LMFDB - Embedded newform 504.2.bu.a.41.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(41,504)] 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("504.41"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bu (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.4
Character	$\chi$	$=$	504.41
Dual form			504.2.bu.a.209.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50601 - 0.855530i) q^{3} +(0.422480 - 0.731757i) q^{5} +(0.327684 + 2.62538i) q^{7} +(1.53614 + 2.57688i) q^{9} +(-0.791371 + 0.456898i) q^{11} +(-0.472651 - 0.272885i) q^{13} +(-1.26230 + 0.740590i) q^{15} +4.77352 q^{17} +3.15579i q^{19} +(1.75260 - 4.23419i) q^{21} +(1.39291 + 0.804196i) q^{23} +(2.14302 + 3.71182i) q^{25} +(-0.108844 - 5.19501i) q^{27} +(5.56478 - 3.21283i) q^{29} +(1.57351 + 0.908468i) q^{31} +(1.58270 - 0.0110519i) q^{33} +(2.05958 + 0.869387i) q^{35} +7.14037 q^{37} +(0.478356 + 0.815336i) q^{39} +(2.82322 - 4.88995i) q^{41} +(-1.84576 - 3.19695i) q^{43} +(2.53463 - 0.0354002i) q^{45} +(6.75196 + 11.6947i) q^{47} +(-6.78525 + 1.72059i) q^{49} +(-7.18897 - 4.08389i) q^{51} +2.49672i q^{53} +0.772122i q^{55} +(2.69987 - 4.75266i) q^{57} +(0.279096 - 0.483409i) q^{59} +(-10.9926 + 6.34661i) q^{61} +(-6.26191 + 4.87734i) q^{63} +(-0.399372 + 0.230577i) q^{65} +(-3.06545 + 5.30951i) q^{67} +(-1.40972 - 2.40280i) q^{69} -9.24488i q^{71} +8.87479i q^{73} +(-0.0518376 - 7.42346i) q^{75} +(-1.45885 - 1.92793i) q^{77} +(-5.58581 - 9.67491i) q^{79} +(-4.28057 + 7.91686i) q^{81} +(0.122120 + 0.211518i) q^{83} +(2.01672 - 3.49306i) q^{85} +(-11.1293 + 0.0777152i) q^{87} +6.19322 q^{89} +(0.561548 - 1.33031i) q^{91} +(-1.59250 - 2.71435i) q^{93} +(2.30927 + 1.33326i) q^{95} +(-12.2408 + 7.06722i) q^{97} +(-2.39302 - 1.33741i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9} + 8 q^{15} - 4 q^{21} + 12 q^{23} - 24 q^{25} - 36 q^{29} + 32 q^{39} + 12 q^{43} + 6 q^{49} + 24 q^{51} + 28 q^{57} - 14 q^{63} + 36 q^{65} - 60 q^{77} - 12 q^{79} - 36 q^{81} - 12 q^{91}+ \cdots + 44 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 + 8 * q^15 - 4 * q^21 + 12 * q^23 - 24 * q^25 - 36 * q^29 + 32 * q^39 + 12 * q^43 + 6 * q^49 + 24 * q^51 + 28 * q^57 - 14 * q^63 + 36 * q^65 - 60 * q^77 - 12 * q^79 - 36 * q^81 - 12 * q^91 + 16 * q^93 - 108 * q^95 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−1.50601	−	0.855530i	−0.869496	−	0.493941i
$3$	−1.50601	−	0.855530i	−0.869496	−	0.493941i
$4$		0			0
$5$	0.422480	−	0.731757i	0.188939	−	0.327252i	−0.755958	−	0.654620i	$-0.772829\pi$
$5$	0.422480	−	0.731757i	0.188939	−	0.327252i	0.944897	+	0.327368i	$0.106162\pi$
$6$		0			0
$7$	0.327684	+	2.62538i	0.123853	+	0.992301i
$7$	0.327684	+	2.62538i	0.123853	+	0.992301i
$8$		0			0
$9$	1.53614	+	2.57688i	0.512045	+	0.858958i
$10$		0			0
$11$	−0.791371	+	0.456898i	−0.238607	+	0.137760i	−0.614537	−	0.788888i	$-0.710657\pi$
$11$	−0.791371	+	0.456898i	−0.238607	+	0.137760i	0.375929	+	0.926648i	$0.377324\pi$
$12$		0			0
$13$	−0.472651	−	0.272885i	−0.131090	−	0.0756848i	0.433021	−	0.901384i	$-0.357448\pi$
$13$	−0.472651	−	0.272885i	−0.131090	−	0.0756848i	−0.564111	+	0.825699i	$0.690781\pi$
$14$		0			0
$15$	−1.26230	+	0.740590i	−0.325925	+	0.191219i
$16$		0			0
$17$	4.77352			1.15775			0.578874	−	0.815417i	$-0.303492\pi$
$17$	4.77352			1.15775			0.578874	+	0.815417i	$0.303492\pi$
$18$		0			0
$19$			3.15579i			0.723988i	0.932180	+	0.361994i	$0.117904\pi$
$19$			3.15579i			0.723988i	−0.932180	+	0.361994i	$0.882096\pi$
$20$		0			0
$21$	1.75260	−	4.23419i	0.382448	−	0.923977i
$22$		0			0
$23$	1.39291	+	0.804196i	0.290441	+	0.167686i	0.638141	−	0.769920i	$-0.279704\pi$
$23$	1.39291	+	0.804196i	0.290441	+	0.167686i	−0.347699	+	0.937606i	$0.613037\pi$
$24$		0			0
$25$	2.14302	+	3.71182i	0.428604	+	0.742364i
$26$		0			0
$27$	−0.108844	−	5.19501i	−0.0209470	−	0.999781i
$28$		0			0
$29$	5.56478	−	3.21283i	1.03335	−	0.596607i	0.115410	−	0.993318i	$-0.463182\pi$
$29$	5.56478	−	3.21283i	1.03335	−	0.596607i	0.917944	+	0.396711i	$0.129848\pi$
$30$		0			0
$31$	1.57351	+	0.908468i	0.282611	+	0.163166i	0.634605	−	0.772837i	$-0.281163\pi$
$31$	1.57351	+	0.908468i	0.282611	+	0.163166i	−0.351994	+	0.936002i	$0.614496\pi$
$32$		0			0
$33$	1.58270	−	0.0110519i	0.275513	−	0.00192390i
$34$		0			0
$35$	2.05958	+	0.869387i	0.348133	+	0.146953i
$36$		0			0
$37$	7.14037			1.17387			0.586935	−	0.809634i	$-0.300334\pi$
$37$	7.14037			1.17387			0.586935	+	0.809634i	$0.300334\pi$
$38$		0			0
$39$	0.478356	+	0.815336i	0.0765983	+	0.130558i
$40$		0			0
$41$	2.82322	−	4.88995i	0.440912	−	0.763683i	−0.556845	−	0.830616i	$-0.687988\pi$
$41$	2.82322	−	4.88995i	0.440912	−	0.763683i	0.997757	+	0.0669338i	$0.0213216\pi$
$42$		0			0
$43$	−1.84576	−	3.19695i	−0.281476	−	0.487531i	0.690273	−	0.723549i	$-0.257491\pi$
$43$	−1.84576	−	3.19695i	−0.281476	−	0.487531i	−0.971748	+	0.236019i	$0.924157\pi$
$44$		0			0
$45$	2.53463	−	0.0354002i	0.377841	−	0.00527715i
$46$		0			0
$47$	6.75196	+	11.6947i	0.984874	+	1.70585i	0.642494	+	0.766291i	$0.277900\pi$
$47$	6.75196	+	11.6947i	0.984874	+	1.70585i	0.342381	+	0.939561i	$0.388767\pi$
$48$		0			0
$49$	−6.78525	+	1.72059i	−0.969321	+	0.245798i
$50$		0			0
$51$	−7.18897	−	4.08389i	−1.00666	−	0.571859i
$52$		0			0
$53$			2.49672i			0.342951i	0.985188	+	0.171476i	$0.0548535\pi$
$53$			2.49672i			0.342951i	−0.985188	+	0.171476i	$0.945147\pi$
$54$		0			0
$55$			0.772122i			0.104113i
$56$		0			0
$57$	2.69987	−	4.75266i	0.357607	−	0.629505i
$58$		0			0
$59$	0.279096	−	0.483409i	0.0363353	−	0.0629345i	−0.847286	−	0.531137i	$-0.821765\pi$
$59$	0.279096	−	0.483409i	0.0363353	−	0.0629345i	0.883621	+	0.468203i	$0.155098\pi$
$60$		0			0
$61$	−10.9926	+	6.34661i	−1.40746	+	0.812600i	−0.995143	−	0.0984388i	$-0.968615\pi$
$61$	−10.9926	+	6.34661i	−1.40746	+	0.812600i	−0.412321	+	0.911039i	$0.635282\pi$
$62$		0			0
$63$	−6.26191	+	4.87734i	−0.788927	+	0.614487i
$64$		0			0
$65$	−0.399372	+	0.230577i	−0.0495360	+	0.0285996i
$66$		0			0
$67$	−3.06545	+	5.30951i	−0.374504	+	0.648660i	−0.990253	−	0.139282i	$-0.955520\pi$
$67$	−3.06545	+	5.30951i	−0.374504	+	0.648660i	0.615748	+	0.787943i	$0.288854\pi$
$68$		0			0
$69$	−1.40972	−	2.40280i	−0.169710	−	0.289263i
$70$		0			0
$71$		−	9.24488i		−	1.09717i	−0.836096	−	0.548583i	$-0.815168\pi$
$71$		−	9.24488i		−	1.09717i	0.836096	−	0.548583i	$-0.184832\pi$
$72$		0			0
$73$			8.87479i			1.03872i	0.854557	+	0.519358i	$0.173829\pi$
$73$			8.87479i			1.03872i	−0.854557	+	0.519358i	$0.826171\pi$
$74$		0			0
$75$	−0.0518376	−	7.42346i	−0.00598569	−	0.857187i
$76$		0			0
$77$	−1.45885	−	1.92793i	−0.166252	−	0.219708i
$78$		0			0
$79$	−5.58581	−	9.67491i	−0.628453	−	1.08851i	−0.987862	−	0.155332i	$-0.950355\pi$
$79$	−5.58581	−	9.67491i	−0.628453	−	1.08851i	0.359410	−	0.933180i	$-0.382978\pi$
$80$		0			0
$81$	−4.28057	+	7.91686i	−0.475619	+	0.879651i
$82$		0			0
$83$	0.122120	+	0.211518i	0.0134044	+	0.0232171i	0.872650	−	0.488347i	$-0.162400\pi$
$83$	0.122120	+	0.211518i	0.0134044	+	0.0232171i	−0.859245	+	0.511564i	$0.829066\pi$
$84$		0			0
$85$	2.01672	−	3.49306i	0.218744	−	0.378875i
$86$		0			0
$87$	−11.1293	+	0.0777152i	−1.19319	+	0.00833195i
$88$		0			0
$89$	6.19322			0.656480			0.328240	−	0.944594i	$-0.393545\pi$
$89$	6.19322			0.656480			0.328240	+	0.944594i	$0.393545\pi$
$90$		0			0
$91$	0.561548	−	1.33031i	0.0588662	−	0.139454i
$92$		0			0
$93$	−1.59250	−	2.71435i	−0.165135	−	0.281465i
$94$		0			0
$95$	2.30927	+	1.33326i	0.236926	+	0.136790i
$96$		0			0
$97$	−12.2408	+	7.06722i	−1.24286	+	0.717568i	−0.969676	−	0.244393i	$-0.921411\pi$
$97$	−12.2408	+	7.06722i	−1.24286	+	0.717568i	−0.273187	+	0.961961i	$0.588078\pi$
$98$		0			0
$99$	−2.39302	−	1.33741i	−0.240508	−	0.134414i
$100$		0			0
$101$	−5.62446	−	9.74186i	−0.559655	−	0.969351i	−0.997525	−	0.0703128i	$-0.977600\pi$
$101$	−5.62446	−	9.74186i	−0.559655	−	0.969351i	0.437870	−	0.899038i	$-0.355733\pi$
$102$		0			0
$103$	1.97803	+	1.14202i	0.194901	+	0.112526i	0.594275	−	0.804262i	$-0.297439\pi$
$103$	1.97803	+	1.14202i	0.194901	+	0.112526i	−0.399374	+	0.916788i	$0.630772\pi$
$104$		0			0
$105$	−2.35797	−	3.07134i	−0.230114	−	0.299732i
$106$		0			0
$107$		−	10.9749i		−	1.06098i	−0.847690	−	0.530492i	$-0.822007\pi$
$107$		−	10.9749i		−	1.06098i	0.847690	−	0.530492i	$-0.177993\pi$
$108$		0			0
$109$	6.21135			0.594939			0.297470	−	0.954731i	$-0.403857\pi$
$109$	6.21135			0.594939			0.297470	+	0.954731i	$0.403857\pi$
$110$		0			0
$111$	−10.7535	−	6.10880i	−1.02067	−	0.579822i
$112$		0			0
$113$	−15.1205	−	8.72980i	−1.42241	−	0.821230i	−0.425908	−	0.904767i	$-0.640045\pi$
$113$	−15.1205	−	8.72980i	−1.42241	−	0.821230i	−0.996505	+	0.0835364i	$0.973379\pi$
$114$		0			0
$115$	1.17695	−	0.679514i	0.109751	−	0.0633650i
$116$		0			0
$117$	−0.0228654	−	1.63715i	−0.00211391	−	0.151355i
$118$		0			0
$119$	1.56420	+	12.5323i	0.143390	+	1.14883i
$120$		0			0
$121$	−5.08249	+	8.80313i	−0.462044	+	0.800284i
$122$		0			0
$123$	−8.43530	+	4.94898i	−0.760585	+	0.446234i
$124$		0			0
$125$	7.84634			0.701798
$126$		0			0
$127$	7.19234			0.638217			0.319109	−	0.947718i	$-0.396617\pi$
$127$	7.19234			0.638217			0.319109	+	0.947718i	$0.396617\pi$
$128$		0			0
$129$	0.0446472	+	6.39375i	0.00393097	+	0.562938i
$130$		0			0
$131$	−2.51594	+	4.35773i	−0.219819	+	0.380737i	−0.954752	−	0.297402i	$-0.903880\pi$
$131$	−2.51594	+	4.35773i	−0.219819	+	0.380737i	0.734934	+	0.678139i	$0.237213\pi$
$132$		0			0
$133$	−8.28515	+	1.03410i	−0.718414	+	0.0896679i
$134$		0			0
$135$	−3.84747	−	2.11514i	−0.331138	−	0.182043i
$136$		0			0
$137$	−1.61383	+	0.931746i	−0.137879	+	0.0796044i	−0.567353	−	0.823475i	$-0.692032\pi$
$137$	−1.61383	+	0.931746i	−0.137879	+	0.0796044i	0.429474	+	0.903079i	$0.358699\pi$
$138$		0			0
$139$	9.90462	+	5.71843i	0.840098	+	0.485031i	0.857298	−	0.514821i	$-0.172142\pi$
$139$	9.90462	+	5.71843i	0.840098	+	0.485031i	−0.0171992	+	0.999852i	$0.505475\pi$
$140$		0			0
$141$	−0.163323	−	23.3889i	−0.0137543	−	1.96970i
$142$		0			0
$143$	0.498724			0.0417054
$144$		0			0
$145$		−	5.42943i		−	0.450889i
$146$		0			0
$147$	11.6907	+	3.21376i	0.964230	+	0.265066i
$148$		0			0
$149$	0.443690	+	0.256164i	0.0363485	+	0.0209858i	0.518064	−	0.855342i	$-0.326653\pi$
$149$	0.443690	+	0.256164i	0.0363485	+	0.0209858i	−0.481716	+	0.876328i	$0.659986\pi$
$150$		0			0
$151$	−5.74808	−	9.95597i	−0.467772	−	0.810205i	0.531550	−	0.847027i	$-0.321610\pi$
$151$	−5.74808	−	9.95597i	−0.467772	−	0.810205i	−0.999322	+	0.0368219i	$0.988277\pi$
$152$		0			0
$153$	7.33277	+	12.3008i	0.592819	+	0.994457i
$154$		0			0
$155$	1.32956	−	0.767619i	0.106793	−	0.0616567i
$156$		0			0
$157$	14.9187	+	8.61334i	1.19065	+	0.687419i	0.958453	−	0.285250i	$-0.0920768\pi$
$157$	14.9187	+	8.61334i	1.19065	+	0.687419i	0.232192	+	0.972670i	$0.425410\pi$
$158$		0			0
$159$	2.13602	−	3.76009i	0.169398	−	0.298195i
$160$		0			0
$161$	−1.65489	+	3.92044i	−0.130423	+	0.308974i
$162$		0			0
$163$	12.7474			0.998450			0.499225	−	0.866473i	$-0.333618\pi$
$163$	12.7474			0.998450			0.499225	+	0.866473i	$0.333618\pi$
$164$		0			0
$165$	0.660574	−	1.16282i	0.0514256	−	0.0905258i
$166$		0			0
$167$	−3.92213	+	6.79333i	−0.303503	+	0.525683i	−0.976927	−	0.213573i	$-0.931490\pi$
$167$	−3.92213	+	6.79333i	−0.303503	+	0.525683i	0.673424	+	0.739257i	$0.264823\pi$
$168$		0			0
$169$	−6.35107	−	11.0004i	−0.488544	−	0.846182i
$170$		0			0
$171$	−8.13208	+	4.84773i	−0.621876	+	0.370715i
$172$		0			0
$173$	−1.00420	−	1.73933i	−0.0763482	−	0.132239i	0.825324	−	0.564660i	$-0.190993\pi$
$173$	−1.00420	−	1.73933i	−0.0763482	−	0.132239i	−0.901672	+	0.432421i	$0.857659\pi$
$174$		0			0
$175$	−9.04271	+	6.84255i	−0.683565	+	0.517248i
$176$		0			0
$177$	−0.833893	+	0.489244i	−0.0626793	+	0.0367738i
$178$		0			0
$179$			11.8357i			0.884641i	0.896857	+	0.442320i	$0.145845\pi$
$179$			11.8357i			0.884641i	−0.896857	+	0.442320i	$0.854155\pi$
$180$		0			0
$181$		−	10.7449i		−	0.798660i	−0.916807	−	0.399330i	$-0.869243\pi$
$181$		−	10.7449i		−	0.798660i	0.916807	−	0.399330i	$-0.130757\pi$
$182$		0			0
$183$	21.9848	−	0.153518i	1.62516	−	0.0113484i
$184$		0			0
$185$	3.01667	−	5.22502i	0.221790	−	0.384151i
$186$		0			0
$187$	−3.77762	+	2.18101i	−0.276247	+	0.159491i
$188$		0			0
$189$	13.6032	−	1.98808i	0.989489	−	0.144611i
$190$		0			0
$191$	2.86793	−	1.65580i	0.207516	−	0.119809i	−0.392640	−	0.919692i	$-0.628438\pi$
$191$	2.86793	−	1.65580i	0.207516	−	0.119809i	0.600156	+	0.799883i	$0.295105\pi$
$192$		0			0
$193$	−11.7223	+	20.3036i	−0.843788	+	1.46148i	0.0428821	+	0.999080i	$0.486346\pi$
$193$	−11.7223	+	20.3036i	−0.843788	+	1.46148i	−0.886670	+	0.462403i	$0.846987\pi$
$194$		0			0
$195$	0.798724	−	0.00557745i	0.0571978	−	0.000399409i
$196$		0			0
$197$		−	17.9144i		−	1.27635i	−0.769893	−	0.638173i	$-0.779690\pi$
$197$		−	17.9144i		−	1.27635i	0.769893	−	0.638173i	$-0.220310\pi$
$198$		0			0
$199$		−	16.0924i		−	1.14076i	−0.821381	−	0.570380i	$-0.806796\pi$
$199$		−	16.0924i		−	1.14076i	0.821381	−	0.570380i	$-0.193204\pi$
$200$		0			0
$201$	9.15905	−	5.37360i	0.646030	−	0.379025i
$202$		0			0
$203$	10.2584	+	13.5569i	0.719997	+	0.951506i
$204$		0			0
$205$	−2.38551	−	4.13182i	−0.166611	−	0.288579i
$206$		0			0
$207$	0.0673846	+	4.82471i	0.00468355	+	0.335340i
$208$		0			0
$209$	−1.44188	−	2.49740i	−0.0997367	−	0.172749i
$210$		0			0
$211$	1.95748	−	3.39046i	0.134759	−	0.233409i	−0.790747	−	0.612144i	$-0.790307\pi$
$211$	1.95748	−	3.39046i	0.134759	−	0.233409i	0.925505	+	0.378735i	$0.123641\pi$
$212$		0			0
$213$	−7.90927	+	13.9229i	−0.541934	+	0.953981i
$214$		0			0
$215$	−3.11919			−0.212727
$216$		0			0
$217$	−1.86946	+	4.42876i	−0.126907	+	0.300644i
$218$		0			0
$219$	7.59265	−	13.3655i	0.513064	−	0.903159i
$220$		0			0
$221$	−2.25621	−	1.30262i	−0.151769	−	0.0876239i
$222$		0			0
$223$	21.6047	−	12.4735i	1.44676	−	0.835288i	0.448474	−	0.893796i	$-0.351968\pi$
$223$	21.6047	−	12.4735i	1.44676	−	0.835288i	0.998287	+	0.0585082i	$0.0186344\pi$
$224$		0			0
$225$	−6.27293	+	11.2242i	−0.418195	+	0.748277i
$226$		0			0
$227$	−11.3878	−	19.7243i	−0.755838	−	1.30915i	−0.944957	−	0.327195i	$-0.893897\pi$
$227$	−11.3878	−	19.7243i	−0.755838	−	1.30915i	0.189119	−	0.981954i	$-0.439437\pi$
$228$		0			0
$229$	−22.3549	−	12.9066i	−1.47725	−	0.852891i	−0.477581	−	0.878588i	$-0.658486\pi$
$229$	−22.3549	−	12.9066i	−1.47725	−	0.852891i	−0.999670	+	0.0256966i	$0.991820\pi$
$230$		0			0
$231$	0.547642	+	4.15158i	0.0360322	+	0.273154i
$232$		0			0
$233$			28.7072i			1.88067i	0.340245	+	0.940337i	$0.389490\pi$
$233$			28.7072i			1.88067i	−0.340245	+	0.940337i	$0.610510\pi$
$234$		0			0
$235$	11.4103			0.744325
$236$		0			0
$237$	0.135115	+	19.3493i	0.00877669	+	1.25687i
$238$		0			0
$239$	20.7087	+	11.9562i	1.33954	+	0.773381i	0.986738	−	0.162318i	$-0.0518971\pi$
$239$	20.7087	+	11.9562i	1.33954	+	0.773381i	0.352797	+	0.935700i	$0.385230\pi$
$240$		0			0
$241$	12.7991	−	7.38955i	0.824461	−	0.476003i	−0.0274914	−	0.999622i	$-0.508752\pi$
$241$	12.7991	−	7.38955i	0.824461	−	0.476003i	0.851952	+	0.523619i	$0.175419\pi$
$242$		0			0
$243$	13.2197	−	8.26072i	0.848044	−	0.529926i
$244$		0			0
$245$	−1.60758	+	5.69207i	−0.102705	+	0.363653i
$246$		0			0
$247$	0.861169	−	1.49159i	0.0547949	−	0.0949075i
$248$		0			0
$249$	−0.00295396	−	0.423025i	−0.000187200	−	0.0268081i
$250$		0			0
$251$	−25.5524			−1.61285			−0.806426	−	0.591334i	$-0.798601\pi$
$251$	−25.5524			−1.61285			−0.806426	+	0.591334i	$0.798601\pi$
$252$		0			0
$253$	−1.46974			−0.0924020
$254$		0			0
$255$	−6.02561	+	3.53522i	−0.377338	+	0.221384i
$256$		0			0
$257$	−2.67566	+	4.63438i	−0.166903	+	0.289085i	−0.937330	−	0.348444i	$-0.886710\pi$
$257$	−2.67566	+	4.63438i	−0.166903	+	0.289085i	0.770426	+	0.637529i	$0.220043\pi$
$258$		0			0
$259$	2.33978	+	18.7462i	0.145387	+	1.16483i
$260$		0			0
$261$	16.8273	+	9.40440i	1.04158	+	0.582118i
$262$		0			0
$263$	−4.09220	+	2.36263i	−0.252336	+	0.145686i	−0.620833	−	0.783943i	$-0.713206\pi$
$263$	−4.09220	+	2.36263i	−0.252336	+	0.145686i	0.368497	+	0.929629i	$0.379872\pi$
$264$		0			0
$265$	1.82700	+	1.05482i	0.112231	+	0.0647969i
$266$		0			0
$267$	−9.32705	−	5.29848i	−0.570806	−	0.324262i
$268$		0			0
$269$	−22.4749			−1.37032			−0.685161	−	0.728392i	$-0.740268\pi$
$269$	−22.4749			−1.37032			−0.685161	+	0.728392i	$0.740268\pi$
$270$		0			0
$271$		−	26.2752i		−	1.59611i	−0.602588	−	0.798053i	$-0.705864\pi$
$271$		−	26.2752i		−	1.59611i	0.602588	−	0.798053i	$-0.294136\pi$
$272$		0			0
$273$	−1.98382	+	1.52304i	−0.120066	+	0.0921785i
$274$		0			0
$275$	−3.39185	−	1.95829i	−0.204536	−	0.118089i
$276$		0			0
$277$	−1.43859	−	2.49171i	−0.0864365	−	0.149712i	0.819566	−	0.572985i	$-0.194215\pi$
$277$	−1.43859	−	2.49171i	−0.0864365	−	0.149712i	−0.906002	+	0.423272i	$0.860881\pi$
$278$		0			0
$279$	0.0761217	+	5.45027i	0.00455728	+	0.326299i
$280$		0			0
$281$	3.15735	−	1.82290i	0.188352	−	0.108745i	−0.402859	−	0.915262i	$-0.631983\pi$
$281$	3.15735	−	1.82290i	0.188352	−	0.108745i	0.591211	+	0.806517i	$0.298650\pi$
$282$		0			0
$283$	22.9147	+	13.2298i	1.36214	+	0.786431i	0.989908	−	0.141709i	$-0.0452598\pi$
$283$	22.9147	+	13.2298i	1.36214	+	0.786431i	0.372231	+	0.928140i	$0.378593\pi$
$284$		0			0
$285$	−2.33715	−	3.98356i	−0.138441	−	0.235966i
$286$		0			0
$287$	13.7631	+	5.80966i	0.812411	+	0.342933i
$288$		0			0
$289$	5.78646			0.340380
$290$		0			0
$291$	24.4810	−	0.170949i	1.43510	−	0.0100212i
$292$		0			0
$293$	8.80499	−	15.2507i	0.514393	−	0.890955i	−0.485468	−	0.874255i	$-0.661351\pi$
$293$	8.80499	−	15.2507i	0.514393	−	0.890955i	0.999861	−	0.0167000i	$-0.00531603\pi$
$294$		0			0
$295$	−0.235826	−	0.408462i	−0.0137303	−	0.0237816i
$296$		0			0
$297$	2.45973	+	4.06145i	0.142728	+	0.235669i
$298$		0			0
$299$	−0.438907	−	0.760209i	−0.0253826	−	0.0439640i
$300$		0			0
$301$	7.78839	−	5.89341i	0.448915	−	0.339691i
$302$		0			0
$303$	0.136050	+	19.4832i	0.00781589	+	1.11928i
$304$		0			0
$305$			10.7253i			0.614127i
$306$		0			0
$307$			19.7066i			1.12472i	0.826894	+	0.562358i	$0.190106\pi$
$307$			19.7066i			1.12472i	−0.826894	+	0.562358i	$0.809894\pi$
$308$		0			0
$309$	−2.00191	−	3.41216i	−0.113885	−	0.194111i
$310$		0			0
$311$	11.9357	−	20.6733i	0.676812	−	1.17227i	−0.299124	−	0.954214i	$-0.596694\pi$
$311$	11.9357	−	20.6733i	0.676812	−	1.17227i	0.975936	−	0.218058i	$-0.0699723\pi$
$312$		0			0
$313$	6.86688	−	3.96459i	0.388139	−	0.224092i	−0.293215	−	0.956047i	$-0.594725\pi$
$313$	6.86688	−	3.96459i	0.388139	−	0.224092i	0.681353	+	0.731955i	$0.261392\pi$
$314$		0			0
$315$	0.923497	+	6.64278i	0.0520332	+	0.374278i
$316$		0			0
$317$	8.42664	−	4.86513i	0.473287	−	0.273253i	−0.244327	−	0.969693i	$-0.578567\pi$
$317$	8.42664	−	4.86513i	0.473287	−	0.273253i	0.717615	+	0.696440i	$0.245234\pi$
$318$		0			0
$319$	−2.93587	+	5.08508i	−0.164377	+	0.284710i
$320$		0			0
$321$	−9.38936	+	16.5283i	−0.524063	+	0.922521i
$322$		0			0
$323$			15.0642i			0.838196i
$324$		0			0
$325$		−	2.33920i		−	0.129755i
$326$		0			0
$327$	−9.35436	−	5.31400i	−0.517297	−	0.293865i
$328$		0			0
$329$	−28.4906	+	21.5586i	−1.57074	+	1.18857i
$330$		0			0
$331$	−15.2451	−	26.4053i	−0.837947	−	1.45137i	−0.891609	−	0.452807i	$-0.850423\pi$
$331$	−15.2451	−	26.4053i	−0.837947	−	1.45137i	0.0536621	−	0.998559i	$-0.482911\pi$
$332$		0			0
$333$	10.9686	+	18.3998i	0.601075	+	1.00831i
$334$		0			0
$335$	2.59018	+	4.48633i	0.141517	+	0.245114i
$336$		0			0
$337$	9.31669	−	16.1370i	0.507512	−	0.879037i	−0.492450	−	0.870341i	$-0.663899\pi$
$337$	9.31669	−	16.1370i	0.507512	−	0.879037i	0.999962	−	0.00869629i	$-0.00276815\pi$
$338$		0			0
$339$	15.3030	+	26.0832i	0.831143	+	1.41664i
$340$		0			0
$341$	−1.66031			−0.0899108
$342$		0			0
$343$	−6.74061	−	17.2500i	−0.363959	−	0.931415i
$344$		0			0
$345$	−2.35385	+	0.0164368i	−0.126727	+	0.000884927i
$346$		0			0
$347$	2.95873	+	1.70822i	0.158833	+	0.0917022i	0.577310	−	0.816525i	$-0.304103\pi$
$347$	2.95873	+	1.70822i	0.158833	+	0.0917022i	−0.418477	+	0.908227i	$0.637436\pi$
$348$		0			0
$349$	11.0696	−	6.39102i	0.592541	−	0.342104i	−0.173561	−	0.984823i	$-0.555527\pi$
$349$	11.0696	−	6.39102i	0.592541	−	0.342104i	0.766101	+	0.642720i	$0.222194\pi$
$350$		0			0
$351$	−1.36620	+	2.48513i	−0.0729222	+	0.132646i
$352$		0			0
$353$	−18.3612	−	31.8025i	−0.977268	−	1.69268i	−0.672237	−	0.740336i	$-0.734666\pi$
$353$	−18.3612	−	31.8025i	−0.977268	−	1.69268i	−0.305031	−	0.952342i	$-0.598667\pi$
$354$		0			0
$355$	−6.76501	−	3.90578i	−0.359049	−	0.207297i
$356$		0			0
$357$	8.36605	−	20.2120i	0.442778	−	1.06973i
$358$		0			0
$359$		−	31.9790i		−	1.68779i	−0.536510	−	0.843894i	$-0.680258\pi$
$359$		−	31.9790i		−	1.68779i	0.536510	−	0.843894i	$-0.319742\pi$
$360$		0			0
$361$	9.04098			0.475841
$362$		0			0
$363$	15.1856	−	8.90938i	0.797038	−	0.467621i
$364$		0			0
$365$	6.49419	+	3.74943i	0.339922	+	0.196254i
$366$		0			0
$367$	24.6434	−	14.2279i	1.28638	−	0.742689i	0.308370	−	0.951267i	$-0.400217\pi$
$367$	24.6434	−	14.2279i	1.28638	−	0.742689i	0.978006	+	0.208577i	$0.0668833\pi$
$368$		0			0
$369$	16.9376	−	0.236561i	0.881739	−	0.0123149i
$370$		0			0
$371$	−6.55485	+	0.818135i	−0.340311	+	0.0424755i
$372$		0			0
$373$	−11.7350	+	20.3257i	−0.607618	+	1.05242i	0.384014	+	0.923327i	$0.374541\pi$
$373$	−11.7350	+	20.3257i	−0.607618	+	1.05242i	−0.991632	+	0.129098i	$0.958792\pi$
$374$		0			0
$375$	−11.8167	−	6.71278i	−0.610210	−	0.346646i
$376$		0			0
$377$	−3.50694			−0.180616
$378$		0			0
$379$	−12.5179			−0.643003			−0.321502	−	0.946909i	$-0.604188\pi$
$379$	−12.5179			−0.643003			−0.321502	+	0.946909i	$0.604188\pi$
$380$		0			0
$381$	−10.8317	−	6.15327i	−0.554927	−	0.315241i
$382$		0			0
$383$	−6.71492	+	11.6306i	−0.343116	+	0.594295i	−0.985010	−	0.172499i	$-0.944816\pi$
$383$	−6.71492	+	11.6306i	−0.343116	+	0.594295i	0.641893	+	0.766794i	$0.278149\pi$
$384$		0			0
$385$	−2.02712	+	0.253012i	−0.103311	+	0.0128947i
$386$		0			0
$387$	5.40280	−	9.66725i	0.274640	−	0.491414i
$388$		0			0
$389$	−4.38955	+	2.53431i	−0.222559	+	0.128495i	−0.607135	−	0.794599i	$-0.707681\pi$
$389$	−4.38955	+	2.53431i	−0.222559	+	0.128495i	0.384576	+	0.923094i	$0.374348\pi$
$390$		0			0
$391$	6.64907	+	3.83884i	0.336258	+	0.194139i
$392$		0			0
$393$	7.51720	−	4.41033i	0.379193	−	0.222472i
$394$		0			0
$395$	−9.43958			−0.474957
$396$		0			0
$397$			1.08699i			0.0545543i	0.999628	+	0.0272771i	$0.00868366\pi$
$397$			1.08699i			0.0545543i	−0.999628	+	0.0272771i	$0.991316\pi$
$398$		0			0
$399$	13.3622	+	5.53083i	0.668948	+	0.276888i
$400$		0			0
$401$	−4.72547	−	2.72825i	−0.235979	−	0.136242i	0.377348	−	0.926071i	$-0.376836\pi$
$401$	−4.72547	−	2.72825i	−0.235979	−	0.136242i	−0.613327	+	0.789829i	$0.710169\pi$
$402$		0			0
$403$	−0.495815	−	0.858777i	−0.0246983	−	0.0427787i
$404$		0			0
$405$	3.98477	+	6.47706i	0.198005	+	0.321848i
$406$		0			0
$407$	−5.65069	+	3.26243i	−0.280094	+	0.161712i
$408$		0			0
$409$	21.4739	+	12.3979i	1.06181	+	0.613039i	0.925934	−	0.377686i	$-0.123280\pi$
$409$	21.4739	+	12.3979i	1.06181	+	0.613039i	0.135881	+	0.990725i	$0.456614\pi$
$410$		0			0
$411$	3.22758	−	0.0225381i	0.159205	−	0.00111172i
$412$		0			0
$413$	1.36059	+	0.574329i	0.0669502	+	0.0282609i
$414$		0			0
$415$	0.206373			0.0101305
$416$		0			0
$417$	−10.0242	−	17.0857i	−0.490885	−	0.836691i
$418$		0			0
$419$	−0.145143	+	0.251394i	−0.00709068	+	0.0122814i	−0.869549	−	0.493847i	$-0.835590\pi$
$419$	−0.145143	+	0.251394i	−0.00709068	+	0.0122814i	0.862458	+	0.506128i	$0.168924\pi$
$420$		0			0
$421$	−2.47275	−	4.28293i	−0.120515	−	0.208737i	0.799456	−	0.600724i	$-0.205121\pi$
$421$	−2.47275	−	4.28293i	−0.120515	−	0.208737i	−0.919971	+	0.391987i	$0.871788\pi$
$422$		0			0
$423$	−19.7639	+	35.3637i	−0.960956	+	1.71944i
$424$		0			0
$425$	10.2297	+	17.7184i	0.496215	+	0.859470i
$426$		0			0
$427$	−20.2644	−	26.7802i	−0.980662	−	1.29598i
$428$		0			0
$429$	−0.751083	−	0.426673i	−0.0362626	−	0.0206000i
$430$		0			0
$431$		−	15.4421i		−	0.743818i	−0.928269	−	0.371909i	$-0.878703\pi$
$431$		−	15.4421i		−	0.743818i	0.928269	−	0.371909i	$-0.121297\pi$
$432$		0			0
$433$		−	20.5683i		−	0.988451i	−0.869334	−	0.494225i	$-0.835452\pi$
$433$		−	20.5683i		−	0.988451i	0.869334	−	0.494225i	$-0.164548\pi$
$434$		0			0
$435$	−4.64504	+	8.17678i	−0.222713	+	0.392046i
$436$		0			0
$437$	−2.53787	+	4.39573i	−0.121403	+	0.210276i
$438$		0			0
$439$	−16.1823	+	9.34286i	−0.772339	+	0.445910i	−0.833708	−	0.552205i	$-0.813787\pi$
$439$	−16.1823	+	9.34286i	−0.772339	+	0.445910i	0.0613693	+	0.998115i	$0.480453\pi$
$440$		0			0
$441$	−14.8568	−	14.8417i	−0.707467	−	0.706746i
$442$		0			0
$443$	−29.4963	+	17.0297i	−1.40141	+	0.809104i	−0.994537	−	0.104380i	$-0.966714\pi$
$443$	−29.4963	+	17.0297i	−1.40141	+	0.809104i	−0.406873	+	0.913485i	$0.633381\pi$
$444$		0			0
$445$	2.61651	−	4.53193i	0.124035	−	0.214834i
$446$		0			0
$447$	−0.449045	−	0.765376i	−0.0212391	−	0.0362011i
$448$		0			0
$449$			12.7995i			0.604045i	0.953301	+	0.302023i	$0.0976618\pi$
$449$			12.7995i			0.604045i	−0.953301	+	0.302023i	$0.902338\pi$
$450$		0			0
$451$			5.15969i			0.242960i
$452$		0			0
$453$	0.139041	+	19.9115i	0.00653270	+	0.935522i
$454$		0			0
$455$	−0.736221	−	0.972947i	−0.0345146	−	0.0456124i
$456$		0			0
$457$	−1.55034	−	2.68526i	−0.0725217	−	0.125611i	0.827484	−	0.561489i	$-0.189771\pi$
$457$	−1.55034	−	2.68526i	−0.0725217	−	0.125611i	−0.900006	+	0.435878i	$0.856438\pi$
$458$		0			0
$459$	−0.519567	−	24.7985i	−0.0242513	−	1.15749i
$460$		0			0
$461$	−2.78519	−	4.82409i	−0.129719	−	0.224680i	0.793849	−	0.608115i	$-0.208074\pi$
$461$	−2.78519	−	4.82409i	−0.129719	−	0.224680i	−0.923568	+	0.383435i	$0.874741\pi$
$462$		0			0
$463$	−3.87498	+	6.71166i	−0.180086	+	0.311917i	−0.941909	−	0.335867i	$-0.890971\pi$
$463$	−3.87498	+	6.71166i	−0.180086	+	0.311917i	0.761824	+	0.647784i	$0.224304\pi$
$464$		0			0
$465$	−2.65905	+	0.0185680i	−0.123310	+	0.000861070i
$466$		0			0
$467$	−17.7545			−0.821579			−0.410789	−	0.911730i	$-0.634747\pi$
$467$	−17.7545			−0.821579			−0.410789	+	0.911730i	$0.634747\pi$
$468$		0			0
$469$	−14.9440	−	6.30813i	−0.690050	−	0.291282i
$470$		0			0
$471$	−15.0988	−	25.7352i	−0.695717	−	1.18582i
$472$		0			0
$473$	2.92136	+	1.68665i	0.134325	+	0.0775523i
$474$		0			0
$475$	−11.7137	+	6.76293i	−0.537463	+	0.310304i
$476$		0			0
$477$	−6.43374	+	3.83531i	−0.294581	+	0.175607i
$478$		0			0
$479$	2.03903	+	3.53171i	0.0931658	+	0.161368i	0.908842	−	0.417141i	$-0.136968\pi$
$479$	2.03903	+	3.53171i	0.0931658	+	0.161368i	−0.815676	+	0.578509i	$0.803635\pi$
$480$		0			0
$481$	−3.37491	−	1.94850i	−0.153882	−	0.0888441i
$482$		0			0
$483$	5.84633	−	4.48841i	0.266017	−	0.204230i
$484$		0			0
$485$			11.9430i			0.542306i
$486$		0			0
$487$	−29.6103			−1.34177			−0.670885	−	0.741561i	$-0.734086\pi$
$487$	−29.6103			−1.34177			−0.670885	+	0.741561i	$0.734086\pi$
$488$		0			0
$489$	−19.1976	−	10.9057i	−0.868148	−	0.493175i
$490$		0			0
$491$	−24.9656	−	14.4139i	−1.12668	−	0.650491i	−0.183584	−	0.983004i	$-0.558770\pi$
$491$	−24.9656	−	14.4139i	−1.12668	−	0.650491i	−0.943099	+	0.332513i	$0.892103\pi$
$492$		0			0
$493$	26.5636	−	15.3365i	1.19636	−	0.690721i
$494$		0			0
$495$	−1.98966	+	1.18609i	−0.0894287	+	0.0533106i
$496$		0			0
$497$	24.2713	−	3.02940i	1.08872	−	0.135887i
$498$		0			0
$499$	−13.9354	+	24.1367i	−0.623832	+	1.08051i	0.364933	+	0.931034i	$0.381092\pi$
$499$	−13.9354	+	24.1367i	−0.623832	+	1.08051i	−0.988765	+	0.149475i	$0.952241\pi$
$500$		0			0
$501$	11.7187	−	6.87532i	0.523551	−	0.307167i
$502$		0			0
$503$	−20.6312			−0.919901			−0.459950	−	0.887945i	$-0.652133\pi$
$503$	−20.6312			−0.919901			−0.459950	+	0.887945i	$0.652133\pi$
$504$		0			0
$505$	−9.50490			−0.422963
$506$		0			0
$507$	0.153626	+	22.0002i	0.00682278	+	0.977063i
$508$		0			0
$509$	−12.4163	+	21.5056i	−0.550341	+	0.953219i	0.447908	+	0.894079i	$0.352169\pi$
$509$	−12.4163	+	21.5056i	−0.550341	+	0.953219i	−0.998250	+	0.0591396i	$0.981164\pi$
$510$		0			0
$511$	−23.2997	+	2.90812i	−1.03072	+	0.128648i
$512$		0			0
$513$	16.3944	−	0.343488i	0.723829	−	0.0151654i
$514$		0			0
$515$	1.67136	−	0.964960i	0.0736489	−	0.0425212i
$516$		0			0
$517$	−10.6866	−	6.16992i	−0.469997	−	0.271353i
$518$		0			0
$519$	0.0242907	+	3.47858i	0.00106624	+	0.152693i
$520$		0			0
$521$	−25.5525			−1.11947			−0.559737	−	0.828670i	$-0.689098\pi$
$521$	−25.5525			−1.11947			−0.559737	+	0.828670i	$0.689098\pi$
$522$		0			0
$523$			25.0505i			1.09538i	0.836681	+	0.547691i	$0.184493\pi$
$523$			25.0505i			1.09538i	−0.836681	+	0.547691i	$0.815507\pi$
$524$		0			0
$525$	19.4724	−	2.56864i	0.849846	−	0.112105i
$526$		0			0
$527$	7.51119	+	4.33659i	0.327192	+	0.188905i
$528$		0			0
$529$	−10.2065	−	17.6782i	−0.443762	−	0.768619i
$530$		0			0
$531$	1.67442	−	0.0233858i	0.0726634	−	0.00101486i
$532$		0			0
$533$	−2.66879	+	1.54083i	−0.115598	+	0.0667407i
$534$		0			0
$535$	−8.03097	−	4.63668i	−0.347209	−	0.200461i
$536$		0			0
$537$	10.1258	−	17.8247i	0.436960	−	0.769191i
$538$		0			0
$539$	4.58352	−	4.46179i	0.197426	−	0.192183i
$540$		0			0
$541$	23.6313			1.01599			0.507995	−	0.861360i	$-0.330387\pi$
$541$	23.6313			1.01599			0.507995	+	0.861360i	$0.330387\pi$
$542$		0			0
$543$	−9.19256	+	16.1819i	−0.394491	+	0.694432i
$544$		0			0
$545$	2.62417	−	4.54520i	0.112407	−	0.194695i
$546$		0			0
$547$	14.0512	+	24.3375i	0.600788	+	1.04060i	0.992702	+	0.120593i	$0.0384797\pi$
$547$	14.0512	+	24.3375i	0.600788	+	1.04060i	−0.391914	+	0.920002i	$0.628187\pi$
$548$		0			0
$549$	−33.2406	−	18.5774i	−1.41868	−	0.792865i
$550$		0			0
$551$	10.1390	+	17.5613i	0.431937	+	0.748136i
$552$		0			0
$553$	23.5699	−	17.8352i	1.00230	−	0.758429i
$554$		0			0
$555$	−9.01330	+	5.28809i	−0.382593	+	0.224467i
$556$		0			0
$557$		−	14.3227i		−	0.606871i	−0.952852	−	0.303436i	$-0.901866\pi$
$557$		−	14.3227i		−	0.606871i	0.952852	−	0.303436i	$-0.0981338\pi$
$558$		0			0
$559$			2.01472i			0.0852138i
$560$		0			0
$561$	7.55506	−	0.0527566i	0.318975	−	0.00222739i
$562$		0			0
$563$	19.2183	−	33.2871i	0.809955	−	1.40288i	−0.102940	−	0.994688i	$-0.532825\pi$
$563$	19.2183	−	33.2871i	0.809955	−	1.40288i	0.912895	−	0.408196i	$-0.133842\pi$
$564$		0			0
$565$	−12.7762	+	7.37634i	−0.537498	+	0.310325i
$566$		0			0
$567$	−22.1875	−	8.64390i	−0.931785	−	0.363010i
$568$		0			0
$569$	22.5883	−	13.0414i	0.946951	−	0.546722i	0.0548183	−	0.998496i	$-0.482542\pi$
$569$	22.5883	−	13.0414i	0.946951	−	0.546722i	0.892132	+	0.451774i	$0.149209\pi$
$570$		0			0
$571$	9.74336	−	16.8760i	0.407747	−	0.706238i	−0.586890	−	0.809667i	$-0.699648\pi$
$571$	9.74336	−	16.8760i	0.407747	−	0.706238i	0.994637	+	0.103428i	$0.0329813\pi$
$572$		0			0
$573$	−5.73571	+	0.0400522i	−0.239613	+	0.00167320i
$574$		0			0
$575$			6.89364i			0.287484i
$576$		0			0
$577$			8.07209i			0.336045i	0.985783	+	0.168023i	$0.0537382\pi$
$577$			8.07209i			0.336045i	−0.985783	+	0.168023i	$0.946262\pi$
$578$		0			0
$579$	35.0242	−	20.5486i	1.45556	−	0.853972i
$580$		0			0
$581$	−0.515298	+	0.389922i	−0.0213782	+	0.0161767i
$582$		0			0
$583$	−1.14075	−	1.97584i	−0.0472450	−	0.0818307i
$584$		0			0
$585$	−1.20766	−	0.674933i	−0.0499305	−	0.0279050i
$586$		0			0
$587$	−16.1825	−	28.0289i	−0.667923	−	1.15688i	−0.978484	−	0.206323i	$-0.933850\pi$
$587$	−16.1825	−	28.0289i	−0.667923	−	1.15688i	0.310561	−	0.950554i	$-0.399483\pi$
$588$		0			0
$589$	−2.86693	+	4.96568i	−0.118130	+	0.204607i
$590$		0			0
$591$	−15.3263	+	26.9793i	−0.630439	+	1.10978i
$592$		0			0
$593$	43.7169			1.79524			0.897619	−	0.440772i	$-0.145295\pi$
$593$	43.7169			1.79524			0.897619	+	0.440772i	$0.145295\pi$
$594$		0			0
$595$	9.83145	+	4.15003i	0.403050	+	0.170135i
$596$		0			0
$597$	−13.7675	+	24.2353i	−0.563467	+	0.991885i
$598$		0			0
$599$	−20.4061	−	11.7814i	−0.833769	−	0.481377i	0.0213724	−	0.999772i	$-0.493196\pi$
$599$	−20.4061	−	11.7814i	−0.833769	−	0.481377i	−0.855141	+	0.518395i	$0.826530\pi$
$600$		0			0
$601$	3.85990	−	2.22851i	0.157449	−	0.0909030i	−0.419206	−	0.907891i	$-0.637691\pi$
$601$	3.85990	−	2.22851i	0.157449	−	0.0909030i	0.576654	+	0.816988i	$0.304358\pi$
$602$		0			0
$603$	−18.3909	+	0.256858i	−0.748936	+	0.0104601i
$604$		0			0
$605$	4.29450	+	7.43830i	0.174596	+	0.302410i
$606$		0			0
$607$	−8.95483	−	5.17007i	−0.363465	−	0.209847i	0.307134	−	0.951666i	$-0.400630\pi$
$607$	−8.95483	−	5.17007i	−0.363465	−	0.209847i	−0.670600	+	0.741819i	$0.733963\pi$
$608$		0			0
$609$	−3.85092	−	29.1932i	−0.156047	−	1.18297i
$610$		0			0
$611$		−	7.37004i		−	0.298160i
$612$		0			0
$613$	2.30558			0.0931214			0.0465607	−	0.998915i	$-0.485174\pi$
$613$	2.30558			0.0931214			0.0465607	+	0.998915i	$0.485174\pi$
$614$		0			0
$615$	0.0577031	+	8.26344i	0.00232682	+	0.333214i
$616$		0			0
$617$	−0.725847	−	0.419068i	−0.0292215	−	0.0168710i	0.485318	−	0.874338i	$-0.338704\pi$
$617$	−0.725847	−	0.419068i	−0.0292215	−	0.0168710i	−0.514540	+	0.857467i	$0.672037\pi$
$618$		0			0
$619$	−21.8761	+	12.6302i	−0.879274	+	0.507649i	−0.870419	−	0.492312i	$-0.836152\pi$
$619$	−21.8761	+	12.6302i	−0.879274	+	0.507649i	−0.00885512	+	0.999961i	$0.502819\pi$
$620$		0			0
$621$	4.02620	−	7.32371i	0.161566	−	0.293890i
$622$		0			0
$623$	2.02942	+	16.2596i	0.0813068	+	0.651425i
$624$		0			0
$625$	−7.40018	+	12.8175i	−0.296007	+	0.512699i
$626$		0			0
$627$	0.0348776	+	4.99468i	0.00139288	+	0.199468i
$628$		0			0
$629$	34.0847			1.35905
$630$		0			0
$631$	8.42854			0.335535			0.167768	−	0.985827i	$-0.446344\pi$
$631$	8.42854			0.335535			0.167768	+	0.985827i	$0.446344\pi$
$632$		0			0
$633$	−5.84863	+	3.43138i	−0.232462	+	0.136385i
$634$		0			0
$635$	3.03862	−	5.26305i	0.120584	−	0.208858i
$636$		0			0
$637$	3.67658	+	1.03836i	0.145671	+	0.0411412i
$638$		0			0
$639$	23.8229	−	14.2014i	0.942419	−	0.561799i
$640$		0			0
$641$	28.3658	−	16.3770i	1.12038	−	0.646853i	0.178884	−	0.983870i	$-0.442751\pi$
$641$	28.3658	−	16.3770i	1.12038	−	0.646853i	0.941498	+	0.337017i	$0.109418\pi$
$642$		0			0
$643$	33.5703	+	19.3818i	1.32388	+	0.764344i	0.984346	−	0.176249i	$-0.0563962\pi$
$643$	33.5703	+	19.3818i	1.32388	+	0.764344i	0.339537	+	0.940593i	$0.389730\pi$
$644$		0			0
$645$	4.69754	+	2.66856i	0.184965	+	0.105075i
$646$		0			0
$647$	33.9121			1.33322			0.666611	−	0.745405i	$-0.267744\pi$
$647$	33.9121			1.33322			0.666611	+	0.745405i	$0.267744\pi$
$648$		0			0
$649$			0.510075i			0.0200222i
$650$		0			0
$651$	6.60436	−	5.07038i	0.258845	−	0.198724i
$652$		0			0
$653$	−8.48007	−	4.89597i	−0.331851	−	0.191594i	0.324812	−	0.945779i	$-0.394699\pi$
$653$	−8.48007	−	4.89597i	−0.331851	−	0.191594i	−0.656663	+	0.754185i	$0.728032\pi$
$654$		0			0
$655$	2.12587	+	3.68211i	0.0830646	+	0.143872i
$656$		0			0
$657$	−22.8692	+	13.6329i	−0.892214	+	0.531870i
$658$		0			0
$659$	−28.8977	+	16.6841i	−1.12569	+	0.649920i	−0.942849	−	0.333221i	$-0.891864\pi$
$659$	−28.8977	+	16.6841i	−1.12569	+	0.649920i	−0.182846	+	0.983142i	$0.558531\pi$
$660$		0			0
$661$	36.8160	+	21.2558i	1.43198	+	0.826753i	0.997272	−	0.0738194i	$-0.0235188\pi$
$661$	36.8160	+	21.2558i	1.43198	+	0.826753i	0.434706	+	0.900572i	$0.356852\pi$
$662$		0			0
$663$	2.28344	+	3.89202i	0.0886815	+	0.151153i
$664$		0			0
$665$	−2.74360	+	6.49961i	−0.106392	+	0.252044i
$666$		0			0
$667$	10.3350			0.400172
$668$		0			0
$669$	−43.2084	+	0.301722i	−1.67053	+	0.0116653i
$670$		0			0
$671$	5.79951	−	10.0450i	0.223888	−	0.387785i
$672$		0			0
$673$	22.7186	+	39.3498i	0.875739	+	1.51682i	0.855974	+	0.517019i	$0.172958\pi$
$673$	22.7186	+	39.3498i	0.875739	+	1.51682i	0.0197649	+	0.999805i	$0.493708\pi$
$674$		0			0
$675$	19.0497	−	11.5370i	0.733223	−	0.444060i
$676$		0			0
$677$	16.2542	+	28.1532i	0.624701	+	1.08201i	0.988599	+	0.150575i	$0.0481124\pi$
$677$	16.2542	+	28.1532i	0.624701	+	1.08201i	−0.363898	+	0.931439i	$0.618554\pi$
$678$		0			0
$679$	−22.5653	−	29.8209i	−0.865975	−	1.14442i
$680$		0			0
$681$	0.275461	+	39.4477i	0.0105557	+	1.51164i
$682$		0			0
$683$		−	24.3776i		−	0.932781i	−0.884579	−	0.466391i	$-0.845554\pi$
$683$		−	24.3776i		−	0.932781i	0.884579	−	0.466391i	$-0.154446\pi$
$684$		0			0
$685$			1.57458i			0.0601615i
$686$		0			0
$687$	22.6247	+	38.5627i	0.863186	+	1.47126i
$688$		0			0
$689$	0.681319	−	1.18008i	0.0259562	−	0.0449575i
$690$		0			0
$691$	−23.5773	+	13.6123i	−0.896922	+	0.517838i	−0.876200	−	0.481947i	$-0.839930\pi$
$691$	−23.5773	+	13.6123i	−0.896922	+	0.517838i	−0.0207214	+	0.999785i	$0.506596\pi$
$692$		0			0
$693$	2.72705	−	6.72085i	0.103592	−	0.255304i
$694$		0			0
$695$	8.36901	−	4.83185i	0.317455	−	0.183283i
$696$		0			0
$697$	13.4767	−	23.3423i	0.510465	−	0.884152i
$698$		0			0
$699$	24.5599	−	43.2334i	0.928941	−	1.63524i
$700$		0			0
$701$			32.8777i			1.24177i	0.783900	+	0.620887i	$0.213227\pi$
$701$			32.8777i			1.24177i	−0.783900	+	0.620887i	$0.786773\pi$
$702$		0			0
$703$			22.5335i			0.849868i
$704$		0			0
$705$	−17.1840	−	9.76184i	−0.647187	−	0.367652i
$706$		0			0
$707$	23.7330	−	17.9586i	0.892573	−	0.675403i
$708$		0			0
$709$	2.02639	+	3.50981i	0.0761026	+	0.131814i	0.901565	−	0.432643i	$-0.142419\pi$
$709$	2.02639	+	3.50981i	0.0761026	+	0.131814i	−0.825463	+	0.564457i	$0.809086\pi$
$710$		0			0
$711$	16.3505	−	29.2559i	0.613190	−	1.09718i
$712$		0			0
$713$	1.46117	+	2.53082i	0.0547213	+	0.0947801i
$714$		0			0
$715$	0.210701	−	0.364945i	0.00787977	−	0.0136482i
$716$		0			0
$717$	−20.9587	−	35.7231i	−0.782716	−	1.33410i
$718$		0			0
$719$	35.0419			1.30684			0.653420	−	0.756995i	$-0.273333\pi$
$719$	35.0419			1.30684			0.653420	+	0.756995i	$0.273333\pi$
$720$		0			0
$721$	−2.35006	+	5.56731i	−0.0875209	+	0.207337i
$722$		0			0
$723$	−25.5975	+	0.178746i	−0.951982	+	0.00664764i
$724$		0			0
$725$	23.8509	+	13.7703i	0.885800	+	0.511417i
$726$		0			0
$727$	0.292512	−	0.168882i	0.0108487	−	0.00626349i	−0.494566	−	0.869140i	$-0.664673\pi$
$727$	0.292512	−	0.168882i	0.0108487	−	0.00626349i	0.505415	+	0.862877i	$0.331340\pi$
$728$		0			0
$729$	−26.9763	+	1.13089i	−0.999122	+	0.0418847i
$730$		0			0
$731$	−8.81077	−	15.2607i	−0.325878	−	0.564437i
$732$		0			0
$733$	−2.16404	−	1.24941i	−0.0799306	−	0.0461479i	0.459502	−	0.888177i	$-0.348028\pi$
$733$	−2.16404	−	1.24941i	−0.0799306	−	0.0461479i	−0.539433	+	0.842029i	$0.681361\pi$
$734$		0			0
$735$	7.29077	−	7.19698i	0.268924	−	0.265465i
$736$		0			0
$737$		−	5.60240i		−	0.206367i
$738$		0			0
$739$	34.0147			1.25125			0.625625	−	0.780124i	$-0.284844\pi$
$739$	34.0147			1.25125			0.625625	+	0.780124i	$0.284844\pi$
$740$		0			0
$741$	−2.57303	+	1.50959i	−0.0945226	+	0.0554563i
$742$		0			0
$743$	30.1013	+	17.3790i	1.10431	+	0.637573i	0.937350	−	0.348390i	$-0.113272\pi$
$743$	30.1013	+	17.3790i	1.10431	+	0.637573i	0.166960	+	0.985964i	$0.446605\pi$
$744$		0			0
$745$	0.374900	−	0.216449i	0.0137353	−	0.00793007i
$746$		0			0
$747$	−0.357462	+	0.639608i	−0.0130789	+	0.0234020i
$748$		0			0
$749$	28.8133	−	3.59630i	1.05281	−	0.131406i
$750$		0			0
$751$	−5.46861	+	9.47191i	−0.199552	+	0.345635i	−0.948383	−	0.317126i	$-0.897282\pi$
$751$	−5.46861	+	9.47191i	−0.199552	+	0.345635i	0.748831	+	0.662761i	$0.230615\pi$
$752$		0			0
$753$	38.4822	+	21.8608i	1.40237	+	0.796653i
$754$		0			0
$755$	−9.71381			−0.353522
$756$		0			0
$757$	−37.5008			−1.36299			−0.681496	−	0.731822i	$-0.738670\pi$
$757$	−37.5008			−1.36299			−0.681496	+	0.731822i	$0.738670\pi$
$758$		0			0
$759$	2.21345	+	1.25741i	0.0803431	+	0.0456411i
$760$		0			0
$761$	−8.94575	+	15.4945i	−0.324283	+	0.561675i	−0.981367	−	0.192143i	$-0.938456\pi$
$761$	−8.94575	+	15.4945i	−0.324283	+	0.561675i	0.657084	+	0.753818i	$0.271790\pi$
$762$		0			0
$763$	2.03536	+	16.3072i	0.0736849	+	0.590359i
$764$		0			0
$765$	12.0991	−	0.168983i	0.437445	−	0.00610960i
$766$		0			0
$767$	−0.263831	+	0.152323i	−0.00952637	+	0.00550005i
$768$		0			0
$769$	−47.0913	−	27.1882i	−1.69816	−	0.980431i	−0.947510	−	0.319727i	$-0.896409\pi$
$769$	−47.0913	−	27.1882i	−1.69816	−	0.980431i	−0.750647	−	0.660704i	$-0.770258\pi$
$770$		0			0
$771$	7.99443	−	4.69032i	0.287912	−	0.168918i
$772$		0			0
$773$	−2.26464			−0.0814533			−0.0407266	−	0.999170i	$-0.512967\pi$
$773$	−2.26464			−0.0814533			−0.0407266	+	0.999170i	$0.512967\pi$
$774$		0			0
$775$			7.78746i			0.279734i
$776$		0			0
$777$	12.5142	−	30.2337i	0.448944	−	1.08463i
$778$		0			0
$779$	15.4317	+	8.90948i	0.552897	+	0.319215i
$780$		0			0
$781$	4.22397	+	7.31613i	0.151146	+	0.261792i
$782$		0			0
$783$	−17.2964	−	28.5594i	−0.618122	−	1.02063i
$784$		0			0
$785$	12.6058	−	7.27793i	0.449919	−	0.259761i
$786$		0			0
$787$	−12.2816	−	7.09078i	−0.437792	−	0.252759i	0.264869	−	0.964284i	$-0.414671\pi$
$787$	−12.2816	−	7.09078i	−0.437792	−	0.252759i	−0.702660	+	0.711525i	$0.748005\pi$
$788$		0			0
$789$	8.18420	−	0.0571499i	0.291365	−	0.00203459i
$790$		0			0
$791$	17.9643	−	42.5576i	0.638738	−	1.51317i
$792$		0			0
$793$	6.92759			0.246006
$794$		0			0
$795$	−1.84905	−	3.15162i	−0.0655790	−	0.111776i
$796$		0			0
$797$	−1.56607	+	2.71252i	−0.0554731	+	0.0960823i	−0.892428	−	0.451189i	$-0.851000\pi$
$797$	−1.56607	+	2.71252i	−0.0554731	+	0.0960823i	0.836955	+	0.547271i	$0.184333\pi$
$798$		0			0
$799$	32.2306	+	55.8250i	1.14024	+	1.97495i
$800$		0			0
$801$	9.51363	+	15.9591i	0.336148	+	0.563889i
$802$		0			0
$803$	−4.05488	−	7.02326i	−0.143094	−	0.247845i
$804$		0			0
$805$	2.16965	+	2.86728i	0.0764702	+	0.101058i
$806$		0			0
$807$	33.8475	+	19.2280i	1.19149	+	0.676857i
$808$		0			0
$809$		−	8.37975i		−	0.294616i	−0.989091	−	0.147308i	$-0.952939\pi$
$809$		−	8.37975i		−	0.294616i	0.989091	−	0.147308i	$-0.0470609\pi$
$810$		0			0
$811$			21.1311i			0.742013i	0.928630	+	0.371006i	$0.120987\pi$
$811$			21.1311i			0.742013i	−0.928630	+	0.371006i	$0.879013\pi$
$812$		0			0
$813$	−22.4792	+	39.5707i	−0.788381	+	1.38781i
$814$		0			0
$815$	5.38551	−	9.32797i	0.188646	−	0.326744i
$816$		0			0
$817$	10.0889	−	5.82484i	0.352966	−	0.203785i
$818$		0			0
$819$	4.29066	−	0.596499i	0.149928	−	0.0208433i
$820$		0			0
$821$	−22.9473	+	13.2486i	−0.800867	+	0.462381i	−0.843774	−	0.536699i	$-0.819671\pi$
$821$	−22.9473	+	13.2486i	−0.800867	+	0.462381i	0.0429075	+	0.999079i	$0.486338\pi$
$822$		0			0
$823$	−3.00916	+	5.21202i	−0.104893	+	0.181679i	−0.913694	−	0.406402i	$-0.866783\pi$
$823$	−3.00916	+	5.21202i	−0.104893	+	0.181679i	0.808802	+	0.588082i	$0.200117\pi$
$824$		0			0
$825$	3.43279	+	5.85103i	0.119514	+	0.203707i
$826$		0			0
$827$			0.447159i			0.0155492i	0.999970	+	0.00777462i	$0.00247476\pi$
$827$			0.447159i			0.0155492i	−0.999970	+	0.00777462i	$0.997525\pi$
$828$		0			0
$829$			23.3395i			0.810614i	0.914181	+	0.405307i	$0.132835\pi$
$829$			23.3395i			0.810614i	−0.914181	+	0.405307i	$0.867165\pi$
$830$		0			0
$831$	0.0347981	+	4.98330i	0.00120713	+	0.172869i
$832$		0			0
$833$	−32.3895	+	8.21326i	−1.12223	+	0.284572i
$834$		0			0
$835$	3.31404	+	5.74009i	0.114687	+	0.198644i
$836$		0			0
$837$	4.54823	−	8.27330i	0.157210	−	0.285967i
$838$		0			0
$839$	11.0244	+	19.0948i	0.380603	+	0.659224i	0.991149	−	0.132757i	$-0.0423830\pi$
$839$	11.0244	+	19.0948i	0.380603	+	0.659224i	−0.610545	+	0.791981i	$0.709050\pi$
$840$		0			0
$841$	6.14453	−	10.6426i	0.211880	−	0.366987i
$842$		0			0
$843$	−6.31455	+	0.0440942i	−0.217485	+	0.00151868i
$844$		0			0
$845$	−10.7328			−0.369220
$846$		0			0
$847$	−24.7770	−	10.4588i	−0.851348	−	0.359369i
$848$		0			0
$849$	−23.1913	−	39.5285i	−0.795924	−	1.35661i
$850$		0			0
$851$	9.94589	+	5.74226i	0.340941	+	0.196842i
$852$		0			0
$853$	−9.94613	+	5.74240i	−0.340549	+	0.196616i	−0.660515	−	0.750813i	$-0.729662\pi$
$853$	−9.94613	+	5.74240i	−0.340549	+	0.196616i	0.319966	+	0.947429i	$0.396329\pi$
$854$		0			0
$855$	0.111716	+	7.99878i	0.00382059	+	0.273552i
$856$		0			0
$857$	−20.1891	−	34.9686i	−0.689648	−	1.19451i	−0.971952	−	0.235180i	$-0.924432\pi$
$857$	−20.1891	−	34.9686i	−0.689648	−	1.19451i	0.282304	−	0.959325i	$-0.408901\pi$
$858$		0			0
$859$	−22.7331	−	13.1250i	−0.775643	−	0.447818i	0.0592409	−	0.998244i	$-0.481132\pi$
$859$	−22.7331	−	13.1250i	−0.775643	−	0.447818i	−0.834884	+	0.550426i	$0.814465\pi$
$860$		0			0
$861$	−15.7571	−	20.5242i	−0.536999	−	0.699462i
$862$		0			0
$863$			39.2987i			1.33774i	0.743378	+	0.668871i	$0.233222\pi$
$863$			39.2987i			1.33774i	−0.743378	+	0.668871i	$0.766778\pi$
$864$		0			0
$865$	−1.69702			−0.0577006
$866$		0			0
$867$	−8.71446	−	4.95049i	−0.295959	−	0.168127i
$868$		0			0
$869$	8.84090	+	5.10430i	0.299907	+	0.173151i
$870$		0			0
$871$	2.89778	−	1.67303i	0.0981875	−	0.0566886i
$872$		0			0
$873$	−37.0149	−	20.6868i	−1.25276	−	0.700141i
$874$		0			0
$875$	2.57112	+	20.5996i	0.0869196	+	0.696395i
$876$		0			0
$877$	7.40252	−	12.8215i	0.249965	−	0.432952i	−0.713551	−	0.700604i	$-0.752914\pi$
$877$	7.40252	−	12.8215i	0.249965	−	0.432952i	0.963516	+	0.267651i	$0.0862475\pi$
$878$		0			0
$879$	−26.3078	+	15.4348i	−0.887341	+	0.520602i
$880$		0			0
$881$	47.2029			1.59031			0.795153	−	0.606409i	$-0.207390\pi$
$881$	47.2029			1.59031			0.795153	+	0.606409i	$0.207390\pi$
$882$		0			0
$883$	−50.0235			−1.68343			−0.841713	−	0.539925i	$-0.818452\pi$
$883$	−50.0235			−1.68343			−0.841713	+	0.539925i	$0.818452\pi$
$884$		0			0
$885$	0.00570439	+	0.816904i	0.000191751	+	0.0274599i
$886$		0			0
$887$	1.91871	−	3.32330i	0.0644239	−	0.111585i	−0.832014	−	0.554754i	$-0.812812\pi$
$887$	1.91871	−	3.32330i	0.0644239	−	0.111585i	0.896438	+	0.443169i	$0.146146\pi$
$888$		0			0
$889$	2.35681	+	18.8826i	0.0790450	+	0.633303i
$890$		0			0
$891$	−0.229682	−	8.22096i	−0.00769464	−	0.275413i
$892$		0			0
$893$	−36.9061	+	21.3078i	−1.23502	+	0.713037i
$894$		0			0
$895$	8.66085	+	5.00034i	0.289500	+	0.167143i
$896$		0			0
$897$	0.0106167	+	1.52038i	0.000354482	+	0.0507640i
$898$		0			0
$899$	11.6750			0.389383
$900$		0			0
$901$			11.9181i			0.397051i
$902$		0			0
$903$	−16.7714	+	2.21234i	−0.558117	+	0.0736221i
$904$		0			0
$905$	−7.86264	−	4.53950i	−0.261363	−	0.150898i
$906$		0			0
$907$	12.9009	+	22.3450i	0.428367	+	0.741954i	0.996728	−	0.0808252i	$-0.0257556\pi$
$907$	12.9009	+	22.3450i	0.428367	+	0.741954i	−0.568361	+	0.822779i	$0.692422\pi$
$908$		0			0
$909$	16.4636	−	29.4584i	0.546063	−	0.977072i
$910$		0			0
$911$	38.0894	−	21.9909i	1.26196	−	0.728592i	0.288505	−	0.957478i	$-0.406842\pi$
$911$	38.0894	−	21.9909i	1.26196	−	0.728592i	0.973453	+	0.228886i	$0.0735084\pi$
$912$		0			0
$913$	−0.193284	−	0.111593i	−0.00639678	−	0.00369318i
$914$		0			0
$915$	9.17579	−	16.1524i	0.303342	−	0.533981i
$916$		0			0
$917$	−12.2651	−	5.17734i	−0.405031	−	0.170971i
$918$		0			0
$919$	13.8634			0.457312			0.228656	−	0.973507i	$-0.426567\pi$
$919$	13.8634			0.457312			0.228656	+	0.973507i	$0.426567\pi$
$920$		0			0
$921$	16.8596	−	29.6784i	0.555543	−	0.977935i
$922$		0			0
$923$	−2.52279	+	4.36960i	−0.0830387	+	0.143827i
$924$		0			0
$925$	15.3020	+	26.5038i	0.503126	+	0.871439i
$926$		0			0
$927$	0.0956911	+	6.85144i	0.00314291	+	0.225031i
$928$		0			0
$929$	13.0022	+	22.5204i	0.426588	+	0.738872i	0.996567	−	0.0827871i	$-0.0263821\pi$
$929$	13.0022	+	22.5204i	0.426588	+	0.738872i	−0.569979	+	0.821659i	$0.693049\pi$
$930$		0			0
$931$	−5.42982	−	21.4128i	−0.177955	−	0.701777i
$932$		0			0
$933$	−35.6619	+	20.9228i	−1.16752	+	0.684981i
$934$		0			0
$935$			3.68574i			0.120537i
$936$		0			0
$937$			12.2999i			0.401819i	0.979610	+	0.200910i	$0.0643898\pi$
$937$			12.2999i			0.401819i	−0.979610	+	0.200910i	$0.935610\pi$
$938$		0			0
$939$	−13.7334	+	0.0958997i	−0.448173	+	0.00312957i
$940$		0			0
$941$	−19.4720	+	33.7264i	−0.634768	+	1.09945i	0.351797	+	0.936076i	$0.385571\pi$
$941$	−19.4720	+	33.7264i	−0.634768	+	1.09945i	−0.986564	+	0.163374i	$0.947762\pi$
$942$		0			0
$943$	7.86496	−	4.54084i	0.256118	−	0.147870i
$944$		0			0
$945$	4.29230	−	10.7942i	0.139629	−	0.351135i
$946$		0			0
$947$	−7.79744	+	4.50186i	−0.253383	+	0.146291i	−0.621312	−	0.783563i	$-0.713400\pi$
$947$	−7.79744	+	4.50186i	−0.253383	+	0.146291i	0.367929	+	0.929854i	$0.380067\pi$
$948$		0			0
$949$	2.42180	−	4.19468i	0.0786150	−	0.136165i
$950$		0			0
$951$	−16.8529	+	0.117683i	−0.546492	+	0.00381612i
$952$		0			0
$953$		−	12.2826i		−	0.397873i	−0.980012	−	0.198937i	$-0.936251\pi$
$953$		−	12.2826i		−	0.397873i	0.980012	−	0.198937i	$-0.0637488\pi$
$954$		0			0
$955$		−	2.79817i		−	0.0905466i
$956$		0			0
$957$	8.77189	−	5.14646i	0.283555	−	0.166361i
$958$		0			0
$959$	−2.97501	−	3.93160i	−0.0960682	−	0.126958i
$960$		0			0
$961$	−13.8494	−	23.9878i	−0.446754	−	0.773801i
$962$		0			0
$963$	28.2809	−	16.8589i	0.911341	−	0.543272i
$964$		0			0
$965$	9.90486	+	17.1557i	0.318849	+	0.552262i
$966$		0			0
$967$	19.6853	−	34.0960i	0.633037	−	1.09645i	−0.353890	−	0.935287i	$-0.615141\pi$
$967$	19.6853	−	34.0960i	0.633037	−	1.09645i	0.986927	−	0.161166i	$-0.0515253\pi$
$968$		0			0
$969$	12.8879	−	22.6869i	0.414019	−	0.728807i
$970$		0			0
$971$	−1.59421			−0.0511608			−0.0255804	−	0.999673i	$-0.508143\pi$
$971$	−1.59421			−0.0511608			−0.0255804	+	0.999673i	$0.508143\pi$
$972$		0			0
$973$	−11.7675	+	27.8772i	−0.377248	+	0.893703i
$974$		0			0
$975$	−2.00125	+	3.52285i	−0.0640914	+	0.112822i
$976$		0			0
$977$	−35.5341	−	20.5156i	−1.13684	−	0.656353i	−0.191192	−	0.981553i	$-0.561235\pi$
$977$	−35.5341	−	20.5156i	−1.13684	−	0.656353i	−0.945646	+	0.325199i	$0.894569\pi$
$978$		0			0
$979$	−4.90114	+	2.82967i	−0.156641	+	0.0904367i
$980$		0			0
$981$	9.54148	+	16.0059i	0.304636	+	0.511028i
$982$		0			0
$983$	−7.72534	−	13.3807i	−0.246400	−	0.426778i	0.716124	−	0.697973i	$-0.245914\pi$
$983$	−7.72534	−	13.3807i	−0.246400	−	0.426778i	−0.962524	+	0.271195i	$0.912581\pi$
$984$		0			0
$985$	−13.1090	−	7.56847i	−0.417687	−	0.241152i
$986$		0			0
$987$	61.3512	−	8.09295i	1.95283	−	0.257601i
$988$		0			0
$989$		−	5.93742i		−	0.188799i
$990$		0			0
$991$	1.86113			0.0591207			0.0295604	−	0.999563i	$-0.490589\pi$
$991$	1.86113			0.0591207			0.0295604	+	0.999563i	$0.490589\pi$
$992$		0			0
$993$	0.368764	+	52.8093i	0.0117024	+	1.67585i
$994$		0			0
$995$	−11.7757	−	6.79872i	−0.373316	−	0.215534i
$996$		0			0
$997$	35.7835	−	20.6596i	1.13328	−	0.654297i	0.188519	−	0.982070i	$-0.439631\pi$
$997$	35.7835	−	20.6596i	1.13328	−	0.654297i	0.944757	+	0.327773i	$0.106298\pi$
$998$		0			0
$999$	−0.777184	−	37.0943i	−0.0245890	−	1.17361i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bu.a.41.4	✓	48
3.2	odd	2		1512.2.bu.a.881.9		48
4.3	odd	2		1008.2.cc.d.545.21		48
7.6	odd	2	inner	504.2.bu.a.41.21	yes	48
9.2	odd	6	inner	504.2.bu.a.209.21	yes	48
9.4	even	3		4536.2.k.a.3401.18		48
9.5	odd	6		4536.2.k.a.3401.31		48
9.7	even	3		1512.2.bu.a.1385.16		48
12.11	even	2		3024.2.cc.d.881.9		48
21.20	even	2		1512.2.bu.a.881.16		48
28.27	even	2		1008.2.cc.d.545.4		48
36.7	odd	6		3024.2.cc.d.2897.16		48
36.11	even	6		1008.2.cc.d.209.4		48
63.13	odd	6		4536.2.k.a.3401.32		48
63.20	even	6	inner	504.2.bu.a.209.4	yes	48
63.34	odd	6		1512.2.bu.a.1385.9		48
63.41	even	6		4536.2.k.a.3401.17		48
84.83	odd	2		3024.2.cc.d.881.16		48
252.83	odd	6		1008.2.cc.d.209.21		48
252.223	even	6		3024.2.cc.d.2897.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bu.a.41.4	✓	48	1.1	even	1	trivial
504.2.bu.a.41.21	yes	48	7.6	odd	2	inner
504.2.bu.a.209.4	yes	48	63.20	even	6	inner
504.2.bu.a.209.21	yes	48	9.2	odd	6	inner
1008.2.cc.d.209.4		48	36.11	even	6
1008.2.cc.d.209.21		48	252.83	odd	6
1008.2.cc.d.545.4		48	28.27	even	2
1008.2.cc.d.545.21		48	4.3	odd	2
1512.2.bu.a.881.9		48	3.2	odd	2
1512.2.bu.a.881.16		48	21.20	even	2
1512.2.bu.a.1385.9		48	63.34	odd	6
1512.2.bu.a.1385.16		48	9.7	even	3
3024.2.cc.d.881.9		48	12.11	even	2
3024.2.cc.d.881.16		48	84.83	odd	2
3024.2.cc.d.2897.9		48	252.223	even	6
3024.2.cc.d.2897.16		48	36.7	odd	6
4536.2.k.a.3401.17		48	63.41	even	6
4536.2.k.a.3401.18		48	9.4	even	3
4536.2.k.a.3401.31		48	9.5	odd	6
4536.2.k.a.3401.32		48	63.13	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bu (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50601 - 0.855530i) q^{3} +(0.422480 - 0.731757i) q^{5} +(0.327684 + 2.62538i) q^{7} +(1.53614 + 2.57688i) q^{9} +(-0.791371 + 0.456898i) q^{11} +(-0.472651 - 0.272885i) q^{13} +(-1.26230 + 0.740590i) q^{15} +4.77352 q^{17} +3.15579i q^{19} +(1.75260 - 4.23419i) q^{21} +(1.39291 + 0.804196i) q^{23} +(2.14302 + 3.71182i) q^{25} +(-0.108844 - 5.19501i) q^{27} +(5.56478 - 3.21283i) q^{29} +(1.57351 + 0.908468i) q^{31} +(1.58270 - 0.0110519i) q^{33} +(2.05958 + 0.869387i) q^{35} +7.14037 q^{37} +(0.478356 + 0.815336i) q^{39} +(2.82322 - 4.88995i) q^{41} +(-1.84576 - 3.19695i) q^{43} +(2.53463 - 0.0354002i) q^{45} +(6.75196 + 11.6947i) q^{47} +(-6.78525 + 1.72059i) q^{49} +(-7.18897 - 4.08389i) q^{51} +2.49672i q^{53} +0.772122i q^{55} +(2.69987 - 4.75266i) q^{57} +(0.279096 - 0.483409i) q^{59} +(-10.9926 + 6.34661i) q^{61} +(-6.26191 + 4.87734i) q^{63} +(-0.399372 + 0.230577i) q^{65} +(-3.06545 + 5.30951i) q^{67} +(-1.40972 - 2.40280i) q^{69} -9.24488i q^{71} +8.87479i q^{73} +(-0.0518376 - 7.42346i) q^{75} +(-1.45885 - 1.92793i) q^{77} +(-5.58581 - 9.67491i) q^{79} +(-4.28057 + 7.91686i) q^{81} +(0.122120 + 0.211518i) q^{83} +(2.01672 - 3.49306i) q^{85} +(-11.1293 + 0.0777152i) q^{87} +6.19322 q^{89} +(0.561548 - 1.33031i) q^{91} +(-1.59250 - 2.71435i) q^{93} +(2.30927 + 1.33326i) q^{95} +(-12.2408 + 7.06722i) q^{97} +(-2.39302 - 1.33741i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9} + 8 q^{15} - 4 q^{21} + 12 q^{23} - 24 q^{25} - 36 q^{29} + 32 q^{39} + 12 q^{43} + 6 q^{49} + 24 q^{51} + 28 q^{57} - 14 q^{63} + 36 q^{65} - 60 q^{77} - 12 q^{79} - 36 q^{81} - 12 q^{91}+ \cdots + 44 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 + 8 * q^15 - 4 * q^21 + 12 * q^23 - 24 * q^25 - 36 * q^29 + 32 * q^39 + 12 * q^43 + 6 * q^49 + 24 * q^51 + 28 * q^57 - 14 * q^63 + 36 * q^65 - 60 * q^77 - 12 * q^79 - 36 * q^81 - 12 * q^91 + 16 * q^93 - 108 * q^95 + 44 * q^99

Introduction

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