LMFDB - Embedded newform 432.3.bc.b.65.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,3,Mod(65,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("432.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	432.bc (of order $18$, degree $6$, 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:	$11.7711474204$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			65.2
Character	$\chi$	$=$	432.65
Dual form			432.3.bc.b.113.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.70588 - 1.29546i) q^{3} +(1.65461 - 4.54600i) q^{5} +(-1.68621 + 9.56295i) q^{7} +(5.64356 + 7.01072i) q^{9} +O(q^{10})$	\(q+(-2.70588 - 1.29546i) q^{3} +(1.65461 - 4.54600i) q^{5} +(-1.68621 + 9.56295i) q^{7} +(5.64356 + 7.01072i) q^{9} +(-5.23790 - 14.3910i) q^{11} +(-6.28432 + 5.27317i) q^{13} +(-10.3663 + 10.1574i) q^{15} +(-9.01220 + 5.20319i) q^{17} +(-7.17439 + 12.4264i) q^{19} +(16.9511 - 23.6918i) q^{21} +(24.2260 - 4.27170i) q^{23} +(1.22274 + 1.02600i) q^{25} +(-6.18868 - 26.2812i) q^{27} +(-20.0134 + 23.8510i) q^{29} +(10.5226 + 59.6766i) q^{31} +(-4.46987 + 45.7258i) q^{33} +(40.6832 + 23.4884i) q^{35} +(-0.367254 - 0.636102i) q^{37} +(23.8358 - 6.12747i) q^{39} +(30.1540 + 35.9362i) q^{41} +(69.9886 - 25.4738i) q^{43} +(41.2086 - 14.0556i) q^{45} +(12.5408 + 2.21127i) q^{47} +(-42.5618 - 15.4912i) q^{49} +(31.1265 - 2.40427i) q^{51} +36.5138i q^{53} -74.0882 q^{55} +(35.5110 - 24.3302i) q^{57} +(-30.5258 + 83.8689i) q^{59} +(-7.06212 + 40.0513i) q^{61} +(-76.5594 + 42.1476i) q^{63} +(13.5737 + 37.2935i) q^{65} +(-61.6114 + 51.6981i) q^{67} +(-71.0865 - 19.8251i) q^{69} +(-0.595295 + 0.343694i) q^{71} +(13.7680 - 23.8468i) q^{73} +(-1.97944 - 4.36025i) q^{75} +(146.453 - 25.8236i) q^{77} +(-97.1709 - 81.5361i) q^{79} +(-17.3004 + 79.1309i) q^{81} +(8.62013 - 10.2731i) q^{83} +(8.74206 + 49.5787i) q^{85} +(85.0518 - 38.6114i) q^{87} +(-146.234 - 84.4283i) q^{89} +(-39.8304 - 68.9883i) q^{91} +(48.8358 - 175.109i) q^{93} +(44.6196 + 53.1756i) q^{95} +(-60.2262 + 21.9205i) q^{97} +(71.3309 - 117.938i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q - 9 * q^5 + 6 * q^9	$ 36 q - 9 q^{5} + 6 q^{9} - 36 q^{11} - 45 q^{15} + 42 q^{21} + 18 q^{23} - 9 q^{25} - 18 q^{29} - 45 q^{31} - 153 q^{33} + 243 q^{35} + 123 q^{39} - 198 q^{41} - 90 q^{43} - 333 q^{45} + 243 q^{47} + 72 q^{49} + 99 q^{51} + 243 q^{57} - 252 q^{59} - 144 q^{61} - 381 q^{63} + 747 q^{65} - 108 q^{67} + 585 q^{69} - 324 q^{71} - 63 q^{73} - 597 q^{75} + 495 q^{77} - 36 q^{79} - 54 q^{81} + 27 q^{83} - 180 q^{85} + 441 q^{87} - 567 q^{89} - 99 q^{91} - 699 q^{93} + 1044 q^{95} - 216 q^{97} + 945 q^{99}+O(q^{100}) $ 36 * q - 9 * q^5 + 6 * q^9 - 36 * q^11 - 45 * q^15 + 42 * q^21 + 18 * q^23 - 9 * q^25 - 18 * q^29 - 45 * q^31 - 153 * q^33 + 243 * q^35 + 123 * q^39 - 198 * q^41 - 90 * q^43 - 333 * q^45 + 243 * q^47 + 72 * q^49 + 99 * q^51 + 243 * q^57 - 252 * q^59 - 144 * q^61 - 381 * q^63 + 747 * q^65 - 108 * q^67 + 585 * q^69 - 324 * q^71 - 63 * q^73 - 597 * q^75 + 495 * q^77 - 36 * q^79 - 54 * q^81 + 27 * q^83 - 180 * q^85 + 441 * q^87 - 567 * q^89 - 99 * q^91 - 699 * q^93 + 1044 * q^95 - 216 * q^97 + 945 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{18}\right)$

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
$3$	−2.70588	−	1.29546i	−0.901960	−	0.431820i
$3$	−2.70588	−	1.29546i	−0.901960	−	0.431820i
$4$		0			0
$5$	1.65461	−	4.54600i	0.330922	−	0.909200i	−0.656951	−	0.753933i	$-0.728154\pi$
$5$	1.65461	−	4.54600i	0.330922	−	0.909200i	0.987873	−	0.155266i	$-0.0496236\pi$
$6$		0			0
$7$	−1.68621	+	9.56295i	−0.240887	+	1.36614i	0.588968	+	0.808156i	$0.299534\pi$
$7$	−1.68621	+	9.56295i	−0.240887	+	1.36614i	−0.829855	+	0.557980i	$0.811577\pi$
$8$		0			0
$9$	5.64356	+	7.01072i	0.627063	+	0.778969i
$10$		0			0
$11$	−5.23790	−	14.3910i	−0.476173	−	1.30827i	−0.912718	−	0.408591i	$-0.866020\pi$
$11$	−5.23790	−	14.3910i	−0.476173	−	1.30827i	0.436545	−	0.899682i	$-0.356202\pi$
$12$		0			0
$13$	−6.28432	+	5.27317i	−0.483409	+	0.405629i	−0.851657	−	0.524099i	$-0.824402\pi$
$13$	−6.28432	+	5.27317i	−0.483409	+	0.405629i	0.368248	+	0.929728i	$0.379958\pi$
$14$		0			0
$15$	−10.3663	+	10.1574i	−0.691089	+	0.677163i
$16$		0			0
$17$	−9.01220	+	5.20319i	−0.530129	+	0.306070i	−0.741069	−	0.671429i	$-0.765681\pi$
$17$	−9.01220	+	5.20319i	−0.530129	+	0.306070i	0.210940	+	0.977499i	$0.432348\pi$
$18$		0			0
$19$	−7.17439	+	12.4264i	−0.377599	+	0.654021i	−0.990712	−	0.135974i	$-0.956584\pi$
$19$	−7.17439	+	12.4264i	−0.377599	+	0.654021i	0.613113	+	0.789995i	$0.289917\pi$
$20$		0			0
$21$	16.9511	−	23.6918i	0.807195	−	1.12818i
$22$		0			0
$23$	24.2260	−	4.27170i	1.05330	−	0.185726i	0.379921	−	0.925019i	$-0.375951\pi$
$23$	24.2260	−	4.27170i	1.05330	−	0.185726i	0.673384	+	0.739293i	$0.264840\pi$
$24$		0			0
$25$	1.22274	+	1.02600i	0.0489096	+	0.0410401i
$26$		0			0
$27$	−6.18868	−	26.2812i	−0.229211	−	0.973377i
$28$		0			0
$29$	−20.0134	+	23.8510i	−0.690116	+	0.822449i	−0.991370	−	0.131095i	$-0.958151\pi$
$29$	−20.0134	+	23.8510i	−0.690116	+	0.822449i	0.301253	+	0.953544i	$0.402595\pi$
$30$		0			0
$31$	10.5226	+	59.6766i	0.339439	+	1.92505i	0.378023	+	0.925796i	$0.376604\pi$
$31$	10.5226	+	59.6766i	0.339439	+	1.92505i	−0.0385845	+	0.999255i	$0.512285\pi$
$32$		0			0
$33$	−4.46987	+	45.7258i	−0.135451	+	1.38563i
$34$		0			0
$35$	40.6832	+	23.4884i	1.16238	+	0.671098i
$36$		0			0
$37$	−0.367254	−	0.636102i	−0.00992578	−	0.0171920i	0.861020	−	0.508571i	$-0.169826\pi$
$37$	−0.367254	−	0.636102i	−0.00992578	−	0.0171920i	−0.870946	+	0.491379i	$0.836493\pi$
$38$		0			0
$39$	23.8358	−	6.12747i	0.611174	−	0.157115i
$40$		0			0
$41$	30.1540	+	35.9362i	0.735465	+	0.876493i	0.996035	−	0.0889623i	$-0.0283551\pi$
$41$	30.1540	+	35.9362i	0.735465	+	0.876493i	−0.260570	+	0.965455i	$0.583911\pi$
$42$		0			0
$43$	69.9886	−	25.4738i	1.62764	−	0.592413i	0.642826	−	0.766012i	$-0.277762\pi$
$43$	69.9886	−	25.4738i	1.62764	−	0.592413i	0.984816	+	0.173599i	$0.0555396\pi$
$44$		0			0
$45$	41.2086	−	14.0556i	0.915747	−	0.312347i
$46$		0			0
$47$	12.5408	+	2.21127i	0.266824	+	0.0470484i	0.305460	−	0.952205i	$-0.401190\pi$
$47$	12.5408	+	2.21127i	0.266824	+	0.0470484i	−0.0386351	+	0.999253i	$0.512301\pi$
$48$		0			0
$49$	−42.5618	−	15.4912i	−0.868609	−	0.316148i
$50$		0			0
$51$	31.1265	−	2.40427i	0.610323	−	0.0471425i
$52$		0			0
$53$			36.5138i			0.688940i	0.938797	+	0.344470i	$0.111941\pi$
$53$			36.5138i			0.688940i	−0.938797	+	0.344470i	$0.888059\pi$
$54$		0			0
$55$	−74.0882			−1.34706
$56$		0			0
$57$	35.5110	−	24.3302i	0.622999	−	0.426846i
$58$		0			0
$59$	−30.5258	+	83.8689i	−0.517386	+	1.42151i	0.356004	+	0.934484i	$0.384139\pi$
$59$	−30.5258	+	83.8689i	−0.517386	+	1.42151i	−0.873390	+	0.487022i	$0.838083\pi$
$60$		0			0
$61$	−7.06212	+	40.0513i	−0.115772	+	0.656578i	0.870592	+	0.492005i	$0.163736\pi$
$61$	−7.06212	+	40.0513i	−0.115772	+	0.656578i	−0.986365	+	0.164573i	$0.947375\pi$
$62$		0			0
$63$	−76.5594	+	42.1476i	−1.21523	+	0.669009i
$64$		0			0
$65$	13.5737	+	37.2935i	0.208827	+	0.573747i
$66$		0			0
$67$	−61.6114	+	51.6981i	−0.919573	+	0.771613i	−0.973916	−	0.226909i	$-0.927138\pi$
$67$	−61.6114	+	51.6981i	−0.919573	+	0.771613i	0.0543434	+	0.998522i	$0.482693\pi$
$68$		0			0
$69$	−71.0865	−	19.8251i	−1.03024	−	0.287321i
$70$		0			0
$71$	−0.595295	+	0.343694i	−0.00838443	+	0.00484075i	−0.504186	−	0.863595i	$-0.668208\pi$
$71$	−0.595295	+	0.343694i	−0.00838443	+	0.00484075i	0.495802	+	0.868436i	$0.334874\pi$
$72$		0			0
$73$	13.7680	−	23.8468i	0.188603	−	0.326669i	−0.756182	−	0.654361i	$-0.772938\pi$
$73$	13.7680	−	23.8468i	0.188603	−	0.326669i	0.944785	+	0.327692i	$0.106271\pi$
$74$		0			0
$75$	−1.97944	−	4.36025i	−0.0263926	−	0.0581366i
$76$		0			0
$77$	146.453	−	25.8236i	1.90198	−	0.335371i
$78$		0			0
$79$	−97.1709	−	81.5361i	−1.23001	−	1.03210i	−0.998238	−	0.0593327i	$-0.981103\pi$
$79$	−97.1709	−	81.5361i	−1.23001	−	1.03210i	−0.231774	−	0.972770i	$-0.574453\pi$
$80$		0			0
$81$	−17.3004	+	79.1309i	−0.213585	+	0.976924i
$82$		0			0
$83$	8.62013	−	10.2731i	0.103857	−	0.123772i	−0.711612	−	0.702573i	$-0.752035\pi$
$83$	8.62013	−	10.2731i	0.103857	−	0.123772i	0.815469	+	0.578801i	$0.196479\pi$
$84$		0			0
$85$	8.74206	+	49.5787i	0.102848	+	0.583279i
$86$		0			0
$87$	85.0518	−	38.6114i	0.977607	−	0.443809i
$88$		0			0
$89$	−146.234	−	84.4283i	−1.64308	−	0.948632i	−0.979730	−	0.200323i	$-0.935801\pi$
$89$	−146.234	−	84.4283i	−1.64308	−	0.948632i	−0.663349	−	0.748310i	$-0.730866\pi$
$90$		0			0
$91$	−39.8304	−	68.9883i	−0.437697	−	0.758113i
$92$		0			0
$93$	48.8358	−	175.109i	0.525116	−	1.88290i
$94$		0			0
$95$	44.6196	+	53.1756i	0.469680	+	0.559743i
$96$		0			0
$97$	−60.2262	+	21.9205i	−0.620888	+	0.225985i	−0.633261	−	0.773939i	$-0.718284\pi$
$97$	−60.2262	+	21.9205i	−0.620888	+	0.225985i	0.0123723	+	0.999923i	$0.496062\pi$
$98$		0			0
$99$	71.3309	−	117.938i	0.720514	−	1.19129i
$100$		0			0
$101$	182.669	+	32.2094i	1.80860	+	0.318905i	0.973065	−	0.230529i	$-0.0740456\pi$
$101$	182.669	+	32.2094i	1.80860	+	0.318905i	0.835537	+	0.549434i	$0.185157\pi$
$102$		0			0
$103$	65.2417	+	23.7460i	0.633415	+	0.230544i	0.638717	−	0.769442i	$-0.279466\pi$
$103$	65.2417	+	23.7460i	0.633415	+	0.230544i	−0.00530214	+	0.999986i	$0.501688\pi$
$104$		0			0
$105$	−79.6553	−	116.260i	−0.758622	−	1.10724i
$106$		0			0
$107$			44.4428i			0.415353i	0.978198	+	0.207677i	$0.0665902\pi$
$107$			44.4428i			0.415353i	−0.978198	+	0.207677i	$0.933410\pi$
$108$		0			0
$109$	5.37221			0.0492863			0.0246432	−	0.999696i	$-0.492155\pi$
$109$	5.37221			0.0492863			0.0246432	+	0.999696i	$0.492155\pi$
$110$		0			0
$111$	0.169699	+	2.19698i	0.00152882	+	0.0197926i
$112$		0			0
$113$	20.2350	−	55.5953i	0.179071	−	0.491994i	−0.817387	−	0.576089i	$-0.804578\pi$
$113$	20.2350	−	55.5953i	0.179071	−	0.491994i	0.996458	+	0.0840959i	$0.0268002\pi$
$114$		0			0
$115$	20.6654	−	117.199i	0.179699	−	1.01912i
$116$		0			0
$117$	−72.4347	−	14.2981i	−0.619100	−	0.122206i
$118$		0			0
$119$	−34.5615	−	94.9569i	−0.290433	−	0.797957i
$120$		0			0
$121$	−86.9742	+	72.9800i	−0.718795	+	0.603141i
$122$		0			0
$123$	−35.0393	−	136.302i	−0.284872	−	1.10815i
$124$		0			0
$125$	111.428	−	64.3328i	0.891422	−	0.514663i
$126$		0			0
$127$	11.7617	−	20.3718i	0.0926117	−	0.160408i	−0.815998	−	0.578055i	$-0.803812\pi$
$127$	11.7617	−	20.3718i	0.0926117	−	0.160408i	0.908609	+	0.417647i	$0.137145\pi$
$128$		0			0
$129$	−222.381	−	21.7386i	−1.72388	−	0.168516i
$130$		0			0
$131$	−98.3090	+	17.3345i	−0.750451	+	0.132325i	−0.535775	−	0.844361i	$-0.679981\pi$
$131$	−98.3090	+	17.3345i	−0.750451	+	0.132325i	−0.214676	+	0.976685i	$0.568869\pi$
$132$		0			0
$133$	−106.736	−	89.5618i	−0.802524	−	0.673397i
$134$		0			0
$135$	−129.714	−	15.3513i	−0.960845	−	0.113713i
$136$		0			0
$137$	−29.3994	+	35.0368i	−0.214594	+	0.255743i	−0.862594	−	0.505898i	$-0.831161\pi$
$137$	−29.3994	+	35.0368i	−0.214594	+	0.255743i	0.648000	+	0.761641i	$0.275606\pi$
$138$		0			0
$139$	16.9605	+	96.1879i	0.122018	+	0.691999i	0.983034	+	0.183422i	$0.0587174\pi$
$139$	16.9605	+	96.1879i	0.122018	+	0.691999i	−0.861016	+	0.508577i	$0.830172\pi$
$140$		0			0
$141$	−31.0691	−	22.2295i	−0.220348	−	0.157656i
$142$		0			0
$143$	108.803	+	62.8174i	0.760860	+	0.439282i
$144$		0			0
$145$	75.3124	+	130.445i	0.519396	+	0.899620i
$146$		0			0
$147$	95.0989	+	97.0546i	0.646931	+	0.660235i
$148$		0			0
$149$	−115.756	−	137.952i	−0.776884	−	0.925854i	0.221905	−	0.975068i	$-0.428773\pi$
$149$	−115.756	−	137.952i	−0.776884	−	0.925854i	−0.998788	+	0.0492145i	$0.984328\pi$
$150$		0			0
$151$	−52.3251	+	19.0448i	−0.346524	+	0.126124i	−0.509418	−	0.860519i	$-0.670139\pi$
$151$	−52.3251	+	19.0448i	−0.346524	+	0.126124i	0.162894	+	0.986644i	$0.447917\pi$
$152$		0			0
$153$	−87.3390	−	33.8174i	−0.570843	−	0.221029i
$154$		0			0
$155$	288.700	+	50.9057i	1.86258	+	0.328424i
$156$		0			0
$157$	−0.737193	−	0.268316i	−0.00469550	−	0.00170902i	0.339671	−	0.940544i	$-0.389684\pi$
$157$	−0.737193	−	0.268316i	−0.00469550	−	0.00170902i	−0.344367	+	0.938835i	$0.611906\pi$
$158$		0			0
$159$	47.3023	−	98.8020i	0.297498	−	0.621396i
$160$		0			0
$161$			238.875i			1.48370i
$162$		0			0
$163$	−292.245			−1.79292			−0.896458	−	0.443128i	$-0.853869\pi$
$163$	−292.245			−1.79292			−0.896458	+	0.443128i	$0.853869\pi$
$164$		0			0
$165$	200.474	+	95.9783i	1.21499	+	0.581687i
$166$		0			0
$167$	86.5719	−	237.854i	0.518395	−	1.42428i	−0.353893	−	0.935286i	$-0.615142\pi$
$167$	86.5719	−	237.854i	0.518395	−	1.42428i	0.872288	−	0.488992i	$-0.162635\pi$
$168$		0			0
$169$	−17.6602	+	100.156i	−0.104498	+	0.592638i
$170$		0			0
$171$	−127.607	+	19.8316i	−0.746241	+	0.115974i
$172$		0			0
$173$	15.4798	+	42.5305i	0.0894788	+	0.245841i	0.976358	−	0.216161i	$-0.0693535\pi$
$173$	15.4798	+	42.5305i	0.0894788	+	0.245841i	−0.886879	+	0.462002i	$0.847131\pi$
$174$		0			0
$175$	−11.8734	+	9.96296i	−0.0678480	+	0.0569312i
$176$		0			0
$177$	191.248	−	187.394i	1.08050	−	1.05872i
$178$		0			0
$179$	−292.829	+	169.065i	−1.63592	+	0.944498i	−0.653701	+	0.756753i	$0.726785\pi$
$179$	−292.829	+	169.065i	−1.63592	+	0.944498i	−0.982218	+	0.187745i	$0.939882\pi$
$180$		0			0
$181$	44.0372	−	76.2746i	0.243299	−	0.421407i	−0.718353	−	0.695679i	$-0.755104\pi$
$181$	44.0372	−	76.2746i	0.243299	−	0.421407i	0.961652	+	0.274272i	$0.0884369\pi$
$182$		0			0
$183$	70.9941	−	99.2252i	0.387946	−	0.542214i
$184$		0			0
$185$	−3.49938	+	0.617035i	−0.0189156	+	0.00333533i
$186$		0			0
$187$	122.084	+	102.441i	0.652857	+	0.547812i
$188$		0			0
$189$	261.761	−	14.8666i	1.38498	−	0.0786593i
$190$		0			0
$191$	−73.2854	+	87.3382i	−0.383693	+	0.457268i	−0.922976	−	0.384857i	$-0.874251\pi$
$191$	−73.2854	+	87.3382i	−0.383693	+	0.457268i	0.539283	+	0.842125i	$0.318695\pi$
$192$		0			0
$193$	−28.7710	−	163.168i	−0.149073	−	0.845432i	−0.964007	−	0.265878i	$-0.914338\pi$
$193$	−28.7710	−	163.168i	−0.149073	−	0.845432i	0.814934	−	0.579554i	$-0.196773\pi$
$194$		0			0
$195$	11.5834	−	118.496i	0.0594022	−	0.607672i
$196$		0			0
$197$	−147.151	−	84.9579i	−0.746962	−	0.431259i	0.0776334	−	0.996982i	$-0.475264\pi$
$197$	−147.151	−	84.9579i	−0.746962	−	0.431259i	−0.824595	+	0.565723i	$0.808597\pi$
$198$		0			0
$199$	143.965	+	249.355i	0.723444	+	1.25304i	0.959611	+	0.281329i	$0.0907753\pi$
$199$	143.965	+	249.355i	0.723444	+	1.25304i	−0.236167	+	0.971712i	$0.575891\pi$
$200$		0			0
$201$	233.686	−	60.0736i	1.16262	−	0.298874i
$202$		0			0
$203$	−194.339	−	231.605i	−0.957337	−	1.14091i
$204$		0			0
$205$	213.259	−	77.6199i	1.04029	−	0.378634i
$206$		0			0
$207$	166.669	+	145.734i	0.805163	+	0.704030i
$208$		0			0
$209$	216.407	+	38.1584i	1.03544	+	0.182576i
$210$		0			0
$211$	−167.189	−	60.8519i	−0.792366	−	0.288398i	−0.0860469	−	0.996291i	$-0.527424\pi$
$211$	−167.189	−	60.8519i	−0.792366	−	0.288398i	−0.706319	+	0.707893i	$0.749646\pi$
$212$		0			0
$213$	2.05604	−	0.158812i	0.00965276	−	0.000745597i
$214$		0			0
$215$		−	360.317i		−	1.67589i
$216$		0			0
$217$	−588.428			−2.71165
$218$		0			0
$219$	−68.1472	+	46.6908i	−0.311174	+	0.213200i
$220$		0			0
$221$	29.1982	−	80.2214i	0.132119	−	0.362993i
$222$		0			0
$223$	−25.5930	+	145.145i	−0.114767	+	0.650874i	0.872099	+	0.489330i	$0.162759\pi$
$223$	−25.5930	+	145.145i	−0.114767	+	0.650874i	−0.986865	+	0.161544i	$0.948352\pi$
$224$		0			0
$225$	−0.292394	+	14.3626i	−0.00129953	+	0.0638338i
$226$		0			0
$227$	108.612	+	298.408i	0.478465	+	1.31457i	0.910796	+	0.412857i	$0.135469\pi$
$227$	108.612	+	298.408i	0.478465	+	1.31457i	−0.432331	+	0.901715i	$0.642309\pi$
$228$		0			0
$229$	71.8167	−	60.2614i	0.313610	−	0.263150i	−0.472372	−	0.881399i	$-0.656602\pi$
$229$	71.8167	−	60.2614i	0.313610	−	0.263150i	0.785982	+	0.618249i	$0.212158\pi$
$230$		0			0
$231$	−429.737	−	119.848i	−1.86033	−	0.518824i
$232$		0			0
$233$	−198.373	+	114.531i	−0.851387	+	0.491549i	−0.861119	−	0.508404i	$-0.830236\pi$
$233$	−198.373	+	114.531i	−0.851387	+	0.491549i	0.00973138	+	0.999953i	$0.496902\pi$
$234$		0			0
$235$	30.8025	−	53.3514i	0.131074	−	0.227027i
$236$		0			0
$237$	157.306	+	346.508i	0.663738	+	1.46206i
$238$		0			0
$239$	397.341	−	70.0620i	1.66252	−	0.293147i	0.738146	−	0.674641i	$-0.235702\pi$
$239$	397.341	−	70.0620i	1.66252	−	0.293147i	0.924371	+	0.381495i	$0.124591\pi$
$240$		0			0
$241$	107.338	+	90.0675i	0.445387	+	0.373724i	0.837721	−	0.546099i	$-0.183888\pi$
$241$	107.338	+	90.0675i	0.445387	+	0.373724i	−0.392334	+	0.919823i	$0.628332\pi$
$242$		0			0
$243$	149.324	−	191.707i	0.614501	−	0.788916i
$244$		0			0
$245$	−140.846	+	167.854i	−0.574883	+	0.685118i
$246$		0			0
$247$	−20.4404	−	115.923i	−0.0827547	−	0.469325i
$248$		0			0
$249$	−36.6334	+	16.6306i	−0.147122	+	0.0667897i
$250$		0			0
$251$	189.721	+	109.536i	0.755862	+	0.436397i	0.827808	−	0.561011i	$-0.189588\pi$
$251$	189.721	+	109.536i	0.755862	+	0.436397i	−0.0719458	+	0.997409i	$0.522921\pi$
$252$		0			0
$253$	−188.367	−	326.262i	−0.744535	−	1.28957i
$254$		0			0
$255$	40.5723	−	145.479i	0.159107	−	0.570506i
$256$		0			0
$257$	−57.7595	−	68.8350i	−0.224745	−	0.267841i	0.641875	−	0.766809i	$-0.278157\pi$
$257$	−57.7595	−	68.8350i	−0.224745	−	0.267841i	−0.866620	+	0.498969i	$0.833712\pi$
$258$		0			0
$259$	6.70228	−	2.43943i	0.0258775	−	0.00941865i
$260$		0			0
$261$	−280.160	−	5.70350i	−1.07341	−	0.0218525i
$262$		0			0
$263$	159.024	+	28.0401i	0.604652	+	0.106617i	0.467589	−	0.883946i	$-0.345123\pi$
$263$	159.024	+	28.0401i	0.604652	+	0.106617i	0.137063	+	0.990562i	$0.456234\pi$
$264$		0			0
$265$	165.992	+	60.4161i	0.626384	+	0.227985i
$266$		0			0
$267$	286.318	+	417.893i	1.07235	+	1.56514i
$268$		0			0
$269$			350.503i			1.30299i	0.758655	+	0.651493i	$0.225857\pi$
$269$			350.503i			1.30299i	−0.758655	+	0.651493i	$0.774143\pi$
$270$		0			0
$271$	60.6565			0.223825			0.111912	−	0.993718i	$-0.464302\pi$
$271$	60.6565			0.223825			0.111912	+	0.993718i	$0.464302\pi$
$272$		0			0
$273$	18.4046	+	238.273i	0.0674163	+	0.872794i
$274$		0			0
$275$	8.36060	−	22.9706i	0.0304022	−	0.0835293i
$276$		0			0
$277$	70.9181	−	402.197i	0.256022	−	1.45197i	−0.537413	−	0.843319i	$-0.680599\pi$
$277$	70.9181	−	402.197i	0.256022	−	1.45197i	0.793435	−	0.608654i	$-0.208290\pi$
$278$		0			0
$279$	−358.991	+	410.560i	−1.28671	+	1.47154i
$280$		0			0
$281$	1.62253	+	4.45786i	0.00577413	+	0.0158643i	0.942546	−	0.334076i	$-0.108424\pi$
$281$	1.62253	+	4.45786i	0.00577413	+	0.0158643i	−0.936772	+	0.349940i	$0.886202\pi$
$282$		0			0
$283$	66.7804	−	56.0354i	0.235973	−	0.198005i	−0.517131	−	0.855906i	$-0.673000\pi$
$283$	66.7804	−	56.0354i	0.235973	−	0.198005i	0.753104	+	0.657901i	$0.228556\pi$
$284$		0			0
$285$	−51.8484	−	201.690i	−0.181924	−	0.707683i
$286$		0			0
$287$	−394.502	+	227.766i	−1.37457	+	0.793609i
$288$		0			0
$289$	−90.3535	+	156.497i	−0.312642	+	0.541512i
$290$		0			0
$291$	191.362	+	18.7063i	0.657601	+	0.0642829i
$292$		0			0
$293$	−254.252	+	44.8315i	−0.867754	+	0.153009i	−0.589764	−	0.807575i	$-0.700779\pi$
$293$	−254.252	+	44.8315i	−0.867754	+	0.153009i	−0.277990	+	0.960584i	$0.589668\pi$
$294$		0			0
$295$	330.760	+	277.540i	1.12122	+	0.940814i
$296$		0			0
$297$	−345.797	+	226.720i	−1.16430	+	0.763366i
$298$		0			0
$299$	−129.719	+	154.593i	−0.433841	+	0.517032i
$300$		0			0
$301$	125.589	+	712.252i	0.417240	+	2.36629i
$302$		0			0
$303$	−452.554	−	323.795i	−1.49358	−	1.06863i
$304$		0			0
$305$	170.388	+	98.3735i	0.558649	+	0.322536i
$306$		0			0
$307$	−189.250	−	327.790i	−0.616449	−	1.06772i	−0.990128	−	0.140163i	$-0.955237\pi$
$307$	−189.250	−	327.790i	−0.616449	−	1.06772i	0.373679	−	0.927558i	$-0.378096\pi$
$308$		0			0
$309$	−145.774	−	148.772i	−0.471761	−	0.481463i
$310$		0			0
$311$	−174.625	−	208.110i	−0.561497	−	0.669165i	0.408366	−	0.912818i	$-0.366099\pi$
$311$	−174.625	−	208.110i	−0.561497	−	0.669165i	−0.969863	+	0.243653i	$0.921654\pi$
$312$		0			0
$313$	382.853	−	139.347i	1.22317	−	0.445198i	0.351918	−	0.936031i	$-0.385530\pi$
$313$	382.853	−	139.347i	1.22317	−	0.445198i	0.871254	+	0.490833i	$0.163307\pi$
$314$		0			0
$315$	64.9271	+	417.777i	0.206118	+	1.32627i
$316$		0			0
$317$	−236.114	−	41.6333i	−0.744840	−	0.131335i	−0.211667	−	0.977342i	$-0.567889\pi$
$317$	−236.114	−	41.6333i	−0.744840	−	0.131335i	−0.533173	+	0.846006i	$0.679000\pi$
$318$		0			0
$319$	448.068	+	163.083i	1.40460	+	0.511233i
$320$		0			0
$321$	57.5739	−	120.257i	0.179358	−	0.374632i
$322$		0			0
$323$		−	149.319i		−	0.462288i
$324$		0			0
$325$	−13.0944			−0.0402904
$326$		0			0
$327$	−14.5365	−	6.95948i	−0.0444543	−	0.0212828i
$328$		0			0
$329$	−42.2926	+	116.198i	−0.128549	+	0.353185i
$330$		0			0
$331$	33.9255	−	192.401i	0.102494	−	0.581272i	−0.889698	−	0.456550i	$-0.849085\pi$
$331$	33.9255	−	192.401i	0.102494	−	0.581272i	0.992192	−	0.124722i	$-0.0398039\pi$
$332$		0			0
$333$	2.38692	−	6.16460i	0.00716791	−	0.0185123i
$334$		0			0
$335$	133.077	+	365.625i	0.397244	+	1.09142i
$336$		0			0
$337$	4.83567	−	4.05761i	0.0143492	−	0.0120404i	−0.635585	−	0.772031i	$-0.719241\pi$
$337$	4.83567	−	4.05761i	0.0143492	−	0.0120404i	0.649934	+	0.759991i	$0.274797\pi$
$338$		0			0
$339$	−126.775	+	124.220i	−0.373968	+	0.366432i
$340$		0			0
$341$	803.690	−	464.011i	2.35686	−	1.36074i
$342$		0			0
$343$	−17.9967	+	31.1712i	−0.0524685	+	0.0908781i
$344$		0			0
$345$	−207.745	+	290.356i	−0.602160	+	0.841612i
$346$		0			0
$347$	368.103	−	64.9065i	1.06082	−	0.187050i	0.384097	−	0.923293i	$-0.374513\pi$
$347$	368.103	−	64.9065i	1.06082	−	0.187050i	0.676718	+	0.736242i	$0.263402\pi$
$348$		0			0
$349$	370.783	+	311.123i	1.06241	+	0.891471i	0.994344	−	0.106209i	$-0.0338713\pi$
$349$	370.783	+	311.123i	1.06241	+	0.891471i	0.0680703	+	0.997681i	$0.478316\pi$
$350$		0			0
$351$	177.477	+	132.525i	0.505632	+	0.377565i
$352$		0			0
$353$	371.609	−	442.866i	1.05272	−	1.25458i	0.0866620	−	0.996238i	$-0.472380\pi$
$353$	371.609	−	442.866i	1.05272	−	1.25458i	0.966054	−	0.258340i	$-0.0831756\pi$
$354$		0			0
$355$	0.577451	+	3.27489i	0.00162662	+	0.00922503i
$356$		0			0
$357$	−29.4937	+	301.715i	−0.0826155	+	0.845140i
$358$		0			0
$359$	−305.985	−	176.661i	−0.852326	−	0.492091i	0.00910901	−	0.999959i	$-0.497100\pi$
$359$	−305.985	−	176.661i	−0.852326	−	0.492091i	−0.861435	+	0.507868i	$0.830434\pi$
$360$		0			0
$361$	77.5563	+	134.331i	0.214837	+	0.372109i
$362$		0			0
$363$	329.884	−	84.8034i	0.908773	−	0.233618i
$364$		0			0
$365$	−85.6271	−	102.046i	−0.234595	−	0.279579i
$366$		0			0
$367$	391.598	−	142.530i	1.06702	−	0.388365i	0.251962	−	0.967737i	$-0.418924\pi$
$367$	391.598	−	142.530i	1.06702	−	0.388365i	0.815063	+	0.579372i	$0.196702\pi$
$368$		0			0
$369$	−81.7624	+	414.210i	−0.221578	+	1.12252i
$370$		0			0
$371$	−349.180	−	61.5699i	−0.941186	−	0.165957i
$372$		0			0
$373$	529.096	+	192.575i	1.41849	+	0.516287i	0.933609	−	0.358294i	$-0.116641\pi$
$373$	529.096	+	192.575i	1.41849	+	0.516287i	0.484879	+	0.874581i	$0.338864\pi$
$374$		0			0
$375$	−384.851	+	29.7266i	−1.02627	+	0.0792709i
$376$		0			0
$377$		−	255.421i		−	0.677510i
$378$		0			0
$379$	43.1728			0.113912			0.0569562	−	0.998377i	$-0.481860\pi$
$379$	43.1728			0.113912			0.0569562	+	0.998377i	$0.481860\pi$
$380$		0			0
$381$	−58.2166	+	39.8869i	−0.152800	+	0.104690i
$382$		0			0
$383$	−18.4613	+	50.7221i	−0.0482019	+	0.132434i	−0.961458	−	0.274953i	$-0.911338\pi$
$383$	−18.4613	+	50.7221i	−0.0482019	+	0.132434i	0.913256	+	0.407387i	$0.133560\pi$
$384$		0			0
$385$	124.928	−	708.502i	0.324488	−	1.84026i
$386$		0			0
$387$	573.575	+	346.908i	1.48211	+	0.896403i
$388$		0			0
$389$	6.35035	+	17.4474i	0.0163248	+	0.0448520i	0.947587	−	0.319497i	$-0.103514\pi$
$389$	6.35035	+	17.4474i	0.0163248	+	0.0448520i	−0.931263	+	0.364349i	$0.881292\pi$
$390$		0			0
$391$	−196.103	+	164.550i	−0.501542	+	0.420844i
$392$		0			0
$393$	288.469	+	80.4504i	0.734017	+	0.204708i
$394$		0			0
$395$	−531.443	+	306.829i	−1.34542	+	0.776781i
$396$		0			0
$397$	−76.9302	+	133.247i	−0.193779	+	0.335635i	−0.946500	−	0.322705i	$-0.895408\pi$
$397$	−76.9302	+	133.247i	−0.193779	+	0.335635i	0.752721	+	0.658340i	$0.228741\pi$
$398$		0			0
$399$	172.790	+	380.615i	0.433057	+	0.953923i
$400$		0			0
$401$	360.952	−	63.6455i	0.900129	−	0.158717i	0.295611	−	0.955308i	$-0.404477\pi$
$401$	360.952	−	63.6455i	0.900129	−	0.158717i	0.604518	+	0.796592i	$0.293366\pi$
$402$		0			0
$403$	−380.812	−	319.539i	−0.944944	−	0.792902i
$404$		0			0
$405$	331.103	+	209.578i	0.817539	+	0.517477i
$406$		0			0
$407$	−7.23052	+	8.61699i	−0.0177654	+	0.0211720i
$408$		0			0
$409$	47.8328	+	271.273i	0.116951	+	0.663260i	0.985766	+	0.168124i	$0.0537707\pi$
$409$	47.8328	+	271.273i	0.116951	+	0.663260i	−0.868815	+	0.495136i	$0.835118\pi$
$410$		0			0
$411$	124.940	−	56.7196i	0.303990	−	0.138004i
$412$		0			0
$413$	−750.561	−	433.337i	−1.81734	−	1.04924i
$414$		0			0
$415$	−32.4384	−	56.1850i	−0.0781648	−	0.135385i
$416$		0			0
$417$	78.7145	−	282.244i	0.188764	−	0.676845i
$418$		0			0
$419$	−80.8046	−	96.2992i	−0.192851	−	0.229831i	0.660951	−	0.750429i	$-0.270153\pi$
$419$	−80.8046	−	96.2992i	−0.192851	−	0.229831i	−0.853802	+	0.520598i	$0.825709\pi$
$420$		0			0
$421$	−137.678	+	50.1109i	−0.327027	+	0.119028i	−0.500316	−	0.865843i	$-0.666783\pi$
$421$	−137.678	+	50.1109i	−0.327027	+	0.119028i	0.173289	+	0.984871i	$0.444561\pi$
$422$		0			0
$423$	55.2719	+	100.399i	0.130666	+	0.237350i
$424$		0			0
$425$	−16.3581	−	2.88437i	−0.0384896	−	0.00678675i
$426$		0			0
$427$	−371.100	−	135.069i	−0.869087	−	0.316322i
$428$		0			0
$429$	−213.030	−	310.926i	−0.496574	−	0.724770i
$430$		0			0
$431$		−	534.529i		−	1.24021i	−0.784520	−	0.620103i	$-0.787091\pi$
$431$		−	534.529i		−	1.24021i	0.784520	−	0.620103i	$-0.212909\pi$
$432$		0			0
$433$	−46.7148			−0.107886			−0.0539431	−	0.998544i	$-0.517179\pi$
$433$	−46.7148			−0.107886			−0.0539431	+	0.998544i	$0.517179\pi$
$434$		0			0
$435$	−34.8000	−	450.532i	−0.0799999	−	1.03571i
$436$		0			0
$437$	−120.725	+	331.689i	−0.276258	+	0.759014i
$438$		0			0
$439$	56.0382	−	317.808i	0.127650	−	0.723937i	−0.852049	−	0.523462i	$-0.824640\pi$
$439$	56.0382	−	317.808i	0.127650	−	0.723937i	0.979699	−	0.200475i	$-0.0642487\pi$
$440$		0			0
$441$	−131.596	−	385.815i	−0.298403	−	0.874863i
$442$		0			0
$443$	2.37683	+	6.53028i	0.00536530	+	0.0147410i	0.942346	−	0.334639i	$-0.108614\pi$
$443$	2.37683	+	6.53028i	0.00536530	+	0.0147410i	−0.936981	+	0.349380i	$0.886392\pi$
$444$		0			0
$445$	−625.771	+	525.084i	−1.40623	+	1.17996i
$446$		0			0
$447$	134.509	+	523.239i	0.300915	+	1.17056i
$448$		0			0
$449$	−711.494	+	410.781i	−1.58462	+	0.914880i	−0.590447	+	0.807076i	$0.701049\pi$
$449$	−711.494	+	410.781i	−1.58462	+	0.914880i	−0.994172	+	0.107804i	$0.965618\pi$
$450$		0			0
$451$	359.214	−	622.177i	0.796484	−	1.37955i
$452$		0			0
$453$	166.257	+	16.2523i	0.367014	+	0.0358769i
$454$		0			0
$455$	−379.525	+	66.9204i	−0.834120	+	0.147078i
$456$		0			0
$457$	4.39384	+	3.68687i	0.00961453	+	0.00806755i	0.647582	−	0.761996i	$-0.275780\pi$
$457$	4.39384	+	3.68687i	0.00961453	+	0.00806755i	−0.637968	+	0.770063i	$0.720225\pi$
$458$		0			0
$459$	192.520	+	204.650i	0.419433	+	0.445861i
$460$		0			0
$461$	−75.4026	+	89.8613i	−0.163563	+	0.194927i	−0.841601	−	0.540100i	$-0.818386\pi$
$461$	−75.4026	+	89.8613i	−0.163563	+	0.194927i	0.678038	+	0.735027i	$0.262831\pi$
$462$		0			0
$463$	75.4724	+	428.025i	0.163007	+	0.924460i	0.951095	+	0.308898i	$0.0999601\pi$
$463$	75.4724	+	428.025i	0.163007	+	0.924460i	−0.788088	+	0.615563i	$0.788929\pi$
$464$		0			0
$465$	−715.242	−	511.745i	−1.53816	−	1.10053i
$466$		0			0
$467$	−419.536	−	242.219i	−0.898365	−	0.518671i	−0.0216955	−	0.999765i	$-0.506906\pi$
$467$	−419.536	−	242.219i	−0.898365	−	0.518671i	−0.876669	+	0.481093i	$0.840240\pi$
$468$		0			0
$469$	−390.497	−	676.360i	−0.832616	−	1.44213i
$470$		0			0
$471$	1.64716	+	1.68104i	0.00349716	+	0.00356908i
$472$		0			0
$473$	−733.187	−	873.778i	−1.55008	−	1.84731i
$474$		0			0
$475$	−21.5219	+	7.83334i	−0.0453093	+	0.0164912i
$476$		0			0
$477$	−255.988	+	206.068i	−0.536663	+	0.432009i
$478$		0			0
$479$	168.511	+	29.7130i	0.351798	+	0.0620314i	0.346755	−	0.937956i	$-0.387284\pi$
$479$	168.511	+	29.7130i	0.351798	+	0.0620314i	0.00504299	+	0.999987i	$0.498395\pi$
$480$		0			0
$481$	5.66222	+	2.06088i	0.0117718	+	0.00428457i
$482$		0			0
$483$	309.453	−	646.367i	0.640690	−	1.33823i
$484$		0			0
$485$			310.058i			0.639295i
$486$		0			0
$487$	144.274			0.296250			0.148125	−	0.988969i	$-0.452676\pi$
$487$	144.274			0.296250			0.148125	+	0.988969i	$0.452676\pi$
$488$		0			0
$489$	790.781	+	378.592i	1.61714	+	0.774218i
$490$		0			0
$491$	−34.2046	+	93.9763i	−0.0696631	+	0.191398i	−0.969638	−	0.244543i	$-0.921362\pi$
$491$	−34.2046	+	93.9763i	−0.0696631	+	0.191398i	0.899975	+	0.435941i	$0.143584\pi$
$492$		0			0
$493$	56.2630	−	319.084i	0.114124	−	0.647228i
$494$		0			0
$495$	−418.121	−	519.411i	−0.844689	−	1.04932i
$496$		0			0
$497$	−2.28294	−	6.27231i	−0.00459343	−	0.0126203i
$498$		0			0
$499$	219.429	−	184.123i	0.439738	−	0.368984i	−0.395873	−	0.918305i	$-0.629558\pi$
$499$	219.429	−	184.123i	0.439738	−	0.368984i	0.835611	+	0.549321i	$0.185114\pi$
$500$		0			0
$501$	−542.384	+	531.455i	−1.08260	+	1.06079i
$502$		0			0
$503$	369.781	−	213.493i	0.735150	−	0.424439i	−0.0851531	−	0.996368i	$-0.527138\pi$
$503$	369.781	−	213.493i	0.735150	−	0.424439i	0.820303	+	0.571929i	$0.193805\pi$
$504$		0			0
$505$	448.669	−	777.118i	0.888454	−	1.53885i
$506$		0			0
$507$	177.534	−	248.132i	0.350166	−	0.489412i
$508$		0			0
$509$	699.518	−	123.344i	1.37430	−	0.242326i	0.562758	−	0.826622i	$-0.309740\pi$
$509$	699.518	−	123.344i	1.37430	−	0.242326i	0.811541	+	0.584296i	$0.198629\pi$
$510$		0			0
$511$	204.831	+	171.873i	0.400843	+	0.336347i
$512$		0			0
$513$	370.981	+	111.648i	0.723159	+	0.217638i
$514$		0			0
$515$	215.899	−	257.298i	0.419221	−	0.499608i
$516$		0			0
$517$	−33.8647	−	192.056i	−0.0655024	−	0.371483i
$518$		0			0
$519$	13.2100	−	135.136i	0.0254529	−	0.260378i
$520$		0			0
$521$	−391.760	−	226.183i	−0.751939	−	0.434132i	0.0744554	−	0.997224i	$-0.476278\pi$
$521$	−391.760	−	226.183i	−0.751939	−	0.434132i	−0.826394	+	0.563092i	$0.809612\pi$
$522$		0			0
$523$	−53.9338	−	93.4160i	−0.103124	−	0.178616i	0.809846	−	0.586642i	$-0.199550\pi$
$523$	−53.9338	−	93.4160i	−0.103124	−	0.178616i	−0.912970	+	0.408026i	$0.866217\pi$
$524$		0			0
$525$	45.0346	−	11.5771i	0.0857802	−	0.0220515i
$526$		0			0
$527$	−405.341	−	483.066i	−0.769147	−	0.916634i
$528$		0			0
$529$	71.5545	−	26.0437i	0.135264	−	0.0492320i
$530$		0			0
$531$	−760.255	+	259.312i	−1.43174	+	0.488346i
$532$		0			0
$533$	−378.995	−	66.8271i	−0.711061	−	0.125379i
$534$		0			0
$535$	202.037	+	73.5354i	0.377639	+	0.137449i
$536$		0			0
$537$	1011.38	−	78.1208i	1.88339	−	0.145476i
$538$		0			0
$539$			693.649i			1.28692i
$540$		0			0
$541$	−38.7755			−0.0716738			−0.0358369	−	0.999358i	$-0.511410\pi$
$541$	−38.7755			−0.0716738			−0.0358369	+	0.999358i	$0.511410\pi$
$542$		0			0
$543$	−217.970	+	149.342i	−0.401418	+	0.275030i
$544$		0			0
$545$	8.88890	−	24.4220i	0.0163099	−	0.0448111i
$546$		0			0
$547$	92.2064	−	522.928i	0.168567	−	0.955994i	−0.776742	−	0.629819i	$-0.783129\pi$
$547$	92.2064	−	522.928i	0.168567	−	0.955994i	0.945310	−	0.326175i	$-0.105760\pi$
$548$		0			0
$549$	−320.644	+	176.521i	−0.584051	+	0.321532i
$550$		0			0
$551$	−152.799	−	419.811i	−0.277311	−	0.761907i
$552$		0			0
$553$	943.576	−	791.754i	1.70629	−	1.43174i
$554$		0			0
$555$	10.2682	+	2.86369i	0.0185013	+	0.00515980i
$556$		0			0
$557$	−324.141	+	187.143i	−0.581942	+	0.335984i	−0.761905	−	0.647689i	$-0.775736\pi$
$557$	−324.141	+	187.143i	−0.581942	+	0.335984i	0.179963	+	0.983673i	$0.442402\pi$
$558$		0			0
$559$	−305.503	+	529.147i	−0.546518	+	0.946596i
$560$		0			0
$561$	−197.637	−	435.348i	−0.352294	−	0.776021i
$562$		0			0
$563$	544.864	−	96.0742i	0.967787	−	0.170647i	0.332653	−	0.943049i	$-0.392056\pi$
$563$	544.864	−	96.0742i	0.967787	−	0.170647i	0.635134	+	0.772402i	$0.280945\pi$
$564$		0			0
$565$	−219.255	−	183.977i	−0.388062	−	0.325623i
$566$		0			0
$567$	−727.553	−	298.874i	−1.28316	−	0.527114i
$568$		0			0
$569$	109.394	−	130.371i	0.192257	−	0.229123i	−0.661301	−	0.750120i	$-0.729995\pi$
$569$	109.394	−	130.371i	0.192257	−	0.229123i	0.853558	+	0.520997i	$0.174440\pi$
$570$		0			0
$571$	144.904	+	821.794i	0.253773	+	1.43922i	0.799202	+	0.601062i	$0.205256\pi$
$571$	144.904	+	821.794i	0.253773	+	1.43922i	−0.545429	+	0.838157i	$0.683633\pi$
$572$		0			0
$573$	311.445	−	141.388i	0.543534	−	0.246751i
$574$		0			0
$575$	34.0049	+	19.6327i	0.0591389	+	0.0341439i
$576$		0			0
$577$	312.331	+	540.973i	0.541301	+	0.937561i	0.998830	+	0.0483663i	$0.0154015\pi$
$577$	312.331	+	540.973i	0.541301	+	0.937561i	−0.457528	+	0.889195i	$0.651265\pi$
$578$		0			0
$579$	−133.527	+	478.786i	−0.230617	+	0.826918i
$580$		0			0
$581$	83.7055	+	99.7564i	0.144071	+	0.171698i
$582$		0			0
$583$	525.471	−	191.256i	0.901323	−	0.328055i
$584$		0			0
$585$	−184.850	+	305.630i	−0.315984	+	0.522445i
$586$		0			0
$587$	−594.734	−	104.868i	−1.01318	−	0.178650i	−0.357676	−	0.933846i	$-0.616431\pi$
$587$	−594.734	−	104.868i	−1.01318	−	0.178650i	−0.655500	+	0.755195i	$0.727542\pi$
$588$		0			0
$589$	−817.059	−	297.385i	−1.38720	−	0.504898i
$590$		0			0
$591$	288.114	+	420.515i	0.487503	+	0.711531i
$592$		0			0
$593$			167.598i			0.282628i	0.989965	+	0.141314i	$0.0451327\pi$
$593$			167.598i			0.282628i	−0.989965	+	0.141314i	$0.954867\pi$
$594$		0			0
$595$	−488.859			−0.821613
$596$		0			0
$597$	−66.5228	−	861.227i	−0.111428	−	1.44259i
$598$		0			0
$599$	191.447	−	525.998i	0.319612	−	0.878126i	−0.671004	−	0.741453i	$-0.734137\pi$
$599$	191.447	−	525.998i	0.319612	−	0.878126i	0.990616	−	0.136673i	$-0.0436409\pi$
$600$		0			0
$601$	−157.626	+	893.940i	−0.262273	+	1.48742i	0.514418	+	0.857539i	$0.328008\pi$
$601$	−157.626	+	893.940i	−0.262273	+	1.48742i	−0.776691	+	0.629882i	$0.783103\pi$
$602$		0			0
$603$	−710.148	−	140.179i	−1.17769	−	0.232469i
$604$		0			0
$605$	187.859	+	516.138i	0.310510	+	0.853120i
$606$		0			0
$607$	−269.576	+	226.201i	−0.444112	+	0.372654i	−0.837246	−	0.546827i	$-0.815835\pi$
$607$	−269.576	+	226.201i	−0.444112	+	0.372654i	0.393133	+	0.919481i	$0.371391\pi$
$608$		0			0
$609$	225.824	+	878.453i	0.370811	+	1.44245i
$610$		0			0
$611$	−90.4705	+	52.2332i	−0.148070	+	0.0854880i
$612$		0			0
$613$	−152.261	+	263.724i	−0.248387	+	0.430219i	−0.963078	−	0.269221i	$-0.913234\pi$
$613$	−152.261	+	263.724i	−0.248387	+	0.430219i	0.714691	+	0.699440i	$0.246567\pi$
$614$		0			0
$615$	−677.607	−	66.2385i	−1.10180	−	0.107705i
$616$		0			0
$617$	500.716	−	88.2897i	0.811533	−	0.143095i	0.247543	−	0.968877i	$-0.420377\pi$
$617$	500.716	−	88.2897i	0.811533	−	0.143095i	0.563990	+	0.825782i	$0.309266\pi$
$618$		0			0
$619$	52.3325	+	43.9122i	0.0845436	+	0.0709405i	0.684080	−	0.729407i	$-0.260204\pi$
$619$	52.3325	+	43.9122i	0.0845436	+	0.0709405i	−0.599536	+	0.800347i	$0.704648\pi$
$620$		0			0
$621$	−262.192	−	610.252i	−0.422210	−	0.982692i
$622$		0			0
$623$	1053.96	−	1256.07i	1.69176	−	2.01616i
$624$		0			0
$625$	−101.158	−	573.698i	−0.161853	−	0.917916i
$626$		0			0
$627$	−536.139	−	383.599i	−0.855086	−	0.611801i
$628$		0			0
$629$	6.61953	+	3.82179i	0.0105239	+	0.00607597i
$630$		0			0
$631$	−62.9443	−	109.023i	−0.0997533	−	0.172778i	0.811829	−	0.583895i	$-0.198472\pi$
$631$	−62.9443	−	109.023i	−0.0997533	−	0.172778i	−0.911582	+	0.411117i	$0.865139\pi$
$632$		0			0
$633$	373.563	+	381.245i	0.590146	+	0.602283i
$634$		0			0
$635$	−73.1494	−	87.1760i	−0.115196	−	0.137285i
$636$		0			0
$637$	349.160	−	127.084i	0.548132	−	0.199504i
$638$		0			0
$639$	−5.76912	−	2.23379i	−0.00902836	−	0.00349576i
$640$		0			0
$641$	525.113	+	92.5916i	0.819209	+	0.144449i	0.567520	−	0.823360i	$-0.307903\pi$
$641$	525.113	+	92.5916i	0.819209	+	0.144449i	0.251689	+	0.967808i	$0.419014\pi$
$642$		0			0
$643$	456.157	+	166.027i	0.709419	+	0.258207i	0.671427	−	0.741071i	$-0.265682\pi$
$643$	456.157	+	166.027i	0.709419	+	0.258207i	0.0379920	+	0.999278i	$0.487904\pi$
$644$		0			0
$645$	−466.777	+	974.975i	−0.723685	+	1.51159i
$646$		0			0
$647$			783.796i			1.21143i	0.795682	+	0.605715i	$0.207113\pi$
$647$			783.796i			1.21143i	−0.795682	+	0.605715i	$0.792887\pi$
$648$		0			0
$649$	1366.85			2.10608
$650$		0			0
$651$	1592.21	+	762.285i	2.44580	+	1.17094i
$652$		0			0
$653$	116.572	−	320.280i	0.178518	−	0.490475i	−0.817869	−	0.575405i	$-0.804845\pi$
$653$	116.572	−	320.280i	0.178518	−	0.490475i	0.996387	+	0.0849302i	$0.0270667\pi$
$654$		0			0
$655$	−83.8602	+	475.595i	−0.128031	+	0.726099i
$656$		0			0
$657$	244.884	−	38.0577i	0.372731	−	0.0579265i
$658$		0			0
$659$	182.181	+	500.537i	0.276450	+	0.759540i	0.997758	+	0.0669256i	$0.0213190\pi$
$659$	182.181	+	500.537i	0.276450	+	0.759540i	−0.721308	+	0.692614i	$0.756459\pi$
$660$		0			0
$661$	−130.190	+	109.242i	−0.196959	+	0.165268i	−0.735933	−	0.677054i	$-0.763256\pi$
$661$	−130.190	+	109.242i	−0.196959	+	0.165268i	0.538974	+	0.842322i	$0.318812\pi$
$662$		0			0
$663$	−182.931	+	179.244i	−0.275913	+	0.270353i
$664$		0			0
$665$	−583.753	+	337.030i	−0.877825	+	0.506812i
$666$		0			0
$667$	−382.960	+	663.306i	−0.574153	+	0.994462i
$668$		0			0
$669$	257.281	−	359.590i	0.384576	−	0.537504i
$670$		0			0
$671$	613.369	−	108.153i	0.914112	−	0.161183i
$672$		0			0
$673$	−668.840	−	561.224i	−0.993819	−	0.833913i	−0.00770313	−	0.999970i	$-0.502452\pi$
$673$	−668.840	−	561.224i	−0.993819	−	0.833913i	−0.986116	+	0.166057i	$0.946896\pi$
$674$		0			0
$675$	19.3974	−	38.4847i	0.0287368	−	0.0570143i
$676$		0			0
$677$	−18.4136	+	21.9445i	−0.0271989	+	0.0324144i	−0.779472	−	0.626437i	$-0.784513\pi$
$677$	−18.4136	+	21.9445i	−0.0271989	+	0.0324144i	0.752274	+	0.658851i	$0.228957\pi$
$678$		0			0
$679$	−108.071	−	612.903i	−0.159162	−	0.902655i
$680$		0			0
$681$	92.6859	−	948.158i	0.136103	−	1.39230i
$682$		0			0
$683$	547.126	+	315.884i	0.801063	+	0.462494i	0.843843	−	0.536590i	$-0.180288\pi$
$683$	547.126	+	315.884i	0.801063	+	0.462494i	−0.0427795	+	0.999085i	$0.513621\pi$
$684$		0			0
$685$	110.633	+	191.622i	0.161508	+	0.279740i
$686$		0			0
$687$	−272.394	+	70.0242i	−0.396497	+	0.101928i
$688$		0			0
$689$	−192.544	−	229.465i	−0.279454	−	0.333040i
$690$		0			0
$691$	−209.825	+	76.3702i	−0.303655	+	0.110521i	−0.489354	−	0.872085i	$-0.662767\pi$
$691$	−209.825	+	76.3702i	−0.303655	+	0.110521i	0.185699	+	0.982607i	$0.440545\pi$
$692$		0			0
$693$	1007.56	+	881.002i	1.45391	+	1.27129i
$694$		0			0
$695$	465.333	+	82.0507i	0.669544	+	0.118059i
$696$		0			0
$697$	−458.737	−	166.967i	−0.658160	−	0.239551i
$698$		0			0
$699$	685.144	−	52.9219i	0.980178	−	0.0757108i
$700$		0			0
$701$		−	489.886i		−	0.698839i	−0.936966	−	0.349419i	$-0.886379\pi$
$701$		−	489.886i		−	0.698839i	0.936966	−	0.349419i	$-0.113621\pi$
$702$		0			0
$703$	10.5393			0.0149919
$704$		0			0
$705$	−152.462	+	104.459i	−0.216259	+	0.148169i
$706$		0			0
$707$	−616.035	+	1692.54i	−0.871336	+	2.39398i
$708$		0			0
$709$	−170.312	+	965.890i	−0.240215	+	1.36233i	0.591133	+	0.806574i	$0.298681\pi$
$709$	−170.312	+	965.890i	−0.240215	+	1.36233i	−0.831348	+	0.555752i	$0.812430\pi$
$710$		0			0
$711$	23.2365	−	1141.39i	0.0326814	−	1.60533i
$712$		0			0
$713$	509.841	+	1400.78i	0.715064	+	1.96462i
$714$		0			0
$715$	465.594	−	390.680i	0.651180	−	0.546405i
$716$		0			0
$717$	−1165.92	−	325.161i	−1.62611	−	0.453502i
$718$		0			0
$719$	372.521	−	215.075i	0.518110	−	0.299131i	−0.218051	−	0.975937i	$-0.569970\pi$
$719$	372.521	−	215.075i	0.518110	−	0.299131i	0.736161	+	0.676807i	$0.236637\pi$
$720$		0			0
$721$	−337.093	+	583.863i	−0.467536	+	0.809796i
$722$		0			0
$723$	−173.766	−	382.764i	−0.240340	−	0.529411i
$724$		0			0
$725$	−48.9423	+	8.62986i	−0.0675067	+	0.0119032i
$726$		0			0
$727$	−264.636	−	222.056i	−0.364011	−	0.305442i	0.442376	−	0.896830i	$-0.354136\pi$
$727$	−264.636	−	222.056i	−0.364011	−	0.305442i	−0.806387	+	0.591388i	$0.798580\pi$
$728$		0			0
$729$	−652.400	+	325.292i	−0.894925	+	0.446216i
$730$		0			0
$731$	−498.206	+	593.739i	−0.681541	+	0.812229i
$732$		0			0
$733$	−29.8989	−	169.565i	−0.0407898	−	0.231331i	0.957597	−	0.288112i	$-0.0930274\pi$
$733$	−29.8989	−	169.565i	−0.0407898	−	0.231331i	−0.998387	+	0.0567810i	$0.981916\pi$
$734$		0			0
$735$	598.561	−	271.732i	0.814369	−	0.369703i
$736$		0			0
$737$	1066.70	+	615.860i	1.44736	+	0.835631i
$738$		0			0
$739$	−10.3839	−	17.9855i	−0.0140513	−	0.0243376i	0.858914	−	0.512119i	$-0.171139\pi$
$739$	−10.3839	−	17.9855i	−0.0140513	−	0.0243376i	−0.872966	+	0.487782i	$0.837806\pi$
$740$		0			0
$741$	−94.8648	+	340.154i	−0.128023	+	0.459048i
$742$		0			0
$743$	−268.303	−	319.751i	−0.361108	−	0.430352i	0.554649	−	0.832084i	$-0.312853\pi$
$743$	−268.303	−	319.751i	−0.361108	−	0.430352i	−0.915757	+	0.401733i	$0.868408\pi$
$744$		0			0
$745$	−818.661	+	297.968i	−1.09887	+	0.399957i
$746$		0			0
$747$	120.670	+	2.45660i	0.161539	+	0.00328862i
$748$		0			0
$749$	−425.004	−	74.9398i	−0.567429	−	0.100053i
$750$		0			0
$751$	641.259	+	233.399i	0.853874	+	0.310785i	0.731619	−	0.681714i	$-0.238765\pi$
$751$	641.259	+	233.399i	0.853874	+	0.310785i	0.122255	+	0.992499i	$0.460987\pi$
$752$		0			0
$753$	−371.464	−	542.167i	−0.493312	−	0.720010i
$754$		0			0
$755$			269.381i			0.356797i
$756$		0			0
$757$	−127.228			−0.168069			−0.0840346	−	0.996463i	$-0.526781\pi$
$757$	−127.228			−0.168069			−0.0840346	+	0.996463i	$0.526781\pi$
$758$		0			0
$759$	87.0399	+	1126.85i	0.114677	+	1.48465i
$760$		0			0
$761$	221.043	−	607.312i	0.290464	−	0.798045i	−0.705534	−	0.708676i	$-0.749293\pi$
$761$	221.043	−	607.312i	0.290464	−	0.798045i	0.995999	−	0.0893686i	$-0.0284849\pi$
$762$		0			0
$763$	−9.05865	+	51.3742i	−0.0118724	+	0.0673318i
$764$		0			0
$765$	−298.246	+	341.089i	−0.389864	+	0.445867i
$766$		0			0
$767$	−250.421	−	688.027i	−0.326494	−	0.897036i
$768$		0			0
$769$	−313.457	+	263.022i	−0.407616	+	0.342031i	−0.823429	−	0.567420i	$-0.807942\pi$
$769$	−313.457	+	263.022i	−0.407616	+	0.342031i	0.415812	+	0.909450i	$0.363497\pi$
$770$		0			0
$771$	67.1170	+	261.084i	0.0870519	+	0.338631i
$772$		0			0
$773$	−492.676	+	284.447i	−0.637356	+	0.367978i	−0.783595	−	0.621272i	$-0.786616\pi$
$773$	−492.676	+	284.447i	−0.637356	+	0.367978i	0.146239	+	0.989249i	$0.453283\pi$
$774$		0			0
$775$	−48.3619	+	83.7652i	−0.0624024	+	0.108084i
$776$		0			0
$777$	−21.2958	−	2.08174i	−0.0274077	−	0.00267920i
$778$		0			0
$779$	−662.895	+	116.886i	−0.850956	+	0.150046i
$780$		0			0
$781$	8.06419	+	6.76666i	0.0103255	+	0.00866410i
$782$		0			0
$783$	750.689	+	378.369i	0.958734	+	0.483229i
$784$		0			0
$785$	−2.43953	+	2.90732i	−0.00310768	+	0.00370359i
$786$		0			0
$787$	−144.258	−	818.127i	−0.183301	−	1.03955i	−0.928119	−	0.372284i	$-0.878575\pi$
$787$	−144.258	−	818.127i	−0.183301	−	1.03955i	0.744818	−	0.667268i	$-0.232536\pi$
$788$		0			0
$789$	−393.974	−	281.882i	−0.499333	−	0.357265i
$790$		0			0
$791$	497.535	+	287.252i	0.628994	+	0.363150i
$792$		0			0
$793$	−166.817	−	288.935i	−0.210361	−	0.364357i
$794$		0			0
$795$	−370.887	−	378.515i	−0.466525	−	0.476119i
$796$		0			0
$797$	513.681	+	612.181i	0.644518	+	0.768107i	0.985077	−	0.172116i	$-0.0550605\pi$
$797$	513.681	+	612.181i	0.644518	+	0.768107i	−0.340558	+	0.940223i	$0.610616\pi$
$798$		0			0
$799$	−124.525	+	45.3235i	−0.155852	+	0.0567253i
$800$		0			0
$801$	−233.378	−	1501.68i	−0.291358	−	1.87476i
$802$		0			0
$803$	−415.296	−	73.2278i	−0.517180	−	0.0911928i
$804$		0			0
$805$	1085.93	+	395.245i	1.34898	+	0.490987i
$806$		0			0
$807$	454.063	−	948.419i	0.562656	−	1.17524i
$808$		0			0
$809$		−	848.662i		−	1.04903i	−0.851403	−	0.524513i	$-0.824247\pi$
$809$		−	848.662i		−	1.04903i	0.851403	−	0.524513i	$-0.175753\pi$
$810$		0			0
$811$	571.138			0.704240			0.352120	−	0.935955i	$-0.385461\pi$
$811$	571.138			0.704240			0.352120	+	0.935955i	$0.385461\pi$
$812$		0			0
$813$	−164.129	−	78.5781i	−0.201881	−	0.0966520i
$814$		0			0
$815$	−483.552	+	1328.55i	−0.593315	+	1.63012i
$816$		0			0
$817$	−185.578	+	1052.47i	−0.227146	+	1.28821i
$818$		0			0
$819$	258.872	−	668.580i	0.316083	−	0.816337i
$820$		0			0
$821$	−176.355	−	484.532i	−0.214805	−	0.590173i	0.784756	−	0.619805i	$-0.212788\pi$
$821$	−176.355	−	484.532i	−0.214805	−	0.590173i	−0.999561	+	0.0296327i	$0.990566\pi$
$822$		0			0
$823$	−1140.75	+	957.205i	−1.38609	+	1.16307i	−0.419194	+	0.907897i	$0.637687\pi$
$823$	−1140.75	+	957.205i	−1.38609	+	1.16307i	−0.966896	+	0.255171i	$0.917868\pi$
$824$		0			0
$825$	−52.3802	+	51.3247i	−0.0634912	+	0.0622118i
$826$		0			0
$827$	1296.29	−	748.416i	1.56747	−	0.904977i	0.571003	−	0.820948i	$-0.306554\pi$
$827$	1296.29	−	748.416i	1.56747	−	0.904977i	0.996463	−	0.0840296i	$-0.0267790\pi$
$828$		0			0
$829$	−393.694	+	681.898i	−0.474902	+	0.822555i	−0.999587	−	0.0287417i	$-0.990850\pi$
$829$	−393.694	+	681.898i	−0.474902	+	0.822555i	0.524684	+	0.851297i	$0.324183\pi$
$830$		0			0
$831$	−712.926	+	996.424i	−0.857913	+	1.19907i
$832$		0			0
$833$	464.179	−	81.8474i	0.557238	−	0.0982561i
$834$		0			0
$835$	−938.043	−	787.112i	−1.12341	−	0.942649i
$836$		0			0
$837$	1503.25	−	645.866i	1.79600	−	0.771644i
$838$		0			0
$839$	−679.426	+	809.709i	−0.809805	+	0.965088i	−0.999861	−	0.0166853i	$-0.994689\pi$
$839$	−679.426	+	809.709i	−0.809805	+	0.965088i	0.190056	+	0.981773i	$0.439133\pi$
$840$		0			0
$841$	−22.2975	−	126.455i	−0.0265130	−	0.150363i
$842$		0			0
$843$	1.38462	−	14.1644i	0.00164249	−	0.0168023i
$844$		0			0
$845$	426.088	+	246.002i	0.504246	+	0.291127i
$846$		0			0
$847$	−551.248	−	954.790i	−0.650824	−	1.12726i
$848$		0			0
$849$	−253.291	+	65.1136i	−0.298341	+	0.0766945i
$850$		0			0
$851$	−11.6143	−	13.8414i	−0.0136479	−	0.0162649i
$852$		0			0
$853$	1201.29	−	437.233i	1.40831	−	0.512583i	0.477676	−	0.878536i	$-0.341479\pi$
$853$	1201.29	−	437.233i	1.40831	−	0.512583i	0.930633	+	0.365953i	$0.119257\pi$
$854$		0			0
$855$	−120.986	+	612.915i	−0.141504	+	0.716860i
$856$		0			0
$857$	1252.41	+	220.834i	1.46139	+	0.257682i	0.847115	−	0.531410i	$-0.178338\pi$
$857$	1252.41	+	220.834i	1.46139	+	0.257682i	0.614275	+	0.789092i	$0.289449\pi$
$858$		0			0
$859$	−1386.42	−	504.615i	−1.61399	−	0.587445i	−0.631767	−	0.775158i	$-0.717670\pi$
$859$	−1386.42	−	504.615i	−1.61399	−	0.587445i	−0.982224	+	0.187714i	$0.939892\pi$
$860$		0			0
$861$	1362.54	−	105.245i	1.58250	−	0.122236i
$862$		0			0
$863$			1077.10i			1.24809i	0.781388	+	0.624045i	$0.214512\pi$
$863$			1077.10i			1.24809i	−0.781388	+	0.624045i	$0.785488\pi$
$864$		0			0
$865$	218.957			0.253129
$866$		0			0
$867$	447.221	−	306.412i	0.515826	−	0.353417i
$868$		0			0
$869$	−664.415	+	1825.47i	−0.764574	+	2.10065i
$870$		0			0
$871$	114.573	−	649.775i	0.131542	−	0.746010i
$872$		0			0
$873$	−493.569	−	298.519i	−0.565371	−	0.341946i
$874$		0			0
$875$	427.322	+	1174.06i	0.488367	+	1.34178i
$876$		0			0
$877$	−391.739	+	328.708i	−0.446681	+	0.374810i	−0.838202	−	0.545359i	$-0.816393\pi$
$877$	−391.739	+	328.708i	−0.446681	+	0.374810i	0.391522	+	0.920169i	$0.371949\pi$
$878$		0			0
$879$	746.053	+	208.065i	0.848752	+	0.236706i
$880$		0			0
$881$	483.529	−	279.166i	0.548842	−	0.316874i	−0.199813	−	0.979834i	$-0.564033\pi$
$881$	483.529	−	279.166i	0.548842	−	0.316874i	0.748655	+	0.662960i	$0.230700\pi$
$882$		0			0
$883$	−485.687	+	841.235i	−0.550042	+	0.952701i	0.448229	+	0.893919i	$0.352055\pi$
$883$	−485.687	+	841.235i	−0.550042	+	0.952701i	−0.998271	+	0.0587818i	$0.981278\pi$
$884$		0			0
$885$	−535.453	−	1179.48i	−0.605031	−	1.33274i
$886$		0			0
$887$	402.172	−	70.9138i	0.453407	−	0.0799479i	0.0577191	−	0.998333i	$-0.481617\pi$
$887$	402.172	−	70.9138i	0.453407	−	0.0799479i	0.395688	+	0.918385i	$0.370506\pi$
$888$		0			0
$889$	174.982	+	146.828i	0.196831	+	0.165160i
$890$		0			0
$891$	1229.39	−	165.509i	1.37979	−	0.185757i
$892$		0			0
$893$	−117.450	+	139.972i	−0.131523	+	0.156743i
$894$		0			0
$895$	284.052	+	1610.94i	0.317376	+	1.79993i
$896$		0			0
$897$	551.272	−	250.264i	0.614573	−	0.279001i
$898$		0			0
$899$	−1633.94	−	943.356i	−1.81751	−	1.04934i
$900$		0			0
$901$	−189.989	−	329.070i	−0.210864	−	0.365227i
$902$		0			0
$903$	582.865	−	2089.96i	0.645476	−	2.31447i
$904$		0			0
$905$	−273.880	−	326.398i	−0.302630	−	0.360660i
$906$		0			0
$907$	290.446	−	105.714i	0.320228	−	0.116553i	−0.176905	−	0.984228i	$-0.556609\pi$
$907$	290.446	−	105.714i	0.320228	−	0.116553i	0.497133	+	0.867675i	$0.334386\pi$
$908$		0			0
$909$	805.092	+	1462.42i	0.885689	+	1.60882i
$910$		0			0
$911$	428.590	+	75.5720i	0.470461	+	0.0829550i	0.403852	−	0.914824i	$-0.367671\pi$
$911$	428.590	+	75.5720i	0.470461	+	0.0829550i	0.0666089	+	0.997779i	$0.478782\pi$
$912$		0			0
$913$	−192.991	−	70.2430i	−0.211381	−	0.0769365i
$914$		0			0
$915$	−333.610	−	486.918i	−0.364601	−	0.532151i
$916$		0			0
$917$		−	969.354i		−	1.05709i
$918$		0			0
$919$	−784.590			−0.853743			−0.426871	−	0.904312i	$-0.640384\pi$
$919$	−784.590			−0.853743			−0.426871	+	0.904312i	$0.640384\pi$
$920$		0			0
$921$	87.4477	+	1132.13i	0.0949486	+	1.22924i
$922$		0			0
$923$	1.92867	−	5.29897i	0.00208956	−	0.00574103i
$924$		0			0
$925$	0.203586	−	1.15459i	0.000220093	−	0.00124821i
$926$		0			0
$927$	201.719	+	591.404i	0.217604	+	0.637976i
$928$		0			0
$929$	−454.441	−	1248.57i	−0.489172	−	1.34399i	−0.901431	−	0.432923i	$-0.857482\pi$
$929$	−454.441	−	1248.57i	−0.489172	−	1.34399i	0.412259	−	0.911067i	$-0.364740\pi$
$930$		0			0
$931$	497.855	−	417.750i	0.534753	−	0.448711i
$932$		0			0
$933$	202.916	+	789.342i	0.217488	+	0.846026i
$934$		0			0
$935$	667.697	−	385.495i	0.714115	−	0.412294i
$936$		0			0
$937$	−100.627	+	174.291i	−0.107392	+	0.186009i	−0.914713	−	0.404104i	$-0.867583\pi$
$937$	−100.627	+	174.291i	−0.107392	+	0.186009i	0.807321	+	0.590113i	$0.200917\pi$
$938$		0			0
$939$	−1216.47	−	118.915i	−1.29550	−	0.126640i
$940$		0			0
$941$	1253.67	−	221.056i	1.33228	−	0.234916i	0.538243	−	0.842790i	$-0.319088\pi$
$941$	1253.67	−	221.056i	1.33228	−	0.234916i	0.794034	+	0.607873i	$0.207977\pi$
$942$		0			0
$943$	884.021	+	741.781i	0.937456	+	0.786619i
$944$		0			0
$945$	365.528	−	1214.56i	0.386802	−	1.28525i
$946$		0			0
$947$	99.6925	−	118.809i	0.105272	−	0.125458i	−0.710836	−	0.703358i	$-0.751683\pi$
$947$	99.6925	−	118.809i	0.105272	−	0.125458i	0.816108	+	0.577900i	$0.196128\pi$
$948$		0			0
$949$	39.2261	+	222.462i	0.0413341	+	0.234418i
$950$		0			0
$951$	584.963	+	418.532i	0.615103	+	0.440096i
$952$		0			0
$953$	1150.65	+	664.330i	1.20740	+	0.697094i	0.962191	−	0.272376i	$-0.0878094\pi$
$953$	1150.65	+	664.330i	1.20740	+	0.697094i	0.245211	+	0.969470i	$0.421143\pi$
$954$		0			0
$955$	275.781	+	477.666i	0.288775	+	0.500174i
$956$		0			0
$957$	−1001.15	−	1021.74i	−1.04613	−	1.06765i
$958$		0			0
$959$	−285.482	−	340.224i	−0.297687	−	0.354770i
$960$		0			0
$961$	−2547.53	+	927.224i	−2.65091	+	0.964853i
$962$		0			0
$963$	−311.576	+	250.816i	−0.323547	+	0.260453i
$964$		0			0
$965$	−789.368	−	139.187i	−0.817998	−	0.144235i
$966$		0			0
$967$	−254.164	−	92.5081i	−0.262837	−	0.0956650i	0.207240	−	0.978290i	$-0.433552\pi$
$967$	−254.164	−	92.5081i	−0.262837	−	0.0956650i	−0.470078	+	0.882625i	$0.655774\pi$
$968$		0			0
$969$	−193.437	+	404.039i	−0.199625	+	0.416965i
$970$		0			0
$971$		−	753.072i		−	0.775564i	−0.921751	−	0.387782i	$-0.873241\pi$
$971$		−	753.072i		−	0.775564i	0.921751	−	0.387782i	$-0.126759\pi$
$972$		0			0
$973$	−948.439			−0.974757
$974$		0			0
$975$	35.4318	+	16.9633i	0.0363403	+	0.0173982i
$976$		0			0
$977$	−406.873	+	1117.87i	−0.416451	+	1.14419i	0.537247	+	0.843425i	$0.319464\pi$
$977$	−406.873	+	1117.87i	−0.416451	+	1.14419i	−0.953698	+	0.300765i	$0.902758\pi$
$978$		0			0
$979$	−449.049	+	2546.68i	−0.458681	+	2.60131i
$980$		0			0
$981$	30.3184	+	37.6630i	0.0309056	+	0.0383925i
$982$		0			0
$983$	−204.955	−	563.108i	−0.208499	−	0.572847i	0.790727	−	0.612168i	$-0.209703\pi$
$983$	−204.955	−	563.108i	−0.208499	−	0.572847i	−0.999227	+	0.0393216i	$0.987480\pi$
$984$		0			0
$985$	−629.697	+	528.378i	−0.639286	+	0.536425i
$986$		0			0
$987$	264.969	−	259.629i	0.268458	−	0.263049i
$988$		0			0
$989$	1586.73	−	916.098i	1.60438	−	0.926287i
$990$		0			0
$991$	483.546	−	837.525i	0.487937	−	0.845132i	−0.511967	−	0.859005i	$-0.671083\pi$
$991$	483.546	−	837.525i	0.487937	−	0.845132i	0.999904	+	0.0138736i	$0.00441625\pi$
$992$		0			0
$993$	−341.046	+	476.665i	−0.343450	+	0.480025i
$994$		0			0
$995$	1371.77	−	241.881i	1.37867	−	0.243096i
$996$		0			0
$997$	929.710	+	780.119i	0.932507	+	0.782467i	0.976266	−	0.216575i	$-0.0694887\pi$
$997$	929.710	+	780.119i	0.932507	+	0.782467i	−0.0437584	+	0.999042i	$0.513933\pi$
$998$		0			0
$999$	−14.4447	+	13.5885i	−0.0144592	+	0.0136021i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.bc.b.65.2		36
4.3	odd	2		108.3.k.a.65.5	yes	36
12.11	even	2		324.3.k.a.197.1		36
27.5	odd	18	inner	432.3.bc.b.113.2		36
108.7	odd	18		2916.3.c.b.1457.29		36
108.47	even	18		2916.3.c.b.1457.8		36
108.59	even	18		108.3.k.a.5.5	✓	36
108.103	odd	18		324.3.k.a.125.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.5.5	✓	36	108.59	even	18
108.3.k.a.65.5	yes	36	4.3	odd	2
324.3.k.a.125.1		36	108.103	odd	18
324.3.k.a.197.1		36	12.11	even	2
432.3.bc.b.65.2		36	1.1	even	1	trivial
432.3.bc.b.113.2		36	27.5	odd	18	inner
2916.3.c.b.1457.8		36	108.47	even	18
2916.3.c.b.1457.29		36	108.7	odd	18

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.bc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.70588 - 1.29546i) q^{3} +(1.65461 - 4.54600i) q^{5} +(-1.68621 + 9.56295i) q^{7} +(5.64356 + 7.01072i) q^{9} +O(q^{10})\)	\(q+(-2.70588 - 1.29546i) q^{3} +(1.65461 - 4.54600i) q^{5} +(-1.68621 + 9.56295i) q^{7} +(5.64356 + 7.01072i) q^{9} +(-5.23790 - 14.3910i) q^{11} +(-6.28432 + 5.27317i) q^{13} +(-10.3663 + 10.1574i) q^{15} +(-9.01220 + 5.20319i) q^{17} +(-7.17439 + 12.4264i) q^{19} +(16.9511 - 23.6918i) q^{21} +(24.2260 - 4.27170i) q^{23} +(1.22274 + 1.02600i) q^{25} +(-6.18868 - 26.2812i) q^{27} +(-20.0134 + 23.8510i) q^{29} +(10.5226 + 59.6766i) q^{31} +(-4.46987 + 45.7258i) q^{33} +(40.6832 + 23.4884i) q^{35} +(-0.367254 - 0.636102i) q^{37} +(23.8358 - 6.12747i) q^{39} +(30.1540 + 35.9362i) q^{41} +(69.9886 - 25.4738i) q^{43} +(41.2086 - 14.0556i) q^{45} +(12.5408 + 2.21127i) q^{47} +(-42.5618 - 15.4912i) q^{49} +(31.1265 - 2.40427i) q^{51} +36.5138i q^{53} -74.0882 q^{55} +(35.5110 - 24.3302i) q^{57} +(-30.5258 + 83.8689i) q^{59} +(-7.06212 + 40.0513i) q^{61} +(-76.5594 + 42.1476i) q^{63} +(13.5737 + 37.2935i) q^{65} +(-61.6114 + 51.6981i) q^{67} +(-71.0865 - 19.8251i) q^{69} +(-0.595295 + 0.343694i) q^{71} +(13.7680 - 23.8468i) q^{73} +(-1.97944 - 4.36025i) q^{75} +(146.453 - 25.8236i) q^{77} +(-97.1709 - 81.5361i) q^{79} +(-17.3004 + 79.1309i) q^{81} +(8.62013 - 10.2731i) q^{83} +(8.74206 + 49.5787i) q^{85} +(85.0518 - 38.6114i) q^{87} +(-146.234 - 84.4283i) q^{89} +(-39.8304 - 68.9883i) q^{91} +(48.8358 - 175.109i) q^{93} +(44.6196 + 53.1756i) q^{95} +(-60.2262 + 21.9205i) q^{97} +(71.3309 - 117.938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q - 9 * q^5 + 6 * q^9	\( 36 q - 9 q^{5} + 6 q^{9} - 36 q^{11} - 45 q^{15} + 42 q^{21} + 18 q^{23} - 9 q^{25} - 18 q^{29} - 45 q^{31} - 153 q^{33} + 243 q^{35} + 123 q^{39} - 198 q^{41} - 90 q^{43} - 333 q^{45} + 243 q^{47} + 72 q^{49} + 99 q^{51} + 243 q^{57} - 252 q^{59} - 144 q^{61} - 381 q^{63} + 747 q^{65} - 108 q^{67} + 585 q^{69} - 324 q^{71} - 63 q^{73} - 597 q^{75} + 495 q^{77} - 36 q^{79} - 54 q^{81} + 27 q^{83} - 180 q^{85} + 441 q^{87} - 567 q^{89} - 99 q^{91} - 699 q^{93} + 1044 q^{95} - 216 q^{97} + 945 q^{99}+O(q^{100}) \) 36 * q - 9 * q^5 + 6 * q^9 - 36 * q^11 - 45 * q^15 + 42 * q^21 + 18 * q^23 - 9 * q^25 - 18 * q^29 - 45 * q^31 - 153 * q^33 + 243 * q^35 + 123 * q^39 - 198 * q^41 - 90 * q^43 - 333 * q^45 + 243 * q^47 + 72 * q^49 + 99 * q^51 + 243 * q^57 - 252 * q^59 - 144 * q^61 - 381 * q^63 + 747 * q^65 - 108 * q^67 + 585 * q^69 - 324 * q^71 - 63 * q^73 - 597 * q^75 + 495 * q^77 - 36 * q^79 - 54 * q^81 + 27 * q^83 - 180 * q^85 + 441 * q^87 - 567 * q^89 - 99 * q^91 - 699 * q^93 + 1044 * q^95 - 216 * q^97 + 945 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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