LMFDB - Embedded newform 1344.2.s.c.239.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(239,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1344.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.s (of order $4$, 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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.19
Character	$\chi$	$=$	1344.239
Dual form			1344.2.s.c.911.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.68331 + 0.408017i) q^{3} +(-2.26080 - 2.26080i) q^{5} +1.00000 q^{7} +(2.66704 + 1.37363i) q^{9} +O(q^{10})$	\(q+(1.68331 + 0.408017i) q^{3} +(-2.26080 - 2.26080i) q^{5} +1.00000 q^{7} +(2.66704 + 1.37363i) q^{9} +(1.82069 - 1.82069i) q^{11} +(0.915413 + 0.915413i) q^{13} +(-2.88318 - 4.72806i) q^{15} -2.93247i q^{17} +(-1.79372 + 1.79372i) q^{19} +(1.68331 + 0.408017i) q^{21} -8.77567i q^{23} +5.22244i q^{25} +(3.92899 + 3.40045i) q^{27} +(-1.67539 + 1.67539i) q^{29} -8.15507i q^{31} +(3.80765 - 2.32191i) q^{33} +(-2.26080 - 2.26080i) q^{35} +(-4.29751 + 4.29751i) q^{37} +(1.16742 + 1.91442i) q^{39} +4.52681 q^{41} +(3.46653 + 3.46653i) q^{43} +(-2.92414 - 9.13517i) q^{45} +8.60844 q^{47} +1.00000 q^{49} +(1.19649 - 4.93624i) q^{51} +(-6.48541 - 6.48541i) q^{53} -8.23243 q^{55} +(-3.75125 + 2.28752i) q^{57} +(8.08166 - 8.08166i) q^{59} +(2.11377 + 2.11377i) q^{61} +(2.66704 + 1.37363i) q^{63} -4.13913i q^{65} +(2.17584 - 2.17584i) q^{67} +(3.58062 - 14.7721i) q^{69} +4.72561i q^{71} -8.88001i q^{73} +(-2.13084 + 8.79096i) q^{75} +(1.82069 - 1.82069i) q^{77} -10.6576i q^{79} +(5.22626 + 7.32709i) q^{81} +(-7.45604 - 7.45604i) q^{83} +(-6.62972 + 6.62972i) q^{85} +(-3.50379 + 2.13661i) q^{87} -11.6283 q^{89} +(0.915413 + 0.915413i) q^{91} +(3.32740 - 13.7275i) q^{93} +8.11049 q^{95} +9.08157 q^{97} +(7.35683 - 2.35490i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} + 40 q^{7}+O(q^{10}) $ 40 * q - 4 * q^3 + 40 * q^7	$ 40 q - 4 q^{3} + 40 q^{7} + 24 q^{13} - 16 q^{19} - 4 q^{21} + 32 q^{27} + 24 q^{33} - 8 q^{37} + 64 q^{39} - 24 q^{43} - 28 q^{45} + 40 q^{49} + 32 q^{51} - 16 q^{55} - 48 q^{61} - 40 q^{67} + 4 q^{69} - 40 q^{75} + 56 q^{81} - 48 q^{85} - 32 q^{87} + 24 q^{91} + 56 q^{93} + 16 q^{97} - 24 q^{99}+O(q^{100}) $ 40 * q - 4 * q^3 + 40 * q^7 + 24 * q^13 - 16 * q^19 - 4 * q^21 + 32 * q^27 + 24 * q^33 - 8 * q^37 + 64 * q^39 - 24 * q^43 - 28 * q^45 + 40 * q^49 + 32 * q^51 - 16 * q^55 - 48 * q^61 - 40 * q^67 + 4 * q^69 - 40 * q^75 + 56 * q^81 - 48 * q^85 - 32 * q^87 + 24 * q^91 + 56 * q^93 + 16 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.68331	+	0.408017i	0.971858	+	0.235568i
$3$	1.68331	+	0.408017i	0.971858	+	0.235568i
$4$		0			0
$5$	−2.26080	−	2.26080i	−1.01106	−	1.01106i	−0.999938	−	0.0111224i	$-0.996460\pi$
$5$	−2.26080	−	2.26080i	−1.01106	−	1.01106i	−0.0111224	−	0.999938i	$-0.503540\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$		0			0
$9$	2.66704	+	1.37363i	0.889015	+	0.457878i
$10$		0			0
$11$	1.82069	−	1.82069i	0.548959	−	0.548959i	−0.377181	−	0.926140i	$-0.623106\pi$
$11$	1.82069	−	1.82069i	0.548959	−	0.548959i	0.926140	+	0.377181i	$0.123106\pi$
$12$		0			0
$13$	0.915413	+	0.915413i	0.253890	+	0.253890i	0.822563	−	0.568674i	$-0.192543\pi$
$13$	0.915413	+	0.915413i	0.253890	+	0.253890i	−0.568674	+	0.822563i	$0.692543\pi$
$14$		0			0
$15$	−2.88318	−	4.72806i	−0.744433	−	1.22078i
$16$		0			0
$17$		−	2.93247i		−	0.711228i	−0.934633	−	0.355614i	$-0.884272\pi$
$17$		−	2.93247i		−	0.711228i	0.934633	−	0.355614i	$-0.115728\pi$
$18$		0			0
$19$	−1.79372	+	1.79372i	−0.411508	+	0.411508i	−0.882264	−	0.470756i	$-0.843981\pi$
$19$	−1.79372	+	1.79372i	−0.411508	+	0.411508i	0.470756	+	0.882264i	$0.343981\pi$
$20$		0			0
$21$	1.68331	+	0.408017i	0.367328	+	0.0890365i
$22$		0			0
$23$		−	8.77567i		−	1.82985i	−0.403619	−	0.914927i	$-0.632248\pi$
$23$		−	8.77567i		−	1.82985i	0.403619	−	0.914927i	$-0.367752\pi$
$24$		0			0
$25$			5.22244i			1.04449i
$26$		0			0
$27$	3.92899	+	3.40045i	0.756134	+	0.654416i
$28$		0			0
$29$	−1.67539	+	1.67539i	−0.311113	+	0.311113i	−0.845340	−	0.534228i	$-0.820602\pi$
$29$	−1.67539	+	1.67539i	−0.311113	+	0.311113i	0.534228	+	0.845340i	$0.320602\pi$
$30$		0			0
$31$		−	8.15507i		−	1.46469i	−0.680931	−	0.732347i	$-0.738425\pi$
$31$		−	8.15507i		−	1.46469i	0.680931	−	0.732347i	$-0.261575\pi$
$32$		0			0
$33$	3.80765	−	2.32191i	0.662827	−	0.404192i
$34$		0			0
$35$	−2.26080	−	2.26080i	−0.382145	−	0.382145i
$36$		0			0
$37$	−4.29751	+	4.29751i	−0.706506	+	0.706506i	−0.965799	−	0.259293i	$-0.916511\pi$
$37$	−4.29751	+	4.29751i	−0.706506	+	0.706506i	0.259293	+	0.965799i	$0.416511\pi$
$38$		0			0
$39$	1.16742	+	1.91442i	0.186936	+	0.306553i
$40$		0			0
$41$	4.52681			0.706969			0.353484	−	0.935440i	$-0.384997\pi$
$41$	4.52681			0.706969			0.353484	+	0.935440i	$0.384997\pi$
$42$		0			0
$43$	3.46653	+	3.46653i	0.528641	+	0.528641i	0.920167	−	0.391526i	$-0.128053\pi$
$43$	3.46653	+	3.46653i	0.528641	+	0.528641i	−0.391526	+	0.920167i	$0.628053\pi$
$44$		0			0
$45$	−2.92414	−	9.13517i	−0.435905	−	1.36179i
$46$		0			0
$47$	8.60844			1.25567			0.627835	−	0.778346i	$-0.283941\pi$
$47$	8.60844			1.25567			0.627835	+	0.778346i	$0.283941\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$		0			0
$51$	1.19649	−	4.93624i	0.167543	−	0.691212i
$52$		0			0
$53$	−6.48541	−	6.48541i	−0.890840	−	0.890840i	0.103762	−	0.994602i	$-0.466912\pi$
$53$	−6.48541	−	6.48541i	−0.890840	−	0.890840i	−0.994602	+	0.103762i	$0.966912\pi$
$54$		0			0
$55$	−8.23243			−1.11006
$56$		0			0
$57$	−3.75125	+	2.28752i	−0.496866	+	0.302989i
$58$		0			0
$59$	8.08166	−	8.08166i	1.05214	−	1.05214i	0.0535782	−	0.998564i	$-0.482937\pi$
$59$	8.08166	−	8.08166i	1.05214	−	1.05214i	0.998564	−	0.0535782i	$-0.0170627\pi$
$60$		0			0
$61$	2.11377	+	2.11377i	0.270641	+	0.270641i	0.829358	−	0.558717i	$-0.188706\pi$
$61$	2.11377	+	2.11377i	0.270641	+	0.270641i	−0.558717	+	0.829358i	$0.688706\pi$
$62$		0			0
$63$	2.66704	+	1.37363i	0.336016	+	0.173062i
$64$		0			0
$65$		−	4.13913i		−	0.513396i
$66$		0			0
$67$	2.17584	−	2.17584i	0.265821	−	0.265821i	−0.561593	−	0.827414i	$-0.689811\pi$
$67$	2.17584	−	2.17584i	0.265821	−	0.265821i	0.827414	+	0.561593i	$0.189811\pi$
$68$		0			0
$69$	3.58062	−	14.7721i	0.431056	−	1.77836i
$70$		0			0
$71$			4.72561i			0.560827i	0.959879	+	0.280413i	$0.0904715\pi$
$71$			4.72561i			0.560827i	−0.959879	+	0.280413i	$0.909528\pi$
$72$		0			0
$73$		−	8.88001i		−	1.03933i	−0.854371	−	0.519663i	$-0.826058\pi$
$73$		−	8.88001i		−	1.03933i	0.854371	−	0.519663i	$-0.173942\pi$
$74$		0			0
$75$	−2.13084	+	8.79096i	−0.246048	+	1.01509i
$76$		0			0
$77$	1.82069	−	1.82069i	0.207487	−	0.207487i
$78$		0			0
$79$		−	10.6576i		−	1.19907i	−0.800349	−	0.599535i	$-0.795352\pi$
$79$		−	10.6576i		−	1.19907i	0.800349	−	0.599535i	$-0.204648\pi$
$80$		0			0
$81$	5.22626	+	7.32709i	0.580695	+	0.814121i
$82$		0			0
$83$	−7.45604	−	7.45604i	−0.818407	−	0.818407i	0.167470	−	0.985877i	$-0.446440\pi$
$83$	−7.45604	−	7.45604i	−0.818407	−	0.818407i	−0.985877	+	0.167470i	$0.946440\pi$
$84$		0			0
$85$	−6.62972	+	6.62972i	−0.719094	+	0.719094i
$86$		0			0
$87$	−3.50379	+	2.13661i	−0.375646	+	0.229069i
$88$		0			0
$89$	−11.6283			−1.23260			−0.616298	−	0.787513i	$-0.711368\pi$
$89$	−11.6283			−1.23260			−0.616298	+	0.787513i	$0.711368\pi$
$90$		0			0
$91$	0.915413	+	0.915413i	0.0959613	+	0.0959613i
$92$		0			0
$93$	3.32740	−	13.7275i	0.345036	−	1.42347i
$94$		0			0
$95$	8.11049			0.832119
$96$		0			0
$97$	9.08157			0.922094			0.461047	−	0.887376i	$-0.347474\pi$
$97$	9.08157			0.922094			0.461047	+	0.887376i	$0.347474\pi$
$98$		0			0
$99$	7.35683	−	2.35490i	0.739389	−	0.236676i
$100$		0			0
$101$	−4.72687	−	4.72687i	−0.470341	−	0.470341i	0.431684	−	0.902025i	$-0.357920\pi$
$101$	−4.72687	−	4.72687i	−0.470341	−	0.470341i	−0.902025	+	0.431684i	$0.857920\pi$
$102$		0			0
$103$	14.7866			1.45696			0.728482	−	0.685065i	$-0.240226\pi$
$103$	14.7866			1.45696			0.728482	+	0.685065i	$0.240226\pi$
$104$		0			0
$105$	−2.88318	−	4.72806i	−0.281369	−	0.461412i
$106$		0			0
$107$	−9.12369	+	9.12369i	−0.882020	+	0.882020i	−0.993740	−	0.111719i	$-0.964364\pi$
$107$	−9.12369	+	9.12369i	−0.882020	+	0.882020i	0.111719	+	0.993740i	$0.464364\pi$
$108$		0			0
$109$	7.45700	+	7.45700i	0.714251	+	0.714251i	0.967422	−	0.253171i	$-0.0814734\pi$
$109$	7.45700	+	7.45700i	0.714251	+	0.714251i	−0.253171	+	0.967422i	$0.581473\pi$
$110$		0			0
$111$	−8.98748	+	5.48057i	−0.853054	+	0.520193i
$112$		0			0
$113$			18.9798i			1.78547i	0.450580	+	0.892736i	$0.351217\pi$
$113$			18.9798i			1.78547i	−0.450580	+	0.892736i	$0.648783\pi$
$114$		0			0
$115$	−19.8400	+	19.8400i	−1.85009	+	1.85009i
$116$		0			0
$117$	1.18400	+	3.69889i	0.109461	+	0.341962i
$118$		0			0
$119$		−	2.93247i		−	0.268819i
$120$		0			0
$121$			4.37017i			0.397288i
$122$		0			0
$123$	7.62001	+	1.84701i	0.687073	+	0.166540i
$124$		0			0
$125$	0.502881	−	0.502881i	0.0449791	−	0.0449791i
$126$		0			0
$127$			20.6001i			1.82796i	0.405757	+	0.913981i	$0.367008\pi$
$127$			20.6001i			1.82796i	−0.405757	+	0.913981i	$0.632992\pi$
$128$		0			0
$129$	4.42083	+	7.24964i	0.389233	+	0.638295i
$130$		0			0
$131$	−8.07416	−	8.07416i	−0.705443	−	0.705443i	0.260131	−	0.965573i	$-0.416234\pi$
$131$	−8.07416	−	8.07416i	−0.705443	−	0.705443i	−0.965573	+	0.260131i	$0.916234\pi$
$132$		0			0
$133$	−1.79372	+	1.79372i	−0.155535	+	0.155535i
$134$		0			0
$135$	−1.19493	−	16.5704i	−0.102843	−	1.42615i
$136$		0			0
$137$	5.22066			0.446031			0.223016	−	0.974815i	$-0.428410\pi$
$137$	5.22066			0.446031			0.223016	+	0.974815i	$0.428410\pi$
$138$		0			0
$139$	11.9868	+	11.9868i	1.01671	+	1.01671i	0.999858	+	0.0168474i	$0.00536296\pi$
$139$	11.9868	+	11.9868i	1.01671	+	1.01671i	0.0168474	+	0.999858i	$0.494637\pi$
$140$		0			0
$141$	14.4907	+	3.51239i	1.22033	+	0.295796i
$142$		0			0
$143$	3.33337			0.278750
$144$		0			0
$145$	7.57546			0.629107
$146$		0			0
$147$	1.68331	+	0.408017i	0.138837	+	0.0336526i
$148$		0			0
$149$	11.7493	+	11.7493i	0.962540	+	0.962540i	0.999323	−	0.0367834i	$-0.0117112\pi$
$149$	11.7493	+	11.7493i	0.962540	+	0.962540i	−0.0367834	+	0.999323i	$0.511711\pi$
$150$		0			0
$151$	−8.14983			−0.663223			−0.331612	−	0.943416i	$-0.607592\pi$
$151$	−8.14983			−0.663223			−0.331612	+	0.943416i	$0.607592\pi$
$152$		0			0
$153$	4.02814	−	7.82102i	0.325656	−	0.632292i
$154$		0			0
$155$	−18.4370	+	18.4370i	−1.48089	+	1.48089i
$156$		0			0
$157$	−10.7876	−	10.7876i	−0.860946	−	0.860946i	0.130502	−	0.991448i	$-0.458341\pi$
$157$	−10.7876	−	10.7876i	−0.860946	−	0.860946i	−0.991448	+	0.130502i	$0.958341\pi$
$158$		0			0
$159$	−8.27079	−	13.5631i	−0.655916	−	1.07562i
$160$		0			0
$161$		−	8.77567i		−	0.691620i
$162$		0			0
$163$	2.26578	−	2.26578i	0.177469	−	0.177469i	−0.612782	−	0.790252i	$-0.709950\pi$
$163$	2.26578	−	2.26578i	0.177469	−	0.177469i	0.790252	+	0.612782i	$0.209950\pi$
$164$		0			0
$165$	−13.8577	−	3.35897i	−1.07882	−	0.261495i
$166$		0			0
$167$			15.2783i			1.18227i	0.806574	+	0.591133i	$0.201319\pi$
$167$			15.2783i			1.18227i	−0.806574	+	0.591133i	$0.798681\pi$
$168$		0			0
$169$		−	11.3240i		−	0.871080i
$170$		0			0
$171$	−7.24785	+	2.32002i	−0.554257	+	0.177416i
$172$		0			0
$173$	−12.5993	+	12.5993i	−0.957903	+	0.957903i	−0.999149	−	0.0412456i	$-0.986867\pi$
$173$	−12.5993	+	12.5993i	−0.957903	+	0.957903i	0.0412456	+	0.999149i	$0.486867\pi$
$174$		0			0
$175$			5.22244i			0.394779i
$176$		0			0
$177$	16.9014	−	10.3065i	1.27038	−	0.774681i
$178$		0			0
$179$	−0.354922	−	0.354922i	−0.0265281	−	0.0265281i	0.693718	−	0.720246i	$-0.255971\pi$
$179$	−0.354922	−	0.354922i	−0.0265281	−	0.0265281i	−0.720246	+	0.693718i	$0.755971\pi$
$180$		0			0
$181$	−3.95505	+	3.95505i	−0.293976	+	0.293976i	−0.838649	−	0.544672i	$-0.816654\pi$
$181$	−3.95505	+	3.95505i	−0.293976	+	0.293976i	0.544672	+	0.838649i	$0.316654\pi$
$182$		0			0
$183$	2.69568	+	4.42059i	0.199270	+	0.326779i
$184$		0			0
$185$	19.4316			1.42864
$186$		0			0
$187$	−5.33911	−	5.33911i	−0.390435	−	0.390435i
$188$		0			0
$189$	3.92899	+	3.40045i	0.285792	+	0.247346i
$190$		0			0
$191$	11.1317			0.805460			0.402730	−	0.915319i	$-0.368061\pi$
$191$	11.1317			0.805460			0.402730	+	0.915319i	$0.368061\pi$
$192$		0			0
$193$	−24.2243			−1.74370			−0.871852	−	0.489769i	$-0.837081\pi$
$193$	−24.2243			−1.74370			−0.871852	+	0.489769i	$0.837081\pi$
$194$		0			0
$195$	1.68883	−	6.96743i	0.120940	−	0.498948i
$196$		0			0
$197$	11.9310	+	11.9310i	0.850048	+	0.850048i	0.990139	−	0.140091i	$-0.0447394\pi$
$197$	11.9310	+	11.9310i	0.850048	+	0.850048i	−0.140091	+	0.990139i	$0.544739\pi$
$198$		0			0
$199$	5.66656			0.401692			0.200846	−	0.979623i	$-0.435631\pi$
$199$	5.66656			0.401692			0.200846	+	0.979623i	$0.435631\pi$
$200$		0			0
$201$	4.55038	−	2.77482i	0.320959	−	0.195721i
$202$		0			0
$203$	−1.67539	+	1.67539i	−0.117590	+	0.117590i
$204$		0			0
$205$	−10.2342	−	10.2342i	−0.714788	−	0.714788i
$206$		0			0
$207$	12.0546	−	23.4051i	0.837850	−	1.62677i
$208$		0			0
$209$			6.53162i			0.451802i
$210$		0			0
$211$	−11.8208	+	11.8208i	−0.813776	+	0.813776i	−0.985198	−	0.171422i	$-0.945164\pi$
$211$	−11.8208	+	11.8208i	−0.813776	+	0.813776i	0.171422	+	0.985198i	$0.445164\pi$
$212$		0			0
$213$	−1.92813	+	7.95465i	−0.132113	+	0.545044i
$214$		0			0
$215$		−	15.6743i		−	1.06898i
$216$		0			0
$217$		−	8.15507i		−	0.553602i
$218$		0			0
$219$	3.62319	−	14.9478i	0.244832	−	1.01008i
$220$		0			0
$221$	2.68442	−	2.68442i	0.180573	−	0.180573i
$222$		0			0
$223$		−	6.81157i		−	0.456136i	−0.973645	−	0.228068i	$-0.926759\pi$
$223$		−	6.81157i		−	0.456136i	0.973645	−	0.228068i	$-0.0732409\pi$
$224$		0			0
$225$	−7.17372	+	13.9285i	−0.478248	+	0.928565i
$226$		0			0
$227$	−0.205032	−	0.205032i	−0.0136084	−	0.0136084i	0.700270	−	0.713878i	$-0.253063\pi$
$227$	−0.205032	−	0.205032i	−0.0136084	−	0.0136084i	−0.713878	+	0.700270i	$0.753063\pi$
$228$		0			0
$229$	−13.3965	+	13.3965i	−0.885266	+	0.885266i	−0.994064	−	0.108798i	$-0.965300\pi$
$229$	−13.3965	+	13.3965i	−0.885266	+	0.885266i	0.108798	+	0.994064i	$0.465300\pi$
$230$		0			0
$231$	3.80765	−	2.32191i	0.250525	−	0.152770i
$232$		0			0
$233$	−6.01646			−0.394151			−0.197076	−	0.980388i	$-0.563144\pi$
$233$	−6.01646			−0.394151			−0.197076	+	0.980388i	$0.563144\pi$
$234$		0			0
$235$	−19.4620	−	19.4620i	−1.26956	−	1.26956i
$236$		0			0
$237$	4.34846	−	17.9399i	0.282463	−	1.16532i
$238$		0			0
$239$	6.89526			0.446017			0.223009	−	0.974816i	$-0.428412\pi$
$239$	6.89526			0.446017			0.223009	+	0.974816i	$0.428412\pi$
$240$		0			0
$241$	10.9906			0.707966			0.353983	−	0.935252i	$-0.384827\pi$
$241$	10.9906			0.707966			0.353983	+	0.935252i	$0.384827\pi$
$242$		0			0
$243$	5.80782	+	14.4661i	0.372572	+	0.928003i
$244$		0			0
$245$	−2.26080	−	2.26080i	−0.144437	−	0.144437i
$246$		0			0
$247$	−3.28399			−0.208955
$248$		0			0
$249$	−9.50862	−	15.5930i	−0.602584	−	0.988166i
$250$		0			0
$251$	11.8940	−	11.8940i	0.750744	−	0.750744i	−0.223874	−	0.974618i	$-0.571871\pi$
$251$	11.8940	−	11.8940i	0.750744	−	0.750744i	0.974618	+	0.223874i	$0.0718706\pi$
$252$		0			0
$253$	−15.9778	−	15.9778i	−1.00451	−	1.00451i
$254$		0			0
$255$	−13.8649	+	8.45482i	−0.868253	+	0.529461i
$256$		0			0
$257$		−	14.6730i		−	0.915275i	−0.889139	−	0.457637i	$-0.848696\pi$
$257$		−	14.6730i		−	0.915275i	0.889139	−	0.457637i	$-0.151304\pi$
$258$		0			0
$259$	−4.29751	+	4.29751i	−0.267034	+	0.267034i
$260$		0			0
$261$	−6.76972	+	2.16697i	−0.419035	+	0.134132i
$262$		0			0
$263$			20.4151i			1.25885i	0.777061	+	0.629425i	$0.216710\pi$
$263$			20.4151i			1.25885i	−0.777061	+	0.629425i	$0.783290\pi$
$264$		0			0
$265$			29.3245i			1.80139i
$266$		0			0
$267$	−19.5740	−	4.74454i	−1.19791	−	0.290361i
$268$		0			0
$269$	−18.6963	+	18.6963i	−1.13993	+	1.13993i	−0.151469	+	0.988462i	$0.548400\pi$
$269$	−18.6963	+	18.6963i	−1.13993	+	1.13993i	−0.988462	+	0.151469i	$0.951600\pi$
$270$		0			0
$271$			5.42038i			0.329265i	0.986355	+	0.164632i	$0.0526438\pi$
$271$			5.42038i			0.329265i	−0.986355	+	0.164632i	$0.947356\pi$
$272$		0			0
$273$	1.16742	+	1.91442i	0.0706553	+	0.115866i
$274$		0			0
$275$	9.50844	+	9.50844i	0.573380	+	0.573380i
$276$		0			0
$277$	−5.12370	+	5.12370i	−0.307854	+	0.307854i	−0.844076	−	0.536223i	$-0.819851\pi$
$277$	−5.12370	+	5.12370i	−0.307854	+	0.307854i	0.536223	+	0.844076i	$0.319851\pi$
$278$		0			0
$279$	11.2021	−	21.7499i	0.670651	−	1.30214i
$280$		0			0
$281$	−5.35336			−0.319355			−0.159677	−	0.987169i	$-0.551045\pi$
$281$	−5.35336			−0.319355			−0.159677	+	0.987169i	$0.551045\pi$
$282$		0			0
$283$	10.6748	+	10.6748i	0.634552	+	0.634552i	0.949206	−	0.314654i	$-0.101889\pi$
$283$	10.6748	+	10.6748i	0.634552	+	0.634552i	−0.314654	+	0.949206i	$0.601889\pi$
$284$		0			0
$285$	13.6524	+	3.30922i	0.808701	+	0.196021i
$286$		0			0
$287$	4.52681			0.267209
$288$		0			0
$289$	8.40064			0.494155
$290$		0			0
$291$	15.2871	+	3.70543i	0.896144	+	0.217216i
$292$		0			0
$293$	−0.265538	−	0.265538i	−0.0155129	−	0.0155129i	0.699308	−	0.714821i	$-0.253492\pi$
$293$	−0.265538	−	0.265538i	−0.0155129	−	0.0155129i	−0.714821	+	0.699308i	$0.753492\pi$
$294$		0			0
$295$	−36.5420			−2.12756
$296$		0			0
$297$	13.3446	−	0.962313i	0.774334	−	0.0558391i
$298$		0			0
$299$	8.03336	−	8.03336i	0.464581	−	0.464581i
$300$		0			0
$301$	3.46653	+	3.46653i	0.199808	+	0.199808i
$302$		0			0
$303$	−6.02813	−	9.88541i	−0.346307	−	0.567902i
$304$		0			0
$305$		−	9.55764i		−	0.547269i
$306$		0			0
$307$	7.28530	−	7.28530i	0.415794	−	0.415794i	−0.467957	−	0.883751i	$-0.655010\pi$
$307$	7.28530	−	7.28530i	0.415794	−	0.415794i	0.883751	+	0.467957i	$0.155010\pi$
$308$		0			0
$309$	24.8903	+	6.03317i	1.41596	+	0.343215i
$310$		0			0
$311$			12.0885i			0.685473i	0.939432	+	0.342737i	$0.111354\pi$
$311$			12.0885i			0.685473i	−0.939432	+	0.342737i	$0.888646\pi$
$312$		0			0
$313$		−	0.942109i		−	0.0532511i	−0.999645	−	0.0266256i	$-0.991524\pi$
$313$		−	0.942109i		−	0.0532511i	0.999645	−	0.0266256i	$-0.00847618\pi$
$314$		0			0
$315$	−2.92414	−	9.13517i	−0.164757	−	0.514708i
$316$		0			0
$317$	3.95890	−	3.95890i	0.222354	−	0.222354i	−0.587135	−	0.809489i	$-0.699744\pi$
$317$	3.95890	−	3.95890i	0.222354	−	0.222354i	0.809489	+	0.587135i	$0.199744\pi$
$318$		0			0
$319$			6.10074i			0.341576i
$320$		0			0
$321$	−19.0806	+	11.6354i	−1.06497	+	0.649422i
$322$		0			0
$323$	5.26003	+	5.26003i	0.292676	+	0.292676i
$324$		0			0
$325$	−4.78068	+	4.78068i	−0.265185	+	0.265185i
$326$		0			0
$327$	9.50984	+	15.5950i	0.525895	+	0.862405i
$328$		0			0
$329$	8.60844			0.474599
$330$		0			0
$331$	16.3244	+	16.3244i	0.897271	+	0.897271i	0.995194	−	0.0979228i	$-0.0312198\pi$
$331$	16.3244	+	16.3244i	0.897271	+	0.897271i	−0.0979228	+	0.995194i	$0.531220\pi$
$332$		0			0
$333$	−17.3649	+	5.55844i	−0.951588	+	0.304601i
$334$		0			0
$335$	−9.83827			−0.537522
$336$		0			0
$337$	−18.4456			−1.00480			−0.502398	−	0.864636i	$-0.667549\pi$
$337$	−18.4456			−1.00480			−0.502398	+	0.864636i	$0.667549\pi$
$338$		0			0
$339$	−7.74409	+	31.9489i	−0.420601	+	1.73523i
$340$		0			0
$341$	−14.8479	−	14.8479i	−0.804057	−	0.804057i
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	−41.4919	+	25.3018i	−2.23385	+	1.36220i
$346$		0			0
$347$	4.16277	−	4.16277i	0.223469	−	0.223469i	−0.586488	−	0.809958i	$-0.699490\pi$
$347$	4.16277	−	4.16277i	0.223469	−	0.223469i	0.809958	+	0.586488i	$0.199490\pi$
$348$		0			0
$349$	−1.74656	−	1.74656i	−0.0934910	−	0.0934910i	0.658814	−	0.752305i	$-0.271058\pi$
$349$	−1.74656	−	1.74656i	−0.0934910	−	0.0934910i	−0.752305	+	0.658814i	$0.771058\pi$
$350$		0			0
$351$	0.483835	+	6.70946i	0.0258252	+	0.358124i
$352$		0			0
$353$		−	12.3621i		−	0.657967i	−0.944336	−	0.328983i	$-0.893294\pi$
$353$		−	12.3621i		−	0.657967i	0.944336	−	0.328983i	$-0.106706\pi$
$354$		0			0
$355$	10.6837	−	10.6837i	0.567030	−	0.567030i
$356$		0			0
$357$	1.19649	−	4.93624i	0.0633252	−	0.261254i
$358$		0			0
$359$			16.2343i			0.856814i	0.903586	+	0.428407i	$0.140925\pi$
$359$			16.2343i			0.856814i	−0.903586	+	0.428407i	$0.859075\pi$
$360$		0			0
$361$			12.5651i			0.661322i
$362$		0			0
$363$	−1.78310	+	7.35634i	−0.0935886	+	0.386108i
$364$		0			0
$365$	−20.0759	+	20.0759i	−1.05082	+	1.05082i
$366$		0			0
$367$		−	25.8770i		−	1.35077i	−0.737465	−	0.675385i	$-0.763977\pi$
$367$		−	25.8770i		−	1.35077i	0.737465	−	0.675385i	$-0.236023\pi$
$368$		0			0
$369$	12.0732	+	6.21818i	0.628506	+	0.323706i
$370$		0			0
$371$	−6.48541	−	6.48541i	−0.336706	−	0.336706i
$372$		0			0
$373$	26.0420	−	26.0420i	1.34841	−	1.34841i	0.461011	−	0.887394i	$-0.347487\pi$
$373$	26.0420	−	26.0420i	1.34841	−	1.34841i	0.887394	−	0.461011i	$-0.152513\pi$
$374$		0			0
$375$	1.05169	−	0.641320i	0.0543089	−	0.0331176i
$376$		0			0
$377$	−3.06735			−0.157977
$378$		0			0
$379$	−5.51674	−	5.51674i	−0.283376	−	0.283376i	0.551078	−	0.834454i	$-0.314217\pi$
$379$	−5.51674	−	5.51674i	−0.283376	−	0.283376i	−0.834454	+	0.551078i	$0.814217\pi$
$380$		0			0
$381$	−8.40518	+	34.6763i	−0.430610	+	1.77652i
$382$		0			0
$383$	10.8580			0.554818			0.277409	−	0.960752i	$-0.410524\pi$
$383$	10.8580			0.554818			0.277409	+	0.960752i	$0.410524\pi$
$384$		0			0
$385$	−8.23243			−0.419564
$386$		0			0
$387$	4.48365	+	14.0071i	0.227917	+	0.712023i
$388$		0			0
$389$	18.0972	+	18.0972i	0.917566	+	0.917566i	0.996852	−	0.0792861i	$-0.0252641\pi$
$389$	18.0972	+	18.0972i	0.917566	+	0.917566i	−0.0792861	+	0.996852i	$0.525264\pi$
$390$		0			0
$391$	−25.7344			−1.30144
$392$		0			0
$393$	−10.2969	−	16.8857i	−0.519410	−	0.851770i
$394$		0			0
$395$	−24.0946	+	24.0946i	−1.21233	+	1.21233i
$396$		0			0
$397$	12.4866	+	12.4866i	0.626683	+	0.626683i	0.947232	−	0.320549i	$-0.103867\pi$
$397$	12.4866	+	12.4866i	0.626683	+	0.626683i	−0.320549	+	0.947232i	$0.603867\pi$
$398$		0			0
$399$	−3.75125	+	2.28752i	−0.187798	+	0.114519i
$400$		0			0
$401$			3.80237i			0.189881i	0.995483	+	0.0949406i	$0.0302661\pi$
$401$			3.80237i			0.189881i	−0.995483	+	0.0949406i	$0.969734\pi$
$402$		0			0
$403$	7.46526	−	7.46526i	0.371871	−	0.371871i
$404$		0			0
$405$	4.74956	−	28.3806i	0.236008	−	1.41024i
$406$		0			0
$407$			15.6489i			0.775686i
$408$		0			0
$409$			8.52624i			0.421595i	0.977530	+	0.210798i	$0.0676061\pi$
$409$			8.52624i			0.421595i	−0.977530	+	0.210798i	$0.932394\pi$
$410$		0			0
$411$	8.78797	+	2.13012i	0.433479	+	0.105071i
$412$		0			0
$413$	8.08166	−	8.08166i	0.397672	−	0.397672i
$414$		0			0
$415$			33.7133i			1.65492i
$416$		0			0
$417$	15.2866	+	25.0682i	0.748589	+	1.22760i
$418$		0			0
$419$	−4.56394	−	4.56394i	−0.222963	−	0.222963i	0.586782	−	0.809745i	$-0.300395\pi$
$419$	−4.56394	−	4.56394i	−0.222963	−	0.222963i	−0.809745	+	0.586782i	$0.800395\pi$
$420$		0			0
$421$	−6.35998	+	6.35998i	−0.309966	+	0.309966i	−0.844896	−	0.534930i	$-0.820338\pi$
$421$	−6.35998	+	6.35998i	−0.309966	+	0.309966i	0.534930	+	0.844896i	$0.320338\pi$
$422$		0			0
$423$	22.9591	+	11.8249i	1.11631	+	0.574944i
$424$		0			0
$425$	15.3146			0.742868
$426$		0			0
$427$	2.11377	+	2.11377i	0.102293	+	0.102293i
$428$		0			0
$429$	5.61108	+	1.36007i	0.270905	+	0.0656647i
$430$		0			0
$431$	−15.4570			−0.744536			−0.372268	−	0.928125i	$-0.621420\pi$
$431$	−15.4570			−0.744536			−0.372268	+	0.928125i	$0.621420\pi$
$432$		0			0
$433$	−6.09769			−0.293036			−0.146518	−	0.989208i	$-0.546807\pi$
$433$	−6.09769			−0.293036			−0.146518	+	0.989208i	$0.546807\pi$
$434$		0			0
$435$	12.7518	+	3.09091i	0.611403	+	0.148198i
$436$		0			0
$437$	15.7411	+	15.7411i	0.753000	+	0.753000i
$438$		0			0
$439$	10.3091			0.492027			0.246013	−	0.969266i	$-0.420879\pi$
$439$	10.3091			0.492027			0.246013	+	0.969266i	$0.420879\pi$
$440$		0			0
$441$	2.66704	+	1.37363i	0.127002	+	0.0654112i
$442$		0			0
$443$	−9.98250	+	9.98250i	−0.474283	+	0.474283i	−0.903297	−	0.429015i	$-0.858861\pi$
$443$	−9.98250	+	9.98250i	−0.474283	+	0.474283i	0.429015	+	0.903297i	$0.358861\pi$
$444$		0			0
$445$	26.2892	+	26.2892i	1.24623	+	1.24623i
$446$		0			0
$447$	14.9838	+	24.5716i	0.708708	+	1.16220i
$448$		0			0
$449$		−	11.0455i		−	0.521268i	−0.965438	−	0.260634i	$-0.916068\pi$
$449$		−	11.0455i		−	0.521268i	0.965438	−	0.260634i	$-0.0839315\pi$
$450$		0			0
$451$	8.24192	−	8.24192i	0.388097	−	0.388097i
$452$		0			0
$453$	−13.7187	−	3.32526i	−0.644559	−	0.156235i
$454$		0			0
$455$		−	4.13913i		−	0.194045i
$456$		0			0
$457$			29.4280i			1.37659i	0.725433	+	0.688293i	$0.241639\pi$
$457$			29.4280i			1.37659i	−0.725433	+	0.688293i	$0.758361\pi$
$458$		0			0
$459$	9.97170	−	11.5216i	0.465439	−	0.537784i
$460$		0			0
$461$	8.61270	−	8.61270i	0.401134	−	0.401134i	−0.477499	−	0.878632i	$-0.658457\pi$
$461$	8.61270	−	8.61270i	0.401134	−	0.401134i	0.878632	+	0.477499i	$0.158457\pi$
$462$		0			0
$463$		−	4.16285i		−	0.193464i	−0.995310	−	0.0967321i	$-0.969161\pi$
$463$		−	4.16285i		−	0.193464i	0.995310	−	0.0967321i	$-0.0308390\pi$
$464$		0			0
$465$	−38.5577	+	23.5125i	−1.78807	+	1.09037i
$466$		0			0
$467$	−4.41317	−	4.41317i	−0.204217	−	0.204217i	0.597587	−	0.801804i	$-0.296126\pi$
$467$	−4.41317	−	4.41317i	−0.204217	−	0.204217i	−0.801804	+	0.597587i	$0.796126\pi$
$468$		0			0
$469$	2.17584	−	2.17584i	0.100471	−	0.100471i
$470$		0			0
$471$	−13.7573	−	22.5604i	−0.633905	−	1.03953i
$472$		0			0
$473$	12.6230			0.580404
$474$		0			0
$475$	−9.36759	−	9.36759i	−0.429815	−	0.429815i
$476$		0			0
$477$	−8.38830	−	26.2055i	−0.384074	−	1.19987i
$478$		0			0
$479$	−19.6658			−0.898553			−0.449277	−	0.893393i	$-0.648318\pi$
$479$	−19.6658			−0.898553			−0.449277	+	0.893393i	$0.648318\pi$
$480$		0			0
$481$	−7.86799			−0.358749
$482$		0			0
$483$	3.58062	−	14.7721i	0.162924	−	0.672156i
$484$		0			0
$485$	−20.5316	−	20.5316i	−0.932292	−	0.932292i
$486$		0			0
$487$	0.727896			0.0329841			0.0164921	−	0.999864i	$-0.494750\pi$
$487$	0.727896			0.0329841			0.0164921	+	0.999864i	$0.494750\pi$
$488$		0			0
$489$	4.73847	−	2.88952i	0.214281	−	0.130669i
$490$		0			0
$491$	2.15522	−	2.15522i	0.0972636	−	0.0972636i	−0.656801	−	0.754064i	$-0.728091\pi$
$491$	2.15522	−	2.15522i	0.0972636	−	0.0972636i	0.754064	+	0.656801i	$0.228091\pi$
$492$		0			0
$493$	4.91303	+	4.91303i	0.221272	+	0.221272i
$494$		0			0
$495$	−21.9563	−	11.3084i	−0.986861	−	0.508273i
$496$		0			0
$497$			4.72561i			0.211973i
$498$		0			0
$499$	25.4814	−	25.4814i	1.14070	−	1.14070i	0.152381	−	0.988322i	$-0.451306\pi$
$499$	25.4814	−	25.4814i	1.14070	−	1.14070i	0.988322	−	0.152381i	$-0.0486940\pi$
$500$		0			0
$501$	−6.23378	+	25.7180i	−0.278505	+	1.14900i
$502$		0			0
$503$		−	18.0159i		−	0.803289i	−0.915796	−	0.401645i	$-0.868439\pi$
$503$		−	18.0159i		−	0.803289i	0.915796	−	0.401645i	$-0.131561\pi$
$504$		0			0
$505$			21.3730i			0.951086i
$506$		0			0
$507$	4.62040	−	19.0618i	0.205199	−	0.846566i
$508$		0			0
$509$	4.60982	−	4.60982i	0.204327	−	0.204327i	−0.597524	−	0.801851i	$-0.703849\pi$
$509$	4.60982	−	4.60982i	0.204327	−	0.204327i	0.801851	+	0.597524i	$0.203849\pi$
$510$		0			0
$511$		−	8.88001i		−	0.392828i
$512$		0			0
$513$	−13.1470	+	0.948059i	−0.580453	+	0.0418578i
$514$		0			0
$515$	−33.4295	−	33.4295i	−1.47308	−	1.47308i
$516$		0			0
$517$	15.6733	−	15.6733i	0.689311	−	0.689311i
$518$		0			0
$519$	−26.3491	+	16.0677i	−1.15660	+	0.705294i
$520$		0			0
$521$	−0.205806			−0.00901651			−0.00450825	−	0.999990i	$-0.501435\pi$
$521$	−0.205806			−0.00901651			−0.00450825	+	0.999990i	$0.501435\pi$
$522$		0			0
$523$	−10.4823	−	10.4823i	−0.458361	−	0.458361i	0.439756	−	0.898117i	$-0.355065\pi$
$523$	−10.4823	−	10.4823i	−0.458361	−	0.458361i	−0.898117	+	0.439756i	$0.855065\pi$
$524$		0			0
$525$	−2.13084	+	8.79096i	−0.0929975	+	0.383669i
$526$		0			0
$527$	−23.9145			−1.04173
$528$		0			0
$529$	−54.0124			−2.34837
$530$		0			0
$531$	32.6554	−	10.4529i	1.41712	−	0.453617i
$532$		0			0
$533$	4.14390	+	4.14390i	0.179492	+	0.179492i
$534$		0			0
$535$	41.2537			1.78355
$536$		0			0
$537$	−0.452629	−	0.742257i	−0.0195324	−	0.0320308i
$538$		0			0
$539$	1.82069	−	1.82069i	0.0784227	−	0.0784227i
$540$		0			0
$541$	−20.1726	−	20.1726i	−0.867286	−	0.867286i	0.124885	−	0.992171i	$-0.460144\pi$
$541$	−20.1726	−	20.1726i	−0.867286	−	0.867286i	−0.992171	+	0.124885i	$0.960144\pi$
$542$		0			0
$543$	−8.27129	+	5.04384i	−0.354955	+	0.216452i
$544$		0			0
$545$		−	33.7176i		−	1.44430i
$546$		0			0
$547$	6.72133	−	6.72133i	0.287383	−	0.287383i	−0.548661	−	0.836045i	$-0.684862\pi$
$547$	6.72133	−	6.72133i	0.287383	−	0.287383i	0.836045	+	0.548661i	$0.184862\pi$
$548$		0			0
$549$	2.73398	+	8.54109i	0.116683	+	0.364525i
$550$		0			0
$551$		−	6.01038i		−	0.256051i
$552$		0			0
$553$		−	10.6576i		−	0.453205i
$554$		0			0
$555$	32.7094	+	7.92842i	1.38844	+	0.336543i
$556$		0			0
$557$	−5.70500	+	5.70500i	−0.241729	+	0.241729i	−0.817565	−	0.575836i	$-0.804677\pi$
$557$	−5.70500	+	5.70500i	−0.241729	+	0.241729i	0.575836	+	0.817565i	$0.304677\pi$
$558$		0			0
$559$			6.34661i			0.268433i
$560$		0			0
$561$	−6.80892	−	11.1658i	−0.287473	−	0.471421i
$562$		0			0
$563$	−20.8412	−	20.8412i	−0.878353	−	0.878353i	0.115011	−	0.993364i	$-0.463310\pi$
$563$	−20.8412	−	20.8412i	−0.878353	−	0.878353i	−0.993364	+	0.115011i	$0.963310\pi$
$564$		0			0
$565$	42.9096	−	42.9096i	1.80522	−	1.80522i
$566$		0			0
$567$	5.22626	+	7.32709i	0.219482	+	0.307709i
$568$		0			0
$569$	7.74936			0.324870			0.162435	−	0.986719i	$-0.448065\pi$
$569$	7.74936			0.324870			0.162435	+	0.986719i	$0.448065\pi$
$570$		0			0
$571$	−4.96436	−	4.96436i	−0.207752	−	0.207752i	0.595559	−	0.803311i	$-0.296930\pi$
$571$	−4.96436	−	4.96436i	−0.207752	−	0.207752i	−0.803311	+	0.595559i	$0.796930\pi$
$572$		0			0
$573$	18.7380	+	4.54191i	0.782792	+	0.189741i
$574$		0			0
$575$	45.8304			1.91126
$576$		0			0
$577$	42.9528			1.78815			0.894073	−	0.447921i	$-0.147835\pi$
$577$	42.9528			1.78815			0.894073	+	0.447921i	$0.147835\pi$
$578$		0			0
$579$	−40.7770	−	9.88392i	−1.69463	−	0.410762i
$580$		0			0
$581$	−7.45604	−	7.45604i	−0.309329	−	0.309329i
$582$		0			0
$583$	−23.6159			−0.978069
$584$		0			0
$585$	5.68565	−	11.0392i	0.235073	−	0.456417i
$586$		0			0
$587$	6.19957	−	6.19957i	0.255884	−	0.255884i	−0.567494	−	0.823378i	$-0.692087\pi$
$587$	6.19957	−	6.19957i	0.255884	−	0.255884i	0.823378	+	0.567494i	$0.192087\pi$
$588$		0			0
$589$	14.6279	+	14.6279i	0.602733	+	0.602733i
$590$		0			0
$591$	15.2155	+	24.9516i	0.625881	+	1.02637i
$592$		0			0
$593$		−	14.7953i		−	0.607569i	−0.952741	−	0.303785i	$-0.901750\pi$
$593$		−	14.7953i		−	0.607569i	0.952741	−	0.303785i	$-0.0982504\pi$
$594$		0			0
$595$	−6.62972	+	6.62972i	−0.271792	+	0.271792i
$596$		0			0
$597$	9.53856	+	2.31205i	0.390387	+	0.0946259i
$598$		0			0
$599$			21.0039i			0.858198i	0.903257	+	0.429099i	$0.141169\pi$
$599$			21.0039i			0.858198i	−0.903257	+	0.429099i	$0.858831\pi$
$600$		0			0
$601$		−	39.2853i		−	1.60248i	−0.598343	−	0.801240i	$-0.704174\pi$
$601$		−	39.2853i		−	1.60248i	0.598343	−	0.801240i	$-0.295826\pi$
$602$		0			0
$603$	8.79186	−	2.81425i	0.358032	−	0.114605i
$604$		0			0
$605$	9.88009	−	9.88009i	0.401683	−	0.401683i
$606$		0			0
$607$			13.5867i			0.551466i	0.961234	+	0.275733i	$0.0889205\pi$
$607$			13.5867i			0.551466i	−0.961234	+	0.275733i	$0.911079\pi$
$608$		0			0
$609$	−3.50379	+	2.13661i	−0.141981	+	0.0865799i
$610$		0			0
$611$	7.88028	+	7.88028i	0.318802	+	0.318802i
$612$		0			0
$613$	7.18766	−	7.18766i	0.290307	−	0.290307i	−0.546895	−	0.837201i	$-0.684190\pi$
$613$	7.18766	−	7.18766i	0.290307	−	0.290307i	0.837201	+	0.546895i	$0.184190\pi$
$614$		0			0
$615$	−13.0516	−	21.4031i	−0.526291	−	0.863054i
$616$		0			0
$617$	25.4655			1.02520			0.512601	−	0.858627i	$-0.328682\pi$
$617$	25.4655			1.02520			0.512601	+	0.858627i	$0.328682\pi$
$618$		0			0
$619$	−24.8928	−	24.8928i	−1.00052	−	1.00052i	−1.00000		0.000524244i	$-0.999833\pi$
$619$	−24.8928	−	24.8928i	−1.00052	−	1.00052i	−0.000524244	−	1.00000i	$-0.500167\pi$
$620$		0			0
$621$	29.8412	−	34.4795i	1.19749	−	1.38362i
$622$		0			0
$623$	−11.6283			−0.465878
$624$		0			0
$625$	23.8383			0.953534
$626$		0			0
$627$	−2.66501	+	10.9947i	−0.106430	+	0.439087i
$628$		0			0
$629$	12.6023	+	12.6023i	0.502487	+	0.502487i
$630$		0			0
$631$	0.512718			0.0204110			0.0102055	−	0.999948i	$-0.496751\pi$
$631$	0.512718			0.0204110			0.0102055	+	0.999948i	$0.496751\pi$
$632$		0			0
$633$	−24.7211	+	15.0749i	−0.982574	+	0.599174i
$634$		0			0
$635$	46.5727	−	46.5727i	1.84818	−	1.84818i
$636$		0			0
$637$	0.915413	+	0.915413i	0.0362700	+	0.0362700i
$638$		0			0
$639$	−6.49126	+	12.6034i	−0.256790	+	0.498583i
$640$		0			0
$641$		−	24.2180i		−	0.956553i	−0.878209	−	0.478277i	$-0.841262\pi$
$641$		−	24.2180i		−	0.956553i	0.878209	−	0.478277i	$-0.158738\pi$
$642$		0			0
$643$	1.22963	−	1.22963i	0.0484917	−	0.0484917i	−0.682445	−	0.730937i	$-0.739083\pi$
$643$	1.22963	−	1.22963i	0.0484917	−	0.0484917i	0.730937	+	0.682445i	$0.239083\pi$
$644$		0			0
$645$	6.39536	−	26.3846i	0.251817	−	1.03889i
$646$		0			0
$647$			32.1398i			1.26355i	0.775153	+	0.631773i	$0.217673\pi$
$647$			32.1398i			1.26355i	−0.775153	+	0.631773i	$0.782327\pi$
$648$		0			0
$649$		−	29.4284i		−	1.15517i
$650$		0			0
$651$	3.32740	−	13.7275i	0.130411	−	0.538023i
$652$		0			0
$653$	4.20090	−	4.20090i	0.164394	−	0.164394i	−0.620116	−	0.784510i	$-0.712915\pi$
$653$	4.20090	−	4.20090i	0.164394	−	0.164394i	0.784510	+	0.620116i	$0.212915\pi$
$654$		0			0
$655$			36.5081i			1.42649i
$656$		0			0
$657$	12.1979	−	23.6834i	0.475885	−	0.923976i
$658$		0			0
$659$	19.3636	+	19.3636i	0.754299	+	0.754299i	0.975279	−	0.220979i	$-0.0709253\pi$
$659$	19.3636	+	19.3636i	0.754299	+	0.754299i	−0.220979	+	0.975279i	$0.570925\pi$
$660$		0			0
$661$	−4.66027	+	4.66027i	−0.181264	+	0.181264i	−0.791906	−	0.610643i	$-0.790911\pi$
$661$	−4.66027	+	4.66027i	−0.181264	+	0.181264i	0.610643	+	0.791906i	$0.290911\pi$
$662$		0			0
$663$	5.61398	−	3.42341i	0.218029	−	0.132954i
$664$		0			0
$665$	8.11049			0.314511
$666$		0			0
$667$	14.7027	+	14.7027i	0.569291	+	0.569291i
$668$		0			0
$669$	2.77923	−	11.4660i	0.107451	−	0.443300i
$670$		0			0
$671$	7.69706			0.297142
$672$		0			0
$673$	−38.8503			−1.49757			−0.748784	−	0.662814i	$-0.769362\pi$
$673$	−38.8503			−1.49757			−0.748784	+	0.662814i	$0.769362\pi$
$674$		0			0
$675$	−17.7586	+	20.5189i	−0.683529	+	0.789773i
$676$		0			0
$677$	3.77109	+	3.77109i	0.144935	+	0.144935i	0.775851	−	0.630916i	$-0.217321\pi$
$677$	3.77109	+	3.77109i	0.144935	+	0.144935i	−0.630916	+	0.775851i	$0.717321\pi$
$678$		0			0
$679$	9.08157			0.348519
$680$		0			0
$681$	−0.261475	−	0.428788i	−0.0100197	−	0.0164312i
$682$		0			0
$683$	−26.2664	+	26.2664i	−1.00506	+	1.00506i	−0.00507032	+	0.999987i	$0.501614\pi$
$683$	−26.2664	+	26.2664i	−1.00506	+	1.00506i	−0.999987	+	0.00507032i	$0.998386\pi$
$684$		0			0
$685$	−11.8029	−	11.8029i	−0.450964	−	0.450964i
$686$		0			0
$687$	−28.0164	+	17.0844i	−1.06889	+	0.651812i
$688$		0			0
$689$		−	11.8737i		−	0.452350i
$690$		0			0
$691$	−16.9641	+	16.9641i	−0.645344	+	0.645344i	−0.951864	−	0.306520i	$-0.900835\pi$
$691$	−16.9641	+	16.9641i	−0.645344	+	0.645344i	0.306520	+	0.951864i	$0.400835\pi$
$692$		0			0
$693$	7.35683	−	2.35490i	0.279463	−	0.0894553i
$694$		0			0
$695$		−	54.1994i		−	2.05590i
$696$		0			0
$697$		−	13.2747i		−	0.502816i
$698$		0			0
$699$	−10.1275	−	2.45481i	−0.383059	−	0.0928496i
$700$		0			0
$701$	−3.53373	+	3.53373i	−0.133467	+	0.133467i	−0.770684	−	0.637217i	$-0.780085\pi$
$701$	−3.53373	+	3.53373i	−0.133467	+	0.133467i	0.637217	+	0.770684i	$0.280085\pi$
$702$		0			0
$703$		−	15.4171i		−	0.581466i
$704$		0			0
$705$	−24.8197	−	40.7013i	−0.934762	−	1.53290i
$706$		0			0
$707$	−4.72687	−	4.72687i	−0.177772	−	0.177772i
$708$		0			0
$709$	36.9985	−	36.9985i	1.38951	−	1.38951i	0.563162	−	0.826346i	$-0.309585\pi$
$709$	36.9985	−	36.9985i	1.38951	−	1.38951i	0.826346	−	0.563162i	$-0.190415\pi$
$710$		0			0
$711$	14.6396	−	28.4242i	0.549027	−	1.06599i
$712$		0			0
$713$	−71.5662			−2.68018
$714$		0			0
$715$	−7.53607	−	7.53607i	−0.281833	−	0.281833i
$716$		0			0
$717$	11.6068	+	2.81338i	0.433465	+	0.105068i
$718$		0			0
$719$	−1.47388			−0.0549663			−0.0274831	−	0.999622i	$-0.508749\pi$
$719$	−1.47388			−0.0549663			−0.0274831	+	0.999622i	$0.508749\pi$
$720$		0			0
$721$	14.7866			0.550681
$722$		0			0
$723$	18.5005	+	4.48434i	0.688042	+	0.166774i
$724$		0			0
$725$	−8.74963	−	8.74963i	−0.324953	−	0.324953i
$726$		0			0
$727$	31.5533			1.17025			0.585124	−	0.810944i	$-0.301046\pi$
$727$	31.5533			1.17025			0.585124	+	0.810944i	$0.301046\pi$
$728$		0			0
$729$	3.87392	+	26.7206i	0.143479	+	0.989653i
$730$		0			0
$731$	10.1655	−	10.1655i	0.375984	−	0.375984i
$732$		0			0
$733$	4.14193	+	4.14193i	0.152986	+	0.152986i	0.779450	−	0.626464i	$-0.215499\pi$
$733$	4.14193	+	4.14193i	0.152986	+	0.152986i	−0.626464	+	0.779450i	$0.715499\pi$
$734$		0			0
$735$	−2.88318	−	4.72806i	−0.106348	−	0.174397i
$736$		0			0
$737$		−	7.92305i		−	0.291849i
$738$		0			0
$739$	−24.0249	+	24.0249i	−0.883769	+	0.883769i	−0.993915	−	0.110147i	$-0.964868\pi$
$739$	−24.0249	+	24.0249i	−0.883769	+	0.883769i	0.110147	+	0.993915i	$0.464868\pi$
$740$		0			0
$741$	−5.52796	−	1.33992i	−0.203075	−	0.0492233i
$742$		0			0
$743$		−	14.1448i		−	0.518923i	−0.965753	−	0.259461i	$-0.916455\pi$
$743$		−	14.1448i		−	0.518923i	0.965753	−	0.259461i	$-0.0835450\pi$
$744$		0			0
$745$		−	53.1256i		−	1.94637i
$746$		0			0
$747$	−9.64373	−	30.1275i	−0.352845	−	1.10231i
$748$		0			0
$749$	−9.12369	+	9.12369i	−0.333372	+	0.333372i
$750$		0			0
$751$			2.98228i			0.108825i	0.998519	+	0.0544125i	$0.0173286\pi$
$751$			2.98228i			0.108825i	−0.998519	+	0.0544125i	$0.982671\pi$
$752$		0			0
$753$	24.8742	−	15.1683i	0.906467	−	0.552764i
$754$		0			0
$755$	18.4251	+	18.4251i	0.670559	+	0.670559i
$756$		0			0
$757$	−11.2382	+	11.2382i	−0.408459	+	0.408459i	−0.881201	−	0.472742i	$-0.843264\pi$
$757$	−11.2382	+	11.2382i	−0.408459	+	0.408459i	0.472742	+	0.881201i	$0.343264\pi$
$758$		0			0
$759$	−20.3763	−	33.4147i	−0.739613	−	1.21288i
$760$		0			0
$761$	46.7489			1.69465			0.847324	−	0.531077i	$-0.178212\pi$
$761$	46.7489			1.69465			0.847324	+	0.531077i	$0.178212\pi$
$762$		0			0
$763$	7.45700	+	7.45700i	0.269961	+	0.269961i
$764$		0			0
$765$	−26.7886	+	8.57495i	−0.968543	+	0.310028i
$766$		0			0
$767$	14.7961			0.534256
$768$		0			0
$769$	45.7155			1.64854			0.824272	−	0.566194i	$-0.191585\pi$
$769$	45.7155			1.64854			0.824272	+	0.566194i	$0.191585\pi$
$770$		0			0
$771$	5.98682	−	24.6991i	0.215610	−	0.889517i
$772$		0			0
$773$	14.0908	+	14.0908i	0.506812	+	0.506812i	0.913546	−	0.406735i	$-0.133333\pi$
$773$	14.0908	+	14.0908i	0.506812	+	0.506812i	−0.406735	+	0.913546i	$0.633333\pi$
$774$		0			0
$775$	42.5893			1.52985
$776$		0			0
$777$	−8.98748	+	5.48057i	−0.322424	+	0.196614i
$778$		0			0
$779$	−8.11984	+	8.11984i	−0.290923	+	0.290923i
$780$		0			0
$781$	8.60387	+	8.60387i	0.307871	+	0.307871i
$782$		0			0
$783$	−12.2797	+	0.885517i	−0.438840	+	0.0316458i
$784$		0			0
$785$			48.7773i			1.74094i
$786$		0			0
$787$	14.7212	−	14.7212i	0.524752	−	0.524752i	−0.394251	−	0.919003i	$-0.628996\pi$
$787$	14.7212	−	14.7212i	0.524752	−	0.524752i	0.919003	+	0.394251i	$0.128996\pi$
$788$		0			0
$789$	−8.32971	+	34.3649i	−0.296546	+	1.22342i
$790$		0			0
$791$			18.9798i			0.674845i
$792$		0			0
$793$			3.86995i			0.137426i
$794$		0			0
$795$	−11.9649	+	49.3621i	−0.424350	+	1.75069i
$796$		0			0
$797$	−5.16925	+	5.16925i	−0.183104	+	0.183104i	−0.792707	−	0.609603i	$-0.791329\pi$
$797$	−5.16925	+	5.16925i	−0.183104	+	0.183104i	0.609603	+	0.792707i	$0.291329\pi$
$798$		0			0
$799$		−	25.2440i		−	0.893067i
$800$		0			0
$801$	−31.0132	−	15.9730i	−1.09580	−	0.564379i
$802$		0			0
$803$	−16.1677	−	16.1677i	−0.570547	−	0.570547i
$804$		0			0
$805$	−19.8400	+	19.8400i	−0.699270	+	0.699270i
$806$		0			0
$807$	−39.0999	+	23.8432i	−1.37638	+	0.839319i
$808$		0			0
$809$	−40.7474			−1.43260			−0.716302	−	0.697790i	$-0.754167\pi$
$809$	−40.7474			−1.43260			−0.716302	+	0.697790i	$0.754167\pi$
$810$		0			0
$811$	3.79131	+	3.79131i	0.133131	+	0.133131i	0.770532	−	0.637401i	$-0.219991\pi$
$811$	3.79131	+	3.79131i	0.133131	+	0.133131i	−0.637401	+	0.770532i	$0.719991\pi$
$812$		0			0
$813$	−2.21161	+	9.12417i	−0.0775644	+	0.319999i
$814$		0			0
$815$	−10.2449			−0.358865
$816$		0			0
$817$	−12.4360			−0.435080
$818$		0			0
$819$	1.18400	+	3.69889i	0.0413725	+	0.129250i
$820$		0			0
$821$	3.18885	+	3.18885i	0.111291	+	0.111291i	0.760560	−	0.649268i	$-0.224925\pi$
$821$	3.18885	+	3.18885i	0.111291	+	0.111291i	−0.649268	+	0.760560i	$0.724925\pi$
$822$		0			0
$823$	48.4703			1.68957			0.844784	−	0.535107i	$-0.179729\pi$
$823$	48.4703			1.68957			0.844784	+	0.535107i	$0.179729\pi$
$824$		0			0
$825$	12.1260	+	19.8852i	0.422174	+	0.692314i
$826$		0			0
$827$	13.1317	−	13.1317i	0.456633	−	0.456633i	−0.440916	−	0.897548i	$-0.645346\pi$
$827$	13.1317	−	13.1317i	0.456633	−	0.456633i	0.897548	+	0.440916i	$0.145346\pi$
$828$		0			0
$829$	22.4142	+	22.4142i	0.778479	+	0.778479i	0.979572	−	0.201093i	$-0.0644494\pi$
$829$	22.4142	+	22.4142i	0.778479	+	0.778479i	−0.201093	+	0.979572i	$0.564449\pi$
$830$		0			0
$831$	−10.7153	+	6.53421i	−0.371710	+	0.226669i
$832$		0			0
$833$		−	2.93247i		−	0.101604i
$834$		0			0
$835$	34.5411	−	34.5411i	1.19534	−	1.19534i
$836$		0			0
$837$	27.7309	−	32.0412i	0.958520	−	1.10751i
$838$		0			0
$839$		−	44.4390i		−	1.53420i	−0.641525	−	0.767102i	$-0.721698\pi$
$839$		−	44.4390i		−	1.53420i	0.641525	−	0.767102i	$-0.278302\pi$
$840$		0			0
$841$			23.3861i			0.806418i
$842$		0			0
$843$	−9.01135	−	2.18426i	−0.310367	−	0.0752299i
$844$		0			0
$845$	−25.6014	+	25.6014i	−0.880715	+	0.880715i
$846$		0			0
$847$			4.37017i			0.150161i
$848$		0			0
$849$	13.6135	+	22.3245i	0.467214	+	0.766175i
$850$		0			0
$851$	37.7135	+	37.7135i	1.29280	+	1.29280i
$852$		0			0
$853$	−28.2563	+	28.2563i	−0.967478	+	0.967478i	−0.999488	−	0.0320095i	$-0.989809\pi$
$853$	−28.2563	+	28.2563i	−0.967478	+	0.967478i	0.0320095	+	0.999488i	$0.489809\pi$
$854$		0			0
$855$	21.6310	+	11.1409i	0.739766	+	0.381009i
$856$		0			0
$857$	14.0907			0.481328			0.240664	−	0.970609i	$-0.422635\pi$
$857$	14.0907			0.481328			0.240664	+	0.970609i	$0.422635\pi$
$858$		0			0
$859$	11.8054	+	11.8054i	0.402796	+	0.402796i	0.879217	−	0.476421i	$-0.158066\pi$
$859$	11.8054	+	11.8054i	0.402796	+	0.402796i	−0.476421	+	0.879217i	$0.658066\pi$
$860$		0			0
$861$	7.62001	+	1.84701i	0.259689	+	0.0629461i
$862$		0			0
$863$	−10.6934			−0.364009			−0.182004	−	0.983298i	$-0.558259\pi$
$863$	−10.6934			−0.364009			−0.182004	+	0.983298i	$0.558259\pi$
$864$		0			0
$865$	56.9688			1.93700
$866$		0			0
$867$	14.1409	+	3.42760i	0.480249	+	0.116407i
$868$		0			0
$869$	−19.4041	−	19.4041i	−0.658239	−	0.658239i
$870$		0			0
$871$	3.98358			0.134978
$872$		0			0
$873$	24.2210	+	12.4748i	0.819755	+	0.422206i
$874$		0			0
$875$	0.502881	−	0.502881i	0.0170005	−	0.0170005i
$876$		0			0
$877$	0.535576	+	0.535576i	0.0180851	+	0.0180851i	0.716092	−	0.698006i	$-0.245929\pi$
$877$	0.535576	+	0.535576i	0.0180851	+	0.0180851i	−0.698006	+	0.716092i	$0.745929\pi$
$878$		0			0
$879$	−0.338638	−	0.555326i	−0.0114220	−	0.0187307i
$880$		0			0
$881$		−	53.6084i		−	1.80611i	−0.429522	−	0.903057i	$-0.641318\pi$
$881$		−	53.6084i		−	1.80611i	0.429522	−	0.903057i	$-0.358682\pi$
$882$		0			0
$883$	8.11686	−	8.11686i	0.273154	−	0.273154i	−0.557215	−	0.830369i	$-0.688130\pi$
$883$	8.11686	−	8.11686i	0.273154	−	0.273154i	0.830369	+	0.557215i	$0.188130\pi$
$884$		0			0
$885$	−61.5114	−	14.9097i	−2.06768	−	0.501186i
$886$		0			0
$887$		−	19.7832i		−	0.664254i	−0.943235	−	0.332127i	$-0.892234\pi$
$887$		−	19.7832i		−	0.664254i	0.943235	−	0.332127i	$-0.107766\pi$
$888$		0			0
$889$			20.6001i			0.690905i
$890$		0			0
$891$	22.8558	+	3.82496i	0.765697	+	0.128141i
$892$		0			0
$893$	−15.4411	+	15.4411i	−0.516718	+	0.516718i
$894$		0			0
$895$			1.60482i			0.0536431i
$896$		0			0
$897$	16.8004	−	10.2449i	0.560948	−	0.342066i
$898$		0			0
$899$	13.6629	+	13.6629i	0.455685	+	0.455685i
$900$		0			0
$901$	−19.0183	+	19.0183i	−0.633590	+	0.633590i
$902$		0			0
$903$	4.42083	+	7.24964i	0.147116	+	0.241253i
$904$		0			0
$905$	17.8832			0.594456
$906$		0			0
$907$	−24.7075	−	24.7075i	−0.820398	−	0.820398i	0.165767	−	0.986165i	$-0.446990\pi$
$907$	−24.7075	−	24.7075i	−0.820398	−	0.820398i	−0.986165	+	0.165767i	$0.946990\pi$
$908$		0			0
$909$	−6.11378	−	19.0998i	−0.202781	−	0.633499i
$910$		0			0
$911$	−39.4269			−1.30627			−0.653135	−	0.757241i	$-0.726547\pi$
$911$	−39.4269			−1.30627			−0.653135	+	0.757241i	$0.726547\pi$
$912$		0			0
$913$	−27.1503			−0.898544
$914$		0			0
$915$	3.89968	−	16.0884i	0.128919	−	0.531868i
$916$		0			0
$917$	−8.07416	−	8.07416i	−0.266632	−	0.266632i
$918$		0			0
$919$	7.10328			0.234315			0.117158	−	0.993113i	$-0.462622\pi$
$919$	7.10328			0.234315			0.117158	+	0.993113i	$0.462622\pi$
$920$		0			0
$921$	15.2359	−	9.29087i	0.502041	−	0.306145i
$922$		0			0
$923$	−4.32588	+	4.32588i	−0.142388	+	0.142388i
$924$		0			0
$925$	−22.4435	−	22.4435i	−0.737937	−	0.737937i
$926$		0			0
$927$	39.4365	+	20.3113i	1.29526	+	0.667112i
$928$		0			0
$929$			17.0263i			0.558615i	0.960202	+	0.279308i	$0.0901049\pi$
$929$			17.0263i			0.558615i	−0.960202	+	0.279308i	$0.909895\pi$
$930$		0			0
$931$	−1.79372	+	1.79372i	−0.0587869	+	0.0587869i
$932$		0			0
$933$	−4.93229	+	20.3486i	−0.161476	+	0.666182i
$934$		0			0
$935$			24.1413i			0.789506i
$936$		0			0
$937$			52.6704i			1.72067i	0.509731	+	0.860334i	$0.329745\pi$
$937$			52.6704i			1.72067i	−0.509731	+	0.860334i	$0.670255\pi$
$938$		0			0
$939$	0.384396	−	1.58586i	0.0125443	−	0.0517525i
$940$		0			0
$941$	−11.0340	+	11.0340i	−0.359698	+	0.359698i	−0.863701	−	0.504004i	$-0.831860\pi$
$941$	−11.0340	+	11.0340i	−0.359698	+	0.359698i	0.504004	+	0.863701i	$0.331860\pi$
$942$		0			0
$943$		−	39.7258i		−	1.29365i
$944$		0			0
$945$	−1.19493	−	16.5704i	−0.0388711	−	0.539035i
$946$		0			0
$947$	−1.96456	−	1.96456i	−0.0638396	−	0.0638396i	0.674466	−	0.738306i	$-0.264374\pi$
$947$	−1.96456	−	1.96456i	−0.0638396	−	0.0638396i	−0.738306	+	0.674466i	$0.764374\pi$
$948$		0			0
$949$	8.12887	−	8.12887i	0.263874	−	0.263874i
$950$		0			0
$951$	8.27934	−	5.04874i	0.268476	−	0.163717i
$952$		0			0
$953$	−32.9580			−1.06761			−0.533807	−	0.845606i	$-0.679239\pi$
$953$	−32.9580			−1.06761			−0.533807	+	0.845606i	$0.679239\pi$
$954$		0			0
$955$	−25.1665	−	25.1665i	−0.814368	−	0.814368i
$956$		0			0
$957$	−2.48920	+	10.2694i	−0.0804645	+	0.331963i
$958$		0			0
$959$	5.22066			0.168584
$960$		0			0
$961$	−35.5052			−1.14533
$962$		0			0
$963$	−36.8659	+	11.8007i	−1.18799	+	0.380271i
$964$		0			0
$965$	54.7663	+	54.7663i	1.76299	+	1.76299i
$966$		0			0
$967$	3.67868			0.118298			0.0591492	−	0.998249i	$-0.481161\pi$
$967$	3.67868			0.118298			0.0591492	+	0.998249i	$0.481161\pi$
$968$		0			0
$969$	6.70806	+	11.0004i	0.215494	+	0.353384i
$970$		0			0
$971$	−19.8765	+	19.8765i	−0.637866	+	0.637866i	−0.950029	−	0.312162i	$-0.898947\pi$
$971$	−19.8765	+	19.8765i	−0.637866	+	0.637866i	0.312162	+	0.950029i	$0.398947\pi$
$972$		0			0
$973$	11.9868	+	11.9868i	0.384279	+	0.384279i
$974$		0			0
$975$	−9.99795	+	6.09676i	−0.320191	+	0.195253i
$976$		0			0
$977$			33.2269i			1.06302i	0.847051	+	0.531511i	$0.178376\pi$
$977$			33.2269i			1.06302i	−0.847051	+	0.531511i	$0.821624\pi$
$978$		0			0
$979$	−21.1715	+	21.1715i	−0.676645	+	0.676645i
$980$		0			0
$981$	9.64496	+	30.1313i	0.307940	+	0.962020i
$982$		0			0
$983$			17.2861i			0.551341i	0.961252	+	0.275671i	$0.0888999\pi$
$983$			17.2861i			0.551341i	−0.961252	+	0.275671i	$0.911100\pi$
$984$		0			0
$985$		−	53.9472i		−	1.71890i
$986$		0			0
$987$	14.4907	+	3.51239i	0.461242	+	0.111801i
$988$		0			0
$989$	30.4211	−	30.4211i	0.967336	−	0.967336i
$990$		0			0
$991$			36.1152i			1.14724i	0.819123	+	0.573618i	$0.194461\pi$
$991$			36.1152i			1.14724i	−0.819123	+	0.573618i	$0.805539\pi$
$992$		0			0
$993$	20.8184	+	34.1396i	0.660651	+	1.08339i
$994$		0			0
$995$	−12.8110	−	12.8110i	−0.406135	−	0.406135i
$996$		0			0
$997$	0.871700	−	0.871700i	0.0276070	−	0.0276070i	−0.693169	−	0.720776i	$-0.743786\pi$
$997$	0.871700	−	0.871700i	0.0276070	−	0.0276070i	0.720776	+	0.693169i	$0.243786\pi$
$998$		0			0
$999$	−31.4983	+	2.27142i	−0.996563	+	0.0718645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.s.c.239.19		40
3.2	odd	2	inner	1344.2.s.c.239.10		40
4.3	odd	2		336.2.s.c.323.8	yes	40
12.11	even	2		336.2.s.c.323.13	yes	40
16.5	even	4		336.2.s.c.155.13	yes	40
16.11	odd	4	inner	1344.2.s.c.911.10		40
48.5	odd	4		336.2.s.c.155.8	✓	40
48.11	even	4	inner	1344.2.s.c.911.19		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.c.155.8	✓	40	48.5	odd	4
336.2.s.c.155.13	yes	40	16.5	even	4
336.2.s.c.323.8	yes	40	4.3	odd	2
336.2.s.c.323.13	yes	40	12.11	even	2
1344.2.s.c.239.10		40	3.2	odd	2	inner
1344.2.s.c.239.19		40	1.1	even	1	trivial
1344.2.s.c.911.10		40	16.11	odd	4	inner
1344.2.s.c.911.19		40	48.11	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.68331 + 0.408017i) q^{3} +(-2.26080 - 2.26080i) q^{5} +1.00000 q^{7} +(2.66704 + 1.37363i) q^{9} +O(q^{10})\)	\(q+(1.68331 + 0.408017i) q^{3} +(-2.26080 - 2.26080i) q^{5} +1.00000 q^{7} +(2.66704 + 1.37363i) q^{9} +(1.82069 - 1.82069i) q^{11} +(0.915413 + 0.915413i) q^{13} +(-2.88318 - 4.72806i) q^{15} -2.93247i q^{17} +(-1.79372 + 1.79372i) q^{19} +(1.68331 + 0.408017i) q^{21} -8.77567i q^{23} +5.22244i q^{25} +(3.92899 + 3.40045i) q^{27} +(-1.67539 + 1.67539i) q^{29} -8.15507i q^{31} +(3.80765 - 2.32191i) q^{33} +(-2.26080 - 2.26080i) q^{35} +(-4.29751 + 4.29751i) q^{37} +(1.16742 + 1.91442i) q^{39} +4.52681 q^{41} +(3.46653 + 3.46653i) q^{43} +(-2.92414 - 9.13517i) q^{45} +8.60844 q^{47} +1.00000 q^{49} +(1.19649 - 4.93624i) q^{51} +(-6.48541 - 6.48541i) q^{53} -8.23243 q^{55} +(-3.75125 + 2.28752i) q^{57} +(8.08166 - 8.08166i) q^{59} +(2.11377 + 2.11377i) q^{61} +(2.66704 + 1.37363i) q^{63} -4.13913i q^{65} +(2.17584 - 2.17584i) q^{67} +(3.58062 - 14.7721i) q^{69} +4.72561i q^{71} -8.88001i q^{73} +(-2.13084 + 8.79096i) q^{75} +(1.82069 - 1.82069i) q^{77} -10.6576i q^{79} +(5.22626 + 7.32709i) q^{81} +(-7.45604 - 7.45604i) q^{83} +(-6.62972 + 6.62972i) q^{85} +(-3.50379 + 2.13661i) q^{87} -11.6283 q^{89} +(0.915413 + 0.915413i) q^{91} +(3.32740 - 13.7275i) q^{93} +8.11049 q^{95} +9.08157 q^{97} +(7.35683 - 2.35490i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} + 40 q^{7}+O(q^{10}) \) 40 * q - 4 * q^3 + 40 * q^7	\( 40 q - 4 q^{3} + 40 q^{7} + 24 q^{13} - 16 q^{19} - 4 q^{21} + 32 q^{27} + 24 q^{33} - 8 q^{37} + 64 q^{39} - 24 q^{43} - 28 q^{45} + 40 q^{49} + 32 q^{51} - 16 q^{55} - 48 q^{61} - 40 q^{67} + 4 q^{69} - 40 q^{75} + 56 q^{81} - 48 q^{85} - 32 q^{87} + 24 q^{91} + 56 q^{93} + 16 q^{97} - 24 q^{99}+O(q^{100}) \) 40 * q - 4 * q^3 + 40 * q^7 + 24 * q^13 - 16 * q^19 - 4 * q^21 + 32 * q^27 + 24 * q^33 - 8 * q^37 + 64 * q^39 - 24 * q^43 - 28 * q^45 + 40 * q^49 + 32 * q^51 - 16 * q^55 - 48 * q^61 - 40 * q^67 + 4 * q^69 - 40 * q^75 + 56 * q^81 - 48 * q^85 - 32 * q^87 + 24 * q^91 + 56 * q^93 + 16 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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