LMFDB - Embedded newform 432.3.bc.b.65.6

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			65.6
Character	$\chi$	$=$	432.65
Dual form			432.3.bc.b.113.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.92720 - 0.656882i) q^{3} +(0.740753 - 2.03520i) q^{5} +(-1.08248 + 6.13906i) q^{7} +(8.13701 - 3.84565i) q^{9} +O(q^{10})$	\(q+(2.92720 - 0.656882i) q^{3} +(0.740753 - 2.03520i) q^{5} +(-1.08248 + 6.13906i) q^{7} +(8.13701 - 3.84565i) q^{9} +(5.10694 + 14.0312i) q^{11} +(9.95988 - 8.35733i) q^{13} +(0.831446 - 6.44403i) q^{15} +(-3.36308 + 1.94167i) q^{17} +(-6.39866 + 11.0828i) q^{19} +(0.863993 + 18.6813i) q^{21} +(35.3663 - 6.23604i) q^{23} +(15.5578 + 13.0545i) q^{25} +(21.2925 - 16.6020i) q^{27} +(7.13197 - 8.49955i) q^{29} +(-6.25720 - 35.4864i) q^{31} +(24.1659 + 37.7175i) q^{33} +(11.6924 + 6.75059i) q^{35} +(-16.3431 - 28.3071i) q^{37} +(23.6648 - 31.0060i) q^{39} +(-14.5164 - 17.3000i) q^{41} +(-58.2594 + 21.2047i) q^{43} +(-1.79915 - 19.4091i) q^{45} +(3.36255 + 0.592908i) q^{47} +(9.52866 + 3.46815i) q^{49} +(-8.56895 + 7.89281i) q^{51} +79.3144i q^{53} +32.3393 q^{55} +(-11.4501 + 36.6448i) q^{57} +(-7.36318 + 20.2302i) q^{59} +(13.7025 - 77.7109i) q^{61} +(14.8005 + 54.1165i) q^{63} +(-9.63104 - 26.4611i) q^{65} +(84.5379 - 70.9357i) q^{67} +(99.4280 - 41.4856i) q^{69} +(-71.2183 + 41.1179i) q^{71} +(-3.09644 + 5.36320i) q^{73} +(54.1160 + 27.9936i) q^{75} +(-91.6666 + 16.1633i) q^{77} +(-49.2237 - 41.3036i) q^{79} +(51.4220 - 62.5842i) q^{81} +(-97.6080 + 116.325i) q^{83} +(1.46049 + 8.28284i) q^{85} +(15.2935 - 29.5648i) q^{87} +(97.5489 + 56.3199i) q^{89} +(40.5248 + 70.1909i) q^{91} +(-41.6264 - 99.7655i) q^{93} +(17.8159 + 21.2322i) q^{95} +(-52.0684 + 18.9513i) q^{97} +(95.5143 + 94.5326i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.92720	−	0.656882i	0.975734	−	0.218961i
$3$	2.92720	−	0.656882i	0.975734	−	0.218961i
$4$		0			0
$5$	0.740753	−	2.03520i	0.148151	−	0.407040i	−0.843313	−	0.537422i	$-0.819398\pi$
$5$	0.740753	−	2.03520i	0.148151	−	0.407040i	0.991464	+	0.130382i	$0.0416204\pi$
$6$		0			0
$7$	−1.08248	+	6.13906i	−0.154640	+	0.877008i	0.804474	+	0.593988i	$0.202447\pi$
$7$	−1.08248	+	6.13906i	−0.154640	+	0.877008i	−0.959114	+	0.283020i	$0.908664\pi$
$8$		0			0
$9$	8.13701	−	3.84565i	0.904113	−	0.427294i
$10$		0			0
$11$	5.10694	+	14.0312i	0.464267	+	1.27556i	0.922247	+	0.386601i	$0.126351\pi$
$11$	5.10694	+	14.0312i	0.464267	+	1.27556i	−0.457979	+	0.888963i	$0.651427\pi$
$12$		0			0
$13$	9.95988	−	8.35733i	0.766144	−	0.642871i	−0.173574	−	0.984821i	$-0.555532\pi$
$13$	9.95988	−	8.35733i	0.766144	−	0.642871i	0.939718	+	0.341949i	$0.111087\pi$
$14$		0			0
$15$	0.831446	−	6.44403i	0.0554297	−	0.429602i
$16$		0			0
$17$	−3.36308	+	1.94167i	−0.197828	+	0.114216i	−0.595642	−	0.803250i	$-0.703102\pi$
$17$	−3.36308	+	1.94167i	−0.197828	+	0.114216i	0.397814	+	0.917466i	$0.369769\pi$
$18$		0			0
$19$	−6.39866	+	11.0828i	−0.336772	+	0.583306i	−0.983824	−	0.179140i	$-0.942668\pi$
$19$	−6.39866	+	11.0828i	−0.336772	+	0.583306i	0.647052	+	0.762446i	$0.276002\pi$
$20$		0			0
$21$	0.863993	+	18.6813i	0.0411425	+	0.889587i
$22$		0			0
$23$	35.3663	−	6.23604i	1.53767	−	0.271132i	0.660318	−	0.750986i	$-0.270422\pi$
$23$	35.3663	−	6.23604i	1.53767	−	0.271132i	0.877348	+	0.479854i	$0.159310\pi$
$24$		0			0
$25$	15.5578	+	13.0545i	0.622311	+	0.522181i
$26$		0			0
$27$	21.2925	−	16.6020i	0.788613	−	0.614890i
$28$		0			0
$29$	7.13197	−	8.49955i	0.245930	−	0.293088i	−0.628932	−	0.777460i	$-0.716508\pi$
$29$	7.13197	−	8.49955i	0.245930	−	0.293088i	0.874862	+	0.484372i	$0.160952\pi$
$30$		0			0
$31$	−6.25720	−	35.4864i	−0.201845	−	1.14472i	−0.902327	−	0.431052i	$-0.858143\pi$
$31$	−6.25720	−	35.4864i	−0.201845	−	1.14472i	0.700482	−	0.713670i	$-0.252968\pi$
$32$		0			0
$33$	24.1659	+	37.7175i	0.732300	+	1.14295i
$34$		0			0
$35$	11.6924	+	6.75059i	0.334068	+	0.192874i
$36$		0			0
$37$	−16.3431	−	28.3071i	−0.441705	−	0.765056i	0.556111	−	0.831108i	$-0.312293\pi$
$37$	−16.3431	−	28.3071i	−0.441705	−	0.765056i	−0.997816	+	0.0660523i	$0.978960\pi$
$38$		0			0
$39$	23.6648	−	31.0060i	0.606789	−	0.795027i
$40$		0			0
$41$	−14.5164	−	17.3000i	−0.354059	−	0.421951i	0.559390	−	0.828905i	$-0.311036\pi$
$41$	−14.5164	−	17.3000i	−0.354059	−	0.421951i	−0.913449	+	0.406954i	$0.866591\pi$
$42$		0			0
$43$	−58.2594	+	21.2047i	−1.35487	+	0.493133i	−0.914465	−	0.404666i	$-0.867388\pi$
$43$	−58.2594	+	21.2047i	−1.35487	+	0.493133i	−0.440406	+	0.897799i	$0.645166\pi$
$44$		0			0
$45$	−1.79915	−	19.4091i	−0.0399812	−	0.431314i
$46$		0			0
$47$	3.36255	+	0.592908i	0.0715435	+	0.0126151i	0.209305	−	0.977850i	$-0.432880\pi$
$47$	3.36255	+	0.592908i	0.0715435	+	0.0126151i	−0.137762	+	0.990465i	$0.543991\pi$
$48$		0			0
$49$	9.52866	+	3.46815i	0.194462	+	0.0707785i
$50$		0			0
$51$	−8.56895	+	7.89281i	−0.168019	+	0.154761i
$52$		0			0
$53$			79.3144i			1.49650i	0.663418	+	0.748249i	$0.269105\pi$
$53$			79.3144i			1.49650i	−0.663418	+	0.748249i	$0.730895\pi$
$54$		0			0
$55$	32.3393			0.587987
$56$		0			0
$57$	−11.4501	+	36.6448i	−0.200879	+	0.642891i
$58$		0			0
$59$	−7.36318	+	20.2302i	−0.124800	+	0.342884i	−0.986321	−	0.164838i	$-0.947290\pi$
$59$	−7.36318	+	20.2302i	−0.124800	+	0.342884i	0.861521	+	0.507722i	$0.169512\pi$
$60$		0			0
$61$	13.7025	−	77.7109i	0.224632	−	1.27395i	−0.638757	−	0.769409i	$-0.720551\pi$
$61$	13.7025	−	77.7109i	0.224632	−	1.27395i	0.863388	−	0.504540i	$-0.168338\pi$
$62$		0			0
$63$	14.8005	+	54.1165i	0.234929	+	0.858991i
$64$		0			0
$65$	−9.63104	−	26.4611i	−0.148170	−	0.407093i
$66$		0			0
$67$	84.5379	−	70.9357i	1.26176	−	1.05874i	0.266267	−	0.963899i	$-0.414210\pi$
$67$	84.5379	−	70.9357i	1.26176	−	1.05874i	0.995492	−	0.0948429i	$-0.0302349\pi$
$68$		0			0
$69$	99.4280	−	41.4856i	1.44099	−	0.601241i
$70$		0			0
$71$	−71.2183	+	41.1179i	−1.00307	+	0.579125i	−0.909157	−	0.416455i	$-0.863272\pi$
$71$	−71.2183	+	41.1179i	−1.00307	+	0.579125i	−0.0939180	+	0.995580i	$0.529939\pi$
$72$		0			0
$73$	−3.09644	+	5.36320i	−0.0424170	+	0.0734685i	−0.886454	−	0.462816i	$-0.846839\pi$
$73$	−3.09644	+	5.36320i	−0.0424170	+	0.0734685i	0.844037	+	0.536284i	$0.180172\pi$
$74$		0			0
$75$	54.1160	+	27.9936i	0.721547	+	0.373248i
$76$		0			0
$77$	−91.6666	+	16.1633i	−1.19048	+	0.209913i
$78$		0			0
$79$	−49.2237	−	41.3036i	−0.623085	−	0.522830i	0.275687	−	0.961248i	$-0.411095\pi$
$79$	−49.2237	−	41.3036i	−0.623085	−	0.522830i	−0.898772	+	0.438417i	$0.855539\pi$
$80$		0			0
$81$	51.4220	−	62.5842i	0.634839	−	0.772644i
$82$		0			0
$83$	−97.6080	+	116.325i	−1.17600	+	1.40150i	−0.278530	+	0.960428i	$0.589847\pi$
$83$	−97.6080	+	116.325i	−1.17600	+	1.40150i	−0.897470	+	0.441075i	$0.854597\pi$
$84$		0			0
$85$	1.46049	+	8.28284i	0.0171822	+	0.0974451i
$86$		0			0
$87$	15.2935	−	29.5648i	0.175788	−	0.339825i
$88$		0			0
$89$	97.5489	+	56.3199i	1.09606	+	0.632808i	0.935182	−	0.354167i	$-0.115236\pi$
$89$	97.5489	+	56.3199i	1.09606	+	0.632808i	0.160873	+	0.986975i	$0.448569\pi$
$90$		0			0
$91$	40.5248	+	70.1909i	0.445327	+	0.771329i
$92$		0			0
$93$	−41.6264	−	99.7655i	−0.447596	−	1.07275i
$94$		0			0
$95$	17.8159	+	21.2322i	0.187536	+	0.223497i
$96$		0			0
$97$	−52.0684	+	18.9513i	−0.536787	+	0.195375i	−0.596166	−	0.802861i	$-0.703310\pi$
$97$	−52.0684	+	18.9513i	−0.536787	+	0.195375i	0.0593790	+	0.998236i	$0.481088\pi$
$98$		0			0
$99$	95.5143	+	94.5326i	0.964791	+	0.954875i
$100$		0			0
$101$	77.5927	+	13.6817i	0.768245	+	0.135462i	0.544017	−	0.839074i	$-0.316903\pi$
$101$	77.5927	+	13.6817i	0.768245	+	0.135462i	0.224228	+	0.974537i	$0.428014\pi$
$102$		0			0
$103$	−49.2174	−	17.9137i	−0.477839	−	0.173919i	0.0918613	−	0.995772i	$-0.470718\pi$
$103$	−49.2174	−	17.9137i	−0.477839	−	0.173919i	−0.569700	+	0.821853i	$0.692941\pi$
$104$		0			0
$105$	38.6603	+	12.0798i	0.368193	+	0.115046i
$106$		0			0
$107$		−	189.920i		−	1.77495i	−0.460854	−	0.887476i	$-0.652457\pi$
$107$		−	189.920i		−	1.77495i	0.460854	−	0.887476i	$-0.347543\pi$
$108$		0			0
$109$	−161.394			−1.48068			−0.740338	−	0.672234i	$-0.765335\pi$
$109$	−161.394			−1.48068			−0.740338	+	0.672234i	$0.765335\pi$
$110$		0			0
$111$	−66.4339	−	72.1250i	−0.598504	−	0.649775i
$112$		0			0
$113$	−71.3701	+	196.088i	−0.631594	+	1.73529i	0.0450545	+	0.998985i	$0.485654\pi$
$113$	−71.3701	+	196.088i	−0.631594	+	1.73529i	−0.676649	+	0.736306i	$0.736568\pi$
$114$		0			0
$115$	13.5061	−	76.5969i	0.117444	−	0.666060i
$116$		0			0
$117$	48.9043	−	106.306i	0.417985	−	0.908597i
$118$		0			0
$119$	−8.27958	−	22.7480i	−0.0695763	−	0.191159i
$120$		0			0
$121$	−78.1025	+	65.5358i	−0.645475	+	0.541618i
$122$		0			0
$123$	−53.8565	−	41.1050i	−0.437858	−	0.334187i
$124$		0			0
$125$	84.9844	−	49.0657i	0.679875	−	0.392526i
$126$		0			0
$127$	28.4088	−	49.2055i	0.223691	−	0.387445i	−0.732235	−	0.681052i	$-0.761523\pi$
$127$	28.4088	−	49.2055i	0.223691	−	0.387445i	0.955926	+	0.293608i	$0.0948559\pi$
$128$		0			0
$129$	−156.608	+	100.340i	−1.21402	+	0.777829i
$130$		0			0
$131$	−136.396	+	24.0503i	−1.04119	+	0.183590i	−0.667998	−	0.744163i	$-0.732849\pi$
$131$	−136.396	+	24.0503i	−1.04119	+	0.183590i	−0.373194	+	0.927753i	$0.621737\pi$
$132$		0			0
$133$	−61.1116	−	51.2787i	−0.459486	−	0.385554i
$134$		0			0
$135$	−18.0160	−	55.6326i	−0.133452	−	0.412093i
$136$		0			0
$137$	−34.3399	+	40.9247i	−0.250656	+	0.298720i	−0.876671	−	0.481091i	$-0.840241\pi$
$137$	−34.3399	+	40.9247i	−0.250656	+	0.298720i	0.626014	+	0.779811i	$0.284685\pi$
$138$		0			0
$139$	−34.7093	−	196.846i	−0.249707	−	1.41616i	−0.809302	−	0.587393i	$-0.800154\pi$
$139$	−34.7093	−	196.846i	−0.249707	−	1.41616i	0.559595	−	0.828767i	$-0.310957\pi$
$140$		0			0
$141$	10.2323	−	0.473235i	0.0725696	−	0.00335627i
$142$		0			0
$143$	168.128	+	97.0687i	1.17572	+	0.678802i
$144$		0			0
$145$	−12.0153	−	20.8111i	−0.0828639	−	0.143525i
$146$		0			0
$147$	30.1705	+	3.89277i	0.205241	+	0.0264814i
$148$		0			0
$149$	−43.0873	−	51.3494i	−0.289176	−	0.344627i	0.601825	−	0.798628i	$-0.294441\pi$
$149$	−43.0873	−	51.3494i	−0.289176	−	0.344627i	−0.891001	+	0.454001i	$0.849996\pi$
$150$		0			0
$151$	−209.460	+	76.2371i	−1.38715	+	0.504881i	−0.924338	−	0.381575i	$-0.875382\pi$
$151$	−209.460	+	76.2371i	−1.38715	+	0.504881i	−0.462812	+	0.886456i	$0.653160\pi$
$152$		0			0
$153$	−19.8984	+	28.7326i	−0.130055	+	0.187795i
$154$		0			0
$155$	−76.8569	−	13.5520i	−0.495851	−	0.0874320i
$156$		0			0
$157$	−113.832	−	41.4314i	−0.725043	−	0.263894i	−0.0469779	−	0.998896i	$-0.514959\pi$
$157$	−113.832	−	41.4314i	−0.725043	−	0.263894i	−0.678065	+	0.735002i	$0.737181\pi$
$158$		0			0
$159$	52.1002	+	232.169i	0.327674	+	1.46018i
$160$		0			0
$161$			223.866i			1.39047i
$162$		0			0
$163$	−70.9962			−0.435560			−0.217780	−	0.975998i	$-0.569881\pi$
$163$	−70.9962			−0.435560			−0.217780	+	0.975998i	$0.569881\pi$
$164$		0			0
$165$	94.6637	−	21.2431i	0.573719	−	0.128746i
$166$		0			0
$167$	−57.0403	+	156.717i	−0.341559	+	0.938425i	0.643384	+	0.765544i	$0.277530\pi$
$167$	−57.0403	+	156.717i	−0.341559	+	0.938425i	−0.984943	+	0.172882i	$0.944692\pi$
$168$		0			0
$169$	0.00765212	−	0.0433973i	4.52788e−5	−	0.000256789i
$170$		0			0
$171$	−9.44541	+	114.788i	−0.0552363	+	0.671275i
$172$		0			0
$173$	−78.3577	−	215.286i	−0.452935	−	1.24443i	−0.930649	−	0.365913i	$-0.880757\pi$
$173$	−78.3577	−	215.286i	−0.452935	−	1.24443i	0.477714	−	0.878515i	$-0.341465\pi$
$174$		0			0
$175$	−96.9835	+	81.3789i	−0.554192	+	0.465022i
$176$		0			0
$177$	−8.26468	+	64.0545i	−0.0466931	+	0.361890i
$178$		0			0
$179$	−129.909	+	75.0033i	−0.725751	+	0.419013i	−0.816866	−	0.576828i	$-0.804290\pi$
$179$	−129.909	+	75.0033i	−0.725751	+	0.419013i	0.0911147	+	0.995840i	$0.470957\pi$
$180$		0			0
$181$	74.7777	−	129.519i	0.413137	−	0.715574i	−0.582094	−	0.813121i	$-0.697767\pi$
$181$	74.7777	−	129.519i	0.413137	−	0.715574i	0.995231	+	0.0975476i	$0.0310998\pi$
$182$		0			0
$183$	−10.9368	−	236.476i	−0.0597639	−	1.29222i
$184$		0			0
$185$	−69.7168	+	12.2929i	−0.376847	+	0.0664483i
$186$		0			0
$187$	−44.4191	−	37.2720i	−0.237535	−	0.199316i
$188$		0			0
$189$	78.8721	+	148.688i	0.417313	+	0.786707i
$190$		0			0
$191$	48.7526	−	58.1011i	0.255249	−	0.304194i	−0.623169	−	0.782087i	$-0.714155\pi$
$191$	48.7526	−	58.1011i	0.255249	−	0.304194i	0.878418	+	0.477893i	$0.158599\pi$
$192$		0			0
$193$	−23.6459	−	134.103i	−0.122518	−	0.694833i	−0.982751	−	0.184932i	$-0.940793\pi$
$193$	−23.6459	−	134.103i	−0.122518	−	0.694833i	0.860234	−	0.509900i	$-0.170318\pi$
$194$		0			0
$195$	−45.5738	−	71.1304i	−0.233712	−	0.364771i
$196$		0			0
$197$	−285.910	−	165.070i	−1.45132	−	0.837919i	−0.452762	−	0.891631i	$-0.649561\pi$
$197$	−285.910	−	165.070i	−1.45132	−	0.837919i	−0.998556	+	0.0537122i	$0.982895\pi$
$198$		0			0
$199$	29.8782	+	51.7505i	0.150141	+	0.260053i	0.931279	−	0.364306i	$-0.118694\pi$
$199$	29.8782	+	51.7505i	0.150141	+	0.260053i	−0.781138	+	0.624359i	$0.785360\pi$
$200$		0			0
$201$	200.863	−	263.175i	0.999319	−	1.30933i
$202$		0			0
$203$	44.4590	+	52.9842i	0.219010	+	0.261006i
$204$		0			0
$205$	−45.9621	+	16.7288i	−0.224205	+	0.0816040i
$206$		0			0
$207$	263.795	−	186.749i	1.27437	−	0.902170i
$208$		0			0
$209$	−188.183	−	33.1817i	−0.900396	−	0.158764i
$210$		0			0
$211$	−10.6114	−	3.86224i	−0.0502911	−	0.0183045i	0.316752	−	0.948508i	$-0.397408\pi$
$211$	−10.6114	−	3.86224i	−0.0502911	−	0.0183045i	−0.367043	+	0.930204i	$0.619630\pi$
$212$		0			0
$213$	−181.461	+	167.142i	−0.851928	+	0.784706i
$214$		0			0
$215$			134.277i			0.624545i
$216$		0			0
$217$	224.626			1.03514
$218$		0			0
$219$	−5.54093	+	17.7332i	−0.0253010	+	0.0809733i
$220$		0			0
$221$	−17.2686	+	47.4452i	−0.0781386	+	0.214684i
$222$		0			0
$223$	−19.2101	+	108.946i	−0.0861441	+	0.488547i	0.910960	+	0.412495i	$0.135343\pi$
$223$	−19.2101	+	108.946i	−0.0861441	+	0.488547i	−0.997104	+	0.0760521i	$0.975768\pi$
$224$		0			0
$225$	176.797	+	46.3951i	0.785764	+	0.206200i
$226$		0			0
$227$	−112.933	−	310.280i	−0.497500	−	1.36687i	−0.893683	−	0.448699i	$-0.851887\pi$
$227$	−112.933	−	310.280i	−0.497500	−	1.36687i	0.396182	−	0.918172i	$-0.370335\pi$
$228$		0			0
$229$	346.931	−	291.110i	1.51498	−	1.27122i	0.661711	−	0.749759i	$-0.269831\pi$
$229$	346.931	−	291.110i	1.51498	−	1.27122i	0.853273	−	0.521464i	$-0.174614\pi$
$230$		0			0
$231$	−257.709	+	107.527i	−1.11562	+	0.465486i
$232$		0			0
$233$	312.892	−	180.648i	1.34289	−	0.775315i	0.355655	−	0.934617i	$-0.384258\pi$
$233$	312.892	−	180.648i	1.34289	−	0.775315i	0.987230	+	0.159302i	$0.0509243\pi$
$234$		0			0
$235$	3.69750	−	6.40426i	0.0157340	−	0.0272522i
$236$		0			0
$237$	−171.219	−	88.5698i	−0.722444	−	0.373712i
$238$		0			0
$239$	125.627	−	22.1514i	0.525636	−	0.0926838i	0.0954677	−	0.995433i	$-0.469565\pi$
$239$	125.627	−	22.1514i	0.525636	−	0.0926838i	0.430168	+	0.902749i	$0.358454\pi$
$240$		0			0
$241$	−100.014	−	83.9215i	−0.414995	−	0.348222i	0.411260	−	0.911518i	$-0.365089\pi$
$241$	−100.014	−	83.9215i	−0.414995	−	0.348222i	−0.826255	+	0.563296i	$0.809533\pi$
$242$		0			0
$243$	109.412	−	216.975i	0.450255	−	0.892900i
$244$		0			0
$245$	14.1168	−	16.8237i	0.0576194	−	0.0686681i
$246$		0			0
$247$	28.8928	+	163.859i	0.116975	+	0.663397i
$248$		0			0
$249$	−209.307	+	404.623i	−0.840589	+	1.62499i
$250$		0			0
$251$	376.247	+	217.226i	1.49899	+	0.865444i	0.999999	−	0.00116146i	$-0.000369704\pi$
$251$	376.247	+	217.226i	1.49899	+	0.865444i	0.498994	+	0.866606i	$0.333703\pi$
$252$		0			0
$253$	268.113	+	464.385i	1.05973	+	1.83551i
$254$		0			0
$255$	9.71598	+	23.2862i	0.0381019	+	0.0913183i
$256$		0			0
$257$	104.428	+	124.452i	0.406334	+	0.484250i	0.929941	−	0.367710i	$-0.119858\pi$
$257$	104.428	+	124.452i	0.406334	+	0.484250i	−0.523606	+	0.851960i	$0.675414\pi$
$258$		0			0
$259$	191.470	−	69.6893i	0.739266	−	0.269071i
$260$		0			0
$261$	25.3466	−	96.5880i	0.0971136	−	0.370069i
$262$		0			0
$263$	297.767	+	52.5043i	1.13219	+	0.199636i	0.708188	−	0.706024i	$-0.249513\pi$
$263$	297.767	+	52.5043i	1.13219	+	0.199636i	0.424005	+	0.905660i	$0.360624\pi$
$264$		0			0
$265$	161.421	+	58.7524i	0.609135	+	0.221707i
$266$		0			0
$267$	322.541	+	100.782i	1.20802	+	0.377459i
$268$		0			0
$269$			252.041i			0.936956i	0.883475	+	0.468478i	$0.155197\pi$
$269$			252.041i			0.936956i	−0.883475	+	0.468478i	$0.844803\pi$
$270$		0			0
$271$	−107.217			−0.395635			−0.197818	−	0.980239i	$-0.563385\pi$
$271$	−107.217			−0.395635			−0.197818	+	0.980239i	$0.563385\pi$
$272$		0			0
$273$	164.731	+	178.843i	0.603411	+	0.655103i
$274$		0			0
$275$	−103.718	+	284.963i	−0.377157	+	1.03623i
$276$		0			0
$277$	−46.8272	+	265.570i	−0.169051	+	0.958738i	0.775737	+	0.631056i	$0.217378\pi$
$277$	−46.8272	+	265.570i	−0.169051	+	0.958738i	−0.944788	+	0.327681i	$0.893733\pi$
$278$		0			0
$279$	−187.383	−	264.690i	−0.671624	−	0.948710i
$280$		0			0
$281$	−5.79982	−	15.9349i	−0.0206399	−	0.0567077i	0.928945	−	0.370218i	$-0.120717\pi$
$281$	−5.79982	−	15.9349i	−0.0206399	−	0.0567077i	−0.949585	+	0.313511i	$0.898495\pi$
$282$		0			0
$283$	250.525	−	210.215i	0.885247	−	0.742810i	−0.0820041	−	0.996632i	$-0.526132\pi$
$283$	250.525	−	210.215i	0.885247	−	0.742810i	0.967251	+	0.253822i	$0.0816876\pi$
$284$		0			0
$285$	66.0978	+	50.4479i	0.231922	+	0.177010i
$286$		0			0
$287$	121.919	−	70.3903i	0.424807	−	0.245262i
$288$		0			0
$289$	−136.960	+	237.221i	−0.473909	+	0.820835i
$290$		0			0
$291$	−139.966	+	89.6771i	−0.480982	+	0.308169i
$292$		0			0
$293$	264.414	−	46.6234i	0.902437	−	0.159124i	0.296870	−	0.954918i	$-0.404057\pi$
$293$	264.414	−	46.6234i	0.902437	−	0.159124i	0.605568	+	0.795794i	$0.292946\pi$
$294$		0			0
$295$	35.7182	+	29.9711i	0.121078	+	0.101597i
$296$		0			0
$297$	341.686	+	213.974i	1.15046	+	0.720452i
$298$		0			0
$299$	300.128	−	357.678i	1.00377	−	1.19625i
$300$		0			0
$301$	−67.1121	−	380.612i	−0.222964	−	1.26449i
$302$		0			0
$303$	236.117	−	10.9202i	0.779263	−	0.0360401i
$304$		0			0
$305$	−148.007	−	85.4519i	−0.485269	−	0.280170i
$306$		0			0
$307$	51.1411	+	88.5790i	0.166583	+	0.288531i	0.937216	−	0.348748i	$-0.113393\pi$
$307$	51.1411	+	88.5790i	0.166583	+	0.288531i	−0.770633	+	0.637279i	$0.780060\pi$
$308$		0			0
$309$	−155.836	−	20.1069i	−0.504325	−	0.0650709i
$310$		0			0
$311$	−300.925	−	358.629i	−0.967605	−	1.15315i	−0.988171	−	0.153358i	$-0.950991\pi$
$311$	−300.925	−	358.629i	−0.967605	−	1.15315i	0.0205661	−	0.999788i	$-0.493453\pi$
$312$		0			0
$313$	−173.348	+	63.0934i	−0.553827	+	0.201576i	−0.603746	−	0.797177i	$-0.706326\pi$
$313$	−173.348	+	63.0934i	−0.553827	+	0.201576i	0.0499192	+	0.998753i	$0.484104\pi$
$314$		0			0
$315$	121.101	+	9.96492i	0.384449	+	0.0316347i
$316$		0			0
$317$	96.3583	+	16.9906i	0.303969	+	0.0535980i	0.323552	−	0.946210i	$-0.395123\pi$
$317$	96.3583	+	16.9906i	0.303969	+	0.0535980i	−0.0195831	+	0.999808i	$0.506234\pi$
$318$		0			0
$319$	155.682	+	56.6634i	0.488030	+	0.177628i
$320$		0			0
$321$	−124.755	−	555.933i	−0.388644	−	1.73188i
$322$		0			0
$323$		−	49.6965i		−	0.153859i
$324$		0			0
$325$	264.055			0.812476
$326$		0			0
$327$	−472.432	+	106.017i	−1.44475	+	0.324210i
$328$		0			0
$329$	−7.27979	+	20.0011i	−0.0221270	+	0.0607935i
$330$		0			0
$331$	18.3892	−	104.290i	0.0555564	−	0.315076i	−0.944347	−	0.328950i	$-0.893305\pi$
$331$	18.3892	−	104.290i	0.0555564	−	0.315076i	0.999904	+	0.0138738i	$0.00441632\pi$
$332$		0			0
$333$	−241.843	−	167.485i	−0.726255	−	0.502958i
$334$		0			0
$335$	−81.7468	−	224.597i	−0.244020	−	0.670440i
$336$		0			0
$337$	−3.17508	+	2.66420i	−0.00942159	+	0.00790565i	−0.647486	−	0.762077i	$-0.724180\pi$
$337$	−3.17508	+	2.66420i	−0.00942159	+	0.00790565i	0.638065	+	0.769983i	$0.279735\pi$
$338$		0			0
$339$	−80.1083	+	620.870i	−0.236308	+	1.83148i
$340$		0			0
$341$	465.961	−	269.023i	1.36646	−	0.788924i
$342$		0			0
$343$	−184.333	+	319.274i	−0.537414	+	0.930828i
$344$		0			0
$345$	−10.7800	−	233.087i	−0.0312464	−	0.675613i
$346$		0			0
$347$	−387.103	+	68.2568i	−1.11557	+	0.196705i	−0.700896	−	0.713264i	$-0.747216\pi$
$347$	−387.103	+	68.2568i	−1.11557	+	0.196705i	−0.414676	+	0.909969i	$0.636105\pi$
$348$		0			0
$349$	−246.286	−	206.658i	−0.705690	−	0.592144i	0.217696	−	0.976017i	$-0.430146\pi$
$349$	−246.286	−	206.658i	−0.705690	−	0.592144i	−0.923386	+	0.383872i	$0.874590\pi$
$350$		0			0
$351$	73.3223	−	343.303i	0.208896	−	0.978071i
$352$		0			0
$353$	112.600	−	134.192i	0.318982	−	0.380147i	−0.582598	−	0.812760i	$-0.697964\pi$
$353$	112.600	−	134.192i	0.318982	−	0.380147i	0.901580	+	0.432613i	$0.142408\pi$
$354$		0			0
$355$	30.9281	+	175.402i	0.0871213	+	0.494089i
$356$		0			0
$357$	−39.1787	−	61.1491i	−0.109744	−	0.171286i
$358$		0			0
$359$	455.354	+	262.899i	1.26840	+	0.732309i	0.974684	−	0.223586i	$-0.0717762\pi$
$359$	455.354	+	262.899i	1.26840	+	0.732309i	0.293711	+	0.955894i	$0.405110\pi$
$360$		0			0
$361$	98.6142	+	170.805i	0.273170	+	0.473143i
$362$		0			0
$363$	−185.573	+	243.141i	−0.511219	+	0.669809i
$364$		0			0
$365$	8.62149	+	10.2747i	0.0236205	+	0.0281498i
$366$		0			0
$367$	304.854	−	110.958i	0.830664	−	0.302337i	0.108533	−	0.994093i	$-0.465385\pi$
$367$	304.854	−	110.958i	0.830664	−	0.302337i	0.722131	+	0.691756i	$0.243163\pi$
$368$		0			0
$369$	−184.650	−	84.9453i	−0.500407	−	0.230204i
$370$		0			0
$371$	−486.916	−	85.8564i	−1.31244	−	0.231419i
$372$		0			0
$373$	227.629	+	82.8503i	0.610267	+	0.222119i	0.628620	−	0.777713i	$-0.283620\pi$
$373$	227.629	+	82.8503i	0.610267	+	0.222119i	−0.0183533	+	0.999832i	$0.505842\pi$
$374$		0			0
$375$	216.536	−	199.450i	0.577429	−	0.531866i
$376$		0			0
$377$		−	144.259i		−	0.382649i
$378$		0			0
$379$	605.266			1.59701			0.798504	−	0.601989i	$-0.205625\pi$
$379$	605.266			1.59701			0.798504	+	0.601989i	$0.205625\pi$
$380$		0			0
$381$	50.8361	−	162.696i	0.133428	−	0.427023i
$382$		0			0
$383$	−92.4520	+	254.010i	−0.241389	+	0.663211i	0.758544	+	0.651622i	$0.225911\pi$
$383$	−92.4520	+	254.010i	−0.241389	+	0.663211i	−0.999933	+	0.0115889i	$0.996311\pi$
$384$		0			0
$385$	−35.0067	+	198.533i	−0.0909265	+	0.515670i
$386$		0			0
$387$	−392.512	+	396.588i	−1.01424	+	1.02478i
$388$		0			0
$389$	56.4976	+	155.226i	0.145238	+	0.399038i	0.990886	−	0.134703i	$-0.0430079\pi$
$389$	56.4976	+	155.226i	0.145238	+	0.399038i	−0.845648	+	0.533741i	$0.820786\pi$
$390$		0			0
$391$	−106.831	+	89.6421i	−0.273226	+	0.229264i
$392$		0			0
$393$	−383.461	+	159.996i	−0.975727	+	0.407115i
$394$		0			0
$395$	−120.524	+	69.5844i	−0.305123	+	0.176163i
$396$		0			0
$397$	−192.854	+	334.032i	−0.485778	+	0.841392i	−0.999866	−	0.0163455i	$-0.994797\pi$
$397$	−192.854	+	334.032i	−0.485778	+	0.841392i	0.514089	+	0.857737i	$0.328130\pi$
$398$		0			0
$399$	−212.570	−	109.960i	−0.532757	−	0.275589i
$400$		0			0
$401$	238.103	−	41.9840i	0.593773	−	0.104698i	0.131317	−	0.991340i	$-0.458079\pi$
$401$	238.103	−	41.9840i	0.593773	−	0.104698i	0.462456	+	0.886642i	$0.346968\pi$
$402$		0			0
$403$	−358.892	−	301.146i	−0.890551	−	0.747261i
$404$		0			0
$405$	−89.2805	−	151.013i	−0.220446	−	0.372873i
$406$		0			0
$407$	313.719	−	373.876i	0.770808	−	0.918614i
$408$		0			0
$409$	26.9195	+	152.668i	0.0658180	+	0.373272i	0.999870	+	0.0161348i	$0.00513609\pi$
$409$	26.9195	+	152.668i	0.0658180	+	0.373272i	−0.934052	+	0.357137i	$0.883753\pi$
$410$		0			0
$411$	−73.6371	+	142.352i	−0.179166	+	0.346355i
$412$		0			0
$413$	−116.224	−	67.1018i	−0.281413	−	0.162474i
$414$		0			0
$415$	164.441	+	284.820i	0.396243	+	0.686313i
$416$		0			0
$417$	−230.906	−	553.409i	−0.553731	−	1.32712i
$418$		0			0
$419$	−308.155	−	367.245i	−0.735453	−	0.876479i	0.260581	−	0.965452i	$-0.416086\pi$
$419$	−308.155	−	367.245i	−0.735453	−	0.876479i	−0.996034	+	0.0889728i	$0.971642\pi$
$420$		0			0
$421$	−647.463	+	235.657i	−1.53792	+	0.559756i	−0.965545	−	0.260238i	$-0.916199\pi$
$421$	−647.463	+	235.657i	−1.53792	+	0.559756i	−0.572372	+	0.819994i	$0.693977\pi$
$422$		0			0
$423$	29.6412	−	8.10667i	0.0700737	−	0.0191647i
$424$		0			0
$425$	−77.6696	−	13.6953i	−0.182752	−	0.0322241i
$426$		0			0
$427$	462.239	+	168.241i	1.08253	+	0.394008i
$428$		0			0
$429$	555.907	+	173.699i	1.29582	+	0.404894i
$430$		0			0
$431$		−	506.298i		−	1.17471i	−0.809331	−	0.587353i	$-0.800170\pi$
$431$		−	506.298i		−	1.17471i	0.809331	−	0.587353i	$-0.199830\pi$
$432$		0			0
$433$	425.824			0.983427			0.491714	−	0.870757i	$-0.336371\pi$
$433$	425.824			0.983427			0.491714	+	0.870757i	$0.336371\pi$
$434$		0			0
$435$	−48.8415	−	53.0256i	−0.112279	−	0.121898i
$436$		0			0
$437$	−157.184	+	431.861i	−0.359690	+	0.988239i
$438$		0			0
$439$	−79.7889	+	452.505i	−0.181751	+	1.03076i	0.748307	+	0.663353i	$0.230867\pi$
$439$	−79.7889	+	452.505i	−0.181751	+	1.03076i	−0.930059	+	0.367411i	$0.880244\pi$
$440$		0			0
$441$	90.8721	−	8.42351i	0.206059	−	0.0191009i
$442$		0			0
$443$	−18.6549	−	51.2541i	−0.0421105	−	0.115698i	0.916855	−	0.399220i	$-0.130719\pi$
$443$	−18.6549	−	51.2541i	−0.0421105	−	0.115698i	−0.958966	+	0.283523i	$0.908497\pi$
$444$		0			0
$445$	186.882	−	156.813i	0.419959	−	0.352388i
$446$		0			0
$447$	−159.856	−	122.007i	−0.357619	−	0.272946i
$448$		0			0
$449$	182.250	−	105.222i	0.405902	−	0.234348i	−0.283125	−	0.959083i	$-0.591371\pi$
$449$	182.250	−	105.222i	0.405902	−	0.234348i	0.689027	+	0.724735i	$0.258038\pi$
$450$		0			0
$451$	168.605	−	292.033i	0.373848	−	0.647523i
$452$		0			0
$453$	−563.052	+	360.751i	−1.24294	+	0.796361i
$454$		0			0
$455$	172.871	−	30.4819i	0.379937	−	0.0669932i
$456$		0			0
$457$	−150.910	−	126.628i	−0.330218	−	0.277086i	0.462571	−	0.886582i	$-0.346927\pi$
$457$	−150.910	−	126.628i	−0.330218	−	0.277086i	−0.792789	+	0.609497i	$0.791372\pi$
$458$		0			0
$459$	−39.3727	+	97.1771i	−0.0857793	+	0.211715i
$460$		0			0
$461$	128.532	−	153.179i	0.278812	−	0.332275i	−0.608406	−	0.793626i	$-0.708191\pi$
$461$	128.532	−	153.179i	0.278812	−	0.332275i	0.887218	+	0.461351i	$0.152635\pi$
$462$		0			0
$463$	−67.1681	−	380.929i	−0.145071	−	0.822741i	−0.967310	−	0.253598i	$-0.918386\pi$
$463$	−67.1681	−	380.929i	−0.145071	−	0.822741i	0.822238	−	0.569143i	$-0.192725\pi$
$464$		0			0
$465$	−233.878	+	10.8166i	−0.502963	+	0.0232615i
$466$		0			0
$467$	−300.701	−	173.610i	−0.643900	−	0.371756i	0.142215	−	0.989836i	$-0.454577\pi$
$467$	−300.701	−	173.610i	−0.643900	−	0.371756i	−0.786115	+	0.618080i	$0.787911\pi$
$468$		0			0
$469$	343.968	+	595.770i	0.733407	+	1.27030i
$470$		0			0
$471$	−360.424	−	46.5040i	−0.765231	−	0.0987346i
$472$		0			0
$473$	−595.055	−	709.159i	−1.25804	−	1.49928i
$474$		0			0
$475$	−244.230	+	88.8924i	−0.514168	+	0.187142i
$476$		0			0
$477$	305.015	+	645.382i	0.639445	+	1.35300i
$478$		0			0
$479$	239.163	+	42.1710i	0.499297	+	0.0880396i	0.417625	−	0.908620i	$-0.362863\pi$
$479$	239.163	+	42.1710i	0.499297	+	0.0880396i	0.0816727	+	0.996659i	$0.473974\pi$
$480$		0			0
$481$	−399.347	−	145.350i	−0.830242	−	0.302183i
$482$		0			0
$483$	147.054	+	655.302i	0.304459	+	1.35673i
$484$		0			0
$485$			120.008i			0.247439i
$486$		0			0
$487$	−294.321			−0.604355			−0.302177	−	0.953252i	$-0.597713\pi$
$487$	−294.321			−0.604355			−0.302177	+	0.953252i	$0.597713\pi$
$488$		0			0
$489$	−207.820	+	46.6361i	−0.424990	+	0.0953704i
$490$		0			0
$491$	81.7251	−	224.538i	0.166446	−	0.457307i	−0.828226	−	0.560394i	$-0.810650\pi$
$491$	81.7251	−	224.538i	0.166446	−	0.457307i	0.994672	+	0.103087i	$0.0328719\pi$
$492$		0			0
$493$	−7.48201	+	42.4326i	−0.0151765	+	0.0860702i
$494$		0			0
$495$	263.145	−	124.366i	0.531607	−	0.251244i
$496$		0			0
$497$	−175.333	−	481.723i	−0.352782	−	0.969261i
$498$		0			0
$499$	184.698	−	154.980i	0.370136	−	0.310581i	−0.438679	−	0.898644i	$-0.644554\pi$
$499$	184.698	−	154.980i	0.370136	−	0.310581i	0.808815	+	0.588063i	$0.200109\pi$
$500$		0			0
$501$	−64.0240	+	496.211i	−0.127792	+	0.990441i
$502$		0			0
$503$	138.798	−	80.1352i	0.275941	−	0.159314i	−0.355644	−	0.934622i	$-0.615738\pi$
$503$	138.798	−	80.1352i	0.275941	−	0.159314i	0.631584	+	0.775307i	$0.282405\pi$
$504$		0			0
$505$	85.3220	−	147.782i	0.168954	−	0.292638i
$506$		0			0
$507$	−0.00610761	−	0.132059i	−1.20466e−5	−	0.000260472i
$508$		0			0
$509$	78.7326	−	13.8827i	0.154681	−	0.0272744i	−0.0957713	−	0.995403i	$-0.530532\pi$
$509$	78.7326	−	13.8827i	0.154681	−	0.0272744i	0.250452	+	0.968129i	$0.419421\pi$
$510$		0			0
$511$	−29.5731	−	24.8148i	−0.0578731	−	0.0485613i
$512$		0			0
$513$	47.7535	+	342.212i	0.0930867	+	0.667080i
$514$		0			0
$515$	−72.9158	+	86.8977i	−0.141584	+	0.168733i
$516$		0			0
$517$	8.85312	+	50.2085i	0.0171240	+	0.0971151i
$518$		0			0
$519$	−370.786	−	578.714i	−0.714424	−	1.11506i
$520$		0			0
$521$	599.564	+	346.158i	1.15079	+	0.664411i	0.949081	−	0.315033i	$-0.102016\pi$
$521$	599.564	+	346.158i	1.15079	+	0.664411i	0.201713	+	0.979445i	$0.435349\pi$
$522$		0			0
$523$	33.5131	+	58.0464i	0.0640786	+	0.110987i	0.896285	−	0.443479i	$-0.146256\pi$
$523$	33.5131	+	58.0464i	0.0640786	+	0.110987i	−0.832206	+	0.554466i	$0.812923\pi$
$524$		0			0
$525$	−230.434	+	301.919i	−0.438922	+	0.575084i
$526$		0			0
$527$	89.9464	+	107.194i	0.170676	+	0.203404i
$528$		0			0
$529$	714.791	−	260.163i	1.35121	−	0.491801i
$530$		0			0
$531$	17.8838	+	192.929i	0.0336795	+	0.363332i
$532$		0			0
$533$	−289.164	−	50.9873i	−0.542521	−	0.0956611i
$534$		0			0
$535$	−386.525	−	140.684i	−0.722477	−	0.262960i
$536$		0			0
$537$	−331.003	+	304.885i	−0.616393	+	0.567756i
$538$		0			0
$539$			151.410i			0.280909i
$540$		0			0
$541$	−584.288			−1.08002			−0.540008	−	0.841660i	$-0.681579\pi$
$541$	−584.288			−1.08002			−0.540008	+	0.841660i	$0.681579\pi$
$542$		0			0
$543$	133.811	−	428.248i	0.246429	−	0.788670i
$544$		0			0
$545$	−119.553	+	328.469i	−0.219363	+	0.602695i
$546$		0			0
$547$	−13.0135	+	73.8033i	−0.0237907	+	0.134924i	−0.994390	−	0.105778i	$-0.966267\pi$
$547$	−13.0135	+	73.8033i	−0.0237907	+	0.134924i	0.970599	+	0.240702i	$0.0773777\pi$
$548$		0			0
$549$	−187.351	−	685.030i	−0.341259	−	1.24778i
$550$		0			0
$551$	48.5638	+	133.428i	0.0881377	+	0.242156i
$552$		0			0
$553$	306.849	−	257.477i	0.554881	−	0.465600i
$554$		0			0
$555$	−196.000	+	81.7796i	−0.353153	+	0.147351i
$556$		0			0
$557$	−460.828	+	266.059i	−0.827340	+	0.477665i	−0.852941	−	0.522007i	$-0.825183\pi$
$557$	−460.828	+	266.059i	−0.827340	+	0.477665i	0.0256012	+	0.999672i	$0.491850\pi$
$558$		0			0
$559$	−403.042	+	698.090i	−0.721006	+	1.24882i
$560$		0			0
$561$	−154.507	−	79.9246i	−0.275413	−	0.142468i
$562$		0			0
$563$	457.883	−	80.7371i	0.813291	−	0.143405i	0.248492	−	0.968634i	$-0.420065\pi$
$563$	457.883	−	80.7371i	0.813291	−	0.143405i	0.564799	+	0.825229i	$0.308954\pi$
$564$		0			0
$565$	346.211	+	290.505i	0.612762	+	0.514168i
$566$		0			0
$567$	328.545	+	383.429i	0.579444	+	0.676241i
$568$		0			0
$569$	324.973	−	387.288i	0.571130	−	0.680647i	−0.400732	−	0.916195i	$-0.631244\pi$
$569$	324.973	−	387.288i	0.571130	−	0.680647i	0.971863	+	0.235549i	$0.0756887\pi$
$570$		0			0
$571$	−4.63998	−	26.3146i	−0.00812605	−	0.0460851i	0.980475	−	0.196643i	$-0.0630041\pi$
$571$	−4.63998	−	26.3146i	−0.00812605	−	0.0460851i	−0.988601	+	0.150558i	$0.951893\pi$
$572$		0			0
$573$	104.543	−	202.098i	0.182449	−	0.352702i
$574$		0			0
$575$	631.630	+	364.672i	1.09849	+	0.634212i
$576$		0			0
$577$	−568.853	−	985.283i	−0.985881	−	1.70760i	−0.637955	−	0.770074i	$-0.720219\pi$
$577$	−568.853	−	985.283i	−0.985881	−	1.70760i	−0.347926	−	0.937522i	$-0.613114\pi$
$578$		0			0
$579$	−157.306	−	377.013i	−0.271686	−	0.651145i
$580$		0			0
$581$	−608.465	−	725.141i	−1.04727	−	1.24809i
$582$		0			0
$583$	−1112.88	+	405.054i	−1.90888	+	0.694775i
$584$		0			0
$585$	−180.128	−	178.276i	−0.307911	−	0.304746i
$586$		0			0
$587$	−413.543	−	72.9187i	−0.704502	−	0.124223i	−0.190091	−	0.981767i	$-0.560878\pi$
$587$	−413.543	−	72.9187i	−0.704502	−	0.124223i	−0.514411	+	0.857544i	$0.671989\pi$
$588$		0			0
$589$	433.327	+	157.718i	0.735699	+	0.267772i
$590$		0			0
$591$	−945.347	−	295.384i	−1.59957	−	0.499805i
$592$		0			0
$593$		−	608.635i		−	1.02637i	−0.858279	−	0.513183i	$-0.828466\pi$
$593$		−	608.635i		−	1.02637i	0.858279	−	0.513183i	$-0.171534\pi$
$594$		0			0
$595$	−52.4298			−0.0881173
$596$		0			0
$597$	121.453	+	131.858i	0.203439	+	0.220867i
$598$		0			0
$599$	−222.904	+	612.422i	−0.372126	+	1.02241i	0.602412	+	0.798185i	$0.294206\pi$
$599$	−222.904	+	612.422i	−0.372126	+	1.02241i	−0.974538	+	0.224223i	$0.928016\pi$
$600$		0			0
$601$	29.5147	−	167.386i	0.0491092	−	0.278512i	−0.950358	−	0.311160i	$-0.899283\pi$
$601$	29.5147	−	167.386i	0.0491092	−	0.278512i	0.999467	+	0.0326472i	$0.0103938\pi$
$602$		0			0
$603$	415.092	−	902.308i	0.688378	−	1.49636i
$604$		0			0
$605$	75.5239	+	207.500i	0.124833	+	0.342976i
$606$		0			0
$607$	275.061	−	230.804i	0.453149	−	0.380237i	−0.387454	−	0.921889i	$-0.626645\pi$
$607$	275.061	−	230.804i	0.453149	−	0.380237i	0.840603	+	0.541652i	$0.182201\pi$
$608$		0			0
$609$	164.945	+	125.891i	0.270845	+	0.206718i
$610$		0			0
$611$	38.4457	−	22.1966i	0.0629225	−	0.0363283i
$612$		0			0
$613$	112.374	−	194.637i	0.183317	−	0.317515i	−0.759691	−	0.650284i	$-0.774650\pi$
$613$	112.374	−	194.637i	0.183317	−	0.317515i	0.943008	+	0.332769i	$0.107983\pi$
$614$		0			0
$615$	−123.551	+	79.1603i	−0.200897	+	0.128716i
$616$		0			0
$617$	−369.095	+	65.0815i	−0.598210	+	0.105481i	−0.464550	−	0.885547i	$-0.653784\pi$
$617$	−369.095	+	65.0815i	−0.598210	+	0.105481i	−0.133660	+	0.991027i	$0.542673\pi$
$618$		0			0
$619$	511.061	+	428.831i	0.825623	+	0.692780i	0.954282	−	0.298909i	$-0.0966226\pi$
$619$	511.061	+	428.831i	0.825623	+	0.692780i	−0.128658	+	0.991689i	$0.541067\pi$
$620$		0			0
$621$	649.508	−	719.934i	1.04591	−	1.15931i
$622$		0			0
$623$	−451.346	+	537.893i	−0.724472	+	0.863392i
$624$		0			0
$625$	51.2603	+	290.712i	0.0820165	+	0.465139i
$626$		0			0
$627$	−572.645	+	26.4843i	−0.913310	+	0.0422397i
$628$		0			0
$629$	109.926	+	63.4659i	0.174763	+	0.100900i
$630$		0			0
$631$	288.004	+	498.837i	0.456425	+	0.790551i	0.998769	−	0.0496058i	$-0.0157965\pi$
$631$	288.004	+	498.837i	0.456425	+	0.790551i	−0.542344	+	0.840156i	$0.682463\pi$
$632$		0			0
$633$	−33.5988	−	4.33511i	−0.0530786	−	0.00684851i
$634$		0			0
$635$	−79.0992	−	94.2667i	−0.124566	−	0.148452i
$636$		0			0
$637$	123.889	−	45.0918i	0.194488	−	0.0707877i
$638$		0			0
$639$	−421.379	+	608.457i	−0.659435	+	0.952203i
$640$		0			0
$641$	−732.193	−	129.105i	−1.14227	−	0.201412i	−0.429670	−	0.902986i	$-0.641370\pi$
$641$	−732.193	−	129.105i	−1.14227	−	0.201412i	−0.712597	+	0.701574i	$0.752481\pi$
$642$		0			0
$643$	−717.060	−	260.989i	−1.11518	−	0.405892i	−0.282289	−	0.959330i	$-0.591094\pi$
$643$	−717.060	−	260.989i	−1.11518	−	0.405892i	−0.832891	+	0.553437i	$0.813316\pi$
$644$		0			0
$645$	88.2042	+	393.056i	0.136751	+	0.609389i
$646$		0			0
$647$		−	128.575i		−	0.198725i	−0.995051	−	0.0993624i	$-0.968320\pi$
$647$		−	128.575i		−	0.198725i	0.995051	−	0.0993624i	$-0.0316803\pi$
$648$		0			0
$649$	−321.457			−0.495311
$650$		0			0
$651$	657.526	−	147.553i	1.01002	−	0.226656i
$652$		0			0
$653$	−61.1625	+	168.042i	−0.0936638	+	0.257339i	−0.977674	−	0.210129i	$-0.932612\pi$
$653$	−61.1625	+	168.042i	−0.0936638	+	0.257339i	0.884010	+	0.467468i	$0.154834\pi$
$654$		0			0
$655$	−52.0886	+	295.409i	−0.0795245	+	0.451006i
$656$		0			0
$657$	−4.57083	+	55.5482i	−0.00695712	+	0.0845483i
$658$		0			0
$659$	69.7138	+	191.537i	0.105787	+	0.290648i	0.981281	−	0.192581i	$-0.0616859\pi$
$659$	69.7138	+	191.537i	0.105787	+	0.290648i	−0.875494	+	0.483229i	$0.839464\pi$
$660$		0			0
$661$	−588.511	+	493.819i	−0.890334	+	0.747079i	−0.968277	−	0.249879i	$-0.919609\pi$
$661$	−588.511	+	493.819i	−0.890334	+	0.747079i	0.0779433	+	0.996958i	$0.475165\pi$
$662$		0			0
$663$	−19.3829	+	150.225i	−0.0292351	+	0.226584i
$664$		0			0
$665$	−149.631	+	86.3896i	−0.225009	+	0.129909i
$666$		0			0
$667$	199.228	−	345.073i	0.298693	−	0.517351i
$668$		0			0
$669$	15.3327	+	331.526i	0.0229189	+	0.495554i
$670$		0			0
$671$	1160.36	−	204.602i	1.72929	−	0.304921i
$672$		0			0
$673$	897.798	+	753.342i	1.33402	+	1.11938i	0.983119	+	0.182967i	$0.0585703\pi$
$673$	897.798	+	753.342i	1.33402	+	1.11938i	0.350905	+	0.936411i	$0.385874\pi$
$674$		0			0
$675$	547.997	+	19.6731i	0.811847	+	0.0291454i
$676$		0			0
$677$	192.459	−	229.364i	0.284283	−	0.338795i	−0.604939	−	0.796272i	$-0.706802\pi$
$677$	192.459	−	229.364i	0.284283	−	0.338795i	0.889221	+	0.457477i	$0.151247\pi$
$678$		0			0
$679$	−59.9803	−	340.165i	−0.0883363	−	0.500980i
$680$		0			0
$681$	−534.393	−	834.068i	−0.784719	−	1.22477i
$682$		0			0
$683$	−812.585	−	469.146i	−1.18973	−	0.686890i	−0.231484	−	0.972839i	$-0.574358\pi$
$683$	−812.585	−	469.146i	−1.18973	−	0.686890i	−0.958245	+	0.285949i	$0.907691\pi$
$684$		0			0
$685$	57.8526	+	100.204i	0.0844564	+	0.146283i
$686$		0			0
$687$	824.313	−	1080.03i	1.19987	−	1.57210i
$688$		0			0
$689$	662.856	+	789.962i	0.962056	+	1.14653i
$690$		0			0
$691$	31.6500	−	11.5197i	0.0458032	−	0.0166710i	−0.319017	−	0.947749i	$-0.603353\pi$
$691$	31.6500	−	11.5197i	0.0458032	−	0.0166710i	0.364820	+	0.931078i	$0.381130\pi$
$692$		0			0
$693$	−683.734	+	484.038i	−0.986629	+	0.698468i
$694$		0			0
$695$	−426.333	−	75.1739i	−0.613428	−	0.108164i
$696$		0			0
$697$	82.4108	+	29.9951i	0.118236	+	0.0430345i
$698$		0			0
$699$	797.234	−	734.328i	1.14054	−	1.05054i
$700$		0			0
$701$			1259.81i			1.79716i	0.438814	+	0.898578i	$0.355399\pi$
$701$			1259.81i			1.79716i	−0.438814	+	0.898578i	$0.644601\pi$
$702$		0			0
$703$	418.296			0.595015
$704$		0			0
$705$	6.61649	−	21.1754i	0.00938509	−	0.0300360i
$706$		0			0
$707$	−167.985	+	461.536i	−0.237603	+	0.652809i
$708$		0			0
$709$	51.2300	−	290.540i	0.0722567	−	0.409788i	−0.927129	−	0.374742i	$-0.877731\pi$
$709$	51.2300	−	290.540i	0.0722567	−	0.409788i	0.999386	−	0.0350457i	$-0.0111577\pi$
$710$		0			0
$711$	−559.373	−	146.791i	−0.786742	−	0.206457i
$712$		0			0
$713$	−442.589	−	1216.00i	−0.620741	−	1.70547i
$714$		0			0
$715$	322.096	−	270.270i	0.450483	−	0.378000i
$716$		0			0
$717$	353.185	−	147.364i	0.492587	−	0.205528i
$718$		0			0
$719$	719.610	−	415.467i	1.00085	−	0.577840i	0.0923493	−	0.995727i	$-0.470562\pi$
$719$	719.610	−	415.467i	1.00085	−	0.577840i	0.908499	+	0.417886i	$0.137229\pi$
$720$		0			0
$721$	163.250	−	282.757i	0.226422	−	0.392174i
$722$		0			0
$723$	−347.887	−	179.958i	−0.481172	−	0.248905i
$724$		0			0
$725$	221.915	−	39.1297i	0.306090	−	0.0539719i
$726$		0			0
$727$	−171.551	−	143.949i	−0.235972	−	0.198004i	0.517132	−	0.855906i	$-0.327000\pi$
$727$	−171.551	−	143.949i	−0.235972	−	0.198004i	−0.753104	+	0.657902i	$0.771444\pi$
$728$		0			0
$729$	177.744	−	706.999i	0.243820	−	0.969821i
$730$		0			0
$731$	154.758	−	184.434i	0.211708	−	0.252303i
$732$		0			0
$733$	−47.7555	−	270.835i	−0.0651508	−	0.369488i	−0.999899	−	0.0141788i	$-0.995487\pi$
$733$	−47.7555	−	270.835i	−0.0651508	−	0.369488i	0.934749	−	0.355309i	$-0.115625\pi$
$734$		0			0
$735$	30.2714	−	58.5194i	0.0411856	−	0.0796182i
$736$		0			0
$737$	1427.04	+	823.904i	1.93629	+	1.11792i
$738$		0			0
$739$	−235.936	−	408.653i	−0.319264	−	0.552981i	0.661071	−	0.750323i	$-0.270102\pi$
$739$	−235.936	−	408.653i	−0.319264	−	0.552981i	−0.980335	+	0.197343i	$0.936769\pi$
$740$		0			0
$741$	192.211	+	460.670i	0.259394	+	0.621686i
$742$		0			0
$743$	245.380	+	292.432i	0.330255	+	0.393583i	0.905464	−	0.424424i	$-0.139523\pi$
$743$	245.380	+	292.432i	0.330255	+	0.393583i	−0.575208	+	0.818007i	$0.695079\pi$
$744$		0			0
$745$	−136.423	+	49.6541i	−0.183119	+	0.0666497i
$746$		0			0
$747$	−346.894	+	1321.90i	−0.464383	+	1.76961i
$748$		0			0
$749$	1165.93	+	205.585i	1.55665	+	0.274479i
$750$		0			0
$751$	1053.31	+	383.374i	1.40255	+	0.510485i	0.928933	−	0.370248i	$-0.120727\pi$
$751$	1053.31	+	383.374i	1.40255	+	0.510485i	0.473613	+	0.880733i	$0.342949\pi$
$752$		0			0
$753$	1244.04	+	388.716i	1.65212	+	0.516223i
$754$		0			0
$755$			482.765i			0.639424i
$756$		0			0
$757$	157.155			0.207602			0.103801	−	0.994598i	$-0.466899\pi$
$757$	157.155			0.207602			0.103801	+	0.994598i	$0.466899\pi$
$758$		0			0
$759$	1089.87	+	1183.23i	1.43592	+	1.55893i
$760$		0			0
$761$	−440.078	+	1209.11i	−0.578290	+	1.58884i	0.212773	+	0.977102i	$0.431751\pi$
$761$	−440.078	+	1209.11i	−0.578290	+	1.58884i	−0.791062	+	0.611736i	$0.790472\pi$
$762$		0			0
$763$	174.706	−	990.806i	0.228972	−	1.29857i
$764$		0			0
$765$	43.7369	+	61.7810i	0.0571724	+	0.0807595i
$766$		0			0
$767$	95.7338	+	263.026i	0.124816	+	0.342929i
$768$		0			0
$769$	−687.236	+	576.660i	−0.893675	+	0.749882i	−0.968944	−	0.247281i	$-0.920463\pi$
$769$	−687.236	+	576.660i	−0.893675	+	0.749882i	0.0752688	+	0.997163i	$0.476019\pi$
$770$		0			0
$771$	387.432	+	295.700i	0.502506	+	0.383528i
$772$		0			0
$773$	−211.789	+	122.276i	−0.273983	+	0.158184i	−0.630696	−	0.776030i	$-0.717231\pi$
$773$	−211.789	+	122.276i	−0.273983	+	0.158184i	0.356713	+	0.934214i	$0.383897\pi$
$774$		0			0
$775$	365.910	−	633.774i	0.472141	−	0.817773i
$776$		0			0
$777$	514.693	−	329.768i	0.662411	−	0.424411i
$778$		0			0
$779$	284.618	−	50.1859i	0.365364	−	0.0644235i
$780$		0			0
$781$	−940.641	−	789.292i	−1.20441	−	1.01062i
$782$		0			0
$783$	10.7479	−	299.382i	0.0137265	−	0.382353i
$784$		0			0
$785$	−168.642	+	200.980i	−0.214831	+	0.256026i
$786$		0			0
$787$	−75.9828	−	430.920i	−0.0965474	−	0.547547i	−0.994262	−	0.106970i	$-0.965885\pi$
$787$	−75.9828	−	430.920i	−0.0965474	−	0.547547i	0.897715	−	0.440577i	$-0.145226\pi$
$788$		0			0
$789$	906.112	−	41.9068i	1.14843	−	0.0531138i
$790$		0			0
$791$	−1126.54	−	650.407i	−1.42419	−	0.822259i
$792$		0			0
$793$	−512.980	−	888.507i	−0.646885	−	1.12044i
$794$		0			0
$795$	511.104	+	65.9456i	0.642899	+	0.0829505i
$796$		0			0
$797$	−275.128	−	327.885i	−0.345204	−	0.411399i	0.565308	−	0.824880i	$-0.308757\pi$
$797$	−275.128	−	327.885i	−0.345204	−	0.411399i	−0.910513	+	0.413481i	$0.864313\pi$
$798$		0			0
$799$	−12.4597	+	4.53497i	−0.0155942	+	0.00567581i
$800$		0			0
$801$	1010.34	+	83.1368i	1.26135	+	0.103791i
$802$		0			0
$803$	−91.0655	−	16.0573i	−0.113407	−	0.0199966i
$804$		0			0
$805$	455.613	+	165.830i	0.565979	+	0.205999i
$806$		0			0
$807$	165.561	+	737.775i	0.205156	+	0.914220i
$808$		0			0
$809$		−	1161.28i		−	1.43545i	−0.696326	−	0.717725i	$-0.745183\pi$
$809$		−	1161.28i		−	1.43545i	0.696326	−	0.717725i	$-0.254817\pi$
$810$		0			0
$811$	611.140			0.753563			0.376782	−	0.926302i	$-0.377031\pi$
$811$	611.140			0.753563			0.376782	+	0.926302i	$0.377031\pi$
$812$		0			0
$813$	−313.846	+	70.4289i	−0.386034	+	0.0866284i
$814$		0			0
$815$	−52.5907	+	144.492i	−0.0645284	+	0.177290i
$816$		0			0
$817$	137.775	−	781.360i	0.168635	−	0.956377i
$818$		0			0
$819$	599.680	+	415.301i	0.732210	+	0.507082i
$820$		0			0
$821$	531.207	+	1459.48i	0.647024	+	1.77769i	0.628440	+	0.777858i	$0.283694\pi$
$821$	531.207	+	1459.48i	0.647024	+	1.77769i	0.0185843	+	0.999827i	$0.494084\pi$
$822$		0			0
$823$	−463.298	+	388.753i	−0.562938	+	0.472361i	−0.879294	−	0.476279i	$-0.841985\pi$
$823$	−463.298	+	388.753i	−0.562938	+	0.472361i	0.316356	+	0.948641i	$0.397541\pi$
$824$		0			0
$825$	−116.417	+	902.275i	−0.141111	+	1.09367i
$826$		0			0
$827$	−79.8064	+	46.0762i	−0.0965010	+	0.0557149i	−0.547474	−	0.836823i	$-0.684410\pi$
$827$	−79.8064	+	46.0762i	−0.0965010	+	0.0557149i	0.450973	+	0.892538i	$0.351077\pi$
$828$		0			0
$829$	−418.250	+	724.429i	−0.504523	+	0.873859i	0.495463	+	0.868629i	$0.334998\pi$
$829$	−418.250	+	724.429i	−0.504523	+	0.873859i	−0.999986	+	0.00523058i	$0.998335\pi$
$830$		0			0
$831$	37.3756	+	808.138i	0.0449766	+	0.972488i
$832$		0			0
$833$	−38.7796	+	6.83789i	−0.0465541	+	0.00820875i
$834$		0			0
$835$	276.698	+	232.177i	0.331375	+	0.278056i
$836$		0			0
$837$	−722.378	−	651.713i	−0.863056	−	0.778629i
$838$		0			0
$839$	−278.941	+	332.429i	−0.332469	+	0.396221i	−0.906218	−	0.422810i	$-0.861044\pi$
$839$	−278.941	+	332.429i	−0.332469	+	0.396221i	0.573750	+	0.819031i	$0.305488\pi$
$840$		0			0
$841$	124.661	+	706.986i	0.148229	+	0.840649i
$842$		0			0
$843$	−27.4445	−	42.8348i	−0.0325558	−	0.0508123i
$844$		0			0
$845$	−0.0826539	−	0.0477203i	−9.78153e−5	−	5.64737e-5i
$846$		0			0
$847$	−317.784	−	550.417i	−0.375187	−	0.649843i
$848$		0			0
$849$	595.250	−	779.908i	0.701119	−	0.918619i
$850$		0			0
$851$	−754.519	−	899.200i	−0.886626	−	1.05664i
$852$		0			0
$853$	375.612	−	136.712i	0.440342	−	0.160271i	−0.112329	−	0.993671i	$-0.535831\pi$
$853$	375.612	−	136.712i	0.440342	−	0.160271i	0.552671	+	0.833400i	$0.313609\pi$
$854$		0			0
$855$	226.620	+	104.253i	0.265053	+	0.121933i
$856$		0			0
$857$	314.017	+	55.3697i	0.366414	+	0.0646087i	0.353824	−	0.935312i	$-0.384881\pi$
$857$	314.017	+	55.3697i	0.366414	+	0.0646087i	0.0125903	+	0.999921i	$0.495992\pi$
$858$		0			0
$859$	−259.079	−	94.2970i	−0.301605	−	0.109775i	0.186785	−	0.982401i	$-0.440193\pi$
$859$	−259.079	−	94.2970i	−0.301605	−	0.109775i	−0.488390	+	0.872626i	$0.662416\pi$
$860$		0			0
$861$	310.645	−	286.133i	0.360795	−	0.332326i
$862$		0			0
$863$			764.036i			0.885325i	0.896688	+	0.442663i	$0.145966\pi$
$863$			764.036i			0.885325i	−0.896688	+	0.442663i	$0.854034\pi$
$864$		0			0
$865$	−496.194			−0.573635
$866$		0			0
$867$	−245.083	+	784.361i	−0.282679	+	0.904684i
$868$		0			0
$869$	328.157	−	901.603i	0.377626	−	1.03752i
$870$		0			0
$871$	249.154	−	1413.02i	0.286055	−	1.62230i
$872$		0			0
$873$	−350.801	+	354.444i	−0.401834	+	0.406007i
$874$		0			0
$875$	209.223	+	574.837i	0.239113	+	0.656956i
$876$		0			0
$877$	611.740	−	513.311i	0.697537	−	0.585303i	−0.223535	−	0.974696i	$-0.571760\pi$
$877$	611.740	−	513.311i	0.697537	−	0.585303i	0.921072	+	0.389393i	$0.127315\pi$
$878$		0			0
$879$	743.367	−	310.165i	0.845697	−	0.352861i
$880$		0			0
$881$	−659.646	+	380.847i	−0.748747	+	0.432290i	−0.825241	−	0.564781i	$-0.808961\pi$
$881$	−659.646	+	380.847i	−0.748747	+	0.432290i	0.0764937	+	0.997070i	$0.475627\pi$
$882$		0			0
$883$	−463.143	+	802.187i	−0.524511	+	0.908479i	0.475082	+	0.879941i	$0.342418\pi$
$883$	−463.143	+	802.187i	−0.524511	+	0.908479i	−0.999593	+	0.0285375i	$0.990915\pi$
$884$		0			0
$885$	124.242	+	64.2688i	0.140386	+	0.0726201i
$886$		0			0
$887$	−169.111	+	29.8188i	−0.190655	+	0.0336176i	−0.268160	−	0.963374i	$-0.586416\pi$
$887$	−169.111	+	29.8188i	−0.190655	+	0.0336176i	0.0775053	+	0.996992i	$0.475305\pi$
$888$		0			0
$889$	271.323	+	227.667i	0.305201	+	0.256094i
$890$		0			0
$891$	1140.74	+	401.898i	1.28029	+	0.451065i
$892$		0			0
$893$	−28.0869	+	33.4726i	−0.0314523	+	0.0374834i
$894$		0			0
$895$	56.4159	+	319.951i	0.0630346	+	0.357487i
$896$		0			0
$897$	643.582	−	1244.14i	0.717482	−	1.38701i
$898$		0			0
$899$	−346.244	−	199.904i	−0.385144	−	0.222363i
$900$		0			0
$901$	−154.003	−	266.740i	−0.170924	−	0.296049i
$902$		0			0
$903$	−446.468	−	1070.04i	−0.494427	−	1.18499i
$904$		0			0
$905$	−208.205	−	248.129i	−0.230061	−	0.274176i
$906$		0			0
$907$	479.601	−	174.560i	0.528777	−	0.192459i	−0.0638151	−	0.997962i	$-0.520327\pi$
$907$	479.601	−	174.560i	0.528777	−	0.192459i	0.592592	+	0.805503i	$0.298105\pi$
$908$		0			0
$909$	683.988	−	187.066i	0.752462	−	0.205793i
$910$		0			0
$911$	653.228	+	115.182i	0.717045	+	0.126434i	0.520255	−	0.854011i	$-0.325837\pi$
$911$	653.228	+	115.182i	0.717045	+	0.126434i	0.196791	+	0.980446i	$0.436948\pi$
$912$		0			0
$913$	−2130.65	−	775.495i	−2.33369	−	0.849392i
$914$		0			0
$915$	−489.378	−	152.912i	−0.534840	−	0.167117i
$916$		0			0
$917$		−	863.378i		−	0.941525i
$918$		0			0
$919$	−63.4363			−0.0690275			−0.0345138	−	0.999404i	$-0.510988\pi$
$919$	−63.4363			−0.0690275			−0.0345138	+	0.999404i	$0.510988\pi$
$920$		0			0
$921$	207.886	+	225.695i	0.225718	+	0.245054i
$922$		0			0
$923$	−365.690	+	1004.72i	−0.396197	+	1.08854i
$924$		0			0
$925$	115.273	−	653.746i	0.124620	−	0.706753i
$926$		0			0
$927$	−469.372	+	43.5091i	−0.506334	+	0.0469353i
$928$		0			0
$929$	444.979	+	1222.57i	0.478987	+	1.31601i	0.910354	+	0.413829i	$0.135809\pi$
$929$	444.979	+	1222.57i	0.478987	+	1.31601i	−0.431368	+	0.902176i	$0.641969\pi$
$930$		0			0
$931$	−99.4075	+	83.4128i	−0.106775	+	0.0895948i
$932$		0			0
$933$	−1116.44	−	852.106i	−1.19662	−	0.913297i
$934$		0			0
$935$	−108.760	+	62.7924i	−0.116320	+	0.0671576i
$936$		0			0
$937$	88.1210	−	152.630i	0.0940459	−	0.162892i	−0.815164	−	0.579230i	$-0.803353\pi$
$937$	88.1210	−	152.630i	0.0940459	−	0.162892i	0.909210	+	0.416338i	$0.136687\pi$
$938$		0			0
$939$	−465.979	+	298.556i	−0.496250	+	0.317951i
$940$		0			0
$941$	1167.87	−	205.926i	1.24109	−	0.218838i	0.485708	−	0.874121i	$-0.338562\pi$
$941$	1167.87	−	205.926i	1.24109	−	0.218838i	0.755383	+	0.655284i	$0.227451\pi$
$942$		0			0
$943$	−621.276	−	521.312i	−0.658829	−	0.552823i
$944$		0			0
$945$	361.034	−	50.3799i	0.382046	−	0.0533121i
$946$		0			0
$947$	−169.717	+	202.261i	−0.179216	+	0.213581i	−0.848172	−	0.529721i	$-0.822297\pi$
$947$	−169.717	+	202.261i	−0.179216	+	0.213581i	0.668957	+	0.743302i	$0.266741\pi$
$948$		0			0
$949$	13.9818	+	79.2948i	0.0147332	+	0.0835561i
$950$		0			0
$951$	293.221	−	13.5612i	0.308329	−	0.0142599i
$952$		0			0
$953$	−117.730	−	67.9713i	−0.123536	−	0.0713235i	0.436959	−	0.899482i	$-0.356056\pi$
$953$	−117.730	−	67.9713i	−0.123536	−	0.0713235i	−0.560495	+	0.828158i	$0.689389\pi$
$954$		0			0
$955$	−82.1337	−	142.260i	−0.0860039	−	0.148963i
$956$		0			0
$957$	492.932	+	63.6010i	0.515081	+	0.0664587i
$958$		0			0
$959$	−214.067	−	255.115i	−0.223219	−	0.266022i
$960$		0			0
$961$	−317.085	+	115.410i	−0.329954	+	0.120093i
$962$		0			0
$963$	−730.365	−	1545.38i	−0.758427	−	1.60476i
$964$		0			0
$965$	−290.442	−	51.2127i	−0.300976	−	0.0530702i
$966$		0			0
$967$	−434.941	−	158.306i	−0.449784	−	0.163708i	0.107189	−	0.994239i	$-0.465815\pi$
$967$	−434.941	−	158.306i	−0.449784	−	0.163708i	−0.556973	+	0.830531i	$0.688037\pi$
$968$		0			0
$969$	−32.6447	−	145.472i	−0.0336890	−	0.150125i
$970$		0			0
$971$			241.390i			0.248599i	0.992245	+	0.124299i	$0.0396683\pi$
$971$			241.390i			0.248599i	−0.992245	+	0.124299i	$0.960332\pi$
$972$		0			0
$973$	1246.02			1.28060
$974$		0			0
$975$	772.941	−	173.453i	0.792760	−	0.177900i
$976$		0			0
$977$	−543.473	+	1493.18i	−0.556267	+	1.52833i	0.268742	+	0.963212i	$0.413392\pi$
$977$	−543.473	+	1493.18i	−0.556267	+	1.52833i	−0.825009	+	0.565119i	$0.808830\pi$
$978$		0			0
$979$	−292.059	+	1656.35i	−0.298324	+	1.69188i
$980$		0			0
$981$	−1313.26	+	620.664i	−1.33870	+	0.632685i
$982$		0			0
$983$	11.4309	+	31.4063i	0.0116286	+	0.0319494i	0.945371	−	0.325996i	$-0.105700\pi$
$983$	11.4309	+	31.4063i	0.0116286	+	0.0319494i	−0.933743	+	0.357945i	$0.883477\pi$
$984$		0			0
$985$	−547.739	+	459.608i	−0.556080	+	0.466607i
$986$		0			0
$987$	−8.17108	+	63.3291i	−0.00827871	+	0.0641632i
$988$		0			0
$989$	−1928.19	+	1113.24i	−1.94963	+	1.12562i
$990$		0			0
$991$	−90.3973	+	156.573i	−0.0912182	+	0.157995i	−0.908024	−	0.418918i	$-0.862409\pi$
$991$	−90.3973	+	156.573i	−0.0912182	+	0.157995i	0.816806	+	0.576913i	$0.195743\pi$
$992$		0			0
$993$	−14.6775	−	317.358i	−0.0147810	−	0.319595i
$994$		0			0
$995$	127.455	−	22.4737i	0.128095	−	0.0225867i
$996$		0			0
$997$	−371.647	−	311.849i	−0.372766	−	0.312787i	0.437089	−	0.899418i	$-0.356010\pi$
$997$	−371.647	−	311.849i	−0.372766	−	0.312787i	−0.809854	+	0.586631i	$0.800454\pi$
$998$		0			0
$999$	−817.941	−	331.401i	−0.818760	−	0.331732i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.bc.b.65.6		36
4.3	odd	2		108.3.k.a.65.1	yes	36
12.11	even	2		324.3.k.a.197.3		36
27.5	odd	18	inner	432.3.bc.b.113.6		36
108.7	odd	18		2916.3.c.b.1457.22		36
108.47	even	18		2916.3.c.b.1457.15		36
108.59	even	18		108.3.k.a.5.1	✓	36
108.103	odd	18		324.3.k.a.125.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.5.1	✓	36	108.59	even	18
108.3.k.a.65.1	yes	36	4.3	odd	2
324.3.k.a.125.3		36	108.103	odd	18
324.3.k.a.197.3		36	12.11	even	2
432.3.bc.b.65.6		36	1.1	even	1	trivial
432.3.bc.b.113.6		36	27.5	odd	18	inner
2916.3.c.b.1457.15		36	108.47	even	18
2916.3.c.b.1457.22		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)

\(f(q)\)	\(=\)	\(q+(2.92720 - 0.656882i) q^{3} +(0.740753 - 2.03520i) q^{5} +(-1.08248 + 6.13906i) q^{7} +(8.13701 - 3.84565i) q^{9} +O(q^{10})\)	\(q+(2.92720 - 0.656882i) q^{3} +(0.740753 - 2.03520i) q^{5} +(-1.08248 + 6.13906i) q^{7} +(8.13701 - 3.84565i) q^{9} +(5.10694 + 14.0312i) q^{11} +(9.95988 - 8.35733i) q^{13} +(0.831446 - 6.44403i) q^{15} +(-3.36308 + 1.94167i) q^{17} +(-6.39866 + 11.0828i) q^{19} +(0.863993 + 18.6813i) q^{21} +(35.3663 - 6.23604i) q^{23} +(15.5578 + 13.0545i) q^{25} +(21.2925 - 16.6020i) q^{27} +(7.13197 - 8.49955i) q^{29} +(-6.25720 - 35.4864i) q^{31} +(24.1659 + 37.7175i) q^{33} +(11.6924 + 6.75059i) q^{35} +(-16.3431 - 28.3071i) q^{37} +(23.6648 - 31.0060i) q^{39} +(-14.5164 - 17.3000i) q^{41} +(-58.2594 + 21.2047i) q^{43} +(-1.79915 - 19.4091i) q^{45} +(3.36255 + 0.592908i) q^{47} +(9.52866 + 3.46815i) q^{49} +(-8.56895 + 7.89281i) q^{51} +79.3144i q^{53} +32.3393 q^{55} +(-11.4501 + 36.6448i) q^{57} +(-7.36318 + 20.2302i) q^{59} +(13.7025 - 77.7109i) q^{61} +(14.8005 + 54.1165i) q^{63} +(-9.63104 - 26.4611i) q^{65} +(84.5379 - 70.9357i) q^{67} +(99.4280 - 41.4856i) q^{69} +(-71.2183 + 41.1179i) q^{71} +(-3.09644 + 5.36320i) q^{73} +(54.1160 + 27.9936i) q^{75} +(-91.6666 + 16.1633i) q^{77} +(-49.2237 - 41.3036i) q^{79} +(51.4220 - 62.5842i) q^{81} +(-97.6080 + 116.325i) q^{83} +(1.46049 + 8.28284i) q^{85} +(15.2935 - 29.5648i) q^{87} +(97.5489 + 56.3199i) q^{89} +(40.5248 + 70.1909i) q^{91} +(-41.6264 - 99.7655i) q^{93} +(17.8159 + 21.2322i) q^{95} +(-52.0684 + 18.9513i) q^{97} +(95.5143 + 94.5326i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) \) 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

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Representations

Groups

Database

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