LMFDB - Embedded newform 234.2.l.b.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(127,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("234.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	234.199
Dual form			234.2.l.b.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +3.00000i q^{5} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{10} +(-2.50000 - 2.59808i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(2.59808 + 4.50000i) q^{17} +(6.00000 - 3.46410i) q^{19} +(-2.59808 + 1.50000i) q^{20} -4.00000 q^{25} +(-0.866025 - 3.50000i) q^{26} +(2.59808 - 4.50000i) q^{29} -6.92820i q^{31} +(-0.866025 + 0.500000i) q^{32} +5.19615i q^{34} +(-1.50000 - 0.866025i) q^{37} +6.92820 q^{38} -3.00000 q^{40} +(-7.79423 - 4.50000i) q^{41} +(2.00000 + 3.46410i) q^{43} -12.0000i q^{47} +(-3.50000 + 6.06218i) q^{49} +(-3.46410 - 2.00000i) q^{50} +(1.00000 - 3.46410i) q^{52} -5.19615 q^{53} +(4.50000 - 2.59808i) q^{58} +(-10.3923 + 6.00000i) q^{59} +(2.50000 + 4.33013i) q^{61} +(3.46410 - 6.00000i) q^{62} -1.00000 q^{64} +(7.79423 - 7.50000i) q^{65} +(12.0000 + 6.92820i) q^{67} +(-2.59808 + 4.50000i) q^{68} +(10.3923 - 6.00000i) q^{71} -8.66025i q^{73} +(-0.866025 - 1.50000i) q^{74} +(6.00000 + 3.46410i) q^{76} +4.00000 q^{79} +(-2.59808 - 1.50000i) q^{80} +(-4.50000 - 7.79423i) q^{82} +12.0000i q^{83} +(-13.5000 + 7.79423i) q^{85} +4.00000i q^{86} +(-5.19615 - 3.00000i) q^{89} +(6.00000 - 10.3923i) q^{94} +(10.3923 + 18.0000i) q^{95} +(-12.0000 + 6.92820i) q^{97} +(-6.06218 + 3.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 6 q^{10} - 10 q^{13} - 2 q^{16} + 24 q^{19} - 16 q^{25} - 6 q^{37} - 12 q^{40} + 8 q^{43} - 14 q^{49} + 4 q^{52} + 18 q^{58} + 10 q^{61} - 4 q^{64} + 48 q^{67} + 24 q^{76} + 16 q^{79} - 18 q^{82}+ \cdots - 48 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 - 6 * q^10 - 10 * q^13 - 2 * q^16 + 24 * q^19 - 16 * q^25 - 6 * q^37 - 12 * q^40 + 8 * q^43 - 14 * q^49 + 4 * q^52 + 18 * q^58 + 10 * q^61 - 4 * q^64 + 48 * q^67 + 24 * q^76 + 16 * q^79 - 18 * q^82 - 54 * q^85 + 24 * q^94 - 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$			3.00000i			1.34164i	0.741620	+	0.670820i	$0.234058\pi$
$5$			3.00000i			1.34164i	−0.741620	+	0.670820i	$0.765942\pi$
$6$		0			0
$7$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$7$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$		0			0
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.59808	+	4.50000i	0.630126	+	1.09141i	0.987526	+	0.157459i	$0.0503301\pi$
$17$	2.59808	+	4.50000i	0.630126	+	1.09141i	−0.357400	+	0.933952i	$0.616337\pi$
$18$		0			0
$19$	6.00000	−	3.46410i	1.37649	−	0.794719i	0.384759	−	0.923017i	$-0.374285\pi$
$19$	6.00000	−	3.46410i	1.37649	−	0.794719i	0.991736	+	0.128298i	$0.0409513\pi$
$20$	−2.59808	+	1.50000i	−0.580948	+	0.335410i
$21$		0			0
$22$		0			0
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$	−4.00000			−0.800000
$26$	−0.866025	−	3.50000i	−0.169842	−	0.686406i
$27$		0			0
$28$		0			0
$29$	2.59808	−	4.50000i	0.482451	−	0.835629i	−0.517346	−	0.855776i	$-0.673080\pi$
$29$	2.59808	−	4.50000i	0.482451	−	0.835629i	0.999797	+	0.0201471i	$0.00641344\pi$
$30$		0			0
$31$		−	6.92820i		−	1.24434i	−0.782881	−	0.622171i	$-0.786251\pi$
$31$		−	6.92820i		−	1.24434i	0.782881	−	0.622171i	$-0.213749\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$			5.19615i			0.891133i
$35$		0			0
$36$		0			0
$37$	−1.50000	−	0.866025i	−0.246598	−	0.142374i	0.371607	−	0.928390i	$-0.378807\pi$
$37$	−1.50000	−	0.866025i	−0.246598	−	0.142374i	−0.618206	+	0.786016i	$0.712140\pi$
$38$	6.92820			1.12390
$39$		0			0
$40$	−3.00000			−0.474342
$41$	−7.79423	−	4.50000i	−1.21725	−	0.702782i	−0.252924	−	0.967486i	$-0.581392\pi$
$41$	−7.79423	−	4.50000i	−1.21725	−	0.702782i	−0.964330	+	0.264704i	$0.914726\pi$
$42$		0			0
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	0.977261	−	0.212041i	$-0.0680112\pi$
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	−0.672264	+	0.740312i	$0.734678\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	12.0000i		−	1.75038i	−0.483779	−	0.875190i	$-0.660736\pi$
$47$		−	12.0000i		−	1.75038i	0.483779	−	0.875190i	$-0.339264\pi$
$48$		0			0
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$	−3.46410	−	2.00000i	−0.489898	−	0.282843i
$51$		0			0
$52$	1.00000	−	3.46410i	0.138675	−	0.480384i
$53$	−5.19615			−0.713746			−0.356873	−	0.934153i	$-0.616157\pi$
$53$	−5.19615			−0.713746			−0.356873	+	0.934153i	$0.616157\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	4.50000	−	2.59808i	0.590879	−	0.341144i
$59$	−10.3923	+	6.00000i	−1.35296	+	0.781133i	−0.988663	−	0.150148i	$-0.952025\pi$
$59$	−10.3923	+	6.00000i	−1.35296	+	0.781133i	−0.364299	+	0.931282i	$0.618692\pi$
$60$		0			0
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	0.980507	−	0.196485i	$-0.0629528\pi$
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	−0.660415	+	0.750901i	$0.729619\pi$
$62$	3.46410	−	6.00000i	0.439941	−	0.762001i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	7.79423	−	7.50000i	0.966755	−	0.930261i
$66$		0			0
$67$	12.0000	+	6.92820i	1.46603	+	0.846415i	0.999279	−	0.0379722i	$-0.0120898\pi$
$67$	12.0000	+	6.92820i	1.46603	+	0.846415i	0.466755	+	0.884387i	$0.345423\pi$
$68$	−2.59808	+	4.50000i	−0.315063	+	0.545705i
$69$		0			0
$70$		0			0
$71$	10.3923	−	6.00000i	1.23334	−	0.712069i	0.265615	−	0.964079i	$-0.414425\pi$
$71$	10.3923	−	6.00000i	1.23334	−	0.712069i	0.967725	+	0.252010i	$0.0810916\pi$
$72$		0			0
$73$		−	8.66025i		−	1.01361i	−0.862062	−	0.506803i	$-0.830827\pi$
$73$		−	8.66025i		−	1.01361i	0.862062	−	0.506803i	$-0.169173\pi$
$74$	−0.866025	−	1.50000i	−0.100673	−	0.174371i
$75$		0			0
$76$	6.00000	+	3.46410i	0.688247	+	0.397360i
$77$		0			0
$78$		0			0
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$	−2.59808	−	1.50000i	−0.290474	−	0.167705i
$81$		0			0
$82$	−4.50000	−	7.79423i	−0.496942	−	0.860729i
$83$			12.0000i			1.31717i	0.752506	+	0.658586i	$0.228845\pi$
$83$			12.0000i			1.31717i	−0.752506	+	0.658586i	$0.771155\pi$
$84$		0			0
$85$	−13.5000	+	7.79423i	−1.46428	+	0.845403i
$86$			4.00000i			0.431331i
$87$		0			0
$88$		0			0
$89$	−5.19615	−	3.00000i	−0.550791	−	0.317999i	0.198650	−	0.980071i	$-0.436344\pi$
$89$	−5.19615	−	3.00000i	−0.550791	−	0.317999i	−0.749441	+	0.662071i	$0.769678\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$	6.00000	−	10.3923i	0.618853	−	1.07188i
$95$	10.3923	+	18.0000i	1.06623	+	1.84676i
$96$		0			0
$97$	−12.0000	+	6.92820i	−1.21842	+	0.703452i	−0.964579	−	0.263795i	$-0.915026\pi$
$97$	−12.0000	+	6.92820i	−1.21842	+	0.703452i	−0.253837	+	0.967247i	$0.581693\pi$
$98$	−6.06218	+	3.50000i	−0.612372	+	0.353553i
$99$		0			0
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	2.59808	−	4.50000i	0.258518	−	0.447767i	−0.707327	−	0.706887i	$-0.750099\pi$
$101$	2.59808	−	4.50000i	0.258518	−	0.447767i	0.965845	+	0.259120i	$0.0834325\pi$
$102$		0			0
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$	2.59808	−	2.50000i	0.254762	−	0.245145i
$105$		0			0
$106$	−4.50000	−	2.59808i	−0.437079	−	0.252347i
$107$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$107$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$108$		0			0
$109$			6.92820i			0.663602i	0.943349	+	0.331801i	$0.107656\pi$
$109$			6.92820i			0.663602i	−0.943349	+	0.331801i	$0.892344\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.79423	+	13.5000i	0.733219	+	1.26997i	0.955500	+	0.294990i	$0.0953165\pi$
$113$	7.79423	+	13.5000i	0.733219	+	1.26997i	−0.222281	+	0.974983i	$0.571350\pi$
$114$		0			0
$115$		0			0
$116$	5.19615			0.482451
$117$		0			0
$118$	−12.0000			−1.10469
$119$		0			0
$120$		0			0
$121$	−5.50000	−	9.52628i	−0.500000	−	0.866025i
$122$			5.00000i			0.452679i
$123$		0			0
$124$	6.00000	−	3.46410i	0.538816	−	0.311086i
$125$			3.00000i			0.268328i
$126$		0			0
$127$	4.00000	−	6.92820i	0.354943	−	0.614779i	−0.632166	−	0.774833i	$-0.717834\pi$
$127$	4.00000	−	6.92820i	0.354943	−	0.614779i	0.987108	+	0.160055i	$0.0511671\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	10.5000	−	2.59808i	0.920911	−	0.227866i
$131$	−20.7846			−1.81596			−0.907980	−	0.419014i	$-0.862376\pi$
$131$	−20.7846			−1.81596			−0.907980	+	0.419014i	$0.862376\pi$
$132$		0			0
$133$		0			0
$134$	6.92820	+	12.0000i	0.598506	+	1.03664i
$135$		0			0
$136$	−4.50000	+	2.59808i	−0.385872	+	0.222783i
$137$	−7.79423	+	4.50000i	−0.665906	+	0.384461i	−0.794524	−	0.607233i	$-0.792279\pi$
$137$	−7.79423	+	4.50000i	−0.665906	+	0.384461i	0.128618	+	0.991694i	$0.458946\pi$
$138$		0			0
$139$	8.00000	+	13.8564i	0.678551	+	1.17529i	0.975417	+	0.220366i	$0.0707252\pi$
$139$	8.00000	+	13.8564i	0.678551	+	1.17529i	−0.296866	+	0.954919i	$0.595942\pi$
$140$		0			0
$141$		0			0
$142$	12.0000			1.00702
$143$		0			0
$144$		0			0
$145$	13.5000	+	7.79423i	1.12111	+	0.647275i
$146$	4.33013	−	7.50000i	0.358364	−	0.620704i
$147$		0			0
$148$		−	1.73205i		−	0.142374i
$149$	−2.59808	+	1.50000i	−0.212843	+	0.122885i	−0.602632	−	0.798019i	$-0.705881\pi$
$149$	−2.59808	+	1.50000i	−0.212843	+	0.122885i	0.389789	+	0.920904i	$0.372548\pi$
$150$		0			0
$151$		−	13.8564i		−	1.12762i	−0.825905	−	0.563809i	$-0.809335\pi$
$151$		−	13.8564i		−	1.12762i	0.825905	−	0.563809i	$-0.190665\pi$
$152$	3.46410	+	6.00000i	0.280976	+	0.486664i
$153$		0			0
$154$		0			0
$155$	20.7846			1.66946
$156$		0			0
$157$	−7.00000			−0.558661			−0.279330	−	0.960195i	$-0.590112\pi$
$157$	−7.00000			−0.558661			−0.279330	+	0.960195i	$0.590112\pi$
$158$	3.46410	+	2.00000i	0.275589	+	0.159111i
$159$		0			0
$160$	−1.50000	−	2.59808i	−0.118585	−	0.205396i
$161$		0			0
$162$		0			0
$163$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$163$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$164$		−	9.00000i		−	0.702782i
$165$		0			0
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$	−10.3923	−	6.00000i	−0.804181	−	0.464294i	0.0407502	−	0.999169i	$-0.487025\pi$
$167$	−10.3923	−	6.00000i	−0.804181	−	0.464294i	−0.844931	+	0.534875i	$0.820359\pi$
$168$		0			0
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$	−15.5885			−1.19558
$171$		0			0
$172$	−2.00000	+	3.46410i	−0.152499	+	0.264135i
$173$	10.3923	+	18.0000i	0.790112	+	1.36851i	0.925897	+	0.377776i	$0.123311\pi$
$173$	10.3923	+	18.0000i	0.790112	+	1.36851i	−0.135785	+	0.990738i	$0.543356\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	10.3923	−	18.0000i	0.776757	−	1.34538i	−0.157044	−	0.987592i	$-0.550196\pi$
$179$	10.3923	−	18.0000i	0.776757	−	1.34538i	0.933801	−	0.357792i	$-0.116470\pi$
$180$		0			0
$181$	−1.00000			−0.0743294			−0.0371647	−	0.999309i	$-0.511833\pi$
$181$	−1.00000			−0.0743294			−0.0371647	+	0.999309i	$0.511833\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.59808	−	4.50000i	0.191014	−	0.330847i
$186$		0			0
$187$		0			0
$188$	10.3923	−	6.00000i	0.757937	−	0.437595i
$189$		0			0
$190$			20.7846i			1.50787i
$191$	−10.3923	−	18.0000i	−0.751961	−	1.30243i	−0.946871	−	0.321613i	$-0.895775\pi$
$191$	−10.3923	−	18.0000i	−0.751961	−	1.30243i	0.194910	−	0.980821i	$-0.437558\pi$
$192$		0			0
$193$	−4.50000	−	2.59808i	−0.323917	−	0.187014i	0.329220	−	0.944253i	$-0.393214\pi$
$193$	−4.50000	−	2.59808i	−0.323917	−	0.187014i	−0.653137	+	0.757240i	$0.726548\pi$
$194$	−13.8564			−0.994832
$195$		0			0
$196$	−7.00000			−0.500000
$197$	−5.19615	−	3.00000i	−0.370211	−	0.213741i	0.303340	−	0.952882i	$-0.401898\pi$
$197$	−5.19615	−	3.00000i	−0.370211	−	0.213741i	−0.673550	+	0.739141i	$0.735232\pi$
$198$		0			0
$199$	4.00000	+	6.92820i	0.283552	+	0.491127i	0.972257	−	0.233915i	$-0.0751537\pi$
$199$	4.00000	+	6.92820i	0.283552	+	0.491127i	−0.688705	+	0.725042i	$0.741820\pi$
$200$		−	4.00000i		−	0.282843i
$201$		0			0
$202$	4.50000	−	2.59808i	0.316619	−	0.182800i
$203$		0			0
$204$		0			0
$205$	13.5000	−	23.3827i	0.942881	−	1.63312i
$206$	−3.46410	−	2.00000i	−0.241355	−	0.139347i
$207$		0			0
$208$	3.50000	−	0.866025i	0.242681	−	0.0600481i
$209$		0			0
$210$		0			0
$211$	−2.00000	+	3.46410i	−0.137686	+	0.238479i	−0.926620	−	0.375999i	$-0.877300\pi$
$211$	−2.00000	+	3.46410i	−0.137686	+	0.238479i	0.788935	+	0.614477i	$0.210633\pi$
$212$	−2.59808	−	4.50000i	−0.178437	−	0.309061i
$213$		0			0
$214$		0			0
$215$	−10.3923	+	6.00000i	−0.708749	+	0.409197i
$216$		0			0
$217$		0			0
$218$	−3.46410	+	6.00000i	−0.234619	+	0.406371i
$219$		0			0
$220$		0			0
$221$	5.19615	−	18.0000i	0.349531	−	1.21081i
$222$		0			0
$223$	−18.0000	−	10.3923i	−1.20537	−	0.695920i	−0.243625	−	0.969870i	$-0.578337\pi$
$223$	−18.0000	−	10.3923i	−1.20537	−	0.695920i	−0.961744	+	0.273949i	$0.911670\pi$
$224$		0			0
$225$		0			0
$226$			15.5885i			1.03693i
$227$	10.3923	−	6.00000i	0.689761	−	0.398234i	−0.113761	−	0.993508i	$-0.536290\pi$
$227$	10.3923	−	6.00000i	0.689761	−	0.398234i	0.803523	+	0.595274i	$0.202957\pi$
$228$		0			0
$229$		−	20.7846i		−	1.37349i	−0.726900	−	0.686743i	$-0.759040\pi$
$229$		−	20.7846i		−	1.37349i	0.726900	−	0.686743i	$-0.240960\pi$
$230$		0			0
$231$		0			0
$232$	4.50000	+	2.59808i	0.295439	+	0.170572i
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$		0			0
$235$	36.0000			2.34838
$236$	−10.3923	−	6.00000i	−0.676481	−	0.390567i
$237$		0			0
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$	7.50000	−	4.33013i	0.483117	−	0.278928i	−0.238597	−	0.971119i	$-0.576688\pi$
$241$	7.50000	−	4.33013i	0.483117	−	0.278928i	0.721715	+	0.692191i	$0.243354\pi$
$242$		−	11.0000i		−	0.707107i
$243$		0			0
$244$	−2.50000	+	4.33013i	−0.160046	+	0.277208i
$245$	−18.1865	−	10.5000i	−1.16190	−	0.670820i
$246$		0			0
$247$	−24.0000	−	6.92820i	−1.52708	−	0.440831i
$248$	6.92820			0.439941
$249$		0			0
$250$	−1.50000	+	2.59808i	−0.0948683	+	0.164317i
$251$	−10.3923	−	18.0000i	−0.655956	−	1.13615i	−0.981653	−	0.190676i	$-0.938932\pi$
$251$	−10.3923	−	18.0000i	−0.655956	−	1.13615i	0.325697	−	0.945474i	$-0.394401\pi$
$252$		0			0
$253$		0			0
$254$	6.92820	−	4.00000i	0.434714	−	0.250982i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.79423	−	13.5000i	0.486191	−	0.842107i	−0.513683	−	0.857980i	$-0.671719\pi$
$257$	7.79423	−	13.5000i	0.486191	−	0.842107i	0.999874	+	0.0158730i	$0.00505273\pi$
$258$		0			0
$259$		0			0
$260$	10.3923	+	3.00000i	0.644503	+	0.186052i
$261$		0			0
$262$	−18.0000	−	10.3923i	−1.11204	−	0.642039i
$263$	−10.3923	+	18.0000i	−0.640817	+	1.10993i	0.344434	+	0.938811i	$0.388071\pi$
$263$	−10.3923	+	18.0000i	−0.640817	+	1.10993i	−0.985251	+	0.171117i	$0.945262\pi$
$264$		0			0
$265$		−	15.5885i		−	0.957591i
$266$		0			0
$267$		0			0
$268$			13.8564i			0.846415i
$269$	10.3923	+	18.0000i	0.633630	+	1.09748i	0.986804	+	0.161922i	$0.0517692\pi$
$269$	10.3923	+	18.0000i	0.633630	+	1.09748i	−0.353174	+	0.935558i	$0.614898\pi$
$270$		0			0
$271$	−18.0000	−	10.3923i	−1.09342	−	0.631288i	−0.158937	−	0.987289i	$-0.550807\pi$
$271$	−18.0000	−	10.3923i	−1.09342	−	0.631288i	−0.934485	+	0.356001i	$0.884140\pi$
$272$	−5.19615			−0.315063
$273$		0			0
$274$	−9.00000			−0.543710
$275$		0			0
$276$		0			0
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	0.996484	+	0.0837823i	$0.0267000\pi$
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	−0.425684	+	0.904872i	$0.639967\pi$
$278$			16.0000i			0.959616i
$279$		0			0
$280$		0			0
$281$			3.00000i			0.178965i	0.995988	+	0.0894825i	$0.0285213\pi$
$281$			3.00000i			0.178965i	−0.995988	+	0.0894825i	$0.971479\pi$
$282$		0			0
$283$	−8.00000	+	13.8564i	−0.475551	+	0.823678i	−0.999608	−	0.0280052i	$-0.991084\pi$
$283$	−8.00000	+	13.8564i	−0.475551	+	0.823678i	0.524057	+	0.851683i	$0.324418\pi$
$284$	10.3923	+	6.00000i	0.616670	+	0.356034i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−5.00000	+	8.66025i	−0.294118	+	0.509427i
$290$	7.79423	+	13.5000i	0.457693	+	0.792747i
$291$		0			0
$292$	7.50000	−	4.33013i	0.438904	−	0.253402i
$293$	−7.79423	+	4.50000i	−0.455344	+	0.262893i	−0.710084	−	0.704117i	$-0.751343\pi$
$293$	−7.79423	+	4.50000i	−0.455344	+	0.262893i	0.254741	+	0.967009i	$0.418010\pi$
$294$		0			0
$295$	−18.0000	−	31.1769i	−1.04800	−	1.81519i
$296$	0.866025	−	1.50000i	0.0503367	−	0.0871857i
$297$		0			0
$298$	−3.00000			−0.173785
$299$		0			0
$300$		0			0
$301$		0			0
$302$	6.92820	−	12.0000i	0.398673	−	0.690522i
$303$		0			0
$304$			6.92820i			0.397360i
$305$	−12.9904	+	7.50000i	−0.743827	+	0.429449i
$306$		0			0
$307$			13.8564i			0.790827i	0.918503	+	0.395413i	$0.129399\pi$
$307$			13.8564i			0.790827i	−0.918503	+	0.395413i	$0.870601\pi$
$308$		0			0
$309$		0			0
$310$	18.0000	+	10.3923i	1.02233	+	0.590243i
$311$	20.7846			1.17859			0.589294	−	0.807919i	$-0.299406\pi$
$311$	20.7846			1.17859			0.589294	+	0.807919i	$0.299406\pi$
$312$		0			0
$313$	22.0000			1.24351			0.621757	−	0.783210i	$-0.286419\pi$
$313$	22.0000			1.24351			0.621757	+	0.783210i	$0.286419\pi$
$314$	−6.06218	−	3.50000i	−0.342108	−	0.197516i
$315$		0			0
$316$	2.00000	+	3.46410i	0.112509	+	0.194871i
$317$		−	9.00000i		−	0.505490i	−0.967533	−	0.252745i	$-0.918667\pi$
$317$		−	9.00000i		−	0.505490i	0.967533	−	0.252745i	$-0.0813334\pi$
$318$		0			0
$319$		0			0
$320$		−	3.00000i		−	0.167705i
$321$		0			0
$322$		0			0
$323$	31.1769	+	18.0000i	1.73473	+	1.00155i
$324$		0			0
$325$	10.0000	+	10.3923i	0.554700	+	0.576461i
$326$		0			0
$327$		0			0
$328$	4.50000	−	7.79423i	0.248471	−	0.430364i
$329$		0			0
$330$		0			0
$331$	12.0000	−	6.92820i	0.659580	−	0.380808i	−0.132537	−	0.991178i	$-0.542312\pi$
$331$	12.0000	−	6.92820i	0.659580	−	0.380808i	0.792117	+	0.610370i	$0.208979\pi$
$332$	−10.3923	+	6.00000i	−0.570352	+	0.329293i
$333$		0			0
$334$	−6.00000	−	10.3923i	−0.328305	−	0.568642i
$335$	−20.7846	+	36.0000i	−1.13558	+	1.96689i
$336$		0			0
$337$	7.00000			0.381314			0.190657	−	0.981657i	$-0.438938\pi$
$337$	7.00000			0.381314			0.190657	+	0.981657i	$0.438938\pi$
$338$	−6.92820	+	11.0000i	−0.376845	+	0.598321i
$339$		0			0
$340$	−13.5000	−	7.79423i	−0.732140	−	0.422701i
$341$		0			0
$342$		0			0
$343$		0			0
$344$	−3.46410	+	2.00000i	−0.186772	+	0.107833i
$345$		0			0
$346$			20.7846i			1.11739i
$347$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$347$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$348$		0			0
$349$	−6.00000	−	3.46410i	−0.321173	−	0.185429i	0.330743	−	0.943721i	$-0.392701\pi$
$349$	−6.00000	−	3.46410i	−0.321173	−	0.185429i	−0.651915	+	0.758292i	$0.726034\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	12.9904	+	7.50000i	0.691408	+	0.399185i	0.804139	−	0.594441i	$-0.202627\pi$
$353$	12.9904	+	7.50000i	0.691408	+	0.399185i	−0.112731	+	0.993626i	$0.535960\pi$
$354$		0			0
$355$	18.0000	+	31.1769i	0.955341	+	1.65470i
$356$		−	6.00000i		−	0.317999i
$357$		0			0
$358$	18.0000	−	10.3923i	0.951330	−	0.549250i
$359$			12.0000i			0.633336i	0.948536	+	0.316668i	$0.102564\pi$
$359$			12.0000i			0.633336i	−0.948536	+	0.316668i	$0.897436\pi$
$360$		0			0
$361$	14.5000	−	25.1147i	0.763158	−	1.32183i
$362$	−0.866025	−	0.500000i	−0.0455173	−	0.0262794i
$363$		0			0
$364$		0			0
$365$	25.9808			1.35990
$366$		0			0
$367$	−16.0000	+	27.7128i	−0.835193	+	1.44660i	0.0586798	+	0.998277i	$0.481311\pi$
$367$	−16.0000	+	27.7128i	−0.835193	+	1.44660i	−0.893873	+	0.448320i	$0.852022\pi$
$368$		0			0
$369$		0			0
$370$	4.50000	−	2.59808i	0.233944	−	0.135068i
$371$		0			0
$372$		0			0
$373$	11.5000	+	19.9186i	0.595447	+	1.03135i	0.993484	+	0.113975i	$0.0363585\pi$
$373$	11.5000	+	19.9186i	0.595447	+	1.03135i	−0.398036	+	0.917370i	$0.630308\pi$
$374$		0			0
$375$		0			0
$376$	12.0000			0.618853
$377$	−18.1865	+	4.50000i	−0.936654	+	0.231762i
$378$		0			0
$379$	−12.0000	−	6.92820i	−0.616399	−	0.355878i	0.159067	−	0.987268i	$-0.449151\pi$
$379$	−12.0000	−	6.92820i	−0.616399	−	0.355878i	−0.775466	+	0.631390i	$0.782485\pi$
$380$	−10.3923	+	18.0000i	−0.533114	+	0.923381i
$381$		0			0
$382$		−	20.7846i		−	1.06343i
$383$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$383$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$384$		0			0
$385$		0			0
$386$	−2.59808	−	4.50000i	−0.132239	−	0.229044i
$387$		0			0
$388$	−12.0000	−	6.92820i	−0.609208	−	0.351726i
$389$	−5.19615			−0.263455			−0.131728	−	0.991286i	$-0.542052\pi$
$389$	−5.19615			−0.263455			−0.131728	+	0.991286i	$0.542052\pi$
$390$		0			0
$391$		0			0
$392$	−6.06218	−	3.50000i	−0.306186	−	0.176777i
$393$		0			0
$394$	−3.00000	−	5.19615i	−0.151138	−	0.261778i
$395$			12.0000i			0.603786i
$396$		0			0
$397$	6.00000	−	3.46410i	0.301131	−	0.173858i	−0.341820	−	0.939766i	$-0.611043\pi$
$397$	6.00000	−	3.46410i	0.301131	−	0.173858i	0.642951	+	0.765907i	$0.277710\pi$
$398$			8.00000i			0.401004i
$399$		0			0
$400$	2.00000	−	3.46410i	0.100000	−	0.173205i
$401$	2.59808	+	1.50000i	0.129742	+	0.0749064i	0.563466	−	0.826139i	$-0.309468\pi$
$401$	2.59808	+	1.50000i	0.129742	+	0.0749064i	−0.433724	+	0.901046i	$0.642801\pi$
$402$		0			0
$403$	−18.0000	+	17.3205i	−0.896644	+	0.862796i
$404$	5.19615			0.258518
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−13.5000	+	7.79423i	−0.667532	+	0.385400i	−0.795141	−	0.606425i	$-0.792603\pi$
$409$	−13.5000	+	7.79423i	−0.667532	+	0.385400i	0.127609	+	0.991825i	$0.459270\pi$
$410$	23.3827	−	13.5000i	1.15479	−	0.666717i
$411$		0			0
$412$	−2.00000	−	3.46410i	−0.0985329	−	0.170664i
$413$		0			0
$414$		0			0
$415$	−36.0000			−1.76717
$416$	3.46410	+	1.00000i	0.169842	+	0.0490290i
$417$		0			0
$418$		0			0
$419$	10.3923	−	18.0000i	0.507697	−	0.879358i	−0.492263	−	0.870447i	$-0.663830\pi$
$419$	10.3923	−	18.0000i	0.507697	−	0.879358i	0.999960	−	0.00891102i	$-0.00283650\pi$
$420$		0			0
$421$			15.5885i			0.759735i	0.925041	+	0.379867i	$0.124030\pi$
$421$			15.5885i			0.759735i	−0.925041	+	0.379867i	$0.875970\pi$
$422$	−3.46410	+	2.00000i	−0.168630	+	0.0973585i
$423$		0			0
$424$		−	5.19615i		−	0.252347i
$425$	−10.3923	−	18.0000i	−0.504101	−	0.873128i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$	−12.0000			−0.578691
$431$	10.3923	+	6.00000i	0.500580	+	0.289010i	0.728953	−	0.684564i	$-0.240007\pi$
$431$	10.3923	+	6.00000i	0.500580	+	0.289010i	−0.228373	+	0.973574i	$0.573341\pi$
$432$		0			0
$433$	−9.50000	−	16.4545i	−0.456541	−	0.790752i	0.542234	−	0.840227i	$-0.317578\pi$
$433$	−9.50000	−	16.4545i	−0.456541	−	0.790752i	−0.998775	+	0.0494752i	$0.984245\pi$
$434$		0			0
$435$		0			0
$436$	−6.00000	+	3.46410i	−0.287348	+	0.165900i
$437$		0			0
$438$		0			0
$439$	2.00000	−	3.46410i	0.0954548	−	0.165333i	−0.814344	−	0.580383i	$-0.802903\pi$
$439$	2.00000	−	3.46410i	0.0954548	−	0.165333i	0.909798	+	0.415051i	$0.136236\pi$
$440$		0			0
$441$		0			0
$442$	13.5000	−	12.9904i	0.642130	−	0.617889i
$443$		0			0			−	1.00000i	$-0.5\pi$
$443$		0			0				1.00000i	$0.5\pi$
$444$		0			0
$445$	9.00000	−	15.5885i	0.426641	−	0.738964i
$446$	−10.3923	−	18.0000i	−0.492090	−	0.852325i
$447$		0			0
$448$		0			0
$449$	25.9808	−	15.0000i	1.22611	−	0.707894i	0.259895	−	0.965637i	$-0.416312\pi$
$449$	25.9808	−	15.0000i	1.22611	−	0.707894i	0.966213	+	0.257743i	$0.0829789\pi$
$450$		0			0
$451$		0			0
$452$	−7.79423	+	13.5000i	−0.366610	+	0.634987i
$453$		0			0
$454$	12.0000			0.563188
$455$		0			0
$456$		0			0
$457$	10.5000	+	6.06218i	0.491169	+	0.283577i	0.725059	−	0.688686i	$-0.241812\pi$
$457$	10.5000	+	6.06218i	0.491169	+	0.283577i	−0.233890	+	0.972263i	$0.575146\pi$
$458$	10.3923	−	18.0000i	0.485601	−	0.841085i
$459$		0			0
$460$		0			0
$461$	−18.1865	+	10.5000i	−0.847031	+	0.489034i	−0.859648	−	0.510887i	$-0.829317\pi$
$461$	−18.1865	+	10.5000i	−0.847031	+	0.489034i	0.0126168	+	0.999920i	$0.495984\pi$
$462$		0			0
$463$		−	6.92820i		−	0.321981i	−0.986956	−	0.160990i	$-0.948531\pi$
$463$		−	6.92820i		−	0.321981i	0.986956	−	0.160990i	$-0.0514688\pi$
$464$	2.59808	+	4.50000i	0.120613	+	0.208907i
$465$		0			0
$466$		0			0
$467$	−41.5692			−1.92359			−0.961797	−	0.273764i	$-0.911731\pi$
$467$	−41.5692			−1.92359			−0.961797	+	0.273764i	$0.911731\pi$
$468$		0			0
$469$		0			0
$470$	31.1769	+	18.0000i	1.43808	+	0.830278i
$471$		0			0
$472$	−6.00000	−	10.3923i	−0.276172	−	0.478345i
$473$		0			0
$474$		0			0
$475$	−24.0000	+	13.8564i	−1.10120	+	0.635776i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−20.7846	−	12.0000i	−0.949673	−	0.548294i	−0.0566937	−	0.998392i	$-0.518056\pi$
$479$	−20.7846	−	12.0000i	−0.949673	−	0.548294i	−0.892979	+	0.450098i	$0.851389\pi$
$480$		0			0
$481$	1.50000	+	6.06218i	0.0683941	+	0.276412i
$482$	8.66025			0.394464
$483$		0			0
$484$	5.50000	−	9.52628i	0.250000	−	0.433013i
$485$	−20.7846	−	36.0000i	−0.943781	−	1.63468i
$486$		0			0
$487$	−6.00000	+	3.46410i	−0.271886	+	0.156973i	−0.629744	−	0.776802i	$-0.716840\pi$
$487$	−6.00000	+	3.46410i	−0.271886	+	0.156973i	0.357858	+	0.933776i	$0.383507\pi$
$488$	−4.33013	+	2.50000i	−0.196016	+	0.113170i
$489$		0			0
$490$	−10.5000	−	18.1865i	−0.474342	−	0.821584i
$491$	10.3923	−	18.0000i	0.468998	−	0.812329i	−0.530374	−	0.847764i	$-0.677948\pi$
$491$	10.3923	−	18.0000i	0.468998	−	0.812329i	0.999372	+	0.0354353i	$0.0112818\pi$
$492$		0			0
$493$	27.0000			1.21602
$494$	−17.3205	−	18.0000i	−0.779287	−	0.809858i
$495$		0			0
$496$	6.00000	+	3.46410i	0.269408	+	0.155543i
$497$		0			0
$498$		0			0
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$	−2.59808	+	1.50000i	−0.116190	+	0.0670820i
$501$		0			0
$502$		−	20.7846i		−	0.927663i
$503$	−10.3923	−	18.0000i	−0.463370	−	0.802580i	0.535756	−	0.844373i	$-0.320027\pi$
$503$	−10.3923	−	18.0000i	−0.463370	−	0.802580i	−0.999126	+	0.0417923i	$0.986693\pi$
$504$		0			0
$505$	13.5000	+	7.79423i	0.600742	+	0.346839i
$506$		0			0
$507$		0			0
$508$	8.00000			0.354943
$509$	−12.9904	−	7.50000i	−0.575789	−	0.332432i	0.183669	−	0.982988i	$-0.441202\pi$
$509$	−12.9904	−	7.50000i	−0.575789	−	0.332432i	−0.759458	+	0.650556i	$0.774536\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	13.5000	−	7.79423i	0.595459	−	0.343789i
$515$		−	12.0000i		−	0.528783i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	7.50000	+	7.79423i	0.328897	+	0.341800i
$521$	15.5885			0.682943			0.341471	−	0.939892i	$-0.389075\pi$
$521$	15.5885			0.682943			0.341471	+	0.939892i	$0.389075\pi$
$522$		0			0
$523$	−4.00000	+	6.92820i	−0.174908	+	0.302949i	−0.940129	−	0.340818i	$-0.889296\pi$
$523$	−4.00000	+	6.92820i	−0.174908	+	0.302949i	0.765222	+	0.643767i	$0.222629\pi$
$524$	−10.3923	−	18.0000i	−0.453990	−	0.786334i
$525$		0			0
$526$	−18.0000	+	10.3923i	−0.784837	+	0.453126i
$527$	31.1769	−	18.0000i	1.35809	−	0.784092i
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	7.79423	−	13.5000i	0.338560	−	0.586403i
$531$		0			0
$532$		0			0
$533$	7.79423	+	31.5000i	0.337606	+	1.36442i
$534$		0			0
$535$		0			0
$536$	−6.92820	+	12.0000i	−0.299253	+	0.518321i
$537$		0			0
$538$			20.7846i			0.896088i
$539$		0			0
$540$		0			0
$541$		−	32.9090i		−	1.41487i	−0.706780	−	0.707433i	$-0.749853\pi$
$541$		−	32.9090i		−	1.41487i	0.706780	−	0.707433i	$-0.250147\pi$
$542$	−10.3923	−	18.0000i	−0.446388	−	0.773166i
$543$		0			0
$544$	−4.50000	−	2.59808i	−0.192936	−	0.111392i
$545$	−20.7846			−0.890315
$546$		0			0
$547$	−4.00000			−0.171028			−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000			−0.171028			−0.0855138	+	0.996337i	$0.527253\pi$
$548$	−7.79423	−	4.50000i	−0.332953	−	0.192230i
$549$		0			0
$550$		0			0
$551$		−	36.0000i		−	1.53365i
$552$		0			0
$553$		0			0
$554$			19.0000i			0.807233i
$555$		0			0
$556$	−8.00000	+	13.8564i	−0.339276	+	0.587643i
$557$	38.9711	+	22.5000i	1.65126	+	0.953356i	0.976555	+	0.215268i	$0.0690627\pi$
$557$	38.9711	+	22.5000i	1.65126	+	0.953356i	0.674705	+	0.738087i	$0.264271\pi$
$558$		0			0
$559$	4.00000	−	13.8564i	0.169182	−	0.586064i
$560$		0			0
$561$		0			0
$562$	−1.50000	+	2.59808i	−0.0632737	+	0.109593i
$563$	−10.3923	−	18.0000i	−0.437983	−	0.758610i	0.559550	−	0.828796i	$-0.310974\pi$
$563$	−10.3923	−	18.0000i	−0.437983	−	0.758610i	−0.997534	+	0.0701867i	$0.977640\pi$
$564$		0			0
$565$	−40.5000	+	23.3827i	−1.70385	+	0.983717i
$566$	−13.8564	+	8.00000i	−0.582428	+	0.336265i
$567$		0			0
$568$	6.00000	+	10.3923i	0.251754	+	0.436051i
$569$	−20.7846	+	36.0000i	−0.871336	+	1.50920i	−0.0107211	+	0.999943i	$0.503413\pi$
$569$	−20.7846	+	36.0000i	−0.871336	+	1.50920i	−0.860615	+	0.509256i	$0.829921\pi$
$570$		0			0
$571$	16.0000			0.669579			0.334790	−	0.942293i	$-0.391335\pi$
$571$	16.0000			0.669579			0.334790	+	0.942293i	$0.391335\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$			43.3013i			1.80266i	0.433138	+	0.901328i	$0.357406\pi$
$577$			43.3013i			1.80266i	−0.433138	+	0.901328i	$0.642594\pi$
$578$	−8.66025	+	5.00000i	−0.360219	+	0.207973i
$579$		0			0
$580$			15.5885i			0.647275i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	8.66025			0.358364
$585$		0			0
$586$	−9.00000			−0.371787
$587$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$587$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$588$		0			0
$589$	−24.0000	−	41.5692i	−0.988903	−	1.71283i
$590$		−	36.0000i		−	1.48210i
$591$		0			0
$592$	1.50000	−	0.866025i	0.0616496	−	0.0355934i
$593$			9.00000i			0.369586i	0.982777	+	0.184793i	$0.0591614\pi$
$593$			9.00000i			0.369586i	−0.982777	+	0.184793i	$0.940839\pi$
$594$		0			0
$595$		0			0
$596$	−2.59808	−	1.50000i	−0.106421	−	0.0614424i
$597$		0			0
$598$		0			0
$599$	20.7846			0.849236			0.424618	−	0.905373i	$-0.360408\pi$
$599$	20.7846			0.849236			0.424618	+	0.905373i	$0.360408\pi$
$600$		0			0
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	−0.249565	−	0.968358i	$-0.580288\pi$
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	0.963405	−	0.268049i	$-0.0863789\pi$
$602$		0			0
$603$		0			0
$604$	12.0000	−	6.92820i	0.488273	−	0.281905i
$605$	28.5788	−	16.5000i	1.16190	−	0.670820i
$606$		0			0
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	0.981454	−	0.191700i	$-0.0614000\pi$
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	−0.656744	+	0.754114i	$0.728067\pi$
$608$	−3.46410	+	6.00000i	−0.140488	+	0.243332i
$609$		0			0
$610$	−15.0000			−0.607332
$611$	−31.1769	+	30.0000i	−1.26128	+	1.21367i
$612$		0			0
$613$	34.5000	+	19.9186i	1.39344	+	0.804504i	0.993695	−	0.112121i	$-0.0357645\pi$
$613$	34.5000	+	19.9186i	1.39344	+	0.804504i	0.399747	+	0.916625i	$0.369098\pi$
$614$	−6.92820	+	12.0000i	−0.279600	+	0.484281i
$615$		0			0
$616$		0			0
$617$	18.1865	−	10.5000i	0.732162	−	0.422714i	−0.0870504	−	0.996204i	$-0.527744\pi$
$617$	18.1865	−	10.5000i	0.732162	−	0.422714i	0.819213	+	0.573490i	$0.194411\pi$
$618$		0			0
$619$			20.7846i			0.835404i	0.908584	+	0.417702i	$0.137164\pi$
$619$			20.7846i			0.835404i	−0.908584	+	0.417702i	$0.862836\pi$
$620$	10.3923	+	18.0000i	0.417365	+	0.722897i
$621$		0			0
$622$	18.0000	+	10.3923i	0.721734	+	0.416693i
$623$		0			0
$624$		0			0
$625$	−29.0000			−1.16000
$626$	19.0526	+	11.0000i	0.761493	+	0.439648i
$627$		0			0
$628$	−3.50000	−	6.06218i	−0.139665	−	0.241907i
$629$		−	9.00000i		−	0.358854i
$630$		0			0
$631$	12.0000	−	6.92820i	0.477712	−	0.275807i	−0.241750	−	0.970339i	$-0.577721\pi$
$631$	12.0000	−	6.92820i	0.477712	−	0.275807i	0.719463	+	0.694531i	$0.244388\pi$
$632$			4.00000i			0.159111i
$633$		0			0
$634$	4.50000	−	7.79423i	0.178718	−	0.309548i
$635$	20.7846	+	12.0000i	0.824812	+	0.476205i
$636$		0			0
$637$	24.5000	−	6.06218i	0.970725	−	0.240192i
$638$		0			0
$639$		0			0
$640$	1.50000	−	2.59808i	0.0592927	−	0.102698i
$641$	−2.59808	−	4.50000i	−0.102618	−	0.177739i	0.810145	−	0.586230i	$-0.199389\pi$
$641$	−2.59808	−	4.50000i	−0.102618	−	0.177739i	−0.912762	+	0.408491i	$0.866055\pi$
$642$		0			0
$643$	30.0000	−	17.3205i	1.18308	−	0.683054i	0.226358	−	0.974044i	$-0.427318\pi$
$643$	30.0000	−	17.3205i	1.18308	−	0.683054i	0.956726	+	0.290990i	$0.0939846\pi$
$644$		0			0
$645$		0			0
$646$	18.0000	+	31.1769i	0.708201	+	1.22664i
$647$	−10.3923	+	18.0000i	−0.408564	+	0.707653i	−0.994729	−	0.102538i	$-0.967304\pi$
$647$	−10.3923	+	18.0000i	−0.408564	+	0.707653i	0.586165	+	0.810191i	$0.300637\pi$
$648$		0			0
$649$		0			0
$650$	3.46410	+	14.0000i	0.135873	+	0.549125i
$651$		0			0
$652$		0			0
$653$	−10.3923	+	18.0000i	−0.406682	+	0.704394i	−0.994516	−	0.104588i	$-0.966648\pi$
$653$	−10.3923	+	18.0000i	−0.406682	+	0.704394i	0.587833	+	0.808982i	$0.299981\pi$
$654$		0			0
$655$		−	62.3538i		−	2.43637i
$656$	7.79423	−	4.50000i	0.304314	−	0.175695i
$657$		0			0
$658$		0			0
$659$	20.7846	+	36.0000i	0.809653	+	1.40236i	0.913104	+	0.407726i	$0.133678\pi$
$659$	20.7846	+	36.0000i	0.809653	+	1.40236i	−0.103451	+	0.994635i	$0.532988\pi$
$660$		0			0
$661$	4.50000	+	2.59808i	0.175030	+	0.101053i	0.584955	−	0.811065i	$-0.301112\pi$
$661$	4.50000	+	2.59808i	0.175030	+	0.101053i	−0.409926	+	0.912119i	$0.634445\pi$
$662$	13.8564			0.538545
$663$		0			0
$664$	−12.0000			−0.465690
$665$		0			0
$666$		0			0
$667$		0			0
$668$		−	12.0000i		−	0.464294i
$669$		0			0
$670$	−36.0000	+	20.7846i	−1.39080	+	0.802980i
$671$		0			0
$672$		0			0
$673$	−2.50000	+	4.33013i	−0.0963679	+	0.166914i	−0.910179	−	0.414216i	$-0.864056\pi$
$673$	−2.50000	+	4.33013i	−0.0963679	+	0.166914i	0.813811	+	0.581130i	$0.197389\pi$
$674$	6.06218	+	3.50000i	0.233506	+	0.134815i
$675$		0			0
$676$	−11.5000	+	6.06218i	−0.442308	+	0.233161i
$677$	−20.7846			−0.798817			−0.399409	−	0.916773i	$-0.630785\pi$
$677$	−20.7846			−0.798817			−0.399409	+	0.916773i	$0.630785\pi$
$678$		0			0
$679$		0			0
$680$	−7.79423	−	13.5000i	−0.298895	−	0.517701i
$681$		0			0
$682$		0			0
$683$	10.3923	−	6.00000i	0.397650	−	0.229584i	−0.287819	−	0.957685i	$-0.592930\pi$
$683$	10.3923	−	6.00000i	0.397650	−	0.229584i	0.685470	+	0.728101i	$0.259597\pi$
$684$		0			0
$685$	−13.5000	−	23.3827i	−0.515808	−	0.893407i
$686$		0			0
$687$		0			0
$688$	−4.00000			−0.152499
$689$	12.9904	+	13.5000i	0.494894	+	0.514309i
$690$		0			0
$691$	12.0000	+	6.92820i	0.456502	+	0.263561i	0.710572	−	0.703624i	$-0.248436\pi$
$691$	12.0000	+	6.92820i	0.456502	+	0.263561i	−0.254071	+	0.967186i	$0.581770\pi$
$692$	−10.3923	+	18.0000i	−0.395056	+	0.684257i
$693$		0			0
$694$		0			0
$695$	−41.5692	+	24.0000i	−1.57681	+	0.910372i
$696$		0			0
$697$		−	46.7654i		−	1.77136i
$698$	−3.46410	−	6.00000i	−0.131118	−	0.227103i
$699$		0			0
$700$		0			0
$701$	−20.7846			−0.785024			−0.392512	−	0.919747i	$-0.628394\pi$
$701$	−20.7846			−0.785024			−0.392512	+	0.919747i	$0.628394\pi$
$702$		0			0
$703$	−12.0000			−0.452589
$704$		0			0
$705$		0			0
$706$	7.50000	+	12.9904i	0.282266	+	0.488899i
$707$		0			0
$708$		0			0
$709$	−22.5000	+	12.9904i	−0.845005	+	0.487864i	−0.858962	−	0.512039i	$-0.828890\pi$
$709$	−22.5000	+	12.9904i	−0.845005	+	0.487864i	0.0139572	+	0.999903i	$0.495557\pi$
$710$			36.0000i			1.35106i
$711$		0			0
$712$	3.00000	−	5.19615i	0.112430	−	0.194734i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	20.7846			0.776757
$717$		0			0
$718$	−6.00000	+	10.3923i	−0.223918	+	0.387837i
$719$	−10.3923	−	18.0000i	−0.387568	−	0.671287i	0.604554	−	0.796564i	$-0.293351\pi$
$719$	−10.3923	−	18.0000i	−0.387568	−	0.671287i	−0.992122	+	0.125277i	$0.960018\pi$
$720$		0			0
$721$		0			0
$722$	25.1147	−	14.5000i	0.934674	−	0.539634i
$723$		0			0
$724$	−0.500000	−	0.866025i	−0.0185824	−	0.0321856i
$725$	−10.3923	+	18.0000i	−0.385961	+	0.668503i
$726$		0			0
$727$	−32.0000			−1.18681			−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000			−1.18681			−0.593407	+	0.804902i	$0.702218\pi$
$728$		0			0
$729$		0			0
$730$	22.5000	+	12.9904i	0.832762	+	0.480796i
$731$	−10.3923	+	18.0000i	−0.384373	+	0.665754i
$732$		0			0
$733$		−	8.66025i		−	0.319874i	−0.987127	−	0.159937i	$-0.948871\pi$
$733$		−	8.66025i		−	0.319874i	0.987127	−	0.159937i	$-0.0511291\pi$
$734$	−27.7128	+	16.0000i	−1.02290	+	0.590571i
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−36.0000	−	20.7846i	−1.32428	−	0.764574i	−0.339873	−	0.940471i	$-0.610384\pi$
$739$	−36.0000	−	20.7846i	−1.32428	−	0.764574i	−0.984409	+	0.175897i	$0.943717\pi$
$740$	5.19615			0.191014
$741$		0			0
$742$		0			0
$743$	20.7846	+	12.0000i	0.762513	+	0.440237i	0.830197	−	0.557470i	$-0.188228\pi$
$743$	20.7846	+	12.0000i	0.762513	+	0.440237i	−0.0676840	+	0.997707i	$0.521561\pi$
$744$		0			0
$745$	−4.50000	−	7.79423i	−0.164867	−	0.285558i
$746$			23.0000i			0.842090i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−10.0000	+	17.3205i	−0.364905	+	0.632034i	−0.988761	−	0.149505i	$-0.952232\pi$
$751$	−10.0000	+	17.3205i	−0.364905	+	0.632034i	0.623856	+	0.781540i	$0.285565\pi$
$752$	10.3923	+	6.00000i	0.378968	+	0.218797i
$753$		0			0
$754$	−18.0000	−	5.19615i	−0.655521	−	0.189233i
$755$	41.5692			1.51286
$756$		0			0
$757$	−5.00000	+	8.66025i	−0.181728	+	0.314762i	−0.942469	−	0.334293i	$-0.891502\pi$
$757$	−5.00000	+	8.66025i	−0.181728	+	0.314762i	0.760741	+	0.649056i	$0.224836\pi$
$758$	−6.92820	−	12.0000i	−0.251644	−	0.435860i
$759$		0			0
$760$	−18.0000	+	10.3923i	−0.652929	+	0.376969i
$761$	−5.19615	+	3.00000i	−0.188360	+	0.108750i	−0.591215	−	0.806514i	$-0.701351\pi$
$761$	−5.19615	+	3.00000i	−0.188360	+	0.108750i	0.402854	+	0.915264i	$0.368018\pi$
$762$		0			0
$763$		0			0
$764$	10.3923	−	18.0000i	0.375980	−	0.651217i
$765$		0			0
$766$		0			0
$767$	41.5692	+	12.0000i	1.50098	+	0.433295i
$768$		0			0
$769$	−12.0000	−	6.92820i	−0.432731	−	0.249837i	0.267778	−	0.963481i	$-0.413711\pi$
$769$	−12.0000	−	6.92820i	−0.432731	−	0.249837i	−0.700509	+	0.713643i	$0.747044\pi$
$770$		0			0
$771$		0			0
$772$		−	5.19615i		−	0.187014i
$773$	36.3731	−	21.0000i	1.30825	−	0.755318i	0.326445	−	0.945216i	$-0.394149\pi$
$773$	36.3731	−	21.0000i	1.30825	−	0.755318i	0.981804	+	0.189899i	$0.0608160\pi$
$774$		0			0
$775$			27.7128i			0.995474i
$776$	−6.92820	−	12.0000i	−0.248708	−	0.430775i
$777$		0			0
$778$	−4.50000	−	2.59808i	−0.161333	−	0.0931455i
$779$	−62.3538			−2.23406
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−3.50000	−	6.06218i	−0.125000	−	0.216506i
$785$		−	21.0000i		−	0.749522i
$786$		0			0
$787$	42.0000	−	24.2487i	1.49714	−	0.864373i	0.497144	−	0.867668i	$-0.334382\pi$
$787$	42.0000	−	24.2487i	1.49714	−	0.864373i	0.999995	+	0.00329499i	$0.00104883\pi$
$788$		−	6.00000i		−	0.213741i
$789$		0			0
$790$	−6.00000	+	10.3923i	−0.213470	+	0.369742i
$791$		0			0
$792$		0			0
$793$	5.00000	−	17.3205i	0.177555	−	0.615069i
$794$	6.92820			0.245873
$795$		0			0
$796$	−4.00000	+	6.92820i	−0.141776	+	0.245564i
$797$	−10.3923	−	18.0000i	−0.368114	−	0.637593i	0.621156	−	0.783687i	$-0.286663\pi$
$797$	−10.3923	−	18.0000i	−0.368114	−	0.637593i	−0.989271	+	0.146094i	$0.953330\pi$
$798$		0			0
$799$	54.0000	−	31.1769i	1.91038	−	1.10296i
$800$	3.46410	−	2.00000i	0.122474	−	0.0707107i
$801$		0			0
$802$	1.50000	+	2.59808i	0.0529668	+	0.0917413i
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−24.2487	+	6.00000i	−0.854124	+	0.211341i
$807$		0			0
$808$	4.50000	+	2.59808i	0.158309	+	0.0914000i
$809$	7.79423	−	13.5000i	0.274030	−	0.474635i	−0.695860	−	0.718178i	$-0.744976\pi$
$809$	7.79423	−	13.5000i	0.274030	−	0.474635i	0.969890	+	0.243543i	$0.0783097\pi$
$810$		0			0
$811$		−	6.92820i		−	0.243282i	−0.992574	−	0.121641i	$-0.961184\pi$
$811$		−	6.92820i		−	0.243282i	0.992574	−	0.121641i	$-0.0388157\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$	24.0000	+	13.8564i	0.839654	+	0.484774i
$818$	−15.5885			−0.545038
$819$		0			0
$820$	27.0000			0.942881
$821$	46.7654	+	27.0000i	1.63212	+	0.942306i	0.983437	+	0.181250i	$0.0580143\pi$
$821$	46.7654	+	27.0000i	1.63212	+	0.942306i	0.648686	+	0.761056i	$0.275319\pi$
$822$		0			0
$823$	26.0000	+	45.0333i	0.906303	+	1.56976i	0.819159	+	0.573567i	$0.194441\pi$
$823$	26.0000	+	45.0333i	0.906303	+	1.56976i	0.0871445	+	0.996196i	$0.472226\pi$
$824$		−	4.00000i		−	0.139347i
$825$		0			0
$826$		0			0
$827$			36.0000i			1.25184i	0.779886	+	0.625921i	$0.215277\pi$
$827$			36.0000i			1.25184i	−0.779886	+	0.625921i	$0.784723\pi$
$828$		0			0
$829$	−18.5000	+	32.0429i	−0.642532	+	1.11290i	0.342334	+	0.939578i	$0.388783\pi$
$829$	−18.5000	+	32.0429i	−0.642532	+	1.11290i	−0.984866	+	0.173319i	$0.944551\pi$
$830$	−31.1769	−	18.0000i	−1.08217	−	0.624789i
$831$		0			0
$832$	2.50000	+	2.59808i	0.0866719	+	0.0900721i
$833$	−36.3731			−1.26025
$834$		0			0
$835$	18.0000	−	31.1769i	0.622916	−	1.07892i
$836$		0			0
$837$		0			0
$838$	18.0000	−	10.3923i	0.621800	−	0.358996i
$839$	41.5692	−	24.0000i	1.43513	−	0.828572i	0.437623	−	0.899158i	$-0.355820\pi$
$839$	41.5692	−	24.0000i	1.43513	−	0.828572i	0.997506	+	0.0705865i	$0.0224871\pi$
$840$		0			0
$841$	1.00000	+	1.73205i	0.0344828	+	0.0597259i
$842$	−7.79423	+	13.5000i	−0.268607	+	0.465241i
$843$		0			0
$844$	−4.00000			−0.137686
$845$	−38.9711	−	1.50000i	−1.34065	−	0.0516016i
$846$		0			0
$847$		0			0
$848$	2.59808	−	4.50000i	0.0892183	−	0.154531i
$849$		0			0
$850$		−	20.7846i		−	0.712906i
$851$		0			0
$852$		0			0
$853$			36.3731i			1.24539i	0.782465	+	0.622695i	$0.213962\pi$
$853$			36.3731i			1.24539i	−0.782465	+	0.622695i	$0.786038\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	25.9808			0.887486			0.443743	−	0.896154i	$-0.353650\pi$
$857$	25.9808			0.887486			0.443743	+	0.896154i	$0.353650\pi$
$858$		0			0
$859$	40.0000			1.36478			0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000			1.36478			0.682391	+	0.730987i	$0.260940\pi$
$860$	−10.3923	−	6.00000i	−0.354375	−	0.204598i
$861$		0			0
$862$	6.00000	+	10.3923i	0.204361	+	0.353963i
$863$		−	24.0000i		−	0.816970i	−0.912765	−	0.408485i	$-0.866057\pi$
$863$		−	24.0000i		−	0.816970i	0.912765	−	0.408485i	$-0.133943\pi$
$864$		0			0
$865$	−54.0000	+	31.1769i	−1.83606	+	1.06005i
$866$		−	19.0000i		−	0.645646i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−12.0000	−	48.4974i	−0.406604	−	1.64327i
$872$	−6.92820			−0.234619
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−16.5000	+	9.52628i	−0.557165	+	0.321680i	−0.752007	−	0.659155i	$-0.770914\pi$
$877$	−16.5000	+	9.52628i	−0.557165	+	0.321680i	0.194842	+	0.980835i	$0.437581\pi$
$878$	3.46410	−	2.00000i	0.116908	−	0.0674967i
$879$		0			0
$880$		0			0
$881$	12.9904	−	22.5000i	0.437657	−	0.758044i	−0.559851	−	0.828593i	$-0.689142\pi$
$881$	12.9904	−	22.5000i	0.437657	−	0.758044i	0.997508	+	0.0705489i	$0.0224751\pi$
$882$		0			0
$883$	−8.00000			−0.269221			−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000			−0.269221			−0.134611	+	0.990899i	$0.542978\pi$
$884$	18.1865	−	4.50000i	0.611679	−	0.151351i
$885$		0			0
$886$		0			0
$887$	10.3923	−	18.0000i	0.348939	−	0.604381i	−0.637122	−	0.770763i	$-0.719875\pi$
$887$	10.3923	−	18.0000i	0.348939	−	0.604381i	0.986061	+	0.166382i	$0.0532086\pi$
$888$		0			0
$889$		0			0
$890$	15.5885	−	9.00000i	0.522526	−	0.301681i
$891$		0			0
$892$		−	20.7846i		−	0.695920i
$893$	−41.5692	−	72.0000i	−1.39106	−	2.40939i
$894$		0			0
$895$	54.0000	+	31.1769i	1.80502	+	1.04213i
$896$		0			0
$897$		0			0
$898$	30.0000			1.00111
$899$	−31.1769	−	18.0000i	−1.03981	−	0.600334i
$900$		0			0
$901$	−13.5000	−	23.3827i	−0.449750	−	0.778990i
$902$		0			0
$903$		0			0
$904$	−13.5000	+	7.79423i	−0.449003	+	0.259232i
$905$		−	3.00000i		−	0.0997234i
$906$		0			0
$907$	−20.0000	+	34.6410i	−0.664089	+	1.15024i	0.315442	+	0.948945i	$0.397847\pi$
$907$	−20.0000	+	34.6410i	−0.664089	+	1.15024i	−0.979531	+	0.201291i	$0.935486\pi$
$908$	10.3923	+	6.00000i	0.344881	+	0.199117i
$909$		0			0
$910$		0			0
$911$	20.7846			0.688625			0.344312	−	0.938855i	$-0.388112\pi$
$911$	20.7846			0.688625			0.344312	+	0.938855i	$0.388112\pi$
$912$		0			0
$913$		0			0
$914$	6.06218	+	10.5000i	0.200519	+	0.347309i
$915$		0			0
$916$	18.0000	−	10.3923i	0.594737	−	0.343371i
$917$		0			0
$918$		0			0
$919$	−8.00000	−	13.8564i	−0.263896	−	0.457081i	0.703378	−	0.710816i	$-0.251674\pi$
$919$	−8.00000	−	13.8564i	−0.263896	−	0.457081i	−0.967274	+	0.253735i	$0.918341\pi$
$920$		0			0
$921$		0			0
$922$	−21.0000			−0.691598
$923$	−41.5692	−	12.0000i	−1.36827	−	0.394985i
$924$		0			0
$925$	6.00000	+	3.46410i	0.197279	+	0.113899i
$926$	3.46410	−	6.00000i	0.113837	−	0.197172i
$927$		0			0
$928$			5.19615i			0.170572i
$929$	−23.3827	+	13.5000i	−0.767161	+	0.442921i	−0.831861	−	0.554984i	$-0.812724\pi$
$929$	−23.3827	+	13.5000i	−0.767161	+	0.442921i	0.0646999	+	0.997905i	$0.479391\pi$
$930$		0			0
$931$			48.4974i			1.58944i
$932$		0			0
$933$		0			0
$934$	−36.0000	−	20.7846i	−1.17796	−	0.680093i
$935$		0			0
$936$		0			0
$937$	−53.0000			−1.73143			−0.865717	−	0.500533i	$-0.833137\pi$
$937$	−53.0000			−1.73143			−0.865717	+	0.500533i	$0.833137\pi$
$938$		0			0
$939$		0			0
$940$	18.0000	+	31.1769i	0.587095	+	1.01688i
$941$			18.0000i			0.586783i	0.955992	+	0.293392i	$0.0947840\pi$
$941$			18.0000i			0.586783i	−0.955992	+	0.293392i	$0.905216\pi$
$942$		0			0
$943$		0			0
$944$		−	12.0000i		−	0.390567i
$945$		0			0
$946$		0			0
$947$	−20.7846	−	12.0000i	−0.675409	−	0.389948i	0.122714	−	0.992442i	$-0.460840\pi$
$947$	−20.7846	−	12.0000i	−0.675409	−	0.389948i	−0.798123	+	0.602494i	$0.794174\pi$
$948$		0			0
$949$	−22.5000	+	21.6506i	−0.730381	+	0.702809i
$950$	−27.7128			−0.899122
$951$		0			0
$952$		0			0
$953$	−20.7846	−	36.0000i	−0.673280	−	1.16615i	−0.976969	−	0.213383i	$-0.931552\pi$
$953$	−20.7846	−	36.0000i	−0.673280	−	1.16615i	0.303689	−	0.952771i	$-0.401782\pi$
$954$		0			0
$955$	54.0000	−	31.1769i	1.74740	−	1.00886i
$956$		0			0
$957$		0			0
$958$	−12.0000	−	20.7846i	−0.387702	−	0.671520i
$959$		0			0
$960$		0			0
$961$	−17.0000			−0.548387
$962$	−1.73205	+	6.00000i	−0.0558436	+	0.193448i
$963$		0			0
$964$	7.50000	+	4.33013i	0.241559	+	0.139464i
$965$	7.79423	−	13.5000i	0.250905	−	0.434580i
$966$		0			0
$967$			6.92820i			0.222796i	0.993776	+	0.111398i	$0.0355328\pi$
$967$			6.92820i			0.222796i	−0.993776	+	0.111398i	$0.964467\pi$
$968$	9.52628	−	5.50000i	0.306186	−	0.176777i
$969$		0			0
$970$		−	41.5692i		−	1.33471i
$971$	20.7846	+	36.0000i	0.667010	+	1.15529i	0.978736	+	0.205123i	$0.0657595\pi$
$971$	20.7846	+	36.0000i	0.667010	+	1.15529i	−0.311726	+	0.950172i	$0.600907\pi$
$972$		0			0
$973$		0			0
$974$	−6.92820			−0.221994
$975$		0			0
$976$	−5.00000			−0.160046
$977$	−2.59808	−	1.50000i	−0.0831198	−	0.0479893i	0.457864	−	0.889022i	$-0.348615\pi$
$977$	−2.59808	−	1.50000i	−0.0831198	−	0.0479893i	−0.540984	+	0.841033i	$0.681948\pi$
$978$		0			0
$979$		0			0
$980$		−	21.0000i		−	0.670820i
$981$		0			0
$982$	18.0000	−	10.3923i	0.574403	−	0.331632i
$983$		−	36.0000i		−	1.14822i	−0.818778	−	0.574111i	$-0.805348\pi$
$983$		−	36.0000i		−	1.14822i	0.818778	−	0.574111i	$-0.194652\pi$
$984$		0			0
$985$	9.00000	−	15.5885i	0.286764	−	0.496690i
$986$	23.3827	+	13.5000i	0.744656	+	0.429928i
$987$		0			0
$988$	−6.00000	−	24.2487i	−0.190885	−	0.771454i
$989$		0			0
$990$		0			0
$991$	−22.0000	+	38.1051i	−0.698853	+	1.21045i	0.270011	+	0.962857i	$0.412973\pi$
$991$	−22.0000	+	38.1051i	−0.698853	+	1.21045i	−0.968864	+	0.247592i	$0.920361\pi$
$992$	3.46410	+	6.00000i	0.109985	+	0.190500i
$993$		0			0
$994$		0			0
$995$	−20.7846	+	12.0000i	−0.658916	+	0.380426i
$996$		0			0
$997$	6.50000	+	11.2583i	0.205857	+	0.356555i	0.950405	−	0.311014i	$-0.100668\pi$
$997$	6.50000	+	11.2583i	0.205857	+	0.356555i	−0.744548	+	0.667568i	$0.767335\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.l.b.199.2	yes	4
3.2	odd	2	inner	234.2.l.b.199.1	yes	4
4.3	odd	2		1872.2.by.i.433.2		4
12.11	even	2		1872.2.by.i.433.1		4
13.4	even	6		3042.2.b.m.1351.3		4
13.6	odd	12		3042.2.a.t.1.2		2
13.7	odd	12		3042.2.a.u.1.2		2
13.9	even	3		3042.2.b.m.1351.1		4
13.10	even	6	inner	234.2.l.b.127.2	yes	4
39.17	odd	6		3042.2.b.m.1351.2		4
39.20	even	12		3042.2.a.t.1.1		2
39.23	odd	6	inner	234.2.l.b.127.1	✓	4
39.32	even	12		3042.2.a.u.1.1		2
39.35	odd	6		3042.2.b.m.1351.4		4
52.23	odd	6		1872.2.by.i.1297.1		4
156.23	even	6		1872.2.by.i.1297.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.l.b.127.1	✓	4	39.23	odd	6	inner
234.2.l.b.127.2	yes	4	13.10	even	6	inner
234.2.l.b.199.1	yes	4	3.2	odd	2	inner
234.2.l.b.199.2	yes	4	1.1	even	1	trivial
1872.2.by.i.433.1		4	12.11	even	2
1872.2.by.i.433.2		4	4.3	odd	2
1872.2.by.i.1297.1		4	52.23	odd	6
1872.2.by.i.1297.2		4	156.23	even	6
3042.2.a.t.1.1		2	39.20	even	12
3042.2.a.t.1.2		2	13.6	odd	12
3042.2.a.u.1.1		2	39.32	even	12
3042.2.a.u.1.2		2	13.7	odd	12
3042.2.b.m.1351.1		4	13.9	even	3
3042.2.b.m.1351.2		4	39.17	odd	6
3042.2.b.m.1351.3		4	13.4	even	6
3042.2.b.m.1351.4		4	39.35	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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +3.00000i q^{5} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{10} +(-2.50000 - 2.59808i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(2.59808 + 4.50000i) q^{17} +(6.00000 - 3.46410i) q^{19} +(-2.59808 + 1.50000i) q^{20} -4.00000 q^{25} +(-0.866025 - 3.50000i) q^{26} +(2.59808 - 4.50000i) q^{29} -6.92820i q^{31} +(-0.866025 + 0.500000i) q^{32} +5.19615i q^{34} +(-1.50000 - 0.866025i) q^{37} +6.92820 q^{38} -3.00000 q^{40} +(-7.79423 - 4.50000i) q^{41} +(2.00000 + 3.46410i) q^{43} -12.0000i q^{47} +(-3.50000 + 6.06218i) q^{49} +(-3.46410 - 2.00000i) q^{50} +(1.00000 - 3.46410i) q^{52} -5.19615 q^{53} +(4.50000 - 2.59808i) q^{58} +(-10.3923 + 6.00000i) q^{59} +(2.50000 + 4.33013i) q^{61} +(3.46410 - 6.00000i) q^{62} -1.00000 q^{64} +(7.79423 - 7.50000i) q^{65} +(12.0000 + 6.92820i) q^{67} +(-2.59808 + 4.50000i) q^{68} +(10.3923 - 6.00000i) q^{71} -8.66025i q^{73} +(-0.866025 - 1.50000i) q^{74} +(6.00000 + 3.46410i) q^{76} +4.00000 q^{79} +(-2.59808 - 1.50000i) q^{80} +(-4.50000 - 7.79423i) q^{82} +12.0000i q^{83} +(-13.5000 + 7.79423i) q^{85} +4.00000i q^{86} +(-5.19615 - 3.00000i) q^{89} +(6.00000 - 10.3923i) q^{94} +(10.3923 + 18.0000i) q^{95} +(-12.0000 + 6.92820i) q^{97} +(-6.06218 + 3.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 6 q^{10} - 10 q^{13} - 2 q^{16} + 24 q^{19} - 16 q^{25} - 6 q^{37} - 12 q^{40} + 8 q^{43} - 14 q^{49} + 4 q^{52} + 18 q^{58} + 10 q^{61} - 4 q^{64} + 48 q^{67} + 24 q^{76} + 16 q^{79} - 18 q^{82}+ \cdots - 48 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 - 6 * q^10 - 10 * q^13 - 2 * q^16 + 24 * q^19 - 16 * q^25 - 6 * q^37 - 12 * q^40 + 8 * q^43 - 14 * q^49 + 4 * q^52 + 18 * q^58 + 10 * q^61 - 4 * q^64 + 48 * q^67 + 24 * q^76 + 16 * q^79 - 18 * q^82 - 54 * q^85 + 24 * q^94 - 48 * q^97

Introduction

L-functions

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