LMFDB - Embedded newform 1323.2.i.b.1097.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1323,2,Mod(521,1323)] 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("1323.521"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1323, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1097.5
Root			$0.827154 + 1.43267i$ of defining polynomial
Character	$\chi$	$=$	1323.1097
Dual form			1323.2.i.b.521.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.09548i q^{2} -2.39104 q^{4} +(-1.04492 - 1.80985i) q^{5} -0.819421i q^{8} +(3.79250 - 2.18960i) q^{10} +(-2.79620 - 1.61439i) q^{11} +(2.68740 + 1.55157i) q^{13} -3.06500 q^{16} +(0.816304 + 1.41388i) q^{17} +(-4.79094 - 2.76605i) q^{19} +(2.49844 + 4.32742i) q^{20} +(3.38292 - 5.85939i) q^{22} +(1.00527 - 0.580391i) q^{23} +(0.316304 - 0.547854i) q^{25} +(-3.25129 + 5.63139i) q^{26} +(7.05749 - 4.07464i) q^{29} -5.96849i q^{31} -8.06150i q^{32} +(-2.96276 + 1.71055i) q^{34} +(2.82656 - 4.89575i) q^{37} +(5.79620 - 10.0393i) q^{38} +(-1.48303 + 0.856225i) q^{40} +(1.35369 - 2.34465i) q^{41} +(-0.974903 - 1.68858i) q^{43} +(6.68583 + 3.86007i) q^{44} +(1.21620 + 2.10652i) q^{46} +8.13518 q^{47} +(1.14802 + 0.662809i) q^{50} +(-6.42568 - 3.70987i) q^{52} +(5.27766 - 3.04706i) q^{53} +6.74759i q^{55} +(8.53834 + 14.7888i) q^{58} -3.96206 q^{59} +4.79219i q^{61} +12.5068 q^{62} +10.7627 q^{64} -6.48504i q^{65} -0.673961 q^{67} +(-1.95182 - 3.38065i) q^{68} -7.01535i q^{71} +(2.96276 - 1.71055i) q^{73} +(10.2590 + 5.92301i) q^{74} +(11.4553 + 6.61374i) q^{76} -14.1595 q^{79} +(3.20267 + 5.54718i) q^{80} +(4.91318 + 2.83662i) q^{82} +(-1.54535 - 2.67662i) q^{83} +(1.70594 - 2.95477i) q^{85} +(3.53839 - 2.04289i) q^{86} +(-1.32286 + 2.29127i) q^{88} +(2.45766 - 4.25679i) q^{89} +(-2.40363 + 1.38774i) q^{92} +17.0471i q^{94} +11.5611i q^{95} +(2.07939 - 1.20054i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 8 q^{4} + 15 q^{10} + 12 q^{11} + 6 q^{13} + 12 q^{16} + 12 q^{17} - 3 q^{19} + 3 q^{20} + 5 q^{22} + 15 q^{23} + 7 q^{25} - 3 q^{26} + 15 q^{29} + 3 q^{34} + 6 q^{37} + 18 q^{38} - 15 q^{40} + 9 q^{41}+ \cdots + 6 q^{97}+O(q^{100}) $ 10 * q - 8 * q^4 + 15 * q^10 + 12 * q^11 + 6 * q^13 + 12 * q^16 + 12 * q^17 - 3 * q^19 + 3 * q^20 + 5 * q^22 + 15 * q^23 + 7 * q^25 - 3 * q^26 + 15 * q^29 + 3 * q^34 + 6 * q^37 + 18 * q^38 - 15 * q^40 + 9 * q^41 + 3 * q^43 + 24 * q^44 - 13 * q^46 + 30 * q^47 - 3 * q^50 + 12 * q^52 - 9 * q^53 + 8 * q^58 - 36 * q^59 - 12 * q^62 + 6 * q^64 + 20 * q^67 - 27 * q^68 - 3 * q^73 + 30 * q^74 + 9 * q^76 - 40 * q^79 + 30 * q^80 - 9 * q^82 + 15 * q^83 + 18 * q^85 - 54 * q^86 - 8 * q^88 - 24 * q^89 - 39 * q^92 + 6 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$			2.09548i			1.48173i	0.671655	+	0.740865i	$0.265584\pi$
$2$			2.09548i			1.48173i	−0.671655	+	0.740865i	$0.734416\pi$
$3$		0			0
$3$		0			0
$4$	−2.39104			−1.19552
$5$	−1.04492	−	1.80985i	−0.467300	−	0.809388i	0.532002	−	0.846743i	$-0.321440\pi$
$5$	−1.04492	−	1.80985i	−0.467300	−	0.809388i	−0.999302	+	0.0373553i	$0.988107\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	0.819421i		−	0.289709i
$9$		0			0
$10$	3.79250	−	2.18960i	1.19929	−	0.692412i
$11$	−2.79620	−	1.61439i	−0.843086	−	0.486756i	0.0152257	−	0.999884i	$-0.495153\pi$
$11$	−2.79620	−	1.61439i	−0.843086	−	0.486756i	−0.858312	+	0.513128i	$0.828487\pi$
$12$		0			0
$13$	2.68740	+	1.55157i	0.745350	+	0.430328i	0.824011	−	0.566573i	$-0.191731\pi$
$13$	2.68740	+	1.55157i	0.745350	+	0.430328i	−0.0786612	+	0.996901i	$0.525065\pi$
$14$		0			0
$15$		0			0
$16$	−3.06500			−0.766251
$17$	0.816304	+	1.41388i	0.197983	+	0.342916i	0.947874	−	0.318645i	$-0.103228\pi$
$17$	0.816304	+	1.41388i	0.197983	+	0.342916i	−0.749891	+	0.661561i	$0.769894\pi$
$18$		0			0
$19$	−4.79094	−	2.76605i	−1.09912	−	0.634575i	−0.163127	−	0.986605i	$-0.552158\pi$
$19$	−4.79094	−	2.76605i	−1.09912	−	0.634575i	−0.935989	+	0.352030i	$0.885491\pi$
$20$	2.49844	+	4.32742i	0.558667	+	0.967640i
$21$		0			0
$22$	3.38292	−	5.85939i	0.721241	−	1.24923i
$23$	1.00527	−	0.580391i	0.209612	−	0.121020i	−0.391519	−	0.920170i	$-0.628050\pi$
$23$	1.00527	−	0.580391i	0.209612	−	0.121020i	0.601131	+	0.799150i	$0.294717\pi$
$24$		0			0
$25$	0.316304	−	0.547854i	0.0632608	−	0.109571i
$26$	−3.25129	+	5.63139i	−0.637630	+	1.10441i
$27$		0			0
$28$		0			0
$29$	7.05749	−	4.07464i	1.31054	−	0.756643i	0.328357	−	0.944554i	$-0.393505\pi$
$29$	7.05749	−	4.07464i	1.31054	−	0.756643i	0.982186	+	0.187911i	$0.0601717\pi$
$30$		0			0
$31$		−	5.96849i		−	1.07197i	−0.844227	−	0.535986i	$-0.819940\pi$
$31$		−	5.96849i		−	1.07197i	0.844227	−	0.535986i	$-0.180060\pi$
$32$		−	8.06150i		−	1.42508i
$33$		0			0
$34$	−2.96276	+	1.71055i	−0.508109	+	0.293357i
$35$		0			0
$36$		0			0
$37$	2.82656	−	4.89575i	0.464684	−	0.804857i	−0.534503	−	0.845167i	$-0.679501\pi$
$37$	2.82656	−	4.89575i	0.464684	−	0.804857i	0.999187	+	0.0403097i	$0.0128345\pi$
$38$	5.79620	−	10.0393i	0.940268	−	1.62859i
$39$		0			0
$40$	−1.48303	+	0.856225i	−0.234487	+	0.135381i
$41$	1.35369	−	2.34465i	0.211410	−	0.366173i	−0.740746	−	0.671785i	$-0.765528\pi$
$41$	1.35369	−	2.34465i	0.211410	−	0.366173i	0.952156	+	0.305612i	$0.0988611\pi$
$42$		0			0
$43$	−0.974903	−	1.68858i	−0.148671	−	0.257506i	0.782065	−	0.623196i	$-0.214166\pi$
$43$	−0.974903	−	1.68858i	−0.148671	−	0.257506i	−0.930737	+	0.365690i	$0.880833\pi$
$44$	6.68583	+	3.86007i	1.00793	+	0.581927i
$45$		0			0
$46$	1.21620	+	2.10652i	0.179319	+	0.310589i
$47$	8.13518			1.18664			0.593319	−	0.804967i	$-0.297817\pi$
$47$	8.13518			1.18664			0.593319	+	0.804967i	$0.297817\pi$
$48$		0			0
$49$		0			0
$50$	1.14802	+	0.662809i	0.162354	+	0.0937353i
$51$		0			0
$52$	−6.42568	−	3.70987i	−0.891082	−	0.514466i
$53$	5.27766	−	3.04706i	0.724943	−	0.418546i	−0.0916264	−	0.995793i	$-0.529207\pi$
$53$	5.27766	−	3.04706i	0.724943	−	0.418546i	0.816569	+	0.577248i	$0.195873\pi$
$54$		0			0
$55$			6.74759i			0.909845i
$56$		0			0
$57$		0			0
$58$	8.53834	+	14.7888i	1.12114	+	1.94187i
$59$	−3.96206			−0.515816			−0.257908	−	0.966170i	$-0.583033\pi$
$59$	−3.96206			−0.515816			−0.257908	+	0.966170i	$0.583033\pi$
$60$		0			0
$61$			4.79219i			0.613577i	0.951778	+	0.306788i	$0.0992544\pi$
$61$			4.79219i			0.613577i	−0.951778	+	0.306788i	$0.900746\pi$
$62$	12.5068			1.58837
$63$		0			0
$64$	10.7627			1.34534
$65$		−	6.48504i		−	0.804370i
$66$		0			0
$67$	−0.673961			−0.0823375			−0.0411687	−	0.999152i	$-0.513108\pi$
$67$	−0.673961			−0.0823375			−0.0411687	+	0.999152i	$0.513108\pi$
$68$	−1.95182	−	3.38065i	−0.236693	−	0.409963i
$69$		0			0
$70$		0			0
$71$		−	7.01535i		−	0.832568i	−0.909235	−	0.416284i	$-0.863332\pi$
$71$		−	7.01535i		−	0.832568i	0.909235	−	0.416284i	$-0.136668\pi$
$72$		0			0
$73$	2.96276	−	1.71055i	0.346765	−	0.200205i	−0.316495	−	0.948594i	$-0.602506\pi$
$73$	2.96276	−	1.71055i	0.346765	−	0.200205i	0.663259	+	0.748390i	$0.269173\pi$
$74$	10.2590	+	5.92301i	1.19258	+	0.688536i
$75$		0			0
$76$	11.4553	+	6.61374i	1.31402	+	0.758648i
$77$		0			0
$78$		0			0
$79$	−14.1595			−1.59306			−0.796532	−	0.604596i	$-0.793335\pi$
$79$	−14.1595			−1.59306			−0.796532	+	0.604596i	$0.793335\pi$
$80$	3.20267	+	5.54718i	0.358069	+	0.620194i
$81$		0			0
$82$	4.91318	+	2.83662i	0.542570	+	0.313253i
$83$	−1.54535	−	2.67662i	−0.169624	−	0.293798i	0.768664	−	0.639653i	$-0.220922\pi$
$83$	−1.54535	−	2.67662i	−0.169624	−	0.293798i	−0.938288	+	0.345856i	$0.887589\pi$
$84$		0			0
$85$	1.70594	−	2.95477i	0.185035	−	0.320490i
$86$	3.53839	−	2.04289i	0.381554	−	0.220291i
$87$		0			0
$88$	−1.32286	+	2.29127i	−0.141018	+	0.244250i
$89$	2.45766	−	4.25679i	0.260511	−	0.451219i	−0.705867	−	0.708345i	$-0.749442\pi$
$89$	2.45766	−	4.25679i	0.260511	−	0.451219i	0.966378	+	0.257126i	$0.0827756\pi$
$90$		0			0
$91$		0			0
$92$	−2.40363	+	1.38774i	−0.250596	+	0.144682i
$93$		0			0
$94$			17.0471i			1.75828i
$95$			11.5611i			1.18615i
$96$		0			0
$97$	2.07939	−	1.20054i	0.211130	−	0.121896i	−0.390706	−	0.920515i	$-0.627769\pi$
$97$	2.07939	−	1.20054i	0.211130	−	0.121896i	0.601837	+	0.798619i	$0.294436\pi$
$98$		0			0
$99$		0			0
$100$	−0.756296	+	1.30994i	−0.0756296	+	0.130994i
$101$	−1.76025	+	3.04885i	−0.175152	+	0.303372i	−0.940214	−	0.340585i	$-0.889375\pi$
$101$	−1.76025	+	3.04885i	−0.175152	+	0.303372i	0.765062	+	0.643957i	$0.222708\pi$
$102$		0			0
$103$	13.5832	−	7.84228i	1.33840	−	0.772723i	0.351826	−	0.936065i	$-0.385561\pi$
$103$	13.5832	−	7.84228i	1.33840	−	0.772723i	0.986569	+	0.163342i	$0.0522275\pi$
$104$	1.27139	−	2.20211i	0.124670	−	0.215935i
$105$		0			0
$106$	6.38506	+	11.0592i	0.620172	+	1.07417i
$107$	−1.41984	−	0.819746i	−0.137261	−	0.0792478i	0.429797	−	0.902926i	$-0.358585\pi$
$107$	−1.41984	−	0.819746i	−0.137261	−	0.0792478i	−0.567058	+	0.823678i	$0.691919\pi$
$108$		0			0
$109$	2.90672	+	5.03459i	0.278414	+	0.482227i	0.970991	−	0.239117i	$-0.0768581\pi$
$109$	2.90672	+	5.03459i	0.278414	+	0.482227i	−0.692577	+	0.721344i	$0.743525\pi$
$110$	−14.1395			−1.34814
$111$		0			0
$112$		0			0
$113$	−13.9931	−	8.07894i	−1.31636	−	0.760003i	−0.333222	−	0.942848i	$-0.608136\pi$
$113$	−13.9931	−	8.07894i	−1.31636	−	0.760003i	−0.983142	+	0.182845i	$0.941469\pi$
$114$		0			0
$115$	−2.10084	−	1.21292i	−0.195904	−	0.113105i
$116$	−16.8748	+	9.74265i	−1.56678	+	0.904582i
$117$		0			0
$118$		−	8.30241i		−	0.764299i
$119$		0			0
$120$		0			0
$121$	−0.287505	−	0.497972i	−0.0261368	−	0.0452702i
$122$	−10.0419			−0.909155
$123$		0			0
$124$			14.2709i			1.28156i
$125$	−11.7712			−1.05285
$126$		0			0
$127$	−9.59240			−0.851188			−0.425594	−	0.904914i	$-0.639935\pi$
$127$	−9.59240			−0.851188			−0.425594	+	0.904914i	$0.639935\pi$
$128$			6.43006i			0.568343i
$129$		0			0
$130$	13.5893			1.19186
$131$	1.23061	+	2.13148i	0.107519	+	0.186228i	0.914765	−	0.403987i	$-0.132376\pi$
$131$	1.23061	+	2.13148i	0.107519	+	0.186228i	−0.807246	+	0.590216i	$0.799043\pi$
$132$		0			0
$133$		0			0
$134$		−	1.41227i		−	0.122002i
$135$		0			0
$136$	1.15856	−	0.668896i	0.0993459	−	0.0573574i
$137$	15.0571	+	8.69322i	1.28641	+	0.742712i	0.978013	−	0.208545i	$-0.0668727\pi$
$137$	15.0571	+	8.69322i	1.28641	+	0.742712i	0.308401	+	0.951256i	$0.400206\pi$
$138$		0			0
$139$	−8.61174	−	4.97199i	−0.730438	−	0.421719i	0.0881443	−	0.996108i	$-0.471906\pi$
$139$	−8.61174	−	4.97199i	−0.730438	−	0.421719i	−0.818582	+	0.574389i	$0.805240\pi$
$140$		0			0
$141$		0			0
$142$	14.7005			1.23364
$143$	−5.00967	−	8.67701i	−0.418930	−	0.725608i
$144$		0			0
$145$	−14.7490	−	8.51532i	−1.22483	−	0.707159i
$146$	3.58442	+	6.20840i	0.296649	+	0.513811i
$147$		0			0
$148$	−6.75843	+	11.7060i	−0.555540	+	0.962223i
$149$	−8.01695	+	4.62859i	−0.656774	+	0.379189i	−0.791047	−	0.611756i	$-0.790464\pi$
$149$	−8.01695	+	4.62859i	−0.656774	+	0.379189i	0.134273	+	0.990944i	$0.457130\pi$
$150$		0			0
$151$	5.98489	−	10.3661i	0.487044	−	0.843584i	−0.512845	−	0.858481i	$-0.671409\pi$
$151$	5.98489	−	10.3661i	0.487044	−	0.843584i	0.999889	+	0.0148966i	$0.00474192\pi$
$152$	−2.26656	+	3.92579i	−0.183842	+	0.318424i
$153$		0			0
$154$		0			0
$155$	−10.8020	+	6.23656i	−0.867641	+	0.500933i
$156$		0			0
$157$			17.8514i			1.42470i	0.701826	+	0.712348i	$0.252368\pi$
$157$			17.8514i			1.42470i	−0.701826	+	0.712348i	$0.747632\pi$
$158$		−	29.6709i		−	2.36049i
$159$		0			0
$160$	−14.5901	+	8.42358i	−1.15345	+	0.665943i
$161$		0			0
$162$		0			0
$163$	−8.91768	+	15.4459i	−0.698486	+	1.20981i	0.270505	+	0.962719i	$0.412809\pi$
$163$	−8.91768	+	15.4459i	−0.698486	+	1.20981i	−0.968991	+	0.247095i	$0.920524\pi$
$164$	−3.23672	+	5.60616i	−0.252745	+	0.437768i
$165$		0			0
$166$	5.60881	−	3.23825i	0.435328	−	0.251337i
$167$	6.16899	−	10.6850i	0.477371	−	0.826830i	−0.522293	−	0.852766i	$-0.674923\pi$
$167$	6.16899	−	10.6850i	0.477371	−	0.826830i	0.999664	+	0.0259359i	$0.00825657\pi$
$168$		0			0
$169$	−1.68526	−	2.91896i	−0.129635	−	0.224535i
$170$	6.19166	+	3.57476i	0.474879	+	0.274171i
$171$		0			0
$172$	2.33103	+	4.03747i	0.177740	+	0.307854i
$173$	9.06736			0.689379			0.344689	−	0.938717i	$-0.387984\pi$
$173$	9.06736			0.689379			0.344689	+	0.938717i	$0.387984\pi$
$174$		0			0
$175$		0			0
$176$	8.57037	+	4.94810i	0.646016	+	0.372977i
$177$		0			0
$178$	8.92002	+	5.14997i	0.668584	+	0.386007i
$179$	−13.0086	+	7.51051i	−0.972307	+	0.561362i	−0.899939	−	0.436016i	$-0.856389\pi$
$179$	−13.0086	+	7.51051i	−0.972307	+	0.561362i	−0.0723682	+	0.997378i	$0.523056\pi$
$180$		0			0
$181$			2.34159i			0.174049i	0.996206	+	0.0870246i	$0.0277359\pi$
$181$			2.34159i			0.174049i	−0.996206	+	0.0870246i	$0.972264\pi$
$182$		0			0
$183$		0			0
$184$	−0.475584	−	0.823736i	−0.0350605	−	0.0607266i
$185$	−11.8141			−0.868589
$186$		0			0
$187$		−	5.27132i		−	0.385477i
$188$	−19.4516			−1.41865
$189$		0			0
$190$	−24.2262			−1.75755
$191$			9.03651i			0.653859i	0.945049	+	0.326929i	$0.106014\pi$
$191$			9.03651i			0.653859i	−0.945049	+	0.326929i	$0.893986\pi$
$192$		0			0
$193$	−5.48269			−0.394652			−0.197326	−	0.980338i	$-0.563226\pi$
$193$	−5.48269			−0.394652			−0.197326	+	0.980338i	$0.563226\pi$
$194$	2.51570	+	4.35733i	0.180617	+	0.312838i
$195$		0			0
$196$		0			0
$197$			2.88946i			0.205865i	0.994688	+	0.102933i	$0.0328226\pi$
$197$			2.88946i			0.205865i	−0.994688	+	0.102933i	$0.967177\pi$
$198$		0			0
$199$	−4.45419	+	2.57163i	−0.315749	+	0.182298i	−0.649496	−	0.760365i	$-0.725020\pi$
$199$	−4.45419	+	2.57163i	−0.315749	+	0.182298i	0.333747	+	0.942663i	$0.391687\pi$
$200$	−0.448923	−	0.259186i	−0.0317437	−	0.0183272i
$201$		0			0
$202$	−6.38881	−	3.68858i	−0.449515	−	0.259528i
$203$		0			0
$204$		0			0
$205$	−5.65795			−0.395168
$206$	16.4334	+	28.4634i	1.14497	+	1.98314i
$207$		0			0
$208$	−8.23688	−	4.75557i	−0.571125	−	0.329739i
$209$	8.93095	+	15.4689i	0.617767	+	1.07000i
$210$		0			0
$211$	7.93224	−	13.7390i	0.546078	−	0.945835i	−0.452460	−	0.891785i	$-0.649454\pi$
$211$	7.93224	−	13.7390i	0.546078	−	0.945835i	0.998538	−	0.0540502i	$-0.0172131\pi$
$212$	−12.6191	+	7.28565i	−0.866684	+	0.500380i
$213$		0			0
$214$	1.71776	−	2.97525i	0.117424	−	0.203384i
$215$	−2.03738	+	3.52885i	−0.138948	+	0.240666i
$216$		0			0
$217$		0			0
$218$	−10.5499	+	6.09099i	−0.714529	+	0.412534i
$219$		0			0
$220$		−	16.1338i		−	1.08774i
$221$			5.06621i			0.340790i
$222$		0			0
$223$	13.5288	−	7.81085i	0.905955	−	0.523053i	0.0268275	−	0.999640i	$-0.491460\pi$
$223$	13.5288	−	7.81085i	0.905955	−	0.523053i	0.879127	+	0.476587i	$0.158126\pi$
$224$		0			0
$225$		0			0
$226$	16.9293	−	29.3224i	1.12612	−	1.95049i
$227$	1.04045	−	1.80211i	0.0690569	−	0.119610i	−0.829430	−	0.558611i	$-0.811334\pi$
$227$	1.04045	−	1.80211i	0.0690569	−	0.119610i	0.898486	+	0.439001i	$0.144668\pi$
$228$		0			0
$229$	−5.57233	+	3.21719i	−0.368230	+	0.212598i	−0.672685	−	0.739929i	$-0.734859\pi$
$229$	−5.57233	+	3.21719i	−0.368230	+	0.212598i	0.304455	+	0.952527i	$0.401526\pi$
$230$	2.54165	−	4.40226i	0.167591	−	0.290277i
$231$		0			0
$232$	−3.33885	−	5.78305i	−0.219206	−	0.379676i
$233$	−13.5222	−	7.80704i	−0.885868	−	0.511456i	−0.0132791	−	0.999912i	$-0.504227\pi$
$233$	−13.5222	−	7.80704i	−0.885868	−	0.511456i	−0.872589	+	0.488456i	$0.837560\pi$
$234$		0			0
$235$	−8.50057	−	14.7234i	−0.554516	−	0.960450i
$236$	9.47344			0.616668
$237$		0			0
$238$		0			0
$239$	14.8777	+	8.58964i	0.962358	+	0.555618i	0.896898	−	0.442238i	$-0.145815\pi$
$239$	14.8777	+	8.58964i	0.962358	+	0.555618i	0.0654600	+	0.997855i	$0.479149\pi$
$240$		0			0
$241$	−9.71544	−	5.60921i	−0.625827	−	0.361321i	0.153307	−	0.988179i	$-0.451008\pi$
$241$	−9.71544	−	5.60921i	−0.625827	−	0.361321i	−0.779134	+	0.626857i	$0.784341\pi$
$242$	1.04349	−	0.602460i	0.0670782	−	0.0387276i
$243$		0			0
$244$		−	11.4583i		−	0.733544i
$245$		0			0
$246$		0			0
$247$	−8.58343	−	14.8669i	−0.546151	−	0.945961i
$248$	−4.89070			−0.310560
$249$		0			0
$250$		−	24.6663i		−	1.56004i
$251$	−11.3837			−0.718535			−0.359267	−	0.933235i	$-0.616973\pi$
$251$	−11.3837			−0.718535			−0.359267	+	0.933235i	$0.616973\pi$
$252$		0			0
$253$	−3.74790			−0.235629
$254$		−	20.1007i		−	1.26123i
$255$		0			0
$256$	8.05134			0.503209
$257$	4.69024	+	8.12373i	0.292569	+	0.506745i	0.974416	−	0.224750i	$-0.0721565\pi$
$257$	4.69024	+	8.12373i	0.292569	+	0.506745i	−0.681847	+	0.731494i	$0.738823\pi$
$258$		0			0
$259$		0			0
$260$			15.5060i			0.961641i
$261$		0			0
$262$	−4.46647	+	2.57872i	−0.275940	+	0.159314i
$263$	7.62367	+	4.40153i	0.470096	+	0.271410i	0.716280	−	0.697813i	$-0.245843\pi$
$263$	7.62367	+	4.40153i	0.470096	+	0.271410i	−0.246184	+	0.969223i	$0.579177\pi$
$264$		0			0
$265$	−11.0294	−	6.36784i	−0.677532	−	0.391173i
$266$		0			0
$267$		0			0
$268$	1.61147			0.0984362
$269$	−8.16473	−	14.1417i	−0.497812	−	0.862236i	0.502184	−	0.864761i	$-0.332530\pi$
$269$	−8.16473	−	14.1417i	−0.497812	−	0.862236i	−0.999997	+	0.00252412i	$0.999197\pi$
$270$		0			0
$271$	12.6186	+	7.28538i	0.766528	+	0.442555i	0.831635	−	0.555323i	$-0.187405\pi$
$271$	12.6186	+	7.28538i	0.766528	+	0.442555i	−0.0651065	+	0.997878i	$0.520739\pi$
$272$	−2.50197	−	4.33355i	−0.151704	−	0.262760i
$273$		0			0
$274$	−18.2165	+	31.5519i	−1.10050	+	1.90612i
$275$	−1.76890	+	1.02127i	−0.106669	+	0.0615851i
$276$		0			0
$277$	−14.3568	+	24.8668i	−0.862618	+	1.49410i	0.00677410	+	0.999977i	$0.497844\pi$
$277$	−14.3568	+	24.8668i	−0.862618	+	1.49410i	−0.869393	+	0.494122i	$0.835490\pi$
$278$	10.4187	−	18.0457i	0.624873	−	1.08231i
$279$		0			0
$280$		0			0
$281$	4.76893	−	2.75334i	0.284490	−	0.164251i	−0.350964	−	0.936389i	$-0.614146\pi$
$281$	4.76893	−	2.75334i	0.284490	−	0.164251i	0.635455	+	0.772138i	$0.280813\pi$
$282$		0			0
$283$		−	30.2829i		−	1.80013i	−0.435756	−	0.900065i	$-0.643519\pi$
$283$		−	30.2829i		−	1.80013i	0.435756	−	0.900065i	$-0.356481\pi$
$284$			16.7740i			0.995353i
$285$		0			0
$286$	18.1825	−	10.4977i	1.07515	−	0.620740i
$287$		0			0
$288$		0			0
$289$	7.16730	−	12.4141i	0.421606	−	0.730242i
$290$	17.8437	−	30.9062i	1.04782	−	1.81487i
$291$		0			0
$292$	−7.08408	+	4.08999i	−0.414564	+	0.239349i
$293$	3.54362	−	6.13773i	0.207021	−	0.358570i	−0.743754	−	0.668453i	$-0.766957\pi$
$293$	3.54362	−	6.13773i	0.207021	−	0.358570i	0.950775	+	0.309883i	$0.100290\pi$
$294$		0			0
$295$	4.14001	+	7.17071i	0.241041	+	0.417495i
$296$	−4.01168	−	2.31615i	−0.233174	−	0.134623i
$297$		0			0
$298$	−9.69912	−	16.7994i	−0.561855	−	0.973161i
$299$	3.60207			0.208313
$300$		0			0
$301$		0			0
$302$	21.7220	+	12.5412i	1.24996	+	0.721667i
$303$		0			0
$304$	14.6842	+	8.47795i	0.842198	+	0.486244i
$305$	8.67313	−	5.00743i	0.496622	−	0.286725i
$306$		0			0
$307$		−	3.11346i		−	0.177695i	−0.996045	−	0.0888473i	$-0.971682\pi$
$307$		−	3.11346i		−	0.177695i	0.996045	−	0.0888473i	$-0.0283183\pi$
$308$		0			0
$309$		0			0
$310$	−13.0686	−	22.6355i	−0.742247	−	1.28561i
$311$	19.4521			1.10303			0.551514	−	0.834166i	$-0.314051\pi$
$311$	19.4521			1.10303			0.551514	+	0.834166i	$0.314051\pi$
$312$		0			0
$313$			25.5447i			1.44387i	0.691959	+	0.721937i	$0.256748\pi$
$313$			25.5447i			1.44387i	−0.691959	+	0.721937i	$0.743252\pi$
$314$	−37.4073			−2.11101
$315$		0			0
$316$	33.8559			1.90454
$317$		−	16.2274i		−	0.911424i	−0.890127	−	0.455712i	$-0.849385\pi$
$317$		−	16.2274i		−	0.911424i	0.890127	−	0.455712i	$-0.150615\pi$
$318$		0			0
$319$	−26.3122			−1.47320
$320$	−11.2461	−	19.4789i	−0.628677	−	1.08890i
$321$		0			0
$322$		0			0
$323$		−	9.03174i		−	0.502540i
$324$		0			0
$325$	1.70007	−	0.981535i	0.0943029	−	0.0544458i
$326$	−32.3665	−	18.6868i	−1.79262	−	1.03497i
$327$		0			0
$328$	−1.92126	−	1.10924i	−0.106084	−	0.0612474i
$329$		0			0
$330$		0			0
$331$	23.3117			1.28132			0.640662	−	0.767823i	$-0.278660\pi$
$331$	23.3117			1.28132			0.640662	+	0.767823i	$0.278660\pi$
$332$	3.69499	+	6.39992i	0.202789	+	0.351241i
$333$		0			0
$334$	22.3902	+	12.9270i	1.22514	+	0.707334i
$335$	0.704232	+	1.21977i	0.0384763	+	0.0666430i
$336$		0			0
$337$	5.93515	−	10.2800i	0.323308	−	0.559986i	−0.657860	−	0.753140i	$-0.728538\pi$
$337$	5.93515	−	10.2800i	0.323308	−	0.559986i	0.981168	+	0.193154i	$0.0618717\pi$
$338$	6.11662	−	3.53143i	0.332700	−	0.192085i
$339$		0			0
$340$	−4.07897	+	7.06498i	−0.221213	+	0.383152i
$341$	−9.63545	+	16.6891i	−0.521789	+	0.903765i
$342$		0			0
$343$		0			0
$344$	−1.38366	+	0.798855i	−0.0746019	+	0.0430714i
$345$		0			0
$346$			19.0005i			1.02147i
$347$		−	21.7060i		−	1.16524i	−0.812745	−	0.582619i	$-0.802028\pi$
$347$		−	21.7060i		−	1.16524i	0.812745	−	0.582619i	$-0.197972\pi$
$348$		0			0
$349$	2.20868	−	1.27518i	0.118228	−	0.0682588i	−0.439720	−	0.898135i	$-0.644922\pi$
$349$	2.20868	−	1.27518i	0.118228	−	0.0682588i	0.557948	+	0.829876i	$0.311589\pi$
$350$		0			0
$351$		0			0
$352$	−13.0144	+	22.5416i	−0.693669	+	1.20147i
$353$	−12.6873	+	21.9751i	−0.675279	+	1.16962i	0.301109	+	0.953590i	$0.402643\pi$
$353$	−12.6873	+	21.9751i	−0.675279	+	1.16962i	−0.976387	+	0.216027i	$0.930690\pi$
$354$		0			0
$355$	−12.6967	+	7.33044i	−0.673871	+	0.389059i
$356$	−5.87636	+	10.1782i	−0.311446	+	0.539441i
$357$		0			0
$358$	−15.7381	−	27.2592i	−0.831786	−	1.44070i
$359$	−9.73735	−	5.62186i	−0.513918	−	0.296711i	0.220525	−	0.975381i	$-0.429223\pi$
$359$	−9.73735	−	5.62186i	−0.513918	−	0.296711i	−0.734443	+	0.678671i	$0.762556\pi$
$360$		0			0
$361$	5.80204	+	10.0494i	0.305371	+	0.528917i
$362$	−4.90676			−0.257894
$363$		0			0
$364$		0			0
$365$	−6.19166	−	3.57476i	−0.324086	−	0.187111i
$366$		0			0
$367$	−2.86810	−	1.65590i	−0.149714	−	0.0864372i	0.423272	−	0.906003i	$-0.360882\pi$
$367$	−2.86810	−	1.65590i	−0.149714	−	0.0864372i	−0.572985	+	0.819566i	$0.694215\pi$
$368$	−3.08114	+	1.77890i	−0.160616	+	0.0927315i
$369$		0			0
$370$		−	24.7562i		−	1.28701i
$371$		0			0
$372$		0			0
$373$	3.32271	+	5.75510i	0.172043	+	0.297988i	0.939134	−	0.343551i	$-0.111630\pi$
$373$	3.32271	+	5.75510i	0.172043	+	0.297988i	−0.767091	+	0.641539i	$0.778296\pi$
$374$	11.0460			0.571173
$375$		0			0
$376$		−	6.66613i		−	0.343780i
$377$	25.2884			1.30242
$378$		0			0
$379$	−3.84940			−0.197730			−0.0988652	−	0.995101i	$-0.531521\pi$
$379$	−3.84940			−0.197730			−0.0988652	+	0.995101i	$0.531521\pi$
$380$		−	27.6432i		−	1.41807i
$381$		0			0
$382$	−18.9358			−0.968842
$383$	−17.1112	−	29.6374i	−0.874339	−	1.51440i	−0.857465	−	0.514542i	$-0.827962\pi$
$383$	−17.1112	−	29.6374i	−0.874339	−	1.51440i	−0.0168739	−	0.999858i	$-0.505371\pi$
$384$		0			0
$385$		0			0
$386$		−	11.4889i		−	0.584768i
$387$		0			0
$388$	−4.97191	+	2.87054i	−0.252411	+	0.145729i
$389$	−11.6737	−	6.73982i	−0.591881	−	0.341723i	0.173960	−	0.984753i	$-0.444344\pi$
$389$	−11.6737	−	6.73982i	−0.591881	−	0.341723i	−0.765841	+	0.643030i	$0.777677\pi$
$390$		0			0
$391$	1.64121	+	0.947550i	0.0829993	+	0.0479197i
$392$		0			0
$393$		0			0
$394$	−6.05480			−0.305036
$395$	14.7954	+	25.6265i	0.744440	+	1.28941i
$396$		0			0
$397$	25.5501	+	14.7513i	1.28232	+	0.740349i	0.977272	−	0.211988i	$-0.0679938\pi$
$397$	25.5501	+	14.7513i	1.28232	+	0.740349i	0.305049	+	0.952337i	$0.401327\pi$
$398$	−5.38880	−	9.33367i	−0.270116	−	0.467855i
$399$		0			0
$400$	−0.969472	+	1.67918i	−0.0484736	+	0.0839588i
$401$	25.1534	−	14.5223i	1.25610	−	0.725209i	0.283786	−	0.958888i	$-0.408410\pi$
$401$	25.1534	−	14.5223i	1.25610	−	0.725209i	0.972314	+	0.233678i	$0.0750763\pi$
$402$		0			0
$403$	9.26052	−	16.0397i	0.461300	−	0.798994i
$404$	4.20884	−	7.28993i	0.209398	−	0.362687i
$405$		0			0
$406$		0			0
$407$	−15.8073	+	9.12634i	−0.783538	+	0.452376i
$408$		0			0
$409$		−	30.2755i		−	1.49703i	−0.663121	−	0.748513i	$-0.730768\pi$
$409$		−	30.2755i		−	1.49703i	0.663121	−	0.748513i	$-0.269232\pi$
$410$		−	11.8561i		−	0.585532i
$411$		0			0
$412$	−32.4781	+	18.7512i	−1.60008	+	0.923806i
$413$		0			0
$414$		0			0
$415$	−3.22952	+	5.59369i	−0.158531	+	0.274583i
$416$	12.5080	−	21.6645i	0.613254	−	1.06219i
$417$		0			0
$418$	−32.4147	+	18.7146i	−1.58545	+	0.915363i
$419$	−18.2902	+	31.6795i	−0.893534	+	1.54765i	−0.0579246	+	0.998321i	$0.518448\pi$
$419$	−18.2902	+	31.6795i	−0.893534	+	1.54765i	−0.835609	+	0.549325i	$0.814885\pi$
$420$		0			0
$421$	3.85999	+	6.68570i	0.188124	+	0.325841i	0.944625	−	0.328152i	$-0.106426\pi$
$421$	3.85999	+	6.68570i	0.188124	+	0.325841i	−0.756501	+	0.653993i	$0.773093\pi$
$422$	28.7899	+	16.6219i	1.40147	+	0.809140i
$423$		0			0
$424$	−2.49682	−	4.32463i	−0.121256	−	0.210022i
$425$	1.03280			0.0500982
$426$		0			0
$427$		0			0
$428$	3.39490	+	1.96005i	0.164099	+	0.0947424i
$429$		0			0
$430$	−7.39464	−	4.26930i	−0.356601	−	0.205884i
$431$	−20.0311	+	11.5650i	−0.964865	+	0.557065i	−0.897667	−	0.440674i	$-0.854739\pi$
$431$	−20.0311	+	11.5650i	−0.964865	+	0.557065i	−0.0671983	+	0.997740i	$0.521406\pi$
$432$		0			0
$433$			34.9265i			1.67846i	0.543776	+	0.839230i	$0.316994\pi$
$433$			34.9265i			1.67846i	−0.543776	+	0.839230i	$0.683006\pi$
$434$		0			0
$435$		0			0
$436$	−6.95010	−	12.0379i	−0.332849	−	0.576512i
$437$	−6.42155			−0.307185
$438$		0			0
$439$		−	38.8952i		−	1.85637i	−0.372122	−	0.928184i	$-0.621370\pi$
$439$		−	38.8952i		−	1.85637i	0.372122	−	0.928184i	$-0.378630\pi$
$440$	5.52912			0.263590
$441$		0			0
$442$	−10.6161			−0.504959
$443$			37.3289i			1.77355i	0.462204	+	0.886774i	$0.347059\pi$
$443$			37.3289i			1.77355i	−0.462204	+	0.886774i	$0.652941\pi$
$444$		0			0
$445$	−10.2722			−0.486948
$446$	16.3675	+	28.3493i	0.775023	+	1.34238i
$447$		0			0
$448$		0			0
$449$			23.9224i			1.12897i	0.825445	+	0.564483i	$0.190924\pi$
$449$			23.9224i			1.12897i	−0.825445	+	0.564483i	$0.809076\pi$
$450$		0			0
$451$	−7.57036	+	4.37075i	−0.356474	+	0.205810i
$452$	33.4582	+	19.3171i	1.57374	+	0.908600i
$453$		0			0
$454$	3.77628	+	2.18024i	0.177230	+	0.102324i
$455$		0			0
$456$		0			0
$457$	9.98063			0.466874			0.233437	−	0.972372i	$-0.425003\pi$
$457$	9.98063			0.466874			0.233437	+	0.972372i	$0.425003\pi$
$458$	−6.74155	−	11.6767i	−0.315012	−	0.545617i
$459$		0			0
$460$	5.02319	+	2.90014i	0.234207	+	0.135220i
$461$	−16.7279	−	28.9735i	−0.779094	−	1.34943i	−0.932465	−	0.361261i	$-0.882346\pi$
$461$	−16.7279	−	28.9735i	−0.779094	−	1.34943i	0.153371	−	0.988169i	$-0.450987\pi$
$462$		0			0
$463$	11.5353	−	19.9798i	0.536092	−	0.928538i	−0.463018	−	0.886349i	$-0.653233\pi$
$463$	11.5353	−	19.9798i	0.536092	−	0.928538i	0.999110	−	0.0421893i	$-0.0134333\pi$
$464$	−21.6312	+	12.4888i	−1.00420	+	0.579778i
$465$		0			0
$466$	16.3595	−	28.3355i	0.757839	−	1.31262i
$467$	−20.1395	+	34.8827i	−0.931946	+	1.61418i	−0.151955	+	0.988387i	$0.548557\pi$
$467$	−20.1395	+	34.8827i	−0.931946	+	1.61418i	−0.779991	+	0.625791i	$0.784776\pi$
$468$		0			0
$469$		0			0
$470$	30.8527	−	17.8128i	1.42313	−	0.821643i
$471$		0			0
$472$			3.24659i			0.149436i
$473$			6.29549i			0.289467i
$474$		0			0
$475$	−3.03078	+	1.74982i	−0.139062	+	0.0802874i
$476$		0			0
$477$		0			0
$478$	−17.9994	+	31.1759i	−0.823275	+	1.42595i
$479$	−0.0777513	+	0.134669i	−0.00355255	+	0.00615319i	−0.867796	−	0.496920i	$-0.834464\pi$
$479$	−0.0777513	+	0.134669i	−0.00355255	+	0.00615319i	0.864244	+	0.503073i	$0.167797\pi$
$480$		0			0
$481$	15.1922	−	8.77123i	0.692705	−	0.399934i
$482$	11.7540	−	20.3585i	0.535380	−	0.927305i
$483$		0			0
$484$	0.687435	+	1.19067i	0.0312471	+	0.0541215i
$485$	−4.34558	−	2.50892i	−0.197323	−	0.113924i
$486$		0			0
$487$	8.25111	+	14.2913i	0.373893	+	0.647602i	0.990161	−	0.139935i	$-0.0446892\pi$
$487$	8.25111	+	14.2913i	0.373893	+	0.647602i	−0.616267	+	0.787537i	$0.711356\pi$
$488$	3.92682			0.177759
$489$		0			0
$490$		0			0
$491$	−8.10003	−	4.67655i	−0.365549	−	0.211050i	0.305963	−	0.952043i	$-0.401022\pi$
$491$	−8.10003	−	4.67655i	−0.365549	−	0.211050i	−0.671512	+	0.740993i	$0.734355\pi$
$492$		0			0
$493$	11.5221	+	6.65230i	0.518930	+	0.299604i
$494$	31.1534	−	17.9864i	1.40166	−	0.809248i
$495$		0			0
$496$			18.2934i			0.821399i
$497$		0			0
$498$		0			0
$499$	−0.998116	−	1.72879i	−0.0446818	−	0.0773912i	0.842820	−	0.538196i	$-0.180894\pi$
$499$	−0.998116	−	1.72879i	−0.0446818	−	0.0773912i	−0.887501	+	0.460805i	$0.847561\pi$
$500$	28.1454			1.25870
$501$		0			0
$502$		−	23.8544i		−	1.06467i
$503$	15.7008			0.700063			0.350032	−	0.936738i	$-0.386171\pi$
$503$	15.7008			0.700063			0.350032	+	0.936738i	$0.386171\pi$
$504$		0			0
$505$	7.35727			0.327394
$506$		−	7.85366i		−	0.349138i
$507$		0			0
$508$	22.9358			1.01761
$509$	−7.59893	−	13.1617i	−0.336817	−	0.583383i	0.647016	−	0.762477i	$-0.276017\pi$
$509$	−7.59893	−	13.1617i	−0.336817	−	0.583383i	−0.983832	+	0.179093i	$0.942684\pi$
$510$		0			0
$511$		0			0
$512$			29.7316i			1.31396i
$513$		0			0
$514$	−17.0231	+	9.82831i	−0.750858	+	0.433508i
$515$	−28.3867	−	16.3890i	−1.25087	−	0.722187i
$516$		0			0
$517$	−22.7476	−	13.1333i	−1.00044	−	0.577603i
$518$		0			0
$519$		0			0
$520$	−5.31397			−0.233033
$521$	−20.6160	−	35.7080i	−0.903204	−	1.56440i	−0.823310	−	0.567592i	$-0.807875\pi$
$521$	−20.6160	−	35.7080i	−0.903204	−	1.56440i	−0.0798940	−	0.996803i	$-0.525458\pi$
$522$		0			0
$523$	−37.0311	−	21.3799i	−1.61926	−	0.934878i	−0.987113	−	0.160026i	$-0.948842\pi$
$523$	−37.0311	−	21.3799i	−1.61926	−	0.934878i	−0.632143	−	0.774852i	$-0.717824\pi$
$524$	−2.94244	−	5.09645i	−0.128541	−	0.222640i
$525$		0			0
$526$	−9.22332	+	15.9753i	−0.402156	+	0.696554i
$527$	8.43872	−	4.87210i	0.367596	−	0.212232i
$528$		0			0
$529$	−10.8263	+	18.7517i	−0.470708	+	0.815291i
$530$	13.3437	−	23.1119i	0.579613	−	1.00392i
$531$		0			0
$532$		0			0
$533$	7.27579	−	4.20068i	0.315149	−	0.181952i
$534$		0			0
$535$			3.42626i			0.148130i
$536$			0.552258i			0.0238539i
$537$		0			0
$538$	29.6337	−	17.1090i	1.27760	−	0.737623i
$539$		0			0
$540$		0			0
$541$	8.04309	−	13.9310i	0.345800	−	0.598942i	−0.639699	−	0.768625i	$-0.720941\pi$
$541$	8.04309	−	13.9310i	0.345800	−	0.598942i	0.985499	+	0.169683i	$0.0542744\pi$
$542$	−15.2664	+	26.4421i	−0.655747	+	1.13579i
$543$		0			0
$544$	11.3980	−	6.58063i	0.488685	−	0.282142i
$545$	6.07456	−	10.5214i	0.260206	−	0.450689i
$546$		0			0
$547$	−5.94015	−	10.2886i	−0.253982	−	0.439910i	0.710636	−	0.703560i	$-0.248407\pi$
$547$	−5.94015	−	10.2886i	−0.253982	−	0.439910i	−0.964619	+	0.263649i	$0.915074\pi$
$548$	−36.0021	−	20.7858i	−1.53794	−	0.887927i
$549$		0			0
$550$	−2.14006	−	3.70669i	−0.0912525	−	0.158054i
$551$	−45.0827			−1.92059
$552$		0			0
$553$		0			0
$554$	−52.1078	−	30.0845i	−2.21385	−	1.27817i
$555$		0			0
$556$	20.5910	+	11.8882i	0.873254	+	0.504173i
$557$	−26.4006	+	15.2424i	−1.11863	+	0.645841i	−0.941051	−	0.338265i	$-0.890160\pi$
$557$	−26.4006	+	15.2424i	−1.11863	+	0.645841i	−0.177579	+	0.984107i	$0.556827\pi$
$558$		0			0
$559$		−	6.05052i		−	0.255910i
$560$		0			0
$561$		0			0
$562$	5.76958	+	9.99320i	0.243375	+	0.421538i
$563$	−22.5371			−0.949828			−0.474914	−	0.880032i	$-0.657521\pi$
$563$	−22.5371			−0.949828			−0.474914	+	0.880032i	$0.657521\pi$
$564$		0			0
$565$			33.7673i			1.42060i
$566$	63.4572			2.66730
$567$		0			0
$568$	−5.74852			−0.241202
$569$			44.5639i			1.86822i	0.356992	+	0.934108i	$0.383802\pi$
$569$			44.5639i			1.86822i	−0.356992	+	0.934108i	$0.616198\pi$
$570$		0			0
$571$	35.2830			1.47655			0.738274	−	0.674501i	$-0.235641\pi$
$571$	35.2830			1.47655			0.738274	+	0.674501i	$0.235641\pi$
$572$	11.9783	+	20.7471i	0.500839	+	0.867479i
$573$		0			0
$574$		0			0
$575$		−	0.734319i		−	0.0306232i
$576$		0			0
$577$	−3.25158	+	1.87730i	−0.135365	+	0.0781531i	−0.566153	−	0.824300i	$-0.691569\pi$
$577$	−3.25158	+	1.87730i	−0.135365	+	0.0781531i	0.430788	+	0.902453i	$0.358236\pi$
$578$	26.0136	+	15.0189i	1.08202	+	0.624705i
$579$		0			0
$580$	35.2654	+	20.3605i	1.46432	+	0.845423i
$581$		0			0
$582$		0			0
$583$	−19.6765			−0.814919
$584$	−1.40166	−	2.42775i	−0.0580011	−	0.100461i
$585$		0			0
$586$	12.8615	+	7.42559i	0.531304	+	0.306748i
$587$	15.8021	+	27.3700i	0.652222	+	1.12968i	0.982583	+	0.185826i	$0.0594961\pi$
$587$	15.8021	+	27.3700i	0.652222	+	1.12968i	−0.330361	+	0.943855i	$0.607171\pi$
$588$		0			0
$589$	−16.5091	+	28.5946i	−0.680246	+	1.17822i
$590$	−15.0261	+	8.67532i	−0.618614	+	0.357157i
$591$		0			0
$592$	−8.66343	+	15.0055i	−0.356065	+	0.616722i
$593$	18.5588	−	32.1448i	0.762120	−	1.32003i	−0.179636	−	0.983733i	$-0.557492\pi$
$593$	18.5588	−	32.1448i	0.762120	−	1.32003i	0.941756	−	0.336297i	$-0.109175\pi$
$594$		0			0
$595$		0			0
$596$	19.1689	−	11.0671i	0.785187	−	0.453328i
$597$		0			0
$598$			7.54806i			0.308663i
$599$			28.3119i			1.15679i	0.815756	+	0.578396i	$0.196321\pi$
$599$			28.3119i			1.15679i	−0.815756	+	0.578396i	$0.803679\pi$
$600$		0			0
$601$	20.8341	−	12.0286i	0.849840	−	0.490655i	−0.0107568	−	0.999942i	$-0.503424\pi$
$601$	20.8341	−	12.0286i	0.849840	−	0.490655i	0.860597	+	0.509287i	$0.170091\pi$
$602$		0			0
$603$		0			0
$604$	−14.3101	+	24.7859i	−0.582271	+	1.00852i
$605$	−0.600836	+	1.04068i	−0.0244274	+	0.0423096i
$606$		0			0
$607$	−8.24496	+	4.76023i	−0.334653	+	0.193212i	−0.657905	−	0.753101i	$-0.728557\pi$
$607$	−8.24496	+	4.76023i	−0.334653	+	0.193212i	0.323252	+	0.946313i	$0.395224\pi$
$608$	−22.2985	+	38.6221i	−0.904323	+	1.56633i
$609$		0			0
$610$	10.4930	+	18.1744i	0.424848	+	0.735859i
$611$	21.8625	+	12.6223i	0.884461	+	0.510644i
$612$		0			0
$613$	1.23108	+	2.13230i	0.0497230	+	0.0861227i	0.889816	−	0.456320i	$-0.150833\pi$
$613$	1.23108	+	2.13230i	0.0497230	+	0.0861227i	−0.840093	+	0.542443i	$0.817499\pi$
$614$	6.52420			0.263295
$615$		0			0
$616$		0			0
$617$	−18.7738	−	10.8390i	−0.755804	−	0.436364i	0.0719831	−	0.997406i	$-0.477067\pi$
$617$	−18.7738	−	10.8390i	−0.755804	−	0.436364i	−0.827787	+	0.561042i	$0.810401\pi$
$618$		0			0
$619$	20.8767	+	12.0532i	0.839105	+	0.484457i	0.856960	−	0.515383i	$-0.172350\pi$
$619$	20.8767	+	12.0532i	0.839105	+	0.484457i	−0.0178550	+	0.999841i	$0.505684\pi$
$620$	25.8281	−	14.9119i	1.03728	−	0.598875i
$621$		0			0
$622$			40.7615i			1.63439i
$623$		0			0
$624$		0			0
$625$	10.7184	+	18.5648i	0.428735	+	0.742591i
$626$	−53.5285			−2.13943
$627$		0			0
$628$		−	42.6834i		−	1.70325i
$629$	9.22934			0.367998
$630$		0			0
$631$	3.37520			0.134365			0.0671824	−	0.997741i	$-0.478599\pi$
$631$	3.37520			0.134365			0.0671824	+	0.997741i	$0.478599\pi$
$632$			11.6026i			0.461525i
$633$		0			0
$634$	34.0043			1.35048
$635$	10.0232	+	17.3608i	0.397761	+	0.688941i
$636$		0			0
$637$		0			0
$638$		−	55.1368i		−	2.18289i
$639$		0			0
$640$	11.6374	−	6.71887i	0.460010	−	0.265587i
$641$	30.9152	+	17.8489i	1.22108	+	0.704989i	0.965148	−	0.261706i	$-0.0842850\pi$
$641$	30.9152	+	17.8489i	1.22108	+	0.704989i	0.255930	+	0.966695i	$0.417618\pi$
$642$		0			0
$643$	3.03956	+	1.75489i	0.119868	+	0.0692060i	0.558735	−	0.829346i	$-0.311287\pi$
$643$	3.03956	+	1.75489i	0.119868	+	0.0692060i	−0.438867	+	0.898552i	$0.644620\pi$
$644$		0			0
$645$		0			0
$646$	18.9258			0.744627
$647$	7.02996	+	12.1762i	0.276376	+	0.478698i	0.970481	−	0.241176i	$-0.0775331\pi$
$647$	7.02996	+	12.1762i	0.276376	+	0.478698i	−0.694105	+	0.719874i	$0.744200\pi$
$648$		0			0
$649$	11.0787	+	6.39629i	0.434877	+	0.251076i
$650$	2.05679	+	3.56246i	0.0806739	+	0.139731i
$651$		0			0
$652$	21.3225	−	36.9317i	0.835055	−	1.44636i
$653$	10.2675	−	5.92792i	0.401797	−	0.231978i	−0.285462	−	0.958390i	$-0.592147\pi$
$653$	10.2675	−	5.92792i	0.401797	−	0.231978i	0.687259	+	0.726412i	$0.258814\pi$
$654$		0			0
$655$	2.57177	−	4.45443i	0.100487	−	0.174049i
$656$	−4.14905	+	7.18637i	−0.161993	+	0.280581i
$657$		0			0
$658$		0			0
$659$	−5.03144	+	2.90491i	−0.195997	+	0.113159i	−0.594787	−	0.803883i	$-0.702764\pi$
$659$	−5.03144	+	2.90491i	−0.195997	+	0.113159i	0.398790	+	0.917042i	$0.369430\pi$
$660$		0			0
$661$			9.71786i			0.377981i	0.981979	+	0.188991i	$0.0605215\pi$
$661$			9.71786i			0.377981i	−0.981979	+	0.188991i	$0.939478\pi$
$662$			48.8491i			1.89858i
$663$		0			0
$664$	−2.19328	+	1.26629i	−0.0851158	+	0.0491416i
$665$		0			0
$666$		0			0
$667$	4.72977	−	8.19220i	0.183137	−	0.317203i
$668$	−14.7503	+	25.5483i	−0.570707	+	0.988493i
$669$		0			0
$670$	−2.55600	+	1.47571i	−0.0987468	+	0.0570115i
$671$	7.73645	−	13.3999i	0.298662	−	0.517298i
$672$		0			0
$673$	13.4646	+	23.3214i	0.519023	+	0.898975i	0.999756	+	0.0221072i	$0.00703750\pi$
$673$	13.4646	+	23.3214i	0.519023	+	0.898975i	−0.480732	+	0.876867i	$0.659629\pi$
$674$	21.5415	+	12.4370i	0.829747	+	0.479055i
$675$		0			0
$676$	4.02953	+	6.97935i	0.154982	+	0.268436i
$677$	45.4112			1.74530			0.872648	−	0.488350i	$-0.162401\pi$
$677$	45.4112			1.74530			0.872648	+	0.488350i	$0.162401\pi$
$678$		0			0
$679$		0			0
$680$	−2.42120	−	1.39788i	−0.0928487	−	0.0536062i
$681$		0			0
$682$	−34.9717	−	20.1909i	−1.33913	−	0.773150i
$683$	37.6543	−	21.7397i	1.44080	−	0.831848i	0.442900	−	0.896571i	$-0.353950\pi$
$683$	37.6543	−	21.7397i	1.44080	−	0.831848i	0.997903	+	0.0647226i	$0.0206162\pi$
$684$		0			0
$685$		−	36.3347i		−	1.38828i
$686$		0			0
$687$		0			0
$688$	2.98808	+	5.17551i	0.113919	+	0.197314i
$689$	18.9109			0.720448
$690$		0			0
$691$			27.3654i			1.04103i	0.853853	+	0.520514i	$0.174260\pi$
$691$			27.3654i			1.04103i	−0.853853	+	0.520514i	$0.825740\pi$
$692$	−21.6804			−0.824166
$693$		0			0
$694$	45.4845			1.72657
$695$			20.7812i			0.788277i
$696$		0			0
$697$	4.42008			0.167422
$698$	2.67212	+	4.62824i	0.101141	+	0.175182i
$699$		0			0
$700$		0			0
$701$			8.26437i			0.312141i	0.987746	+	0.156070i	$0.0498827\pi$
$701$			8.26437i			0.312141i	−0.987746	+	0.156070i	$0.950117\pi$
$702$		0			0
$703$	−27.0838	+	15.6368i	−1.02148	+	0.589754i
$704$	−30.0947	−	17.3752i	−1.13424	−	0.654852i
$705$		0			0
$706$	−46.0484	−	26.5861i	−1.73306	−	1.00058i
$707$		0			0
$708$		0			0
$709$	42.8171			1.60803			0.804015	−	0.594608i	$-0.202693\pi$
$709$	42.8171			1.60803			0.804015	+	0.594608i	$0.202693\pi$
$710$	−15.3608	−	26.6057i	−0.576481	−	0.998494i
$711$		0			0
$712$	−3.48810	−	2.01385i	−0.130722	−	0.0754724i
$713$	−3.46405	−	5.99992i	−0.129730	−	0.224699i
$714$		0			0
$715$	−10.4694	+	18.1335i	−0.391532	+	0.678153i
$716$	31.1041	−	17.9579i	1.16241	−	0.671120i
$717$		0			0
$718$	11.7805	−	20.4044i	0.439645	−	0.761487i
$719$	−11.5725	+	20.0442i	−0.431583	+	0.747523i	−0.997010	−	0.0772751i	$-0.975378\pi$
$719$	−11.5725	+	20.0442i	−0.431583	+	0.747523i	0.565427	+	0.824798i	$0.308711\pi$
$720$		0			0
$721$		0			0
$722$	−21.0584	+	12.1581i	−0.783712	+	0.452477i
$723$		0			0
$724$		−	5.59884i		−	0.208079i
$725$		−	5.15530i		−	0.191463i
$726$		0			0
$727$	4.76878	−	2.75326i	0.176864	−	0.102113i	−0.408954	−	0.912555i	$-0.634106\pi$
$727$	4.76878	−	2.75326i	0.176864	−	0.102113i	0.585819	+	0.810442i	$0.300773\pi$
$728$		0			0
$729$		0			0
$730$	7.49084	−	12.9745i	0.277248	−	0.480208i
$731$	1.59163	−	2.75679i	0.0588687	−	0.101964i
$732$		0			0
$733$	3.45543	−	1.99499i	0.127629	−	0.0736867i	−0.434826	−	0.900514i	$-0.643190\pi$
$733$	3.45543	−	1.99499i	0.127629	−	0.0736867i	0.562455	+	0.826828i	$0.309857\pi$
$734$	3.46991	−	6.01005i	0.128077	−	0.221835i
$735$		0			0
$736$	−4.67882	−	8.10395i	−0.172463	−	0.298716i
$737$	1.88453	+	1.08803i	0.0694176	+	0.0400783i
$738$		0			0
$739$	0.871657	+	1.50976i	0.0320644	+	0.0555372i	0.881612	−	0.471974i	$-0.156458\pi$
$739$	0.871657	+	1.50976i	0.0320644	+	0.0555372i	−0.849548	+	0.527512i	$0.823125\pi$
$740$	28.2480			1.03842
$741$		0			0
$742$		0			0
$743$	−8.70204	−	5.02413i	−0.319247	−	0.184317i	0.331810	−	0.943346i	$-0.392341\pi$
$743$	−8.70204	−	5.02413i	−0.319247	−	0.184317i	−0.651057	+	0.759029i	$0.725674\pi$
$744$		0			0
$745$	16.7541	+	9.67296i	0.613821	+	0.354390i
$746$	−12.0597	+	6.96267i	−0.441537	+	0.254921i
$747$		0			0
$748$			12.6040i			0.460846i
$749$		0			0
$750$		0			0
$751$	11.6725	+	20.2174i	0.425936	+	0.737743i	0.996507	−	0.0835052i	$-0.0266115\pi$
$751$	11.6725	+	20.2174i	0.425936	+	0.737743i	−0.570571	+	0.821248i	$0.693278\pi$
$752$	−24.9344			−0.909262
$753$		0			0
$754$			52.9913i			1.92983i
$755$	−25.0148			−0.910383
$756$		0			0
$757$	−14.3334			−0.520957			−0.260479	−	0.965480i	$-0.583880\pi$
$757$	−14.3334			−0.520957			−0.260479	+	0.965480i	$0.583880\pi$
$758$		−	8.06634i		−	0.292983i
$759$		0			0
$760$	9.47344			0.343638
$761$	11.3178	+	19.6029i	0.410268	+	0.710606i	0.994919	−	0.100680i	$-0.0321017\pi$
$761$	11.3178	+	19.6029i	0.410268	+	0.710606i	−0.584650	+	0.811285i	$0.698768\pi$
$762$		0			0
$763$		0			0
$764$		−	21.6067i		−	0.781702i
$765$		0			0
$766$	62.1046	−	35.8561i	2.24393	−	1.29553i
$767$	−10.6476	−	6.14741i	−0.384463	−	0.221970i
$768$		0			0
$769$	42.6873	+	24.6455i	1.53934	+	0.888741i	0.998877	+	0.0473762i	$0.0150860\pi$
$769$	42.6873	+	24.6455i	1.53934	+	0.888741i	0.540468	+	0.841365i	$0.318247\pi$
$770$		0			0
$771$		0			0
$772$	13.1093			0.471815
$773$	11.0083	+	19.0670i	0.395943	+	0.685793i	0.993221	−	0.116241i	$-0.0370845\pi$
$773$	11.0083	+	19.0670i	0.395943	+	0.685793i	−0.597278	+	0.802034i	$0.703751\pi$
$774$		0			0
$775$	−3.26986	−	1.88785i	−0.117457	−	0.0678137i
$776$	−0.983745	−	1.70390i	−0.0353144	−	0.0611663i
$777$		0			0
$778$	14.1232	−	24.4621i	0.506340	−	0.877007i
$779$	−12.9708	+	7.48872i	−0.464729	+	0.268311i
$780$		0			0
$781$	−11.3255	+	19.6163i	−0.405258	+	0.701927i
$782$	−1.98557	+	3.43911i	−0.0710040	+	0.122982i
$783$		0			0
$784$		0			0
$785$	32.3083	−	18.6532i	1.15313	−	0.665761i
$786$		0			0
$787$			10.8554i			0.386954i	0.981105	+	0.193477i	$0.0619765\pi$
$787$			10.8554i			0.386954i	−0.981105	+	0.193477i	$0.938024\pi$
$788$		−	6.90881i		−	0.246116i
$789$		0			0
$790$	−53.6998	+	31.0036i	−1.91055	+	1.10306i
$791$		0			0
$792$		0			0
$793$	−7.43542	+	12.8785i	−0.264039	+	0.457330i
$794$	−30.9112	+	53.5397i	−1.09700	+	1.90005i
$795$		0			0
$796$	10.6502	−	6.14887i	0.377485	−	0.217941i
$797$	−1.98299	+	3.43465i	−0.0702412	+	0.121661i	−0.899007	−	0.437934i	$-0.855710\pi$
$797$	−1.98299	+	3.43465i	−0.0702412	+	0.121661i	0.828766	+	0.559596i	$0.189044\pi$
$798$		0			0
$799$	6.64078	+	11.5022i	0.234934	+	0.406917i
$800$	−4.41653	−	2.54988i	−0.156148	−	0.0901520i
$801$		0			0
$802$	30.4312	+	52.7084i	1.07456	+	1.86120i
$803$	−11.0460			−0.389803
$804$		0			0
$805$		0			0
$806$	33.6109	+	19.4053i	1.18389	+	0.683521i
$807$		0			0
$808$	2.49829	+	1.44239i	0.0878896	+	0.0507431i
$809$	36.0199	−	20.7961i	1.26639	−	0.731152i	0.292088	−	0.956391i	$-0.405650\pi$
$809$	36.0199	−	20.7961i	1.26639	−	0.731152i	0.974303	+	0.225240i	$0.0723166\pi$
$810$		0			0
$811$			13.3293i			0.468056i	0.972230	+	0.234028i	$0.0751907\pi$
$811$			13.3293i			0.468056i	−0.972230	+	0.234028i	$0.924809\pi$
$812$		0			0
$813$		0			0
$814$	−19.1241	−	33.1239i	−0.670299	−	1.16099i
$815$	37.2729			1.30561
$816$		0			0
$817$			10.7865i			0.377372i
$818$	63.4417			2.21819
$819$		0			0
$820$	13.5284			0.472432
$821$		−	38.6054i		−	1.34734i	−0.739034	−	0.673668i	$-0.764718\pi$
$821$		−	38.6054i		−	1.34734i	0.739034	−	0.673668i	$-0.235282\pi$
$822$		0			0
$823$	−10.6976			−0.372896			−0.186448	−	0.982465i	$-0.559698\pi$
$823$	−10.6976			−0.372896			−0.186448	+	0.982465i	$0.559698\pi$
$824$	−6.42613	−	11.1304i	−0.223865	−	0.387745i
$825$		0			0
$826$		0			0
$827$		−	11.7079i		−	0.407125i	−0.979062	−	0.203562i	$-0.934748\pi$
$827$		−	11.7079i		−	0.407125i	0.979062	−	0.203562i	$-0.0652520\pi$
$828$		0			0
$829$	15.0948	−	8.71498i	0.524263	−	0.302684i	−0.214414	−	0.976743i	$-0.568784\pi$
$829$	15.0948	−	8.71498i	0.524263	−	0.302684i	0.738677	+	0.674059i	$0.235451\pi$
$830$	−11.7215	−	6.76740i	−0.406858	−	0.234900i
$831$		0			0
$832$	28.9237	+	16.6991i	1.00275	+	0.578937i
$833$		0			0
$834$		0			0
$835$	−25.7843			−0.892302
$836$	−21.3543	−	36.9867i	−0.738553	−	1.27921i
$837$		0			0
$838$	−66.3838	−	38.3267i	−2.29319	−	1.32397i
$839$	−0.704502	−	1.22023i	−0.0243221	−	0.0421271i	0.853608	−	0.520916i	$-0.174409\pi$
$839$	−0.704502	−	1.22023i	−0.0243221	−	0.0421271i	−0.877930	+	0.478789i	$0.841076\pi$
$840$		0			0
$841$	18.7055	−	32.3988i	0.645016	−	1.11720i
$842$	−14.0097	+	8.08853i	−0.482808	+	0.278749i
$843$		0			0
$844$	−18.9663	+	32.8506i	−0.652848	+	1.13077i
$845$	−3.52191	+	6.10012i	−0.121157	+	0.209851i
$846$		0			0
$847$		0			0
$848$	−16.1761	+	9.33925i	−0.555488	+	0.320711i
$849$		0			0
$850$			2.16421i			0.0742319i
$851$		−	6.56205i		−	0.224944i
$852$		0			0
$853$	−28.0716	+	16.2071i	−0.961153	+	0.554922i	−0.896528	−	0.442987i	$-0.853919\pi$
$853$	−28.0716	+	16.2071i	−0.961153	+	0.554922i	−0.0646255	+	0.997910i	$0.520585\pi$
$854$		0			0
$855$		0			0
$856$	−0.671716	+	1.16345i	−0.0229588	+	0.0397658i
$857$	22.2270	−	38.4982i	0.759258	−	1.31507i	−0.183971	−	0.982932i	$-0.558895\pi$
$857$	22.2270	−	38.4982i	0.759258	−	1.31507i	0.943229	−	0.332142i	$-0.107771\pi$
$858$		0			0
$859$	−13.5528	+	7.82472i	−0.462416	+	0.266976i	−0.713060	−	0.701103i	$-0.752691\pi$
$859$	−13.5528	+	7.82472i	−0.462416	+	0.266976i	0.250644	+	0.968079i	$0.419358\pi$
$860$	4.87147	−	8.43763i	0.166116	−	0.287721i
$861$		0			0
$862$	−24.2342	−	41.9748i	−0.825420	−	1.42967i
$863$	−15.6911	−	9.05927i	−0.534132	−	0.308381i	0.208565	−	0.978008i	$-0.433121\pi$
$863$	−15.6911	−	9.05927i	−0.534132	−	0.308381i	−0.742697	+	0.669627i	$0.766454\pi$
$864$		0			0
$865$	−9.47462	−	16.4105i	−0.322147	−	0.557975i
$866$	−73.1878			−2.48702
$867$		0			0
$868$		0			0
$869$	39.5927	+	22.8589i	1.34309	+	0.775434i
$870$		0			0
$871$	−1.81120	−	1.04570i	−0.0613703	−	0.0354321i
$872$	4.12545	−	2.38183i	0.139705	−	0.0806589i
$873$		0			0
$874$		−	13.4562i		−	0.455164i
$875$		0			0
$876$		0			0
$877$	1.38926	+	2.40628i	0.0469121	+	0.0812542i	0.888528	−	0.458822i	$-0.151729\pi$
$877$	1.38926	+	2.40628i	0.0469121	+	0.0812542i	−0.841616	+	0.540077i	$0.818395\pi$
$878$	81.5042			2.75063
$879$		0			0
$880$		−	20.6814i		−	0.697170i
$881$	1.96106			0.0660696			0.0330348	−	0.999454i	$-0.489483\pi$
$881$	1.96106			0.0660696			0.0330348	+	0.999454i	$0.489483\pi$
$882$		0			0
$883$	−36.9657			−1.24400			−0.621998	−	0.783019i	$-0.713679\pi$
$883$	−36.9657			−1.24400			−0.621998	+	0.783019i	$0.713679\pi$
$884$		−	12.1135i		−	0.407422i
$885$		0			0
$886$	−78.2219			−2.62792
$887$	−11.2584	−	19.5001i	−0.378020	−	0.654750i	0.612754	−	0.790274i	$-0.290062\pi$
$887$	−11.2584	−	19.5001i	−0.378020	−	0.654750i	−0.990774	+	0.135524i	$0.956728\pi$
$888$		0			0
$889$		0			0
$890$		−	21.5251i		−	0.721525i
$891$		0			0
$892$	−32.3479	+	18.6761i	−1.08309	+	0.625321i
$893$	−38.9751	−	22.5023i	−1.30425	−	0.753011i
$894$		0			0
$895$	27.1857	+	15.6957i	0.908719	+	0.524649i
$896$		0			0
$897$		0			0
$898$	−50.1289			−1.67282
$899$	−24.3195	−	42.1225i	−0.811099	−	1.40487i
$900$		0			0
$901$	8.61635	+	4.97465i	0.287052	+	0.165730i
$902$	−9.15882	−	15.8635i	−0.304955	−	0.528198i
$903$		0			0
$904$	−6.62005	+	11.4663i	−0.220180	+	0.381362i
$905$	4.23792	−	2.44676i	0.140873	−	0.0813332i
$906$		0			0
$907$	9.55982	−	16.5581i	0.317428	−	0.549802i	−0.662522	−	0.749042i	$-0.730514\pi$
$907$	9.55982	−	16.5581i	0.317428	−	0.549802i	0.979951	+	0.199240i	$0.0638473\pi$
$908$	−2.48775	+	4.30891i	−0.0825589	+	0.142996i
$909$		0			0
$910$		0			0
$911$	−4.92610	+	2.84408i	−0.163209	+	0.0942287i	−0.579380	−	0.815058i	$-0.696705\pi$
$911$	−4.92610	+	2.84408i	−0.163209	+	0.0942287i	0.416171	+	0.909286i	$0.363372\pi$
$912$		0			0
$913$			9.97917i			0.330262i
$914$			20.9142i			0.691781i
$915$		0			0
$916$	13.3237	−	7.69242i	0.440226	−	0.254165i
$917$		0			0
$918$		0			0
$919$	−10.9255	+	18.9235i	−0.360399	+	0.624230i	−0.988027	−	0.154284i	$-0.950693\pi$
$919$	−10.9255	+	18.9235i	−0.360399	+	0.624230i	0.627627	+	0.778514i	$0.284026\pi$
$920$	−0.993890	+	1.72147i	−0.0327676	+	0.0567551i
$921$		0			0
$922$	60.7134	−	35.0529i	1.99949	−	1.15441i
$923$	10.8848	−	18.8530i	0.358278	−	0.620555i
$924$		0			0
$925$	−1.78811	−	3.09709i	−0.0587926	−	0.101832i
$926$	41.8672	+	24.1720i	1.37584	+	0.794343i
$927$		0			0
$928$	−32.8477	−	56.8940i	−1.07828	−	1.86764i
$929$	16.1761			0.530721			0.265361	−	0.964149i	$-0.414509\pi$
$929$	16.1761			0.530721			0.265361	+	0.964149i	$0.414509\pi$
$930$		0			0
$931$		0			0
$932$	32.3321	+	18.6669i	1.05907	+	0.611456i
$933$		0			0
$934$	−73.0960	−	42.2020i	−2.39177	−	1.38089i
$935$	−9.54029	+	5.50809i	−0.312001	+	0.180134i
$936$		0			0
$937$		−	14.0440i		−	0.458799i	−0.973332	−	0.229400i	$-0.926324\pi$
$937$		−	14.0440i		−	0.458799i	0.973332	−	0.229400i	$-0.0736762\pi$
$938$		0			0
$939$		0			0
$940$	20.3252	+	35.2043i	0.662936	+	1.14824i
$941$	43.1868			1.40785			0.703924	−	0.710275i	$-0.251429\pi$
$941$	43.1868			1.40785			0.703924	+	0.710275i	$0.251429\pi$
$942$		0			0
$943$		−	3.14267i		−	0.102339i
$944$	12.1437			0.395244
$945$		0			0
$946$	−13.1921			−0.428911
$947$			19.1952i			0.623759i	0.950122	+	0.311879i	$0.100959\pi$
$947$			19.1952i			0.623759i	−0.950122	+	0.311879i	$0.899041\pi$
$948$		0			0
$949$	10.6161			0.344615
$950$	−3.66672	−	6.35095i	−0.118964	−	0.206052i
$951$		0			0
$952$		0			0
$953$			5.62718i			0.182282i	0.995838	+	0.0911411i	$0.0290514\pi$
$953$			5.62718i			0.182282i	−0.995838	+	0.0911411i	$0.970949\pi$
$954$		0			0
$955$	16.3547	−	9.44239i	0.529225	−	0.305548i
$956$	−35.5732	−	20.5382i	−1.15052	−	0.664252i
$957$		0			0
$958$	−0.282197	−	0.162926i	−0.00911736	−	0.00526391i
$959$		0			0
$960$		0			0
$961$	−4.62282			−0.149123
$962$	18.3799	+	31.8350i	0.592593	+	1.02640i
$963$		0			0
$964$	23.2300	+	13.4119i	0.748189	+	0.431967i
$965$	5.72894	+	9.92282i	0.184421	+	0.319427i
$966$		0			0
$967$	−7.62091	+	13.1998i	−0.245072	+	0.424477i	−0.962152	−	0.272514i	$-0.912145\pi$
$967$	−7.62091	+	13.1998i	−0.245072	+	0.424477i	0.717080	+	0.696991i	$0.245478\pi$
$968$	−0.408049	+	0.235587i	−0.0131152	+	0.00757206i
$969$		0			0
$970$	5.25740	−	9.10608i	0.168805	−	0.292379i
$971$	20.4479	−	35.4168i	0.656205	−	1.13658i	−0.325386	−	0.945581i	$-0.605494\pi$
$971$	20.4479	−	35.4168i	0.656205	−	1.13658i	0.981590	−	0.190998i	$-0.0611725\pi$
$972$		0			0
$973$		0			0
$974$	−29.9472	+	17.2900i	−0.959571	+	0.554009i
$975$		0			0
$976$		−	14.6881i		−	0.470154i
$977$		−	10.3726i		−	0.331850i	−0.986138	−	0.165925i	$-0.946939\pi$
$977$		−	10.3726i		−	0.331850i	0.986138	−	0.165925i	$-0.0530609\pi$
$978$		0			0
$979$	−13.7442	+	7.93522i	−0.439267	+	0.253611i
$980$		0			0
$981$		0			0
$982$	9.79963	−	16.9735i	0.312719	−	0.541645i
$983$	1.05850	−	1.83338i	0.0337609	−	0.0584756i	−0.848651	−	0.528953i	$-0.822585\pi$
$983$	1.05850	−	1.83338i	0.0337609	−	0.0584756i	0.882412	+	0.470477i	$0.155918\pi$
$984$		0			0
$985$	5.22947	−	3.01924i	0.166625	−	0.0962009i
$986$	−13.9398	+	24.1444i	−0.443932	+	0.768914i
$987$		0			0
$988$	20.5234	+	35.5475i	0.652935	+	1.13092i
$989$	−1.96007	−	1.13165i	−0.0623267	−	0.0359843i
$990$		0			0
$991$	−17.0581	−	29.5456i	−0.541870	−	0.938546i	−0.998797	−	0.0490418i	$-0.984383\pi$
$991$	−17.0581	−	29.5456i	−0.541870	−	0.938546i	0.456927	−	0.889504i	$-0.348950\pi$
$992$	−48.1149			−1.52765
$993$		0			0
$994$		0			0
$995$	9.30850	+	5.37427i	0.295099	+	0.170376i
$996$		0			0
$997$	−39.6843	−	22.9118i	−1.25682	−	0.725623i	−0.284361	−	0.958717i	$-0.591782\pi$
$997$	−39.6843	−	22.9118i	−1.25682	−	0.725623i	−0.972454	+	0.233094i	$0.925115\pi$
$998$	3.62264	−	2.09153i	0.114673	−	0.0662064i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.i.b.1097.5		10
3.2	odd	2		441.2.i.b.68.1		10
7.2	even	3		1323.2.o.d.881.5		10
7.3	odd	6		1323.2.s.b.962.1		10
7.4	even	3		189.2.s.b.17.1		10
7.5	odd	6		1323.2.o.c.881.5		10
7.6	odd	2		189.2.i.b.152.5		10
9.2	odd	6		1323.2.s.b.656.1		10
9.7	even	3		441.2.s.b.362.5		10
21.2	odd	6		441.2.o.c.293.1		10
21.5	even	6		441.2.o.d.293.1		10
21.11	odd	6		63.2.s.b.59.5	yes	10
21.17	even	6		441.2.s.b.374.5		10
21.20	even	2		63.2.i.b.5.1	✓	10
28.11	odd	6		3024.2.df.b.17.5		10
28.27	even	2		3024.2.ca.b.2609.5		10
63.2	odd	6		1323.2.o.c.440.5		10
63.4	even	3		567.2.p.d.80.5		10
63.11	odd	6		189.2.i.b.143.1		10
63.13	odd	6		567.2.p.c.404.1		10
63.16	even	3		441.2.o.d.146.1		10
63.20	even	6		189.2.s.b.89.1		10
63.25	even	3		63.2.i.b.38.5	yes	10
63.32	odd	6		567.2.p.c.80.1		10
63.34	odd	6		63.2.s.b.47.5	yes	10
63.38	even	6	inner	1323.2.i.b.521.1		10
63.41	even	6		567.2.p.d.404.5		10
63.47	even	6		1323.2.o.d.440.5		10
63.52	odd	6		441.2.i.b.227.5		10
63.61	odd	6		441.2.o.c.146.1		10
84.11	even	6		1008.2.df.b.689.3		10
84.83	odd	2		1008.2.ca.b.257.5		10
252.11	even	6		3024.2.ca.b.2033.5		10
252.83	odd	6		3024.2.df.b.1601.5		10
252.151	odd	6		1008.2.ca.b.353.5		10
252.223	even	6		1008.2.df.b.929.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.1	✓	10	21.20	even	2
63.2.i.b.38.5	yes	10	63.25	even	3
63.2.s.b.47.5	yes	10	63.34	odd	6
63.2.s.b.59.5	yes	10	21.11	odd	6
189.2.i.b.143.1		10	63.11	odd	6
189.2.i.b.152.5		10	7.6	odd	2
189.2.s.b.17.1		10	7.4	even	3
189.2.s.b.89.1		10	63.20	even	6
441.2.i.b.68.1		10	3.2	odd	2
441.2.i.b.227.5		10	63.52	odd	6
441.2.o.c.146.1		10	63.61	odd	6
441.2.o.c.293.1		10	21.2	odd	6
441.2.o.d.146.1		10	63.16	even	3
441.2.o.d.293.1		10	21.5	even	6
441.2.s.b.362.5		10	9.7	even	3
441.2.s.b.374.5		10	21.17	even	6
567.2.p.c.80.1		10	63.32	odd	6
567.2.p.c.404.1		10	63.13	odd	6
567.2.p.d.80.5		10	63.4	even	3
567.2.p.d.404.5		10	63.41	even	6
1008.2.ca.b.257.5		10	84.83	odd	2
1008.2.ca.b.353.5		10	252.151	odd	6
1008.2.df.b.689.3		10	84.11	even	6
1008.2.df.b.929.3		10	252.223	even	6
1323.2.i.b.521.1		10	63.38	even	6	inner
1323.2.i.b.1097.5		10	1.1	even	1	trivial
1323.2.o.c.440.5		10	63.2	odd	6
1323.2.o.c.881.5		10	7.5	odd	6
1323.2.o.d.440.5		10	63.47	even	6
1323.2.o.d.881.5		10	7.2	even	3
1323.2.s.b.656.1		10	9.2	odd	6
1323.2.s.b.962.1		10	7.3	odd	6
3024.2.ca.b.2033.5		10	252.11	even	6
3024.2.ca.b.2609.5		10	28.27	even	2
3024.2.df.b.17.5		10	28.11	odd	6
3024.2.df.b.1601.5		10	252.83	odd	6

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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.09548i q^{2} -2.39104 q^{4} +(-1.04492 - 1.80985i) q^{5} -0.819421i q^{8} +(3.79250 - 2.18960i) q^{10} +(-2.79620 - 1.61439i) q^{11} +(2.68740 + 1.55157i) q^{13} -3.06500 q^{16} +(0.816304 + 1.41388i) q^{17} +(-4.79094 - 2.76605i) q^{19} +(2.49844 + 4.32742i) q^{20} +(3.38292 - 5.85939i) q^{22} +(1.00527 - 0.580391i) q^{23} +(0.316304 - 0.547854i) q^{25} +(-3.25129 + 5.63139i) q^{26} +(7.05749 - 4.07464i) q^{29} -5.96849i q^{31} -8.06150i q^{32} +(-2.96276 + 1.71055i) q^{34} +(2.82656 - 4.89575i) q^{37} +(5.79620 - 10.0393i) q^{38} +(-1.48303 + 0.856225i) q^{40} +(1.35369 - 2.34465i) q^{41} +(-0.974903 - 1.68858i) q^{43} +(6.68583 + 3.86007i) q^{44} +(1.21620 + 2.10652i) q^{46} +8.13518 q^{47} +(1.14802 + 0.662809i) q^{50} +(-6.42568 - 3.70987i) q^{52} +(5.27766 - 3.04706i) q^{53} +6.74759i q^{55} +(8.53834 + 14.7888i) q^{58} -3.96206 q^{59} +4.79219i q^{61} +12.5068 q^{62} +10.7627 q^{64} -6.48504i q^{65} -0.673961 q^{67} +(-1.95182 - 3.38065i) q^{68} -7.01535i q^{71} +(2.96276 - 1.71055i) q^{73} +(10.2590 + 5.92301i) q^{74} +(11.4553 + 6.61374i) q^{76} -14.1595 q^{79} +(3.20267 + 5.54718i) q^{80} +(4.91318 + 2.83662i) q^{82} +(-1.54535 - 2.67662i) q^{83} +(1.70594 - 2.95477i) q^{85} +(3.53839 - 2.04289i) q^{86} +(-1.32286 + 2.29127i) q^{88} +(2.45766 - 4.25679i) q^{89} +(-2.40363 + 1.38774i) q^{92} +17.0471i q^{94} +11.5611i q^{95} +(2.07939 - 1.20054i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 8 q^{4} + 15 q^{10} + 12 q^{11} + 6 q^{13} + 12 q^{16} + 12 q^{17} - 3 q^{19} + 3 q^{20} + 5 q^{22} + 15 q^{23} + 7 q^{25} - 3 q^{26} + 15 q^{29} + 3 q^{34} + 6 q^{37} + 18 q^{38} - 15 q^{40} + 9 q^{41}+ \cdots + 6 q^{97}+O(q^{100}) \) 10 * q - 8 * q^4 + 15 * q^10 + 12 * q^11 + 6 * q^13 + 12 * q^16 + 12 * q^17 - 3 * q^19 + 3 * q^20 + 5 * q^22 + 15 * q^23 + 7 * q^25 - 3 * q^26 + 15 * q^29 + 3 * q^34 + 6 * q^37 + 18 * q^38 - 15 * q^40 + 9 * q^41 + 3 * q^43 + 24 * q^44 - 13 * q^46 + 30 * q^47 - 3 * q^50 + 12 * q^52 - 9 * q^53 + 8 * q^58 - 36 * q^59 - 12 * q^62 + 6 * q^64 + 20 * q^67 - 27 * q^68 - 3 * q^73 + 30 * q^74 + 9 * q^76 - 40 * q^79 + 30 * q^80 - 9 * q^82 + 15 * q^83 + 18 * q^85 - 54 * q^86 - 8 * q^88 - 24 * q^89 - 39 * q^92 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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