LMFDB - Embedded newform 300.2.x.a.17.2

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			17.2
Character	$\chi$	$=$	300.17
Dual form			300.2.x.a.53.2

$q$-expansion

$f(q)$	$=$	$q+(-1.58605 + 0.696021i) q^{3} +(-1.99640 - 1.00718i) q^{5} +(0.814380 + 0.814380i) q^{7} +(2.03111 - 2.20785i) q^{9} +O(q^{10})$	\(q+(-1.58605 + 0.696021i) q^{3} +(-1.99640 - 1.00718i) q^{5} +(0.814380 + 0.814380i) q^{7} +(2.03111 - 2.20785i) q^{9} +(3.46407 - 1.12554i) q^{11} +(-2.63271 - 5.16697i) q^{13} +(3.86740 + 0.207896i) q^{15} +(-0.902627 + 0.142962i) q^{17} +(4.29919 - 5.91733i) q^{19} +(-1.85847 - 0.724821i) q^{21} +(3.05909 - 6.00381i) q^{23} +(2.97120 + 4.02144i) q^{25} +(-1.68473 + 4.91545i) q^{27} +(-4.30536 + 3.12803i) q^{29} +(-1.78920 - 1.29993i) q^{31} +(-4.71078 + 4.19623i) q^{33} +(-0.805601 - 2.44605i) q^{35} +(2.74637 - 1.39935i) q^{37} +(7.77193 + 6.36266i) q^{39} +(2.66555 + 0.866089i) q^{41} +(-3.01283 + 3.01283i) q^{43} +(-6.27859 + 2.36206i) q^{45} +(-0.998165 + 6.30217i) q^{47} -5.67357i q^{49} +(1.33211 - 0.854993i) q^{51} +(-8.04180 - 1.27370i) q^{53} +(-8.04927 - 1.24189i) q^{55} +(-2.70014 + 12.3775i) q^{57} +(1.98388 - 6.10574i) q^{59} +(-4.21356 - 12.9680i) q^{61} +(3.45212 - 0.143935i) q^{63} +(0.0518720 + 12.9669i) q^{65} +(0.976557 + 6.16574i) q^{67} +(-0.673095 + 11.6515i) q^{69} +(5.88318 + 8.09750i) q^{71} +(-8.26387 - 4.21065i) q^{73} +(-7.51147 - 4.31019i) q^{75} +(3.73768 + 1.90445i) q^{77} +(4.29102 + 5.90609i) q^{79} +(-0.749199 - 8.96876i) q^{81} +(-0.190258 - 1.20124i) q^{83} +(1.94599 + 0.623695i) q^{85} +(4.65135 - 7.95784i) q^{87} +(3.41396 + 10.5071i) q^{89} +(2.06386 - 6.35190i) q^{91} +(3.74254 + 0.816433i) q^{93} +(-14.5427 + 7.48329i) q^{95} +(3.84712 + 0.609325i) q^{97} +(4.55086 - 9.93423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{20}\right)$

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
$3$	−1.58605	+	0.696021i	−0.915706	+	0.401848i
$3$	−1.58605	+	0.696021i	−0.915706	+	0.401848i
$4$		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	0.844058	−	0.536252i	$-0.180160\pi$
$7$	0.814380	+	0.814380i	0.307807	+	0.307807i	−0.536252	+	0.844058i	$0.680160\pi$
$8$		0			0
$9$	2.03111	−	2.20785i	0.677036	−	0.735950i
$10$		0			0
$11$	3.46407	−	1.12554i	1.04446	−	0.339364i	0.263965	−	0.964532i	$-0.414970\pi$
$11$	3.46407	−	1.12554i	1.04446	−	0.339364i	0.780490	+	0.625168i	$0.214970\pi$
$12$		0			0
$13$	−2.63271	−	5.16697i	−0.730181	−	1.43306i	−0.894691	−	0.446686i	$-0.852604\pi$
$13$	−2.63271	−	5.16697i	−0.730181	−	1.43306i	0.164510	−	0.986375i	$-0.447396\pi$
$14$		0			0
$15$	3.86740	+	0.207896i	0.998558	+	0.0536785i
$16$		0			0
$17$	−0.902627	+	0.142962i	−0.218919	+	0.0346734i	−0.264930	−	0.964268i	$-0.585349\pi$
$17$	−0.902627	+	0.142962i	−0.218919	+	0.0346734i	0.0460112	+	0.998941i	$0.485349\pi$
$18$		0			0
$19$	4.29919	−	5.91733i	0.986302	−	1.35753i	0.0529373	−	0.998598i	$-0.483142\pi$
$19$	4.29919	−	5.91733i	0.986302	−	1.35753i	0.933364	−	0.358930i	$-0.116858\pi$
$20$		0			0
$21$	−1.85847	−	0.724821i	−0.405552	−	0.158169i
$22$		0			0
$23$	3.05909	−	6.00381i	0.637865	−	1.25188i	−0.315174	−	0.949034i	$-0.602063\pi$
$23$	3.05909	−	6.00381i	0.637865	−	1.25188i	0.953039	−	0.302847i	$-0.0979372\pi$
$24$		0			0
$25$	2.97120	+	4.02144i	0.594239	+	0.804289i
$26$		0			0
$27$	−1.68473	+	4.91545i	−0.324226	+	0.945980i
$28$		0			0
$29$	−4.30536	+	3.12803i	−0.799486	+	0.580861i	−0.910763	−	0.412929i	$-0.864506\pi$
$29$	−4.30536	+	3.12803i	−0.799486	+	0.580861i	0.111277	+	0.993789i	$0.464506\pi$
$30$		0			0
$31$	−1.78920	−	1.29993i	−0.321350	−	0.233475i	0.415401	−	0.909638i	$-0.363641\pi$
$31$	−1.78920	−	1.29993i	−0.321350	−	0.233475i	−0.736751	+	0.676164i	$0.763641\pi$
$32$		0			0
$33$	−4.71078	+	4.19623i	−0.820041	+	0.730470i
$34$		0			0
$35$	−0.805601	−	2.44605i	−0.136171	−	0.413458i
$36$		0			0
$37$	2.74637	−	1.39935i	0.451501	−	0.230051i	−0.213427	−	0.976959i	$-0.568462\pi$
$37$	2.74637	−	1.39935i	0.451501	−	0.230051i	0.664927	+	0.746908i	$0.268462\pi$
$38$		0			0
$39$	7.77193	+	6.36266i	1.24450	+	1.01884i
$40$		0			0
$41$	2.66555	+	0.866089i	0.416289	+	0.135260i	0.509670	−	0.860370i	$-0.329768\pi$
$41$	2.66555	+	0.866089i	0.416289	+	0.135260i	−0.0933813	+	0.995630i	$0.529768\pi$
$42$		0			0
$43$	−3.01283	+	3.01283i	−0.459453	+	0.459453i	−0.898476	−	0.439023i	$-0.855325\pi$
$43$	−3.01283	+	3.01283i	−0.459453	+	0.459453i	0.439023	+	0.898476i	$0.355325\pi$
$44$		0			0
$45$	−6.27859	+	2.36206i	−0.935957	+	0.352115i
$46$		0			0
$47$	−0.998165	+	6.30217i	−0.145597	+	0.919265i	0.801424	+	0.598096i	$0.204076\pi$
$47$	−0.998165	+	6.30217i	−0.145597	+	0.919265i	−0.947022	+	0.321169i	$0.895924\pi$
$48$		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	$-0.638891\pi$
$53$	−8.04180	−	1.27370i	−1.10463	−	0.174956i	−0.682002	+	0.731350i	$0.738891\pi$
$54$		0			0
$55$	−8.04927	−	1.24189i	−1.08536	−	0.167457i
$56$		0			0
$57$	−2.70014	+	12.3775i	−0.357643	+	1.63944i
$58$		0			0
$59$	1.98388	−	6.10574i	0.258279	−	0.794900i	−0.734887	−	0.678189i	$-0.762765\pi$
$59$	1.98388	−	6.10574i	0.258279	−	0.794900i	0.993166	−	0.116711i	$-0.0372350\pi$
$60$		0			0
$61$	−4.21356	−	12.9680i	−0.539492	−	1.66038i	−0.733739	−	0.679432i	$-0.762226\pi$
$61$	−4.21356	−	12.9680i	−0.539492	−	1.66038i	0.194247	−	0.980953i	$-0.437774\pi$
$62$		0			0
$63$	3.45212	−	0.143935i	0.434926	−	0.0181341i
$64$		0			0
$65$	0.0518720	+	12.9669i	0.00643393	+	1.60835i
$66$		0			0
$67$	0.976557	+	6.16574i	0.119305	+	0.753265i	0.972712	+	0.232018i	$0.0745328\pi$
$67$	0.976557	+	6.16574i	0.119305	+	0.753265i	−0.853406	+	0.521247i	$0.825467\pi$
$68$		0			0
$69$	−0.673095	+	11.6515i	−0.0810311	+	1.40268i
$70$		0			0
$71$	5.88318	+	8.09750i	0.698205	+	0.960996i	0.999971	+	0.00761427i	$0.00242372\pi$
$71$	5.88318	+	8.09750i	0.698205	+	0.960996i	−0.301766	+	0.953382i	$0.597576\pi$
$72$		0			0
$73$	−8.26387	−	4.21065i	−0.967212	−	0.492819i	−0.102306	−	0.994753i	$-0.532622\pi$
$73$	−8.26387	−	4.21065i	−0.967212	−	0.492819i	−0.864906	+	0.501934i	$0.832622\pi$
$74$		0			0
$75$	−7.51147	−	4.31019i	−0.867350	−	0.497698i
$76$		0			0
$77$	3.73768	+	1.90445i	0.425949	+	0.217032i
$78$		0			0
$79$	4.29102	+	5.90609i	0.482778	+	0.664487i	0.979036	−	0.203689i	$-0.0652930\pi$
$79$	4.29102	+	5.90609i	0.482778	+	0.664487i	−0.496258	+	0.868175i	$0.665293\pi$
$80$		0			0
$81$	−0.749199	−	8.96876i	−0.0832444	−	0.996529i
$82$		0			0
$83$	−0.190258	−	1.20124i	−0.0208835	−	0.131853i	0.975044	−	0.222012i	$-0.0712625\pi$
$83$	−0.190258	−	1.20124i	−0.0208835	−	0.131853i	−0.995927	+	0.0901590i	$0.971262\pi$
$84$		0			0
$85$	1.94599	+	0.623695i	0.211072	+	0.0676492i
$86$		0			0
$87$	4.65135	−	7.95784i	0.498677	−	0.853170i
$88$		0			0
$89$	3.41396	+	10.5071i	0.361879	+	1.11375i	0.951913	+	0.306369i	$0.0991143\pi$
$89$	3.41396	+	10.5071i	0.361879	+	1.11375i	−0.590034	+	0.807378i	$0.700886\pi$
$90$		0			0
$91$	2.06386	−	6.35190i	0.216351	−	0.665860i
$92$		0			0
$93$	3.74254	+	0.816433i	0.388084	+	0.0846602i
$94$		0			0
$95$	−14.5427	+	7.48329i	−1.49205	+	0.767769i
$96$		0			0
$97$	3.84712	+	0.609325i	0.390616	+	0.0618675i	0.348654	−	0.937252i	$-0.386639\pi$
$97$	3.84712	+	0.609325i	0.390616	+	0.0618675i	0.0419626	+	0.999119i	$0.486639\pi$
$98$		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	0.776009	+	0.630722i	$0.217241\pi$
$103$	−1.59260	+	10.0553i	−0.156923	+	0.990775i	−0.932932	+	0.360053i	$0.882759\pi$
$104$		0			0
$105$	2.98023	+	3.31884i	0.290840	+	0.323885i
$106$		0			0
$107$	12.7040	−	12.7040i	1.22814	−	1.22814i	0.263470	−	0.964668i	$-0.415133\pi$
$107$	12.7040	−	12.7040i	1.22814	−	1.22814i	0.964668	−	0.263470i	$-0.0848669\pi$
$108$		0			0
$109$	7.48884	+	2.43327i	0.717301	+	0.233065i	0.644853	−	0.764307i	$-0.276919\pi$
$109$	7.48884	+	2.43327i	0.717301	+	0.233065i	0.0724482	+	0.997372i	$0.476919\pi$
$110$		0			0
$111$	−3.38191	+	4.13097i	−0.320996	+	0.392094i
$112$		0			0
$113$	16.6927	−	8.50535i	1.57032	−	0.800116i	0.570540	−	0.821270i	$-0.306734\pi$
$113$	16.6927	−	8.50535i	1.57032	−	0.800116i	0.999776	+	0.0211535i	$0.00673389\pi$
$114$		0			0
$115$	−12.1541	+	8.90494i	−1.13337	+	0.830390i
$116$		0			0
$117$	−16.7552	−	4.68207i	−1.54902	−	0.432857i
$118$		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
$123$	−4.83051	+	0.481618i	−0.435552	+	0.0434261i
$124$		0			0
$125$	−1.88138	−	11.0209i	−0.168276	−	0.985740i
$126$		0			0
$127$	3.30459	−	6.48562i	0.293235	−	0.575505i	−0.696645	−	0.717416i	$-0.745325\pi$
$127$	3.30459	−	6.48562i	0.293235	−	0.575505i	0.989879	+	0.141911i	$0.0453246\pi$
$128$		0			0
$129$	2.68151	−	6.87550i	0.236094	−	0.605354i
$130$		0			0
$131$	−3.48009	+	4.78993i	−0.304057	+	0.418498i	−0.933516	−	0.358535i	$-0.883276\pi$
$131$	−3.48009	+	4.78993i	−0.304057	+	0.418498i	0.629460	+	0.777033i	$0.283276\pi$
$132$		0			0
$133$	8.32012	−	1.31778i	0.721446	−	0.114266i
$134$		0			0
$135$	8.31411	−	8.11638i	0.715565	−	0.698547i
$136$		0			0
$137$	−2.92241	−	5.73556i	−0.249679	−	0.490022i	0.731818	−	0.681500i	$-0.238672\pi$
$137$	−2.92241	−	5.73556i	−0.249679	−	0.490022i	−0.981497	+	0.191478i	$0.938672\pi$
$138$		0			0
$139$	−2.67670	+	0.869713i	−0.227035	+	0.0737681i	−0.420325	−	0.907373i	$-0.638084\pi$
$139$	−2.67670	+	0.869713i	−0.227035	+	0.0737681i	0.193290	+	0.981142i	$0.438084\pi$
$140$		0			0
$141$	−2.80330	−	10.6903i	−0.236081	−	0.900285i
$142$		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
$147$	3.94893	+	8.99857i	0.325702	+	0.742189i
$148$		0			0
$149$	−21.8247			−1.78795			−0.893974	−	0.448119i	$-0.852094\pi$
$149$	−21.8247			−1.78795			−0.893974	+	0.448119i	$0.852094\pi$
$150$		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
$153$	−1.51770	+	2.28324i	−0.122698	+	0.184589i
$154$		0			0
$155$	2.26270	+	4.39722i	0.181744	+	0.353193i
$156$		0			0
$157$	10.3925	+	10.3925i	0.829410	+	0.829410i	0.987435	−	0.158025i	$-0.0505126\pi$
$157$	10.3925	+	10.3925i	0.829410	+	0.829410i	−0.158025	+	0.987435i	$0.550513\pi$
$158$		0			0
$159$	13.6412	−	3.57712i	1.08182	−	0.283684i
$160$		0			0
$161$	7.38065	−	2.39812i	0.581677	−	0.188998i
$162$		0			0
$163$	3.53766	+	6.94305i	0.277091	+	0.543822i	0.987048	−	0.160423i	$-0.0512859\pi$
$163$	3.53766	+	6.94305i	0.277091	+	0.543822i	−0.709957	+	0.704245i	$0.751286\pi$
$164$		0			0
$165$	13.6309	−	3.63276i	1.06117	−	0.282810i
$166$		0			0
$167$	−0.370295	+	0.0586489i	−0.0286543	+	0.00453839i	−0.170745	−	0.985315i	$-0.554617\pi$
$167$	−0.370295	+	0.0586489i	−0.0286543	+	0.00453839i	0.142091	+	0.989854i	$0.454617\pi$
$168$		0			0
$169$	−12.1253	+	16.6890i	−0.932714	+	1.28377i
$170$		0			0
$171$	−4.33245	−	21.5107i	−0.331311	−	1.64496i
$172$		0			0
$173$	5.57182	−	10.9353i	0.423618	−	0.831397i	−0.576282	−	0.817251i	$-0.695497\pi$
$173$	5.57182	−	10.9353i	0.423618	−	0.831397i	0.999900	−	0.0141460i	$-0.00450296\pi$
$174$		0			0
$175$	−0.855300	+	5.69466i	−0.0646546	+	0.430476i
$176$		0			0
$177$	1.10320	+	11.0648i	0.0829217	+	0.831684i
$178$		0			0
$179$	−4.46475	+	3.24383i	−0.333711	+	0.242455i	−0.742004	−	0.670396i	$-0.766124\pi$
$179$	−4.46475	+	3.24383i	−0.333711	+	0.242455i	0.408293	+	0.912851i	$0.366124\pi$
$180$		0			0
$181$	8.04985	+	5.84856i	0.598340	+	0.434720i	0.845289	−	0.534309i	$-0.179428\pi$
$181$	8.04985	+	5.84856i	0.598340	+	0.434720i	−0.246949	+	0.969028i	$0.579428\pi$
$182$		0			0
$183$	15.7089	+	17.6352i	1.16124	+	1.30363i
$184$		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
$189$	−5.37506	+	2.63104i	−0.390978	+	0.191380i
$190$		0			0
$191$	9.80442	+	3.18565i	0.709423	+	0.230505i	0.641431	−	0.767181i	$-0.278341\pi$
$191$	9.80442	+	3.18565i	0.709423	+	0.230505i	0.0679914	+	0.997686i	$0.478341\pi$
$192$		0			0
$193$	−0.238354	+	0.238354i	−0.0171571	+	0.0171571i	−0.715633	−	0.698476i	$-0.753862\pi$
$193$	−0.238354	+	0.238354i	−0.0171571	+	0.0171571i	0.698476	+	0.715633i	$0.253862\pi$
$194$		0			0
$195$	−9.10753	−	20.5301i	−0.652204	−	1.47019i
$196$		0			0
$197$	−0.296468	+	1.87183i	−0.0211225	+	0.133362i	−0.995996	−	0.0893965i	$-0.971506\pi$
$197$	−0.296468	+	1.87183i	−0.0211225	+	0.133362i	0.974874	+	0.222759i	$0.0715062\pi$
$198$		0			0
$199$		−	18.6398i		−	1.32134i	−0.750676	−	0.660670i	$-0.770272\pi$
$199$		−	18.6398i		−	1.32134i	0.750676	−	0.660670i	$-0.229728\pi$
$200$		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
$207$	−7.04216	−	18.9484i	−0.489464	−	1.31701i
$208$		0			0
$209$	8.23247	−	25.3369i	0.569452	−	1.75259i
$210$		0			0
$211$	7.77153	+	23.9183i	0.535014	+	1.64660i	0.743618	+	0.668604i	$0.233108\pi$
$211$	7.77153	+	23.9183i	0.535014	+	1.64660i	−0.208604	+	0.978000i	$0.566892\pi$
$212$		0			0
$213$	−14.9670	−	8.74822i	−1.02552	−	0.599418i
$214$		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
$219$	16.0376	+	0.926472i	1.08372	+	0.0626052i
$220$		0			0
$221$	3.11503	+	4.28748i	0.209540	+	0.288407i
$222$		0			0
$223$	4.28530	+	2.18347i	0.286965	+	0.146216i	0.591548	−	0.806270i	$-0.298517\pi$
$223$	4.28530	+	2.18347i	0.286965	+	0.146216i	−0.304583	+	0.952486i	$0.598517\pi$
$224$		0			0
$225$	14.9136	+	1.60803i	0.994237	+	0.107202i
$226$		0			0
$227$	11.3411	+	5.77860i	0.752738	+	0.383539i	0.787868	−	0.615844i	$-0.211185\pi$
$227$	11.3411	+	5.77860i	0.752738	+	0.383539i	−0.0351307	+	0.999383i	$0.511185\pi$
$228$		0			0
$229$	0.0954879	+	0.131428i	0.00631002	+	0.00868500i	0.812160	−	0.583434i	$-0.198291\pi$
$229$	0.0954879	+	0.131428i	0.00631002	+	0.00868500i	−0.805850	+	0.592119i	$0.798291\pi$
$230$		0			0
$231$	−7.25369	−	0.419037i	−0.477258	−	0.0275706i
$232$		0			0
$233$	0.939042	+	5.92888i	0.0615187	+	0.388414i	0.999166	+	0.0408262i	$0.0129990\pi$
$233$	0.939042	+	5.92888i	0.0615187	+	0.388414i	−0.937648	+	0.347587i	$0.887001\pi$
$234$		0			0
$235$	8.34012	−	11.5763i	0.544049	−	0.755154i
$236$		0			0
$237$	−10.9165	−	6.38070i	−0.709105	−	0.414471i
$238$		0			0
$239$	3.44778	+	10.6112i	0.223019	+	0.686380i	0.998487	+	0.0549938i	$0.0175139\pi$
$239$	3.44778	+	10.6112i	0.223019	+	0.686380i	−0.775468	+	0.631387i	$0.782486\pi$
$240$		0			0
$241$	−8.68635	+	26.7338i	−0.559537	+	1.72208i	0.124114	+	0.992268i	$0.460391\pi$
$241$	−8.68635	+	26.7338i	−0.559537	+	1.72208i	−0.683650	+	0.729810i	$0.739609\pi$
$242$		0			0
$243$	7.43072	+	13.7034i	0.476681	+	0.879076i
$244$		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
$255$	−3.52054	+	0.365239i	−0.220465	+	0.0228722i
$256$		0			0
$257$	12.8233	−	12.8233i	0.799894	−	0.799894i	−0.183184	−	0.983079i	$-0.558641\pi$
$257$	12.8233	−	12.8233i	0.799894	−	0.799894i	0.983079	+	0.183184i	$0.0586405\pi$
$258$		0			0
$259$	3.37619	+	1.09699i	0.209786	+	0.0681637i
$260$		0			0
$261$	−1.83844	+	15.8590i	−0.113797	+	0.981645i
$262$		0			0
$263$	−18.6904	+	9.52321i	−1.15250	+	0.587226i	−0.922512	−	0.385968i	$-0.873868\pi$
$263$	−18.6904	+	9.52321i	−1.15250	+	0.587226i	−0.229984	+	0.973194i	$0.573868\pi$
$264$		0			0
$265$	14.7718	+	10.6423i	0.907423	+	0.653751i
$266$		0			0
$267$	−12.7279	−	14.2886i	−0.778932	−	0.874446i
$268$		0			0
$269$	−10.9550	−	7.95929i	−0.667940	−	0.485287i	0.201395	−	0.979510i	$-0.435452\pi$
$269$	−10.9550	−	7.95929i	−0.667940	−	0.485287i	−0.869335	+	0.494223i	$0.835452\pi$
$270$		0			0
$271$	1.95011	−	1.41684i	0.118461	−	0.0860669i	−0.526977	−	0.849879i	$-0.676675\pi$
$271$	1.95011	−	1.41684i	0.118461	−	0.0860669i	0.645438	+	0.763812i	$0.276675\pi$
$272$		0			0
$273$	1.14768	+	11.5109i	0.0694607	+	0.696673i
$274$		0			0
$275$	14.8187	+	10.5863i	0.893602	+	0.638380i
$276$		0			0
$277$	−4.61588	+	9.05917i	−0.277341	+	0.544313i	−0.987095	−	0.160137i	$-0.948806\pi$
$277$	−4.61588	+	9.05917i	−0.277341	+	0.544313i	0.709753	+	0.704450i	$0.248806\pi$
$278$		0			0
$279$	−6.50412	+	1.30999i	−0.389391	+	0.0784269i
$280$		0			0
$281$	3.75864	−	5.17333i	0.224222	−	0.308615i	−0.682054	−	0.731302i	$-0.738913\pi$
$281$	3.75864	−	5.17333i	0.224222	−	0.308615i	0.906276	+	0.422687i	$0.138913\pi$
$282$		0			0
$283$	−12.2845	+	1.94568i	−0.730239	+	0.115658i	−0.510472	−	0.859894i	$-0.670529\pi$
$283$	−12.2845	+	1.94568i	−0.730239	+	0.115658i	−0.219766	+	0.975553i	$0.570529\pi$
$284$		0			0
$285$	17.8569	−	21.9909i	1.05775	−	1.30263i
$286$		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
$291$	−6.52583	+	1.71126i	−0.382551	+	0.100316i
$292$		0			0
$293$	20.0058	+	20.0058i	1.16875	+	1.16875i	0.982503	+	0.186248i	$0.0596329\pi$
$293$	20.0058	+	20.0058i	1.16875	+	1.16875i	0.186248	+	0.982503i	$0.440367\pi$
$294$		0			0
$295$	−10.1102	+	10.1914i	−0.588636	+	0.593364i
$296$		0			0
$297$	−0.303452	+	18.9237i	−0.0176081	+	1.09806i
$298$		0			0
$299$	−39.0752			−2.25978
$300$		0			0
$301$	−4.90718			−0.282845
$302$		0			0
$303$	1.27511	+	2.90563i	0.0732529	+	0.166924i
$304$		0			0
$305$	−4.64913	+	30.1331i	−0.266208	+	1.72542i
$306$		0			0
$307$	1.67900	+	1.67900i	0.0958255	+	0.0958255i	0.753394	−	0.657569i	$-0.228415\pi$
$307$	1.67900	+	1.67900i	0.0958255	+	0.0958255i	−0.657569	+	0.753394i	$0.728415\pi$
$308$		0			0
$309$	−4.47274	−	17.0566i	−0.254445	−	0.970318i
$310$		0			0
$311$	−16.6707	+	5.41664i	−0.945310	+	0.307150i	−0.740808	−	0.671717i	$-0.765557\pi$
$311$	−16.6707	+	5.41664i	−0.945310	+	0.307150i	−0.204501	+	0.978866i	$0.565557\pi$
$312$		0			0
$313$	7.60246	+	14.9207i	0.429716	+	0.843366i	0.999763	+	0.0217538i	$0.00692499\pi$
$313$	7.60246	+	14.9207i	0.429716	+	0.843366i	−0.570047	+	0.821612i	$0.693075\pi$
$314$		0			0
$315$	−7.03677	−	3.18954i	−0.396477	−	0.179710i
$316$		0			0
$317$	10.0629	−	1.59380i	0.565187	−	0.0895168i	0.132699	−	0.991156i	$-0.457636\pi$
$317$	10.0629	−	1.59380i	0.565187	−	0.0895168i	0.432488	+	0.901640i	$0.357636\pi$
$318$		0			0
$319$	−11.3933	+	15.6816i	−0.637904	+	0.878000i
$320$		0			0
$321$	−11.3069	+	28.9913i	−0.631088	+	1.61814i
$322$		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
$327$	−13.5713	+	1.35310i	−0.750494	+	0.0748268i
$328$		0			0
$329$	−5.94524	+	4.31947i	−0.327772	+	0.238140i
$330$		0			0
$331$	21.8809	+	15.8974i	1.20268	+	0.873801i	0.994546	−	0.104298i	$-0.0332597\pi$
$331$	21.8809	+	15.8974i	1.20268	+	0.873801i	0.208138	+	0.978099i	$0.433260\pi$
$332$		0			0
$333$	2.48863	−	8.90580i	0.136376	−	0.488035i
$334$		0			0
$335$	4.26038	−	13.2928i	0.232770	−	0.726264i
$336$		0			0
$337$	13.4244	−	6.84007i	0.731273	−	0.372602i	−0.0483675	−	0.998830i	$-0.515402\pi$
$337$	13.4244	−	6.84007i	0.731273	−	0.372602i	0.779640	+	0.626227i	$0.215402\pi$
$338$		0			0
$339$	−20.5555	+	25.1084i	−1.11642	+	1.36370i
$340$		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
$345$	13.0789	−	22.5832i	0.704145	−	1.21584i
$346$		0			0
$347$	1.70896	−	10.7899i	0.0917415	−	0.579233i	−0.898402	−	0.439175i	$-0.855271\pi$
$347$	1.70896	−	10.7899i	0.0917415	−	0.579233i	0.990143	−	0.140059i	$-0.0447291\pi$
$348$		0			0
$349$			4.93794i			0.264322i	0.991228	+	0.132161i	$0.0421916\pi$
$349$			4.93794i			0.264322i	−0.991228	+	0.132161i	$0.957808\pi$
$350$		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	$-0.424564\pi$
$353$	2.96257	+	0.469225i	0.157682	+	0.0249744i	−0.0770944	+	0.997024i	$0.524564\pi$
$354$		0			0
$355$	−3.58955	−	22.0912i	−0.190513	−	1.17248i
$356$		0			0
$357$	1.78113	+	0.388552i	0.0942674	+	0.0205644i
$358$		0			0
$359$	9.84389	−	30.2964i	0.519540	−	1.59898i	−0.255325	−	0.966855i	$-0.582183\pi$
$359$	9.84389	−	30.2964i	0.519540	−	1.59898i	0.774866	−	0.632126i	$-0.217817\pi$
$360$		0			0
$361$	−10.6604	−	32.8093i	−0.561074	−	1.72681i
$362$		0			0
$363$	−1.98107	+	3.38935i	−0.103979	+	0.177895i
$364$		0			0
$365$	12.2571	+	16.7293i	0.641565	+	0.875651i
$366$		0			0
$367$	−4.72166	−	29.8114i	−0.246469	−	1.55614i	−0.731621	−	0.681712i	$-0.761236\pi$
$367$	−4.72166	−	29.8114i	−0.246469	−	1.55614i	0.485152	−	0.874430i	$-0.338764\pi$
$368$		0			0
$369$	7.32621	−	4.12601i	0.381387	−	0.214791i
$370$		0			0
$371$	−5.51180	−	7.58635i	−0.286159	−	0.393864i
$372$		0			0
$373$	17.7102	+	9.02378i	0.916998	+	0.467234i	0.847768	−	0.530367i	$-0.177946\pi$
$373$	17.7102	+	9.02378i	0.916998	+	0.467234i	0.0692297	+	0.997601i	$0.477946\pi$
$374$		0			0
$375$	10.6548	+	16.1702i	0.550209	+	0.835027i
$376$		0			0
$377$	27.4972	+	14.0105i	1.41618	+	0.721579i
$378$		0			0
$379$	−8.60609	−	11.8453i	−0.442065	−	0.608450i	0.528604	−	0.848868i	$-0.322716\pi$
$379$	−8.60609	−	11.8453i	−0.442065	−	0.608450i	−0.970669	+	0.240418i	$0.922716\pi$
$380$		0			0
$381$	−0.727111	+	12.5866i	−0.0372510	+	0.644830i
$382$		0			0
$383$	−4.01050	−	25.3213i	−0.204927	−	1.29386i	−0.848795	−	0.528722i	$-0.822671\pi$
$383$	−4.01050	−	25.3213i	−0.204927	−	1.29386i	0.643868	−	0.765137i	$-0.277329\pi$
$384$		0			0
$385$	−5.54379	−	7.56653i	−0.282538	−	0.385626i
$386$		0			0
$387$	0.532493	+	12.7713i	0.0270681	+	0.649200i
$388$		0			0
$389$	−3.42204	−	10.5320i	−0.173504	−	0.533991i	0.826058	−	0.563586i	$-0.190578\pi$
$389$	−3.42204	−	10.5320i	−0.173504	−	0.533991i	−0.999562	+	0.0295942i	$0.990578\pi$
$390$		0			0
$391$	−1.90291	+	5.85654i	−0.0962341	+	0.296178i
$392$		0			0
$393$	2.18570	−	10.0193i	0.110254	−	0.505406i
$394$		0			0
$395$	−2.61812	−	16.1127i	−0.131732	−	0.810718i
$396$		0			0
$397$	−34.8560	−	5.52065i	−1.74937	−	0.277074i	−0.802029	−	0.597286i	$-0.796246\pi$
$397$	−34.8560	−	5.52065i	−1.74937	−	0.277074i	−0.947346	+	0.320212i	$0.896246\pi$
$398$		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
$405$	−7.53742	+	18.6598i	−0.374537	+	0.927212i
$406$		0			0
$407$	7.93859	−	7.93859i	0.393501	−	0.393501i
$408$		0			0
$409$	15.1592	+	4.92552i	0.749574	+	0.243551i	0.658798	−	0.752320i	$-0.271065\pi$
$409$	15.1592	+	4.92552i	0.749574	+	0.243551i	0.0907761	+	0.995871i	$0.471065\pi$
$410$		0			0
$411$	8.62717	+	7.06282i	0.425547	+	0.348383i
$412$		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
$417$	3.64004	−	3.24245i	0.178254	−	0.158784i
$418$		0			0
$419$	28.4906	+	20.6996i	1.39186	+	1.01124i	0.995659	+	0.0930769i	$0.0296702\pi$
$419$	28.4906	+	20.6996i	1.39186	+	1.01124i	0.396197	+	0.918166i	$0.370330\pi$
$420$		0			0
$421$	−1.21908	+	0.885714i	−0.0594143	+	0.0431670i	−0.617096	−	0.786888i	$-0.711691\pi$
$421$	−1.21908	+	0.885714i	−0.0594143	+	0.0431670i	0.557682	+	0.830055i	$0.311691\pi$
$422$		0			0
$423$	11.8869	+	15.0042i	0.577959	+	0.729528i
$424$		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
$429$	34.0839	+	13.2930i	1.64559	+	0.641794i
$430$		0			0
$431$	−3.75782	+	5.17220i	−0.181008	+	0.249136i	−0.889873	−	0.456208i	$-0.849207\pi$
$431$	−3.75782	+	5.17220i	−0.181008	+	0.249136i	0.708865	+	0.705344i	$0.249207\pi$
$432$		0			0
$433$	22.5721	−	3.57506i	1.08474	−	0.171807i	0.411634	−	0.911349i	$-0.364958\pi$
$433$	22.5721	−	3.57506i	1.08474	−	0.171807i	0.673110	+	0.739542i	$0.264958\pi$
$434$		0			0
$435$	−17.3009	+	11.2023i	−0.829513	+	0.537108i
$436$		0			0
$437$	−22.3749	−	43.9132i	−1.07034	−	2.10065i
$438$		0			0
$439$	−1.74365	+	0.566545i	−0.0832197	+	0.0270397i	−0.350331	−	0.936626i	$-0.613931\pi$
$439$	−1.74365	+	0.566545i	−0.0832197	+	0.0270397i	0.267111	+	0.963666i	$0.413931\pi$
$440$		0			0
$441$	−12.5264	−	11.5236i	−0.596495	−	0.548745i
$442$		0			0
$443$	−6.75410	−	6.75410i	−0.320897	−	0.320897i	0.528214	−	0.849111i	$-0.322862\pi$
$443$	−6.75410	−	6.75410i	−0.320897	−	0.320897i	−0.849111	+	0.528214i	$0.822862\pi$
$444$		0			0
$445$	3.76686	−	24.4147i	0.178566	−	1.15737i
$446$		0			0
$447$	34.6150	−	15.1905i	1.63724	−	0.718484i
$448$		0			0
$449$	−24.0642			−1.13566			−0.567830	−	0.823146i	$-0.692217\pi$
$449$	−24.0642			−1.13566			−0.567830	+	0.823146i	$0.692217\pi$
$450$		0			0
$451$	10.2085			0.480697
$452$		0			0
$453$	12.3659	−	5.42665i	0.581001	−	0.254966i
$454$		0			0
$455$	−10.5178	+	10.6022i	−0.493080	+	0.497041i
$456$		0			0
$457$	15.7146	+	15.7146i	0.735097	+	0.735097i	0.971625	−	0.236528i	$-0.0760095\pi$
$457$	15.7146	+	15.7146i	0.735097	+	0.735097i	−0.236528	+	0.971625i	$0.576010\pi$
$458$		0			0
$459$	0.817958	−	4.67768i	0.0381790	−	0.218335i
$460$		0			0
$461$	−8.27650	+	2.68920i	−0.385475	+	0.125248i	−0.495342	−	0.868698i	$-0.664957\pi$
$461$	−8.27650	+	2.68920i	−0.385475	+	0.125248i	0.109867	+	0.993946i	$0.464957\pi$
$462$		0			0
$463$	−6.79566	−	13.3372i	−0.315821	−	0.619834i	0.677460	−	0.735560i	$-0.263081\pi$
$463$	−6.79566	−	13.3372i	−0.315821	−	0.619834i	−0.993281	+	0.115726i	$0.963081\pi$
$464$		0			0
$465$	−6.64931	−	5.39932i	−0.308354	−	0.250388i
$466$		0			0
$467$	−32.4831	+	5.14481i	−1.50314	+	0.238074i	−0.853067	−	0.521801i	$-0.825261\pi$
$467$	−32.4831	+	5.14481i	−1.50314	+	0.238074i	−0.650070	+	0.759874i	$0.725261\pi$
$468$		0			0
$469$	−4.22596	+	5.81654i	−0.195137	+	0.268583i
$470$		0			0
$471$	−23.7164	−	9.24960i	−1.09279	−	0.426199i
$472$		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
$477$	−19.1459	+	15.1681i	−0.876630	+	0.694498i
$478$		0			0
$479$	22.4708	−	16.3260i	1.02672	−	0.745953i	0.0590677	−	0.998254i	$-0.481187\pi$
$479$	22.4708	−	16.3260i	1.02672	−	0.745953i	0.967649	+	0.252301i	$0.0811872\pi$
$480$		0			0
$481$	−14.4608	−	10.5064i	−0.659355	−	0.479049i
$482$		0			0
$483$	−10.0369	+	8.94062i	−0.456696	+	0.406812i
$484$		0			0
$485$	−7.06669	−	5.09118i	−0.320882	−	0.231179i
$486$		0			0
$487$	28.0023	−	14.2679i	1.26891	−	0.646540i	0.315700	−	0.948859i	$-0.397761\pi$
$487$	28.0023	−	14.2679i	1.26891	−	0.646540i	0.953207	+	0.302319i	$0.0977607\pi$
$488$		0			0
$489$	−10.4434	−	8.54973i	−0.472268	−	0.386632i
$490$		0			0
$491$	11.6547	+	3.78683i	0.525968	+	0.170897i	0.559952	−	0.828525i	$-0.310820\pi$
$491$	11.6547	+	3.78683i	0.525968	+	0.170897i	−0.0339840	+	0.999422i	$0.510820\pi$
$492$		0			0
$493$	3.43895	−	3.43895i	0.154883	−	0.154883i
$494$		0			0
$495$	−19.0908	+	15.2492i	−0.858069	+	0.685398i
$496$		0			0
$497$	−1.80330	+	11.3856i	−0.0808890	+	0.510713i
$498$		0			0
$499$		−	2.58376i		−	0.115665i	−0.998326	−	0.0578324i	$-0.981581\pi$
$499$		−	2.58376i		−	0.115665i	0.998326	−	0.0578324i	$-0.0184189\pi$
$500$		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	$-0.215772\pi$
$503$	29.7370	+	4.70988i	1.32591	+	0.210003i	0.546995	+	0.837136i	$0.315772\pi$
$504$		0			0
$505$	−1.84514	+	3.65738i	−0.0821076	+	0.162751i
$506$		0			0
$507$	7.61539	−	34.9091i	0.338211	−	1.55037i
$508$		0			0
$509$	−10.5395	+	32.4372i	−0.467155	+	1.43776i	0.389097	+	0.921197i	$0.372787\pi$
$509$	−10.5395	+	32.4372i	−0.467155	+	1.43776i	−0.856252	+	0.516559i	$0.827213\pi$
$510$		0			0
$511$	−3.30086	−	10.1590i	−0.146021	−	0.449407i
$512$		0			0
$513$	21.8434	+	31.1016i	0.964409	+	1.37317i
$514$		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
$519$	−1.22597	+	21.2221i	−0.0538142	+	0.931545i
$520$		0			0
$521$	7.87830	+	10.8435i	0.345154	+	0.475064i	0.945938	−	0.324347i	$-0.105145\pi$
$521$	7.87830	+	10.8435i	0.345154	+	0.475064i	−0.600784	+	0.799412i	$0.705145\pi$
$522$		0			0
$523$	11.1465	+	5.67941i	0.487401	+	0.248343i	0.680380	−	0.732860i	$-0.261815\pi$
$523$	11.1465	+	5.67941i	0.487401	+	0.248343i	−0.192979	+	0.981203i	$0.561815\pi$
$524$		0			0
$525$	−2.60706	−	9.62733i	−0.113781	−	0.420171i
$526$		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
$531$	−9.45109	−	16.7815i	−0.410143	−	0.728256i
$532$		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
$537$	4.82354	−	8.25243i	0.208151	−	0.356119i
$538$		0			0
$539$	−6.38585	−	19.6536i	−0.275058	−	0.846541i
$540$		0			0
$541$	1.14874	−	3.53545i	0.0493881	−	0.152001i	−0.923321	−	0.384029i	$-0.874536\pi$
$541$	1.14874	−	3.53545i	0.0493881	−	0.152001i	0.972709	+	0.232028i	$0.0745362\pi$
$542$		0			0
$543$	−16.8382	−	3.67323i	−0.722595	−	0.157634i
$544$		0			0
$545$	−12.5000	−	12.4003i	−0.535439	−	0.531173i
$546$		0			0
$547$	−2.64836	−	0.419459i	−0.113236	−	0.0179348i	0.0995594	−	0.995032i	$-0.468257\pi$
$547$	−2.64836	−	0.419459i	−0.113236	−	0.0179348i	−0.212795	+	0.977097i	$0.568257\pi$
$548$		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
$555$	10.9122	−	4.84087i	0.463199	−	0.205484i
$556$		0			0
$557$	−19.5853	+	19.5853i	−0.829857	+	0.829857i	−0.987497	−	0.157639i	$-0.949612\pi$
$557$	−19.5853	+	19.5853i	−0.829857	+	0.829857i	0.157639	+	0.987497i	$0.449612\pi$
$558$		0			0
$559$	23.4991	+	7.63533i	0.993908	+	0.322940i
$560$		0			0
$561$	3.65218	−	4.46110i	0.154195	−	0.188348i
$562$		0			0
$563$	−14.2772	+	7.27459i	−0.601712	+	0.306587i	−0.728183	−	0.685383i	$-0.759635\pi$
$563$	−14.2772	+	7.27459i	−0.601712	+	0.306587i	0.126471	+	0.991970i	$0.459635\pi$
$564$		0			0
$565$	−41.8916	+	0.167580i	−1.76239	+	0.00705015i
$566$		0			0
$567$	6.69385	−	7.91411i	0.281115	−	0.332361i
$568$		0			0
$569$	29.7086	+	21.5845i	1.24545	+	0.904871i	0.997949	−	0.0640170i	$-0.0203912\pi$
$569$	29.7086	+	21.5845i	1.24545	+	0.904871i	0.247499	+	0.968888i	$0.420391\pi$
$570$		0			0
$571$	34.0496	−	24.7385i	1.42493	−	1.03527i	0.433997	−	0.900914i	$-0.357103\pi$
$571$	34.0496	−	24.7385i	1.42493	−	1.03527i	0.990933	−	0.134358i	$-0.0428971\pi$
$572$		0			0
$573$	−17.7676	+	1.77149i	−0.742251	+	0.0740050i
$574$		0			0
$575$	33.2332	−	5.53652i	1.38592	−	0.230889i
$576$		0			0
$577$	19.4132	−	38.1006i	0.808182	−	1.58615i	−0.00202117	−	0.999998i	$-0.500643\pi$
$577$	19.4132	−	38.1006i	0.808182	−	1.58615i	0.810203	−	0.586149i	$-0.199357\pi$
$578$		0			0
$579$	0.212141	−	0.543940i	0.00881630	−	0.0226054i
$580$		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
$585$	28.7344	+	26.2227i	1.18802	+	1.08418i
$586$		0			0
$587$	0.114338	+	0.224402i	0.00471925	+	0.00926205i	0.893354	−	0.449353i	$-0.148346\pi$
$587$	0.114338	+	0.224402i	0.00471925	+	0.00926205i	−0.888635	+	0.458615i	$0.848346\pi$
$588$		0			0
$589$	−15.3842	+	4.99864i	−0.633897	+	0.205966i
$590$		0			0
$591$	−0.832618	−	3.17516i	−0.0342493	−	0.130609i
$592$		0			0
$593$	−14.4925	−	14.4925i	−0.595137	−	0.595137i	0.343878	−	0.939014i	$-0.388259\pi$
$593$	−14.4925	−	14.4925i	−0.595137	−	0.595137i	−0.939014	+	0.343878i	$0.888259\pi$
$594$		0			0
$595$	1.07685	+	2.09270i	0.0441466	+	0.0857923i
$596$		0			0
$597$	12.9737	+	29.5637i	0.530978	+	1.20996i
$598$		0			0
$599$	16.6754			0.681340			0.340670	−	0.940183i	$-0.389346\pi$
$599$	16.6754			0.681340			0.340670	+	0.940183i	$0.389346\pi$
$600$		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
$603$	15.5965	+	10.3672i	0.635139	+	0.422184i
$604$		0			0
$605$	−5.00265	+	0.812870i	−0.203387	+	0.0330479i
$606$		0			0
$607$	7.49042	+	7.49042i	0.304027	+	0.304027i	0.842587	−	0.538560i	$-0.181032\pi$
$607$	7.49042	+	7.49042i	0.304027	+	0.304027i	−0.538560	+	0.842587i	$0.681032\pi$
$608$		0			0
$609$	10.2687	−	2.69274i	0.416107	−	0.109115i
$610$		0			0
$611$	35.1910	−	11.4343i	1.42368	−	0.462580i
$612$		0			0
$613$	−9.77730	−	19.1890i	−0.394902	−	0.775038i	0.604872	−	0.796323i	$-0.293224\pi$
$613$	−9.77730	−	19.1890i	−0.394902	−	0.775038i	−0.999773	+	0.0212848i	$0.993224\pi$
$614$		0			0
$615$	10.1287	+	3.90367i	0.408428	+	0.157411i
$616$		0			0
$617$	9.79635	−	1.55159i	0.394386	−	0.0624646i	0.0439081	−	0.999036i	$-0.486019\pi$
$617$	9.79635	−	1.55159i	0.394386	−	0.0624646i	0.350478	+	0.936571i	$0.386019\pi$
$618$		0			0
$619$	4.81151	−	6.62247i	0.193391	−	0.266180i	−0.701299	−	0.712867i	$-0.747396\pi$
$619$	4.81151	−	6.62247i	0.193391	−	0.266180i	0.894690	+	0.446687i	$0.147396\pi$
$620$		0			0
$621$	24.3577	+	25.1516i	0.977442	+	1.00930i
$622$		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
$627$	4.57794	+	45.9156i	0.182825	+	1.83369i
$628$		0			0
$629$	−2.27890	+	1.65572i	−0.0908656	+	0.0660177i
$630$		0			0
$631$	−0.620208	−	0.450607i	−0.0246901	−	0.0179384i	0.575372	−	0.817892i	$-0.304857\pi$
$631$	−0.620208	−	0.450607i	−0.0246901	−	0.0179384i	−0.600062	+	0.799954i	$0.704857\pi$
$632$		0			0
$633$	−28.9737	−	32.5265i	−1.15160	−	1.29281i
$634$		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
$639$	29.8274	+	3.45772i	1.17995	+	0.136785i
$640$		0			0
$641$	−16.9921	−	5.52105i	−0.671146	−	0.218068i	−0.0464310	−	0.998922i	$-0.514785\pi$
$641$	−16.9921	−	5.52105i	−0.671146	−	0.218068i	−0.624715	+	0.780853i	$0.714785\pi$
$642$		0			0
$643$	5.47671	−	5.47671i	0.215980	−	0.215980i	−0.590822	−	0.806802i	$-0.701196\pi$
$643$	5.47671	−	5.47671i	0.215980	−	0.215980i	0.806802	+	0.590822i	$0.201196\pi$
$644$		0			0
$645$	−12.2782	+	11.0255i	−0.483453	+	0.434128i
$646$		0			0
$647$	−5.84782	+	36.9217i	−0.229902	+	1.45154i	0.554963	+	0.831875i	$0.312732\pi$
$647$	−5.84782	+	36.9217i	−0.229902	+	1.45154i	−0.784865	+	0.619667i	$0.787268\pi$
$648$		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	$-0.227006\pi$
$653$	32.5406	+	5.15393i	1.27341	+	0.201689i	0.517115	+	0.855916i	$0.327006\pi$
$654$		0			0
$655$	11.7719	−	6.05753i	0.459967	−	0.236687i
$656$		0			0
$657$	−26.0813	+	9.69309i	−1.01753	+	0.378163i
$658$		0			0
$659$	−5.58239	+	17.1808i	−0.217459	+	0.669270i	0.781511	+	0.623892i	$0.214449\pi$
$659$	−5.58239	+	17.1808i	−0.217459	+	0.669270i	−0.998970	+	0.0453785i	$0.985551\pi$
$660$		0			0
$661$	5.43861	+	16.7383i	0.211537	+	0.651045i	0.999381	+	0.0351703i	$0.0111974\pi$
$661$	5.43861	+	16.7383i	0.211537	+	0.651045i	−0.787844	+	0.615875i	$0.788803\pi$
$662$		0			0
$663$	−7.92477	−	4.63202i	−0.307773	−	0.179893i
$664$		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
$669$	−8.31644	−	0.480431i	−0.321532	−	0.0185745i
$670$		0			0
$671$	−29.1921	−	40.1795i	−1.12695	−	1.55111i
$672$		0			0
$673$	−44.4567	−	22.6518i	−1.71368	−	0.873164i	−0.981354	−	0.192211i	$-0.938434\pi$
$673$	−44.4567	−	22.6518i	−1.71368	−	0.873164i	−0.732327	−	0.680953i	$-0.761566\pi$
$674$		0			0
$675$	−24.7729	+	7.82974i	−0.953508	+	0.301367i
$676$		0			0
$677$	13.4384	+	6.84718i	0.516478	+	0.263159i	0.692744	−	0.721184i	$-0.256402\pi$
$677$	13.4384	+	6.84718i	0.516478	+	0.263159i	−0.176266	+	0.984343i	$0.556402\pi$
$678$		0			0
$679$	2.63680	+	3.62924i	0.101191	+	0.139278i
$680$		0			0
$681$	−22.0096	−	1.27147i	−0.843411	−	0.0487228i
$682$		0			0
$683$	2.11149	+	13.3314i	0.0807939	+	0.510113i	0.994585	+	0.103928i	$0.0331411\pi$
$683$	2.11149	+	13.3314i	0.0807939	+	0.510113i	−0.913791	+	0.406185i	$0.866859\pi$
$684$		0			0
$685$	0.0575801	+	14.3938i	0.00220002	+	0.549960i
$686$		0			0
$687$	−0.242925	−	0.141989i	−0.00926818	−	0.00541724i
$688$		0			0
$689$	14.5905	+	44.9050i	0.555855	+	1.71075i
$690$		0			0
$691$	−1.08757	+	3.34720i	−0.0413731	+	0.127333i	−0.969610	−	0.244657i	$-0.921325\pi$
$691$	−1.08757	+	3.34720i	−0.0413731	+	0.127333i	0.928237	+	0.371991i	$0.121325\pi$
$692$		0			0
$693$	11.7964	−	4.38411i	0.448107	−	0.166539i
$694$		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
$705$	−5.17050	+	24.1655i	−0.194732	+	0.910125i
$706$		0			0
$707$	1.49194	−	1.49194i	0.0561101	−	0.0561101i
$708$		0			0
$709$	12.6101	+	4.09726i	0.473581	+	0.153876i	0.536076	−	0.844170i	$-0.319906\pi$
$709$	12.6101	+	4.09726i	0.473581	+	0.153876i	−0.0624957	+	0.998045i	$0.519906\pi$
$710$		0			0
$711$	21.7553	+	2.52197i	0.815887	+	0.0945811i
$712$		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
$717$	−12.8540	−	14.4301i	−0.480040	−	0.538903i
$718$		0			0
$719$	−18.6310	−	13.5362i	−0.694820	−	0.504816i	0.183421	−	0.983034i	$-0.441283\pi$
$719$	−18.6310	−	13.5362i	−0.694820	−	0.504816i	−0.878241	+	0.478218i	$0.841283\pi$
$720$		0			0
$721$	−9.48579	+	6.89183i	−0.353269	+	0.256665i
$722$		0			0
$723$	−4.83034	−	48.4471i	−0.179642	−	1.80177i
$724$		0			0
$725$	−25.3713	−	8.01979i	−0.942265	−	0.297847i
$726$		0			0
$727$	−10.3618	+	20.3362i	−0.384299	+	0.754229i	−0.999415	−	0.0342075i	$-0.989109\pi$
$727$	−10.3618	+	20.3362i	−0.384299	+	0.754229i	0.615116	+	0.788437i	$0.289109\pi$
$728$		0			0
$729$	−21.3234	−	16.5624i	−0.789755	−	0.613422i
$730$		0			0
$731$	2.28875	−	3.15019i	0.0846523	−	0.116514i
$732$		0			0
$733$	−13.2294	+	2.09532i	−0.488638	+	0.0773926i	−0.395892	−	0.918297i	$-0.629564\pi$
$733$	−13.2294	+	2.09532i	−0.488638	+	0.0773926i	−0.0927459	+	0.995690i	$0.529564\pi$
$734$		0			0
$735$	1.17951	−	21.9420i	0.0435070	−	0.809342i
$736$		0			0
$737$	10.3227	+	20.2594i	0.380240	+	0.746263i
$738$		0			0
$739$	15.0540	−	4.89134i	0.553770	−	0.179931i	−0.0187462	−	0.999824i	$-0.505967\pi$
$739$	15.0540	−	4.89134i	0.553770	−	0.179931i	0.572516	+	0.819894i	$0.305967\pi$
$740$		0			0
$741$	71.0629	−	18.6348i	2.61056	−	0.684565i
$742$		0			0
$743$	7.06750	+	7.06750i	0.259281	+	0.259281i	0.824762	−	0.565480i	$-0.191309\pi$
$743$	7.06750	+	7.06750i	0.259281	+	0.259281i	−0.565480	+	0.824762i	$0.691309\pi$
$744$		0			0
$745$	43.5707	+	21.9813i	1.59631	+	0.805332i
$746$		0			0
$747$	−3.03859	−	2.01979i	−0.111176	−	0.0739001i
$748$		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
$753$	−19.5824	−	44.6231i	−0.713621	−	1.62615i
$754$		0			0
$755$	15.5652	+	7.85262i	0.566477	+	0.285786i
$756$		0			0
$757$	10.5818	+	10.5818i	0.384604	+	0.384604i	0.872758	−	0.488154i	$-0.162330\pi$
$757$	10.5818	+	10.5818i	0.384604	+	0.384604i	−0.488154	+	0.872758i	$0.662330\pi$
$758$		0			0
$759$	10.7827	+	41.1193i	0.391386	+	1.49254i
$760$		0			0
$761$	−36.8728	+	11.9807i	−1.33664	+	0.434300i	−0.888176	−	0.459503i	$-0.848027\pi$
$761$	−36.8728	+	11.9807i	−1.33664	+	0.434300i	−0.448460	+	0.893803i	$0.648027\pi$
$762$		0			0
$763$	4.11715	+	8.08037i	0.149051	+	0.292529i
$764$		0			0
$765$	5.32954	−	3.02966i	0.192690	−	0.109538i
$766$		0			0
$767$	−36.7712	+	5.82398i	−1.32773	+	0.210292i
$768$		0			0
$769$	30.1156	−	41.4506i	1.08600	−	1.49475i	0.233252	−	0.972416i	$-0.425063\pi$
$769$	30.1156	−	41.4506i	1.08600	−	1.49475i	0.852744	−	0.522329i	$-0.174937\pi$
$770$		0			0
$771$	−11.4131	+	29.2636i	−0.411032	+	1.05390i
$772$		0			0
$773$	−10.0630	+	19.7497i	−0.361940	+	0.710347i	−0.998126	−	0.0611885i	$-0.980511\pi$
$773$	−10.0630	+	19.7497i	−0.361940	+	0.710347i	0.636186	+	0.771535i	$0.280511\pi$
$774$		0			0
$775$	−0.0884689	−	11.0575i	−0.00317790	−	0.397198i
$776$		0			0
$777$	−6.11833	+	0.610019i	−0.219494	+	0.0218843i
$778$		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
$783$	−8.12232	−	26.4327i	−0.290268	−	0.944628i
$784$		0			0
$785$	−10.2805	−	31.2146i	−0.366925	−	1.11410i
$786$		0			0
$787$	7.51983	−	3.83155i	0.268053	−	0.136580i	−0.314798	−	0.949159i	$-0.601937\pi$
$787$	7.51983	−	3.83155i	0.268053	−	0.136580i	0.582852	+	0.812579i	$0.301937\pi$
$788$		0			0
$789$	23.0155	−	28.1132i	0.819373	−	1.00086i
$790$		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
$795$	−30.8360	−	6.59775i	−1.09364	−	0.233998i
$796$		0			0
$797$	3.19808	−	20.1919i	0.113282	−

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)

\(f(q)\)	\(=\)	\(q+(-1.58605 + 0.696021i) q^{3} +(-1.99640 - 1.00718i) q^{5} +(0.814380 + 0.814380i) q^{7} +(2.03111 - 2.20785i) q^{9} +O(q^{10})\)	\(q+(-1.58605 + 0.696021i) q^{3} +(-1.99640 - 1.00718i) q^{5} +(0.814380 + 0.814380i) q^{7} +(2.03111 - 2.20785i) q^{9} +(3.46407 - 1.12554i) q^{11} +(-2.63271 - 5.16697i) q^{13} +(3.86740 + 0.207896i) q^{15} +(-0.902627 + 0.142962i) q^{17} +(4.29919 - 5.91733i) q^{19} +(-1.85847 - 0.724821i) q^{21} +(3.05909 - 6.00381i) q^{23} +(2.97120 + 4.02144i) q^{25} +(-1.68473 + 4.91545i) q^{27} +(-4.30536 + 3.12803i) q^{29} +(-1.78920 - 1.29993i) q^{31} +(-4.71078 + 4.19623i) q^{33} +(-0.805601 - 2.44605i) q^{35} +(2.74637 - 1.39935i) q^{37} +(7.77193 + 6.36266i) q^{39} +(2.66555 + 0.866089i) q^{41} +(-3.01283 + 3.01283i) q^{43} +(-6.27859 + 2.36206i) q^{45} +(-0.998165 + 6.30217i) q^{47} -5.67357i q^{49} +(1.33211 - 0.854993i) q^{51} +(-8.04180 - 1.27370i) q^{53} +(-8.04927 - 1.24189i) q^{55} +(-2.70014 + 12.3775i) q^{57} +(1.98388 - 6.10574i) q^{59} +(-4.21356 - 12.9680i) q^{61} +(3.45212 - 0.143935i) q^{63} +(0.0518720 + 12.9669i) q^{65} +(0.976557 + 6.16574i) q^{67} +(-0.673095 + 11.6515i) q^{69} +(5.88318 + 8.09750i) q^{71} +(-8.26387 - 4.21065i) q^{73} +(-7.51147 - 4.31019i) q^{75} +(3.73768 + 1.90445i) q^{77} +(4.29102 + 5.90609i) q^{79} +(-0.749199 - 8.96876i) q^{81} +(-0.190258 - 1.20124i) q^{83} +(1.94599 + 0.623695i) q^{85} +(4.65135 - 7.95784i) q^{87} +(3.41396 + 10.5071i) q^{89} +(2.06386 - 6.35190i) q^{91} +(3.74254 + 0.816433i) q^{93} +(-14.5427 + 7.48329i) q^{95} +(3.84712 + 0.609325i) q^{97} +(4.55086 - 9.93423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \)	\( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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