LMFDB - Embedded newform 320.2.q.c.209.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [320,2,Mod(49,320)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(320, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("320.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	320.q (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0] 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:	$2.55521286468$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.534694406811304329216.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 - 2x^12 + 4x^10 + 4x^8 + 16x^6 - 32x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			209.3
Root			$0.841995 + 1.13624i$ of defining polynomial
Character	$\chi$	$=$	320.209
Dual form			320.2.q.c.49.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.734294 + 0.734294i) q^{3} +(-1.17216 - 1.90421i) q^{5} -1.71452 q^{7} +1.92163i q^{9} +(-2.82684 + 2.82684i) q^{11} +(-2.59462 + 2.59462i) q^{13} +(2.25896 + 0.537540i) q^{15} +1.89939i q^{17} +(-2.89623 - 2.89623i) q^{19} +(1.25896 - 1.25896i) q^{21} -2.00613 q^{23} +(-2.25207 + 4.46410i) q^{25} +(-3.61392 - 3.61392i) q^{27} +(-6.72307 - 6.72307i) q^{29} +7.11778 q^{31} -4.15146i q^{33} +(2.00970 + 3.26482i) q^{35} +(2.25207 + 2.25207i) q^{37} -3.81042i q^{39} +1.59630i q^{41} +(8.06886 + 8.06886i) q^{43} +(3.65919 - 2.25246i) q^{45} -4.43823i q^{47} -4.06040 q^{49} +(-1.39471 - 1.39471i) q^{51} +(0.481758 + 0.481758i) q^{53} +(8.69642 + 2.06939i) q^{55} +4.25336 q^{57} +(-3.08580 + 3.08580i) q^{59} +(3.46410 + 3.46410i) q^{61} -3.29468i q^{63} +(7.98203 + 1.89939i) q^{65} +(-1.80454 + 1.80454i) q^{67} +(1.47309 - 1.47309i) q^{69} -0.379150i q^{71} +8.37718 q^{73} +(-1.62428 - 4.93164i) q^{75} +(4.84668 - 4.84668i) q^{77} -11.2566 q^{79} -0.457524 q^{81} +(8.24890 - 8.24890i) q^{83} +(3.61685 - 2.22640i) q^{85} +9.87341 q^{87} -11.9820i q^{89} +(4.44854 - 4.44854i) q^{91} +(-5.22654 + 5.22654i) q^{93} +(-2.12019 + 8.90989i) q^{95} +6.50543i q^{97} +(-5.43213 - 5.43213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{5} - 8 q^{11} + 8 q^{19} - 16 q^{21} - 16 q^{29} - 16 q^{31} + 24 q^{35} + 8 q^{45} + 16 q^{49} + 16 q^{51} + 24 q^{59} + 32 q^{69} - 48 q^{75} - 16 q^{79} - 16 q^{81} + 16 q^{91} - 32 q^{95}+ \cdots - 88 q^{99}+O(q^{100}) $ 16 * q - 8 * q^5 - 8 * q^11 + 8 * q^19 - 16 * q^21 - 16 * q^29 - 16 * q^31 + 24 * q^35 + 8 * q^45 + 16 * q^49 + 16 * q^51 + 24 * q^59 + 32 * q^69 - 48 * q^75 - 16 * q^79 - 16 * q^81 + 16 * q^91 - 32 * q^95 - 88 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.734294	+	0.734294i	−0.423945	+	0.423945i	−0.886559	−	0.462615i	$-0.846911\pi$
$3$	−0.734294	+	0.734294i	−0.423945	+	0.423945i	0.462615	+	0.886559i	$0.346911\pi$
$4$		0			0
$5$	−1.17216	−	1.90421i	−0.524207	−	0.851591i
$5$	−1.17216	−	1.90421i	−0.524207	−	0.851591i
$6$		0			0
$7$	−1.71452			−0.648029			−0.324015	−	0.946052i	$-0.605033\pi$
$7$	−1.71452			−0.648029			−0.324015	+	0.946052i	$0.605033\pi$
$8$		0			0
$9$			1.92163i			0.640542i
$10$		0			0
$11$	−2.82684	+	2.82684i	−0.852324	+	0.852324i	−0.990419	−	0.138095i	$-0.955902\pi$
$11$	−2.82684	+	2.82684i	−0.852324	+	0.852324i	0.138095	+	0.990419i	$0.455902\pi$
$12$		0			0
$13$	−2.59462	+	2.59462i	−0.719618	+	0.719618i	−0.968527	−	0.248909i	$-0.919928\pi$
$13$	−2.59462	+	2.59462i	−0.719618	+	0.719618i	0.248909	+	0.968527i	$0.419928\pi$
$14$		0			0
$15$	2.25896	+	0.537540i	0.583262	+	0.138792i
$16$		0			0
$17$			1.89939i			0.460671i	0.973111	+	0.230335i	$0.0739823\pi$
$17$			1.89939i			0.460671i	−0.973111	+	0.230335i	$0.926018\pi$
$18$		0			0
$19$	−2.89623	−	2.89623i	−0.664440	−	0.664440i	0.291983	−	0.956423i	$-0.405685\pi$
$19$	−2.89623	−	2.89623i	−0.664440	−	0.664440i	−0.956423	+	0.291983i	$0.905685\pi$
$20$		0			0
$21$	1.25896	−	1.25896i	0.274729	−	0.274729i
$22$		0			0
$23$	−2.00613			−0.418306			−0.209153	−	0.977883i	$-0.567071\pi$
$23$	−2.00613			−0.418306			−0.209153	+	0.977883i	$0.567071\pi$
$24$		0			0
$25$	−2.25207	+	4.46410i	−0.450413	+	0.892820i
$26$		0			0
$27$	−3.61392	−	3.61392i	−0.695499	−	0.695499i
$28$		0			0
$29$	−6.72307	−	6.72307i	−1.24844	−	1.24844i	−0.956408	−	0.292034i	$-0.905668\pi$
$29$	−6.72307	−	6.72307i	−1.24844	−	1.24844i	−0.292034	−	0.956408i	$-0.594332\pi$
$30$		0			0
$31$	7.11778			1.27839			0.639195	−	0.769044i	$-0.279268\pi$
$31$	7.11778			1.27839			0.639195	+	0.769044i	$0.279268\pi$
$32$		0			0
$33$		−	4.15146i		−	0.722676i
$34$		0			0
$35$	2.00970	+	3.26482i	0.339702	+	0.551856i
$36$		0			0
$37$	2.25207	+	2.25207i	0.370237	+	0.370237i	0.867564	−	0.497326i	$-0.165685\pi$
$37$	2.25207	+	2.25207i	0.370237	+	0.370237i	−0.497326	+	0.867564i	$0.665685\pi$
$38$		0			0
$39$		−	3.81042i		−	0.610156i
$40$		0			0
$41$			1.59630i			0.249301i	0.992201	+	0.124650i	$0.0397809\pi$
$41$			1.59630i			0.249301i	−0.992201	+	0.124650i	$0.960219\pi$
$42$		0			0
$43$	8.06886	+	8.06886i	1.23049	+	1.23049i	0.963776	+	0.266715i	$0.0859381\pi$
$43$	8.06886	+	8.06886i	1.23049	+	1.23049i	0.266715	+	0.963776i	$0.414062\pi$
$44$		0			0
$45$	3.65919	−	2.25246i	0.545480	−	0.335777i
$46$		0			0
$47$		−	4.43823i		−	0.647383i	−0.946163	−	0.323691i	$-0.895076\pi$
$47$		−	4.43823i		−	0.647383i	0.946163	−	0.323691i	$-0.104924\pi$
$48$		0			0
$49$	−4.06040			−0.580058
$50$		0			0
$51$	−1.39471	−	1.39471i	−0.195299	−	0.195299i
$52$		0			0
$53$	0.481758	+	0.481758i	0.0661746	+	0.0661746i	0.739420	−	0.673245i	$-0.235100\pi$
$53$	0.481758	+	0.481758i	0.0661746	+	0.0661746i	−0.673245	+	0.739420i	$0.735100\pi$
$54$		0			0
$55$	8.69642	+	2.06939i	1.17263	+	0.279036i
$56$		0			0
$57$	4.25336			0.563372
$58$		0			0
$59$	−3.08580	+	3.08580i	−0.401737	+	0.401737i	−0.878845	−	0.477108i	$-0.841685\pi$
$59$	−3.08580	+	3.08580i	−0.401737	+	0.401737i	0.477108	+	0.878845i	$0.341685\pi$
$60$		0			0
$61$	3.46410	+	3.46410i	0.443533	+	0.443533i	0.893197	−	0.449665i	$-0.148457\pi$
$61$	3.46410	+	3.46410i	0.443533	+	0.443533i	−0.449665	+	0.893197i	$0.648457\pi$
$62$		0			0
$63$		−	3.29468i		−	0.415090i
$64$		0			0
$65$	7.98203	+	1.89939i	0.990049	+	0.235591i
$66$		0			0
$67$	−1.80454	+	1.80454i	−0.220460	+	0.220460i	−0.808692	−	0.588232i	$-0.799824\pi$
$67$	−1.80454	+	1.80454i	−0.220460	+	0.220460i	0.588232	+	0.808692i	$0.299824\pi$
$68$		0			0
$69$	1.47309	−	1.47309i	0.177339	−	0.177339i
$70$		0			0
$71$		−	0.379150i		−	0.0449969i	−0.999747	−	0.0224984i	$-0.992838\pi$
$71$		−	0.379150i		−	0.0449969i	0.999747	−	0.0224984i	$-0.00716208\pi$
$72$		0			0
$73$	8.37718			0.980475			0.490237	−	0.871589i	$-0.336910\pi$
$73$	8.37718			0.980475			0.490237	+	0.871589i	$0.336910\pi$
$74$		0			0
$75$	−1.62428	−	4.93164i	−0.187556	−	0.569456i
$76$		0			0
$77$	4.84668	−	4.84668i	0.552331	−	0.552331i
$78$		0			0
$79$	−11.2566			−1.26646			−0.633231	−	0.773963i	$-0.718272\pi$
$79$	−11.2566			−1.26646			−0.633231	+	0.773963i	$0.718272\pi$
$80$		0			0
$81$	−0.457524			−0.0508360
$82$		0			0
$83$	8.24890	−	8.24890i	0.905435	−	0.905435i	−0.0904649	−	0.995900i	$-0.528835\pi$
$83$	8.24890	−	8.24890i	0.905435	−	0.905435i	0.995900	+	0.0904649i	$0.0288353\pi$
$84$		0			0
$85$	3.61685	−	2.22640i	0.392303	−	0.241487i
$86$		0			0
$87$	9.87341			1.05854
$88$		0			0
$89$		−	11.9820i		−	1.27009i	−0.772474	−	0.635046i	$-0.780981\pi$
$89$		−	11.9820i		−	1.27009i	0.772474	−	0.635046i	$-0.219019\pi$
$90$		0			0
$91$	4.44854	−	4.44854i	0.466334	−	0.466334i
$92$		0			0
$93$	−5.22654	+	5.22654i	−0.541967	+	0.541967i
$94$		0			0
$95$	−2.12019	+	8.90989i	−0.217526	+	0.914136i
$96$		0			0
$97$			6.50543i			0.660526i	0.943889	+	0.330263i	$0.107137\pi$
$97$			6.50543i			0.660526i	−0.943889	+	0.330263i	$0.892863\pi$
$98$		0			0
$99$	−5.43213	−	5.43213i	−0.545949	−	0.545949i
$100$		0			0
$101$	−6.72307	+	6.72307i	−0.668970	+	0.668970i	−0.957478	−	0.288508i	$-0.906841\pi$
$101$	−6.72307	+	6.72307i	−0.668970	+	0.668970i	0.288508	+	0.957478i	$0.406841\pi$
$102$		0			0
$103$	−15.1733			−1.49506			−0.747532	−	0.664225i	$-0.768762\pi$
$103$	−15.1733			−1.49506			−0.747532	+	0.664225i	$0.768762\pi$
$104$		0			0
$105$	−3.87305	−	0.921626i	−0.377971	−	0.0899415i
$106$		0			0
$107$	1.69781	+	1.69781i	0.164134	+	0.164134i	0.784395	−	0.620262i	$-0.212974\pi$
$107$	1.69781	+	1.69781i	0.164134	+	0.164134i	−0.620262	+	0.784395i	$0.712974\pi$
$108$		0			0
$109$	3.11120	+	3.11120i	0.297999	+	0.297999i	0.840230	−	0.542231i	$-0.182420\pi$
$109$	3.11120	+	3.11120i	0.297999	+	0.297999i	−0.542231	+	0.840230i	$0.682420\pi$
$110$		0			0
$111$	−3.30735			−0.313920
$112$		0			0
$113$		−	15.8259i		−	1.48877i	−0.667748	−	0.744387i	$-0.732742\pi$
$113$		−	15.8259i		−	1.48877i	0.667748	−	0.744387i	$-0.267258\pi$
$114$		0			0
$115$	2.35151	+	3.82010i	0.219279	+	0.356226i
$116$		0			0
$117$	−4.98589	−	4.98589i	−0.460946	−	0.460946i
$118$		0			0
$119$		−	3.25656i		−	0.298528i
$120$		0			0
$121$		−	4.98203i		−	0.452912i
$122$		0			0
$123$	−1.17216	−	1.17216i	−0.105690	−	0.105690i
$124$		0			0
$125$	11.1404	−	0.944243i	0.996427	−	0.0844556i
$126$		0			0
$127$			18.3239i			1.62598i	0.582276	+	0.812991i	$0.302162\pi$
$127$			18.3239i			1.62598i	−0.582276	+	0.812991i	$0.697838\pi$
$128$		0			0
$129$	−11.8498			−1.04332
$130$		0			0
$131$	10.2036	+	10.2036i	0.891491	+	0.891491i	0.994663	−	0.103172i	$-0.0328994\pi$
$131$	10.2036	+	10.2036i	0.891491	+	0.891491i	−0.103172	+	0.994663i	$0.532899\pi$
$132$		0			0
$133$	4.96565	+	4.96565i	0.430577	+	0.430577i
$134$		0			0
$135$	−2.64557	+	11.1178i	−0.227695	+	0.956866i
$136$		0			0
$137$	−14.9845			−1.28021			−0.640107	−	0.768286i	$-0.721110\pi$
$137$	−14.9845			−1.28021			−0.640107	+	0.768286i	$0.721110\pi$
$138$		0			0
$139$	8.29094	−	8.29094i	0.703228	−	0.703228i	−0.261874	−	0.965102i	$-0.584340\pi$
$139$	8.29094	−	8.29094i	0.703228	−	0.703228i	0.965102	+	0.261874i	$0.0843404\pi$
$140$		0			0
$141$	3.25896	+	3.25896i	0.274454	+	0.274454i
$142$		0			0
$143$		−	14.6691i		−	1.22670i
$144$		0			0
$145$	−4.92163	+	20.6827i	−0.408719	+	1.71760i
$146$		0			0
$147$	2.98153	−	2.98153i	0.245912	−	0.245912i
$148$		0			0
$149$	−7.30735	+	7.30735i	−0.598642	+	0.598642i	−0.939951	−	0.341309i	$-0.889130\pi$
$149$	−7.30735	+	7.30735i	−0.598642	+	0.598642i	0.341309	+	0.939951i	$0.389130\pi$
$150$		0			0
$151$			4.56873i			0.371798i	0.982569	+	0.185899i	$0.0595197\pi$
$151$			4.56873i			0.371798i	−0.982569	+	0.185899i	$0.940480\pi$
$152$		0			0
$153$	−3.64992			−0.295079
$154$		0			0
$155$	−8.34320	−	13.5538i	−0.670142	−	1.08867i
$156$		0			0
$157$	−1.52966	+	1.52966i	−0.122080	+	0.122080i	−0.765507	−	0.643427i	$-0.777512\pi$
$157$	−1.52966	+	1.52966i	−0.122080	+	0.122080i	0.643427	+	0.765507i	$0.277512\pi$
$158$		0			0
$159$	−0.707504			−0.0561087
$160$		0			0
$161$	3.43955			0.271075
$162$		0			0
$163$	−10.1361	+	10.1361i	−0.793918	+	0.793918i	−0.982129	−	0.188211i	$-0.939731\pi$
$163$	−10.1361	+	10.1361i	−0.793918	+	0.793918i	0.188211	+	0.982129i	$0.439731\pi$
$164$		0			0
$165$	−7.90527	+	4.86619i	−0.615424	+	0.378832i
$166$		0			0
$167$	−2.57967			−0.199621			−0.0998105	−	0.995006i	$-0.531824\pi$
$167$	−2.57967			−0.199621			−0.0998105	+	0.995006i	$0.531824\pi$
$168$		0			0
$169$		−	0.464102i		−	0.0357001i
$170$		0			0
$171$	5.56547	−	5.56547i	0.425602	−	0.425602i
$172$		0			0
$173$	−14.1773	+	14.1773i	−1.07788	+	1.07788i	−0.0811779	+	0.996700i	$0.525868\pi$
$173$	−14.1773	+	14.1773i	−1.07788	+	1.07788i	−0.996700	+	0.0811779i	$0.974132\pi$
$174$		0			0
$175$	3.86122	−	7.65381i	0.291881	−	0.578574i
$176$		0			0
$177$		−	4.53177i		−	0.340629i
$178$		0			0
$179$	9.88067	+	9.88067i	0.738516	+	0.738516i	0.972291	−	0.233775i	$-0.0751079\pi$
$179$	9.88067	+	9.88067i	0.738516	+	0.738516i	−0.233775	+	0.972291i	$0.575108\pi$
$180$		0			0
$181$	6.20514	−	6.20514i	0.461224	−	0.461224i	−0.437832	−	0.899057i	$-0.644254\pi$
$181$	6.20514	−	6.20514i	0.461224	−	0.461224i	0.899057	+	0.437832i	$0.144254\pi$
$182$		0			0
$183$	−5.08733			−0.376067
$184$		0			0
$185$	1.64863	−	6.92820i	0.121209	−	0.509372i
$186$		0			0
$187$	−5.36928	−	5.36928i	−0.392641	−	0.392641i
$188$		0			0
$189$	6.19615	+	6.19615i	0.450704	+	0.450704i
$190$		0			0
$191$	−18.9282			−1.36960			−0.684798	−	0.728733i	$-0.740110\pi$
$191$	−18.9282			−1.36960			−0.684798	+	0.728733i	$0.740110\pi$
$192$		0			0
$193$		−	4.42987i		−	0.318869i	−0.987209	−	0.159434i	$-0.949033\pi$
$193$		−	4.42987i		−	0.318869i	0.987209	−	0.159434i	$-0.0509670\pi$
$194$		0			0
$195$	−7.25587	+	4.46644i	−0.519603	+	0.319849i
$196$		0			0
$197$	−6.39341	−	6.39341i	−0.455511	−	0.455511i	0.441667	−	0.897179i	$-0.354387\pi$
$197$	−6.39341	−	6.39341i	−0.455511	−	0.455511i	−0.897179	+	0.441667i	$0.854387\pi$
$198$		0			0
$199$			5.85641i			0.415150i	0.978219	+	0.207575i	$0.0665570\pi$
$199$			5.85641i			0.415150i	−0.978219	+	0.207575i	$0.933443\pi$
$200$		0			0
$201$		−	2.65013i		−	0.186926i
$202$		0			0
$203$	11.5269	+	11.5269i	0.809027	+	0.809027i
$204$		0			0
$205$	3.03970	−	1.87113i	0.212302	−	0.130685i
$206$		0			0
$207$		−	3.85503i		−	0.267943i
$208$		0			0
$209$	16.3743			1.13264
$210$		0			0
$211$	−7.60373	−	7.60373i	−0.523462	−	0.523462i	0.395153	−	0.918615i	$-0.370692\pi$
$211$	−7.60373	−	7.60373i	−0.523462	−	0.523462i	−0.918615	+	0.395153i	$0.870692\pi$
$212$		0			0
$213$	0.278408	+	0.278408i	0.0190762	+	0.0190762i
$214$		0			0
$215$	5.90682	−	24.8229i	0.402842	−	1.69291i
$216$		0			0
$217$	−12.2036			−0.828435
$218$		0			0
$219$	−6.15131	+	6.15131i	−0.415667	+	0.415667i
$220$		0			0
$221$	−4.92820	−	4.92820i	−0.331507	−	0.331507i
$222$		0			0
$223$			9.22430i			0.617705i	0.951110	+	0.308853i	$0.0999450\pi$
$223$			9.22430i			0.617705i	−0.951110	+	0.308853i	$0.900055\pi$
$224$		0			0
$225$	−8.57833	−	4.32763i	−0.571889	−	0.288508i
$226$		0			0
$227$	−9.21725	+	9.21725i	−0.611770	+	0.611770i	−0.943407	−	0.331637i	$-0.892399\pi$
$227$	−9.21725	+	9.21725i	−0.611770	+	0.611770i	0.331637	+	0.943407i	$0.392399\pi$
$228$		0			0
$229$	1.63811	−	1.63811i	0.108250	−	0.108250i	−0.650907	−	0.759157i	$-0.725611\pi$
$229$	1.63811	−	1.63811i	0.108250	−	0.108250i	0.759157	+	0.650907i	$0.225611\pi$
$230$		0			0
$231$			7.11778i			0.468315i
$232$		0			0
$233$	12.3798			0.811026			0.405513	−	0.914089i	$-0.367093\pi$
$233$	12.3798			0.811026			0.405513	+	0.914089i	$0.367093\pi$
$234$		0			0
$235$	−8.45134	+	5.20233i	−0.551305	+	0.339363i
$236$		0			0
$237$	8.26562	−	8.26562i	0.536910	−	0.536910i
$238$		0			0
$239$	7.77449			0.502890			0.251445	−	0.967872i	$-0.419094\pi$
$239$	7.77449			0.502890			0.251445	+	0.967872i	$0.419094\pi$
$240$		0			0
$241$	−3.47068			−0.223566			−0.111783	−	0.993733i	$-0.535656\pi$
$241$	−3.47068			−0.223566			−0.111783	+	0.993733i	$0.535656\pi$
$242$		0			0
$243$	11.1777	−	11.1777i	0.717051	−	0.717051i
$244$		0			0
$245$	4.75946	+	7.73188i	0.304071	+	0.493972i
$246$		0			0
$247$	15.0292			0.956286
$248$		0			0
$249$			12.1142i			0.767708i
$250$		0			0
$251$	−8.94765	+	8.94765i	−0.564771	+	0.564771i	−0.930659	−	0.365888i	$-0.880765\pi$
$251$	−8.94765	+	8.94765i	−0.564771	+	0.564771i	0.365888	+	0.930659i	$0.380765\pi$
$252$		0			0
$253$	5.67100	−	5.67100i	0.356533	−	0.356533i
$254$		0			0
$255$	−1.02100	+	4.29066i	−0.0639375	+	0.268692i
$256$		0			0
$257$		−	3.62228i		−	0.225952i	−0.993598	−	0.112976i	$-0.963962\pi$
$257$		−	3.62228i		−	0.225952i	0.993598	−	0.112976i	$-0.0360383\pi$
$258$		0			0
$259$	−3.86122	−	3.86122i	−0.239925	−	0.239925i
$260$		0			0
$261$	12.9192	−	12.9192i	0.799680	−	0.799680i
$262$		0			0
$263$	−13.7416			−0.847345			−0.423673	−	0.905815i	$-0.639259\pi$
$263$	−13.7416			−0.847345			−0.423673	+	0.905815i	$0.639259\pi$
$264$		0			0
$265$	0.352672	−	1.48207i	0.0216644	−	0.0910429i
$266$		0			0
$267$	8.79833	+	8.79833i	0.538449	+	0.538449i
$268$		0			0
$269$	−4.22240	−	4.22240i	−0.257444	−	0.257444i	0.566570	−	0.824014i	$-0.308270\pi$
$269$	−4.22240	−	4.22240i	−0.257444	−	0.257444i	−0.824014	+	0.566570i	$0.808270\pi$
$270$		0			0
$271$	5.40015			0.328036			0.164018	−	0.986457i	$-0.447555\pi$
$271$	5.40015			0.328036			0.164018	+	0.986457i	$0.447555\pi$
$272$		0			0
$273$			6.53307i			0.395399i
$274$		0			0
$275$	−6.25307	−	18.9855i	−0.377074	−	1.14487i
$276$		0			0
$277$	5.08733	+	5.08733i	0.305668	+	0.305668i	0.843227	−	0.537558i	$-0.180653\pi$
$277$	5.08733	+	5.08733i	0.305668	+	0.305668i	−0.537558	+	0.843227i	$0.680653\pi$
$278$		0			0
$279$			13.6777i			0.818863i
$280$		0			0
$281$			21.2780i			1.26934i	0.772784	+	0.634669i	$0.218864\pi$
$281$			21.2780i			1.26934i	−0.772784	+	0.634669i	$0.781136\pi$
$282$		0			0
$283$	4.08521	+	4.08521i	0.242840	+	0.242840i	0.818024	−	0.575184i	$-0.195069\pi$
$283$	4.08521	+	4.08521i	0.242840	+	0.242840i	−0.575184	+	0.818024i	$0.695069\pi$
$284$		0			0
$285$	−4.98564	−	8.09931i	−0.295324	−	0.479762i
$286$		0			0
$287$		−	2.73690i		−	0.161554i
$288$		0			0
$289$	13.3923			0.787783
$290$		0			0
$291$	−4.77689	−	4.77689i	−0.280026	−	0.280026i
$292$		0			0
$293$	7.40400	+	7.40400i	0.432547	+	0.432547i	0.889494	−	0.456947i	$-0.151057\pi$
$293$	7.40400	+	7.40400i	0.432547	+	0.432547i	−0.456947	+	0.889494i	$0.651057\pi$
$294$		0			0
$295$	9.49310	+	2.25896i	0.552709	+	0.131522i
$296$		0			0
$297$	20.4319			1.18558
$298$		0			0
$299$	5.20514	−	5.20514i	0.301021	−	0.301021i
$300$		0			0
$301$	−13.8343	−	13.8343i	−0.797394	−	0.797394i
$302$		0			0
$303$		−	9.87341i		−	0.567212i
$304$		0			0
$305$	2.53590	−	10.6569i	0.145205	−	0.610212i
$306$		0			0
$307$	16.6634	−	16.6634i	0.951030	−	0.951030i	−0.0478262	−	0.998856i	$-0.515229\pi$
$307$	16.6634	−	16.6634i	0.951030	−	0.951030i	0.998856	+	0.0478262i	$0.0152294\pi$
$308$		0			0
$309$	11.1416	−	11.1416i	0.633825	−	0.633825i
$310$		0			0
$311$		−	21.9072i		−	1.24224i	−0.783714	−	0.621122i	$-0.786677\pi$
$311$		−	21.9072i		−	1.24224i	0.783714	−	0.621122i	$-0.213323\pi$
$312$		0			0
$313$	12.4820			0.705525			0.352763	−	0.935713i	$-0.385242\pi$
$313$	12.4820			0.705525			0.352763	+	0.935713i	$0.385242\pi$
$314$		0			0
$315$	−6.27377	+	3.86190i	−0.353487	+	0.217593i
$316$		0			0
$317$	−4.24325	+	4.24325i	−0.238324	+	0.238324i	−0.816156	−	0.577832i	$-0.803899\pi$
$317$	−4.24325	+	4.24325i	−0.238324	+	0.238324i	0.577832	+	0.816156i	$0.303899\pi$
$318$		0			0
$319$	38.0100			2.12815
$320$		0			0
$321$	−2.49338			−0.139167
$322$		0			0
$323$	5.50108	−	5.50108i	0.306088	−	0.306088i
$324$		0			0
$325$	−5.73939	−	17.4259i	−0.318364	−	0.966615i
$326$		0			0
$327$	−4.56907			−0.252670
$328$		0			0
$329$			7.60946i			0.419523i
$330$		0			0
$331$	−1.10377	+	1.10377i	−0.0606688	+	0.0606688i	−0.736790	−	0.676121i	$-0.763659\pi$
$331$	−1.10377	+	1.10377i	−0.0606688	+	0.0606688i	0.676121	+	0.736790i	$0.263659\pi$
$332$		0			0
$333$	−4.32763	+	4.32763i	−0.237152	+	0.237152i
$334$		0			0
$335$	5.55146	+	1.32102i	0.303309	+	0.0721749i
$336$		0			0
$337$			7.47635i			0.407263i	0.979048	+	0.203631i	$0.0652744\pi$
$337$			7.47635i			0.407263i	−0.979048	+	0.203631i	$0.934726\pi$
$338$		0			0
$339$	11.6208	+	11.6208i	0.631158	+	0.631158i
$340$		0			0
$341$	−20.1208	+	20.1208i	−1.08960	+	1.08960i
$342$		0			0
$343$	18.9633			1.02392
$344$		0			0
$345$	−4.53177	−	1.07837i	−0.243982	−	0.0580577i
$346$		0			0
$347$	−8.56074	−	8.56074i	−0.459565	−	0.459565i	0.438948	−	0.898512i	$-0.355351\pi$
$347$	−8.56074	−	8.56074i	−0.459565	−	0.459565i	−0.898512	+	0.438948i	$0.855351\pi$
$348$		0			0
$349$	7.91567	+	7.91567i	0.423716	+	0.423716i	0.886481	−	0.462765i	$-0.153143\pi$
$349$	7.91567	+	7.91567i	0.423716	+	0.423716i	−0.462765	+	0.886481i	$0.653143\pi$
$350$		0			0
$351$	18.7535			1.00099
$352$		0			0
$353$			9.67314i			0.514849i	0.966298	+	0.257425i	$0.0828739\pi$
$353$			9.67314i			0.514849i	−0.966298	+	0.257425i	$0.917126\pi$
$354$		0			0
$355$	−0.721984	+	0.444426i	−0.0383189	+	0.0235877i
$356$		0			0
$357$	2.39127	+	2.39127i	0.126559	+	0.126559i
$358$		0			0
$359$		−	17.0867i		−	0.901799i	−0.892575	−	0.450900i	$-0.851103\pi$
$359$		−	17.0867i		−	0.901799i	0.892575	−	0.450900i	$-0.148897\pi$
$360$		0			0
$361$		−	2.22373i		−	0.117038i
$362$		0			0
$363$	3.65827	+	3.65827i	0.192010	+	0.192010i
$364$		0			0
$365$	−9.81943	−	15.9519i	−0.513972	−	0.834963i
$366$		0			0
$367$		−	13.4500i		−	0.702086i	−0.936359	−	0.351043i	$-0.885827\pi$
$367$		−	13.4500i		−	0.702086i	0.936359	−	0.351043i	$-0.114173\pi$
$368$		0			0
$369$	−3.06750			−0.159688
$370$		0			0
$371$	−0.825987	−	0.825987i	−0.0428831	−	0.0428831i
$372$		0			0
$373$	−12.0271	−	12.0271i	−0.622740	−	0.622740i	0.323491	−	0.946231i	$-0.395143\pi$
$373$	−12.0271	−	12.0271i	−0.622740	−	0.622740i	−0.946231	+	0.323491i	$0.895143\pi$
$374$		0			0
$375$	−7.48697	+	8.87367i	−0.386625	+	0.458234i
$376$		0			0
$377$	34.8876			1.79680
$378$		0			0
$379$	−19.1552	+	19.1552i	−0.983936	+	0.983936i	−0.999873	−	0.0159369i	$-0.994927\pi$
$379$	−19.1552	+	19.1552i	−0.983936	+	0.983936i	0.0159369	+	0.999873i	$0.494927\pi$
$380$		0			0
$381$	−13.4551	−	13.4551i	−0.689327	−	0.689327i
$382$		0			0
$383$			17.7503i			0.907000i	0.891256	+	0.453500i	$0.149825\pi$
$383$			17.7503i			0.907000i	−0.891256	+	0.453500i	$0.850175\pi$
$384$		0			0
$385$	−14.9102	−	3.54802i	−0.759896	−	0.180824i
$386$		0			0
$387$	−15.5053	+	15.5053i	−0.788181	+	0.788181i
$388$		0			0
$389$	−1.18654	+	1.18654i	−0.0601602	+	0.0601602i	−0.736547	−	0.676387i	$-0.763545\pi$
$389$	−1.18654	+	1.18654i	−0.0601602	+	0.0601602i	0.676387	+	0.736547i	$0.263545\pi$
$390$		0			0
$391$		−	3.81042i		−	0.192701i
$392$		0			0
$393$	−14.9848			−0.755886
$394$		0			0
$395$	13.1945	+	21.4349i	0.663889	+	1.07851i
$396$		0			0
$397$	−4.74478	+	4.74478i	−0.238134	+	0.238134i	−0.816077	−	0.577943i	$-0.803855\pi$
$397$	−4.74478	+	4.74478i	−0.238134	+	0.238134i	0.577943	+	0.816077i	$0.303855\pi$
$398$		0			0
$399$	−7.29250			−0.365081
$400$		0			0
$401$	0.632677			0.0315944			0.0157972	−	0.999875i	$-0.494971\pi$
$401$	0.632677			0.0315944			0.0157972	+	0.999875i	$0.494971\pi$
$402$		0			0
$403$	−18.4679	+	18.4679i	−0.919953	+	0.919953i
$404$		0			0
$405$	0.536293	+	0.871224i	0.0266486	+	0.0432915i
$406$		0			0
$407$	−12.7324			−0.631124
$408$		0			0
$409$			26.3809i			1.30445i	0.758024	+	0.652226i	$0.226165\pi$
$409$			26.3809i			1.30445i	−0.758024	+	0.652226i	$0.773835\pi$
$410$		0			0
$411$	11.0030	−	11.0030i	0.542739	−	0.542739i
$412$		0			0
$413$	5.29069	−	5.29069i	0.260338	−	0.260338i
$414$		0			0
$415$	−25.3767	−	6.03862i	−1.24570	−	0.296424i
$416$		0			0
$417$			12.1760i			0.596260i
$418$		0			0
$419$	1.37589	+	1.37589i	0.0672167	+	0.0672167i	0.739916	−	0.672699i	$-0.234865\pi$
$419$	1.37589	+	1.37589i	0.0672167	+	0.0672167i	−0.672699	+	0.739916i	$0.734865\pi$
$420$		0			0
$421$	6.65671	−	6.65671i	0.324428	−	0.324428i	−0.526035	−	0.850463i	$-0.676322\pi$
$421$	6.65671	−	6.65671i	0.324428	−	0.324428i	0.850463	+	0.526035i	$0.176322\pi$
$422$		0			0
$423$	8.52862			0.414676
$424$		0			0
$425$	−8.47908	−	4.27756i	−0.411296	−	0.207492i
$426$		0			0
$427$	−5.93929	−	5.93929i	−0.287422	−	0.287422i
$428$		0			0
$429$	10.7715	+	10.7715i	0.520051	+	0.520051i
$430$		0			0
$431$	−4.08798			−0.196911			−0.0984556	−	0.995141i	$-0.531390\pi$
$431$	−4.08798			−0.196911			−0.0984556	+	0.995141i	$0.531390\pi$
$432$		0			0
$433$		−	29.2913i		−	1.40765i	−0.710373	−	0.703826i	$-0.751474\pi$
$433$		−	29.2913i		−	1.40765i	0.710373	−	0.703826i	$-0.248526\pi$
$434$		0			0
$435$	−11.5732	−	18.8011i	−0.554895	−	0.901443i
$436$		0			0
$437$	5.81020	+	5.81020i	0.277940	+	0.277940i
$438$		0			0
$439$			26.9790i			1.28764i	0.765178	+	0.643819i	$0.222651\pi$
$439$			26.9790i			1.28764i	−0.765178	+	0.643819i	$0.777349\pi$
$440$		0			0
$441$		−	7.80258i		−	0.371551i
$442$		0			0
$443$	−14.5286	−	14.5286i	−0.690276	−	0.690276i	0.272017	−	0.962293i	$-0.412309\pi$
$443$	−14.5286	−	14.5286i	−0.690276	−	0.690276i	−0.962293	+	0.272017i	$0.912309\pi$
$444$		0			0
$445$	−22.8164	+	14.0449i	−1.08160	+	0.665792i
$446$		0			0
$447$		−	10.7315i		−	0.507582i
$448$		0			0
$449$	23.1572			1.09286			0.546428	−	0.837506i	$-0.315987\pi$
$449$	23.1572			1.09286			0.546428	+	0.837506i	$0.315987\pi$
$450$		0			0
$451$	−4.51249	−	4.51249i	−0.212485	−	0.212485i
$452$		0			0
$453$	−3.35479	−	3.35479i	−0.157622	−	0.157622i
$454$		0			0
$455$	−13.6854	−	3.25656i	−0.641581	−	0.152670i
$456$		0			0
$457$	−37.7026			−1.76365			−0.881827	−	0.471572i	$-0.843687\pi$
$457$	−37.7026			−1.76365			−0.881827	+	0.471572i	$0.843687\pi$
$458$		0			0
$459$	6.86425	−	6.86425i	0.320396	−	0.320396i
$460$		0			0
$461$	11.3737	+	11.3737i	0.529727	+	0.529727i	0.920491	−	0.390764i	$-0.127789\pi$
$461$	11.3737	+	11.3737i	0.529727	+	0.529727i	−0.390764	+	0.920491i	$0.627789\pi$
$462$		0			0
$463$		−	7.94895i		−	0.369419i	−0.982793	−	0.184710i	$-0.940866\pi$
$463$		−	7.94895i		−	0.369419i	0.982793	−	0.184710i	$-0.0591344\pi$
$464$		0			0
$465$	16.0788	+	3.82609i	0.745637	+	0.177431i
$466$		0			0
$467$	−5.34999	+	5.34999i	−0.247568	+	0.247568i	−0.819972	−	0.572404i	$-0.806011\pi$
$467$	−5.34999	+	5.34999i	−0.247568	+	0.247568i	0.572404	+	0.819972i	$0.306011\pi$
$468$		0			0
$469$	3.09394	−	3.09394i	0.142865	−	0.142865i
$470$		0			0
$471$		−	2.24643i		−	0.103510i
$472$		0			0
$473$	−45.6187			−2.09755
$474$		0			0
$475$	19.4515	−	6.40656i	0.892498	−	0.293953i
$476$		0			0
$477$	−0.925759	+	0.925759i	−0.0423876	+	0.0423876i
$478$		0			0
$479$	9.58973			0.438166			0.219083	−	0.975706i	$-0.429693\pi$
$479$	9.58973			0.438166			0.219083	+	0.975706i	$0.429693\pi$
$480$		0			0
$481$	−11.6865			−0.532859
$482$		0			0
$483$	−2.52564	+	2.52564i	−0.114921	+	0.114921i
$484$		0			0
$485$	12.3877	−	7.62543i	0.562498	−	0.346253i
$486$		0			0
$487$	−36.6487			−1.66071			−0.830357	−	0.557232i	$-0.811863\pi$
$487$	−36.6487			−1.66071			−0.830357	+	0.557232i	$0.811863\pi$
$488$		0			0
$489$		−	14.8857i		−	0.673154i
$490$		0			0
$491$	−23.4273	+	23.4273i	−1.05726	+	1.05726i	−0.0590019	+	0.998258i	$0.518792\pi$
$491$	−23.4273	+	23.4273i	−1.05726	+	1.05726i	−0.998258	+	0.0590019i	$0.981208\pi$
$492$		0			0
$493$	12.7697	−	12.7697i	0.575120	−	0.575120i
$494$		0			0
$495$	−3.97659	+	16.7113i	−0.178735	+	0.751116i
$496$		0			0
$497$			0.650063i			0.0291593i
$498$		0			0
$499$	9.50152	+	9.50152i	0.425346	+	0.425346i	0.887040	−	0.461693i	$-0.152758\pi$
$499$	9.50152	+	9.50152i	0.425346	+	0.425346i	−0.461693	+	0.887040i	$0.652758\pi$
$500$		0			0
$501$	1.89424	−	1.89424i	0.0846283	−	0.0846283i
$502$		0			0
$503$	20.6875			0.922411			0.461206	−	0.887293i	$-0.347417\pi$
$503$	20.6875			0.922411			0.461206	+	0.887293i	$0.347417\pi$
$504$		0			0
$505$	20.6827	+	4.92163i	0.920368	+	0.219009i
$506$		0			0
$507$	0.340787	+	0.340787i	0.0151349	+	0.0151349i
$508$		0			0
$509$	11.6381	+	11.6381i	0.515850	+	0.515850i	0.916313	−	0.400463i	$-0.131151\pi$
$509$	11.6381	+	11.6381i	0.515850	+	0.515850i	−0.400463	+	0.916313i	$0.631151\pi$
$510$		0			0
$511$	−14.3629			−0.635377
$512$		0			0
$513$			20.9335i			0.924235i
$514$		0			0
$515$	17.7855	+	28.8931i	0.783724	+	1.27318i
$516$		0			0
$517$	12.5462	+	12.5462i	0.551780	+	0.551780i
$518$		0			0
$519$		−	20.8205i		−	0.913921i
$520$		0			0
$521$		−	5.18654i		−	0.227227i	−0.993525	−	0.113613i	$-0.963758\pi$
$521$		−	5.18654i		−	0.227227i	0.993525	−	0.113613i	$-0.0362425\pi$
$522$		0			0
$523$	−26.9589	−	26.9589i	−1.17883	−	1.17883i	−0.980043	−	0.198788i	$-0.936300\pi$
$523$	−26.9589	−	26.9589i	−1.17883	−	1.17883i	−0.198788	−	0.980043i	$-0.563700\pi$
$524$		0			0
$525$	2.78488	+	8.45542i	0.121542	+	0.369025i
$526$		0			0
$527$			13.5195i			0.588917i
$528$		0			0
$529$	−18.9755			−0.825020
$530$		0			0
$531$	−5.92976	−	5.92976i	−0.257330	−	0.257330i
$532$		0			0
$533$	−4.14180	−	4.14180i	−0.179401	−	0.179401i
$534$		0			0
$535$	1.24288	−	5.22311i	0.0537345	−	0.225815i
$536$		0			0
$537$	−14.5106			−0.626179
$538$		0			0
$539$	11.4781	−	11.4781i	0.494397	−	0.494397i
$540$		0			0
$541$	27.4945	+	27.4945i	1.18208	+	1.18208i	0.979204	+	0.202878i	$0.0650294\pi$
$541$	27.4945	+	27.4945i	1.18208	+	1.18208i	0.202878	+	0.979204i	$0.434971\pi$
$542$		0			0
$543$			9.11278i			0.391067i
$544$		0			0
$545$	2.27756	−	9.57123i	0.0975598	−	0.409986i
$546$		0			0
$547$	22.5197	−	22.5197i	0.962873	−	0.962873i	−0.0364619	−	0.999335i	$-0.511609\pi$
$547$	22.5197	−	22.5197i	0.962873	−	0.962873i	0.999335	+	0.0364619i	$0.0116088\pi$
$548$		0			0
$549$	−6.65671	+	6.65671i	−0.284101	+	0.284101i
$550$		0			0
$551$			38.9431i			1.65903i
$552$		0			0
$553$	19.2996			0.820704
$554$		0			0
$555$	3.87676	+	6.29791i	0.164559	+	0.267331i
$556$		0			0
$557$	−13.7333	+	13.7333i	−0.581897	+	0.581897i	−0.935424	−	0.353527i	$-0.884982\pi$
$557$	−13.7333	+	13.7333i	−0.581897	+	0.581897i	0.353527	+	0.935424i	$0.384982\pi$
$558$		0			0
$559$	−41.8713			−1.77097
$560$		0			0
$561$	7.88525			0.332916
$562$		0			0
$563$	−0.229223	+	0.229223i	−0.00966061	+	0.00966061i	−0.711921	−	0.702260i	$-0.752174\pi$
$563$	−0.229223	+	0.229223i	−0.00966061	+	0.00966061i	0.702260	+	0.711921i	$0.252174\pi$
$564$		0			0
$565$	−30.1359	+	18.5505i	−1.26783	+	0.780427i
$566$		0			0
$567$	0.784437			0.0329433
$568$		0			0
$569$		−	23.0376i		−	0.965787i	−0.875679	−	0.482894i	$-0.839586\pi$
$569$		−	23.0376i		−	0.965787i	0.875679	−	0.482894i	$-0.160414\pi$
$570$		0			0
$571$	11.8610	−	11.8610i	0.496367	−	0.496367i	−0.413938	−	0.910305i	$-0.635847\pi$
$571$	11.8610	−	11.8610i	0.496367	−	0.496367i	0.910305	+	0.413938i	$0.135847\pi$
$572$		0			0
$573$	13.8989	−	13.8989i	0.580633	−	0.580633i
$574$		0			0
$575$	4.51793	−	8.95556i	0.188411	−	0.373473i
$576$		0			0
$577$		−	39.7168i		−	1.65343i	−0.562621	−	0.826715i	$-0.690207\pi$
$577$		−	39.7168i		−	1.65343i	0.562621	−	0.826715i	$-0.309793\pi$
$578$		0			0
$579$	3.25282	+	3.25282i	0.135183	+	0.135183i
$580$		0			0
$581$	−14.1429	+	14.1429i	−0.586748	+	0.586748i
$582$		0			0
$583$	−2.72371			−0.112804
$584$		0			0
$585$	−3.64992	+	15.3385i	−0.150906	+	0.634168i
$586$		0			0
$587$	8.63887	+	8.63887i	0.356564	+	0.356564i	0.862545	−	0.505980i	$-0.168869\pi$
$587$	8.63887	+	8.63887i	0.356564	+	0.356564i	−0.505980	+	0.862545i	$0.668869\pi$
$588$		0			0
$589$	−20.6147	−	20.6147i	−0.849414	−	0.849414i
$590$		0			0
$591$	9.38927			0.386223
$592$		0			0
$593$			45.8229i			1.88172i	0.338795	+	0.940860i	$0.389981\pi$
$593$			45.8229i			1.88172i	−0.338795	+	0.940860i	$0.610019\pi$
$594$		0			0
$595$	−6.20118	+	3.81722i	−0.254224	+	0.156491i
$596$		0			0
$597$	−4.30032	−	4.30032i	−0.176000	−	0.176000i
$598$		0			0
$599$			17.0609i			0.697090i	0.937292	+	0.348545i	$0.113324\pi$
$599$			17.0609i			0.697090i	−0.937292	+	0.348545i	$0.886676\pi$
$600$		0			0
$601$		−	38.0363i		−	1.55153i	−0.631020	−	0.775766i	$-0.717364\pi$
$601$		−	38.0363i		−	1.55153i	0.631020	−	0.775766i	$-0.282636\pi$
$602$		0			0
$603$	−3.46766	−	3.46766i	−0.141214	−	0.141214i
$604$		0			0
$605$	−9.48685	+	5.83975i	−0.385695	+	0.237420i
$606$		0			0
$607$			8.67169i			0.351973i	0.984393	+	0.175987i	$0.0563115\pi$
$607$			8.67169i			0.351973i	−0.984393	+	0.175987i	$0.943688\pi$
$608$		0			0
$609$	−16.9282			−0.685965
$610$		0			0
$611$	11.5155	+	11.5155i	0.465868	+	0.465868i
$612$		0			0
$613$	−13.9739	−	13.9739i	−0.564401	−	0.564401i	0.366153	−	0.930554i	$-0.380675\pi$
$613$	−13.9739	−	13.9739i	−0.564401	−	0.564401i	−0.930554	+	0.366153i	$0.880675\pi$
$614$		0			0
$615$	−0.858077	+	3.60599i	−0.0346010	+	0.145408i
$616$		0			0
$617$	37.3904			1.50528			0.752641	−	0.658431i	$-0.228780\pi$
$617$	37.3904			1.50528			0.752641	+	0.658431i	$0.228780\pi$
$618$		0			0
$619$	23.2754	−	23.2754i	0.935516	−	0.935516i	−0.0625269	−	0.998043i	$-0.519916\pi$
$619$	23.2754	−	23.2754i	0.935516	−	0.935516i	0.998043	+	0.0625269i	$0.0199159\pi$
$620$		0			0
$621$	7.24998	+	7.24998i	0.290932	+	0.290932i
$622$		0			0
$623$			20.5435i			0.823058i
$624$		0			0
$625$	−14.8564	−	20.1069i	−0.594256	−	0.804276i
$626$		0			0
$627$	−12.0236	+	12.0236i	−0.480175	+	0.480175i
$628$		0			0
$629$	−4.27756	+	4.27756i	−0.170557	+	0.170557i
$630$		0			0
$631$		−	19.1834i		−	0.763680i	−0.924228	−	0.381840i	$-0.875290\pi$
$631$		−	19.1834i		−	0.763680i	0.924228	−	0.381840i	$-0.124710\pi$
$632$		0			0
$633$	11.1667			0.443838
$634$		0			0
$635$	34.8926	−	21.4786i	1.38467	−	0.852352i
$636$		0			0
$637$	10.5352	−	10.5352i	0.417420	−	0.417420i
$638$		0			0
$639$	0.728585			0.0288224
$640$		0			0
$641$	−16.1765			−0.638933			−0.319466	−	0.947598i	$-0.603504\pi$
$641$	−16.1765			−0.638933			−0.319466	+	0.947598i	$0.603504\pi$
$642$		0			0
$643$	15.0289	−	15.0289i	0.592681	−	0.592681i	−0.345674	−	0.938355i	$-0.612350\pi$
$643$	15.0289	−	15.0289i	0.592681	−	0.592681i	0.938355	+	0.345674i	$0.112350\pi$
$644$		0			0
$645$	13.8899	+	22.5646i	0.546916	+	0.888481i
$646$		0			0
$647$	49.3812			1.94138			0.970688	−	0.240345i	$-0.0772606\pi$
$647$	49.3812			1.94138			0.970688	+	0.240345i	$0.0772606\pi$
$648$		0			0
$649$		−	17.4461i		−	0.684821i
$650$		0			0
$651$	8.96103	−	8.96103i	0.351210	−	0.351210i
$652$		0			0
$653$	19.8685	−	19.8685i	0.777514	−	0.777514i	−0.201893	−	0.979408i	$-0.564709\pi$
$653$	19.8685	−	19.8685i	0.777514	−	0.777514i	0.979408	+	0.201893i	$0.0647094\pi$
$654$		0			0
$655$	7.46954	−	31.3901i	0.291859	−	1.22651i
$656$		0			0
$657$			16.0978i			0.628035i
$658$		0			0
$659$	−4.94765	−	4.94765i	−0.192733	−	0.192733i	0.604143	−	0.796876i	$-0.293516\pi$
$659$	−4.94765	−	4.94765i	−0.192733	−	0.192733i	−0.796876	+	0.604143i	$0.793516\pi$
$660$		0			0
$661$	12.1602	−	12.1602i	0.472977	−	0.472977i	−0.429899	−	0.902877i	$-0.641451\pi$
$661$	12.1602	−	12.1602i	0.472977	−	0.472977i	0.902877	+	0.429899i	$0.141451\pi$
$662$		0			0
$663$	7.23750			0.281081
$664$		0			0
$665$	3.63511	−	15.2762i	0.140964	−	0.592387i
$666$		0			0
$667$	13.4873	+	13.4873i	0.522231	+	0.522231i
$668$		0			0
$669$	−6.77335	−	6.77335i	−0.261873	−	0.261873i
$670$		0			0
$671$	−19.5849			−0.756067
$672$		0			0
$673$			32.9882i			1.27160i	0.771853	+	0.635801i	$0.219330\pi$
$673$			32.9882i			1.27160i	−0.771853	+	0.635801i	$0.780670\pi$
$674$		0			0
$675$	24.2717	−	7.99412i	0.934217	−	0.307694i
$676$		0			0
$677$	−18.4610	−	18.4610i	−0.709513	−	0.709513i	0.256920	−	0.966433i	$-0.417292\pi$
$677$	−18.4610	−	18.4610i	−0.709513	−	0.709513i	−0.966433	+	0.256920i	$0.917292\pi$
$678$		0			0
$679$		−	11.1537i		−	0.428040i
$680$		0			0
$681$		−	13.5363i		−	0.518713i
$682$		0			0
$683$	−12.2374	−	12.2374i	−0.468251	−	0.468251i	0.433097	−	0.901347i	$-0.357421\pi$
$683$	−12.2374	−	12.2374i	−0.468251	−	0.468251i	−0.901347	+	0.433097i	$0.857421\pi$
$684$		0			0
$685$	17.5643	+	28.5337i	0.671097	+	1.09022i
$686$		0			0
$687$			2.40571i			0.0917837i
$688$		0			0
$689$	−2.49996			−0.0952409
$690$		0			0
$691$	9.46014	+	9.46014i	0.359881	+	0.359881i	0.863769	−	0.503888i	$-0.168098\pi$
$691$	9.46014	+	9.46014i	0.359881	+	0.359881i	−0.503888	+	0.863769i	$0.668098\pi$
$692$		0			0
$693$	9.31352	+	9.31352i	0.353791	+	0.353791i
$694$		0			0
$695$	−25.5061	−	6.06939i	−0.967500	−	0.230225i
$696$		0			0
$697$	−3.03201			−0.114845
$698$		0			0
$699$	−9.09039	+	9.09039i	−0.343830	+	0.343830i
$700$		0			0
$701$	−5.14714	−	5.14714i	−0.194405	−	0.194405i	0.603192	−	0.797596i	$-0.293895\pi$
$701$	−5.14714	−	5.14714i	−0.194405	−	0.194405i	−0.797596	+	0.603192i	$0.793895\pi$
$702$		0			0
$703$		−	13.0450i		−	0.492001i
$704$		0			0
$705$	2.38573	−	10.0258i	0.0898517	−	0.377594i
$706$		0			0
$707$	11.5269	−	11.5269i	0.433512	−	0.433512i
$708$		0			0
$709$	−18.0125	+	18.0125i	−0.676472	+	0.676472i	−0.959200	−	0.282728i	$-0.908761\pi$
$709$	−18.0125	+	18.0125i	−0.676472	+	0.676472i	0.282728	+	0.959200i	$0.408761\pi$
$710$		0			0
$711$		−	21.6309i		−	0.811222i
$712$		0			0
$713$	−14.2792			−0.534759
$714$		0			0
$715$	−27.9332	+	17.1946i	−1.04464	+	0.643043i
$716$		0			0
$717$	−5.70875	+	5.70875i	−0.213197	+	0.213197i
$718$		0			0
$719$	−34.5017			−1.28669			−0.643347	−	0.765574i	$-0.722455\pi$
$719$	−34.5017			−1.28669			−0.643347	+	0.765574i	$0.722455\pi$
$720$		0			0
$721$	26.0149			0.968846
$722$		0			0
$723$	2.54850	−	2.54850i	0.0947796	−	0.0947796i
$724$		0			0
$725$	45.1532	−	14.8717i	1.67695	−	0.552320i
$726$		0			0
$727$	−12.8421			−0.476288			−0.238144	−	0.971230i	$-0.576539\pi$
$727$	−12.8421			−0.476288			−0.238144	+	0.971230i	$0.576539\pi$
$728$		0			0
$729$			15.0429i			0.557143i
$730$		0			0
$731$	−15.3259	+	15.3259i	−0.566851	+	0.566851i
$732$		0			0
$733$	24.1490	−	24.1490i	0.891965	−	0.891965i	−0.102743	−	0.994708i	$-0.532762\pi$
$733$	24.1490	−	24.1490i	0.891965	−	0.891965i	0.994708	+	0.102743i	$0.0327618\pi$
$734$		0			0
$735$	−9.17231	−	2.18263i	−0.338326	−	0.0805075i
$736$		0			0
$737$		−	10.2023i		−	0.375807i
$738$		0			0
$739$	−35.9398	−	35.9398i	−1.32207	−	1.32207i	−0.912101	−	0.409966i	$-0.865540\pi$
$739$	−35.9398	−	35.9398i	−1.32207	−	1.32207i	−0.409966	−	0.912101i	$-0.634460\pi$
$740$		0			0
$741$	−11.0359	+	11.0359i	−0.405412	+	0.405412i
$742$		0			0
$743$	45.9502			1.68575			0.842875	−	0.538109i	$-0.180861\pi$
$743$	45.9502			1.68575			0.842875	+	0.538109i	$0.180861\pi$
$744$		0			0
$745$	22.4802	+	5.34935i	0.823610	+	0.195985i
$746$		0			0
$747$	15.8513	+	15.8513i	0.579969	+	0.579969i
$748$		0			0
$749$	−2.91094	−	2.91094i	−0.106363	−	0.106363i
$750$		0			0
$751$	24.4820			0.893361			0.446680	−	0.894694i	$-0.352606\pi$
$751$	24.4820			0.893361			0.446680	+	0.894694i	$0.352606\pi$
$752$		0			0
$753$		−	13.1404i		−	0.478863i
$754$		0			0
$755$	8.69983	−	5.35529i	0.316619	−	0.194899i
$756$		0			0
$757$	17.0328	+	17.0328i	0.619067	+	0.619067i	0.945292	−	0.326225i	$-0.105777\pi$
$757$	17.0328	+	17.0328i	0.619067	+	0.619067i	−0.326225	+	0.945292i	$0.605777\pi$
$758$		0			0
$759$			8.32835i			0.302300i
$760$		0			0
$761$			8.53590i			0.309426i	0.987959	+	0.154713i	$0.0494453\pi$
$761$			8.53590i			0.309426i	−0.987959	+	0.154713i	$0.950555\pi$
$762$		0			0
$763$	−5.33423	−	5.33423i	−0.193112	−	0.193112i
$764$		0			0
$765$	4.27831	+	6.95024i	0.154683	+	0.251286i
$766$		0			0
$767$		−	16.0130i		−	0.578195i
$768$		0			0
$769$	−1.87438			−0.0675917			−0.0337959	−	0.999429i	$-0.510760\pi$
$769$	−1.87438			−0.0675917			−0.0337959	+	0.999429i	$0.510760\pi$
$770$		0			0
$771$	2.65982	+	2.65982i	0.0957911	+	0.0957911i
$772$		0			0
$773$	21.5374	+	21.5374i	0.774645	+	0.774645i	0.978915	−	0.204270i	$-0.0654820\pi$
$773$	21.5374	+	21.5374i	0.774645	+	0.774645i	−0.204270	+	0.978915i	$0.565482\pi$
$774$		0			0
$775$	−16.0297	+	31.7745i	−0.575804	+	1.14137i
$776$		0			0
$777$	5.67054			0.203429
$778$		0			0
$779$	4.62326	−	4.62326i	0.165645	−	0.165645i
$780$		0			0
$781$	1.07180	+	1.07180i	0.0383519	+	0.0383519i
$782$		0			0
$783$			48.5932i			1.73658i
$784$		0			0
$785$	4.70580	+	1.11979i	0.167957	+	0.0399669i
$786$		0			0
$787$	7.03687	−	7.03687i	0.250837	−	0.250837i	−0.570477	−	0.821314i	$-0.693241\pi$
$787$	7.03687	−	7.03687i	0.250837	−	0.250837i	0.821314	+	0.570477i	$0.193241\pi$
$788$		0			0
$789$	10.0904	−	10.0904i	0.359227	−	0.359227i
$790$		0			0
$791$			27.1339i			0.964770i
$792$		0			0
$793$	−17.9761			−0.638348
$794$		0			0
$795$	0.829311	+	1.34724i	0.0294126	+	0.0477817i
$796$		0			0
$797$	−8.07933	+	8.07933i	−0.286185	+	0.286185i	−0.835569	−	0.549385i	$-0.814862\pi$
$797$	−8.07933	+	8.07933i	−0.286185	+	0.286185i	0.549385	+	0.835569i	$0.314862\pi$
$798$		0			0
$799$	8.42995			0.298230
$800$		0			0
$801$	23.0250			0.813548
$802$		0			0
$803$	−23.6809	+	23.6809i	−0.835682	+	0.835682i
$804$		0			0
$805$	−4.03172	−	6.54965i	−0.142099	−	0.230845i
$806$		0			0
$807$	6.20097			0.218284
$808$		0			0
$809$			5.40185i			0.189919i	0.995481	+	0.0949595i	$0.0302722\pi$
$809$			5.40185i			0.189919i	−0.995481	+	0.0949595i	$0.969728\pi$
$810$		0			0
$811$	10.3478	−	10.3478i	0.363360	−	0.363360i	−0.501688	−	0.865049i	$-0.667288\pi$
$811$	10.3478	−	10.3478i	0.363360	−	0.363360i	0.865049	+	0.501688i	$0.167288\pi$
$812$		0			0
$813$	−3.96530	+	3.96530i	−0.139069	+	0.139069i
$814$		0			0
$815$	31.1824	+	7.42011i	1.09227	+	0.259915i
$816$		0			0
$817$		−	46.7385i		−	1.63517i
$818$		0			0
$819$	8.54843	+	8.54843i	0.298706	+	0.298706i
$820$		0			0
$821$	10.7321	−	10.7321i	0.374551	−	0.374551i	−0.494581	−	0.869132i	$-0.664678\pi$
$821$	10.7321	−	10.7321i	0.374551	−	0.374551i	0.869132	+	0.494581i	$0.164678\pi$
$822$		0			0
$823$	3.51588			0.122556			0.0612780	−	0.998121i	$-0.480482\pi$
$823$	3.51588			0.122556			0.0612780	+	0.998121i	$0.480482\pi$
$824$		0			0
$825$	18.5325	+	9.34935i	0.645220	+	0.325503i
$826$		0			0
$827$	27.7375	+	27.7375i	0.964529	+	0.964529i	0.999392	−	0.0348631i	$-0.0110995\pi$
$827$	27.7375	+	27.7375i	0.964529	+	0.964529i	−0.0348631	+	0.999392i	$0.511100\pi$
$828$		0			0
$829$	−19.5849	−	19.5849i	−0.680212	−	0.680212i	0.279836	−	0.960048i	$-0.409720\pi$
$829$	−19.5849	−	19.5849i	−0.680212	−	0.680212i	−0.960048	+	0.279836i	$0.909720\pi$
$830$		0			0
$831$	−7.47119			−0.259173
$832$		0			0
$833$		−	7.71231i		−	0.267216i
$834$		0			0
$835$	3.02380	+	4.91225i	0.104643	+	0.169995i
$836$		0			0
$837$	−25.7231	−	25.7231i	−0.889119	−	0.889119i
$838$		0			0
$839$		−	40.0520i		−	1.38275i	−0.722496	−	0.691375i	$-0.757005\pi$
$839$		−	40.0520i		−	1.38275i	0.722496	−	0.691375i	$-0.242995\pi$
$840$		0			0
$841$			61.3992i			2.11722i
$842$		0			0
$843$	−15.6243	−	15.6243i	−0.538129	−	0.538129i
$844$		0			0
$845$	−0.883749	+	0.544003i	−0.0304019	+	0.0187143i
$846$		0			0
$847$			8.54182i			0.293500i
$848$		0			0
$849$	−5.99948			−0.205902
$850$		0			0
$851$	−4.51793	−	4.51793i	−0.154873	−	0.154873i
$852$		0			0
$853$	−13.7328	−	13.7328i	−0.470202	−	0.470202i	0.431778	−	0.901980i	$-0.357886\pi$
$853$	−13.7328	−	13.7328i	−0.470202	−	0.470202i	−0.901980	+	0.431778i	$0.857886\pi$
$854$		0			0
$855$	−17.1215	−	4.07420i	−0.585542	−	0.139335i
$856$		0			0
$857$	−39.9485			−1.36462			−0.682308	−	0.731065i	$-0.739024\pi$
$857$	−39.9485			−1.36462			−0.682308	+	0.731065i	$0.739024\pi$
$858$		0			0
$859$	−33.6366	+	33.6366i	−1.14766	+	1.14766i	−0.160654	+	0.987011i	$0.551360\pi$
$859$	−33.6366	+	33.6366i	−1.14766	+	1.14766i	−0.987011	+	0.160654i	$0.948640\pi$
$860$		0			0
$861$	2.00969	+	2.00969i	0.0684900	+	0.0684900i
$862$		0			0
$863$		−	16.5303i		−	0.562697i	−0.959606	−	0.281349i	$-0.909218\pi$
$863$		−	16.5303i		−	0.562697i	0.959606	−	0.281349i	$-0.0907817\pi$
$864$		0			0
$865$	43.6146	+	10.3785i	1.48294	+	0.352879i
$866$		0			0
$867$	−9.83388	+	9.83388i	−0.333976	+	0.333976i
$868$		0			0
$869$	31.8205	−	31.8205i	1.07944	−	1.07944i
$870$		0			0
$871$		−	9.36421i		−	0.317294i
$872$		0			0
$873$	−12.5010			−0.423095
$874$		0			0
$875$	−19.1005	+	1.61893i	−0.645714	+	0.0547297i
$876$		0			0
$877$	9.66381	−	9.66381i	0.326324	−	0.326324i	−0.524863	−	0.851187i	$-0.675883\pi$
$877$	9.66381	−	9.66381i	0.326324	−	0.326324i	0.851187	+	0.524863i	$0.175883\pi$
$878$		0			0
$879$	−10.8734			−0.366752
$880$		0			0
$881$	−43.4299			−1.46319			−0.731596	−	0.681739i	$-0.761224\pi$
$881$	−43.4299			−1.46319			−0.731596	+	0.681739i	$0.761224\pi$
$882$		0			0
$883$	−22.3879	+	22.3879i	−0.753413	+	0.753413i	−0.975115	−	0.221701i	$-0.928839\pi$
$883$	−22.3879	+	22.3879i	−0.753413	+	0.753413i	0.221701	+	0.975115i	$0.428839\pi$
$884$		0			0
$885$	−8.62946	+	5.31198i	−0.290076	+	0.178560i
$886$		0			0
$887$	−31.6913			−1.06409			−0.532045	−	0.846716i	$-0.678576\pi$
$887$	−31.6913			−1.06409			−0.532045	+	0.846716i	$0.678576\pi$
$888$		0			0
$889$		−	31.4168i		−	1.05368i
$890$		0			0
$891$	1.29335	−	1.29335i	0.0433288	−	0.0433288i
$892$		0			0
$893$	−12.8541	+	12.8541i	−0.430147	+	0.430147i
$894$		0			0
$895$	7.23315	−	30.3967i	0.241778	−	1.01605i
$896$		0			0
$897$			7.64420i			0.255232i
$898$		0			0
$899$	−47.8533	−	47.8533i	−1.59600	−	1.59600i
$900$		0			0
$901$	−0.915049	+	0.915049i	−0.0304847	+	0.0304847i
$902$		0			0
$903$	20.3168			0.676102
$904$		0			0
$905$	−19.0893	−	4.54248i	−0.634551	−	0.150997i
$906$		0			0
$907$	−24.9184	−	24.9184i	−0.827401	−	0.827401i	0.159755	−	0.987157i	$-0.448929\pi$
$907$	−24.9184	−	24.9184i	−0.827401	−	0.827401i	−0.987157	+	0.159755i	$0.948929\pi$
$908$		0			0
$909$	−12.9192	−	12.9192i	−0.428503	−	0.428503i
$910$		0			0
$911$	47.0459			1.55870			0.779350	−	0.626589i	$-0.215549\pi$
$911$	47.0459			1.55870			0.779350	+	0.626589i	$0.215549\pi$
$912$		0			0
$913$			46.6366i			1.54345i
$914$		0			0
$915$	5.96319	+	9.68738i	0.197137	+	0.320255i
$916$		0			0
$917$	−17.4943	−	17.4943i	−0.577712	−	0.577712i
$918$		0			0
$919$		−	12.5442i		−	0.413796i	−0.978362	−	0.206898i	$-0.933663\pi$
$919$		−	12.5442i		−	0.413796i	0.978362	−	0.206898i	$-0.0663369\pi$
$920$		0			0
$921$			24.4716i			0.806368i
$922$		0			0
$923$	0.983751	+	0.983751i	0.0323806	+	0.0323806i
$924$		0			0
$925$	−15.1252	+	4.98165i	−0.497315	+	0.163796i
$926$		0			0
$927$		−	29.1573i		−	0.957652i
$928$		0			0
$929$	−26.7421			−0.877380			−0.438690	−	0.898639i	$-0.644557\pi$
$929$	−26.7421			−0.877380			−0.438690	+	0.898639i	$0.644557\pi$
$930$		0			0
$931$	11.7599	+	11.7599i	0.385414	+	0.385414i
$932$		0			0
$933$	16.0863	+	16.0863i	0.526642	+	0.526642i
$934$		0			0
$935$	−3.93058	+	16.5179i	−0.128544	+	0.540194i
$936$		0			0
$937$	−3.06580			−0.100155			−0.0500777	−	0.998745i	$-0.515947\pi$
$937$	−3.06580			−0.100155			−0.0500777	+	0.998745i	$0.515947\pi$
$938$		0			0
$939$	−9.16546	+	9.16546i	−0.299104	+	0.299104i
$940$		0			0
$941$	−14.6023	−	14.6023i	−0.476020	−	0.476020i	0.427836	−	0.903856i	$-0.359276\pi$
$941$	−14.6023	−	14.6023i	−0.476020	−	0.476020i	−0.903856	+	0.427836i	$0.859276\pi$
$942$		0			0
$943$		−	3.20239i		−	0.104284i
$944$		0			0
$945$	4.53590	−	19.0617i	0.147553	−	0.620077i
$946$		0			0
$947$	−29.4872	+	29.4872i	−0.958204	+	0.958204i	−0.999161	−	0.0409570i	$-0.986959\pi$
$947$	−29.4872	+	29.4872i	−0.958204	+	0.958204i	0.0409570	+	0.999161i	$0.486959\pi$
$948$		0			0
$949$	−21.7356	+	21.7356i	−0.705567	+	0.705567i
$950$		0			0
$951$		−	6.23158i		−	0.202073i
$952$		0			0
$953$	33.6807			1.09103			0.545513	−	0.838103i	$-0.316335\pi$
$953$	33.6807			1.09103			0.545513	+	0.838103i	$0.316335\pi$
$954$		0			0
$955$	22.1870	+	36.0434i	0.717953	+	1.16634i
$956$		0			0
$957$	−27.9105	+	27.9105i	−0.902219	+	0.902219i
$958$		0			0
$959$	25.6913			0.829616
$960$		0			0
$961$	19.6628			0.634283
$962$		0			0
$963$	−3.26256	+	3.26256i	−0.105134	+	0.105134i
$964$		0			0
$965$	−8.43541	+	5.19253i	−0.271546	+	0.167153i
$966$		0			0
$967$	−8.70089			−0.279802			−0.139901	−	0.990166i	$-0.544678\pi$
$967$	−8.70089			−0.279802			−0.139901	+	0.990166i	$0.544678\pi$
$968$		0			0
$969$			8.07881i			0.259529i
$970$		0			0
$971$	5.87523	−	5.87523i	0.188545	−	0.188545i	−0.606522	−	0.795067i	$-0.707436\pi$
$971$	5.87523	−	5.87523i	0.188545	−	0.188545i	0.795067	+	0.606522i	$0.207436\pi$
$972$		0			0
$973$	−14.2150	+	14.2150i	−0.455713	+	0.455713i
$974$		0			0
$975$	17.0101	+	8.58132i	0.544760	+	0.274822i
$976$		0			0
$977$			41.8541i			1.33903i	0.742798	+	0.669516i	$0.233498\pi$
$977$			41.8541i			1.33903i	−0.742798	+	0.669516i	$0.766502\pi$
$978$		0			0
$979$	33.8713	+	33.8713i	1.08253	+	1.08253i
$980$		0			0
$981$	−5.97856	+	5.97856i	−0.190881	+	0.190881i
$982$		0			0
$983$	−57.4539			−1.83250			−0.916248	−	0.400612i	$-0.868797\pi$
$983$	−57.4539			−1.83250			−0.916248	+	0.400612i	$0.868797\pi$
$984$		0			0
$985$	−4.68030	+	19.6685i	−0.149127	+	0.626692i
$986$		0			0
$987$	−5.58758	−	5.58758i	−0.177854	−	0.177854i
$988$		0			0
$989$	−16.1872	−	16.1872i	−0.514722	−	0.514722i
$990$		0			0
$991$	−12.8205			−0.407258			−0.203629	−	0.979048i	$-0.565274\pi$
$991$	−12.8205			−0.407258			−0.203629	+	0.979048i	$0.565274\pi$
$992$		0			0
$993$		−	1.62099i		−	0.0514404i
$994$		0			0
$995$	11.1519	−	6.86467i	0.353538	−	0.217625i
$996$		0			0
$997$	15.0860	+	15.0860i	0.477777	+	0.477777i	0.904420	−	0.426643i	$-0.140304\pi$
$997$	15.0860	+	15.0860i	0.477777	+	0.477777i	−0.426643	+	0.904420i	$0.640304\pi$
$998$		0			0
$999$		−	16.2776i		−	0.514999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.2.q.c.209.3		16
4.3	odd	2		80.2.q.c.29.4	✓	16
5.2	odd	4		1600.2.l.h.401.6		16
5.3	odd	4		1600.2.l.h.401.3		16
5.4	even	2	inner	320.2.q.c.209.6		16
8.3	odd	2		640.2.q.e.289.3		16
8.5	even	2		640.2.q.f.289.6		16
12.11	even	2		720.2.bm.f.109.5		16
16.3	odd	4		640.2.q.e.609.6		16
16.5	even	4	inner	320.2.q.c.49.6		16
16.11	odd	4		80.2.q.c.69.5	yes	16
16.13	even	4		640.2.q.f.609.3		16
20.3	even	4		400.2.l.i.301.1		16
20.7	even	4		400.2.l.i.301.8		16
20.19	odd	2		80.2.q.c.29.5	yes	16
40.19	odd	2		640.2.q.e.289.6		16
40.29	even	2		640.2.q.f.289.3		16
48.11	even	4		720.2.bm.f.469.4		16
60.59	even	2		720.2.bm.f.109.4		16
80.19	odd	4		640.2.q.e.609.3		16
80.27	even	4		400.2.l.i.101.8		16
80.29	even	4		640.2.q.f.609.6		16
80.37	odd	4		1600.2.l.h.1201.6		16
80.43	even	4		400.2.l.i.101.1		16
80.53	odd	4		1600.2.l.h.1201.3		16
80.59	odd	4		80.2.q.c.69.4	yes	16
80.69	even	4	inner	320.2.q.c.49.3		16
240.59	even	4		720.2.bm.f.469.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.c.29.4	✓	16	4.3	odd	2
80.2.q.c.29.5	yes	16	20.19	odd	2
80.2.q.c.69.4	yes	16	80.59	odd	4
80.2.q.c.69.5	yes	16	16.11	odd	4
320.2.q.c.49.3		16	80.69	even	4	inner
320.2.q.c.49.6		16	16.5	even	4	inner
320.2.q.c.209.3		16	1.1	even	1	trivial
320.2.q.c.209.6		16	5.4	even	2	inner
400.2.l.i.101.1		16	80.43	even	4
400.2.l.i.101.8		16	80.27	even	4
400.2.l.i.301.1		16	20.3	even	4
400.2.l.i.301.8		16	20.7	even	4
640.2.q.e.289.3		16	8.3	odd	2
640.2.q.e.289.6		16	40.19	odd	2
640.2.q.e.609.3		16	80.19	odd	4
640.2.q.e.609.6		16	16.3	odd	4
640.2.q.f.289.3		16	40.29	even	2
640.2.q.f.289.6		16	8.5	even	2
640.2.q.f.609.3		16	16.13	even	4
640.2.q.f.609.6		16	80.29	even	4
720.2.bm.f.109.4		16	60.59	even	2
720.2.bm.f.109.5		16	12.11	even	2
720.2.bm.f.469.4		16	48.11	even	4
720.2.bm.f.469.5		16	240.59	even	4
1600.2.l.h.401.3		16	5.3	odd	4
1600.2.l.h.401.6		16	5.2	odd	4
1600.2.l.h.1201.3		16	80.53	odd	4
1600.2.l.h.1201.6		16	80.37	odd	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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	320.q (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.734294 + 0.734294i) q^{3} +(-1.17216 - 1.90421i) q^{5} -1.71452 q^{7} +1.92163i q^{9} +(-2.82684 + 2.82684i) q^{11} +(-2.59462 + 2.59462i) q^{13} +(2.25896 + 0.537540i) q^{15} +1.89939i q^{17} +(-2.89623 - 2.89623i) q^{19} +(1.25896 - 1.25896i) q^{21} -2.00613 q^{23} +(-2.25207 + 4.46410i) q^{25} +(-3.61392 - 3.61392i) q^{27} +(-6.72307 - 6.72307i) q^{29} +7.11778 q^{31} -4.15146i q^{33} +(2.00970 + 3.26482i) q^{35} +(2.25207 + 2.25207i) q^{37} -3.81042i q^{39} +1.59630i q^{41} +(8.06886 + 8.06886i) q^{43} +(3.65919 - 2.25246i) q^{45} -4.43823i q^{47} -4.06040 q^{49} +(-1.39471 - 1.39471i) q^{51} +(0.481758 + 0.481758i) q^{53} +(8.69642 + 2.06939i) q^{55} +4.25336 q^{57} +(-3.08580 + 3.08580i) q^{59} +(3.46410 + 3.46410i) q^{61} -3.29468i q^{63} +(7.98203 + 1.89939i) q^{65} +(-1.80454 + 1.80454i) q^{67} +(1.47309 - 1.47309i) q^{69} -0.379150i q^{71} +8.37718 q^{73} +(-1.62428 - 4.93164i) q^{75} +(4.84668 - 4.84668i) q^{77} -11.2566 q^{79} -0.457524 q^{81} +(8.24890 - 8.24890i) q^{83} +(3.61685 - 2.22640i) q^{85} +9.87341 q^{87} -11.9820i q^{89} +(4.44854 - 4.44854i) q^{91} +(-5.22654 + 5.22654i) q^{93} +(-2.12019 + 8.90989i) q^{95} +6.50543i q^{97} +(-5.43213 - 5.43213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{5} - 8 q^{11} + 8 q^{19} - 16 q^{21} - 16 q^{29} - 16 q^{31} + 24 q^{35} + 8 q^{45} + 16 q^{49} + 16 q^{51} + 24 q^{59} + 32 q^{69} - 48 q^{75} - 16 q^{79} - 16 q^{81} + 16 q^{91} - 32 q^{95}+ \cdots - 88 q^{99}+O(q^{100}) \) 16 * q - 8 * q^5 - 8 * q^11 + 8 * q^19 - 16 * q^21 - 16 * q^29 - 16 * q^31 + 24 * q^35 + 8 * q^45 + 16 * q^49 + 16 * q^51 + 24 * q^59 + 32 * q^69 - 48 * q^75 - 16 * q^79 - 16 * q^81 + 16 * q^91 - 32 * q^95 - 88 * q^99

Introduction

L-functions

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