LMFDB - Embedded newform 300.2.x.a.53.9

Newspace parameters

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.x (of order $20$, degree $8$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			53.9
Character	$\chi$	$=$	300.53
Dual form			300.2.x.a.17.9

$q$-expansion

$f(q)$	$=$	$q+(1.29334 - 1.15207i) q^{3} +(1.99640 - 1.00718i) q^{5} +(0.814380 - 0.814380i) q^{7} +(0.345460 - 2.98004i) q^{9} +O(q^{10})$	\(q+(1.29334 - 1.15207i) q^{3} +(1.99640 - 1.00718i) q^{5} +(0.814380 - 0.814380i) q^{7} +(0.345460 - 2.98004i) q^{9} +(-3.46407 - 1.12554i) q^{11} +(-2.63271 + 5.16697i) q^{13} +(1.42168 - 3.60261i) q^{15} +(0.902627 + 0.142962i) q^{17} +(4.29919 + 5.91733i) q^{19} +(0.115046 - 1.99149i) q^{21} +(-3.05909 - 6.00381i) q^{23} +(2.97120 - 4.02144i) q^{25} +(-2.98643 - 4.25221i) q^{27} +(4.30536 + 3.12803i) q^{29} +(-1.78920 + 1.29993i) q^{31} +(-5.77692 + 2.53514i) q^{33} +(0.805601 - 2.44605i) q^{35} +(2.74637 + 1.39935i) q^{37} +(2.54774 + 9.71572i) q^{39} +(-2.66555 + 0.866089i) q^{41} +(-3.01283 - 3.01283i) q^{43} +(-2.31175 - 6.29729i) q^{45} +(0.998165 + 6.30217i) q^{47} +5.67357i q^{49} +(1.33211 - 0.854993i) q^{51} +(8.04180 - 1.27370i) q^{53} +(-8.04927 + 1.24189i) q^{55} +(12.3775 + 2.70014i) q^{57} +(-1.98388 - 6.10574i) q^{59} +(-4.21356 + 12.9680i) q^{61} +(-2.14555 - 2.70822i) q^{63} +(-0.0518720 + 12.9669i) q^{65} +(0.976557 - 6.16574i) q^{67} +(-10.8733 - 4.24068i) q^{69} +(-5.88318 + 8.09750i) q^{71} +(-8.26387 + 4.21065i) q^{73} +(-0.790225 - 8.62413i) q^{75} +(-3.73768 + 1.90445i) q^{77} +(4.29102 - 5.90609i) q^{79} +(-8.76132 - 2.05897i) q^{81} +(0.190258 - 1.20124i) q^{83} +(1.94599 - 0.623695i) q^{85} +(9.17202 - 0.914482i) q^{87} +(-3.41396 + 10.5071i) q^{89} +(2.06386 + 6.35190i) q^{91} +(-0.816433 + 3.74254i) q^{93} +(14.5427 + 7.48329i) q^{95} +(3.84712 - 0.609325i) q^{97} +(-4.55086 + 9.93423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80q - 2q^{3} + 4q^{7} + O(q^{10}) $	$ 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{20}\right)$

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			0
$2$		0			0
$3$	1.29334	−	1.15207i	0.746711	−	0.665149i
$3$	1.29334	−	1.15207i	0.746711	−	0.665149i
$4$		0			0
$5$	1.99640	−	1.00718i	0.892815	−	0.450423i
$5$	1.99640	−	1.00718i	0.892815	−	0.450423i
$6$		0			0
$7$	0.814380	−	0.814380i	0.307807	−	0.307807i	−0.536252	−	0.844058i	$-0.680160\pi$
$7$	0.814380	−	0.814380i	0.307807	−	0.307807i	0.844058	+	0.536252i	$0.180160\pi$
$8$		0			0
$9$	0.345460	−	2.98004i	0.115153	−	0.993348i
$10$		0			0
$11$	−3.46407	−	1.12554i	−1.04446	−	0.339364i	−0.263965	−	0.964532i	$-0.585030\pi$
$11$	−3.46407	−	1.12554i	−1.04446	−	0.339364i	−0.780490	+	0.625168i	$0.785030\pi$
$12$		0			0
$13$	−2.63271	+	5.16697i	−0.730181	+	1.43306i	0.164510	+	0.986375i	$0.447396\pi$
$13$	−2.63271	+	5.16697i	−0.730181	+	1.43306i	−0.894691	+	0.446686i	$0.852604\pi$
$14$		0			0
$15$	1.42168	−	3.60261i	0.367077	−	0.930191i
$16$		0			0
$17$	0.902627	+	0.142962i	0.218919	+	0.0346734i	0.264930	−	0.964268i	$-0.414651\pi$
$17$	0.902627	+	0.142962i	0.218919	+	0.0346734i	−0.0460112	+	0.998941i	$0.514651\pi$
$18$		0			0
$19$	4.29919	+	5.91733i	0.986302	+	1.35753i	0.933364	+	0.358930i	$0.116858\pi$
$19$	4.29919	+	5.91733i	0.986302	+	1.35753i	0.0529373	+	0.998598i	$0.483142\pi$
$20$		0			0
$21$	0.115046	−	1.99149i	0.0251051	−	0.434580i
$22$		0			0
$23$	−3.05909	−	6.00381i	−0.637865	−	1.25188i	−0.953039	−	0.302847i	$-0.902063\pi$
$23$	−3.05909	−	6.00381i	−0.637865	−	1.25188i	0.315174	−	0.949034i	$-0.397937\pi$
$24$		0			0
$25$	2.97120	−	4.02144i	0.594239	−	0.804289i
$26$		0			0
$27$	−2.98643	−	4.25221i	−0.574738	−	0.818337i
$28$		0			0
$29$	4.30536	+	3.12803i	0.799486	+	0.580861i	0.910763	−	0.412929i	$-0.135494\pi$
$29$	4.30536	+	3.12803i	0.799486	+	0.580861i	−0.111277	+	0.993789i	$0.535494\pi$
$30$		0			0
$31$	−1.78920	+	1.29993i	−0.321350	+	0.233475i	−0.736751	−	0.676164i	$-0.763641\pi$
$31$	−1.78920	+	1.29993i	−0.321350	+	0.233475i	0.415401	+	0.909638i	$0.363641\pi$
$32$		0			0
$33$	−5.77692	+	2.53514i	−1.00563	+	0.441312i
$34$		0			0
$35$	0.805601	−	2.44605i	0.136171	−	0.413458i
$36$		0			0
$37$	2.74637	+	1.39935i	0.451501	+	0.230051i	0.664927	−	0.746908i	$-0.268462\pi$
$37$	2.74637	+	1.39935i	0.451501	+	0.230051i	−0.213427	+	0.976959i	$0.568462\pi$
$38$		0			0
$39$	2.54774	+	9.71572i	0.407965	+	1.55576i
$40$		0			0
$41$	−2.66555	+	0.866089i	−0.416289	+	0.135260i	−0.509670	−	0.860370i	$-0.670232\pi$
$41$	−2.66555	+	0.866089i	−0.416289	+	0.135260i	0.0933813	+	0.995630i	$0.470232\pi$
$42$		0			0
$43$	−3.01283	−	3.01283i	−0.459453	−	0.459453i	0.439023	−	0.898476i	$-0.355325\pi$
$43$	−3.01283	−	3.01283i	−0.459453	−	0.459453i	−0.898476	+	0.439023i	$0.855325\pi$
$44$		0			0
$45$	−2.31175	−	6.29729i	−0.344616	−	0.938744i
$46$		0			0
$47$	0.998165	+	6.30217i	0.145597	+	0.919265i	0.947022	+	0.321169i	$0.104076\pi$
$47$	0.998165	+	6.30217i	0.145597	+	0.919265i	−0.801424	+	0.598096i	$0.795924\pi$
$48$		0			0
$49$			5.67357i			0.810510i
$50$		0			0
$51$	1.33211	−	0.854993i	0.186532	−	0.119723i
$52$		0			0
$53$	8.04180	−	1.27370i	1.10463	−	0.174956i	0.422623	−	0.906305i	$-0.361109\pi$
$53$	8.04180	−	1.27370i	1.10463	−	0.174956i	0.682002	+	0.731350i	$0.261109\pi$
$54$		0			0
$55$	−8.04927	+	1.24189i	−1.08536	+	0.167457i
$56$		0			0
$57$	12.3775	+	2.70014i	1.63944	+	0.357643i
$58$		0			0
$59$	−1.98388	−	6.10574i	−0.258279	−	0.794900i	−0.993166	−	0.116711i	$-0.962765\pi$
$59$	−1.98388	−	6.10574i	−0.258279	−	0.794900i	0.734887	−	0.678189i	$-0.237235\pi$
$60$		0			0
$61$	−4.21356	+	12.9680i	−0.539492	+	1.66038i	0.194247	+	0.980953i	$0.437774\pi$
$61$	−4.21356	+	12.9680i	−0.539492	+	1.66038i	−0.733739	+	0.679432i	$0.762226\pi$
$62$		0			0
$63$	−2.14555	−	2.70822i	−0.270314	−	0.341204i
$64$		0			0
$65$	−0.0518720	+	12.9669i	−0.00643393	+	1.60835i
$66$		0			0
$67$	0.976557	−	6.16574i	0.119305	−	0.753265i	−0.853406	−	0.521247i	$-0.825467\pi$
$67$	0.976557	−	6.16574i	0.119305	−	0.753265i	0.972712	−	0.232018i	$-0.0745328\pi$
$68$		0			0
$69$	−10.8733	−	4.24068i	−1.30899	−	0.510517i
$70$		0			0
$71$	−5.88318	+	8.09750i	−0.698205	+	0.960996i	0.301766	+	0.953382i	$0.402424\pi$
$71$	−5.88318	+	8.09750i	−0.698205	+	0.960996i	−0.999971	+	0.00761427i	$0.997576\pi$
$72$		0			0
$73$	−8.26387	+	4.21065i	−0.967212	+	0.492819i	−0.864906	−	0.501934i	$-0.832622\pi$
$73$	−8.26387	+	4.21065i	−0.967212	+	0.492819i	−0.102306	+	0.994753i	$0.532622\pi$
$74$		0			0
$75$	−0.790225	−	8.62413i	−0.0912473	−	0.995828i
$76$		0			0
$77$	−3.73768	+	1.90445i	−0.425949	+	0.217032i
$78$		0			0
$79$	4.29102	−	5.90609i	0.482778	−	0.664487i	−0.496258	−	0.868175i	$-0.665293\pi$
$79$	4.29102	−	5.90609i	0.482778	−	0.664487i	0.979036	+	0.203689i	$0.0652930\pi$
$80$		0			0
$81$	−8.76132	−	2.05897i	−0.973479	−	0.228774i
$82$		0			0
$83$	0.190258	−	1.20124i	0.0208835	−	0.131853i	−0.975044	−	0.222012i	$-0.928738\pi$
$83$	0.190258	−	1.20124i	0.0208835	−	0.131853i	0.995927	+	0.0901590i	$0.0287375\pi$
$84$		0			0
$85$	1.94599	−	0.623695i	0.211072	−	0.0676492i
$86$		0			0
$87$	9.17202	−	0.914482i	0.983344	−	0.0980427i
$88$		0			0
$89$	−3.41396	+	10.5071i	−0.361879	+	1.11375i	0.590034	+	0.807378i	$0.299114\pi$
$89$	−3.41396	+	10.5071i	−0.361879	+	1.11375i	−0.951913	+	0.306369i	$0.900886\pi$
$90$		0			0
$91$	2.06386	+	6.35190i	0.216351	+	0.665860i
$92$		0			0
$93$	−0.816433	+	3.74254i	−0.0846602	+	0.388084i
$94$		0			0
$95$	14.5427	+	7.48329i	1.49205	+	0.767769i
$96$		0			0
$97$	3.84712	−	0.609325i	0.390616	−	0.0618675i	0.0419626	−	0.999119i	$-0.486639\pi$
$97$	3.84712	−	0.609325i	0.390616	−	0.0618675i	0.348654	+	0.937252i	$0.386639\pi$
$98$		0			0
$99$	−4.55086	+	9.93423i	−0.457379	+	0.998428i
$100$		0			0
$101$		−	1.83199i		−	0.182290i	−0.995838	−	0.0911450i	$-0.970947\pi$
$101$		−	1.83199i		−	0.182290i	0.995838	−	0.0911450i	$-0.0290527\pi$
$102$		0			0
$103$	−1.59260	−	10.0553i	−0.156923	−	0.990775i	−0.932932	−	0.360053i	$-0.882759\pi$
$103$	−1.59260	−	10.0553i	−0.156923	−	0.990775i	0.776009	−	0.630722i	$-0.217241\pi$
$104$		0			0
$105$	−1.77611	−	4.09168i	−0.173330	−	0.399307i
$106$		0			0
$107$	−12.7040	−	12.7040i	−1.22814	−	1.22814i	−0.964668	−	0.263470i	$-0.915133\pi$
$107$	−12.7040	−	12.7040i	−1.22814	−	1.22814i	−0.263470	−	0.964668i	$-0.584867\pi$
$108$		0			0
$109$	7.48884	−	2.43327i	0.717301	−	0.233065i	0.0724482	−	0.997372i	$-0.476919\pi$
$109$	7.48884	−	2.43327i	0.717301	−	0.233065i	0.644853	+	0.764307i	$0.276919\pi$
$110$		0			0
$111$	5.16414	−	1.35419i	0.490159	−	0.128534i
$112$		0			0
$113$	−16.6927	−	8.50535i	−1.57032	−	0.800116i	−0.570540	−	0.821270i	$-0.693266\pi$
$113$	−16.6927	−	8.50535i	−1.57032	−	0.800116i	−0.999776	+	0.0211535i	$0.993266\pi$
$114$		0			0
$115$	−12.1541	−	8.90494i	−1.13337	−	0.830390i
$116$		0			0
$117$	14.4883	+	9.63056i	1.33945	+	0.890345i
$118$		0			0
$119$	0.851507	−	0.618656i	0.0780575	−	0.0567121i
$120$		0			0
$121$	1.83371	+	1.33227i	0.166701	+	0.121116i
$122$		0			0
$123$	−2.44966	+	4.19105i	−0.220879	+	0.377894i
$124$		0			0
$125$	1.88138	−	11.0209i	0.168276	−	0.985740i
$126$		0			0
$127$	3.30459	+	6.48562i	0.293235	+	0.575505i	0.989879	−	0.141911i	$-0.0453246\pi$
$127$	3.30459	+	6.48562i	0.293235	+	0.575505i	−0.696645	+	0.717416i	$0.745325\pi$
$128$		0			0
$129$	−7.36762	−	0.425618i	−0.648683	−	0.0374736i
$130$		0			0
$131$	3.48009	+	4.78993i	0.304057	+	0.418498i	0.933516	−	0.358535i	$-0.116724\pi$
$131$	3.48009	+	4.78993i	0.304057	+	0.418498i	−0.629460	+	0.777033i	$0.716724\pi$
$132$		0			0
$133$	8.32012	+	1.31778i	0.721446	+	0.114266i
$134$		0			0
$135$	−10.2448	−	5.48123i	−0.881733	−	0.471749i
$136$		0			0
$137$	2.92241	−	5.73556i	0.249679	−	0.490022i	−0.731818	−	0.681500i	$-0.761328\pi$
$137$	2.92241	−	5.73556i	0.249679	−	0.490022i	0.981497	+	0.191478i	$0.0613280\pi$
$138$		0			0
$139$	−2.67670	−	0.869713i	−0.227035	−	0.0737681i	0.193290	−	0.981142i	$-0.438084\pi$
$139$	−2.67670	−	0.869713i	−0.227035	−	0.0737681i	−0.420325	+	0.907373i	$0.638084\pi$
$140$		0			0
$141$	8.55152	+	7.00089i	0.720168	+	0.589581i
$142$		0			0
$143$	14.9355	−	14.9355i	1.24897	−	1.24897i
$144$		0			0
$145$	11.7457	+	1.90853i	0.975426	+	0.158495i
$146$		0			0
$147$	6.53636	+	7.33786i	0.539110	+	0.605216i
$148$		0			0
$149$	21.8247			1.78795			0.893974	−	0.448119i	$-0.147906\pi$
$149$	21.8247			1.78795			0.893974	+	0.448119i	$0.147906\pi$
$150$		0			0
$151$	−7.79667			−0.634484			−0.317242	−	0.948345i	$-0.602757\pi$
$151$	−7.79667			−0.634484			−0.317242	+	0.948345i	$0.602757\pi$
$152$		0			0
$153$	0.737855	−	2.64048i	0.0596520	−	0.213470i
$154$		0			0
$155$	−2.26270	+	4.39722i	−0.181744	+	0.353193i
$156$		0			0
$157$	10.3925	−	10.3925i	0.829410	−	0.829410i	−0.158025	−	0.987435i	$-0.550513\pi$
$157$	10.3925	−	10.3925i	0.829410	−	0.829410i	0.987435	+	0.158025i	$0.0505126\pi$
$158$		0			0
$159$	8.93339	−	10.9121i	0.708464	−	0.865382i
$160$		0			0
$161$	−7.38065	−	2.39812i	−0.581677	−	0.188998i
$162$		0			0
$163$	3.53766	−	6.94305i	0.277091	−	0.543822i	−0.709957	−	0.704245i	$-0.751286\pi$
$163$	3.53766	−	6.94305i	0.277091	−	0.543822i	0.987048	+	0.160423i	$0.0512859\pi$
$164$		0			0
$165$	−8.97969	+	10.8795i	−0.699068	+	0.846970i
$166$		0			0
$167$	0.370295	+	0.0586489i	0.0286543	+	0.00453839i	0.170745	−	0.985315i	$-0.445383\pi$
$167$	0.370295	+	0.0586489i	0.0286543	+	0.00453839i	−0.142091	+	0.989854i	$0.545383\pi$
$168$		0			0
$169$	−12.1253	−	16.6890i	−0.932714	−	1.28377i
$170$		0			0
$171$	19.1191	−	10.7676i	1.46207	−	0.823417i
$172$		0			0
$173$	−5.57182	−	10.9353i	−0.423618	−	0.831397i	−0.999900	−	0.0141460i	$-0.995497\pi$
$173$	−5.57182	−	10.9353i	−0.423618	−	0.831397i	0.576282	−	0.817251i	$-0.304503\pi$
$174$		0			0
$175$	−0.855300	−	5.69466i	−0.0646546	−	0.430476i
$176$		0			0
$177$	−9.60008	−	5.61124i	−0.721586	−	0.421766i
$178$		0			0
$179$	4.46475	+	3.24383i	0.333711	+	0.242455i	0.742004	−	0.670396i	$-0.233876\pi$
$179$	4.46475	+	3.24383i	0.333711	+	0.242455i	−0.408293	+	0.912851i	$0.633876\pi$
$180$		0			0
$181$	8.04985	−	5.84856i	0.598340	−	0.434720i	−0.246949	−	0.969028i	$-0.579428\pi$
$181$	8.04985	−	5.84856i	0.598340	−	0.434720i	0.845289	+	0.534309i	$0.179428\pi$
$182$		0			0
$183$	9.49052	+	21.6264i	0.701559	+	1.59867i
$184$		0			0
$185$	6.89223	+	0.0275712i	0.506727	+	0.00202708i
$186$		0			0
$187$	−2.96585	−	1.51118i	−0.216884	−	0.110508i
$188$		0			0
$189$	−5.89500	−	1.03082i	−0.428798	−	0.0749814i
$190$		0			0
$191$	−9.80442	+	3.18565i	−0.709423	+	0.230505i	−0.641431	−	0.767181i	$-0.721659\pi$
$191$	−9.80442	+	3.18565i	−0.709423	+	0.230505i	−0.0679914	+	0.997686i	$0.521659\pi$
$192$		0			0
$193$	−0.238354	−	0.238354i	−0.0171571	−	0.0171571i	0.698476	−	0.715633i	$-0.253862\pi$
$193$	−0.238354	−	0.238354i	−0.0171571	−	0.0171571i	−0.715633	+	0.698476i	$0.753862\pi$
$194$		0			0
$195$	14.8717	+	16.8304i	1.06499	+	1.20525i
$196$		0			0
$197$	0.296468	+	1.87183i	0.0211225	+	0.133362i	0.995996	−	0.0893965i	$-0.0284938\pi$
$197$	0.296468	+	1.87183i	0.0211225	+	0.133362i	−0.974874	+	0.222759i	$0.928494\pi$
$198$		0			0
$199$			18.6398i			1.32134i	0.750676	+	0.660670i	$0.229728\pi$
$199$			18.6398i			1.32134i	−0.750676	+	0.660670i	$0.770272\pi$
$200$		0			0
$201$	−5.84035	−	9.09946i	−0.411947	−	0.641826i
$202$		0			0
$203$	6.05361	−	0.958797i	0.424880	−	0.0672944i
$204$		0			0
$205$	−4.44919	+	4.41373i	−0.310745	+	0.308268i
$206$		0			0
$207$	−18.9484	+	7.04216i	−1.31701	+	0.489464i
$208$		0			0
$209$	−8.23247	−	25.3369i	−0.569452	−	1.75259i
$210$		0			0
$211$	7.77153	−	23.9183i	0.535014	−	1.64660i	−0.208604	−	0.978000i	$-0.566892\pi$
$211$	7.77153	−	23.9183i	0.535014	−	1.64660i	0.743618	−	0.668604i	$-0.233108\pi$
$212$		0			0
$213$	1.71995	+	17.2507i	0.117849	+	1.18200i
$214$		0			0
$215$	−9.04926	−	2.98036i	−0.617155	−	0.203259i
$216$		0			0
$217$	−0.398452	+	2.51573i	−0.0270487	+	0.170779i
$218$		0			0
$219$	−5.83702	+	14.9664i	−0.394429	+	1.01133i
$220$		0			0
$221$	−3.11503	+	4.28748i	−0.209540	+	0.288407i
$222$		0			0
$223$	4.28530	−	2.18347i	0.286965	−	0.146216i	−0.304583	−	0.952486i	$-0.598517\pi$
$223$	4.28530	−	2.18347i	0.286965	−	0.146216i	0.591548	+	0.806270i	$0.298517\pi$
$224$		0			0
$225$	−10.9576	−	10.2435i	−0.730510	−	0.682902i
$226$		0			0
$227$	−11.3411	+	5.77860i	−0.752738	+	0.383539i	−0.787868	−	0.615844i	$-0.788815\pi$
$227$	−11.3411	+	5.77860i	−0.752738	+	0.383539i	0.0351307	+	0.999383i	$0.488815\pi$
$228$		0			0
$229$	0.0954879	−	0.131428i	0.00631002	−	0.00868500i	−0.805850	−	0.592119i	$-0.798291\pi$
$229$	0.0954879	−	0.131428i	0.00631002	−	0.00868500i	0.812160	+	0.583434i	$0.198291\pi$
$230$		0			0
$231$	−2.64004	+	6.76918i	−0.173702	+	0.445379i
$232$		0			0
$233$	−0.939042	+	5.92888i	−0.0615187	+	0.388414i	0.937648	+	0.347587i	$0.112999\pi$
$233$	−0.939042	+	5.92888i	−0.0615187	+	0.388414i	−0.999166	+	0.0408262i	$0.987001\pi$
$234$		0			0
$235$	8.34012	+	11.5763i	0.544049	+	0.755154i
$236$		0			0
$237$	−1.25448	−	12.5821i	−0.0814875	−	0.817298i
$238$		0			0
$239$	−3.44778	+	10.6112i	−0.223019	+	0.686380i	0.775468	+	0.631387i	$0.217514\pi$
$239$	−3.44778	+	10.6112i	−0.223019	+	0.686380i	−0.998487	+	0.0549938i	$0.982486\pi$
$240$		0			0
$241$	−8.68635	−	26.7338i	−0.559537	−	1.72208i	−0.683650	−	0.729810i	$-0.739609\pi$
$241$	−8.68635	−	26.7338i	−0.559537	−	1.72208i	0.124114	−	0.992268i	$-0.460391\pi$
$242$		0			0
$243$	−13.7034	+	7.43072i	−0.879076	+	0.476681i
$244$		0			0
$245$	5.71428	+	11.3267i	0.365072	+	0.723636i
$246$		0			0
$247$	−41.8932	+	6.63523i	−2.66560	+	0.422189i
$248$		0			0
$249$	−1.13785	−	1.77280i	−0.0721081	−	0.112347i
$250$		0			0
$251$			28.1347i			1.77585i	0.459991	+	0.887924i	$0.347853\pi$
$251$			28.1347i			1.77585i	−0.459991	+	0.887924i	$0.652147\pi$
$252$		0			0
$253$	3.83936	+	24.2407i	0.241378	+	1.52400i
$254$		0			0
$255$	1.79829	−	3.04857i	0.112613	−	0.190909i
$256$		0			0
$257$	−12.8233	−	12.8233i	−0.799894	−	0.799894i	0.183184	−	0.983079i	$-0.441359\pi$
$257$	−12.8233	−	12.8233i	−0.799894	−	0.799894i	−0.983079	+	0.183184i	$0.941359\pi$
$258$		0			0
$259$	3.37619	−	1.09699i	0.209786	−	0.0681637i
$260$		0			0
$261$	10.8090	−	11.7496i	0.669060	−	0.727280i
$262$		0			0
$263$	18.6904	+	9.52321i	1.15250	+	0.587226i	0.922512	−	0.385968i	$-0.126132\pi$
$263$	18.6904	+	9.52321i	1.15250	+	0.587226i	0.229984	+	0.973194i	$0.426132\pi$
$264$		0			0
$265$	14.7718	−	10.6423i	0.907423	−	0.653751i
$266$		0			0
$267$	7.68950	+	17.5223i	0.470590	+	1.07235i
$268$		0			0
$269$	10.9550	−	7.95929i	0.667940	−	0.485287i	−0.201395	−	0.979510i	$-0.564548\pi$
$269$	10.9550	−	7.95929i	0.667940	−	0.485287i	0.869335	+	0.494223i	$0.164548\pi$
$270$		0			0
$271$	1.95011	+	1.41684i	0.118461	+	0.0860669i	0.645438	−	0.763812i	$-0.276675\pi$
$271$	1.95011	+	1.41684i	0.118461	+	0.0860669i	−0.526977	+	0.849879i	$0.676675\pi$
$272$		0			0
$273$	9.98712	+	5.83746i	0.604448	+	0.353299i
$274$		0			0
$275$	−14.8187	+	10.5863i	−0.893602	+	0.638380i
$276$		0			0
$277$	−4.61588	−	9.05917i	−0.277341	−	0.544313i	0.709753	−	0.704450i	$-0.248806\pi$
$277$	−4.61588	−	9.05917i	−0.277341	−	0.544313i	−0.987095	+	0.160137i	$0.948806\pi$
$278$		0			0
$279$	3.25576	+	5.78097i	0.194917	+	0.346098i
$280$		0			0
$281$	−3.75864	−	5.17333i	−0.224222	−	0.308615i	0.682054	−	0.731302i	$-0.261087\pi$
$281$	−3.75864	−	5.17333i	−0.224222	−	0.308615i	−0.906276	+	0.422687i	$0.861087\pi$
$282$		0			0
$283$	−12.2845	−	1.94568i	−0.730239	−	0.115658i	−0.219766	−	0.975553i	$-0.570529\pi$
$283$	−12.2845	−	1.94568i	−0.730239	−	0.115658i	−0.510472	+	0.859894i	$0.670529\pi$
$284$		0			0
$285$	27.4299	−	7.07576i	1.62481	−	0.419132i
$286$		0			0
$287$	−1.46544	+	2.87609i	−0.0865024	+	0.169770i
$288$		0			0
$289$	−15.3737	−	4.99521i	−0.904333	−	0.293836i
$290$		0			0
$291$	4.27366	−	5.22023i	0.250526	−	0.306015i
$292$		0			0
$293$	−20.0058	+	20.0058i	−1.16875	+	1.16875i	−0.186248	+	0.982503i	$0.559633\pi$
$293$	−20.0058	+	20.0058i	−1.16875	+	1.16875i	−0.982503	+	0.186248i	$0.940367\pi$
$294$		0			0
$295$	−10.1102	−	10.1914i	−0.588636	−	0.593364i
$296$		0			0
$297$	5.55914	+	18.0913i	0.322574	+	1.04976i
$298$		0			0
$299$	39.0752			2.25978
$300$		0			0
$301$	−4.90718			−0.282845
$302$		0			0
$303$	−2.11059	−	2.36939i	−0.121250	−	0.136118i
$304$		0			0
$305$	4.64913	+	30.1331i	0.266208	+	1.72542i
$306$		0			0
$307$	1.67900	−	1.67900i	0.0958255	−	0.0958255i	−0.657569	−	0.753394i	$-0.728415\pi$
$307$	1.67900	−	1.67900i	0.0958255	−	0.0958255i	0.753394	+	0.657569i	$0.228415\pi$
$308$		0			0
$309$	−13.6442	−	11.1701i	−0.776190	−	0.635445i
$310$		0			0
$311$	16.6707	+	5.41664i	0.945310	+	0.307150i	0.740808	−	0.671717i	$-0.234443\pi$
$311$	16.6707	+	5.41664i	0.945310	+	0.307150i	0.204501	+	0.978866i	$0.434443\pi$
$312$		0			0
$313$	7.60246	−	14.9207i	0.429716	−	0.843366i	−0.570047	−	0.821612i	$-0.693075\pi$
$313$	7.60246	−	14.9207i	0.429716	−	0.843366i	0.999763	−	0.0217538i	$-0.00692499\pi$
$314$		0			0
$315$	−7.01103	−	3.24574i	−0.395027	−	0.182877i
$316$		0			0
$317$	−10.0629	−	1.59380i	−0.565187	−	0.0895168i	−0.132699	−	0.991156i	$-0.542364\pi$
$317$	−10.0629	−	1.59380i	−0.565187	−	0.0895168i	−0.432488	+	0.901640i	$0.642364\pi$
$318$		0			0
$319$	−11.3933	−	15.6816i	−0.637904	−	0.878000i
$320$		0			0
$321$	−31.0664	−	1.79467i	−1.73396	−	0.100169i
$322$		0			0
$323$	3.03461	+	5.95576i	0.168850	+	0.331388i
$324$		0			0
$325$	12.9564	+	25.9394i	0.718692	+	1.43886i
$326$		0			0
$327$	6.88232	−	11.7747i	0.380593	−	0.651144i
$328$		0			0
$329$	5.94524	+	4.31947i	0.327772	+	0.238140i
$330$		0			0
$331$	21.8809	−	15.8974i	1.20268	−	0.873801i	0.208138	−	0.978099i	$-0.433260\pi$
$331$	21.8809	−	15.8974i	1.20268	−	0.873801i	0.994546	+	0.104298i	$0.0332597\pi$
$332$		0			0
$333$	5.11887	−	7.70089i	0.280513	−	0.422006i
$334$		0			0
$335$	−4.26038	−	13.2928i	−0.232770	−	0.726264i
$336$		0			0
$337$	13.4244	+	6.84007i	0.731273	+	0.372602i	0.779640	−	0.626227i	$-0.215402\pi$
$337$	13.4244	+	6.84007i	0.731273	+	0.372602i	−0.0483675	+	0.998830i	$0.515402\pi$
$338$		0			0
$339$	−31.3881	+	8.23087i	−1.70477	+	0.447039i
$340$		0			0
$341$	7.66104	−	2.48922i	0.414869	−	0.134799i
$342$		0			0
$343$	10.3211	+	10.3211i	0.557287	+	0.557287i
$344$		0			0
$345$	−25.9785	+	2.48523i	−1.39863	+	0.133800i
$346$		0			0
$347$	−1.70896	−	10.7899i	−0.0917415	−	0.579233i	−0.990143	−	0.140059i	$-0.955271\pi$
$347$	−1.70896	−	10.7899i	−0.0917415	−	0.579233i	0.898402	−	0.439175i	$-0.144729\pi$
$348$		0			0
$349$		−	4.93794i		−	0.264322i	−0.991228	−	0.132161i	$-0.957808\pi$
$349$		−	4.93794i		−	0.264322i	0.991228	−	0.132161i	$-0.0421916\pi$
$350$		0			0
$351$	29.8334	−	4.23600i	1.59239	−	0.226101i
$352$		0			0
$353$	−2.96257	+	0.469225i	−0.157682	+	0.0249744i	−0.234776	−	0.972049i	$-0.575436\pi$
$353$	−2.96257	+	0.469225i	−0.157682	+	0.0249744i	0.0770944	+	0.997024i	$0.475436\pi$
$354$		0			0
$355$	−3.58955	+	22.0912i	−0.190513	+	1.17248i
$356$		0			0
$357$	0.388552	−	1.78113i	0.0205644	−	0.0942674i
$358$		0			0
$359$	−9.84389	−	30.2964i	−0.519540	−	1.59898i	−0.774866	−	0.632126i	$-0.782183\pi$
$359$	−9.84389	−	30.2964i	−0.519540	−	1.59898i	0.255325	−	0.966855i	$-0.417817\pi$
$360$		0			0
$361$	−10.6604	+	32.8093i	−0.561074	+	1.72681i
$362$		0			0
$363$	3.90649	−	0.389491i	0.205038	−	0.0204430i
$364$		0			0
$365$	−12.2571	+	16.7293i	−0.641565	+	0.875651i
$366$		0			0
$367$	−4.72166	+	29.8114i	−0.246469	+	1.55614i	0.485152	+	0.874430i	$0.338764\pi$
$367$	−4.72166	+	29.8114i	−0.246469	+	1.55614i	−0.731621	+	0.681712i	$0.761236\pi$
$368$		0			0
$369$	1.66014	+	8.24265i	0.0864236	+	0.429095i
$370$		0			0
$371$	5.51180	−	7.58635i	0.286159	−	0.393864i
$372$		0			0
$373$	17.7102	−	9.02378i	0.916998	−	0.467234i	0.0692297	−	0.997601i	$-0.477946\pi$
$373$	17.7102	−	9.02378i	0.916998	−	0.467234i	0.847768	+	0.530367i	$0.177946\pi$
$374$		0			0
$375$	−10.2636	−	16.4213i	−0.530011	−	0.847991i
$376$		0			0
$377$	−27.4972	+	14.0105i	−1.41618	+	0.721579i
$378$		0			0
$379$	−8.60609	+	11.8453i	−0.442065	+	0.608450i	−0.970669	−	0.240418i	$-0.922716\pi$
$379$	−8.60609	+	11.8453i	−0.442065	+	0.608450i	0.528604	+	0.848868i	$0.322716\pi$
$380$		0			0
$381$	11.7459	+	4.58099i	0.601758	+	0.234691i
$382$		0			0
$383$	4.01050	−	25.3213i	0.204927	−	1.29386i	−0.643868	−	0.765137i	$-0.722671\pi$
$383$	4.01050	−	25.3213i	0.204927	−	1.29386i	0.848795	−	0.528722i	$-0.177329\pi$
$384$		0			0
$385$	−5.54379	+	7.56653i	−0.282538	+	0.385626i
$386$		0			0
$387$	−10.0192	+	7.93756i	−0.509304	+	0.403489i
$388$		0			0
$389$	3.42204	−	10.5320i	0.173504	−	0.533991i	−0.826058	−	0.563586i	$-0.809422\pi$
$389$	3.42204	−	10.5320i	0.173504	−	0.533991i	0.999562	+	0.0295942i	$0.00942151\pi$
$390$		0			0
$391$	−1.90291	−	5.85654i	−0.0962341	−	0.296178i
$392$		0			0
$393$	10.0193	+	2.18570i	0.505406	+	0.110254i
$394$		0			0
$395$	2.61812	−	16.1127i	0.131732	−	0.810718i
$396$		0			0
$397$	−34.8560	+	5.52065i	−1.74937	+	0.277074i	−0.947346	−	0.320212i	$-0.896246\pi$
$397$	−34.8560	+	5.52065i	−1.74937	+	0.277074i	−0.802029	+	0.597286i	$0.796246\pi$
$398$		0			0
$399$	12.2789	−	7.88105i	0.614715	−	0.394546i
$400$		0			0
$401$		−	28.2805i		−	1.41226i	−0.708081	−	0.706131i	$-0.750439\pi$
$401$		−	28.2805i		−	1.41226i	0.708081	−	0.706131i	$-0.249561\pi$
$402$		0			0
$403$	−2.00627	−	12.6671i	−0.0999395	−	0.630993i
$404$		0			0
$405$	−19.5648	+	4.71366i	−0.972183	+	0.234224i
$406$		0			0
$407$	−7.93859	−	7.93859i	−0.393501	−	0.393501i
$408$		0			0
$409$	15.1592	−	4.92552i	0.749574	−	0.243551i	0.0907761	−	0.995871i	$-0.471065\pi$
$409$	15.1592	−	4.92552i	0.749574	−	0.243551i	0.658798	+	0.752320i	$0.271065\pi$
$410$		0			0
$411$	−2.82810	−	10.7849i	−0.139500	−	0.531978i
$412$		0			0
$413$	−6.58802	−	3.35676i	−0.324175	−	0.165176i
$414$		0			0
$415$	−0.830029	−	2.58977i	−0.0407445	−	0.127127i
$416$		0			0
$417$	−4.46386	+	1.95892i	−0.218596	+	0.0959287i
$418$		0			0
$419$	−28.4906	+	20.6996i	−1.39186	+	1.01124i	−0.396197	+	0.918166i	$0.629670\pi$
$419$	−28.4906	+	20.6996i	−1.39186	+	1.01124i	−0.995659	+	0.0930769i	$0.970330\pi$
$420$		0			0
$421$	−1.21908	−	0.885714i	−0.0594143	−	0.0431670i	0.557682	−	0.830055i	$-0.311691\pi$
$421$	−1.21908	−	0.885714i	−0.0594143	−	0.0431670i	−0.617096	+	0.786888i	$0.711691\pi$
$422$		0			0
$423$	19.1256	−	0.797431i	0.929916	−	0.0387724i
$424$		0			0
$425$	3.25680	−	3.20510i	0.157978	−	0.155470i
$426$		0			0
$427$	7.12945	+	13.9923i	0.345018	+	0.677137i
$428$		0			0
$429$	2.10992	−	36.5235i	0.101868	−	1.76337i
$430$		0			0
$431$	3.75782	+	5.17220i	0.181008	+	0.249136i	0.889873	−	0.456208i	$-0.150793\pi$
$431$	3.75782	+	5.17220i	0.181008	+	0.249136i	−0.708865	+	0.705344i	$0.750793\pi$
$432$		0			0
$433$	22.5721	+	3.57506i	1.08474	+	0.171807i	0.673110	−	0.739542i	$-0.264958\pi$
$433$	22.5721	+	3.57506i	1.08474	+	0.171807i	0.411634	+	0.911349i	$0.364958\pi$
$434$		0			0
$435$	17.3899	−	11.0635i	0.833784	−	0.530454i
$436$		0			0
$437$	22.3749	−	43.9132i	1.07034	−	2.10065i
$438$		0			0
$439$	−1.74365	−	0.566545i	−0.0832197	−	0.0270397i	0.267111	−	0.963666i	$-0.413931\pi$
$439$	−1.74365	−	0.566545i	−0.0832197	−	0.0270397i	−0.350331	+	0.936626i	$0.613931\pi$
$440$		0			0
$441$	16.9075	+	1.95999i	0.805118	+	0.0933328i
$442$		0			0
$443$	6.75410	−	6.75410i	0.320897	−	0.320897i	−0.528214	−	0.849111i	$-0.677138\pi$
$443$	6.75410	−	6.75410i	0.320897	−	0.320897i	0.849111	+	0.528214i	$0.177138\pi$
$444$		0			0
$445$	3.76686	+	24.4147i	0.178566	+	1.15737i
$446$		0			0
$447$	28.2268	−	25.1436i	1.33508	−	1.18925i
$448$		0			0
$449$	24.0642			1.13566			0.567830	−	0.823146i	$-0.307783\pi$
$449$	24.0642			1.13566			0.567830	+	0.823146i	$0.307783\pi$
$450$		0			0
$451$	10.2085			0.480697
$452$		0			0
$453$	−10.0838	+	8.98233i	−0.473776	+	0.422027i
$454$		0			0
$455$	10.5178	+	10.6022i	0.493080	+	0.497041i
$456$		0			0
$457$	15.7146	−	15.7146i	0.735097	−	0.735097i	−0.236528	−	0.971625i	$-0.576010\pi$
$457$	15.7146	−	15.7146i	0.735097	−	0.735097i	0.971625	+	0.236528i	$0.0760095\pi$
$458$		0			0
$459$	−2.08773	−	4.26510i	−0.0974468	−	0.199078i
$460$		0			0
$461$	8.27650	+	2.68920i	0.385475	+	0.125248i	0.495342	−	0.868698i	$-0.335043\pi$
$461$	8.27650	+	2.68920i	0.385475	+	0.125248i	−0.109867	+	0.993946i	$0.535043\pi$
$462$		0			0
$463$	−6.79566	+	13.3372i	−0.315821	+	0.619834i	−0.993281	−	0.115726i	$-0.963081\pi$
$463$	−6.79566	+	13.3372i	−0.315821	+	0.619834i	0.677460	+	0.735560i	$0.263081\pi$
$464$		0			0
$465$	2.13948	+	8.29389i	0.0992158	+	0.384620i
$466$		0			0
$467$	32.4831	+	5.14481i	1.50314	+	0.238074i	0.853067	−	0.521801i	$-0.174739\pi$
$467$	32.4831	+	5.14481i	1.50314	+	0.238074i	0.650070	+	0.759874i	$0.274739\pi$
$468$		0			0
$469$	−4.22596	−	5.81654i	−0.195137	−	0.268583i
$470$		0			0
$471$	1.46813	−	25.4139i	0.0676478	−	1.17101i
$472$		0			0
$473$	7.04558	+	13.8277i	0.323956	+	0.635800i
$474$		0			0
$475$	36.5699	+	0.292588i	1.67794	+	0.0134249i
$476$		0			0
$477$	−1.01755	−	24.4049i	−0.0465905	−	1.11742i
$478$		0			0
$479$	−22.4708	−	16.3260i	−1.02672	−	0.745953i	−0.0590677	−	0.998254i	$-0.518813\pi$
$479$	−22.4708	−	16.3260i	−1.02672	−	0.745953i	−0.967649	+	0.252301i	$0.918813\pi$
$480$		0			0
$481$	−14.4608	+	10.5064i	−0.659355	+	0.479049i
$482$		0			0
$483$	−12.3085	+	5.40146i	−0.560056	+	0.245775i
$484$		0			0
$485$	7.06669	−	5.09118i	0.320882	−	0.231179i
$486$		0			0
$487$	28.0023	+	14.2679i	1.26891	+	0.646540i	0.953207	−	0.302319i	$-0.0977607\pi$
$487$	28.0023	+	14.2679i	1.26891	+	0.646540i	0.315700	+	0.948859i	$0.397761\pi$
$488$		0			0
$489$	−3.42349	−	13.0554i	−0.154816	−	0.590384i
$490$		0			0
$491$	−11.6547	+	3.78683i	−0.525968	+	0.170897i	−0.559952	−	0.828525i	$-0.689180\pi$
$491$	−11.6547	+	3.78683i	−0.525968	+	0.170897i	0.0339840	+	0.999422i	$0.489180\pi$
$492$		0			0
$493$	3.43895	+	3.43895i	0.154883	+	0.154883i
$494$		0			0
$495$	0.920195	+	24.4162i	0.0413597	+	1.09743i
$496$		0			0
$497$	1.80330	+	11.3856i	0.0808890	+	0.510713i
$498$		0			0
$499$			2.58376i			0.115665i	0.998326	+	0.0578324i	$0.0184189\pi$
$499$			2.58376i			0.115665i	−0.998326	+	0.0578324i	$0.981581\pi$
$500$		0			0
$501$	0.546485	−	0.350753i	0.0244151	−	0.0156705i
$502$		0			0
$503$	−29.7370	+	4.70988i	−1.32591	+	0.210003i	−0.778913	−	0.627132i	$-0.784228\pi$
$503$	−29.7370	+	4.70988i	−1.32591	+	0.210003i	−0.546995	+	0.837136i	$0.684228\pi$
$504$		0			0
$505$	−1.84514	−	3.65738i	−0.0821076	−	0.162751i
$506$		0			0
$507$	−34.9091	−	7.61539i	−1.55037	−	0.338211i
$508$		0			0
$509$	10.5395	+	32.4372i	0.467155	+	1.43776i	0.856252	+	0.516559i	$0.172787\pi$
$509$	10.5395	+	32.4372i	0.467155	+	1.43776i	−0.389097	+	0.921197i	$0.627213\pi$
$510$		0			0
$511$	−3.30086	+	10.1590i	−0.146021	+	0.449407i
$512$		0			0
$513$	12.3225	−	35.9527i	0.544050	−	1.58735i
$514$		0			0
$515$	−13.3069	−	18.4703i	−0.586371	−	0.813898i
$516$		0			0
$517$	3.63565	−	22.9546i	0.159896	−	1.00954i
$518$		0			0
$519$	−19.8045	−	7.72395i	−0.869323	−	0.339044i
$520$		0			0
$521$	−7.87830	+	10.8435i	−0.345154	+	0.475064i	−0.945938	−	0.324347i	$-0.894855\pi$
$521$	−7.87830	+	10.8435i	−0.345154	+	0.475064i	0.600784	+	0.799412i	$0.294855\pi$
$522$		0			0
$523$	11.1465	−	5.67941i	0.487401	−	0.248343i	−0.192979	−	0.981203i	$-0.561815\pi$
$523$	11.1465	−	5.67941i	0.487401	−	0.248343i	0.680380	+	0.732860i	$0.261815\pi$
$524$		0			0
$525$	−7.66686	−	6.37977i	−0.334609	−	0.278436i
$526$		0			0
$527$	−1.80082	+	0.917566i	−0.0784451	+	0.0399698i
$528$		0			0
$529$	−13.1686	+	18.1251i	−0.572549	+	0.788046i
$530$		0			0
$531$	−18.8807	+	3.80275i	−0.819354	+	0.165025i
$532$		0			0
$533$	2.54254	−	16.0530i	0.110130	−	0.695332i
$534$		0			0
$535$	−38.1572	−	12.5670i	−1.64968	−	0.543319i
$536$		0			0
$537$	9.51156	−	0.948335i	0.410454	−	0.0409237i
$538$		0			0
$539$	6.38585	−	19.6536i	0.275058	−	0.846541i
$540$		0			0
$541$	1.14874	+	3.53545i	0.0493881	+	0.152001i	0.972709	−	0.232028i	$-0.0745362\pi$
$541$	1.14874	+	3.53545i	0.0493881	+	0.152001i	−0.923321	+	0.384029i	$0.874536\pi$
$542$		0			0
$543$	3.67323	−	16.8382i	0.157634	−	0.722595i
$544$		0			0
$545$	12.5000	−	12.4003i	0.535439	−	0.531173i
$546$		0			0
$547$	−2.64836	+	0.419459i	−0.113236	+	0.0179348i	−0.212795	−	0.977097i	$-0.568257\pi$
$547$	−2.64836	+	0.419459i	−0.113236	+	0.0179348i	0.0995594	+	0.995032i	$0.468257\pi$
$548$		0			0
$549$	37.1896	+	17.0365i	1.58722	+	0.727101i
$550$		0			0
$551$			38.9242i			1.65823i
$552$		0			0
$553$	−1.31527	−	8.30432i	−0.0559312	−	0.353136i
$554$		0			0
$555$	8.94577	−	7.90469i	0.379727	−	0.335535i
$556$		0			0
$557$	19.5853	+	19.5853i	0.829857	+	0.829857i	0.987497	−	0.157639i	$-0.0503884\pi$
$557$	19.5853	+	19.5853i	0.829857	+	0.829857i	−0.157639	+	0.987497i	$0.550388\pi$
$558$		0			0
$559$	23.4991	−	7.63533i	0.993908	−	0.322940i
$560$		0			0
$561$	−5.57684	+	1.46241i	−0.235454	+	0.0617429i
$562$		0			0
$563$	14.2772	+	7.27459i	0.601712	+	0.306587i	0.728183	−	0.685383i	$-0.240365\pi$
$563$	14.2772	+	7.27459i	0.601712	+	0.306587i	−0.126471	+	0.991970i	$0.540365\pi$
$564$		0			0
$565$	−41.8916	−	0.167580i	−1.76239	−	0.00705015i
$566$		0			0
$567$	−8.81182	+	5.45826i	−0.370062	+	0.229225i
$568$		0			0
$569$	−29.7086	+	21.5845i	−1.24545	+	0.904871i	−0.997949	−	0.0640170i	$-0.979609\pi$
$569$	−29.7086	+	21.5845i	−1.24545	+	0.904871i	−0.247499	+	0.968888i	$0.579609\pi$
$570$		0			0
$571$	34.0496	+	24.7385i	1.42493	+	1.03527i	0.990933	+	0.134358i	$0.0428971\pi$
$571$	34.0496	+	24.7385i	1.42493	+	1.03527i	0.433997	+	0.900914i	$0.357103\pi$
$572$		0			0
$573$	−9.01035	+	15.4155i	−0.376413	+	0.643993i
$574$		0			0
$575$	−33.2332	−	5.53652i	−1.38592	−	0.230889i
$576$		0			0
$577$	19.4132	+	38.1006i	0.808182	+	1.58615i	0.810203	+	0.586149i	$0.199357\pi$
$577$	19.4132	+	38.1006i	0.808182	+	1.58615i	−0.00202117	+	0.999998i	$0.500643\pi$
$578$		0			0
$579$	−0.582873	−	0.0336718i	−0.0242234	−	0.00139935i
$580$		0			0
$581$	−0.823323	−	1.13321i	−0.0341572	−	0.0470133i
$582$		0			0
$583$	−29.2909	−	4.63922i	−1.21311	−	0.192137i
$584$		0			0
$585$	38.6241	+	4.63413i	1.59691	+	0.191598i
$586$		0			0
$587$	−0.114338	+	0.224402i	−0.00471925	+	0.00926205i	−0.893354	−	0.449353i	$-0.851654\pi$
$587$	−0.114338	+	0.224402i	−0.00471925	+	0.00926205i	0.888635	+	0.458615i	$0.151654\pi$
$588$		0			0
$589$	−15.3842	−	4.99864i	−0.633897	−	0.205966i
$590$		0			0
$591$	2.53991	+	2.07936i	0.104478	+	0.0855333i
$592$		0			0
$593$	14.4925	−	14.4925i	0.595137	−	0.595137i	−0.343878	−	0.939014i	$-0.611741\pi$
$593$	14.4925	−	14.4925i	0.595137	−	0.595137i	0.939014	+	0.343878i	$0.111741\pi$
$594$		0			0
$595$	1.07685	−	2.09270i	0.0441466	−	0.0857923i
$596$		0			0
$597$	21.4744	+	24.1076i	0.878889	+	0.986659i
$598$		0			0
$599$	−16.6754			−0.681340			−0.340670	−	0.940183i	$-0.610654\pi$
$599$	−16.6754			−0.681340			−0.340670	+	0.940183i	$0.610654\pi$
$600$		0			0
$601$	−21.5251			−0.878028			−0.439014	−	0.898480i	$-0.644672\pi$
$601$	−21.5251			−0.878028			−0.439014	+	0.898480i	$0.644672\pi$
$602$		0			0
$603$	−18.0368	−	5.04019i	−0.734515	−	0.205253i
$604$		0			0
$605$	5.00265	+	0.812870i	0.203387	+	0.0330479i
$606$		0			0
$607$	7.49042	−	7.49042i	0.304027	−	0.304027i	−0.538560	−	0.842587i	$-0.681032\pi$
$607$	7.49042	−	7.49042i	0.304027	−	0.304027i	0.842587	+	0.538560i	$0.181032\pi$
$608$		0			0
$609$	6.72477	−	8.21424i	0.272501	−	0.332858i
$610$		0			0
$611$	−35.1910	−	11.4343i	−1.42368	−	0.462580i
$612$		0			0
$613$	−9.77730	+	19.1890i	−0.394902	+	0.775038i	−0.999773	−	0.0212848i	$-0.993224\pi$
$613$	−9.77730	+	19.1890i	−0.394902	+	0.775038i	0.604872	+	0.796323i	$0.293224\pi$
$614$		0			0
$615$	−0.669376	+	10.8342i	−0.0269918	+	0.436879i
$616$		0			0
$617$	−9.79635	−	1.55159i	−0.394386	−	0.0624646i	−0.0439081	−	0.999036i	$-0.513981\pi$
$617$	−9.79635	−	1.55159i	−0.394386	−	0.0624646i	−0.350478	+	0.936571i	$0.613981\pi$
$618$		0			0
$619$	4.81151	+	6.62247i	0.193391	+	0.266180i	0.894690	−	0.446687i	$-0.147396\pi$
$619$	4.81151	+	6.62247i	0.193391	+	0.266180i	−0.701299	+	0.712867i	$0.747396\pi$
$620$		0			0
$621$	−16.3937	+	30.9378i	−0.657855	+	1.24149i
$622$		0			0
$623$	5.77649	+	11.3370i	0.231430	+	0.454208i
$624$		0			0
$625$	−7.34400	−	23.8970i	−0.293760	−	0.955879i
$626$		0			0
$627$	−39.8374	−	23.2849i	−1.59095	−	0.929909i
$628$		0			0
$629$	2.27890	+	1.65572i	0.0908656	+	0.0660177i
$630$		0			0
$631$	−0.620208	+	0.450607i	−0.0246901	+	0.0179384i	−0.600062	−	0.799954i	$-0.704857\pi$
$631$	−0.620208	+	0.450607i	−0.0246901	+	0.0179384i	0.575372	+	0.817892i	$0.304857\pi$
$632$		0			0
$633$	−17.5044	−	39.8879i	−0.695737	−	1.58540i
$634$		0			0
$635$	13.1294	+	9.61956i	0.521025	+	0.381741i
$636$		0			0
$637$	−29.3152	−	14.9368i	−1.16151	−	0.591819i
$638$		0			0
$639$	22.0985	+	20.3295i	0.874203	+	0.804222i
$640$		0			0
$641$	16.9921	−	5.52105i	0.671146	−	0.218068i	0.0464310	−	0.998922i	$-0.485215\pi$
$641$	16.9921	−	5.52105i	0.671146	−	0.218068i	0.624715	+	0.780853i	$0.285215\pi$
$642$		0			0
$643$	5.47671	+	5.47671i	0.215980	+	0.215980i	0.806802	−	0.590822i	$-0.201196\pi$
$643$	5.47671	+	5.47671i	0.215980	+	0.215980i	−0.590822	+	0.806802i	$0.701196\pi$
$644$		0			0
$645$	−15.1374	+	6.57079i	−0.596033	+	0.258724i
$646$		0			0
$647$	5.84782	+	36.9217i	0.229902	+	1.45154i	0.784865	+	0.619667i	$0.212732\pi$
$647$	5.84782	+	36.9217i	0.229902	+	1.45154i	−0.554963	+	0.831875i	$0.687268\pi$
$648$		0			0
$649$			23.3836i			0.917888i
$650$		0			0
$651$	2.38297	+	3.71274i	0.0933958	+	0.145514i
$652$		0			0
$653$	−32.5406	+	5.15393i	−1.27341	+	0.201689i	−0.756298	−	0.654227i	$-0.772994\pi$
$653$	−32.5406	+	5.15393i	−1.27341	+	0.201689i	−0.517115	+	0.855916i	$0.672994\pi$
$654$		0			0
$655$	11.7719	+	6.05753i	0.459967	+	0.236687i
$656$		0			0
$657$	9.69309	+	26.0813i	0.378163	+	1.01753i
$658$		0			0
$659$	5.58239	+	17.1808i	0.217459	+	0.669270i	0.998970	+	0.0453785i	$0.0144494\pi$
$659$	5.58239	+	17.1808i	0.217459	+	0.669270i	−0.781511	+	0.623892i	$0.785551\pi$
$660$		0			0
$661$	5.43861	−	16.7383i	0.211537	−	0.651045i	−0.787844	−	0.615875i	$-0.788803\pi$
$661$	5.43861	−	16.7383i	0.211537	−	0.651045i	0.999381	−	0.0351703i	$-0.0111974\pi$
$662$		0			0
$663$	0.910682	+	9.13391i	0.0353680	+	0.354732i
$664$		0			0
$665$	17.9375	−	5.74902i	0.695586	−	0.222937i
$666$		0			0
$667$	5.60959	−	35.4175i	0.217204	−	1.37137i
$668$		0			0
$669$	3.02684	−	7.76095i	0.117024	−	0.300056i
$670$		0			0
$671$	29.1921	−	40.1795i	1.12695	−	1.55111i
$672$		0			0
$673$	−44.4567	+	22.6518i	−1.71368	+	0.873164i	−0.732327	+	0.680953i	$0.761566\pi$
$673$	−44.4567	+	22.6518i	−1.71368	+	0.873164i	−0.981354	+	0.192211i	$0.938434\pi$
$674$		0			0
$675$	−25.9733	−	0.624383i	−0.999711	−	0.0240325i
$676$		0			0
$677$	−13.4384	+	6.84718i	−0.516478	+	0.263159i	−0.692744	−	0.721184i	$-0.743598\pi$
$677$	−13.4384	+	6.84718i	−0.516478	+	0.263159i	0.176266	+	0.984343i	$0.443598\pi$
$678$		0			0
$679$	2.63680	−	3.62924i	0.101191	−	0.139278i
$680$		0			0
$681$	−8.01059	+	20.5395i	−0.306966	+	0.787075i
$682$		0			0
$683$	−2.11149	+	13.3314i	−0.0807939	+	0.510113i	0.913791	+	0.406185i	$0.133141\pi$
$683$	−2.11149	+	13.3314i	−0.0807939	+	0.510113i	−0.994585	+	0.103928i	$0.966859\pi$
$684$		0			0
$685$	0.0575801	−	14.3938i	0.00220002	−	0.549960i
$686$		0			0
$687$	−0.0279160	−	0.279990i	−0.00106506	−	0.0106823i
$688$		0			0
$689$	−14.5905	+	44.9050i	−0.555855	+	1.71075i
$690$		0			0
$691$	−1.08757	−	3.34720i	−0.0413731	−	0.127333i	0.928237	−	0.371991i	$-0.121325\pi$
$691$	−1.08757	−	3.34720i	−0.0413731	−	0.127333i	−0.969610	+	0.244657i	$0.921325\pi$
$692$		0			0
$693$	4.38411	+	11.7964i	0.166539	+	0.448107i
$694$		0			0
$695$	−6.21971	+	0.959617i	−0.235927	+	0.0364003i
$696$		0			0
$697$	−2.52981	+	0.400683i	−0.0958236	+	0.0151770i
$698$		0			0
$699$	5.61599	+	8.74990i	0.212416	+	0.330952i
$700$		0			0
$701$		−	40.9855i		−	1.54800i	−0.633184	−	0.774001i	$-0.718253\pi$
$701$		−	40.9855i		−	1.54800i	0.633184	−	0.774001i	$-0.281747\pi$
$702$		0			0
$703$	3.52678	+	22.2672i	0.133015	+	0.839825i
$704$		0			0
$705$	24.1233	+	5.36367i	0.908538	+	0.202007i
$706$		0			0
$707$	−1.49194	−	1.49194i	−0.0561101	−	0.0561101i
$708$		0			0
$709$	12.6101	−	4.09726i	0.473581	−	0.153876i	−0.0624957	−	0.998045i	$-0.519906\pi$
$709$	12.6101	−	4.09726i	0.473581	−	0.153876i	0.536076	+	0.844170i	$0.319906\pi$
$710$		0			0
$711$	−16.1180	−	14.8277i	−0.604473	−	0.556084i
$712$		0			0
$713$	13.2779	+	6.76542i	0.497261	+	0.253367i
$714$		0			0
$715$	14.7745	−	44.8599i	0.552536	−	1.67766i
$716$		0			0
$717$	7.76569	+	17.6960i	0.290015	+	0.660868i
$718$		0			0
$719$	18.6310	−	13.5362i	0.694820	−	0.504816i	−0.183421	−	0.983034i	$-0.558717\pi$
$719$	18.6310	−	13.5362i	0.694820	−	0.504816i	0.878241	+	0.478218i	$0.158717\pi$
$720$		0			0
$721$	−9.48579	−	6.89183i	−0.353269	−	0.256665i
$722$		0			0
$723$	−42.0337	−	24.5687i	−1.56325	−	0.913718i
$724$		0			0
$725$	25.3713	−	8.01979i	0.942265	−	0.297847i
$726$		0			0
$727$	−10.3618	−	20.3362i	−0.384299	−	0.754229i	0.615116	−	0.788437i	$-0.289109\pi$
$727$	−10.3618	−	20.3362i	−0.384299	−	0.754229i	−0.999415	+	0.0342075i	$0.989109\pi$
$728$		0			0
$729$	−9.16250	+	25.3978i	−0.339352	+	0.940660i
$730$		0			0
$731$	−2.28875	−	3.15019i	−0.0846523	−	0.116514i
$732$		0			0
$733$	−13.2294	−	2.09532i	−0.488638	−	0.0773926i	−0.0927459	−	0.995690i	$-0.529564\pi$
$733$	−13.2294	−	2.09532i	−0.488638	−	0.0773926i	−0.395892	+	0.918297i	$0.629564\pi$
$734$		0			0
$735$	20.4397	+	8.06601i	0.753929	+	0.297519i
$736$		0			0
$737$	−10.3227	+	20.2594i	−0.380240	+	0.746263i
$738$		0			0
$739$	15.0540	+	4.89134i	0.553770	+	0.179931i	0.572516	−	0.819894i	$-0.305967\pi$
$739$	15.0540	+	4.89134i	0.553770	+	0.179931i	−0.0187462	+	0.999824i	$0.505967\pi$
$740$		0			0
$741$	−46.5379	+	56.8456i	−1.70961	+	2.08827i
$742$		0			0
$743$	−7.06750	+	7.06750i	−0.259281	+	0.259281i	−0.824762	−	0.565480i	$-0.808691\pi$
$743$	−7.06750	+	7.06750i	−0.259281	+	0.259281i	0.565480	+	0.824762i	$0.308691\pi$
$744$		0			0
$745$	43.5707	−	21.9813i	1.59631	−	0.805332i
$746$		0			0
$747$	−3.51402	−	0.981955i	−0.128571	−	0.0359279i
$748$		0			0
$749$	−20.6917			−0.756058
$750$		0			0
$751$	−51.2590			−1.87047			−0.935234	−	0.354031i	$-0.884811\pi$
$751$	−51.2590			−1.87047			−0.935234	+	0.354031i	$0.884811\pi$
$752$		0			0
$753$	32.4132	+	36.3878i	1.18120	+	1.32604i
$754$		0			0
$755$	−15.5652	+	7.85262i	−0.566477	+	0.285786i
$756$		0			0
$757$	10.5818	−	10.5818i	0.384604	−	0.384604i	−0.488154	−	0.872758i	$-0.662330\pi$
$757$	10.5818	−	10.5818i	0.384604	−	0.384604i	0.872758	+	0.488154i	$0.162330\pi$
$758$		0			0
$759$	32.8927	+	26.9283i	1.19393	+	0.977436i
$760$		0			0
$761$	36.8728	+	11.9807i	1.33664	+	0.434300i	0.888176	−	0.459503i	$-0.151973\pi$
$761$	36.8728	+	11.9807i	1.33664	+	0.434300i	0.448460	+	0.893803i	$0.351973\pi$
$762$		0			0
$763$	4.11715	−	8.08037i	0.149051	−	0.292529i
$764$		0			0
$765$	−1.18638	−	6.01460i	−0.0428936	−	0.217458i
$766$		0			0
$767$	36.7712	+	5.82398i	1.32773	+	0.210292i
$768$		0			0
$769$	30.1156	+	41.4506i	1.08600	+	1.49475i	0.852744	+	0.522329i	$0.174937\pi$
$769$	30.1156	+	41.4506i	1.08600	+	1.49475i	0.233252	+	0.972416i	$0.425063\pi$
$770$		0			0
$771$	−31.3582	−	1.81152i	−1.12934	−	0.0652405i
$772$		0			0
$773$	10.0630	+	19.7497i	0.361940	+	0.710347i	0.998126	−	0.0611885i	$-0.0194891\pi$
$773$	10.0630	+	19.7497i	0.361940	+	0.710347i	−0.636186	+	0.771535i	$0.719489\pi$
$774$		0			0
$775$	−0.0884689	+	11.0575i	−0.00317790	+	0.397198i
$776$		0			0
$777$	3.10275	−	5.30840i	0.111311	−	0.190438i
$778$		0			0
$779$	−16.5846	−	12.0494i	−0.594206	−	0.431716i
$780$		0			0
$781$	29.4938	−	21.4285i	1.05537	−	0.766772i
$782$		0			0
$783$	0.443366	−	27.6489i	0.0158446	−	0.988092i
$784$		0			0
$785$	10.2805	−	31.2146i	0.366925	−	1.11410i
$786$		0			0
$787$	7.51983	+	3.83155i	0.268053	+	0.136580i	0.582852	−	0.812579i	$-0.301937\pi$
$787$	7.51983	+	3.83155i	0.268053	+	0.136580i	−0.314798	+	0.949159i	$0.601937\pi$
$788$		0			0
$789$	35.1444	−	9.21588i	1.25117	−	0.328094i
$790$		0			0
$791$	−20.5208	+	6.66761i	−0.729635	+	0.237073i
$792$		0			0
$793$	−55.9124	−	55.9124i	−1.98551	−	1.98551i
$794$		0			0
$795$	6.84424	−	30.7823i	0.242740	−	1.09173i
$796$		0			0
$797$	−3.19808	−	20.1919i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.x (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29334 - 1.15207i) q^{3} +(1.99640 - 1.00718i) q^{5} +(0.814380 - 0.814380i) q^{7} +(0.345460 - 2.98004i) q^{9} +O(q^{10})\)	\(q+(1.29334 - 1.15207i) q^{3} +(1.99640 - 1.00718i) q^{5} +(0.814380 - 0.814380i) q^{7} +(0.345460 - 2.98004i) q^{9} +(-3.46407 - 1.12554i) q^{11} +(-2.63271 + 5.16697i) q^{13} +(1.42168 - 3.60261i) q^{15} +(0.902627 + 0.142962i) q^{17} +(4.29919 + 5.91733i) q^{19} +(0.115046 - 1.99149i) q^{21} +(-3.05909 - 6.00381i) q^{23} +(2.97120 - 4.02144i) q^{25} +(-2.98643 - 4.25221i) q^{27} +(4.30536 + 3.12803i) q^{29} +(-1.78920 + 1.29993i) q^{31} +(-5.77692 + 2.53514i) q^{33} +(0.805601 - 2.44605i) q^{35} +(2.74637 + 1.39935i) q^{37} +(2.54774 + 9.71572i) q^{39} +(-2.66555 + 0.866089i) q^{41} +(-3.01283 - 3.01283i) q^{43} +(-2.31175 - 6.29729i) q^{45} +(0.998165 + 6.30217i) q^{47} +5.67357i q^{49} +(1.33211 - 0.854993i) q^{51} +(8.04180 - 1.27370i) q^{53} +(-8.04927 + 1.24189i) q^{55} +(12.3775 + 2.70014i) q^{57} +(-1.98388 - 6.10574i) q^{59} +(-4.21356 + 12.9680i) q^{61} +(-2.14555 - 2.70822i) q^{63} +(-0.0518720 + 12.9669i) q^{65} +(0.976557 - 6.16574i) q^{67} +(-10.8733 - 4.24068i) q^{69} +(-5.88318 + 8.09750i) q^{71} +(-8.26387 + 4.21065i) q^{73} +(-0.790225 - 8.62413i) q^{75} +(-3.73768 + 1.90445i) q^{77} +(4.29102 - 5.90609i) q^{79} +(-8.76132 - 2.05897i) q^{81} +(0.190258 - 1.20124i) q^{83} +(1.94599 - 0.623695i) q^{85} +(9.17202 - 0.914482i) q^{87} +(-3.41396 + 10.5071i) q^{89} +(2.06386 + 6.35190i) q^{91} +(-0.816433 + 3.74254i) q^{93} +(14.5427 + 7.48329i) q^{95} +(3.84712 - 0.609325i) q^{97} +(-4.55086 + 9.93423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \)	\( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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