LMFDB - Embedded newform 1764.2.l.d.949.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1764,2,Mod(949,1764)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1764.949"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1764, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.l (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			949.1
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	1764.949
Dual form			1764.2.l.d.961.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73025 - 0.0789082i) q^{3} +2.05408 q^{5} +(2.98755 + 0.273062i) q^{9} -5.05408 q^{11} +(0.500000 - 0.866025i) q^{13} +(-3.55408 - 0.162084i) q^{15} +(-0.136673 + 0.236725i) q^{17} +(2.69076 + 4.66053i) q^{19} -5.32743 q^{23} -0.780738 q^{25} +(-5.14766 - 0.708209i) q^{27} +(4.16372 + 7.21177i) q^{29} +(5.08113 + 8.80077i) q^{31} +(8.74484 + 0.398809i) q^{33} +(-4.08113 - 7.06872i) q^{37} +(-0.933463 + 1.45899i) q^{39} +(2.52704 - 4.37697i) q^{41} +(-2.30039 - 3.98439i) q^{43} +(6.13667 + 0.560893i) q^{45} +(-0.690757 + 1.19643i) q^{47} +(0.255158 - 0.398809i) q^{51} +(-1.71780 + 2.97532i) q^{53} -10.3815 q^{55} +(-4.28794 - 8.27621i) q^{57} +(-0.890369 - 1.54216i) q^{59} +(-0.390369 + 0.676139i) q^{61} +(1.02704 - 1.77889i) q^{65} +(4.19076 + 7.25860i) q^{67} +(9.21780 + 0.420378i) q^{69} -7.78074 q^{71} +(-4.69076 + 8.12463i) q^{73} +(1.35087 + 0.0616067i) q^{75} +(-6.47150 + 11.2090i) q^{79} +(8.85087 + 1.63157i) q^{81} +(2.86333 + 4.95943i) q^{83} +(-0.280738 + 0.486253i) q^{85} +(-6.63521 - 12.8067i) q^{87} +(6.90856 + 11.9660i) q^{89} +(-8.09718 - 15.6285i) q^{93} +(5.52704 + 9.57312i) q^{95} +(1.10963 + 1.92194i) q^{97} +(-15.0993 - 1.38008i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{3} - 6 q^{5} - 4 q^{9} - 12 q^{11} + 3 q^{13} - 3 q^{15} - 3 q^{19} - 12 q^{23} + 12 q^{25} - 7 q^{27} + 15 q^{29} + 3 q^{31} + 15 q^{33} + 3 q^{37} - 2 q^{39} + 6 q^{41} - 3 q^{43} + 36 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) $ 6 * q - 4 * q^3 - 6 * q^5 - 4 * q^9 - 12 * q^11 + 3 * q^13 - 3 * q^15 - 3 * q^19 - 12 * q^23 + 12 * q^25 - 7 * q^27 + 15 * q^29 + 3 * q^31 + 15 * q^33 + 3 * q^37 - 2 * q^39 + 6 * q^41 - 3 * q^43 + 36 * q^45 + 15 * q^47 + 39 * q^51 + 18 * q^53 - 24 * q^55 + 7 * q^57 + 3 * q^59 + 6 * q^61 - 3 * q^65 + 6 * q^67 + 27 * q^69 - 30 * q^71 - 9 * q^73 - 13 * q^75 - 3 * q^79 + 32 * q^81 + 18 * q^83 + 15 * q^85 + 6 * q^87 - 6 * q^89 - 35 * q^93 + 24 * q^95 + 15 * q^97 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.73025	−	0.0789082i	−0.998962	−	0.0455577i
$3$	−1.73025	−	0.0789082i	−0.998962	−	0.0455577i
$4$		0			0
$5$	2.05408			0.918614			0.459307	−	0.888277i	$-0.348098\pi$
$5$	2.05408			0.918614			0.459307	+	0.888277i	$0.348098\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	2.98755	+	0.273062i	0.995849	+	0.0910208i
$10$		0			0
$11$	−5.05408			−1.52386			−0.761932	−	0.647657i	$-0.775749\pi$
$11$	−5.05408			−1.52386			−0.761932	+	0.647657i	$0.775749\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	0.926995	+	0.375073i	$0.122382\pi$
$14$		0			0
$15$	−3.55408	−	0.162084i	−0.917661	−	0.0418500i
$16$		0			0
$17$	−0.136673	+	0.236725i	−0.0331481	+	0.0574142i	−0.882124	−	0.471018i	$-0.843887\pi$
$17$	−0.136673	+	0.236725i	−0.0331481	+	0.0574142i	0.848975	+	0.528432i	$0.177220\pi$
$18$		0			0
$19$	2.69076	+	4.66053i	0.617302	+	1.06920i	0.989976	+	0.141236i	$0.0451077\pi$
$19$	2.69076	+	4.66053i	0.617302	+	1.06920i	−0.372674	+	0.927962i	$0.621559\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−5.32743			−1.11085			−0.555423	−	0.831568i	$-0.687444\pi$
$23$	−5.32743			−1.11085			−0.555423	+	0.831568i	$0.687444\pi$
$24$		0			0
$25$	−0.780738			−0.156148
$26$		0			0
$27$	−5.14766	−	0.708209i	−0.990668	−	0.136295i
$28$		0			0
$29$	4.16372	+	7.21177i	0.773183	+	1.33919i	0.935810	+	0.352504i	$0.114670\pi$
$29$	4.16372	+	7.21177i	0.773183	+	1.33919i	−0.162628	+	0.986687i	$0.551997\pi$
$30$		0			0
$31$	5.08113	+	8.80077i	0.912597	+	1.58066i	0.810382	+	0.585903i	$0.199260\pi$
$31$	5.08113	+	8.80077i	0.912597	+	1.58066i	0.102216	+	0.994762i	$0.467407\pi$
$32$		0			0
$33$	8.74484	+	0.398809i	1.52228	+	0.0694237i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.08113	−	7.06872i	−0.670933	−	1.16209i	−0.977640	−	0.210286i	$-0.932560\pi$
$37$	−4.08113	−	7.06872i	−0.670933	−	1.16209i	0.306707	−	0.951804i	$-0.400773\pi$
$38$		0			0
$39$	−0.933463	+	1.45899i	−0.149474	+	0.233625i
$40$		0			0
$41$	2.52704	−	4.37697i	0.394658	−	0.683567i	−0.598400	−	0.801198i	$-0.704197\pi$
$41$	2.52704	−	4.37697i	0.394658	−	0.683567i	0.993057	+	0.117631i	$0.0375299\pi$
$42$		0			0
$43$	−2.30039	−	3.98439i	−0.350806	−	0.607614i	0.635585	−	0.772031i	$-0.280759\pi$
$43$	−2.30039	−	3.98439i	−0.350806	−	0.607614i	−0.986391	+	0.164417i	$0.947426\pi$
$44$		0			0
$45$	6.13667	+	0.560893i	0.914801	+	0.0836130i
$46$		0			0
$47$	−0.690757	+	1.19643i	−0.100757	+	0.174517i	−0.911997	−	0.410197i	$-0.865460\pi$
$47$	−0.690757	+	1.19643i	−0.100757	+	0.174517i	0.811240	+	0.584714i	$0.198793\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	0.255158	−	0.398809i	0.0357293	−	0.0558444i
$52$		0			0
$53$	−1.71780	+	2.97532i	−0.235958	+	0.408691i	−0.959551	−	0.281536i	$-0.909156\pi$
$53$	−1.71780	+	2.97532i	−0.235958	+	0.408691i	0.723593	+	0.690227i	$0.242489\pi$
$54$		0			0
$55$	−10.3815			−1.39984
$56$		0			0
$57$	−4.28794	−	8.27621i	−0.567951	−	1.09621i
$58$		0			0
$59$	−0.890369	−	1.54216i	−0.115916	−	0.200773i	0.802229	−	0.597016i	$-0.203647\pi$
$59$	−0.890369	−	1.54216i	−0.115916	−	0.200773i	−0.918146	+	0.396243i	$0.870314\pi$
$60$		0			0
$61$	−0.390369	+	0.676139i	−0.0499816	+	0.0865707i	−0.889934	−	0.456090i	$-0.849250\pi$
$61$	−0.390369	+	0.676139i	−0.0499816	+	0.0865707i	0.839952	+	0.542660i	$0.182583\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.02704	−	1.77889i	0.127389	−	0.220644i
$66$		0			0
$67$	4.19076	+	7.25860i	0.511982	+	0.886780i	0.999904	+	0.0138919i	$0.00442207\pi$
$67$	4.19076	+	7.25860i	0.511982	+	0.886780i	−0.487921	+	0.872888i	$0.662245\pi$
$68$		0			0
$69$	9.21780	+	0.420378i	1.10969	+	0.0506076i
$70$		0			0
$71$	−7.78074			−0.923404			−0.461702	−	0.887035i	$-0.652761\pi$
$71$	−7.78074			−0.923404			−0.461702	+	0.887035i	$0.652761\pi$
$72$		0			0
$73$	−4.69076	+	8.12463i	−0.549012	+	0.950916i	0.449331	+	0.893365i	$0.351662\pi$
$73$	−4.69076	+	8.12463i	−0.549012	+	0.950916i	−0.998343	+	0.0575506i	$0.981671\pi$
$74$		0			0
$75$	1.35087	+	0.0616067i	0.155985	+	0.00711373i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−6.47150	+	11.2090i	−0.728100	+	1.26111i	0.229585	+	0.973289i	$0.426263\pi$
$79$	−6.47150	+	11.2090i	−0.728100	+	1.26111i	−0.957685	+	0.287818i	$0.907070\pi$
$80$		0			0
$81$	8.85087	+	1.63157i	0.983430	+	0.181286i
$82$		0			0
$83$	2.86333	+	4.95943i	0.314291	+	0.544368i	0.979287	−	0.202479i	$-0.0648999\pi$
$83$	2.86333	+	4.95943i	0.314291	+	0.544368i	−0.664996	+	0.746847i	$0.731567\pi$
$84$		0			0
$85$	−0.280738	+	0.486253i	−0.0304503	+	0.0527415i
$86$		0			0
$87$	−6.63521	−	12.8067i	−0.711369	−	1.37303i
$88$		0			0
$89$	6.90856	+	11.9660i	0.732306	+	1.26839i	0.955895	+	0.293707i	$0.0948890\pi$
$89$	6.90856	+	11.9660i	0.732306	+	1.26839i	−0.223590	+	0.974683i	$0.571778\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−8.09718	−	15.6285i	−0.839638	−	1.62060i
$94$		0			0
$95$	5.52704	+	9.57312i	0.567063	+	0.982181i
$96$		0			0
$97$	1.10963	+	1.92194i	0.112666	+	0.195143i	0.916844	−	0.399245i	$-0.130728\pi$
$97$	1.10963	+	1.92194i	0.112666	+	0.195143i	−0.804178	+	0.594388i	$0.797394\pi$
$98$		0			0
$99$	−15.0993	−	1.38008i	−1.51754	−	0.138703i
$100$		0			0
$101$	2.72665			0.271312			0.135656	−	0.990756i	$-0.456686\pi$
$101$	2.72665			0.271312			0.135656	+	0.990756i	$0.456686\pi$
$102$		0			0
$103$	17.9823			1.77185			0.885924	−	0.463831i	$-0.153525\pi$
$103$	17.9823			1.77185			0.885924	+	0.463831i	$0.153525\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.554084	−	0.959702i	−0.0535653	−	0.0927779i	0.837999	−	0.545671i	$-0.183725\pi$
$107$	−0.554084	−	0.959702i	−0.0535653	−	0.0927779i	−0.891565	+	0.452893i	$0.850392\pi$
$108$		0			0
$109$	−1.69076	+	2.92848i	−0.161945	+	0.280497i	−0.935566	−	0.353151i	$-0.885110\pi$
$109$	−1.69076	+	2.92848i	−0.161945	+	0.280497i	0.773621	+	0.633649i	$0.218443\pi$
$110$		0			0
$111$	6.50360	+	12.5527i	0.617294	+	1.19145i
$112$		0			0
$113$	−9.43560	+	16.3429i	−0.887626	+	1.53741i	−0.0449531	+	0.998989i	$0.514314\pi$
$113$	−9.43560	+	16.3429i	−0.887626	+	1.53741i	−0.842673	+	0.538425i	$0.819020\pi$
$114$		0			0
$115$	−10.9430			−1.02044
$116$		0			0
$117$	1.73025	−	2.45076i	0.159962	−	0.226573i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	14.5438			1.32216
$122$		0			0
$123$	−4.71780	+	7.37385i	−0.425390	+	0.664878i
$124$		0			0
$125$	−11.8741			−1.06205
$126$		0			0
$127$	17.1623			1.52290			0.761452	−	0.648221i	$-0.224487\pi$
$127$	17.1623			1.52290			0.761452	+	0.648221i	$0.224487\pi$
$128$		0			0
$129$	3.66585	+	7.07552i	0.322760	+	0.622965i
$130$		0			0
$131$	−17.8889			−1.56296			−0.781481	−	0.623930i	$-0.785535\pi$
$131$	−17.8889			−1.56296			−0.781481	+	0.623930i	$0.785535\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−10.5737	−	1.45472i	−0.910042	−	0.125202i
$136$		0			0
$137$	−4.49261			−0.383829			−0.191915	−	0.981412i	$-0.561470\pi$
$137$	−4.49261			−0.383829			−0.191915	+	0.981412i	$0.561470\pi$
$138$		0			0
$139$	−9.07227	+	15.7136i	−0.769500	+	1.33281i	0.168334	+	0.985730i	$0.446161\pi$
$139$	−9.07227	+	15.7136i	−0.769500	+	1.33281i	−0.937834	+	0.347083i	$0.887172\pi$
$140$		0			0
$141$	1.28959	−	2.01561i	0.108603	−	0.169745i
$142$		0			0
$143$	−2.52704	+	4.37697i	−0.211322	+	0.366020i
$144$		0			0
$145$	8.55262	+	14.8136i	0.710257	+	1.23020i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.50739			−0.369260			−0.184630	−	0.982808i	$-0.559109\pi$
$149$	−4.50739			−0.369260			−0.184630	+	0.982808i	$0.559109\pi$
$150$		0			0
$151$	−10.9823			−0.893726			−0.446863	−	0.894602i	$-0.647459\pi$
$151$	−10.9823			−0.893726			−0.446863	+	0.894602i	$0.647459\pi$
$152$		0			0
$153$	−0.472958	+	0.669906i	−0.0382364	+	0.0541587i
$154$		0			0
$155$	10.4371	+	18.0775i	0.838325	+	1.45202i
$156$		0			0
$157$	−2.08998	−	3.61995i	−0.166799	−	0.288904i	0.770494	−	0.637447i	$-0.220010\pi$
$157$	−2.08998	−	3.61995i	−0.166799	−	0.288904i	−0.937293	+	0.348544i	$0.886676\pi$
$158$		0			0
$159$	3.20700	−	5.01250i	0.254332	−	0.397517i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	2.80924	+	4.86575i	0.220037	+	0.381115i	0.954819	−	0.297188i	$-0.0960489\pi$
$163$	2.80924	+	4.86575i	0.220037	+	0.381115i	−0.734782	+	0.678303i	$0.762716\pi$
$164$		0			0
$165$	17.9626	+	0.819187i	1.39839	+	0.0637736i
$166$		0			0
$167$	5.44592	−	9.43260i	0.421418	−	0.729917i	−0.574661	−	0.818392i	$-0.694866\pi$
$167$	5.44592	−	9.43260i	0.421418	−	0.729917i	0.996078	+	0.0884750i	$0.0281993\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$		0			0
$171$	6.76615	+	14.6583i	0.517420	+	1.12095i
$172$		0			0
$173$	−7.30039	+	12.6446i	−0.555038	+	0.961354i	0.442862	+	0.896590i	$0.353963\pi$
$173$	−7.30039	+	12.6446i	−0.555038	+	0.961354i	−0.997901	+	0.0647648i	$0.979370\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.41887	+	2.73859i	0.106649	+	0.205845i
$178$		0			0
$179$	11.7448	−	20.3427i	0.877851	−	1.52048i	0.0241559	−	0.999708i	$-0.492310\pi$
$179$	11.7448	−	20.3427i	0.877851	−	1.52048i	0.853695	−	0.520774i	$-0.174356\pi$
$180$		0			0
$181$	−1.39922			−0.104003			−0.0520017	−	0.998647i	$-0.516560\pi$
$181$	−1.39922			−0.104003			−0.0520017	+	0.998647i	$0.516560\pi$
$182$		0			0
$183$	0.728790	−	1.13909i	0.0538737	−	0.0842038i
$184$		0			0
$185$	−8.38298	−	14.5197i	−0.616329	−	1.06751i
$186$		0			0
$187$	0.690757	−	1.19643i	0.0505132	−	0.0874914i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−11.6819	+	20.2336i	−0.845273	+	1.46406i	0.0401112	+	0.999195i	$0.487229\pi$
$191$	−11.6819	+	20.2336i	−0.845273	+	1.46406i	−0.885384	+	0.464860i	$0.846105\pi$
$192$		0			0
$193$	7.27188	+	12.5953i	0.523442	+	0.906628i	0.999628	+	0.0272830i	$0.00868552\pi$
$193$	7.27188	+	12.5953i	0.523442	+	0.906628i	−0.476186	+	0.879345i	$0.657981\pi$
$194$		0			0
$195$	−1.91741	+	2.99689i	−0.137309	+	0.214611i
$196$		0			0
$197$	−17.3422			−1.23558			−0.617791	−	0.786343i	$-0.711972\pi$
$197$	−17.3422			−1.23558			−0.617791	+	0.786343i	$0.711972\pi$
$198$		0			0
$199$	5.77188	−	9.99720i	0.409158	−	0.708682i	−0.585638	−	0.810573i	$-0.699156\pi$
$199$	5.77188	−	9.99720i	0.409158	−	0.708682i	0.994796	+	0.101891i	$0.0324892\pi$
$200$		0			0
$201$	−6.67830	−	12.8899i	−0.471051	−	0.909184i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	5.19076	−	8.99066i	0.362538	−	0.627935i
$206$		0			0
$207$	−15.9159	−	1.45472i	−1.10623	−	0.101110i
$208$		0			0
$209$	−13.5993	−	23.5547i	−0.940684	−	1.62931i
$210$		0			0
$211$	12.2630	−	21.2402i	0.844222	−	1.46223i	−0.0420736	−	0.999115i	$-0.513396\pi$
$211$	12.2630	−	21.2402i	0.844222	−	1.46223i	0.886295	−	0.463120i	$-0.153270\pi$
$212$		0			0
$213$	13.4626	+	0.613964i	0.922445	+	0.0420681i
$214$		0			0
$215$	−4.72519	−	8.18427i	−0.322255	−	0.558163i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	8.75729	−	13.6875i	0.591763	−	0.924917i
$220$		0			0
$221$	0.136673	+	0.236725i	0.00919363	+	0.0159238i
$222$		0			0
$223$	−4.28074	−	7.41446i	−0.286659	−	0.496509i	0.686351	−	0.727271i	$-0.259211\pi$
$223$	−4.28074	−	7.41446i	−0.286659	−	0.496509i	−0.973010	+	0.230762i	$0.925878\pi$
$224$		0			0
$225$	−2.33249	−	0.213190i	−0.155499	−	0.0142127i
$226$		0			0
$227$	−21.1986			−1.40700			−0.703501	−	0.710694i	$-0.748381\pi$
$227$	−21.1986			−1.40700			−0.703501	+	0.710694i	$0.748381\pi$
$228$		0			0
$229$	−4.56148			−0.301431			−0.150715	−	0.988577i	$-0.548158\pi$
$229$	−4.56148			−0.301431			−0.150715	+	0.988577i	$0.548158\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−6.75370	−	11.6977i	−0.442449	−	0.766345i	0.555421	−	0.831569i	$-0.312557\pi$
$233$	−6.75370	−	11.6977i	−0.442449	−	0.766345i	−0.997871	+	0.0652244i	$0.979224\pi$
$234$		0			0
$235$	−1.41887	+	2.45756i	−0.0925571	+	0.160314i
$236$		0			0
$237$	12.0818	−	18.8837i	0.784797	−	1.22663i
$238$		0			0
$239$	6.82743	−	11.8255i	0.441630	−	0.764925i	−0.556181	−	0.831061i	$-0.687734\pi$
$239$	6.82743	−	11.8255i	0.441630	−	0.764925i	0.997811	+	0.0661361i	$0.0210672\pi$
$240$		0			0
$241$	3.21926			0.207371			0.103685	−	0.994610i	$-0.466936\pi$
$241$	3.21926			0.207371			0.103685	+	0.994610i	$0.466936\pi$
$242$		0			0
$243$	−15.1855	−	3.52144i	−0.974150	−	0.225901i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	5.38151			0.342418
$248$		0			0
$249$	−4.56294	−	8.80700i	−0.289164	−	0.558121i
$250$		0			0
$251$	4.38151			0.276559			0.138279	−	0.990393i	$-0.455843\pi$
$251$	4.38151			0.276559			0.138279	+	0.990393i	$0.455843\pi$
$252$		0			0
$253$	26.9253			1.69278
$254$		0			0
$255$	0.524117	−	0.819187i	0.0328215	−	0.0512995i
$256$		0			0
$257$	11.4533			0.714438			0.357219	−	0.934021i	$-0.383725\pi$
$257$	11.4533			0.714438			0.357219	+	0.934021i	$0.383725\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	10.4700	+	22.6824i	0.648079	+	1.40401i
$262$		0			0
$263$	−6.83482			−0.421453			−0.210727	−	0.977545i	$-0.567583\pi$
$263$	−6.83482			−0.421453			−0.210727	+	0.977545i	$0.567583\pi$
$264$		0			0
$265$	−3.52850	+	6.11155i	−0.216754	+	0.375429i
$266$		0			0
$267$	−11.0093	−	21.2493i	−0.673760	−	1.30044i
$268$		0			0
$269$	−4.83628	+	8.37669i	−0.294873	+	0.510736i	−0.974955	−	0.222400i	$-0.928611\pi$
$269$	−4.83628	+	8.37669i	−0.294873	+	0.510736i	0.680082	+	0.733136i	$0.261944\pi$
$270$		0			0
$271$	6.41887	+	11.1178i	0.389919	+	0.675359i	0.992438	−	0.122745i	$-0.0391697\pi$
$271$	6.41887	+	11.1178i	0.389919	+	0.675359i	−0.602519	+	0.798104i	$0.705836\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.94592			0.237948
$276$		0			0
$277$	11.5831			0.695959			0.347980	−	0.937502i	$-0.386868\pi$
$277$	11.5831			0.695959			0.347980	+	0.937502i	$0.386868\pi$
$278$		0			0
$279$	12.7769	+	27.6802i	0.764936	+	1.65717i
$280$		0			0
$281$	2.46410	+	4.26795i	0.146996	+	0.254605i	0.930116	−	0.367266i	$-0.119706\pi$
$281$	2.46410	+	4.26795i	0.146996	+	0.254605i	−0.783120	+	0.621871i	$0.786373\pi$
$282$		0			0
$283$	9.30039	+	16.1087i	0.552851	+	0.957565i	0.998067	+	0.0621426i	$0.0197934\pi$
$283$	9.30039	+	16.1087i	0.552851	+	0.957565i	−0.445217	+	0.895423i	$0.646873\pi$
$284$		0			0
$285$	−8.80778	−	17.0000i	−0.521728	−	1.00700i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.46264	+	14.6577i	0.497802	+	0.862219i
$290$		0			0
$291$	−1.76829	−	3.41300i	−0.103659	−	0.200073i
$292$		0			0
$293$	12.3801	−	21.4429i	0.723250	−	1.25271i	−0.236440	−	0.971646i	$-0.575981\pi$
$293$	12.3801	−	21.4429i	0.723250	−	1.25271i	0.959690	−	0.281060i	$-0.0906861\pi$
$294$		0			0
$295$	−1.82889	−	3.16774i	−0.106482	−	0.184433i
$296$		0			0
$297$	26.0167	+	3.57935i	1.50964	+	0.207695i
$298$		0			0
$299$	−2.66372	+	4.61369i	−0.154047	+	0.266817i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−4.71780	−	0.215155i	−0.271030	−	0.0123604i
$304$		0			0
$305$	−0.801851	+	1.38885i	−0.0459138	+	0.0795251i
$306$		0			0
$307$	21.9430			1.25235			0.626176	−	0.779681i	$-0.284619\pi$
$307$	21.9430			1.25235			0.626176	+	0.779681i	$0.284619\pi$
$308$		0			0
$309$	−31.1139	−	1.41895i	−1.77001	−	0.0807213i
$310$		0			0
$311$	−13.5811	−	23.5232i	−0.770115	−	1.33388i	−0.937499	−	0.347987i	$-0.886865\pi$
$311$	−13.5811	−	23.5232i	−0.770115	−	1.33388i	0.167384	−	0.985892i	$-0.446468\pi$
$312$		0			0
$313$	4.27188	−	7.39912i	0.241461	−	0.418223i	−0.719670	−	0.694317i	$-0.755707\pi$
$313$	4.27188	−	7.39912i	0.241461	−	0.418223i	0.961131	+	0.276094i	$0.0890400\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.199612	+	0.345738i	−0.0112113	+	0.0194186i	−0.871577	−	0.490259i	$-0.836902\pi$
$317$	−0.199612	+	0.345738i	−0.0112113	+	0.0194186i	0.860365	+	0.509678i	$0.170235\pi$
$318$		0			0
$319$	−21.0438	−	36.4489i	−1.17822	−	2.04075i
$320$		0			0
$321$	0.882977	+	1.70425i	0.0492830	+	0.0951219i
$322$		0			0
$323$	−1.47102			−0.0818495
$324$		0			0
$325$	−0.390369	+	0.676139i	−0.0216538	+	0.0375054i
$326$		0			0
$327$	3.15652	−	4.93359i	0.174556	−	0.272828i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	2.80924	−	4.86575i	0.154410	−	0.267446i	−0.778434	−	0.627726i	$-0.783986\pi$
$331$	2.80924	−	4.86575i	0.154410	−	0.267446i	0.932844	+	0.360281i	$0.117319\pi$
$332$		0			0
$333$	−10.2624	−	22.2325i	−0.562374	−	1.21834i
$334$		0			0
$335$	8.60817	+	14.9098i	0.470314	+	0.814609i
$336$		0			0
$337$	14.4911	−	25.0994i	0.789383	−	1.36725i	−0.136962	−	0.990576i	$-0.543734\pi$
$337$	14.4911	−	25.0994i	0.789383	−	1.36725i	0.926345	−	0.376675i	$-0.122933\pi$
$338$		0			0
$339$	17.6156	−	27.5329i	0.956746	−	1.49538i
$340$		0			0
$341$	−25.6804	−	44.4798i	−1.39067	−	2.40872i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	18.9341	+	0.863492i	1.01938	+	0.0464889i
$346$		0			0
$347$	−17.2345	−	29.8511i	−0.925198	−	1.60249i	−0.791243	−	0.611502i	$-0.790566\pi$
$347$	−17.2345	−	29.8511i	−0.925198	−	1.60249i	−0.133955	−	0.990987i	$-0.542768\pi$
$348$		0			0
$349$	−8.78074	−	15.2087i	−0.470022	−	0.814102i	0.529390	−	0.848378i	$-0.322421\pi$
$349$	−8.78074	−	15.2087i	−0.470022	−	0.814102i	−0.999412	+	0.0342762i	$0.989087\pi$
$350$		0			0
$351$	−3.18716	+	4.10390i	−0.170118	+	0.219050i
$352$		0			0
$353$	32.8889			1.75050			0.875250	−	0.483671i	$-0.160697\pi$
$353$	32.8889			1.75050			0.875250	+	0.483671i	$0.160697\pi$
$354$		0			0
$355$	−15.9823			−0.848252
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.48181	−	2.56657i	−0.0782071	−	0.135459i	0.824269	−	0.566198i	$-0.191586\pi$
$359$	−1.48181	−	2.56657i	−0.0782071	−	0.135459i	−0.902476	+	0.430739i	$0.858253\pi$
$360$		0			0
$361$	−4.98035	+	8.62622i	−0.262124	+	0.454012i
$362$		0			0
$363$	−25.1644	−	1.14762i	−1.32079	−	0.0602346i
$364$		0			0
$365$	−9.63521	+	16.6887i	−0.504330	+	0.873525i
$366$		0			0
$367$	13.3638			0.697585			0.348792	−	0.937200i	$-0.386592\pi$
$367$	13.3638			0.697585			0.348792	+	0.937200i	$0.386592\pi$
$368$		0			0
$369$	8.74484	−	12.3863i	0.455238	−	0.644808i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	4.60078			0.238219			0.119110	−	0.992881i	$-0.461996\pi$
$373$	4.60078			0.238219			0.119110	+	0.992881i	$0.461996\pi$
$374$		0			0
$375$	20.5452	+	0.936966i	1.06095	+	0.0483847i
$376$		0			0
$377$	8.32743			0.428884
$378$		0			0
$379$	−2.21926			−0.113996			−0.0569979	−	0.998374i	$-0.518153\pi$
$379$	−2.21926			−0.113996			−0.0569979	+	0.998374i	$0.518153\pi$
$380$		0			0
$381$	−29.6950	−	1.35424i	−1.52132	−	0.0693800i
$382$		0			0
$383$	−31.0335			−1.58574			−0.792868	−	0.609394i	$-0.791413\pi$
$383$	−31.0335			−1.58574			−0.792868	+	0.609394i	$0.791413\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−5.78453	−	12.5317i	−0.294044	−	0.637022i
$388$		0			0
$389$	−24.8348			−1.25918			−0.629588	−	0.776929i	$-0.716776\pi$
$389$	−24.8348			−1.25918			−0.629588	+	0.776929i	$0.716776\pi$
$390$		0			0
$391$	0.728116	−	1.26113i	0.0368224	−	0.0637783i
$392$		0			0
$393$	30.9523	+	1.41158i	1.56134	+	0.0712049i
$394$		0			0
$395$	−13.2930	+	23.0241i	−0.668843	+	1.15847i
$396$		0			0
$397$	−8.86186	−	15.3492i	−0.444764	−	0.770354i	0.553272	−	0.833001i	$-0.313379\pi$
$397$	−8.86186	−	15.3492i	−0.444764	−	0.770354i	−0.998036	+	0.0626467i	$0.980046\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	30.1770			1.50697			0.753485	−	0.657466i	$-0.228371\pi$
$401$	30.1770			1.50697			0.753485	+	0.657466i	$0.228371\pi$
$402$		0			0
$403$	10.1623			0.506218
$404$		0			0
$405$	18.1804	+	3.35139i	0.903393	+	0.166532i
$406$		0			0
$407$	20.6264	+	35.7259i	1.02241	+	1.77087i
$408$		0			0
$409$	−8.38151	−	14.5172i	−0.414439	−	0.717830i	0.580930	−	0.813953i	$-0.302689\pi$
$409$	−8.38151	−	14.5172i	−0.414439	−	0.717830i	−0.995369	+	0.0961236i	$0.969356\pi$
$410$		0			0
$411$	7.77335	+	0.354504i	0.383431	+	0.0174864i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	5.88151	+	10.1871i	0.288712	+	0.500064i
$416$		0			0
$417$	16.9373	−	26.4727i	0.829421	−	1.29637i
$418$		0			0
$419$	−1.44445	+	2.50187i	−0.0705662	+	0.122224i	−0.899150	−	0.437641i	$-0.855814\pi$
$419$	−1.44445	+	2.50187i	−0.0705662	+	0.122224i	0.828583	+	0.559866i	$0.189147\pi$
$420$		0			0
$421$	0.0899807	+	0.155851i	0.00438539	+	0.00759572i	0.868210	−	0.496197i	$-0.165271\pi$
$421$	0.0899807	+	0.155851i	0.00438539	+	0.00759572i	−0.863824	+	0.503793i	$0.831937\pi$
$422$		0			0
$423$	−2.39037	+	3.38576i	−0.116224	+	0.164621i
$424$		0			0
$425$	0.106706	−	0.184820i	0.00517600	−	0.00896509i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	4.71780	−	7.37385i	0.227778	−	0.356013i
$430$		0			0
$431$	2.38298	−	4.12744i	0.114784	−	0.198812i	−0.802909	−	0.596101i	$-0.796716\pi$
$431$	2.38298	−	4.12744i	0.114784	−	0.198812i	0.917693	+	0.397289i	$0.130049\pi$
$432$		0			0
$433$	−27.7630			−1.33421			−0.667103	−	0.744965i	$-0.732466\pi$
$433$	−27.7630			−1.33421			−0.667103	+	0.744965i	$0.732466\pi$
$434$		0			0
$435$	−13.6293	−	26.3061i	−0.653474	−	1.26128i
$436$		0			0
$437$	−14.3348	−	24.8286i	−0.685728	−	1.18771i
$438$		0			0
$439$	2.32889	−	4.03376i	0.111152	−	0.192521i	−0.805083	−	0.593162i	$-0.797879\pi$
$439$	2.32889	−	4.03376i	0.111152	−	0.192521i	0.916235	+	0.400641i	$0.131213\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.38151	−	2.39285i	0.0656377	−	0.113688i	−0.831339	−	0.555766i	$-0.812425\pi$
$443$	1.38151	−	2.39285i	0.0656377	−	0.113688i	0.896977	+	0.442078i	$0.145758\pi$
$444$		0			0
$445$	14.1908	+	24.5791i	0.672706	+	1.16516i
$446$		0			0
$447$	7.79893	+	0.355670i	0.368877	+	0.0168226i
$448$		0			0
$449$	19.9430			0.941168			0.470584	−	0.882355i	$-0.344043\pi$
$449$	19.9430			0.941168			0.470584	+	0.882355i	$0.344043\pi$
$450$		0			0
$451$	−12.7719	+	22.1216i	−0.601405	+	1.04166i
$452$		0			0
$453$	19.0021	+	0.866593i	0.892798	+	0.0407161i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−13.6908	+	23.7131i	−0.640427	+	1.10925i	0.344911	+	0.938635i	$0.387909\pi$
$457$	−13.6908	+	23.7131i	−0.640427	+	1.10925i	−0.985338	+	0.170616i	$0.945424\pi$
$458$		0			0
$459$	0.871198	−	1.12179i	0.0406640	−	0.0523605i
$460$		0			0
$461$	3.02558	+	5.24046i	0.140915	+	0.244072i	0.927842	−	0.372975i	$-0.121662\pi$
$461$	3.02558	+	5.24046i	0.140915	+	0.244072i	−0.786926	+	0.617047i	$0.788329\pi$
$462$		0			0
$463$	8.77188	−	15.1933i	0.407664	−	0.706095i	−0.586964	−	0.809613i	$-0.699677\pi$
$463$	8.77188	−	15.1933i	0.407664	−	0.706095i	0.994628	+	0.103519i	$0.0330101\pi$
$464$		0			0
$465$	−16.6323	−	32.1022i	−0.771304	−	1.48871i
$466$		0			0
$467$	11.8078	+	20.4517i	0.546399	+	0.946391i	0.998517	+	0.0544328i	$0.0173351\pi$
$467$	11.8078	+	20.4517i	0.546399	+	0.946391i	−0.452119	+	0.891958i	$0.649332\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	3.33055	+	6.42835i	0.153464	+	0.296203i
$472$		0			0
$473$	11.6264	+	20.1374i	0.534580	+	0.925920i
$474$		0			0
$475$	−2.10078	−	3.63865i	−0.0963902	−	0.166953i
$476$		0			0
$477$	−5.94445	+	8.41983i	−0.272178	+	0.385518i
$478$		0			0
$479$	38.2527			1.74781			0.873906	−	0.486096i	$-0.161579\pi$
$479$	38.2527			1.74781			0.873906	+	0.486096i	$0.161579\pi$
$480$		0			0
$481$	−8.16225			−0.372167
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.27928	+	3.94782i	0.103497	+	0.179261i
$486$		0			0
$487$	3.28959	−	5.69774i	0.149066	−	0.258189i	−0.781817	−	0.623508i	$-0.785707\pi$
$487$	3.28959	−	5.69774i	0.149066	−	0.258189i	0.930882	+	0.365319i	$0.119040\pi$
$488$		0			0
$489$	−4.47675	−	8.64065i	−0.202446	−	0.390744i
$490$		0			0
$491$	1.02704	−	1.77889i	0.0463498	−	0.0802801i	−0.841920	−	0.539603i	$-0.818574\pi$
$491$	1.02704	−	1.77889i	0.0463498	−	0.0802801i	0.888270	+	0.459323i	$0.151908\pi$
$492$		0			0
$493$	−2.27627			−0.102518
$494$		0			0
$495$	−31.0153	−	2.83480i	−1.39403	−	0.127415i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−16.3245			−0.730785			−0.365393	−	0.930854i	$-0.619065\pi$
$499$	−16.3245			−0.730785			−0.365393	+	0.930854i	$0.619065\pi$
$500$		0			0
$501$	−10.1671	+	15.8911i	−0.454233	+	0.709960i
$502$		0			0
$503$	−5.60078			−0.249726			−0.124863	−	0.992174i	$-0.539849\pi$
$503$	−5.60078			−0.249726			−0.124863	+	0.992174i	$0.539849\pi$
$504$		0			0
$505$	5.60078			0.249231
$506$		0			0
$507$	−9.56148	−	18.4548i	−0.424640	−	0.819605i
$508$		0			0
$509$	0.672570			0.0298111			0.0149056	−	0.999889i	$-0.495255\pi$
$509$	0.672570			0.0298111			0.0149056	+	0.999889i	$0.495255\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−10.5505	−	25.8965i	−0.465815	−	1.14336i
$514$		0			0
$515$	36.9371			1.62764
$516$		0			0
$517$	3.49115	−	6.04684i	0.153540	−	0.265940i
$518$		0			0
$519$	13.6293	−	21.3024i	0.598259	−	0.935070i
$520$		0			0
$521$	−13.2267	+	22.9092i	−0.579470	+	1.00367i	0.416070	+	0.909333i	$0.363407\pi$
$521$	−13.2267	+	22.9092i	−0.579470	+	1.00367i	−0.995540	+	0.0943392i	$0.969926\pi$
$522$		0			0
$523$	−13.6534	−	23.6484i	−0.597021	−	1.03407i	−0.993258	−	0.115923i	$-0.963017\pi$
$523$	−13.6534	−	23.6484i	−0.597021	−	1.03407i	0.396237	−	0.918148i	$-0.370316\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.77781			−0.121003
$528$		0			0
$529$	5.38151			0.233979
$530$		0			0
$531$	−2.23891	−	4.85041i	−0.0971605	−	0.210490i
$532$		0			0
$533$	−2.52704	−	4.37697i	−0.109458	−	0.189587i
$534$		0			0
$535$	−1.13814	−	1.97131i	−0.0492059	−	0.0852271i
$536$		0			0
$537$	−21.9267	+	34.2712i	−0.946209	+	1.47891i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	9.66225	+	16.7355i	0.415413	+	0.719516i	0.995472	−	0.0950586i	$-0.0303038\pi$
$541$	9.66225	+	16.7355i	0.415413	+	0.719516i	−0.580059	+	0.814574i	$0.696971\pi$
$542$		0			0
$543$	2.42101	+	0.110410i	0.103895	+	0.00473816i
$544$		0			0
$545$	−3.47296	+	6.01534i	−0.148765	+	0.257669i
$546$		0			0
$547$	9.17111	+	15.8848i	0.392128	+	0.679186i	0.992730	−	0.120362i	$-0.0384056\pi$
$547$	9.17111	+	15.8848i	0.392128	+	0.679186i	−0.600602	+	0.799548i	$0.705072\pi$
$548$		0			0
$549$	−1.35087	+	1.91340i	−0.0576539	+	0.0816620i
$550$		0			0
$551$	−22.4071	+	38.8102i	−0.954574	+	1.65337i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	13.3589	+	25.7843i	0.567055	+	1.09448i
$556$		0			0
$557$	−4.59931	+	7.96625i	−0.194879	+	0.337541i	−0.946861	−	0.321643i	$-0.895765\pi$
$557$	−4.59931	+	7.96625i	−0.194879	+	0.337541i	0.751982	+	0.659184i	$0.229098\pi$
$558$		0			0
$559$	−4.60078			−0.194592
$560$		0			0
$561$	−1.28959	+	2.01561i	−0.0544466	+	0.0850993i
$562$		0			0
$563$	−16.5811	−	28.7194i	−0.698811	−	1.21038i	−0.968879	−	0.247535i	$-0.920379\pi$
$563$	−16.5811	−	28.7194i	−0.698811	−	1.21038i	0.270068	−	0.962841i	$-0.412954\pi$
$564$		0			0
$565$	−19.3815	+	33.5698i	−0.815386	+	1.41229i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−13.1008	+	22.6912i	−0.549213	+	0.951265i	0.449116	+	0.893474i	$0.351739\pi$
$569$	−13.1008	+	22.6912i	−0.549213	+	0.951265i	−0.998329	+	0.0577914i	$0.981594\pi$
$570$		0			0
$571$	−4.89037	−	8.47037i	−0.204656	−	0.354474i	0.745367	−	0.666654i	$-0.232274\pi$
$571$	−4.89037	−	8.47037i	−0.204656	−	0.354474i	−0.950023	+	0.312180i	$0.898941\pi$
$572$		0			0
$573$	21.8092	−	34.0875i	0.911094	−	1.42403i
$574$		0			0
$575$	4.15933			0.173456
$576$		0			0
$577$	−18.1534	+	31.4426i	−0.755736	+	1.30897i	0.189272	+	0.981925i	$0.439387\pi$
$577$	−18.1534	+	31.4426i	−0.755736	+	1.30897i	−0.945008	+	0.327048i	$0.893946\pi$
$578$		0			0
$579$	−11.5883	−	22.3668i	−0.481594	−	0.929533i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	8.68190	−	15.0375i	0.359568	−	0.622789i
$584$		0			0
$585$	3.55408	−	5.03407i	0.146943	−	0.208133i
$586$		0			0
$587$	12.0737	+	20.9123i	0.498336	+	0.863144i	0.999998	−	0.00191995i	$-0.000611139\pi$
$587$	12.0737	+	20.9123i	0.498336	+	0.863144i	−0.501662	+	0.865064i	$0.667278\pi$
$588$		0			0
$589$	−27.3442	+	47.3615i	−1.12670	+	1.95150i
$590$		0			0
$591$	30.0064	+	1.36844i	1.23430	+	0.0562903i
$592$		0			0
$593$	−20.7448	−	35.9311i	−0.851889	−	1.47551i	−0.879502	−	0.475896i	$-0.842124\pi$
$593$	−20.7448	−	35.9311i	−0.851889	−	1.47551i	0.0276133	−	0.999619i	$-0.491209\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−10.7757	+	16.8422i	−0.441019	+	0.689306i
$598$		0			0
$599$	11.3422	+	19.6453i	0.463430	+	0.802685i	0.999129	−	0.0417243i	$-0.0132851\pi$
$599$	11.3422	+	19.6453i	0.463430	+	0.802685i	−0.535699	+	0.844409i	$0.679952\pi$
$600$		0			0
$601$	20.1249	+	34.8573i	0.820912	+	1.42186i	0.905004	+	0.425403i	$0.139867\pi$
$601$	20.1249	+	34.8573i	0.820912	+	1.42186i	−0.0840927	+	0.996458i	$0.526799\pi$
$602$		0			0
$603$	10.5380	+	22.8298i	0.429142	+	0.929700i
$604$		0			0
$605$	29.8741			1.21456
$606$		0			0
$607$	17.3245			0.703180			0.351590	−	0.936154i	$-0.385641\pi$
$607$	17.3245			0.703180			0.351590	+	0.936154i	$0.385641\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.690757	+	1.19643i	0.0279450	+	0.0484022i
$612$		0			0
$613$	16.4823	−	28.5482i	0.665713	−	1.15305i	−0.313378	−	0.949629i	$-0.601461\pi$
$613$	16.4823	−	28.5482i	0.665713	−	1.15305i	0.979091	−	0.203421i	$-0.0652060\pi$
$614$		0			0
$615$	−9.69076	+	15.1465i	−0.390769	+	0.610766i
$616$		0			0
$617$	13.4700	−	23.3308i	0.542283	−	0.939262i	−0.456489	−	0.889729i	$-0.650893\pi$
$617$	13.4700	−	23.3308i	0.542283	−	0.939262i	0.998772	−	0.0495330i	$-0.0157733\pi$
$618$		0			0
$619$	−1.98229			−0.0796750			−0.0398375	−	0.999206i	$-0.512684\pi$
$619$	−1.98229			−0.0796750			−0.0398375	+	0.999206i	$0.512684\pi$
$620$		0			0
$621$	27.4238	+	3.77293i	1.10048	+	0.151403i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−20.4868			−0.819470
$626$		0			0
$627$	21.6716	+	41.8287i	0.865480	+	1.67048i
$628$		0			0
$629$	2.23112			0.0889606
$630$		0			0
$631$	−25.4868			−1.01461			−0.507306	−	0.861766i	$-0.669359\pi$
$631$	−25.4868			−1.01461			−0.507306	+	0.861766i	$0.669359\pi$
$632$		0			0
$633$	−22.8942	+	35.7832i	−0.909961	+	1.42226i
$634$		0			0
$635$	35.2527			1.39896
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−23.2453	−	2.12463i	−0.919571	−	0.0840489i
$640$		0			0
$641$	−40.0846			−1.58325			−0.791623	−	0.611009i	$-0.790764\pi$
$641$	−40.0846			−1.58325			−0.791623	+	0.611009i	$0.790764\pi$
$642$		0			0
$643$	−3.50885	+	6.07751i	−0.138376	+	0.239674i	−0.926882	−	0.375353i	$-0.877521\pi$
$643$	−3.50885	+	6.07751i	−0.138376	+	0.239674i	0.788506	+	0.615027i	$0.210855\pi$
$644$		0			0
$645$	7.52997	+	14.5337i	0.296492	+	0.572264i
$646$		0			0
$647$	5.90709	−	10.2314i	0.232232	−	0.402237i	−0.726233	−	0.687449i	$-0.758731\pi$
$647$	5.90709	−	10.2314i	0.232232	−	0.402237i	0.958465	+	0.285212i	$0.0920639\pi$
$648$		0			0
$649$	4.50000	+	7.79423i	0.176640	+	0.305950i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.273346			0.0106969			0.00534843	−	0.999986i	$-0.498298\pi$
$653$	0.273346			0.0106969			0.00534843	+	0.999986i	$0.498298\pi$
$654$		0			0
$655$	−36.7453			−1.43576
$656$		0			0
$657$	−16.2324	+	22.9918i	−0.633286	+	0.896997i
$658$		0			0
$659$	−7.39970	−	12.8167i	−0.288251	−	0.499266i	0.685141	−	0.728410i	$-0.259741\pi$
$659$	−7.39970	−	12.8167i	−0.288251	−	0.499266i	−0.973392	+	0.229144i	$0.926407\pi$
$660$		0			0
$661$	4.50885	+	7.80956i	0.175374	+	0.303757i	0.940291	−	0.340372i	$-0.110553\pi$
$661$	4.50885	+	7.80956i	0.175374	+	0.303757i	−0.764917	+	0.644129i	$0.777220\pi$
$662$		0			0
$663$	−0.217799	−	0.420378i	−0.00845863	−	0.0163261i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−22.1819	−	38.4202i	−0.858887	−	1.48764i
$668$		0			0
$669$	6.82170	+	13.1667i	0.263742	+	0.509053i
$670$		0			0
$671$	1.97296	−	3.41726i	0.0761652	−	0.131922i
$672$		0			0
$673$	−11.9803	−	20.7506i	−0.461809	−	0.799876i	0.537243	−	0.843428i	$-0.319466\pi$
$673$	−11.9803	−	20.7506i	−0.461809	−	0.799876i	−0.999051	+	0.0435519i	$0.986133\pi$
$674$		0			0
$675$	4.01898	+	0.552926i	0.154690	+	0.0212821i
$676$		0			0
$677$	3.32889	−	5.76581i	0.127940	−	0.221598i	−0.794938	−	0.606690i	$-0.792497\pi$
$677$	3.32889	−	5.76581i	0.127940	−	0.221598i	0.922878	+	0.385092i	$0.125830\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	36.6790	+	1.67275i	1.40554	+	0.0640998i
$682$		0			0
$683$	15.0364	−	26.0438i	0.575351	−	0.996537i	−0.420652	−	0.907222i	$-0.638199\pi$
$683$	15.0364	−	26.0438i	0.575351	−	0.996537i	0.996003	−	0.0893152i	$-0.0284678\pi$
$684$		0			0
$685$	−9.22820			−0.352591
$686$		0			0
$687$	7.89251	+	0.359938i	0.301118	+	0.0137325i
$688$		0			0
$689$	1.71780	+	2.97532i	0.0654429	+	0.113351i
$690$		0			0
$691$	1.63814	−	2.83733i	0.0623176	−	0.107937i	−0.833183	−	0.552997i	$-0.813484\pi$
$691$	1.63814	−	2.83733i	0.0623176	−	0.107937i	0.895501	+	0.445060i	$0.146817\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−18.6352	+	32.2771i	−0.706874	+	1.22434i
$696$		0			0
$697$	0.690757	+	1.19643i	0.0261643	+	0.0453179i
$698$		0			0
$699$	10.7626	+	20.7730i	0.407077	+	0.785706i
$700$		0			0
$701$	−32.2891			−1.21954			−0.609771	−	0.792578i	$-0.708739\pi$
$701$	−32.2891			−1.21954			−0.609771	+	0.792578i	$0.708739\pi$
$702$		0			0
$703$	21.9626	−	38.0404i	0.828337	−	1.43472i
$704$		0			0
$705$	2.64893	−	4.14024i	0.0997645	−	0.155930i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	24.5438	−	42.5111i	0.921761	−	1.59654i	0.125071	−	0.992148i	$-0.460084\pi$
$709$	24.5438	−	42.5111i	0.921761	−	1.59654i	0.796690	−	0.604388i	$-0.206582\pi$
$710$		0			0
$711$	−22.3946	+	31.7202i	−0.839865	+	1.18960i
$712$		0			0
$713$	−27.0693	−	46.8855i	−1.01376	−	1.75588i
$714$		0			0
$715$	−5.19076	+	8.99066i	−0.194123	+	0.336231i
$716$		0			0
$717$	−12.7463	+	19.9223i	−0.476019	+	0.744011i
$718$		0			0
$719$	20.9808	+	36.3399i	0.782453	+	1.35525i	0.930509	+	0.366269i	$0.119365\pi$
$719$	20.9808	+	36.3399i	0.782453	+	1.35525i	−0.148056	+	0.988979i	$0.547302\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−5.57014	−	0.254026i	−0.207156	−	0.00944734i
$724$		0			0
$725$	−3.25077	−	5.63050i	−0.120731	−	0.209112i
$726$		0			0
$727$	14.2434	+	24.6703i	0.528258	+	0.914969i	0.999457	+	0.0329425i	$0.0104878\pi$
$727$	14.2434	+	24.6703i	0.528258	+	0.914969i	−0.471200	+	0.882027i	$0.656179\pi$
$728$		0			0
$729$	25.9969	+	7.29124i	0.962847	+	0.270046i
$730$		0			0
$731$	1.25760			0.0465142
$732$		0			0
$733$	28.5261			1.05363			0.526817	−	0.849979i	$-0.323385\pi$
$733$	28.5261			1.05363			0.526817	+	0.849979i	$0.323385\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−21.1804	−	36.6856i	−0.780192	−	1.35133i
$738$		0			0
$739$	−3.92967	+	6.80639i	−0.144555	+	0.250377i	−0.929207	−	0.369560i	$-0.879508\pi$
$739$	−3.92967	+	6.80639i	−0.144555	+	0.250377i	0.784652	+	0.619937i	$0.212842\pi$
$740$		0			0
$741$	−9.31138	−	0.424646i	−0.342062	−	0.0155998i
$742$		0			0
$743$	3.37364	−	5.84332i	0.123767	−	0.214371i	−0.797483	−	0.603341i	$-0.793836\pi$
$743$	3.37364	−	5.84332i	0.123767	−	0.214371i	0.921250	+	0.388970i	$0.127169\pi$
$744$		0			0
$745$	−9.25856			−0.339207
$746$		0			0
$747$	7.20009	+	15.5984i	0.263438	+	0.570715i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	22.1800			0.809358			0.404679	−	0.914459i	$-0.367383\pi$
$751$	22.1800			0.809358			0.404679	+	0.914459i	$0.367383\pi$
$752$		0			0
$753$	−7.58113	−	0.345738i	−0.276272	−	0.0125994i
$754$		0			0
$755$	−22.5586			−0.820990
$756$		0			0
$757$	−20.3815			−0.740779			−0.370389	−	0.928877i	$-0.620776\pi$
$757$	−20.3815			−0.740779			−0.370389	+	0.928877i	$0.620776\pi$
$758$		0			0
$759$	−46.5875	−	2.12463i	−1.69102	−	0.0771191i
$760$		0			0
$761$	40.6549			1.47374			0.736869	−	0.676036i	$-0.236304\pi$
$761$	40.6549			1.47374			0.736869	+	0.676036i	$0.236304\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.971495	+	1.37604i	−0.0351245	+	0.0497510i
$766$		0			0
$767$	−1.78074			−0.0642987
$768$		0			0
$769$	16.9518	−	29.3615i	0.611299	−	1.05880i	−0.379723	−	0.925100i	$-0.623981\pi$
$769$	16.9518	−	29.3615i	0.611299	−	1.05880i	0.991022	−	0.133701i	$-0.0426861\pi$
$770$		0			0
$771$	−19.8171	−	0.903760i	−0.713696	−	0.0325481i
$772$		0			0
$773$	4.37412	−	7.57620i	0.157326	−	0.272497i	−0.776577	−	0.630022i	$-0.783046\pi$
$773$	4.37412	−	7.57620i	0.157326	−	0.272497i	0.933904	+	0.357525i	$0.116379\pi$
$774$		0			0
$775$	−3.96703	−	6.87110i	−0.142500	−	0.246817i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	27.1986			0.974492
$780$		0			0
$781$	39.3245			1.40714
$782$		0			0
$783$	−16.3260	−	40.0725i	−0.583442	−	1.43208i
$784$		0			0
$785$	−4.29300	−	7.43569i	−0.153224	−	0.265391i
$786$		0			0
$787$	−4.64260	−	8.04122i	−0.165491	−	0.286639i	0.771339	−	0.636425i	$-0.219588\pi$
$787$	−4.64260	−	8.04122i	−0.165491	−	0.286639i	−0.936830	+	0.349786i	$0.886254\pi$
$788$		0			0
$789$	11.8260	+	0.539324i	0.421016	+	0.0192004i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	0.390369	+	0.676139i	0.0138624	+	0.0240104i
$794$		0			0
$795$	6.58746	−	10.2961i	0.233633	−	0.365165i
$796$		0			0
$797$	−11.2271	+	19.4460i	−0.397685	+	0.688811i	−0.993440	−	0.114355i	$-0.963520\pi$
$797$	−11.2271	+	19.4460i	−0.397685	+	0.688811i	0.595754	+	0.803167i	$0.296853\pi$
$798$		0			0
$799$	−0.188816	−	0.327039i	−0.00667983	−	0.0115698i
$800$		0			0
$801$	17.3722	+	37.6354i	0.613816	+	1.32978i
$802$		0			0
$803$	23.7075	−	41.0626i	0.836619	−	1.44907i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	9.02898	−	14.1122i	0.317835	−	0.496772i
$808$		0			0
$809$	2.70107	−	4.67840i	0.0949647	−	0.164484i	−0.814629	−	0.579982i	$-0.803060\pi$
$809$	2.70107	−	4.67840i	0.0949647	−	0.164484i	0.909594	+	0.415498i	$0.136393\pi$
$810$		0			0
$811$	−0.0177088			−0.000621841			−0.000310920	−	1.00000i	$-0.500099\pi$
$811$	−0.0177088			−0.000621841			−0.000310920		1.00000i	$0.500099\pi$
$812$		0			0
$813$	−10.2290	−	19.7431i	−0.358746	−	0.692422i
$814$		0			0
$815$	5.77042	+	9.99466i	0.202129	+	0.350098i
$816$		0			0
$817$	12.3796	−	21.4420i	0.433106	−	0.750162i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.528505	−	0.915397i	0.0184449	−	0.0319476i	−0.856656	−	0.515889i	$-0.827462\pi$
$821$	0.528505	−	0.915397i	0.0184449	−	0.0319476i	0.875101	+	0.483941i	$0.160795\pi$
$822$		0			0
$823$	−6.76303	−	11.7139i	−0.235744	−	0.408321i	0.723744	−	0.690068i	$-0.242419\pi$
$823$	−6.76303	−	11.7139i	−0.235744	−	0.408321i	−0.959489	+	0.281747i	$0.909086\pi$
$824$		0			0
$825$	−6.82743	−	0.311365i	−0.237701	−	0.0108403i
$826$		0			0
$827$	−49.3068			−1.71457			−0.857283	−	0.514846i	$-0.827849\pi$
$827$	−49.3068			−1.71457			−0.857283	+	0.514846i	$0.827849\pi$
$828$		0			0
$829$	26.8530	−	46.5108i	0.932644	−	1.61539i	0.153861	−	0.988093i	$-0.450829\pi$
$829$	26.8530	−	46.5108i	0.932644	−	1.61539i	0.778783	−	0.627294i	$-0.215837\pi$
$830$		0			0
$831$	−20.0416	−	0.914000i	−0.695236	−	0.0317063i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	11.1864	−	19.3754i	0.387120	−	0.670512i
$836$		0			0
$837$	−19.9231	−	48.9019i	−0.688645	−	1.69030i
$838$		0			0
$839$	18.7163	+	32.4176i	0.646160	+	1.11918i	0.984032	+	0.177990i	$0.0569593\pi$
$839$	18.7163	+	32.4176i	0.646160	+	1.11918i	−0.337873	+	0.941192i	$0.609707\pi$
$840$		0			0
$841$	−20.1730	+	34.9407i	−0.695622	+	1.20485i
$842$		0			0
$843$	−3.92674	−	7.57907i	−0.135244	−	0.261037i
$844$		0			0
$845$	12.3245	+	21.3467i	0.423976	+	0.734348i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−14.8209	−	28.6061i	−0.508652	−	0.981758i
$850$		0			0
$851$	21.7419	+	37.6581i	0.745303	+	1.29090i
$852$		0			0
$853$	10.3092	+	17.8561i	0.352982	+	0.611382i	0.986770	−	0.162124i	$-0.0518344\pi$
$853$	10.3092	+	17.8561i	0.352982	+	0.611382i	−0.633789	+	0.773506i	$0.718501\pi$
$854$		0			0
$855$	13.8982	+	30.1094i	0.475310	+	1.02972i
$856$		0			0
$857$	20.8889			0.713551			0.356776	−	0.934190i	$-0.383876\pi$
$857$	20.8889			0.713551			0.356776	+	0.934190i	$0.383876\pi$
$858$		0			0
$859$	26.8860			0.917338			0.458669	−	0.888607i	$-0.348326\pi$
$859$	26.8860			0.917338			0.458669	+	0.888607i	$0.348326\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−13.4071	−	23.2218i	−0.456383	−	0.790478i	0.542384	−	0.840131i	$-0.317522\pi$
$863$	−13.4071	−	23.2218i	−0.456383	−	0.790478i	−0.998767	+	0.0496527i	$0.984189\pi$
$864$		0			0
$865$	−14.9956	+	25.9732i	−0.509866	+	0.883114i
$866$		0			0
$867$	−13.4859	−	26.0293i	−0.458005	−	0.884003i
$868$		0			0
$869$	32.7075	−	56.6510i	1.10953	−	1.92175i
$870$		0			0
$871$	8.38151			0.283997
$872$		0			0
$873$	2.79027	+	6.04488i	0.0944362	+	0.204588i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−37.9076			−1.28005			−0.640024	−	0.768355i	$-0.721076\pi$
$877$	−37.9076			−1.28005			−0.640024	+	0.768355i	$0.721076\pi$
$878$		0			0
$879$	−23.1126	+	36.1247i	−0.779570	+	1.21846i
$880$		0			0
$881$	7.47782			0.251934			0.125967	−	0.992034i	$-0.459797\pi$
$881$	7.47782			0.251934			0.125967	+	0.992034i	$0.459797\pi$
$882$		0			0
$883$	5.07472			0.170778			0.0853889	−	0.996348i	$-0.472787\pi$
$883$	5.07472			0.170778			0.0853889	+	0.996348i	$0.472787\pi$
$884$		0			0
$885$	2.91449	+	5.62530i	0.0979694	+	0.189092i
$886$		0			0
$887$	18.5231			0.621946			0.310973	−	0.950419i	$-0.399345\pi$
$887$	18.5231			0.621946			0.310973	+	0.950419i	$0.399345\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−44.7331	−	8.24611i	−1.49861	−	0.276255i
$892$		0			0
$893$	−7.43464			−0.248791
$894$		0			0
$895$	24.1249	−	41.7855i	0.806406	−	1.39674i
$896$		0			0
$897$	4.97296	−	7.77266i	0.166042	−	0.259522i
$898$		0			0
$899$	−42.3127	+	73.2878i	−1.41121	+	2.44428i
$900$		0			0
$901$	−0.469554	−	0.813291i	−0.0156431	−	0.0270947i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.87412			−0.0955391
$906$		0			0
$907$	−49.6490			−1.64857			−0.824284	−	0.566176i	$-0.808422\pi$
$907$	−49.6490			−1.64857			−0.824284	+	0.566176i	$0.808422\pi$
$908$		0			0
$909$	8.14601	+	0.744547i	0.270186	+	0.0246951i
$910$		0			0
$911$	−11.9808	−	20.7514i	−0.396943	−	0.687525i	0.596404	−	0.802684i	$-0.296595\pi$
$911$	−11.9808	−	20.7514i	−0.396943	−	0.687525i	−0.993347	+	0.115159i	$0.963262\pi$
$912$		0			0
$913$	−14.4715	−	25.0654i	−0.478937	−	0.829543i
$914$		0			0
$915$	1.49700	−	2.33978i	0.0494892	−	0.0773508i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	9.41887	+	16.3140i	0.310700	+	0.538148i	0.978514	−	0.206180i	$-0.0661032\pi$
$919$	9.41887	+	16.3140i	0.310700	+	0.538148i	−0.667814	+	0.744328i	$0.732770\pi$
$920$		0			0
$921$	−37.9669	−	1.73148i	−1.25105	−	0.0570543i
$922$		0			0
$923$	−3.89037	+	6.73832i	−0.128053	+	0.221794i
$924$		0			0
$925$	3.18629	+	5.51882i	0.104765	+	0.181458i
$926$		0			0
$927$	53.7229	+	4.91029i	1.76449	+	0.161275i
$928$		0			0
$929$	−7.45185	+	12.9070i	−0.244487	+	0.423464i	−0.961987	−	0.273094i	$-0.911953\pi$
$929$	−7.45185	+	12.9070i	−0.244487	+	0.423464i	0.717500	+	0.696558i	$0.245286\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	21.6426	+	41.7727i	0.708547	+	1.36758i
$934$		0			0
$935$	1.41887	−	2.45756i	0.0464021	−	0.0803708i
$936$		0			0
$937$	3.94299			0.128812			0.0644059	−	0.997924i	$-0.479485\pi$
$937$	3.94299			0.128812			0.0644059	+	0.997924i	$0.479485\pi$
$938$		0			0
$939$	−7.97529	+	12.4653i	−0.260264	+	0.406788i
$940$		0			0
$941$	21.4056	+	37.0756i	0.697804	+	1.20863i	0.969226	+	0.246171i	$0.0791725\pi$
$941$	21.4056	+	37.0756i	0.697804	+	1.20863i	−0.271423	+	0.962460i	$0.587494\pi$
$942$		0			0
$943$	−13.4626	+	23.3180i	−0.438404	+	0.759338i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	13.5919	−	23.5419i	0.441678	−	0.765009i	−0.556136	−	0.831091i	$-0.687717\pi$
$947$	13.5919	−	23.5419i	0.441678	−	0.765009i	0.997814	+	0.0660823i	$0.0210500\pi$
$948$		0			0
$949$	4.69076	+	8.12463i	0.152268	+	0.263737i
$950$		0			0
$951$	0.372660	−	0.582462i	0.0120843	−	0.0188876i
$952$		0			0
$953$	1.12295			0.0363760			0.0181880	−	0.999835i	$-0.494210\pi$
$953$	1.12295			0.0363760			0.0181880	+	0.999835i	$0.494210\pi$
$954$		0			0
$955$	−23.9956	+	41.5616i	−0.776480	+	1.34490i
$956$		0			0
$957$	33.5349	+	64.7263i	1.08403	+	2.09230i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−36.1357	+	62.5889i	−1.16567	+	2.01900i
$962$		0			0
$963$	−1.39329	−	3.01845i	−0.0448983	−	0.0972683i
$964$		0			0
$965$	14.9371	+	25.8717i	0.480841	+	0.832841i
$966$		0			0
$967$	4.75223	−	8.23111i	0.152822	−	0.264695i	−0.779442	−	0.626474i	$-0.784497\pi$
$967$	4.75223	−	8.23111i	0.152822	−	0.264695i	0.932264	+	0.361780i	$0.117831\pi$
$968$		0			0
$969$	2.54523	+	0.116075i	0.0817646	+	0.00372888i
$970$		0			0
$971$	12.2989	+	21.3024i	0.394691	+	0.683625i	0.993062	−	0.117594i	$-0.0375182\pi$
$971$	12.2989	+	21.3024i	0.394691	+	0.683625i	−0.598370	+	0.801220i	$0.704185\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	0.728790	−	1.13909i	0.0233400	−	0.0364800i
$976$		0			0
$977$	12.7016	+	21.9997i	0.406359	+	0.703834i	0.994479	−	0.104940i	$-0.0334650\pi$
$977$	12.7016	+	21.9997i	0.406359	+	0.703834i	−0.588120	+	0.808774i	$0.700132\pi$
$978$		0			0
$979$	−34.9164	−	60.4770i	−1.11593	−	1.93285i
$980$		0			0
$981$	−5.85087	+	8.28728i	−0.186804	+	0.264593i
$982$		0			0
$983$	22.8535			0.728913			0.364457	−	0.931220i	$-0.381255\pi$
$983$	22.8535			0.728913			0.364457	+	0.931220i	$0.381255\pi$
$984$		0			0
$985$	−35.6224			−1.13502
$986$		0			0
$987$		0			0
$988$		0			0
$989$	12.2552	+	21.2266i	0.389691	+	0.674965i
$990$		0			0
$991$	−12.2345	+	21.1908i	−0.388642	+	0.673149i	−0.992267	−	0.124120i	$-0.960389\pi$
$991$	−12.2345	+	21.1908i	−0.388642	+	0.673149i	0.603625	+	0.797269i	$0.293723\pi$
$992$		0			0
$993$	−5.24465	+	8.19731i	−0.166434	+	0.260134i
$994$		0			0
$995$	11.8559	−	20.5351i	0.375858	−	0.651006i
$996$		0			0
$997$	26.0000			0.823428			0.411714	−	0.911313i	$-0.364930\pi$
$997$	26.0000			0.823428			0.411714	+	0.911313i	$0.364930\pi$
$998$		0			0
$999$	16.0021	+	39.2777i	0.506285	+	1.24269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.l.d.949.1		6
3.2	odd	2		5292.2.l.g.361.1		6
7.2	even	3		1764.2.i.f.373.2		6
7.3	odd	6		1764.2.j.d.589.2		6
7.4	even	3		252.2.j.b.85.2	✓	6
7.5	odd	6		1764.2.i.e.373.2		6
7.6	odd	2		1764.2.l.g.949.3		6
9.2	odd	6		5292.2.i.d.2125.3		6
9.7	even	3		1764.2.i.f.1537.2		6
21.2	odd	6		5292.2.i.d.1549.3		6
21.5	even	6		5292.2.i.g.1549.1		6
21.11	odd	6		756.2.j.a.253.3		6
21.17	even	6		5292.2.j.e.1765.1		6
21.20	even	2		5292.2.l.d.361.3		6
28.11	odd	6		1008.2.r.g.337.2		6
63.2	odd	6		5292.2.l.g.3313.1		6
63.4	even	3		2268.2.a.g.1.3		3
63.11	odd	6		756.2.j.a.505.3		6
63.16	even	3	inner	1764.2.l.d.961.1		6
63.20	even	6		5292.2.i.g.2125.1		6
63.25	even	3		252.2.j.b.169.2	yes	6
63.32	odd	6		2268.2.a.j.1.1		3
63.34	odd	6		1764.2.i.e.1537.2		6
63.38	even	6		5292.2.j.e.3529.1		6
63.47	even	6		5292.2.l.d.3313.3		6
63.52	odd	6		1764.2.j.d.1177.2		6
63.61	odd	6		1764.2.l.g.961.3		6
84.11	even	6		3024.2.r.i.1009.3		6
252.11	even	6		3024.2.r.i.2017.3		6
252.67	odd	6		9072.2.a.bt.1.3		3
252.95	even	6		9072.2.a.bz.1.1		3
252.151	odd	6		1008.2.r.g.673.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.j.b.85.2	✓	6	7.4	even	3
252.2.j.b.169.2	yes	6	63.25	even	3
756.2.j.a.253.3		6	21.11	odd	6
756.2.j.a.505.3		6	63.11	odd	6
1008.2.r.g.337.2		6	28.11	odd	6
1008.2.r.g.673.2		6	252.151	odd	6
1764.2.i.e.373.2		6	7.5	odd	6
1764.2.i.e.1537.2		6	63.34	odd	6
1764.2.i.f.373.2		6	7.2	even	3
1764.2.i.f.1537.2		6	9.7	even	3
1764.2.j.d.589.2		6	7.3	odd	6
1764.2.j.d.1177.2		6	63.52	odd	6
1764.2.l.d.949.1		6	1.1	even	1	trivial
1764.2.l.d.961.1		6	63.16	even	3	inner
1764.2.l.g.949.3		6	7.6	odd	2
1764.2.l.g.961.3		6	63.61	odd	6
2268.2.a.g.1.3		3	63.4	even	3
2268.2.a.j.1.1		3	63.32	odd	6
3024.2.r.i.1009.3		6	84.11	even	6
3024.2.r.i.2017.3		6	252.11	even	6
5292.2.i.d.1549.3		6	21.2	odd	6
5292.2.i.d.2125.3		6	9.2	odd	6
5292.2.i.g.1549.1		6	21.5	even	6
5292.2.i.g.2125.1		6	63.20	even	6
5292.2.j.e.1765.1		6	21.17	even	6
5292.2.j.e.3529.1		6	63.38	even	6
5292.2.l.d.361.3		6	21.20	even	2
5292.2.l.d.3313.3		6	63.47	even	6
5292.2.l.g.361.1		6	3.2	odd	2
5292.2.l.g.3313.1		6	63.2	odd	6
9072.2.a.bt.1.3		3	252.67	odd	6
9072.2.a.bz.1.1		3	252.95	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73025 - 0.0789082i) q^{3} +2.05408 q^{5} +(2.98755 + 0.273062i) q^{9} -5.05408 q^{11} +(0.500000 - 0.866025i) q^{13} +(-3.55408 - 0.162084i) q^{15} +(-0.136673 + 0.236725i) q^{17} +(2.69076 + 4.66053i) q^{19} -5.32743 q^{23} -0.780738 q^{25} +(-5.14766 - 0.708209i) q^{27} +(4.16372 + 7.21177i) q^{29} +(5.08113 + 8.80077i) q^{31} +(8.74484 + 0.398809i) q^{33} +(-4.08113 - 7.06872i) q^{37} +(-0.933463 + 1.45899i) q^{39} +(2.52704 - 4.37697i) q^{41} +(-2.30039 - 3.98439i) q^{43} +(6.13667 + 0.560893i) q^{45} +(-0.690757 + 1.19643i) q^{47} +(0.255158 - 0.398809i) q^{51} +(-1.71780 + 2.97532i) q^{53} -10.3815 q^{55} +(-4.28794 - 8.27621i) q^{57} +(-0.890369 - 1.54216i) q^{59} +(-0.390369 + 0.676139i) q^{61} +(1.02704 - 1.77889i) q^{65} +(4.19076 + 7.25860i) q^{67} +(9.21780 + 0.420378i) q^{69} -7.78074 q^{71} +(-4.69076 + 8.12463i) q^{73} +(1.35087 + 0.0616067i) q^{75} +(-6.47150 + 11.2090i) q^{79} +(8.85087 + 1.63157i) q^{81} +(2.86333 + 4.95943i) q^{83} +(-0.280738 + 0.486253i) q^{85} +(-6.63521 - 12.8067i) q^{87} +(6.90856 + 11.9660i) q^{89} +(-8.09718 - 15.6285i) q^{93} +(5.52704 + 9.57312i) q^{95} +(1.10963 + 1.92194i) q^{97} +(-15.0993 - 1.38008i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{3} - 6 q^{5} - 4 q^{9} - 12 q^{11} + 3 q^{13} - 3 q^{15} - 3 q^{19} - 12 q^{23} + 12 q^{25} - 7 q^{27} + 15 q^{29} + 3 q^{31} + 15 q^{33} + 3 q^{37} - 2 q^{39} + 6 q^{41} - 3 q^{43} + 36 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) \) 6 * q - 4 * q^3 - 6 * q^5 - 4 * q^9 - 12 * q^11 + 3 * q^13 - 3 * q^15 - 3 * q^19 - 12 * q^23 + 12 * q^25 - 7 * q^27 + 15 * q^29 + 3 * q^31 + 15 * q^33 + 3 * q^37 - 2 * q^39 + 6 * q^41 - 3 * q^43 + 36 * q^45 + 15 * q^47 + 39 * q^51 + 18 * q^53 - 24 * q^55 + 7 * q^57 + 3 * q^59 + 6 * q^61 - 3 * q^65 + 6 * q^67 + 27 * q^69 - 30 * q^71 - 9 * q^73 - 13 * q^75 - 3 * q^79 + 32 * q^81 + 18 * q^83 + 15 * q^85 + 6 * q^87 - 6 * q^89 - 35 * q^93 + 24 * q^95 + 15 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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