406i	−0.883903	+	0.236841i	−0.211813	+	0.977310i	$0.567937\pi$
$230$		0			0
$231$	14.1961	+	15.5572i	0.934032	+	1.02359i
$232$		0			0
$233$	−10.6523	−	6.15010i	−0.697854	−	0.402906i	0.108694	−	0.994075i	$-0.465333\pi$
$233$	−10.6523	−	6.15010i	−0.697854	−	0.402906i	−0.806548	+	0.591169i	$0.798667\pi$
$234$		0			0
$235$	0.995035	−	3.71352i	0.0649089	−	0.242243i
$236$		0			0
$237$	−18.5369	+	18.5369i	−1.20410	+	1.20410i
$238$		0			0
$239$		−	7.20218i		−	0.465870i	−0.972492	−	0.232935i	$-0.925167\pi$
$239$		−	7.20218i		−	0.465870i	0.972492	−	0.232935i	$-0.0748329\pi$
$240$		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
$243$	0.212722	−	0.0569986i	0.0136461	−	0.00365646i
$244$		0			0
$245$	4.97063	+	1.83266i	0.317562	+	0.117084i
$246$		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	−0.487369	−	0.873196i	$-0.662043\pi$
$251$	6.11266	−	6.11266i	0.385828	−	0.385828i	0.873196	+	0.487369i	$0.162043\pi$
$252$		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
$259$	0.478413	−	10.4574i	0.0297272	−	0.649790i
$260$		0			0
$261$	0.00162522	+	0.00606542i	0.000100599	+	0.000375440i
$262$		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
$269$	10.0057	+	2.68103i	0.610061	+	0.163465i	0.550605	−	0.834766i	$-0.314397\pi$
$269$	10.0057	+	2.68103i	0.610061	+	0.163465i	0.0594553	+	0.998231i	$0.481064\pi$
$270$		0			0
$271$	−12.3322	+	21.3601i	−0.749131	+	1.29753i	0.199109	+	0.979977i	$0.436195\pi$
$271$	−12.3322	+	21.3601i	−0.749131	+	1.29753i	−0.948240	+	0.317555i	$0.897138\pi$
$272$		0			0
$273$	4.03720	+	18.3919i	0.244342	+	1.11313i
$274$		0			0
$275$	−5.24764	−	19.5845i	−0.316445	−	1.18099i
$276$		0			0
$277$	−10.3610	−	2.77622i	−0.622531	−	0.166807i	−0.0662529	−	0.997803i	$-0.521104\pi$
$277$	−10.3610	−	2.77622i	−0.622531	−	0.166807i	−0.556278	+	0.830996i	$0.687771\pi$
$278$		0			0
$279$			0.141158i			0.00845093i
$280$		0			0
$281$		−	6.46396i		−	0.385608i	−0.981237	−	0.192804i	$-0.938242\pi$
$281$		−	6.46396i		−	0.385608i	0.981237	−	0.192804i	$-0.0617581\pi$
$282$		0			0
$283$	−19.0327	−	5.09979i	−1.13138	−	0.303151i	−0.355897	−	0.934525i	$-0.615825\pi$
$283$	−19.0327	−	5.09979i	−1.13138	−	0.303151i	−0.775478	+	0.631374i	$0.782491\pi$
$284$		0			0
$285$	1.89639	+	7.07742i	0.112332	+	0.419230i
$286$		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
$291$	14.7667	+	3.95673i	0.865641	+	0.231948i
$292$		0			0
$293$	2.96394	+	2.96394i	0.173155	+	0.173155i	0.788364	−	0.615209i	$-0.210928\pi$
$293$	2.96394	+	2.96394i	0.173155	+	0.173155i	−0.615209	+	0.788364i	$0.710928\pi$
$294$		0			0
$295$	4.09933			0.238672
$296$		0			0
$297$	−11.8560	−	20.5352i	−0.687954	−	1.19157i
$298$		0			0
$299$	−2.14372	−	8.00046i	−0.123974	−	0.462679i
$300$		0			0
$301$	−6.52959	−	12.6073i	−0.376359	−	0.726672i
$302$		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	0.417356	−	0.908743i	$-0.362957\pi$
$307$	−8.60981	−	8.60981i	−0.491388	−	0.491388i	−0.908743	+	0.417356i	$0.862957\pi$
$308$		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	−0.956920	−	0.290352i	$-0.906228\pi$
$313$	−4.01618	+	6.95623i	−0.227008	+	0.393190i	0.729912	+	0.683541i	$0.239561\pi$
$314$		0			0
$315$	0.0357401	+	0.0228738i	0.00201372	+	0.00128879i
$316$		0			0
$317$	9.01190	−	2.41473i	0.506159	−	0.135625i	0.00330181	−	0.999995i	$-0.498949\pi$
$317$	9.01190	−	2.41473i	0.506159	−	0.135625i	0.502857	+	0.864370i	$0.332282\pi$
$318$		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
$325$	4.69176	−	17.5099i	0.260252	−	0.971273i
$326$		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
$331$	−4.96046	+	1.32915i	−0.272652	+	0.0730568i	−0.392554	−	0.919729i	$-0.628408\pi$
$331$	−4.96046	+	1.32915i	−0.272652	+	0.0730568i	0.119903	+	0.992786i	$0.461742\pi$
$332$		0			0
$333$	0.0217014	−	0.0809907i	0.00118923	−	0.00443827i
$334$		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
$339$	−8.31587	+	31.0353i	−0.451656	+	1.68560i
$340$		0			0
$341$	29.4661	−	7.89541i	1.59568	−	0.427561i
$342$		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
$347$	−2.24815	+	8.39020i	−0.120687	+	0.450410i	−0.999649	−	0.0264814i	$-0.991570\pi$
$347$	−2.24815	+	8.39020i	−0.120687	+	0.450410i	0.878962	+	0.476891i	$0.158236\pi$
$348$		0			0
$349$	15.6677	−	15.6677i	0.838672	−	0.838672i	−0.150012	−	0.988684i	$-0.547931\pi$
$349$	15.6677	−	15.6677i	0.838672	−	0.838672i	0.988684	+	0.150012i	$0.0479313\pi$
$350$		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
$355$	5.30367	−	1.42111i	0.281490	−	0.0754249i
$356$		0			0
$357$	−0.554347	+	12.1172i	−0.0293391	+	0.641308i
$358$		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	$0.0481022\pi$
$367$	11.9671	+	20.7276i	0.624676	+	1.08197i	−0.363928	+	0.931427i	$0.618564\pi$
$368$		0			0
$369$	0.0925831	+	0.0534529i	0.00481968	+	0.00278264i
$370$		0			0
$371$	−24.7623	−	15.8480i	−1.28560	−	0.822786i
$372$		0			0
$373$	0.612436	+	2.28564i	0.0317107	+	0.118346i	0.979967	−	0.199160i	$-0.0638213\pi$
$373$	0.612436	+	2.28564i	0.0317107	+	0.118346i	−0.948256	+	0.317506i	$0.897155\pi$
$374$		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	$-0.187795\pi$
$379$	5.34619	+	5.34619i	0.274615	+	0.274615i	−0.556340	+	0.830955i	$0.687795\pi$
$380$		0			0
$381$	−21.9380	−	5.87828i	−1.12392	−	0.301153i
$382$		0			0
$383$	12.5700	−	21.7718i	0.642296	−	1.11249i	−0.342623	−	0.939473i	$-0.611315\pi$
$383$	12.5700	−	21.7718i	0.642296	−	1.11249i	0.984919	−	0.173016i	$-0.0553514\pi$
$384$		0			0
$385$	2.77573	−	8.73996i	0.141464	−	0.445429i
$386$		0			0
$387$	−0.0294330	−	0.109845i	−0.00149616	−	0.00558375i
$388$		0			0
$389$	−6.08010	−	1.62916i	−0.308273	−	0.0826016i	0.101366	−	0.994849i	$-0.467679\pi$
$389$	−6.08010	−	1.62916i	−0.308273	−	0.0826016i	−0.409639	+	0.912248i	$0.634345\pi$
$390$		0			0
$391$		−	5.33557i		−	0.269831i
$392$		0			0
$393$			14.9346i			0.753350i
$394$		0			0
$395$	11.0255	+	2.95427i	0.554753	+	0.148646i
$396$		0			0
$397$	4.67347	+	17.4416i	0.234555	+	0.875371i	0.978349	+	0.206962i	$0.0663577\pi$
$397$	4.67347	+	17.4416i	0.234555	+	0.875371i	−0.743794	+	0.668409i	$0.766976\pi$
$398$		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
$403$	26.3447	+	7.05905i	1.31232	+	0.351636i
$404$		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	$0.0989637\pi$
$409$	14.9850	+	25.9548i	0.740963	+	1.28338i	−0.211095	+	0.977466i	$0.567703\pi$
$410$		0			0
$411$	10.3860	+	38.7612i	0.512305	+	1.91195i
$412$		0			0
$413$	−12.0704	−	7.72511i	−0.593946	−	0.380128i
$414$		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	0.997802	−	0.0662653i	$-0.0211084\pi$
$419$	19.0681	+	19.0681i	0.931537	+	0.931537i	−0.0662653	+	0.997802i	$0.521108\pi$
$420$		0			0
$421$	1.12116	−	1.12116i	0.0546418	−	0.0546418i	−0.679258	−	0.733900i	$-0.737698\pi$
$421$	1.12116	−	1.12116i	0.0546418	−	0.0546418i	0.733900	+	0.679258i	$0.237698\pi$
$422$		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
$427$	−0.732036	+	16.0012i	−0.0354257	+	0.774351i
$428$		0			0
$429$	31.4830	−	8.43585i	1.52001	−	0.407287i
$430$		0			0
$431$	−14.2383	+	8.22048i	−0.685834	+	0.395966i	−0.802049	−	0.597258i	$-0.796257\pi$
$431$	−14.2383	+	8.22048i	−0.685834	+	0.395966i	0.116216	+	0.993224i	$0.462924\pi$
$432$		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
$437$	−2.91616	+	10.8833i	−0.139499	+	0.520617i
$438$		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
$443$	33.5974	−	9.00239i	1.59626	−	0.427717i	0.652350	−	0.757918i	$-0.273783\pi$
$443$	33.5974	−	9.00239i	1.59626	−	0.427717i	0.943910	+	0.330202i	$0.107117\pi$
$444$		0			0
$445$	1.53779	−	5.73910i	0.0728982	−	0.272060i
$446$		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
$451$	5.97956	−	22.3160i	0.281567	−	1.05082i
$452$		0			0
$453$	−2.73223	+	0.732100i	−0.128372	+	0.0343970i
$454$		0			0
$455$	6.05628	−	5.52638i	0.283923	−	0.259081i
$456$		0			0
$457$	26.0860	+	15.0607i	1.22025	+	0.704512i	0.964971	−	0.262356i	$-0.0844993\pi$
$457$	26.0860	+	15.0607i	1.22025	+	0.704512i	0.255279	+	0.966867i	$0.417833\pi$
$458$		0			0
$459$	3.53464	−	13.1914i	0.164983	−	0.615724i
$460$		0			0
$461$	2.37946	−	2.37946i	0.110822	−	0.110822i	−0.649521	−	0.760344i	$-0.725031\pi$
$461$	2.37946	−	2.37946i	0.110822	−	0.110822i	0.760344	+	0.649521i	$0.225031\pi$
$462$		0			0
$463$		−	1.23324i		−	0.0573136i	−0.999589	−	0.0286568i	$-0.990877\pi$
$463$		−	1.23324i		−	0.0573136i	0.999589	−	0.0286568i	$-0.00912299\pi$
$464$		0			0
$465$	7.58845	−	4.38120i	0.351906	−	0.203173i
$466$		0			0
$467$	30.7990	−	8.25258i	1.42521	−	0.381884i	0.537881	−	0.843021i	$-0.319225\pi$
$467$	30.7990	−	8.25258i	1.42521	−	0.381884i	0.887329	+	0.461137i	$0.152558\pi$
$468$		0			0
$469$	21.3172	+	13.6431i	0.984339	+	0.629980i
$470$		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	0.976964	−	0.213404i	$-0.0684552\pi$
$479$	6.64611	+	11.5114i	0.303668	+	0.525969i	−0.673296	+	0.739373i	$0.735122\pi$
$480$		0			0
$481$	−14.0303	−	8.10037i	−0.639725	−	0.369345i
$482$		0			0
$483$	4.27824	+	8.26040i	0.194667	+	0.375861i
$484$		0			0
$485$	−1.72281	−	6.42963i	−0.0782290	−	0.291955i
$486$		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	$-0.322578\pi$
$491$	−7.08341	−	7.08341i	−0.319670	−	0.319670i	−0.848640	+	0.528970i	$0.822578\pi$
$492$		0			0
$493$	0.754942	+	0.202286i	0.0340009	+	0.00911051i
$494$		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
$499$	−5.87786	−	21.9365i	−0.263129	−	0.982011i	−0.963386	−	0.268120i	$-0.913598\pi$
$499$	−5.87786	−	21.9365i	−0.263129	−	0.982011i	0.700256	−	0.713891i	$-0.253069\pi$
$500$		0			0
$501$	−5.35158	−	1.43395i	−0.239091	−	0.0640642i
$502$		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
$507$	6.32191	+	1.69395i	0.280766	+	0.0752310i
$508$		0			0
$509$	−1.40903	−	5.25856i	−0.0624540	−	0.233081i	0.927643	−	0.373469i	$-0.121832\pi$
$509$	−1.40903	−	5.25856i	−0.0624540	−	0.233081i	−0.990097	+	0.140388i	$0.955165\pi$
$510$		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
$515$	−9.96122	−	2.66910i	−0.438944	−	0.117615i
$516$		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	0.916967	−	0.398963i	$-0.130630\pi$
$521$	2.57861	+	4.46629i	0.112971	+	0.195672i	−0.803996	+	0.594635i	$0.797297\pi$
$522$		0			0
$523$	−1.98945	−	7.42474i	−0.0869928	−	0.324661i	0.908691	−	0.417469i	$-0.137083\pi$
$523$	−1.98945	−	7.42474i	−0.0869928	−	0.324661i	−0.995684	+	0.0928072i	$0.970416\pi$
$524$		0			0
$525$	−0.930458	+	20.3384i	−0.0406085	+	0.887639i
$526$		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
$539$	−24.6434	+	20.5039i	−1.06147	+	0.883163i
$540$		0			0
$541$	7.55039	−	2.02312i	0.324617	−	0.0869808i	−0.0928305	−	0.995682i	$-0.529591\pi$
$541$	7.55039	−	2.02312i	0.324617	−	0.0869808i	0.417447	+	0.908701i	$0.362925\pi$
$542$		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	$-0.783304\pi$
$547$	−3.45431	+	3.45431i	−0.147696	+	0.147696i	0.629392	+	0.777088i	$0.283304\pi$
$548$		0			0
$549$	−0.0332060	+	0.123927i	−0.00141720	+	0.00528906i
$550$		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
$555$	−5.02749	+	1.34711i	−0.213405	+	0.0571817i
$556$		0			0
$557$	−7.47554	+	27.8991i	−0.316749	+	1.18212i	0.605602	+	0.795768i	$0.292933\pi$
$557$	−7.47554	+	27.8991i	−0.316749	+	1.18212i	−0.922350	+	0.386354i	$0.873734\pi$
$558$		0			0
$559$	−21.9726			−0.929342
$560$		0			0
$561$	20.9963			0.886463
$562$		0			0
$563$	−0.243342	+	0.908166i	−0.0102557	+	0.0382746i	−0.970864	−	0.239631i	$-0.922974\pi$
$563$	−0.243342	+	0.908166i	−0.0102557	+	0.0382746i	0.960608	+	0.277906i	$0.0896402\pi$
$564$		0			0
$565$	13.5132	−	3.62084i	0.568503	−	0.152330i
$566$		0			0
$567$	5.14116	+	23.4211i	0.215909	+	0.983596i
$568$		0			0
$569$	−11.5141	−	6.64769i	−0.482698	−	0.278686i	0.238842	−	0.971058i	$-0.423232\pi$
$569$	−11.5141	−	6.64769i	−0.482698	−	0.278686i	−0.721540	+	0.692373i	$0.756565\pi$
$570$		0			0
$571$	−2.11813	+	7.90497i	−0.0886410	+	0.330813i	−0.995979	−	0.0895898i	$-0.971444\pi$
$571$	−2.11813	+	7.90497i	−0.0886410	+	0.330813i	0.907338	+	0.420402i	$0.138111\pi$
$572$		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
$579$	−8.96716	+	2.40274i	−0.372662	+	0.0998546i
$580$		0			0
$581$	−13.7757	−	26.5981i	−0.571513	−	1.10347i
$582$		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	−0.488616	−	0.872499i	$-0.662498\pi$
$587$	9.30074	−	9.30074i	0.383883	−	0.383883i	0.872499	+	0.488616i	$0.162498\pi$
$588$		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
$595$	4.68981	−	2.42895i	0.192264	−	0.0995774i
$596$		0			0
$597$	4.69033	+	17.5046i	0.191963	+	0.716414i
$598$		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	$-0.660483\pi$
$601$	−23.6858			−0.966164			−0.483082	+	0.875575i	$0.660483\pi$
$602$		0			0
$603$	0.143344	+	0.143344i	0.00583742	+	0.00583742i
$604$		0			0
$605$	−7.29097	−	1.95361i	−0.296420	−	0.0794255i
$606$		0			0
$607$	2.86300	−	4.95886i	0.116206	−	0.201274i	−0.802055	−	0.597250i	$-0.796260\pi$
$607$	2.86300	−	4.95886i	0.116206	−	0.201274i	0.918261	+	0.395976i	$0.129593\pi$
$608$		0			0
$609$	−1.33098	+	0.292163i	−0.0539341	+	0.0118391i
$610$		0			0
$611$	5.38338	+	20.0910i	0.217788	+	0.812796i
$612$		0			0
$613$	2.17496	+	0.582780i	0.0878459	+	0.0235383i	0.302474	−	0.953158i	$-0.402187\pi$
$613$	2.17496	+	0.582780i	0.0878459	+	0.0235383i	−0.214628	+	0.976696i	$0.568854\pi$
$614$		0			0
$615$		−	6.63616i		−	0.267596i
$616$		0			0
$617$			12.2572i			0.493457i	0.969085	+	0.246729i	$0.0793556\pi$
$617$			12.2572i			0.493457i	−0.969085	+	0.246729i	$0.920644\pi$
$618$		0			0
$619$	7.21445	+	1.93311i	0.289973	+	0.0776981i	0.400873	−	0.916133i	$-0.368707\pi$
$619$	7.21445	+	1.93311i	0.289973	+	0.0776981i	−0.110900	+	0.993832i	$0.535373\pi$
$620$		0			0
$621$	−2.71077	−	10.1167i	−0.108779	−	0.405970i
$622$		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
$627$	−42.8272	−	11.4755i	−1.71036	−	0.458288i
$628$		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
$635$	2.55948	+	9.55211i	0.101570	+	0.379064i
$636$		0			0
$637$	−28.2470	+	4.85941i	−1.11919	+	0.192537i
$638$		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	0.646743	−	0.762708i	$-0.276131\pi$
$643$	−2.94059	−	2.94059i	−0.115965	−	0.115965i	−0.762708	+	0.646743i	$0.776131\pi$
$644$		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
$651$	−30.6004	−	1.39993i	−1.19932	−	0.0548677i
$652$		0			0
$653$	−11.8827	+	3.18397i	−0.465007	+	0.124598i	−0.483713	−	0.875227i	$-0.660712\pi$
$653$	−11.8827	+	3.18397i	−0.465007	+	0.124598i	0.0187058	+	0.999825i	$0.494045\pi$
$654$		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	$-0.959429\pi$
$659$	−22.1996	+	22.1996i	−0.864775	+	0.864775i	0.127114	+	0.991888i	$0.459429\pi$
$660$		0			0
$661$	−0.253956	+	0.947777i	−0.00987774	+	0.0368642i	−0.970689	−	0.240340i	$-0.922741\pi$
$661$	−0.253956	+	0.947777i	−0.00987774	+	0.0368642i	0.960811	+	0.277204i	$0.0894078\pi$
$662$		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
$667$	0.578976	−	0.155136i	0.0224181	−	0.00600690i
$668$		0			0
$669$	5.81146	−	21.6887i	0.224684	−	0.838532i
$670$		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
$675$	5.93280	−	22.1415i	0.228354	−	0.852227i
$676$		0			0
$677$	7.13755	−	1.91250i	0.274318	−	0.0735033i	−0.119037	−	0.992890i	$-0.537981\pi$
$677$	7.13755	−	1.91250i	0.274318	−	0.0735033i	0.393356	+	0.919386i	$0.371314\pi$
$678$		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
$683$	−0.510463	+	1.90507i	−0.0195323	+	0.0728956i	−0.975004	−	0.222187i	$-0.928680\pi$
$683$	−0.510463	+	1.90507i	−0.0195323	+	0.0728956i	0.955472	+	0.295083i	$0.0953472\pi$
$684$		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
$691$	0.216289	−	0.0579544i	0.00822801	−	0.00220469i	−0.254703	−	0.967019i	$-0.581978\pi$
$691$	0.216289	−	0.0579544i	0.00822801	−	0.00220469i	0.262931	+	0.964815i	$0.415311\pi$
$692$		0			0
$693$	−0.228007	+	0.118090i	−0.00866127	+	0.00448586i
$694$		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	$-0.0876898\pi$
$701$	18.2761	+	18.2761i	0.690279	+	0.690279i	−0.272014	+	0.962293i	$0.587690\pi$
$702$		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
$707$	−3.28997	+	5.14054i	−0.123732	+	0.193330i
$708$		0			0
$709$	0.446105	+	1.66489i	0.0167538	+	0.0625261i	0.973797	−	0.227420i	$-0.0730292\pi$
$709$	0.446105	+	1.66489i	0.0167538	+	0.0625261i	−0.957043	+	0.289946i	$0.906362\pi$
$710$		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
$717$	12.0920	+	3.24003i	0.451582	+	0.121001i
$718$		0			0
$719$	−25.5064	+	44.1784i	−0.951229	+	1.64758i	−0.208457	+	0.978031i	$0.566844\pi$
$719$	−25.5064	+	44.1784i	−0.951229	+	1.64758i	−0.742771	+	0.669545i	$0.766489\pi$
$720$		0			0
$721$	24.3008	+	26.6309i	0.905009	+	0.991785i
$722$		0			0
$723$	10.7728	+	40.2045i	0.400644	+	1.49522i
$724$		0			0
$725$	1.26715	+	0.339532i	0.0470609	+	0.0126099i
$726$		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
$731$	−13.6721	−	3.66342i	−0.505680	−	0.135496i
$732$		0			0
$733$	10.8083	+	40.3371i	0.399213	+	1.48988i	0.814484	+	0.580186i	$0.197020\pi$
$733$	10.8083	+	40.3371i	0.399213	+	1.48988i	−0.415271	+	0.909698i	$0.636313\pi$
$734$		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
$739$	17.3991	+	4.66207i	0.640036	+	0.171497i	0.564220	−	0.825625i	$-0.309177\pi$
$739$	17.3991	+	4.66207i	0.640036	+	0.171497i	0.0758162	+	0.997122i	$0.475844\pi$
$740$		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
$747$	−0.0620958	−	0.231745i	−0.00227197	−	0.00847910i
$748$		0			0
$749$	12.4871	+	0.571271i	0.456269	+	0.0208738i
$750$		0			0
$751$	−0.399765	−	0.230804i	−0.0145876	−	0.00842217i	0.492688	−	0.870206i	$-0.336014\pi$
$751$	−0.399765	−	0.230804i	−0.0145876	−	0.00842217i	−0.507276	+	0.861784i	$0.669348\pi$
$752$		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	$-0.792931\pi$
$757$	−5.23204	+	5.23204i	−0.190162	+	0.190162i	0.605604	+	0.795766i	$0.292931\pi$
$758$		0			0
$759$	13.9450	−	8.05117i	0.506173	−	0.292239i
$760$		0			0
$761$	10.6052	−	18.3687i	0.384437	−	0.665864i	−0.607254	−	0.794508i	$-0.707729\pi$
$761$	10.6052	−	18.3687i	0.384437	−	0.665864i	0.991691	+	0.128644i	$0.0410623\pi$
$762$		0			0
$763$	11.7521	−	18.3625i	0.425454	−	0.664767i
$764$		0			0
$765$	0.0408616	−	0.0109488i	0.00147735	−	0.000395856i
$766$		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
$773$	−12.5926	+	46.9962i	−0.452924	+	1.69034i	0.241196	+	0.970476i	$0.422460\pi$
$773$	−12.5926	+	46.9962i	−0.452924	+	1.69034i	−0.694120	+	0.719859i	$0.744206\pi$
$774$		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
$779$	−27.1414	+	7.27251i	−0.972441	+	0.260565i
$780$		0			0
$781$	−8.59952	+	32.0938i	−0.307715	+	1.14841i
$782$		0			0
$783$	1.53421			0.0548282
$784$		0			0
$785$	−18.2049			−0.649762
$786$		0			0
$787$	3.47299	−	12.9614i	0.123799	−	0.462023i	−0.875995	−	0.482319i	$-0.839794\pi$
$787$	3.47299	−	12.9614i	0.123799	−	0.462023i	0.999794	+	0.0202968i	$0.00646112\pi$
$788$		0			0
$789$	−17.7560	+	4.75770i	−0.632130	+	0.169379i
$790$		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
$795$	−3.78327	+	14.1194i	−0.134179	+	0.500762i
$796$		0			0
$797$	−6.22856	+	6.22856i	−0.220627	+	0.220627i	−0.808762	−	0.588135i	$-0.799862\pi$
$797$	−6.22856	+	6.22856i	−0.220627	+	0.220627i	0.588135	+	0.808762i	$0.299862\pi$
$798$		0			0
$799$			13.3989i			0.474017i
$800$		0			0
$801$	−0.144080	+	0.0831847i	−0.00509082	+	0.00293919i
$802$		0			0
$803$	−29.1635	+	7.81434i	−1.02916	+	0.275762i
$804$		0			0
$805$	2.18342	−	3.41158i	0.0769555	−	0.120242i
$806$		0			0
$807$	−9.00253	+	15.5928i	−0.316904	+	0.548894i
$808$		0			0
$809$	1.49336	−	0.862190i	0.0525036	−	0.0303130i	−0.473518	−	0.880784i	$-0.657016\pi$
$809$	1.49336	−	0.862190i	0.0525036	−	0.0303130i	0.526022	+	0.850471i	$0.323683\pi$
$810$		0			0
$811$	29.5809	−	29.5809i	1.03872	−	1.03872i	0.0395050	−	0.999219i	$-0.487422\pi$
$811$	29.5809	−	29.5809i	1.03872	−	1.03872i	0.999219	−	0.0395050i	$-0.0125781\pi$
$812$		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
$819$	−0.229333	−	0.0104917i	−0.00801354	−	0.000366611i
$820$		0			0
$821$	−9.77105	−	36.4661i	−0.341012	−	1.27267i	−0.897202	−	0.441620i	$-0.854404\pi$
$821$	−9.77105	−	36.4661i	−0.341012	−	1.27267i	0.556190	−	0.831055i	$-0.312263\pi$
$822$		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	$-0.462510\pi$
$827$	−25.1791	−	25.1791i	−0.875565	−	0.875565i	−0.993072	+	0.117507i	$0.962510\pi$
$828$		0			0
$829$	22.7086	+	6.08475i	0.788702	+	0.211332i	0.630618	−	0.776094i	$-0.282802\pi$
$829$	22.7086	+	6.08475i	0.788702	+	0.211332i	0.158084	+	0.987426i	$0.449468\pi$
$830$		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
$835$	0.624362	+	2.33015i	0.0216069	+	0.0806382i
$836$		0			0
$837$	33.3133	+	8.92628i	1.15148	+	0.308537i
$838$		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
$843$	10.8525	+	2.90793i	0.373782	+	0.100154i
$844$		0			0
$845$	−0.737569	−	2.75264i	−0.0253731	−	0.0946938i
$846$		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
$851$	−7.73099	−	2.07151i	−0.265015	−	0.0710106i
$852$		0			0
$853$	−2.88131	−	2.88131i	−0.0986542	−	0.0986542i	0.656057	−	0.754711i	$-0.272223\pi$
$853$	−2.88131	−	2.88131i	−0.0986542	−	0.0986542i	−0.754711	+	0.656057i	$0.772223\pi$
$854$		0			0
$855$	−0.0893318			−0.00305508
$856$		0			0
$857$	7.75242	+	13.4276i	0.264817	+	0.458677i	0.967516	−	0.252811i	$-0.0813550\pi$
$857$	7.75242	+	13.4276i	0.264817	+	0.458677i	−0.702698	+	0.711488i	$0.748022\pi$
$858$		0			0
$859$	−6.34616	−	23.6842i	−0.216528	−	0.808094i	−0.985623	−	0.168960i	$-0.945959\pi$
$859$	−6.34616	−	23.6842i	−0.216528	−	0.808094i	0.769095	−	0.639135i	$-0.220707\pi$
$860$		0			0
$861$	−12.5057	+	19.5401i	−0.426194	+	0.665924i
$862$		0			0
$863$	−40.7734	−	23.5405i	−1.38794	−	0.801329i	−0.394860	−	0.918741i	$-0.629207\pi$
$863$	−40.7734	−	23.5405i	−1.38794	−	0.801329i	−0.993083	+	0.117412i	$0.962540\pi$
$864$		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
$875$	16.7619	−	8.68134i	0.566655	−	0.293483i
$876$		0			0
$877$	−19.5661	+	5.24273i	−0.660701	+	0.177034i	−0.573563	−	0.819162i	$-0.694439\pi$
$877$	−19.5661	+	5.24273i	−0.660701	+	0.177034i	−0.0871389	+	0.996196i	$0.527772\pi$
$878$		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	$-0.672467\pi$
$883$	10.1351	−	10.1351i	0.341074	−	0.341074i	0.856771	+	0.515697i	$0.172467\pi$
$884$		0			0
$885$	−1.84416	+	6.88249i	−0.0619907	+	0.231352i
$886$		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
$891$	40.0920	−	10.7426i	1.34313	−	0.359891i
$892$		0			0
$893$	7.32316	−	27.3304i	0.245060	−	0.914577i
$894$		0			0
$895$	5.50881			0.184139
$896$		0			0
$897$	14.3966			0.480689
$898$		0			0
$899$	−0.510848	+	1.90651i	−0.0170377	+	0.0635857i
$900$		0			0
$901$	−28.3107	+	7.58584i	−0.943168	+	0.252721i
$902$		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
$907$	−2.16076	+	8.06405i	−0.0717467	+	0.267762i	−0.992476	−	0.122440i	$-0.960928\pi$
$907$	−2.16076	+	8.06405i	−0.0717467	+	0.267762i	0.920729	+	0.390202i	$0.127595\pi$
$908$		0			0
$909$	−0.0345667	+	0.0345667i	−0.00114650	+	0.00114650i
$910$		0			0
$911$		−	8.93090i		−	0.295894i	−0.988995	−	0.147947i	$-0.952734\pi$
$911$		−	8.93090i		−	0.295894i	0.988995	−	0.147947i	$-0.0472665\pi$
$912$		0			0
$913$	−44.9023	+	25.9244i	−1.48605	+	0.857972i
$914$		0			0
$915$	7.69273	−	2.06126i	0.254314	−	0.0681432i
$916$		0			0
$917$	−22.7091	−	1.03891i	−0.749919	−	0.0343080i
$918$		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
$931$	36.5824	+	13.4878i	1.19894	+	0.442045i
$932$		0			0
$933$	−2.59210	−	9.67386i	−0.0848617	−	0.316708i
$934$		0			0
$935$	−4.57103	−	7.91725i	−0.149489	−	0.258922i
$936$		0			0
$937$	14.3493			0.468771			0.234385	−	0.972144i	$-0.424692\pi$
$937$	14.3493			0.468771			0.234385	+	0.972144i	$0.424692\pi$
$938$		0			0
$939$	−9.87228	−	9.87228i	−0.322170	−	0.322170i
$940$		0			0
$941$	31.7588	+	8.50975i	1.03531	+	0.277410i	0.736168	−	0.676799i	$-0.236633\pi$
$941$	31.7588	+	8.50975i	1.03531	+	0.277410i	0.299141	+	0.954209i	$0.403300\pi$
$942$		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
$947$	−13.0783	−	48.8089i	−0.424988	−	1.58608i	−0.763950	−	0.645276i	$-0.776742\pi$
$947$	−13.0783	−	48.8089i	−0.424988	−	1.58608i	0.338962	−	0.940800i	$-0.389924\pi$
$948$		0			0
$949$	−26.0742	−	6.98657i	−0.846405	−	0.226794i
$950$		0			0
$951$			16.2167i			0.525861i
$952$		0			0
$953$		−	12.5441i		−	0.406345i	−0.979143	−	0.203172i	$-0.934875\pi$
$953$		−	12.5441i		−	0.406345i	0.979143	−	0.203172i	$-0.0651252\pi$
$954$		0			0
$955$	−3.48398	−	0.933528i	−0.112739	−	0.0302083i
$956$		0			0
$957$	0.610485	+	2.27836i	0.0197342	+	0.0736489i
$958$		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
$963$	0.0967106	+	0.0259135i	0.00311646	+	0.000835052i
$964$		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
$971$	5.14459	+	19.1999i	0.165098	+	0.616153i	0.998028	+	0.0627745i	$0.0199949\pi$
$971$	5.14459	+	19.1999i	0.165098	+	0.616153i	−0.832930	+	0.553378i	$0.813338\pi$
$972$		0			0
$973$	20.2462	−	10.4859i	0.649063	−	0.336163i
$974$		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
$987$	−10.7437	−	20.7438i	−0.341974	−	0.660282i
$988$		0			0
$989$	−10.4853	+	2.80953i	−0.333414	+	0.0893379i
$990$		0			0
$991$	32.1531	−	18.5636i	1.02138	−	0.589693i	0.106875	−	0.994272i	$-0.465915\pi$
$991$	32.1531	−	18.5636i	1.02138	−	0.589693i	0.914503	+	0.404579i	$0.132582\pi$
$992$		0			0
$993$		−	8.92622i		−	0.283265i
$994$		0			0
$995$	5.57949	−	5.57949i	0.176882	−	0.176882i
$996$		0			0
$997$	14.9373	−	55.7466i	0.473067	−	1.76551i	−0.155582	−	0.987823i	$-0.549725\pi$
$997$	14.9373	−	55.7466i	0.473067	−	1.76551i	0.628649	−	0.777689i	$-0.283608\pi$
$998$		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	448.2.z.a.47.4		56
4.3	odd	2		112.2.v.a.19.6	yes	56
7.3	odd	6	inner	448.2.z.a.367.4		56
8.3	odd	2		896.2.z.b.607.4		56
8.5	even	2		896.2.z.a.607.11		56
16.3	odd	4		896.2.z.a.159.11		56
16.5	even	4		112.2.v.a.75.5	yes	56
16.11	odd	4	inner	448.2.z.a.271.4		56
16.13	even	4		896.2.z.b.159.4		56
28.3	even	6		112.2.v.a.3.5	✓	56
28.11	odd	6		784.2.w.f.227.5		56
28.19	even	6		784.2.j.a.195.25		56
28.23	odd	6		784.2.j.a.195.26		56
28.27	even	2		784.2.w.f.19.6		56
56.3	even	6		896.2.z.b.479.4		56
56.45	odd	6		896.2.z.a.479.11		56
112.3	even	12		896.2.z.a.31.11		56
112.5	odd	12		784.2.j.a.587.26		56
112.37	even	12		784.2.j.a.587.25		56
112.45	odd	12		896.2.z.b.31.4		56
112.53	even	12		784.2.w.f.619.6		56
112.59	even	12	inner	448.2.z.a.143.4		56
112.69	odd	4		784.2.w.f.411.5		56
112.101	odd	12		112.2.v.a.59.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.5	✓	56	28.3	even	6
112.2.v.a.19.6	yes	56	4.3	odd	2
112.2.v.a.59.6	yes	56	112.101	odd	12
112.2.v.a.75.5	yes	56	16.5	even	4
448.2.z.a.47.4		56	1.1	even	1	trivial
448.2.z.a.143.4		56	112.59	even	12	inner
448.2.z.a.271.4		56	16.11	odd	4	inner
448.2.z.a.367.4		56	7.3	odd	6	inner
784.2.j.a.195.25		56	28.19	even	6
784.2.j.a.195.26		56	28.23	odd	6
784.2.j.a.587.25		56	112.37	even	12
784.2.j.a.587.26		56	112.5	odd	12
784.2.w.f.19.6		56	28.27	even	2
784.2.w.f.227.5		56	28.11	odd	6
784.2.w.f.411.5		56	112.69	odd	4
784.2.w.f.619.6		56	112.53	even	12
896.2.z.a.31.11		56	112.3	even	12
896.2.z.a.159.11		56	16.3	odd	4
896.2.z.a.479.11		56	56.45	odd	6
896.2.z.a.607.11		56	8.5	even	2
896.2.z.b.31.4		56	112.45	odd	12
896.2.z.b.159.4		56	16.13	even	4
896.2.z.b.479.4		56	56.3	even	6
896.2.z.b.607.4		56	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.z (of order \(12\), degree \(4\), not minimal)

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

Fields

Representations

Groups

Database

Properties

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