LMFDB - Embedded newform 420.2.bv.b.233.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(53,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 9, 8]))

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

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

chi := DirichletCharacter("420.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.bv (of order $12$, degree $4$, 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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.303595776.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			233.1
Root			$-0.396143 + 1.68614i$ of defining polynomial
Character	$\chi$	$=$	420.233
Dual form			420.2.bv.b.137.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18614 + 1.26217i) q^{3} +(1.86603 - 1.23205i) q^{5} +(-1.94831 - 1.79000i) q^{7} +(-0.186141 - 2.99422i) q^{9} +O(q^{10})$	\(q+(-1.18614 + 1.26217i) q^{3} +(1.86603 - 1.23205i) q^{5} +(-1.94831 - 1.79000i) q^{7} +(-0.186141 - 2.99422i) q^{9} +(2.00626 - 1.15831i) q^{11} +(-2.00000 - 2.00000i) q^{13} +(-0.658312 + 3.81662i) q^{15} +(0.847944 - 3.16457i) q^{17} +(0.274205 + 0.158312i) q^{19} +(4.57025 - 0.335907i) q^{21} +(-0.423972 - 1.58228i) q^{23} +(1.96410 - 4.59808i) q^{25} +(4.00000 + 3.31662i) q^{27} +7.31662 q^{29} +(3.00000 + 5.19615i) q^{31} +(-0.917716 + 3.90616i) q^{33} +(-5.84096 - 0.939764i) q^{35} +(-1.46410 - 5.46410i) q^{37} +(4.89662 - 0.152056i) q^{39} -9.63325i q^{41} +(1.84169 + 1.84169i) q^{43} +(-4.03637 - 5.35796i) q^{45} +(-6.83013 + 1.83013i) q^{47} +(0.591820 + 6.97494i) q^{49} +(2.98844 + 4.82387i) q^{51} +(9.99470 + 2.67807i) q^{53} +(2.31662 - 4.63325i) q^{55} +(-0.525063 + 0.158312i) q^{57} +(-6.15831 - 10.6665i) q^{59} +(-4.65831 + 8.06843i) q^{61} +(-4.99699 + 6.16686i) q^{63} +(-6.19615 - 1.26795i) q^{65} +(-9.77844 - 2.62012i) q^{67} +(2.50000 + 1.34169i) q^{69} -2.31662i q^{71} +(-2.42794 + 9.06119i) q^{73} +(3.47385 + 7.93299i) q^{75} +(-5.98218 - 1.33444i) q^{77} +(4.92195 + 2.84169i) q^{79} +(-8.93070 + 1.11469i) q^{81} +(-3.84169 + 3.84169i) q^{83} +(-2.31662 - 6.94987i) q^{85} +(-8.67855 + 9.23482i) q^{87} +(-8.29156 + 14.3614i) q^{89} +(0.316625 + 7.47661i) q^{91} +(-10.1168 - 2.37686i) q^{93} +(0.706723 - 0.0424197i) q^{95} +(-9.31662 + 9.31662i) q^{97} +(-3.84169 - 5.79156i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 8 q^{5} + 6 q^{7} + 10 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 + 8 * q^5 + 6 * q^7 + 10 * q^9	$ 8 q + 2 q^{3} + 8 q^{5} + 6 q^{7} + 10 q^{9} - 16 q^{13} + 8 q^{15} + 4 q^{17} + 14 q^{21} - 2 q^{23} - 12 q^{25} + 32 q^{27} + 32 q^{29} + 24 q^{31} - 22 q^{33} + 16 q^{37} - 4 q^{39} + 28 q^{43} - 20 q^{45} - 20 q^{47} - 24 q^{51} + 16 q^{53} - 8 q^{55} - 44 q^{57} - 36 q^{59} - 24 q^{61} + 22 q^{63} - 8 q^{65} - 22 q^{67} + 20 q^{69} + 6 q^{75} - 16 q^{77} - 14 q^{81} - 44 q^{83} + 8 q^{85} + 8 q^{87} - 24 q^{91} - 12 q^{93} - 12 q^{95} - 48 q^{97} - 44 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 8 * q^5 + 6 * q^7 + 10 * q^9 - 16 * q^13 + 8 * q^15 + 4 * q^17 + 14 * q^21 - 2 * q^23 - 12 * q^25 + 32 * q^27 + 32 * q^29 + 24 * q^31 - 22 * q^33 + 16 * q^37 - 4 * q^39 + 28 * q^43 - 20 * q^45 - 20 * q^47 - 24 * q^51 + 16 * q^53 - 8 * q^55 - 44 * q^57 - 36 * q^59 - 24 * q^61 + 22 * q^63 - 8 * q^65 - 22 * q^67 + 20 * q^69 + 6 * q^75 - 16 * q^77 - 14 * q^81 - 44 * q^83 + 8 * q^85 + 8 * q^87 - 24 * q^91 - 12 * q^93 - 12 * q^95 - 48 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.18614	+	1.26217i	−0.684819	+	0.728714i
$3$	−1.18614	+	1.26217i	−0.684819	+	0.728714i
$4$		0			0
$5$	1.86603	−	1.23205i	0.834512	−	0.550990i
$5$	1.86603	−	1.23205i	0.834512	−	0.550990i
$6$		0			0
$7$	−1.94831	−	1.79000i	−0.736392	−	0.676555i
$7$	−1.94831	−	1.79000i	−0.736392	−	0.676555i
$8$		0			0
$9$	−0.186141	−	2.99422i	−0.0620469	−	0.998073i
$10$		0			0
$11$	2.00626	−	1.15831i	0.604909	−	0.349244i	−0.166061	−	0.986115i	$-0.553105\pi$
$11$	2.00626	−	1.15831i	0.604909	−	0.349244i	0.770970	+	0.636871i	$0.219772\pi$
$12$		0			0
$13$	−2.00000	−	2.00000i	−0.554700	−	0.554700i	0.373094	−	0.927794i	$-0.378297\pi$
$13$	−2.00000	−	2.00000i	−0.554700	−	0.554700i	−0.927794	+	0.373094i	$0.878297\pi$
$14$		0			0
$15$	−0.658312	+	3.81662i	−0.169976	+	0.985448i
$16$		0			0
$17$	0.847944	−	3.16457i	0.205657	−	0.767521i	−0.783592	−	0.621276i	$-0.786615\pi$
$17$	0.847944	−	3.16457i	0.205657	−	0.767521i	0.989248	−	0.146245i	$-0.0467187\pi$
$18$		0			0
$19$	0.274205	+	0.158312i	0.0629070	+	0.0363194i	0.531124	−	0.847294i	$-0.321770\pi$
$19$	0.274205	+	0.158312i	0.0629070	+	0.0363194i	−0.468217	+	0.883614i	$0.655103\pi$
$20$		0			0
$21$	4.57025	−	0.335907i	0.997310	−	0.0733010i
$22$		0			0
$23$	−0.423972	−	1.58228i	−0.0884042	−	0.329929i	0.907533	−	0.419981i	$-0.137963\pi$
$23$	−0.423972	−	1.58228i	−0.0884042	−	0.329929i	−0.995937	+	0.0900521i	$0.971297\pi$
$24$		0			0
$25$	1.96410	−	4.59808i	0.392820	−	0.919615i
$26$		0			0
$27$	4.00000	+	3.31662i	0.769800	+	0.638285i
$28$		0			0
$29$	7.31662			1.35866			0.679332	−	0.733831i	$-0.262270\pi$
$29$	7.31662			1.35866			0.679332	+	0.733831i	$0.262270\pi$
$30$		0			0
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$		0			0
$33$	−0.917716	+	3.90616i	−0.159754	+	0.679974i
$34$		0			0
$35$	−5.84096	−	0.939764i	−0.987303	−	0.158849i
$36$		0			0
$37$	−1.46410	−	5.46410i	−0.240697	−	0.898293i	−0.975498	−	0.220010i	$-0.929391\pi$
$37$	−1.46410	−	5.46410i	−0.240697	−	0.898293i	0.734801	−	0.678283i	$-0.237276\pi$
$38$		0			0
$39$	4.89662	−	0.152056i	0.784087	−	0.0243485i
$40$		0			0
$41$		−	9.63325i		−	1.50446i	−0.658900	−	0.752230i	$-0.728978\pi$
$41$		−	9.63325i		−	1.50446i	0.658900	−	0.752230i	$-0.271022\pi$
$42$		0			0
$43$	1.84169	+	1.84169i	0.280855	+	0.280855i	0.833450	−	0.552595i	$-0.186362\pi$
$43$	1.84169	+	1.84169i	0.280855	+	0.280855i	−0.552595	+	0.833450i	$0.686362\pi$
$44$		0			0
$45$	−4.03637	−	5.35796i	−0.601707	−	0.798717i
$46$		0			0
$47$	−6.83013	+	1.83013i	−0.996276	+	0.266951i	−0.719885	−	0.694094i	$-0.755805\pi$
$47$	−6.83013	+	1.83013i	−0.996276	+	0.266951i	−0.276392	+	0.961045i	$0.589139\pi$
$48$		0			0
$49$	0.591820	+	6.97494i	0.0845458	+	0.996420i
$50$		0			0
$51$	2.98844	+	4.82387i	0.418465	+	0.675477i
$52$		0			0
$53$	9.99470	+	2.67807i	1.37288	+	0.367861i	0.868529	−	0.495639i	$-0.165066\pi$
$53$	9.99470	+	2.67807i	1.37288	+	0.367861i	0.504348	+	0.863500i	$0.331733\pi$
$54$		0			0
$55$	2.31662	−	4.63325i	0.312374	−	0.624747i
$56$		0			0
$57$	−0.525063	+	0.158312i	−0.0695463	+	0.0209690i
$58$		0			0
$59$	−6.15831	−	10.6665i	−0.801744	−	1.38866i	−0.918467	−	0.395497i	$-0.870572\pi$
$59$	−6.15831	−	10.6665i	−0.801744	−	1.38866i	0.116723	−	0.993164i	$-0.462761\pi$
$60$		0			0
$61$	−4.65831	+	8.06843i	−0.596436	+	1.03306i	0.396907	+	0.917859i	$0.370084\pi$
$61$	−4.65831	+	8.06843i	−0.596436	+	1.03306i	−0.993343	+	0.115198i	$0.963250\pi$
$62$		0			0
$63$	−4.99699	+	6.16686i	−0.629561	+	0.776951i
$64$		0			0
$65$	−6.19615	−	1.26795i	−0.768538	−	0.157270i
$66$		0			0
$67$	−9.77844	−	2.62012i	−1.19463	−	0.320099i	−0.393913	−	0.919148i	$-0.628879\pi$
$67$	−9.77844	−	2.62012i	−1.19463	−	0.320099i	−0.800713	+	0.599048i	$0.795546\pi$
$68$		0			0
$69$	2.50000	+	1.34169i	0.300965	+	0.161520i
$70$		0			0
$71$		−	2.31662i		−	0.274933i	−0.990506	−	0.137466i	$-0.956104\pi$
$71$		−	2.31662i		−	0.274933i	0.990506	−	0.137466i	$-0.0438959\pi$
$72$		0			0
$73$	−2.42794	+	9.06119i	−0.284169	+	1.06053i	0.665276	+	0.746597i	$0.268314\pi$
$73$	−2.42794	+	9.06119i	−0.284169	+	1.06053i	−0.949445	+	0.313934i	$0.898353\pi$
$74$		0			0
$75$	3.47385	+	7.93299i	0.401125	+	0.916023i
$76$		0			0
$77$	−5.98218	−	1.33444i	−0.681733	−	0.152074i
$78$		0			0
$79$	4.92195	+	2.84169i	0.553762	+	0.319715i	0.750638	−	0.660714i	$-0.229746\pi$
$79$	4.92195	+	2.84169i	0.553762	+	0.319715i	−0.196876	+	0.980428i	$0.563080\pi$
$80$		0			0
$81$	−8.93070	+	1.11469i	−0.992300	+	0.123855i
$82$		0			0
$83$	−3.84169	+	3.84169i	−0.421680	+	0.421680i	−0.885782	−	0.464102i	$-0.846377\pi$
$83$	−3.84169	+	3.84169i	−0.421680	+	0.421680i	0.464102	+	0.885782i	$0.346377\pi$
$84$		0			0
$85$	−2.31662	−	6.94987i	−0.251273	−	0.753820i
$86$		0			0
$87$	−8.67855	+	9.23482i	−0.930438	+	0.990076i
$88$		0			0
$89$	−8.29156	+	14.3614i	−0.878904	+	1.52231i	−0.0263586	+	0.999653i	$0.508391\pi$
$89$	−8.29156	+	14.3614i	−0.878904	+	1.52231i	−0.852545	+	0.522654i	$0.824942\pi$
$90$		0			0
$91$	0.316625	+	7.47661i	0.0331913	+	0.783762i
$92$		0			0
$93$	−10.1168	−	2.37686i	−1.04907	−	0.246469i
$94$		0			0
$95$	0.706723	−	0.0424197i	0.0725082	−	0.00435217i
$96$		0			0
$97$	−9.31662	+	9.31662i	−0.945960	+	0.945960i	−0.998613	−	0.0526529i	$-0.983232\pi$
$97$	−9.31662	+	9.31662i	−0.945960	+	0.945960i	0.0526529	+	0.998613i	$0.483232\pi$
$98$		0			0
$99$	−3.84169	−	5.79156i	−0.386104	−	0.582074i
$100$		0			0
$101$	2.32387	−	1.34169i	0.231234	−	0.133503i	−0.379907	−	0.925025i	$-0.624044\pi$
$101$	2.32387	−	1.34169i	0.231234	−	0.133503i	0.611141	+	0.791522i	$0.290711\pi$
$102$		0			0
$103$	13.8080	−	3.69985i	1.36055	−	0.364557i	0.496530	−	0.868020i	$-0.334607\pi$
$103$	13.8080	−	3.69985i	1.36055	−	0.364557i	0.864017	+	0.503462i	$0.167941\pi$
$104$		0			0
$105$	8.11434	−	6.25759i	0.791879	−	0.610678i
$106$		0			0
$107$	−5.24784	+	1.40616i	−0.507328	+	0.135938i	−0.503399	−	0.864054i	$-0.667917\pi$
$107$	−5.24784	+	1.40616i	−0.507328	+	0.135938i	−0.00392920	+	0.999992i	$0.501251\pi$
$108$		0			0
$109$	16.0935	−	9.29156i	1.54147	−	0.889970i	0.542728	−	0.839909i	$-0.317392\pi$
$109$	16.0935	−	9.29156i	1.54147	−	0.889970i	0.998746	−	0.0500614i	$-0.0159417\pi$
$110$		0			0
$111$	8.63325	+	4.63325i	0.819432	+	0.439769i
$112$		0			0
$113$	9.63325	−	9.63325i	0.906220	−	0.906220i	−0.0897449	−	0.995965i	$-0.528605\pi$
$113$	9.63325	−	9.63325i	0.906220	−	0.906220i	0.995965	+	0.0897449i	$0.0286052\pi$
$114$		0			0
$115$	−2.74060	−	2.43023i	−0.255562	−	0.226620i
$116$		0			0
$117$	−5.61616	+	6.36072i	−0.519214	+	0.588049i
$118$		0			0
$119$	−7.31662	+	4.64774i	−0.670714	+	0.426058i
$120$		0			0
$121$	−2.81662	+	4.87854i	−0.256057	+	0.443503i
$122$		0			0
$123$	12.1588	+	11.4264i	1.09632	+	1.03028i
$124$		0			0
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$	5.63325	−	5.63325i	0.499870	−	0.499870i	−0.411527	−	0.911397i	$-0.635005\pi$
$127$	5.63325	−	5.63325i	0.499870	−	0.499870i	0.911397	+	0.411527i	$0.135005\pi$
$128$		0			0
$129$	−4.50902	+	0.140020i	−0.396997	+	0.0123281i
$130$		0			0
$131$	8.66025	+	5.00000i	0.756650	+	0.436852i	0.828092	−	0.560593i	$-0.189427\pi$
$131$	8.66025	+	5.00000i	0.756650	+	0.436852i	−0.0714417	+	0.997445i	$0.522760\pi$
$132$		0			0
$133$	−0.250858	−	0.799268i	−0.0217521	−	0.0693053i
$134$		0			0
$135$	11.5504	+	1.26070i	0.994096	+	0.108504i
$136$		0			0
$137$	−2.54383	+	9.49370i	−0.217334	+	0.811102i	0.767998	+	0.640453i	$0.221253\pi$
$137$	−2.54383	+	9.49370i	−0.217334	+	0.811102i	−0.985332	+	0.170649i	$0.945413\pi$
$138$		0			0
$139$		−	5.68338i		−	0.482058i	−0.970518	−	0.241029i	$-0.922515\pi$
$139$		−	5.68338i		−	0.482058i	0.970518	−	0.241029i	$-0.0774848\pi$
$140$		0			0
$141$	5.79156	−	10.7916i	0.487738	−	0.908813i
$142$		0			0
$143$	−6.32914	−	1.69589i	−0.529269	−	0.141817i
$144$		0			0
$145$	13.6530	−	9.01445i	1.13382	−	0.748610i
$146$		0			0
$147$	−9.50553	−	7.52628i	−0.784003	−	0.620757i
$148$		0			0
$149$	4.81662	−	8.34264i	0.394593	−	0.683456i	−0.598456	−	0.801156i	$-0.704219\pi$
$149$	4.81662	−	8.34264i	0.394593	−	0.683456i	0.993049	+	0.117700i	$0.0375522\pi$
$150$		0			0
$151$	1.68338	+	2.91569i	0.136991	+	0.237276i	0.926356	−	0.376648i	$-0.122923\pi$
$151$	1.68338	+	2.91569i	0.136991	+	0.237276i	−0.789365	+	0.613924i	$0.789590\pi$
$152$		0			0
$153$	−9.63325	−	1.94987i	−0.778802	−	0.157638i
$154$		0			0
$155$	12.0000	+	6.00000i	0.963863	+	0.481932i
$156$		0			0
$157$	−7.26264	−	1.94602i	−0.579622	−	0.155309i	−0.0429162	−	0.999079i	$-0.513665\pi$
$157$	−7.26264	−	1.94602i	−0.579622	−	0.155309i	−0.536706	+	0.843769i	$0.680332\pi$
$158$		0			0
$159$	−15.2353	+	9.43843i	−1.20824	+	0.748516i
$160$		0			0
$161$	−2.00626	+	3.84169i	−0.158115	+	0.302767i
$162$		0			0
$163$	1.36603	−	0.366025i	0.106995	−	0.0286693i	−0.204924	−	0.978778i	$-0.565695\pi$
$163$	1.36603	−	0.366025i	0.106995	−	0.0286693i	0.311919	+	0.950109i	$0.399028\pi$
$164$		0			0
$165$	3.10010	+	8.41966i	0.241343	+	0.655469i
$166$		0			0
$167$	13.1082	+	13.1082i	1.01434	+	1.01434i	0.999896	+	0.0144463i	$0.00459856\pi$
$167$	13.1082	+	13.1082i	1.01434	+	1.01434i	0.0144463	+	0.999896i	$0.495401\pi$
$168$		0			0
$169$		−	5.00000i		−	0.384615i
$170$		0			0
$171$	0.422981	−	0.850499i	0.0323462	−	0.0650393i
$172$		0			0
$173$	2.54383	+	9.49370i	0.193404	+	0.721793i	0.992674	+	0.120821i	$0.0385529\pi$
$173$	2.54383	+	9.49370i	0.193404	+	0.721793i	−0.799270	+	0.600972i	$0.794780\pi$
$174$		0			0
$175$	−12.0572	+	5.44274i	−0.911440	+	0.411432i
$176$		0			0
$177$	20.7676	+	4.87915i	1.56099	+	0.366739i
$178$		0			0
$179$	−9.63325	−	16.6853i	−0.720023	−	1.24712i	−0.960990	−	0.276583i	$-0.910798\pi$
$179$	−9.63325	−	16.6853i	−0.720023	−	1.24712i	0.240967	−	0.970533i	$-0.422535\pi$
$180$		0			0
$181$	−10.2665			−0.763103			−0.381551	−	0.924348i	$-0.624610\pi$
$181$	−10.2665			−0.763103			−0.381551	+	0.924348i	$0.624610\pi$
$182$		0			0
$183$	−4.65831	−	15.4499i	−0.344352	−	1.14209i
$184$		0			0
$185$	−9.46410	−	8.39230i	−0.695815	−	0.617015i
$186$		0			0
$187$	−1.96437	−	7.33112i	−0.143649	−	0.536104i
$188$		0			0
$189$	−1.85649	−	13.6218i	−0.135040	−	0.990840i
$190$		0			0
$191$	2.00626	+	1.15831i	0.145168	+	0.0838125i	0.570825	−	0.821072i	$-0.306624\pi$
$191$	2.00626	+	1.15831i	0.145168	+	0.0838125i	−0.425657	+	0.904885i	$0.639957\pi$
$192$		0			0
$193$	−5.10601	+	19.0559i	−0.367539	+	1.37167i	0.496408	+	0.868089i	$0.334652\pi$
$193$	−5.10601	+	19.0559i	−0.367539	+	1.37167i	−0.863947	+	0.503583i	$0.832015\pi$
$194$		0			0
$195$	8.94987	−	6.31662i	0.640914	−	0.452343i
$196$		0			0
$197$	15.0000	+	15.0000i	1.06871	+	1.06871i	0.997459	+	0.0712470i	$0.0226979\pi$
$197$	15.0000	+	15.0000i	1.06871	+	1.06871i	0.0712470	+	0.997459i	$0.477302\pi$
$198$		0			0
$199$	−2.82887	+	1.63325i	−0.200533	+	0.115778i	−0.596904	−	0.802312i	$-0.703603\pi$
$199$	−2.82887	+	1.63325i	−0.200533	+	0.115778i	0.396371	+	0.918090i	$0.370269\pi$
$200$		0			0
$201$	14.9056	−	9.23420i	1.05136	−	0.651330i
$202$		0			0
$203$	−14.2551	−	13.0967i	−1.00051	−	0.919211i
$204$		0			0
$205$	−11.8687	−	17.9759i	−0.828943	−	1.25549i
$206$		0			0
$207$	−4.65879	+	1.56399i	−0.323808	+	0.108705i
$208$		0			0
$209$	0.733501			0.0507373
$210$		0			0
$211$	−4.94987			−0.340763			−0.170382	−	0.985378i	$-0.554500\pi$
$211$	−4.94987			−0.340763			−0.170382	+	0.985378i	$0.554500\pi$
$212$		0			0
$213$	2.92397	+	2.74784i	0.200347	+	0.188279i
$214$		0			0
$215$	5.70569	+	1.16758i	0.389125	+	0.0796285i
$216$		0			0
$217$	3.45617	−	15.4937i	0.234620	−	1.05178i
$218$		0			0
$219$	−8.55687	−	13.8123i	−0.578220	−	0.933349i
$220$		0			0
$221$	−8.02502	+	4.63325i	−0.539822	+	0.311666i
$222$		0			0
$223$	11.3166	+	11.3166i	0.757817	+	0.757817i	0.975925	−	0.218108i	$-0.0699883\pi$
$223$	11.3166	+	11.3166i	0.757817	+	0.757817i	−0.218108	+	0.975925i	$0.569988\pi$
$224$		0			0
$225$	−14.1332	−	5.02506i	−0.942217	−	0.335004i
$226$		0			0
$227$	7.18627	−	26.8195i	0.476969	−	1.78007i	−0.136811	−	0.990597i	$-0.543685\pi$
$227$	7.18627	−	26.8195i	0.476969	−	1.78007i	0.613780	−	0.789477i	$-0.289648\pi$
$228$		0			0
$229$	6.92820	+	4.00000i	0.457829	+	0.264327i	0.711131	−	0.703060i	$-0.248183\pi$
$229$	6.92820	+	4.00000i	0.457829	+	0.264327i	−0.253302	+	0.967387i	$0.581517\pi$
$230$		0			0
$231$	8.78000	−	5.96769i	0.577682	−	0.392645i
$232$		0			0
$233$	4.50820	+	16.8248i	0.295342	+	1.10223i	0.940945	+	0.338558i	$0.109939\pi$
$233$	4.50820	+	16.8248i	0.295342	+	1.10223i	−0.645604	+	0.763673i	$0.723394\pi$
$234$		0			0
$235$	−10.4904	+	11.8301i	−0.684317	+	0.771712i
$236$		0			0
$237$	−9.42481	+	2.84169i	−0.612207	+	0.184587i
$238$		0			0
$239$	28.5330			1.84565			0.922823	−	0.385224i	$-0.125876\pi$
$239$	28.5330			1.84565			0.922823	+	0.385224i	$0.125876\pi$
$240$		0			0
$241$	1.31662	+	2.28046i	0.0848113	+	0.146897i	0.905311	−	0.424750i	$-0.139638\pi$
$241$	1.31662	+	2.28046i	0.0848113	+	0.146897i	−0.820500	+	0.571647i	$0.806305\pi$
$242$		0			0
$243$	9.18614	−	12.5942i	0.589291	−	0.807921i
$244$		0			0
$245$	9.69783	+	12.2863i	0.619572	+	0.784940i
$246$		0			0
$247$	−0.231785	−	0.865035i	−0.0147482	−	0.0550409i
$248$		0			0
$249$	−0.292077	−	9.40564i	−0.0185096	−	0.596058i
$250$		0			0
$251$			9.26650i			0.584896i	0.956281	+	0.292448i	$0.0944699\pi$
$251$			9.26650i			0.584896i	−0.956281	+	0.292448i	$0.905530\pi$
$252$		0			0
$253$	−2.68338	−	2.68338i	−0.168702	−	0.168702i
$254$		0			0
$255$	11.5198	+	5.31956i	0.721395	+	0.333124i
$256$		0			0
$257$	19.9894	−	5.35614i	1.24690	−	0.334107i	0.425764	−	0.904834i	$-0.360005\pi$
$257$	19.9894	−	5.35614i	1.24690	−	0.334107i	0.821140	+	0.570727i	$0.193339\pi$
$258$		0			0
$259$	−6.92820	+	13.2665i	−0.430498	+	0.824340i
$260$		0			0
$261$	−1.36192	−	21.9076i	−0.0843008	−	1.35605i
$262$		0			0
$263$	5.24784	+	1.40616i	0.323596	+	0.0867072i	0.416960	−	0.908925i	$-0.363095\pi$
$263$	5.24784	+	1.40616i	0.323596	+	0.0867072i	−0.0933643	+	0.995632i	$0.529762\pi$
$264$		0			0
$265$	21.9499	−	7.31662i	1.34837	−	0.449457i
$266$		0			0
$267$	−8.29156	−	27.5000i	−0.507435	−	1.68297i
$268$		0			0
$269$	2.13325	+	3.69490i	0.130067	+	0.225282i	0.923702	−	0.383112i	$-0.125148\pi$
$269$	2.13325	+	3.69490i	0.130067	+	0.225282i	−0.793635	+	0.608394i	$0.791814\pi$
$270$		0			0
$271$	−14.1082	+	24.4361i	−0.857011	+	1.48439i	0.0177551	+	0.999842i	$0.494348\pi$
$271$	−14.1082	+	24.4361i	−0.857011	+	1.48439i	−0.874766	+	0.484545i	$0.838985\pi$
$272$		0			0
$273$	−9.81231	−	8.46868i	−0.593868	−	0.512548i
$274$		0			0
$275$	−1.38552	−	11.5000i	−0.0835499	−	0.693474i
$276$		0			0
$277$	8.62867	+	2.31205i	0.518447	+	0.138917i	0.508548	−	0.861034i	$-0.330182\pi$
$277$	8.62867	+	2.31205i	0.518447	+	0.138917i	0.00989859	+	0.999951i	$0.496849\pi$
$278$		0			0
$279$	15.0000	−	9.94987i	0.898027	−	0.595683i
$280$		0			0
$281$			24.6332i			1.46950i	0.678340	+	0.734748i	$0.262700\pi$
$281$			24.6332i			1.46950i	−0.678340	+	0.734748i	$0.737300\pi$
$282$		0			0
$283$	6.45422	−	24.0875i	0.383663	−	1.43185i	−0.456600	−	0.889672i	$-0.650933\pi$
$283$	6.45422	−	24.0875i	0.383663	−	1.43185i	0.840263	−	0.542179i	$-0.182401\pi$
$284$		0			0
$285$	−0.784732	+	0.942319i	−0.0464835	+	0.0558182i
$286$		0			0
$287$	−17.2435	+	18.7686i	−1.01785	+	1.10787i
$288$		0			0
$289$	5.42695	+	3.13325i	0.319232	+	0.184309i
$290$		0			0
$291$	−0.708327	−	22.8100i	−0.0415228	−	1.33714i
$292$		0			0
$293$	−5.36675	+	5.36675i	−0.313529	+	0.313529i	−0.846275	−	0.532746i	$-0.821160\pi$
$293$	−5.36675	+	5.36675i	−0.313529	+	0.313529i	0.532746	+	0.846275i	$0.321160\pi$
$294$		0			0
$295$	−24.6332	−	12.3166i	−1.43420	−	0.717102i
$296$		0			0
$297$	11.8667	+	2.02075i	0.688576	+	0.117256i
$298$		0			0
$299$	−2.31662	+	4.01251i	−0.133974	+	0.232050i
$300$		0			0
$301$	−0.291562	−	6.88479i	−0.0168054	−	0.396833i
$302$		0			0
$303$	−1.06300	+	4.52455i	−0.0610678	+	0.259928i
$304$		0			0
$305$	1.24819	+	20.7952i	0.0714712	+	1.19073i
$306$		0			0
$307$	9.47494	−	9.47494i	0.540763	−	0.540763i	−0.382989	−	0.923753i	$-0.625105\pi$
$307$	9.47494	−	9.47494i	0.540763	−	0.540763i	0.923753	+	0.382989i	$0.125105\pi$
$308$		0			0
$309$	−11.7084	+	21.8166i	−0.666070	+	1.24110i
$310$		0			0
$311$	−2.00626	+	1.15831i	−0.113764	+	0.0656819i	−0.555802	−	0.831314i	$-0.687589\pi$
$311$	−2.00626	+	1.15831i	−0.113764	+	0.0656819i	0.442038	+	0.896996i	$0.354256\pi$
$312$		0			0
$313$	12.2258	−	3.27588i	0.691041	−	0.185164i	0.103826	−	0.994595i	$-0.466891\pi$
$313$	12.2258	−	3.27588i	0.691041	−	0.185164i	0.587214	+	0.809432i	$0.300225\pi$
$314$		0			0
$315$	−1.72662	+	17.6641i	−0.0972839	+	0.995257i
$316$		0			0
$317$	−9.49370	+	2.54383i	−0.533220	+	0.142876i	−0.515375	−	0.856965i	$-0.672347\pi$
$317$	−9.49370	+	2.54383i	−0.533220	+	0.142876i	−0.0178450	+	0.999841i	$0.505681\pi$
$318$		0			0
$319$	14.6790	−	8.47494i	0.821867	−	0.474505i
$320$		0			0
$321$	4.44987	−	8.29156i	0.248368	−	0.462790i
$322$		0			0
$323$	0.733501	−	0.733501i	0.0408131	−	0.0408131i
$324$		0			0
$325$	−13.1244	+	5.26795i	−0.728008	+	0.292213i
$326$		0			0
$327$	−7.36158	+	31.3338i	−0.407097	+	1.73276i
$328$		0			0
$329$	16.5831	+	8.66025i	0.914257	+	0.477455i
$330$		0			0
$331$	−4.31662	+	7.47661i	−0.237263	+	0.410952i	−0.959928	−	0.280247i	$-0.909584\pi$
$331$	−4.31662	+	7.47661i	−0.237263	+	0.410952i	0.722665	+	0.691199i	$0.242917\pi$
$332$		0			0
$333$	−16.0882	+	5.40093i	−0.881627	+	0.295969i
$334$		0			0
$335$	−21.4749	+	7.15831i	−1.17330	+	0.391100i
$336$		0			0
$337$	−4.36675	+	4.36675i	−0.237872	+	0.237872i	−0.815968	−	0.578096i	$-0.803796\pi$
$337$	−4.36675	+	4.36675i	−0.237872	+	0.237872i	0.578096	+	0.815968i	$0.303796\pi$
$338$		0			0
$339$	0.732399	+	23.5852i	0.0397785	+	1.28097i
$340$		0			0
$341$	12.0375	+	6.94987i	0.651869	+	0.376357i
$342$		0			0
$343$	11.3321	−	14.6487i	0.611874	−	0.790955i
$344$		0			0
$345$	6.31809	−	0.576504i	0.340155	−	0.0310379i
$346$		0			0
$347$	4.21847	−	15.7435i	0.226459	−	0.845157i	−0.755356	−	0.655315i	$-0.772536\pi$
$347$	4.21847	−	15.7435i	0.226459	−	0.845157i	0.981815	−	0.189842i	$-0.0607975\pi$
$348$		0			0
$349$			11.0000i			0.588817i	0.955680	+	0.294408i	$0.0951225\pi$
$349$			11.0000i			0.588817i	−0.955680	+	0.294408i	$0.904877\pi$
$350$		0			0
$351$	−1.36675	−	14.6332i	−0.0729517	−	0.781065i
$352$		0			0
$353$	−13.1593	−	3.52601i	−0.700397	−	0.187671i	−0.108989	−	0.994043i	$-0.534761\pi$
$353$	−13.1593	−	3.52601i	−0.700397	−	0.187671i	−0.591408	+	0.806372i	$0.701428\pi$
$354$		0			0
$355$	−2.85420	−	4.32288i	−0.151485	−	0.229435i
$356$		0			0
$357$	2.81231	−	14.7477i	0.148843	−	0.780531i
$358$		0			0
$359$	−14.6332	+	25.3455i	−0.772313	+	1.33769i	0.163979	+	0.986464i	$0.447567\pi$
$359$	−14.6332	+	25.3455i	−0.772313	+	1.33769i	−0.936292	+	0.351222i	$0.885766\pi$
$360$		0			0
$361$	−9.44987	−	16.3677i	−0.497362	−	0.861456i
$362$		0			0
$363$	−2.81662	−	9.34169i	−0.147834	−	0.490311i
$364$		0			0
$365$	6.63325	+	19.8997i	0.347200	+	1.04160i
$366$		0			0
$367$	26.5348	+	7.10997i	1.38510	+	0.371138i	0.872973	−	0.487769i	$-0.162189\pi$
$367$	26.5348	+	7.10997i	1.38510	+	0.371138i	0.512132	+	0.858907i	$0.328856\pi$
$368$		0			0
$369$	−28.8441	+	1.79314i	−1.50156	+	0.0933471i
$370$		0			0
$371$	−14.6790	−	23.1082i	−0.762097	−	1.19972i
$372$		0			0
$373$	5.89662	−	1.57999i	0.305315	−	0.0818090i	−0.102909	−	0.994691i	$-0.532815\pi$
$373$	5.89662	−	1.57999i	0.305315	−	0.0818090i	0.408224	+	0.912882i	$0.366148\pi$
$374$		0			0
$375$	16.2561	+	10.5232i	0.839463	+	0.543416i
$376$		0			0
$377$	−14.6332	−	14.6332i	−0.753651	−	0.753651i
$378$		0			0
$379$			38.2164i			1.96304i	0.191351	+	0.981522i	$0.438713\pi$
$379$			38.2164i			1.96304i	−0.191351	+	0.981522i	$0.561287\pi$
$380$		0			0
$381$	0.428286	+	13.7919i	0.0219418	+	0.706582i
$382$		0			0
$383$	−8.32394	−	31.0654i	−0.425334	−	1.58737i	−0.763193	−	0.646170i	$-0.776370\pi$
$383$	−8.32394	−	31.0654i	−0.425334	−	1.58737i	0.337860	−	0.941197i	$-0.390297\pi$
$384$		0			0
$385$	−12.8070	+	4.88025i	−0.652705	+	0.248721i
$386$		0			0
$387$	5.17160	−	5.85723i	0.262887	−	0.297740i
$388$		0			0
$389$	−2.31662	−	4.01251i	−0.117458	−	0.203442i	0.801302	−	0.598260i	$-0.204141\pi$
$389$	−2.31662	−	4.01251i	−0.117458	−	0.203442i	−0.918759	+	0.394818i	$0.870808\pi$
$390$		0			0
$391$	−5.36675			−0.271408
$392$		0			0
$393$	−16.5831	+	5.00000i	−0.836508	+	0.252217i
$394$		0			0
$395$	12.6856	−	0.761428i	0.638281	−	0.0383116i
$396$		0			0
$397$	2.33039	+	8.69714i	0.116959	+	0.436497i	0.999426	−	0.0338773i	$-0.0107855\pi$
$397$	2.33039	+	8.69714i	0.116959	+	0.436497i	−0.882467	+	0.470374i	$0.844119\pi$
$398$		0			0
$399$	1.30636	+	0.631419i	0.0654000	+	0.0316105i
$400$		0			0
$401$	−28.3046	−	16.3417i	−1.41347	−	0.816065i	−0.417753	−	0.908561i	$-0.637182\pi$
$401$	−28.3046	−	16.3417i	−1.41347	−	0.816065i	−0.995713	+	0.0924958i	$0.970516\pi$
$402$		0			0
$403$	4.39230	−	16.3923i	0.218796	−	0.816559i
$404$		0			0
$405$	−15.2916	+	13.0831i	−0.759844	+	0.650106i
$406$		0			0
$407$	−9.26650	−	9.26650i	−0.459323	−	0.459323i
$408$		0			0
$409$	−5.23956	+	3.02506i	−0.259080	+	0.149580i	−0.623915	−	0.781492i	$-0.714459\pi$
$409$	−5.23956	+	3.02506i	−0.259080	+	0.149580i	0.364835	+	0.931072i	$0.381125\pi$
$410$		0			0
$411$	−8.96532	−	14.4716i	−0.442227	−	0.713832i
$412$		0			0
$413$	−7.09472	+	31.8050i	−0.349109	+	1.56502i
$414$		0			0
$415$	−2.43553	+	11.9018i	−0.119556	+	0.584238i
$416$		0			0
$417$	7.17338	+	6.74128i	0.351282	+	0.330122i
$418$		0			0
$419$	−0.733501			−0.0358339			−0.0179169	−	0.999839i	$-0.505703\pi$
$419$	−0.733501			−0.0358339			−0.0179169	+	0.999839i	$0.505703\pi$
$420$		0			0
$421$	21.3166			1.03891			0.519454	−	0.854498i	$-0.326135\pi$
$421$	21.3166			1.03891			0.519454	+	0.854498i	$0.326135\pi$
$422$		0			0
$423$	6.75117	+	20.1102i	0.328253	+	0.977793i
$424$		0			0
$425$	−12.8855	−	10.1144i	−0.625038	−	0.490623i
$426$		0			0
$427$	23.5183	−	7.38144i	1.13813	−	0.357213i
$428$		0			0
$429$	9.64774	−	5.97688i	0.465797	−	0.288566i
$430$		0			0
$431$	−10.6665	+	6.15831i	−0.513788	+	0.296635i	−0.734389	−	0.678729i	$-0.762531\pi$
$431$	−10.6665	+	6.15831i	−0.513788	+	0.296635i	0.220602	+	0.975364i	$0.429198\pi$
$432$		0			0
$433$	−13.9499	−	13.9499i	−0.670388	−	0.670388i	0.287417	−	0.957805i	$-0.407203\pi$
$433$	−13.9499	−	13.9499i	−0.670388	−	0.670388i	−0.957805	+	0.287417i	$0.907203\pi$
$434$		0			0
$435$	−4.81662	+	27.9248i	−0.230939	+	1.33889i
$436$		0			0
$437$	0.134240	−	0.500990i	0.00642157	−	0.0239656i
$438$		0			0
$439$	−33.9190	−	19.5831i	−1.61886	−	0.934652i	−0.987215	−	0.159397i	$-0.949045\pi$
$439$	−33.9190	−	19.5831i	−1.61886	−	0.934652i	−0.631649	−	0.775254i	$-0.717622\pi$
$440$		0			0
$441$	20.7743	−	3.07036i	0.989254	−	0.146208i
$442$		0			0
$443$	1.27192	+	4.74685i	0.0604305	+	0.225530i	0.989536	−	0.144284i	$-0.0460880\pi$
$443$	1.27192	+	4.74685i	0.0604305	+	0.225530i	−0.929106	+	0.369814i	$0.879421\pi$
$444$		0			0
$445$	2.22172	+	37.0144i	0.105320	+	1.75465i
$446$		0			0
$447$	4.81662	+	15.9749i	0.227819	+	0.755589i
$448$		0			0
$449$	−8.89975			−0.420005			−0.210003	−	0.977701i	$-0.567347\pi$
$449$	−8.89975			−0.420005			−0.210003	+	0.977701i	$0.567347\pi$
$450$		0			0
$451$	−11.1583	−	19.3268i	−0.525424	−	0.910062i
$452$		0			0
$453$	−5.67681	−	1.33372i	−0.266720	−	0.0626635i
$454$		0			0
$455$	9.80240	+	13.5615i	0.459543	+	0.635771i
$456$		0			0
$457$	10.0961	+	37.6792i	0.472277	+	1.76256i	0.631559	+	0.775328i	$0.282415\pi$
$457$	10.0961	+	37.6792i	0.472277	+	1.76256i	−0.159282	+	0.987233i	$0.550918\pi$
$458$		0			0
$459$	13.8875	−	9.84596i	0.648211	−	0.459570i
$460$		0			0
$461$		−	5.36675i		−	0.249954i	−0.992160	−	0.124977i	$-0.960114\pi$
$461$		−	5.36675i		−	0.249954i	0.992160	−	0.124977i	$-0.0398858\pi$
$462$		0			0
$463$	9.15831	+	9.15831i	0.425623	+	0.425623i	0.887134	−	0.461511i	$-0.152693\pi$
$463$	9.15831	+	9.15831i	0.425623	+	0.425623i	−0.461511	+	0.887134i	$0.652693\pi$
$464$		0			0
$465$	−21.8067	+	8.02918i	−1.01126	+	0.372344i
$466$		0			0
$467$	2.08327	−	0.558212i	0.0964024	−	0.0258310i	−0.210295	−	0.977638i	$-0.567443\pi$
$467$	2.08327	−	0.558212i	0.0964024	−	0.0258310i	0.306698	+	0.951807i	$0.400776\pi$
$468$		0			0
$469$	14.3614	+	22.6082i	0.663148	+	1.04395i
$470$		0			0
$471$	11.0707	−	6.85843i	0.510112	−	0.316020i
$472$		0			0
$473$	5.82815	+	1.56165i	0.267978	+	0.0718046i
$474$		0			0
$475$	1.26650	−	0.949874i	0.0581110	−	0.0435832i
$476$		0			0
$477$	6.15831	−	30.4248i	0.281970	−	1.39306i
$478$		0			0
$479$	4.63325	+	8.02502i	0.211699	+	0.366673i	0.952246	−	0.305331i	$-0.0987672\pi$
$479$	4.63325	+	8.02502i	0.211699	+	0.366673i	−0.740548	+	0.672004i	$0.765434\pi$
$480$		0			0
$481$	−8.00000	+	13.8564i	−0.364769	+	0.631798i
$482$		0			0
$483$	−2.46916	−	7.08902i	−0.112351	−	0.322561i
$484$		0			0
$485$	−5.90650	+	28.8636i	−0.268201	+	1.31063i
$486$		0			0
$487$	−34.0137	−	9.11394i	−1.54131	−	0.412992i	−0.614619	−	0.788824i	$-0.710690\pi$
$487$	−34.0137	−	9.11394i	−1.54131	−	0.412992i	−0.926688	+	0.375832i	$0.877357\pi$
$488$		0			0
$489$	−1.15831	+	2.15831i	−0.0523807	+	0.0976023i
$490$		0			0
$491$		−	3.89975i		−	0.175993i	−0.996121	−	0.0879966i	$-0.971954\pi$
$491$		−	3.89975i		−	0.175993i	0.996121	−	0.0879966i	$-0.0280465\pi$
$492$		0			0
$493$	6.20408	−	23.1540i	0.279418	−	1.04280i
$494$		0			0
$495$	−14.3042	−	6.07405i	−0.642925	−	0.273008i
$496$		0			0
$497$	−4.14675	+	4.51350i	−0.186007	+	0.202458i
$498$		0			0
$499$	−13.0338	−	7.52506i	−0.583473	−	0.336868i	0.179040	−	0.983842i	$-0.442701\pi$
$499$	−13.0338	−	7.52506i	−0.583473	−	0.336868i	−0.762512	+	0.646974i	$0.776034\pi$
$500$		0			0
$501$	−32.0929	+	0.996592i	−1.43380	+	0.0445245i
$502$		0			0
$503$	4.20844	−	4.20844i	0.187645	−	0.187645i	−0.607032	−	0.794677i	$-0.707640\pi$
$503$	4.20844	−	4.20844i	0.187645	−	0.187645i	0.794677	+	0.607032i	$0.207640\pi$
$504$		0			0
$505$	2.68338	−	5.36675i	0.119409	−	0.238817i
$506$		0			0
$507$	6.31084	+	5.93070i	0.280274	+	0.263392i
$508$		0			0
$509$	20.6082	−	35.6944i	0.913442	−	1.58213i	0.104275	−	0.994548i	$-0.466748\pi$
$509$	20.6082	−	35.6944i	0.913442	−	1.58213i	0.809167	−	0.587579i	$-0.199919\pi$
$510$		0			0
$511$	20.9499	−	13.3080i	0.926768	−	0.588711i
$512$		0			0
$513$	0.571758	+	1.54269i	0.0252437	+	0.0681112i
$514$		0			0
$515$	21.2077	−	23.9162i	0.934525	−	1.05387i
$516$		0			0
$517$	−11.5831	+	11.5831i	−0.509425	+	0.509425i
$518$		0			0
$519$	−15.0000	−	8.05013i	−0.658427	−	0.353361i
$520$		0			0
$521$	16.6853	−	9.63325i	0.730995	−	0.422040i	−0.0877909	−	0.996139i	$-0.527981\pi$
$521$	16.6853	−	9.63325i	0.730995	−	0.422040i	0.818786	+	0.574099i	$0.194647\pi$
$522$		0			0
$523$	−10.4272	+	2.79396i	−0.455950	+	0.122171i	−0.479482	−	0.877552i	$-0.659175\pi$
$523$	−10.4272	+	2.79396i	−0.455950	+	0.122171i	0.0235320	+	0.999723i	$0.492509\pi$
$524$		0			0
$525$	7.43190	−	21.6741i	0.324355	−	0.945935i
$526$		0			0
$527$	18.9874	−	5.08766i	0.827105	−	0.221622i
$528$		0			0
$529$	17.5947	−	10.1583i	0.764988	−	0.441666i
$530$		0			0
$531$	−30.7916	+	20.4248i	−1.33624	+	0.886361i
$532$		0			0
$533$	−19.2665	+	19.2665i	−0.834525	+	0.834525i
$534$		0			0
$535$	−8.06015	+	9.08953i	−0.348471	+	0.392975i
$536$		0			0
$537$	32.4860	+	7.63230i	1.40188	+	0.329358i
$538$		0			0
$539$	9.26650	+	13.3080i	0.399136	+	0.573216i
$540$		0			0
$541$	−9.13325	+	15.8193i	−0.392669	+	0.680123i	−0.992801	−	0.119779i	$-0.961782\pi$
$541$	−9.13325	+	15.8193i	−0.392669	+	0.680123i	0.600132	+	0.799901i	$0.295115\pi$
$542$		0			0
$543$	12.1775	−	12.9581i	0.522587	−	0.556083i
$544$		0			0
$545$	18.5831	−	37.1662i	0.796014	−	1.59203i
$546$		0			0
$547$	16.1082	−	16.1082i	0.688736	−	0.688736i	−0.273216	−	0.961953i	$-0.588087\pi$
$547$	16.1082	−	16.1082i	0.688736	−	0.688736i	0.961953	+	0.273216i	$0.0880875\pi$
$548$		0			0
$549$	25.0258	+	12.4461i	1.06807	+	0.531189i
$550$		0			0
$551$	2.00626	+	1.15831i	0.0854694	+	0.0493458i
$552$		0			0
$553$	−4.50286	−	14.3468i	−0.191481	−	0.610086i
$554$		0			0
$555$	21.8183	−	1.99084i	0.926134	−	0.0845065i
$556$		0			0
$557$	2.67807	−	9.99470i	0.113473	−	0.423489i	−0.885695	−	0.464268i	$-0.846317\pi$
$557$	2.67807	−	9.99470i	0.113473	−	0.423489i	0.999168	+	0.0407793i	$0.0129841\pi$
$558$		0			0
$559$		−	7.36675i		−	0.311580i
$560$		0			0
$561$	11.5831	+	6.21637i	0.489040	+	0.262455i
$562$		0			0
$563$	10.5750	+	2.83356i	0.445683	+	0.119420i	0.474679	−	0.880159i	$-0.342564\pi$
$563$	10.5750	+	2.83356i	0.445683	+	0.119420i	−0.0289957	+	0.999580i	$0.509231\pi$
$564$		0			0
$565$	6.10724	−	29.8445i	0.256933	−	1.25557i
$566$		0			0
$567$	19.3951	+	13.8142i	0.814516	+	0.580141i
$568$		0			0
$569$	−12.3166	+	21.3330i	−0.516340	+	0.894327i	0.483480	+	0.875355i	$0.339372\pi$
$569$	−12.3166	+	21.3330i	−0.516340	+	0.894327i	−0.999820	+	0.0189715i	$0.993961\pi$
$570$		0			0
$571$	−10.4749	−	18.1431i	−0.438362	−	0.759266i	0.559201	−	0.829032i	$-0.311108\pi$
$571$	−10.4749	−	18.1431i	−0.438362	−	0.759266i	−0.997563	+	0.0697661i	$0.977775\pi$
$572$		0			0
$573$	−3.84169	+	1.15831i	−0.160489	+	0.0483892i
$574$		0			0
$575$	−8.10819	−	1.15831i	−0.338135	−	0.0483050i
$576$		0			0
$577$	25.9545	+	6.95448i	1.08050	+	0.289519i	0.754800	−	0.655955i	$-0.227734\pi$
$577$	25.9545	+	6.95448i	1.08050	+	0.289519i	0.325699	+	0.945474i	$0.394400\pi$
$578$		0			0
$579$	−17.9953	−	29.0476i	−0.747859	−	1.20718i
$580$		0			0
$581$	14.3614	−	0.608187i	0.595812	−	0.0252318i
$582$		0			0
$583$	23.1540	−	6.20408i	0.958939	−	0.256947i
$584$		0			0
$585$	−2.64316	+	18.7887i	−0.109281	+	0.776815i
$586$		0			0
$587$	0.366750	+	0.366750i	0.0151374	+	0.0151374i	0.714635	−	0.699498i	$-0.246593\pi$
$587$	0.366750	+	0.366750i	0.0151374	+	0.0151374i	−0.699498	+	0.714635i	$0.746593\pi$
$588$		0			0
$589$			1.89975i			0.0782778i
$590$		0			0
$591$	−36.7246	+	1.14042i	−1.51065	+	0.0469108i
$592$		0			0
$593$	−9.73010	−	36.3132i	−0.399567	−	1.49121i	−0.813860	−	0.581061i	$-0.802638\pi$
$593$	−9.73010	−	36.3132i	−0.399567	−	1.49121i	0.414292	−	0.910144i	$-0.364029\pi$
$594$		0			0
$595$	−7.92675	+	17.6873i	−0.324965	+	0.725107i
$596$		0			0
$597$	1.29400	−	5.50778i	0.0529600	−	0.225418i
$598$		0			0
$599$	−14.2665	−	24.7103i	−0.582913	−	1.00964i	−0.995132	−	0.0985506i	$-0.968579\pi$
$599$	−14.2665	−	24.7103i	−0.582913	−	1.00964i	0.412219	−	0.911085i	$-0.364754\pi$
$600$		0			0
$601$	−4.53300			−0.184905			−0.0924524	−	0.995717i	$-0.529471\pi$
$601$	−4.53300			−0.184905			−0.0924524	+	0.995717i	$0.529471\pi$
$602$		0			0
$603$	−6.02506	+	29.7665i	−0.245360	+	1.21219i
$604$		0			0
$605$	0.754712	+	12.5737i	0.0306834	+	0.511194i
$606$		0			0
$607$	−2.87026	−	10.7119i	−0.116500	−	0.434784i	0.882895	−	0.469571i	$-0.155591\pi$
$607$	−2.87026	−	10.7119i	−0.116500	−	0.434784i	−0.999395	+	0.0347868i	$0.988925\pi$
$608$		0			0
$609$	33.4388	−	2.45771i	1.35501	−	0.0995913i
$610$		0			0
$611$	17.3205	+	10.0000i	0.700713	+	0.404557i
$612$		0			0
$613$	−5.58793	+	20.8544i	−0.225694	+	0.842302i	0.756431	+	0.654074i	$0.226941\pi$
$613$	−5.58793	+	20.8544i	−0.225694	+	0.842302i	−0.982125	+	0.188229i	$0.939725\pi$
$614$		0			0
$615$	36.7665	+	6.34169i	1.48257	+	0.255722i
$616$		0			0
$617$	−1.58312	−	1.58312i	−0.0637342	−	0.0637342i	0.674521	−	0.738255i	$-0.264350\pi$
$617$	−1.58312	−	1.58312i	−0.0637342	−	0.0637342i	−0.738255	+	0.674521i	$0.764350\pi$
$618$		0			0
$619$	−29.6322	+	17.1082i	−1.19102	+	0.687636i	−0.958538	−	0.284964i	$-0.908018\pi$
$619$	−29.6322	+	17.1082i	−1.19102	+	0.687636i	−0.232483	+	0.972601i	$0.574685\pi$
$620$		0			0
$621$	3.55196	−	7.73529i	0.142535	−	0.310407i
$622$		0			0
$623$	41.8614	−	13.1386i	1.67714	−	0.526387i
$624$		0			0
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$		0			0
$627$	−0.870035	+	0.925802i	−0.0347459	+	0.0369730i
$628$		0			0
$629$	−18.5330			−0.738959
$630$		0			0
$631$	4.31662			0.171842			0.0859211	−	0.996302i	$-0.472617\pi$
$631$	4.31662			0.171842			0.0859211	+	0.996302i	$0.472617\pi$
$632$		0			0
$633$	5.87125	−	6.24758i	0.233361	−	0.248319i
$634$		0			0
$635$	3.57134	−	17.4522i	0.141724	−	0.692571i
$636$		0			0
$637$	12.7662	−	15.1335i	0.505817	−	0.599612i
$638$		0			0
$639$	−6.93648	+	0.431218i	−0.274403	+	0.0170587i
$640$		0			0
$641$	0.952846	−	0.550126i	0.0376351	−	0.0217287i	−0.481064	−	0.876685i	$-0.659750\pi$
$641$	0.952846	−	0.550126i	0.0376351	−	0.0217287i	0.518700	+	0.854957i	$0.326416\pi$
$642$		0			0
$643$	16.8997	+	16.8997i	0.666461	+	0.666461i	0.956895	−	0.290434i	$-0.0937997\pi$
$643$	16.8997	+	16.8997i	0.666461	+	0.666461i	−0.290434	+	0.956895i	$0.593800\pi$
$644$		0			0
$645$	−8.24144	+	5.81662i	−0.324506	+	0.229029i
$646$		0			0
$647$	4.93217	−	18.4071i	0.193904	−	0.723658i	−0.798644	−	0.601803i	$-0.794449\pi$
$647$	4.93217	−	18.4071i	0.193904	−	0.723658i	0.992548	−	0.121855i	$-0.0388842\pi$
$648$		0			0
$649$	−24.7103	−	14.2665i	−0.969964	−	0.560009i
$650$		0			0
$651$	15.4562	+	22.7400i	0.605775	+	0.891250i
$652$		0			0
$653$	−12.4082	−	46.3079i	−0.485569	−	1.81217i	−0.577484	−	0.816402i	$-0.695965\pi$
$653$	−12.4082	−	46.3079i	−0.485569	−	1.81217i	0.0919148	−	0.995767i	$-0.470701\pi$
$654$		0			0
$655$	22.3205	−	1.33975i	0.872134	−	0.0523482i
$656$		0			0
$657$	27.5831	+	5.58312i	1.07612	+	0.217818i
$658$		0			0
$659$	3.05013			0.118816			0.0594080	−	0.998234i	$-0.481079\pi$
$659$	3.05013			0.118816			0.0594080	+	0.998234i	$0.481079\pi$
$660$		0			0
$661$	−0.658312	−	1.14023i	−0.0256054	−	0.0443498i	0.852939	−	0.522011i	$-0.174818\pi$
$661$	−0.658312	−	1.14023i	−0.0256054	−	0.0443498i	−0.878544	+	0.477661i	$0.841485\pi$
$662$		0			0
$663$	3.67086	−	15.6246i	0.142565	−	0.606810i
$664$		0			0
$665$	−1.45285	−	1.18238i	−0.0563389	−	0.0458509i
$666$		0			0
$667$	−3.10204	−	11.5770i	−0.120112	−	0.448262i
$668$		0			0
$669$	−27.7066	+	0.860383i	−1.07120	+	0.0332643i
$670$		0			0
$671$			21.5831i			0.833207i
$672$		0			0
$673$	7.26650	+	7.26650i	0.280103	+	0.280103i	0.833150	−	0.553047i	$-0.186535\pi$
$673$	7.26650	+	7.26650i	0.280103	+	0.280103i	−0.553047	+	0.833150i	$0.686535\pi$
$674$		0			0
$675$	23.1065	−	11.8781i	0.889370	−	0.457189i
$676$		0			0
$677$	38.9768	−	10.4438i	1.49800	−	0.401388i	0.585570	−	0.810622i	$-0.300871\pi$
$677$	38.9768	−	10.4438i	1.49800	−	0.401388i	0.912430	+	0.409234i	$0.134204\pi$
$678$		0			0
$679$	34.8284	−	1.47494i	1.33659	−	0.0566029i
$680$		0			0
$681$	25.3268	+	40.8820i	0.970526	+	1.56660i
$682$		0			0
$683$	−19.4091	−	5.20065i	−0.742668	−	0.198997i	−0.132405	−	0.991196i	$-0.542270\pi$
$683$	−19.4091	−	5.20065i	−0.742668	−	0.198997i	−0.610264	+	0.792198i	$0.708936\pi$
$684$		0			0
$685$	6.94987	+	20.8496i	0.265541	+	0.796623i
$686$		0			0
$687$	−13.2665	+	4.00000i	−0.506149	+	0.152610i
$688$		0			0
$689$	−14.6332	−	25.3455i	−0.557482	−	0.965588i
$690$		0			0
$691$	−22.4248	+	38.8409i	−0.853080	+	1.47758i	0.0253348	+	0.999679i	$0.491935\pi$
$691$	−22.4248	+	38.8409i	−0.853080	+	1.47758i	−0.878415	+	0.477899i	$0.841399\pi$
$692$		0			0
$693$	−2.88208	+	18.1604i	−0.109481	+	0.689855i
$694$		0			0
$695$	−7.00221	−	10.6053i	−0.265609	−	0.402283i
$696$		0			0
$697$	−30.4851	−	8.16845i	−1.15470	−	0.309402i
$698$		0			0
$699$	−26.5831	−	14.2665i	−1.00547	−	0.539609i
$700$		0			0
$701$		−	19.6332i		−	0.741538i	−0.928725	−	0.370769i	$-0.879094\pi$
$701$		−	19.6332i		−	0.741538i	0.928725	−	0.370769i	$-0.120906\pi$
$702$		0			0
$703$	0.463571	−	1.73007i	0.0174839	−	0.0652508i
$704$		0			0
$705$	−2.48855	−	27.2728i	−0.0937242	−	1.02715i
$706$		0			0
$707$	−6.92924	−	1.54570i	−0.260601	−	0.0581320i
$708$		0			0
$709$	−8.25582	−	4.76650i	−0.310054	−	0.179010i	0.336897	−	0.941542i	$-0.390623\pi$
$709$	−8.25582	−	4.76650i	−0.310054	−	0.179010i	−0.646951	+	0.762532i	$0.723956\pi$
$710$		0			0
$711$	7.59246	−	15.2663i	0.284740	−	0.572533i
$712$		0			0
$713$	6.94987	−	6.94987i	0.260275	−	0.260275i
$714$		0			0
$715$	−13.8997	+	4.63325i	−0.519821	+	0.173274i
$716$		0			0
$717$	−33.8441	+	36.0135i	−1.26393	+	1.34495i
$718$		0			0
$719$	−5.79156	+	10.0313i	−0.215989	+	0.374104i	−0.953578	−	0.301146i	$-0.902631\pi$
$719$	−5.79156	+	10.0313i	−0.215989	+	0.374104i	0.737589	+	0.675250i	$0.235964\pi$
$720$		0			0
$721$	−33.5251	−	17.5079i	−1.24854	−	0.652028i
$722$		0			0
$723$	−4.44003	−	1.04314i	−0.165126	−	0.0387950i
$724$		0			0
$725$	14.3706	−	33.6424i	0.533710	−	1.24945i
$726$		0			0
$727$	−8.20844	+	8.20844i	−0.304434	+	0.304434i	−0.842746	−	0.538312i	$-0.819062\pi$
$727$	−8.20844	+	8.20844i	−0.304434	+	0.304434i	0.538312	+	0.842746i	$0.319062\pi$
$728$		0			0
$729$	5.00000	+	26.5330i	0.185185	+	0.982704i
$730$		0			0
$731$	7.38979	−	4.26650i	0.273321	−	0.157802i
$732$		0			0
$733$	−16.7563	+	4.48985i	−0.618910	+	0.165836i	−0.554632	−	0.832096i	$-0.687141\pi$
$733$	−16.7563	+	4.48985i	−0.618910	+	0.165836i	−0.0642777	+	0.997932i	$0.520474\pi$
$734$		0			0
$735$	−27.0103	−	2.33293i	−0.996291	−	0.0860515i
$736$		0			0
$737$	−22.6530	+	6.06984i	−0.834433	+	0.223586i
$738$		0			0
$739$	16.4111	−	9.47494i	0.603691	−	0.348541i	−0.166801	−	0.985991i	$-0.553344\pi$
$739$	16.4111	−	9.47494i	0.603691	−	0.348541i	0.770492	+	0.637449i	$0.220010\pi$
$740$		0			0
$741$	1.36675	+	0.733501i	0.0502088	+	0.0269458i
$742$		0			0
$743$	−6.15831	+	6.15831i	−0.225927	+	0.225927i	−0.810989	−	0.585062i	$-0.801070\pi$
$743$	−6.15831	+	6.15831i	−0.225927	+	0.225927i	0.585062	+	0.810989i	$0.301070\pi$
$744$		0			0
$745$	−1.29061	−	21.5019i	−0.0472843	−	0.787769i
$746$		0			0
$747$	12.2180	+	10.7878i	0.447031	+	0.394704i
$748$		0			0
$749$	12.7414	+	6.65400i	0.465562	+	0.243132i
$750$		0			0
$751$	19.9499	−	34.5542i	0.727981	−	1.26090i	−0.229754	−	0.973249i	$-0.573792\pi$
$751$	19.9499	−	34.5542i	0.727981	−	1.26090i	0.957735	−	0.287652i	$-0.0928746\pi$
$752$		0			0
$753$	−11.6959	−	10.9914i	−0.426222	−	0.400548i
$754$		0			0
$755$	6.73350	+	3.36675i	0.245057	+	0.122529i
$756$		0			0
$757$	−14.3166	+	14.3166i	−0.520347	+	0.520347i	−0.917676	−	0.397329i	$-0.869937\pi$
$757$	−14.3166	+	14.3166i	−0.520347	+	0.520347i	0.397329	+	0.917676i	$0.369937\pi$
$758$		0			0
$759$	6.56973	−	0.204012i	0.238466	−	0.00740518i
$760$		0			0
$761$	−17.3205	−	10.0000i	−0.627868	−	0.362500i	0.152058	−	0.988372i	$-0.451410\pi$
$761$	−17.3205	−	10.0000i	−0.627868	−	0.362500i	−0.779926	+	0.625872i	$0.784743\pi$
$762$		0			0
$763$	−47.9869	−	10.7044i	−1.73724	−	0.387525i
$764$		0			0
$765$	−20.3782	+	8.23014i	−0.736777	+	0.297561i
$766$		0			0
$767$	−9.01640	+	33.6496i	−0.325563	+	1.21502i
$768$		0			0
$769$		−	46.5330i		−	1.67802i	−0.544114	−	0.839011i	$-0.683134\pi$
$769$		−	46.5330i		−	1.67802i	0.544114	−	0.839011i	$-0.316866\pi$
$770$		0			0
$771$	−16.9499	+	31.5831i	−0.610435	+	1.13744i
$772$		0			0
$773$	36.8142	+	9.86434i	1.32412	+	0.354796i	0.850518	−	0.525946i	$-0.176289\pi$
$773$	36.8142	+	9.86434i	1.32412	+	0.354796i	0.473597	+	0.880742i	$0.342955\pi$
$774$		0			0
$775$	29.7846	−	3.58846i	1.06989	−	0.128901i
$776$		0			0
$777$	−8.52674	−	24.4805i	−0.305895	−	0.878233i
$778$		0			0
$779$	1.52506	−	2.64149i	0.0546410	−	0.0946411i
$780$		0			0
$781$	−2.68338	−	4.64774i	−0.0960187	−	0.166309i
$782$		0			0
$783$	29.2665	+	24.2665i	1.04590	+	0.867214i
$784$		0			0
$785$	−15.9499	+	5.31662i	−0.569275	+	0.189758i
$786$		0			0
$787$	21.1392	+	5.66422i	0.753530	+	0.201908i	0.615083	−	0.788462i	$-0.289122\pi$
$787$	21.1392	+	5.66422i	0.753530	+	0.201908i	0.138446	+	0.990370i	$0.455789\pi$
$788$		0			0
$789$	−7.99949	+	4.95577i	−0.284789	+	0.176430i
$790$		0			0
$791$	−36.0120	+	1.52506i	−1.28044	+	0.0542250i
$792$		0			0
$793$	25.4535	−	6.82024i	0.903880	−	0.242194i
$794$		0			0
$795$	−16.8008	+	36.3830i	−0.595864	+	1.29037i
$796$		0			0
$797$	−15.3668	−	15.3668i	−0.544318	−	0.544318i	0.380474	−	0.924792i	$-0.375761\pi$
$797$	−15.3668	−	15.3668i	−0.544318	−	0.544318i	−0.924792	+	0.380474i	$0.875761\pi$
$798$		0			0
$799$			23.1662i			0.819563i
$800$		0			0
$801$	44.5446	+	22.1535i	1.57391	+	0.782756i
$802$		0			0
$803$	5.62462	+	20.9914i	0.198489	+	0.740769i
$804$		0			0
$805$	0.989430	+	9.64050i	0.0348728	+	0.339783i
$806$		0			0
$807$	−7.19392	−	1.69015i	−0.253238	−	0.0594960i
$808$		0			0
$809$	−0.608187	−	1.05341i	−0.0213827	−	0.0370359i	0.855136	−	0.518404i	$-0.173474\pi$
$809$	−0.608187	−	1.05341i	−0.0213827	−	0.0370359i	−0.876519	+	0.481368i	$0.840140\pi$
$810$		0			0
$811$	12.0000			0.421377			0.210688	−	0.977553i	$-0.432429\pi$
$811$	12.0000			0.421377			0.210688	+	0.977553i	$0.432429\pi$
$812$		0			0
$813$	−14.1082	−	46.7916i	−0.494796	−	1.64105i
$814$		0			0
$815$	2.09808	−	2.36603i	0.0734924	−	0.0828783i
$816$		0			0
$817$	0.213438	+	0.796562i	0.00746726	+	0.0278682i
$818$		0			0
$819$	22.3277	−	2.33975i	0.780193	−	0.0817573i
$820$		0			0
$821$	8.02502	+	4.63325i	0.280075	+	0.161702i	0.633457	−	0.773777i	$-0.281635\pi$
$821$	8.02502	+	4.63325i	0.280075	+	0.161702i	−0.353382	+	0.935479i	$0.614968\pi$
$822$		0			0
$823$	−10.0749	+	37.5999i	−0.351188	+	1.31065i	0.534026	+	0.845468i	$0.320678\pi$
$823$	−10.0749	+	37.5999i	−0.351188	+	1.31065i	−0.885214	+	0.465183i	$0.845988\pi$
$824$		0			0
$825$	16.1583	+	11.8918i	0.562560	+	0.414020i
$826$		0			0
$827$	−6.52506	−	6.52506i	−0.226899	−	0.226899i	0.584497	−	0.811396i	$-0.301292\pi$
$827$	−6.52506	−	6.52506i	−0.226899	−	0.226899i	−0.811396	+	0.584497i	$0.801292\pi$
$828$		0			0
$829$	25.8071	−	14.8997i	0.896318	−	0.517490i	0.0203145	−	0.999794i	$-0.493533\pi$
$829$	25.8071	−	14.8997i	0.896318	−	0.517490i	0.876004	+	0.482304i	$0.160200\pi$
$830$		0			0
$831$	−13.1530	+	8.14843i	−0.456273	+	0.282666i
$832$		0			0
$833$	22.5745	+	4.04150i	0.782160	+	0.140030i
$834$		0			0
$835$	40.6102	+	8.31026i	1.40537	+	0.287588i
$836$		0			0
$837$	−5.23369	+	30.7345i	−0.180903	+	1.06234i
$838$		0			0
$839$	−46.9499			−1.62089			−0.810445	−	0.585815i	$-0.800775\pi$
$839$	−46.9499			−1.62089			−0.810445	+	0.585815i	$0.800775\pi$
$840$		0			0
$841$	24.5330			0.845965
$842$		0			0
$843$	−31.0913	−	29.2185i	−1.07084	−	1.00634i
$844$		0			0
$845$	−6.16025	−	9.33013i	−0.211919	−	0.320966i
$846$		0			0
$847$	14.2202	−	4.46315i	0.488613	−	0.153356i
$848$		0			0
$849$	22.7468	+	36.7174i	0.780670	+	1.26014i
$850$		0			0
$851$	−8.02502	+	4.63325i	−0.275094	+	0.158826i
$852$		0			0
$853$	7.63325	+	7.63325i	0.261357	+	0.261357i	0.825605	−	0.564248i	$-0.190834\pi$
$853$	7.63325	+	7.63325i	0.261357	+	0.261357i	−0.564248	+	0.825605i	$0.690834\pi$
$854$		0			0
$855$	−0.258564	−	2.10819i	−0.00884269	−	0.0720985i
$856$		0			0
$857$	−6.33832	+	23.6549i	−0.216513	+	0.808038i	0.769115	+	0.639110i	$0.220697\pi$
$857$	−6.33832	+	23.6549i	−0.216513	+	0.808038i	−0.985628	+	0.168928i	$0.945970\pi$
$858$		0			0
$859$	38.1051	+	22.0000i	1.30013	+	0.750630i	0.980426	−	0.196887i	$-0.0630833\pi$
$859$	38.1051	+	22.0000i	1.30013	+	0.750630i	0.319704	+	0.947518i	$0.396417\pi$
$860$		0			0
$861$	−3.23588	−	44.0263i	−0.110278	−	1.50041i
$862$		0			0
$863$	13.8143	+	51.5558i	0.470245	+	1.75498i	0.638886	+	0.769301i	$0.279395\pi$
$863$	13.8143	+	51.5558i	0.470245	+	1.75498i	−0.168641	+	0.985677i	$0.553938\pi$
$864$		0			0
$865$	16.4436	+	14.5814i	0.559098	+	0.495781i
$866$		0			0
$867$	−10.3918	+	3.13325i	−0.352924	+	0.106411i
$868$		0			0
$869$	13.1662			0.446634
$870$		0			0
$871$	14.3166	+	24.7971i	0.485100	+	0.840218i
$872$		0			0
$873$	29.6302	+	26.1618i	1.00283	+	0.885443i
$874$		0			0
$875$	−15.7933	+	25.0114i	−0.533913	+	0.845540i
$876$		0			0
$877$	2.21450	+	8.26463i	0.0747783	+	0.279077i	0.993183	−	0.116566i	$-0.0371886\pi$
$877$	2.21450	+	8.26463i	0.0747783	+	0.279077i	−0.918405	+	0.395642i	$0.870522\pi$
$878$		0			0
$879$	−0.408025	−	13.1395i	−0.0137623	−	0.443183i
$880$		0			0
$881$		−	33.5330i		−	1.12976i	−0.825175	−	0.564878i	$-0.808923\pi$
$881$		−	33.5330i		−	1.12976i	0.825175	−	0.564878i	$-0.191077\pi$
$882$		0			0
$883$	−6.26650	−	6.26650i	−0.210884	−	0.210884i	0.593759	−	0.804643i	$-0.297643\pi$
$883$	−6.26650	−	6.26650i	−0.210884	−	0.210884i	−0.804643	+	0.593759i	$0.797643\pi$
$884$		0			0
$885$	44.7642	−	16.4821i	1.50473	−	0.554039i
$886$		0			0
$887$	4.74685	−	1.27192i	0.159384	−	0.0427067i	−0.178245	−	0.983986i	$-0.557042\pi$
$887$	4.74685	−	1.27192i	0.159384	−	0.0427067i	0.337629	+	0.941279i	$0.390375\pi$
$888$		0			0
$889$	−21.0588	+	0.891813i	−0.706290	+	0.0299105i
$890$		0			0
$891$	−16.6261	+	12.5809i	−0.556996	+	0.421476i
$892$		0			0
$893$	−2.16259	−	0.579464i	−0.0723682	−	0.0193910i
$894$		0			0
$895$	−38.5330	−	19.2665i	−1.28802	−	0.644008i
$896$		0			0
$897$	−2.31662	−	7.68338i	−0.0773499	−	0.256540i
$898$		0			0
$899$	21.9499	+	38.0183i	0.732069	+	1.26798i
$900$		0			0
$901$	16.9499	−	29.3580i	0.564682	−	0.978058i
$902$		0			0
$903$	9.03561	+	7.79833i	0.300686	+	0.259512i
$904$		0			0
$905$	−19.1575	+	12.6488i	−0.636818	+	0.420462i
$906$		0			0
$907$	−18.7712	−	5.02971i	−0.623286	−	0.167009i	−0.0666648	−	0.997775i	$-0.521236\pi$
$907$	−18.7712	−	5.02971i	−0.623286	−	0.167009i	−0.556621	+	0.830766i	$0.687902\pi$
$908$		0			0
$909$	−4.44987	−	6.70844i	−0.147593	−	0.222505i
$910$		0			0
$911$		−	26.9499i		−	0.892889i	−0.894811	−	0.446445i	$-0.852690\pi$
$911$		−	26.9499i		−	0.892889i	0.894811	−	0.446445i	$-0.147310\pi$
$912$		0			0
$913$	−3.25753	+	12.1573i	−0.107809	+	0.402347i
$914$		0			0
$915$	−27.7276	−	23.0906i	−0.916645	−	0.763351i
$916$		0			0
$917$	−7.92287	−	25.2434i	−0.261636	−	0.833610i
$918$		0			0
$919$	−33.0964	−	19.1082i	−1.09175	−	0.630321i	−0.157707	−	0.987486i	$-0.550410\pi$
$919$	−33.0964	−	19.1082i	−1.09175	−	0.630321i	−0.934041	+	0.357165i	$0.883743\pi$
$920$		0			0
$921$	0.720363	+	23.1976i	0.0237368	+	0.764386i
$922$		0			0
$923$	−4.63325	+	4.63325i	−0.152505	+	0.152505i
$924$		0			0
$925$	−28.0000	−	4.00000i	−0.920634	−	0.131519i
$926$		0			0
$927$	−13.6484	−	40.6556i	−0.448273	−	1.33531i
$928$		0			0
$929$	0.550126	−	0.952846i	0.0180490	−	0.0312618i	−0.856860	−	0.515549i	$-0.827588\pi$
$929$	0.550126	−	0.952846i	0.0180490	−	0.0312618i	0.874909	+	0.484288i	$0.160921\pi$
$930$		0			0
$931$	−0.941939	+	2.00626i	−0.0308708	+	0.0657524i
$932$		0			0
$933$	0.917716	−	3.90616i	0.0300447	−	0.127882i
$934$		0			0
$935$	−12.6979	−	11.2599i	−0.415265	−	0.368237i
$936$		0			0
$937$	−14.0000	+	14.0000i	−0.457360	+	0.457360i	−0.897788	−	0.440428i	$-0.854827\pi$
$937$	−14.0000	+	14.0000i	−0.457360	+	0.457360i	0.440428	+	0.897788i	$0.354827\pi$
$938$		0			0
$939$	−10.3668	+	19.3166i	−0.338306	+	0.630374i
$940$		0			0
$941$	16.6853	−	9.63325i	0.543925	−	0.314035i	−0.202743	−	0.979232i	$-0.564986\pi$
$941$	16.6853	−	9.63325i	0.543925	−	0.314035i	0.746668	+	0.665197i	$0.231652\pi$
$942$		0			0
$943$	−15.2425	+	4.08423i	−0.496365	+	0.133001i
$944$		0			0
$945$	−20.2470	−	23.1313i	−0.658635	−	0.752462i
$946$		0			0
$947$	−43.0640	+	11.5390i	−1.39939	+	0.374966i	−0.878127	−	0.478428i	$-0.841207\pi$
$947$	−43.0640	+	11.5390i	−1.39939	+	0.374966i	−0.521266	+	0.853394i	$0.674540\pi$
$948$		0			0
$949$	22.9783	−	13.2665i	0.745906	−	0.430649i
$950$		0			0
$951$	8.05013	−	15.0000i	0.261043	−	0.486408i
$952$		0			0
$953$	−20.0000	+	20.0000i	−0.647864	+	0.647864i	−0.952476	−	0.304613i	$-0.901473\pi$
$953$	−20.0000	+	20.0000i	−0.647864	+	0.647864i	0.304613	+	0.952476i	$0.401473\pi$
$954$		0			0
$955$	5.17082	−	0.310369i	0.167324	−	0.0100433i
$956$		0			0
$957$	−6.71458	+	28.5799i	−0.217052	+	0.923856i
$958$		0			0
$959$	21.9499	−	13.9432i	0.708798	−	0.450250i
$960$		0			0
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$		0			0
$963$	5.18717	+	15.4515i	0.167154	+	0.497916i
$964$		0			0
$965$	13.9499	+	41.8496i	0.449062	+	1.34719i
$966$		0			0
$967$	−27.1082	+	27.1082i	−0.871741	+	0.871741i	−0.992662	−	0.120922i	$-0.961415\pi$
$967$	−27.1082	+	27.1082i	−0.871741	+	0.871741i	0.120922	+	0.992662i	$0.461415\pi$
$968$		0			0
$969$	0.0557668	+	1.79584i	0.00179149	+	0.0576906i
$970$		0			0
$971$	12.0375	+	6.94987i	0.386303	+	0.223032i	0.680557	−	0.732695i	$-0.261738\pi$
$971$	12.0375	+	6.94987i	0.386303	+	0.223032i	−0.294254	+	0.955727i	$0.595071\pi$
$972$		0			0
$973$	−10.1732	+	11.0730i	−0.326139	+	0.354983i
$974$		0			0
$975$	8.91829	−	22.8137i	0.285614	−	0.730623i
$976$		0			0
$977$	−1.83013	+	6.83013i	−0.0585510	+	0.218515i	−0.989002	−	0.147900i	$-0.952748\pi$
$977$	−1.83013	+	6.83013i	−0.0585510	+	0.218515i	0.930451	+	0.366416i	$0.119415\pi$
$978$		0			0
$979$			38.4169i			1.22781i
$980$		0			0
$981$	−30.8166	−	46.4578i	−0.983899	−	1.48328i
$982$		0			0
$983$	−14.7415	−	3.94999i	−0.470182	−	0.125985i	0.0159452	−	0.999873i	$-0.494924\pi$
$983$	−14.7415	−	3.94999i	−0.470182	−	0.125985i	−0.486128	+	0.873888i	$0.661591\pi$
$984$		0			0
$985$	46.4711	+	9.50962i	1.48069	+	0.303002i
$986$		0			0
$987$	−30.6006	+	10.6584i	−0.974028	+	0.339261i
$988$		0			0
$989$	2.13325	−	3.69490i	0.0678334	−	0.117491i
$990$		0			0
$991$	27.2665	+	47.2270i	0.866149	+	1.50021i	0.865902	+	0.500214i	$0.166745\pi$
$991$	27.2665	+	47.2270i	0.866149	+	1.50021i	0.000247028		1.00000i	$0.499921\pi$
$992$		0			0
$993$	−4.31662	−	14.3166i	−0.136984	−	0.454324i
$994$		0			0
$995$	−3.26650	+	6.53300i	−0.103555	+	0.207110i
$996$		0			0
$997$	5.96509	+	1.59834i	0.188916	+	0.0506200i	0.352037	−	0.935986i	$-0.385489\pi$
$997$	5.96509	+	1.59834i	0.188916	+	0.0506200i	−0.163120	+	0.986606i	$0.552156\pi$
$998$		0			0
$999$	12.2660	−	26.7123i	0.388078	−	0.845139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.bv.b.233.1	yes	8
3.2	odd	2		420.2.bv.a.233.2	yes	8
5.2	odd	4		420.2.bv.a.317.2	yes	8
7.4	even	3	inner	420.2.bv.b.53.2	yes	8
15.2	even	4	inner	420.2.bv.b.317.2	yes	8
21.11	odd	6		420.2.bv.a.53.2	✓	8
35.32	odd	12		420.2.bv.a.137.2	yes	8
105.32	even	12	inner	420.2.bv.b.137.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bv.a.53.2	✓	8	21.11	odd	6
420.2.bv.a.137.2	yes	8	35.32	odd	12
420.2.bv.a.233.2	yes	8	3.2	odd	2
420.2.bv.a.317.2	yes	8	5.2	odd	4
420.2.bv.b.53.2	yes	8	7.4	even	3	inner
420.2.bv.b.137.1	yes	8	105.32	even	12	inner
420.2.bv.b.233.1	yes	8	1.1	even	1	trivial
420.2.bv.b.317.2	yes	8	15.2	even	4	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:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18614 + 1.26217i) q^{3} +(1.86603 - 1.23205i) q^{5} +(-1.94831 - 1.79000i) q^{7} +(-0.186141 - 2.99422i) q^{9} +O(q^{10})\)	\(q+(-1.18614 + 1.26217i) q^{3} +(1.86603 - 1.23205i) q^{5} +(-1.94831 - 1.79000i) q^{7} +(-0.186141 - 2.99422i) q^{9} +(2.00626 - 1.15831i) q^{11} +(-2.00000 - 2.00000i) q^{13} +(-0.658312 + 3.81662i) q^{15} +(0.847944 - 3.16457i) q^{17} +(0.274205 + 0.158312i) q^{19} +(4.57025 - 0.335907i) q^{21} +(-0.423972 - 1.58228i) q^{23} +(1.96410 - 4.59808i) q^{25} +(4.00000 + 3.31662i) q^{27} +7.31662 q^{29} +(3.00000 + 5.19615i) q^{31} +(-0.917716 + 3.90616i) q^{33} +(-5.84096 - 0.939764i) q^{35} +(-1.46410 - 5.46410i) q^{37} +(4.89662 - 0.152056i) q^{39} -9.63325i q^{41} +(1.84169 + 1.84169i) q^{43} +(-4.03637 - 5.35796i) q^{45} +(-6.83013 + 1.83013i) q^{47} +(0.591820 + 6.97494i) q^{49} +(2.98844 + 4.82387i) q^{51} +(9.99470 + 2.67807i) q^{53} +(2.31662 - 4.63325i) q^{55} +(-0.525063 + 0.158312i) q^{57} +(-6.15831 - 10.6665i) q^{59} +(-4.65831 + 8.06843i) q^{61} +(-4.99699 + 6.16686i) q^{63} +(-6.19615 - 1.26795i) q^{65} +(-9.77844 - 2.62012i) q^{67} +(2.50000 + 1.34169i) q^{69} -2.31662i q^{71} +(-2.42794 + 9.06119i) q^{73} +(3.47385 + 7.93299i) q^{75} +(-5.98218 - 1.33444i) q^{77} +(4.92195 + 2.84169i) q^{79} +(-8.93070 + 1.11469i) q^{81} +(-3.84169 + 3.84169i) q^{83} +(-2.31662 - 6.94987i) q^{85} +(-8.67855 + 9.23482i) q^{87} +(-8.29156 + 14.3614i) q^{89} +(0.316625 + 7.47661i) q^{91} +(-10.1168 - 2.37686i) q^{93} +(0.706723 - 0.0424197i) q^{95} +(-9.31662 + 9.31662i) q^{97} +(-3.84169 - 5.79156i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 8 q^{5} + 6 q^{7} + 10 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 + 8 * q^5 + 6 * q^7 + 10 * q^9	\( 8 q + 2 q^{3} + 8 q^{5} + 6 q^{7} + 10 q^{9} - 16 q^{13} + 8 q^{15} + 4 q^{17} + 14 q^{21} - 2 q^{23} - 12 q^{25} + 32 q^{27} + 32 q^{29} + 24 q^{31} - 22 q^{33} + 16 q^{37} - 4 q^{39} + 28 q^{43} - 20 q^{45} - 20 q^{47} - 24 q^{51} + 16 q^{53} - 8 q^{55} - 44 q^{57} - 36 q^{59} - 24 q^{61} + 22 q^{63} - 8 q^{65} - 22 q^{67} + 20 q^{69} + 6 q^{75} - 16 q^{77} - 14 q^{81} - 44 q^{83} + 8 q^{85} + 8 q^{87} - 24 q^{91} - 12 q^{93} - 12 q^{95} - 48 q^{97} - 44 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 8 * q^5 + 6 * q^7 + 10 * q^9 - 16 * q^13 + 8 * q^15 + 4 * q^17 + 14 * q^21 - 2 * q^23 - 12 * q^25 + 32 * q^27 + 32 * q^29 + 24 * q^31 - 22 * q^33 + 16 * q^37 - 4 * q^39 + 28 * q^43 - 20 * q^45 - 20 * q^47 - 24 * q^51 + 16 * q^53 - 8 * q^55 - 44 * q^57 - 36 * q^59 - 24 * q^61 + 22 * q^63 - 8 * q^65 - 22 * q^67 + 20 * q^69 + 6 * q^75 - 16 * q^77 - 14 * q^81 - 44 * q^83 + 8 * q^85 + 8 * q^87 - 24 * q^91 - 12 * q^93 - 12 * q^95 - 48 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

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Representations

Groups

Database

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