LMFDB - Embedded newform 644.2.y.a.261.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(9,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 22, 30]))

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

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

chi := DirichletCharacter("644.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.y (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			261.16
Character	$\chi$	$=$	644.261
Dual form			644.2.y.a.417.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.97820 - 2.77799i) q^{3} +(3.68583 - 0.710386i) q^{5} +(-1.93087 + 1.80879i) q^{7} +(-2.82276 - 8.15583i) q^{9} +O(q^{10})$	\(q+(1.97820 - 2.77799i) q^{3} +(3.68583 - 0.710386i) q^{5} +(-1.93087 + 1.80879i) q^{7} +(-2.82276 - 8.15583i) q^{9} +(-2.00401 + 1.57597i) q^{11} +(-0.391321 + 0.251487i) q^{13} +(5.31786 - 11.6445i) q^{15} +(-2.85941 - 2.72644i) q^{17} +(0.488477 - 0.465762i) q^{19} +(1.20515 + 8.94210i) q^{21} +(4.50612 + 1.64161i) q^{23} +(8.43888 - 3.37842i) q^{25} +(-18.4242 - 5.40983i) q^{27} +(1.26245 - 0.370688i) q^{29} +(5.31369 - 0.507396i) q^{31} +(0.413703 + 8.68470i) q^{33} +(-5.83194 + 8.03857i) q^{35} +(2.76491 + 7.98869i) q^{37} +(-0.0754828 + 1.58458i) q^{39} +(1.24082 + 1.43198i) q^{41} +(5.22179 + 11.4341i) q^{43} +(-16.1980 - 28.0558i) q^{45} +(-3.71502 + 6.43460i) q^{47} +(0.456548 - 6.98510i) q^{49} +(-13.2305 + 2.54997i) q^{51} +(0.262450 - 5.50950i) q^{53} +(-6.26690 + 7.23238i) q^{55} +(-0.327578 - 2.27835i) q^{57} +(-4.99004 - 2.57254i) q^{59} +(-2.09478 - 2.94171i) q^{61} +(20.2026 + 10.6421i) q^{63} +(-1.26369 + 1.20493i) q^{65} +(6.10550 - 2.44428i) q^{67} +(13.4744 - 9.27053i) q^{69} +(0.274109 - 1.90647i) q^{71} +(-1.13958 - 4.69742i) q^{73} +(7.30857 - 30.1263i) q^{75} +(1.01889 - 6.66783i) q^{77} +(0.642995 + 13.4981i) q^{79} +(-31.1231 + 24.4755i) q^{81} +(-6.54603 + 7.55452i) q^{83} +(-12.4761 - 8.01791i) q^{85} +(1.46760 - 4.24036i) q^{87} +(2.89144 + 0.276099i) q^{89} +(0.300705 - 1.19341i) q^{91} +(9.10199 - 15.7651i) q^{93} +(1.46957 - 2.06373i) q^{95} +(3.97227 + 4.58425i) q^{97} +(18.5102 + 11.8958i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 6 q^{5} - 2 q^{7} + 12 q^{9}+O(q^{10}) $ 320 * q + 6 * q^5 - 2 * q^7 + 12 * q^9	$ 320 q + 6 q^{5} - 2 q^{7} + 12 q^{9} - 2 q^{11} - 16 q^{15} + 4 q^{17} - 50 q^{21} + 25 q^{23} + 44 q^{25} + 54 q^{27} + 12 q^{29} + 2 q^{31} - 12 q^{33} - 22 q^{35} - 44 q^{37} - 4 q^{39} + 12 q^{41} + 76 q^{43} - 114 q^{45} - 10 q^{47} - 74 q^{49} - 30 q^{51} - 20 q^{53} + 32 q^{55} + 52 q^{57} - 32 q^{59} + 74 q^{61} + 87 q^{63} - 75 q^{65} - 8 q^{67} + 10 q^{69} + 8 q^{73} + 118 q^{75} + 5 q^{77} - 40 q^{79} - 44 q^{81} - 52 q^{83} - 100 q^{85} + 84 q^{87} + 36 q^{89} + 30 q^{91} - 12 q^{93} - 25 q^{95} + 72 q^{97} + 2 q^{99}+O(q^{100}) $ 320 * q + 6 * q^5 - 2 * q^7 + 12 * q^9 - 2 * q^11 - 16 * q^15 + 4 * q^17 - 50 * q^21 + 25 * q^23 + 44 * q^25 + 54 * q^27 + 12 * q^29 + 2 * q^31 - 12 * q^33 - 22 * q^35 - 44 * q^37 - 4 * q^39 + 12 * q^41 + 76 * q^43 - 114 * q^45 - 10 * q^47 - 74 * q^49 - 30 * q^51 - 20 * q^53 + 32 * q^55 + 52 * q^57 - 32 * q^59 + 74 * q^61 + 87 * q^63 - 75 * q^65 - 8 * q^67 + 10 * q^69 + 8 * q^73 + 118 * q^75 + 5 * q^77 - 40 * q^79 - 44 * q^81 - 52 * q^83 - 100 * q^85 + 84 * q^87 + 36 * q^89 + 30 * q^91 - 12 * q^93 - 25 * q^95 + 72 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{11}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.97820	−	2.77799i	1.14211	−	1.60387i	0.428120	−	0.903722i	$-0.359176\pi$
$3$	1.97820	−	2.77799i	1.14211	−	1.60387i	0.713994	−	0.700152i	$-0.246884\pi$
$4$		0			0
$5$	3.68583	−	0.710386i	1.64835	−	0.317694i	0.721301	−	0.692622i	$-0.243545\pi$
$5$	3.68583	−	0.710386i	1.64835	−	0.317694i	0.927054	+	0.374928i	$0.122332\pi$
$6$		0			0
$7$	−1.93087	+	1.80879i	−0.729802	+	0.683659i
$7$	−1.93087	+	1.80879i	−0.729802	+	0.683659i
$8$		0			0
$9$	−2.82276	−	8.15583i	−0.940921	−	2.71861i
$10$		0			0
$11$	−2.00401	+	1.57597i	−0.604231	+	0.475173i	−0.872794	−	0.488090i	$-0.837694\pi$
$11$	−2.00401	+	1.57597i	−0.604231	+	0.475173i	0.268562	+	0.963262i	$0.413452\pi$
$12$		0			0
$13$	−0.391321	+	0.251487i	−0.108533	+	0.0697499i	−0.593781	−	0.804626i	$-0.702366\pi$
$13$	−0.391321	+	0.251487i	−0.108533	+	0.0697499i	0.485248	+	0.874376i	$0.338729\pi$
$14$		0			0
$15$	5.31786	−	11.6445i	1.37307	−	3.00660i
$16$		0			0
$17$	−2.85941	−	2.72644i	−0.693508	−	0.661258i	0.258963	−	0.965887i	$-0.416619\pi$
$17$	−2.85941	−	2.72644i	−0.693508	−	0.661258i	−0.952471	+	0.304629i	$0.901468\pi$
$18$		0			0
$19$	0.488477	−	0.465762i	0.112064	−	0.106853i	−0.631976	−	0.774988i	$-0.717756\pi$
$19$	0.488477	−	0.465762i	0.112064	−	0.106853i	0.744040	+	0.668135i	$0.232907\pi$
$20$		0			0
$21$	1.20515	+	8.94210i	0.262986	+	1.95133i
$22$		0			0
$23$	4.50612	+	1.64161i	0.939591	+	0.342299i
$23$	4.50612	+	1.64161i	0.939591	+	0.342299i
$24$		0			0
$25$	8.43888	−	3.37842i	1.68778	−	0.675684i
$26$		0			0
$27$	−18.4242	−	5.40983i	−3.54574	−	1.04112i
$28$		0			0
$29$	1.26245	−	0.370688i	0.234431	−	0.0688350i	−0.162407	−	0.986724i	$-0.551926\pi$
$29$	1.26245	−	0.370688i	0.234431	−	0.0688350i	0.396838	+	0.917889i	$0.370108\pi$
$30$		0			0
$31$	5.31369	−	0.507396i	0.954367	−	0.0911310i	0.393760	−	0.919213i	$-0.371174\pi$
$31$	5.31369	−	0.507396i	0.954367	−	0.0911310i	0.560607	+	0.828082i	$0.310568\pi$
$32$		0			0
$33$	0.413703	+	8.68470i	0.0720165	+	1.51181i
$34$		0			0
$35$	−5.83194	+	8.03857i	−0.985778	+	1.35877i
$36$		0			0
$37$	2.76491	+	7.98869i	0.454549	+	1.31333i	0.906845	+	0.421465i	$0.138484\pi$
$37$	2.76491	+	7.98869i	0.454549	+	1.31333i	−0.452296	+	0.891868i	$0.649395\pi$
$38$		0			0
$39$	−0.0754828	+	1.58458i	−0.0120869	+	0.253736i
$40$		0			0
$41$	1.24082	+	1.43198i	0.193784	+	0.223638i	0.844323	−	0.535834i	$-0.180003\pi$
$41$	1.24082	+	1.43198i	0.193784	+	0.223638i	−0.650540	+	0.759472i	$0.725457\pi$
$42$		0			0
$43$	5.22179	+	11.4341i	0.796315	+	1.74369i	0.657617	+	0.753352i	$0.271564\pi$
$43$	5.22179	+	11.4341i	0.796315	+	1.74369i	0.138698	+	0.990335i	$0.455708\pi$
$44$		0			0
$45$	−16.1980	−	28.0558i	−2.41466	−	4.18231i
$46$		0			0
$47$	−3.71502	+	6.43460i	−0.541891	+	0.938583i	0.456905	+	0.889516i	$0.348958\pi$
$47$	−3.71502	+	6.43460i	−0.541891	+	0.938583i	−0.998795	+	0.0490669i	$0.984375\pi$
$48$		0			0
$49$	0.456548	−	6.98510i	0.0652211	−	0.997871i
$50$		0			0
$51$	−13.2305	+	2.54997i	−1.85264	+	0.357067i
$52$		0			0
$53$	0.262450	−	5.50950i	0.0360502	−	0.756788i	−0.906396	−	0.422429i	$-0.861177\pi$
$53$	0.262450	−	5.50950i	0.0360502	−	0.756788i	0.942446	−	0.334358i	$-0.108520\pi$
$54$		0			0
$55$	−6.26690	+	7.23238i	−0.845028	+	0.975214i
$56$		0			0
$57$	−0.327578	−	2.27835i	−0.0433887	−	0.301775i
$58$		0			0
$59$	−4.99004	−	2.57254i	−0.649647	−	0.334916i	0.101708	−	0.994814i	$-0.467569\pi$
$59$	−4.99004	−	2.57254i	−0.649647	−	0.334916i	−0.751355	+	0.659898i	$0.770600\pi$
$60$		0			0
$61$	−2.09478	−	2.94171i	−0.268209	−	0.376647i	0.658403	−	0.752666i	$-0.271232\pi$
$61$	−2.09478	−	2.94171i	−0.268209	−	0.376647i	−0.926612	+	0.376018i	$0.877293\pi$
$62$		0			0
$63$	20.2026	+	10.6421i	2.54529	+	1.34078i
$64$		0			0
$65$	−1.26369	+	1.20493i	−0.156742	+	0.149453i
$66$		0			0
$67$	6.10550	−	2.44428i	0.745906	−	0.298616i	0.0326001	−	0.999468i	$-0.489621\pi$
$67$	6.10550	−	2.44428i	0.745906	−	0.298616i	0.713306	+	0.700853i	$0.247197\pi$
$68$		0			0
$69$	13.4744	−	9.27053i	1.62212	−	1.11604i
$70$		0			0
$71$	0.274109	−	1.90647i	0.0325308	−	0.226256i	−0.967070	−	0.254510i	$-0.918086\pi$
$71$	0.274109	−	1.90647i	0.0325308	−	0.226256i	0.999601	+	0.0282541i	$0.00899476\pi$
$72$		0			0
$73$	−1.13958	−	4.69742i	−0.133378	−	0.549792i	−0.998810	−	0.0487658i	$-0.984471\pi$
$73$	−1.13958	−	4.69742i	−0.133378	−	0.549792i	0.865432	−	0.501026i	$-0.167044\pi$
$74$		0			0
$75$	7.30857	−	30.1263i	0.843921	−	3.47869i
$76$		0			0
$77$	1.01889	−	6.66783i	0.116113	−	0.759870i
$78$		0			0
$79$	0.642995	+	13.4981i	0.0723426	+	1.51866i	0.685137	+	0.728415i	$0.259743\pi$
$79$	0.642995	+	13.4981i	0.0723426	+	1.51866i	−0.612794	+	0.790243i	$0.709954\pi$
$80$		0			0
$81$	−31.1231	+	24.4755i	−3.45812	+	2.71949i
$82$		0			0
$83$	−6.54603	+	7.55452i	−0.718520	+	0.829216i	−0.991128	−	0.132909i	$-0.957568\pi$
$83$	−6.54603	+	7.55452i	−0.718520	+	0.829216i	0.272608	+	0.962125i	$0.412114\pi$
$84$		0			0
$85$	−12.4761	−	8.01791i	−1.35322	−	0.869665i
$86$		0			0
$87$	1.46760	−	4.24036i	0.157344	−	0.454615i
$88$		0			0
$89$	2.89144	+	0.276099i	0.306492	+	0.0292665i	0.247169	−	0.968972i	$-0.420500\pi$
$89$	2.89144	+	0.276099i	0.306492	+	0.0292665i	0.0593233	+	0.998239i	$0.481106\pi$
$90$		0			0
$91$	0.300705	−	1.19341i	0.0315224	−	0.125103i
$92$		0			0
$93$	9.10199	−	15.7651i	0.943832	−	1.63477i
$94$		0			0
$95$	1.46957	−	2.06373i	0.150775	−	0.211734i
$96$		0			0
$97$	3.97227	+	4.58425i	0.403323	+	0.465460i	0.920685	−	0.390307i	$-0.127631\pi$
$97$	3.97227	+	4.58425i	0.403323	+	0.465460i	−0.517361	+	0.855767i	$0.673086\pi$
$98$		0			0
$99$	18.5102	+	11.8958i	1.86034	+	1.19557i
$100$		0			0
$101$	4.29028	+	0.826883i	0.426899	+	0.0822780i	0.398175	−	0.917309i	$-0.369644\pi$
$101$	4.29028	+	0.826883i	0.426899	+	0.0822780i	0.0287235	+	0.999587i	$0.490856\pi$
$102$		0			0
$103$	−14.7176	−	5.89203i	−1.45017	−	0.580559i	−0.492982	−	0.870039i	$-0.664093\pi$
$103$	−14.7176	−	5.89203i	−1.45017	−	0.580559i	−0.957184	+	0.289480i	$0.906517\pi$
$104$		0			0
$105$	10.7943	+	32.1030i	1.05342	+	3.13293i
$106$		0			0
$107$	6.83136	+	9.59330i	0.660412	+	0.927419i	0.999913	−	0.0131864i	$-0.00419748\pi$
$107$	6.83136	+	9.59330i	0.660412	+	0.927419i	−0.339501	+	0.940606i	$0.610258\pi$
$108$		0			0
$109$	−1.97296	−	1.88122i	−0.188976	−	0.180188i	0.589685	−	0.807634i	$-0.299252\pi$
$109$	−1.97296	−	1.88122i	−0.188976	−	0.180188i	−0.778660	+	0.627446i	$0.784101\pi$
$110$		0			0
$111$	27.6621	+	8.12231i	2.62557	+	0.770936i
$112$		0			0
$113$	0.721219	−	5.01619i	0.0678466	−	0.471884i	−0.927366	−	0.374154i	$-0.877933\pi$
$113$	0.721219	−	5.01619i	0.0678466	−	0.471884i	0.995213	−	0.0977292i	$-0.0311579\pi$
$114$		0			0
$115$	17.7750	+	2.84962i	1.65753	+	0.265728i
$116$		0			0
$117$	3.15569	+	2.48166i	0.291744	+	0.229430i
$118$		0			0
$119$	10.4527	+	0.0923393i	0.958198	+	0.00846473i
$120$		0			0
$121$	−1.06098	+	4.37341i	−0.0964526	+	0.397583i
$122$		0			0
$123$	6.43262	−	0.614241i	0.580010	−	0.0553842i
$124$		0			0
$125$	12.9154	−	8.30023i	1.15519	−	0.742395i
$126$		0			0
$127$	−0.118370	−	0.823281i	−0.0105036	−	0.0730544i	0.983895	−	0.178745i	$-0.0572037\pi$
$127$	−0.118370	−	0.823281i	−0.0105036	−	0.0730544i	−0.994399	+	0.105691i	$0.966295\pi$
$128$		0			0
$129$	42.0936	+	8.11288i	3.70614	+	0.714299i
$130$		0			0
$131$	−9.14681	+	4.71551i	−0.799160	+	0.411996i	−0.808892	−	0.587957i	$-0.799933\pi$
$131$	−9.14681	+	4.71551i	−0.799160	+	0.411996i	0.00973187	+	0.999953i	$0.496902\pi$
$132$		0			0
$133$	−0.100721	+	1.78288i	−0.00873365	+	0.154595i
$134$		0			0
$135$	−71.7516	−	6.85144i	−6.17539	−	0.589678i
$136$		0			0
$137$	−4.06893	−	7.04760i	−0.347632	−	0.602117i	0.638196	−	0.769874i	$-0.279681\pi$
$137$	−4.06893	−	7.04760i	−0.347632	−	0.602117i	−0.985828	+	0.167757i	$0.946348\pi$
$138$		0			0
$139$	−18.6212			−1.57943			−0.789713	−	0.613476i	$-0.789771\pi$
$139$	−18.6212			−1.57943			−0.789713	+	0.613476i	$0.789771\pi$
$140$		0			0
$141$	10.5262	+	23.0492i	0.886467	+	1.94109i
$142$		0			0
$143$	0.387876	−	1.12069i	0.0324358	−	0.0937170i
$144$		0			0
$145$	4.38984	−	2.26312i	0.364556	−	0.187942i
$146$		0			0
$147$	−18.5014	−	15.0862i	−1.52597	−	1.24429i
$148$		0			0
$149$	4.58851	+	1.83696i	0.375906	+	0.150490i	0.551919	−	0.833898i	$-0.313896\pi$
$149$	4.58851	+	1.83696i	0.375906	+	0.150490i	−0.176013	+	0.984388i	$0.556320\pi$
$150$		0			0
$151$	−15.5264	−	8.00440i	−1.26352	−	0.651389i	−0.309432	−	0.950921i	$-0.600139\pi$
$151$	−15.5264	−	8.00440i	−1.26352	−	0.651389i	−0.954086	+	0.299532i	$0.903169\pi$
$152$		0			0
$153$	−14.1650	+	31.0169i	−1.14517	+	2.50757i
$154$		0			0
$155$	19.2249	−	5.64495i	1.54418	−	0.453413i
$156$		0			0
$157$	−2.17745	−	8.97558i	−0.173780	−	0.716329i	−0.990292	−	0.139002i	$-0.955611\pi$
$157$	−2.17745	−	8.97558i	−0.173780	−	0.716329i	0.816513	−	0.577328i	$-0.195904\pi$
$158$		0			0
$159$	−14.7862	−	11.6280i	−1.17262	−	0.922157i
$160$		0			0
$161$	−11.6701	+	4.98089i	−0.919731	+	0.392549i
$162$		0			0
$163$	−3.70714	−	2.91533i	−0.290366	−	0.228346i	0.462341	−	0.886702i	$-0.347010\pi$
$163$	−3.70714	−	2.91533i	−0.290366	−	0.228346i	−0.752706	+	0.658356i	$0.771252\pi$
$164$		0			0
$165$	7.69433	+	31.7165i	0.599003	+	2.46912i
$166$		0			0
$167$	−3.65815	+	1.07413i	−0.283076	+	0.0831187i	−0.420189	−	0.907437i	$-0.638036\pi$
$167$	−3.65815	+	1.07413i	−0.283076	+	0.0831187i	0.137112	+	0.990556i	$0.456218\pi$
$168$		0			0
$169$	−5.31051	+	11.6284i	−0.408501	+	0.894492i
$170$		0			0
$171$	−5.17753	−	2.66920i	−0.395935	−	0.204119i
$172$		0			0
$173$	−16.4435	−	6.58299i	−1.25018	−	0.500495i	−0.350299	−	0.936638i	$-0.613920\pi$
$173$	−16.4435	−	6.58299i	−1.25018	−	0.500495i	−0.899878	+	0.436142i	$0.856344\pi$
$174$		0			0
$175$	−10.1836	+	21.7875i	−0.769805	+	1.64698i
$176$		0			0
$177$	−17.0178	+	8.77328i	−1.27913	+	0.659440i
$178$		0			0
$179$	3.42477	−	9.89523i	0.255980	−	0.739604i	−0.741650	−	0.670787i	$-0.765956\pi$
$179$	3.42477	−	9.89523i	0.255980	−	0.739604i	0.997629	−	0.0688170i	$-0.0219225\pi$
$180$		0			0
$181$	2.49314	+	5.45922i	0.185314	+	0.405780i	0.979373	−	0.202060i	$-0.0647635\pi$
$181$	2.49314	+	5.45922i	0.185314	+	0.405780i	−0.794060	+	0.607840i	$0.792036\pi$
$182$		0			0
$183$	−12.3159			−0.910420
$184$		0			0
$185$	15.8661	+	27.4808i	1.16650	+	2.02043i
$186$		0			0
$187$	10.0271	+	0.957468i	0.733251	+	0.0700170i
$188$		0			0
$189$	45.3600	−	22.8798i	3.29946	−	1.66426i
$190$		0			0
$191$	15.8215	−	8.15657i	1.14481	−	0.590188i	0.221845	−	0.975082i	$-0.428792\pi$
$191$	15.8215	−	8.15657i	1.14481	−	0.590188i	0.922961	+	0.384894i	$0.125762\pi$
$192$		0			0
$193$	1.80541	+	0.347963i	0.129956	+	0.0250470i	0.253814	−	0.967253i	$-0.418315\pi$
$193$	1.80541	+	0.347963i	0.129956	+	0.0250470i	−0.123858	+	0.992300i	$0.539527\pi$
$194$		0			0
$195$	0.847446	+	5.89411i	0.0606869	+	0.422086i
$196$		0			0
$197$	13.9845	−	8.98728i	0.996353	−	0.640317i	0.0625261	−	0.998043i	$-0.480084\pi$
$197$	13.9845	−	8.98728i	0.996353	−	0.640317i	0.933826	+	0.357726i	$0.116448\pi$
$198$		0			0
$199$	−11.5240	+	1.10041i	−0.816917	+	0.0780061i	−0.495144	−	0.868811i	$-0.664885\pi$
$199$	−11.5240	+	1.10041i	−0.816917	+	0.0780061i	−0.321773	+	0.946817i	$0.604279\pi$
$200$		0			0
$201$	5.28773	−	21.7963i	0.372967	−	1.53739i
$202$		0			0
$203$	−1.76713	+	2.99926i	−0.124028	+	0.210507i
$204$		0			0
$205$	5.59072	+	4.39659i	0.390473	+	0.307071i
$206$		0			0
$207$	0.669003	−	41.3850i	0.0464989	−	2.87646i
$208$		0			0
$209$	−0.244885	+	1.70321i	−0.0169391	+	0.117814i
$210$		0			0
$211$	−10.9962	−	3.22878i	−0.757011	−	0.222279i	−0.119621	−	0.992820i	$-0.538168\pi$
$211$	−10.9962	−	3.22878i	−0.757011	−	0.222279i	−0.637390	+	0.770541i	$0.719986\pi$
$212$		0			0
$213$	−4.75391	−	4.53285i	−0.325733	−	0.310586i
$214$		0			0
$215$	27.3693	+	38.4348i	1.86657	+	2.62123i
$216$		0			0
$217$	−9.34229	+	10.5911i	−0.634196	+	0.718969i
$218$		0			0
$219$	−15.3037	−	6.12669i	−1.03413	−	0.414003i
$220$		0			0
$221$	1.80461	+	0.347810i	0.121391	+	0.0233962i
$222$		0			0
$223$	17.9907	+	11.5619i	1.20475	+	0.774245i	0.979772	−	0.200119i	$-0.0641330\pi$
$223$	17.9907	+	11.5619i	1.20475	+	0.774245i	0.224977	+	0.974364i	$0.427769\pi$
$224$		0			0
$225$	−51.3748	−	59.2897i	−3.42498	−	3.95264i
$226$		0			0
$227$	16.1367	−	22.6609i	1.07103	−	1.50405i	0.222485	−	0.974936i	$-0.428583\pi$
$227$	16.1367	−	22.6609i	1.07103	−	1.50405i	0.848548	−	0.529119i	$-0.177477\pi$
$228$		0			0
$229$	4.05267	−	7.01942i	0.267808	−	0.463856i	−0.700488	−	0.713664i	$-0.747034\pi$
$229$	4.05267	−	7.01942i	0.267808	−	0.463856i	0.968295	+	0.249808i	$0.0803675\pi$
$230$		0			0
$231$	−16.5076	−	16.0208i	−1.08612	−	1.05409i
$232$		0			0
$233$	9.38795	+	0.896440i	0.615025	+	0.0587278i	0.397919	−	0.917420i	$-0.369732\pi$
$233$	9.38795	+	0.896440i	0.615025	+	0.0587278i	0.217106	+	0.976148i	$0.430338\pi$
$234$		0			0
$235$	−9.12189	+	26.3560i	−0.595046	+	1.71927i
$236$		0			0
$237$	38.7696	+	24.9157i	2.51836	+	1.61845i
$238$		0			0
$239$	14.6995	−	16.9642i	0.950834	−	1.09732i	−0.0443225	−	0.999017i	$-0.514113\pi$
$239$	14.6995	−	16.9642i	0.950834	−	1.09732i	0.995156	−	0.0983036i	$-0.0313416\pi$
$240$		0			0
$241$	−17.1183	+	13.4620i	−1.10269	+	0.867162i	−0.991943	−	0.126687i	$-0.959565\pi$
$241$	−17.1183	+	13.4620i	−1.10269	+	0.867162i	−0.110743	+	0.993849i	$0.535323\pi$
$242$		0			0
$243$	3.68397	+	77.3361i	0.236327	+	4.96112i
$244$		0			0
$245$	−3.27936	−	26.0702i	−0.209510	−	1.66557i
$246$		0			0
$247$	−0.0740184	+	0.305108i	−0.00470968	+	0.0194136i
$248$		0			0
$249$	8.03705	+	33.1292i	0.509327	+	2.09947i
$250$		0			0
$251$	−2.39359	+	16.6478i	−0.151082	+	1.05080i	0.763328	+	0.646011i	$0.223564\pi$
$251$	−2.39359	+	16.6478i	−0.151082	+	1.05080i	−0.914410	+	0.404788i	$0.867345\pi$
$252$		0			0
$253$	−11.6174	+	3.81171i	−0.730382	+	0.239640i
$254$		0			0
$255$	−46.9539	+	18.7975i	−2.94037	+	1.17715i
$256$		0			0
$257$	12.7328	−	12.1407i	0.794249	−	0.757315i	−0.179787	−	0.983705i	$-0.557541\pi$
$257$	12.7328	−	12.1407i	0.794249	−	0.757315i	0.974037	+	0.226390i	$0.0726925\pi$
$258$		0			0
$259$	−19.7886	−	10.4240i	−1.22960	−	0.647716i
$260$		0			0
$261$	−6.58686	−	9.24995i	−0.407716	−	0.572558i
$262$		0			0
$263$	−1.97222	−	1.01675i	−0.121612	−	0.0626954i	0.396347	−	0.918101i	$-0.370278\pi$
$263$	−1.97222	−	1.01675i	−0.121612	−	0.0626954i	−0.517959	+	0.855405i	$0.673308\pi$
$264$		0			0
$265$	−2.94653	−	20.4935i	−0.181004	−	1.25891i
$266$		0			0
$267$	6.48685	−	7.48623i	0.396989	−	0.458150i
$268$		0			0
$269$	−0.255517	+	5.36397i	−0.0155792	+	0.327047i	0.977602	+	0.210463i	$0.0674973\pi$
$269$	−0.255517	+	5.36397i	−0.0155792	+	0.327047i	−0.993181	+	0.116583i	$0.962806\pi$
$270$		0			0
$271$	−9.16874	+	1.76713i	−0.556961	+	0.107345i	−0.459961	−	0.887939i	$-0.652137\pi$
$271$	−9.16874	+	1.76713i	−0.556961	+	0.107345i	−0.0969998	+	0.995284i	$0.530925\pi$
$272$		0			0
$273$	−2.72042	−	3.19615i	−0.164648	−	0.193440i
$274$		0			0
$275$	−11.5873	+	20.0698i	−0.698741	+	1.21025i
$276$		0			0
$277$	0.633604	+	1.09743i	0.0380696	+	0.0659385i	0.884432	−	0.466668i	$-0.154546\pi$
$277$	0.633604	+	1.09743i	0.0380696	+	0.0659385i	−0.846363	+	0.532607i	$0.821212\pi$
$278$		0			0
$279$	−19.1375	−	41.9053i	−1.14573	−	2.50881i
$280$		0			0
$281$	2.74868	+	3.17214i	0.163972	+	0.189234i	0.831789	−	0.555091i	$-0.187317\pi$
$281$	2.74868	+	3.17214i	0.163972	+	0.189234i	−0.667817	+	0.744325i	$0.732771\pi$
$282$		0			0
$283$	0.745801	−	15.6563i	0.0443332	−	0.930669i	−0.861688	−	0.507438i	$-0.830593\pi$
$283$	0.745801	−	15.6563i	0.0443332	−	0.930669i	0.906022	−	0.423231i	$-0.139104\pi$
$284$		0			0
$285$	−2.82591	−	8.16492i	−0.167392	−	0.483648i
$286$		0			0
$287$	−4.98602	−	0.520593i	−0.294316	−	0.0307297i
$288$		0			0
$289$	−0.0661549	−	1.38876i	−0.00389146	−	0.0816919i
$290$		0			0
$291$	20.5930	−	1.96639i	1.20718	−	0.115272i
$292$		0			0
$293$	21.6971	−	6.37083i	1.26756	−	0.372188i	0.422254	−	0.906478i	$-0.361239\pi$
$293$	21.6971	−	6.37083i	1.26756	−	0.372188i	0.845301	+	0.534290i	$0.179421\pi$
$294$		0			0
$295$	−20.2199	−	5.93711i	−1.17725	−	0.345672i
$296$		0			0
$297$	45.4480	−	18.1946i	2.63716	−	1.05576i
$298$		0			0
$299$	−2.17618	+	0.490833i	−0.125852	+	0.0283856i
$300$		0			0
$301$	−30.7646	−	12.6327i	−1.77324	−	0.728138i
$302$		0			0
$303$	10.7841	−	10.2826i	0.619530	−	0.590721i
$304$		0			0
$305$	−9.81076	−	9.35454i	−0.561763	−	0.535640i
$306$		0			0
$307$	10.0894	−	22.0926i	0.575831	−	1.26089i	−0.367804	−	0.929903i	$-0.619890\pi$
$307$	10.0894	−	22.0926i	0.575831	−	1.26089i	0.943634	−	0.330990i	$-0.107383\pi$
$308$		0			0
$309$	−45.4823	+	29.2297i	−2.58740	+	1.66282i
$310$		0			0
$311$	8.91877	−	7.01380i	0.505737	−	0.397716i	−0.332432	−	0.943127i	$-0.607869\pi$
$311$	8.91877	−	7.01380i	0.505737	−	0.397716i	0.838168	+	0.545412i	$0.183627\pi$
$312$		0			0
$313$	2.81428	+	8.13133i	0.159073	+	0.459610i	0.996169	−	0.0874448i	$-0.0278701\pi$
$313$	2.81428	+	8.13133i	0.159073	+	0.459610i	−0.837097	+	0.547055i	$0.815749\pi$
$314$		0			0
$315$	82.0234	+	24.8734i	4.62150	+	1.40146i
$316$		0			0
$317$	−21.7926	+	4.20018i	−1.22399	+	0.235905i	−0.759994	−	0.649930i	$-0.774798\pi$
$317$	−21.7926	+	4.20018i	−1.22399	+	0.235905i	−0.463999	+	0.885836i	$0.653586\pi$
$318$		0			0
$319$	−1.94576	+	2.73244i	−0.108942	+	0.152987i
$320$		0			0
$321$	40.1639			2.24173
$322$		0			0
$323$	−2.66662			−0.148375
$324$		0			0
$325$	−2.45269	+	3.44432i	−0.136051	+	0.191056i
$326$		0			0
$327$	−9.12892	+	1.75946i	−0.504831	+	0.0972981i
$328$		0			0
$329$	−4.46562	−	19.1441i	−0.246197	−	1.05545i
$330$		0			0
$331$	1.56103	+	4.51029i	0.0858017	+	0.247908i	0.979737	−	0.200288i	$-0.0641879\pi$
$331$	1.56103	+	4.51029i	0.0858017	+	0.247908i	−0.893935	+	0.448196i	$0.852067\pi$
$332$		0			0
$333$	57.3497	−	45.1003i	3.14275	−	2.47148i
$334$		0			0
$335$	20.7675	−	13.3465i	1.13465	−	0.729195i
$336$		0			0
$337$	3.77009	−	8.25535i	0.205370	−	0.449697i	−0.778719	−	0.627373i	$-0.784130\pi$
$337$	3.77009	−	8.25535i	0.205370	−	0.449697i	0.984089	+	0.177675i	$0.0568576\pi$
$338$		0			0
$339$	−12.5082	−	11.9266i	−0.679353	−	0.647762i
$340$		0			0
$341$	−9.84904	+	9.39104i	−0.533355	+	0.508553i
$342$		0			0
$343$	11.7530	+	14.3131i	0.634605	+	0.772837i
$344$		0			0
$345$	43.0787	−	43.7416i	2.31928	−	2.35497i
$346$		0			0
$347$	−12.5679	+	5.03143i	−0.674681	+	0.270102i	−0.683598	−	0.729859i	$-0.739586\pi$
$347$	−12.5679	+	5.03143i	−0.674681	+	0.270102i	0.00891697	+	0.999960i	$0.497162\pi$
$348$		0			0
$349$	−29.7148	−	8.72504i	−1.59060	−	0.467041i	−0.637686	−	0.770296i	$-0.720108\pi$
$349$	−29.7148	−	8.72504i	−1.59060	−	0.467041i	−0.952909	+	0.303255i	$0.901926\pi$
$350$		0			0
$351$	8.57028	−	2.51646i	0.457448	−	0.134319i
$352$		0			0
$353$	6.63125	−	0.633207i	0.352946	−	0.0337022i	0.0829224	−	0.996556i	$-0.473575\pi$
$353$	6.63125	−	0.633207i	0.352946	−	0.0337022i	0.270023	+	0.962854i	$0.412969\pi$
$354$		0			0
$355$	−0.344010	−	7.22165i	−0.0182581	−	0.383286i
$356$		0			0
$357$	20.9341	−	28.8549i	1.10795	−	1.52716i
$358$		0			0
$359$	−4.34762	−	12.5616i	−0.229459	−	0.662978i	−0.999682	−	0.0252037i	$-0.991977\pi$
$359$	−4.34762	−	12.5616i	−0.229459	−	0.662978i	0.770223	−	0.637774i	$-0.220145\pi$
$360$		0			0
$361$	−0.882381	+	18.5235i	−0.0464411	+	0.974919i
$362$		0			0
$363$	10.0505	+	11.5989i	0.527513	+	0.608783i
$364$		0			0
$365$	−7.53730	−	16.5044i	−0.394520	−	0.863879i
$366$		0			0
$367$	4.20614	+	7.28524i	0.219559	+	0.380287i	0.954673	−	0.297656i	$-0.0962050\pi$
$367$	4.20614	+	7.28524i	0.219559	+	0.380287i	−0.735115	+	0.677943i	$0.762872\pi$
$368$		0			0
$369$	8.17647	−	14.1621i	0.425650	−	0.737248i
$370$		0			0
$371$	9.45877	+	11.1129i	0.491075	+	0.576951i
$372$		0			0
$373$	−20.6039	+	3.97108i	−1.06683	+	0.205615i	−0.692307	−	0.721603i	$-0.743406\pi$
$373$	−20.6039	+	3.97108i	−1.06683	+	0.205615i	−0.374523	+	0.927218i	$0.622194\pi$
$374$		0			0
$375$	2.49128	−	52.2984i	0.128649	−	2.70068i
$376$		0			0
$377$	−0.400800	+	0.462547i	−0.0206422	+	0.0238224i
$378$		0			0
$379$	−0.389034	−	2.70579i	−0.0199833	−	0.138987i	0.977387	−	0.211457i	$-0.0678209\pi$
$379$	−0.389034	−	2.70579i	−0.0199833	−	0.138987i	−0.997371	+	0.0724701i	$0.976912\pi$
$380$		0			0
$381$	−2.52123	−	1.29978i	−0.129166	−	0.0665899i
$382$		0			0
$383$	−11.1110	−	15.6032i	−0.567744	−	0.797285i	0.426493	−	0.904491i	$-0.359749\pi$
$383$	−11.1110	−	15.6032i	−0.567744	−	0.797285i	−0.994237	+	0.107206i	$0.965810\pi$
$384$		0			0
$385$	−0.981287	−	25.3003i	−0.0500110	−	1.28942i
$386$		0			0
$387$	78.5149	−	74.8638i	3.99114	−	3.80554i
$388$		0			0
$389$	−24.8763	+	9.95896i	−1.26128	+	0.504939i	−0.903388	−	0.428825i	$-0.858928\pi$
$389$	−24.8763	+	9.95896i	−1.26128	+	0.504939i	−0.357890	+	0.933764i	$0.616504\pi$
$390$		0			0
$391$	−8.40907	−	16.9797i	−0.425265	−	0.858700i
$392$		0			0
$393$	−4.99457	+	34.7380i	−0.251943	+	1.75230i
$394$		0			0
$395$	11.9589	+	49.2951i	0.601715	+	2.48030i
$396$		0			0
$397$	2.53666	−	10.4563i	0.127311	−	0.524784i	−0.872062	−	0.489395i	$-0.837218\pi$
$397$	2.53666	−	10.4563i	0.127311	−	0.524784i	0.999374	−	0.0353895i	$-0.0112672\pi$
$398$		0			0
$399$	4.75358	+	3.80669i	0.237976	+	0.190573i
$400$		0			0
$401$	−0.180949	−	3.79859i	−0.00903616	−	0.189692i	−0.998872	−	0.0474793i	$-0.984881\pi$
$401$	−0.180949	−	3.79859i	−0.00903616	−	0.189692i	0.989836	−	0.142213i	$-0.0454218\pi$
$402$		0			0
$403$	−1.95176	+	1.53488i	−0.0972239	+	0.0764577i
$404$		0			0
$405$	−97.3274	+	112.322i	−4.83624	+	5.58132i
$406$		0			0
$407$	−18.1308	−	11.6520i	−0.898713	−	0.577567i
$408$		0			0
$409$	5.58566	−	16.1387i	0.276193	−	0.798008i	−0.718538	−	0.695488i	$-0.755188\pi$
$409$	5.58566	−	16.1387i	0.276193	−	0.798008i	0.994731	−	0.102520i	$-0.0326905\pi$
$410$		0			0
$411$	−27.6273	−	2.63809i	−1.36276	−	0.130127i
$412$		0			0
$413$	14.2883	−	4.05868i	0.703082	−	0.199715i
$414$		0			0
$415$	−18.7609	+	32.4949i	−0.920939	+	1.59511i
$416$		0			0
$417$	−36.8364	+	51.7294i	−1.80388	+	2.53320i
$418$		0			0
$419$	−21.6144	−	24.9443i	−1.05593	−	1.21861i	−0.975073	−	0.221885i	$-0.928779\pi$
$419$	−21.6144	−	24.9443i	−1.05593	−	1.21861i	−0.0808595	−	0.996726i	$-0.525767\pi$
$420$		0			0
$421$	−5.15547	−	3.31322i	−0.251262	−	0.161476i	0.408947	−	0.912558i	$-0.365896\pi$
$421$	−5.15547	−	3.31322i	−0.251262	−	0.161476i	−0.660209	+	0.751082i	$0.729532\pi$
$422$		0			0
$423$	62.9661	+	12.1357i	3.06152	+	0.590059i
$424$		0			0
$425$	−33.3412	−	13.3478i	−1.61729	−	0.647464i
$426$		0			0
$427$	9.36570	+	1.89105i	0.453238	+	0.0915141i
$428$		0			0
$429$	−2.34598	−	3.29447i	−0.113265	−	0.159058i
$430$		0			0
$431$	−19.8527	−	18.9296i	−0.956273	−	0.911805i	0.0399001	−	0.999204i	$-0.487296\pi$
$431$	−19.8527	−	18.9296i	−0.956273	−	0.911805i	−0.996173	+	0.0873990i	$0.972145\pi$
$432$		0			0
$433$	−14.1540	−	4.15600i	−0.680200	−	0.199725i	−0.0766598	−	0.997057i	$-0.524426\pi$
$433$	−14.1540	−	4.15600i	−0.680200	−	0.199725i	−0.603540	+	0.797333i	$0.706244\pi$
$434$		0			0
$435$	2.39705	−	16.6718i	0.114930	−	0.799353i
$436$		0			0
$437$	2.96573	−	1.29689i	0.141870	−	0.0620386i
$438$		0			0
$439$	12.3352	+	9.70052i	0.588728	+	0.462981i	0.867542	−	0.497365i	$-0.165699\pi$
$439$	12.3352	+	9.70052i	0.588728	+	0.462981i	−0.278814	+	0.960345i	$0.589941\pi$
$440$		0			0
$441$	−58.2580	+	15.9937i	−2.77419	+	0.761606i
$442$		0			0
$443$	3.22573	−	13.2966i	0.153259	−	0.631742i	−0.842415	−	0.538829i	$-0.818867\pi$
$443$	3.22573	−	13.2966i	0.153259	−	0.631742i	0.995674	−	0.0929129i	$-0.0296178\pi$
$444$		0			0
$445$	10.8535	−	1.03639i	0.514506	−	0.0491294i
$446$		0			0
$447$	14.1801	−	9.11297i	0.670694	−	0.431029i
$448$		0			0
$449$	1.74635	+	12.1461i	0.0824154	+	0.573211i	0.988627	+	0.150387i	$0.0480521\pi$
$449$	1.74635	+	12.1461i	0.0824154	+	0.573211i	−0.906212	+	0.422824i	$0.861039\pi$
$450$		0			0
$451$	−4.74338	−	0.914211i	−0.223357	−	0.0430485i
$452$		0			0
$453$	−52.9504	+	27.2978i	−2.48783	+	1.28256i
$454$		0			0
$455$	0.260567	−	4.61232i	0.0122156	−	0.216229i
$456$		0			0
$457$	22.4589	+	2.14456i	1.05058	+	0.100318i	0.606036	−	0.795438i	$-0.292759\pi$
$457$	22.4589	+	2.14456i	1.05058	+	0.100318i	0.444546	+	0.895756i	$0.353365\pi$
$458$		0			0
$459$	37.9327	+	65.7013i	1.77055	+	3.06667i
$460$		0			0
$461$	29.2900			1.36417			0.682086	−	0.731272i	$-0.261073\pi$
$461$	29.2900			1.36417			0.682086	+	0.731272i	$0.261073\pi$
$462$		0			0
$463$	1.65304	+	3.61966i	0.0768234	+	0.168220i	0.944147	−	0.329525i	$-0.106889\pi$
$463$	1.65304	+	3.61966i	0.0768234	+	0.168220i	−0.867323	+	0.497745i	$0.834161\pi$
$464$		0			0
$465$	22.3491	−	64.5735i	1.03642	−	2.99452i
$466$		0			0
$467$	−9.30396	+	4.79653i	−0.430536	+	0.221957i	−0.659852	−	0.751395i	$-0.729381\pi$
$467$	−9.30396	+	4.79653i	−0.430536	+	0.221957i	0.229316	+	0.973352i	$0.426351\pi$
$468$		0			0
$469$	−7.36777	+	15.7632i	−0.340212	+	0.727876i
$470$		0			0
$471$	−29.2415	−	11.7065i	−1.34738	−	0.539409i
$472$		0			0
$473$	−28.4843	−	14.6847i	−1.30971	−	0.675203i
$474$		0			0
$475$	2.54866	−	5.58079i	0.116941	−	0.256064i
$476$		0			0
$477$	−45.6754	+	13.4115i	−2.09133	+	0.614071i
$478$		0			0
$479$	−6.80398	−	28.0464i	−0.310882	−	1.28147i	−0.886108	−	0.463478i	$-0.846601\pi$
$479$	−6.80398	−	28.0464i	−0.310882	−	1.28147i	0.575227	−	0.817994i	$-0.304914\pi$
$480$		0			0
$481$	−3.09102	−	2.43081i	−0.140938	−	0.110835i
$482$		0			0
$483$	−9.24888	+	42.2726i	−0.420838	+	1.92347i
$484$		0			0
$485$	17.8977	+	14.0749i	0.812694	+	0.639110i
$486$		0			0
$487$	0.629974	+	2.59679i	0.0285468	+	0.117672i	0.984302	−	0.176491i	$-0.0564745\pi$
$487$	0.629974	+	2.59679i	0.0285468	+	0.117672i	−0.955755	+	0.294162i	$0.904959\pi$
$488$		0			0
$489$	−15.4322	+	4.53131i	−0.697869	+	0.204913i
$490$		0			0
$491$	−9.11864	+	19.9670i	−0.411518	+	0.901100i	0.584453	+	0.811428i	$0.301309\pi$
$491$	−9.11864	+	19.9670i	−0.411518	+	0.901100i	−0.995971	+	0.0896721i	$0.971418\pi$
$492$		0			0
$493$	−4.62051	−	2.38204i	−0.208097	−	0.107282i
$494$		0			0
$495$	76.6761	+	30.6965i	3.44633	+	1.37970i
$496$		0			0
$497$	2.91914	+	4.17696i	0.130941	+	0.187362i
$498$		0			0
$499$	−27.4452	+	14.1490i	−1.22861	+	0.633395i	−0.945478	−	0.325685i	$-0.894405\pi$
$499$	−27.4452	+	14.1490i	−1.22861	+	0.633395i	−0.283136	+	0.959080i	$0.591375\pi$
$500$		0			0
$501$	−4.25262	+	12.2872i	−0.189993	+	0.548949i
$502$		0			0
$503$	5.66113	+	12.3962i	0.252417	+	0.552717i	0.992844	−	0.119420i	$-0.0381036\pi$
$503$	5.66113	+	12.3962i	0.252417	+	0.552717i	−0.740426	+	0.672138i	$0.765376\pi$
$504$		0			0
$505$	16.4007			0.729820
$506$		0			0
$507$	21.7983	+	37.7558i	0.968098	+	1.67679i
$508$		0			0
$509$	25.1568	+	2.40218i	1.11505	+	0.106475i	0.636277	−	0.771461i	$-0.280474\pi$
$509$	25.1568	+	2.40218i	1.11505	+	0.106475i	0.478778	+	0.877936i	$0.341080\pi$
$510$		0			0
$511$	10.6971	+	7.00887i	0.473210	+	0.310054i
$512$		0			0
$513$	−11.5195	+	5.93870i	−0.508597	+	0.262200i
$514$		0			0
$515$	−58.4322	−	11.2619i	−2.57483	−	0.496258i
$516$		0			0
$517$	−2.69581	−	18.7497i	−0.118561	−	0.824613i
$518$		0			0
$519$	−50.8160	+	32.6575i	−2.23058	+	1.43350i
$520$		0			0
$521$	−21.2984	+	2.03375i	−0.933098	+	0.0891000i	−0.550519	−	0.834823i	$-0.685570\pi$
$521$	−21.2984	+	2.03375i	−0.933098	+	0.0891000i	−0.382579	+	0.923923i	$0.624964\pi$
$522$		0			0
$523$	4.88699	−	20.1445i	0.213693	−	0.880855i	−0.759433	−	0.650585i	$-0.774524\pi$
$523$	4.88699	−	20.1445i	0.213693	−	0.880855i	0.973127	−	0.230270i	$-0.0739611\pi$
$524$		0			0
$525$	40.3803	+	71.3898i	1.76234	+	3.11571i
$526$		0			0
$527$	−16.5774	−	13.0366i	−0.722122	−	0.567883i
$528$		0			0
$529$	17.6102	+	14.7946i	0.765662	+	0.643243i
$530$		0			0
$531$	−6.89555	+	47.9596i	−0.299241	+	2.08127i
$532$		0			0
$533$	−0.845684	−	0.248315i	−0.0366307	−	0.0107557i
$534$		0			0
$535$	31.9942	+	30.5064i	1.38323	+	1.31891i
$536$		0			0
$537$	−20.7140	−	29.0887i	−0.893875	−	1.25527i
$538$		0			0
$539$	10.0934	+	14.7177i	0.434752	+	0.633936i
$540$		0			0
$541$	9.73734	+	3.89824i	0.418641	+	0.167599i	0.571413	−	0.820663i	$-0.306396\pi$
$541$	9.73734	+	3.89824i	0.418641	+	0.167599i	−0.152772	+	0.988262i	$0.548820\pi$
$542$		0			0
$543$	20.0976	+	3.87349i	0.862470	+	0.166227i
$544$		0			0
$545$	−8.60841	−	5.53229i	−0.368744	−	0.236977i
$546$		0			0
$547$	29.1170	+	33.6028i	1.24495	+	1.43675i	0.857197	+	0.514989i	$0.172204\pi$
$547$	29.1170	+	33.6028i	1.24495	+	1.43675i	0.387755	+	0.921763i	$0.373251\pi$
$548$		0			0
$549$	−18.0790	+	25.3884i	−0.771594	+	1.08355i
$550$		0			0
$551$	0.444024	−	0.769072i	0.0189161	−	0.0327636i
$552$		0			0
$553$	−25.6568	−	24.9001i	−1.09104	−	1.05886i
$554$		0			0
$555$	107.728	+	10.2867i	4.57279	+	0.436648i
$556$		0			0
$557$	−8.57683	+	24.7811i	−0.363412	+	1.05001i	0.604040	+	0.796954i	$0.293557\pi$
$557$	−8.57683	+	24.7811i	−0.363412	+	1.05001i	−0.967452	+	0.253056i	$0.918564\pi$
$558$		0			0
$559$	−4.91893	−	3.16120i	−0.208049	−	0.133705i
$560$		0			0
$561$	22.4954	−	25.9610i	0.949754	−	1.09608i
$562$		0			0
$563$	2.73244	−	2.14882i	0.115159	−	0.0905618i	−0.558919	−	0.829222i	$-0.688784\pi$
$563$	2.73244	−	2.14882i	0.115159	−	0.0905618i	0.674078	+	0.738660i	$0.264541\pi$
$564$		0			0
$565$	−0.905138	−	19.0012i	−0.0380794	−	0.799386i
$566$		0			0
$567$	15.8237	−	103.554i	0.664534	−	4.34887i
$568$		0			0
$569$	−2.74729	+	11.3245i	−0.115172	+	0.474746i	0.884789	+	0.465991i	$0.154302\pi$
$569$	−2.74729	+	11.3245i	−0.115172	+	0.474746i	−0.999962	+	0.00875536i	$0.997213\pi$
$570$		0			0
$571$	−0.126543	−	0.521618i	−0.00529567	−	0.0218290i	0.969102	−	0.246659i	$-0.0793326\pi$
$571$	−0.126543	−	0.521618i	−0.00529567	−	0.0218290i	−0.974398	+	0.224830i	$0.927817\pi$
$572$		0			0
$573$	8.63926	−	60.0874i	0.360910	−	2.51019i
$574$		0			0
$575$	43.5727	−	1.37020i	1.81711	−	0.0571413i
$576$		0			0
$577$	−25.0476	+	10.0276i	−1.04275	+	0.417453i	−0.828890	−	0.559412i	$-0.811027\pi$
$577$	−25.0476	+	10.0276i	−1.04275	+	0.417453i	−0.213857	+	0.976865i	$0.568603\pi$
$578$		0			0
$579$	4.53809	−	4.32706i	0.188597	−	0.179826i
$580$		0			0
$581$	−1.02499	−	26.4272i	−0.0425239	−	1.09639i
$582$		0			0
$583$	8.15685	+	11.4547i	0.337822	+	0.474405i
$584$		0			0
$585$	13.3943	+	6.90524i	0.553786	+	0.285497i
$586$		0			0
$587$	3.21677	+	22.3731i	0.132770	+	0.923437i	0.941921	+	0.335836i	$0.109019\pi$
$587$	3.21677	+	22.3731i	0.132770	+	0.923437i	−0.809150	+	0.587602i	$0.800072\pi$
$588$		0			0
$589$	2.35929	−	2.72276i	0.0972128	−	0.112189i
$590$		0			0
$591$	2.69749	−	56.6274i	0.110960	−	2.32934i
$592$		0			0
$593$	−9.37936	+	1.80772i	−0.385164	+	0.0742343i	−0.378158	−	0.925741i	$-0.623442\pi$
$593$	−9.37936	+	1.80772i	−0.385164	+	0.0742343i	−0.00700637	+	0.999975i	$0.502230\pi$
$594$		0			0
$595$	38.5925	−	7.08511i	1.58214	−	0.290461i
$596$		0			0
$597$	−19.7399	+	34.1905i	−0.807900	+	1.39932i
$598$		0			0
$599$	−9.50684	−	16.4663i	−0.388439	−	0.672796i	0.603801	−	0.797135i	$-0.293652\pi$
$599$	−9.50684	−	16.4663i	−0.388439	−	0.672796i	−0.992240	+	0.124339i	$0.960319\pi$
$600$		0			0
$601$	−12.1606	−	26.6280i	−0.496041	−	1.08618i	−0.977736	−	0.209839i	$-0.932706\pi$
$601$	−12.1606	−	26.6280i	−0.496041	−	1.08618i	0.481695	−	0.876339i	$-0.340021\pi$
$602$		0			0
$603$	−37.1695	−	42.8959i	−1.51366	−	1.74686i
$604$		0			0
$605$	−0.803778	+	16.8734i	−0.0326782	+	0.686000i
$606$		0			0
$607$	0.454787	+	1.31402i	0.0184592	+	0.0533344i	0.953854	−	0.300271i	$-0.0970770\pi$
$607$	0.454787	+	1.31402i	0.0184592	+	0.0533344i	−0.935395	+	0.353605i	$0.884956\pi$
$608$		0			0
$609$	4.83617	+	10.8422i	0.195972	+	0.439348i
$610$		0			0
$611$	−0.164452	−	3.45227i	−0.00665302	−	0.139664i
$612$		0			0
$613$	11.3519	−	1.08397i	0.458497	−	0.0437812i	0.136748	−	0.990606i	$-0.456335\pi$
$613$	11.3519	−	1.08397i	0.458497	−	0.0437812i	0.321750	+	0.946825i	$0.395729\pi$
$614$		0			0
$615$	23.2732	−	6.83364i	0.938467	−	0.275559i
$616$		0			0
$617$	15.3737	+	4.51411i	0.618920	+	0.181731i	0.576137	−	0.817353i	$-0.304559\pi$
$617$	15.3737	+	4.51411i	0.618920	+	0.181731i	0.0427831	+	0.999084i	$0.486378\pi$
$618$		0			0
$619$	−39.1425	+	15.6703i	−1.57327	+	0.629842i	−0.984012	−	0.178104i	$-0.943004\pi$
$619$	−39.1425	+	15.6703i	−1.57327	+	0.629842i	−0.589257	+	0.807946i	$0.700579\pi$
$620$		0			0
$621$	−74.1408	−	54.6227i	−2.97517	−	2.19193i
$622$		0			0
$623$	−6.08242	+	4.69691i	−0.243687	+	0.188178i
$624$		0			0
$625$	8.81388	−	8.40402i	0.352555	−	0.336161i
$626$		0			0
$627$	4.24708	+	4.04959i	0.169612	+	0.161725i
$628$		0			0
$629$	13.8747	−	30.3813i	0.553219	−	1.21138i
$630$		0			0
$631$	11.1152	−	7.14329i	0.442488	−	0.284370i	−0.300365	−	0.953824i	$-0.597108\pi$
$631$	11.1152	−	7.14329i	0.442488	−	0.284370i	0.742853	+	0.669455i	$0.233472\pi$
$632$		0			0
$633$	−30.7222	+	24.1602i	−1.22110	+	0.960283i
$634$		0			0
$635$	−1.02114	−	2.95039i	−0.0405227	−	0.117083i
$636$		0			0
$637$	1.57800	+	2.84823i	0.0625228	+	0.112851i
$638$		0			0
$639$	−16.3226	+	3.14592i	−0.645712	+	0.124451i
$640$		0			0
$641$	−1.32450	+	1.86000i	−0.0523146	+	0.0734656i	−0.839905	−	0.542734i	$-0.817389\pi$
$641$	−1.32450	+	1.86000i	−0.0523146	+	0.0734656i	0.787590	+	0.616200i	$0.211329\pi$
$642$		0			0
$643$	41.3787			1.63182			0.815908	−	0.578182i	$-0.196238\pi$
$643$	41.3787			1.63182			0.815908	+	0.578182i	$0.196238\pi$
$644$		0			0
$645$	160.913			6.33596
$646$		0			0
$647$	−21.5447	+	30.2554i	−0.847011	+	1.18946i	0.133118	+	0.991100i	$0.457501\pi$
$647$	−21.5447	+	30.2554i	−0.847011	+	1.18946i	−0.980129	+	0.198361i	$0.936438\pi$
$648$		0			0
$649$	14.0543	−	2.70875i	0.551681	−	0.106328i
$650$		0			0
$651$	10.9410	+	46.9040i	0.428812	+	1.83831i
$652$		0			0
$653$	14.6481	+	42.3230i	0.573226	+	1.65623i	0.741865	+	0.670550i	$0.233942\pi$
$653$	14.6481	+	42.3230i	0.573226	+	1.65623i	−0.168639	+	0.985678i	$0.553937\pi$
$654$		0			0
$655$	−30.3638	+	23.8783i	−1.18641	+	0.933004i
$656$		0			0
$657$	−35.0946	+	22.5540i	−1.36917	+	0.879914i
$658$		0			0
$659$	−6.48988	+	14.2109i	−0.252810	+	0.553576i	−0.992903	−	0.118928i	$-0.962054\pi$
$659$	−6.48988	+	14.2109i	−0.252810	+	0.553576i	0.740093	+	0.672504i	$0.234781\pi$
$660$		0			0
$661$	12.4939	+	11.9129i	0.485955	+	0.463357i	0.893004	−	0.450049i	$-0.148594\pi$
$661$	12.4939	+	11.9129i	0.485955	+	0.463357i	−0.407049	+	0.913406i	$0.633442\pi$
$662$		0			0
$663$	4.53609	−	4.32515i	0.176167	−	0.167975i
$664$		0			0
$665$	0.895291	+	6.64295i	0.0347179	+	0.257602i
$666$		0			0
$667$	6.29727	+	0.402083i	0.243831	+	0.0155687i
$668$		0			0
$669$	67.7082	−	27.1063i	2.61775	−	1.04799i
$670$		0			0
$671$	8.83400	+	2.59390i	0.341033	+	0.100136i
$672$		0			0
$673$	−27.8124	+	8.16646i	−1.07209	+	0.314794i	−0.769710	−	0.638393i	$-0.779599\pi$
$673$	−27.8124	+	8.16646i	−1.07209	+	0.314794i	−0.302380	+	0.953187i	$0.597781\pi$
$674$		0			0
$675$	−173.756	+	16.5917i	−6.68788	+	0.638615i
$676$		0			0
$677$	0.578232	+	12.1386i	0.0222233	+	0.466524i	0.982361	+	0.186996i	$0.0598750\pi$
$677$	0.578232	+	12.1386i	0.0222233	+	0.466524i	−0.960137	+	0.279528i	$0.909822\pi$
$678$		0			0
$679$	−15.9619	−	1.66659i	−0.612562	−	0.0639579i
$680$		0			0
$681$	−31.0300	−	89.6554i	−1.18907	−	3.43560i
$682$		0			0
$683$	1.96336	−	41.2160i	0.0751259	−	1.57709i	−0.575572	−	0.817751i	$-0.695221\pi$
$683$	1.96336	−	41.2160i	0.0751259	−	1.57709i	0.650698	−	0.759336i	$-0.274476\pi$
$684$		0			0
$685$	−20.0039	−	23.0858i	−0.764311	−	0.882061i
$686$		0			0
$687$	−11.4829	−	25.1441i	−0.438101	−	0.959306i
$688$		0			0
$689$	1.28286	+	2.22199i	0.0488733	+	0.0846510i
$690$		0			0
$691$	−1.13318	+	1.96272i	−0.0431080	+	0.0746653i	−0.886774	−	0.462203i	$-0.847059\pi$
$691$	−1.13318	+	1.96272i	−0.0431080	+	0.0746653i	0.843666	+	0.536868i	$0.180393\pi$
$692$		0			0
$693$	−57.2578	+	10.5118i	−2.17504	+	0.399311i
$694$		0			0
$695$	−68.6345	+	13.2282i	−2.60345	+	0.501775i
$696$		0			0
$697$	0.356204	−	7.47764i	0.0134922	−	0.283236i
$698$		0			0
$699$	21.0615	−	24.3063i	0.796620	−	0.919349i
$700$		0			0
$701$	4.27879	+	29.7596i	0.161608	+	1.12400i	0.895604	+	0.444852i	$0.146744\pi$
$701$	4.27879	+	29.7596i	0.161608	+	1.12400i	−0.733997	+	0.679153i	$0.762347\pi$
$702$		0			0
$703$	5.07142	+	2.61450i	0.191272	+	0.0986077i
$704$		0			0
$705$	55.1717	+	77.4778i	2.07789	+	2.91798i
$706$		0			0
$707$	−9.77964	+	6.16361i	−0.367801	+	0.231806i
$708$		0			0
$709$	8.13144	−	7.75332i	0.305383	−	0.291182i	−0.521855	−	0.853034i	$-0.674760\pi$
$709$	8.13144	−	7.75332i	0.305383	−	0.291182i	0.827237	+	0.561853i	$0.189911\pi$
$710$		0			0
$711$	108.273	−	43.3461i	4.06057	−	1.62561i
$712$		0			0
$713$	24.7771	+	6.43662i	0.927908	+	0.241053i
$714$		0			0
$715$	0.633520	−	4.40623i	0.0236923	−	0.164784i
$716$		0			0
$717$	−18.0477	−	74.3937i	−0.674004	−	2.77828i
$718$		0			0
$719$	4.13717	−	17.0537i	0.154291	−	0.635994i	−0.841166	−	0.540777i	$-0.818130\pi$
$719$	4.13717	−	17.0537i	0.154291	−	0.635994i	0.995457	−	0.0952172i	$-0.0303546\pi$
$720$		0			0
$721$	39.0752	−	15.2443i	1.45524	−	0.567726i
$722$		0			0
$723$	3.53386	+	74.1849i	0.131426	+	2.75897i
$724$		0			0
$725$	9.40131	−	7.39327i	0.349156	−	0.274579i
$726$		0			0
$727$	−16.6428	+	19.2068i	−0.617246	+	0.712339i	−0.975182	−	0.221407i	$-0.928935\pi$
$727$	−16.6428	+	19.2068i	−0.617246	+	0.712339i	0.357936	+	0.933746i	$0.383481\pi$
$728$		0			0
$729$	122.201	+	78.5336i	4.52595	+	2.90865i
$730$		0			0
$731$	16.2432	−	46.9317i	0.600777	−	1.73583i
$732$		0			0
$733$	−0.229353	−	0.0219005i	−0.00847134	−	0.000808915i	0.0908195	−	0.995867i	$-0.471051\pi$
$733$	−0.229353	−	0.0219005i	−0.00847134	−	0.000808915i	−0.0992909	+	0.995058i	$0.531657\pi$
$734$		0			0
$735$	−78.9101	−	42.4621i	−2.91064	−	1.56624i
$736$		0			0
$737$	−8.38338	+	14.5204i	−0.308806	+	0.534867i
$738$		0			0
$739$	−12.6634	+	17.7833i	−0.465831	+	0.654168i	−0.978938	−	0.204156i	$-0.934555\pi$
$739$	−12.6634	+	17.7833i	−0.465831	+	0.654168i	0.513107	+	0.858325i	$0.328494\pi$
$740$		0			0
$741$	0.701164	+	0.809187i	0.0257579	+	0.0297262i
$742$		0			0
$743$	37.2875	+	23.9632i	1.36795	+	0.879125i	0.998738	−	0.0502215i	$-0.0159927\pi$
$743$	37.2875	+	23.9632i	1.36795	+	0.879125i	0.369208	+	0.929347i	$0.379629\pi$
$744$		0			0
$745$	18.2175	+	3.51113i	0.667436	+	0.128638i
$746$		0			0
$747$	80.0913	+	32.0637i	2.93039	+	1.17315i
$748$		0			0
$749$	−30.5428	−	6.16695i	−1.11601	−	0.225336i
$750$		0			0
$751$	−11.8993	−	16.7102i	−0.434211	−	0.609764i	0.538262	−	0.842777i	$-0.319081\pi$
$751$	−11.8993	−	16.7102i	−0.434211	−	0.609764i	−0.972474	+	0.233013i	$0.925142\pi$
$752$		0			0
$753$	41.5124	+	39.5820i	1.51280	+	1.44245i
$754$		0			0
$755$	−62.9139	−	18.4732i	−2.28967	−	0.672308i
$756$		0			0
$757$	4.10791	−	28.5711i	0.149305	−	1.03844i	−0.768057	−	0.640381i	$-0.778776\pi$
$757$	4.10791	−	28.5711i	0.149305	−	1.03844i	0.917362	−	0.398055i	$-0.130315\pi$
$758$		0			0
$759$	−12.3927	+	39.8134i	−0.449827	+	1.44514i
$760$		0			0
$761$	32.2488	+	25.3607i	1.16902	+	0.919326i	0.997825	−	0.0659113i	$-0.0209954\pi$
$761$	32.2488	+	25.3607i	1.16902	+	0.919326i	0.171193	+	0.985238i	$0.445238\pi$
$762$		0			0
$763$	7.21228	+	0.0637133i	0.261102	+	0.00230658i
$764$		0			0
$765$	−30.1757	+	124.386i	−1.09100	+	4.49718i
$766$		0			0
$767$	2.59967	−	0.248238i	0.0938686	−	0.00896336i
$768$		0			0
$769$	20.0186	−	12.8652i	0.721891	−	0.463931i	−0.127403	−	0.991851i	$-0.540664\pi$
$769$	20.0186	−	12.8652i	0.721891	−	0.463931i	0.849294	+	0.527920i	$0.177028\pi$
$770$		0			0
$771$	−8.53874	−	59.3882i	−0.307515	−	2.13882i
$772$		0			0
$773$	41.2449	+	7.94930i	1.48348	+	0.285916i	0.865750	−	0.500477i	$-0.166842\pi$
$773$	41.2449	+	7.94930i	1.48348	+	0.285916i	0.617726	+	0.786394i	$0.288054\pi$
$774$		0			0
$775$	43.1274	−	22.2337i	1.54918	−	0.798659i
$776$		0			0
$777$	−68.1035	+	34.3517i	−2.44320	+	1.23236i
$778$		0			0
$779$	1.27307	+	0.121564i	0.0456126	+	0.00435548i
$780$		0			0
$781$	2.45522	+	4.25257i	0.0878548	+	0.152169i
$782$		0			0
$783$	−25.2649			−0.902895
$784$		0			0
$785$	−14.4019	−	31.5357i	−0.514024	−	1.12556i
$786$		0			0
$787$	6.13597	−	17.7287i	0.218724	−	0.631961i	−0.781246	−	0.624223i	$-0.785416\pi$
$787$	6.13597	−	17.7287i	0.218724	−	0.631961i	0.999970	−	0.00773780i	$-0.00246304\pi$
$788$		0			0
$789$	−6.72595	+	3.46747i	−0.239450	+	0.123445i
$790$		0			0
$791$	7.68066	+	10.9902i	0.273093	+	0.390765i
$792$		0			0
$793$	1.55953	+	0.624343i	0.0553807	+	0.0221711i
$794$		0			0
$795$	−62.7597	−	32.3549i	−2.22586	−	1.14751i
$796$		0			0
$797$	6.90323	−	15.1160i	0.244525	−	0.535435i	−0.747081	−	0.664733i	$-0.768545\pi$
$797$	6.90323	−	15.1160i	0.244525	−	0.535435i	0.991606	+	0.129298i	$0.0412724\pi$
$798$		0			0
$799$	28.1663	−	8.27036i	0.996451	−	0.292584i
$800$		0			0
$801$	−5.91004	−	24.3615i	−0.208821	−	0.860771i
$802$		0			0
$803$	9.68673	+	7.61773i	0.341837	+	0.268824i
$804$		0			0
$805$	−39.4756	+	26.6490i	−1.39133	+	0.939253i
$806$		0			0
$807$	14.3956	+	11.3208i	0.506749	+	0.398512i
$808$		0			0
$809$	−4.59458	−	18.9391i	−0.161537	−	0.665864i	−0.993771	−	0.111440i	$-0.964454\pi$
$809$	−4.59458	−	18.9391i	−0.161537	−	0.665864i	0.832234	−	0.554424i	$-0.187061\pi$
$810$		0			0
$811$	−19.3160	+	5.67168i	−0.678276	+	0.199160i	−0.602685	−	0.797979i	$-0.705902\pi$
$811$	−19.3160	+	5.67168i	−0.678276	+	0.199160i	−0.0755906	+	0.997139i	$0.524084\pi$
$812$		0			0
$813$	−13.2285	+	28.9664i	−0.463944	+	1.01590i
$814$		0			0
$815$	−15.7349	−	8.11191i	−0.551170	−	0.284148i
$816$		0			0
$817$	7.87630	+	3.15319i	0.275557	+	0.110316i
$818$		0			0
$819$	−10.5821	+	0.916209i	−0.369767	+	0.0320149i
$820$		0			0
$821$	17.9939	−	9.27650i	0.627991	−	0.323752i	−0.114686	−	0.993402i	$-0.536586\pi$
$821$	17.9939	−	9.27650i	0.627991	−	0.323752i	0.742677	+	0.669650i	$0.233556\pi$
$822$		0			0
$823$	−4.92451	+	14.2284i	−0.171658	+	0.495972i	−0.997711	−	0.0676195i	$-0.978460\pi$
$823$	−4.92451	+	14.2284i	−0.171658	+	0.495972i	0.826054	+	0.563592i	$0.190581\pi$
$824$		0			0
$825$	32.8317	+	71.8915i	1.14305	+	2.50294i
$826$		0			0
$827$	−45.0559			−1.56675			−0.783374	−	0.621550i	$-0.786503\pi$
$827$	−45.0559			−1.56675			−0.783374	+	0.621550i	$0.786503\pi$
$828$		0			0
$829$	−1.59485	−	2.76235i	−0.0553913	−	0.0959405i	0.837000	−	0.547203i	$-0.184307\pi$
$829$	−1.59485	−	2.76235i	−0.0553913	−	0.0959405i	−0.892391	+	0.451262i	$0.850974\pi$
$830$		0			0
$831$	4.30206	+	0.410797i	0.149237	+	0.0142504i
$832$		0			0
$833$	−20.3499	+	18.7285i	−0.705082	+	0.648903i
$834$		0			0
$835$	−12.7203	+	6.55776i	−0.440204	+	0.226941i
$836$		0			0
$837$	−100.645	−	19.3978i	−3.47881	−	0.670486i
$838$		0			0
$839$	−0.793602	−	5.51962i	−0.0273982	−	0.190558i	0.971526	−	0.236933i	$-0.0761423\pi$
$839$	−0.793602	−	5.51962i	−0.0273982	−	0.190558i	−0.998924	+	0.0463747i	$0.985233\pi$
$840$		0			0
$841$	−22.9400	+	14.7426i	−0.791034	+	0.508367i
$842$		0			0
$843$	14.2496	−	1.36067i	0.490783	−	0.0468641i
$844$		0			0
$845$	−11.3130	+	46.6328i	−0.389179	+	1.60422i
$846$		0			0
$847$	−5.86197	−	10.3636i	−0.201420	−	0.356097i
$848$		0			0
$849$	−42.0177	−	33.0431i	−1.44204	−	1.13403i
$850$		0			0
$851$	−0.655293	+	40.5369i	−0.0224631	+	1.38959i
$852$		0			0
$853$	3.42020	−	23.7880i	0.117106	−	0.814487i	−0.843611	−	0.536955i	$-0.819575\pi$
$853$	3.42020	−	23.7880i	0.117106	−	0.814487i	0.960716	−	0.277532i	$-0.0895164\pi$
$854$		0			0
$855$	−20.9797	−	6.16019i	−0.717490	−	0.210674i
$856$		0			0
$857$	−13.6800	−	13.0438i	−0.467299	−	0.445568i	0.419479	−	0.907765i	$-0.362213\pi$
$857$	−13.6800	−	13.0438i	−0.467299	−	0.445568i	−0.886777	+	0.462197i	$0.847061\pi$
$858$		0			0
$859$	−18.3454	−	25.7626i	−0.625938	−	0.879008i	0.372866	−	0.927885i	$-0.378375\pi$
$859$	−18.3454	−	25.7626i	−0.625938	−	0.879008i	−0.998805	+	0.0488775i	$0.984436\pi$
$860$		0			0
$861$	−11.3095	+	12.8213i	−0.385428	+	0.436949i
$862$		0			0
$863$	42.9495	+	17.1944i	1.46202	+	0.585303i	0.960111	−	0.279619i	$-0.0902082\pi$
$863$	42.9495	+	17.1944i	1.46202	+	0.585303i	0.501906	+	0.864922i	$0.332632\pi$
$864$		0			0
$865$	−65.2845	−	12.5826i	−2.21974	−	0.427820i
$866$		0			0
$867$	−3.98884	−	2.56347i	−0.135468	−	0.0870600i
$868$		0			0
$869$	−22.5612	−	26.0370i	−0.765336	−	0.883245i
$870$		0			0
$871$	−1.77451	+	2.49195i	−0.0601270	+	0.0844366i
$872$		0			0
$873$	26.1756	−	45.3375i	0.885910	−	1.53444i
$874$		0			0
$875$	−9.92464	+	39.3880i	−0.335514	+	1.33156i
$876$		0			0
$877$	4.05648	+	0.387347i	0.136978	+	0.0130798i	0.163320	−	0.986573i	$-0.447780\pi$
$877$	4.05648	+	0.387347i	0.136978	+	0.0130798i	−0.0263420	+	0.999653i	$0.508386\pi$
$878$		0			0
$879$	25.2230	−	72.8770i	0.850750	−	2.45808i
$880$		0			0
$881$	7.82539	+	5.02908i	0.263644	+	0.169434i	0.665784	−	0.746144i	$-0.268097\pi$
$881$	7.82539	+	5.02908i	0.263644	+	0.169434i	−0.402140	+	0.915578i	$0.631733\pi$
$882$		0			0
$883$	26.9598	−	31.1133i	0.907270	−	1.04705i	−0.0914165	−	0.995813i	$-0.529139\pi$
$883$	26.9598	−	31.1133i	0.907270	−	1.04705i	0.998687	−	0.0512329i	$-0.0163151\pi$
$884$		0			0
$885$	−56.4923	+	44.4260i	−1.89897	+	1.49336i
$886$		0			0
$887$	0.114459	+	2.40278i	0.00384315	+	0.0806776i	0.999974	−	0.00720431i	$-0.00229322\pi$
$887$	0.114459	+	2.40278i	0.00384315	+	0.0806776i	−0.996131	+	0.0878819i	$0.971990\pi$
$888$		0			0
$889$	1.71770	+	1.37555i	0.0576099	+	0.0461343i
$890$		0			0
$891$	23.7983	−	98.0980i	0.797274	−	3.28641i
$892$		0			0
$893$	1.18229	+	4.87346i	0.0395638	+	0.163084i
$894$		0			0
$895$	5.59371	−	38.9051i	0.186977	−	1.30045i
$896$		0			0
$897$	−2.94140	+	7.01639i	−0.0982103	+	0.234270i
$898$		0			0
$899$	6.52017	−	2.61028i	0.217460	−	0.0870578i
$900$		0			0
$901$	−15.7718	+	15.0383i	−0.525433	+	0.501000i
$902$		0			0
$903$	−95.9520	+	60.4736i	−3.19308	+	2.01244i
$904$		0			0
$905$	13.0675	+	18.3507i	0.434377	+	0.609997i
$906$		0			0
$907$	−5.83824	−	3.00982i	−0.193856	−	0.0999396i	0.358566	−	0.933504i	$-0.383266\pi$
$907$	−5.83824	−	3.00982i	−0.193856	−	0.0999396i	−0.552422	+	0.833565i	$0.686296\pi$
$908$		0			0
$909$	−5.36651	−	37.3249i	−0.177996	−	1.23799i
$910$		0			0
$911$	19.6067	−	22.6274i	0.649600	−	0.749678i	−0.331442	−	0.943476i	$-0.607535\pi$
$911$	19.6067	−	22.6274i	0.649600	−	0.749678i	0.981042	+	0.193798i	$0.0620805\pi$
$912$		0			0
$913$	1.21260	−	25.4557i	0.0401313	−	0.842460i
$914$		0			0
$915$	−45.3945	+	8.74907i	−1.50070	+	0.289235i
$916$		0			0
$917$	9.13197	−	25.6497i	0.301564	−	0.847028i
$918$		0			0
$919$	−16.9805	+	29.4112i	−0.560137	+	0.970185i	0.437347	+	0.899293i	$0.355918\pi$
$919$	−16.9805	+	29.4112i	−0.560137	+	0.970185i	−0.997484	+	0.0708923i	$0.977415\pi$
$920$		0			0
$921$	−41.4144	−	71.7318i	−1.36465	−	2.36364i
$922$		0			0
$923$	0.372188	+	0.814977i	0.0122507	+	0.0268253i
$924$		0			0
$925$	50.3219	+	58.0746i	1.65457	+	1.90948i
$926$		0			0
$927$	−6.51020	+	136.666i	−0.213823	+	4.48870i
$928$		0			0
$929$	−12.0105	−	34.7020i	−0.394051	−	1.13853i	−0.951321	−	0.308203i	$-0.900272\pi$
$929$	−12.0105	−	34.7020i	−0.394051	−	1.13853i	0.557270	−	0.830331i	$-0.311849\pi$
$930$		0			0
$931$	−3.03038	−	3.62470i	−0.0993166	−	0.118795i
$932$		0			0
$933$	−1.84117	−	38.6509i	−0.0602772	−	1.26537i
$934$		0			0
$935$	37.6382	−	3.59402i	1.23090	−	0.117537i
$936$		0			0
$937$	−6.63192	+	1.94731i	−0.216656	+	0.0636158i	−0.388259	−	0.921550i	$-0.626923\pi$
$937$	−6.63192	+	1.94731i	−0.216656	+	0.0636158i	0.171603	+	0.985166i	$0.445105\pi$
$938$		0			0
$939$	28.1560	+	8.26734i	0.918835	+	0.269794i
$940$		0			0
$941$	39.8333	−	15.9469i	1.29853	−	0.519853i	0.383612	−	0.923494i	$-0.374680\pi$
$941$	39.8333	−	15.9469i	1.29853	−	0.519853i	0.914917	+	0.403642i	$0.132256\pi$
$942$		0			0
$943$	3.24053	+	8.48963i	0.105526	+	0.276460i
$944$		0			0
$945$	150.936	−	116.554i	4.90995	−	3.79151i
$946$		0			0
$947$	33.6646	−	32.0991i	1.09395	−	1.04308i	0.0950865	−	0.995469i	$-0.469687\pi$
$947$	33.6646	−	32.0991i	1.09395	−	1.04308i	0.998866	−	0.0476125i	$-0.0151613\pi$
$948$		0			0
$949$	1.62728	+	1.55161i	0.0528239	+	0.0503675i
$950$		0			0
$951$	−31.4420	+	68.8484i	−1.01958	+	2.23256i
$952$		0			0
$953$	26.6846	−	17.1492i	0.864399	−	0.555516i	−0.0316354	−	0.999499i	$-0.510072\pi$
$953$	26.6846	−	17.1492i	0.864399	−	0.555516i	0.896035	+	0.443984i	$0.146435\pi$
$954$		0			0
$955$	52.5212	−	41.3031i	1.69955	−	1.33654i
$956$		0			0
$957$	3.74159	+	10.8106i	0.120949	+	0.349458i
$958$		0			0
$959$	20.6042	+	6.24817i	0.665345	+	0.201764i
$960$		0			0
$961$	−2.46195	+	0.474502i	−0.0794178	+	0.0153065i
$962$		0			0
$963$	58.9581	−	82.7950i	1.89990	−	2.66803i
$964$		0			0
$965$	6.90161			0.222171
$966$		0			0
$967$	−39.0063			−1.25436			−0.627179	−	0.778875i	$-0.715791\pi$
$967$	−39.0063			−1.25436			−0.627179	+	0.778875i	$0.715791\pi$
$968$		0			0
$969$	−5.27511	+	7.40786i	−0.169461	+	0.237975i
$970$		0			0
$971$	13.0522	−	2.51560i	0.418864	−	0.0807295i	0.0245357	−	0.999699i	$-0.492189\pi$
$971$	13.0522	−	2.51560i	0.418864	−	0.0807295i	0.394329	+	0.918969i	$0.370977\pi$
$972$		0			0
$973$	35.9551	−	33.6818i	1.15267	−	1.07979i
$974$		0			0
$975$	4.71638	+	13.6271i	0.151045	+	0.436416i
$976$		0			0
$977$	12.7835	−	10.0531i	0.408982	−	0.321627i	−0.392384	−	0.919801i	$-0.628350\pi$
$977$	12.7835	−	10.0531i	0.408982	−	0.321627i	0.801366	+	0.598175i	$0.204107\pi$
$978$		0			0
$979$	−6.22960	+	4.00352i	−0.199099	+	0.127953i
$980$		0			0
$981$	−9.77369	+	21.4014i	−0.312050	+	0.683294i
$982$		0			0
$983$	−10.9008	−	10.3939i	−0.347681	−	0.331514i	0.496035	−	0.868302i	$-0.334789\pi$
$983$	−10.9008	−	10.3939i	−0.347681	−	0.331514i	−0.843717	+	0.536789i	$0.819637\pi$
$984$		0			0
$985$	45.1600	−	43.0600i	1.43892	−	1.37201i
$986$		0			0
$987$	−62.0160	−	25.4654i	−1.97399	−	0.810572i
$988$		0			0
$989$	4.75963	+	60.0957i	0.151347	+	1.91093i
$990$		0			0
$991$	28.1708	−	11.2779i	0.894876	−	0.358254i	0.121790	−	0.992556i	$-0.461136\pi$
$991$	28.1708	−	11.2779i	0.894876	−	0.358254i	0.773086	+	0.634302i	$0.218712\pi$
$992$		0			0
$993$	15.6176	+	4.58573i	0.495608	+	0.145524i
$994$		0			0
$995$	−41.6939	+	12.2424i	−1.32179	+	0.388112i
$996$		0			0
$997$	38.6088	−	3.68669i	1.22275	−	0.116759i	0.536360	−	0.843989i	$-0.319799\pi$
$997$	38.6088	−	3.68669i	1.22275	−	0.116759i	0.686393	+	0.727231i	$0.259193\pi$
$998$		0			0
$999$	−7.72382	−	162.143i	−0.244371	−	5.12997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.y.a.261.16	yes	320
7.4	even	3	inner	644.2.y.a.445.1	yes	320
23.3	even	11	inner	644.2.y.a.233.1	✓	320
161.95	even	33	inner	644.2.y.a.417.16	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.y.a.233.1	✓	320	23.3	even	11	inner
644.2.y.a.261.16	yes	320	1.1	even	1	trivial
644.2.y.a.417.16	yes	320	161.95	even	33	inner
644.2.y.a.445.1	yes	320	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.97820 - 2.77799i) q^{3} +(3.68583 - 0.710386i) q^{5} +(-1.93087 + 1.80879i) q^{7} +(-2.82276 - 8.15583i) q^{9} +O(q^{10})\)	\(q+(1.97820 - 2.77799i) q^{3} +(3.68583 - 0.710386i) q^{5} +(-1.93087 + 1.80879i) q^{7} +(-2.82276 - 8.15583i) q^{9} +(-2.00401 + 1.57597i) q^{11} +(-0.391321 + 0.251487i) q^{13} +(5.31786 - 11.6445i) q^{15} +(-2.85941 - 2.72644i) q^{17} +(0.488477 - 0.465762i) q^{19} +(1.20515 + 8.94210i) q^{21} +(4.50612 + 1.64161i) q^{23} +(8.43888 - 3.37842i) q^{25} +(-18.4242 - 5.40983i) q^{27} +(1.26245 - 0.370688i) q^{29} +(5.31369 - 0.507396i) q^{31} +(0.413703 + 8.68470i) q^{33} +(-5.83194 + 8.03857i) q^{35} +(2.76491 + 7.98869i) q^{37} +(-0.0754828 + 1.58458i) q^{39} +(1.24082 + 1.43198i) q^{41} +(5.22179 + 11.4341i) q^{43} +(-16.1980 - 28.0558i) q^{45} +(-3.71502 + 6.43460i) q^{47} +(0.456548 - 6.98510i) q^{49} +(-13.2305 + 2.54997i) q^{51} +(0.262450 - 5.50950i) q^{53} +(-6.26690 + 7.23238i) q^{55} +(-0.327578 - 2.27835i) q^{57} +(-4.99004 - 2.57254i) q^{59} +(-2.09478 - 2.94171i) q^{61} +(20.2026 + 10.6421i) q^{63} +(-1.26369 + 1.20493i) q^{65} +(6.10550 - 2.44428i) q^{67} +(13.4744 - 9.27053i) q^{69} +(0.274109 - 1.90647i) q^{71} +(-1.13958 - 4.69742i) q^{73} +(7.30857 - 30.1263i) q^{75} +(1.01889 - 6.66783i) q^{77} +(0.642995 + 13.4981i) q^{79} +(-31.1231 + 24.4755i) q^{81} +(-6.54603 + 7.55452i) q^{83} +(-12.4761 - 8.01791i) q^{85} +(1.46760 - 4.24036i) q^{87} +(2.89144 + 0.276099i) q^{89} +(0.300705 - 1.19341i) q^{91} +(9.10199 - 15.7651i) q^{93} +(1.46957 - 2.06373i) q^{95} +(3.97227 + 4.58425i) q^{97} +(18.5102 + 11.8958i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 6 q^{5} - 2 q^{7} + 12 q^{9}+O(q^{10}) \) 320 * q + 6 * q^5 - 2 * q^7 + 12 * q^9	\( 320 q + 6 q^{5} - 2 q^{7} + 12 q^{9} - 2 q^{11} - 16 q^{15} + 4 q^{17} - 50 q^{21} + 25 q^{23} + 44 q^{25} + 54 q^{27} + 12 q^{29} + 2 q^{31} - 12 q^{33} - 22 q^{35} - 44 q^{37} - 4 q^{39} + 12 q^{41} + 76 q^{43} - 114 q^{45} - 10 q^{47} - 74 q^{49} - 30 q^{51} - 20 q^{53} + 32 q^{55} + 52 q^{57} - 32 q^{59} + 74 q^{61} + 87 q^{63} - 75 q^{65} - 8 q^{67} + 10 q^{69} + 8 q^{73} + 118 q^{75} + 5 q^{77} - 40 q^{79} - 44 q^{81} - 52 q^{83} - 100 q^{85} + 84 q^{87} + 36 q^{89} + 30 q^{91} - 12 q^{93} - 25 q^{95} + 72 q^{97} + 2 q^{99}+O(q^{100}) \) 320 * q + 6 * q^5 - 2 * q^7 + 12 * q^9 - 2 * q^11 - 16 * q^15 + 4 * q^17 - 50 * q^21 + 25 * q^23 + 44 * q^25 + 54 * q^27 + 12 * q^29 + 2 * q^31 - 12 * q^33 - 22 * q^35 - 44 * q^37 - 4 * q^39 + 12 * q^41 + 76 * q^43 - 114 * q^45 - 10 * q^47 - 74 * q^49 - 30 * q^51 - 20 * q^53 + 32 * q^55 + 52 * q^57 - 32 * q^59 + 74 * q^61 + 87 * q^63 - 75 * q^65 - 8 * q^67 + 10 * q^69 + 8 * q^73 + 118 * q^75 + 5 * q^77 - 40 * q^79 - 44 * q^81 - 52 * q^83 - 100 * q^85 + 84 * q^87 + 36 * q^89 + 30 * q^91 - 12 * q^93 - 25 * q^95 + 72 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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