LMFDB - Embedded newform 1716.2.q.b.133.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1716,2,Mod(133,1716)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1716, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1716.133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1716.q (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:	$13.7023289869$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 19 x^{10} - 28 x^{9} + 301 x^{8} - 319 x^{7} + 1300 x^{6} - 1174 x^{5} + 4000 x^{4} + \cdots + 324 $ x^12 + 19x^10 - 28x^9 + 301x^8 - 319x^7 + 1300x^6 - 1174x^5 + 4000x^4 - 2676x^3 + 3889x^2 + 954x + 324
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.5
Root			$-0.955509 + 1.65499i$ of defining polynomial
Character	$\chi$	$=$	1716.133
Dual form			1716.2.q.b.529.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} +1.91102 q^{5} +(-2.19058 + 3.79419i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{3} +1.91102 q^{5} +(-2.19058 + 3.79419i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(-2.62951 + 2.46691i) q^{13} +(-0.955509 - 1.65499i) q^{15} +(0.520977 - 0.902358i) q^{17} +(-0.479023 + 0.829693i) q^{19} +4.38115 q^{21} +(-0.434533 - 0.752633i) q^{23} -1.34801 q^{25} +1.00000 q^{27} +(-5.14174 - 8.90576i) q^{29} -3.95297 q^{31} +(-0.500000 + 0.866025i) q^{33} +(-4.18623 + 7.25077i) q^{35} +(-3.56127 - 6.16829i) q^{37} +(3.45117 + 1.04377i) q^{39} +(-5.94222 - 10.2922i) q^{41} +(-3.77994 + 6.54705i) q^{43} +(-0.955509 + 1.65499i) q^{45} -2.20242 q^{47} +(-6.09725 - 10.5608i) q^{49} -1.04195 q^{51} +5.46133 q^{53} +(-0.955509 - 1.65499i) q^{55} +0.958046 q^{57} +(1.74730 - 3.02641i) q^{59} +(-1.84975 + 3.20387i) q^{61} +(-2.19058 - 3.79419i) q^{63} +(-5.02505 + 4.71432i) q^{65} +(1.69492 + 2.93569i) q^{67} +(-0.434533 + 0.752633i) q^{69} +(-0.281566 + 0.487687i) q^{71} +13.4771 q^{73} +(0.674003 + 1.16741i) q^{75} +4.38115 q^{77} -2.51237 q^{79} +(-0.500000 - 0.866025i) q^{81} -10.6354 q^{83} +(0.995596 - 1.72442i) q^{85} +(-5.14174 + 8.90576i) q^{87} +(5.78783 + 10.0248i) q^{89} +(-3.59979 - 15.3808i) q^{91} +(1.97649 + 3.42337i) q^{93} +(-0.915422 + 1.58556i) q^{95} +(5.56895 - 9.64571i) q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 2 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 + 2 * q^7 - 6 * q^9	$ 12 q - 6 q^{3} + 2 q^{7} - 6 q^{9} - 6 q^{11} - 4 q^{13} + 5 q^{17} - 7 q^{19} - 4 q^{21} + 5 q^{23} + 16 q^{25} + 12 q^{27} - 22 q^{31} - 6 q^{33} - 33 q^{37} + 8 q^{39} - 14 q^{41} - 4 q^{47} - 10 q^{51} + 10 q^{53} + 14 q^{57} - 30 q^{59} - 9 q^{61} + 2 q^{63} + 4 q^{65} + 14 q^{67} + 5 q^{69} + 3 q^{71} - 6 q^{73} - 8 q^{75} - 4 q^{77} + 2 q^{79} - 6 q^{81} + 8 q^{83} + q^{85} - 32 q^{89} + 16 q^{91} + 11 q^{93} + q^{95} + 10 q^{97} + 12 q^{99}+O(q^{100}) $ 12 * q - 6 * q^3 + 2 * q^7 - 6 * q^9 - 6 * q^11 - 4 * q^13 + 5 * q^17 - 7 * q^19 - 4 * q^21 + 5 * q^23 + 16 * q^25 + 12 * q^27 - 22 * q^31 - 6 * q^33 - 33 * q^37 + 8 * q^39 - 14 * q^41 - 4 * q^47 - 10 * q^51 + 10 * q^53 + 14 * q^57 - 30 * q^59 - 9 * q^61 + 2 * q^63 + 4 * q^65 + 14 * q^67 + 5 * q^69 + 3 * q^71 - 6 * q^73 - 8 * q^75 - 4 * q^77 + 2 * q^79 - 6 * q^81 + 8 * q^83 + q^85 - 32 * q^89 + 16 * q^91 + 11 * q^93 + q^95 + 10 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1716\mathbb{Z}\right)^\times$.

$n$	$859$	$925$	$937$	$1145$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$	1.91102			0.854634			0.427317	−	0.904102i	$-0.359459\pi$
$5$	1.91102			0.854634			0.427317	+	0.904102i	$0.359459\pi$
$6$		0			0
$7$	−2.19058	+	3.79419i	−0.827960	+	1.43407i	0.0716756	+	0.997428i	$0.477165\pi$
$7$	−2.19058	+	3.79419i	−0.827960	+	1.43407i	−0.899636	+	0.436641i	$0.856168\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	−2.62951	+	2.46691i	−0.729296	+	0.684199i
$13$	−2.62951	+	2.46691i	−0.729296	+	0.684199i
$14$		0			0
$15$	−0.955509	−	1.65499i	−0.246711	−	0.427317i
$16$		0			0
$17$	0.520977	−	0.902358i	0.126355	−	0.218854i	−0.795907	−	0.605420i	$-0.793005\pi$
$17$	0.520977	−	0.902358i	0.126355	−	0.218854i	0.922262	+	0.386566i	$0.126339\pi$
$18$		0			0
$19$	−0.479023	+	0.829693i	−0.109895	+	0.190345i	−0.915728	−	0.401799i	$-0.868385\pi$
$19$	−0.479023	+	0.829693i	−0.109895	+	0.190345i	0.805832	+	0.592144i	$0.201718\pi$
$20$		0			0
$21$	4.38115			0.956046
$22$		0			0
$23$	−0.434533	−	0.752633i	−0.0906063	−	0.156935i	0.817160	−	0.576411i	$-0.195547\pi$
$23$	−0.434533	−	0.752633i	−0.0906063	−	0.156935i	−0.907766	+	0.419476i	$0.862214\pi$
$24$		0			0
$25$	−1.34801			−0.269601
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−5.14174	−	8.90576i	−0.954798	−	1.65376i	−0.734830	−	0.678251i	$-0.762738\pi$
$29$	−5.14174	−	8.90576i	−0.954798	−	1.65376i	−0.219967	−	0.975507i	$-0.570595\pi$
$30$		0			0
$31$	−3.95297			−0.709975			−0.354987	−	0.934871i	$-0.615515\pi$
$31$	−3.95297			−0.709975			−0.354987	+	0.934871i	$0.615515\pi$
$32$		0			0
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$		0			0
$35$	−4.18623	+	7.25077i	−0.707603	+	1.22560i
$36$		0			0
$37$	−3.56127	−	6.16829i	−0.585469	−	1.01406i	−0.994817	−	0.101683i	$-0.967577\pi$
$37$	−3.56127	−	6.16829i	−0.585469	−	1.01406i	0.409348	−	0.912378i	$-0.365756\pi$
$38$		0			0
$39$	3.45117	+	1.04377i	0.552629	+	0.167137i
$40$		0			0
$41$	−5.94222	−	10.2922i	−0.928018	−	1.60738i	−0.786633	−	0.617420i	$-0.788178\pi$
$41$	−5.94222	−	10.2922i	−0.928018	−	1.60738i	−0.141385	−	0.989955i	$-0.545156\pi$
$42$		0			0
$43$	−3.77994	+	6.54705i	−0.576436	+	0.998416i	0.419448	+	0.907779i	$0.362224\pi$
$43$	−3.77994	+	6.54705i	−0.576436	+	0.998416i	−0.995884	+	0.0906368i	$0.971110\pi$
$44$		0			0
$45$	−0.955509	+	1.65499i	−0.142439	+	0.246711i
$46$		0			0
$47$	−2.20242			−0.321256			−0.160628	−	0.987015i	$-0.551352\pi$
$47$	−2.20242			−0.321256			−0.160628	+	0.987015i	$0.551352\pi$
$48$		0			0
$49$	−6.09725	−	10.5608i	−0.871036	−	1.50868i
$50$		0			0
$51$	−1.04195			−0.145903
$52$		0			0
$53$	5.46133			0.750171			0.375086	−	0.926990i	$-0.377613\pi$
$53$	5.46133			0.750171			0.375086	+	0.926990i	$0.377613\pi$
$54$		0			0
$55$	−0.955509	−	1.65499i	−0.128841	−	0.223159i
$56$		0			0
$57$	0.958046			0.126896
$58$		0			0
$59$	1.74730	−	3.02641i	0.227479	−	0.394005i	−0.729581	−	0.683894i	$-0.760285\pi$
$59$	1.74730	−	3.02641i	0.227479	−	0.394005i	0.957060	+	0.289889i	$0.0936185\pi$
$60$		0			0
$61$	−1.84975	+	3.20387i	−0.236837	+	0.410213i	−0.959805	−	0.280668i	$-0.909444\pi$
$61$	−1.84975	+	3.20387i	−0.236837	+	0.410213i	0.722968	+	0.690881i	$0.242777\pi$
$62$		0			0
$63$	−2.19058	−	3.79419i	−0.275987	−	0.478023i
$64$		0			0
$65$	−5.02505	+	4.71432i	−0.623281	+	0.584739i
$66$		0			0
$67$	1.69492	+	2.93569i	0.207067	+	0.358651i	0.950789	−	0.309838i	$-0.100275\pi$
$67$	1.69492	+	2.93569i	0.207067	+	0.358651i	−0.743722	+	0.668489i	$0.766941\pi$
$68$		0			0
$69$	−0.434533	+	0.752633i	−0.0523116	+	0.0906063i
$70$		0			0
$71$	−0.281566	+	0.487687i	−0.0334158	+	0.0578778i	−0.882250	−	0.470782i	$-0.843972\pi$
$71$	−0.281566	+	0.487687i	−0.0334158	+	0.0578778i	0.848834	+	0.528660i	$0.177305\pi$
$72$		0			0
$73$	13.4771			1.57738			0.788688	−	0.614794i	$-0.210761\pi$
$73$	13.4771			1.57738			0.788688	+	0.614794i	$0.210761\pi$
$74$		0			0
$75$	0.674003	+	1.16741i	0.0778272	+	0.134801i
$76$		0			0
$77$	4.38115			0.499279
$78$		0			0
$79$	−2.51237			−0.282664			−0.141332	−	0.989962i	$-0.545138\pi$
$79$	−2.51237			−0.282664			−0.141332	+	0.989962i	$0.545138\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−10.6354			−1.16739			−0.583693	−	0.811975i	$-0.698393\pi$
$83$	−10.6354			−1.16739			−0.583693	+	0.811975i	$0.698393\pi$
$84$		0			0
$85$	0.995596	−	1.72442i	0.107988	−	0.187040i
$86$		0			0
$87$	−5.14174	+	8.90576i	−0.551253	+	0.954798i
$88$		0			0
$89$	5.78783	+	10.0248i	0.613509	+	1.06263i	0.990644	+	0.136470i	$0.0435758\pi$
$89$	5.78783	+	10.0248i	0.613509	+	1.06263i	−0.377136	+	0.926158i	$0.623091\pi$
$90$		0			0
$91$	−3.59979	−	15.3808i	−0.377360	−	1.61235i
$92$		0			0
$93$	1.97649	+	3.42337i	0.204952	+	0.354987i
$94$		0			0
$95$	−0.915422	+	1.58556i	−0.0939204	+	0.162675i
$96$		0			0
$97$	5.56895	−	9.64571i	0.565441	−	0.979373i	−0.431567	−	0.902081i	$-0.642039\pi$
$97$	5.56895	−	9.64571i	0.565441	−	0.979373i	0.997008	−	0.0772922i	$-0.0246274\pi$
$98$		0			0
$99$	1.00000			0.100504
$100$		0			0
$101$	4.10399	+	7.10832i	0.408362	+	0.707304i	0.994706	−	0.102758i	$-0.0327667\pi$
$101$	4.10399	+	7.10832i	0.408362	+	0.707304i	−0.586344	+	0.810062i	$0.699433\pi$
$102$		0			0
$103$	−15.4108			−1.51847			−0.759236	−	0.650815i	$-0.774427\pi$
$103$	−15.4108			−1.51847			−0.759236	+	0.650815i	$0.774427\pi$
$104$		0			0
$105$	8.37247			0.817069
$106$		0			0
$107$	4.82009	+	8.34864i	0.465976	+	0.807093i	0.999245	−	0.0388520i	$-0.0123701\pi$
$107$	4.82009	+	8.34864i	0.465976	+	0.807093i	−0.533269	+	0.845946i	$0.679037\pi$
$108$		0			0
$109$	−19.3645			−1.85479			−0.927394	−	0.374087i	$-0.877956\pi$
$109$	−19.3645			−1.85479			−0.927394	+	0.374087i	$0.877956\pi$
$110$		0			0
$111$	−3.56127	+	6.16829i	−0.338020	+	0.585469i
$112$		0			0
$113$	−2.81711	+	4.87937i	−0.265011	+	0.459013i	−0.967567	−	0.252616i	$-0.918709\pi$
$113$	−2.81711	+	4.87937i	−0.265011	+	0.459013i	0.702555	+	0.711629i	$0.252042\pi$
$114$		0			0
$115$	−0.830400	−	1.43830i	−0.0774352	−	0.134122i
$116$		0			0
$117$	−0.821653	−	3.51068i	−0.0759619	−	0.324563i
$118$		0			0
$119$	2.28248	+	3.95337i	0.209235	+	0.362405i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	−5.94222	+	10.2922i	−0.535792	+	0.928018i
$124$		0			0
$125$	−12.1312			−1.08504
$126$		0			0
$127$	7.41690	+	12.8464i	0.658143	+	1.13994i	0.981096	+	0.193522i	$0.0619912\pi$
$127$	7.41690	+	12.8464i	0.658143	+	1.13994i	−0.322953	+	0.946415i	$0.604675\pi$
$128$		0			0
$129$	7.55988			0.665611
$130$		0			0
$131$	−10.4096			−0.909494			−0.454747	−	0.890621i	$-0.650270\pi$
$131$	−10.4096			−0.909494			−0.454747	+	0.890621i	$0.650270\pi$
$132$		0			0
$133$	−2.09867	−	3.63501i	−0.181978	−	0.315195i
$134$		0			0
$135$	1.91102			0.164474
$136$		0			0
$137$	5.01247	−	8.68186i	0.428244	−	0.741741i	−0.568473	−	0.822702i	$-0.692466\pi$
$137$	5.01247	−	8.68186i	0.428244	−	0.741741i	0.996717	+	0.0809609i	$0.0257989\pi$
$138$		0			0
$139$	−7.70378	+	13.3433i	−0.653426	+	1.13177i	0.328860	+	0.944379i	$0.393336\pi$
$139$	−7.70378	+	13.3433i	−0.653426	+	1.13177i	−0.982286	+	0.187388i	$0.939998\pi$
$140$		0			0
$141$	1.10121	+	1.90735i	0.0927387	+	0.160628i
$142$		0			0
$143$	3.45117	+	1.04377i	0.288601	+	0.0872843i
$144$		0			0
$145$	−9.82597	−	17.0191i	−0.816002	−	1.41336i
$146$		0			0
$147$	−6.09725	+	10.5608i	−0.502893	+	0.871036i
$148$		0			0
$149$	−9.96358	+	17.2574i	−0.816248	+	1.41378i	0.0921801	+	0.995742i	$0.470616\pi$
$149$	−9.96358	+	17.2574i	−0.816248	+	1.41378i	−0.908428	+	0.418041i	$0.862717\pi$
$150$		0			0
$151$	11.3906			0.926955			0.463477	−	0.886109i	$-0.346602\pi$
$151$	11.3906			0.926955			0.463477	+	0.886109i	$0.346602\pi$
$152$		0			0
$153$	0.520977	+	0.902358i	0.0421185	+	0.0729513i
$154$		0			0
$155$	−7.55421			−0.606768
$156$		0			0
$157$	7.97743			0.636668			0.318334	−	0.947979i	$-0.396877\pi$
$157$	7.97743			0.636668			0.318334	+	0.947979i	$0.396877\pi$
$158$		0			0
$159$	−2.73066	−	4.72965i	−0.216556	−	0.375086i
$160$		0			0
$161$	3.80751			0.300074
$162$		0			0
$163$	9.01571	−	15.6157i	0.706165	−	1.22311i	−0.260104	−	0.965581i	$-0.583757\pi$
$163$	9.01571	−	15.6157i	0.706165	−	1.22311i	0.966269	−	0.257533i	$-0.0829097\pi$
$164$		0			0
$165$	−0.955509	+	1.65499i	−0.0743863	+	0.128841i
$166$		0			0
$167$	6.72691	+	11.6513i	0.520544	+	0.901608i	0.999715	+	0.0238866i	$0.00760405\pi$
$167$	6.72691	+	11.6513i	0.520544	+	0.901608i	−0.479171	+	0.877722i	$0.659063\pi$
$168$		0			0
$169$	0.828676	−	12.9736i	0.0637443	−	0.997966i
$170$		0			0
$171$	−0.479023	−	0.829693i	−0.0366318	−	0.0634482i
$172$		0			0
$173$	−4.07335	+	7.05526i	−0.309691	+	0.536401i	−0.978295	−	0.207218i	$-0.933559\pi$
$173$	−4.07335	+	7.05526i	−0.309691	+	0.536401i	0.668603	+	0.743619i	$0.266892\pi$
$174$		0			0
$175$	2.95291	−	5.11459i	0.223219	−	0.386627i
$176$		0			0
$177$	−3.49459			−0.262670
$178$		0			0
$179$	−3.44676	−	5.96997i	−0.257623	−	0.446216i	0.707982	−	0.706231i	$-0.249606\pi$
$179$	−3.44676	−	5.96997i	−0.257623	−	0.446216i	−0.965605	+	0.260015i	$0.916273\pi$
$180$		0			0
$181$	−9.29684			−0.691029			−0.345514	−	0.938413i	$-0.612296\pi$
$181$	−9.29684			−0.691029			−0.345514	+	0.938413i	$0.612296\pi$
$182$		0			0
$183$	3.69951			0.273475
$184$		0			0
$185$	−6.80565	−	11.7877i	−0.500361	−	0.866651i
$186$		0			0
$187$	−1.04195			−0.0761952
$188$		0			0
$189$	−2.19058	+	3.79419i	−0.159341	+	0.275987i
$190$		0			0
$191$	3.46041	−	5.99361i	0.250387	−	0.433683i	−0.713246	−	0.700914i	$-0.752776\pi$
$191$	3.46041	−	5.99361i	0.250387	−	0.433683i	0.963632	+	0.267232i	$0.0861089\pi$
$192$		0			0
$193$	−9.71648	−	16.8294i	−0.699408	−	1.21141i	−0.968672	−	0.248343i	$-0.920114\pi$
$193$	−9.71648	−	16.8294i	−0.699408	−	1.21141i	0.269264	−	0.963066i	$-0.413219\pi$
$194$		0			0
$195$	6.59524	+	1.99466i	0.472295	+	0.142841i
$196$		0			0
$197$	6.24050	+	10.8089i	0.444617	+	0.770099i	0.998025	−	0.0628106i	$-0.0200064\pi$
$197$	6.24050	+	10.8089i	0.444617	+	0.770099i	−0.553408	+	0.832910i	$0.686673\pi$
$198$		0			0
$199$	−10.6069	+	18.3718i	−0.751906	+	1.30234i	0.194991	+	0.980805i	$0.437532\pi$
$199$	−10.6069	+	18.3718i	−0.751906	+	1.30234i	−0.946898	+	0.321535i	$0.895801\pi$
$200$		0			0
$201$	1.69492	−	2.93569i	0.119550	−	0.207067i
$202$		0			0
$203$	45.0535			3.16214
$204$		0			0
$205$	−11.3557	−	19.6686i	−0.793116	−	1.37372i
$206$		0			0
$207$	0.869065			0.0604042
$208$		0			0
$209$	0.958046			0.0662695
$210$		0			0
$211$	5.33374	+	9.23831i	0.367190	+	0.635992i	0.989125	−	0.147077i	$-0.0469866\pi$
$211$	5.33374	+	9.23831i	0.367190	+	0.635992i	−0.621935	+	0.783069i	$0.713653\pi$
$212$		0			0
$213$	0.563133			0.0385852
$214$		0			0
$215$	−7.22354	+	12.5115i	−0.492641	+	0.853280i
$216$		0			0
$217$	8.65929	−	14.9983i	0.587831	−	1.01815i
$218$		0			0
$219$	−6.73855	−	11.6715i	−0.455349	−	0.788688i
$220$		0			0
$221$	0.856125	+	3.65797i	0.0575892	+	0.246062i
$222$		0			0
$223$	−11.6992	−	20.2637i	−0.783439	−	1.35696i	−0.929927	−	0.367743i	$-0.880131\pi$
$223$	−11.6992	−	20.2637i	−0.783439	−	1.35696i	0.146489	−	0.989212i	$-0.453203\pi$
$224$		0			0
$225$	0.674003	−	1.16741i	0.0449336	−	0.0778272i
$226$		0			0
$227$	−10.3580	+	17.9406i	−0.687486	+	1.19076i	0.285162	+	0.958479i	$0.407952\pi$
$227$	−10.3580	+	17.9406i	−0.687486	+	1.19076i	−0.972649	+	0.232282i	$0.925381\pi$
$228$		0			0
$229$	−9.58954			−0.633695			−0.316847	−	0.948477i	$-0.602624\pi$
$229$	−9.58954			−0.633695			−0.316847	+	0.948477i	$0.602624\pi$
$230$		0			0
$231$	−2.19058	−	3.79419i	−0.144129	−	0.249639i
$232$		0			0
$233$	13.4017			0.877976			0.438988	−	0.898493i	$-0.355337\pi$
$233$	13.4017			0.877976			0.438988	+	0.898493i	$0.355337\pi$
$234$		0			0
$235$	−4.20887			−0.274556
$236$		0			0
$237$	1.25619	+	2.17578i	0.0815980	+	0.141332i
$238$		0			0
$239$	−21.7225			−1.40511			−0.702557	−	0.711628i	$-0.747958\pi$
$239$	−21.7225			−1.40511			−0.702557	+	0.711628i	$0.747958\pi$
$240$		0			0
$241$	−1.60535	+	2.78055i	−0.103410	+	0.179111i	−0.913087	−	0.407764i	$-0.866309\pi$
$241$	−1.60535	+	2.78055i	−0.103410	+	0.179111i	0.809678	+	0.586875i	$0.199642\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	−11.6520	−	20.1818i	−0.744417	−	1.28937i
$246$		0			0
$247$	−0.787182	−	3.36340i	−0.0500872	−	0.214008i
$248$		0			0
$249$	5.31769	+	9.21052i	0.336995	+	0.583693i
$250$		0			0
$251$	4.79497	−	8.30513i	0.302656	−	0.524215i	−0.674081	−	0.738658i	$-0.735460\pi$
$251$	4.79497	−	8.30513i	0.302656	−	0.524215i	0.976737	+	0.214442i	$0.0687934\pi$
$252$		0			0
$253$	−0.434533	+	0.752633i	−0.0273188	+	0.0473176i
$254$		0			0
$255$	−1.99119			−0.124693
$256$		0			0
$257$	5.41671	+	9.38203i	0.337885	+	0.585235i	0.984035	−	0.177976i	$-0.0569550\pi$
$257$	5.41671	+	9.38203i	0.337885	+	0.585235i	−0.646149	+	0.763211i	$0.723622\pi$
$258$		0			0
$259$	31.2049			1.93898
$260$		0			0
$261$	10.2835			0.636532
$262$		0			0
$263$	−2.81291	−	4.87210i	−0.173451	−	0.300426i	0.766173	−	0.642634i	$-0.222159\pi$
$263$	−2.81291	−	4.87210i	−0.173451	−	0.300426i	−0.939624	+	0.342208i	$0.888825\pi$
$264$		0			0
$265$	10.4367			0.641121
$266$		0			0
$267$	5.78783	−	10.0248i	0.354209	−	0.613509i
$268$		0			0
$269$	−0.275296	+	0.476827i	−0.0167851	+	0.0290727i	−0.874296	−	0.485393i	$-0.838676\pi$
$269$	−0.275296	+	0.476827i	−0.0167851	+	0.0290727i	0.857511	+	0.514466i	$0.172010\pi$
$270$		0			0
$271$	−4.84107	−	8.38497i	−0.294074	−	0.509351i	0.680695	−	0.732567i	$-0.261678\pi$
$271$	−4.84107	−	8.38497i	−0.294074	−	0.509351i	−0.974769	+	0.223216i	$0.928344\pi$
$272$		0			0
$273$	−11.5203	+	10.8079i	−0.697240	+	0.654125i
$274$		0			0
$275$	0.674003	+	1.16741i	0.0406439	+	0.0703974i
$276$		0			0
$277$	−1.38254	+	2.39463i	−0.0830688	+	0.143879i	−0.904567	−	0.426332i	$-0.859805\pi$
$277$	−1.38254	+	2.39463i	−0.0830688	+	0.143879i	0.821498	+	0.570212i	$0.193139\pi$
$278$		0			0
$279$	1.97649	−	3.42337i	0.118329	−	0.204952i
$280$		0			0
$281$	26.3007			1.56897			0.784485	−	0.620148i	$-0.212928\pi$
$281$	26.3007			1.56897			0.784485	+	0.620148i	$0.212928\pi$
$282$		0			0
$283$	−1.56092	−	2.70360i	−0.0927872	−	0.160712i	0.815896	−	0.578199i	$-0.196244\pi$
$283$	−1.56092	−	2.70360i	−0.0927872	−	0.160712i	−0.908683	+	0.417487i	$0.862911\pi$
$284$		0			0
$285$	1.83084			0.108450
$286$		0			0
$287$	52.0675			3.07345
$288$		0			0
$289$	7.95717	+	13.7822i	0.468069	+	0.810719i
$290$		0			0
$291$	−11.1379			−0.652915
$292$		0			0
$293$	9.11222	−	15.7828i	0.532342	−	0.922043i	−0.466945	−	0.884286i	$-0.654646\pi$
$293$	9.11222	−	15.7828i	0.532342	−	0.922043i	0.999287	−	0.0377566i	$-0.0120212\pi$
$294$		0			0
$295$	3.33912	−	5.78352i	0.194411	−	0.336730i
$296$		0			0
$297$	−0.500000	−	0.866025i	−0.0290129	−	0.0502519i
$298$		0			0
$299$	2.99929	+	0.907103i	0.173453	+	0.0524591i
$300$		0			0
$301$	−16.5605	−	28.6836i	−0.954532	−	1.65330i
$302$		0			0
$303$	4.10399	−	7.10832i	0.235768	−	0.408362i
$304$		0			0
$305$	−3.53491	+	6.12265i	−0.202409	+	0.350582i
$306$		0			0
$307$	19.5998			1.11862			0.559311	−	0.828958i	$-0.311066\pi$
$307$	19.5998			1.11862			0.559311	+	0.828958i	$0.311066\pi$
$308$		0			0
$309$	7.70540	+	13.3462i	0.438345	+	0.759236i
$310$		0			0
$311$	−12.1143			−0.686941			−0.343470	−	0.939164i	$-0.611602\pi$
$311$	−12.1143			−0.686941			−0.343470	+	0.939164i	$0.611602\pi$
$312$		0			0
$313$	−4.67020			−0.263975			−0.131988	−	0.991251i	$-0.542136\pi$
$313$	−4.67020			−0.263975			−0.131988	+	0.991251i	$0.542136\pi$
$314$		0			0
$315$	−4.18623	−	7.25077i	−0.235868	−	0.408535i
$316$		0			0
$317$	8.09099			0.454436			0.227218	−	0.973844i	$-0.427037\pi$
$317$	8.09099			0.454436			0.227218	+	0.973844i	$0.427037\pi$
$318$		0			0
$319$	−5.14174	+	8.90576i	−0.287882	+	0.498627i
$320$		0			0
$321$	4.82009	−	8.34864i	0.269031	−	0.465976i
$322$		0			0
$323$	0.499120	+	0.864501i	0.0277718	+	0.0481021i
$324$		0			0
$325$	3.54460	−	3.32542i	0.196619	−	0.184461i
$326$		0			0
$327$	9.68227	+	16.7702i	0.535431	+	0.927394i
$328$		0			0
$329$	4.82457	−	8.35641i	0.265987	−	0.460704i
$330$		0			0
$331$	8.76724	−	15.1853i	0.481891	−	0.834660i	−0.517893	−	0.855445i	$-0.673283\pi$
$331$	8.76724	−	15.1853i	0.481891	−	0.834660i	0.999784	+	0.0207857i	$0.00661678\pi$
$332$		0			0
$333$	7.12253			0.390312
$334$		0			0
$335$	3.23902	+	5.61015i	0.176967	+	0.306515i
$336$		0			0
$337$	−30.4412			−1.65824			−0.829119	−	0.559073i	$-0.811157\pi$
$337$	−30.4412			−1.65824			−0.829119	+	0.559073i	$0.811157\pi$
$338$		0			0
$339$	5.63422			0.306009
$340$		0			0
$341$	1.97649	+	3.42337i	0.107033	+	0.185386i
$342$		0			0
$343$	22.7579			1.22881
$344$		0			0
$345$	−0.830400	+	1.43830i	−0.0447072	+	0.0774352i
$346$		0			0
$347$	−0.493120	+	0.854108i	−0.0264721	+	0.0458509i	−0.878958	−	0.476899i	$-0.841761\pi$
$347$	−0.493120	+	0.854108i	−0.0264721	+	0.0458509i	0.852486	+	0.522750i	$0.175094\pi$
$348$		0			0
$349$	12.4221	+	21.5157i	0.664940	+	1.15171i	0.979302	+	0.202407i	$0.0648762\pi$
$349$	12.4221	+	21.5157i	0.664940	+	1.15171i	−0.314362	+	0.949303i	$0.601790\pi$
$350$		0			0
$351$	−2.62951	+	2.46691i	−0.140353	+	0.131674i
$352$		0			0
$353$	−1.22763	−	2.12631i	−0.0653399	−	0.113172i	0.831505	−	0.555518i	$-0.187480\pi$
$353$	−1.22763	−	2.12631i	−0.0653399	−	0.113172i	−0.896845	+	0.442346i	$0.854146\pi$
$354$		0			0
$355$	−0.538079	+	0.931979i	−0.0285582	+	0.0494643i
$356$		0			0
$357$	2.28248	−	3.95337i	0.120802	−	0.209235i
$358$		0			0
$359$	31.2582			1.64974			0.824871	−	0.565321i	$-0.191248\pi$
$359$	31.2582			1.64974			0.824871	+	0.565321i	$0.191248\pi$
$360$		0			0
$361$	9.04107	+	15.6596i	0.475846	+	0.824189i
$362$		0			0
$363$	1.00000			0.0524864
$364$		0			0
$365$	25.7550			1.34808
$366$		0			0
$367$	2.22391	+	3.85193i	0.116087	+	0.201069i	0.918214	−	0.396085i	$-0.129631\pi$
$367$	2.22391	+	3.85193i	0.116087	+	0.201069i	−0.802127	+	0.597154i	$0.796298\pi$
$368$		0			0
$369$	11.8844			0.618679
$370$		0			0
$371$	−11.9635	+	20.7213i	−0.621112	+	1.07580i
$372$		0			0
$373$	−5.20833	+	9.02108i	−0.269677	+	0.467094i	−0.968778	−	0.247928i	$-0.920250\pi$
$373$	−5.20833	+	9.02108i	−0.269677	+	0.467094i	0.699101	+	0.715022i	$0.253584\pi$
$374$		0			0
$375$	6.06558	+	10.5059i	0.313225	+	0.542522i
$376$		0			0
$377$	35.4900	+	10.7336i	1.82783	+	0.552807i
$378$		0			0
$379$	11.0421	+	19.1254i	0.567193	+	0.982407i	0.996842	+	0.0794109i	$0.0253039\pi$
$379$	11.0421	+	19.1254i	0.567193	+	0.982407i	−0.429649	+	0.902996i	$0.641363\pi$
$380$		0			0
$381$	7.41690	−	12.8464i	0.379979	−	0.658143i
$382$		0			0
$383$	−3.14154	+	5.44131i	−0.160525	+	0.278038i	−0.935057	−	0.354497i	$-0.884652\pi$
$383$	−3.14154	+	5.44131i	−0.160525	+	0.278038i	0.774532	+	0.632535i	$0.217985\pi$
$384$		0			0
$385$	8.37247			0.426700
$386$		0			0
$387$	−3.77994	−	6.54705i	−0.192145	−	0.332805i
$388$		0			0
$389$	−8.36952			−0.424351			−0.212176	−	0.977232i	$-0.568055\pi$
$389$	−8.36952			−0.424351			−0.212176	+	0.977232i	$0.568055\pi$
$390$		0			0
$391$	−0.905526			−0.0457944
$392$		0			0
$393$	5.20482	+	9.01500i	0.262548	+	0.454747i
$394$		0			0
$395$	−4.80119			−0.241574
$396$		0			0
$397$	−14.5517	+	25.2042i	−0.730327	+	1.26496i	0.226417	+	0.974031i	$0.427299\pi$
$397$	−14.5517	+	25.2042i	−0.730327	+	1.26496i	−0.956744	+	0.290933i	$0.906034\pi$
$398$		0			0
$399$	−2.09867	+	3.63501i	−0.105065	+	0.181978i
$400$		0			0
$401$	−19.4083	−	33.6162i	−0.969205	−	1.67871i	−0.697866	−	0.716228i	$-0.745867\pi$
$401$	−19.4083	−	33.6162i	−0.969205	−	1.67871i	−0.271338	−	0.962484i	$-0.587466\pi$
$402$		0			0
$403$	10.3944	−	9.75164i	0.517782	−	0.485764i
$404$		0			0
$405$	−0.955509	−	1.65499i	−0.0474796	−	0.0822372i
$406$		0			0
$407$	−3.56127	+	6.16829i	−0.176525	+	0.305751i
$408$		0			0
$409$	12.6506	−	21.9115i	0.625532	−	1.08345i	−0.362906	−	0.931826i	$-0.618215\pi$
$409$	12.6506	−	21.9115i	0.625532	−	1.08345i	0.988438	−	0.151627i	$-0.0484514\pi$
$410$		0			0
$411$	−10.0249			−0.494494
$412$		0			0
$413$	7.65518	+	13.2592i	0.376687	+	0.652440i
$414$		0			0
$415$	−20.3244			−0.997687
$416$		0			0
$417$	15.4076			0.754511
$418$		0			0
$419$	3.87284	+	6.70796i	0.189201	+	0.327705i	0.944984	−	0.327117i	$-0.106077\pi$
$419$	3.87284	+	6.70796i	0.189201	+	0.327705i	−0.755783	+	0.654822i	$0.772744\pi$
$420$		0			0
$421$	6.78226			0.330547			0.165274	−	0.986248i	$-0.447149\pi$
$421$	6.78226			0.330547			0.165274	+	0.986248i	$0.447149\pi$
$422$		0			0
$423$	1.10121	−	1.90735i	0.0535427	−	0.0927387i
$424$		0			0
$425$	−0.702280	+	1.21639i	−0.0340656	+	0.0590033i
$426$		0			0
$427$	−8.10405	−	14.0366i	−0.392183	−	0.679280i
$428$		0			0
$429$	−0.821653	−	3.51068i	−0.0396698	−	0.169497i
$430$		0			0
$431$	7.55282	+	13.0819i	0.363807	+	0.630132i	0.988584	−	0.150671i	$-0.0481436\pi$
$431$	7.55282	+	13.0819i	0.363807	+	0.630132i	−0.624777	+	0.780803i	$0.714810\pi$
$432$		0			0
$433$	10.5685	−	18.3052i	0.507891	−	0.879694i	−0.492067	−	0.870557i	$-0.663758\pi$
$433$	10.5685	−	18.3052i	0.507891	−	0.879694i	0.999958	−	0.00913629i	$-0.00290821\pi$
$434$		0			0
$435$	−9.82597	+	17.0191i	−0.471119	+	0.816002i
$436$		0			0
$437$	0.832605			0.0398289
$438$		0			0
$439$	−6.57931	−	11.3957i	−0.314014	−	0.543887i	0.665214	−	0.746653i	$-0.268340\pi$
$439$	−6.57931	−	11.3957i	−0.314014	−	0.543887i	−0.979227	+	0.202766i	$0.935007\pi$
$440$		0			0
$441$	12.1945			0.580691
$442$		0			0
$443$	−34.5853			−1.64320			−0.821600	−	0.570065i	$-0.806918\pi$
$443$	−34.5853			−1.64320			−0.821600	+	0.570065i	$0.806918\pi$
$444$		0			0
$445$	11.0607	+	19.1576i	0.524325	+	0.908158i
$446$		0			0
$447$	19.9272			0.942522
$448$		0			0
$449$	−13.0640	+	22.6274i	−0.616526	+	1.06785i	0.373588	+	0.927595i	$0.378127\pi$
$449$	−13.0640	+	22.6274i	−0.616526	+	1.06785i	−0.990115	+	0.140260i	$0.955206\pi$
$450$		0			0
$451$	−5.94222	+	10.2922i	−0.279808	+	0.484642i
$452$		0			0
$453$	−5.69530	−	9.86456i	−0.267589	−	0.463477i
$454$		0			0
$455$	−6.87927	−	29.3931i	−0.322505	−	1.37797i
$456$		0			0
$457$	−2.17028	−	3.75903i	−0.101521	−	0.175840i	0.810790	−	0.585337i	$-0.199038\pi$
$457$	−2.17028	−	3.75903i	−0.101521	−	0.175840i	−0.912312	+	0.409497i	$0.865704\pi$
$458$		0			0
$459$	0.520977	−	0.902358i	0.0243171	−	0.0421185i
$460$		0			0
$461$	14.6321	−	25.3436i	0.681486	−	1.18037i	−0.293041	−	0.956100i	$-0.594667\pi$
$461$	14.6321	−	25.3436i	0.681486	−	1.18037i	0.974527	−	0.224269i	$-0.0719993\pi$
$462$		0			0
$463$	14.8486			0.690071			0.345036	−	0.938590i	$-0.387867\pi$
$463$	14.8486			0.690071			0.345036	+	0.938590i	$0.387867\pi$
$464$		0			0
$465$	3.77710	+	6.54213i	0.175159	+	0.303384i
$466$		0			0
$467$	−3.35457			−0.155231			−0.0776155	−	0.996983i	$-0.524731\pi$
$467$	−3.35457			−0.155231			−0.0776155	+	0.996983i	$0.524731\pi$
$468$		0			0
$469$	−14.8514			−0.685774
$470$		0			0
$471$	−3.98872	−	6.90866i	−0.183790	−	0.318334i
$472$		0			0
$473$	7.55988			0.347604
$474$		0			0
$475$	0.645727	−	1.11843i	0.0296280	−	0.0513171i
$476$		0			0
$477$	−2.73066	+	4.72965i	−0.125029	+	0.216556i
$478$		0			0
$479$	−15.2019	−	26.3304i	−0.694592	−	1.20307i	−0.970318	−	0.241832i	$-0.922252\pi$
$479$	−15.2019	−	26.3304i	−0.694592	−	1.20307i	0.275726	−	0.961236i	$-0.411082\pi$
$480$		0			0
$481$	24.5810	+	7.43427i	1.12080	+	0.338974i
$482$		0			0
$483$	−1.90375	−	3.29740i	−0.0866238	−	0.150037i
$484$		0			0
$485$	10.6424	−	18.4331i	0.483245	−	0.837005i
$486$		0			0
$487$	8.92830	−	15.4643i	0.404580	−	0.700753i	−0.589693	−	0.807628i	$-0.700751\pi$
$487$	8.92830	−	15.4643i	0.404580	−	0.700753i	0.994272	+	0.106875i	$0.0340844\pi$
$488$		0			0
$489$	−18.0314			−0.815409
$490$		0			0
$491$	−19.7146	−	34.1467i	−0.889708	−	1.54102i	−0.840220	−	0.542245i	$-0.817574\pi$
$491$	−19.7146	−	34.1467i	−0.889708	−	1.54102i	−0.0494883	−	0.998775i	$-0.515759\pi$
$492$		0			0
$493$	−10.7149			−0.482575
$494$		0			0
$495$	1.91102			0.0858939
$496$		0			0
$497$	−1.23359	−	2.13663i	−0.0553339	−	0.0958410i
$498$		0			0
$499$	−10.0948			−0.451904			−0.225952	−	0.974138i	$-0.572549\pi$
$499$	−10.0948			−0.451904			−0.225952	+	0.974138i	$0.572549\pi$
$500$		0			0
$501$	6.72691	−	11.6513i	0.300536	−	0.520544i
$502$		0			0
$503$	−14.7440	+	25.5373i	−0.657402	+	1.13865i	0.323884	+	0.946097i	$0.395011\pi$
$503$	−14.7440	+	25.5373i	−0.657402	+	1.13865i	−0.981286	+	0.192556i	$0.938322\pi$
$504$		0			0
$505$	7.84280	+	13.5841i	0.349000	+	0.604486i
$506$		0			0
$507$	−11.6498	+	5.76913i	−0.517385	+	0.256216i
$508$		0			0
$509$	1.25180	+	2.16818i	0.0554851	+	0.0961030i	0.892434	−	0.451178i	$-0.148996\pi$
$509$	1.25180	+	2.16818i	0.0554851	+	0.0961030i	−0.836949	+	0.547281i	$0.815663\pi$
$510$		0			0
$511$	−29.5226	+	51.1347i	−1.30600	+	2.26207i
$512$		0			0
$513$	−0.479023	+	0.829693i	−0.0211494	+	0.0366318i
$514$		0			0
$515$	−29.4503			−1.29774
$516$		0			0
$517$	1.10121	+	1.90735i	0.0484312	+	0.0838853i
$518$		0			0
$519$	8.14671			0.357601
$520$		0			0
$521$	13.4621			0.589787			0.294893	−	0.955530i	$-0.404716\pi$
$521$	13.4621			0.589787			0.294893	+	0.955530i	$0.404716\pi$
$522$		0			0
$523$	−4.98246	−	8.62988i	−0.217868	−	0.377358i	0.736288	−	0.676668i	$-0.236577\pi$
$523$	−4.98246	−	8.62988i	−0.217868	−	0.377358i	−0.954156	+	0.299310i	$0.903244\pi$
$524$		0			0
$525$	−5.90582			−0.257751
$526$		0			0
$527$	−2.05941	+	3.56700i	−0.0897092	+	0.155381i
$528$		0			0
$529$	11.1224	−	19.2645i	0.483581	−	0.837587i
$530$		0			0
$531$	1.74730	+	3.02641i	0.0758262	+	0.131335i
$532$		0			0
$533$	41.0152	+	12.4046i	1.77656	+	0.537303i
$534$		0			0
$535$	9.21128	+	15.9544i	0.398238	+	0.689769i
$536$		0			0
$537$	−3.44676	+	5.96997i	−0.148739	+	0.257623i
$538$		0			0
$539$	−6.09725	+	10.5608i	−0.262627	+	0.454884i
$540$		0			0
$541$	−31.8778			−1.37053			−0.685266	−	0.728293i	$-0.740314\pi$
$541$	−31.8778			−1.37053			−0.685266	+	0.728293i	$0.740314\pi$
$542$		0			0
$543$	4.64842	+	8.05130i	0.199483	+	0.345514i
$544$		0			0
$545$	−37.0060			−1.58516
$546$		0			0
$547$	7.42045			0.317275			0.158638	−	0.987337i	$-0.449290\pi$
$547$	7.42045			0.317275			0.158638	+	0.987337i	$0.449290\pi$
$548$		0			0
$549$	−1.84975	−	3.20387i	−0.0789455	−	0.136738i
$550$		0			0
$551$	9.85206			0.419712
$552$		0			0
$553$	5.50354	−	9.53242i	0.234034	−	0.405360i
$554$		0			0
$555$	−6.80565	+	11.7877i	−0.288884	+	0.500361i
$556$		0			0
$557$	−19.0173	−	32.9390i	−0.805790	−	1.39567i	−0.915757	−	0.401733i	$-0.868408\pi$
$557$	−19.0173	−	32.9390i	−0.805790	−	1.39567i	0.109967	−	0.993935i	$-0.464925\pi$
$558$		0			0
$559$	−6.21160	−	26.5403i	−0.262723	−	1.12254i
$560$		0			0
$561$	0.520977	+	0.902358i	0.0219957	+	0.0380976i
$562$		0			0
$563$	−0.735616	+	1.27412i	−0.0310025	+	0.0536979i	−0.881110	−	0.472911i	$-0.843203\pi$
$563$	−0.735616	+	1.27412i	−0.0310025	+	0.0536979i	0.850108	+	0.526609i	$0.176537\pi$
$564$		0			0
$565$	−5.38355	+	9.32458i	−0.226487	+	0.392288i
$566$		0			0
$567$	4.38115			0.183991
$568$		0			0
$569$	17.5829	+	30.4544i	0.737112	+	1.27672i	0.953790	+	0.300473i	$0.0971444\pi$
$569$	17.5829	+	30.4544i	0.737112	+	1.27672i	−0.216678	+	0.976243i	$0.569522\pi$
$570$		0			0
$571$	−46.2860			−1.93701			−0.968504	−	0.248998i	$-0.919899\pi$
$571$	−46.2860			−1.93701			−0.968504	+	0.248998i	$0.919899\pi$
$572$		0			0
$573$	−6.92083			−0.289122
$574$		0			0
$575$	0.585753	+	1.01455i	0.0244276	+	0.0423098i
$576$		0			0
$577$	2.80024			0.116576			0.0582878	−	0.998300i	$-0.481436\pi$
$577$	2.80024			0.116576			0.0582878	+	0.998300i	$0.481436\pi$
$578$		0			0
$579$	−9.71648	+	16.8294i	−0.403803	+	0.699408i
$580$		0			0
$581$	23.2976	−	40.3527i	0.966549	−	1.67411i
$582$		0			0
$583$	−2.73066	−	4.72965i	−0.113093	−	0.195882i
$584$		0			0
$585$	−1.57020	−	6.70898i	−0.0649196	−	0.277382i
$586$		0			0
$587$	−10.8649	−	18.8186i	−0.448443	−	0.776727i	0.549842	−	0.835269i	$-0.314688\pi$
$587$	−10.8649	−	18.8186i	−0.448443	−	0.776727i	−0.998285	+	0.0585423i	$0.981355\pi$
$588$		0			0
$589$	1.89357	−	3.27975i	0.0780230	−	0.135140i
$590$		0			0
$591$	6.24050	−	10.8089i	0.256700	−	0.444617i
$592$		0			0
$593$	1.50045			0.0616162			0.0308081	−	0.999525i	$-0.490192\pi$
$593$	1.50045			0.0616162			0.0308081	+	0.999525i	$0.490192\pi$
$594$		0			0
$595$	4.36186	+	7.55496i	0.178819	+	0.309723i
$596$		0			0
$597$	21.2139			0.868227
$598$		0			0
$599$	31.9260			1.30446			0.652231	−	0.758020i	$-0.273833\pi$
$599$	31.9260			1.30446			0.652231	+	0.758020i	$0.273833\pi$
$600$		0			0
$601$	7.73841	+	13.4033i	0.315656	+	0.546733i	0.979577	−	0.201070i	$-0.0644420\pi$
$601$	7.73841	+	13.4033i	0.315656	+	0.546733i	−0.663921	+	0.747803i	$0.731109\pi$
$602$		0			0
$603$	−3.38984			−0.138045
$604$		0			0
$605$	−0.955509	+	1.65499i	−0.0388470	+	0.0672849i
$606$		0			0
$607$	15.9132	−	27.5624i	0.645896	−	1.11872i	−0.338198	−	0.941075i	$-0.609817\pi$
$607$	15.9132	−	27.5624i	0.645896	−	1.11872i	0.984094	−	0.177650i	$-0.0568494\pi$
$608$		0			0
$609$	−22.5268	−	39.0175i	−0.912831	−	1.58107i
$610$		0			0
$611$	5.79130	−	5.43319i	0.234291	−	0.219803i
$612$		0			0
$613$	3.21253	+	5.56426i	0.129753	+	0.224738i	0.923581	−	0.383404i	$-0.125248\pi$
$613$	3.21253	+	5.56426i	0.129753	+	0.224738i	−0.793828	+	0.608142i	$0.791915\pi$
$614$		0			0
$615$	−11.3557	+	19.6686i	−0.457906	+	0.793116i
$616$		0			0
$617$	−6.28718	+	10.8897i	−0.253112	+	0.438403i	−0.964381	−	0.264517i	$-0.914788\pi$
$617$	−6.28718	+	10.8897i	−0.253112	+	0.438403i	0.711269	+	0.702920i	$0.248121\pi$
$618$		0			0
$619$	−9.06312			−0.364278			−0.182139	−	0.983273i	$-0.558302\pi$
$619$	−9.06312			−0.364278			−0.182139	+	0.983273i	$0.558302\pi$
$620$		0			0
$621$	−0.434533	−	0.752633i	−0.0174372	−	0.0302021i
$622$		0			0
$623$	−50.7147			−2.03184
$624$		0			0
$625$	−16.4428			−0.657714
$626$		0			0
$627$	−0.479023	−	0.829693i	−0.0191303	−	0.0331347i
$628$		0			0
$629$	−7.42135			−0.295909
$630$		0			0
$631$	−9.48581	+	16.4299i	−0.377624	+	0.654064i	−0.990716	−	0.135947i	$-0.956592\pi$
$631$	−9.48581	+	16.4299i	−0.377624	+	0.654064i	0.613092	+	0.790012i	$0.289926\pi$
$632$		0			0
$633$	5.33374	−	9.23831i	0.211997	−	0.367190i
$634$		0			0
$635$	14.1738	+	24.5498i	0.562471	+	0.974229i
$636$		0			0
$637$	42.0853	+	12.7282i	1.66748	+	0.504311i
$638$		0			0
$639$	−0.281566	−	0.487687i	−0.0111386	−	0.0192926i
$640$		0			0
$641$	−10.0503	+	17.4075i	−0.396961	+	0.687557i	−0.993349	−	0.115139i	$-0.963269\pi$
$641$	−10.0503	+	17.4075i	−0.396961	+	0.687557i	0.596388	+	0.802696i	$0.296602\pi$
$642$		0			0
$643$	11.4932	−	19.9068i	0.453247	−	0.785048i	−0.545338	−	0.838216i	$-0.683599\pi$
$643$	11.4932	−	19.9068i	0.453247	−	0.785048i	0.998586	+	0.0531685i	$0.0169321\pi$
$644$		0			0
$645$	14.4471			0.568853
$646$		0			0
$647$	9.69501	+	16.7922i	0.381150	+	0.660171i	0.991227	−	0.132171i	$-0.0421948\pi$
$647$	9.69501	+	16.7922i	0.381150	+	0.660171i	−0.610077	+	0.792342i	$0.708861\pi$
$648$		0			0
$649$	−3.49459			−0.137175
$650$		0			0
$651$	−17.3186			−0.678769
$652$		0			0
$653$	−7.23117	−	12.5248i	−0.282977	−	0.490131i	0.689139	−	0.724629i	$-0.257989\pi$
$653$	−7.23117	−	12.5248i	−0.282977	−	0.490131i	−0.972117	+	0.234498i	$0.924656\pi$
$654$		0			0
$655$	−19.8930			−0.777284
$656$		0			0
$657$	−6.73855	+	11.6715i	−0.262896	+	0.455349i
$658$		0			0
$659$	15.2841	−	26.4729i	0.595385	−	1.03124i	−0.398107	−	0.917339i	$-0.630333\pi$
$659$	15.2841	−	26.4729i	0.595385	−	1.03124i	0.993492	−	0.113898i	$-0.0363339\pi$
$660$		0			0
$661$	2.13850	+	3.70399i	0.0831781	+	0.144069i	0.904613	−	0.426233i	$-0.140160\pi$
$661$	2.13850	+	3.70399i	0.0831781	+	0.144069i	−0.821435	+	0.570302i	$0.806826\pi$
$662$		0			0
$663$	2.73983	−	2.57041i	0.106406	−	0.0998264i
$664$		0			0
$665$	−4.01061	−	6.94657i	−0.155525	−	0.269377i
$666$		0			0
$667$	−4.46851	+	7.73969i	−0.173021	+	0.299682i
$668$		0			0
$669$	−11.6992	+	20.2637i	−0.452319	+	0.783439i
$670$		0			0
$671$	3.69951			0.142818
$672$		0			0
$673$	21.1676	+	36.6634i	0.815952	+	1.41327i	0.908642	+	0.417575i	$0.137120\pi$
$673$	21.1676	+	36.6634i	0.815952	+	1.41327i	−0.0926906	+	0.995695i	$0.529547\pi$
$674$		0			0
$675$	−1.34801			−0.0518848
$676$		0			0
$677$	−1.04873			−0.0403058			−0.0201529	−	0.999797i	$-0.506415\pi$
$677$	−1.04873			−0.0403058			−0.0201529	+	0.999797i	$0.506415\pi$
$678$		0			0
$679$	24.3984	+	42.2593i	0.936326	+	1.62176i
$680$		0			0
$681$	20.7160			0.793841
$682$		0			0
$683$	−7.93198	+	13.7386i	−0.303509	+	0.525692i	−0.976928	−	0.213568i	$-0.931491\pi$
$683$	−7.93198	+	13.7386i	−0.303509	+	0.525692i	0.673420	+	0.739261i	$0.264825\pi$
$684$		0			0
$685$	9.57893	−	16.5912i	0.365992	−	0.633917i
$686$		0			0
$687$	4.79477	+	8.30478i	0.182932	+	0.316847i
$688$		0			0
$689$	−14.3606	+	13.4726i	−0.547096	+	0.513266i
$690$		0			0
$691$	15.0415	+	26.0527i	0.572206	+	0.991090i	0.996339	+	0.0854904i	$0.0272457\pi$
$691$	15.0415	+	26.0527i	0.572206	+	0.991090i	−0.424133	+	0.905600i	$0.639421\pi$
$692$		0			0
$693$	−2.19058	+	3.79419i	−0.0832131	+	0.144129i
$694$		0			0
$695$	−14.7221	+	25.4994i	−0.558440	+	0.967246i
$696$		0			0
$697$	−12.3830			−0.469041
$698$		0			0
$699$	−6.70086	−	11.6062i	−0.253450	−	0.438988i
$700$		0			0
$701$	25.7592			0.972912			0.486456	−	0.873705i	$-0.338289\pi$
$701$	25.7592			0.972912			0.486456	+	0.873705i	$0.338289\pi$
$702$		0			0
$703$	6.82372			0.257361
$704$		0			0
$705$	2.10444	+	3.64499i	0.0792576	+	0.137278i
$706$		0			0
$707$	−35.9604			−1.35243
$708$		0			0
$709$	−9.08437	+	15.7346i	−0.341171	+	0.590925i	−0.984650	−	0.174538i	$-0.944157\pi$
$709$	−9.08437	+	15.7346i	−0.341171	+	0.590925i	0.643480	+	0.765463i	$0.277490\pi$
$710$		0			0
$711$	1.25619	−	2.17578i	0.0471107	−	0.0815980i
$712$		0			0
$713$	1.71770	+	2.97514i	0.0643282	+	0.111420i
$714$		0			0
$715$	6.59524	+	1.99466i	0.246648	+	0.0745961i
$716$		0			0
$717$	10.8613	+	18.8123i	0.405621	+	0.702557i
$718$		0			0
$719$	−7.21238	+	12.4922i	−0.268977	+	0.465881i	−0.968598	−	0.248633i	$-0.920019\pi$
$719$	−7.21238	+	12.4922i	−0.268977	+	0.465881i	0.699621	+	0.714514i	$0.253352\pi$
$720$		0			0
$721$	33.7586	−	58.4715i	1.25723	−	2.17759i
$722$		0			0
$723$	3.21070			0.119407
$724$		0			0
$725$	6.93110	+	12.0050i	0.257415	+	0.445855i
$726$		0			0
$727$	44.7045			1.65800			0.828998	−	0.559251i	$-0.188911\pi$
$727$	44.7045			1.65800			0.828998	+	0.559251i	$0.188911\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	3.93852	+	6.82172i	0.145672	+	0.252311i
$732$		0			0
$733$	2.05531			0.0759144			0.0379572	−	0.999279i	$-0.487915\pi$
$733$	2.05531			0.0759144			0.0379572	+	0.999279i	$0.487915\pi$
$734$		0			0
$735$	−11.6520	+	20.1818i	−0.429789	+	0.744417i
$736$		0			0
$737$	1.69492	−	2.93569i	0.0624332	−	0.108137i
$738$		0			0
$739$	−3.28948	−	5.69755i	−0.121006	−	0.209588i	0.799159	−	0.601120i	$-0.205279\pi$
$739$	−3.28948	−	5.69755i	−0.121006	−	0.209588i	−0.920165	+	0.391532i	$0.871945\pi$
$740$		0			0
$741$	−2.51920	+	2.36342i	−0.0925450	+	0.0868223i
$742$		0			0
$743$	−8.39196	−	14.5353i	−0.307871	−	0.533249i	0.670025	−	0.742338i	$-0.266283\pi$
$743$	−8.39196	−	14.5353i	−0.307871	−	0.533249i	−0.977896	+	0.209090i	$0.932950\pi$
$744$		0			0
$745$	−19.0406	+	32.9793i	−0.697593	+	1.20827i
$746$		0			0
$747$	5.31769	−	9.21052i	0.194564	−	0.336995i
$748$		0			0
$749$	−42.2351			−1.54324
$750$		0			0
$751$	−14.1423	−	24.4952i	−0.516060	−	0.893842i	−0.999826	−	0.0186451i	$-0.994065\pi$
$751$	−14.1423	−	24.4952i	−0.516060	−	0.893842i	0.483766	−	0.875197i	$-0.339269\pi$
$752$		0			0
$753$	−9.58994			−0.349477
$754$		0			0
$755$	21.7677			0.792207
$756$		0			0
$757$	−9.20744	−	15.9478i	−0.334650	−	0.579631i	0.648767	−	0.760987i	$-0.275285\pi$
$757$	−9.20744	−	15.9478i	−0.334650	−	0.579631i	−0.983418	+	0.181356i	$0.941951\pi$
$758$		0			0
$759$	0.869065			0.0315451
$760$		0			0
$761$	−24.7816	+	42.9230i	−0.898333	+	1.55596i	−0.0687082	+	0.997637i	$0.521888\pi$
$761$	−24.7816	+	42.9230i	−0.898333	+	1.55596i	−0.829625	+	0.558321i	$0.811446\pi$
$762$		0			0
$763$	42.4195	−	73.4728i	1.53569	−	2.65989i
$764$		0			0
$765$	0.995596	+	1.72442i	0.0359959	+	0.0623467i
$766$		0			0
$767$	2.87135	+	12.2684i	0.103678	+	0.442987i
$768$		0			0
$769$	−19.9055	−	34.4773i	−0.717810	−	1.24328i	−0.961866	−	0.273522i	$-0.911811\pi$
$769$	−19.9055	−	34.4773i	−0.717810	−	1.24328i	0.244056	−	0.969761i	$-0.421522\pi$
$770$		0			0
$771$	5.41671	−	9.38203i	0.195078	−	0.337885i
$772$		0			0
$773$	−14.5650	+	25.2273i	−0.523867	+	0.907365i	0.475747	+	0.879582i	$0.342178\pi$
$773$	−14.5650	+	25.2273i	−0.523867	+	0.907365i	−0.999614	+	0.0277824i	$0.991155\pi$
$774$		0			0
$775$	5.32863			0.191410
$776$		0			0
$777$	−15.6025	−	27.0242i	−0.559735	−	0.969489i
$778$		0			0
$779$	11.3858			0.407940
$780$		0			0
$781$	0.563133			0.0201505
$782$		0			0
$783$	−5.14174	−	8.90576i	−0.183751	−	0.318266i
$784$		0			0
$785$	15.2450			0.544118
$786$		0			0
$787$	4.74204	−	8.21346i	0.169036	−	0.292778i	−0.769046	−	0.639194i	$-0.779268\pi$
$787$	4.74204	−	8.21346i	0.169036	−	0.292778i	0.938081	+	0.346416i	$0.112601\pi$
$788$		0			0
$789$	−2.81291	+	4.87210i	−0.100142	+	0.173451i
$790$		0			0
$791$	−12.3422	−	21.3773i	−0.438837	−	0.760089i
$792$		0			0
$793$	−3.03971	−	12.9878i	−0.107943	−	0.461210i
$794$		0			0
$795$	−5.21835	−	9.03845i	−0.185076	−	0.320561i
$796$		0			0
$797$	13.7124	−	23.7506i	0.485718	−	0.841288i	−0.514147	−	0.857702i	$-0.671892\pi$
$797$	13.7124	−	23.7506i	0.485718	−	0.841288i	0.999865	+	0.0164137i	$0.00522488\pi$
$798$		0			0
$799$	−1.14741	+	1.98737i	−0.0405925	+	0.0703082i
$800$		0			0
$801$	−11.5757			−0.409006
$802$		0			0
$803$	−6.73855	−	11.6715i	−0.237798	−	0.411879i
$804$		0			0
$805$	7.27622			0.256453
$806$		0			0
$807$	0.550592			0.0193818
$808$		0			0
$809$	−19.3911	−	33.5864i	−0.681754	−	1.18083i	−0.974445	−	0.224626i	$-0.927884\pi$
$809$	−19.3911	−	33.5864i	−0.681754	−	1.18083i	0.292691	−	0.956207i	$-0.405449\pi$
$810$		0			0
$811$	27.8455			0.977786			0.488893	−	0.872344i	$-0.337401\pi$
$811$	27.8455			0.977786			0.488893	+	0.872344i	$0.337401\pi$
$812$		0			0
$813$	−4.84107	+	8.38497i	−0.169784	+	0.294074i
$814$		0			0
$815$	17.2292	−	29.8418i	0.603512	−	1.04531i
$816$		0			0
$817$	−3.62136	−	6.27238i	−0.126695	−	0.219443i
$818$		0			0
$819$	15.1201	+	4.57291i	0.528339	+	0.159790i
$820$		0			0
$821$	−22.9822	−	39.8064i	−0.802085	−	1.38925i	−0.918242	−	0.396021i	$-0.870391\pi$
$821$	−22.9822	−	39.8064i	−0.802085	−	1.38925i	0.116157	−	0.993231i	$-0.462942\pi$
$822$		0			0
$823$	−4.66798	+	8.08518i	−0.162716	+	0.281832i	−0.935842	−	0.352421i	$-0.885359\pi$
$823$	−4.66798	+	8.08518i	−0.162716	+	0.281832i	0.773126	+	0.634252i	$0.218692\pi$
$824$		0			0
$825$	0.674003	−	1.16741i	0.0234658	−	0.0406439i
$826$		0			0
$827$	−9.31623			−0.323957			−0.161978	−	0.986794i	$-0.551788\pi$
$827$	−9.31623			−0.323957			−0.161978	+	0.986794i	$0.551788\pi$
$828$		0			0
$829$	4.18025	+	7.24041i	0.145186	+	0.251470i	0.929442	−	0.368967i	$-0.120289\pi$
$829$	4.18025	+	7.24041i	0.145186	+	0.251470i	−0.784256	+	0.620437i	$0.786955\pi$
$830$		0			0
$831$	2.76508			0.0959195
$832$		0			0
$833$	−12.7061			−0.440241
$834$		0			0
$835$	12.8552	+	22.2659i	0.444874	+	0.770545i
$836$		0			0
$837$	−3.95297			−0.136635
$838$		0			0
$839$	−21.3635	+	37.0026i	−0.737549	+	1.27747i	0.216048	+	0.976383i	$0.430683\pi$
$839$	−21.3635	+	37.0026i	−0.737549	+	1.27747i	−0.953596	+	0.301089i	$0.902650\pi$
$840$		0			0
$841$	−38.3750	+	66.4675i	−1.32328	+	2.29198i
$842$		0			0
$843$	−13.1504	−	22.7771i	−0.452922	−	0.784485i
$844$		0			0
$845$	1.58361	−	24.7927i	0.0544780	−	0.852896i
$846$		0			0
$847$	−2.19058	−	3.79419i	−0.0752691	−	0.130370i
$848$		0			0
$849$	−1.56092	+	2.70360i	−0.0535707	+	0.0927872i
$850$		0			0
$851$	−3.09497	+	5.36065i	−0.106094	+	0.183761i
$852$		0			0
$853$	−34.8591			−1.19355			−0.596776	−	0.802408i	$-0.703552\pi$
$853$	−34.8591			−1.19355			−0.596776	+	0.802408i	$0.703552\pi$
$854$		0			0
$855$	−0.915422	−	1.58556i	−0.0313068	−	0.0542249i
$856$		0			0
$857$	30.4183			1.03907			0.519535	−	0.854449i	$-0.326105\pi$
$857$	30.4183			1.03907			0.519535	+	0.854449i	$0.326105\pi$
$858$		0			0
$859$	22.3280			0.761823			0.380912	−	0.924611i	$-0.375610\pi$
$859$	22.3280			0.761823			0.380912	+	0.924611i	$0.375610\pi$
$860$		0			0
$861$	−26.0338	−	45.0918i	−0.887228	−	1.53672i
$862$		0			0
$863$	−5.66749			−0.192924			−0.0964618	−	0.995337i	$-0.530753\pi$
$863$	−5.66749			−0.192924			−0.0964618	+	0.995337i	$0.530753\pi$
$864$		0			0
$865$	−7.78426	+	13.4827i	−0.264673	+	0.458427i
$866$		0			0
$867$	7.95717	−	13.7822i	0.270240	−	0.468069i
$868$		0			0
$869$	1.25619	+	2.17578i	0.0426132	+	0.0738082i
$870$		0			0
$871$	−11.6989	−	3.53821i	−0.396402	−	0.119888i
$872$		0			0
$873$	5.56895	+	9.64571i	0.188480	+	0.326458i
$874$		0			0
$875$	26.5742	−	46.0279i	0.898373	−	1.55603i
$876$		0			0
$877$	−20.5871	+	35.6579i	−0.695178	+	1.20408i	0.274943	+	0.961460i	$0.411341\pi$
$877$	−20.5871	+	35.6579i	−0.695178	+	1.20408i	−0.970121	+	0.242622i	$0.921992\pi$
$878$		0			0
$879$	−18.2244			−0.614695
$880$		0			0
$881$	21.9236	+	37.9728i	0.738625	+	1.27934i	0.953115	+	0.302610i	$0.0978579\pi$
$881$	21.9236	+	37.9728i	0.738625	+	1.27934i	−0.214489	+	0.976726i	$0.568809\pi$
$882$		0			0
$883$	−29.4256			−0.990250			−0.495125	−	0.868822i	$-0.664878\pi$
$883$	−29.4256			−0.990250			−0.495125	+	0.868822i	$0.664878\pi$
$884$		0			0
$885$	−6.67824			−0.224486
$886$		0			0
$887$	19.2312	+	33.3093i	0.645719	+	1.11842i	0.984135	+	0.177422i	$0.0567756\pi$
$887$	19.2312	+	33.3093i	0.645719	+	1.11842i	−0.338416	+	0.940997i	$0.609891\pi$
$888$		0			0
$889$	−64.9891			−2.17967
$890$		0			0
$891$	−0.500000	+	0.866025i	−0.0167506	+	0.0290129i
$892$		0			0
$893$	1.05501	−	1.82733i	0.0353046	−	0.0611494i
$894$		0			0
$895$	−6.58683	−	11.4087i	−0.220173	−	0.381352i
$896$		0			0
$897$	−0.714070	−	3.05101i	−0.0238421	−	0.101870i
$898$		0			0
$899$	20.3252	+	35.2042i	0.677882	+	1.17413i
$900$		0			0
$901$	2.84522	−	4.92807i	0.0947882	−	0.164178i
$902$		0			0
$903$	−16.5605	+	28.6836i	−0.551099	+	0.954532i
$904$		0			0
$905$	−17.7664			−0.590576
$906$		0			0
$907$	−27.2581	−	47.2124i	−0.905090	−	1.56766i	−0.820796	−	0.571221i	$-0.806470\pi$
$907$	−27.2581	−	47.2124i	−0.905090	−	1.56766i	−0.0842938	−	0.996441i	$-0.526863\pi$
$908$		0			0
$909$	−8.20798			−0.272242
$910$		0			0
$911$	−27.1135			−0.898309			−0.449154	−	0.893454i	$-0.648275\pi$
$911$	−27.1135			−0.898309			−0.449154	+	0.893454i	$0.648275\pi$
$912$		0			0
$913$	5.31769	+	9.21052i	0.175990	+	0.304824i
$914$		0			0
$915$	7.06983			0.233721
$916$		0			0
$917$	22.8031	−	39.4961i	0.753024	−	1.30428i
$918$		0			0
$919$	−20.5189	+	35.5397i	−0.676855	+	1.17235i	0.299067	+	0.954232i	$0.403324\pi$
$919$	−20.5189	+	35.5397i	−0.676855	+	1.17235i	−0.975923	+	0.218116i	$0.930009\pi$
$920$		0			0
$921$	−9.79992	−	16.9740i	−0.322918	−	0.559311i
$922$		0			0
$923$	−0.462700	−	1.97698i	−0.0152299	−	0.0650731i
$924$		0			0
$925$	4.80061	+	8.31490i	0.157843	+	0.273392i
$926$		0			0
$927$	7.70540	−	13.3462i	0.253079	−	0.438345i
$928$		0			0
$929$	7.66091	−	13.2691i	0.251346	−	0.435344i	−0.712550	−	0.701621i	$-0.752460\pi$
$929$	7.66091	−	13.2691i	0.251346	−	0.435344i	0.963897	+	0.266276i	$0.0857934\pi$
$930$		0			0
$931$	11.6829			0.382892
$932$		0			0
$933$	6.05717	+	10.4913i	0.198303	+	0.343470i
$934$		0			0
$935$	−1.99119			−0.0651190
$936$		0			0
$937$	31.6779			1.03487			0.517436	−	0.855722i	$-0.326887\pi$
$937$	31.6779			1.03487			0.517436	+	0.855722i	$0.326887\pi$
$938$		0			0
$939$	2.33510	+	4.04451i	0.0762031	+	0.131988i
$940$		0			0
$941$	4.09477			0.133486			0.0667429	−	0.997770i	$-0.478739\pi$
$941$	4.09477			0.133486			0.0667429	+	0.997770i	$0.478739\pi$
$942$		0			0
$943$	−5.16417	+	8.94461i	−0.168169	+	0.291277i
$944$		0			0
$945$	−4.18623	+	7.25077i	−0.136178	+	0.235868i
$946$		0			0
$947$	−8.50740	−	14.7352i	−0.276453	−	0.478831i	0.694047	−	0.719929i	$-0.255826\pi$
$947$	−8.50740	−	14.7352i	−0.276453	−	0.478831i	−0.970501	+	0.241098i	$0.922492\pi$
$948$		0			0
$949$	−35.4382	+	33.2468i	−1.15037	+	1.07924i
$950$		0			0
$951$	−4.04550	−	7.00701i	−0.131184	−	0.227218i
$952$		0			0
$953$	11.9701	−	20.7329i	0.387751	−	0.671604i	−0.604396	−	0.796684i	$-0.706585\pi$
$953$	11.9701	−	20.7329i	0.387751	−	0.671604i	0.992147	+	0.125080i	$0.0399187\pi$
$954$		0			0
$955$	6.61292	−	11.4539i	0.213989	−	0.370640i
$956$		0			0
$957$	10.2835			0.332418
$958$		0			0
$959$	21.9604	+	38.0365i	0.709139	+	1.22826i
$960$		0			0
$961$	−15.3740			−0.495936
$962$		0			0
$963$	−9.64018			−0.310650
$964$		0			0
$965$	−18.5684	−	32.1614i	−0.597737	−	1.03531i
$966$		0			0
$967$	−19.0038			−0.611121			−0.305561	−	0.952173i	$-0.598844\pi$
$967$	−19.0038			−0.611121			−0.305561	+	0.952173i	$0.598844\pi$
$968$		0			0
$969$	0.499120	−	0.864501i	0.0160340	−	0.0277718i
$970$		0			0
$971$	25.0291	−	43.3517i	0.803222	−	1.39122i	−0.114263	−	0.993451i	$-0.536451\pi$
$971$	25.0291	−	43.3517i	0.803222	−	1.39122i	0.917485	−	0.397771i	$-0.130216\pi$
$972$		0			0
$973$	−33.7514	−	58.4592i	−1.08202	−	1.87412i
$974$		0			0
$975$	−4.65220	−	1.40701i	−0.148989	−	0.0450603i
$976$		0			0
$977$	−17.7405	−	30.7274i	−0.567567	−	0.983056i	−0.996806	−	0.0798644i	$-0.974551\pi$
$977$	−17.7405	−	30.7274i	−0.567567	−	0.983056i	0.429238	−	0.903191i	$-0.358782\pi$
$978$		0			0
$979$	5.78783	−	10.0248i	0.184980	−	0.320394i
$980$		0			0
$981$	9.68227	−	16.7702i	0.309131	−	0.535431i
$982$		0			0
$983$	−55.8896			−1.78260			−0.891301	−	0.453411i	$-0.850207\pi$
$983$	−55.8896			−1.78260			−0.891301	+	0.453411i	$0.850207\pi$
$984$		0			0
$985$	11.9257	+	20.6559i	0.379985	+	0.658153i
$986$		0			0
$987$	−9.64915			−0.307136
$988$		0			0
$989$	6.57003			0.208915
$990$		0			0
$991$	31.4079	+	54.4002i	0.997706	+	1.72808i	0.557477	+	0.830192i	$0.311769\pi$
$991$	31.4079	+	54.4002i	0.997706	+	1.72808i	0.440229	+	0.897886i	$0.354897\pi$
$992$		0			0
$993$	−17.5345			−0.556440
$994$		0			0
$995$	−20.2701	+	35.1088i	−0.642605	+	1.11302i
$996$		0			0
$997$	12.8150	−	22.1962i	0.405854	−	0.702960i	−0.588566	−	0.808449i	$-0.700307\pi$
$997$	12.8150	−	22.1962i	0.405854	−	0.702960i	0.994420	+	0.105489i	$0.0336407\pi$
$998$		0			0
$999$	−3.56127	−	6.16829i	−0.112673	−	0.195156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1716.2.q.b.133.5	✓	12
13.9	even	3	inner	1716.2.q.b.529.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1716.2.q.b.133.5	✓	12	1.1	even	1	trivial
1716.2.q.b.529.5	yes	12	13.9	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:	\( N \)	\(=\)	\( 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1716.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +1.91102 q^{5} +(-2.19058 + 3.79419i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{3} +1.91102 q^{5} +(-2.19058 + 3.79419i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(-2.62951 + 2.46691i) q^{13} +(-0.955509 - 1.65499i) q^{15} +(0.520977 - 0.902358i) q^{17} +(-0.479023 + 0.829693i) q^{19} +4.38115 q^{21} +(-0.434533 - 0.752633i) q^{23} -1.34801 q^{25} +1.00000 q^{27} +(-5.14174 - 8.90576i) q^{29} -3.95297 q^{31} +(-0.500000 + 0.866025i) q^{33} +(-4.18623 + 7.25077i) q^{35} +(-3.56127 - 6.16829i) q^{37} +(3.45117 + 1.04377i) q^{39} +(-5.94222 - 10.2922i) q^{41} +(-3.77994 + 6.54705i) q^{43} +(-0.955509 + 1.65499i) q^{45} -2.20242 q^{47} +(-6.09725 - 10.5608i) q^{49} -1.04195 q^{51} +5.46133 q^{53} +(-0.955509 - 1.65499i) q^{55} +0.958046 q^{57} +(1.74730 - 3.02641i) q^{59} +(-1.84975 + 3.20387i) q^{61} +(-2.19058 - 3.79419i) q^{63} +(-5.02505 + 4.71432i) q^{65} +(1.69492 + 2.93569i) q^{67} +(-0.434533 + 0.752633i) q^{69} +(-0.281566 + 0.487687i) q^{71} +13.4771 q^{73} +(0.674003 + 1.16741i) q^{75} +4.38115 q^{77} -2.51237 q^{79} +(-0.500000 - 0.866025i) q^{81} -10.6354 q^{83} +(0.995596 - 1.72442i) q^{85} +(-5.14174 + 8.90576i) q^{87} +(5.78783 + 10.0248i) q^{89} +(-3.59979 - 15.3808i) q^{91} +(1.97649 + 3.42337i) q^{93} +(-0.915422 + 1.58556i) q^{95} +(5.56895 - 9.64571i) q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 2 * q^7 - 6 * q^9	\( 12 q - 6 q^{3} + 2 q^{7} - 6 q^{9} - 6 q^{11} - 4 q^{13} + 5 q^{17} - 7 q^{19} - 4 q^{21} + 5 q^{23} + 16 q^{25} + 12 q^{27} - 22 q^{31} - 6 q^{33} - 33 q^{37} + 8 q^{39} - 14 q^{41} - 4 q^{47} - 10 q^{51} + 10 q^{53} + 14 q^{57} - 30 q^{59} - 9 q^{61} + 2 q^{63} + 4 q^{65} + 14 q^{67} + 5 q^{69} + 3 q^{71} - 6 q^{73} - 8 q^{75} - 4 q^{77} + 2 q^{79} - 6 q^{81} + 8 q^{83} + q^{85} - 32 q^{89} + 16 q^{91} + 11 q^{93} + q^{95} + 10 q^{97} + 12 q^{99}+O(q^{100}) \) 12 * q - 6 * q^3 + 2 * q^7 - 6 * q^9 - 6 * q^11 - 4 * q^13 + 5 * q^17 - 7 * q^19 - 4 * q^21 + 5 * q^23 + 16 * q^25 + 12 * q^27 - 22 * q^31 - 6 * q^33 - 33 * q^37 + 8 * q^39 - 14 * q^41 - 4 * q^47 - 10 * q^51 + 10 * q^53 + 14 * q^57 - 30 * q^59 - 9 * q^61 + 2 * q^63 + 4 * q^65 + 14 * q^67 + 5 * q^69 + 3 * q^71 - 6 * q^73 - 8 * q^75 - 4 * q^77 + 2 * q^79 - 6 * q^81 + 8 * q^83 + q^85 - 32 * q^89 + 16 * q^91 + 11 * q^93 + q^95 + 10 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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