LMFDB - Embedded newform 495.3.j.c.298.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [495,3,Mod(298,495)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(495, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("495.298"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	495.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4877730858$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			298.12
Character	$\chi$	$=$	495.298
Dual form			495.3.j.c.397.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.692901 - 0.692901i) q^{2} +3.03978i q^{4} +(4.55660 + 2.05850i) q^{5} +(3.68149 - 3.68149i) q^{7} +(4.87787 + 4.87787i) q^{8} +(4.58361 - 1.73093i) q^{10} +3.31662 q^{11} +(8.16727 + 8.16727i) q^{13} -5.10182i q^{14} -5.39934 q^{16} +(-8.96365 + 8.96365i) q^{17} -15.2705i q^{19} +(-6.25738 + 13.8510i) q^{20} +(2.29809 - 2.29809i) q^{22} +(-15.0992 - 15.0992i) q^{23} +(16.5251 + 18.7595i) q^{25} +11.3182 q^{26} +(11.1909 + 11.1909i) q^{28} +17.7614i q^{29} +49.7660 q^{31} +(-23.2527 + 23.2527i) q^{32} +12.4219i q^{34} +(24.3534 - 9.19671i) q^{35} +(-26.1351 + 26.1351i) q^{37} +(-10.5810 - 10.5810i) q^{38} +(12.1854 + 32.2676i) q^{40} -12.6463 q^{41} +(30.0705 + 30.0705i) q^{43} +10.0818i q^{44} -20.9245 q^{46} +(34.2331 - 34.2331i) q^{47} +21.8932i q^{49} +(24.4488 + 1.54821i) q^{50} +(-24.8267 + 24.8267i) q^{52} +(-55.2796 - 55.2796i) q^{53} +(15.1125 + 6.82728i) q^{55} +35.9157 q^{56} +(12.3069 + 12.3069i) q^{58} +57.6796i q^{59} +96.1575 q^{61} +(34.4829 - 34.4829i) q^{62} +10.6263i q^{64} +(20.4026 + 54.0273i) q^{65} +(64.4666 - 64.4666i) q^{67} +(-27.2475 - 27.2475i) q^{68} +(10.5021 - 23.2469i) q^{70} -48.5204 q^{71} +(-59.7343 - 59.7343i) q^{73} +36.2181i q^{74} +46.4189 q^{76} +(12.2101 - 12.2101i) q^{77} +27.3519i q^{79} +(-24.6026 - 11.1145i) q^{80} +(-8.76261 + 8.76261i) q^{82} +(9.39902 + 9.39902i) q^{83} +(-59.2955 + 22.3921i) q^{85} +41.6718 q^{86} +(16.1781 + 16.1781i) q^{88} -120.444i q^{89} +60.1355 q^{91} +(45.8982 - 45.8982i) q^{92} -47.4403i q^{94} +(31.4344 - 69.5816i) q^{95} +(35.0156 - 35.0156i) q^{97} +(15.1699 + 15.1699i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{10} - 88 q^{13} - 296 q^{16} + 168 q^{25} + 248 q^{28} - 32 q^{31} - 24 q^{37} + 296 q^{40} - 48 q^{43} + 48 q^{46} + 64 q^{52} + 104 q^{58} + 576 q^{61} - 544 q^{67} - 1048 q^{70} - 408 q^{73}+ \cdots + 712 q^{97}+O(q^{100}) $ 40 * q + 24 * q^10 - 88 * q^13 - 296 * q^16 + 168 * q^25 + 248 * q^28 - 32 * q^31 - 24 * q^37 + 296 * q^40 - 48 * q^43 + 48 * q^46 + 64 * q^52 + 104 * q^58 + 576 * q^61 - 544 * q^67 - 1048 * q^70 - 408 * q^73 - 96 * q^76 - 280 * q^82 + 160 * q^85 + 264 * q^88 + 528 * q^91 + 712 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.692901	−	0.692901i	0.346451	−	0.346451i	−0.512335	−	0.858786i	$-0.671219\pi$
$2$	0.692901	−	0.692901i	0.346451	−	0.346451i	0.858786	+	0.512335i	$0.171219\pi$
$3$		0			0
$3$		0			0
$4$			3.03978i			0.759944i
$5$	4.55660	+	2.05850i	0.911319	+	0.411700i
$5$	4.55660	+	2.05850i	0.911319	+	0.411700i
$6$		0			0
$7$	3.68149	−	3.68149i	0.525927	−	0.525927i	−0.393428	−	0.919355i	$-0.628711\pi$
$7$	3.68149	−	3.68149i	0.525927	−	0.525927i	0.919355	+	0.393428i	$0.128711\pi$
$8$	4.87787	+	4.87787i	0.609734	+	0.609734i
$9$		0			0
$10$	4.58361	−	1.73093i	0.458361	−	0.173093i
$11$	3.31662			0.301511
$11$	3.31662			0.301511
$12$		0			0
$13$	8.16727	+	8.16727i	0.628251	+	0.628251i	0.947628	−	0.319376i	$-0.103473\pi$
$13$	8.16727	+	8.16727i	0.628251	+	0.628251i	−0.319376	+	0.947628i	$0.603473\pi$
$14$		−	5.10182i		−	0.364416i
$15$		0			0
$16$	−5.39934			−0.337459
$17$	−8.96365	+	8.96365i	−0.527274	+	0.527274i	−0.919759	−	0.392485i	$-0.871616\pi$
$17$	−8.96365	+	8.96365i	−0.527274	+	0.527274i	0.392485	+	0.919759i	$0.371616\pi$
$18$		0			0
$19$		−	15.2705i		−	0.803711i	−0.915703	−	0.401856i	$-0.868365\pi$
$19$		−	15.2705i		−	0.803711i	0.915703	−	0.401856i	$-0.131635\pi$
$20$	−6.25738	+	13.8510i	−0.312869	+	0.692551i
$21$		0			0
$22$	2.29809	−	2.29809i	0.104459	−	0.104459i
$23$	−15.0992	−	15.0992i	−0.656487	−	0.656487i	0.298060	−	0.954547i	$-0.403660\pi$
$23$	−15.0992	−	15.0992i	−0.656487	−	0.656487i	−0.954547	+	0.298060i	$0.903660\pi$
$24$		0			0
$25$	16.5251	+	18.7595i	0.661006	+	0.750381i
$26$	11.3182			0.435316
$27$		0			0
$28$	11.1909	+	11.1909i	0.399675	+	0.399675i
$29$			17.7614i			0.612461i	0.951957	+	0.306230i	$0.0990678\pi$
$29$			17.7614i			0.612461i	−0.951957	+	0.306230i	$0.900932\pi$
$30$		0			0
$31$	49.7660			1.60535			0.802677	−	0.596414i	$-0.203408\pi$
$31$	49.7660			1.60535			0.802677	+	0.596414i	$0.203408\pi$
$32$	−23.2527	+	23.2527i	−0.726646	+	0.726646i
$33$		0			0
$34$			12.4219i			0.365349i
$35$	24.3534	−	9.19671i	0.695812	−	0.262763i
$36$		0			0
$37$	−26.1351	+	26.1351i	−0.706355	+	0.706355i	−0.965767	−	0.259412i	$-0.916471\pi$
$37$	−26.1351	+	26.1351i	−0.706355	+	0.706355i	0.259412	+	0.965767i	$0.416471\pi$
$38$	−10.5810	−	10.5810i	−0.278446	−	0.278446i
$39$		0			0
$40$	12.1854	+	32.2676i	0.304634	+	0.806690i
$41$	−12.6463			−0.308445			−0.154223	−	0.988036i	$-0.549287\pi$
$41$	−12.6463			−0.308445			−0.154223	+	0.988036i	$0.549287\pi$
$42$		0			0
$43$	30.0705	+	30.0705i	0.699315	+	0.699315i	0.964263	−	0.264948i	$-0.0853547\pi$
$43$	30.0705	+	30.0705i	0.699315	+	0.699315i	−0.264948	+	0.964263i	$0.585355\pi$
$44$			10.0818i			0.229132i
$45$		0			0
$46$	−20.9245			−0.454881
$47$	34.2331	−	34.2331i	0.728364	−	0.728364i	−0.241930	−	0.970294i	$-0.577780\pi$
$47$	34.2331	−	34.2331i	0.728364	−	0.728364i	0.970294	+	0.241930i	$0.0777805\pi$
$48$		0			0
$49$			21.8932i			0.446801i
$50$	24.4488	+	1.54821i	0.488976	+	0.0309642i
$51$		0			0
$52$	−24.8267	+	24.8267i	−0.477436	+	0.477436i
$53$	−55.2796	−	55.2796i	−1.04301	−	1.04301i	−0.999032	−	0.0439782i	$-0.985997\pi$
$53$	−55.2796	−	55.2796i	−1.04301	−	1.04301i	−0.0439782	−	0.999032i	$-0.514003\pi$
$54$		0			0
$55$	15.1125	+	6.82728i	0.274773	+	0.124132i
$56$	35.9157			0.641351
$57$		0			0
$58$	12.3069	+	12.3069i	0.212187	+	0.212187i
$59$			57.6796i			0.977620i	0.872390	+	0.488810i	$0.162569\pi$
$59$			57.6796i			0.977620i	−0.872390	+	0.488810i	$0.837431\pi$
$60$		0			0
$61$	96.1575			1.57635			0.788176	−	0.615450i	$-0.211026\pi$
$61$	96.1575			1.57635			0.788176	+	0.615450i	$0.211026\pi$
$62$	34.4829	−	34.4829i	0.556176	−	0.556176i
$63$		0			0
$64$			10.6263i			0.166036i
$65$	20.4026	+	54.0273i	0.313886	+	0.831189i
$66$		0			0
$67$	64.4666	−	64.4666i	0.962189	−	0.962189i	−0.0371222	−	0.999311i	$-0.511819\pi$
$67$	64.4666	−	64.4666i	0.962189	−	0.962189i	0.999311	+	0.0371222i	$0.0118191\pi$
$68$	−27.2475	−	27.2475i	−0.400698	−	0.400698i
$69$		0			0
$70$	10.5021	−	23.2469i	0.150030	−	0.332099i
$71$	−48.5204			−0.683385			−0.341693	−	0.939812i	$-0.611000\pi$
$71$	−48.5204			−0.683385			−0.341693	+	0.939812i	$0.611000\pi$
$72$		0			0
$73$	−59.7343	−	59.7343i	−0.818278	−	0.818278i	0.167581	−	0.985858i	$-0.446405\pi$
$73$	−59.7343	−	59.7343i	−0.818278	−	0.818278i	−0.985858	+	0.167581i	$0.946405\pi$
$74$			36.2181i			0.489434i
$75$		0			0
$76$	46.4189			0.610776
$77$	12.2101	−	12.2101i	0.158573	−	0.158573i
$78$		0			0
$79$			27.3519i			0.346226i	0.984902	+	0.173113i	$0.0553827\pi$
$79$			27.3519i			0.346226i	−0.984902	+	0.173113i	$0.944617\pi$
$80$	−24.6026	−	11.1145i	−0.307532	−	0.138932i
$81$		0			0
$82$	−8.76261	+	8.76261i	−0.106861	+	0.106861i
$83$	9.39902	+	9.39902i	0.113241	+	0.113241i	0.761457	−	0.648216i	$-0.224484\pi$
$83$	9.39902	+	9.39902i	0.113241	+	0.113241i	−0.648216	+	0.761457i	$0.724484\pi$
$84$		0			0
$85$	−59.2955	+	22.3921i	−0.697594	+	0.263436i
$86$	41.6718			0.484556
$87$		0			0
$88$	16.1781	+	16.1781i	0.183842	+	0.183842i
$89$		−	120.444i		−	1.35330i	−0.736305	−	0.676649i	$-0.763431\pi$
$89$		−	120.444i		−	1.35330i	0.736305	−	0.676649i	$-0.236569\pi$
$90$		0			0
$91$	60.1355			0.660829
$92$	45.8982	−	45.8982i	0.498893	−	0.498893i
$93$		0			0
$94$		−	47.4403i		−	0.504684i
$95$	31.4344	−	69.5816i	0.330888	−	0.732438i
$96$		0			0
$97$	35.0156	−	35.0156i	0.360985	−	0.360985i	−0.503190	−	0.864176i	$-0.667841\pi$
$97$	35.0156	−	35.0156i	0.360985	−	0.360985i	0.864176	+	0.503190i	$0.167841\pi$
$98$	15.1699	+	15.1699i	0.154794	+	0.154794i
$99$		0			0
$100$	−57.0247	+	50.2327i	−0.570247	+	0.502327i
$101$	−138.348			−1.36978			−0.684892	−	0.728644i	$-0.740151\pi$
$101$	−138.348			−1.36978			−0.684892	+	0.728644i	$0.740151\pi$
$102$		0			0
$103$	−53.3996	−	53.3996i	−0.518443	−	0.518443i	0.398657	−	0.917100i	$-0.369476\pi$
$103$	−53.3996	−	53.3996i	−0.518443	−	0.518443i	−0.917100	+	0.398657i	$0.869476\pi$
$104$			79.6778i			0.766132i
$105$		0			0
$106$	−76.6066			−0.722704
$107$	−31.8185	+	31.8185i	−0.297369	+	0.297369i	−0.839983	−	0.542613i	$-0.817435\pi$
$107$	−31.8185	+	31.8185i	−0.297369	+	0.297369i	0.542613	+	0.839983i	$0.317435\pi$
$108$		0			0
$109$		−	128.209i		−	1.17623i	−0.808777	−	0.588115i	$-0.799870\pi$
$109$		−	128.209i		−	1.17623i	0.808777	−	0.588115i	$-0.200130\pi$
$110$	15.2021	−	5.74086i	0.138201	−	0.0521896i
$111$		0			0
$112$	−19.8776	+	19.8776i	−0.177479	+	0.177479i
$113$	−6.33251	−	6.33251i	−0.0560399	−	0.0560399i	0.678531	−	0.734571i	$-0.262617\pi$
$113$	−6.33251	−	6.33251i	−0.0560399	−	0.0560399i	−0.734571	+	0.678531i	$0.762617\pi$
$114$		0			0
$115$	−37.7192	−	99.8827i	−0.327993	−	0.868546i
$116$	−53.9906			−0.465436
$117$		0			0
$118$	39.9663	+	39.9663i	0.338697	+	0.338697i
$119$			65.9992i			0.554615i
$120$		0			0
$121$	11.0000			0.0909091
$122$	66.6276	−	66.6276i	0.546128	−	0.546128i
$123$		0			0
$124$			151.277i			1.21998i
$125$	36.6819	+	119.497i	0.293455	+	0.955973i
$126$		0			0
$127$	−77.9047	+	77.9047i	−0.613423	+	0.613423i	−0.943836	−	0.330413i	$-0.892812\pi$
$127$	−77.9047	+	77.9047i	−0.613423	+	0.613423i	0.330413	+	0.943836i	$0.392812\pi$
$128$	−85.6478	−	85.6478i	−0.669123	−	0.669123i
$129$		0			0
$130$	51.5726	+	23.2986i	0.396712	+	0.179220i
$131$	−164.860			−1.25847			−0.629236	−	0.777215i	$-0.716632\pi$
$131$	−164.860			−1.25847			−0.629236	+	0.777215i	$0.716632\pi$
$132$		0			0
$133$	−56.2183	−	56.2183i	−0.422694	−	0.422694i
$134$		−	89.3380i		−	0.666702i
$135$		0			0
$136$	−87.4471			−0.642993
$137$	93.1512	−	93.1512i	0.679936	−	0.679936i	−0.280050	−	0.959985i	$-0.590351\pi$
$137$	93.1512	−	93.1512i	0.679936	−	0.679936i	0.959985	+	0.280050i	$0.0903510\pi$
$138$		0			0
$139$		−	89.7778i		−	0.645884i	−0.946419	−	0.322942i	$-0.895328\pi$
$139$		−	89.7778i		−	0.645884i	0.946419	−	0.322942i	$-0.104672\pi$
$140$	27.9559	+	74.0289i	0.199685	+	0.528778i
$141$		0			0
$142$	−33.6198	+	33.6198i	−0.236759	+	0.236759i
$143$	27.0878	+	27.0878i	0.189425	+	0.189425i
$144$		0			0
$145$	−36.5618	+	80.9314i	−0.252150	+	0.558147i
$146$	−82.7799			−0.566986
$147$		0			0
$148$	−79.4450	−	79.4450i	−0.536790	−	0.536790i
$149$			244.498i			1.64093i	0.571699	+	0.820463i	$0.306284\pi$
$149$			244.498i			1.64093i	−0.571699	+	0.820463i	$0.693716\pi$
$150$		0			0
$151$	−174.477			−1.15548			−0.577738	−	0.816222i	$-0.696065\pi$
$151$	−174.477			−1.15548			−0.577738	+	0.816222i	$0.696065\pi$
$152$	74.4876	−	74.4876i	0.490050	−	0.490050i
$153$		0			0
$154$		−	16.9208i		−	0.109875i
$155$	226.763	+	102.443i	1.46299	+	0.660925i
$156$		0			0
$157$	83.4260	−	83.4260i	0.531376	−	0.531376i	−0.389606	−	0.920982i	$-0.627389\pi$
$157$	83.4260	−	83.4260i	0.531376	−	0.531376i	0.920982	+	0.389606i	$0.127389\pi$
$158$	18.9522	+	18.9522i	0.119950	+	0.119950i
$159$		0			0
$160$	−153.819	+	58.0874i	−0.961368	+	0.363046i
$161$	−111.175			−0.690529
$162$		0			0
$163$	−156.440	−	156.440i	−0.959755	−	0.959755i	0.0394656	−	0.999221i	$-0.487434\pi$
$163$	−156.440	−	156.440i	−0.959755	−	0.959755i	−0.999221	+	0.0394656i	$0.987434\pi$
$164$		−	38.4418i		−	0.234401i
$165$		0			0
$166$	13.0252			0.0784649
$167$	−6.71225	+	6.71225i	−0.0401931	+	0.0401931i	−0.726918	−	0.686725i	$-0.759048\pi$
$167$	−6.71225	+	6.71225i	−0.0401931	+	0.0401931i	0.686725	+	0.726918i	$0.259048\pi$
$168$		0			0
$169$		−	35.5914i		−	0.210600i
$170$	−25.5704	+	56.6014i	−0.150414	+	0.332949i
$171$		0			0
$172$	−91.4077	+	91.4077i	−0.531440	+	0.531440i
$173$	−41.6087	−	41.6087i	−0.240513	−	0.240513i	0.576550	−	0.817062i	$-0.304399\pi$
$173$	−41.6087	−	41.6087i	−0.240513	−	0.240513i	−0.817062	+	0.576550i	$0.804399\pi$
$174$		0			0
$175$	129.900	+	8.22587i	0.742287	+	0.0470050i
$176$	−17.9076			−0.101748
$177$		0			0
$178$	−83.4555	−	83.4555i	−0.468851	−	0.468851i
$179$			35.8421i			0.200235i	0.994976	+	0.100118i	$0.0319219\pi$
$179$			35.8421i			0.200235i	−0.994976	+	0.100118i	$0.968078\pi$
$180$		0			0
$181$	76.1361			0.420642			0.210321	−	0.977632i	$-0.432549\pi$
$181$	76.1361			0.420642			0.210321	+	0.977632i	$0.432549\pi$
$182$	41.6679	−	41.6679i	0.228945	−	0.228945i
$183$		0			0
$184$		−	147.304i		−	0.800565i
$185$	−172.887	+	65.2880i	−0.934522	+	0.352908i
$186$		0			0
$187$	−29.7291	+	29.7291i	−0.158979	+	0.158979i
$188$	104.061	+	104.061i	0.553515	+	0.553515i
$189$		0			0
$190$	−26.4322	−	69.9941i	−0.139117	−	0.368390i
$191$	327.166			1.71291			0.856455	−	0.516222i	$-0.172662\pi$
$191$	327.166			1.71291			0.856455	+	0.516222i	$0.172662\pi$
$192$		0			0
$193$	−45.7105	−	45.7105i	−0.236842	−	0.236842i	0.578699	−	0.815541i	$-0.303561\pi$
$193$	−45.7105	−	45.7105i	−0.236842	−	0.236842i	−0.815541	+	0.578699i	$0.803561\pi$
$194$		−	48.5247i		−	0.250127i
$195$		0			0
$196$	−66.5506			−0.339544
$197$	93.2886	−	93.2886i	0.473546	−	0.473546i	−0.429514	−	0.903060i	$-0.641315\pi$
$197$	93.2886	−	93.2886i	0.473546	−	0.473546i	0.903060	+	0.429514i	$0.141315\pi$
$198$		0			0
$199$		−	249.951i		−	1.25603i	−0.778200	−	0.628017i	$-0.783867\pi$
$199$		−	249.951i		−	1.25603i	0.778200	−	0.628017i	$-0.216133\pi$
$200$	−10.8990	+	172.114i	−0.0544952	+	0.860570i
$201$		0			0
$202$	−95.8617	+	95.8617i	−0.474563	+	0.474563i
$203$	65.3883	+	65.3883i	0.322110	+	0.322110i
$204$		0			0
$205$	−57.6239	−	26.0324i	−0.281092	−	0.126987i
$206$	−74.0013			−0.359230
$207$		0			0
$208$	−44.0978	−	44.0978i	−0.212009	−	0.212009i
$209$		−	50.6466i		−	0.242328i
$210$		0			0
$211$	154.127			0.730462			0.365231	−	0.930917i	$-0.380990\pi$
$211$	154.127			0.730462			0.365231	+	0.930917i	$0.380990\pi$
$212$	168.037	−	168.037i	0.792630	−	0.792630i
$213$		0			0
$214$			44.0941i			0.206047i
$215$	75.1191	+	198.920i	0.349391	+	0.925208i
$216$		0			0
$217$	183.213	−	183.213i	0.844299	−	0.844299i
$218$	−88.8362	−	88.8362i	−0.407506	−	0.407506i
$219$		0			0
$220$	−20.7534	+	45.9387i	−0.0943336	+	0.208812i
$221$	−146.417			−0.662521
$222$		0			0
$223$	185.905	+	185.905i	0.833653	+	0.833653i	0.988014	−	0.154362i	$-0.0493320\pi$
$223$	185.905	+	185.905i	0.833653	+	0.833653i	−0.154362	+	0.988014i	$0.549332\pi$
$224$			171.209i			0.764326i
$225$		0			0
$226$	−8.77561			−0.0388302
$227$	150.732	−	150.732i	0.664018	−	0.664018i	−0.292306	−	0.956325i	$-0.594423\pi$
$227$	150.732	−	150.732i	0.664018	−	0.664018i	0.956325	+	0.292306i	$0.0944227\pi$
$228$		0			0
$229$		−	172.693i		−	0.754120i	−0.926189	−	0.377060i	$-0.876935\pi$
$229$		−	172.693i		−	0.754120i	0.926189	−	0.377060i	$-0.123065\pi$
$230$	−95.3446	−	43.0732i	−0.414542	−	0.187275i
$231$		0			0
$232$	−86.6376	+	86.6376i	−0.373438	+	0.373438i
$233$	−295.327	−	295.327i	−1.26750	−	1.26750i	−0.947377	−	0.320121i	$-0.896276\pi$
$233$	−295.327	−	295.327i	−1.26750	−	1.26750i	−0.320121	−	0.947377i	$-0.603724\pi$
$234$		0			0
$235$	226.455	−	85.5175i	0.963639	−	0.363904i
$236$	−175.333			−0.742936
$237$		0			0
$238$	45.7310	+	45.7310i	0.192147	+	0.192147i
$239$		−	178.384i		−	0.746376i	−0.927756	−	0.373188i	$-0.878265\pi$
$239$		−	178.384i		−	0.746376i	0.927756	−	0.373188i	$-0.121735\pi$
$240$		0			0
$241$	−280.305			−1.16309			−0.581546	−	0.813513i	$-0.697552\pi$
$241$	−280.305			−1.16309			−0.581546	+	0.813513i	$0.697552\pi$
$242$	7.62191	−	7.62191i	0.0314955	−	0.0314955i
$243$		0			0
$244$			292.297i			1.19794i
$245$	−45.0673	+	99.7587i	−0.183948	+	0.407178i
$246$		0			0
$247$	124.718	−	124.718i	0.504933	−	0.504933i
$248$	242.752	+	242.752i	0.978838	+	0.978838i
$249$		0			0
$250$	108.216	+	57.3824i	0.432865	+	0.229530i
$251$	−293.526			−1.16943			−0.584713	−	0.811240i	$-0.698793\pi$
$251$	−293.526			−1.16943			−0.584713	+	0.811240i	$0.698793\pi$
$252$		0			0
$253$	−50.0784	−	50.0784i	−0.197938	−	0.197938i
$254$			107.961i			0.425042i
$255$		0			0
$256$	−161.196			−0.629672
$257$	171.250	−	171.250i	0.666344	−	0.666344i	−0.290524	−	0.956868i	$-0.593830\pi$
$257$	171.250	−	171.250i	0.666344	−	0.666344i	0.956868	+	0.290524i	$0.0938296\pi$
$258$		0			0
$259$			192.433i			0.742983i
$260$	−164.231	+	62.0194i	−0.631657	+	0.238536i
$261$		0			0
$262$	−114.232	+	114.232i	−0.435998	+	0.435998i
$263$	−308.433	−	308.433i	−1.17275	−	1.17275i	−0.981552	−	0.191198i	$-0.938763\pi$
$263$	−308.433	−	308.433i	−1.17275	−	1.17275i	−0.191198	−	0.981552i	$-0.561237\pi$
$264$		0			0
$265$	−138.094	−	365.680i	−0.521108	−	1.37992i
$266$	−77.9074			−0.292885
$267$		0			0
$268$	195.964	+	195.964i	0.731209	+	0.731209i
$269$			212.116i			0.788536i	0.918996	+	0.394268i	$0.129002\pi$
$269$			212.116i			0.788536i	−0.918996	+	0.394268i	$0.870998\pi$
$270$		0			0
$271$	200.258			0.738959			0.369479	−	0.929239i	$-0.379536\pi$
$271$	200.258			0.738959			0.369479	+	0.929239i	$0.379536\pi$
$272$	48.3978	−	48.3978i	0.177933	−	0.177933i
$273$		0			0
$274$		−	129.089i		−	0.471128i
$275$	54.8077	+	62.2183i	0.199301	+	0.226248i
$276$		0			0
$277$	−183.873	+	183.873i	−0.663801	+	0.663801i	−0.956274	−	0.292473i	$-0.905522\pi$
$277$	−183.873	+	183.873i	−0.663801	+	0.663801i	0.292473	+	0.956274i	$0.405522\pi$
$278$	−62.2072	−	62.2072i	−0.223767	−	0.223767i
$279$		0			0
$280$	163.653	+	73.9325i	0.584476	+	0.264045i
$281$	323.782			1.15225			0.576125	−	0.817362i	$-0.304564\pi$
$281$	323.782			1.15225			0.576125	+	0.817362i	$0.304564\pi$
$282$		0			0
$283$	267.253	+	267.253i	0.944357	+	0.944357i	0.998531	−	0.0541745i	$-0.0172527\pi$
$283$	267.253	+	267.253i	0.944357	+	0.944357i	−0.0541745	+	0.998531i	$0.517253\pi$
$284$		−	147.491i		−	0.519335i
$285$		0			0
$286$	37.5383			0.131253
$287$	−46.5571	+	46.5571i	−0.162220	+	0.162220i
$288$		0			0
$289$			128.306i			0.443965i
$290$	30.7437	+	81.4112i	0.106013	+	0.280728i
$291$		0			0
$292$	181.579	−	181.579i	0.621845	−	0.621845i
$293$	−258.183	−	258.183i	−0.881171	−	0.881171i	0.112483	−	0.993654i	$-0.464120\pi$
$293$	−258.183	−	258.183i	−0.881171	−	0.881171i	−0.993654	+	0.112483i	$0.964120\pi$
$294$		0			0
$295$	−118.734	+	262.823i	−0.402486	+	0.890924i
$296$	−254.968			−0.861377
$297$		0			0
$298$	169.413	+	169.413i	0.568500	+	0.568500i
$299$		−	246.639i		−	0.824878i
$300$		0			0
$301$	221.409			0.735578
$302$	−120.895	+	120.895i	−0.400316	+	0.400316i
$303$		0			0
$304$			82.4507i			0.271219i
$305$	438.151	+	197.940i	1.43656	+	0.648985i
$306$		0			0
$307$	17.0001	−	17.0001i	0.0553748	−	0.0553748i	−0.678877	−	0.734252i	$-0.737533\pi$
$307$	17.0001	−	17.0001i	0.0553748	−	0.0553748i	0.734252	+	0.678877i	$0.237533\pi$
$308$	37.1160	+	37.1160i	0.120507	+	0.120507i
$309$		0			0
$310$	228.108	−	86.1415i	0.735831	−	0.277876i
$311$	68.2297			0.219388			0.109694	−	0.993965i	$-0.465013\pi$
$311$	68.2297			0.219388			0.109694	+	0.993965i	$0.465013\pi$
$312$		0			0
$313$	−199.246	−	199.246i	−0.636568	−	0.636568i	0.313139	−	0.949707i	$-0.398619\pi$
$313$	−199.246	−	199.246i	−0.636568	−	0.636568i	−0.949707	+	0.313139i	$0.898619\pi$
$314$		−	115.612i		−	0.368191i
$315$		0			0
$316$	−83.1436			−0.263113
$317$	83.4496	−	83.4496i	0.263248	−	0.263248i	−0.563124	−	0.826372i	$-0.690401\pi$
$317$	83.4496	−	83.4496i	0.263248	−	0.263248i	0.826372	+	0.563124i	$0.190401\pi$
$318$		0			0
$319$			58.9078i			0.184664i
$320$	−21.8742	+	48.4197i	−0.0683570	+	0.151312i
$321$		0			0
$322$	−77.0334	+	77.0334i	−0.239234	+	0.239234i
$323$	136.880	+	136.880i	0.423776	+	0.423776i
$324$		0			0
$325$	−18.2488	+	288.179i	−0.0561502	+	0.886706i
$326$	−216.795			−0.665016
$327$		0			0
$328$	−61.6868	−	61.6868i	−0.188070	−	0.188070i
$329$		−	252.058i		−	0.766133i
$330$		0			0
$331$	189.354			0.572065			0.286033	−	0.958220i	$-0.407663\pi$
$331$	189.354			0.572065			0.286033	+	0.958220i	$0.407663\pi$
$332$	−28.5709	+	28.5709i	−0.0860569	+	0.0860569i
$333$		0			0
$334$			9.30185i			0.0278499i
$335$	426.453	−	161.044i	1.27299	−	0.480728i
$336$		0			0
$337$	327.468	−	327.468i	0.971716	−	0.971716i	−0.0278952	−	0.999611i	$-0.508880\pi$
$337$	327.468	−	327.468i	0.971716	−	0.971716i	0.999611	+	0.0278952i	$0.00888047\pi$
$338$	−24.6613	−	24.6613i	−0.0729626	−	0.0729626i
$339$		0			0
$340$	−68.0668	−	180.245i	−0.200197	−	0.530132i
$341$	165.055			0.484032
$342$		0			0
$343$	260.993	+	260.993i	0.760912	+	0.760912i
$344$			293.360i			0.852792i
$345$		0			0
$346$	−57.6614			−0.166651
$347$	304.837	−	304.837i	0.878494	−	0.878494i	−0.114885	−	0.993379i	$-0.536650\pi$
$347$	304.837	−	304.837i	0.878494	−	0.878494i	0.993379	+	0.114885i	$0.0366500\pi$
$348$		0			0
$349$			410.903i			1.17737i	0.808361	+	0.588687i	$0.200355\pi$
$349$			410.903i			1.17737i	−0.808361	+	0.588687i	$0.799645\pi$
$350$	95.7077	−	84.3083i	0.273451	−	0.240881i
$351$		0			0
$352$	−77.1204	+	77.1204i	−0.219092	+	0.219092i
$353$	215.002	+	215.002i	0.609071	+	0.609071i	0.942703	−	0.333633i	$-0.108274\pi$
$353$	215.002	+	215.002i	0.609071	+	0.609071i	−0.333633	+	0.942703i	$0.608274\pi$
$354$		0			0
$355$	−221.088	−	99.8793i	−0.622782	−	0.281350i
$356$	366.121			1.02843
$357$		0			0
$358$	24.8351	+	24.8351i	0.0693717	+	0.0693717i
$359$			356.681i			0.993540i	0.867882	+	0.496770i	$0.165481\pi$
$359$			356.681i			0.993540i	−0.867882	+	0.496770i	$0.834519\pi$
$360$		0			0
$361$	127.811			0.354048
$362$	52.7548	−	52.7548i	0.145732	−	0.145732i
$363$		0			0
$364$			182.798i			0.502193i
$365$	−149.222	−	395.148i	−0.408827	−	1.08260i
$366$		0			0
$367$	82.8049	−	82.8049i	0.225626	−	0.225626i	−0.585236	−	0.810863i	$-0.698998\pi$
$367$	82.8049	−	82.8049i	0.225626	−	0.225626i	0.810863	+	0.585236i	$0.198998\pi$
$368$	81.5257	+	81.5257i	0.221537	+	0.221537i
$369$		0			0
$370$	−74.5551	+	165.031i	−0.201500	+	0.446031i
$371$	−407.022			−1.09710
$372$		0			0
$373$	−51.3189	−	51.3189i	−0.137584	−	0.137584i	0.634960	−	0.772545i	$-0.281016\pi$
$373$	−51.3189	−	51.3189i	−0.137584	−	0.137584i	−0.772545	+	0.634960i	$0.781016\pi$
$374$			41.1986i			0.110157i
$375$		0			0
$376$	333.969			0.888216
$377$	−145.062	+	145.062i	−0.384779	+	0.384779i
$378$		0			0
$379$			743.254i			1.96109i	0.196287	+	0.980546i	$0.437112\pi$
$379$			743.254i			1.96109i	−0.196287	+	0.980546i	$0.562888\pi$
$380$	211.512	+	95.5535i	0.556611	+	0.251457i
$381$		0			0
$382$	226.694	−	226.694i	0.593439	−	0.593439i
$383$	−369.744	−	369.744i	−0.965390	−	0.965390i	0.0340308	−	0.999421i	$-0.489166\pi$
$383$	−369.744	−	369.744i	−0.965390	−	0.965390i	−0.999421	+	0.0340308i	$0.989166\pi$
$384$		0			0
$385$	80.7712	−	30.5020i	0.209795	−	0.0792261i
$386$	−63.3457			−0.164108
$387$		0			0
$388$	106.439	+	106.439i	0.274329	+	0.274329i
$389$			742.252i			1.90810i	0.299644	+	0.954051i	$0.403132\pi$
$389$			742.252i			1.90810i	−0.299644	+	0.954051i	$0.596868\pi$
$390$		0			0
$391$	270.688			0.692297
$392$	−106.792	+	106.792i	−0.272430	+	0.272430i
$393$		0			0
$394$		−	129.280i		−	0.328121i
$395$	−56.3039	+	124.632i	−0.142542	+	0.315523i
$396$		0			0
$397$	−70.6003	+	70.6003i	−0.177835	+	0.177835i	−0.790411	−	0.612577i	$-0.790133\pi$
$397$	−70.6003	+	70.6003i	−0.177835	+	0.177835i	0.612577	+	0.790411i	$0.290133\pi$
$398$	−173.191	−	173.191i	−0.435154	−	0.435154i
$399$		0			0
$400$	−89.2248	−	101.289i	−0.223062	−	0.253222i
$401$	162.318			0.404783			0.202391	−	0.979305i	$-0.435129\pi$
$401$	162.318			0.404783			0.202391	+	0.979305i	$0.435129\pi$
$402$		0			0
$403$	406.452	+	406.452i	1.00857	+	1.00857i
$404$		−	420.547i		−	1.04096i
$405$		0			0
$406$	90.6153			0.223190
$407$	−86.6804	+	86.6804i	−0.212974	+	0.212974i
$408$		0			0
$409$		−	3.19036i		−	0.00780038i	−0.999992	−	0.00390019i	$-0.998759\pi$
$409$		−	3.19036i		−	0.00780038i	0.999992	−	0.00390019i	$-0.00124147\pi$
$410$	−57.9655	+	21.8898i	−0.141379	+	0.0533898i
$411$		0			0
$412$	162.323	−	162.323i	0.393987	−	0.393987i
$413$	212.347	+	212.347i	0.514157	+	0.514157i
$414$		0			0
$415$	23.4796	+	62.1754i	0.0565774	+	0.149820i
$416$	−379.822			−0.913033
$417$		0			0
$418$	−35.0931	−	35.0931i	−0.0839547	−	0.0839547i
$419$			656.966i			1.56794i	0.620800	+	0.783969i	$0.286808\pi$
$419$			656.966i			1.56794i	−0.620800	+	0.783969i	$0.713192\pi$
$420$		0			0
$421$	−713.995			−1.69595			−0.847975	−	0.530037i	$-0.822178\pi$
$421$	−713.995			−1.69595			−0.847975	+	0.530037i	$0.822178\pi$
$422$	106.795	−	106.795i	0.253069	−	0.253069i
$423$		0			0
$424$		−	539.293i		−	1.27192i
$425$	−316.280	−	20.0282i	−0.744187	−	0.0471253i
$426$		0			0
$427$	354.003	−	354.003i	0.829046	−	0.829046i
$428$	−96.7211	−	96.7211i	−0.225984	−	0.225984i
$429$		0			0
$430$	189.882	+	85.7816i	0.441586	+	0.199492i
$431$	−811.634			−1.88314			−0.941571	−	0.336816i	$-0.890650\pi$
$431$	−811.634			−1.88314			−0.941571	+	0.336816i	$0.890650\pi$
$432$		0			0
$433$	−25.0648	−	25.0648i	−0.0578863	−	0.0578863i	0.677571	−	0.735457i	$-0.263033\pi$
$433$	−25.0648	−	25.0648i	−0.0578863	−	0.0578863i	−0.735457	+	0.677571i	$0.763033\pi$
$434$		−	253.897i		−	0.585016i
$435$		0			0
$436$	389.727			0.893869
$437$	−230.573	+	230.573i	−0.527626	+	0.527626i
$438$		0			0
$439$			276.543i			0.629939i	0.949102	+	0.314969i	$0.101994\pi$
$439$			276.543i			0.629939i	−0.949102	+	0.314969i	$0.898006\pi$
$440$	40.4143	+	107.019i	0.0918508	+	0.243226i
$441$		0			0
$442$	−101.453	+	101.453i	−0.229531	+	0.229531i
$443$	−321.159	−	321.159i	−0.724965	−	0.724965i	0.244647	−	0.969612i	$-0.421328\pi$
$443$	−321.159	−	321.159i	−0.724965	−	0.724965i	−0.969612	+	0.244647i	$0.921328\pi$
$444$		0			0
$445$	247.933	−	548.813i	0.557154	−	1.23329i
$446$	257.627			0.577639
$447$		0			0
$448$	39.1206	+	39.1206i	0.0873227	+	0.0873227i
$449$		−	195.462i		−	0.435327i	−0.976024	−	0.217663i	$-0.930156\pi$
$449$		−	195.462i		−	0.435327i	0.976024	−	0.217663i	$-0.0698435\pi$
$450$		0			0
$451$	−41.9429			−0.0929998
$452$	19.2494	−	19.2494i	0.0425872	−	0.0425872i
$453$		0			0
$454$		−	208.885i		−	0.460099i
$455$	274.013	+	123.789i	0.602226	+	0.272064i
$456$		0			0
$457$	−308.165	+	308.165i	−0.674322	+	0.674322i	−0.958709	−	0.284388i	$-0.908210\pi$
$457$	−308.165	+	308.165i	−0.674322	+	0.674322i	0.284388	+	0.958709i	$0.408210\pi$
$458$	−119.660	−	119.660i	−0.261265	−	0.261265i
$459$		0			0
$460$	303.621	−	114.658i	0.660046	−	0.249257i
$461$	743.850			1.61356			0.806779	−	0.590854i	$-0.201209\pi$
$461$	743.850			1.61356			0.806779	+	0.590854i	$0.201209\pi$
$462$		0			0
$463$	−380.768	−	380.768i	−0.822393	−	0.822393i	0.164058	−	0.986451i	$-0.447542\pi$
$463$	−380.768	−	380.768i	−0.822393	−	0.822393i	−0.986451	+	0.164058i	$0.947542\pi$
$464$		−	95.8996i		−	0.206680i
$465$		0			0
$466$	−409.265			−0.878251
$467$	352.366	−	352.366i	0.754531	−	0.754531i	−0.220790	−	0.975321i	$-0.570864\pi$
$467$	352.366	−	352.366i	0.754531	−	0.754531i	0.975321	+	0.220790i	$0.0708637\pi$
$468$		0			0
$469$		−	474.667i		−	1.01208i
$470$	97.6560	−	216.166i	0.207779	−	0.459928i
$471$		0			0
$472$	−281.353	+	281.353i	−0.596088	+	0.596088i
$473$	99.7327	+	99.7327i	0.210851	+	0.210851i
$474$		0			0
$475$	286.468	−	252.347i	0.603090	−	0.531258i
$476$	−200.623			−0.421477
$477$		0			0
$478$	−123.602	−	123.602i	−0.258583	−	0.258583i
$479$			831.630i			1.73618i	0.496406	+	0.868090i	$0.334653\pi$
$479$			831.630i			1.73618i	−0.496406	+	0.868090i	$0.665347\pi$
$480$		0			0
$481$	−426.905			−0.887537
$482$	−194.224	+	194.224i	−0.402954	+	0.402954i
$483$		0			0
$484$			33.4375i			0.0690858i
$485$	231.631	−	87.4722i	0.477591	−	0.180355i
$486$		0			0
$487$	54.4187	−	54.4187i	0.111743	−	0.111743i	−0.649025	−	0.760767i	$-0.724823\pi$
$487$	54.4187	−	54.4187i	0.111743	−	0.111743i	0.760767	+	0.649025i	$0.224823\pi$
$488$	469.044	+	469.044i	0.961155	+	0.961155i
$489$		0			0
$490$	37.8957	+	100.350i	0.0773382	+	0.204796i
$491$	−151.009			−0.307554			−0.153777	−	0.988106i	$-0.549144\pi$
$491$	−151.009			−0.307554			−0.153777	+	0.988106i	$0.549144\pi$
$492$		0			0
$493$	−159.207	−	159.207i	−0.322935	−	0.322935i
$494$		−	172.835i		−	0.349869i
$495$		0			0
$496$	−268.703			−0.541740
$497$	−178.627	+	178.627i	−0.359411	+	0.359411i
$498$		0			0
$499$			469.179i			0.940238i	0.882603	+	0.470119i	$0.155789\pi$
$499$			469.179i			0.940238i	−0.882603	+	0.470119i	$0.844211\pi$
$500$	−363.243	+	111.505i	−0.726486	+	0.223009i
$501$		0			0
$502$	−203.384	+	203.384i	−0.405148	+	0.405148i
$503$	254.121	+	254.121i	0.505211	+	0.505211i	0.913053	−	0.407842i	$-0.133718\pi$
$503$	254.121	+	254.121i	0.505211	+	0.505211i	−0.407842	+	0.913053i	$0.633718\pi$
$504$		0			0
$505$	−630.397	−	284.790i	−1.24831	−	0.563941i
$506$	−69.3988			−0.137152
$507$		0			0
$508$	−236.813	−	236.813i	−0.466167	−	0.466167i
$509$			58.9749i			0.115864i	0.998321	+	0.0579322i	$0.0184507\pi$
$509$			58.9749i			0.115864i	−0.998321	+	0.0579322i	$0.981549\pi$
$510$		0			0
$511$	−439.822			−0.860709
$512$	230.898	−	230.898i	0.450973	−	0.450973i
$513$		0			0
$514$		−	237.319i		−	0.461710i
$515$	−133.397	−	353.244i	−0.259024	−	0.685910i
$516$		0			0
$517$	113.538	−	113.538i	0.219610	−	0.219610i
$518$	133.337	+	133.337i	0.257407	+	0.257407i
$519$		0			0
$520$	−164.017	+	363.059i	−0.315417	+	0.698191i
$521$	869.983			1.66983			0.834916	−	0.550377i	$-0.185516\pi$
$521$	869.983			1.66983			0.834916	+	0.550377i	$0.185516\pi$
$522$		0			0
$523$	418.179	+	418.179i	0.799577	+	0.799577i	0.983029	−	0.183452i	$-0.0587271\pi$
$523$	418.179	+	418.179i	0.799577	+	0.799577i	−0.183452	+	0.983029i	$0.558727\pi$
$524$		−	501.137i		−	0.956368i
$525$		0			0
$526$	−427.427			−0.812600
$527$	−446.085	+	446.085i	−0.846461	+	0.846461i
$528$		0			0
$529$		−	73.0279i		−	0.138049i
$530$	−349.065	−	157.695i	−0.658614	−	0.297537i
$531$		0			0
$532$	170.891	−	170.891i	0.321224	−	0.321224i
$533$	−103.285	−	103.285i	−0.193781	−	0.193781i
$534$		0			0
$535$	−210.482	+	79.4856i	−0.393425	+	0.148571i
$536$	628.920			1.17336
$537$		0			0
$538$	146.976	+	146.976i	0.273189	+	0.273189i
$539$			72.6117i			0.134716i
$540$		0			0
$541$	−198.651			−0.367193			−0.183596	−	0.983002i	$-0.558774\pi$
$541$	−198.651			−0.367193			−0.183596	+	0.983002i	$0.558774\pi$
$542$	138.759	−	138.759i	0.256013	−	0.256013i
$543$		0			0
$544$		−	416.858i		−	0.766283i
$545$	263.919	−	584.197i	0.484254	−	1.07192i
$546$		0			0
$547$	−118.406	+	118.406i	−0.216464	+	0.216464i	−0.807007	−	0.590543i	$-0.798914\pi$
$547$	−118.406	+	118.406i	−0.216464	+	0.216464i	0.590543	+	0.807007i	$0.298914\pi$
$548$	283.159	+	283.159i	0.516713	+	0.516713i
$549$		0			0
$550$	81.0875	+	5.13482i	0.147432	+	0.00933604i
$551$	271.225			0.492242
$552$		0			0
$553$	100.696	+	100.696i	0.182090	+	0.182090i
$554$			254.812i			0.459949i
$555$		0			0
$556$	272.904			0.490835
$557$	−483.193	+	483.193i	−0.867492	+	0.867492i	−0.992194	−	0.124702i	$-0.960202\pi$
$557$	−483.193	+	483.193i	−0.867492	+	0.867492i	0.124702	+	0.992194i	$0.460202\pi$
$558$		0			0
$559$			491.189i			0.878691i
$560$	−131.492	+	49.6561i	−0.234808	+	0.0886717i
$561$		0			0
$562$	224.349	−	224.349i	0.399198	−	0.399198i
$563$	−264.442	−	264.442i	−0.469701	−	0.469701i	0.432117	−	0.901818i	$-0.357767\pi$
$563$	−264.442	−	264.442i	−0.469701	−	0.469701i	−0.901818	+	0.432117i	$0.857767\pi$
$564$		0			0
$565$	−15.8192	−	41.8902i	−0.0279986	−	0.0741419i
$566$	370.360			0.654346
$567$		0			0
$568$	−236.676	−	236.676i	−0.416683	−	0.416683i
$569$			94.2465i			0.165635i	0.996565	+	0.0828177i	$0.0263919\pi$
$569$			94.2465i			0.165635i	−0.996565	+	0.0828177i	$0.973608\pi$
$570$		0			0
$571$	588.505			1.03066			0.515328	−	0.856993i	$-0.327670\pi$
$571$	588.505			1.03066			0.515328	+	0.856993i	$0.327670\pi$
$572$	−82.3407	+	82.3407i	−0.143952	+	0.143952i
$573$		0			0
$574$			64.5189i			0.112402i
$575$	33.7374	−	532.770i	0.0586738	−	0.926557i
$576$		0			0
$577$	−758.203	+	758.203i	−1.31404	+	1.31404i	−0.395635	+	0.918408i	$0.629475\pi$
$577$	−758.203	+	758.203i	−1.31404	+	1.31404i	−0.918408	+	0.395635i	$0.870525\pi$
$578$	88.9033	+	88.9033i	0.153812	+	0.153812i
$579$		0			0
$580$	−246.013	−	111.140i	−0.424161	−	0.191620i
$581$	69.2048			0.119113
$582$		0			0
$583$	−183.342	−	183.342i	−0.314480	−	0.314480i
$584$		−	582.752i		−	0.997863i
$585$		0			0
$586$	−357.791			−0.610564
$587$	−74.4278	+	74.4278i	−0.126793	+	0.126793i	−0.767656	−	0.640862i	$-0.778577\pi$
$587$	−74.4278	+	74.4278i	−0.126793	+	0.126793i	0.640862	+	0.767656i	$0.278577\pi$
$588$		0			0
$589$		−	759.952i		−	1.29024i
$590$	99.8395	+	264.381i	0.169219	+	0.448103i
$591$		0			0
$592$	141.112	−	141.112i	0.238366	−	0.238366i
$593$	−760.346	−	760.346i	−1.28220	−	1.28220i	−0.939412	−	0.342790i	$-0.888628\pi$
$593$	−760.346	−	760.346i	−1.28220	−	1.28220i	−0.342790	−	0.939412i	$-0.611372\pi$
$594$		0			0
$595$	−135.860	+	300.732i	−0.228335	+	0.505432i
$596$	−743.219			−1.24701
$597$		0			0
$598$	−170.896	−	170.896i	−0.285780	−	0.285780i
$599$		−	553.984i		−	0.924848i	−0.886659	−	0.462424i	$-0.846980\pi$
$599$		−	553.984i		−	0.924848i	0.886659	−	0.462424i	$-0.153020\pi$
$600$		0			0
$601$	−907.051			−1.50924			−0.754618	−	0.656164i	$-0.772178\pi$
$601$	−907.051			−1.50924			−0.754618	+	0.656164i	$0.772178\pi$
$602$	153.415	−	153.415i	0.254841	−	0.254841i
$603$		0			0
$604$		−	530.371i		−	0.878097i
$605$	50.1226	+	22.6435i	0.0828472	+	0.0374273i
$606$		0			0
$607$	−466.312	+	466.312i	−0.768224	+	0.768224i	−0.977794	−	0.209570i	$-0.932794\pi$
$607$	−466.312	+	466.312i	−0.768224	+	0.768224i	0.209570	+	0.977794i	$0.432794\pi$
$608$	355.081	+	355.081i	0.584014	+	0.584014i
$609$		0			0
$610$	440.748	−	166.442i	0.722538	−	0.272856i
$611$	559.182			0.915191
$612$		0			0
$613$	−542.769	−	542.769i	−0.885431	−	0.885431i	0.108649	−	0.994080i	$-0.465348\pi$
$613$	−542.769	−	542.769i	−0.885431	−	0.885431i	−0.994080	+	0.108649i	$0.965348\pi$
$614$		−	23.5588i		−	0.0383693i
$615$		0			0
$616$	119.119			0.193375
$617$	−368.002	+	368.002i	−0.596438	+	0.596438i	−0.939363	−	0.342925i	$-0.888582\pi$
$617$	−368.002	+	368.002i	−0.596438	+	0.596438i	0.342925	+	0.939363i	$0.388582\pi$
$618$		0			0
$619$		−	349.062i		−	0.563912i	−0.959427	−	0.281956i	$-0.909017\pi$
$619$		−	349.062i		−	0.563912i	0.959427	−	0.281956i	$-0.0909832\pi$
$620$	−311.405	+	689.310i	−0.502266	+	1.11179i
$621$		0			0
$622$	47.2764	−	47.2764i	0.0760071	−	0.0760071i
$623$	−443.412	−	443.412i	−0.711737	−	0.711737i
$624$		0			0
$625$	−78.8395	+	620.008i	−0.126143	+	0.992012i
$626$	−276.115			−0.441079
$627$		0			0
$628$	253.596	+	253.596i	0.403816	+	0.403816i
$629$		−	468.533i		−	0.744885i
$630$		0			0
$631$	−197.799			−0.313470			−0.156735	−	0.987641i	$-0.550097\pi$
$631$	−197.799			−0.313470			−0.156735	+	0.987641i	$0.550097\pi$
$632$	−133.419	+	133.419i	−0.211106	+	0.211106i
$633$		0			0
$634$		−	115.645i		−	0.182405i
$635$	−515.347	+	194.613i	−0.811571	+	0.306478i
$636$		0			0
$637$	−178.808	+	178.808i	−0.280703	+	0.280703i
$638$	40.8173	+	40.8173i	0.0639769	+	0.0639769i
$639$		0			0
$640$	−213.956	−	566.568i	−0.334307	−	0.885263i
$641$	−557.454			−0.869663			−0.434832	−	0.900512i	$-0.643192\pi$
$641$	−557.454			−0.869663			−0.434832	+	0.900512i	$0.643192\pi$
$642$		0			0
$643$	124.138	+	124.138i	0.193061	+	0.193061i	0.797017	−	0.603956i	$-0.206410\pi$
$643$	124.138	+	124.138i	0.193061	+	0.193061i	−0.603956	+	0.797017i	$0.706410\pi$
$644$		−	337.948i		−	0.524763i
$645$		0			0
$646$	189.688			0.293635
$647$	−70.4444	+	70.4444i	−0.108879	+	0.108879i	−0.759447	−	0.650569i	$-0.774531\pi$
$647$	−70.4444	+	70.4444i	−0.108879	+	0.108879i	0.650569	+	0.759447i	$0.274531\pi$
$648$		0			0
$649$			191.301i			0.294763i
$650$	187.035	+	212.324i	0.287747	+	0.326653i
$651$		0			0
$652$	475.543	−	475.543i	0.729360	−	0.729360i
$653$	764.443	+	764.443i	1.17066	+	1.17066i	0.982052	+	0.188612i	$0.0603988\pi$
$653$	764.443	+	764.443i	1.17066	+	1.17066i	0.188612	+	0.982052i	$0.439601\pi$
$654$		0			0
$655$	−751.199	−	339.364i	−1.14687	−	0.518113i
$656$	68.2814			0.104088
$657$		0			0
$658$	−174.651	−	174.651i	−0.265427	−	0.265427i
$659$		−	361.616i		−	0.548735i	−0.961625	−	0.274367i	$-0.911532\pi$
$659$		−	361.616i		−	0.548735i	0.961625	−	0.274367i	$-0.0884684\pi$
$660$		0			0
$661$	4.35847			0.00659376			0.00329688	−	0.999995i	$-0.498951\pi$
$661$	4.35847			0.00659376			0.00329688	+	0.999995i	$0.498951\pi$
$662$	131.203	−	131.203i	0.198192	−	0.198192i
$663$		0			0
$664$			91.6944i			0.138094i
$665$	−140.439	−	371.889i	−0.211186	−	0.559232i
$666$		0			0
$667$	268.183	−	268.183i	0.402073	−	0.402073i
$668$	−20.4037	−	20.4037i	−0.0305445	−	0.0305445i
$669$		0			0
$670$	183.903	−	407.077i	0.274481	−	0.607578i
$671$	318.918			0.475288
$672$		0			0
$673$	−805.217	−	805.217i	−1.19646	−	1.19646i	−0.975219	−	0.221240i	$-0.928990\pi$
$673$	−805.217	−	805.217i	−1.19646	−	1.19646i	−0.221240	−	0.975219i	$-0.571010\pi$
$674$		−	453.806i		−	0.673303i
$675$		0			0
$676$	108.190			0.160044
$677$	−302.616	+	302.616i	−0.446996	+	0.446996i	−0.894355	−	0.447358i	$-0.852365\pi$
$677$	−302.616	+	302.616i	−0.446996	+	0.446996i	0.447358	+	0.894355i	$0.352365\pi$
$678$		0			0
$679$		−	257.819i		−	0.379704i
$680$	−398.461	−	180.010i	−0.585972	−	0.264721i
$681$		0			0
$682$	114.367	−	114.367i	0.167693	−	0.167693i
$683$	444.248	+	444.248i	0.650437	+	0.650437i	0.953098	−	0.302661i	$-0.0978751\pi$
$683$	444.248	+	444.248i	0.650437	+	0.650437i	−0.302661	+	0.953098i	$0.597875\pi$
$684$		0			0
$685$	616.204	−	232.700i	0.899568	−	0.339709i
$686$	361.685			0.527237
$687$		0			0
$688$	−162.361	−	162.361i	−0.235990	−	0.235990i
$689$		−	902.966i		−	1.31055i
$690$		0			0
$691$	522.237			0.755770			0.377885	−	0.925853i	$-0.376652\pi$
$691$	522.237			0.755770			0.377885	+	0.925853i	$0.376652\pi$
$692$	126.481	−	126.481i	0.182776	−	0.182776i
$693$		0			0
$694$		−	422.444i		−	0.608709i
$695$	184.808	−	409.081i	0.265911	−	0.588606i
$696$		0			0
$697$	113.357	−	113.357i	0.162635	−	0.162635i
$698$	284.715	+	284.715i	0.407902	+	0.407902i
$699$		0			0
$700$	−25.0048	+	394.867i	−0.0357211	+	0.564096i
$701$	414.800			0.591727			0.295863	−	0.955230i	$-0.404393\pi$
$701$	414.800			0.591727			0.295863	+	0.955230i	$0.404393\pi$
$702$		0			0
$703$	399.097	+	399.097i	0.567706	+	0.567706i
$704$			35.2434i			0.0500617i
$705$		0			0
$706$	297.950			0.422026
$707$	−509.328	+	509.328i	−0.720407	+	0.720407i
$708$		0			0
$709$			64.4155i			0.0908540i	0.998968	+	0.0454270i	$0.0144648\pi$
$709$			64.4155i			0.0908540i	−0.998968	+	0.0454270i	$0.985535\pi$
$710$	−222.398	+	83.9855i	−0.313237	+	0.118289i
$711$		0			0
$712$	587.508	−	587.508i	0.825152	−	0.825152i
$713$	−751.426	−	751.426i	−1.05389	−	1.05389i
$714$		0			0
$715$	67.6678	+	179.188i	0.0946403	+	0.250613i
$716$	−108.952			−0.152168
$717$		0			0
$718$	247.145	+	247.145i	0.344212	+	0.344212i
$719$		−	684.369i		−	0.951834i	−0.879490	−	0.475917i	$-0.842116\pi$
$719$		−	684.369i		−	0.951834i	0.879490	−	0.475917i	$-0.157884\pi$
$720$		0			0
$721$	−393.180			−0.545326
$722$	88.5607	−	88.5607i	0.122660	−	0.122660i
$723$		0			0
$724$			231.437i			0.319664i
$725$	−333.195	+	293.509i	−0.459579	+	0.404840i
$726$		0			0
$727$	−542.160	+	542.160i	−0.745750	+	0.745750i	−0.973678	−	0.227928i	$-0.926805\pi$
$727$	−542.160	+	542.160i	−0.745750	+	0.745750i	0.227928	+	0.973678i	$0.426805\pi$
$728$	293.333	+	293.333i	0.402930	+	0.402930i
$729$		0			0
$730$	−377.195	−	170.403i	−0.516705	−	0.233428i
$731$	−539.084			−0.737461
$732$		0			0
$733$	−186.770	−	186.770i	−0.254803	−	0.254803i	0.568134	−	0.822936i	$-0.307666\pi$
$733$	−186.770	−	186.770i	−0.254803	−	0.254803i	−0.822936	+	0.568134i	$0.807666\pi$
$734$		−	114.751i		−	0.156337i
$735$		0			0
$736$	702.194			0.954068
$737$	213.812	−	213.812i	0.290111	−	0.290111i
$738$		0			0
$739$		−	252.800i		−	0.342084i	−0.985264	−	0.171042i	$-0.945287\pi$
$739$		−	252.800i		−	0.342084i	0.985264	−	0.171042i	$-0.0547133\pi$
$740$	−198.461	−	525.536i	−0.268191	−	0.710184i
$741$		0			0
$742$	−282.026	+	282.026i	−0.380090	+	0.380090i
$743$	966.342	+	966.342i	1.30059	+	1.30059i	0.927990	+	0.372605i	$0.121535\pi$
$743$	966.342	+	966.342i	1.30059	+	1.30059i	0.372605	+	0.927990i	$0.378465\pi$
$744$		0			0
$745$	−503.300	+	1114.08i	−0.675570	+	1.49541i
$746$	−71.1179			−0.0953323
$747$		0			0
$748$	−90.3697	−	90.3697i	−0.120815	−	0.120815i
$749$			234.279i			0.312789i
$750$		0			0
$751$	1248.62			1.66261			0.831307	−	0.555814i	$-0.187593\pi$
$751$	1248.62			1.66261			0.831307	+	0.555814i	$0.187593\pi$
$752$	−184.836	+	184.836i	−0.245793	+	0.245793i
$753$		0			0
$754$			201.027i			0.266614i
$755$	−795.021	−	359.161i	−1.05301	−	0.475710i
$756$		0			0
$757$	−111.550	+	111.550i	−0.147357	+	0.147357i	−0.776936	−	0.629579i	$-0.783227\pi$
$757$	−111.550	+	111.550i	−0.147357	+	0.147357i	0.629579	+	0.776936i	$0.283227\pi$
$758$	515.002	+	515.002i	0.679422	+	0.679422i
$759$		0			0
$760$	492.743	−	186.077i	0.648346	−	0.244838i
$761$	752.350			0.988633			0.494317	−	0.869282i	$-0.335418\pi$
$761$	752.350			0.988633			0.494317	+	0.869282i	$0.335418\pi$
$762$		0			0
$763$	−472.001	−	472.001i	−0.618612	−	0.618612i
$764$			994.510i			1.30171i
$765$		0			0
$766$	−512.393			−0.668920
$767$	−471.085	+	471.085i	−0.614191	+	0.614191i
$768$		0			0
$769$			1143.74i			1.48730i	0.668568	+	0.743651i	$0.266908\pi$
$769$			1143.74i			1.48730i	−0.668568	+	0.743651i	$0.733092\pi$
$770$	34.8315	−	77.1014i	0.0452358	−	0.100132i
$771$		0			0
$772$	138.950	−	138.950i	0.179987	−	0.179987i
$773$	654.811	+	654.811i	0.847103	+	0.847103i	0.989771	−	0.142667i	$-0.0455679\pi$
$773$	654.811	+	654.811i	0.847103	+	0.847103i	−0.142667	+	0.989771i	$0.545568\pi$
$774$		0			0
$775$	822.389	+	933.586i	1.06115	+	1.20463i
$776$	341.603			0.440210
$777$		0			0
$778$	514.307	+	514.307i	0.661063	+	0.661063i
$779$			193.115i			0.247901i
$780$		0			0
$781$	−160.924			−0.206048
$782$	187.560	−	187.560i	0.239847	−	0.239847i
$783$		0			0
$784$		−	118.209i		−	0.150777i
$785$	551.871	−	208.406i	0.703020	−	0.265485i
$786$		0			0
$787$	−281.035	+	281.035i	−0.357096	+	0.357096i	−0.862741	−	0.505645i	$-0.831254\pi$
$787$	−281.035	+	281.035i	−0.357096	+	0.357096i	0.505645	+	0.862741i	$0.331254\pi$
$788$	283.576	+	283.576i	0.359869	+	0.359869i
$789$		0			0
$790$	47.3443	+	125.370i	0.0599295	+	0.158697i
$791$	−46.6262			−0.0589459
$792$		0			0
$793$	785.344	+	785.344i	0.990345	+	0.990345i
$794$			97.8381i			0.123222i
$795$		0			0
$796$	759.794			0.954515
$797$	−133.596	+	133.596i	−0.167624	+	0.167624i	−0.785934	−	0.618310i	$-0.787818\pi$
$797$	−133.596	+	133.596i	−0.167624	+	0.167624i	0.618310	+	0.785934i	$0.287818\pi$
$798$		0			0
$799$			613.707i			0.768094i
$800$	−820.463	−	51.9554i	−1.02558	−	0.0649443i
$801$		0			0
$802$	112.470	−	112.470i	0.140237	−	0.140237i
$803$	−198.116	−	198.116i	−0.246720	−	0.246720i
$804$		0			0
$805$	−506.580	−	228.854i	−0.629293	−	0.284291i
$806$	563.262			0.698836
$807$		0			0
$808$	−674.845	−	674.845i	−0.835204	−	0.835204i
$809$			263.012i			0.325107i	0.986700	+	0.162553i	$0.0519730\pi$
$809$			263.012i			0.325107i	−0.986700	+	0.162553i	$0.948027\pi$
$810$		0			0
$811$	−796.014			−0.981522			−0.490761	−	0.871294i	$-0.663281\pi$
$811$	−796.014			−0.981522			−0.490761	+	0.871294i	$0.663281\pi$
$812$	−198.766	+	198.766i	−0.244785	+	0.244785i
$813$		0			0
$814$			120.122i			0.147570i
$815$	−390.802	−	1034.87i	−0.479512	−	1.26978i
$816$		0			0
$817$	459.193	−	459.193i	0.562047	−	0.562047i
$818$	−2.21060	−	2.21060i	−0.00270245	−	0.00270245i
$819$		0			0
$820$	79.1325	−	175.164i	0.0965031	−	0.213614i
$821$	405.321			0.493691			0.246846	−	0.969055i	$-0.420606\pi$
$821$	405.321			0.493691			0.246846	+	0.969055i	$0.420606\pi$
$822$		0			0
$823$	−178.127	−	178.127i	−0.216436	−	0.216436i	0.590559	−	0.806995i	$-0.298907\pi$
$823$	−178.127	−	178.127i	−0.216436	−	0.216436i	−0.806995	+	0.590559i	$0.798907\pi$
$824$		−	520.953i		−	0.632224i
$825$		0			0
$826$	294.271			0.356260
$827$	38.9361	−	38.9361i	0.0470812	−	0.0470812i	−0.683174	−	0.730255i	$-0.739401\pi$
$827$	38.9361	−	38.9361i	0.0470812	−	0.0470812i	0.730255	+	0.683174i	$0.239401\pi$
$828$		0			0
$829$			171.269i			0.206597i	0.994650	+	0.103299i	$0.0329397\pi$
$829$			171.269i			0.206597i	−0.994650	+	0.103299i	$0.967060\pi$
$830$	59.3505	+	26.8124i	0.0715066	+	0.0323040i
$831$		0			0
$832$	−86.7878	+	86.7878i	−0.104312	+	0.104312i
$833$	−196.243	−	196.243i	−0.235586	−	0.235586i
$834$		0			0
$835$	−44.4022	+	16.7678i	−0.0531763	+	0.0200812i
$836$	153.954			0.184156
$837$		0			0
$838$	455.212	+	455.212i	0.543213	+	0.543213i
$839$			465.310i			0.554600i	0.960783	+	0.277300i	$0.0894397\pi$
$839$			465.310i			0.554600i	−0.960783	+	0.277300i	$0.910560\pi$
$840$		0			0
$841$	525.534			0.624892
$842$	−494.728	+	494.728i	−0.587563	+	0.587563i
$843$		0			0
$844$			468.513i			0.555110i
$845$	73.2650	−	162.176i	0.0867042	−	0.191924i
$846$		0			0
$847$	40.4964	−	40.4964i	0.0478116	−	0.0478116i
$848$	298.473	+	298.473i	0.351973	+	0.351973i
$849$		0			0
$850$	−233.028	+	205.273i	−0.274151	+	0.241498i
$851$	789.240			0.927426
$852$		0			0
$853$	554.474	+	554.474i	0.650028	+	0.650028i	0.953000	−	0.302971i	$-0.0979786\pi$
$853$	554.474	+	554.474i	0.650028	+	0.650028i	−0.302971	+	0.953000i	$0.597979\pi$
$854$		−	490.578i		−	0.574447i
$855$		0			0
$856$	−310.413			−0.362632
$857$	−995.353	+	995.353i	−1.16144	+	1.16144i	−0.177278	+	0.984161i	$0.556729\pi$
$857$	−995.353	+	995.353i	−1.16144	+	1.16144i	−0.984161	+	0.177278i	$0.943271\pi$
$858$		0			0
$859$			660.228i			0.768601i	0.923208	+	0.384300i	$0.125557\pi$
$859$			660.228i			0.768601i	−0.923208	+	0.384300i	$0.874443\pi$
$860$	−604.671	+	228.345i	−0.703106	+	0.265518i
$861$		0			0
$862$	−562.382	+	562.382i	−0.652416	+	0.652416i
$863$	553.402	+	553.402i	0.641253	+	0.641253i	0.950864	−	0.309610i	$-0.100199\pi$
$863$	553.402	+	553.402i	0.641253	+	0.641253i	−0.309610	+	0.950864i	$0.600199\pi$
$864$		0			0
$865$	−103.942	−	275.245i	−0.120165	−	0.318203i
$866$	−34.7348			−0.0401095
$867$		0			0
$868$	556.926	+	556.926i	0.641620	+	0.641620i
$869$			90.7160i			0.104391i
$870$		0			0
$871$	1053.03			1.20899
$872$	625.387	−	625.387i	0.717187	−	0.717187i
$873$		0			0
$874$			319.528i			0.365593i
$875$	574.970	+	304.882i	0.657108	+	0.348436i
$876$		0			0
$877$	863.196	−	863.196i	0.984260	−	0.984260i	−0.0156176	−	0.999878i	$-0.504971\pi$
$877$	863.196	−	863.196i	0.984260	−	0.984260i	0.999878	+	0.0156176i	$0.00497145\pi$
$878$	191.617	+	191.617i	0.218243	+	0.218243i
$879$		0			0
$880$	−81.5976	−	36.8628i	−0.0927245	−	0.0418895i
$881$	498.888			0.566275			0.283137	−	0.959079i	$-0.408625\pi$
$881$	498.888			0.566275			0.283137	+	0.959079i	$0.408625\pi$
$882$		0			0
$883$	206.575	+	206.575i	0.233947	+	0.233947i	0.814338	−	0.580391i	$-0.197100\pi$
$883$	206.575	+	206.575i	0.233947	+	0.233947i	−0.580391	+	0.814338i	$0.697100\pi$
$884$		−	445.075i		−	0.503479i
$885$		0			0
$886$	−445.064			−0.502329
$887$	−182.818	+	182.818i	−0.206108	+	0.206108i	−0.802611	−	0.596503i	$-0.796556\pi$
$887$	−182.818	+	182.818i	−0.206108	+	0.206108i	0.596503	+	0.802611i	$0.296556\pi$
$888$		0			0
$889$			573.611i			0.645232i
$890$	−208.480	−	552.066i	−0.234247	−	0.620299i
$891$		0			0
$892$	−565.108	+	565.108i	−0.633529	+	0.633529i
$893$	−522.757	−	522.757i	−0.585394	−	0.585394i
$894$		0			0
$895$	−73.7811	+	163.318i	−0.0824370	+	0.182478i
$896$	−630.623			−0.703820
$897$		0			0
$898$	−135.436	−	135.436i	−0.150819	−	0.150819i
$899$			883.911i			0.983216i
$900$		0			0
$901$	991.014			1.09990
$902$	−29.0623	+	29.0623i	−0.0322198	+	0.0322198i
$903$		0			0
$904$		−	61.7784i		−	0.0683389i
$905$	346.922	+	156.726i	0.383339	+	0.173178i
$906$		0			0
$907$	910.065	−	910.065i	1.00338	−	1.00338i	0.00338553	−	0.999994i	$-0.498922\pi$
$907$	910.065	−	910.065i	1.00338	−	1.00338i	0.999994	−	0.00338553i	$-0.00107765\pi$
$908$	458.192	+	458.192i	0.504617	+	0.504617i
$909$		0			0
$910$	275.638	−	104.090i	0.302898	−	0.114385i
$911$	493.142			0.541320			0.270660	−	0.962675i	$-0.412758\pi$
$911$	493.142			0.541320			0.270660	+	0.962675i	$0.412758\pi$
$912$		0			0
$913$	31.1730	+	31.1730i	0.0341435	+	0.0341435i
$914$			427.056i			0.467238i
$915$		0			0
$916$	524.949			0.573089
$917$	−606.930	+	606.930i	−0.661864	+	0.661864i
$918$		0			0
$919$		−	464.091i		−	0.504996i	−0.967597	−	0.252498i	$-0.918748\pi$
$919$		−	464.091i		−	0.504996i	0.967597	−	0.252498i	$-0.0812521\pi$
$920$	303.225	−	671.205i	0.329593	−	0.729570i
$921$		0			0
$922$	515.415	−	515.415i	0.559018	−	0.559018i
$923$	−396.279	−	396.279i	−0.429338	−	0.429338i
$924$		0			0
$925$	−922.170	−	58.3959i	−0.996940	−	0.0631308i
$926$	−527.669			−0.569837
$927$		0			0
$928$	−412.999	−	412.999i	−0.445043	−	0.445043i
$929$			1150.61i			1.23855i	0.785176	+	0.619273i	$0.212573\pi$
$929$			1150.61i			1.23855i	−0.785176	+	0.619273i	$0.787427\pi$
$930$		0			0
$931$	334.321			0.359099
$932$	897.728	−	897.728i	0.963227	−	0.963227i
$933$		0			0
$934$		−	488.310i		−	0.522815i
$935$	−196.661	+	74.2660i	−0.210332	+	0.0794289i
$936$		0			0
$937$	−740.662	+	740.662i	−0.790461	+	0.790461i	−0.981569	−	0.191108i	$-0.938792\pi$
$937$	−740.662	+	740.662i	−0.790461	+	0.790461i	0.191108	+	0.981569i	$0.438792\pi$
$938$	−328.897	−	328.897i	−0.350637	−	0.350637i
$939$		0			0
$940$	259.954	+	688.373i	0.276547	+	0.732312i
$941$	−1596.26			−1.69635			−0.848173	−	0.529719i	$-0.822297\pi$
$941$	−1596.26			−1.69635			−0.848173	+	0.529719i	$0.822297\pi$
$942$		0			0
$943$	190.948	+	190.948i	0.202490	+	0.202490i
$944$		−	311.431i		−	0.329906i
$945$		0			0
$946$	138.210			0.146099
$947$	761.299	−	761.299i	0.803906	−	0.803906i	−0.179798	−	0.983704i	$-0.557544\pi$
$947$	761.299	−	761.299i	0.803906	−	0.803906i	0.983704	+	0.179798i	$0.0575444\pi$
$948$		0			0
$949$		−	975.732i		−	1.02817i
$950$	23.6419	−	373.346i	0.0248862	−	0.392995i
$951$		0			0
$952$	−321.936	+	321.936i	−0.338168	+	0.338168i
$953$	400.371	+	400.371i	0.420117	+	0.420117i	0.885244	−	0.465127i	$-0.153991\pi$
$953$	400.371	+	400.371i	0.420117	+	0.420117i	−0.465127	+	0.885244i	$0.653991\pi$
$954$		0			0
$955$	1490.76	+	673.471i	1.56101	+	0.705205i
$956$	542.247			0.567204
$957$		0			0
$958$	576.238	+	576.238i	0.601501	+	0.601501i
$959$		−	685.871i		−	0.715193i
$960$		0			0
$961$	1515.65			1.57716
$962$	−295.803	+	295.803i	−0.307488	+	0.307488i
$963$		0			0
$964$		−	852.065i		−	0.883885i
$965$	−114.189	−	302.379i	−0.118331	−	0.313347i
$966$		0			0
$967$	−533.179	+	533.179i	−0.551375	+	0.551375i	−0.926837	−	0.375463i	$-0.877484\pi$
$967$	−533.179	+	533.179i	−0.551375	+	0.551375i	0.375463	+	0.926837i	$0.377484\pi$
$968$	53.6566	+	53.6566i	0.0554303	+	0.0554303i
$969$		0			0
$970$	99.8881	−	221.107i	0.102977	−	0.227946i
$971$	211.859			0.218186			0.109093	−	0.994032i	$-0.465205\pi$
$971$	211.859			0.218186			0.109093	+	0.994032i	$0.465205\pi$
$972$		0			0
$973$	−330.516	−	330.516i	−0.339688	−	0.339688i
$974$		−	75.4135i		−	0.0774266i
$975$		0			0
$976$	−519.187			−0.531953
$977$	−327.740	+	327.740i	−0.335456	+	0.335456i	−0.854654	−	0.519198i	$-0.826231\pi$
$977$	−327.740	+	327.740i	−0.335456	+	0.335456i	0.519198	+	0.854654i	$0.326231\pi$
$978$		0			0
$979$		−	399.466i		−	0.408035i
$980$	−303.244	−	136.994i	−0.309433	−	0.139790i
$981$		0			0
$982$	−104.634	+	104.634i	−0.106552	+	0.106552i
$983$	−879.861	−	879.861i	−0.895077	−	0.895077i	0.0999187	−	0.994996i	$-0.468142\pi$
$983$	−879.861	−	879.861i	−0.895077	−	0.895077i	−0.994996	+	0.0999187i	$0.968142\pi$
$984$		0			0
$985$	617.113	−	233.044i	0.626511	−	0.236593i
$986$	−220.629			−0.223762
$987$		0			0
$988$	379.116	+	379.116i	0.383721	+	0.383721i
$989$		−	908.083i		−	0.918183i
$990$		0			0
$991$	1357.79			1.37012			0.685062	−	0.728484i	$-0.259775\pi$
$991$	1357.79			1.37012			0.685062	+	0.728484i	$0.259775\pi$
$992$	−1157.19	+	1157.19i	−1.16652	+	1.16652i
$993$		0			0
$994$			247.542i			0.249036i
$995$	514.524	−	1138.92i	0.517109	−	1.14465i
$996$		0			0
$997$	−555.302	+	555.302i	−0.556973	+	0.556973i	−0.928444	−	0.371471i	$-0.878853\pi$
$997$	−555.302	+	555.302i	−0.556973	+	0.556973i	0.371471	+	0.928444i	$0.378853\pi$
$998$	325.095	+	325.095i	0.325746	+	0.325746i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.3.j.c.298.12	yes	40
3.2	odd	2	inner	495.3.j.c.298.9	✓	40
5.2	odd	4	inner	495.3.j.c.397.12	yes	40
15.2	even	4	inner	495.3.j.c.397.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.3.j.c.298.9	✓	40	3.2	odd	2	inner
495.3.j.c.298.12	yes	40	1.1	even	1	trivial
495.3.j.c.397.9	yes	40	15.2	even	4	inner
495.3.j.c.397.12	yes	40	5.2	odd	4	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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	495.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.692901 - 0.692901i) q^{2} +3.03978i q^{4} +(4.55660 + 2.05850i) q^{5} +(3.68149 - 3.68149i) q^{7} +(4.87787 + 4.87787i) q^{8} +(4.58361 - 1.73093i) q^{10} +3.31662 q^{11} +(8.16727 + 8.16727i) q^{13} -5.10182i q^{14} -5.39934 q^{16} +(-8.96365 + 8.96365i) q^{17} -15.2705i q^{19} +(-6.25738 + 13.8510i) q^{20} +(2.29809 - 2.29809i) q^{22} +(-15.0992 - 15.0992i) q^{23} +(16.5251 + 18.7595i) q^{25} +11.3182 q^{26} +(11.1909 + 11.1909i) q^{28} +17.7614i q^{29} +49.7660 q^{31} +(-23.2527 + 23.2527i) q^{32} +12.4219i q^{34} +(24.3534 - 9.19671i) q^{35} +(-26.1351 + 26.1351i) q^{37} +(-10.5810 - 10.5810i) q^{38} +(12.1854 + 32.2676i) q^{40} -12.6463 q^{41} +(30.0705 + 30.0705i) q^{43} +10.0818i q^{44} -20.9245 q^{46} +(34.2331 - 34.2331i) q^{47} +21.8932i q^{49} +(24.4488 + 1.54821i) q^{50} +(-24.8267 + 24.8267i) q^{52} +(-55.2796 - 55.2796i) q^{53} +(15.1125 + 6.82728i) q^{55} +35.9157 q^{56} +(12.3069 + 12.3069i) q^{58} +57.6796i q^{59} +96.1575 q^{61} +(34.4829 - 34.4829i) q^{62} +10.6263i q^{64} +(20.4026 + 54.0273i) q^{65} +(64.4666 - 64.4666i) q^{67} +(-27.2475 - 27.2475i) q^{68} +(10.5021 - 23.2469i) q^{70} -48.5204 q^{71} +(-59.7343 - 59.7343i) q^{73} +36.2181i q^{74} +46.4189 q^{76} +(12.2101 - 12.2101i) q^{77} +27.3519i q^{79} +(-24.6026 - 11.1145i) q^{80} +(-8.76261 + 8.76261i) q^{82} +(9.39902 + 9.39902i) q^{83} +(-59.2955 + 22.3921i) q^{85} +41.6718 q^{86} +(16.1781 + 16.1781i) q^{88} -120.444i q^{89} +60.1355 q^{91} +(45.8982 - 45.8982i) q^{92} -47.4403i q^{94} +(31.4344 - 69.5816i) q^{95} +(35.0156 - 35.0156i) q^{97} +(15.1699 + 15.1699i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{10} - 88 q^{13} - 296 q^{16} + 168 q^{25} + 248 q^{28} - 32 q^{31} - 24 q^{37} + 296 q^{40} - 48 q^{43} + 48 q^{46} + 64 q^{52} + 104 q^{58} + 576 q^{61} - 544 q^{67} - 1048 q^{70} - 408 q^{73}+ \cdots + 712 q^{97}+O(q^{100}) \) 40 * q + 24 * q^10 - 88 * q^13 - 296 * q^16 + 168 * q^25 + 248 * q^28 - 32 * q^31 - 24 * q^37 + 296 * q^40 - 48 * q^43 + 48 * q^46 + 64 * q^52 + 104 * q^58 + 576 * q^61 - 544 * q^67 - 1048 * q^70 - 408 * q^73 - 96 * q^76 - 280 * q^82 + 160 * q^85 + 264 * q^88 + 528 * q^91 + 712 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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