LMFDB - Embedded newform 1040.2.da.f.881.7

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22x^{14} + 183x^{12} + 730x^{10} + 1485x^{8} + 1552x^{6} + 812x^{4} + 192x^{2} + 16 $ x^16 + 22x^14 + 183x^12 + 730x^10 + 1485x^8 + 1552x^6 + 812x^4 + 192*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 520)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.7
Root			$-0.956612i$ of defining polynomial
Character	$\chi$	$=$	1040.881
Dual form			1040.2.da.f.641.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.52075 + 2.63402i) q^{3} -1.00000i q^{5} +(2.67664 + 1.54536i) q^{7} +(-3.12538 + 5.41331i) q^{9} +O(q^{10})$	\(q+(1.52075 + 2.63402i) q^{3} -1.00000i q^{5} +(2.67664 + 1.54536i) q^{7} +(-3.12538 + 5.41331i) q^{9} +(5.36505 - 3.09751i) q^{11} +(2.54049 + 2.55850i) q^{13} +(2.63402 - 1.52075i) q^{15} +(3.24262 - 5.61638i) q^{17} +(-2.65678 - 1.53389i) q^{19} +9.40042i q^{21} +(-0.896274 - 1.55239i) q^{23} -1.00000 q^{25} -9.88720 q^{27} +(-1.49128 - 2.58297i) q^{29} +4.34508i q^{31} +(16.3178 + 9.42110i) q^{33} +(1.54536 - 2.67664i) q^{35} +(-8.31867 + 4.80279i) q^{37} +(-2.87569 + 10.5825i) q^{39} +(-6.40038 + 3.69526i) q^{41} +(2.64990 - 4.58977i) q^{43} +(5.41331 + 3.12538i) q^{45} -3.46118i q^{47} +(1.27625 + 2.21053i) q^{49} +19.7249 q^{51} -7.82172 q^{53} +(-3.09751 - 5.36505i) q^{55} -9.33068i q^{57} +(-1.21101 - 0.699176i) q^{59} +(-4.92252 + 8.52605i) q^{61} +(-16.7310 + 9.65965i) q^{63} +(2.55850 - 2.54049i) q^{65} +(1.52639 - 0.881260i) q^{67} +(2.72602 - 4.72161i) q^{69} +(3.60493 + 2.08131i) q^{71} -11.7104i q^{73} +(-1.52075 - 2.63402i) q^{75} +19.1470 q^{77} -6.58127 q^{79} +(-5.65985 - 9.80314i) q^{81} +4.46298i q^{83} +(-5.61638 - 3.24262i) q^{85} +(4.53573 - 7.85612i) q^{87} +(-10.0616 + 5.80904i) q^{89} +(2.84617 + 10.7741i) q^{91} +(-11.4450 + 6.60779i) q^{93} +(-1.53389 + 2.65678i) q^{95} +(-10.6392 - 6.14254i) q^{97} +38.7236i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9}+O(q^{10}) $ 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9	$ 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9} + 6 q^{11} - 2 q^{13} + 4 q^{17} - 30 q^{19} - 6 q^{23} - 16 q^{25} - 44 q^{27} - 16 q^{29} + 24 q^{33} + 6 q^{35} - 24 q^{37} + 8 q^{39} - 24 q^{41} - 6 q^{43} + 12 q^{45} - 4 q^{49} + 40 q^{51} + 4 q^{53} + 6 q^{55} - 12 q^{59} - 2 q^{61} + 60 q^{63} - 10 q^{65} + 6 q^{67} + 52 q^{69} - 72 q^{71} - 4 q^{75} + 32 q^{77} - 36 q^{79} - 28 q^{81} + 22 q^{87} + 24 q^{89} + 22 q^{91} - 96 q^{93} - 10 q^{95} + 60 q^{97}+O(q^{100}) $ 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9 + 6 * q^11 - 2 * q^13 + 4 * q^17 - 30 * q^19 - 6 * q^23 - 16 * q^25 - 44 * q^27 - 16 * q^29 + 24 * q^33 + 6 * q^35 - 24 * q^37 + 8 * q^39 - 24 * q^41 - 6 * q^43 + 12 * q^45 - 4 * q^49 + 40 * q^51 + 4 * q^53 + 6 * q^55 - 12 * q^59 - 2 * q^61 + 60 * q^63 - 10 * q^65 + 6 * q^67 + 52 * q^69 - 72 * q^71 - 4 * q^75 + 32 * q^77 - 36 * q^79 - 28 * q^81 + 22 * q^87 + 24 * q^89 + 22 * q^91 - 96 * q^93 - 10 * q^95 + 60 * 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
$3$	1.52075	+	2.63402i	0.878007	+	1.52075i	0.853525	+	0.521053i	$0.174460\pi$
$3$	1.52075	+	2.63402i	0.878007	+	1.52075i	0.0244825	+	0.999700i	$0.492206\pi$
$4$		0			0
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	2.67664	+	1.54536i	1.01167	+	0.584090i	0.911681	−	0.410898i	$-0.134785\pi$
$7$	2.67664	+	1.54536i	1.01167	+	0.584090i	0.0999920	+	0.994988i	$0.468118\pi$
$8$		0			0
$9$	−3.12538	+	5.41331i	−1.04179	+	1.80444i
$10$		0			0
$11$	5.36505	−	3.09751i	1.61762	−	0.933935i	0.630091	−	0.776521i	$-0.283018\pi$
$11$	5.36505	−	3.09751i	1.61762	−	0.933935i	0.987533	−	0.157414i	$-0.0503157\pi$
$12$		0			0
$13$	2.54049	+	2.55850i	0.704605	+	0.709600i
$13$	2.54049	+	2.55850i	0.704605	+	0.709600i
$14$		0			0
$15$	2.63402	−	1.52075i	0.680101	−	0.392657i
$16$		0			0
$17$	3.24262	−	5.61638i	0.786450	−	1.36217i	−0.141678	−	0.989913i	$-0.545250\pi$
$17$	3.24262	−	5.61638i	0.786450	−	1.36217i	0.928129	−	0.372259i	$-0.121417\pi$
$18$		0			0
$19$	−2.65678	−	1.53389i	−0.609507	−	0.351899i	0.163266	−	0.986582i	$-0.447797\pi$
$19$	−2.65678	−	1.53389i	−0.609507	−	0.351899i	−0.772772	+	0.634683i	$0.781131\pi$
$20$		0			0
$21$			9.40042i			2.05134i
$22$		0			0
$23$	−0.896274	−	1.55239i	−0.186886	−	0.323696i	0.757324	−	0.653039i	$-0.226506\pi$
$23$	−0.896274	−	1.55239i	−0.186886	−	0.323696i	−0.944210	+	0.329343i	$0.893173\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−9.88720			−1.90279
$28$		0			0
$29$	−1.49128	−	2.58297i	−0.276923	−	0.479645i	0.693695	−	0.720269i	$-0.255981\pi$
$29$	−1.49128	−	2.58297i	−0.276923	−	0.479645i	−0.970619	+	0.240623i	$0.922648\pi$
$30$		0			0
$31$			4.34508i			0.780399i	0.920730	+	0.390199i	$0.127594\pi$
$31$			4.34508i			0.780399i	−0.920730	+	0.390199i	$0.872406\pi$
$32$		0			0
$33$	16.3178	+	9.42110i	2.84057	+	1.64000i
$34$		0			0
$35$	1.54536	−	2.67664i	0.261213	−	0.452434i
$36$		0			0
$37$	−8.31867	+	4.80279i	−1.36758	+	0.789574i	−0.990619	−	0.136655i	$-0.956365\pi$
$37$	−8.31867	+	4.80279i	−1.36758	+	0.789574i	−0.376963	+	0.926228i	$0.623032\pi$
$38$		0			0
$39$	−2.87569	+	10.5825i	−0.460478	+	1.69456i
$40$		0			0
$41$	−6.40038	+	3.69526i	−0.999571	+	0.577102i	−0.908121	−	0.418707i	$-0.862483\pi$
$41$	−6.40038	+	3.69526i	−0.999571	+	0.577102i	−0.0914495	+	0.995810i	$0.529150\pi$
$42$		0			0
$43$	2.64990	−	4.58977i	0.404106	−	0.699933i	−0.590111	−	0.807322i	$-0.700916\pi$
$43$	2.64990	−	4.58977i	0.404106	−	0.699933i	0.994217	+	0.107390i	$0.0342492\pi$
$44$		0			0
$45$	5.41331	+	3.12538i	0.806969	+	0.465904i
$46$		0			0
$47$		−	3.46118i		−	0.504864i	−0.967615	−	0.252432i	$-0.918770\pi$
$47$		−	3.46118i		−	0.504864i	0.967615	−	0.252432i	$-0.0812305\pi$
$48$		0			0
$49$	1.27625	+	2.21053i	0.182322	+	0.315790i
$50$		0			0
$51$	19.7249			2.76204
$52$		0			0
$53$	−7.82172			−1.07440			−0.537198	−	0.843456i	$-0.680517\pi$
$53$	−7.82172			−1.07440			−0.537198	+	0.843456i	$0.680517\pi$
$54$		0			0
$55$	−3.09751	−	5.36505i	−0.417669	−	0.723423i
$56$		0			0
$57$		−	9.33068i		−	1.23588i
$58$		0			0
$59$	−1.21101	−	0.699176i	−0.157660	−	0.0910250i	0.419094	−	0.907943i	$-0.362348\pi$
$59$	−1.21101	−	0.699176i	−0.157660	−	0.0910250i	−0.576754	+	0.816918i	$0.695681\pi$
$60$		0			0
$61$	−4.92252	+	8.52605i	−0.630264	+	1.09165i	0.357234	+	0.934015i	$0.383720\pi$
$61$	−4.92252	+	8.52605i	−0.630264	+	1.09165i	−0.987498	+	0.157634i	$0.949613\pi$
$62$		0			0
$63$	−16.7310	+	9.65965i	−2.10791	+	1.21700i
$64$		0			0
$65$	2.55850	−	2.54049i	0.317343	−	0.315109i
$66$		0			0
$67$	1.52639	−	0.881260i	0.186478	−	0.107663i	−0.403855	−	0.914823i	$-0.632330\pi$
$67$	1.52639	−	0.881260i	0.186478	−	0.107663i	0.590333	+	0.807160i	$0.298997\pi$
$68$		0			0
$69$	2.72602	−	4.72161i	0.328175	−	0.568415i
$70$		0			0
$71$	3.60493	+	2.08131i	0.427826	+	0.247005i	0.698420	−	0.715688i	$-0.253887\pi$
$71$	3.60493	+	2.08131i	0.427826	+	0.247005i	−0.270594	+	0.962694i	$0.587220\pi$
$72$		0			0
$73$		−	11.7104i		−	1.37060i	−0.728263	−	0.685298i	$-0.759672\pi$
$73$		−	11.7104i		−	1.37060i	0.728263	−	0.685298i	$-0.240328\pi$
$74$		0			0
$75$	−1.52075	−	2.63402i	−0.175601	−	0.304151i
$76$		0			0
$77$	19.1470			2.18201
$78$		0			0
$79$	−6.58127			−0.740451			−0.370225	−	0.928942i	$-0.620720\pi$
$79$	−6.58127			−0.740451			−0.370225	+	0.928942i	$0.620720\pi$
$80$		0			0
$81$	−5.65985	−	9.80314i	−0.628872	−	1.08924i
$82$		0			0
$83$			4.46298i			0.489875i	0.969539	+	0.244938i	$0.0787675\pi$
$83$			4.46298i			0.489875i	−0.969539	+	0.244938i	$0.921233\pi$
$84$		0			0
$85$	−5.61638	−	3.24262i	−0.609182	−	0.351711i
$86$		0			0
$87$	4.53573	−	7.85612i	0.486281	−	0.842264i
$88$		0			0
$89$	−10.0616	+	5.80904i	−1.06652	+	0.615757i	−0.927229	−	0.374494i	$-0.877816\pi$
$89$	−10.0616	+	5.80904i	−1.06652	+	0.615757i	−0.139294	+	0.990251i	$0.544483\pi$
$90$		0			0
$91$	2.84617	+	10.7741i	0.298360	+	1.12944i
$92$		0			0
$93$	−11.4450	+	6.60779i	−1.18679	+	0.685196i
$94$		0			0
$95$	−1.53389	+	2.65678i	−0.157374	+	0.272580i
$96$		0			0
$97$	−10.6392	−	6.14254i	−1.08025	−	0.623681i	−0.149284	−	0.988794i	$-0.547697\pi$
$97$	−10.6392	−	6.14254i	−1.08025	−	0.623681i	−0.930963	+	0.365114i	$0.881030\pi$
$98$		0			0
$99$			38.7236i			3.89187i
$100$		0			0
$101$	−5.08529	−	8.80797i	−0.506005	−	0.876426i	−0.999976	−	0.00694776i	$-0.997788\pi$
$101$	−5.08529	−	8.80797i	−0.506005	−	0.876426i	0.493971	−	0.869478i	$-0.335545\pi$
$102$		0			0
$103$	−6.53156			−0.643573			−0.321787	−	0.946812i	$-0.604283\pi$
$103$	−6.53156			−0.643573			−0.321787	+	0.946812i	$0.604283\pi$
$104$		0			0
$105$	9.40042			0.917387
$106$		0			0
$107$	9.10227	+	15.7656i	0.879949	+	1.52412i	0.851395	+	0.524525i	$0.175757\pi$
$107$	9.10227	+	15.7656i	0.879949	+	1.52412i	0.0285544	+	0.999592i	$0.490910\pi$
$108$		0			0
$109$			14.6401i			1.40227i	0.713028	+	0.701135i	$0.247323\pi$
$109$			14.6401i			1.40227i	−0.713028	+	0.701135i	$0.752677\pi$
$110$		0			0
$111$	−25.3013	−	14.6077i	−2.40149	−	1.38650i
$112$		0			0
$113$	1.36006	−	2.35569i	0.127943	−	0.221604i	−0.794936	−	0.606693i	$-0.792496\pi$
$113$	1.36006	−	2.35569i	0.127943	−	0.221604i	0.922880	+	0.385089i	$0.125829\pi$
$114$		0			0
$115$	−1.55239	+	0.896274i	−0.144761	+	0.0835780i
$116$		0			0
$117$	−21.7900	+	5.75618i	−2.01448	+	0.532159i
$118$		0			0
$119$	17.3586	−	10.0220i	1.59126	−	0.918715i
$120$		0			0
$121$	13.6892	−	23.7104i	1.24447	−	2.15549i
$122$		0			0
$123$	−19.4668	−	11.2392i	−1.75526	−	1.01340i
$124$		0			0
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	−3.70643	−	6.41972i	−0.328892	−	0.569658i	0.653400	−	0.757013i	$-0.273342\pi$
$127$	−3.70643	−	6.41972i	−0.328892	−	0.569658i	−0.982292	+	0.187354i	$0.940009\pi$
$128$		0			0
$129$	16.1194			1.41923
$130$		0			0
$131$	12.2800			1.07291			0.536456	−	0.843929i	$-0.319763\pi$
$131$	12.2800			1.07291			0.536456	+	0.843929i	$0.319763\pi$
$132$		0			0
$133$	−4.74082	−	8.21134i	−0.411081	−	0.712014i
$134$		0			0
$135$			9.88720i			0.850954i
$136$		0			0
$137$	−12.6117	−	7.28134i	−1.07749	−	0.622087i	−0.147269	−	0.989096i	$-0.547048\pi$
$137$	−12.6117	−	7.28134i	−1.07749	−	0.622087i	−0.930217	+	0.367009i	$0.880382\pi$
$138$		0			0
$139$	1.22468	−	2.12121i	0.103876	−	0.179919i	−0.809402	−	0.587255i	$-0.800209\pi$
$139$	1.22468	−	2.12121i	0.103876	−	0.179919i	0.913278	+	0.407336i	$0.133542\pi$
$140$		0			0
$141$	9.11681	−	5.26359i	0.767774	−	0.443274i
$142$		0			0
$143$	21.5548	+	5.85728i	1.80251	+	0.489810i
$144$		0			0
$145$	−2.58297	+	1.49128i	−0.214504	+	0.123844i
$146$		0			0
$147$	−3.88173	+	6.72335i	−0.320159	+	0.554532i
$148$		0			0
$149$	6.99549	+	4.03885i	0.573092	+	0.330875i	0.758384	−	0.651809i	$-0.225989\pi$
$149$	6.99549	+	4.03885i	0.573092	+	0.330875i	−0.185291	+	0.982684i	$0.559323\pi$
$150$		0			0
$151$		−	5.14185i		−	0.418438i	−0.977869	−	0.209219i	$-0.932908\pi$
$151$		−	5.14185i		−	0.418438i	0.977869	−	0.209219i	$-0.0670922\pi$
$152$		0			0
$153$	20.2688	+	35.1066i	1.63864	+	2.83820i
$154$		0			0
$155$	4.34508			0.349005
$156$		0			0
$157$	10.4778			0.836217			0.418109	−	0.908397i	$-0.362693\pi$
$157$	10.4778			0.836217			0.418109	+	0.908397i	$0.362693\pi$
$158$		0			0
$159$	−11.8949	−	20.6026i	−0.943328	−	1.63389i
$160$		0			0
$161$		−	5.54025i		−	0.436633i
$162$		0			0
$163$	−0.773712	−	0.446703i	−0.0606018	−	0.0349885i	0.469393	−	0.882989i	$-0.344473\pi$
$163$	−0.773712	−	0.446703i	−0.0606018	−	0.0349885i	−0.529995	+	0.848001i	$0.677806\pi$
$164$		0			0
$165$	9.42110	−	16.3178i	0.733432	−	1.27034i
$166$		0			0
$167$	−6.78586	+	3.91782i	−0.525105	+	0.303170i	−0.739021	−	0.673682i	$-0.764712\pi$
$167$	−6.78586	+	3.91782i	−0.525105	+	0.303170i	0.213916	+	0.976852i	$0.431378\pi$
$168$		0			0
$169$	−0.0918374	+	12.9997i	−0.00706442	+	0.999975i
$170$		0			0
$171$	16.6069	−	9.58799i	1.26996	−	0.733212i
$172$		0			0
$173$	9.61828	−	16.6593i	0.731264	−	1.26659i	−0.225079	−	0.974341i	$-0.572264\pi$
$173$	9.61828	−	16.6593i	0.731264	−	1.26659i	0.956343	−	0.292246i	$-0.0944026\pi$
$174$		0			0
$175$	−2.67664	−	1.54536i	−0.202335	−	0.116818i
$176$		0			0
$177$		−	4.25310i		−	0.319682i
$178$		0			0
$179$	−0.115064	−	0.199297i	−0.00860032	−	0.0148962i	0.861693	−	0.507430i	$-0.169404\pi$
$179$	−0.115064	−	0.199297i	−0.00860032	−	0.0148962i	−0.870294	+	0.492533i	$0.836071\pi$
$180$		0			0
$181$	9.26780			0.688870			0.344435	−	0.938810i	$-0.388071\pi$
$181$	9.26780			0.688870			0.344435	+	0.938810i	$0.388071\pi$
$182$		0			0
$183$	−29.9437			−2.21350
$184$		0			0
$185$	4.80279	+	8.31867i	0.353108	+	0.611601i
$186$		0			0
$187$		−	40.1762i		−	2.93798i
$188$		0			0
$189$	−26.4644	−	15.2792i	−1.92500	−	1.11140i
$190$		0			0
$191$	1.07946	−	1.86968i	0.0781070	−	0.135285i	−0.824326	−	0.566115i	$-0.808446\pi$
$191$	1.07946	−	1.86968i	0.0781070	−	0.135285i	0.902433	+	0.430830i	$0.141779\pi$
$192$		0			0
$193$	17.8233	−	10.2903i	1.28295	−	0.740710i	0.305561	−	0.952173i	$-0.401156\pi$
$193$	17.8233	−	10.2903i	1.28295	−	0.740710i	0.977386	+	0.211463i	$0.0678227\pi$
$194$		0			0
$195$	10.5825	+	2.87569i	0.757832	+	0.205932i
$196$		0			0
$197$	−5.37114	+	3.10103i	−0.382678	+	0.220939i	−0.678983	−	0.734154i	$-0.737579\pi$
$197$	−5.37114	+	3.10103i	−0.382678	+	0.220939i	0.296305	+	0.955093i	$0.404246\pi$
$198$		0			0
$199$	2.42864	−	4.20652i	0.172161	−	0.298192i	−0.767014	−	0.641631i	$-0.778258\pi$
$199$	2.42864	−	4.20652i	0.172161	−	0.298192i	0.939175	+	0.343438i	$0.111592\pi$
$200$		0			0
$201$	4.64252	+	2.68036i	0.327458	+	0.189058i
$202$		0			0
$203$		−	9.21822i		−	0.646992i
$204$		0			0
$205$	3.69526	+	6.40038i	0.258088	+	0.447022i
$206$		0			0
$207$	11.2048			0.778787
$208$		0			0
$209$	−19.0050			−1.31460
$210$		0			0
$211$	0.494607	+	0.856684i	0.0340501	+	0.0589766i	0.882548	−	0.470222i	$-0.155826\pi$
$211$	0.494607	+	0.856684i	0.0340501	+	0.0589766i	−0.848498	+	0.529198i	$0.822493\pi$
$212$		0			0
$213$			12.6606i			0.867490i
$214$		0			0
$215$	−4.58977	−	2.64990i	−0.313019	−	0.180722i
$216$		0			0
$217$	−6.71469	+	11.6302i	−0.455823	+	0.789508i
$218$		0			0
$219$	30.8454	−	17.8086i	2.08434	−	1.20339i
$220$		0			0
$221$	22.6073	−	5.97211i	1.52073	−	0.401728i
$222$		0			0
$223$	−2.08118	+	1.20157i	−0.139366	+	0.0804632i	−0.568062	−	0.822986i	$-0.692307\pi$
$223$	−2.08118	+	1.20157i	−0.139366	+	0.0804632i	0.428696	+	0.903449i	$0.358973\pi$
$224$		0			0
$225$	3.12538	−	5.41331i	0.208359	−	0.360888i
$226$		0			0
$227$	22.9049	+	13.2242i	1.52025	+	0.877720i	0.999715	+	0.0238823i	$0.00760270\pi$
$227$	22.9049	+	13.2242i	1.52025	+	0.877720i	0.520540	+	0.853837i	$0.325731\pi$
$228$		0			0
$229$			0.715271i			0.0472664i	0.999721	+	0.0236332i	$0.00752339\pi$
$229$			0.715271i			0.0472664i	−0.999721	+	0.0236332i	$0.992477\pi$
$230$		0			0
$231$	29.1179	+	50.4337i	1.91582	+	3.31830i
$232$		0			0
$233$	−9.27534			−0.607648			−0.303824	−	0.952728i	$-0.598263\pi$
$233$	−9.27534			−0.607648			−0.303824	+	0.952728i	$0.598263\pi$
$234$		0			0
$235$	−3.46118			−0.225782
$236$		0			0
$237$	−10.0085	−	17.3352i	−0.650121	−	1.12604i
$238$		0			0
$239$			12.8779i			0.833001i	0.909136	+	0.416500i	$0.136744\pi$
$239$			12.8779i			0.833001i	−0.909136	+	0.416500i	$0.863256\pi$
$240$		0			0
$241$	−3.02528	−	1.74664i	−0.194875	−	0.112511i	0.399388	−	0.916782i	$-0.369223\pi$
$241$	−3.02528	−	1.74664i	−0.194875	−	0.112511i	−0.594263	+	0.804271i	$0.702556\pi$
$242$		0			0
$243$	2.38366	−	4.12863i	0.152912	−	0.264852i
$244$		0			0
$245$	2.21053	−	1.27625i	0.141226	−	0.0815367i
$246$		0			0
$247$	−2.82505	−	10.6942i	−0.179754	−	0.680456i
$248$		0			0
$249$	−11.7556	+	6.78708i	−0.744979	+	0.430114i
$250$		0			0
$251$	−5.53107	+	9.58010i	−0.349118	+	0.604690i	−0.986093	−	0.166194i	$-0.946852\pi$
$251$	−5.53107	+	9.58010i	−0.349118	+	0.604690i	0.636975	+	0.770884i	$0.280185\pi$
$252$		0			0
$253$	−9.61712	−	5.55244i	−0.604623	−	0.349079i
$254$		0			0
$255$		−	19.7249i		−	1.23522i
$256$		0			0
$257$	−0.281244	−	0.487129i	−0.0175435	−	0.0303863i	0.857120	−	0.515116i	$-0.172251\pi$
$257$	−0.281244	−	0.487129i	−0.0175435	−	0.0303863i	−0.874664	+	0.484730i	$0.838918\pi$
$258$		0			0
$259$	−29.6881			−1.84473
$260$		0			0
$261$	18.6432			1.15399
$262$		0			0
$263$	5.50854	+	9.54107i	0.339671	+	0.588328i	0.984371	−	0.176108i	$-0.0563509\pi$
$263$	5.50854	+	9.54107i	0.339671	+	0.588328i	−0.644700	+	0.764436i	$0.723018\pi$
$264$		0			0
$265$			7.82172i			0.480485i
$266$		0			0
$267$	−30.6023	−	17.6682i	−1.87283	−	1.08128i
$268$		0			0
$269$	7.82588	−	13.5548i	0.477152	−	0.826452i	−0.522505	−	0.852636i	$-0.675002\pi$
$269$	7.82588	−	13.5548i	0.477152	−	0.826452i	0.999657	+	0.0261842i	$0.00833564\pi$
$270$		0			0
$271$	17.8011	−	10.2775i	1.08134	−	0.624312i	0.150082	−	0.988674i	$-0.452046\pi$
$271$	17.8011	−	10.2775i	1.08134	−	0.624312i	0.931257	+	0.364362i	$0.118713\pi$
$272$		0			0
$273$	−24.0510	+	23.8817i	−1.45563	+	1.44538i
$274$		0			0
$275$	−5.36505	+	3.09751i	−0.323525	+	0.186787i
$276$		0			0
$277$	−13.8840	+	24.0478i	−0.834210	+	1.44489i	0.0604628	+	0.998170i	$0.480742\pi$
$277$	−13.8840	+	24.0478i	−0.834210	+	1.44489i	−0.894672	+	0.446723i	$0.852591\pi$
$278$		0			0
$279$	−23.5213	−	13.5800i	−1.40818	−	0.813014i
$280$		0			0
$281$		−	22.7781i		−	1.35883i	−0.733755	−	0.679414i	$-0.762234\pi$
$281$		−	22.7781i		−	1.35883i	0.733755	−	0.679414i	$-0.237766\pi$
$282$		0			0
$283$	−2.25409	−	3.90420i	−0.133992	−	0.232081i	0.791220	−	0.611532i	$-0.209446\pi$
$283$	−2.25409	−	3.90420i	−0.133992	−	0.232081i	−0.925212	+	0.379451i	$0.876113\pi$
$284$		0			0
$285$	−9.33068			−0.552702
$286$		0			0
$287$	−22.8420			−1.34832
$288$		0			0
$289$	−12.5291	−	21.7011i	−0.737009	−	1.27654i
$290$		0			0
$291$		−	37.3652i		−	2.19038i
$292$		0			0
$293$	−8.50606	−	4.91097i	−0.496929	−	0.286902i	0.230515	−	0.973069i	$-0.425959\pi$
$293$	−8.50606	−	4.91097i	−0.496929	−	0.286902i	−0.727445	+	0.686166i	$0.759292\pi$
$294$		0			0
$295$	−0.699176	+	1.21101i	−0.0407076	+	0.0705076i
$296$		0			0
$297$	−53.0453	+	30.6257i	−3.07800	+	1.77708i
$298$		0			0
$299$	1.69482	−	6.23695i	0.0980140	−	0.360692i
$300$		0			0
$301$	14.1856	−	8.19009i	0.817647	−	0.472069i
$302$		0			0
$303$	15.4669	−	26.7895i	0.888552	−	1.53902i
$304$		0			0
$305$	8.52605	+	4.92252i	0.488200	+	0.281862i
$306$		0			0
$307$			19.5716i			1.11701i	0.829501	+	0.558505i	$0.188625\pi$
$307$			19.5716i			1.11701i	−0.829501	+	0.558505i	$0.811375\pi$
$308$		0			0
$309$	−9.93289	−	17.2043i	−0.565062	−	0.978716i
$310$		0			0
$311$	8.70881			0.493831			0.246916	−	0.969037i	$-0.420583\pi$
$311$	8.70881			0.493831			0.246916	+	0.969037i	$0.420583\pi$
$312$		0			0
$313$	−3.24505			−0.183421			−0.0917105	−	0.995786i	$-0.529233\pi$
$313$	−3.24505			−0.183421			−0.0917105	+	0.995786i	$0.529233\pi$
$314$		0			0
$315$	9.65965	+	16.7310i	0.544259	+	0.942685i
$316$		0			0
$317$			20.7194i			1.16372i	0.813290	+	0.581858i	$0.197674\pi$
$317$			20.7194i			1.16372i	−0.813290	+	0.581858i	$0.802326\pi$
$318$		0			0
$319$	−16.0016	−	9.23851i	−0.895915	−	0.517257i
$320$		0			0
$321$	−27.6846	+	47.9511i	−1.54520	+	2.67637i
$322$		0			0
$323$	−17.2298	+	9.94765i	−0.958694	+	0.553502i
$324$		0			0
$325$	−2.54049	−	2.55850i	−0.140921	−	0.141920i
$326$		0			0
$327$	−38.5624	+	22.2640i	−2.13251	+	1.23120i
$328$		0			0
$329$	5.34875	−	9.26431i	0.294886	−	0.510758i
$330$		0			0
$331$	4.07951	+	2.35531i	0.224230	+	0.129459i	0.607907	−	0.794008i	$-0.292009\pi$
$331$	4.07951	+	2.35531i	0.224230	+	0.129459i	−0.383677	+	0.923467i	$0.625342\pi$
$332$		0			0
$333$		−	60.0421i		−	3.29029i
$334$		0			0
$335$	−0.881260	−	1.52639i	−0.0481484	−	0.0833955i
$336$		0			0
$337$	2.62561			0.143026			0.0715131	−	0.997440i	$-0.477217\pi$
$337$	2.62561			0.143026			0.0715131	+	0.997440i	$0.477217\pi$
$338$		0			0
$339$	8.27324			0.449341
$340$		0			0
$341$	13.4589	+	23.3116i	0.728842	+	1.26239i
$342$		0			0
$343$		−	13.7459i		−	0.742211i
$344$		0			0
$345$	−4.72161	−	2.72602i	−0.254203	−	0.146764i
$346$		0			0
$347$	3.71375	−	6.43240i	0.199364	−	0.345309i	−0.748958	−	0.662617i	$-0.769446\pi$
$347$	3.71375	−	6.43240i	0.199364	−	0.345309i	0.948323	+	0.317308i	$0.102779\pi$
$348$		0			0
$349$	9.73318	−	5.61946i	0.521005	−	0.300803i	−0.216341	−	0.976318i	$-0.569412\pi$
$349$	9.73318	−	5.61946i	0.521005	−	0.300803i	0.737346	+	0.675515i	$0.236079\pi$
$350$		0			0
$351$	−25.1183	−	25.2964i	−1.34072	−	1.35022i
$352$		0			0
$353$	3.02944	−	1.74905i	0.161241	−	0.0930924i	−0.417208	−	0.908811i	$-0.636991\pi$
$353$	3.02944	−	1.74905i	0.161241	−	0.0930924i	0.578449	+	0.815718i	$0.303658\pi$
$354$		0			0
$355$	2.08131	−	3.60493i	0.110464	−	0.191330i
$356$		0			0
$357$	52.7963	+	30.4820i	2.79428	+	1.61328i
$358$		0			0
$359$		−	32.3856i		−	1.70925i	−0.519246	−	0.854625i	$-0.673787\pi$
$359$		−	32.3856i		−	1.70925i	0.519246	−	0.854625i	$-0.326213\pi$
$360$		0			0
$361$	−4.79435	−	8.30406i	−0.252334	−	0.437056i
$362$		0			0
$363$	83.2714			4.37062
$364$		0			0
$365$	−11.7104			−0.612949
$366$		0			0
$367$	6.25931	+	10.8414i	0.326734	+	0.565919i	0.981862	−	0.189599i	$-0.0607187\pi$
$367$	6.25931	+	10.8414i	0.326734	+	0.565919i	−0.655128	+	0.755518i	$0.727385\pi$
$368$		0			0
$369$		−	46.1963i		−	2.40488i
$370$		0			0
$371$	−20.9359	−	12.0873i	−1.08694	−	0.627544i
$372$		0			0
$373$	8.65692	−	14.9942i	0.448238	−	0.776372i	−0.550033	−	0.835143i	$-0.685385\pi$
$373$	8.65692	−	14.9942i	0.448238	−	0.776372i	0.998271	+	0.0587712i	$0.0187183\pi$
$374$		0			0
$375$	−2.63402	+	1.52075i	−0.136020	+	0.0785313i
$376$		0			0
$377$	2.81995	−	10.3774i	0.145235	−	0.534465i
$378$		0			0
$379$	−12.3989	+	7.15848i	−0.636886	+	0.367706i	−0.783414	−	0.621500i	$-0.786524\pi$
$379$	−12.3989	+	7.15848i	−0.636886	+	0.367706i	0.146528	+	0.989207i	$0.453190\pi$
$380$		0			0
$381$	11.2731	−	19.5256i	0.577540	−	1.00033i
$382$		0			0
$383$	−24.4985	−	14.1442i	−1.25182	−	0.722736i	−0.280346	−	0.959899i	$-0.590449\pi$
$383$	−24.4985	−	14.1442i	−1.25182	−	0.722736i	−0.971470	+	0.237163i	$0.923782\pi$
$384$		0			0
$385$		−	19.1470i		−	0.975824i
$386$		0			0
$387$	16.5639	+	28.6895i	0.841990	+	1.45837i
$388$		0			0
$389$	12.7931			0.648638			0.324319	−	0.945948i	$-0.394865\pi$
$389$	12.7931			0.648638			0.324319	+	0.945948i	$0.394865\pi$
$390$		0			0
$391$	−11.6251			−0.587907
$392$		0			0
$393$	18.6749	+	32.3459i	0.942024	+	1.63163i
$394$		0			0
$395$			6.58127i			0.331140i
$396$		0			0
$397$	−13.9023	−	8.02648i	−0.697735	−	0.402838i	0.108768	−	0.994067i	$-0.465309\pi$
$397$	−13.9023	−	8.02648i	−0.697735	−	0.402838i	−0.806503	+	0.591229i	$0.798643\pi$
$398$		0			0
$399$	14.4192	−	24.9748i	0.721864	−	1.25031i
$400$		0			0
$401$	−16.9103	+	9.76314i	−0.844458	+	0.487548i	−0.858777	−	0.512349i	$-0.828775\pi$
$401$	−16.9103	+	9.76314i	−0.844458	+	0.487548i	0.0143191	+	0.999897i	$0.495442\pi$
$402$		0			0
$403$	−11.1169	+	11.0386i	−0.553771	+	0.549873i
$404$		0			0
$405$	−9.80314	+	5.65985i	−0.487122	+	0.281240i
$406$		0			0
$407$	−29.7534	+	51.5344i	−1.47482	+	2.55447i
$408$		0			0
$409$	13.1641	+	7.60030i	0.650923	+	0.375810i	0.788810	−	0.614637i	$-0.210698\pi$
$409$	13.1641	+	7.60030i	0.650923	+	0.375810i	−0.137887	+	0.990448i	$0.544031\pi$
$410$		0			0
$411$		−	44.2925i		−	2.18479i
$412$		0			0
$413$	−2.16095	−	3.74288i	−0.106334	−	0.184175i
$414$		0			0
$415$	4.46298			0.219079
$416$		0			0
$417$	7.44975			0.364816
$418$		0			0
$419$	−9.67886	−	16.7643i	−0.472843	−	0.818989i	0.526673	−	0.850068i	$-0.323439\pi$
$419$	−9.67886	−	16.7643i	−0.472843	−	0.818989i	−0.999517	+	0.0310787i	$0.990106\pi$
$420$		0			0
$421$			30.6285i			1.49274i	0.665530	+	0.746371i	$0.268205\pi$
$421$			30.6285i			1.49274i	−0.665530	+	0.746371i	$0.731795\pi$
$422$		0			0
$423$	18.7364	+	10.8175i	0.910996	+	0.525964i
$424$		0			0
$425$	−3.24262	+	5.61638i	−0.157290	+	0.272434i
$426$		0			0
$427$	−26.3516	+	15.2141i	−1.27524	+	0.736261i
$428$		0			0
$429$	17.3514	+	65.6834i	0.837732	+	3.17122i
$430$		0			0
$431$	13.3769	−	7.72314i	0.644341	−	0.372011i	−0.141943	−	0.989875i	$-0.545335\pi$
$431$	13.3769	−	7.72314i	0.644341	−	0.372011i	0.786285	+	0.617864i	$0.212002\pi$
$432$		0			0
$433$	−13.3779	+	23.1713i	−0.642903	+	1.11354i	0.341879	+	0.939744i	$0.388937\pi$
$433$	−13.3779	+	23.1713i	−0.642903	+	1.11354i	−0.984782	+	0.173796i	$0.944397\pi$
$434$		0			0
$435$	−7.85612	−	4.53573i	−0.376672	−	0.217472i
$436$		0			0
$437$			5.49915i			0.263060i
$438$		0			0
$439$	14.5047	+	25.1229i	0.692272	+	1.19905i	0.971092	+	0.238707i	$0.0767236\pi$
$439$	14.5047	+	25.1229i	0.692272	+	1.19905i	−0.278819	+	0.960344i	$0.589943\pi$
$440$		0			0
$441$	−15.9551			−0.759766
$442$		0			0
$443$	19.9797			0.949264			0.474632	−	0.880184i	$-0.342581\pi$
$443$	19.9797			0.949264			0.474632	+	0.880184i	$0.342581\pi$
$444$		0			0
$445$	5.80904	+	10.0616i	0.275375	+	0.476964i
$446$		0			0
$447$			24.5683i			1.16204i
$448$		0			0
$449$	24.2193	+	13.9830i	1.14298	+	0.659900i	0.947167	−	0.320741i	$-0.103932\pi$
$449$	24.2193	+	13.9830i	1.14298	+	0.659900i	0.195814	+	0.980641i	$0.437265\pi$
$450$		0			0
$451$	−22.8922	+	39.6505i	−1.07795	+	1.86707i
$452$		0			0
$453$	13.5438	−	7.81949i	0.636341	−	0.367392i
$454$		0			0
$455$	10.7741	−	2.84617i	0.505099	−	0.133430i
$456$		0			0
$457$	28.0087	−	16.1708i	1.31019	−	0.756439i	0.328064	−	0.944656i	$-0.393604\pi$
$457$	28.0087	−	16.1708i	1.31019	−	0.756439i	0.982128	+	0.188216i	$0.0602706\pi$
$458$		0			0
$459$	−32.0604	+	55.5303i	−1.49645	+	2.59193i
$460$		0			0
$461$	−1.68552	−	0.973133i	−0.0785023	−	0.0453233i	0.460235	−	0.887797i	$-0.347765\pi$
$461$	−1.68552	−	0.973133i	−0.0785023	−	0.0453233i	−0.538737	+	0.842474i	$0.681098\pi$
$462$		0			0
$463$			36.4860i			1.69565i	0.530279	+	0.847823i	$0.322087\pi$
$463$			36.4860i			1.69565i	−0.530279	+	0.847823i	$0.677913\pi$
$464$		0			0
$465$	6.60779	+	11.4450i	0.306429	+	0.530750i
$466$		0			0
$467$	35.9368			1.66296			0.831479	−	0.555556i	$-0.187495\pi$
$467$	35.9368			1.66296			0.831479	+	0.555556i	$0.187495\pi$
$468$		0			0
$469$	5.44745			0.251540
$470$		0			0
$471$	15.9341	+	27.5987i	0.734205	+	1.27168i
$472$		0			0
$473$		−	32.8324i		−	1.50964i
$474$		0			0
$475$	2.65678	+	1.53389i	0.121901	+	0.0703798i
$476$		0			0
$477$	24.4458	−	42.3414i	1.11930	−	1.93868i
$478$		0			0
$479$	−15.6767	+	9.05094i	−0.716286	+	0.413548i	−0.813384	−	0.581727i	$-0.802377\pi$
$479$	−15.6767	+	9.05094i	−0.716286	+	0.413548i	0.0970982	+	0.995275i	$0.469044\pi$
$480$		0			0
$481$	−33.4214	−	9.08189i	−1.52389	−	0.414099i
$482$		0			0
$483$	14.5931	−	8.42536i	0.664011	−	0.383367i
$484$		0			0
$485$	−6.14254	+	10.6392i	−0.278918	+	0.483101i
$486$		0			0
$487$	−11.7913	−	6.80773i	−0.534317	−	0.308488i	0.208456	−	0.978032i	$-0.433156\pi$
$487$	−11.7913	−	6.80773i	−0.534317	−	0.308488i	−0.742772	+	0.669544i	$0.766490\pi$
$488$		0			0
$489$		−	2.71730i		−	0.122881i
$490$		0			0
$491$	18.5371	+	32.1071i	0.836565	+	1.44897i	0.892749	+	0.450553i	$0.148773\pi$
$491$	18.5371	+	32.1071i	0.836565	+	1.44897i	−0.0561840	+	0.998420i	$0.517893\pi$
$492$		0			0
$493$	−19.3426			−0.871146
$494$		0			0
$495$	38.7236			1.74050
$496$		0			0
$497$	6.43272	+	11.1418i	0.288547	+	0.499778i
$498$		0			0
$499$			10.5828i			0.473749i	0.971540	+	0.236875i	$0.0761231\pi$
$499$			10.5828i			0.473749i	−0.971540	+	0.236875i	$0.923877\pi$
$500$		0			0
$501$	−20.6392	−	11.9161i	−0.922093	−	0.532370i
$502$		0			0
$503$	−5.43223	+	9.40891i	−0.242211	+	0.419522i	−0.961344	−	0.275351i	$-0.911206\pi$
$503$	−5.43223	+	9.40891i	−0.242211	+	0.419522i	0.719133	+	0.694873i	$0.244539\pi$
$504$		0			0
$505$	−8.80797	+	5.08529i	−0.391950	+	0.226292i
$506$		0			0
$507$	−34.3811	+	19.5274i	−1.52692	+	0.867242i
$508$		0			0
$509$	−11.6029	+	6.69892i	−0.514288	+	0.296924i	−0.734595	−	0.678506i	$-0.762628\pi$
$509$	−11.6029	+	6.69892i	−0.514288	+	0.296924i	0.220306	+	0.975431i	$0.429294\pi$
$510$		0			0
$511$	18.0967	−	31.3444i	0.800551	−	1.38659i
$512$		0			0
$513$	26.2681	+	15.1659i	1.15976	+	0.669591i
$514$		0			0
$515$			6.53156i			0.287815i
$516$		0			0
$517$	−10.7210	−	18.5694i	−0.471511	−	0.816680i
$518$		0			0
$519$	58.5081			2.56822
$520$		0			0
$521$	18.5320			0.811900			0.405950	−	0.913895i	$-0.366941\pi$
$521$	18.5320			0.811900			0.405950	+	0.913895i	$0.366941\pi$
$522$		0			0
$523$	−17.5432	−	30.3858i	−0.767113	−	1.32868i	−0.939122	−	0.343583i	$-0.888359\pi$
$523$	−17.5432	−	30.3858i	−0.767113	−	1.32868i	0.172010	−	0.985095i	$-0.444974\pi$
$524$		0			0
$525$		−	9.40042i		−	0.410268i
$526$		0			0
$527$	24.4036	+	14.0894i	1.06304	+	0.613745i
$528$		0			0
$529$	9.89338	−	17.1358i	0.430147	−	0.745037i
$530$		0			0
$531$	7.56972	−	4.37038i	0.328498	−	0.189658i
$532$		0			0
$533$	−25.7144	−	6.98760i	−1.11381	−	0.302666i
$534$		0			0
$535$	15.7656	−	9.10227i	0.681606	−	0.393525i
$536$		0			0
$537$	0.349969	−	0.606164i	0.0151023	−	0.0261579i
$538$		0			0
$539$	13.6943	+	7.90641i	0.589856	+	0.340553i
$540$		0			0
$541$			41.0429i			1.76457i	0.470714	+	0.882286i	$0.343996\pi$
$541$			41.0429i			1.76457i	−0.470714	+	0.882286i	$0.656004\pi$
$542$		0			0
$543$	14.0940	+	24.4116i	0.604833	+	1.04760i
$544$		0			0
$545$	14.6401			0.627115
$546$		0			0
$547$	27.7275			1.18554			0.592771	−	0.805371i	$-0.298034\pi$
$547$	27.7275			1.18554			0.592771	+	0.805371i	$0.298034\pi$
$548$		0			0
$549$	−30.7695	−	53.2943i	−1.31321	−	2.27454i
$550$		0			0
$551$			9.14984i			0.389796i
$552$		0			0
$553$	−17.6157	−	10.1704i	−0.749094	−	0.432490i
$554$		0			0
$555$	−14.6077	+	25.3013i	−0.620063	+	1.07398i
$556$		0			0
$557$	−12.0043	+	6.93067i	−0.508637	+	0.293662i	−0.732273	−	0.681011i	$-0.761541\pi$
$557$	−12.0043	+	6.93067i	−0.508637	+	0.293662i	0.223636	+	0.974673i	$0.428207\pi$
$558$		0			0
$559$	18.4750	−	4.88047i	0.781408	−	0.206422i
$560$		0			0
$561$	105.825	−	61.0981i	4.46794	−	2.57956i
$562$		0			0
$563$	16.6980	−	28.9218i	0.703738	−	1.21891i	−0.263407	−	0.964685i	$-0.584846\pi$
$563$	16.6980	−	28.9218i	0.703738	−	1.21891i	0.967145	−	0.254225i	$-0.0818203\pi$
$564$		0			0
$565$	−2.35569	−	1.36006i	−0.0991045	−	0.0572180i
$566$		0			0
$567$		−	34.9859i		−	1.46927i
$568$		0			0
$569$	14.7539	+	25.5546i	0.618517	+	1.07130i	0.989757	+	0.142766i	$0.0455995\pi$
$569$	14.7539	+	25.5546i	0.618517	+	1.07130i	−0.371240	+	0.928537i	$0.621067\pi$
$570$		0			0
$571$	−40.4206			−1.69155			−0.845775	−	0.533540i	$-0.820861\pi$
$571$	−40.4206			−1.69155			−0.845775	+	0.533540i	$0.820861\pi$
$572$		0			0
$573$	6.56637			0.274314
$574$		0			0
$575$	0.896274	+	1.55239i	0.0373772	+	0.0647393i
$576$		0			0
$577$			16.2824i			0.677847i	0.940814	+	0.338924i	$0.110063\pi$
$577$			16.2824i			0.677847i	−0.940814	+	0.338924i	$0.889937\pi$
$578$		0			0
$579$	54.2096	+	31.2979i	2.25287	+	1.30070i
$580$		0			0
$581$	−6.89689	+	11.9458i	−0.286131	+	0.495594i
$582$		0			0
$583$	−41.9639	+	24.2279i	−1.73797	+	1.00342i
$584$		0			0
$585$	5.75618	+	21.7900i	0.237989	+	0.900904i
$586$		0			0
$587$	6.62733	−	3.82629i	0.273539	−	0.157928i	−0.356956	−	0.934121i	$-0.616185\pi$
$587$	6.62733	−	3.82629i	0.273539	−	0.157928i	0.630495	+	0.776193i	$0.282852\pi$
$588$		0			0
$589$	6.66488	−	11.5439i	0.274622	−	0.475658i
$590$		0			0
$591$	−16.3363	−	9.43179i	−0.671987	−	0.387972i
$592$		0			0
$593$		−	14.4087i		−	0.591695i	−0.955235	−	0.295848i	$-0.904398\pi$
$593$		−	14.4087i		−	0.591695i	0.955235	−	0.295848i	$-0.0956021\pi$
$594$		0			0
$595$	−10.0220	−	17.3586i	−0.410862	−	0.711634i
$596$		0			0
$597$	14.7734			0.604636
$598$		0			0
$599$	−3.99980			−0.163427			−0.0817136	−	0.996656i	$-0.526039\pi$
$599$	−3.99980			−0.163427			−0.0817136	+	0.996656i	$0.526039\pi$
$600$		0			0
$601$	0.0101359	+	0.0175559i	0.000413451	+	0.000716119i	0.866232	−	0.499642i	$-0.166535\pi$
$601$	0.0101359	+	0.0175559i	0.000413451	+	0.000716119i	−0.865819	+	0.500358i	$0.833202\pi$
$602$		0			0
$603$			11.0171i			0.448651i
$604$		0			0
$605$	−23.7104	−	13.6892i	−0.963963	−	0.556544i
$606$		0			0
$607$	5.89836	−	10.2163i	0.239407	−	0.414665i	−0.721137	−	0.692792i	$-0.756380\pi$
$607$	5.89836	−	10.2163i	0.239407	−	0.414665i	0.960544	+	0.278127i	$0.0897136\pi$
$608$		0			0
$609$	24.2810	−	14.0186i	0.983916	−	0.568064i
$610$		0			0
$611$	8.85541	−	8.79308i	0.358252	−	0.355730i
$612$		0			0
$613$	−17.1624	+	9.90874i	−0.693184	+	0.400210i	−0.804804	−	0.593541i	$-0.797730\pi$
$613$	−17.1624	+	9.90874i	−0.693184	+	0.400210i	0.111620	+	0.993751i	$0.464396\pi$
$614$		0			0
$615$	−11.2392	+	19.4668i	−0.453206	+	0.784976i
$616$		0			0
$617$	−7.71489	−	4.45419i	−0.310590	−	0.179319i	0.336601	−	0.941647i	$-0.390723\pi$
$617$	−7.71489	−	4.45419i	−0.310590	−	0.179319i	−0.647190	+	0.762328i	$0.724056\pi$
$618$		0			0
$619$		−	17.6823i		−	0.710710i	−0.934731	−	0.355355i	$-0.884360\pi$
$619$		−	17.6823i		−	0.710710i	0.934731	−	0.355355i	$-0.115640\pi$
$620$		0			0
$621$	8.86164	+	15.3488i	0.355605	+	0.615927i
$622$		0			0
$623$	−35.9082			−1.43863
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−28.9019	−	50.0596i	−1.15423	−	1.99919i
$628$		0			0
$629$			62.2944i			2.48384i
$630$		0			0
$631$	−12.1488	−	7.01411i	−0.483636	−	0.279227i	0.238295	−	0.971193i	$-0.423412\pi$
$631$	−12.1488	−	7.01411i	−0.483636	−	0.279227i	−0.721930	+	0.691966i	$0.756745\pi$
$632$		0			0
$633$	−1.50435	+	2.60561i	−0.0597925	+	0.103564i
$634$		0			0
$635$	−6.41972	+	3.70643i	−0.254759	+	0.147085i
$636$		0			0
$637$	−2.41334	+	8.88112i	−0.0956202	+	0.351883i
$638$		0			0
$639$	−22.5335	+	13.0097i	−0.891412	+	0.514657i
$640$		0			0
$641$	0.933393	−	1.61668i	0.0368668	−	0.0638552i	−0.847003	−	0.531588i	$-0.821596\pi$
$641$	0.933393	−	1.61668i	0.0368668	−	0.0638552i	0.883870	+	0.467733i	$0.154929\pi$
$642$		0			0
$643$	−20.9377	−	12.0884i	−0.825702	−	0.476719i	0.0266766	−	0.999644i	$-0.491508\pi$
$643$	−20.9377	−	12.0884i	−0.825702	−	0.476719i	−0.852379	+	0.522925i	$0.824841\pi$
$644$		0			0
$645$		−	16.1194i		−	0.634700i
$646$		0			0
$647$	−15.0185	−	26.0128i	−0.590438	−	1.02267i	−0.994173	−	0.107793i	$-0.965622\pi$
$647$	−15.0185	−	26.0128i	−0.590438	−	1.02267i	0.403735	−	0.914876i	$-0.367712\pi$
$648$		0			0
$649$	−8.66283			−0.340046
$650$		0			0
$651$	−40.8455			−1.60086
$652$		0			0
$653$	−11.5424	−	19.9920i	−0.451689	−	0.782347i	0.546803	−	0.837262i	$-0.315845\pi$
$653$	−11.5424	−	19.9920i	−0.451689	−	0.782347i	−0.998491	+	0.0549141i	$0.982512\pi$
$654$		0			0
$655$		−	12.2800i		−	0.479820i
$656$		0			0
$657$	63.3919	+	36.5993i	2.47315	+	1.42788i
$658$		0			0
$659$	−9.25948	+	16.0379i	−0.360698	+	0.624747i	−0.988076	−	0.153968i	$-0.950795\pi$
$659$	−9.25948	+	16.0379i	−0.360698	+	0.624747i	0.627378	+	0.778715i	$0.284128\pi$
$660$		0			0
$661$	−10.3917	+	5.99967i	−0.404192	+	0.233360i	−0.688291	−	0.725435i	$-0.741639\pi$
$661$	−10.3917	+	5.99967i	−0.404192	+	0.233360i	0.284099	+	0.958795i	$0.408305\pi$
$662$		0			0
$663$	50.1108	+	50.4661i	1.94614	+	1.95994i
$664$		0			0
$665$	−8.21134	+	4.74082i	−0.318422	+	0.183841i
$666$		0			0
$667$	−2.67319	+	4.63010i	−0.103506	+	0.179278i
$668$		0			0
$669$	−6.32994	−	3.65459i	−0.244729	−	0.141295i
$670$		0			0
$671$			60.9902i			2.35450i
$672$		0			0
$673$	−22.2641	−	38.5625i	−0.858218	−	1.48648i	−0.873628	−	0.486595i	$-0.838239\pi$
$673$	−22.2641	−	38.5625i	−0.858218	−	1.48648i	0.0154099	−	0.999881i	$-0.495095\pi$
$674$		0			0
$675$	9.88720			0.380558
$676$		0			0
$677$	4.47823			0.172112			0.0860561	−	0.996290i	$-0.472574\pi$
$677$	4.47823			0.172112			0.0860561	+	0.996290i	$0.472574\pi$
$678$		0			0
$679$	−18.9848	−	32.8827i	−0.728571	−	1.26192i
$680$		0			0
$681$			80.4428i			3.08258i
$682$		0			0
$683$	3.98035	+	2.29806i	0.152304	+	0.0879326i	0.574215	−	0.818704i	$-0.305307\pi$
$683$	3.98035	+	2.29806i	0.152304	+	0.0879326i	−0.421911	+	0.906637i	$0.638641\pi$
$684$		0			0
$685$	−7.28134	+	12.6117i	−0.278206	+	0.481867i
$686$		0			0
$687$	−1.88404	+	1.08775i	−0.0718805	+	0.0415003i
$688$		0			0
$689$	−19.8710	−	20.0119i	−0.757025	−	0.762392i
$690$		0			0
$691$	2.86876	−	1.65628i	0.109133	−	0.0630078i	−0.444440	−	0.895809i	$-0.646597\pi$
$691$	2.86876	−	1.65628i	0.109133	−	0.0630078i	0.553573	+	0.832801i	$0.313264\pi$
$692$		0			0
$693$	−59.8418	+	103.649i	−2.27320	+	3.93730i
$694$		0			0
$695$	−2.12121	−	1.22468i	−0.0804621	−	0.0464548i
$696$		0			0
$697$			47.9293i			1.81545i
$698$		0			0
$699$	−14.1055	−	24.4314i	−0.533519	−	0.924082i
$700$		0			0
$701$	44.4676			1.67952			0.839759	−	0.542959i	$-0.182696\pi$
$701$	44.4676			1.67952			0.839759	+	0.542959i	$0.182696\pi$
$702$		0			0
$703$	29.4678			1.11140
$704$		0			0
$705$	−5.26359	−	9.11681i	−0.198238	−	0.343359i
$706$		0			0
$707$		−	31.4343i		−	1.18221i
$708$		0			0
$709$	13.8293	+	7.98436i	0.519371	+	0.299859i	0.736677	−	0.676244i	$-0.236394\pi$
$709$	13.8293	+	7.98436i	0.519371	+	0.299859i	−0.217306	+	0.976103i	$0.569727\pi$
$710$		0			0
$711$	20.5690	−	35.6265i	0.771396	−	1.33610i
$712$		0			0
$713$	6.74526	−	3.89438i	0.252612	−	0.145846i
$714$		0			0
$715$	5.85728	−	21.5548i	0.219050	−	0.806105i
$716$		0			0
$717$	−33.9206	+	19.5841i	−1.26679	+	0.731381i
$718$		0			0
$719$	−17.2084	+	29.8058i	−0.641764	+	1.11157i	0.343274	+	0.939235i	$0.388464\pi$
$719$	−17.2084	+	29.8058i	−0.641764	+	1.11157i	−0.985039	+	0.172333i	$0.944869\pi$
$720$		0			0
$721$	−17.4826	−	10.0936i	−0.651086	−	0.375905i
$722$		0			0
$723$		−	10.6249i		−	0.395143i
$724$		0			0
$725$	1.49128	+	2.58297i	0.0553847	+	0.0959291i
$726$		0			0
$727$	7.77676			0.288424			0.144212	−	0.989547i	$-0.453935\pi$
$727$	7.77676			0.288424			0.144212	+	0.989547i	$0.453935\pi$
$728$		0			0
$729$	−19.4592			−0.720712
$730$		0			0
$731$	−17.1852	−	29.7657i	−0.635619	−	1.10092i
$732$		0			0
$733$			0.931223i			0.0343955i	0.999852	+	0.0171978i	$0.00547448\pi$
$733$			0.931223i			0.0343955i	−0.999852	+	0.0171978i	$0.994526\pi$
$734$		0			0
$735$	6.72335	+	3.88173i	0.247994	+	0.143180i
$736$		0			0
$737$	5.45943	−	9.45601i	0.201101	−	0.348317i
$738$		0			0
$739$	−33.3027	+	19.2273i	−1.22506	+	0.707288i	−0.965992	−	0.258572i	$-0.916748\pi$
$739$	−33.3027	+	19.2273i	−1.22506	+	0.707288i	−0.259066	+	0.965860i	$0.583415\pi$
$740$		0			0
$741$	23.8725	−	23.7045i	0.876980	−	0.870806i
$742$		0			0
$743$	36.8202	−	21.2582i	1.35080	−	0.779886i	0.362440	−	0.932007i	$-0.381944\pi$
$743$	36.8202	−	21.2582i	1.35080	−	0.779886i	0.988362	+	0.152121i	$0.0486103\pi$
$744$		0			0
$745$	4.03885	−	6.99549i	0.147972	−	0.256295i
$746$		0			0
$747$	−24.1595	−	13.9485i	−0.883950	−	0.510349i
$748$		0			0
$749$			56.2650i			2.05588i
$750$		0			0
$751$	7.05453	+	12.2188i	0.257423	+	0.445870i	0.965551	−	0.260214i	$-0.0837932\pi$
$751$	7.05453	+	12.2188i	0.257423	+	0.445870i	−0.708128	+	0.706085i	$0.750460\pi$
$752$		0			0
$753$	−33.6456			−1.22611
$754$		0			0
$755$	−5.14185			−0.187131
$756$		0			0
$757$	−12.5112	−	21.6700i	−0.454727	−	0.787610i	0.543946	−	0.839120i	$-0.316930\pi$
$757$	−12.5112	−	21.6700i	−0.454727	−	0.787610i	−0.998672	+	0.0515105i	$0.983596\pi$
$758$		0			0
$759$		−	33.7756i		−	1.22598i
$760$		0			0
$761$	−14.2177	−	8.20862i	−0.515393	−	0.297562i	0.219655	−	0.975578i	$-0.429507\pi$
$761$	−14.2177	−	8.20862i	−0.515393	−	0.297562i	−0.735048	+	0.678015i	$0.762840\pi$
$762$		0			0
$763$	−22.6242	+	39.1863i	−0.819052	+	1.41864i
$764$		0			0
$765$	35.1066	−	20.2688i	1.26928	−	0.732821i
$766$		0			0
$767$	−1.28771	−	4.87461i	−0.0464966	−	0.176012i
$768$		0			0
$769$	−16.6459	+	9.61052i	−0.600267	+	0.346564i	−0.769146	−	0.639073i	$-0.779318\pi$
$769$	−16.6459	+	9.61052i	−0.600267	+	0.346564i	0.168880	+	0.985637i	$0.445985\pi$
$770$		0			0
$771$	0.855406	−	1.48161i	0.0308067	−	0.0533588i
$772$		0			0
$773$	−11.1605	−	6.44353i	−0.401416	−	0.231758i	0.285679	−	0.958325i	$-0.407781\pi$
$773$	−11.1605	−	6.44353i	−0.401416	−	0.231758i	−0.687095	+	0.726568i	$0.741114\pi$
$774$		0			0
$775$		−	4.34508i		−	0.156080i
$776$		0			0
$777$	−45.1482	−	78.1990i	−1.61968	−	2.80537i
$778$		0			0
$779$	22.6725			0.812327
$780$		0			0
$781$	25.7875			0.922749
$782$		0			0
$783$	14.7446	+	25.5383i	0.526928	+	0.912665i
$784$		0			0
$785$		−	10.4778i		−	0.373968i
$786$		0			0
$787$	16.5436	+	9.55146i	0.589716	+	0.340473i	0.764985	−	0.644048i	$-0.222746\pi$
$787$	16.5436	+	9.55146i	0.589716	+	0.340473i	−0.175269	+	0.984521i	$0.556080\pi$
$788$		0			0
$789$	−16.7543	+	29.0192i	−0.596467	+	1.03311i
$790$		0			0
$791$	7.28075	−	4.20354i	0.258874	−	0.149461i
$792$		0			0
$793$	−34.3195	+	9.06607i	−1.21872	+	0.321946i
$794$		0			0
$795$	−20.6026	+	11.8949i	−0.730698	+	0.421869i
$796$		0			0
$797$	7.11560	−	12.3246i	0.252048	−	0.436559i	−0.712042	−	0.702137i	$-0.752229\pi$
$797$	7.11560	−	12.3246i	0.252048	−	0.436559i	0.964089	+	0.265578i	$0.0855627\pi$
$798$		0			0
$799$	−19.4393	−	11.2233i	−0.687712	−	0.397051i
$800$		0			0
$801$		−	72.6218i		−	2.56597i
$802$		0			0
$803$	−36.2730	−	62.8267i	−1.28005	−	2.21711i
$804$		0			0
$805$	−5.54025			−0.195268
$806$		0			0
$807$	47.6049			1.67577
$808$		0			0
$809$	16.8637	+	29.2087i	0.592895	+	1.02692i	0.993840	+	0.110823i	$0.0353485\pi$
$809$	16.8637	+	29.2087i	0.592895	+	1.02692i	−0.400945	+	0.916102i	$0.631318\pi$
$810$		0			0
$811$			44.7248i			1.57050i	0.619178	+	0.785251i	$0.287466\pi$
$811$			44.7248i			1.57050i	−0.619178	+	0.785251i	$0.712534\pi$
$812$		0			0
$813$	54.1421	+	31.2590i	1.89885	+	1.09630i
$814$		0			0
$815$	−0.446703	+	0.773712i	−0.0156473	+	0.0271020i
$816$		0			0
$817$	−14.0804	+	8.12933i	−0.492611	+	0.284409i
$818$		0			0
$819$	−67.2191	−	18.2660i	−2.34883	−	0.638267i
$820$		0			0
$821$	−24.3917	+	14.0825i	−0.851275	+	0.491484i	−0.861081	−	0.508468i	$-0.830212\pi$
$821$	−24.3917	+	14.0825i	−0.851275	+	0.491484i	0.00980561	+	0.999952i	$0.496879\pi$
$822$		0			0
$823$	−18.7557	+	32.4859i	−0.653784	+	1.13239i	0.328413	+	0.944534i	$0.393486\pi$
$823$	−18.7557	+	32.4859i	−0.653784	+	1.13239i	−0.982197	+	0.187853i	$0.939847\pi$
$824$		0			0
$825$	−16.3178	−	9.42110i	−0.568114	−	0.328001i
$826$		0			0
$827$			8.70866i			0.302830i	0.988470	+	0.151415i	$0.0483829\pi$
$827$			8.70866i			0.302830i	−0.988470	+	0.151415i	$0.951617\pi$
$828$		0			0
$829$	−17.4190	−	30.1705i	−0.604986	−	1.04787i	−0.992054	−	0.125815i	$-0.959846\pi$
$829$	−17.4190	−	30.1705i	−0.604986	−	1.04787i	0.387068	−	0.922051i	$-0.373488\pi$
$830$		0			0
$831$	−84.4566			−2.92977
$832$		0			0
$833$	16.5536			0.573548
$834$		0			0
$835$	3.91782	+	6.78586i	0.135582	+	0.234834i
$836$		0			0
$837$		−	42.9606i		−	1.48494i
$838$		0			0
$839$	29.8823	+	17.2525i	1.03165	+	0.595624i	0.917457	−	0.397835i	$-0.130238\pi$
$839$	29.8823	+	17.2525i	1.03165	+	0.595624i	0.114193	+	0.993459i	$0.463572\pi$
$840$		0			0
$841$	10.0522	−	17.4109i	0.346627	−	0.600375i
$842$		0			0
$843$	59.9980	−	34.6399i	2.06644	−	1.19306i
$844$		0			0
$845$	12.9997	+	0.0918374i	0.447202	+	0.00315930i
$846$		0			0
$847$	73.2819	−	42.3093i	2.51800	−	1.45377i
$848$		0			0
$849$	6.85584	−	11.8747i	0.235292	−	0.407537i
$850$		0			0
$851$	14.9116	+	8.60923i	0.511164	+	0.295121i
$852$		0			0
$853$			13.3341i			0.456552i	0.973596	+	0.228276i	$0.0733088\pi$
$853$			13.3341i			0.456552i	−0.973596	+	0.228276i	$0.926691\pi$
$854$		0			0
$855$	−9.58799	−	16.6069i	−0.327902	−	0.567943i
$856$		0			0
$857$	43.0304			1.46989			0.734946	−	0.678126i	$-0.237208\pi$
$857$	43.0304			1.46989			0.734946	+	0.678126i	$0.237208\pi$
$858$		0			0
$859$	49.9836			1.70542			0.852708	−	0.522387i	$-0.174958\pi$
$859$	49.9836			1.70542			0.852708	+	0.522387i	$0.174958\pi$
$860$		0			0
$861$	−34.7370	−	60.1662i	−1.18383	−	2.05046i
$862$		0			0
$863$		−	35.0715i		−	1.19385i	−0.802298	−	0.596923i	$-0.796390\pi$
$863$		−	35.0715i		−	1.19385i	0.802298	−	0.596923i	$-0.203610\pi$
$864$		0			0
$865$	−16.6593	−	9.61828i	−0.566435	−	0.327031i
$866$		0			0
$867$	38.1075	−	66.0041i	1.29420	−	2.24162i
$868$		0			0
$869$	−35.3088	+	20.3856i	−1.19777	+	0.691533i
$870$		0			0
$871$	6.13247	+	1.66643i	0.207791	+	0.0564648i
$872$		0			0
$873$	66.5030	−	38.3955i	2.25079	−	1.29949i
$874$		0			0
$875$	−1.54536	+	2.67664i	−0.0522426	+	0.0904868i
$876$		0			0
$877$	−33.9697	−	19.6124i	−1.14707	−	0.662264i	−0.198902	−	0.980019i	$-0.563737\pi$
$877$	−33.9697	−	19.6124i	−1.14707	−	0.662264i	−0.948173	+	0.317756i	$0.897071\pi$
$878$		0			0
$879$		−	29.8735i		−	1.00761i
$880$		0			0
$881$	0.814739	+	1.41117i	0.0274493	+	0.0475435i	0.879424	−	0.476040i	$-0.157928\pi$
$881$	0.814739	+	1.41117i	0.0274493	+	0.0475435i	−0.851974	+	0.523583i	$0.824595\pi$
$882$		0			0
$883$	31.0710			1.04562			0.522812	−	0.852448i	$-0.324883\pi$
$883$	31.0710			1.04562			0.522812	+	0.852448i	$0.324883\pi$
$884$		0			0
$885$	−4.25310			−0.142966
$886$		0			0
$887$	−14.4181	−	24.9729i	−0.484113	−	0.838508i	0.515721	−	0.856757i	$-0.327524\pi$
$887$	−14.4181	−	24.9729i	−0.484113	−	0.838508i	−0.999833	+	0.0182490i	$0.994191\pi$
$888$		0			0
$889$		−	22.9110i		−	0.768411i
$890$		0			0
$891$	−60.7307	−	35.0629i	−2.03456	−	1.17465i
$892$		0			0
$893$	−5.30907	+	9.19558i	−0.177661	+	0.307718i
$894$		0			0
$895$	−0.199297	+	0.115064i	−0.00666178	+	0.00384618i
$896$		0			0
$897$	19.0057	−	5.02067i	0.634581	−	0.167635i
$898$		0			0
$899$	11.2232	−	6.47972i	0.374315	−	0.216111i
$900$		0			0
$901$	−25.3629	+	43.9298i	−0.844960	+	1.46351i
$902$		0			0
$903$	43.1457	+	24.9102i	1.43580	+	0.828959i
$904$		0			0
$905$		−	9.26780i		−	0.308072i
$906$		0			0
$907$	15.5786	+	26.9830i	0.517279	+	0.895954i	0.999799	+	0.0200688i	$0.00638854\pi$
$907$	15.5786	+	26.9830i	0.517279	+	0.895954i	−0.482519	+	0.875885i	$0.660278\pi$
$908$		0			0
$909$	63.5738			2.10861
$910$		0			0
$911$	49.4868			1.63957			0.819786	−	0.572670i	$-0.194093\pi$
$911$	49.4868			1.63957			0.819786	+	0.572670i	$0.194093\pi$
$912$		0			0
$913$	13.8241	+	23.9441i	0.457512	+	0.792434i
$914$		0			0
$915$			29.9437i			0.989909i
$916$		0			0
$917$	32.8692	+	18.9770i	1.08544	+	0.626676i
$918$		0			0
$919$	5.47785	−	9.48792i	0.180698	−	0.312978i	−0.761421	−	0.648258i	$-0.775498\pi$
$919$	5.47785	−	9.48792i	0.180698	−	0.312978i	0.942118	+	0.335281i	$0.108831\pi$
$920$		0			0
$921$	−51.5520	+	29.7636i	−1.69870	+	0.980742i
$922$		0			0
$923$	3.83326	+	14.5107i	0.126173	+	0.477627i
$924$		0			0
$925$	8.31867	−	4.80279i	0.273516	−	0.157915i
$926$		0			0
$927$	20.4136	−	35.3574i	0.670470	−	1.16129i
$928$		0			0
$929$	−27.1056	−	15.6494i	−0.889307	−	0.513442i	−0.0155913	−	0.999878i	$-0.504963\pi$
$929$	−27.1056	−	15.6494i	−0.889307	−	0.513442i	−0.873716	+	0.486437i	$0.838296\pi$
$930$		0			0
$931$		−	7.83053i		−	0.256635i
$932$		0			0
$933$	13.2439	+	22.9392i	0.433587	+	0.750995i
$934$		0			0
$935$	−40.1762			−1.31390
$936$		0			0
$937$	−50.9022			−1.66290			−0.831451	−	0.555598i	$-0.812489\pi$
$937$	−50.9022			−1.66290			−0.831451	+	0.555598i	$0.812489\pi$
$938$		0			0
$939$	−4.93491	−	8.54752i	−0.161045	−	0.278938i
$940$		0			0
$941$			26.0815i			0.850232i	0.905139	+	0.425116i	$0.139767\pi$
$941$			26.0815i			0.850232i	−0.905139	+	0.425116i	$0.860233\pi$
$942$		0			0
$943$	11.4730	+	6.62393i	0.373612	+	0.215705i
$944$		0			0
$945$	−15.2792	+	26.4644i	−0.497034	+	0.860888i
$946$		0			0
$947$	−36.4093	+	21.0209i	−1.18314	+	0.683089i	−0.956740	−	0.290945i	$-0.906030\pi$
$947$	−36.4093	+	21.0209i	−1.18314	+	0.683089i	−0.226405	+	0.974033i	$0.572697\pi$
$948$		0			0
$949$	29.9610	−	29.7501i	0.972574	−	0.965728i
$950$		0			0
$951$	−54.5753	+	31.5091i	−1.76973	+	1.02175i
$952$		0			0
$953$	−9.52765	+	16.5024i	−0.308631	+	0.534564i	−0.978063	−	0.208309i	$-0.933204\pi$
$953$	−9.52765	+	16.5024i	−0.308631	+	0.534564i	0.669432	+	0.742873i	$0.266537\pi$
$954$		0			0
$955$	−1.86968	−	1.07946i	−0.0605014	−	0.0349305i
$956$		0			0
$957$		−	56.1979i		−	1.81662i
$958$		0			0
$959$	−22.5045	−	38.9790i	−0.726710	−	1.25870i
$960$		0			0
$961$	12.1203			0.390978
$962$		0			0
$963$	−113.792			−3.66690
$964$		0			0
$965$	−10.2903	−	17.8233i	−0.331256	−	0.573751i
$966$		0			0
$967$			13.7596i			0.442479i	0.975220	+	0.221239i	$0.0710102\pi$
$967$			13.7596i			0.442479i	−0.975220	+	0.221239i	$0.928990\pi$
$968$		0			0
$969$	−52.4047	−	30.2558i	−1.68348	−	0.971958i
$970$		0			0
$971$	−0.644841	+	1.11690i	−0.0206939	+	0.0358429i	−0.876187	−	0.481971i	$-0.839921\pi$
$971$	−0.644841	+	1.11690i	−0.0206939	+	0.0358429i	0.855493	+	0.517814i	$0.173254\pi$
$972$		0			0
$973$	6.55605	−	3.78514i	0.210177	−	0.121346i
$974$		0			0
$975$	2.87569	−	10.5825i	0.0920957	−	0.338913i
$976$		0			0
$977$	42.5589	−	24.5714i	1.36158	−	0.786109i	0.371746	−	0.928334i	$-0.378759\pi$
$977$	42.5589	−	24.5714i	1.36158	−	0.786109i	0.989834	+	0.142225i	$0.0454258\pi$
$978$		0			0
$979$	−35.9872	+	62.3316i	−1.15016	+	1.99213i
$980$		0			0
$981$	−79.2517	−	45.7560i	−2.53031	−	1.46088i
$982$		0			0
$983$		−	55.0670i		−	1.75637i	−0.478325	−	0.878183i	$-0.658756\pi$
$983$		−	55.0670i		−	1.75637i	0.478325	−	0.878183i	$-0.341244\pi$
$984$		0			0
$985$	3.10103	+	5.37114i	0.0988069	+	0.171139i
$986$		0			0
$987$	32.5365			1.03565
$988$		0			0
$989$	−9.50016			−0.302088
$990$		0			0
$991$	19.8975	+	34.4634i	0.632063	+	1.09477i	0.987129	+	0.159925i	$0.0511251\pi$
$991$	19.8975	+	34.4634i	0.632063	+	1.09477i	−0.355066	+	0.934841i	$0.615542\pi$
$992$		0			0
$993$			14.3274i			0.454665i
$994$		0			0
$995$	−4.20652	−	2.42864i	−0.133356	−	0.0769929i
$996$		0			0
$997$	−24.2267	+	41.9619i	−0.767268	+	1.32895i	0.171771	+	0.985137i	$0.445051\pi$
$997$	−24.2267	+	41.9619i	−0.767268	+	1.32895i	−0.939039	+	0.343810i	$0.888282\pi$
$998$		0			0
$999$	82.2484	−	47.4861i	2.60222	−	1.50239i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.da.f.881.7		16
4.3	odd	2		520.2.bu.b.361.2	yes	16
13.4	even	6	inner	1040.2.da.f.641.7		16
52.11	even	12		6760.2.a.bl.1.7		8
52.15	even	12		6760.2.a.bk.1.7		8
52.43	odd	6		520.2.bu.b.121.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.bu.b.121.2	✓	16	52.43	odd	6
520.2.bu.b.361.2	yes	16	4.3	odd	2
1040.2.da.f.641.7		16	13.4	even	6	inner
1040.2.da.f.881.7		16	1.1	even	1	trivial
6760.2.a.bk.1.7		8	52.15	even	12
6760.2.a.bl.1.7		8	52.11	even	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)

\(f(q)\)	\(=\)	\(q+(1.52075 + 2.63402i) q^{3} -1.00000i q^{5} +(2.67664 + 1.54536i) q^{7} +(-3.12538 + 5.41331i) q^{9} +O(q^{10})\)	\(q+(1.52075 + 2.63402i) q^{3} -1.00000i q^{5} +(2.67664 + 1.54536i) q^{7} +(-3.12538 + 5.41331i) q^{9} +(5.36505 - 3.09751i) q^{11} +(2.54049 + 2.55850i) q^{13} +(2.63402 - 1.52075i) q^{15} +(3.24262 - 5.61638i) q^{17} +(-2.65678 - 1.53389i) q^{19} +9.40042i q^{21} +(-0.896274 - 1.55239i) q^{23} -1.00000 q^{25} -9.88720 q^{27} +(-1.49128 - 2.58297i) q^{29} +4.34508i q^{31} +(16.3178 + 9.42110i) q^{33} +(1.54536 - 2.67664i) q^{35} +(-8.31867 + 4.80279i) q^{37} +(-2.87569 + 10.5825i) q^{39} +(-6.40038 + 3.69526i) q^{41} +(2.64990 - 4.58977i) q^{43} +(5.41331 + 3.12538i) q^{45} -3.46118i q^{47} +(1.27625 + 2.21053i) q^{49} +19.7249 q^{51} -7.82172 q^{53} +(-3.09751 - 5.36505i) q^{55} -9.33068i q^{57} +(-1.21101 - 0.699176i) q^{59} +(-4.92252 + 8.52605i) q^{61} +(-16.7310 + 9.65965i) q^{63} +(2.55850 - 2.54049i) q^{65} +(1.52639 - 0.881260i) q^{67} +(2.72602 - 4.72161i) q^{69} +(3.60493 + 2.08131i) q^{71} -11.7104i q^{73} +(-1.52075 - 2.63402i) q^{75} +19.1470 q^{77} -6.58127 q^{79} +(-5.65985 - 9.80314i) q^{81} +4.46298i q^{83} +(-5.61638 - 3.24262i) q^{85} +(4.53573 - 7.85612i) q^{87} +(-10.0616 + 5.80904i) q^{89} +(2.84617 + 10.7741i) q^{91} +(-11.4450 + 6.60779i) q^{93} +(-1.53389 + 2.65678i) q^{95} +(-10.6392 - 6.14254i) q^{97} +38.7236i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9}+O(q^{10}) \) 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9	\( 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9} + 6 q^{11} - 2 q^{13} + 4 q^{17} - 30 q^{19} - 6 q^{23} - 16 q^{25} - 44 q^{27} - 16 q^{29} + 24 q^{33} + 6 q^{35} - 24 q^{37} + 8 q^{39} - 24 q^{41} - 6 q^{43} + 12 q^{45} - 4 q^{49} + 40 q^{51} + 4 q^{53} + 6 q^{55} - 12 q^{59} - 2 q^{61} + 60 q^{63} - 10 q^{65} + 6 q^{67} + 52 q^{69} - 72 q^{71} - 4 q^{75} + 32 q^{77} - 36 q^{79} - 28 q^{81} + 22 q^{87} + 24 q^{89} + 22 q^{91} - 96 q^{93} - 10 q^{95} + 60 q^{97}+O(q^{100}) \) 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9 + 6 * q^11 - 2 * q^13 + 4 * q^17 - 30 * q^19 - 6 * q^23 - 16 * q^25 - 44 * q^27 - 16 * q^29 + 24 * q^33 + 6 * q^35 - 24 * q^37 + 8 * q^39 - 24 * q^41 - 6 * q^43 + 12 * q^45 - 4 * q^49 + 40 * q^51 + 4 * q^53 + 6 * q^55 - 12 * q^59 - 2 * q^61 + 60 * q^63 - 10 * q^65 + 6 * q^67 + 52 * q^69 - 72 * q^71 - 4 * q^75 + 32 * q^77 - 36 * q^79 - 28 * q^81 + 22 * q^87 + 24 * q^89 + 22 * q^91 - 96 * q^93 - 10 * q^95 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more