LMFDB - Embedded newform 252.2.bm.a.185.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(173,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 5]))

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

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

chi := DirichletCharacter("252.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bm (of order $6$, degree $2$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.4
Root			$-1.61108 + 0.635951i$ of defining polynomial
Character	$\chi$	$=$	252.185
Dual form			252.2.bm.a.173.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.127742 - 1.72733i) q^{3} +2.18300 q^{5} +(2.64473 + 0.0736382i) q^{7} +(-2.96736 - 0.441307i) q^{9} +O(q^{10})$	\(q+(0.127742 - 1.72733i) q^{3} +2.18300 q^{5} +(2.64473 + 0.0736382i) q^{7} +(-2.96736 - 0.441307i) q^{9} +1.46518i q^{11} +(-2.92752 - 1.69021i) q^{13} +(0.278862 - 3.77077i) q^{15} +(-1.32136 + 2.28866i) q^{17} +(6.87816 - 3.97111i) q^{19} +(0.465041 - 4.55892i) q^{21} -4.00964i q^{23} -0.234498 q^{25} +(-1.14134 + 5.06925i) q^{27} +(-6.71261 + 3.87553i) q^{29} +(0.612252 - 0.353484i) q^{31} +(2.53086 + 0.187166i) q^{33} +(5.77345 + 0.160752i) q^{35} +(1.41738 + 2.45498i) q^{37} +(-3.29352 + 4.84090i) q^{39} +(-3.74173 + 6.48086i) q^{41} +(-1.27112 - 2.20164i) q^{43} +(-6.47776 - 0.963374i) q^{45} +(-6.27538 + 10.8693i) q^{47} +(6.98915 + 0.389506i) q^{49} +(3.78448 + 2.57478i) q^{51} +(2.41675 + 1.39531i) q^{53} +3.19850i q^{55} +(-5.98079 - 12.3881i) q^{57} +(6.71650 + 11.6333i) q^{59} +(6.75061 + 3.89747i) q^{61} +(-7.81537 - 1.38565i) q^{63} +(-6.39079 - 3.68972i) q^{65} +(-2.92029 - 5.05809i) q^{67} +(-6.92598 - 0.512200i) q^{69} -11.6854i q^{71} +(-3.95924 - 2.28587i) q^{73} +(-0.0299553 + 0.405056i) q^{75} +(-0.107894 + 3.87501i) q^{77} +(-4.69189 + 8.12659i) q^{79} +(8.61050 + 2.61904i) q^{81} +(-1.70847 - 2.95917i) q^{83} +(-2.88452 + 4.99614i) q^{85} +(5.83685 + 12.0900i) q^{87} +(-4.61937 - 8.00099i) q^{89} +(-7.61803 - 4.68571i) q^{91} +(-0.532375 - 1.10272i) q^{93} +(15.0150 - 8.66894i) q^{95} +(-6.38394 + 3.68577i) q^{97} +(0.646596 - 4.34773i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{7}+O(q^{10}) $ 16 * q - q^7	$ 16 q - q^{7} + 3 q^{13} - 3 q^{15} - 9 q^{17} + 16 q^{25} - 9 q^{27} + 6 q^{29} + 6 q^{31} - 27 q^{33} + 15 q^{35} + q^{37} - 3 q^{39} + 6 q^{41} - 2 q^{43} - 15 q^{45} - 18 q^{47} + 13 q^{49} + 15 q^{51} + 15 q^{57} - 15 q^{59} + 3 q^{61} - 9 q^{63} - 39 q^{65} - 7 q^{67} - 21 q^{69} - 15 q^{75} - 45 q^{77} - q^{79} + 6 q^{85} - 3 q^{87} - 21 q^{89} + 9 q^{91} - 69 q^{93} + 6 q^{95} + 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q - q^7 + 3 * q^13 - 3 * q^15 - 9 * q^17 + 16 * q^25 - 9 * q^27 + 6 * q^29 + 6 * q^31 - 27 * q^33 + 15 * q^35 + q^37 - 3 * q^39 + 6 * q^41 - 2 * q^43 - 15 * q^45 - 18 * q^47 + 13 * q^49 + 15 * q^51 + 15 * q^57 - 15 * q^59 + 3 * q^61 - 9 * q^63 - 39 * q^65 - 7 * q^67 - 21 * q^69 - 15 * q^75 - 45 * q^77 - q^79 + 6 * q^85 - 3 * q^87 - 21 * q^89 + 9 * q^91 - 69 * q^93 + 6 * q^95 + 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.127742	−	1.72733i	0.0737520	−	0.997277i
$3$	0.127742	−	1.72733i	0.0737520	−	0.997277i
$4$		0			0
$5$	2.18300			0.976269			0.488134	−	0.872769i	$-0.337678\pi$
$5$	2.18300			0.976269			0.488134	+	0.872769i	$0.337678\pi$
$6$		0			0
$7$	2.64473	+	0.0736382i	0.999613	+	0.0278326i
$7$	2.64473	+	0.0736382i	0.999613	+	0.0278326i
$8$		0			0
$9$	−2.96736	−	0.441307i	−0.989121	−	0.147102i
$10$		0			0
$11$			1.46518i			0.441770i	0.975300	+	0.220885i	$0.0708945\pi$
$11$			1.46518i			0.441770i	−0.975300	+	0.220885i	$0.929106\pi$
$12$		0			0
$13$	−2.92752	−	1.69021i	−0.811948	−	0.468779i	0.0356837	−	0.999363i	$-0.488639\pi$
$13$	−2.92752	−	1.69021i	−0.811948	−	0.468779i	−0.847632	+	0.530585i	$0.821972\pi$
$14$		0			0
$15$	0.278862	−	3.77077i	0.0720017	−	0.973610i
$16$		0			0
$17$	−1.32136	+	2.28866i	−0.320476	+	0.555081i	−0.980586	−	0.196088i	$-0.937176\pi$
$17$	−1.32136	+	2.28866i	−0.320476	+	0.555081i	0.660110	+	0.751169i	$0.270509\pi$
$18$		0			0
$19$	6.87816	−	3.97111i	1.57796	−	0.911034i	0.582813	−	0.812606i	$-0.301952\pi$
$19$	6.87816	−	3.97111i	1.57796	−	0.911034i	0.995144	−	0.0984279i	$-0.0313814\pi$
$20$		0			0
$21$	0.465041	−	4.55892i	0.101480	−	0.994838i
$22$		0			0
$23$		−	4.00964i		−	0.836068i	−0.908431	−	0.418034i	$-0.862719\pi$
$23$		−	4.00964i		−	0.836068i	0.908431	−	0.418034i	$-0.137281\pi$
$24$		0			0
$25$	−0.234498			−0.0468996
$26$		0			0
$27$	−1.14134	+	5.06925i	−0.219651	+	0.975578i
$28$		0			0
$29$	−6.71261	+	3.87553i	−1.24650	+	0.719667i	−0.970410	−	0.241464i	$-0.922372\pi$
$29$	−6.71261	+	3.87553i	−1.24650	+	0.719667i	−0.276091	+	0.961132i	$0.589039\pi$
$30$		0			0
$31$	0.612252	−	0.353484i	0.109964	−	0.0634876i	−0.444009	−	0.896022i	$-0.646444\pi$
$31$	0.612252	−	0.353484i	0.109964	−	0.0634876i	0.553973	+	0.832534i	$0.313111\pi$
$32$		0			0
$33$	2.53086	+	0.187166i	0.440567	+	0.0325814i
$34$		0			0
$35$	5.77345	+	0.160752i	0.975890	+	0.0271721i
$36$		0			0
$37$	1.41738	+	2.45498i	0.233016	+	0.403596i	0.958694	−	0.284438i	$-0.0918071\pi$
$37$	1.41738	+	2.45498i	0.233016	+	0.403596i	−0.725678	+	0.688034i	$0.758474\pi$
$38$		0			0
$39$	−3.29352	+	4.84090i	−0.527385	+	0.775164i
$40$		0			0
$41$	−3.74173	+	6.48086i	−0.584360	+	1.01214i	0.410595	+	0.911818i	$0.365321\pi$
$41$	−3.74173	+	6.48086i	−0.584360	+	1.01214i	−0.994955	+	0.100323i	$0.968012\pi$
$42$		0			0
$43$	−1.27112	−	2.20164i	−0.193844	−	0.335748i	0.752677	−	0.658390i	$-0.228762\pi$
$43$	−1.27112	−	2.20164i	−0.193844	−	0.335748i	−0.946521	+	0.322642i	$0.895429\pi$
$44$		0			0
$45$	−6.47776	−	0.963374i	−0.965648	−	0.143611i
$46$		0			0
$47$	−6.27538	+	10.8693i	−0.915358	+	1.58545i	−0.108983	+	0.994044i	$0.534759\pi$
$47$	−6.27538	+	10.8693i	−0.915358	+	1.58545i	−0.806376	+	0.591403i	$0.798574\pi$
$48$		0			0
$49$	6.98915	+	0.389506i	0.998451	+	0.0556437i
$50$		0			0
$51$	3.78448	+	2.57478i	0.529933	+	0.360541i
$52$		0			0
$53$	2.41675	+	1.39531i	0.331966	+	0.191661i	0.656714	−	0.754140i	$-0.271946\pi$
$53$	2.41675	+	1.39531i	0.331966	+	0.191661i	−0.324748	+	0.945801i	$0.605279\pi$
$54$		0			0
$55$			3.19850i			0.431286i
$56$		0			0
$57$	−5.98079	−	12.3881i	−0.792176	−	1.64085i
$58$		0			0
$59$	6.71650	+	11.6333i	0.874414	+	1.51453i	0.857385	+	0.514675i	$0.172087\pi$
$59$	6.71650	+	11.6333i	0.874414	+	1.51453i	0.0170287	+	0.999855i	$0.494579\pi$
$60$		0			0
$61$	6.75061	+	3.89747i	0.864327	+	0.499020i	0.865459	−	0.500980i	$-0.167027\pi$
$61$	6.75061	+	3.89747i	0.864327	+	0.499020i	−0.00113176	+	0.999999i	$0.500360\pi$
$62$		0			0
$63$	−7.81537	−	1.38565i	−0.984644	−	0.174575i
$64$		0			0
$65$	−6.39079	−	3.68972i	−0.792680	−	0.457654i
$66$		0			0
$67$	−2.92029	−	5.05809i	−0.356770	−	0.617945i	0.630649	−	0.776068i	$-0.282789\pi$
$67$	−2.92029	−	5.05809i	−0.356770	−	0.617945i	−0.987419	+	0.158124i	$0.949455\pi$
$68$		0			0
$69$	−6.92598	−	0.512200i	−0.833791	−	0.0616616i
$70$		0			0
$71$		−	11.6854i		−	1.38680i	−0.720554	−	0.693398i	$-0.756113\pi$
$71$		−	11.6854i		−	1.38680i	0.720554	−	0.693398i	$-0.243887\pi$
$72$		0			0
$73$	−3.95924	−	2.28587i	−0.463394	−	0.267541i	0.250076	−	0.968226i	$-0.419544\pi$
$73$	−3.95924	−	2.28587i	−0.463394	−	0.267541i	−0.713470	+	0.700685i	$0.752878\pi$
$74$		0			0
$75$	−0.0299553	+	0.405056i	−0.00345894	+	0.0467719i
$76$		0			0
$77$	−0.107894	+	3.87501i	−0.0122956	+	0.441599i
$78$		0			0
$79$	−4.69189	+	8.12659i	−0.527879	+	0.914312i	0.471593	+	0.881816i	$0.343679\pi$
$79$	−4.69189	+	8.12659i	−0.527879	+	0.914312i	−0.999472	+	0.0324963i	$0.989654\pi$
$80$		0			0
$81$	8.61050	+	2.61904i	0.956722	+	0.291004i
$82$		0			0
$83$	−1.70847	−	2.95917i	−0.187529	−	0.324811i	0.756896	−	0.653535i	$-0.226715\pi$
$83$	−1.70847	−	2.95917i	−0.187529	−	0.324811i	−0.944426	+	0.328724i	$0.893381\pi$
$84$		0			0
$85$	−2.88452	+	4.99614i	−0.312871	+	0.541908i
$86$		0			0
$87$	5.83685	+	12.0900i	0.625776	+	1.29618i
$88$		0			0
$89$	−4.61937	−	8.00099i	−0.489653	−	0.848103i	0.510276	−	0.860010i	$-0.329543\pi$
$89$	−4.61937	−	8.00099i	−0.489653	−	0.848103i	−0.999929	+	0.0119070i	$0.996210\pi$
$90$		0			0
$91$	−7.61803	−	4.68571i	−0.798586	−	0.491196i
$92$		0			0
$93$	−0.532375	−	1.10272i	−0.0552047	−	0.114347i
$94$		0			0
$95$	15.0150	−	8.66894i	1.54051	−	0.889414i
$96$		0			0
$97$	−6.38394	+	3.68577i	−0.648191	+	0.374233i	−0.787763	−	0.615979i	$-0.788761\pi$
$97$	−6.38394	+	3.68577i	−0.648191	+	0.374233i	0.139572	+	0.990212i	$0.455427\pi$
$98$		0			0
$99$	0.646596	−	4.34773i	0.0649853	−	0.436964i
$100$		0			0
$101$	7.92714			0.788780			0.394390	−	0.918943i	$-0.370956\pi$
$101$	7.92714			0.788780			0.394390	+	0.918943i	$0.370956\pi$
$102$		0			0
$103$			3.77385i			0.371849i	0.982564	+	0.185924i	$0.0595280\pi$
$103$			3.77385i			0.371849i	−0.982564	+	0.185924i	$0.940472\pi$
$104$		0			0
$105$	1.01519	−	9.95213i	0.0990720	−	0.971229i
$106$		0			0
$107$	6.88241	−	3.97356i	0.665347	−	0.384138i	−0.128964	−	0.991649i	$-0.541165\pi$
$107$	6.88241	−	3.97356i	0.665347	−	0.384138i	0.794311	+	0.607511i	$0.207832\pi$
$108$		0			0
$109$	0.505142	−	0.874932i	0.0483838	−	0.0838033i	−0.840819	−	0.541316i	$-0.817926\pi$
$109$	0.505142	−	0.874932i	0.0483838	−	0.0838033i	0.889203	+	0.457513i	$0.151260\pi$
$110$		0			0
$111$	4.42163	−	2.13469i	0.419682	−	0.202616i
$112$		0			0
$113$	−10.5557	−	6.09431i	−0.992992	−	0.573304i	−0.0868250	−	0.996224i	$-0.527672\pi$
$113$	−10.5557	−	6.09431i	−0.992992	−	0.573304i	−0.906167	+	0.422919i	$0.861005\pi$
$114$		0			0
$115$		−	8.75305i		−	0.816226i
$116$		0			0
$117$	7.94112	+	6.30739i	0.734157	+	0.583118i
$118$		0			0
$119$	−3.66316	+	5.95557i	−0.335801	+	0.545946i
$120$		0			0
$121$	8.85324			0.804840
$122$		0			0
$123$	10.7166	+	7.29109i	0.966286	+	0.657416i
$124$		0			0
$125$	−11.4269			−1.02206
$126$		0			0
$127$	6.79350			0.602826			0.301413	−	0.953494i	$-0.402542\pi$
$127$	6.79350			0.602826			0.301413	+	0.953494i	$0.402542\pi$
$128$		0			0
$129$	−3.96535	+	1.91441i	−0.349130	+	0.168554i
$130$		0			0
$131$	13.7358			1.20010			0.600051	−	0.799961i	$-0.295147\pi$
$131$	13.7358			1.20010			0.600051	+	0.799961i	$0.295147\pi$
$132$		0			0
$133$	18.4833	−	9.99599i	1.60270	−	0.866762i
$134$		0			0
$135$	−2.49155	+	11.0662i	−0.214439	+	0.952427i
$136$		0			0
$137$		−	20.0950i		−	1.71683i	−0.512954	−	0.858416i	$-0.671449\pi$
$137$		−	20.0950i		−	1.71683i	0.512954	−	0.858416i	$-0.328551\pi$
$138$		0			0
$139$	−8.51403	−	4.91558i	−0.722151	−	0.416934i	0.0933930	−	0.995629i	$-0.470229\pi$
$139$	−8.51403	−	4.91558i	−0.722151	−	0.416934i	−0.815544	+	0.578695i	$0.803562\pi$
$140$		0			0
$141$	17.9732	+	12.2281i	1.51362	+	1.02980i
$142$		0			0
$143$	2.47646	−	4.28936i	0.207092	−	0.358694i
$144$		0			0
$145$	−14.6536	+	8.46029i	−1.21692	+	0.702589i
$146$		0			0
$147$	1.56562	−	12.0228i	0.129130	−	0.991628i
$148$		0			0
$149$			20.0354i			1.64136i	0.571386	+	0.820682i	$0.306406\pi$
$149$			20.0354i			1.64136i	−0.571386	+	0.820682i	$0.693594\pi$
$150$		0			0
$151$	−22.2337			−1.80935			−0.904675	−	0.426103i	$-0.859886\pi$
$151$	−22.2337			−1.80935			−0.904675	+	0.426103i	$0.859886\pi$
$152$		0			0
$153$	4.93094	−	6.20815i	0.398643	−	0.501899i
$154$		0			0
$155$	1.33655	−	0.771657i	0.107354	−	0.0619810i
$156$		0			0
$157$	6.95305	−	4.01435i	0.554914	−	0.320380i	−0.196188	−	0.980566i	$-0.562856\pi$
$157$	6.95305	−	4.01435i	0.554914	−	0.320380i	0.751102	+	0.660187i	$0.229523\pi$
$158$		0			0
$159$	2.71889	−	3.99629i	0.215622	−	0.316927i
$160$		0			0
$161$	0.295263	−	10.6044i	0.0232700	−	0.835744i
$162$		0			0
$163$	−6.22604	−	10.7838i	−0.487661	−	0.844654i	0.512238	−	0.858844i	$-0.328817\pi$
$163$	−6.22604	−	10.7838i	−0.487661	−	0.844654i	−0.999899	+	0.0141893i	$0.995483\pi$
$164$		0			0
$165$	5.52488	+	0.408584i	0.430111	+	0.0318082i
$166$		0			0
$167$	9.85984	−	17.0777i	0.762978	−	1.32152i	−0.178332	−	0.983970i	$-0.557070\pi$
$167$	9.85984	−	17.0777i	0.762978	−	1.32152i	0.941309	−	0.337546i	$-0.109597\pi$
$168$		0			0
$169$	−0.786412	−	1.36211i	−0.0604933	−	0.104777i
$170$		0			0
$171$	−22.1625	+	8.74834i	−1.69481	+	0.669002i
$172$		0			0
$173$	0.913733	−	1.58263i	0.0694699	−	0.120325i	−0.829198	−	0.558955i	$-0.811203\pi$
$173$	0.913733	−	1.58263i	0.0694699	−	0.120325i	0.898668	+	0.438629i	$0.144536\pi$
$174$		0			0
$175$	−0.620183	−	0.0172680i	−0.0468814	−	0.00130534i
$176$		0			0
$177$	20.9526	−	10.1156i	1.57489	−	0.760333i
$178$		0			0
$179$	−12.1182	−	6.99645i	−0.905757	−	0.522939i	−0.0266934	−	0.999644i	$-0.508498\pi$
$179$	−12.1182	−	6.99645i	−0.905757	−	0.522939i	−0.879064	+	0.476705i	$0.841831\pi$
$180$		0			0
$181$			16.3594i			1.21599i	0.793942	+	0.607994i	$0.208025\pi$
$181$			16.3594i			1.21599i	−0.793942	+	0.607994i	$0.791975\pi$
$182$		0			0
$183$	7.59456	−	11.1627i	0.561406	−	0.825170i
$184$		0			0
$185$	3.09415	+	5.35923i	0.227486	+	0.394018i
$186$		0			0
$187$	−3.35330	−	1.93603i	−0.245218	−	0.141577i
$188$		0			0
$189$	−3.39183	+	13.3227i	−0.246719	+	0.969087i
$190$		0			0
$191$	−11.8326	−	6.83153i	−0.856173	−	0.494312i	0.00655557	−	0.999979i	$-0.497913\pi$
$191$	−11.8326	−	6.83153i	−0.856173	−	0.494312i	−0.862729	+	0.505667i	$0.831247\pi$
$192$		0			0
$193$	2.18885	+	3.79119i	0.157557	+	0.272896i	0.933987	−	0.357307i	$-0.116305\pi$
$193$	2.18885	+	3.79119i	0.157557	+	0.272896i	−0.776430	+	0.630203i	$0.782972\pi$
$194$		0			0
$195$	−7.18976	+	10.5677i	−0.514869	+	0.756768i
$196$		0			0
$197$			1.00603i			0.0716767i	0.999358	+	0.0358384i	$0.0114101\pi$
$197$			1.00603i			0.0716767i	−0.999358	+	0.0358384i	$0.988590\pi$
$198$		0			0
$199$	−5.67639	−	3.27726i	−0.402388	−	0.232319i	0.285126	−	0.958490i	$-0.407965\pi$
$199$	−5.67639	−	3.27726i	−0.402388	−	0.232319i	−0.687514	+	0.726171i	$0.741298\pi$
$200$		0			0
$201$	−9.11006	+	4.39819i	−0.642574	+	0.310224i
$202$		0			0
$203$	−18.0384	+	9.75540i	−1.26605	+	0.684695i
$204$		0			0
$205$	−8.16820	+	14.1477i	−0.570492	+	0.988121i
$206$		0			0
$207$	−1.76948	+	11.8981i	−0.122987	+	0.826972i
$208$		0			0
$209$	5.81840	+	10.0778i	0.402467	+	0.697094i
$210$		0			0
$211$	−9.11202	+	15.7825i	−0.627297	+	1.08651i	0.360794	+	0.932645i	$0.382506\pi$
$211$	−9.11202	+	15.7825i	−0.627297	+	1.08651i	−0.988092	+	0.153866i	$0.950828\pi$
$212$		0			0
$213$	−20.1845	−	1.49271i	−1.38302	−	0.102279i
$214$		0			0
$215$	−2.77486	−	4.80620i	−0.189244	−	0.327780i
$216$		0			0
$217$	1.64527	−	0.889784i	0.111688	−	0.0604024i
$218$		0			0
$219$	−4.45422	+	6.54693i	−0.300989	+	0.442401i
$220$		0			0
$221$	7.73660	−	4.46673i	0.520420	−	0.300464i
$222$		0			0
$223$	8.71705	−	5.03279i	0.583737	−	0.337021i	−0.178880	−	0.983871i	$-0.557247\pi$
$223$	8.71705	−	5.03279i	0.583737	−	0.337021i	0.762617	+	0.646850i	$0.223914\pi$
$224$		0			0
$225$	0.695841	+	0.103486i	0.0463894	+	0.00689904i
$226$		0			0
$227$	19.8874			1.31998			0.659988	−	0.751276i	$-0.270561\pi$
$227$	19.8874			1.31998			0.659988	+	0.751276i	$0.270561\pi$
$228$		0			0
$229$			17.7655i			1.17398i	0.809595	+	0.586988i	$0.199687\pi$
$229$			17.7655i			1.17398i	−0.809595	+	0.586988i	$0.800313\pi$
$230$		0			0
$231$	6.67966	+	0.681371i	0.439489	+	0.0448309i
$232$		0			0
$233$	13.9077	−	8.02962i	0.911124	−	0.526038i	0.0303317	−	0.999540i	$-0.490344\pi$
$233$	13.9077	−	8.02962i	0.911124	−	0.526038i	0.880793	+	0.473502i	$0.157010\pi$
$234$		0			0
$235$	−13.6992	+	23.7277i	−0.893636	+	1.54782i
$236$		0			0
$237$	13.4380	+	9.14256i	0.872890	+	0.593873i
$238$		0			0
$239$	−7.11117	−	4.10564i	−0.459983	−	0.265572i	0.252054	−	0.967713i	$-0.418894\pi$
$239$	−7.11117	−	4.10564i	−0.459983	−	0.265572i	−0.712037	+	0.702142i	$0.752227\pi$
$240$		0			0
$241$		−	28.4765i		−	1.83433i	−0.398505	−	0.917166i	$-0.630471\pi$
$241$		−	28.4765i		−	1.83433i	0.398505	−	0.917166i	$-0.369529\pi$
$242$		0			0
$243$	5.62387	−	14.5386i	0.360772	−	0.932654i
$244$		0			0
$245$	15.2573	+	0.850293i	0.974756	+	0.0543232i
$246$		0			0
$247$	−26.8479			−1.70829
$248$		0			0
$249$	−5.32971	+	2.57310i	−0.337757	+	0.163063i
$250$		0			0
$251$	−0.656343			−0.0414280			−0.0207140	−	0.999785i	$-0.506594\pi$
$251$	−0.656343			−0.0414280			−0.0207140	+	0.999785i	$0.506594\pi$
$252$		0			0
$253$	5.87486			0.369349
$254$		0			0
$255$	8.26153	+	5.62075i	0.517357	+	0.351985i
$256$		0			0
$257$	−7.64084			−0.476623			−0.238311	−	0.971189i	$-0.576594\pi$
$257$	−7.64084			−0.476623			−0.238311	+	0.971189i	$0.576594\pi$
$258$		0			0
$259$	3.56781	+	6.59712i	0.221693	+	0.409925i
$260$		0			0
$261$	21.6291	−	8.53778i	1.33880	−	0.528475i
$262$		0			0
$263$			6.62669i			0.408619i	0.978906	+	0.204310i	$0.0654949\pi$
$263$			6.62669i			0.408619i	−0.978906	+	0.204310i	$0.934505\pi$
$264$		0			0
$265$	5.27577	+	3.04597i	0.324088	+	0.187112i
$266$		0			0
$267$	−14.4105	+	6.95714i	−0.881907	+	0.425770i
$268$		0			0
$269$	−4.38347	+	7.59239i	−0.267265	+	0.462916i	−0.968154	−	0.250354i	$-0.919453\pi$
$269$	−4.38347	+	7.59239i	−0.267265	+	0.462916i	0.700890	+	0.713270i	$0.252786\pi$
$270$		0			0
$271$	14.2608	−	8.23346i	0.866280	−	0.500147i	0.000169619	−	1.00000i	$-0.499946\pi$
$271$	14.2608	−	8.23346i	0.866280	−	0.500147i	0.866110	+	0.499853i	$0.166613\pi$
$272$		0			0
$273$	−9.06693	+	12.5603i	−0.548755	+	0.760185i
$274$		0			0
$275$		−	0.343583i		−	0.0207188i
$276$		0			0
$277$	−17.7746			−1.06797			−0.533987	−	0.845493i	$-0.679307\pi$
$277$	−17.7746			−1.06797			−0.533987	+	0.845493i	$0.679307\pi$
$278$		0			0
$279$	−1.97277	+	0.778725i	−0.118107	+	0.0466210i
$280$		0			0
$281$	−14.0252	+	8.09748i	−0.836676	+	0.483055i	−0.856133	−	0.516755i	$-0.827140\pi$
$281$	−14.0252	+	8.09748i	−0.836676	+	0.483055i	0.0194568	+	0.999811i	$0.493806\pi$
$282$		0			0
$283$	24.5717	−	14.1865i	1.46063	−	0.843298i	0.461594	−	0.887091i	$-0.347278\pi$
$283$	24.5717	−	14.1865i	1.46063	−	0.843298i	0.999041	+	0.0437937i	$0.0139444\pi$
$284$		0			0
$285$	−13.0561	−	27.0434i	−0.773376	−	1.60191i
$286$		0			0
$287$	−10.3731	+	16.8646i	−0.612304	+	0.995484i
$288$		0			0
$289$	5.00804	+	8.67417i	0.294590	+	0.510246i
$290$		0			0
$291$	5.55106	+	11.4980i	0.325409	+	0.674027i
$292$		0			0
$293$	4.38260	−	7.59088i	0.256034	−	0.443464i	−0.709142	−	0.705066i	$-0.750917\pi$
$293$	4.38260	−	7.59088i	0.256034	−	0.443464i	0.965176	+	0.261602i	$0.0842507\pi$
$294$		0			0
$295$	14.6621	+	25.3956i	0.853663	+	1.47859i
$296$		0			0
$297$	−7.42739	−	1.67228i	−0.430981	−	0.0970353i
$298$		0			0
$299$	−6.77711	+	11.7383i	−0.391931	+	0.678844i
$300$		0			0
$301$	−3.19964	−	5.91635i	−0.184424	−	0.341013i
$302$		0			0
$303$	1.01263	−	13.6928i	0.0581741	−	0.786632i
$304$		0			0
$305$	14.7366	+	8.50818i	0.843816	+	0.487177i
$306$		0			0
$307$		−	12.8497i		−	0.733372i	−0.930345	−	0.366686i	$-0.880492\pi$
$307$		−	12.8497i		−	0.733372i	0.930345	−	0.366686i	$-0.119508\pi$
$308$		0			0
$309$	6.51871	+	0.482080i	0.370836	+	0.0274246i
$310$		0			0
$311$	−3.29671	−	5.71007i	−0.186939	−	0.323789i	0.757289	−	0.653080i	$-0.226523\pi$
$311$	−3.29671	−	5.71007i	−0.186939	−	0.323789i	−0.944228	+	0.329291i	$0.893190\pi$
$312$		0			0
$313$	−2.95711	−	1.70729i	−0.167146	−	0.0965018i	0.414093	−	0.910234i	$-0.364099\pi$
$313$	−2.95711	−	1.70729i	−0.167146	−	0.0965018i	−0.581239	+	0.813733i	$0.697432\pi$
$314$		0			0
$315$	−17.0610	−	3.02487i	−0.961277	−	0.170432i
$316$		0			0
$317$	−27.8003	−	16.0505i	−1.56142	−	0.901485i	−0.997114	−	0.0759182i	$-0.975811\pi$
$317$	−27.8003	−	16.0505i	−1.56142	−	0.901485i	−0.564304	−	0.825567i	$-0.690855\pi$
$318$		0			0
$319$	−5.67836	−	9.83521i	−0.317927	−	0.550666i
$320$		0			0
$321$	−5.98449	−	12.3958i	−0.334022	−	0.691866i
$322$		0			0
$323$			20.9890i			1.16786i
$324$		0			0
$325$	0.686498	+	0.396350i	0.0380801	+	0.0219855i
$326$		0			0
$327$	−1.44677	−	0.984315i	−0.0800066	−	0.0544327i
$328$		0			0
$329$	−17.3971	+	28.2842i	−0.959131	+	1.55936i
$330$		0			0
$331$	14.4416	−	25.0137i	0.793784	−	1.37487i	−0.129824	−	0.991537i	$-0.541441\pi$
$331$	14.4416	−	25.0137i	0.793784	−	1.37487i	0.923608	−	0.383338i	$-0.125225\pi$
$332$		0			0
$333$	−3.12249	−	7.91032i	−0.171111	−	0.433483i
$334$		0			0
$335$	−6.37501	−	11.0418i	−0.348304	−	0.603280i
$336$		0			0
$337$	4.82568	−	8.35833i	0.262872	−	0.455307i	−0.704132	−	0.710069i	$-0.748664\pi$
$337$	4.82568	−	8.35833i	0.262872	−	0.455307i	0.967004	+	0.254762i	$0.0819971\pi$
$338$		0			0
$339$	−11.8753	+	17.4546i	−0.644978	+	0.948006i
$340$		0			0
$341$	0.517919	+	0.897063i	0.0280469	+	0.0485787i
$342$		0			0
$343$	18.4557	+	1.54481i	0.996515	+	0.0834117i
$344$		0			0
$345$	−15.1194	−	1.11813i	−0.814004	−	0.0601983i
$346$		0			0
$347$	10.6758	−	6.16367i	0.573106	−	0.330883i	−0.185283	−	0.982685i	$-0.559320\pi$
$347$	10.6758	−	6.16367i	0.573106	−	0.330883i	0.758389	+	0.651802i	$0.225987\pi$
$348$		0			0
$349$	10.2211	−	5.90115i	0.547123	−	0.315881i	−0.200838	−	0.979624i	$-0.564366\pi$
$349$	10.2211	−	5.90115i	0.547123	−	0.315881i	0.747961	+	0.663743i	$0.231033\pi$
$350$		0			0
$351$	11.9094	−	12.9112i	0.635676	−	0.689151i
$352$		0			0
$353$	13.1971			0.702411			0.351205	−	0.936298i	$-0.385772\pi$
$353$	13.1971			0.702411			0.351205	+	0.936298i	$0.385772\pi$
$354$		0			0
$355$		−	25.5092i		−	1.35389i
$356$		0			0
$357$	9.81931	+	7.08827i	0.519693	+	0.375151i
$358$		0			0
$359$	5.22483	−	3.01656i	0.275756	−	0.159208i	−0.355745	−	0.934583i	$-0.615773\pi$
$359$	5.22483	−	3.01656i	0.275756	−	0.159208i	0.631501	+	0.775375i	$0.282439\pi$
$360$		0			0
$361$	22.0394	−	38.1733i	1.15997	−	2.00912i
$362$		0			0
$363$	1.13093	−	15.2925i	0.0593585	−	0.802648i
$364$		0			0
$365$	−8.64304	−	4.99006i	−0.452397	−	0.261192i
$366$		0			0
$367$			17.1767i			0.896618i	0.893879	+	0.448309i	$0.147974\pi$
$367$			17.1767i			0.896618i	−0.893879	+	0.448309i	$0.852026\pi$
$368$		0			0
$369$	13.9631	−	17.5798i	0.726891	−	0.915169i
$370$		0			0
$371$	6.28889	+	3.86818i	0.326503	+	0.200826i
$372$		0			0
$373$	4.71804			0.244291			0.122146	−	0.992512i	$-0.461023\pi$
$373$	4.71804			0.244291			0.122146	+	0.992512i	$0.461023\pi$
$374$		0			0
$375$	−1.45970	+	19.7381i	−0.0753786	+	1.01927i
$376$		0			0
$377$	26.2017			1.34946
$378$		0			0
$379$	9.34015			0.479771			0.239886	−	0.970801i	$-0.422890\pi$
$379$	9.34015			0.479771			0.239886	+	0.970801i	$0.422890\pi$
$380$		0			0
$381$	0.867816	−	11.7346i	0.0444596	−	0.601184i
$382$		0			0
$383$	5.70071			0.291293			0.145646	−	0.989337i	$-0.453474\pi$
$383$	5.70071			0.291293			0.145646	+	0.989337i	$0.453474\pi$
$384$		0			0
$385$	−0.235532	+	8.45916i	−0.0120038	+	0.431119i
$386$		0			0
$387$	2.80027	+	7.09403i	0.142346	+	0.360610i
$388$		0			0
$389$		−	7.66342i		−	0.388551i	−0.980947	−	0.194275i	$-0.937764\pi$
$389$		−	7.66342i		−	0.388551i	0.980947	−	0.194275i	$-0.0622355\pi$
$390$		0			0
$391$	9.17668	+	5.29816i	0.464085	+	0.267939i
$392$		0			0
$393$	1.75464	−	23.7263i	0.0885100	−	1.19683i
$394$		0			0
$395$	−10.2424	+	17.7404i	−0.515351	+	0.892615i
$396$		0			0
$397$	−1.12810	+	0.651310i	−0.0566178	+	0.0326883i	−0.528042	−	0.849218i	$-0.677074\pi$
$397$	−1.12810	+	0.651310i	−0.0566178	+	0.0326883i	0.471424	+	0.881907i	$0.343740\pi$
$398$		0			0
$399$	−14.9053	−	33.2037i	−0.746199	−	1.66226i
$400$		0			0
$401$		−	9.45443i		−	0.472132i	−0.971737	−	0.236066i	$-0.924142\pi$
$401$		−	9.45443i		−	0.472132i	0.971737	−	0.236066i	$-0.0758581\pi$
$402$		0			0
$403$	−2.38984			−0.119047
$404$		0			0
$405$	18.7967	+	5.71736i	0.934018	+	0.284098i
$406$		0			0
$407$	−3.59700	+	2.07673i	−0.178296	+	0.102940i
$408$		0			0
$409$	−16.5182	+	9.53678i	−0.816771	+	0.471563i	−0.849302	−	0.527908i	$-0.822977\pi$
$409$	−16.5182	+	9.53678i	−0.816771	+	0.471563i	0.0325304	+	0.999471i	$0.489643\pi$
$410$		0			0
$411$	−34.7108	−	2.56698i	−1.71216	−	0.126620i
$412$		0			0
$413$	16.9067	+	31.2615i	0.831922	+	1.53828i
$414$		0			0
$415$	−3.72961	−	6.45987i	−0.183079	−	0.317102i
$416$		0			0
$417$	−9.57845	+	14.0786i	−0.469059	+	0.689434i
$418$		0			0
$419$	4.20003	−	7.27466i	0.205185	−	0.355390i	−0.745007	−	0.667057i	$-0.767554\pi$
$419$	4.20003	−	7.27466i	0.205185	−	0.355390i	0.950192	+	0.311666i	$0.100887\pi$
$420$		0			0
$421$	19.7178	+	34.1522i	0.960985	+	1.66448i	0.720035	+	0.693938i	$0.244126\pi$
$421$	19.7178	+	34.1522i	0.960985	+	1.66448i	0.240951	+	0.970537i	$0.422541\pi$
$422$		0			0
$423$	23.4180	−	29.4837i	1.13862	−	1.43355i
$424$		0			0
$425$	0.309855	−	0.536685i	0.0150302	−	0.0260331i
$426$		0			0
$427$	17.5665	+	10.8048i	0.850103	+	0.522883i
$428$		0			0
$429$	−7.09280	−	4.82561i	−0.342444	−	0.232983i
$430$		0			0
$431$	−10.3340	−	5.96634i	−0.497772	−	0.287389i	0.230021	−	0.973186i	$-0.426120\pi$
$431$	−10.3340	−	5.96634i	−0.497772	−	0.287389i	−0.727793	+	0.685797i	$0.759454\pi$
$432$		0			0
$433$		−	12.2121i		−	0.586875i	−0.955978	−	0.293437i	$-0.905201\pi$
$433$		−	12.2121i		−	0.586875i	0.955978	−	0.293437i	$-0.0947992\pi$
$434$		0			0
$435$	12.7419	+	26.3925i	0.610925	+	1.26542i
$436$		0			0
$437$	−15.9227	−	27.5789i	−0.761686	−	1.31928i
$438$		0			0
$439$	14.4639	+	8.35076i	0.690326	+	0.398560i	0.803734	−	0.594989i	$-0.202843\pi$
$439$	14.4639	+	8.35076i	0.690326	+	0.398560i	−0.113408	+	0.993548i	$0.536177\pi$
$440$		0			0
$441$	−20.5675	−	4.24017i	−0.979404	−	0.201913i
$442$		0			0
$443$	26.2403	+	15.1499i	1.24672	+	0.719791i	0.970453	−	0.241291i	$-0.0775708\pi$
$443$	26.2403	+	15.1499i	1.24672	+	0.719791i	0.276262	+	0.961082i	$0.410904\pi$
$444$		0			0
$445$	−10.0841	−	17.4662i	−0.478033	−	0.827977i
$446$		0			0
$447$	34.6078	+	2.55936i	1.63689	+	0.121054i
$448$		0			0
$449$			30.1253i			1.42170i	0.703343	+	0.710851i	$0.251690\pi$
$449$			30.1253i			1.42170i	−0.703343	+	0.710851i	$0.748310\pi$
$450$		0			0
$451$	−9.49566	−	5.48232i	−0.447133	−	0.258152i
$452$		0			0
$453$	−2.84018	+	38.4050i	−0.133443	+	1.80442i
$454$		0			0
$455$	−16.6302	−	10.2289i	−0.779635	−	0.479539i
$456$		0			0
$457$	−12.6159	+	21.8513i	−0.590146	+	1.02216i	0.404067	+	0.914730i	$0.367596\pi$
$457$	−12.6159	+	21.8513i	−0.590146	+	1.02216i	−0.994212	+	0.107433i	$0.965737\pi$
$458$		0			0
$459$	−10.0937	−	9.31043i	−0.471132	−	0.434574i
$460$		0			0
$461$	12.3174	+	21.3344i	0.573680	+	0.993643i	0.996184	+	0.0872820i	$0.0278181\pi$
$461$	12.3174	+	21.3344i	0.573680	+	0.993643i	−0.422503	+	0.906361i	$0.638849\pi$
$462$		0			0
$463$	−6.33215	+	10.9676i	−0.294280	+	0.509708i	−0.974817	−	0.223006i	$-0.928413\pi$
$463$	−6.33215	+	10.9676i	−0.294280	+	0.509708i	0.680537	+	0.732713i	$0.261746\pi$
$464$		0			0
$465$	−1.16218	−	2.40724i	−0.0538946	−	0.111633i
$466$		0			0
$467$	−10.4723	−	18.1385i	−0.484599	−	0.839350i	0.515245	−	0.857043i	$-0.327701\pi$
$467$	−10.4723	−	18.1385i	−0.484599	−	0.839350i	−0.999843	+	0.0176932i	$0.994368\pi$
$468$		0			0
$469$	−7.35090	−	13.5923i	−0.339433	−	0.627635i
$470$		0			0
$471$	−6.04592	−	12.5230i	−0.278581	−	0.577031i
$472$		0			0
$473$	3.22581	−	1.86242i	0.148323	−	0.0856344i
$474$		0			0
$475$	−1.61291	+	0.931217i	−0.0740056	+	0.0427271i
$476$		0			0
$477$	−6.55562	−	5.20692i	−0.300161	−	0.238409i
$478$		0			0
$479$	31.7705			1.45163			0.725816	−	0.687889i	$-0.241463\pi$
$479$	31.7705			1.45163			0.725816	+	0.687889i	$0.241463\pi$
$480$		0			0
$481$		−	9.58267i		−	0.436932i
$482$		0			0
$483$	−18.2796	−	1.86465i	−0.831751	−	0.0848443i
$484$		0			0
$485$	−13.9362	+	8.04605i	−0.632809	+	0.365352i
$486$		0			0
$487$	−17.7821	+	30.7995i	−0.805784	+	1.39566i	0.109977	+	0.993934i	$0.464922\pi$
$487$	−17.7821	+	30.7995i	−0.805784	+	1.39566i	−0.915761	+	0.401724i	$0.868411\pi$
$488$		0			0
$489$	−19.4226	+	9.37691i	−0.878320	+	0.424038i
$490$		0			0
$491$	2.75734	+	1.59195i	0.124437	+	0.0718437i	0.560926	−	0.827866i	$-0.310445\pi$
$491$	2.75734	+	1.59195i	0.124437	+	0.0718437i	−0.436490	+	0.899709i	$0.643778\pi$
$492$		0			0
$493$		−	20.4838i		−	0.922544i
$494$		0			0
$495$	1.41152	−	9.49112i	0.0634431	−	0.426594i
$496$		0			0
$497$	0.860489	−	30.9046i	0.0385982	−	1.38626i
$498$		0			0
$499$	32.0427			1.43443			0.717215	−	0.696852i	$-0.245417\pi$
$499$	32.0427			1.43443			0.717215	+	0.696852i	$0.245417\pi$
$500$		0			0
$501$	−28.2395	−	19.2128i	−1.26165	−	0.858364i
$502$		0			0
$503$	−11.6608			−0.519930			−0.259965	−	0.965618i	$-0.583711\pi$
$503$	−11.6608			−0.519930			−0.259965	+	0.965618i	$0.583711\pi$
$504$		0			0
$505$	17.3050			0.770061
$506$		0			0
$507$	−2.45327	+	1.18440i	−0.108954	+	0.0526010i
$508$		0			0
$509$	−26.8854			−1.19167			−0.595836	−	0.803106i	$-0.703179\pi$
$509$	−26.8854			−1.19167			−0.595836	+	0.803106i	$0.703179\pi$
$510$		0			0
$511$	−10.3028	−	6.33705i	−0.455769	−	0.280335i
$512$		0			0
$513$	12.2802	+	39.3995i	0.542185	+	1.73953i
$514$		0			0
$515$			8.23834i			0.363024i
$516$		0			0
$517$	−15.9255	−	9.19459i	−0.700402	−	0.404378i
$518$		0			0
$519$	−2.61701	−	1.78049i	−0.114874	−	0.0781549i
$520$		0			0
$521$	−17.0385	+	29.5116i	−0.746471	+	1.29293i	0.203033	+	0.979172i	$0.434920\pi$
$521$	−17.0385	+	29.5116i	−0.746471	+	1.29293i	−0.949504	+	0.313754i	$0.898413\pi$
$522$		0			0
$523$	4.71003	−	2.71933i	0.205955	−	0.118908i	−0.393475	−	0.919335i	$-0.628727\pi$
$523$	4.71003	−	2.71933i	0.205955	−	0.118908i	0.599430	+	0.800427i	$0.295394\pi$
$524$		0			0
$525$	−0.109051	+	1.06906i	−0.00475938	+	0.0466575i
$526$		0			0
$527$			1.86831i			0.0813850i
$528$		0			0
$529$	6.92280			0.300991
$530$		0			0
$531$	−14.7964	−	37.4843i	−0.642111	−	1.62668i
$532$		0			0
$533$	21.9080	−	12.6486i	0.948940	−	0.547871i
$534$		0			0
$535$	15.0243	−	8.67429i	0.649558	−	0.375022i
$536$		0			0
$537$	−13.6332	+	20.0384i	−0.588316	+	0.864722i
$538$		0			0
$539$	−0.570698	+	10.2404i	−0.0245817	+	0.441085i
$540$		0			0
$541$	11.8329	+	20.4952i	0.508737	+	0.881158i	0.999949	+	0.0101183i	$0.00322080\pi$
$541$	11.8329	+	20.4952i	0.508737	+	0.881158i	−0.491212	+	0.871040i	$0.663446\pi$
$542$		0			0
$543$	28.2582	+	2.08979i	1.21268	+	0.0896815i
$544$		0			0
$545$	1.10273	−	1.90998i	0.0472356	−	0.0818145i
$546$		0			0
$547$	−12.0824	−	20.9273i	−0.516606	−	0.894788i	−0.999814	−	0.0192822i	$-0.993862\pi$
$547$	−12.0824	−	20.9273i	−0.516606	−	0.894788i	0.483208	−	0.875505i	$-0.339471\pi$
$548$		0			0
$549$	−18.3115	−	14.5443i	−0.781518	−	0.620735i
$550$		0			0
$551$	−30.7803	+	53.3130i	−1.31128	+	2.27121i
$552$		0			0
$553$	−13.0072	+	21.1471i	−0.553122	+	0.899266i
$554$		0			0
$555$	9.65243	−	4.66003i	0.409723	−	0.197807i
$556$		0			0
$557$	7.36315	+	4.25111i	0.311987	+	0.180126i	0.647815	−	0.761798i	$-0.275683\pi$
$557$	7.36315	+	4.25111i	0.311987	+	0.180126i	−0.335829	+	0.941923i	$0.609016\pi$
$558$		0			0
$559$			8.59381i			0.363480i
$560$		0			0
$561$	−3.77253	+	5.54496i	−0.159276	+	0.234108i
$562$		0			0
$563$	0.473776	+	0.820605i	0.0199673	+	0.0345844i	0.875836	−	0.482608i	$-0.160310\pi$
$563$	0.473776	+	0.820605i	0.0199673	+	0.0345844i	−0.855869	+	0.517192i	$0.826977\pi$
$564$		0			0
$565$	−23.0430	−	13.3039i	−0.969427	−	0.559699i
$566$		0			0
$567$	22.5795	+	7.56069i	0.948252	+	0.317519i
$568$		0			0
$569$	−15.7859	−	9.11401i	−0.661781	−	0.382079i	0.131175	−	0.991359i	$-0.458125\pi$
$569$	−15.7859	−	9.11401i	−0.661781	−	0.382079i	−0.792955	+	0.609280i	$0.791458\pi$
$570$		0			0
$571$	6.12121	+	10.6023i	0.256165	+	0.443691i	0.965211	−	0.261471i	$-0.0842077\pi$
$571$	6.12121	+	10.6023i	0.256165	+	0.443691i	−0.709046	+	0.705162i	$0.750874\pi$
$572$		0			0
$573$	−13.3118	+	19.5661i	−0.556110	+	0.817385i
$574$		0			0
$575$			0.940253i			0.0392112i
$576$		0			0
$577$	−10.2500	−	5.91784i	−0.426713	−	0.246363i	0.271232	−	0.962514i	$-0.412569\pi$
$577$	−10.2500	−	5.91784i	−0.426713	−	0.246363i	−0.697945	+	0.716151i	$0.745902\pi$
$578$		0			0
$579$	6.82827	−	3.29657i	0.283773	−	0.137001i
$580$		0			0
$581$	−4.30054	−	7.95199i	−0.178416	−	0.329904i
$582$		0			0
$583$	−2.04439	+	3.54098i	−0.0846699	+	0.146653i
$584$		0			0
$585$	17.3355	+	13.7690i	0.716734	+	0.569280i
$586$		0			0
$587$	−3.57681	−	6.19521i	−0.147631	−	0.255704i	0.782721	−	0.622373i	$-0.213831\pi$
$587$	−3.57681	−	6.19521i	−0.147631	−	0.255704i	−0.930351	+	0.366669i	$0.880498\pi$
$588$		0			0
$589$	2.80745	−	4.86264i	0.115679	−	0.200362i
$590$		0			0
$591$	1.73775	+	0.128513i	0.0714815	+	0.00528630i
$592$		0			0
$593$	−13.4811	−	23.3500i	−0.553603	−	0.958869i	−0.998011	−	0.0630442i	$-0.979919\pi$
$593$	−13.4811	−	23.3500i	−0.553603	−	0.958869i	0.444408	−	0.895825i	$-0.353414\pi$
$594$		0			0
$595$	−7.99668	+	13.0010i	−0.327832	+	0.532990i
$596$		0			0
$597$	−6.38604	+	9.38637i	−0.261363	+	0.384158i
$598$		0			0
$599$	−30.5223	+	17.6221i	−1.24711	+	0.720018i	−0.970532	−	0.240974i	$-0.922533\pi$
$599$	−30.5223	+	17.6221i	−1.24711	+	0.720018i	−0.276576	+	0.960992i	$0.589200\pi$
$600$		0			0
$601$	−3.39266	+	1.95875i	−0.138389	+	0.0798991i	−0.567596	−	0.823307i	$-0.692126\pi$
$601$	−3.39266	+	1.95875i	−0.138389	+	0.0798991i	0.429207	+	0.903206i	$0.358793\pi$
$602$		0			0
$603$	6.43340	+	16.2979i	0.261988	+	0.663704i
$604$		0			0
$605$	19.3266			0.785740
$606$		0			0
$607$			14.4772i			0.587613i	0.955865	+	0.293807i	$0.0949222\pi$
$607$			14.4772i			0.587613i	−0.955865	+	0.293807i	$0.905078\pi$
$608$		0			0
$609$	14.5466	+	32.4045i	0.589457	+	1.31310i
$610$		0			0
$611$	36.7426	−	21.2134i	1.48645	−	0.858201i
$612$		0			0
$613$	−6.51761	+	11.2888i	−0.263244	+	0.455952i	−0.967102	−	0.254389i	$-0.918126\pi$
$613$	−6.51761	+	11.2888i	−0.263244	+	0.455952i	0.703858	+	0.710341i	$0.251459\pi$
$614$		0			0
$615$	23.3944	+	15.9165i	0.943355	+	0.641814i
$616$		0			0
$617$	−3.14491	−	1.81571i	−0.126609	−	0.0730979i	0.435358	−	0.900258i	$-0.356622\pi$
$617$	−3.14491	−	1.81571i	−0.126609	−	0.0730979i	−0.561967	+	0.827160i	$0.689955\pi$
$618$		0			0
$619$		−	16.4818i		−	0.662460i	−0.943550	−	0.331230i	$-0.892536\pi$
$619$		−	16.4818i		−	0.662460i	0.943550	−	0.331230i	$-0.107464\pi$
$620$		0			0
$621$	20.3259	+	4.57637i	0.815649	+	0.183643i
$622$		0			0
$623$	−11.6278	−	21.5006i	−0.465858	−	0.861403i
$624$		0			0
$625$	−23.7725			−0.950901
$626$		0			0
$627$	18.1509	−	8.76296i	0.724878	−	0.349959i
$628$		0			0
$629$	−7.49147			−0.298704
$630$		0			0
$631$	−34.8383			−1.38689			−0.693446	−	0.720508i	$-0.743909\pi$
$631$	−34.8383			−1.38689			−0.693446	+	0.720508i	$0.743909\pi$
$632$		0			0
$633$	26.0976	+	17.7556i	1.03729	+	0.705721i
$634$		0			0
$635$	14.8302			0.588520
$636$		0			0
$637$	−19.8026	−	12.9534i	−0.784606	−	0.513232i
$638$		0			0
$639$	−5.15683	+	34.6747i	−0.204001	+	1.37171i
$640$		0			0
$641$		−	8.37779i		−	0.330903i	−0.986218	−	0.165451i	$-0.947092\pi$
$641$		−	8.37779i		−	0.330903i	0.986218	−	0.165451i	$-0.0529081\pi$
$642$		0			0
$643$	18.0021	+	10.3935i	0.709934	+	0.409881i	0.811037	−	0.584995i	$-0.198904\pi$
$643$	18.0021	+	10.3935i	0.709934	+	0.409881i	−0.101103	+	0.994876i	$0.532237\pi$
$644$		0			0
$645$	−8.65637	+	4.17915i	−0.340844	+	0.164554i
$646$		0			0
$647$	−4.74770	+	8.22325i	−0.186651	+	0.323289i	−0.944132	−	0.329568i	$-0.893097\pi$
$647$	−4.74770	+	8.22325i	−0.186651	+	0.323289i	0.757480	+	0.652858i	$0.226430\pi$
$648$		0			0
$649$	−17.0450	+	9.84091i	−0.669073	+	0.386290i
$650$		0			0
$651$	−1.32678	−	2.95559i	−0.0520007	−	0.115839i
$652$		0			0
$653$		−	7.67583i		−	0.300379i	−0.988657	−	0.150189i	$-0.952012\pi$
$653$		−	7.67583i		−	0.300379i	0.988657	−	0.150189i	$-0.0479883\pi$
$654$		0			0
$655$	29.9853			1.17162
$656$		0			0
$657$	10.7397	+	8.53025i	0.418997	+	0.332797i
$658$		0			0
$659$	38.0493	−	21.9678i	1.48219	−	0.855743i	0.482395	−	0.875954i	$-0.339767\pi$
$659$	38.0493	−	21.9678i	1.48219	−	0.855743i	0.999796	+	0.0202102i	$0.00643354\pi$
$660$		0			0
$661$	−22.1649	+	12.7969i	−0.862115	+	0.497742i	−0.864720	−	0.502254i	$-0.832504\pi$
$661$	−22.1649	+	12.7969i	−0.862115	+	0.497742i	0.00260513	+	0.999997i	$0.499171\pi$
$662$		0			0
$663$	−6.72724	−	13.9343i	−0.261264	−	0.541162i
$664$		0			0
$665$	40.3490	−	21.8213i	1.56467	−	0.846193i
$666$		0			0
$667$	15.5395	+	26.9151i	0.601691	+	1.04216i
$668$		0			0
$669$	−7.57977	−	15.7002i	−0.293051	−	0.607003i
$670$		0			0
$671$	−5.71051	+	9.89089i	−0.220452	+	0.381834i
$672$		0			0
$673$	−7.64671	−	13.2445i	−0.294759	−	0.510538i	0.680170	−	0.733055i	$-0.261906\pi$
$673$	−7.64671	−	13.2445i	−0.294759	−	0.510538i	−0.974929	+	0.222517i	$0.928573\pi$
$674$		0			0
$675$	0.267642	−	1.18873i	0.0103016	−	0.0457543i
$676$		0			0
$677$	22.6459	−	39.2238i	0.870352	−	1.50749i	0.00871898	−	0.999962i	$-0.497225\pi$
$677$	22.6459	−	39.2238i	0.870352	−	1.50749i	0.861633	−	0.507532i	$-0.169442\pi$
$678$		0			0
$679$	−17.1552	+	9.27776i	−0.658356	+	0.356048i
$680$		0			0
$681$	2.54047	−	34.3523i	0.0973509	−	1.31638i
$682$		0			0
$683$	−24.0891	−	13.9079i	−0.921744	−	0.532169i	−0.0375529	−	0.999295i	$-0.511956\pi$
$683$	−24.0891	−	13.9079i	−0.921744	−	0.532169i	−0.884191	+	0.467126i	$0.845290\pi$
$684$		0			0
$685$		−	43.8674i		−	1.67609i
$686$		0			0
$687$	30.6869	+	2.26940i	1.17078	+	0.0865831i
$688$		0			0
$689$	−4.71672	−	8.16961i	−0.179693	−	0.311237i
$690$		0			0
$691$	14.1115	+	8.14729i	0.536828	+	0.309938i	0.743792	−	0.668411i	$-0.233025\pi$
$691$	14.1115	+	8.14729i	0.536828	+	0.309938i	−0.206965	+	0.978348i	$0.566359\pi$
$692$		0			0
$693$	2.03023	−	11.4510i	0.0771220	−	0.434986i
$694$		0			0
$695$	−18.5862	−	10.7307i	−0.705013	−	0.407040i
$696$		0			0
$697$	−9.88831	−	17.1271i	−0.374546	−	0.648733i
$698$		0			0
$699$	−12.0932	−	25.0490i	−0.457408	−	0.947439i
$700$		0			0
$701$		−	0.393403i		−	0.0148586i	−0.999972	−	0.00742932i	$-0.997635\pi$
$701$		−	0.393403i		−	0.0148586i	0.999972	−	0.00742932i	$-0.00236485\pi$
$702$		0			0
$703$	19.4980	+	11.2572i	0.735379	+	0.424572i
$704$		0			0
$705$	39.2356	+	26.6941i	1.47770	+	1.00536i
$706$		0			0
$707$	20.9651	+	0.583740i	0.788474	+	0.0219538i
$708$		0			0
$709$	16.3183	−	28.2641i	0.612846	−	1.06148i	−0.377912	−	0.925841i	$-0.623358\pi$
$709$	16.3183	−	28.2641i	0.612846	−	1.06148i	0.990758	−	0.135639i	$-0.0433087\pi$
$710$		0			0
$711$	17.5089	−	22.0440i	0.656633	−	0.826714i
$712$		0			0
$713$	−1.41734	−	2.45491i	−0.0530799	−	0.0919372i
$714$		0			0
$715$	5.40612	−	9.36368i	0.202178	−	0.350182i
$716$		0			0
$717$	−8.00020	+	11.7589i	−0.298773	+	0.439144i
$718$		0			0
$719$	−0.106604	−	0.184643i	−0.00397565	−	0.00688602i	0.864031	−	0.503439i	$-0.167932\pi$
$719$	−0.106604	−	0.184643i	−0.00397565	−	0.00688602i	−0.868006	+	0.496553i	$0.834599\pi$
$720$		0			0
$721$	−0.277900	+	9.98081i	−0.0103495	+	0.371705i
$722$		0			0
$723$	−49.1884	−	3.63765i	−1.82934	−	0.135286i
$724$		0			0
$725$	1.57409	−	0.908804i	0.0584604	−	0.0337521i
$726$		0			0
$727$	−31.8208	+	18.3717i	−1.18017	+	0.681370i	−0.956053	−	0.293193i	$-0.905282\pi$
$727$	−31.8208	+	18.3717i	−1.18017	+	0.681370i	−0.224114	+	0.974563i	$0.571949\pi$
$728$		0			0
$729$	−24.3947	−	11.5715i	−0.903507	−	0.428574i
$730$		0			0
$731$	6.71841			0.248489
$732$		0			0
$733$		−	10.8753i		−	0.401689i	−0.979623	−	0.200844i	$-0.935631\pi$
$733$		−	10.8753i		−	0.401689i	0.979623	−	0.200844i	$-0.0643685\pi$
$734$		0			0
$735$	3.41775	−	26.2459i	0.126065	−	0.968095i
$736$		0			0
$737$	7.41104	−	4.27877i	0.272989	−	0.157610i
$738$		0			0
$739$	6.91282	−	11.9734i	0.254292	−	0.440447i	−0.710411	−	0.703787i	$-0.751491\pi$
$739$	6.91282	−	11.9734i	0.254292	−	0.440447i	0.964703	+	0.263340i	$0.0848242\pi$
$740$		0			0
$741$	−3.42961	+	46.3753i	−0.125990	+	1.70364i
$742$		0			0
$743$	−15.8751	−	9.16552i	−0.582403	−	0.336250i	0.179685	−	0.983724i	$-0.442492\pi$
$743$	−15.8751	−	9.16552i	−0.582403	−	0.336250i	−0.762088	+	0.647474i	$0.775825\pi$
$744$		0			0
$745$			43.7373i			1.60241i
$746$		0			0
$747$	3.76377	+	9.53488i	0.137709	+	0.348863i
$748$		0			0
$749$	18.4947	−	10.0022i	0.675781	−	0.365471i
$750$		0			0
$751$	−19.9417			−0.727682			−0.363841	−	0.931461i	$-0.618535\pi$
$751$	−19.9417			−0.727682			−0.363841	+	0.931461i	$0.618535\pi$
$752$		0			0
$753$	−0.0838426	+	1.13372i	−0.00305540	+	0.0413152i
$754$		0			0
$755$	−48.5362			−1.76641
$756$		0			0
$757$	−46.9292			−1.70567			−0.852836	−	0.522178i	$-0.825119\pi$
$757$	−46.9292			−1.70567			−0.852836	+	0.522178i	$0.825119\pi$
$758$		0			0
$759$	0.750467	−	10.1478i	0.0272402	−	0.368343i
$760$		0			0
$761$	53.5538			1.94132			0.970661	−	0.240452i	$-0.0772956\pi$
$761$	53.5538			1.94132			0.970661	+	0.240452i	$0.0772956\pi$
$762$		0			0
$763$	1.40039	−	2.27676i	0.0506976	−	0.0824242i
$764$		0			0
$765$	10.7643	−	13.5524i	0.389183	−	0.489988i
$766$		0			0
$767$		−	45.4091i		−	1.63963i
$768$		0			0
$769$	34.7306	+	20.0517i	1.25242	+	0.723085i	0.971589	−	0.236673i	$-0.0760570\pi$
$769$	34.7306	+	20.0517i	1.25242	+	0.723085i	0.280830	+	0.959758i	$0.409390\pi$
$770$		0			0
$771$	−0.976058	+	13.1983i	−0.0351519	+	0.475325i
$772$		0			0
$773$	7.82375	−	13.5511i	0.281401	−	0.487400i	−0.690329	−	0.723495i	$-0.742534\pi$
$773$	7.82375	−	13.5511i	0.281401	−	0.487400i	0.971730	+	0.236095i	$0.0758677\pi$
$774$		0			0
$775$	−0.143572	+	0.0828913i	−0.00515726	+	0.00297755i
$776$		0			0
$777$	11.8512	−	5.32007i	0.425159	−	0.190856i
$778$		0			0
$779$			59.4352i			2.12949i
$780$		0			0
$781$	17.1212			0.612645
$782$		0			0
$783$	−11.9847	−	38.4512i	−0.428297	−	1.37413i
$784$		0			0
$785$	15.1785	−	8.76333i	0.541745	−	0.312777i
$786$		0			0
$787$	−39.9920	+	23.0894i	−1.42556	+	0.823048i	−0.996766	−	0.0803536i	$-0.974395\pi$
$787$	−39.9920	+	23.0894i	−1.42556	+	0.823048i	−0.428795	+	0.903402i	$0.641062\pi$
$788$		0			0
$789$	11.4465	+	0.846508i	0.407506	+	0.0301365i
$790$		0			0
$791$	−27.4680	−	16.8951i	−0.976651	−	0.600720i
$792$		0			0
$793$	−13.1750	−	22.8198i	−0.467859	−	0.810356i
$794$		0			0
$795$	5.93534	−	8.72392i	0.210505	−	0.309406i
$796$		0			0
$797$	16.9388	−	29.3388i	0.600002	−	1.03923i	−0.392818	−	0.919616i	$-0.628500\pi$
$797$	16.9388	−	29.3388i	0.600002	−	1.03923i	0.992820	−	0.119618i	$-0.0381669\pi$
$798$		0			0
$799$	−16.5840	−	28.7244i	−0.586701	−	1.01620i
$800$		0			0
$801$	10.1765	+	25.7804i	0.359568	+	0.910906i
$802$		0			0
$803$	3.34922	−	5.80102i	0.118191	−	0.204714i
$804$		0			0
$805$	0.644559	−	23.1494i	0.0227177	−	0.815910i
$806$		0			0
$807$	12.5546	+	8.54158i	0.441944	+	0.300678i
$808$		0			0
$809$	33.7873	+	19.5071i	1.18790	+	0.685834i	0.957829	−	0.287340i	$-0.0927711\pi$
$809$	33.7873	+	19.5071i	1.18790	+	0.685834i	0.230070	+	0.973174i	$0.426104\pi$
$810$		0			0
$811$			7.73397i			0.271577i	0.990738	+	0.135788i	$0.0433567\pi$
$811$			7.73397i			0.271577i	−0.990738	+	0.135788i	$0.956643\pi$
$812$		0			0
$813$	−12.4002	−	25.6849i	−0.434895	−	0.900807i
$814$		0			0
$815$	−13.5915	−	23.5411i	−0.476088	−	0.824609i
$816$		0			0
$817$	−17.4859	−	10.0955i	−0.611755	−	0.353197i
$818$		0			0
$819$	20.5376	+	17.2661i	0.717643	+	0.603326i
$820$		0			0
$821$	−0.443638	−	0.256134i	−0.0154831	−	0.00893915i	0.492238	−	0.870460i	$-0.336179\pi$
$821$	−0.443638	−	0.256134i	−0.0154831	−	0.00893915i	−0.507722	+	0.861521i	$0.669512\pi$
$822$		0			0
$823$	24.1753	+	41.8728i	0.842698	+	1.45960i	0.887606	+	0.460604i	$0.152367\pi$
$823$	24.1753	+	41.8728i	0.842698	+	1.45960i	−0.0449080	+	0.998991i	$0.514299\pi$
$824$		0			0
$825$	−0.593482	−	0.0438900i	−0.0206624	−	0.00152805i
$826$		0			0
$827$		−	17.3086i		−	0.601879i	−0.953643	−	0.300940i	$-0.902700\pi$
$827$		−	17.3086i		−	0.601879i	0.953643	−	0.300940i	$-0.0973003\pi$
$828$		0			0
$829$	33.0205	+	19.0644i	1.14685	+	0.662134i	0.948118	−	0.317919i	$-0.102984\pi$
$829$	33.0205	+	19.0644i	1.14685	+	0.662134i	0.198733	+	0.980054i	$0.436317\pi$
$830$		0			0
$831$	−2.27057	+	30.7027i	−0.0787652	+	1.06507i
$832$		0			0
$833$	−10.1266	+	15.4811i	−0.350866	+	0.536388i
$834$		0			0
$835$	21.5241	−	37.2808i	0.744871	−	1.29015i
$836$		0			0
$837$	1.09311	+	3.50711i	0.0377835	+	0.121223i
$838$		0			0
$839$	15.2026	+	26.3317i	0.524852	+	0.909071i	0.999581	+	0.0289389i	$0.00921281\pi$
$839$	15.2026	+	26.3317i	0.524852	+	0.909071i	−0.474729	+	0.880132i	$0.657454\pi$
$840$		0			0
$841$	15.5394	−	26.9151i	0.535842	−	0.928106i
$842$		0			0
$843$	12.1954	+	25.2607i	0.420033	+	0.870024i
$844$		0			0
$845$	−1.71674	−	2.97348i	−0.0590577	−	0.102291i
$846$		0			0
$847$	23.4144	+	0.651937i	0.804528	+	0.0224008i
$848$		0			0
$849$	−21.3659	−	44.2557i	−0.733276	−	1.51885i
$850$		0			0
$851$	9.84358	−	5.68319i	0.337434	−	0.194817i
$852$		0			0
$853$	−27.7143	+	16.0008i	−0.948919	+	0.547858i	−0.892745	−	0.450563i	$-0.851223\pi$
$853$	−27.7143	+	16.0008i	−0.948919	+	0.547858i	−0.0561738	+	0.998421i	$0.517890\pi$
$854$		0			0
$855$	−48.3807	+	19.0976i	−1.65459	+	0.653126i
$856$		0			0
$857$	−45.1549			−1.54246			−0.771230	−	0.636556i	$-0.780358\pi$
$857$	−45.1549			−1.54246			−0.771230	+	0.636556i	$0.780358\pi$
$858$		0			0
$859$			18.2340i			0.622137i	0.950388	+	0.311068i	$0.100687\pi$
$859$			18.2340i			0.622137i	−0.950388	+	0.311068i	$0.899313\pi$
$860$		0			0
$861$	27.8057	+	20.0721i	0.947614	+	0.684055i
$862$		0			0
$863$	6.61966	−	3.82186i	0.225336	−	0.130098i	−0.383083	−	0.923714i	$-0.625138\pi$
$863$	6.61966	−	3.82186i	0.225336	−	0.130098i	0.608419	+	0.793616i	$0.291804\pi$
$864$		0			0
$865$	1.99468	−	3.45489i	0.0678213	−	0.117470i
$866$		0			0
$867$	15.6229	−	7.54249i	0.530583	−	0.256157i
$868$		0			0
$869$	−11.9069	−	6.87448i	−0.403915	−	0.233201i
$870$		0			0
$871$			19.7436i			0.668985i
$872$		0			0
$873$	20.5700	−	8.11975i	0.696190	−	0.274812i
$874$		0			0
$875$	−30.2211	−	0.841458i	−1.02166	−	0.0284465i
$876$		0			0
$877$	16.0316			0.541350			0.270675	−	0.962671i	$-0.412753\pi$
$877$	16.0316			0.541350			0.270675	+	0.962671i	$0.412753\pi$
$878$		0			0
$879$	−12.5521	−	8.53988i	−0.423373	−	0.288043i
$880$		0			0
$881$	−24.7532			−0.833958			−0.416979	−	0.908916i	$-0.636911\pi$
$881$	−24.7532			−0.833958			−0.416979	+	0.908916i	$0.636911\pi$
$882$		0			0
$883$	−11.6958			−0.393595			−0.196798	−	0.980444i	$-0.563054\pi$
$883$	−11.6958			−0.393595			−0.196798	+	0.980444i	$0.563054\pi$
$884$		0			0
$885$	45.7396	−	22.0823i	1.53752	−	0.742289i
$886$		0			0
$887$	55.0859			1.84960			0.924801	−	0.380451i	$-0.124231\pi$
$887$	55.0859			1.84960			0.924801	+	0.380451i	$0.124231\pi$
$888$		0			0
$889$	17.9669	+	0.500261i	0.602592	+	0.0167782i
$890$		0			0
$891$	−3.83737	+	12.6160i	−0.128557	+	0.422651i
$892$		0			0
$893$			99.6808i			3.33569i
$894$		0			0
$895$	−26.4541	−	15.2733i	−0.884262	−	0.510529i
$896$		0			0
$897$	19.4102	+	13.2058i	0.648089	+	0.440929i
$898$		0			0
$899$	−2.73987	+	4.74560i	−0.0913799	+	0.158275i
$900$		0			0
$901$	−6.38677	+	3.68741i	−0.212774	+	0.122845i
$902$		0			0
$903$	−10.6282	+	4.77108i	−0.353686	+	0.158771i
$904$		0			0
$905$			35.7127i			1.18713i
$906$		0			0
$907$	−25.8767			−0.859220			−0.429610	−	0.903014i	$-0.641349\pi$
$907$	−25.8767			−0.859220			−0.429610	+	0.903014i	$0.641349\pi$
$908$		0			0
$909$	−23.5227	−	3.49830i	−0.780199	−	0.116031i
$910$		0			0
$911$	−3.86306	+	2.23034i	−0.127989	+	0.0738944i	−0.562627	−	0.826711i	$-0.690209\pi$
$911$	−3.86306	+	2.23034i	−0.127989	+	0.0738944i	0.434639	+	0.900605i	$0.356876\pi$
$912$		0			0
$913$	4.33572	−	2.50323i	0.143491	−	0.0828448i
$914$		0			0
$915$	16.5790	−	24.3682i	0.548083	−	0.805587i
$916$		0			0
$917$	36.3274	+	1.01148i	1.19964	+	0.0334020i
$918$		0			0
$919$	−21.2352	−	36.7805i	−0.700485	−	1.21328i	−0.968296	−	0.249804i	$-0.919634\pi$
$919$	−21.2352	−	36.7805i	−0.700485	−	1.21328i	0.267811	−	0.963471i	$-0.413700\pi$
$920$		0			0
$921$	−22.1958	−	1.64145i	−0.731375	−	0.0540877i
$922$		0			0
$923$	−19.7507	+	34.2091i	−0.650101	+	1.12601i
$924$		0			0
$925$	−0.332373	−	0.575688i	−0.0109284	−	0.0189285i
$926$		0			0
$927$	1.66543	−	11.1984i	0.0546998	−	0.367804i
$928$		0			0
$929$	−7.72508	+	13.3802i	−0.253452	+	0.438991i	−0.964474	−	0.264178i	$-0.914899\pi$
$929$	−7.72508	+	13.3802i	−0.253452	+	0.438991i	0.711022	+	0.703170i	$0.248233\pi$
$930$		0			0
$931$	49.6193	−	25.0756i	1.62621	−	0.821819i
$932$		0			0
$933$	−10.2843	+	4.96511i	−0.336694	+	0.162550i
$934$		0			0
$935$	−7.32027	−	4.22636i	−0.239398	−	0.138217i
$936$		0			0
$937$			46.1410i			1.50736i	0.657241	+	0.753680i	$0.271723\pi$
$937$			46.1410i			1.50736i	−0.657241	+	0.753680i	$0.728277\pi$
$938$		0			0
$939$	−3.32681	+	4.88983i	−0.108566	+	0.159574i
$940$		0			0
$941$	−20.5052	−	35.5161i	−0.668451	−	1.15779i	−0.978337	−	0.207017i	$-0.933624\pi$
$941$	−20.5052	−	35.5161i	−0.668451	−	1.15779i	0.309886	−	0.950774i	$-0.399709\pi$
$942$		0			0
$943$	25.9859	+	15.0030i	0.846218	+	0.488564i
$944$		0			0
$945$	−7.40437	+	29.0836i	−0.240864	+	0.946089i
$946$		0			0
$947$	−8.50657	−	4.91127i	−0.276426	−	0.159595i	0.355378	−	0.934723i	$-0.384352\pi$
$947$	−8.50657	−	4.91127i	−0.276426	−	0.159595i	−0.631804	+	0.775128i	$0.717685\pi$
$948$		0			0
$949$	7.72718	+	13.3839i	0.250835	+	0.434459i
$950$		0			0
$951$	−31.2758	+	45.9700i	−1.01419	+	1.49068i
$952$		0			0
$953$		−	17.0826i		−	0.553359i	−0.960962	−	0.276679i	$-0.910766\pi$
$953$		−	17.0826i		−	0.553359i	0.960962	−	0.276679i	$-0.0892340\pi$
$954$		0			0
$955$	−25.8305	−	14.9132i	−0.835855	−	0.482581i
$956$		0			0
$957$	−17.7141	+	8.55205i	−0.572614	+	0.276449i
$958$		0			0
$959$	1.47976	−	53.1458i	0.0477840	−	1.71617i
$960$		0			0
$961$	−15.2501	+	26.4139i	−0.491939	+	0.852063i
$962$		0			0
$963$	−22.1762	+	8.75374i	−0.714617	+	0.282085i
$964$		0			0
$965$	4.77826	+	8.27619i	0.153818	+	0.266420i
$966$		0			0
$967$	21.3240	−	36.9343i	0.685735	−	1.18773i	−0.287471	−	0.957789i	$-0.592814\pi$
$967$	21.3240	−	36.9343i	0.685735	−	1.18773i	0.973205	−	0.229938i	$-0.0738523\pi$
$968$		0			0
$969$	36.2550	+	2.68118i	1.16468	+	0.0861318i
$970$		0			0
$971$	−11.7562	−	20.3623i	−0.377275	−	0.653459i	0.613390	−	0.789780i	$-0.289805\pi$
$971$	−11.7562	−	20.3623i	−0.377275	−	0.653459i	−0.990665	+	0.136321i	$0.956472\pi$
$972$		0			0
$973$	−22.1553	−	13.6273i	−0.710267	−	0.436872i
$974$		0			0
$975$	0.772323	−	1.13518i	0.0247341	−	0.0363549i
$976$		0			0
$977$	−30.1944	+	17.4327i	−0.966003	+	0.557722i	−0.898015	−	0.439964i	$-0.854991\pi$
$977$	−30.1944	+	17.4327i	−0.966003	+	0.557722i	−0.0679878	+	0.997686i	$0.521658\pi$
$978$		0			0
$979$	11.7229	−	6.76824i	0.374666	−	0.216314i
$980$		0			0
$981$	−1.88505	+	2.37332i	−0.0601851	+	0.0757742i
$982$		0			0
$983$	−26.3608			−0.840780			−0.420390	−	0.907343i	$-0.638107\pi$
$983$	−26.3608			−0.840780			−0.420390	+	0.907343i	$0.638107\pi$
$984$		0			0
$985$			2.19617i			0.0699757i
$986$		0			0
$987$	46.6338	+	33.6636i	1.48437	+	1.07152i
$988$		0			0
$989$	−8.82780	+	5.09673i	−0.280708	+	0.162067i
$990$		0			0
$991$	0.0805213	−	0.139467i	0.00255784	−	0.00443031i	−0.864744	−	0.502214i	$-0.832519\pi$
$991$	0.0805213	−	0.139467i	0.00255784	−	0.00443031i	0.867301	+	0.497783i	$0.165852\pi$
$992$		0			0
$993$	−41.3621	−	28.1408i	−1.31259	−	0.893022i
$994$		0			0
$995$	−12.3916	−	7.15427i	−0.392839	−	0.226806i
$996$		0			0
$997$			16.8378i			0.533259i	0.963799	+	0.266629i	$0.0859100\pi$
$997$			16.8378i			0.533259i	−0.963799	+	0.266629i	$0.914090\pi$
$998$		0			0
$999$	−14.0626	+	4.38310i	−0.444922	+	0.138675i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bm.a.185.4	yes	16
3.2	odd	2		756.2.bm.a.17.3		16
4.3	odd	2		1008.2.df.d.689.5		16
7.2	even	3		1764.2.w.b.509.7		16
7.3	odd	6		1764.2.x.a.293.7		16
7.4	even	3		1764.2.x.b.293.2		16
7.5	odd	6		252.2.w.a.5.2	✓	16
7.6	odd	2		1764.2.bm.a.1697.5		16
9.2	odd	6		252.2.w.a.101.2	yes	16
9.4	even	3		2268.2.t.a.1781.3		16
9.5	odd	6		2268.2.t.b.1781.6		16
9.7	even	3		756.2.w.a.521.3		16
12.11	even	2		3024.2.df.d.17.3		16
21.2	odd	6		5292.2.w.b.1097.6		16
21.5	even	6		756.2.w.a.341.3		16
21.11	odd	6		5292.2.x.b.881.6		16
21.17	even	6		5292.2.x.a.881.3		16
21.20	even	2		5292.2.bm.a.2285.6		16
28.19	even	6		1008.2.ca.d.257.7		16
36.7	odd	6		3024.2.ca.d.2033.3		16
36.11	even	6		1008.2.ca.d.353.7		16
63.2	odd	6		1764.2.bm.a.1685.5		16
63.5	even	6		2268.2.t.a.2105.3		16
63.11	odd	6		1764.2.x.a.1469.7		16
63.16	even	3		5292.2.bm.a.4625.6		16
63.20	even	6		1764.2.w.b.1109.7		16
63.25	even	3		5292.2.x.a.4409.3		16
63.34	odd	6		5292.2.w.b.521.6		16
63.38	even	6		1764.2.x.b.1469.2		16
63.40	odd	6		2268.2.t.b.2105.6		16
63.47	even	6	inner	252.2.bm.a.173.4	yes	16
63.52	odd	6		5292.2.x.b.4409.6		16
63.61	odd	6		756.2.bm.a.89.3		16
84.47	odd	6		3024.2.ca.d.2609.3		16
252.47	odd	6		1008.2.df.d.929.5		16
252.187	even	6		3024.2.df.d.1601.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.2	✓	16	7.5	odd	6
252.2.w.a.101.2	yes	16	9.2	odd	6
252.2.bm.a.173.4	yes	16	63.47	even	6	inner
252.2.bm.a.185.4	yes	16	1.1	even	1	trivial
756.2.w.a.341.3		16	21.5	even	6
756.2.w.a.521.3		16	9.7	even	3
756.2.bm.a.17.3		16	3.2	odd	2
756.2.bm.a.89.3		16	63.61	odd	6
1008.2.ca.d.257.7		16	28.19	even	6
1008.2.ca.d.353.7		16	36.11	even	6
1008.2.df.d.689.5		16	4.3	odd	2
1008.2.df.d.929.5		16	252.47	odd	6
1764.2.w.b.509.7		16	7.2	even	3
1764.2.w.b.1109.7		16	63.20	even	6
1764.2.x.a.293.7		16	7.3	odd	6
1764.2.x.a.1469.7		16	63.11	odd	6
1764.2.x.b.293.2		16	7.4	even	3
1764.2.x.b.1469.2		16	63.38	even	6
1764.2.bm.a.1685.5		16	63.2	odd	6
1764.2.bm.a.1697.5		16	7.6	odd	2
2268.2.t.a.1781.3		16	9.4	even	3
2268.2.t.a.2105.3		16	63.5	even	6
2268.2.t.b.1781.6		16	9.5	odd	6
2268.2.t.b.2105.6		16	63.40	odd	6
3024.2.ca.d.2033.3		16	36.7	odd	6
3024.2.ca.d.2609.3		16	84.47	odd	6
3024.2.df.d.17.3		16	12.11	even	2
3024.2.df.d.1601.3		16	252.187	even	6
5292.2.w.b.521.6		16	63.34	odd	6
5292.2.w.b.1097.6		16	21.2	odd	6
5292.2.x.a.881.3		16	21.17	even	6
5292.2.x.a.4409.3		16	63.25	even	3
5292.2.x.b.881.6		16	21.11	odd	6
5292.2.x.b.4409.6		16	63.52	odd	6
5292.2.bm.a.2285.6		16	21.20	even	2
5292.2.bm.a.4625.6		16	63.16	even	3

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.127742 - 1.72733i) q^{3} +2.18300 q^{5} +(2.64473 + 0.0736382i) q^{7} +(-2.96736 - 0.441307i) q^{9} +O(q^{10})\)	\(q+(0.127742 - 1.72733i) q^{3} +2.18300 q^{5} +(2.64473 + 0.0736382i) q^{7} +(-2.96736 - 0.441307i) q^{9} +1.46518i q^{11} +(-2.92752 - 1.69021i) q^{13} +(0.278862 - 3.77077i) q^{15} +(-1.32136 + 2.28866i) q^{17} +(6.87816 - 3.97111i) q^{19} +(0.465041 - 4.55892i) q^{21} -4.00964i q^{23} -0.234498 q^{25} +(-1.14134 + 5.06925i) q^{27} +(-6.71261 + 3.87553i) q^{29} +(0.612252 - 0.353484i) q^{31} +(2.53086 + 0.187166i) q^{33} +(5.77345 + 0.160752i) q^{35} +(1.41738 + 2.45498i) q^{37} +(-3.29352 + 4.84090i) q^{39} +(-3.74173 + 6.48086i) q^{41} +(-1.27112 - 2.20164i) q^{43} +(-6.47776 - 0.963374i) q^{45} +(-6.27538 + 10.8693i) q^{47} +(6.98915 + 0.389506i) q^{49} +(3.78448 + 2.57478i) q^{51} +(2.41675 + 1.39531i) q^{53} +3.19850i q^{55} +(-5.98079 - 12.3881i) q^{57} +(6.71650 + 11.6333i) q^{59} +(6.75061 + 3.89747i) q^{61} +(-7.81537 - 1.38565i) q^{63} +(-6.39079 - 3.68972i) q^{65} +(-2.92029 - 5.05809i) q^{67} +(-6.92598 - 0.512200i) q^{69} -11.6854i q^{71} +(-3.95924 - 2.28587i) q^{73} +(-0.0299553 + 0.405056i) q^{75} +(-0.107894 + 3.87501i) q^{77} +(-4.69189 + 8.12659i) q^{79} +(8.61050 + 2.61904i) q^{81} +(-1.70847 - 2.95917i) q^{83} +(-2.88452 + 4.99614i) q^{85} +(5.83685 + 12.0900i) q^{87} +(-4.61937 - 8.00099i) q^{89} +(-7.61803 - 4.68571i) q^{91} +(-0.532375 - 1.10272i) q^{93} +(15.0150 - 8.66894i) q^{95} +(-6.38394 + 3.68577i) q^{97} +(0.646596 - 4.34773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7}+O(q^{10}) \) 16 * q - q^7	\( 16 q - q^{7} + 3 q^{13} - 3 q^{15} - 9 q^{17} + 16 q^{25} - 9 q^{27} + 6 q^{29} + 6 q^{31} - 27 q^{33} + 15 q^{35} + q^{37} - 3 q^{39} + 6 q^{41} - 2 q^{43} - 15 q^{45} - 18 q^{47} + 13 q^{49} + 15 q^{51} + 15 q^{57} - 15 q^{59} + 3 q^{61} - 9 q^{63} - 39 q^{65} - 7 q^{67} - 21 q^{69} - 15 q^{75} - 45 q^{77} - q^{79} + 6 q^{85} - 3 q^{87} - 21 q^{89} + 9 q^{91} - 69 q^{93} + 6 q^{95} + 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q - q^7 + 3 * q^13 - 3 * q^15 - 9 * q^17 + 16 * q^25 - 9 * q^27 + 6 * q^29 + 6 * q^31 - 27 * q^33 + 15 * q^35 + q^37 - 3 * q^39 + 6 * q^41 - 2 * q^43 - 15 * q^45 - 18 * q^47 + 13 * q^49 + 15 * q^51 + 15 * q^57 - 15 * q^59 + 3 * q^61 - 9 * q^63 - 39 * q^65 - 7 * q^67 - 21 * q^69 - 15 * q^75 - 45 * q^77 - q^79 + 6 * q^85 - 3 * q^87 - 21 * q^89 + 9 * q^91 - 69 * q^93 + 6 * q^95 + 3 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more