LMFDB - Embedded newform 880.2.cd.b.289.4

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 = [16,0,0,0,-6] 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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} + 10 x^{13} - 109 x^{12} + 280 x^{11} - 198 x^{10} - 1168 x^{9} + \cdots + 390625 $ x^16 - 4x^15 + 8x^14 + 10x^13 - 109x^12 + 280x^11 - 198x^10 - 1168x^9 + 4281x^8 - 5840x^7 - 4950x^6 + 35000x^5 - 68125x^4 + 31250x^3 + 125000x^2 - 312500*x + 390625
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			289.4
Root			$1.19237 - 1.89162i$ of defining polynomial
Character	$\chi$	$=$	880.289
Dual form			880.2.cd.b.609.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.53884 - 0.500000i) q^{3} +(-0.829496 + 2.07652i) q^{5} +(-4.76878 - 1.54947i) q^{7} +(-0.309017 + 0.224514i) q^{9} +(0.969425 - 3.17178i) q^{11} +(-1.37249 - 1.88906i) q^{13} +(-0.238203 + 3.61018i) q^{15} +(-0.0359433 + 0.0494717i) q^{17} +(-0.636930 - 1.96027i) q^{19} -8.11314 q^{21} -3.91525i q^{23} +(-3.62387 - 3.44493i) q^{25} +(-3.21644 + 4.42705i) q^{27} +(1.27844 - 3.93464i) q^{29} +(-7.18170 + 5.21781i) q^{31} +(-0.0941007 - 5.36559i) q^{33} +(7.17320 - 8.61720i) q^{35} +(-4.33385 - 1.40815i) q^{37} +(-3.05657 - 2.22073i) q^{39} +(-1.41525 - 4.35570i) q^{41} -3.61803i q^{43} +(-0.209880 - 0.827913i) q^{45} +(-8.44260 + 2.74317i) q^{47} +(14.6773 + 10.6637i) q^{49} +(-0.0305752 + 0.0941007i) q^{51} +(-1.30598 - 1.79753i) q^{53} +(5.78214 + 4.64401i) q^{55} +(-1.96027 - 2.69808i) q^{57} +(0.599137 - 1.84396i) q^{59} +(7.84211 + 5.69763i) q^{61} +(1.82151 - 0.591846i) q^{63} +(5.06115 - 1.28302i) q^{65} +2.49573i q^{67} +(-1.95763 - 6.02495i) q^{69} +(7.13254 + 5.18210i) q^{71} +(5.13205 + 1.66751i) q^{73} +(-7.29903 - 3.48927i) q^{75} +(-9.53757 + 13.6235i) q^{77} +(5.38417 - 3.91183i) q^{79} +(-2.38197 + 7.33094i) q^{81} +(-6.49620 + 8.94125i) q^{83} +(-0.0729142 - 0.115674i) q^{85} -6.69401i q^{87} -6.09017 q^{89} +(3.61803 + 11.1352i) q^{91} +(-8.44260 + 11.6202i) q^{93} +(4.59887 + 0.303437i) q^{95} +(-4.29216 - 5.90765i) q^{97} +(0.412541 + 1.19778i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{5} + 4 q^{9} + 20 q^{11} - 2 q^{15} + 16 q^{19} - 16 q^{21} + 16 q^{29} + 4 q^{31} + 48 q^{35} + 8 q^{39} + 40 q^{41} - 4 q^{45} + 84 q^{49} + 4 q^{51} - 32 q^{55} + 20 q^{61} + 72 q^{65} + 56 q^{71}+ \cdots + 20 q^{99}+O(q^{100}) $ 16 * q - 6 * q^5 + 4 * q^9 + 20 * q^11 - 2 * q^15 + 16 * q^19 - 16 * q^21 + 16 * q^29 + 4 * q^31 + 48 * q^35 + 8 * q^39 + 40 * q^41 - 4 * q^45 + 84 * q^49 + 4 * q^51 - 32 * q^55 + 20 * q^61 + 72 * q^65 + 56 * q^71 - 32 * q^75 - 36 * q^79 - 56 * q^81 - 54 * q^85 - 8 * q^89 + 40 * q^91 + 50 * q^95 + 20 * q^99

Character values

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

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$-1$	$e\left(\frac{4}{5}\right)$	$1$

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
$3$	1.53884	−	0.500000i	0.888451	−	0.288675i	0.170989	−	0.985273i	$-0.445304\pi$
$3$	1.53884	−	0.500000i	0.888451	−	0.288675i	0.717462	+	0.696598i	$0.245304\pi$
$4$		0			0
$5$	−0.829496	+	2.07652i	−0.370962	+	0.928648i
$5$	−0.829496	+	2.07652i	−0.370962	+	0.928648i
$6$		0			0
$7$	−4.76878	−	1.54947i	−1.80243	−	0.585645i	−0.802491	−	0.596664i	$-0.796493\pi$
$7$	−4.76878	−	1.54947i	−1.80243	−	0.585645i	−0.999939	+	0.0110184i	$0.996493\pi$
$8$		0			0
$9$	−0.309017	+	0.224514i	−0.103006	+	0.0748380i
$10$		0			0
$11$	0.969425	−	3.17178i	0.292293	−	0.956329i
$11$	0.969425	−	3.17178i	0.292293	−	0.956329i
$12$		0			0
$13$	−1.37249	−	1.88906i	−0.380659	−	0.523932i	0.575100	−	0.818083i	$-0.304963\pi$
$13$	−1.37249	−	1.88906i	−0.380659	−	0.523932i	−0.955759	+	0.294151i	$0.904963\pi$
$14$		0			0
$15$	−0.238203	+	3.61018i	−0.0615037	+	0.932146i
$16$		0			0
$17$	−0.0359433	+	0.0494717i	−0.00871753	+	0.0119986i	−0.813354	−	0.581770i	$-0.802360\pi$
$17$	−0.0359433	+	0.0494717i	−0.00871753	+	0.0119986i	0.804636	+	0.593768i	$0.202360\pi$
$18$		0			0
$19$	−0.636930	−	1.96027i	−0.146122	−	0.449717i	0.851032	−	0.525114i	$-0.175977\pi$
$19$	−0.636930	−	1.96027i	−0.146122	−	0.449717i	−0.997154	+	0.0753974i	$0.975977\pi$
$20$		0			0
$21$	−8.11314			−1.77043
$22$		0			0
$23$		−	3.91525i		−	0.816387i	−0.912896	−	0.408193i	$-0.866159\pi$
$23$		−	3.91525i		−	0.816387i	0.912896	−	0.408193i	$-0.133841\pi$
$24$		0			0
$25$	−3.62387	−	3.44493i	−0.724775	−	0.688986i
$26$		0			0
$27$	−3.21644	+	4.42705i	−0.619004	+	0.851986i
$28$		0			0
$29$	1.27844	−	3.93464i	0.237401	−	0.730644i	−0.759393	−	0.650632i	$-0.774504\pi$
$29$	1.27844	−	3.93464i	0.237401	−	0.730644i	0.996794	−	0.0800122i	$-0.0254959\pi$
$30$		0			0
$31$	−7.18170	+	5.21781i	−1.28987	+	0.937147i	−0.999803	−	0.0198592i	$-0.993678\pi$
$31$	−7.18170	+	5.21781i	−1.28987	+	0.937147i	−0.290069	+	0.957006i	$0.593678\pi$
$32$		0			0
$33$	−0.0941007	−	5.36559i	−0.0163808	−	0.934029i
$34$		0			0
$35$	7.17320	−	8.61720i	1.21249	−	1.45657i
$36$		0			0
$37$	−4.33385	−	1.40815i	−0.712481	−	0.231499i	−0.0697209	−	0.997567i	$-0.522211\pi$
$37$	−4.33385	−	1.40815i	−0.712481	−	0.231499i	−0.642760	+	0.766067i	$0.722211\pi$
$38$		0			0
$39$	−3.05657	−	2.22073i	−0.489443	−	0.355601i
$40$		0			0
$41$	−1.41525	−	4.35570i	−0.221025	−	0.680246i	−0.998671	−	0.0515429i	$-0.983586\pi$
$41$	−1.41525	−	4.35570i	−0.221025	−	0.680246i	0.777646	−	0.628703i	$-0.216414\pi$
$42$		0			0
$43$		−	3.61803i		−	0.551745i	−0.961194	−	0.275873i	$-0.911033\pi$
$43$		−	3.61803i		−	0.551745i	0.961194	−	0.275873i	$-0.0889668\pi$
$44$		0			0
$45$	−0.209880	−	0.827913i	−0.0312870	−	0.123418i
$46$		0			0
$47$	−8.44260	+	2.74317i	−1.23148	+	0.400132i	−0.851250	−	0.524760i	$-0.824155\pi$
$47$	−8.44260	+	2.74317i	−1.23148	+	0.400132i	−0.380229	+	0.924892i	$0.624155\pi$
$48$		0			0
$49$	14.6773	+	10.6637i	2.09676	+	1.52338i
$50$		0			0
$51$	−0.0305752	+	0.0941007i	−0.00428138	+	0.0131767i
$52$		0			0
$53$	−1.30598	−	1.79753i	−0.179391	−	0.246910i	0.709847	−	0.704356i	$-0.248764\pi$
$53$	−1.30598	−	1.79753i	−0.179391	−	0.246910i	−0.889237	+	0.457446i	$0.848764\pi$
$54$		0			0
$55$	5.78214	+	4.64401i	0.779664	+	0.626199i
$56$		0			0
$57$	−1.96027	−	2.69808i	−0.259644	−	0.357370i
$58$		0			0
$59$	0.599137	−	1.84396i	0.0780011	−	0.240063i	−0.904451	−	0.426577i	$-0.859719\pi$
$59$	0.599137	−	1.84396i	0.0780011	−	0.240063i	0.982452	+	0.186515i	$0.0597192\pi$
$60$		0			0
$61$	7.84211	+	5.69763i	1.00408	+	0.729506i	0.962959	−	0.269648i	$-0.0869073\pi$
$61$	7.84211	+	5.69763i	1.00408	+	0.729506i	0.0411202	+	0.999154i	$0.486907\pi$
$62$		0			0
$63$	1.82151	−	0.591846i	0.229489	−	0.0745655i
$64$		0			0
$65$	5.06115	−	1.28302i	0.627758	−	0.159139i
$66$		0			0
$67$			2.49573i			0.304902i	0.988311	+	0.152451i	$0.0487167\pi$
$67$			2.49573i			0.304902i	−0.988311	+	0.152451i	$0.951283\pi$
$68$		0			0
$69$	−1.95763	−	6.02495i	−0.235670	−	0.725319i
$70$		0			0
$71$	7.13254	+	5.18210i	0.846477	+	0.615002i	0.924172	−	0.381975i	$-0.124756\pi$
$71$	7.13254	+	5.18210i	0.846477	+	0.615002i	−0.0776953	+	0.996977i	$0.524756\pi$
$72$		0			0
$73$	5.13205	+	1.66751i	0.600662	+	0.195167i	0.593535	−	0.804808i	$-0.297732\pi$
$73$	5.13205	+	1.66751i	0.600662	+	0.195167i	0.00712611	+	0.999975i	$0.497732\pi$
$74$		0			0
$75$	−7.29903	−	3.48927i	−0.842820	−	0.402906i
$76$		0			0
$77$	−9.53757	+	13.6235i	−1.08691	+	1.55254i
$78$		0			0
$79$	5.38417	−	3.91183i	0.605766	−	0.440115i	−0.242155	−	0.970238i	$-0.577854\pi$
$79$	5.38417	−	3.91183i	0.605766	−	0.440115i	0.847921	+	0.530123i	$0.177854\pi$
$80$		0			0
$81$	−2.38197	+	7.33094i	−0.264663	+	0.814549i
$82$		0			0
$83$	−6.49620	+	8.94125i	−0.713050	+	0.981429i	0.286676	+	0.958028i	$0.407450\pi$
$83$	−6.49620	+	8.94125i	−0.713050	+	0.981429i	−0.999726	+	0.0234017i	$0.992550\pi$
$84$		0			0
$85$	−0.0729142	−	0.115674i	−0.00790865	−	0.0125466i
$86$		0			0
$87$		−	6.69401i		−	0.717673i
$88$		0			0
$89$	−6.09017			−0.645557			−0.322778	−	0.946475i	$-0.604617\pi$
$89$	−6.09017			−0.645557			−0.322778	+	0.946475i	$0.604617\pi$
$90$		0			0
$91$	3.61803	+	11.1352i	0.379273	+	1.16728i
$92$		0			0
$93$	−8.44260	+	11.6202i	−0.875456	+	1.20496i
$94$		0			0
$95$	4.59887	+	0.303437i	0.471834	+	0.0311320i
$96$		0			0
$97$	−4.29216	−	5.90765i	−0.435802	−	0.599831i	0.533470	−	0.845819i	$-0.320888\pi$
$97$	−4.29216	−	5.90765i	−0.435802	−	0.599831i	−0.969273	+	0.245988i	$0.920888\pi$
$98$		0			0
$99$	0.412541	+	1.19778i	0.0414620	+	0.120382i
$100$		0			0
$101$	0.179498	−	0.130413i	0.0178608	−	0.0129766i	−0.578819	−	0.815456i	$-0.696486\pi$
$101$	0.179498	−	0.130413i	0.0178608	−	0.0129766i	0.596680	+	0.802479i	$0.296486\pi$
$102$		0			0
$103$	−0.538341	−	0.174918i	−0.0530443	−	0.0172351i	0.282375	−	0.959304i	$-0.408878\pi$
$103$	−0.538341	−	0.174918i	−0.0530443	−	0.0172351i	−0.335419	+	0.942069i	$0.608878\pi$
$104$		0			0
$105$	6.72982	−	16.8471i	0.656763	−	1.64411i
$106$		0			0
$107$	2.12087	−	0.689113i	0.205033	−	0.0666191i	−0.204700	−	0.978825i	$-0.565622\pi$
$107$	2.12087	−	0.689113i	0.205033	−	0.0666191i	0.409733	+	0.912206i	$0.365622\pi$
$108$		0			0
$109$	−7.86288			−0.753127			−0.376563	−	0.926391i	$-0.622894\pi$
$109$	−7.86288			−0.753127			−0.376563	+	0.926391i	$0.622894\pi$
$110$		0			0
$111$	−7.37319			−0.699832
$112$		0			0
$113$	11.9469	−	3.88177i	1.12387	−	0.365166i	0.312624	−	0.949877i	$-0.398792\pi$
$113$	11.9469	−	3.88177i	1.12387	−	0.365166i	0.811242	+	0.584710i	$0.198792\pi$
$114$		0			0
$115$	8.13010	+	3.24769i	0.758136	+	0.302848i
$116$		0			0
$117$	0.848243	+	0.275611i	0.0784200	+	0.0254802i
$118$		0			0
$119$	0.248061	−	0.180227i	0.0227397	−	0.0165214i
$120$		0			0
$121$	−9.12043	−	6.14961i	−0.829130	−	0.559056i
$122$		0			0
$123$	−4.35570	−	5.99511i	−0.392740	−	0.540560i
$124$		0			0
$125$	10.1595	−	4.66749i	0.908689	−	0.417473i
$126$		0			0
$127$	8.50112	−	11.7008i	0.754353	−	1.03828i	−0.243310	−	0.969949i	$-0.578233\pi$
$127$	8.50112	−	11.7008i	0.754353	−	1.03828i	0.997663	−	0.0683289i	$-0.0217667\pi$
$128$		0			0
$129$	−1.80902	−	5.56758i	−0.159275	−	0.490198i
$130$		0			0
$131$	−15.3256			−1.33900			−0.669502	−	0.742810i	$-0.733493\pi$
$131$	−15.3256			−1.33900			−0.669502	+	0.742810i	$0.733493\pi$
$132$		0			0
$133$			10.3350i			0.896159i
$134$		0			0
$135$	−6.52484	−	10.3512i	−0.561569	−	0.890892i
$136$		0			0
$137$	0.649130	−	0.893451i	0.0554589	−	0.0763326i	−0.780387	−	0.625297i	$-0.784978\pi$
$137$	0.649130	−	0.893451i	0.0554589	−	0.0763326i	0.835846	+	0.548964i	$0.184978\pi$
$138$		0			0
$139$	−3.06115	+	9.42125i	−0.259643	+	0.799100i	0.733236	+	0.679974i	$0.238009\pi$
$139$	−3.06115	+	9.42125i	−0.259643	+	0.799100i	−0.992879	+	0.119126i	$0.961991\pi$
$140$		0			0
$141$	−11.6202	+	8.44260i	−0.978600	+	0.710995i
$142$		0			0
$143$	−7.32222	+	2.52192i	−0.612315	+	0.210894i
$144$		0			0
$145$	7.10990	+	5.91848i	0.590445	+	0.491503i
$146$		0			0
$147$	27.9179	+	9.07108i	2.30263	+	0.748170i
$148$		0			0
$149$	7.11314	+	5.16800i	0.582731	+	0.423379i	0.839708	−	0.543039i	$-0.182726\pi$
$149$	7.11314	+	5.16800i	0.582731	+	0.423379i	−0.256977	+	0.966418i	$0.582726\pi$
$150$		0			0
$151$	−6.67177	−	20.5336i	−0.542941	−	1.67100i	−0.725835	−	0.687868i	$-0.758547\pi$
$151$	−6.67177	−	20.5336i	−0.542941	−	1.67100i	0.182894	−	0.983133i	$-0.441453\pi$
$152$		0			0
$153$		−	0.0233574i		−	0.00188833i
$154$		0			0
$155$	−4.87770	−	19.2411i	−0.391786	−	1.54548i
$156$		0			0
$157$	3.24760	−	1.05521i	0.259186	−	0.0842148i	−0.176542	−	0.984293i	$-0.556491\pi$
$157$	3.24760	−	1.05521i	0.259186	−	0.0842148i	0.435728	+	0.900078i	$0.356491\pi$
$158$		0			0
$159$	−2.90847	−	2.11313i	−0.230657	−	0.167582i
$160$		0			0
$161$	−6.06657	+	18.6710i	−0.478113	+	1.47148i
$162$		0			0
$163$	10.2336	+	14.0853i	0.801554	+	1.10324i	0.992572	+	0.121657i	$0.0388209\pi$
$163$	10.2336	+	14.0853i	0.801554	+	1.10324i	−0.191019	+	0.981586i	$0.561179\pi$
$164$		0			0
$165$	11.2198	+	4.25533i	0.873461	+	0.331277i
$166$		0			0
$167$	−1.94321	−	2.67460i	−0.150370	−	0.206967i	0.727186	−	0.686440i	$-0.240828\pi$
$167$	−1.94321	−	2.67460i	−0.150370	−	0.206967i	−0.877556	+	0.479473i	$0.840828\pi$
$168$		0			0
$169$	2.33237	−	7.17831i	0.179413	−	0.552178i
$170$		0			0
$171$	0.636930	+	0.462757i	0.0487073	+	0.0353879i
$172$		0			0
$173$	−4.87758	+	1.58482i	−0.370836	+	0.120492i	−0.488505	−	0.872561i	$-0.662458\pi$
$173$	−4.87758	+	1.58482i	−0.370836	+	0.120492i	0.117670	+	0.993053i	$0.462458\pi$
$174$		0			0
$175$	11.9436	+	22.0432i	0.902855	+	1.66631i
$176$		0			0
$177$		−	3.13712i		−	0.235801i
$178$		0			0
$179$	−4.46201	−	13.7327i	−0.333507	−	1.02643i	−0.967453	−	0.253051i	$-0.918566\pi$
$179$	−4.46201	−	13.7327i	−0.333507	−	1.02643i	0.633947	−	0.773377i	$-0.281434\pi$
$180$		0			0
$181$	−9.63223	−	6.99822i	−0.715958	−	0.520174i	0.169132	−	0.985593i	$-0.445903\pi$
$181$	−9.63223	−	6.99822i	−0.715958	−	0.520174i	−0.885090	+	0.465419i	$0.845903\pi$
$182$		0			0
$183$	14.9166	+	4.84669i	1.10267	+	0.358278i
$184$		0			0
$185$	6.51898	−	7.83128i	0.479285	−	0.575767i
$186$		0			0
$187$	0.122069	+	0.161963i	0.00892658	+	0.0118439i
$188$		0			0
$189$	22.1981	−	16.1279i	1.61467	−	1.17313i
$190$		0			0
$191$	−3.25026	+	10.0033i	−0.235181	+	0.723812i	0.761917	+	0.647675i	$0.224259\pi$
$191$	−3.25026	+	10.0033i	−0.235181	+	0.723812i	−0.997097	+	0.0761369i	$0.975741\pi$
$192$		0			0
$193$	2.86174	−	3.93885i	0.205993	−	0.283525i	−0.693503	−	0.720453i	$-0.743934\pi$
$193$	2.86174	−	3.93885i	0.205993	−	0.283525i	0.899496	+	0.436929i	$0.143934\pi$
$194$		0			0
$195$	7.14680	−	4.50494i	0.511793	−	0.322606i
$196$		0			0
$197$			15.9760i			1.13824i	0.822253	+	0.569122i	$0.192717\pi$
$197$			15.9760i			1.13824i	−0.822253	+	0.569122i	$0.807283\pi$
$198$		0			0
$199$	16.7076			1.18437			0.592184	−	0.805803i	$-0.298266\pi$
$199$	16.7076			1.18437			0.592184	+	0.805803i	$0.298266\pi$
$200$		0			0
$201$	1.24787	+	3.84054i	0.0880177	+	0.270891i
$202$		0			0
$203$	−12.1932	+	16.7825i	−0.855797	+	1.17790i
$204$		0			0
$205$	10.2186	+	0.674234i	0.713701	+	0.0470906i
$206$		0			0
$207$	0.879029	+	1.20988i	0.0610967	+	0.0840924i
$208$		0			0
$209$	−6.83501	+	0.119871i	−0.472788	+	0.00829167i
$210$		0			0
$211$	−12.7388	+	9.25526i	−0.876974	+	0.637159i	−0.932449	−	0.361301i	$-0.882333\pi$
$211$	−12.7388	+	9.25526i	−0.876974	+	0.637159i	0.0554754	+	0.998460i	$0.482333\pi$
$212$		0			0
$213$	13.5669	+	4.40815i	0.929589	+	0.302042i
$214$		0			0
$215$	7.51292	+	3.00114i	0.512377	+	0.204676i
$216$		0			0
$217$	42.3328	−	13.7548i	2.87374	−	0.933735i
$218$		0			0
$219$	8.73117			0.589998
$220$		0			0
$221$	0.142787			0.00960488
$222$		0			0
$223$	13.8432	−	4.49794i	0.927011	−	0.301204i	0.193671	−	0.981067i	$-0.437961\pi$
$223$	13.8432	−	4.49794i	0.927011	−	0.301204i	0.733340	+	0.679862i	$0.237961\pi$
$224$		0			0
$225$	1.89327	+	0.250932i	0.126218	+	0.0167288i
$226$		0			0
$227$	−9.35512	−	3.03966i	−0.620921	−	0.201749i	−0.0183719	−	0.999831i	$-0.505848\pi$
$227$	−9.35512	−	3.03966i	−0.620921	−	0.201749i	−0.602549	+	0.798082i	$0.705848\pi$
$228$		0			0
$229$	−12.5785	+	9.13881i	−0.831210	+	0.603909i	−0.919901	−	0.392150i	$-0.871732\pi$
$229$	−12.5785	+	9.13881i	−0.831210	+	0.603909i	0.0886913	+	0.996059i	$0.471732\pi$
$230$		0			0
$231$	−7.86508	+	25.7331i	−0.517484	+	1.69312i
$232$		0			0
$233$	−15.2217	−	20.9509i	−0.997206	−	1.37254i	−0.927024	−	0.375002i	$-0.877642\pi$
$233$	−15.2217	−	20.9509i	−0.997206	−	1.37254i	−0.0701824	−	0.997534i	$-0.522358\pi$
$234$		0			0
$235$	1.30686	−	19.8067i	0.0852501	−	1.29204i
$236$		0			0
$237$	6.32947	−	8.71177i	0.411143	−	0.565890i
$238$		0			0
$239$	6.17911	+	19.0173i	0.399693	+	1.23013i	0.925246	+	0.379369i	$0.123859\pi$
$239$	6.17911	+	19.0173i	0.399693	+	1.23013i	−0.525552	+	0.850761i	$0.676141\pi$
$240$		0			0
$241$	9.01381			0.580630			0.290315	−	0.956931i	$-0.406240\pi$
$241$	9.01381			0.580630			0.290315	+	0.956931i	$0.406240\pi$
$242$		0			0
$243$		−	3.94427i		−	0.253025i
$244$		0			0
$245$	−34.3181	+	21.6323i	−2.19251	+	1.38203i
$246$		0			0
$247$	−2.82890	+	3.89364i	−0.179998	+	0.247747i
$248$		0			0
$249$	−5.52599	+	17.0073i	−0.350196	+	1.07779i
$250$		0			0
$251$	1.06115	−	0.770971i	0.0669792	−	0.0486632i	−0.553792	−	0.832655i	$-0.686820\pi$
$251$	1.06115	−	0.770971i	0.0669792	−	0.0486632i	0.620771	+	0.783992i	$0.286820\pi$
$252$		0			0
$253$	−12.4183	−	3.79554i	−0.780734	−	0.238624i
$254$		0			0
$255$	−0.170040	−	0.141546i	−0.0106483	−	0.00886397i
$256$		0			0
$257$	−4.24551	−	1.37945i	−0.264827	−	0.0860477i	0.173594	−	0.984817i	$-0.444462\pi$
$257$	−4.24551	−	1.37945i	−0.264827	−	0.0860477i	−0.438421	+	0.898770i	$0.644462\pi$
$258$		0			0
$259$	18.4853	+	13.4304i	1.14862	+	0.834522i
$260$		0			0
$261$	0.488321	+	1.50290i	0.0302263	+	0.0930271i
$262$		0			0
$263$		−	14.1791i		−	0.874320i	−0.899384	−	0.437160i	$-0.855984\pi$
$263$		−	14.1791i		−	0.874320i	0.899384	−	0.437160i	$-0.144016\pi$
$264$		0			0
$265$	4.81592	−	1.22086i	0.295840	−	0.0749966i
$266$		0			0
$267$	−9.37181	+	3.04508i	−0.573545	+	0.186356i
$268$		0			0
$269$	−25.8847	−	18.8063i	−1.57822	−	1.14664i	−0.918702	−	0.394952i	$-0.870761\pi$
$269$	−25.8847	−	18.8063i	−1.57822	−	1.14664i	−0.659516	−	0.751691i	$-0.729239\pi$
$270$		0			0
$271$	−0.327988	+	1.00944i	−0.0199238	+	0.0613192i	−0.960524	−	0.278197i	$-0.910263\pi$
$271$	−0.327988	+	1.00944i	−0.0199238	+	0.0613192i	0.940600	+	0.339516i	$0.110263\pi$
$272$		0			0
$273$	11.1352	+	15.3262i	0.673931	+	0.927586i
$274$		0			0
$275$	−14.4396	+	8.15454i	−0.870744	+	0.491737i
$276$		0			0
$277$	−3.89892	−	5.36641i	−0.234264	−	0.322436i	0.675659	−	0.737214i	$-0.263859\pi$
$277$	−3.89892	−	5.36641i	−0.234264	−	0.322436i	−0.909923	+	0.414778i	$0.863859\pi$
$278$		0			0
$279$	1.04780	−	3.22478i	0.0627299	−	0.193063i
$280$		0			0
$281$	−12.6582	−	9.19674i	−0.755126	−	0.548631i	0.142285	−	0.989826i	$-0.454555\pi$
$281$	−12.6582	−	9.19674i	−0.755126	−	0.548631i	−0.897412	+	0.441194i	$0.854555\pi$
$282$		0			0
$283$	21.3993	−	6.95305i	1.27205	−	0.413316i	0.406280	−	0.913749i	$-0.366826\pi$
$283$	21.3993	−	6.95305i	1.27205	−	0.413316i	0.865775	+	0.500433i	$0.166826\pi$
$284$		0			0
$285$	7.22866	−	1.83249i	0.428189	−	0.108548i
$286$		0			0
$287$			22.9643i			1.35554i
$288$		0			0
$289$	5.25213	+	16.1644i	0.308949	+	0.950847i
$290$		0			0
$291$	−9.55877	−	6.94485i	−0.560345	−	0.407115i
$292$		0			0
$293$	17.2985	+	5.62063i	1.01059	+	0.328360i	0.767089	−	0.641540i	$-0.221704\pi$
$293$	17.2985	+	5.62063i	1.01059	+	0.328360i	0.243500	+	0.969901i	$0.421704\pi$
$294$		0			0
$295$	3.33203	+	2.77367i	0.193998	+	0.161490i
$296$		0			0
$297$	10.9236	+	14.4935i	0.633849	+	0.841001i
$298$		0			0
$299$	−7.39616	+	5.37363i	−0.427731	+	0.310765i
$300$		0			0
$301$	−5.60604	+	17.2536i	−0.323127	+	0.994482i
$302$		0			0
$303$	0.211013	−	0.290435i	0.0121224	−	0.0166850i
$304$		0			0
$305$	−18.3362	+	11.5581i	−1.04993	+	0.661817i
$306$		0			0
$307$		−	12.3820i		−	0.706676i	−0.935496	−	0.353338i	$-0.885047\pi$
$307$		−	12.3820i		−	0.706676i	0.935496	−	0.353338i	$-0.114953\pi$
$308$		0			0
$309$	−0.915880			−0.0521026
$310$		0			0
$311$	−2.90784	−	8.94941i	−0.164889	−	0.507475i	0.834140	−	0.551553i	$-0.185965\pi$
$311$	−2.90784	−	8.94941i	−0.164889	−	0.507475i	−0.999028	+	0.0440788i	$0.985965\pi$
$312$		0			0
$313$	−8.95297	+	12.3227i	−0.506052	+	0.696520i	−0.983247	−	0.182277i	$-0.941653\pi$
$313$	−8.95297	+	12.3227i	−0.506052	+	0.696520i	0.477196	+	0.878797i	$0.341653\pi$
$314$		0			0
$315$	−0.281959	+	4.27334i	−0.0158866	+	0.240776i
$316$		0			0
$317$	7.90964	+	10.8867i	0.444250	+	0.611457i	0.971150	−	0.238470i	$-0.0766459\pi$
$317$	7.90964	+	10.8867i	0.444250	+	0.611457i	−0.526900	+	0.849927i	$0.676646\pi$
$318$		0			0
$319$	−11.2405	−	7.86928i	−0.629346	−	0.440595i
$320$		0			0
$321$	2.91913	−	2.12087i	0.162930	−	0.118376i
$322$		0			0
$323$	0.119871	+	0.0389485i	0.00666982	+	0.00216715i
$324$		0			0
$325$	−1.53398	+	11.5738i	−0.0850900	+	0.642001i
$326$		0			0
$327$	−12.0997	+	3.93144i	−0.669116	+	0.217409i
$328$		0			0
$329$	44.5114			2.45399
$330$		0			0
$331$	3.82236			0.210096			0.105048	−	0.994467i	$-0.466500\pi$
$331$	3.82236			0.210096			0.105048	+	0.994467i	$0.466500\pi$
$332$		0			0
$333$	1.65538	−	0.537867i	0.0907145	−	0.0294749i
$334$		0			0
$335$	−5.18244	−	2.07020i	−0.283147	−	0.113107i
$336$		0			0
$337$	−9.00338	−	2.92538i	−0.490445	−	0.159355i	0.0533455	−	0.998576i	$-0.483012\pi$
$337$	−9.00338	−	2.92538i	−0.490445	−	0.159355i	−0.543791	+	0.839221i	$0.683012\pi$
$338$		0			0
$339$	16.4434	−	11.9469i	0.893086	−	0.648865i
$340$		0			0
$341$	9.58765	+	27.8371i	0.519201	+	1.50746i
$342$		0			0
$343$	−32.8390	−	45.1989i	−1.77314	−	2.44051i
$344$		0			0
$345$	14.1348	+	0.932624i	0.760991	+	0.0502108i
$346$		0			0
$347$	9.72341	−	13.3831i	0.521980	−	0.718444i	−0.463902	−	0.885887i	$-0.653551\pi$
$347$	9.72341	−	13.3831i	0.521980	−	0.718444i	0.985882	+	0.167443i	$0.0535510\pi$
$348$		0			0
$349$	−9.03161	−	27.7964i	−0.483451	−	1.48791i	−0.834212	−	0.551444i	$-0.814077\pi$
$349$	−9.03161	−	27.7964i	−0.483451	−	1.48791i	0.350761	−	0.936465i	$-0.385923\pi$
$350$		0			0
$351$	12.7775			0.682012
$352$		0			0
$353$		−	27.9200i		−	1.48603i	−0.669272	−	0.743017i	$-0.733394\pi$
$353$		−	27.9200i		−	1.48603i	0.669272	−	0.743017i	$-0.266606\pi$
$354$		0			0
$355$	−16.6771	+	10.5123i	−0.885131	+	0.557937i
$356$		0			0
$357$	0.291613	−	0.401371i	0.0154338	−	0.0212428i
$358$		0			0
$359$	5.25768	−	16.1815i	0.277490	−	0.854025i	−0.711060	−	0.703131i	$-0.751785\pi$
$359$	5.25768	−	16.1815i	0.277490	−	0.854025i	0.988550	−	0.150894i	$-0.0482152\pi$
$360$		0			0
$361$	11.9343	−	8.67081i	0.628123	−	0.456358i
$362$		0			0
$363$	−17.1097	−	4.90307i	−0.898027	−	0.257344i
$364$		0			0
$365$	−7.71963	+	9.27363i	−0.404064	+	0.485404i
$366$		0			0
$367$	27.9983	+	9.09719i	1.46150	+	0.474870i	0.928527	−	0.371264i	$-0.121075\pi$
$367$	27.9983	+	9.09719i	1.46150	+	0.474870i	0.532971	+	0.846133i	$0.321075\pi$
$368$		0			0
$369$	1.41525	+	1.02824i	0.0736751	+	0.0535281i
$370$		0			0
$371$	3.44273	+	10.5956i	0.178738	+	0.550098i
$372$		0			0
$373$		−	16.0743i		−	0.832297i	−0.909297	−	0.416149i	$-0.863380\pi$
$373$		−	16.0743i		−	0.832297i	0.909297	−	0.416149i	$-0.136620\pi$
$374$		0			0
$375$	13.3000	−	12.2623i	0.686812	−	0.633220i
$376$		0			0
$377$	−9.18743	+	2.98518i	−0.473177	+	0.153744i
$378$		0			0
$379$	−14.6618	−	10.6524i	−0.753125	−	0.547178i	0.143669	−	0.989626i	$-0.454110\pi$
$379$	−14.6618	−	10.6524i	−0.753125	−	0.547178i	−0.896794	+	0.442448i	$0.854110\pi$
$380$		0			0
$381$	7.23149	−	22.2562i	0.370480	−	1.14022i
$382$		0			0
$383$	7.76587	+	10.6888i	0.396817	+	0.546172i	0.959942	−	0.280200i	$-0.0904008\pi$
$383$	7.76587	+	10.6888i	0.396817	+	0.546172i	−0.563124	+	0.826372i	$0.690401\pi$
$384$		0			0
$385$	−20.3780	−	31.1056i	−1.03856	−	1.58529i
$386$		0			0
$387$	0.812299	+	1.11803i	0.0412915	+	0.0568329i
$388$		0			0
$389$	8.19653	−	25.2263i	0.415580	−	1.27902i	−0.496150	−	0.868237i	$-0.665254\pi$
$389$	8.19653	−	25.2263i	0.415580	−	1.27902i	0.911731	−	0.410788i	$-0.134746\pi$
$390$		0			0
$391$	0.193694	+	0.140727i	0.00979553	+	0.00711687i
$392$		0			0
$393$	−23.5837	+	7.66280i	−1.18964	+	0.386537i
$394$		0			0
$395$	3.65684	+	14.4252i	0.183996	+	0.725810i
$396$		0			0
$397$		−	30.3246i		−	1.52195i	−0.648783	−	0.760974i	$-0.724722\pi$
$397$		−	30.3246i		−	1.52195i	0.648783	−	0.760974i	$-0.275278\pi$
$398$		0			0
$399$	5.16751	+	15.9039i	0.258699	+	0.796193i
$400$		0			0
$401$	−15.7565	−	11.4478i	−0.786844	−	0.571676i	0.120181	−	0.992752i	$-0.461652\pi$
$401$	−15.7565	−	11.4478i	−0.786844	−	0.571676i	−0.907025	+	0.421076i	$0.861652\pi$
$402$		0			0
$403$	19.7136	+	6.40532i	0.982002	+	0.319072i
$404$		0			0
$405$	−13.2470	−	11.0272i	−0.658249	−	0.547945i
$406$		0			0
$407$	−8.66771	+	12.3809i	−0.429642	+	0.613701i
$408$		0			0
$409$	−22.9197	+	16.6521i	−1.13330	+	0.823394i	−0.986172	−	0.165723i	$-0.947004\pi$
$409$	−22.9197	+	16.6521i	−1.13330	+	0.823394i	−0.147132	+	0.989117i	$0.547004\pi$
$410$		0			0
$411$	0.552183	−	1.69944i	0.0272372	−	0.0838274i
$412$		0			0
$413$	−5.71431	+	7.86508i	−0.281183	+	0.387015i
$414$		0			0
$415$	−13.1781	−	20.9062i	−0.646888	−	1.02625i
$416$		0			0
$417$			16.0284i			0.784914i
$418$		0			0
$419$	−15.4826			−0.756374			−0.378187	−	0.925729i	$-0.623452\pi$
$419$	−15.4826			−0.756374			−0.378187	+	0.925729i	$0.623452\pi$
$420$		0			0
$421$	6.63964	+	20.4347i	0.323596	+	0.995927i	0.972070	+	0.234690i	$0.0754076\pi$
$421$	6.63964	+	20.4347i	0.323596	+	0.995927i	−0.648474	+	0.761237i	$0.724592\pi$
$422$		0			0
$423$	1.99303	−	2.74317i	0.0969043	−	0.133377i
$424$		0			0
$425$	0.300680	−	0.0554570i	0.0145851	−	0.00269006i
$426$		0			0
$427$	−28.5690	−	39.3219i	−1.38255	−	1.90292i
$428$		0			0
$429$	−10.0068	+	7.54195i	−0.483132	+	0.364129i
$430$		0			0
$431$	21.3896	−	15.5404i	1.03030	−	0.748557i	0.0619316	−	0.998080i	$-0.480274\pi$
$431$	21.3896	−	15.5404i	1.03030	−	0.748557i	0.968369	+	0.249523i	$0.0802739\pi$
$432$		0			0
$433$	31.2725	+	10.1611i	1.50286	+	0.488309i	0.940851	−	0.338821i	$-0.110028\pi$
$433$	31.2725	+	10.1611i	1.50286	+	0.488309i	0.562010	+	0.827130i	$0.310028\pi$
$434$		0			0
$435$	13.9002	+	5.55265i	0.666466	+	0.266229i
$436$		0			0
$437$	−7.67495	+	2.49374i	−0.367143	+	0.119292i
$438$		0			0
$439$	−12.1796			−0.581299			−0.290649	−	0.956830i	$-0.593871\pi$
$439$	−12.1796			−0.581299			−0.290649	+	0.956830i	$0.593871\pi$
$440$		0			0
$441$	−6.92969			−0.329985
$442$		0			0
$443$	−15.7961	+	5.13247i	−0.750496	+	0.243851i	−0.659195	−	0.751972i	$-0.729103\pi$
$443$	−15.7961	+	5.13247i	−0.750496	+	0.243851i	−0.0913015	+	0.995823i	$0.529103\pi$
$444$		0			0
$445$	5.05177	−	12.6464i	0.239477	−	0.599495i
$446$		0			0
$447$	13.5300	+	4.39616i	0.639947	+	0.207931i
$448$		0			0
$449$	−4.33928	+	3.15267i	−0.204783	+	0.148784i	−0.685450	−	0.728119i	$-0.740395\pi$
$449$	−4.33928	+	3.15267i	−0.204783	+	0.148784i	0.480667	+	0.876903i	$0.340395\pi$
$450$		0			0
$451$	−15.1873	+	0.266353i	−0.715143	+	0.0125421i
$452$		0			0
$453$	−20.5336	−	28.2621i	−0.964753	−	1.32787i
$454$		0			0
$455$	−26.1235	−	1.72365i	−1.22469	−	0.0808061i
$456$		0			0
$457$	2.12330	−	2.92247i	0.0993237	−	0.136707i	−0.756462	−	0.654037i	$-0.773074\pi$
$457$	2.12330	−	2.92247i	0.0993237	−	0.136707i	0.855786	+	0.517330i	$0.173074\pi$
$458$		0			0
$459$	−0.103404	−	0.318246i	−0.00482650	−	0.0148544i
$460$		0			0
$461$	−40.6625			−1.89384			−0.946922	−	0.321464i	$-0.895825\pi$
$461$	−40.6625			−1.89384			−0.946922	+	0.321464i	$0.895825\pi$
$462$		0			0
$463$			2.11880i			0.0984690i	0.998787	+	0.0492345i	$0.0156782\pi$
$463$			2.11880i			0.0984690i	−0.998787	+	0.0492345i	$0.984322\pi$
$464$		0			0
$465$	−17.1266	−	27.1702i	−0.794225	−	1.25999i
$466$		0			0
$467$	−8.08494	+	11.1280i	−0.374126	+	0.514941i	−0.954017	−	0.299754i	$-0.903095\pi$
$467$	−8.08494	+	11.1280i	−0.374126	+	0.514941i	0.579890	+	0.814695i	$0.303095\pi$
$468$		0			0
$469$	3.86707	−	11.9016i	0.178565	−	0.549565i
$470$		0			0
$471$	4.46993	−	3.24760i	0.205964	−	0.149641i
$472$		0			0
$473$	−11.4756	−	3.50741i	−0.527650	−	0.161271i
$474$		0			0
$475$	−4.44484	+	9.29795i	−0.203943	+	0.426619i
$476$		0			0
$477$	0.807142	+	0.262256i	0.0369565	+	0.0120079i
$478$		0			0
$479$	−25.4118	−	18.4628i	−1.16110	−	0.843586i	−0.171180	−	0.985240i	$-0.554758\pi$
$479$	−25.4118	−	18.4628i	−1.16110	−	0.843586i	−0.989916	+	0.141654i	$0.954758\pi$
$480$		0			0
$481$	3.28806	+	10.1196i	0.149922	+	0.461414i
$482$		0			0
$483$			31.7650i			1.44536i
$484$		0			0
$485$	15.8277	−	4.01238i	0.718698	−	0.182193i
$486$		0			0
$487$	7.14274	−	2.32082i	0.323668	−	0.105166i	−0.142676	−	0.989769i	$-0.545571\pi$
$487$	7.14274	−	2.32082i	0.323668	−	0.105166i	0.466344	+	0.884603i	$0.345571\pi$
$488$		0			0
$489$	22.7905	+	16.5582i	1.03062	+	0.748789i
$490$		0			0
$491$	−3.48008	+	10.7106i	−0.157054	+	0.483361i	−0.998363	−	0.0571923i	$-0.981785\pi$
$491$	−3.48008	+	10.7106i	−0.157054	+	0.483361i	0.841310	+	0.540554i	$0.181785\pi$
$492$		0			0
$493$	0.148702	+	0.204671i	0.00669719	+	0.00921790i
$494$		0			0
$495$	−2.82943	−	0.136907i	−0.127173	−	0.00615353i
$496$		0			0
$497$	−25.9840	−	35.7640i	−1.16554	−	1.60423i
$498$		0			0
$499$	−8.33753	+	25.6603i	−0.373239	+	1.14871i	0.571420	+	0.820658i	$0.306393\pi$
$499$	−8.33753	+	25.6603i	−0.373239	+	1.14871i	−0.944659	+	0.328054i	$0.893607\pi$
$500$		0			0
$501$	−4.32760	−	3.14419i	−0.193343	−	0.140472i
$502$		0			0
$503$	−30.5818	+	9.93662i	−1.36357	+	0.443052i	−0.897235	−	0.441554i	$-0.854427\pi$
$503$	−30.5818	+	9.93662i	−1.36357	+	0.443052i	−0.466339	+	0.884606i	$0.654427\pi$
$504$		0			0
$505$	0.121913	+	0.480909i	0.00542504	+	0.0214002i
$506$		0			0
$507$		−	12.2125i		−	0.542375i
$508$		0			0
$509$	−3.64048	−	11.2043i	−0.161362	−	0.496620i	0.837388	−	0.546609i	$-0.184081\pi$
$509$	−3.64048	−	11.2043i	−0.161362	−	0.496620i	−0.998750	+	0.0499888i	$0.984081\pi$
$510$		0			0
$511$	−21.8899	−	15.9039i	−0.968352	−	0.703549i
$512$		0			0
$513$	10.7269	+	3.48537i	0.473603	+	0.153883i
$514$		0			0
$515$	0.809772	−	0.972783i	0.0356828	−	0.0428659i
$516$		0			0
$517$	0.516268	+	29.4374i	0.0227054	+	1.29465i
$518$		0			0
$519$	−6.71341	+	4.87758i	−0.294686	+	0.214102i
$520$		0			0
$521$	0.718847	−	2.21238i	0.0314933	−	0.0969263i	−0.934074	−	0.357079i	$-0.883773\pi$
$521$	0.718847	−	2.21238i	0.0314933	−	0.0969263i	0.965568	+	0.260152i	$0.0837728\pi$
$522$		0			0
$523$	−0.901612	+	1.24096i	−0.0394248	+	0.0542635i	−0.828274	−	0.560323i	$-0.810677\pi$
$523$	−0.901612	+	1.24096i	−0.0394248	+	0.0542635i	0.788850	+	0.614586i	$0.210677\pi$
$524$		0			0
$525$	29.4010	+	27.9492i	1.28316	+	1.21980i
$526$		0			0
$527$		−	0.542836i		−	0.0236463i
$528$		0			0
$529$	7.67080			0.333513
$530$		0			0
$531$	0.228850	+	0.704328i	0.00993125	+	0.0305652i
$532$		0			0
$533$	−6.28578	+	8.65163i	−0.272267	+	0.374744i
$534$		0			0
$535$	−0.328298	+	4.97565i	−0.0141935	+	0.215116i
$536$		0			0
$537$	−13.7327	−	18.9014i	−0.592608	−	0.815655i
$538$		0			0
$539$	48.0515	−	36.2156i	2.06972	−	1.55992i
$540$		0			0
$541$	12.4927	−	9.07650i	0.537104	−	0.390229i	−0.285904	−	0.958258i	$-0.592294\pi$
$541$	12.4927	−	9.07650i	0.537104	−	0.390229i	0.823008	+	0.568029i	$0.192294\pi$
$542$		0			0
$543$	−18.3216	−	5.95305i	−0.786255	−	0.255470i
$544$		0			0
$545$	6.52222	−	16.3274i	0.279381	−	0.699390i
$546$		0			0
$547$	10.1261	−	3.29017i	0.432960	−	0.140677i	−0.0844251	−	0.996430i	$-0.526905\pi$
$547$	10.1261	−	3.29017i	0.432960	−	0.140677i	0.517385	+	0.855752i	$0.326905\pi$
$548$		0			0
$549$	−3.70254			−0.158021
$550$		0			0
$551$	−8.52724			−0.363272
$552$		0			0
$553$	−31.7372	+	10.3120i	−1.34960	+	0.438513i
$554$		0			0
$555$	6.11603	−	15.3106i	0.259611	−	0.649898i
$556$		0			0
$557$	−32.2595	−	10.4818i	−1.36688	−	0.444126i	−0.468545	−	0.883439i	$-0.655222\pi$
$557$	−32.2595	−	10.4818i	−1.36688	−	0.444126i	−0.898334	+	0.439313i	$0.855222\pi$
$558$		0			0
$559$	−6.83470	+	4.96570i	−0.289077	+	0.210027i
$560$		0			0
$561$	0.268827	+	0.188201i	0.0113499	+	0.00794587i
$562$		0			0
$563$	0.789857	+	1.08714i	0.0332885	+	0.0458177i	0.825337	−	0.564641i	$-0.190985\pi$
$563$	0.789857	+	1.08714i	0.0332885	+	0.0458177i	−0.792048	+	0.610458i	$0.790985\pi$
$564$		0			0
$565$	−1.84930	+	28.0278i	−0.0778006	+	1.17914i
$566$		0			0
$567$	22.7182	−	31.2689i	0.954073	−	1.31317i
$568$		0			0
$569$	9.70595	+	29.8718i	0.406894	+	1.25229i	0.919303	+	0.393550i	$0.128753\pi$
$569$	9.70595	+	29.8718i	0.406894	+	1.25229i	−0.512409	+	0.858742i	$0.671247\pi$
$570$		0			0
$571$	−9.25361			−0.387252			−0.193626	−	0.981075i	$-0.562025\pi$
$571$	−9.25361			−0.387252			−0.193626	+	0.981075i	$0.562025\pi$
$572$		0			0
$573$			17.0186i			0.710962i
$574$		0			0
$575$	−13.4878	+	14.1884i	−0.562479	+	0.591696i
$576$		0			0
$577$	−25.4998	+	35.0975i	−1.06157	+	1.46113i	−0.183244	+	0.983068i	$0.558660\pi$
$577$	−25.4998	+	35.0975i	−1.06157	+	1.46113i	−0.878327	+	0.478060i	$0.841340\pi$
$578$		0			0
$579$	2.43434	−	7.49214i	0.101168	−	0.311363i
$580$		0			0
$581$	44.8332	−	32.5732i	1.85999	−	1.35136i
$582$		0			0
$583$	−6.96744	+	2.39973i	−0.288562	+	0.0993865i
$584$		0			0
$585$	−1.27592	+	1.53277i	−0.0527530	+	0.0633724i
$586$		0			0
$587$	−3.05524	−	0.992708i	−0.126103	−	0.0409734i	0.245285	−	0.969451i	$-0.421118\pi$
$587$	−3.05524	−	0.992708i	−0.126103	−	0.0409734i	−0.371389	+	0.928477i	$0.621118\pi$
$588$		0			0
$589$	14.8026	+	10.7547i	0.609929	+	0.443139i
$590$		0			0
$591$	7.98801	+	24.5846i	0.328583	+	1.01127i
$592$		0			0
$593$			0.0315027i			0.00129366i	1.00000		0.000646829i	$0.000205892\pi$
$593$			0.0315027i			0.00129366i	−1.00000		0.000646829i	$0.999794\pi$
$594$		0			0
$595$	0.168479	+	0.664600i	0.00690696	+	0.0272460i
$596$		0			0
$597$	25.7103	−	8.35379i	1.05225	−	0.341898i
$598$		0			0
$599$	8.50993	+	6.18283i	0.347706	+	0.252623i	0.747906	−	0.663804i	$-0.231059\pi$
$599$	8.50993	+	6.18283i	0.347706	+	0.252623i	−0.400200	+	0.916428i	$0.631059\pi$
$600$		0			0
$601$	7.45305	−	22.9381i	0.304016	−	0.935665i	−0.676026	−	0.736877i	$-0.736300\pi$
$601$	7.45305	−	22.9381i	0.304016	−	0.935665i	0.980043	−	0.198788i	$-0.0637005\pi$
$602$		0			0
$603$	−0.560327	−	0.771224i	−0.0228183	−	0.0314067i
$604$		0			0
$605$	20.3352	−	13.8377i	0.826742	−	0.562582i
$606$		0			0
$607$	−1.46340	−	2.01420i	−0.0593975	−	0.0817537i	0.778285	−	0.627911i	$-0.216090\pi$
$607$	−1.46340	−	2.01420i	−0.0593975	−	0.0817537i	−0.837682	+	0.546158i	$0.816090\pi$
$608$		0			0
$609$	−10.3722	+	31.9223i	−0.420302	+	1.29356i
$610$		0			0
$611$	16.7694	+	12.1836i	0.678415	+	0.492898i
$612$		0			0
$613$	35.7338	−	11.6106i	1.44328	−	0.468949i	0.520359	−	0.853948i	$-0.325798\pi$
$613$	35.7338	−	11.6106i	1.44328	−	0.468949i	0.922917	+	0.384999i	$0.125798\pi$
$614$		0			0
$615$	16.0620	−	4.07178i	0.647682	−	0.164190i
$616$		0			0
$617$			45.5803i			1.83499i	0.397744	+	0.917496i	$0.369793\pi$
$617$			45.5803i			1.83499i	−0.397744	+	0.917496i	$0.630207\pi$
$618$		0			0
$619$	1.77382	+	5.45924i	0.0712957	+	0.219425i	0.980355	−	0.197241i	$-0.0631982\pi$
$619$	1.77382	+	5.45924i	0.0712957	+	0.219425i	−0.909059	+	0.416667i	$0.863198\pi$
$620$		0			0
$621$	17.3330	+	12.5932i	0.695550	+	0.505347i
$622$		0			0
$623$	29.0427	+	9.43655i	1.16357	+	0.378067i
$624$		0			0
$625$	1.26491	+	24.9680i	0.0505964	+	0.998719i
$626$		0			0
$627$	−10.4581	+	3.60197i	−0.417655	+	0.143849i
$628$		0			0
$629$	0.225437	−	0.163789i	0.00898875	−	0.00653071i
$630$		0			0
$631$	−3.70103	+	11.3906i	−0.147336	+	0.453453i	−0.997304	−	0.0733811i	$-0.976621\pi$
$631$	−3.70103	+	11.3906i	−0.147336	+	0.453453i	0.849968	+	0.526834i	$0.176621\pi$
$632$		0			0
$633$	−14.9753	+	20.6118i	−0.595216	+	0.819245i
$634$		0			0
$635$	17.2453	+	27.3585i	0.684358	+	1.08569i
$636$		0			0
$637$		−	42.3621i		−	1.67845i
$638$		0			0
$639$	−3.36753			−0.133217
$640$		0			0
$641$	−10.8526	−	33.4007i	−0.428650	−	1.31925i	−0.899455	−	0.437013i	$-0.856036\pi$
$641$	−10.8526	−	33.4007i	−0.428650	−	1.31925i	0.470805	−	0.882237i	$-0.343964\pi$
$642$		0			0
$643$	−20.9529	+	28.8392i	−0.826302	+	1.13731i	0.162298	+	0.986742i	$0.448109\pi$
$643$	−20.9529	+	28.8392i	−0.826302	+	1.13731i	−0.988600	+	0.150565i	$0.951891\pi$
$644$		0			0
$645$	13.0618	+	0.861826i	0.514307	+	0.0339344i
$646$		0			0
$647$	11.8476	+	16.3068i	0.465778	+	0.641088i	0.975694	−	0.219136i	$-0.0703238\pi$
$647$	11.8476	+	16.3068i	0.465778	+	0.641088i	−0.509917	+	0.860224i	$0.670324\pi$
$648$		0			0
$649$	−5.26781	−	3.68791i	−0.206780	−	0.144763i
$650$		0			0
$651$	58.2661	−	42.3328i	2.28363	−	1.65915i
$652$		0			0
$653$	−23.1905	−	7.53504i	−0.907513	−	0.294869i	−0.182178	−	0.983266i	$-0.558315\pi$
$653$	−23.1905	−	7.53504i	−0.907513	−	0.294869i	−0.725334	+	0.688397i	$0.758315\pi$
$654$		0			0
$655$	12.7125	−	31.8239i	0.496720	−	1.24346i
$656$		0			0
$657$	−1.96027	+	0.636930i	−0.0764774	+	0.0248490i
$658$		0			0
$659$	−6.98788			−0.272209			−0.136104	−	0.990694i	$-0.543458\pi$
$659$	−6.98788			−0.272209			−0.136104	+	0.990694i	$0.543458\pi$
$660$		0			0
$661$	−3.61827			−0.140735			−0.0703673	−	0.997521i	$-0.522417\pi$
$661$	−3.61827			−0.140735			−0.0703673	+	0.997521i	$0.522417\pi$
$662$		0			0
$663$	0.219726	−	0.0713934i	0.00853346	−	0.00277269i
$664$		0			0
$665$	−21.4609	−	8.57285i	−0.832216	−	0.332441i
$666$		0			0
$667$	−15.4051	−	5.00542i	−0.596488	−	0.193811i
$668$		0			0
$669$	19.0536	−	13.8432i	0.736653	−	0.535210i
$670$		0			0
$671$	25.6740	−	19.3501i	0.991133	−	0.747001i
$672$		0			0
$673$	4.68377	+	6.44665i	0.180546	+	0.248500i	0.889692	−	0.456562i	$-0.150919\pi$
$673$	4.68377	+	6.44665i	0.180546	+	0.248500i	−0.709146	+	0.705062i	$0.750919\pi$
$674$		0			0
$675$	26.9069	−	4.96266i	1.03565	−	0.191013i
$676$		0			0
$677$	8.48443	−	11.6778i	0.326083	−	0.448815i	−0.614229	−	0.789128i	$-0.710533\pi$
$677$	8.48443	−	11.6778i	0.326083	−	0.448815i	0.940312	+	0.340313i	$0.110533\pi$
$678$		0			0
$679$	11.3146	+	34.8229i	0.434216	+	1.33638i
$680$		0			0
$681$	−15.9159			−0.609898
$682$		0			0
$683$		−	29.6723i		−	1.13538i	−0.823242	−	0.567690i	$-0.807837\pi$
$683$		−	29.6723i		−	1.13538i	0.823242	−	0.567690i	$-0.192163\pi$
$684$		0			0
$685$	1.31682	+	2.08904i	0.0503130	+	0.0798183i
$686$		0			0
$687$	−14.7869	+	20.3524i	−0.564156	+	0.776493i
$688$		0			0
$689$	−1.60321	+	4.93417i	−0.0610774	+	0.187977i
$690$		0			0
$691$	26.1812	−	19.0218i	0.995980	−	0.723622i	0.0347577	−	0.999396i	$-0.488934\pi$
$691$	26.1812	−	19.0218i	0.995980	−	0.723622i	0.961223	+	0.275774i	$0.0889341\pi$
$692$		0			0
$693$	−0.111386	−	6.35120i	−0.00423121	−	0.241262i
$694$		0			0
$695$	−17.0242	−	14.1714i	−0.645765	−	0.537553i
$696$		0			0
$697$	0.266353	+	0.0865432i	0.0100888	+	0.00327806i
$698$		0			0
$699$	−33.8992	−	24.6292i	−1.28219	−	0.931562i
$700$		0			0
$701$	5.86089	+	18.0380i	0.221363	+	0.681284i	0.998640	+	0.0521266i	$0.0165999\pi$
$701$	5.86089	+	18.0380i	0.221363	+	0.681284i	−0.777278	+	0.629157i	$0.783400\pi$
$702$		0			0
$703$			9.39242i			0.354242i
$704$		0			0
$705$	−7.89228	−	31.1328i	−0.297241	−	1.17253i
$706$		0			0
$707$	−1.05806	+	0.343785i	−0.0397925	+	0.0129294i
$708$		0			0
$709$	6.78617	+	4.93044i	0.254860	+	0.185167i	0.707878	−	0.706335i	$-0.249653\pi$
$709$	6.78617	+	4.93044i	0.254860	+	0.185167i	−0.453018	+	0.891501i	$0.649653\pi$
$710$		0			0
$711$	−0.785540	+	2.41764i	−0.0294600	+	0.0906687i
$712$		0			0
$713$	20.4290	+	28.1182i	0.765074	+	1.05303i
$714$		0			0
$715$	0.836934	−	17.2967i	0.0312995	−	0.646859i
$716$		0			0
$717$	19.0173	+	26.1751i	0.710216	+	0.977528i
$718$		0			0
$719$	2.33218	−	7.17771i	0.0869756	−	0.267684i	−0.898104	−	0.439783i	$-0.855055\pi$
$719$	2.33218	−	7.17771i	0.0869756	−	0.267684i	0.985079	+	0.172100i	$0.0550552\pi$
$720$		0			0
$721$	2.29620	+	1.66829i	0.0855150	+	0.0621303i
$722$		0			0
$723$	13.8708	−	4.50690i	0.515861	−	0.167614i
$724$		0			0
$725$	−18.1875	+	9.85449i	−0.675466	+	0.365987i
$726$		0			0
$727$			24.2826i			0.900593i	0.892879	+	0.450297i	$0.148682\pi$
$727$			24.2826i			0.900593i	−0.892879	+	0.450297i	$0.851318\pi$
$728$		0			0
$729$	−9.11803	−	28.0624i	−0.337705	−	1.03935i
$730$		0			0
$731$	0.178990	+	0.130044i	0.00662019	+	0.00480985i
$732$		0			0
$733$	20.3541	+	6.61345i	0.751796	+	0.244273i	0.659754	−	0.751482i	$-0.270660\pi$
$733$	20.3541	+	6.61345i	0.751796	+	0.244273i	0.0920424	+	0.995755i	$0.470660\pi$
$734$		0			0
$735$	−41.9941	+	50.4477i	−1.54897	+	1.86079i
$736$		0			0
$737$	7.91593	+	2.41943i	0.291587	+	0.0891207i
$738$		0			0
$739$	−28.4419	+	20.6642i	−1.04625	+	0.760147i	−0.971496	−	0.237055i	$-0.923818\pi$
$739$	−28.4419	+	20.6642i	−1.04625	+	0.760147i	−0.0747558	+	0.997202i	$0.523818\pi$
$740$		0			0
$741$	−2.40640	+	7.40615i	−0.0884015	+	0.272072i
$742$		0			0
$743$	20.0435	−	27.5875i	0.735324	−	1.01209i	−0.263550	−	0.964646i	$-0.584893\pi$
$743$	20.0435	−	27.5875i	0.735324	−	1.01209i	0.998874	−	0.0474407i	$-0.0151065\pi$
$744$		0			0
$745$	−16.6318	+	10.4837i	−0.609341	+	0.384095i
$746$		0			0
$747$		−	4.22148i		−	0.154456i
$748$		0			0
$749$	−11.1817			−0.408572
$750$		0			0
$751$	11.0690	+	34.0669i	0.403914	+	1.24312i	0.921799	+	0.387669i	$0.126720\pi$
$751$	11.0690	+	34.0669i	0.403914	+	1.24312i	−0.517884	+	0.855451i	$0.673280\pi$
$752$		0			0
$753$	1.24746	−	1.71698i	0.0454599	−	0.0625701i
$754$		0			0
$755$	48.1727	+	3.17847i	1.75318	+	0.115676i
$756$		0			0
$757$	14.2408	+	19.6008i	0.517592	+	0.712404i	0.985176	−	0.171544i	$-0.0548756\pi$
$757$	14.2408	+	19.6008i	0.517592	+	0.712404i	−0.467584	+	0.883948i	$0.654876\pi$
$758$		0			0
$759$	−21.0076	+	0.368428i	−0.762528	+	0.0133731i
$760$		0			0
$761$	−8.62191	+	6.26419i	−0.312544	+	0.227077i	−0.732987	−	0.680242i	$-0.761875\pi$
$761$	−8.62191	+	6.26419i	−0.312544	+	0.227077i	0.420443	+	0.907319i	$0.361875\pi$
$762$		0			0
$763$	37.4964	+	12.1833i	1.35746	+	0.441065i
$764$		0			0
$765$	0.0485020	+	0.0193748i	0.00175359	+	0.000700499i
$766$		0			0
$767$	−4.30566	+	1.39899i	−0.155468	+	0.0505147i
$768$		0			0
$769$	−25.8297			−0.931444			−0.465722	−	0.884931i	$-0.654205\pi$
$769$	−25.8297			−0.931444			−0.465722	+	0.884931i	$0.654205\pi$
$770$		0			0
$771$	−7.22289			−0.260126
$772$		0			0
$773$	11.4679	−	3.72614i	0.412471	−	0.134020i	−0.0954286	−	0.995436i	$-0.530422\pi$
$773$	11.4679	−	3.72614i	0.412471	−	0.134020i	0.507899	+	0.861416i	$0.330422\pi$
$774$		0			0
$775$	44.0006	+	5.83177i	1.58055	+	0.209484i
$776$		0			0
$777$	35.1612	+	11.4246i	1.26140	+	0.409854i
$778$		0			0
$779$	−7.63693	+	5.54855i	−0.273621	+	0.198798i
$780$		0			0
$781$	23.3510	−	17.5992i	0.835563	−	0.629750i
$782$		0			0
$783$	13.3068	+	18.3153i	0.475547	+	0.654534i
$784$		0			0
$785$	−0.502707	+	7.61899i	−0.0179424	+	0.271933i
$786$		0			0
$787$	−10.6725	+	14.6895i	−0.380435	+	0.523624i	−0.955700	−	0.294343i	$-0.904899\pi$
$787$	−10.6725	+	14.6895i	−0.380435	+	0.523624i	0.575265	+	0.817967i	$0.304899\pi$
$788$		0			0
$789$	−7.08954	−	21.8194i	−0.252394	−	0.776790i
$790$		0			0
$791$	−62.9867			−2.23955
$792$		0			0
$793$		−	22.6342i		−	0.803762i
$794$		0			0
$795$	6.80051	−	4.28666i	0.241189	−	0.152032i
$796$		0			0
$797$	−0.946725	+	1.30306i	−0.0335347	+	0.0461566i	−0.825455	−	0.564468i	$-0.809081\pi$
$797$	−0.946725	+	1.30306i	−0.0335347	+	0.0461566i	0.791920	+	0.610624i	$0.209081\pi$
$798$		0			0
$799$	0.167746	−	0.516268i	0.00593441	−	0.0182642i
$800$		0			0
$801$	1.88197	−	1.36733i	0.0664960	−	0.0483122i
$802$		0			0
$803$	10.2641	−	14.6612i	0.362213	−	0.517384i
$804$		0			0
$805$	−33.7385	−	28.0849i	−1.18913	−	0.989862i
$806$		0			0
$807$	−49.2356	−	15.9976i	−1.73318	−	0.563143i
$808$		0			0
$809$	20.7273	+	15.0593i	0.728733	+	0.529455i	0.889162	−	0.457592i	$-0.151288\pi$
$809$	20.7273	+	15.0593i	0.728733	+	0.529455i	−0.160429	+	0.987047i	$0.551288\pi$
$810$		0			0
$811$	−13.5506	−	41.7045i	−0.475827	−	1.46444i	−0.844839	−	0.535020i	$-0.820304\pi$
$811$	−13.5506	−	41.7045i	−0.475827	−	1.46444i	0.369012	−	0.929424i	$-0.379696\pi$
$812$		0			0
$813$			1.71737i			0.0602306i
$814$		0			0
$815$	−37.7370	+	9.56650i	−1.32187	+	0.335100i
$816$		0			0
$817$	−7.09233	+	2.30444i	−0.248129	+	0.0806220i
$818$		0			0
$819$	−3.61803	−	2.62866i	−0.126424	−	0.0918527i
$820$		0			0
$821$	−5.43938	+	16.7407i	−0.189836	+	0.584254i	−0.999998	−	0.00195152i	$-0.999379\pi$
$821$	−5.43938	+	16.7407i	−0.189836	+	0.584254i	0.810163	+	0.586205i	$0.199379\pi$
$822$		0			0
$823$	−7.43854	−	10.2383i	−0.259291	−	0.356884i	0.659447	−	0.751751i	$-0.270791\pi$
$823$	−7.43854	−	10.2383i	−0.259291	−	0.356884i	−0.918738	+	0.394867i	$0.870791\pi$
$824$		0			0
$825$	−18.1431	+	19.7684i	−0.631660	+	0.688246i
$826$		0			0
$827$	−5.19856	−	7.15520i	−0.180772	−	0.248811i	0.709009	−	0.705200i	$-0.249143\pi$
$827$	−5.19856	−	7.15520i	−0.180772	−	0.248811i	−0.889780	+	0.456389i	$0.849143\pi$
$828$		0			0
$829$	−11.6571	+	35.8767i	−0.404866	+	1.24605i	0.516141	+	0.856504i	$0.327368\pi$
$829$	−11.6571	+	35.8767i	−0.404866	+	1.24605i	−0.921007	+	0.389546i	$0.872632\pi$
$830$		0			0
$831$	−8.68303	−	6.30859i	−0.301211	−	0.218843i
$832$		0			0
$833$	−1.05510	+	0.342823i	−0.0365571	+	0.0118781i
$834$		0			0
$835$	7.16576	−	1.81655i	0.247981	−	0.0628643i
$836$		0			0
$837$		−	48.5765i		−	1.67905i
$838$		0			0
$839$	−11.8934	−	36.6041i	−0.410606	−	1.26372i	−0.916123	−	0.400898i	$-0.868698\pi$
$839$	−11.8934	−	36.6041i	−0.410606	−	1.26372i	0.505517	−	0.862817i	$-0.331302\pi$
$840$		0			0
$841$	9.61452	+	6.98536i	0.331535	+	0.240874i
$842$		0			0
$843$	−24.0774	−	7.82321i	−0.829269	−	0.269446i
$844$		0			0
$845$	12.9712	+	10.7976i	0.446223	+	0.371449i
$846$		0			0
$847$	33.9647	+	43.4580i	1.16704	+	1.49324i
$848$		0			0
$849$	29.4536	−	21.3993i	1.01084	−	0.734421i
$850$		0			0
$851$	−5.51328	+	16.9681i	−0.188993	+	0.581660i
$852$		0			0
$853$	29.9122	−	41.1706i	1.02417	−	1.40965i	0.114936	−	0.993373i	$-0.463334\pi$
$853$	29.9122	−	41.1706i	1.02417	−	1.40965i	0.909237	−	0.416280i	$-0.136666\pi$
$854$		0			0
$855$	−1.48926	+	0.938744i	−0.0509315	+	0.0321044i
$856$		0			0
$857$		−	11.5197i		−	0.393506i	−0.980453	−	0.196753i	$-0.936960\pi$
$857$		−	11.5197i		−	0.393506i	0.980453	−	0.196753i	$-0.0630397\pi$
$858$		0			0
$859$	23.9497			0.817153			0.408577	−	0.912724i	$-0.366025\pi$
$859$	23.9497			0.817153			0.408577	+	0.912724i	$0.366025\pi$
$860$		0			0
$861$	11.4821	+	35.3384i	0.391310	+	1.20433i
$862$		0			0
$863$	23.5170	−	32.3684i	0.800530	−	1.10183i	−0.192187	−	0.981358i	$-0.561558\pi$
$863$	23.5170	−	32.3684i	0.800530	−	1.10183i	0.992716	−	0.120476i	$-0.0384421\pi$
$864$		0			0
$865$	0.755018	−	11.4430i	0.0256714	−	0.389074i
$866$		0			0
$867$	16.1644	+	22.2484i	0.548972	+	0.755595i
$868$		0			0
$869$	−7.18793	−	20.8696i	−0.243834	−	0.707954i
$870$		0			0
$871$	4.71460	−	3.42536i	0.159748	−	0.116064i
$872$		0			0
$873$	2.65270	+	0.861914i	0.0897802	+	0.0291714i
$874$		0			0
$875$	−55.6804	+	6.51646i	−1.88234	+	0.220297i
$876$		0			0
$877$	−24.7104	+	8.02891i	−0.834413	+	0.271117i	−0.694903	−	0.719104i	$-0.744553\pi$
$877$	−24.7104	+	8.02891i	−0.834413	+	0.271117i	−0.139510	+	0.990221i	$0.544553\pi$
$878$		0			0
$879$	29.4300			0.992648
$880$		0			0
$881$	25.1372			0.846893			0.423446	−	0.905921i	$-0.360820\pi$
$881$	25.1372			0.846893			0.423446	+	0.905921i	$0.360820\pi$
$882$		0			0
$883$	41.3431	−	13.4332i	1.39131	−	0.452063i	0.484937	−	0.874549i	$-0.338843\pi$
$883$	41.3431	−	13.4332i	1.39131	−	0.452063i	0.906369	+	0.422486i	$0.138843\pi$
$884$		0			0
$885$	6.51430	+	2.60223i	0.218976	+	0.0874731i
$886$		0			0
$887$	−27.2078	−	8.84036i	−0.913549	−	0.296830i	−0.185731	−	0.982601i	$-0.559465\pi$
$887$	−27.2078	−	8.84036i	−0.913549	−	0.296830i	−0.727818	+	0.685770i	$0.759465\pi$
$888$		0			0
$889$	−58.6701	+	42.6263i	−1.96773	+	1.42964i
$890$		0			0
$891$	20.9430	+	14.6619i	0.701617	+	0.491191i
$892$		0			0
$893$	10.7547	+	14.8026i	0.359892	+	0.495349i
$894$		0			0
$895$	32.2174	+	2.12573i	1.07691	+	0.0710553i
$896$		0			0
$897$	−8.69471	+	11.9672i	−0.290308	+	0.399575i
$898$		0			0
$899$	11.3488	+	34.9281i	0.378504	+	1.16492i
$900$		0			0
$901$	0.135868			0.00452643
$902$		0			0
$903$			29.3536i			0.976827i
$904$		0			0
$905$	22.5219	−	14.1965i	0.748652	−	0.471908i
$906$		0			0
$907$	−28.0438	+	38.5990i	−0.931179	+	1.28166i	0.0282187	+	0.999602i	$0.491017\pi$
$907$	−28.0438	+	38.5990i	−0.931179	+	1.28166i	−0.959398	+	0.282056i	$0.908983\pi$
$908$		0			0
$909$	−0.0261885	+	0.0805998i	−0.000868617	+	0.00267333i
$910$		0			0
$911$	40.3003	−	29.2799i	1.33521	−	0.970085i	0.335602	−	0.942004i	$-0.391060\pi$
$911$	40.3003	−	29.2799i	1.33521	−	0.970085i	0.999606	−	0.0280809i	$-0.00893959\pi$
$912$		0			0
$913$	22.0621	+	29.2724i	0.730150	+	0.968775i
$914$		0			0
$915$	−22.4375	+	26.9543i	−0.741761	+	0.891081i
$916$		0			0
$917$	73.0845	+	23.7466i	2.41346	+	0.784182i
$918$		0			0
$919$	34.7058	+	25.2153i	1.14484	+	0.831775i	0.987786	−	0.155815i	$-0.0498005\pi$
$919$	34.7058	+	25.2153i	1.14484	+	0.831775i	0.157053	+	0.987590i	$0.449801\pi$
$920$		0			0
$921$	−6.19098	−	19.0539i	−0.204000	−	0.627847i
$922$		0			0
$923$		−	20.5862i		−	0.677602i
$924$		0			0
$925$	10.8543	+	20.0328i	0.356889	+	0.658674i
$926$		0			0
$927$	0.205628	−	0.0668126i	0.00675371	−	0.00219441i
$928$		0			0
$929$	−3.20719	−	2.33016i	−0.105224	−	0.0764500i	0.533929	−	0.845529i	$-0.320715\pi$
$929$	−3.20719	−	2.33016i	−0.105224	−	0.0764500i	−0.639153	+	0.769079i	$0.720715\pi$
$930$		0			0
$931$	11.5553	−	35.5635i	0.378709	−	1.16555i
$932$		0			0
$933$	−8.94941	−	12.3178i	−0.292991	−	0.403267i
$934$		0			0
$935$	−0.437576	+	0.119131i	−0.0143103	+	0.00389601i
$936$		0			0
$937$	1.24563	+	1.71446i	0.0406929	+	0.0560090i	0.828879	−	0.559429i	$-0.188979\pi$
$937$	1.24563	+	1.71446i	0.0406929	+	0.0560090i	−0.788186	+	0.615437i	$0.788979\pi$
$938$		0			0
$939$	−7.61585	+	23.4392i	−0.248534	+	0.764909i
$940$		0			0
$941$	−4.08118	−	2.96515i	−0.133043	−	0.0966612i	0.519274	−	0.854608i	$-0.326203\pi$
$941$	−4.08118	−	2.96515i	−0.133043	−	0.0966612i	−0.652316	+	0.757947i	$0.726203\pi$
$942$		0			0
$943$	−17.0537	+	5.54107i	−0.555344	+	0.180442i
$944$		0			0
$945$	15.0766	+	59.4728i	0.490442	+	1.93465i
$946$		0			0
$947$			0.986192i			0.0320470i	0.999872	+	0.0160235i	$0.00510065\pi$
$947$			0.986192i			0.0320470i	−0.999872	+	0.0160235i	$0.994899\pi$
$948$		0			0
$949$	−3.89364	−	11.9834i	−0.126393	−	0.388998i
$950$		0			0
$951$	17.6150	+	12.7981i	0.571206	+	0.415006i
$952$		0			0
$953$	−21.8386	−	7.09580i	−0.707422	−	0.229855i	−0.0668608	−	0.997762i	$-0.521298\pi$
$953$	−21.8386	−	7.09580i	−0.707422	−	0.229855i	−0.640562	+	0.767907i	$0.721298\pi$
$954$		0			0
$955$	−18.0759	−	15.0469i	−0.584924	−	0.486907i
$956$		0			0
$957$	−21.2320	−	6.48934i	−0.686331	−	0.209770i
$958$		0			0
$959$	−4.47994	+	3.25486i	−0.144665	+	0.105105i
$960$		0			0
$961$	14.7718	−	45.4628i	0.476508	−	1.46654i
$962$		0			0
$963$	−0.500670	+	0.689113i	−0.0161339	+	0.0222064i
$964$		0			0
$965$	5.80530	+	9.20972i	0.186879	+	0.296472i
$966$		0			0
$967$		−	20.1267i		−	0.647231i	−0.946189	−	0.323616i	$-0.895102\pi$
$967$		−	20.1267i		−	0.647231i	0.946189	−	0.323616i	$-0.104898\pi$
$968$		0			0
$969$	0.203937			0.00655141
$970$		0			0
$971$	6.77852	+	20.8621i	0.217533	+	0.669498i	0.998964	+	0.0455060i	$0.0144900\pi$
$971$	6.77852	+	20.8621i	0.217533	+	0.669498i	−0.781431	+	0.623991i	$0.785510\pi$
$972$		0			0
$973$	29.1959	−	40.1847i	0.935978	−	1.28826i
$974$		0			0
$975$	3.42637	+	18.5773i	0.109732	+	0.594950i
$976$		0			0
$977$	−34.7133	−	47.7788i	−1.11058	−	1.52858i	−0.820562	−	0.571557i	$-0.806340\pi$
$977$	−34.7133	−	47.7788i	−1.11058	−	1.52858i	−0.290015	−	0.957022i	$-0.593660\pi$
$978$		0			0
$979$	−5.90396	+	19.3167i	−0.188691	+	0.617365i
$980$		0			0
$981$	2.42976	−	1.76533i	0.0775763	−	0.0563625i
$982$		0			0
$983$	45.9751	+	14.9382i	1.46638	+	0.476455i	0.930012	−	0.367530i	$-0.119796\pi$
$983$	45.9751	+	14.9382i	1.46638	+	0.476455i	0.536367	+	0.843985i	$0.319796\pi$
$984$		0			0
$985$	−33.1745	−	13.2520i	−1.05703	−	0.422245i
$986$		0			0
$987$	68.4960	−	22.2557i	2.18025	−	0.708406i
$988$		0			0
$989$	−14.1655			−0.450437
$990$		0			0
$991$	55.0154			1.74762			0.873811	−	0.486266i	$-0.161641\pi$
$991$	55.0154			1.74762			0.873811	+	0.486266i	$0.161641\pi$
$992$		0			0
$993$	5.88201	−	1.91118i	0.186660	−	0.0606495i
$994$		0			0
$995$	−13.8589	+	34.6936i	−0.439356	+	1.09986i
$996$		0			0
$997$	−21.8457	−	7.09810i	−0.691861	−	0.224799i	−0.0580799	−	0.998312i	$-0.518498\pi$
$997$	−21.8457	−	7.09810i	−0.691861	−	0.224799i	−0.633781	+	0.773513i	$0.718498\pi$
$998$		0			0
$999$	20.1736	−	14.6569i	0.638263	−	0.463725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.cd.b.289.4		16
4.3	odd	2		110.2.j.b.69.2	yes	16
5.4	even	2	inner	880.2.cd.b.289.2		16
11.4	even	5	inner	880.2.cd.b.609.2		16
12.11	even	2		990.2.ba.h.289.3		16
20.3	even	4		550.2.h.j.201.2		8
20.7	even	4		550.2.h.n.201.1		8
20.19	odd	2		110.2.j.b.69.4	yes	16
44.15	odd	10		110.2.j.b.59.4	yes	16
44.31	odd	10		1210.2.b.k.969.7		8
44.35	even	10		1210.2.b.l.969.3		8
55.4	even	10	inner	880.2.cd.b.609.4		16
60.59	even	2		990.2.ba.h.289.1		16
132.59	even	10		990.2.ba.h.829.1		16
220.59	odd	10		110.2.j.b.59.2	✓	16
220.79	even	10		1210.2.b.l.969.5		8
220.103	even	20		550.2.h.j.301.2		8
220.119	odd	10		1210.2.b.k.969.1		8
220.123	odd	20		6050.2.a.da.1.1		4
220.147	even	20		550.2.h.n.301.1		8
220.163	even	20		6050.2.a.di.1.2		4
220.167	odd	20		6050.2.a.dl.1.4		4
220.207	even	20		6050.2.a.dd.1.3		4
660.59	even	10		990.2.ba.h.829.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.j.b.59.2	✓	16	220.59	odd	10
110.2.j.b.59.4	yes	16	44.15	odd	10
110.2.j.b.69.2	yes	16	4.3	odd	2
110.2.j.b.69.4	yes	16	20.19	odd	2
550.2.h.j.201.2		8	20.3	even	4
550.2.h.j.301.2		8	220.103	even	20
550.2.h.n.201.1		8	20.7	even	4
550.2.h.n.301.1		8	220.147	even	20
880.2.cd.b.289.2		16	5.4	even	2	inner
880.2.cd.b.289.4		16	1.1	even	1	trivial
880.2.cd.b.609.2		16	11.4	even	5	inner
880.2.cd.b.609.4		16	55.4	even	10	inner
990.2.ba.h.289.1		16	60.59	even	2
990.2.ba.h.289.3		16	12.11	even	2
990.2.ba.h.829.1		16	132.59	even	10
990.2.ba.h.829.3		16	660.59	even	10
1210.2.b.k.969.1		8	220.119	odd	10
1210.2.b.k.969.7		8	44.31	odd	10
1210.2.b.l.969.3		8	44.35	even	10
1210.2.b.l.969.5		8	220.79	even	10
6050.2.a.da.1.1		4	220.123	odd	20
6050.2.a.dd.1.3		4	220.207	even	20
6050.2.a.di.1.2		4	220.163	even	20
6050.2.a.dl.1.4		4	220.167	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)

\(f(q)\)	\(=\)	\(q+(1.53884 - 0.500000i) q^{3} +(-0.829496 + 2.07652i) q^{5} +(-4.76878 - 1.54947i) q^{7} +(-0.309017 + 0.224514i) q^{9} +(0.969425 - 3.17178i) q^{11} +(-1.37249 - 1.88906i) q^{13} +(-0.238203 + 3.61018i) q^{15} +(-0.0359433 + 0.0494717i) q^{17} +(-0.636930 - 1.96027i) q^{19} -8.11314 q^{21} -3.91525i q^{23} +(-3.62387 - 3.44493i) q^{25} +(-3.21644 + 4.42705i) q^{27} +(1.27844 - 3.93464i) q^{29} +(-7.18170 + 5.21781i) q^{31} +(-0.0941007 - 5.36559i) q^{33} +(7.17320 - 8.61720i) q^{35} +(-4.33385 - 1.40815i) q^{37} +(-3.05657 - 2.22073i) q^{39} +(-1.41525 - 4.35570i) q^{41} -3.61803i q^{43} +(-0.209880 - 0.827913i) q^{45} +(-8.44260 + 2.74317i) q^{47} +(14.6773 + 10.6637i) q^{49} +(-0.0305752 + 0.0941007i) q^{51} +(-1.30598 - 1.79753i) q^{53} +(5.78214 + 4.64401i) q^{55} +(-1.96027 - 2.69808i) q^{57} +(0.599137 - 1.84396i) q^{59} +(7.84211 + 5.69763i) q^{61} +(1.82151 - 0.591846i) q^{63} +(5.06115 - 1.28302i) q^{65} +2.49573i q^{67} +(-1.95763 - 6.02495i) q^{69} +(7.13254 + 5.18210i) q^{71} +(5.13205 + 1.66751i) q^{73} +(-7.29903 - 3.48927i) q^{75} +(-9.53757 + 13.6235i) q^{77} +(5.38417 - 3.91183i) q^{79} +(-2.38197 + 7.33094i) q^{81} +(-6.49620 + 8.94125i) q^{83} +(-0.0729142 - 0.115674i) q^{85} -6.69401i q^{87} -6.09017 q^{89} +(3.61803 + 11.1352i) q^{91} +(-8.44260 + 11.6202i) q^{93} +(4.59887 + 0.303437i) q^{95} +(-4.29216 - 5.90765i) q^{97} +(0.412541 + 1.19778i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{5} + 4 q^{9} + 20 q^{11} - 2 q^{15} + 16 q^{19} - 16 q^{21} + 16 q^{29} + 4 q^{31} + 48 q^{35} + 8 q^{39} + 40 q^{41} - 4 q^{45} + 84 q^{49} + 4 q^{51} - 32 q^{55} + 20 q^{61} + 72 q^{65} + 56 q^{71}+ \cdots + 20 q^{99}+O(q^{100}) \) 16 * q - 6 * q^5 + 4 * q^9 + 20 * q^11 - 2 * q^15 + 16 * q^19 - 16 * q^21 + 16 * q^29 + 4 * q^31 + 48 * q^35 + 8 * q^39 + 40 * q^41 - 4 * q^45 + 84 * q^49 + 4 * q^51 - 32 * q^55 + 20 * q^61 + 72 * q^65 + 56 * q^71 - 32 * q^75 - 36 * q^79 - 56 * q^81 - 54 * q^85 - 8 * q^89 + 40 * q^91 + 50 * q^95 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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