LMFDB - Embedded newform 804.2.ba.b.41.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(41,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 33, 53]))

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

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

chi := DirichletCharacter("804.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.ba (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			41.19
Character	$\chi$	$=$	804.41
Dual form			804.2.ba.b.353.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.59370 + 0.678318i) q^{3} +(0.306661 - 2.13288i) q^{5} +(-0.233782 - 2.44828i) q^{7} +(2.07977 + 2.16207i) q^{9} +O(q^{10})$	\(q+(1.59370 + 0.678318i) q^{3} +(0.306661 - 2.13288i) q^{5} +(-0.233782 - 2.44828i) q^{7} +(2.07977 + 2.16207i) q^{9} +(2.54950 - 1.02066i) q^{11} +(-4.81545 - 5.05030i) q^{13} +(1.93549 - 3.19115i) q^{15} +(-0.521893 + 0.180629i) q^{17} +(-2.78507 - 0.265942i) q^{19} +(1.28813 - 4.06040i) q^{21} +(2.01683 - 0.0960734i) q^{23} +(0.342350 + 0.100523i) q^{25} +(1.84795 + 4.85645i) q^{27} +(2.51027 - 1.44930i) q^{29} +(-0.313059 + 0.328327i) q^{31} +(4.75547 + 0.102736i) q^{33} +(-5.29357 - 0.252164i) q^{35} +(-1.36757 + 2.36869i) q^{37} +(-4.24868 - 11.3151i) q^{39} +(-6.42149 - 1.23764i) q^{41} +(0.627825 + 0.544013i) q^{43} +(5.24922 - 3.77286i) q^{45} +(5.40598 - 10.4861i) q^{47} +(0.934085 - 0.180030i) q^{49} +(-0.954266 - 0.0661411i) q^{51} +(8.67995 + 10.0172i) q^{53} +(-1.39512 - 5.75075i) q^{55} +(-4.25818 - 2.31300i) q^{57} +(3.75489 + 12.7880i) q^{59} +(-2.25071 + 5.62201i) q^{61} +(4.80715 - 5.59731i) q^{63} +(-12.2484 + 8.72202i) q^{65} +(-8.15679 + 0.683270i) q^{67} +(3.27939 + 1.21494i) q^{69} +(8.87305 + 3.07099i) q^{71} +(9.59379 + 3.84077i) q^{73} +(0.477417 + 0.392426i) q^{75} +(-3.09490 - 6.00326i) q^{77} +(4.42862 - 1.07437i) q^{79} +(-0.349130 + 8.99323i) q^{81} +(6.35474 - 8.08070i) q^{83} +(0.225215 + 1.16852i) q^{85} +(4.98371 - 0.606996i) q^{87} +(1.12214 - 1.74608i) q^{89} +(-11.2388 + 12.9702i) q^{91} +(-0.721633 + 0.310901i) q^{93} +(-1.42130 + 5.85866i) q^{95} +(7.31896 + 4.22560i) q^{97} +(7.50911 + 3.38945i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) $ 440 * q - 12 * q^7 + 4 * q^9	$ 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) $ 440 * q - 12 * q^7 + 4 * q^9 - 2 * q^15 - 10 * q^19 + 22 * q^21 - 68 * q^25 + 50 * q^31 + 11 * q^33 - 22 * q^37 - 45 * q^39 + 22 * q^43 + 22 * q^45 - 18 * q^49 - 6 * q^51 + 126 * q^55 - 183 * q^57 - 56 * q^61 - 141 * q^63 - 12 * q^67 + 33 * q^69 + 356 * q^73 + 165 * q^75 + 228 * q^79 + 24 * q^81 - 6 * q^85 + 75 * q^87 - 4 * q^91 - 75 * q^93 + 12 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{53}{66}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.59370	+	0.678318i	0.920124	+	0.391627i
$3$	1.59370	+	0.678318i	0.920124	+	0.391627i
$4$		0			0
$5$	0.306661	−	2.13288i	0.137143	−	0.953851i	−0.798774	−	0.601631i	$-0.794518\pi$
$5$	0.306661	−	2.13288i	0.137143	−	0.953851i	0.935917	−	0.352220i	$-0.114573\pi$
$6$		0			0
$7$	−0.233782	−	2.44828i	−0.0883614	−	0.925362i	−0.925595	−	0.378516i	$-0.876434\pi$
$7$	−0.233782	−	2.44828i	−0.0883614	−	0.925362i	0.837233	−	0.546846i	$-0.184172\pi$
$8$		0			0
$9$	2.07977	+	2.16207i	0.693256	+	0.720691i
$10$		0			0
$11$	2.54950	−	1.02066i	0.768702	−	0.307742i	0.0460363	−	0.998940i	$-0.485341\pi$
$11$	2.54950	−	1.02066i	0.768702	−	0.307742i	0.722665	+	0.691198i	$0.242917\pi$
$12$		0			0
$13$	−4.81545	−	5.05030i	−1.33557	−	1.40070i	−0.850267	−	0.526352i	$-0.823559\pi$
$13$	−4.81545	−	5.05030i	−1.33557	−	1.40070i	−0.485299	−	0.874348i	$-0.661289\pi$
$14$		0			0
$15$	1.93549	−	3.19115i	0.499743	−	0.823952i
$16$		0			0
$17$	−0.521893	+	0.180629i	−0.126578	+	0.0438090i	−0.389622	−	0.920975i	$-0.627395\pi$
$17$	−0.521893	+	0.180629i	−0.126578	+	0.0438090i	0.263045	+	0.964784i	$0.415273\pi$
$18$		0			0
$19$	−2.78507	−	0.265942i	−0.638940	−	0.0610113i	−0.229442	−	0.973322i	$-0.573690\pi$
$19$	−2.78507	−	0.265942i	−0.638940	−	0.0610113i	−0.409498	+	0.912311i	$0.634296\pi$
$20$		0			0
$21$	1.28813	−	4.06040i	0.281094	−	0.886053i
$22$		0			0
$23$	2.01683	−	0.0960734i	0.420538	−	0.0200327i	0.163753	−	0.986501i	$-0.447640\pi$
$23$	2.01683	−	0.0960734i	0.420538	−	0.0200327i	0.256785	+	0.966469i	$0.417337\pi$
$24$		0			0
$25$	0.342350	+	0.100523i	0.0684700	+	0.0201046i
$26$		0			0
$27$	1.84795	+	4.85645i	0.355639	+	0.934623i
$28$		0			0
$29$	2.51027	−	1.44930i	0.466145	−	0.269129i	−0.248480	−	0.968637i	$-0.579931\pi$
$29$	2.51027	−	1.44930i	0.466145	−	0.269129i	0.714625	+	0.699508i	$0.246598\pi$
$30$		0			0
$31$	−0.313059	+	0.328327i	−0.0562271	+	0.0589693i	−0.751247	−	0.660021i	$-0.770547\pi$
$31$	−0.313059	+	0.328327i	−0.0562271	+	0.0589693i	0.695020	+	0.718991i	$0.255396\pi$
$32$		0			0
$33$	4.75547	+	0.102736i	0.827821	+	0.0178841i
$34$		0			0
$35$	−5.29357	−	0.252164i	−0.894776	−	0.0426234i
$36$		0			0
$37$	−1.36757	+	2.36869i	−0.224826	+	0.389411i	−0.956267	−	0.292494i	$-0.905515\pi$
$37$	−1.36757	+	2.36869i	−0.224826	+	0.389411i	0.731441	+	0.681905i	$0.238848\pi$
$38$		0			0
$39$	−4.24868	−	11.3151i	−0.680333	−	1.81186i
$40$		0			0
$41$	−6.42149	−	1.23764i	−1.00287	−	0.193287i	−0.338720	−	0.940887i	$-0.609994\pi$
$41$	−6.42149	−	1.23764i	−1.00287	−	0.193287i	−0.664149	+	0.747600i	$0.731206\pi$
$42$		0			0
$43$	0.627825	+	0.544013i	0.0957424	+	0.0829613i	0.701417	−	0.712751i	$-0.252551\pi$
$43$	0.627825	+	0.544013i	0.0957424	+	0.0829613i	−0.605674	+	0.795713i	$0.707097\pi$
$44$		0			0
$45$	5.24922	−	3.77286i	0.782507	−	0.562425i
$46$		0			0
$47$	5.40598	−	10.4861i	0.788543	−	1.52956i	−0.0586520	−	0.998278i	$-0.518680\pi$
$47$	5.40598	−	10.4861i	0.788543	−	1.52956i	0.847195	−	0.531282i	$-0.178289\pi$
$48$		0			0
$49$	0.934085	−	0.180030i	0.133441	−	0.0257186i
$50$		0			0
$51$	−0.954266	−	0.0661411i	−0.133624	−	0.00926161i
$52$		0			0
$53$	8.67995	+	10.0172i	1.19228	+	1.37597i	0.908929	+	0.416951i	$0.136901\pi$
$53$	8.67995	+	10.0172i	1.19228	+	1.37597i	0.283353	+	0.959016i	$0.408553\pi$
$54$		0			0
$55$	−1.39512	−	5.75075i	−0.188118	−	0.775431i
$56$		0			0
$57$	−4.25818	−	2.31300i	−0.564010	−	0.306364i
$58$		0			0
$59$	3.75489	+	12.7880i	0.488845	+	1.66485i	0.721595	+	0.692315i	$0.243409\pi$
$59$	3.75489	+	12.7880i	0.488845	+	1.66485i	−0.232750	+	0.972536i	$0.574773\pi$
$60$		0			0
$61$	−2.25071	+	5.62201i	−0.288174	+	0.719824i	0.711676	+	0.702508i	$0.247936\pi$
$61$	−2.25071	+	5.62201i	−0.288174	+	0.719824i	−0.999850	+	0.0173163i	$0.994488\pi$
$62$		0			0
$63$	4.80715	−	5.59731i	0.605644	−	0.705194i
$64$		0			0
$65$	−12.2484	+	8.72202i	−1.51922	+	1.08183i
$66$		0			0
$67$	−8.15679	+	0.683270i	−0.996510	+	0.0834747i
$67$	−8.15679	+	0.683270i	−0.996510	+	0.0834747i
$68$		0			0
$69$	3.27939	+	1.21494i	0.394793	+	0.146262i
$70$		0			0
$71$	8.87305	+	3.07099i	1.05304	+	0.364460i	0.798117	−	0.602502i	$-0.205830\pi$
$71$	8.87305	+	3.07099i	1.05304	+	0.364460i	0.254920	+	0.966962i	$0.417951\pi$
$72$		0			0
$73$	9.59379	+	3.84077i	1.12287	+	0.449528i	0.857431	−	0.514600i	$-0.172059\pi$
$73$	9.59379	+	3.84077i	1.12287	+	0.449528i	0.265437	+	0.964128i	$0.414484\pi$
$74$		0			0
$75$	0.477417	+	0.392426i	0.0551274	+	0.0453135i
$76$		0			0
$77$	−3.09490	−	6.00326i	−0.352696	−	0.684135i
$78$		0			0
$79$	4.42862	−	1.07437i	0.498259	−	0.120876i	0.0212489	−	0.999774i	$-0.493236\pi$
$79$	4.42862	−	1.07437i	0.498259	−	0.120876i	0.477010	+	0.878898i	$0.341721\pi$
$80$		0			0
$81$	−0.349130	+	8.99323i	−0.0387922	+	0.999247i
$82$		0			0
$83$	6.35474	−	8.08070i	0.697523	−	0.886972i	−0.300237	−	0.953865i	$-0.597066\pi$
$83$	6.35474	−	8.08070i	0.697523	−	0.886972i	0.997760	+	0.0668921i	$0.0213083\pi$
$84$		0			0
$85$	0.225215	+	1.16852i	0.0244280	+	0.126744i
$86$		0			0
$87$	4.98371	−	0.606996i	0.534309	−	0.0650768i
$88$		0			0
$89$	1.12214	−	1.74608i	0.118947	−	0.185084i	−0.776675	−	0.629902i	$-0.783095\pi$
$89$	1.12214	−	1.74608i	0.118947	−	0.185084i	0.895621	+	0.444817i	$0.146731\pi$
$90$		0			0
$91$	−11.2388	+	12.9702i	−1.17814	+	1.35965i
$92$		0			0
$93$	−0.721633	+	0.310901i	−0.0748299	+	0.0322390i
$94$		0			0
$95$	−1.42130	+	5.85866i	−0.145822	+	0.601086i
$96$		0			0
$97$	7.31896	+	4.22560i	0.743128	+	0.429045i	0.823205	−	0.567744i	$-0.192183\pi$
$97$	7.31896	+	4.22560i	0.743128	+	0.429045i	−0.0800776	+	0.996789i	$0.525517\pi$
$98$		0			0
$99$	7.50911	+	3.38945i	0.754694	+	0.340653i
$100$		0			0
$101$	−0.426724	+	0.599250i	−0.0424607	+	0.0596276i	−0.835260	−	0.549854i	$-0.814683\pi$
$101$	−0.426724	+	0.599250i	−0.0424607	+	0.0596276i	0.792800	+	0.609482i	$0.208623\pi$
$102$		0			0
$103$	−9.36794	−	8.93231i	−0.923050	−	0.880127i	0.0700322	−	0.997545i	$-0.477690\pi$
$103$	−9.36794	−	8.93231i	−0.923050	−	0.880127i	−0.993083	+	0.117418i	$0.962538\pi$
$104$		0			0
$105$	−8.26531	−	3.99260i	−0.806612	−	0.389638i
$106$		0			0
$107$	4.80701	−	0.691144i	0.464711	−	0.0668154i	0.0940174	−	0.995571i	$-0.470029\pi$
$107$	4.80701	−	0.691144i	0.464711	−	0.0668154i	0.370694	+	0.928755i	$0.379120\pi$
$108$		0			0
$109$	−2.08024	+	7.08464i	−0.199251	+	0.678586i	0.797875	+	0.602823i	$0.205957\pi$
$109$	−2.08024	+	7.08464i	−0.199251	+	0.678586i	−0.997126	+	0.0757630i	$0.975861\pi$
$110$		0			0
$111$	−3.78622	+	2.84734i	−0.359372	+	0.270258i
$112$		0			0
$113$	1.78929	−	1.40711i	0.168322	−	0.132370i	−0.530445	−	0.847720i	$-0.677975\pi$
$113$	1.78929	−	1.40711i	0.168322	−	0.132370i	0.698767	+	0.715350i	$0.253733\pi$
$114$		0			0
$115$	0.413571	−	4.33111i	0.0385657	−	0.403878i
$116$		0			0
$117$	0.904101	−	20.9148i	0.0835842	−	1.93357i
$118$		0			0
$119$	0.564239	+	1.23551i	0.0517237	+	0.113259i
$120$		0			0
$121$	−2.50290	+	2.38651i	−0.227537	+	0.216956i
$122$		0			0
$123$	−9.39442	−	6.32825i	−0.847067	−	0.570599i
$124$		0			0
$125$	4.79509	−	10.4998i	0.428886	−	0.939128i
$126$		0			0
$127$	−15.4009	+	1.47061i	−1.36661	+	0.130496i	−0.752432	−	0.658670i	$-0.771120\pi$
$127$	−15.4009	+	1.47061i	−1.36661	+	0.130496i	−0.614181	+	0.789165i	$0.710513\pi$
$128$		0			0
$129$	0.631551	+	1.29286i	0.0556050	+	0.113830i
$130$		0			0
$131$	−3.50834	−	5.45908i	−0.306525	−	0.476962i	0.653481	−	0.756943i	$-0.273308\pi$
$131$	−3.50834	−	5.45908i	−0.306525	−	0.476962i	−0.960005	+	0.279981i	$0.909672\pi$
$132$		0			0
$133$			6.88081i			0.596642i
$134$		0			0
$135$	10.9249	−	2.45217i	0.940265	−	0.211049i
$136$		0			0
$137$	−10.3235	+	6.63453i	−0.881999	+	0.566826i	−0.901401	−	0.432985i	$-0.857460\pi$
$137$	−10.3235	+	6.63453i	−0.881999	+	0.566826i	0.0194019	+	0.999812i	$0.493824\pi$
$138$		0			0
$139$	−9.86849	−	1.41887i	−0.837034	−	0.120347i	−0.289549	−	0.957163i	$-0.593505\pi$
$139$	−9.86849	−	1.41887i	−0.837034	−	0.120347i	−0.547485	+	0.836816i	$0.684415\pi$
$140$		0			0
$141$	15.7285	−	13.0448i	1.32458	−	1.09857i
$142$		0			0
$143$	−17.4316	−	7.96076i	−1.45771	−	0.665712i
$144$		0			0
$145$	−2.32138	−	5.79853i	−0.192780	−	0.481542i
$146$		0			0
$147$	1.61077	+	0.346693i	0.132854	+	0.0285947i
$148$		0			0
$149$	−18.0782	+	8.25602i	−1.48102	+	0.676359i	−0.981766	−	0.190096i	$-0.939120\pi$
$149$	−18.0782	+	8.25602i	−1.48102	+	0.676359i	−0.499255	+	0.866455i	$0.666393\pi$
$150$		0			0
$151$	2.76478	+	7.98830i	0.224994	+	0.650079i	0.999839	+	0.0179272i	$0.00570670\pi$
$151$	2.76478	+	7.98830i	0.224994	+	0.650079i	−0.774845	+	0.632151i	$0.782172\pi$
$152$		0			0
$153$	−1.47595	−	0.752705i	−0.119323	−	0.0608526i
$154$		0			0
$155$	0.604278	+	0.768401i	0.0485367	+	0.0617195i
$156$		0			0
$157$	0.0842720	+	1.76909i	0.00672563	+	0.141188i	0.999732	+	0.0231313i	$0.00736357\pi$
$157$	0.0842720	+	1.76909i	0.00672563	+	0.141188i	−0.993007	+	0.118057i	$0.962333\pi$
$158$		0			0
$159$	7.03839	+	21.8522i	0.558181	+	1.73299i
$160$		0			0
$161$	−0.706714	−	4.91530i	−0.0556968	−	0.387380i
$162$		0			0
$163$	−3.78670	−	6.55876i	−0.296598	−	0.513722i	0.678758	−	0.734362i	$-0.262519\pi$
$163$	−3.78670	−	6.55876i	−0.296598	−	0.513722i	−0.975355	+	0.220640i	$0.929185\pi$
$164$		0			0
$165$	1.67744	−	10.1113i	0.130589	−	0.787165i
$166$		0			0
$167$	−9.87190	−	7.02975i	−0.763910	−	0.543978i	0.130381	−	0.991464i	$-0.458380\pi$
$167$	−9.87190	−	7.02975i	−0.763910	−	0.543978i	−0.894291	+	0.447486i	$0.852319\pi$
$168$		0			0
$169$	−1.69839	+	35.6536i	−0.130646	+	2.74259i
$170$		0			0
$171$	−5.21732	−	6.57463i	−0.398978	−	0.502775i
$172$		0			0
$173$	20.3597	+	4.93922i	1.54792	+	0.375522i	0.916537	−	0.399949i	$-0.130972\pi$
$173$	20.3597	+	4.93922i	1.54792	+	0.375522i	0.631384	+	0.775471i	$0.282487\pi$
$174$		0			0
$175$	0.166073	−	0.861669i	0.0125539	−	0.0651361i
$176$		0			0
$177$	−2.69015	+	22.9272i	−0.202204	+	1.72331i
$178$		0			0
$179$	8.09006	+	5.19917i	0.604679	+	0.388604i	0.806859	−	0.590745i	$-0.201166\pi$
$179$	8.09006	+	5.19917i	0.604679	+	0.388604i	−0.202179	+	0.979349i	$0.564802\pi$
$180$		0			0
$181$	5.87750	+	3.03006i	0.436871	+	0.225223i	0.662609	−	0.748965i	$-0.269449\pi$
$181$	5.87750	+	3.03006i	0.436871	+	0.225223i	−0.225738	+	0.974188i	$0.572479\pi$
$182$		0			0
$183$	−7.40047	+	7.43310i	−0.547059	+	0.549471i
$184$		0			0
$185$	4.63275	+	3.64323i	0.340606	+	0.267856i
$186$		0			0
$187$	−1.14620	+	0.993190i	−0.0838186	+	0.0726292i
$188$		0			0
$189$	11.4579	−	5.65966i	0.833441	−	0.411680i
$190$		0			0
$191$	3.46682	−	1.78727i	0.250850	−	0.129322i	−0.328216	−	0.944603i	$-0.606447\pi$
$191$	3.46682	−	1.78727i	0.250850	−	0.129322i	0.579067	+	0.815280i	$0.303417\pi$
$192$		0			0
$193$	26.3811	−	7.74620i	1.89896	−	0.557584i	0.908879	−	0.417060i	$-0.136939\pi$
$193$	26.3811	−	7.74620i	1.89896	−	0.557584i	0.990077	−	0.140524i	$-0.0448787\pi$
$194$		0			0
$195$	−25.4365	+	5.59200i	−1.82155	+	0.400452i
$196$		0			0
$197$	−5.55240	+	16.0426i	−0.395592	+	1.14299i	0.554813	+	0.831975i	$0.312790\pi$
$197$	−5.55240	+	16.0426i	−0.395592	+	1.14299i	−0.950405	+	0.311014i	$0.899331\pi$
$198$		0			0
$199$	7.13663	+	10.0220i	0.505902	+	0.710440i	0.985995	−	0.166778i	$-0.0533363\pi$
$199$	7.13663	+	10.0220i	0.505902	+	0.710440i	−0.480092	+	0.877218i	$0.659397\pi$
$200$		0			0
$201$	−13.4630	−	4.44397i	−0.949604	−	0.313453i
$202$		0			0
$203$	−4.13515	−	5.80701i	−0.290231	−	0.407572i
$204$		0			0
$205$	−4.60896	+	13.3167i	−0.321903	+	0.930079i
$206$		0			0
$207$	4.40226	+	4.16073i	0.305978	+	0.289190i
$208$		0			0
$209$	−7.37197	+	2.16461i	−0.509930	+	0.149729i
$210$		0			0
$211$	−16.8027	+	8.66237i	−1.15674	+	0.596342i	−0.926316	−	0.376748i	$-0.877042\pi$
$211$	−16.8027	+	8.66237i	−1.15674	+	0.596342i	−0.230426	+	0.973090i	$0.574012\pi$
$212$		0			0
$213$	12.0579	+	10.9130i	0.826192	+	0.747746i
$214$		0			0
$215$	1.35284	−	1.17224i	0.0922631	−	0.0799464i
$216$		0			0
$217$	0.877024	+	0.689699i	0.0595363	+	0.0468198i
$218$		0			0
$219$	12.6844	+	12.6287i	0.857130	+	0.853368i
$220$		0			0
$221$	3.42538	+	1.76591i	0.230416	+	0.118788i
$222$		0			0
$223$	−14.0431	−	9.02498i	−0.940399	−	0.604358i	−0.0218910	−	0.999760i	$-0.506969\pi$
$223$	−14.0431	−	9.02498i	−0.940399	−	0.604358i	−0.918508	+	0.395403i	$0.870605\pi$
$224$		0			0
$225$	0.494670	+	0.949251i	0.0329780	+	0.0632834i
$226$		0			0
$227$	−1.17258	+	6.08393i	−0.0778270	+	0.403805i	0.922034	+	0.387110i	$0.126527\pi$
$227$	−1.17258	+	6.08393i	−0.0778270	+	0.403805i	−0.999861	+	0.0166949i	$0.994686\pi$
$228$		0			0
$229$	−3.04756	−	0.739331i	−0.201389	−	0.0488563i	0.133796	−	0.991009i	$-0.457283\pi$
$229$	−3.04756	−	0.739331i	−0.201389	−	0.0488563i	−0.335184	+	0.942153i	$0.608799\pi$
$230$		0			0
$231$	−0.860217	−	11.6667i	−0.0565982	−	0.767615i
$232$		0			0
$233$	0.317294	−	6.66082i	0.0207866	−	0.436365i	−0.964354	−	0.264616i	$-0.914755\pi$
$233$	0.317294	−	6.66082i	0.0207866	−	0.436365i	0.985141	−	0.171750i	$-0.0549420\pi$
$234$		0			0
$235$	−20.7078	−	14.7460i	−1.35083	−	0.961921i
$236$		0			0
$237$	7.78666	+	1.29179i	0.505798	+	0.0839106i
$238$		0			0
$239$	−12.4911	−	21.6352i	−0.807981	−	1.39946i	−0.914260	−	0.405127i	$-0.867227\pi$
$239$	−12.4911	−	21.6352i	−0.807981	−	1.39946i	0.106279	−	0.994336i	$-0.466106\pi$
$240$		0			0
$241$	0.00925738	+	0.0643865i	0.000596320	+	0.00414750i	0.990117	−	0.140241i	$-0.0447877\pi$
$241$	0.00925738	+	0.0643865i	0.000596320	+	0.00414750i	−0.989521	+	0.144388i	$0.953879\pi$
$242$		0			0
$243$	−6.65668	+	14.0957i	−0.427026	+	0.904239i
$244$		0			0
$245$	−0.0975342	−	2.04749i	−0.00623123	−	0.130810i
$246$		0			0
$247$	12.0683	+	15.3461i	0.767887	+	0.976448i
$248$		0			0
$249$	15.6088	−	8.56769i	0.989170	−	0.542955i
$250$		0			0
$251$	−8.13828	−	23.5140i	−0.513684	−	1.48419i	−0.841923	−	0.539597i	$-0.818577\pi$
$251$	−8.13828	−	23.5140i	−0.513684	−	1.48419i	0.328240	−	0.944594i	$-0.393545\pi$
$252$		0			0
$253$	5.04384	−	2.30344i	0.317103	−	0.144816i
$254$		0			0
$255$	−0.433707	+	2.01505i	−0.0271598	+	0.126187i
$256$		0			0
$257$	5.53208	+	13.8185i	0.345082	+	0.861972i	0.994805	+	0.101801i	$0.0324605\pi$
$257$	5.53208	+	13.8185i	0.345082	+	0.861972i	−0.649723	+	0.760171i	$0.725115\pi$
$258$		0			0
$259$	6.11893	+	2.79442i	0.380212	+	0.173637i
$260$		0			0
$261$	8.35427	+	2.41317i	0.517117	+	0.149371i
$262$		0			0
$263$	−13.2735	−	1.90845i	−0.818482	−	0.117680i	−0.279660	−	0.960099i	$-0.590222\pi$
$263$	−13.2735	−	1.90845i	−0.818482	−	0.117680i	−0.538823	+	0.842419i	$0.681131\pi$
$264$		0			0
$265$	24.0272	−	15.4414i	1.47598	−	0.948555i
$266$		0			0
$267$	2.97276	−	2.02157i	0.181930	−	0.123718i
$268$		0			0
$269$			9.15469i			0.558171i	0.960266	+	0.279086i	$0.0900313\pi$
$269$			9.15469i			0.558171i	−0.960266	+	0.279086i	$0.909969\pi$
$270$		0			0
$271$	−6.35792	−	9.89311i	−0.386216	−	0.600964i	0.592652	−	0.805459i	$-0.298081\pi$
$271$	−6.35792	−	9.89311i	−0.386216	−	0.600964i	−0.978868	+	0.204495i	$0.934445\pi$
$272$		0			0
$273$	−26.7092	+	13.0472i	−1.61651	+	0.789653i
$274$		0			0
$275$	0.975420	−	0.0931413i	0.0588200	−	0.00561663i
$276$		0			0
$277$	−4.72997	+	10.3572i	−0.284196	+	0.622303i	−0.996858	−	0.0792046i	$-0.974762\pi$
$277$	−4.72997	+	10.3572i	−0.284196	+	0.622303i	0.712662	+	0.701507i	$0.247489\pi$
$278$		0			0
$279$	−1.36096	+	0.00598686i	−0.0814784	+	0.000358424i
$280$		0			0
$281$	14.5314	−	13.8556i	0.866869	−	0.826558i	−0.119204	−	0.992870i	$-0.538034\pi$
$281$	14.5314	−	13.8556i	0.866869	−	0.826558i	0.986073	+	0.166312i	$0.0531859\pi$
$282$		0			0
$283$	0.292674	+	0.640866i	0.0173976	+	0.0380955i	0.918131	−	0.396276i	$-0.129698\pi$
$283$	0.292674	+	0.640866i	0.0173976	+	0.0380955i	−0.900734	+	0.434372i	$0.856970\pi$
$284$		0			0
$285$	−6.23916	+	8.37286i	−0.369576	+	0.495966i
$286$		0			0
$287$	−1.52886	+	16.0109i	−0.0902457	+	0.945096i
$288$		0			0
$289$	−13.1232	+	10.3202i	−0.771950	+	0.607069i
$290$		0			0
$291$	8.79793	+	11.6989i	0.515744	+	0.685804i
$292$		0			0
$293$	−4.70974	+	16.0399i	−0.275146	+	0.937061i	0.699748	+	0.714390i	$0.253296\pi$
$293$	−4.70974	+	16.0399i	−0.275146	+	0.937061i	−0.974894	+	0.222671i	$0.928522\pi$
$294$		0			0
$295$	28.4266	−	4.08713i	1.65506	−	0.237962i
$296$		0			0
$297$	9.66815	+	10.4953i	0.561003	+	0.609002i
$298$		0			0
$299$	−10.1971	−	9.72295i	−0.589716	−	0.562293i
$300$		0			0
$301$	1.18512	−	1.66427i	0.0683093	−	0.0959270i
$302$		0			0
$303$	−1.08655	+	0.665571i	−0.0624209	+	0.0382361i
$304$		0			0
$305$	11.3008	+	6.52454i	0.647084	+	0.373594i
$306$		0			0
$307$	2.60375	−	10.7328i	0.148604	−	0.612554i	−0.847984	−	0.530021i	$-0.822184\pi$
$307$	2.60375	−	10.7328i	0.148604	−	0.612554i	0.996588	−	0.0825328i	$-0.0263009\pi$
$308$		0			0
$309$	−8.87074	−	20.5899i	−0.504639	−	1.17132i
$310$		0			0
$311$	−8.51947	+	9.83200i	−0.483095	+	0.557521i	−0.944007	−	0.329924i	$-0.892977\pi$
$311$	−8.51947	+	9.83200i	−0.483095	+	0.557521i	0.460912	+	0.887446i	$0.347522\pi$
$312$		0			0
$313$	7.14245	−	11.1139i	0.403715	−	0.628193i	−0.578560	−	0.815640i	$-0.696385\pi$
$313$	7.14245	−	11.1139i	0.403715	−	0.628193i	0.982275	+	0.187447i	$0.0600213\pi$
$314$		0			0
$315$	−10.4642	−	11.9695i	−0.589590	−	0.674406i
$316$		0			0
$317$	1.34794	+	6.99379i	0.0757080	+	0.392810i	0.999940	+	0.0109782i	$0.00349455\pi$
$317$	1.34794	+	6.99379i	0.0757080	+	0.392810i	−0.924232	+	0.381832i	$0.875293\pi$
$318$		0			0
$319$	4.92066	−	6.25713i	0.275504	−	0.350332i
$320$		0			0
$321$	8.12975	+	2.15921i	0.453759	+	0.120515i
$322$		0			0
$323$	1.50155	−	0.364271i	0.0835483	−	0.0202686i
$324$		0			0
$325$	−1.14090	−	2.21303i	−0.0632856	−	0.122757i
$326$		0			0
$327$	−8.12093	+	9.87974i	−0.449088	+	0.546351i
$328$		0			0
$329$	−26.9368	−	10.7839i	−1.48507	−	0.594534i
$330$		0			0
$331$	15.5053	+	5.36642i	0.852246	+	0.294965i	0.718052	−	0.695990i	$-0.245034\pi$
$331$	15.5053	+	5.36642i	0.852246	+	0.294965i	0.134195	+	0.990955i	$0.457155\pi$
$332$		0			0
$333$	−7.96551	+	1.96955i	−0.436507	+	0.107931i
$334$		0			0
$335$	−1.04404	+	17.6069i	−0.0570420	+	0.961970i
$336$		0			0
$337$	−17.8277	+	12.6951i	−0.971138	+	0.691544i	−0.951302	−	0.308259i	$-0.900254\pi$
$337$	−17.8277	+	12.6951i	−0.971138	+	0.691544i	−0.0198353	+	0.999803i	$0.506314\pi$
$338$		0			0
$339$	3.80606	−	1.02881i	0.206717	−	0.0558772i
$340$		0			0
$341$	−0.463031	+	1.15660i	−0.0250746	+	0.0626332i
$342$		0			0
$343$	−5.50942	−	18.7634i	−0.297481	−	1.01313i
$344$		0			0
$345$	3.59698	−	6.62196i	0.193655	−	0.356514i
$346$		0			0
$347$	1.18614	+	4.88934i	0.0636754	+	0.262473i	0.994747	−	0.102363i	$-0.0326402\pi$
$347$	1.18614	+	4.88934i	0.0636754	+	0.262473i	−0.931072	+	0.364836i	$0.881125\pi$
$348$		0			0
$349$	−11.0268	−	12.7256i	−0.590252	−	0.681187i	0.379525	−	0.925182i	$-0.376088\pi$
$349$	−11.0268	−	12.7256i	−0.590252	−	0.681187i	−0.969777	+	0.243995i	$0.921542\pi$
$350$		0			0
$351$	15.6278	−	32.7187i	0.834149	−	1.74639i
$352$		0			0
$353$	13.7779	−	2.65548i	0.733325	−	0.141337i	0.191100	−	0.981571i	$-0.438794\pi$
$353$	13.7779	−	2.65548i	0.733325	−	0.141337i	0.542224	+	0.840234i	$0.317582\pi$
$354$		0			0
$355$	9.27106	−	17.9834i	0.492057	−	0.954457i
$356$		0			0
$357$	0.0611585	+	2.35177i	0.00323685	+	0.124469i
$358$		0			0
$359$	19.3650	+	16.7799i	1.02205	+	0.885609i	0.993483	−	0.113983i	$-0.0363608\pi$
$359$	19.3650	+	16.7799i	1.02205	+	0.885609i	0.0285650	+	0.999592i	$0.490906\pi$
$360$		0			0
$361$	−10.9707	−	2.11444i	−0.577407	−	0.111286i
$362$		0			0
$363$	−5.60770	+	2.10562i	−0.294328	+	0.110517i
$364$		0			0
$365$	11.1339	−	19.2845i	0.582777	−	1.00940i
$366$		0			0
$367$	16.1306	+	0.768397i	0.842012	+	0.0401100i	0.464155	−	0.885754i	$-0.346358\pi$
$367$	16.1306	+	0.768397i	0.842012	+	0.0401100i	0.377857	+	0.925864i	$0.376661\pi$
$368$		0			0
$369$	−10.6793	−	16.4577i	−0.555944	−	0.856756i
$370$		0			0
$371$	22.4957	−	23.5928i	1.16792	−	1.22488i
$372$		0			0
$373$	10.0070	−	5.77757i	0.518145	−	0.299151i	−0.218030	−	0.975942i	$-0.569963\pi$
$373$	10.0070	−	5.77757i	0.518145	−	0.299151i	0.736175	+	0.676791i	$0.236630\pi$
$374$		0			0
$375$	14.7641	−	13.4809i	0.762416	−	0.696151i
$376$		0			0
$377$	−19.4075	−	5.69855i	−0.999536	−	0.293490i
$378$		0			0
$379$	33.6176	−	1.60140i	1.72682	−	0.0822586i	0.839485	−	0.543383i	$-0.182857\pi$
$379$	33.6176	−	1.60140i	1.72682	−	0.0822586i	0.887335	+	0.461124i	$0.152554\pi$
$380$		0			0
$381$	−25.5421	−	8.10303i	−1.30856	−	0.415131i
$382$		0			0
$383$	34.1052	+	3.25665i	1.74269	+	0.166407i	0.917312	−	0.398170i	$-0.130355\pi$
$383$	34.1052	+	3.25665i	1.74269	+	0.166407i	0.825380	+	0.564577i	$0.190961\pi$
$384$		0			0
$385$	−13.7533	+	4.76006i	−0.700933	+	0.242595i
$386$		0			0
$387$	0.129533	+	2.48883i	0.00658453	+	0.126514i
$388$		0			0
$389$	−17.0865	−	17.9198i	−0.866318	−	0.908568i	0.130239	−	0.991483i	$-0.458426\pi$
$389$	−17.0865	−	17.9198i	−0.866318	−	0.908568i	−0.996557	+	0.0829147i	$0.973577\pi$
$390$		0			0
$391$	−1.03522	+	0.414438i	−0.0523531	+	0.0209590i
$392$		0			0
$393$	−1.88825	−	11.0799i	−0.0952494	−	0.558907i
$394$		0			0
$395$	−0.933415	−	9.77516i	−0.0469652	−	0.491842i
$396$		0			0
$397$	1.99460	−	13.8728i	0.100106	−	0.696254i	−0.876529	−	0.481350i	$-0.840147\pi$
$397$	1.99460	−	13.8728i	0.100106	−	0.696254i	0.976635	−	0.214905i	$-0.0689441\pi$
$398$		0			0
$399$	−4.66738	+	10.9660i	−0.233661	+	0.548984i
$400$		0			0
$401$	18.0622			0.901983			0.450991	−	0.892528i	$-0.351070\pi$
$401$	18.0622			0.901983			0.450991	+	0.892528i	$0.351070\pi$
$402$		0			0
$403$	3.16567			0.157693
$404$		0			0
$405$	19.0744	+	3.50252i	0.947813	+	0.174042i
$406$		0			0
$407$	−1.06896	+	7.43480i	−0.0529865	+	0.368529i
$408$		0			0
$409$	−1.56485	−	16.3879i	−0.0773770	−	0.810328i	−0.947977	−	0.318338i	$-0.896875\pi$
$409$	−1.56485	−	16.3879i	−0.0773770	−	0.810328i	0.870600	−	0.491991i	$-0.163731\pi$
$410$		0			0
$411$	−20.9530	+	3.57082i	−1.03353	+	0.176136i
$412$		0			0
$413$	30.4307	−	12.1826i	1.49740	−	0.599467i
$414$		0			0
$415$	−15.2864	−	16.0319i	−0.750379	−	0.786975i
$416$		0			0
$417$	−14.7650	−	8.95524i	−0.723044	−	0.438540i
$418$		0			0
$419$	−25.6749	+	8.88615i	−1.25430	+	0.434117i	−0.871810	−	0.489843i	$-0.837054\pi$
$419$	−25.6749	+	8.88615i	−1.25430	+	0.434117i	−0.382488	+	0.923960i	$0.624933\pi$
$420$		0			0
$421$	−27.0960	−	2.58736i	−1.32058	−	0.126100i	−0.589153	−	0.808021i	$-0.700539\pi$
$421$	−27.0960	−	2.58736i	−1.32058	−	0.126100i	−0.731426	+	0.681921i	$0.761145\pi$
$422$		0			0
$423$	33.9150	−	10.1206i	1.64900	−	0.492081i
$424$		0			0
$425$	−0.196827	+	0.00937605i	−0.00954754	+	0.000454805i
$426$		0			0
$427$	14.2904	+	4.19605i	0.691562	+	0.203061i
$428$		0			0
$429$	−22.3809	−	24.5113i	−1.08056	−	1.18341i
$430$		0			0
$431$	29.7965	−	17.2030i	1.43525	−	0.828640i	0.437733	−	0.899105i	$-0.355782\pi$
$431$	29.7965	−	17.2030i	1.43525	−	0.828640i	0.997514	+	0.0704650i	$0.0224483\pi$
$432$		0			0
$433$	12.8252	−	13.4507i	0.616342	−	0.646400i	−0.339388	−	0.940646i	$-0.610220\pi$
$433$	12.8252	−	13.4507i	0.616342	−	0.646400i	0.955730	+	0.294246i	$0.0950685\pi$
$434$		0			0
$435$	0.233662	−	10.8158i	0.0112032	−	0.518576i
$436$		0			0
$437$	−5.64257	−	0.268789i	−0.269921	−	0.0128579i
$438$		0			0
$439$	−2.80865	+	4.86473i	−0.134050	+	0.232181i	−0.925234	−	0.379397i	$-0.876131\pi$
$439$	−2.80865	+	4.86473i	−0.134050	+	0.232181i	0.791184	+	0.611578i	$0.209465\pi$
$440$		0			0
$441$	2.33192	+	1.64514i	0.111044	+	0.0783400i
$442$		0			0
$443$	−18.3930	−	3.54496i	−0.873878	−	0.168426i	−0.267457	−	0.963570i	$-0.586183\pi$
$443$	−18.3930	−	3.54496i	−0.873878	−	0.168426i	−0.606421	+	0.795144i	$0.707395\pi$
$444$		0			0
$445$	−3.38006	−	2.92884i	−0.160230	−	0.138840i
$446$		0			0
$447$	−34.4114	+	0.894878i	−1.62760	+	0.0423263i
$448$		0			0
$449$	3.99949	−	7.75792i	0.188747	−	0.366119i	−0.775407	−	0.631462i	$-0.782455\pi$
$449$	3.99949	−	7.75792i	0.188747	−	0.366119i	0.964154	+	0.265343i	$0.0854853\pi$
$450$		0			0
$451$	−17.6348	+	3.39882i	−0.830389	+	0.160044i
$452$		0			0
$453$	−1.01238	+	14.6064i	−0.0475658	+	0.686267i
$454$		0			0
$455$	24.2174	+	27.9484i	1.13533	+	1.31024i
$456$		0			0
$457$	8.20283	+	33.8125i	0.383712	+	1.58168i	0.756645	+	0.653826i	$0.226837\pi$
$457$	8.20283	+	33.8125i	0.383712	+	1.58168i	−0.372933	+	0.927858i	$0.621648\pi$
$458$		0			0
$459$	−1.84165	−	2.20075i	−0.0859608	−	0.102722i
$460$		0			0
$461$	7.58595	+	25.8354i	0.353313	+	1.20327i	0.924092	+	0.382170i	$0.124823\pi$
$461$	7.58595	+	25.8354i	0.353313	+	1.20327i	−0.570779	+	0.821104i	$0.693359\pi$
$462$		0			0
$463$	11.8761	−	29.6651i	0.551929	−	1.37865i	−0.345884	−	0.938277i	$-0.612421\pi$
$463$	11.8761	−	29.6651i	0.551929	−	1.37865i	0.897814	−	0.440376i	$-0.145155\pi$
$464$		0			0
$465$	0.441817	+	1.63449i	0.0204888	+	0.0757979i
$466$		0			0
$467$	7.86651	−	5.60171i	0.364018	−	0.259216i	−0.383382	−	0.923590i	$-0.625241\pi$
$467$	7.86651	−	5.60171i	0.364018	−	0.259216i	0.747401	+	0.664373i	$0.231301\pi$
$468$		0			0
$469$	3.57975	+	19.8103i	0.165297	+	0.914757i
$470$		0			0
$471$	−1.06570	+	2.87656i	−0.0491048	+	0.132545i
$472$		0			0
$473$	2.15589	+	0.746161i	0.0991280	+	0.0343085i
$474$		0			0
$475$	−0.926737	−	0.371009i	−0.0425216	−	0.0170231i
$476$		0			0
$477$	−3.60564	+	39.6001i	−0.165091	+	1.81316i
$478$		0			0
$479$	12.3046	+	23.8677i	0.562214	+	1.09054i	0.983038	+	0.183400i	$0.0587105\pi$
$479$	12.3046	+	23.8677i	0.562214	+	1.09054i	−0.420825	+	0.907142i	$0.638259\pi$
$480$		0			0
$481$	18.5480	−	4.49971i	0.845718	−	0.205169i
$482$		0			0
$483$	2.20785	−	8.31290i	0.100461	−	0.378250i
$484$		0			0
$485$	11.2571	−	14.3146i	0.511160	−	0.649993i
$486$		0			0
$487$	−6.53877	−	33.9264i	−0.296300	−	1.53735i	−0.759151	−	0.650915i	$-0.774385\pi$
$487$	−6.53877	−	33.9264i	−0.296300	−	1.53735i	0.462851	−	0.886436i	$-0.346827\pi$
$488$		0			0
$489$	−1.58594	−	13.0213i	−0.0717189	−	0.588844i
$490$		0			0
$491$	4.02285	−	6.25968i	0.181549	−	0.282495i	−0.738537	−	0.674213i	$-0.764483\pi$
$491$	4.02285	−	6.25968i	0.181549	−	0.282495i	0.920085	+	0.391718i	$0.128119\pi$
$492$		0			0
$493$	−1.04830	+	1.20981i	−0.0472133	+	0.0544870i
$494$		0			0
$495$	9.53203	−	14.9766i	0.428433	−	0.673147i
$496$		0			0
$497$	5.44428	−	22.4416i	0.244209	−	1.00665i
$498$		0			0
$499$	−4.30141	−	2.48342i	−0.192557	−	0.111173i	0.400622	−	0.916243i	$-0.368794\pi$
$499$	−4.30141	−	2.48342i	−0.192557	−	0.111173i	−0.593179	+	0.805070i	$0.702127\pi$
$500$		0			0
$501$	−10.9644	−	17.8996i	−0.489855	−	0.799695i
$502$		0			0
$503$	−0.0854197	+	0.119955i	−0.00380867	+	0.00534853i	−0.816476	−	0.577380i	$-0.804075\pi$
$503$	−0.0854197	+	0.119955i	−0.00380867	+	0.00534853i	0.812667	+	0.582728i	$0.198015\pi$
$504$		0			0
$505$	1.14727	+	1.09392i	0.0510527	+	0.0486786i
$506$		0			0
$507$	−26.8912	+	55.6692i	−1.19428	+	2.47236i
$508$		0			0
$509$	6.04361	−	0.868940i	0.267878	−	0.0385151i	−0.00706679	−	0.999975i	$-0.502249\pi$
$509$	6.04361	−	0.868940i	0.267878	−	0.0385151i	0.274945	+	0.961460i	$0.411340\pi$
$510$		0			0
$511$	7.16043	−	24.3862i	0.316759	−	1.07878i
$512$		0			0
$513$	−3.85515	−	14.0170i	−0.170209	−	0.618866i
$514$		0			0
$515$	−21.9243	+	17.2414i	−0.966099	+	0.759749i
$516$		0			0
$517$	3.07970	−	32.2520i	0.135445	−	1.41844i
$518$		0			0
$519$	29.0970	+	21.6820i	1.27721	+	0.951735i
$520$		0			0
$521$	−10.9594	−	23.9977i	−0.480140	−	1.05136i	−0.982425	−	0.186658i	$-0.940234\pi$
$521$	−10.9594	−	23.9977i	−0.480140	−	1.05136i	0.502285	−	0.864702i	$-0.332493\pi$
$522$		0			0
$523$	15.1168	−	14.4138i	0.661011	−	0.630273i	−0.283414	−	0.958998i	$-0.591467\pi$
$523$	15.1168	−	14.4138i	0.661011	−	0.630273i	0.944426	+	0.328724i	$0.106619\pi$
$524$		0			0
$525$	0.849157	−	1.26059i	0.0370602	−	0.0550168i
$526$		0			0
$527$	0.104078	−	0.227899i	0.00453371	−	0.00992744i
$528$		0			0
$529$	−18.8375	+	1.79876i	−0.819021	+	0.0782070i
$530$		0			0
$531$	−19.8392	+	34.7144i	−0.860950	+	1.50647i
$532$		0			0
$533$	24.6719	+	38.3902i	1.06866	+	1.66287i
$534$		0			0
$535$		−	10.4647i		−	0.452428i
$536$		0			0
$537$	9.36645	+	13.7736i	0.404192	+	0.594373i
$538$		0			0
$539$	2.19770	−	1.41237i	0.0946614	−	0.0608352i
$540$		0			0
$541$	32.9306	+	4.73471i	1.41580	+	0.203561i	0.807369	−	0.590047i	$-0.200891\pi$
$541$	32.9306	+	4.73471i	1.41580	+	0.203561i	0.608430	+	0.793608i	$0.291800\pi$
$542$		0			0
$543$	7.31164	+	8.81584i	0.313772	+	0.378324i
$544$		0			0
$545$	14.4727	+	6.60948i	0.619944	+	0.283119i
$546$		0			0
$547$	6.50868	+	16.2579i	0.278291	+	0.695137i	0.999996	+	0.00293625i	$0.000934640\pi$
$547$	6.50868	+	16.2579i	0.278291	+	0.695137i	−0.721705	+	0.692201i	$0.756641\pi$
$548$		0			0
$549$	−16.8362	+	6.82626i	−0.718550	+	0.291338i
$550$		0			0
$551$	−7.37671	+	3.36883i	−0.314258	+	0.143517i
$552$		0			0
$553$	−3.66569	−	10.5913i	−0.155881	−	0.450389i
$554$		0			0
$555$	4.91194	+	8.94870i	0.208500	+	0.379851i
$556$		0			0
$557$	−16.6237	−	21.1388i	−0.704369	−	0.895679i	0.293818	−	0.955861i	$-0.405074\pi$
$557$	−16.6237	−	21.1388i	−0.704369	−	0.895679i	−0.998187	+	0.0601829i	$0.980832\pi$
$558$		0			0
$559$	−0.275829	−	5.79037i	−0.0116663	−	0.244907i
$560$		0			0
$561$	−2.50040	+	0.805358i	−0.105567	+	0.0340022i
$562$		0			0
$563$	6.20782	+	43.1764i	0.261629	+	1.81967i	0.520622	+	0.853788i	$0.325700\pi$
$563$	6.20782	+	43.1764i	0.261629	+	1.81967i	−0.258993	+	0.965879i	$0.583391\pi$
$564$		0			0
$565$	−2.45249	−	4.24784i	−0.103177	−	0.178708i
$566$		0			0
$567$	22.0995	−	1.24769i	0.928094	−	0.0523980i
$568$		0			0
$569$	24.2621	+	17.2770i	1.01712	+	0.724289i	0.961680	−	0.274173i	$-0.0884040\pi$
$569$	24.2621	+	17.2770i	1.01712	+	0.724289i	0.0554414	+	0.998462i	$0.482343\pi$
$570$		0			0
$571$	−0.750998	+	15.7654i	−0.0314283	+	0.659761i	0.927109	+	0.374793i	$0.122286\pi$
$571$	−0.750998	+	15.7654i	−0.0314283	+	0.659761i	−0.958537	+	0.284968i	$0.908017\pi$
$572$		0			0
$573$	6.73741	−	0.496766i	0.281460	−	0.0207527i
$574$		0			0
$575$	0.700119	+	0.169847i	0.0291970	+	0.00708312i
$576$		0			0
$577$	7.92014	−	41.0936i	0.329720	−	1.71075i	−0.317343	−	0.948311i	$-0.602791\pi$
$577$	7.92014	−	41.0936i	0.329720	−	1.71075i	0.647063	−	0.762437i	$-0.275997\pi$
$578$		0			0
$579$	47.2981	+	5.54968i	1.96564	+	0.230637i
$580$		0			0
$581$	−21.2694	−	13.6690i	−0.882405	−	0.567087i
$582$		0			0
$583$	32.3537	+	16.6795i	1.33995	+	0.690793i
$584$		0			0
$585$	−44.3314	−	8.34209i	−1.83288	−	0.344903i
$586$		0			0
$587$	−26.8181	−	21.0900i	−1.10690	−	0.870477i	−0.114489	−	0.993425i	$-0.536523\pi$
$587$	−26.8181	−	21.0900i	−1.10690	−	0.870477i	−0.992413	+	0.122947i	$0.960765\pi$
$588$		0			0
$589$	0.959209	−	0.831159i	0.0395235	−	0.0342473i
$590$		0			0
$591$	−19.7309	+	21.8008i	−0.811620	+	0.896767i
$592$		0			0
$593$	−26.4914	+	13.6573i	−1.08787	+	0.560837i	−0.906341	−	0.422548i	$-0.861136\pi$
$593$	−26.4914	+	13.6573i	−1.08787	+	0.560837i	−0.181532	+	0.983385i	$0.558105\pi$
$594$		0			0
$595$	2.80822	−	0.824569i	0.115126	−	0.0338040i
$596$		0			0
$597$	4.57555	+	20.8130i	0.187265	+	0.851818i
$598$		0			0
$599$	4.85131	−	14.0169i	0.198219	−	0.572717i	−0.801460	−	0.598049i	$-0.795943\pi$
$599$	4.85131	−	14.0169i	0.198219	−	0.572717i	0.999679	+	0.0253316i	$0.00806417\pi$
$600$		0			0
$601$	22.9200	+	32.1867i	0.934927	+	1.31292i	0.949743	+	0.313031i	$0.101344\pi$
$601$	22.9200	+	32.1867i	0.934927	+	1.31292i	−0.0148163	+	0.999890i	$0.504716\pi$
$602$		0			0
$603$	−18.4415	−	16.2145i	−0.750996	−	0.660307i
$604$		0			0
$605$	4.32259	+	6.07023i	0.175738	+	0.246790i
$606$		0			0
$607$	−4.68718	+	13.5427i	−0.190247	+	0.549682i	−0.999274	−	0.0380889i	$-0.987873\pi$
$607$	−4.68718	+	13.5427i	−0.190247	+	0.549682i	0.809028	+	0.587771i	$0.199994\pi$
$608$		0			0
$609$	−2.65120	−	12.0596i	−0.107432	−	0.488679i
$610$		0			0
$611$	−78.9903	+	23.1937i	−3.19561	+	0.938315i
$612$		0			0
$613$	14.1715	−	7.30591i	0.572381	−	0.295083i	−0.147633	−	0.989042i	$-0.547165\pi$
$613$	14.1715	−	7.30591i	0.572381	−	0.295083i	0.720014	+	0.693959i	$0.244135\pi$
$614$		0			0
$615$	−16.3783	+	18.0965i	−0.660435	+	0.729722i
$616$		0			0
$617$	−10.1060	+	8.75690i	−0.406852	+	0.352539i	−0.834117	−	0.551587i	$-0.814022\pi$
$617$	−10.1060	+	8.75690i	−0.406852	+	0.352539i	0.427265	+	0.904126i	$0.359477\pi$
$618$		0			0
$619$	−35.1858	−	27.6704i	−1.41424	−	1.11217i	−0.977102	−	0.212770i	$-0.931751\pi$
$619$	−35.1858	−	27.6704i	−1.41424	−	1.11217i	−0.437133	−	0.899397i	$-0.644006\pi$
$620$		0			0
$621$	4.19358	+	9.61709i	0.168283	+	0.385920i
$622$		0			0
$623$	−4.53723	−	2.33911i	−0.181780	−	0.0937143i
$624$		0			0
$625$	−19.4234	−	12.4827i	−0.776937	−	0.499307i
$626$		0			0
$627$	−13.2170	−	1.55081i	−0.527836	−	0.0619333i
$628$		0			0
$629$	0.285868	−	1.48323i	0.0113983	−	0.0591401i
$630$		0			0
$631$	32.3998	+	7.86012i	1.28982	+	0.312906i	0.821274	−	0.570534i	$-0.193264\pi$
$631$	32.3998	+	7.86012i	1.28982	+	0.312906i	0.468544	+	0.883440i	$0.344779\pi$
$632$		0			0
$633$	−32.6543	+	2.40768i	−1.29789	+	0.0956967i
$634$		0			0
$635$	−1.58624	+	33.2993i	−0.0629480	+	1.32144i
$636$		0			0
$637$	−5.40724	−	3.85048i	−0.214243	−	0.152562i
$638$		0			0
$639$	11.8142	+	25.5711i	0.467361	+	1.01158i
$640$		0			0
$641$	−5.04283	−	8.73443i	−0.199180	−	0.344989i	0.749083	−	0.662476i	$-0.230494\pi$
$641$	−5.04283	−	8.73443i	−0.199180	−	0.344989i	−0.948263	+	0.317487i	$0.897161\pi$
$642$		0			0
$643$	1.46628	+	10.1982i	0.0578245	+	0.402178i	0.998092	+	0.0617419i	$0.0196656\pi$
$643$	1.46628	+	10.1982i	0.0578245	+	0.402178i	−0.940268	+	0.340436i	$0.889425\pi$
$644$		0			0
$645$	2.95118	−	0.950550i	0.116203	−	0.0374279i
$646$		0			0
$647$	2.21980	+	46.5994i	0.0872694	+	1.83201i	0.441969	+	0.897030i	$0.354280\pi$
$647$	2.21980	+	46.5994i	0.0872694	+	1.83201i	−0.354700	+	0.934980i	$0.615417\pi$
$648$		0			0
$649$	22.6253	+	28.7704i	0.888120	+	1.12934i
$650$		0			0
$651$	0.929879	+	1.69408i	0.0364448	+	0.0663961i
$652$		0			0
$653$	−14.8700	−	42.9640i	−0.581907	−	1.68131i	−0.722607	−	0.691259i	$-0.757056\pi$
$653$	−14.8700	−	42.9640i	−0.581907	−	1.68131i	0.140700	−	0.990052i	$-0.455065\pi$
$654$		0			0
$655$	−12.7194	+	5.80875i	−0.496988	+	0.226967i
$656$		0			0
$657$	11.6488	+	28.7304i	0.454464	+	1.12088i
$658$		0			0
$659$	−9.29668	−	23.2220i	−0.362147	−	0.904600i	−0.991809	−	0.127731i	$-0.959231\pi$
$659$	−9.29668	−	23.2220i	−0.362147	−	0.904600i	0.629662	−	0.776870i	$-0.283194\pi$
$660$		0			0
$661$	−1.56815	−	0.716148i	−0.0609938	−	0.0278549i	0.384685	−	0.923048i	$-0.374310\pi$
$661$	−1.56815	−	0.716148i	−0.0609938	−	0.0278549i	−0.445678	+	0.895193i	$0.647037\pi$
$662$		0			0
$663$	4.26119	+	5.13782i	0.165491	+	0.199537i
$664$		0			0
$665$	14.6759	+	2.11008i	0.569107	+	0.0818253i
$666$		0			0
$667$	4.92354	−	3.16417i	0.190640	−	0.122517i
$668$		0			0
$669$	−16.2588	−	23.9089i	−0.628600	−	0.924370i
$670$		0			0
$671$			16.6305i			0.642013i
$672$		0			0
$673$	−1.62999	−	2.53631i	−0.0628314	−	0.0977675i	0.808416	−	0.588611i	$-0.200325\pi$
$673$	−1.62999	−	2.53631i	−0.0628314	−	0.0977675i	−0.871248	+	0.490844i	$0.836689\pi$
$674$		0			0
$675$	0.144463	+	1.84837i	0.00556036	+	0.0711437i
$676$		0			0
$677$	−29.1487	+	2.78336i	−1.12028	+	0.106973i	−0.638718	−	0.769441i	$-0.720535\pi$
$677$	−29.1487	+	2.78336i	−1.12028	+	0.106973i	−0.481558	+	0.876414i	$0.659929\pi$
$678$		0			0
$679$	8.63441	−	18.9067i	0.331358	−	0.725574i
$680$		0			0
$681$	−5.99559	+	8.90058i	−0.229751	+	0.341071i
$682$		0			0
$683$	5.63357	−	5.37160i	0.215563	−	0.205539i	−0.574602	−	0.818433i	$-0.694843\pi$
$683$	5.63357	−	5.37160i	0.215563	−	0.205539i	0.790165	+	0.612894i	$0.209995\pi$
$684$		0			0
$685$	10.9848	+	24.0534i	0.419708	+	0.919032i
$686$		0			0
$687$	−4.35540	−	3.24549i	−0.166169	−	0.123823i
$688$		0			0
$689$	8.79196	−	92.0736i	0.334947	−	3.50772i
$690$		0			0
$691$	−11.2652	+	8.85907i	−0.428549	+	0.337015i	−0.809023	−	0.587777i	$-0.800003\pi$
$691$	−11.2652	+	8.85907i	−0.428549	+	0.337015i	0.380474	+	0.924792i	$0.375761\pi$
$692$		0			0
$693$	6.54283	−	19.1768i	0.248542	−	0.728466i
$694$		0			0
$695$	−6.05256	+	20.6131i	−0.229587	+	0.781901i
$696$		0			0
$697$	3.57489	−	0.513991i	0.135408	−	0.0194688i
$698$		0			0
$699$	5.02383	−	10.4001i	0.190019	−	0.393369i
$700$		0			0
$701$	−18.2157	−	17.3687i	−0.687999	−	0.656006i	0.263144	−	0.964757i	$-0.415241\pi$
$701$	−18.2157	−	17.3687i	−0.687999	−	0.656006i	−0.951143	+	0.308751i	$0.900089\pi$
$702$		0			0
$703$	4.43870	−	6.23329i	0.167409	−	0.235093i
$704$		0			0
$705$	−22.9996	−	37.5472i	−0.866215	−	1.41411i
$706$		0			0
$707$	1.56689	+	0.904646i	0.0589291	+	0.0340227i
$708$		0			0
$709$	−6.67711	+	27.5234i	−0.250764	+	1.03366i	0.697602	+	0.716486i	$0.254250\pi$
$709$	−6.67711	+	27.5234i	−0.250764	+	1.03366i	−0.948366	+	0.317178i	$0.897265\pi$
$710$		0			0
$711$	11.5334	+	7.34056i	0.432535	+	0.275293i
$712$		0			0
$713$	−0.599844	+	0.692257i	−0.0224643	+	0.0259252i
$714$		0			0
$715$	−22.3249	+	34.7382i	−0.834904	+	1.29914i
$716$		0			0
$717$	−5.23150	−	42.9530i	−0.195374	−	1.60411i
$718$		0			0
$719$	0.513994	+	2.66685i	0.0191687	+	0.0994569i	0.990253	−	0.139280i	$-0.0444788\pi$
$719$	0.513994	+	2.66685i	0.0191687	+	0.0994569i	−0.971084	+	0.238737i	$0.923267\pi$
$720$		0			0
$721$	−19.6787	+	25.0235i	−0.732874	+	0.931925i
$722$		0			0
$723$	−0.0289210	+	0.108892i	−0.00107559	+	0.00404975i
$724$		0			0
$725$	1.00508	−	0.243829i	0.0373277	−	0.00905560i
$726$		0			0
$727$	16.5228	+	32.0498i	0.612798	+	1.18866i	0.967307	+	0.253610i	$0.0816179\pi$
$727$	16.5228	+	32.0498i	0.612798	+	1.18866i	−0.354508	+	0.935053i	$0.615352\pi$
$728$		0			0
$729$	−20.1701	+	17.9490i	−0.747042	+	0.664777i
$730$		0			0
$731$	−0.425922	−	0.170513i	−0.0157533	−	0.00630667i
$732$		0			0
$733$	6.38116	+	2.20854i	0.235694	+	0.0815743i	0.442362	−	0.896837i	$-0.354141\pi$
$733$	6.38116	+	2.20854i	0.235694	+	0.0815743i	−0.206668	+	0.978411i	$0.566262\pi$
$734$		0			0
$735$	1.23341	−	3.32925i	0.0454951	−	0.122801i
$736$		0			0
$737$	−20.0983	+	10.0673i	−0.740330	+	0.370835i
$738$		0			0
$739$	−9.54596	+	6.79764i	−0.351154	+	0.250055i	−0.741999	−	0.670401i	$-0.766122\pi$
$739$	−9.54596	+	6.79764i	−0.351154	+	0.250055i	0.390845	+	0.920456i	$0.372183\pi$
$740$		0			0
$741$	8.82372	+	32.6432i	0.324147	+	1.19918i
$742$		0			0
$743$	13.4166	−	33.5130i	0.492207	−	1.22947i	−0.449573	−	0.893244i	$-0.648424\pi$
$743$	13.4166	−	33.5130i	0.492207	−	1.22947i	0.941780	−	0.336230i	$-0.109152\pi$
$744$		0			0
$745$	12.0652	+	41.0902i	0.442034	+	1.50543i
$746$		0			0
$747$	30.6875	−	3.06658i	1.12280	−	0.112200i
$748$		0			0
$749$	−2.81591	−	11.6073i	−0.102891	−	0.424122i
$750$		0			0
$751$	−24.0876	−	27.7986i	−0.878971	−	1.01439i	−0.999764	−	0.0217085i	$-0.993089\pi$
$751$	−24.0876	−	27.7986i	−0.878971	−	1.01439i	0.120794	−	0.992678i	$-0.461456\pi$
$752$		0			0
$753$	2.98000	−	42.9947i	0.108597	−	1.56681i
$754$		0			0
$755$	17.8859	−	3.44722i	0.650934	−	0.125457i
$756$		0			0
$757$	−16.4736	+	31.9542i	−0.598742	+	1.16140i	0.373547	+	0.927611i	$0.378142\pi$
$757$	−16.4736	+	31.9542i	−0.598742	+	1.16140i	−0.972288	+	0.233785i	$0.924889\pi$
$758$		0			0
$759$	9.60084	−	0.249673i	0.348489	−	0.00906255i
$760$		0			0
$761$	−0.118608	−	0.102774i	−0.00429952	−	0.00372556i	0.652708	−	0.757609i	$-0.273633\pi$
$761$	−0.118608	−	0.102774i	−0.00429952	−	0.00372556i	−0.657008	+	0.753884i	$0.728178\pi$
$762$		0			0
$763$	17.8315	+	3.43674i	0.645544	+	0.124418i
$764$		0			0
$765$	−2.05804	+	2.91719i	−0.0744087	+	0.105471i
$766$		0			0
$767$	46.5016	−	80.5431i	1.67908	−	2.90824i
$768$		0			0
$769$	−46.3240	−	2.20669i	−1.67049	−	0.0795751i	−0.809148	−	0.587605i	$-0.800071\pi$
$769$	−46.3240	−	2.20669i	−1.67049	−	0.0795751i	−0.861340	+	0.508030i	$0.830374\pi$
$770$		0			0
$771$	−0.556839	+	25.7750i	−0.0200541	+	0.928264i
$772$		0			0
$773$	−28.4381	+	29.8250i	−1.02285	+	1.07273i	−0.0255199	+	0.999674i	$0.508124\pi$
$773$	−28.4381	+	29.8250i	−1.02285	+	1.07273i	−0.997328	+	0.0730574i	$0.976724\pi$
$774$		0			0
$775$	−0.140180	+	0.0809331i	−0.00503542	+	0.00290720i
$776$		0			0
$777$	7.85624	+	8.60406i	0.281841	+	0.308669i
$778$		0			0
$779$	17.5552	+	5.15467i	0.628980	+	0.184685i
$780$		0			0
$781$	25.7562	−	1.22692i	0.921631	−	0.0439027i
$782$		0			0
$783$	11.6773	+	9.51273i	0.417313	+	0.339957i
$784$		0			0
$785$	3.79908	+	0.362768i	0.135595	+	0.0129478i
$786$		0			0
$787$	23.0071	−	7.96283i	0.820114	−	0.283844i	0.115385	−	0.993321i	$-0.463190\pi$
$787$	23.0071	−	7.96283i	0.820114	−	0.283844i	0.704729	+	0.709477i	$0.251069\pi$
$788$		0			0
$789$	−19.8595	−	12.0452i	−0.707018	−	0.428820i
$790$		0			0
$791$	−3.86331	−	4.05172i	−0.137363	−	0.144063i
$792$		0			0
$793$	39.2310	−	15.7057i	1.39313	−	0.557727i
$794$		0			0
$795$	48.7664	−	8.31080i	1.72956	−	0.294754i
$796$		0			0
$797$	2.68671	+	28.1365i	0.0951681	+	0.996645i	0.909349	+	0.416034i	$0.136580\pi$
$797$	2.68671	+	28.1365i	0.0951681	+	0.996645i	−0.814181	+	0.580611i	$0.802814\pi$
$798$		0			0
$799$	−0.927243	+	6.44912i	−0.0328035	+	0.228153i
$800$		0			0
$801$	6.10895	−	1.20530i	0.215849	−	0.0425871i
$802$		0			0
$803$	28.3795			1.00149
$804$		0			0
$805$	−10.7004			−0.377141
$806$		0			0
$807$	−6.20980	+	14.5898i	−0.218595	+	0.513587i
$808$		0			0
$809$	−1.33803	+	9.30620i	−0.0470426	+	0.327188i	0.952687	+	0.303952i	$0.0983062\pi$
$809$	−1.33803	+	9.30620i	−0.0470426	+	0.327188i	−0.999730	+	0.0232366i	$0.992603\pi$
$810$		0			0
$811$	2.07284	+	21.7078i	0.0727873	+	0.762263i	0.956015	+	0.293318i	$0.0947596\pi$
$811$	2.07284	+	21.7078i	0.0727873	+	0.762263i	−0.883227	+	0.468945i	$0.844634\pi$
$812$		0			0
$813$	−3.42194	−	20.0794i	−0.120013	−	0.704214i
$814$		0			0
$815$	−15.1503	+	6.06525i	−0.530690	+	0.212456i
$816$		0			0
$817$	−1.60386	−	1.68208i	−0.0561120	−	0.0588486i
$818$		0			0
$819$	−51.4166	+	2.67602i	−1.79664	+	0.0935077i
$820$		0			0
$821$	−30.1184	+	10.4241i	−1.05114	+	0.363803i	−0.797388	−	0.603466i	$-0.793786\pi$
$821$	−30.1184	+	10.4241i	−1.05114	+	0.363803i	−0.253751	+	0.967269i	$0.581665\pi$
$822$		0			0
$823$	−11.0091	−	1.05125i	−0.383755	−	0.0366441i	−0.0986037	−	0.995127i	$-0.531438\pi$
$823$	−11.0091	−	1.05125i	−0.383755	−	0.0366441i	−0.285151	+	0.958483i	$0.592044\pi$
$824$		0			0
$825$	1.61771	+	0.513206i	0.0563214	+	0.0178675i
$826$		0			0
$827$	−28.6623	+	1.36535i	−0.996685	+	0.0474780i	−0.539580	−	0.841934i	$-0.681417\pi$
$827$	−28.6623	+	1.36535i	−0.996685	+	0.0474780i	−0.457106	+	0.889412i	$0.651114\pi$
$828$		0			0
$829$	−11.4805	−	3.37097i	−0.398733	−	0.117079i	0.0762173	−	0.997091i	$-0.475716\pi$
$829$	−11.4805	−	3.37097i	−0.398733	−	0.117079i	−0.474950	+	0.880013i	$0.657534\pi$
$830$		0			0
$831$	−14.5636	+	13.2978i	−0.505206	+	0.461297i
$832$		0			0
$833$	−0.454974	+	0.262679i	−0.0157639	+	0.00910130i
$834$		0			0
$835$	−18.0209	+	18.8998i	−0.623639	+	0.654054i
$836$		0			0
$837$	−2.17302	−	0.913622i	−0.0751106	−	0.0315794i
$838$		0			0
$839$	7.50028	+	0.357283i	0.258939	+	0.0123348i	0.176650	−	0.984274i	$-0.443474\pi$
$839$	7.50028	+	0.357283i	0.258939	+	0.0123348i	0.0822887	+	0.996609i	$0.473777\pi$
$840$		0			0
$841$	−10.2990	+	17.8385i	−0.355139	+	0.615119i
$842$		0			0
$843$	32.5572	−	12.2248i	1.12133	−	0.421046i
$844$		0			0
$845$	75.5239	+	14.5560i	2.59810	+	0.500743i
$846$		0			0
$847$	6.42798	+	5.56988i	0.220868	+	0.191383i
$848$		0			0
$849$	0.0317232	+	1.21987i	0.00108874	+	0.0418660i
$850$		0			0
$851$	−2.53058	+	4.90864i	−0.0867471	+	0.168266i
$852$		0			0
$853$	7.14229	−	1.37656i	0.244547	−	0.0471327i	−0.0655045	−	0.997852i	$-0.520866\pi$
$853$	7.14229	−	1.37656i	0.244547	−	0.0471327i	0.310052	+	0.950720i	$0.399654\pi$
$854$		0			0
$855$	−15.6228	+	9.11171i	−0.534289	+	0.311614i
$856$		0			0
$857$	2.53153	+	2.92154i	0.0864755	+	0.0997980i	0.797338	−	0.603533i	$-0.206241\pi$
$857$	2.53153	+	2.92154i	0.0864755	+	0.0997980i	−0.710863	+	0.703331i	$0.751695\pi$
$858$		0			0
$859$	−1.00173	−	4.12919i	−0.0341786	−	0.140886i	0.952166	−	0.305582i	$-0.0988510\pi$
$859$	−1.00173	−	4.12919i	−0.0341786	−	0.140886i	−0.986344	+	0.164696i	$0.947336\pi$
$860$		0			0
$861$	−13.2971	+	24.4796i	−0.453163	+	0.834263i
$862$		0			0
$863$	−1.22638	−	4.17668i	−0.0417466	−	0.142176i	0.935983	−	0.352046i	$-0.114514\pi$
$863$	−1.22638	−	4.17668i	−0.0417466	−	0.142176i	−0.977729	+	0.209870i	$0.932696\pi$
$864$		0			0
$865$	16.7783	−	41.9101i	0.570478	−	1.42499i
$866$		0			0
$867$	−27.9148	+	7.54558i	−0.948035	+	0.256261i
$868$		0			0
$869$	10.1942	−	7.25924i	0.345814	−	0.246253i
$870$		0			0
$871$	42.7293	+	37.9039i	1.44783	+	1.28433i
$872$		0			0
$873$	6.08567	+	24.6124i	0.205969	+	0.833004i
$874$		0			0
$875$	−26.8274	−	9.28505i	−0.906931	−	0.313892i
$876$		0			0
$877$	−33.1871	−	13.2861i	−1.12065	−	0.448641i	−0.263992	−	0.964525i	$-0.585039\pi$
$877$	−33.1871	−	13.2861i	−1.12065	−	0.448641i	−0.856658	+	0.515884i	$0.827463\pi$
$878$		0			0
$879$	−18.3861	+	22.3681i	−0.620147	+	0.754457i
$880$		0			0
$881$	3.25892	+	6.32142i	0.109796	+	0.212974i	0.937331	−	0.348439i	$-0.113288\pi$
$881$	3.25892	+	6.32142i	0.109796	+	0.212974i	−0.827536	+	0.561413i	$0.810258\pi$
$882$		0			0
$883$	−3.38521	+	0.821244i	−0.113922	+	0.0276371i	−0.292314	−	0.956322i	$-0.594425\pi$
$883$	−3.38521	+	0.821244i	−0.113922	+	0.0276371i	0.178393	+	0.983959i	$0.442910\pi$
$884$		0			0
$885$	48.0759	+	12.7686i	1.61605	+	0.429213i
$886$		0			0
$887$	6.30023	−	8.01140i	0.211541	−	0.268996i	−0.668690	−	0.743541i	$-0.733145\pi$
$887$	6.30023	−	8.01140i	0.211541	−	0.268996i	0.880231	+	0.474545i	$0.157387\pi$
$888$		0			0
$889$	7.20094	+	37.3620i	0.241512	+	1.25308i
$890$		0			0
$891$	8.28896	+	23.2845i	0.277690	+	0.780061i
$892$		0			0
$893$	−17.8448	+	27.7670i	−0.597152	+	0.929187i
$894$		0			0
$895$	13.5701	−	15.6607i	0.453598	−	0.523480i
$896$		0			0
$897$	−9.65594	−	22.4124i	−0.322402	−	0.748328i
$898$		0			0
$899$	−0.310017	+	1.27791i	−0.0103396	+	0.0426206i
$900$		0			0
$901$	−6.33940	−	3.66005i	−0.211196	−	0.121934i
$902$		0			0
$903$	3.01764	−	1.84846i	0.100421	−	0.0615129i
$904$		0			0
$905$	8.26515	−	11.6068i	0.274743	−	0.385822i
$906$		0			0
$907$	−1.53755	−	1.46605i	−0.0510534	−	0.0486793i	0.664123	−	0.747623i	$-0.268805\pi$
$907$	−1.53755	−	1.46605i	−0.0510534	−	0.0486793i	−0.715176	+	0.698944i	$0.753654\pi$
$908$		0			0
$909$	−2.18311	+	0.323692i	−0.0724092	+	0.0107362i
$910$		0			0
$911$	−29.7778	+	4.28140i	−0.986583	+	0.141849i	−0.616674	−	0.787219i	$-0.711520\pi$
$911$	−29.7778	+	4.28140i	−0.986583	+	0.141849i	−0.369909	+	0.929068i	$0.620611\pi$
$912$		0			0
$913$	7.95369	−	27.0878i	0.263229	−	0.896474i
$914$		0			0
$915$	13.5844	+	18.0637i	0.449088	+	0.597169i
$916$		0			0
$917$	−12.5452	+	9.86562i	−0.414278	+	0.325791i
$918$		0			0
$919$	−1.50036	+	15.7125i	−0.0494923	+	0.518306i	0.936401	+	0.350932i	$0.114135\pi$
$919$	−1.50036	+	15.7125i	−0.0494923	+	0.518306i	−0.985893	+	0.167375i	$0.946471\pi$
$920$		0			0
$921$	11.4299	−	15.3387i	0.376627	−	0.505428i
$922$		0			0
$923$	−27.2183	−	59.5997i	−0.895901	−	1.96175i
$924$		0			0
$925$	−0.706294	+	0.673450i	−0.0232228	+	0.0221429i
$926$		0			0
$927$	−0.170819	−	38.8313i	−0.00561044	−	1.27539i
$928$		0			0
$929$	−17.5384	+	38.4038i	−0.575418	+	1.25999i	0.368445	+	0.929650i	$0.379890\pi$
$929$	−17.5384	+	38.4038i	−0.575418	+	1.25999i	−0.943862	+	0.330339i	$0.892837\pi$
$930$		0			0
$931$	−2.64937	+	0.252984i	−0.0868297	+	0.00829123i
$932$		0			0
$933$	−20.2467	+	9.89035i	−0.662848	+	0.323796i
$934$		0			0
$935$	1.76685	+	2.74928i	0.0577823	+	0.0899110i
$936$		0			0
$937$		−	41.0031i		−	1.33951i	−0.742581	−	0.669756i	$-0.766399\pi$
$937$		−	41.0031i		−	1.33951i	0.742581	−	0.669756i	$-0.233601\pi$
$938$		0			0
$939$	18.9217	−	12.8673i	0.617486	−	0.419910i
$940$		0			0
$941$	−37.4772	+	24.0851i	−1.22172	+	0.785152i	−0.982581	−	0.185833i	$-0.940502\pi$
$941$	−37.4772	+	24.0851i	−1.22172	+	0.785152i	−0.239139	+	0.970985i	$0.576865\pi$
$942$		0			0
$943$	−13.0700	−	1.87918i	−0.425616	−	0.0611944i
$944$		0			0
$945$	−8.55765	−	26.1739i	−0.278380	−	0.851437i
$946$		0			0
$947$	15.7829	+	7.20782i	0.512876	+	0.234223i	0.655004	−	0.755626i	$-0.272667\pi$
$947$	15.7829	+	7.20782i	0.512876	+	0.234223i	−0.142128	+	0.989848i	$0.545394\pi$
$948$		0			0
$949$	−26.8013	−	66.9465i	−0.870009	−	2.17318i
$950$		0			0
$951$	−2.59580	+	12.0603i	−0.0841745	+	0.391083i
$952$		0			0
$953$	35.4125	−	16.1724i	1.14712	−	0.523874i	0.251136	−	0.967952i	$-0.419196\pi$
$953$	35.4125	−	16.1724i	1.14712	−	0.523874i	0.895988	+	0.444078i	$0.146469\pi$
$954$		0			0
$955$	−2.74888	−	7.94238i	−0.0889518	−	0.257009i
$956$		0			0
$957$	12.0864	−	6.63422i	0.390698	−	0.214454i
$958$		0			0
$959$	18.6566	+	23.7239i	0.602455	+	0.766083i
$960$		0			0
$961$	1.46525	+	30.7593i	0.0472660	+	0.992236i
$962$		0			0
$963$	11.4918	+	8.95569i	0.370317	+	0.288593i
$964$		0			0
$965$	−8.43161	−	58.6431i	−0.271423	−	1.88779i
$966$		0			0
$967$	−26.8720	−	46.5436i	−0.864145	−	1.49674i	−0.867894	−	0.496750i	$-0.834527\pi$
$967$	−26.8720	−	46.5436i	−0.864145	−	1.49674i	0.00374909	−	0.999993i	$-0.498807\pi$
$968$		0			0
$969$	2.64011	+	0.437987i	0.0848125	+	0.0140702i
$970$		0			0
$971$	−9.99233	−	7.11551i	−0.320669	−	0.228348i	0.408375	−	0.912814i	$-0.366096\pi$
$971$	−9.99233	−	7.11551i	−0.320669	−	0.228348i	−0.729044	+	0.684467i	$0.760035\pi$
$972$		0			0
$973$	−1.16672	+	24.4925i	−0.0374034	+	0.785194i
$974$		0			0
$975$	−0.317109	−	4.30081i	−0.0101556	−	0.137736i
$976$		0			0
$977$	25.7156	+	6.23853i	0.822714	+	0.199588i	0.624954	−	0.780662i	$-0.285118\pi$
$977$	25.7156	+	6.23853i	0.822714	+	0.199588i	0.197761	+	0.980250i	$0.436633\pi$
$978$		0			0
$979$	1.07873	−	5.59696i	0.0344762	−	0.178880i
$980$		0			0
$981$	−19.6439	+	10.2368i	−0.627183	+	0.326835i
$982$		0			0
$983$	−20.3730	−	13.0929i	−0.649799	−	0.417600i	0.173794	−	0.984782i	$-0.444397\pi$
$983$	−20.3730	−	13.0929i	−0.649799	−	0.417600i	−0.823593	+	0.567182i	$0.808034\pi$
$984$		0			0
$985$	32.5142	+	16.7622i	1.03599	+	0.534089i
$986$		0			0
$987$	−35.6143	−	35.4580i	−1.13362	−	1.12864i
$988$		0			0
$989$	1.31848	+	1.03687i	0.0419253	+	0.0329704i
$990$		0			0
$991$	21.8626	−	18.9441i	0.694490	−	0.601779i	−0.234398	−	0.972141i	$-0.575312\pi$
$991$	21.8626	−	18.9441i	0.694490	−	0.601779i	0.928887	+	0.370362i	$0.120766\pi$
$992$		0			0
$993$	21.0706	+	19.0700i	0.668656	+	0.605168i
$994$		0			0
$995$	23.5642	−	12.1482i	0.747035	−	0.385123i
$996$		0			0
$997$	−19.8213	+	5.82007i	−0.627748	+	0.184324i	−0.580106	−	0.814541i	$-0.696989\pi$
$997$	−19.8213	+	5.82007i	−0.627748	+	0.184324i	−0.0476422	+	0.998864i	$0.515171\pi$
$998$		0			0
$999$	−14.0306	−	2.26427i	−0.443909	−	0.0716384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.ba.b.41.19	yes	440
3.2	odd	2	inner	804.2.ba.b.41.12	✓	440
67.18	odd	66	inner	804.2.ba.b.353.12	yes	440
201.152	even	66	inner	804.2.ba.b.353.19	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.ba.b.41.12	✓	440	3.2	odd	2	inner
804.2.ba.b.41.19	yes	440	1.1	even	1	trivial
804.2.ba.b.353.12	yes	440	67.18	odd	66	inner
804.2.ba.b.353.19	yes	440	201.152	even	66	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.ba (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.59370 + 0.678318i) q^{3} +(0.306661 - 2.13288i) q^{5} +(-0.233782 - 2.44828i) q^{7} +(2.07977 + 2.16207i) q^{9} +O(q^{10})\)	\(q+(1.59370 + 0.678318i) q^{3} +(0.306661 - 2.13288i) q^{5} +(-0.233782 - 2.44828i) q^{7} +(2.07977 + 2.16207i) q^{9} +(2.54950 - 1.02066i) q^{11} +(-4.81545 - 5.05030i) q^{13} +(1.93549 - 3.19115i) q^{15} +(-0.521893 + 0.180629i) q^{17} +(-2.78507 - 0.265942i) q^{19} +(1.28813 - 4.06040i) q^{21} +(2.01683 - 0.0960734i) q^{23} +(0.342350 + 0.100523i) q^{25} +(1.84795 + 4.85645i) q^{27} +(2.51027 - 1.44930i) q^{29} +(-0.313059 + 0.328327i) q^{31} +(4.75547 + 0.102736i) q^{33} +(-5.29357 - 0.252164i) q^{35} +(-1.36757 + 2.36869i) q^{37} +(-4.24868 - 11.3151i) q^{39} +(-6.42149 - 1.23764i) q^{41} +(0.627825 + 0.544013i) q^{43} +(5.24922 - 3.77286i) q^{45} +(5.40598 - 10.4861i) q^{47} +(0.934085 - 0.180030i) q^{49} +(-0.954266 - 0.0661411i) q^{51} +(8.67995 + 10.0172i) q^{53} +(-1.39512 - 5.75075i) q^{55} +(-4.25818 - 2.31300i) q^{57} +(3.75489 + 12.7880i) q^{59} +(-2.25071 + 5.62201i) q^{61} +(4.80715 - 5.59731i) q^{63} +(-12.2484 + 8.72202i) q^{65} +(-8.15679 + 0.683270i) q^{67} +(3.27939 + 1.21494i) q^{69} +(8.87305 + 3.07099i) q^{71} +(9.59379 + 3.84077i) q^{73} +(0.477417 + 0.392426i) q^{75} +(-3.09490 - 6.00326i) q^{77} +(4.42862 - 1.07437i) q^{79} +(-0.349130 + 8.99323i) q^{81} +(6.35474 - 8.08070i) q^{83} +(0.225215 + 1.16852i) q^{85} +(4.98371 - 0.606996i) q^{87} +(1.12214 - 1.74608i) q^{89} +(-11.2388 + 12.9702i) q^{91} +(-0.721633 + 0.310901i) q^{93} +(-1.42130 + 5.85866i) q^{95} +(7.31896 + 4.22560i) q^{97} +(7.50911 + 3.38945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) \) 440 * q - 12 * q^7 + 4 * q^9	\( 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) \) 440 * q - 12 * q^7 + 4 * q^9 - 2 * q^15 - 10 * q^19 + 22 * q^21 - 68 * q^25 + 50 * q^31 + 11 * q^33 - 22 * q^37 - 45 * q^39 + 22 * q^43 + 22 * q^45 - 18 * q^49 - 6 * q^51 + 126 * q^55 - 183 * q^57 - 56 * q^61 - 141 * q^63 - 12 * q^67 + 33 * q^69 + 356 * q^73 + 165 * q^75 + 228 * q^79 + 24 * q^81 - 6 * q^85 + 75 * q^87 - 4 * q^91 - 75 * q^93 + 12 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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