LMFDB - Embedded newform 960.2.y.f.943.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [960,2,Mod(847,960)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("960.847"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(960, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.y (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,20,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 3 x^{18} - 6 x^{17} + 2 x^{16} + 4 x^{14} + 20 x^{13} - 24 x^{12} + 40 x^{11} + \cdots + 1024 $ x^20 - 2x^19 + 3x^18 - 6x^17 + 2x^16 + 4x^14 + 20x^13 - 24x^12 + 40x^11 - 124x^10 + 80x^9 - 96x^8 + 160x^7 + 64x^6 + 128x^4 - 768x^3 + 768x^2 - 1024*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{17} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			943.2
Root			$-1.41400 - 0.0245121i$ of defining polynomial
Character	$\chi$	$=$	960.943
Dual form			960.2.y.f.847.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{3} +(-1.85415 - 1.24985i) q^{5} +(-1.96536 + 1.96536i) q^{7} +1.00000 q^{9} +(2.59268 + 2.59268i) q^{11} +0.328451i q^{13} +(-1.85415 - 1.24985i) q^{15} +(3.36908 - 3.36908i) q^{17} +(0.361062 + 0.361062i) q^{19} +(-1.96536 + 1.96536i) q^{21} +(6.27687 + 6.27687i) q^{23} +(1.87574 + 4.63482i) q^{25} +1.00000 q^{27} +(-3.99896 + 3.99896i) q^{29} +3.02085i q^{31} +(2.59268 + 2.59268i) q^{33} +(6.10048 - 1.18766i) q^{35} -7.87281i q^{37} +0.328451i q^{39} +7.90024i q^{41} +5.87147i q^{43} +(-1.85415 - 1.24985i) q^{45} +(5.51736 + 5.51736i) q^{47} -0.725284i q^{49} +(3.36908 - 3.36908i) q^{51} +13.6546 q^{53} +(-1.56676 - 8.04769i) q^{55} +(0.361062 + 0.361062i) q^{57} +(5.41759 - 5.41759i) q^{59} +(-1.32047 - 1.32047i) q^{61} +(-1.96536 + 1.96536i) q^{63} +(0.410514 - 0.608997i) q^{65} -9.81578i q^{67} +(6.27687 + 6.27687i) q^{69} -8.07691 q^{71} +(-0.167116 + 0.167116i) q^{73} +(1.87574 + 4.63482i) q^{75} -10.1911 q^{77} -5.94905 q^{79} +1.00000 q^{81} -2.80013 q^{83} +(-10.4576 + 2.03593i) q^{85} +(-3.99896 + 3.99896i) q^{87} -10.2825 q^{89} +(-0.645524 - 0.645524i) q^{91} +3.02085i q^{93} +(-0.218189 - 1.12074i) q^{95} +(0.537048 - 0.537048i) q^{97} +(2.59268 + 2.59268i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{3} + 4 q^{7} + 20 q^{9} - 8 q^{11} + 12 q^{17} - 16 q^{19} + 4 q^{21} + 16 q^{23} + 4 q^{25} + 20 q^{27} - 8 q^{33} + 28 q^{35} + 12 q^{51} + 8 q^{53} + 4 q^{55} - 16 q^{57} + 16 q^{59} - 12 q^{61}+ \cdots - 8 q^{99}+O(q^{100}) $ 20 * q + 20 * q^3 + 4 * q^7 + 20 * q^9 - 8 * q^11 + 12 * q^17 - 16 * q^19 + 4 * q^21 + 16 * q^23 + 4 * q^25 + 20 * q^27 - 8 * q^33 + 28 * q^35 + 12 * q^51 + 8 * q^53 + 4 * q^55 - 16 * q^57 + 16 * q^59 - 12 * q^61 + 4 * q^63 + 4 * q^65 + 16 * q^69 - 20 * q^73 + 4 * q^75 - 48 * q^79 + 20 * q^81 + 24 * q^83 + 4 * q^85 + 40 * q^89 + 24 * q^91 + 72 * q^95 - 28 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	−1.85415	−	1.24985i	−0.829201	−	0.558950i
$5$	−1.85415	−	1.24985i	−0.829201	−	0.558950i
$6$		0			0
$7$	−1.96536	+	1.96536i	−0.742836	+	0.742836i	−0.973123	−	0.230286i	$-0.926034\pi$
$7$	−1.96536	+	1.96536i	−0.742836	+	0.742836i	0.230286	+	0.973123i	$0.426034\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	2.59268	+	2.59268i	0.781723	+	0.781723i	0.980122	−	0.198398i	$-0.0635739\pi$
$11$	2.59268	+	2.59268i	0.781723	+	0.781723i	−0.198398	+	0.980122i	$0.563574\pi$
$12$		0			0
$13$			0.328451i			0.0910958i	0.998962	+	0.0455479i	$0.0145034\pi$
$13$			0.328451i			0.0910958i	−0.998962	+	0.0455479i	$0.985497\pi$
$14$		0			0
$15$	−1.85415	−	1.24985i	−0.478739	−	0.322710i
$16$		0			0
$17$	3.36908	−	3.36908i	0.817121	−	0.817121i	−0.168569	−	0.985690i	$-0.553914\pi$
$17$	3.36908	−	3.36908i	0.817121	−	0.817121i	0.985690	+	0.168569i	$0.0539144\pi$
$18$		0			0
$19$	0.361062	+	0.361062i	0.0828332	+	0.0828332i	0.747309	−	0.664476i	$-0.231345\pi$
$19$	0.361062	+	0.361062i	0.0828332	+	0.0828332i	−0.664476	+	0.747309i	$0.731345\pi$
$20$		0			0
$21$	−1.96536	+	1.96536i	−0.428877	+	0.428877i
$22$		0			0
$23$	6.27687	+	6.27687i	1.30882	+	1.30882i	0.922269	+	0.386550i	$0.126333\pi$
$23$	6.27687	+	6.27687i	1.30882	+	1.30882i	0.386550	+	0.922269i	$0.373667\pi$
$24$		0			0
$25$	1.87574	+	4.63482i	0.375149	+	0.926965i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−3.99896	+	3.99896i	−0.742588	+	0.742588i	−0.973075	−	0.230487i	$-0.925968\pi$
$29$	−3.99896	+	3.99896i	−0.742588	+	0.742588i	0.230487	+	0.973075i	$0.425968\pi$
$30$		0			0
$31$			3.02085i			0.542561i	0.962500	+	0.271281i	$0.0874472\pi$
$31$			3.02085i			0.542561i	−0.962500	+	0.271281i	$0.912553\pi$
$32$		0			0
$33$	2.59268	+	2.59268i	0.451328	+	0.451328i
$34$		0			0
$35$	6.10048	−	1.18766i	1.03117	−	0.200752i
$36$		0			0
$37$		−	7.87281i		−	1.29428i	−0.762370	−	0.647141i	$-0.775964\pi$
$37$		−	7.87281i		−	1.29428i	0.762370	−	0.647141i	$-0.224036\pi$
$38$		0			0
$39$			0.328451i			0.0525942i
$40$		0			0
$41$			7.90024i			1.23381i	0.787038	+	0.616905i	$0.211614\pi$
$41$			7.90024i			1.23381i	−0.787038	+	0.616905i	$0.788386\pi$
$42$		0			0
$43$			5.87147i			0.895391i	0.894186	+	0.447695i	$0.147755\pi$
$43$			5.87147i			0.895391i	−0.894186	+	0.447695i	$0.852245\pi$
$44$		0			0
$45$	−1.85415	−	1.24985i	−0.276400	−	0.186317i
$46$		0			0
$47$	5.51736	+	5.51736i	0.804790	+	0.804790i	0.983840	−	0.179050i	$-0.0573023\pi$
$47$	5.51736	+	5.51736i	0.804790	+	0.804790i	−0.179050	+	0.983840i	$0.557302\pi$
$48$		0			0
$49$		−	0.725284i		−	0.103612i
$50$		0			0
$51$	3.36908	−	3.36908i	0.471765	−	0.471765i
$52$		0			0
$53$	13.6546			1.87560			0.937801	−	0.347173i	$-0.112858\pi$
$53$	13.6546			1.87560			0.937801	+	0.347173i	$0.112858\pi$
$54$		0			0
$55$	−1.56676	−	8.04769i	−0.211261	−	1.08515i
$56$		0			0
$57$	0.361062	+	0.361062i	0.0478238	+	0.0478238i
$58$		0			0
$59$	5.41759	−	5.41759i	0.705310	−	0.705310i	−0.260236	−	0.965545i	$-0.583800\pi$
$59$	5.41759	−	5.41759i	0.705310	−	0.705310i	0.965545	+	0.260236i	$0.0838002\pi$
$60$		0			0
$61$	−1.32047	−	1.32047i	−0.169069	−	0.169069i	0.617501	−	0.786570i	$-0.288145\pi$
$61$	−1.32047	−	1.32047i	−0.169069	−	0.169069i	−0.786570	+	0.617501i	$0.788145\pi$
$62$		0			0
$63$	−1.96536	+	1.96536i	−0.247612	+	0.247612i
$64$		0			0
$65$	0.410514	−	0.608997i	0.0509180	−	0.0755367i
$66$		0			0
$67$		−	9.81578i		−	1.19919i	−0.800304	−	0.599594i	$-0.795329\pi$
$67$		−	9.81578i		−	1.19919i	0.800304	−	0.599594i	$-0.204671\pi$
$68$		0			0
$69$	6.27687	+	6.27687i	0.755647	+	0.755647i
$70$		0			0
$71$	−8.07691			−0.958553			−0.479276	−	0.877664i	$-0.659101\pi$
$71$	−8.07691			−0.958553			−0.479276	+	0.877664i	$0.659101\pi$
$72$		0			0
$73$	−0.167116	+	0.167116i	−0.0195595	+	0.0195595i	−0.716819	−	0.697259i	$-0.754403\pi$
$73$	−0.167116	+	0.167116i	−0.0195595	+	0.0195595i	0.697259	+	0.716819i	$0.254403\pi$
$74$		0			0
$75$	1.87574	+	4.63482i	0.216592	+	0.535183i
$76$		0			0
$77$	−10.1911			−1.16139
$78$		0			0
$79$	−5.94905			−0.669320			−0.334660	−	0.942339i	$-0.608621\pi$
$79$	−5.94905			−0.669320			−0.334660	+	0.942339i	$0.608621\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−2.80013			−0.307354			−0.153677	−	0.988121i	$-0.549112\pi$
$83$	−2.80013			−0.307354			−0.153677	+	0.988121i	$0.549112\pi$
$84$		0			0
$85$	−10.4576	+	2.03593i	−1.13429	+	0.220828i
$86$		0			0
$87$	−3.99896	+	3.99896i	−0.428733	+	0.428733i
$88$		0			0
$89$	−10.2825			−1.08994			−0.544972	−	0.838454i	$-0.683460\pi$
$89$	−10.2825			−1.08994			−0.544972	+	0.838454i	$0.683460\pi$
$90$		0			0
$91$	−0.645524	−	0.645524i	−0.0676693	−	0.0676693i
$92$		0			0
$93$			3.02085i			0.313248i
$94$		0			0
$95$	−0.218189	−	1.12074i	−0.0223857	−	0.114985i
$96$		0			0
$97$	0.537048	−	0.537048i	0.0545290	−	0.0545290i	−0.679316	−	0.733845i	$-0.737724\pi$
$97$	0.537048	−	0.537048i	0.0545290	−	0.0545290i	0.733845	+	0.679316i	$0.237724\pi$
$98$		0			0
$99$	2.59268	+	2.59268i	0.260574	+	0.260574i
$100$		0			0
$101$	7.00905	−	7.00905i	0.697426	−	0.697426i	−0.266428	−	0.963855i	$-0.585844\pi$
$101$	7.00905	−	7.00905i	0.697426	−	0.697426i	0.963855	+	0.266428i	$0.0858436\pi$
$102$		0			0
$103$	−8.14591	−	8.14591i	−0.802640	−	0.802640i	0.180867	−	0.983507i	$-0.442109\pi$
$103$	−8.14591	−	8.14591i	−0.802640	−	0.802640i	−0.983507	+	0.180867i	$0.942109\pi$
$104$		0			0
$105$	6.10048	−	1.18766i	0.595346	−	0.115904i
$106$		0			0
$107$	−12.8117			−1.23855			−0.619275	−	0.785174i	$-0.712573\pi$
$107$	−12.8117			−1.23855			−0.619275	+	0.785174i	$0.712573\pi$
$108$		0			0
$109$	4.65039	−	4.65039i	0.445427	−	0.445427i	−0.448404	−	0.893831i	$-0.648007\pi$
$109$	4.65039	−	4.65039i	0.445427	−	0.445427i	0.893831	+	0.448404i	$0.148007\pi$
$110$		0			0
$111$		−	7.87281i		−	0.747254i
$112$		0			0
$113$	8.92382	+	8.92382i	0.839482	+	0.839482i	0.988791	−	0.149308i	$-0.0477047\pi$
$113$	8.92382	+	8.92382i	0.839482	+	0.839482i	−0.149308	+	0.988791i	$0.547705\pi$
$114$		0			0
$115$	−3.79311	−	19.4834i	−0.353709	−	1.81684i
$116$		0			0
$117$			0.328451i			0.0303653i
$118$		0			0
$119$			13.2429i			1.21398i
$120$		0			0
$121$			2.44401i			0.222183i
$122$		0			0
$123$			7.90024i			0.712341i
$124$		0			0
$125$	2.31493	−	10.9381i	0.207053	−	0.978330i
$126$		0			0
$127$	8.89383	+	8.89383i	0.789199	+	0.789199i	0.981363	−	0.192164i	$-0.0615504\pi$
$127$	8.89383	+	8.89383i	0.789199	+	0.789199i	−0.192164	+	0.981363i	$0.561550\pi$
$128$		0			0
$129$			5.87147i			0.516954i
$130$		0			0
$131$	−5.04824	+	5.04824i	−0.441067	+	0.441067i	−0.892371	−	0.451303i	$-0.850959\pi$
$131$	−5.04824	+	5.04824i	−0.441067	+	0.441067i	0.451303	+	0.892371i	$0.350959\pi$
$132$		0			0
$133$	−1.41923			−0.123063
$134$		0			0
$135$	−1.85415	−	1.24985i	−0.159580	−	0.107570i
$136$		0			0
$137$	8.94353	+	8.94353i	0.764097	+	0.764097i	0.977060	−	0.212963i	$-0.0683114\pi$
$137$	8.94353	+	8.94353i	0.764097	+	0.764097i	−0.212963	+	0.977060i	$0.568311\pi$
$138$		0			0
$139$	1.67569	−	1.67569i	0.142130	−	0.142130i	−0.632462	−	0.774592i	$-0.717955\pi$
$139$	1.67569	−	1.67569i	0.142130	−	0.142130i	0.774592	+	0.632462i	$0.217955\pi$
$140$		0			0
$141$	5.51736	+	5.51736i	0.464646	+	0.464646i
$142$		0			0
$143$	−0.851568	+	0.851568i	−0.0712117	+	0.0712117i
$144$		0			0
$145$	12.4128	−	2.41657i	1.03082	−	0.200685i
$146$		0			0
$147$		−	0.725284i		−	0.0598204i
$148$		0			0
$149$	−1.65655	−	1.65655i	−0.135710	−	0.135710i	0.635988	−	0.771699i	$-0.280593\pi$
$149$	−1.65655	−	1.65655i	−0.135710	−	0.135710i	−0.771699	+	0.635988i	$0.780593\pi$
$150$		0			0
$151$	−9.40919			−0.765709			−0.382854	−	0.923809i	$-0.625059\pi$
$151$	−9.40919			−0.765709			−0.382854	+	0.923809i	$0.625059\pi$
$152$		0			0
$153$	3.36908	−	3.36908i	0.272374	−	0.272374i
$154$		0			0
$155$	3.77562	−	5.60112i	0.303265	−	0.449892i
$156$		0			0
$157$	−15.5285			−1.23931			−0.619655	−	0.784874i	$-0.712728\pi$
$157$	−15.5285			−1.23931			−0.619655	+	0.784874i	$0.712728\pi$
$158$		0			0
$159$	13.6546			1.08288
$160$		0			0
$161$	−24.6726			−1.94448
$162$		0			0
$163$	−4.41190			−0.345567			−0.172783	−	0.984960i	$-0.555276\pi$
$163$	−4.41190			−0.345567			−0.172783	+	0.984960i	$0.555276\pi$
$164$		0			0
$165$	−1.56676	−	8.04769i	−0.121972	−	0.626512i
$166$		0			0
$167$	1.70055	−	1.70055i	0.131593	−	0.131593i	−0.638243	−	0.769835i	$-0.720338\pi$
$167$	1.70055	−	1.70055i	0.131593	−	0.131593i	0.769835	+	0.638243i	$0.220338\pi$
$168$		0			0
$169$	12.8921			0.991702
$170$		0			0
$171$	0.361062	+	0.361062i	0.0276111	+	0.0276111i
$172$		0			0
$173$		−	15.0010i		−	1.14051i	−0.821469	−	0.570253i	$-0.806845\pi$
$173$		−	15.0010i		−	1.14051i	0.821469	−	0.570253i	$-0.193155\pi$
$174$		0			0
$175$	−12.7956	−	5.42258i	−0.967257	−	0.409909i
$176$		0			0
$177$	5.41759	−	5.41759i	0.407211	−	0.407211i
$178$		0			0
$179$	8.06006	+	8.06006i	0.602437	+	0.602437i	0.940959	−	0.338521i	$-0.109927\pi$
$179$	8.06006	+	8.06006i	0.602437	+	0.602437i	−0.338521	+	0.940959i	$0.609927\pi$
$180$		0			0
$181$	−12.4443	+	12.4443i	−0.924979	+	0.924979i	−0.997376	−	0.0723968i	$-0.976935\pi$
$181$	−12.4443	+	12.4443i	−0.924979	+	0.924979i	0.0723968	+	0.997376i	$0.476935\pi$
$182$		0			0
$183$	−1.32047	−	1.32047i	−0.0976119	−	0.0976119i
$184$		0			0
$185$	−9.83984	+	14.5974i	−0.723440	+	1.07322i
$186$		0			0
$187$	17.4699			1.27753
$188$		0			0
$189$	−1.96536	+	1.96536i	−0.142959	+	0.142959i
$190$		0			0
$191$			13.0787i			0.946340i	0.880971	+	0.473170i	$0.156890\pi$
$191$			13.0787i			0.946340i	−0.880971	+	0.473170i	$0.843110\pi$
$192$		0			0
$193$	−15.0162	−	15.0162i	−1.08089	−	1.08089i	−0.996427	−	0.0844610i	$-0.973083\pi$
$193$	−15.0162	−	15.0162i	−1.08089	−	1.08089i	−0.0844610	−	0.996427i	$-0.526917\pi$
$194$		0			0
$195$	0.410514	−	0.608997i	0.0293975	−	0.0436111i
$196$		0			0
$197$		−	4.49246i		−	0.320074i	−0.987111	−	0.160037i	$-0.948839\pi$
$197$		−	4.49246i		−	0.320074i	0.987111	−	0.160037i	$-0.0511614\pi$
$198$		0			0
$199$			2.17777i			0.154378i	0.997016	+	0.0771890i	$0.0245945\pi$
$199$			2.17777i			0.154378i	−0.997016	+	0.0771890i	$0.975406\pi$
$200$		0			0
$201$		−	9.81578i		−	0.692352i
$202$		0			0
$203$		−	15.7188i		−	1.10324i
$204$		0			0
$205$	9.87412	−	14.6482i	0.689639	−	1.02308i
$206$		0			0
$207$	6.27687	+	6.27687i	0.436273	+	0.436273i
$208$		0			0
$209$			1.87224i			0.129505i
$210$		0			0
$211$	−13.3900	+	13.3900i	−0.921807	+	0.921807i	−0.997157	−	0.0753502i	$-0.975993\pi$
$211$	−13.3900	+	13.3900i	−0.921807	+	0.921807i	0.0753502	+	0.997157i	$0.475993\pi$
$212$		0			0
$213$	−8.07691			−0.553421
$214$		0			0
$215$	7.33846	−	10.8866i	0.500479	−	0.742459i
$216$		0			0
$217$	−5.93707	−	5.93707i	−0.403034	−	0.403034i
$218$		0			0
$219$	−0.167116	+	0.167116i	−0.0112927	+	0.0112927i
$220$		0			0
$221$	1.10658	+	1.10658i	0.0744363	+	0.0744363i
$222$		0			0
$223$	13.9939	−	13.9939i	0.937100	−	0.937100i	−0.0610360	−	0.998136i	$-0.519440\pi$
$223$	13.9939	−	13.9939i	0.937100	−	0.937100i	0.998136	+	0.0610360i	$0.0194405\pi$
$224$		0			0
$225$	1.87574	+	4.63482i	0.125050	+	0.308988i
$226$		0			0
$227$		−	27.3648i		−	1.81626i	−0.418685	−	0.908132i	$-0.637509\pi$
$227$		−	27.3648i		−	1.81626i	0.418685	−	0.908132i	$-0.362491\pi$
$228$		0			0
$229$	−6.18602	−	6.18602i	−0.408783	−	0.408783i	0.472531	−	0.881314i	$-0.343341\pi$
$229$	−6.18602	−	6.18602i	−0.408783	−	0.408783i	−0.881314	+	0.472531i	$0.843341\pi$
$230$		0			0
$231$	−10.1911			−0.670526
$232$		0			0
$233$	16.9076	−	16.9076i	1.10765	−	1.10765i	0.114196	−	0.993458i	$-0.463571\pi$
$233$	16.9076	−	16.9076i	1.10765	−	1.10765i	0.993458	−	0.114196i	$-0.0364293\pi$
$234$		0			0
$235$	−3.33414	−	17.1259i	−0.217495	−	1.11717i
$236$		0			0
$237$	−5.94905			−0.386432
$238$		0			0
$239$	−1.90480			−0.123212			−0.0616058	−	0.998101i	$-0.519622\pi$
$239$	−1.90480			−0.123212			−0.0616058	+	0.998101i	$0.519622\pi$
$240$		0			0
$241$	−23.0653			−1.48577			−0.742884	−	0.669420i	$-0.766543\pi$
$241$	−23.0653			−1.48577			−0.742884	+	0.669420i	$0.766543\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−0.906496	+	1.34478i	−0.0579139	+	0.0859151i
$246$		0			0
$247$	−0.118591	+	0.118591i	−0.00754576	+	0.00754576i
$248$		0			0
$249$	−2.80013			−0.177451
$250$		0			0
$251$	−17.1103	−	17.1103i	−1.07999	−	1.07999i	−0.996509	−	0.0834806i	$-0.973396\pi$
$251$	−17.1103	−	17.1103i	−1.07999	−	1.07999i	−0.0834806	−	0.996509i	$-0.526604\pi$
$252$		0			0
$253$			32.5479i			2.04627i
$254$		0			0
$255$	−10.4576	+	2.03593i	−0.654882	+	0.127495i
$256$		0			0
$257$	4.11987	−	4.11987i	0.256990	−	0.256990i	−0.566838	−	0.823829i	$-0.691834\pi$
$257$	4.11987	−	4.11987i	0.256990	−	0.256990i	0.823829	+	0.566838i	$0.191834\pi$
$258$		0			0
$259$	15.4729	+	15.4729i	0.961440	+	0.961440i
$260$		0			0
$261$	−3.99896	+	3.99896i	−0.247529	+	0.247529i
$262$		0			0
$263$	17.0258	+	17.0258i	1.04985	+	1.04985i	0.998690	+	0.0511644i	$0.0162933\pi$
$263$	17.0258	+	17.0258i	1.04985	+	1.04985i	0.0511644	+	0.998690i	$0.483707\pi$
$264$		0			0
$265$	−25.3177	−	17.0662i	−1.55525	−	1.04837i
$266$		0			0
$267$	−10.2825			−0.629280
$268$		0			0
$269$	2.02914	−	2.02914i	0.123719	−	0.123719i	−0.642536	−	0.766255i	$-0.722118\pi$
$269$	2.02914	−	2.02914i	0.123719	−	0.123719i	0.766255	+	0.642536i	$0.222118\pi$
$270$		0			0
$271$		−	17.1830i		−	1.04379i	−0.853009	−	0.521896i	$-0.825225\pi$
$271$		−	17.1830i		−	1.04379i	0.853009	−	0.521896i	$-0.174775\pi$
$272$		0			0
$273$	−0.645524	−	0.645524i	−0.0390689	−	0.0390689i
$274$		0			0
$275$	−7.15342	+	16.8798i	−0.431367	+	1.01789i
$276$		0			0
$277$			6.31808i			0.379617i	0.981821	+	0.189808i	$0.0607866\pi$
$277$			6.31808i			0.379617i	−0.981821	+	0.189808i	$0.939213\pi$
$278$		0			0
$279$			3.02085i			0.180854i
$280$		0			0
$281$			19.5262i			1.16483i	0.812890	+	0.582417i	$0.197893\pi$
$281$			19.5262i			1.16483i	−0.812890	+	0.582417i	$0.802107\pi$
$282$		0			0
$283$			24.8436i			1.47680i	0.674363	+	0.738400i	$0.264418\pi$
$283$			24.8436i			1.47680i	−0.674363	+	0.738400i	$0.735582\pi$
$284$		0			0
$285$	−0.218189	−	1.12074i	−0.0129244	−	0.0663867i
$286$		0			0
$287$	−15.5268	−	15.5268i	−0.916519	−	0.916519i
$288$		0			0
$289$		−	5.70137i		−	0.335375i
$290$		0			0
$291$	0.537048	−	0.537048i	0.0314823	−	0.0314823i
$292$		0			0
$293$	29.0203			1.69539			0.847693	−	0.530487i	$-0.177991\pi$
$293$	29.0203			1.69539			0.847693	+	0.530487i	$0.177991\pi$
$294$		0			0
$295$	−16.8162	+	3.27384i	−0.979077	+	0.190610i
$296$		0			0
$297$	2.59268	+	2.59268i	0.150443	+	0.150443i
$298$		0			0
$299$	−2.06164	+	2.06164i	−0.119228	+	0.119228i
$300$		0			0
$301$	−11.5396	−	11.5396i	−0.665129	−	0.665129i
$302$		0			0
$303$	7.00905	−	7.00905i	0.402659	−	0.402659i
$304$		0			0
$305$	0.797958	+	4.09874i	0.0456909	+	0.234693i
$306$		0			0
$307$			5.46765i			0.312055i	0.987753	+	0.156028i	$0.0498689\pi$
$307$			5.46765i			0.312055i	−0.987753	+	0.156028i	$0.950131\pi$
$308$		0			0
$309$	−8.14591	−	8.14591i	−0.463404	−	0.463404i
$310$		0			0
$311$	20.7682			1.17765			0.588827	−	0.808259i	$-0.299590\pi$
$311$	20.7682			1.17765			0.588827	+	0.808259i	$0.299590\pi$
$312$		0			0
$313$	3.63603	−	3.63603i	0.205520	−	0.205520i	−0.596840	−	0.802360i	$-0.703577\pi$
$313$	3.63603	−	3.63603i	0.205520	−	0.205520i	0.802360	+	0.596840i	$0.203577\pi$
$314$		0			0
$315$	6.10048	−	1.18766i	0.343723	−	0.0669173i
$316$		0			0
$317$	13.7806			0.773993			0.386996	−	0.922081i	$-0.373513\pi$
$317$	13.7806			0.773993			0.386996	+	0.922081i	$0.373513\pi$
$318$		0			0
$319$	−20.7361			−1.16100
$320$		0			0
$321$	−12.8117			−0.715077
$322$		0			0
$323$	2.43289			0.135370
$324$		0			0
$325$	−1.52231	+	0.616089i	−0.0844426	+	0.0341745i
$326$		0			0
$327$	4.65039	−	4.65039i	0.257167	−	0.257167i
$328$		0			0
$329$	−21.6872			−1.19565
$330$		0			0
$331$	−1.33711	−	1.33711i	−0.0734944	−	0.0734944i	0.669404	−	0.742898i	$-0.266550\pi$
$331$	−1.33711	−	1.33711i	−0.0734944	−	0.0734944i	−0.742898	+	0.669404i	$0.766550\pi$
$332$		0			0
$333$		−	7.87281i		−	0.431427i
$334$		0			0
$335$	−12.2683	+	18.1999i	−0.670287	+	0.994369i
$336$		0			0
$337$	17.7527	−	17.7527i	0.967049	−	0.967049i	−0.0324256	−	0.999474i	$-0.510323\pi$
$337$	17.7527	−	17.7527i	0.967049	−	0.967049i	0.999474	+	0.0324256i	$0.0103232\pi$
$338$		0			0
$339$	8.92382	+	8.92382i	0.484675	+	0.484675i
$340$		0			0
$341$	−7.83212	+	7.83212i	−0.424133	+	0.424133i
$342$		0			0
$343$	−12.3321	−	12.3321i	−0.665870	−	0.665870i
$344$		0			0
$345$	−3.79311	−	19.4834i	−0.204214	−	1.04895i
$346$		0			0
$347$	−17.7610			−0.953463			−0.476732	−	0.879049i	$-0.658179\pi$
$347$	−17.7610			−0.953463			−0.476732	+	0.879049i	$0.658179\pi$
$348$		0			0
$349$	4.63321	−	4.63321i	0.248010	−	0.248010i	−0.572143	−	0.820154i	$-0.693888\pi$
$349$	4.63321	−	4.63321i	0.248010	−	0.248010i	0.820154	+	0.572143i	$0.193888\pi$
$350$		0			0
$351$			0.328451i			0.0175314i
$352$		0			0
$353$	−12.5956	−	12.5956i	−0.670398	−	0.670398i	0.287409	−	0.957808i	$-0.407206\pi$
$353$	−12.5956	−	12.5956i	−0.670398	−	0.670398i	−0.957808	+	0.287409i	$0.907206\pi$
$354$		0			0
$355$	14.9758	+	10.0949i	0.794833	+	0.535783i
$356$		0			0
$357$			13.2429i			0.700889i
$358$		0			0
$359$		−	11.1031i		−	0.585999i	−0.956113	−	0.293000i	$-0.905347\pi$
$359$		−	11.1031i		−	0.585999i	0.956113	−	0.293000i	$-0.0946535\pi$
$360$		0			0
$361$		−	18.7393i		−	0.986277i
$362$		0			0
$363$			2.44401i			0.128277i
$364$		0			0
$365$	0.518729	−	0.100988i	0.0271515	−	0.00528596i
$366$		0			0
$367$	13.4477	+	13.4477i	0.701963	+	0.701963i	0.964832	−	0.262869i	$-0.0846687\pi$
$367$	13.4477	+	13.4477i	0.701963	+	0.701963i	−0.262869	+	0.964832i	$0.584669\pi$
$368$		0			0
$369$			7.90024i			0.411270i
$370$		0			0
$371$	−26.8362	+	26.8362i	−1.39327	+	1.39327i
$372$		0			0
$373$	−10.8013			−0.559268			−0.279634	−	0.960107i	$-0.590213\pi$
$373$	−10.8013			−0.559268			−0.279634	+	0.960107i	$0.590213\pi$
$374$		0			0
$375$	2.31493	−	10.9381i	0.119542	−	0.564839i
$376$		0			0
$377$	−1.31346	−	1.31346i	−0.0676466	−	0.0676466i
$378$		0			0
$379$	−10.8059	+	10.8059i	−0.555061	+	0.555061i	−0.927897	−	0.372836i	$-0.878385\pi$
$379$	−10.8059	+	10.8059i	−0.555061	+	0.555061i	0.372836	+	0.927897i	$0.378385\pi$
$380$		0			0
$381$	8.89383	+	8.89383i	0.455644	+	0.455644i
$382$		0			0
$383$	17.8896	−	17.8896i	0.914118	−	0.914118i	−0.0824750	−	0.996593i	$-0.526282\pi$
$383$	17.8896	−	17.8896i	0.914118	−	0.914118i	0.996593	+	0.0824750i	$0.0262825\pi$
$384$		0			0
$385$	18.8959	+	12.7374i	0.963022	+	0.649157i
$386$		0			0
$387$			5.87147i			0.298464i
$388$		0			0
$389$	15.1376	+	15.1376i	0.767509	+	0.767509i	0.977667	−	0.210159i	$-0.0673981\pi$
$389$	15.1376	+	15.1376i	0.767509	+	0.767509i	−0.210159	+	0.977667i	$0.567398\pi$
$390$		0			0
$391$	42.2945			2.13893
$392$		0			0
$393$	−5.04824	+	5.04824i	−0.254650	+	0.254650i
$394$		0			0
$395$	11.0304	+	7.43542i	0.555001	+	0.374117i
$396$		0			0
$397$	17.2400			0.865251			0.432626	−	0.901574i	$-0.357587\pi$
$397$	17.2400			0.865251			0.432626	+	0.901574i	$0.357587\pi$
$398$		0			0
$399$	−1.41923			−0.0710505
$400$		0			0
$401$	−9.32631			−0.465734			−0.232867	−	0.972509i	$-0.574811\pi$
$401$	−9.32631			−0.465734			−0.232867	+	0.972509i	$0.574811\pi$
$402$		0			0
$403$	−0.992201			−0.0494251
$404$		0			0
$405$	−1.85415	−	1.24985i	−0.0921335	−	0.0621056i
$406$		0			0
$407$	20.4117	−	20.4117i	1.01177	−	1.01177i
$408$		0			0
$409$	25.0691			1.23959			0.619793	−	0.784765i	$-0.287216\pi$
$409$	25.0691			1.23959			0.619793	+	0.784765i	$0.287216\pi$
$410$		0			0
$411$	8.94353	+	8.94353i	0.441152	+	0.441152i
$412$		0			0
$413$			21.2950i			1.04786i
$414$		0			0
$415$	5.19186	+	3.49975i	0.254858	+	0.171796i
$416$		0			0
$417$	1.67569	−	1.67569i	0.0820588	−	0.0820588i
$418$		0			0
$419$	−19.5372	−	19.5372i	−0.954452	−	0.954452i	0.0445546	−	0.999007i	$-0.485813\pi$
$419$	−19.5372	−	19.5372i	−0.954452	−	0.954452i	−0.999007	+	0.0445546i	$0.985813\pi$
$420$		0			0
$421$	19.4102	−	19.4102i	0.945996	−	0.945996i	−0.0526183	−	0.998615i	$-0.516757\pi$
$421$	19.4102	−	19.4102i	0.945996	−	0.945996i	0.998615	+	0.0526183i	$0.0167567\pi$
$422$		0			0
$423$	5.51736	+	5.51736i	0.268263	+	0.268263i
$424$		0			0
$425$	21.9346	+	9.29555i	1.06398	+	0.450901i
$426$		0			0
$427$	5.19040			0.251181
$428$		0			0
$429$	−0.851568	+	0.851568i	−0.0411141	+	0.0411141i
$430$		0			0
$431$		−	18.4295i		−	0.887718i	−0.896097	−	0.443859i	$-0.853609\pi$
$431$		−	18.4295i		−	0.887718i	0.896097	−	0.443859i	$-0.146391\pi$
$432$		0			0
$433$	24.9318	+	24.9318i	1.19815	+	1.19815i	0.974721	+	0.223425i	$0.0717238\pi$
$433$	24.9318	+	24.9318i	1.19815	+	1.19815i	0.223425	+	0.974721i	$0.428276\pi$
$434$		0			0
$435$	12.4128	−	2.41657i	0.595147	−	0.115865i
$436$		0			0
$437$			4.53268i			0.216827i
$438$		0			0
$439$		−	13.7877i		−	0.658050i	−0.944321	−	0.329025i	$-0.893280\pi$
$439$		−	13.7877i		−	0.658050i	0.944321	−	0.329025i	$-0.106720\pi$
$440$		0			0
$441$		−	0.725284i		−	0.0345373i
$442$		0			0
$443$			3.84992i			0.182915i	0.995809	+	0.0914577i	$0.0291526\pi$
$443$			3.84992i			0.182915i	−0.995809	+	0.0914577i	$0.970847\pi$
$444$		0			0
$445$	19.0653	+	12.8516i	0.903783	+	0.609225i
$446$		0			0
$447$	−1.65655	−	1.65655i	−0.0783524	−	0.0783524i
$448$		0			0
$449$			16.4518i			0.776410i	0.921573	+	0.388205i	$0.126905\pi$
$449$			16.4518i			0.776410i	−0.921573	+	0.388205i	$0.873095\pi$
$450$		0			0
$451$	−20.4828	+	20.4828i	−0.964498	+	0.964498i
$452$		0			0
$453$	−9.40919			−0.442082
$454$		0			0
$455$	0.390089	+	2.00371i	0.0182877	+	0.0939352i
$456$		0			0
$457$	−10.1758	−	10.1758i	−0.476005	−	0.476005i	0.427846	−	0.903851i	$-0.359272\pi$
$457$	−10.1758	−	10.1758i	−0.476005	−	0.476005i	−0.903851	+	0.427846i	$0.859272\pi$
$458$		0			0
$459$	3.36908	−	3.36908i	0.157255	−	0.157255i
$460$		0			0
$461$	21.3206	+	21.3206i	0.992997	+	0.992997i	0.999976	−	0.00697835i	$-0.00222130\pi$
$461$	21.3206	+	21.3206i	0.992997	+	0.992997i	−0.00697835	+	0.999976i	$0.502221\pi$
$462$		0			0
$463$	−4.62419	+	4.62419i	−0.214904	+	0.214904i	−0.806347	−	0.591443i	$-0.798559\pi$
$463$	−4.62419	+	4.62419i	−0.214904	+	0.214904i	0.591443	+	0.806347i	$0.298559\pi$
$464$		0			0
$465$	3.77562	−	5.60112i	0.175090	−	0.259746i
$466$		0			0
$467$		−	22.4668i		−	1.03964i	−0.854276	−	0.519819i	$-0.825999\pi$
$467$		−	22.4668i		−	1.03964i	0.854276	−	0.519819i	$-0.174001\pi$
$468$		0			0
$469$	19.2916	+	19.2916i	0.890801	+	0.890801i
$470$		0			0
$471$	−15.5285			−0.715516
$472$		0			0
$473$	−15.2229	+	15.2229i	−0.699948	+	0.699948i
$474$		0			0
$475$	−0.996198	+	2.35072i	−0.0457087	+	0.107858i
$476$		0			0
$477$	13.6546			0.625201
$478$		0			0
$479$	−15.4368			−0.705323			−0.352662	−	0.935751i	$-0.614723\pi$
$479$	−15.4368			−0.705323			−0.352662	+	0.935751i	$0.614723\pi$
$480$		0			0
$481$	2.58583			0.117904
$482$		0			0
$483$	−24.6726			−1.12264
$484$		0			0
$485$	−1.66700	+	0.324537i	−0.0756945	+	0.0147365i
$486$		0			0
$487$	−7.05304	+	7.05304i	−0.319604	+	0.319604i	−0.848615	−	0.529011i	$-0.822563\pi$
$487$	−7.05304	+	7.05304i	−0.319604	+	0.319604i	0.529011	+	0.848615i	$0.322563\pi$
$488$		0			0
$489$	−4.41190			−0.199513
$490$		0			0
$491$	4.18235	+	4.18235i	0.188747	+	0.188747i	0.795154	−	0.606407i	$-0.207390\pi$
$491$	4.18235	+	4.18235i	0.188747	+	0.188747i	−0.606407	+	0.795154i	$0.707390\pi$
$492$		0			0
$493$			26.9456i			1.21357i
$494$		0			0
$495$	−1.56676	−	8.04769i	−0.0704204	−	0.361717i
$496$		0			0
$497$	15.8740	−	15.8740i	0.712048	−	0.712048i
$498$		0			0
$499$	12.8087	+	12.8087i	0.573395	+	0.573395i	0.933076	−	0.359680i	$-0.117114\pi$
$499$	12.8087	+	12.8087i	0.573395	+	0.573395i	−0.359680	+	0.933076i	$0.617114\pi$
$500$		0			0
$501$	1.70055	−	1.70055i	0.0759750	−	0.0759750i
$502$		0			0
$503$	13.5229	+	13.5229i	0.602956	+	0.602956i	0.941096	−	0.338140i	$-0.109798\pi$
$503$	13.5229	+	13.5229i	0.602956	+	0.602956i	−0.338140	+	0.941096i	$0.609798\pi$
$504$		0			0
$505$	−21.7561	+	4.23556i	−0.968133	+	0.188480i
$506$		0			0
$507$	12.8921			0.572559
$508$		0			0
$509$	9.46330	−	9.46330i	0.419454	−	0.419454i	−0.465562	−	0.885015i	$-0.654148\pi$
$509$	9.46330	−	9.46330i	0.419454	−	0.419454i	0.885015	+	0.465562i	$0.154148\pi$
$510$		0			0
$511$		−	0.656887i		−	0.0290590i
$512$		0			0
$513$	0.361062	+	0.361062i	0.0159413	+	0.0159413i
$514$		0			0
$515$	4.92256	+	25.2849i	0.216914	+	1.11419i
$516$		0			0
$517$			28.6096i			1.25825i
$518$		0			0
$519$		−	15.0010i		−	0.658472i
$520$		0			0
$521$		−	40.1350i		−	1.75834i	−0.476504	−	0.879172i	$-0.658096\pi$
$521$		−	40.1350i		−	1.75834i	0.476504	−	0.879172i	$-0.341904\pi$
$522$		0			0
$523$		−	26.6375i		−	1.16477i	−0.812911	−	0.582387i	$-0.802119\pi$
$523$		−	26.6375i		−	1.16477i	0.812911	−	0.582387i	$-0.197881\pi$
$524$		0			0
$525$	−12.7956	−	5.42258i	−0.558446	−	0.236661i
$526$		0			0
$527$	10.1775	+	10.1775i	0.443338	+	0.443338i
$528$		0			0
$529$			55.7983i			2.42601i
$530$		0			0
$531$	5.41759	−	5.41759i	0.235103	−	0.235103i
$532$		0			0
$533$	−2.59484			−0.112395
$534$		0			0
$535$	23.7547	+	16.0127i	1.02701	+	0.692288i
$536$		0			0
$537$	8.06006	+	8.06006i	0.347817	+	0.347817i
$538$		0			0
$539$	1.88043	−	1.88043i	0.0809959	−	0.0809959i
$540$		0			0
$541$	13.3757	+	13.3757i	0.575067	+	0.575067i	0.933540	−	0.358473i	$-0.116703\pi$
$541$	13.3757	+	13.3757i	0.575067	+	0.575067i	−0.358473	+	0.933540i	$0.616703\pi$
$542$		0			0
$543$	−12.4443	+	12.4443i	−0.534037	+	0.534037i
$544$		0			0
$545$	−14.4348	+	2.81023i	−0.618320	+	0.120377i
$546$		0			0
$547$		−	22.1477i		−	0.946967i	−0.880803	−	0.473484i	$-0.842996\pi$
$547$		−	22.1477i		−	0.946967i	0.880803	−	0.473484i	$-0.157004\pi$
$548$		0			0
$549$	−1.32047	−	1.32047i	−0.0563563	−	0.0563563i
$550$		0			0
$551$	−2.88774			−0.123022
$552$		0			0
$553$	11.6920	−	11.6920i	0.497195	−	0.497195i
$554$		0			0
$555$	−9.83984	+	14.5974i	−0.417678	+	0.619624i
$556$		0			0
$557$	−43.6968			−1.85149			−0.925746	−	0.378146i	$-0.876562\pi$
$557$	−43.6968			−1.85149			−0.925746	+	0.378146i	$0.876562\pi$
$558$		0			0
$559$	−1.92849			−0.0815663
$560$		0			0
$561$	17.4699			0.737580
$562$		0			0
$563$	2.28960			0.0964951			0.0482475	−	0.998835i	$-0.484636\pi$
$563$	2.28960			0.0964951			0.0482475	+	0.998835i	$0.484636\pi$
$564$		0			0
$565$	−5.39265	−	27.6995i	−0.226871	−	1.16533i
$566$		0			0
$567$	−1.96536	+	1.96536i	−0.0825374	+	0.0825374i
$568$		0			0
$569$	−3.49978			−0.146718			−0.0733592	−	0.997306i	$-0.523372\pi$
$569$	−3.49978			−0.146718			−0.0733592	+	0.997306i	$0.523372\pi$
$570$		0			0
$571$	18.9855	+	18.9855i	0.794519	+	0.794519i	0.982225	−	0.187707i	$-0.0601054\pi$
$571$	18.9855	+	18.9855i	0.794519	+	0.794519i	−0.187707	+	0.982225i	$0.560105\pi$
$572$		0			0
$573$			13.0787i			0.546370i
$574$		0			0
$575$	−17.3184	+	40.8660i	−0.722227	+	1.70423i
$576$		0			0
$577$	−21.0061	+	21.0061i	−0.874494	+	0.874494i	−0.992958	−	0.118464i	$-0.962203\pi$
$577$	−21.0061	+	21.0061i	−0.874494	+	0.874494i	0.118464	+	0.992958i	$0.462203\pi$
$578$		0			0
$579$	−15.0162	−	15.0162i	−0.624051	−	0.624051i
$580$		0			0
$581$	5.50326	−	5.50326i	0.228314	−	0.228314i
$582$		0			0
$583$	35.4020	+	35.4020i	1.46620	+	1.46620i
$584$		0			0
$585$	0.410514	−	0.608997i	0.0169727	−	0.0251789i
$586$		0			0
$587$	8.65348			0.357167			0.178584	−	0.983925i	$-0.442848\pi$
$587$	8.65348			0.357167			0.178584	+	0.983925i	$0.442848\pi$
$588$		0			0
$589$	−1.09071	+	1.09071i	−0.0449421	+	0.0449421i
$590$		0			0
$591$		−	4.49246i		−	0.184795i
$592$		0			0
$593$	−14.6188	−	14.6188i	−0.600323	−	0.600323i	0.340075	−	0.940398i	$-0.389548\pi$
$593$	−14.6188	−	14.6188i	−0.600323	−	0.600323i	−0.940398	+	0.340075i	$0.889548\pi$
$594$		0			0
$595$	16.5517	−	24.5543i	0.678552	−	1.00663i
$596$		0			0
$597$			2.17777i			0.0891302i
$598$		0			0
$599$		−	1.77632i		−	0.0725785i	−0.999341	−	0.0362892i	$-0.988446\pi$
$599$		−	1.77632i		−	0.0725785i	0.999341	−	0.0362892i	$-0.0115538\pi$
$600$		0			0
$601$			18.3608i			0.748952i	0.927237	+	0.374476i	$0.122177\pi$
$601$			18.3608i			0.748952i	−0.927237	+	0.374476i	$0.877823\pi$
$602$		0			0
$603$		−	9.81578i		−	0.399730i
$604$		0			0
$605$	3.05465	−	4.53157i	0.124189	−	0.184234i
$606$		0			0
$607$	10.3710	+	10.3710i	0.420946	+	0.420946i	0.885529	−	0.464583i	$-0.153796\pi$
$607$	10.3710	+	10.3710i	0.420946	+	0.420946i	−0.464583	+	0.885529i	$0.653796\pi$
$608$		0			0
$609$		−	15.7188i		−	0.636957i
$610$		0			0
$611$	−1.81218	+	1.81218i	−0.0733130	+	0.0733130i
$612$		0			0
$613$	2.01402			0.0813455			0.0406727	−	0.999173i	$-0.487050\pi$
$613$	2.01402			0.0813455			0.0406727	+	0.999173i	$0.487050\pi$
$614$		0			0
$615$	9.87412	−	14.6482i	0.398163	−	0.590674i
$616$		0			0
$617$	−17.7461	−	17.7461i	−0.714431	−	0.714431i	0.253028	−	0.967459i	$-0.418573\pi$
$617$	−17.7461	−	17.7461i	−0.714431	−	0.714431i	−0.967459	+	0.253028i	$0.918573\pi$
$618$		0			0
$619$	−19.7692	+	19.7692i	−0.794590	+	0.794590i	−0.982237	−	0.187647i	$-0.939914\pi$
$619$	−19.7692	+	19.7692i	−0.794590	+	0.794590i	0.187647	+	0.982237i	$0.439914\pi$
$620$		0			0
$621$	6.27687	+	6.27687i	0.251882	+	0.251882i
$622$		0			0
$623$	20.2089	−	20.2089i	0.809651	−	0.809651i
$624$		0			0
$625$	−17.9632	+	17.3875i	−0.718527	+	0.695499i
$626$		0			0
$627$			1.87224i			0.0747700i
$628$		0			0
$629$	−26.5241	−	26.5241i	−1.05759	−	1.05759i
$630$		0			0
$631$	4.44887			0.177107			0.0885534	−	0.996071i	$-0.471776\pi$
$631$	4.44887			0.177107			0.0885534	+	0.996071i	$0.471776\pi$
$632$		0			0
$633$	−13.3900	+	13.3900i	−0.532205	+	0.532205i
$634$		0			0
$635$	−5.37453	−	27.6064i	−0.213282	−	1.09553i
$636$		0			0
$637$	0.238220			0.00943861
$638$		0			0
$639$	−8.07691			−0.319518
$640$		0			0
$641$	8.90582			0.351759			0.175879	−	0.984412i	$-0.443723\pi$
$641$	8.90582			0.351759			0.175879	+	0.984412i	$0.443723\pi$
$642$		0			0
$643$	31.8622			1.25652			0.628261	−	0.778003i	$-0.283767\pi$
$643$	31.8622			1.25652			0.628261	+	0.778003i	$0.283767\pi$
$644$		0			0
$645$	7.33846	−	10.8866i	0.288952	−	0.428659i
$646$		0			0
$647$	−22.4710	+	22.4710i	−0.883426	+	0.883426i	−0.993881	−	0.110455i	$-0.964769\pi$
$647$	−22.4710	+	22.4710i	−0.883426	+	0.883426i	0.110455	+	0.993881i	$0.464769\pi$
$648$		0			0
$649$	28.0922			1.10271
$650$		0			0
$651$	−5.93707	−	5.93707i	−0.232692	−	0.232692i
$652$		0			0
$653$		−	24.4911i		−	0.958410i	−0.877703	−	0.479205i	$-0.840925\pi$
$653$		−	24.4911i		−	0.958410i	0.877703	−	0.479205i	$-0.159075\pi$
$654$		0			0
$655$	15.6698	−	3.05065i	0.612268	−	0.119199i
$656$		0			0
$657$	−0.167116	+	0.167116i	−0.00651982	+	0.00651982i
$658$		0			0
$659$	−1.67655	−	1.67655i	−0.0653092	−	0.0653092i	0.673698	−	0.739007i	$-0.264705\pi$
$659$	−1.67655	−	1.67655i	−0.0653092	−	0.0653092i	−0.739007	+	0.673698i	$0.764705\pi$
$660$		0			0
$661$	5.00448	−	5.00448i	0.194652	−	0.194652i	−0.603051	−	0.797703i	$-0.706048\pi$
$661$	5.00448	−	5.00448i	0.194652	−	0.194652i	0.797703	+	0.603051i	$0.206048\pi$
$662$		0			0
$663$	1.10658	+	1.10658i	0.0429758	+	0.0429758i
$664$		0			0
$665$	2.63147	+	1.77383i	0.102044	+	0.0687862i
$666$		0			0
$667$	−50.2019			−1.94383
$668$		0			0
$669$	13.9939	−	13.9939i	0.541035	−	0.541035i
$670$		0			0
$671$		−	6.84712i		−	0.264330i
$672$		0			0
$673$	−33.7116	−	33.7116i	−1.29948	−	1.29948i	−0.928731	−	0.370753i	$-0.879099\pi$
$673$	−33.7116	−	33.7116i	−1.29948	−	1.29948i	−0.370753	−	0.928731i	$-0.620901\pi$
$674$		0			0
$675$	1.87574	+	4.63482i	0.0721974	+	0.178394i
$676$		0			0
$677$		−	20.5805i		−	0.790972i	−0.918472	−	0.395486i	$-0.870576\pi$
$677$		−	20.5805i		−	0.790972i	0.918472	−	0.395486i	$-0.129424\pi$
$678$		0			0
$679$			2.11099i			0.0810122i
$680$		0			0
$681$		−	27.3648i		−	1.04862i
$682$		0			0
$683$		−	9.74375i		−	0.372834i	−0.982471	−	0.186417i	$-0.940312\pi$
$683$		−	9.74375i		−	0.372834i	0.982471	−	0.186417i	$-0.0596876\pi$
$684$		0			0
$685$	−5.40456	−	27.7607i	−0.206498	−	1.06068i
$686$		0			0
$687$	−6.18602	−	6.18602i	−0.236011	−	0.236011i
$688$		0			0
$689$			4.48486i			0.170859i
$690$		0			0
$691$	−0.547587	+	0.547587i	−0.0208312	+	0.0208312i	−0.717446	−	0.696614i	$-0.754689\pi$
$691$	−0.547587	+	0.547587i	−0.0208312	+	0.0208312i	0.696614	+	0.717446i	$0.254689\pi$
$692$		0			0
$693$	−10.1911			−0.387128
$694$		0			0
$695$	−5.20134	+	1.01262i	−0.197298	+	0.0384107i
$696$		0			0
$697$	26.6165	+	26.6165i	1.00817	+	1.00817i
$698$		0			0
$699$	16.9076	−	16.9076i	0.639505	−	0.639505i
$700$		0			0
$701$	23.4694	+	23.4694i	0.886428	+	0.886428i	0.994178	−	0.107750i	$-0.0343645\pi$
$701$	23.4694	+	23.4694i	0.886428	+	0.886428i	−0.107750	+	0.994178i	$0.534364\pi$
$702$		0			0
$703$	2.84257	−	2.84257i	0.107210	−	0.107210i
$704$		0			0
$705$	−3.33414	−	17.1259i	−0.125571	−	0.644999i
$706$		0			0
$707$			27.5506i			1.03615i
$708$		0			0
$709$	−4.85224	−	4.85224i	−0.182230	−	0.182230i	0.610097	−	0.792327i	$-0.291130\pi$
$709$	−4.85224	−	4.85224i	−0.182230	−	0.182230i	−0.792327	+	0.610097i	$0.791130\pi$
$710$		0			0
$711$	−5.94905			−0.223107
$712$		0			0
$713$	−18.9615	+	18.9615i	−0.710114	+	0.710114i
$714$		0			0
$715$	2.64327	−	0.514602i	0.0988526	−	0.0192450i
$716$		0			0
$717$	−1.90480			−0.0711362
$718$		0			0
$719$	−4.46550			−0.166535			−0.0832676	−	0.996527i	$-0.526536\pi$
$719$	−4.46550			−0.166535			−0.0832676	+	0.996527i	$0.526536\pi$
$720$		0			0
$721$	32.0193			1.19246
$722$		0			0
$723$	−23.0653			−0.857809
$724$		0			0
$725$	−26.0355	−	11.0334i	−0.966934	−	0.409772i
$726$		0			0
$727$	−8.26309	+	8.26309i	−0.306461	+	0.306461i	−0.843535	−	0.537074i	$-0.819530\pi$
$727$	−8.26309	+	8.26309i	−0.306461	+	0.306461i	0.537074	+	0.843535i	$0.319530\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	19.7814	+	19.7814i	0.731643	+	0.731643i
$732$		0			0
$733$		−	4.71219i		−	0.174049i	−0.996206	−	0.0870244i	$-0.972264\pi$
$733$		−	4.71219i		−	0.174049i	0.996206	−	0.0870244i	$-0.0277358\pi$
$734$		0			0
$735$	−0.906496	+	1.34478i	−0.0334366	+	0.0496031i
$736$		0			0
$737$	25.4492	−	25.4492i	0.937434	−	0.937434i
$738$		0			0
$739$	−0.159375	−	0.159375i	−0.00586271	−	0.00586271i	0.704169	−	0.710032i	$-0.251320\pi$
$739$	−0.159375	−	0.159375i	−0.00586271	−	0.00586271i	−0.710032	+	0.704169i	$0.751320\pi$
$740$		0			0
$741$	−0.118591	+	0.118591i	−0.00435655	+	0.00435655i
$742$		0			0
$743$	−16.1456	−	16.1456i	−0.592324	−	0.592324i	0.345934	−	0.938259i	$-0.387562\pi$
$743$	−16.1456	−	16.1456i	−0.592324	−	0.592324i	−0.938259	+	0.345934i	$0.887562\pi$
$744$		0			0
$745$	1.00105	+	5.14195i	0.0366758	+	0.188386i
$746$		0			0
$747$	−2.80013			−0.102451
$748$		0			0
$749$	25.1795	−	25.1795i	0.920040	−	0.920040i
$750$		0			0
$751$		−	23.4293i		−	0.854946i	−0.904028	−	0.427473i	$-0.859404\pi$
$751$		−	23.4293i		−	0.854946i	0.904028	−	0.427473i	$-0.140596\pi$
$752$		0			0
$753$	−17.1103	−	17.1103i	−0.623533	−	0.623533i
$754$		0			0
$755$	17.4460	+	11.7601i	0.634926	+	0.427993i
$756$		0			0
$757$			21.6310i			0.786191i	0.919498	+	0.393096i	$0.128596\pi$
$757$			21.6310i			0.786191i	−0.919498	+	0.393096i	$0.871404\pi$
$758$		0			0
$759$			32.5479i			1.18141i
$760$		0			0
$761$		−	5.69977i		−	0.206617i	−0.994649	−	0.103308i	$-0.967057\pi$
$761$		−	5.69977i		−	0.206617i	0.994649	−	0.103308i	$-0.0329428\pi$
$762$		0			0
$763$			18.2794i			0.661758i
$764$		0			0
$765$	−10.4576	+	2.03593i	−0.378096	+	0.0736092i
$766$		0			0
$767$	1.77941	+	1.77941i	0.0642507	+	0.0642507i
$768$		0			0
$769$		−	37.8742i		−	1.36578i	−0.730522	−	0.682889i	$-0.760723\pi$
$769$		−	37.8742i		−	1.36578i	0.730522	−	0.682889i	$-0.239277\pi$
$770$		0			0
$771$	4.11987	−	4.11987i	0.148374	−	0.148374i
$772$		0			0
$773$	1.09218			0.0392830			0.0196415	−	0.999807i	$-0.493748\pi$
$773$	1.09218			0.0392830			0.0196415	+	0.999807i	$0.493748\pi$
$774$		0			0
$775$	−14.0011	+	5.66635i	−0.502935	+	0.203541i
$776$		0			0
$777$	15.4729	+	15.4729i	0.555088	+	0.555088i
$778$		0			0
$779$	−2.85247	+	2.85247i	−0.102200	+	0.102200i
$780$		0			0
$781$	−20.9409	−	20.9409i	−0.749323	−	0.749323i
$782$		0			0
$783$	−3.99896	+	3.99896i	−0.142911	+	0.142911i
$784$		0			0
$785$	28.7922	+	19.4083i	1.02764	+	0.692713i
$786$		0			0
$787$		−	3.77885i		−	0.134701i	−0.997729	−	0.0673507i	$-0.978545\pi$
$787$		−	3.77885i		−	0.134701i	0.997729	−	0.0673507i	$-0.0214546\pi$
$788$		0			0
$789$	17.0258	+	17.0258i	0.606134	+	0.606134i
$790$		0			0
$791$	−35.0770			−1.24720
$792$		0			0
$793$	0.433709	−	0.433709i	0.0154015	−	0.0154015i
$794$		0			0
$795$	−25.3177	−	17.0662i	−0.897925	−	0.605276i
$796$		0			0
$797$	−18.4489			−0.653492			−0.326746	−	0.945112i	$-0.605952\pi$
$797$	−18.4489			−0.653492			−0.326746	+	0.945112i	$0.605952\pi$
$798$		0			0
$799$	37.1769			1.31522
$800$		0			0
$801$	−10.2825			−0.363315
$802$		0			0
$803$	−0.866559			−0.0305802
$804$		0			0
$805$	45.7468	+	30.8371i	1.61236	+	1.08687i
$806$		0			0
$807$	2.02914	−	2.02914i	0.0714293	−	0.0714293i
$808$		0			0
$809$	−36.4892			−1.28289			−0.641446	−	0.767168i	$-0.721665\pi$
$809$	−36.4892			−1.28289			−0.641446	+	0.767168i	$0.721665\pi$
$810$		0			0
$811$	7.01356	+	7.01356i	0.246279	+	0.246279i	0.819442	−	0.573162i	$-0.194284\pi$
$811$	7.01356	+	7.01356i	0.246279	+	0.246279i	−0.573162	+	0.819442i	$0.694284\pi$
$812$		0			0
$813$		−	17.1830i		−	0.602634i
$814$		0			0
$815$	8.18032	+	5.51422i	0.286544	+	0.193155i
$816$		0			0
$817$	−2.11996	+	2.11996i	−0.0741681	+	0.0741681i
$818$		0			0
$819$	−0.645524	−	0.645524i	−0.0225564	−	0.0225564i
$820$		0			0
$821$	−33.0652	+	33.0652i	−1.15398	+	1.15398i	−0.168235	+	0.985747i	$0.553807\pi$
$821$	−33.0652	+	33.0652i	−1.15398	+	1.15398i	−0.985747	+	0.168235i	$0.946193\pi$
$822$		0			0
$823$	−34.1975	−	34.1975i	−1.19205	−	1.19205i	−0.976490	−	0.215561i	$-0.930842\pi$
$823$	−34.1975	−	34.1975i	−1.19205	−	1.19205i	−0.215561	−	0.976490i	$-0.569158\pi$
$824$		0			0
$825$	−7.15342	+	16.8798i	−0.249050	+	0.587681i
$826$		0			0
$827$	−2.06318			−0.0717439			−0.0358720	−	0.999356i	$-0.511421\pi$
$827$	−2.06318			−0.0717439			−0.0358720	+	0.999356i	$0.511421\pi$
$828$		0			0
$829$	−19.1593	+	19.1593i	−0.665430	+	0.665430i	−0.956655	−	0.291225i	$-0.905937\pi$
$829$	−19.1593	+	19.1593i	−0.665430	+	0.665430i	0.291225	+	0.956655i	$0.405937\pi$
$830$		0			0
$831$			6.31808i			0.219172i
$832$		0			0
$833$	−2.44354	−	2.44354i	−0.0846635	−	0.0846635i
$834$		0			0
$835$	−5.27851	+	1.02764i	−0.182670	+	0.0355630i
$836$		0			0
$837$			3.02085i			0.104416i
$838$		0			0
$839$		−	33.2213i		−	1.14693i	−0.819231	−	0.573463i	$-0.805600\pi$
$839$		−	33.2213i		−	1.14693i	0.819231	−	0.573463i	$-0.194400\pi$
$840$		0			0
$841$		−	2.98333i		−	0.102874i
$842$		0			0
$843$			19.5262i			0.672517i
$844$		0			0
$845$	−23.9039	−	16.1132i	−0.822320	−	0.554312i
$846$		0			0
$847$	−4.80337	−	4.80337i	−0.165046	−	0.165046i
$848$		0			0
$849$			24.8436i			0.852631i
$850$		0			0
$851$	49.4166	−	49.4166i	1.69398	−	1.69398i
$852$		0			0
$853$	−28.7388			−0.983998			−0.491999	−	0.870596i	$-0.663734\pi$
$853$	−28.7388			−0.983998			−0.491999	+	0.870596i	$0.663734\pi$
$854$		0			0
$855$	−0.218189	−	1.12074i	−0.00746191	−	0.0383284i
$856$		0			0
$857$	6.08056	+	6.08056i	0.207708	+	0.207708i	0.803293	−	0.595585i	$-0.203080\pi$
$857$	6.08056	+	6.08056i	0.207708	+	0.207708i	−0.595585	+	0.803293i	$0.703080\pi$
$858$		0			0
$859$	7.01497	−	7.01497i	0.239348	−	0.239348i	−0.577232	−	0.816580i	$-0.695867\pi$
$859$	7.01497	−	7.01497i	0.239348	−	0.239348i	0.816580	+	0.577232i	$0.195867\pi$
$860$		0			0
$861$	−15.5268	−	15.5268i	−0.529153	−	0.529153i
$862$		0			0
$863$	18.1343	−	18.1343i	0.617300	−	0.617300i	−0.327538	−	0.944838i	$-0.606219\pi$
$863$	18.1343	−	18.1343i	0.617300	−	0.617300i	0.944838	+	0.327538i	$0.106219\pi$
$864$		0			0
$865$	−18.7490	+	27.8141i	−0.637487	+	0.945709i
$866$		0			0
$867$		−	5.70137i		−	0.193629i
$868$		0			0
$869$	−15.4240	−	15.4240i	−0.523223	−	0.523223i
$870$		0			0
$871$	3.22400			0.109241
$872$		0			0
$873$	0.537048	−	0.537048i	0.0181763	−	0.0181763i
$874$		0			0
$875$	16.9476	+	26.0469i	0.572932	+	0.880546i
$876$		0			0
$877$	−49.4950			−1.67133			−0.835665	−	0.549240i	$-0.814917\pi$
$877$	−49.4950			−1.67133			−0.835665	+	0.549240i	$0.814917\pi$
$878$		0			0
$879$	29.0203			0.978832
$880$		0			0
$881$	4.94736			0.166681			0.0833404	−	0.996521i	$-0.473441\pi$
$881$	4.94736			0.166681			0.0833404	+	0.996521i	$0.473441\pi$
$882$		0			0
$883$	−11.9844			−0.403308			−0.201654	−	0.979457i	$-0.564632\pi$
$883$	−11.9844			−0.403308			−0.201654	+	0.979457i	$0.564632\pi$
$884$		0			0
$885$	−16.8162	+	3.27384i	−0.565270	+	0.110049i
$886$		0			0
$887$	−11.2856	+	11.2856i	−0.378932	+	0.378932i	−0.870717	−	0.491785i	$-0.836345\pi$
$887$	−11.2856	+	11.2856i	−0.378932	+	0.378932i	0.491785	+	0.870717i	$0.336345\pi$
$888$		0			0
$889$	−34.9591			−1.17249
$890$		0			0
$891$	2.59268	+	2.59268i	0.0868582	+	0.0868582i
$892$		0			0
$893$			3.98422i			0.133327i
$894$		0			0
$895$	−4.87069	−	25.0184i	−0.162809	−	0.836274i
$896$		0			0
$897$	−2.06164	+	2.06164i	−0.0688362	+	0.0688362i
$898$		0			0
$899$	−12.0803	−	12.0803i	−0.402899	−	0.402899i
$900$		0			0
$901$	46.0034	−	46.0034i	1.53259	−	1.53259i
$902$		0			0
$903$	−11.5396	−	11.5396i	−0.384012	−	0.384012i
$904$		0			0
$905$	38.6272	−	7.52009i	1.28401	−	0.249976i
$906$		0			0
$907$	26.9222			0.893938			0.446969	−	0.894549i	$-0.352503\pi$
$907$	26.9222			0.893938			0.446969	+	0.894549i	$0.352503\pi$
$908$		0			0
$909$	7.00905	−	7.00905i	0.232475	−	0.232475i
$910$		0			0
$911$			35.0373i			1.16084i	0.814319	+	0.580418i	$0.197111\pi$
$911$			35.0373i			1.16084i	−0.814319	+	0.580418i	$0.802889\pi$
$912$		0			0
$913$	−7.25985	−	7.25985i	−0.240266	−	0.240266i
$914$		0			0
$915$	0.797958	+	4.09874i	0.0263797	+	0.135500i
$916$		0			0
$917$		−	19.8432i		−	0.655282i
$918$		0			0
$919$		−	9.58700i		−	0.316246i	−0.987419	−	0.158123i	$-0.949456\pi$
$919$		−	9.58700i		−	0.316246i	0.987419	−	0.158123i	$-0.0505442\pi$
$920$		0			0
$921$			5.46765i			0.180165i
$922$		0			0
$923$		−	2.65286i		−	0.0873201i
$924$		0			0
$925$	36.4891	−	14.7674i	1.19975	−	0.485549i
$926$		0			0
$927$	−8.14591	−	8.14591i	−0.267547	−	0.267547i
$928$		0			0
$929$		−	37.6651i		−	1.23575i	−0.786275	−	0.617877i	$-0.787993\pi$
$929$		−	37.6651i		−	1.23575i	0.786275	−	0.617877i	$-0.212007\pi$
$930$		0			0
$931$	0.261872	−	0.261872i	0.00858251	−	0.00858251i
$932$		0			0
$933$	20.7682			0.679919
$934$		0			0
$935$	−32.3918	−	21.8348i	−1.05933	−	0.714074i
$936$		0			0
$937$	7.96119	+	7.96119i	0.260081	+	0.260081i	0.825087	−	0.565006i	$-0.191126\pi$
$937$	7.96119	+	7.96119i	0.260081	+	0.260081i	−0.565006	+	0.825087i	$0.691126\pi$
$938$		0			0
$939$	3.63603	−	3.63603i	0.118657	−	0.118657i
$940$		0			0
$941$	−18.5116	−	18.5116i	−0.603460	−	0.603460i	0.337769	−	0.941229i	$-0.390328\pi$
$941$	−18.5116	−	18.5116i	−0.603460	−	0.603460i	−0.941229	+	0.337769i	$0.890328\pi$
$942$		0			0
$943$	−49.5888	+	49.5888i	−1.61483	+	1.61483i
$944$		0			0
$945$	6.10048	−	1.18766i	0.198449	−	0.0386347i
$946$		0			0
$947$			28.4982i			0.926066i	0.886341	+	0.463033i	$0.153239\pi$
$947$			28.4982i			0.926066i	−0.886341	+	0.463033i	$0.846761\pi$
$948$		0			0
$949$	−0.0548894	−	0.0548894i	−0.00178179	−	0.00178179i
$950$		0			0
$951$	13.7806			0.446865
$952$		0			0
$953$	16.4326	−	16.4326i	0.532304	−	0.532304i	−0.388953	−	0.921257i	$-0.627163\pi$
$953$	16.4326	−	16.4326i	0.532304	−	0.532304i	0.921257	+	0.388953i	$0.127163\pi$
$954$		0			0
$955$	16.3464	−	24.2498i	0.528957	−	0.784706i
$956$		0			0
$957$	−20.7361			−0.670302
$958$		0			0
$959$	−35.1545			−1.13520
$960$		0			0
$961$	21.8744			0.705627
$962$		0			0
$963$	−12.8117			−0.412850
$964$		0			0
$965$	9.07425	+	46.6102i	0.292111	+	1.50044i
$966$		0			0
$967$	−17.0971	+	17.0971i	−0.549806	+	0.549806i	−0.926385	−	0.376578i	$-0.877101\pi$
$967$	−17.0971	+	17.0971i	−0.549806	+	0.549806i	0.376578	+	0.926385i	$0.377101\pi$
$968$		0			0
$969$	2.43289			0.0781557
$970$		0			0
$971$	18.3662	+	18.3662i	0.589400	+	0.589400i	0.937469	−	0.348069i	$-0.113162\pi$
$971$	18.3662	+	18.3662i	0.589400	+	0.589400i	−0.348069	+	0.937469i	$0.613162\pi$
$972$		0			0
$973$			6.58666i			0.211159i
$974$		0			0
$975$	−1.52231	+	0.616089i	−0.0487529	+	0.0197306i
$976$		0			0
$977$	−15.4378	+	15.4378i	−0.493898	+	0.493898i	−0.909532	−	0.415634i	$-0.863560\pi$
$977$	−15.4378	+	15.4378i	−0.493898	+	0.493898i	0.415634	+	0.909532i	$0.363560\pi$
$978$		0			0
$979$	−26.6593	−	26.6593i	−0.852035	−	0.852035i
$980$		0			0
$981$	4.65039	−	4.65039i	0.148476	−	0.148476i
$982$		0			0
$983$	−7.27569	−	7.27569i	−0.232059	−	0.232059i	0.581493	−	0.813551i	$-0.302469\pi$
$983$	−7.27569	−	7.27569i	−0.232059	−	0.232059i	−0.813551	+	0.581493i	$0.802469\pi$
$984$		0			0
$985$	−5.61490	+	8.32969i	−0.178906	+	0.265406i
$986$		0			0
$987$	−21.6872			−0.690312
$988$		0			0
$989$	−36.8545	+	36.8545i	−1.17190	+	1.17190i
$990$		0			0
$991$		−	33.6571i		−	1.06915i	−0.845120	−	0.534577i	$-0.820471\pi$
$991$		−	33.6571i		−	1.06915i	0.845120	−	0.534577i	$-0.179529\pi$
$992$		0			0
$993$	−1.33711	−	1.33711i	−0.0424320	−	0.0424320i
$994$		0			0
$995$	2.72189	−	4.03791i	0.0862897	−	0.128010i
$996$		0			0
$997$			23.5114i			0.744614i	0.928110	+	0.372307i	$0.121433\pi$
$997$			23.5114i			0.744614i	−0.928110	+	0.372307i	$0.878567\pi$
$998$		0			0
$999$		−	7.87281i		−	0.249085i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.y.f.943.2		20
4.3	odd	2		240.2.y.f.163.6	✓	20
5.2	odd	4		960.2.bc.f.367.7		20
8.3	odd	2		1920.2.y.l.223.9		20
8.5	even	2		1920.2.y.k.223.9		20
12.11	even	2		720.2.z.h.163.5		20
16.3	odd	4		1920.2.bc.l.1183.4		20
16.5	even	4		240.2.bc.f.43.1	yes	20
16.11	odd	4		960.2.bc.f.463.7		20
16.13	even	4		1920.2.bc.k.1183.4		20
20.7	even	4		240.2.bc.f.67.1	yes	20
40.27	even	4		1920.2.bc.k.607.4		20
40.37	odd	4		1920.2.bc.l.607.4		20
48.5	odd	4		720.2.bd.h.523.10		20
60.47	odd	4		720.2.bd.h.307.10		20
80.27	even	4	inner	960.2.y.f.847.2		20
80.37	odd	4		240.2.y.f.187.6	yes	20
80.67	even	4		1920.2.y.k.1567.9		20
80.77	odd	4		1920.2.y.l.1567.9		20
240.197	even	4		720.2.z.h.667.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.f.163.6	✓	20	4.3	odd	2
240.2.y.f.187.6	yes	20	80.37	odd	4
240.2.bc.f.43.1	yes	20	16.5	even	4
240.2.bc.f.67.1	yes	20	20.7	even	4
720.2.z.h.163.5		20	12.11	even	2
720.2.z.h.667.5		20	240.197	even	4
720.2.bd.h.307.10		20	60.47	odd	4
720.2.bd.h.523.10		20	48.5	odd	4
960.2.y.f.847.2		20	80.27	even	4	inner
960.2.y.f.943.2		20	1.1	even	1	trivial
960.2.bc.f.367.7		20	5.2	odd	4
960.2.bc.f.463.7		20	16.11	odd	4
1920.2.y.k.223.9		20	8.5	even	2
1920.2.y.k.1567.9		20	80.67	even	4
1920.2.y.l.223.9		20	8.3	odd	2
1920.2.y.l.1567.9		20	80.77	odd	4
1920.2.bc.k.607.4		20	40.27	even	4
1920.2.bc.k.1183.4		20	16.13	even	4
1920.2.bc.l.607.4		20	40.37	odd	4
1920.2.bc.l.1183.4		20	16.3	odd	4

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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.y (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +(-1.85415 - 1.24985i) q^{5} +(-1.96536 + 1.96536i) q^{7} +1.00000 q^{9} +(2.59268 + 2.59268i) q^{11} +0.328451i q^{13} +(-1.85415 - 1.24985i) q^{15} +(3.36908 - 3.36908i) q^{17} +(0.361062 + 0.361062i) q^{19} +(-1.96536 + 1.96536i) q^{21} +(6.27687 + 6.27687i) q^{23} +(1.87574 + 4.63482i) q^{25} +1.00000 q^{27} +(-3.99896 + 3.99896i) q^{29} +3.02085i q^{31} +(2.59268 + 2.59268i) q^{33} +(6.10048 - 1.18766i) q^{35} -7.87281i q^{37} +0.328451i q^{39} +7.90024i q^{41} +5.87147i q^{43} +(-1.85415 - 1.24985i) q^{45} +(5.51736 + 5.51736i) q^{47} -0.725284i q^{49} +(3.36908 - 3.36908i) q^{51} +13.6546 q^{53} +(-1.56676 - 8.04769i) q^{55} +(0.361062 + 0.361062i) q^{57} +(5.41759 - 5.41759i) q^{59} +(-1.32047 - 1.32047i) q^{61} +(-1.96536 + 1.96536i) q^{63} +(0.410514 - 0.608997i) q^{65} -9.81578i q^{67} +(6.27687 + 6.27687i) q^{69} -8.07691 q^{71} +(-0.167116 + 0.167116i) q^{73} +(1.87574 + 4.63482i) q^{75} -10.1911 q^{77} -5.94905 q^{79} +1.00000 q^{81} -2.80013 q^{83} +(-10.4576 + 2.03593i) q^{85} +(-3.99896 + 3.99896i) q^{87} -10.2825 q^{89} +(-0.645524 - 0.645524i) q^{91} +3.02085i q^{93} +(-0.218189 - 1.12074i) q^{95} +(0.537048 - 0.537048i) q^{97} +(2.59268 + 2.59268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{3} + 4 q^{7} + 20 q^{9} - 8 q^{11} + 12 q^{17} - 16 q^{19} + 4 q^{21} + 16 q^{23} + 4 q^{25} + 20 q^{27} - 8 q^{33} + 28 q^{35} + 12 q^{51} + 8 q^{53} + 4 q^{55} - 16 q^{57} + 16 q^{59} - 12 q^{61}+ \cdots - 8 q^{99}+O(q^{100}) \) 20 * q + 20 * q^3 + 4 * q^7 + 20 * q^9 - 8 * q^11 + 12 * q^17 - 16 * q^19 + 4 * q^21 + 16 * q^23 + 4 * q^25 + 20 * q^27 - 8 * q^33 + 28 * q^35 + 12 * q^51 + 8 * q^53 + 4 * q^55 - 16 * q^57 + 16 * q^59 - 12 * q^61 + 4 * q^63 + 4 * q^65 + 16 * q^69 - 20 * q^73 + 4 * q^75 - 48 * q^79 + 20 * q^81 + 24 * q^83 + 4 * q^85 + 40 * q^89 + 24 * q^91 + 72 * q^95 - 28 * q^97 - 8 * q^99

Introduction

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