LMFDB - Embedded newform 1040.2.dh.b.529.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(289,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("1040.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.dh (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:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.6
Root			$-0.531325 - 1.98293i$ of defining polynomial
Character	$\chi$	$=$	1040.529
Dual form			1040.2.dh.b.289.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.91766 + 1.10716i) q^{3} +(2.21432 + 0.311108i) q^{5} +(-3.38028 + 1.95161i) q^{7} +(0.951606 + 1.64823i) q^{9} +O(q^{10})$	\(q+(1.91766 + 1.10716i) q^{3} +(2.21432 + 0.311108i) q^{5} +(-3.38028 + 1.95161i) q^{7} +(0.951606 + 1.64823i) q^{9} +(0.533338 - 0.923769i) q^{11} +(-2.24483 + 2.82148i) q^{13} +(3.90186 + 3.04820i) q^{15} +(-1.13545 + 0.655554i) q^{17} +(3.29605 + 5.70893i) q^{19} -8.64296 q^{21} +(1.85991 + 1.07382i) q^{23} +(4.80642 + 1.37778i) q^{25} -2.42864i q^{27} +(-4.52543 + 7.83827i) q^{29} +6.92396 q^{31} +(2.04552 - 1.18098i) q^{33} +(-8.09218 + 3.26985i) q^{35} +(4.34809 + 2.51037i) q^{37} +(-7.42864 + 2.92525i) q^{39} +(2.97703 - 5.15637i) q^{41} +(-1.73205 + 1.00000i) q^{43} +(1.59438 + 3.94576i) q^{45} -0.0967881i q^{47} +(4.11753 - 7.13177i) q^{49} -2.90321 q^{51} -1.49532i q^{53} +(1.46837 - 1.87959i) q^{55} +14.5970i q^{57} +(-3.59210 - 6.22171i) q^{59} +(-3.94370 - 6.83068i) q^{61} +(-6.43339 - 3.71432i) q^{63} +(-5.84855 + 5.54927i) q^{65} +(7.29942 + 4.21432i) q^{67} +(2.37778 + 4.11844i) q^{69} +(-7.73975 - 13.4056i) q^{71} -15.3526i q^{73} +(7.69165 + 7.96360i) q^{75} +4.16346i q^{77} +4.30174 q^{79} +(5.54371 - 9.60199i) q^{81} -9.69381i q^{83} +(-2.71820 + 1.09836i) q^{85} +(-17.3564 + 10.0207i) q^{87} +(2.26271 - 3.91914i) q^{89} +(2.08173 - 13.9184i) q^{91} +(13.2778 + 7.66593i) q^{93} +(5.52242 + 13.6668i) q^{95} +(3.68949 - 2.13013i) q^{97} +2.03011 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{9}+O(q^{10}) $ 12 * q - 2 * q^9	$ 12 q - 2 q^{9} + 6 q^{11} - 4 q^{15} + 26 q^{19} - 24 q^{21} + 4 q^{25} - 28 q^{29} - 24 q^{31} + 6 q^{35} - 36 q^{39} - 4 q^{41} + 12 q^{45} - 4 q^{49} - 8 q^{51} - 12 q^{55} - 16 q^{59} - 8 q^{61} - 10 q^{65} + 28 q^{69} - 40 q^{71} + 8 q^{75} - 56 q^{79} + 26 q^{81} - 16 q^{85} + 14 q^{89} + 38 q^{91} + 8 q^{95} + 52 q^{99}+O(q^{100}) $ 12 * q - 2 * q^9 + 6 * q^11 - 4 * q^15 + 26 * q^19 - 24 * q^21 + 4 * q^25 - 28 * q^29 - 24 * q^31 + 6 * q^35 - 36 * q^39 - 4 * q^41 + 12 * q^45 - 4 * q^49 - 8 * q^51 - 12 * q^55 - 16 * q^59 - 8 * q^61 - 10 * q^65 + 28 * q^69 - 40 * q^71 + 8 * q^75 - 56 * q^79 + 26 * q^81 - 16 * q^85 + 14 * q^89 + 38 * q^91 + 8 * q^95 + 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.91766	+	1.10716i	1.10716	+	0.639219i	0.938092	−	0.346385i	$-0.112591\pi$
$3$	1.91766	+	1.10716i	1.10716	+	0.639219i	0.169068	+	0.985604i	$0.445924\pi$
$4$		0			0
$5$	2.21432	+	0.311108i	0.990274	+	0.139132i
$5$	2.21432	+	0.311108i	0.990274	+	0.139132i
$6$		0			0
$7$	−3.38028	+	1.95161i	−1.27763	+	0.737638i	−0.976411	−	0.215919i	$-0.930725\pi$
$7$	−3.38028	+	1.95161i	−1.27763	+	0.737638i	−0.301215	+	0.953556i	$0.597392\pi$
$8$		0			0
$9$	0.951606	+	1.64823i	0.317202	+	0.549410i
$10$		0			0
$11$	0.533338	−	0.923769i	0.160808	−	0.278527i	−0.774351	−	0.632756i	$-0.781923\pi$
$11$	0.533338	−	0.923769i	0.160808	−	0.278527i	0.935159	+	0.354229i	$0.115257\pi$
$12$		0			0
$13$	−2.24483	+	2.82148i	−0.622603	+	0.782538i
$13$	−2.24483	+	2.82148i	−0.622603	+	0.782538i
$14$		0			0
$15$	3.90186	+	3.04820i	1.00746	+	0.787043i
$16$		0			0
$17$	−1.13545	+	0.655554i	−0.275388	+	0.158995i	−0.631334	−	0.775511i	$-0.717492\pi$
$17$	−1.13545	+	0.655554i	−0.275388	+	0.158995i	0.355946	+	0.934507i	$0.384159\pi$
$18$		0			0
$19$	3.29605	+	5.70893i	0.756166	+	1.30972i	0.944792	+	0.327669i	$0.106263\pi$
$19$	3.29605	+	5.70893i	0.756166	+	1.30972i	−0.188626	+	0.982049i	$0.560403\pi$
$20$		0			0
$21$	−8.64296			−1.88605
$22$		0			0
$23$	1.85991	+	1.07382i	0.387819	+	0.223907i	0.681215	−	0.732084i	$-0.261452\pi$
$23$	1.85991	+	1.07382i	0.387819	+	0.223907i	−0.293396	+	0.955991i	$0.594785\pi$
$24$		0			0
$25$	4.80642	+	1.37778i	0.961285	+	0.275557i
$26$		0			0
$27$		−	2.42864i		−	0.467392i
$28$		0			0
$29$	−4.52543	+	7.83827i	−0.840351	+	1.45553i	0.0492475	+	0.998787i	$0.484318\pi$
$29$	−4.52543	+	7.83827i	−0.840351	+	1.45553i	−0.889598	+	0.456744i	$0.849016\pi$
$30$		0			0
$31$	6.92396			1.24358			0.621790	−	0.783184i	$-0.286406\pi$
$31$	6.92396			1.24358			0.621790	+	0.783184i	$0.286406\pi$
$32$		0			0
$33$	2.04552	−	1.18098i	0.356079	−	0.205582i
$34$		0			0
$35$	−8.09218	+	3.26985i	−1.36783	+	0.552705i
$36$		0			0
$37$	4.34809	+	2.51037i	0.714822	+	0.412703i	0.812844	−	0.582482i	$-0.197918\pi$
$37$	4.34809	+	2.51037i	0.714822	+	0.412703i	−0.0980220	+	0.995184i	$0.531252\pi$
$38$		0			0
$39$	−7.42864	+	2.92525i	−1.18953	+	0.468414i
$40$		0			0
$41$	2.97703	−	5.15637i	0.464935	−	0.805290i	−0.534264	−	0.845318i	$-0.679411\pi$
$41$	2.97703	−	5.15637i	0.464935	−	0.805290i	0.999199	+	0.0400274i	$0.0127445\pi$
$42$		0			0
$43$	−1.73205	+	1.00000i	−0.264135	+	0.152499i	−0.626219	−	0.779647i	$-0.715399\pi$
$43$	−1.73205	+	1.00000i	−0.264135	+	0.152499i	0.362084	+	0.932145i	$0.382065\pi$
$44$		0			0
$45$	1.59438	+	3.94576i	0.237677	+	0.588199i
$46$		0			0
$47$		−	0.0967881i		−	0.0141180i	−0.999975	−	0.00705900i	$-0.997753\pi$
$47$		−	0.0967881i		−	0.0141180i	0.999975	−	0.00705900i	$-0.00224697\pi$
$48$		0			0
$49$	4.11753	−	7.13177i	0.588219	−	1.01882i
$50$		0			0
$51$	−2.90321			−0.406531
$52$		0			0
$53$		−	1.49532i		−	0.205397i	−0.994713	−	0.102699i	$-0.967252\pi$
$53$		−	1.49532i		−	0.205397i	0.994713	−	0.102699i	$-0.0327478\pi$
$54$		0			0
$55$	1.46837	−	1.87959i	0.197995	−	0.253444i
$56$		0			0
$57$			14.5970i			1.93342i
$58$		0			0
$59$	−3.59210	−	6.22171i	−0.467652	−	0.809997i	0.531665	−	0.846955i	$-0.321567\pi$
$59$	−3.59210	−	6.22171i	−0.467652	−	0.809997i	−0.999317	+	0.0369577i	$0.988233\pi$
$60$		0			0
$61$	−3.94370	−	6.83068i	−0.504938	−	0.874579i	−0.999984	−	0.00571183i	$-0.998182\pi$
$61$	−3.94370	−	6.83068i	−0.504938	−	0.874579i	0.495045	−	0.868867i	$-0.335151\pi$
$62$		0			0
$63$	−6.43339	−	3.71432i	−0.810531	−	0.467960i
$64$		0			0
$65$	−5.84855	+	5.54927i	−0.725424	+	0.688303i
$66$		0			0
$67$	7.29942	+	4.21432i	0.891766	+	0.514861i	0.874520	−	0.484990i	$-0.161177\pi$
$67$	7.29942	+	4.21432i	0.891766	+	0.514861i	0.0172460	+	0.999851i	$0.494510\pi$
$68$		0			0
$69$	2.37778	+	4.11844i	0.286252	+	0.495802i
$70$		0			0
$71$	−7.73975	−	13.4056i	−0.918539	−	1.59096i	−0.801636	−	0.597813i	$-0.796037\pi$
$71$	−7.73975	−	13.4056i	−0.918539	−	1.59096i	−0.116903	−	0.993143i	$-0.537297\pi$
$72$		0			0
$73$		−	15.3526i		−	1.79689i	−0.439091	−	0.898443i	$-0.644699\pi$
$73$		−	15.3526i		−	1.79689i	0.439091	−	0.898443i	$-0.355301\pi$
$74$		0			0
$75$	7.69165	+	7.96360i	0.888155	+	0.919557i
$76$		0			0
$77$			4.16346i			0.474471i
$78$		0			0
$79$	4.30174			0.483984			0.241992	−	0.970278i	$-0.422199\pi$
$79$	4.30174			0.483984			0.241992	+	0.970278i	$0.422199\pi$
$80$		0			0
$81$	5.54371	−	9.60199i	0.615968	−	1.06689i
$82$		0			0
$83$		−	9.69381i		−	1.06403i	−0.846734	−	0.532017i	$-0.821434\pi$
$83$		−	9.69381i		−	1.06403i	0.846734	−	0.532017i	$-0.178566\pi$
$84$		0			0
$85$	−2.71820	+	1.09836i	−0.294831	+	0.119134i
$86$		0			0
$87$	−17.3564	+	10.0207i	−1.86081	+	1.07434i
$88$		0			0
$89$	2.26271	−	3.91914i	0.239847	−	0.415428i	−0.720823	−	0.693119i	$-0.756236\pi$
$89$	2.26271	−	3.91914i	0.239847	−	0.415428i	0.960670	+	0.277692i	$0.0895693\pi$
$90$		0			0
$91$	2.08173	−	13.9184i	0.218225	−	1.45905i
$92$		0			0
$93$	13.2778	+	7.66593i	1.37684	+	0.794919i
$94$		0			0
$95$	5.52242	+	13.6668i	0.566588	+	1.40219i
$96$		0			0
$97$	3.68949	−	2.13013i	0.374611	−	0.216282i	−0.300860	−	0.953668i	$-0.597274\pi$
$97$	3.68949	−	2.13013i	0.374611	−	0.216282i	0.675471	+	0.737387i	$0.263940\pi$
$98$		0			0
$99$	2.03011			0.204034
$100$		0			0
$101$	−0.729376	+	1.26332i	−0.0725756	+	0.125705i	−0.900029	−	0.435829i	$-0.856455\pi$
$101$	−0.729376	+	1.26332i	−0.0725756	+	0.125705i	0.827454	+	0.561534i	$0.189789\pi$
$102$		0			0
$103$			10.2444i			1.00941i	0.863291	+	0.504707i	$0.168399\pi$
$103$			10.2444i			1.00941i	−0.863291	+	0.504707i	$0.831601\pi$
$104$		0			0
$105$	−19.1383	−	2.68889i	−1.86770	−	0.262409i
$106$		0			0
$107$	1.91766	+	1.10716i	0.185387	+	0.107033i	0.589821	−	0.807534i	$-0.299198\pi$
$107$	1.91766	+	1.10716i	0.185387	+	0.107033i	−0.404434	+	0.914567i	$0.632532\pi$
$108$		0			0
$109$	−0.133353			−0.0127729			−0.00638645	−	0.999980i	$-0.502033\pi$
$109$	−0.133353			−0.0127729			−0.00638645	+	0.999980i	$0.502033\pi$
$110$		0			0
$111$	5.55877	+	9.62806i	0.527615	+	0.913855i
$112$		0			0
$113$	−12.1244	+	7.00000i	−1.14056	+	0.658505i	−0.946570	−	0.322498i	$-0.895477\pi$
$113$	−12.1244	+	7.00000i	−1.14056	+	0.658505i	−0.193993	+	0.981003i	$0.562144\pi$
$114$		0			0
$115$	3.78437	+	2.95642i	0.352894	+	0.275687i
$116$		0			0
$117$	−6.78664	−	1.01506i	−0.627425	−	0.0938419i
$118$		0			0
$119$	2.55877	−	4.43191i	0.234562	−	0.406273i
$120$		0			0
$121$	4.93110	+	8.54092i	0.448282	+	0.776447i
$122$		0			0
$123$	11.4179	−	6.59210i	1.02951	−	0.594390i
$124$		0			0
$125$	10.2143	+	4.54617i	0.913597	+	0.406622i
$126$		0			0
$127$	−8.65214	−	4.99532i	−0.767753	−	0.443263i	0.0643192	−	0.997929i	$-0.479512\pi$
$127$	−8.65214	−	4.99532i	−0.767753	−	0.443263i	−0.832073	+	0.554667i	$0.812846\pi$
$128$		0			0
$129$	−4.42864			−0.389920
$130$		0			0
$131$	−9.25581			−0.808684			−0.404342	−	0.914608i	$-0.632499\pi$
$131$	−9.25581			−0.808684			−0.404342	+	0.914608i	$0.632499\pi$
$132$		0			0
$133$	−22.2832	−	12.8652i	−1.93220	−	1.11555i
$134$		0			0
$135$	0.755569	−	5.37778i	0.0650290	−	0.462846i
$136$		0			0
$137$	12.8090	−	7.39530i	1.09435	−	0.631823i	0.159619	−	0.987179i	$-0.448974\pi$
$137$	12.8090	−	7.39530i	1.09435	−	0.631823i	0.934731	+	0.355356i	$0.115640\pi$
$138$		0			0
$139$	6.34691	+	10.9932i	0.538338	+	0.932428i	0.998994	+	0.0448494i	$0.0142808\pi$
$139$	6.34691	+	10.9932i	0.538338	+	0.932428i	−0.460656	+	0.887579i	$0.652386\pi$
$140$		0			0
$141$	0.107160	−	0.185606i	0.00902449	−	0.0156309i
$142$		0			0
$143$	1.40914	+	3.57851i	0.117838	+	0.299250i
$144$		0			0
$145$	−12.4593	+	15.9485i	−1.03469	+	1.32445i
$146$		0			0
$147$	15.7920	−	9.11753i	1.30250	−	0.752001i
$148$		0			0
$149$	3.64296	+	6.30979i	0.298443	+	0.516918i	0.975780	−	0.218755i	$-0.0701994\pi$
$149$	3.64296	+	6.30979i	0.298443	+	0.516918i	−0.677337	+	0.735673i	$0.736866\pi$
$150$		0			0
$151$	−20.1082			−1.63638			−0.818190	−	0.574949i	$-0.805022\pi$
$151$	−20.1082			−1.63638			−0.818190	+	0.574949i	$0.805022\pi$
$152$		0			0
$153$	−2.16101	−	1.24766i	−0.174707	−	0.100867i
$154$		0			0
$155$	15.3319	+	2.15410i	1.23148	+	0.173021i
$156$		0			0
$157$			1.98418i			0.158355i	0.996861	+	0.0791773i	$0.0252293\pi$
$157$			1.98418i			0.158355i	−0.996861	+	0.0791773i	$0.974771\pi$
$158$		0			0
$159$	1.65555	−	2.86750i	0.131294	−	0.227408i
$160$		0			0
$161$	−8.38271			−0.660650
$162$		0			0
$163$	4.07308	−	2.35159i	0.319028	−	0.184191i	−0.331931	−	0.943304i	$-0.607700\pi$
$163$	4.07308	−	2.35159i	0.319028	−	0.184191i	0.650959	+	0.759113i	$0.274367\pi$
$164$		0			0
$165$	4.89685	−	1.97869i	0.381219	−	0.154041i
$166$		0			0
$167$	8.39642	+	4.84767i	0.649734	+	0.375124i	0.788354	−	0.615221i	$-0.210933\pi$
$167$	8.39642	+	4.84767i	0.649734	+	0.375124i	−0.138620	+	0.990346i	$0.544267\pi$
$168$		0			0
$169$	−2.92149	−	12.6675i	−0.224730	−	0.974421i
$170$		0			0
$171$	−6.27309	+	10.8653i	−0.479715	+	0.830890i
$172$		0			0
$173$	20.8466	−	12.0358i	1.58494	−	0.915065i	0.590816	−	0.806806i	$-0.298806\pi$
$173$	20.8466	−	12.0358i	1.58494	−	0.915065i	0.994123	−	0.108259i	$-0.0345275\pi$
$174$		0			0
$175$	−18.9360	+	4.72295i	−1.43142	+	0.357021i
$176$		0			0
$177$		−	15.9081i		−	1.19573i
$178$		0			0
$179$	−1.52543	+	2.64212i	−0.114016	+	0.197481i	−0.917386	−	0.397999i	$-0.869705\pi$
$179$	−1.52543	+	2.64212i	−0.114016	+	0.197481i	0.803370	+	0.595480i	$0.203038\pi$
$180$		0			0
$181$	10.6430			0.791085			0.395542	−	0.918448i	$-0.370557\pi$
$181$	10.6430			0.791085			0.395542	+	0.918448i	$0.370557\pi$
$182$		0			0
$183$		−	17.4652i		−	1.29107i
$184$		0			0
$185$	8.84707	+	6.91149i	0.650449	+	0.508143i
$186$		0			0
$187$			1.39853i			0.102270i
$188$		0			0
$189$	4.73975	+	8.20948i	0.344766	+	0.597152i
$190$		0			0
$191$	7.36519	+	12.7569i	0.532926	+	0.923056i	0.999261	+	0.0384470i	$0.0122411\pi$
$191$	7.36519	+	12.7569i	0.532926	+	0.923056i	−0.466334	+	0.884609i	$0.654426\pi$
$192$		0			0
$193$	12.1244	+	7.00000i	0.872730	+	0.503871i	0.868255	−	0.496119i	$-0.165242\pi$
$193$	12.1244	+	7.00000i	0.872730	+	0.503871i	0.00447566	+	0.999990i	$0.498575\pi$
$194$		0			0
$195$	−17.3595	+	4.16632i	−1.24314	+	0.298357i
$196$		0			0
$197$	−9.01776	−	5.20641i	−0.642489	−	0.370941i	0.143084	−	0.989711i	$-0.454298\pi$
$197$	−9.01776	−	5.20641i	−0.642489	−	0.370941i	−0.785573	+	0.618769i	$0.787632\pi$
$198$		0			0
$199$	2.18421	+	3.78316i	0.154834	+	0.268181i	0.932999	−	0.359880i	$-0.117182\pi$
$199$	2.18421	+	3.78316i	0.154834	+	0.268181i	−0.778164	+	0.628061i	$0.783849\pi$
$200$		0			0
$201$	9.33185	+	16.1632i	0.658218	+	1.14007i
$202$		0			0
$203$		−	35.3274i		−	2.47950i
$204$		0			0
$205$	8.19629	−	10.4917i	0.572454	−	0.732771i
$206$		0			0
$207$			4.08742i			0.284095i
$208$		0			0
$209$	7.03164			0.486389
$210$		0			0
$211$	2.74766	−	4.75908i	0.189157	−	0.327629i	−0.755813	−	0.654788i	$-0.772758\pi$
$211$	2.74766	−	4.75908i	0.189157	−	0.327629i	0.944969	+	0.327159i	$0.106091\pi$
$212$		0			0
$213$		−	34.2766i		−	2.34859i
$214$		0			0
$215$	−4.14642	+	1.67547i	−0.282784	+	0.114266i
$216$		0			0
$217$	−23.4049	+	13.5128i	−1.58883	+	0.917311i
$218$		0			0
$219$	16.9978	−	29.4410i	1.14860	−	1.98944i
$220$		0			0
$221$	0.699264	−	4.67526i	0.0470376	−	0.314492i
$222$		0			0
$223$	−17.4043	−	10.0484i	−1.16548	−	0.672890i	−0.212869	−	0.977081i	$-0.568281\pi$
$223$	−17.4043	−	10.0484i	−1.16548	−	0.672890i	−0.952611	+	0.304191i	$0.901614\pi$
$224$		0			0
$225$	2.30292	+	9.23320i	0.153528	+	0.615547i
$226$		0			0
$227$	16.7654	−	9.67952i	1.11276	−	0.642453i	0.173218	−	0.984884i	$-0.444584\pi$
$227$	16.7654	−	9.67952i	1.11276	−	0.642453i	0.939543	+	0.342431i	$0.111250\pi$
$228$		0			0
$229$	−15.7255			−1.03917			−0.519584	−	0.854420i	$-0.673913\pi$
$229$	−15.7255			−1.03917			−0.519584	+	0.854420i	$0.673913\pi$
$230$		0			0
$231$	−4.60962	+	7.98410i	−0.303291	+	0.525315i
$232$		0			0
$233$		−	14.8825i		−	0.974983i	−0.873128	−	0.487491i	$-0.837912\pi$
$233$		−	14.8825i		−	0.974983i	0.873128	−	0.487491i	$-0.162088\pi$
$234$		0			0
$235$	0.0301115	−	0.214320i	0.00196426	−	0.0139807i
$236$		0			0
$237$	8.24926	+	4.76271i	0.535847	+	0.309372i
$238$		0			0
$239$	4.42219			0.286047			0.143024	−	0.989719i	$-0.454317\pi$
$239$	4.42219			0.286047			0.143024	+	0.989719i	$0.454317\pi$
$240$		0			0
$241$	5.64050	+	9.76963i	0.363336	+	0.629317i	0.988508	−	0.151170i	$-0.0483042\pi$
$241$	5.64050	+	9.76963i	0.363336	+	0.629317i	−0.625171	+	0.780488i	$0.714971\pi$
$242$		0			0
$243$	14.9521	−	8.63259i	0.959176	−	0.553781i
$244$		0			0
$245$	11.3363	−	14.5110i	0.724249	−	0.927076i
$246$		0			0
$247$	−23.5067	−	3.51582i	−1.49570	−	0.223706i
$248$		0			0
$249$	10.7326	−	18.5894i	0.680151	−	1.17806i
$250$		0			0
$251$	1.32616	+	2.29698i	0.0837067	+	0.144984i	0.904839	−	0.425753i	$-0.139991\pi$
$251$	1.32616	+	2.29698i	0.0837067	+	0.144984i	−0.821133	+	0.570737i	$0.806657\pi$
$252$		0			0
$253$	1.98393	−	1.14542i	0.124728	−	0.0720120i
$254$		0			0
$255$	−6.42864	−	0.903212i	−0.402577	−	0.0565613i
$256$		0			0
$257$	3.55219	+	2.05086i	0.221579	+	0.127929i	0.606681	−	0.794945i	$-0.292500\pi$
$257$	3.55219	+	2.05086i	0.221579	+	0.127929i	−0.385102	+	0.922874i	$0.625834\pi$
$258$		0			0
$259$	−19.5970			−1.21770
$260$		0			0
$261$	−17.2257			−1.06624
$262$		0			0
$263$	−9.35479	−	5.40099i	−0.576841	−	0.333039i	0.183036	−	0.983106i	$-0.441407\pi$
$263$	−9.35479	−	5.40099i	−0.576841	−	0.333039i	−0.759877	+	0.650067i	$0.774741\pi$
$264$		0			0
$265$	0.465205	−	3.31111i	0.0285773	−	0.203400i
$266$		0			0
$267$	8.67822	−	5.01037i	0.531098	−	0.306630i
$268$		0			0
$269$	−9.29137	−	16.0931i	−0.566505	−	0.981215i	−0.996908	−	0.0785782i	$-0.974962\pi$
$269$	−9.29137	−	16.0931i	−0.566505	−	0.981215i	0.430403	−	0.902637i	$-0.358371\pi$
$270$		0			0
$271$	9.88739	−	17.1255i	0.600616	−	1.04030i	−0.392112	−	0.919918i	$-0.628255\pi$
$271$	9.88739	−	17.1255i	0.600616	−	1.04030i	0.992728	−	0.120380i	$-0.0384113\pi$
$272$		0			0
$273$	19.4020	−	24.3859i	1.17426	−	1.47590i
$274$		0			0
$275$	3.83620	−	3.70520i	0.231332	−	0.223432i
$276$		0			0
$277$	−0.177493	+	0.102476i	−0.0106645	+	0.00615718i	−0.505323	−	0.862930i	$-0.668627\pi$
$277$	−0.177493	+	0.102476i	−0.0106645	+	0.00615718i	0.494658	+	0.869088i	$0.335293\pi$
$278$		0			0
$279$	6.58888	+	11.4123i	0.394466	+	0.683235i
$280$		0			0
$281$	−20.4558			−1.22029			−0.610146	−	0.792289i	$-0.708889\pi$
$281$	−20.4558			−1.22029			−0.610146	+	0.792289i	$0.708889\pi$
$282$		0			0
$283$	1.24535	+	0.719004i	0.0740284	+	0.0427403i	0.536557	−	0.843864i	$-0.319725\pi$
$283$	1.24535	+	0.719004i	0.0740284	+	0.0427403i	−0.462529	+	0.886604i	$0.653058\pi$
$284$		0			0
$285$	−4.54125	+	32.3225i	−0.269000	+	1.91462i
$286$		0			0
$287$			23.2400i			1.37181i
$288$		0			0
$289$	−7.64050	+	13.2337i	−0.449441	+	0.778455i
$290$		0			0
$291$	9.43356			0.553005
$292$		0			0
$293$	−18.1126	+	10.4573i	−1.05815	+	0.610922i	−0.924919	−	0.380164i	$-0.875868\pi$
$293$	−18.1126	+	10.4573i	−1.05815	+	0.610922i	−0.133228	+	0.991085i	$0.542534\pi$
$294$		0			0
$295$	−6.01845	−	14.8944i	−0.350407	−	0.867184i
$296$		0			0
$297$	−2.24350	−	1.29529i	−0.130181	−	0.0751601i
$298$		0			0
$299$	−7.20495	+	2.83716i	−0.416673	+	0.164077i
$300$		0			0
$301$	3.90321	−	6.76056i	0.224977	−	0.389672i
$302$		0			0
$303$	−2.79738	+	1.61507i	−0.160706	+	0.0927834i
$304$		0			0
$305$	−6.60752	−	16.3522i	−0.378346	−	0.936326i
$306$		0			0
$307$			12.5303i			0.715145i	0.933885	+	0.357572i	$0.116395\pi$
$307$			12.5303i			0.715145i	−0.933885	+	0.357572i	$0.883605\pi$
$308$		0			0
$309$	−11.3422	+	19.6453i	−0.645237	+	1.11758i
$310$		0			0
$311$	9.78123			0.554643			0.277321	−	0.960777i	$-0.410553\pi$
$311$	9.78123			0.554643			0.277321	+	0.960777i	$0.410553\pi$
$312$		0			0
$313$			17.2128i			0.972924i	0.873702	+	0.486462i	$0.161713\pi$
$313$			17.2128i			0.972924i	−0.873702	+	0.486462i	$0.838287\pi$
$314$		0			0
$315$	−13.0900	−	10.2262i	−0.737540	−	0.576179i
$316$		0			0
$317$		−	13.7447i		−	0.771978i	−0.922503	−	0.385989i	$-0.873860\pi$
$317$		−	13.7447i		−	0.771978i	0.922503	−	0.385989i	$-0.126140\pi$
$318$		0			0
$319$	4.82717	+	8.36090i	0.270269	+	0.468120i
$320$		0			0
$321$	2.45161	+	4.24631i	0.136835	+	0.237006i
$322$		0			0
$323$	−7.48502	−	4.32148i	−0.416478	−	0.240454i
$324$		0			0
$325$	−14.6770	+	10.4683i	−0.814133	+	0.580679i
$326$		0			0
$327$	−0.255726	−	0.147643i	−0.0141417	−	0.00816469i
$328$		0			0
$329$	0.188892	+	0.327171i	0.0104140	+	0.0180375i
$330$		0			0
$331$	9.69381	+	16.7902i	0.532820	+	0.922872i	0.999265	+	0.0383216i	$0.0122011\pi$
$331$	9.69381	+	16.7902i	0.532820	+	0.922872i	−0.466445	+	0.884550i	$0.654466\pi$
$332$		0			0
$333$			9.55554i			0.523640i
$334$		0			0
$335$	14.8521	+	11.6028i	0.811459	+	0.633926i
$336$		0			0
$337$		−	0.555539i		−	0.0302621i	−0.999886	−	0.0151311i	$-0.995183\pi$
$337$		−	0.555539i		−	0.0302621i	0.999886	−	0.0151311i	$-0.00481655\pi$
$338$		0			0
$339$	−31.0005			−1.68371
$340$		0			0
$341$	3.69281	−	6.39614i	0.199977	−	0.346370i
$342$		0			0
$343$			4.82071i			0.260294i
$344$		0			0
$345$	3.98389	+	9.85930i	0.214486	+	0.530807i
$346$		0			0
$347$	5.78890	−	3.34222i	0.310764	−	0.179420i	−0.336504	−	0.941682i	$-0.609245\pi$
$347$	5.78890	−	3.34222i	0.310764	−	0.179420i	0.647269	+	0.762262i	$0.275911\pi$
$348$		0			0
$349$	5.29137	−	9.16492i	0.283240	−	0.490587i	−0.688941	−	0.724818i	$-0.741924\pi$
$349$	5.29137	−	9.16492i	0.283240	−	0.490587i	0.972181	+	0.234231i	$0.0752572\pi$
$350$		0			0
$351$	6.85236	+	5.45188i	0.365752	+	0.291000i
$352$		0			0
$353$	7.97557	+	4.60470i	0.424497	+	0.245083i	0.696999	−	0.717072i	$-0.254518\pi$
$353$	7.97557	+	4.60470i	0.424497	+	0.245083i	−0.272503	+	0.962155i	$0.587851\pi$
$354$		0			0
$355$	−12.9677	−	32.0923i	−0.688253	−	1.70328i
$356$		0			0
$357$	9.81367	−	5.66593i	0.519395	−	0.299873i
$358$		0			0
$359$	−4.19358			−0.221328			−0.110664	−	0.993858i	$-0.535298\pi$
$359$	−4.19358			−0.221328			−0.110664	+	0.993858i	$0.535298\pi$
$360$		0			0
$361$	−12.2279	+	21.1794i	−0.643575	+	1.11470i
$362$		0			0
$363$			21.8381i			1.14620i
$364$		0			0
$365$	4.77631	−	33.9956i	0.250004	−	1.77941i
$366$		0			0
$367$	−12.0970	−	6.98418i	−0.631456	−	0.364571i	0.149860	−	0.988707i	$-0.452118\pi$
$367$	−12.0970	−	6.98418i	−0.631456	−	0.364571i	−0.781316	+	0.624136i	$0.785451\pi$
$368$		0			0
$369$	11.3319			0.589913
$370$		0			0
$371$	2.91827	+	5.05459i	0.151509	+	0.262421i
$372$		0			0
$373$	10.2606	−	5.92396i	0.531273	−	0.306731i	−0.210262	−	0.977645i	$-0.567432\pi$
$373$	10.2606	−	5.92396i	0.531273	−	0.306731i	0.741535	+	0.670914i	$0.234098\pi$
$374$		0			0
$375$	14.5542	+	20.0269i	0.751577	+	1.03418i
$376$		0			0
$377$	−11.9567	−	30.3640i	−0.615802	−	1.56382i
$378$		0			0
$379$	−0.303197	+	0.525153i	−0.0155742	+	0.0269753i	−0.873707	−	0.486452i	$-0.838291\pi$
$379$	−0.303197	+	0.525153i	−0.0155742	+	0.0269753i	0.858133	+	0.513427i	$0.171624\pi$
$380$		0			0
$381$	−11.0612	−	19.1586i	−0.566684	−	0.981525i
$382$		0			0
$383$	30.1201	−	17.3899i	1.53907	−	0.888580i	0.540172	−	0.841555i	$-0.318359\pi$
$383$	30.1201	−	17.3899i	1.53907	−	0.888580i	0.998894	−	0.0470252i	$-0.0149741\pi$
$384$		0			0
$385$	−1.29529	+	9.21924i	−0.0660139	+	0.469856i
$386$		0			0
$387$	−3.29646	−	1.90321i	−0.167568	−	0.0967457i
$388$		0			0
$389$	18.6844			0.947339			0.473670	−	0.880703i	$-0.342929\pi$
$389$	18.6844			0.947339			0.473670	+	0.880703i	$0.342929\pi$
$390$		0			0
$391$	−2.81579			−0.142401
$392$		0			0
$393$	−17.7495	−	10.2477i	−0.895342	−	0.516926i
$394$		0			0
$395$	9.52543	+	1.33830i	0.479276	+	0.0673374i
$396$		0			0
$397$	−19.8968	+	11.4874i	−0.998590	+	0.576536i	−0.907831	−	0.419337i	$-0.862263\pi$
$397$	−19.8968	+	11.4874i	−0.998590	+	0.576536i	−0.0907594	+	0.995873i	$0.528929\pi$
$398$		0			0
$399$	−28.4876	−	49.3420i	−1.42617	−	2.47019i
$400$		0			0
$401$	2.18667	−	3.78742i	0.109197	−	0.189135i	−0.806248	−	0.591577i	$-0.798505\pi$
$401$	2.18667	−	3.78742i	0.109197	−	0.189135i	0.915445	+	0.402443i	$0.131839\pi$
$402$		0			0
$403$	−15.5431	+	19.5358i	−0.774256	+	0.973147i
$404$		0			0
$405$	15.2628	−	19.5372i	0.758415	−	0.970810i
$406$		0			0
$407$	4.63801	−	2.67775i	0.229897	−	0.132731i
$408$		0			0
$409$	−1.88493	−	3.26479i	−0.0932038	−	0.161434i	0.815654	−	0.578540i	$-0.196377\pi$
$409$	−1.88493	−	3.26479i	−0.0932038	−	0.161434i	−0.908858	+	0.417107i	$0.863044\pi$
$410$		0			0
$411$	32.7511			1.61549
$412$		0			0
$413$	24.2846	+	14.0207i	1.19497	+	0.689916i
$414$		0			0
$415$	3.01582	−	21.4652i	0.148041	−	1.05369i
$416$		0			0
$417$			28.1082i			1.37646i
$418$		0			0
$419$	−3.72615	+	6.45388i	−0.182034	+	0.315293i	−0.942573	−	0.334000i	$-0.891602\pi$
$419$	−3.72615	+	6.45388i	−0.182034	+	0.315293i	0.760539	+	0.649292i	$0.224935\pi$
$420$		0			0
$421$	27.6751			1.34880			0.674400	−	0.738366i	$-0.264402\pi$
$421$	27.6751			1.34880			0.674400	+	0.738366i	$0.264402\pi$
$422$		0			0
$423$	0.159529	−	0.0921041i	0.00775657	−	0.00447825i
$424$		0			0
$425$	−6.36068	+	1.58646i	−0.308538	+	0.0769547i
$426$		0			0
$427$	26.6616	+	15.3931i	1.29024	+	0.744923i
$428$		0			0
$429$	−1.25973	+	8.42249i	−0.0608201	+	0.406642i
$430$		0			0
$431$	9.84468	−	17.0515i	0.474202	−	0.821342i	−0.525362	−	0.850879i	$-0.676070\pi$
$431$	9.84468	−	17.0515i	0.474202	−	0.821342i	0.999564	+	0.0295373i	$0.00940339\pi$
$432$		0			0
$433$	−11.9046	+	6.87310i	−0.572097	+	0.330300i	−0.757986	−	0.652270i	$-0.773817\pi$
$433$	−11.9046	+	6.87310i	−0.572097	+	0.330300i	0.185890	+	0.982571i	$0.440483\pi$
$434$		0			0
$435$	−41.5502	+	16.7894i	−1.99218	+	0.804990i
$436$		0			0
$437$			14.1575i			0.677244i
$438$		0			0
$439$	−20.9114	+	36.2195i	−0.998045	+	1.72866i	−0.444894	+	0.895583i	$0.646758\pi$
$439$	−20.9114	+	36.2195i	−0.998045	+	1.72866i	−0.553151	+	0.833081i	$0.686575\pi$
$440$		0			0
$441$	15.6731			0.746337
$442$		0			0
$443$			23.6829i			1.12521i	0.826726	+	0.562605i	$0.190201\pi$
$443$			23.6829i			1.12521i	−0.826726	+	0.562605i	$0.809799\pi$
$444$		0			0
$445$	6.22965	−	7.97427i	0.295314	−	0.378017i
$446$		0			0
$447$			16.1334i			0.763081i
$448$		0			0
$449$	3.52789	+	6.11048i	0.166491	+	0.288371i	0.937184	−	0.348836i	$-0.113423\pi$
$449$	3.52789	+	6.11048i	0.166491	+	0.288371i	−0.770693	+	0.637207i	$0.780090\pi$
$450$		0			0
$451$	−3.17553	−	5.50018i	−0.149530	−	0.258993i
$452$		0			0
$453$	−38.5606	−	22.2630i	−1.81173	−	1.04600i
$454$		0			0
$455$	8.93975	−	30.1722i	0.419102	−	1.41449i
$456$		0			0
$457$	−30.8994	−	17.8398i	−1.44541	−	0.834509i	−0.447209	−	0.894430i	$-0.647582\pi$
$457$	−30.8994	−	17.8398i	−1.44541	−	0.834509i	−0.998203	+	0.0599208i	$0.980915\pi$
$458$		0			0
$459$	1.59210	+	2.75761i	0.0743131	+	0.128714i
$460$		0			0
$461$	7.30074	+	12.6452i	0.340029	+	0.588948i	0.984438	−	0.175734i	$-0.0562297\pi$
$461$	7.30074	+	12.6452i	0.340029	+	0.588948i	−0.644409	+	0.764681i	$0.722896\pi$
$462$		0			0
$463$		−	30.7511i		−	1.42913i	−0.699571	−	0.714563i	$-0.746626\pi$
$463$		−	30.7511i		−	1.42913i	0.699571	−	0.714563i	$-0.253374\pi$
$464$		0			0
$465$	27.0163	+	21.1056i	1.25285	+	0.978750i
$466$		0			0
$467$		−	20.5620i		−	0.951496i	−0.879582	−	0.475748i	$-0.842178\pi$
$467$		−	20.5620i		−	0.951496i	0.879582	−	0.475748i	$-0.157822\pi$
$468$		0			0
$469$	−32.8988			−1.51912
$470$		0			0
$471$	−2.19680	+	3.80497i	−0.101223	+	0.175324i
$472$		0			0
$473$			2.13335i			0.0980917i
$474$		0			0
$475$	7.97655	+	31.9808i	0.365989	+	1.46738i
$476$		0			0
$477$	2.46462	−	1.42295i	0.112847	−	0.0651525i
$478$		0			0
$479$	−5.96666	+	10.3346i	−0.272624	+	0.472198i	−0.969533	−	0.244961i	$-0.921225\pi$
$479$	−5.96666	+	10.3346i	−0.272624	+	0.472198i	0.696909	+	0.717159i	$0.254558\pi$
$480$		0			0
$481$	−16.8437	+	6.63270i	−0.768006	+	0.302425i
$482$		0			0
$483$	−16.0752	−	9.28100i	−0.731445	−	0.422300i
$484$		0			0
$485$	8.83240	−	3.56895i	0.401059	−	0.162058i
$486$		0			0
$487$	−24.2244	+	13.9859i	−1.09771	+	0.633764i	−0.935619	−	0.353012i	$-0.885158\pi$
$487$	−24.2244	+	13.9859i	−1.09771	+	0.633764i	−0.162092	+	0.986776i	$0.551824\pi$
$488$		0			0
$489$	10.4143			0.470953
$490$		0			0
$491$	−10.3906	+	17.9971i	−0.468922	+	0.812197i	−0.999369	−	0.0355214i	$-0.988691\pi$
$491$	−10.3906	+	17.9971i	−0.468922	+	0.812197i	0.530447	+	0.847718i	$0.322024\pi$
$492$		0			0
$493$		−	11.8666i		−	0.534447i
$494$		0			0
$495$	4.49532	+	0.631584i	0.202049	+	0.0283876i
$496$		0			0
$497$	52.3250	+	30.2099i	2.34710	+	1.35510i
$498$		0			0
$499$	34.2908			1.53507			0.767534	−	0.641008i	$-0.221483\pi$
$499$	34.2908			1.53507			0.767534	+	0.641008i	$0.221483\pi$
$500$		0			0
$501$	10.7343	+	18.5923i	0.479573	+	0.830645i
$502$		0			0
$503$	17.5160	−	10.1128i	0.780998	−	0.450910i	−0.0557857	−	0.998443i	$-0.517766\pi$
$503$	17.5160	−	10.1128i	0.780998	−	0.450910i	0.836784	+	0.547533i	$0.184433\pi$
$504$		0			0
$505$	−2.00810	+	2.57047i	−0.0893592	+	0.114384i
$506$		0			0
$507$	8.42249	−	27.5264i	0.374056	−	1.22249i
$508$		0			0
$509$	−13.6889	+	23.7099i	−0.606749	+	1.05092i	0.385023	+	0.922907i	$0.374194\pi$
$509$	−13.6889	+	23.7099i	−0.606749	+	1.05092i	−0.991772	+	0.128014i	$0.959140\pi$
$510$		0			0
$511$	29.9622	+	51.8961i	1.32545	+	2.29575i
$512$		0			0
$513$	13.8649	−	8.00492i	0.612152	−	0.353426i
$514$		0			0
$515$	−3.18712	+	22.6844i	−0.140441	+	0.999596i
$516$		0			0
$517$	−0.0894098	−	0.0516208i	−0.00393224	−	0.00227028i
$518$		0			0
$519$	53.3022			2.33971
$520$		0			0
$521$	−31.2034			−1.36705			−0.683523	−	0.729929i	$-0.739553\pi$
$521$	−31.2034			−1.36705			−0.683523	+	0.729929i	$0.739553\pi$
$522$		0			0
$523$	−8.52854	−	4.92396i	−0.372927	−	0.215310i	0.301809	−	0.953368i	$-0.402409\pi$
$523$	−8.52854	−	4.92396i	−0.372927	−	0.215310i	−0.674736	+	0.738059i	$0.735743\pi$
$524$		0			0
$525$	−41.5417	−	11.9081i	−1.81303	−	0.519714i
$526$		0			0
$527$	−7.86182	+	4.53903i	−0.342466	+	0.197723i
$528$		0			0
$529$	−9.19381	−	15.9242i	−0.399731	−	0.692355i
$530$		0			0
$531$	6.83654	−	11.8412i	0.296680	−	0.513865i
$532$		0			0
$533$	7.86567	+	19.9748i	0.340700	+	0.865205i
$534$		0			0
$535$	3.90186	+	3.04820i	0.168692	+	0.131785i
$536$		0			0
$537$	−5.85049	+	3.37778i	−0.252467	+	0.145762i
$538$		0			0
$539$	−4.39207	−	7.60730i	−0.189180	−	0.327669i
$540$		0			0
$541$	41.6149			1.78916			0.894581	−	0.446905i	$-0.147474\pi$
$541$	41.6149			1.78916			0.894581	+	0.446905i	$0.147474\pi$
$542$		0			0
$543$	20.4095	+	11.7835i	0.875857	+	0.505677i
$544$		0			0
$545$	−0.295286	−	0.0414872i	−0.0126487	−	0.00177712i
$546$		0			0
$547$			6.77430i			0.289648i	0.989457	+	0.144824i	$0.0462617\pi$
$547$			6.77430i			0.289648i	−0.989457	+	0.144824i	$0.953738\pi$
$548$		0			0
$549$	7.50569	−	13.0002i	0.320335	−	0.554836i
$550$		0			0
$551$	−59.6642			−2.54178
$552$		0			0
$553$	−14.5411	+	8.39530i	−0.618350	+	0.357005i
$554$		0			0
$555$	9.31352	+	23.0490i	0.395337	+	0.978375i
$556$		0			0
$557$	22.0360	+	12.7225i	0.933694	+	0.539068i	0.887978	−	0.459886i	$-0.152110\pi$
$557$	22.0360	+	12.7225i	0.933694	+	0.539068i	0.0457158	+	0.998954i	$0.485443\pi$
$558$		0			0
$559$	1.06668	−	7.13177i	0.0451156	−	0.301642i
$560$		0			0
$561$	−1.54839	+	2.68190i	−0.0653732	+	0.113230i
$562$		0			0
$563$	−11.4179	+	6.59210i	−0.481205	+	0.277824i	−0.720919	−	0.693020i	$-0.756280\pi$
$563$	−11.4179	+	6.59210i	−0.481205	+	0.277824i	0.239713	+	0.970844i	$0.422947\pi$
$564$		0			0
$565$	−29.0250	+	11.7283i	−1.22109	+	0.493411i
$566$		0			0
$567$			43.2766i			1.81744i
$568$		0			0
$569$	−12.2304	+	21.1836i	−0.512724	+	0.888064i	0.487167	+	0.873309i	$0.338030\pi$
$569$	−12.2304	+	21.1836i	−0.512724	+	0.888064i	−0.999891	+	0.0147555i	$0.995303\pi$
$570$		0			0
$571$	−24.3526			−1.01912			−0.509562	−	0.860434i	$-0.670193\pi$
$571$	−24.3526			−1.01912			−0.509562	+	0.860434i	$0.670193\pi$
$572$		0			0
$573$			32.6178i			1.36263i
$574$		0			0
$575$	7.46004	+	7.72380i	0.311105	+	0.322105i
$576$		0			0
$577$			42.0479i			1.75048i	0.483690	+	0.875239i	$0.339296\pi$
$577$			42.0479i			1.75048i	−0.483690	+	0.875239i	$0.660704\pi$
$578$		0			0
$579$	15.5002	+	26.8472i	0.644168	+	1.11573i
$580$		0			0
$581$	18.9185	+	32.7678i	0.784872	+	1.35944i
$582$		0			0
$583$	−1.38133	−	0.797509i	−0.0572087	−	0.0330295i
$584$		0			0
$585$	−14.7120	−	4.35903i	−0.608266	−	0.180224i
$586$		0			0
$587$	6.36195	+	3.67307i	0.262586	+	0.151604i	0.625513	−	0.780213i	$-0.284890\pi$
$587$	6.36195	+	3.67307i	0.262586	+	0.151604i	−0.362928	+	0.931817i	$0.618223\pi$
$588$		0			0
$589$	22.8217	+	39.5284i	0.940353	+	1.62874i
$590$		0			0
$591$	−11.5287	−	19.9682i	−0.474225	−	0.821383i
$592$		0			0
$593$			4.19358i			0.172210i	0.996286	+	0.0861048i	$0.0274420\pi$
$593$			4.19358i			0.172210i	−0.996286	+	0.0861048i	$0.972558\pi$
$594$		0			0
$595$	7.04473	−	9.01762i	0.288806	−	0.369686i
$596$		0			0
$597$			9.67307i			0.395892i
$598$		0			0
$599$	9.33630			0.381471			0.190735	−	0.981641i	$-0.438913\pi$
$599$	9.33630			0.381471			0.190735	+	0.981641i	$0.438913\pi$
$600$		0			0
$601$	1.48571	−	2.57333i	0.0606034	−	0.104968i	−0.834132	−	0.551565i	$-0.814031\pi$
$601$	1.48571	−	2.57333i	0.0606034	−	0.104968i	0.894735	+	0.446597i	$0.147364\pi$
$602$		0			0
$603$			16.0415i			0.653260i
$604$		0			0
$605$	8.26189	+	20.4464i	0.335893	+	0.831265i
$606$		0			0
$607$	−14.8464	+	8.57160i	−0.602599	+	0.347910i	−0.770063	−	0.637968i	$-0.779775\pi$
$607$	−14.8464	+	8.57160i	−0.602599	+	0.347910i	0.167465	+	0.985878i	$0.446442\pi$
$608$		0			0
$609$	39.1131	−	67.7459i	1.58494	−	2.74520i
$610$		0			0
$611$	0.273086	+	0.217273i	0.0110479	+	0.00878991i
$612$		0			0
$613$	25.3610	+	14.6422i	1.02432	+	0.591393i	0.915353	−	0.402653i	$-0.131912\pi$
$613$	25.3610	+	14.6422i	1.02432	+	0.591393i	0.108969	+	0.994045i	$0.465245\pi$
$614$		0			0
$615$	27.3336	−	11.0448i	1.10220	−	0.445371i
$616$		0			0
$617$	11.4453	−	6.60793i	0.460769	−	0.266025i	−0.251599	−	0.967832i	$-0.580956\pi$
$617$	11.4453	−	6.60793i	0.460769	−	0.266025i	0.712368	+	0.701807i	$0.247623\pi$
$618$		0			0
$619$	−18.9333			−0.760995			−0.380497	−	0.924782i	$-0.624247\pi$
$619$	−18.9333			−0.760995			−0.380497	+	0.924782i	$0.624247\pi$
$620$		0			0
$621$	2.60793	−	4.51706i	0.104652	−	0.181263i
$622$		0			0
$623$			17.6637i			0.707681i
$624$		0			0
$625$	21.2034	+	13.2444i	0.848137	+	0.529777i
$626$		0			0
$627$	13.4843	+	7.78515i	0.538510	+	0.310909i
$628$		0			0
$629$	−6.58274			−0.262471
$630$		0			0
$631$	1.21432	+	2.10326i	0.0483413	+	0.0837296i	0.889184	−	0.457551i	$-0.151273\pi$
$631$	1.21432	+	2.10326i	0.0483413	+	0.0837296i	−0.840842	+	0.541280i	$0.817940\pi$
$632$		0			0
$633$	10.5381	−	6.08419i	0.418853	−	0.241825i
$634$		0			0
$635$	−17.6045	−	13.7530i	−0.698614	−	0.545770i
$636$		0			0
$637$	10.8790	+	27.6271i	0.431042	+	1.09463i
$638$		0			0
$639$	14.7304	−	25.5138i	0.582725	−	1.00931i
$640$		0			0
$641$	−7.54371	−	13.0661i	−0.297959	−	0.516079i	0.677710	−	0.735329i	$-0.262972\pi$
$641$	−7.54371	−	13.0661i	−0.297959	−	0.516079i	−0.975669	+	0.219250i	$0.929639\pi$
$642$		0			0
$643$	5.80513	−	3.35159i	0.228932	−	0.132174i	−0.381147	−	0.924514i	$-0.624471\pi$
$643$	5.80513	−	3.35159i	0.228932	−	0.132174i	0.610079	+	0.792340i	$0.291138\pi$
$644$		0			0
$645$	−9.80642	−	1.37778i	−0.386128	−	0.0542502i
$646$		0			0
$647$	−19.3759	−	11.1867i	−0.761744	−	0.439793i	0.0681773	−	0.997673i	$-0.478282\pi$
$647$	−19.3759	−	11.1867i	−0.761744	−	0.439793i	−0.829922	+	0.557880i	$0.811615\pi$
$648$		0			0
$649$	−7.66323			−0.300808
$650$		0			0
$651$	−59.8435			−2.34545
$652$		0			0
$653$	−14.2139	−	8.20641i	−0.556234	−	0.321142i	0.195399	−	0.980724i	$-0.437400\pi$
$653$	−14.2139	−	8.20641i	−0.556234	−	0.321142i	−0.751632	+	0.659582i	$0.770733\pi$
$654$		0			0
$655$	−20.4953	−	2.87955i	−0.800818	−	0.112513i
$656$		0			0
$657$	25.3046	−	14.6096i	0.987227	−	0.569976i
$658$		0			0
$659$	−4.33407	−	7.50684i	−0.168832	−	0.292425i	0.769178	−	0.639035i	$-0.220666\pi$
$659$	−4.33407	−	7.50684i	−0.168832	−	0.292425i	−0.938009	+	0.346610i	$0.887333\pi$
$660$		0			0
$661$	−8.71509	+	15.0950i	−0.338978	+	0.587126i	−0.984241	−	0.176834i	$-0.943414\pi$
$661$	−8.71509	+	15.0950i	−0.338978	+	0.587126i	0.645263	+	0.763960i	$0.276748\pi$
$662$		0			0
$663$	6.51721	−	8.19135i	0.253108	−	0.318126i
$664$		0			0
$665$	−45.3396	−	35.4201i	−1.75819	−	1.37353i
$666$		0			0
$667$	−16.8338	+	9.71900i	−0.651808	+	0.376321i
$668$		0			0
$669$	−22.2504	−	38.5387i	−0.860249	−	1.48999i
$670$		0			0
$671$	−8.41329			−0.324792
$672$		0			0
$673$	−35.0593	−	20.2415i	−1.35144	−	0.780253i	−0.362987	−	0.931794i	$-0.618243\pi$
$673$	−35.0593	−	20.2415i	−1.35144	−	0.780253i	−0.988451	+	0.151541i	$0.951576\pi$
$674$		0			0
$675$	3.34614	−	11.6731i	0.128793	−	0.449297i
$676$		0			0
$677$		−	40.0228i		−	1.53820i	−0.639129	−	0.769100i	$-0.720705\pi$
$677$		−	40.0228i		−	1.53820i	0.639129	−	0.769100i	$-0.279295\pi$
$678$		0			0
$679$	−8.31433	+	14.4008i	−0.319075	+	0.552654i
$680$		0			0
$681$	42.8671			1.64267
$682$		0			0
$683$	−37.5064	+	21.6543i	−1.43514	+	0.828580i	−0.997507	−	0.0705721i	$-0.977518\pi$
$683$	−37.5064	+	21.6543i	−1.43514	+	0.828580i	−0.437636	+	0.899152i	$0.644184\pi$
$684$		0			0
$685$	30.6640	−	12.3906i	1.17161	−	0.473419i
$686$		0			0
$687$	−30.1560	−	17.4106i	−1.15052	−	0.664256i
$688$		0			0
$689$	4.21900	+	3.35673i	0.160731	+	0.127881i
$690$		0			0
$691$	14.1741	−	24.5502i	0.539207	−	0.933934i	−0.459740	−	0.888054i	$-0.652057\pi$
$691$	14.1741	−	24.5502i	0.539207	−	0.933934i	0.998947	−	0.0458806i	$-0.0146094\pi$
$692$		0			0
$693$	−6.86235	+	3.96198i	−0.260679	+	0.150503i
$694$		0			0
$695$	10.6340	+	26.3170i	0.403371	+	0.998259i
$696$		0			0
$697$			7.80642i			0.295689i
$698$		0			0
$699$	16.4773	−	28.5395i	0.623228	−	1.07946i
$700$		0			0
$701$	12.8080			0.483750			0.241875	−	0.970307i	$-0.422238\pi$
$701$	12.8080			0.483750			0.241875	+	0.970307i	$0.422238\pi$
$702$		0			0
$703$			33.0973i			1.24829i
$704$		0			0
$705$	0.295030	−	0.377654i	0.0111115	−	0.0142233i
$706$		0			0
$707$		−	5.69381i		−	0.214138i
$708$		0			0
$709$	1.26126	+	2.18456i	0.0473675	+	0.0820429i	0.888737	−	0.458417i	$-0.151583\pi$
$709$	1.26126	+	2.18456i	0.0473675	+	0.0820429i	−0.841370	+	0.540460i	$0.818250\pi$
$710$		0			0
$711$	4.09356	+	7.09026i	0.153521	+	0.265905i
$712$		0			0
$713$	12.8780	+	7.43509i	0.482283	+	0.278446i
$714$		0			0
$715$	2.00699	+	8.36235i	0.0750572	+	0.312734i
$716$		0			0
$717$	8.48024	+	4.89607i	0.316700	+	0.182847i
$718$		0			0
$719$	−8.51114	−	14.7417i	−0.317412	−	0.549773i	0.662535	−	0.749031i	$-0.269480\pi$
$719$	−8.51114	−	14.7417i	−0.317412	−	0.549773i	−0.979947	+	0.199257i	$0.936147\pi$
$720$		0			0
$721$	−19.9931	−	34.6291i	−0.744582	−	1.28965i
$722$		0			0
$723$			24.9797i			0.929006i
$724$		0			0
$725$	−32.5506	+	31.4390i	−1.20890	+	1.16761i
$726$		0			0
$727$		−	30.5353i		−	1.13249i	−0.824237	−	0.566245i	$-0.808395\pi$
$727$		−	30.5353i		−	1.13249i	0.824237	−	0.566245i	$-0.191605\pi$
$728$		0			0
$729$	4.96836			0.184013
$730$		0			0
$731$	1.31111	−	2.27091i	0.0484931	−	0.0839925i
$732$		0			0
$733$			24.4499i			0.903076i	0.892252	+	0.451538i	$0.149124\pi$
$733$			24.4499i			0.903076i	−0.892252	+	0.451538i	$0.850876\pi$
$734$		0			0
$735$	37.8051	−	15.2761i	1.39446	−	0.563468i
$736$		0			0
$737$	7.78612	−	4.49532i	0.286805	−	0.165587i
$738$		0			0
$739$	5.39776	−	9.34920i	0.198560	−	0.343916i	−0.749502	−	0.662002i	$-0.769707\pi$
$739$	5.39776	−	9.34920i	0.198560	−	0.343916i	0.948062	+	0.318086i	$0.103040\pi$
$740$		0			0
$741$	−41.1852	−	32.7678i	−1.51298	−	1.20376i
$742$		0			0
$743$	25.9248	+	14.9677i	0.951087	+	0.549110i	0.893418	−	0.449225i	$-0.148300\pi$
$743$	25.9248	+	14.9677i	0.951087	+	0.549110i	0.0576686	+	0.998336i	$0.481633\pi$
$744$		0			0
$745$	6.10365	+	15.1052i	0.223620	+	0.553413i
$746$		0			0
$747$	15.9776	−	9.22469i	0.584591	−	0.337514i
$748$		0			0
$749$	−8.64296			−0.315807
$750$		0			0
$751$	13.4588	−	23.3112i	0.491117	−	0.850639i	−0.508831	−	0.860866i	$-0.669922\pi$
$751$	13.4588	−	23.3112i	0.491117	−	0.850639i	0.999948	+	0.0102272i	$0.00325549\pi$
$752$		0			0
$753$			5.87310i			0.214028i
$754$		0			0
$755$	−44.5259	−	6.25581i	−1.62046	−	0.227672i
$756$		0			0
$757$	−31.0960	−	17.9533i	−1.13020	−	0.652524i	−0.186218	−	0.982508i	$-0.559623\pi$
$757$	−31.0960	−	17.9533i	−1.13020	−	0.652524i	−0.943986	+	0.329985i	$0.892956\pi$
$758$		0			0
$759$	5.07265			0.184126
$760$		0			0
$761$	−11.2699	−	19.5200i	−0.408532	−	0.707598i	0.586193	−	0.810171i	$-0.300626\pi$
$761$	−11.2699	−	19.5200i	−0.408532	−	0.707598i	−0.994725	+	0.102573i	$0.967293\pi$
$762$		0			0
$763$	0.450771	−	0.260253i	0.0163190	−	0.00942178i
$764$		0			0
$765$	−4.39700	−	3.43502i	−0.158974	−	0.124193i
$766$		0			0
$767$	25.6181	+	3.83161i	0.925015	+	0.138352i
$768$		0			0
$769$	1.23729	−	2.14304i	0.0446177	−	0.0772801i	−0.842854	−	0.538142i	$-0.819126\pi$
$769$	1.23729	−	2.14304i	0.0446177	−	0.0772801i	0.887472	+	0.460862i	$0.152460\pi$
$770$		0			0
$771$	4.54125	+	7.86567i	0.163549	+	0.283275i
$772$		0			0
$773$	−38.2788	+	22.1003i	−1.37679	+	0.794891i	−0.991772	−	0.128018i	$-0.959139\pi$
$773$	−38.2788	+	22.1003i	−1.37679	+	0.794891i	−0.385019	+	0.922908i	$0.625805\pi$
$774$		0			0
$775$	33.2795	+	9.53972i	1.19543	+	0.342677i
$776$		0			0
$777$	−37.5804	−	21.6970i	−1.34819	−	0.778377i
$778$		0			0
$779$	39.2498			1.40627
$780$		0			0
$781$	−16.5116			−0.590832
$782$		0			0
$783$	19.0363	+	10.9906i	0.680303	+	0.392773i
$784$		0			0
$785$	−0.617293	+	4.39361i	−0.0220321	+	0.156815i
$786$		0			0
$787$	29.4714	−	17.0153i	1.05054	−	0.606530i	0.127740	−	0.991808i	$-0.459228\pi$
$787$	29.4714	−	17.0153i	1.05054	−	0.606530i	0.922801	+	0.385278i	$0.125894\pi$
$788$		0			0
$789$	−11.9595	−	20.7145i	−0.425770	−	0.737455i
$790$		0			0
$791$	27.3225	−	47.3239i	0.971476	−	1.68265i
$792$		0			0
$793$	28.1255	+	4.20665i	0.998767	+	0.149382i
$794$		0			0
$795$	4.55803	−	5.83451i	0.161657	−	0.206929i
$796$		0			0
$797$	−7.04754	+	4.06890i	−0.249637	+	0.144128i	−0.619598	−	0.784919i	$-0.712704\pi$
$797$	−7.04754	+	4.06890i	−0.249637	+	0.144128i	0.369961	+	0.929047i	$0.379371\pi$
$798$		0			0
$799$	0.0634498	+	0.109898i	0.00224469	+	0.00388792i
$800$		0			0
$801$	8.61285			0.304320
$802$		0			0
$803$	−14.1823	−	8.18813i	−0.500481	−	0.288953i
$804$		0			0
$805$	−18.5620	−	2.60793i	−0.654224	−	0.0919173i
$806$		0			0
$807$		−	41.1481i		−	1.44848i
$808$		0			0
$809$	−3.92618	+	6.80034i	−0.138037	+	0.239087i	−0.926754	−	0.375670i	$-0.877413\pi$
$809$	−3.92618	+	6.80034i	−0.138037	+	0.239087i	0.788716	+	0.614757i	$0.210746\pi$
$810$		0			0
$811$	−9.33477			−0.327788			−0.163894	−	0.986478i	$-0.552405\pi$
$811$	−9.33477			−0.327788			−0.163894	+	0.986478i	$0.552405\pi$
$812$		0			0
$813$	37.9213	−	21.8938i	1.32996	−	0.767851i
$814$		0			0
$815$	9.75069	−	3.94001i	0.341552	−	0.138012i
$816$		0			0
$817$	−11.4179	−	6.59210i	−0.399460	−	0.230629i
$818$		0			0
$819$	24.9217	−	9.81367i	0.870836	−	0.342917i
$820$		0			0
$821$	23.7659	−	41.1638i	0.829437	−	1.43663i	−0.0690434	−	0.997614i	$-0.521995\pi$
$821$	23.7659	−	41.1638i	0.829437	−	1.43663i	0.898480	−	0.439013i	$-0.144672\pi$
$822$		0			0
$823$	1.20131	−	0.693576i	0.0418750	−	0.0241765i	−0.478916	−	0.877861i	$-0.658970\pi$
$823$	1.20131	−	0.693576i	0.0418750	−	0.0241765i	0.520791	+	0.853684i	$0.325637\pi$
$824$		0			0
$825$	11.4588	−	2.85801i	0.398943	−	0.0995032i
$826$		0			0
$827$		−	31.5131i		−	1.09582i	−0.836537	−	0.547910i	$-0.815424\pi$
$827$		−	31.5131i		−	1.09582i	0.836537	−	0.547910i	$-0.184576\pi$
$828$		0			0
$829$	−14.4128	+	24.9637i	−0.500578	+	0.867026i	0.499422	+	0.866359i	$0.333546\pi$
$829$	−14.4128	+	24.9637i	−0.500578	+	0.867026i	−1.00000		0.000667386i	$0.999788\pi$
$830$		0			0
$831$	−0.453829			−0.0157431
$832$		0			0
$833$			10.7971i			0.374096i
$834$		0			0
$835$	17.0842	+	13.3465i	0.591223	+	0.461874i
$836$		0			0
$837$		−	16.8158i		−	0.581239i
$838$		0			0
$839$	−4.21755	−	7.30500i	−0.145606	−	0.252197i	0.783993	−	0.620770i	$-0.213180\pi$
$839$	−4.21755	−	7.30500i	−0.145606	−	0.252197i	−0.929599	+	0.368573i	$0.879846\pi$
$840$		0			0
$841$	−26.4590	−	45.8283i	−0.912379	−	1.58029i
$842$		0			0
$843$	−39.2273	−	22.6479i	−1.35106	−	0.780034i
$844$		0			0
$845$	−2.52817	−	28.9587i	−0.0869718	−	0.996211i
$846$		0			0
$847$	−33.3370	−	19.2471i	−1.14547	−	0.661339i
$848$		0			0
$849$	1.59210	+	2.75761i	0.0546409	+	0.0946408i
$850$		0			0
$851$	5.39138	+	9.33815i	0.184814	+	0.320108i
$852$		0			0
$853$		−	40.0656i		−	1.37182i	−0.727686	−	0.685910i	$-0.759404\pi$
$853$		−	40.0656i		−	1.37182i	0.727686	−	0.685910i	$-0.240596\pi$
$854$		0			0
$855$	−17.2709	+	22.1076i	−0.590652	+	0.756066i
$856$		0			0
$857$		−	32.0479i		−	1.09474i	−0.836892	−	0.547368i	$-0.815630\pi$
$857$		−	32.0479i		−	1.09474i	0.836892	−	0.547368i	$-0.184370\pi$
$858$		0			0
$859$	−26.6894			−0.910630			−0.455315	−	0.890331i	$-0.650473\pi$
$859$	−26.6894			−0.910630			−0.455315	+	0.890331i	$0.650473\pi$
$860$		0			0
$861$	−25.7304	+	44.5663i	−0.876889	+	1.51882i
$862$		0			0
$863$		−	30.6593i		−	1.04365i	−0.853052	−	0.521827i	$-0.825251\pi$
$863$		−	30.6593i		−	1.04365i	0.853052	−	0.521827i	$-0.174749\pi$
$864$		0			0
$865$	49.9055	−	20.1656i	1.69684	−	0.685650i
$866$		0			0
$867$	−29.3037	+	16.9185i	−0.995206	+	0.574583i
$868$		0			0
$869$	2.29428	−	3.97381i	0.0778282	−	0.134802i
$870$		0			0
$871$	−28.2766	+	11.1347i	−0.958114	+	0.377286i
$872$		0			0
$873$	7.02188	+	4.05408i	0.237654	+	0.137210i
$874$		0			0
$875$	−43.3996	+	4.56699i	−1.46717	+	0.154393i
$876$		0			0
$877$	−18.1263	+	10.4652i	−0.612081	+	0.353385i	−0.773779	−	0.633455i	$-0.781636\pi$
$877$	−18.1263	+	10.4652i	−0.612081	+	0.353385i	0.161699	+	0.986840i	$0.448303\pi$
$878$		0			0
$879$	−46.3116			−1.56205
$880$		0			0
$881$	−10.7351	+	18.5937i	−0.361673	+	0.626437i	−0.988236	−	0.152934i	$-0.951128\pi$
$881$	−10.7351	+	18.5937i	−0.361673	+	0.626437i	0.626563	+	0.779371i	$0.284461\pi$
$882$		0			0
$883$			7.73530i			0.260314i	0.991493	+	0.130157i	$0.0415481\pi$
$883$			7.73530i			0.260314i	−0.991493	+	0.130157i	$0.958452\pi$
$884$		0			0
$885$	4.94914	−	35.2257i	0.166364	−	1.18410i
$886$		0			0
$887$	41.9559	+	24.2232i	1.40874	+	0.813337i	0.995267	−	0.0971796i	$-0.0309821\pi$
$887$	41.9559	+	24.2232i	1.40874	+	0.813337i	0.413473	+	0.910516i	$0.364315\pi$
$888$		0			0
$889$	38.9956			1.30787
$890$		0			0
$891$	−5.91335	−	10.2422i	−0.198105	−	0.343127i
$892$		0			0
$893$	0.552556	−	0.319019i	0.0184906	−	0.0106755i
$894$		0			0
$895$	−4.19977	+	5.37592i	−0.140383	+	0.179697i
$896$		0			0
$897$	−16.9578	−	2.53633i	−0.566205	−	0.0846855i
$898$		0			0
$899$	−31.3339	+	54.2718i	−1.04504	+	1.81007i
$900$		0			0
$901$	0.980260	+	1.69786i	0.0326572	+	0.0565639i
$902$		0			0
$903$	14.9700	−	8.64296i	0.498172	−	0.287620i
$904$		0			0
$905$	23.5669	+	3.31111i	0.783391	+	0.110065i
$906$		0			0
$907$	−10.4017	−	6.00545i	−0.345384	−	0.199408i	0.317266	−	0.948337i	$-0.397235\pi$
$907$	−10.4017	−	6.00545i	−0.345384	−	0.199408i	−0.662650	+	0.748929i	$0.730568\pi$
$908$		0			0
$909$	−2.77631			−0.0920845
$910$		0			0
$911$	8.10171			0.268422			0.134211	−	0.990953i	$-0.457150\pi$
$911$	8.10171			0.268422			0.134211	+	0.990953i	$0.457150\pi$
$912$		0			0
$913$	−8.95485	−	5.17008i	−0.296362	−	0.171105i
$914$		0			0
$915$	5.43356	−	38.6735i	0.179628	−	1.27851i
$916$		0			0
$917$	31.2872	−	18.0637i	1.03320	−	0.596516i
$918$		0			0
$919$	−8.29682	−	14.3705i	−0.273687	−	0.474039i	0.696116	−	0.717929i	$-0.254910\pi$
$919$	−8.29682	−	14.3705i	−0.273687	−	0.474039i	−0.969803	+	0.243890i	$0.921576\pi$
$920$		0			0
$921$	−13.8731	+	24.0289i	−0.457134	+	0.791780i
$922$		0			0
$923$	55.1981	+	8.25581i	1.81687	+	0.271743i
$924$		0			0
$925$	17.4400	+	18.0566i	0.573424	+	0.593699i
$926$		0			0
$927$	−16.8852	+	9.74866i	−0.554582	+	0.320188i
$928$		0			0
$929$	28.5605	+	49.4682i	0.937038	+	1.62300i	0.770958	+	0.636886i	$0.219778\pi$
$929$	28.5605	+	49.4682i	0.937038	+	1.62300i	0.166080	+	0.986112i	$0.446889\pi$
$930$		0			0
$931$	54.2864			1.77916
$932$		0			0
$933$	18.7571	+	10.8294i	0.614078	+	0.354538i
$934$		0			0
$935$	−0.435093	+	3.09679i	−0.0142291	+	0.101276i
$936$		0			0
$937$			11.1842i			0.365372i	0.983171	+	0.182686i	$0.0584792\pi$
$937$			11.1842i			0.365372i	−0.983171	+	0.182686i	$0.941521\pi$
$938$		0			0
$939$	−19.0573	+	33.0082i	−0.621912	+	1.07718i
$940$		0			0
$941$	−7.68598			−0.250556			−0.125278	−	0.992122i	$-0.539982\pi$
$941$	−7.68598			−0.250556			−0.125278	+	0.992122i	$0.539982\pi$
$942$		0			0
$943$	11.0741	−	6.39361i	0.360621	−	0.208204i
$944$		0			0
$945$	7.94128	+	19.6530i	0.258330	+	0.639312i
$946$		0			0
$947$	−17.9047	−	10.3373i	−0.581826	−	0.335917i	0.180033	−	0.983661i	$-0.442380\pi$
$947$	−17.9047	−	10.3373i	−0.581826	−	0.335917i	−0.761859	+	0.647743i	$0.775713\pi$
$948$		0			0
$949$	43.3170	+	34.4639i	1.40613	+	1.11875i
$950$		0			0
$951$	15.2175	−	26.3576i	0.493463	−	0.854703i
$952$		0			0
$953$	−26.8254	+	15.4876i	−0.868959	+	0.501694i	−0.867002	−	0.498304i	$-0.833956\pi$
$953$	−26.8254	+	15.4876i	−0.868959	+	0.501694i	−0.00195715	+	0.999998i	$0.500623\pi$
$954$		0			0
$955$	12.3401	+	30.5392i	0.399317	+	0.988225i
$956$		0			0
$957$			21.3778i			0.691046i
$958$		0			0
$959$	−28.8654	+	49.9964i	−0.932113	+	1.61447i
$960$		0			0
$961$	16.9412			0.546489
$962$		0			0
$963$			4.21432i			0.135805i
$964$		0			0
$965$	24.6694	+	19.2722i	0.794138	+	0.620395i
$966$		0			0
$967$		−	0.529873i		−	0.0170396i	−0.999964	−	0.00851979i	$-0.997288\pi$
$967$		−	0.529873i		−	0.0170396i	0.999964	−	0.00851979i	$-0.00271197\pi$
$968$		0			0
$969$	−9.56914	−	16.5742i	−0.307405	−	0.532441i
$970$		0			0
$971$	−17.1620	−	29.7255i	−0.550755	−	0.953936i	−0.998220	−	0.0596344i	$-0.981007\pi$
$971$	−17.1620	−	29.7255i	−0.550755	−	0.953936i	0.447465	−	0.894301i	$-0.352327\pi$
$972$		0			0
$973$	−42.9087	−	24.7733i	−1.37559	−	0.794196i
$974$		0			0
$975$	−39.7355	+	3.82491i	−1.27256	+	0.122495i
$976$		0			0
$977$	17.2931	+	9.98418i	0.553255	+	0.319422i	0.750434	−	0.660945i	$-0.229845\pi$
$977$	17.2931	+	9.98418i	0.553255	+	0.319422i	−0.197179	+	0.980368i	$0.563178\pi$
$978$		0			0
$979$	−2.41358	−	4.18045i	−0.0771385	−	0.133608i
$980$		0			0
$981$	−0.126900	−	0.219797i	−0.00405159	−	0.00701756i
$982$		0			0
$983$			20.8524i			0.665087i	0.943088	+	0.332543i	$0.107907\pi$
$983$			20.8524i			0.665087i	−0.943088	+	0.332543i	$0.892093\pi$
$984$		0			0
$985$	−18.3485	−	14.3342i	−0.584631	−	0.456724i
$986$		0			0
$987$			0.836535i			0.0266272i
$988$		0			0
$989$	−4.29529			−0.136582
$990$		0			0
$991$	−1.47949	+	2.56256i	−0.0469977	+	0.0814024i	−0.888567	−	0.458746i	$-0.848299\pi$
$991$	−1.47949	+	2.56256i	−0.0469977	+	0.0814024i	0.841570	+	0.540149i	$0.181632\pi$
$992$		0			0
$993$			42.9304i			1.36236i
$994$		0			0
$995$	3.65956	+	9.05665i	0.116016	+	0.287115i
$996$		0			0
$997$	18.2281	−	10.5240i	0.577288	−	0.333297i	−0.182767	−	0.983156i	$-0.558505\pi$
$997$	18.2281	−	10.5240i	0.577288	−	0.333297i	0.760055	+	0.649859i	$0.225172\pi$
$998$		0			0
$999$	6.09679	−	10.5599i	0.192894	−	0.334102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.dh.b.529.6		12
4.3	odd	2		130.2.n.a.9.4	yes	12
5.4	even	2	inner	1040.2.dh.b.529.1		12
12.11	even	2		1170.2.bp.h.919.1		12
13.3	even	3	inner	1040.2.dh.b.289.1		12
20.3	even	4		650.2.e.k.451.3		6
20.7	even	4		650.2.e.j.451.1		6
20.19	odd	2		130.2.n.a.9.3	✓	12
52.3	odd	6		130.2.n.a.29.3	yes	12
52.7	even	12		1690.2.c.c.1689.6		6
52.19	even	12		1690.2.c.b.1689.6		6
52.35	odd	6		1690.2.b.c.339.3		6
52.43	odd	6		1690.2.b.b.339.6		6
60.59	even	2		1170.2.bp.h.919.4		12
65.29	even	6	inner	1040.2.dh.b.289.6		12
156.107	even	6		1170.2.bp.h.289.4		12
260.3	even	12		650.2.e.k.601.3		6
260.19	even	12		1690.2.c.c.1689.1		6
260.43	even	12		8450.2.a.ca.1.1		3
260.59	even	12		1690.2.c.b.1689.1		6
260.87	even	12		8450.2.a.cb.1.3		3
260.107	even	12		650.2.e.j.601.1		6
260.139	odd	6		1690.2.b.c.339.4		6
260.147	even	12		8450.2.a.bt.1.3		3
260.159	odd	6		130.2.n.a.29.4	yes	12
260.199	odd	6		1690.2.b.b.339.1		6
260.243	even	12		8450.2.a.bu.1.1		3
780.419	even	6		1170.2.bp.h.289.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.n.a.9.3	✓	12	20.19	odd	2
130.2.n.a.9.4	yes	12	4.3	odd	2
130.2.n.a.29.3	yes	12	52.3	odd	6
130.2.n.a.29.4	yes	12	260.159	odd	6
650.2.e.j.451.1		6	20.7	even	4
650.2.e.j.601.1		6	260.107	even	12
650.2.e.k.451.3		6	20.3	even	4
650.2.e.k.601.3		6	260.3	even	12
1040.2.dh.b.289.1		12	13.3	even	3	inner
1040.2.dh.b.289.6		12	65.29	even	6	inner
1040.2.dh.b.529.1		12	5.4	even	2	inner
1040.2.dh.b.529.6		12	1.1	even	1	trivial
1170.2.bp.h.289.1		12	780.419	even	6
1170.2.bp.h.289.4		12	156.107	even	6
1170.2.bp.h.919.1		12	12.11	even	2
1170.2.bp.h.919.4		12	60.59	even	2
1690.2.b.b.339.1		6	260.199	odd	6
1690.2.b.b.339.6		6	52.43	odd	6
1690.2.b.c.339.3		6	52.35	odd	6
1690.2.b.c.339.4		6	260.139	odd	6
1690.2.c.b.1689.1		6	260.59	even	12
1690.2.c.b.1689.6		6	52.19	even	12
1690.2.c.c.1689.1		6	260.19	even	12
1690.2.c.c.1689.6		6	52.7	even	12
8450.2.a.bt.1.3		3	260.147	even	12
8450.2.a.bu.1.1		3	260.243	even	12
8450.2.a.ca.1.1		3	260.43	even	12
8450.2.a.cb.1.3		3	260.87	even	12

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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.dh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.91766 + 1.10716i) q^{3} +(2.21432 + 0.311108i) q^{5} +(-3.38028 + 1.95161i) q^{7} +(0.951606 + 1.64823i) q^{9} +O(q^{10})\)	\(q+(1.91766 + 1.10716i) q^{3} +(2.21432 + 0.311108i) q^{5} +(-3.38028 + 1.95161i) q^{7} +(0.951606 + 1.64823i) q^{9} +(0.533338 - 0.923769i) q^{11} +(-2.24483 + 2.82148i) q^{13} +(3.90186 + 3.04820i) q^{15} +(-1.13545 + 0.655554i) q^{17} +(3.29605 + 5.70893i) q^{19} -8.64296 q^{21} +(1.85991 + 1.07382i) q^{23} +(4.80642 + 1.37778i) q^{25} -2.42864i q^{27} +(-4.52543 + 7.83827i) q^{29} +6.92396 q^{31} +(2.04552 - 1.18098i) q^{33} +(-8.09218 + 3.26985i) q^{35} +(4.34809 + 2.51037i) q^{37} +(-7.42864 + 2.92525i) q^{39} +(2.97703 - 5.15637i) q^{41} +(-1.73205 + 1.00000i) q^{43} +(1.59438 + 3.94576i) q^{45} -0.0967881i q^{47} +(4.11753 - 7.13177i) q^{49} -2.90321 q^{51} -1.49532i q^{53} +(1.46837 - 1.87959i) q^{55} +14.5970i q^{57} +(-3.59210 - 6.22171i) q^{59} +(-3.94370 - 6.83068i) q^{61} +(-6.43339 - 3.71432i) q^{63} +(-5.84855 + 5.54927i) q^{65} +(7.29942 + 4.21432i) q^{67} +(2.37778 + 4.11844i) q^{69} +(-7.73975 - 13.4056i) q^{71} -15.3526i q^{73} +(7.69165 + 7.96360i) q^{75} +4.16346i q^{77} +4.30174 q^{79} +(5.54371 - 9.60199i) q^{81} -9.69381i q^{83} +(-2.71820 + 1.09836i) q^{85} +(-17.3564 + 10.0207i) q^{87} +(2.26271 - 3.91914i) q^{89} +(2.08173 - 13.9184i) q^{91} +(13.2778 + 7.66593i) q^{93} +(5.52242 + 13.6668i) q^{95} +(3.68949 - 2.13013i) q^{97} +2.03011 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{9}+O(q^{10}) \) 12 * q - 2 * q^9	\( 12 q - 2 q^{9} + 6 q^{11} - 4 q^{15} + 26 q^{19} - 24 q^{21} + 4 q^{25} - 28 q^{29} - 24 q^{31} + 6 q^{35} - 36 q^{39} - 4 q^{41} + 12 q^{45} - 4 q^{49} - 8 q^{51} - 12 q^{55} - 16 q^{59} - 8 q^{61} - 10 q^{65} + 28 q^{69} - 40 q^{71} + 8 q^{75} - 56 q^{79} + 26 q^{81} - 16 q^{85} + 14 q^{89} + 38 q^{91} + 8 q^{95} + 52 q^{99}+O(q^{100}) \) 12 * q - 2 * q^9 + 6 * q^11 - 4 * q^15 + 26 * q^19 - 24 * q^21 + 4 * q^25 - 28 * q^29 - 24 * q^31 + 6 * q^35 - 36 * q^39 - 4 * q^41 + 12 * q^45 - 4 * q^49 - 8 * q^51 - 12 * q^55 - 16 * q^59 - 8 * q^61 - 10 * q^65 + 28 * q^69 - 40 * q^71 + 8 * q^75 - 56 * q^79 + 26 * q^81 - 16 * q^85 + 14 * q^89 + 38 * q^91 + 8 * q^95 + 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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