LMFDB - Embedded newform 405.3.n.a.179.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(44,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("405.44");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.n (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			179.33
Character	$\chi$	$=$	405.179
Dual form			405.3.n.a.224.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.50983 + 1.27747i) q^{2} +(7.62280 + 6.39629i) q^{4} +(3.38697 + 3.67811i) q^{5} +(1.03030 + 1.22786i) q^{7} +(11.1135 + 19.2491i) q^{8} +(7.18899 + 17.2363i) q^{10} +(-11.9341 + 2.10430i) q^{11} +(-4.71168 - 12.9452i) q^{13} +(2.04761 + 5.62576i) q^{14} +(7.50440 + 42.5596i) q^{16} +(8.93265 - 15.4718i) q^{17} +(-14.5705 - 25.2368i) q^{19} +(2.29194 + 49.7015i) q^{20} +(-44.5747 - 7.85972i) q^{22} +(22.0238 + 18.4801i) q^{23} +(-2.05692 + 24.9152i) q^{25} -51.4546i q^{26} +15.9498i q^{28} +(6.96737 - 19.1427i) q^{29} +(-5.05373 - 4.24059i) q^{31} +(-12.5909 + 71.4065i) q^{32} +(51.1169 - 42.8922i) q^{34} +(-1.02662 + 7.94827i) q^{35} +(33.0454 + 19.0788i) q^{37} +(-18.9005 - 107.190i) q^{38} +(-33.1593 + 106.073i) q^{40} +(16.8042 + 46.1691i) q^{41} +(23.8547 - 4.20622i) q^{43} +(-104.431 - 60.2930i) q^{44} +(53.6918 + 92.9970i) q^{46} +(-5.12070 + 4.29678i) q^{47} +(8.06263 - 45.7255i) q^{49} +(-39.0480 + 84.8206i) q^{50} +(46.8852 - 128.816i) q^{52} -35.3575 q^{53} +(-48.1601 - 36.7675i) q^{55} +(-12.1850 + 33.4781i) q^{56} +(48.9086 - 58.2870i) q^{58} +(-81.0242 - 14.2868i) q^{59} +(-42.3934 + 35.5723i) q^{61} +(-12.3205 - 21.3398i) q^{62} +(-48.9797 + 84.8352i) q^{64} +(31.6556 - 61.1751i) q^{65} +(10.5187 + 28.8998i) q^{67} +(167.054 - 60.8026i) q^{68} +(-13.7570 + 26.5856i) q^{70} +(-46.8725 - 27.0619i) q^{71} +(80.6986 - 46.5914i) q^{73} +(91.6111 + 109.178i) q^{74} +(50.3540 - 285.572i) q^{76} +(-14.8794 - 12.4853i) q^{77} +(27.1542 + 9.88334i) q^{79} +(-131.121 + 171.750i) q^{80} +183.513i q^{82} +(25.7526 + 9.37318i) q^{83} +(87.1615 - 19.5472i) q^{85} +(89.0992 + 15.7106i) q^{86} +(-173.135 - 206.334i) q^{88} +(-41.9166 + 24.2006i) q^{89} +(11.0405 - 19.1227i) q^{91} +(49.6785 + 281.741i) q^{92} +(-23.4618 + 8.53941i) q^{94} +(43.4739 - 139.068i) q^{95} +(133.103 - 23.4697i) q^{97} +(86.7116 - 150.189i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 12 q^{4} - 3 q^{5} - 3 q^{10} - 6 q^{11} + 48 q^{14} + 12 q^{16} - 6 q^{19} - 63 q^{20} - 15 q^{25} - 96 q^{29} - 102 q^{31} + 12 q^{34} + 252 q^{35} + 117 q^{40} - 96 q^{41} + 666 q^{44} - 6 q^{46}+ \cdots + 543 q^{95}+O(q^{100}) $ 204 * q - 12 * q^4 - 3 * q^5 - 3 * q^10 - 6 * q^11 + 48 * q^14 + 12 * q^16 - 6 * q^19 - 63 * q^20 - 15 * q^25 - 96 * q^29 - 102 * q^31 + 12 * q^34 + 252 * q^35 + 117 * q^40 - 96 * q^41 + 666 * q^44 - 6 * q^46 + 60 * q^49 - 48 * q^50 - 12 * q^55 - 294 * q^56 - 510 * q^59 + 132 * q^61 - 486 * q^64 - 147 * q^65 - 141 * q^70 + 18 * q^71 + 954 * q^74 + 84 * q^76 - 48 * q^79 + 69 * q^85 + 1506 * q^86 - 792 * q^89 - 6 * q^91 + 492 * q^94 + 543 * q^95

Character values

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

$n$	$82$	$326$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	3.50983	+	1.27747i	1.75492	+	0.638737i	0.999857	−	0.0169199i	$-0.00538603\pi$
$2$	3.50983	+	1.27747i	1.75492	+	0.638737i	0.755059	+	0.655657i	$0.227608\pi$
$3$		0			0
$3$		0			0
$4$	7.62280	+	6.39629i	1.90570	+	1.59907i
$5$	3.38697	+	3.67811i	0.677393	+	0.735621i
$5$	3.38697	+	3.67811i	0.677393	+	0.735621i
$6$		0			0
$7$	1.03030	+	1.22786i	0.147185	+	0.175409i	0.834600	−	0.550857i	$-0.185699\pi$
$7$	1.03030	+	1.22786i	0.147185	+	0.175409i	−0.687415	+	0.726265i	$0.741254\pi$
$8$	11.1135	+	19.2491i	1.38918	+	2.40614i
$9$		0			0
$10$	7.18899	+	17.2363i	0.718899	+	1.72363i
$11$	−11.9341	+	2.10430i	−1.08491	+	0.191300i	−0.687387	−	0.726291i	$-0.741242\pi$
$11$	−11.9341	+	2.10430i	−1.08491	+	0.191300i	−0.397527	+	0.917591i	$0.630131\pi$
$12$		0			0
$13$	−4.71168	−	12.9452i	−0.362437	−	0.995786i	−0.978165	−	0.207828i	$-0.933361\pi$
$13$	−4.71168	−	12.9452i	−0.362437	−	0.995786i	0.615729	−	0.787958i	$-0.288862\pi$
$14$	2.04761	+	5.62576i	0.146258	+	0.401840i
$15$		0			0
$16$	7.50440	+	42.5596i	0.469025	+	2.65997i
$17$	8.93265	−	15.4718i	0.525450	−	0.910106i	−0.474111	−	0.880465i	$-0.657230\pi$
$17$	8.93265	−	15.4718i	0.525450	−	0.910106i	0.999561	−	0.0296407i	$-0.00943630\pi$
$18$		0			0
$19$	−14.5705	−	25.2368i	−0.766866	−	1.32825i	−0.939254	−	0.343222i	$-0.888482\pi$
$19$	−14.5705	−	25.2368i	−0.766866	−	1.32825i	0.172388	−	0.985029i	$-0.444852\pi$
$20$	2.29194	+	49.7015i	0.114597	+	2.48507i
$21$		0			0
$22$	−44.5747	−	7.85972i	−2.02612	−	0.357260i
$23$	22.0238	+	18.4801i	0.957555	+	0.803484i	0.980554	−	0.196251i	$-0.0628769\pi$
$23$	22.0238	+	18.4801i	0.957555	+	0.803484i	−0.0229985	+	0.999735i	$0.507321\pi$
$24$		0			0
$25$	−2.05692	+	24.9152i	−0.0822769	+	0.996610i
$26$		−	51.4546i		−	1.97902i
$27$		0			0
$28$			15.9498i			0.569636i
$29$	6.96737	−	19.1427i	0.240254	−	0.660092i	−0.759698	−	0.650276i	$-0.774653\pi$
$29$	6.96737	−	19.1427i	0.240254	−	0.660092i	0.999952	−	0.00981620i	$-0.00312464\pi$
$30$		0			0
$31$	−5.05373	−	4.24059i	−0.163024	−	0.136793i	0.557626	−	0.830092i	$-0.311712\pi$
$31$	−5.05373	−	4.24059i	−0.163024	−	0.136793i	−0.720650	+	0.693299i	$0.756157\pi$
$32$	−12.5909	+	71.4065i	−0.393466	+	2.23145i
$33$		0			0
$34$	51.1169	−	42.8922i	1.50344	−	1.26153i
$35$	−1.02662	+	7.94827i	−0.0293320	+	0.227093i
$36$		0			0
$37$	33.0454	+	19.0788i	0.893118	+	0.515642i	0.874961	−	0.484193i	$-0.160887\pi$
$37$	33.0454	+	19.0788i	0.893118	+	0.515642i	0.0181570	+	0.999835i	$0.494220\pi$
$38$	−18.9005	−	107.190i	−0.497382	−	2.82080i
$39$		0			0
$40$	−33.1593	+	106.073i	−0.828982	+	2.65182i
$41$	16.8042	+	46.1691i	0.409858	+	1.12608i	0.957266	+	0.289210i	$0.0933925\pi$
$41$	16.8042	+	46.1691i	0.409858	+	1.12608i	−0.547408	+	0.836866i	$0.684385\pi$
$42$		0			0
$43$	23.8547	−	4.20622i	0.554760	−	0.0978191i	0.110762	−	0.993847i	$-0.464671\pi$
$43$	23.8547	−	4.20622i	0.554760	−	0.0978191i	0.443998	+	0.896028i	$0.353560\pi$
$44$	−104.431	−	60.2930i	−2.37342	−	1.37030i
$45$		0			0
$46$	53.6918	+	92.9970i	1.16721	+	2.02167i
$47$	−5.12070	+	4.29678i	−0.108951	+	0.0914209i	−0.695636	−	0.718395i	$-0.744877\pi$
$47$	−5.12070	+	4.29678i	−0.108951	+	0.0914209i	0.586685	+	0.809815i	$0.300433\pi$
$48$		0			0
$49$	8.06263	−	45.7255i	0.164543	−	0.933173i
$50$	−39.0480	+	84.8206i	−0.780961	+	1.69641i
$51$		0			0
$52$	46.8852	−	128.816i	0.901639	−	2.47723i
$53$	−35.3575			−0.667123			−0.333562	−	0.942728i	$-0.608251\pi$
$53$	−35.3575			−0.667123			−0.333562	+	0.942728i	$0.608251\pi$
$54$		0			0
$55$	−48.1601	−	36.7675i	−0.875637	−	0.668501i
$56$	−12.1850	+	33.4781i	−0.217590	+	0.597824i
$57$		0			0
$58$	48.9086	−	58.2870i	0.843251	−	1.00495i
$59$	−81.0242	−	14.2868i	−1.37329	−	0.242148i	−0.562168	−	0.827023i	$-0.690033\pi$
$59$	−81.0242	−	14.2868i	−1.37329	−	0.242148i	−0.811124	+	0.584874i	$0.801144\pi$
$60$		0			0
$61$	−42.3934	+	35.5723i	−0.694974	+	0.583153i	−0.920339	−	0.391122i	$-0.872087\pi$
$61$	−42.3934	+	35.5723i	−0.694974	+	0.583153i	0.225365	+	0.974274i	$0.427643\pi$
$62$	−12.3205	−	21.3398i	−0.198718	−	0.344190i
$63$		0			0
$64$	−48.9797	+	84.8352i	−0.765307	+	1.32555i
$65$	31.6556	−	61.1751i	0.487009	−	0.941155i
$66$		0			0
$67$	10.5187	+	28.8998i	0.156995	+	0.431340i	0.993106	−	0.117220i	$-0.0373983\pi$
$67$	10.5187	+	28.8998i	0.156995	+	0.431340i	−0.836111	+	0.548560i	$0.815176\pi$
$68$	167.054	−	60.8026i	2.45667	−	0.894156i
$69$		0			0
$70$	−13.7570	+	26.5856i	−0.196528	+	0.379794i
$71$	−46.8725	−	27.0619i	−0.660176	−	0.381153i	0.132168	−	0.991227i	$-0.457806\pi$
$71$	−46.8725	−	27.0619i	−0.660176	−	0.381153i	−0.792344	+	0.610074i	$0.791140\pi$
$72$		0			0
$73$	80.6986	−	46.5914i	1.10546	−	0.638238i	0.167811	−	0.985819i	$-0.446330\pi$
$73$	80.6986	−	46.5914i	1.10546	−	0.638238i	0.937650	+	0.347581i	$0.112997\pi$
$74$	91.6111	+	109.178i	1.23799	+	1.47538i
$75$		0			0
$76$	50.3540	−	285.572i	0.662553	−	3.75752i
$77$	−14.8794	−	12.4853i	−0.193239	−	0.162147i
$78$		0			0
$79$	27.1542	+	9.88334i	0.343725	+	0.125106i	0.508114	−	0.861290i	$-0.330343\pi$
$79$	27.1542	+	9.88334i	0.343725	+	0.125106i	−0.164389	+	0.986396i	$0.552565\pi$
$80$	−131.121	+	171.750i	−1.63902	+	2.14687i
$81$		0			0
$82$			183.513i			2.23796i
$83$	25.7526	+	9.37318i	0.310272	+	0.112930i	0.492463	−	0.870333i	$-0.336097\pi$
$83$	25.7526	+	9.37318i	0.310272	+	0.112930i	−0.182191	+	0.983263i	$0.558319\pi$
$84$		0			0
$85$	87.1615	−	19.5472i	1.02543	−	0.229967i
$86$	89.0992	+	15.7106i	1.03604	+	0.182681i
$87$		0			0
$88$	−173.135	−	206.334i	−1.96744	−	2.34470i
$89$	−41.9166	+	24.2006i	−0.470973	+	0.271917i	−0.716647	−	0.697436i	$-0.754324\pi$
$89$	−41.9166	+	24.2006i	−0.470973	+	0.271917i	0.245674	+	0.969353i	$0.420991\pi$
$90$		0			0
$91$	11.0405	−	19.1227i	0.121324	−	0.210140i
$92$	49.6785	+	281.741i	0.539984	+	3.06240i
$93$		0			0
$94$	−23.4618	+	8.53941i	−0.249594	+	0.0908448i
$95$	43.4739	−	139.068i	0.457620	−	1.46387i
$96$		0			0
$97$	133.103	−	23.4697i	1.37220	−	0.241956i	0.561528	−	0.827458i	$-0.310214\pi$
$97$	133.103	−	23.4697i	1.37220	−	0.241956i	0.810671	+	0.585502i	$0.199103\pi$
$98$	86.7116	−	150.189i	0.884812	−	1.53254i
$99$		0			0
$100$	−175.045	+	176.767i	−1.75045	+	1.76767i
$101$	−93.6071	−	111.557i	−0.926803	−	1.10452i	−0.994281	−	0.106799i	$-0.965940\pi$
$101$	−93.6071	−	111.557i	−0.926803	−	1.10452i	0.0674781	−	0.997721i	$-0.478505\pi$
$102$		0			0
$103$	−13.4708	−	2.37526i	−0.130784	−	0.0230608i	0.107873	−	0.994165i	$-0.465596\pi$
$103$	−13.4708	−	2.37526i	−0.130784	−	0.0230608i	−0.238657	+	0.971104i	$0.576707\pi$
$104$	196.821	−	234.562i	1.89251	−	2.25540i
$105$		0			0
$106$	−124.099	−	45.1683i	−1.17075	−	0.426116i
$107$	−123.329			−1.15261			−0.576306	−	0.817234i	$-0.695506\pi$
$107$	−123.329			−1.15261			−0.576306	+	0.817234i	$0.695506\pi$
$108$		0			0
$109$	−135.797			−1.24584			−0.622920	−	0.782285i	$-0.714054\pi$
$109$	−135.797			−1.24584			−0.622920	+	0.782285i	$0.714054\pi$
$110$	−122.064	−	190.571i	−1.10967	−	1.73246i
$111$		0			0
$112$	−44.5255	+	53.0634i	−0.397549	+	0.473780i
$113$	16.9029	−	95.8613i	0.149584	−	0.848330i	−0.813988	−	0.580881i	$-0.802708\pi$
$113$	16.9029	−	95.8613i	0.149584	−	0.848330i	0.963572	−	0.267449i	$-0.0861808\pi$
$114$		0			0
$115$	6.62186	+	143.597i	0.0575814	+	1.24867i
$116$	175.553	−	101.356i	1.51339	−	0.873755i
$117$		0			0
$118$	−266.130	−	153.650i	−2.25534	−	1.30212i
$119$	28.2005	−	4.97251i	0.236979	−	0.0417858i
$120$		0			0
$121$	24.2908	−	8.84111i	0.200750	−	0.0730671i
$122$	−194.236	+	70.6963i	−1.59210	+	0.579478i
$123$		0			0
$124$	−11.3996	−	64.6503i	−0.0919322	−	0.521373i
$125$	−98.6076	+	76.8215i	−0.788861	+	0.614572i
$126$		0			0
$127$	−192.478	+	111.127i	−1.51558	+	0.875019i	−0.515745	+	0.856742i	$0.672485\pi$
$127$	−192.478	+	111.127i	−1.51558	+	0.875019i	−0.999833	+	0.0182767i	$0.994182\pi$
$128$	−58.1075	+	48.7580i	−0.453965	+	0.380922i
$129$		0			0
$130$	189.255	−	174.275i	1.45581	−	1.34058i
$131$	−10.0305	+	11.9539i	−0.0765690	+	0.0912514i	−0.802969	−	0.596021i	$-0.796748\pi$
$131$	−10.0305	+	11.9539i	−0.0765690	+	0.0912514i	0.726400	+	0.687272i	$0.241192\pi$
$132$		0			0
$133$	15.9753	−	43.8919i	0.120115	−	0.330014i
$134$			114.871i			0.857245i
$135$		0			0
$136$	397.091			2.91979
$137$	−6.93037	−	2.52245i	−0.0505867	−	0.0184120i	0.316603	−	0.948558i	$-0.397458\pi$
$137$	−6.93037	−	2.52245i	−0.0505867	−	0.0184120i	−0.367190	+	0.930146i	$0.619680\pi$
$138$		0			0
$139$	114.438	+	96.0245i	0.823292	+	0.690824i	0.953740	−	0.300631i	$-0.0971974\pi$
$139$	114.438	+	96.0245i	0.823292	+	0.690824i	−0.130449	+	0.991455i	$0.541642\pi$
$140$	−58.6651	+	54.0215i	−0.419037	+	0.385868i
$141$		0			0
$142$	−129.944	−	154.861i	−0.915097	−	1.09057i
$143$	83.4700	+	144.574i	0.583706	+	1.01101i
$144$		0			0
$145$	94.0070	−	39.2089i	0.648324	−	0.270406i
$146$	342.758	−	60.4375i	2.34766	−	0.413955i
$147$		0			0
$148$	129.865	+	356.801i	0.877466	+	2.41082i
$149$	74.0973	+	203.581i	0.497297	+	1.36631i	0.893877	+	0.448313i	$0.147975\pi$
$149$	74.0973	+	203.581i	0.497297	+	1.36631i	−0.396579	+	0.918000i	$0.629803\pi$
$150$		0			0
$151$	2.21211	+	12.5455i	0.0146497	+	0.0830828i	0.991256	−	0.131952i	$-0.0421245\pi$
$151$	2.21211	+	12.5455i	0.0146497	+	0.0830828i	−0.976606	+	0.215035i	$0.931013\pi$
$152$	323.857	−	560.937i	2.13064	−	3.69037i
$153$		0			0
$154$	−36.2746	−	62.8294i	−0.235549	−	0.407983i
$155$	−1.51950	−	32.9509i	−0.00980323	−	0.212586i
$156$		0			0
$157$	−85.3324	−	15.0464i	−0.543519	−	0.0958370i	−0.104854	−	0.994488i	$-0.533437\pi$
$157$	−85.3324	−	15.0464i	−0.543519	−	0.0958370i	−0.438665	+	0.898651i	$0.644549\pi$
$158$	82.6811	+	69.3777i	0.523298	+	0.439099i
$159$		0			0
$160$	−305.286	+	195.541i	−1.90804	+	1.22213i
$161$			46.0822i			0.286225i
$162$		0			0
$163$			44.5111i			0.273075i	0.990635	+	0.136537i	$0.0435973\pi$
$163$			44.5111i			0.273075i	−0.990635	+	0.136537i	$0.956403\pi$
$164$	−167.216	+	459.422i	−1.01961	+	2.80136i
$165$		0			0
$166$	78.4133	+	65.7965i	0.472369	+	0.396365i
$167$	−11.7528	+	66.6535i	−0.0703761	+	0.399123i	0.929188	+	0.369607i	$0.120508\pi$
$167$	−11.7528	+	66.6535i	−0.0703761	+	0.399123i	−0.999564	+	0.0295159i	$0.990603\pi$
$168$		0			0
$169$	−15.9174	+	13.3563i	−0.0941856	+	0.0790311i
$170$	330.893	+	42.7391i	1.94643	+	0.251406i
$171$		0			0
$172$	208.743	+	120.518i	1.21362	+	0.700687i
$173$	1.72745	+	9.79683i	0.00998523	+	0.0566291i	0.989393	−	0.145262i	$-0.0464025\pi$
$173$	1.72745	+	9.79683i	0.00998523	+	0.0566291i	−0.979408	+	0.201891i	$0.935291\pi$
$174$		0			0
$175$	−32.7117	+	23.1445i	−0.186924	+	0.132254i
$176$	−179.116	−	492.117i	−1.01770	−	2.79612i
$177$		0			0
$178$	−178.036	+	31.3925i	−1.00020	+	0.176363i
$179$	−183.909	−	106.180i	−1.02743	−	0.593184i	−0.111179	−	0.993800i	$-0.535463\pi$
$179$	−183.909	−	106.180i	−1.02743	−	0.593184i	−0.916246	+	0.400616i	$0.868796\pi$
$180$		0			0
$181$	−76.4143	−	132.353i	−0.422178	−	0.731234i	0.573974	−	0.818874i	$-0.305401\pi$
$181$	−76.4143	−	132.353i	−0.422178	−	0.731234i	−0.996152	+	0.0876392i	$0.972068\pi$
$182$	63.1791	−	53.0136i	0.347138	−	0.291283i
$183$		0			0
$184$	−110.965	+	629.316i	−0.603073	+	3.42020i
$185$	41.7499	+	186.163i	0.225675	+	1.00629i
$186$		0			0
$187$	−74.0455	+	203.438i	−0.395965	+	1.08790i
$188$	−66.5175			−0.353817
$189$		0			0
$190$	330.242	−	432.568i	1.73811	−	2.27667i
$191$	−25.7878	+	70.8514i	−0.135015	+	0.370950i	−0.988714	−	0.149817i	$-0.952132\pi$
$191$	−25.7878	+	70.8514i	−0.135015	+	0.370950i	0.853699	+	0.520767i	$0.174354\pi$
$192$		0			0
$193$	86.3157	−	102.867i	0.447231	−	0.532990i	−0.494580	−	0.869132i	$-0.664678\pi$
$193$	86.3157	−	102.867i	0.447231	−	0.532990i	0.941811	+	0.336143i	$0.109122\pi$
$194$	497.152	+	87.6613i	2.56264	+	0.451862i
$195$		0			0
$196$	353.933	−	296.985i	1.80578	−	1.51523i
$197$	−34.3090	−	59.4249i	−0.174157	−	0.301649i	0.765712	−	0.643184i	$-0.222387\pi$
$197$	−34.3090	−	59.4249i	−0.174157	−	0.301649i	−0.939869	+	0.341534i	$0.889053\pi$
$198$		0			0
$199$	30.4787	−	52.7906i	0.153159	−	0.265279i	−0.779228	−	0.626740i	$-0.784389\pi$
$199$	30.4787	−	52.7906i	0.153159	−	0.265279i	0.932387	+	0.361461i	$0.117722\pi$
$200$	−502.456	+	237.301i	−2.51228	+	1.18650i
$201$		0			0
$202$	−186.034	−	511.125i	−0.920962	−	2.53032i
$203$	30.6830	−	11.1677i	0.151148	−	0.0550133i
$204$		0			0
$205$	−112.900	+	218.181i	−0.550730	+	1.06430i
$206$	−44.2458	−	25.5453i	−0.214785	−	0.124006i
$207$		0			0
$208$	515.585	−	297.673i	2.47877	−	1.43112i
$209$	226.990	+	270.517i	1.08608	+	1.29434i
$210$		0			0
$211$	−65.8918	+	373.691i	−0.312284	+	1.77105i	0.274780	+	0.961507i	$0.411395\pi$
$211$	−65.8918	+	373.691i	−0.312284	+	1.77105i	−0.587064	+	0.809541i	$0.699716\pi$
$212$	−269.523	−	226.157i	−1.27134	−	1.06678i
$213$		0			0
$214$	−432.866	−	157.550i	−2.02274	−	0.736216i
$215$	96.2659	+	73.4936i	0.447748	+	0.341831i
$216$		0			0
$217$		−	10.5744i		−	0.0487297i
$218$	−476.623	−	173.477i	−2.18634	−	0.795764i
$219$		0			0
$220$	−131.939	−	588.317i	−0.599721	−	2.67417i
$221$	−242.374	−	42.7370i	−1.09671	−	0.193380i
$222$		0			0
$223$	192.748	+	229.708i	0.864339	+	1.03008i	0.999231	+	0.0392192i	$0.0124871\pi$
$223$	192.748	+	229.708i	0.864339	+	1.03008i	−0.134891	+	0.990860i	$0.543068\pi$
$224$	−100.650	+	58.1101i	−0.449329	+	0.259420i
$225$		0			0
$226$	181.787	−	314.864i	0.804367	−	1.39320i
$227$	−20.9629	−	118.887i	−0.0923476	−	0.523729i	−0.995528	−	0.0944679i	$-0.969885\pi$
$227$	−20.9629	−	118.887i	−0.0923476	−	0.523729i	0.903180	−	0.429261i	$-0.141226\pi$
$228$		0			0
$229$	175.173	−	63.7578i	0.764948	−	0.278418i	0.0700666	−	0.997542i	$-0.477679\pi$
$229$	175.173	−	63.7578i	0.764948	−	0.278418i	0.694882	+	0.719124i	$0.255457\pi$
$230$	−160.200	+	512.462i	−0.696523	+	2.22809i
$231$		0			0
$232$	445.911	−	78.6262i	1.92203	−	0.338906i
$233$	−73.0177	+	126.470i	−0.313381	+	0.542791i	−0.979092	−	0.203418i	$-0.934795\pi$
$233$	−73.0177	+	126.470i	−0.313381	+	0.542791i	0.665711	+	0.746209i	$0.268128\pi$
$234$		0			0
$235$	−33.1477	−	4.28144i	−0.141054	−	0.0182189i
$236$	−526.249	−	627.159i	−2.22987	−	2.65746i
$237$		0			0
$238$	105.331	+	18.5727i	0.442568	+	0.0780368i
$239$	135.434	−	161.404i	0.566668	−	0.675329i	−0.404275	−	0.914637i	$-0.632476\pi$
$239$	135.434	−	161.404i	0.566668	−	0.675329i	0.970944	+	0.239308i	$0.0769206\pi$
$240$		0			0
$241$	73.8445	+	26.8772i	0.306409	+	0.111524i	0.490648	−	0.871358i	$-0.336760\pi$
$241$	73.8445	+	26.8772i	0.306409	+	0.111524i	−0.184240	+	0.982881i	$0.558982\pi$
$242$	96.5508			0.398970
$243$		0			0
$244$	−550.687			−2.25691
$245$	195.491	−	125.215i	0.797922	−	0.511083i
$246$		0			0
$247$	−258.044	+	307.525i	−1.04471	+	1.24504i
$248$	25.4629	−	144.408i	0.102673	−	0.582288i
$249$		0			0
$250$	−444.234	+	143.662i	−1.77693	+	0.574647i
$251$	28.4525	−	16.4271i	0.113357	−	0.0654465i	−0.442250	−	0.896892i	$-0.645820\pi$
$251$	28.4525	−	16.4271i	0.113357	−	0.0654465i	0.555606	+	0.831445i	$0.312486\pi$
$252$		0			0
$253$	−301.720	−	174.198i	−1.19257	−	0.688531i
$254$	−817.529	+	144.152i	−3.21862	+	0.567529i
$255$		0			0
$256$	101.972	−	37.1147i	0.398328	−	0.144979i
$257$	−267.150	+	97.2345i	−1.03949	+	0.378344i	−0.804688	−	0.593698i	$-0.797667\pi$
$257$	−267.150	+	97.2345i	−1.03949	+	0.378344i	−0.234805	+	0.972043i	$0.575445\pi$
$258$		0			0
$259$	10.6205	+	60.2319i	0.0410058	+	0.232556i
$260$	632.598	−	263.847i	2.43307	−	1.01480i
$261$		0			0
$262$	−50.4763	+	29.1425i	−0.192658	+	0.111231i
$263$	−219.036	+	183.793i	−0.832838	+	0.698834i	−0.955941	−	0.293560i	$-0.905160\pi$
$263$	−219.036	+	183.793i	−0.832838	+	0.698834i	0.123102	+	0.992394i	$0.460716\pi$
$264$		0			0
$265$	−119.755	−	130.049i	−0.451905	−	0.490750i
$266$	112.142	−	133.645i	0.421585	−	0.502425i
$267$		0			0
$268$	−104.670	+	287.578i	−0.390559	+	1.07305i
$269$		−	143.973i		−	0.535215i	−0.963528	−	0.267607i	$-0.913767\pi$
$269$		−	143.973i		−	0.535215i	0.963528	−	0.267607i	$-0.0862330\pi$
$270$		0			0
$271$	−386.716			−1.42699			−0.713497	−	0.700658i	$-0.752890\pi$
$271$	−386.716			−1.42699			−0.713497	+	0.700658i	$0.752890\pi$
$272$	725.508	+	264.063i	2.66731	+	0.970820i
$273$		0			0
$274$	−21.1021	−	17.7068i	−0.0770149	−	0.0646232i
$275$	−27.8816	−	301.668i	−0.101388	−	1.09698i
$276$		0			0
$277$	132.179	+	157.524i	0.477179	+	0.568680i	0.949909	−	0.312528i	$-0.101176\pi$
$277$	132.179	+	157.524i	0.477179	+	0.568680i	−0.472730	+	0.881208i	$0.656731\pi$
$278$	278.988	+	483.221i	1.00355	+	1.73820i
$279$		0			0
$280$	−164.406	+	68.5714i	−0.587166	+	0.244898i
$281$	498.789	−	87.9499i	1.77505	−	0.312989i	0.812271	−	0.583280i	$-0.198231\pi$
$281$	498.789	−	87.9499i	1.77505	−	0.312989i	0.962779	+	0.270291i	$0.0871200\pi$
$282$		0			0
$283$	−146.487	−	402.471i	−0.517623	−	1.42216i	−0.873131	−	0.487485i	$-0.837914\pi$
$283$	−146.487	−	402.471i	−0.517623	−	1.42216i	0.355508	−	0.934673i	$-0.384308\pi$
$284$	−184.204	−	506.097i	−0.648607	−	1.78203i
$285$		0			0
$286$	108.276	+	614.062i	0.378586	+	2.14707i
$287$	−39.3759	+	68.2011i	−0.137198	+	0.237635i
$288$		0			0
$289$	−15.0844	−	26.1269i	−0.0521952	−	0.0904047i
$290$	380.037	−	17.5251i	1.31047	−	0.0604313i
$291$		0			0
$292$	913.161	+	161.015i	3.12726	+	0.551421i
$293$	258.409	+	216.831i	0.881942	+	0.740037i	0.966577	−	0.256375i	$-0.0825282\pi$
$293$	258.409	+	216.831i	0.881942	+	0.740037i	−0.0846357	+	0.996412i	$0.526973\pi$
$294$		0			0
$295$	−221.878	−	346.404i	−0.752129	−	1.17425i
$296$			848.125i			2.86529i
$297$		0			0
$298$			809.191i			2.71541i
$299$	135.461	−	372.175i	0.453046	−	1.24473i
$300$		0			0
$301$	29.7421	+	24.9566i	0.0988108	+	0.0829121i
$302$	−8.26242	+	46.8585i	−0.0273590	+	0.155161i
$303$		0			0
$304$	964.724	−	809.500i	3.17343	−	2.66283i
$305$	−274.424	−	35.4453i	−0.899750	−	0.116214i
$306$		0			0
$307$	90.5911	+	52.3028i	0.295085	+	0.170367i	0.640233	−	0.768181i	$-0.278838\pi$
$307$	90.5911	+	52.3028i	0.295085	+	0.170367i	−0.345148	+	0.938548i	$0.612171\pi$
$308$	−33.5631	−	190.346i	−0.108971	−	0.618007i
$309$		0			0
$310$	36.7607	−	117.593i	0.118583	−	0.379333i
$311$	124.512	+	342.094i	0.400360	+	1.09998i	0.962107	+	0.272671i	$0.0879070\pi$
$311$	124.512	+	342.094i	0.400360	+	1.09998i	−0.561748	+	0.827309i	$0.689871\pi$
$312$		0			0
$313$	259.852	−	45.8188i	0.830197	−	0.146386i	0.257629	−	0.966244i	$-0.417059\pi$
$313$	259.852	−	45.8188i	0.830197	−	0.146386i	0.572567	+	0.819858i	$0.305948\pi$
$314$	−280.281	−	161.820i	−0.892615	−	0.515351i
$315$		0			0
$316$	143.775	+	249.025i	0.454983	+	0.788054i
$317$	−319.270	+	267.899i	−1.00716	+	0.845107i	−0.987960	−	0.154708i	$-0.950556\pi$
$317$	−319.270	+	267.899i	−1.00716	+	0.845107i	−0.0191996	+	0.999816i	$0.506112\pi$
$318$		0			0
$319$	−42.8671	+	243.111i	−0.134380	+	0.762104i
$320$	−477.925	+	107.182i	−1.49352	+	0.334943i
$321$		0			0
$322$	−58.8688	+	161.741i	−0.182822	+	0.502300i
$323$	−520.611			−1.61180
$324$		0			0
$325$	332.225	−	90.7652i	1.02223	−	0.279277i
$326$	−56.8618	+	156.227i	−0.174423	+	0.479223i
$327$		0			0
$328$	−701.961	+	836.565i	−2.14013	+	2.55050i
$329$	−10.5517	−	1.86055i	−0.0320720	−	0.00565517i
$330$		0			0
$331$	−55.6735	+	46.7156i	−0.168198	+	0.141135i	−0.723001	−	0.690847i	$-0.757238\pi$
$331$	−55.6735	+	46.7156i	−0.168198	+	0.141135i	0.554803	+	0.831982i	$0.312793\pi$
$332$	136.353	+	236.171i	0.410703	+	0.711358i
$333$		0			0
$334$	−126.399	+	218.929i	−0.378439	+	0.655475i
$335$	−70.6702	+	136.571i	−0.210956	+	0.407676i
$336$		0			0
$337$	−30.3392	−	83.3563i	−0.0900273	−	0.247348i	0.886505	−	0.462719i	$-0.153126\pi$
$337$	−30.3392	−	83.3563i	−0.0900273	−	0.247348i	−0.976532	+	0.215371i	$0.930904\pi$
$338$	−72.9296	+	26.5442i	−0.215768	+	0.0785331i
$339$		0			0
$340$	789.444	+	408.505i	2.32189	+	1.20149i
$341$	69.2350	+	39.9728i	0.203035	+	0.117222i
$342$		0			0
$343$	132.469	−	76.4811i	0.386207	−	0.222977i
$344$	346.074	+	412.435i	1.00603	+	1.19894i
$345$		0			0
$346$	−6.45215	+	36.5920i	−0.0186478	+	0.105757i
$347$	305.192	+	256.086i	0.879515	+	0.738001i	0.966079	−	0.258246i	$-0.0831444\pi$
$347$	305.192	+	256.086i	0.879515	+	0.738001i	−0.0865644	+	0.996246i	$0.527589\pi$
$348$		0			0
$349$	414.030	+	150.695i	1.18633	+	0.431790i	0.858435	−	0.512923i	$-0.171437\pi$
$349$	414.030	+	150.695i	1.18633	+	0.431790i	0.327899	+	0.944713i	$0.393660\pi$
$350$	−144.379	+	39.4449i	−0.412512	+	0.112700i
$351$		0			0
$352$		−	878.664i		−	2.49621i
$353$	361.633	+	131.624i	1.02446	+	0.372871i	0.798967	−	0.601375i	$-0.205380\pi$
$353$	361.633	+	131.624i	1.02446	+	0.372871i	0.225488	+	0.974246i	$0.427602\pi$
$354$		0			0
$355$	−59.2192	−	264.060i	−0.166815	−	0.743830i
$356$	−474.316	−	83.6347i	−1.33235	−	0.234929i
$357$		0			0
$358$	−509.848	−	607.613i	−1.42416	−	1.69724i
$359$	−88.2741	+	50.9651i	−0.245889	+	0.141964i	−0.617880	−	0.786272i	$-0.712008\pi$
$359$	−88.2741	+	50.9651i	−0.245889	+	0.141964i	0.371991	+	0.928236i	$0.378675\pi$
$360$		0			0
$361$	−244.097	+	422.788i	−0.676168	+	1.17116i
$362$	−99.1232	−	562.155i	−0.273821	−	1.55292i
$363$		0			0
$364$	206.474	−	75.1504i	0.567236	−	0.206457i
$365$	444.691	+	139.015i	1.21833	+	0.380862i
$366$		0			0
$367$	−513.441	+	90.5336i	−1.39902	+	0.246686i	−0.821742	−	0.569860i	$-0.806997\pi$
$367$	−513.441	+	90.5336i	−1.39902	+	0.246686i	−0.577281	+	0.816545i	$0.695886\pi$
$368$	−621.232	+	1076.00i	−1.68813	+	2.92393i
$369$		0			0
$370$	−91.2840	+	706.737i	−0.246714	+	1.91010i
$371$	−36.4288	−	43.4141i	−0.0981908	−	0.117019i
$372$		0			0
$373$	62.8021	+	11.0737i	0.168370	+	0.0296882i	0.257198	−	0.966359i	$-0.417201\pi$
$373$	62.8021	+	11.0737i	0.168370	+	0.0296882i	−0.0888274	+	0.996047i	$0.528312\pi$
$374$	−519.774	+	619.443i	−1.38977	+	1.65626i
$375$		0			0
$376$	−139.618	−	50.8168i	−0.371325	−	0.135151i
$377$	−280.634			−0.744388
$378$		0			0
$379$	270.107			0.712684			0.356342	−	0.934356i	$-0.384024\pi$
$379$	270.107			0.712684			0.356342	+	0.934356i	$0.384024\pi$
$380$	1220.91	−	782.014i	3.21292	−	2.05793i
$381$		0			0
$382$	−181.022	+	215.733i	−0.473879	+	0.564746i
$383$	5.06194	−	28.7077i	0.0132165	−	0.0749547i	−0.977486	−	0.211000i	$-0.932328\pi$
$383$	5.06194	−	28.7077i	0.0132165	−	0.0749547i	0.990703	+	0.136045i	$0.0434392\pi$
$384$		0			0
$385$	−4.47377	−	97.0154i	−0.0116202	−	0.251988i
$386$	434.363	−	250.780i	1.12529	−	0.649689i
$387$		0			0
$388$	1164.74	+	672.462i	3.00190	+	1.73315i
$389$	497.062	−	87.6455i	1.27780	−	0.225310i	0.506752	−	0.862092i	$-0.330846\pi$
$389$	497.062	−	87.6455i	1.27780	−	0.225310i	0.771044	+	0.636782i	$0.219735\pi$
$390$		0			0
$391$	482.652	−	175.671i	1.23440	−	0.449286i
$392$	969.778	−	352.970i	2.47392	−	0.900435i
$393$		0			0
$394$	−44.5050	−	252.400i	−0.112957	−	0.640610i
$395$	55.6185	+	133.351i	0.140806	+	0.337597i
$396$		0			0
$397$	−172.126	+	99.3771i	−0.433567	+	0.250320i	−0.700865	−	0.713294i	$-0.747203\pi$
$397$	−172.126	+	99.3771i	−0.433567	+	0.250320i	0.267298	+	0.963614i	$0.413869\pi$
$398$	174.414	−	146.350i	0.438225	−	0.367715i
$399$		0			0
$400$	−1075.82	+	99.4322i	−2.68955	+	0.248580i
$401$	−243.584	+	290.292i	−0.607440	+	0.723919i	−0.978857	−	0.204547i	$-0.934428\pi$
$401$	−243.584	+	290.292i	−0.607440	+	0.723919i	0.371416	+	0.928466i	$0.378872\pi$
$402$		0			0
$403$	−31.0838	+	85.4020i	−0.0771310	+	0.211916i
$404$		−	1449.11i		−	3.58691i
$405$		0			0
$406$	121.959			0.300391
$407$	−434.513	−	158.150i	−1.06760	−	0.388574i
$408$		0			0
$409$	126.040	+	105.760i	0.308167	+	0.258583i	0.783734	−	0.621097i	$-0.213313\pi$
$409$	126.040	+	105.760i	0.308167	+	0.258583i	−0.475567	+	0.879680i	$0.657757\pi$
$410$	−674.979	+	621.551i	−1.64629	+	1.51598i
$411$		0			0
$412$	−87.4921	−	104.269i	−0.212360	−	0.253080i
$413$	−65.9369	−	114.206i	−0.159654	−	0.276528i
$414$		0			0
$415$	52.7476	+	126.467i	0.127103	+	0.304741i
$416$	983.697	−	173.452i	2.36466	−	0.416953i
$417$		0			0
$418$	451.120	+	1239.44i	1.07923	+	2.96517i
$419$	−166.490	−	457.429i	−0.397352	−	1.09172i	−0.963569	−	0.267460i	$-0.913816\pi$
$419$	−166.490	−	457.429i	−0.397352	−	1.09172i	0.566217	−	0.824256i	$-0.308406\pi$
$420$		0			0
$421$	−109.527	−	621.157i	−0.260159	−	1.47543i	−0.782476	−	0.622681i	$-0.786043\pi$
$421$	−109.527	−	621.157i	−0.260159	−	1.47543i	0.522317	−	0.852751i	$-0.325068\pi$
$422$	−708.650	+	1227.42i	−1.67927	+	2.90857i
$423$		0			0
$424$	−392.945	−	680.601i	−0.926757	−	1.60519i
$425$	367.110	+	254.383i	0.863788	+	0.598549i
$426$		0			0
$427$	−87.3557	−	15.4032i	−0.204580	−	0.0360730i
$428$	−940.116	−	788.851i	−2.19653	−	1.84311i
$429$		0			0
$430$	243.991	+	380.927i	0.567420	+	0.885878i
$431$		−	538.952i		−	1.25047i	−0.780437	−	0.625235i	$-0.785003\pi$
$431$		−	538.952i		−	1.25047i	0.780437	−	0.625235i	$-0.214997\pi$
$432$		0			0
$433$		−	142.952i		−	0.330144i	−0.986282	−	0.165072i	$-0.947214\pi$
$433$		−	142.952i		−	0.330144i	0.986282	−	0.165072i	$-0.0527856\pi$
$434$	13.5085	−	37.1142i	0.0311255	−	0.0855166i
$435$		0			0
$436$	−1035.15	−	868.594i	−2.37420	−	1.99219i
$437$	145.483	−	825.073i	0.332912	−	1.88804i
$438$		0			0
$439$	120.959	−	101.496i	0.275532	−	0.231199i	−0.494541	−	0.869154i	$-0.664664\pi$
$439$	120.959	−	101.496i	0.275532	−	0.231199i	0.770074	+	0.637955i	$0.220219\pi$
$440$	172.517	−	1335.65i	0.392083	−	3.03558i
$441$		0			0
$442$	−796.095	−	459.626i	−1.80112	−	1.03988i
$443$	33.6677	+	190.939i	0.0759993	+	0.431013i	0.998938	+	0.0460672i	$0.0146688\pi$
$443$	33.6677	+	190.939i	0.0759993	+	0.431013i	−0.922939	+	0.384946i	$0.874220\pi$
$444$		0			0
$445$	−230.982	−	72.2073i	−0.519062	−	0.162263i
$446$	383.066	+	1052.47i	0.858893	+	2.35979i
$447$		0			0
$448$	−154.630	+	27.2654i	−0.345155	+	0.0608602i
$449$	34.7894	+	20.0857i	0.0774820	+	0.0447343i	0.538240	−	0.842791i	$-0.319089\pi$
$449$	34.7894	+	20.0857i	0.0774820	+	0.0447343i	−0.460758	+	0.887526i	$0.652423\pi$
$450$		0			0
$451$	−297.695	−	515.624i	−0.660079	−	1.14329i
$452$	742.004	−	622.616i	1.64160	−	1.37747i
$453$		0			0
$454$	78.2982	−	444.051i	0.172463	−	0.978087i
$455$	107.729	−	24.1598i	0.236767	−	0.0530986i
$456$		0			0
$457$	−75.2035	+	206.620i	−0.164559	+	0.452122i	−0.994375	−	0.105915i	$-0.966223\pi$
$457$	−75.2035	+	206.620i	−0.164559	+	0.452122i	0.829816	+	0.558037i	$0.188445\pi$
$458$	696.277			1.52026
$459$		0			0
$460$	−868.013	+	1136.97i	−1.88698	+	2.47167i
$461$	−239.621	+	658.355i	−0.519786	+	1.42810i	0.350970	+	0.936387i	$0.385852\pi$
$461$	−239.621	+	658.355i	−0.519786	+	1.42810i	−0.870757	+	0.491714i	$0.836370\pi$
$462$		0			0
$463$	−93.8008	+	111.787i	−0.202593	+	0.241441i	−0.857769	−	0.514035i	$-0.828150\pi$
$463$	−93.8008	+	111.787i	−0.202593	+	0.241441i	0.655176	+	0.755477i	$0.272595\pi$
$464$	866.990	+	152.874i	1.86851	+	0.329469i
$465$		0			0
$466$	−417.842	+	350.611i	−0.896658	+	0.752385i
$467$	−137.204	−	237.644i	−0.293798	−	0.508873i	0.680907	−	0.732370i	$-0.261586\pi$
$467$	−137.204	−	237.644i	−0.293798	−	0.508873i	−0.974705	+	0.223497i	$0.928253\pi$
$468$		0			0
$469$	−24.6476	+	42.6909i	−0.0525535	+	0.0910253i
$470$	−110.873	−	57.3724i	−0.235901	−	0.122069i
$471$		0			0
$472$	−625.454	−	1718.42i	−1.32511	−	3.64072i
$473$	−275.832	+	100.395i	−0.583154	+	0.212251i
$474$		0			0
$475$	658.751	−	311.116i	1.38684	−	0.654982i
$476$	246.772	+	142.474i	0.518429	+	0.299315i
$477$		0			0
$478$	681.539	−	393.487i	1.42581	−	0.823194i
$479$	−68.8982	−	82.1097i	−0.143838	−	0.171419i	0.689316	−	0.724461i	$-0.257911\pi$
$479$	−68.8982	−	82.1097i	−0.143838	−	0.171419i	−0.833153	+	0.553042i	$0.813467\pi$
$480$		0			0
$481$	91.2796	−	517.673i	0.189771	−	1.07624i
$482$	224.847	+	188.669i	0.466487	+	0.391429i
$483$		0			0
$484$	241.714	+	87.9767i	0.499409	+	0.181770i
$485$	537.140	+	410.077i	1.10751	+	0.845519i
$486$		0			0
$487$		−	532.318i		−	1.09305i	−0.837441	−	0.546527i	$-0.815949\pi$
$487$		−	532.318i		−	1.09305i	0.837441	−	0.546527i	$-0.184051\pi$
$488$	−1155.87	−	420.704i	−2.36859	−	0.862097i
$489$		0			0
$490$	846.100	−	189.750i	1.72673	−	0.387245i
$491$	203.492	+	35.8811i	0.414444	+	0.0730776i	0.376982	−	0.926220i	$-0.376962\pi$
$491$	203.492	+	35.8811i	0.414444	+	0.0730776i	0.0374614	+	0.999298i	$0.488073\pi$
$492$		0			0
$493$	−233.935	−	278.793i	−0.474513	−	0.565502i
$494$	−1298.55	+	749.717i	−2.62864	+	1.51765i
$495$		0			0
$496$	142.552	−	246.908i	0.287404	−	0.497798i
$497$	−15.0644	−	85.4347i	−0.0303108	−	0.171901i
$498$		0			0
$499$	−554.526	+	201.831i	−1.11127	+	0.404471i	−0.831461	−	0.555584i	$-0.812495\pi$
$499$	−554.526	+	201.831i	−1.11127	+	0.404471i	−0.279813	+	0.960054i	$0.590273\pi$
$500$	−1243.04	−	45.1280i	−2.48608	−	0.0902559i
$501$		0			0
$502$	120.849	−	21.3089i	0.240734	−	0.0424480i
$503$	366.904	−	635.497i	0.729432	−	1.26341i	−0.227691	−	0.973733i	$-0.573118\pi$
$503$	366.904	−	635.497i	0.729432	−	1.26341i	0.957123	−	0.289680i	$-0.0935490\pi$
$504$		0			0
$505$	93.2729	−	722.135i	0.184699	−	1.42997i
$506$	−836.454	−	996.847i	−1.65307	−	1.97005i
$507$		0			0
$508$	−2178.03	−	384.045i	−4.28745	−	0.755994i
$509$	572.292	−	682.031i	1.12435	−	1.33994i	0.190741	−	0.981640i	$-0.438911\pi$
$509$	572.292	−	682.031i	1.12435	−	1.33994i	0.933605	−	0.358303i	$-0.116645\pi$
$510$		0			0
$511$	140.351	+	51.0837i	0.274660	+	0.0999681i
$512$	708.733			1.38424
$513$		0			0
$514$	−1061.86			−2.06588
$515$	−36.8886	−	57.5918i	−0.0716283	−	0.111829i
$516$		0			0
$517$	52.0691	−	62.0535i	0.100714	−	0.120026i
$518$	−39.6685	+	224.971i	−0.0765802	+	0.434308i
$519$		0			0
$520$	1529.37	−	70.5255i	2.94109	−	0.135626i
$521$	173.520	−	100.182i	0.333052	−	0.192288i	−0.324143	−	0.946008i	$-0.605076\pi$
$521$	173.520	−	100.182i	0.333052	−	0.192288i	0.657195	+	0.753720i	$0.271743\pi$
$522$		0			0
$523$	514.780	+	297.208i	0.984283	+	0.568276i	0.903560	−	0.428461i	$-0.140944\pi$
$523$	514.780	+	297.208i	0.984283	+	0.568276i	0.0807223	+	0.996737i	$0.474277\pi$
$524$	−152.922	+	26.9642i	−0.291835	+	0.0514584i
$525$		0			0
$526$	−1003.57	+	365.271i	−1.90793	+	0.694431i
$527$	−110.753	+	40.3107i	−0.210157	+	0.0764909i
$528$		0			0
$529$	51.6711	+	293.041i	0.0976769	+	0.553953i
$530$	−254.185	−	609.433i	−0.479595	−	1.14987i
$531$		0			0
$532$	402.522	−	232.396i	0.756621	−	0.436835i
$533$	518.494	−	435.068i	0.972783	−	0.816262i
$534$		0			0
$535$	−417.713	−	453.619i	−0.780771	−	0.847885i
$536$	−439.396	+	523.652i	−0.819770	+	0.976963i
$537$		0			0
$538$	183.921	−	505.320i	0.341861	−	0.939257i
$539$			562.656i			1.04389i
$540$		0			0
$541$	446.693			0.825681			0.412840	−	0.910803i	$-0.364537\pi$
$541$	446.693			0.825681			0.412840	+	0.910803i	$0.364537\pi$
$542$	−1357.31	−	494.019i	−2.50426	−	0.911475i
$543$		0			0
$544$	992.317	+	832.653i	1.82411	+	1.53061i
$545$	−459.938	−	499.474i	−0.843924	−	0.916466i
$546$		0			0
$547$	341.647	+	407.160i	0.624584	+	0.744350i	0.981851	−	0.189652i	$-0.0607359\pi$
$547$	341.647	+	407.160i	0.624584	+	0.744350i	−0.357267	+	0.934002i	$0.616292\pi$
$548$	−36.6945	−	63.5568i	−0.0669608	−	0.115980i
$549$		0			0
$550$	287.514	−	1094.42i	0.522752	−	1.98986i
$551$	−584.617	+	103.084i	−1.06101	+	0.187085i
$552$		0			0
$553$	15.8416	+	43.5244i	0.0286466	+	0.0787060i
$554$	262.691	+	721.738i	0.474172	+	1.30278i
$555$		0			0
$556$	258.134	+	1463.95i	0.464270	+	2.63301i
$557$	−128.583	+	222.713i	−0.230850	+	0.399844i	−0.958058	−	0.286573i	$-0.907484\pi$
$557$	−128.583	+	222.713i	−0.230850	+	0.399844i	0.727209	+	0.686417i	$0.240817\pi$
$558$		0			0
$559$	−166.846	−	288.986i	−0.298472	−	0.516969i
$560$	−345.979	+	15.9545i	−0.617820	+	0.0284902i
$561$		0			0
$562$	1863.02	+	328.500i	3.31498	+	0.584520i
$563$	361.325	+	303.188i	0.641786	+	0.538522i	0.904566	−	0.426333i	$-0.140195\pi$
$563$	361.325	+	303.188i	0.641786	+	0.538522i	−0.262780	+	0.964856i	$0.584639\pi$
$564$		0			0
$565$	409.838	−	262.508i	0.725377	−	0.464616i
$566$		−	1599.74i		−	2.82639i
$567$		0			0
$568$		−	1203.01i		−	2.11797i
$569$	35.4016	−	97.2651i	0.0622173	−	0.170941i	−0.904689	−	0.426073i	$-0.859897\pi$
$569$	35.4016	−	97.2651i	0.0622173	−	0.170941i	0.966906	+	0.255132i	$0.0821190\pi$
$570$		0			0
$571$	462.971	+	388.479i	0.810807	+	0.680348i	0.950800	−	0.309804i	$-0.100264\pi$
$571$	462.971	+	388.479i	0.810807	+	0.680348i	−0.139993	+	0.990153i	$0.544708\pi$
$572$	−288.464	+	1635.96i	−0.504307	+	2.86007i
$573$		0			0
$574$	−225.328	+	189.073i	−0.392558	+	0.329395i
$575$	−505.738	+	510.715i	−0.879545	+	0.888200i
$576$		0			0
$577$	−219.729	−	126.861i	−0.380813	−	0.219863i	0.297359	−	0.954766i	$-0.403894\pi$
$577$	−219.729	−	126.861i	−0.380813	−	0.219863i	−0.678172	+	0.734903i	$0.737228\pi$
$578$	−19.5672	−	110.971i	−0.0338533	−	0.191992i
$579$		0			0
$580$	967.388	+	302.415i	1.66791	+	0.521404i
$581$	15.0239	+	41.2778i	0.0258587	+	0.0710461i
$582$		0			0
$583$	421.959	−	74.4027i	0.723771	−	0.127620i
$584$	1793.68	+	1035.58i	3.07138	+	1.77326i
$585$		0			0
$586$	629.976	+	1091.15i	1.07504	+	1.86203i
$587$	402.386	−	337.642i	0.685496	−	0.575199i	−0.232111	−	0.972689i	$-0.574563\pi$
$587$	402.386	−	337.642i	0.685496	−	0.575199i	0.917606	+	0.397490i	$0.130119\pi$
$588$		0			0
$589$	−33.3835	+	189.327i	−0.0566783	+	0.321439i
$590$	−336.232	−	1499.26i	−0.569885	−	2.54113i
$591$		0			0
$592$	−563.998	+	1549.57i	−0.952699	+	2.61752i
$593$	841.771			1.41951			0.709757	−	0.704447i	$-0.248805\pi$
$593$	841.771			1.41951			0.709757	+	0.704447i	$0.248805\pi$
$594$		0			0
$595$	113.804	+	86.8827i	0.191267	+	0.146021i
$596$	−737.332	+	2025.80i	−1.23713	+	3.39900i
$597$		0			0
$598$	950.888	−	1133.22i	1.59011	−	1.89502i
$599$	−607.717	−	107.157i	−1.01455	−	0.178893i	−0.358437	−	0.933554i	$-0.616690\pi$
$599$	−607.717	−	107.157i	−1.01455	−	0.178893i	−0.656115	+	0.754661i	$0.727801\pi$
$600$		0			0
$601$	687.872	−	577.193i	1.14455	−	0.960388i	0.144968	−	0.989436i	$-0.453692\pi$
$601$	687.872	−	577.193i	1.14455	−	0.960388i	0.999578	+	0.0290485i	$0.00924772\pi$
$602$	72.5083	+	125.588i	0.120446	+	0.208618i
$603$		0			0
$604$	−63.3822	+	109.781i	−0.104937	+	0.181757i
$605$	114.791	+	59.3994i	0.189736	+	0.0981809i
$606$		0			0
$607$	305.379	+	839.023i	0.503096	+	1.38225i	0.888236	+	0.459388i	$0.151931\pi$
$607$	305.379	+	839.023i	0.503096	+	1.38225i	−0.385140	+	0.922858i	$0.625847\pi$
$608$	1985.53	−	722.672i	3.26567	−	1.18861i
$609$		0			0
$610$	−917.901	−	474.976i	−1.50476	−	0.778650i
$611$	79.7499	+	46.0436i	0.130524	+	0.0753578i
$612$		0			0
$613$	−499.634	+	288.464i	−0.815063	+	0.470577i	−0.848711	−	0.528857i	$-0.822621\pi$
$613$	−499.634	+	288.464i	−0.815063	+	0.470577i	0.0336481	+	0.999434i	$0.489287\pi$
$614$	251.144	+	299.302i	0.409029	+	0.487462i
$615$		0			0
$616$	74.9691	−	425.171i	0.121703	−	0.690212i
$617$	−235.192	−	197.349i	−0.381186	−	0.319853i	0.431982	−	0.901882i	$-0.357815\pi$
$617$	−235.192	−	197.349i	−0.381186	−	0.319853i	−0.813168	+	0.582029i	$0.802259\pi$
$618$		0			0
$619$	−278.964	−	101.535i	−0.450668	−	0.164030i	0.106707	−	0.994291i	$-0.465969\pi$
$619$	−278.964	−	101.535i	−0.450668	−	0.164030i	−0.557375	+	0.830261i	$0.688192\pi$
$620$	199.181	−	260.897i	0.321259	−	0.420802i
$621$		0			0
$622$			1359.75i			2.18610i
$623$	−72.9016	−	26.5340i	−0.117017	−	0.0425907i
$624$		0			0
$625$	−616.538	−	102.497i	−0.986461	−	0.163996i
$626$	970.567	+	171.137i	1.55043	+	0.273382i
$627$		0			0
$628$	−554.231	−	660.507i	−0.882533	−	1.05176i
$629$	590.365	−	340.848i	0.938578	−	0.541888i
$630$		0			0
$631$	−152.227	+	263.664i	−0.241247	+	0.417851i	−0.961070	−	0.276306i	$-0.910890\pi$
$631$	−152.227	+	263.664i	−0.241247	+	0.417851i	0.719823	+	0.694158i	$0.244223\pi$
$632$	111.533	+	632.533i	0.176476	+	1.00084i
$633$		0			0
$634$	−1462.82	+	532.422i	−2.30728	+	0.839782i
$635$	−1060.66	−	331.571i	−1.67032	−	0.522159i
$636$		0			0
$637$	−629.915	+	111.071i	−0.988877	+	0.174366i
$638$	−461.024	+	798.518i	−0.722609	+	1.25160i
$639$		0			0
$640$	−376.145	−	48.5839i	−0.587727	−	0.0759124i
$641$	−710.009	−	846.156i	−1.10766	−	1.32006i	−0.942657	−	0.333762i	$-0.891682\pi$
$641$	−710.009	−	846.156i	−1.10766	−	1.32006i	−0.165001	−	0.986293i	$-0.552763\pi$
$642$		0			0
$643$	−421.371	−	74.2990i	−0.655320	−	0.115551i	−0.163905	−	0.986476i	$-0.552409\pi$
$643$	−421.371	−	74.2990i	−0.655320	−	0.115551i	−0.491415	+	0.870926i	$0.663520\pi$
$644$	−294.755	+	351.275i	−0.457694	+	0.545458i
$645$		0			0
$646$	−1827.26	−	665.067i	−2.82857	−	1.02952i
$647$	−839.214			−1.29709			−0.648543	−	0.761178i	$-0.724621\pi$
$647$	−839.214			−1.29709			−0.648543	+	0.761178i	$0.724621\pi$
$648$		0			0
$649$	997.011			1.53623
$650$	1282.00	+	105.838i	1.97231	+	0.162828i
$651$		0			0
$652$	−284.706	+	339.300i	−0.436666	+	0.520398i
$653$	218.407	−	1238.65i	0.334468	−	1.89686i	−0.0979579	−	0.995191i	$-0.531231\pi$
$653$	218.407	−	1238.65i	0.334468	−	1.89686i	0.432426	−	0.901670i	$-0.357658\pi$
$654$		0			0
$655$	−77.9409	+	3.59417i	−0.118994	+	0.00548729i
$656$	−1838.83	+	1061.65i	−2.80310	+	1.61837i
$657$		0			0
$658$	−34.6579	−	20.0097i	−0.0526716	−	0.0304099i
$659$	−102.328	+	18.0433i	−0.155278	+	0.0273798i	−0.250747	−	0.968053i	$-0.580676\pi$
$659$	−102.328	+	18.0433i	−0.155278	+	0.0273798i	0.0954686	+	0.995432i	$0.469565\pi$
$660$		0			0
$661$	−528.130	+	192.224i	−0.798986	+	0.290807i	−0.709066	−	0.705142i	$-0.750883\pi$
$661$	−528.130	+	192.224i	−0.798986	+	0.290807i	−0.0899200	+	0.995949i	$0.528661\pi$
$662$	−255.083	+	92.8425i	−0.385321	+	0.140245i
$663$		0			0
$664$	105.776	+	599.883i	0.159301	+	0.903438i
$665$	215.547	−	89.9014i	0.324131	−	0.135190i
$666$		0			0
$667$	507.207	−	292.836i	0.760430	−	0.439035i
$668$	−515.924	+	432.912i	−0.772342	+	0.648072i
$669$		0			0
$670$	−422.507	+	389.063i	−0.630607	+	0.580692i
$671$	431.071	−	513.730i	0.642430	−	0.765619i
$672$		0			0
$673$	−83.8135	+	230.276i	−0.124537	+	0.342163i	−0.986256	−	0.165222i	$-0.947166\pi$
$673$	−83.8135	+	230.276i	−0.124537	+	0.342163i	0.861719	+	0.507386i	$0.169388\pi$
$674$		−	331.324i		−	0.491579i
$675$		0			0
$676$	−206.765			−0.305866
$677$	1015.64	+	369.663i	1.50021	+	0.546031i	0.956115	−	0.292992i	$-0.0946511\pi$
$677$	1015.64	+	369.663i	1.50021	+	0.546031i	0.544094	+	0.839024i	$0.316873\pi$
$678$		0			0
$679$	165.953	+	139.252i	0.244409	+	0.205083i
$680$	1344.93	+	1460.54i	1.97784	+	2.14786i
$681$		0			0
$682$	191.939	+	228.744i	0.281435	+	0.335401i
$683$	−428.494	−	742.173i	−0.627370	−	1.08664i	−0.988077	−	0.153958i	$-0.950798\pi$
$683$	−428.494	−	742.173i	−0.627370	−	1.08664i	0.360707	−	0.932679i	$-0.382535\pi$
$684$		0			0
$685$	−14.1951	−	34.0341i	−0.0207228	−	0.0496848i
$686$	562.647	−	99.2098i	0.820185	−	0.144621i
$687$		0			0
$688$	358.030	+	983.679i	0.520392	+	1.42977i
$689$	166.593	+	457.711i	0.241790	+	0.664312i
$690$		0			0
$691$	−214.349	−	1215.63i	−0.310201	−	1.75924i	−0.597951	−	0.801533i	$-0.704018\pi$
$691$	−214.349	−	1215.63i	−0.310201	−	1.75924i	0.287749	−	0.957706i	$-0.407093\pi$
$692$	−49.4954	+	85.7285i	−0.0715251	+	0.123885i
$693$		0			0
$694$	744.028	+	1288.69i	1.07209	+	1.85691i
$695$	34.4078	+	746.145i	0.0495076	+	1.07359i
$696$		0			0
$697$	864.425	+	152.421i	1.24021	+	0.218682i
$698$	1260.67	+	1057.83i	1.80611	+	1.51551i
$699$		0			0
$700$	−397.394	−	32.8076i	−0.567705	−	0.0468679i
$701$			691.765i			0.986826i	0.869795	+	0.493413i	$0.164251\pi$
$701$			691.765i			0.986826i	−0.869795	+	0.493413i	$0.835749\pi$
$702$		0			0
$703$		−	1111.95i		−	1.58171i
$704$	406.007	−	1115.50i	0.576715	−	1.58451i
$705$		0			0
$706$	1101.12	+	923.953i	1.55967	+	1.30871i
$707$	40.5328	−	229.873i	0.0573307	−	0.325139i
$708$		0			0
$709$	199.020	−	166.998i	0.280705	−	0.235540i	−0.491554	−	0.870847i	$-0.663571\pi$
$709$	199.020	−	166.998i	0.280705	−	0.235540i	0.772259	+	0.635307i	$0.219127\pi$
$710$	129.480	−	1002.46i	0.182366	−	1.41191i
$711$		0			0
$712$	−931.679	−	537.905i	−1.30854	−	0.755485i
$713$	−32.9357	−	186.787i	−0.0461931	−	0.261974i
$714$		0			0
$715$	−249.049	+	796.679i	−0.348321	+	1.11424i
$716$	−722.744	−	1985.72i	−1.00942	−	2.77336i
$717$		0			0
$718$	−374.934	+	66.1110i	−0.522192	+	0.0920765i
$719$	687.917	+	397.169i	0.956769	+	0.552391i	0.895177	−	0.445711i	$-0.147049\pi$
$719$	687.917	+	397.169i	0.956769	+	0.552391i	0.0615920	+	0.998101i	$0.480382\pi$
$720$		0			0
$721$	−10.9624	−	18.9875i	−0.0152045	−	0.0263349i
$722$	−1396.84	+	1172.09i	−1.93468	+	1.62339i
$723$		0			0
$724$	264.080	−	1497.67i	0.364751	−	2.06861i
$725$	462.613	+	212.969i	0.638087	+	0.293750i
$726$		0			0
$727$	29.4405	−	80.8871i	0.0404959	−	0.111261i	−0.917797	−	0.397051i	$-0.870034\pi$
$727$	29.4405	−	80.8871i	0.0404959	−	0.111261i	0.958292	+	0.285790i	$0.0922558\pi$
$728$	490.794			0.674167
$729$		0			0
$730$	1383.20	+	1056.00i	1.89480	+	1.44658i
$731$	148.007	−	406.647i	0.202473	−	0.556289i
$732$		0			0
$733$	166.327	−	198.220i	0.226912	−	0.270423i	−0.640561	−	0.767907i	$-0.721298\pi$
$733$	166.327	−	198.220i	0.226912	−	0.270423i	0.867473	+	0.497484i	$0.165743\pi$
$734$	−1917.75	−	338.151i	−2.61273	−	0.460696i
$735$		0			0
$736$	−1596.90	+	1339.96i	−2.16970	+	1.82060i
$737$	−186.344	−	322.757i	−0.252841	−	0.437934i
$738$		0			0
$739$	−157.730	+	273.197i	−0.213438	+	0.369685i	−0.952788	−	0.303636i	$-0.901799\pi$
$739$	−157.730	+	273.197i	−0.213438	+	0.369685i	0.739350	+	0.673321i	$0.235133\pi$
$740$	−872.504	+	1686.13i	−1.17906	+	2.27856i
$741$		0			0
$742$	−72.3985	−	198.913i	−0.0975721	−	0.268077i
$743$	−219.384	+	79.8494i	−0.295268	+	0.107469i	−0.485407	−	0.874288i	$-0.661328\pi$
$743$	−219.384	+	79.8494i	−0.295268	+	0.107469i	0.190139	+	0.981757i	$0.439106\pi$
$744$		0			0
$745$	−497.826	+	962.059i	−0.668223	+	1.29135i
$746$	206.278	+	119.095i	0.276513	+	0.159645i
$747$		0			0
$748$	−1865.68	+	1077.15i	−2.49423	+	1.44004i
$749$	−127.066	−	151.431i	−0.169648	−	0.202178i
$750$		0			0
$751$	−163.837	+	929.165i	−0.218158	+	1.23724i	0.657183	+	0.753731i	$0.271748\pi$
$751$	−163.837	+	929.165i	−0.218158	+	1.23724i	−0.875341	+	0.483506i	$0.839363\pi$
$752$	−221.297	−	185.690i	−0.294278	−	0.246929i
$753$		0			0
$754$	−984.979	−	358.503i	−1.30634	−	0.475468i
$755$	−38.6514	+	50.6276i	−0.0511939	+	0.0670564i
$756$		0			0
$757$		−	197.402i		−	0.260769i	−0.991464	−	0.130384i	$-0.958379\pi$
$757$		−	197.402i		−	0.260769i	0.991464	−	0.130384i	$-0.0416211\pi$
$758$	948.031	+	345.055i	1.25070	+	0.455218i
$759$		0			0
$760$	3160.08	−	708.693i	4.15800	−	0.932491i
$761$	−7.30341	−	1.28779i	−0.00959713	−	0.00169223i	0.168848	−	0.985642i	$-0.445995\pi$
$761$	−7.30341	−	1.28779i	−0.00959713	−	0.00169223i	−0.178445	+	0.983950i	$0.557107\pi$
$762$		0			0
$763$	−139.911	−	166.739i	−0.183369	−	0.218531i
$764$	−649.761	+	375.140i	−0.850472	+	0.491020i
$765$		0			0
$766$	54.4398	−	94.2926i	0.0710703	−	0.123097i
$767$	196.815	+	1116.19i	0.256603	+	1.45527i
$768$		0			0
$769$	1240.22	−	451.405i	1.61278	−	0.587003i	0.630790	−	0.775954i	$-0.282731\pi$
$769$	1240.22	−	451.405i	1.61278	−	0.587003i	0.981986	+	0.188951i	$0.0605088\pi$
$770$	108.232	−	346.223i	0.140562	−	0.449640i
$771$		0			0
$772$	1315.93	−	232.035i	1.70458	−	0.300563i
$773$	−238.322	+	412.785i	−0.308307	+	0.534004i	−0.977992	−	0.208641i	$-0.933096\pi$
$773$	−238.322	+	412.785i	−0.308307	+	0.534004i	0.669685	+	0.742645i	$0.266429\pi$
$774$		0			0
$775$	116.050	−	117.192i	0.149742	−	0.151216i
$776$	1931.01	+	2301.29i	2.48842	+	2.96558i
$777$		0			0
$778$	1856.57	+	327.363i	2.38634	+	0.420776i
$779$	920.315	−	1096.79i	1.18141	−	1.40794i
$780$		0			0
$781$	616.325	+	224.324i	0.789149	+	0.287227i
$782$	1918.44			2.45325
$783$		0			0
$784$	2006.56			2.55939
$785$	−233.676	−	364.823i	−0.297676	−	0.464743i
$786$		0			0
$787$	−470.940	+	561.245i	−0.598400	+	0.713145i	−0.977197	−	0.212335i	$-0.931893\pi$
$787$	−470.940	+	561.245i	−0.598400	+	0.713145i	0.378797	+	0.925480i	$0.376338\pi$
$788$	118.568	−	672.434i	0.150467	−	0.853343i
$789$		0			0
$790$	24.8596	+	539.090i	0.0314679	+	0.682392i
$791$	135.119	−	78.0113i	0.170821	−	0.0986236i
$792$		0			0
$793$	660.235	+	381.187i	0.832579	+	0.480690i
$794$	−731.086	+	128.910i	−0.920763	+	0.162355i
$795$		0			0
$796$	569.997	−	207.462i	0.716076	−	0.260630i
$797$	−545.314	+	198.478i	−0.684209	+	0.249032i	−0.660653	−	0.750691i	$-0.729721\pi$
$797$	−545.314	+	198.478i	−0.684209	+	0.249032i	−0.0235551	+	0.999723i	$0.507498\pi$
$798$		0			0
$799$	20.7375	+	117.608i	0.0259543	+	0.147194i
$800$	−1753.21	−	460.583i	−2.19151	−	0.575729i
$801$		0			0
$802$	−1225.78	+	707.703i	−1.52840	+	0.882423i
$803$	−865.020	+	725.838i	−1.07723	+	0.903907i
$804$		0			0
$805$	−169.495	+	156.079i	−0.210553	+	0.193887i
$806$	−218.198	+	260.038i	−0.270717	+	0.322628i
$807$		0			0
$808$	1107.06	−	3041.63i	1.37013	−	3.76440i
$809$			459.833i			0.568397i	0.958765	+	0.284199i	$0.0917275\pi$
$809$			459.833i			0.568397i	−0.958765	+	0.284199i	$0.908272\pi$
$810$		0			0
$811$	−1419.14			−1.74986			−0.874931	−	0.484248i	$-0.839093\pi$
$811$	−1419.14			−1.74986			−0.874931	+	0.484248i	$0.839093\pi$
$812$	305.322	+	111.128i	0.376013	+	0.136857i
$813$		0			0
$814$	−1323.03	−	1110.16i	−1.62535	−	1.36383i
$815$	−163.717	+	150.758i	−0.200879	+	0.184979i
$816$		0			0
$817$	−453.725	−	540.728i	−0.555355	−	0.661846i
$818$	307.274	+	532.215i	0.375641	+	0.650629i
$819$		0			0
$820$	−2256.16	+	941.009i	−2.75141	+	1.14757i
$821$	−1297.62	+	228.805i	−1.58053	+	0.278691i	−0.893884	−	0.448299i	$-0.852030\pi$
$821$	−1297.62	+	228.805i	−1.58053	+	0.278691i	−0.686649	+	0.726989i	$0.740919\pi$
$822$		0			0
$823$	49.4573	+	135.883i	0.0600940	+	0.165107i	0.966106	−	0.258144i	$-0.0831110\pi$
$823$	49.4573	+	135.883i	0.0600940	+	0.165107i	−0.906012	+	0.423251i	$0.860889\pi$
$824$	−103.985	−	285.698i	−0.126196	−	0.346721i
$825$		0			0
$826$	−85.5322	−	485.077i	−0.103550	−	0.587260i
$827$	548.614	−	950.226i	0.663378	−	1.14900i	−0.316345	−	0.948644i	$-0.602456\pi$
$827$	548.614	−	950.226i	0.663378	−	1.14900i	0.979722	−	0.200360i	$-0.0642111\pi$
$828$		0			0
$829$	562.861	+	974.904i	0.678964	+	1.17600i	0.975293	+	0.220914i	$0.0709041\pi$
$829$	562.861	+	974.904i	0.678964	+	1.17600i	−0.296329	+	0.955086i	$0.595763\pi$
$830$	23.5764	+	511.263i	0.0284053	+	0.615979i
$831$		0			0
$832$	1328.99	+	234.336i	1.59734	+	0.281654i
$833$	−635.434	−	533.193i	−0.762826	−	0.640087i
$834$		0			0
$835$	−284.965	+	182.525i	−0.341276	+	0.218593i
$836$			3513.99i			4.20334i
$837$		0			0
$838$		−	1818.19i		−	2.16967i
$839$	−204.373	+	561.510i	−0.243591	+	0.669261i	0.756296	+	0.654230i	$0.227007\pi$
$839$	−204.373	+	561.510i	−0.243591	+	0.669261i	−0.999887	+	0.0150315i	$0.995215\pi$
$840$		0			0
$841$	326.345	+	273.836i	0.388044	+	0.325608i
$842$	409.092	−	2320.07i	0.485857	−	2.75543i
$843$		0			0
$844$	−2892.52	+	2427.11i	−3.42715	+	2.87572i
$845$	−103.037	−	13.3086i	−0.121938	−	0.0157498i
$846$		0			0
$847$	35.8824	+	20.7167i	0.0423641	+	0.0244589i
$848$	−265.337	−	1504.80i	−0.312898	−	1.77453i
$849$		0			0
$850$	963.525	+	1361.82i	1.13356	+	1.60214i
$851$	375.206	+	1030.87i	0.440900	+	1.21136i
$852$		0			0
$853$	−53.6769	+	9.46469i	−0.0629272	+	0.0110958i	−0.205023	−	0.978757i	$-0.565727\pi$
$853$	−53.6769	+	9.46469i	−0.0629272	+	0.0110958i	0.142096	+	0.989853i	$0.454616\pi$
$854$	−286.927	−	165.657i	−0.335980	−	0.193978i
$855$		0			0
$856$	−1370.62	−	2373.98i	−1.60119	−	2.77334i
$857$	−218.563	+	183.396i	−0.255033	+	0.213998i	−0.761336	−	0.648358i	$-0.775456\pi$
$857$	−218.563	+	183.396i	−0.255033	+	0.213998i	0.506303	+	0.862356i	$0.331012\pi$
$858$		0			0
$859$	177.600	−	1007.22i	0.206752	−	1.17255i	−0.687908	−	0.725798i	$-0.741471\pi$
$859$	177.600	−	1007.22i	0.206752	−	1.17255i	0.894659	−	0.446749i	$-0.147418\pi$
$860$	263.729	+	1175.97i	0.306661	+	1.36741i
$861$		0			0
$862$	688.498	−	1891.63i	0.798721	−	2.19447i
$863$	649.495			0.752601			0.376300	−	0.926498i	$-0.377196\pi$
$863$	649.495			0.752601			0.376300	+	0.926498i	$0.377196\pi$
$864$		0			0
$865$	−30.1830	+	39.5353i	−0.0348936	+	0.0457055i
$866$	182.618	−	501.739i	0.210875	−	0.579375i
$867$		0			0
$868$	67.6366	−	80.6062i	0.0779223	−	0.0928642i
$869$	−344.858	−	60.8077i	−0.396844	−	0.0699744i
$870$		0			0
$871$	324.554	−	272.333i	0.372622	−	0.312667i
$872$	−1509.17	−	2613.96i	−1.73070	−	2.99766i
$873$		0			0
$874$	1564.63	−	2710.02i	1.79019	−	3.10071i
$875$	−195.921	−	41.9275i	−0.223910	−	0.0479171i
$876$		0			0
$877$	−551.626	−	1515.58i	−0.628992	−	1.72814i	−0.683826	−	0.729645i	$-0.739685\pi$
$877$	−551.626	−	1515.58i	−0.628992	−	1.72814i	0.0548340	−	0.998495i	$-0.482537\pi$
$878$	554.204	−	201.714i	0.631212	−	0.229742i
$879$		0			0
$880$	1203.40	−	2325.59i	1.36750	−	2.64272i
$881$	969.613	+	559.806i	1.10058	+	0.635421i	0.936374	−	0.351004i	$-0.114160\pi$
$881$	969.613	+	559.806i	1.10058	+	0.635421i	0.164208	+	0.986426i	$0.447493\pi$
$882$		0			0
$883$	−328.990	+	189.942i	−0.372582	+	0.215110i	−0.674586	−	0.738196i	$-0.735678\pi$
$883$	−328.990	+	189.942i	−0.372582	+	0.215110i	0.302004	+	0.953307i	$0.402344\pi$
$884$	−1574.21	−	1876.07i	−1.78078	−	2.12225i
$885$		0			0
$886$	−125.752	+	713.173i	−0.141932	+	0.804936i
$887$	321.634	+	269.883i	0.362609	+	0.304265i	0.805830	−	0.592148i	$-0.201720\pi$
$887$	321.634	+	269.883i	0.362609	+	0.304265i	−0.443221	+	0.896413i	$0.646164\pi$
$888$		0			0
$889$	−334.759	−	121.842i	−0.376557	−	0.137056i
$890$	−718.467	−	548.509i	−0.807266	−	0.616303i
$891$		0			0
$892$			2983.89i			3.34516i
$893$	183.048	+	66.6240i	0.204981	+	0.0746069i
$894$		0			0
$895$	−232.353	−	1036.07i	−0.259612	−	1.15761i
$896$	−119.736	−	21.1127i	−0.133634	−	0.0235633i
$897$		0			0
$898$	96.4460	+	114.940i	0.107401	+	0.127995i
$899$	−116.387	+	67.1963i	−0.129463	+	0.0747456i
$900$		0			0
$901$	−315.836	+	547.045i	−0.350540	+	0.607153i
$902$	−386.165	−	2190.05i	−0.428121	−	2.42799i
$903$		0			0
$904$	2033.10	−	739.986i	2.24900	−	0.818569i
$905$	227.997	−	729.336i	0.251931	−	0.805896i
$906$		0			0
$907$	−816.196	+	143.917i	−0.899885	+	0.158674i	−0.604407	−	0.796675i	$-0.706590\pi$
$907$	−816.196	+	143.917i	−0.899885	+	0.158674i	−0.295478	+	0.955350i	$0.595479\pi$
$908$	600.637	−	1040.33i	0.661494	−	1.14574i
$909$		0			0
$910$	408.975	+	52.8243i	0.449423	+	0.0580487i
$911$	240.268	+	286.340i	0.263740	+	0.314314i	0.881621	−	0.471959i	$-0.156453\pi$
$911$	240.268	+	286.340i	0.263740	+	0.314314i	−0.617880	+	0.786272i	$0.712008\pi$
$912$		0			0
$913$	−327.057	−	57.6689i	−0.358222	−	0.0631642i
$914$	−527.903	+	629.130i	−0.577574	+	0.688326i
$915$		0			0
$916$	1743.12	+	634.445i	1.90297	+	0.692626i
$917$	−25.0122			−0.0272761
$918$		0			0
$919$	670.084			0.729144			0.364572	−	0.931175i	$-0.381215\pi$
$919$	670.084			0.729144			0.364572	+	0.931175i	$0.381215\pi$
$920$	−2690.53	+	1723.33i	−2.92449	+	1.87319i
$921$		0			0
$922$	−1682.06	+	2004.60i	−1.82436	+	2.17419i
$923$	−129.474	+	734.282i	−0.140275	+	0.795538i
$924$		0			0
$925$	−543.323	+	784.090i	−0.587377	+	0.847665i
$926$	−472.030	+	272.527i	−0.509752	+	0.294305i
$927$		0			0
$928$	1279.19	+	738.539i	1.37843	+	0.795839i
$929$	254.515	−	44.8778i	0.273966	−	0.0483076i	−0.0349770	−	0.999388i	$-0.511136\pi$
$929$	254.515	−	44.8778i	0.273966	−	0.0483076i	0.308943	+	0.951080i	$0.400025\pi$
$930$		0			0
$931$	−1271.44	+	462.766i	−1.36567	+	0.497064i
$932$	−1365.54	+	497.016i	−1.46517	+	0.533279i
$933$		0			0
$934$	−177.978	−	1009.36i	−0.190555	−	1.08069i
$935$	−999.057	+	416.691i	−1.06851	+	0.445659i
$936$		0			0
$937$	1183.51	−	683.299i	1.26308	−	0.729241i	0.289413	−	0.957204i	$-0.406540\pi$
$937$	1183.51	−	683.299i	1.26308	−	0.729241i	0.973670	+	0.227963i	$0.0732064\pi$
$938$	−141.045	+	118.351i	−0.150368	+	0.126174i
$939$		0			0
$940$	−225.293	−	244.659i	−0.239673	−	0.260275i
$941$	404.676	−	482.275i	0.430049	−	0.512513i	−0.506887	−	0.862012i	$-0.669204\pi$
$941$	404.676	−	482.275i	0.430049	−	0.512513i	0.936937	+	0.349500i	$0.113648\pi$
$942$		0			0
$943$	−483.120	+	1327.36i	−0.512322	+	1.40759i
$944$		−	3555.57i		−	3.76649i
$945$		0			0
$946$	−1096.37			−1.15896
$947$	449.992	+	163.784i	0.475177	+	0.172950i	0.568496	−	0.822686i	$-0.307526\pi$
$947$	449.992	+	163.784i	0.475177	+	0.172950i	−0.0933193	+	0.995636i	$0.529748\pi$
$948$		0			0
$949$	−983.361	−	825.138i	−1.03621	−	0.869482i
$950$	2709.55	−	250.429i	2.85215	−	0.263610i
$951$		0			0
$952$	409.122	+	487.573i	0.429750	+	0.512156i
$953$	243.506	+	421.765i	0.255516	+	0.442566i	0.965035	−	0.262120i	$-0.0844215\pi$
$953$	243.506	+	421.765i	0.255516	+	0.442566i	−0.709520	+	0.704685i	$0.751088\pi$
$954$		0			0
$955$	−347.941	+	145.121i	−0.364336	+	0.151959i
$956$	2064.77	−	364.074i	2.15980	−	0.380831i
$957$		0			0
$958$	−136.928	−	376.207i	−0.142931	−	0.392700i
$959$	−4.04313	−	11.1084i	−0.00421599	−	0.0115833i
$960$		0			0
$961$	−159.318	−	903.539i	−0.165784	−	0.940207i
$962$	981.689	−	1700.34i	1.02047	−	1.76750i
$963$		0			0
$964$	390.987	+	677.210i	0.405588	+	0.702500i
$965$	670.704	−	30.9289i	0.695030	−	0.0320507i
$966$		0			0
$967$	−159.464	−	28.1178i	−0.164906	−	0.0290774i	0.0905855	−	0.995889i	$-0.471126\pi$
$967$	−159.464	−	28.1178i	−0.164906	−	0.0290774i	−0.255491	+	0.966811i	$0.582237\pi$
$968$	440.138	+	369.320i	0.454688	+	0.381529i
$969$		0			0
$970$	1361.41	+	2125.48i	1.40351	+	2.19122i
$971$		−	1357.14i		−	1.39768i	−0.715280	−	0.698838i	$-0.753701\pi$
$971$		−	1357.14i		−	1.39768i	0.715280	−	0.698838i	$-0.246299\pi$
$972$		0			0
$973$			239.447i			0.246092i
$974$	680.022	−	1868.34i	0.698174	−	1.91822i
$975$		0			0
$976$	−1832.08	−	1537.30i	−1.87713	−	1.57510i
$977$	−244.318	+	1385.60i	−0.250070	+	1.41822i	0.558348	+	0.829607i	$0.311435\pi$
$977$	−244.318	+	1385.60i	−0.250070	+	1.41822i	−0.808418	+	0.588609i	$0.799676\pi$
$978$		0			0
$979$	449.310	−	377.016i	0.458948	−	0.385103i
$980$	2291.10	+	295.925i	2.33786	+	0.301964i
$981$		0			0
$982$	668.385	+	385.892i	0.680636	+	0.392966i
$983$	147.248	+	835.086i	0.149795	+	0.849528i	0.963391	+	0.268099i	$0.0863953\pi$
$983$	147.248	+	835.086i	0.149795	+	0.849528i	−0.813597	+	0.581430i	$0.802494\pi$
$984$		0			0
$985$	102.368	−	327.462i	0.103927	−	0.332449i
$986$	−464.921	−	1277.36i	−0.471522	−	1.29550i
$987$		0			0
$988$	−3934.04	+	693.678i	−3.98182	+	0.702103i
$989$	603.101	+	348.201i	0.609809	+	0.352073i
$990$		0			0
$991$	161.951	+	280.507i	0.163422	+	0.283055i	0.936094	−	0.351751i	$-0.114414\pi$
$991$	161.951	+	280.507i	0.163422	+	0.283055i	−0.772672	+	0.634805i	$0.781080\pi$
$992$	366.437	−	307.477i	0.369392	−	0.309956i
$993$		0			0
$994$	56.2670	−	319.106i	0.0566066	−	0.321032i
$995$	297.400	−	66.6962i	0.298894	−	0.0670314i
$996$		0			0
$997$	148.115	−	406.943i	0.148561	−	0.408168i	−0.842983	−	0.537940i	$-0.819203\pi$
$997$	148.115	−	406.943i	0.148561	−	0.408168i	0.991544	+	0.129773i	$0.0414248\pi$
$998$	−2204.13			−2.20854
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.n.a.179.33		204
3.2	odd	2		135.3.n.a.104.2	yes	204
5.4	even	2	inner	405.3.n.a.179.2		204
15.14	odd	2		135.3.n.a.104.33	yes	204
27.7	even	9		135.3.n.a.74.33	yes	204
27.20	odd	18	inner	405.3.n.a.224.2		204
135.34	even	18		135.3.n.a.74.2	✓	204
135.74	odd	18	inner	405.3.n.a.224.33		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.n.a.74.2	✓	204	135.34	even	18
135.3.n.a.74.33	yes	204	27.7	even	9
135.3.n.a.104.2	yes	204	3.2	odd	2
135.3.n.a.104.33	yes	204	15.14	odd	2
405.3.n.a.179.2		204	5.4	even	2	inner
405.3.n.a.179.33		204	1.1	even	1	trivial
405.3.n.a.224.2		204	27.20	odd	18	inner
405.3.n.a.224.33		204	135.74	odd	18	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.n (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.50983 + 1.27747i) q^{2} +(7.62280 + 6.39629i) q^{4} +(3.38697 + 3.67811i) q^{5} +(1.03030 + 1.22786i) q^{7} +(11.1135 + 19.2491i) q^{8} +(7.18899 + 17.2363i) q^{10} +(-11.9341 + 2.10430i) q^{11} +(-4.71168 - 12.9452i) q^{13} +(2.04761 + 5.62576i) q^{14} +(7.50440 + 42.5596i) q^{16} +(8.93265 - 15.4718i) q^{17} +(-14.5705 - 25.2368i) q^{19} +(2.29194 + 49.7015i) q^{20} +(-44.5747 - 7.85972i) q^{22} +(22.0238 + 18.4801i) q^{23} +(-2.05692 + 24.9152i) q^{25} -51.4546i q^{26} +15.9498i q^{28} +(6.96737 - 19.1427i) q^{29} +(-5.05373 - 4.24059i) q^{31} +(-12.5909 + 71.4065i) q^{32} +(51.1169 - 42.8922i) q^{34} +(-1.02662 + 7.94827i) q^{35} +(33.0454 + 19.0788i) q^{37} +(-18.9005 - 107.190i) q^{38} +(-33.1593 + 106.073i) q^{40} +(16.8042 + 46.1691i) q^{41} +(23.8547 - 4.20622i) q^{43} +(-104.431 - 60.2930i) q^{44} +(53.6918 + 92.9970i) q^{46} +(-5.12070 + 4.29678i) q^{47} +(8.06263 - 45.7255i) q^{49} +(-39.0480 + 84.8206i) q^{50} +(46.8852 - 128.816i) q^{52} -35.3575 q^{53} +(-48.1601 - 36.7675i) q^{55} +(-12.1850 + 33.4781i) q^{56} +(48.9086 - 58.2870i) q^{58} +(-81.0242 - 14.2868i) q^{59} +(-42.3934 + 35.5723i) q^{61} +(-12.3205 - 21.3398i) q^{62} +(-48.9797 + 84.8352i) q^{64} +(31.6556 - 61.1751i) q^{65} +(10.5187 + 28.8998i) q^{67} +(167.054 - 60.8026i) q^{68} +(-13.7570 + 26.5856i) q^{70} +(-46.8725 - 27.0619i) q^{71} +(80.6986 - 46.5914i) q^{73} +(91.6111 + 109.178i) q^{74} +(50.3540 - 285.572i) q^{76} +(-14.8794 - 12.4853i) q^{77} +(27.1542 + 9.88334i) q^{79} +(-131.121 + 171.750i) q^{80} +183.513i q^{82} +(25.7526 + 9.37318i) q^{83} +(87.1615 - 19.5472i) q^{85} +(89.0992 + 15.7106i) q^{86} +(-173.135 - 206.334i) q^{88} +(-41.9166 + 24.2006i) q^{89} +(11.0405 - 19.1227i) q^{91} +(49.6785 + 281.741i) q^{92} +(-23.4618 + 8.53941i) q^{94} +(43.4739 - 139.068i) q^{95} +(133.103 - 23.4697i) q^{97} +(86.7116 - 150.189i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 12 q^{4} - 3 q^{5} - 3 q^{10} - 6 q^{11} + 48 q^{14} + 12 q^{16} - 6 q^{19} - 63 q^{20} - 15 q^{25} - 96 q^{29} - 102 q^{31} + 12 q^{34} + 252 q^{35} + 117 q^{40} - 96 q^{41} + 666 q^{44} - 6 q^{46}+ \cdots + 543 q^{95}+O(q^{100}) \) 204 * q - 12 * q^4 - 3 * q^5 - 3 * q^10 - 6 * q^11 + 48 * q^14 + 12 * q^16 - 6 * q^19 - 63 * q^20 - 15 * q^25 - 96 * q^29 - 102 * q^31 + 12 * q^34 + 252 * q^35 + 117 * q^40 - 96 * q^41 + 666 * q^44 - 6 * q^46 + 60 * q^49 - 48 * q^50 - 12 * q^55 - 294 * q^56 - 510 * q^59 + 132 * q^61 - 486 * q^64 - 147 * q^65 - 141 * q^70 + 18 * q^71 + 954 * q^74 + 84 * q^76 - 48 * q^79 + 69 * q^85 + 1506 * q^86 - 792 * q^89 - 6 * q^91 + 492 * q^94 + 543 * q^95

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