LMFDB - Embedded newform 108.3.k.a.65.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(5,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("108.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.k (of order $18$, degree $6$, 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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			65.1
Character	$\chi$	$=$	108.65
Dual form			108.3.k.a.5.1

$q$-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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$

Coefficient data

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

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

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

$2$		0			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	$-0.797553\pi$
$7$	1.08248	−	6.13906i	0.154640	−	0.877008i	0.959114	−	0.283020i	$-0.0913363\pi$
$8$		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	$-0.873649\pi$
$11$	−5.10694	−	14.0312i	−0.464267	−	1.27556i	0.457979	−	0.888963i	$-0.348573\pi$
$12$		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	−0.647052	−	0.762446i	$-0.723998\pi$
$19$	6.39866	−	11.0828i	0.336772	−	0.583306i	0.983824	+	0.179140i	$0.0573316\pi$
$20$		0			0
$21$	0.863993	+	18.6813i	0.0411425	+	0.889587i
$22$		0			0
$23$	−35.3663	+	6.23604i	−1.53767	+	0.271132i	−0.877348	−	0.479854i	$-0.840690\pi$
$23$	−35.3663	+	6.23604i	−1.53767	+	0.271132i	−0.660318	+	0.750986i	$0.729578\pi$
$24$		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	$0.141857\pi$
$31$	6.25720	+	35.4864i	0.201845	+	1.14472i	−0.700482	+	0.713670i	$0.747032\pi$
$32$		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	0.440406	−	0.897799i	$-0.354834\pi$
$43$	58.2594	−	21.2047i	1.35487	−	0.493133i	0.914465	+	0.404666i	$0.132612\pi$
$44$		0			0
$45$	−1.79915	−	19.4091i	−0.0399812	−	0.431314i
$46$		0			0
$47$	−3.36255	−	0.592908i	−0.0715435	−	0.0126151i	0.137762	−	0.990465i	$-0.456009\pi$
$47$	−3.36255	−	0.592908i	−0.0715435	−	0.0126151i	−0.209305	+	0.977850i	$0.567120\pi$
$48$		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	−0.861521	−	0.507722i	$-0.830488\pi$
$59$	7.36318	−	20.2302i	0.124800	−	0.342884i	0.986321	+	0.164838i	$0.0527100\pi$
$60$		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	$0.585790\pi$
$67$	−84.5379	+	70.9357i	−1.26176	+	1.05874i	−0.995492	+	0.0948429i	$0.969765\pi$
$68$		0			0
$69$	99.4280	−	41.4856i	1.44099	−	0.601241i
$70$		0			0
$71$	71.2183	−	41.1179i	1.00307	−	0.579125i	0.0939180	−	0.995580i	$-0.470061\pi$
$71$	71.2183	−	41.1179i	1.00307	−	0.579125i	0.909157	+	0.416455i	$0.136728\pi$
$72$		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	0.898772	−	0.438417i	$-0.144461\pi$
$79$	49.2237	+	41.3036i	0.623085	+	0.522830i	−0.275687	+	0.961248i	$0.588905\pi$
$80$		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	$-0.410153\pi$
$83$	97.6080	−	116.325i	1.17600	−	1.40150i	0.897470	−	0.441075i	$-0.145403\pi$
$84$		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	0.569700	−	0.821853i	$-0.307059\pi$
$103$	49.2174	+	17.9137i	0.477839	+	0.173919i	−0.0918613	+	0.995772i	$0.529282\pi$
$104$		0			0
$105$	38.6603	+	12.0798i	0.368193	+	0.115046i
$106$		0			0
$107$			189.920i			1.77495i	0.460854	+	0.887476i	$0.347543\pi$
$107$			189.920i			1.77495i	−0.460854	+	0.887476i	$0.652457\pi$
$108$		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	−0.955926	−	0.293608i	$-0.905144\pi$
$127$	−28.4088	+	49.2055i	−0.223691	+	0.387445i	0.732235	+	0.681052i	$0.238477\pi$
$128$		0			0
$129$	−156.608	+	100.340i	−1.21402	+	0.777829i
$130$		0			0
$131$	136.396	−	24.0503i	1.04119	−	0.183590i	0.373194	−	0.927753i	$-0.378263\pi$
$131$	136.396	−	24.0503i	1.04119	−	0.183590i	0.667998	+	0.744163i	$0.267151\pi$
$132$		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	$0.199846\pi$
$139$	34.7093	+	196.846i	0.249707	+	1.41616i	−0.559595	+	0.828767i	$0.689043\pi$
$140$		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	0.462812	−	0.886456i	$-0.346840\pi$
$151$	209.460	−	76.2371i	1.38715	−	0.504881i	0.924338	+	0.381575i	$0.124618\pi$
$152$		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	$-0.430119\pi$
$163$	70.9962			0.435560			0.217780	+	0.975998i	$0.430119\pi$
$164$		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	$-0.722470\pi$
$167$	57.0403	−	156.717i	0.341559	−	0.938425i	0.984943	−	0.172882i	$-0.0553078\pi$
$168$		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	−0.0911147	−	0.995840i	$-0.529043\pi$
$179$	129.909	−	75.0033i	0.725751	−	0.419013i	0.816866	+	0.576828i	$0.195710\pi$
$180$		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	−0.878418	−	0.477893i	$-0.841401\pi$
$191$	−48.7526	+	58.1011i	−0.255249	+	0.304194i	0.623169	+	0.782087i	$0.285845\pi$
$192$		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	0.781138	−	0.624359i	$-0.214640\pi$
$199$	−29.8782	−	51.7505i	−0.150141	−	0.260053i	−0.931279	+	0.364306i	$0.881306\pi$
$200$		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	0.367043	−	0.930204i	$-0.380370\pi$
$211$	10.6114	+	3.86224i	0.0502911	+	0.0183045i	−0.316752	+	0.948508i	$0.602592\pi$
$212$		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	$-0.864657\pi$
$223$	19.2101	−	108.946i	0.0861441	−	0.488547i	0.997104	−	0.0760521i	$-0.0242315\pi$
$224$		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	$0.148113\pi$
$227$	112.933	+	310.280i	0.497500	+	1.36687i	−0.396182	+	0.918172i	$0.629665\pi$
$228$		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	−0.430168	−	0.902749i	$-0.641546\pi$
$239$	−125.627	+	22.1514i	−0.525636	+	0.0926838i	−0.0954677	+	0.995433i	$0.530435\pi$
$240$		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	−0.498994	−	0.866606i	$-0.666297\pi$
$251$	−376.247	−	217.226i	−1.49899	−	0.865444i	−0.999999	+	0.00116146i	$0.999630\pi$
$252$		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	−0.424005	−	0.905660i	$-0.639376\pi$
$263$	−297.767	−	52.5043i	−1.13219	−	0.199636i	−0.708188	+	0.706024i	$0.750487\pi$
$264$		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	$-0.436615\pi$
$271$	107.217			0.395635			0.197818	+	0.980239i	$0.436615\pi$
$272$		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	−0.967251	−	0.253822i	$-0.918312\pi$
$283$	−250.525	+	210.215i	−0.885247	+	0.742810i	0.0820041	+	0.996632i	$0.473868\pi$
$284$		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	0.770633	−	0.637279i	$-0.219940\pi$
$307$	−51.1411	−	88.5790i	−0.166583	−	0.288531i	−0.937216	+	0.348748i	$0.886607\pi$
$308$		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	$0.0490087\pi$
$311$	300.925	+	358.629i	0.967605	+	1.15315i	−0.0205661	+	0.999788i	$0.506547\pi$
$312$		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	−0.999904	−	0.0138738i	$-0.995584\pi$
$331$	−18.3892	+	104.290i	−0.0555564	+	0.315076i	0.944347	+	0.328950i	$0.106695\pi$
$332$		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	0.414676	−	0.909969i	$-0.363895\pi$
$347$	387.103	−	68.2568i	1.11557	−	0.196705i	0.700896	+	0.713264i	$0.252784\pi$
$348$		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	−0.293711	−	0.955894i	$-0.594890\pi$
$359$	−455.354	−	262.899i	−1.26840	−	0.732309i	−0.974684	+	0.223586i	$0.928224\pi$
$360$		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	−0.722131	−	0.691756i	$-0.756837\pi$
$367$	−304.854	+	110.958i	−0.830664	+	0.302337i	−0.108533	+	0.994093i	$0.534615\pi$
$368$		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	$-0.794375\pi$
$379$	−605.266			−1.59701			−0.798504	+	0.601989i	$0.794375\pi$
$380$		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	$-0.774089\pi$
$383$	92.4520	−	254.010i	0.241389	−	0.663211i	0.999933	−	0.0115889i	$-0.00368896\pi$
$384$		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	0.996034	−	0.0889728i	$-0.0283584\pi$
$419$	308.155	+	367.245i	0.735453	+	0.876479i	−0.260581	+	0.965452i	$0.583914\pi$
$420$		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	$0.199830\pi$
$431$			506.298i			1.17471i	−0.809331	+	0.587353i	$0.800170\pi$
$432$		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	$-0.769133\pi$
$439$	79.7889	−	452.505i	0.181751	−	1.03076i	0.930059	−	0.367411i	$-0.119756\pi$
$440$		0			0
$441$	90.8721	−	8.42351i	0.206059	−	0.0191009i
$442$		0			0
$443$	18.6549	+	51.2541i	0.0421105	+	0.115698i	0.958966	−	0.283523i	$-0.0915031\pi$
$443$	18.6549	+	51.2541i	0.0421105	+	0.115698i	−0.916855	+	0.399220i	$0.869281\pi$
$444$		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	$0.0816139\pi$
$463$	67.1681	+	380.929i	0.145071	+	0.822741i	−0.822238	+	0.569143i	$0.807275\pi$
$464$		0			0
$465$	−233.878	+	10.8166i	−0.502963	+	0.0232615i
$466$		0			0
$467$	300.701	+	173.610i	0.643900	+	0.371756i	0.786115	−	0.618080i	$-0.212089\pi$
$467$	300.701	+	173.610i	0.643900	+	0.371756i	−0.142215	+	0.989836i	$0.545423\pi$
$468$		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	−0.0816727	−	0.996659i	$-0.526026\pi$
$479$	−239.163	−	42.1710i	−0.499297	−	0.0880396i	−0.417625	+	0.908620i	$0.637137\pi$
$480$		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	$-0.402287\pi$
$487$	294.321			0.604355			0.302177	+	0.953252i	$0.402287\pi$
$488$		0			0
$489$	−207.820	+	46.6361i	−0.424990	+	0.0953704i
$490$		0			0
$491$	−81.7251	+	224.538i	−0.166446	+	0.457307i	−0.994672	−	0.103087i	$-0.967128\pi$
$491$	−81.7251	+	224.538i	−0.166446	+	0.457307i	0.828226	+	0.560394i	$0.189350\pi$
$492$		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	−0.808815	−	0.588063i	$-0.799891\pi$
$499$	−184.698	+	154.980i	−0.370136	+	0.310581i	0.438679	+	0.898644i	$0.355446\pi$
$500$		0			0
$501$	−64.0240	+	496.211i	−0.127792	+	0.990441i
$502$		0			0
$503$	−138.798	+	80.1352i	−0.275941	+	0.159314i	−0.631584	−	0.775307i	$-0.717595\pi$
$503$	−138.798	+	80.1352i	−0.275941	+	0.159314i	0.355644	+	0.934622i	$0.384262\pi$
$504$		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	0.832206	−	0.554466i	$-0.187077\pi$
$523$	−33.5131	−	58.0464i	−0.0640786	−	0.110987i	−0.896285	+	0.443479i	$0.853744\pi$
$524$		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	−0.970599	−	0.240702i	$-0.922622\pi$
$547$	13.0135	−	73.8033i	0.0237907	−	0.134924i	0.994390	+	0.105778i	$0.0337334\pi$
$548$		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	−0.564799	−	0.825229i	$-0.691046\pi$
$563$	−457.883	+	80.7371i	−0.813291	+	0.143405i	−0.248492	+	0.968634i	$0.579935\pi$
$564$		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	0.988601	−	0.150558i	$-0.0481070\pi$
$571$	4.63998	+	26.3146i	0.00812605	+	0.0460851i	−0.980475	+	0.196643i	$0.936996\pi$
$572$		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	0.514411	−	0.857544i	$-0.328011\pi$
$587$	413.543	+	72.9187i	0.704502	+	0.124223i	0.190091	+	0.981767i	$0.439122\pi$
$588$		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	$-0.705794\pi$
$599$	222.904	−	612.422i	0.372126	−	1.02241i	0.974538	−	0.224223i	$-0.0719843\pi$
$600$		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	−0.840603	−	0.541652i	$-0.817799\pi$
$607$	−275.061	+	230.804i	−0.453149	+	0.380237i	0.387454	+	0.921889i	$0.373355\pi$
$608$		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	0.128658	−	0.991689i	$-0.458933\pi$
$619$	−511.061	−	428.831i	−0.825623	−	0.692780i	−0.954282	+	0.298909i	$0.903377\pi$
$620$		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	0.542344	−	0.840156i	$-0.317537\pi$
$631$	−288.004	−	498.837i	−0.456425	−	0.790551i	−0.998769	+	0.0496058i	$0.984204\pi$
$632$		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	0.832891	−	0.553437i	$-0.186684\pi$
$643$	717.060	+	260.989i	1.11518	+	0.405892i	0.282289	+	0.959330i	$0.408906\pi$
$644$		0			0
$645$	88.2042	+	393.056i	0.136751	+	0.609389i
$646$		0			0
$647$			128.575i			0.198725i	0.995051	+	0.0993624i	$0.0316803\pi$
$647$			128.575i			0.198725i	−0.995051	+	0.0993624i	$0.968320\pi$
$648$		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	0.875494	−	0.483229i	$-0.160536\pi$
$659$	−69.7138	−	191.537i	−0.105787	−	0.290648i	−0.981281	+	0.192581i	$0.938314\pi$
$660$		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	0.958245	−	0.285949i	$-0.0923087\pi$
$683$	812.585	+	469.146i	1.18973	+	0.686890i	0.231484	+	0.972839i	$0.425642\pi$
$684$		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	−0.364820	−	0.931078i	$-0.618870\pi$
$691$	−31.6500	+	11.5197i	−0.0458032	+	0.0166710i	0.319017	+	0.947749i	$0.396647\pi$
$692$		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	−0.908499	−	0.417886i	$-0.862771\pi$
$719$	−719.610	+	415.467i	−1.00085	+	0.577840i	−0.0923493	+	0.995727i	$0.529438\pi$
$720$		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	0.753104	−	0.657902i	$-0.228556\pi$
$727$	171.551	+	143.949i	0.235972	+	0.198004i	−0.517132	+	0.855906i	$0.673000\pi$
$728$		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	0.980335	−	0.197343i	$-0.0632311\pi$
$739$	235.936	+	408.653i	0.319264	+	0.552981i	−0.661071	+	0.750323i	$0.729898\pi$
$740$		0			0
$741$	192.211	+	460.670i	0.259394	+	0.621686i
$742$		0			0
$743$	−245.380	−	292.432i	−0.330255	−	0.393583i	0.575208	−	0.818007i	$-0.304921\pi$
$743$	−245.380	−	292.432i	−0.330255	−	0.393583i	−0.905464	+	0.424424i	$0.860477\pi$
$744$		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	−0.473613	−	0.880733i	$-0.657051\pi$
$751$	−1053.31	−	383.374i	−1.40255	−	0.510485i	−0.928933	+	0.370248i	$0.879273\pi$
$752$		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	$0.0341150\pi$
$787$	75.9828	+	430.920i	0.0965474	+	0.547547i	−0.897715	+	0.440577i	$0.854774\pi$
$788$		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	$-0.622969\pi$
$811$	−611.140			−0.753563			−0.376782	+	0.926302i	$0.622969\pi$
$812$		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	−0.316356	−	0.948641i	$-0.602459\pi$
$823$	463.298	−	388.753i	0.562938	−	0.472361i	0.879294	+	0.476279i	$0.158015\pi$
$824$		0			0
$825$	−116.417	+	902.275i	−0.141111	+	1.09367i
$826$		0			0
$827$	79.8064	−	46.0762i	0.0965010	−	0.0557149i	−0.450973	−	0.892538i	$-0.648923\pi$
$827$	79.8064	−	46.0762i	0.0965010	−	0.0557149i	0.547474	+	0.836823i	$0.315590\pi$
$828$		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	−0.573750	−	0.819031i	$-0.694512\pi$
$839$	278.941	−	332.429i	0.332469	−	0.396221i	0.906218	+	0.422810i	$0.138956\pi$
$840$		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	0.488390	−	0.872626i	$-0.337584\pi$
$859$	259.079	+	94.2970i	0.301605	+	0.109775i	−0.186785	+	0.982401i	$0.559807\pi$
$860$		0			0
$861$	310.645	−	286.133i	0.360795	−	0.332326i
$862$		0			0
$863$		−	764.036i		−	0.885325i	−0.896688	−	0.442663i	$-0.854034\pi$
$863$		−	764.036i		−	0.885325i	0.896688	−	0.442663i	$-0.145966\pi$
$864$		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	$-0.657582\pi$
$883$	463.143	−	802.187i	0.524511	−	0.908479i	0.999593	−	0.0285375i	$-0.00908500\pi$
$884$		0			0
$885$	124.242	+	64.2688i	0.140386	+	0.0726201i
$886$		0			0
$887$	169.111	−	29.8188i	0.190655	−	0.0336176i	−0.0775053	−	0.996992i	$-0.524695\pi$
$887$	169.111	−	29.8188i	0.190655	−	0.0336176i	0.268160	+	0.963374i	$0.413584\pi$
$888$		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	−0.592592	−	0.805503i	$-0.701895\pi$
$907$	−479.601	+	174.560i	−0.528777	+	0.192459i	0.0638151	+	0.997962i	$0.479673\pi$
$908$		0			0
$909$	683.988	−	187.066i	0.752462	−	0.205793i
$910$		0			0
$911$	−653.228	−	115.182i	−0.717045	−	0.126434i	−0.196791	−	0.980446i	$-0.563052\pi$
$911$	−653.228	−	115.182i	−0.717045	−	0.126434i	−0.520255	+	0.854011i	$0.674163\pi$
$912$		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	$-0.489012\pi$
$919$	63.4363			0.0690275			0.0345138	+	0.999404i	$0.489012\pi$
$920$		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	−0.668957	−	0.743302i	$-0.733259\pi$
$947$	169.717	−	202.261i	0.179216	−	0.213581i	0.848172	+	0.529721i	$0.177703\pi$
$948$		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	0.556973	−	0.830531i	$-0.311963\pi$
$967$	434.941	+	158.306i	0.449784	+	0.163708i	−0.107189	+	0.994239i	$0.534185\pi$
$968$		0			0
$969$	−32.6447	−	145.472i	−0.0336890	−	0.150125i
$970$		0			0
$971$		−	241.390i		−	0.248599i	−0.992245	−	0.124299i	$-0.960332\pi$
$971$		−	241.390i		−	0.248599i	0.992245	−	0.124299i	$-0.0396683\pi$
$972$		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	0.933743	−	0.357945i	$-0.116523\pi$
$983$	−11.4309	−	31.4063i	−0.0116286	−	0.0319494i	−0.945371	+	0.325996i	$0.894300\pi$
$984$		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	−0.816806	−	0.576913i	$-0.804257\pi$
$991$	90.3973	−	156.573i	0.0912182	−	0.157995i	0.908024	+	0.418918i	$0.137591\pi$
$992$		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	108.3.k.a.65.1	yes	36
3.2	odd	2		324.3.k.a.197.3		36
4.3	odd	2		432.3.bc.b.65.6		36
27.5	odd	18	inner	108.3.k.a.5.1	✓	36
27.7	even	9		2916.3.c.b.1457.22		36
27.20	odd	18		2916.3.c.b.1457.15		36
27.22	even	9		324.3.k.a.125.3		36
108.59	even	18		432.3.bc.b.113.6		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.5.1	✓	36	27.5	odd	18	inner
108.3.k.a.65.1	yes	36	1.1	even	1	trivial
324.3.k.a.125.3		36	27.22	even	9
324.3.k.a.197.3		36	3.2	odd	2
432.3.bc.b.65.6		36	4.3	odd	2
432.3.bc.b.113.6		36	108.59	even	18
2916.3.c.b.1457.15		36	27.20	odd	18
2916.3.c.b.1457.22		36	27.7	even	9

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.k (of order \(18\), degree \(6\), 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

Fields

Representations

Groups

Database

Properties

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