LMFDB - Embedded newform 405.3.l.h.217.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(28,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 9])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.28"); S:= CuspForms(chi, 3); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [8,4,0,0,4,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			217.1
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	405.217
Dual form			405.3.l.h.28.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.307007 + 0.0822623i) q^{2} +(-3.37662 + 1.94949i) q^{4} +(3.87453 + 3.16038i) q^{5} +(-4.71209 + 1.26260i) q^{7} +(1.77526 - 1.77526i) q^{8} +(-1.44949 - 0.651531i) q^{10} +(-5.67423 + 9.82806i) q^{11} +(7.58214 + 2.03163i) q^{13} +(1.34278 - 0.775255i) q^{14} +(7.39898 - 12.8154i) q^{16} +(-17.3485 - 17.3485i) q^{17} +8.69694i q^{19} +(-19.2439 - 3.11802i) q^{20} +(0.933552 - 3.48406i) q^{22} +(-15.7783 - 4.22778i) q^{23} +(5.02402 + 24.4900i) q^{25} -2.49490 q^{26} +(13.4495 - 13.4495i) q^{28} +(-30.4377 - 17.5732i) q^{29} +(-5.34847 - 9.26382i) q^{31} +(-3.81647 + 14.2433i) q^{32} +(6.75323 + 3.89898i) q^{34} +(-22.2474 - 10.0000i) q^{35} +(-6.04541 - 6.04541i) q^{37} +(-0.715430 - 2.67002i) q^{38} +(12.4888 - 1.26781i) q^{40} +(-0.348469 - 0.603566i) q^{41} +(-9.69781 - 36.1927i) q^{43} -44.2474i q^{44} +5.19184 q^{46} +(-60.4431 + 16.1957i) q^{47} +(-21.8256 + 12.6010i) q^{49} +(-3.55701 - 7.10531i) q^{50} +(-29.5626 + 7.92127i) q^{52} +(-0.696938 + 0.696938i) q^{53} +(-53.0454 + 20.1464i) q^{55} +(-6.12372 + 10.6066i) q^{56} +(10.7902 + 2.89123i) q^{58} +(-34.5840 + 19.9671i) q^{59} +(-2.95459 + 5.11750i) q^{61} +(2.40408 + 2.40408i) q^{62} +54.5051i q^{64} +(22.9565 + 31.8340i) q^{65} +(-16.5081 + 61.6091i) q^{67} +(92.3998 + 24.7584i) q^{68} +(7.65275 + 1.23995i) q^{70} -68.0000 q^{71} +(77.7878 - 77.7878i) q^{73} +(2.35329 + 1.35867i) q^{74} +(-16.9546 - 29.3662i) q^{76} +(14.3286 - 53.4750i) q^{77} +(21.2132 + 12.2474i) q^{79} +(69.1691 - 26.2702i) q^{80} +(0.156633 + 0.156633i) q^{82} +(4.81193 + 17.9584i) q^{83} +(-12.3895 - 122.045i) q^{85} +(5.95459 + 10.3137i) q^{86} +(7.37410 + 27.5205i) q^{88} +82.1816i q^{89} -38.2929 q^{91} +(61.5192 - 16.4840i) q^{92} +(17.2242 - 9.94439i) q^{94} +(-27.4856 + 33.6966i) q^{95} +(33.5986 - 9.00273i) q^{97} +(5.66403 - 5.66403i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 4 q^{5} - 4 q^{7} + 24 q^{8} + 8 q^{10} - 16 q^{11} + 32 q^{13} + 20 q^{16} - 80 q^{17} + 36 q^{20} - 20 q^{22} - 56 q^{23} - 16 q^{25} + 176 q^{26} + 88 q^{28} + 16 q^{31} + 76 q^{32} - 80 q^{35}+ \cdots - 376 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 + 24 * q^8 + 8 * q^10 - 16 * q^11 + 32 * q^13 + 20 * q^16 - 80 * q^17 + 36 * q^20 - 20 * q^22 - 56 * q^23 - 16 * q^25 + 176 * q^26 + 88 * q^28 + 16 * q^31 + 76 * q^32 - 80 * q^35 + 128 * q^37 + 96 * q^38 - 48 * q^40 + 56 * q^41 + 8 * q^43 - 272 * q^46 - 128 * q^47 - 164 * q^50 + 80 * q^52 + 112 * q^53 - 248 * q^55 + 12 * q^58 - 200 * q^61 + 176 * q^62 + 112 * q^65 + 200 * q^67 + 104 * q^68 + 60 * q^70 - 544 * q^71 + 152 * q^73 - 312 * q^76 - 88 * q^77 + 328 * q^80 + 256 * q^82 + 16 * q^83 - 232 * q^85 + 224 * q^86 - 12 * q^88 - 32 * q^91 - 104 * q^92 - 144 * q^95 + 20 * q^97 - 376 * q^98

Character values

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

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.307007	+	0.0822623i	−0.153504	+	0.0411312i	−0.334752	−	0.942306i	$-0.608653\pi$
$2$	−0.307007	+	0.0822623i	−0.153504	+	0.0411312i	0.181249	+	0.983437i	$0.441986\pi$
$3$		0			0
$3$		0			0
$4$	−3.37662	+	1.94949i	−0.844154	+	0.487372i
$5$	3.87453	+	3.16038i	0.774907	+	0.632076i
$5$	3.87453	+	3.16038i	0.774907	+	0.632076i
$6$		0			0
$7$	−4.71209	+	1.26260i	−0.673156	+	0.180372i	−0.579176	−	0.815203i	$-0.696626\pi$
$7$	−4.71209	+	1.26260i	−0.673156	+	0.180372i	−0.0939798	+	0.995574i	$0.529959\pi$
$8$	1.77526	−	1.77526i	0.221907	−	0.221907i
$9$		0			0
$10$	−1.44949	−	0.651531i	−0.144949	−	0.0651531i
$11$	−5.67423	+	9.82806i	−0.515840	+	0.893460i	0.483991	+	0.875073i	$0.339187\pi$
$11$	−5.67423	+	9.82806i	−0.515840	+	0.893460i	−0.999831	+	0.0183875i	$0.994147\pi$
$12$		0			0
$13$	7.58214	+	2.03163i	0.583241	+	0.156279i	0.538362	−	0.842713i	$-0.319043\pi$
$13$	7.58214	+	2.03163i	0.583241	+	0.156279i	0.0448789	+	0.998992i	$0.485710\pi$
$14$	1.34278	−	0.775255i	0.0959129	−	0.0553754i
$15$		0			0
$16$	7.39898	−	12.8154i	0.462436	−	0.800963i
$17$	−17.3485	−	17.3485i	−1.02050	−	1.02050i	−0.999785	−	0.0207127i	$-0.993406\pi$
$17$	−17.3485	−	17.3485i	−1.02050	−	1.02050i	−0.0207127	−	0.999785i	$-0.506594\pi$
$18$		0			0
$19$			8.69694i			0.457734i	0.973458	+	0.228867i	$0.0735020\pi$
$19$			8.69694i			0.457734i	−0.973458	+	0.228867i	$0.926498\pi$
$20$	−19.2439	−	3.11802i	−0.962197	−	0.155901i
$21$		0			0
$22$	0.933552	−	3.48406i	0.0424342	−	0.158366i
$23$	−15.7783	−	4.22778i	−0.686013	−	0.183817i	−0.101056	−	0.994881i	$-0.532222\pi$
$23$	−15.7783	−	4.22778i	−0.686013	−	0.183817i	−0.584957	+	0.811064i	$0.698889\pi$
$24$		0			0
$25$	5.02402	+	24.4900i	0.200961	+	0.979599i
$26$	−2.49490			−0.0959576
$27$		0			0
$28$	13.4495	−	13.4495i	0.480339	−	0.480339i
$29$	−30.4377	−	17.5732i	−1.04958	−	0.605973i	−0.127045	−	0.991897i	$-0.540549\pi$
$29$	−30.4377	−	17.5732i	−1.04958	−	0.605973i	−0.922531	+	0.385924i	$0.873883\pi$
$30$		0			0
$31$	−5.34847	−	9.26382i	−0.172531	−	0.298833i	0.766773	−	0.641918i	$-0.221861\pi$
$31$	−5.34847	−	9.26382i	−0.172531	−	0.298833i	−0.939304	+	0.343086i	$0.888528\pi$
$32$	−3.81647	+	14.2433i	−0.119265	+	0.445102i
$33$		0			0
$34$	6.75323	+	3.89898i	0.198624	+	0.114676i
$35$	−22.2474	−	10.0000i	−0.635641	−	0.285714i
$36$		0			0
$37$	−6.04541	−	6.04541i	−0.163389	−	0.163389i	0.620677	−	0.784066i	$-0.286858\pi$
$37$	−6.04541	−	6.04541i	−0.163389	−	0.163389i	−0.784066	+	0.620677i	$0.786858\pi$
$38$	−0.715430	−	2.67002i	−0.0188271	−	0.0702638i
$39$		0			0
$40$	12.4888	−	1.26781i	0.312219	−	0.0316952i
$41$	−0.348469	−	0.603566i	−0.00849925	−	0.0147211i	0.861744	−	0.507343i	$-0.169372\pi$
$41$	−0.348469	−	0.603566i	−0.00849925	−	0.0147211i	−0.870244	+	0.492621i	$0.836039\pi$
$42$		0			0
$43$	−9.69781	−	36.1927i	−0.225530	−	0.841691i	−0.982191	−	0.187883i	$-0.939837\pi$
$43$	−9.69781	−	36.1927i	−0.225530	−	0.841691i	0.756661	−	0.653807i	$-0.226829\pi$
$44$		−	44.2474i		−	1.00562i
$45$		0			0
$46$	5.19184			0.112866
$47$	−60.4431	+	16.1957i	−1.28602	+	0.344589i	−0.836149	−	0.548502i	$-0.815198\pi$
$47$	−60.4431	+	16.1957i	−1.28602	+	0.344589i	−0.449875	+	0.893091i	$0.648532\pi$
$48$		0			0
$49$	−21.8256	+	12.6010i	−0.445421	+	0.257164i
$50$	−3.55701	−	7.10531i	−0.0711403	−	0.142106i
$51$		0			0
$52$	−29.5626	+	7.92127i	−0.568512	+	0.152332i
$53$	−0.696938	+	0.696938i	−0.0131498	+	0.0131498i	−0.713651	−	0.700501i	$-0.752960\pi$
$53$	−0.696938	+	0.696938i	−0.0131498	+	0.0131498i	0.700501	+	0.713651i	$0.252960\pi$
$54$		0			0
$55$	−53.0454	+	20.1464i	−0.964462	+	0.366299i
$56$	−6.12372	+	10.6066i	−0.109352	+	0.189404i
$57$		0			0
$58$	10.7902	+	2.89123i	0.186038	+	0.0498487i
$59$	−34.5840	+	19.9671i	−0.586170	+	0.338425i	−0.763582	−	0.645711i	$-0.776561\pi$
$59$	−34.5840	+	19.9671i	−0.586170	+	0.338425i	0.177412	+	0.984137i	$0.443228\pi$
$60$		0			0
$61$	−2.95459	+	5.11750i	−0.0484359	+	0.0838935i	−0.889227	−	0.457466i	$-0.848757\pi$
$61$	−2.95459	+	5.11750i	−0.0484359	+	0.0838935i	0.840791	+	0.541360i	$0.182090\pi$
$62$	2.40408	+	2.40408i	0.0387755	+	0.0387755i
$63$		0			0
$64$			54.5051i			0.851642i
$65$	22.9565	+	31.8340i	0.353177	+	0.489754i
$66$		0			0
$67$	−16.5081	+	61.6091i	−0.246390	+	0.919539i	0.726290	+	0.687388i	$0.241243\pi$
$67$	−16.5081	+	61.6091i	−0.246390	+	0.919539i	−0.972680	+	0.232151i	$0.925424\pi$
$68$	92.3998	+	24.7584i	1.35882	+	0.364095i
$69$		0			0
$70$	7.65275	+	1.23995i	0.109325	+	0.0177135i
$71$	−68.0000			−0.957746			−0.478873	−	0.877884i	$-0.658955\pi$
$71$	−68.0000			−0.957746			−0.478873	+	0.877884i	$0.658955\pi$
$72$		0			0
$73$	77.7878	−	77.7878i	1.06559	−	1.06559i	0.0678931	−	0.997693i	$-0.478372\pi$
$73$	77.7878	−	77.7878i	1.06559	−	1.06559i	0.997693	−	0.0678931i	$-0.0216277\pi$
$74$	2.35329	+	1.35867i	0.0318013	+	0.0183605i
$75$		0			0
$76$	−16.9546	−	29.3662i	−0.223087	−	0.386398i
$77$	14.3286	−	53.4750i	0.186086	−	0.694481i
$78$		0			0
$79$	21.2132	+	12.2474i	0.268522	+	0.155031i	0.628216	−	0.778039i	$-0.283786\pi$
$79$	21.2132	+	12.2474i	0.268522	+	0.155031i	−0.359694	+	0.933070i	$0.617119\pi$
$80$	69.1691	−	26.2702i	0.864614	−	0.328377i
$81$		0			0
$82$	0.156633	+	0.156633i	0.00191016	+	0.00191016i
$83$	4.81193	+	17.9584i	0.0579750	+	0.216366i	0.988836	−	0.149008i	$-0.0476079\pi$
$83$	4.81193	+	17.9584i	0.0579750	+	0.216366i	−0.930861	+	0.365373i	$0.880941\pi$
$84$		0			0
$85$	−12.3895	−	122.045i	−0.145759	−	1.43582i
$86$	5.95459	+	10.3137i	0.0692394	+	0.119926i
$87$		0			0
$88$	7.37410	+	27.5205i	0.0837966	+	0.312733i
$89$			82.1816i			0.923389i	0.887039	+	0.461695i	$0.152758\pi$
$89$			82.1816i			0.923389i	−0.887039	+	0.461695i	$0.847242\pi$
$90$		0			0
$91$	−38.2929			−0.420801
$92$	61.5192	−	16.4840i	0.668687	−	0.179174i
$93$		0			0
$94$	17.2242	−	9.94439i	0.183236	−	0.105791i
$95$	−27.4856	+	33.6966i	−0.289322	+	0.354701i
$96$		0			0
$97$	33.5986	−	9.00273i	0.346378	−	0.0928117i	−0.0814359	−	0.996679i	$-0.525951\pi$
$97$	33.5986	−	9.00273i	0.346378	−	0.0928117i	0.427814	+	0.903867i	$0.359284\pi$
$98$	5.66403	−	5.66403i	0.0577962	−	0.0577962i
$99$		0			0
$100$	−64.7071	−	72.8990i	−0.647071	−	0.728990i
$101$	52.8105	−	91.4704i	0.522876	−	0.905647i	−0.476770	−	0.879028i	$-0.658192\pi$
$101$	52.8105	−	91.4704i	0.522876	−	0.905647i	0.999646	−	0.0266193i	$-0.00847419\pi$
$102$		0			0
$103$	121.914	+	32.6668i	1.18363	+	0.317154i	0.796367	−	0.604814i	$-0.206753\pi$
$103$	121.914	+	32.6668i	1.18363	+	0.317154i	0.387267	+	0.921968i	$0.373419\pi$
$104$	17.0669	−	9.85357i	0.164105	−	0.0947459i
$105$		0			0
$106$	0.156633	−	0.271297i	0.00147767	−	0.00255940i
$107$	68.7423	+	68.7423i	0.642452	+	0.642452i	0.951158	−	0.308706i	$-0.0998958\pi$
$107$	68.7423	+	68.7423i	0.642452	+	0.642452i	−0.308706	+	0.951158i	$0.599896\pi$
$108$		0			0
$109$			68.6969i			0.630247i	0.949051	+	0.315124i	$0.102046\pi$
$109$			68.6969i			0.630247i	−0.949051	+	0.315124i	$0.897954\pi$
$110$	14.6280	−	10.5487i	0.132982	−	0.0958976i
$111$		0			0
$112$	−18.6839	+	69.7293i	−0.166821	+	0.622583i
$113$	−133.381	−	35.7392i	−1.18036	−	0.316276i	−0.385290	−	0.922796i	$-0.625899\pi$
$113$	−133.381	−	35.7392i	−1.18036	−	0.316276i	−0.795069	+	0.606519i	$0.792565\pi$
$114$		0			0
$115$	−47.7721	−	66.2460i	−0.415410	−	0.576053i
$116$	137.035			1.18134
$117$		0			0
$118$	8.97500	−	8.97500i	0.0760593	−	0.0760593i
$119$	103.652	+	59.8434i	0.871023	+	0.502885i
$120$		0			0
$121$	−3.89388	−	6.74439i	−0.0321808	−	0.0557388i
$122$	0.486103	−	1.81416i	0.00398445	−	0.0148702i
$123$		0			0
$124$	36.1194	+	20.8536i	0.291286	+	0.168174i
$125$	−57.9319	+	110.765i	−0.463455	+	0.886120i
$126$		0			0
$127$	164.621	+	164.621i	1.29623	+	1.29623i	0.930865	+	0.365362i	$0.119055\pi$
$127$	164.621	+	164.621i	1.29623	+	1.29623i	0.365362	+	0.930865i	$0.380945\pi$
$128$	−19.7496	−	73.7065i	−0.154294	−	0.575832i
$129$		0			0
$130$	−9.66656	−	7.88482i	−0.0743582	−	0.0606525i
$131$	−53.0681	−	91.9167i	−0.405100	−	0.701654i	0.589233	−	0.807963i	$-0.299430\pi$
$131$	−53.0681	−	91.9167i	−0.405100	−	0.701654i	−0.994333	+	0.106309i	$0.966097\pi$
$132$		0			0
$133$	−10.9808	−	40.9808i	−0.0825621	−	0.308126i
$134$		−	20.2724i		−	0.151287i
$135$		0			0
$136$	−61.5959			−0.452911
$137$	227.622	−	60.9912i	1.66148	−	0.445191i	0.698684	−	0.715431i	$-0.253769\pi$
$137$	227.622	−	60.9912i	1.66148	−	0.445191i	0.962793	+	0.270239i	$0.0871028\pi$
$138$		0			0
$139$	−165.559	+	95.5857i	−1.19107	+	0.687667i	−0.958550	−	0.284924i	$-0.908032\pi$
$139$	−165.559	+	95.5857i	−1.19107	+	0.687667i	−0.232524	+	0.972591i	$0.574698\pi$
$140$	94.6160	−	9.60502i	0.675828	−	0.0686073i
$141$		0			0
$142$	20.8765	−	5.59384i	0.147018	−	0.0393932i
$143$	−62.9898	+	62.9898i	−0.440488	+	0.440488i
$144$		0			0
$145$	−62.3939	−	164.283i	−0.430303	−	1.13298i
$146$	−17.4824	+	30.2804i	−0.119742	+	0.207400i
$147$		0			0
$148$	32.1985	+	8.62756i	0.217557	+	0.0582943i
$149$	73.4853	−	42.4268i	0.493190	−	0.284744i	−0.232707	−	0.972547i	$-0.574758\pi$
$149$	73.4853	−	42.4268i	0.493190	−	0.284744i	0.725897	+	0.687803i	$0.241425\pi$
$150$		0			0
$151$	−74.4847	+	129.011i	−0.493276	+	0.854379i	−0.999970	−	0.00774676i	$-0.997534\pi$
$151$	−74.4847	+	129.011i	−0.493276	+	0.854379i	0.506694	+	0.862126i	$0.330867\pi$
$152$	15.4393	+	15.4393i	0.101574	+	0.101574i
$153$		0			0
$154$			17.5959i			0.114259i
$155$	8.55436	−	52.7962i	0.0551894	−	0.340620i
$156$		0			0
$157$	6.16884	−	23.0224i	0.0392919	−	0.146640i	−0.943493	−	0.331392i	$-0.892482\pi$
$157$	6.16884	−	23.0224i	0.0392919	−	0.146640i	0.982785	+	0.184753i	$0.0591484\pi$
$158$	−7.52011	−	2.01501i	−0.0475956	−	0.0127532i
$159$		0			0
$160$	−59.8011	+	43.1245i	−0.373757	+	0.269528i
$161$	79.6867			0.494949
$162$		0			0
$163$	130.606	−	130.606i	0.801265	−	0.801265i	−0.182029	−	0.983293i	$-0.558266\pi$
$163$	130.606	−	130.606i	0.801265	−	0.801265i	0.983293	+	0.182029i	$0.0582664\pi$
$164$	2.35329	+	1.35867i	0.0143493	+	0.00828460i
$165$		0			0
$166$	−2.95459	−	5.11750i	−0.0177987	−	0.0308283i
$167$	−16.4840	+	61.5192i	−0.0987068	+	0.368379i	−0.997555	−	0.0698806i	$-0.977738\pi$
$167$	−16.4840	+	61.5192i	−0.0987068	+	0.368379i	0.898849	+	0.438259i	$0.144405\pi$
$168$		0			0
$169$	−92.9970	−	53.6918i	−0.550278	−	0.317703i
$170$	13.8434	+	36.4495i	0.0814316	+	0.214409i
$171$		0			0
$172$	103.303	+	103.303i	0.600599	+	0.600599i
$173$	53.6707	+	200.302i	0.310235	+	1.15781i	0.928344	+	0.371722i	$0.121232\pi$
$173$	53.6707	+	200.302i	0.310235	+	1.15781i	−0.618109	+	0.786092i	$0.712101\pi$
$174$		0			0
$175$	−54.5947	−	109.056i	−0.311970	−	0.623175i
$176$	83.9671	+	145.435i	0.477086	+	0.826337i
$177$		0			0
$178$	−6.76045	−	25.2304i	−0.0379801	−	0.141744i
$179$			183.712i			1.02632i	0.858292	+	0.513161i	$0.171526\pi$
$179$			183.712i			1.02632i	−0.858292	+	0.513161i	$0.828474\pi$
$180$		0			0
$181$	−286.272			−1.58162			−0.790808	−	0.612064i	$-0.790339\pi$
$181$	−286.272			−1.58162			−0.790808	+	0.612064i	$0.790339\pi$
$182$	11.7562	−	3.15006i	0.0645944	−	0.0173080i
$183$		0			0
$184$	−35.5159	+	20.5051i	−0.193021	+	0.111441i
$185$	−4.31736	−	42.5289i	−0.0233371	−	0.229886i
$186$		0			0
$187$	268.941	−	72.0626i	1.43819	−	0.385361i
$188$	172.520	−	172.520i	0.917659	−	0.917659i
$189$		0			0
$190$	5.66632	−	12.6061i	0.0298228	−	0.0663480i
$191$	−24.0454	+	41.6479i	−0.125892	+	0.218052i	−0.922081	−	0.386996i	$-0.873513\pi$
$191$	−24.0454	+	41.6479i	−0.125892	+	0.218052i	0.796189	+	0.605048i	$0.206846\pi$
$192$		0			0
$193$	349.109	+	93.5434i	1.80885	+	0.484681i	0.995303	−	0.0968131i	$-0.0308649\pi$
$193$	349.109	+	93.5434i	1.80885	+	0.484681i	0.813551	+	0.581494i	$0.197532\pi$
$194$	−9.57444	+	5.52781i	−0.0493528	+	0.0284938i
$195$		0			0
$196$	49.1311	−	85.0976i	0.250669	−	0.434171i
$197$	−96.6969	−	96.6969i	−0.490847	−	0.490847i	0.417726	−	0.908573i	$-0.362827\pi$
$197$	−96.6969	−	96.6969i	−0.490847	−	0.490847i	−0.908573	+	0.417726i	$0.862827\pi$
$198$		0			0
$199$			192.606i			0.967870i	0.875104	+	0.483935i	$0.160793\pi$
$199$			192.606i			0.967870i	−0.875104	+	0.483935i	$0.839207\pi$
$200$	52.3949	+	34.5571i	0.261974	+	0.172785i
$201$		0			0
$202$	−8.68862	+	32.4264i	−0.0430130	+	0.160527i
$203$	165.613	+	44.3759i	0.815828	+	0.218601i
$204$		0			0
$205$	0.557343	−	3.43983i	0.00271874	−	0.0167797i
$206$	−40.1158			−0.194737
$207$		0			0
$208$	82.1362	−	82.1362i	0.394886	−	0.394886i
$209$	−85.4741	−	49.3485i	−0.408967	−	0.236117i
$210$		0			0
$211$	−73.6061	−	127.490i	−0.348844	−	0.604216i	0.637200	−	0.770698i	$-0.280092\pi$
$211$	−73.6061	−	127.490i	−0.348844	−	0.604216i	−0.986044	+	0.166482i	$0.946759\pi$
$212$	0.994619	−	3.71197i	0.00469160	−	0.0175093i
$213$		0			0
$214$	−26.7593	−	15.4495i	−0.125043	−	0.0721939i
$215$	76.8082	−	170.879i	0.357247	−	0.794784i
$216$		0			0
$217$	36.8990	+	36.8990i	0.170041	+	0.170041i
$218$	−5.65117	−	21.0905i	−0.0259228	−	0.0967452i
$219$		0			0
$220$	139.839	−	171.438i	0.635630	−	0.779265i
$221$	−96.2929	−	166.784i	−0.435714	−	0.754679i
$222$		0			0
$223$	61.2833	+	228.712i	0.274813	+	1.02562i	0.955967	+	0.293475i	$0.0948119\pi$
$223$	61.2833	+	228.712i	0.274813	+	1.02562i	−0.681154	+	0.732141i	$0.738521\pi$
$224$		−	71.9342i		−	0.321135i
$225$		0			0
$226$	43.8888			0.194198
$227$	−345.839	+	92.6672i	−1.52352	+	0.408225i	−0.920898	−	0.389803i	$-0.872543\pi$
$227$	−345.839	+	92.6672i	−1.52352	+	0.408225i	−0.602620	+	0.798028i	$0.705876\pi$
$228$		0			0
$229$	−194.165	+	112.101i	−0.847881	+	0.489524i	−0.859935	−	0.510403i	$-0.829496\pi$
$229$	−194.165	+	112.101i	−0.847881	+	0.489524i	0.0120546	+	0.999927i	$0.496163\pi$
$230$	20.1159	+	16.4082i	0.0874606	+	0.0713399i
$231$		0			0
$232$	−85.2316	+	22.8377i	−0.367378	+	0.0984386i
$233$	−205.712	+	205.712i	−0.882883	+	0.882883i	−0.993827	−	0.110944i	$-0.964613\pi$
$233$	−205.712	+	205.712i	−0.882883	+	0.882883i	0.110944	+	0.993827i	$0.464613\pi$
$234$		0			0
$235$	−285.373	−	128.272i	−1.21436	−	0.545840i
$236$	77.8513	−	134.842i	0.329878	−	0.571366i
$237$		0			0
$238$	−36.7447	−	9.84571i	−0.154389	−	0.0413685i
$239$	−299.470	+	172.899i	−1.25301	+	0.723427i	−0.971706	−	0.236192i	$-0.924101\pi$
$239$	−299.470	+	172.899i	−1.25301	+	0.723427i	−0.281305	+	0.959618i	$0.590767\pi$
$240$		0			0
$241$	−50.7878	+	87.9670i	−0.210738	+	0.365008i	−0.951946	−	0.306267i	$-0.900920\pi$
$241$	−50.7878	+	87.9670i	−0.210738	+	0.365008i	0.741208	+	0.671275i	$0.234253\pi$
$242$	1.75026	+	1.75026i	0.00723247	+	0.00723247i
$243$		0			0
$244$		−	23.0398i		−	0.0944254i
$245$	−124.388	−	20.1541i	−0.507706	−	0.0822616i
$246$		0			0
$247$	−17.6689	+	65.9414i	−0.0715342	+	0.266969i
$248$	−25.9405	−	6.95075i	−0.104599	−	0.0280272i
$249$		0			0
$250$	8.67372	−	38.7713i	0.0346949	−	0.155085i
$251$	−331.258			−1.31975			−0.659876	−	0.751375i	$-0.729391\pi$
$251$	−331.258			−1.31975			−0.659876	+	0.751375i	$0.729391\pi$
$252$		0			0
$253$	131.081	−	131.081i	0.518105	−	0.518105i
$254$	−64.0819	−	36.9977i	−0.252291	−	0.145660i
$255$		0			0
$256$	−96.8837	−	167.807i	−0.378452	−	0.655498i
$257$	12.1657	−	45.4029i	0.0473373	−	0.176665i	−0.938210	−	0.346067i	$-0.887517\pi$
$257$	12.1657	−	45.4029i	0.0473373	−	0.176665i	0.985547	+	0.169402i	$0.0541836\pi$
$258$		0			0
$259$	36.1194	+	20.8536i	0.139457	+	0.0805157i
$260$	−139.576	−	62.7378i	−0.536829	−	0.241299i
$261$		0			0
$262$	23.8536	+	23.8536i	0.0910442	+	0.0910442i
$263$	−101.812	−	379.969i	−0.387119	−	1.44475i	−0.834799	−	0.550555i	$-0.814416\pi$
$263$	−101.812	−	379.969i	−0.387119	−	1.44475i	0.447679	−	0.894194i	$-0.352251\pi$
$264$		0			0
$265$	−4.90290	+	0.497722i	−0.0185015	+	0.00187820i
$266$	6.74235	+	11.6781i	0.0253472	+	0.0439026i
$267$		0			0
$268$	−64.3648	−	240.213i	−0.240167	−	0.896316i
$269$		−	488.499i		−	1.81598i	−0.418988	−	0.907992i	$-0.637615\pi$
$269$		−	488.499i		−	1.81598i	0.418988	−	0.907992i	$-0.362385\pi$
$270$		0			0
$271$	131.576			0.485518			0.242759	−	0.970087i	$-0.421947\pi$
$271$	131.576			0.485518			0.242759	+	0.970087i	$0.421947\pi$
$272$	−350.689	+	93.9668i	−1.28930	+	0.345466i
$273$		0			0
$274$	−64.8644	+	37.4495i	−0.236731	+	0.136677i
$275$	−269.197	−	89.5856i	−0.978896	−	0.325766i
$276$		0			0
$277$	−138.665	+	37.1551i	−0.500595	+	0.134134i	−0.500276	−	0.865866i	$-0.666768\pi$
$277$	−138.665	+	37.1551i	−0.500595	+	0.134134i	−0.000318873		1.00000i	$0.500102\pi$
$278$	42.9648	−	42.9648i	0.154550	−	0.154550i
$279$		0			0
$280$	−57.2474	+	21.7423i	−0.204455	+	0.0776512i
$281$	−171.652	+	297.309i	−0.610860	+	1.05804i	0.380236	+	0.924889i	$0.375843\pi$
$281$	−171.652	+	297.309i	−0.610860	+	1.05804i	−0.991096	+	0.133150i	$0.957491\pi$
$282$		0			0
$283$	−1.62808	−	0.436242i	−0.00575293	−	0.00154149i	0.255941	−	0.966692i	$-0.417615\pi$
$283$	−1.62808	−	0.436242i	−0.00575293	−	0.00154149i	−0.261694	+	0.965151i	$0.584281\pi$
$284$	229.610	−	132.565i	0.808485	−	0.466779i
$285$		0			0
$286$	14.1566	−	24.5200i	0.0494987	−	0.0857343i
$287$	2.40408	+	2.40408i	0.00837659	+	0.00837659i
$288$		0			0
$289$			312.939i			1.08283i
$290$	32.6696	+	45.3033i	0.112654	+	0.156218i
$291$		0			0
$292$	−111.013	+	414.306i	−0.380181	+	1.41886i
$293$	−131.911	−	35.3454i	−0.450207	−	0.120633i	0.0265892	−	0.999646i	$-0.491535\pi$
$293$	−131.911	−	35.3454i	−0.450207	−	0.120633i	−0.476796	+	0.879014i	$0.658202\pi$
$294$		0			0
$295$	−197.100	−	31.9354i	−0.668137	−	0.108256i
$296$	−21.4643			−0.0725145
$297$		0			0
$298$	−19.0704	+	19.0704i	−0.0639946	+	0.0639946i
$299$	−111.044	−	64.1112i	−0.371384	−	0.214419i
$300$		0			0
$301$	91.3939	+	158.299i	0.303634	+	0.525910i
$302$	12.2546	−	45.7347i	0.0405780	−	0.151439i
$303$		0			0
$304$	111.455	+	64.3485i	0.366628	+	0.211673i
$305$	−27.6209	+	10.4903i	−0.0905604	+	0.0343945i
$306$		0			0
$307$	−124.969	−	124.969i	−0.407066	−	0.407066i	0.473648	−	0.880714i	$-0.342937\pi$
$307$	−124.969	−	124.969i	−0.407066	−	0.407066i	−0.880714	+	0.473648i	$0.842937\pi$
$308$	55.8669	+	208.498i	0.181386	+	0.676942i
$309$		0			0
$310$	1.71689	+	16.9125i	0.00553835	+	0.0545565i
$311$	293.151	+	507.752i	0.942608	+	1.63264i	0.760472	+	0.649371i	$0.224968\pi$
$311$	293.151	+	507.752i	0.942608	+	1.63264i	0.182136	+	0.983273i	$0.441699\pi$
$312$		0			0
$313$	−37.4713	−	139.845i	−0.119717	−	0.446788i	0.879880	−	0.475196i	$-0.157623\pi$
$313$	−37.4713	−	139.845i	−0.119717	−	0.446788i	−0.999596	+	0.0284079i	$0.990956\pi$
$314$			7.57551i			0.0241258i
$315$		0			0
$316$	−95.5051			−0.302231
$317$	148.601	−	39.8174i	0.468772	−	0.125607i	−0.0166979	−	0.999861i	$-0.505315\pi$
$317$	148.601	−	39.8174i	0.468772	−	0.125607i	0.485469	+	0.874254i	$0.338649\pi$
$318$		0			0
$319$	345.421	−	199.429i	1.08283	−	0.625170i
$320$	−172.257	+	211.182i	−0.538302	+	0.659943i
$321$		0			0
$322$	−24.4644	+	6.55522i	−0.0759764	+	0.0203578i
$323$	150.879	−	150.879i	0.467116	−	0.467116i
$324$		0			0
$325$	−11.6617	+	195.893i	−0.0358823	+	0.602749i
$326$	−29.3531	+	50.8410i	−0.0900401	+	0.155954i
$327$		0			0
$328$	−1.69011	−	0.452863i	−0.00515276	−	0.00138068i
$329$	264.365	−	152.631i	0.803541	−	0.463924i
$330$		0			0
$331$	122.712	−	212.543i	0.370730	−	0.642124i	−0.618948	−	0.785432i	$-0.712441\pi$
$331$	122.712	−	212.543i	0.370730	−	0.642124i	0.989678	+	0.143308i	$0.0457741\pi$
$332$	−51.2577	−	51.2577i	−0.154391	−	0.154391i
$333$		0			0
$334$		−	20.2429i		−	0.0606074i
$335$	−258.669	+	186.535i	−0.772148	+	0.556820i
$336$		0			0
$337$	78.2592	−	292.067i	0.232223	−	0.866669i	−0.747158	−	0.664647i	$-0.768582\pi$
$337$	78.2592	−	292.067i	0.232223	−	0.866669i	0.979381	−	0.202022i	$-0.0647513\pi$
$338$	32.9676	+	8.83363i	0.0975372	+	0.0261350i
$339$		0			0
$340$	279.760	+	387.946i	0.822823	+	1.14102i
$341$	121.394			0.355994
$342$		0			0
$343$	255.959	−	255.959i	0.746237	−	0.746237i
$344$	−81.4674	−	47.0352i	−0.236824	−	0.136730i
$345$		0			0
$346$	−32.9546	−	57.0790i	−0.0952445	−	0.164968i
$347$	−58.5824	+	218.632i	−0.168825	+	0.630064i	0.828696	+	0.559699i	$0.189083\pi$
$347$	−58.5824	+	218.632i	−0.168825	+	0.630064i	−0.997521	+	0.0703655i	$0.977583\pi$
$348$		0			0
$349$	258.084	+	149.005i	0.739494	+	0.426947i	0.821885	−	0.569653i	$-0.192922\pi$
$349$	258.084	+	149.005i	0.739494	+	0.426947i	−0.0823911	+	0.996600i	$0.526256\pi$
$350$	25.7321	+	28.9898i	0.0735204	+	0.0828280i
$351$		0			0
$352$	−118.328	−	118.328i	−0.336159	−	0.336159i
$353$	−8.24285	−	30.7627i	−0.0233509	−	0.0871466i	0.953267	−	0.302129i	$-0.0976973\pi$
$353$	−8.24285	−	30.7627i	−0.0233509	−	0.0871466i	−0.976618	+	0.214982i	$0.931031\pi$
$354$		0			0
$355$	−263.468	−	214.906i	−0.742164	−	0.605368i
$356$	−160.212	−	277.496i	−0.450034	−	0.779482i
$357$		0			0
$358$	−15.1126	−	56.4008i	−0.0422138	−	0.157544i
$359$			48.2724i			0.134464i	0.997737	+	0.0672318i	$0.0214167\pi$
$359$			48.2724i			0.134464i	−0.997737	+	0.0672318i	$0.978583\pi$
$360$		0			0
$361$	285.363			0.790480
$362$	87.8877	−	23.5494i	0.242784	−	0.0650537i
$363$		0			0
$364$	129.300	−	74.6515i	0.355220	−	0.205087i
$365$	547.230	−	55.5525i	1.49926	−	0.152199i
$366$		0			0
$367$	−200.136	+	53.6263i	−0.545330	+	0.146121i	−0.520958	−	0.853582i	$-0.674425\pi$
$367$	−200.136	+	53.6263i	−0.545330	+	0.146121i	−0.0243716	+	0.999703i	$0.507759\pi$
$368$	−170.924	+	170.924i	−0.464467	+	0.464467i
$369$		0			0
$370$	4.82399	+	12.7015i	0.0130378	+	0.0343284i
$371$	2.40408	−	4.16399i	0.00648001	−	0.0112237i
$372$		0			0
$373$	−117.760	−	31.5538i	−0.315712	−	0.0845947i	0.0974836	−	0.995237i	$-0.468921\pi$
$373$	−117.760	−	31.5538i	−0.315712	−	0.0845947i	−0.413195	+	0.910642i	$0.635587\pi$
$374$	−76.6388	+	44.2474i	−0.204917	+	0.118309i
$375$		0			0
$376$	−78.5505	+	136.053i	−0.208911	+	0.361844i
$377$	−195.081	−	195.081i	−0.517455	−	0.517455i
$378$		0			0
$379$		−	210.000i		−	0.554090i	−0.960857	−	0.277045i	$-0.910645\pi$
$379$		−	210.000i		−	0.554090i	0.960857	−	0.277045i	$-0.0893551\pi$
$380$	27.1172	−	167.363i	0.0713611	−	0.440430i
$381$		0			0
$382$	3.95606	−	14.7642i	0.0103562	−	0.0386498i
$383$	14.5224	+	3.89126i	0.0379174	+	0.0101599i	0.277728	−	0.960660i	$-0.410419\pi$
$383$	14.5224	+	3.89126i	0.0379174	+	0.0101599i	−0.239810	+	0.970820i	$0.577085\pi$
$384$		0			0
$385$	224.518	−	161.907i	0.583163	−	0.420538i
$386$	−114.874			−0.297601
$387$		0			0
$388$	−95.8990	+	95.8990i	−0.247162	+	0.247162i
$389$	463.616	+	267.669i	1.19181	+	0.688094i	0.958718	−	0.284360i	$-0.0917809\pi$
$389$	463.616	+	267.669i	1.19181	+	0.688094i	0.233096	+	0.972454i	$0.425114\pi$
$390$		0			0
$391$	200.384	+	347.075i	0.512490	+	0.887659i
$392$	−16.3760	+	61.1160i	−0.0417755	+	0.155908i
$393$		0			0
$394$	37.6412	+	21.7321i	0.0955360	+	0.0551577i
$395$	43.4847	+	114.495i	0.110088	+	0.289860i
$396$		0			0
$397$	118.742	+	118.742i	0.299099	+	0.299099i	0.840661	−	0.541562i	$-0.182167\pi$
$397$	118.742	+	118.742i	0.299099	+	0.299099i	−0.541562	+	0.840661i	$0.682167\pi$
$398$	−15.8442	−	59.1315i	−0.0398096	−	0.148572i
$399$		0			0
$400$	351.022	+	116.816i	0.877554	+	0.292040i
$401$	−210.151	−	363.992i	−0.524067	−	0.907711i	−0.999607	−	0.0280172i	$-0.991081\pi$
$401$	−210.151	−	363.992i	−0.524067	−	0.907711i	0.475540	−	0.879694i	$-0.342253\pi$
$402$		0			0
$403$	−21.7322	−	81.1057i	−0.0539260	−	0.201255i
$404$			411.814i			1.01934i
$405$		0			0
$406$	−54.4949			−0.134224
$407$	93.7177	−	25.1116i	0.230265	−	0.0616992i
$408$		0			0
$409$	−446.099	+	257.555i	−1.09071	+	0.629719i	−0.933764	−	0.357889i	$-0.883497\pi$
$409$	−446.099	+	257.555i	−1.09071	+	0.629719i	−0.156941	+	0.987608i	$0.550163\pi$
$410$	0.111860	+	1.10190i	0.000272830	+	0.00268757i
$411$		0			0
$412$	−475.341	+	127.367i	−1.15374	+	0.309144i
$413$	137.753	−	137.753i	0.333541	−	0.333541i
$414$		0			0
$415$	−38.1112	+	84.7878i	−0.0918343	+	0.204308i
$416$	−57.8740	+	100.241i	−0.139120	+	0.240963i
$417$		0			0
$418$	30.3007	+	8.11904i	0.0724896	+	0.0194235i
$419$	−76.7312	+	44.3008i	−0.183129	+	0.105730i	−0.588762	−	0.808306i	$-0.700385\pi$
$419$	−76.7312	+	44.3008i	−0.183129	+	0.105730i	0.405633	+	0.914036i	$0.367051\pi$
$420$		0			0
$421$	128.576	−	222.699i	0.305405	−	0.528977i	−0.671946	−	0.740600i	$-0.734541\pi$
$421$	128.576	−	222.699i	0.305405	−	0.528977i	0.977351	+	0.211623i	$0.0678748\pi$
$422$	33.0852	+	33.0852i	0.0784009	+	0.0784009i
$423$		0			0
$424$			2.47449i			0.00583605i
$425$	337.705	−	512.023i	0.794599	−	1.20476i
$426$		0			0
$427$	7.46094	−	27.8446i	0.0174729	−	0.0652099i
$428$	−366.129	−	98.1040i	−0.855441	−	0.229215i
$429$		0			0
$430$	−9.52379	+	58.7794i	−0.0221483	+	0.136696i
$431$	804.636			1.86690			0.933452	−	0.358702i	$-0.116781\pi$
$431$	804.636			1.86690			0.933452	+	0.358702i	$0.116781\pi$
$432$		0			0
$433$	−344.848	+	344.848i	−0.796416	+	0.796416i	−0.982528	−	0.186113i	$-0.940411\pi$
$433$	−344.848	+	344.848i	−0.796416	+	0.796416i	0.186113	+	0.982528i	$0.440411\pi$
$434$	−14.3636	−	8.29286i	−0.0330960	−	0.0191080i
$435$		0			0
$436$	−133.924	−	231.963i	−0.307165	−	0.532026i
$437$	36.7687	−	137.223i	0.0841390	−	0.314011i
$438$		0			0
$439$	−374.927	−	216.464i	−0.854048	−	0.493085i	0.00796652	−	0.999968i	$-0.497464\pi$
$439$	−374.927	−	216.464i	−0.854048	−	0.493085i	−0.862015	+	0.506883i	$0.830797\pi$
$440$	−58.4041	+	129.934i	−0.132737	+	0.295305i
$441$		0			0
$442$	43.2827	+	43.2827i	0.0979246	+	0.0979246i
$443$	89.7240	+	334.855i	0.202537	+	0.755880i	0.990186	+	0.139755i	$0.0446315\pi$
$443$	89.7240	+	334.855i	0.202537	+	0.755880i	−0.787649	+	0.616124i	$0.788702\pi$
$444$		0			0
$445$	−259.725	+	318.415i	−0.583652	+	0.715540i
$446$	−37.6288	−	65.1750i	−0.0843696	−	0.146132i
$447$		0			0
$448$	−68.8182	−	256.833i	−0.153612	−	0.573288i
$449$			386.091i			0.859890i	0.902855	+	0.429945i	$0.141467\pi$
$449$			386.091i			0.859890i	−0.902855	+	0.429945i	$0.858533\pi$
$450$		0			0
$451$	7.90918			0.0175370
$452$	520.048	−	139.346i	1.15055	−	0.308289i
$453$		0			0
$454$	98.5519	−	56.8990i	0.217075	−	0.125328i
$455$	−148.367	−	121.020i	−0.326081	−	0.265978i
$456$		0			0
$457$	305.644	−	81.8971i	0.668805	−	0.179206i	0.0915887	−	0.995797i	$-0.470806\pi$
$457$	305.644	−	81.8971i	0.668805	−	0.179206i	0.577217	+	0.816591i	$0.304139\pi$
$458$	50.3883	−	50.3883i	0.110018	−	0.110018i
$459$		0			0
$460$	290.454	+	130.556i	0.631422	+	0.283818i
$461$	361.310	−	625.807i	0.783753	−	1.35750i	−0.145989	−	0.989286i	$-0.546636\pi$
$461$	361.310	−	625.807i	0.783753	−	1.35750i	0.929741	−	0.368213i	$-0.120030\pi$
$462$		0			0
$463$	177.176	+	47.4741i	0.382669	+	0.102536i	0.445025	−	0.895518i	$-0.353195\pi$
$463$	177.176	+	47.4741i	0.382669	+	0.102536i	−0.0623562	+	0.998054i	$0.519861\pi$
$464$	−450.416	+	260.048i	−0.970724	+	0.560448i
$465$		0			0
$466$	46.2327	−	80.0773i	0.0992117	−	0.171840i
$467$	415.258	+	415.258i	0.889203	+	0.889203i	0.994446	−	0.105244i	$-0.0335623\pi$
$467$	415.258	+	415.258i	0.889203	+	0.889203i	−0.105244	+	0.994446i	$0.533562\pi$
$468$		0			0
$469$		−	311.151i		−	0.663435i
$470$	98.1637	+	15.9051i	0.208859	+	0.0338406i
$471$		0			0
$472$	−25.9488	+	96.8421i	−0.0549762	+	0.205174i
$473$	410.732	+	110.055i	0.868355	+	0.232675i
$474$		0			0
$475$	−212.988	+	43.6936i	−0.448396	+	0.0919865i
$476$	−466.656			−0.980370
$477$		0			0
$478$	77.7163	−	77.7163i	0.162586	−	0.162586i
$479$	−264.094	−	152.474i	−0.551344	−	0.318318i	0.198320	−	0.980137i	$-0.436451\pi$
$479$	−264.094	−	152.474i	−0.551344	−	0.318318i	−0.749664	+	0.661819i	$0.769785\pi$
$480$		0			0
$481$	−33.5551	−	58.1191i	−0.0697611	−	0.120830i
$482$	8.35584	−	31.1844i	0.0173358	−	0.0646980i
$483$		0			0
$484$	26.2962	+	15.1821i	0.0543311	+	0.0313681i
$485$	158.631	+	71.3031i	0.327074	+	0.147017i
$486$		0			0
$487$	−429.318	−	429.318i	−0.881556	−	0.881556i	0.112137	−	0.993693i	$-0.464231\pi$
$487$	−429.318	−	429.318i	−0.881556	−	0.881556i	−0.993693	+	0.112137i	$0.964231\pi$
$488$	3.83972	+	14.3300i	0.00786828	+	0.0293648i
$489$		0			0
$490$	39.8459	−	4.04499i	0.0813183	−	0.00825509i
$491$	207.159	+	358.810i	0.421912	+	0.730773i	0.996127	−	0.0879316i	$-0.0280257\pi$
$491$	207.159	+	358.810i	0.421912	+	0.730773i	−0.574214	+	0.818705i	$0.694692\pi$
$492$		0			0
$493$	223.179	+	832.916i	0.452696	+	1.68948i
$494$		−	21.6980i		−	0.0439230i
$495$		0			0
$496$	−158.293			−0.319139
$497$	320.422	−	85.8569i	0.644713	−	0.172750i
$498$		0			0
$499$	318.338	−	183.792i	0.637951	−	0.368321i	−0.145874	−	0.989303i	$-0.546599\pi$
$499$	318.338	−	183.792i	0.637951	−	0.368321i	0.783825	+	0.620982i	$0.213266\pi$
$500$	−20.3216	−	486.949i	−0.0406433	−	0.973897i
$501$		0			0
$502$	101.698	−	27.2500i	0.202587	−	0.0542829i
$503$	−9.59133	+	9.59133i	−0.0190683	+	0.0190683i	−0.716577	−	0.697508i	$-0.754292\pi$
$503$	−9.59133	+	9.59133i	−0.0190683	+	0.0190683i	0.697508	+	0.716577i	$0.254292\pi$
$504$		0			0
$505$	493.697	−	187.504i	0.977618	−	0.371295i
$506$	−29.4597	+	51.0257i	−0.0582207	+	0.100841i
$507$		0			0
$508$	−876.788	−	234.935i	−1.72596	−	0.462470i
$509$	673.325	−	388.745i	1.32284	−	0.763742i	0.338659	−	0.940909i	$-0.390027\pi$
$509$	673.325	−	388.745i	1.32284	−	0.763742i	0.984181	+	0.177167i	$0.0566933\pi$
$510$		0			0
$511$	−268.328	+	464.758i	−0.525104	+	0.909507i
$512$	259.376	+	259.376i	0.506593	+	0.506593i
$513$		0			0
$514$			14.9398i			0.0290658i
$515$	369.121	+	511.864i	0.716741	+	0.993911i
$516$		0			0
$517$	183.796	−	685.937i	0.355505	−	1.32676i
$518$	−12.8044	−	3.43093i	−0.0247189	−	0.00662341i
$519$		0			0
$520$	97.2672	+	15.7598i	0.187052	+	0.0303074i
$521$	321.605			0.617284			0.308642	−	0.951178i	$-0.400125\pi$
$521$	321.605			0.617284			0.308642	+	0.951178i	$0.400125\pi$
$522$		0			0
$523$	−582.454	+	582.454i	−1.11368	+	1.11368i	−0.121030	+	0.992649i	$0.538620\pi$
$523$	−582.454	+	582.454i	−1.11368	+	1.11368i	−0.992649	+	0.121030i	$0.961380\pi$
$524$	358.381	+	206.911i	0.683934	+	0.394869i
$525$		0			0
$526$	62.5143	+	108.278i	0.118848	+	0.205852i
$527$	−67.9254	+	253.501i	−0.128891	+	0.481026i
$528$		0			0
$529$	−227.047	−	131.086i	−0.429201	−	0.247799i
$530$	1.46428	−	0.556128i	0.00276280	−	0.00104930i
$531$		0			0
$532$	116.969	+	116.969i	0.219867	+	0.219867i
$533$	−1.41592	−	5.28428i	−0.00265651	−	0.00991423i
$534$		0			0
$535$	49.0927	+	483.596i	0.0917620	+	0.903918i
$536$	80.0658	+	138.678i	0.149377	+	0.258728i
$537$		0			0
$538$	40.1851	+	149.973i	0.0746935	+	0.278760i
$539$		−	286.005i		−	0.530621i
$540$		0			0
$541$	460.697			0.851566			0.425783	−	0.904825i	$-0.359999\pi$
$541$	460.697			0.851566			0.425783	+	0.904825i	$0.359999\pi$
$542$	−40.3946	+	10.8237i	−0.0745288	+	0.0199699i
$543$		0			0
$544$	313.309	−	180.889i	0.575935	−	0.332516i
$545$	−217.108	+	266.169i	−0.398364	+	0.488383i
$546$		0			0
$547$	904.005	−	242.227i	1.65266	−	0.442829i	0.692304	−	0.721606i	$-0.256596\pi$
$547$	904.005	−	242.227i	1.65266	−	0.442829i	0.960356	+	0.278777i	$0.0899291\pi$
$548$	−649.691	+	649.691i	−1.18557	+	1.18557i
$549$		0			0
$550$	90.0148	+	5.35867i	0.163663	+	0.00974304i
$551$	152.833	−	264.715i	0.277374	−	0.480426i
$552$		0			0
$553$	−115.422	−	30.9273i	−0.208720	−	0.0559264i
$554$	39.5146	−	22.8138i	0.0713260	−	0.0411801i
$555$		0			0
$556$	372.687	−	645.512i	0.670300	−	1.16099i
$557$	125.909	+	125.909i	0.226049	+	0.226049i	0.811040	−	0.584991i	$-0.198902\pi$
$557$	125.909	+	125.909i	0.226049	+	0.226049i	−0.584991	+	0.811040i	$0.698902\pi$
$558$		0			0
$559$		−	294.120i		−	0.526155i
$560$	−292.763	+	211.120i	−0.522790	+	0.377001i
$561$		0			0
$562$	28.2409	−	105.397i	0.0502507	−	0.187538i
$563$	273.218	+	73.2084i	0.485289	+	0.130033i	0.493164	−	0.869936i	$-0.335840\pi$
$563$	273.218	+	73.2084i	0.485289	+	0.130033i	−0.00787538	+	0.999969i	$0.502507\pi$
$564$		0			0
$565$	−403.838	−	560.006i	−0.714757	−	0.991161i
$566$	0.535718			0.000946498
$567$		0			0
$568$	−120.717	+	120.717i	−0.212531	+	0.212531i
$569$	519.476	+	299.919i	0.912962	+	0.527099i	0.881383	−	0.472402i	$-0.156613\pi$
$569$	519.476	+	299.919i	0.912962	+	0.527099i	0.0315793	+	0.999501i	$0.489946\pi$
$570$		0			0
$571$	123.985	+	214.749i	0.217137	+	0.376092i	0.953932	−	0.300024i	$-0.0969948\pi$
$571$	123.985	+	214.749i	0.217137	+	0.376092i	−0.736795	+	0.676117i	$0.763662\pi$
$572$	89.8943	−	335.490i	0.157158	−	0.586521i
$573$		0			0
$574$	−0.935836	−	0.540305i	−0.00163038	−	0.000941298i
$575$	24.2679	−	407.650i	0.0422050	−	0.708957i
$576$		0			0
$577$	−292.121	−	292.121i	−0.506276	−	0.506276i	0.407105	−	0.913381i	$-0.366538\pi$
$577$	−292.121	−	292.121i	−0.506276	−	0.506276i	−0.913381	+	0.407105i	$0.866538\pi$
$578$	−25.7431	−	96.0745i	−0.0445382	−	0.166219i
$579$		0			0
$580$	530.947	+	433.083i	0.915427	+	0.746695i
$581$	−45.3485	−	78.5459i	−0.0780524	−	0.135191i
$582$		0			0
$583$	−2.89496	−	10.8041i	−0.00496563	−	0.0185320i
$584$		−	276.186i		−	0.472922i
$585$		0			0
$586$	43.4051			0.0740702
$587$	−834.938	+	223.721i	−1.42238	+	0.381126i	−0.886328	−	0.463058i	$-0.846752\pi$
$587$	−834.938	+	223.721i	−1.42238	+	0.381126i	−0.536053	+	0.844184i	$0.680085\pi$
$588$		0			0
$589$	80.5669	−	46.5153i	0.136786	−	0.0789734i
$590$	63.1384	−	6.40954i	0.107014	−	0.0108636i
$591$		0			0
$592$	−122.204	+	32.7445i	−0.206426	+	0.0553117i
$593$	524.742	−	524.742i	0.884894	−	0.884894i	−0.109133	−	0.994027i	$-0.534807\pi$
$593$	524.742	−	524.742i	0.884894	−	0.884894i	0.994027	+	0.109133i	$0.0348074\pi$
$594$		0			0
$595$	212.474	+	559.444i	0.357100	+	0.940242i
$596$	−165.421	+	286.518i	−0.277552	+	0.480735i
$597$		0			0
$598$	39.3652	+	10.5479i	0.0658281	+	0.0176386i
$599$	−319.441	+	184.429i	−0.533290	+	0.307895i	−0.742355	−	0.670007i	$-0.766291\pi$
$599$	−319.441	+	184.429i	−0.533290	+	0.307895i	0.209065	+	0.977902i	$0.432958\pi$
$600$		0			0
$601$	−466.242	+	807.555i	−0.775777	+	1.34368i	0.158580	+	0.987346i	$0.449308\pi$
$601$	−466.242	+	807.555i	−0.775777	+	1.34368i	−0.934357	+	0.356339i	$0.884025\pi$
$602$	−41.0806	−	41.0806i	−0.0682402	−	0.0682402i
$603$		0			0
$604$		−	580.829i		−	0.961637i
$605$	6.22788	−	38.4375i	0.0102940	−	0.0635331i
$606$		0			0
$607$	187.995	−	701.605i	0.309711	−	1.15586i	−0.619103	−	0.785310i	$-0.712504\pi$
$607$	187.995	−	701.605i	0.309711	−	1.15586i	0.928814	−	0.370547i	$-0.120830\pi$
$608$	−123.873	−	33.1916i	−0.203738	−	0.0545914i
$609$		0			0
$610$	7.61686	−	5.49276i	0.0124867	−	0.00900453i
$611$	−491.192			−0.803915
$612$		0			0
$613$	−615.287	+	615.287i	−1.00373	+	1.00373i	−0.00373821	+	0.999993i	$0.501190\pi$
$613$	−615.287	+	615.287i	−1.00373	+	1.00373i	−0.999993	+	0.00373821i	$0.998810\pi$
$614$	48.6468	+	28.0862i	0.0792293	+	0.0457430i
$615$		0			0
$616$	−69.4949	−	120.369i	−0.112816	−	0.195404i
$617$	200.125	−	746.876i	0.324352	−	1.21050i	−0.590610	−	0.806957i	$-0.701113\pi$
$617$	200.125	−	746.876i	0.324352	−	1.21050i	0.914962	−	0.403540i	$-0.132220\pi$
$618$		0			0
$619$	−132.389	−	76.4347i	−0.213875	−	0.123481i	0.389236	−	0.921138i	$-0.372739\pi$
$619$	−132.389	−	76.4347i	−0.213875	−	0.123481i	−0.603111	+	0.797657i	$0.706072\pi$
$620$	74.0408	+	194.949i	0.119421	+	0.314434i
$621$		0			0
$622$	−131.768	−	131.768i	−0.211846	−	0.211846i
$623$	−103.763	−	387.247i	−0.166553	−	0.621585i
$624$		0			0
$625$	−574.519	+	246.076i	−0.919230	+	0.393722i
$626$	23.0079	+	39.8509i	0.0367539	+	0.0636595i
$627$		0			0
$628$	24.0522	+	89.7639i	0.0382996	+	0.142936i
$629$			209.757i			0.333477i
$630$		0			0
$631$	−41.4847			−0.0657444			−0.0328722	−	0.999460i	$-0.510465\pi$
$631$	−41.4847			−0.0657444			−0.0328722	+	0.999460i	$0.510465\pi$
$632$	59.4012	−	15.9165i	0.0939892	−	0.0251843i
$633$		0			0
$634$	−42.3460	+	24.4485i	−0.0667918	+	0.0385622i
$635$	117.565	+	1158.09i	0.185141	+	1.82377i
$636$		0			0
$637$	−191.085	+	51.2012i	−0.299977	+	0.0803786i
$638$	−89.6413	+	89.6413i	−0.140504	+	0.140504i
$639$		0			0
$640$	156.420	−	347.994i	0.244406	−	0.543741i
$641$	−23.6061	+	40.8870i	−0.0368270	+	0.0637863i	−0.883851	−	0.467768i	$-0.845058\pi$
$641$	−23.6061	+	40.8870i	−0.0368270	+	0.0637863i	0.847024	+	0.531554i	$0.178392\pi$
$642$		0			0
$643$	−628.880	−	168.508i	−0.978041	−	0.262065i	−0.265822	−	0.964022i	$-0.585643\pi$
$643$	−628.880	−	168.508i	−0.978041	−	0.262065i	−0.712219	+	0.701957i	$0.752310\pi$
$644$	−269.071	+	155.348i	−0.417813	+	0.241224i
$645$		0			0
$646$	−33.9092	+	58.7324i	−0.0524910	+	0.0909171i
$647$	−281.287	−	281.287i	−0.434756	−	0.434756i	0.455487	−	0.890243i	$-0.349465\pi$
$647$	−281.287	−	281.287i	−0.434756	−	0.434756i	−0.890243	+	0.455487i	$0.849465\pi$
$648$		0			0
$649$		−	453.192i		−	0.698293i
$650$	−12.5344	−	61.1000i	−0.0192837	−	0.0940000i
$651$		0			0
$652$	−186.391	+	695.622i	−0.285876	+	1.06690i
$653$	−122.700	−	32.8775i	−0.187903	−	0.0503484i	0.163641	−	0.986520i	$-0.447676\pi$
$653$	−122.700	−	32.8775i	−0.187903	−	0.0503484i	−0.351543	+	0.936172i	$0.614343\pi$
$654$		0			0
$655$	84.8773	−	523.849i	0.129584	−	0.799770i
$656$	−10.3133			−0.0157214
$657$		0			0
$658$	−68.6061	+	68.6061i	−0.104265	+	0.104265i
$659$	−936.379	−	540.619i	−1.42091	−	0.820362i	−0.424532	−	0.905413i	$-0.639561\pi$
$659$	−936.379	−	540.619i	−1.42091	−	0.820362i	−0.996377	+	0.0850507i	$0.972895\pi$
$660$		0			0
$661$	316.196	+	547.668i	0.478361	+	0.828545i	0.999692	−	0.0248092i	$-0.00789783\pi$
$661$	316.196	+	547.668i	0.478361	+	0.828545i	−0.521332	+	0.853354i	$0.674564\pi$
$662$	−20.1891	+	75.3468i	−0.0304971	+	0.113817i
$663$		0			0
$664$	40.4231	+	23.3383i	0.0608781	+	0.0351480i
$665$	86.9694	−	193.485i	0.130781	−	0.290954i
$666$		0			0
$667$	405.959	+	405.959i	0.608634	+	0.608634i
$668$	−64.2709	−	239.862i	−0.0962139	−	0.359075i
$669$		0			0
$670$	64.0686	−	78.5463i	0.0956248	−	0.117233i
$671$	−33.5301	−	58.0758i	−0.0499703	−	0.0865512i
$672$		0			0
$673$	85.3911	+	318.684i	0.126881	+	0.473527i	0.999900	−	0.0141597i	$-0.00450734\pi$
$673$	85.3911	+	318.684i	0.126881	+	0.473527i	−0.873018	+	0.487687i	$0.837841\pi$
$674$			96.1046i			0.142588i
$675$		0			0
$676$	418.687			0.619359
$677$	66.0996	−	17.7113i	0.0976360	−	0.0261615i	−0.209670	−	0.977772i	$-0.567239\pi$
$677$	66.0996	−	17.7113i	0.0976360	−	0.0261615i	0.307306	+	0.951611i	$0.400572\pi$
$678$		0			0
$679$	−146.953	+	84.8434i	−0.216426	+	0.124953i
$680$	−238.655	−	194.666i	−0.350964	−	0.286274i
$681$		0			0
$682$	−37.2688	+	9.98614i	−0.0546463	+	0.0146424i
$683$	213.410	−	213.410i	0.312459	−	0.312459i	−0.533402	−	0.845862i	$-0.679087\pi$
$683$	213.410	−	213.410i	0.312459	−	0.312459i	0.845862	+	0.533402i	$0.179087\pi$
$684$		0			0
$685$	1074.69	+	483.060i	1.56888	+	0.705197i
$686$	−57.5255	+	99.6371i	−0.0838564	+	0.145244i
$687$		0			0
$688$	−535.578	−	143.508i	−0.778457	−	0.208587i
$689$	−6.70020	+	3.86836i	−0.00972453	+	0.00561446i
$690$		0			0
$691$	−75.5607	+	130.875i	−0.109350	+	0.189399i	−0.915507	−	0.402302i	$-0.868210\pi$
$691$	−75.5607	+	130.875i	−0.109350	+	0.189399i	0.806157	+	0.591701i	$0.201544\pi$
$692$	−571.712	−	571.712i	−0.826173	−	0.826173i
$693$		0			0
$694$		−	71.9408i		−	0.103661i
$695$	−943.552	−	152.880i	−1.35763	−	0.219971i
$696$		0			0
$697$	−4.42555	+	16.5164i	−0.00634942	+	0.0236964i
$698$	−91.4910	−	24.5149i	−0.131076	−	0.0351217i
$699$		0			0
$700$	396.948	+	261.807i	0.567069	+	0.374010i
$701$	−745.680			−1.06374			−0.531869	−	0.846827i	$-0.678510\pi$
$701$	−745.680			−1.06374			−0.531869	+	0.846827i	$0.678510\pi$
$702$		0			0
$703$	52.5765	−	52.5765i	0.0747888	−	0.0747888i
$704$	−535.680	−	309.275i	−0.760908	−	0.439311i
$705$		0			0
$706$	5.06123	+	8.76631i	0.00716888	+	0.0124169i
$707$	−133.357	+	497.695i	−0.188624	+	0.703954i
$708$		0			0
$709$	−622.715	−	359.524i	−0.878300	−	0.507087i	−0.00820246	−	0.999966i	$-0.502611\pi$
$709$	−622.715	−	359.524i	−0.878300	−	0.507087i	−0.870097	+	0.492880i	$0.835944\pi$
$710$	98.5653	+	44.3041i	0.138824	+	0.0624001i
$711$		0			0
$712$	145.893	+	145.893i	0.204906	+	0.204906i
$713$	45.2243	+	168.779i	0.0634282	+	0.236717i
$714$		0			0
$715$	−443.128	+	44.9845i	−0.619759	+	0.0629154i
$716$	−358.144	−	620.324i	−0.500201	−	0.866374i
$717$		0			0
$718$	−3.97100	−	14.8200i	−0.00553065	−	0.0206407i
$719$		−	605.271i		−	0.841824i	−0.907101	−	0.420912i	$-0.861710\pi$
$719$		−	605.271i		−	0.841824i	0.907101	−	0.420912i	$-0.138290\pi$
$720$		0			0
$721$	−615.716			−0.853975
$722$	−87.6086	+	23.4746i	−0.121342	+	0.0325134i
$723$		0			0
$724$	966.632	−	558.085i	1.33513	−	0.770836i
$725$	277.448	−	833.707i	0.382687	−	1.14994i
$726$		0			0
$727$	336.214	−	90.0884i	0.462468	−	0.123918i	−0.0200593	−	0.999799i	$-0.506386\pi$
$727$	336.214	−	90.0884i	0.462468	−	0.123918i	0.482528	+	0.875881i	$0.339719\pi$
$728$	−67.9796	+	67.9796i	−0.0933786	+	0.0933786i
$729$		0			0
$730$	−163.434	+	62.0714i	−0.223882	+	0.0850294i
$731$	−459.646	+	796.130i	−0.628791	+	1.08910i
$732$		0			0
$733$	369.869	+	99.1060i	0.504596	+	0.135206i	0.502132	−	0.864791i	$-0.332549\pi$
$733$	369.869	+	99.1060i	0.504596	+	0.135206i	0.00246376	+	0.999997i	$0.499216\pi$
$734$	57.0318	−	32.9273i	0.0776999	−	0.0448601i
$735$		0			0
$736$	120.435	−	208.599i	0.163634	−	0.283423i
$737$	−511.828	−	511.828i	−0.694474	−	0.694474i
$738$		0			0
$739$		−	515.666i		−	0.697789i	−0.937162	−	0.348895i	$-0.886557\pi$
$739$		−	515.666i		−	0.697789i	0.937162	−	0.348895i	$-0.113443\pi$
$740$	97.4877	+	135.187i	0.131740	+	0.182685i
$741$		0			0
$742$	−0.395531	+	1.47614i	−0.000533060	+	0.00198941i
$743$	−574.689	−	153.987i	−0.773471	−	0.207251i	−0.149567	−	0.988752i	$-0.547788\pi$
$743$	−574.689	−	153.987i	−0.773471	−	0.207251i	−0.623904	+	0.781501i	$0.714455\pi$
$744$		0			0
$745$	418.806	+	67.8575i	0.562156	+	0.0910839i
$746$	38.7490			0.0519424
$747$		0			0
$748$	−767.626	+	767.626i	−1.02624	+	1.02624i
$749$	−410.714	−	237.126i	−0.548350	−	0.316590i
$750$		0			0
$751$	429.893	+	744.597i	0.572428	+	0.991474i	0.996316	+	0.0857596i	$0.0273317\pi$
$751$	429.893	+	744.597i	0.572428	+	0.991474i	−0.423888	+	0.905715i	$0.639335\pi$
$752$	−239.663	+	894.435i	−0.318701	+	1.18941i
$753$		0			0
$754$	75.9389	+	43.8434i	0.100715	+	0.0581477i
$755$	−696.318	+	264.459i	−0.922275	+	0.350276i
$756$		0			0
$757$	−956.075	−	956.075i	−1.26298	−	1.26298i	−0.949642	−	0.313337i	$-0.898553\pi$
$757$	−956.075	−	956.075i	−1.26298	−	1.26298i	−0.313337	−	0.949642i	$-0.601447\pi$
$758$	17.2751	+	64.4715i	0.0227904	+	0.0850548i
$759$		0			0
$760$	11.0260	+	108.614i	0.0145080	+	0.142913i
$761$	161.379	+	279.517i	0.212062	+	0.367302i	0.952360	−	0.304977i	$-0.0986488\pi$
$761$	161.379	+	279.517i	0.212062	+	0.367302i	−0.740298	+	0.672279i	$0.765315\pi$
$762$		0			0
$763$	−86.7368	−	323.706i	−0.113679	−	0.424255i
$764$		−	187.505i		−	0.245426i
$765$		0			0
$766$	−4.77858			−0.00623835
$767$	−302.786	+	81.1314i	−0.394767	+	0.105778i
$768$		0			0
$769$	599.638	−	346.201i	0.779763	−	0.450196i	−0.0565833	−	0.998398i	$-0.518021\pi$
$769$	599.638	−	346.201i	0.779763	−	0.450196i	0.836346	+	0.548202i	$0.184687\pi$
$770$	−55.6098	+	68.1760i	−0.0722205	+	0.0885402i
$771$		0			0
$772$	−1361.17	+	364.724i	−1.76317	+	0.472440i
$773$	375.226	−	375.226i	0.485415	−	0.485415i	−0.421441	−	0.906856i	$-0.638475\pi$
$773$	375.226	−	375.226i	0.485415	−	0.485415i	0.906856	+	0.421441i	$0.138475\pi$
$774$		0			0
$775$	200.000	−	177.526i	0.258065	−	0.229065i
$776$	43.6640	−	75.6283i	0.0562681	−	0.0974592i
$777$		0			0
$778$	−164.352	−	44.0381i	−0.211250	−	0.0566042i
$779$	5.24918	−	3.03062i	0.00673836	−	0.00389039i
$780$		0			0
$781$	385.848	−	668.308i	0.494043	−	0.855708i
$782$	−90.0704	−	90.0704i	−0.115180	−	0.115180i
$783$		0			0
$784$			372.939i			0.475687i
$785$	96.6609	−	69.7052i	0.123135	−	0.0887965i
$786$		0			0
$787$	333.445	−	1244.44i	0.423692	−	1.58124i	−0.343072	−	0.939309i	$-0.611467\pi$
$787$	333.445	−	1244.44i	0.423692	−	1.58124i	0.766763	−	0.641930i	$-0.221866\pi$
$788$	515.018	+	137.999i	0.653576	+	0.175125i
$789$		0			0
$790$	−22.7687	−	31.5736i	−0.0288212	−	0.0399666i
$791$	673.626			0.851613
$792$		0			0
$793$	−32.7990	+	32.7990i	−0.0413606	+	0.0413606i
$794$	−46.2228	−	26.6867i	−0.0582151	−	0.0336105i
$795$		0			0
$796$	−375.484	−	650.357i	−0.471713	−	0.817031i
$797$	−2.64154	+	9.85838i	−0.00331436	+	0.0123694i	−0.967563	−	0.252629i	$-0.918705\pi$
$797$	−2.64154	+	9.85838i	−0.00331436	+	0.0123694i	0.964249	+	0.264998i	$0.0853714\pi$
$798$		0			0
$799$	1329.57	+	767.626i	1.66404	+	0.960733i
$800$	−367.991	−	21.9069i	−0.459989	−	0.0273836i
$801$		0			0
$802$	94.4607	+	94.4607i	0.117781	+	0.117781i
$803$	323.117	+	1205.89i	0.402387	+	1.50173i
$804$		0			0
$805$	308.749	+	251.840i	0.383539	+	0.312845i
$806$	13.3439	+	23.1123i	0.0165557	+	0.0286753i
$807$		0			0
$808$	−68.6313	−	256.135i	−0.0849397	−	0.316999i
$809$		−	150.000i		−	0.185414i	−0.995693	−	0.0927070i	$-0.970448\pi$
$809$		−	150.000i		−	0.185414i	0.995693	−	0.0927070i	$-0.0295520\pi$
$810$		0			0
$811$	1336.85			1.64839			0.824197	−	0.566304i	$-0.191627\pi$
$811$	1336.85			1.64839			0.824197	+	0.566304i	$0.191627\pi$
$812$	−645.722	+	173.021i	−0.795224	+	0.213080i
$813$		0			0
$814$	−26.7063	+	15.4189i	−0.0328087	+	0.0189421i
$815$	918.803	−	93.2730i	1.12737	−	0.114445i
$816$		0			0
$817$	314.766	−	84.3412i	0.385270	−	0.103233i
$818$	115.768	−	115.768i	0.141526	−	0.141526i
$819$		0			0
$820$	4.82399	+	12.7015i	0.00588291	+	0.0154897i
$821$	16.9467	−	29.3525i	0.0206415	−	0.0357521i	−0.855520	−	0.517770i	$-0.826762\pi$
$821$	16.9467	−	29.3525i	0.0206415	−	0.0357521i	0.876162	+	0.482017i	$0.160096\pi$
$822$		0			0
$823$	−657.920	−	176.289i	−0.799417	−	0.214203i	−0.164089	−	0.986446i	$-0.552468\pi$
$823$	−657.920	−	176.289i	−0.799417	−	0.214203i	−0.635328	+	0.772242i	$0.719135\pi$
$824$	274.421	−	158.437i	0.333035	−	0.192278i
$825$		0			0
$826$	−30.9592	+	53.6229i	−0.0374808	+	0.0649187i
$827$	350.756	+	350.756i	0.424131	+	0.424131i	0.886623	−	0.462492i	$-0.153045\pi$
$827$	350.756	+	350.756i	0.424131	+	0.424131i	−0.462492	+	0.886623i	$0.653045\pi$
$828$		0			0
$829$		−	697.423i		−	0.841283i	−0.907227	−	0.420641i	$-0.861805\pi$
$829$		−	697.423i		−	0.841283i	0.907227	−	0.420641i	$-0.138195\pi$
$830$	4.72558	−	29.1656i	0.00569347	−	0.0351392i
$831$		0			0
$832$	−110.734	+	413.265i	−0.133094	+	0.496713i
$833$	597.249	+	160.032i	0.716986	+	0.192116i
$834$		0			0
$835$	−258.292	+	186.263i	−0.309332	+	0.223069i
$836$	384.817			0.460308
$837$		0			0
$838$	19.9127	−	19.9127i	0.0237622	−	0.0237622i
$839$	−62.6764	−	36.1862i	−0.0747037	−	0.0431302i	0.462183	−	0.886785i	$-0.347066\pi$
$839$	−62.6764	−	36.1862i	−0.0747037	−	0.0431302i	−0.536887	+	0.843654i	$0.680400\pi$
$840$		0			0
$841$	197.136	+	341.449i	0.234406	+	0.406004i
$842$	−21.1538	+	78.9472i	−0.0251233	+	0.0937615i
$843$		0			0
$844$	497.079	+	286.989i	0.588956	+	0.340034i
$845$	−190.633	−	501.936i	−0.225602	−	0.594008i
$846$		0			0
$847$	26.8638	+	26.8638i	0.0317164	+	0.0317164i
$848$	3.77492	+	14.0882i	0.00445155	+	0.0166134i
$849$		0			0
$850$	−61.5576	+	184.975i	−0.0724207	+	0.217618i
$851$	69.8275	+	120.945i	0.0820535	+	0.142121i
$852$		0			0
$853$	−27.2945	−	101.864i	−0.0319982	−	0.119419i	0.948079	−	0.318034i	$-0.103022\pi$
$853$	−27.2945	−	101.864i	−0.0319982	−	0.119419i	−0.980078	+	0.198615i	$0.936356\pi$
$854$			9.16225i			0.0107286i
$855$		0			0
$856$	244.070			0.285129
$857$	400.486	−	107.310i	0.467311	−	0.125216i	−0.0174768	−	0.999847i	$-0.505563\pi$
$857$	400.486	−	107.310i	0.467311	−	0.125216i	0.484788	+	0.874632i	$0.338897\pi$
$858$		0			0
$859$	−681.447	+	393.434i	−0.793303	+	0.458014i	−0.841124	−	0.540842i	$-0.818106\pi$
$859$	−681.447	+	393.434i	−0.793303	+	0.458014i	0.0478212	+	0.998856i	$0.484772\pi$
$860$	73.7744	+	726.728i	0.0857842	+	0.845032i
$861$		0			0
$862$	−247.029	+	66.1912i	−0.286577	+	0.0767879i
$863$	−1072.68	+	1072.68i	−1.24297	+	1.24297i	−0.284204	+	0.958764i	$0.591729\pi$
$863$	−1072.68	+	1072.68i	−1.24297	+	1.24297i	−0.958764	+	0.284204i	$0.908271\pi$
$864$		0			0
$865$	−425.081	+	945.696i	−0.491423	+	1.09329i
$866$	77.5028	−	134.239i	0.0894952	−	0.155010i
$867$		0			0
$868$	−196.528	−	52.6595i	−0.226415	−	0.0606676i
$869$	−240.737	+	138.990i	−0.277028	+	0.159942i
$870$		0			0
$871$	−250.334	+	433.591i	−0.287410	+	0.497808i
$872$	121.955	+	121.955i	0.139856	+	0.139856i
$873$		0			0
$874$			45.1531i			0.0516626i
$875$	133.128	−	595.080i	0.152147	−	0.680091i
$876$		0			0
$877$	87.6483	−	327.108i	0.0999411	−	0.372985i	−0.897781	−	0.440442i	$-0.854822\pi$
$877$	87.6483	−	327.108i	0.0999411	−	0.372985i	0.997722	+	0.0674567i	$0.0214884\pi$
$878$	132.912	+	35.6137i	0.151381	+	0.0405623i
$879$		0			0
$880$	−134.297	+	828.862i	−0.152610	+	0.941888i
$881$	62.8490			0.0713382			0.0356691	−	0.999364i	$-0.488644\pi$
$881$	62.8490			0.0713382			0.0356691	+	0.999364i	$0.488644\pi$
$882$		0			0
$883$	−158.061	+	158.061i	−0.179005	+	0.179005i	−0.790922	−	0.611917i	$-0.790399\pi$
$883$	−158.061	+	158.061i	−0.179005	+	0.179005i	0.611917	+	0.790922i	$0.290399\pi$
$884$	650.288	+	375.444i	0.735620	+	0.424710i
$885$		0			0
$886$	−55.0918	−	95.4219i	−0.0621804	−	0.107700i
$887$	11.0564	−	41.2630i	0.0124649	−	0.0465198i	−0.959413	−	0.282004i	$-0.909001\pi$
$887$	11.0564	−	41.2630i	0.0124649	−	0.0465198i	0.971878	+	0.235484i	$0.0756676\pi$
$888$		0			0
$889$	−983.559	−	567.858i	−1.10637	−	0.638761i
$890$	53.5439	−	119.121i	0.0601616	−	0.133844i
$891$		0			0
$892$	−652.803	−	652.803i	−0.731841	−	0.731841i
$893$	−140.853	−	525.670i	−0.157730	−	0.588657i
$894$		0			0
$895$	−580.599	+	711.797i	−0.648713	+	0.795304i
$896$	186.124	+	322.376i	0.207727	+	0.359794i
$897$		0			0
$898$	−31.7607	−	118.533i	−0.0353683	−	0.131996i
$899$			375.959i			0.418197i
$900$		0			0
$901$	24.1816			0.0268387
$902$	−2.42818	+	0.650628i	−0.00269199	+	0.000721317i
$903$		0			0
$904$	−300.231	+	173.338i	−0.332114	+	0.191746i
$905$	−1109.17	−	904.729i	−1.22560	−	0.999701i
$906$		0			0
$907$	−780.467	+	209.126i	−0.860493	+	0.230568i	−0.661972	−	0.749528i	$-0.730280\pi$
$907$	−780.467	+	209.126i	−0.860493	+	0.230568i	−0.198521	+	0.980097i	$0.563614\pi$
$908$	987.110	−	987.110i	1.08713	−	1.08713i
$909$		0			0
$910$	55.5051	+	24.9490i	0.0609946	+	0.0274165i
$911$	−86.6811	+	150.136i	−0.0951494	+	0.164804i	−0.909671	−	0.415330i	$-0.863666\pi$
$911$	−86.6811	+	150.136i	−0.0951494	+	0.164804i	0.814522	+	0.580133i	$0.197000\pi$
$912$		0			0
$913$	−203.800	−	54.6080i	−0.223220	−	0.0598116i
$914$	−87.0979	+	50.2860i	−0.0952931	+	0.0550175i
$915$		0			0
$916$	437.080	−	757.044i	0.477161	−	0.826467i
$917$	366.116	+	366.116i	0.399254	+	0.399254i
$918$		0			0
$919$			1147.42i			1.24856i	0.781202	+	0.624278i	$0.214607\pi$
$919$			1147.42i			1.24856i	−0.781202	+	0.624278i	$0.785393\pi$
$920$	−202.411	−	32.7959i	−0.220012	−	0.0356477i
$921$		0			0
$922$	−59.4444	+	221.850i	−0.0644733	+	0.240618i
$923$	−515.585	−	138.151i	−0.558597	−	0.149676i
$924$		0			0
$925$	117.680	−	178.424i	0.127221	−	0.192891i
$926$	−58.2995			−0.0629584
$927$		0			0
$928$	366.464	−	366.464i	0.394897	−	0.394897i
$929$	190.779	+	110.146i	0.205360	+	0.118565i	0.599153	−	0.800635i	$-0.295504\pi$
$929$	190.779	+	110.146i	0.205360	+	0.118565i	−0.393793	+	0.919199i	$0.628837\pi$
$930$		0			0
$931$	−109.590	−	189.816i	−0.117712	−	0.203884i
$932$	293.576	−	1095.64i	0.314996	−	1.17558i
$933$		0			0
$934$	−161.647	−	93.3270i	−0.173070	−	0.0999219i
$935$	1269.77	+	570.747i	1.35804	+	0.610425i
$936$		0			0
$937$	−396.090	−	396.090i	−0.422721	−	0.422721i	0.463418	−	0.886140i	$-0.346623\pi$
$937$	−396.090	−	396.090i	−0.422721	−	0.422721i	−0.886140	+	0.463418i	$0.846623\pi$
$938$	25.5960	+	95.5256i	0.0272879	+	0.101840i
$939$		0			0
$940$	1213.66	−	123.206i	1.29113	−	0.131070i
$941$	−92.8854	−	160.882i	−0.0987093	−	0.170970i	0.812441	−	0.583043i	$-0.198138\pi$
$941$	−92.8854	−	160.882i	−0.0987093	−	0.170970i	−0.911151	+	0.412073i	$0.864805\pi$
$942$		0			0
$943$	2.94650	+	10.9965i	0.00312461	+	0.0116612i
$944$			590.944i			0.626000i
$945$		0			0
$946$	−135.151			−0.142866
$947$	1154.55	−	309.361i	1.21917	−	0.326675i	0.408814	−	0.912618i	$-0.365942\pi$
$947$	1154.55	−	309.361i	1.21917	−	0.326675i	0.810352	+	0.585943i	$0.199276\pi$
$948$		0			0
$949$	747.833	−	431.762i	0.788022	−	0.454965i
$950$	61.7945	−	30.9351i	0.0650468	−	0.0325633i
$951$		0			0
$952$	290.246	−	77.7711i	0.304880	−	0.0816923i
$953$	−630.499	+	630.499i	−0.661594	+	0.661594i	−0.955756	−	0.294161i	$-0.904960\pi$
$953$	−630.499	+	630.499i	−0.661594	+	0.661594i	0.294161	+	0.955756i	$0.404960\pi$
$954$		0			0
$955$	−224.788	+	85.3735i	−0.235380	+	0.0893963i
$956$	674.130	−	1167.63i	0.705156	−	1.22137i
$957$		0			0
$958$	93.6215	+	25.0858i	0.0977260	+	0.0261856i
$959$	−995.570	+	574.792i	−1.03813	+	0.599366i
$960$		0			0
$961$	423.288	−	733.156i	0.440466	−	0.762909i
$962$	15.0827	+	15.0827i	0.0156785	+	0.0156785i
$963$		0			0
$964$		−	396.041i		−	0.410831i
$965$	1057.00	+	1465.75i	1.09534	+	1.51891i
$966$		0			0
$967$	−139.708	+	521.399i	−0.144476	+	0.539192i	0.855302	+	0.518130i	$0.173372\pi$
$967$	−139.708	+	521.399i	−0.144476	+	0.539192i	−0.999778	+	0.0210624i	$0.993295\pi$
$968$	−18.8856	−	5.06039i	−0.0195100	−	0.00522768i
$969$		0			0
$970$	−54.5665	−	8.84119i	−0.0562541	−	0.00911463i
$971$	−1000.44			−1.03032			−0.515159	−	0.857095i	$-0.672267\pi$
$971$	−1000.44			−1.03032			−0.515159	+	0.857095i	$0.672267\pi$
$972$		0			0
$973$	659.444	−	659.444i	0.677743	−	0.677743i
$974$	167.120	+	96.4870i	0.171581	+	0.0990626i
$975$		0			0
$976$	43.7219	+	75.7286i	0.0447971	+	0.0775908i
$977$	217.295	−	810.957i	0.222411	−	0.830048i	−0.761015	−	0.648735i	$-0.775298\pi$
$977$	217.295	−	810.957i	0.222411	−	0.830048i	0.983425	−	0.181313i	$-0.0580348\pi$
$978$		0			0
$979$	−807.686	−	466.318i	−0.825011	−	0.476321i
$980$	459.301	−	174.441i	0.468674	−	0.178001i
$981$		0			0
$982$	−93.1158	−	93.1158i	−0.0948226	−	0.0948226i
$983$	−445.576	−	1662.91i	−0.453282	−	1.69167i	−0.693090	−	0.720852i	$-0.743751\pi$
$983$	−445.576	−	1662.91i	−0.453282	−	1.69167i	0.239807	−	0.970820i	$-0.422916\pi$
$984$		0			0
$985$	−69.0566	−	680.254i	−0.0701082	−	0.690614i
$986$	−137.035	−	237.352i	−0.138981	−	0.240722i
$987$		0			0
$988$	−68.8908	−	257.104i	−0.0697276	−	0.260227i
$989$			612.059i			0.618867i
$990$		0			0
$991$	−544.061			−0.549002			−0.274501	−	0.961587i	$-0.588513\pi$
$991$	−544.061			−0.549002			−0.274501	+	0.961587i	$0.588513\pi$
$992$	152.359	−	40.8245i	0.153588	−	0.0411538i
$993$		0			0
$994$	−91.3091	+	52.7173i	−0.0918603	+	0.0530356i
$995$	−608.708	+	746.259i	−0.611767	+	0.750009i
$996$		0			0
$997$	432.666	−	115.932i	0.433967	−	0.116281i	−0.0352205	−	0.999380i	$-0.511213\pi$
$997$	432.666	−	115.932i	0.433967	−	0.116281i	0.469188	+	0.883098i	$0.344547\pi$
$998$	−82.6128	+	82.6128i	−0.0827783	+	0.0827783i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.l.h.217.1		8
3.2	odd	2		405.3.l.f.217.2		8
5.3	odd	4	inner	405.3.l.h.298.2		8
9.2	odd	6		45.3.g.b.37.1		4
9.4	even	3	inner	405.3.l.h.352.2		8
9.5	odd	6		405.3.l.f.352.1		8
9.7	even	3		15.3.f.a.7.2	✓	4
15.8	even	4		405.3.l.f.298.1		8
36.7	odd	6		240.3.bg.a.97.2		4
36.11	even	6		720.3.bh.k.577.2		4
45.2	even	12		225.3.g.a.118.2		4
45.7	odd	12		75.3.f.c.43.1		4
45.13	odd	12	inner	405.3.l.h.28.1		8
45.23	even	12		405.3.l.f.28.2		8
45.29	odd	6		225.3.g.a.82.2		4
45.34	even	6		75.3.f.c.7.1		4
45.38	even	12		45.3.g.b.28.1		4
45.43	odd	12		15.3.f.a.13.2	yes	4
72.43	odd	6		960.3.bg.h.577.1		4
72.61	even	6		960.3.bg.i.577.2		4
180.7	even	12		1200.3.bg.k.193.1		4
180.43	even	12		240.3.bg.a.193.2		4
180.79	odd	6		1200.3.bg.k.1057.1		4
180.83	odd	12		720.3.bh.k.433.2		4
360.43	even	12		960.3.bg.h.193.1		4
360.133	odd	12		960.3.bg.i.193.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.3.f.a.7.2	✓	4	9.7	even	3
15.3.f.a.13.2	yes	4	45.43	odd	12
45.3.g.b.28.1		4	45.38	even	12
45.3.g.b.37.1		4	9.2	odd	6
75.3.f.c.7.1		4	45.34	even	6
75.3.f.c.43.1		4	45.7	odd	12
225.3.g.a.82.2		4	45.29	odd	6
225.3.g.a.118.2		4	45.2	even	12
240.3.bg.a.97.2		4	36.7	odd	6
240.3.bg.a.193.2		4	180.43	even	12
405.3.l.f.28.2		8	45.23	even	12
405.3.l.f.217.2		8	3.2	odd	2
405.3.l.f.298.1		8	15.8	even	4
405.3.l.f.352.1		8	9.5	odd	6
405.3.l.h.28.1		8	45.13	odd	12	inner
405.3.l.h.217.1		8	1.1	even	1	trivial
405.3.l.h.298.2		8	5.3	odd	4	inner
405.3.l.h.352.2		8	9.4	even	3	inner
720.3.bh.k.433.2		4	180.83	odd	12
720.3.bh.k.577.2		4	36.11	even	6
960.3.bg.h.193.1		4	360.43	even	12
960.3.bg.h.577.1		4	72.43	odd	6
960.3.bg.i.193.2		4	360.133	odd	12
960.3.bg.i.577.2		4	72.61	even	6
1200.3.bg.k.193.1		4	180.7	even	12
1200.3.bg.k.1057.1		4	180.79	odd	6

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.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.307007 + 0.0822623i) q^{2} +(-3.37662 + 1.94949i) q^{4} +(3.87453 + 3.16038i) q^{5} +(-4.71209 + 1.26260i) q^{7} +(1.77526 - 1.77526i) q^{8} +(-1.44949 - 0.651531i) q^{10} +(-5.67423 + 9.82806i) q^{11} +(7.58214 + 2.03163i) q^{13} +(1.34278 - 0.775255i) q^{14} +(7.39898 - 12.8154i) q^{16} +(-17.3485 - 17.3485i) q^{17} +8.69694i q^{19} +(-19.2439 - 3.11802i) q^{20} +(0.933552 - 3.48406i) q^{22} +(-15.7783 - 4.22778i) q^{23} +(5.02402 + 24.4900i) q^{25} -2.49490 q^{26} +(13.4495 - 13.4495i) q^{28} +(-30.4377 - 17.5732i) q^{29} +(-5.34847 - 9.26382i) q^{31} +(-3.81647 + 14.2433i) q^{32} +(6.75323 + 3.89898i) q^{34} +(-22.2474 - 10.0000i) q^{35} +(-6.04541 - 6.04541i) q^{37} +(-0.715430 - 2.67002i) q^{38} +(12.4888 - 1.26781i) q^{40} +(-0.348469 - 0.603566i) q^{41} +(-9.69781 - 36.1927i) q^{43} -44.2474i q^{44} +5.19184 q^{46} +(-60.4431 + 16.1957i) q^{47} +(-21.8256 + 12.6010i) q^{49} +(-3.55701 - 7.10531i) q^{50} +(-29.5626 + 7.92127i) q^{52} +(-0.696938 + 0.696938i) q^{53} +(-53.0454 + 20.1464i) q^{55} +(-6.12372 + 10.6066i) q^{56} +(10.7902 + 2.89123i) q^{58} +(-34.5840 + 19.9671i) q^{59} +(-2.95459 + 5.11750i) q^{61} +(2.40408 + 2.40408i) q^{62} +54.5051i q^{64} +(22.9565 + 31.8340i) q^{65} +(-16.5081 + 61.6091i) q^{67} +(92.3998 + 24.7584i) q^{68} +(7.65275 + 1.23995i) q^{70} -68.0000 q^{71} +(77.7878 - 77.7878i) q^{73} +(2.35329 + 1.35867i) q^{74} +(-16.9546 - 29.3662i) q^{76} +(14.3286 - 53.4750i) q^{77} +(21.2132 + 12.2474i) q^{79} +(69.1691 - 26.2702i) q^{80} +(0.156633 + 0.156633i) q^{82} +(4.81193 + 17.9584i) q^{83} +(-12.3895 - 122.045i) q^{85} +(5.95459 + 10.3137i) q^{86} +(7.37410 + 27.5205i) q^{88} +82.1816i q^{89} -38.2929 q^{91} +(61.5192 - 16.4840i) q^{92} +(17.2242 - 9.94439i) q^{94} +(-27.4856 + 33.6966i) q^{95} +(33.5986 - 9.00273i) q^{97} +(5.66403 - 5.66403i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 4 q^{5} - 4 q^{7} + 24 q^{8} + 8 q^{10} - 16 q^{11} + 32 q^{13} + 20 q^{16} - 80 q^{17} + 36 q^{20} - 20 q^{22} - 56 q^{23} - 16 q^{25} + 176 q^{26} + 88 q^{28} + 16 q^{31} + 76 q^{32} - 80 q^{35}+ \cdots - 376 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 + 24 * q^8 + 8 * q^10 - 16 * q^11 + 32 * q^13 + 20 * q^16 - 80 * q^17 + 36 * q^20 - 20 * q^22 - 56 * q^23 - 16 * q^25 + 176 * q^26 + 88 * q^28 + 16 * q^31 + 76 * q^32 - 80 * q^35 + 128 * q^37 + 96 * q^38 - 48 * q^40 + 56 * q^41 + 8 * q^43 - 272 * q^46 - 128 * q^47 - 164 * q^50 + 80 * q^52 + 112 * q^53 - 248 * q^55 + 12 * q^58 - 200 * q^61 + 176 * q^62 + 112 * q^65 + 200 * q^67 + 104 * q^68 + 60 * q^70 - 544 * q^71 + 152 * q^73 - 312 * q^76 - 88 * q^77 + 328 * q^80 + 256 * q^82 + 16 * q^83 - 232 * q^85 + 224 * q^86 - 12 * q^88 - 32 * q^91 - 104 * q^92 - 144 * q^95 + 20 * q^97 - 376 * q^98

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