LMFDB - Embedded newform 1360.2.bt.f.1041.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1360,2,Mod(81,1360)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1360, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1360.81"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1360 = 2^{4} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1360.bt (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,4] 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:	$10.8596546749$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 38 x^{18} + 597 x^{16} + 5004 x^{14} + 24072 x^{12} + 66452 x^{10} + 99328 x^{8} + 70784 x^{6} + \cdots + 16 $ x^20 + 38x^18 + 597x^16 + 5004x^14 + 24072x^12 + 66452x^10 + 99328x^8 + 70784x^6 + 19972x^4 + 1104*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 680)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1041.1
Root			$-2.91112i$ of defining polynomial
Character	$\chi$	$=$	1360.1041
Dual form			1360.2.bt.f.81.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.05847 + 2.05847i) q^{3} +(-0.707107 + 0.707107i) q^{5} +(-2.82095 - 2.82095i) q^{7} -5.47464i q^{9} +(-4.19898 - 4.19898i) q^{11} -2.09669 q^{13} -2.91112i q^{15} +(3.90859 + 1.31259i) q^{17} +2.76433i q^{19} +11.6137 q^{21} +(4.94663 + 4.94663i) q^{23} -1.00000i q^{25} +(5.09398 + 5.09398i) q^{27} +(-3.23769 + 3.23769i) q^{29} +(2.83189 - 2.83189i) q^{31} +17.2870 q^{33} +3.98942 q^{35} +(1.73551 - 1.73551i) q^{37} +(4.31599 - 4.31599i) q^{39} +(-6.82233 - 6.82233i) q^{41} +8.10856i q^{43} +(3.87115 + 3.87115i) q^{45} -2.89927 q^{47} +8.91549i q^{49} +(-10.7477 + 5.34380i) q^{51} +7.53227i q^{53} +5.93825 q^{55} +(-5.69030 - 5.69030i) q^{57} +5.43616i q^{59} +(-10.1370 - 10.1370i) q^{61} +(-15.4437 + 15.4437i) q^{63} +(1.48259 - 1.48259i) q^{65} +10.9061 q^{67} -20.3650 q^{69} +(2.59393 - 2.59393i) q^{71} +(0.889261 - 0.889261i) q^{73} +(2.05847 + 2.05847i) q^{75} +23.6902i q^{77} +(3.27892 + 3.27892i) q^{79} -4.54775 q^{81} -2.84677i q^{83} +(-3.69194 + 1.83565i) q^{85} -13.3294i q^{87} +13.9998 q^{89} +(5.91466 + 5.91466i) q^{91} +11.6588i q^{93} +(-1.95468 - 1.95468i) q^{95} +(1.92396 - 1.92396i) q^{97} +(-22.9879 + 22.9879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} - 4 q^{7} - 12 q^{11} + 4 q^{13} + 4 q^{17} + 16 q^{21} + 4 q^{23} + 16 q^{27} - 4 q^{29} + 4 q^{31} + 16 q^{33} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} - 4 q^{47} + 4 q^{51} + 8 q^{55}+ \cdots - 52 q^{99}+O(q^{100}) $ 20 * q + 4 * q^3 - 4 * q^7 - 12 * q^11 + 4 * q^13 + 4 * q^17 + 16 * q^21 + 4 * q^23 + 16 * q^27 - 4 * q^29 + 4 * q^31 + 16 * q^33 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 - 4 * q^47 + 4 * q^51 + 8 * q^55 - 24 * q^57 - 24 * q^61 - 60 * q^63 - 4 * q^65 + 56 * q^67 + 24 * q^69 + 40 * q^71 - 20 * q^73 - 4 * q^75 + 8 * q^79 + 4 * q^81 - 12 * q^85 + 28 * q^89 + 4 * q^95 + 24 * q^97 - 52 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1360\mathbb{Z}\right)^\times$.

$n$	$241$	$341$	$511$	$817$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.05847	+	2.05847i	−1.18846	+	1.18846i	−0.210968	+	0.977493i	$0.567662\pi$
$3$	−2.05847	+	2.05847i	−1.18846	+	1.18846i	−0.977493	+	0.210968i	$0.932338\pi$
$4$		0			0
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$		0			0
$7$	−2.82095	−	2.82095i	−1.06622	−	1.06622i	−0.997646	−	0.0685719i	$-0.978156\pi$
$7$	−2.82095	−	2.82095i	−1.06622	−	1.06622i	−0.0685719	−	0.997646i	$-0.521844\pi$
$8$		0			0
$9$		−	5.47464i		−	1.82488i
$10$		0			0
$11$	−4.19898	−	4.19898i	−1.26604	−	1.26604i	−0.948117	−	0.317922i	$-0.897015\pi$
$11$	−4.19898	−	4.19898i	−1.26604	−	1.26604i	−0.317922	−	0.948117i	$-0.602985\pi$
$12$		0			0
$13$	−2.09669			−0.581518			−0.290759	−	0.956796i	$-0.593908\pi$
$13$	−2.09669			−0.581518			−0.290759	+	0.956796i	$0.593908\pi$
$14$		0			0
$15$		−	2.91112i		−	0.751649i
$16$		0			0
$17$	3.90859	+	1.31259i	0.947973	+	0.318351i
$17$	3.90859	+	1.31259i	0.947973	+	0.318351i
$18$		0			0
$19$			2.76433i			0.634181i	0.948395	+	0.317090i	$0.102706\pi$
$19$			2.76433i			0.634181i	−0.948395	+	0.317090i	$0.897294\pi$
$20$		0			0
$21$	11.6137			2.53432
$22$		0			0
$23$	4.94663	+	4.94663i	1.03144	+	1.03144i	0.999489	+	0.0319542i	$0.0101731\pi$
$23$	4.94663	+	4.94663i	1.03144	+	1.03144i	0.0319542	+	0.999489i	$0.489827\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$		0			0
$27$	5.09398	+	5.09398i	0.980337	+	0.980337i
$28$		0			0
$29$	−3.23769	+	3.23769i	−0.601224	+	0.601224i	−0.940637	−	0.339413i	$-0.889772\pi$
$29$	−3.23769	+	3.23769i	−0.601224	+	0.601224i	0.339413	+	0.940637i	$0.389772\pi$
$30$		0			0
$31$	2.83189	−	2.83189i	0.508623	−	0.508623i	−0.405481	−	0.914104i	$-0.632896\pi$
$31$	2.83189	−	2.83189i	0.508623	−	0.508623i	0.914104	+	0.405481i	$0.132896\pi$
$32$		0			0
$33$	17.2870			3.00928
$34$		0			0
$35$	3.98942			0.674336
$36$		0			0
$37$	1.73551	−	1.73551i	0.285316	−	0.285316i	−0.549909	−	0.835225i	$-0.685337\pi$
$37$	1.73551	−	1.73551i	0.285316	−	0.285316i	0.835225	+	0.549909i	$0.185337\pi$
$38$		0			0
$39$	4.31599	−	4.31599i	0.691112	−	0.691112i
$40$		0			0
$41$	−6.82233	−	6.82233i	−1.06547	−	1.06547i	−0.997701	−	0.0677679i	$-0.978412\pi$
$41$	−6.82233	−	6.82233i	−1.06547	−	1.06547i	−0.0677679	−	0.997701i	$-0.521588\pi$
$42$		0			0
$43$			8.10856i			1.23654i	0.785964	+	0.618272i	$0.212167\pi$
$43$			8.10856i			1.23654i	−0.785964	+	0.618272i	$0.787833\pi$
$44$		0			0
$45$	3.87115	+	3.87115i	0.577078	+	0.577078i
$46$		0			0
$47$	−2.89927			−0.422902			−0.211451	−	0.977389i	$-0.567819\pi$
$47$	−2.89927			−0.422902			−0.211451	+	0.977389i	$0.567819\pi$
$48$		0			0
$49$			8.91549i			1.27364i
$50$		0			0
$51$	−10.7477	+	5.34380i	−1.50498	+	0.748281i
$52$		0			0
$53$			7.53227i			1.03464i	0.855793	+	0.517318i	$0.173070\pi$
$53$			7.53227i			1.03464i	−0.855793	+	0.517318i	$0.826930\pi$
$54$		0			0
$55$	5.93825			0.800713
$56$		0			0
$57$	−5.69030	−	5.69030i	−0.753699	−	0.753699i
$58$		0			0
$59$			5.43616i			0.707727i	0.935297	+	0.353864i	$0.115132\pi$
$59$			5.43616i			0.707727i	−0.935297	+	0.353864i	$0.884868\pi$
$60$		0			0
$61$	−10.1370	−	10.1370i	−1.29792	−	1.29792i	−0.929767	−	0.368149i	$-0.879992\pi$
$61$	−10.1370	−	10.1370i	−1.29792	−	1.29792i	−0.368149	−	0.929767i	$-0.620008\pi$
$62$		0			0
$63$	−15.4437	+	15.4437i	−1.94572	+	1.94572i
$64$		0			0
$65$	1.48259	−	1.48259i	0.183892	−	0.183892i
$66$		0			0
$67$	10.9061			1.33240			0.666198	−	0.745775i	$-0.267920\pi$
$67$	10.9061			1.33240			0.666198	+	0.745775i	$0.267920\pi$
$68$		0			0
$69$	−20.3650			−2.45166
$70$		0			0
$71$	2.59393	−	2.59393i	0.307843	−	0.307843i	−0.536230	−	0.844072i	$-0.680152\pi$
$71$	2.59393	−	2.59393i	0.307843	−	0.307843i	0.844072	+	0.536230i	$0.180152\pi$
$72$		0			0
$73$	0.889261	−	0.889261i	0.104080	−	0.104080i	−0.653149	−	0.757229i	$-0.726553\pi$
$73$	0.889261	−	0.889261i	0.104080	−	0.104080i	0.757229	+	0.653149i	$0.226553\pi$
$74$		0			0
$75$	2.05847	+	2.05847i	0.237692	+	0.237692i
$76$		0			0
$77$			23.6902i			2.69975i
$78$		0			0
$79$	3.27892	+	3.27892i	0.368907	+	0.368907i	0.867078	−	0.498172i	$-0.165995\pi$
$79$	3.27892	+	3.27892i	0.368907	+	0.368907i	−0.498172	+	0.867078i	$0.665995\pi$
$80$		0			0
$81$	−4.54775			−0.505306
$82$		0			0
$83$		−	2.84677i		−	0.312473i	−0.987720	−	0.156237i	$-0.950064\pi$
$83$		−	2.84677i		−	0.312473i	0.987720	−	0.156237i	$-0.0499362\pi$
$84$		0			0
$85$	−3.69194	+	1.83565i	−0.400447	+	0.199104i
$86$		0			0
$87$		−	13.3294i		−	1.42906i
$88$		0			0
$89$	13.9998			1.48397			0.741987	−	0.670414i	$-0.233883\pi$
$89$	13.9998			1.48397			0.741987	+	0.670414i	$0.233883\pi$
$90$		0			0
$91$	5.91466	+	5.91466i	0.620025	+	0.620025i
$92$		0			0
$93$			11.6588i			1.20896i
$94$		0			0
$95$	−1.95468	−	1.95468i	−0.200546	−	0.200546i
$96$		0			0
$97$	1.92396	−	1.92396i	0.195349	−	0.195349i	−0.602654	−	0.798003i	$-0.705890\pi$
$97$	1.92396	−	1.92396i	0.195349	−	0.195349i	0.798003	+	0.602654i	$0.205890\pi$
$98$		0			0
$99$	−22.9879	+	22.9879i	−2.31037	+	2.31037i
$100$		0			0
$101$	11.5378			1.14805			0.574027	−	0.818837i	$-0.305381\pi$
$101$	11.5378			1.14805			0.574027	+	0.818837i	$0.305381\pi$
$102$		0			0
$103$	−10.1567			−1.00077			−0.500385	−	0.865803i	$-0.666808\pi$
$103$	−10.1567			−1.00077			−0.500385	+	0.865803i	$0.666808\pi$
$104$		0			0
$105$	−8.21213	+	8.21213i	−0.801422	+	0.801422i
$106$		0			0
$107$	5.57763	−	5.57763i	0.539210	−	0.539210i	−0.384087	−	0.923297i	$-0.625484\pi$
$107$	5.57763	−	5.57763i	0.539210	−	0.539210i	0.923297	+	0.384087i	$0.125484\pi$
$108$		0			0
$109$	−1.38413	−	1.38413i	−0.132576	−	0.132576i	0.637705	−	0.770281i	$-0.279884\pi$
$109$	−1.38413	−	1.38413i	−0.132576	−	0.132576i	−0.770281	+	0.637705i	$0.779884\pi$
$110$		0			0
$111$			7.14501i			0.678174i
$112$		0			0
$113$	14.2440	+	14.2440i	1.33996	+	1.33996i	0.896093	+	0.443866i	$0.146393\pi$
$113$	14.2440	+	14.2440i	1.33996	+	1.33996i	0.443866	+	0.896093i	$0.353607\pi$
$114$		0			0
$115$	−6.99559			−0.652342
$116$		0			0
$117$			11.4786i			1.06120i
$118$		0			0
$119$	−7.32317	−	14.7287i	−0.671314	−	1.35018i
$120$		0			0
$121$			24.2628i			2.20571i
$122$		0			0
$123$	28.0872			2.53254
$124$		0			0
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$		0			0
$127$			4.63445i			0.411241i	0.978632	+	0.205620i	$0.0659212\pi$
$127$			4.63445i			0.411241i	−0.978632	+	0.205620i	$0.934079\pi$
$128$		0			0
$129$	−16.6913	−	16.6913i	−1.46958	−	1.46958i
$130$		0			0
$131$	13.3285	−	13.3285i	1.16452	−	1.16452i	0.181043	−	0.983475i	$-0.442053\pi$
$131$	13.3285	−	13.3285i	1.16452	−	1.16452i	0.983475	−	0.181043i	$-0.0579474\pi$
$132$		0			0
$133$	7.79803	−	7.79803i	0.676175	−	0.676175i
$134$		0			0
$135$	−7.20398			−0.620020
$136$		0			0
$137$	0.159296			0.0136096			0.00680479	−	0.999977i	$-0.497834\pi$
$137$	0.159296			0.0136096			0.00680479	+	0.999977i	$0.497834\pi$
$138$		0			0
$139$	12.1081	−	12.1081i	1.02699	−	1.02699i	0.0273687	−	0.999625i	$-0.491287\pi$
$139$	12.1081	−	12.1081i	1.02699	−	1.02699i	0.999625	−	0.0273687i	$-0.00871281\pi$
$140$		0			0
$141$	5.96808	−	5.96808i	0.502603	−	0.502603i
$142$		0			0
$143$	8.80397	+	8.80397i	0.736225	+	0.736225i
$144$		0			0
$145$		−	4.57879i		−	0.380248i
$146$		0			0
$147$	−18.3523	−	18.3523i	−1.51367	−	1.51367i
$148$		0			0
$149$	3.66668			0.300386			0.150193	−	0.988657i	$-0.452010\pi$
$149$	3.66668			0.300386			0.150193	+	0.988657i	$0.452010\pi$
$150$		0			0
$151$			12.9239i			1.05173i	0.850568	+	0.525865i	$0.176258\pi$
$151$			12.9239i			1.05173i	−0.850568	+	0.525865i	$0.823742\pi$
$152$		0			0
$153$	7.18598	−	21.3981i	0.580952	−	1.72994i
$154$		0			0
$155$			4.00490i			0.321682i
$156$		0			0
$157$	−4.71806			−0.376542			−0.188271	−	0.982117i	$-0.560288\pi$
$157$	−4.71806			−0.376542			−0.188271	+	0.982117i	$0.560288\pi$
$158$		0			0
$159$	−15.5050	−	15.5050i	−1.22963	−	1.22963i
$160$		0			0
$161$		−	27.9084i		−	2.19949i
$162$		0			0
$163$	8.67514	+	8.67514i	0.679489	+	0.679489i	0.959885	−	0.280395i	$-0.0904656\pi$
$163$	8.67514	+	8.67514i	0.679489	+	0.679489i	−0.280395	+	0.959885i	$0.590466\pi$
$164$		0			0
$165$	−12.2237	+	12.2237i	−0.951617	+	0.951617i
$166$		0			0
$167$	5.70359	−	5.70359i	0.441357	−	0.441357i	−0.451111	−	0.892468i	$-0.648972\pi$
$167$	5.70359	−	5.70359i	0.441357	−	0.441357i	0.892468	+	0.451111i	$0.148972\pi$
$168$		0			0
$169$	−8.60388			−0.661837
$170$		0			0
$171$	15.1337			1.15730
$172$		0			0
$173$	−13.6664	+	13.6664i	−1.03904	+	1.03904i	−0.0398333	+	0.999206i	$0.512683\pi$
$173$	−13.6664	+	13.6664i	−1.03904	+	1.03904i	−0.999206	+	0.0398333i	$0.987317\pi$
$174$		0			0
$175$	−2.82095	+	2.82095i	−0.213244	+	0.213244i
$176$		0			0
$177$	−11.1902	−	11.1902i	−0.841106	−	0.841106i
$178$		0			0
$179$			14.7409i			1.10179i	0.834575	+	0.550895i	$0.185713\pi$
$179$			14.7409i			1.10179i	−0.834575	+	0.550895i	$0.814287\pi$
$180$		0			0
$181$	4.34077	+	4.34077i	0.322647	+	0.322647i	0.849782	−	0.527135i	$-0.176734\pi$
$181$	4.34077	+	4.34077i	0.322647	+	0.322647i	−0.527135	+	0.849782i	$0.676734\pi$
$182$		0			0
$183$	41.7337			3.08505
$184$		0			0
$185$			2.45438i			0.180450i
$186$		0			0
$187$	−10.9005	−	21.9236i	−0.797126	−	1.60322i
$188$		0			0
$189$		−	28.7397i		−	2.09051i
$190$		0			0
$191$	−9.49122			−0.686761			−0.343380	−	0.939196i	$-0.611572\pi$
$191$	−9.49122			−0.686761			−0.343380	+	0.939196i	$0.611572\pi$
$192$		0			0
$193$	3.18113	+	3.18113i	0.228983	+	0.228983i	0.812268	−	0.583285i	$-0.198233\pi$
$193$	3.18113	+	3.18113i	0.228983	+	0.228983i	−0.583285	+	0.812268i	$0.698233\pi$
$194$		0			0
$195$			6.10373i			0.437097i
$196$		0			0
$197$	8.97616	+	8.97616i	0.639525	+	0.639525i	0.950438	−	0.310913i	$-0.100635\pi$
$197$	8.97616	+	8.97616i	0.639525	+	0.639525i	−0.310913	+	0.950438i	$0.600635\pi$
$198$		0			0
$199$	−16.8897	+	16.8897i	−1.19728	+	1.19728i	−0.222298	+	0.974979i	$0.571356\pi$
$199$	−16.8897	+	16.8897i	−1.19728	+	1.19728i	−0.974979	+	0.222298i	$0.928644\pi$
$200$		0			0
$201$	−22.4500	+	22.4500i	−1.58350	+	1.58350i
$202$		0			0
$203$	18.2667			1.28207
$204$		0			0
$205$	9.64823			0.673862
$206$		0			0
$207$	27.0810	−	27.0810i	1.88226	−	1.88226i
$208$		0			0
$209$	11.6074	−	11.6074i	0.802897	−	0.802897i
$210$		0			0
$211$	6.98903	+	6.98903i	0.481145	+	0.481145i	0.905497	−	0.424352i	$-0.139498\pi$
$211$	6.98903	+	6.98903i	0.481145	+	0.481145i	−0.424352	+	0.905497i	$0.639498\pi$
$212$		0			0
$213$			10.6791i			0.731718i
$214$		0			0
$215$	−5.73362	−	5.73362i	−0.391029	−	0.391029i
$216$		0			0
$217$	−15.9772			−1.08461
$218$		0			0
$219$			3.66104i			0.247390i
$220$		0			0
$221$	−8.19512	−	2.75211i	−0.551264	−	0.185127i
$222$		0			0
$223$		−	15.3642i		−	1.02886i	−0.857531	−	0.514432i	$-0.828003\pi$
$223$		−	15.3642i		−	1.02886i	0.857531	−	0.514432i	$-0.171997\pi$
$224$		0			0
$225$	−5.47464			−0.364976
$226$		0			0
$227$	12.9872	+	12.9872i	0.861990	+	0.861990i	0.991569	−	0.129579i	$-0.0413625\pi$
$227$	12.9872	+	12.9872i	0.861990	+	0.861990i	−0.129579	+	0.991569i	$0.541363\pi$
$228$		0			0
$229$		−	25.2673i		−	1.66971i	−0.550471	−	0.834854i	$-0.685552\pi$
$229$		−	25.2673i		−	1.66971i	0.550471	−	0.834854i	$-0.314448\pi$
$230$		0			0
$231$	−48.7656	−	48.7656i	−3.20854	−	3.20854i
$232$		0			0
$233$	−6.43800	+	6.43800i	−0.421768	+	0.421768i	−0.885812	−	0.464044i	$-0.846398\pi$
$233$	−6.43800	+	6.43800i	−0.421768	+	0.421768i	0.464044	+	0.885812i	$0.346398\pi$
$234$		0			0
$235$	2.05010	−	2.05010i	0.133733	−	0.133733i
$236$		0			0
$237$	−13.4991			−0.876863
$238$		0			0
$239$	9.90234			0.640529			0.320265	−	0.947328i	$-0.396228\pi$
$239$	9.90234			0.640529			0.320265	+	0.947328i	$0.396228\pi$
$240$		0			0
$241$	−0.262472	+	0.262472i	−0.0169073	+	0.0169073i	−0.715510	−	0.698603i	$-0.753806\pi$
$241$	−0.262472	+	0.262472i	−0.0169073	+	0.0169073i	0.698603	+	0.715510i	$0.253806\pi$
$242$		0			0
$243$	−5.92051	+	5.92051i	−0.379801	+	0.379801i
$244$		0			0
$245$	−6.30421	−	6.30421i	−0.402761	−	0.402761i
$246$		0			0
$247$		−	5.79595i		−	0.368788i
$248$		0			0
$249$	5.86000	+	5.86000i	0.371362	+	0.371362i
$250$		0			0
$251$	24.0817			1.52002			0.760011	−	0.649911i	$-0.225194\pi$
$251$	24.0817			1.52002			0.760011	+	0.649911i	$0.225194\pi$
$252$		0			0
$253$		−	41.5416i		−	2.61170i
$254$		0			0
$255$	3.82112	−	11.3784i	0.239288	−	0.712543i
$256$		0			0
$257$			5.67250i			0.353841i	0.984225	+	0.176920i	$0.0566135\pi$
$257$			5.67250i			0.353841i	−0.984225	+	0.176920i	$0.943386\pi$
$258$		0			0
$259$	−9.79157			−0.608418
$260$		0			0
$261$	17.7252	+	17.7252i	1.09716	+	1.09716i
$262$		0			0
$263$		−	24.0031i		−	1.48009i	−0.672555	−	0.740047i	$-0.734803\pi$
$263$		−	24.0031i		−	1.48009i	0.672555	−	0.740047i	$-0.265197\pi$
$264$		0			0
$265$	−5.32612	−	5.32612i	−0.327181	−	0.327181i
$266$		0			0
$267$	−28.8182	+	28.8182i	−1.76365	+	1.76365i
$268$		0			0
$269$	12.6651	−	12.6651i	0.772204	−	0.772204i	−0.206288	−	0.978491i	$-0.566138\pi$
$269$	12.6651	−	12.6651i	0.772204	−	0.772204i	0.978491	+	0.206288i	$0.0661383\pi$
$270$		0			0
$271$	−1.45621			−0.0884586			−0.0442293	−	0.999021i	$-0.514083\pi$
$271$	−1.45621			−0.0884586			−0.0442293	+	0.999021i	$0.514083\pi$
$272$		0			0
$273$	−24.3504			−1.47375
$274$		0			0
$275$	−4.19898	+	4.19898i	−0.253208	+	0.253208i
$276$		0			0
$277$	−9.01170	+	9.01170i	−0.541460	+	0.541460i	−0.923957	−	0.382497i	$-0.875064\pi$
$277$	−9.01170	+	9.01170i	−0.541460	+	0.541460i	0.382497	+	0.923957i	$0.375064\pi$
$278$		0			0
$279$	−15.5036	−	15.5036i	−0.928176	−	0.928176i
$280$		0			0
$281$		−	15.8563i		−	0.945908i	−0.881087	−	0.472954i	$-0.843188\pi$
$281$		−	15.8563i		−	0.945908i	0.881087	−	0.472954i	$-0.156812\pi$
$282$		0			0
$283$	−2.73612	−	2.73612i	−0.162645	−	0.162645i	0.621092	−	0.783737i	$-0.286689\pi$
$283$	−2.73612	−	2.73612i	−0.162645	−	0.162645i	−0.783737	+	0.621092i	$0.786689\pi$
$284$		0			0
$285$	8.04730			0.476681
$286$		0			0
$287$			38.4909i			2.27204i
$288$		0			0
$289$	13.5542	+	10.2608i	0.797305	+	0.603576i
$290$		0			0
$291$			7.92087i			0.464329i
$292$		0			0
$293$	18.3190			1.07021			0.535104	−	0.844786i	$-0.320272\pi$
$293$	18.3190			1.07021			0.535104	+	0.844786i	$0.320272\pi$
$294$		0			0
$295$	−3.84394	−	3.84394i	−0.223803	−	0.223803i
$296$		0			0
$297$		−	42.7790i		−	2.48229i
$298$		0			0
$299$	−10.3716	−	10.3716i	−0.599803	−	0.599803i
$300$		0			0
$301$	22.8738	−	22.8738i	1.31843	−	1.31843i
$302$		0			0
$303$	−23.7503	+	23.7503i	−1.36442	+	1.36442i
$304$		0			0
$305$	14.3360			0.820874
$306$		0			0
$307$	−6.82114			−0.389303			−0.194651	−	0.980872i	$-0.562358\pi$
$307$	−6.82114			−0.389303			−0.194651	+	0.980872i	$0.562358\pi$
$308$		0			0
$309$	20.9073	−	20.9073i	1.18938	−	1.18938i
$310$		0			0
$311$	9.76974	−	9.76974i	0.553991	−	0.553991i	−0.373599	−	0.927590i	$-0.621876\pi$
$311$	9.76974	−	9.76974i	0.553991	−	0.553991i	0.927590	+	0.373599i	$0.121876\pi$
$312$		0			0
$313$	2.55820	+	2.55820i	0.144598	+	0.144598i	0.775700	−	0.631102i	$-0.217397\pi$
$313$	2.55820	+	2.55820i	0.144598	+	0.144598i	−0.631102	+	0.775700i	$0.717397\pi$
$314$		0			0
$315$		−	21.8406i		−	1.23058i
$316$		0			0
$317$	−10.7924	−	10.7924i	−0.606161	−	0.606161i	0.335780	−	0.941940i	$-0.391000\pi$
$317$	−10.7924	−	10.7924i	−0.606161	−	0.606161i	−0.941940	+	0.335780i	$0.891000\pi$
$318$		0			0
$319$	27.1900			1.52235
$320$		0			0
$321$			22.9628i			1.28166i
$322$		0			0
$323$	−3.62844	+	10.8046i	−0.201892	+	0.601186i
$324$		0			0
$325$			2.09669i			0.116304i
$326$		0			0
$327$	5.69841			0.315123
$328$		0			0
$329$	8.17870	+	8.17870i	0.450906	+	0.450906i
$330$		0			0
$331$			27.3436i			1.50294i	0.659767	+	0.751470i	$0.270655\pi$
$331$			27.3436i			1.50294i	−0.659767	+	0.751470i	$0.729345\pi$
$332$		0			0
$333$	−9.50129	−	9.50129i	−0.520668	−	0.520668i
$334$		0			0
$335$	−7.71180	+	7.71180i	−0.421341	+	0.421341i
$336$		0			0
$337$	−5.41215	+	5.41215i	−0.294818	+	0.294818i	−0.838980	−	0.544162i	$-0.816848\pi$
$337$	−5.41215	+	5.41215i	−0.294818	+	0.294818i	0.544162	+	0.838980i	$0.316848\pi$
$338$		0			0
$339$	−58.6417			−3.18498
$340$		0			0
$341$	−23.7821			−1.28787
$342$		0			0
$343$	5.40351	−	5.40351i	0.291762	−	0.291762i
$344$		0			0
$345$	14.4002	−	14.4002i	0.775283	−	0.775283i
$346$		0			0
$347$	−23.3630	−	23.3630i	−1.25419	−	1.25419i	−0.953824	−	0.300365i	$-0.902892\pi$
$347$	−23.3630	−	23.3630i	−1.25419	−	1.25419i	−0.300365	−	0.953824i	$-0.597108\pi$
$348$		0			0
$349$			0.517999i			0.0277278i	0.999904	+	0.0138639i	$0.00441316\pi$
$349$			0.517999i			0.0277278i	−0.999904	+	0.0138639i	$0.995587\pi$
$350$		0			0
$351$	−10.6805	−	10.6805i	−0.570084	−	0.570084i
$352$		0			0
$353$	31.2253			1.66195			0.830976	−	0.556308i	$-0.187782\pi$
$353$	31.2253			1.66195			0.830976	+	0.556308i	$0.187782\pi$
$354$		0			0
$355$			3.66837i			0.194697i
$356$		0			0
$357$	45.3932	+	15.2441i	2.40246	+	0.806802i
$358$		0			0
$359$		−	11.6951i		−	0.617243i	−0.951185	−	0.308622i	$-0.900132\pi$
$359$		−	11.6951i		−	0.617243i	0.951185	−	0.308622i	$-0.0998677\pi$
$360$		0			0
$361$	11.3585			0.597815
$362$		0			0
$363$	−49.9444	−	49.9444i	−2.62140	−	2.62140i
$364$		0			0
$365$			1.25760i			0.0658260i
$366$		0			0
$367$	−0.454347	−	0.454347i	−0.0237167	−	0.0237167i	0.695149	−	0.718866i	$-0.255338\pi$
$367$	−0.454347	−	0.454347i	−0.0237167	−	0.0237167i	−0.718866	+	0.695149i	$0.755338\pi$
$368$		0			0
$369$	−37.3498	+	37.3498i	−1.94435	+	1.94435i
$370$		0			0
$371$	21.2481	−	21.2481i	1.10315	−	1.10315i
$372$		0			0
$373$	−13.9448			−0.722035			−0.361017	−	0.932559i	$-0.617571\pi$
$373$	−13.9448			−0.722035			−0.361017	+	0.932559i	$0.617571\pi$
$374$		0			0
$375$	−2.91112			−0.150330
$376$		0			0
$377$	6.78845	−	6.78845i	0.349623	−	0.349623i
$378$		0			0
$379$	15.0574	−	15.0574i	0.773447	−	0.773447i	−0.205261	−	0.978707i	$-0.565804\pi$
$379$	15.0574	−	15.0574i	0.773447	−	0.773447i	0.978707	+	0.205261i	$0.0658042\pi$
$380$		0			0
$381$	−9.53989	−	9.53989i	−0.488743	−	0.488743i
$382$		0			0
$383$		−	27.7632i		−	1.41863i	−0.704889	−	0.709317i	$-0.749003\pi$
$383$		−	27.7632i		−	1.41863i	0.704889	−	0.709317i	$-0.250997\pi$
$384$		0			0
$385$	−16.7515	−	16.7515i	−0.853735	−	0.853735i
$386$		0			0
$387$	44.3914			2.25654
$388$		0			0
$389$		−	15.8342i		−	0.802828i	−0.915897	−	0.401414i	$-0.868519\pi$
$389$		−	15.8342i		−	0.802828i	0.915897	−	0.401414i	$-0.131481\pi$
$390$		0			0
$391$	12.8414	+	25.8273i	0.649420	+	1.30614i
$392$		0			0
$393$			54.8729i			2.76797i
$394$		0			0
$395$	−4.63709			−0.233317
$396$		0			0
$397$	11.4157	+	11.4157i	0.572936	+	0.572936i	0.932948	−	0.360012i	$-0.117227\pi$
$397$	11.4157	+	11.4157i	0.572936	+	0.572936i	−0.360012	+	0.932948i	$0.617227\pi$
$398$		0			0
$399$			32.1041i			1.60721i
$400$		0			0
$401$	1.96450	+	1.96450i	0.0981022	+	0.0981022i	0.754455	−	0.656352i	$-0.227901\pi$
$401$	1.96450	+	1.96450i	0.0981022	+	0.0981022i	−0.656352	+	0.754455i	$0.727901\pi$
$402$		0			0
$403$	−5.93761	+	5.93761i	−0.295774	+	0.295774i
$404$		0			0
$405$	3.21574	−	3.21574i	0.159792	−	0.159792i
$406$		0			0
$407$	−14.5747			−0.722443
$408$		0			0
$409$	−3.92333			−0.193996			−0.0969982	−	0.995285i	$-0.530924\pi$
$409$	−3.92333			−0.193996			−0.0969982	+	0.995285i	$0.530924\pi$
$410$		0			0
$411$	−0.327907	+	0.327907i	−0.0161745	+	0.0161745i
$412$		0			0
$413$	15.3351	−	15.3351i	0.754592	−	0.754592i
$414$		0			0
$415$	2.01297	+	2.01297i	0.0988127	+	0.0988127i
$416$		0			0
$417$			49.8484i			2.44108i
$418$		0			0
$419$	−7.79273	−	7.79273i	−0.380700	−	0.380700i	0.490654	−	0.871354i	$-0.336758\pi$
$419$	−7.79273	−	7.79273i	−0.380700	−	0.380700i	−0.871354	+	0.490654i	$0.836758\pi$
$420$		0			0
$421$	−13.7575			−0.670502			−0.335251	−	0.942129i	$-0.608821\pi$
$421$	−13.7575			−0.670502			−0.335251	+	0.942129i	$0.608821\pi$
$422$		0			0
$423$			15.8725i			0.771746i
$424$		0			0
$425$	1.31259	−	3.90859i	0.0636702	−	0.189595i
$426$		0			0
$427$			57.1922i			2.76772i
$428$		0			0
$429$	−36.2455			−1.74995
$430$		0			0
$431$	9.54879	+	9.54879i	0.459949	+	0.459949i	0.898639	−	0.438690i	$-0.144557\pi$
$431$	9.54879	+	9.54879i	0.459949	+	0.459949i	−0.438690	+	0.898639i	$0.644557\pi$
$432$		0			0
$433$		−	3.19820i		−	0.153696i	−0.997043	−	0.0768478i	$-0.975514\pi$
$433$		−	3.19820i		−	0.153696i	0.997043	−	0.0768478i	$-0.0244856\pi$
$434$		0			0
$435$	9.42532	+	9.42532i	0.451910	+	0.451910i
$436$		0			0
$437$	−13.6741	+	13.6741i	−0.654122	+	0.654122i
$438$		0			0
$439$	−14.2608	+	14.2608i	−0.680632	+	0.680632i	−0.960143	−	0.279511i	$-0.909828\pi$
$439$	−14.2608	+	14.2608i	−0.680632	+	0.680632i	0.279511	+	0.960143i	$0.409828\pi$
$440$		0			0
$441$	48.8091			2.32424
$442$		0			0
$443$	−13.4708			−0.640017			−0.320009	−	0.947415i	$-0.603686\pi$
$443$	−13.4708			−0.640017			−0.320009	+	0.947415i	$0.603686\pi$
$444$		0			0
$445$	−9.89935	+	9.89935i	−0.469274	+	0.469274i
$446$		0			0
$447$	−7.54778	+	7.54778i	−0.356998	+	0.356998i
$448$		0			0
$449$	17.4688	+	17.4688i	0.824402	+	0.824402i	0.986736	−	0.162334i	$-0.0519022\pi$
$449$	17.4688	+	17.4688i	0.824402	+	0.824402i	−0.162334	+	0.986736i	$0.551902\pi$
$450$		0			0
$451$			57.2936i			2.69785i
$452$		0			0
$453$	−26.6035	−	26.6035i	−1.24994	−	1.24994i
$454$		0			0
$455$	−8.36460			−0.392138
$456$		0			0
$457$			0.458058i			0.0214271i	0.999943	+	0.0107135i	$0.00341029\pi$
$457$			0.458058i			0.0214271i	−0.999943	+	0.0107135i	$0.996590\pi$
$458$		0			0
$459$	13.2240	+	26.5966i	0.617242	+	1.24142i
$460$		0			0
$461$		−	32.3110i		−	1.50487i	−0.658664	−	0.752437i	$-0.728878\pi$
$461$		−	32.3110i		−	1.50487i	0.658664	−	0.752437i	$-0.271122\pi$
$462$		0			0
$463$	11.4592			0.532555			0.266278	−	0.963896i	$-0.414206\pi$
$463$	11.4592			0.532555			0.266278	+	0.963896i	$0.414206\pi$
$464$		0			0
$465$	−8.24399	−	8.24399i	−0.382306	−	0.382306i
$466$		0			0
$467$		−	34.5948i		−	1.60086i	−0.599429	−	0.800428i	$-0.704606\pi$
$467$		−	34.5948i		−	1.60086i	0.599429	−	0.800428i	$-0.295394\pi$
$468$		0			0
$469$	−30.7656	−	30.7656i	−1.42063	−	1.42063i
$470$		0			0
$471$	9.71200	−	9.71200i	0.447505	−	0.447505i
$472$		0			0
$473$	34.0476	−	34.0476i	1.56551	−	1.56551i
$474$		0			0
$475$	2.76433			0.126836
$476$		0			0
$477$	41.2365			1.88809
$478$		0			0
$479$	−30.3280	+	30.3280i	−1.38572	+	1.38572i	−0.551641	+	0.834082i	$0.685998\pi$
$479$	−30.3280	+	30.3280i	−1.38572	+	1.38572i	−0.834082	+	0.551641i	$0.814002\pi$
$480$		0			0
$481$	−3.63883	+	3.63883i	−0.165917	+	0.165917i
$482$		0			0
$483$	57.4487	+	57.4487i	2.61401	+	2.61401i
$484$		0			0
$485$			2.72090i			0.123550i
$486$		0			0
$487$	−6.53184	−	6.53184i	−0.295986	−	0.295986i	0.543453	−	0.839439i	$-0.317116\pi$
$487$	−6.53184	−	6.53184i	−0.295986	−	0.295986i	−0.839439	+	0.543453i	$0.817116\pi$
$488$		0			0
$489$	−35.7151			−1.61509
$490$		0			0
$491$			16.8643i			0.761074i	0.924766	+	0.380537i	$0.124261\pi$
$491$			16.8643i			0.761074i	−0.924766	+	0.380537i	$0.875739\pi$
$492$		0			0
$493$	−16.9046	+	8.40504i	−0.761345	+	0.378544i
$494$		0			0
$495$		−	32.5098i		−	1.46121i
$496$		0			0
$497$	−14.6347			−0.656455
$498$		0			0
$499$	5.12740	+	5.12740i	0.229534	+	0.229534i	0.812498	−	0.582964i	$-0.198107\pi$
$499$	5.12740	+	5.12740i	0.229534	+	0.229534i	−0.582964	+	0.812498i	$0.698107\pi$
$500$		0			0
$501$			23.4814i			1.04907i
$502$		0			0
$503$	7.43245	+	7.43245i	0.331396	+	0.331396i	0.853117	−	0.521720i	$-0.174709\pi$
$503$	7.43245	+	7.43245i	0.331396	+	0.331396i	−0.521720	+	0.853117i	$0.674709\pi$
$504$		0			0
$505$	−8.15845	+	8.15845i	−0.363046	+	0.363046i
$506$		0			0
$507$	17.7109	−	17.7109i	0.786567	−	0.786567i
$508$		0			0
$509$	−22.7759			−1.00953			−0.504763	−	0.863258i	$-0.668420\pi$
$509$	−22.7759			−1.00953			−0.504763	+	0.863258i	$0.668420\pi$
$510$		0			0
$511$	−5.01712			−0.221944
$512$		0			0
$513$	−14.0814	+	14.0814i	−0.621711	+	0.621711i
$514$		0			0
$515$	7.18187	−	7.18187i	0.316471	−	0.316471i
$516$		0			0
$517$	12.1740	+	12.1740i	0.535411	+	0.535411i
$518$		0			0
$519$		−	56.2640i		−	2.46972i
$520$		0			0
$521$	−1.57543	−	1.57543i	−0.0690208	−	0.0690208i	0.671754	−	0.740775i	$-0.265541\pi$
$521$	−1.57543	−	1.57543i	−0.0690208	−	0.0690208i	−0.740775	+	0.671754i	$0.765541\pi$
$522$		0			0
$523$	−18.2385			−0.797513			−0.398757	−	0.917057i	$-0.630558\pi$
$523$	−18.2385			−0.797513			−0.398757	+	0.917057i	$0.630558\pi$
$524$		0			0
$525$		−	11.6137i		−	0.506863i
$526$		0			0
$527$	14.7858	−	7.35159i	0.644082	−	0.320240i
$528$		0			0
$529$			25.9383i			1.12775i
$530$		0			0
$531$	29.7610			1.29152
$532$		0			0
$533$	14.3043	+	14.3043i	0.619590	+	0.619590i
$534$		0			0
$535$			7.88796i			0.341026i
$536$		0			0
$537$	−30.3439	−	30.3439i	−1.30943	−	1.30943i
$538$		0			0
$539$	37.4359	−	37.4359i	1.61248	−	1.61248i
$540$		0			0
$541$	−5.62690	+	5.62690i	−0.241919	+	0.241919i	−0.817644	−	0.575724i	$-0.804720\pi$
$541$	−5.62690	+	5.62690i	−0.241919	+	0.241919i	0.575724	+	0.817644i	$0.304720\pi$
$542$		0			0
$543$	−17.8707			−0.766906
$544$		0			0
$545$	1.95746			0.0838484
$546$		0			0
$547$	−8.47076	+	8.47076i	−0.362183	+	0.362183i	−0.864616	−	0.502433i	$-0.832438\pi$
$547$	−8.47076	+	8.47076i	−0.362183	+	0.362183i	0.502433	+	0.864616i	$0.332438\pi$
$548$		0			0
$549$	−55.4967	+	55.4967i	−2.36854	+	2.36854i
$550$		0			0
$551$	−8.95005	−	8.95005i	−0.381285	−	0.381285i
$552$		0			0
$553$		−	18.4993i		−	0.786670i
$554$		0			0
$555$	−5.05228	−	5.05228i	−0.214458	−	0.214458i
$556$		0			0
$557$	47.0602			1.99400			0.997002	−	0.0773775i	$-0.0246547\pi$
$557$	47.0602			1.99400			0.997002	+	0.0773775i	$0.0246547\pi$
$558$		0			0
$559$		−	17.0012i		−	0.719073i
$560$		0			0
$561$	67.5677	+	22.6908i	2.85271	+	0.958006i
$562$		0			0
$563$			14.2723i			0.601505i	0.953702	+	0.300752i	$0.0972378\pi$
$563$			14.2723i			0.601505i	−0.953702	+	0.300752i	$0.902762\pi$
$564$		0			0
$565$	−20.1440			−0.847464
$566$		0			0
$567$	12.8290	+	12.8290i	0.538766	+	0.538766i
$568$		0			0
$569$			34.8997i			1.46307i	0.681802	+	0.731537i	$0.261197\pi$
$569$			34.8997i			1.46307i	−0.681802	+	0.731537i	$0.738803\pi$
$570$		0			0
$571$	−11.6490	−	11.6490i	−0.487494	−	0.487494i	0.420020	−	0.907515i	$-0.362023\pi$
$571$	−11.6490	−	11.6490i	−0.487494	−	0.487494i	−0.907515	+	0.420020i	$0.862023\pi$
$572$		0			0
$573$	19.5374	−	19.5374i	0.816188	−	0.816188i
$574$		0			0
$575$	4.94663	−	4.94663i	0.206289	−	0.206289i
$576$		0			0
$577$	43.2867			1.80205			0.901024	−	0.433768i	$-0.142816\pi$
$577$	43.2867			1.80205			0.901024	+	0.433768i	$0.142816\pi$
$578$		0			0
$579$	−13.0966			−0.544274
$580$		0			0
$581$	−8.03058	+	8.03058i	−0.333165	+	0.333165i
$582$		0			0
$583$	31.6278	−	31.6278i	1.30989	−	1.30989i
$584$		0			0
$585$	−8.11662	−	8.11662i	−0.335581	−	0.335581i
$586$		0			0
$587$			15.9381i			0.657835i	0.944359	+	0.328917i	$0.106684\pi$
$587$			15.9381i			0.657835i	−0.944359	+	0.328917i	$0.893316\pi$
$588$		0			0
$589$	7.82829	+	7.82829i	0.322559	+	0.322559i
$590$		0			0
$591$	−36.9544			−1.52010
$592$		0			0
$593$		−	13.4044i		−	0.550454i	−0.961379	−	0.275227i	$-0.911247\pi$
$593$		−	13.4044i		−	0.550454i	0.961379	−	0.275227i	$-0.0887530\pi$
$594$		0			0
$595$	15.5930	+	5.23649i	0.639252	+	0.214675i
$596$		0			0
$597$		−	69.5339i		−	2.84583i
$598$		0			0
$599$	32.0456			1.30935			0.654674	−	0.755911i	$-0.272806\pi$
$599$	32.0456			1.30935			0.654674	+	0.755911i	$0.272806\pi$
$600$		0			0
$601$	−6.15901	−	6.15901i	−0.251231	−	0.251231i	0.570244	−	0.821475i	$-0.306849\pi$
$601$	−6.15901	−	6.15901i	−0.251231	−	0.251231i	−0.821475	+	0.570244i	$0.806849\pi$
$602$		0			0
$603$		−	59.7072i		−	2.43146i
$604$		0			0
$605$	−17.1564	−	17.1564i	−0.697506	−	0.697506i
$606$		0			0
$607$	−4.72727	+	4.72727i	−0.191874	+	0.191874i	−0.796505	−	0.604631i	$-0.793320\pi$
$607$	−4.72727	+	4.72727i	−0.191874	+	0.191874i	0.604631	+	0.796505i	$0.293320\pi$
$608$		0			0
$609$	−37.6016	+	37.6016i	−1.52369	+	1.52369i
$610$		0			0
$611$	6.07889			0.245925
$612$		0			0
$613$	−36.4982			−1.47415			−0.737074	−	0.675812i	$-0.763793\pi$
$613$	−36.4982			−1.47415			−0.737074	+	0.675812i	$0.763793\pi$
$614$		0			0
$615$	−19.8606	+	19.8606i	−0.800858	+	0.800858i
$616$		0			0
$617$	−8.42292	+	8.42292i	−0.339094	+	0.339094i	−0.856026	−	0.516932i	$-0.827074\pi$
$617$	−8.42292	+	8.42292i	−0.339094	+	0.339094i	0.516932	+	0.856026i	$0.327074\pi$
$618$		0			0
$619$	−4.71037	−	4.71037i	−0.189326	−	0.189326i	0.606079	−	0.795405i	$-0.292742\pi$
$619$	−4.71037	−	4.71037i	−0.189326	−	0.189326i	−0.795405	+	0.606079i	$0.792742\pi$
$620$		0			0
$621$			50.3961i			2.02232i
$622$		0			0
$623$	−39.4927	−	39.4927i	−1.58224	−	1.58224i
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$			47.7869i			1.90842i
$628$		0			0
$629$	9.06142	−	4.50538i	0.361303	−	0.179641i
$630$		0			0
$631$			10.9619i			0.436388i	0.975905	+	0.218194i	$0.0700166\pi$
$631$			10.9619i			0.436388i	−0.975905	+	0.218194i	$0.929983\pi$
$632$		0			0
$633$	−28.7735			−1.14364
$634$		0			0
$635$	−3.27705	−	3.27705i	−0.130046	−	0.130046i
$636$		0			0
$637$		−	18.6931i		−	0.740646i
$638$		0			0
$639$	−14.2008	−	14.2008i	−0.561776	−	0.561776i
$640$		0			0
$641$	−2.15336	+	2.15336i	−0.0850524	+	0.0850524i	−0.748353	−	0.663301i	$-0.769155\pi$
$641$	−2.15336	+	2.15336i	−0.0850524	+	0.0850524i	0.663301	+	0.748353i	$0.269155\pi$
$642$		0			0
$643$	3.35423	−	3.35423i	0.132278	−	0.132278i	−0.637868	−	0.770146i	$-0.720183\pi$
$643$	3.35423	−	3.35423i	0.132278	−	0.132278i	0.770146	+	0.637868i	$0.220183\pi$
$644$		0			0
$645$	23.6050			0.929447
$646$		0			0
$647$	40.1686			1.57919			0.789595	−	0.613629i	$-0.210291\pi$
$647$	40.1686			1.57919			0.789595	+	0.613629i	$0.210291\pi$
$648$		0			0
$649$	22.8263	−	22.8263i	0.896010	−	0.896010i
$650$		0			0
$651$	32.8888	−	32.8888i	1.28901	−	1.28901i
$652$		0			0
$653$	−6.83933	−	6.83933i	−0.267644	−	0.267644i	0.560506	−	0.828150i	$-0.310607\pi$
$653$	−6.83933	−	6.83933i	−0.267644	−	0.267644i	−0.828150	+	0.560506i	$0.810607\pi$
$654$		0			0
$655$			18.8494i			0.736506i
$656$		0			0
$657$	−4.86838	−	4.86838i	−0.189934	−	0.189934i
$658$		0			0
$659$	41.3724			1.61164			0.805819	−	0.592161i	$-0.201725\pi$
$659$	41.3724			1.61164			0.805819	+	0.592161i	$0.201725\pi$
$660$		0			0
$661$			38.9890i			1.51650i	0.651966	+	0.758248i	$0.273945\pi$
$661$			38.9890i			1.51650i	−0.651966	+	0.758248i	$0.726055\pi$
$662$		0			0
$663$	22.5346	−	11.2043i	0.875171	−	0.435139i
$664$		0			0
$665$			11.0281i			0.427651i
$666$		0			0
$667$	−32.0313			−1.24026
$668$		0			0
$669$	31.6268	+	31.6268i	1.22276	+	1.22276i
$670$		0			0
$671$			85.1304i			3.28642i
$672$		0			0
$673$	−15.7018	−	15.7018i	−0.605258	−	0.605258i	0.336445	−	0.941703i	$-0.390775\pi$
$673$	−15.7018	−	15.7018i	−0.605258	−	0.605258i	−0.941703	+	0.336445i	$0.890775\pi$
$674$		0			0
$675$	5.09398	−	5.09398i	0.196067	−	0.196067i
$676$		0			0
$677$	8.42888	−	8.42888i	0.323948	−	0.323948i	−0.526331	−	0.850279i	$-0.676433\pi$
$677$	8.42888	−	8.42888i	0.323948	−	0.323948i	0.850279	+	0.526331i	$0.176433\pi$
$678$		0			0
$679$	−10.8548			−0.416569
$680$		0			0
$681$	−53.4676			−2.04888
$682$		0			0
$683$	−14.2584	+	14.2584i	−0.545583	+	0.545583i	−0.925160	−	0.379577i	$-0.876069\pi$
$683$	−14.2584	+	14.2584i	−0.545583	+	0.545583i	0.379577	+	0.925160i	$0.376069\pi$
$684$		0			0
$685$	−0.112639	+	0.112639i	−0.00430373	+	0.00430373i
$686$		0			0
$687$	52.0121	+	52.0121i	1.98438	+	1.98438i
$688$		0			0
$689$		−	15.7929i		−	0.601660i
$690$		0			0
$691$	−13.0060	−	13.0060i	−0.494771	−	0.494771i	0.415035	−	0.909806i	$-0.363769\pi$
$691$	−13.0060	−	13.0060i	−0.494771	−	0.494771i	−0.909806	+	0.415035i	$0.863769\pi$
$692$		0			0
$693$	129.695			4.92671
$694$		0			0
$695$			17.1234i			0.649528i
$696$		0			0
$697$	−17.7108	−	35.6207i	−0.670843	−	1.34923i
$698$		0			0
$699$		−	26.5049i		−	1.00251i
$700$		0			0
$701$	47.4735			1.79305			0.896525	−	0.442994i	$-0.146084\pi$
$701$	47.4735			1.79305			0.896525	+	0.442994i	$0.146084\pi$
$702$		0			0
$703$	4.79752	+	4.79752i	0.180942	+	0.180942i
$704$		0			0
$705$			8.44014i			0.317874i
$706$		0			0
$707$	−32.5475	−	32.5475i	−1.22408	−	1.22408i
$708$		0			0
$709$	−8.88457	+	8.88457i	−0.333667	+	0.333667i	−0.853977	−	0.520310i	$-0.825816\pi$
$709$	−8.88457	+	8.88457i	−0.333667	+	0.333667i	0.520310	+	0.853977i	$0.325816\pi$
$710$		0			0
$711$	17.9509	−	17.9509i	0.673211	−	0.673211i
$712$		0			0
$713$	28.0167			1.04923
$714$		0			0
$715$	−12.4507			−0.465629
$716$		0			0
$717$	−20.3837	+	20.3837i	−0.761244	+	0.761244i
$718$		0			0
$719$	12.8819	−	12.8819i	0.480413	−	0.480413i	−0.424850	−	0.905264i	$-0.639673\pi$
$719$	12.8819	−	12.8819i	0.480413	−	0.480413i	0.905264	+	0.424850i	$0.139673\pi$
$720$		0			0
$721$	28.6515	+	28.6515i	1.06704	+	1.06704i
$722$		0			0
$723$		−	1.08059i		−	0.0401874i
$724$		0			0
$725$	3.23769	+	3.23769i	0.120245	+	0.120245i
$726$		0			0
$727$	−42.0417			−1.55924			−0.779621	−	0.626252i	$-0.784588\pi$
$727$	−42.0417			−1.55924			−0.779621	+	0.626252i	$0.784588\pi$
$728$		0			0
$729$		−	38.0177i		−	1.40806i
$730$		0			0
$731$	−10.6433	+	31.6931i	−0.393655	+	1.17221i
$732$		0			0
$733$			5.75421i			0.212537i	0.994337	+	0.106268i	$0.0338902\pi$
$733$			5.75421i			0.212537i	−0.994337	+	0.106268i	$0.966110\pi$
$734$		0			0
$735$	25.9541			0.957331
$736$		0			0
$737$	−45.7946	−	45.7946i	−1.68687	−	1.68687i
$738$		0			0
$739$		−	44.6567i		−	1.64272i	−0.570408	−	0.821361i	$-0.693215\pi$
$739$		−	44.6567i		−	1.64272i	0.570408	−	0.821361i	$-0.306785\pi$
$740$		0			0
$741$	11.9308	+	11.9308i	0.438290	+	0.438290i
$742$		0			0
$743$	10.0237	−	10.0237i	0.367733	−	0.367733i	−0.498917	−	0.866650i	$-0.666269\pi$
$743$	10.0237	−	10.0237i	0.367733	−	0.367733i	0.866650	+	0.498917i	$0.166269\pi$
$744$		0			0
$745$	−2.59274	+	2.59274i	−0.0949905	+	0.0949905i
$746$		0			0
$747$	−15.5850			−0.570226
$748$		0			0
$749$	−31.4684			−1.14983
$750$		0			0
$751$	0.387773	−	0.387773i	0.0141500	−	0.0141500i	−0.699996	−	0.714146i	$-0.746815\pi$
$751$	0.387773	−	0.387773i	0.0141500	−	0.0141500i	0.714146	+	0.699996i	$0.246815\pi$
$752$		0			0
$753$	−49.5715	+	49.5715i	−1.80649	+	1.80649i
$754$		0			0
$755$	−9.13855	−	9.13855i	−0.332586	−	0.332586i
$756$		0			0
$757$			5.35045i			0.194466i	0.995262	+	0.0972328i	$0.0309991\pi$
$757$			5.35045i			0.194466i	−0.995262	+	0.0972328i	$0.969001\pi$
$758$		0			0
$759$	85.5122	+	85.5122i	3.10390	+	3.10390i
$760$		0			0
$761$	−5.74506			−0.208258			−0.104129	−	0.994564i	$-0.533206\pi$
$761$	−5.74506			−0.208258			−0.104129	+	0.994564i	$0.533206\pi$
$762$		0			0
$763$			7.80913i			0.282710i
$764$		0			0
$765$	10.0495	+	20.2120i	0.363341	+	0.730767i
$766$		0			0
$767$		−	11.3980i		−	0.411556i
$768$		0			0
$769$	19.9110			0.718008			0.359004	−	0.933336i	$-0.383116\pi$
$769$	19.9110			0.718008			0.359004	+	0.933336i	$0.383116\pi$
$770$		0			0
$771$	−11.6767	−	11.6767i	−0.420526	−	0.420526i
$772$		0			0
$773$			3.80237i			0.136762i	0.997659	+	0.0683808i	$0.0217833\pi$
$773$			3.80237i			0.136762i	−0.997659	+	0.0683808i	$0.978217\pi$
$774$		0			0
$775$	−2.83189	−	2.83189i	−0.101725	−	0.101725i
$776$		0			0
$777$	20.1557	−	20.1557i	0.723082	−	0.723082i
$778$		0			0
$779$	18.8592	−	18.8592i	0.675700	−	0.675700i
$780$		0			0
$781$	−21.7837			−0.779482
$782$		0			0
$783$	−32.9855			−1.17881
$784$		0			0
$785$	3.33617	−	3.33617i	0.119073	−	0.119073i
$786$		0			0
$787$	7.00665	−	7.00665i	0.249760	−	0.249760i	−0.571112	−	0.820872i	$-0.693488\pi$
$787$	7.00665	−	7.00665i	0.249760	−	0.249760i	0.820872	+	0.571112i	$0.193488\pi$
$788$		0			0
$789$	49.4098	+	49.4098i	1.75904	+	1.75904i
$790$		0			0
$791$		−	80.3629i		−	2.85738i
$792$		0			0
$793$	21.2543	+	21.2543i	0.754762	+	0.754762i
$794$		0			0
$795$	21.9274			0.777684
$796$		0			0
$797$			31.9487i			1.13168i	0.824515	+	0.565841i	$0.191448\pi$
$797$			31.9487i			1.13168i	−0.824515	+	0.565841i	$0.808552\pi$
$798$		0			0
$799$	−11.3321	−	3.80557i	−0.400900	−	0.134631i
$800$		0			0
$801$		−	76.6438i		−	2.70808i
$802$		0			0
$803$	−7.46797			−0.263539
$804$		0			0
$805$	19.7342	+	19.7342i	0.695539	+	0.695539i
$806$		0			0
$807$			52.1415i			1.83547i
$808$		0			0
$809$	−11.2944	−	11.2944i	−0.397092	−	0.397092i	0.480114	−	0.877206i	$-0.340595\pi$
$809$	−11.2944	−	11.2944i	−0.397092	−	0.397092i	−0.877206	+	0.480114i	$0.840595\pi$
$810$		0			0
$811$	−32.9954	+	32.9954i	−1.15863	+	1.15863i	−0.173855	+	0.984771i	$0.555622\pi$
$811$	−32.9954	+	32.9954i	−1.15863	+	1.15863i	−0.984771	+	0.173855i	$0.944378\pi$
$812$		0			0
$813$	2.99758	−	2.99758i	0.105130	−	0.105130i
$814$		0			0
$815$	−12.2685			−0.429747
$816$		0			0
$817$	−22.4147			−0.784192
$818$		0			0
$819$	32.3806	−	32.3806i	1.13147	−	1.13147i
$820$		0			0
$821$	−31.4040	+	31.4040i	−1.09601	+	1.09601i	−0.101134	+	0.994873i	$0.532247\pi$
$821$	−31.4040	+	31.4040i	−1.09601	+	1.09601i	−0.994873	+	0.101134i	$0.967753\pi$
$822$		0			0
$823$	8.35292	+	8.35292i	0.291165	+	0.291165i	0.837540	−	0.546376i	$-0.183993\pi$
$823$	8.35292	+	8.35292i	0.291165	+	0.291165i	−0.546376	+	0.837540i	$0.683993\pi$
$824$		0			0
$825$		−	17.2870i		−	0.601855i
$826$		0			0
$827$	34.2825	+	34.2825i	1.19212	+	1.19212i	0.976471	+	0.215648i	$0.0691863\pi$
$827$	34.2825	+	34.2825i	1.19212	+	1.19212i	0.215648	+	0.976471i	$0.430814\pi$
$828$		0			0
$829$	32.1189			1.11554			0.557768	−	0.829997i	$-0.311658\pi$
$829$	32.1189			1.11554			0.557768	+	0.829997i	$0.311658\pi$
$830$		0			0
$831$		−	37.1007i		−	1.28701i
$832$		0			0
$833$	−11.7024	+	34.8470i	−0.405465	+	1.20738i
$834$		0			0
$835$			8.06609i			0.279139i
$836$		0			0
$837$	28.8512			0.997244
$838$		0			0
$839$	5.02151	+	5.02151i	0.173362	+	0.173362i	0.788455	−	0.615093i	$-0.210882\pi$
$839$	5.02151	+	5.02151i	0.173362	+	0.173362i	−0.615093	+	0.788455i	$0.710882\pi$
$840$		0			0
$841$			8.03470i			0.277059i
$842$		0			0
$843$	32.6398	+	32.6398i	1.12417	+	1.12417i
$844$		0			0
$845$	6.08386	−	6.08386i	0.209291	−	0.209291i
$846$		0			0
$847$	68.4441	−	68.4441i	2.35177	−	2.35177i
$848$		0			0
$849$	11.2645			0.386595
$850$		0			0
$851$	17.1699			0.588575
$852$		0			0
$853$	−8.61501	+	8.61501i	−0.294972	+	0.294972i	−0.839041	−	0.544068i	$-0.816883\pi$
$853$	−8.61501	+	8.61501i	−0.294972	+	0.294972i	0.544068	+	0.839041i	$0.316883\pi$
$854$		0			0
$855$	−10.7011	+	10.7011i	−0.365971	+	0.365971i
$856$		0			0
$857$	14.7705	+	14.7705i	0.504551	+	0.504551i	0.912849	−	0.408298i	$-0.133878\pi$
$857$	14.7705	+	14.7705i	0.504551	+	0.504551i	−0.408298	+	0.912849i	$0.633878\pi$
$858$		0			0
$859$			7.89536i			0.269386i	0.990887	+	0.134693i	$0.0430049\pi$
$859$			7.89536i			0.269386i	−0.990887	+	0.134693i	$0.956995\pi$
$860$		0			0
$861$	−79.2325	−	79.2325i	−2.70024	−	2.70024i
$862$		0			0
$863$	−14.4016			−0.490237			−0.245119	−	0.969493i	$-0.578827\pi$
$863$	−14.4016			−0.490237			−0.245119	+	0.969493i	$0.578827\pi$
$864$		0			0
$865$		−	19.3273i		−	0.657146i
$866$		0			0
$867$	−49.0226	+	6.77937i	−1.66489	+	0.230240i
$868$		0			0
$869$		−	27.5362i		−	0.934101i
$870$		0			0
$871$	−22.8668			−0.774813
$872$		0			0
$873$	−10.5330	−	10.5330i	−0.356488	−	0.356488i
$874$		0			0
$875$		−	3.98942i		−	0.134867i
$876$		0			0
$877$	11.0389	+	11.0389i	0.372757	+	0.372757i	0.868480	−	0.495724i	$-0.165097\pi$
$877$	11.0389	+	11.0389i	0.372757	+	0.372757i	−0.495724	+	0.868480i	$0.665097\pi$
$878$		0			0
$879$	−37.7092	+	37.7092i	−1.27190	+	1.27190i
$880$		0			0
$881$	−11.9814	+	11.9814i	−0.403663	+	0.403663i	−0.879522	−	0.475858i	$-0.842137\pi$
$881$	−11.9814	+	11.9814i	−0.403663	+	0.403663i	0.475858	+	0.879522i	$0.342137\pi$
$882$		0			0
$883$	23.3753			0.786642			0.393321	−	0.919401i	$-0.371326\pi$
$883$	23.3753			0.786642			0.393321	+	0.919401i	$0.371326\pi$
$884$		0			0
$885$	15.8253			0.531962
$886$		0			0
$887$	−14.8185	+	14.8185i	−0.497556	+	0.497556i	−0.910676	−	0.413121i	$-0.864439\pi$
$887$	−14.8185	+	14.8185i	−0.497556	+	0.497556i	0.413121	+	0.910676i	$0.364439\pi$
$888$		0			0
$889$	13.0735	−	13.0735i	0.438472	−	0.438472i
$890$		0			0
$891$	19.0959	+	19.0959i	0.639736	+	0.639736i
$892$		0			0
$893$		−	8.01454i		−	0.268196i
$894$		0			0
$895$	−10.4234	−	10.4234i	−0.348417	−	0.348417i
$896$		0			0
$897$	42.6992			1.42569
$898$		0			0
$899$			18.3376i			0.611593i
$900$		0			0
$901$	−9.88682	+	29.4406i	−0.329378	+	0.980808i
$902$		0			0
$903$			94.1704i			3.13379i
$904$		0			0
$905$	−6.13877			−0.204060
$906$		0			0
$907$	−32.7366	−	32.7366i	−1.08700	−	1.08700i	−0.995836	−	0.0911645i	$-0.970941\pi$
$907$	−32.7366	−	32.7366i	−1.08700	−	1.08700i	−0.0911645	−	0.995836i	$-0.529059\pi$
$908$		0			0
$909$		−	63.1653i		−	2.09506i
$910$		0			0
$911$	37.7922	+	37.7922i	1.25211	+	1.25211i	0.954771	+	0.297341i	$0.0961000\pi$
$911$	37.7922	+	37.7922i	1.25211	+	1.25211i	0.297341	+	0.954771i	$0.403900\pi$
$912$		0			0
$913$	−11.9535	+	11.9535i	−0.395603	+	0.395603i
$914$		0			0
$915$	−29.5102	+	29.5102i	−0.975577	+	0.975577i
$916$		0			0
$917$	−75.1981			−2.48326
$918$		0			0
$919$	5.67563			0.187222			0.0936108	−	0.995609i	$-0.470159\pi$
$919$	5.67563			0.187222			0.0936108	+	0.995609i	$0.470159\pi$
$920$		0			0
$921$	14.0411	−	14.0411i	0.462671	−	0.462671i
$922$		0			0
$923$	−5.43867	+	5.43867i	−0.179016	+	0.179016i
$924$		0			0
$925$	−1.73551	−	1.73551i	−0.0570632	−	0.0570632i
$926$		0			0
$927$			55.6043i			1.82628i
$928$		0			0
$929$	38.6326	+	38.6326i	1.26750	+	1.26750i	0.947377	+	0.320119i	$0.103723\pi$
$929$	38.6326	+	38.6326i	1.26750	+	1.26750i	0.320119	+	0.947377i	$0.396277\pi$
$930$		0			0
$931$	−24.6454			−0.807719
$932$		0			0
$933$			40.2215i			1.31679i
$934$		0			0
$935$	23.2102	+	7.79451i	0.759054	+	0.254908i
$936$		0			0
$937$			0.717134i			0.0234278i	0.999931	+	0.0117139i	$0.00372873\pi$
$937$			0.717134i			0.0234278i	−0.999931	+	0.0117139i	$0.996271\pi$
$938$		0			0
$939$	−10.5320			−0.343699
$940$		0			0
$941$	−1.45190	−	1.45190i	−0.0473305	−	0.0473305i	0.683045	−	0.730376i	$-0.260655\pi$
$941$	−1.45190	−	1.45190i	−0.0473305	−	0.0473305i	−0.730376	+	0.683045i	$0.760655\pi$
$942$		0			0
$943$		−	67.4951i		−	2.19794i
$944$		0			0
$945$	20.3220	+	20.3220i	0.661076	+	0.661076i
$946$		0			0
$947$	−17.4393	+	17.4393i	−0.566701	+	0.566701i	−0.931203	−	0.364502i	$-0.881239\pi$
$947$	−17.4393	+	17.4393i	−0.566701	+	0.566701i	0.364502	+	0.931203i	$0.381239\pi$
$948$		0			0
$949$	−1.86451	+	1.86451i	−0.0605245	+	0.0605245i
$950$		0			0
$951$	44.4317			1.44080
$952$		0			0
$953$	−8.89683			−0.288197			−0.144098	−	0.989563i	$-0.546028\pi$
$953$	−8.89683			−0.288197			−0.144098	+	0.989563i	$0.546028\pi$
$954$		0			0
$955$	6.71131	−	6.71131i	0.217173	−	0.217173i
$956$		0			0
$957$	−55.9699	+	55.9699i	−1.80925	+	1.80925i
$958$		0			0
$959$	−0.449366	−	0.449366i	−0.0145108	−	0.0145108i
$960$		0			0
$961$			14.9608i			0.482605i
$962$		0			0
$963$	−30.5355	−	30.5355i	−0.983992	−	0.983992i
$964$		0			0
$965$	−4.49880			−0.144821
$966$		0			0
$967$			11.9808i			0.385277i	0.981270	+	0.192639i	$0.0617045\pi$
$967$			11.9808i			0.385277i	−0.981270	+	0.192639i	$0.938295\pi$
$968$		0			0
$969$	−14.7720	−	29.7101i	−0.474545	−	0.954427i
$970$		0			0
$971$			6.41275i			0.205795i	0.994692	+	0.102897i	$0.0328114\pi$
$971$			6.41275i			0.205795i	−0.994692	+	0.102897i	$0.967189\pi$
$972$		0			0
$973$	−68.3125			−2.19000
$974$		0			0
$975$	−4.31599	−	4.31599i	−0.138222	−	0.138222i
$976$		0			0
$977$		−	7.73116i		−	0.247342i	−0.992323	−	0.123671i	$-0.960533\pi$
$977$		−	7.73116i		−	0.247342i	0.992323	−	0.123671i	$-0.0394667\pi$
$978$		0			0
$979$	−58.7848	−	58.7848i	−1.87877	−	1.87877i
$980$		0			0
$981$	−7.57763	+	7.57763i	−0.241935	+	0.241935i
$982$		0			0
$983$	−10.6322	+	10.6322i	−0.339113	+	0.339113i	−0.856034	−	0.516920i	$-0.827078\pi$
$983$	−10.6322	+	10.6322i	−0.339113	+	0.339113i	0.516920	+	0.856034i	$0.327078\pi$
$984$		0			0
$985$	−12.6942			−0.404471
$986$		0			0
$987$	−33.6713			−1.07177
$988$		0			0
$989$	−40.1100	+	40.1100i	−1.27543	+	1.27543i
$990$		0			0
$991$	−2.34983	+	2.34983i	−0.0746448	+	0.0746448i	−0.743444	−	0.668799i	$-0.766809\pi$
$991$	−2.34983	+	2.34983i	−0.0746448	+	0.0746448i	0.668799	+	0.743444i	$0.266809\pi$
$992$		0			0
$993$	−56.2861	−	56.2861i	−1.78619	−	1.78619i
$994$		0			0
$995$		−	23.8856i		−	0.757224i
$996$		0			0
$997$	26.2242	+	26.2242i	0.830528	+	0.830528i	0.987589	−	0.157061i	$-0.0502018\pi$
$997$	26.2242	+	26.2242i	0.830528	+	0.830528i	−0.157061	+	0.987589i	$0.550202\pi$
$998$		0			0
$999$	17.6813			0.559412

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1360.2.bt.f.1041.1		20
4.3	odd	2		680.2.bd.b.361.10	yes	20
17.13	even	4	inner	1360.2.bt.f.81.1		20
68.47	odd	4		680.2.bd.b.81.10	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.bd.b.81.10	✓	20	68.47	odd	4
680.2.bd.b.361.10	yes	20	4.3	odd	2
1360.2.bt.f.81.1		20	17.13	even	4	inner
1360.2.bt.f.1041.1		20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1360 = 2^{4} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1360.bt (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.05847 + 2.05847i) q^{3} +(-0.707107 + 0.707107i) q^{5} +(-2.82095 - 2.82095i) q^{7} -5.47464i q^{9} +(-4.19898 - 4.19898i) q^{11} -2.09669 q^{13} -2.91112i q^{15} +(3.90859 + 1.31259i) q^{17} +2.76433i q^{19} +11.6137 q^{21} +(4.94663 + 4.94663i) q^{23} -1.00000i q^{25} +(5.09398 + 5.09398i) q^{27} +(-3.23769 + 3.23769i) q^{29} +(2.83189 - 2.83189i) q^{31} +17.2870 q^{33} +3.98942 q^{35} +(1.73551 - 1.73551i) q^{37} +(4.31599 - 4.31599i) q^{39} +(-6.82233 - 6.82233i) q^{41} +8.10856i q^{43} +(3.87115 + 3.87115i) q^{45} -2.89927 q^{47} +8.91549i q^{49} +(-10.7477 + 5.34380i) q^{51} +7.53227i q^{53} +5.93825 q^{55} +(-5.69030 - 5.69030i) q^{57} +5.43616i q^{59} +(-10.1370 - 10.1370i) q^{61} +(-15.4437 + 15.4437i) q^{63} +(1.48259 - 1.48259i) q^{65} +10.9061 q^{67} -20.3650 q^{69} +(2.59393 - 2.59393i) q^{71} +(0.889261 - 0.889261i) q^{73} +(2.05847 + 2.05847i) q^{75} +23.6902i q^{77} +(3.27892 + 3.27892i) q^{79} -4.54775 q^{81} -2.84677i q^{83} +(-3.69194 + 1.83565i) q^{85} -13.3294i q^{87} +13.9998 q^{89} +(5.91466 + 5.91466i) q^{91} +11.6588i q^{93} +(-1.95468 - 1.95468i) q^{95} +(1.92396 - 1.92396i) q^{97} +(-22.9879 + 22.9879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} - 4 q^{7} - 12 q^{11} + 4 q^{13} + 4 q^{17} + 16 q^{21} + 4 q^{23} + 16 q^{27} - 4 q^{29} + 4 q^{31} + 16 q^{33} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} - 4 q^{47} + 4 q^{51} + 8 q^{55}+ \cdots - 52 q^{99}+O(q^{100}) \) 20 * q + 4 * q^3 - 4 * q^7 - 12 * q^11 + 4 * q^13 + 4 * q^17 + 16 * q^21 + 4 * q^23 + 16 * q^27 - 4 * q^29 + 4 * q^31 + 16 * q^33 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 - 4 * q^47 + 4 * q^51 + 8 * q^55 - 24 * q^57 - 24 * q^61 - 60 * q^63 - 4 * q^65 + 56 * q^67 + 24 * q^69 + 40 * q^71 - 20 * q^73 - 4 * q^75 + 8 * q^79 + 4 * q^81 - 12 * q^85 + 28 * q^89 + 4 * q^95 + 24 * q^97 - 52 * q^99

Introduction

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