LMFDB - Embedded newform 405.3.s.a.37.34

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(37,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.37"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([28, 9])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.s (of order $36$, degree $12$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$408$
Relative dimension:	$34$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			37.34
Character	$\chi$	$=$	405.37
Dual form			405.3.s.a.208.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.75348 + 0.328387i) q^{2} +(10.0415 + 1.77059i) q^{4} +(4.26277 + 2.61320i) q^{5} +(1.74995 - 2.49919i) q^{7} +(22.5515 + 6.04267i) q^{8} +(15.1421 + 11.2084i) q^{10} +(-8.21269 - 2.98918i) q^{11} +(-14.9670 + 1.30944i) q^{13} +(7.38912 - 8.80601i) q^{14} +(44.3363 + 16.1371i) q^{16} +(-24.1418 + 6.46879i) q^{17} +(23.0066 - 13.2829i) q^{19} +(38.1778 + 33.7882i) q^{20} +(-29.8446 - 13.9168i) q^{22} +(-16.6632 - 23.7975i) q^{23} +(11.3424 + 22.2789i) q^{25} -56.6083 q^{26} +(21.9973 - 21.9973i) q^{28} +(-3.19342 - 3.80577i) q^{29} +(-2.35330 + 13.3462i) q^{31} +(76.4778 + 35.6622i) q^{32} +(-92.7402 + 16.3526i) q^{34} +(13.9905 - 6.08049i) q^{35} +(21.6691 - 5.80622i) q^{37} +(90.7169 - 42.3020i) q^{38} +(80.3413 + 84.6902i) q^{40} +(10.7753 + 9.04151i) q^{41} +(21.6979 - 10.1179i) q^{43} +(-77.1755 - 44.5573i) q^{44} +(-54.7302 - 94.7954i) q^{46} +(-13.8013 + 19.7104i) q^{47} +(13.5754 + 37.2980i) q^{49} +(35.2572 + 87.3482i) q^{50} +(-152.610 - 13.3517i) q^{52} +(-35.7379 + 35.7379i) q^{53} +(-27.1975 - 34.2036i) q^{55} +(54.5659 - 45.7863i) q^{56} +(-10.7367 - 15.3335i) q^{58} +(7.15372 + 19.6547i) q^{59} +(-13.4180 - 76.0970i) q^{61} +(-13.2158 + 49.3221i) q^{62} +(111.904 + 64.6080i) q^{64} +(-67.2226 - 33.5299i) q^{65} +(-8.95949 - 102.407i) q^{67} +(-253.875 + 22.2112i) q^{68} +(54.5099 - 18.2287i) q^{70} +(12.6791 - 21.9608i) q^{71} +(86.6915 + 23.2289i) q^{73} +(83.2413 - 14.6777i) q^{74} +(254.541 - 92.6453i) q^{76} +(-21.8424 + 15.2942i) q^{77} +(-6.63920 - 7.91230i) q^{79} +(146.826 + 184.649i) q^{80} +(37.4756 + 37.4756i) q^{82} +(-6.03693 + 69.0024i) q^{83} +(-119.815 - 35.5126i) q^{85} +(84.7654 - 30.8521i) q^{86} +(-167.146 - 117.037i) q^{88} +(-61.3185 + 35.4023i) q^{89} +(-22.9190 + 39.6969i) q^{91} +(-125.188 - 268.467i) q^{92} +(-58.2757 + 69.4503i) q^{94} +(132.783 + 3.49913i) q^{95} +(-32.6054 - 69.9225i) q^{97} +(38.7067 + 144.455i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8} - 6 q^{10} + 60 q^{11} - 12 q^{13} - 24 q^{16} + 6 q^{17} + 300 q^{20} - 12 q^{22} + 156 q^{23} + 6 q^{25} + 48 q^{26} - 24 q^{28} - 24 q^{31} - 72 q^{32}+ \cdots + 1032 q^{98}+O(q^{100}) $ 408 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 6 * q^8 - 6 * q^10 + 60 * q^11 - 12 * q^13 - 24 * q^16 + 6 * q^17 + 300 * q^20 - 12 * q^22 + 156 * q^23 + 6 * q^25 + 48 * q^26 - 24 * q^28 - 24 * q^31 - 72 * q^32 - 156 * q^35 - 6 * q^37 + 252 * q^38 - 108 * q^40 + 384 * q^41 - 12 * q^43 - 12 * q^46 + 210 * q^47 - 276 * q^50 - 60 * q^52 - 516 * q^53 - 24 * q^55 - 912 * q^56 - 12 * q^58 - 312 * q^61 + 6 * q^62 - 420 * q^65 - 480 * q^67 + 540 * q^68 - 12 * q^70 + 12 * q^71 - 6 * q^73 - 216 * q^76 + 876 * q^77 + 1644 * q^80 - 24 * q^82 + 372 * q^83 - 12 * q^85 - 516 * q^86 + 348 * q^88 - 12 * q^91 - 2082 * q^92 - 198 * q^95 + 600 * q^97 + 1032 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	3.75348	+	0.328387i	1.87674	+	0.164193i	0.967632	−	0.252367i	$-0.0812089\pi$
$2$	3.75348	+	0.328387i	1.87674	+	0.164193i	0.909108	+	0.416560i	$0.136764\pi$
$3$		0			0
$3$		0			0
$4$	10.0415	+	1.77059i	2.51039	+	0.442649i
$5$	4.26277	+	2.61320i	0.852553	+	0.522640i
$5$	4.26277	+	2.61320i	0.852553	+	0.522640i
$6$		0			0
$7$	1.74995	−	2.49919i	0.249993	−	0.357027i	−0.674467	−	0.738305i	$-0.735627\pi$
$7$	1.74995	−	2.49919i	0.249993	−	0.357027i	0.924461	+	0.381277i	$0.124516\pi$
$8$	22.5515	+	6.04267i	2.81894	+	0.755334i
$9$		0			0
$10$	15.1421	+	11.2084i	1.51421	+	1.12084i
$11$	−8.21269	−	2.98918i	−0.746608	−	0.271743i	−0.0594306	−	0.998232i	$-0.518928\pi$
$11$	−8.21269	−	2.98918i	−0.746608	−	0.271743i	−0.687178	+	0.726489i	$0.741151\pi$
$12$		0			0
$13$	−14.9670	+	1.30944i	−1.15131	+	0.100726i	−0.646785	−	0.762672i	$-0.723887\pi$
$13$	−14.9670	+	1.30944i	−1.15131	+	0.100726i	−0.504522	+	0.863399i	$0.668331\pi$
$14$	7.38912	−	8.80601i	0.527794	−	0.629000i
$15$		0			0
$16$	44.3363	+	16.1371i	2.77102	+	1.00857i
$17$	−24.1418	+	6.46879i	−1.42011	+	0.380517i	−0.885522	−	0.464597i	$-0.846199\pi$
$17$	−24.1418	+	6.46879i	−1.42011	+	0.380517i	−0.534586	+	0.845114i	$0.679533\pi$
$18$		0			0
$19$	23.0066	−	13.2829i	1.21088	−	0.699100i	0.247926	−	0.968779i	$-0.420251\pi$
$19$	23.0066	−	13.2829i	1.21088	−	0.699100i	0.962950	+	0.269679i	$0.0869177\pi$
$20$	38.1778	+	33.7882i	1.90889	+	1.68941i
$21$		0			0
$22$	−29.8446	−	13.9168i	−1.35657	−	0.632580i
$23$	−16.6632	−	23.7975i	−0.724487	−	1.03467i	−0.997359	−	0.0726240i	$-0.976863\pi$
$23$	−16.6632	−	23.7975i	−0.724487	−	1.03467i	0.272873	−	0.962050i	$-0.412026\pi$
$24$		0			0
$25$	11.3424	+	22.2789i	0.453694	+	0.891157i
$26$	−56.6083			−2.17724
$27$		0			0
$28$	21.9973	−	21.9973i	0.785617	−	0.785617i
$29$	−3.19342	−	3.80577i	−0.110118	−	0.131233i	0.708170	−	0.706042i	$-0.249521\pi$
$29$	−3.19342	−	3.80577i	−0.110118	−	0.131233i	−0.818288	+	0.574809i	$0.805077\pi$
$30$		0			0
$31$	−2.35330	+	13.3462i	−0.0759130	+	0.430524i	0.923037	+	0.384711i	$0.125699\pi$
$31$	−2.35330	+	13.3462i	−0.0759130	+	0.430524i	−0.998950	+	0.0458129i	$0.985412\pi$
$32$	76.4778	+	35.6622i	2.38993	+	1.11444i
$33$		0			0
$34$	−92.7402	+	16.3526i	−2.72765	+	0.480959i
$35$	13.9905	−	6.08049i	0.399730	−	0.173728i
$36$		0			0
$37$	21.6691	−	5.80622i	0.585652	−	0.156925i	0.0461868	−	0.998933i	$-0.485293\pi$
$37$	21.6691	−	5.80622i	0.585652	−	0.156925i	0.539465	+	0.842008i	$0.318626\pi$
$38$	90.7169	−	42.3020i	2.38729	−	1.11321i
$39$		0			0
$40$	80.3413	+	84.6902i	2.00853	+	2.11726i
$41$	10.7753	+	9.04151i	0.262811	+	0.220525i	0.764665	−	0.644427i	$-0.222904\pi$
$41$	10.7753	+	9.04151i	0.262811	+	0.220525i	−0.501854	+	0.864952i	$0.667349\pi$
$42$		0			0
$43$	21.6979	−	10.1179i	0.504603	−	0.235300i	−0.153610	−	0.988131i	$-0.549090\pi$
$43$	21.6979	−	10.1179i	0.504603	−	0.235300i	0.658214	+	0.752831i	$0.271312\pi$
$44$	−77.1755	−	44.5573i	−1.75399	−	1.01267i
$45$		0			0
$46$	−54.7302	−	94.7954i	−1.18979	−	2.06077i
$47$	−13.8013	+	19.7104i	−0.293646	+	0.419369i	−0.938683	−	0.344782i	$-0.887953\pi$
$47$	−13.8013	+	19.7104i	−0.293646	+	0.419369i	0.645037	+	0.764151i	$0.276842\pi$
$48$		0			0
$49$	13.5754	+	37.2980i	0.277048	+	0.761184i
$50$	35.2572	+	87.3482i	0.705144	+	1.74696i
$51$		0			0
$52$	−152.610	−	13.3517i	−2.93481	−	0.256763i
$53$	−35.7379	+	35.7379i	−0.674300	+	0.674300i	−0.958704	−	0.284404i	$-0.908204\pi$
$53$	−35.7379	+	35.7379i	−0.674300	+	0.674300i	0.284404	+	0.958704i	$0.408204\pi$
$54$		0			0
$55$	−27.1975	−	34.2036i	−0.494500	−	0.621883i
$56$	54.5659	−	45.7863i	0.974392	−	0.817612i
$57$		0			0
$58$	−10.7367	−	15.3335i	−0.185115	−	0.264371i
$59$	7.15372	+	19.6547i	0.121250	+	0.333130i	0.985437	−	0.170039i	$-0.0543894\pi$
$59$	7.15372	+	19.6547i	0.121250	+	0.333130i	−0.864188	+	0.503169i	$0.832167\pi$
$60$		0			0
$61$	−13.4180	−	76.0970i	−0.219966	−	1.24749i	−0.872077	−	0.489368i	$-0.837227\pi$
$61$	−13.4180	−	76.0970i	−0.219966	−	1.24749i	0.652111	−	0.758124i	$-0.273884\pi$
$62$	−13.2158	+	49.3221i	−0.213158	+	0.795517i
$63$		0			0
$64$	111.904	+	64.6080i	1.74851	+	1.00950i
$65$	−67.2226	−	33.5299i	−1.03419	−	0.515845i
$66$		0			0
$67$	−8.95949	−	102.407i	−0.133724	−	1.52847i	−0.705884	−	0.708328i	$-0.749450\pi$
$67$	−8.95949	−	102.407i	−0.133724	−	1.52847i	0.572160	−	0.820142i	$-0.306106\pi$
$68$	−253.875	+	22.2112i	−3.73345	+	0.326635i
$69$		0			0
$70$	54.5099	−	18.2287i	0.778713	−	0.260410i
$71$	12.6791	−	21.9608i	0.178579	−	0.309308i	−0.762815	−	0.646617i	$-0.776183\pi$
$71$	12.6791	−	21.9608i	0.178579	−	0.309308i	0.941394	+	0.337309i	$0.109517\pi$
$72$		0			0
$73$	86.6915	+	23.2289i	1.18755	+	0.318204i	0.797919	−	0.602765i	$-0.205934\pi$
$73$	86.6915	+	23.2289i	1.18755	+	0.318204i	0.389635	+	0.920969i	$0.372601\pi$
$74$	83.2413	−	14.6777i	1.12488	−	0.198347i
$75$		0			0
$76$	254.541	−	92.6453i	3.34922	−	1.21902i
$77$	−21.8424	+	15.2942i	−0.283667	+	0.198626i
$78$		0			0
$79$	−6.63920	−	7.91230i	−0.0840406	−	0.100156i	0.722386	−	0.691490i	$-0.243046\pi$
$79$	−6.63920	−	7.91230i	−0.0840406	−	0.100156i	−0.806426	+	0.591335i	$0.798601\pi$
$80$	146.826	+	184.649i	1.83532	+	2.30811i
$81$		0			0
$82$	37.4756	+	37.4756i	0.457019	+	0.457019i
$83$	−6.03693	+	69.0024i	−0.0727341	+	0.831354i	0.868960	+	0.494883i	$0.164789\pi$
$83$	−6.03693	+	69.0024i	−0.0727341	+	0.831354i	−0.941694	+	0.336471i	$0.890766\pi$
$84$		0			0
$85$	−119.815	−	35.5126i	−1.40959	−	0.417795i
$86$	84.7654	−	30.8521i	0.985644	−	0.358745i
$87$		0			0
$88$	−167.146	−	117.037i	−1.89939	−	1.32997i
$89$	−61.3185	+	35.4023i	−0.688972	+	0.397778i	−0.803227	−	0.595673i	$-0.796885\pi$
$89$	−61.3185	+	35.4023i	−0.688972	+	0.397778i	0.114255	+	0.993452i	$0.463552\pi$
$90$		0			0
$91$	−22.9190	+	39.6969i	−0.251857	+	0.436229i
$92$	−125.188	−	268.467i	−1.36074	−	2.91812i
$93$		0			0
$94$	−58.2757	+	69.4503i	−0.619954	+	0.738833i
$95$	132.783	+	3.49913i	1.39771	+	0.0368330i
$96$		0			0
$97$	−32.6054	−	69.9225i	−0.336138	−	0.720850i	0.663488	−	0.748187i	$-0.269075\pi$
$97$	−32.6054	−	69.9225i	−0.336138	−	0.720850i	−0.999626	+	0.0273363i	$0.991298\pi$
$98$	38.7067	+	144.455i	0.394966	+	1.47403i
$99$		0			0
$100$	74.4478	+	243.798i	0.744478	+	2.43798i
$101$	−31.7898	−	180.289i	−0.314750	−	1.78504i	−0.573617	−	0.819124i	$-0.694460\pi$
$101$	−31.7898	−	180.289i	−0.314750	−	1.78504i	0.258867	−	0.965913i	$-0.416651\pi$
$102$		0			0
$103$	−77.3039	+	165.779i	−0.750523	+	1.60950i	0.0415948	+	0.999135i	$0.486756\pi$
$103$	−77.3039	+	165.779i	−0.750523	+	1.60950i	−0.792118	+	0.610368i	$0.791022\pi$
$104$	−345.441	−	60.9106i	−3.32155	−	0.585679i
$105$		0			0
$106$	−145.877	+	122.406i	−1.37620	+	1.15477i
$107$	5.45487	+	5.45487i	0.0509801	+	0.0509801i	0.732137	−	0.681157i	$-0.238523\pi$
$107$	5.45487	+	5.45487i	0.0509801	+	0.0509801i	−0.681157	+	0.732137i	$0.738523\pi$
$108$		0			0
$109$			30.3525i			0.278463i	0.990260	+	0.139231i	$0.0444632\pi$
$109$			30.3525i			0.278463i	−0.990260	+	0.139231i	$0.955537\pi$
$110$	−90.8532	−	137.314i	−0.825938	−	1.24831i
$111$		0			0
$112$	117.916	−	82.5659i	1.05282	−	0.737195i
$113$	8.63948	−	18.5274i	0.0764556	−	0.163959i	−0.864365	−	0.502865i	$-0.832279\pi$
$113$	8.63948	−	18.5274i	0.0764556	−	0.163959i	0.940820	+	0.338906i	$0.110057\pi$
$114$		0			0
$115$	−8.84362	−	144.987i	−0.0769010	−	1.26076i
$116$	−25.3284	−	43.8700i	−0.218348	−	0.378190i
$117$		0			0
$118$	20.3970	+	76.1227i	0.172856	+	0.645107i
$119$	−26.0804	+	71.6552i	−0.219163	+	0.602144i
$120$		0			0
$121$	−34.1782	−	28.6789i	−0.282465	−	0.237016i
$122$	−25.3748	−	290.035i	−0.207990	−	2.37733i
$123$		0			0
$124$	−47.2616	+	129.850i	−0.381142	+	1.04718i
$125$	−9.86954	+	124.610i	−0.0789563	+	0.996878i
$126$		0			0
$127$	−13.0107	+	48.5567i	−0.102447	+	0.382336i	−0.998043	−	0.0625315i	$-0.980083\pi$
$127$	−13.0107	+	48.5567i	−0.102447	+	0.382336i	0.895596	+	0.444868i	$0.146749\pi$
$128$	122.321	+	85.6504i	0.955637	+	0.669144i
$129$		0			0
$130$	−241.308	−	147.929i	−1.85622	−	1.13791i
$131$	−35.4480	+	201.036i	−0.270596	+	1.53462i	0.482018	+	0.876161i	$0.339904\pi$
$131$	−35.4480	+	201.036i	−0.270596	+	1.53462i	−0.752614	+	0.658462i	$0.771207\pi$
$132$		0			0
$133$	7.06405	−	80.7425i	0.0531132	−	0.607086i
$134$		−	387.327i		−	2.89050i
$135$		0			0
$136$	−583.525			−4.29062
$137$	−37.1184	−	3.24744i	−0.270937	−	0.0237039i	−0.0491224	−	0.998793i	$-0.515642\pi$
$137$	−37.1184	−	3.24744i	−0.270937	−	0.0237039i	−0.221815	+	0.975089i	$0.571198\pi$
$138$		0			0
$139$	182.916	+	32.2530i	1.31594	+	0.232036i	0.787173	−	0.616732i	$-0.211544\pi$
$139$	182.916	+	32.2530i	1.31594	+	0.232036i	0.528766	+	0.848768i	$0.322655\pi$
$140$	151.253	−	36.2859i	1.08038	−	0.259185i
$141$		0			0
$142$	54.8024	−	78.2659i	0.385932	−	0.551169i
$143$	126.833	+	33.9849i	0.886947	+	0.237657i
$144$		0			0
$145$	−3.66756	−	24.5681i	−0.0252935	−	0.169435i
$146$	317.767	+	115.658i	2.17648	+	0.792175i
$147$		0			0
$148$	227.872	−	19.9362i	1.53967	−	0.134704i
$149$	−25.6513	+	30.5701i	−0.172157	+	0.205168i	−0.845223	−	0.534414i	$-0.820532\pi$
$149$	−25.6513	+	30.5701i	−0.172157	+	0.205168i	0.673066	+	0.739582i	$0.264977\pi$
$150$		0			0
$151$	143.221	+	52.1282i	0.948484	+	0.345220i	0.769511	−	0.638634i	$-0.220500\pi$
$151$	143.221	+	52.1282i	0.948484	+	0.345220i	0.178973	+	0.983854i	$0.442722\pi$
$152$	599.100	−	160.528i	3.94145	−	1.05611i
$153$		0			0
$154$	−87.0072	+	50.2337i	−0.564982	+	0.326193i
$155$	−44.9080	+	50.7423i	−0.289729	+	0.327369i
$156$		0			0
$157$	111.147	+	51.8286i	0.707942	+	0.330119i	0.743023	−	0.669266i	$-0.233391\pi$
$157$	111.147	+	51.8286i	0.707942	+	0.330119i	−0.0350814	+	0.999384i	$0.511169\pi$
$158$	−22.3218	−	31.8789i	−0.141277	−	0.201765i
$159$		0			0
$160$	232.814	+	351.871i	1.45509	+	2.19920i
$161$	−88.6343			−0.550524
$162$		0			0
$163$	20.2656	−	20.2656i	0.124329	−	0.124329i	−0.642205	−	0.766533i	$-0.721980\pi$
$163$	20.2656	−	20.2656i	0.124329	−	0.124329i	0.766533	+	0.642205i	$0.221980\pi$
$164$	92.1913	+	109.869i	0.562142	+	0.669935i
$165$		0			0
$166$	−45.3190	+	257.017i	−0.273006	+	1.54829i
$167$	120.543	+	56.2102i	0.721815	+	0.336588i	0.748571	−	0.663054i	$-0.230740\pi$
$167$	120.543	+	56.2102i	0.721815	+	0.336588i	−0.0267565	+	0.999642i	$0.508518\pi$
$168$		0			0
$169$	55.8638	−	9.85029i	0.330555	−	0.0582858i
$170$	−438.062	−	172.642i	−2.57684	−	1.01554i
$171$		0			0
$172$	235.795	−	63.1812i	1.37090	−	0.367333i
$173$	19.7354	−	9.20275i	0.114077	−	0.0531951i	−0.364742	−	0.931109i	$-0.618843\pi$
$173$	19.7354	−	9.20275i	0.114077	−	0.0531951i	0.478819	+	0.877914i	$0.341065\pi$
$174$		0			0
$175$	75.5279	+	10.6404i	0.431588	+	0.0608021i
$176$	−315.884	−	265.058i	−1.79480	−	1.50601i
$177$		0			0
$178$	−241.784	+	112.746i	−1.35833	+	0.633402i
$179$	186.793	+	107.845i	1.04354	+	0.602487i	0.920833	−	0.389957i	$-0.127510\pi$
$179$	186.793	+	107.845i	1.04354	+	0.602487i	0.122704	+	0.992443i	$0.460843\pi$
$180$		0			0
$181$	12.7646	+	22.1089i	0.0705224	+	0.122148i	0.899130	−	0.437681i	$-0.144200\pi$
$181$	12.7646	+	22.1089i	0.0705224	+	0.122148i	−0.828608	+	0.559829i	$0.810867\pi$
$182$	−99.0619	+	141.475i	−0.544296	+	0.777335i
$183$		0			0
$184$	−231.980	−	637.361i	−1.26076	−	3.46392i
$185$	107.543	+	31.8752i	0.581315	+	0.172298i
$186$		0			0
$187$	217.606	+	19.0380i	1.16367	+	0.101808i
$188$	−173.486	+	173.486i	−0.922797	+	0.922797i
$189$		0			0
$190$	497.249	+	56.7381i	2.61710	+	0.298621i
$191$	241.803	−	202.897i	1.26599	−	1.06229i	0.270969	−	0.962588i	$-0.412656\pi$
$191$	241.803	−	202.897i	1.26599	−	1.06229i	0.995017	−	0.0997005i	$-0.0317885\pi$
$192$		0			0
$193$	54.2892	+	77.5331i	0.281291	+	0.401726i	0.934789	−	0.355203i	$-0.115588\pi$
$193$	54.2892	+	77.5331i	0.281291	+	0.401726i	−0.653498	+	0.756928i	$0.726699\pi$
$194$	−99.4221	−	273.160i	−0.512485	−	1.40804i
$195$		0			0
$196$	70.2779	+	398.566i	0.358561	+	2.03350i
$197$	26.1273	−	97.5085i	0.132626	−	0.494967i	−0.867370	−	0.497663i	$-0.834192\pi$
$197$	26.1273	−	97.5085i	0.132626	−	0.494967i	0.999996	+	0.00269614i	$0.000858211\pi$
$198$		0			0
$199$	−10.4704	−	6.04508i	−0.0526150	−	0.0303773i	0.473462	−	0.880814i	$-0.343004\pi$
$199$	−10.4704	−	6.04508i	−0.0526150	−	0.0303773i	−0.526077	+	0.850437i	$0.676338\pi$
$200$	121.163	+	570.963i	0.605817	+	2.85481i
$201$		0			0
$202$	−60.1178	−	687.149i	−0.297613	−	3.40173i
$203$	−15.0997	+	1.32105i	−0.0743826	+	0.00650764i
$204$		0			0
$205$	22.3051	+	66.6998i	0.108805	+	0.325365i
$206$	−344.598	+	596.862i	−1.67281	+	2.89739i
$207$		0			0
$208$	−684.712	−	183.468i	−3.29189	−	0.882058i
$209$	−228.651	+	40.3174i	−1.09403	+	0.192906i
$210$		0			0
$211$	−43.6801	+	15.8982i	−0.207015	+	0.0753471i	−0.443446	−	0.896301i	$-0.646244\pi$
$211$	−43.6801	+	15.8982i	−0.207015	+	0.0753471i	0.236432	+	0.971648i	$0.424022\pi$
$212$	−422.141	+	295.586i	−1.99123	+	1.39428i
$213$		0			0
$214$	18.6834	+	22.2661i	0.0873058	+	0.104047i
$215$	118.933	+	13.5708i	0.553179	+	0.0631199i
$216$		0			0
$217$	29.2367	+	29.2367i	0.134731	+	0.134731i
$218$	−9.96735	+	113.927i	−0.0457218	+	0.522603i
$219$		0			0
$220$	−212.544	−	391.612i	−0.966108	−	1.78006i
$221$	352.860	−	128.431i	1.59665	−	0.581134i
$222$		0			0
$223$	−85.5949	−	59.9342i	−0.383834	−	0.268763i	0.365696	−	0.930735i	$-0.380831\pi$
$223$	−85.5949	−	59.9342i	−0.383834	−	0.268763i	−0.749529	+	0.661971i	$0.769720\pi$
$224$	222.959	−	128.726i	0.995353	−	0.574667i
$225$		0			0
$226$	38.5123	−	66.7052i	0.170408	−	0.295156i
$227$	−46.1908	−	99.0566i	−0.203484	−	0.436373i	0.777911	−	0.628375i	$-0.216280\pi$
$227$	−46.1908	−	99.0566i	−0.203484	−	0.436373i	−0.981394	+	0.192002i	$0.938502\pi$
$228$		0			0
$229$	−186.679	+	222.475i	−0.815192	+	0.971508i	−0.999936	−	0.0112785i	$-0.996410\pi$
$229$	−186.679	+	222.475i	−0.815192	+	0.971508i	0.184744	+	0.982787i	$0.440854\pi$
$230$	14.4176	−	547.112i	0.0626854	−	2.37875i
$231$		0			0
$232$	−49.0195	−	105.123i	−0.211291	−	0.453115i
$233$	−77.6767	−	289.894i	−0.333377	−	1.24418i	−0.905618	−	0.424093i	$-0.860593\pi$
$233$	−77.6767	−	289.894i	−0.333377	−	1.24418i	0.572242	−	0.820085i	$-0.306074\pi$
$234$		0			0
$235$	−110.339	+	47.9550i	−0.469528	+	0.204064i
$236$	37.0339	+	210.030i	0.156923	+	0.889956i
$237$		0			0
$238$	−121.423	+	260.392i	−0.510179	+	1.09408i
$239$	59.1436	+	10.4286i	0.247463	+	0.0436344i	0.296004	−	0.955187i	$-0.404346\pi$
$239$	59.1436	+	10.4286i	0.247463	+	0.0436344i	−0.0485408	+	0.998821i	$0.515457\pi$
$240$		0			0
$241$	352.232	−	295.558i	1.46154	−	1.22638i	0.537967	−	0.842966i	$-0.319193\pi$
$241$	352.232	−	295.558i	1.46154	−	1.22638i	0.923577	−	0.383414i	$-0.125252\pi$
$242$	−118.869	−	118.869i	−0.491196	−	0.491196i
$243$		0			0
$244$		−	787.889i		−	3.22905i
$245$	−39.5986	+	194.468i	−0.161627	+	0.793746i
$246$		0			0
$247$	−326.947	+	228.931i	−1.32367	+	0.926846i
$248$	−133.718	+	286.758i	−0.539184	+	1.15628i
$249$		0			0
$250$	−77.9653	+	464.479i	−0.311861	+	1.85792i
$251$	43.4873	+	75.3221i	0.173256	+	0.300088i	0.939556	−	0.342394i	$-0.111238\pi$
$251$	43.4873	+	75.3221i	0.173256	+	0.300088i	−0.766300	+	0.642483i	$0.777905\pi$
$252$		0			0
$253$	65.7148	+	245.251i	0.259742	+	0.969371i
$254$	−64.7809	+	177.984i	−0.255043	+	0.700724i
$255$		0			0
$256$	35.0638	+	29.4220i	0.136968	+	0.114930i
$257$	16.0932	+	183.946i	0.0626194	+	0.715743i	0.961004	+	0.276534i	$0.0891858\pi$
$257$	16.0932	+	183.946i	0.0626194	+	0.715743i	−0.898385	+	0.439209i	$0.855259\pi$
$258$		0			0
$259$	23.4091	−	64.3159i	0.0903826	−	0.248324i
$260$	−615.651	−	455.716i	−2.36789	−	1.75275i
$261$		0			0
$262$	−199.071	+	742.943i	−0.759813	+	2.83566i
$263$	−288.870	−	202.269i	−1.09836	−	0.769083i	−0.123603	−	0.992332i	$-0.539445\pi$
$263$	−288.870	−	202.269i	−1.09836	−	0.769083i	−0.974762	+	0.223248i	$0.928334\pi$
$264$		0			0
$265$	−245.733	+	58.9520i	−0.927293	+	0.222460i
$266$	53.0295	−	300.746i	0.199359	−	1.13062i
$267$		0			0
$268$	91.3550	−	1044.19i	0.340877	−	3.89624i
$269$			359.275i			1.33560i	0.744342	+	0.667798i	$0.232763\pi$
$269$			359.275i			1.33560i	−0.744342	+	0.667798i	$0.767237\pi$
$270$		0			0
$271$	350.436			1.29312			0.646562	−	0.762862i	$-0.276206\pi$
$271$	350.436			1.29312			0.646562	+	0.762862i	$0.276206\pi$
$272$	−1174.75	−	102.777i	−4.31893	−	0.377857i
$273$		0			0
$274$	−138.257	−	24.3784i	−0.504586	−	0.0889722i
$275$	−26.5556	−	216.874i	−0.0965659	−	0.788634i
$276$		0			0
$277$	−77.3848	+	110.517i	−0.279368	+	0.398978i	−0.934174	−	0.356819i	$-0.883861\pi$
$277$	−77.3848	+	110.517i	−0.279368	+	0.398978i	0.654806	+	0.755797i	$0.272750\pi$
$278$	675.978	+	181.128i	2.43158	+	0.651539i
$279$		0			0
$280$	352.251	−	52.5843i	1.25804	−	0.187801i
$281$	11.3445	+	4.12907i	0.0403720	+	0.0146942i	0.362127	−	0.932129i	$-0.382051\pi$
$281$	11.3445	+	4.12907i	0.0403720	+	0.0146942i	−0.321755	+	0.946823i	$0.604273\pi$
$282$		0			0
$283$	248.503	−	21.7412i	0.878102	−	0.0768240i	0.360817	−	0.932637i	$-0.382498\pi$
$283$	248.503	−	21.7412i	0.878102	−	0.0768240i	0.517286	+	0.855813i	$0.326942\pi$
$284$	166.201	−	198.071i	0.585216	−	0.697434i
$285$		0			0
$286$	464.907	+	169.212i	1.62555	+	0.591651i
$287$	41.4527	−	11.1072i	0.144434	−	0.0387011i
$288$		0			0
$289$	290.702	−	167.837i	1.00589	−	0.580751i
$290$	−5.69824	−	93.4204i	−0.0196491	−	0.322139i
$291$		0			0
$292$	829.387	+	386.749i	2.84037	+	1.32448i
$293$	10.4865	+	14.9763i	0.0357901	+	0.0511136i	0.836648	−	0.547740i	$-0.184512\pi$
$293$	10.4865	+	14.9763i	0.0357901	+	0.0511136i	−0.800858	+	0.598854i	$0.795623\pi$
$294$		0			0
$295$	−20.8670	+	102.477i	−0.0707356	+	0.347381i
$296$	523.757			1.76945
$297$		0			0
$298$	−106.321	+	106.321i	−0.356781	+	0.356781i
$299$	280.559	+	334.358i	0.938326	+	1.11825i
$300$		0			0
$301$	12.6838	−	71.9332i	0.0421388	−	0.238981i
$302$	520.459	+	242.694i	1.72338	+	0.803623i
$303$		0			0
$304$	1234.38	−	217.654i	4.06045	−	0.715968i
$305$	141.659	−	359.448i	0.464456	−	1.17852i
$306$		0			0
$307$	−473.261	+	126.810i	−1.54157	+	0.413062i	−0.926772	−	0.375625i	$-0.877428\pi$
$307$	−473.261	+	126.810i	−1.54157	+	0.413062i	−0.614796	+	0.788687i	$0.710761\pi$
$308$	−246.411	+	114.903i	−0.800035	+	0.373062i
$309$		0			0
$310$	−185.224	+	175.713i	−0.597498	+	0.566816i
$311$	157.780	+	132.394i	0.507333	+	0.425703i	0.860189	−	0.509975i	$-0.170345\pi$
$311$	157.780	+	132.394i	0.507333	+	0.425703i	−0.352857	+	0.935677i	$0.614790\pi$
$312$		0			0
$313$	−465.356	+	216.999i	−1.48676	+	0.693288i	−0.985133	−	0.171796i	$-0.945043\pi$
$313$	−465.356	+	216.999i	−1.48676	+	0.693288i	−0.501628	+	0.865084i	$0.667265\pi$
$314$	400.168	+	231.037i	1.27442	+	0.735786i
$315$		0			0
$316$	−52.6584	−	91.2070i	−0.166640	−	0.288630i
$317$	263.349	−	376.101i	0.830753	−	1.18644i	−0.149514	−	0.988760i	$-0.547771\pi$
$317$	263.349	−	376.101i	0.830753	−	1.18644i	0.980267	−	0.197679i	$-0.0633402\pi$
$318$		0			0
$319$	14.8504	+	40.8013i	0.0465531	+	0.127904i
$320$	308.188	+	567.838i	0.963089	+	1.77449i
$321$		0			0
$322$	−332.687	−	29.1064i	−1.03319	−	0.0903924i
$323$	−469.499	+	469.499i	−1.45356	+	1.45356i
$324$		0			0
$325$	−198.934	−	318.597i	−0.612104	−	0.980297i
$326$	82.7215	−	69.4116i	0.253747	−	0.212919i
$327$		0			0
$328$	188.364	+	269.011i	0.574280	+	0.820157i
$329$	25.1083	+	68.9844i	0.0763170	+	0.209679i
$330$		0			0
$331$	−47.9543	−	271.962i	−0.144877	−	0.821638i	−0.967466	−	0.253001i	$-0.918582\pi$
$331$	−47.9543	−	271.962i	−0.144877	−	0.821638i	0.822589	−	0.568636i	$-0.192529\pi$
$332$	−182.795	+	682.202i	−0.550588	+	2.05482i
$333$		0			0
$334$	433.997	+	250.568i	1.29939	+	0.750205i
$335$	229.419	−	459.952i	0.684833	−	1.37299i
$336$		0			0
$337$	28.0105	+	320.162i	0.0831173	+	0.950036i	0.917208	+	0.398408i	$0.130437\pi$
$337$	28.0105	+	320.162i	0.0831173	+	0.950036i	−0.834091	+	0.551627i	$0.814007\pi$
$338$	212.918	−	18.6279i	0.629936	−	0.0551122i
$339$		0			0
$340$	−1140.25	−	568.745i	−3.35368	−	1.67278i
$341$	59.2212	−	102.574i	0.173669	−	0.300804i
$342$		0			0
$343$	261.374	+	70.0349i	0.762022	+	0.204183i
$344$	550.461	−	97.0612i	1.60018	−	0.282155i
$345$		0			0
$346$	77.0984	−	28.0615i	0.222828	−	0.0811026i
$347$	−360.044	+	252.105i	−1.03759	+	0.726528i	−0.962675	−	0.270661i	$-0.912758\pi$
$347$	−360.044	+	252.105i	−1.03759	+	0.726528i	−0.0749155	+	0.997190i	$0.523869\pi$
$348$		0			0
$349$	129.078	+	153.829i	0.369851	+	0.440771i	0.918584	−	0.395227i	$-0.129334\pi$
$349$	129.078	+	153.829i	0.369851	+	0.440771i	−0.548733	+	0.835998i	$0.684890\pi$
$350$	279.998	+	64.7408i	0.799995	+	0.184974i
$351$		0			0
$352$	−521.488	−	521.488i	−1.48150	−	1.48150i
$353$	24.8659	−	284.218i	0.0704415	−	0.805150i	−0.876008	−	0.482297i	$-0.839802\pi$
$353$	24.8659	−	284.218i	0.0704415	−	0.805150i	0.946449	−	0.322853i	$-0.104642\pi$
$354$		0			0
$355$	111.436	−	60.4809i	0.313905	−	0.170369i
$356$	−678.416	+	246.923i	−1.90566	+	0.693604i
$357$		0			0
$358$	665.710	+	466.135i	1.85952	+	1.30205i
$359$	−163.907	+	94.6319i	−0.456566	+	0.263599i	−0.710599	−	0.703597i	$-0.751576\pi$
$359$	−163.907	+	94.6319i	−0.456566	+	0.263599i	0.254033	+	0.967196i	$0.418243\pi$
$360$		0			0
$361$	172.371	−	298.555i	0.477481	−	0.827021i
$362$	40.6512	+	87.1768i	0.112296	+	0.240820i
$363$		0			0
$364$	−300.429	+	358.037i	−0.825354	+	0.983619i
$365$	308.844	+	325.562i	0.846147	+	0.891950i
$366$		0			0
$367$	−185.946	−	398.763i	−0.506666	−	1.08655i	−0.978762	−	0.205001i	$-0.934280\pi$
$367$	−185.946	−	398.763i	−0.506666	−	1.08655i	0.472096	−	0.881547i	$-0.343498\pi$
$368$	−354.762	−	1323.99i	−0.964027	−	3.59780i
$369$		0			0
$370$	393.194	+	154.959i	1.06269	+	0.418807i
$371$	26.7762	+	151.856i	0.0721732	+	0.409314i
$372$		0			0
$373$	115.252	−	247.160i	0.308988	−	0.662626i	−0.689085	−	0.724680i	$-0.741987\pi$
$373$	115.252	−	247.160i	0.308988	−	0.662626i	0.998073	+	0.0620543i	$0.0197652\pi$
$374$	810.527	+	142.918i	2.16719	+	0.382133i
$375$		0			0
$376$	−430.345	+	361.102i	−1.14453	+	0.960378i
$377$	52.7793	+	52.7793i	0.139998	+	0.139998i
$378$		0			0
$379$			373.089i			0.984403i	0.870481	+	0.492202i	$0.163808\pi$
$379$			373.089i			0.984403i	−0.870481	+	0.492202i	$0.836192\pi$
$380$	1327.15	+	270.241i	3.49250	+	0.711161i
$381$		0			0
$382$	974.233	−	682.165i	2.55035	−	1.78577i
$383$	−153.867	+	329.969i	−0.401742	+	0.861538i	0.596520	+	0.802598i	$0.296550\pi$
$383$	−153.867	+	329.969i	−0.401742	+	0.861538i	−0.998262	+	0.0589394i	$0.981228\pi$
$384$		0			0
$385$	−133.076	+	8.11705i	−0.345651	+	0.0210832i
$386$	178.313	+	308.847i	0.461950	+	0.800121i
$387$		0			0
$388$	−203.604	−	759.860i	−0.524753	−	1.95840i
$389$	186.117	−	511.351i	0.478449	−	1.31453i	−0.432361	−	0.901701i	$-0.642319\pi$
$389$	186.117	−	511.351i	0.478449	−	1.31453i	0.910810	−	0.412827i	$-0.135458\pi$
$390$		0			0
$391$	556.221	+	466.725i	1.42256	+	1.19367i
$392$	80.7660	+	923.159i	0.206036	+	2.35500i
$393$		0			0
$394$	130.089	−	357.416i	0.330175	−	0.907148i
$395$	−7.62495	−	51.0778i	−0.0193037	−	0.129311i
$396$		0			0
$397$	−30.6816	+	114.505i	−0.0772837	+	0.288427i	−0.993741	−	0.111705i	$-0.964369\pi$
$397$	−30.6816	+	114.505i	−0.0772837	+	0.288427i	0.916458	+	0.400132i	$0.131036\pi$
$398$	−37.3153	−	26.1284i	−0.0937570	−	0.0656493i
$399$		0			0
$400$	143.361	+	1170.80i	0.358402	+	2.92700i
$401$	28.2142	−	160.011i	0.0703596	−	0.399029i	−0.929206	−	0.369562i	$-0.879508\pi$
$401$	28.2142	−	160.011i	0.0703596	−	0.399029i	0.999566	−	0.0294672i	$-0.00938106\pi$
$402$		0			0
$403$	17.7457	−	202.835i	0.0440341	−	0.503312i
$404$		−	1866.66i		−	4.62045i
$405$		0			0
$406$	−57.1101			−0.140665
$407$	−195.318	−	17.0881i	−0.479896	−	0.0419855i
$408$		0			0
$409$	241.096	+	42.5117i	0.589476	+	0.103941i	0.460427	−	0.887698i	$-0.347696\pi$
$409$	241.096	+	42.5117i	0.589476	+	0.103941i	0.129049	+	0.991638i	$0.458807\pi$
$410$	61.8184	+	257.681i	0.150777	+	0.628490i
$411$		0			0
$412$	−1069.78	+	1527.80i	−2.59655	+	3.70825i
$413$	61.6395	+	16.5163i	0.149248	+	0.0399909i
$414$		0			0
$415$	−206.051	+	278.365i	−0.496509	+	0.670760i
$416$	−1191.34	−	433.612i	−2.86380	−	1.04234i
$417$		0			0
$418$	−871.478	+	76.2445i	−2.08488	+	0.182403i
$419$	39.9401	−	47.5987i	0.0953223	−	0.113601i	−0.716275	−	0.697819i	$-0.754154\pi$
$419$	39.9401	−	47.5987i	0.0953223	−	0.113601i	0.811597	+	0.584218i	$0.198599\pi$
$420$		0			0
$421$	20.0465	+	7.29634i	0.0476165	+	0.0173310i	0.365719	−	0.930725i	$-0.380823\pi$
$421$	20.0465	+	7.29634i	0.0476165	+	0.0173310i	−0.318102	+	0.948056i	$0.603045\pi$
$422$	−169.173	+	45.3298i	−0.400884	+	0.107417i
$423$		0			0
$424$	−1021.90	+	589.993i	−2.41014	+	1.39149i
$425$	−417.943	−	464.483i	−0.983396	−	1.09290i
$426$		0			0
$427$	−213.662	−	99.6322i	−0.500379	−	0.233331i
$428$	45.1169	+	64.4337i	0.105413	+	0.150546i
$429$		0			0
$430$	441.958	+	89.9938i	1.02781	+	0.209288i
$431$	486.219			1.12812			0.564059	−	0.825734i	$-0.309239\pi$
$431$	486.219			1.12812			0.564059	+	0.825734i	$0.309239\pi$
$432$		0			0
$433$	−120.602	+	120.602i	−0.278526	+	0.278526i	−0.832520	−	0.553995i	$-0.813103\pi$
$433$	−120.602	+	120.602i	−0.278526	+	0.278526i	0.553995	+	0.832520i	$0.313103\pi$
$434$	100.138	+	119.340i	0.230733	+	0.274977i
$435$		0			0
$436$	−53.7419	+	304.785i	−0.123261	+	0.699049i
$437$	−699.464	−	326.165i	−1.60060	−	0.746374i
$438$		0			0
$439$	427.090	−	75.3075i	0.972870	−	0.171543i	0.335448	−	0.942059i	$-0.391112\pi$
$439$	427.090	−	75.3075i	0.972870	−	0.171543i	0.637421	+	0.770515i	$0.280001\pi$
$440$	−406.664	−	935.689i	−0.924237	−	2.12657i
$441$		0			0
$442$	1366.63	−	366.187i	3.09192	−	0.828478i
$443$	271.289	−	126.504i	0.612392	−	0.285563i	−0.0915725	−	0.995798i	$-0.529189\pi$
$443$	271.289	−	126.504i	0.612392	−	0.285563i	0.703964	+	0.710236i	$0.251412\pi$
$444$		0			0
$445$	−353.900	−	9.32607i	−0.795281	−	0.0209575i
$446$	−301.597	−	253.070i	−0.676227	−	0.567421i
$447$		0			0
$448$	357.295	−	166.610i	0.797534	−	0.371896i
$449$	−624.818	−	360.739i	−1.39158	−	0.803428i	−0.398087	−	0.917347i	$-0.630326\pi$
$449$	−624.818	−	360.739i	−1.39158	−	0.803428i	−0.993490	+	0.113920i	$0.963659\pi$
$450$		0			0
$451$	−61.4672	−	106.464i	−0.136291	−	0.236063i
$452$	119.558	−	170.747i	0.264509	−	0.377758i
$453$		0			0
$454$	−140.847	−	386.975i	−0.310237	−	0.852368i
$455$	−201.434	+	109.326i	−0.442713	+	0.240278i
$456$		0			0
$457$	−726.121	−	63.5274i	−1.58889	−	0.139010i	−0.741858	−	0.670557i	$-0.766055\pi$
$457$	−726.121	−	63.5274i	−1.58889	−	0.139010i	−0.847029	+	0.531547i	$0.821611\pi$
$458$	−773.754	+	773.754i	−1.68942	+	1.68942i
$459$		0			0
$460$	167.910	−	1471.56i	0.365023	−	3.19904i
$461$	−684.108	+	574.034i	−1.48396	+	1.24519i	−0.582142	+	0.813087i	$0.697785\pi$
$461$	−684.108	+	574.034i	−1.48396	+	1.24519i	−0.901822	+	0.432107i	$0.857770\pi$
$462$		0			0
$463$	−340.262	−	485.944i	−0.734907	−	1.04956i	−0.996435	−	0.0843598i	$-0.973115\pi$
$463$	−340.262	−	485.944i	−0.734907	−	1.04956i	0.261529	−	0.965196i	$-0.415773\pi$
$464$	−80.1704	−	220.266i	−0.172781	−	0.474712i
$465$		0			0
$466$	−196.361	−	1113.62i	−0.421375	−	2.38974i
$467$	−32.2601	+	120.396i	−0.0690794	+	0.257808i	−0.991826	−	0.127600i	$-0.959273\pi$
$467$	−32.2601	+	120.396i	−0.0690794	+	0.257808i	0.922746	+	0.385408i	$0.125939\pi$
$468$		0			0
$469$	−271.615	−	156.817i	−0.579136	−	0.334364i
$470$	−429.903	+	143.764i	−0.914688	+	0.305881i
$471$		0			0
$472$	42.5607	+	486.471i	0.0901710	+	1.03066i
$473$	−208.443	+	18.2364i	−0.440682	+	0.0385547i
$474$		0			0
$475$	556.878	+	361.904i	1.17238	+	0.761904i
$476$	−388.759	+	673.351i	−0.816721	+	1.41460i
$477$		0			0
$478$	218.570	+	58.5656i	0.457259	+	0.122522i
$479$	−291.942	+	51.4772i	−0.609482	+	0.107468i	−0.469866	−	0.882738i	$-0.655698\pi$
$479$	−291.942	+	51.4772i	−0.609482	+	0.107468i	−0.139616	+	0.990206i	$0.544587\pi$
$480$		0			0
$481$	−316.719	+	115.276i	−0.658459	+	0.239659i
$482$	1419.15	−	993.701i	2.94430	−	2.06162i
$483$		0			0
$484$	−292.423	−	348.496i	−0.604180	−	0.720034i
$485$	43.7324	−	383.268i	0.0901699	−	0.790243i
$486$		0			0
$487$	−187.665	−	187.665i	−0.385349	−	0.385349i	0.487676	−	0.873025i	$-0.337845\pi$
$487$	−187.665	−	187.665i	−0.385349	−	0.385349i	−0.873025	+	0.487676i	$0.837845\pi$
$488$	157.233	−	1797.19i	0.322200	−	3.68276i
$489$		0			0
$490$	−212.493	+	716.927i	−0.433660	+	1.46312i
$491$	223.725	−	81.4291i	0.455651	−	0.165843i	−0.103990	−	0.994578i	$-0.533161\pi$
$491$	223.725	−	81.4291i	0.455651	−	0.165843i	0.559641	+	0.828735i	$0.310939\pi$
$492$		0			0
$493$	101.714	+	71.2207i	0.206316	+	0.144464i
$494$	−1302.37	+	751.922i	−2.63637	+	1.52211i
$495$		0			0
$496$	−319.707	+	553.748i	−0.644570	+	1.11643i
$497$	−32.6965	−	70.1180i	−0.0657878	−	0.141082i
$498$		0			0
$499$	206.163	−	245.695i	0.413152	−	0.492375i	−0.518831	−	0.854877i	$-0.673633\pi$
$499$	206.163	−	245.695i	0.413152	−	0.492375i	0.931983	+	0.362501i	$0.118077\pi$
$500$	−319.739	+	1233.80i	−0.639477	+	2.46760i
$501$		0			0
$502$	138.494	+	297.001i	0.275884	+	0.591635i
$503$	209.119	+	780.441i	0.415743	+	1.55157i	0.783344	+	0.621589i	$0.213513\pi$
$503$	209.119	+	780.441i	0.415743	+	1.55157i	−0.367601	+	0.929984i	$0.619821\pi$
$504$		0			0
$505$	335.618	−	851.602i	0.664591	−	1.68634i
$506$	166.122	+	942.124i	0.328304	+	1.86190i
$507$		0			0
$508$	−216.622	+	464.547i	−0.426421	+	0.914463i
$509$	−14.3637	−	2.53271i	−0.0282195	−	0.00497586i	0.159521	−	0.987195i	$-0.449005\pi$
$509$	−14.3637	−	2.53271i	−0.0282195	−	0.00497586i	−0.187740	+	0.982219i	$0.560116\pi$
$510$		0			0
$511$	209.760	−	176.009i	0.410488	−	0.344441i
$512$	−300.411	−	300.411i	−0.586740	−	0.586740i
$513$		0			0
$514$			695.722i			1.35355i
$515$	−762.742	+	504.665i	−1.48105	+	0.979933i
$516$		0			0
$517$	172.264	−	120.621i	0.333199	−	0.233309i
$518$	108.986	−	233.721i	0.210398	−	0.451199i
$519$		0			0
$520$	−1313.36	−	1162.36i	−2.52570	−	2.23530i
$521$	−193.021	−	334.321i	−0.370481	−	0.641692i	0.619159	−	0.785266i	$-0.287474\pi$
$521$	−193.021	−	334.321i	−0.370481	−	0.641692i	−0.989640	+	0.143574i	$0.954140\pi$
$522$		0			0
$523$	39.5642	+	147.655i	0.0756485	+	0.282324i	0.993380	−	0.114878i	$-0.0366478\pi$
$523$	39.5642	+	147.655i	0.0756485	+	0.282324i	−0.917731	+	0.397202i	$0.869981\pi$
$524$	−711.905	+	1955.94i	−1.35860	+	3.73272i
$525$		0			0
$526$	−1017.85	−	854.073i	−1.93507	−	1.62371i
$527$	−29.5210	−	337.426i	−0.0560170	−	0.640277i
$528$		0			0
$529$	−107.731	+	295.987i	−0.203650	+	0.559523i
$530$	−941.712	+	140.580i	−1.77682	+	0.265245i
$531$		0			0
$532$	213.896	−	798.271i	0.402060	−	1.50051i
$533$	−173.113	−	121.215i	−0.324789	−	0.227420i
$534$		0			0
$535$	8.99816	+	37.5075i	0.0168190	+	0.0701075i
$536$	416.764	−	2363.59i	0.777545	−	4.40968i
$537$		0			0
$538$	−117.981	+	1348.53i	−0.219296	+	2.50657i
$539$		−	346.896i		−	0.643592i
$540$		0			0
$541$	−596.238			−1.10210			−0.551051	−	0.834471i	$-0.685773\pi$
$541$	−596.238			−1.10210			−0.551051	+	0.834471i	$0.685773\pi$
$542$	1315.36	+	115.079i	2.42686	+	0.212322i
$543$		0			0
$544$	−2077.01	−	366.232i	−3.81802	−	0.673221i
$545$	−79.3171	+	129.385i	−0.145536	+	0.237405i
$546$		0			0
$547$	24.2447	−	34.6251i	0.0443231	−	0.0632999i	−0.796379	−	0.604798i	$-0.793254\pi$
$547$	24.2447	−	34.6251i	0.0443231	−	0.0632999i	0.840702	+	0.541498i	$0.182143\pi$
$548$	−366.976	−	98.3309i	−0.669664	−	0.179436i
$549$		0			0
$550$	−28.4573	−	822.754i	−0.0517406	−	1.49592i
$551$	−124.021	−	45.1401i	−0.225084	−	0.0819240i
$552$		0			0
$553$	−31.3926	+	2.74650i	−0.0567679	+	0.00496655i
$554$	−326.755	+	389.411i	−0.589810	+	0.702908i
$555$		0			0
$556$	1779.65	+	647.739i	3.20080	+	1.16500i
$557$	369.552	−	99.0213i	0.663469	−	0.177776i	0.0886581	−	0.996062i	$-0.471742\pi$
$557$	369.552	−	99.0213i	0.663469	−	0.177776i	0.574811	+	0.818286i	$0.305075\pi$
$558$		0			0
$559$	−311.504	+	179.847i	−0.557252	+	0.321730i
$560$	718.411	−	43.8200i	1.28288	−	0.0782500i
$561$		0			0
$562$	41.2256	+	19.2238i	0.0733551	+	0.0342060i
$563$	−144.583	−	206.487i	−0.256809	−	0.366761i	0.669957	−	0.742400i	$-0.266312\pi$
$563$	−144.583	−	206.487i	−0.256809	−	0.366761i	−0.926766	+	0.375638i	$0.877423\pi$
$564$		0			0
$565$	85.2440	−	56.4014i	0.150874	−	0.0998254i
$566$	939.890			1.66058
$567$		0			0
$568$	418.635	−	418.635i	0.737034	−	0.737034i
$569$	457.282	+	544.967i	0.803658	+	0.957763i	0.999739	−	0.0228251i	$-0.00726609\pi$
$569$	457.282	+	544.967i	0.803658	+	0.957763i	−0.196081	+	0.980588i	$0.562822\pi$
$570$		0			0
$571$	9.87196	−	55.9867i	0.0172889	−	0.0980502i	−0.974942	−	0.222458i	$-0.928592\pi$
$571$	9.87196	−	55.9867i	0.0172889	−	0.0980502i	0.992231	+	0.124408i	$0.0397031\pi$
$572$	1213.43	+	565.832i	2.12138	+	0.989216i
$573$		0			0
$574$	159.239	−	28.0782i	0.277420	−	0.0489167i
$575$	341.183	−	641.158i	0.593362	−	1.11506i
$576$		0			0
$577$	−430.452	+	115.339i	−0.746017	+	0.199895i	−0.611751	−	0.791051i	$-0.709534\pi$
$577$	−430.452	+	115.339i	−0.746017	+	0.199895i	−0.134266	+	0.990945i	$0.542868\pi$
$578$	1146.26	−	534.510i	1.98315	−	0.924757i
$579$		0			0
$580$	6.67228	−	253.196i	0.0115039	−	0.436544i
$581$	161.886	+	135.838i	0.278633	+	0.233801i
$582$		0			0
$583$	400.331	−	186.678i	0.686675	−	0.320202i
$584$	1814.66	+	1047.70i	3.10730	+	1.79400i
$585$		0			0
$586$	34.4429	+	59.6568i	0.0587763	+	0.101803i
$587$	−514.229	+	734.395i	−0.876028	+	1.25110i	0.0908509	+	0.995865i	$0.471041\pi$
$587$	−514.229	+	734.395i	−0.876028	+	1.25110i	−0.966879	+	0.255234i	$0.917848\pi$
$588$		0			0
$589$	123.135	+	338.311i	0.209058	+	0.574382i
$590$	−111.976	+	377.795i	−0.189790	+	0.640330i
$591$		0			0
$592$	1054.43	+	92.2503i	1.78112	+	0.155828i
$593$	536.873	−	536.873i	0.905351	−	0.905351i	−0.0905416	−	0.995893i	$-0.528860\pi$
$593$	536.873	−	536.873i	0.905351	−	0.905351i	0.995893	+	0.0905416i	$0.0288598\pi$
$594$		0			0
$595$	−298.424	+	237.296i	−0.501553	+	0.398817i
$596$	−311.706	+	261.553i	−0.522997	+	0.438847i
$597$		0			0
$598$	943.275	+	1347.14i	1.57738	+	2.25274i
$599$	−72.2154	−	198.410i	−0.120560	−	0.331236i	0.864703	−	0.502284i	$-0.167507\pi$
$599$	−72.2154	−	198.410i	−0.120560	−	0.331236i	−0.985263	+	0.171048i	$0.945285\pi$
$600$		0			0
$601$	−167.417	−	949.470i	−0.278564	−	1.57982i	−0.727407	−	0.686206i	$-0.759275\pi$
$601$	−167.417	−	949.470i	−0.278564	−	1.57982i	0.448843	−	0.893611i	$-0.351836\pi$
$602$	71.2302	−	265.835i	0.118323	−	0.441586i
$603$		0			0
$604$	1345.86	+	777.034i	2.22825	+	1.28648i
$605$	−70.7500	−	211.566i	−0.116942	−	0.349696i
$606$		0			0
$607$	−3.18451	−	36.3991i	−0.00524631	−	0.0599656i	0.993120	−	0.117099i	$-0.0373595\pi$
$607$	−3.18451	−	36.3991i	−0.00524631	−	0.0599656i	−0.998367	+	0.0571335i	$0.981804\pi$
$608$	2233.19	−	195.379i	3.67302	−	0.321347i
$609$		0			0
$610$	649.753	−	1302.66i	1.06517	−	2.13551i
$611$	180.755	−	313.077i	0.295835	−	0.512401i
$612$		0			0
$613$	−1112.65	−	298.135i	−1.81510	−	0.486353i	−0.818934	−	0.573888i	$-0.805434\pi$
$613$	−1112.65	−	298.135i	−1.81510	−	0.486353i	−0.996161	+	0.0875346i	$0.972101\pi$
$614$	−1818.02	+	320.566i	−2.96094	+	0.522094i
$615$		0			0
$616$	−584.997	+	212.921i	−0.949670	+	0.345652i
$617$	283.392	−	198.434i	0.459307	−	0.321610i	−0.320920	−	0.947106i	$-0.603992\pi$
$617$	283.392	−	198.434i	0.459307	−	0.321610i	0.780227	+	0.625496i	$0.215103\pi$
$618$		0			0
$619$	−426.792	−	508.631i	−0.689487	−	0.821698i	0.301807	−	0.953369i	$-0.402410\pi$
$619$	−426.792	−	508.631i	−0.689487	−	0.821698i	−0.991294	+	0.131671i	$0.957966\pi$
$620$	−540.790	+	430.017i	−0.872241	+	0.693575i
$621$		0			0
$622$	548.749	+	548.749i	0.882234	+	0.882234i
$623$	−18.8275	+	215.199i	−0.0302207	+	0.345424i
$624$		0			0
$625$	−367.702	+	505.391i	−0.588323	+	0.808626i
$626$	−1817.96	+	661.685i	−2.90410	+	1.05700i
$627$		0			0
$628$	1024.32	+	717.235i	1.63108	+	1.14209i
$629$	−485.573	+	280.346i	−0.771977	+	0.445701i
$630$		0			0
$631$	285.716	−	494.875i	0.452799	−	0.784270i	−0.545760	−	0.837942i	$-0.683759\pi$
$631$	285.716	−	494.875i	0.452799	−	0.784270i	0.998559	+	0.0536712i	$0.0170923\pi$
$632$	−101.913	−	218.553i	−0.161255	−	0.345812i
$633$		0			0
$634$	1111.98	−	1325.21i	1.75391	−	2.09023i
$635$	−182.350	+	172.986i	−0.287165	+	0.272419i
$636$		0			0
$637$	−252.022	−	540.463i	−0.395639	−	0.848450i
$638$	42.3422	+	158.023i	0.0663672	+	0.247686i
$639$		0			0
$640$	297.606	+	684.759i	0.465010	+	1.06994i
$641$	−84.2379	−	477.737i	−0.131416	−	0.745299i	−0.977288	−	0.211913i	$-0.932031\pi$
$641$	−84.2379	−	477.737i	−0.131416	−	0.745299i	0.845872	−	0.533386i	$-0.179081\pi$
$642$		0			0
$643$	212.723	−	456.186i	0.330829	−	0.709465i	−0.668587	−	0.743634i	$-0.733101\pi$
$643$	212.723	−	456.186i	0.330829	−	0.709465i	0.999416	+	0.0341686i	$0.0108783\pi$
$644$	−890.025	−	156.935i	−1.38203	−	0.243689i
$645$		0			0
$646$	−1916.43	+	1608.08i	−2.96661	+	2.48928i
$647$	−802.350	−	802.350i	−1.24011	−	1.24011i	−0.959955	−	0.280153i	$-0.909615\pi$
$647$	−802.350	−	802.350i	−1.24011	−	1.24011i	−0.280153	−	0.959955i	$-0.590385\pi$
$648$		0			0
$649$		−	182.802i		−	0.281667i
$650$	−642.072	−	1261.17i	−0.987802	−	1.94027i
$651$		0			0
$652$	239.380	−	167.616i	0.367147	−	0.257079i
$653$	−337.025	+	722.752i	−0.516118	+	1.10682i	0.459668	+	0.888091i	$0.347968\pi$
$653$	−337.025	+	722.752i	−0.516118	+	1.10682i	−0.975786	+	0.218727i	$0.929809\pi$
$654$		0			0
$655$	−676.453	+	764.335i	−1.03275	+	1.16692i
$656$	331.832	+	574.749i	0.505841	+	0.876142i
$657$		0			0
$658$	71.5898	+	267.177i	0.108799	+	0.406044i
$659$	254.736	−	699.880i	0.386549	−	1.06203i	−0.581996	−	0.813192i	$-0.697728\pi$
$659$	254.736	−	699.880i	0.386549	−	1.06203i	0.968544	−	0.248842i	$-0.0800499\pi$
$660$		0			0
$661$	415.794	+	348.892i	0.629037	+	0.527825i	0.900630	−	0.434587i	$-0.143106\pi$
$661$	415.794	+	348.892i	0.629037	+	0.527825i	−0.271592	+	0.962412i	$0.587550\pi$
$662$	−90.6865	−	1036.55i	−0.136989	−	1.56579i
$663$		0			0
$664$	−553.101	+	1519.63i	−0.832983	+	2.28860i
$665$	241.109	−	325.727i	0.362570	−	0.489814i
$666$		0			0
$667$	−37.3552	+	139.412i	−0.0560048	+	0.209013i
$668$	1110.91	+	777.870i	1.66304	+	1.16448i
$669$		0			0
$670$	1012.16	−	1651.08i	1.51069	−	2.46430i
$671$	−117.270	+	665.070i	−0.174769	+	0.991162i
$672$		0			0
$673$	−110.861	+	1267.15i	−0.164727	+	1.88284i	0.243417	+	0.969922i	$0.421732\pi$
$673$	−110.861	+	1267.15i	−0.164727	+	1.88284i	−0.408144	+	0.912918i	$0.633824\pi$
$674$			1210.92i			1.79662i
$675$		0			0
$676$	578.399			0.855620
$677$	596.336	+	52.1727i	0.880851	+	0.0770645i	0.518601	−	0.855016i	$-0.326453\pi$
$677$	596.336	+	52.1727i	0.880851	+	0.0770645i	0.362250	+	0.932081i	$0.382009\pi$
$678$		0			0
$679$	−231.808	−	40.8739i	−0.341396	−	0.0601973i
$680$	−2487.43	−	1524.87i	−3.65798	−	2.24245i
$681$		0			0
$682$	255.970	−	365.563i	0.375322	−	0.536016i
$683$	747.832	+	200.381i	1.09492	+	0.293384i	0.760696	−	0.649109i	$-0.224858\pi$
$683$	747.832	+	200.381i	1.09492	+	0.293384i	0.334227	+	0.942493i	$0.391525\pi$
$684$		0			0
$685$	−149.741	−	110.841i	−0.218600	−	0.161811i
$686$	958.062	+	348.706i	1.39659	+	0.508318i
$687$		0			0
$688$	1125.28	−	98.4493i	1.63558	−	0.143095i
$689$	488.092	−	581.686i	0.708407	−	0.844247i
$690$		0			0
$691$	−79.8263	−	29.0544i	−0.115523	−	0.0420469i	0.283612	−	0.958939i	$-0.408467\pi$
$691$	−79.8263	−	29.0544i	−0.115523	−	0.0420469i	−0.399135	+	0.916892i	$0.630689\pi$
$692$	214.468	−	57.4665i	0.309925	−	0.0830440i
$693$		0			0
$694$	−1434.21	+	828.039i	−2.06658	+	1.19314i
$695$	695.443	+	615.482i	1.00064	+	0.885586i
$696$		0			0
$697$	−318.622	−	148.576i	−0.457134	−	0.213165i
$698$	433.976	+	619.782i	0.621742	+	0.887940i
$699$		0			0
$700$	739.577	+	240.575i	1.05654	+	0.343679i
$701$	430.049			0.613479			0.306740	−	0.951793i	$-0.400762\pi$
$701$	430.049			0.613479			0.306740	+	0.951793i	$0.400762\pi$
$702$		0			0
$703$	421.411	−	421.411i	0.599446	−	0.599446i
$704$	−725.912	−	865.108i	−1.03112	−	1.22885i
$705$		0			0
$706$	186.667	−	1058.64i	0.264401	−	1.49949i
$707$	−506.207	−	236.048i	−0.715993	−	0.333873i
$708$		0			0
$709$	316.132	−	55.7426i	0.445885	−	0.0786215i	0.0538023	−	0.998552i	$-0.482866\pi$
$709$	316.132	−	55.7426i	0.445885	−	0.0786215i	0.392082	+	0.919930i	$0.371755\pi$
$710$	438.135	−	190.420i	0.617091	−	0.268197i
$711$		0			0
$712$	−1596.75	+	427.849i	−2.24263	+	0.600911i
$713$	356.821	−	166.388i	0.500450	−	0.233364i
$714$		0			0
$715$	451.852	+	476.311i	0.631961	+	0.666170i
$716$	1684.74	+	1413.67i	2.35299	+	1.97439i
$717$		0			0
$718$	−646.298	+	301.374i	−0.900137	+	0.419741i
$719$	483.899	+	279.379i	0.673016	+	0.388566i	0.797219	−	0.603691i	$-0.206304\pi$
$719$	483.899	+	279.379i	0.673016	+	0.388566i	−0.124202	+	0.992257i	$0.539637\pi$
$720$		0			0
$721$	279.035	+	483.302i	0.387011	+	0.670322i
$722$	745.031	−	1064.01i	1.03190	−	1.47370i
$723$		0			0
$724$	89.0300	+	244.608i	0.122970	+	0.337856i
$725$	48.5675	−	114.312i	0.0669897	−	0.157672i
$726$		0			0
$727$	783.774	+	68.5713i	1.07809	+	0.0943210i	0.612341	−	0.790594i	$-0.290228\pi$
$727$	783.774	+	68.5713i	1.07809	+	0.0943210i	0.465753	+	0.884915i	$0.345784\pi$
$728$	−756.734	+	756.734i	−1.03947	+	1.03947i
$729$		0			0
$730$	1052.33	+	1323.41i	1.44155	+	1.81289i
$731$	−458.378	+	384.625i	−0.627056	+	0.526162i
$732$		0			0
$733$	−719.641	−	1027.75i	−0.981774	−	1.40212i	−0.914592	−	0.404378i	$-0.867488\pi$
$733$	−719.641	−	1027.75i	−0.981774	−	1.40212i	−0.0671824	−	0.997741i	$-0.521401\pi$
$734$	−566.997	−	1557.81i	−0.772476	−	2.12236i
$735$		0			0
$736$	−425.693	−	2414.23i	−0.578387	−	3.28020i
$737$	−232.532	+	867.823i	−0.315512	+	1.17751i
$738$		0			0
$739$	−236.827	−	136.732i	−0.320469	−	0.185023i	0.331132	−	0.943584i	$-0.392569\pi$
$739$	−236.827	−	136.732i	−0.320469	−	0.185023i	−0.651602	+	0.758561i	$0.725903\pi$
$740$	1023.46	+	510.492i	1.38306	+	0.689854i
$741$		0			0
$742$	50.6367	+	578.780i	0.0682435	+	0.780027i
$743$	−1104.17	+	96.6026i	−1.48610	+	0.130017i	−0.801103	−	0.598527i	$-0.795753\pi$
$743$	−1104.17	+	96.6026i	−1.48610	+	0.130017i	−0.684999	+	0.728544i	$0.740197\pi$
$744$		0			0
$745$	−189.232	+	63.2810i	−0.254002	+	0.0849409i
$746$	513.761	−	889.861i	0.688688	−	1.19284i
$747$		0			0
$748$	2151.39	+	576.463i	2.87619	+	0.770673i
$749$	23.1785	−	4.08700i	0.0309460	−	0.00545661i
$750$		0			0
$751$	−165.200	+	60.1277i	−0.219973	+	0.0800636i	−0.449656	−	0.893202i	$-0.648453\pi$
$751$	−165.200	+	60.1277i	−0.219973	+	0.0800636i	0.229683	+	0.973266i	$0.426231\pi$
$752$	−929.969	+	651.172i	−1.23666	+	0.865920i
$753$		0			0
$754$	180.774	+	215.438i	0.239753	+	0.285727i
$755$	474.297	+	596.476i	0.628207	+	0.790035i
$756$		0			0
$757$	−712.642	−	712.642i	−0.941402	−	0.941402i	0.0569733	−	0.998376i	$-0.481855\pi$
$757$	−712.642	−	712.642i	−0.941402	−	0.941402i	−0.998376	+	0.0569733i	$0.981855\pi$
$758$	−122.517	+	1400.38i	−0.161633	+	1.84747i
$759$		0			0
$760$	2973.31	+	881.274i	3.91226	+	1.15957i
$761$	435.097	−	158.362i	0.571744	−	0.208098i	−0.0399372	−	0.999202i	$-0.512716\pi$
$761$	435.097	−	158.362i	0.571744	−	0.208098i	0.611681	+	0.791104i	$0.290494\pi$
$762$		0			0
$763$	75.8566	+	53.1154i	0.0994189	+	0.0696139i
$764$	2787.33	−	1609.26i	3.64833	−	2.10637i
$765$		0			0
$766$	−685.894	+	1188.00i	−0.895423	+	1.55092i
$767$	−132.806	−	284.804i	−0.173150	−	0.371322i
$768$		0			0
$769$	−284.787	+	339.396i	−0.370334	+	0.441347i	−0.918739	−	0.394866i	$-0.870791\pi$
$769$	−284.787	+	339.396i	−0.370334	+	0.441347i	0.548405	+	0.836213i	$0.315235\pi$
$770$	−502.162	−	13.2331i	−0.652159	−	0.0171859i
$771$		0			0
$772$	407.868	+	874.676i	0.528326	+	1.13300i
$773$	−298.276	−	1113.18i	−0.385868	−	1.44008i	−0.836795	−	0.547517i	$-0.815573\pi$
$773$	−298.276	−	1113.18i	−0.385868	−	1.44008i	0.450927	−	0.892561i	$-0.351094\pi$
$774$		0			0
$775$	−324.032	+	98.9488i	−0.418106	+	0.127676i
$776$	−312.784	−	1773.88i	−0.403072	−	2.28593i
$777$		0			0
$778$	866.506	−	1858.23i	1.11376	−	2.38847i
$779$	368.000	+	64.8883i	0.472401	+	0.0832970i
$780$		0			0
$781$	−169.774	+	142.458i	−0.217381	+	0.182404i
$782$	1934.50	+	1934.50i	2.47378	+	2.47378i
$783$		0			0
$784$			1872.72i			2.38868i
$785$	338.354	+	511.382i	0.431025	+	0.651443i
$786$		0			0
$787$	760.113	−	532.237i	0.965837	−	0.676286i	0.0196158	−	0.999808i	$-0.493756\pi$
$787$	760.113	−	532.237i	0.965837	−	0.676286i	0.946221	+	0.323522i	$0.104867\pi$
$788$	435.007	−	932.875i	0.552039	−	1.18385i
$789$		0			0
$790$	−11.8468	−	194.224i	−0.0149960	−	0.245853i
$791$	−31.1849	−	54.0138i	−0.0394247	−	0.0682855i
$792$		0			0
$793$	300.471	+	1121.37i	0.378904	+	1.41409i
$794$	−152.765	+	419.718i	−0.192399	+	0.528612i
$795$		0			0
$796$	−94.4355	−	79.2408i	−0.118638	−	0.0995487i
$797$	27.1813	+	310.684i	0.0341045	+	0.389817i	0.993994	+	0.109437i	$0.0349048\pi$
$797$	27.1813	+	310.684i	0.0341045	+	0.389817i	−0.959889	+	0.280380i	$0.909540\pi$
$798$		0			0
$799$	205.688	−	565.123i	0.257432	−	0.707287i
$800$	72.9229	+	2108.34i	0.0911536	+	2.63542i
$801$		0			0
$802$	158.447	−	591.331i	0.197565	−	0.737321i
$803$	−642.535	−	449.908i	−0.800168	−	0.560284i
$804$		0			0
$805$	−377.828	−	231.619i	−0.469351	−	0.287726i
$806$	133.217	−	755.508i	0.165281	−	0.937355i
$807$		0			0
$808$	372.517	−	4257.89i	0.461035	−	5.26966i
$809$			458.912i			0.567258i	0.958934	+	0.283629i	$0.0915385\pi$
$809$			458.912i			0.567258i	−0.958934	+	0.283629i	$0.908462\pi$
$810$		0			0
$811$	−581.518			−0.717039			−0.358519	−	0.933522i	$-0.616718\pi$
$811$	−581.518			−0.717039			−0.358519	+	0.933522i	$0.616718\pi$
$812$	−153.963	−	13.4700i	−0.189610	−	0.0165887i
$813$		0			0
$814$	−727.510	−	128.280i	−0.893746	−	0.157592i
$815$	139.346	−	33.4294i	0.170976	−	0.0410177i
$816$		0			0
$817$	364.802	−	520.991i	0.446514	−	0.637688i
$818$	890.988	+	238.740i	1.08923	+	0.291858i
$819$		0			0
$820$	105.879	+	709.262i	0.129121	+	0.864953i
$821$	−334.376	−	121.703i	−0.407279	−	0.148238i	0.130253	−	0.991481i	$-0.458421\pi$
$821$	−334.376	−	121.703i	−0.407279	−	0.148238i	−0.537532	+	0.843243i	$0.680643\pi$
$822$		0			0
$823$	681.301	−	59.6061i	0.827826	−	0.0724254i	0.334636	−	0.942347i	$-0.391387\pi$
$823$	681.301	−	59.6061i	0.827826	−	0.0724254i	0.493189	+	0.869922i	$0.335831\pi$
$824$	−2745.07	+	3271.45i	−3.33139	+	3.97020i
$825$		0			0
$826$	225.939	+	82.2351i	0.273534	+	0.0995582i
$827$	229.843	−	61.5862i	0.277924	−	0.0744695i	−0.117165	−	0.993112i	$-0.537381\pi$
$827$	229.843	−	61.5862i	0.277924	−	0.0744695i	0.395089	+	0.918643i	$0.370714\pi$
$828$		0			0
$829$	−289.902	+	167.375i	−0.349701	+	0.201900i	−0.664553	−	0.747241i	$-0.731378\pi$
$829$	−289.902	+	167.375i	−0.349701	+	0.201900i	0.314853	+	0.949140i	$0.398045\pi$
$830$	−864.821	+	977.175i	−1.04195	+	1.17732i
$831$		0			0
$832$	−1759.47	−	820.456i	−2.11475	−	0.986125i
$833$	−569.007	−	812.626i	−0.683082	−	0.975542i
$834$		0			0
$835$	366.959	+	554.614i	0.439471	+	0.664209i
$836$	−2367.40			−2.83182
$837$		0			0
$838$	165.545	−	165.545i	0.197548	−	0.197548i
$839$	−126.171	−	150.364i	−0.150382	−	0.179218i	0.685594	−	0.727984i	$-0.259542\pi$
$839$	−126.171	−	150.364i	−0.150382	−	0.179218i	−0.835976	+	0.548765i	$0.815098\pi$
$840$		0			0
$841$	141.752	−	803.917i	0.168552	−	0.955906i
$842$	72.8482	+	33.9697i	0.0865181	+	0.0403440i
$843$		0			0
$844$	−466.764	+	82.3032i	−0.553038	+	0.0975156i
$845$	263.875	+	103.994i	0.312278	+	0.123070i
$846$		0			0
$847$	−131.484	+	35.2312i	−0.155236	+	0.0415952i
$848$	−2161.20	+	1007.78i	−2.54858	+	1.18842i
$849$		0			0
$850$	−1416.21	−	1880.68i	−1.66613	−	2.21256i
$851$	−499.250	−	418.921i	−0.586663	−	0.492269i
$852$		0			0
$853$	−307.011	+	143.161i	−0.359919	+	0.167833i	−0.594163	−	0.804345i	$-0.702516\pi$
$853$	−307.011	+	143.161i	−0.359919	+	0.167833i	0.234244	+	0.972178i	$0.424739\pi$
$854$	−769.258	−	444.131i	−0.900770	−	0.520060i
$855$		0			0
$856$	90.0538	+	155.978i	0.105203	+	0.182217i
$857$	−914.569	+	1306.14i	−1.06717	+	1.52408i	−0.233084	+	0.972457i	$0.574882\pi$
$857$	−914.569	+	1306.14i	−1.06717	+	1.52408i	−0.834091	+	0.551627i	$0.814007\pi$
$858$		0			0
$859$	399.816	+	1098.49i	0.465444	+	1.27880i	0.921338	+	0.388762i	$0.127097\pi$
$859$	399.816	+	1098.49i	0.465444	+	1.27880i	−0.455894	+	0.890034i	$0.650680\pi$
$860$	1170.25	+	346.854i	1.36075	+	0.403319i
$861$		0			0
$862$	1825.01	+	159.668i	2.11719	+	0.185230i
$863$	373.723	−	373.723i	0.433051	−	0.433051i	−0.456614	−	0.889665i	$-0.650938\pi$
$863$	373.723	−	373.723i	0.433051	−	0.433051i	0.889665	+	0.456614i	$0.150938\pi$
$864$		0			0
$865$	108.176	+	12.3433i	0.125059	+	0.0142697i
$866$	−492.280	+	413.072i	−0.568452	+	0.476988i
$867$		0			0
$868$	241.815	+	345.347i	0.278589	+	0.397866i
$869$	30.8745	+	84.8270i	0.0355288	+	0.0976145i
$870$		0			0
$871$	268.193	+	1521.00i	0.307914	+	1.74627i
$872$	−183.410	+	684.495i	−0.210332	+	0.784971i
$873$		0			0
$874$	−2518.32	−	1453.95i	−2.88137	−	1.66356i
$875$	294.153	+	242.727i	0.336174	+	0.277402i
$876$		0			0
$877$	−4.43847	−	50.7319i	−0.00506097	−	0.0578471i	0.993244	−	0.116043i	$-0.0370209\pi$
$877$	−4.43847	−	50.7319i	−0.00506097	−	0.0578471i	−0.998305	+	0.0581955i	$0.981465\pi$
$878$	1627.80	−	142.414i	1.85399	−	0.162203i
$879$		0			0
$880$	−653.890	−	1955.35i	−0.743056	−	2.22199i
$881$	174.009	−	301.392i	0.197513	−	0.342102i	−0.750209	−	0.661201i	$-0.770047\pi$
$881$	174.009	−	301.392i	0.197513	−	0.342102i	0.947721	+	0.319099i	$0.103380\pi$
$882$		0			0
$883$	644.574	+	172.713i	0.729982	+	0.195598i	0.604621	−	0.796513i	$-0.293324\pi$
$883$	644.574	+	172.713i	0.729982	+	0.195598i	0.125361	+	0.992111i	$0.459991\pi$
$884$	3770.66	−	664.869i	4.26545	−	0.752114i
$885$		0			0
$886$	1059.82	−	385.744i	1.19619	−	0.435377i
$887$	−421.577	+	295.192i	−0.475284	+	0.332798i	−0.786551	−	0.617525i	$-0.788136\pi$
$887$	−421.577	+	295.192i	−0.475284	+	0.332798i	0.311267	+	0.950323i	$0.399247\pi$
$888$		0			0
$889$	98.5843	+	117.488i	0.110894	+	0.132158i
$890$	−1325.29	−	151.221i	−1.48909	−	0.169912i
$891$		0			0
$892$	−753.385	−	753.385i	−0.844602	−	0.844602i
$893$	−55.7120	+	636.791i	−0.0623875	+	0.713092i
$894$		0			0
$895$	514.435	+	947.847i	0.574788	+	1.05905i
$896$	428.114	−	155.821i	0.477806	−	0.173907i
$897$		0			0
$898$	−2226.78	−	1559.21i	−2.47971	−	1.73631i
$899$	58.3078	−	33.6640i	0.0648585	−	0.0374461i
$900$		0			0
$901$	631.598	−	1093.96i	0.700997	−	1.21416i
$902$	−195.754	−	419.797i	−0.217023	−	0.465407i
$903$		0			0
$904$	306.789	−	365.616i	0.339368	−	0.404443i
$905$	−3.36258	+	127.601i	−0.00371556	+	0.140996i
$906$		0			0
$907$	306.690	+	657.700i	0.338137	+	0.725138i	0.999693	−	0.0247580i	$-0.00788152\pi$
$907$	306.690	+	657.700i	0.338137	+	0.725138i	−0.661556	+	0.749895i	$0.730104\pi$
$908$	−288.438	−	1076.47i	−0.317663	−	1.18554i
$909$		0			0
$910$	−791.981	+	344.206i	−0.870308	+	0.378249i
$911$	−118.300	−	670.913i	−0.129857	−	0.736458i	−0.978304	−	0.207176i	$-0.933573\pi$
$911$	−118.300	−	670.913i	−0.129857	−	0.736458i	0.848446	−	0.529282i	$-0.177539\pi$
$912$		0			0
$913$	255.840	−	548.650i	0.280219	−	0.600931i
$914$	−2704.62	−	476.898i	−2.95910	−	0.521770i
$915$		0			0
$916$	−2268.46	+	1903.46i	−2.47648	+	2.07802i
$917$	440.394	+	440.394i	0.480256	+	0.480256i
$918$		0			0
$919$			1623.73i			1.76685i	0.468574	+	0.883424i	$0.344768\pi$
$919$			1623.73i			1.76685i	−0.468574	+	0.883424i	$0.655232\pi$
$920$	676.674	−	3323.13i	0.735515	−	3.61210i
$921$		0			0
$922$	−2756.29	+	1929.97i	−2.98947	+	2.09325i
$923$	−161.012	+	345.290i	−0.174444	+	0.374096i
$924$		0			0
$925$	375.135	+	416.909i	0.405552	+	0.450712i
$926$	−1117.59	−	1935.72i	−1.20690	−	2.09041i
$927$		0			0
$928$	−108.504	−	404.941i	−0.116922	−	0.436358i
$929$	14.1415	−	38.8534i	0.0152223	−	0.0418228i	−0.931849	−	0.362847i	$-0.881805\pi$
$929$	14.1415	−	38.8534i	0.0152223	−	0.0418228i	0.947071	+	0.321024i	$0.104027\pi$
$930$		0			0
$931$	807.749	+	677.782i	0.867614	+	0.728015i
$932$	−266.710	−	3048.51i	−0.286170	−	3.27094i
$933$		0			0
$934$	−160.624	+	441.311i	−0.171974	+	0.472496i
$935$	877.853	+	649.803i	0.938880	+	0.694976i
$936$		0			0
$937$	−82.7125	+	308.687i	−0.0882737	+	0.329442i	−0.995914	−	0.0903068i	$-0.971215\pi$
$937$	−82.7125	+	308.687i	−0.0882737	+	0.329442i	0.907640	+	0.419749i	$0.137882\pi$
$938$	−968.004	−	677.803i	−1.03199	−	0.722605i
$939$		0			0
$940$	−1192.88	+	286.176i	−1.26902	+	0.304443i
$941$	194.531	−	1103.24i	0.206728	−	1.17241i	−0.687969	−	0.725740i	$-0.741497\pi$
$941$	194.531	−	1103.24i	0.206728	−	1.17241i	0.894697	−	0.446674i	$-0.147392\pi$
$942$		0			0
$943$	35.6153	−	407.085i	0.0377681	−	0.431691i
$944$			986.857i			1.04540i
$945$		0			0
$946$	−788.374			−0.833376
$947$	633.129	+	55.3916i	0.668563	+	0.0584916i	0.416384	−	0.909189i	$-0.363297\pi$
$947$	633.129	+	55.3916i	0.668563	+	0.0584916i	0.252179	+	0.967681i	$0.418853\pi$
$948$		0			0
$949$	−1327.93	−	234.149i	−1.39929	−	0.246733i
$950$	1971.39	+	1541.27i	2.07514	+	1.62239i
$951$		0			0
$952$	−1021.14	+	1458.34i	−1.07263	+	1.53187i
$953$	−1460.67	−	391.386i	−1.53271	−	0.410688i	−0.608807	−	0.793319i	$-0.708352\pi$
$953$	−1460.67	−	391.386i	−1.53271	−	0.410688i	−0.923901	+	0.382631i	$0.875018\pi$
$954$		0			0
$955$	1560.96	−	233.022i	1.63452	−	0.244002i
$956$	575.428	+	209.439i	0.601912	+	0.219078i
$957$		0			0
$958$	−1112.70	+	97.3488i	−1.16148	+	0.101617i
$959$	−73.0714	+	87.0831i	−0.0761954	+	0.0908061i
$960$		0			0
$961$	730.460	+	265.866i	0.760104	+	0.276655i
$962$	−1226.65	+	328.681i	−1.27511	+	0.341664i
$963$		0			0
$964$	4060.26	−	2344.19i	4.21189	−	2.43174i
$965$	28.8128	+	472.374i	0.0298578	+	0.489507i
$966$		0			0
$967$	795.561	+	370.976i	0.822710	+	0.383636i	0.787934	−	0.615759i	$-0.211151\pi$
$967$	795.561	+	370.976i	0.822710	+	0.383636i	0.0347756	+	0.999395i	$0.488928\pi$
$968$	−597.475	−	853.282i	−0.617226	−	0.881490i
$969$		0			0
$970$	290.009	−	1424.23i	0.298978	−	1.46827i
$971$	195.094			0.200920			0.100460	−	0.994941i	$-0.467968\pi$
$971$	195.094			0.200920			0.100460	+	0.994941i	$0.467968\pi$
$972$		0			0
$973$	400.700	−	400.700i	0.411819	−	0.411819i
$974$	−642.770	−	766.023i	−0.659928	−	0.786471i
$975$		0			0
$976$	633.083	−	3590.39i	0.648650	−	3.67868i
$977$	−518.912	−	241.973i	−0.531128	−	0.247669i	0.138504	−	0.990362i	$-0.455771\pi$
$977$	−518.912	−	241.973i	−0.531128	−	0.247669i	−0.669632	+	0.742693i	$0.733548\pi$
$978$		0			0
$979$	609.414	−	107.456i	0.622486	−	0.109761i
$980$	−741.955	+	1882.64i	−0.757096	+	1.92106i
$981$		0			0
$982$	866.486	−	232.174i	0.882369	−	0.236430i
$983$	1349.02	−	629.058i	1.37235	−	0.639937i	0.410083	−	0.912048i	$-0.365500\pi$
$983$	1349.02	−	629.058i	1.37235	−	0.639937i	0.962266	+	0.272111i	$0.0877218\pi$
$984$		0			0
$985$	366.184	−	347.380i	0.371761	−	0.352670i
$986$	358.392	+	300.727i	0.363481	+	0.304997i
$987$		0			0
$988$	−3688.40	+	1719.93i	−3.73320	+	1.74082i
$989$	−602.338	−	347.760i	−0.609037	−	0.351628i
$990$		0			0
$991$	−758.343	−	1313.49i	−0.765230	−	1.32542i	−0.940125	−	0.340830i	$-0.889292\pi$
$991$	−758.343	−	1313.49i	−0.765230	−	1.32542i	0.174895	−	0.984587i	$-0.444042\pi$
$992$	−655.931	+	936.767i	−0.661221	+	0.944322i
$993$		0			0
$994$	−99.7000	−	273.923i	−0.100302	−	0.275577i
$995$	−28.8358	−	53.1300i	−0.0289807	−	0.0533970i
$996$		0			0
$997$	−1365.17	−	119.437i	−1.36928	−	0.119796i	−0.621328	−	0.783551i	$-0.713406\pi$
$997$	−1365.17	−	119.437i	−1.36928	−	0.119796i	−0.747951	+	0.663754i	$0.768962\pi$
$998$	854.511	−	854.511i	0.856223	−	0.856223i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.s.a.37.34		408
3.2	odd	2		135.3.r.a.22.1	✓	408
5.3	odd	4	inner	405.3.s.a.118.34		408
15.8	even	4		135.3.r.a.103.1	yes	408
27.11	odd	18		135.3.r.a.97.1	yes	408
27.16	even	9	inner	405.3.s.a.127.34		408
135.38	even	36		135.3.r.a.43.1	yes	408
135.43	odd	36	inner	405.3.s.a.208.34		408

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.r.a.22.1	✓	408	3.2	odd	2
135.3.r.a.43.1	yes	408	135.38	even	36
135.3.r.a.97.1	yes	408	27.11	odd	18
135.3.r.a.103.1	yes	408	15.8	even	4
405.3.s.a.37.34		408	1.1	even	1	trivial
405.3.s.a.118.34		408	5.3	odd	4	inner
405.3.s.a.127.34		408	27.16	even	9	inner
405.3.s.a.208.34		408	135.43	odd	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.75348 + 0.328387i) q^{2} +(10.0415 + 1.77059i) q^{4} +(4.26277 + 2.61320i) q^{5} +(1.74995 - 2.49919i) q^{7} +(22.5515 + 6.04267i) q^{8} +(15.1421 + 11.2084i) q^{10} +(-8.21269 - 2.98918i) q^{11} +(-14.9670 + 1.30944i) q^{13} +(7.38912 - 8.80601i) q^{14} +(44.3363 + 16.1371i) q^{16} +(-24.1418 + 6.46879i) q^{17} +(23.0066 - 13.2829i) q^{19} +(38.1778 + 33.7882i) q^{20} +(-29.8446 - 13.9168i) q^{22} +(-16.6632 - 23.7975i) q^{23} +(11.3424 + 22.2789i) q^{25} -56.6083 q^{26} +(21.9973 - 21.9973i) q^{28} +(-3.19342 - 3.80577i) q^{29} +(-2.35330 + 13.3462i) q^{31} +(76.4778 + 35.6622i) q^{32} +(-92.7402 + 16.3526i) q^{34} +(13.9905 - 6.08049i) q^{35} +(21.6691 - 5.80622i) q^{37} +(90.7169 - 42.3020i) q^{38} +(80.3413 + 84.6902i) q^{40} +(10.7753 + 9.04151i) q^{41} +(21.6979 - 10.1179i) q^{43} +(-77.1755 - 44.5573i) q^{44} +(-54.7302 - 94.7954i) q^{46} +(-13.8013 + 19.7104i) q^{47} +(13.5754 + 37.2980i) q^{49} +(35.2572 + 87.3482i) q^{50} +(-152.610 - 13.3517i) q^{52} +(-35.7379 + 35.7379i) q^{53} +(-27.1975 - 34.2036i) q^{55} +(54.5659 - 45.7863i) q^{56} +(-10.7367 - 15.3335i) q^{58} +(7.15372 + 19.6547i) q^{59} +(-13.4180 - 76.0970i) q^{61} +(-13.2158 + 49.3221i) q^{62} +(111.904 + 64.6080i) q^{64} +(-67.2226 - 33.5299i) q^{65} +(-8.95949 - 102.407i) q^{67} +(-253.875 + 22.2112i) q^{68} +(54.5099 - 18.2287i) q^{70} +(12.6791 - 21.9608i) q^{71} +(86.6915 + 23.2289i) q^{73} +(83.2413 - 14.6777i) q^{74} +(254.541 - 92.6453i) q^{76} +(-21.8424 + 15.2942i) q^{77} +(-6.63920 - 7.91230i) q^{79} +(146.826 + 184.649i) q^{80} +(37.4756 + 37.4756i) q^{82} +(-6.03693 + 69.0024i) q^{83} +(-119.815 - 35.5126i) q^{85} +(84.7654 - 30.8521i) q^{86} +(-167.146 - 117.037i) q^{88} +(-61.3185 + 35.4023i) q^{89} +(-22.9190 + 39.6969i) q^{91} +(-125.188 - 268.467i) q^{92} +(-58.2757 + 69.4503i) q^{94} +(132.783 + 3.49913i) q^{95} +(-32.6054 - 69.9225i) q^{97} +(38.7067 + 144.455i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8} - 6 q^{10} + 60 q^{11} - 12 q^{13} - 24 q^{16} + 6 q^{17} + 300 q^{20} - 12 q^{22} + 156 q^{23} + 6 q^{25} + 48 q^{26} - 24 q^{28} - 24 q^{31} - 72 q^{32}+ \cdots + 1032 q^{98}+O(q^{100}) \) 408 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 6 * q^8 - 6 * q^10 + 60 * q^11 - 12 * q^13 - 24 * q^16 + 6 * q^17 + 300 * q^20 - 12 * q^22 + 156 * q^23 + 6 * q^25 + 48 * q^26 - 24 * q^28 - 24 * q^31 - 72 * q^32 - 156 * q^35 - 6 * q^37 + 252 * q^38 - 108 * q^40 + 384 * q^41 - 12 * q^43 - 12 * q^46 + 210 * q^47 - 276 * q^50 - 60 * q^52 - 516 * q^53 - 24 * q^55 - 912 * q^56 - 12 * q^58 - 312 * q^61 + 6 * q^62 - 420 * q^65 - 480 * q^67 + 540 * q^68 - 12 * q^70 + 12 * q^71 - 6 * q^73 - 216 * q^76 + 876 * q^77 + 1644 * q^80 - 24 * q^82 + 372 * q^83 - 12 * q^85 - 516 * q^86 + 348 * q^88 - 12 * q^91 - 2082 * q^92 - 198 * q^95 + 600 * q^97 + 1032 * q^98

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