LMFDB - Embedded newform 880.2.cm.c.833.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(17,880)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 0, 5, 18]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("880.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.cm (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			833.6
Character	$\chi$	$=$	880.833
Dual form			880.2.cm.c.337.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.45771 - 2.86091i) q^{3} +(-1.70643 - 1.44502i) q^{5} +(1.35828 - 0.692077i) q^{7} +(-4.29653 - 5.91367i) q^{9} +(2.70495 - 1.91918i) q^{11} +(-0.165595 + 1.04553i) q^{13} +(-6.62155 + 2.77553i) q^{15} +(0.347837 + 2.19616i) q^{17} +(-1.91500 - 5.89375i) q^{19} -4.89475i q^{21} +(3.05791 + 3.05791i) q^{23} +(0.823819 + 4.93167i) q^{25} +(-13.6675 + 2.16472i) q^{27} +(-1.39938 + 4.30686i) q^{29} +(-2.32781 + 1.69125i) q^{31} +(-1.54760 - 10.5362i) q^{33} +(-3.31788 - 0.781760i) q^{35} +(-0.631904 - 1.24018i) q^{37} +(2.74977 + 1.99782i) q^{39} +(2.38365 - 0.774496i) q^{41} +(6.40957 - 6.40957i) q^{43} +(-1.21365 + 16.2999i) q^{45} +(-3.99740 - 2.03678i) q^{47} +(-2.74855 + 3.78305i) q^{49} +(6.79005 + 2.20622i) q^{51} +(3.75665 + 0.594995i) q^{53} +(-7.38907 - 0.633749i) q^{55} +(-19.6530 - 3.11273i) q^{57} +(4.27154 + 1.38791i) q^{59} +(3.48115 - 4.79140i) q^{61} +(-9.92860 - 5.05887i) q^{63} +(1.79339 - 1.54483i) q^{65} +(-5.40776 + 5.40776i) q^{67} +(13.2059 - 4.29086i) q^{69} +(7.19862 + 5.23010i) q^{71} +(-5.17847 - 10.1633i) q^{73} +(15.3099 + 4.83204i) q^{75} +(2.34584 - 4.47882i) q^{77} +(-4.69179 + 3.40879i) q^{79} +(-6.95367 + 21.4012i) q^{81} +(-1.26330 + 0.200087i) q^{83} +(2.57994 - 4.25022i) q^{85} +(10.2816 + 10.2816i) q^{87} +10.5518i q^{89} +(0.498662 + 1.53472i) q^{91} +(1.44526 + 9.12499i) q^{93} +(-5.24880 + 12.8245i) q^{95} +(1.09605 - 6.92020i) q^{97} +(-22.9713 - 7.75031i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{3} - 8 q^{5} + 20 q^{7} - 12 q^{11} + 16 q^{15} - 20 q^{17} + 8 q^{23} - 20 q^{25} - 8 q^{27} - 16 q^{31} - 104 q^{33} + 20 q^{37} - 20 q^{41} + 16 q^{45} - 40 q^{47} - 40 q^{51} - 96 q^{55}+ \cdots + 72 q^{97}+O(q^{100}) $ 48 * q + 4 * q^3 - 8 * q^5 + 20 * q^7 - 12 * q^11 + 16 * q^15 - 20 * q^17 + 8 * q^23 - 20 * q^25 - 8 * q^27 - 16 * q^31 - 104 * q^33 + 20 * q^37 - 20 * q^41 + 16 * q^45 - 40 * q^47 - 40 * q^51 - 96 * q^55 + 80 * q^61 - 100 * q^63 + 56 * q^71 - 20 * q^73 + 76 * q^75 - 96 * q^77 - 68 * q^81 - 80 * q^85 + 68 * q^91 + 76 * q^93 - 20 * q^95 + 72 * q^97

Character values

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

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{10}\right)$	$1$

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
$3$	1.45771	−	2.86091i	0.841606	−	1.65175i	0.0863983	−	0.996261i	$-0.472464\pi$
$3$	1.45771	−	2.86091i	0.841606	−	1.65175i	0.755208	−	0.655485i	$-0.227536\pi$
$4$		0			0
$5$	−1.70643	−	1.44502i	−0.763139	−	0.646234i
$5$	−1.70643	−	1.44502i	−0.763139	−	0.646234i
$6$		0			0
$7$	1.35828	−	0.692077i	0.513381	−	0.261581i	−0.178052	−	0.984021i	$-0.556980\pi$
$7$	1.35828	−	0.692077i	0.513381	−	0.261581i	0.691433	+	0.722440i	$0.256980\pi$
$8$		0			0
$9$	−4.29653	−	5.91367i	−1.43218	−	1.97122i
$10$		0			0
$11$	2.70495	−	1.91918i	0.815572	−	0.578656i
$11$	2.70495	−	1.91918i	0.815572	−	0.578656i
$12$		0			0
$13$	−0.165595	+	1.04553i	−0.0459279	+	0.289977i	−0.999952	−	0.00975110i	$-0.996896\pi$
$13$	−0.165595	+	1.04553i	−0.0459279	+	0.289977i	0.954025	+	0.299728i	$0.0968961\pi$
$14$		0			0
$15$	−6.62155	+	2.77553i	−1.70968	+	0.716638i
$16$		0			0
$17$	0.347837	+	2.19616i	0.0843629	+	0.532646i	0.993286	+	0.115683i	$0.0369057\pi$
$17$	0.347837	+	2.19616i	0.0843629	+	0.532646i	−0.908923	+	0.416963i	$0.863094\pi$
$18$		0			0
$19$	−1.91500	−	5.89375i	−0.439330	−	1.35212i	−0.888583	−	0.458715i	$-0.848310\pi$
$19$	−1.91500	−	5.89375i	−0.439330	−	1.35212i	0.449253	−	0.893405i	$-0.351690\pi$
$20$		0			0
$21$		−	4.89475i		−	1.06812i
$22$		0			0
$23$	3.05791	+	3.05791i	0.637617	+	0.637617i	0.949967	−	0.312350i	$-0.101116\pi$
$23$	3.05791	+	3.05791i	0.637617	+	0.637617i	−0.312350	+	0.949967i	$0.601116\pi$
$24$		0			0
$25$	0.823819	+	4.93167i	0.164764	+	0.986333i
$26$		0			0
$27$	−13.6675	+	2.16472i	−2.63031	+	0.416601i
$28$		0			0
$29$	−1.39938	+	4.30686i	−0.259859	+	0.799763i	0.732975	+	0.680256i	$0.238131\pi$
$29$	−1.39938	+	4.30686i	−0.259859	+	0.799763i	−0.992833	+	0.119507i	$0.961869\pi$
$30$		0			0
$31$	−2.32781	+	1.69125i	−0.418087	+	0.303758i	−0.776868	−	0.629664i	$-0.783193\pi$
$31$	−2.32781	+	1.69125i	−0.418087	+	0.303758i	0.358781	+	0.933422i	$0.383193\pi$
$32$		0			0
$33$	−1.54760	−	10.5362i	−0.269402	−	1.83412i
$34$		0			0
$35$	−3.31788	−	0.781760i	−0.560823	−	0.132142i
$36$		0			0
$37$	−0.631904	−	1.24018i	−0.103884	−	0.203885i	0.833213	−	0.552952i	$-0.186499\pi$
$37$	−0.631904	−	1.24018i	−0.103884	−	0.203885i	−0.937098	+	0.349067i	$0.886499\pi$
$38$		0			0
$39$	2.74977	+	1.99782i	0.440316	+	0.319908i
$40$		0			0
$41$	2.38365	−	0.774496i	0.372264	−	0.120956i	−0.116909	−	0.993143i	$-0.537299\pi$
$41$	2.38365	−	0.774496i	0.372264	−	0.120956i	0.489173	+	0.872187i	$0.337299\pi$
$42$		0			0
$43$	6.40957	−	6.40957i	0.977450	−	0.977450i	−0.0223009	−	0.999751i	$-0.507099\pi$
$43$	6.40957	−	6.40957i	0.977450	−	0.977450i	0.999751	+	0.0223009i	$0.00709920\pi$
$44$		0			0
$45$	−1.21365	+	16.2999i	−0.180920	+	2.42984i
$46$		0			0
$47$	−3.99740	−	2.03678i	−0.583081	−	0.297095i	0.137460	−	0.990507i	$-0.456106\pi$
$47$	−3.99740	−	2.03678i	−0.583081	−	0.297095i	−0.720541	+	0.693413i	$0.756106\pi$
$48$		0			0
$49$	−2.74855	+	3.78305i	−0.392650	+	0.540436i
$50$		0			0
$51$	6.79005	+	2.20622i	0.950797	+	0.308933i
$52$		0			0
$53$	3.75665	+	0.594995i	0.516016	+	0.0817288i	0.409011	−	0.912530i	$-0.365874\pi$
$53$	3.75665	+	0.594995i	0.516016	+	0.0817288i	0.107005	+	0.994258i	$0.465874\pi$
$54$		0			0
$55$	−7.38907	−	0.633749i	−0.996342	−	0.0854548i
$56$		0			0
$57$	−19.6530	−	3.11273i	−2.60310	−	0.412291i
$58$		0			0
$59$	4.27154	+	1.38791i	0.556107	+	0.180690i	0.573569	−	0.819158i	$-0.305559\pi$
$59$	4.27154	+	1.38791i	0.556107	+	0.180690i	−0.0174620	+	0.999848i	$0.505559\pi$
$60$		0			0
$61$	3.48115	−	4.79140i	0.445716	−	0.613475i	−0.525754	−	0.850636i	$-0.676217\pi$
$61$	3.48115	−	4.79140i	0.445716	−	0.613475i	0.971470	+	0.237161i	$0.0762169\pi$
$62$		0			0
$63$	−9.92860	−	5.05887i	−1.25089	−	0.637358i
$64$		0			0
$65$	1.79339	−	1.54483i	0.222443	−	0.191613i
$66$		0			0
$67$	−5.40776	+	5.40776i	−0.660663	+	0.660663i	−0.955536	−	0.294873i	$-0.904723\pi$
$67$	−5.40776	+	5.40776i	−0.660663	+	0.660663i	0.294873	+	0.955536i	$0.404723\pi$
$68$		0			0
$69$	13.2059	−	4.29086i	1.58980	−	0.516559i
$70$		0			0
$71$	7.19862	+	5.23010i	0.854319	+	0.620699i	0.926334	−	0.376704i	$-0.122943\pi$
$71$	7.19862	+	5.23010i	0.854319	+	0.620699i	−0.0720143	+	0.997404i	$0.522943\pi$
$72$		0			0
$73$	−5.17847	−	10.1633i	−0.606094	−	1.18953i	−0.966485	−	0.256725i	$-0.917357\pi$
$73$	−5.17847	−	10.1633i	−0.606094	−	1.18953i	0.360391	−	0.932801i	$-0.382643\pi$
$74$		0			0
$75$	15.3099	+	4.83204i	1.76784	+	0.557956i
$76$		0			0
$77$	2.34584	−	4.47882i	0.267334	−	0.510409i
$78$		0			0
$79$	−4.69179	+	3.40879i	−0.527868	+	0.383518i	−0.819560	−	0.572994i	$-0.805782\pi$
$79$	−4.69179	+	3.40879i	−0.527868	+	0.383518i	0.291692	+	0.956512i	$0.405782\pi$
$80$		0			0
$81$	−6.95367	+	21.4012i	−0.772631	+	2.37791i
$82$		0			0
$83$	−1.26330	+	0.200087i	−0.138665	+	0.0219624i	−0.225381	−	0.974271i	$-0.572363\pi$
$83$	−1.26330	+	0.200087i	−0.138665	+	0.0219624i	0.0867161	+	0.996233i	$0.472363\pi$
$84$		0			0
$85$	2.57994	−	4.25022i	0.279833	−	0.461002i
$86$		0			0
$87$	10.2816	+	10.2816i	1.10231	+	1.10231i
$88$		0			0
$89$			10.5518i			1.11849i	0.829004	+	0.559243i	$0.188908\pi$
$89$			10.5518i			1.11849i	−0.829004	+	0.559243i	$0.811092\pi$
$90$		0			0
$91$	0.498662	+	1.53472i	0.0522740	+	0.160883i
$92$		0			0
$93$	1.44526	+	9.12499i	0.149866	+	0.946218i
$94$		0			0
$95$	−5.24880	+	12.8245i	−0.538515	+	1.31577i
$96$		0			0
$97$	1.09605	−	6.92020i	0.111287	−	0.702639i	−0.867451	−	0.497523i	$-0.834243\pi$
$97$	1.09605	−	6.92020i	0.111287	−	0.702639i	0.978738	−	0.205116i	$-0.0657572\pi$
$98$		0			0
$99$	−22.9713	−	7.75031i	−2.30870	−	0.778936i
$100$		0			0
$101$	10.3519	+	14.2481i	1.03005	+	1.41774i	0.904912	+	0.425599i	$0.139937\pi$
$101$	10.3519	+	14.2481i	1.03005	+	1.41774i	0.125136	+	0.992140i	$0.460063\pi$
$102$		0			0
$103$	2.86217	−	1.45835i	0.282018	−	0.143695i	−0.307260	−	0.951625i	$-0.599412\pi$
$103$	2.86217	−	1.45835i	0.282018	−	0.143695i	0.589278	+	0.807930i	$0.299412\pi$
$104$		0			0
$105$	−7.07303	+	8.35256i	−0.690257	+	0.815127i
$106$		0			0
$107$	7.49892	−	14.7175i	0.724948	−	1.42279i	−0.174006	−	0.984745i	$-0.555671\pi$
$107$	7.49892	−	14.7175i	0.724948	−	1.42279i	0.898953	−	0.438045i	$-0.144329\pi$
$108$		0			0
$109$	−1.88801			−0.180839			−0.0904195	−	0.995904i	$-0.528821\pi$
$109$	−1.88801			−0.180839			−0.0904195	+	0.995904i	$0.528821\pi$
$110$		0			0
$111$	−4.46917			−0.424195
$112$		0			0
$113$	1.81113	−	3.55455i	0.170377	−	0.334384i	−0.789991	−	0.613118i	$-0.789915\pi$
$113$	1.81113	−	3.55455i	0.170377	−	0.334384i	0.960368	+	0.278734i	$0.0899149\pi$
$114$		0			0
$115$	−0.799364	−	9.63685i	−0.0745411	−	0.898641i
$116$		0			0
$117$	6.89439	−	3.51287i	0.637387	−	0.324765i
$118$		0			0
$119$	1.99237	+	2.74226i	0.182640	+	0.251383i
$120$		0			0
$121$	3.63346	−	10.3826i	0.330314	−	0.943871i
$122$		0			0
$123$	1.25890	−	7.94840i	0.113511	−	0.716683i
$124$		0			0
$125$	5.72058	−	9.60599i	0.511664	−	0.859186i
$126$		0			0
$127$	−2.65395	−	16.7564i	−0.235500	−	1.48689i	−0.767995	−	0.640456i	$-0.778746\pi$
$127$	−2.65395	−	16.7564i	−0.235500	−	1.48689i	0.532495	−	0.846433i	$-0.321254\pi$
$128$		0			0
$129$	−8.99392	−	27.6805i	−0.791871	−	2.43713i
$130$		0			0
$131$		−	9.77651i		−	0.854177i	−0.904210	−	0.427089i	$-0.859539\pi$
$131$		−	9.77651i		−	0.854177i	0.904210	−	0.427089i	$-0.140461\pi$
$132$		0			0
$133$	−6.68003	−	6.68003i	−0.579232	−	0.579232i
$134$		0			0
$135$	26.4507	+	16.0559i	2.27652	+	1.38187i
$136$		0			0
$137$	−2.44036	+	0.386515i	−0.208494	+	0.0330222i	−0.259808	−	0.965660i	$-0.583659\pi$
$137$	−2.44036	+	0.386515i	−0.208494	+	0.0330222i	0.0513136	+	0.998683i	$0.483659\pi$
$138$		0			0
$139$	2.32161	−	7.14518i	0.196916	−	0.606046i	−0.803032	−	0.595935i	$-0.796781\pi$
$139$	2.32161	−	7.14518i	0.196916	−	0.606046i	0.999949	−	0.0101112i	$-0.00321854\pi$
$140$		0			0
$141$	−11.6541	+	8.46717i	−0.981449	+	0.713065i
$142$		0			0
$143$	1.55864	+	3.14590i	0.130340	+	0.263074i
$144$		0			0
$145$	8.61146	−	5.32722i	0.715143	−	0.442401i
$146$		0			0
$147$	6.81639	+	13.3779i	0.562206	+	1.10339i
$148$		0			0
$149$	0.0269615	+	0.0195887i	0.00220877	+	0.00160477i	0.588889	−	0.808214i	$-0.299565\pi$
$149$	0.0269615	+	0.0195887i	0.00220877	+	0.00160477i	−0.586680	+	0.809819i	$0.699565\pi$
$150$		0			0
$151$	20.1481	−	6.54653i	1.63963	−	0.532749i	0.663176	−	0.748463i	$-0.269208\pi$
$151$	20.1481	−	6.54653i	1.63963	−	0.532749i	0.976457	+	0.215714i	$0.0692079\pi$
$152$		0			0
$153$	11.4929	−	11.4929i	0.929142	−	0.929142i
$154$		0			0
$155$	6.41615	+	0.477730i	0.515357	+	0.0383722i
$156$		0			0
$157$	1.75037	+	0.891858i	0.139695	+	0.0711780i	0.522441	−	0.852676i	$-0.325022\pi$
$157$	1.75037	+	0.891858i	0.139695	+	0.0711780i	−0.382746	+	0.923854i	$0.625022\pi$
$158$		0			0
$159$	7.17831	−	9.88010i	0.569277	−	0.783543i
$160$		0			0
$161$	6.26979	+	2.03718i	0.494129	+	0.160552i
$162$		0			0
$163$	2.15047	+	0.340601i	0.168438	+	0.0266779i	0.240084	−	0.970752i	$-0.422825\pi$
$163$	2.15047	+	0.340601i	0.168438	+	0.0266779i	−0.0716458	+	0.997430i	$0.522825\pi$
$164$		0			0
$165$	−12.5842	+	20.2156i	−0.979677	+	1.57378i
$166$		0			0
$167$	−21.1879	−	3.35583i	−1.63957	−	0.259682i	−0.732530	−	0.680735i	$-0.761661\pi$
$167$	−21.1879	−	3.35583i	−1.63957	−	0.259682i	−0.907036	+	0.421053i	$0.861661\pi$
$168$		0			0
$169$	11.2980	+	3.67095i	0.869079	+	0.282381i
$170$		0			0
$171$	−26.6259	+	36.6474i	−2.03613	+	2.80249i
$172$		0			0
$173$	11.7553	+	5.98965i	0.893742	+	0.455384i	0.839635	−	0.543151i	$-0.182769\pi$
$173$	11.7553	+	5.98965i	0.893742	+	0.455384i	0.0541069	+	0.998535i	$0.482769\pi$
$174$		0			0
$175$	4.53207	+	6.12843i	0.342592	+	0.463266i
$176$		0			0
$177$	10.1973	−	10.1973i	0.766477	−	0.766477i
$178$		0			0
$179$	12.8887	−	4.18779i	0.963346	−	0.313010i	0.215219	−	0.976566i	$-0.430953\pi$
$179$	12.8887	−	4.18779i	0.963346	−	0.313010i	0.748127	+	0.663555i	$0.230953\pi$
$180$		0			0
$181$	−13.9517	−	10.1365i	−1.03702	−	0.753441i	−0.0673204	−	0.997731i	$-0.521445\pi$
$181$	−13.9517	−	10.1365i	−1.03702	−	0.753441i	−0.969702	+	0.244290i	$0.921445\pi$
$182$		0			0
$183$	−8.63324	−	16.9437i	−0.638188	−	1.25251i
$184$		0			0
$185$	−0.713789	+	3.02940i	−0.0524788	+	0.222726i
$186$		0			0
$187$	5.15571	+	5.27292i	0.377023	+	0.385594i
$188$		0			0
$189$	−17.0661	+	12.3993i	−1.24138	+	0.901914i
$190$		0			0
$191$	3.89136	−	11.9764i	0.281569	−	0.866580i	−0.705837	−	0.708374i	$-0.749429\pi$
$191$	3.89136	−	11.9764i	0.281569	−	0.866580i	0.987406	−	0.158206i	$-0.0505709\pi$
$192$		0			0
$193$	−3.78808	+	0.599973i	−0.272672	+	0.0431870i	−0.291273	−	0.956640i	$-0.594079\pi$
$193$	−3.78808	+	0.599973i	−0.272672	+	0.0431870i	0.0186009	+	0.999827i	$0.494079\pi$
$194$		0			0
$195$	−1.80539	−	7.38263i	−0.129287	−	0.528681i
$196$		0			0
$197$	7.40013	+	7.40013i	0.527238	+	0.527238i	0.919748	−	0.392510i	$-0.128393\pi$
$197$	7.40013	+	7.40013i	0.527238	+	0.527238i	−0.392510	+	0.919748i	$0.628393\pi$
$198$		0			0
$199$			9.10742i			0.645608i	0.946466	+	0.322804i	$0.104625\pi$
$199$			9.10742i			0.645608i	−0.946466	+	0.322804i	$0.895375\pi$
$200$		0			0
$201$	7.58818	+	23.3540i	0.535229	+	1.64727i
$202$		0			0
$203$	1.07993	+	6.81839i	0.0757960	+	0.478557i
$204$		0			0
$205$	−5.18670	−	2.12281i	−0.362255	−	0.148263i
$206$		0			0
$207$	4.94505	−	31.2218i	0.343705	−	2.17007i
$208$		0			0
$209$	−16.4912	−	12.2671i	−1.14072	−	0.848530i
$210$		0			0
$211$	14.7378	+	20.2849i	1.01459	+	1.39647i	0.915926	+	0.401347i	$0.131458\pi$
$211$	14.7378	+	20.2849i	1.01459	+	1.39647i	0.0986665	+	0.995121i	$0.468542\pi$
$212$		0			0
$213$	25.4563	−	12.9706i	1.74424	−	0.888734i
$214$		0			0
$215$	−20.1995	+	1.67552i	−1.37759	+	0.114270i
$216$		0			0
$217$	−1.99133	+	3.90821i	−0.135181	+	0.265307i
$218$		0			0
$219$	−36.6250			−2.47489
$220$		0			0
$221$	−2.35374			−0.158330
$222$		0			0
$223$	2.26373	−	4.44282i	0.151590	−	0.297513i	−0.802706	−	0.596375i	$-0.796607\pi$
$223$	2.26373	−	4.44282i	0.151590	−	0.297513i	0.954296	+	0.298862i	$0.0966071\pi$
$224$		0			0
$225$	25.6247	−	26.0608i	1.70831	−	1.73739i
$226$		0			0
$227$	−1.81833	+	0.926486i	−0.120687	+	0.0614931i	−0.513292	−	0.858214i	$-0.671574\pi$
$227$	−1.81833	+	0.926486i	−0.120687	+	0.0614931i	0.392605	+	0.919707i	$0.371574\pi$
$228$		0			0
$229$	0.895888	+	1.23308i	0.0592020	+	0.0814845i	0.837591	−	0.546297i	$-0.183963\pi$
$229$	0.895888	+	1.23308i	0.0592020	+	0.0814845i	−0.778389	+	0.627782i	$0.783963\pi$
$230$		0			0
$231$	−9.39394	−	13.2400i	−0.618076	−	0.871131i
$232$		0			0
$233$	−3.47122	+	21.9164i	−0.227407	+	1.43579i	0.564642	+	0.825336i	$0.309014\pi$
$233$	−3.47122	+	21.9164i	−0.227407	+	1.43579i	−0.792050	+	0.610457i	$0.790986\pi$
$234$		0			0
$235$	3.87810	+	9.25196i	0.252980	+	0.603531i
$236$		0			0
$237$	2.91297	+	18.3918i	0.189218	+	1.19468i
$238$		0			0
$239$	7.65870	+	23.5711i	0.495400	+	1.52468i	0.816332	+	0.577583i	$0.196004\pi$
$239$	7.65870	+	23.5711i	0.495400	+	1.52468i	−0.320932	+	0.947102i	$0.603996\pi$
$240$		0			0
$241$		−	0.0562577i		−	0.00362387i	−0.999998	−	0.00181194i	$-0.999423\pi$
$241$		−	0.0562577i		−	0.00362387i	0.999998	−	0.00181194i	$-0.000576758\pi$
$242$		0			0
$243$	21.7359	+	21.7359i	1.39436	+	1.39436i
$244$		0			0
$245$	10.1568	−	2.48381i	0.648895	−	0.158685i
$246$		0			0
$247$	6.47920	−	1.02620i	0.412262	−	0.0652958i
$248$		0			0
$249$	−1.26909	+	3.90585i	−0.0804251	+	0.247523i
$250$		0			0
$251$	−6.81505	+	4.95143i	−0.430162	+	0.312531i	−0.781714	−	0.623637i	$-0.785654\pi$
$251$	−6.81505	+	4.95143i	−0.430162	+	0.312531i	0.351551	+	0.936169i	$0.385654\pi$
$252$		0			0
$253$	14.1402	+	2.40278i	0.888984	+	0.151062i
$254$		0			0
$255$	−8.39871	−	13.5765i	−0.525948	−	0.850196i
$256$		0			0
$257$	4.76675	+	9.35527i	0.297342	+	0.583566i	0.990547	−	0.137175i	$-0.0438021\pi$
$257$	4.76675	+	9.35527i	0.297342	+	0.583566i	−0.693205	+	0.720740i	$0.743802\pi$
$258$		0			0
$259$	−1.71660	−	1.24718i	−0.106664	−	0.0774963i
$260$		0			0
$261$	31.4818	−	10.2291i	1.94868	−	0.633163i
$262$		0			0
$263$	−3.20922	+	3.20922i	−0.197889	+	0.197889i	−0.799095	−	0.601205i	$-0.794687\pi$
$263$	−3.20922	+	3.20922i	−0.197889	+	0.197889i	0.601205	+	0.799095i	$0.294687\pi$
$264$		0			0
$265$	−5.55069	−	6.44376i	−0.340976	−	0.395837i
$266$		0			0
$267$	30.1877	+	15.3814i	1.84746	+	0.941325i
$268$		0			0
$269$	−15.2248	+	20.9551i	−0.928272	+	1.27766i	0.0322573	+	0.999480i	$0.489730\pi$
$269$	−15.2248	+	20.9551i	−0.928272	+	1.27766i	−0.960530	+	0.278178i	$0.910270\pi$
$270$		0			0
$271$	−20.4415	−	6.64186i	−1.24173	−	0.403464i	−0.386783	−	0.922171i	$-0.626414\pi$
$271$	−20.4415	−	6.64186i	−1.24173	−	0.403464i	−0.854952	+	0.518707i	$0.826414\pi$
$272$		0			0
$273$	5.11760	+	0.810549i	0.309731	+	0.0490566i
$274$		0			0
$275$	11.6932	+	11.7588i	0.705124	+	0.709084i
$276$		0			0
$277$	−13.5625	−	2.14809i	−0.814893	−	0.129066i	−0.264943	−	0.964264i	$-0.585353\pi$
$277$	−13.5625	−	2.14809i	−0.814893	−	0.129066i	−0.549950	+	0.835198i	$0.685353\pi$
$278$		0			0
$279$	20.0030	+	6.49937i	1.19755	+	0.389107i
$280$		0			0
$281$	5.82266	−	8.01420i	0.347351	−	0.478087i	−0.599220	−	0.800585i	$-0.704522\pi$
$281$	5.82266	−	8.01420i	0.347351	−	0.478087i	0.946570	+	0.322498i	$0.104522\pi$
$282$		0			0
$283$	1.83534	+	0.935154i	0.109100	+	0.0555891i	0.507689	−	0.861541i	$-0.330500\pi$
$283$	1.83534	+	0.935154i	0.109100	+	0.0555891i	−0.398589	+	0.917130i	$0.630500\pi$
$284$		0			0
$285$	29.0385	+	33.7107i	1.72009	+	1.99685i
$286$		0			0
$287$	2.70165	−	2.70165i	0.159473	−	0.159473i
$288$		0			0
$289$	11.4658	−	3.72548i	0.674461	−	0.219146i
$290$		0			0
$291$	−18.2003	−	13.2233i	−1.06692	−	0.775164i
$292$		0			0
$293$	−8.91767	−	17.5019i	−0.520976	−	1.02247i	−0.990234	−	0.139412i	$-0.955479\pi$
$293$	−8.91767	−	17.5019i	−0.520976	−	1.02247i	0.469259	−	0.883061i	$-0.344521\pi$
$294$		0			0
$295$	−5.28353	−	8.54083i	−0.307619	−	0.497266i
$296$		0			0
$297$	−32.8154	+	32.0859i	−1.90414	+	1.86181i
$298$		0			0
$299$	−3.70350	+	2.69075i	−0.214179	+	0.155610i
$300$		0			0
$301$	4.27006	−	13.1419i	0.246122	−	0.757486i
$302$		0			0
$303$	55.8524	−	8.84616i	3.20864	−	0.508199i
$304$		0			0
$305$	−12.8640	+	3.14584i	−0.736592	+	0.180131i
$306$		0			0
$307$	8.35315	+	8.35315i	0.476740	+	0.476740i	0.904087	−	0.427348i	$-0.140552\pi$
$307$	8.35315	+	8.35315i	0.476740	+	0.476740i	−0.427348	+	0.904087i	$0.640552\pi$
$308$		0			0
$309$		−	10.3142i		−	0.586757i
$310$		0			0
$311$	4.29712	+	13.2252i	0.243667	+	0.749931i	0.995853	+	0.0909796i	$0.0289998\pi$
$311$	4.29712	+	13.2252i	0.243667	+	0.749931i	−0.752185	+	0.658952i	$0.771000\pi$
$312$		0			0
$313$	4.72303	+	29.8201i	0.266962	+	1.68553i	0.648530	+	0.761189i	$0.275384\pi$
$313$	4.72303	+	29.8201i	0.266962	+	1.68553i	−0.381569	+	0.924341i	$0.624616\pi$
$314$		0			0
$315$	9.63229	+	22.9797i	0.542718	+	1.29476i
$316$		0			0
$317$	4.79669	−	30.2851i	0.269409	−	1.70098i	−0.367485	−	0.930029i	$-0.619781\pi$
$317$	4.79669	−	30.2851i	0.269409	−	1.70098i	0.636894	−	0.770951i	$-0.280219\pi$
$318$		0			0
$319$	4.48040	+	14.3355i	0.250854	+	0.802633i
$320$		0			0
$321$	−31.1741	−	42.9074i	−1.73997	−	2.39486i
$322$		0			0
$323$	12.2775	−	6.25570i	0.683139	−	0.348076i
$324$		0			0
$325$	−5.29262	+	0.0446648i	−0.293581	+	0.00247756i
$326$		0			0
$327$	−2.75217	+	5.40143i	−0.152195	+	0.298700i
$328$		0			0
$329$	−6.83919			−0.377057
$330$		0			0
$331$	−14.2522			−0.783372			−0.391686	−	0.920099i	$-0.628108\pi$
$331$	−14.2522			−0.783372			−0.391686	+	0.920099i	$0.628108\pi$
$332$		0			0
$333$	−4.61903	+	9.06535i	−0.253121	+	0.496778i
$334$		0			0
$335$	17.0423	−	1.41364i	0.931121	−	0.0772353i
$336$		0			0
$337$	12.2410	−	6.23713i	0.666812	−	0.339758i	−0.0876027	−	0.996155i	$-0.527921\pi$
$337$	12.2410	−	6.23713i	0.666812	−	0.339758i	0.754415	+	0.656398i	$0.227921\pi$
$338$		0			0
$339$	−7.52914	−	10.3630i	−0.408927	−	0.562839i
$340$		0			0
$341$	−3.05077	+	9.04224i	−0.165208	+	0.489665i
$342$		0			0
$343$	−2.78444	+	17.5803i	−0.150346	+	0.949246i
$344$		0			0
$345$	−28.7354	−	11.7608i	−1.54706	−	0.633179i
$346$		0			0
$347$	2.77431	+	17.5163i	0.148933	+	0.940326i	0.943072	+	0.332589i	$0.107922\pi$
$347$	2.77431	+	17.5163i	0.148933	+	0.940326i	−0.794139	+	0.607737i	$0.792078\pi$
$348$		0			0
$349$	5.50175	+	16.9327i	0.294502	+	0.906384i	0.983388	+	0.181515i	$0.0581000\pi$
$349$	5.50175	+	16.9327i	0.294502	+	0.906384i	−0.688886	+	0.724870i	$0.741900\pi$
$350$		0			0
$351$		−	14.6482i		−	0.781865i
$352$		0			0
$353$	12.3974	+	12.3974i	0.659845	+	0.659845i	0.955343	−	0.295499i	$-0.0954858\pi$
$353$	12.3974	+	12.3974i	0.659845	+	0.659845i	−0.295499	+	0.955343i	$0.595486\pi$
$354$		0			0
$355$	−4.72634	−	19.3270i	−0.250848	−	1.02577i
$356$		0			0
$357$	10.7496	−	1.70258i	0.568932	−	0.0901099i
$358$		0			0
$359$	2.37480	−	7.30888i	0.125337	−	0.385748i	−0.868625	−	0.495470i	$-0.834996\pi$
$359$	2.37480	−	7.30888i	0.125337	−	0.385748i	0.993962	+	0.109722i	$0.0349959\pi$
$360$		0			0
$361$	−15.6978	+	11.4051i	−0.826200	+	0.600270i
$362$		0			0
$363$	−24.4071	−	25.5297i	−1.28104	−	1.33996i
$364$		0			0
$365$	−5.84952	+	24.8260i	−0.306178	+	1.29945i
$366$		0			0
$367$	−16.4293	−	32.2443i	−0.857603	−	1.68314i	−0.721464	−	0.692452i	$-0.756531\pi$
$367$	−16.4293	−	32.2443i	−0.857603	−	1.68314i	−0.136139	−	0.990690i	$-0.543469\pi$
$368$		0			0
$369$	−14.8215	−	10.7685i	−0.771579	−	0.560585i
$370$		0			0
$371$	5.51436	−	1.79172i	0.286291	−	0.0930217i
$372$		0			0
$373$	−11.5350	+	11.5350i	−0.597259	+	0.597259i	−0.939582	−	0.342323i	$-0.888786\pi$
$373$	−11.5350	+	11.5350i	−0.597259	+	0.597259i	0.342323	+	0.939582i	$0.388786\pi$
$374$		0			0
$375$	−19.1429	−	30.3687i	−0.988536	−	1.56823i
$376$		0			0
$377$	−4.27121	−	2.17629i	−0.219978	−	0.112085i
$378$		0			0
$379$	−3.86753	+	5.32320i	−0.198662	+	0.273434i	−0.896712	−	0.442614i	$-0.854051\pi$
$379$	−3.86753	+	5.32320i	−0.198662	+	0.273434i	0.698050	+	0.716049i	$0.254051\pi$
$380$		0			0
$381$	−51.8071	−	16.8332i	−2.65416	−	0.862389i
$382$		0			0
$383$	−28.9091	−	4.57876i	−1.47719	−	0.233963i	−0.634733	−	0.772731i	$-0.718890\pi$
$383$	−28.9091	−	4.57876i	−1.47719	−	0.233963i	−0.842454	+	0.538768i	$0.818890\pi$
$384$		0			0
$385$	−10.4750	+	4.25300i	−0.533856	+	0.216753i
$386$		0			0
$387$	−65.4430	−	10.3652i	−3.32665	−	0.526890i
$388$		0			0
$389$	−4.21993	−	1.37114i	−0.213959	−	0.0695195i	0.200076	−	0.979780i	$-0.435881\pi$
$389$	−4.21993	−	1.37114i	−0.213959	−	0.0695195i	−0.414035	+	0.910261i	$0.635881\pi$
$390$		0			0
$391$	−5.65199	+	7.77930i	−0.285833	+	0.393416i
$392$		0			0
$393$	−27.9697	−	14.2513i	−1.41088	−	0.718881i
$394$		0			0
$395$	12.9320	+	0.962884i	0.650679	+	0.0484480i
$396$		0			0
$397$	6.59354	−	6.59354i	0.330920	−	0.330920i	−0.522016	−	0.852936i	$-0.674820\pi$
$397$	6.59354	−	6.59354i	0.330920	−	0.330920i	0.852936	+	0.522016i	$0.174820\pi$
$398$		0			0
$399$	−28.8485	+	9.37344i	−1.44423	+	0.469259i
$400$		0			0
$401$	−7.12541	−	5.17691i	−0.355826	−	0.258523i	0.395483	−	0.918473i	$-0.370577\pi$
$401$	−7.12541	−	5.17691i	−0.355826	−	0.258523i	−0.751309	+	0.659951i	$0.770577\pi$
$402$		0			0
$403$	−1.38278	−	2.71385i	−0.0688811	−	0.135187i
$404$		0			0
$405$	42.7912	−	26.4715i	2.12631	−	1.31538i
$406$		0			0
$407$	−4.08940	−	2.14188i	−0.202704	−	0.106169i
$408$		0			0
$409$	14.0728	−	10.2245i	0.695853	−	0.505567i	−0.182726	−	0.983164i	$-0.558492\pi$
$409$	14.0728	−	10.2245i	0.695853	−	0.505567i	0.878579	+	0.477597i	$0.158492\pi$
$410$		0			0
$411$	−2.45154	+	7.54507i	−0.120926	+	0.372171i
$412$		0			0
$413$	6.76247	−	1.07107i	0.332759	−	0.0527039i
$414$		0			0
$415$	2.44486	+	1.48406i	0.120014	+	0.0728497i
$416$		0			0
$417$	−17.0575	−	17.0575i	−0.835309	−	0.835309i
$418$		0			0
$419$			16.4015i			0.801265i	0.916239	+	0.400632i	$0.131210\pi$
$419$			16.4015i			0.801265i	−0.916239	+	0.400632i	$0.868790\pi$
$420$		0			0
$421$	8.15001	+	25.0832i	0.397207	+	1.22248i	0.927229	+	0.374494i	$0.122184\pi$
$421$	8.15001	+	25.0832i	0.397207	+	1.22248i	−0.530022	+	0.847984i	$0.677816\pi$
$422$		0			0
$423$	5.13013	+	32.3904i	0.249436	+	1.57487i
$424$		0			0
$425$	−10.5442	+	3.52465i	−0.511467	+	0.170971i
$426$		0			0
$427$	1.41236	−	8.91727i	0.0683488	−	0.431537i
$428$		0			0
$429$	11.2722	+	0.126690i	0.544226	+	0.00611667i
$430$		0			0
$431$	5.58501	+	7.68711i	0.269020	+	0.370275i	0.922059	−	0.387050i	$-0.126506\pi$
$431$	5.58501	+	7.68711i	0.269020	+	0.370275i	−0.653038	+	0.757325i	$0.726506\pi$
$432$		0			0
$433$	−22.2230	+	11.3232i	−1.06797	+	0.544158i	−0.897414	−	0.441190i	$-0.854557\pi$
$433$	−22.2230	+	11.3232i	−1.06797	+	0.544158i	−0.170557	+	0.985348i	$0.554557\pi$
$434$		0			0
$435$	−2.68771	−	32.4021i	−0.128866	−	1.55356i
$436$		0			0
$437$	12.1667	−	23.8784i	0.582011	−	1.14226i
$438$		0			0
$439$	−1.69115			−0.0807143			−0.0403571	−	0.999185i	$-0.512850\pi$
$439$	−1.69115			−0.0807143			−0.0403571	+	0.999185i	$0.512850\pi$
$440$		0			0
$441$	34.1809			1.62766
$442$		0			0
$443$	−9.21964	+	18.0946i	−0.438038	+	0.859698i	0.561444	+	0.827515i	$0.310246\pi$
$443$	−9.21964	+	18.0946i	−0.438038	+	0.859698i	−0.999482	+	0.0321835i	$0.989754\pi$
$444$		0			0
$445$	15.2476	−	18.0059i	0.722804	−	0.853561i
$446$		0			0
$447$	0.0953432	−	0.0485798i	0.00450958	−	0.00229775i
$448$		0			0
$449$	24.7166	+	34.0195i	1.16645	+	1.60548i	0.683806	+	0.729664i	$0.260323\pi$
$449$	24.7166	+	34.0195i	1.16645	+	1.60548i	0.482643	+	0.875817i	$0.339677\pi$
$450$		0			0
$451$	4.96125	−	6.66964i	0.233616	−	0.314061i
$452$		0			0
$453$	10.6410	−	67.1849i	0.499960	−	3.15662i
$454$		0			0
$455$	1.36678	−	3.33948i	0.0640755	−	0.156557i
$456$		0			0
$457$	1.58324	+	9.99618i	0.0740608	+	0.467602i	0.996648	+	0.0818123i	$0.0260708\pi$
$457$	1.58324	+	9.99618i	0.0740608	+	0.467602i	−0.922587	+	0.385789i	$0.873929\pi$
$458$		0			0
$459$	−9.50814	−	29.2630i	−0.443802	−	1.36588i
$460$		0			0
$461$		−	27.4513i		−	1.27854i	−0.768984	−	0.639268i	$-0.779237\pi$
$461$		−	27.4513i		−	1.27854i	0.768984	−	0.639268i	$-0.220763\pi$
$462$		0			0
$463$	−12.8080	−	12.8080i	−0.595237	−	0.595237i	0.343804	−	0.939041i	$-0.388284\pi$
$463$	−12.8080	−	12.8080i	−0.595237	−	0.595237i	−0.939041	+	0.343804i	$0.888284\pi$
$464$		0			0
$465$	10.7196	−	17.6596i	0.497109	−	0.818945i
$466$		0			0
$467$	21.5674	−	3.41594i	0.998021	−	0.158071i	0.364010	−	0.931395i	$-0.381407\pi$
$467$	21.5674	−	3.41594i	0.998021	−	0.158071i	0.634011	+	0.773324i	$0.281407\pi$
$468$		0			0
$469$	−3.60265	+	11.0878i	−0.166355	+	0.511988i
$470$		0			0
$471$	5.10305	−	3.70758i	0.235136	−	0.170836i
$472$		0			0
$473$	5.03639	−	29.6387i	0.231573	−	1.36279i
$474$		0			0
$475$	27.4884	−	14.2995i	1.26125	−	0.656106i
$476$		0			0
$477$	−12.6220	−	24.7720i	−0.577920	−	1.13423i
$478$		0			0
$479$	5.27636	+	3.83350i	0.241083	+	0.175157i	0.701766	−	0.712408i	$-0.252395\pi$
$479$	5.27636	+	3.83350i	0.241083	+	0.175157i	−0.460683	+	0.887565i	$0.652395\pi$
$480$		0			0
$481$	1.40128	−	0.455305i	0.0638931	−	0.0207601i
$482$		0			0
$483$	14.9677	−	14.9677i	0.681054	−	0.681054i
$484$		0			0
$485$	−11.8702	+	10.2250i	−0.538997	+	0.464294i
$486$		0			0
$487$	2.61310	+	1.33144i	0.118411	+	0.0603334i	0.512193	−	0.858871i	$-0.328833\pi$
$487$	2.61310	+	1.33144i	0.118411	+	0.0603334i	−0.393782	+	0.919204i	$0.628833\pi$
$488$		0			0
$489$	4.10918	−	5.65580i	0.185824	−	0.255764i
$490$		0			0
$491$	−12.6664	−	4.11555i	−0.571625	−	0.185732i	0.00892018	−	0.999960i	$-0.497161\pi$
$491$	−12.6664	−	4.11555i	−0.571625	−	0.185732i	−0.580545	+	0.814228i	$0.697161\pi$
$492$		0			0
$493$	−9.94529	−	1.57518i	−0.447913	−	0.0709425i
$494$		0			0
$495$	27.9996	+	46.4194i	1.25849	+	2.08640i
$496$		0			0
$497$	13.3974	+	2.12193i	0.600954	+	0.0951818i
$498$		0			0
$499$	−22.2265	−	7.22182i	−0.994994	−	0.323293i	−0.234130	−	0.972205i	$-0.575224\pi$
$499$	−22.2265	−	7.22182i	−0.994994	−	0.323293i	−0.760863	+	0.648912i	$0.775224\pi$
$500$		0			0
$501$	−40.4864	+	55.7247i	−1.80880	+	2.48960i
$502$		0			0
$503$	−20.7030	−	10.5487i	−0.923103	−	0.470344i	−0.0732197	−	0.997316i	$-0.523327\pi$
$503$	−20.7030	−	10.5487i	−0.923103	−	0.470344i	−0.849883	+	0.526972i	$0.823327\pi$
$504$		0			0
$505$	2.92410	−	39.2721i	0.130121	−	1.74758i
$506$		0			0
$507$	26.9714	−	26.9714i	1.19784	−	1.19784i
$508$		0			0
$509$	−21.9064	+	7.11784i	−0.970986	+	0.315493i	−0.751214	−	0.660059i	$-0.770531\pi$
$509$	−21.9064	+	7.11784i	−0.970986	+	0.315493i	−0.219772	+	0.975551i	$0.570531\pi$
$510$		0			0
$511$	−14.0676	−	10.2207i	−0.622314	−	0.452138i
$512$		0			0
$513$	38.9316	+	76.4075i	1.71887	+	3.37347i
$514$		0			0
$515$	−6.99144	−	1.64733i	−0.308080	−	0.0725899i
$516$		0			0
$517$	−14.7217	+	2.16238i	−0.647460	+	0.0951014i
$518$		0			0
$519$	34.2716	−	24.8998i	1.50436	−	1.09298i
$520$		0			0
$521$	−9.62530	+	29.6236i	−0.421692	+	1.29783i	0.484435	+	0.874827i	$0.339025\pi$
$521$	−9.62530	+	29.6236i	−0.421692	+	1.29783i	−0.906127	+	0.423007i	$0.860975\pi$
$522$		0			0
$523$	−5.13797	+	0.813774i	−0.224668	+	0.0355838i	−0.267753	−	0.963488i	$-0.586281\pi$
$523$	−5.13797	+	0.813774i	−0.224668	+	0.0355838i	0.0430856	+	0.999071i	$0.486281\pi$
$524$		0			0
$525$	24.1393	−	4.03239i	1.05352	−	0.175988i
$526$		0			0
$527$	−4.52395	−	4.52395i	−0.197067	−	0.197067i
$528$		0			0
$529$		−	4.29842i		−	0.186888i
$530$		0			0
$531$	−10.1452	−	31.2236i	−0.440263	−	1.35499i
$532$		0			0
$533$	0.415035	+	2.62043i	0.0179772	+	0.113503i
$534$		0			0
$535$	−34.0634	+	14.2782i	−1.47269	+	0.617301i
$536$		0			0
$537$	6.80704	−	42.9779i	0.293745	−	1.85463i
$538$		0			0
$539$	−0.174297	+	15.5079i	−0.00750749	+	0.667973i
$540$		0			0
$541$	7.63567	+	10.5096i	0.328283	+	0.451843i	0.940974	−	0.338480i	$-0.109913\pi$
$541$	7.63567	+	10.5096i	0.328283	+	0.451843i	−0.612690	+	0.790323i	$0.709913\pi$
$542$		0			0
$543$	−49.3371	+	25.1385i	−2.11726	+	1.07880i
$544$		0			0
$545$	3.22177	+	2.72822i	0.138005	+	0.116864i
$546$		0			0
$547$	−2.13624	+	4.19261i	−0.0913391	+	0.179263i	−0.932156	−	0.362056i	$-0.882075\pi$
$547$	−2.13624	+	4.19261i	−0.0913391	+	0.179263i	0.840817	+	0.541319i	$0.182075\pi$
$548$		0			0
$549$	−43.2916			−1.84764
$550$		0			0
$551$	28.0634			1.19554
$552$		0			0
$553$	−4.01362	+	7.87716i	−0.170676	+	0.334971i
$554$		0			0
$555$	7.62634	+	6.45806i	0.323720	+	0.274129i
$556$		0			0
$557$	−29.1897	+	14.8729i	−1.23681	+	0.630185i	−0.945243	−	0.326366i	$-0.894176\pi$
$557$	−29.1897	+	14.8729i	−1.23681	+	0.630185i	−0.291564	+	0.956551i	$0.594176\pi$
$558$		0			0
$559$	5.63999	+	7.76278i	0.238546	+	0.328331i
$560$		0			0
$561$	22.6008	−	7.06365i	0.954209	−	0.298228i
$562$		0			0
$563$	0.520168	−	3.28421i	0.0219225	−	0.138413i	−0.974299	−	0.225257i	$-0.927678\pi$
$563$	0.520168	−	3.28421i	0.0219225	−	0.138413i	0.996222	+	0.0868434i	$0.0276780\pi$
$564$		0			0
$565$	−8.22698	+	3.44847i	−0.346112	+	0.145078i
$566$		0			0
$567$	5.36627	+	33.8813i	0.225362	+	1.42288i
$568$		0			0
$569$	−2.18501	−	6.72478i	−0.0916005	−	0.281917i	0.894752	−	0.446563i	$-0.147352\pi$
$569$	−2.18501	−	6.72478i	−0.0916005	−	0.281917i	−0.986353	+	0.164645i	$0.947352\pi$
$570$		0			0
$571$		−	24.2620i		−	1.01533i	−0.861553	−	0.507667i	$-0.830508\pi$
$571$		−	24.2620i		−	1.01533i	0.861553	−	0.507667i	$-0.169492\pi$
$572$		0			0
$573$	−28.5908	−	28.5908i	−1.19440	−	1.19440i
$574$		0			0
$575$	−12.5614	+	17.5997i	−0.523847	+	0.733959i
$576$		0			0
$577$	6.36086	−	1.00746i	0.264806	−	0.0419412i	−0.0226195	−	0.999744i	$-0.507201\pi$
$577$	6.36086	−	1.00746i	0.264806	−	0.0419412i	0.287426	+	0.957803i	$0.407201\pi$
$578$		0			0
$579$	−3.80544	+	11.7119i	−0.158149	+	0.486731i
$580$		0			0
$581$	−1.57744	+	1.14607i	−0.0654430	+	0.0475471i
$582$		0			0
$583$	11.3034	−	5.60028i	0.468141	−	0.231940i
$584$		0			0
$585$	−16.8410	−	3.96808i	−0.696289	−	0.164060i
$586$		0			0
$587$	−2.50306	−	4.91253i	−0.103312	−	0.202762i	0.833564	−	0.552423i	$-0.186297\pi$
$587$	−2.50306	−	4.91253i	−0.103312	−	0.202762i	−0.936876	+	0.349661i	$0.886297\pi$
$588$		0			0
$589$	14.4256	+	10.4808i	0.594395	+	0.431853i
$590$		0			0
$591$	31.9583	−	10.3839i	1.31459	−	0.427136i
$592$		0			0
$593$	−11.4901	+	11.4901i	−0.471841	+	0.471841i	−0.902510	−	0.430669i	$-0.858278\pi$
$593$	−11.4901	+	11.4901i	−0.471841	+	0.471841i	0.430669	+	0.902510i	$0.358278\pi$
$594$		0			0
$595$	0.562787	−	7.55850i	0.0230720	−	0.309868i
$596$		0			0
$597$	26.0555	+	13.2759i	1.06638	+	0.543348i
$598$		0			0
$599$	−24.2507	+	33.3782i	−0.990856	+	1.36380i	−0.0600854	+	0.998193i	$0.519137\pi$
$599$	−24.2507	+	33.3782i	−0.990856	+	1.36380i	−0.930771	+	0.365603i	$0.880863\pi$
$600$		0			0
$601$	42.1453	+	13.6938i	1.71914	+	0.558583i	0.991812	−	0.127705i	$-0.0407609\pi$
$601$	42.1453	+	13.6938i	1.71914	+	0.558583i	0.727330	+	0.686288i	$0.240761\pi$
$602$		0			0
$603$	55.2143	+	8.74509i	2.24850	+	0.356127i
$604$		0			0
$605$	−21.2033	+	12.4667i	−0.862037	+	0.506845i
$606$		0			0
$607$	16.6706	+	2.64036i	0.676638	+	0.107169i	0.485290	−	0.874353i	$-0.338714\pi$
$607$	16.6706	+	2.64036i	0.676638	+	0.107169i	0.191348	+	0.981522i	$0.438714\pi$
$608$		0			0
$609$	21.0810	+	6.84963i	0.854245	+	0.277561i
$610$		0			0
$611$	2.79146	−	3.84212i	0.112930	−	0.155435i
$612$		0			0
$613$	−21.6696	−	11.0412i	−0.875225	−	0.445949i	−0.0421512	−	0.999111i	$-0.513421\pi$
$613$	−21.6696	−	11.0412i	−0.875225	−	0.445949i	−0.833074	+	0.553162i	$0.813421\pi$
$614$		0			0
$615$	−13.6338	+	11.7443i	−0.549770	+	0.473574i
$616$		0			0
$617$	−2.46606	+	2.46606i	−0.0992799	+	0.0992799i	−0.755002	−	0.655722i	$-0.772364\pi$
$617$	−2.46606	+	2.46606i	−0.0992799	+	0.0992799i	0.655722	+	0.755002i	$0.272364\pi$
$618$		0			0
$619$	28.7652	−	9.34637i	1.15617	−	0.375662i	0.332706	−	0.943031i	$-0.392038\pi$
$619$	28.7652	−	9.34637i	1.15617	−	0.375662i	0.823464	+	0.567369i	$0.192038\pi$
$620$		0			0
$621$	−48.4135	−	35.1745i	−1.94277	−	1.41150i
$622$		0			0
$623$	7.30265	+	14.3323i	0.292574	+	0.574210i
$624$		0			0
$625$	−23.6426	+	8.12560i	−0.945706	+	0.325024i
$626$		0			0
$627$	−59.1342	+	29.2980i	−2.36159	+	1.17005i
$628$		0			0
$629$	2.50383	−	1.81914i	0.0998344	−	0.0725339i
$630$		0			0
$631$	−9.75833	+	30.0330i	−0.388473	+	1.19560i	0.545456	+	0.838139i	$0.316356\pi$
$631$	−9.75833	+	30.0330i	−0.388473	+	1.19560i	−0.933929	+	0.357458i	$0.883644\pi$
$632$		0			0
$633$	79.5165	−	12.5942i	3.16050	−	0.500573i
$634$		0			0
$635$	−19.6846	+	32.4286i	−0.781158	+	1.28689i
$636$		0			0
$637$	−3.50014	−	3.50014i	−0.138681	−	0.138681i
$638$		0			0
$639$		−	65.0416i		−	2.57300i
$640$		0			0
$641$	−1.51513	−	4.66309i	−0.0598440	−	0.184181i	0.916665	−	0.399655i	$-0.130870\pi$
$641$	−1.51513	−	4.66309i	−0.0598440	−	0.184181i	−0.976509	+	0.215474i	$0.930870\pi$
$642$		0			0
$643$	−2.56190	−	16.1752i	−0.101031	−	0.637888i	−0.985290	−	0.170890i	$-0.945336\pi$
$643$	−2.56190	−	16.1752i	−0.101031	−	0.637888i	0.884259	−	0.466998i	$-0.154664\pi$
$644$		0			0
$645$	−24.6514	+	60.2312i	−0.970646	+	2.37160i
$646$		0			0
$647$	−6.72843	+	42.4816i	−0.264522	+	1.67012i	0.395185	+	0.918602i	$0.370681\pi$
$647$	−6.72843	+	42.4816i	−0.264522	+	1.67012i	−0.659707	+	0.751523i	$0.729319\pi$
$648$		0			0
$649$	14.2179	−	4.44366i	0.558102	−	0.174429i
$650$		0			0
$651$	8.27826	+	11.3940i	0.324451	+	0.446568i
$652$		0			0
$653$	−3.03452	+	1.54616i	−0.118750	+	0.0605061i	−0.512356	−	0.858773i	$-0.671227\pi$
$653$	−3.03452	+	1.54616i	−0.118750	+	0.0605061i	0.393606	+	0.919279i	$0.371227\pi$
$654$		0			0
$655$	−14.1273	+	16.6829i	−0.551998	+	0.651856i
$656$		0			0
$657$	−37.8530	+	74.2907i	−1.47679	+	2.89836i
$658$		0			0
$659$	1.70430			0.0663902			0.0331951	−	0.999449i	$-0.489432\pi$
$659$	1.70430			0.0663902			0.0331951	+	0.999449i	$0.489432\pi$
$660$		0			0
$661$	−3.81557			−0.148409			−0.0742043	−	0.997243i	$-0.523642\pi$
$661$	−3.81557			−0.148409			−0.0742043	+	0.997243i	$0.523642\pi$
$662$		0			0
$663$	−3.43107	+	6.73385i	−0.133252	+	0.261521i
$664$		0			0
$665$	1.74622	+	21.0518i	0.0677156	+	0.816354i
$666$		0			0
$667$	−17.4491	+	8.89078i	−0.675634	+	0.344252i
$668$		0			0
$669$	−9.41064	−	12.9526i	−0.363836	−	0.500778i
$670$		0			0
$671$	0.220754	−	19.6414i	0.00852212	−	0.758249i
$672$		0			0
$673$	4.12434	−	26.0401i	0.158982	−	1.00377i	−0.771179	−	0.636619i	$-0.780333\pi$
$673$	4.12434	−	26.0401i	0.158982	−	1.00377i	0.930161	−	0.367153i	$-0.119667\pi$
$674$		0			0
$675$	−21.9352	−	65.6203i	−0.844288	−	2.52572i
$676$		0			0
$677$	−1.85111	−	11.6875i	−0.0711440	−	0.449185i	−0.997386	−	0.0722563i	$-0.976980\pi$
$677$	−1.85111	−	11.6875i	−0.0711440	−	0.449185i	0.926242	−	0.376929i	$-0.123020\pi$
$678$		0			0
$679$	−3.30057	−	10.1581i	−0.126664	−	0.389832i
$680$		0			0
$681$			6.55262i			0.251097i
$682$		0			0
$683$	19.2371	+	19.2371i	0.736087	+	0.736087i	0.971818	−	0.235731i	$-0.0757484\pi$
$683$	19.2371	+	19.2371i	0.736087	+	0.736087i	−0.235731	+	0.971818i	$0.575748\pi$
$684$		0			0
$685$	4.72283	+	2.86681i	0.180450	+	0.109535i
$686$		0			0
$687$	4.83368	−	0.765580i	0.184416	−	0.0292087i
$688$		0			0
$689$	−1.24417	+	3.82916i	−0.0473990	+	0.145879i
$690$		0			0
$691$	2.86279	−	2.07994i	0.108906	−	0.0791246i	−0.531999	−	0.846745i	$-0.678559\pi$
$691$	2.86279	−	2.07994i	0.108906	−	0.0791246i	0.640905	+	0.767620i	$0.278559\pi$
$692$		0			0
$693$	−36.5652	+	5.37084i	−1.38900	+	0.204021i
$694$		0			0
$695$	−14.2866	+	8.83799i	−0.541922	+	0.335244i
$696$		0			0
$697$	2.53004	+	4.96548i	0.0958320	+	0.188081i
$698$		0			0
$699$	57.6408	+	41.8785i	2.18018	+	1.58399i
$700$		0			0
$701$	37.5991	−	12.2167i	1.42010	−	0.461418i	0.504466	−	0.863432i	$-0.331689\pi$
$701$	37.5991	−	12.2167i	1.42010	−	0.461418i	0.915634	+	0.402013i	$0.131689\pi$
$702$		0			0
$703$	−6.09923	+	6.09923i	−0.230037	+	0.230037i
$704$		0			0
$705$	32.1221	+	2.39173i	1.20979	+	0.0900779i
$706$		0			0
$707$	23.9215	+	12.1886i	0.899660	+	0.458400i
$708$		0			0
$709$	23.7291	−	32.6603i	0.891166	−	1.22658i	−0.0820353	−	0.996629i	$-0.526142\pi$
$709$	23.7291	−	32.6603i	0.891166	−	1.22658i	0.973201	−	0.229955i	$-0.0738580\pi$
$710$		0			0
$711$	40.3169	+	13.0997i	1.51200	+	0.491279i
$712$		0			0
$713$	−12.2899	−	1.94653i	−0.460261	−	0.0728982i
$714$		0			0
$715$	1.88620	−	7.62054i	0.0705398	−	0.284992i
$716$		0			0
$717$	78.5987	+	12.4488i	2.93532	+	0.464910i
$718$		0			0
$719$	−6.32991	−	2.05671i	−0.236066	−	0.0767024i	0.188595	−	0.982055i	$-0.439607\pi$
$719$	−6.32991	−	2.05671i	−0.236066	−	0.0767024i	−0.424661	+	0.905353i	$0.639607\pi$
$720$		0			0
$721$	2.87833	−	3.96168i	0.107195	−	0.147541i
$722$		0			0
$723$	−0.160948	−	0.0820071i	−0.00598572	−	0.00304988i
$724$		0			0
$725$	−22.3928	−	3.35322i	−0.831648	−	0.124535i
$726$		0			0
$727$	−13.3487	+	13.3487i	−0.495074	+	0.495074i	−0.909901	−	0.414826i	$-0.863842\pi$
$727$	−13.3487	+	13.3487i	−0.495074	+	0.495074i	0.414826	+	0.909901i	$0.363842\pi$
$728$		0			0
$729$	29.6653	−	9.63884i	1.09871	−	0.356994i
$730$		0			0
$731$	16.3059	+	11.8469i	0.603096	+	0.438175i
$732$		0			0
$733$	−12.6624	−	24.8515i	−0.467698	−	0.917909i	−0.997559	−	0.0698250i	$-0.977756\pi$
$733$	−12.6624	−	24.8515i	−0.467698	−	0.917909i	0.529861	−	0.848084i	$-0.322244\pi$
$734$		0			0
$735$	7.69969	−	32.6783i	0.284007	−	1.20536i
$736$		0			0
$737$	−4.24920	+	25.0062i	−0.156521	+	0.921115i
$738$		0			0
$739$	−8.88327	+	6.45407i	−0.326776	+	0.237417i	−0.739061	−	0.673638i	$-0.764731\pi$
$739$	−8.88327	+	6.45407i	−0.326776	+	0.237417i	0.412285	+	0.911055i	$0.364731\pi$
$740$		0			0
$741$	6.50889	−	20.0323i	0.239110	−	0.735905i
$742$		0			0
$743$	23.8652	−	3.77987i	0.875527	−	0.138670i	0.297534	−	0.954711i	$-0.403836\pi$
$743$	23.8652	−	3.77987i	0.875527	−	0.138670i	0.577994	+	0.816041i	$0.303836\pi$
$744$		0			0
$745$	−0.0177019	−	0.0723867i	−0.000648546	−	0.00265204i
$746$		0			0
$747$	6.61105	+	6.61105i	0.241886	+	0.241886i
$748$		0			0
$749$		−	25.1802i		−	0.920065i
$750$		0			0
$751$	15.1449	+	46.6112i	0.552645	+	1.70087i	0.702082	+	0.712096i	$0.252254\pi$
$751$	15.1449	+	46.6112i	0.552645	+	1.70087i	−0.149437	+	0.988771i	$0.547746\pi$
$752$		0			0
$753$	4.23123	+	26.7150i	0.154195	+	0.973547i
$754$		0			0
$755$	−43.8413	−	17.9433i	−1.59555	−	0.653024i
$756$		0			0
$757$	−7.91360	+	49.9645i	−0.287625	+	1.81599i	0.244869	+	0.969556i	$0.421255\pi$
$757$	−7.91360	+	49.9645i	−0.287625	+	1.81599i	−0.532493	+	0.846434i	$0.678745\pi$
$758$		0			0
$759$	27.4863	−	36.9511i	0.997690	−	1.34124i
$760$		0			0
$761$	18.7749	+	25.8415i	0.680591	+	0.936753i	0.999941	−	0.0108837i	$-0.00346445\pi$
$761$	18.7749	+	25.8415i	0.680591	+	0.936753i	−0.319350	+	0.947637i	$0.603464\pi$
$762$		0			0
$763$	−2.56445	+	1.30665i	−0.0928392	+	0.0473040i
$764$		0			0
$765$	−36.2192	+	3.00434i	−1.30951	+	0.108622i
$766$		0			0
$767$	−2.15844	+	4.23618i	−0.0779368	+	0.152960i
$768$		0			0
$769$	−41.4875			−1.49608			−0.748039	−	0.663655i	$-0.769004\pi$
$769$	−41.4875			−1.49608			−0.748039	+	0.663655i	$0.769004\pi$
$770$		0			0
$771$	33.7131			1.21415
$772$		0			0
$773$	9.90821	−	19.4460i	0.356373	−	0.699422i	−0.641322	−	0.767272i	$-0.721614\pi$
$773$	9.90821	−	19.4460i	0.356373	−	0.699422i	0.997696	+	0.0678495i	$0.0216138\pi$
$774$		0			0
$775$	−10.2584	−	10.0867i	−0.368492	−	0.362325i
$776$		0			0
$777$	−6.07038	+	3.09301i	−0.217774	+	0.110961i
$778$		0			0
$779$	−9.12937	−	12.5655i	−0.327094	−	0.450206i
$780$		0			0
$781$	29.5094	+	0.331662i	1.05593	+	0.0118678i
$782$		0			0
$783$	9.80293	−	61.8933i	0.350328	−	2.21189i
$784$		0			0
$785$	−1.69813	−	4.05122i	−0.0606089	−	0.144594i
$786$		0			0
$787$	−4.74219	−	29.9410i	−0.169041	−	1.06728i	−0.915637	−	0.402005i	$-0.868313\pi$
$787$	−4.74219	−	29.9410i	−0.169041	−	1.06728i	0.746596	−	0.665277i	$-0.231687\pi$
$788$		0			0
$789$	4.50319	+	13.8594i	0.160318	+	0.493407i
$790$		0			0
$791$		−	6.08151i		−	0.216234i
$792$		0			0
$793$	4.43308	+	4.43308i	0.157423	+	0.157423i
$794$		0			0
$795$	−26.5263	+	6.48689i	−0.940790	+	0.230066i
$796$		0			0
$797$	53.0278	−	8.39878i	1.87834	−	0.297500i	0.890744	−	0.454505i	$-0.150184\pi$
$797$	53.0278	−	8.39878i	1.87834	−	0.297500i	0.987598	+	0.157004i	$0.0501837\pi$
$798$		0			0
$799$	3.08264	−	9.48739i	0.109056	−	0.335640i
$800$		0			0
$801$	62.3997	−	45.3361i	2.20479	−	1.60187i
$802$		0			0
$803$	−33.5128	−	17.5528i	−1.18264	−	0.619424i
$804$		0			0
$805$	−7.75521	−	12.5363i	−0.273335	−	0.441847i
$806$		0			0
$807$	37.7574	+	74.1031i	1.32912	+	2.60855i
$808$		0			0
$809$	25.4737	+	18.5077i	0.895608	+	0.650697i	0.937334	−	0.348432i	$-0.113286\pi$
$809$	25.4737	+	18.5077i	0.895608	+	0.650697i	−0.0417260	+	0.999129i	$0.513286\pi$
$810$		0			0
$811$	6.48163	−	2.10601i	0.227601	−	0.0739520i	−0.192996	−	0.981199i	$-0.561821\pi$
$811$	6.48163	−	2.10601i	0.227601	−	0.0739520i	0.420597	+	0.907247i	$0.361821\pi$
$812$		0			0
$813$	−48.7995	+	48.7995i	−1.71147	+	1.71147i
$814$		0			0
$815$	−3.17746	−	3.68869i	−0.111301	−	0.129209i
$816$		0			0
$817$	−50.0507	−	25.5021i	−1.75105	−	0.892206i
$818$		0			0
$819$	6.93333	−	9.54290i	0.242270	−	0.333456i
$820$		0			0
$821$	−0.216685	−	0.0704052i	−0.00756235	−	0.00245716i	0.305233	−	0.952278i	$-0.401266\pi$
$821$	−0.216685	−	0.0704052i	−0.00756235	−	0.00245716i	−0.312796	+	0.949820i	$0.601266\pi$
$822$		0			0
$823$	−22.6675	−	3.59018i	−0.790139	−	0.125146i	−0.251695	−	0.967807i	$-0.580988\pi$
$823$	−22.6675	−	3.59018i	−0.790139	−	0.125146i	−0.538445	+	0.842661i	$0.680988\pi$
$824$		0			0
$825$	50.6861	−	16.3122i	1.76466	−	0.567916i
$826$		0			0
$827$	39.9523	+	6.32782i	1.38928	+	0.220040i	0.805847	−	0.592124i	$-0.201710\pi$
$827$	39.9523	+	6.32782i	1.38928	+	0.220040i	0.583430	+	0.812164i	$0.301710\pi$
$828$		0			0
$829$	25.8477	+	8.39841i	0.897726	+	0.291689i	0.721298	−	0.692625i	$-0.243546\pi$
$829$	25.8477	+	8.39841i	0.897726	+	0.291689i	0.176428	+	0.984314i	$0.443546\pi$
$830$		0			0
$831$	−25.9156	+	35.6698i	−0.899004	+	1.23737i
$832$		0			0
$833$	−9.26422	−	4.72036i	−0.320986	−	0.163551i
$834$		0			0
$835$	31.3064	+	36.3434i	1.08340	+	1.25772i
$836$		0			0
$837$	28.1543	−	28.1543i	0.973154	−	0.973154i
$838$		0			0
$839$	−20.9575	+	6.80951i	−0.723533	+	0.235090i	−0.647554	−	0.762019i	$-0.724208\pi$
$839$	−20.9575	+	6.80951i	−0.723533	+	0.235090i	−0.0759789	+	0.997109i	$0.524208\pi$
$840$		0			0
$841$	6.87075	+	4.99189i	0.236922	+	0.172134i
$842$		0			0
$843$	−14.4402	−	28.3404i	−0.497346	−	0.976096i
$844$		0			0
$845$	−13.9747	−	22.5901i	−0.480744	−	0.777124i
$846$		0			0
$847$	−2.25030	−	16.6171i	−0.0773212	−	0.570969i
$848$		0			0
$849$	5.35078	−	3.88757i	0.183638	−	0.133421i
$850$		0			0
$851$	1.86005	−	5.72466i	0.0637619	−	0.196239i
$852$		0			0
$853$	−36.1266	+	5.72190i	−1.23695	+	0.195914i	−0.740444	−	0.672118i	$-0.765385\pi$
$853$	−36.1266	+	5.72190i	−1.23695	+	0.195914i	−0.496508	+	0.868032i	$0.665385\pi$
$854$		0			0
$855$	98.3915	−	24.0612i	3.36492	−	0.822877i
$856$		0			0
$857$	8.98140	+	8.98140i	0.306799	+	0.306799i	0.843666	−	0.536868i	$-0.180393\pi$
$857$	8.98140	+	8.98140i	0.306799	+	0.306799i	−0.536868	+	0.843666i	$0.680393\pi$
$858$		0			0
$859$		−	54.6972i		−	1.86624i	−0.359559	−	0.933122i	$-0.617073\pi$
$859$		−	54.6972i		−	1.86624i	0.359559	−	0.933122i	$-0.382927\pi$
$860$		0			0
$861$	−3.79096	−	11.6674i	−0.129196	−	0.397624i
$862$		0			0
$863$	2.23202	+	14.0924i	0.0759788	+	0.479711i	0.996111	+	0.0881040i	$0.0280808\pi$
$863$	2.23202	+	14.0924i	0.0759788	+	0.479711i	−0.920132	+	0.391607i	$0.871919\pi$
$864$		0			0
$865$	−11.4045	−	27.2077i	−0.387765	−	0.925088i
$866$		0			0
$867$	6.05557	−	38.2334i	0.205658	−	1.29847i
$868$		0			0
$869$	−6.14895	+	18.2250i	−0.208589	+	0.618241i
$870$		0			0
$871$	−4.75846	−	6.54946i	−0.161234	−	0.221920i
$872$		0			0
$873$	−45.6330	+	23.2512i	−1.54444	+	0.786932i
$874$		0			0
$875$	1.12205	−	17.0067i	0.0379322	−	0.574931i
$876$		0			0
$877$	6.98490	−	13.7086i	0.235863	−	0.462908i	−0.742488	−	0.669860i	$-0.766354\pi$
$877$	6.98490	−	13.7086i	0.235863	−	0.462908i	0.978351	+	0.206952i	$0.0663543\pi$
$878$		0			0
$879$	−63.0707			−2.12732
$880$		0			0
$881$	−27.4651			−0.925323			−0.462662	−	0.886535i	$-0.653106\pi$
$881$	−27.4651			−0.925323			−0.462662	+	0.886535i	$0.653106\pi$
$882$		0			0
$883$	−24.6520	+	48.3824i	−0.829607	+	1.62820i	−0.0526752	+	0.998612i	$0.516775\pi$
$883$	−24.6520	+	48.3824i	−0.829607	+	1.62820i	−0.776932	+	0.629584i	$0.783225\pi$
$884$		0			0
$885$	−32.1364	+	2.66567i	−1.08025	+	0.0896055i
$886$		0			0
$887$	52.7376	−	26.8712i	1.77076	−	0.902246i	0.834432	−	0.551111i	$-0.185796\pi$
$887$	52.7376	−	26.8712i	1.77076	−	0.902246i	0.936325	−	0.351134i	$-0.114204\pi$
$888$		0			0
$889$	−15.2015	−	20.9231i	−0.509843	−	0.701738i
$890$		0			0
$891$	22.2636	+	71.2345i	0.745858	+	2.38645i
$892$		0			0
$893$	−4.34926	+	27.4601i	−0.145542	+	0.918918i
$894$		0			0
$895$	−28.0451	−	11.4783i	−0.937446	−	0.383677i
$896$		0			0
$897$	2.29938	+	14.5177i	0.0767740	+	0.484732i
$898$		0			0
$899$	−4.02649	−	12.3922i	−0.134291	−	0.413305i
$900$		0			0
$901$			8.45716i			0.281749i
$902$		0			0
$903$	−31.3733	−	31.3733i	−1.04404	−	1.04404i
$904$		0			0
$905$	9.16015	+	37.4578i	0.304494	+	1.24514i
$906$		0			0
$907$	14.9623	−	2.36980i	0.496817	−	0.0786880i	0.0970022	−	0.995284i	$-0.469075\pi$
$907$	14.9623	−	2.36980i	0.496817	−	0.0786880i	0.399814	+	0.916596i	$0.369075\pi$
$908$		0			0
$909$	39.7815	−	122.435i	1.31947	−	4.06091i
$910$		0			0
$911$	−5.44856	+	3.95861i	−0.180519	+	0.131155i	−0.674375	−	0.738389i	$-0.735587\pi$
$911$	−5.44856	+	3.95861i	−0.180519	+	0.131155i	0.493856	+	0.869544i	$0.335587\pi$
$912$		0			0
$913$	−3.03315	+	2.96573i	−0.100383	+	0.0981512i
$914$		0			0
$915$	−9.75198	+	41.3885i	−0.322391	+	1.36826i
$916$		0			0
$917$	−6.76610	−	13.2792i	−0.223436	−	0.438518i
$918$		0			0
$919$	47.2044	+	34.2960i	1.55713	+	1.13132i	0.938315	+	0.345782i	$0.112386\pi$
$919$	47.2044	+	34.2960i	1.55713	+	1.13132i	0.618813	+	0.785538i	$0.287614\pi$
$920$		0			0
$921$	36.0740	−	11.7212i	1.18868	−	0.386226i
$922$		0			0
$923$	−6.66028	+	6.66028i	−0.219226	+	0.219226i
$924$		0			0
$925$	5.59558	−	4.13802i	0.183982	−	0.136057i
$926$		0			0
$927$	−20.9216	−	10.6601i	−0.687155	−	0.350123i
$928$		0			0
$929$	−5.89306	+	8.11110i	−0.193345	+	0.266117i	−0.894672	−	0.446723i	$-0.852591\pi$
$929$	−5.89306	+	8.11110i	−0.193345	+	0.266117i	0.701327	+	0.712839i	$0.252591\pi$
$930$		0			0
$931$	27.5598	+	8.95473i	0.903237	+	0.293480i
$932$		0			0
$933$	44.1000	+	6.98475i	1.44377	+	0.228670i
$934$		0			0
$935$	−1.17838	−	16.4480i	−0.0385371	−	0.537907i
$936$		0			0
$937$	−41.2128	−	6.52746i	−1.34636	−	0.213243i	−0.558710	−	0.829363i	$-0.688703\pi$
$937$	−41.2128	−	6.52746i	−1.34636	−	0.213243i	−0.787652	+	0.616120i	$0.788703\pi$
$938$		0			0
$939$	92.1972	+	29.9567i	3.00874	+	0.977600i
$940$		0			0
$941$	14.4754	−	19.9237i	0.471885	−	0.649494i	−0.505035	−	0.863099i	$-0.668520\pi$
$941$	14.4754	−	19.9237i	0.471885	−	0.649494i	0.976920	+	0.213605i	$0.0685205\pi$
$942$		0			0
$943$	9.65732	+	4.92065i	0.314486	+	0.160238i
$944$		0			0
$945$	47.0394	+	3.50244i	1.53019	+	0.113934i
$946$		0			0
$947$	6.72877	−	6.72877i	0.218656	−	0.218656i	−0.589276	−	0.807932i	$-0.700587\pi$
$947$	6.72877	−	6.72877i	0.218656	−	0.218656i	0.807932	+	0.589276i	$0.200587\pi$
$948$		0			0
$949$	11.4836	−	3.73124i	0.372772	−	0.121121i
$950$		0			0
$951$	−79.6507	−	57.8696i	−2.58285	−	1.87655i
$952$		0			0
$953$	−15.9429	−	31.2897i	−0.516441	−	1.01357i	−0.991064	−	0.133384i	$-0.957416\pi$
$953$	−15.9429	−	31.2897i	−0.516441	−	1.01357i	0.474623	−	0.880189i	$-0.342584\pi$
$954$		0			0
$955$	−23.9465	+	14.8138i	−0.774889	+	0.479362i
$956$		0			0
$957$	47.5436	+	8.07890i	1.53687	+	0.261154i
$958$		0			0
$959$	−3.04719	+	2.21391i	−0.0983989	+	0.0714910i
$960$		0			0
$961$	−7.02117	+	21.6089i	−0.226489	+	0.697062i
$962$		0			0
$963$	−119.253	+	18.8879i	−3.84289	+	0.608654i
$964$		0			0
$965$	7.33108	+	4.45005i	0.235996	+	0.143252i
$966$		0			0
$967$	−43.6347	−	43.6347i	−1.40320	−	1.40320i	−0.789685	−	0.613512i	$-0.789756\pi$
$967$	−43.6347	−	43.6347i	−1.40320	−	1.40320i	−0.613512	−	0.789685i	$-0.710244\pi$
$968$		0			0
$969$		−	44.2438i		−	1.42131i
$970$		0			0
$971$	−8.80597	−	27.1020i	−0.282597	−	0.869744i	−0.987109	−	0.160052i	$-0.948834\pi$
$971$	−8.80597	−	27.1020i	−0.282597	−	0.869744i	0.704512	−	0.709693i	$-0.251166\pi$
$972$		0			0
$973$	−1.79163	−	11.3119i	−0.0574369	−	0.362642i
$974$		0			0
$975$	−7.58729	+	15.2068i	−0.242988	+	0.487007i
$976$		0			0
$977$	−8.07944	+	51.0116i	−0.258484	+	1.63201i	0.427236	+	0.904140i	$0.359487\pi$
$977$	−8.07944	+	51.0116i	−0.258484	+	1.63201i	−0.685720	+	0.727865i	$0.740513\pi$
$978$		0			0
$979$	20.2508	+	28.5420i	0.647219	+	0.912206i
$980$		0			0
$981$	8.11191	+	11.1651i	0.258993	+	0.356474i
$982$		0			0
$983$	48.6352	−	24.7809i	1.55122	−	0.790387i	0.552161	−	0.833737i	$-0.313803\pi$
$983$	48.6352	−	24.7809i	1.55122	−	0.790387i	0.999060	+	0.0433506i	$0.0138033\pi$
$984$		0			0
$985$	−1.93446	−	23.3212i	−0.0616371	−	0.743075i
$986$		0			0
$987$	−9.96952	+	19.5663i	−0.317333	+	0.622802i
$988$		0			0
$989$	39.1997			1.24648
$990$		0			0
$991$	−1.67436			−0.0531879			−0.0265939	−	0.999646i	$-0.508466\pi$
$991$	−1.67436			−0.0531879			−0.0265939	+	0.999646i	$0.508466\pi$
$992$		0			0
$993$	−20.7755	+	40.7742i	−0.659291	+	1.29393i
$994$		0			0
$995$	13.1604	−	15.5412i	0.417214	−	0.492689i
$996$		0			0
$997$	−26.6089	+	13.5579i	−0.842713	+	0.429384i	−0.821375	−	0.570389i	$-0.806793\pi$
$997$	−26.6089	+	13.5579i	−0.842713	+	0.429384i	−0.0213379	+	0.999772i	$0.506793\pi$
$998$		0			0
$999$	11.3212	+	15.5823i	0.358187	+	0.493002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.cm.c.833.6		48
4.3	odd	2		110.2.k.a.63.1	yes	48
5.2	odd	4	inner	880.2.cm.c.657.1		48
11.7	odd	10	inner	880.2.cm.c.513.1		48
12.11	even	2		990.2.bh.c.613.6		48
20.3	even	4		550.2.bh.b.107.1		48
20.7	even	4		110.2.k.a.107.6	yes	48
20.19	odd	2		550.2.bh.b.393.6		48
44.7	even	10		110.2.k.a.73.6	yes	48
55.7	even	20	inner	880.2.cm.c.337.6		48
60.47	odd	4		990.2.bh.c.217.2		48
132.95	odd	10		990.2.bh.c.73.2		48
220.7	odd	20		110.2.k.a.7.1	✓	48
220.139	even	10		550.2.bh.b.293.1		48
220.183	odd	20		550.2.bh.b.7.6		48
660.227	even	20		990.2.bh.c.667.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.k.a.7.1	✓	48	220.7	odd	20
110.2.k.a.63.1	yes	48	4.3	odd	2
110.2.k.a.73.6	yes	48	44.7	even	10
110.2.k.a.107.6	yes	48	20.7	even	4
550.2.bh.b.7.6		48	220.183	odd	20
550.2.bh.b.107.1		48	20.3	even	4
550.2.bh.b.293.1		48	220.139	even	10
550.2.bh.b.393.6		48	20.19	odd	2
880.2.cm.c.337.6		48	55.7	even	20	inner
880.2.cm.c.513.1		48	11.7	odd	10	inner
880.2.cm.c.657.1		48	5.2	odd	4	inner
880.2.cm.c.833.6		48	1.1	even	1	trivial
990.2.bh.c.73.2		48	132.95	odd	10
990.2.bh.c.217.2		48	60.47	odd	4
990.2.bh.c.613.6		48	12.11	even	2
990.2.bh.c.667.6		48	660.227	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.cm (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.45771 - 2.86091i) q^{3} +(-1.70643 - 1.44502i) q^{5} +(1.35828 - 0.692077i) q^{7} +(-4.29653 - 5.91367i) q^{9} +(2.70495 - 1.91918i) q^{11} +(-0.165595 + 1.04553i) q^{13} +(-6.62155 + 2.77553i) q^{15} +(0.347837 + 2.19616i) q^{17} +(-1.91500 - 5.89375i) q^{19} -4.89475i q^{21} +(3.05791 + 3.05791i) q^{23} +(0.823819 + 4.93167i) q^{25} +(-13.6675 + 2.16472i) q^{27} +(-1.39938 + 4.30686i) q^{29} +(-2.32781 + 1.69125i) q^{31} +(-1.54760 - 10.5362i) q^{33} +(-3.31788 - 0.781760i) q^{35} +(-0.631904 - 1.24018i) q^{37} +(2.74977 + 1.99782i) q^{39} +(2.38365 - 0.774496i) q^{41} +(6.40957 - 6.40957i) q^{43} +(-1.21365 + 16.2999i) q^{45} +(-3.99740 - 2.03678i) q^{47} +(-2.74855 + 3.78305i) q^{49} +(6.79005 + 2.20622i) q^{51} +(3.75665 + 0.594995i) q^{53} +(-7.38907 - 0.633749i) q^{55} +(-19.6530 - 3.11273i) q^{57} +(4.27154 + 1.38791i) q^{59} +(3.48115 - 4.79140i) q^{61} +(-9.92860 - 5.05887i) q^{63} +(1.79339 - 1.54483i) q^{65} +(-5.40776 + 5.40776i) q^{67} +(13.2059 - 4.29086i) q^{69} +(7.19862 + 5.23010i) q^{71} +(-5.17847 - 10.1633i) q^{73} +(15.3099 + 4.83204i) q^{75} +(2.34584 - 4.47882i) q^{77} +(-4.69179 + 3.40879i) q^{79} +(-6.95367 + 21.4012i) q^{81} +(-1.26330 + 0.200087i) q^{83} +(2.57994 - 4.25022i) q^{85} +(10.2816 + 10.2816i) q^{87} +10.5518i q^{89} +(0.498662 + 1.53472i) q^{91} +(1.44526 + 9.12499i) q^{93} +(-5.24880 + 12.8245i) q^{95} +(1.09605 - 6.92020i) q^{97} +(-22.9713 - 7.75031i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{3} - 8 q^{5} + 20 q^{7} - 12 q^{11} + 16 q^{15} - 20 q^{17} + 8 q^{23} - 20 q^{25} - 8 q^{27} - 16 q^{31} - 104 q^{33} + 20 q^{37} - 20 q^{41} + 16 q^{45} - 40 q^{47} - 40 q^{51} - 96 q^{55}+ \cdots + 72 q^{97}+O(q^{100}) \) 48 * q + 4 * q^3 - 8 * q^5 + 20 * q^7 - 12 * q^11 + 16 * q^15 - 20 * q^17 + 8 * q^23 - 20 * q^25 - 8 * q^27 - 16 * q^31 - 104 * q^33 + 20 * q^37 - 20 * q^41 + 16 * q^45 - 40 * q^47 - 40 * q^51 - 96 * q^55 + 80 * q^61 - 100 * q^63 + 56 * q^71 - 20 * q^73 + 76 * q^75 - 96 * q^77 - 68 * q^81 - 80 * q^85 + 68 * q^91 + 76 * q^93 - 20 * q^95 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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