LMFDB - Embedded newform 672.2.bd.a.527.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [672,2,Mod(431,672)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(672, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("672.431"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bd (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			527.9
Character	$\chi$	$=$	672.527
Dual form			672.2.bd.a.431.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.996948 - 1.41637i) q^{3} +(-1.00081 + 1.73346i) q^{5} +(-2.50986 + 0.837013i) q^{7} +(-1.01219 + 2.82409i) q^{9} +(3.33711 - 1.92668i) q^{11} -2.05924i q^{13} +(3.45297 - 0.310649i) q^{15} +(4.92484 - 2.84336i) q^{17} +(0.232846 - 0.403301i) q^{19} +(3.68772 + 2.72043i) q^{21} +(-0.711115 + 1.23169i) q^{23} +(0.496746 + 0.860389i) q^{25} +(5.00905 - 1.38183i) q^{27} +9.25829 q^{29} +(4.99699 - 2.88502i) q^{31} +(-6.05580 - 2.80577i) q^{33} +(1.06098 - 5.18844i) q^{35} +(0.569094 + 0.328567i) q^{37} +(-2.91663 + 2.05295i) q^{39} -8.42924i q^{41} -6.77074 q^{43} +(-3.88243 - 4.58098i) q^{45} +(-1.79536 + 3.10966i) q^{47} +(5.59882 - 4.20157i) q^{49} +(-8.93705 - 4.14070i) q^{51} +(1.50566 + 2.60789i) q^{53} +7.71298i q^{55} +(-0.803357 + 0.0722746i) q^{57} +(5.72041 - 3.30268i) q^{59} +(-8.50530 - 4.91054i) q^{61} +(0.176663 - 7.93529i) q^{63} +(3.56960 + 2.06091i) q^{65} +(3.78271 + 6.55184i) q^{67} +(2.45347 - 0.220728i) q^{69} +14.0426 q^{71} +(-2.02113 - 3.50071i) q^{73} +(0.723397 - 1.56134i) q^{75} +(-6.76302 + 7.62890i) q^{77} +(0.00488142 + 0.00281829i) q^{79} +(-6.95094 - 5.71703i) q^{81} +8.56466i q^{83} +11.3827i q^{85} +(-9.23003 - 13.1131i) q^{87} +(8.14017 + 4.69973i) q^{89} +(1.72361 + 5.16840i) q^{91} +(-9.06798 - 4.20137i) q^{93} +(0.466070 + 0.807257i) q^{95} -4.17304 q^{97} +(2.06332 + 11.3744i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{3} - 2 q^{9} + 4 q^{19} - 16 q^{25} + 8 q^{27} - 14 q^{33} + 16 q^{43} - 16 q^{49} + 34 q^{51} + 4 q^{57} + 36 q^{67} + 4 q^{73} - 10 q^{81} - 72 q^{91} - 32 q^{97} + 44 q^{99}+O(q^{100}) $ 56 * q + 2 * q^3 - 2 * q^9 + 4 * q^19 - 16 * q^25 + 8 * q^27 - 14 * q^33 + 16 * q^43 - 16 * q^49 + 34 * q^51 + 4 * q^57 + 36 * q^67 + 4 * q^73 - 10 * q^81 - 72 * q^91 - 32 * q^97 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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
$3$	−0.996948	−	1.41637i	−0.575588	−	0.817740i
$3$	−0.996948	−	1.41637i	−0.575588	−	0.817740i
$4$		0			0
$5$	−1.00081	+	1.73346i	−0.447577	+	0.775227i	−0.998228	−	0.0595094i	$-0.981046\pi$
$5$	−1.00081	+	1.73346i	−0.447577	+	0.775227i	0.550650	+	0.834736i	$0.314380\pi$
$6$		0			0
$7$	−2.50986	+	0.837013i	−0.948639	+	0.316361i
$7$	−2.50986	+	0.837013i	−0.948639	+	0.316361i
$8$		0			0
$9$	−1.01219	+	2.82409i	−0.337397	+	0.941362i
$10$		0			0
$11$	3.33711	−	1.92668i	1.00618	−	0.580916i	0.0961058	−	0.995371i	$-0.469361\pi$
$11$	3.33711	−	1.92668i	1.00618	−	0.580916i	0.910070	+	0.414455i	$0.136028\pi$
$12$		0			0
$13$		−	2.05924i		−	0.571129i	−0.958359	−	0.285565i	$-0.907819\pi$
$13$		−	2.05924i		−	0.571129i	0.958359	−	0.285565i	$-0.0921811\pi$
$14$		0			0
$15$	3.45297	−	0.310649i	0.891554	−	0.0802093i
$16$		0			0
$17$	4.92484	−	2.84336i	1.19445	−	0.689616i	0.235137	−	0.971962i	$-0.424446\pi$
$17$	4.92484	−	2.84336i	1.19445	−	0.689616i	0.959313	+	0.282346i	$0.0911127\pi$
$18$		0			0
$19$	0.232846	−	0.403301i	0.0534185	−	0.0925235i	−0.838080	−	0.545548i	$-0.816322\pi$
$19$	0.232846	−	0.403301i	0.0534185	−	0.0925235i	0.891498	+	0.453024i	$0.149655\pi$
$20$		0			0
$21$	3.68772	+	2.72043i	0.804726	+	0.593646i
$22$		0			0
$23$	−0.711115	+	1.23169i	−0.148278	+	0.256825i	−0.930591	−	0.366061i	$-0.880706\pi$
$23$	−0.711115	+	1.23169i	−0.148278	+	0.256825i	0.782313	+	0.622885i	$0.214040\pi$
$24$		0			0
$25$	0.496746	+	0.860389i	0.0993492	+	0.172078i
$26$		0			0
$27$	5.00905	−	1.38183i	0.963991	−	0.265934i
$28$		0			0
$29$	9.25829			1.71922			0.859611	−	0.510949i	$-0.170706\pi$
$29$	9.25829			1.71922			0.859611	+	0.510949i	$0.170706\pi$
$30$		0			0
$31$	4.99699	−	2.88502i	0.897486	−	0.518164i	0.0211026	−	0.999777i	$-0.493282\pi$
$31$	4.99699	−	2.88502i	0.897486	−	0.518164i	0.876384	+	0.481613i	$0.159949\pi$
$32$		0			0
$33$	−6.05580	−	2.80577i	−1.05418	−	0.488422i
$34$		0			0
$35$	1.06098	−	5.18844i	0.179338	−	0.877006i
$36$		0			0
$37$	0.569094	+	0.328567i	0.0935586	+	0.0540161i	0.546049	−	0.837753i	$-0.316131\pi$
$37$	0.569094	+	0.328567i	0.0935586	+	0.0540161i	−0.452491	+	0.891769i	$0.649464\pi$
$38$		0			0
$39$	−2.91663	+	2.05295i	−0.467035	+	0.328735i
$40$		0			0
$41$		−	8.42924i		−	1.31643i	−0.752832	−	0.658213i	$-0.771313\pi$
$41$		−	8.42924i		−	1.31643i	0.752832	−	0.658213i	$-0.228687\pi$
$42$		0			0
$43$	−6.77074			−1.03253			−0.516264	−	0.856430i	$-0.672678\pi$
$43$	−6.77074			−1.03253			−0.516264	+	0.856430i	$0.672678\pi$
$44$		0			0
$45$	−3.88243	−	4.58098i	−0.578758	−	0.682892i
$46$		0			0
$47$	−1.79536	+	3.10966i	−0.261881	+	0.453590i	−0.966742	−	0.255755i	$-0.917676\pi$
$47$	−1.79536	+	3.10966i	−0.261881	+	0.453590i	0.704861	+	0.709345i	$0.251009\pi$
$48$		0			0
$49$	5.59882	−	4.20157i	0.799831	−	0.600225i
$50$		0			0
$51$	−8.93705	−	4.14070i	−1.25144	−	0.579815i
$52$		0			0
$53$	1.50566	+	2.60789i	0.206819	+	0.358221i	0.950711	−	0.310079i	$-0.100356\pi$
$53$	1.50566	+	2.60789i	0.206819	+	0.358221i	−0.743892	+	0.668300i	$0.767022\pi$
$54$		0			0
$55$			7.71298i			1.04002i
$56$		0			0
$57$	−0.803357	+	0.0722746i	−0.106407	+	0.00957300i
$58$		0			0
$59$	5.72041	−	3.30268i	0.744735	−	0.429973i	−0.0790537	−	0.996870i	$-0.525190\pi$
$59$	5.72041	−	3.30268i	0.744735	−	0.429973i	0.823788	+	0.566898i	$0.191857\pi$
$60$		0			0
$61$	−8.50530	−	4.91054i	−1.08899	−	0.628730i	−0.155684	−	0.987807i	$-0.549758\pi$
$61$	−8.50530	−	4.91054i	−1.08899	−	0.628730i	−0.933308	+	0.359077i	$0.883092\pi$
$62$		0			0
$63$	0.176663	−	7.93529i	0.0222575	−	0.999752i
$64$		0			0
$65$	3.56960	+	2.06091i	0.442755	+	0.255624i
$66$		0			0
$67$	3.78271	+	6.55184i	0.462131	+	0.800435i	0.999067	−	0.0431883i	$-0.0137515\pi$
$67$	3.78271	+	6.55184i	0.462131	+	0.800435i	−0.536936	+	0.843623i	$0.680418\pi$
$68$		0			0
$69$	2.45347	−	0.220728i	0.295363	−	0.0265725i
$70$		0			0
$71$	14.0426			1.66655			0.833274	−	0.552861i	$-0.186464\pi$
$71$	14.0426			1.66655			0.833274	+	0.552861i	$0.186464\pi$
$72$		0			0
$73$	−2.02113	−	3.50071i	−0.236556	−	0.409727i	0.723168	−	0.690672i	$-0.242685\pi$
$73$	−2.02113	−	3.50071i	−0.236556	−	0.409727i	−0.959724	+	0.280946i	$0.909352\pi$
$74$		0			0
$75$	0.723397	−	1.56134i	0.0835307	−	0.180288i
$76$		0			0
$77$	−6.76302	+	7.62890i	−0.770718	+	0.869394i
$78$		0			0
$79$	0.00488142	+	0.00281829i	0.000549203	+	0.000317082i	0.500275	−	0.865867i	$-0.333232\pi$
$79$	0.00488142	+	0.00281829i	0.000549203	+	0.000317082i	−0.499725	+	0.866184i	$0.666566\pi$
$80$		0			0
$81$	−6.95094	−	5.71703i	−0.772327	−	0.635226i
$82$		0			0
$83$			8.56466i			0.940093i	0.882642	+	0.470047i	$0.155763\pi$
$83$			8.56466i			0.940093i	−0.882642	+	0.470047i	$0.844237\pi$
$84$		0			0
$85$			11.3827i			1.23463i
$86$		0			0
$87$	−9.23003	−	13.1131i	−0.989564	−	1.40588i
$88$		0			0
$89$	8.14017	+	4.69973i	0.862857	+	0.498170i	0.864968	−	0.501827i	$-0.167339\pi$
$89$	8.14017	+	4.69973i	0.862857	+	0.498170i	−0.00211125	+	0.999998i	$0.500672\pi$
$90$		0			0
$91$	1.72361	+	5.16840i	0.180683	+	0.541795i
$92$		0			0
$93$	−9.06798	−	4.20137i	−0.940306	−	0.435661i
$94$		0			0
$95$	0.466070	+	0.807257i	0.0478178	+	0.0828228i
$96$		0			0
$97$	−4.17304			−0.423708			−0.211854	−	0.977301i	$-0.567950\pi$
$97$	−4.17304			−0.423708			−0.211854	+	0.977301i	$0.567950\pi$
$98$		0			0
$99$	2.06332	+	11.3744i	0.207372	+	1.14317i
$100$		0			0
$101$	−5.27692	−	9.13990i	−0.525073	−	0.909454i	−0.999574	−	0.0291983i	$-0.990705\pi$
$101$	−5.27692	−	9.13990i	−0.525073	−	0.909454i	0.474500	−	0.880255i	$-0.342629\pi$
$102$		0			0
$103$	9.20735	+	5.31587i	0.907227	+	0.523788i	0.879538	−	0.475829i	$-0.157852\pi$
$103$	9.20735	+	5.31587i	0.907227	+	0.523788i	0.0276894	+	0.999617i	$0.491185\pi$
$104$		0			0
$105$	−8.40647	+	3.66987i	−0.820387	+	0.358143i
$106$		0			0
$107$	4.86572	+	2.80922i	0.470386	+	0.271578i	0.716401	−	0.697688i	$-0.245788\pi$
$107$	4.86572	+	2.80922i	0.470386	+	0.271578i	−0.246015	+	0.969266i	$0.579121\pi$
$108$		0			0
$109$	9.15046	−	5.28302i	0.876456	−	0.506022i	0.00696746	−	0.999976i	$-0.497782\pi$
$109$	9.15046	−	5.28302i	0.876456	−	0.506022i	0.869488	+	0.493954i	$0.164449\pi$
$110$		0			0
$111$	−0.101986	−	1.13361i	−0.00968009	−	0.107598i
$112$		0			0
$113$			15.9104i			1.49673i	0.663288	+	0.748364i	$0.269160\pi$
$113$			15.9104i			1.49673i	−0.663288	+	0.748364i	$0.730840\pi$
$114$		0			0
$115$	−1.42339	−	2.46538i	−0.132731	−	0.229898i
$116$		0			0
$117$	5.81546	+	2.08434i	0.537640	+	0.192697i
$118$		0			0
$119$	−9.98075	+	11.2586i	−0.914934	+	1.03207i
$120$		0			0
$121$	1.92419	−	3.33279i	0.174926	−	0.302981i
$122$		0			0
$123$	−11.9389	+	8.40351i	−1.07649	+	0.757719i
$124$		0			0
$125$	−11.9967			−1.07302
$126$		0			0
$127$		−	17.8415i		−	1.58317i	−0.611056	−	0.791587i	$-0.709255\pi$
$127$		−	17.8415i		−	1.58317i	0.611056	−	0.791587i	$-0.290745\pi$
$128$		0			0
$129$	6.75007	+	9.58985i	0.594311	+	0.844339i
$130$		0			0
$131$	2.10794	+	1.21702i	0.184172	+	0.106332i	0.589251	−	0.807950i	$-0.299423\pi$
$131$	2.10794	+	1.21702i	0.184172	+	0.106332i	−0.405080	+	0.914281i	$0.632756\pi$
$132$		0			0
$133$	−0.246843	+	1.20712i	−0.0214040	+	0.104671i
$134$		0			0
$135$	−2.61777	+	10.0659i	−0.225302	+	0.866338i
$136$		0			0
$137$	−2.69513	+	1.55603i	−0.230260	+	0.132941i	−0.610692	−	0.791868i	$-0.709109\pi$
$137$	−2.69513	+	1.55603i	−0.230260	+	0.132941i	0.380432	+	0.924809i	$0.375775\pi$
$138$		0			0
$139$	−7.95494			−0.674729			−0.337364	−	0.941374i	$-0.609535\pi$
$139$	−7.95494			−0.674729			−0.337364	+	0.941374i	$0.609535\pi$
$140$		0			0
$141$	6.19430	−	0.557275i	0.521654	−	0.0469310i
$142$		0			0
$143$	−3.96749	−	6.87189i	−0.331778	−	0.574656i
$144$		0			0
$145$	−9.26582	+	16.0489i	−0.769485	+	1.33279i
$146$		0			0
$147$	−11.5327	−	3.74123i	−0.951201	−	0.308572i
$148$		0			0
$149$	−5.27692	+	9.13990i	−0.432302	+	0.748769i	−0.997071	−	0.0764797i	$-0.975632\pi$
$149$	−5.27692	+	9.13990i	−0.432302	+	0.748769i	0.564769	+	0.825249i	$0.308965\pi$
$150$		0			0
$151$	−15.2482	+	8.80356i	−1.24088	+	0.716424i	−0.969274	−	0.245984i	$-0.920889\pi$
$151$	−15.2482	+	8.80356i	−1.24088	+	0.716424i	−0.271608	+	0.962408i	$0.587556\pi$
$152$		0			0
$153$	3.04501	+	16.7862i	0.246175	+	1.35708i
$154$		0			0
$155$			11.5494i			0.927674i
$156$		0			0
$157$	2.13267	−	1.23130i	0.170206	−	0.0982682i	−0.412477	−	0.910968i	$-0.635336\pi$
$157$	2.13267	−	1.23130i	0.170206	−	0.0982682i	0.582683	+	0.812700i	$0.302003\pi$
$158$		0			0
$159$	2.19266	−	4.73250i	0.173889	−	0.375312i
$160$		0			0
$161$	0.753863	−	3.68658i	0.0594127	−	0.290543i
$162$		0			0
$163$	4.83382	−	8.37243i	0.378614	−	0.655779i	−0.612247	−	0.790667i	$-0.709734\pi$
$163$	4.83382	−	8.37243i	0.378614	−	0.655779i	0.990861	+	0.134888i	$0.0430674\pi$
$164$		0			0
$165$	10.9244	−	7.68944i	0.850465	−	0.598622i
$166$		0			0
$167$	−12.7380			−0.985699			−0.492850	−	0.870114i	$-0.664045\pi$
$167$	−12.7380			−0.985699			−0.492850	+	0.870114i	$0.664045\pi$
$168$		0			0
$169$	8.75955			0.673811
$170$		0			0
$171$	0.903272	+	1.06579i	0.0690749	+	0.0815033i
$172$		0			0
$173$	5.87501	−	10.1758i	0.446668	−	0.773652i	−0.551498	−	0.834176i	$-0.685944\pi$
$173$	5.87501	−	10.1758i	0.446668	−	0.773652i	0.998167	+	0.0605236i	$0.0192770\pi$
$174$		0			0
$175$	−1.96692	−	1.74368i	−0.148685	−	0.131810i
$176$		0			0
$177$	−10.3808	−	4.80960i	−0.780266	−	0.361512i
$178$		0			0
$179$	8.89943	−	5.13809i	0.665175	−	0.384039i	−0.129071	−	0.991635i	$-0.541200\pi$
$179$	8.89943	−	5.13809i	0.665175	−	0.384039i	0.794246	+	0.607597i	$0.207866\pi$
$180$		0			0
$181$		−	4.76352i		−	0.354070i	−0.984205	−	0.177035i	$-0.943349\pi$
$181$		−	4.76352i		−	0.354070i	0.984205	−	0.177035i	$-0.0566505\pi$
$182$		0			0
$183$	1.52422	+	16.9422i	0.112673	+	1.25240i
$184$		0			0
$185$	−1.13911	+	0.657668i	−0.0837494	+	0.0483527i
$186$		0			0
$187$	10.9565	−	18.9772i	0.801217	−	1.38775i
$188$		0			0
$189$	−11.4154	+	7.66085i	−0.830348	+	0.557245i
$190$		0			0
$191$	−1.19496	+	2.06973i	−0.0864644	+	0.149761i	−0.906014	−	0.423247i	$-0.860890\pi$
$191$	−1.19496	+	2.06973i	−0.0864644	+	0.149761i	0.819550	+	0.573008i	$0.194224\pi$
$192$		0			0
$193$	−3.18130	−	5.51018i	−0.228995	−	0.396631i	0.728515	−	0.685029i	$-0.240211\pi$
$193$	−3.18130	−	5.51018i	−0.228995	−	0.396631i	−0.957511	+	0.288398i	$0.906877\pi$
$194$		0			0
$195$	−0.639700	−	7.11049i	−0.0458099	−	0.509192i
$196$		0			0
$197$	16.9051			1.20444			0.602219	−	0.798331i	$-0.294284\pi$
$197$	16.9051			1.20444			0.602219	+	0.798331i	$0.294284\pi$
$198$		0			0
$199$	−11.2472	+	6.49358i	−0.797293	+	0.460318i	−0.842524	−	0.538659i	$-0.818931\pi$
$199$	−11.2472	+	6.49358i	−0.797293	+	0.460318i	0.0452304	+	0.998977i	$0.485598\pi$
$200$		0			0
$201$	5.50865	−	11.8895i	0.388550	−	0.838624i
$202$		0			0
$203$	−23.2370	+	7.74931i	−1.63092	+	0.543895i
$204$		0			0
$205$	14.6117	+	8.43610i	1.02053	+	0.589202i
$206$		0			0
$207$	−2.75861	−	3.25495i	−0.191737	−	0.226235i
$208$		0			0
$209$		−	1.79448i		−	0.124127i
$210$		0			0
$211$	4.34903			0.299400			0.149700	−	0.988731i	$-0.452169\pi$
$211$	4.34903			0.299400			0.149700	+	0.988731i	$0.452169\pi$
$212$		0			0
$213$	−13.9997	−	19.8894i	−0.959244	−	1.36280i
$214$		0			0
$215$	6.77624	−	11.7368i	0.462136	−	0.800443i
$216$		0			0
$217$	−10.1270	+	11.4235i	−0.687464	+	0.775480i
$218$		0			0
$219$	−2.94332	+	6.35269i	−0.198891	+	0.429275i
$220$		0			0
$221$	−5.85515	−	10.1414i	−0.393860	−	0.682185i
$222$		0			0
$223$		−	25.7814i		−	1.72645i	−0.504820	−	0.863225i	$-0.668441\pi$
$223$		−	25.7814i		−	1.72645i	0.504820	−	0.863225i	$-0.331559\pi$
$224$		0			0
$225$	−2.93262	+	0.531976i	−0.195508	+	0.0354651i
$226$		0			0
$227$	−1.40958	+	0.813824i	−0.0935574	+	0.0540154i	−0.546049	−	0.837753i	$-0.683869\pi$
$227$	−1.40958	+	0.813824i	−0.0935574	+	0.0540154i	0.452491	+	0.891769i	$0.350535\pi$
$228$		0			0
$229$	−12.1735	−	7.02837i	−0.804448	−	0.464448i	0.0405764	−	0.999176i	$-0.487081\pi$
$229$	−12.1735	−	7.02837i	−0.804448	−	0.464448i	−0.845024	+	0.534728i	$0.820414\pi$
$230$		0			0
$231$	17.5477	+	1.97331i	1.15455	+	0.129834i
$232$		0			0
$233$	−15.5827	−	8.99668i	−1.02086	−	0.589392i	−0.106505	−	0.994312i	$-0.533966\pi$
$233$	−15.5827	−	8.99668i	−1.02086	−	0.589392i	−0.914352	+	0.404920i	$0.867299\pi$
$234$		0			0
$235$	−3.59364	−	6.22438i	−0.234424	−	0.406033i
$236$		0			0
$237$	−0.000874789	−	0.00972357i	−5.68236e−5	−	0.000631614i
$238$		0			0
$239$	16.0533			1.03840			0.519200	−	0.854653i	$-0.326230\pi$
$239$	16.0533			1.03840			0.519200	+	0.854653i	$0.326230\pi$
$240$		0			0
$241$	3.64298	+	6.30983i	0.234665	+	0.406452i	0.959175	−	0.282812i	$-0.0912673\pi$
$241$	3.64298	+	6.30983i	0.234665	+	0.406452i	−0.724510	+	0.689264i	$0.757934\pi$
$242$		0			0
$243$	−1.16769	+	15.5447i	−0.0749075	+	0.997190i
$244$		0			0
$245$	1.67988	+	13.9103i	0.107324	+	0.888697i
$246$		0			0
$247$	−0.830491	−	0.479484i	−0.0528429	−	0.0305089i
$248$		0			0
$249$	12.1307	−	8.53852i	0.768752	−	0.541106i
$250$		0			0
$251$		−	22.3471i		−	1.41053i	−0.708942	−	0.705267i	$-0.750827\pi$
$251$		−	22.3471i		−	1.41053i	0.708942	−	0.705267i	$-0.249173\pi$
$252$		0			0
$253$			5.48036i			0.344547i
$254$		0			0
$255$	16.1221	−	11.3479i	1.00960	−	0.710636i
$256$		0			0
$257$	2.61954	+	1.51239i	0.163402	+	0.0943404i	0.579471	−	0.814993i	$-0.303259\pi$
$257$	2.61954	+	1.51239i	0.163402	+	0.0943404i	−0.416069	+	0.909333i	$0.636592\pi$
$258$		0			0
$259$	−1.70336	−	0.348318i	−0.105842	−	0.0216434i
$260$		0			0
$261$	−9.37116	+	26.1462i	−0.580060	+	1.61841i
$262$		0			0
$263$	−10.7454	−	18.6116i	−0.662590	−	1.14764i	−0.979933	−	0.199329i	$-0.936124\pi$
$263$	−10.7454	−	18.6116i	−0.662590	−	1.14764i	0.317342	−	0.948311i	$-0.397210\pi$
$264$		0			0
$265$	−6.02755			−0.370270
$266$		0			0
$267$	−1.45878	−	16.2149i	−0.0892760	−	0.992333i
$268$		0			0
$269$	10.9385	+	18.9460i	0.666929	+	1.15516i	0.978758	+	0.205017i	$0.0657250\pi$
$269$	10.9385	+	18.9460i	0.666929	+	1.15516i	−0.311829	+	0.950138i	$0.600942\pi$
$270$		0			0
$271$	9.03323	+	5.21534i	0.548729	+	0.316809i	0.748609	−	0.663011i	$-0.230722\pi$
$271$	9.03323	+	5.21534i	0.548729	+	0.316809i	−0.199880	+	0.979820i	$0.564055\pi$
$272$		0			0
$273$	5.60200	−	7.59388i	0.339049	−	0.459603i
$274$		0			0
$275$	3.31539	+	1.91414i	0.199925	+	0.115427i
$276$		0			0
$277$	−18.7719	+	10.8380i	−1.12790	+	0.651191i	−0.943405	−	0.331643i	$-0.892397\pi$
$277$	−18.7719	+	10.8380i	−1.12790	+	0.651191i	−0.184492	+	0.982834i	$0.559064\pi$
$278$		0			0
$279$	3.08962	+	17.0321i	0.184971	+	1.01969i
$280$		0			0
$281$			8.35022i			0.498132i	0.968487	+	0.249066i	$0.0801236\pi$
$281$			8.35022i			0.498132i	−0.968487	+	0.249066i	$0.919876\pi$
$282$		0			0
$283$	11.3999	+	19.7453i	0.677656	+	1.17374i	0.975685	+	0.219178i	$0.0703376\pi$
$283$	11.3999	+	19.7453i	0.677656	+	1.17374i	−0.298028	+	0.954557i	$0.596329\pi$
$284$		0			0
$285$	0.678725	−	1.46492i	0.0402042	−	0.0867743i
$286$		0			0
$287$	7.05538	+	21.1562i	0.416466	+	1.24881i
$288$		0			0
$289$	7.66938	−	13.2838i	0.451140	−	0.781398i
$290$		0			0
$291$	4.16030	+	5.91056i	0.243881	+	0.346483i
$292$		0			0
$293$	−6.51811			−0.380792			−0.190396	−	0.981707i	$-0.560977\pi$
$293$	−6.51811			−0.380792			−0.190396	+	0.981707i	$0.560977\pi$
$294$		0			0
$295$			13.2215i			0.769784i
$296$		0			0
$297$	14.0534	−	14.2621i	0.815459	−	0.827574i
$298$		0			0
$299$	2.53633	+	1.46435i	0.146680	+	0.0846858i
$300$		0			0
$301$	16.9936	−	5.66719i	0.979496	−	0.326652i
$302$		0			0
$303$	−7.68463	+	16.5861i	−0.441471	+	0.952844i
$304$		0			0
$305$	17.0244	−	9.82906i	0.974817	−	0.562811i
$306$		0			0
$307$	12.7577			0.728122			0.364061	−	0.931375i	$-0.381390\pi$
$307$	12.7577			0.728122			0.364061	+	0.931375i	$0.381390\pi$
$308$		0			0
$309$	−1.65003	−	18.3406i	−0.0938669	−	1.04336i
$310$		0			0
$311$	4.72369	+	8.18167i	0.267856	+	0.463940i	0.968308	−	0.249760i	$-0.0803516\pi$
$311$	4.72369	+	8.18167i	0.267856	+	0.463940i	−0.700452	+	0.713699i	$0.747018\pi$
$312$		0			0
$313$	2.87628	−	4.98187i	0.162577	−	0.281592i	−0.773215	−	0.634144i	$-0.781353\pi$
$313$	2.87628	−	4.98187i	0.162577	−	0.281592i	0.935792	+	0.352552i	$0.114686\pi$
$314$		0			0
$315$	13.5787	+	8.24798i	0.765073	+	0.464721i
$316$		0			0
$317$	6.69015	−	11.5877i	0.375756	−	0.650829i	−0.614684	−	0.788774i	$-0.710716\pi$
$317$	6.69015	−	11.5877i	0.375756	−	0.650829i	0.990440	+	0.137945i	$0.0440496\pi$
$318$		0			0
$319$	30.8959	−	17.8378i	1.72984	−	0.998723i
$320$		0			0
$321$	−0.871974	−	9.69229i	−0.0486688	−	0.540971i
$322$		0			0
$323$		−	2.64826i		−	0.147353i
$324$		0			0
$325$	1.77174	−	1.02292i	0.0982787	−	0.0567412i
$326$		0			0
$327$	−16.6052	−	7.69352i	−0.918272	−	0.425453i
$328$		0			0
$329$	1.90329	−	9.30756i	0.104932	−	0.513142i
$330$		0			0
$331$	−2.24337	+	3.88563i	−0.123307	+	0.213573i	−0.921070	−	0.389398i	$-0.872683\pi$
$331$	−2.24337	+	3.88563i	−0.123307	+	0.213573i	0.797763	+	0.602971i	$0.206017\pi$
$332$		0			0
$333$	−1.50393	+	1.27460i	−0.0824151	+	0.0698477i
$334$		0			0
$335$	−15.1431			−0.827358
$336$		0			0
$337$	−9.02628			−0.491693			−0.245846	−	0.969309i	$-0.579066\pi$
$337$	−9.02628			−0.491693			−0.245846	+	0.969309i	$0.579066\pi$
$338$		0			0
$339$	22.5350	−	15.8619i	1.22393	−	0.861499i
$340$		0			0
$341$	11.1170	−	19.2552i	0.602019	−	1.04273i
$342$		0			0
$343$	−10.5355	+	15.2317i	−0.568863	+	0.822432i
$344$		0			0
$345$	−2.07284	+	4.47389i	−0.111598	+	0.240866i
$346$		0			0
$347$	0.882015	−	0.509232i	0.0473491	−	0.0273370i	−0.476139	−	0.879370i	$-0.657964\pi$
$347$	0.882015	−	0.509232i	0.0473491	−	0.0273370i	0.523488	+	0.852033i	$0.324631\pi$
$348$		0			0
$349$			9.91220i			0.530588i	0.964168	+	0.265294i	$0.0854690\pi$
$349$			9.91220i			0.530588i	−0.964168	+	0.265294i	$0.914531\pi$
$350$		0			0
$351$	−2.84552	−	10.3148i	−0.151883	−	0.550564i
$352$		0			0
$353$	−20.6381	+	11.9154i	−1.09845	+	0.634192i	−0.935814	−	0.352494i	$-0.885334\pi$
$353$	−20.6381	+	11.9154i	−1.09845	+	0.634192i	−0.162638	+	0.986686i	$0.552000\pi$
$354$		0			0
$355$	−14.0540	+	24.3422i	−0.745909	+	1.29195i
$356$		0			0
$357$	25.8966	+	2.91217i	1.37059	+	0.154129i
$358$		0			0
$359$	−1.66057	+	2.87619i	−0.0876414	+	0.151799i	−0.906514	−	0.422176i	$-0.861266\pi$
$359$	−1.66057	+	2.87619i	−0.0876414	+	0.151799i	0.818872	+	0.573976i	$0.194600\pi$
$360$		0			0
$361$	9.39157	+	16.2667i	0.494293	+	0.856140i
$362$		0			0
$363$	−6.63876	+	0.597261i	−0.348445	+	0.0313481i
$364$		0			0
$365$	8.09111			0.423508
$366$		0			0
$367$	−6.76756	+	3.90725i	−0.353264	+	0.203957i	−0.666122	−	0.745843i	$-0.732047\pi$
$367$	−6.76756	+	3.90725i	−0.353264	+	0.203957i	0.312858	+	0.949800i	$0.398714\pi$
$368$		0			0
$369$	23.8049	+	8.53200i	1.23923	+	0.444158i
$370$		0			0
$371$	−5.96184	−	5.28518i	−0.309524	−	0.274393i
$372$		0			0
$373$	−27.0847	−	15.6374i	−1.40239	−	0.809673i	−0.407756	−	0.913091i	$-0.633689\pi$
$373$	−27.0847	−	15.6374i	−1.40239	−	0.809673i	−0.994638	+	0.103418i	$0.967022\pi$
$374$		0			0
$375$	11.9601	+	16.9918i	0.617618	+	0.877451i
$376$		0			0
$377$		−	19.0650i		−	0.981898i
$378$		0			0
$379$	−19.1714			−0.984768			−0.492384	−	0.870378i	$-0.663874\pi$
$379$	−19.1714			−0.984768			−0.492384	+	0.870378i	$0.663874\pi$
$380$		0			0
$381$	−25.2701	+	17.7870i	−1.29463	+	0.911256i
$382$		0			0
$383$	13.9774	−	24.2095i	0.714209	−	1.23705i	−0.249054	−	0.968490i	$-0.580120\pi$
$383$	13.9774	−	24.2095i	0.714209	−	1.23705i	0.963264	−	0.268558i	$-0.0865469\pi$
$384$		0			0
$385$	−6.45587	−	19.3585i	−0.329021	−	0.986602i
$386$		0			0
$387$	6.85328	−	19.1212i	0.348372	−	0.971983i
$388$		0			0
$389$	−7.27120	−	12.5941i	−0.368664	−	0.638545i	0.620693	−	0.784054i	$-0.286851\pi$
$389$	−7.27120	−	12.5941i	−0.368664	−	0.638545i	−0.989357	+	0.145509i	$0.953518\pi$
$390$		0			0
$391$			8.08782i			0.409019i
$392$		0			0
$393$	−0.377759	−	4.19892i	−0.0190554	−	0.211808i
$394$		0			0
$395$	−0.00977078	+	0.00564117i	−0.000491622	+	0.000283838i
$396$		0			0
$397$	31.2547	+	18.0449i	1.56863	+	0.905647i	0.996330	+	0.0856008i	$0.0272810\pi$
$397$	31.2547	+	18.0449i	1.56863	+	0.905647i	0.572297	+	0.820046i	$0.306052\pi$
$398$		0			0
$399$	1.95582	−	0.853819i	0.0979135	−	0.0427444i
$400$		0			0
$401$	−2.65616	−	1.53353i	−0.132642	−	0.0765811i	0.432211	−	0.901773i	$-0.357734\pi$
$401$	−2.65616	−	1.53353i	−0.132642	−	0.0765811i	−0.564853	+	0.825192i	$0.691067\pi$
$402$		0			0
$403$	−5.94093	−	10.2900i	−0.295939	−	0.512581i
$404$		0			0
$405$	16.8668	−	6.32749i	0.838120	−	0.314415i
$406$		0			0
$407$	2.53217			0.125515
$408$		0			0
$409$	−13.6122	−	23.5770i	−0.673080	−	1.16581i	−0.977026	−	0.213119i	$-0.931638\pi$
$409$	−13.6122	−	23.5770i	−0.673080	−	1.16581i	0.303947	−	0.952689i	$-0.401696\pi$
$410$		0			0
$411$	4.89081	+	2.26601i	0.241246	+	0.111774i
$412$		0			0
$413$	−11.5931	+	13.0773i	−0.570457	+	0.643494i
$414$		0			0
$415$	−14.8465	−	8.57162i	−0.728785	−	0.420764i
$416$		0			0
$417$	7.93066	+	11.2671i	0.388366	+	0.551753i
$418$		0			0
$419$		−	8.16587i		−	0.398929i	−0.979905	−	0.199465i	$-0.936080\pi$
$419$		−	8.16587i		−	0.398929i	0.979905	−	0.199465i	$-0.0639203\pi$
$420$		0			0
$421$		−	7.30698i		−	0.356121i	−0.984020	−	0.178060i	$-0.943018\pi$
$421$		−	7.30698i		−	0.356121i	0.984020	−	0.178060i	$-0.0569822\pi$
$422$		0			0
$423$	−6.96470	−	8.21783i	−0.338635	−	0.399564i
$424$		0			0
$425$	4.89279	+	2.82485i	0.237335	+	0.137026i
$426$		0			0
$427$	25.4573	+	5.20573i	1.23197	+	0.251923i
$428$		0			0
$429$	−5.77774	+	12.4703i	−0.278952	+	0.602073i
$430$		0			0
$431$	1.44464	+	2.50219i	0.0695858	+	0.120526i	0.898719	−	0.438525i	$-0.144499\pi$
$431$	1.44464	+	2.50219i	0.0695858	+	0.120526i	−0.829133	+	0.559051i	$0.811166\pi$
$432$		0			0
$433$	23.0768			1.10900			0.554499	−	0.832184i	$-0.312910\pi$
$433$	23.0768			1.10900			0.554499	+	0.832184i	$0.312910\pi$
$434$		0			0
$435$	31.9686	−	2.87608i	1.53278	−	0.137898i
$436$		0			0
$437$	0.331160	+	0.573586i	0.0158415	+	0.0274384i
$438$		0			0
$439$	2.57178	+	1.48482i	0.122744	+	0.0708664i	0.560115	−	0.828415i	$-0.310757\pi$
$439$	2.57178	+	1.48482i	0.122744	+	0.0708664i	−0.437371	+	0.899281i	$0.644090\pi$
$440$		0			0
$441$	6.19854	+	20.0644i	0.295168	+	0.955445i
$442$		0			0
$443$	−17.0338	−	9.83448i	−0.809301	−	0.467250i	0.0374121	−	0.999300i	$-0.488089\pi$
$443$	−17.0338	−	9.83448i	−0.809301	−	0.467250i	−0.846713	+	0.532050i	$0.821422\pi$
$444$		0			0
$445$	−16.2936	+	9.40711i	−0.772390	+	0.445940i
$446$		0			0
$447$	18.2063	−	1.63794i	0.861127	−	0.0774719i
$448$		0			0
$449$		−	36.3243i		−	1.71425i	−0.515111	−	0.857124i	$-0.672249\pi$
$449$		−	36.3243i		−	1.71425i	0.515111	−	0.857124i	$-0.327751\pi$
$450$		0			0
$451$	−16.2404	−	28.1293i	−0.764733	−	1.32456i
$452$		0			0
$453$	27.6707	+	12.8204i	1.30009	+	0.602354i
$454$		0			0
$455$	−10.6842	−	2.18480i	−0.500884	−	0.102425i
$456$		0			0
$457$	−13.7632	+	23.8385i	−0.643814	+	1.11512i	0.340760	+	0.940150i	$0.389316\pi$
$457$	−13.7632	+	23.8385i	−0.643814	+	1.11512i	−0.984574	+	0.174968i	$0.944018\pi$
$458$		0			0
$459$	20.7397	−	21.0478i	0.968047	−	0.982428i
$460$		0			0
$461$	−19.4067			−0.903861			−0.451931	−	0.892053i	$-0.649265\pi$
$461$	−19.4067			−0.903861			−0.451931	+	0.892053i	$0.649265\pi$
$462$		0			0
$463$			8.27807i			0.384715i	0.981325	+	0.192357i	$0.0616132\pi$
$463$			8.27807i			0.384715i	−0.981325	+	0.192357i	$0.938387\pi$
$464$		0			0
$465$	16.3583	−	11.5142i	0.758596	−	0.533958i
$466$		0			0
$467$	−13.6618	−	7.88767i	−0.632194	−	0.364998i	0.149407	−	0.988776i	$-0.452264\pi$
$467$	−13.6618	−	7.88767i	−0.632194	−	0.364998i	−0.781601	+	0.623778i	$0.785597\pi$
$468$		0			0
$469$	−14.9781	−	13.2780i	−0.691622	−	0.613123i
$470$		0			0
$471$	−3.87013	−	1.79310i	−0.178326	−	0.0826218i
$472$		0			0
$473$	−22.5947	+	13.0450i	−1.03890	+	0.599812i
$474$		0			0
$475$	0.462661			0.0212283
$476$		0			0
$477$	−8.88892	+	1.61245i	−0.406996	+	0.0738289i
$478$		0			0
$479$	6.21288	+	10.7610i	0.283874	+	0.491684i	0.972335	−	0.233589i	$-0.0750470\pi$
$479$	6.21288	+	10.7610i	0.283874	+	0.491684i	−0.688462	+	0.725273i	$0.741714\pi$
$480$		0			0
$481$	0.676597	−	1.17190i	0.0308502	−	0.0534340i
$482$		0			0
$483$	−5.97311	+	2.60758i	−0.271786	+	0.118649i
$484$		0			0
$485$	4.17643	−	7.23379i	0.189642	−	0.328470i
$486$		0			0
$487$	13.8846	−	8.01628i	0.629172	−	0.363252i	−0.151260	−	0.988494i	$-0.548333\pi$
$487$	13.8846	−	8.01628i	0.629172	−	0.363252i	0.780431	+	0.625242i	$0.215000\pi$
$488$		0			0
$489$	−16.6775	+	1.50040i	−0.754183	+	0.0678506i
$490$		0			0
$491$			9.44091i			0.426062i	0.977045	+	0.213031i	$0.0683336\pi$
$491$			9.44091i			0.426062i	−0.977045	+	0.213031i	$0.931666\pi$
$492$		0			0
$493$	45.5956	−	26.3247i	2.05352	−	1.18560i
$494$		0			0
$495$	−21.7821	−	7.80701i	−0.979034	−	0.350899i
$496$		0			0
$497$	−35.2449	+	11.7538i	−1.58095	+	0.527231i
$498$		0			0
$499$	−15.9322	+	27.5954i	−0.713225	+	1.23534i	0.250415	+	0.968139i	$0.419433\pi$
$499$	−15.9322	+	27.5954i	−0.713225	+	1.23534i	−0.963640	+	0.267203i	$0.913900\pi$
$500$		0			0
$501$	12.6992	+	18.0417i	0.567357	+	0.806046i
$502$		0			0
$503$	5.16274			0.230195			0.115098	−	0.993354i	$-0.463282\pi$
$503$	5.16274			0.230195			0.115098	+	0.993354i	$0.463282\pi$
$504$		0			0
$505$	21.1248			0.940043
$506$		0			0
$507$	−8.73281	−	12.4067i	−0.387838	−	0.551002i
$508$		0			0
$509$	1.78554	−	3.09264i	0.0791426	−	0.137079i	−0.823738	−	0.566971i	$-0.808115\pi$
$509$	1.78554	−	3.09264i	0.0791426	−	0.137079i	0.902880	+	0.429892i	$0.141448\pi$
$510$		0			0
$511$	8.00290	+	7.09458i	0.354028	+	0.313846i
$512$		0			0
$513$	0.609041	−	2.34191i	0.0268898	−	0.103398i
$514$		0			0
$515$	−18.4297	+	10.6404i	−0.812109	+	0.468871i
$516$		0			0
$517$			13.8363i			0.608522i
$518$		0			0
$519$	−20.2698	+	1.82358i	−0.889743	+	0.0800464i
$520$		0			0
$521$	−5.95306	+	3.43700i	−0.260808	+	0.150578i	−0.624703	−	0.780862i	$-0.714780\pi$
$521$	−5.95306	+	3.43700i	−0.260808	+	0.150578i	0.363895	+	0.931440i	$0.381447\pi$
$522$		0			0
$523$	6.59397	−	11.4211i	0.288334	−	0.499410i	−0.685078	−	0.728470i	$-0.740232\pi$
$523$	6.59397	−	11.4211i	0.288334	−	0.499410i	0.973412	+	0.229060i	$0.0735652\pi$
$524$		0			0
$525$	−0.508768	+	4.52424i	−0.0222045	+	0.197454i
$526$		0			0
$527$	16.4063	−	28.4165i	0.714668	−	1.23784i
$528$		0			0
$529$	10.4886	+	18.1668i	0.456027	+	0.789863i
$530$		0			0
$531$	3.53691	+	19.4979i	0.153489	+	0.846137i
$532$		0			0
$533$	−17.3578			−0.751850
$534$		0			0
$535$	−9.73934	+	5.62301i	−0.421069	+	0.243104i
$536$		0			0
$537$	−16.1497	−	7.48245i	−0.696910	−	0.322892i
$538$		0			0
$539$	10.5888	−	24.8082i	0.456091	−	1.06857i
$540$		0			0
$541$	2.61534	+	1.50996i	0.112442	+	0.0649185i	0.555166	−	0.831739i	$-0.312655\pi$
$541$	2.61534	+	1.50996i	0.112442	+	0.0649185i	−0.442724	+	0.896658i	$0.645988\pi$
$542$		0			0
$543$	−6.74689	+	4.74898i	−0.289537	+	0.203798i
$544$		0			0
$545$			21.1493i			0.905936i
$546$		0			0
$547$	8.67520			0.370925			0.185462	−	0.982651i	$-0.440622\pi$
$547$	8.67520			0.370925			0.185462	+	0.982651i	$0.440622\pi$
$548$		0			0
$549$	22.4768	−	19.0493i	0.959286	−	0.813005i
$550$		0			0
$551$	2.15575	−	3.73388i	0.0918382	−	0.159068i
$552$		0			0
$553$	−0.0146106	−	0.00298771i	−0.000621308	−	0.000127050i
$554$		0			0
$555$	2.06714	+	0.957744i	0.0877451	+	0.0406539i
$556$		0			0
$557$	−3.73163	−	6.46337i	−0.158114	−	0.273862i	0.776075	−	0.630641i	$-0.217208\pi$
$557$	−3.73163	−	6.46337i	−0.158114	−	0.273862i	−0.934189	+	0.356780i	$0.883875\pi$
$558$		0			0
$559$			13.9425i			0.589707i
$560$		0			0
$561$	−37.8017	+	3.40086i	−1.59599	+	0.143584i
$562$		0			0
$563$	−35.8665	+	20.7076i	−1.51159	+	0.872720i	−0.511687	+	0.859172i	$0.670979\pi$
$563$	−35.8665	+	20.7076i	−1.51159	+	0.872720i	−0.999908	+	0.0135474i	$0.995688\pi$
$564$		0			0
$565$	−27.5801	−	15.9234i	−1.16030	−	0.669901i
$566$		0			0
$567$	22.2311	+	8.53094i	0.933620	+	0.358266i
$568$		0			0
$569$	29.0674	+	16.7821i	1.21857	+	0.703541i	0.964612	−	0.263674i	$-0.0849343\pi$
$569$	29.0674	+	16.7821i	1.21857	+	0.703541i	0.253958	+	0.967215i	$0.418268\pi$
$570$		0			0
$571$	−11.7720	−	20.3898i	−0.492645	−	0.853286i	0.507319	−	0.861758i	$-0.330636\pi$
$571$	−11.7720	−	20.3898i	−0.492645	−	0.853286i	−0.999964	+	0.00847253i	$0.997303\pi$
$572$		0			0
$573$	4.12282	−	0.370912i	0.172233	−	0.0154951i
$574$		0			0
$575$	−1.41297			−0.0589251
$576$		0			0
$577$	11.5230	+	19.9584i	0.479708	+	0.830879i	0.999729	−	0.0232743i	$-0.00740910\pi$
$577$	11.5230	+	19.9584i	0.479708	+	0.830879i	−0.520021	+	0.854154i	$0.674076\pi$
$578$		0			0
$579$	−4.63284	+	9.99925i	−0.192534	+	0.415554i
$580$		0			0
$581$	−7.16873	−	21.4961i	−0.297409	−	0.891809i
$582$		0			0
$583$	10.0491	+	5.80186i	0.416192	+	0.240289i
$584$		0			0
$585$	−9.43331	+	7.99483i	−0.390019	+	0.330546i
$586$		0			0
$587$			35.2560i			1.45517i	0.686017	+	0.727585i	$0.259358\pi$
$587$			35.2560i			1.45517i	−0.686017	+	0.727585i	$0.740642\pi$
$588$		0			0
$589$		−	2.68705i		−	0.110718i
$590$		0			0
$591$	−16.8535	−	23.9438i	−0.693260	−	0.984916i
$592$		0			0
$593$	−15.9344	−	9.19971i	−0.654346	−	0.377787i	0.135773	−	0.990740i	$-0.456648\pi$
$593$	−15.9344	−	9.19971i	−0.654346	−	0.377787i	−0.790119	+	0.612953i	$0.789981\pi$
$594$		0			0
$595$	−9.52745	−	28.5690i	−0.390587	−	1.17121i
$596$		0			0
$597$	20.4102	+	9.45642i	0.835333	+	0.387025i
$598$		0			0
$599$	−3.46929	−	6.00898i	−0.141751	−	0.245520i	0.786405	−	0.617711i	$-0.211940\pi$
$599$	−3.46929	−	6.00898i	−0.141751	−	0.245520i	−0.928156	+	0.372191i	$0.878607\pi$
$600$		0			0
$601$	17.3861			0.709194			0.354597	−	0.935019i	$-0.384618\pi$
$601$	17.3861			0.709194			0.354597	+	0.935019i	$0.384618\pi$
$602$		0			0
$603$	−22.3318	+	4.05098i	−0.909421	+	0.164969i
$604$		0			0
$605$	3.85150	+	6.67099i	0.156586	+	0.271214i
$606$		0			0
$607$	−21.1329	−	12.2011i	−0.857757	−	0.495226i	0.00550324	−	0.999985i	$-0.498248\pi$
$607$	−21.1329	−	12.2011i	−0.857757	−	0.495226i	−0.863261	+	0.504758i	$0.831582\pi$
$608$		0			0
$609$	34.1420	+	25.1865i	1.38350	+	1.02061i
$610$		0			0
$611$	6.40352	+	3.69707i	0.259059	+	0.149568i
$612$		0			0
$613$	−7.71712	+	4.45548i	−0.311692	+	0.179955i	−0.647683	−	0.761910i	$-0.724262\pi$
$613$	−7.71712	+	4.45548i	−0.311692	+	0.179955i	0.335992	+	0.941865i	$0.390929\pi$
$614$		0			0
$615$	−2.61854	−	29.1059i	−0.105590	−	1.17366i
$616$		0			0
$617$			43.3713i			1.74606i	0.487664	+	0.873031i	$0.337849\pi$
$617$			43.3713i			1.74606i	−0.487664	+	0.873031i	$0.662151\pi$
$618$		0			0
$619$	18.4061	+	31.8804i	0.739806	+	1.28138i	0.952583	+	0.304280i	$0.0984159\pi$
$619$	18.4061	+	31.8804i	0.739806	+	1.28138i	−0.212777	+	0.977101i	$0.568251\pi$
$620$		0			0
$621$	−1.86002	+	7.15222i	−0.0746401	+	0.287009i
$622$		0			0
$623$	−24.3644	−	4.98225i	−0.976141	−	0.199610i
$624$		0			0
$625$	9.52276	−	16.4939i	0.380910	−	0.659756i
$626$		0			0
$627$	−2.54164	+	1.78900i	−0.101503	+	0.0714457i
$628$		0			0
$629$	3.73693			0.149001
$630$		0			0
$631$		−	23.1113i		−	0.920045i	−0.887907	−	0.460023i	$-0.847841\pi$
$631$		−	23.1113i		−	0.920045i	0.887907	−	0.460023i	$-0.152159\pi$
$632$		0			0
$633$	−4.33576	−	6.15983i	−0.172331	−	0.244831i
$634$		0			0
$635$	30.9275	+	17.8560i	1.22732	+	0.708593i
$636$		0			0
$637$	−8.65203	−	11.5293i	−0.342806	−	0.456807i
$638$		0			0
$639$	−14.2138	+	39.6575i	−0.562288	+	1.56882i
$640$		0			0
$641$	−12.0471	+	6.95538i	−0.475831	+	0.274721i	−0.718677	−	0.695344i	$-0.755252\pi$
$641$	−12.0471	+	6.95538i	−0.475831	+	0.274721i	0.242847	+	0.970065i	$0.421919\pi$
$642$		0			0
$643$	−13.6551			−0.538505			−0.269252	−	0.963070i	$-0.586777\pi$
$643$	−13.6551			−0.538505			−0.269252	+	0.963070i	$0.586777\pi$
$644$		0			0
$645$	−23.3792	+	2.10332i	−0.920554	+	0.0828183i
$646$		0			0
$647$	15.7948	+	27.3574i	0.620958	+	1.07553i	0.989308	+	0.145843i	$0.0465895\pi$
$647$	15.7948	+	27.3574i	0.620958	+	1.07553i	−0.368350	+	0.929687i	$0.620077\pi$
$648$		0			0
$649$	12.7264	−	22.0428i	0.499556	−	0.865256i
$650$		0			0
$651$	26.2760	+	2.95484i	1.02984	+	0.115809i
$652$		0			0
$653$	15.3505	−	26.5879i	0.600713	−	1.04047i	−0.392000	−	0.919965i	$-0.628217\pi$
$653$	15.3505	−	26.5879i	0.600713	−	1.04047i	0.992713	−	0.120500i	$-0.0384498\pi$
$654$		0			0
$655$	−4.21931	+	2.43602i	−0.164862	+	0.0951832i
$656$		0			0
$657$	11.9321	−	2.16447i	0.465514	−	0.0844442i
$658$		0			0
$659$			20.0419i			0.780720i	0.920662	+	0.390360i	$0.127649\pi$
$659$			20.0419i			0.780720i	−0.920662	+	0.390360i	$0.872351\pi$
$660$		0			0
$661$	−27.8066	+	16.0541i	−1.08155	+	0.624434i	−0.931314	−	0.364216i	$-0.881337\pi$
$661$	−27.8066	+	16.0541i	−1.08155	+	0.624434i	−0.150237	+	0.988650i	$0.548004\pi$
$662$		0			0
$663$	−8.52669	+	18.4035i	−0.331149	+	0.714733i
$664$		0			0
$665$	−1.84546	−	1.63600i	−0.0715637	−	0.0634413i
$666$		0			0
$667$	−6.58371	+	11.4033i	−0.254922	+	0.441538i
$668$		0			0
$669$	−36.5159	+	25.7027i	−1.41179	+	0.993724i
$670$		0			0
$671$	−37.8441			−1.46096
$672$		0			0
$673$	−39.5520			−1.52462			−0.762308	−	0.647214i	$-0.775934\pi$
$673$	−39.5520			−1.52462			−0.762308	+	0.647214i	$0.775934\pi$
$674$		0			0
$675$	3.67714	+	3.62331i	0.141533	+	0.139461i
$676$		0			0
$677$	−20.5606	+	35.6119i	−0.790206	+	1.36868i	0.135633	+	0.990759i	$0.456693\pi$
$677$	−20.5606	+	35.6119i	−0.790206	+	1.36868i	−0.925839	+	0.377918i	$0.876640\pi$
$678$		0			0
$679$	10.4738	−	3.49289i	0.401946	−	0.134045i
$680$		0			0
$681$	2.55795	+	1.18515i	0.0980210	+	0.0454150i
$682$		0			0
$683$	−1.63043	+	0.941329i	−0.0623866	+	0.0360189i	−0.530869	−	0.847454i	$-0.678134\pi$
$683$	−1.63043	+	0.941329i	−0.0623866	+	0.0360189i	0.468482	+	0.883473i	$0.344801\pi$
$684$		0			0
$685$		−	6.22919i		−	0.238005i
$686$		0			0
$687$	2.18159	+	24.2491i	0.0832327	+	0.925159i
$688$		0			0
$689$	5.37025	−	3.10052i	0.204590	−	0.118120i
$690$		0			0
$691$	−4.71705	+	8.17016i	−0.179445	+	0.310808i	−0.941691	−	0.336480i	$-0.890763\pi$
$691$	−4.71705	+	8.17016i	−0.179445	+	0.310808i	0.762246	+	0.647288i	$0.224097\pi$
$692$		0			0
$693$	−14.6992	−	26.8213i	−0.558377	−	1.01886i
$694$		0			0
$695$	7.96141	−	13.7896i	0.301993	−	0.523068i
$696$		0			0
$697$	−23.9674	−	41.5127i	−0.907829	−	1.57241i
$698$		0			0
$699$	2.79254	+	31.0401i	0.105624	+	1.17404i
$700$		0			0
$701$	23.3839			0.883197			0.441598	−	0.897213i	$-0.354412\pi$
$701$	23.3839			0.883197			0.441598	+	0.897213i	$0.354412\pi$
$702$		0			0
$703$	0.265022	−	0.153011i	0.00999551	−	0.00577091i
$704$		0			0
$705$	−5.23332	+	11.2953i	−0.197098	+	0.425405i
$706$		0			0
$707$	20.8946	+	18.5230i	0.785821	+	0.696630i
$708$		0			0
$709$	19.2646	+	11.1224i	0.723496	+	0.417711i	0.816038	−	0.577998i	$-0.196166\pi$
$709$	19.2646	+	11.1224i	0.723496	+	0.417711i	−0.0925419	+	0.995709i	$0.529499\pi$
$710$		0			0
$711$	−0.0129000	+	0.0109329i	−0.000483789	+	0.000410016i
$712$		0			0
$713$			8.20631i			0.307329i
$714$		0			0
$715$	15.8829			0.593985
$716$		0			0
$717$	−16.0043	−	22.7373i	−0.597690	−	0.849141i
$718$		0			0
$719$	−21.5877	+	37.3910i	−0.805086	+	1.39445i	0.111148	+	0.993804i	$0.464547\pi$
$719$	−21.5877	+	37.3910i	−0.805086	+	1.39445i	−0.916233	+	0.400645i	$0.868786\pi$
$720$		0			0
$721$	−27.5586	−	5.63543i	−1.02634	−	0.209874i
$722$		0			0
$723$	5.30518	−	11.4504i	0.197302	−	0.425844i
$724$		0			0
$725$	4.59902	+	7.96574i	0.170803	+	0.295840i
$726$		0			0
$727$		−	18.5349i		−	0.687423i	−0.939075	−	0.343712i	$-0.888316\pi$
$727$		−	18.5349i		−	0.687423i	0.939075	−	0.343712i	$-0.111684\pi$
$728$		0			0
$729$	23.1811	−	13.8433i	0.858558	−	0.512716i
$730$		0			0
$731$	−33.3448	+	19.2516i	−1.23330	+	0.712048i
$732$		0			0
$733$	−7.89497	−	4.55816i	−0.291607	−	0.168360i	0.347059	−	0.937843i	$-0.387180\pi$
$733$	−7.89497	−	4.55816i	−0.291607	−	0.168360i	−0.638666	+	0.769484i	$0.720514\pi$
$734$		0			0
$735$	18.0274	−	16.2472i	0.664949	−	0.599287i
$736$		0			0
$737$	25.2466	+	14.5761i	0.929970	+	0.536919i
$738$		0			0
$739$	16.9014	+	29.2741i	0.621728	+	1.07686i	0.989164	+	0.146815i	$0.0469023\pi$
$739$	16.9014	+	29.2741i	0.621728	+	1.07686i	−0.367436	+	0.930049i	$0.619764\pi$
$740$		0			0
$741$	0.148830	+	1.65430i	0.00546742	+	0.0607723i
$742$		0			0
$743$	−19.4548			−0.713726			−0.356863	−	0.934157i	$-0.616154\pi$
$743$	−19.4548			−0.713726			−0.356863	+	0.934157i	$0.616154\pi$
$744$		0			0
$745$	−10.5624	−	18.2947i	−0.386977	−	0.670264i
$746$		0			0
$747$	−24.1873	−	8.66907i	−0.884969	−	0.317185i
$748$		0			0
$749$	−14.5636	−	2.97810i	−0.532143	−	0.108817i
$750$		0			0
$751$	10.6440	+	6.14534i	0.388407	+	0.224247i	0.681470	−	0.731847i	$-0.261341\pi$
$751$	10.6440	+	6.14534i	0.388407	+	0.224247i	−0.293063	+	0.956093i	$0.594675\pi$
$752$		0			0
$753$	−31.6516	+	22.2788i	−1.15345	+	0.811886i
$754$		0			0
$755$		−	35.2429i		−	1.28262i
$756$		0			0
$757$		−	10.4294i		−	0.379064i	−0.981875	−	0.189532i	$-0.939303\pi$
$757$		−	10.4294i		−	0.379064i	0.981875	−	0.189532i	$-0.0606970\pi$
$758$		0			0
$759$	7.76220	−	5.46363i	0.281750	−	0.198317i
$760$		0			0
$761$	−21.5087	−	12.4181i	−0.779691	−	0.450155i	0.0566301	−	0.998395i	$-0.481964\pi$
$761$	−21.5087	−	12.4181i	−0.779691	−	0.450155i	−0.836321	+	0.548241i	$0.815298\pi$
$762$		0			0
$763$	−18.5445	+	20.9187i	−0.671354	+	0.757308i
$764$		0			0
$765$	−32.1457	−	11.5215i	−1.16223	−	0.416559i
$766$		0			0
$767$	−6.80100	−	11.7797i	−0.245570	−	0.425340i
$768$		0			0
$769$	0.929396			0.0335149			0.0167574	−	0.999860i	$-0.494666\pi$
$769$	0.929396			0.0335149			0.0167574	+	0.999860i	$0.494666\pi$
$770$		0			0
$771$	−0.469442	−	5.21800i	−0.0169065	−	0.187922i
$772$		0			0
$773$	15.9577	+	27.6396i	0.573959	+	0.994127i	0.996154	+	0.0876213i	$0.0279265\pi$
$773$	15.9577	+	27.6396i	0.573959	+	0.994127i	−0.422195	+	0.906505i	$0.638740\pi$
$774$		0			0
$775$	4.96447	+	2.86624i	0.178329	+	0.102958i
$776$		0			0
$777$	1.20482	+	2.75984i	0.0432226	+	0.0990088i
$778$		0			0
$779$	−3.39952	−	1.96271i	−0.121800	−	0.0703215i
$780$		0			0
$781$	46.8616	−	27.0555i	1.67684	−	0.968123i
$782$		0			0
$783$	46.3752	−	12.7934i	1.65732	−	0.457200i
$784$		0			0
$785$			4.92919i			0.175930i
$786$		0			0
$787$	3.93891	+	6.82240i	0.140407	+	0.243192i	0.927650	−	0.373451i	$-0.121826\pi$
$787$	3.93891	+	6.82240i	0.140407	+	0.243192i	−0.787243	+	0.616643i	$0.788492\pi$
$788$		0			0
$789$	−15.6482	+	33.7742i	−0.557092	+	1.20239i
$790$		0			0
$791$	−13.3172	−	39.9330i	−0.473506	−	1.41985i
$792$		0			0
$793$	−10.1120	+	17.5144i	−0.359086	+	0.621956i
$794$		0			0
$795$	6.00916	+	8.53723i	0.213123	+	0.302784i
$796$		0			0
$797$	−5.89418			−0.208782			−0.104391	−	0.994536i	$-0.533289\pi$
$797$	−5.89418			−0.208782			−0.104391	+	0.994536i	$0.533289\pi$
$798$		0			0
$799$			20.4194i			0.722388i
$800$		0			0
$801$	−21.5119	+	18.2315i	−0.760084	+	0.644180i
$802$		0			0
$803$	−13.4895	−	7.78815i	−0.476033	−	0.274838i
$804$		0			0
$805$	5.63606	+	4.99637i	0.198645	+	0.176099i
$806$		0			0
$807$	15.9294	−	34.3810i	0.560740	−	1.21027i
$808$		0			0
$809$	35.6151	−	20.5624i	1.25216	−	0.722936i	0.280623	−	0.959818i	$-0.409459\pi$
$809$	35.6151	−	20.5624i	1.25216	−	0.722936i	0.971538	+	0.236882i	$0.0761256\pi$
$810$		0			0
$811$	−17.5373			−0.615819			−0.307909	−	0.951416i	$-0.599629\pi$
$811$	−17.5373			−0.615819			−0.307909	+	0.951416i	$0.599629\pi$
$812$		0			0
$813$	−1.61882	−	17.9938i	−0.0567746	−	0.631069i
$814$		0			0
$815$	9.67551	+	16.7585i	0.338918	+	0.587024i
$816$		0			0
$817$	−1.57654	+	2.73064i	−0.0551561	+	0.0955331i
$818$		0			0
$819$	−16.3406	−	0.363791i	−0.570988	−	0.0127119i
$820$		0			0
$821$	13.1411	−	22.7610i	0.458626	−	0.794364i	−0.540262	−	0.841497i	$-0.681675\pi$
$821$	13.1411	−	22.7610i	0.458626	−	0.794364i	0.998889	+	0.0471324i	$0.0150083\pi$
$822$		0			0
$823$	10.8805	−	6.28189i	0.379272	−	0.218973i	−0.298229	−	0.954494i	$-0.596396\pi$
$823$	10.8805	−	6.28189i	0.379272	−	0.218973i	0.677502	+	0.735521i	$0.263063\pi$
$824$		0			0
$825$	−0.594143	−	6.60410i	−0.0206854	−	0.229925i
$826$		0			0
$827$		−	27.2104i		−	0.946197i	−0.881010	−	0.473098i	$-0.843136\pi$
$827$		−	27.2104i		−	0.946197i	0.881010	−	0.473098i	$-0.156864\pi$
$828$		0			0
$829$	−37.1390	+	21.4422i	−1.28989	+	0.744718i	−0.978634	−	0.205608i	$-0.934083\pi$
$829$	−37.1390	+	21.4422i	−1.28989	+	0.744718i	−0.311255	+	0.950326i	$0.600749\pi$
$830$		0			0
$831$	34.0652	+	15.7831i	1.18171	+	0.547508i
$832$		0			0
$833$	15.6267	−	36.6115i	0.541434	−	1.26851i
$834$		0			0
$835$	12.7484	−	22.0809i	0.441177	−	0.764140i
$836$		0			0
$837$	21.0436	−	21.3562i	0.727372	−	0.738178i
$838$		0			0
$839$	43.8842			1.51505			0.757526	−	0.652805i	$-0.226408\pi$
$839$	43.8842			1.51505			0.757526	+	0.652805i	$0.226408\pi$
$840$		0			0
$841$	56.7160			1.95572
$842$		0			0
$843$	11.8270	−	8.32473i	0.407342	−	0.286719i
$844$		0			0
$845$	−8.76667	+	15.1843i	−0.301583	+	0.522356i
$846$		0			0
$847$	−2.03986	+	9.97540i	−0.0700903	+	0.342759i
$848$		0			0
$849$	16.6014	−	35.8315i	0.569759	−	1.22973i
$850$		0			0
$851$	−0.809383	+	0.467298i	−0.0277453	+	0.0160188i
$852$		0			0
$853$			45.0262i			1.54167i	0.637036	+	0.770834i	$0.280160\pi$
$853$			45.0262i			1.54167i	−0.637036	+	0.770834i	$0.719840\pi$
$854$		0			0
$855$	−2.75152	+	0.499124i	−0.0940999	+	0.0170697i
$856$		0			0
$857$	−2.63945	+	1.52389i	−0.0901621	+	0.0520551i	−0.544403	−	0.838824i	$-0.683244\pi$
$857$	−2.63945	+	1.52389i	−0.0901621	+	0.0520551i	0.454241	+	0.890879i	$0.349910\pi$
$858$		0			0
$859$	18.4182	−	31.9013i	0.628421	−	1.08846i	−0.359447	−	0.933165i	$-0.617035\pi$
$859$	18.4182	−	31.9013i	0.628421	−	1.08846i	0.987869	−	0.155292i	$-0.0496320\pi$
$860$		0			0
$861$	22.9311	−	31.0847i	0.781491	−	1.05936i
$862$		0			0
$863$	23.1013	−	40.0125i	0.786376	−	1.36204i	−0.141798	−	0.989896i	$-0.545288\pi$
$863$	23.1013	−	40.0125i	0.786376	−	1.36204i	0.928174	−	0.372147i	$-0.121378\pi$
$864$		0			0
$865$	11.7596	+	20.3682i	0.399837	+	0.692538i
$866$		0			0
$867$	−26.4607	+	2.38055i	−0.898651	+	0.0808478i
$868$		0			0
$869$	0.0217198			0.000736793
$870$		0			0
$871$	13.4918	−	7.78949i	0.457152	−	0.263937i
$872$		0			0
$873$	4.22391	−	11.7850i	0.142958	−	0.398863i
$874$		0			0
$875$	30.1101	−	10.0414i	1.01791	−	0.339462i
$876$		0			0
$877$	20.3134	+	11.7280i	0.685935	+	0.396025i	0.802087	−	0.597207i	$-0.203723\pi$
$877$	20.3134	+	11.7280i	0.685935	+	0.396025i	−0.116152	+	0.993231i	$0.537056\pi$
$878$		0			0
$879$	6.49821	+	9.23203i	0.219179	+	0.311389i
$880$		0			0
$881$		−	16.7672i		−	0.564900i	−0.959282	−	0.282450i	$-0.908853\pi$
$881$		−	16.7672i		−	0.564900i	0.959282	−	0.282450i	$-0.0911471\pi$
$882$		0			0
$883$	18.5641			0.624731			0.312365	−	0.949962i	$-0.398879\pi$
$883$	18.5641			0.624731			0.312365	+	0.949962i	$0.398879\pi$
$884$		0			0
$885$	18.7265	−	13.1811i	0.629483	−	0.443078i
$886$		0			0
$887$	−19.6635	+	34.0581i	−0.660234	+	1.14356i	0.320320	+	0.947309i	$0.396210\pi$
$887$	−19.6635	+	34.0581i	−0.660234	+	1.14356i	−0.980554	+	0.196250i	$0.937124\pi$
$888$		0			0
$889$	14.9335	+	44.7796i	0.500855	+	1.50186i
$890$		0			0
$891$	−34.2109	−	5.68611i	−1.14611	−	0.190492i
$892$		0			0
$893$	0.836085	+	1.44814i	0.0279785	+	0.0484602i
$894$		0			0
$895$			20.5691i			0.687548i
$896$		0			0
$897$	−0.454531	−	5.05226i	−0.0151763	−	0.168690i
$898$		0			0
$899$	46.2636	−	26.7103i	1.54298	−	0.890839i
$900$		0			0
$901$	14.8303	+	8.56229i	0.494070	+	0.285251i
$902$		0			0
$903$	−24.9686	−	18.4193i	−0.830902	−	0.612956i
$904$		0			0
$905$	8.25737	+	4.76740i	0.274484	+	0.158474i
$906$		0			0
$907$	−12.8800	−	22.3088i	−0.427674	−	0.740753i	0.568992	−	0.822343i	$-0.307333\pi$
$907$	−12.8800	−	22.3088i	−0.427674	−	0.740753i	−0.996666	+	0.0815902i	$0.974000\pi$
$908$		0			0
$909$	31.1531	−	5.65117i	1.03328	−	0.187437i
$910$		0			0
$911$	0.887972			0.0294198			0.0147099	−	0.999892i	$-0.495318\pi$
$911$	0.887972			0.0294198			0.0147099	+	0.999892i	$0.495318\pi$
$912$		0			0
$913$	16.5014	+	28.5812i	0.546115	+	0.945899i
$914$		0			0
$915$	−30.8940	−	14.3138i	−1.02133	−	0.473199i
$916$		0			0
$917$	−6.30930	−	1.29018i	−0.208352	−	0.0426055i
$918$		0			0
$919$	−37.8224	−	21.8368i	−1.24764	−	0.720328i	−0.277006	−	0.960868i	$-0.589342\pi$
$919$	−37.8224	−	21.8368i	−1.24764	−	0.720328i	−0.970639	+	0.240540i	$0.922675\pi$
$920$		0			0
$921$	−12.7188	−	18.0696i	−0.419098	−	0.595414i
$922$		0			0
$923$		−	28.9170i		−	0.951814i
$924$		0			0
$925$			0.652857i			0.0214658i
$926$		0			0
$927$	−24.3321	+	20.6217i	−0.799170	+	0.677305i
$928$		0			0
$929$	−10.6999	−	6.17761i	−0.351053	−	0.202681i	0.314096	−	0.949391i	$-0.398299\pi$
$929$	−10.6999	−	6.17761i	−0.351053	−	0.202681i	−0.665149	+	0.746711i	$0.731632\pi$
$930$		0			0
$931$	−0.390836	−	3.23633i	−0.0128091	−	0.106066i
$932$		0			0
$933$	6.87897	−	14.8472i	0.225207	−	0.486074i
$934$		0			0
$935$	21.9308	+	37.9852i	0.717213	+	1.24225i
$936$		0			0
$937$	−60.8875			−1.98911			−0.994553	−	0.104228i	$-0.966763\pi$
$937$	−60.8875			−1.98911			−0.994553	+	0.104228i	$0.966763\pi$
$938$		0			0
$939$	−9.92366	+	0.892790i	−0.323847	+	0.0291351i
$940$		0			0
$941$	20.1874	+	34.9656i	0.658090	+	1.13985i	0.981109	+	0.193453i	$0.0619688\pi$
$941$	20.1874	+	34.9656i	0.658090	+	1.13985i	−0.323019	+	0.946392i	$0.604698\pi$
$942$		0			0
$943$	10.3822	+	5.99416i	0.338091	+	0.195197i
$944$		0			0
$945$	−1.85508	−	27.4552i	−0.0603457	−	0.893118i
$946$		0			0
$947$	49.1278	+	28.3640i	1.59644	+	0.921705i	0.992166	+	0.124928i	$0.0398699\pi$
$947$	49.1278	+	28.3640i	1.59644	+	0.921705i	0.604273	+	0.796777i	$0.293463\pi$
$948$		0			0
$949$	−7.20878	+	4.16199i	−0.234007	+	0.135104i
$950$		0			0
$951$	−23.0821	+	2.07660i	−0.748490	+	0.0673385i
$952$		0			0
$953$		−	57.3370i		−	1.85733i	−0.370922	−	0.928664i	$-0.620958\pi$
$953$		−	57.3370i		−	1.85733i	0.370922	−	0.928664i	$-0.379042\pi$
$954$		0			0
$955$	−2.39187	−	4.14283i	−0.0773990	−	0.134059i
$956$		0			0
$957$	−56.0664	−	25.9766i	−1.81237	−	0.839705i
$958$		0			0
$959$	5.46198	−	6.16128i	0.176376	−	0.198958i
$960$		0			0
$961$	1.14663	−	1.98602i	0.0369880	−	0.0640651i
$962$		0			0
$963$	−12.8585	+	10.8977i	−0.414360	+	0.351175i
$964$		0			0
$965$	12.7356			0.409972
$966$		0			0
$967$		−	8.50633i		−	0.273545i	−0.990602	−	0.136773i	$-0.956327\pi$
$967$		−	8.50633i		−	0.273545i	0.990602	−	0.136773i	$-0.0436729\pi$
$968$		0			0
$969$	−3.75090	+	2.64017i	−0.120496	+	0.0848146i
$970$		0			0
$971$	−19.5026	−	11.2598i	−0.625867	−	0.361344i	0.153283	−	0.988182i	$-0.451015\pi$
$971$	−19.5026	−	11.2598i	−0.625867	−	0.361344i	−0.779150	+	0.626838i	$0.784349\pi$
$972$		0			0
$973$	19.9658	−	6.65838i	0.640074	−	0.213458i
$974$		0			0
$975$	−3.21516	−	1.48965i	−0.102968	−	0.0477068i
$976$		0			0
$977$	28.7960	−	16.6254i	0.921267	−	0.531894i	0.0372277	−	0.999307i	$-0.488147\pi$
$977$	28.7960	−	16.6254i	0.921267	−	0.531894i	0.884039	+	0.467413i	$0.154814\pi$
$978$		0			0
$979$	36.2195			1.15758
$980$		0			0
$981$	5.65770	+	31.1891i	0.180637	+	0.995793i
$982$		0			0
$983$	5.17748	+	8.96766i	0.165136	+	0.286024i	0.936704	−	0.350123i	$-0.113860\pi$
$983$	5.17748	+	8.96766i	0.165136	+	0.286024i	−0.771568	+	0.636147i	$0.780527\pi$
$984$		0			0
$985$	−16.9188	+	29.3043i	−0.539079	+	0.933712i
$986$		0			0
$987$	−15.0804	+	6.58339i	−0.480014	+	0.209552i
$988$		0			0
$989$	4.81477	−	8.33943i	0.153101	−	0.265178i
$990$		0			0
$991$	−49.0627	+	28.3264i	−1.55853	+	0.899817i	−0.561130	+	0.827728i	$0.689633\pi$
$991$	−49.0627	+	28.3264i	−1.55853	+	0.899817i	−0.997398	+	0.0720892i	$0.977033\pi$
$992$		0			0
$993$	7.74000	−	0.696335i	0.245621	−	0.0220975i
$994$		0			0
$995$		−	25.9954i		−	0.824111i
$996$		0			0
$997$	−12.1911	+	7.03856i	−0.386097	+	0.222913i	−0.680468	−	0.732778i	$-0.738223\pi$
$997$	−12.1911	+	7.03856i	−0.386097	+	0.222913i	0.294370	+	0.955691i	$0.404890\pi$
$998$		0			0
$999$	3.30464	+	0.859413i	0.104554	+	0.0271906i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bd.a.527.9		56
3.2	odd	2	inner	672.2.bd.a.527.12		56
4.3	odd	2		168.2.v.a.107.14	yes	56
7.4	even	3	inner	672.2.bd.a.431.11		56
8.3	odd	2	inner	672.2.bd.a.527.10		56
8.5	even	2		168.2.v.a.107.24	yes	56
12.11	even	2		168.2.v.a.107.15	yes	56
21.11	odd	6	inner	672.2.bd.a.431.10		56
24.5	odd	2		168.2.v.a.107.5	yes	56
24.11	even	2	inner	672.2.bd.a.527.11		56
28.11	odd	6		168.2.v.a.11.5	✓	56
56.11	odd	6	inner	672.2.bd.a.431.12		56
56.53	even	6		168.2.v.a.11.15	yes	56
84.11	even	6		168.2.v.a.11.24	yes	56
168.11	even	6	inner	672.2.bd.a.431.9		56
168.53	odd	6		168.2.v.a.11.14	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.v.a.11.5	✓	56	28.11	odd	6
168.2.v.a.11.14	yes	56	168.53	odd	6
168.2.v.a.11.15	yes	56	56.53	even	6
168.2.v.a.11.24	yes	56	84.11	even	6
168.2.v.a.107.5	yes	56	24.5	odd	2
168.2.v.a.107.14	yes	56	4.3	odd	2
168.2.v.a.107.15	yes	56	12.11	even	2
168.2.v.a.107.24	yes	56	8.5	even	2
672.2.bd.a.431.9		56	168.11	even	6	inner
672.2.bd.a.431.10		56	21.11	odd	6	inner
672.2.bd.a.431.11		56	7.4	even	3	inner
672.2.bd.a.431.12		56	56.11	odd	6	inner
672.2.bd.a.527.9		56	1.1	even	1	trivial
672.2.bd.a.527.10		56	8.3	odd	2	inner
672.2.bd.a.527.11		56	24.11	even	2	inner
672.2.bd.a.527.12		56	3.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bd (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.996948 - 1.41637i) q^{3} +(-1.00081 + 1.73346i) q^{5} +(-2.50986 + 0.837013i) q^{7} +(-1.01219 + 2.82409i) q^{9} +(3.33711 - 1.92668i) q^{11} -2.05924i q^{13} +(3.45297 - 0.310649i) q^{15} +(4.92484 - 2.84336i) q^{17} +(0.232846 - 0.403301i) q^{19} +(3.68772 + 2.72043i) q^{21} +(-0.711115 + 1.23169i) q^{23} +(0.496746 + 0.860389i) q^{25} +(5.00905 - 1.38183i) q^{27} +9.25829 q^{29} +(4.99699 - 2.88502i) q^{31} +(-6.05580 - 2.80577i) q^{33} +(1.06098 - 5.18844i) q^{35} +(0.569094 + 0.328567i) q^{37} +(-2.91663 + 2.05295i) q^{39} -8.42924i q^{41} -6.77074 q^{43} +(-3.88243 - 4.58098i) q^{45} +(-1.79536 + 3.10966i) q^{47} +(5.59882 - 4.20157i) q^{49} +(-8.93705 - 4.14070i) q^{51} +(1.50566 + 2.60789i) q^{53} +7.71298i q^{55} +(-0.803357 + 0.0722746i) q^{57} +(5.72041 - 3.30268i) q^{59} +(-8.50530 - 4.91054i) q^{61} +(0.176663 - 7.93529i) q^{63} +(3.56960 + 2.06091i) q^{65} +(3.78271 + 6.55184i) q^{67} +(2.45347 - 0.220728i) q^{69} +14.0426 q^{71} +(-2.02113 - 3.50071i) q^{73} +(0.723397 - 1.56134i) q^{75} +(-6.76302 + 7.62890i) q^{77} +(0.00488142 + 0.00281829i) q^{79} +(-6.95094 - 5.71703i) q^{81} +8.56466i q^{83} +11.3827i q^{85} +(-9.23003 - 13.1131i) q^{87} +(8.14017 + 4.69973i) q^{89} +(1.72361 + 5.16840i) q^{91} +(-9.06798 - 4.20137i) q^{93} +(0.466070 + 0.807257i) q^{95} -4.17304 q^{97} +(2.06332 + 11.3744i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} - 2 q^{9} + 4 q^{19} - 16 q^{25} + 8 q^{27} - 14 q^{33} + 16 q^{43} - 16 q^{49} + 34 q^{51} + 4 q^{57} + 36 q^{67} + 4 q^{73} - 10 q^{81} - 72 q^{91} - 32 q^{97} + 44 q^{99}+O(q^{100}) \) 56 * q + 2 * q^3 - 2 * q^9 + 4 * q^19 - 16 * q^25 + 8 * q^27 - 14 * q^33 + 16 * q^43 - 16 * q^49 + 34 * q^51 + 4 * q^57 + 36 * q^67 + 4 * q^73 - 10 * q^81 - 72 * q^91 - 32 * q^97 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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