LMFDB - Embedded newform 861.2.i.c.739.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [861,2,Mod(247,861)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(861, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("861.247");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 861 = 3 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	861.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.87511961403$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.7873200.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 12x^{4} + 36x^{2} + 12 $ x^6 + 12x^4 + 36x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			739.3
Root			$-2.08243i$ of defining polynomial
Character	$\chi$	$=$	861.739
Dual form			861.2.i.c.247.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(1.97169 + 3.41507i) q^{5} +(2.63994 - 0.175189i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(1.97169 + 3.41507i) q^{5} +(2.63994 - 0.175189i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(2.13994 - 3.70649i) q^{11} +(-1.00000 - 1.73205i) q^{12} -4.60687 q^{13} +3.94338 q^{15} +(-2.00000 - 3.46410i) q^{16} +(1.00000 - 1.73205i) q^{17} +(3.47169 + 6.01314i) q^{19} +7.88676 q^{20} +(1.16825 - 2.37385i) q^{21} +(-2.97169 - 5.14712i) q^{23} +(-5.27513 + 9.13679i) q^{25} -1.00000 q^{27} +(2.33651 - 4.74771i) q^{28} +7.88676 q^{29} +(-4.61164 + 7.98759i) q^{31} +(-2.13994 - 3.70649i) q^{33} +(5.80344 + 8.67017i) q^{35} -2.00000 q^{36} +(0.500000 + 0.866025i) q^{37} +(-2.30344 + 3.98967i) q^{39} -1.00000 q^{41} -6.66349 q^{43} +(-4.27989 - 7.41299i) q^{44} +(1.97169 - 3.41507i) q^{45} +(1.46693 + 2.54079i) q^{47} -4.00000 q^{48} +(6.93862 - 0.924978i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(-4.60687 + 7.97934i) q^{52} +(4.60687 - 7.97934i) q^{53} +16.8772 q^{55} +6.94338 q^{57} +(-6.60687 + 11.4434i) q^{59} +(3.94338 - 6.83014i) q^{60} +(-4.43862 - 7.68791i) q^{61} +(-1.47169 - 2.19866i) q^{63} -8.00000 q^{64} +(-9.08333 - 15.7328i) q^{65} +(1.30344 - 2.25762i) q^{67} +(-2.00000 - 3.46410i) q^{68} -5.94338 q^{69} +7.21374 q^{71} +(3.33175 - 5.77075i) q^{73} +(5.27513 + 9.13679i) q^{75} +13.8868 q^{76} +(5.00000 - 10.1598i) q^{77} +(-1.19180 - 2.06426i) q^{79} +(7.88676 - 13.6603i) q^{80} +(-0.500000 + 0.866025i) q^{81} -4.59735 q^{83} +(-2.94338 - 4.39733i) q^{84} +7.88676 q^{85} +(3.94338 - 6.83014i) q^{87} +(-3.46693 - 6.00489i) q^{89} +(-12.1619 + 0.807073i) q^{91} -11.8868 q^{92} +(4.61164 + 7.98759i) q^{93} +(-13.6902 + 23.7121i) q^{95} -9.77352 q^{97} -4.27989 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} + 6 q^{4} + 3 q^{7} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 + 6 * q^4 + 3 * q^7 - 3 * q^9	$ 6 q + 3 q^{3} + 6 q^{4} + 3 q^{7} - 3 q^{9} - 6 q^{12} - 6 q^{13} - 12 q^{16} + 6 q^{17} + 9 q^{19} + 6 q^{21} - 6 q^{23} - 9 q^{25} - 6 q^{27} + 12 q^{28} - 3 q^{31} + 24 q^{35} - 12 q^{36} + 3 q^{37} - 3 q^{39} - 6 q^{41} - 42 q^{43} - 24 q^{48} + 21 q^{49} - 6 q^{51} - 6 q^{52} + 6 q^{53} + 60 q^{55} + 18 q^{57} - 18 q^{59} - 6 q^{61} + 3 q^{63} - 48 q^{64} - 18 q^{65} - 3 q^{67} - 12 q^{68} - 12 q^{69} + 21 q^{73} + 9 q^{75} + 36 q^{76} + 30 q^{77} - 21 q^{79} - 3 q^{81} - 12 q^{83} + 6 q^{84} - 12 q^{89} - 3 q^{91} - 24 q^{92} + 3 q^{93} - 24 q^{95} + 36 q^{97}+O(q^{100}) $ 6 * q + 3 * q^3 + 6 * q^4 + 3 * q^7 - 3 * q^9 - 6 * q^12 - 6 * q^13 - 12 * q^16 + 6 * q^17 + 9 * q^19 + 6 * q^21 - 6 * q^23 - 9 * q^25 - 6 * q^27 + 12 * q^28 - 3 * q^31 + 24 * q^35 - 12 * q^36 + 3 * q^37 - 3 * q^39 - 6 * q^41 - 42 * q^43 - 24 * q^48 + 21 * q^49 - 6 * q^51 - 6 * q^52 + 6 * q^53 + 60 * q^55 + 18 * q^57 - 18 * q^59 - 6 * q^61 + 3 * q^63 - 48 * q^64 - 18 * q^65 - 3 * q^67 - 12 * q^68 - 12 * q^69 + 21 * q^73 + 9 * q^75 + 36 * q^76 + 30 * q^77 - 21 * q^79 - 3 * q^81 - 12 * q^83 + 6 * q^84 - 12 * q^89 - 3 * q^91 - 24 * q^92 + 3 * q^93 - 24 * q^95 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/861\mathbb{Z}\right)^\times$.

$n$	$211$	$493$	$575$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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		0.866025	−	0.500000i	$-0.166667\pi$
$2$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	1.97169	+	3.41507i	0.881767	+	1.52726i	0.849375	+	0.527790i	$0.176979\pi$
$5$	1.97169	+	3.41507i	0.881767	+	1.52726i	0.0323916	+	0.999475i	$0.489688\pi$
$6$		0			0
$7$	2.63994	−	0.175189i	0.997805	−	0.0662152i
$7$	2.63994	−	0.175189i	0.997805	−	0.0662152i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	2.13994	−	3.70649i	0.645218	−	1.11755i	−0.339034	−	0.940774i	$-0.610100\pi$
$11$	2.13994	−	3.70649i	0.645218	−	1.11755i	0.984251	−	0.176775i	$-0.0565666\pi$
$12$	−1.00000	−	1.73205i	−0.288675	−	0.500000i
$13$	−4.60687			−1.27772			−0.638858	−	0.769324i	$-0.720593\pi$
$13$	−4.60687			−1.27772			−0.638858	+	0.769324i	$0.720593\pi$
$14$		0			0
$15$	3.94338			1.01818
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$		0			0
$19$	3.47169	+	6.01314i	0.796460	+	1.37951i	0.921908	+	0.387410i	$0.126630\pi$
$19$	3.47169	+	6.01314i	0.796460	+	1.37951i	−0.125447	+	0.992100i	$0.540037\pi$
$20$	7.88676			1.76353
$21$	1.16825	−	2.37385i	0.254934	−	0.518017i
$22$		0			0
$23$	−2.97169	−	5.14712i	−0.619640	−	1.07325i	−0.989551	−	0.144181i	$-0.953945\pi$
$23$	−2.97169	−	5.14712i	−0.619640	−	1.07325i	0.369911	−	0.929067i	$-0.379388\pi$
$24$		0			0
$25$	−5.27513	+	9.13679i	−1.05503	+	1.82736i
$26$		0			0
$27$	−1.00000			−0.192450
$28$	2.33651	−	4.74771i	0.441559	−	0.897232i
$29$	7.88676			1.46453			0.732267	−	0.681017i	$-0.238462\pi$
$29$	7.88676			1.46453			0.732267	+	0.681017i	$0.238462\pi$
$30$		0			0
$31$	−4.61164	+	7.98759i	−0.828274	+	1.43461i	0.0711169	+	0.997468i	$0.477344\pi$
$31$	−4.61164	+	7.98759i	−0.828274	+	1.43461i	−0.899391	+	0.437145i	$0.855990\pi$
$32$		0			0
$33$	−2.13994	−	3.70649i	−0.372517	−	0.645218i
$34$		0			0
$35$	5.80344	+	8.67017i	0.980960	+	1.46553i
$36$	−2.00000			−0.333333
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$		0			0
$39$	−2.30344	+	3.98967i	−0.368845	+	0.638858i
$40$		0			0
$41$	−1.00000			−0.156174
$41$	−1.00000			−0.156174
$42$		0			0
$43$	−6.66349			−1.01617			−0.508086	−	0.861306i	$-0.669647\pi$
$43$	−6.66349			−1.01617			−0.508086	+	0.861306i	$0.669647\pi$
$44$	−4.27989	−	7.41299i	−0.645218	−	1.11755i
$45$	1.97169	−	3.41507i	0.293922	−	0.509088i
$46$		0			0
$47$	1.46693	+	2.54079i	0.213973	+	0.370613i	0.952954	−	0.303113i	$-0.0980261\pi$
$47$	1.46693	+	2.54079i	0.213973	+	0.370613i	−0.738981	+	0.673726i	$0.764693\pi$
$48$	−4.00000			−0.577350
$49$	6.93862	−	0.924978i	0.991231	−	0.132140i
$50$		0			0
$51$	−1.00000	−	1.73205i	−0.140028	−	0.242536i
$52$	−4.60687	+	7.97934i	−0.638858	+	1.10653i
$53$	4.60687	−	7.97934i	0.632803	−	1.09605i	−0.354174	−	0.935180i	$-0.615238\pi$
$53$	4.60687	−	7.97934i	0.632803	−	1.09605i	0.986976	−	0.160866i	$-0.0514289\pi$
$54$		0			0
$55$	16.8772			2.27573
$56$		0			0
$57$	6.94338			0.919673
$58$		0			0
$59$	−6.60687	+	11.4434i	−0.860141	+	1.48981i	0.0116503	+	0.999932i	$0.496292\pi$
$59$	−6.60687	+	11.4434i	−0.860141	+	1.48981i	−0.871792	+	0.489877i	$0.837042\pi$
$60$	3.94338	−	6.83014i	0.509088	−	0.881767i
$61$	−4.43862	−	7.68791i	−0.568307	−	0.984336i	−0.996734	−	0.0807597i	$-0.974265\pi$
$61$	−4.43862	−	7.68791i	−0.568307	−	0.984336i	0.428427	−	0.903576i	$-0.359068\pi$
$62$		0			0
$63$	−1.47169	−	2.19866i	−0.185416	−	0.277006i
$64$	−8.00000			−1.00000
$65$	−9.08333	−	15.7328i	−1.12665	−	1.95141i
$66$		0			0
$67$	1.30344	−	2.25762i	0.159240	−	0.275812i	−0.775355	−	0.631526i	$-0.782429\pi$
$67$	1.30344	−	2.25762i	0.159240	−	0.275812i	0.934595	+	0.355714i	$0.115762\pi$
$68$	−2.00000	−	3.46410i	−0.242536	−	0.420084i
$69$	−5.94338			−0.715499
$70$		0			0
$71$	7.21374			0.856114			0.428057	−	0.903752i	$-0.359198\pi$
$71$	7.21374			0.856114			0.428057	+	0.903752i	$0.359198\pi$
$72$		0			0
$73$	3.33175	−	5.77075i	0.389951	−	0.675416i	−0.602491	−	0.798125i	$-0.705825\pi$
$73$	3.33175	−	5.77075i	0.389951	−	0.675416i	0.992443	+	0.122710i	$0.0391585\pi$
$74$		0			0
$75$	5.27513	+	9.13679i	0.609119	+	1.05503i
$76$	13.8868			1.59292
$77$	5.00000	−	10.1598i	0.569803	−	1.15782i
$78$		0			0
$79$	−1.19180	−	2.06426i	−0.134088	−	0.232247i	0.791161	−	0.611608i	$-0.209477\pi$
$79$	−1.19180	−	2.06426i	−0.134088	−	0.232247i	−0.925249	+	0.379361i	$0.876144\pi$
$80$	7.88676	−	13.6603i	0.881767	−	1.52726i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−4.59735			−0.504624			−0.252312	−	0.967646i	$-0.581191\pi$
$83$	−4.59735			−0.504624			−0.252312	+	0.967646i	$0.581191\pi$
$84$	−2.94338	−	4.39733i	−0.321149	−	0.479788i
$85$	7.88676			0.855439
$86$		0			0
$87$	3.94338	−	6.83014i	0.422775	−	0.732267i
$88$		0			0
$89$	−3.46693	−	6.00489i	−0.367494	−	0.636518i	0.621679	−	0.783272i	$-0.286451\pi$
$89$	−3.46693	−	6.00489i	−0.367494	−	0.636518i	−0.989173	+	0.146754i	$0.953117\pi$
$90$		0			0
$91$	−12.1619	+	0.807073i	−1.27491	+	0.0846042i
$92$	−11.8868			−1.23928
$93$	4.61164	+	7.98759i	0.478204	+	0.828274i
$94$		0			0
$95$	−13.6902	+	23.7121i	−1.40458	+	2.43281i
$96$		0			0
$97$	−9.77352			−0.992351			−0.496175	−	0.868222i	$-0.665263\pi$
$97$	−9.77352			−0.992351			−0.496175	+	0.868222i	$0.665263\pi$
$98$		0			0
$99$	−4.27989			−0.430145
$100$	10.5503	+	18.2736i	1.05503	+	1.82736i
$101$	−6.88676	+	11.9282i	−0.685258	+	1.18690i	0.288097	+	0.957601i	$0.406977\pi$
$101$	−6.88676	+	11.9282i	−0.685258	+	1.18690i	−0.973356	+	0.229301i	$0.926356\pi$
$102$		0			0
$103$	−2.44338	−	4.23206i	−0.240753	−	0.416997i	0.720176	−	0.693792i	$-0.244061\pi$
$103$	−2.44338	−	4.23206i	−0.240753	−	0.416997i	−0.960929	+	0.276795i	$0.910728\pi$
$104$		0			0
$105$	10.4103	−	0.690837i	1.01594	−	0.0674187i
$106$		0			0
$107$	1.97169	+	3.41507i	0.190611	+	0.330147i	0.945453	−	0.325759i	$-0.105620\pi$
$107$	1.97169	+	3.41507i	0.190611	+	0.330147i	−0.754842	+	0.655906i	$0.772287\pi$
$108$	−1.00000	+	1.73205i	−0.0962250	+	0.166667i
$109$	−8.07856	+	13.9925i	−0.773786	+	1.34024i	0.161688	+	0.986842i	$0.448306\pi$
$109$	−8.07856	+	13.9925i	−0.773786	+	1.34024i	−0.935474	+	0.353395i	$0.885027\pi$
$110$		0			0
$111$	1.00000			0.0949158
$112$	−5.88676	−	8.79466i	−0.556247	−	0.831017i
$113$	7.28942			0.685731			0.342865	−	0.939385i	$-0.388603\pi$
$113$	7.28942			0.685731			0.342865	+	0.939385i	$0.388603\pi$
$114$		0			0
$115$	11.7185	−	20.2971i	1.09276	−	1.89271i
$116$	7.88676	−	13.6603i	0.732267	−	1.26832i
$117$	2.30344	+	3.98967i	0.212953	+	0.368845i
$118$		0			0
$119$	2.33651	−	4.74771i	0.214187	−	0.435222i
$120$		0			0
$121$	−3.65873	−	6.33710i	−0.332612	−	0.576100i
$122$		0			0
$123$	−0.500000	+	0.866025i	−0.0450835	+	0.0780869i
$124$	9.22327	+	15.9752i	0.828274	+	1.43461i
$125$	−21.8868			−1.95761
$126$		0			0
$127$	5.67302			0.503399			0.251699	−	0.967805i	$-0.419011\pi$
$127$	5.67302			0.503399			0.251699	+	0.967805i	$0.419011\pi$
$128$		0			0
$129$	−3.33175	+	5.77075i	−0.293344	+	0.508086i
$130$		0			0
$131$	5.02831	+	8.70929i	0.439325	+	0.760934i	0.997638	−	0.0686970i	$-0.0218842\pi$
$131$	5.02831	+	8.70929i	0.439325	+	0.760934i	−0.558312	+	0.829631i	$0.688551\pi$
$132$	−8.55978			−0.745033
$133$	10.2185	+	15.2662i	0.886057	+	1.32374i
$134$		0			0
$135$	−1.97169	−	3.41507i	−0.169696	−	0.293922i
$136$		0			0
$137$	2.60687	−	4.51523i	0.222720	−	0.385763i	−0.732913	−	0.680322i	$-0.761840\pi$
$137$	2.60687	−	4.51523i	0.222720	−	0.385763i	0.955633	+	0.294560i	$0.0951731\pi$
$138$		0			0
$139$	−5.54073			−0.469958			−0.234979	−	0.972000i	$-0.575502\pi$
$139$	−5.54073			−0.469958			−0.234979	+	0.972000i	$0.575502\pi$
$140$	20.8206	−	1.38167i	1.75966	−	0.116773i
$141$	2.93385			0.247075
$142$		0			0
$143$	−9.85845	+	17.0753i	−0.824405	+	1.42791i
$144$	−2.00000	+	3.46410i	−0.166667	+	0.288675i
$145$	15.5503	+	26.9338i	1.29138	+	2.23673i
$146$		0			0
$147$	2.66825	−	6.47151i	0.220074	−	0.533761i
$148$	2.00000			0.164399
$149$	−4.13994	−	7.17059i	−0.339157	−	0.587438i	0.645117	−	0.764084i	$-0.276809\pi$
$149$	−4.13994	−	7.17059i	−0.339157	−	0.587438i	−0.984274	+	0.176646i	$0.943475\pi$
$150$		0			0
$151$	−1.84127	+	3.18918i	−0.149841	+	0.259532i	−0.931168	−	0.364589i	$-0.881209\pi$
$151$	−1.84127	+	3.18918i	−0.149841	+	0.259532i	0.781328	+	0.624121i	$0.214543\pi$
$152$		0			0
$153$	−2.00000			−0.161690
$154$		0			0
$155$	−36.3709			−2.92138
$156$	4.60687	+	7.97934i	0.368845	+	0.638858i
$157$	5.00000	−	8.66025i	0.399043	−	0.691164i	−0.594565	−	0.804048i	$-0.702676\pi$
$157$	5.00000	−	8.66025i	0.399043	−	0.691164i	0.993608	+	0.112884i	$0.0360089\pi$
$158$		0			0
$159$	−4.60687	−	7.97934i	−0.365349	−	0.632803i
$160$		0			0
$161$	−8.74682	−	13.0675i	−0.689346	−	1.02986i
$162$		0			0
$163$	7.71851	+	13.3688i	0.604560	+	1.04713i	0.992121	+	0.125285i	$0.0399844\pi$
$163$	7.71851	+	13.3688i	0.604560	+	1.04713i	−0.387561	+	0.921844i	$0.626682\pi$
$164$	−1.00000	+	1.73205i	−0.0780869	+	0.135250i
$165$	8.43862	−	14.6161i	0.656945	−	1.13786i
$166$		0			0
$167$	1.21374			0.0939223			0.0469612	−	0.998897i	$-0.485046\pi$
$167$	1.21374			0.0939223			0.0469612	+	0.998897i	$0.485046\pi$
$168$		0			0
$169$	8.22327			0.632559
$170$		0			0
$171$	3.47169	−	6.01314i	0.265487	−	0.459837i
$172$	−6.66349	+	11.5415i	−0.508086	+	0.880032i
$173$	0.393128	+	0.680917i	0.0298890	+	0.0517692i	0.880583	−	0.473892i	$-0.157151\pi$
$173$	0.393128	+	0.680917i	0.0298890	+	0.0517692i	−0.850694	+	0.525661i	$0.823818\pi$
$174$		0			0
$175$	−12.3254	+	25.0448i	−0.931711	+	1.89321i
$176$	−17.1196			−1.29044
$177$	6.60687	+	11.4434i	0.496603	+	0.860141i
$178$		0			0
$179$	−12.2233	+	21.1713i	−0.913610	+	1.58242i	−0.104687	+	0.994505i	$0.533384\pi$
$179$	−12.2233	+	21.1713i	−0.913610	+	1.58242i	−0.808923	+	0.587914i	$0.799949\pi$
$180$	−3.94338	−	6.83014i	−0.293922	−	0.509088i
$181$	−19.5032			−1.44966			−0.724829	−	0.688929i	$-0.758081\pi$
$181$	−19.5032			−1.44966			−0.724829	+	0.688929i	$0.758081\pi$
$182$		0			0
$183$	−8.87724			−0.656224
$184$		0			0
$185$	−1.97169	+	3.41507i	−0.144962	+	0.251081i
$186$		0			0
$187$	−4.27989	−	7.41299i	−0.312977	−	0.542091i
$188$	5.86771			0.427947
$189$	−2.63994	+	0.175189i	−0.192028	+	0.0127431i
$190$		0			0
$191$	−6.41031	−	11.1030i	−0.463834	−	0.803383i	0.535314	−	0.844653i	$-0.320193\pi$
$191$	−6.41031	−	11.1030i	−0.463834	−	0.803383i	−0.999148	+	0.0412695i	$0.986860\pi$
$192$	−4.00000	+	6.92820i	−0.288675	+	0.500000i
$193$	−3.96693	+	6.87092i	−0.285546	+	0.494580i	−0.972741	−	0.231893i	$-0.925508\pi$
$193$	−3.96693	+	6.87092i	−0.285546	+	0.494580i	0.687196	+	0.726472i	$0.258841\pi$
$194$		0			0
$195$	−18.1667			−1.30094
$196$	5.33651	−	12.9430i	0.381179	−	0.924501i
$197$	21.7545			1.54994			0.774971	−	0.631997i	$-0.217764\pi$
$197$	21.7545			1.54994			0.774971	+	0.631997i	$0.217764\pi$
$198$		0			0
$199$	−3.60687	+	6.24729i	−0.255684	+	0.442858i	−0.965081	−	0.261951i	$-0.915634\pi$
$199$	−3.60687	+	6.24729i	−0.255684	+	0.442858i	0.709397	+	0.704809i	$0.248967\pi$
$200$		0			0
$201$	−1.30344	−	2.25762i	−0.0919373	−	0.159240i
$202$		0			0
$203$	20.8206	−	1.38167i	1.46132	−	0.0969744i
$204$	−4.00000			−0.280056
$205$	−1.97169	−	3.41507i	−0.137709	−	0.238519i
$206$		0			0
$207$	−2.97169	+	5.14712i	−0.206547	+	0.357749i
$208$	9.21374	+	15.9587i	0.638858	+	1.10653i
$209$	29.7169			2.05556
$210$		0			0
$211$	−25.1196			−1.72930			−0.864651	−	0.502373i	$-0.832460\pi$
$211$	−25.1196			−1.72930			−0.864651	+	0.502373i	$0.832460\pi$
$212$	−9.21374	−	15.9587i	−0.632803	−	1.09605i
$213$	3.60687	−	6.24729i	0.247139	−	0.428057i
$214$		0			0
$215$	−13.1383	−	22.7563i	−0.896027	−	1.55197i
$216$		0			0
$217$	−10.7751	+	21.8947i	−0.731463	+	1.48631i
$218$		0			0
$219$	−3.33175	−	5.77075i	−0.225139	−	0.389951i
$220$	16.8772	−	29.2322i	1.13786	−	1.97084i
$221$	−4.60687	+	7.97934i	−0.309892	+	0.536748i
$222$		0			0
$223$	−8.89629			−0.595740			−0.297870	−	0.954607i	$-0.596276\pi$
$223$	−8.89629			−0.595740			−0.297870	+	0.954607i	$0.596276\pi$
$224$		0			0
$225$	10.5503			0.703350
$226$		0			0
$227$	6.60687	−	11.4434i	0.438514	−	0.759528i	−0.559062	−	0.829126i	$-0.688838\pi$
$227$	6.60687	−	11.4434i	0.438514	−	0.759528i	0.997575	+	0.0695985i	$0.0221718\pi$
$228$	6.94338	−	12.0263i	0.459837	−	0.796460i
$229$	−1.74205	−	3.01733i	−0.115118	−	0.199390i	0.802709	−	0.596371i	$-0.203391\pi$
$229$	−1.74205	−	3.01733i	−0.115118	−	0.199390i	−0.917827	+	0.396981i	$0.870058\pi$
$230$		0			0
$231$	−6.29867	−	9.41004i	−0.414422	−	0.619135i
$232$		0			0
$233$	2.86006	+	4.95376i	0.187368	+	0.324532i	0.944372	−	0.328879i	$-0.106671\pi$
$233$	2.86006	+	4.95376i	0.187368	+	0.324532i	−0.757004	+	0.653411i	$0.773338\pi$
$234$		0			0
$235$	−5.78465	+	10.0193i	−0.377349	+	0.653588i
$236$	13.2137	+	22.8869i	0.860141	+	1.48981i
$237$	−2.38360			−0.154832
$238$		0			0
$239$	−8.44654			−0.546361			−0.273181	−	0.961963i	$-0.588076\pi$
$239$	−8.44654			−0.546361			−0.273181	+	0.961963i	$0.588076\pi$
$240$	−7.88676	−	13.6603i	−0.509088	−	0.881767i
$241$	4.83175	−	8.36883i	0.311240	−	0.539084i	−0.667391	−	0.744707i	$-0.732589\pi$
$241$	4.83175	−	8.36883i	0.311240	−	0.539084i	0.978631	+	0.205624i	$0.0659223\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−17.7545			−1.13661
$245$	16.8397	+	21.8721i	1.07585	+	1.39736i
$246$		0			0
$247$	−15.9936	−	27.7018i	−1.01765	−	1.76262i
$248$		0			0
$249$	−2.29867	+	3.98142i	−0.145672	+	0.252312i
$250$		0			0
$251$	13.1571			0.830470			0.415235	−	0.909714i	$-0.363699\pi$
$251$	13.1571			0.830470			0.415235	+	0.909714i	$0.363699\pi$
$252$	−5.27989	+	0.350378i	−0.332602	+	0.0220717i
$253$	−25.4370			−1.59921
$254$		0			0
$255$	3.94338	−	6.83014i	0.246944	−	0.427720i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−4.07380	−	7.05603i	−0.254117	−	0.440143i	0.710539	−	0.703658i	$-0.248451\pi$
$257$	−4.07380	−	7.05603i	−0.254117	−	0.440143i	−0.964655	+	0.263515i	$0.915118\pi$
$258$		0			0
$259$	1.47169	+	2.19866i	0.0914464	+	0.136618i
$260$	−36.3333			−2.25330
$261$	−3.94338	−	6.83014i	−0.244089	−	0.422775i
$262$		0			0
$263$	5.47645	−	9.48550i	0.337693	−	0.584901i	−0.646306	−	0.763079i	$-0.723687\pi$
$263$	5.47645	−	9.48550i	0.337693	−	0.584901i	0.983998	+	0.178178i	$0.0570202\pi$
$264$		0			0
$265$	36.3333			2.23194
$266$		0			0
$267$	−6.93385			−0.424345
$268$	−2.60687	−	4.51523i	−0.159240	−	0.275812i
$269$	9.27036	−	16.0567i	0.565224	−	0.978997i	−0.431805	−	0.901967i	$-0.642123\pi$
$269$	9.27036	−	16.0567i	0.565224	−	0.978997i	0.997029	−	0.0770296i	$-0.0245436\pi$
$270$		0			0
$271$	−10.8206	−	18.7419i	−0.657306	−	1.13849i	−0.981310	−	0.192431i	$-0.938363\pi$
$271$	−10.8206	−	18.7419i	−0.657306	−	1.13849i	0.324005	−	0.946055i	$-0.394971\pi$
$272$	−8.00000			−0.485071
$273$	−5.38200	+	10.9360i	−0.325733	+	0.661879i
$274$		0			0
$275$	22.5770	+	39.1044i	1.36144	+	2.35809i
$276$	−5.94338	+	10.2942i	−0.357749	+	0.619640i
$277$	−4.33175	+	7.50280i	−0.260269	+	0.450800i	−0.966313	−	0.257368i	$-0.917145\pi$
$277$	−4.33175	+	7.50280i	−0.260269	+	0.450800i	0.706044	+	0.708168i	$0.250478\pi$
$278$		0			0
$279$	9.22327			0.552183
$280$		0			0
$281$	−20.1476			−1.20190			−0.600952	−	0.799285i	$-0.705212\pi$
$281$	−20.1476			−1.20190			−0.600952	+	0.799285i	$0.705212\pi$
$282$		0			0
$283$	9.77989	−	16.9393i	0.581354	−	1.00693i	−0.413965	−	0.910293i	$-0.635856\pi$
$283$	9.77989	−	16.9393i	0.581354	−	1.00693i	0.995319	−	0.0966421i	$-0.0308102\pi$
$284$	7.21374	−	12.4946i	0.428057	−	0.741416i
$285$	13.6902	+	23.7121i	0.810937	+	1.40458i
$286$		0			0
$287$	−2.63994	+	0.175189i	−0.155831	+	0.0103411i
$288$		0			0
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$		0			0
$291$	−4.88676	+	8.46412i	−0.286467	+	0.496175i
$292$	−6.66349	−	11.5415i	−0.389951	−	0.675416i
$293$	12.0534			0.704168			0.352084	−	0.935968i	$-0.385473\pi$
$293$	12.0534			0.704168			0.352084	+	0.935968i	$0.385473\pi$
$294$		0			0
$295$	−52.1068			−3.03378
$296$		0			0
$297$	−2.13994	+	3.70649i	−0.124172	+	0.215073i
$298$		0			0
$299$	13.6902	+	23.7121i	0.791725	+	1.37131i
$300$	21.1005			1.21824
$301$	−17.5912	+	1.16737i	−1.01394	+	0.0672861i
$302$		0			0
$303$	6.88676	+	11.9282i	0.395634	+	0.685258i
$304$	13.8868	−	24.0526i	0.796460	−	1.37951i
$305$	17.5032	−	30.3164i	1.00223	−	1.73591i
$306$		0			0
$307$	6.77352			0.386585			0.193293	−	0.981141i	$-0.438083\pi$
$307$	6.77352			0.386585			0.193293	+	0.981141i	$0.438083\pi$
$308$	−12.5973	−	18.8201i	−0.717800	−	1.07237i
$309$	−4.88676			−0.277998
$310$		0			0
$311$	−8.09285	+	14.0172i	−0.458904	+	0.794844i	−0.998903	−	0.0468209i	$-0.985091\pi$
$311$	−8.09285	+	14.0172i	−0.458904	+	0.794844i	0.540000	+	0.841665i	$0.318424\pi$
$312$		0			0
$313$	14.5172	+	25.1445i	0.820560	+	1.42125i	0.905266	+	0.424845i	$0.139671\pi$
$313$	14.5172	+	25.1445i	0.820560	+	1.42125i	−0.0847066	+	0.996406i	$0.526995\pi$
$314$		0			0
$315$	4.60687	−	9.36101i	0.259568	−	0.527433i
$316$	−4.76720			−0.268176
$317$	5.13042	+	8.88615i	0.288153	+	0.499096i	0.973369	−	0.229244i	$-0.0736255\pi$
$317$	5.13042	+	8.88615i	0.288153	+	0.499096i	−0.685216	+	0.728340i	$0.740292\pi$
$318$		0			0
$319$	16.8772	−	29.2322i	0.944944	−	1.63669i
$320$	−15.7735	−	27.3205i	−0.881767	−	1.52726i
$321$	3.94338			0.220098
$322$		0			0
$323$	13.8868			0.772680
$324$	1.00000	+	1.73205i	0.0555556	+	0.0962250i
$325$	24.3018	−	42.0920i	1.34802	−	2.33484i
$326$		0			0
$327$	8.07856	+	13.9925i	0.446746	+	0.773786i
$328$		0			0
$329$	4.31773	+	6.45056i	0.238044	+	0.355631i
$330$		0			0
$331$	7.79867	+	13.5077i	0.428654	+	0.742450i	0.996754	−	0.0805093i	$-0.0256547\pi$
$331$	7.79867	+	13.5077i	0.428654	+	0.742450i	−0.568100	+	0.822960i	$0.692321\pi$
$332$	−4.59735	+	7.96284i	−0.252312	+	0.437017i
$333$	0.500000	−	0.866025i	0.0273998	−	0.0474579i
$334$		0			0
$335$	10.2799			0.561650
$336$	−10.5598	+	0.700756i	−0.576083	+	0.0382293i
$337$	−27.0000			−1.47078			−0.735392	−	0.677642i	$-0.763002\pi$
$337$	−27.0000			−1.47078			−0.735392	+	0.677642i	$0.763002\pi$
$338$		0			0
$339$	3.64471	−	6.31282i	0.197953	−	0.342865i
$340$	7.88676	−	13.6603i	0.427720	−	0.740832i
$341$	19.7373	+	34.1860i	1.06883	+	1.85128i
$342$		0			0
$343$	18.1555	−	3.65746i	0.980306	−	0.197484i
$344$		0			0
$345$	−11.7185	−	20.2971i	−0.630903	−	1.09276i
$346$		0			0
$347$	−11.2704	+	19.5208i	−0.605025	+	1.04793i	0.387023	+	0.922070i	$0.373503\pi$
$347$	−11.2704	+	19.5208i	−0.605025	+	1.04793i	−0.992048	+	0.125864i	$0.959830\pi$
$348$	−7.88676	−	13.6603i	−0.422775	−	0.732267i
$349$	5.10371			0.273195			0.136598	−	0.990627i	$-0.456383\pi$
$349$	5.10371			0.273195			0.136598	+	0.990627i	$0.456383\pi$
$350$		0			0
$351$	4.60687			0.245897
$352$		0			0
$353$	1.05662	−	1.83012i	0.0562382	−	0.0974073i	−0.836536	−	0.547912i	$-0.815423\pi$
$353$	1.05662	−	1.83012i	0.0562382	−	0.0974073i	0.892774	+	0.450505i	$0.148756\pi$
$354$		0			0
$355$	14.2233	+	24.6354i	0.754893	+	1.30751i
$356$	−13.8677			−0.734987
$357$	−2.94338	−	4.39733i	−0.155780	−	0.232731i
$358$		0			0
$359$	−7.42144	−	12.8543i	−0.391688	−	0.678424i	0.600984	−	0.799261i	$-0.294776\pi$
$359$	−7.42144	−	12.8543i	−0.391688	−	0.678424i	−0.992672	+	0.120837i	$0.961442\pi$
$360$		0			0
$361$	−14.6053	+	25.2971i	−0.768698	+	1.33142i
$362$		0			0
$363$	−7.31746			−0.384067
$364$	−10.7640	+	21.8721i	−0.564187	+	1.14641i
$365$	26.2767			1.37538
$366$		0			0
$367$	−7.21851	+	12.5028i	−0.376803	+	0.652642i	−0.990595	−	0.136826i	$-0.956310\pi$
$367$	−7.21851	+	12.5028i	−0.376803	+	0.652642i	0.613792	+	0.789468i	$0.289643\pi$
$368$	−11.8868	+	20.5885i	−0.619640	+	1.07325i
$369$	0.500000	+	0.866025i	0.0260290	+	0.0450835i
$370$		0			0
$371$	10.7640	−	21.8721i	0.558839	−	1.13554i
$372$	18.4465			0.956409
$373$	4.38676	+	7.59809i	0.227138	+	0.393414i	0.956959	−	0.290224i	$-0.0937298\pi$
$373$	4.38676	+	7.59809i	0.227138	+	0.393414i	−0.729821	+	0.683639i	$0.760397\pi$
$374$		0			0
$375$	−10.9434	+	18.9545i	−0.565114	+	0.978806i
$376$		0			0
$377$	−36.3333			−1.87126
$378$		0			0
$379$	15.7449			0.808763			0.404382	−	0.914590i	$-0.367487\pi$
$379$	15.7449			0.808763			0.404382	+	0.914590i	$0.367487\pi$
$380$	27.3804	+	47.4242i	1.40458	+	2.43281i
$381$	2.83651	−	4.91298i	0.145319	−	0.251699i
$382$		0			0
$383$	−6.15713	−	10.6645i	−0.314614	−	0.544928i	0.664741	−	0.747074i	$-0.268542\pi$
$383$	−6.15713	−	10.6645i	−0.314614	−	0.544928i	−0.979355	+	0.202146i	$0.935209\pi$
$384$		0			0
$385$	44.5550	−	2.95670i	2.27073	−	0.150688i
$386$		0			0
$387$	3.33175	+	5.77075i	0.169362	+	0.293344i
$388$	−9.77352	+	16.9282i	−0.496175	+	0.859401i
$389$	7.98122	−	13.8239i	0.404664	−	0.700898i	−0.589619	−	0.807682i	$-0.700722\pi$
$389$	7.98122	−	13.8239i	0.404664	−	0.700898i	0.994282	+	0.106784i	$0.0340552\pi$
$390$		0			0
$391$	−11.8868			−0.601139
$392$		0			0
$393$	10.0566			0.507289
$394$		0			0
$395$	4.69972	−	8.14016i	0.236469	−	0.409576i
$396$	−4.27989	+	7.41299i	−0.215073	+	0.372517i
$397$	−17.1997	−	29.7908i	−0.863229	−	1.49516i	−0.868795	−	0.495173i	$-0.835105\pi$
$397$	−17.1997	−	29.7908i	−0.863229	−	1.49516i	0.00556515	−	0.999985i	$-0.498229\pi$
$398$		0			0
$399$	18.3301	−	1.21640i	0.917655	−	0.0608963i
$400$	42.2010			2.11005
$401$	4.00953	+	6.94470i	0.200226	+	0.346802i	0.948601	−	0.316474i	$-0.102499\pi$
$401$	4.00953	+	6.94470i	0.200226	+	0.346802i	−0.748375	+	0.663276i	$0.769166\pi$
$402$		0			0
$403$	21.2452	−	36.7978i	1.05830	−	1.83303i
$404$	13.7735	+	23.8564i	0.685258	+	1.18690i
$405$	−3.94338			−0.195948
$406$		0			0
$407$	4.27989			0.212146
$408$		0			0
$409$	−1.65873	+	2.87300i	−0.0820188	+	0.142061i	−0.904117	−	0.427285i	$-0.859470\pi$
$409$	−1.65873	+	2.87300i	−0.0820188	+	0.142061i	0.822098	+	0.569346i	$0.192803\pi$
$410$		0			0
$411$	−2.60687	−	4.51523i	−0.128588	−	0.222720i
$412$	−9.77352			−0.481507
$413$	−15.4370	+	31.3675i	−0.759606	+	1.54349i
$414$		0			0
$415$	−9.06454	−	15.7002i	−0.444961	−	0.770695i
$416$		0			0
$417$	−2.77036	+	4.79841i	−0.135665	+	0.234979i
$418$		0			0
$419$	1.44022			0.0703594			0.0351797	−	0.999381i	$-0.488800\pi$
$419$	1.44022			0.0703594			0.0351797	+	0.999381i	$0.488800\pi$
$420$	9.21374	−	18.7220i	0.449585	−	0.913541i
$421$	35.5000			1.73016			0.865081	−	0.501632i	$-0.167267\pi$
$421$	35.5000			1.73016			0.865081	+	0.501632i	$0.167267\pi$
$422$		0			0
$423$	1.46693	−	2.54079i	0.0713244	−	0.123538i
$424$		0			0
$425$	10.5503	+	18.2736i	0.511762	+	0.886399i
$426$		0			0
$427$	−13.0645	−	19.5181i	−0.632238	−	0.944545i
$428$	7.88676			0.381221
$429$	9.85845	+	17.0753i	0.475971	+	0.824405i
$430$		0			0
$431$	13.0722	−	22.6417i	0.629666	−	1.09061i	−0.357953	−	0.933740i	$-0.616525\pi$
$431$	13.0722	−	22.6417i	0.629666	−	1.09061i	0.987619	−	0.156873i	$-0.0501414\pi$
$432$	2.00000	+	3.46410i	0.0962250	+	0.166667i
$433$	22.9968			1.10516			0.552578	−	0.833461i	$-0.313644\pi$
$433$	22.9968			1.10516			0.552578	+	0.833461i	$0.313644\pi$
$434$		0			0
$435$	31.1005			1.49116
$436$	16.1571	+	27.9850i	0.773786	+	1.34024i
$437$	20.6336	−	35.7384i	0.987038	−	1.70960i
$438$		0			0
$439$	16.0455	+	27.7916i	0.765809	+	1.32642i	0.939818	+	0.341677i	$0.110995\pi$
$439$	16.0455	+	27.7916i	0.765809	+	1.32642i	−0.174008	+	0.984744i	$0.555672\pi$
$440$		0			0
$441$	−4.27036	−	5.54653i	−0.203351	−	0.264120i
$442$		0			0
$443$	−1.38360	−	2.39647i	−0.0657369	−	0.113860i	0.831284	−	0.555848i	$-0.187606\pi$
$443$	−1.38360	−	2.39647i	−0.0657369	−	0.113860i	−0.897021	+	0.441989i	$0.854273\pi$
$444$	1.00000	−	1.73205i	0.0474579	−	0.0821995i
$445$	13.6714	−	23.6796i	0.648087	−	1.12252i
$446$		0			0
$447$	−8.27989			−0.391625
$448$	−21.1196	+	1.40151i	−0.997805	+	0.0662152i
$449$	−5.81109			−0.274242			−0.137121	−	0.990554i	$-0.543785\pi$
$449$	−5.81109			−0.274242			−0.137121	+	0.990554i	$0.543785\pi$
$450$		0			0
$451$	−2.13994	+	3.70649i	−0.100766	+	0.174532i
$452$	7.28942	−	12.6256i	0.342865	−	0.593860i
$453$	1.84127	+	3.18918i	0.0865105	+	0.149841i
$454$		0			0
$455$	−26.7357	−	39.9424i	−1.25339	−	1.87253i
$456$		0			0
$457$	−9.08809	−	15.7410i	−0.425123	−	0.736334i	0.571309	−	0.820735i	$-0.306436\pi$
$457$	−9.08809	−	15.7410i	−0.425123	−	0.736334i	−0.996432	+	0.0844006i	$0.973102\pi$
$458$		0			0
$459$	−1.00000	+	1.73205i	−0.0466760	+	0.0808452i
$460$	−23.4370	−	40.5941i	−1.09276	−	1.89271i
$461$	−20.5032			−0.954927			−0.477464	−	0.878651i	$-0.658444\pi$
$461$	−20.5032			−0.954927			−0.477464	+	0.878651i	$0.658444\pi$
$462$		0			0
$463$	−14.7201			−0.684102			−0.342051	−	0.939681i	$-0.611121\pi$
$463$	−14.7201			−0.684102			−0.342051	+	0.939681i	$0.611121\pi$
$464$	−15.7735	−	27.3205i	−0.732267	−	1.26832i
$465$	−18.1854	+	31.4981i	−0.843329	+	1.46069i
$466$		0			0
$467$	−10.5786	−	18.3226i	−0.489517	−	0.847869i	0.510410	−	0.859931i	$-0.329494\pi$
$467$	−10.5786	−	18.3226i	−0.489517	−	0.847869i	−0.999927	+	0.0120622i	$0.996160\pi$
$468$	9.21374			0.425905
$469$	3.04549	−	6.18833i	0.140628	−	0.285751i
$470$		0			0
$471$	−5.00000	−	8.66025i	−0.230388	−	0.399043i
$472$		0			0
$473$	−14.2595	+	24.6982i	−0.655653	+	1.13562i
$474$		0			0
$475$	−73.2544			−3.36114
$476$	−5.88676	−	8.79466i	−0.269819	−	0.403103i
$477$	−9.21374			−0.421868
$478$		0			0
$479$	13.7468	−	23.8102i	0.628108	−	1.08792i	−0.359823	−	0.933021i	$-0.617163\pi$
$479$	13.7468	−	23.8102i	0.628108	−	1.08792i	0.987931	−	0.154895i	$-0.0495038\pi$
$480$		0			0
$481$	−2.30344	−	3.98967i	−0.105028	−	0.181913i
$482$		0			0
$483$	−15.6902	+	1.04121i	−0.713929	+	0.0473769i
$484$	−14.6349			−0.665223
$485$	−19.2704	−	33.3772i	−0.875022	−	1.51558i
$486$		0			0
$487$	7.04073	−	12.1949i	0.319046	−	0.552603i	−0.661243	−	0.750171i	$-0.729971\pi$
$487$	7.04073	−	12.1949i	0.319046	−	0.552603i	0.980289	+	0.197568i	$0.0633043\pi$
$488$		0			0
$489$	15.4370			0.698086
$490$		0			0
$491$	12.6730			0.571925			0.285963	−	0.958241i	$-0.407687\pi$
$491$	12.6730			0.571925			0.285963	+	0.958241i	$0.407687\pi$
$492$	1.00000	+	1.73205i	0.0450835	+	0.0780869i
$493$	7.88676	−	13.6603i	0.355202	−	0.615228i
$494$		0			0
$495$	−8.43862	−	14.6161i	−0.379288	−	0.656945i
$496$	36.8931			1.65655
$497$	19.0439	−	1.26377i	0.854235	−	0.0566877i
$498$		0			0
$499$	15.0219	+	26.0188i	0.672475	+	1.16476i	0.977200	+	0.212320i	$0.0681019\pi$
$499$	15.0219	+	26.0188i	0.672475	+	1.16476i	−0.304726	+	0.952440i	$0.598565\pi$
$500$	−21.8868	+	37.9090i	−0.978806	+	1.69534i
$501$	0.606872	−	1.05113i	0.0271130	−	0.0469612i
$502$		0			0
$503$	−30.5941			−1.36413			−0.682063	−	0.731294i	$-0.738917\pi$
$503$	−30.5941			−1.36413			−0.682063	+	0.731294i	$0.738917\pi$
$504$		0			0
$505$	−54.3143			−2.41695
$506$		0			0
$507$	4.11164	−	7.12156i	0.182604	−	0.316280i
$508$	5.67302	−	9.82595i	0.251699	−	0.435956i
$509$	−3.99047	−	6.91170i	−0.176875	−	0.306356i	0.763934	−	0.645295i	$-0.223265\pi$
$509$	−3.99047	−	6.91170i	−0.176875	−	0.306356i	−0.940808	+	0.338939i	$0.889932\pi$
$510$		0			0
$511$	7.78465	−	15.8182i	0.344373	−	0.699754i
$512$		0			0
$513$	−3.47169	−	6.01314i	−0.153279	−	0.265487i
$514$		0			0
$515$	9.63518	−	16.6886i	0.424577	−	0.735389i
$516$	6.66349	+	11.5415i	0.293344	+	0.508086i
$517$	12.5566			0.552237
$518$		0			0
$519$	0.786256			0.0345128
$520$		0			0
$521$	−11.2405	+	19.4690i	−0.492453	+	0.852954i	−0.999962	−	0.00869260i	$-0.997233\pi$
$521$	−11.2405	+	19.4690i	−0.492453	+	0.852954i	0.507509	+	0.861646i	$0.330566\pi$
$522$		0			0
$523$	−7.83491	−	13.5705i	−0.342597	−	0.593395i	0.642318	−	0.766439i	$-0.277973\pi$
$523$	−7.83491	−	13.5705i	−0.342597	−	0.593395i	−0.984914	+	0.173044i	$0.944640\pi$
$524$	20.1132			0.878651
$525$	15.5267	+	23.1965i	0.677641	+	1.01238i
$526$		0			0
$527$	9.22327	+	15.9752i	0.401772	+	0.695889i
$528$	−8.55978	+	14.8260i	−0.372517	+	0.645218i
$529$	−6.16189	+	10.6727i	−0.267908	+	0.464031i
$530$		0			0
$531$	13.2137			0.573428
$532$	36.6603	−	2.43281i	1.58942	−	0.105476i
$533$	4.60687			0.199546
$534$		0			0
$535$	−7.77513	+	13.4669i	−0.336148	+	0.582225i
$536$		0			0
$537$	12.2233	+	21.1713i	0.527473	+	0.913610i
$538$		0			0
$539$	11.4198	−	27.6973i	0.491887	−	1.19301i
$540$	−7.88676			−0.339392
$541$	−6.33175	−	10.9669i	−0.272223	−	0.471504i	0.697208	−	0.716869i	$-0.254426\pi$
$541$	−6.33175	−	10.9669i	−0.272223	−	0.471504i	−0.969431	+	0.245365i	$0.921092\pi$
$542$		0			0
$543$	−9.75158	+	16.8902i	−0.418480	+	0.724829i
$544$		0			0
$545$	−63.7137			−2.72920
$546$		0			0
$547$	44.0687			1.88424			0.942121	−	0.335272i	$-0.108828\pi$
$547$	44.0687			1.88424			0.942121	+	0.335272i	$0.108828\pi$
$548$	−5.21374	−	9.03047i	−0.222720	−	0.385763i
$549$	−4.43862	+	7.68791i	−0.189436	+	0.328112i
$550$		0			0
$551$	27.3804	+	47.4242i	1.16644	+	2.02034i
$552$		0			0
$553$	−3.50792	−	5.24074i	−0.149172	−	0.222859i
$554$		0			0
$555$	1.97169	+	3.41507i	0.0836936	+	0.144962i
$556$	−5.54073	+	9.59682i	−0.234979	+	0.406996i
$557$	10.7373	−	18.5975i	0.454954	−	0.788003i	−0.543732	−	0.839259i	$-0.682989\pi$
$557$	10.7373	−	18.5975i	0.454954	−	0.788003i	0.998686	+	0.0512562i	$0.0163225\pi$
$558$		0			0
$559$	30.6979			1.29838
$560$	18.4275	−	37.4440i	0.778704	−	1.58230i
$561$	−8.55978			−0.361394
$562$		0			0
$563$	−11.0833	+	19.1969i	−0.467106	+	0.809052i	−0.999294	−	0.0375744i	$-0.988037\pi$
$563$	−11.0833	+	19.1969i	−0.467106	+	0.809052i	0.532187	+	0.846627i	$0.321370\pi$
$564$	2.93385	−	5.08159i	0.123538	−	0.213973i
$565$	14.3725	+	24.8939i	0.604654	+	1.04729i
$566$		0			0
$567$	−1.16825	+	2.37385i	−0.0490621	+	0.0996925i
$568$		0			0
$569$	−9.84893	−	17.0588i	−0.412888	−	0.715144i	0.582316	−	0.812963i	$-0.302147\pi$
$569$	−9.84893	−	17.0588i	−0.412888	−	0.715144i	−0.995204	+	0.0978189i	$0.968813\pi$
$570$		0			0
$571$	8.32249	−	14.4150i	0.348285	−	0.603248i	−0.637660	−	0.770318i	$-0.720097\pi$
$571$	8.32249	−	14.4150i	0.348285	−	0.603248i	0.985945	+	0.167070i	$0.0534307\pi$
$572$	19.7169	+	34.1507i	0.824405	+	1.42791i
$573$	−12.8206			−0.535589
$574$		0			0
$575$	62.7042			2.61494
$576$	4.00000	+	6.92820i	0.166667	+	0.288675i
$577$	21.3114	−	36.9124i	0.887204	−	1.53668i	0.0440364	−	0.999030i	$-0.485978\pi$
$577$	21.3114	−	36.9124i	0.887204	−	1.53668i	0.843167	−	0.537652i	$-0.180688\pi$
$578$		0			0
$579$	3.96693	+	6.87092i	0.164860	+	0.285546i
$580$	62.2010			2.58276
$581$	−12.1367	+	0.805404i	−0.503517	+	0.0334138i
$582$		0			0
$583$	−19.7169	−	34.1507i	−0.816591	−	1.41438i
$584$		0			0
$585$	−9.08333	+	15.7328i	−0.375549	+	0.650470i
$586$		0			0
$587$	9.26716			0.382497			0.191248	−	0.981542i	$-0.438746\pi$
$587$	9.26716			0.382497			0.191248	+	0.981542i	$0.438746\pi$
$588$	−8.54073	−	11.0931i	−0.352214	−	0.457470i
$589$	−64.0407			−2.63875
$590$		0			0
$591$	10.8772	−	18.8399i	0.447430	−	0.774971i
$592$	2.00000	−	3.46410i	0.0821995	−	0.142374i
$593$	−3.79391	−	6.57124i	−0.155797	−	0.269849i	0.777552	−	0.628819i	$-0.216461\pi$
$593$	−3.79391	−	6.57124i	−0.155797	−	0.269849i	−0.933349	+	0.358970i	$0.883128\pi$
$594$		0			0
$595$	20.8206	−	1.38167i	0.853562	−	0.0566431i
$596$	−16.5598			−0.678315
$597$	3.60687	+	6.24729i	0.147619	+	0.255684i
$598$		0			0
$599$	−5.70133	+	9.87499i	−0.232950	+	0.403481i	−0.958675	−	0.284504i	$-0.908171\pi$
$599$	−5.70133	+	9.87499i	−0.232950	+	0.403481i	0.725725	+	0.687985i	$0.241504\pi$
$600$		0			0
$601$	29.0534			1.18511			0.592557	−	0.805529i	$-0.298119\pi$
$601$	29.0534			1.18511			0.592557	+	0.805529i	$0.298119\pi$
$602$		0			0
$603$	−2.60687			−0.106160
$604$	3.68254	+	6.37835i	0.149841	+	0.259532i
$605$	14.4278	−	24.9896i	0.586572	−	1.01597i
$606$		0			0
$607$	−20.0032	−	34.6465i	−0.811903	−	1.40626i	−0.911530	−	0.411233i	$-0.865098\pi$
$607$	−20.0032	−	34.6465i	−0.811903	−	1.40626i	0.0996271	−	0.995025i	$-0.468235\pi$
$608$		0			0
$609$	9.21374	−	18.7220i	0.373360	−	0.758655i
$610$		0			0
$611$	−6.75795	−	11.7051i	−0.273397	−	0.473538i
$612$	−2.00000	+	3.46410i	−0.0808452	+	0.140028i
$613$	6.28942	−	10.8936i	0.254027	−	0.439988i	−0.710604	−	0.703592i	$-0.751578\pi$
$613$	6.28942	−	10.8936i	0.254027	−	0.439988i	0.964631	+	0.263605i	$0.0849114\pi$
$614$		0			0
$615$	−3.94338			−0.159012
$616$		0			0
$617$	31.8677			1.28295			0.641473	−	0.767146i	$-0.278324\pi$
$617$	31.8677			1.28295			0.641473	+	0.767146i	$0.278324\pi$
$618$		0			0
$619$	1.26560	−	2.19208i	0.0508688	−	0.0881073i	−0.839470	−	0.543406i	$-0.817134\pi$
$619$	1.26560	−	2.19208i	0.0508688	−	0.0881073i	0.890339	+	0.455299i	$0.150468\pi$
$620$	−36.3709	+	62.9962i	−1.46069	+	2.52999i
$621$	2.97169	+	5.14712i	0.119250	+	0.206547i
$622$		0			0
$623$	−10.2045	−	15.2452i	−0.408834	−	0.610787i
$624$	18.4275			0.737690
$625$	−16.7783	−	29.0608i	−0.671131	−	1.16243i
$626$		0			0
$627$	14.8585	−	25.7356i	0.593389	−	1.02778i
$628$	−10.0000	−	17.3205i	−0.399043	−	0.691164i
$629$	2.00000			0.0797452
$630$		0			0
$631$	−27.2137			−1.08336			−0.541681	−	0.840584i	$-0.682212\pi$
$631$	−27.2137			−1.08336			−0.541681	+	0.840584i	$0.682212\pi$
$632$		0			0
$633$	−12.5598	+	21.7542i	−0.499206	+	0.864651i
$634$		0			0
$635$	11.1854	+	19.3737i	0.443880	+	0.768823i
$636$	−18.4275			−0.730697
$637$	−31.9653	+	4.26126i	−1.26651	+	0.168837i
$638$		0			0
$639$	−3.60687	−	6.24729i	−0.142686	−	0.247139i
$640$		0			0
$641$	3.58969	−	6.21753i	0.141784	−	0.245578i	−0.786384	−	0.617738i	$-0.788049\pi$
$641$	3.58969	−	6.21753i	0.141784	−	0.245578i	0.928169	+	0.372160i	$0.121383\pi$
$642$		0			0
$643$	26.3423			1.03884			0.519419	−	0.854520i	$-0.326148\pi$
$643$	26.3423			1.03884			0.519419	+	0.854520i	$0.326148\pi$
$644$	−31.3804	+	2.08243i	−1.23656	+	0.0820592i
$645$	−26.2767			−1.03464
$646$		0			0
$647$	−1.00953	+	1.74855i	−0.0396886	+	0.0687426i	−0.885187	−	0.465235i	$-0.845970\pi$
$647$	−1.00953	+	1.74855i	−0.0396886	+	0.0687426i	0.845499	+	0.533977i	$0.179303\pi$
$648$		0			0
$649$	28.2767	+	48.9767i	1.10996	+	1.92250i
$650$		0			0
$651$	13.5738	+	20.2789i	0.531999	+	0.794792i
$652$	30.8740			1.20912
$653$	16.4008	+	28.4070i	0.641812	+	1.11165i	0.985028	+	0.172395i	$0.0551505\pi$
$653$	16.4008	+	28.4070i	0.641812	+	1.11165i	−0.343216	+	0.939257i	$0.611516\pi$
$654$		0			0
$655$	−19.8285	+	34.3440i	−0.774765	+	1.34193i
$656$	2.00000	+	3.46410i	0.0780869	+	0.135250i
$657$	−6.66349			−0.259968
$658$		0			0
$659$	15.5470			0.605627			0.302813	−	0.953050i	$-0.402074\pi$
$659$	15.5470			0.605627			0.302813	+	0.953050i	$0.402074\pi$
$660$	−16.8772	−	29.2322i	−0.656945	−	1.13786i
$661$	1.79102	−	3.10214i	0.0696626	−	0.120659i	−0.829090	−	0.559115i	$-0.811141\pi$
$661$	1.79102	−	3.10214i	0.0696626	−	0.120659i	0.898753	+	0.438456i	$0.144474\pi$
$662$		0			0
$663$	4.60687	+	7.97934i	0.178916	+	0.309892i
$664$		0			0
$665$	−31.9873	+	64.9971i	−1.24041	+	2.52048i
$666$		0			0
$667$	−23.4370	−	40.5941i	−0.907485	−	1.57181i
$668$	1.21374	−	2.10227i	0.0469612	−	0.0813391i
$669$	−4.44814	+	7.70441i	−0.171975	+	0.297870i
$670$		0			0
$671$	−37.9936			−1.46673
$672$		0			0
$673$	25.5000			0.982951			0.491476	−	0.870891i	$-0.336458\pi$
$673$	25.5000			0.982951			0.491476	+	0.870891i	$0.336458\pi$
$674$		0			0
$675$	5.27513	−	9.13679i	0.203040	−	0.351675i
$676$	8.22327	−	14.2431i	0.316280	−	0.547812i
$677$	−16.5881	−	28.7314i	−0.637532	−	1.10424i	−0.985973	−	0.166907i	$-0.946622\pi$
$677$	−16.5881	−	28.7314i	−0.637532	−	1.10424i	0.348441	−	0.937331i	$-0.386711\pi$
$678$		0			0
$679$	−25.8016	+	1.71221i	−0.990173	+	0.0657087i
$680$		0			0
$681$	−6.60687	−	11.4434i	−0.253176	−	0.438514i
$682$		0			0
$683$	−15.0738	+	26.1086i	−0.576783	+	0.999017i	0.419063	+	0.907957i	$0.362359\pi$
$683$	−15.0738	+	26.1086i	−0.576783	+	0.999017i	−0.995845	+	0.0910599i	$0.970975\pi$
$684$	−6.94338	−	12.0263i	−0.265487	−	0.459837i
$685$	20.5598			0.785549
$686$		0			0
$687$	−3.48411			−0.132927
$688$	13.3270	+	23.0830i	0.508086	+	0.880032i
$689$	−21.2233	+	36.7598i	−0.808542	+	1.40044i
$690$		0			0
$691$	20.6838	+	35.8254i	0.786850	+	1.36286i	0.927888	+	0.372860i	$0.121623\pi$
$691$	20.6838	+	35.8254i	0.786850	+	1.36286i	−0.141038	+	0.990004i	$0.545044\pi$
$692$	1.57251			0.0597779
$693$	−11.2987	+	0.749789i	−0.429201	+	0.0284821i
$694$		0			0
$695$	−10.9246	−	18.9220i	−0.414394	−	0.717751i
$696$		0			0
$697$	−1.00000	+	1.73205i	−0.0378777	+	0.0656061i
$698$		0			0
$699$	5.72011			0.216354
$700$	31.0534	+	46.3929i	1.17371	+	1.75349i
$701$	25.0629			0.946614			0.473307	−	0.880897i	$-0.343060\pi$
$701$	25.0629			0.946614			0.473307	+	0.880897i	$0.343060\pi$
$702$		0			0
$703$	−3.47169	+	6.01314i	−0.130937	+	0.226790i
$704$	−17.1196	+	29.6519i	−0.645218	+	1.11755i
$705$	5.78465	+	10.0193i	0.217863	+	0.377349i
$706$		0			0
$707$	−16.0910	+	32.6963i	−0.605164	+	1.22967i
$708$	26.4275			0.993206
$709$	−3.55978	−	6.16572i	−0.133690	−	0.231558i	0.791406	−	0.611291i	$-0.209349\pi$
$709$	−3.55978	−	6.16572i	−0.133690	−	0.231558i	−0.925096	+	0.379732i	$0.876016\pi$
$710$		0			0
$711$	−1.19180	+	2.06426i	−0.0446960	+	0.0774158i
$712$		0			0
$713$	54.8174			2.05293
$714$		0			0
$715$	−77.7513			−2.90773
$716$	24.4465	+	42.3427i	0.913610	+	1.58242i
$717$	−4.22327	+	7.31492i	−0.157721	+	0.273181i
$718$		0			0
$719$	−7.67115	−	13.2868i	−0.286085	−	0.495515i	0.686786	−	0.726859i	$-0.259021\pi$
$719$	−7.67115	−	13.2868i	−0.286085	−	0.495515i	−0.972872	+	0.231345i	$0.925687\pi$
$720$	−15.7735			−0.587845
$721$	−7.19180	−	10.7444i	−0.267837	−	0.400141i
$722$		0			0
$723$	−4.83175	−	8.36883i	−0.179695	−	0.311240i
$724$	−19.5032	+	33.7805i	−0.724829	+	1.25544i
$725$	−41.6037	+	72.0597i	−1.54512	+	2.67623i
$726$		0			0
$727$	−31.7264			−1.17667			−0.588334	−	0.808618i	$-0.700216\pi$
$727$	−31.7264			−1.17667			−0.588334	+	0.808618i	$0.700216\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−6.66349	+	11.5415i	−0.246458	+	0.426878i
$732$	−8.87724	+	15.3758i	−0.328112	+	0.568307i
$733$	−20.9841	−	36.3455i	−0.775066	−	1.34245i	−0.934758	−	0.355286i	$-0.884383\pi$
$733$	−20.9841	−	36.3455i	−0.775066	−	1.34245i	0.159692	−	0.987167i	$-0.448950\pi$
$734$		0			0
$735$	27.3616	−	3.64754i	1.00925	−	0.134542i
$736$		0			0
$737$	−5.57856	−	9.66235i	−0.205489	−	0.355917i
$738$		0			0
$739$	3.44498	−	5.96689i	0.126726	−	0.219495i	−0.795680	−	0.605717i	$-0.792887\pi$
$739$	3.44498	−	5.96689i	0.126726	−	0.219495i	0.922406	+	0.386221i	$0.126220\pi$
$740$	3.94338	+	6.83014i	0.144962	+	0.251081i
$741$	−31.9873			−1.17508
$742$		0			0
$743$	7.44022			0.272955			0.136478	−	0.990643i	$-0.456422\pi$
$743$	7.44022			0.272955			0.136478	+	0.990643i	$0.456422\pi$
$744$		0			0
$745$	16.3254	−	28.2764i	0.598116	−	1.03597i
$746$		0			0
$747$	2.29867	+	3.98142i	0.0841040	+	0.145672i
$748$	−17.1196			−0.625953
$749$	5.80344	+	8.67017i	0.212053	+	0.316801i
$750$		0			0
$751$	1.42620	+	2.47025i	0.0520428	+	0.0901408i	0.890873	−	0.454252i	$-0.150093\pi$
$751$	1.42620	+	2.47025i	0.0520428	+	0.0901408i	−0.838830	+	0.544393i	$0.816760\pi$
$752$	5.86771	−	10.1632i	0.213973	−	0.370613i
$753$	6.57856	−	11.3944i	0.239736	−	0.415235i
$754$		0			0
$755$	−14.5217			−0.528498
$756$	−2.33651	+	4.74771i	−0.0849780	+	0.172672i
$757$	−11.5884			−0.421186			−0.210593	−	0.977574i	$-0.567539\pi$
$757$	−11.5884			−0.421186			−0.210593	+	0.977574i	$0.567539\pi$
$758$		0			0
$759$	−12.7185	+	22.0291i	−0.461653	+	0.799606i
$760$		0			0
$761$	−3.55025	−	6.14922i	−0.128697	−	0.222909i	0.794475	−	0.607297i	$-0.207746\pi$
$761$	−3.55025	−	6.14922i	−0.128697	−	0.222909i	−0.923172	+	0.384388i	$0.874413\pi$
$762$		0			0
$763$	−18.8756	+	38.3547i	−0.683344	+	1.38853i
$764$	−25.6412			−0.927667
$765$	−3.94338	−	6.83014i	−0.142573	−	0.246944i
$766$		0			0
$767$	30.4370	−	52.7185i	1.09902	−	1.90355i
$768$	8.00000	+	13.8564i	0.288675	+	0.500000i
$769$	−21.6698			−0.781433			−0.390717	−	0.920511i	$-0.627773\pi$
$769$	−21.6698			−0.781433			−0.390717	+	0.920511i	$0.627773\pi$
$770$		0			0
$771$	−8.14760			−0.293429
$772$	7.93385	+	13.7418i	0.285546	+	0.494580i
$773$	16.0077	−	27.7261i	0.575755	−	0.997237i	−0.420204	−	0.907430i	$-0.638041\pi$
$773$	16.0077	−	27.7261i	0.575755	−	0.997237i	0.995959	−	0.0898077i	$-0.0286252\pi$
$774$		0			0
$775$	−48.6539	−	84.2711i	−1.74770	−	3.02711i
$776$		0			0
$777$	2.63994	−	0.175189i	0.0947075	−	0.00628487i
$778$		0			0
$779$	−3.47169	−	6.01314i	−0.124386	−	0.215443i
$780$	−18.1667	+	31.4656i	−0.650470	+	1.12665i
$781$	15.4370	−	26.7377i	0.552380	−	0.956750i
$782$		0			0
$783$	−7.88676			−0.281850
$784$	−17.0815	−	22.1861i	−0.610052	−	0.792361i
$785$	39.4338			1.40745
$786$		0			0
$787$	−15.7942	+	27.3563i	−0.563002	+	0.975148i	0.434231	+	0.900802i	$0.357020\pi$
$787$	−15.7942	+	27.3563i	−0.563002	+	0.975148i	−0.997233	+	0.0743459i	$0.976313\pi$
$788$	21.7545	−	37.6798i	0.774971	−	1.34229i
$789$	−5.47645	−	9.48550i	−0.194967	−	0.337693i
$790$		0			0
$791$	19.2437	−	1.27702i	0.684226	−	0.0454058i
$792$		0			0
$793$	20.4481	+	35.4172i	0.726135	+	1.25770i
$794$		0			0
$795$	18.1667	−	31.4656i	0.644305	−	1.11597i
$796$	7.21374	+	12.4946i	0.255684	+	0.442858i
$797$	35.1762			1.24600			0.623002	−	0.782220i	$-0.285913\pi$
$797$	35.1762			1.24600			0.623002	+	0.782220i	$0.285913\pi$
$798$		0			0
$799$	5.86771			0.207585
$800$		0			0
$801$	−3.46693	+	6.00489i	−0.122498	+	0.212173i
$802$		0			0
$803$	−14.2595	−	24.6982i	−0.503207	−	0.871580i
$804$	−5.21374			−0.183875
$805$	27.3804	−	55.6360i	0.965032	−	1.96091i
$806$		0			0
$807$	−9.27036	−	16.0567i	−0.326332	−	0.565224i
$808$		0			0
$809$	−16.4198	+	28.4400i	−0.577291	+	0.999897i	0.418498	+	0.908218i	$0.362557\pi$
$809$	−16.4198	+	28.4400i	−0.577291	+	0.999897i	−0.995789	+	0.0916790i	$0.970777\pi$
$810$		0			0
$811$	6.31746			0.221836			0.110918	−	0.993830i	$-0.464621\pi$
$811$	6.31746			0.221836			0.110918	+	0.993830i	$0.464621\pi$
$812$	18.4275	−	37.4440i	0.646678	−	1.31403i
$813$	−21.6412			−0.758991
$814$		0			0
$815$	−30.4370	+	52.7185i	−1.06616	+	1.84665i
$816$	−4.00000	+	6.92820i	−0.140028	+	0.242536i
$817$	−23.1336	−	40.0685i	−0.809341	−	1.40182i
$818$		0			0
$819$	6.77989	+	10.1290i	0.236909	+	0.353935i
$820$	−7.88676			−0.275418
$821$	−17.5598	−	30.4144i	−0.612841	−	1.06147i	−0.990759	−	0.135632i	$-0.956693\pi$
$821$	−17.5598	−	30.4144i	−0.612841	−	1.06147i	0.377919	−	0.925839i	$-0.376640\pi$
$822$		0			0
$823$	19.0439	−	32.9850i	0.663828	−	1.14978i	−0.315773	−	0.948835i	$-0.602264\pi$
$823$	19.0439	−	32.9850i	0.663828	−	1.14978i	0.979602	−	0.200949i	$-0.0644027\pi$
$824$		0			0
$825$	45.1539			1.57206
$826$		0			0
$827$	−17.1196			−0.595305			−0.297653	−	0.954674i	$-0.596204\pi$
$827$	−17.1196			−0.595305			−0.297653	+	0.954674i	$0.596204\pi$
$828$	5.94338	+	10.2942i	0.206547	+	0.357749i
$829$	−18.6100	+	32.2335i	−0.646353	+	1.11952i	0.337634	+	0.941277i	$0.390373\pi$
$829$	−18.6100	+	32.2335i	−0.646353	+	1.11952i	−0.983987	+	0.178239i	$0.942960\pi$
$830$		0			0
$831$	4.33175	+	7.50280i	0.150267	+	0.260269i
$832$	36.8550			1.27772
$833$	5.33651	−	12.9430i	0.184899	−	0.448449i
$834$		0			0
$835$	2.39313	+	4.14502i	0.0828176	+	0.143444i
$836$	29.7169	−	51.4712i	1.02778	−	1.78017i
$837$	4.61164	−	7.98759i	0.159401	−	0.276091i
$838$		0			0
$839$	49.0597			1.69373			0.846865	−	0.531808i	$-0.178487\pi$
$839$	49.0597			1.69373			0.846865	+	0.531808i	$0.178487\pi$
$840$		0			0
$841$	33.2010			1.14486
$842$		0			0
$843$	−10.0738	+	17.4483i	−0.346960	+	0.600952i
$844$	−25.1196	+	43.5084i	−0.864651	+	1.49762i
$845$	16.2137	+	28.0830i	0.557770	+	0.966086i
$846$		0			0
$847$	−10.7690	−	16.0886i	−0.370028	−	0.552812i
$848$	−36.8550			−1.26561
$849$	−9.77989	−	16.9393i	−0.335645	−	0.581354i
$850$		0			0
$851$	2.97169	−	5.14712i	0.101868	−	0.176441i
$852$	−7.21374	−	12.4946i	−0.247139	−	0.428057i
$853$	−4.10371			−0.140508			−0.0702542	−	0.997529i	$-0.522381\pi$
$853$	−4.10371			−0.140508			−0.0702542	+	0.997529i	$0.522381\pi$
$854$		0			0
$855$	27.3804			0.936390
$856$		0			0
$857$	0.355562	−	0.615851i	0.0121458	−	0.0210371i	−0.859889	−	0.510482i	$-0.829467\pi$
$857$	0.355562	−	0.615851i	0.0121458	−	0.0210371i	0.872034	+	0.489445i	$0.162800\pi$
$858$		0			0
$859$	−4.28149	−	7.41576i	−0.146083	−	0.253023i	0.783694	−	0.621147i	$-0.213333\pi$
$859$	−4.28149	−	7.41576i	−0.146083	−	0.253023i	−0.929776	+	0.368125i	$0.880000\pi$
$860$	−52.5534			−1.79205
$861$	−1.16825	+	2.37385i	−0.0398140	+	0.0809007i
$862$		0			0
$863$	21.9590	+	38.0340i	0.747492	+	1.29469i	0.949022	+	0.315211i	$0.102075\pi$
$863$	21.9590	+	38.0340i	0.747492	+	1.29469i	−0.201530	+	0.979482i	$0.564591\pi$
$864$		0			0
$865$	−1.55025	+	2.68512i	−0.0527102	+	0.0912967i
$866$		0			0
$867$	13.0000			0.441503
$868$	27.1476	+	40.5578i	0.921450	+	1.37662i
$869$	−10.2016			−0.346064
$870$		0			0
$871$	−6.00476	+	10.4006i	−0.203464	+	0.352409i
$872$		0			0
$873$	4.88676	+	8.46412i	0.165392	+	0.286467i
$874$		0			0
$875$	−57.7798	+	3.83432i	−1.95332	+	0.129624i
$876$	−13.3270			−0.450277
$877$	−4.23440	−	7.33420i	−0.142986	−	0.247658i	0.785634	−	0.618691i	$-0.212337\pi$
$877$	−4.23440	−	7.33420i	−0.142986	−	0.247658i	−0.928620	+	0.371033i	$0.879004\pi$
$878$		0			0
$879$	6.02671	−	10.4386i	0.203276	−	0.352084i
$880$	−33.7545	−	58.4645i	−1.13786	−	1.97084i
$881$	28.3524			0.955215			0.477608	−	0.878573i	$-0.341504\pi$
$881$	28.3524			0.955215			0.477608	+	0.878573i	$0.341504\pi$
$882$		0			0
$883$	−44.4904			−1.49722			−0.748611	−	0.663009i	$-0.769279\pi$
$883$	−44.4904			−1.49722			−0.748611	+	0.663009i	$0.769279\pi$
$884$	9.21374	+	15.9587i	0.309892	+	0.536748i
$885$	−26.0534	+	45.1258i	−0.875776	+	1.51689i
$886$		0			0
$887$	−7.28942	−	12.6256i	−0.244755	−	0.423927i	0.717308	−	0.696756i	$-0.245374\pi$
$887$	−7.28942	−	12.6256i	−0.244755	−	0.423927i	−0.962063	+	0.272829i	$0.912041\pi$
$888$		0			0
$889$	14.9765	−	0.993850i	0.502294	−	0.0333326i
$890$		0			0
$891$	2.13994	+	3.70649i	0.0716909	+	0.124172i
$892$	−8.89629	+	15.4088i	−0.297870	+	0.515926i
$893$	−10.1854	+	17.6417i	−0.340843	+	0.590357i
$894$		0			0
$895$	−96.4020			−3.22236
$896$		0			0
$897$	27.3804			0.914205
$898$		0			0
$899$	−36.3709	+	62.9962i	−1.21304	+	2.10104i
$900$	10.5503	−	18.2736i	0.351675	−	0.609119i
$901$	−9.21374	−	15.9587i	−0.306954	−	0.531660i
$902$		0			0
$903$	−7.78465	+	15.8182i	−0.259057	+	0.526395i
$904$		0			0
$905$	−38.4542	−	66.6046i	−1.27826	−	2.21401i
$906$		0			0
$907$	21.9920	−	38.0913i	0.730233	−	1.26480i	−0.226550	−	0.974000i	$-0.572745\pi$
$907$	21.9920	−	38.0913i	0.730233	−	1.26480i	0.956783	−	0.290802i	$-0.0939220\pi$
$908$	−13.2137	−	22.8869i	−0.438514	−	0.759528i
$909$	13.7735			0.456839
$910$		0			0
$911$	29.6412			0.982058			0.491029	−	0.871143i	$-0.336621\pi$
$911$	29.6412			0.982058			0.491029	+	0.871143i	$0.336621\pi$
$912$	−13.8868	−	24.0526i	−0.459837	−	0.796460i
$913$	−9.83807	+	17.0400i	−0.325592	+	0.563943i
$914$		0			0
$915$	−17.5032	−	30.3164i	−0.578637	−	1.00223i
$916$	−6.96822			−0.230236
$917$	14.8002	+	22.1111i	0.488747	+	0.730174i
$918$		0			0
$919$	19.4246	+	33.6444i	0.640758	+	1.10983i	0.985264	+	0.171042i	$0.0547133\pi$
$919$	19.4246	+	33.6444i	0.640758	+	1.10983i	−0.344505	+	0.938784i	$0.611953\pi$
$920$		0			0
$921$	3.38676	−	5.86604i	0.111598	−	0.193293i
$922$		0			0
$923$	−33.2328			−1.09387
$924$	−22.5973	+	1.49958i	−0.743398	+	0.0493325i
$925$	−10.5503			−0.346890
$926$		0			0
$927$	−2.44338	+	4.23206i	−0.0802512	+	0.138999i
$928$		0			0
$929$	4.82062	+	8.34955i	0.158159	+	0.273940i	0.934205	−	0.356737i	$-0.116111\pi$
$929$	4.82062	+	8.34955i	0.158159	+	0.273940i	−0.776046	+	0.630677i	$0.782777\pi$
$930$		0			0
$931$	29.6508	+	38.5117i	0.971764	+	1.26217i
$932$	11.4402			0.374737
$933$	8.09285	+	14.0172i	0.264948	+	0.458904i
$934$		0			0
$935$	16.8772	−	29.2322i	0.551945	−	0.955996i
$936$		0			0
$937$	−11.7106			−0.382568			−0.191284	−	0.981535i	$-0.561265\pi$
$937$	−11.7106			−0.382568			−0.191284	+	0.981535i	$0.561265\pi$
$938$		0			0
$939$	29.0344			0.947501
$940$	11.5693	+	20.0386i	0.377349	+	0.653588i
$941$	21.7074	−	37.5983i	0.707640	−	1.22567i	−0.258090	−	0.966121i	$-0.583093\pi$
$941$	21.7074	−	37.5983i	0.707640	−	1.22567i	0.965730	−	0.259548i	$-0.0835736\pi$
$942$		0			0
$943$	2.97169	+	5.14712i	0.0967716	+	0.167613i
$944$	52.8550			1.72028
$945$	−5.80344	−	8.67017i	−0.188786	−	0.282041i
$946$		0			0
$947$	6.79231	+	11.7646i	0.220720	+	0.382299i	0.955027	−	0.296519i	$-0.0958259\pi$
$947$	6.79231	+	11.7646i	0.220720	+	0.382299i	−0.734307	+	0.678818i	$0.762493\pi$
$948$	−2.38360	+	4.12852i	−0.0774158	+	0.134088i
$949$	−15.3489	+	26.5851i	−0.498247	+	0.862989i
$950$		0			0
$951$	10.2608			0.332730
$952$		0			0
$953$	57.0254			1.84723			0.923617	−	0.383318i	$-0.125219\pi$
$953$	57.0254			1.84723			0.923617	+	0.383318i	$0.125219\pi$
$954$		0			0
$955$	25.2783	−	43.7833i	0.817986	−	1.41679i
$956$	−8.44654	+	14.6298i	−0.273181	+	0.473163i
$957$	−16.8772	−	29.2322i	−0.545564	−	0.944944i
$958$		0			0
$959$	6.09098	−	12.3767i	0.196688	−	0.399663i
$960$	−31.5470			−1.01818
$961$	−27.0344	−	46.8249i	−0.872076	−	1.51048i
$962$		0			0
$963$	1.97169	−	3.41507i	0.0635368	−	0.110049i
$964$	−9.66349	−	16.7377i	−0.311240	−	0.539084i
$965$	−31.2862			−1.00714
$966$		0			0
$967$	−11.7042			−0.376381			−0.188190	−	0.982133i	$-0.560262\pi$
$967$	−11.7042			−0.376381			−0.188190	+	0.982133i	$0.560262\pi$
$968$		0			0
$969$	6.94338	−	12.0263i	0.223054	−	0.386340i
$970$		0			0
$971$	−0.393128	−	0.680917i	−0.0126161	−	0.0218517i	0.859648	−	0.510886i	$-0.170683\pi$
$971$	−0.393128	−	0.680917i	−0.0126161	−	0.0218517i	−0.872265	+	0.489034i	$0.837349\pi$
$972$	2.00000			0.0641500
$973$	−14.6272	+	0.970674i	−0.468927	+	0.0311184i
$974$		0			0
$975$	−24.3018	−	42.0920i	−0.778282	−	1.34802i
$976$	−17.7545	+	30.7516i	−0.568307	+	0.984336i
$977$	11.1196	−	19.2596i	0.355746	−	0.616171i	−0.631499	−	0.775377i	$-0.717560\pi$
$977$	11.1196	−	19.2596i	0.355746	−	0.616171i	0.987245	+	0.159206i	$0.0508934\pi$
$978$		0			0
$979$	−29.6761			−0.948453
$980$	54.7232	−	7.29508i	1.74807	−	0.233033i
$981$	16.1571			0.515857
$982$		0			0
$983$	−8.43096	+	14.6029i	−0.268906	+	0.465759i	−0.968580	−	0.248704i	$-0.919995\pi$
$983$	−8.43096	+	14.6029i	−0.268906	+	0.465759i	0.699674	+	0.714463i	$0.253329\pi$
$984$		0			0
$985$	42.8931	+	74.2930i	1.36669	+	2.36717i
$986$		0			0
$987$	7.74521	−	0.513979i	0.246533	−	0.0163601i
$988$	−63.9745			−2.03530
$989$	19.8018	+	34.2978i	0.629662	+	1.09061i
$990$		0			0
$991$	9.31296	−	16.1305i	0.295836	−	0.512403i	−0.679343	−	0.733821i	$-0.737735\pi$
$991$	9.31296	−	16.1305i	0.295836	−	0.512403i	0.975179	+	0.221418i	$0.0710685\pi$
$992$		0			0
$993$	15.5973			0.494967
$994$		0			0
$995$	−28.4465			−0.901816
$996$	4.59735	+	7.96284i	0.145672	+	0.252312i
$997$	−4.85529	+	8.40961i	−0.153769	+	0.266335i	−0.932610	−	0.360886i	$-0.882474\pi$
$997$	−4.85529	+	8.40961i	−0.153769	+	0.266335i	0.778841	+	0.627221i	$0.215808\pi$
$998$		0			0
$999$	−0.500000	−	0.866025i	−0.0158193	−	0.0273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	861.2.i.c.739.3	yes	6
7.2	even	3	inner	861.2.i.c.247.3	✓	6
7.3	odd	6		6027.2.a.q.1.3		3
7.4	even	3		6027.2.a.p.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.c.247.3	✓	6	7.2	even	3	inner
861.2.i.c.739.3	yes	6	1.1	even	1	trivial
6027.2.a.p.1.1		3	7.4	even	3
6027.2.a.q.1.3		3	7.3	odd	6

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:	\( N \)	\(=\)	\( 861 = 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	861.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(1.97169 + 3.41507i) q^{5} +(2.63994 - 0.175189i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(1.97169 + 3.41507i) q^{5} +(2.63994 - 0.175189i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(2.13994 - 3.70649i) q^{11} +(-1.00000 - 1.73205i) q^{12} -4.60687 q^{13} +3.94338 q^{15} +(-2.00000 - 3.46410i) q^{16} +(1.00000 - 1.73205i) q^{17} +(3.47169 + 6.01314i) q^{19} +7.88676 q^{20} +(1.16825 - 2.37385i) q^{21} +(-2.97169 - 5.14712i) q^{23} +(-5.27513 + 9.13679i) q^{25} -1.00000 q^{27} +(2.33651 - 4.74771i) q^{28} +7.88676 q^{29} +(-4.61164 + 7.98759i) q^{31} +(-2.13994 - 3.70649i) q^{33} +(5.80344 + 8.67017i) q^{35} -2.00000 q^{36} +(0.500000 + 0.866025i) q^{37} +(-2.30344 + 3.98967i) q^{39} -1.00000 q^{41} -6.66349 q^{43} +(-4.27989 - 7.41299i) q^{44} +(1.97169 - 3.41507i) q^{45} +(1.46693 + 2.54079i) q^{47} -4.00000 q^{48} +(6.93862 - 0.924978i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(-4.60687 + 7.97934i) q^{52} +(4.60687 - 7.97934i) q^{53} +16.8772 q^{55} +6.94338 q^{57} +(-6.60687 + 11.4434i) q^{59} +(3.94338 - 6.83014i) q^{60} +(-4.43862 - 7.68791i) q^{61} +(-1.47169 - 2.19866i) q^{63} -8.00000 q^{64} +(-9.08333 - 15.7328i) q^{65} +(1.30344 - 2.25762i) q^{67} +(-2.00000 - 3.46410i) q^{68} -5.94338 q^{69} +7.21374 q^{71} +(3.33175 - 5.77075i) q^{73} +(5.27513 + 9.13679i) q^{75} +13.8868 q^{76} +(5.00000 - 10.1598i) q^{77} +(-1.19180 - 2.06426i) q^{79} +(7.88676 - 13.6603i) q^{80} +(-0.500000 + 0.866025i) q^{81} -4.59735 q^{83} +(-2.94338 - 4.39733i) q^{84} +7.88676 q^{85} +(3.94338 - 6.83014i) q^{87} +(-3.46693 - 6.00489i) q^{89} +(-12.1619 + 0.807073i) q^{91} -11.8868 q^{92} +(4.61164 + 7.98759i) q^{93} +(-13.6902 + 23.7121i) q^{95} -9.77352 q^{97} -4.27989 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} + 6 q^{4} + 3 q^{7} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 + 6 * q^4 + 3 * q^7 - 3 * q^9	\( 6 q + 3 q^{3} + 6 q^{4} + 3 q^{7} - 3 q^{9} - 6 q^{12} - 6 q^{13} - 12 q^{16} + 6 q^{17} + 9 q^{19} + 6 q^{21} - 6 q^{23} - 9 q^{25} - 6 q^{27} + 12 q^{28} - 3 q^{31} + 24 q^{35} - 12 q^{36} + 3 q^{37} - 3 q^{39} - 6 q^{41} - 42 q^{43} - 24 q^{48} + 21 q^{49} - 6 q^{51} - 6 q^{52} + 6 q^{53} + 60 q^{55} + 18 q^{57} - 18 q^{59} - 6 q^{61} + 3 q^{63} - 48 q^{64} - 18 q^{65} - 3 q^{67} - 12 q^{68} - 12 q^{69} + 21 q^{73} + 9 q^{75} + 36 q^{76} + 30 q^{77} - 21 q^{79} - 3 q^{81} - 12 q^{83} + 6 q^{84} - 12 q^{89} - 3 q^{91} - 24 q^{92} + 3 q^{93} - 24 q^{95} + 36 q^{97}+O(q^{100}) \) 6 * q + 3 * q^3 + 6 * q^4 + 3 * q^7 - 3 * q^9 - 6 * q^12 - 6 * q^13 - 12 * q^16 + 6 * q^17 + 9 * q^19 + 6 * q^21 - 6 * q^23 - 9 * q^25 - 6 * q^27 + 12 * q^28 - 3 * q^31 + 24 * q^35 - 12 * q^36 + 3 * q^37 - 3 * q^39 - 6 * q^41 - 42 * q^43 - 24 * q^48 + 21 * q^49 - 6 * q^51 - 6 * q^52 + 6 * q^53 + 60 * q^55 + 18 * q^57 - 18 * q^59 - 6 * q^61 + 3 * q^63 - 48 * q^64 - 18 * q^65 - 3 * q^67 - 12 * q^68 - 12 * q^69 + 21 * q^73 + 9 * q^75 + 36 * q^76 + 30 * q^77 - 21 * q^79 - 3 * q^81 - 12 * q^83 + 6 * q^84 - 12 * q^89 - 3 * q^91 - 24 * q^92 + 3 * q^93 - 24 * q^95 + 36 * q^97

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