LMFDB - Embedded newform 1248.2.ca.a.433.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1248,2,Mod(49,1248)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1248, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1248.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1248 = 2^{5} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1248.ca (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$9.96533017226$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.12960000.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1 $ x^8 - 3x^6 + 8x^4 - 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			433.4
Root			$-0.535233 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	1248.433
Dual form			1248.2.ca.a.49.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{3} +2.23607 q^{5} +(0.436492 - 0.252009i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-1.98406 + 3.43649i) q^{11} +(2.59808 - 2.50000i) q^{13} +(1.93649 + 1.11803i) q^{15} +(0.936492 + 1.62205i) q^{17} +(1.98406 + 3.43649i) q^{19} +0.504017 q^{21} +(0.563508 - 0.976025i) q^{23} +1.00000i q^{27} +(1.84205 + 1.06351i) q^{29} +4.47214i q^{31} +(-3.43649 + 1.98406i) q^{33} +(0.976025 - 0.563508i) q^{35} +(5.33816 - 9.24597i) q^{37} +(3.50000 - 0.866025i) q^{39} +(4.93649 + 2.85008i) q^{41} +(0.976025 - 0.563508i) q^{43} +(1.11803 + 1.93649i) q^{45} +0.504017i q^{47} +(-3.37298 + 5.84218i) q^{49} +1.87298i q^{51} -0.127017i q^{53} +(-4.43649 + 7.68423i) q^{55} +3.96812i q^{57} +(-5.70017 - 9.87298i) q^{59} +(-0.866025 + 0.500000i) q^{61} +(0.436492 + 0.252009i) q^{63} +(5.80948 - 5.59017i) q^{65} +(7.68423 - 13.3095i) q^{67} +(0.976025 - 0.563508i) q^{69} +(-7.30948 + 4.22013i) q^{71} -4.18812i q^{73} +2.00000i q^{77} -14.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +7.43222 q^{83} +(2.09406 + 3.62702i) q^{85} +(1.06351 + 1.84205i) q^{87} +(13.7460 + 7.93624i) q^{89} +(0.504017 - 1.74597i) q^{91} +(-2.23607 + 3.87298i) q^{93} +(4.43649 + 7.68423i) q^{95} +(-15.0000 + 8.66025i) q^{97} -3.96812 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{7} + 4 q^{9} - 8 q^{17} + 20 q^{23} - 12 q^{33} + 28 q^{39} + 24 q^{41} + 4 q^{49} - 20 q^{55} - 12 q^{63} - 12 q^{71} - 112 q^{79} - 4 q^{81} + 24 q^{87} + 48 q^{89} + 20 q^{95} - 120 q^{97}+O(q^{100}) $ 8 * q - 12 * q^7 + 4 * q^9 - 8 * q^17 + 20 * q^23 - 12 * q^33 + 28 * q^39 + 24 * q^41 + 4 * q^49 - 20 * q^55 - 12 * q^63 - 12 * q^71 - 112 * q^79 - 4 * q^81 + 24 * q^87 + 48 * q^89 + 20 * q^95 - 120 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1248\mathbb{Z}\right)^\times$.

$n$	$703$	$769$	$833$	$1093$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$		0			0
$5$	2.23607			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$5$	2.23607			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$6$		0			0
$7$	0.436492	−	0.252009i	0.164978	−	0.0952503i	−0.415238	−	0.909713i	$-0.636302\pi$
$7$	0.436492	−	0.252009i	0.164978	−	0.0952503i	0.580216	+	0.814463i	$0.302968\pi$
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−1.98406	+	3.43649i	−0.598216	+	1.03614i	0.394868	+	0.918738i	$0.370790\pi$
$11$	−1.98406	+	3.43649i	−0.598216	+	1.03614i	−0.993084	+	0.117403i	$0.962543\pi$
$12$		0			0
$13$	2.59808	−	2.50000i	0.720577	−	0.693375i
$13$	2.59808	−	2.50000i	0.720577	−	0.693375i
$14$		0			0
$15$	1.93649	+	1.11803i	0.500000	+	0.288675i
$16$		0			0
$17$	0.936492	+	1.62205i	0.227133	+	0.393405i	0.956957	−	0.290229i	$-0.0937316\pi$
$17$	0.936492	+	1.62205i	0.227133	+	0.393405i	−0.729825	+	0.683635i	$0.760398\pi$
$18$		0			0
$19$	1.98406	+	3.43649i	0.455174	+	0.788385i	0.998698	−	0.0510085i	$-0.0162436\pi$
$19$	1.98406	+	3.43649i	0.455174	+	0.788385i	−0.543524	+	0.839394i	$0.682910\pi$
$20$		0			0
$21$	0.504017			0.109986
$22$		0			0
$23$	0.563508	−	0.976025i	0.117500	−	0.203515i	−0.801277	−	0.598294i	$-0.795845\pi$
$23$	0.563508	−	0.976025i	0.117500	−	0.203515i	0.918776	+	0.394779i	$0.129179\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	1.84205	+	1.06351i	0.342060	+	0.197489i	0.661183	−	0.750225i	$-0.270055\pi$
$29$	1.84205	+	1.06351i	0.342060	+	0.197489i	−0.319123	+	0.947713i	$0.603388\pi$
$30$		0			0
$31$			4.47214i			0.803219i	0.915811	+	0.401610i	$0.131549\pi$
$31$			4.47214i			0.803219i	−0.915811	+	0.401610i	$0.868451\pi$
$32$		0			0
$33$	−3.43649	+	1.98406i	−0.598216	+	0.345380i
$34$		0			0
$35$	0.976025	−	0.563508i	0.164978	−	0.0952503i
$36$		0			0
$37$	5.33816	−	9.24597i	0.877588	−	1.52003i	0.0236086	−	0.999721i	$-0.492484\pi$
$37$	5.33816	−	9.24597i	0.877588	−	1.52003i	0.853980	−	0.520306i	$-0.174182\pi$
$38$		0			0
$39$	3.50000	−	0.866025i	0.560449	−	0.138675i
$40$		0			0
$41$	4.93649	+	2.85008i	0.770950	+	0.445108i	0.833214	−	0.552951i	$-0.186498\pi$
$41$	4.93649	+	2.85008i	0.770950	+	0.445108i	−0.0622631	+	0.998060i	$0.519832\pi$
$42$		0			0
$43$	0.976025	−	0.563508i	0.148842	−	0.0859342i	−0.423729	−	0.905789i	$-0.639279\pi$
$43$	0.976025	−	0.563508i	0.148842	−	0.0859342i	0.572572	+	0.819855i	$0.305946\pi$
$44$		0			0
$45$	1.11803	+	1.93649i	0.166667	+	0.288675i
$46$		0			0
$47$			0.504017i			0.0735185i	0.999324	+	0.0367592i	$0.0117035\pi$
$47$			0.504017i			0.0735185i	−0.999324	+	0.0367592i	$0.988297\pi$
$48$		0			0
$49$	−3.37298	+	5.84218i	−0.481855	+	0.834597i
$50$		0			0
$51$			1.87298i			0.262270i
$52$		0			0
$53$		−	0.127017i		−	0.0174471i	−0.999962	−	0.00872354i	$-0.997223\pi$
$53$		−	0.127017i		−	0.0174471i	0.999962	−	0.00872354i	$-0.00277682\pi$
$54$		0			0
$55$	−4.43649	+	7.68423i	−0.598216	+	1.03614i
$56$		0			0
$57$			3.96812i			0.525590i
$58$		0			0
$59$	−5.70017	−	9.87298i	−0.742099	−	1.28535i	−0.951538	−	0.307531i	$-0.900497\pi$
$59$	−5.70017	−	9.87298i	−0.742099	−	1.28535i	0.209439	−	0.977822i	$-0.432836\pi$
$60$		0			0
$61$	−0.866025	+	0.500000i	−0.110883	+	0.0640184i	−0.554416	−	0.832240i	$-0.687058\pi$
$61$	−0.866025	+	0.500000i	−0.110883	+	0.0640184i	0.443533	+	0.896258i	$0.353725\pi$
$62$		0			0
$63$	0.436492	+	0.252009i	0.0549928	+	0.0317501i
$64$		0			0
$65$	5.80948	−	5.59017i	0.720577	−	0.693375i
$66$		0			0
$67$	7.68423	−	13.3095i	0.938778	−	1.62601i	0.171024	−	0.985267i	$-0.445293\pi$
$67$	7.68423	−	13.3095i	0.938778	−	1.62601i	0.767754	−	0.640744i	$-0.221374\pi$
$68$		0			0
$69$	0.976025	−	0.563508i	0.117500	−	0.0678384i
$70$		0			0
$71$	−7.30948	+	4.22013i	−0.867475	+	0.500837i	−0.866508	−	0.499163i	$-0.833641\pi$
$71$	−7.30948	+	4.22013i	−0.867475	+	0.500837i	−0.000966726		1.00000i	$0.500308\pi$
$72$		0			0
$73$		−	4.18812i		−	0.490182i	−0.969500	−	0.245091i	$-0.921182\pi$
$73$		−	4.18812i		−	0.490182i	0.969500	−	0.245091i	$-0.0788179\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			2.00000i			0.227921i
$78$		0			0
$79$	−14.0000			−1.57512			−0.787562	−	0.616236i	$-0.788657\pi$
$79$	−14.0000			−1.57512			−0.787562	+	0.616236i	$0.788657\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	7.43222			0.815792			0.407896	−	0.913028i	$-0.366263\pi$
$83$	7.43222			0.815792			0.407896	+	0.913028i	$0.366263\pi$
$84$		0			0
$85$	2.09406	+	3.62702i	0.227133	+	0.393405i
$86$		0			0
$87$	1.06351	+	1.84205i	0.114020	+	0.197489i
$88$		0			0
$89$	13.7460	+	7.93624i	1.45707	+	0.841239i	0.998866	−	0.0476078i	$-0.0151598\pi$
$89$	13.7460	+	7.93624i	1.45707	+	0.841239i	0.458203	+	0.888847i	$0.348493\pi$
$90$		0			0
$91$	0.504017	−	1.74597i	0.0528354	−	0.183027i
$92$		0			0
$93$	−2.23607	+	3.87298i	−0.231869	+	0.401610i
$94$		0			0
$95$	4.43649	+	7.68423i	0.455174	+	0.788385i
$96$		0			0
$97$	−15.0000	+	8.66025i	−1.52302	+	0.879316i	−0.523390	+	0.852093i	$0.675333\pi$
$97$	−15.0000	+	8.66025i	−1.52302	+	0.879316i	−0.999629	+	0.0272222i	$0.991334\pi$
$98$		0			0
$99$	−3.96812			−0.398811
$100$		0			0
$101$	−0.110000	−	0.0635083i	−0.0109454	−	0.00631931i	0.494517	−	0.869168i	$-0.335345\pi$
$101$	−0.110000	−	0.0635083i	−0.0109454	−	0.00631931i	−0.505463	+	0.862848i	$0.668678\pi$
$102$		0			0
$103$	12.6190			1.24338			0.621691	−	0.783263i	$-0.286446\pi$
$103$	12.6190			1.24338			0.621691	+	0.783263i	$0.286446\pi$
$104$		0			0
$105$	1.12702			0.109986
$106$		0			0
$107$	5.95218	+	3.43649i	0.575419	+	0.332218i	0.759311	−	0.650728i	$-0.225536\pi$
$107$	5.95218	+	3.43649i	0.575419	+	0.332218i	−0.183892	+	0.982946i	$0.558870\pi$
$108$		0			0
$109$	−11.4003			−1.09195			−0.545977	−	0.837800i	$-0.683841\pi$
$109$	−11.4003			−1.09195			−0.545977	+	0.837800i	$0.683841\pi$
$110$		0			0
$111$	9.24597	−	5.33816i	0.877588	−	0.506676i
$112$		0			0
$113$	−1.06351	−	1.84205i	−0.100046	−	0.173286i	0.811657	−	0.584134i	$-0.198566\pi$
$113$	−1.06351	−	1.84205i	−0.100046	−	0.173286i	−0.911704	+	0.410849i	$0.865232\pi$
$114$		0			0
$115$	1.26004	−	2.18246i	0.117500	−	0.203515i
$116$		0			0
$117$	3.46410	+	1.00000i	0.320256	+	0.0924500i
$118$		0			0
$119$	0.817542	+	0.472008i	0.0749439	+	0.0432689i
$120$		0			0
$121$	−2.37298	−	4.11013i	−0.215726	−	0.373648i
$122$		0			0
$123$	2.85008	+	4.93649i	0.256983	+	0.445108i
$124$		0			0
$125$	−11.1803			−1.00000
$126$		0			0
$127$	8.87298	−	15.3685i	0.787350	−	1.36373i	−0.140235	−	0.990118i	$-0.544786\pi$
$127$	8.87298	−	15.3685i	0.787350	−	1.36373i	0.927585	−	0.373612i	$-0.121881\pi$
$128$		0			0
$129$	1.12702			0.0992283
$130$		0			0
$131$			3.74597i			0.327287i	0.986520	+	0.163643i	$0.0523246\pi$
$131$			3.74597i			0.327287i	−0.986520	+	0.163643i	$0.947675\pi$
$132$		0			0
$133$	1.73205	+	1.00000i	0.150188	+	0.0867110i
$134$		0			0
$135$			2.23607i			0.192450i
$136$		0			0
$137$	−11.8095	+	6.81820i	−1.00895	+	0.582518i	−0.910885	−	0.412661i	$-0.864599\pi$
$137$	−11.8095	+	6.81820i	−1.00895	+	0.582518i	−0.0980670	+	0.995180i	$0.531266\pi$
$138$		0			0
$139$	4.97615	−	2.87298i	0.422072	−	0.243683i	−0.273892	−	0.961761i	$-0.588311\pi$
$139$	4.97615	−	2.87298i	0.422072	−	0.243683i	0.695963	+	0.718077i	$0.254978\pi$
$140$		0			0
$141$	−0.252009	+	0.436492i	−0.0212230	+	0.0367592i
$142$		0			0
$143$	3.43649	+	13.8884i	0.287374	+	1.16141i
$144$		0			0
$145$	4.11895	+	2.37808i	0.342060	+	0.197489i
$146$		0			0
$147$	−5.84218	+	3.37298i	−0.481855	+	0.278199i
$148$		0			0
$149$	11.2903	+	19.5554i	0.924941	+	1.60204i	0.791657	+	0.610966i	$0.209219\pi$
$149$	11.2903	+	19.5554i	0.924941	+	1.60204i	0.133284	+	0.991078i	$0.457448\pi$
$150$		0			0
$151$		−	6.42419i		−	0.522793i	−0.965232	−	0.261396i	$-0.915817\pi$
$151$		−	6.42419i		−	0.522793i	0.965232	−	0.261396i	$-0.0841830\pi$
$152$		0			0
$153$	−0.936492	+	1.62205i	−0.0757109	+	0.131135i
$154$		0			0
$155$			10.0000i			0.803219i
$156$		0			0
$157$		−	16.7460i		−	1.33647i	−0.743949	−	0.668237i	$-0.767049\pi$
$157$		−	16.7460i		−	1.33647i	0.743949	−	0.668237i	$-0.232951\pi$
$158$		0			0
$159$	0.0635083	−	0.110000i	0.00503654	−	0.00872354i
$160$		0			0
$161$		−	0.568036i		−	0.0447675i
$162$		0			0
$163$	−4.97615	−	8.61895i	−0.389762	−	0.675088i	0.602655	−	0.798002i	$-0.294110\pi$
$163$	−4.97615	−	8.61895i	−0.389762	−	0.675088i	−0.992417	+	0.122914i	$0.960776\pi$
$164$		0			0
$165$	−7.68423	+	4.43649i	−0.598216	+	0.345380i
$166$		0			0
$167$	−15.8730	−	9.16427i	−1.22829	−	0.709153i	−0.261617	−	0.965172i	$-0.584256\pi$
$167$	−15.8730	−	9.16427i	−1.22829	−	0.709153i	−0.966672	+	0.256019i	$0.917589\pi$
$168$		0			0
$169$	0.500000	−	12.9904i	0.0384615	−	0.999260i
$170$		0			0
$171$	−1.98406	+	3.43649i	−0.151725	+	0.262795i
$172$		0			0
$173$	−11.6844	+	6.74597i	−0.888345	+	0.512886i	−0.873401	−	0.487002i	$-0.838090\pi$
$173$	−11.6844	+	6.74597i	−0.888345	+	0.512886i	−0.0149443	+	0.999888i	$0.504757\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	11.4003i		−	0.856902i
$178$		0			0
$179$	11.1483	+	6.43649i	0.833265	+	0.481086i	0.854969	−	0.518678i	$-0.173576\pi$
$179$	11.1483	+	6.43649i	0.833265	+	0.481086i	−0.0217040	+	0.999764i	$0.506909\pi$
$180$		0			0
$181$		−	14.7460i		−	1.09606i	−0.836459	−	0.548030i	$-0.815378\pi$
$181$		−	14.7460i		−	1.09606i	0.836459	−	0.548030i	$-0.184622\pi$
$182$		0			0
$183$	−1.00000			−0.0739221
$184$		0			0
$185$	11.9365	−	20.6746i	0.877588	−	1.52003i
$186$		0			0
$187$	−7.43222			−0.543498
$188$		0			0
$189$	0.252009	+	0.436492i	0.0183309	+	0.0317501i
$190$		0			0
$191$	2.12702	+	3.68410i	0.153906	+	0.266572i	0.932660	−	0.360757i	$-0.117482\pi$
$191$	2.12702	+	3.68410i	0.153906	+	0.266572i	−0.778754	+	0.627329i	$0.784148\pi$
$192$		0			0
$193$	−16.1190	−	9.30628i	−1.16027	−	0.669881i	−0.208899	−	0.977937i	$-0.566988\pi$
$193$	−16.1190	−	9.30628i	−1.16027	−	0.669881i	−0.951368	+	0.308056i	$0.900321\pi$
$194$		0			0
$195$	7.82624	−	1.93649i	0.560449	−	0.138675i
$196$		0			0
$197$	5.70017	−	9.87298i	0.406120	−	0.703421i	−0.588331	−	0.808620i	$-0.700215\pi$
$197$	5.70017	−	9.87298i	0.406120	−	0.703421i	0.994451	+	0.105199i	$0.0335481\pi$
$198$		0			0
$199$	0.436492	+	0.756026i	0.0309421	+	0.0535932i	0.881082	−	0.472964i	$-0.156816\pi$
$199$	0.436492	+	0.756026i	0.0309421	+	0.0535932i	−0.850140	+	0.526557i	$0.823483\pi$
$200$		0			0
$201$	13.3095	−	7.68423i	0.938778	−	0.542004i
$202$		0			0
$203$	1.07205			0.0752434
$204$		0			0
$205$	11.0383	+	6.37298i	0.770950	+	0.445108i
$206$		0			0
$207$	1.12702			0.0783331
$208$		0			0
$209$	−15.7460			−1.08917
$210$		0			0
$211$	−12.1244	−	7.00000i	−0.834675	−	0.481900i	0.0207756	−	0.999784i	$-0.493386\pi$
$211$	−12.1244	−	7.00000i	−0.834675	−	0.481900i	−0.855451	+	0.517884i	$0.826720\pi$
$212$		0			0
$213$	−8.44025			−0.578317
$214$		0			0
$215$	2.18246	−	1.26004i	0.148842	−	0.0859342i
$216$		0			0
$217$	1.12702	+	1.95205i	0.0765069	+	0.132514i
$218$		0			0
$219$	2.09406	−	3.62702i	0.141503	−	0.245091i
$220$		0			0
$221$	6.48820	+	1.87298i	0.436444	+	0.125990i
$222$		0			0
$223$	−18.4919	−	10.6763i	−1.23831	−	0.714939i	−0.269563	−	0.962983i	$-0.586879\pi$
$223$	−18.4919	−	10.6763i	−1.23831	−	0.714939i	−0.968749	+	0.248043i	$0.920212\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.68423	−	13.3095i	−0.510020	−	0.883381i	−0.999933	−	0.0116092i	$-0.996305\pi$
$227$	−7.68423	−	13.3095i	−0.510020	−	0.883381i	0.489912	−	0.871772i	$-0.337029\pi$
$228$		0			0
$229$	2.01607			0.133226			0.0666128	−	0.997779i	$-0.478781\pi$
$229$	2.01607			0.133226			0.0666128	+	0.997779i	$0.478781\pi$
$230$		0			0
$231$	−1.00000	+	1.73205i	−0.0657952	+	0.113961i
$232$		0			0
$233$	22.0000			1.44127			0.720634	−	0.693316i	$-0.243851\pi$
$233$	22.0000			1.44127			0.720634	+	0.693316i	$0.243851\pi$
$234$		0			0
$235$			1.12702i			0.0735185i
$236$		0			0
$237$	−12.1244	−	7.00000i	−0.787562	−	0.454699i
$238$		0			0
$239$		−	11.9044i		−	0.770029i	−0.922911	−	0.385014i	$-0.874196\pi$
$239$		−	11.9044i		−	0.770029i	0.922911	−	0.385014i	$-0.125804\pi$
$240$		0			0
$241$	−13.5000	+	7.79423i	−0.869611	+	0.502070i	−0.867219	−	0.497927i	$-0.834095\pi$
$241$	−13.5000	+	7.79423i	−0.869611	+	0.502070i	−0.00239235	+	0.999997i	$0.500762\pi$
$242$		0			0
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	−7.54222	+	13.0635i	−0.481855	+	0.834597i
$246$		0			0
$247$	13.7460	+	3.96812i	0.874635	+	0.252485i
$248$		0			0
$249$	6.43649	+	3.71611i	0.407896	+	0.235499i
$250$		0			0
$251$	−27.0528	+	15.6190i	−1.70756	+	0.985859i	−0.769992	+	0.638054i	$0.779740\pi$
$251$	−27.0528	+	15.6190i	−1.70756	+	0.985859i	−0.937567	+	0.347806i	$0.886927\pi$
$252$		0			0
$253$	2.23607	+	3.87298i	0.140580	+	0.243492i
$254$		0			0
$255$			4.18812i			0.262270i
$256$		0			0
$257$	−11.6825	+	20.2346i	−0.728732	+	1.26220i	0.228688	+	0.973500i	$0.426557\pi$
$257$	−11.6825	+	20.2346i	−0.728732	+	1.26220i	−0.957419	+	0.288701i	$0.906777\pi$
$258$		0			0
$259$		−	5.38105i		−	0.334362i
$260$		0			0
$261$			2.12702i			0.131659i
$262$		0			0
$263$	4.43649	−	7.68423i	0.273566	−	0.473830i	−0.696206	−	0.717842i	$-0.745130\pi$
$263$	4.43649	−	7.68423i	0.273566	−	0.473830i	0.969772	+	0.244012i	$0.0784635\pi$
$264$		0			0
$265$		−	0.284018i		−	0.0174471i
$266$		0			0
$267$	7.93624	+	13.7460i	0.485690	+	0.841239i
$268$		0			0
$269$	−3.68410	+	2.12702i	−0.224624	+	0.129686i	−0.608089	−	0.793869i	$-0.708064\pi$
$269$	−3.68410	+	2.12702i	−0.224624	+	0.129686i	0.383466	+	0.923555i	$0.374730\pi$
$270$		0			0
$271$	−20.2379	−	11.6844i	−1.22936	−	0.709774i	−0.262468	−	0.964941i	$-0.584536\pi$
$271$	−20.2379	−	11.6844i	−1.22936	−	0.709774i	−0.966897	+	0.255167i	$0.917870\pi$
$272$		0			0
$273$	1.30948	−	1.26004i	0.0792530	−	0.0762613i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−12.7704	+	7.37298i	−0.767298	+	0.443000i	−0.831910	−	0.554911i	$-0.812752\pi$
$277$	−12.7704	+	7.37298i	−0.767298	+	0.443000i	0.0646120	+	0.997910i	$0.479419\pi$
$278$		0			0
$279$	−3.87298	+	2.23607i	−0.231869	+	0.133870i
$280$		0			0
$281$		−	19.1166i		−	1.14040i	−0.821506	−	0.570200i	$-0.806866\pi$
$281$		−	19.1166i		−	1.14040i	0.821506	−	0.570200i	$-0.193134\pi$
$282$		0			0
$283$	−2.26808	−	1.30948i	−0.134823	−	0.0778402i	0.431071	−	0.902318i	$-0.358136\pi$
$283$	−2.26808	−	1.30948i	−0.134823	−	0.0778402i	−0.565895	+	0.824478i	$0.691469\pi$
$284$		0			0
$285$			8.87298i			0.525590i
$286$		0			0
$287$	2.87298			0.169587
$288$		0			0
$289$	6.74597	−	11.6844i	0.396822	−	0.687315i
$290$		0			0
$291$	−17.3205			−1.01535
$292$		0			0
$293$	−14.2504	−	24.6825i	−0.832519	−	1.44196i	−0.896035	−	0.443984i	$-0.853565\pi$
$293$	−14.2504	−	24.6825i	−0.832519	−	1.44196i	0.0635162	−	0.997981i	$-0.479769\pi$
$294$		0			0
$295$	−12.7460	−	22.0767i	−0.742099	−	1.28535i
$296$		0			0
$297$	−3.43649	−	1.98406i	−0.199405	−	0.115127i
$298$		0			0
$299$	−0.976025	−	3.94456i	−0.0564450	−	0.228120i
$300$		0			0
$301$	0.284018	−	0.491933i	0.0163705	−	0.0283546i
$302$		0			0
$303$	−0.0635083	−	0.110000i	−0.00364846	−	0.00631931i
$304$		0			0
$305$	−1.93649	+	1.11803i	−0.110883	+	0.0640184i
$306$		0			0
$307$	5.41615			0.309116			0.154558	−	0.987984i	$-0.450605\pi$
$307$	5.41615			0.309116			0.154558	+	0.987984i	$0.450605\pi$
$308$		0			0
$309$	10.9283	+	6.30948i	0.621691	+	0.358933i
$310$		0			0
$311$	10.6190			0.602145			0.301073	−	0.953601i	$-0.402655\pi$
$311$	10.6190			0.602145			0.301073	+	0.953601i	$0.402655\pi$
$312$		0			0
$313$	4.00000			0.226093			0.113047	−	0.993590i	$-0.463939\pi$
$313$	4.00000			0.226093			0.113047	+	0.993590i	$0.463939\pi$
$314$		0			0
$315$	0.976025	+	0.563508i	0.0549928	+	0.0317501i
$316$		0			0
$317$	23.0207			1.29297			0.646485	−	0.762927i	$-0.276238\pi$
$317$	23.0207			1.29297			0.646485	+	0.762927i	$0.276238\pi$
$318$		0			0
$319$	−7.30948	+	4.22013i	−0.409252	+	0.236282i
$320$		0			0
$321$	3.43649	+	5.95218i	0.191806	+	0.332218i
$322$		0			0
$323$	−3.71611	+	6.43649i	−0.206770	+	0.358136i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−9.87298	−	5.70017i	−0.545977	−	0.315220i
$328$		0			0
$329$	0.127017	+	0.219999i	0.00700265	+	0.0121290i
$330$		0			0
$331$	8.44025	+	14.6190i	0.463918	+	0.803530i	0.999152	−	0.0411739i	$-0.0131098\pi$
$331$	8.44025	+	14.6190i	0.463918	+	0.803530i	−0.535234	+	0.844704i	$0.679776\pi$
$332$		0			0
$333$	10.6763			0.585059
$334$		0			0
$335$	17.1825	−	29.7609i	0.938778	−	1.62601i
$336$		0			0
$337$	−13.0000			−0.708155			−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000			−0.708155			−0.354078	+	0.935216i	$0.615205\pi$
$338$		0			0
$339$		−	2.12702i		−	0.115524i
$340$		0			0
$341$	−15.3685	−	8.87298i	−0.832249	−	0.480499i
$342$		0			0
$343$			6.92820i			0.374088i
$344$		0			0
$345$	2.18246	−	1.26004i	0.117500	−	0.0678384i
$346$		0			0
$347$	−12.8804	+	7.43649i	−0.691455	+	0.399212i	−0.804157	−	0.594417i	$-0.797383\pi$
$347$	−12.8804	+	7.43649i	−0.691455	+	0.399212i	0.112702	+	0.993629i	$0.464050\pi$
$348$		0			0
$349$	−0.219999	+	0.381050i	−0.0117763	+	0.0203971i	−0.871853	−	0.489767i	$-0.837082\pi$
$349$	−0.219999	+	0.381050i	−0.0117763	+	0.0203971i	0.860077	+	0.510164i	$0.170415\pi$
$350$		0			0
$351$	2.50000	+	2.59808i	0.133440	+	0.138675i
$352$		0			0
$353$	−12.1905	−	7.03820i	−0.648836	−	0.374606i	0.139174	−	0.990268i	$-0.455555\pi$
$353$	−12.1905	−	7.03820i	−0.648836	−	0.374606i	−0.788010	+	0.615662i	$0.788889\pi$
$354$		0			0
$355$	−16.3445	+	9.43649i	−0.867475	+	0.500837i
$356$		0			0
$357$	0.472008	+	0.817542i	0.0249813	+	0.0432689i
$358$		0			0
$359$		−	17.3845i		−	0.917520i	−0.888560	−	0.458760i	$-0.848294\pi$
$359$		−	17.3845i		−	0.917520i	0.888560	−	0.458760i	$-0.151706\pi$
$360$		0			0
$361$	1.62702	−	2.81808i	0.0856325	−	0.148320i
$362$		0			0
$363$		−	4.74597i		−	0.249099i
$364$		0			0
$365$		−	9.36492i		−	0.490182i
$366$		0			0
$367$	−11.3095	+	19.5886i	−0.590350	+	1.02252i	0.403835	+	0.914832i	$0.367677\pi$
$367$	−11.3095	+	19.5886i	−0.590350	+	1.02252i	−0.994185	+	0.107684i	$0.965656\pi$
$368$		0			0
$369$			5.70017i			0.296739i
$370$		0			0
$371$	−0.0320093	−	0.0554417i	−0.00166184	−	0.00287839i
$372$		0			0
$373$	−0.426027	+	0.245967i	−0.0220588	+	0.0127357i	−0.510989	−	0.859587i	$-0.670721\pi$
$373$	−0.426027	+	0.245967i	−0.0220588	+	0.0127357i	0.488930	+	0.872323i	$0.337387\pi$
$374$		0			0
$375$	−9.68246	−	5.59017i	−0.500000	−	0.288675i
$376$		0			0
$377$	7.44456	−	1.84205i	0.383414	−	0.0948704i
$378$		0			0
$379$	12.4084	−	21.4919i	0.637375	−	1.10397i	−0.348631	−	0.937260i	$-0.613353\pi$
$379$	12.4084	−	21.4919i	0.637375	−	1.10397i	0.986007	−	0.166706i	$-0.0533132\pi$
$380$		0			0
$381$	15.3685	−	8.87298i	0.787350	−	0.454577i
$382$		0			0
$383$	4.25403	−	2.45607i	0.217371	−	0.125499i	−0.387361	−	0.921928i	$-0.626613\pi$
$383$	4.25403	−	2.45607i	0.217371	−	0.125499i	0.604732	+	0.796429i	$0.293280\pi$
$384$		0			0
$385$			4.47214i			0.227921i
$386$		0			0
$387$	0.976025	+	0.563508i	0.0496141	+	0.0286447i
$388$		0			0
$389$			11.6190i			0.589104i	0.955635	+	0.294552i	$0.0951704\pi$
$389$			11.6190i			0.589104i	−0.955635	+	0.294552i	$0.904830\pi$
$390$		0			0
$391$	2.11088			0.106752
$392$		0			0
$393$	−1.87298	+	3.24410i	−0.0944795	+	0.163643i
$394$		0			0
$395$	−31.3050			−1.57512
$396$		0			0
$397$	−14.1404	−	24.4919i	−0.709688	−	1.22921i	−0.964973	−	0.262349i	$-0.915503\pi$
$397$	−14.1404	−	24.4919i	−0.709688	−	1.22921i	0.255285	−	0.966866i	$-0.417831\pi$
$398$		0			0
$399$	1.00000	+	1.73205i	0.0500626	+	0.0867110i
$400$		0			0
$401$	−14.8095	−	8.55025i	−0.739550	−	0.426979i	0.0823557	−	0.996603i	$-0.473756\pi$
$401$	−14.8095	−	8.55025i	−0.739550	−	0.426979i	−0.821906	+	0.569624i	$0.807089\pi$
$402$		0			0
$403$	11.1803	+	11.6190i	0.556932	+	0.578781i
$404$		0			0
$405$	−1.11803	+	1.93649i	−0.0555556	+	0.0962250i
$406$		0			0
$407$	21.1825	+	36.6891i	1.04998	+	1.81861i
$408$		0			0
$409$	28.1190	−	16.2345i	1.39039	−	0.802744i	0.397034	−	0.917804i	$-0.370039\pi$
$409$	28.1190	−	16.2345i	1.39039	−	0.802744i	0.993359	+	0.115060i	$0.0367061\pi$
$410$		0			0
$411$	−13.6364			−0.672634
$412$		0			0
$413$	−4.97615	−	2.87298i	−0.244860	−	0.141370i
$414$		0			0
$415$	16.6190			0.815792
$416$		0			0
$417$	5.74597			0.281381
$418$		0			0
$419$	22.5167	+	13.0000i	1.10001	+	0.635092i	0.936224	−	0.351404i	$-0.114296\pi$
$419$	22.5167	+	13.0000i	1.10001	+	0.635092i	0.163787	+	0.986496i	$0.447629\pi$
$420$		0			0
$421$	−12.1244			−0.590905			−0.295452	−	0.955357i	$-0.595470\pi$
$421$	−12.1244			−0.590905			−0.295452	+	0.955357i	$0.595470\pi$
$422$		0			0
$423$	−0.436492	+	0.252009i	−0.0212230	+	0.0122531i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.252009	+	0.436492i	−0.0121956	+	0.0211233i
$428$		0			0
$429$	−3.96812	+	13.7460i	−0.191583	+	0.663662i
$430$		0			0
$431$	−25.3095	−	14.6124i	−1.21911	−	0.703856i	−0.254386	−	0.967103i	$-0.581873\pi$
$431$	−25.3095	−	14.6124i	−1.21911	−	0.703856i	−0.964729	+	0.263247i	$0.915207\pi$
$432$		0			0
$433$	5.62702	+	9.74628i	0.270417	+	0.468376i	0.968969	−	0.247183i	$-0.0795050\pi$
$433$	5.62702	+	9.74628i	0.270417	+	0.468376i	−0.698552	+	0.715560i	$0.746172\pi$
$434$		0			0
$435$	2.37808	+	4.11895i	0.114020	+	0.197489i
$436$		0			0
$437$	4.47214			0.213931
$438$		0			0
$439$	−4.56351	+	7.90423i	−0.217804	+	0.377248i	−0.954136	−	0.299372i	$-0.903223\pi$
$439$	−4.56351	+	7.90423i	−0.217804	+	0.377248i	0.736332	+	0.676620i	$0.236556\pi$
$440$		0			0
$441$	−6.74597			−0.321237
$442$		0			0
$443$		−	36.7298i		−	1.74509i	−0.488536	−	0.872544i	$-0.662469\pi$
$443$		−	36.7298i		−	1.74509i	0.488536	−	0.872544i	$-0.337531\pi$
$444$		0			0
$445$	30.7369	+	17.7460i	1.45707	+	0.841239i
$446$		0			0
$447$			22.5807i			1.06803i
$448$		0			0
$449$	−19.7460	+	11.4003i	−0.931870	+	0.538015i	−0.887402	−	0.460996i	$-0.847492\pi$
$449$	−19.7460	+	11.4003i	−0.931870	+	0.538015i	−0.0444673	+	0.999011i	$0.514159\pi$
$450$		0			0
$451$	−19.5886	+	11.3095i	−0.922390	+	0.532542i
$452$		0			0
$453$	3.21209	−	5.56351i	0.150917	−	0.261396i
$454$		0			0
$455$	1.12702	−	3.90410i	0.0528354	−	0.183027i
$456$		0			0
$457$	36.3569	+	20.9906i	1.70070	+	0.981901i	0.945049	+	0.326928i	$0.106013\pi$
$457$	36.3569	+	20.9906i	1.70070	+	0.981901i	0.755652	+	0.654973i	$0.227320\pi$
$458$		0			0
$459$	−1.62205	+	0.936492i	−0.0757109	+	0.0437117i
$460$		0			0
$461$	−2.56607	−	4.44456i	−0.119514	−	0.207004i	0.800061	−	0.599918i	$-0.204800\pi$
$461$	−2.56607	−	4.44456i	−0.119514	−	0.207004i	−0.919575	+	0.392914i	$0.871467\pi$
$462$		0			0
$463$			21.8567i			1.01577i	0.861426	+	0.507883i	$0.169572\pi$
$463$			21.8567i			1.01577i	−0.861426	+	0.507883i	$0.830428\pi$
$464$		0			0
$465$	−5.00000	+	8.66025i	−0.231869	+	0.401610i
$466$		0			0
$467$			26.3649i			1.22002i	0.792393	+	0.610011i	$0.208835\pi$
$467$			26.3649i			1.22002i	−0.792393	+	0.610011i	$0.791165\pi$
$468$		0			0
$469$		−	7.74597i		−	0.357676i
$470$		0			0
$471$	8.37298	−	14.5024i	0.385807	−	0.668237i
$472$		0			0
$473$			4.47214i			0.205629i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.110000	−	0.0635083i	0.00503654	−	0.00290785i
$478$		0			0
$479$	18.1109	+	10.4563i	0.827507	+	0.477762i	0.852998	−	0.521913i	$-0.174782\pi$
$479$	18.1109	+	10.4563i	0.827507	+	0.477762i	−0.0254911	+	0.999675i	$0.508115\pi$
$480$		0			0
$481$	−9.24597	−	37.3671i	−0.421580	−	1.70379i
$482$		0			0
$483$	0.284018	−	0.491933i	0.0129233	−	0.0223837i
$484$		0			0
$485$	−33.5410	+	19.3649i	−1.52302	+	0.879316i
$486$		0			0
$487$	−6.92843	+	4.00013i	−0.313957	+	0.181263i	−0.648696	−	0.761048i	$-0.724685\pi$
$487$	−6.92843	+	4.00013i	−0.313957	+	0.181263i	0.334739	+	0.942311i	$0.391352\pi$
$488$		0			0
$489$		−	9.95231i		−	0.450059i
$490$		0			0
$491$	27.5888	+	15.9284i	1.24507	+	0.718840i	0.970121	−	0.242620i	$-0.0780068\pi$
$491$	27.5888	+	15.9284i	1.24507	+	0.718840i	0.274946	+	0.961460i	$0.411340\pi$
$492$		0			0
$493$			3.98387i			0.179424i
$494$		0			0
$495$	−8.87298			−0.398811
$496$		0			0
$497$	−2.12702	+	3.68410i	−0.0954097	+	0.165255i
$498$		0			0
$499$	−15.8725			−0.710550			−0.355275	−	0.934762i	$-0.615613\pi$
$499$	−15.8725			−0.710550			−0.355275	+	0.934762i	$0.615613\pi$
$500$		0			0
$501$	−9.16427	−	15.8730i	−0.409429	−	0.709153i
$502$		0			0
$503$	−1.30948	−	2.26808i	−0.0583866	−	0.101129i	0.835355	−	0.549711i	$-0.185262\pi$
$503$	−1.30948	−	2.26808i	−0.0583866	−	0.101129i	−0.893741	+	0.448583i	$0.851929\pi$
$504$		0			0
$505$	−0.245967	−	0.142009i	−0.0109454	−	0.00631931i
$506$		0			0
$507$	6.92820	−	11.0000i	0.307692	−	0.488527i
$508$		0			0
$509$	11.2903	−	19.5554i	0.500436	−	0.866780i	−0.499564	−	0.866277i	$-0.666507\pi$
$509$	11.2903	−	19.5554i	0.500436	−	0.866780i	1.00000		0.000502947i	$-0.000160093\pi$
$510$		0			0
$511$	−1.05544	−	1.82808i	−0.0466900	−	0.0808694i
$512$		0			0
$513$	−3.43649	+	1.98406i	−0.151725	+	0.0875984i
$514$		0			0
$515$	28.2168			1.24338
$516$		0			0
$517$	−1.73205	−	1.00000i	−0.0761755	−	0.0439799i
$518$		0			0
$519$	−13.4919			−0.592230
$520$		0			0
$521$	−17.6190			−0.771900			−0.385950	−	0.922520i	$-0.626126\pi$
$521$	−17.6190			−0.771900			−0.385950	+	0.922520i	$0.626126\pi$
$522$		0			0
$523$	3.78013	+	2.18246i	0.165293	+	0.0954322i	0.580365	−	0.814357i	$-0.302910\pi$
$523$	3.78013	+	2.18246i	0.165293	+	0.0954322i	−0.415071	+	0.909789i	$0.636243\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−7.25403	+	4.18812i	−0.315991	+	0.182437i
$528$		0			0
$529$	10.8649	+	18.8186i	0.472388	+	0.818199i
$530$		0			0
$531$	5.70017	−	9.87298i	0.247366	−	0.428451i
$532$		0			0
$533$	19.9506	−	4.93649i	0.864156	−	0.213823i
$534$		0			0
$535$	13.3095	+	7.68423i	0.575419	+	0.332218i
$536$		0			0
$537$	6.43649	+	11.1483i	0.277755	+	0.481086i
$538$		0			0
$539$	−13.3844	−	23.1825i	−0.576507	−	0.998539i
$540$		0			0
$541$	29.4449			1.26593			0.632967	−	0.774179i	$-0.281837\pi$
$541$	29.4449			1.26593			0.632967	+	0.774179i	$0.281837\pi$
$542$		0			0
$543$	7.37298	−	12.7704i	0.316405	−	0.548030i
$544$		0			0
$545$	−25.4919			−1.09195
$546$		0			0
$547$		−	14.3649i		−	0.614199i	−0.951677	−	0.307100i	$-0.900641\pi$
$547$		−	14.3649i		−	0.614199i	0.951677	−	0.307100i	$-0.0993585\pi$
$548$		0			0
$549$	−0.866025	−	0.500000i	−0.0369611	−	0.0213395i
$550$		0			0
$551$			8.44025i			0.359567i
$552$		0			0
$553$	−6.11088	+	3.52812i	−0.259861	+	0.150031i
$554$		0			0
$555$	20.6746	−	11.9365i	0.877588	−	0.506676i
$556$		0			0
$557$	0.614017	−	1.06351i	0.0260167	−	0.0450623i	−0.852724	−	0.522362i	$-0.825051\pi$
$557$	0.614017	−	1.06351i	0.0260167	−	0.0450623i	0.878741	+	0.477300i	$0.158384\pi$
$558$		0			0
$559$	1.12702	−	3.90410i	0.0476677	−	0.165126i
$560$		0			0
$561$	−6.43649	−	3.71611i	−0.271749	−	0.156894i
$562$		0			0
$563$	32.0290	−	18.4919i	1.34986	−	0.779342i	0.361631	−	0.932321i	$-0.382220\pi$
$563$	32.0290	−	18.4919i	1.34986	−	0.779342i	0.988229	+	0.152979i	$0.0488868\pi$
$564$		0			0
$565$	−2.37808	−	4.11895i	−0.100046	−	0.173286i
$566$		0			0
$567$			0.504017i			0.0211667i
$568$		0			0
$569$	−11.4919	+	19.9046i	−0.481767	+	0.834445i	−0.999781	−	0.0209273i	$-0.993338\pi$
$569$	−11.4919	+	19.9046i	−0.481767	+	0.834445i	0.518014	+	0.855372i	$0.326671\pi$
$570$		0			0
$571$		−	6.61895i		−	0.276994i	−0.990363	−	0.138497i	$-0.955773\pi$
$571$		−	6.61895i		−	0.276994i	0.990363	−	0.138497i	$-0.0442272\pi$
$572$		0			0
$573$			4.25403i			0.177715i
$574$		0			0
$575$		0			0
$576$		0			0
$577$			8.22026i			0.342214i	0.985252	+	0.171107i	$0.0547343\pi$
$577$			8.22026i			0.342214i	−0.985252	+	0.171107i	$0.945266\pi$
$578$		0			0
$579$	−9.30628	−	16.1190i	−0.386756	−	0.669881i
$580$		0			0
$581$	3.24410	−	1.87298i	0.134588	−	0.0777044i
$582$		0			0
$583$	0.436492	+	0.252009i	0.0180776	+	0.0104371i
$584$		0			0
$585$	7.74597	+	2.23607i	0.320256	+	0.0924500i
$586$		0			0
$587$	−4.47214	+	7.74597i	−0.184585	+	0.319710i	−0.943437	−	0.331553i	$-0.892427\pi$
$587$	−4.47214	+	7.74597i	−0.184585	+	0.319710i	0.758852	+	0.651263i	$0.225761\pi$
$588$		0			0
$589$	−15.3685	+	8.87298i	−0.633246	+	0.365605i
$590$		0			0
$591$	9.87298	−	5.70017i	0.406120	−	0.234474i
$592$		0			0
$593$			15.0844i			0.619444i	0.950827	+	0.309722i	$0.100236\pi$
$593$			15.0844i			0.619444i	−0.950827	+	0.309722i	$0.899764\pi$
$594$		0			0
$595$	1.82808	+	1.05544i	0.0749439	+	0.0432689i
$596$		0			0
$597$			0.872983i			0.0357288i
$598$		0			0
$599$	10.0000			0.408589			0.204294	−	0.978909i	$-0.434510\pi$
$599$	10.0000			0.408589			0.204294	+	0.978909i	$0.434510\pi$
$600$		0			0
$601$	−7.24597	+	12.5504i	−0.295569	+	0.511941i	−0.975117	−	0.221690i	$-0.928843\pi$
$601$	−7.24597	+	12.5504i	−0.295569	+	0.511941i	0.679548	+	0.733631i	$0.262176\pi$
$602$		0			0
$603$	15.3685			0.625852
$604$		0			0
$605$	−5.30615	−	9.19052i	−0.215726	−	0.373648i
$606$		0			0
$607$	5.74597	+	9.95231i	0.233222	+	0.403952i	0.958754	−	0.284236i	$-0.0917399\pi$
$607$	5.74597	+	9.95231i	0.233222	+	0.403952i	−0.725533	+	0.688188i	$0.758407\pi$
$608$		0			0
$609$	0.928425	+	0.536026i	0.0376217	+	0.0217209i
$610$		0			0
$611$	1.26004	+	1.30948i	0.0509759	+	0.0529757i
$612$		0			0
$613$	−19.4786	+	33.7379i	−0.786733	+	1.36266i	0.141226	+	0.989977i	$0.454896\pi$
$613$	−19.4786	+	33.7379i	−0.786733	+	1.36266i	−0.927958	+	0.372684i	$0.878438\pi$
$614$		0			0
$615$	6.37298	+	11.0383i	0.256983	+	0.445108i
$616$		0			0
$617$	29.4284	−	16.9905i	1.18474	−	0.684012i	0.227637	−	0.973746i	$-0.426900\pi$
$617$	29.4284	−	16.9905i	1.18474	−	0.684012i	0.957107	+	0.289734i	$0.0935668\pi$
$618$		0			0
$619$	40.1212			1.61261			0.806303	−	0.591502i	$-0.201465\pi$
$619$	40.1212			1.61261			0.806303	+	0.591502i	$0.201465\pi$
$620$		0			0
$621$	0.976025	+	0.563508i	0.0391665	+	0.0226128i
$622$		0			0
$623$	8.00000			0.320513
$624$		0			0
$625$	−25.0000			−1.00000
$626$		0			0
$627$	−13.6364	−	7.87298i	−0.544586	−	0.314417i
$628$		0			0
$629$	19.9966			0.797316
$630$		0			0
$631$	−12.0000	+	6.92820i	−0.477712	+	0.275807i	−0.719463	−	0.694531i	$-0.755612\pi$
$631$	−12.0000	+	6.92820i	−0.477712	+	0.275807i	0.241750	+	0.970339i	$0.422279\pi$
$632$		0			0
$633$	−7.00000	−	12.1244i	−0.278225	−	0.481900i
$634$		0			0
$635$	19.8406	−	34.3649i	0.787350	−	1.36373i
$636$		0			0
$637$	5.84218	+	23.6109i	0.231476	+	0.935497i
$638$		0			0
$639$	−7.30948	−	4.22013i	−0.289158	−	0.166946i
$640$		0			0
$641$	9.68246	+	16.7705i	0.382434	+	0.662395i	0.991410	−	0.130794i	$-0.0417526\pi$
$641$	9.68246	+	16.7705i	0.382434	+	0.662395i	−0.608975	+	0.793189i	$0.708419\pi$
$642$		0			0
$643$	25.0367	+	43.3649i	0.987353	+	1.71015i	0.630974	+	0.775804i	$0.282655\pi$
$643$	25.0367	+	43.3649i	0.987353	+	1.71015i	0.356379	+	0.934342i	$0.384011\pi$
$644$		0			0
$645$	2.52009			0.0992283
$646$		0			0
$647$	−15.8730	+	27.4928i	−0.624031	+	1.08085i	0.364696	+	0.931127i	$0.381173\pi$
$647$	−15.8730	+	27.4928i	−0.624031	+	1.08085i	−0.988727	+	0.149727i	$0.952160\pi$
$648$		0			0
$649$	45.2379			1.77574
$650$		0			0
$651$			2.25403i			0.0883425i
$652$		0			0
$653$	23.5887	+	13.6190i	0.923098	+	0.532951i	0.884622	−	0.466309i	$-0.154416\pi$
$653$	23.5887	+	13.6190i	0.923098	+	0.532951i	0.0384757	+	0.999260i	$0.487750\pi$
$654$		0			0
$655$			8.37624i			0.327287i
$656$		0			0
$657$	3.62702	−	2.09406i	0.141503	−	0.0816970i
$658$		0			0
$659$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$659$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$660$		0			0
$661$	2.81808	−	4.88105i	0.109610	−	0.189851i	−0.806002	−	0.591913i	$-0.798373\pi$
$661$	2.81808	−	4.88105i	0.109610	−	0.189851i	0.915612	+	0.402062i	$0.131706\pi$
$662$		0			0
$663$	4.68246	+	4.86615i	0.181852	+	0.188986i
$664$		0			0
$665$	3.87298	+	2.23607i	0.150188	+	0.0867110i
$666$		0			0
$667$	2.07602	−	1.19859i	0.0803839	−	0.0464097i
$668$		0			0
$669$	−10.6763	−	18.4919i	−0.412770	−	0.714939i
$670$		0			0
$671$		−	3.96812i		−	0.153188i
$672$		0			0
$673$	12.1190	−	20.9906i	0.467151	−	0.809130i	−0.532145	−	0.846654i	$-0.678614\pi$
$673$	12.1190	−	20.9906i	0.467151	−	0.809130i	0.999296	+	0.0375239i	$0.0119470\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			0.254033i			0.00976329i	0.999988	+	0.00488165i	$0.00155388\pi$
$677$			0.254033i			0.00976329i	−0.999988	+	0.00488165i	$0.998446\pi$
$678$		0			0
$679$	−4.36492	+	7.56026i	−0.167510	+	0.290136i
$680$		0			0
$681$		−	15.3685i		−	0.588921i
$682$		0			0
$683$	−18.1085	−	31.3649i	−0.692904	−	1.20015i	−0.970882	−	0.239558i	$-0.922998\pi$
$683$	−18.1085	−	31.3649i	−0.692904	−	1.20015i	0.277978	−	0.960587i	$-0.410336\pi$
$684$		0			0
$685$	−26.4068	+	15.2460i	−1.00895	+	0.582518i
$686$		0			0
$687$	1.74597	+	1.00803i	0.0666128	+	0.0384589i
$688$		0			0
$689$	−0.317542	−	0.329999i	−0.0120974	−	0.0125720i
$690$		0			0
$691$	1.19602	−	2.07157i	0.0454989	−	0.0788064i	−0.842379	−	0.538885i	$-0.818846\pi$
$691$	1.19602	−	2.07157i	0.0454989	−	0.0788064i	0.887878	+	0.460079i	$0.152179\pi$
$692$		0			0
$693$	−1.73205	+	1.00000i	−0.0657952	+	0.0379869i
$694$		0			0
$695$	11.1270	−	6.42419i	0.422072	−	0.243683i
$696$		0			0
$697$			10.6763i			0.404395i
$698$		0			0
$699$	19.0526	+	11.0000i	0.720634	+	0.416058i
$700$		0			0
$701$			28.2540i			1.06714i	0.845756	+	0.533570i	$0.179150\pi$
$701$			28.2540i			1.06714i	−0.845756	+	0.533570i	$0.820850\pi$
$702$		0			0
$703$	42.3649			1.59782
$704$		0			0
$705$	−0.563508	+	0.976025i	−0.0212230	+	0.0367592i
$706$		0			0
$707$	−0.0640186			−0.00240767
$708$		0			0
$709$	11.4783	+	19.8810i	0.431078	+	0.746649i	0.996966	−	0.0778331i	$-0.0248001\pi$
$709$	11.4783	+	19.8810i	0.431078	+	0.746649i	−0.565889	+	0.824482i	$0.691467\pi$
$710$		0			0
$711$	−7.00000	−	12.1244i	−0.262521	−	0.454699i
$712$		0			0
$713$	4.36492	+	2.52009i	0.163467	+	0.0943780i
$714$		0			0
$715$	7.68423	+	31.0554i	0.287374	+	1.16141i
$716$		0			0
$717$	5.95218	−	10.3095i	0.222288	−	0.385014i
$718$		0			0
$719$	24.4919	+	42.4213i	0.913395	+	1.58205i	0.809234	+	0.587486i	$0.199882\pi$
$719$	24.4919	+	42.4213i	0.913395	+	1.58205i	0.104161	+	0.994560i	$0.466784\pi$
$720$		0			0
$721$	5.50807	−	3.18008i	0.205131	−	0.118433i
$722$		0			0
$723$	−15.5885			−0.579741
$724$		0			0
$725$		0			0
$726$		0			0
$727$	32.8730			1.21919			0.609596	−	0.792712i	$-0.291332\pi$
$727$	32.8730			1.21919			0.609596	+	0.792712i	$0.291332\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	1.82808	+	1.05544i	0.0676139	+	0.0390369i
$732$		0			0
$733$	−40.9732			−1.51338			−0.756691	−	0.653773i	$-0.773185\pi$
$733$	−40.9732			−1.51338			−0.756691	+	0.653773i	$0.773185\pi$
$734$		0			0
$735$	−13.0635	+	7.54222i	−0.481855	+	0.278199i
$736$		0			0
$737$	30.4919	+	52.8136i	1.12318	+	1.94541i
$738$		0			0
$739$	5.98419	−	10.3649i	0.220132	−	0.381280i	−0.734716	−	0.678375i	$-0.762685\pi$
$739$	5.98419	−	10.3649i	0.220132	−	0.381280i	0.954848	+	0.297095i	$0.0960179\pi$
$740$		0			0
$741$	9.92030	+	10.3095i	0.364431	+	0.378728i
$742$		0			0
$743$	−30.0000	−	17.3205i	−1.10059	−	0.635428i	−0.164216	−	0.986424i	$-0.552510\pi$
$743$	−30.0000	−	17.3205i	−1.10059	−	0.635428i	−0.936377	+	0.350997i	$0.885843\pi$
$744$		0			0
$745$	25.2460	+	43.7273i	0.924941	+	1.60204i
$746$		0			0
$747$	3.71611	+	6.43649i	0.135965	+	0.235499i
$748$		0			0
$749$	3.46410			0.126576
$750$		0			0
$751$	13.4365	−	23.2727i	0.490305	−	0.849232i	−0.509633	−	0.860392i	$-0.670219\pi$
$751$	13.4365	−	23.2727i	0.490305	−	0.849232i	0.999938	+	0.0111594i	$0.00355222\pi$
$752$		0			0
$753$	−31.2379			−1.13837
$754$		0			0
$755$		−	14.3649i		−	0.522793i
$756$		0			0
$757$	42.6413	+	24.6190i	1.54982	+	0.894791i	0.998154	+	0.0607279i	$0.0193422\pi$
$757$	42.6413	+	24.6190i	1.54982	+	0.894791i	0.551669	+	0.834063i	$0.313991\pi$
$758$		0			0
$759$			4.47214i			0.162328i
$760$		0			0
$761$	12.8730	−	7.43222i	0.466645	−	0.269418i	−0.248189	−	0.968712i	$-0.579835\pi$
$761$	12.8730	−	7.43222i	0.466645	−	0.269418i	0.714834	+	0.699294i	$0.246502\pi$
$762$		0			0
$763$	−4.97615	+	2.87298i	−0.180149	+	0.104009i
$764$		0			0
$765$	−2.09406	+	3.62702i	−0.0757109	+	0.131135i
$766$		0			0
$767$	−39.4919	−	11.4003i	−1.42597	−	0.411642i
$768$		0			0
$769$	−6.49193	−	3.74812i	−0.234105	−	0.135161i	0.378359	−	0.925659i	$-0.376488\pi$
$769$	−6.49193	−	3.74812i	−0.234105	−	0.135161i	−0.612464	+	0.790498i	$0.709822\pi$
$770$		0			0
$771$	−20.2346	+	11.6825i	−0.728732	+	0.420733i
$772$		0			0
$773$	11.9044	+	20.6190i	0.428170	+	0.741612i	0.996711	−	0.0810431i	$-0.0258251\pi$
$773$	11.9044	+	20.6190i	0.428170	+	0.741612i	−0.568541	+	0.822655i	$0.692492\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	2.69052	−	4.66013i	0.0965220	−	0.167181i
$778$		0			0
$779$			22.6190i			0.810408i
$780$		0			0
$781$		−	33.4919i		−	1.19844i
$782$		0			0
$783$	−1.06351	+	1.84205i	−0.0380067	+	0.0658295i
$784$		0			0
$785$		−	37.4451i		−	1.33647i
$786$		0			0
$787$	−10.1723	−	17.6190i	−0.362604	−	0.628048i	0.625785	−	0.779996i	$-0.284779\pi$
$787$	−10.1723	−	17.6190i	−0.362604	−	0.628048i	−0.988389	+	0.151948i	$0.951445\pi$
$788$		0			0
$789$	7.68423	−	4.43649i	0.273566	−	0.157943i
$790$		0			0
$791$	−0.928425	−	0.536026i	−0.0330110	−	0.0190589i
$792$		0			0
$793$	−1.00000	+	3.46410i	−0.0355110	+	0.123014i
$794$		0			0
$795$	0.142009	−	0.245967i	0.00503654	−	0.00872354i
$796$		0			0
$797$	0.439999	−	0.254033i	0.0155855	−	0.00899832i	−0.492187	−	0.870490i	$-0.663802\pi$
$797$	0.439999	−	0.254033i	0.0155855	−	0.00899832i	0.507773	+	0.861491i	$0.330469\pi$
$798$		0			0
$799$	−0.817542	+	0.472008i	−0.0289225	+	0.0166984i
$800$		0			0
$801$			15.8725i			0.560826i
$802$		0			0
$803$	14.3924	+	8.30948i	0.507898	+	0.293235i
$804$		0			0
$805$		−	1.27017i		−	0.0447675i
$806$		0			0
$807$	−4.25403			−0.149749
$808$		0			0
$809$	−10.0635	+	17.4305i	−0.353814	+	0.612824i	−0.986914	−	0.161246i	$-0.948449\pi$
$809$	−10.0635	+	17.4305i	−0.353814	+	0.612824i	0.633100	+	0.774070i	$0.281782\pi$
$810$		0			0
$811$	−8.50427			−0.298625			−0.149313	−	0.988790i	$-0.547706\pi$
$811$	−8.50427			−0.298625			−0.149313	+	0.988790i	$0.547706\pi$
$812$		0			0
$813$	−11.6844	−	20.2379i	−0.409788	−	0.709774i
$814$		0			0
$815$	−11.1270	−	19.2726i	−0.389762	−	0.675088i
$816$		0			0
$817$	3.87298	+	2.23607i	0.135499	+	0.0782301i
$818$		0			0
$819$	1.76406	−	0.436492i	0.0616412	−	0.0152523i
$820$		0			0
$821$	22.8647	−	39.6028i	0.797983	−	1.38215i	−0.122944	−	0.992414i	$-0.539234\pi$
$821$	22.8647	−	39.6028i	0.797983	−	1.38215i	0.920927	−	0.389734i	$-0.127433\pi$
$822$		0			0
$823$	16.1270	+	27.9328i	0.562152	+	0.973677i	0.997308	+	0.0733215i	$0.0233599\pi$
$823$	16.1270	+	27.9328i	0.562152	+	0.973677i	−0.435156	+	0.900355i	$0.643307\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.568036			0.0197525			0.00987627	−	0.999951i	$-0.496856\pi$
$827$	0.568036			0.0197525			0.00987627	+	0.999951i	$0.496856\pi$
$828$		0			0
$829$	14.0624	+	8.11895i	0.488409	+	0.281983i	0.723914	−	0.689890i	$-0.242341\pi$
$829$	14.0624	+	8.11895i	0.488409	+	0.281983i	−0.235505	+	0.971873i	$0.575675\pi$
$830$		0			0
$831$	−14.7460			−0.511532
$832$		0			0
$833$	−12.6351			−0.437780
$834$		0			0
$835$	−35.4931	−	20.4919i	−1.22829	−	0.709153i
$836$		0			0
$837$	−4.47214			−0.154580
$838$		0			0
$839$	−6.00000	+	3.46410i	−0.207143	+	0.119594i	−0.599983	−	0.800013i	$-0.704826\pi$
$839$	−6.00000	+	3.46410i	−0.207143	+	0.119594i	0.392840	+	0.919607i	$0.371493\pi$
$840$		0			0
$841$	−12.2379	−	21.1967i	−0.421997	−	0.730919i
$842$		0			0
$843$	9.55829	−	16.5554i	0.329205	−	0.570200i
$844$		0			0
$845$	1.11803	−	29.0474i	0.0384615	−	0.999260i
$846$		0			0
$847$	−2.07157	−	1.19602i	−0.0711802	−	0.0410959i
$848$		0			0
$849$	−1.30948	−	2.26808i	−0.0449411	−	0.0778402i
$850$		0			0
$851$	−6.01620	−	10.4204i	−0.206233	−	0.357205i
$852$		0			0
$853$	1.29205			0.0442390			0.0221195	−	0.999755i	$-0.492959\pi$
$853$	1.29205			0.0442390			0.0221195	+	0.999755i	$0.492959\pi$
$854$		0			0
$855$	−4.43649	+	7.68423i	−0.151725	+	0.262795i
$856$		0			0
$857$	7.61895			0.260258			0.130129	−	0.991497i	$-0.458461\pi$
$857$	7.61895			0.260258			0.130129	+	0.991497i	$0.458461\pi$
$858$		0			0
$859$			41.6028i			1.41947i	0.704469	+	0.709735i	$0.251185\pi$
$859$			41.6028i			1.41947i	−0.704469	+	0.709735i	$0.748815\pi$
$860$		0			0
$861$	2.48808	+	1.43649i	0.0847934	+	0.0489555i
$862$		0			0
$863$			48.5614i			1.65305i	0.562900	+	0.826525i	$0.309686\pi$
$863$			48.5614i			1.65305i	−0.562900	+	0.826525i	$0.690314\pi$
$864$		0			0
$865$	−26.1270	+	15.0844i	−0.888345	+	0.512886i
$866$		0			0
$867$	11.6844	−	6.74597i	0.396822	−	0.229105i
$868$		0			0
$869$	27.7768	−	48.1109i	0.942264	−	1.63205i
$870$		0			0
$871$	−13.3095	−	53.7896i	−0.450974	−	1.82259i
$872$		0			0
$873$	−15.0000	−	8.66025i	−0.507673	−	0.293105i
$874$		0			0
$875$	−4.88013	+	2.81754i	−0.164978	+	0.0952503i
$876$		0			0
$877$	−2.59808	−	4.50000i	−0.0877308	−	0.151954i	0.818821	−	0.574049i	$-0.194628\pi$
$877$	−2.59808	−	4.50000i	−0.0877308	−	0.151954i	−0.906552	+	0.422095i	$0.861295\pi$
$878$		0			0
$879$		−	28.5008i		−	0.961310i
$880$		0			0
$881$	21.5554	−	37.3351i	0.726221	−	1.25785i	−0.232248	−	0.972657i	$-0.574608\pi$
$881$	21.5554	−	37.3351i	0.726221	−	1.25785i	0.958469	−	0.285196i	$-0.0920586\pi$
$882$		0			0
$883$			10.9839i			0.369637i	0.982773	+	0.184818i	$0.0591697\pi$
$883$			10.9839i			0.369637i	−0.982773	+	0.184818i	$0.940830\pi$
$884$		0			0
$885$		−	25.4919i		−	0.856902i
$886$		0			0
$887$	−10.1270	+	17.5405i	−0.340032	+	0.588953i	−0.984438	−	0.175731i	$-0.943771\pi$
$887$	−10.1270	+	17.5405i	−0.340032	+	0.588953i	0.644406	+	0.764683i	$0.277105\pi$
$888$		0			0
$889$		−	8.94427i		−	0.299981i
$890$		0			0
$891$	−1.98406	−	3.43649i	−0.0664685	−	0.115127i
$892$		0			0
$893$	−1.73205	+	1.00000i	−0.0579609	+	0.0334637i
$894$		0			0
$895$	24.9284	+	14.3924i	0.833265	+	0.481086i
$896$		0			0
$897$	1.12702	−	3.90410i	0.0376300	−	0.130354i
$898$		0			0
$899$	−4.75615	+	8.23790i	−0.158627	+	0.274749i
$900$		0			0
$901$	0.206028	−	0.118950i	0.00686377	−	0.00396280i
$902$		0			0
$903$	0.491933	−	0.284018i	0.0163705	−	0.00945152i
$904$		0			0
$905$		−	32.9730i		−	1.09606i
$906$		0			0
$907$	0.439999	+	0.254033i	0.0146099	+	0.00843504i	0.507287	−	0.861777i	$-0.330648\pi$
$907$	0.439999	+	0.254033i	0.0146099	+	0.00843504i	−0.492677	+	0.870212i	$0.663982\pi$
$908$		0			0
$909$		−	0.127017i		−	0.00421288i
$910$		0			0
$911$	−38.7298			−1.28318			−0.641588	−	0.767049i	$-0.721724\pi$
$911$	−38.7298			−1.28318			−0.641588	+	0.767049i	$0.721724\pi$
$912$		0			0
$913$	−14.7460	+	25.5408i	−0.488020	+	0.845276i
$914$		0			0
$915$	−2.23607			−0.0739221
$916$		0			0
$917$	0.944016	+	1.63508i	0.0311741	+	0.0539952i
$918$		0			0
$919$	15.1270	+	26.2008i	0.498994	+	0.864283i	0.999999	−	0.00116097i	$-0.000369547\pi$
$919$	15.1270	+	26.2008i	0.498994	+	0.864283i	−0.501005	+	0.865444i	$0.667036\pi$
$920$		0			0
$921$	4.69052	+	2.70808i	0.154558	+	0.0892341i
$922$		0			0
$923$	−8.44025	+	29.2379i	−0.277814	+	0.962377i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	6.30948	+	10.9283i	0.207230	+	0.358933i
$928$		0			0
$929$	−11.4284	+	6.59820i	−0.374954	+	0.216480i	−0.675621	−	0.737249i	$-0.736124\pi$
$929$	−11.4284	+	6.59820i	−0.374954	+	0.216480i	0.300666	+	0.953729i	$0.402791\pi$
$930$		0			0
$931$	−26.7688			−0.877312
$932$		0			0
$933$	9.19628	+	5.30948i	0.301073	+	0.173824i
$934$		0			0
$935$	−16.6190			−0.543498
$936$		0			0
$937$	−34.2379			−1.11850			−0.559252	−	0.828998i	$-0.688911\pi$
$937$	−34.2379			−1.11850			−0.559252	+	0.828998i	$0.688911\pi$
$938$		0			0
$939$	3.46410	+	2.00000i	0.113047	+	0.0652675i
$940$		0			0
$941$	−34.6410			−1.12926			−0.564632	−	0.825342i	$-0.690982\pi$
$941$	−34.6410			−1.12926			−0.564632	+	0.825342i	$0.690982\pi$
$942$		0			0
$943$	5.56351	−	3.21209i	0.181173	−	0.104600i
$944$		0			0
$945$	0.563508	+	0.976025i	0.0183309	+	0.0317501i
$946$		0			0
$947$	3.96812	−	6.87298i	0.128947	−	0.223342i	−0.794322	−	0.607497i	$-0.792174\pi$
$947$	3.96812	−	6.87298i	0.128947	−	0.223342i	0.923269	+	0.384155i	$0.125507\pi$
$948$		0			0
$949$	−10.4703	−	10.8810i	−0.339880	−	0.353214i
$950$		0			0
$951$	19.9365	+	11.5103i	0.646485	+	0.373248i
$952$		0			0
$953$	2.25403	+	3.90410i	0.0730153	+	0.126466i	0.900221	−	0.435432i	$-0.143404\pi$
$953$	2.25403	+	3.90410i	0.0730153	+	0.126466i	−0.827206	+	0.561899i	$0.810071\pi$
$954$		0			0
$955$	4.75615	+	8.23790i	0.153906	+	0.266572i
$956$		0			0
$957$	−8.44025			−0.272835
$958$		0			0
$959$	−3.43649	+	5.95218i	−0.110970	+	0.192206i
$960$		0			0
$961$	11.0000			0.354839
$962$		0			0
$963$			6.87298i			0.221479i
$964$		0			0
$965$	−36.0431	−	20.8095i	−1.16027	−	0.669881i
$966$		0			0
$967$		−	33.6970i		−	1.08362i	−0.840500	−	0.541811i	$-0.817739\pi$
$967$		−	33.6970i		−	1.08362i	0.840500	−	0.541811i	$-0.182261\pi$
$968$		0			0
$969$	−6.43649	+	3.71611i	−0.206770	+	0.119379i
$970$		0			0
$971$	−29.8569	+	17.2379i	−0.958154	+	0.553191i	−0.895604	−	0.444851i	$-0.853257\pi$
$971$	−29.8569	+	17.2379i	−0.958154	+	0.553191i	−0.0625497	+	0.998042i	$0.519923\pi$
$972$		0			0
$973$	1.44803	−	2.50807i	0.0464218	−	0.0804049i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−15.3014	−	8.83427i	−0.489535	−	0.282633i	0.234846	−	0.972033i	$-0.424541\pi$
$977$	−15.3014	−	8.83427i	−0.489535	−	0.282633i	−0.724382	+	0.689399i	$0.757875\pi$
$978$		0			0
$979$	−54.5456	+	31.4919i	−1.74329	+	1.00649i
$980$		0			0
$981$	−5.70017	−	9.87298i	−0.181992	−	0.315220i
$982$		0			0
$983$		−	0.439999i		−	0.0140338i	−0.999975	−	0.00701689i	$-0.997766\pi$
$983$		−	0.439999i		−	0.0140338i	0.999975	−	0.00701689i	$-0.00223356\pi$
$984$		0			0
$985$	12.7460	−	22.0767i	0.406120	−	0.703421i
$986$		0			0
$987$			0.254033i			0.00808597i
$988$		0			0
$989$		−	1.27017i		−	0.0403889i
$990$		0			0
$991$	13.1825	−	22.8327i	0.418755	−	0.725304i	−0.577060	−	0.816702i	$-0.695800\pi$
$991$	13.1825	−	22.8327i	0.418755	−	0.725304i	0.995814	+	0.0913976i	$0.0291334\pi$
$992$		0			0
$993$			16.8805i			0.535687i
$994$		0			0
$995$	0.976025	+	1.69052i	0.0309421	+	0.0535932i
$996$		0			0
$997$	33.3350	−	19.2460i	1.05573	−	0.609526i	0.131482	−	0.991319i	$-0.458027\pi$
$997$	33.3350	−	19.2460i	1.05573	−	0.609526i	0.924248	+	0.381793i	$0.124693\pi$
$998$		0			0
$999$	9.24597	+	5.33816i	0.292529	+	0.168892i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1248.2.ca.a.433.4		8
4.3	odd	2		312.2.bk.a.277.2	yes	8
8.3	odd	2		312.2.bk.a.277.1	yes	8
8.5	even	2	inner	1248.2.ca.a.433.1		8
12.11	even	2		936.2.dg.c.901.3		8
13.10	even	6	inner	1248.2.ca.a.49.1		8
24.11	even	2		936.2.dg.c.901.4		8
52.23	odd	6		312.2.bk.a.205.1	✓	8
104.75	odd	6		312.2.bk.a.205.2	yes	8
104.101	even	6	inner	1248.2.ca.a.49.4		8
156.23	even	6		936.2.dg.c.829.4		8
312.179	even	6		936.2.dg.c.829.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bk.a.205.1	✓	8	52.23	odd	6
312.2.bk.a.205.2	yes	8	104.75	odd	6
312.2.bk.a.277.1	yes	8	8.3	odd	2
312.2.bk.a.277.2	yes	8	4.3	odd	2
936.2.dg.c.829.3		8	312.179	even	6
936.2.dg.c.829.4		8	156.23	even	6
936.2.dg.c.901.3		8	12.11	even	2
936.2.dg.c.901.4		8	24.11	even	2
1248.2.ca.a.49.1		8	13.10	even	6	inner
1248.2.ca.a.49.4		8	104.101	even	6	inner
1248.2.ca.a.433.1		8	8.5	even	2	inner
1248.2.ca.a.433.4		8	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1248.ca (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{3} +2.23607 q^{5} +(0.436492 - 0.252009i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-1.98406 + 3.43649i) q^{11} +(2.59808 - 2.50000i) q^{13} +(1.93649 + 1.11803i) q^{15} +(0.936492 + 1.62205i) q^{17} +(1.98406 + 3.43649i) q^{19} +0.504017 q^{21} +(0.563508 - 0.976025i) q^{23} +1.00000i q^{27} +(1.84205 + 1.06351i) q^{29} +4.47214i q^{31} +(-3.43649 + 1.98406i) q^{33} +(0.976025 - 0.563508i) q^{35} +(5.33816 - 9.24597i) q^{37} +(3.50000 - 0.866025i) q^{39} +(4.93649 + 2.85008i) q^{41} +(0.976025 - 0.563508i) q^{43} +(1.11803 + 1.93649i) q^{45} +0.504017i q^{47} +(-3.37298 + 5.84218i) q^{49} +1.87298i q^{51} -0.127017i q^{53} +(-4.43649 + 7.68423i) q^{55} +3.96812i q^{57} +(-5.70017 - 9.87298i) q^{59} +(-0.866025 + 0.500000i) q^{61} +(0.436492 + 0.252009i) q^{63} +(5.80948 - 5.59017i) q^{65} +(7.68423 - 13.3095i) q^{67} +(0.976025 - 0.563508i) q^{69} +(-7.30948 + 4.22013i) q^{71} -4.18812i q^{73} +2.00000i q^{77} -14.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +7.43222 q^{83} +(2.09406 + 3.62702i) q^{85} +(1.06351 + 1.84205i) q^{87} +(13.7460 + 7.93624i) q^{89} +(0.504017 - 1.74597i) q^{91} +(-2.23607 + 3.87298i) q^{93} +(4.43649 + 7.68423i) q^{95} +(-15.0000 + 8.66025i) q^{97} -3.96812 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{7} + 4 q^{9} - 8 q^{17} + 20 q^{23} - 12 q^{33} + 28 q^{39} + 24 q^{41} + 4 q^{49} - 20 q^{55} - 12 q^{63} - 12 q^{71} - 112 q^{79} - 4 q^{81} + 24 q^{87} + 48 q^{89} + 20 q^{95} - 120 q^{97}+O(q^{100}) \) 8 * q - 12 * q^7 + 4 * q^9 - 8 * q^17 + 20 * q^23 - 12 * q^33 + 28 * q^39 + 24 * q^41 + 4 * q^49 - 20 * q^55 - 12 * q^63 - 12 * q^71 - 112 * q^79 - 4 * q^81 + 24 * q^87 + 48 * q^89 + 20 * q^95 - 120 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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