LMFDB - Embedded newform 1040.2.da.b.881.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(641,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

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

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

chi := DirichletCharacter("1040.641");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.da (of order $6$, degree $2$, not 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:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.2
Root			$-1.27597 + 0.609843i$ of defining polynomial
Character	$\chi$	$=$	1040.881
Dual form			1040.2.da.b.641.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.800098 - 1.38581i) q^{3} -1.00000i q^{5} +(0.287734 + 0.166123i) q^{7} +(0.219687 - 0.380509i) q^{9} +O(q^{10})$	\(q+(-0.800098 - 1.38581i) q^{3} -1.00000i q^{5} +(0.287734 + 0.166123i) q^{7} +(0.219687 - 0.380509i) q^{9} +(-4.65213 + 2.68591i) q^{11} +(-3.55193 - 0.619491i) q^{13} +(-1.38581 + 0.800098i) q^{15} +(-2.53215 + 4.38581i) q^{17} +(1.96410 + 1.13397i) q^{19} -0.531659i q^{21} +(1.41959 + 2.45880i) q^{23} -1.00000 q^{25} -5.50367 q^{27} +(1.45174 + 2.51448i) q^{29} -5.46410i q^{31} +(7.44432 + 4.29798i) q^{33} +(0.166123 - 0.287734i) q^{35} +(-5.17191 + 2.98601i) q^{37} +(1.98340 + 5.41796i) q^{39} +(3.23205 - 1.86603i) q^{41} +(2.53215 - 4.38581i) q^{43} +(-0.380509 - 0.219687i) q^{45} +8.34285i q^{47} +(-3.44481 - 5.96658i) q^{49} +8.10387 q^{51} -1.56063 q^{53} +(2.68591 + 4.65213i) q^{55} -3.62916i q^{57} +(-2.34461 - 1.35366i) q^{59} +(-7.05193 + 12.2143i) q^{61} +(0.126423 - 0.0729902i) q^{63} +(-0.619491 + 3.55193i) q^{65} +(-8.94799 + 5.16612i) q^{67} +(2.27162 - 3.93456i) q^{69} +(11.0828 + 6.39866i) q^{71} +9.68922i q^{73} +(0.800098 + 1.38581i) q^{75} -1.78477 q^{77} -4.51851 q^{79} +(3.74441 + 6.48552i) q^{81} +4.26371i q^{83} +(4.38581 + 2.53215i) q^{85} +(2.32306 - 4.02367i) q^{87} +(-2.79366 + 1.61292i) q^{89} +(-0.919100 - 0.768307i) q^{91} +(-7.57221 + 4.37182i) q^{93} +(1.13397 - 1.96410i) q^{95} +(2.17191 + 1.25396i) q^{97} +2.36023i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 6 * q^7 - 4 * q^9	$ 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9} + 6 q^{15} - 2 q^{17} - 12 q^{19} + 10 q^{23} - 8 q^{25} + 4 q^{27} - 8 q^{29} + 42 q^{33} - 10 q^{35} + 6 q^{37} + 12 q^{41} + 2 q^{43} + 12 q^{49} + 8 q^{51} - 24 q^{53} + 12 q^{59} - 28 q^{61} + 24 q^{63} - 8 q^{65} - 6 q^{67} - 16 q^{69} + 2 q^{75} - 36 q^{77} + 16 q^{79} + 8 q^{81} + 18 q^{85} - 22 q^{87} + 24 q^{89} - 28 q^{91} + 16 q^{95} - 30 q^{97}+O(q^{100}) $ 8 * q - 2 * q^3 + 6 * q^7 - 4 * q^9 + 6 * q^15 - 2 * q^17 - 12 * q^19 + 10 * q^23 - 8 * q^25 + 4 * q^27 - 8 * q^29 + 42 * q^33 - 10 * q^35 + 6 * q^37 + 12 * q^41 + 2 * q^43 + 12 * q^49 + 8 * q^51 - 24 * q^53 + 12 * q^59 - 28 * q^61 + 24 * q^63 - 8 * q^65 - 6 * q^67 - 16 * q^69 + 2 * q^75 - 36 * q^77 + 16 * q^79 + 8 * q^81 + 18 * q^85 - 22 * q^87 + 24 * q^89 - 28 * q^91 + 16 * q^95 - 30 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.800098	−	1.38581i	−0.461937	−	0.800098i	0.537121	−	0.843505i	$-0.319512\pi$
$3$	−0.800098	−	1.38581i	−0.461937	−	0.800098i	−0.999057	+	0.0434075i	$0.986179\pi$
$4$		0			0
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	0.287734	+	0.166123i	0.108753	+	0.0627887i	0.553390	−	0.832922i	$-0.313334\pi$
$7$	0.287734	+	0.166123i	0.108753	+	0.0627887i	−0.444637	+	0.895711i	$0.646667\pi$
$8$		0			0
$9$	0.219687	−	0.380509i	0.0732290	−	0.126836i
$10$		0			0
$11$	−4.65213	+	2.68591i	−1.40267	+	0.809832i	−0.994666	−	0.103149i	$-0.967108\pi$
$11$	−4.65213	+	2.68591i	−1.40267	+	0.809832i	−0.408004	+	0.912980i	$0.633775\pi$
$12$		0			0
$13$	−3.55193	−	0.619491i	−0.985129	−	0.171816i
$13$	−3.55193	−	0.619491i	−0.985129	−	0.171816i
$14$		0			0
$15$	−1.38581	+	0.800098i	−0.357815	+	0.206584i
$16$		0			0
$17$	−2.53215	+	4.38581i	−0.614136	+	1.06372i	0.376399	+	0.926458i	$0.377162\pi$
$17$	−2.53215	+	4.38581i	−0.614136	+	1.06372i	−0.990535	+	0.137258i	$0.956171\pi$
$18$		0			0
$19$	1.96410	+	1.13397i	0.450596	+	0.260152i	0.708082	−	0.706130i	$-0.249561\pi$
$19$	1.96410	+	1.13397i	0.450596	+	0.260152i	−0.257486	+	0.966282i	$0.582894\pi$
$20$		0			0
$21$		−	0.531659i		−	0.116018i
$22$		0			0
$23$	1.41959	+	2.45880i	0.296005	+	0.512695i	0.975218	−	0.221246i	$-0.0710122\pi$
$23$	1.41959	+	2.45880i	0.296005	+	0.512695i	−0.679213	+	0.733941i	$0.737679\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−5.50367			−1.05918
$28$		0			0
$29$	1.45174	+	2.51448i	0.269581	+	0.466928i	0.968754	−	0.248025i	$-0.0797815\pi$
$29$	1.45174	+	2.51448i	0.269581	+	0.466928i	−0.699173	+	0.714953i	$0.746448\pi$
$30$		0			0
$31$		−	5.46410i		−	0.981382i	−0.871334	−	0.490691i	$-0.836744\pi$
$31$		−	5.46410i		−	0.981382i	0.871334	−	0.490691i	$-0.163256\pi$
$32$		0			0
$33$	7.44432	+	4.29798i	1.29589	+	0.748182i
$34$		0			0
$35$	0.166123	−	0.287734i	0.0280800	−	0.0486359i
$36$		0			0
$37$	−5.17191	+	2.98601i	−0.850257	+	0.490896i	−0.860738	−	0.509049i	$-0.829997\pi$
$37$	−5.17191	+	2.98601i	−0.850257	+	0.490896i	0.0104803	+	0.999945i	$0.496664\pi$
$38$		0			0
$39$	1.98340	+	5.41796i	0.317598	+	0.867568i
$40$		0			0
$41$	3.23205	−	1.86603i	0.504762	−	0.291424i	−0.225916	−	0.974147i	$-0.572538\pi$
$41$	3.23205	−	1.86603i	0.504762	−	0.291424i	0.730678	+	0.682723i	$0.239204\pi$
$42$		0			0
$43$	2.53215	−	4.38581i	0.386149	−	0.668830i	−0.605779	−	0.795633i	$-0.707138\pi$
$43$	2.53215	−	4.38581i	0.386149	−	0.668830i	0.991928	+	0.126803i	$0.0404717\pi$
$44$		0			0
$45$	−0.380509	−	0.219687i	−0.0567229	−	0.0327490i
$46$		0			0
$47$			8.34285i			1.21693i	0.793581	+	0.608465i	$0.208214\pi$
$47$			8.34285i			1.21693i	−0.793581	+	0.608465i	$0.791786\pi$
$48$		0			0
$49$	−3.44481	−	5.96658i	−0.492115	−	0.852368i
$50$		0			0
$51$	8.10387			1.13477
$52$		0			0
$53$	−1.56063			−0.214369			−0.107184	−	0.994239i	$-0.534183\pi$
$53$	−1.56063			−0.214369			−0.107184	+	0.994239i	$0.534183\pi$
$54$		0			0
$55$	2.68591	+	4.65213i	0.362168	+	0.627293i
$56$		0			0
$57$		−	3.62916i		−	0.480694i
$58$		0			0
$59$	−2.34461	−	1.35366i	−0.305242	−	0.176232i	0.339553	−	0.940587i	$-0.389724\pi$
$59$	−2.34461	−	1.35366i	−0.305242	−	0.176232i	−0.644795	+	0.764355i	$0.723057\pi$
$60$		0			0
$61$	−7.05193	+	12.2143i	−0.902908	+	1.56388i	−0.0792059	+	0.996858i	$0.525238\pi$
$61$	−7.05193	+	12.2143i	−0.902908	+	1.56388i	−0.823702	+	0.567023i	$0.808095\pi$
$62$		0			0
$63$	0.126423	−	0.0729902i	0.0159278	−	0.00919590i
$64$		0			0
$65$	−0.619491	+	3.55193i	−0.0768384	+	0.440563i
$66$		0			0
$67$	−8.94799	+	5.16612i	−1.09317	+	0.631142i	−0.934419	−	0.356176i	$-0.884080\pi$
$67$	−8.94799	+	5.16612i	−1.09317	+	0.631142i	−0.158752	+	0.987319i	$0.550747\pi$
$68$		0			0
$69$	2.27162	−	3.93456i	0.273471	−	0.473666i
$70$		0			0
$71$	11.0828	+	6.39866i	1.31529	+	0.759382i	0.982967	−	0.183785i	$-0.0588349\pi$
$71$	11.0828	+	6.39866i	1.31529	+	0.759382i	0.332321	+	0.943166i	$0.392168\pi$
$72$		0			0
$73$			9.68922i			1.13404i	0.823705	+	0.567019i	$0.191903\pi$
$73$			9.68922i			1.13404i	−0.823705	+	0.567019i	$0.808097\pi$
$74$		0			0
$75$	0.800098	+	1.38581i	0.0923873	+	0.160020i
$76$		0			0
$77$	−1.78477			−0.203393
$78$		0			0
$79$	−4.51851			−0.508372			−0.254186	−	0.967155i	$-0.581808\pi$
$79$	−4.51851			−0.508372			−0.254186	+	0.967155i	$0.581808\pi$
$80$		0			0
$81$	3.74441	+	6.48552i	0.416046	+	0.720613i
$82$		0			0
$83$			4.26371i			0.468003i	0.972236	+	0.234001i	$0.0751821\pi$
$83$			4.26371i			0.468003i	−0.972236	+	0.234001i	$0.924818\pi$
$84$		0			0
$85$	4.38581	+	2.53215i	0.475708	+	0.274650i
$86$		0			0
$87$	2.32306	−	4.02367i	0.249059	−	0.431382i
$88$		0			0
$89$	−2.79366	+	1.61292i	−0.296127	+	0.170969i	−0.640702	−	0.767790i	$-0.721356\pi$
$89$	−2.79366	+	1.61292i	−0.296127	+	0.170969i	0.344575	+	0.938759i	$0.388023\pi$
$90$		0			0
$91$	−0.919100	−	0.768307i	−0.0963478	−	0.0805405i
$92$		0			0
$93$	−7.57221	+	4.37182i	−0.785201	+	0.453336i
$94$		0			0
$95$	1.13397	−	1.96410i	0.116343	−	0.201513i
$96$		0			0
$97$	2.17191	+	1.25396i	0.220524	+	0.127320i	0.606193	−	0.795318i	$-0.292696\pi$
$97$	2.17191	+	1.25396i	0.220524	+	0.127320i	−0.385669	+	0.922637i	$0.626029\pi$
$98$		0			0
$99$			2.36023i			0.237213i
$100$		0			0
$101$	6.22336	+	10.7792i	0.619247	+	1.07257i	0.989623	+	0.143686i	$0.0458955\pi$
$101$	6.22336	+	10.7792i	0.619247	+	1.07257i	−0.370376	+	0.928882i	$0.620771\pi$
$102$		0			0
$103$	−15.0247			−1.48043			−0.740215	−	0.672370i	$-0.765276\pi$
$103$	−15.0247			−1.48043			−0.740215	+	0.672370i	$0.765276\pi$
$104$		0			0
$105$	−0.531659			−0.0518846
$106$		0			0
$107$	−6.53215	−	11.3140i	−0.631487	−	1.09377i	−0.987248	−	0.159190i	$-0.949112\pi$
$107$	−6.53215	−	11.3140i	−0.631487	−	1.09377i	0.355761	−	0.934577i	$-0.384222\pi$
$108$		0			0
$109$		−	11.2325i		−	1.07587i	−0.842985	−	0.537937i	$-0.819204\pi$
$109$		−	11.2325i		−	1.07587i	0.842985	−	0.537937i	$-0.180796\pi$
$110$		0			0
$111$	8.27607	+	4.77819i	0.785530	+	0.453526i
$112$		0			0
$113$	9.17191	−	15.8862i	0.862821	−	1.49445i	−0.00637349	−	0.999980i	$-0.502029\pi$
$113$	9.17191	−	15.8862i	0.862821	−	1.49445i	0.869195	−	0.494470i	$-0.164638\pi$
$114$		0			0
$115$	2.45880	−	1.41959i	0.229284	−	0.132377i
$116$		0			0
$117$	−1.01603	+	1.21545i	−0.0939325	+	0.112368i
$118$		0			0
$119$	−1.45717	+	0.841298i	−0.133579	+	0.0771216i
$120$		0			0
$121$	8.92820	−	15.4641i	0.811655	−	1.40583i
$122$		0			0
$123$	−5.17191	−	2.98601i	−0.466336	−	0.269239i
$124$		0			0
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	−1.61998	−	2.80589i	−0.143750	−	0.248982i	0.785156	−	0.619298i	$-0.212583\pi$
$127$	−1.61998	−	2.80589i	−0.143750	−	0.248982i	−0.928906	+	0.370316i	$0.879249\pi$
$128$		0			0
$129$	−8.10387			−0.713506
$130$		0			0
$131$	−0.175664			−0.0153478			−0.00767390	−	0.999971i	$-0.502443\pi$
$131$	−0.175664			−0.0153478			−0.00767390	+	0.999971i	$0.502443\pi$
$132$		0			0
$133$	0.376759	+	0.652566i	0.0326692	+	0.0565846i
$134$		0			0
$135$			5.50367i			0.473681i
$136$		0			0
$137$	−15.5736	−	8.99144i	−1.33054	−	0.768190i	−0.345162	−	0.938543i	$-0.612176\pi$
$137$	−15.5736	−	8.99144i	−1.33054	−	0.768190i	−0.985383	+	0.170353i	$0.945509\pi$
$138$		0			0
$139$	5.99307	−	10.3803i	0.508325	−	0.880445i	−0.491628	−	0.870805i	$-0.663598\pi$
$139$	5.99307	−	10.3803i	0.508325	−	0.880445i	0.999954	−	0.00964021i	$-0.00306862\pi$
$140$		0			0
$141$	11.5616	−	6.67510i	0.973663	−	0.562144i
$142$		0			0
$143$	18.1879	−	6.65821i	1.52095	−	0.556788i
$144$		0			0
$145$	2.51448	−	1.45174i	0.208816	−	0.120560i
$146$		0			0
$147$	−5.51236	+	9.54769i	−0.454652	+	0.787481i
$148$		0			0
$149$	2.95350	+	1.70520i	0.241960	+	0.139696i	0.616077	−	0.787686i	$-0.288721\pi$
$149$	2.95350	+	1.70520i	0.241960	+	0.139696i	−0.374117	+	0.927381i	$0.622054\pi$
$150$		0			0
$151$			7.96141i			0.647890i	0.946076	+	0.323945i	$0.105009\pi$
$151$			7.96141i			0.647890i	−0.946076	+	0.323945i	$0.894991\pi$
$152$		0			0
$153$	1.11256	+	1.92701i	0.0899451	+	0.155790i
$154$		0			0
$155$	−5.46410			−0.438887
$156$		0			0
$157$	−16.4329			−1.31148			−0.655742	−	0.754985i	$-0.727644\pi$
$157$	−16.4329			−1.31148			−0.655742	+	0.754985i	$0.727644\pi$
$158$		0			0
$159$	1.24865	+	2.16273i	0.0990247	+	0.171516i
$160$		0			0
$161$			0.943307i			0.0743430i
$162$		0			0
$163$	−15.4215	−	8.90361i	−1.20791	−	0.697384i	−0.245604	−	0.969370i	$-0.578986\pi$
$163$	−15.4215	−	8.90361i	−1.20791	−	0.697384i	−0.962301	+	0.271986i	$0.912320\pi$
$164$		0			0
$165$	4.29798	−	7.44432i	0.334597	−	0.579539i
$166$		0			0
$167$	−5.45047	+	3.14683i	−0.421770	+	0.243509i	−0.695834	−	0.718202i	$-0.744965\pi$
$167$	−5.45047	+	3.14683i	−0.421770	+	0.243509i	0.274064	+	0.961711i	$0.411632\pi$
$168$		0			0
$169$	12.2325	+	4.40078i	0.940959	+	0.338522i
$170$		0			0
$171$	0.862975	−	0.498239i	0.0659933	−	0.0381013i
$172$		0			0
$173$	7.98756	−	13.8349i	0.607283	−	1.05184i	−0.384404	−	0.923165i	$-0.625593\pi$
$173$	7.98756	−	13.8349i	0.607283	−	1.05184i	0.991686	−	0.128679i	$-0.0410738\pi$
$174$		0			0
$175$	−0.287734	−	0.166123i	−0.0217506	−	0.0125577i
$176$		0			0
$177$			4.33225i			0.325632i
$178$		0			0
$179$	−11.8087	−	20.4533i	−0.882625	−	1.52875i	−0.848412	−	0.529336i	$-0.822441\pi$
$179$	−11.8087	−	20.4533i	−0.882625	−	1.52875i	−0.0342123	−	0.999415i	$-0.510892\pi$
$180$		0			0
$181$	2.62590			0.195182			0.0975909	−	0.995227i	$-0.468886\pi$
$181$	2.62590			0.195182			0.0975909	+	0.995227i	$0.468886\pi$
$182$		0			0
$183$	22.5689			1.66834
$184$		0			0
$185$	2.98601	+	5.17191i	0.219536	+	0.380247i
$186$		0			0
$187$		−	27.2045i		−	1.98939i
$188$		0			0
$189$	−1.58359	−	0.914288i	−0.115189	−	0.0665046i
$190$		0			0
$191$	−1.00791	+	1.74575i	−0.0729298	+	0.126318i	−0.900184	−	0.435509i	$-0.856568\pi$
$191$	−1.00791	+	1.74575i	−0.0729298	+	0.126318i	0.827254	+	0.561828i	$0.189902\pi$
$192$		0			0
$193$	−19.7636	+	11.4105i	−1.42262	+	0.821348i	−0.996522	−	0.0833298i	$-0.973445\pi$
$193$	−19.7636	+	11.4105i	−1.42262	+	0.821348i	−0.426095	+	0.904678i	$0.640111\pi$
$194$		0			0
$195$	5.41796	−	1.98340i	0.387988	−	0.142034i
$196$		0			0
$197$	−0.556877	+	0.321513i	−0.0396758	+	0.0229068i	−0.519707	−	0.854345i	$-0.673959\pi$
$197$	−0.556877	+	0.321513i	−0.0396758	+	0.0229068i	0.480031	+	0.877252i	$0.340625\pi$
$198$		0			0
$199$	−1.53342	+	2.65596i	−0.108701	+	0.188276i	−0.915244	−	0.402899i	$-0.868003\pi$
$199$	−1.53342	+	2.65596i	−0.108701	+	0.188276i	0.806543	+	0.591175i	$0.201336\pi$
$200$		0			0
$201$	14.3185	+	8.26681i	1.00995	+	0.583096i
$202$		0			0
$203$			0.964670i			0.0677065i
$204$		0			0
$205$	−1.86603	−	3.23205i	−0.130329	−	0.225736i
$206$		0			0
$207$	1.24746			0.0867045
$208$		0			0
$209$	−12.1830			−0.842716
$210$		0			0
$211$	−4.10020	−	7.10175i	−0.282269	−	0.488904i	0.689674	−	0.724120i	$-0.257754\pi$
$211$	−4.10020	−	7.10175i	−0.282269	−	0.488904i	−0.971943	+	0.235215i	$0.924420\pi$
$212$		0			0
$213$		−	20.4782i		−	1.40314i
$214$		0			0
$215$	−4.38581	−	2.53215i	−0.299110	−	0.172691i
$216$		0			0
$217$	0.907714	−	1.57221i	0.0616197	−	0.106728i
$218$		0			0
$219$	13.4274	−	7.75232i	0.907341	−	0.523854i
$220$		0			0
$221$	11.7110	−	14.0095i	0.787767	−	0.942378i
$222$		0			0
$223$	−8.87174	+	5.12210i	−0.594095	+	0.343001i	−0.766715	−	0.641987i	$-0.778110\pi$
$223$	−8.87174	+	5.12210i	−0.594095	+	0.343001i	0.172620	+	0.984989i	$0.444777\pi$
$224$		0			0
$225$	−0.219687	+	0.380509i	−0.0146458	+	0.0253673i
$226$		0			0
$227$	6.10012	+	3.52190i	0.404879	+	0.233757i	0.688587	−	0.725154i	$-0.258231\pi$
$227$	6.10012	+	3.52190i	0.404879	+	0.233757i	−0.283708	+	0.958911i	$0.591565\pi$
$228$		0			0
$229$		−	1.32899i		−	0.0878219i	−0.999035	−	0.0439109i	$-0.986018\pi$
$229$		−	1.32899i		−	0.0878219i	0.999035	−	0.0439109i	$-0.0139818\pi$
$230$		0			0
$231$	1.42799	+	2.47335i	0.0939547	+	0.162734i
$232$		0			0
$233$	1.24746			0.0817238			0.0408619	−	0.999165i	$-0.486990\pi$
$233$	1.24746			0.0817238			0.0408619	+	0.999165i	$0.486990\pi$
$234$		0			0
$235$	8.34285			0.544227
$236$		0			0
$237$	3.61525	+	6.26180i	0.234836	+	0.406748i
$238$		0			0
$239$			9.94207i			0.643099i	0.946893	+	0.321549i	$0.104204\pi$
$239$			9.94207i			0.643099i	−0.946893	+	0.321549i	$0.895796\pi$
$240$		0			0
$241$	−19.5608	−	11.2934i	−1.26002	−	0.727475i	−0.286944	−	0.957947i	$-0.592640\pi$
$241$	−19.5608	−	11.2934i	−1.26002	−	0.727475i	−0.973079	+	0.230472i	$0.925973\pi$
$242$		0			0
$243$	−2.26371	+	3.92086i	−0.145217	+	0.251523i
$244$		0			0
$245$	−5.96658	+	3.44481i	−0.381191	+	0.220081i
$246$		0			0
$247$	−6.27387	−	5.24455i	−0.399197	−	0.333702i
$248$		0			0
$249$	5.90869	−	3.41139i	0.374448	−	0.216188i
$250$		0			0
$251$	3.38418	−	5.86157i	0.213608	−	0.369979i	−0.739233	−	0.673449i	$-0.764812\pi$
$251$	3.38418	−	5.86157i	0.213608	−	0.369979i	0.952841	+	0.303470i	$0.0981453\pi$
$252$		0			0
$253$	−13.2082	−	7.62577i	−0.830394	−	0.479428i
$254$		0			0
$255$		−	8.10387i		−	0.507484i
$256$		0			0
$257$	−5.12691	−	8.88007i	−0.319808	−	0.553924i	0.660640	−	0.750703i	$-0.270285\pi$
$257$	−5.12691	−	8.88007i	−0.319808	−	0.553924i	−0.980448	+	0.196779i	$0.936952\pi$
$258$		0			0
$259$	−1.98418			−0.123291
$260$		0			0
$261$	1.27571			0.0789645
$262$		0			0
$263$	9.32850	+	16.1574i	0.575220	+	0.996310i	0.996018	+	0.0891555i	$0.0284168\pi$
$263$	9.32850	+	16.1574i	0.575220	+	0.996310i	−0.420798	+	0.907154i	$0.638250\pi$
$264$		0			0
$265$			1.56063i			0.0958685i
$266$		0			0
$267$	4.47040	+	2.58098i	0.273584	+	0.157954i
$268$		0			0
$269$	−8.97894	+	15.5520i	−0.547456	+	0.948221i	0.450992	+	0.892528i	$0.351070\pi$
$269$	−8.97894	+	15.5520i	−0.547456	+	0.948221i	−0.998448	+	0.0556934i	$0.982263\pi$
$270$		0			0
$271$	26.7582	−	15.4488i	1.62544	−	0.938450i	0.640014	−	0.768363i	$-0.278929\pi$
$271$	26.7582	−	15.4488i	1.62544	−	0.938450i	0.985429	−	0.170086i	$-0.0544047\pi$
$272$		0			0
$273$	−0.329358	+	1.88842i	−0.0199337	+	0.114292i
$274$		0			0
$275$	4.65213	−	2.68591i	0.280534	−	0.161966i
$276$		0			0
$277$	13.2522	−	22.9536i	0.796250	−	1.37915i	−0.125792	−	0.992057i	$-0.540147\pi$
$277$	13.2522	−	22.9536i	0.796250	−	1.37915i	0.922042	−	0.387089i	$-0.126519\pi$
$278$		0			0
$279$	−2.07914	−	1.20039i	−0.124475	−	0.0718656i
$280$		0			0
$281$		−	4.97766i		−	0.296942i	−0.988917	−	0.148471i	$-0.952565\pi$
$281$		−	4.97766i		−	0.296942i	0.988917	−	0.148471i	$-0.0474352\pi$
$282$		0			0
$283$	6.29317	+	10.9001i	0.374090	+	0.647943i	0.990190	−	0.139725i	$-0.0446218\pi$
$283$	6.29317	+	10.9001i	0.374090	+	0.647943i	−0.616100	+	0.787668i	$0.711288\pi$
$284$		0			0
$285$	−3.62916			−0.214973
$286$		0			0
$287$	1.23996			0.0731926
$288$		0			0
$289$	−4.32355	−	7.48861i	−0.254327	−	0.440507i
$290$		0			0
$291$		−	4.01315i		−	0.235255i
$292$		0			0
$293$	14.6511	+	8.45880i	0.855925	+	0.494168i	0.862645	−	0.505809i	$-0.168806\pi$
$293$	14.6511	+	8.45880i	0.855925	+	0.494168i	−0.00672072	+	0.999977i	$0.502139\pi$
$294$		0			0
$295$	−1.35366	+	2.34461i	−0.0788132	+	0.136508i
$296$		0			0
$297$	25.6038	−	14.7824i	1.48568	−	0.857759i
$298$		0			0
$299$	−3.51908	−	9.61292i	−0.203514	−	0.555929i
$300$		0			0
$301$	1.45717	−	0.841298i	0.0839899	−	0.0484916i
$302$		0			0
$303$	9.95859	−	17.2488i	0.572106	−	0.990917i
$304$		0			0
$305$	12.2143	+	7.05193i	0.699389	+	0.403793i
$306$		0			0
$307$		−	4.30426i		−	0.245657i	−0.992428	−	0.122828i	$-0.960803\pi$
$307$		−	4.30426i		−	0.245657i	0.992428	−	0.122828i	$-0.0391965\pi$
$308$		0			0
$309$	12.0213	+	20.8214i	0.683865	+	1.18449i
$310$		0			0
$311$	−2.22512			−0.126175			−0.0630875	−	0.998008i	$-0.520095\pi$
$311$	−2.22512			−0.126175			−0.0630875	+	0.998008i	$0.520095\pi$
$312$		0			0
$313$	7.20887			0.407469			0.203735	−	0.979026i	$-0.434692\pi$
$313$	7.20887			0.407469			0.203735	+	0.979026i	$0.434692\pi$
$314$		0			0
$315$	−0.0729902	−	0.126423i	−0.00411253	−	0.00712311i
$316$		0			0
$317$		−	0.321644i		−	0.0180653i	−0.999959	−	0.00903266i	$-0.997125\pi$
$317$		−	0.321644i		−	0.0180653i	0.999959	−	0.00903266i	$-0.00287522\pi$
$318$		0			0
$319$	−13.5073	−	7.79847i	−0.756266	−	0.436630i
$320$		0			0
$321$	−10.4527	+	18.1046i	−0.583414	+	1.01050i
$322$		0			0
$323$	−9.94679	+	5.74278i	−0.553454	+	0.319537i
$324$		0			0
$325$	3.55193	+	0.619491i	0.197026	+	0.0343632i
$326$		0			0
$327$	−15.5661	+	8.98707i	−0.860805	+	0.496986i
$328$		0			0
$329$	−1.38594	+	2.40052i	−0.0764094	+	0.132345i
$330$		0			0
$331$	14.4037	+	8.31600i	0.791701	+	0.457089i	0.840561	−	0.541717i	$-0.182225\pi$
$331$	14.4037	+	8.31600i	0.791701	+	0.457089i	−0.0488600	+	0.998806i	$0.515559\pi$
$332$		0			0
$333$			2.62395i			0.143791i
$334$		0			0
$335$	5.16612	+	8.94799i	0.282255	+	0.488881i
$336$		0			0
$337$	−24.2186			−1.31927			−0.659636	−	0.751586i	$-0.729289\pi$
$337$	−24.2186			−1.31927			−0.659636	+	0.751586i	$0.729289\pi$
$338$		0			0
$339$	−29.3537			−1.59427
$340$		0			0
$341$	14.6761	+	25.4197i	0.794754	+	1.37655i
$342$		0			0
$343$		−	4.61478i		−	0.249174i
$344$		0			0
$345$	−3.93456	−	2.27162i	−0.211830	−	0.122300i
$346$		0			0
$347$	−3.13680	+	5.43309i	−0.168392	+	0.291664i	−0.937855	−	0.347028i	$-0.887191\pi$
$347$	−3.13680	+	5.43309i	−0.168392	+	0.291664i	0.769463	+	0.638692i	$0.220524\pi$
$348$		0			0
$349$	−6.12275	+	3.53497i	−0.327743	+	0.189223i	−0.654839	−	0.755769i	$-0.727263\pi$
$349$	−6.12275	+	3.53497i	−0.327743	+	0.189223i	0.327095	+	0.944991i	$0.393930\pi$
$350$		0			0
$351$	19.5487	+	3.40948i	1.04343	+	0.181984i
$352$		0			0
$353$	−18.8705	+	10.8949i	−1.00438	+	0.579878i	−0.909541	−	0.415615i	$-0.863566\pi$
$353$	−18.8705	+	10.8949i	−1.00438	+	0.579878i	−0.0948371	+	0.995493i	$0.530233\pi$
$354$		0			0
$355$	6.39866	−	11.0828i	0.339606	−	0.588214i
$356$		0			0
$357$	2.33176	+	1.34624i	0.123410	+	0.0712506i
$358$		0			0
$359$			23.9737i			1.26528i	0.774444	+	0.632642i	$0.218029\pi$
$359$			23.9737i			1.26528i	−0.774444	+	0.632642i	$0.781971\pi$
$360$		0			0
$361$	−6.92820	−	12.0000i	−0.364642	−	0.631579i
$362$		0			0
$363$	−28.5737			−1.49973
$364$		0			0
$365$	9.68922			0.507157
$366$		0			0
$367$	3.19566	+	5.53505i	0.166812	+	0.288927i	0.937297	−	0.348531i	$-0.113319\pi$
$367$	3.19566	+	5.53505i	0.166812	+	0.288927i	−0.770485	+	0.637458i	$0.779986\pi$
$368$		0			0
$369$		−	1.63977i		−	0.0853628i
$370$		0			0
$371$	−0.449045	−	0.259256i	−0.0233133	−	0.0134599i
$372$		0			0
$373$	10.0401	−	17.3899i	0.519855	−	0.900414i	−0.479879	−	0.877335i	$-0.659319\pi$
$373$	10.0401	−	17.3899i	0.519855	−	0.900414i	0.999734	−	0.0230798i	$-0.00734719\pi$
$374$		0			0
$375$	1.38581	−	0.800098i	0.0715629	−	0.0413169i
$376$		0			0
$377$	−3.59878	−	9.83062i	−0.185346	−	0.506302i
$378$		0			0
$379$	4.73007	−	2.73091i	0.242968	−	0.140277i	−0.373572	−	0.927601i	$-0.621867\pi$
$379$	4.73007	−	2.73091i	0.242968	−	0.140277i	0.616540	+	0.787324i	$0.288534\pi$
$380$		0			0
$381$	−2.59229	+	4.48997i	−0.132807	+	0.230028i
$382$		0			0
$383$	−4.90842	−	2.83388i	−0.250808	−	0.144804i	0.369326	−	0.929300i	$-0.379589\pi$
$383$	−4.90842	−	2.83388i	−0.250808	−	0.144804i	−0.620134	+	0.784496i	$0.712922\pi$
$384$		0			0
$385$			1.78477i			0.0909602i
$386$		0			0
$387$	−1.11256	−	1.92701i	−0.0565546	−	0.0979554i
$388$		0			0
$389$	−10.6174			−0.538325			−0.269162	−	0.963095i	$-0.586747\pi$
$389$	−10.6174			−0.538325			−0.269162	+	0.963095i	$0.586747\pi$
$390$		0			0
$391$	−14.3784			−0.727149
$392$		0			0
$393$	0.140548	+	0.243436i	0.00708971	+	0.0122797i
$394$		0			0
$395$			4.51851i			0.227351i
$396$		0			0
$397$	24.2780	+	14.0169i	1.21848	+	0.703487i	0.964592	−	0.263748i	$-0.0849586\pi$
$397$	24.2780	+	14.0169i	1.21848	+	0.703487i	0.253884	+	0.967235i	$0.418292\pi$
$398$		0			0
$399$	0.602888	−	1.04423i	0.0301822	−	0.0522770i
$400$		0			0
$401$	19.4979	−	11.2571i	0.973680	−	0.562155i	0.0733241	−	0.997308i	$-0.476639\pi$
$401$	19.4979	−	11.2571i	0.973680	−	0.562155i	0.900356	+	0.435154i	$0.143306\pi$
$402$		0			0
$403$	−3.38496	+	19.4081i	−0.168617	+	0.966788i
$404$		0			0
$405$	6.48552	−	3.74441i	0.322268	−	0.186061i
$406$		0			0
$407$	16.0403	−	27.7826i	0.795087	−	1.37713i
$408$		0			0
$409$	−3.71328	−	2.14386i	−0.183610	−	0.106007i	0.405378	−	0.914149i	$-0.367140\pi$
$409$	−3.71328	−	2.14386i	−0.183610	−	0.106007i	−0.588988	+	0.808142i	$0.700473\pi$
$410$		0			0
$411$			28.7761i			1.41942i
$412$		0			0
$413$	−0.449749	−	0.778989i	−0.0221307	−	0.0383315i
$414$		0			0
$415$	4.26371			0.209297
$416$		0			0
$417$	−19.1802			−0.939257
$418$		0			0
$419$	8.85578	+	15.3387i	0.432633	+	0.749343i	0.997099	−	0.0761137i	$-0.0242512\pi$
$419$	8.85578	+	15.3387i	0.432633	+	0.749343i	−0.564466	+	0.825456i	$0.690918\pi$
$420$		0			0
$421$			12.8787i			0.627672i	0.949477	+	0.313836i	$0.101614\pi$
$421$			12.8787i			0.627672i	−0.949477	+	0.313836i	$0.898386\pi$
$422$		0			0
$423$	3.17453	+	1.83281i	0.154351	+	0.0891145i
$424$		0			0
$425$	2.53215	−	4.38581i	0.122827	−	0.212743i
$426$		0			0
$427$	−4.05816	+	2.34298i	−0.196388	+	0.113385i
$428$		0			0
$429$	−23.7792	−	19.8778i	−1.14807	−	0.959710i
$430$		0			0
$431$	−8.22590	+	4.74923i	−0.396228	+	0.228762i	−0.684855	−	0.728679i	$-0.740134\pi$
$431$	−8.22590	+	4.74923i	−0.396228	+	0.228762i	0.288627	+	0.957442i	$0.406801\pi$
$432$		0			0
$433$	−0.698141	+	1.20922i	−0.0335505	+	0.0581112i	−0.882313	−	0.470663i	$-0.844015\pi$
$433$	−0.698141	+	1.20922i	−0.0335505	+	0.0581112i	0.848763	+	0.528774i	$0.177348\pi$
$434$		0			0
$435$	−4.02367	−	2.32306i	−0.192920	−	0.111382i
$436$		0			0
$437$			6.43911i			0.308024i
$438$		0			0
$439$	−2.08090	−	3.60422i	−0.0993159	−	0.172020i	0.812086	−	0.583538i	$-0.198332\pi$
$439$	−2.08090	−	3.60422i	−0.0993159	−	0.172020i	−0.911402	+	0.411518i	$0.864999\pi$
$440$		0			0
$441$	−3.02711			−0.144148
$442$		0			0
$443$	−9.54563			−0.453526			−0.226763	−	0.973950i	$-0.572814\pi$
$443$	−9.54563			−0.453526			−0.226763	+	0.973950i	$0.572814\pi$
$444$		0			0
$445$	1.61292	+	2.79366i	0.0764596	+	0.132432i
$446$		0			0
$447$		−	5.45732i		−	0.258122i
$448$		0			0
$449$	18.8075	+	10.8585i	0.887582	+	0.512446i	0.873151	−	0.487450i	$-0.162073\pi$
$449$	18.8075	+	10.8585i	0.887582	+	0.512446i	0.0144310	+	0.999896i	$0.495406\pi$
$450$		0			0
$451$	−10.0239	+	17.3620i	−0.472009	+	0.817544i
$452$		0			0
$453$	11.0330	−	6.36991i	0.518376	−	0.299284i
$454$		0			0
$455$	−0.768307	+	0.919100i	−0.0360188	+	0.0430881i
$456$		0			0
$457$	4.08989	−	2.36130i	0.191317	−	0.110457i	−0.401282	−	0.915955i	$-0.631435\pi$
$457$	4.08989	−	2.36130i	0.191317	−	0.110457i	0.592599	+	0.805498i	$0.298102\pi$
$458$		0			0
$459$	13.9361	−	24.1381i	0.650482	−	1.12667i
$460$		0			0
$461$	1.54283	+	0.890753i	0.0718568	+	0.0414865i	0.535498	−	0.844537i	$-0.320124\pi$
$461$	1.54283	+	0.890753i	0.0718568	+	0.0414865i	−0.463641	+	0.886023i	$0.653457\pi$
$462$		0			0
$463$			6.80200i			0.316116i	0.987430	+	0.158058i	$0.0505232\pi$
$463$			6.80200i			0.316116i	−0.987430	+	0.158058i	$0.949477\pi$
$464$		0			0
$465$	4.37182	+	7.57221i	0.202738	+	0.351153i
$466$		0			0
$467$	18.2374			0.843927			0.421963	−	0.906613i	$-0.361341\pi$
$467$	18.2374			0.843927			0.421963	+	0.906613i	$0.361341\pi$
$468$		0			0
$469$	−3.43285			−0.158514
$470$		0			0
$471$	13.1479	+	22.7728i	0.605823	+	1.04932i
$472$		0			0
$473$			27.2045i			1.25086i
$474$		0			0
$475$	−1.96410	−	1.13397i	−0.0901192	−	0.0520303i
$476$		0			0
$477$	−0.342849	+	0.593832i	−0.0156980	+	0.0271897i
$478$		0			0
$479$	−30.4674	+	17.5904i	−1.39209	+	0.803724i	−0.993547	−	0.113425i	$-0.963818\pi$
$479$	−30.4674	+	17.5904i	−1.39209	+	0.803724i	−0.398544	+	0.917149i	$0.630485\pi$
$480$		0			0
$481$	20.2201	−	7.40214i	0.921957	−	0.337508i
$482$		0			0
$483$	1.30724	−	0.754738i	0.0594817	−	0.0343418i
$484$		0			0
$485$	1.25396	−	2.17191i	0.0569392	−	0.0986215i
$486$		0			0
$487$	−8.92352	−	5.15200i	−0.404363	−	0.233459i	0.284002	−	0.958824i	$-0.408338\pi$
$487$	−8.92352	−	5.15200i	−0.404363	−	0.233459i	−0.688365	+	0.725364i	$0.741671\pi$
$488$		0			0
$489$			28.4950i			1.28859i
$490$		0			0
$491$	−4.66599	−	8.08174i	−0.210573	−	0.364724i	0.741321	−	0.671151i	$-0.234200\pi$
$491$	−4.66599	−	8.08174i	−0.210573	−	0.364724i	−0.951894	+	0.306427i	$0.900866\pi$
$492$		0			0
$493$	−14.7041			−0.662238
$494$		0			0
$495$	2.36023			0.106085
$496$		0			0
$497$	2.12593	+	3.68222i	0.0953611	+	0.165170i
$498$		0			0
$499$		−	23.9421i		−	1.07179i	−0.844283	−	0.535897i	$-0.819974\pi$
$499$		−	23.9421i		−	1.07179i	0.844283	−	0.535897i	$-0.180026\pi$
$500$		0			0
$501$	8.72181	+	5.03554i	0.389662	+	0.224971i
$502$		0			0
$503$	21.0721	−	36.4980i	0.939560	−	1.62737i	0.173266	−	0.984875i	$-0.444568\pi$
$503$	21.0721	−	36.4980i	0.939560	−	1.62737i	0.766294	−	0.642490i	$-0.222099\pi$
$504$		0			0
$505$	10.7792	−	6.22336i	0.479667	−	0.276936i
$506$		0			0
$507$	−3.68852	−	20.4729i	−0.163813	−	0.909235i
$508$		0			0
$509$	−29.0640	+	16.7801i	−1.28824	+	0.743765i	−0.978340	−	0.207005i	$-0.933629\pi$
$509$	−29.0640	+	16.7801i	−1.28824	+	0.743765i	−0.309899	+	0.950770i	$0.600295\pi$
$510$		0			0
$511$	−1.60960	+	2.78792i	−0.0712047	+	0.123330i
$512$		0			0
$513$	−10.8098	−	6.24102i	−0.477263	−	0.275548i
$514$		0			0
$515$			15.0247i			0.662069i
$516$		0			0
$517$	−22.4081	−	38.8120i	−0.985508	−	1.70695i
$518$		0			0
$519$	−25.5633			−1.12210
$520$		0			0
$521$	12.4649			0.546098			0.273049	−	0.962000i	$-0.411968\pi$
$521$	12.4649			0.546098			0.273049	+	0.962000i	$0.411968\pi$
$522$		0			0
$523$	−2.82978	−	4.90132i	−0.123738	−	0.214320i	0.797501	−	0.603317i	$-0.206155\pi$
$523$	−2.82978	−	4.90132i	−0.123738	−	0.214320i	−0.921239	+	0.388998i	$0.872821\pi$
$524$		0			0
$525$			0.531659i			0.0232035i
$526$		0			0
$527$	23.9645	+	13.8359i	1.04391	+	0.602702i
$528$		0			0
$529$	7.46953	−	12.9376i	0.324762	−	0.562505i
$530$		0			0
$531$	−1.03016	+	0.594763i	−0.0447051	+	0.0258105i
$532$		0			0
$533$	−12.6360	+	4.62577i	−0.547327	+	0.200364i
$534$		0			0
$535$	−11.3140	+	6.53215i	−0.489147	+	0.282409i
$536$		0			0
$537$	−18.8963	+	32.7293i	−0.815433	+	1.41237i
$538$		0			0
$539$	32.0514	+	18.5049i	1.38055	+	0.797061i
$540$		0			0
$541$			15.4750i			0.665321i	0.943047	+	0.332660i	$0.107946\pi$
$541$			15.4750i			0.665321i	−0.943047	+	0.332660i	$0.892054\pi$
$542$		0			0
$543$	−2.10098	−	3.63900i	−0.0901616	−	0.156165i
$544$		0			0
$545$	−11.2325			−0.481146
$546$		0			0
$547$	−25.1765			−1.07647			−0.538234	−	0.842795i	$-0.680908\pi$
$547$	−25.1765			−1.07647			−0.538234	+	0.842795i	$0.680908\pi$
$548$		0			0
$549$	3.09843	+	5.36665i	0.132238	+	0.229043i
$550$		0			0
$551$			6.58493i			0.280528i
$552$		0			0
$553$	−1.30013	−	0.750630i	−0.0552871	−	0.0319200i
$554$		0			0
$555$	4.77819	−	8.27607i	0.202823	−	0.351300i
$556$		0			0
$557$	−36.6752	+	21.1744i	−1.55398	+	0.897190i	−0.556167	+	0.831071i	$0.687728\pi$
$557$	−36.6752	+	21.1744i	−1.55398	+	0.897190i	−0.997812	+	0.0661194i	$0.978938\pi$
$558$		0			0
$559$	−11.7110	+	14.0095i	−0.495322	+	0.592537i
$560$		0			0
$561$	−37.7002	+	21.7662i	−1.59171	+	0.918971i
$562$		0			0
$563$	−11.8953	+	20.6032i	−0.501326	+	0.868322i	0.498673	+	0.866790i	$0.333821\pi$
$563$	−11.8953	+	20.6032i	−0.501326	+	0.868322i	−0.999999	+	0.00153173i	$0.999512\pi$
$564$		0			0
$565$	−15.8862	−	9.17191i	−0.668338	−	0.385865i
$566$		0			0
$567$			2.48814i			0.104492i
$568$		0			0
$569$	−13.3710	−	23.1593i	−0.560543	−	0.970889i	−0.997449	−	0.0713817i	$-0.977259\pi$
$569$	−13.3710	−	23.1593i	−0.560543	−	0.970889i	0.436906	−	0.899507i	$-0.356074\pi$
$570$		0			0
$571$	−16.7159			−0.699539			−0.349769	−	0.936836i	$-0.613740\pi$
$571$	−16.7159			−0.699539			−0.349769	+	0.936836i	$0.613740\pi$
$572$		0			0
$573$	3.22571			0.134756
$574$		0			0
$575$	−1.41959	−	2.45880i	−0.0592010	−	0.102539i
$576$		0			0
$577$		−	20.6768i		−	0.860786i	−0.902642	−	0.430393i	$-0.858375\pi$
$577$		−	20.6768i		−	0.860786i	0.902642	−	0.430393i	$-0.141625\pi$
$578$		0			0
$579$	31.6257	+	18.2591i	1.31432	+	0.758822i
$580$		0			0
$581$	−0.708301	+	1.22681i	−0.0293853	+	0.0508968i
$582$		0			0
$583$	7.26023	−	4.19170i	0.300688	−	0.173602i
$584$		0			0
$585$	1.21545	+	1.01603i	0.0502526	+	0.0420079i
$586$		0			0
$587$	−18.0109	+	10.3986i	−0.743388	+	0.429196i	−0.823300	−	0.567606i	$-0.807870\pi$
$587$	−18.0109	+	10.3986i	−0.743388	+	0.429196i	0.0799116	+	0.996802i	$0.474536\pi$
$588$		0			0
$589$	6.19615	−	10.7321i	0.255308	−	0.442206i
$590$		0			0
$591$	0.891111	+	0.514483i	0.0366554	+	0.0211630i
$592$		0			0
$593$			21.8475i			0.897169i	0.893740	+	0.448585i	$0.148072\pi$
$593$			21.8475i			0.897169i	−0.893740	+	0.448585i	$0.851928\pi$
$594$		0			0
$595$	0.841298	+	1.45717i	0.0344898	+	0.0597381i
$596$		0			0
$597$	4.90755			0.200853
$598$		0			0
$599$	3.58040			0.146291			0.0731456	−	0.997321i	$-0.476696\pi$
$599$	3.58040			0.146291			0.0731456	+	0.997321i	$0.476696\pi$
$600$		0			0
$601$	−10.6743	−	18.4885i	−0.435414	−	0.754160i	0.561915	−	0.827195i	$-0.310065\pi$
$601$	−10.6743	−	18.4885i	−0.435414	−	0.754160i	−0.997329	+	0.0730352i	$0.976731\pi$
$602$		0			0
$603$			4.53972i			0.184872i
$604$		0			0
$605$	−15.4641	−	8.92820i	−0.628705	−	0.362983i
$606$		0			0
$607$	−1.64988	+	2.85767i	−0.0669665	+	0.115989i	−0.897565	−	0.440883i	$-0.854665\pi$
$607$	−1.64988	+	2.85767i	−0.0669665	+	0.115989i	0.830598	+	0.556872i	$0.187999\pi$
$608$		0			0
$609$	1.33685	−	0.771830i	0.0541718	−	0.0312761i
$610$		0			0
$611$	5.16832	−	29.6332i	0.209088	−	1.19883i
$612$		0			0
$613$	8.56183	−	4.94318i	0.345809	−	0.199653i	−0.317029	−	0.948416i	$-0.602685\pi$
$613$	8.56183	−	4.94318i	0.345809	−	0.199653i	0.662838	+	0.748763i	$0.269352\pi$
$614$		0			0
$615$	−2.98601	+	5.17191i	−0.120407	+	0.208552i
$616$		0			0
$617$	39.5920	+	22.8584i	1.59391	+	0.920246i	0.992626	+	0.121213i	$0.0386785\pi$
$617$	39.5920	+	22.8584i	1.59391	+	0.920246i	0.601287	+	0.799033i	$0.294655\pi$
$618$		0			0
$619$			19.9143i			0.800425i	0.916422	+	0.400212i	$0.131064\pi$
$619$			19.9143i			0.800425i	−0.916422	+	0.400212i	$0.868936\pi$
$620$		0			0
$621$	−7.81295	−	13.5324i	−0.313523	−	0.543038i
$622$		0			0
$623$	−1.07177			−0.0429397
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	9.74760	+	16.8833i	0.389282	+	0.674255i
$628$		0			0
$629$		−	30.2440i		−	1.20591i
$630$		0			0
$631$	−12.6403	−	7.29790i	−0.503204	−	0.290525i	0.226832	−	0.973934i	$-0.427163\pi$
$631$	−12.6403	−	7.29790i	−0.503204	−	0.290525i	−0.730036	+	0.683409i	$0.760497\pi$
$632$		0			0
$633$	−6.56112	+	11.3642i	−0.260781	+	0.451686i
$634$		0			0
$635$	−2.80589	+	1.61998i	−0.111348	+	0.0642870i
$636$		0			0
$637$	8.53948	+	23.3269i	0.338346	+	0.924246i
$638$		0			0
$639$	4.86950	−	2.81140i	0.192634	−	0.111217i
$640$		0			0
$641$	−7.08183	+	12.2661i	−0.279716	+	0.484482i	−0.971314	−	0.237801i	$-0.923573\pi$
$641$	−7.08183	+	12.2661i	−0.279716	+	0.484482i	0.691598	+	0.722282i	$0.256907\pi$
$642$		0			0
$643$	14.5246	+	8.38581i	0.572796	+	0.330704i	0.758265	−	0.651946i	$-0.226047\pi$
$643$	14.5246	+	8.38581i	0.572796	+	0.330704i	−0.185469	+	0.982650i	$0.559380\pi$
$644$		0			0
$645$			8.10387i			0.319089i
$646$		0			0
$647$	1.49584	+	2.59087i	0.0588075	+	0.101858i	0.893930	−	0.448206i	$-0.147937\pi$
$647$	1.49584	+	2.59087i	0.0588075	+	0.101858i	−0.835123	+	0.550063i	$0.814604\pi$
$648$		0			0
$649$	14.5432			0.570872
$650$		0			0
$651$	−2.90504			−0.113858
$652$		0			0
$653$	5.83217	+	10.1016i	0.228230	+	0.395307i	0.957284	−	0.289150i	$-0.0933727\pi$
$653$	5.83217	+	10.1016i	0.228230	+	0.395307i	−0.729053	+	0.684457i	$0.760039\pi$
$654$		0			0
$655$			0.175664i			0.00686374i
$656$		0			0
$657$	3.68683	+	2.12859i	0.143837	+	0.0830444i
$658$		0			0
$659$	−0.905237	+	1.56792i	−0.0352630	+	0.0610773i	−0.883118	−	0.469150i	$-0.844560\pi$
$659$	−0.905237	+	1.56792i	−0.0352630	+	0.0610773i	0.847855	+	0.530228i	$0.177894\pi$
$660$		0			0
$661$	10.6872	−	6.17028i	0.415686	−	0.239996i	−0.277544	−	0.960713i	$-0.589520\pi$
$661$	10.6872	−	6.17028i	0.415686	−	0.239996i	0.693230	+	0.720717i	$0.256187\pi$
$662$		0			0
$663$	−28.7844	−	5.02027i	−1.11789	−	0.194971i
$664$		0			0
$665$	0.652566	−	0.376759i	0.0253054	−	0.0146101i
$666$		0			0
$667$	−4.12174	+	7.13907i	−0.159594	+	0.276426i
$668$		0			0
$669$	14.1965	+	8.19636i	0.548869	+	0.316890i
$670$		0			0
$671$		−	75.7634i		−	2.92481i
$672$		0			0
$673$	4.63313	+	8.02481i	0.178594	+	0.309334i	0.941399	−	0.337295i	$-0.109512\pi$
$673$	4.63313	+	8.02481i	0.178594	+	0.309334i	−0.762805	+	0.646628i	$0.776178\pi$
$674$		0			0
$675$	5.50367			0.211836
$676$		0			0
$677$	13.8984			0.534158			0.267079	−	0.963675i	$-0.413941\pi$
$677$	13.8984			0.534158			0.267079	+	0.963675i	$0.413941\pi$
$678$		0			0
$679$	0.416622	+	0.721611i	0.0159885	+	0.0276929i
$680$		0			0
$681$		−	11.2715i		−	0.431924i
$682$		0			0
$683$	32.6935	+	18.8756i	1.25098	+	0.722255i	0.971305	−	0.237838i	$-0.0764388\pi$
$683$	32.6935	+	18.8756i	1.25098	+	0.722255i	0.279678	+	0.960094i	$0.409772\pi$
$684$		0			0
$685$	−8.99144	+	15.5736i	−0.343545	+	0.595038i
$686$		0			0
$687$	−1.84172	+	1.06332i	−0.0702661	+	0.0405681i
$688$		0			0
$689$	5.54324	+	0.966794i	0.211181	+	0.0368319i
$690$		0			0
$691$	1.43146	−	0.826456i	0.0544554	−	0.0314399i	−0.472525	−	0.881317i	$-0.656657\pi$
$691$	1.43146	−	0.826456i	0.0544554	−	0.0314399i	0.526981	+	0.849877i	$0.323324\pi$
$692$		0			0
$693$	−0.392090	+	0.679120i	−0.0148943	+	0.0257976i
$694$		0			0
$695$	−10.3803	−	5.99307i	−0.393747	−	0.227330i
$696$		0			0
$697$			18.9002i			0.715897i
$698$		0			0
$699$	−0.998090	−	1.72874i	−0.0377512	−	0.0653871i
$700$		0			0
$701$	−20.4819			−0.773590			−0.386795	−	0.922166i	$-0.626418\pi$
$701$	−20.4819			−0.773590			−0.386795	+	0.922166i	$0.626418\pi$
$702$		0			0
$703$	−13.5442			−0.510830
$704$		0			0
$705$	−6.67510	−	11.5616i	−0.251399	−	0.435435i
$706$		0			0
$707$			4.13538i			0.155527i
$708$		0			0
$709$	19.0021	+	10.9709i	0.713639	+	0.412020i	0.812407	−	0.583091i	$-0.198157\pi$
$709$	19.0021	+	10.9709i	0.713639	+	0.412020i	−0.0987679	+	0.995110i	$0.531490\pi$
$710$		0			0
$711$	−0.992658	+	1.71933i	−0.0372276	+	0.0644801i
$712$		0			0
$713$	13.4351	−	7.75678i	0.503150	−	0.290494i
$714$		0			0
$715$	−6.65821	−	18.1879i	−0.249003	−	0.680191i
$716$		0			0
$717$	13.7778	−	7.95463i	0.514542	−	0.297071i
$718$		0			0
$719$	−19.4237	+	33.6429i	−0.724384	+	1.25467i	0.234844	+	0.972033i	$0.424542\pi$
$719$	−19.4237	+	33.6429i	−0.724384	+	1.25467i	−0.959227	+	0.282636i	$0.908791\pi$
$720$		0			0
$721$	−4.32312	−	2.49596i	−0.161002	−	0.0929543i
$722$		0			0
$723$			36.1434i			1.34419i
$724$		0			0
$725$	−1.45174	−	2.51448i	−0.0539162	−	0.0933856i
$726$		0			0
$727$	−30.6598			−1.13711			−0.568555	−	0.822645i	$-0.692497\pi$
$727$	−30.6598			−1.13711			−0.568555	+	0.822645i	$0.692497\pi$
$728$		0			0
$729$	29.7112			1.10042
$730$		0			0
$731$	12.8236	+	22.2110i	0.474296	+	0.821505i
$732$		0			0
$733$			24.3858i			0.900709i	0.892850	+	0.450355i	$0.148702\pi$
$733$			24.3858i			0.900709i	−0.892850	+	0.450355i	$0.851298\pi$
$734$		0			0
$735$	9.54769	+	5.51236i	0.352172	+	0.203327i
$736$		0			0
$737$	27.7515	−	48.0669i	1.02224	−	1.77057i
$738$		0			0
$739$	33.1504	−	19.1394i	1.21946	−	0.704054i	0.254656	−	0.967032i	$-0.418038\pi$
$739$	33.1504	−	19.1394i	1.21946	−	0.704054i	0.964802	+	0.262977i	$0.0847044\pi$
$740$		0			0
$741$	−2.24823	+	12.8905i	−0.0825909	+	0.473546i
$742$		0			0
$743$	34.6479	−	20.0040i	1.27111	−	0.733874i	0.295910	−	0.955216i	$-0.404377\pi$
$743$	34.6479	−	20.0040i	1.27111	−	0.733874i	0.975196	+	0.221342i	$0.0710437\pi$
$744$		0			0
$745$	1.70520	−	2.95350i	0.0624738	−	0.108208i
$746$		0			0
$747$	1.62238	+	0.936681i	0.0593598	+	0.0342714i
$748$		0			0
$749$		−	4.34057i		−	0.158601i
$750$		0			0
$751$	−12.8010	−	22.1720i	−0.467115	−	0.809067i	0.532179	−	0.846632i	$-0.321373\pi$
$751$	−12.8010	−	22.1720i	−0.467115	−	0.809067i	−0.999294	+	0.0375648i	$0.988040\pi$
$752$		0			0
$753$	−10.8307			−0.394693
$754$		0			0
$755$	7.96141			0.289745
$756$		0			0
$757$	0.924239	+	1.60083i	0.0335920	+	0.0581831i	0.882333	−	0.470626i	$-0.155972\pi$
$757$	0.924239	+	1.60083i	0.0335920	+	0.0581831i	−0.848741	+	0.528809i	$0.822639\pi$
$758$		0			0
$759$			24.4055i			0.885862i
$760$		0			0
$761$	22.7006	+	13.1062i	0.822896	+	0.475099i	0.851414	−	0.524494i	$-0.175745\pi$
$761$	22.7006	+	13.1062i	0.822896	+	0.475099i	−0.0285179	+	0.999593i	$0.509079\pi$
$762$		0			0
$763$	1.86597	−	3.23196i	0.0675528	−	0.117005i
$764$		0			0
$765$	1.92701	−	1.11256i	0.0696712	−	0.0402247i
$766$		0			0
$767$	7.48932	+	6.26058i	0.270424	+	0.226056i
$768$		0			0
$769$	−38.4078	+	22.1747i	−1.38502	+	0.799641i	−0.992749	−	0.120208i	$-0.961644\pi$
$769$	−38.4078	+	22.1747i	−1.38502	+	0.799641i	−0.392271	+	0.919850i	$0.628310\pi$
$770$		0			0
$771$	−8.20406	+	14.2099i	−0.295462	+	0.511755i
$772$		0			0
$773$	20.1471	+	11.6319i	0.724640	+	0.418371i	0.816458	−	0.577405i	$-0.195935\pi$
$773$	20.1471	+	11.6319i	0.724640	+	0.418371i	−0.0918181	+	0.995776i	$0.529268\pi$
$774$		0			0
$775$			5.46410i			0.196276i
$776$		0			0
$777$	1.58754	+	2.74970i	0.0569526	+	0.0986448i
$778$		0			0
$779$	8.46410			0.303258
$780$		0			0
$781$	−68.7449			−2.45989
$782$		0			0
$783$	−7.98989	−	13.8389i	−0.285535	−	0.494562i
$784$		0			0
$785$			16.4329i			0.586514i
$786$		0			0
$787$	41.4942	+	23.9567i	1.47911	+	0.853963i	0.999721	−	0.0236408i	$-0.00752582\pi$
$787$	41.4942	+	23.9567i	1.47911	+	0.853963i	0.479387	+	0.877604i	$0.340859\pi$
$788$		0			0
$789$	14.9274	−	25.8551i	0.531430	−	0.920464i
$790$		0			0
$791$	5.27814	−	3.04734i	0.187669	−	0.108351i
$792$		0			0
$793$	32.6147	−	39.0158i	1.15818	−	1.38549i
$794$		0			0
$795$	2.16273	−	1.24865i	0.0767042	−	0.0442852i
$796$		0			0
$797$	−10.3476	+	17.9225i	−0.366530	+	0.634849i	−0.989020	−	0.147779i	$-0.952788\pi$
$797$	−10.3476	+	17.9225i	−0.366530	+	0.634849i	0.622490	+	0.782627i	$0.286121\pi$
$798$		0			0
$799$	−36.5902	−	21.1253i	−1.29447	−	0.747361i
$800$		0			0
$801$			1.41735i			0.0500795i
$802$		0			0
$803$	−26.0244	−	45.0755i	−0.918380	−	1.59068i
$804$		0			0
$805$	0.943307			0.0332472
$806$		0			0
$807$	28.7361			1.01156
$808$		0			0
$809$	−7.94574	−	13.7624i	−0.279357	−	0.483861i	0.691868	−	0.722024i	$-0.256788\pi$
$809$	−7.94574	−	13.7624i	−0.279357	−	0.483861i	−0.971225	+	0.238163i	$0.923455\pi$
$810$		0			0
$811$			23.8796i			0.838525i	0.907865	+	0.419263i	$0.137711\pi$
$811$			23.8796i			0.838525i	−0.907865	+	0.419263i	$0.862289\pi$
$812$		0			0
$813$	−42.8183	−	24.7212i	−1.50170	−	0.867009i
$814$		0			0
$815$	−8.90361	+	15.4215i	−0.311880	+	0.540192i
$816$		0			0
$817$	9.94679	−	5.74278i	0.347994	−	0.200915i
$818$		0			0
$819$	−0.494262	+	0.180939i	−0.0172709	+	0.00632250i
$820$		0			0
$821$	13.7782	−	7.95484i	0.480862	−	0.277626i	−0.239914	−	0.970794i	$-0.577119\pi$
$821$	13.7782	−	7.95484i	0.480862	−	0.277626i	0.720776	+	0.693169i	$0.243786\pi$
$822$		0			0
$823$	7.40573	−	12.8271i	0.258147	−	0.447124i	−0.707598	−	0.706615i	$-0.750221\pi$
$823$	7.40573	−	12.8271i	0.258147	−	0.447124i	0.965746	+	0.259491i	$0.0835547\pi$
$824$		0			0
$825$	−7.44432	−	4.29798i	−0.259178	−	0.149636i
$826$		0			0
$827$			33.9498i			1.18055i	0.807202	+	0.590275i	$0.200981\pi$
$827$			33.9498i			1.18055i	−0.807202	+	0.590275i	$0.799019\pi$
$828$		0			0
$829$	11.6573	+	20.1910i	0.404875	+	0.701264i	0.994307	−	0.106554i	$-0.0339818\pi$
$829$	11.6573	+	20.1910i	0.404875	+	0.701264i	−0.589432	+	0.807818i	$0.700648\pi$
$830$		0			0
$831$	−42.4124			−1.47127
$832$		0			0
$833$	34.8910			1.20890
$834$		0			0
$835$	3.14683	+	5.45047i	0.108900	+	0.188621i
$836$		0			0
$837$			30.0726i			1.03946i
$838$		0			0
$839$	12.8111	+	7.39649i	0.442288	+	0.255355i	0.704568	−	0.709637i	$-0.251141\pi$
$839$	12.8111	+	7.39649i	0.442288	+	0.255355i	−0.262280	+	0.964992i	$0.584474\pi$
$840$		0			0
$841$	10.2849	−	17.8140i	0.354652	−	0.614276i
$842$		0			0
$843$	−6.89809	+	3.98261i	−0.237583	+	0.137169i
$844$		0			0
$845$	4.40078	−	12.2325i	0.151392	−	0.420809i
$846$		0			0
$847$	5.13789	−	2.96636i	0.176540	−	0.101925i
$848$		0			0
$849$	10.0703	−	17.4423i	0.345612	−	0.598617i
$850$		0			0
$851$	−14.6840	−	8.47780i	−0.503360	−	0.290615i
$852$		0			0
$853$			16.3452i			0.559650i	0.960051	+	0.279825i	$0.0902765\pi$
$853$			16.3452i			0.559650i	−0.960051	+	0.279825i	$0.909724\pi$
$854$		0			0
$855$	−0.498239	−	0.862975i	−0.0170394	−	0.0295131i
$856$		0			0
$857$	34.1418			1.16626			0.583132	−	0.812378i	$-0.301827\pi$
$857$	34.1418			1.16626			0.583132	+	0.812378i	$0.301827\pi$
$858$		0			0
$859$	45.1996			1.54219			0.771096	−	0.636719i	$-0.219709\pi$
$859$	45.1996			1.54219			0.771096	+	0.636719i	$0.219709\pi$
$860$		0			0
$861$	−0.992090	−	1.71835i	−0.0338103	−	0.0585612i
$862$		0			0
$863$		−	4.75058i		−	0.161712i	−0.996726	−	0.0808559i	$-0.974235\pi$
$863$		−	4.75058i		−	0.161712i	0.996726	−	0.0808559i	$-0.0257653\pi$
$864$		0			0
$865$	−13.8349	−	7.98756i	−0.470399	−	0.271585i
$866$		0			0
$867$	−6.91853	+	11.9832i	−0.234966	+	0.406972i
$868$		0			0
$869$	21.0207	−	12.1363i	0.713079	−	0.411696i
$870$		0			0
$871$	34.9830	−	12.8065i	1.18535	−	0.433933i
$872$		0			0
$873$	0.954282	−	0.550955i	0.0322975	−	0.0186470i
$874$		0			0
$875$	−0.166123	+	0.287734i	−0.00561599	+	0.00972718i
$876$		0			0
$877$	−1.95294	−	1.12753i	−0.0659462	−	0.0380741i	0.466664	−	0.884434i	$-0.345456\pi$
$877$	−1.95294	−	1.12753i	−0.0659462	−	0.0380741i	−0.532611	+	0.846360i	$0.678789\pi$
$878$		0			0
$879$		−	27.0715i		−	0.913098i
$880$		0			0
$881$	−1.49152	−	2.58339i	−0.0502507	−	0.0870367i	0.839806	−	0.542887i	$-0.182669\pi$
$881$	−1.49152	−	2.58339i	−0.0502507	−	0.0870367i	−0.890057	+	0.455850i	$0.849335\pi$
$882$		0			0
$883$	28.2874			0.951947			0.475973	−	0.879460i	$-0.342096\pi$
$883$	28.2874			0.951947			0.475973	+	0.879460i	$0.342096\pi$
$884$		0			0
$885$	4.33225			0.145627
$886$		0			0
$887$	−13.9908	−	24.2328i	−0.469766	−	0.813658i	0.529637	−	0.848225i	$-0.322328\pi$
$887$	−13.9908	−	24.2328i	−0.469766	−	0.813658i	−0.999402	+	0.0345665i	$0.988995\pi$
$888$		0			0
$889$		−	1.07647i		−	0.0361035i
$890$		0			0
$891$	−34.8390	−	20.1143i	−1.16715	−	0.673855i
$892$		0			0
$893$	−9.46058	+	16.3862i	−0.316586	+	0.548343i
$894$		0			0
$895$	−20.4533	+	11.8087i	−0.683678	+	0.394722i
$896$		0			0
$897$	−10.5061	+	12.5681i	−0.350787	+	0.419635i
$898$		0			0
$899$	13.7394	−	7.93244i	0.458234	−	0.264562i
$900$		0			0
$901$	3.95174	−	6.84461i	0.131651	−	0.228027i
$902$		0			0
$903$	−2.33176	−	1.34624i	−0.0775960	−	0.0448001i
$904$		0			0
$905$		−	2.62590i		−	0.0872879i
$906$		0			0
$907$	−8.27600	−	14.3344i	−0.274800	−	0.475967i	0.695285	−	0.718734i	$-0.255278\pi$
$907$	−8.27600	−	14.3344i	−0.274800	−	0.475967i	−0.970085	+	0.242767i	$0.921945\pi$
$908$		0			0
$909$	5.46876			0.181387
$910$		0			0
$911$	−7.04863			−0.233532			−0.116766	−	0.993159i	$-0.537253\pi$
$911$	−7.04863			−0.233532			−0.116766	+	0.993159i	$0.537253\pi$
$912$		0			0
$913$	−11.4519	−	19.8353i	−0.379004	−	0.656454i
$914$		0			0
$915$		−	22.5689i		−	0.746106i
$916$		0			0
$917$	−0.0505443	−	0.0291818i	−0.00166912	−	0.000963668i
$918$		0			0
$919$	8.27188	−	14.3273i	0.272864	−	0.472615i	−0.696730	−	0.717334i	$-0.745362\pi$
$919$	8.27188	−	14.3273i	0.272864	−	0.472615i	0.969594	+	0.244719i	$0.0786957\pi$
$920$		0			0
$921$	−5.96488	+	3.44383i	−0.196550	+	0.113478i
$922$		0			0
$923$	−35.4015	−	29.5933i	−1.16525	−	0.974076i
$924$		0			0
$925$	5.17191	−	2.98601i	0.170051	−	0.0981793i
$926$		0			0
$927$	−3.30074	+	5.71704i	−0.108410	+	0.187772i
$928$		0			0
$929$	−29.3035	−	16.9184i	−0.961416	−	0.555074i	−0.0648073	−	0.997898i	$-0.520643\pi$
$929$	−29.3035	−	16.9184i	−0.961416	−	0.555074i	−0.896609	+	0.442824i	$0.853977\pi$
$930$		0			0
$931$		−	15.6253i		−	0.512098i
$932$		0			0
$933$	1.78031	+	3.08359i	0.0582848	+	0.100952i
$934$		0			0
$935$	−27.2045			−0.889681
$936$		0			0
$937$	−30.4606			−0.995104			−0.497552	−	0.867434i	$-0.665768\pi$
$937$	−30.4606			−0.995104			−0.497552	+	0.867434i	$0.665768\pi$
$938$		0			0
$939$	−5.76780	−	9.99012i	−0.188225	−	0.326015i
$940$		0			0
$941$		−	38.2101i		−	1.24561i	−0.782375	−	0.622807i	$-0.785992\pi$
$941$		−	38.2101i		−	1.24561i	0.782375	−	0.622807i	$-0.214008\pi$
$942$		0			0
$943$	9.17637	+	5.29798i	0.298824	+	0.172526i
$944$		0			0
$945$	−0.914288	+	1.58359i	−0.0297418	+	0.0515143i
$946$		0			0
$947$	45.4215	−	26.2241i	1.47600	−	0.852169i	0.476367	−	0.879247i	$-0.341953\pi$
$947$	45.4215	−	26.2241i	1.47600	−	0.852169i	0.999633	+	0.0270773i	$0.00862003\pi$
$948$		0			0
$949$	6.00239	−	34.4155i	0.194846	−	1.11717i
$950$		0			0
$951$	−0.445737	+	0.257347i	−0.0144540	+	0.00834504i
$952$		0			0
$953$	19.8750	−	34.4245i	0.643814	−	1.11512i	−0.340760	−	0.940150i	$-0.610684\pi$
$953$	19.8750	−	34.4245i	0.643814	−	1.11512i	0.984574	−	0.174969i	$-0.0559824\pi$
$954$		0			0
$955$	1.74575	+	1.00791i	0.0564912	+	0.0326152i
$956$		0			0
$957$			24.9581i			0.806782i
$958$		0			0
$959$	−2.98737	−	5.17428i	−0.0964673	−	0.167086i
$960$		0			0
$961$	1.14359			0.0368901
$962$		0			0
$963$	−5.74011			−0.184972
$964$		0			0
$965$	11.4105	+	19.7636i	0.367318	+	0.636214i
$966$		0			0
$967$		−	25.7857i		−	0.829214i	−0.910001	−	0.414607i	$-0.863919\pi$
$967$		−	25.7857i		−	0.829214i	0.910001	−	0.414607i	$-0.136081\pi$
$968$		0			0
$969$	15.9168	+	9.18958i	0.511322	+	0.295212i
$970$		0			0
$971$	−27.7626	+	48.0863i	−0.890945	+	1.54316i	−0.0522005	+	0.998637i	$0.516623\pi$
$971$	−27.7626	+	48.0863i	−0.890945	+	1.54316i	−0.838744	+	0.544525i	$0.816710\pi$
$972$		0			0
$973$	3.44882	−	1.99118i	0.110564	−	0.0638342i
$974$		0			0
$975$	−1.98340	−	5.41796i	−0.0635195	−	0.173514i
$976$		0			0
$977$	−35.0879	+	20.2580i	−1.12256	+	0.648112i	−0.942054	−	0.335461i	$-0.891108\pi$
$977$	−35.0879	+	20.2580i	−1.12256	+	0.648112i	−0.180509	+	0.983573i	$0.557774\pi$
$978$		0			0
$979$	8.66430	−	15.0070i	0.276912	−	0.479626i
$980$		0			0
$981$	−4.27405	−	2.46762i	−0.136460	−	0.0787852i
$982$		0			0
$983$			34.8059i			1.11014i	0.831805	+	0.555068i	$0.187308\pi$
$983$			34.8059i			1.11014i	−0.831805	+	0.555068i	$0.812692\pi$
$984$		0			0
$985$	0.321513	+	0.556877i	0.0102443	+	0.0177436i
$986$		0			0
$987$	4.43555			0.141185
$988$		0			0
$989$	14.3784			0.457208
$990$		0			0
$991$	21.9427	+	38.0059i	0.697034	+	1.20730i	0.969490	+	0.245130i	$0.0788307\pi$
$991$	21.9427	+	38.0059i	0.697034	+	1.20730i	−0.272456	+	0.962168i	$0.587836\pi$
$992$		0			0
$993$		−	26.6145i		−	0.844584i
$994$		0			0
$995$	2.65596	+	1.53342i	0.0841997	+	0.0486127i
$996$		0			0
$997$	2.74569	−	4.75567i	0.0869568	−	0.150614i	−0.819267	−	0.573413i	$-0.805619\pi$
$997$	2.74569	−	4.75567i	0.0869568	−	0.150614i	0.906223	+	0.422799i	$0.138952\pi$
$998$		0			0
$999$	28.4645	−	16.4340i	0.900577	−	0.519949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.da.b.881.2		8
4.3	odd	2		65.2.m.a.36.2	✓	8
12.11	even	2		585.2.bu.c.361.3		8
13.4	even	6	inner	1040.2.da.b.641.2		8
20.3	even	4		325.2.m.b.49.3		8
20.7	even	4		325.2.m.c.49.2		8
20.19	odd	2		325.2.n.d.101.3		8
52.3	odd	6		845.2.c.g.506.4		8
52.7	even	12		845.2.e.n.191.2		8
52.11	even	12		845.2.a.l.1.3		4
52.15	even	12		845.2.a.m.1.2		4
52.19	even	12		845.2.e.m.191.3		8
52.23	odd	6		845.2.c.g.506.5		8
52.31	even	4		845.2.e.m.146.3		8
52.35	odd	6		845.2.m.g.316.3		8
52.43	odd	6		65.2.m.a.56.2	yes	8
52.47	even	4		845.2.e.n.146.2		8
52.51	odd	2		845.2.m.g.361.3		8
156.11	odd	12		7605.2.a.cj.1.2		4
156.95	even	6		585.2.bu.c.316.3		8
156.119	odd	12		7605.2.a.cf.1.3		4
260.43	even	12		325.2.m.c.199.2		8
260.119	even	12		4225.2.a.bi.1.3		4
260.147	even	12		325.2.m.b.199.3		8
260.199	odd	6		325.2.n.d.251.3		8
260.219	even	12		4225.2.a.bl.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.2	✓	8	4.3	odd	2
65.2.m.a.56.2	yes	8	52.43	odd	6
325.2.m.b.49.3		8	20.3	even	4
325.2.m.b.199.3		8	260.147	even	12
325.2.m.c.49.2		8	20.7	even	4
325.2.m.c.199.2		8	260.43	even	12
325.2.n.d.101.3		8	20.19	odd	2
325.2.n.d.251.3		8	260.199	odd	6
585.2.bu.c.316.3		8	156.95	even	6
585.2.bu.c.361.3		8	12.11	even	2
845.2.a.l.1.3		4	52.11	even	12
845.2.a.m.1.2		4	52.15	even	12
845.2.c.g.506.4		8	52.3	odd	6
845.2.c.g.506.5		8	52.23	odd	6
845.2.e.m.146.3		8	52.31	even	4
845.2.e.m.191.3		8	52.19	even	12
845.2.e.n.146.2		8	52.47	even	4
845.2.e.n.191.2		8	52.7	even	12
845.2.m.g.316.3		8	52.35	odd	6
845.2.m.g.361.3		8	52.51	odd	2
1040.2.da.b.641.2		8	13.4	even	6	inner
1040.2.da.b.881.2		8	1.1	even	1	trivial
4225.2.a.bi.1.3		4	260.119	even	12
4225.2.a.bl.1.2		4	260.219	even	12
7605.2.a.cf.1.3		4	156.119	odd	12
7605.2.a.cj.1.2		4	156.11	odd	12

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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.da (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.800098 - 1.38581i) q^{3} -1.00000i q^{5} +(0.287734 + 0.166123i) q^{7} +(0.219687 - 0.380509i) q^{9} +O(q^{10})\)	\(q+(-0.800098 - 1.38581i) q^{3} -1.00000i q^{5} +(0.287734 + 0.166123i) q^{7} +(0.219687 - 0.380509i) q^{9} +(-4.65213 + 2.68591i) q^{11} +(-3.55193 - 0.619491i) q^{13} +(-1.38581 + 0.800098i) q^{15} +(-2.53215 + 4.38581i) q^{17} +(1.96410 + 1.13397i) q^{19} -0.531659i q^{21} +(1.41959 + 2.45880i) q^{23} -1.00000 q^{25} -5.50367 q^{27} +(1.45174 + 2.51448i) q^{29} -5.46410i q^{31} +(7.44432 + 4.29798i) q^{33} +(0.166123 - 0.287734i) q^{35} +(-5.17191 + 2.98601i) q^{37} +(1.98340 + 5.41796i) q^{39} +(3.23205 - 1.86603i) q^{41} +(2.53215 - 4.38581i) q^{43} +(-0.380509 - 0.219687i) q^{45} +8.34285i q^{47} +(-3.44481 - 5.96658i) q^{49} +8.10387 q^{51} -1.56063 q^{53} +(2.68591 + 4.65213i) q^{55} -3.62916i q^{57} +(-2.34461 - 1.35366i) q^{59} +(-7.05193 + 12.2143i) q^{61} +(0.126423 - 0.0729902i) q^{63} +(-0.619491 + 3.55193i) q^{65} +(-8.94799 + 5.16612i) q^{67} +(2.27162 - 3.93456i) q^{69} +(11.0828 + 6.39866i) q^{71} +9.68922i q^{73} +(0.800098 + 1.38581i) q^{75} -1.78477 q^{77} -4.51851 q^{79} +(3.74441 + 6.48552i) q^{81} +4.26371i q^{83} +(4.38581 + 2.53215i) q^{85} +(2.32306 - 4.02367i) q^{87} +(-2.79366 + 1.61292i) q^{89} +(-0.919100 - 0.768307i) q^{91} +(-7.57221 + 4.37182i) q^{93} +(1.13397 - 1.96410i) q^{95} +(2.17191 + 1.25396i) q^{97} +2.36023i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 6 * q^7 - 4 * q^9	\( 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9} + 6 q^{15} - 2 q^{17} - 12 q^{19} + 10 q^{23} - 8 q^{25} + 4 q^{27} - 8 q^{29} + 42 q^{33} - 10 q^{35} + 6 q^{37} + 12 q^{41} + 2 q^{43} + 12 q^{49} + 8 q^{51} - 24 q^{53} + 12 q^{59} - 28 q^{61} + 24 q^{63} - 8 q^{65} - 6 q^{67} - 16 q^{69} + 2 q^{75} - 36 q^{77} + 16 q^{79} + 8 q^{81} + 18 q^{85} - 22 q^{87} + 24 q^{89} - 28 q^{91} + 16 q^{95} - 30 q^{97}+O(q^{100}) \) 8 * q - 2 * q^3 + 6 * q^7 - 4 * q^9 + 6 * q^15 - 2 * q^17 - 12 * q^19 + 10 * q^23 - 8 * q^25 + 4 * q^27 - 8 * q^29 + 42 * q^33 - 10 * q^35 + 6 * q^37 + 12 * q^41 + 2 * q^43 + 12 * q^49 + 8 * q^51 - 24 * q^53 + 12 * q^59 - 28 * q^61 + 24 * q^63 - 8 * q^65 - 6 * q^67 - 16 * q^69 + 2 * q^75 - 36 * q^77 + 16 * q^79 + 8 * q^81 + 18 * q^85 - 22 * q^87 + 24 * q^89 - 28 * q^91 + 16 * q^95 - 30 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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