LMFDB - Embedded newform 864.2.bi.a.767.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(95,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 17]))

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

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

chi := DirichletCharacter("864.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bi (of order $18$, degree $6$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			767.13
Character	$\chi$	$=$	864.767
Dual form			864.2.bi.a.383.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.903983 - 1.47743i) q^{3} +(-1.26017 + 3.46229i) q^{5} +(-1.82330 - 0.321498i) q^{7} +(-1.36563 + 2.67115i) q^{9} +O(q^{10})$	\(q+(-0.903983 - 1.47743i) q^{3} +(-1.26017 + 3.46229i) q^{5} +(-1.82330 - 0.321498i) q^{7} +(-1.36563 + 2.67115i) q^{9} +(2.49231 - 0.907128i) q^{11} +(4.15274 - 3.48456i) q^{13} +(6.25448 - 1.26803i) q^{15} +(-5.06828 + 2.92617i) q^{17} +(-6.05539 - 3.49608i) q^{19} +(1.17324 + 2.98444i) q^{21} +(-0.349489 - 1.98205i) q^{23} +(-6.56919 - 5.51221i) q^{25} +(5.18096 - 0.397052i) q^{27} +(4.64086 - 5.53076i) q^{29} +(5.28973 - 0.932722i) q^{31} +(-3.59323 - 2.86220i) q^{33} +(3.41079 - 5.90766i) q^{35} +(-1.56888 - 2.71739i) q^{37} +(-8.90222 - 2.98542i) q^{39} +(-5.45081 - 6.49602i) q^{41} +(-3.31701 - 9.11341i) q^{43} +(-7.52738 - 8.09431i) q^{45} +(-1.04884 + 5.94826i) q^{47} +(-3.35677 - 1.22177i) q^{49} +(8.90488 + 4.84285i) q^{51} -2.61696i q^{53} +9.77224i q^{55} +(0.308740 + 12.1068i) q^{57} +(1.31447 + 0.478427i) q^{59} +(-1.08453 + 6.15068i) q^{61} +(3.34872 - 4.43128i) q^{63} +(6.83140 + 18.7691i) q^{65} +(-6.80221 - 8.10655i) q^{67} +(-2.61242 + 2.30809i) q^{69} +(-3.21225 - 5.56378i) q^{71} +(-0.960323 + 1.66333i) q^{73} +(-2.20549 + 14.6885i) q^{75} +(-4.83588 + 0.852697i) q^{77} +(-4.70796 + 5.61073i) q^{79} +(-5.27012 - 7.29560i) q^{81} +(-1.31562 - 1.10393i) q^{83} +(-3.74436 - 21.2353i) q^{85} +(-12.3666 - 1.85685i) q^{87} +(8.51242 + 4.91465i) q^{89} +(-8.69198 + 5.01832i) q^{91} +(-6.15986 - 6.97207i) q^{93} +(19.7353 - 16.5598i) q^{95} +(5.07136 - 1.84583i) q^{97} +(-0.980495 + 7.89615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * q	$ 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) $ 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{13}{18}\right)$	$-1$

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
$3$	−0.903983	−	1.47743i	−0.521915	−	0.852997i
$3$	−0.903983	−	1.47743i	−0.521915	−	0.852997i
$4$		0			0
$5$	−1.26017	+	3.46229i	−0.563565	+	1.54838i	0.250805	+	0.968038i	$0.419305\pi$
$5$	−1.26017	+	3.46229i	−0.563565	+	1.54838i	−0.814371	+	0.580345i	$0.802918\pi$
$6$		0			0
$7$	−1.82330	−	0.321498i	−0.689144	−	0.121515i	−0.181900	−	0.983317i	$-0.558225\pi$
$7$	−1.82330	−	0.321498i	−0.689144	−	0.121515i	−0.507244	+	0.861802i	$0.669336\pi$
$8$		0			0
$9$	−1.36563	+	2.67115i	−0.455209	+	0.890384i
$10$		0			0
$11$	2.49231	−	0.907128i	0.751461	−	0.273509i	0.0622404	−	0.998061i	$-0.480175\pi$
$11$	2.49231	−	0.907128i	0.751461	−	0.273509i	0.689220	+	0.724552i	$0.257953\pi$
$12$		0			0
$13$	4.15274	−	3.48456i	1.15176	−	0.966443i	0.152003	−	0.988380i	$-0.451428\pi$
$13$	4.15274	−	3.48456i	1.15176	−	0.966443i	0.999759	+	0.0219366i	$0.00698318\pi$
$14$		0			0
$15$	6.25448	−	1.26803i	1.61490	−	0.327405i
$16$		0			0
$17$	−5.06828	+	2.92617i	−1.22924	+	0.709702i	−0.966871	−	0.255266i	$-0.917837\pi$
$17$	−5.06828	+	2.92617i	−1.22924	+	0.709702i	−0.262368	+	0.964968i	$0.584504\pi$
$18$		0			0
$19$	−6.05539	−	3.49608i	−1.38920	−	0.802056i	−0.395976	−	0.918261i	$-0.629594\pi$
$19$	−6.05539	−	3.49608i	−1.38920	−	0.802056i	−0.993225	+	0.116205i	$0.962927\pi$
$20$		0			0
$21$	1.17324	+	2.98444i	0.256023	+	0.651258i
$22$		0			0
$23$	−0.349489	−	1.98205i	−0.0728735	−	0.413286i	−0.999320	−	0.0368607i	$-0.988264\pi$
$23$	−0.349489	−	1.98205i	−0.0728735	−	0.413286i	0.926447	−	0.376425i	$-0.122847\pi$
$24$		0			0
$25$	−6.56919	−	5.51221i	−1.31384	−	1.10244i
$26$		0			0
$27$	5.18096	−	0.397052i	0.997076	−	0.0764127i
$28$		0			0
$29$	4.64086	−	5.53076i	0.861786	−	1.02704i	−0.137546	−	0.990495i	$-0.543922\pi$
$29$	4.64086	−	5.53076i	0.861786	−	1.02704i	0.999332	−	0.0365413i	$-0.0116340\pi$
$30$		0			0
$31$	5.28973	−	0.932722i	0.950064	−	0.167522i	0.322921	−	0.946426i	$-0.395335\pi$
$31$	5.28973	−	0.932722i	0.950064	−	0.167522i	0.627143	+	0.778904i	$0.284224\pi$
$32$		0			0
$33$	−3.59323	−	2.86220i	−0.625501	−	0.498245i
$34$		0			0
$35$	3.41079	−	5.90766i	0.576529	−	0.998577i
$36$		0			0
$37$	−1.56888	−	2.71739i	−0.257923	−	0.446736i	0.707762	−	0.706451i	$-0.249705\pi$
$37$	−1.56888	−	2.71739i	−0.257923	−	0.446736i	−0.965685	+	0.259715i	$0.916371\pi$
$38$		0			0
$39$	−8.90222	−	2.98542i	−1.42550	−	0.478049i
$40$		0			0
$41$	−5.45081	−	6.49602i	−0.851273	−	1.01451i	−0.999673	−	0.0255802i	$-0.991857\pi$
$41$	−5.45081	−	6.49602i	−0.851273	−	1.01451i	0.148400	−	0.988927i	$-0.452588\pi$
$42$		0			0
$43$	−3.31701	−	9.11341i	−0.505839	−	1.38978i	−0.885493	−	0.464653i	$-0.846179\pi$
$43$	−3.31701	−	9.11341i	−0.505839	−	1.38978i	0.379654	−	0.925129i	$-0.376043\pi$
$44$		0			0
$45$	−7.52738	−	8.09431i	−1.12212	−	1.20663i
$46$		0			0
$47$	−1.04884	+	5.94826i	−0.152989	+	0.867643i	0.807613	+	0.589713i	$0.200759\pi$
$47$	−1.04884	+	5.94826i	−0.152989	+	0.867643i	−0.960601	+	0.277930i	$0.910352\pi$
$48$		0			0
$49$	−3.35677	−	1.22177i	−0.479539	−	0.174538i
$50$		0			0
$51$	8.90488	+	4.84285i	1.24693	+	0.678134i
$52$		0			0
$53$		−	2.61696i		−	0.359467i	−0.983715	−	0.179733i	$-0.942477\pi$
$53$		−	2.61696i		−	0.359467i	0.983715	−	0.179733i	$-0.0575235\pi$
$54$		0			0
$55$			9.77224i			1.31769i
$56$		0			0
$57$	0.308740	+	12.1068i	0.0408936	+	1.60359i
$58$		0			0
$59$	1.31447	+	0.478427i	0.171129	+	0.0622859i	0.426164	−	0.904646i	$-0.359865\pi$
$59$	1.31447	+	0.478427i	0.171129	+	0.0622859i	−0.255035	+	0.966932i	$0.582087\pi$
$60$		0			0
$61$	−1.08453	+	6.15068i	−0.138860	+	0.787514i	0.833234	+	0.552921i	$0.186487\pi$
$61$	−1.08453	+	6.15068i	−0.138860	+	0.787514i	−0.972094	+	0.234593i	$0.924624\pi$
$62$		0			0
$63$	3.34872	−	4.43128i	0.421900	−	0.558289i
$64$		0			0
$65$	6.83140	+	18.7691i	0.847331	+	2.32802i
$66$		0			0
$67$	−6.80221	−	8.10655i	−0.831022	−	0.990373i	−0.999989	−	0.00475131i	$-0.998488\pi$
$67$	−6.80221	−	8.10655i	−0.831022	−	0.990373i	0.168967	−	0.985622i	$-0.445957\pi$
$68$		0			0
$69$	−2.61242	+	2.30809i	−0.314498	+	0.277861i
$70$		0			0
$71$	−3.21225	−	5.56378i	−0.381224	−	0.660299i	0.610013	−	0.792391i	$-0.291164\pi$
$71$	−3.21225	−	5.56378i	−0.381224	−	0.660299i	−0.991238	+	0.132092i	$0.957831\pi$
$72$		0			0
$73$	−0.960323	+	1.66333i	−0.112397	+	0.194678i	−0.916736	−	0.399493i	$-0.869186\pi$
$73$	−0.960323	+	1.66333i	−0.112397	+	0.194678i	0.804339	+	0.594171i	$0.202520\pi$
$74$		0			0
$75$	−2.20549	+	14.6885i	−0.254668	+	1.69608i
$76$		0			0
$77$	−4.83588	+	0.852697i	−0.551100	+	0.0971738i
$78$		0			0
$79$	−4.70796	+	5.61073i	−0.529687	+	0.631257i	−0.962843	−	0.270063i	$-0.912956\pi$
$79$	−4.70796	+	5.61073i	−0.529687	+	0.631257i	0.433156	+	0.901319i	$0.357400\pi$
$80$		0			0
$81$	−5.27012	−	7.29560i	−0.585569	−	0.810623i
$82$		0			0
$83$	−1.31562	−	1.10393i	−0.144408	−	0.121173i	0.567722	−	0.823220i	$-0.307825\pi$
$83$	−1.31562	−	1.10393i	−0.144408	−	0.121173i	−0.712130	+	0.702048i	$0.752269\pi$
$84$		0			0
$85$	−3.74436	−	21.2353i	−0.406133	−	2.30330i
$86$		0			0
$87$	−12.3666	−	1.85685i	−1.32584	−	0.199075i
$88$		0			0
$89$	8.51242	+	4.91465i	0.902315	+	0.520952i	0.877951	−	0.478751i	$-0.158910\pi$
$89$	8.51242	+	4.91465i	0.902315	+	0.520952i	0.0243645	+	0.999703i	$0.492244\pi$
$90$		0			0
$91$	−8.69198	+	5.01832i	−0.911167	+	0.526063i
$92$		0			0
$93$	−6.15986	−	6.97207i	−0.638748	−	0.722970i
$94$		0			0
$95$	19.7353	−	16.5598i	2.02479	−	1.69900i
$96$		0			0
$97$	5.07136	−	1.84583i	0.514919	−	0.187415i	−0.0714732	−	0.997443i	$-0.522770\pi$
$97$	5.07136	−	1.84583i	0.514919	−	0.187415i	0.586392	+	0.810027i	$0.300548\pi$
$98$		0			0
$99$	−0.980495	+	7.89615i	−0.0985435	+	0.793593i
$100$		0			0
$101$	16.1653	+	2.85038i	1.60851	+	0.283624i	0.904470	−	0.426537i	$-0.140267\pi$
$101$	16.1653	+	2.85038i	1.60851	+	0.283624i	0.704039	+	0.710161i	$0.251378\pi$
$102$		0			0
$103$	2.00870	−	5.51886i	0.197923	−	0.543789i	−0.800536	−	0.599285i	$-0.795452\pi$
$103$	2.00870	−	5.51886i	0.197923	−	0.543789i	0.998459	+	0.0554956i	$0.0176739\pi$
$104$		0			0
$105$	−11.8115	+	0.301208i	−1.15268	+	0.0293949i
$106$		0			0
$107$	−6.67916			−0.645699			−0.322849	−	0.946450i	$-0.604641\pi$
$107$	−6.67916			−0.645699			−0.322849	+	0.946450i	$0.604641\pi$
$108$		0			0
$109$	1.34286			0.128623			0.0643113	−	0.997930i	$-0.479515\pi$
$109$	1.34286			0.128623			0.0643113	+	0.997930i	$0.479515\pi$
$110$		0			0
$111$	−2.59652	+	4.77440i	−0.246450	+	0.453166i
$112$		0			0
$113$	1.27305	−	3.49766i	0.119758	−	0.329033i	−0.865300	−	0.501254i	$-0.832872\pi$
$113$	1.27305	−	3.49766i	0.119758	−	0.329033i	0.985058	+	0.172221i	$0.0550944\pi$
$114$		0			0
$115$	7.30285	+	1.28769i	0.680994	+	0.120078i
$116$		0			0
$117$	3.63670	+	15.8512i	0.336213	+	1.46545i
$118$		0			0
$119$	10.1818	−	3.70586i	0.933362	−	0.339716i
$120$		0			0
$121$	−3.03775	+	2.54897i	−0.276159	+	0.231725i
$122$		0			0
$123$	−4.67001	+	13.9255i	−0.421080	+	1.25562i
$124$		0			0
$125$	11.4088	−	6.58690i	1.02044	−	0.589150i
$126$		0			0
$127$	−15.0186	−	8.67100i	−1.33269	−	0.769427i	−0.346976	−	0.937874i	$-0.612791\pi$
$127$	−15.0186	−	8.67100i	−1.33269	−	0.769427i	−0.985711	+	0.168447i	$0.946125\pi$
$128$		0			0
$129$	−10.4659	+	13.1390i	−0.921475	+	1.15683i
$130$		0			0
$131$	−2.33086	−	13.2189i	−0.203648	−	1.15494i	−0.899553	−	0.436811i	$-0.856108\pi$
$131$	−2.33086	−	13.2189i	−0.203648	−	1.15494i	0.695905	−	0.718133i	$-0.255003\pi$
$132$		0			0
$133$	9.91683	+	8.32121i	0.859898	+	0.721540i
$134$		0			0
$135$	−5.15418	+	18.4383i	−0.443601	+	1.58692i
$136$		0			0
$137$	6.42491	−	7.65691i	0.548917	−	0.654174i	−0.418245	−	0.908334i	$-0.637355\pi$
$137$	6.42491	−	7.65691i	0.548917	−	0.654174i	0.967162	+	0.254160i	$0.0817990\pi$
$138$		0			0
$139$	17.8192	−	3.14200i	1.51140	−	0.266501i	0.644354	−	0.764727i	$-0.277126\pi$
$139$	17.8192	−	3.14200i	1.51140	−	0.266501i	0.867047	+	0.498226i	$0.166015\pi$
$140$		0			0
$141$	9.73630	−	3.82754i	0.819945	−	0.322337i
$142$		0			0
$143$	7.18898	−	12.4517i	0.601173	−	1.04126i
$144$		0			0
$145$	13.3008	+	23.0377i	1.10457	+	1.91318i
$146$		0			0
$147$	1.22939	+	6.06387i	0.101398	+	0.500139i
$148$		0			0
$149$	6.93552	+	8.26544i	0.568180	+	0.677131i	0.971256	−	0.238036i	$-0.0765035\pi$
$149$	6.93552	+	8.26544i	0.568180	+	0.677131i	−0.403076	+	0.915166i	$0.632059\pi$
$150$		0			0
$151$	5.33743	+	14.6645i	0.434354	+	1.19338i	0.943114	+	0.332469i	$0.107882\pi$
$151$	5.33743	+	14.6645i	0.434354	+	1.19338i	−0.508760	+	0.860908i	$0.669896\pi$
$152$		0			0
$153$	−0.894872	−	17.5342i	−0.0723461	−	1.41756i
$154$		0			0
$155$	−3.43661	+	19.4900i	−0.276035	+	1.56547i
$156$		0			0
$157$	−4.20202	−	1.52941i	−0.335357	−	0.122060i	0.168852	−	0.985641i	$-0.445994\pi$
$157$	−4.20202	−	1.52941i	−0.335357	−	0.122060i	−0.504210	+	0.863581i	$0.668216\pi$
$158$		0			0
$159$	−3.86638	+	2.36569i	−0.306624	+	0.187611i
$160$		0			0
$161$			3.72624i			0.293669i
$162$		0			0
$163$		−	6.14887i		−	0.481617i	−0.970573	−	0.240809i	$-0.922587\pi$
$163$		−	6.14887i		−	0.481617i	0.970573	−	0.240809i	$-0.0774126\pi$
$164$		0			0
$165$	14.4379	−	8.83395i	1.12399	−	0.687722i
$166$		0			0
$167$	−9.79636	−	3.56558i	−0.758065	−	0.275913i	−0.0660697	−	0.997815i	$-0.521046\pi$
$167$	−9.79636	−	3.56558i	−0.758065	−	0.275913i	−0.691995	+	0.721902i	$0.743268\pi$
$168$		0			0
$169$	2.84564	−	16.1384i	0.218896	−	1.24142i
$170$		0			0
$171$	17.6080	−	11.4005i	1.34652	−	0.871820i
$172$		0			0
$173$	4.65596	+	12.7922i	0.353986	+	0.972569i	0.981076	+	0.193622i	$0.0620237\pi$
$173$	4.65596	+	12.7922i	0.353986	+	0.972569i	−0.627090	+	0.778947i	$0.715754\pi$
$174$		0			0
$175$	10.2055	+	12.1624i	0.771461	+	0.919392i
$176$		0			0
$177$	−0.481412	−	2.37453i	−0.0361851	−	0.178481i
$178$		0			0
$179$	7.94695	+	13.7645i	0.593983	+	1.02881i	0.993690	+	0.112166i	$0.0357788\pi$
$179$	7.94695	+	13.7645i	0.593983	+	1.02881i	−0.399706	+	0.916643i	$0.630888\pi$
$180$		0			0
$181$	1.47317	−	2.55160i	0.109500	−	0.189659i	−0.806068	−	0.591823i	$-0.798408\pi$
$181$	1.47317	−	2.55160i	0.109500	−	0.189659i	0.915568	+	0.402164i	$0.131742\pi$
$182$		0			0
$183$	10.0676	−	3.95779i	0.744220	−	0.292568i
$184$		0			0
$185$	11.3854	−	2.00756i	0.837074	−	0.147599i
$186$		0			0
$187$	−9.97733	+	11.8905i	−0.729615	+	0.869521i
$188$		0			0
$189$	−9.57412	−	0.941720i	−0.696414	−	0.0685001i
$190$		0			0
$191$	−12.4978	−	10.4869i	−0.904309	−	0.758806i	0.0667187	−	0.997772i	$-0.478747\pi$
$191$	−12.4978	−	10.4869i	−0.904309	−	0.758806i	−0.971028	+	0.238966i	$0.923191\pi$
$192$		0			0
$193$	−3.03999	−	17.2407i	−0.218823	−	1.24101i	−0.874147	−	0.485661i	$-0.838579\pi$
$193$	−3.03999	−	17.2407i	−0.218823	−	1.24101i	0.655324	−	0.755348i	$-0.272532\pi$
$194$		0			0
$195$	21.5547	−	27.0599i	1.54356	−	1.93780i
$196$		0			0
$197$	−7.93394	−	4.58066i	−0.565270	−	0.326359i	0.189988	−	0.981786i	$-0.439155\pi$
$197$	−7.93394	−	4.58066i	−0.565270	−	0.326359i	−0.755258	+	0.655428i	$0.772488\pi$
$198$		0			0
$199$	−6.79914	+	3.92549i	−0.481978	+	0.278270i	−0.721241	−	0.692685i	$-0.756428\pi$
$199$	−6.79914	+	3.92549i	−0.481978	+	0.278270i	0.239262	+	0.970955i	$0.423094\pi$
$200$		0			0
$201$	−5.82782	+	17.3780i	−0.411063	+	1.22575i
$202$		0			0
$203$	−10.2398	+	8.59223i	−0.718695	+	0.603057i
$204$		0			0
$205$	29.3600	−	10.6862i	2.05059	−	0.746355i
$206$		0			0
$207$	5.77163	+	1.77320i	0.401156	+	0.123246i
$208$		0			0
$209$	−18.2633	−	3.22031i	−1.26330	−	0.222754i
$210$		0			0
$211$	−2.92530	+	8.03719i	−0.201386	+	0.553303i	−0.998739	−	0.0502106i	$-0.984011\pi$
$211$	−2.92530	+	8.03719i	−0.201386	+	0.553303i	0.797353	+	0.603513i	$0.206233\pi$
$212$		0			0
$213$	−5.31630	+	9.77546i	−0.364267	+	0.669803i
$214$		0			0
$215$	35.7332			2.43699
$216$		0			0
$217$	−9.94465			−0.675087
$218$		0			0
$219$	3.32558	−	0.0848064i	0.224722	−	0.00573069i
$220$		0			0
$221$	−10.8508	+	29.8124i	−0.729905	+	2.00540i
$222$		0			0
$223$	−3.75162	−	0.661511i	−0.251227	−	0.0442981i	0.0466164	−	0.998913i	$-0.485156\pi$
$223$	−3.75162	−	0.661511i	−0.251227	−	0.0442981i	−0.297843	+	0.954615i	$0.596267\pi$
$224$		0			0
$225$	23.6950	−	10.0197i	1.57967	−	0.667980i
$226$		0			0
$227$	−13.0258	+	4.74099i	−0.864551	+	0.314671i	−0.735958	−	0.677027i	$-0.763268\pi$
$227$	−13.0258	+	4.74099i	−0.864551	+	0.314671i	−0.128592	+	0.991698i	$0.541046\pi$
$228$		0			0
$229$	−10.9532	+	9.19080i	−0.723806	+	0.607345i	−0.928435	−	0.371494i	$-0.878846\pi$
$229$	−10.9532	+	9.19080i	−0.723806	+	0.607345i	0.204629	+	0.978840i	$0.434401\pi$
$230$		0			0
$231$	5.63136	+	6.37388i	0.370516	+	0.419370i
$232$		0			0
$233$	6.41217	−	3.70207i	0.420075	−	0.242530i	−0.275034	−	0.961434i	$-0.588689\pi$
$233$	6.41217	−	3.70207i	0.420075	−	0.242530i	0.695109	+	0.718904i	$0.255356\pi$
$234$		0			0
$235$	−19.2729	−	11.1272i	−1.25722	−	0.725859i
$236$		0			0
$237$	12.5454	+	1.88370i	0.814912	+	0.122359i
$238$		0			0
$239$	0.155109	+	0.879669i	0.0100332	+	0.0569010i	0.989413	−	0.145125i	$-0.0463585\pi$
$239$	0.155109	+	0.879669i	0.0100332	+	0.0569010i	−0.979380	+	0.202026i	$0.935247\pi$
$240$		0			0
$241$	−2.52904	−	2.12211i	−0.162910	−	0.136697i	0.557689	−	0.830050i	$-0.311688\pi$
$241$	−2.52904	−	2.12211i	−0.162910	−	0.136697i	−0.720598	+	0.693353i	$0.756133\pi$
$242$		0			0
$243$	−6.01468	+	14.3814i	−0.385842	+	0.922565i
$244$		0			0
$245$	8.46021	−	10.0825i	0.540503	−	0.644146i
$246$		0			0
$247$	−37.3287	+	6.58206i	−2.37517	+	0.418807i
$248$		0			0
$249$	−0.441695	+	2.94168i	−0.0279913	+	0.186421i
$250$		0			0
$251$	−11.1221	+	19.2641i	−0.702023	+	1.21594i	0.265732	+	0.964047i	$0.414386\pi$
$251$	−11.1221	+	19.2641i	−0.702023	+	1.21594i	−0.967755	+	0.251893i	$0.918947\pi$
$252$		0			0
$253$	−2.66901	−	4.62286i	−0.167799	−	0.290637i
$254$		0			0
$255$	−27.9890	+	24.7284i	−1.75274	+	1.54856i
$256$		0			0
$257$	11.0437	+	13.1614i	0.688887	+	0.820984i	0.991221	−	0.132218i	$-0.0422100\pi$
$257$	11.0437	+	13.1614i	0.688887	+	0.820984i	−0.302333	+	0.953202i	$0.597766\pi$
$258$		0			0
$259$	1.98692	+	5.45901i	0.123461	+	0.339207i
$260$		0			0
$261$	8.43582	+	19.9494i	0.522164	+	1.23484i
$262$		0			0
$263$	−4.37797	+	24.8287i	−0.269957	+	1.53100i	0.484581	+	0.874746i	$0.338972\pi$
$263$	−4.37797	+	24.8287i	−0.269957	+	1.53100i	−0.754538	+	0.656256i	$0.772139\pi$
$264$		0			0
$265$	9.06066	+	3.29781i	0.556592	+	0.202583i
$266$		0			0
$267$	−0.434014	−	17.0193i	−0.0265612	−	1.04157i
$268$		0			0
$269$		−	14.1101i		−	0.860310i	−0.902755	−	0.430155i	$-0.858459\pi$
$269$		−	14.1101i		−	0.860310i	0.902755	−	0.430155i	$-0.141541\pi$
$270$		0			0
$271$		−	4.92075i		−	0.298914i	−0.988768	−	0.149457i	$-0.952247\pi$
$271$		−	4.92075i		−	0.298914i	0.988768	−	0.149457i	$-0.0477526\pi$
$272$		0			0
$273$	15.2716	+	8.30536i	0.924282	+	0.502663i
$274$		0			0
$275$	−21.3728	−	7.77905i	−1.28883	−	0.469094i
$276$		0			0
$277$	2.91617	−	16.5384i	0.175216	−	0.993699i	−0.762678	−	0.646778i	$-0.776116\pi$
$277$	2.91617	−	16.5384i	0.175216	−	0.993699i	0.937894	−	0.346921i	$-0.112773\pi$
$278$		0			0
$279$	−4.73236	+	15.4034i	−0.283319	+	0.922179i
$280$		0			0
$281$	5.11831	+	14.0624i	0.305333	+	0.838895i	0.993550	+	0.113391i	$0.0361712\pi$
$281$	5.11831	+	14.0624i	0.305333	+	0.838895i	−0.688218	+	0.725504i	$0.741607\pi$
$282$		0			0
$283$	−15.0741	−	17.9646i	−0.896060	−	1.06788i	−0.997330	−	0.0730239i	$-0.976735\pi$
$283$	−15.0741	−	17.9646i	−0.896060	−	1.06788i	0.101270	−	0.994859i	$-0.467709\pi$
$284$		0			0
$285$	−42.3064	−	14.1877i	−2.50602	−	0.840409i
$286$		0			0
$287$	7.85002	+	13.5966i	0.463372	+	0.802584i
$288$		0			0
$289$	8.62499	−	14.9389i	0.507353	−	0.878761i
$290$		0			0
$291$	−7.31151	−	5.82401i	−0.428609	−	0.341410i
$292$		0			0
$293$	−23.0887	+	4.07116i	−1.34885	+	0.237840i	−0.800965	−	0.598711i	$-0.795680\pi$
$293$	−23.0887	+	4.07116i	−1.34885	+	0.237840i	−0.547890	+	0.836551i	$0.684569\pi$
$294$		0			0
$295$	−3.31290	+	3.94817i	−0.192885	+	0.229871i
$296$		0			0
$297$	12.5524	−	5.68937i	0.728364	−	0.330131i
$298$		0			0
$299$	−8.35791	−	7.01312i	−0.483351	−	0.405579i
$300$		0			0
$301$	3.11798	+	17.6829i	0.179717	+	1.01923i
$302$		0			0
$303$	−10.4019	−	26.4599i	−0.597575	−	1.52008i
$304$		0			0
$305$	−19.9287	−	11.5059i	−1.14112	−	0.658824i
$306$		0			0
$307$	27.8381	−	16.0723i	1.58881	−	0.917297i	0.595301	−	0.803503i	$-0.297033\pi$
$307$	27.8381	−	16.0723i	1.58881	−	0.917297i	0.993504	−	0.113794i	$-0.0363004\pi$
$308$		0			0
$309$	−9.96959	+	2.02123i	−0.567150	+	0.114984i
$310$		0			0
$311$	−9.56035	+	8.02209i	−0.542118	+	0.454891i	−0.872261	−	0.489040i	$-0.837347\pi$
$311$	−9.56035	+	8.02209i	−0.542118	+	0.454891i	0.330144	+	0.943931i	$0.392903\pi$
$312$		0			0
$313$	−4.38722	+	1.59682i	−0.247980	+	0.0902574i	−0.463020	−	0.886348i	$-0.653234\pi$
$313$	−4.38722	+	1.59682i	−0.247980	+	0.0902574i	0.215040	+	0.976605i	$0.431012\pi$
$314$		0			0
$315$	11.1224	+	17.1784i	0.626676	+	0.967894i
$316$		0			0
$317$	−27.1885	−	4.79406i	−1.52706	−	0.269261i	−0.653855	−	0.756620i	$-0.726849\pi$
$317$	−27.1885	−	4.79406i	−1.52706	−	0.269261i	−0.873202	+	0.487359i	$0.837960\pi$
$318$		0			0
$319$	6.54937	−	17.9942i	0.366694	−	1.00748i
$320$		0			0
$321$	6.03785	+	9.86802i	0.337000	+	0.550779i
$322$		0			0
$323$	40.9206			2.27688
$324$		0			0
$325$	−46.4878			−2.57868
$326$		0			0
$327$	−1.21392	−	1.98399i	−0.0671301	−	0.109715i
$328$		0			0
$329$	3.82470	−	10.5083i	0.210863	−	0.579341i
$330$		0			0
$331$	−12.8470	−	2.26528i	−0.706137	−	0.124511i	−0.190964	−	0.981597i	$-0.561161\pi$
$331$	−12.8470	−	2.26528i	−0.706137	−	0.124511i	−0.515173	+	0.857086i	$0.672272\pi$
$332$		0			0
$333$	9.40107	−	0.479790i	0.515175	−	0.0262923i
$334$		0			0
$335$	36.6392	−	13.3356i	2.00181	−	0.728600i
$336$		0			0
$337$	12.3248	−	10.3417i	0.671375	−	0.563351i	−0.242097	−	0.970252i	$-0.577835\pi$
$337$	12.3248	−	10.3417i	0.671375	−	0.563351i	0.913472	+	0.406901i	$0.133391\pi$
$338$		0			0
$339$	−6.31838	+	1.28099i	−0.343168	+	0.0695737i
$340$		0			0
$341$	12.3376	−	7.12310i	0.668117	−	0.385737i
$342$		0			0
$343$	16.9513	+	9.78685i	0.915286	+	0.528440i
$344$		0			0
$345$	−4.69918	−	11.9535i	−0.252995	−	0.643556i
$346$		0			0
$347$	−0.113527	−	0.643846i	−0.00609447	−	0.0345635i	0.981609	−	0.190903i	$-0.0611416\pi$
$347$	−0.113527	−	0.643846i	−0.00609447	−	0.0345635i	−0.987703	+	0.156340i	$0.950031\pi$
$348$		0			0
$349$	21.4694	+	18.0149i	1.14923	+	0.964318i	0.999701	−	0.0244400i	$-0.00778026\pi$
$349$	21.4694	+	18.0149i	1.14923	+	0.964318i	0.149528	+	0.988758i	$0.452225\pi$
$350$		0			0
$351$	20.1316	−	19.7022i	1.07455	−	1.05163i
$352$		0			0
$353$	−3.04356	+	3.62718i	−0.161992	+	0.193055i	−0.840935	−	0.541137i	$-0.817994\pi$
$353$	−3.04356	+	3.62718i	−0.161992	+	0.193055i	0.678942	+	0.734192i	$0.262439\pi$
$354$		0			0
$355$	23.3114	−	4.11043i	1.23724	−	0.218159i
$356$		0			0
$357$	−14.6793	−	11.6929i	−0.776913	−	0.618853i
$358$		0			0
$359$	6.37413	−	11.0403i	0.336414	−	0.582685i	−0.647342	−	0.762200i	$-0.724119\pi$
$359$	6.37413	−	11.0403i	0.336414	−	0.582685i	0.983755	+	0.179514i	$0.0574527\pi$
$360$		0			0
$361$	14.9451	+	25.8857i	0.786586	+	1.36241i
$362$		0			0
$363$	6.51201	+	2.18384i	0.341792	+	0.114622i
$364$		0			0
$365$	−4.54875	−	5.42099i	−0.238093	−	0.283748i
$366$		0			0
$367$	9.46924	+	26.0165i	0.494290	+	1.35805i	0.896719	+	0.442600i	$0.145944\pi$
$367$	9.46924	+	26.0165i	0.494290	+	1.35805i	−0.402429	+	0.915451i	$0.631834\pi$
$368$		0			0
$369$	24.7956	−	5.68880i	1.29081	−	0.296147i
$370$		0			0
$371$	−0.841346	+	4.77151i	−0.0436805	+	0.247724i
$372$		0			0
$373$	−22.3852	−	8.14756i	−1.15906	−	0.421865i	−0.310301	−	0.950638i	$-0.600430\pi$
$373$	−22.3852	−	8.14756i	−1.15906	−	0.421865i	−0.848763	+	0.528774i	$0.822652\pi$
$374$		0			0
$375$	−20.0451	−	10.9014i	−1.03513	−	0.562945i
$376$		0			0
$377$		−	39.1392i		−	2.01577i
$378$		0			0
$379$		−	4.22856i		−	0.217206i	−0.994085	−	0.108603i	$-0.965362\pi$
$379$		−	4.22856i		−	0.217206i	0.994085	−	0.108603i	$-0.0346378\pi$
$380$		0			0
$381$	0.765739	+	30.0275i	0.0392300	+	1.53835i
$382$		0			0
$383$	−7.51651	−	2.73579i	−0.384076	−	0.139792i	0.142764	−	0.989757i	$-0.454401\pi$
$383$	−7.51651	−	2.73579i	−0.384076	−	0.139792i	−0.526840	+	0.849965i	$0.676623\pi$
$384$		0			0
$385$	3.14175	−	17.8178i	0.160119	−	0.908078i
$386$		0			0
$387$	28.8731	+	3.58528i	1.46770	+	0.182250i
$388$		0			0
$389$	−2.59136	−	7.11969i	−0.131387	−	0.360983i	0.856502	−	0.516143i	$-0.172633\pi$
$389$	−2.59136	−	7.11969i	−0.131387	−	0.360983i	−0.987889	+	0.155160i	$0.950411\pi$
$390$		0			0
$391$	7.57113	+	9.02293i	0.382889	+	0.456309i
$392$		0			0
$393$	−17.4231	+	15.3934i	−0.878878	+	0.776494i
$394$		0			0
$395$	−13.4931	−	23.3708i	−0.678914	−	1.17591i
$396$		0			0
$397$	0.228404	−	0.395607i	0.0114633	−	0.0198549i	−0.860237	−	0.509895i	$-0.829684\pi$
$397$	0.228404	−	0.395607i	0.0114633	−	0.0198549i	0.871700	+	0.490040i	$0.163018\pi$
$398$		0			0
$399$	3.32939	−	22.1737i	0.166678	−	1.11007i
$400$		0			0
$401$	−25.8193	+	4.55265i	−1.28936	+	0.227348i	−0.775949	−	0.630796i	$-0.782728\pi$
$401$	−25.8193	+	4.55265i	−1.28936	+	0.227348i	−0.513408	+	0.858145i	$0.671617\pi$
$402$		0			0
$403$	18.7167	−	22.3057i	0.932347	−	1.11113i
$404$		0			0
$405$	31.9007	−	9.05298i	1.58516	−	0.449846i
$406$		0			0
$407$	−6.37517	−	5.34940i	−0.316005	−	0.265160i
$408$		0			0
$409$	0.279484	+	1.58503i	0.0138196	+	0.0783748i	0.990938	−	0.134323i	$-0.0428860\pi$
$409$	0.279484	+	1.58503i	0.0138196	+	0.0783748i	−0.977118	+	0.212698i	$0.931775\pi$
$410$		0			0
$411$	−17.1206	−	2.57067i	−0.844497	−	0.126802i
$412$		0			0
$413$	−2.24286	−	1.29492i	−0.110364	−	0.0637186i
$414$		0			0
$415$	5.48004	−	3.16390i	0.269005	−	0.155310i
$416$		0			0
$417$	−20.7503	−	23.4863i	−1.01615	−	1.15013i
$418$		0			0
$419$	−19.2396	+	16.1439i	−0.939916	+	0.788683i	−0.977571	−	0.210608i	$-0.932456\pi$
$419$	−19.2396	+	16.1439i	−0.939916	+	0.788683i	0.0376548	+	0.999291i	$0.488011\pi$
$420$		0			0
$421$	−5.15496	+	1.87625i	−0.251237	+	0.0914428i	−0.464569	−	0.885537i	$-0.653791\pi$
$421$	−5.15496	+	1.87625i	−0.251237	+	0.0914428i	0.213332	+	0.976980i	$0.431568\pi$
$422$		0			0
$423$	−14.4564	−	10.9247i	−0.702894	−	0.531178i
$424$		0			0
$425$	49.4242	+	8.71482i	2.39743	+	0.422731i
$426$		0			0
$427$	3.95486	−	10.8659i	0.191389	−	0.525837i
$428$		0			0
$429$	−24.8953	+	0.634861i	−1.20196	+	0.0306514i
$430$		0			0
$431$	−16.0621			−0.773685			−0.386843	−	0.922146i	$-0.626434\pi$
$431$	−16.0621			−0.773685			−0.386843	+	0.922146i	$0.626434\pi$
$432$		0			0
$433$	−38.9404			−1.87136			−0.935678	−	0.352855i	$-0.885211\pi$
$433$	−38.9404			−1.87136			−0.935678	+	0.352855i	$0.885211\pi$
$434$		0			0
$435$	22.0130	−	40.4768i	1.05544	−	1.94071i
$436$		0			0
$437$	−4.81311	+	13.2239i	−0.230242	+	0.632586i
$438$		0			0
$439$	21.2507	+	3.74706i	1.01424	+	0.178838i	0.655975	−	0.754783i	$-0.272258\pi$
$439$	21.2507	+	3.74706i	1.01424	+	0.178838i	0.358264	+	0.933620i	$0.383369\pi$
$440$		0			0
$441$	7.84762	−	7.29798i	0.373696	−	0.347523i
$442$		0			0
$443$	−29.3171	+	10.6705i	−1.39290	+	0.506973i	−0.926062	−	0.377372i	$-0.876828\pi$
$443$	−29.3171	+	10.6705i	−1.39290	+	0.506973i	−0.466834	+	0.884345i	$0.654605\pi$
$444$		0			0
$445$	−27.7430	+	23.2792i	−1.31515	+	1.10354i
$446$		0			0
$447$	5.94204	−	17.7186i	0.281049	−	0.838061i
$448$		0			0
$449$	−10.3417	+	5.97080i	−0.488056	+	0.281779i	−0.723768	−	0.690044i	$-0.757591\pi$
$449$	−10.3417	+	5.97080i	−0.488056	+	0.281779i	0.235711	+	0.971823i	$0.424258\pi$
$450$		0			0
$451$	−19.4778	−	11.2455i	−0.917175	−	0.529531i
$452$		0			0
$453$	16.8409	−	21.1421i	0.791252	−	0.993345i
$454$		0			0
$455$	−6.42149	−	36.4181i	−0.301044	−	1.70731i
$456$		0			0
$457$	16.6152	+	13.9418i	0.777227	+	0.652171i	0.942549	−	0.334069i	$-0.108422\pi$
$457$	16.6152	+	13.9418i	0.777227	+	0.652171i	−0.165322	+	0.986240i	$0.552866\pi$
$458$		0			0
$459$	−25.0967	+	17.1728i	−1.17142	+	0.801556i
$460$		0			0
$461$	9.33490	−	11.1249i	0.434769	−	0.518138i	−0.503523	−	0.863982i	$-0.667963\pi$
$461$	9.33490	−	11.1249i	0.434769	−	0.518138i	0.938292	+	0.345844i	$0.112407\pi$
$462$		0			0
$463$	40.6512	−	7.16790i	1.88922	−	0.333120i	0.895504	−	0.445054i	$-0.146815\pi$
$463$	40.6512	−	7.16790i	1.88922	−	0.333120i	0.993716	+	0.111933i	$0.0357044\pi$
$464$		0			0
$465$	31.9018	−	12.5412i	1.47941	−	0.581586i
$466$		0			0
$467$	8.29661	−	14.3702i	0.383922	−	0.664972i	−0.607697	−	0.794169i	$-0.707907\pi$
$467$	8.29661	−	14.3702i	0.383922	−	0.664972i	0.991619	+	0.129197i	$0.0412400\pi$
$468$		0			0
$469$	9.79625	+	16.9676i	0.452349	+	0.783491i
$470$		0			0
$471$	1.53895	+	7.59076i	0.0709111	+	0.349764i
$472$		0			0
$473$	−16.5340	−	19.7045i	−0.760236	−	0.906014i
$474$		0			0
$475$	20.5079	+	56.3450i	0.940967	+	2.58529i
$476$		0			0
$477$	6.99029	+	3.57379i	0.320064	+	0.163633i
$478$		0			0
$479$	2.51415	−	14.2584i	0.114874	−	0.651485i	−0.871938	−	0.489616i	$-0.837137\pi$
$479$	2.51415	−	14.2584i	0.114874	−	0.651485i	0.986812	−	0.161868i	$-0.0517520\pi$
$480$		0			0
$481$	−15.9841	−	5.81772i	−0.728811	−	0.265265i
$482$		0			0
$483$	5.50528	−	3.36846i	0.250499	−	0.153270i
$484$		0			0
$485$			19.8846i			0.902912i
$486$		0			0
$487$			20.2055i			0.915598i	0.889056	+	0.457799i	$0.151362\pi$
$487$			20.2055i			0.915598i	−0.889056	+	0.457799i	$0.848638\pi$
$488$		0			0
$489$	−9.08456	+	5.55848i	−0.410818	+	0.251363i
$490$		0			0
$491$	23.1244	+	8.41658i	1.04359	+	0.379835i	0.806239	−	0.591590i	$-0.201500\pi$
$491$	23.1244	+	8.41658i	1.04359	+	0.379835i	0.237348	+	0.971425i	$0.423722\pi$
$492$		0			0
$493$	−7.33722	+	41.6114i	−0.330452	+	1.87408i
$494$		0			0
$495$	−26.1032	−	13.3452i	−1.17325	−	0.599824i
$496$		0			0
$497$	4.06817	+	11.1772i	0.182482	+	0.501366i
$498$		0			0
$499$	−23.3606	−	27.8401i	−1.04577	−	1.24630i	−0.968429	−	0.249290i	$-0.919803\pi$
$499$	−23.3606	−	27.8401i	−1.04577	−	1.24630i	−0.0773373	−	0.997005i	$-0.524642\pi$
$500$		0			0
$501$	3.58783	+	17.6967i	0.160292	+	0.790631i
$502$		0			0
$503$	5.84283	+	10.1201i	0.260519	+	0.451232i	0.966380	−	0.257118i	$-0.0827730\pi$
$503$	5.84283	+	10.1201i	0.260519	+	0.451232i	−0.705861	+	0.708350i	$0.749440\pi$
$504$		0			0
$505$	−30.2399	+	52.3770i	−1.34566	+	2.33075i
$506$		0			0
$507$	−26.4159	+	10.3846i	−1.17317	+	0.461198i
$508$		0			0
$509$	0.543863	−	0.0958977i	0.0241063	−	0.00425059i	−0.161582	−	0.986859i	$-0.551660\pi$
$509$	0.543863	−	0.0958977i	0.0241063	−	0.00425059i	0.185688	+	0.982609i	$0.440549\pi$
$510$		0			0
$511$	2.28572	−	2.72401i	0.101114	−	0.120503i
$512$		0			0
$513$	−32.7608	−	15.7087i	−1.44643	−	0.693558i
$514$		0			0
$515$	16.5766	+	13.9094i	0.730452	+	0.612922i
$516$		0			0
$517$	2.78180	+	15.7764i	0.122343	+	0.693844i
$518$		0			0
$519$	14.6907	−	18.4428i	0.644848	−	0.809548i
$520$		0			0
$521$	−19.0586	−	11.0035i	−0.834972	−	0.482071i	0.0205802	−	0.999788i	$-0.493449\pi$
$521$	−19.0586	−	11.0035i	−0.834972	−	0.482071i	−0.855552	+	0.517717i	$0.826782\pi$
$522$		0			0
$523$	15.9584	−	9.21361i	0.697814	−	0.402883i	−0.108719	−	0.994073i	$-0.534675\pi$
$523$	15.9584	−	9.21361i	0.697814	−	0.402883i	0.806533	+	0.591190i	$0.201342\pi$
$524$		0			0
$525$	8.74359	−	26.0725i	0.381602	−	1.13790i
$526$		0			0
$527$	−24.0805	+	20.2060i	−1.04896	+	0.880186i
$528$		0			0
$529$	17.8065	−	6.48105i	0.774198	−	0.281785i
$530$		0			0
$531$	−3.07302	+	2.85779i	−0.133358	+	0.124018i
$532$		0			0
$533$	−45.2716	−	7.98260i	−1.96093	−	0.345765i
$534$		0			0
$535$	8.41688	−	23.1252i	0.363893	−	0.999789i
$536$		0			0
$537$	13.1523	−	24.1840i	0.567563	−	1.04362i
$538$		0			0
$539$	−9.47442			−0.408092
$540$		0			0
$541$	25.2185			1.08423			0.542115	−	0.840304i	$-0.317624\pi$
$541$	25.2185			1.08423			0.542115	+	0.840304i	$0.317624\pi$
$542$		0			0
$543$	−5.10155	+	0.130096i	−0.218929	+	0.00558295i
$544$		0			0
$545$	−1.69223	+	4.64937i	−0.0724873	+	0.199157i
$546$		0			0
$547$	3.69708	+	0.651894i	0.158076	+	0.0278730i	0.252126	−	0.967694i	$-0.418870\pi$
$547$	3.69708	+	0.651894i	0.158076	+	0.0278730i	−0.0940502	+	0.995567i	$0.529981\pi$
$548$		0			0
$549$	−14.9483	−	11.2965i	−0.637980	−	0.482122i
$550$		0			0
$551$	−47.4382	+	17.2661i	−2.02093	+	0.735560i
$552$		0			0
$553$	10.3879	−	8.71647i	0.441738	−	0.370662i
$554$		0			0
$555$	−13.2583	−	15.0064i	−0.562783	−	0.636988i
$556$		0			0
$557$	32.0500	−	18.5041i	1.35800	−	0.784044i	0.368649	−	0.929569i	$-0.379820\pi$
$557$	32.0500	−	18.5041i	1.35800	−	0.784044i	0.989355	+	0.145525i	$0.0464870\pi$
$558$		0			0
$559$	−45.5309	−	26.2873i	−1.92575	−	1.11183i
$560$		0			0
$561$	26.5868	+	3.99203i	1.12250	+	0.168543i
$562$		0			0
$563$	−2.44551	−	13.8692i	−0.103066	−	0.584517i	−0.991975	−	0.126433i	$-0.959647\pi$
$563$	−2.44551	−	13.8692i	−0.103066	−	0.584517i	0.888909	−	0.458084i	$-0.151464\pi$
$564$		0			0
$565$	10.5057	+	8.81531i	0.441977	+	0.370863i
$566$		0			0
$567$	7.26351	+	14.9964i	0.305039	+	0.629791i
$568$		0			0
$569$	−9.94279	+	11.8494i	−0.416823	+	0.496751i	−0.933073	−	0.359688i	$-0.882883\pi$
$569$	−9.94279	+	11.8494i	−0.416823	+	0.496751i	0.516250	+	0.856438i	$0.327328\pi$
$570$		0			0
$571$	23.1039	−	4.07385i	0.966870	−	0.170485i	0.332149	−	0.943227i	$-0.392226\pi$
$571$	23.1039	−	4.07385i	0.966870	−	0.170485i	0.634721	+	0.772742i	$0.281115\pi$
$572$		0			0
$573$	−4.19591	+	27.9447i	−0.175287	+	1.16741i
$574$		0			0
$575$	−8.62961	+	14.9469i	−0.359880	+	0.623330i
$576$		0			0
$577$	−1.73316	−	3.00192i	−0.0721523	−	0.124971i	0.827692	−	0.561183i	$-0.189653\pi$
$577$	−1.73316	−	3.00192i	−0.0721523	−	0.124971i	−0.899844	+	0.436211i	$0.856320\pi$
$578$		0			0
$579$	−22.7238	+	20.0767i	−0.944371	+	0.834357i
$580$		0			0
$581$	2.04386	+	2.43578i	0.0847935	+	0.101053i
$582$		0			0
$583$	−2.37391	−	6.52228i	−0.0983175	−	0.270125i
$584$		0			0
$585$	−59.4644	−	7.38392i	−2.45855	−	0.305287i
$586$		0			0
$587$	4.12961	−	23.4202i	0.170447	−	0.966655i	−0.772821	−	0.634624i	$-0.781155\pi$
$587$	4.12961	−	23.4202i	0.170447	−	0.966655i	0.943268	−	0.332031i	$-0.107734\pi$
$588$		0			0
$589$	−35.2922	−	12.8453i	−1.45419	−	0.529282i
$590$		0			0
$591$	0.404520	+	15.8627i	0.0166397	+	0.652505i
$592$		0			0
$593$		−	32.2934i		−	1.32613i	−0.748562	−	0.663065i	$-0.769255\pi$
$593$		−	32.2934i		−	1.32613i	0.748562	−	0.663065i	$-0.230745\pi$
$594$		0			0
$595$			39.9223i			1.63665i
$596$		0			0
$597$	11.9460	+	6.49672i	0.488916	+	0.265893i
$598$		0			0
$599$	1.34749	+	0.490444i	0.0550567	+	0.0200390i	0.369402	−	0.929270i	$-0.379563\pi$
$599$	1.34749	+	0.490444i	0.0550567	+	0.0200390i	−0.314345	+	0.949309i	$0.601785\pi$
$600$		0			0
$601$	−1.19771	+	6.79258i	−0.0488558	+	0.277075i	−0.999443	−	0.0333839i	$-0.989372\pi$
$601$	−1.19771	+	6.79258i	−0.0488558	+	0.277075i	0.950587	+	0.310459i	$0.100483\pi$
$602$		0			0
$603$	30.9431	−	7.09920i	1.26010	−	0.289102i
$604$		0			0
$605$	−4.99720	−	13.7297i	−0.203165	−	0.558191i
$606$		0			0
$607$	23.2765	+	27.7399i	0.944765	+	1.12593i	0.991898	+	0.127039i	$0.0405473\pi$
$607$	23.2765	+	27.7399i	0.944765	+	1.12593i	−0.0471324	+	0.998889i	$0.515008\pi$
$608$		0			0
$609$	21.9511	+	7.36144i	0.889503	+	0.298301i
$610$		0			0
$611$	16.3715	+	28.3563i	0.662321	+	1.14717i
$612$		0			0
$613$	22.5730	−	39.0976i	0.911715	−	1.57914i	0.100074	−	0.994980i	$-0.468092\pi$
$613$	22.5730	−	39.0976i	0.911715	−	1.57914i	0.811641	−	0.584156i	$-0.198574\pi$
$614$		0			0
$615$	−42.3291	−	33.7174i	−1.70687	−	1.35962i
$616$		0			0
$617$	−2.15564	+	0.380098i	−0.0867829	+	0.0153022i	−0.216871	−	0.976200i	$-0.569585\pi$
$617$	−2.15564	+	0.380098i	−0.0867829	+	0.0153022i	0.130088	+	0.991502i	$0.458474\pi$
$618$		0			0
$619$	−15.9794	+	19.0435i	−0.642265	+	0.765421i	−0.984726	−	0.174111i	$-0.944295\pi$
$619$	−15.9794	+	19.0435i	−0.642265	+	0.765421i	0.342462	+	0.939532i	$0.388739\pi$
$620$		0			0
$621$	−2.59767	−	10.1302i	−0.104241	−	0.406509i
$622$		0			0
$623$	−13.9407	−	11.6976i	−0.558522	−	0.468655i
$624$		0			0
$625$	0.983090	+	5.57538i	0.0393236	+	0.223015i
$626$		0			0
$627$	11.7519	+	29.8940i	0.469327	+	1.19385i
$628$		0			0
$629$	15.9031	+	9.18165i	0.634098	+	0.366097i
$630$		0			0
$631$	33.7405	−	19.4801i	1.34319	−	0.775489i	0.355913	−	0.934519i	$-0.384170\pi$
$631$	33.7405	−	19.4801i	1.34319	−	0.775489i	0.987274	+	0.159030i	$0.0508368\pi$
$632$		0			0
$633$	14.5188	−	2.94355i	0.577072	−	0.116996i
$634$		0			0
$635$	48.9475	−	41.0719i	1.94242	−	1.62989i
$636$		0			0
$637$	−18.1971	+	6.62321i	−0.720996	+	0.262421i
$638$		0			0
$639$	19.2485	−	0.982359i	0.761457	−	0.0388615i
$640$		0			0
$641$	38.6258	+	6.81077i	1.52563	+	0.269009i	0.872641	−	0.488362i	$-0.162405\pi$
$641$	38.6258	+	6.81077i	1.52563	+	0.269009i	0.652985	+	0.757371i	$0.273516\pi$
$642$		0			0
$643$	−5.46122	+	15.0046i	−0.215370	+	0.591723i	−0.999586	−	0.0287639i	$-0.990843\pi$
$643$	−5.46122	+	15.0046i	−0.215370	+	0.591723i	0.784217	+	0.620487i	$0.213065\pi$
$644$		0			0
$645$	−32.3023	−	52.7935i	−1.27190	−	2.07874i
$646$		0			0
$647$	−21.3153			−0.837989			−0.418994	−	0.907989i	$-0.637617\pi$
$647$	−21.3153			−0.837989			−0.418994	+	0.907989i	$0.637617\pi$
$648$		0			0
$649$	3.71006			0.145633
$650$		0			0
$651$	8.98980	+	14.6926i	0.352338	+	0.575848i
$652$		0			0
$653$	8.74056	−	24.0145i	0.342045	−	0.939760i	−0.642756	−	0.766071i	$-0.722209\pi$
$653$	8.74056	−	24.0145i	0.342045	−	0.939760i	0.984801	−	0.173689i	$-0.0555687\pi$
$654$		0			0
$655$	48.7051	+	8.58802i	1.90306	+	0.335562i
$656$		0			0
$657$	−3.13156	−	4.83666i	−0.122174	−	0.188696i
$658$		0			0
$659$	−7.32137	+	2.66476i	−0.285200	+	0.103804i	−0.480659	−	0.876907i	$-0.659603\pi$
$659$	−7.32137	+	2.66476i	−0.285200	+	0.103804i	0.195459	+	0.980712i	$0.437380\pi$
$660$		0			0
$661$	8.29887	−	6.96358i	0.322789	−	0.270852i	−0.466965	−	0.884276i	$-0.654653\pi$
$661$	8.29887	−	6.96358i	0.322789	−	0.270852i	0.789754	+	0.613424i	$0.210208\pi$
$662$		0			0
$663$	53.8548	−	10.9185i	2.09155	−	0.424040i
$664$		0			0
$665$	−41.3073	+	23.8488i	−1.60183	+	0.924816i
$666$		0			0
$667$	−12.5842	−	7.26548i	−0.487261	−	0.281320i
$668$		0			0
$669$	2.41406	+	6.14077i	0.0933329	+	0.237416i
$670$		0			0
$671$	2.87646	+	16.3132i	0.111045	+	0.629765i
$672$		0			0
$673$	−28.1083	−	23.5857i	−1.08350	−	0.909162i	−0.0872906	−	0.996183i	$-0.527821\pi$
$673$	−28.1083	−	23.5857i	−1.08350	−	0.909162i	−0.996206	+	0.0870209i	$0.972265\pi$
$674$		0			0
$675$	−36.2234	−	25.9502i	−1.39424	−	0.998825i
$676$		0			0
$677$	−28.3072	+	33.7352i	−1.08793	+	1.29655i	−0.135843	+	0.990730i	$0.543374\pi$
$677$	−28.3072	+	33.7352i	−1.08793	+	1.29655i	−0.952090	+	0.305818i	$0.901070\pi$
$678$		0			0
$679$	−9.84006	+	1.73507i	−0.377627	+	0.0665858i
$680$		0			0
$681$	18.7796	+	14.9589i	0.719635	+	0.573228i
$682$		0			0
$683$	−5.56826	+	9.64450i	−0.213063	+	0.369037i	−0.952672	−	0.304001i	$-0.901677\pi$
$683$	−5.56826	+	9.64450i	−0.213063	+	0.369037i	0.739608	+	0.673038i	$0.235011\pi$
$684$		0			0
$685$	18.4140	+	31.8939i	0.703561	+	1.21860i
$686$		0			0
$687$	23.4803	+	7.87426i	0.895829	+	0.300422i
$688$		0			0
$689$	−9.11895	−	10.8675i	−0.347404	−	0.414020i
$690$		0			0
$691$	−14.2413	−	39.1275i	−0.541763	−	1.48848i	−0.844578	−	0.535432i	$-0.820149\pi$
$691$	−14.2413	−	39.1275i	−0.541763	−	1.48848i	0.302815	−	0.953049i	$-0.402073\pi$
$692$		0			0
$693$	4.32633	−	14.0819i	0.164344	−	0.534925i
$694$		0			0
$695$	−11.5767	+	65.6545i	−0.439128	+	2.49042i
$696$		0			0
$697$	46.6347	+	16.9736i	1.76642	+	0.642923i
$698$		0			0
$699$	−11.2661	−	6.12695i	−0.426121	−	0.231743i
$700$		0			0
$701$		−	25.9804i		−	0.981266i	−0.871366	−	0.490633i	$-0.836766\pi$
$701$		−	25.9804i		−	0.981266i	0.871366	−	0.490633i	$-0.163234\pi$
$702$		0			0
$703$			21.9398i			0.827474i
$704$		0			0
$705$	0.982646	+	38.5332i	0.0370086	+	1.45125i
$706$		0			0
$707$	−28.5579	−	10.3942i	−1.07403	−	0.390915i
$708$		0			0
$709$	7.95930	−	45.1394i	0.298918	−	1.69525i	−0.351921	−	0.936030i	$-0.614471\pi$
$709$	7.95930	−	45.1394i	0.298918	−	1.69525i	0.650838	−	0.759216i	$-0.274418\pi$
$710$		0			0
$711$	−8.55780	−	20.2379i	−0.320943	−	0.758979i
$712$		0			0
$713$	−3.69740	−	10.1585i	−0.138469	−	0.380440i
$714$		0			0
$715$	34.0520	+	40.5816i	1.27347	+	1.51766i
$716$		0			0
$717$	1.15944	−	1.02437i	0.0433000	−	0.0382558i
$718$		0			0
$719$	9.42826	+	16.3302i	0.351615	+	0.609014i	0.986533	−	0.163565i	$-0.0522994\pi$
$719$	9.42826	+	16.3302i	0.351615	+	0.609014i	−0.634918	+	0.772580i	$0.718966\pi$
$720$		0			0
$721$	−5.43677	+	9.41677i	−0.202476	+	0.350699i
$722$		0			0
$723$	−0.849077	+	5.65484i	−0.0315775	+	0.210306i
$724$		0			0
$725$	−60.9734	+	10.7513i	−2.26450	+	0.399292i
$726$		0			0
$727$	−7.24734	+	8.63704i	−0.268789	+	0.320330i	−0.883508	−	0.468416i	$-0.844825\pi$
$727$	−7.24734	+	8.63704i	−0.268789	+	0.320330i	0.614719	+	0.788746i	$0.289269\pi$
$728$		0			0
$729$	26.6847	−	4.11422i	0.988322	−	0.152379i
$730$		0			0
$731$	43.4789	+	36.4832i	1.60813	+	1.34938i
$732$		0			0
$733$	−2.58787	−	14.6765i	−0.0955850	−	0.542090i	−0.994567	−	0.104103i	$-0.966803\pi$
$733$	−2.58787	−	14.6765i	−0.0955850	−	0.542090i	0.898981	−	0.437987i	$-0.144308\pi$
$734$		0			0
$735$	−22.5441	−	3.38501i	−0.831552	−	0.124858i
$736$		0			0
$737$	−24.3069	−	14.0336i	−0.895356	−	0.516934i
$738$		0			0
$739$	−39.5092	+	22.8106i	−1.45337	+	0.839103i	−0.998671	−	0.0515420i	$-0.983586\pi$
$739$	−39.5092	+	22.8106i	−1.45337	+	0.839103i	−0.454699	+	0.890645i	$0.650253\pi$
$740$		0			0
$741$	43.4691	+	49.2007i	1.59688	+	1.80743i
$742$		0			0
$743$	4.34795	−	3.64836i	0.159511	−	0.133846i	−0.559539	−	0.828804i	$-0.689022\pi$
$743$	4.34795	−	3.64836i	0.159511	−	0.133846i	0.719050	+	0.694959i	$0.244577\pi$
$744$		0			0
$745$	−37.3573	+	13.5969i	−1.36866	+	0.498153i
$746$		0			0
$747$	4.74542	−	2.00665i	0.173626	−	0.0734196i
$748$		0			0
$749$	12.1781	+	2.14733i	0.444979	+	0.0784619i
$750$		0			0
$751$	0.876064	−	2.40696i	0.0319680	−	0.0878314i	−0.922682	−	0.385562i	$-0.874008\pi$
$751$	0.876064	−	2.40696i	0.0319680	−	0.0878314i	0.954650	+	0.297731i	$0.0962298\pi$
$752$		0			0
$753$	38.5157	−	0.982199i	1.40359	−	0.0357933i
$754$		0			0
$755$	−57.4987			−2.09259
$756$		0			0
$757$	26.9266			0.978665			0.489333	−	0.872097i	$-0.337240\pi$
$757$	26.9266			0.978665			0.489333	+	0.872097i	$0.337240\pi$
$758$		0			0
$759$	−4.41723	+	8.12227i	−0.160335	+	0.294820i
$760$		0			0
$761$	5.95945	−	16.3734i	0.216030	−	0.593537i	−0.783585	−	0.621284i	$-0.786611\pi$
$761$	5.95945	−	16.3734i	0.216030	−	0.593537i	0.999615	+	0.0277475i	$0.00883344\pi$
$762$		0			0
$763$	−2.44844	−	0.431726i	−0.0886396	−	0.0156295i
$764$		0			0
$765$	61.8363	+	18.9978i	2.23569	+	0.686867i
$766$		0			0
$767$	7.12575	−	2.59356i	0.257296	−	0.0936480i
$768$		0			0
$769$	36.6697	−	30.7695i	1.32234	−	1.10958i	0.336540	−	0.941669i	$-0.390743\pi$
$769$	36.6697	−	30.7695i	1.32234	−	1.10958i	0.985803	−	0.167908i	$-0.0537012\pi$
$770$		0			0
$771$	9.46175	−	28.2140i	0.340757	−	1.01610i
$772$		0			0
$773$	−3.94788	+	2.27931i	−0.141995	+	0.0819811i	−0.569315	−	0.822120i	$-0.692791\pi$
$773$	−3.94788	+	2.27931i	−0.141995	+	0.0819811i	0.427319	+	0.904101i	$0.359458\pi$
$774$		0			0
$775$	−39.8906	−	23.0309i	−1.43291	−	0.827293i
$776$		0			0
$777$	6.26919	−	7.87040i	0.224906	−	0.282349i
$778$		0			0
$779$	10.2961	+	58.3924i	0.368898	+	2.09212i
$780$		0			0
$781$	−13.0530	−	10.9528i	−0.467073	−	0.391921i
$782$		0			0
$783$	21.8481	−	30.4973i	0.780788	−	1.08989i
$784$		0			0
$785$	10.5905	−	12.6213i	0.377991	−	0.450473i
$786$		0			0
$787$	−10.3263	+	1.82081i	−0.368094	+	0.0649050i	−0.354636	−	0.935004i	$-0.615395\pi$
$787$	−10.3263	+	1.82081i	−0.368094	+	0.0649050i	−0.0134584	+	0.999909i	$0.504284\pi$
$788$		0			0
$789$	40.6404	−	15.9766i	1.44684	−	0.568780i
$790$		0			0
$791$	−3.44564	+	5.96802i	−0.122513	+	0.212199i
$792$		0			0
$793$	16.9287	+	29.3213i	0.601154	+	1.04123i
$794$		0			0
$795$	−3.31839	−	16.3677i	−0.117691	−	0.580503i
$796$		0			0
$797$	1.06540	+	1.26969i	0.0377384	+	0.0449749i	0.784584	−	0.620023i	$-0.212877\pi$
$797$	1.06540	+	1.26969i	0.0377384	+	0.0449749i	−0.746845	+	0.664998i	$0.768432\pi$
$798$		0			0
$799$	−12.0898	−	33.2166i	−0.427708	−	1.17512i
$800$		0			0
$801$	−24.7526	+	16.0264i	−0.874590	+	0.566265i
$802$		0			0
$803$	−0.884574	+	5.01667i	−0.0312160	+	0.177034i
$804$		0			0
$805$	−12.9013	−	4.69570i	−0.454712	−	0.165502i
$806$		0			0
$807$	−20.8468	+	12.7553i	−0.733842	+	0.449009i
$808$		0			0
$809$			22.5641i			0.793312i	0.917967	+	0.396656i	$0.129829\pi$
$809$			22.5641i			0.793312i	−0.917967	+	0.396656i	$0.870171\pi$
$810$		0			0
$811$			27.7581i			0.974719i	0.873201	+	0.487360i	$0.162040\pi$
$811$			27.7581i			0.974719i	−0.873201	+	0.487360i	$0.837960\pi$
$812$		0			0
$813$	−7.27009	+	4.44828i	−0.254973	+	0.156008i
$814$		0			0
$815$	21.2892	+	7.74863i	0.745727	+	0.271423i
$816$		0			0
$817$	−11.7754	+	66.7817i	−0.411970	+	2.33640i
$818$		0			0
$819$	−1.53468	−	30.0708i	−0.0536262	−	1.05076i
$820$		0			0
$821$	−13.3896	−	36.7876i	−0.467300	−	1.28390i	−0.919890	−	0.392177i	$-0.871722\pi$
$821$	−13.3896	−	36.7876i	−0.467300	−	1.28390i	0.452590	−	0.891719i	$-0.350500\pi$
$822$		0			0
$823$	7.37753	+	8.79220i	0.257164	+	0.306477i	0.879143	−	0.476557i	$-0.158116\pi$
$823$	7.37753	+	8.79220i	0.257164	+	0.306477i	−0.621979	+	0.783034i	$0.713671\pi$
$824$		0			0
$825$	7.82759	+	38.6090i	0.272522	+	1.34419i
$826$		0			0
$827$	−6.76144	−	11.7112i	−0.235118	−	0.407237i	0.724189	−	0.689602i	$-0.242214\pi$
$827$	−6.76144	−	11.7112i	−0.235118	−	0.407237i	−0.959307	+	0.282365i	$0.908881\pi$
$828$		0			0
$829$	14.2033	−	24.6008i	0.493299	−	0.854420i	−0.506671	−	0.862140i	$-0.669124\pi$
$829$	14.2033	−	24.6008i	0.493299	−	0.854420i	0.999970	+	0.00771994i	$0.00245736\pi$
$830$		0			0
$831$	−27.0706	+	10.6420i	−0.939070	+	0.369168i
$832$		0			0
$833$	20.5882	−	3.63025i	0.713338	−	0.125781i
$834$		0			0
$835$	24.6902	−	29.4246i	0.854438	−	1.01828i
$836$		0			0
$837$	27.0355	−	6.93269i	0.934485	−	0.239629i
$838$		0			0
$839$	27.7563	+	23.2903i	0.958255	+	0.804071i	0.980668	−	0.195678i	$-0.0626907\pi$
$839$	27.7563	+	23.2903i	0.958255	+	0.804071i	−0.0224137	+	0.999749i	$0.507135\pi$
$840$		0			0
$841$	−4.01594	−	22.7756i	−0.138481	−	0.785364i
$842$		0			0
$843$	16.1495	−	20.2742i	0.556218	−	0.698280i
$844$		0			0
$845$	52.2900	+	30.1896i	1.79883	+	1.03855i
$846$		0			0
$847$	6.35822	−	3.67092i	0.218471	−	0.126134i
$848$		0			0
$849$	−12.9148	+	38.5106i	−0.443234	+	1.32168i
$850$		0			0
$851$	−4.83769	+	4.05930i	−0.165834	+	0.139151i
$852$		0			0
$853$	31.7811	−	11.5674i	1.08816	−	0.396059i	0.265223	−	0.964187i	$-0.414554\pi$
$853$	31.7811	−	11.5674i	1.08816	−	0.396059i	0.822940	+	0.568128i	$0.192332\pi$
$854$		0			0
$855$	17.2829	+	75.3305i	0.591062	+	2.57625i
$856$		0			0
$857$	32.8566	+	5.79350i	1.12236	+	0.197902i	0.703876	−	0.710323i	$-0.251451\pi$
$857$	32.8566	+	5.79350i	1.12236	+	0.197902i	0.418483	+	0.908225i	$0.362562\pi$
$858$		0			0
$859$	11.8066	−	32.4385i	0.402838	−	1.10679i	−0.558040	−	0.829814i	$-0.688446\pi$
$859$	11.8066	−	32.4385i	0.402838	−	1.10679i	0.960878	−	0.276973i	$-0.0893313\pi$
$860$		0			0
$861$	12.9919	−	23.8890i	0.442761	−	0.814136i
$862$		0			0
$863$	21.7325			0.739782			0.369891	−	0.929075i	$-0.379395\pi$
$863$	21.7325			0.739782			0.369891	+	0.929075i	$0.379395\pi$
$864$		0			0
$865$	−50.1574			−1.70540
$866$		0			0
$867$	−29.8681	+	0.761676i	−1.01438	+	0.0258679i
$868$		0			0
$869$	−6.64407	+	18.2544i	−0.225385	+	0.619239i
$870$		0			0
$871$	−56.4956	−	9.96169i	−1.91428	−	0.337539i
$872$		0			0
$873$	−1.99511	+	16.0671i	−0.0675243	+	0.543789i
$874$		0			0
$875$	−22.9195	+	8.34201i	−0.774820	+	0.282011i
$876$		0			0
$877$	−17.6058	+	14.7730i	−0.594507	+	0.498850i	−0.889675	−	0.456595i	$-0.849069\pi$
$877$	−17.6058	+	14.7730i	−0.594507	+	0.498850i	0.295168	+	0.955445i	$0.404624\pi$
$878$		0			0
$879$	26.8867	+	30.4318i	0.906864	+	1.02644i
$880$		0			0
$881$	−21.8868	+	12.6363i	−0.737385	+	0.425729i	−0.821118	−	0.570759i	$-0.806649\pi$
$881$	−21.8868	+	12.6363i	−0.737385	+	0.425729i	0.0837329	+	0.996488i	$0.473316\pi$
$882$		0			0
$883$	31.0141	+	17.9060i	1.04371	+	0.602584i	0.920881	−	0.389844i	$-0.127471\pi$
$883$	31.0141	+	17.9060i	1.04371	+	0.602584i	0.122826	+	0.992428i	$0.460804\pi$
$884$		0			0
$885$	8.82797	+	1.32552i	0.296749	+	0.0445570i
$886$		0			0
$887$	0.860725	+	4.88141i	0.0289003	+	0.163902i	0.995842	−	0.0910950i	$-0.0290367\pi$
$887$	0.860725	+	4.88141i	0.0289003	+	0.163902i	−0.966942	+	0.254997i	$0.917926\pi$
$888$		0			0
$889$	24.5958	+	20.6383i	0.824916	+	0.692187i
$890$		0			0
$891$	−19.7528	−	13.4023i	−0.661745	−	0.448992i
$892$		0			0
$893$	27.1467	−	32.3522i	0.908430	−	1.08263i
$894$		0			0
$895$	−57.6713	+	10.1690i	−1.92774	+	0.339912i
$896$		0			0
$897$	−2.80602	+	18.6880i	−0.0936902	+	0.623975i
$898$		0			0
$899$	19.3902	−	33.5849i	0.646700	−	1.12012i
$900$		0			0
$901$	7.65767	+	13.2635i	0.255114	+	0.441871i
$902$		0			0
$903$	23.3068	−	20.5917i	0.775600	−	0.685248i
$904$		0			0
$905$	6.97795	+	8.31600i	0.231955	+	0.276433i
$906$		0			0
$907$	−5.99534	−	16.4721i	−0.199072	−	0.546946i	0.799483	−	0.600689i	$-0.205107\pi$
$907$	−5.99534	−	16.4721i	−0.199072	−	0.546946i	−0.998555	+	0.0537431i	$0.982885\pi$
$908$		0			0
$909$	−29.6896	+	39.2875i	−0.984743	+	1.30308i
$910$		0			0
$911$	1.68255	−	9.54221i	0.0557453	−	0.316148i	−0.944166	−	0.329470i	$-0.893130\pi$
$911$	1.68255	−	9.54221i	0.0557453	−	0.316148i	0.999911	+	0.0133228i	$0.00424092\pi$
$912$		0			0
$913$	−4.28034	−	1.55792i	−0.141659	−	0.0515595i
$914$		0			0
$915$	1.01609	+	39.8445i	0.0335908	+	1.31722i
$916$		0			0
$917$			24.8515i			0.820669i
$918$		0			0
$919$			29.4750i			0.972290i	0.873878	+	0.486145i	$0.161597\pi$
$919$			29.4750i			0.972290i	−0.873878	+	0.486145i	$0.838403\pi$
$920$		0			0
$921$	−48.9110	−	26.5999i	−1.61167	−	0.876496i
$922$		0			0
$923$	−32.7270	−	11.9116i	−1.07722	−	0.392077i
$924$		0			0
$925$	−4.67250	+	26.4991i	−0.153631	+	0.871283i
$926$		0			0
$927$	11.9986	+	12.9023i	0.394085	+	0.423766i
$928$		0			0
$929$	10.8744	+	29.8772i	0.356777	+	0.980238i	0.980140	+	0.198305i	$0.0635437\pi$
$929$	10.8744	+	29.8772i	0.356777	+	0.980238i	−0.623363	+	0.781933i	$0.714234\pi$
$930$		0			0
$931$	16.0552	+	19.1338i	0.526187	+	0.627085i
$932$		0			0
$933$	20.4945	+	6.87296i	0.670960	+	0.225011i
$934$		0			0
$935$	−28.5953	−	49.5285i	−0.935166	−	1.61975i
$936$		0			0
$937$	18.4158	−	31.8971i	0.601618	−	1.04203i	−0.390958	−	0.920409i	$-0.627856\pi$
$937$	18.4158	−	31.8971i	0.601618	−	1.04203i	0.992576	−	0.121625i	$-0.0388105\pi$
$938$		0			0
$939$	6.32516	+	5.03833i	0.206414	+	0.164420i
$940$		0			0
$941$	48.3802	−	8.53074i	1.57715	−	0.278094i	0.684558	−	0.728958i	$-0.259995\pi$
$941$	48.3802	−	8.53074i	1.57715	−	0.278094i	0.892593	+	0.450864i	$0.148884\pi$
$942$		0			0
$943$	−10.9704	+	13.0741i	−0.357247	+	0.425750i
$944$		0			0
$945$	15.3255	−	31.9616i	0.498539	−	1.03971i
$946$		0			0
$947$	35.7835	+	30.0259i	1.16281	+	0.975712i	0.999940	−	0.0109360i	$-0.00348111\pi$
$947$	35.7835	+	30.0259i	1.16281	+	0.975712i	0.162868	+	0.986648i	$0.447926\pi$
$948$		0			0
$949$	1.80800	+	10.2537i	0.0586901	+	0.332848i
$950$		0			0
$951$	17.4950	+	44.5029i	0.567315	+	1.44311i
$952$		0			0
$953$	−27.4348	−	15.8395i	−0.888699	−	0.513090i	−0.0151821	−	0.999885i	$-0.504833\pi$
$953$	−27.4348	−	15.8395i	−0.888699	−	0.513090i	−0.873517	+	0.486794i	$0.838166\pi$
$954$		0			0
$955$	52.0580	−	30.0557i	1.68456	−	0.972580i
$956$		0			0
$957$	−32.5058	+	6.59023i	−1.05076	+	0.213032i
$958$		0			0
$959$	−14.1762	+	11.8953i	−0.457775	+	0.384119i
$960$		0			0
$961$	−2.01919	+	0.734927i	−0.0651353	+	0.0237073i
$962$		0			0
$963$	9.12125	−	17.8411i	0.293928	−	0.574920i
$964$		0			0
$965$	63.5230	+	11.2008i	2.04488	+	0.360567i
$966$		0			0
$967$	12.4580	−	34.2280i	0.400621	−	1.10070i	−0.561358	−	0.827573i	$-0.689721\pi$
$967$	12.4580	−	34.2280i	0.400621	−	1.10070i	0.961979	−	0.273124i	$-0.0880570\pi$
$968$		0			0
$969$	−36.9915	−	60.4575i	−1.18834	−	1.94217i
$970$		0			0
$971$	16.1822			0.519312			0.259656	−	0.965701i	$-0.416391\pi$
$971$	16.1822			0.519312			0.259656	+	0.965701i	$0.416391\pi$
$972$		0			0
$973$	−33.4999			−1.07396
$974$		0			0
$975$	42.0242	+	68.6827i	1.34585	+	2.19961i
$976$		0			0
$977$	−2.76897	+	7.60767i	−0.0885871	+	0.243391i	−0.976073	−	0.217444i	$-0.930228\pi$
$977$	−2.76897	+	7.60767i	−0.0885871	+	0.243391i	0.887486	+	0.460835i	$0.152450\pi$
$978$		0			0
$979$	25.6738	+	4.52699i	0.820539	+	0.144683i
$980$		0			0
$981$	−1.83385	+	3.58699i	−0.0585502	+	0.114524i
$982$		0			0
$983$	5.20539	−	1.89461i	0.166026	−	0.0604286i	−0.257670	−	0.966233i	$-0.582955\pi$
$983$	5.20539	−	1.89461i	0.166026	−	0.0604286i	0.423696	+	0.905804i	$0.360732\pi$
$984$		0			0
$985$	25.8577	−	21.6972i	0.823895	−	0.691330i
$986$		0			0
$987$	−18.9828	+	3.84857i	−0.604229	+	0.122501i
$988$		0			0
$989$	−16.9040	+	9.75951i	−0.537515	+	0.310334i
$990$		0			0
$991$	8.89718	+	5.13679i	0.282628	+	0.163175i	0.634613	−	0.772830i	$-0.281160\pi$
$991$	8.89718	+	5.13679i	0.282628	+	0.163175i	−0.351984	+	0.936006i	$0.614493\pi$
$992$		0			0
$993$	8.26671	+	21.0284i	0.262336	+	0.667318i
$994$		0			0
$995$	−5.02309	−	28.4874i	−0.159243	−	0.903111i
$996$		0			0
$997$	6.32998	+	5.31148i	0.200472	+	0.168216i	0.737497	−	0.675350i	$-0.236007\pi$
$997$	6.32998	+	5.31148i	0.200472	+	0.168216i	−0.537025	+	0.843566i	$0.680452\pi$
$998$		0			0
$999$	−9.20727	−	13.4557i	−0.291305	−	0.425721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bi.a.767.13	yes	216
4.3	odd	2	inner	864.2.bi.a.767.24	yes	216
27.5	odd	18	inner	864.2.bi.a.383.24	yes	216
108.59	even	18	inner	864.2.bi.a.383.13	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.bi.a.383.13	✓	216	108.59	even	18	inner
864.2.bi.a.383.24	yes	216	27.5	odd	18	inner
864.2.bi.a.767.13	yes	216	1.1	even	1	trivial
864.2.bi.a.767.24	yes	216	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bi (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.903983 - 1.47743i) q^{3} +(-1.26017 + 3.46229i) q^{5} +(-1.82330 - 0.321498i) q^{7} +(-1.36563 + 2.67115i) q^{9} +O(q^{10})\)	\(q+(-0.903983 - 1.47743i) q^{3} +(-1.26017 + 3.46229i) q^{5} +(-1.82330 - 0.321498i) q^{7} +(-1.36563 + 2.67115i) q^{9} +(2.49231 - 0.907128i) q^{11} +(4.15274 - 3.48456i) q^{13} +(6.25448 - 1.26803i) q^{15} +(-5.06828 + 2.92617i) q^{17} +(-6.05539 - 3.49608i) q^{19} +(1.17324 + 2.98444i) q^{21} +(-0.349489 - 1.98205i) q^{23} +(-6.56919 - 5.51221i) q^{25} +(5.18096 - 0.397052i) q^{27} +(4.64086 - 5.53076i) q^{29} +(5.28973 - 0.932722i) q^{31} +(-3.59323 - 2.86220i) q^{33} +(3.41079 - 5.90766i) q^{35} +(-1.56888 - 2.71739i) q^{37} +(-8.90222 - 2.98542i) q^{39} +(-5.45081 - 6.49602i) q^{41} +(-3.31701 - 9.11341i) q^{43} +(-7.52738 - 8.09431i) q^{45} +(-1.04884 + 5.94826i) q^{47} +(-3.35677 - 1.22177i) q^{49} +(8.90488 + 4.84285i) q^{51} -2.61696i q^{53} +9.77224i q^{55} +(0.308740 + 12.1068i) q^{57} +(1.31447 + 0.478427i) q^{59} +(-1.08453 + 6.15068i) q^{61} +(3.34872 - 4.43128i) q^{63} +(6.83140 + 18.7691i) q^{65} +(-6.80221 - 8.10655i) q^{67} +(-2.61242 + 2.30809i) q^{69} +(-3.21225 - 5.56378i) q^{71} +(-0.960323 + 1.66333i) q^{73} +(-2.20549 + 14.6885i) q^{75} +(-4.83588 + 0.852697i) q^{77} +(-4.70796 + 5.61073i) q^{79} +(-5.27012 - 7.29560i) q^{81} +(-1.31562 - 1.10393i) q^{83} +(-3.74436 - 21.2353i) q^{85} +(-12.3666 - 1.85685i) q^{87} +(8.51242 + 4.91465i) q^{89} +(-8.69198 + 5.01832i) q^{91} +(-6.15986 - 6.97207i) q^{93} +(19.7353 - 16.5598i) q^{95} +(5.07136 - 1.84583i) q^{97} +(-0.980495 + 7.89615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) \) 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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