LMFDB - Embedded newform 1008.2.df.d.689.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(689,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1008.689");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.df (of order $6$, degree $2$, not 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:	$8.04892052375$
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:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			689.5
Root			$-1.61108 - 0.635951i$ of defining polynomial
Character	$\chi$	$=$	1008.689
Dual form			1008.2.df.d.929.5

$q$-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 $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−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	$-0.929106\pi$
$11$		−	1.46518i		−	0.441770i	0.975300	−	0.220885i	$-0.0708945\pi$
$12$		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	$0.698048\pi$
$19$	−6.87816	+	3.97111i	−1.57796	+	0.911034i	−0.995144	+	0.0984279i	$0.968619\pi$
$20$		0			0
$21$	0.465041	−	4.55892i	0.101480	−	0.994838i
$22$		0			0
$23$			4.00964i			0.836068i	0.908431	+	0.418034i	$0.137281\pi$
$23$			4.00964i			0.836068i	−0.908431	+	0.418034i	$0.862719\pi$
$24$		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	−0.553973	−	0.832534i	$-0.686889\pi$
$31$	−0.612252	+	0.353484i	−0.109964	+	0.0634876i	0.444009	+	0.896022i	$0.353556\pi$
$32$		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	0.946521	−	0.322642i	$-0.104571\pi$
$43$	1.27112	+	2.20164i	0.193844	+	0.335748i	−0.752677	+	0.658390i	$0.771238\pi$
$44$		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	$-0.465241\pi$
$47$	6.27538	−	10.8693i	0.915358	−	1.58545i	0.806376	−	0.591403i	$-0.201426\pi$
$48$		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	$-0.827913\pi$
$59$	−6.71650	−	11.6333i	−0.874414	−	1.51453i	−0.0170287	−	0.999855i	$-0.505421\pi$
$60$		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	0.987419	−	0.158124i	$-0.0505445\pi$
$67$	2.92029	+	5.05809i	0.356770	+	0.617945i	−0.630649	+	0.776068i	$0.717211\pi$
$68$		0			0
$69$	−6.92598	−	0.512200i	−0.833791	−	0.0616616i
$70$		0			0
$71$			11.6854i			1.38680i	0.720554	+	0.693398i	$0.243887\pi$
$71$			11.6854i			1.38680i	−0.720554	+	0.693398i	$0.756113\pi$
$72$		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	$-0.656321\pi$
$79$	4.69189	−	8.12659i	0.527879	−	0.914312i	0.999472	−	0.0324963i	$-0.0103457\pi$
$80$		0			0
$81$	8.61050	+	2.61904i	0.956722	+	0.291004i
$82$		0			0
$83$	1.70847	+	2.95917i	0.187529	+	0.324811i	0.944426	−	0.328724i	$-0.106619\pi$
$83$	1.70847	+	2.95917i	0.187529	+	0.324811i	−0.756896	+	0.653535i	$0.773285\pi$
$84$		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	$-0.940472\pi$
$103$		−	3.77385i		−	0.371849i	0.982564	−	0.185924i	$-0.0595280\pi$
$104$		0			0
$105$	1.01519	−	9.95213i	0.0990720	−	0.971229i
$106$		0			0
$107$	−6.88241	+	3.97356i	−0.665347	+	0.384138i	−0.794311	−	0.607511i	$-0.792168\pi$
$107$	−6.88241	+	3.97356i	−0.665347	+	0.384138i	0.128964	+	0.991649i	$0.458835\pi$
$108$		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	$-0.597458\pi$
$127$	−6.79350			−0.602826			−0.301413	+	0.953494i	$0.597458\pi$
$128$		0			0
$129$	−3.96535	+	1.91441i	−0.349130	+	0.168554i
$130$		0			0
$131$	−13.7358			−1.20010			−0.600051	−	0.799961i	$-0.704853\pi$
$131$	−13.7358			−1.20010			−0.600051	+	0.799961i	$0.704853\pi$
$132$		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	0.815544	−	0.578695i	$-0.196438\pi$
$139$	8.51403	+	4.91558i	0.722151	+	0.416934i	−0.0933930	+	0.995629i	$0.529771\pi$
$140$		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	$-0.140114\pi$
$151$	22.2337			1.80935			0.904675	+	0.426103i	$0.140114\pi$
$152$		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	0.999899	−	0.0141893i	$-0.00451676\pi$
$163$	6.22604	+	10.7838i	0.487661	+	0.844654i	−0.512238	+	0.858844i	$0.671183\pi$
$164$		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	$0.442930\pi$
$167$	−9.85984	+	17.0777i	−0.762978	+	1.32152i	−0.941309	+	0.337546i	$0.890403\pi$
$168$		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	0.879064	−	0.476705i	$-0.158169\pi$
$179$	12.1182	+	6.99645i	0.905757	+	0.522939i	0.0266934	+	0.999644i	$0.491502\pi$
$180$		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	0.862729	−	0.505667i	$-0.168753\pi$
$191$	11.8326	+	6.83153i	0.856173	+	0.494312i	−0.00655557	+	0.999979i	$0.502087\pi$
$192$		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	0.687514	−	0.726171i	$-0.258702\pi$
$199$	5.67639	+	3.27726i	0.402388	+	0.232319i	−0.285126	+	0.958490i	$0.592035\pi$
$200$		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	$-0.617494\pi$
$211$	9.11202	−	15.7825i	0.627297	−	1.08651i	0.988092	−	0.153866i	$-0.0491723\pi$
$212$		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	−0.762617	−	0.646850i	$-0.776086\pi$
$223$	−8.71705	+	5.03279i	−0.583737	+	0.337021i	0.178880	+	0.983871i	$0.442753\pi$
$224$		0			0
$225$	0.695841	+	0.103486i	0.0463894	+	0.00689904i
$226$		0			0
$227$	−19.8874			−1.31998			−0.659988	−	0.751276i	$-0.729439\pi$
$227$	−19.8874			−1.31998			−0.659988	+	0.751276i	$0.729439\pi$
$228$		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	0.712037	−	0.702142i	$-0.247773\pi$
$239$	7.11117	+	4.10564i	0.459983	+	0.265572i	−0.252054	+	0.967713i	$0.581106\pi$
$240$		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	$-0.493406\pi$
$251$	0.656343			0.0414280			0.0207140	+	0.999785i	$0.493406\pi$
$252$		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	$-0.934505\pi$
$263$		−	6.62669i		−	0.408619i	0.978906	−	0.204310i	$-0.0654949\pi$
$264$		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	−0.866110	−	0.499853i	$-0.833387\pi$
$271$	−14.2608	+	8.23346i	−0.866280	+	0.500147i	−0.000169619		1.00000i	$0.500054\pi$
$272$		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	−0.999041	−	0.0437937i	$-0.986056\pi$
$283$	−24.5717	+	14.1865i	−1.46063	+	0.843298i	−0.461594	+	0.887091i	$0.652722\pi$
$284$		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	$0.119508\pi$
$307$			12.8497i			0.733372i	−0.930345	+	0.366686i	$0.880492\pi$
$308$		0			0
$309$	6.51871	+	0.482080i	0.370836	+	0.0274246i
$310$		0			0
$311$	3.29671	+	5.71007i	0.186939	+	0.323789i	0.944228	−	0.329291i	$-0.106810\pi$
$311$	3.29671	+	5.71007i	0.186939	+	0.323789i	−0.757289	+	0.653080i	$0.773477\pi$
$312$		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	$0.458559\pi$
$331$	−14.4416	+	25.0137i	−0.793784	+	1.37487i	−0.923608	+	0.383338i	$0.874775\pi$
$332$		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	−0.758389	−	0.651802i	$-0.774013\pi$
$347$	−10.6758	+	6.16367i	−0.573106	+	0.330883i	0.185283	+	0.982685i	$0.440680\pi$
$348$		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	−0.631501	−	0.775375i	$-0.717561\pi$
$359$	−5.22483	+	3.01656i	−0.275756	+	0.159208i	0.355745	+	0.934583i	$0.384227\pi$
$360$		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	$-0.852026\pi$
$367$		−	17.1767i		−	0.896618i	0.893879	−	0.448309i	$-0.147974\pi$
$368$		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	$-0.577110\pi$
$379$	−9.34015			−0.479771			−0.239886	+	0.970801i	$0.577110\pi$
$380$		0			0
$381$	0.867816	−	11.7346i	0.0444596	−	0.601184i
$382$		0			0
$383$	−5.70071			−0.291293			−0.145646	−	0.989337i	$-0.546526\pi$
$383$	−5.70071			−0.291293			−0.145646	+	0.989337i	$0.546526\pi$
$384$		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	−0.950192	−	0.311666i	$-0.899113\pi$
$419$	−4.20003	+	7.27466i	−0.205185	+	0.355390i	0.745007	+	0.667057i	$0.232446\pi$
$420$		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	0.727793	−	0.685797i	$-0.240546\pi$
$431$	10.3340	+	5.96634i	0.497772	+	0.287389i	−0.230021	+	0.973186i	$0.573880\pi$
$432$		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	0.113408	−	0.993548i	$-0.463823\pi$
$439$	−14.4639	−	8.35076i	−0.690326	−	0.398560i	−0.803734	+	0.594989i	$0.797157\pi$
$440$		0			0
$441$	−20.5675	−	4.24017i	−0.979404	−	0.201913i
$442$		0			0
$443$	−26.2403	−	15.1499i	−1.24672	−	0.719791i	−0.276262	−	0.961082i	$-0.589096\pi$
$443$	−26.2403	−	15.1499i	−1.24672	−	0.719791i	−0.970453	+	0.241291i	$0.922429\pi$
$444$		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	−0.680537	−	0.732713i	$-0.738254\pi$
$463$	6.33215	−	10.9676i	0.294280	−	0.509708i	0.974817	+	0.223006i	$0.0715869\pi$
$464$		0			0
$465$	−1.16218	−	2.40724i	−0.0538946	−	0.111633i
$466$		0			0
$467$	10.4723	+	18.1385i	0.484599	+	0.839350i	0.999843	−	0.0176932i	$-0.00563223\pi$
$467$	10.4723	+	18.1385i	0.484599	+	0.839350i	−0.515245	+	0.857043i	$0.672299\pi$
$468$		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	$-0.758537\pi$
$479$	−31.7705			−1.45163			−0.725816	+	0.687889i	$0.758537\pi$
$480$		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	$-0.535078\pi$
$487$	17.7821	−	30.7995i	0.805784	−	1.39566i	0.915761	−	0.401724i	$-0.131589\pi$
$488$		0			0
$489$	−19.4226	+	9.37691i	−0.878320	+	0.424038i
$490$		0			0
$491$	−2.75734	−	1.59195i	−0.124437	−	0.0718437i	0.436490	−	0.899709i	$-0.356222\pi$
$491$	−2.75734	−	1.59195i	−0.124437	−	0.0718437i	−0.560926	+	0.827866i	$0.689555\pi$
$492$		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	$-0.754583\pi$
$499$	−32.0427			−1.43443			−0.717215	+	0.696852i	$0.754583\pi$
$500$		0			0
$501$	−28.2395	−	19.2128i	−1.26165	−	0.858364i
$502$		0			0
$503$	11.6608			0.519930			0.259965	−	0.965618i	$-0.416289\pi$
$503$	11.6608			0.519930			0.259965	+	0.965618i	$0.416289\pi$
$504$		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	−0.599430	−	0.800427i	$-0.704606\pi$
$523$	−4.71003	+	2.71933i	−0.205955	+	0.118908i	0.393475	+	0.919335i	$0.371273\pi$
$524$		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	$0.00613809\pi$
$547$	12.0824	+	20.9273i	0.516606	+	0.894788i	−0.483208	+	0.875505i	$0.660529\pi$
$548$		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	0.855869	−	0.517192i	$-0.173023\pi$
$563$	−0.473776	−	0.820605i	−0.0199673	−	0.0345844i	−0.875836	+	0.482608i	$0.839690\pi$
$564$		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	0.709046	−	0.705162i	$-0.249126\pi$
$571$	−6.12121	−	10.6023i	−0.256165	−	0.443691i	−0.965211	+	0.261471i	$0.915792\pi$
$572$		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	0.930351	−	0.366669i	$-0.119502\pi$
$587$	3.57681	+	6.19521i	0.147631	+	0.255704i	−0.782721	+	0.622373i	$0.786169\pi$
$588$		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	0.276576	−	0.960992i	$-0.410800\pi$
$599$	30.5223	−	17.6221i	1.24711	−	0.720018i	0.970532	+	0.240974i	$0.0774668\pi$
$600$		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	$-0.905078\pi$
$607$		−	14.4772i		−	0.587613i	0.955865	−	0.293807i	$-0.0949222\pi$
$608$		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	$0.107464\pi$
$619$			16.4818i			0.662460i	−0.943550	+	0.331230i	$0.892536\pi$
$620$		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	$-0.256091\pi$
$631$	34.8383			1.38689			0.693446	+	0.720508i	$0.256091\pi$
$632$		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	0.101103	−	0.994876i	$-0.467763\pi$
$643$	−18.0021	−	10.3935i	−0.709934	−	0.409881i	−0.811037	+	0.584995i	$0.801096\pi$
$644$		0			0
$645$	−8.65637	+	4.17915i	−0.340844	+	0.164554i
$646$		0			0
$647$	4.74770	−	8.22325i	0.186651	−	0.323289i	−0.757480	−	0.652858i	$-0.773570\pi$
$647$	4.74770	−	8.22325i	0.186651	−	0.323289i	0.944132	+	0.329568i	$0.106903\pi$
$648$		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	−0.999796	−	0.0202102i	$-0.993566\pi$
$659$	−38.0493	+	21.9678i	−1.48219	+	0.855743i	−0.482395	+	0.875954i	$0.660233\pi$
$660$		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	0.884191	−	0.467126i	$-0.154710\pi$
$683$	24.0891	+	13.9079i	0.921744	+	0.532169i	0.0375529	+	0.999295i	$0.488044\pi$
$684$		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	0.206965	−	0.978348i	$-0.433641\pi$
$691$	−14.1115	−	8.14729i	−0.536828	−	0.309938i	−0.743792	+	0.668411i	$0.766975\pi$
$692$		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	0.868006	−	0.496553i	$-0.165401\pi$
$719$	0.106604	+	0.184643i	0.00397565	+	0.00688602i	−0.864031	+	0.503439i	$0.832068\pi$
$720$		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	0.224114	−	0.974563i	$-0.428051\pi$
$727$	31.8208	−	18.3717i	1.18017	−	0.681370i	0.956053	+	0.293193i	$0.0947180\pi$
$728$		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	−0.964703	−	0.263340i	$-0.915176\pi$
$739$	−6.91282	+	11.9734i	−0.254292	+	0.440447i	0.710411	+	0.703787i	$0.248509\pi$
$740$		0			0
$741$	−3.42961	+	46.3753i	−0.125990	+	1.70364i
$742$		0			0
$743$	15.8751	+	9.16552i	0.582403	+	0.336250i	0.762088	−	0.647474i	$-0.224175\pi$
$743$	15.8751	+	9.16552i	0.582403	+	0.336250i	−0.179685	+	0.983724i	$0.557508\pi$
$744$		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	$-0.381465\pi$
$751$	19.9417			0.727682			0.363841	+	0.931461i	$0.381465\pi$
$752$		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	0.428795	−	0.903402i	$-0.358938\pi$
$787$	39.9920	−	23.0894i	1.42556	−	0.823048i	0.996766	+	0.0803536i	$0.0256050\pi$
$788$		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	$-0.956643\pi$
$811$		−	7.73397i		−	0.271577i	0.990738	−	0.135788i	$-0.0433567\pi$
$812$		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	$-0.847633\pi$
$823$	−24.1753	−	41.8728i	−0.842698	−	1.45960i	0.0449080	−	0.998991i	$-0.485701\pi$
$824$		0			0
$825$	−0.593482	−	0.0438900i	−0.0206624	−	0.00152805i
$826$		0			0
$827$			17.3086i			0.601879i	0.953643	+	0.300940i	$0.0973003\pi$
$827$			17.3086i			0.601879i	−0.953643	+	0.300940i	$0.902700\pi$
$828$		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	$-0.990787\pi$
$839$	−15.2026	−	26.3317i	−0.524852	−	0.909071i	0.474729	−	0.880132i	$-0.342546\pi$
$840$		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	$-0.899313\pi$
$859$		−	18.2340i		−	0.622137i	0.950388	−	0.311068i	$-0.100687\pi$
$860$		0			0
$861$	27.8057	+	20.0721i	0.947614	+	0.684055i
$862$		0			0
$863$	−6.61966	+	3.82186i	−0.225336	+	0.130098i	−0.608419	−	0.793616i	$-0.708196\pi$
$863$	−6.61966	+	3.82186i	−0.225336	+	0.130098i	0.383083	+	0.923714i	$0.374862\pi$
$864$		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	$-0.436946\pi$
$883$	11.6958			0.393595			0.196798	+	0.980444i	$0.436946\pi$
$884$		0			0
$885$	45.7396	−	22.0823i	1.53752	−	0.742289i
$886$		0			0
$887$	−55.0859			−1.84960			−0.924801	−	0.380451i	$-0.875769\pi$
$887$	−55.0859			−1.84960			−0.924801	+	0.380451i	$0.875769\pi$
$888$		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	$-0.358651\pi$
$907$	25.8767			0.859220			0.429610	+	0.903014i	$0.358651\pi$
$908$		0			0
$909$	−23.5227	−	3.49830i	−0.780199	−	0.116031i
$910$		0			0
$911$	3.86306	−	2.23034i	0.127989	−	0.0738944i	−0.434639	−	0.900605i	$-0.643124\pi$
$911$	3.86306	−	2.23034i	0.127989	−	0.0738944i	0.562627	+	0.826711i	$0.309791\pi$
$912$		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	$0.0803663\pi$
$919$	21.2352	+	36.7805i	0.700485	+	1.21328i	−0.267811	+	0.963471i	$0.586300\pi$
$920$		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	0.631804	−	0.775128i	$-0.282315\pi$
$947$	8.50657	+	4.91127i	0.276426	+	0.159595i	−0.355378	+	0.934723i	$0.615648\pi$
$948$		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	$0.407186\pi$
$967$	−21.3240	+	36.9343i	−0.685735	+	1.18773i	−0.973205	+	0.229938i	$0.926148\pi$
$968$		0			0
$969$	36.2550	+	2.68118i	1.16468	+	0.0861318i
$970$		0			0
$971$	11.7562	+	20.3623i	0.377275	+	0.653459i	0.990665	−	0.136321i	$-0.0435280\pi$
$971$	11.7562	+	20.3623i	0.377275	+	0.653459i	−0.613390	+	0.789780i	$0.710195\pi$
$972$		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	$-0.361893\pi$
$983$	26.3608			0.840780			0.420390	+	0.907343i	$0.361893\pi$
$984$		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	−0.867301	−	0.497783i	$-0.834148\pi$
$991$	−0.0805213	+	0.139467i	−0.00255784	+	0.00443031i	0.864744	+	0.502214i	$0.167481\pi$
$992$		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	1008.2.df.d.689.5		16
3.2	odd	2		3024.2.df.d.17.3		16
4.3	odd	2		252.2.bm.a.185.4	yes	16
7.5	odd	6		1008.2.ca.d.257.7		16
9.2	odd	6		1008.2.ca.d.353.7		16
9.7	even	3		3024.2.ca.d.2033.3		16
12.11	even	2		756.2.bm.a.17.3		16
21.5	even	6		3024.2.ca.d.2609.3		16
28.3	even	6		1764.2.x.a.293.7		16
28.11	odd	6		1764.2.x.b.293.2		16
28.19	even	6		252.2.w.a.5.2	✓	16
28.23	odd	6		1764.2.w.b.509.7		16
28.27	even	2		1764.2.bm.a.1697.5		16
36.7	odd	6		756.2.w.a.521.3		16
36.11	even	6		252.2.w.a.101.2	yes	16
36.23	even	6		2268.2.t.b.1781.6		16
36.31	odd	6		2268.2.t.a.1781.3		16
63.47	even	6	inner	1008.2.df.d.929.5		16
63.61	odd	6		3024.2.df.d.1601.3		16
84.11	even	6		5292.2.x.b.881.6		16
84.23	even	6		5292.2.w.b.1097.6		16
84.47	odd	6		756.2.w.a.341.3		16
84.59	odd	6		5292.2.x.a.881.3		16
84.83	odd	2		5292.2.bm.a.2285.6		16
252.11	even	6		1764.2.x.a.1469.7		16
252.47	odd	6		252.2.bm.a.173.4	yes	16
252.79	odd	6		5292.2.bm.a.4625.6		16
252.83	odd	6		1764.2.w.b.1109.7		16
252.103	even	6		2268.2.t.b.2105.6		16
252.115	even	6		5292.2.x.b.4409.6		16
252.131	odd	6		2268.2.t.a.2105.3		16
252.151	odd	6		5292.2.x.a.4409.3		16
252.187	even	6		756.2.bm.a.89.3		16
252.191	even	6		1764.2.bm.a.1685.5		16
252.223	even	6		5292.2.w.b.521.6		16
252.227	odd	6		1764.2.x.b.1469.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.2	✓	16	28.19	even	6
252.2.w.a.101.2	yes	16	36.11	even	6
252.2.bm.a.173.4	yes	16	252.47	odd	6
252.2.bm.a.185.4	yes	16	4.3	odd	2
756.2.w.a.341.3		16	84.47	odd	6
756.2.w.a.521.3		16	36.7	odd	6
756.2.bm.a.17.3		16	12.11	even	2
756.2.bm.a.89.3		16	252.187	even	6
1008.2.ca.d.257.7		16	7.5	odd	6
1008.2.ca.d.353.7		16	9.2	odd	6
1008.2.df.d.689.5		16	1.1	even	1	trivial
1008.2.df.d.929.5		16	63.47	even	6	inner
1764.2.w.b.509.7		16	28.23	odd	6
1764.2.w.b.1109.7		16	252.83	odd	6
1764.2.x.a.293.7		16	28.3	even	6
1764.2.x.a.1469.7		16	252.11	even	6
1764.2.x.b.293.2		16	28.11	odd	6
1764.2.x.b.1469.2		16	252.227	odd	6
1764.2.bm.a.1685.5		16	252.191	even	6
1764.2.bm.a.1697.5		16	28.27	even	2
2268.2.t.a.1781.3		16	36.31	odd	6
2268.2.t.a.2105.3		16	252.131	odd	6
2268.2.t.b.1781.6		16	36.23	even	6
2268.2.t.b.2105.6		16	252.103	even	6
3024.2.ca.d.2033.3		16	9.7	even	3
3024.2.ca.d.2609.3		16	21.5	even	6
3024.2.df.d.17.3		16	3.2	odd	2
3024.2.df.d.1601.3		16	63.61	odd	6
5292.2.w.b.521.6		16	252.223	even	6
5292.2.w.b.1097.6		16	84.23	even	6
5292.2.x.a.881.3		16	84.59	odd	6
5292.2.x.a.4409.3		16	252.151	odd	6
5292.2.x.b.881.6		16	84.11	even	6
5292.2.x.b.4409.6		16	252.115	even	6
5292.2.bm.a.2285.6		16	84.83	odd	2
5292.2.bm.a.4625.6		16	252.79	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.df (of order \(6\), degree \(2\), not 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

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