LMFDB - Embedded newform 880.2.cd.a.609.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(49,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 5, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("880.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.cd (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			609.2
Root			$0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	880.609
Dual form			880.2.cd.a.289.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.17557 + 0.381966i) q^{3} +(1.03025 - 1.98459i) q^{5} +(-0.587785 + 0.190983i) q^{7} +(-1.19098 - 0.865300i) q^{9} +(-1.69098 - 2.85317i) q^{11} +(1.40008 - 1.92705i) q^{13} +(1.96917 - 1.93950i) q^{15} +(3.80423 + 5.23607i) q^{17} +(1.11803 - 3.44095i) q^{19} -0.763932 q^{21} -4.61803i q^{23} +(-2.87718 - 4.08924i) q^{25} +(-3.24920 - 4.47214i) q^{27} +(-1.38197 - 4.25325i) q^{29} +(1.61803 + 1.17557i) q^{31} +(-0.898056 - 4.00000i) q^{33} +(-0.226543 + 1.36327i) q^{35} +(5.34307 - 1.73607i) q^{37} +(2.38197 - 1.73060i) q^{39} +(0.190983 - 0.587785i) q^{41} +8.47214i q^{43} +(-2.94427 + 1.47214i) q^{45} +(9.59632 + 3.11803i) q^{47} +(-5.35410 + 3.88998i) q^{49} +(2.47214 + 7.60845i) q^{51} +(-4.16750 + 5.73607i) q^{53} +(-7.40450 + 0.416429i) q^{55} +(2.62866 - 3.61803i) q^{57} +(-3.35410 - 10.3229i) q^{59} +(5.61803 - 4.08174i) q^{61} +(0.865300 + 0.281153i) q^{63} +(-2.38197 - 4.76393i) q^{65} +9.23607i q^{67} +(1.76393 - 5.42882i) q^{69} +(1.61803 - 1.17557i) q^{71} +(-1.45309 + 0.472136i) q^{73} +(-1.82037 - 5.90617i) q^{75} +(1.53884 + 1.35410i) q^{77} +(5.00000 + 3.63271i) q^{79} +(-0.746711 - 2.29814i) q^{81} +(-5.98385 - 8.23607i) q^{83} +(14.3107 - 2.15537i) q^{85} -5.52786i q^{87} -11.3820 q^{89} +(-0.454915 + 1.40008i) q^{91} +(1.45309 + 2.00000i) q^{93} +(-5.67702 - 5.76388i) q^{95} +(-5.42882 + 7.47214i) q^{97} +(-0.454915 + 4.86128i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{5} - 14 q^{9} - 18 q^{11} - 12 q^{15} - 24 q^{21} - 6 q^{25} - 20 q^{29} + 4 q^{31} + 4 q^{35} + 28 q^{39} + 6 q^{41} + 48 q^{45} - 16 q^{49} - 16 q^{51} - 4 q^{55} + 36 q^{61} - 28 q^{65} + 32 q^{69}+ \cdots - 26 q^{99}+O(q^{100}) $ 8 * q + 4 * q^5 - 14 * q^9 - 18 * q^11 - 12 * q^15 - 24 * q^21 - 6 * q^25 - 20 * q^29 + 4 * q^31 + 4 * q^35 + 28 * q^39 + 6 * q^41 + 48 * q^45 - 16 * q^49 - 16 * q^51 - 4 * q^55 + 36 * q^61 - 28 * q^65 + 32 * q^69 + 4 * q^71 - 32 * q^75 + 40 * q^79 - 82 * q^81 + 16 * q^85 - 100 * q^89 - 26 * q^91 - 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{5}\right)$	$1$

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
$3$	1.17557	+	0.381966i	0.678716	+	0.220528i	0.628033	−	0.778187i	$-0.283860\pi$
$3$	1.17557	+	0.381966i	0.678716	+	0.220528i	0.0506828	+	0.998715i	$0.483860\pi$
$4$		0			0
$5$	1.03025	−	1.98459i	0.460741	−	0.887535i
$5$	1.03025	−	1.98459i	0.460741	−	0.887535i
$6$		0			0
$7$	−0.587785	+	0.190983i	−0.222162	+	0.0721848i	−0.417983	−	0.908455i	$-0.637263\pi$
$7$	−0.587785	+	0.190983i	−0.222162	+	0.0721848i	0.195821	+	0.980640i	$0.437263\pi$
$8$		0			0
$9$	−1.19098	−	0.865300i	−0.396994	−	0.288433i
$10$		0			0
$11$	−1.69098	−	2.85317i	−0.509851	−	0.860263i
$11$	−1.69098	−	2.85317i	−0.509851	−	0.860263i
$12$		0			0
$13$	1.40008	−	1.92705i	0.388314	−	0.534468i	−0.569449	−	0.822026i	$-0.692844\pi$
$13$	1.40008	−	1.92705i	0.388314	−	0.534468i	0.957763	+	0.287559i	$0.0928436\pi$
$14$		0			0
$15$	1.96917	−	1.93950i	0.508439	−	0.500777i
$16$		0			0
$17$	3.80423	+	5.23607i	0.922660	+	1.26993i	0.962654	+	0.270733i	$0.0872661\pi$
$17$	3.80423	+	5.23607i	0.922660	+	1.26993i	−0.0399941	+	0.999200i	$0.512734\pi$
$18$		0			0
$19$	1.11803	−	3.44095i	0.256495	−	0.789409i	−0.737037	−	0.675852i	$-0.763776\pi$
$19$	1.11803	−	3.44095i	0.256495	−	0.789409i	0.993532	−	0.113557i	$-0.0362244\pi$
$20$		0			0
$21$	−0.763932			−0.166704
$22$		0			0
$23$		−	4.61803i		−	0.962927i	−0.876466	−	0.481463i	$-0.840105\pi$
$23$		−	4.61803i		−	0.962927i	0.876466	−	0.481463i	$-0.159895\pi$
$24$		0			0
$25$	−2.87718	−	4.08924i	−0.575435	−	0.817848i
$26$		0			0
$27$	−3.24920	−	4.47214i	−0.625308	−	0.860663i
$28$		0			0
$29$	−1.38197	−	4.25325i	−0.256625	−	0.789809i	−0.993505	−	0.113787i	$-0.963702\pi$
$29$	−1.38197	−	4.25325i	−0.256625	−	0.789809i	0.736881	−	0.676023i	$-0.236298\pi$
$30$		0			0
$31$	1.61803	+	1.17557i	0.290607	+	0.211139i	0.723531	−	0.690292i	$-0.242518\pi$
$31$	1.61803	+	1.17557i	0.290607	+	0.211139i	−0.432923	+	0.901431i	$0.642518\pi$
$32$		0			0
$33$	−0.898056	−	4.00000i	−0.156331	−	0.696311i
$34$		0			0
$35$	−0.226543	+	1.36327i	−0.0382927	+	0.230435i
$36$		0			0
$37$	5.34307	−	1.73607i	0.878395	−	0.285408i	0.165104	−	0.986276i	$-0.447204\pi$
$37$	5.34307	−	1.73607i	0.878395	−	0.285408i	0.713291	+	0.700868i	$0.247204\pi$
$38$		0			0
$39$	2.38197	−	1.73060i	0.381420	−	0.277118i
$40$		0			0
$41$	0.190983	−	0.587785i	0.0298265	−	0.0917966i	−0.935035	−	0.354555i	$-0.884632\pi$
$41$	0.190983	−	0.587785i	0.0298265	−	0.0917966i	0.964862	+	0.262759i	$0.0846323\pi$
$42$		0			0
$43$			8.47214i			1.29199i	0.763342	+	0.645994i	$0.223557\pi$
$43$			8.47214i			1.29199i	−0.763342	+	0.645994i	$0.776443\pi$
$44$		0			0
$45$	−2.94427	+	1.47214i	−0.438906	+	0.219453i
$46$		0			0
$47$	9.59632	+	3.11803i	1.39977	+	0.454812i	0.909116	−	0.416544i	$-0.136759\pi$
$47$	9.59632	+	3.11803i	1.39977	+	0.454812i	0.490652	+	0.871356i	$0.336759\pi$
$48$		0			0
$49$	−5.35410	+	3.88998i	−0.764872	+	0.555712i
$50$		0			0
$51$	2.47214	+	7.60845i	0.346168	+	1.06540i
$52$		0			0
$53$	−4.16750	+	5.73607i	−0.572450	+	0.787910i	−0.992842	−	0.119433i	$-0.961892\pi$
$53$	−4.16750	+	5.73607i	−0.572450	+	0.787910i	0.420393	+	0.907342i	$0.361892\pi$
$54$		0			0
$55$	−7.40450	+	0.416429i	−0.998422	+	0.0561513i
$56$		0			0
$57$	2.62866	−	3.61803i	0.348174	−	0.479220i
$58$		0			0
$59$	−3.35410	−	10.3229i	−0.436667	−	1.34392i	−0.891369	−	0.453279i	$-0.850254\pi$
$59$	−3.35410	−	10.3229i	−0.436667	−	1.34392i	0.454702	−	0.890644i	$-0.349746\pi$
$60$		0			0
$61$	5.61803	−	4.08174i	0.719316	−	0.522613i	−0.166850	−	0.985982i	$-0.553360\pi$
$61$	5.61803	−	4.08174i	0.719316	−	0.522613i	0.886165	+	0.463369i	$0.153360\pi$
$62$		0			0
$63$	0.865300	+	0.281153i	0.109018	+	0.0354219i
$64$		0			0
$65$	−2.38197	−	4.76393i	−0.295447	−	0.590893i
$66$		0			0
$67$			9.23607i			1.12837i	0.825650	+	0.564183i	$0.190809\pi$
$67$			9.23607i			1.12837i	−0.825650	+	0.564183i	$0.809191\pi$
$68$		0			0
$69$	1.76393	−	5.42882i	0.212352	−	0.653554i
$70$		0			0
$71$	1.61803	−	1.17557i	0.192025	−	0.139515i	−0.487619	−	0.873057i	$-0.662134\pi$
$71$	1.61803	−	1.17557i	0.192025	−	0.139515i	0.679644	+	0.733542i	$0.262134\pi$
$72$		0			0
$73$	−1.45309	+	0.472136i	−0.170071	+	0.0552593i	−0.392815	−	0.919618i	$-0.628499\pi$
$73$	−1.45309	+	0.472136i	−0.170071	+	0.0552593i	0.222744	+	0.974877i	$0.428499\pi$
$74$		0			0
$75$	−1.82037	−	5.90617i	−0.210199	−	0.681986i
$76$		0			0
$77$	1.53884	+	1.35410i	0.175367	+	0.154314i
$78$		0			0
$79$	5.00000	+	3.63271i	0.562544	+	0.408712i	0.832389	−	0.554192i	$-0.186973\pi$
$79$	5.00000	+	3.63271i	0.562544	+	0.408712i	−0.269845	+	0.962904i	$0.586973\pi$
$80$		0			0
$81$	−0.746711	−	2.29814i	−0.0829679	−	0.255349i
$82$		0			0
$83$	−5.98385	−	8.23607i	−0.656813	−	0.904026i	0.342557	−	0.939497i	$-0.388707\pi$
$83$	−5.98385	−	8.23607i	−0.656813	−	0.904026i	−0.999371	+	0.0354710i	$0.988707\pi$
$84$		0			0
$85$	14.3107	−	2.15537i	1.55222	−	0.233782i
$86$		0			0
$87$		−	5.52786i		−	0.592649i
$88$		0			0
$89$	−11.3820			−1.20649			−0.603243	−	0.797557i	$-0.706125\pi$
$89$	−11.3820			−1.20649			−0.603243	+	0.797557i	$0.706125\pi$
$90$		0			0
$91$	−0.454915	+	1.40008i	−0.0476881	+	0.146769i
$92$		0			0
$93$	1.45309	+	2.00000i	0.150678	+	0.207390i
$94$		0			0
$95$	−5.67702	−	5.76388i	−0.582450	−	0.591361i
$96$		0			0
$97$	−5.42882	+	7.47214i	−0.551214	+	0.758680i	−0.990176	−	0.139825i	$-0.955346\pi$
$97$	−5.42882	+	7.47214i	−0.551214	+	0.758680i	0.438963	+	0.898505i	$0.355346\pi$
$98$		0			0
$99$	−0.454915	+	4.86128i	−0.0457207	+	0.488577i
$100$		0			0
$101$	15.9443	+	11.5842i	1.58651	+	1.15267i	0.908710	+	0.417428i	$0.137068\pi$
$101$	15.9443	+	11.5842i	1.58651	+	1.15267i	0.677804	+	0.735242i	$0.262932\pi$
$102$		0			0
$103$	6.51864	−	2.11803i	0.642301	−	0.208696i	0.0302843	−	0.999541i	$-0.490359\pi$
$103$	6.51864	−	2.11803i	0.642301	−	0.208696i	0.612016	+	0.790845i	$0.290359\pi$
$104$		0			0
$105$	−0.787040	+	1.51609i	−0.0768072	+	0.147955i
$106$		0			0
$107$	14.6619	+	4.76393i	1.41742	+	0.460547i	0.914781	−	0.403951i	$-0.132363\pi$
$107$	14.6619	+	4.76393i	1.41742	+	0.460547i	0.502636	+	0.864498i	$0.332363\pi$
$108$		0			0
$109$	5.52786			0.529473			0.264737	−	0.964321i	$-0.414715\pi$
$109$	5.52786			0.529473			0.264737	+	0.964321i	$0.414715\pi$
$110$		0			0
$111$	6.94427			0.659121
$112$		0			0
$113$	8.95554	+	2.90983i	0.842466	+	0.273734i	0.698287	−	0.715818i	$-0.253946\pi$
$113$	8.95554	+	2.90983i	0.842466	+	0.273734i	0.144179	+	0.989552i	$0.453946\pi$
$114$		0			0
$115$	−9.16489	−	4.75772i	−0.854631	−	0.443660i
$116$		0			0
$117$	−3.33495	+	1.08359i	−0.308317	+	0.100178i
$118$		0			0
$119$	−3.23607	−	2.35114i	−0.296650	−	0.215529i
$120$		0			0
$121$	−5.28115	+	9.64932i	−0.480105	+	0.877211i
$122$		0			0
$123$	0.449028	−	0.618034i	0.0404875	−	0.0557262i
$124$		0			0
$125$	−11.0797	+	1.49707i	−0.990995	+	0.133902i
$126$		0			0
$127$	−1.67760	−	2.30902i	−0.148863	−	0.204892i	0.728073	−	0.685500i	$-0.240416\pi$
$127$	−1.67760	−	2.30902i	−0.148863	−	0.204892i	−0.876936	+	0.480608i	$0.840416\pi$
$128$		0			0
$129$	−3.23607	+	9.95959i	−0.284920	+	0.876893i
$130$		0			0
$131$	8.00000			0.698963			0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000			0.698963			0.349482	+	0.936943i	$0.386358\pi$
$132$		0			0
$133$			2.23607i			0.193892i
$134$		0			0
$135$	−12.2228	+	1.84090i	−1.05197	+	0.158440i
$136$		0			0
$137$	−12.5882	−	17.3262i	−1.07549	−	1.48028i	−0.864394	−	0.502814i	$-0.832298\pi$
$137$	−12.5882	−	17.3262i	−1.07549	−	1.48028i	−0.211092	−	0.977466i	$-0.567702\pi$
$138$		0			0
$139$	0.100813	+	0.310271i	0.00855085	+	0.0263168i	0.955241	−	0.295829i	$-0.0955959\pi$
$139$	0.100813	+	0.310271i	0.00855085	+	0.0263168i	−0.946690	+	0.322146i	$0.895596\pi$
$140$		0			0
$141$	10.0902	+	7.33094i	0.849746	+	0.617376i
$142$		0			0
$143$	−7.86572	−	0.736068i	−0.657765	−	0.0615531i
$144$		0			0
$145$	−9.86472	−	1.63928i	−0.819221	−	0.136135i
$146$		0			0
$147$	−7.77997	+	2.52786i	−0.641681	+	0.208495i
$148$		0			0
$149$	17.5623	−	12.7598i	1.43876	−	1.04532i	0.450460	−	0.892796i	$-0.351260\pi$
$149$	17.5623	−	12.7598i	1.43876	−	1.04532i	0.988300	−	0.152524i	$-0.0487401\pi$
$150$		0			0
$151$	−4.23607	+	13.0373i	−0.344726	+	1.06096i	0.617004	+	0.786960i	$0.288346\pi$
$151$	−4.23607	+	13.0373i	−0.344726	+	1.06096i	−0.961730	+	0.273998i	$0.911654\pi$
$152$		0			0
$153$		−	9.52786i		−	0.770282i
$154$		0			0
$155$	4.00000	−	2.00000i	0.321288	−	0.160644i
$156$		0			0
$157$	−5.84510	−	1.89919i	−0.466489	−	0.151572i	0.0663350	−	0.997797i	$-0.478869\pi$
$157$	−5.84510	−	1.89919i	−0.466489	−	0.151572i	−0.532824	+	0.846226i	$0.678869\pi$
$158$		0			0
$159$	−7.09017	+	5.15131i	−0.562287	+	0.408525i
$160$		0			0
$161$	0.881966	+	2.71441i	0.0695087	+	0.213926i
$162$		0			0
$163$	−5.53483	+	7.61803i	−0.433521	+	0.596690i	−0.968757	−	0.248012i	$-0.920223\pi$
$163$	−5.53483	+	7.61803i	−0.433521	+	0.596690i	0.535236	+	0.844703i	$0.320223\pi$
$164$		0			0
$165$	−8.86357	−	2.33872i	−0.690028	−	0.182069i
$166$		0			0
$167$	−7.83297	+	10.7812i	−0.606133	+	0.834271i	−0.996252	−	0.0864937i	$-0.972434\pi$
$167$	−7.83297	+	10.7812i	−0.606133	+	0.834271i	0.390119	+	0.920764i	$0.372434\pi$
$168$		0			0
$169$	2.26393	+	6.96767i	0.174149	+	0.535974i
$170$		0			0
$171$	−4.30902	+	3.13068i	−0.329519	+	0.239409i
$172$		0			0
$173$	1.76336	+	0.572949i	0.134065	+	0.0435605i	0.375281	−	0.926911i	$-0.377546\pi$
$173$	1.76336	+	0.572949i	0.134065	+	0.0435605i	−0.241216	+	0.970472i	$0.577546\pi$
$174$		0			0
$175$	2.47214	+	1.85410i	0.186876	+	0.140157i
$176$		0			0
$177$		−	13.4164i		−	1.00844i
$178$		0			0
$179$	−2.86475	+	8.81678i	−0.214121	+	0.658997i	0.785094	+	0.619377i	$0.212615\pi$
$179$	−2.86475	+	8.81678i	−0.214121	+	0.658997i	−0.999215	+	0.0396200i	$0.987385\pi$
$180$		0			0
$181$	−16.0902	+	11.6902i	−1.19597	+	0.868925i	−0.993883	−	0.110442i	$-0.964773\pi$
$181$	−16.0902	+	11.6902i	−1.19597	+	0.868925i	−0.202090	+	0.979367i	$0.564773\pi$
$182$		0			0
$183$	8.16348	−	2.65248i	0.603462	−	0.196077i
$184$		0			0
$185$	2.05931	−	12.3924i	0.151403	−	0.911105i
$186$		0			0
$187$	8.50651	−	19.7082i	0.622057	−	1.44121i
$188$		0			0
$189$	2.76393	+	2.00811i	0.201046	+	0.146069i
$190$		0			0
$191$	2.79837	+	8.61251i	0.202483	+	0.623179i	0.999807	+	0.0196279i	$0.00624817\pi$
$191$	2.79837	+	8.61251i	0.202483	+	0.623179i	−0.797324	+	0.603551i	$0.793752\pi$
$192$		0			0
$193$	−7.77997	−	10.7082i	−0.560014	−	0.770793i	0.431314	−	0.902202i	$-0.358050\pi$
$193$	−7.77997	−	10.7082i	−0.560014	−	0.770793i	−0.991328	+	0.131408i	$0.958050\pi$
$194$		0			0
$195$	−0.980509	−	6.51017i	−0.0702157	−	0.466203i
$196$		0			0
$197$			26.2148i			1.86773i	0.357631	+	0.933863i	$0.383585\pi$
$197$			26.2148i			1.86773i	−0.357631	+	0.933863i	$0.616415\pi$
$198$		0			0
$199$	−5.52786			−0.391860			−0.195930	−	0.980618i	$-0.562773\pi$
$199$	−5.52786			−0.391860			−0.195930	+	0.980618i	$0.562773\pi$
$200$		0			0
$201$	−3.52786	+	10.8576i	−0.248836	+	0.765840i
$202$		0			0
$203$	1.62460	+	2.23607i	0.114024	+	0.156941i
$204$		0			0
$205$	−0.969751	−	0.984587i	−0.0677304	−	0.0687666i
$206$		0			0
$207$	−3.99598	+	5.50000i	−0.277740	+	0.382276i
$208$		0			0
$209$	−11.7082	+	2.62866i	−0.809873	+	0.181828i
$210$		0			0
$211$	21.4164	+	15.5599i	1.47437	+	1.07119i	0.979319	+	0.202324i	$0.0648494\pi$
$211$	21.4164	+	15.5599i	1.47437	+	1.07119i	0.495048	+	0.868866i	$0.335151\pi$
$212$		0			0
$213$	2.35114	−	0.763932i	0.161098	−	0.0523438i
$214$		0			0
$215$	16.8137	+	8.72841i	1.14668	+	0.595272i
$216$		0			0
$217$	−1.17557	−	0.381966i	−0.0798029	−	0.0259295i
$218$		0			0
$219$	−1.88854			−0.127616
$220$		0			0
$221$	15.4164			1.03702
$222$		0			0
$223$	−18.1558	−	5.89919i	−1.21580	−	0.395039i	−0.370252	−	0.928931i	$-0.620729\pi$
$223$	−18.1558	−	5.89919i	−1.21580	−	0.395039i	−0.845552	+	0.533893i	$0.820729\pi$
$224$		0			0
$225$	−0.111750	+	7.35983i	−0.00744999	+	0.490655i
$226$		0			0
$227$	−11.4127	+	3.70820i	−0.757486	+	0.246122i	−0.662199	−	0.749328i	$-0.730377\pi$
$227$	−11.4127	+	3.70820i	−0.757486	+	0.246122i	−0.0952867	+	0.995450i	$0.530377\pi$
$228$		0			0
$229$	−5.85410	−	4.25325i	−0.386850	−	0.281063i	0.377314	−	0.926086i	$-0.376848\pi$
$229$	−5.85410	−	4.25325i	−0.386850	−	0.281063i	−0.764163	+	0.645023i	$0.776848\pi$
$230$		0			0
$231$	1.29180	+	2.17963i	0.0849939	+	0.143409i
$232$		0			0
$233$	−11.2412	+	15.4721i	−0.736433	+	1.01361i	0.262383	+	0.964964i	$0.415492\pi$
$233$	−11.2412	+	15.4721i	−0.736433	+	1.01361i	−0.998816	+	0.0486494i	$0.984508\pi$
$234$		0			0
$235$	16.0746	−	15.8324i	1.04859	−	1.03279i
$236$		0			0
$237$	4.49028	+	6.18034i	0.291675	+	0.401456i
$238$		0			0
$239$	2.23607	−	6.88191i	0.144639	−	0.445154i	−0.852325	−	0.523012i	$-0.824808\pi$
$239$	2.23607	−	6.88191i	0.144639	−	0.445154i	0.996964	+	0.0778584i	$0.0248082\pi$
$240$		0			0
$241$	−4.90983			−0.316270			−0.158135	−	0.987418i	$-0.550548\pi$
$241$	−4.90983			−0.316270			−0.158135	+	0.987418i	$0.550548\pi$
$242$		0			0
$243$			13.5967i			0.872232i
$244$		0			0
$245$	2.20395	+	14.6333i	0.140805	+	0.934889i
$246$		0			0
$247$	−5.06555	−	6.97214i	−0.322313	−	0.443626i
$248$		0			0
$249$	−3.88854	−	11.9677i	−0.246426	−	0.758423i
$250$		0			0
$251$	5.50000	+	3.99598i	0.347157	+	0.252224i	0.747675	−	0.664064i	$-0.231170\pi$
$251$	5.50000	+	3.99598i	0.347157	+	0.252224i	−0.400518	+	0.916289i	$0.631170\pi$
$252$		0			0
$253$	−13.1760	+	7.80902i	−0.828370	+	0.490949i
$254$		0			0
$255$	17.6466	+	2.93243i	1.10507	+	0.183636i
$256$		0			0
$257$	19.9192	−	6.47214i	1.24252	−	0.403721i	0.387288	−	0.921959i	$-0.373412\pi$
$257$	19.9192	−	6.47214i	1.24252	−	0.403721i	0.855236	+	0.518238i	$0.173412\pi$
$258$		0			0
$259$	−2.80902	+	2.04087i	−0.174544	+	0.126814i
$260$		0			0
$261$	−2.03444	+	6.26137i	−0.125929	+	0.387569i
$262$		0			0
$263$		−	5.14590i		−	0.317310i	−0.987334	−	0.158655i	$-0.949284\pi$
$263$		−	5.14590i		−	0.317310i	0.987334	−	0.158655i	$-0.0507157\pi$
$264$		0			0
$265$	7.09017	+	14.1803i	0.435546	+	0.871091i
$266$		0			0
$267$	−13.3803	−	4.34752i	−0.818861	−	0.266064i
$268$		0			0
$269$	18.0902	−	13.1433i	1.10298	−	0.801360i	0.121434	−	0.992600i	$-0.461251\pi$
$269$	18.0902	−	13.1433i	1.10298	−	0.801360i	0.981543	+	0.191240i	$0.0612508\pi$
$270$		0			0
$271$	0.437694	+	1.34708i	0.0265880	+	0.0818295i	0.963470	−	0.267816i	$-0.0863020\pi$
$271$	0.437694	+	1.34708i	0.0265880	+	0.0818295i	−0.936882	+	0.349646i	$0.886302\pi$
$272$		0			0
$273$	−1.06957	+	1.47214i	−0.0647333	+	0.0890977i
$274$		0			0
$275$	−6.80203	+	15.1239i	−0.410178	+	0.912005i
$276$		0			0
$277$	0.0202444	−	0.0278640i	0.00121637	−	0.00167419i	−0.808408	−	0.588622i	$-0.799671\pi$
$277$	0.0202444	−	0.0278640i	0.00121637	−	0.00167419i	0.809625	+	0.586948i	$0.199671\pi$
$278$		0			0
$279$	−0.909830	−	2.80017i	−0.0544701	−	0.167642i
$280$		0			0
$281$	7.32624	−	5.32282i	0.437047	−	0.317533i	−0.347414	−	0.937712i	$-0.612940\pi$
$281$	7.32624	−	5.32282i	0.437047	−	0.317533i	0.784460	+	0.620179i	$0.212940\pi$
$282$		0			0
$283$	0.171513	+	0.0557281i	0.0101954	+	0.00331269i	0.314110	−	0.949387i	$-0.398294\pi$
$283$	0.171513	+	0.0557281i	0.0101954	+	0.00331269i	−0.303915	+	0.952699i	$0.598294\pi$
$284$		0			0
$285$	−4.47214	−	8.94427i	−0.264906	−	0.529813i
$286$		0			0
$287$			0.381966i			0.0225467i
$288$		0			0
$289$	−7.69098	+	23.6704i	−0.452411	+	1.39238i
$290$		0			0
$291$	−9.23607	+	6.71040i	−0.541428	+	0.393370i
$292$		0			0
$293$	28.3929	−	9.22542i	1.65873	−	0.538955i	0.678127	−	0.734945i	$-0.262792\pi$
$293$	28.3929	−	9.22542i	1.65873	−	0.538955i	0.980606	+	0.195990i	$0.0627919\pi$
$294$		0			0
$295$	−23.9422	−	3.97861i	−1.39397	−	0.231644i
$296$		0			0
$297$	−7.26543	+	16.8328i	−0.421583	+	0.976739i
$298$		0			0
$299$	−8.89919	−	6.46564i	−0.514653	−	0.373917i
$300$		0			0
$301$	−1.61803	−	4.97980i	−0.0932619	−	0.287031i
$302$		0			0
$303$	14.3188	+	19.7082i	0.822596	+	1.13221i
$304$		0			0
$305$	−2.31260	−	15.3547i	−0.132419	−	0.879207i
$306$		0			0
$307$		−	15.2361i		−	0.869568i	−0.900535	−	0.434784i	$-0.856825\pi$
$307$		−	15.2361i		−	0.869568i	0.900535	−	0.434784i	$-0.143175\pi$
$308$		0			0
$309$	8.47214			0.481963
$310$		0			0
$311$	1.29180	−	3.97574i	0.0732510	−	0.225444i	−0.907727	−	0.419561i	$-0.862184\pi$
$311$	1.29180	−	3.97574i	0.0732510	−	0.225444i	0.980978	+	0.194117i	$0.0621842\pi$
$312$		0			0
$313$	−6.77591	−	9.32624i	−0.382997	−	0.527150i	0.573378	−	0.819291i	$-0.305632\pi$
$313$	−6.77591	−	9.32624i	−0.382997	−	0.527150i	−0.956375	+	0.292141i	$0.905632\pi$
$314$		0			0
$315$	1.44945	−	1.42761i	0.0816671	−	0.0804365i
$316$		0			0
$317$	8.45351	−	11.6353i	0.474796	−	0.653501i	−0.502698	−	0.864462i	$-0.667659\pi$
$317$	8.45351	−	11.6353i	0.474796	−	0.653501i	0.977494	+	0.210961i	$0.0676593\pi$
$318$		0			0
$319$	−9.79837	+	11.1352i	−0.548604	+	0.623449i
$320$		0			0
$321$	15.4164	+	11.2007i	0.860460	+	0.625161i
$322$		0			0
$323$	22.2703	−	7.23607i	1.23915	−	0.402626i
$324$		0			0
$325$	−11.9085	−	0.180815i	−0.660562	−	0.0100298i
$326$		0			0
$327$	6.49839	+	2.11146i	0.359362	+	0.116764i
$328$		0			0
$329$	−6.23607			−0.343806
$330$		0			0
$331$	6.09017			0.334746			0.167373	−	0.985894i	$-0.446472\pi$
$331$	6.09017			0.334746			0.167373	+	0.985894i	$0.446472\pi$
$332$		0			0
$333$	−7.86572	−	2.55573i	−0.431039	−	0.140053i
$334$		0			0
$335$	18.3298	+	9.51545i	1.00146	+	0.519884i
$336$		0			0
$337$	−1.73060	+	0.562306i	−0.0942718	+	0.0306308i	−0.355773	−	0.934572i	$-0.615782\pi$
$337$	−1.73060	+	0.562306i	−0.0942718	+	0.0306308i	0.261501	+	0.965203i	$0.415782\pi$
$338$		0			0
$339$	9.41641	+	6.84142i	0.511429	+	0.371575i
$340$		0			0
$341$	0.618034	−	6.60440i	0.0334684	−	0.357648i
$342$		0			0
$343$	4.94704	−	6.80902i	0.267115	−	0.367652i
$344$		0			0
$345$	−8.95669	−	9.09372i	−0.482212	−	0.489589i
$346$		0			0
$347$	−1.55909	−	2.14590i	−0.0836961	−	0.115198i	0.765116	−	0.643893i	$-0.222682\pi$
$347$	−1.55909	−	2.14590i	−0.0836961	−	0.115198i	−0.848812	+	0.528695i	$0.822682\pi$
$348$		0			0
$349$	2.23607	−	6.88191i	0.119694	−	0.368380i	−0.873203	−	0.487356i	$-0.837961\pi$
$349$	2.23607	−	6.88191i	0.119694	−	0.368380i	0.992897	+	0.118976i	$0.0379612\pi$
$350$		0			0
$351$	−13.1672			−0.702812
$352$		0			0
$353$			16.0000i			0.851594i	0.904819	+	0.425797i	$0.140006\pi$
$353$			16.0000i			0.851594i	−0.904819	+	0.425797i	$0.859994\pi$
$354$		0			0
$355$	−0.666045	−	4.42226i	−0.0353500	−	0.234709i
$356$		0			0
$357$	−2.90617	−	4.00000i	−0.153811	−	0.211702i
$358$		0			0
$359$	−10.0000	−	30.7768i	−0.527780	−	1.62434i	−0.758753	−	0.651379i	$-0.774191\pi$
$359$	−10.0000	−	30.7768i	−0.527780	−	1.62434i	0.230973	−	0.972960i	$-0.425809\pi$
$360$		0			0
$361$	4.78115	+	3.47371i	0.251640	+	0.182827i
$362$		0			0
$363$	−9.89408	+	9.32624i	−0.519305	+	0.489501i
$364$		0			0
$365$	−0.560044	+	3.37019i	−0.0293140	+	0.176404i
$366$		0			0
$367$	−28.4257	+	9.23607i	−1.48381	+	0.482119i	−0.935248	−	0.353992i	$-0.884824\pi$
$367$	−28.4257	+	9.23607i	−1.48381	+	0.482119i	−0.548561	+	0.836111i	$0.684824\pi$
$368$		0			0
$369$	−0.736068	+	0.534785i	−0.0383182	+	0.0278398i
$370$		0			0
$371$	1.35410	−	4.16750i	0.0703015	−	0.216366i
$372$		0			0
$373$		−	6.56231i		−	0.339783i	−0.985463	−	0.169892i	$-0.945658\pi$
$373$		−	6.56231i		−	0.339783i	0.985463	−	0.169892i	$-0.0543418\pi$
$374$		0			0
$375$	−13.5967	−	2.47214i	−0.702133	−	0.127661i
$376$		0			0
$377$	−10.1311	−	3.29180i	−0.521779	−	0.169536i
$378$		0			0
$379$	−25.9164	+	18.8294i	−1.33124	+	0.967200i	−0.331519	+	0.943449i	$0.607561\pi$
$379$	−25.9164	+	18.8294i	−1.33124	+	0.967200i	−0.999718	+	0.0237512i	$0.992439\pi$
$380$		0			0
$381$	−1.09017	−	3.35520i	−0.0558511	−	0.171892i
$382$		0			0
$383$	13.0575	−	17.9721i	0.667208	−	0.918333i	−0.332485	−	0.943109i	$-0.607887\pi$
$383$	13.0575	−	17.9721i	0.667208	−	0.918333i	0.999693	+	0.0247753i	$0.00788704\pi$
$384$		0			0
$385$	4.27272	−	1.65890i	0.217758	−	0.0845456i
$386$		0			0
$387$	7.33094	−	10.0902i	0.372652	−	0.512912i
$388$		0			0
$389$	−7.76393	−	23.8949i	−0.393647	−	1.21152i	−0.930010	−	0.367534i	$-0.880202\pi$
$389$	−7.76393	−	23.8949i	−0.393647	−	1.21152i	0.536363	−	0.843987i	$-0.319798\pi$
$390$		0			0
$391$	24.1803	−	17.5680i	1.22285	−	0.888454i
$392$		0			0
$393$	9.40456	+	3.05573i	0.474398	+	0.154141i
$394$		0			0
$395$	12.3607	−	6.18034i	0.621933	−	0.310967i
$396$		0			0
$397$		−	12.3262i		−	0.618636i	−0.950959	−	0.309318i	$-0.899899\pi$
$397$		−	12.3262i		−	0.618636i	0.950959	−	0.309318i	$-0.100101\pi$
$398$		0			0
$399$	−0.854102	+	2.62866i	−0.0427586	+	0.131597i
$400$		0			0
$401$	−0.0729490	+	0.0530006i	−0.00364290	+	0.00264672i	−0.589605	−	0.807692i	$-0.700717\pi$
$401$	−0.0729490	+	0.0530006i	−0.00364290	+	0.00264672i	0.585962	+	0.810338i	$0.300717\pi$
$402$		0			0
$403$	4.53077	−	1.47214i	0.225694	−	0.0733323i
$404$		0			0
$405$	−5.33016	−	0.885743i	−0.264858	−	0.0440129i
$406$		0			0
$407$	−13.9883	−	12.3090i	−0.693376	−	0.610135i
$408$		0			0
$409$	21.0172	+	15.2699i	1.03923	+	0.755048i	0.970136	−	0.242562i	$-0.0779877\pi$
$409$	21.0172	+	15.2699i	1.03923	+	0.755048i	0.0690987	+	0.997610i	$0.477988\pi$
$410$		0			0
$411$	−8.18034	−	25.1765i	−0.403506	−	1.24187i
$412$		0			0
$413$	3.94298	+	5.42705i	0.194022	+	0.267048i
$414$		0			0
$415$	−22.5101	+	3.39028i	−1.10498	+	0.166422i
$416$		0			0
$417$			0.403252i			0.0197473i
$418$		0			0
$419$	35.9787			1.75768			0.878838	−	0.477121i	$-0.158320\pi$
$419$	35.9787			1.75768			0.878838	+	0.477121i	$0.158320\pi$
$420$		0			0
$421$	0.618034	−	1.90211i	0.0301211	−	0.0927033i	−0.934866	−	0.355001i	$-0.884480\pi$
$421$	0.618034	−	1.90211i	0.0301211	−	0.0927033i	0.964987	+	0.262298i	$0.0844804\pi$
$422$		0			0
$423$	−8.73102	−	12.0172i	−0.424517	−	0.584297i
$424$		0			0
$425$	10.4661	−	30.6215i	0.507680	−	1.48536i
$426$		0			0
$427$	−2.52265	+	3.47214i	−0.122080	+	0.168028i
$428$		0			0
$429$	−8.96556	−	3.86974i	−0.432861	−	0.186833i
$430$		0			0
$431$	22.7984	+	16.5640i	1.09816	+	0.797859i	0.980758	−	0.195225i	$-0.0625438\pi$
$431$	22.7984	+	16.5640i	1.09816	+	0.797859i	0.117401	+	0.993085i	$0.462544\pi$
$432$		0			0
$433$	7.05342	−	2.29180i	0.338966	−	0.110137i	−0.134588	−	0.990902i	$-0.542971\pi$
$433$	7.05342	−	2.29180i	0.338966	−	0.110137i	0.473554	+	0.880765i	$0.342971\pi$
$434$		0			0
$435$	−10.9705	−	5.69507i	−0.525997	−	0.273058i
$436$		0			0
$437$	−15.8904	−	5.16312i	−0.760143	−	0.246985i
$438$		0			0
$439$	−6.18034			−0.294972			−0.147486	−	0.989064i	$-0.547118\pi$
$439$	−6.18034			−0.294972			−0.147486	+	0.989064i	$0.547118\pi$
$440$		0			0
$441$	9.74265			0.463936
$442$		0			0
$443$	0.171513	+	0.0557281i	0.00814885	+	0.00264772i	0.313089	−	0.949724i	$-0.398636\pi$
$443$	0.171513	+	0.0557281i	0.00814885	+	0.00264772i	−0.304940	+	0.952372i	$0.598636\pi$
$444$		0			0
$445$	−11.7263	+	22.5885i	−0.555878	+	1.07080i
$446$		0			0
$447$	25.5195	−	8.29180i	1.20703	−	0.392188i
$448$		0			0
$449$	−16.8713	−	12.2577i	−0.796207	−	0.578478i	0.113592	−	0.993527i	$-0.463764\pi$
$449$	−16.8713	−	12.2577i	−0.796207	−	0.578478i	−0.909799	+	0.415049i	$0.863764\pi$
$450$		0			0
$451$	−2.00000	+	0.449028i	−0.0941763	+	0.0211439i
$452$		0			0
$453$	−9.95959	+	13.7082i	−0.467943	+	0.644068i
$454$		0			0
$455$	2.30991	+	2.34525i	0.108290	+	0.109947i
$456$		0			0
$457$	4.80828	+	6.61803i	0.224922	+	0.309579i	0.906532	−	0.422137i	$-0.138720\pi$
$457$	4.80828	+	6.61803i	0.224922	+	0.309579i	−0.681610	+	0.731716i	$0.738720\pi$
$458$		0			0
$459$	11.0557	−	34.0260i	0.516037	−	1.58820i
$460$		0			0
$461$	−9.70820			−0.452156			−0.226078	−	0.974109i	$-0.572590\pi$
$461$	−9.70820			−0.452156			−0.226078	+	0.974109i	$0.572590\pi$
$462$		0			0
$463$		−	1.32624i		−	0.0616355i	−0.999525	−	0.0308178i	$-0.990189\pi$
$463$		−	1.32624i		−	0.0616355i	0.999525	−	0.0308178i	$-0.00981115\pi$
$464$		0			0
$465$	5.46621	−	0.823277i	0.253490	−	0.0381786i
$466$		0			0
$467$	10.9637	+	15.0902i	0.507337	+	0.698290i	0.983467	−	0.181085i	$-0.0579609\pi$
$467$	10.9637	+	15.0902i	0.507337	+	0.698290i	−0.476130	+	0.879375i	$0.657961\pi$
$468$		0			0
$469$	−1.76393	−	5.42882i	−0.0814508	−	0.250680i
$470$		0			0
$471$	−6.14590	−	4.46526i	−0.283188	−	0.205748i
$472$		0			0
$473$	24.1724	−	14.3262i	1.11145	−	0.658721i
$474$		0			0
$475$	−17.2877	+	5.32832i	−0.793212	+	0.244480i
$476$		0			0
$477$	9.92684	−	3.22542i	0.454519	−	0.147682i
$478$		0			0
$479$	22.0344	−	16.0090i	1.00678	−	0.731468i	0.0432482	−	0.999064i	$-0.486229\pi$
$479$	22.0344	−	16.0090i	1.00678	−	0.731468i	0.963531	+	0.267596i	$0.0862294\pi$
$480$		0			0
$481$	4.13525	−	12.7270i	0.188551	−	0.580302i
$482$		0			0
$483$			3.52786i			0.160523i
$484$		0			0
$485$	9.23607	+	18.4721i	0.419388	+	0.838776i
$486$		0			0
$487$	38.9403	+	12.6525i	1.76455	+	0.573338i	0.997656	−	0.0684303i	$-0.0217991\pi$
$487$	38.9403	+	12.6525i	1.76455	+	0.573338i	0.766898	+	0.641769i	$0.221799\pi$
$488$		0			0
$489$	−9.41641	+	6.84142i	−0.425825	+	0.309380i
$490$		0			0
$491$	−8.11803	−	24.9847i	−0.366362	−	1.12755i	−0.949124	−	0.314903i	$-0.898028\pi$
$491$	−8.11803	−	24.9847i	−0.366362	−	1.12755i	0.582762	−	0.812643i	$-0.301972\pi$
$492$		0			0
$493$	17.0130	−	23.4164i	0.766228	−	1.05462i
$494$		0			0
$495$	9.17897	+	5.91115i	0.412564	+	0.265686i
$496$		0			0
$497$	−0.726543	+	1.00000i	−0.0325899	+	0.0448561i
$498$		0			0
$499$	−0.100813	−	0.310271i	−0.00451301	−	0.0138896i	0.948775	−	0.315954i	$-0.102324\pi$
$499$	−0.100813	−	0.310271i	−0.00451301	−	0.0138896i	−0.953288	+	0.302064i	$0.902324\pi$
$500$		0			0
$501$	−13.3262	+	9.68208i	−0.595372	+	0.432563i
$502$		0			0
$503$	−11.7759	−	3.82624i	−0.525064	−	0.170604i	0.0344785	−	0.999405i	$-0.489023\pi$
$503$	−11.7759	−	3.82624i	−0.525064	−	0.170604i	−0.559542	+	0.828802i	$0.689023\pi$
$504$		0			0
$505$	39.4164	−	19.7082i	1.75401	−	0.877004i
$506$		0			0
$507$			9.05573i			0.402179i
$508$		0			0
$509$	3.61803	−	11.1352i	0.160367	−	0.493557i	−0.838298	−	0.545212i	$-0.816449\pi$
$509$	3.61803	−	11.1352i	0.160367	−	0.493557i	0.998665	+	0.0516541i	$0.0164493\pi$
$510$		0			0
$511$	0.763932	−	0.555029i	0.0337944	−	0.0245530i
$512$		0			0
$513$	−19.0211	+	6.18034i	−0.839803	+	0.272869i
$514$		0			0
$515$	2.51240	−	15.1189i	0.110709	−	0.666219i
$516$		0			0
$517$	−7.33094	−	32.6525i	−0.322414	−	1.43605i
$518$		0			0
$519$	1.85410	+	1.34708i	0.0813860	+	0.0591304i
$520$		0			0
$521$	−9.60739	−	29.5685i	−0.420907	−	1.29542i	−0.906859	−	0.421434i	$-0.861527\pi$
$521$	−9.60739	−	29.5685i	−0.420907	−	1.29542i	0.485952	−	0.873986i	$-0.338473\pi$
$522$		0			0
$523$	0.661030	+	0.909830i	0.0289048	+	0.0397841i	0.823225	−	0.567716i	$-0.192173\pi$
$523$	0.661030	+	0.909830i	0.0289048	+	0.0397841i	−0.794320	+	0.607500i	$0.792173\pi$
$524$		0			0
$525$	2.19797	+	3.12390i	0.0959271	+	0.136338i
$526$		0			0
$527$			12.9443i			0.563861i
$528$		0			0
$529$	1.67376			0.0727723
$530$		0			0
$531$	−4.93769	+	15.1967i	−0.214278	+	0.659479i
$532$		0			0
$533$	−0.865300	−	1.19098i	−0.0374803	−	0.0515872i
$534$		0			0
$535$	24.5598	−	24.1897i	1.06181	−	1.04581i
$536$		0			0
$537$	−6.73542	+	9.27051i	−0.290655	+	0.400052i
$538$		0			0
$539$	20.1525	+	8.69827i	0.868029	+	0.374661i
$540$		0			0
$541$	−12.7984	−	9.29856i	−0.550245	−	0.399776i	0.277631	−	0.960688i	$-0.410451\pi$
$541$	−12.7984	−	9.29856i	−0.550245	−	0.399776i	−0.827876	+	0.560911i	$0.810451\pi$
$542$		0			0
$543$	−23.3804	+	7.59675i	−1.00335	+	0.326008i
$544$		0			0
$545$	5.69507	−	10.9705i	0.243950	−	0.469926i
$546$		0			0
$547$	18.9151	+	6.14590i	0.808753	+	0.262780i	0.684069	−	0.729417i	$-0.260209\pi$
$547$	18.9151	+	6.14590i	0.808753	+	0.262780i	0.124683	+	0.992197i	$0.460209\pi$
$548$		0			0
$549$	−10.2229			−0.436303
$550$		0			0
$551$	−16.1803			−0.689306
$552$		0			0
$553$	−3.63271	−	1.18034i	−0.154479	−	0.0501932i
$554$		0			0
$555$	7.15433	−	13.7815i	0.303684	−	0.584993i
$556$		0			0
$557$	−10.0453	+	3.26393i	−0.425635	+	0.138297i	−0.513999	−	0.857791i	$-0.671836\pi$
$557$	−10.0453	+	3.26393i	−0.425635	+	0.138297i	0.0883634	+	0.996088i	$0.471836\pi$
$558$		0			0
$559$	16.3262	+	11.8617i	0.690526	+	0.501697i
$560$		0			0
$561$	17.5279	−	19.9192i	0.740027	−	0.840989i
$562$		0			0
$563$	−26.8011	+	36.8885i	−1.12953	+	1.55467i	−0.340575	+	0.940217i	$0.610622\pi$
$563$	−26.8011	+	36.8885i	−1.12953	+	1.55467i	−0.788956	+	0.614450i	$0.789378\pi$
$564$		0			0
$565$	15.0012	−	14.7752i	0.631107	−	0.621597i
$566$		0			0
$567$	0.877812	+	1.20820i	0.0368646	+	0.0507398i
$568$		0			0
$569$	−1.80902	+	5.56758i	−0.0758379	+	0.233405i	−0.981788	−	0.189979i	$-0.939158\pi$
$569$	−1.80902	+	5.56758i	−0.0758379	+	0.233405i	0.905950	+	0.423384i	$0.139158\pi$
$570$		0			0
$571$	−44.6869			−1.87009			−0.935045	−	0.354530i	$-0.884641\pi$
$571$	−44.6869			−1.87009			−0.935045	+	0.354530i	$0.884641\pi$
$572$		0			0
$573$			11.1935i			0.467615i
$574$		0			0
$575$	−18.8842	+	13.2869i	−0.787527	+	0.554102i
$576$		0			0
$577$	10.3026	+	14.1803i	0.428904	+	0.590335i	0.967701	−	0.252100i	$-0.0811212\pi$
$577$	10.3026	+	14.1803i	0.428904	+	0.590335i	−0.538797	+	0.842435i	$0.681121\pi$
$578$		0			0
$579$	−5.05573	−	15.5599i	−0.210109	−	0.646649i
$580$		0			0
$581$	5.09017	+	3.69822i	0.211176	+	0.153428i
$582$		0			0
$583$	23.4131	+	2.19098i	0.969673	+	0.0907412i
$584$		0			0
$585$	−1.28535	+	7.73488i	−0.0531426	+	0.319798i
$586$		0			0
$587$	22.9969	−	7.47214i	0.949182	−	0.308408i	0.206799	−	0.978383i	$-0.433695\pi$
$587$	22.9969	−	7.47214i	0.949182	−	0.308408i	0.742383	+	0.669975i	$0.233695\pi$
$588$		0			0
$589$	5.85410	−	4.25325i	0.241214	−	0.175252i
$590$		0			0
$591$	−10.0132	+	30.8173i	−0.411886	+	1.26766i
$592$		0			0
$593$		−	6.11146i		−	0.250967i	−0.992096	−	0.125484i	$-0.959952\pi$
$593$		−	6.11146i		−	0.250967i	0.992096	−	0.125484i	$-0.0400483\pi$
$594$		0			0
$595$	−8.00000	+	4.00000i	−0.327968	+	0.163984i
$596$		0			0
$597$	−6.49839	−	2.11146i	−0.265962	−	0.0864161i
$598$		0			0
$599$	5.00000	−	3.63271i	0.204294	−	0.148429i	−0.480934	−	0.876757i	$-0.659702\pi$
$599$	5.00000	−	3.63271i	0.204294	−	0.148429i	0.685228	+	0.728328i	$0.259702\pi$
$600$		0			0
$601$	0.0278640	+	0.0857567i	0.00113660	+	0.00349809i	0.951623	−	0.307267i	$-0.0994146\pi$
$601$	0.0278640	+	0.0857567i	0.00113660	+	0.00349809i	−0.950487	+	0.310766i	$0.899415\pi$
$602$		0			0
$603$	7.99197	−	11.0000i	0.325458	−	0.447955i
$604$		0			0
$605$	13.7090	+	20.4221i	0.557351	+	0.830277i
$606$		0			0
$607$	−19.7072	+	27.1246i	−0.799890	+	1.10095i	0.192916	+	0.981215i	$0.438206\pi$
$607$	−19.7072	+	27.1246i	−0.799890	+	1.10095i	−0.992805	+	0.119739i	$0.961794\pi$
$608$		0			0
$609$	1.05573	+	3.24920i	0.0427803	+	0.131664i
$610$		0			0
$611$	19.4443	−	14.1271i	0.786631	−	0.571521i
$612$		0			0
$613$	5.70634	+	1.85410i	0.230477	+	0.0748865i	0.421979	−	0.906606i	$-0.361336\pi$
$613$	5.70634	+	1.85410i	0.230477	+	0.0748865i	−0.191502	+	0.981492i	$0.561336\pi$
$614$		0			0
$615$	−0.763932	−	1.52786i	−0.0308047	−	0.0616094i
$616$		0			0
$617$			9.05573i			0.364570i	0.983246	+	0.182285i	$0.0583493\pi$
$617$			9.05573i			0.364570i	−0.983246	+	0.182285i	$0.941651\pi$
$618$		0			0
$619$	−2.29837	+	7.07367i	−0.0923794	+	0.284315i	−0.986562	−	0.163388i	$-0.947758\pi$
$619$	−2.29837	+	7.07367i	−0.0923794	+	0.284315i	0.894182	+	0.447703i	$0.147758\pi$
$620$		0			0
$621$	−20.6525	+	15.0049i	−0.828755	+	0.602126i
$622$		0			0
$623$	6.69015	−	2.17376i	0.268035	−	0.0870899i
$624$		0			0
$625$	−8.44373	+	23.5309i	−0.337749	+	0.941236i
$626$		0			0
$627$	−14.7679	−	1.38197i	−0.589772	−	0.0551904i
$628$		0			0
$629$	29.4164	+	21.3723i	1.17291	+	0.852168i
$630$		0			0
$631$	−8.38197	−	25.7970i	−0.333681	−	1.02696i	−0.967368	−	0.253375i	$-0.918459\pi$
$631$	−8.38197	−	25.7970i	−0.333681	−	1.02696i	0.633687	−	0.773589i	$-0.281541\pi$
$632$		0			0
$633$	19.2331	+	26.4721i	0.764448	+	1.05217i
$634$		0			0
$635$	−6.31079	+	0.950480i	−0.250436	+	0.0377187i
$636$		0			0
$637$			15.7639i			0.624590i
$638$		0			0
$639$	−2.94427			−0.116474
$640$		0			0
$641$	9.50000	−	29.2380i	0.375227	−	1.15483i	−0.568098	−	0.822961i	$-0.692320\pi$
$641$	9.50000	−	29.2380i	0.375227	−	1.15483i	0.943325	−	0.331870i	$-0.107680\pi$
$642$		0			0
$643$	−12.2452	−	16.8541i	−0.482904	−	0.664661i	0.496155	−	0.868234i	$-0.334745\pi$
$643$	−12.2452	−	16.8541i	−0.482904	−	0.664661i	−0.979060	+	0.203573i	$0.934745\pi$
$644$		0			0
$645$	16.4317	+	16.6831i	0.646999	+	0.656897i
$646$		0			0
$647$	16.3270	−	22.4721i	0.641879	−	0.883471i	−0.356835	−	0.934167i	$-0.616144\pi$
$647$	16.3270	−	22.4721i	0.641879	−	0.883471i	0.998714	+	0.0506966i	$0.0161442\pi$
$648$		0			0
$649$	−23.7812	+	27.0256i	−0.933492	+	1.06085i
$650$		0			0
$651$	−1.23607	−	0.898056i	−0.0484453	−	0.0351976i
$652$		0			0
$653$	−27.7849	+	9.02786i	−1.08731	+	0.353288i	−0.797205	−	0.603708i	$-0.793689\pi$
$653$	−27.7849	+	9.02786i	−1.08731	+	0.353288i	−0.290102	+	0.956996i	$0.593689\pi$
$654$		0			0
$655$	8.24199	−	15.8767i	0.322041	−	0.620354i
$656$		0			0
$657$	2.13914	+	0.695048i	0.0834558	+	0.0271164i
$658$		0			0
$659$	−11.3820			−0.443378			−0.221689	−	0.975117i	$-0.571157\pi$
$659$	−11.3820			−0.443378			−0.221689	+	0.975117i	$0.571157\pi$
$660$		0			0
$661$	−5.88854			−0.229038			−0.114519	−	0.993421i	$-0.536533\pi$
$661$	−5.88854			−0.229038			−0.114519	+	0.993421i	$0.536533\pi$
$662$		0			0
$663$	18.1231	+	5.88854i	0.703842	+	0.228692i
$664$		0			0
$665$	4.43767	+	2.30371i	0.172086	+	0.0893339i
$666$		0			0
$667$	−19.6417	+	6.38197i	−0.760529	+	0.247111i
$668$		0			0
$669$	−19.0902	−	13.8698i	−0.738069	−	0.536238i
$670$		0			0
$671$	−21.1459	−	9.12705i	−0.816328	−	0.352346i
$672$		0			0
$673$	1.28157	−	1.76393i	0.0494010	−	0.0679946i	−0.783602	−	0.621263i	$-0.786620\pi$
$673$	1.28157	−	1.76393i	0.0494010	−	0.0679946i	0.833003	+	0.553269i	$0.186620\pi$
$674$		0			0
$675$	−8.93912	+	26.1539i	−0.344067	+	1.00666i
$676$		0			0
$677$	9.68208	+	13.3262i	0.372113	+	0.512169i	0.953474	−	0.301477i	$-0.0974796\pi$
$677$	9.68208	+	13.3262i	0.372113	+	0.512169i	−0.581361	+	0.813646i	$0.697480\pi$
$678$		0			0
$679$	1.76393	−	5.42882i	0.0676935	−	0.208339i
$680$		0			0
$681$	−14.8328			−0.568395
$682$		0			0
$683$		−	15.5967i		−	0.596793i	−0.954442	−	0.298396i	$-0.903548\pi$
$683$		−	15.5967i		−	0.596793i	0.954442	−	0.298396i	$-0.0964518\pi$
$684$		0			0
$685$	−47.3545	+	7.13215i	−1.80932	+	0.272505i
$686$		0			0
$687$	−5.25731	−	7.23607i	−0.200579	−	0.276073i
$688$		0			0
$689$	5.21885	+	16.0620i	0.198822	+	0.611912i
$690$		0			0
$691$	31.6803	+	23.0171i	1.20518	+	0.875612i	0.994784	−	0.102005i	$-0.0325256\pi$
$691$	31.6803	+	23.0171i	1.20518	+	0.875612i	0.210393	+	0.977617i	$0.432526\pi$
$692$		0			0
$693$	−0.661030	−	2.94427i	−0.0251105	−	0.111844i
$694$		0			0
$695$	0.719622	+	0.119584i	0.0272968	+	0.00453607i
$696$		0			0
$697$	3.80423	−	1.23607i	0.144095	−	0.0468194i
$698$		0			0
$699$	−19.1246	+	13.8948i	−0.723359	+	0.525551i
$700$		0			0
$701$	−8.20163	+	25.2420i	−0.309771	+	0.953378i	0.668082	+	0.744087i	$0.267115\pi$
$701$	−8.20163	+	25.2420i	−0.309771	+	0.953378i	−0.977854	+	0.209290i	$0.932885\pi$
$702$		0			0
$703$		−	20.3262i		−	0.766619i
$704$		0			0
$705$	24.9443	−	12.4721i	0.939456	−	0.469728i
$706$		0			0
$707$	−11.5842	−	3.76393i	−0.435668	−	0.141557i
$708$		0			0
$709$	−3.61803	+	2.62866i	−0.135878	+	0.0987212i	−0.653648	−	0.756799i	$-0.726762\pi$
$709$	−3.61803	+	2.62866i	−0.135878	+	0.0987212i	0.517770	+	0.855520i	$0.326762\pi$
$710$		0			0
$711$	−2.81153	−	8.65300i	−0.105441	−	0.324513i
$712$		0			0
$713$	5.42882	−	7.47214i	0.203311	−	0.279834i
$714$		0			0
$715$	−9.56444	+	14.8519i	−0.357690	+	0.555429i
$716$		0			0
$717$	5.25731	−	7.23607i	0.196338	−	0.270236i
$718$		0			0
$719$	6.05573	+	18.6376i	0.225841	+	0.695066i	0.998205	+	0.0598864i	$0.0190738\pi$
$719$	6.05573	+	18.6376i	0.225841	+	0.695066i	−0.772365	+	0.635179i	$0.780926\pi$
$720$		0			0
$721$	−3.42705	+	2.48990i	−0.127630	+	0.0927287i
$722$		0			0
$723$	−5.77185	−	1.87539i	−0.214657	−	0.0697464i
$724$		0			0
$725$	−13.4164	+	17.8885i	−0.498273	+	0.664364i
$726$		0			0
$727$		−	31.7426i		−	1.17727i	−0.808399	−	0.588635i	$-0.799666\pi$
$727$		−	31.7426i		−	1.17727i	0.808399	−	0.588635i	$-0.200334\pi$
$728$		0			0
$729$	−7.43363	+	22.8784i	−0.275320	+	0.847347i
$730$		0			0
$731$	−44.3607	+	32.2299i	−1.64074	+	1.19207i
$732$		0			0
$733$	−8.95554	+	2.90983i	−0.330780	+	0.107477i	−0.469699	−	0.882827i	$-0.655637\pi$
$733$	−8.95554	+	2.90983i	−0.330780	+	0.107477i	0.138918	+	0.990304i	$0.455637\pi$
$734$		0			0
$735$	−2.99853	+	18.0444i	−0.110603	+	0.665576i
$736$		0			0
$737$	26.3521	−	15.6180i	0.970691	−	0.575298i
$738$		0			0
$739$	−6.97214	−	5.06555i	−0.256474	−	0.186339i	0.452117	−	0.891959i	$-0.350669\pi$
$739$	−6.97214	−	5.06555i	−0.256474	−	0.186339i	−0.708591	+	0.705619i	$0.750669\pi$
$740$		0			0
$741$	−3.29180	−	10.1311i	−0.120927	−	0.372175i
$742$		0			0
$743$	9.21281	+	12.6803i	0.337985	+	0.465197i	0.943852	−	0.330370i	$-0.107173\pi$
$743$	9.21281	+	12.6803i	0.337985	+	0.465197i	−0.605867	+	0.795566i	$0.707173\pi$
$744$		0			0
$745$	−7.22932	−	47.9997i	−0.264862	−	1.75857i
$746$		0			0
$747$			14.9868i			0.548340i
$748$		0			0
$749$	−9.52786			−0.348141
$750$		0			0
$751$	7.14590	−	21.9928i	0.260758	−	0.802529i	−0.731883	−	0.681430i	$-0.761358\pi$
$751$	7.14590	−	21.9928i	0.260758	−	0.802529i	0.992640	−	0.121099i	$-0.0386418\pi$
$752$		0			0
$753$	4.93931	+	6.79837i	0.179998	+	0.247747i
$754$		0			0
$755$	21.5094	+	21.8385i	0.782808	+	0.794784i
$756$		0			0
$757$	−4.54328	+	6.25329i	−0.165128	+	0.227280i	−0.883560	−	0.468318i	$-0.844860\pi$
$757$	−4.54328	+	6.25329i	−0.165128	+	0.227280i	0.718432	+	0.695597i	$0.244860\pi$
$758$		0			0
$759$	−18.4721	+	4.14725i	−0.670496	+	0.150536i
$760$		0			0
$761$	8.38197	+	6.08985i	0.303846	+	0.220757i	0.729251	−	0.684246i	$-0.239868\pi$
$761$	8.38197	+	6.08985i	0.303846	+	0.220757i	−0.425405	+	0.905003i	$0.639868\pi$
$762$		0			0
$763$	−3.24920	+	1.05573i	−0.117629	+	0.0382199i
$764$		0			0
$765$	−18.9089	−	9.81607i	−0.683652	−	0.354901i
$766$		0			0
$767$	−24.5887	−	7.98936i	−0.887847	−	0.288479i
$768$		0			0
$769$	37.0344			1.33550			0.667748	−	0.744387i	$-0.267258\pi$
$769$	37.0344			1.33550			0.667748	+	0.744387i	$0.267258\pi$
$770$		0			0
$771$	25.8885			0.932353
$772$		0			0
$773$	−37.5200	−	12.1910i	−1.34950	−	0.438479i	−0.456976	−	0.889479i	$-0.651068\pi$
$773$	−37.5200	−	12.1910i	−1.34950	−	0.438479i	−0.892524	+	0.451000i	$0.851068\pi$
$774$		0			0
$775$	0.151820	−	9.99885i	0.00545353	−	0.359169i
$776$		0			0
$777$	−4.08174	+	1.32624i	−0.146432	+	0.0475785i
$778$		0			0
$779$	−1.80902	−	1.31433i	−0.0648148	−	0.0470907i
$780$		0			0
$781$	−6.09017	−	2.62866i	−0.217923	−	0.0940607i
$782$		0			0
$783$	−14.5309	+	20.0000i	−0.519290	+	0.714742i
$784$		0			0
$785$	−9.79101	+	9.64347i	−0.349456	+	0.344190i
$786$		0			0
$787$	10.9637	+	15.0902i	0.390812	+	0.537906i	0.958408	−	0.285400i	$-0.0921266\pi$
$787$	10.9637	+	15.0902i	0.390812	+	0.537906i	−0.567596	+	0.823307i	$0.692127\pi$
$788$		0			0
$789$	1.96556	−	6.04937i	0.0699757	−	0.215363i
$790$		0			0
$791$	−5.81966			−0.206923
$792$		0			0
$793$		−	16.5410i		−	0.587389i
$794$		0			0
$795$	2.91859	+	19.3782i	0.103512	+	0.687274i
$796$		0			0
$797$	3.30220	+	4.54508i	0.116970	+	0.160995i	0.863487	−	0.504371i	$-0.168276\pi$
$797$	3.30220	+	4.54508i	0.116970	+	0.160995i	−0.746517	+	0.665366i	$0.768276\pi$
$798$		0			0
$799$	20.1803	+	62.1087i	0.713929	+	2.19725i
$800$		0			0
$801$	13.5557	+	9.84881i	0.478968	+	0.347991i
$802$		0			0
$803$	3.80423	+	3.34752i	0.134248	+	0.118132i
$804$		0			0
$805$	6.29563	+	1.04618i	0.221892	+	0.0368730i
$806$		0			0
$807$	26.2866	−	8.54102i	0.925331	−	0.300658i
$808$		0			0
$809$	−2.07295	+	1.50609i	−0.0728810	+	0.0529512i	−0.623629	−	0.781720i	$-0.714342\pi$
$809$	−2.07295	+	1.50609i	−0.0728810	+	0.0529512i	0.550748	+	0.834671i	$0.314342\pi$
$810$		0			0
$811$	13.0238	−	40.0831i	0.457327	−	1.40751i	−0.411053	−	0.911611i	$-0.634839\pi$
$811$	13.0238	−	40.0831i	0.457327	−	1.40751i	0.868381	−	0.495898i	$-0.165161\pi$
$812$		0			0
$813$			1.75078i			0.0614024i
$814$		0			0
$815$	9.41641	+	18.8328i	0.329842	+	0.659685i
$816$		0			0
$817$	29.1522	+	9.47214i	1.01991	+	0.331388i
$818$		0			0
$819$	1.75329	−	1.27384i	0.0612649	−	0.0445115i
$820$		0			0
$821$	0.819660	+	2.52265i	0.0286063	+	0.0880412i	0.964340	−	0.264665i	$-0.0852614\pi$
$821$	0.819660	+	2.52265i	0.0286063	+	0.0880412i	−0.935734	+	0.352706i	$0.885261\pi$
$822$		0			0
$823$	−3.79171	+	5.21885i	−0.132171	+	0.181918i	−0.869973	−	0.493100i	$-0.835864\pi$
$823$	−3.79171	+	5.21885i	−0.132171	+	0.181918i	0.737802	+	0.675017i	$0.235864\pi$
$824$		0			0
$825$	−13.7731	+	15.1811i	−0.479517	+	0.528537i
$826$		0			0
$827$	5.19180	−	7.14590i	0.180537	−	0.248487i	−0.709152	−	0.705056i	$-0.750922\pi$
$827$	5.19180	−	7.14590i	0.180537	−	0.248487i	0.889688	+	0.456569i	$0.150922\pi$
$828$		0			0
$829$	7.88854	+	24.2784i	0.273980	+	0.843225i	0.989487	+	0.144619i	$0.0461958\pi$
$829$	7.88854	+	24.2784i	0.273980	+	0.843225i	−0.715507	+	0.698606i	$0.753804\pi$
$830$		0			0
$831$	0.0344419	−	0.0250235i	0.00119477	−	0.000868055i
$832$		0			0
$833$	−40.7364	−	13.2361i	−1.41143	−	0.458603i
$834$		0			0
$835$	13.3262	+	26.6525i	0.461173	+	0.922347i
$836$		0			0
$837$		−	11.0557i		−	0.382142i
$838$		0			0
$839$	−2.23607	+	6.88191i	−0.0771976	+	0.237590i	−0.982207	−	0.187802i	$-0.939864\pi$
$839$	−2.23607	+	6.88191i	−0.0771976	+	0.237590i	0.905009	+	0.425392i	$0.139864\pi$
$840$		0			0
$841$	7.28115	−	5.29007i	0.251074	−	0.182416i
$842$		0			0
$843$	10.6456	−	3.45898i	0.366656	−	0.119134i
$844$		0			0
$845$	16.1604	+	2.68546i	0.555933	+	0.0923826i
$846$		0			0
$847$	1.26133	−	6.68034i	0.0433397	−	0.229539i
$848$		0			0
$849$	0.180340	+	0.131025i	0.00618925	+	0.00449675i
$850$		0			0
$851$	−8.01722	−	24.6745i	−0.274827	−	0.845830i
$852$		0			0
$853$	−3.09793	−	4.26393i	−0.106071	−	0.145994i	0.752682	−	0.658385i	$-0.228760\pi$
$853$	−3.09793	−	4.26393i	−0.106071	−	0.145994i	−0.858753	+	0.512391i	$0.828760\pi$
$854$		0			0
$855$	1.77376	+	11.7770i	0.0606612	+	0.402765i
$856$		0			0
$857$		−	8.18034i		−	0.279435i	−0.990191	−	0.139718i	$-0.955381\pi$
$857$		−	8.18034i		−	0.279435i	0.990191	−	0.139718i	$-0.0446195\pi$
$858$		0			0
$859$	8.61803			0.294044			0.147022	−	0.989133i	$-0.453031\pi$
$859$	8.61803			0.294044			0.147022	+	0.989133i	$0.453031\pi$
$860$		0			0
$861$	−0.145898	+	0.449028i	−0.00497219	+	0.0153028i
$862$		0			0
$863$	13.5393	+	18.6353i	0.460883	+	0.634351i	0.974692	−	0.223554i	$-0.0717658\pi$
$863$	13.5393	+	18.6353i	0.460883	+	0.634351i	−0.513808	+	0.857905i	$0.671766\pi$
$864$		0			0
$865$	2.95376	−	2.90925i	0.100431	−	0.0989176i
$866$		0			0
$867$	−18.0826	+	24.8885i	−0.614117	+	0.845259i
$868$		0			0
$869$	1.90983	−	20.4087i	0.0647865	−	0.692318i
$870$		0			0
$871$	17.7984	+	12.9313i	0.603075	+	0.438160i
$872$		0			0
$873$	12.9313	−	4.20163i	0.437657	−	0.142203i
$874$		0			0
$875$	6.22654	−	2.99598i	0.210496	−	0.101283i
$876$		0			0
$877$	49.3287	+	16.0279i	1.66571	+	0.541223i	0.982057	−	0.188583i	$-0.0603896\pi$
$877$	49.3287	+	16.0279i	1.66571	+	0.541223i	0.683654	+	0.729806i	$0.260390\pi$
$878$		0			0
$879$	36.9017			1.24466
$880$		0			0
$881$	6.79837			0.229043			0.114522	−	0.993421i	$-0.463467\pi$
$881$	6.79837			0.229043			0.114522	+	0.993421i	$0.463467\pi$
$882$		0			0
$883$	−13.5923	−	4.41641i	−0.457418	−	0.148624i	0.0712400	−	0.997459i	$-0.477304\pi$
$883$	−13.5923	−	4.41641i	−0.457418	−	0.148624i	−0.528657	+	0.848835i	$0.677304\pi$
$884$		0			0
$885$	−26.6260	−	13.8222i	−0.895024	−	0.464629i
$886$		0			0
$887$	−37.2425	+	12.1008i	−1.25048	+	0.406306i	−0.858093	−	0.513495i	$-0.828351\pi$
$887$	−37.2425	+	12.1008i	−1.25048	+	0.406306i	−0.392387	+	0.919800i	$0.628351\pi$
$888$		0			0
$889$	1.42705	+	1.03681i	0.0478618	+	0.0347736i
$890$		0			0
$891$	−5.29431	+	6.01661i	−0.177366	+	0.201564i
$892$		0			0
$893$	21.4580	−	29.5344i	0.718066	−	0.988332i
$894$		0			0
$895$	14.5463	+	14.7688i	0.486228	+	0.493667i
$896$		0			0
$897$	−7.99197	−	11.0000i	−0.266844	−	0.367279i
$898$		0			0
$899$	2.76393	−	8.50651i	0.0921823	−	0.283708i
$900$		0			0
$901$	−45.8885			−1.52877
$902$		0			0
$903$		−	6.47214i		−	0.215379i
$904$		0			0
$905$	6.62333	+	43.9762i	0.220167	+	1.46182i
$906$		0			0
$907$	−17.3310	−	23.8541i	−0.575467	−	0.792062i	0.417722	−	0.908575i	$-0.362829\pi$
$907$	−17.3310	−	23.8541i	−0.575467	−	0.792062i	−0.993189	+	0.116512i	$0.962829\pi$
$908$		0			0
$909$	−8.96556	−	27.5932i	−0.297369	−	0.915207i
$910$		0			0
$911$	−19.5623	−	14.2128i	−0.648128	−	0.470893i	0.214505	−	0.976723i	$-0.431186\pi$
$911$	−19.5623	−	14.2128i	−0.648128	−	0.470893i	−0.862633	+	0.505830i	$0.831186\pi$
$912$		0			0
$913$	−13.3803	+	31.0000i	−0.442823	+	1.02595i
$914$		0			0
$915$	3.14635	−	18.9339i	0.104015	−	0.625934i
$916$		0			0
$917$	−4.70228	+	1.52786i	−0.155283	+	0.0504545i
$918$		0			0
$919$	−8.09017	+	5.87785i	−0.266870	+	0.193892i	−0.713170	−	0.700991i	$-0.752741\pi$
$919$	−8.09017	+	5.87785i	−0.266870	+	0.193892i	0.446300	+	0.894883i	$0.352741\pi$
$920$		0			0
$921$	5.81966	−	17.9111i	0.191764	−	0.590190i
$922$		0			0
$923$		−	4.76393i		−	0.156807i
$924$		0			0
$925$	−22.4721	−	16.8541i	−0.738879	−	0.554159i
$926$		0			0
$927$	−9.59632	−	3.11803i	−0.315185	−	0.102410i
$928$		0			0
$929$	−5.26393	+	3.82447i	−0.172704	+	0.125477i	−0.670779	−	0.741657i	$-0.734040\pi$
$929$	−5.26393	+	3.82447i	−0.172704	+	0.125477i	0.498075	+	0.867134i	$0.334040\pi$
$930$		0			0
$931$	7.39919	+	22.7724i	0.242499	+	0.746334i
$932$		0			0
$933$	3.03719	−	4.18034i	0.0994333	−	0.136858i
$934$		0			0
$935$	−30.3488	−	37.1863i	−0.992513	−	1.21612i
$936$		0			0
$937$	−31.3319	+	43.1246i	−1.02357	+	1.40882i	−0.113895	+	0.993493i	$0.536333\pi$
$937$	−31.3319	+	43.1246i	−1.02357	+	1.40882i	−0.909672	+	0.415327i	$0.863667\pi$
$938$		0			0
$939$	−4.40325	−	13.5518i	−0.143695	−	0.442247i
$940$		0			0
$941$	−16.0902	+	11.6902i	−0.524525	+	0.381089i	−0.818306	−	0.574783i	$-0.805086\pi$
$941$	−16.0902	+	11.6902i	−0.524525	+	0.381089i	0.293781	+	0.955873i	$0.405086\pi$
$942$		0			0
$943$	−2.71441	−	0.881966i	−0.0883934	−	0.0287208i
$944$		0			0
$945$	6.83282	−	3.41641i	0.222272	−	0.111136i
$946$		0			0
$947$		−	28.0000i		−	0.909878i	−0.890523	−	0.454939i	$-0.849661\pi$
$947$		−	28.0000i		−	0.909878i	0.890523	−	0.454939i	$-0.150339\pi$
$948$		0			0
$949$	−1.12461	+	3.46120i	−0.0365064	+	0.112355i
$950$		0			0
$951$	14.3820	−	10.4491i	0.466367	−	0.338836i
$952$		0			0
$953$	6.43288	−	2.09017i	0.208381	−	0.0677072i	−0.202966	−	0.979186i	$-0.565058\pi$
$953$	6.43288	−	2.09017i	0.208381	−	0.0677072i	0.411348	+	0.911478i	$0.365058\pi$
$954$		0			0
$955$	19.9753	+	3.31941i	0.646386	+	0.107414i
$956$		0			0
$957$	−15.7719	+	9.34752i	−0.509834	+	0.302163i
$958$		0			0
$959$	10.7082	+	7.77997i	0.345786	+	0.251228i
$960$		0			0
$961$	−8.34346	−	25.6785i	−0.269144	−	0.828340i
$962$		0			0
$963$	−13.3398	−	18.3607i	−0.429870	−	0.591665i
$964$		0			0
$965$	−29.2667	+	4.40791i	−0.942127	+	0.141896i
$966$		0			0
$967$			44.5623i			1.43303i	0.697573	+	0.716514i	$0.254263\pi$
$967$			44.5623i			1.43303i	−0.697573	+	0.716514i	$0.745737\pi$
$968$		0			0
$969$	28.9443			0.929824
$970$		0			0
$971$	10.8647	−	33.4382i	0.348666	−	1.07308i	−0.610925	−	0.791688i	$-0.709202\pi$
$971$	10.8647	−	33.4382i	0.348666	−	1.07308i	0.959592	−	0.281396i	$-0.0907975\pi$
$972$		0			0
$973$	−0.118513	−	0.163119i	−0.00379935	−	0.00522935i
$974$		0			0
$975$	−13.9302	−	4.76119i	−0.446122	−	0.152480i
$976$		0			0
$977$	−5.19180	+	7.14590i	−0.166100	+	0.228618i	−0.883951	−	0.467580i	$-0.845126\pi$
$977$	−5.19180	+	7.14590i	−0.166100	+	0.228618i	0.717851	+	0.696197i	$0.245126\pi$
$978$		0			0
$979$	19.2467	+	32.4747i	0.615128	+	1.03790i
$980$		0			0
$981$	−6.58359	−	4.78326i	−0.210198	−	0.152718i
$982$		0			0
$983$	−21.1275	+	6.86475i	−0.673863	+	0.218951i	−0.625907	−	0.779898i	$-0.715271\pi$
$983$	−21.1275	+	6.86475i	−0.673863	+	0.218951i	−0.0479565	+	0.998849i	$0.515271\pi$
$984$		0			0
$985$	52.0255	+	27.0077i	1.65767	+	0.860538i
$986$		0			0
$987$	−7.33094	−	2.38197i	−0.233346	−	0.0758188i
$988$		0			0
$989$	39.1246			1.24409
$990$		0			0
$991$	−35.8197			−1.13785			−0.568925	−	0.822390i	$-0.692640\pi$
$991$	−35.8197			−1.13785			−0.568925	+	0.822390i	$0.692640\pi$
$992$		0			0
$993$	7.15942	+	2.32624i	0.227197	+	0.0738209i
$994$		0			0
$995$	−5.69507	+	10.9705i	−0.180546	+	0.347789i
$996$		0			0
$997$	−25.6255	+	8.32624i	−0.811569	+	0.263695i	−0.685262	−	0.728297i	$-0.740312\pi$
$997$	−25.6255	+	8.32624i	−0.811569	+	0.263695i	−0.126307	+	0.991991i	$0.540312\pi$
$998$		0			0
$999$	−25.1246	−	18.2541i	−0.794908	−	0.577534i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.cd.a.609.2		8
4.3	odd	2		110.2.j.a.59.2	yes	8
5.4	even	2	inner	880.2.cd.a.609.1		8
11.3	even	5	inner	880.2.cd.a.289.1		8
12.11	even	2		990.2.ba.b.829.1		8
20.3	even	4		550.2.h.d.301.1		4
20.7	even	4		550.2.h.e.301.1		4
20.19	odd	2		110.2.j.a.59.1	✓	8
44.3	odd	10		110.2.j.a.69.1	yes	8
44.27	odd	10		1210.2.b.f.969.3		4
44.39	even	10		1210.2.b.g.969.1		4
55.14	even	10	inner	880.2.cd.a.289.2		8
60.59	even	2		990.2.ba.b.829.2		8
132.47	even	10		990.2.ba.b.289.2		8
220.3	even	20		550.2.h.d.201.1		4
220.27	even	20		6050.2.a.ce.1.1		2
220.39	even	10		1210.2.b.g.969.4		4
220.47	even	20		550.2.h.e.201.1		4
220.83	odd	20		6050.2.a.bv.1.2		2
220.127	odd	20		6050.2.a.ct.1.1		2
220.159	odd	10		1210.2.b.f.969.2		4
220.179	odd	10		110.2.j.a.69.2	yes	8
220.203	even	20		6050.2.a.cl.1.2		2
660.179	even	10		990.2.ba.b.289.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.j.a.59.1	✓	8	20.19	odd	2
110.2.j.a.59.2	yes	8	4.3	odd	2
110.2.j.a.69.1	yes	8	44.3	odd	10
110.2.j.a.69.2	yes	8	220.179	odd	10
550.2.h.d.201.1		4	220.3	even	20
550.2.h.d.301.1		4	20.3	even	4
550.2.h.e.201.1		4	220.47	even	20
550.2.h.e.301.1		4	20.7	even	4
880.2.cd.a.289.1		8	11.3	even	5	inner
880.2.cd.a.289.2		8	55.14	even	10	inner
880.2.cd.a.609.1		8	5.4	even	2	inner
880.2.cd.a.609.2		8	1.1	even	1	trivial
990.2.ba.b.289.1		8	660.179	even	10
990.2.ba.b.289.2		8	132.47	even	10
990.2.ba.b.829.1		8	12.11	even	2
990.2.ba.b.829.2		8	60.59	even	2
1210.2.b.f.969.2		4	220.159	odd	10
1210.2.b.f.969.3		4	44.27	odd	10
1210.2.b.g.969.1		4	44.39	even	10
1210.2.b.g.969.4		4	220.39	even	10
6050.2.a.bv.1.2		2	220.83	odd	20
6050.2.a.ce.1.1		2	220.27	even	20
6050.2.a.cl.1.2		2	220.203	even	20
6050.2.a.ct.1.1		2	220.127	odd	20

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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.cd (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.17557 + 0.381966i) q^{3} +(1.03025 - 1.98459i) q^{5} +(-0.587785 + 0.190983i) q^{7} +(-1.19098 - 0.865300i) q^{9} +(-1.69098 - 2.85317i) q^{11} +(1.40008 - 1.92705i) q^{13} +(1.96917 - 1.93950i) q^{15} +(3.80423 + 5.23607i) q^{17} +(1.11803 - 3.44095i) q^{19} -0.763932 q^{21} -4.61803i q^{23} +(-2.87718 - 4.08924i) q^{25} +(-3.24920 - 4.47214i) q^{27} +(-1.38197 - 4.25325i) q^{29} +(1.61803 + 1.17557i) q^{31} +(-0.898056 - 4.00000i) q^{33} +(-0.226543 + 1.36327i) q^{35} +(5.34307 - 1.73607i) q^{37} +(2.38197 - 1.73060i) q^{39} +(0.190983 - 0.587785i) q^{41} +8.47214i q^{43} +(-2.94427 + 1.47214i) q^{45} +(9.59632 + 3.11803i) q^{47} +(-5.35410 + 3.88998i) q^{49} +(2.47214 + 7.60845i) q^{51} +(-4.16750 + 5.73607i) q^{53} +(-7.40450 + 0.416429i) q^{55} +(2.62866 - 3.61803i) q^{57} +(-3.35410 - 10.3229i) q^{59} +(5.61803 - 4.08174i) q^{61} +(0.865300 + 0.281153i) q^{63} +(-2.38197 - 4.76393i) q^{65} +9.23607i q^{67} +(1.76393 - 5.42882i) q^{69} +(1.61803 - 1.17557i) q^{71} +(-1.45309 + 0.472136i) q^{73} +(-1.82037 - 5.90617i) q^{75} +(1.53884 + 1.35410i) q^{77} +(5.00000 + 3.63271i) q^{79} +(-0.746711 - 2.29814i) q^{81} +(-5.98385 - 8.23607i) q^{83} +(14.3107 - 2.15537i) q^{85} -5.52786i q^{87} -11.3820 q^{89} +(-0.454915 + 1.40008i) q^{91} +(1.45309 + 2.00000i) q^{93} +(-5.67702 - 5.76388i) q^{95} +(-5.42882 + 7.47214i) q^{97} +(-0.454915 + 4.86128i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{5} - 14 q^{9} - 18 q^{11} - 12 q^{15} - 24 q^{21} - 6 q^{25} - 20 q^{29} + 4 q^{31} + 4 q^{35} + 28 q^{39} + 6 q^{41} + 48 q^{45} - 16 q^{49} - 16 q^{51} - 4 q^{55} + 36 q^{61} - 28 q^{65} + 32 q^{69}+ \cdots - 26 q^{99}+O(q^{100}) \) 8 * q + 4 * q^5 - 14 * q^9 - 18 * q^11 - 12 * q^15 - 24 * q^21 - 6 * q^25 - 20 * q^29 + 4 * q^31 + 4 * q^35 + 28 * q^39 + 6 * q^41 + 48 * q^45 - 16 * q^49 - 16 * q^51 - 4 * q^55 + 36 * q^61 - 28 * q^65 + 32 * q^69 + 4 * q^71 - 32 * q^75 + 40 * q^79 - 82 * q^81 + 16 * q^85 - 100 * q^89 - 26 * q^91 - 26 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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