LMFDB - Embedded newform 459.3.i.a.152.27

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,3,Mod(152,459)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("459.152"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	459.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$12.5068441341$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 153)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			152.27
Character	$\chi$	$=$	459.152
Dual form			459.3.i.a.305.27

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.44623 - 1.41233i) q^{2} +(1.98938 - 3.44570i) q^{4} +(1.84354 - 3.19311i) q^{5} +(-1.20670 + 0.696687i) q^{7} +0.0600221i q^{8} -10.4148i q^{10} +(-9.91827 - 17.1789i) q^{11} +(8.79901 - 15.2403i) q^{13} +(-1.96791 + 3.40852i) q^{14} +(8.04227 + 13.9296i) q^{16} +(-10.4620 - 13.3995i) q^{17} +17.1257 q^{19} +(-7.33500 - 12.7046i) q^{20} +(-48.5248 - 28.0158i) q^{22} +(8.76780 - 15.1863i) q^{23} +(5.70269 + 9.87734i) q^{25} -49.7086i q^{26} +5.54389i q^{28} +(-6.20471 - 10.7469i) q^{29} +(29.8091 + 17.2103i) q^{31} +(39.1386 + 22.5967i) q^{32} +(-44.5171 - 18.0024i) q^{34} +5.13750i q^{35} +13.0363i q^{37} +(41.8935 - 24.1872i) q^{38} +(0.191657 + 0.110653i) q^{40} +(-15.2683 + 26.4454i) q^{41} +(-17.3388 - 30.0317i) q^{43} -78.9246 q^{44} -49.5322i q^{46} +(-74.8051 + 43.1887i) q^{47} +(-23.5293 + 40.7539i) q^{49} +(27.9002 + 16.1082i) q^{50} +(-35.0091 - 60.6375i) q^{52} -11.8546i q^{53} -73.1391 q^{55} +(-0.0418166 - 0.0724285i) q^{56} +(-30.3564 - 17.5263i) q^{58} +(77.9699 + 45.0160i) q^{59} +(-1.04031 + 0.600624i) q^{61} +97.2267 q^{62} +63.3182 q^{64} +(-32.4427 - 56.1925i) q^{65} +(29.0384 - 50.2960i) q^{67} +(-66.9835 + 9.39240i) q^{68} +(7.25586 + 12.5675i) q^{70} +119.490 q^{71} +108.335i q^{73} +(18.4117 + 31.8899i) q^{74} +(34.0694 - 59.0100i) q^{76} +(23.9367 + 13.8199i) q^{77} +(-2.99178 + 1.72730i) q^{79} +59.3052 q^{80} +86.2557i q^{82} +(37.0145 - 21.3704i) q^{83} +(-62.0733 + 8.70389i) q^{85} +(-84.8297 - 48.9765i) q^{86} +(1.03112 - 0.595315i) q^{88} -43.3483i q^{89} +24.5206i q^{91} +(-34.8849 - 60.4224i) q^{92} +(-121.994 + 211.300i) q^{94} +(31.5720 - 54.6843i) q^{95} +(42.1943 - 24.3609i) q^{97} +132.925i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 62 q^{4} - 2 q^{13} - 106 q^{16} - 32 q^{19} - 132 q^{25} - 27 q^{34} + 102 q^{38} + 58 q^{43} + 312 q^{47} + 152 q^{49} + 90 q^{50} + 70 q^{52} + 92 q^{55} + 258 q^{59} - 16 q^{64} + 82 q^{67}+ \cdots - 18 q^{94}+O(q^{100}) $ 68 * q + 6 * q^2 + 62 * q^4 - 2 * q^13 - 106 * q^16 - 32 * q^19 - 132 * q^25 - 27 * q^34 + 102 * q^38 + 58 * q^43 + 312 * q^47 + 152 * q^49 + 90 * q^50 + 70 * q^52 + 92 * q^55 + 258 * q^59 - 16 * q^64 + 82 * q^67 + 333 * q^68 + 204 * q^70 + 34 * q^76 + 60 * q^77 + 690 * q^83 - 44 * q^85 + 1248 * q^86 - 18 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	2.44623	−	1.41233i	1.22312	−	0.706167i	0.257536	−	0.966269i	$-0.417089\pi$
$2$	2.44623	−	1.41233i	1.22312	−	0.706167i	0.965581	+	0.260102i	$0.0837561\pi$
$3$		0			0
$3$		0			0
$4$	1.98938	−	3.44570i	0.497344	−	0.861425i
$5$	1.84354	−	3.19311i	0.368709	−	0.638623i	−0.620655	−	0.784084i	$-0.713133\pi$
$5$	1.84354	−	3.19311i	0.368709	−	0.638623i	0.989364	+	0.145461i	$0.0464666\pi$
$6$		0			0
$7$	−1.20670	+	0.696687i	−0.172385	+	0.0995267i	−0.583710	−	0.811962i	$-0.698400\pi$
$7$	−1.20670	+	0.696687i	−0.172385	+	0.0995267i	0.411325	+	0.911489i	$0.365066\pi$
$8$			0.0600221i			0.00750276i
$9$		0			0
$10$		−	10.4148i		−	1.04148i
$11$	−9.91827	−	17.1789i	−0.901661	−	1.56172i	−0.825338	−	0.564639i	$-0.809016\pi$
$11$	−9.91827	−	17.1789i	−0.901661	−	1.56172i	−0.0763223	−	0.997083i	$-0.524318\pi$
$12$		0			0
$13$	8.79901	−	15.2403i	0.676847	−	1.17233i	−0.299079	−	0.954228i	$-0.596679\pi$
$13$	8.79901	−	15.2403i	0.676847	−	1.17233i	0.975925	−	0.218105i	$-0.0699874\pi$
$14$	−1.96791	+	3.40852i	−0.140565	+	0.243466i
$15$		0			0
$16$	8.04227	+	13.9296i	0.502642	+	0.870602i
$17$	−10.4620	−	13.3995i	−0.615413	−	0.788205i
$17$	−10.4620	−	13.3995i	−0.615413	−	0.788205i
$18$		0			0
$19$	17.1257			0.901352			0.450676	−	0.892688i	$-0.351183\pi$
$19$	17.1257			0.901352			0.450676	+	0.892688i	$0.351183\pi$
$20$	−7.33500	−	12.7046i	−0.366750	−	0.635230i
$21$		0			0
$22$	−48.5248	−	28.0158i	−2.20567	−	1.27345i
$23$	8.76780	−	15.1863i	0.381209	−	0.660273i	−0.610027	−	0.792381i	$-0.708841\pi$
$23$	8.76780	−	15.1863i	0.381209	−	0.660273i	0.991235	+	0.132108i	$0.0421747\pi$
$24$		0			0
$25$	5.70269	+	9.87734i	0.228107	+	0.395094i
$26$		−	49.7086i		−	1.91187i
$27$		0			0
$28$			5.54389i			0.197996i
$29$	−6.20471	−	10.7469i	−0.213956	−	0.370582i	0.738993	−	0.673713i	$-0.235301\pi$
$29$	−6.20471	−	10.7469i	−0.213956	−	0.370582i	−0.952949	+	0.303131i	$0.901968\pi$
$30$		0			0
$31$	29.8091	+	17.2103i	0.961584	+	0.555171i	0.896660	−	0.442719i	$-0.145986\pi$
$31$	29.8091	+	17.2103i	0.961584	+	0.555171i	0.0649238	+	0.997890i	$0.479320\pi$
$32$	39.1386	+	22.5967i	1.22308	+	0.706147i
$33$		0			0
$34$	−44.5171	−	18.0024i	−1.30933	−	0.529482i
$35$			5.13750i			0.146786i
$36$		0			0
$37$			13.0363i			0.352333i	0.984360	+	0.176167i	$0.0563698\pi$
$37$			13.0363i			0.352333i	−0.984360	+	0.176167i	$0.943630\pi$
$38$	41.8935	−	24.1872i	1.10246	−	0.636505i
$39$		0			0
$40$	0.191657	+	0.110653i	0.00479143	+	0.00276633i
$41$	−15.2683	+	26.4454i	−0.372397	+	0.645011i	−0.989934	−	0.141531i	$-0.954797\pi$
$41$	−15.2683	+	26.4454i	−0.372397	+	0.645011i	0.617537	+	0.786542i	$0.288131\pi$
$42$		0			0
$43$	−17.3388	−	30.0317i	−0.403229	−	0.698413i	0.590885	−	0.806756i	$-0.298779\pi$
$43$	−17.3388	−	30.0317i	−0.403229	−	0.698413i	−0.994114	+	0.108343i	$0.965445\pi$
$44$	−78.9246			−1.79374
$45$		0			0
$46$		−	49.5322i		−	1.07679i
$47$	−74.8051	+	43.1887i	−1.59160	+	0.918909i	−0.598564	+	0.801075i	$0.704262\pi$
$47$	−74.8051	+	43.1887i	−1.59160	+	0.918909i	−0.993033	+	0.117834i	$0.962405\pi$
$48$		0			0
$49$	−23.5293	+	40.7539i	−0.480189	+	0.831711i
$50$	27.9002	+	16.1082i	0.558004	+	0.322164i
$51$		0			0
$52$	−35.0091	−	60.6375i	−0.673251	−	1.16611i
$53$		−	11.8546i		−	0.223672i	−0.993727	−	0.111836i	$-0.964327\pi$
$53$		−	11.8546i		−	0.223672i	0.993727	−	0.111836i	$-0.0356731\pi$
$54$		0			0
$55$	−73.1391			−1.32980
$56$	−0.0418166	−	0.0724285i	−0.000746725	−	0.00129337i
$57$		0			0
$58$	−30.3564	−	17.5263i	−0.523385	−	0.302177i
$59$	77.9699	+	45.0160i	1.32152	+	0.762982i	0.983972	−	0.178324i	$-0.0570676\pi$
$59$	77.9699	+	45.0160i	1.32152	+	0.762982i	0.337553	+	0.941307i	$0.390401\pi$
$60$		0			0
$61$	−1.04031	+	0.600624i	−0.0170543	+	0.00984629i	−0.508503	−	0.861060i	$-0.669801\pi$
$61$	−1.04031	+	0.600624i	−0.0170543	+	0.00984629i	0.491449	+	0.870907i	$0.336468\pi$
$62$	97.2267			1.56817
$63$		0			0
$64$	63.3182			0.989347
$65$	−32.4427	−	56.1925i	−0.499119	−	0.864499i
$66$		0			0
$67$	29.0384	−	50.2960i	0.433409	−	0.750687i	−0.563755	−	0.825942i	$-0.690644\pi$
$67$	29.0384	−	50.2960i	0.433409	−	0.750687i	0.997164	+	0.0752549i	$0.0239771\pi$
$68$	−66.9835	+	9.39240i	−0.985051	+	0.138124i
$69$		0			0
$70$	7.25586	+	12.5675i	0.103655	+	0.179536i
$71$	119.490			1.68296			0.841481	−	0.540287i	$-0.181684\pi$
$71$	119.490			1.68296			0.841481	+	0.540287i	$0.181684\pi$
$72$		0			0
$73$			108.335i			1.48404i	0.670377	+	0.742021i	$0.266133\pi$
$73$			108.335i			1.48404i	−0.670377	+	0.742021i	$0.733867\pi$
$74$	18.4117	+	31.8899i	0.248806	+	0.430945i
$75$		0			0
$76$	34.0694	−	59.0100i	0.448282	−	0.776447i
$77$	23.9367	+	13.8199i	0.310866	+	0.179479i
$78$		0			0
$79$	−2.99178	+	1.72730i	−0.0378706	+	0.0218646i	−0.518816	−	0.854886i	$-0.673627\pi$
$79$	−2.99178	+	1.72730i	−0.0378706	+	0.0218646i	0.480945	+	0.876751i	$0.340294\pi$
$80$	59.3052			0.741314
$81$		0			0
$82$			86.2557i			1.05190i
$83$	37.0145	−	21.3704i	0.445958	−	0.257474i	−0.260163	−	0.965565i	$-0.583776\pi$
$83$	37.0145	−	21.3704i	0.445958	−	0.257474i	0.706122	+	0.708090i	$0.250443\pi$
$84$		0			0
$85$	−62.0733	+	8.70389i	−0.730274	+	0.102399i
$86$	−84.8297	−	48.9765i	−0.986392	−	0.569494i
$87$		0			0
$88$	1.03112	−	0.595315i	0.0117172	−	0.00676494i
$89$		−	43.3483i		−	0.487060i	−0.969893	−	0.243530i	$-0.921695\pi$
$89$		−	43.3483i		−	0.487060i	0.969893	−	0.243530i	$-0.0783054\pi$
$90$		0			0
$91$			24.5206i			0.269457i
$92$	−34.8849	−	60.4224i	−0.379183	−	0.656765i
$93$		0			0
$94$	−121.994	+	211.300i	−1.29781	+	2.24787i
$95$	31.5720	−	54.6843i	0.332337	−	0.575624i
$96$		0			0
$97$	42.1943	−	24.3609i	0.434993	−	0.251143i	−0.266478	−	0.963841i	$-0.585860\pi$
$97$	42.1943	−	24.3609i	0.434993	−	0.251143i	0.701471	+	0.712698i	$0.252527\pi$
$98$			132.925i			1.35637i
$99$		0			0
$100$	45.3791			0.453791
$101$	−49.3410	+	28.4870i	−0.488524	+	0.282050i	−0.723962	−	0.689840i	$-0.757681\pi$
$101$	−49.3410	+	28.4870i	−0.488524	+	0.282050i	0.235438	+	0.971889i	$0.424348\pi$
$102$		0			0
$103$	30.2358	−	52.3700i	0.293552	−	0.508446i	−0.681095	−	0.732195i	$-0.738496\pi$
$103$	30.2358	−	52.3700i	0.293552	−	0.508446i	0.974647	+	0.223749i	$0.0718294\pi$
$104$	0.914756	+	0.528135i	0.00879573	+	0.00507822i
$105$		0			0
$106$	−16.7427	−	28.9991i	−0.157950	−	0.273577i
$107$	−2.02648			−0.0189390			−0.00946952	−	0.999955i	$-0.503014\pi$
$107$	−2.02648			−0.0189390			−0.00946952	+	0.999955i	$0.503014\pi$
$108$		0			0
$109$			57.0549i			0.523440i	0.965144	+	0.261720i	$0.0842896\pi$
$109$			57.0549i			0.523440i	−0.965144	+	0.261720i	$0.915710\pi$
$110$	−178.915	+	103.297i	−1.62650	+	0.939062i
$111$		0			0
$112$	−19.4092	−	11.2059i	−0.173296	−	0.100053i
$113$	−86.9813	+	150.656i	−0.769746	+	1.33324i	0.167954	+	0.985795i	$0.446284\pi$
$113$	−86.9813	+	150.656i	−0.769746	+	1.33324i	−0.937701	+	0.347445i	$0.887049\pi$
$114$		0			0
$115$	−32.3276	−	55.9931i	−0.281110	−	0.486897i
$116$	−49.3740			−0.425638
$117$		0			0
$118$	254.310			2.15517
$119$	21.9597	+	8.88036i	0.184536	+	0.0746249i
$120$		0			0
$121$	−136.244	+	235.982i	−1.12598	+	1.95026i
$122$	−1.69656	+	2.93853i	−0.0139063	+	0.0240863i
$123$		0			0
$124$	118.603	−	68.4755i	0.956476	−	0.552222i
$125$	134.230			1.07384
$126$		0			0
$127$	44.1786			0.347863			0.173932	−	0.984758i	$-0.444353\pi$
$127$	44.1786			0.347863			0.173932	+	0.984758i	$0.444353\pi$
$128$	−1.66336	+	0.960340i	−0.0129950	+	0.00750265i
$129$		0			0
$130$	−158.725	−	91.6399i	−1.22096	−	0.704923i
$131$	10.9841	−	19.0250i	0.0838479	−	0.145229i	−0.821052	−	0.570854i	$-0.806612\pi$
$131$	10.9841	−	19.0250i	0.0838479	−	0.145229i	0.904900	+	0.425625i	$0.139946\pi$
$132$		0			0
$133$	−20.6655	+	11.9312i	−0.155380	+	0.0897086i
$134$		−	164.048i		−	1.22424i
$135$		0			0
$136$	0.804264	−	0.627952i	0.00591371	−	0.00461730i
$137$	61.9886	−	35.7891i	0.452471	−	0.261234i	−0.256402	−	0.966570i	$-0.582537\pi$
$137$	61.9886	−	35.7891i	0.452471	−	0.261234i	0.708873	+	0.705336i	$0.249204\pi$
$138$		0			0
$139$	167.030	+	96.4351i	1.20166	+	0.693778i	0.960924	−	0.276813i	$-0.0892784\pi$
$139$	167.030	+	96.4351i	1.20166	+	0.693778i	0.240734	+	0.970591i	$0.422612\pi$
$140$	17.7023	+	10.2204i	0.126445	+	0.0730029i
$141$		0			0
$142$	292.301	−	168.760i	2.05846	−	1.18845i
$143$	−349.084			−2.44114
$144$		0			0
$145$	−45.7546			−0.315549
$146$	153.005	+	265.013i	1.04798	+	1.81516i
$147$		0			0
$148$	44.9193	+	25.9342i	0.303509	+	0.175231i
$149$	−107.129	−	61.8512i	−0.718989	−	0.415108i	0.0953916	−	0.995440i	$-0.469590\pi$
$149$	−107.129	−	61.8512i	−0.718989	−	0.415108i	−0.814380	+	0.580331i	$0.802923\pi$
$150$		0			0
$151$	36.8378	+	63.8049i	0.243959	+	0.422549i	0.961838	−	0.273618i	$-0.0882205\pi$
$151$	36.8378	+	63.8049i	0.243959	+	0.422549i	−0.717879	+	0.696167i	$0.754887\pi$
$152$			1.02792i			0.00676263i
$153$		0			0
$154$	78.0730			0.506968
$155$	109.909	−	63.4559i	0.709089	−	0.409393i
$156$		0			0
$157$	3.12950	−	5.42045i	0.0199331	−	0.0345252i	−0.855887	−	0.517163i	$-0.826988\pi$
$157$	3.12950	−	5.42045i	0.0199331	−	0.0345252i	0.875820	+	0.482638i	$0.160321\pi$
$158$	−4.87906	+	8.45078i	−0.0308801	+	0.0534860i
$159$		0			0
$160$	144.308	−	83.3161i	0.901923	−	0.520725i
$161$			24.4336i			0.151762i
$162$		0			0
$163$			47.6644i			0.292420i	0.989254	+	0.146210i	$0.0467074\pi$
$163$			47.6644i			0.292420i	−0.989254	+	0.146210i	$0.953293\pi$
$164$	60.7487	+	105.220i	0.370419	+	0.641584i
$165$		0			0
$166$	60.3642	−	104.554i	0.363640	−	0.629842i
$167$	−61.6977	+	106.864i	−0.369447	+	0.639902i	−0.989479	−	0.144675i	$-0.953786\pi$
$167$	−61.6977	+	106.864i	−0.369447	+	0.639902i	0.620032	+	0.784577i	$0.287120\pi$
$168$		0			0
$169$	−70.3451	−	121.841i	−0.416243	−	0.720954i
$170$	−139.553	+	108.960i	−0.820900	+	0.640941i
$171$		0			0
$172$	−137.974			−0.802173
$173$	−63.7569	−	110.430i	−0.368537	−	0.638325i	0.620800	−	0.783969i	$-0.286808\pi$
$173$	−63.7569	−	110.430i	−0.368537	−	0.638325i	−0.989337	+	0.145644i	$0.953475\pi$
$174$		0			0
$175$	−13.7628	−	7.94598i	−0.0786448	−	0.0454056i
$176$	159.531	−	276.315i	0.906425	−	1.56997i
$177$		0			0
$178$	−61.2223	−	106.040i	−0.343946	−	0.595731i
$179$		−	176.481i		−	0.985925i	−0.870050	−	0.492963i	$-0.835914\pi$
$179$		−	176.481i		−	0.985925i	0.870050	−	0.492963i	$-0.164086\pi$
$180$		0			0
$181$		−	184.304i		−	1.01825i	−0.860692	−	0.509126i	$-0.829969\pi$
$181$		−	184.304i		−	1.01825i	0.860692	−	0.509126i	$-0.170031\pi$
$182$	34.6313	+	59.9832i	0.190282	+	0.329578i
$183$		0			0
$184$	0.911511	+	0.526261i	0.00495387	+	0.00286012i
$185$	41.6265	+	24.0331i	0.225008	+	0.129908i
$186$		0			0
$187$	−126.424	+	312.626i	−0.676063	+	1.67180i
$188$			343.674i			1.82806i
$189$		0			0
$190$		−	178.361i		−	0.938741i
$191$	43.0602	−	24.8608i	0.225446	−	0.130161i	−0.383023	−	0.923739i	$-0.625117\pi$
$191$	43.0602	−	24.8608i	0.225446	−	0.130161i	0.608469	+	0.793577i	$0.291784\pi$
$192$		0			0
$193$	70.3903	+	40.6399i	0.364717	+	0.210569i	0.671148	−	0.741324i	$-0.265802\pi$
$193$	70.3903	+	40.6399i	0.364717	+	0.210569i	−0.306431	+	0.951893i	$0.599135\pi$
$194$	68.8115	−	119.185i	0.354698	−	0.614356i
$195$		0			0
$196$	93.6170	+	162.149i	0.477638	+	0.827293i
$197$	197.609			1.00309			0.501546	−	0.865131i	$-0.332765\pi$
$197$	197.609			1.00309			0.501546	+	0.865131i	$0.332765\pi$
$198$		0			0
$199$		−	356.582i		−	1.79187i	−0.444187	−	0.895934i	$-0.646507\pi$
$199$		−	356.582i		−	1.79187i	0.444187	−	0.895934i	$-0.353493\pi$
$200$	−0.592859	+	0.342287i	−0.00296429	+	0.00171144i
$201$		0			0
$202$	−80.4664	+	139.372i	−0.398348	+	0.689960i
$203$	14.9744	+	8.64549i	0.0737656	+	0.0425886i
$204$		0			0
$205$	56.2955	+	97.5067i	0.274612	+	0.475642i
$206$		−	170.812i		−	0.829186i
$207$		0			0
$208$	283.056			1.36085
$209$	−169.857	−	294.201i	−0.812714	−	1.40766i
$210$		0			0
$211$	−152.648	−	88.1313i	−0.723450	−	0.417684i	0.0925713	−	0.995706i	$-0.470491\pi$
$211$	−152.648	−	88.1313i	−0.723450	−	0.417684i	−0.816021	+	0.578022i	$0.803825\pi$
$212$	−40.8474	−	23.5833i	−0.192676	−	0.111242i
$213$		0			0
$214$	−4.95724	+	2.86206i	−0.0231647	+	0.0133741i
$215$	−127.860			−0.594696
$216$		0			0
$217$	−47.9608			−0.221017
$218$	80.5806	+	139.570i	0.369636	+	0.640228i
$219$		0			0
$220$	−145.501	+	252.015i	−0.661368	+	1.14552i
$221$	−296.268	+	41.5426i	−1.34058	+	0.187976i
$222$		0			0
$223$	−124.855	−	216.256i	−0.559889	−	0.969756i	−0.997505	−	0.0705940i	$-0.977511\pi$
$223$	−124.855	−	216.256i	−0.559889	−	0.969756i	0.437616	−	0.899162i	$-0.355823\pi$
$224$	−62.9714			−0.281122
$225$		0			0
$226$			491.387i			2.17428i
$227$	141.368	+	244.856i	0.622766	+	1.07866i	0.988968	+	0.148128i	$0.0473246\pi$
$227$	141.368	+	244.856i	0.622766	+	1.07866i	−0.366202	+	0.930535i	$0.619342\pi$
$228$		0			0
$229$	160.551	−	278.083i	0.701096	−	1.21433i	−0.266986	−	0.963700i	$-0.586028\pi$
$229$	160.551	−	278.083i	0.701096	−	1.21433i	0.968082	−	0.250634i	$-0.0806390\pi$
$230$	−158.162	−	91.3149i	−0.687661	−	0.397021i
$231$		0			0
$232$	0.645050	−	0.372420i	0.00278039	−	0.00160526i
$233$	308.597			1.32445			0.662225	−	0.749305i	$-0.269612\pi$
$233$	308.597			1.32445			0.662225	+	0.749305i	$0.269612\pi$
$234$		0			0
$235$			318.481i			1.35524i
$236$	310.223	−	179.107i	1.31450	−	0.758929i
$237$		0			0
$238$	66.2607	−	9.29106i	0.278406	−	0.0390381i
$239$	345.060	+	199.221i	1.44377	+	0.833559i	0.998098	−	0.0616393i	$-0.0196328\pi$
$239$	345.060	+	199.221i	1.44377	+	0.833559i	0.445668	+	0.895198i	$0.352966\pi$
$240$		0			0
$241$	−257.575	+	148.711i	−1.06878	+	0.617058i	−0.927847	−	0.372962i	$-0.878342\pi$
$241$	−257.575	+	148.711i	−1.06878	+	0.617058i	−0.140929	+	0.990020i	$0.545009\pi$
$242$			769.688i			3.18053i
$243$		0			0
$244$			4.77947i			0.0195880i
$245$	86.7545	+	150.263i	0.354100	+	0.613319i
$246$		0			0
$247$	150.689	−	261.001i	0.610077	−	1.05668i
$248$	−1.03300	+	1.78920i	−0.00416531	+	0.00721453i
$249$		0			0
$250$	328.358	−	189.577i	1.31343	−	0.758310i
$251$		−	129.889i		−	0.517488i	−0.965946	−	0.258744i	$-0.916691\pi$
$251$		−	129.889i		−	0.517488i	0.965946	−	0.258744i	$-0.0833085\pi$
$252$		0			0
$253$	−347.845			−1.37488
$254$	108.071	−	62.3950i	0.425478	−	0.245650i
$255$		0			0
$256$	−129.349	+	224.039i	−0.505270	+	0.875153i
$257$	−247.879	−	143.113i	−0.964510	−	0.556860i	−0.0669517	−	0.997756i	$-0.521327\pi$
$257$	−247.879	−	143.113i	−0.964510	−	0.556860i	−0.897558	+	0.440896i	$0.854661\pi$
$258$		0			0
$259$	−9.08225	−	15.7309i	−0.0350666	−	0.0607371i
$260$	−258.163			−0.992935
$261$		0			0
$262$		−	62.0528i		−	0.236843i
$263$	−392.362	+	226.530i	−1.49187	+	0.861333i	−0.999957	−	0.00931071i	$-0.997036\pi$
$263$	−392.362	+	226.530i	−1.49187	+	0.861333i	−0.491915	+	0.870643i	$0.663703\pi$
$264$		0			0
$265$	−37.8531	−	21.8545i	−0.142842	−	0.0824698i
$266$	−33.7018	+	58.3733i	−0.126699	+	0.219448i
$267$		0			0
$268$	−115.537	−	200.115i	−0.431107	−	0.746699i
$269$	−492.362			−1.83034			−0.915171	−	0.403065i	$-0.867945\pi$
$269$	−492.362			−1.83034			−0.915171	+	0.403065i	$0.867945\pi$
$270$		0			0
$271$	−368.404			−1.35943			−0.679713	−	0.733478i	$-0.737896\pi$
$271$	−368.404			−1.35943			−0.679713	+	0.733478i	$0.737896\pi$
$272$	102.511	−	253.494i	0.376880	−	0.931965i
$273$		0			0
$274$	101.092	−	175.097i	0.368950	−	0.639041i
$275$	113.122	−	195.932i	0.411351	−	0.712481i
$276$		0			0
$277$	64.1297	−	37.0253i	0.231515	−	0.133665i	−0.379756	−	0.925087i	$-0.623992\pi$
$277$	64.1297	−	37.0253i	0.231515	−	0.133665i	0.611271	+	0.791421i	$0.290659\pi$
$278$	544.794			1.95969
$279$		0			0
$280$	−0.308363			−0.00110130
$281$	−27.0876	+	15.6390i	−0.0963971	+	0.0556549i	−0.547424	−	0.836856i	$-0.684391\pi$
$281$	−27.0876	+	15.6390i	−0.0963971	+	0.0556549i	0.451027	+	0.892511i	$0.351058\pi$
$282$		0			0
$283$	−161.385	−	93.1759i	−0.570267	−	0.329244i	0.186989	−	0.982362i	$-0.440127\pi$
$283$	−161.385	−	93.1759i	−0.570267	−	0.329244i	−0.757256	+	0.653118i	$0.773460\pi$
$284$	237.711	−	411.728i	0.837011	−	1.44974i
$285$		0			0
$286$	−853.940	+	493.023i	−2.98581	+	1.72386i
$287$		−	42.5489i		−	0.148254i
$288$		0			0
$289$	−70.0920	+	280.371i	−0.242533	+	0.970143i
$290$	−111.927	+	64.6208i	−0.385954	+	0.222831i
$291$		0			0
$292$	373.290	+	215.519i	1.27839	+	0.738079i
$293$	−226.180	−	130.585i	−0.771945	−	0.445683i	0.0616231	−	0.998099i	$-0.480372\pi$
$293$	−226.180	−	130.585i	−0.771945	−	0.445683i	−0.833568	+	0.552417i	$0.813706\pi$
$294$		0			0
$295$	287.482	−	165.978i	0.974516	−	0.562637i
$296$	−0.782468			−0.00264347
$297$		0			0
$298$	−349.418			−1.17254
$299$	−154.296	−	267.248i	−0.516040	−	0.893807i
$300$		0			0
$301$	41.8455	+	24.1595i	0.139022	+	0.0802641i
$302$	180.228	+	104.055i	0.596781	+	0.344551i
$303$		0			0
$304$	137.729	+	238.554i	0.453057	+	0.784719i
$305$			4.42911i			0.0145217i
$306$		0			0
$307$	443.373			1.44421			0.722106	−	0.691783i	$-0.243174\pi$
$307$	443.373			1.44421			0.722106	+	0.691783i	$0.243174\pi$
$308$	95.2382	−	54.9858i	0.309215	−	0.178525i
$309$		0			0
$310$	179.242	−	310.456i	0.578199	−	1.00147i
$311$	−148.284	+	256.836i	−0.476799	+	0.825840i	−0.999647	−	0.0265862i	$-0.991536\pi$
$311$	−148.284	+	256.836i	−0.476799	+	0.825840i	0.522848	+	0.852426i	$0.324870\pi$
$312$		0			0
$313$	−433.167	+	250.089i	−1.38392	+	0.799006i	−0.992621	−	0.121258i	$-0.961307\pi$
$313$	−433.167	+	250.089i	−1.38392	+	0.799006i	−0.391298	+	0.920264i	$0.627974\pi$
$314$		−	17.6796i		−	0.0563044i
$315$		0			0
$316$			13.7450i			0.0434969i
$317$	189.329	+	327.928i	0.597254	+	1.03447i	0.993225	+	0.116211i	$0.0370748\pi$
$317$	189.329	+	327.928i	0.597254	+	1.03447i	−0.395971	+	0.918263i	$0.629592\pi$
$318$		0			0
$319$	−123.080	+	213.181i	−0.385831	+	0.668278i
$320$	116.730	−	202.182i	0.364781	−	0.631820i
$321$		0			0
$322$	34.5085	+	59.7704i	0.107169	+	0.185622i
$323$	−179.169	−	229.475i	−0.554704	−	0.710450i
$324$		0			0
$325$	200.712			0.617575
$326$	67.3180	+	116.598i	0.206497	+	0.357663i
$327$		0			0
$328$	−1.58731	−	0.916434i	−0.00483936	−	0.00279401i
$329$	60.1781	−	104.231i	0.182912	−	0.316813i
$330$		0			0
$331$	−82.0944	−	142.192i	−0.248019	−	0.429582i	0.714957	−	0.699169i	$-0.246446\pi$
$331$	−82.0944	−	142.192i	−0.248019	−	0.429582i	−0.962976	+	0.269587i	$0.913113\pi$
$332$		−	170.055i		−	0.512213i
$333$		0			0
$334$			348.551i			1.04357i
$335$	−107.067	−	185.446i	−0.319604	−	0.553570i
$336$		0			0
$337$	46.6553	+	26.9365i	0.138443	+	0.0799301i	0.567622	−	0.823289i	$-0.307864\pi$
$337$	46.6553	+	26.9365i	0.138443	+	0.0799301i	−0.429179	+	0.903220i	$0.641197\pi$
$338$	−344.161	−	198.702i	−1.01823	−	0.587875i
$339$		0			0
$340$	−93.4960	+	231.201i	−0.274988	+	0.680003i
$341$		−	682.785i		−	2.00230i
$342$		0			0
$343$		−	133.845i		−	0.390220i
$344$	1.80257	−	1.04071i	0.00524002	−	0.00302533i
$345$		0			0
$346$	−311.929	−	180.092i	−0.901528	−	0.520497i
$347$	66.4656	−	115.122i	0.191543	−	0.331763i	−0.754218	−	0.656624i	$-0.771984\pi$
$347$	66.4656	−	115.122i	0.191543	−	0.331763i	0.945762	+	0.324861i	$0.105317\pi$
$348$		0			0
$349$	100.388	+	173.877i	0.287644	+	0.498214i	0.973247	−	0.229762i	$-0.0737947\pi$
$349$	100.388	+	173.877i	0.287644	+	0.498214i	−0.685603	+	0.727976i	$0.740461\pi$
$350$	−44.8895			−0.128256
$351$		0			0
$352$		−	896.481i		−	2.54682i
$353$	351.282	−	202.813i	0.995133	−	0.574540i	0.0883284	−	0.996091i	$-0.471848\pi$
$353$	351.282	−	202.813i	0.995133	−	0.574540i	0.906805	+	0.421551i	$0.138514\pi$
$354$		0			0
$355$	220.286	−	381.546i	0.620523	−	1.07478i
$356$	−149.365	−	86.2361i	−0.419566	−	0.242236i
$357$		0			0
$358$	−249.250	−	431.713i	−0.696228	−	1.20590i
$359$			485.639i			1.35276i	0.736555	+	0.676378i	$0.236451\pi$
$359$			485.639i			1.35276i	−0.736555	+	0.676378i	$0.763549\pi$
$360$		0			0
$361$	−67.7107			−0.187564
$362$	−260.298	−	450.850i	−0.719056	−	1.24544i
$363$		0			0
$364$	84.4907	+	48.7807i	0.232117	+	0.134013i
$365$	345.926	+	199.721i	0.947743	+	0.547180i
$366$		0			0
$367$	−160.726	+	92.7954i	−0.437946	+	0.252848i	−0.702726	−	0.711460i	$-0.748034\pi$
$367$	−160.726	+	92.7954i	−0.437946	+	0.252848i	0.264780	+	0.964309i	$0.414701\pi$
$368$	282.052			0.766446
$369$		0			0
$370$	135.771			0.366948
$371$	8.25895	+	14.3049i	0.0222613	+	0.0385578i
$372$		0			0
$373$	115.761	−	200.505i	0.310352	−	0.537546i	−0.668086	−	0.744084i	$-0.732886\pi$
$373$	115.761	−	200.505i	0.310352	−	0.537546i	0.978439	+	0.206538i	$0.0662197\pi$
$374$	132.271	+	943.309i	0.353665	+	2.52222i
$375$		0			0
$376$	−2.59228	−	4.48996i	−0.00689435	−	0.0119414i
$377$	−218.381			−0.579261
$378$		0			0
$379$		−	384.647i		−	1.01490i	−0.861681	−	0.507450i	$-0.830588\pi$
$379$		−	384.647i		−	1.01490i	0.861681	−	0.507450i	$-0.169412\pi$
$380$	−125.617	−	217.575i	−0.330571	−	0.572566i
$381$		0			0
$382$	70.2235	−	121.631i	0.183831	−	0.318405i
$383$	550.654	+	317.920i	1.43774	+	0.830079i	0.997692	−	0.0678966i	$-0.0216288\pi$
$383$	550.654	+	317.920i	1.43774	+	0.830079i	0.440046	+	0.897975i	$0.354962\pi$
$384$		0			0
$385$	88.2567	−	50.9551i	0.229238	−	0.132351i
$386$	229.588			0.594788
$387$		0			0
$388$		−	193.852i		−	0.499618i
$389$	−98.7344	+	57.0043i	−0.253816	+	0.146541i	−0.621510	−	0.783406i	$-0.713481\pi$
$389$	−98.7344	+	57.0043i	−0.253816	+	0.146541i	0.367694	+	0.929947i	$0.380147\pi$
$390$		0			0
$391$	−295.217	+	41.3952i	−0.755031	+	0.105870i
$392$	−2.44613	−	1.41227i	−0.00624013	−	0.00360274i
$393$		0			0
$394$	483.398	−	279.090i	1.22690	−	0.708350i
$395$			12.7375i			0.0322467i
$396$		0			0
$397$		−	319.137i		−	0.803871i	−0.915668	−	0.401936i	$-0.868338\pi$
$397$		−	319.137i		−	0.803871i	0.915668	−	0.401936i	$-0.131662\pi$
$398$	−503.613	−	872.283i	−1.26536	−	2.19167i
$399$		0			0
$400$	−91.7251	+	158.873i	−0.229313	+	0.397181i
$401$	−387.164	+	670.588i	−0.965496	+	1.67229i	−0.257221	+	0.966353i	$0.582807\pi$
$401$	−387.164	+	670.588i	−0.965496	+	1.67229i	−0.708276	+	0.705936i	$0.750527\pi$
$402$		0			0
$403$	524.581	−	302.867i	1.30169	−	0.751531i
$404$			226.685i			0.561103i
$405$		0			0
$406$	48.8413			0.120299
$407$	223.950	−	129.298i	0.550247	−	0.317685i
$408$		0			0
$409$	9.35760	−	16.2078i	0.0228792	−	0.0396280i	−0.854359	−	0.519683i	$-0.826050\pi$
$409$	9.35760	−	16.2078i	0.0228792	−	0.0396280i	0.877238	+	0.480055i	$0.159383\pi$
$410$	275.424	+	159.016i	0.671766	+	0.387844i
$411$		0			0
$412$	−120.301	−	208.367i	−0.291992	−	0.505745i
$413$	−125.448			−0.303749
$414$		0			0
$415$		−	157.589i		−	0.379732i
$416$	688.763	−	397.657i	1.65568	−	0.955907i
$417$		0			0
$418$	−831.021	−	479.790i	−1.98809	−	1.14782i
$419$	289.963	−	502.231i	0.692036	−	1.19864i	−0.279133	−	0.960252i	$-0.590047\pi$
$419$	289.963	−	502.231i	0.692036	−	1.19864i	0.971170	−	0.238390i	$-0.0766196\pi$
$420$		0			0
$421$	149.481	+	258.909i	0.355062	+	0.614985i	0.987128	−	0.159929i	$-0.0511266\pi$
$421$	149.481	+	258.909i	0.355062	+	0.614985i	−0.632067	+	0.774914i	$0.717793\pi$
$422$	−497.883			−1.17982
$423$		0			0
$424$	0.711538			0.00167816
$425$	72.6896	−	179.750i	0.171034	−	0.422941i
$426$		0			0
$427$	0.836894	−	1.44954i	0.00195994	−	0.00339471i
$428$	−4.03142	+	6.98263i	−0.00941921	+	0.0163146i
$429$		0			0
$430$	−312.775	+	180.581i	−0.727383	+	0.419955i
$431$	210.336			0.488018			0.244009	−	0.969773i	$-0.421537\pi$
$431$	210.336			0.488018			0.244009	+	0.969773i	$0.421537\pi$
$432$		0			0
$433$	−530.660			−1.22554			−0.612771	−	0.790260i	$-0.709945\pi$
$433$	−530.660			−1.22554			−0.612771	+	0.790260i	$0.709945\pi$
$434$	−117.323	+	67.7366i	−0.270330	+	0.156075i
$435$		0			0
$436$	196.594	+	113.504i	0.450904	+	0.260329i
$437$	150.155	−	260.075i	0.343603	−	0.595138i
$438$		0			0
$439$	−231.727	+	133.788i	−0.527853	+	0.304756i	−0.740142	−	0.672451i	$-0.765242\pi$
$439$	−231.727	+	133.788i	−0.527853	+	0.304756i	0.212289	+	0.977207i	$0.431908\pi$
$440$		−	4.38996i		−	0.00997718i
$441$		0			0
$442$	−666.069	+	520.052i	−1.50694	+	1.17659i
$443$	−674.555	+	389.455i	−1.52270	+	0.879130i	−0.523058	+	0.852297i	$0.675209\pi$
$443$	−674.555	+	389.455i	−1.52270	+	0.879130i	−0.999640	+	0.0268335i	$0.991458\pi$
$444$		0			0
$445$	−138.416	−	79.9146i	−0.311048	−	0.179583i
$446$	−610.850	−	352.674i	−1.36962	−	0.790750i
$447$		0			0
$448$	−76.4060	+	44.1130i	−0.170549	+	0.0984665i
$449$	−80.4398			−0.179153			−0.0895766	−	0.995980i	$-0.528551\pi$
$449$	−80.4398			−0.179153			−0.0895766	+	0.995980i	$0.528551\pi$
$450$		0			0
$451$	605.739			1.34310
$452$	346.077	+	599.423i	0.765657	+	1.32616i
$453$		0			0
$454$	691.638	+	399.318i	1.52343	+	0.879554i
$455$	78.2971	+	45.2049i	0.172082	+	0.0993514i
$456$		0			0
$457$	218.961	+	379.252i	0.479127	+	0.829872i	0.999713	−	0.0239367i	$-0.00762001\pi$
$457$	218.961	+	379.252i	0.479127	+	0.829872i	−0.520587	+	0.853809i	$0.674287\pi$
$458$		−	907.007i		−	1.98036i
$459$		0			0
$460$	−257.247			−0.559233
$461$	−657.551	+	379.637i	−1.42636	+	0.823509i	−0.996831	−	0.0795452i	$-0.974653\pi$
$461$	−657.551	+	379.637i	−1.42636	+	0.823509i	−0.429527	+	0.903054i	$0.641320\pi$
$462$		0			0
$463$	248.865	−	431.047i	0.537506	−	0.930987i	−0.461532	−	0.887124i	$-0.652700\pi$
$463$	248.865	−	431.047i	0.537506	−	0.930987i	0.999038	−	0.0438634i	$-0.0139666\pi$
$464$	99.8000	−	172.859i	0.215086	−	0.372540i
$465$		0			0
$466$	754.900	−	435.842i	1.61996	−	0.935283i
$467$			56.4240i			0.120822i	0.998174	+	0.0604112i	$0.0192412\pi$
$467$			56.4240i			0.120822i	−0.998174	+	0.0604112i	$0.980759\pi$
$468$		0			0
$469$			80.9228i			0.172543i
$470$	449.802	+	779.080i	0.957026	+	1.65762i
$471$		0			0
$472$	−2.70195	+	4.67992i	−0.00572447	+	0.00991508i
$473$	−343.942	+	595.726i	−0.727151	+	1.25946i
$474$		0			0
$475$	97.6624	+	169.156i	0.205605	+	0.356119i
$476$	74.2852	−	58.0003i	0.156061	−	0.121849i
$477$		0			0
$478$	1125.46			2.35453
$479$	−149.317	−	258.625i	−0.311727	−	0.539927i	0.667009	−	0.745049i	$-0.267574\pi$
$479$	−149.317	−	258.625i	−0.311727	−	0.539927i	−0.978736	+	0.205122i	$0.934241\pi$
$480$		0			0
$481$	198.678	+	114.707i	0.413052	+	0.238476i
$482$	−420.059	+	727.563i	−0.871492	+	1.50947i
$483$		0			0
$484$	542.081	+	938.912i	1.12000	+	1.93990i
$485$		−	179.642i		−	0.370395i
$486$		0			0
$487$		−	768.554i		−	1.57814i	−0.614303	−	0.789070i	$-0.710563\pi$
$487$		−	768.554i		−	1.57814i	0.614303	−	0.789070i	$-0.289437\pi$
$488$	−0.0360507	−	0.0624416i	−7.38744e−5	−	0.000127954i
$489$		0			0
$490$	424.443	+	245.053i	0.866211	+	0.500107i
$491$	49.6394	+	28.6593i	0.101099	+	0.0583693i	0.549697	−	0.835364i	$-0.314743\pi$
$491$	49.6394	+	28.6593i	0.101099	+	0.0583693i	−0.448598	+	0.893734i	$0.648077\pi$
$492$		0			0
$493$	−79.0887	+	195.574i	−0.160423	+	0.396702i
$494$		−	851.293i		−	1.72327i
$495$		0			0
$496$			553.639i			1.11621i
$497$	−144.189	+	83.2474i	−0.290118	+	0.167500i
$498$		0			0
$499$	−187.998	−	108.541i	−0.376750	−	0.217517i	0.299653	−	0.954048i	$-0.403129\pi$
$499$	−187.998	−	108.541i	−0.376750	−	0.217517i	−0.676404	+	0.736531i	$0.736462\pi$
$500$	267.034	−	462.516i	0.534067	−	0.925031i
$501$		0			0
$502$	−183.447	−	317.740i	−0.365433	−	0.632948i
$503$	449.219			0.893080			0.446540	−	0.894764i	$-0.352656\pi$
$503$	449.219			0.893080			0.446540	+	0.894764i	$0.352656\pi$
$504$		0			0
$505$			210.068i			0.415977i
$506$	−850.911	+	491.274i	−1.68164	+	0.970897i
$507$		0			0
$508$	87.8879	−	152.226i	0.173008	−	0.299658i
$509$	114.228	+	65.9498i	0.224417	+	0.129567i	0.607994	−	0.793942i	$-0.291974\pi$
$509$	114.228	+	65.9498i	0.224417	+	0.129567i	−0.383577	+	0.923509i	$0.625308\pi$
$510$		0			0
$511$	−75.4757	−	130.728i	−0.147702	−	0.255827i
$512$			723.054i			1.41221i
$513$		0			0
$514$	−808.494			−1.57294
$515$	−111.482	−	193.093i	−0.216470	−	0.374937i
$516$		0			0
$517$	1483.87	+	856.715i	2.87016	+	1.65709i
$518$	−44.4346	−	25.6543i	−0.0857811	−	0.0495258i
$519$		0			0
$520$	3.37279	−	1.94728i	0.00648613	−	0.00374477i
$521$	736.381			1.41340			0.706700	−	0.707514i	$-0.250183\pi$
$521$	736.381			1.41340			0.706700	+	0.707514i	$0.250183\pi$
$522$		0			0
$523$	92.6839			0.177216			0.0886079	−	0.996067i	$-0.471758\pi$
$523$	92.6839			0.177216			0.0886079	+	0.996067i	$0.471758\pi$
$524$	−43.7029	−	75.6957i	−0.0834025	−	0.144457i
$525$		0			0
$526$	−639.873	+	1108.29i	−1.21649	+	2.10702i
$527$	−81.2546	−	579.481i	−0.154183	−	1.09958i
$528$		0			0
$529$	110.752	+	191.827i	0.209360	+	0.362622i
$530$	−123.463			−0.232950
$531$		0			0
$532$			94.9429i			0.178464i
$533$	268.691	+	465.387i	0.504112	+	0.873147i
$534$		0			0
$535$	−3.73590	+	6.47077i	−0.00698299	+	0.0120949i
$536$	3.01887	+	1.74295i	0.00563222	+	0.00325177i
$537$		0			0
$538$	−1204.43	+	695.380i	−2.23872	+	1.29253i
$539$	933.478			1.73187
$540$		0			0
$541$			875.030i			1.61743i	0.588200	+	0.808716i	$0.299837\pi$
$541$			875.030i			1.61743i	−0.588200	+	0.808716i	$0.700163\pi$
$542$	−901.203	+	520.310i	−1.66274	+	0.959982i
$543$		0			0
$544$	−106.685	−	760.845i	−0.196113	−	1.39861i
$545$	182.183	+	105.183i	0.334280	+	0.192997i
$546$		0			0
$547$	−435.805	+	251.612i	−0.796718	+	0.459985i	−0.842322	−	0.538974i	$-0.818812\pi$
$547$	−435.805	+	251.612i	−0.796718	+	0.459985i	0.0456041	+	0.998960i	$0.485479\pi$
$548$		−	284.792i		−	0.519693i
$549$		0			0
$550$		−	639.062i		−	1.16193i
$551$	−106.260	−	184.048i	−0.192849	−	0.334025i
$552$		0			0
$553$	2.40678	−	4.16867i	0.00435223	−	0.00753828i
$554$	104.584	−	181.145i	0.188780	−	0.326977i
$555$		0			0
$556$	664.573	−	383.691i	1.19527	−	0.690092i
$557$		−	228.618i		−	0.410446i	−0.978715	−	0.205223i	$-0.934208\pi$
$557$		−	228.618i		−	0.410446i	0.978715	−	0.205223i	$-0.0657919\pi$
$558$		0			0
$559$	−610.258			−1.09170
$560$	−71.5634	+	41.3171i	−0.127792	+	0.0737806i
$561$		0			0
$562$	−44.1750	+	76.5134i	−0.0786033	+	0.136145i
$563$	−507.200	−	292.832i	−0.900888	−	0.520128i	−0.0233997	−	0.999726i	$-0.507449\pi$
$563$	−507.200	−	292.832i	−0.900888	−	0.520128i	−0.877488	+	0.479598i	$0.840782\pi$
$564$		0			0
$565$	320.708	+	555.482i	0.567624	+	0.983154i
$566$	−526.382			−0.930004
$567$		0			0
$568$			7.17205i			0.0126269i
$569$	−205.791	+	118.814i	−0.361672	+	0.208811i	−0.669814	−	0.742529i	$-0.733626\pi$
$569$	−205.791	+	118.814i	−0.361672	+	0.208811i	0.308142	+	0.951340i	$0.400293\pi$
$570$		0			0
$571$	802.747	+	463.466i	1.40586	+	0.811675i	0.994986	−	0.100016i	$-0.0318896\pi$
$571$	802.747	+	463.466i	1.40586	+	0.811675i	0.410876	+	0.911691i	$0.365223\pi$
$572$	−694.458	+	1202.84i	−1.21409	+	2.10286i
$573$		0			0
$574$	−60.0932	−	104.085i	−0.104692	−	0.181332i
$575$	200.000			0.347826
$576$		0			0
$577$	−114.402			−0.198270			−0.0991352	−	0.995074i	$-0.531608\pi$
$577$	−114.402			−0.198270			−0.0991352	+	0.995074i	$0.531608\pi$
$578$	224.516	+	784.847i	0.388437	+	1.35787i
$579$		0			0
$580$	−91.0232	+	157.657i	−0.156936	+	0.271822i
$581$	−29.7769	+	51.5751i	−0.0512511	+	0.0887696i
$582$		0			0
$583$	−203.650	+	117.577i	−0.349313	+	0.201676i
$584$	−6.50249			−0.0111344
$585$		0			0
$586$	−737.719			−1.25891
$587$	18.0108	−	10.3985i	0.0306828	−	0.0177147i	−0.484580	−	0.874747i	$-0.661028\pi$
$587$	18.0108	−	10.3985i	0.0306828	−	0.0177147i	0.515263	+	0.857032i	$0.327694\pi$
$588$		0			0
$589$	510.501	+	294.738i	0.866726	+	0.500404i
$590$	468.832	−	812.042i	0.794631	−	1.37634i
$591$		0			0
$592$	−181.591	+	104.842i	−0.306742	+	0.177098i
$593$			995.431i			1.67864i	0.543640	+	0.839318i	$0.317046\pi$
$593$			995.431i			1.67864i	−0.543640	+	0.839318i	$0.682954\pi$
$594$		0			0
$595$	68.8398	−	53.7486i	0.115697	−	0.0903338i
$596$	−426.241	+	246.090i	−0.715169	+	0.412903i
$597$		0			0
$598$	−754.888	−	435.835i	−1.26235	−	0.728820i
$599$	508.130	+	293.369i	0.848297	+	0.489765i	0.860076	−	0.510166i	$-0.170416\pi$
$599$	508.130	+	293.369i	0.848297	+	0.489765i	−0.0117787	+	0.999931i	$0.503749\pi$
$600$		0			0
$601$	325.334	−	187.832i	0.541321	−	0.312532i	−0.204293	−	0.978910i	$-0.565489\pi$
$601$	325.334	−	187.832i	0.541321	−	0.312532i	0.745614	+	0.666378i	$0.232156\pi$
$602$	136.485			0.226719
$603$		0			0
$604$	293.137			0.485326
$605$	502.344	+	870.085i	0.830320	+	1.43816i
$606$		0			0
$607$	−123.401	−	71.2454i	−0.203296	−	0.117373i	0.394896	−	0.918726i	$-0.370781\pi$
$607$	−123.401	−	71.2454i	−0.203296	−	0.117373i	−0.598192	+	0.801353i	$0.704114\pi$
$608$	670.276	+	386.984i	1.10243	+	0.636487i
$609$		0			0
$610$	6.25538	+	10.8346i	0.0102547	+	0.0177617i
$611$			1520.07i			2.48784i
$612$		0			0
$613$	−785.715			−1.28175			−0.640877	−	0.767644i	$-0.721429\pi$
$613$	−785.715			−1.28175			−0.640877	+	0.767644i	$0.721429\pi$
$614$	1084.59	−	626.191i	1.76644	−	1.01985i
$615$		0			0
$616$	−0.829497	+	1.43673i	−0.00134659	+	0.00233235i
$617$	329.263	−	570.301i	0.533652	−	0.924313i	−0.465575	−	0.885008i	$-0.654152\pi$
$617$	329.263	−	570.301i	0.533652	−	0.924313i	0.999227	−	0.0393043i	$-0.0125142\pi$
$618$		0			0
$619$	953.354	−	550.419i	1.54015	−	0.889207i	0.541323	−	0.840815i	$-0.317924\pi$
$619$	953.354	−	550.419i	1.54015	−	0.889207i	0.998828	−	0.0483917i	$-0.0154096\pi$
$620$		−	504.950i		−	0.814436i
$621$		0			0
$622$			837.709i			1.34680i
$623$	30.2002	+	52.3083i	0.0484755	+	0.0839620i
$624$		0			0
$625$	104.892	−	181.678i	0.167827	−	0.290684i
$626$	−706.418	+	1223.55i	−1.12846	+	1.95456i
$627$		0			0
$628$	−12.4515	−	21.5666i	−0.0198272	−	0.0343418i
$629$	174.680	−	136.387i	0.277711	−	0.216831i
$630$		0			0
$631$	479.339			0.759650			0.379825	−	0.925058i	$-0.375984\pi$
$631$	479.339			0.759650			0.379825	+	0.925058i	$0.375984\pi$
$632$	−0.103676	−	0.179573i	−0.000164045	−	0.000284134i
$633$		0			0
$634$	926.288	+	534.793i	1.46102	+	0.843522i
$635$	81.4453	−	141.067i	0.128260	−	0.222153i
$636$		0			0
$637$	414.068	+	717.187i	0.650029	+	1.12588i
$638$			695.320i			1.08984i
$639$		0			0
$640$			7.08172i			0.0110652i
$641$	−129.365	−	224.067i	−0.201818	−	0.349558i	0.747297	−	0.664491i	$-0.231351\pi$
$641$	−129.365	−	224.067i	−0.201818	−	0.349558i	−0.949114	+	0.314932i	$0.898018\pi$
$642$		0			0
$643$	−794.502	−	458.706i	−1.23562	−	0.713384i	−0.267422	−	0.963579i	$-0.586172\pi$
$643$	−794.502	−	458.706i	−1.23562	−	0.713384i	−0.968195	+	0.250195i	$0.919505\pi$
$644$	84.1910	+	48.6077i	0.130731	+	0.0754778i
$645$		0			0
$646$	−762.386	−	308.303i	−1.18016	−	0.477250i
$647$		−	194.253i		−	0.300236i	−0.988668	−	0.150118i	$-0.952035\pi$
$647$		−	194.253i		−	0.300236i	0.988668	−	0.150118i	$-0.0479653\pi$
$648$		0			0
$649$		−	1785.92i		−	2.75180i
$650$	490.988	−	283.472i	0.755367	−	0.436111i
$651$		0			0
$652$	164.237	+	94.8223i	0.251897	+	0.145433i
$653$	34.9563	−	60.5460i	0.0535318	−	0.0927198i	−0.838018	−	0.545643i	$-0.816285\pi$
$653$	34.9563	−	60.5460i	0.0535318	−	0.0927198i	0.891550	+	0.452923i	$0.149619\pi$
$654$		0			0
$655$	−40.4993	−	70.1468i	−0.0618310	−	0.107094i
$656$	−491.167			−0.748730
$657$		0			0
$658$		−	339.966i		−	0.516666i
$659$	207.820	−	119.985i	0.315356	−	0.182071i	−0.333965	−	0.942586i	$-0.608387\pi$
$659$	207.820	−	119.985i	0.315356	−	0.182071i	0.649321	+	0.760515i	$0.275053\pi$
$660$		0			0
$661$	88.4982	−	153.283i	0.133885	−	0.231896i	−0.791286	−	0.611446i	$-0.790588\pi$
$661$	88.4982	−	153.283i	0.133885	−	0.231896i	0.925171	+	0.379550i	$0.123921\pi$
$662$	−401.644	−	231.889i	−0.606713	−	0.350286i
$663$		0			0
$664$	1.28269	+	2.22169i	0.00193177	+	0.00334592i
$665$			87.9832i			0.132306i
$666$		0			0
$667$	−217.607			−0.326247
$668$	245.480	+	425.184i	0.367485	+	0.636502i
$669$		0			0
$670$	−523.823	−	302.430i	−0.781826	−	0.451387i
$671$	20.6362	+	11.9143i	0.0307543	+	0.0177560i
$672$		0			0
$673$	−192.239	+	110.989i	−0.285645	+	0.164917i	−0.635976	−	0.771709i	$-0.719402\pi$
$673$	−192.239	+	110.989i	−0.285645	+	0.164917i	0.350331	+	0.936626i	$0.386069\pi$
$674$	152.173			0.225776
$675$		0			0
$676$	−559.771			−0.828064
$677$	−188.617	−	326.694i	−0.278607	−	0.482561i	0.692432	−	0.721483i	$-0.256539\pi$
$677$	−188.617	−	326.694i	−0.278607	−	0.482561i	−0.971039	+	0.238922i	$0.923206\pi$
$678$		0			0
$679$	−33.9439	+	58.7925i	−0.0499910	+	0.0865869i
$680$	−0.522426	−	3.72577i	−0.000768273	−	0.00547907i
$681$		0			0
$682$	−964.321	−	1670.25i	−1.41396	−	2.44905i
$683$	539.646			0.790111			0.395055	−	0.918657i	$-0.370725\pi$
$683$	539.646			0.790111			0.395055	+	0.918657i	$0.370725\pi$
$684$		0			0
$685$		−	263.915i		−	0.385278i
$686$	−189.035	−	327.417i	−0.275561	−	0.477285i
$687$		0			0
$688$	278.887	−	483.047i	0.405359	−	0.702103i
$689$	−180.668	−	104.309i	−0.262218	−	0.151392i
$690$		0			0
$691$	−451.625	+	260.746i	−0.653582	+	0.377346i	−0.789827	−	0.613329i	$-0.789830\pi$
$691$	−451.625	+	260.746i	−0.653582	+	0.377346i	0.136245	+	0.990675i	$0.456497\pi$
$692$	−507.346			−0.733159
$693$		0			0
$694$		−	375.486i		−	0.541047i
$695$	615.856	−	355.565i	0.886124	−	0.511604i
$696$		0			0
$697$	514.092	−	72.0859i	0.737578	−	0.103423i
$698$	491.144	+	283.562i	0.703645	+	0.406250i
$699$		0			0
$700$	−54.7589	+	31.6151i	−0.0782270	+	0.0451644i
$701$			795.541i			1.13487i	0.823420	+	0.567433i	$0.192063\pi$
$701$			795.541i			1.13487i	−0.823420	+	0.567433i	$0.807937\pi$
$702$		0			0
$703$			223.256i			0.317577i
$704$	−628.007	−	1087.74i	−0.892055	−	1.54509i
$705$		0			0
$706$	572.879	−	992.255i	0.811443	−	1.40546i
$707$	39.6931	−	68.7504i	0.0561430	−	0.0972425i
$708$		0			0
$709$	524.674	−	302.920i	0.740019	−	0.427250i	−0.0820571	−	0.996628i	$-0.526149\pi$
$709$	524.674	−	302.920i	0.740019	−	0.427250i	0.822076	+	0.569377i	$0.192816\pi$
$710$		−	1244.47i		−	1.75277i
$711$		0			0
$712$	2.60186			0.00365429
$713$	522.720	−	301.793i	0.733128	−	0.423272i
$714$		0			0
$715$	−643.551	+	1114.66i	−0.900072	+	1.55897i
$716$	−608.099	−	351.086i	−0.849301	−	0.490344i
$717$		0			0
$718$	685.885	+	1187.99i	0.955272	+	1.65458i
$719$	85.3362			0.118687			0.0593437	−	0.998238i	$-0.481099\pi$
$719$	85.3362			0.118687			0.0593437	+	0.998238i	$0.481099\pi$
$720$		0			0
$721$			84.2596i			0.116865i
$722$	−165.636	+	95.6302i	−0.229413	+	0.132452i
$723$		0			0
$724$	−635.055	−	366.649i	−0.877148	−	0.506422i
$725$	70.7670	−	122.572i	0.0976097	−	0.169065i
$726$		0			0
$727$	227.901	+	394.736i	0.313482	+	0.542966i	0.979114	−	0.203314i	$-0.0651712\pi$
$727$	227.901	+	394.736i	0.313482	+	0.542966i	−0.665632	+	0.746280i	$0.731838\pi$
$728$	−1.47178			−0.00202167
$729$		0			0
$730$	1128.29			1.54560
$731$	−221.010	+	546.524i	−0.302340	+	0.747639i
$732$		0			0
$733$	−391.901	+	678.792i	−0.534653	+	0.926046i	0.464527	+	0.885559i	$0.346224\pi$
$733$	−391.901	+	678.792i	−0.534653	+	0.926046i	−0.999180	+	0.0404872i	$0.987109\pi$
$734$	−262.116	+	453.999i	−0.357107	+	0.618527i
$735$		0			0
$736$	686.319	−	396.247i	0.932499	−	0.538379i
$737$	−1152.04			−1.56315
$738$		0			0
$739$	153.070			0.207131			0.103565	−	0.994623i	$-0.466975\pi$
$739$	153.070			0.207131			0.103565	+	0.994623i	$0.466975\pi$
$740$	165.621	−	95.6216i	0.223813	−	0.129218i
$741$		0			0
$742$	40.4067	+	23.3288i	0.0544564	+	0.0314404i
$743$	208.917	−	361.854i	0.281180	−	0.487018i	−0.690496	−	0.723337i	$-0.742608\pi$
$743$	208.917	−	361.854i	0.281180	−	0.487018i	0.971676	+	0.236318i	$0.0759409\pi$
$744$		0			0
$745$	−394.995	+	228.051i	−0.530195	+	0.306108i
$746$		−	653.975i		−	0.876642i
$747$		0			0
$748$	825.711	+	1057.55i	1.10389	+	1.41384i
$749$	2.44534	−	1.41182i	0.00326481	−	0.00188494i
$750$		0			0
$751$	−298.480	−	172.328i	−0.397444	−	0.229464i	0.287937	−	0.957649i	$-0.407031\pi$
$751$	−298.480	−	172.328i	−0.397444	−	0.229464i	−0.685380	+	0.728185i	$0.740364\pi$
$752$	−1203.21	−	694.671i	−1.60001	−	0.923765i
$753$		0			0
$754$	−534.212	+	308.427i	−0.708504	+	0.409055i
$755$	271.648			0.359799
$756$		0			0
$757$	−612.380			−0.808956			−0.404478	−	0.914548i	$-0.632547\pi$
$757$	−612.380			−0.808956			−0.404478	+	0.914548i	$0.632547\pi$
$758$	−543.250	−	940.936i	−0.716688	−	1.24134i
$759$		0			0
$760$	3.28226	+	1.89502i	0.00431877	+	0.00249344i
$761$	−689.897	−	398.312i	−0.906567	−	0.523407i	−0.0272418	−	0.999629i	$-0.508672\pi$
$761$	−689.897	−	398.312i	−0.906567	−	0.523407i	−0.879325	+	0.476222i	$0.842006\pi$
$762$		0			0
$763$	−39.7494	−	68.8480i	−0.0520962	−	0.0902333i
$764$		−	197.830i		−	0.258940i
$765$		0			0
$766$	1796.04			2.34470
$767$	1372.12	−	792.192i	1.78894	−	1.03284i
$768$		0			0
$769$	−133.749	+	231.661i	−0.173926	+	0.301249i	−0.939789	−	0.341755i	$-0.888979\pi$
$769$	−133.749	+	231.661i	−0.173926	+	0.301249i	0.765863	+	0.643004i	$0.222312\pi$
$770$	143.931	−	249.296i	0.186924	−	0.323761i
$771$		0			0
$772$	280.066	−	161.696i	0.362779	−	0.209451i
$773$		−	218.543i		−	0.282721i	−0.989958	−	0.141361i	$-0.954852\pi$
$773$		−	218.543i		−	0.282721i	0.989958	−	0.141361i	$-0.0451477\pi$
$774$		0			0
$775$			392.580i			0.506554i
$776$	1.46219	+	2.53259i	0.00188427	+	0.00326365i
$777$		0			0
$778$	−161.018	+	278.892i	−0.206964	+	0.358473i
$779$	−261.480	+	452.896i	−0.335661	+	0.581382i
$780$		0			0
$781$	−1185.14	−	2052.72i	−1.51746	−	2.62832i
$782$	−663.706	+	518.207i	−0.848729	+	0.662669i
$783$		0			0
$784$	−756.915			−0.965452
$785$	−11.5387	−	19.9857i	−0.0146990	−	0.0254595i
$786$		0			0
$787$	−1306.69	−	754.419i	−1.66034	−	0.958601i	−0.972549	−	0.232696i	$-0.925245\pi$
$787$	−1306.69	−	754.419i	−1.66034	−	0.958601i	−0.687795	−	0.725905i	$-0.741421\pi$
$788$	393.119	−	680.901i	0.498881	−	0.864088i
$789$		0			0
$790$	17.9895	+	31.1588i	0.0227716	+	0.0394415i
$791$		−	242.395i		−	0.306441i
$792$		0			0
$793$			21.1396i			0.0266577i
$794$	−450.728	−	780.684i	−0.567668	−	0.983229i
$795$		0			0
$796$	−1228.67	−	709.375i	−1.54356	−	0.891175i
$797$	−593.926	−	342.903i	−0.745202	−	0.430243i	0.0787556	−	0.996894i	$-0.474905\pi$
$797$	−593.926	−	342.903i	−0.745202	−	0.430243i	−0.823958	+	0.566651i	$0.808239\pi$
$798$		0			0
$799$	1361.32	+	550.507i	1.70378	+	0.688996i
$800$			515.448i			0.644310i
$801$		0			0
$802$			2187.22i			2.72721i
$803$	1861.08	−	1074.50i	2.31766	−	1.33810i
$804$		0			0
$805$	78.0194	+	45.0445i	0.0969185	+	0.0559559i
$806$	855.499	−	1481.77i	1.06141	−	1.83842i
$807$		0			0
$808$	−1.70985	−	2.96155i	−0.00211615	−	0.00366528i
$809$	−228.169			−0.282039			−0.141019	−	0.990007i	$-0.545038\pi$
$809$	−228.169			−0.282039			−0.141019	+	0.990007i	$0.545038\pi$
$810$		0			0
$811$			63.4735i			0.0782657i	0.999234	+	0.0391328i	$0.0124595\pi$
$811$			63.4735i			0.0782657i	−0.999234	+	0.0391328i	$0.987540\pi$
$812$	59.5795	−	34.3982i	0.0733738	−	0.0423624i
$813$		0			0
$814$	365.224	−	632.586i	0.448678	−	0.777132i
$815$	152.198	+	87.8714i	0.186746	+	0.107818i
$816$		0			0
$817$	−296.940	−	514.314i	−0.363451	−	0.629516i
$818$		−	52.8643i		−	0.0646262i
$819$		0			0
$820$	447.972			0.546307
$821$	339.051	+	587.254i	0.412973	+	0.715291i	0.995213	−	0.0977260i	$-0.0311569\pi$
$821$	339.051	+	587.254i	0.412973	+	0.715291i	−0.582240	+	0.813017i	$0.697824\pi$
$822$		0			0
$823$	389.065	+	224.627i	0.472740	+	0.272936i	0.717386	−	0.696676i	$-0.245338\pi$
$823$	389.065	+	224.627i	0.472740	+	0.272936i	−0.244646	+	0.969612i	$0.578672\pi$
$824$	3.14335	+	1.81482i	0.00381475	+	0.00220245i
$825$		0			0
$826$	−306.876	+	177.175i	−0.371520	+	0.214497i
$827$	−1047.69			−1.26686			−0.633430	−	0.773800i	$-0.718353\pi$
$827$	−1047.69			−1.26686			−0.633430	+	0.773800i	$0.718353\pi$
$828$		0			0
$829$	838.983			1.01204			0.506021	−	0.862521i	$-0.331116\pi$
$829$	838.983			1.01204			0.506021	+	0.862521i	$0.331116\pi$
$830$	−222.568	−	385.499i	−0.268154	−	0.464457i
$831$		0			0
$832$	557.138	−	964.991i	0.669637	−	1.15984i
$833$	792.244	−	111.088i	0.951073	−	0.133359i
$834$		0			0
$835$	227.485	+	394.016i	0.272437	+	0.471875i
$836$	−1351.64			−1.61679
$837$		0			0
$838$		−	1638.10i		−	1.95477i
$839$	21.6089	+	37.4278i	0.0257556	+	0.0446100i	0.878616	−	0.477529i	$-0.158468\pi$
$839$	21.6089	+	37.4278i	0.0257556	+	0.0446100i	−0.852860	+	0.522139i	$0.825134\pi$
$840$		0			0
$841$	343.503	−	594.965i	0.408446	−	0.707449i
$842$	731.331	+	422.234i	0.868564	+	0.501465i
$843$		0			0
$844$	−607.348	+	350.652i	−0.719607	+	0.415465i
$845$	−518.737			−0.613890
$846$		0			0
$847$		−	379.678i		−	0.448262i
$848$	165.130	−	95.3380i	0.194729	−	0.112427i
$849$		0			0
$850$	−76.0513	−	542.373i	−0.0894722	−	0.638086i
$851$	197.973	+	114.300i	0.232636	+	0.134313i
$852$		0			0
$853$	1071.00	−	618.341i	1.25557	−	0.724902i	0.283357	−	0.959014i	$-0.408552\pi$
$853$	1071.00	−	618.341i	1.25557	−	0.724902i	0.972209	+	0.234113i	$0.0752185\pi$
$854$		−	4.72790i		−	0.00553618i
$855$		0			0
$856$		−	0.121633i		−	0.000142095i
$857$	153.442	+	265.770i	0.179046	+	0.310117i	0.941554	−	0.336862i	$-0.109366\pi$
$857$	153.442	+	265.770i	0.179046	+	0.310117i	−0.762508	+	0.646979i	$0.776032\pi$
$858$		0			0
$859$	−37.9520	+	65.7347i	−0.0441815	+	0.0765247i	−0.887271	−	0.461249i	$-0.847401\pi$
$859$	−37.9520	+	65.7347i	−0.0441815	+	0.0765247i	0.843089	+	0.537774i	$0.180735\pi$
$860$	−254.361	+	440.566i	−0.295769	+	0.512286i
$861$		0			0
$862$	514.531	−	297.065i	0.596904	−	0.344622i
$863$		−	264.341i		−	0.306305i	−0.988203	−	0.153152i	$-0.951057\pi$
$863$		−	264.341i		−	0.306305i	0.988203	−	0.153152i	$-0.0489425\pi$
$864$		0			0
$865$	−470.155			−0.543532
$866$	−1298.12	+	749.469i	−1.49898	+	0.865438i
$867$		0			0
$868$	−95.4120	+	165.258i	−0.109922	+	0.190390i
$869$	59.3465	+	34.2637i	0.0682929	+	0.0394289i
$870$		0			0
$871$	−511.019	−	885.111i	−0.586704	−	1.01620i
$872$	−3.42455			−0.00392724
$873$		0			0
$874$		−	848.274i		−	0.970565i
$875$	−161.975	+	93.5162i	−0.185114	+	0.106876i
$876$		0			0
$877$	−483.379	−	279.079i	−0.551173	−	0.318220i	0.198422	−	0.980117i	$-0.436418\pi$
$877$	−483.379	−	279.079i	−0.551173	−	0.318220i	−0.749595	+	0.661897i	$0.769752\pi$
$878$	−377.906	+	654.553i	−0.430417	+	0.745504i
$879$		0			0
$880$	−588.204	−	1018.80i	−0.668414	−	1.15773i
$881$	−615.701			−0.698866			−0.349433	−	0.936961i	$-0.613626\pi$
$881$	−615.701			−0.698866			−0.349433	+	0.936961i	$0.613626\pi$
$882$		0			0
$883$	1536.97			1.74062			0.870311	−	0.492502i	$-0.163918\pi$
$883$	1536.97			1.74062			0.870311	+	0.492502i	$0.163918\pi$
$884$	−446.245	+	1103.49i	−0.504802	+	1.24830i
$885$		0			0
$886$	−1100.08	+	1905.40i	−1.24163	+	2.15056i
$887$	320.893	−	555.804i	0.361774	−	0.626611i	−0.626479	−	0.779438i	$-0.715505\pi$
$887$	320.893	−	555.804i	0.361774	−	0.626611i	0.988253	+	0.152828i	$0.0488379\pi$
$888$		0			0
$889$	−53.3103	+	30.7787i	−0.0599666	+	0.0346217i
$890$	−451.464			−0.507263
$891$		0			0
$892$	−993.535			−1.11383
$893$	−1281.09	+	739.637i	−1.43459	+	0.828261i
$894$		0			0
$895$	−563.523	−	325.350i	−0.629634	−	0.363520i
$896$	1.33811	−	2.31768i	0.00149343	−	0.00258670i
$897$		0			0
$898$	−196.775	+	113.608i	−0.219125	+	0.126512i
$899$		−	427.140i		−	0.475127i
$900$		0			0
$901$	−158.846	+	124.023i	−0.176299	+	0.137651i
$902$	1481.78	−	855.507i	1.64277	−	0.948455i
$903$		0			0
$904$	−9.04269	−	5.22080i	−0.0100030	−	0.00577522i
$905$	−588.503	−	339.772i	−0.650279	−	0.375439i
$906$		0			0
$907$	−1383.50	+	798.765i	−1.52536	+	0.880667i	−0.525813	+	0.850600i	$0.676239\pi$
$907$	−1383.50	+	798.765i	−1.52536	+	0.880667i	−0.999548	+	0.0300668i	$0.990428\pi$
$908$	1124.94			1.23892
$909$		0			0
$910$	255.378			0.280635
$911$	544.648	+	943.358i	0.597858	+	1.03552i	0.993137	+	0.116959i	$0.0373145\pi$
$911$	544.648	+	943.358i	0.597858	+	1.03552i	−0.395279	+	0.918561i	$0.629352\pi$
$912$		0			0
$913$	−734.240	−	423.914i	−0.804206	−	0.464309i
$914$	1071.26	+	618.492i	1.17206	+	0.676687i
$915$		0			0
$916$	−638.792	−	1106.42i	−0.697372	−	1.20788i
$917$			30.6099i			0.0333805i
$918$		0			0
$919$	1463.53			1.59253			0.796264	−	0.604949i	$-0.206807\pi$
$919$	1463.53			1.59253			0.796264	+	0.604949i	$0.206807\pi$
$920$	3.36082	−	1.94037i	0.00365307	−	0.00210910i
$921$		0			0
$922$	−1072.35	+	1857.36i	−1.16307	+	2.01450i
$923$	1051.40	−	1821.07i	1.13911	−	1.97299i
$924$		0			0
$925$	−128.764	+	74.3422i	−0.139205	+	0.0803699i
$926$		−	1405.92i		−	1.51827i
$927$		0			0
$928$		−	560.824i		−	0.604336i
$929$	−199.305	−	345.206i	−0.214537	−	0.371589i	0.738592	−	0.674152i	$-0.235491\pi$
$929$	−199.305	−	345.206i	−0.214537	−	0.371589i	−0.953129	+	0.302564i	$0.902158\pi$
$930$		0			0
$931$	−402.955	+	697.938i	−0.432819	+	0.749665i
$932$	613.915	−	1063.33i	0.658707	−	1.14091i
$933$		0			0
$934$	79.6896	+	138.026i	0.0853207	+	0.147780i
$935$	765.183	+	980.025i	0.818377	+	1.04816i
$936$		0			0
$937$	−125.284			−0.133707			−0.0668536	−	0.997763i	$-0.521296\pi$
$937$	−125.284			−0.133707			−0.0668536	+	0.997763i	$0.521296\pi$
$938$	114.290	+	197.956i	0.121844	+	0.211041i
$939$		0			0
$940$	1097.39	+	633.579i	1.16744	+	0.674020i
$941$	−232.137	+	402.073i	−0.246692	+	0.427282i	−0.962606	−	0.270906i	$-0.912677\pi$
$941$	−232.137	+	402.073i	−0.246692	+	0.427282i	0.715914	+	0.698188i	$0.246010\pi$
$942$		0			0
$943$	267.738	+	463.736i	0.283922	+	0.491767i
$944$			1448.12i			1.53403i
$945$		0			0
$946$			1943.05i			2.05396i
$947$	−411.814	−	713.284i	−0.434862	−	0.753203i	0.562422	−	0.826850i	$-0.309870\pi$
$947$	−411.814	−	713.284i	−0.434862	−	0.753203i	−0.997284	+	0.0736468i	$0.976536\pi$
$948$		0			0
$949$	1651.06	+	953.241i	1.73979	+	1.00447i
$950$	477.810	+	275.864i	0.502958	+	0.290383i
$951$		0			0
$952$	−0.533018	+	1.31807i	−0.000559892	+	0.00138453i
$953$			926.275i			0.971957i	0.873971	+	0.485978i	$0.161537\pi$
$953$			926.275i			0.971957i	−0.873971	+	0.485978i	$0.838463\pi$
$954$		0			0
$955$		−	183.328i		−	0.191966i
$956$	1372.91	−	792.649i	1.43610	−	0.829131i
$957$		0			0
$958$	−730.530	−	421.772i	−0.762557	−	0.440263i
$959$	−49.8676	+	86.3733i	−0.0519996	+	0.0900660i
$960$		0			0
$961$	111.888	+	193.796i	0.116429	+	0.201661i
$962$	648.018			0.673615
$963$		0			0
$964$			1183.37i			1.22756i
$965$	259.535	−	149.843i	0.268949	−	0.155278i
$966$		0			0
$967$	685.245	−	1186.88i	0.708630	−	1.22738i	−0.256736	−	0.966482i	$-0.582647\pi$
$967$	685.245	−	1186.88i	0.708630	−	1.22738i	0.965366	−	0.260901i	$-0.0840196\pi$
$968$	−14.1641	−	8.17765i	−0.0146323	−	0.00844798i
$969$		0			0
$970$	−253.714	−	439.446i	−0.261561	−	0.453037i
$971$			182.369i			0.187815i	0.995581	+	0.0939076i	$0.0299358\pi$
$971$			182.369i			0.187815i	−0.995581	+	0.0939076i	$0.970064\pi$
$972$		0			0
$973$	−268.740			−0.276198
$974$	−1085.46	−	1880.06i	−1.11443	−	1.93025i
$975$		0			0
$976$	−16.7329	−	9.66076i	−0.0171444	−	0.00989832i
$977$	−366.032	−	211.328i	−0.374649	−	0.216303i	0.300839	−	0.953675i	$-0.402733\pi$
$977$	−366.032	−	211.328i	−0.374649	−	0.216303i	−0.675487	+	0.737372i	$0.736067\pi$
$978$		0			0
$979$	−744.679	+	429.940i	−0.760652	+	0.439163i
$980$	690.349			0.704437
$981$		0			0
$982$	161.906			0.164874
$983$	807.232	+	1398.17i	0.821192	+	1.42235i	0.904795	+	0.425848i	$0.140024\pi$
$983$	807.232	+	1398.17i	0.821192	+	1.42235i	−0.0836025	+	0.996499i	$0.526643\pi$
$984$		0			0
$985$	364.301	−	630.988i	0.369849	−	0.640597i
$986$	82.7464	+	590.119i	0.0839213	+	0.598498i
$987$		0			0
$988$	−599.554	−	1038.46i	−0.606836	−	1.05107i
$989$	−608.094			−0.614857
$990$		0			0
$991$			651.023i			0.656936i	0.944515	+	0.328468i	$0.106532\pi$
$991$			651.023i			0.656936i	−0.944515	+	0.328468i	$0.893468\pi$
$992$	777.792	+	1347.18i	0.784064	+	1.35804i
$993$		0			0
$994$	−235.146	+	407.285i	−0.236566	+	0.409744i
$995$	−1138.61	−	657.375i	−1.14433	−	0.660678i
$996$		0			0
$997$	−1123.30	+	648.540i	−1.12668	+	0.650491i	−0.943099	−	0.332513i	$-0.892104\pi$
$997$	−1123.30	+	648.540i	−1.12668	+	0.650491i	−0.183585	+	0.983004i	$0.558770\pi$
$998$	−613.185			−0.614413
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.3.i.a.152.27		68
3.2	odd	2		153.3.i.a.50.8	yes	68
9.2	odd	6	inner	459.3.i.a.305.28		68
9.7	even	3		153.3.i.a.101.7	yes	68
17.16	even	2	inner	459.3.i.a.152.28		68
51.50	odd	2		153.3.i.a.50.7	✓	68
153.16	even	6		153.3.i.a.101.8	yes	68
153.101	odd	6	inner	459.3.i.a.305.27		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.i.a.50.7	✓	68	51.50	odd	2
153.3.i.a.50.8	yes	68	3.2	odd	2
153.3.i.a.101.7	yes	68	9.7	even	3
153.3.i.a.101.8	yes	68	153.16	even	6
459.3.i.a.152.27		68	1.1	even	1	trivial
459.3.i.a.152.28		68	17.16	even	2	inner
459.3.i.a.305.27		68	153.101	odd	6	inner
459.3.i.a.305.28		68	9.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	459.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.44623 - 1.41233i) q^{2} +(1.98938 - 3.44570i) q^{4} +(1.84354 - 3.19311i) q^{5} +(-1.20670 + 0.696687i) q^{7} +0.0600221i q^{8} -10.4148i q^{10} +(-9.91827 - 17.1789i) q^{11} +(8.79901 - 15.2403i) q^{13} +(-1.96791 + 3.40852i) q^{14} +(8.04227 + 13.9296i) q^{16} +(-10.4620 - 13.3995i) q^{17} +17.1257 q^{19} +(-7.33500 - 12.7046i) q^{20} +(-48.5248 - 28.0158i) q^{22} +(8.76780 - 15.1863i) q^{23} +(5.70269 + 9.87734i) q^{25} -49.7086i q^{26} +5.54389i q^{28} +(-6.20471 - 10.7469i) q^{29} +(29.8091 + 17.2103i) q^{31} +(39.1386 + 22.5967i) q^{32} +(-44.5171 - 18.0024i) q^{34} +5.13750i q^{35} +13.0363i q^{37} +(41.8935 - 24.1872i) q^{38} +(0.191657 + 0.110653i) q^{40} +(-15.2683 + 26.4454i) q^{41} +(-17.3388 - 30.0317i) q^{43} -78.9246 q^{44} -49.5322i q^{46} +(-74.8051 + 43.1887i) q^{47} +(-23.5293 + 40.7539i) q^{49} +(27.9002 + 16.1082i) q^{50} +(-35.0091 - 60.6375i) q^{52} -11.8546i q^{53} -73.1391 q^{55} +(-0.0418166 - 0.0724285i) q^{56} +(-30.3564 - 17.5263i) q^{58} +(77.9699 + 45.0160i) q^{59} +(-1.04031 + 0.600624i) q^{61} +97.2267 q^{62} +63.3182 q^{64} +(-32.4427 - 56.1925i) q^{65} +(29.0384 - 50.2960i) q^{67} +(-66.9835 + 9.39240i) q^{68} +(7.25586 + 12.5675i) q^{70} +119.490 q^{71} +108.335i q^{73} +(18.4117 + 31.8899i) q^{74} +(34.0694 - 59.0100i) q^{76} +(23.9367 + 13.8199i) q^{77} +(-2.99178 + 1.72730i) q^{79} +59.3052 q^{80} +86.2557i q^{82} +(37.0145 - 21.3704i) q^{83} +(-62.0733 + 8.70389i) q^{85} +(-84.8297 - 48.9765i) q^{86} +(1.03112 - 0.595315i) q^{88} -43.3483i q^{89} +24.5206i q^{91} +(-34.8849 - 60.4224i) q^{92} +(-121.994 + 211.300i) q^{94} +(31.5720 - 54.6843i) q^{95} +(42.1943 - 24.3609i) q^{97} +132.925i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 62 q^{4} - 2 q^{13} - 106 q^{16} - 32 q^{19} - 132 q^{25} - 27 q^{34} + 102 q^{38} + 58 q^{43} + 312 q^{47} + 152 q^{49} + 90 q^{50} + 70 q^{52} + 92 q^{55} + 258 q^{59} - 16 q^{64} + 82 q^{67}+ \cdots - 18 q^{94}+O(q^{100}) \) 68 * q + 6 * q^2 + 62 * q^4 - 2 * q^13 - 106 * q^16 - 32 * q^19 - 132 * q^25 - 27 * q^34 + 102 * q^38 + 58 * q^43 + 312 * q^47 + 152 * q^49 + 90 * q^50 + 70 * q^52 + 92 * q^55 + 258 * q^59 - 16 * q^64 + 82 * q^67 + 333 * q^68 + 204 * q^70 + 34 * q^76 + 60 * q^77 + 690 * q^83 - 44 * q^85 + 1248 * q^86 - 18 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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