LMFDB - Embedded newform 405.3.s.a.118.28

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			118.28
Character	$\chi$	$=$	405.118
Dual form			405.3.s.a.127.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.227920 - 2.60513i) q^{2} +(-2.79554 - 0.492929i) q^{4} +(-2.63268 + 4.25076i) q^{5} +(4.66090 + 3.26360i) q^{7} +(0.786031 - 2.93351i) q^{8} +(10.4738 + 7.82731i) q^{10} +(-12.9139 - 4.70027i) q^{11} +(-0.714473 - 8.16646i) q^{13} +(9.56441 - 11.3984i) q^{14} +(-18.1329 - 6.59984i) q^{16} +(-7.23092 - 26.9862i) q^{17} +(26.2098 - 15.1322i) q^{19} +(9.45509 - 10.5855i) q^{20} +(-15.1882 + 32.5711i) q^{22} +(14.8089 - 10.3693i) q^{23} +(-11.1380 - 22.3818i) q^{25} -21.4376 q^{26} +(-11.4210 - 11.4210i) q^{28} +(-21.2227 - 25.2922i) q^{29} +(4.67998 - 26.5415i) q^{31} +(-16.1924 + 34.7246i) q^{32} +(-71.9506 + 12.6868i) q^{34} +(-26.1434 + 11.2204i) q^{35} +(10.0842 + 37.6347i) q^{37} +(-33.4478 - 71.7290i) q^{38} +(10.4003 + 11.0642i) q^{40} +(0.528369 + 0.443354i) q^{41} +(-3.77375 - 8.09284i) q^{43} +(33.7844 + 19.5054i) q^{44} +(-23.6382 - 40.9426i) q^{46} +(32.6681 + 22.8744i) q^{47} +(-5.68607 - 15.6223i) q^{49} +(-60.8461 + 23.9147i) q^{50} +(-2.02815 + 23.1819i) q^{52} +(29.6344 + 29.6344i) q^{53} +(53.9778 - 42.5196i) q^{55} +(13.2374 - 11.1075i) q^{56} +(-70.7267 + 49.5234i) q^{58} +(36.4412 + 100.121i) q^{59} +(10.9532 + 62.1185i) q^{61} +(-68.0774 - 18.2413i) q^{62} +(19.9262 + 11.5044i) q^{64} +(36.5947 + 18.4626i) q^{65} +(-76.4475 + 6.68829i) q^{67} +(6.91206 + 79.0052i) q^{68} +(23.2720 + 70.6645i) q^{70} +(16.7490 - 29.0101i) q^{71} +(3.38369 - 12.6281i) q^{73} +(100.342 - 17.6930i) q^{74} +(-80.7297 + 29.3832i) q^{76} +(-44.8505 - 64.0532i) q^{77} +(-45.0676 - 53.7094i) q^{79} +(75.7925 - 59.7035i) q^{80} +(1.27542 - 1.27542i) q^{82} +(-18.4793 - 1.61673i) q^{83} +(133.749 + 40.3090i) q^{85} +(-21.9430 + 7.98661i) q^{86} +(-23.9390 + 34.1884i) q^{88} +(71.9769 - 41.5559i) q^{89} +(23.3220 - 40.3948i) q^{91} +(-46.5103 + 21.6881i) q^{92} +(67.0366 - 79.8911i) q^{94} +(-4.67845 + 151.250i) q^{95} +(-24.7633 + 11.5473i) q^{97} +(-41.9942 + 11.2523i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	0.227920	−	2.60513i	0.113960	−	1.30257i	−0.696833	−	0.717233i	$-0.745408\pi$
$2$	0.227920	−	2.60513i	0.113960	−	1.30257i	0.810793	−	0.585333i	$-0.199036\pi$
$3$		0			0
$3$		0			0
$4$	−2.79554	−	0.492929i	−0.698885	−	0.123232i
$5$	−2.63268	+	4.25076i	−0.526536	+	0.850153i
$5$	−2.63268	+	4.25076i	−0.526536	+	0.850153i
$6$		0			0
$7$	4.66090	+	3.26360i	0.665843	+	0.466228i	0.856990	−	0.515333i	$-0.172332\pi$
$7$	4.66090	+	3.26360i	0.665843	+	0.466228i	−0.191147	+	0.981561i	$0.561221\pi$
$8$	0.786031	−	2.93351i	0.0982538	−	0.366688i
$9$		0			0
$10$	10.4738	+	7.82731i	1.04738	+	0.782731i
$11$	−12.9139	−	4.70027i	−1.17399	−	0.427297i	−0.319914	−	0.947447i	$-0.603654\pi$
$11$	−12.9139	−	4.70027i	−1.17399	−	0.427297i	−0.854075	+	0.520149i	$0.825876\pi$
$12$		0			0
$13$	−0.714473	−	8.16646i	−0.0549595	−	0.628189i	−0.972862	−	0.231384i	$-0.925674\pi$
$13$	−0.714473	−	8.16646i	−0.0549595	−	0.628189i	0.917903	−	0.396805i	$-0.129881\pi$
$14$	9.56441	−	11.3984i	0.683172	−	0.814173i
$15$		0			0
$16$	−18.1329	−	6.59984i	−1.13331	−	0.412490i
$17$	−7.23092	−	26.9862i	−0.425348	−	1.58742i	−0.763161	−	0.646208i	$-0.776354\pi$
$17$	−7.23092	−	26.9862i	−0.425348	−	1.58742i	0.337813	−	0.941213i	$-0.390313\pi$
$18$		0			0
$19$	26.2098	−	15.1322i	1.37946	−	0.796434i	0.387369	−	0.921925i	$-0.373384\pi$
$19$	26.2098	−	15.1322i	1.37946	−	0.796434i	0.992095	+	0.125491i	$0.0400507\pi$
$20$	9.45509	−	10.5855i	0.472754	−	0.529273i
$21$		0			0
$22$	−15.1882	+	32.5711i	−0.690370	+	1.48050i
$23$	14.8089	−	10.3693i	0.643867	−	0.450840i	−0.205490	−	0.978659i	$-0.565879\pi$
$23$	14.8089	−	10.3693i	0.643867	−	0.450840i	0.849357	+	0.527819i	$0.176990\pi$
$24$		0			0
$25$	−11.1380	−	22.3818i	−0.445520	−	0.895272i
$26$	−21.4376			−0.824522
$27$		0			0
$28$	−11.4210	−	11.4210i	−0.407893	−	0.407893i
$29$	−21.2227	−	25.2922i	−0.731817	−	0.872146i	0.263904	−	0.964549i	$-0.414990\pi$
$29$	−21.2227	−	25.2922i	−0.731817	−	0.872146i	−0.995722	+	0.0924028i	$0.970545\pi$
$30$		0			0
$31$	4.67998	−	26.5415i	0.150967	−	0.856176i	−0.811414	−	0.584472i	$-0.801302\pi$
$31$	4.67998	−	26.5415i	0.150967	−	0.856176i	0.962381	−	0.271704i	$-0.0875872\pi$
$32$	−16.1924	+	34.7246i	−0.506011	+	1.08514i
$33$		0			0
$34$	−71.9506	+	12.6868i	−2.11619	+	0.373142i
$35$	−26.1434	+	11.2204i	−0.746955	+	0.320582i
$36$		0			0
$37$	10.0842	+	37.6347i	0.272546	+	1.01715i	0.957468	+	0.288539i	$0.0931694\pi$
$37$	10.0842	+	37.6347i	0.272546	+	1.01715i	−0.684922	+	0.728616i	$0.740164\pi$
$38$	−33.4478	−	71.7290i	−0.880204	−	1.88760i
$39$		0			0
$40$	10.4003	+	11.0642i	0.260007	+	0.276605i
$41$	0.528369	+	0.443354i	0.0128870	+	0.0108135i	0.649208	−	0.760611i	$-0.275100\pi$
$41$	0.528369	+	0.443354i	0.0128870	+	0.0108135i	−0.636321	+	0.771424i	$0.719545\pi$
$42$		0			0
$43$	−3.77375	−	8.09284i	−0.0877617	−	0.188206i	0.857528	−	0.514437i	$-0.171999\pi$
$43$	−3.77375	−	8.09284i	−0.0877617	−	0.188206i	−0.945290	+	0.326231i	$0.894221\pi$
$44$	33.7844	+	19.5054i	0.767826	+	0.443305i
$45$		0			0
$46$	−23.6382	−	40.9426i	−0.513875	−	0.890057i
$47$	32.6681	+	22.8744i	0.695065	+	0.486690i	0.866930	−	0.498431i	$-0.166090\pi$
$47$	32.6681	+	22.8744i	0.695065	+	0.486690i	−0.171864	+	0.985121i	$0.554979\pi$
$48$		0			0
$49$	−5.68607	−	15.6223i	−0.116042	−	0.318823i
$50$	−60.8461	+	23.9147i	−1.21692	+	0.478294i
$51$		0			0
$52$	−2.02815	+	23.1819i	−0.0390029	+	0.445805i
$53$	29.6344	+	29.6344i	0.559139	+	0.559139i	0.929062	−	0.369923i	$-0.120616\pi$
$53$	29.6344	+	29.6344i	0.559139	+	0.559139i	−0.369923	+	0.929062i	$0.620616\pi$
$54$		0			0
$55$	53.9778	−	42.5196i	0.981415	−	0.773083i
$56$	13.2374	−	11.1075i	0.236382	−	0.198348i
$57$		0			0
$58$	−70.7267	+	49.5234i	−1.21943	+	0.853851i
$59$	36.4412	+	100.121i	0.617647	+	1.69697i	0.712673	+	0.701496i	$0.247484\pi$
$59$	36.4412	+	100.121i	0.617647	+	1.69697i	−0.0950262	+	0.995475i	$0.530293\pi$
$60$		0			0
$61$	10.9532	+	62.1185i	0.179560	+	1.01834i	0.932748	+	0.360530i	$0.117404\pi$
$61$	10.9532	+	62.1185i	0.179560	+	1.01834i	−0.753188	+	0.657806i	$0.771485\pi$
$62$	−68.0774	−	18.2413i	−1.09802	−	0.294214i
$63$		0			0
$64$	19.9262	+	11.5044i	0.311347	+	0.179756i
$65$	36.5947	+	18.4626i	0.562995	+	0.284040i
$66$		0			0
$67$	−76.4475	+	6.68829i	−1.14101	+	0.0998252i	−0.641952	−	0.766745i	$-0.721875\pi$
$67$	−76.4475	+	6.68829i	−1.14101	+	0.0998252i	−0.499055	+	0.866570i	$0.666320\pi$
$68$	6.91206	+	79.0052i	0.101648	+	1.16184i
$69$		0			0
$70$	23.2720	+	70.6645i	0.332457	+	1.00949i
$71$	16.7490	−	29.0101i	0.235901	−	0.408593i	−0.723633	−	0.690185i	$-0.757529\pi$
$71$	16.7490	−	29.0101i	0.235901	−	0.408593i	0.959534	+	0.281592i	$0.0908624\pi$
$72$		0			0
$73$	3.38369	−	12.6281i	0.0463519	−	0.172988i	−0.938870	−	0.344273i	$-0.888125\pi$
$73$	3.38369	−	12.6281i	0.0463519	−	0.172988i	0.985221	+	0.171285i	$0.0547920\pi$
$74$	100.342	−	17.6930i	1.35597	−	0.239094i
$75$		0			0
$76$	−80.7297	+	29.3832i	−1.06223	+	0.386621i
$77$	−44.8505	−	64.0532i	−0.582474	−	0.831860i
$78$		0			0
$79$	−45.0676	−	53.7094i	−0.570475	−	0.679866i	0.401253	−	0.915967i	$-0.368575\pi$
$79$	−45.0676	−	53.7094i	−0.570475	−	0.679866i	−0.971729	+	0.236101i	$0.924130\pi$
$80$	75.7925	−	59.7035i	0.947406	−	0.746293i
$81$		0			0
$82$	1.27542	−	1.27542i	0.0155539	−	0.0155539i
$83$	−18.4793	−	1.61673i	−0.222642	−	0.0194786i	−0.0247110	−	0.999695i	$-0.507867\pi$
$83$	−18.4793	−	1.61673i	−0.222642	−	0.0194786i	−0.197931	+	0.980216i	$0.563422\pi$
$84$		0			0
$85$	133.749	+	40.3090i	1.57351	+	0.474224i
$86$	−21.9430	+	7.98661i	−0.255152	+	0.0928676i
$87$		0			0
$88$	−23.9390	+	34.1884i	−0.272034	+	0.388504i
$89$	71.9769	−	41.5559i	0.808730	−	0.466920i	−0.0377849	−	0.999286i	$-0.512030\pi$
$89$	71.9769	−	41.5559i	0.808730	−	0.466920i	0.846515	+	0.532366i	$0.178697\pi$
$90$		0			0
$91$	23.3220	−	40.3948i	0.256285	−	0.443899i
$92$	−46.5103	+	21.6881i	−0.505547	+	0.235740i
$93$		0			0
$94$	67.0366	−	79.8911i	0.713156	−	0.849906i
$95$	−4.67845	+	151.250i	−0.0492469	+	1.59211i
$96$		0			0
$97$	−24.7633	+	11.5473i	−0.255292	+	0.119044i	−0.546051	−	0.837752i	$-0.683870\pi$
$97$	−24.7633	+	11.5473i	−0.255292	+	0.119044i	0.290760	+	0.956796i	$0.406092\pi$
$98$	−41.9942	+	11.2523i	−0.428513	+	0.114820i
$99$		0			0
$100$	20.1041	+	68.0595i	0.201041	+	0.680595i
$101$	−11.1922	−	63.4739i	−0.110814	−	0.628455i	−0.988738	−	0.149656i	$-0.952183\pi$
$101$	−11.1922	−	63.4739i	−0.110814	−	0.628455i	0.877925	−	0.478799i	$-0.158928\pi$
$102$		0			0
$103$	−41.1498	−	19.1885i	−0.399513	−	0.186296i	0.212469	−	0.977168i	$-0.431850\pi$
$103$	−41.1498	−	19.1885i	−0.399513	−	0.186296i	−0.611982	+	0.790872i	$0.709627\pi$
$104$	−24.5180	−	4.32318i	−0.235750	−	0.0415690i
$105$		0			0
$106$	83.9557	−	70.4472i	0.792035	−	0.664596i
$107$	−45.9700	+	45.9700i	−0.429626	+	0.429626i	−0.888501	−	0.458875i	$-0.848253\pi$
$107$	−45.9700	+	45.9700i	−0.429626	+	0.429626i	0.458875	+	0.888501i	$0.348253\pi$
$108$		0			0
$109$			7.40551i			0.0679405i	0.999423	+	0.0339702i	$0.0108151\pi$
$109$			7.40551i			0.0679405i	−0.999423	+	0.0339702i	$0.989185\pi$
$110$	−98.4665	−	150.311i	−0.895150	−	1.36646i
$111$		0			0
$112$	−62.9765	−	89.9397i	−0.562290	−	0.803033i
$113$	−170.252	−	79.3898i	−1.50665	−	0.702565i	−0.518366	−	0.855159i	$-0.673459\pi$
$113$	−170.252	−	79.3898i	−1.50665	−	0.702565i	−0.988289	+	0.152594i	$0.951237\pi$
$114$		0			0
$115$	5.09038	+	90.2484i	0.0442642	+	0.784769i
$116$	46.8616	+	81.1667i	0.403980	+	0.699713i
$117$		0			0
$118$	269.135	−	72.1145i	2.28080	−	0.611140i
$119$	54.3694	−	149.379i	0.456886	−	1.25528i
$120$		0			0
$121$	51.9844	+	43.6201i	0.429623	+	0.360497i
$122$	164.323	−	14.3764i	1.34691	−	0.117840i
$123$		0			0
$124$	−26.1661	+	71.8908i	−0.211017	+	0.579765i
$125$	124.463	+	11.5791i	0.995700	+	0.0926331i
$126$		0			0
$127$	−2.49220	−	0.667782i	−0.0196236	−	0.00525813i	0.248994	−	0.968505i	$-0.419900\pi$
$127$	−2.49220	−	0.667782i	−0.0196236	−	0.00525813i	−0.268617	+	0.963247i	$0.586567\pi$
$128$	−53.3929	+	76.2529i	−0.417132	+	0.595726i
$129$		0			0
$130$	56.4382	−	91.1260i	0.434140	−	0.700969i
$131$	22.4868	−	127.529i	0.171655	−	0.973505i	−0.770279	−	0.637707i	$-0.779883\pi$
$131$	22.4868	−	127.529i	0.171655	−	0.973505i	0.941934	−	0.335798i	$-0.109006\pi$
$132$		0			0
$133$	171.547	+	15.0084i	1.28983	+	0.112845i
$134$			200.680i			1.49761i
$135$		0			0
$136$	−84.8478			−0.623881
$137$	−18.5233	+	211.722i	−0.135206	+	1.54542i	0.561147	+	0.827716i	$0.310360\pi$
$137$	−18.5233	+	211.722i	−0.135206	+	1.54542i	−0.696353	+	0.717699i	$0.745195\pi$
$138$		0			0
$139$	−0.262808	−	0.0463401i	−0.00189070	−	0.000333382i	0.172703	−	0.984974i	$-0.444750\pi$
$139$	−0.262808	−	0.0463401i	−0.00189070	−	0.000333382i	−0.174593	+	0.984641i	$0.555861\pi$
$140$	78.6159	−	18.4802i	0.561542	−	0.132001i
$141$		0			0
$142$	−71.7578	−	50.2454i	−0.505337	−	0.353841i
$143$	−29.1579	+	108.819i	−0.203902	+	0.760972i
$144$		0			0
$145$	163.384	−	23.6264i	1.12679	−	0.162940i
$146$	−32.1267	−	11.6932i	−0.220046	−	0.0800901i
$147$		0			0
$148$	−9.63951	−	110.180i	−0.0651318	−	0.744460i
$149$	100.493	−	119.762i	0.674447	−	0.803774i	−0.314935	−	0.949113i	$-0.601983\pi$
$149$	100.493	−	119.762i	0.674447	−	0.803774i	0.989382	+	0.145339i	$0.0464273\pi$
$150$		0			0
$151$	204.837	+	74.5544i	1.35653	+	0.493738i	0.914981	−	0.403498i	$-0.132206\pi$
$151$	204.837	+	74.5544i	1.35653	+	0.493738i	0.441553	+	0.897235i	$0.354428\pi$
$152$	−23.7888	−	88.7810i	−0.156505	−	0.584086i
$153$		0			0
$154$	−177.089	+	102.243i	−1.14993	+	0.663913i
$155$	100.501	+	89.7687i	0.648391	+	0.579153i
$156$		0			0
$157$	49.9753	−	107.172i	0.318314	−	0.682627i	−0.680426	−	0.732817i	$-0.738205\pi$
$157$	49.9753	−	107.172i	0.318314	−	0.682627i	0.998740	+	0.0501905i	$0.0159829\pi$
$158$	−150.192	+	105.166i	−0.950582	+	0.665605i
$159$		0			0
$160$	−104.977	−	160.249i	−0.656106	−	1.00155i
$161$	102.864			0.638909
$162$		0			0
$163$	−113.010	−	113.010i	−0.693315	−	0.693315i	0.269645	−	0.962960i	$-0.413094\pi$
$163$	−113.010	−	113.010i	−0.693315	−	0.693315i	−0.962960	+	0.269645i	$0.913094\pi$
$164$	−1.25853	−	1.49986i	−0.00767398	−	0.00914550i
$165$		0			0
$166$	−8.42357	+	47.7725i	−0.0507444	+	0.287786i
$167$	−67.6957	+	145.174i	−0.405364	+	0.869305i	0.592598	+	0.805498i	$0.298102\pi$
$167$	−67.6957	+	145.174i	−0.405364	+	0.869305i	−0.997962	+	0.0638074i	$0.979676\pi$
$168$		0			0
$169$	100.252	−	17.6771i	0.593206	−	0.104598i
$170$	135.494	−	339.246i	0.797025	−	1.99556i
$171$		0			0
$172$	6.56048	+	24.4841i	0.0381423	+	0.142349i
$173$	25.5416	+	54.7740i	0.147639	+	0.316613i	0.966194	−	0.257815i	$-0.0830024\pi$
$173$	25.5416	+	54.7740i	0.147639	+	0.316613i	−0.818555	+	0.574428i	$0.805225\pi$
$174$		0			0
$175$	21.1321	−	140.669i	0.120755	−	0.803824i
$176$	203.145	+	170.459i	1.15423	+	0.968518i
$177$		0			0
$178$	−91.8537	−	196.981i	−0.516032	−	1.10663i
$179$	236.166	+	136.351i	1.31936	+	0.761735i	0.983626	−	0.180221i	$-0.0576813\pi$
$179$	236.166	+	136.351i	1.31936	+	0.761735i	0.335737	+	0.941956i	$0.391015\pi$
$180$		0			0
$181$	−93.8465	−	162.547i	−0.518489	−	0.898049i	−0.999769	−	0.0214826i	$-0.993161\pi$
$181$	−93.8465	−	162.547i	−0.518489	−	0.898049i	0.481280	−	0.876567i	$-0.340172\pi$
$182$	−99.9183	−	69.9636i	−0.549002	−	0.384415i
$183$		0			0
$184$	−18.7782	−	51.5927i	−0.102056	−	0.280395i
$185$	−186.525	−	56.2147i	−1.00824	−	0.303863i
$186$		0			0
$187$	−33.4630	+	382.483i	−0.178946	+	2.04537i
$188$	−80.0494	−	80.0494i	−0.425795	−	0.425795i
$189$		0			0
$190$	392.960	+	46.6608i	2.06821	+	0.245583i
$191$	101.563	−	85.2213i	0.531742	−	0.446185i	−0.336960	−	0.941519i	$-0.609399\pi$
$191$	101.563	−	85.2213i	0.531742	−	0.446185i	0.868702	+	0.495334i	$0.164954\pi$
$192$		0			0
$193$	−77.3222	+	54.1416i	−0.400633	+	0.280526i	−0.756478	−	0.654019i	$-0.773082\pi$
$193$	−77.3222	+	54.1416i	−0.400633	+	0.280526i	0.355846	+	0.934545i	$0.384193\pi$
$194$	24.4382	+	67.1435i	0.125970	+	0.346101i
$195$		0			0
$196$	8.19492	+	46.4757i	0.0418108	+	0.237121i
$197$	202.958	+	54.3825i	1.03024	+	0.276053i	0.734065	−	0.679079i	$-0.237621\pi$
$197$	202.958	+	54.3825i	1.03024	+	0.276053i	0.296180	+	0.955132i	$0.404287\pi$
$198$		0			0
$199$	118.108	+	68.1897i	0.593508	+	0.342662i	0.766483	−	0.642264i	$-0.222005\pi$
$199$	118.108	+	68.1897i	0.593508	+	0.342662i	−0.172975	+	0.984926i	$0.555338\pi$
$200$	−74.4120	+	15.0806i	−0.372060	+	0.0754029i
$201$		0			0
$202$	−167.909	+	14.6901i	−0.831232	+	0.0727234i
$203$	−16.3732	−	187.147i	−0.0806563	−	0.921906i
$204$		0			0
$205$	−3.27562	+	1.07876i	−0.0159786	+	0.00526225i
$206$	−59.3673	+	102.827i	−0.288191	+	0.499161i
$207$		0			0
$208$	−40.9419	+	152.797i	−0.196836	+	0.734602i
$209$	−409.596	+	72.2228i	−1.95979	+	0.345564i
$210$		0			0
$211$	223.645	−	81.4002i	1.05993	−	0.385783i	0.247528	−	0.968881i	$-0.420382\pi$
$211$	223.645	−	81.4002i	1.05993	−	0.385783i	0.812402	+	0.583098i	$0.198160\pi$
$212$	−68.2364	−	97.4517i	−0.321870	−	0.459678i
$213$		0			0
$214$	109.280	+	130.235i	0.510656	+	0.608576i
$215$	44.3359	+	5.26452i	0.206213	+	0.0244862i
$216$		0			0
$217$	108.434	−	108.434i	0.499694	−	0.499694i
$218$	19.2923	+	1.68786i	0.0884970	+	0.00774248i
$219$		0			0
$220$	−171.856	+	92.2579i	−0.781165	+	0.419354i
$221$	−215.215	+	78.3319i	−0.973825	+	0.354443i
$222$		0			0
$223$	6.71950	−	9.59643i	0.0301323	−	0.0430333i	−0.803803	−	0.594895i	$-0.797194\pi$
$223$	6.71950	−	9.59643i	0.0301323	−	0.0430333i	0.833936	+	0.551862i	$0.186082\pi$
$224$	−188.798	+	109.003i	−0.842849	+	0.486619i
$225$		0			0
$226$	−245.625	+	425.435i	−1.08684	+	1.88245i
$227$	−217.750	+	101.538i	−0.959249	+	0.447305i	−0.838213	−	0.545343i	$-0.816399\pi$
$227$	−217.750	+	101.538i	−0.959249	+	0.447305i	−0.121036	+	0.992648i	$0.538622\pi$
$228$		0			0
$229$	−89.8856	+	107.121i	−0.392513	+	0.467779i	−0.925722	−	0.378204i	$-0.876542\pi$
$229$	−89.8856	+	107.121i	−0.392513	+	0.467779i	0.533209	+	0.845984i	$0.320986\pi$
$230$	236.269	+	7.30826i	1.02726	+	0.0317750i
$231$		0			0
$232$	−90.8766	+	42.3765i	−0.391710	+	0.182657i
$233$	106.050	−	28.4159i	0.455149	−	0.121957i	−0.0239588	−	0.999713i	$-0.507627\pi$
$233$	106.050	−	28.4159i	0.455149	−	0.121957i	0.479108	+	0.877756i	$0.340960\pi$
$234$		0			0
$235$	−183.238	+	78.6432i	−0.779738	+	0.334652i
$236$	−52.5200	−	297.856i	−0.222543	−	1.26210i
$237$		0			0
$238$	−376.759	−	175.686i	−1.58302	−	0.738176i
$239$	−170.015	−	29.9783i	−0.711361	−	0.125432i	−0.193753	−	0.981050i	$-0.562066\pi$
$239$	−170.015	−	29.9783i	−0.711361	−	0.125432i	−0.517608	+	0.855618i	$0.673177\pi$
$240$		0			0
$241$	−178.536	+	149.809i	−0.740813	+	0.621616i	−0.933056	−	0.359732i	$-0.882868\pi$
$241$	−178.536	+	149.809i	−0.740813	+	0.621616i	0.192243	+	0.981347i	$0.438424\pi$
$242$	125.484	−	125.484i	0.518531	−	0.518531i
$243$		0			0
$244$		−	179.054i		−	0.733827i
$245$	81.3765	+	16.9585i	0.332149	+	0.0692183i
$246$		0			0
$247$	−142.303	−	203.230i	−0.576126	−	0.822793i
$248$	−74.1809	−	34.5911i	−0.299117	−	0.139480i
$249$		0			0
$250$	58.5327	−	321.602i	0.234131	−	1.28641i
$251$	−31.3082	−	54.2275i	−0.124734	−	0.216046i	0.796895	−	0.604118i	$-0.206474\pi$
$251$	−31.3082	−	54.2275i	−0.124734	−	0.216046i	−0.921629	+	0.388072i	$0.873141\pi$
$252$		0			0
$253$	−239.980	+	64.3023i	−0.948536	+	0.254159i
$254$	−2.30768	+	6.34030i	−0.00908536	+	0.0249618i
$255$		0			0
$256$	256.983	+	215.634i	1.00384	+	0.842321i
$257$	78.1350	−	6.83592i	0.304027	−	0.0265989i	0.0658785	−	0.997828i	$-0.479015\pi$
$257$	78.1350	−	6.83592i	0.304027	−	0.0265989i	0.238149	+	0.971229i	$0.423459\pi$
$258$		0			0
$259$	−75.8232	+	208.322i	−0.292754	+	0.804334i
$260$	−93.2011	−	69.6516i	−0.358466	−	0.267891i
$261$		0			0
$262$	−327.105	−	87.6476i	−1.24849	−	0.334533i
$263$	−42.2612	+	60.3552i	−0.160689	+	0.229488i	−0.891420	−	0.453178i	$-0.850290\pi$
$263$	−42.2612	+	60.3552i	−0.160689	+	0.229488i	0.730731	+	0.682665i	$0.239179\pi$
$264$		0			0
$265$	−203.987	+	47.9509i	−0.769760	+	0.180947i
$266$	78.1978	−	443.482i	0.293977	−	1.66722i
$267$		0			0
$268$	217.009	+	18.9858i	0.809734	+	0.0708426i
$269$			133.665i			0.496895i	0.968645	+	0.248447i	$0.0799203\pi$
$269$			133.665i			0.496895i	−0.968645	+	0.248447i	$0.920080\pi$
$270$		0			0
$271$	−167.480			−0.618006			−0.309003	−	0.951061i	$-0.599995\pi$
$271$	−167.480			−0.618006			−0.309003	+	0.951061i	$0.599995\pi$
$272$	−46.9867	+	537.061i	−0.172745	+	1.97449i
$273$		0			0
$274$	547.342	+	96.5111i	1.99760	+	0.352230i
$275$	38.6342	+	341.388i	0.140488	+	1.24141i
$276$		0			0
$277$	437.853	+	306.588i	1.58070	+	1.10682i	0.941112	+	0.338096i	$0.109783\pi$
$277$	437.853	+	306.588i	1.58070	+	1.10682i	0.639585	+	0.768720i	$0.279106\pi$
$278$	−0.180621	+	0.674087i	−0.000649716	+	0.00242477i
$279$		0			0
$280$	12.3655	+	85.5115i	0.0441625	+	0.305398i
$281$	468.626	+	170.566i	1.66771	+	0.606996i	0.991546	−	0.129759i	$-0.0414202\pi$
$281$	468.626	+	170.566i	1.66771	+	0.606996i	0.676161	+	0.736754i	$0.263642\pi$
$282$		0			0
$283$	−2.93131	−	33.5050i	−0.0103580	−	0.118392i	0.989255	−	0.146198i	$-0.0467036\pi$
$283$	−2.93131	−	33.5050i	−0.0103580	−	0.118392i	−0.999613	+	0.0278056i	$0.991148\pi$
$284$	−61.1224	+	72.8429i	−0.215220	+	0.256489i
$285$		0			0
$286$	276.842	+	100.762i	0.967979	+	0.352316i
$287$	1.01574	+	3.79081i	0.00353918	+	0.0132084i
$288$		0			0
$289$	−425.686	+	245.770i	−1.47296	+	0.850414i
$290$	−24.3114	−	431.022i	−0.0838324	−	1.48628i
$291$		0			0
$292$	−15.6840	+	33.6344i	−0.0537123	+	0.115186i
$293$	145.787	−	102.081i	0.497568	−	0.348401i	−0.297700	−	0.954660i	$-0.596219\pi$
$293$	145.787	−	102.081i	0.497568	−	0.348401i	0.795267	+	0.606259i	$0.207331\pi$
$294$		0			0
$295$	−521.530	−	108.684i	−1.76790	−	0.368422i
$296$	118.328			0.399757
$297$		0			0
$298$	−289.093	−	289.093i	−0.970109	−	0.970109i
$299$	−95.2613	−	113.528i	−0.318600	−	0.379692i
$300$		0			0
$301$	8.82269	−	50.0359i	0.0293113	−	0.166232i
$302$	240.910	−	516.634i	0.797716	−	1.71071i
$303$		0			0
$304$	−575.130	+	101.411i	−1.89188	+	0.333589i
$305$	−292.887	−	116.979i	−0.960286	−	0.383537i
$306$		0			0
$307$	31.5341	+	117.687i	0.102717	+	0.383345i	0.998076	−	0.0620000i	$-0.0197479\pi$
$307$	31.5341	+	117.687i	0.102717	+	0.383345i	−0.895359	+	0.445345i	$0.853081\pi$
$308$	93.8077	+	201.171i	0.304571	+	0.653154i
$309$		0			0
$310$	256.765	−	241.357i	0.828275	−	0.778573i
$311$	−457.010	−	383.477i	−1.46949	−	1.23305i	−0.916610	−	0.399783i	$-0.869085\pi$
$311$	−457.010	−	383.477i	−1.46949	−	1.23305i	−0.552877	−	0.833263i	$-0.686470\pi$
$312$		0			0
$313$	−105.281	−	225.776i	−0.336361	−	0.721328i	0.663273	−	0.748377i	$-0.269167\pi$
$313$	−105.281	−	225.776i	−0.336361	−	0.721328i	−0.999634	+	0.0270491i	$0.991389\pi$
$314$	−267.808	−	154.619i	−0.852892	−	0.492417i
$315$		0			0
$316$	99.5132	+	172.362i	0.314915	+	0.545449i
$317$	455.409	+	318.881i	1.43662	+	1.00593i	0.994018	+	0.109214i	$0.0348335\pi$
$317$	455.409	+	318.881i	1.43662	+	1.00593i	0.442602	+	0.896718i	$0.354055\pi$
$318$		0			0
$319$	155.187	+	426.373i	0.486480	+	1.33659i
$320$	−101.362	+	54.4141i	−0.316755	+	0.170044i
$321$		0			0
$322$	23.4448	−	267.975i	0.0728099	−	0.832221i
$323$	−597.882	−	597.882i	−1.85103	−	1.85103i
$324$		0			0
$325$	−174.822	+	106.949i	−0.537915	+	0.329074i
$326$	−320.164	+	268.650i	−0.982099	+	0.824079i
$327$		0			0
$328$	1.71589	−	1.20148i	0.00523139	−	0.00366306i
$329$	77.6097	+	213.231i	0.235896	+	0.648118i
$330$		0			0
$331$	−87.1410	−	494.201i	−0.263266	−	1.49305i	−0.773929	−	0.633273i	$-0.781711\pi$
$331$	−87.1410	−	494.201i	−0.263266	−	1.49305i	0.510663	−	0.859781i	$-0.329400\pi$
$332$	50.8626	+	13.6286i	0.153201	+	0.0410500i
$333$		0			0
$334$	362.768	+	209.444i	1.08613	+	0.627079i
$335$	172.831	−	342.568i	0.515915	−	1.02259i
$336$		0			0
$337$	−107.639	+	9.41717i	−0.319403	+	0.0279441i	−0.245730	−	0.969338i	$-0.579028\pi$
$337$	−107.639	+	9.41717i	−0.319403	+	0.0279441i	−0.0736729	+	0.997282i	$0.523472\pi$
$338$	−23.2019	−	265.198i	−0.0686445	−	0.784611i
$339$		0			0
$340$	−354.030	−	178.614i	−1.04126	−	0.525335i
$341$	−185.189	+	320.756i	−0.543075	+	0.940634i
$342$		0			0
$343$	96.6430	−	360.677i	0.281758	−	1.05154i
$344$	−26.7067	+	4.70911i	−0.0776357	+	0.0136893i
$345$		0			0
$346$	148.515	−	54.0551i	0.429234	−	0.156229i
$347$	173.998	+	248.495i	0.501435	+	0.716123i	0.987468	−	0.157817i	$-0.0504456\pi$
$347$	173.998	+	248.495i	0.501435	+	0.716123i	−0.486034	+	0.873940i	$0.661557\pi$
$348$		0			0
$349$	35.3610	+	42.1416i	0.101321	+	0.120749i	0.814322	−	0.580413i	$-0.197109\pi$
$349$	35.3610	+	42.1416i	0.101321	+	0.120749i	−0.713001	+	0.701163i	$0.752665\pi$
$350$	−361.646	−	87.1133i	−1.03327	−	0.248895i
$351$		0			0
$352$	372.321	−	372.321i	1.05773	−	1.05773i
$353$	636.855	+	55.7176i	1.80412	+	0.157840i	0.939044	−	0.343798i	$-0.111713\pi$
$353$	636.855	+	55.7176i	1.80412	+	0.157840i	0.865078	+	0.501638i	$0.167269\pi$
$354$		0			0
$355$	79.2204	+	147.570i	0.223156	+	0.415691i
$356$	−221.698	+	80.6916i	−0.622749	+	0.226662i
$357$		0			0
$358$	409.038	−	584.167i	1.14256	−	1.63175i
$359$	87.4299	−	50.4777i	0.243537	−	0.140606i	−0.373264	−	0.927725i	$-0.621761\pi$
$359$	87.4299	−	50.4777i	0.243537	−	0.140606i	0.616802	+	0.787119i	$0.288428\pi$
$360$		0			0
$361$	277.469	−	480.591i	0.768613	−	1.33128i
$362$	−444.846	+	207.435i	−1.22886	+	0.573025i
$363$		0			0
$364$	−85.1092	+	101.429i	−0.233817	+	0.278652i
$365$	44.7709	+	47.6290i	0.122660	+	0.130491i
$366$		0			0
$367$	177.604	−	82.8180i	0.483934	−	0.225662i	−0.165311	−	0.986241i	$-0.552863\pi$
$367$	177.604	−	82.8180i	0.483934	−	0.225662i	0.649245	+	0.760579i	$0.275085\pi$
$368$	−336.965	+	90.2895i	−0.915666	+	0.245352i
$369$		0			0
$370$	−188.959	+	473.109i	−0.510701	+	1.27867i
$371$	41.4082	+	234.837i	0.111612	+	0.632985i
$372$		0			0
$373$	551.415	+	257.129i	1.47832	+	0.689354i	0.983711	−	0.179760i	$-0.0575320\pi$
$373$	551.415	+	257.129i	1.47832	+	0.689354i	0.494613	+	0.869113i	$0.335310\pi$
$374$	988.793	+	174.351i	2.64383	+	0.466179i
$375$		0			0
$376$	92.7804	−	77.8520i	0.246756	−	0.207053i
$377$	−191.385	+	191.385i	−0.507653	+	0.507653i
$378$		0			0
$379$		−	710.326i		−	1.87421i	−0.349045	−	0.937106i	$-0.613494\pi$
$379$		−	710.326i		−	1.87421i	0.349045	−	0.937106i	$-0.386506\pi$
$380$	87.6343	−	420.519i	0.230617	−	1.10663i
$381$		0			0
$382$	−198.865	−	284.008i	−0.520588	−	0.743477i
$383$	−238.881	−	111.392i	−0.623710	−	0.290841i	0.0849561	−	0.996385i	$-0.472925\pi$
$383$	−238.881	−	111.392i	−0.623710	−	0.290841i	−0.708666	+	0.705544i	$0.750703\pi$
$384$		0			0
$385$	390.352	−	22.0175i	1.01390	−	0.0571882i
$386$	123.423	+	213.774i	0.319748	+	0.553820i
$387$		0			0
$388$	74.9188	−	20.0744i	0.193090	−	0.0517382i
$389$	129.260	−	355.140i	0.332289	−	0.912955i	−0.655227	−	0.755432i	$-0.727427\pi$
$389$	129.260	−	355.140i	0.332289	−	0.912955i	0.987515	−	0.157523i	$-0.0503509\pi$
$390$		0			0
$391$	−386.911	−	324.657i	−0.989542	−	0.830324i
$392$	−50.2977	+	4.40047i	−0.128310	+	0.0112257i
$393$		0			0
$394$	187.932	−	516.338i	0.476984	−	1.31050i
$395$	346.955	−	50.1718i	0.878366	−	0.127017i
$396$		0			0
$397$	321.590	+	86.1697i	0.810050	+	0.217052i	0.639992	−	0.768382i	$-0.278938\pi$
$397$	321.590	+	86.1697i	0.810050	+	0.217052i	0.170058	+	0.985434i	$0.445604\pi$
$398$	204.562	−	292.145i	0.513976	−	0.734034i
$399$		0			0
$400$	54.2479	+	479.356i	0.135620	+	1.19839i
$401$	15.5961	−	88.4496i	0.0388929	−	0.220573i	−0.959166	−	0.282842i	$-0.908723\pi$
$401$	15.5961	−	88.4496i	0.0388929	−	0.220573i	0.998059	+	0.0622696i	$0.0198338\pi$
$402$		0			0
$403$	−220.094	−	19.2557i	−0.546138	−	0.0477809i
$404$			182.961i			0.452873i
$405$		0			0
$406$	−491.274			−1.21004
$407$	46.6672	−	533.409i	0.114661	−	1.31059i
$408$		0			0
$409$	−66.3266	−	11.6952i	−0.162168	−	0.0285946i	0.0919747	−	0.995761i	$-0.470682\pi$
$409$	−66.3266	−	11.6952i	−0.162168	−	0.0285946i	−0.254142	+	0.967167i	$0.581793\pi$
$410$	2.06374	+	8.77929i	0.00503351	+	0.0214129i
$411$		0			0
$412$	105.577	+	73.9260i	0.256256	+	0.179432i
$413$	−156.907	+	585.585i	−0.379920	+	1.41788i
$414$		0			0
$415$	55.5223	−	74.2947i	0.133789	−	0.179023i
$416$	295.146	+	107.424i	0.709486	+	0.258232i
$417$		0			0
$418$	94.7951	+	1083.51i	0.226783	+	2.59214i
$419$	−313.309	+	373.388i	−0.747755	+	0.891140i	−0.997008	−	0.0772984i	$-0.975371\pi$
$419$	−313.309	+	373.388i	−0.747755	+	0.891140i	0.249253	+	0.968438i	$0.419815\pi$
$420$		0			0
$421$	626.052	+	227.864i	1.48706	+	0.541245i	0.952674	−	0.303995i	$-0.0983207\pi$
$421$	626.052	+	227.864i	1.48706	+	0.541245i	0.534386	+	0.845241i	$0.320543\pi$
$422$	−161.085	−	601.178i	−0.381718	−	1.42459i
$423$		0			0
$424$	110.226	−	63.6391i	0.259967	−	0.150092i
$425$	−523.461	+	462.413i	−1.23167	+	1.08803i
$426$		0			0
$427$	−151.678	+	325.275i	−0.355218	+	0.761767i
$428$	151.171	−	105.851i	0.353203	−	0.247315i
$429$		0			0
$430$	23.8198	−	114.301i	0.0553949	−	0.265816i
$431$	463.226			1.07477			0.537385	−	0.843337i	$-0.319412\pi$
$431$	463.226			1.07477			0.537385	+	0.843337i	$0.319412\pi$
$432$		0			0
$433$	136.418	+	136.418i	0.315052	+	0.315052i	0.846863	−	0.531811i	$-0.178488\pi$
$433$	136.418	+	136.418i	0.315052	+	0.315052i	−0.531811	+	0.846863i	$0.678488\pi$
$434$	−257.770	−	307.198i	−0.593939	−	0.707829i
$435$		0			0
$436$	3.65039	−	20.7024i	0.00837246	−	0.0474826i
$437$	231.228	−	495.871i	0.529126	−	1.13472i
$438$		0			0
$439$	−774.274	+	136.525i	−1.76372	+	0.310992i	−0.959157	−	0.282873i	$-0.908712\pi$
$439$	−774.274	+	136.525i	−1.76372	+	0.310992i	−0.804565	+	0.593865i	$0.797601\pi$
$440$	−82.3031	−	191.766i	−0.187053	−	0.435832i
$441$		0			0
$442$	155.013	+	578.518i	0.350709	+	1.30886i
$443$	−79.9036	−	171.354i	−0.180369	−	0.386803i	0.795247	−	0.606285i	$-0.207341\pi$
$443$	−79.9036	−	171.354i	−0.180369	−	0.386803i	−0.975617	+	0.219482i	$0.929563\pi$
$444$		0			0
$445$	−12.8479	+	415.360i	−0.0288717	+	0.933394i
$446$	−23.4685	−	19.6924i	−0.0526199	−	0.0441534i
$447$		0			0
$448$	55.3283	+	118.652i	0.123501	+	0.264848i
$449$	−687.568	−	396.968i	−1.53133	−	0.884115i	−0.999301	−	0.0373913i	$-0.988095\pi$
$449$	−687.568	−	396.968i	−1.53133	−	0.884115i	−0.532032	−	0.846724i	$-0.678571\pi$
$450$		0			0
$451$	−4.73941	−	8.20889i	−0.0105087	−	0.0182015i
$452$	436.813	+	305.859i	0.966400	+	0.676680i
$453$		0			0
$454$	214.891	+	590.409i	0.473329	+	1.30046i
$455$	110.310	+	205.483i	0.242439	+	0.451610i
$456$		0			0
$457$	−1.89953	+	21.7117i	−0.00415652	+	0.0475093i	−0.997990	−	0.0633763i	$-0.979813\pi$
$457$	−1.89953	+	21.7117i	−0.00415652	+	0.0475093i	0.993833	+	0.110886i	$0.0353687\pi$
$458$	258.579	+	258.579i	0.564583	+	0.564583i
$459$		0			0
$460$	30.2557	−	254.802i	0.0657733	−	0.553918i
$461$	74.4549	−	62.4751i	0.161507	−	0.135521i	−0.558452	−	0.829537i	$-0.688605\pi$
$461$	74.4549	−	62.4751i	0.161507	−	0.135521i	0.719960	+	0.694016i	$0.244160\pi$
$462$		0			0
$463$	28.2390	−	19.7732i	0.0609914	−	0.0427066i	−0.542683	−	0.839938i	$-0.682592\pi$
$463$	28.2390	−	19.7732i	0.0609914	−	0.0427066i	0.603675	+	0.797231i	$0.293703\pi$
$464$	217.905	+	598.688i	0.469622	+	1.29028i
$465$		0			0
$466$	−49.8564	−	282.750i	−0.106988	−	0.606760i
$467$	−96.1818	−	25.7718i	−0.205957	−	0.0551859i	0.154366	−	0.988014i	$-0.450667\pi$
$467$	−96.1818	−	25.7718i	−0.205957	−	0.0551859i	−0.360322	+	0.932828i	$0.617333\pi$
$468$		0			0
$469$	−378.142	−	218.320i	−0.806273	−	0.465502i
$470$	163.112	+	495.285i	0.347048	+	1.05380i
$471$		0			0
$472$	322.350	−	28.2020i	0.682945	−	0.0597500i
$473$	10.6953	+	122.248i	0.0226116	+	0.258452i
$474$		0			0
$475$	−630.611	−	418.080i	−1.32760	−	0.880168i
$476$	−225.625	+	390.794i	−0.474002	+	0.820995i
$477$		0			0
$478$	−116.847	+	436.080i	−0.244450	+	0.912301i
$479$	42.4814	−	7.49061i	0.0886876	−	0.0156380i	−0.129128	−	0.991628i	$-0.541218\pi$
$479$	42.4814	−	7.49061i	0.0886876	−	0.0156380i	0.217816	+	0.975990i	$0.430107\pi$
$480$		0			0
$481$	300.138	−	109.241i	0.623987	−	0.227113i
$482$	349.582	+	499.254i	0.725273	+	1.03580i
$483$		0			0
$484$	−123.823	−	147.566i	−0.255832	−	0.304889i
$485$	16.1089	−	135.663i	0.0332143	−	0.279718i
$486$		0			0
$487$	328.967	−	328.967i	0.675497	−	0.675497i	−0.283481	−	0.958978i	$-0.591489\pi$
$487$	328.967	−	328.967i	0.675497	−	0.675497i	0.958978	+	0.283481i	$0.0914893\pi$
$488$	190.834	+	16.6958i	0.391054	+	0.0342128i
$489$		0			0
$490$	62.7264	−	208.131i	0.128013	−	0.424758i
$491$	784.475	−	285.526i	1.59771	−	0.581519i	0.618752	−	0.785586i	$-0.287638\pi$
$491$	784.475	−	285.526i	1.59771	−	0.581519i	0.978957	+	0.204067i	$0.0654162\pi$
$492$		0			0
$493$	−529.081	+	755.606i	−1.07319	+	1.53267i
$494$	−561.874	+	324.398i	−1.13740	+	0.656677i
$495$		0			0
$496$	−260.031	+	450.387i	−0.524256	+	0.908038i
$497$	172.743	−	80.5513i	0.347571	−	0.162075i
$498$		0			0
$499$	−98.5930	+	117.499i	−0.197581	+	0.235468i	−0.855734	−	0.517417i	$-0.826894\pi$
$499$	−98.5930	+	117.499i	−0.197581	+	0.235468i	0.658152	+	0.752885i	$0.271338\pi$
$500$	−342.232	−	93.7211i	−0.684464	−	0.187442i
$501$		0			0
$502$	−148.406	+	69.2026i	−0.295628	+	0.137854i
$503$	−73.8842	+	19.7972i	−0.146887	+	0.0393583i	−0.331513	−	0.943451i	$-0.607559\pi$
$503$	−73.8842	+	19.7972i	−0.146887	+	0.0393583i	0.184626	+	0.982809i	$0.440893\pi$
$504$		0			0
$505$	299.278	+	119.531i	0.592630	+	0.236696i
$506$	112.820	+	639.834i	0.222965	+	1.26449i
$507$		0			0
$508$	6.63787	+	3.09529i	0.0130667	+	0.00609309i
$509$	−86.9868	−	15.3381i	−0.170898	−	0.0301338i	0.0875445	−	0.996161i	$-0.472098\pi$
$509$	−86.9868	−	15.3381i	−0.170898	−	0.0301338i	−0.258442	+	0.966027i	$0.583209\pi$
$510$		0			0
$511$	56.9841	−	47.8153i	0.111515	−	0.0935721i
$512$	357.035	−	357.035i	0.697335	−	0.697335i
$513$		0			0
$514$		−	205.110i		−	0.399047i
$515$	189.900	−	124.401i	0.368738	−	0.241555i
$516$		0			0
$517$	−314.356	−	448.946i	−0.608038	−	0.868368i
$518$	525.426	+	245.010i	1.01434	+	0.472993i
$519$		0			0
$520$	82.9248	−	92.8385i	0.159471	−	0.178536i
$521$	343.130	+	594.318i	0.658598	+	1.14073i	0.980979	+	0.194115i	$0.0621835\pi$
$521$	343.130	+	594.318i	0.658598	+	1.14073i	−0.322381	+	0.946610i	$0.604483\pi$
$522$		0			0
$523$	−169.317	+	45.3683i	−0.323741	+	0.0867462i	−0.417030	−	0.908893i	$-0.636929\pi$
$523$	−169.317	+	45.3683i	−0.323741	+	0.0867462i	0.0932883	+	0.995639i	$0.470262\pi$
$524$	−125.726	+	345.428i	−0.239934	+	0.659214i
$525$		0			0
$526$	147.601	+	123.852i	0.280611	+	0.235460i
$527$	−750.093	+	65.6246i	−1.42333	+	0.124525i
$528$		0			0
$529$	−69.1470	+	189.980i	−0.130713	+	0.359130i
$530$	78.4260	+	542.341i	0.147974	+	1.02328i
$531$		0			0
$532$	−472.168	−	126.517i	−0.887533	−	0.237814i
$533$	3.24313	−	4.63167i	0.00608467	−	0.00868981i
$534$		0			0
$535$	−74.3833	−	316.432i	−0.139034	−	0.591461i
$536$	−40.4699	+	229.516i	−0.0755036	+	0.428202i
$537$		0			0
$538$	348.214	+	30.4648i	0.647239	+	0.0566261i
$539$			228.471i			0.423880i
$540$		0			0
$541$	518.161			0.957784			0.478892	−	0.877874i	$-0.341039\pi$
$541$	518.161			0.957784			0.478892	+	0.877874i	$0.341039\pi$
$542$	−38.1719	+	436.307i	−0.0704278	+	0.804994i
$543$		0			0
$544$	1054.17	+	185.879i	1.93781	+	0.341689i
$545$	−31.4791	−	19.4963i	−0.0577598	−	0.0357731i
$546$		0			0
$547$	700.415	+	490.436i	1.28047	+	0.896592i	0.998033	−	0.0626950i	$-0.0199695\pi$
$547$	700.415	+	490.436i	1.28047	+	0.896592i	0.282433	+	0.959287i	$0.408858\pi$
$548$	156.146	−	582.746i	0.284939	−	1.06341i
$549$		0			0
$550$	898.165	−	22.8384i	1.63303	−	0.0415244i
$551$	−938.971	−	341.758i	−1.70412	−	0.620250i
$552$		0			0
$553$	−34.7694	−	397.417i	−0.0628742	−	0.718656i
$554$	898.498	−	1070.79i	1.62184	−	1.93283i
$555$		0			0
$556$	0.711847	+	0.259091i	0.00128030	+	0.000465991i
$557$	54.2859	+	202.598i	0.0974612	+	0.363730i	0.997381	−	0.0723250i	$-0.0230419\pi$
$557$	54.2859	+	202.598i	0.0974612	+	0.363730i	−0.899920	+	0.436055i	$0.856375\pi$
$558$		0			0
$559$	−63.3936	+	36.6003i	−0.113405	+	0.0654747i
$560$	548.109	−	30.9156i	0.978767	−	0.0552065i
$561$		0			0
$562$	551.155	−	1181.96i	0.980704	−	2.10313i
$563$	89.6853	−	62.7983i	0.159299	−	0.111542i	−0.491209	−	0.871042i	$-0.663445\pi$
$563$	89.6853	−	62.7983i	0.159299	−	0.111542i	0.650508	+	0.759499i	$0.274556\pi$
$564$		0			0
$565$	785.686	−	514.693i	1.39060	−	0.910961i
$566$	−87.9531			−0.155394
$567$		0			0
$568$	−71.9362	−	71.9362i	−0.126648	−	0.126648i
$569$	−115.386	−	137.512i	−0.202787	−	0.241672i	0.655060	−	0.755576i	$-0.272643\pi$
$569$	−115.386	−	137.512i	−0.202787	−	0.241672i	−0.857848	+	0.513904i	$0.828199\pi$
$570$		0			0
$571$	−99.5175	+	564.392i	−0.174286	+	0.988427i	0.764678	+	0.644412i	$0.222898\pi$
$571$	−99.5175	+	564.392i	−0.174286	+	0.988427i	−0.938964	+	0.344014i	$0.888213\pi$
$572$	135.152	−	289.835i	0.236280	−	0.506704i
$573$		0			0
$574$	10.1071	−	1.78215i	0.0176081	−	0.00310479i
$575$	−397.026	−	215.957i	−0.690480	−	0.375578i
$576$		0			0
$577$	88.5245	+	330.378i	0.153422	+	0.572579i	0.999235	+	0.0390997i	$0.0124490\pi$
$577$	88.5245	+	330.378i	0.153422	+	0.572579i	−0.845813	+	0.533479i	$0.820884\pi$
$578$	543.241	+	1164.98i	0.939863	+	2.01554i
$579$		0			0
$580$	−468.392	−	14.4883i	−0.807573	−	0.0249798i
$581$	−80.8537	−	67.8443i	−0.139163	−	0.116772i
$582$		0			0
$583$	−243.405	−	521.984i	−0.417505	−	0.895342i
$584$	−34.3849	−	19.8522i	−0.0588783	−	0.0339934i
$585$		0			0
$586$	−232.708	−	403.062i	−0.397112	−	0.687818i
$587$	−717.413	−	502.338i	−1.22217	−	0.855772i	−0.229111	−	0.973400i	$-0.573582\pi$
$587$	−717.413	−	502.338i	−1.22217	−	0.855772i	−0.993058	+	0.117628i	$0.962471\pi$
$588$		0			0
$589$	−278.971	−	766.465i	−0.473634	−	1.30130i
$590$	−402.004	+	1333.88i	−0.681363	+	2.26082i
$591$		0			0
$592$	65.5274	−	748.981i	0.110688	−	1.26517i
$593$	−26.3100	−	26.3100i	−0.0443676	−	0.0443676i	0.684575	−	0.728942i	$-0.259988\pi$
$593$	−26.3100	−	26.3100i	−0.0443676	−	0.0443676i	−0.728942	+	0.684575i	$0.759988\pi$
$594$		0			0
$595$	491.836	+	624.378i	0.826615	+	1.04937i
$596$	−339.965	+	285.265i	−0.570411	+	0.478632i
$597$		0			0
$598$	−317.468	+	222.293i	−0.530882	+	0.371728i
$599$	−373.022	−	1024.87i	−0.622741	−	1.71097i	−0.700176	−	0.713970i	$-0.746895\pi$
$599$	−373.022	−	1024.87i	−0.622741	−	1.71097i	0.0774351	−	0.996997i	$-0.475327\pi$
$600$		0			0
$601$	−195.015	−	1105.98i	−0.324484	−	1.84024i	−0.513277	−	0.858223i	$-0.671569\pi$
$601$	−195.015	−	1105.98i	−0.324484	−	1.84024i	0.188793	−	0.982017i	$-0.439543\pi$
$602$	−128.339	−	34.3884i	−0.213188	−	0.0571237i
$603$		0			0
$604$	−535.878	−	309.390i	−0.887216	−	0.512234i
$605$	−322.277	+	106.136i	−0.532690	+	0.175431i
$606$		0			0
$607$	−713.135	+	62.3913i	−1.17485	+	0.102786i	−0.657817	−	0.753178i	$-0.728520\pi$
$607$	−713.135	+	62.3913i	−1.17485	+	0.102786i	−0.517035	+	0.855964i	$0.672964\pi$
$608$	101.063	+	1155.15i	0.166222	+	1.89992i
$609$		0			0
$610$	−371.500	+	736.348i	−0.609016	+	1.20713i
$611$	163.463	−	283.126i	0.267533	−	0.463381i
$612$		0			0
$613$	−278.779	+	1040.42i	−0.454778	+	1.69725i	0.233963	+	0.972245i	$0.424830\pi$
$613$	−278.779	+	1040.42i	−0.454778	+	1.69725i	−0.688741	+	0.725007i	$0.741836\pi$
$614$	313.777	−	55.3273i	0.511037	−	0.0901097i
$615$		0			0
$616$	−223.154	+	81.2215i	−0.362263	+	0.131853i
$617$	−59.3078	−	84.7003i	−0.0961228	−	0.137278i	0.768210	−	0.640198i	$-0.221148\pi$
$617$	−59.3078	−	84.7003i	−0.0961228	−	0.137278i	−0.864333	+	0.502920i	$0.832259\pi$
$618$		0			0
$619$	377.183	+	449.509i	0.609342	+	0.726185i	0.979199	−	0.202903i	$-0.0650377\pi$
$619$	377.183	+	449.509i	0.609342	+	0.726185i	−0.369857	+	0.929089i	$0.620593\pi$
$620$	−236.704	−	300.492i	−0.381780	−	0.484664i
$621$		0			0
$622$	−1103.17	+	1103.17i	−1.77359	+	1.77359i
$623$	471.099	+	41.2158i	0.756178	+	0.0661570i
$624$		0			0
$625$	−376.890	+	498.577i	−0.603024	+	0.797723i
$626$	−612.171	+	222.812i	−0.977910	+	0.355930i
$627$		0			0
$628$	−192.536	+	274.970i	−0.306586	+	0.437851i
$629$	942.699	−	544.268i	1.49873	−	0.865290i
$630$		0			0
$631$	−47.0582	+	81.5072i	−0.0745771	+	0.129171i	−0.900902	−	0.434022i	$-0.857094\pi$
$631$	−47.0582	+	81.5072i	−0.0745771	+	0.129171i	0.826325	+	0.563193i	$0.190427\pi$
$632$	−192.981	+	89.9887i	−0.305350	+	0.142387i
$633$		0			0
$634$	934.523	−	1113.72i	1.47401	−	1.75666i
$635$	9.39974	−	8.83569i	0.0148027	−	0.0139145i
$636$		0			0
$637$	−123.517	+	57.5968i	−0.193904	+	0.0904188i
$638$	1146.13	−	307.104i	1.79644	−	0.481355i
$639$		0			0
$640$	−183.567	−	427.710i	−0.286823	−	0.668297i
$641$	−28.4464	−	161.328i	−0.0443782	−	0.251681i	0.954546	−	0.298065i	$-0.0963413\pi$
$641$	−28.4464	−	161.328i	−0.0443782	−	0.251681i	−0.998924	+	0.0463842i	$0.985230\pi$
$642$		0			0
$643$	190.018	+	88.6070i	0.295518	+	0.137803i	0.564723	−	0.825280i	$-0.308983\pi$
$643$	190.018	+	88.6070i	0.295518	+	0.137803i	−0.269205	+	0.963083i	$0.586761\pi$
$644$	−287.561	−	50.7048i	−0.446524	−	0.0787342i
$645$		0			0
$646$	−1693.83	+	1421.29i	−2.62203	+	2.20014i
$647$	575.686	−	575.686i	0.889778	−	0.889778i	−0.104723	−	0.994501i	$-0.533396\pi$
$647$	575.686	−	575.686i	0.889778	−	0.889778i	0.994501	+	0.104723i	$0.0333957\pi$
$648$		0			0
$649$		−	1464.24i		−	2.25614i
$650$	238.771	+	479.811i	0.367341	+	0.738171i
$651$		0			0
$652$	260.219	+	371.631i	0.399108	+	0.569986i
$653$	−329.524	−	153.660i	−0.504631	−	0.235313i	0.153595	−	0.988134i	$-0.450915\pi$
$653$	−329.524	−	153.660i	−0.504631	−	0.235313i	−0.658226	+	0.752820i	$0.728693\pi$
$654$		0			0
$655$	482.896	+	431.330i	0.737245	+	0.658519i
$656$	−6.65480	−	11.5264i	−0.0101445	−	0.0175708i
$657$		0			0
$658$	573.183	−	153.584i	0.871100	−	0.233410i
$659$	232.026	−	637.485i	0.352087	−	0.967352i	−0.629611	−	0.776911i	$-0.716786\pi$
$659$	232.026	−	637.485i	0.352087	−	0.967352i	0.981698	−	0.190442i	$-0.0609921\pi$
$660$		0			0
$661$	−125.268	−	105.112i	−0.189512	−	0.159020i	0.543095	−	0.839671i	$-0.317252\pi$
$661$	−125.268	−	105.112i	−0.189512	−	0.159020i	−0.732607	+	0.680652i	$0.761697\pi$
$662$	−1307.32	+	114.376i	−1.97480	+	0.172773i
$663$		0			0
$664$	−19.2679	+	52.9382i	−0.0290180	+	0.0797263i
$665$	−515.425	+	689.693i	−0.775075	+	1.03713i
$666$		0			0
$667$	−576.549	−	154.486i	−0.864392	−	0.231613i
$668$	260.807	−	372.470i	0.390429	−	0.557590i
$669$		0			0
$670$	−853.044	−	528.327i	−1.27320	−	0.788547i
$671$	150.526	−	853.673i	0.224330	−	1.27224i
$672$		0			0
$673$	1146.56	+	100.311i	1.70365	+	0.149050i	0.897016	−	0.441998i	$-0.145730\pi$
$673$	1146.56	+	100.311i	1.70365	+	0.149050i	0.806636	+	0.591049i	$0.201286\pi$
$674$			282.560i			0.419228i
$675$		0			0
$676$	−288.972			−0.427473
$677$	35.6905	−	407.945i	0.0527187	−	0.602577i	−0.923182	−	0.384363i	$-0.874421\pi$
$677$	35.6905	−	407.945i	0.0527187	−	0.602577i	0.975901	−	0.218214i	$-0.0700232\pi$
$678$		0			0
$679$	−153.105	−	26.9965i	−0.225486	−	0.0397593i
$680$	223.377	−	360.668i	0.328496	−	0.530394i
$681$		0			0
$682$	793.404	+	555.548i	1.16335	+	0.814586i
$683$	142.470	−	531.706i	0.208595	−	0.778485i	−0.779729	−	0.626117i	$-0.784643\pi$
$683$	142.470	−	531.706i	0.208595	−	0.778485i	0.988324	−	0.152369i	$-0.0486901\pi$
$684$		0			0
$685$	−851.214	−	636.134i	−1.24265	−	0.928663i
$686$	−917.584	−	333.973i	−1.33759	−	0.486841i
$687$		0			0
$688$	15.0177	+	171.653i	0.0218280	+	0.249496i
$689$	220.835	−	263.181i	0.320515	−	0.381975i
$690$		0			0
$691$	−65.4999	−	23.8400i	−0.0947901	−	0.0345008i	0.294190	−	0.955747i	$-0.404950\pi$
$691$	−65.4999	−	23.8400i	−0.0947901	−	0.0345008i	−0.388980	+	0.921246i	$0.627172\pi$
$692$	−44.4027	−	165.713i	−0.0641658	−	0.239470i
$693$		0			0
$694$	687.019	−	396.651i	0.989941	−	0.571543i
$695$	0.888869	−	0.995135i	0.00127895	−	0.00143185i
$696$		0			0
$697$	8.14383	−	17.4645i	0.0116841	−	0.0250567i
$698$	117.844	−	82.5151i	0.168831	−	0.118217i
$699$		0			0
$700$	−128.416	+	382.830i	−0.183451	+	0.546900i
$701$	−516.228			−0.736417			−0.368208	−	0.929743i	$-0.620029\pi$
$701$	−516.228			−0.736417			−0.368208	+	0.929743i	$0.620029\pi$
$702$		0			0
$703$	833.802	+	833.802i	1.18606	+	1.18606i
$704$	−203.251	−	242.225i	−0.288708	−	0.344069i
$705$		0			0
$706$	290.303	−	1646.39i	0.411195	−	2.33200i
$707$	154.988	−	332.372i	0.219219	−	0.470116i
$708$		0			0
$709$	−110.908	+	19.5560i	−0.156428	+	0.0275825i	−0.251314	−	0.967906i	$-0.580863\pi$
$709$	−110.908	+	19.5560i	−0.156428	+	0.0275825i	0.0948855	+	0.995488i	$0.469751\pi$
$710$	402.497	−	172.746i	0.566897	−	0.243304i
$711$		0			0
$712$	−65.3284	−	243.809i	−0.0917534	−	0.342428i
$713$	−205.912	−	441.579i	−0.288796	−	0.619326i
$714$		0			0
$715$	−385.800	−	410.429i	−0.539581	−	0.574027i
$716$	−593.000	−	497.586i	−0.828213	−	0.694953i
$717$		0			0
$718$	−111.574	−	239.271i	−0.155396	−	0.333247i
$719$	306.341	+	176.866i	0.426065	+	0.245989i	0.697669	−	0.716420i	$-0.254221\pi$
$719$	306.341	+	176.866i	0.426065	+	0.245989i	−0.271604	+	0.962409i	$0.587554\pi$
$720$		0			0
$721$	−129.172	−	223.732i	−0.179156	−	0.310308i
$722$	−1188.76	−	832.381i	−1.64649	−	1.15288i
$723$		0			0
$724$	182.228	+	500.666i	0.251696	+	0.691528i
$725$	−329.708	+	756.707i	−0.454769	+	1.04373i
$726$		0			0
$727$	22.1374	−	253.031i	0.0304503	−	0.348049i	−0.965652	−	0.259840i	$-0.916330\pi$
$727$	22.1374	−	253.031i	0.0304503	−	0.348049i	0.996102	−	0.0882088i	$-0.0281143\pi$
$728$	−100.167	−	100.167i	−0.137592	−	0.137592i
$729$		0			0
$730$	134.284	−	105.779i	0.183951	−	0.144902i
$731$	−191.107	+	160.358i	−0.261432	+	0.219368i
$732$		0			0
$733$	−424.701	+	297.379i	−0.579402	+	0.405701i	−0.826209	−	0.563363i	$-0.809507\pi$
$733$	−424.701	+	297.379i	−0.579402	+	0.405701i	0.246808	+	0.969064i	$0.420618\pi$
$734$	−175.273	−	481.557i	−0.238791	−	0.656073i
$735$		0			0
$736$	120.279	+	682.139i	0.163423	+	0.926819i
$737$	1018.67	+	272.952i	1.38218	+	0.370355i
$738$		0			0
$739$	593.622	+	342.728i	0.803277	+	0.463772i	0.844616	−	0.535373i	$-0.179829\pi$
$739$	593.622	+	342.728i	0.803277	+	0.463772i	−0.0413386	+	0.999145i	$0.513162\pi$
$740$	493.728	+	249.094i	0.667199	+	0.336613i
$741$		0			0
$742$	621.220	−	54.3498i	0.837224	−	0.0732476i
$743$	35.6070	+	406.990i	0.0479233	+	0.547766i	0.981767	+	0.190086i	$0.0608767\pi$
$743$	35.6070	+	406.990i	0.0479233	+	0.547766i	−0.933844	+	0.357680i	$0.883568\pi$
$744$		0			0
$745$	244.517	+	742.466i	0.328210	+	0.996599i
$746$	795.533	−	1377.90i	1.06640	−	1.84706i
$747$		0			0
$748$	282.084	−	1052.75i	0.377118	−	1.40742i
$749$	−364.289	+	64.2339i	−0.486367	+	0.0857596i
$750$		0			0
$751$	−881.970	+	321.011i	−1.17439	+	0.427445i	−0.854219	−	0.519914i	$-0.825964\pi$
$751$	−881.970	+	321.011i	−1.17439	+	0.427445i	−0.320176	+	0.947358i	$0.603742\pi$
$752$	−441.400	−	630.384i	−0.586968	−	0.838277i
$753$		0			0
$754$	454.963	+	542.204i	0.603399	+	0.719103i
$755$	−856.182	+	674.434i	−1.13402	+	0.893290i
$756$		0			0
$757$	−661.648	+	661.648i	−0.874040	+	0.874040i	−0.992910	−	0.118870i	$-0.962073\pi$
$757$	−661.648	+	661.648i	−0.874040	+	0.874040i	0.118870	+	0.992910i	$0.462073\pi$
$758$	−1850.49	−	161.897i	−2.44129	−	0.213585i
$759$		0			0
$760$	440.015	+	132.611i	0.578968	+	0.174489i
$761$	344.002	−	125.206i	0.452039	−	0.164529i	−0.105960	−	0.994370i	$-0.533792\pi$
$761$	344.002	−	125.206i	0.452039	−	0.164529i	0.557999	+	0.829842i	$0.311569\pi$
$762$		0			0
$763$	−24.1686	+	34.5163i	−0.0316758	+	0.0452377i
$764$	−325.931	+	188.176i	−0.426611	+	0.246304i
$765$		0			0
$766$	−344.637	+	596.928i	−0.449917	+	0.779280i
$767$	791.601	−	369.129i	1.03207	−	0.481264i
$768$		0			0
$769$	336.653	−	401.207i	0.437780	−	0.521726i	−0.501370	−	0.865233i	$-0.667171\pi$
$769$	336.653	−	401.207i	0.437780	−	0.521726i	0.939150	+	0.343507i	$0.111615\pi$
$770$	31.6105	−	1021.94i	0.0410525	−	1.32719i
$771$		0			0
$772$	242.845	−	113.241i	0.314566	−	0.146685i
$773$	101.742	−	27.2616i	0.131619	−	0.0352673i	−0.192408	−	0.981315i	$-0.561630\pi$
$773$	101.742	−	27.2616i	0.131619	−	0.0352673i	0.324027	+	0.946048i	$0.394963\pi$
$774$		0			0
$775$	−646.171	+	190.872i	−0.833770	+	0.246287i
$776$	14.4094	+	81.7198i	0.0185688	+	0.105309i
$777$		0			0
$778$	−895.725	−	417.683i	−1.15132	−	0.536868i
$779$	20.5574	+	3.62482i	0.0263894	+	0.00465317i
$780$		0			0
$781$	−352.650	+	295.909i	−0.451537	+	0.378884i
$782$	−933.958	+	933.958i	−1.19432	+	1.19432i
$783$		0			0
$784$			320.806i			0.409191i
$785$	323.996	+	494.584i	0.412733	+	0.630043i
$786$		0			0
$787$	465.668	+	665.042i	0.591700	+	0.845035i	0.997626	−	0.0688712i	$-0.0219398\pi$
$787$	465.668	+	665.042i	0.591700	+	0.845035i	−0.405926	+	0.913906i	$0.633051\pi$
$788$	−540.571	−	252.072i	−0.686004	−	0.319889i
$789$		0			0
$790$	−51.6266	−	915.298i	−0.0653501	−	1.15860i
$791$	−534.431	−	925.662i	−0.675640	−	1.17024i
$792$		0			0
$793$	499.462	−	133.831i	0.629839	−	0.168765i
$794$	297.780	−	818.144i	0.375038	−	1.03041i
$795$		0			0
$796$	−296.563	−	248.846i	−0.372567	−	0.312621i
$797$	−946.575	+	82.8146i	−1.18767	+	0.103908i	−0.663814	−	0.747897i	$-0.731063\pi$
$797$	−946.575	+	82.8146i	−1.18767	+	0.103908i	−0.523858	+	0.851805i	$0.675508\pi$
$798$		0			0
$799$	381.073	−	1046.99i	0.476937	−	1.31037i
$800$	957.550	−	24.3485i	1.19694	−	0.0304356i
$801$		0			0
$802$	−226.868	−	60.7892i	−0.282878	−	0.0757970i
$803$	−103.052	+	147.174i	−0.128334	+	0.183280i
$804$		0			0
$805$	−270.809	+	437.252i	−0.336408	+	0.543170i
$806$	−100.327	+	568.984i	−0.124476	+	0.705936i
$807$		0			0
$808$	−194.999	−	17.0602i	−0.241335	−	0.0211141i
$809$			985.730i			1.21845i	0.792996	+	0.609227i	$0.208520\pi$
$809$			985.730i			1.21845i	−0.792996	+	0.609227i	$0.791480\pi$
$810$		0			0
$811$	−590.003			−0.727501			−0.363750	−	0.931496i	$-0.618504\pi$
$811$	−590.003			−0.727501			−0.363750	+	0.931496i	$0.618504\pi$
$812$	−46.4781	+	531.247i	−0.0572391	+	0.654246i
$813$		0			0
$814$	−1378.96	−	243.149i	−1.69406	−	0.298708i
$815$	777.900	−	182.860i	0.954479	−	0.224368i
$816$		0			0
$817$	−221.372	−	155.006i	−0.270957	−	0.189726i
$818$	−45.5846	+	170.124i	−0.0557269	+	0.207976i
$819$		0			0
$820$	9.68887	−	1.40107i	0.0118157	−	0.00170863i
$821$	−679.549	−	247.336i	−0.827709	−	0.301261i	−0.106791	−	0.994282i	$-0.534058\pi$
$821$	−679.549	−	247.336i	−0.827709	−	0.301261i	−0.720918	+	0.693020i	$0.756280\pi$
$822$		0			0
$823$	−112.760	−	1288.85i	−0.137011	−	1.56604i	−0.684364	−	0.729141i	$-0.739920\pi$
$823$	−112.760	−	1288.85i	−0.137011	−	1.56604i	0.547353	−	0.836902i	$-0.315636\pi$
$824$	−88.6345	+	105.630i	−0.107566	+	0.128192i
$825$		0			0
$826$	1489.76	+	542.230i	1.80359	+	0.656452i
$827$	412.833	+	1540.72i	0.499194	+	1.86302i	0.505145	+	0.863035i	$0.331439\pi$
$827$	412.833	+	1540.72i	0.499194	+	1.86302i	−0.00595087	+	0.999982i	$0.501894\pi$
$828$		0			0
$829$	891.879	−	514.927i	1.07585	−	0.621142i	0.146076	−	0.989273i	$-0.453336\pi$
$829$	891.879	−	514.927i	1.07585	−	0.621142i	0.929774	+	0.368132i	$0.120002\pi$
$830$	−180.893	−	161.576i	−0.217943	−	0.194670i
$831$		0			0
$832$	79.7134	−	170.946i	0.0958094	−	0.205464i
$833$	−380.472	+	266.409i	−0.456749	+	0.319819i
$834$		0			0
$835$	−438.879	−	669.955i	−0.525604	−	0.802342i
$836$	1180.64			1.41225
$837$		0			0
$838$	901.315	+	901.315i	1.07556	+	1.07556i
$839$	−259.990	−	309.844i	−0.309881	−	0.369302i	0.588516	−	0.808485i	$-0.299712\pi$
$839$	−259.990	−	309.844i	−0.309881	−	0.369302i	−0.898397	+	0.439184i	$0.855268\pi$
$840$		0			0
$841$	−43.2559	+	245.316i	−0.0514338	+	0.291696i
$842$	736.306	−	1579.01i	0.874473	−	1.87531i
$843$		0			0
$844$	−665.333	+	117.316i	−0.788310	+	0.139000i
$845$	−188.790	+	472.685i	−0.223420	+	0.559391i
$846$		0			0
$847$	99.9357	+	372.965i	0.117988	+	0.440337i
$848$	−341.775	−	732.939i	−0.403037	−	0.864315i
$849$		0			0
$850$	1085.34	+	1469.08i	1.27687	+	1.72833i
$851$	539.583	+	452.764i	0.634058	+	0.532038i
$852$		0			0
$853$	87.7886	+	188.263i	0.102918	+	0.220707i	0.951023	−	0.309120i	$-0.100034\pi$
$853$	87.7886	+	188.263i	0.102918	+	0.220707i	−0.848106	+	0.529827i	$0.822257\pi$
$854$	812.813	+	469.278i	0.951772	+	0.549506i
$855$		0			0
$856$	98.7194	+	170.987i	0.115326	+	0.199751i
$857$	437.567	+	306.388i	0.510580	+	0.357512i	0.800300	−	0.599599i	$-0.204673\pi$
$857$	437.567	+	306.388i	0.510580	+	0.357512i	−0.289720	+	0.957111i	$0.593562\pi$
$858$		0			0
$859$	−91.0704	−	250.214i	−0.106019	−	0.291285i	0.875328	−	0.483530i	$-0.160645\pi$
$859$	−91.0704	−	250.214i	−0.106019	−	0.291285i	−0.981347	+	0.192245i	$0.938423\pi$
$860$	−121.348	−	36.5716i	−0.141102	−	0.0425251i
$861$		0			0
$862$	105.578	−	1206.77i	0.122481	−	1.39996i
$863$	414.792	+	414.792i	0.480639	+	0.480639i	0.905336	−	0.424697i	$-0.139619\pi$
$863$	414.792	+	414.792i	0.480639	+	0.480639i	−0.424697	+	0.905336i	$0.639619\pi$
$864$		0			0
$865$	−300.074	−	35.6314i	−0.346907	−	0.0411924i
$866$	386.478	−	324.294i	0.446279	−	0.374473i
$867$		0			0
$868$	−356.580	+	249.680i	−0.410807	+	0.287650i
$869$	329.548	+	905.427i	0.379227	+	1.04192i
$870$		0			0
$871$	109.239	+	619.527i	0.125418	+	0.711282i
$872$	21.7241	+	5.82096i	0.0249130	+	0.00667541i
$873$		0			0
$874$	−1239.11	−	715.399i	−1.41774	−	0.818534i
$875$	542.318	+	460.165i	0.619792	+	0.525903i
$876$		0			0
$877$	−75.5182	+	6.60699i	−0.0861097	+	0.00753362i	−0.130129	−	0.991497i	$-0.541539\pi$
$877$	−75.5182	+	6.60699i	−0.0861097	+	0.00753362i	0.0440195	+	0.999031i	$0.485984\pi$
$878$	179.195	+	2048.20i	0.204094	+	2.33281i
$879$		0			0
$880$	−1259.40	+	414.758i	−1.43113	+	0.471316i
$881$	−476.501	+	825.323i	−0.540863	+	0.936803i	0.457991	+	0.888957i	$0.348569\pi$
$881$	−476.501	+	825.323i	−0.540863	+	0.936803i	−0.998855	+	0.0478462i	$0.984764\pi$
$882$		0			0
$883$	−176.672	+	659.350i	−0.200082	+	0.746716i	0.790811	+	0.612061i	$0.209659\pi$
$883$	−176.672	+	659.350i	−0.200082	+	0.746716i	−0.990893	+	0.134655i	$0.957007\pi$
$884$	640.255	−	112.894i	0.724270	−	0.127708i
$885$		0			0
$886$	−464.611	+	169.105i	−0.524392	+	0.190863i
$887$	558.367	+	797.431i	0.629501	+	0.899021i	0.999550	−	0.0299916i	$-0.00954805\pi$
$887$	558.367	+	797.431i	0.629501	+	0.899021i	−0.370049	+	0.929012i	$0.620659\pi$
$888$		0			0
$889$	−9.43651	−	11.2460i	−0.0106147	−	0.0126502i
$890$	1079.14	+	128.139i	1.21252	+	0.143977i
$891$		0			0
$892$	−23.5150	+	23.5150i	−0.0263621	+	0.0263621i
$893$	1202.37	+	105.193i	1.34643	+	0.117798i
$894$		0			0
$895$	−1201.34	+	644.919i	−1.34228	+	0.720580i
$896$	−497.718	+	181.154i	−0.555489	+	0.202181i
$897$		0			0
$898$	−1190.86	+	1700.73i	−1.32613	+	1.89391i
$899$	−770.615	+	444.915i	−0.857191	+	0.494900i
$900$		0			0
$901$	585.434	−	1014.00i	0.649761	−	1.12542i
$902$	−22.4655	+	10.4758i	−0.0249063	+	0.0116140i
$903$		0			0
$904$	−366.714	+	437.032i	−0.405657	+	0.483443i
$905$	938.017	+	29.0146i	1.03648	+	0.0320604i
$906$		0			0
$907$	−1100.10	+	512.987i	−1.21290	+	0.565586i	−0.920513	−	0.390712i	$-0.872229\pi$
$907$	−1100.10	+	512.987i	−1.21290	+	0.565586i	−0.292391	+	0.956299i	$0.594451\pi$
$908$	658.779	−	176.519i	0.725527	−	0.194404i
$909$		0			0
$910$	560.452	−	240.538i	0.615881	−	0.264327i
$911$	−97.3307	−	551.990i	−0.106839	−	0.605916i	−0.990470	−	0.137731i	$-0.956019\pi$
$911$	−97.3307	−	551.990i	−0.106839	−	0.605916i	0.883630	−	0.468185i	$-0.155092\pi$
$912$		0			0
$913$	231.040	+	107.736i	0.253056	+	0.118002i
$914$	56.1290	+	9.89707i	0.0614103	+	0.0108283i
$915$		0			0
$916$	304.082	−	255.155i	0.331967	−	0.278554i
$917$	521.013	−	521.013i	0.568171	−	0.568171i
$918$		0			0
$919$			647.257i			0.704306i	0.935943	+	0.352153i	$0.114550\pi$
$919$			647.257i			0.704306i	−0.935943	+	0.352153i	$0.885450\pi$
$920$	268.746	+	56.0054i	0.292115	+	0.0608754i
$921$		0			0
$922$	−145.786	−	208.204i	−0.158119	−	0.225818i
$923$	−248.877	−	116.053i	−0.269639	−	0.125735i
$924$		0			0
$925$	730.015	−	644.878i	0.789206	−	0.697165i
$926$	−45.0755	−	78.0730i	−0.0486776	−	0.0843121i
$927$		0			0
$928$	1221.91	−	327.410i	1.31671	−	0.352812i
$929$	−489.817	+	1345.76i	−0.527251	+	1.44861i	0.335042	+	0.942203i	$0.391249\pi$
$929$	−489.817	+	1345.76i	−0.527251	+	1.44861i	−0.862294	+	0.506408i	$0.830973\pi$
$930$		0			0
$931$	−385.432	−	323.416i	−0.413998	−	0.347385i
$932$	−310.473	+	27.1629i	−0.333126	+	0.0291447i
$933$		0			0
$934$	−89.0608	+	244.692i	−0.0953541	+	0.261983i
$935$	−1537.75	−	1149.20i	−1.64465	−	1.22909i
$936$		0			0
$937$	1488.49	+	398.840i	1.58857	+	0.425656i	0.941566	−	0.336829i	$-0.109355\pi$
$937$	1488.49	+	398.840i	1.58857	+	0.425656i	0.647005	+	0.762486i	$0.276021\pi$
$938$	−654.939	+	935.350i	−0.698230	+	0.997175i
$939$		0			0
$940$	551.016	−	129.527i	0.586187	−	0.137794i
$941$	60.4078	−	342.590i	0.0641954	−	0.364070i	−0.935740	−	0.352691i	$-0.885267\pi$
$941$	60.4078	−	342.590i	0.0641954	−	0.364070i	0.999935	−	0.0113791i	$-0.00362216\pi$
$942$		0			0
$943$	12.4219	+	1.08677i	0.0131727	+	0.00115246i
$944$		−	2056.00i		−	2.17796i
$945$		0			0
$946$	320.909			0.339227
$947$	−65.7115	+	751.086i	−0.0693891	+	0.793121i	0.879167	+	0.476513i	$0.158100\pi$
$947$	−65.7115	+	751.086i	−0.0693891	+	0.793121i	−0.948556	+	0.316608i	$0.897456\pi$
$948$		0			0
$949$	−105.545	−	18.6103i	−0.111217	−	0.0196105i
$950$	−1232.88	+	1547.54i	−1.29777	+	1.62899i
$951$		0			0
$952$	−395.467	−	276.909i	−0.415407	−	0.290871i
$953$	−91.6247	+	341.948i	−0.0961435	+	0.358812i	−0.997190	−	0.0749094i	$-0.976133\pi$
$953$	−91.6247	+	341.948i	−0.0961435	+	0.358812i	0.901047	+	0.433722i	$0.142800\pi$
$954$		0			0
$955$	94.8733	+	656.080i	0.0993438	+	0.686994i
$956$	460.507	+	167.611i	0.481702	+	0.175325i
$957$		0			0
$958$	−9.83170	−	112.377i	−0.0102627	−	0.117304i
$959$	−777.310	+	926.362i	−0.810542	+	0.965967i
$960$		0			0
$961$	220.497	+	80.2545i	0.229446	+	0.0835114i
$962$	−216.181	−	806.797i	−0.224720	−	0.838666i
$963$		0			0
$964$	572.949	−	330.793i	0.594346	−	0.343146i
$965$	−26.5785	−	471.216i	−0.0275425	−	0.488306i
$966$		0			0
$967$	160.494	−	344.180i	0.165971	−	0.355925i	−0.805678	−	0.592353i	$-0.798199\pi$
$967$	160.494	−	344.180i	0.165971	−	0.355925i	0.971649	+	0.236428i	$0.0759768\pi$
$968$	168.821	−	118.210i	0.174402	−	0.122118i
$969$		0			0
$970$	−349.749	−	72.8862i	−0.360566	−	0.0751404i
$971$	15.4343			0.0158953			0.00794765	−	0.999968i	$-0.497470\pi$
$971$	15.4343			0.0158953			0.00794765	+	0.999968i	$0.497470\pi$
$972$		0			0
$973$	−1.07368	−	1.07368i	−0.00110348	−	0.00110348i
$974$	−782.025	−	931.981i	−0.802900	−	0.956859i
$975$		0			0
$976$	211.359	−	1198.68i	0.216557	−	1.22815i
$977$	−626.075	+	1342.62i	−0.640813	+	1.37423i	0.270582	+	0.962697i	$0.412784\pi$
$977$	−626.075	+	1342.62i	−0.640813	+	1.37423i	−0.911395	+	0.411532i	$0.864994\pi$
$978$		0			0
$979$	−1124.83	+	198.337i	−1.14895	+	0.202592i
$980$	−219.132	−	87.5210i	−0.223604	−	0.0893071i
$981$		0			0
$982$	−565.035	−	2108.74i	−0.575392	−	2.14739i
$983$	−349.672	−	749.873i	−0.355719	−	0.762841i	0.644279	−	0.764790i	$-0.277157\pi$
$983$	−349.672	−	749.873i	−0.355719	−	0.762841i	−0.999998	+	0.00194892i	$0.999380\pi$
$984$		0			0
$985$	−765.491	+	719.556i	−0.777148	+	0.730514i
$986$	1847.87	+	1550.54i	1.87410	+	1.57256i
$987$		0			0
$988$	297.636	+	638.282i	0.301251	+	0.646035i
$989$	−139.803	−	80.7151i	−0.141358	−	0.0816129i
$990$		0			0
$991$	423.252	+	733.093i	0.427095	+	0.739751i	0.996614	−	0.0822277i	$-0.0262035\pi$
$991$	423.252	+	733.093i	0.427095	+	0.739751i	−0.569518	+	0.821979i	$0.692870\pi$
$992$	845.863	+	592.279i	0.852684	+	0.597056i
$993$		0			0
$994$	−170.475	−	468.377i	−0.171504	−	0.471204i
$995$	−600.799	+	322.528i	−0.603818	+	0.324149i
$996$		0			0
$997$	−34.8884	+	398.777i	−0.0349934	+	0.399977i	0.958417	+	0.285370i	$0.0921164\pi$
$997$	−34.8884	+	398.777i	−0.0349934	+	0.399977i	−0.993411	+	0.114607i	$0.963439\pi$
$998$	283.628	+	283.628i	0.284197	+	0.284197i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.s.a.118.28		408
3.2	odd	2		135.3.r.a.103.7	yes	408
5.2	odd	4	inner	405.3.s.a.37.28		408
15.2	even	4		135.3.r.a.22.7	✓	408
27.11	odd	18		135.3.r.a.43.7	yes	408
27.16	even	9	inner	405.3.s.a.208.28		408
135.92	even	36		135.3.r.a.97.7	yes	408
135.97	odd	36	inner	405.3.s.a.127.28		408

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.r.a.22.7	✓	408	15.2	even	4
135.3.r.a.43.7	yes	408	27.11	odd	18
135.3.r.a.97.7	yes	408	135.92	even	36
135.3.r.a.103.7	yes	408	3.2	odd	2
405.3.s.a.37.28		408	5.2	odd	4	inner
405.3.s.a.118.28		408	1.1	even	1	trivial
405.3.s.a.127.28		408	135.97	odd	36	inner
405.3.s.a.208.28		408	27.16	even	9	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)

\(f(q)\)	\(=\)	\(q+(0.227920 - 2.60513i) q^{2} +(-2.79554 - 0.492929i) q^{4} +(-2.63268 + 4.25076i) q^{5} +(4.66090 + 3.26360i) q^{7} +(0.786031 - 2.93351i) q^{8} +(10.4738 + 7.82731i) q^{10} +(-12.9139 - 4.70027i) q^{11} +(-0.714473 - 8.16646i) q^{13} +(9.56441 - 11.3984i) q^{14} +(-18.1329 - 6.59984i) q^{16} +(-7.23092 - 26.9862i) q^{17} +(26.2098 - 15.1322i) q^{19} +(9.45509 - 10.5855i) q^{20} +(-15.1882 + 32.5711i) q^{22} +(14.8089 - 10.3693i) q^{23} +(-11.1380 - 22.3818i) q^{25} -21.4376 q^{26} +(-11.4210 - 11.4210i) q^{28} +(-21.2227 - 25.2922i) q^{29} +(4.67998 - 26.5415i) q^{31} +(-16.1924 + 34.7246i) q^{32} +(-71.9506 + 12.6868i) q^{34} +(-26.1434 + 11.2204i) q^{35} +(10.0842 + 37.6347i) q^{37} +(-33.4478 - 71.7290i) q^{38} +(10.4003 + 11.0642i) q^{40} +(0.528369 + 0.443354i) q^{41} +(-3.77375 - 8.09284i) q^{43} +(33.7844 + 19.5054i) q^{44} +(-23.6382 - 40.9426i) q^{46} +(32.6681 + 22.8744i) q^{47} +(-5.68607 - 15.6223i) q^{49} +(-60.8461 + 23.9147i) q^{50} +(-2.02815 + 23.1819i) q^{52} +(29.6344 + 29.6344i) q^{53} +(53.9778 - 42.5196i) q^{55} +(13.2374 - 11.1075i) q^{56} +(-70.7267 + 49.5234i) q^{58} +(36.4412 + 100.121i) q^{59} +(10.9532 + 62.1185i) q^{61} +(-68.0774 - 18.2413i) q^{62} +(19.9262 + 11.5044i) q^{64} +(36.5947 + 18.4626i) q^{65} +(-76.4475 + 6.68829i) q^{67} +(6.91206 + 79.0052i) q^{68} +(23.2720 + 70.6645i) q^{70} +(16.7490 - 29.0101i) q^{71} +(3.38369 - 12.6281i) q^{73} +(100.342 - 17.6930i) q^{74} +(-80.7297 + 29.3832i) q^{76} +(-44.8505 - 64.0532i) q^{77} +(-45.0676 - 53.7094i) q^{79} +(75.7925 - 59.7035i) q^{80} +(1.27542 - 1.27542i) q^{82} +(-18.4793 - 1.61673i) q^{83} +(133.749 + 40.3090i) q^{85} +(-21.9430 + 7.98661i) q^{86} +(-23.9390 + 34.1884i) q^{88} +(71.9769 - 41.5559i) q^{89} +(23.3220 - 40.3948i) q^{91} +(-46.5103 + 21.6881i) q^{92} +(67.0366 - 79.8911i) q^{94} +(-4.67845 + 151.250i) q^{95} +(-24.7633 + 11.5473i) q^{97} +(-41.9942 + 11.2523i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8} - 6 q^{10} + 60 q^{11} - 12 q^{13} - 24 q^{16} + 6 q^{17} + 300 q^{20} - 12 q^{22} + 156 q^{23} + 6 q^{25} + 48 q^{26} - 24 q^{28} - 24 q^{31} - 72 q^{32}+ \cdots + 1032 q^{98}+O(q^{100}) \) 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

Introduction

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