LMFDB - Embedded newform 300.2.x.a.53.4

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			53.4
Character	$\chi$	$=$	300.53
Dual form			300.2.x.a.17.4

$q$-expansion

$f(q)$	$=$	$q+(-0.719024 + 1.57576i) q^{3} +(-1.13602 - 1.92599i) q^{5} +(3.00936 - 3.00936i) q^{7} +(-1.96601 - 2.26601i) q^{9} +O(q^{10})$	\(q+(-0.719024 + 1.57576i) q^{3} +(-1.13602 - 1.92599i) q^{5} +(3.00936 - 3.00936i) q^{7} +(-1.96601 - 2.26601i) q^{9} +(2.76163 + 0.897307i) q^{11} +(0.404807 - 0.794479i) q^{13} +(3.85172 - 0.405257i) q^{15} +(3.19333 + 0.505773i) q^{17} +(0.694208 + 0.955496i) q^{19} +(2.57821 + 6.90582i) q^{21} +(-2.51796 - 4.94177i) q^{23} +(-2.41891 + 4.37594i) q^{25} +(4.98429 - 1.46864i) q^{27} +(6.77941 + 4.92553i) q^{29} +(6.19212 - 4.49884i) q^{31} +(-3.39961 + 3.70646i) q^{33} +(-9.21471 - 2.37731i) q^{35} +(-8.57635 - 4.36987i) q^{37} +(0.960839 + 1.20913i) q^{39} +(-8.73412 + 2.83789i) q^{41} +(-1.45614 - 1.45614i) q^{43} +(-2.13089 + 6.36076i) q^{45} +(-1.10756 - 6.99286i) q^{47} -11.1125i q^{49} +(-3.09305 + 4.66824i) q^{51} +(2.56331 - 0.405989i) q^{53} +(-1.40906 - 6.33824i) q^{55} +(-2.00478 + 0.406879i) q^{57} +(3.44583 + 10.6052i) q^{59} +(-2.69549 + 8.29586i) q^{61} +(-12.7357 - 0.902808i) q^{63} +(-1.99003 + 0.122889i) q^{65} +(0.616819 - 3.89444i) q^{67} +(9.59749 - 0.414436i) q^{69} +(-0.265914 + 0.366000i) q^{71} +(-2.68754 + 1.36937i) q^{73} +(-5.15616 - 6.95802i) q^{75} +(11.0110 - 5.61041i) q^{77} +(2.07296 - 2.85319i) q^{79} +(-1.26961 + 8.91000i) q^{81} +(-2.20859 + 13.9445i) q^{83} +(-2.65357 - 6.72490i) q^{85} +(-12.6360 + 7.14112i) q^{87} +(-2.41968 + 7.44701i) q^{89} +(-1.17266 - 3.60908i) q^{91} +(2.63679 + 12.9920i) q^{93} +(1.05164 - 2.42251i) q^{95} +(-1.51448 + 0.239870i) q^{97} +(-3.39608 - 8.02199i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.719024	+	1.57576i	−0.415128	+	0.909763i
$3$	−0.719024	+	1.57576i	−0.415128	+	0.909763i
$4$		0			0
$5$	−1.13602	−	1.92599i	−0.508044	−	0.861331i
$5$	−1.13602	−	1.92599i	−0.508044	−	0.861331i
$6$		0			0
$7$	3.00936	−	3.00936i	1.13743	−	1.13743i	0.148522	−	0.988909i	$-0.452548\pi$
$7$	3.00936	−	3.00936i	1.13743	−	1.13743i	0.988909	−	0.148522i	$-0.0474516\pi$
$8$		0			0
$9$	−1.96601	−	2.26601i	−0.655337	−	0.755337i
$10$		0			0
$11$	2.76163	+	0.897307i	0.832662	+	0.270548i	0.694166	−	0.719815i	$-0.255773\pi$
$11$	2.76163	+	0.897307i	0.832662	+	0.270548i	0.138496	+	0.990363i	$0.455773\pi$
$12$		0			0
$13$	0.404807	−	0.794479i	0.112273	−	0.220349i	−0.828032	−	0.560681i	$-0.810539\pi$
$13$	0.404807	−	0.794479i	0.112273	−	0.220349i	0.940305	+	0.340332i	$0.110539\pi$
$14$		0			0
$15$	3.85172	−	0.405257i	0.994510	−	0.104637i
$16$		0			0
$17$	3.19333	+	0.505773i	0.774496	+	0.122668i	0.531157	−	0.847273i	$-0.321757\pi$
$17$	3.19333	+	0.505773i	0.774496	+	0.122668i	0.243339	+	0.969941i	$0.421757\pi$
$18$		0			0
$19$	0.694208	+	0.955496i	0.159262	+	0.219206i	0.881189	−	0.472763i	$-0.156743\pi$
$19$	0.694208	+	0.955496i	0.159262	+	0.219206i	−0.721927	+	0.691969i	$0.756743\pi$
$20$		0			0
$21$	2.57821	+	6.90582i	0.562613	+	1.50697i
$22$		0			0
$23$	−2.51796	−	4.94177i	−0.525030	−	1.03043i	−0.989458	−	0.144819i	$-0.953740\pi$
$23$	−2.51796	−	4.94177i	−0.525030	−	1.03043i	0.464428	−	0.885611i	$-0.346260\pi$
$24$		0			0
$25$	−2.41891	+	4.37594i	−0.483782	+	0.875189i
$26$		0			0
$27$	4.98429	−	1.46864i	0.959226	−	0.282639i
$28$		0			0
$29$	6.77941	+	4.92553i	1.25890	+	0.914648i	0.998703	−	0.0509065i	$-0.0162111\pi$
$29$	6.77941	+	4.92553i	1.25890	+	0.914648i	0.260201	+	0.965554i	$0.416211\pi$
$30$		0			0
$31$	6.19212	−	4.49884i	1.11214	−	0.808015i	0.129139	−	0.991627i	$-0.458779\pi$
$31$	6.19212	−	4.49884i	1.11214	−	0.808015i	0.982999	+	0.183611i	$0.0587787\pi$
$32$		0			0
$33$	−3.39961	+	3.70646i	−0.591796	+	0.645213i
$34$		0			0
$35$	−9.21471	−	2.37731i	−1.55757	−	0.401839i
$36$		0			0
$37$	−8.57635	−	4.36987i	−1.40994	−	0.718402i	−0.427335	−	0.904093i	$-0.640548\pi$
$37$	−8.57635	−	4.36987i	−1.40994	−	0.718402i	−0.982608	+	0.185691i	$0.940548\pi$
$38$		0			0
$39$	0.960839	+	1.20913i	0.153857	+	0.193615i
$40$		0			0
$41$	−8.73412	+	2.83789i	−1.36404	+	0.443204i	−0.897390	−	0.441238i	$-0.854540\pi$
$41$	−8.73412	+	2.83789i	−1.36404	+	0.443204i	−0.466651	+	0.884442i	$0.654540\pi$
$42$		0			0
$43$	−1.45614	−	1.45614i	−0.222059	−	0.222059i	0.587306	−	0.809365i	$-0.300188\pi$
$43$	−1.45614	−	1.45614i	−0.222059	−	0.222059i	−0.809365	+	0.587306i	$0.800188\pi$
$44$		0			0
$45$	−2.13089	+	6.36076i	−0.317655	+	0.948206i
$46$		0			0
$47$	−1.10756	−	6.99286i	−0.161554	−	1.02001i	−0.926603	−	0.376041i	$-0.877285\pi$
$47$	−1.10756	−	6.99286i	−0.161554	−	1.02001i	0.765049	−	0.643973i	$-0.222715\pi$
$48$		0			0
$49$		−	11.1125i		−	1.58750i
$50$		0			0
$51$	−3.09305	+	4.66824i	−0.433114	+	0.653684i
$52$		0			0
$53$	2.56331	−	0.405989i	0.352098	−	0.0557668i	0.0221195	−	0.999755i	$-0.492959\pi$
$53$	2.56331	−	0.405989i	0.352098	−	0.0557668i	0.329978	+	0.943989i	$0.392959\pi$
$54$		0			0
$55$	−1.40906	−	6.33824i	−0.189998	−	0.854648i
$56$		0			0
$57$	−2.00478	+	0.406879i	−0.265540	+	0.0538924i
$58$		0			0
$59$	3.44583	+	10.6052i	0.448609	+	1.38068i	0.878477	+	0.477785i	$0.158560\pi$
$59$	3.44583	+	10.6052i	0.448609	+	1.38068i	−0.429867	+	0.902892i	$0.641440\pi$
$60$		0			0
$61$	−2.69549	+	8.29586i	−0.345122	+	1.06218i	0.616397	+	0.787436i	$0.288592\pi$
$61$	−2.69549	+	8.29586i	−0.345122	+	1.06218i	−0.961519	+	0.274740i	$0.911408\pi$
$62$		0			0
$63$	−12.7357	−	0.902808i	−1.60454	−	0.113743i
$64$		0			0
$65$	−1.99003	+	0.122889i	−0.246833	+	0.0152425i
$66$		0			0
$67$	0.616819	−	3.89444i	0.0753564	−	0.475782i	−0.920933	−	0.389720i	$-0.872572\pi$
$67$	0.616819	−	3.89444i	0.0753564	−	0.475782i	0.996290	−	0.0860617i	$-0.0274282\pi$
$68$		0			0
$69$	9.59749	−	0.414436i	1.15540	−	0.0498923i
$70$		0			0
$71$	−0.265914	+	0.366000i	−0.0315582	+	0.0434362i	−0.824505	−	0.565855i	$-0.808546\pi$
$71$	−0.265914	+	0.366000i	−0.0315582	+	0.0434362i	0.792946	+	0.609292i	$0.208546\pi$
$72$		0			0
$73$	−2.68754	+	1.36937i	−0.314553	+	0.160273i	−0.604139	−	0.796879i	$-0.706483\pi$
$73$	−2.68754	+	1.36937i	−0.314553	+	0.160273i	0.289585	+	0.957152i	$0.406483\pi$
$74$		0			0
$75$	−5.15616	−	6.95802i	−0.595383	−	0.803442i
$76$		0			0
$77$	11.0110	−	5.61041i	1.25483	−	0.639366i
$78$		0			0
$79$	2.07296	−	2.85319i	0.233227	−	0.321009i	−0.676322	−	0.736606i	$-0.736427\pi$
$79$	2.07296	−	2.85319i	0.233227	−	0.321009i	0.909549	+	0.415597i	$0.136427\pi$
$80$		0			0
$81$	−1.26961	+	8.91000i	−0.141067	+	0.990000i
$82$		0			0
$83$	−2.20859	+	13.9445i	−0.242424	+	1.53060i	0.503161	+	0.864193i	$0.332170\pi$
$83$	−2.20859	+	13.9445i	−0.242424	+	1.53060i	−0.745585	+	0.666411i	$0.767830\pi$
$84$		0			0
$85$	−2.65357	−	6.72490i	−0.287820	−	0.729418i
$86$		0			0
$87$	−12.6360	+	7.14112i	−1.35472	+	0.765608i
$88$		0			0
$89$	−2.41968	+	7.44701i	−0.256486	+	0.789382i	0.737048	+	0.675841i	$0.236219\pi$
$89$	−2.41968	+	7.44701i	−0.256486	+	0.789382i	−0.993533	+	0.113541i	$0.963781\pi$
$90$		0			0
$91$	−1.17266	−	3.60908i	−0.122928	−	0.378335i
$92$		0			0
$93$	2.63679	+	12.9920i	0.273422	+	1.34721i
$94$		0			0
$95$	1.05164	−	2.42251i	0.107896	−	0.248544i
$96$		0			0
$97$	−1.51448	+	0.239870i	−0.153772	+	0.0243551i	−0.232846	−	0.972514i	$-0.574804\pi$
$97$	−1.51448	+	0.239870i	−0.153772	+	0.0243551i	0.0790736	+	0.996869i	$0.474804\pi$
$98$		0			0
$99$	−3.39608	−	8.02199i	−0.341319	−	0.806240i
$100$		0			0
$101$			4.19521i			0.417439i	0.977976	+	0.208719i	$0.0669296\pi$
$101$			4.19521i			0.417439i	−0.977976	+	0.208719i	$0.933070\pi$
$102$		0			0
$103$	2.94153	+	18.5721i	0.289838	+	1.82996i	0.516854	+	0.856074i	$0.327103\pi$
$103$	2.94153	+	18.5721i	0.289838	+	1.82996i	−0.227016	+	0.973891i	$0.572897\pi$
$104$		0			0
$105$	10.3717	−	12.8108i	1.01217	−	1.25020i
$106$		0			0
$107$	1.62455	+	1.62455i	0.157051	+	0.157051i	0.781259	−	0.624208i	$-0.214578\pi$
$107$	1.62455	+	1.62455i	0.157051	+	0.157051i	−0.624208	+	0.781259i	$0.714578\pi$
$108$		0			0
$109$	−2.44163	+	0.793334i	−0.233866	+	0.0759876i	−0.423605	−	0.905847i	$-0.639236\pi$
$109$	−2.44163	+	0.793334i	−0.233866	+	0.0759876i	0.189740	+	0.981834i	$0.439236\pi$
$110$		0			0
$111$	13.0524	−	10.3722i	1.23888	−	0.984485i
$112$		0			0
$113$	−4.59551	−	2.34153i	−0.432310	−	0.220273i	0.224274	−	0.974526i	$-0.427999\pi$
$113$	−4.59551	−	2.34153i	−0.432310	−	0.220273i	−0.656583	+	0.754253i	$0.727999\pi$
$114$		0			0
$115$	−6.65736	+	10.4635i	−0.620802	+	0.975729i
$116$		0			0
$117$	−2.59615	+	0.644657i	−0.240014	+	0.0595985i
$118$		0			0
$119$	11.1319	−	8.08782i	1.02046	−	0.741409i
$120$		0			0
$121$	−2.07776	−	1.50958i	−0.188888	−	0.137235i
$122$		0			0
$123$	1.80822	−	15.8034i	0.163042	−	1.42494i
$124$		0			0
$125$	11.1760	−	0.312362i	0.999610	−	0.0279385i
$126$		0			0
$127$	6.30372	+	12.3717i	0.559364	+	1.09781i	0.981532	+	0.191297i	$0.0612693\pi$
$127$	6.30372	+	12.3717i	0.559364	+	1.09781i	−0.422168	+	0.906518i	$0.638731\pi$
$128$		0			0
$129$	3.34151	−	1.24752i	0.294204	−	0.109838i
$130$		0			0
$131$	−6.21317	−	8.55169i	−0.542847	−	0.747165i	0.446173	−	0.894947i	$-0.352787\pi$
$131$	−6.21317	−	8.55169i	−0.542847	−	0.747165i	−0.989020	+	0.147782i	$0.952787\pi$
$132$		0			0
$133$	4.96455	+	0.786308i	0.430481	+	0.0681815i
$134$		0			0
$135$	−8.49084	−	7.93130i	−0.730775	−	0.682618i
$136$		0			0
$137$	9.93006	−	19.4888i	0.848382	−	1.66504i	0.106701	−	0.994291i	$-0.465971\pi$
$137$	9.93006	−	19.4888i	0.848382	−	1.66504i	0.741681	−	0.670752i	$-0.234029\pi$
$138$		0			0
$139$	13.6780	+	4.44425i	1.16015	+	0.376956i	0.824958	−	0.565193i	$-0.191198\pi$
$139$	13.6780	+	4.44425i	1.16015	+	0.376956i	0.335193	+	0.942150i	$0.391198\pi$
$140$		0			0
$141$	11.8154	+	3.28279i	0.995037	+	0.276461i
$142$		0			0
$143$	1.83082	−	1.83082i	0.153101	−	0.153101i
$144$		0			0
$145$	1.78499	−	18.6526i	0.148235	−	1.54902i
$146$		0			0
$147$	17.5106	+	7.99014i	1.44425	+	0.659016i
$148$		0			0
$149$	−19.6307			−1.60821			−0.804106	−	0.594487i	$-0.797355\pi$
$149$	−19.6307			−1.60821			−0.804106	+	0.594487i	$0.797355\pi$
$150$		0			0
$151$	7.05432			0.574072			0.287036	−	0.957920i	$-0.407330\pi$
$151$	7.05432			0.574072			0.287036	+	0.957920i	$0.407330\pi$
$152$		0			0
$153$	−5.13203	−	8.23047i	−0.414900	−	0.665394i
$154$		0			0
$155$	−15.6991	−	6.81521i	−1.26098	−	0.547411i
$156$		0			0
$157$	−12.4751	+	12.4751i	−0.995620	+	0.995620i	−0.999990	−	0.00437087i	$-0.998609\pi$
$157$	−12.4751	+	12.4751i	−0.995620	+	0.995620i	0.00437087	+	0.999990i	$0.498609\pi$
$158$		0			0
$159$	−1.20334	+	4.33107i	−0.0954312	+	0.343476i
$160$		0			0
$161$	−22.4490	−	7.29412i	−1.76923	−	0.574857i
$162$		0			0
$163$	4.70822	−	9.24039i	0.368776	−	0.723764i	−0.629820	−	0.776741i	$-0.716871\pi$
$163$	4.70822	−	9.24039i	0.368776	−	0.723764i	0.998596	+	0.0529778i	$0.0168712\pi$
$164$		0			0
$165$	11.0007	+	2.33701i	0.856400	+	0.181936i
$166$		0			0
$167$	−4.64134	−	0.735116i	−0.359158	−	0.0568850i	−0.0257518	−	0.999668i	$-0.508198\pi$
$167$	−4.64134	−	0.735116i	−0.359158	−	0.0568850i	−0.333406	+	0.942783i	$0.608198\pi$
$168$		0			0
$169$	7.17388	+	9.87400i	0.551837	+	0.759538i
$170$		0			0
$171$	0.800343	−	3.45160i	0.0612037	−	0.263950i
$172$		0			0
$173$	5.89408	+	11.5678i	0.448119	+	0.879483i	0.998992	+	0.0448938i	$0.0142949\pi$
$173$	5.89408	+	11.5678i	0.448119	+	0.879483i	−0.550873	+	0.834589i	$0.685705\pi$
$174$		0			0
$175$	5.88942	+	20.4482i	0.445198	+	1.54574i
$176$		0			0
$177$	−19.1888	−	2.19559i	−1.44232	−	0.165030i
$178$		0			0
$179$	9.64168	+	7.00509i	0.720653	+	0.523585i	0.886593	−	0.462551i	$-0.153066\pi$
$179$	9.64168	+	7.00509i	0.720653	+	0.523585i	−0.165940	+	0.986136i	$0.553066\pi$
$180$		0			0
$181$	2.03092	−	1.47555i	0.150957	−	0.109677i	−0.509743	−	0.860327i	$-0.670259\pi$
$181$	2.03092	−	1.47555i	0.150957	−	0.109677i	0.660700	+	0.750650i	$0.270259\pi$
$182$		0			0
$183$	−11.1341	−	10.2123i	−0.823058	−	0.754918i
$184$		0			0
$185$	1.32658	+	21.4823i	0.0975320	+	1.57941i
$186$		0			0
$187$	8.36495	+	4.26215i	0.611705	+	0.311679i
$188$		0			0
$189$	10.5799	−	19.4192i	0.769571	−	1.41254i
$190$		0			0
$191$	4.35419	−	1.41476i	0.315058	−	0.102369i	−0.147219	−	0.989104i	$-0.547032\pi$
$191$	4.35419	−	1.41476i	0.315058	−	0.102369i	0.462278	+	0.886735i	$0.347032\pi$
$192$		0			0
$193$	−0.834752	−	0.834752i	−0.0600868	−	0.0600868i	0.676425	−	0.736512i	$-0.263528\pi$
$193$	−0.834752	−	0.834752i	−0.0600868	−	0.0600868i	−0.736512	+	0.676425i	$0.763528\pi$
$194$		0			0
$195$	1.23724	−	3.22416i	0.0886004	−	0.230887i
$196$		0			0
$197$	−3.31070	−	20.9029i	−0.235878	−	1.48927i	−0.766819	−	0.641863i	$-0.778162\pi$
$197$	−3.31070	−	20.9029i	−0.235878	−	1.48927i	0.530941	−	0.847409i	$-0.321838\pi$
$198$		0			0
$199$		−	12.1010i		−	0.857815i	−0.903348	−	0.428908i	$-0.858899\pi$
$199$		−	12.1010i		−	0.857815i	0.903348	−	0.428908i	$-0.141101\pi$
$200$		0			0
$201$	5.69318	+	3.77215i	0.401566	+	0.266067i
$202$		0			0
$203$	35.2244	−	5.57899i	2.47227	−	0.391569i
$204$		0			0
$205$	15.3879	+	13.5980i	1.07474	+	0.949723i
$206$		0			0
$207$	−6.24777	+	15.4213i	−0.434250	+	1.07185i
$208$		0			0
$209$	1.05977	+	3.26164i	0.0733059	+	0.225612i
$210$		0			0
$211$	−6.11917	+	18.8329i	−0.421261	+	1.29651i	0.485269	+	0.874365i	$0.338722\pi$
$211$	−6.11917	+	18.8329i	−0.421261	+	1.29651i	−0.906530	+	0.422142i	$0.861278\pi$
$212$		0			0
$213$	−0.385527	−	0.682179i	−0.0264159	−	0.0467421i
$214$		0			0
$215$	−1.15031	+	4.45871i	−0.0784503	+	0.304082i
$216$		0			0
$217$	5.09569	−	32.1729i	0.345918	−	2.18404i
$218$		0			0
$219$	−0.225388	−	5.21952i	−0.0152303	−	0.352703i
$220$		0			0
$221$	1.69451	−	2.33229i	0.113985	−	0.156887i
$222$		0			0
$223$	−6.45454	+	3.28875i	−0.432228	+	0.220231i	−0.656548	−	0.754285i	$-0.727984\pi$
$223$	−6.45454	+	3.28875i	−0.432228	+	0.220231i	0.224320	+	0.974516i	$0.427984\pi$
$224$		0			0
$225$	14.6715	−	3.12188i	0.978102	−	0.208125i
$226$		0			0
$227$	−1.65327	+	0.842383i	−0.109731	+	0.0559109i	−0.507995	−	0.861360i	$-0.669613\pi$
$227$	−1.65327	+	0.842383i	−0.109731	+	0.0559109i	0.398263	+	0.917271i	$0.369613\pi$
$228$		0			0
$229$	−13.9886	+	19.2537i	−0.924394	+	1.27232i	0.0376122	+	0.999292i	$0.488025\pi$
$229$	−13.9886	+	19.2537i	−0.924394	+	1.27232i	−0.962006	+	0.273027i	$0.911975\pi$
$230$		0			0
$231$	0.923430	+	21.3847i	0.0607573	+	1.40701i
$232$		0			0
$233$	0.810240	−	5.11565i	0.0530806	−	0.335138i	−0.946830	−	0.321735i	$-0.895734\pi$
$233$	0.810240	−	5.11565i	0.0530806	−	0.335138i	0.999910	−	0.0134021i	$-0.00426616\pi$
$234$		0			0
$235$	−12.2100	+	10.0772i	−0.796493	+	0.657364i
$236$		0			0
$237$	3.00542	+	5.31800i	0.195223	+	0.345441i
$238$		0			0
$239$	−1.51663	+	4.66771i	−0.0981026	+	0.301929i	−0.988050	−	0.154135i	$-0.950741\pi$
$239$	−1.51663	+	4.66771i	−0.0981026	+	0.301929i	0.889947	+	0.456064i	$0.150741\pi$
$240$		0			0
$241$	1.76890	+	5.44413i	0.113945	+	0.350687i	0.991726	−	0.128376i	$-0.0409765\pi$
$241$	1.76890	+	5.44413i	0.113945	+	0.350687i	−0.877780	+	0.479063i	$0.840976\pi$
$242$		0			0
$243$	−13.1271	−	8.40709i	−0.842104	−	0.539315i
$244$		0			0
$245$	−21.4026	+	12.6240i	−1.36736	+	0.806520i
$246$		0			0
$247$	1.04014	−	0.164742i	0.0661827	−	0.0104823i
$248$		0			0
$249$	−20.3850	−	13.5066i	−1.29185	−	0.855945i
$250$		0			0
$251$		−	20.3411i		−	1.28392i	−0.766738	−	0.641961i	$-0.778121\pi$
$251$		−	20.3411i		−	1.28392i	0.766738	−	0.641961i	$-0.221879\pi$
$252$		0			0
$253$	−2.51937	−	15.9067i	−0.158392	−	1.00005i
$254$		0			0
$255$	12.5048	+	0.653980i	0.783080	+	0.0409538i
$256$		0			0
$257$	16.9061	+	16.9061i	1.05458	+	1.05458i	0.998422	+	0.0561541i	$0.0178838\pi$
$257$	16.9061	+	16.9061i	1.05458	+	1.05458i	0.0561541	+	0.998422i	$0.482116\pi$
$258$		0			0
$259$	−38.9598	+	12.6588i	−2.42085	+	0.786581i
$260$		0			0
$261$	−2.16709	−	25.0459i	−0.134139	−	1.55030i
$262$		0			0
$263$	9.39006	+	4.78447i	0.579016	+	0.295023i	0.718865	−	0.695150i	$-0.244662\pi$
$263$	9.39006	+	4.78447i	0.579016	+	0.295023i	−0.139850	+	0.990173i	$0.544662\pi$
$264$		0			0
$265$	−3.69391	−	4.47571i	−0.226915	−	0.274941i
$266$		0			0
$267$	−9.99486	−	9.16740i	−0.611676	−	0.561036i
$268$		0			0
$269$	−6.24078	+	4.53419i	−0.380507	+	0.276454i	−0.761554	−	0.648101i	$-0.775563\pi$
$269$	−6.24078	+	4.53419i	−0.380507	+	0.276454i	0.381048	+	0.924555i	$0.375563\pi$
$270$		0			0
$271$	−16.4232	−	11.9322i	−0.997641	−	0.724828i	−0.0360598	−	0.999350i	$-0.511481\pi$
$271$	−16.4232	−	11.9322i	−0.997641	−	0.724828i	−0.961581	+	0.274521i	$0.911481\pi$
$272$		0			0
$273$	6.53021	+	0.747187i	0.395226	+	0.0452218i
$274$		0			0
$275$	−10.6067	+	9.91422i	−0.639607	+	0.597850i
$276$		0			0
$277$	8.84515	+	17.3596i	0.531453	+	1.04304i	0.988161	+	0.153419i	$0.0490285\pi$
$277$	8.84515	+	17.3596i	0.531453	+	1.04304i	−0.456708	+	0.889617i	$0.650971\pi$
$278$		0			0
$279$	−22.3682	−	5.18665i	−1.33915	−	0.310516i
$280$		0			0
$281$	−1.43495	−	1.97505i	−0.0856022	−	0.117821i	0.764068	−	0.645136i	$-0.223199\pi$
$281$	−1.43495	−	1.97505i	−0.0856022	−	0.117821i	−0.849670	+	0.527314i	$0.823199\pi$
$282$		0			0
$283$	−8.06450	−	1.27729i	−0.479385	−	0.0759271i	−0.0879343	−	0.996126i	$-0.528027\pi$
$283$	−8.06450	−	1.27729i	−0.479385	−	0.0759271i	−0.391450	+	0.920199i	$0.628027\pi$
$284$		0			0
$285$	3.06112	+	3.39897i	0.181325	+	0.201338i
$286$		0			0
$287$	−17.7439	+	34.8244i	−1.04739	+	2.05562i
$288$		0			0
$289$	−6.22643	−	2.02309i	−0.366260	−	0.119005i
$290$		0			0
$291$	0.710971	−	2.55892i	0.0416779	−	0.150007i
$292$		0			0
$293$	11.2030	−	11.2030i	0.654488	−	0.654488i	−0.299582	−	0.954070i	$-0.596847\pi$
$293$	11.2030	−	11.2030i	0.654488	−	0.654488i	0.954070	+	0.299582i	$0.0968473\pi$
$294$		0			0
$295$	16.5110	−	18.6844i	0.961307	−	1.08785i
$296$		0			0
$297$	15.0826	+	0.416608i	0.875179	+	0.0241741i
$298$		0			0
$299$	−4.94542			−0.286001
$300$		0			0
$301$	−8.76407			−0.505153
$302$		0			0
$303$	−6.61062	−	3.01645i	−0.379770	−	0.173291i
$304$		0			0
$305$	19.0399	−	4.23278i	1.09022	−	0.242368i
$306$		0			0
$307$	−2.43888	+	2.43888i	−0.139194	+	0.139194i	−0.773270	−	0.634076i	$-0.781380\pi$
$307$	−2.43888	+	2.43888i	−0.139194	+	0.139194i	0.634076	+	0.773270i	$0.281380\pi$
$308$		0			0
$309$	−31.3801	−	8.71865i	−1.78515	−	0.495987i
$310$		0			0
$311$	9.68418	+	3.14658i	0.549139	+	0.178426i	0.570429	−	0.821347i	$-0.306777\pi$
$311$	9.68418	+	3.14658i	0.549139	+	0.178426i	−0.0212893	+	0.999773i	$0.506777\pi$
$312$		0			0
$313$	−1.29485	+	2.54128i	−0.0731892	+	0.143642i	−0.924702	−	0.380692i	$-0.875686\pi$
$313$	−1.29485	+	2.54128i	−0.0731892	+	0.143642i	0.851513	+	0.524334i	$0.175686\pi$
$314$		0			0
$315$	12.7292	+	25.5544i	0.717209	+	1.43983i
$316$		0			0
$317$	−23.8744	−	3.78133i	−1.34092	−	0.212381i	−0.555589	−	0.831457i	$-0.687507\pi$
$317$	−23.8744	−	3.78133i	−1.34092	−	0.212381i	−0.785331	+	0.619076i	$0.787507\pi$
$318$		0			0
$319$	14.3025	+	19.6857i	0.800786	+	1.10219i
$320$		0			0
$321$	−3.72798	+	1.39180i	−0.208075	+	0.0776828i
$322$		0			0
$323$	1.73357	+	3.40232i	0.0964584	+	0.189310i
$324$		0			0
$325$	2.49740	+	3.69319i	0.138531	+	0.204861i
$326$		0			0
$327$	0.505489	−	4.41784i	0.0279536	−	0.244307i
$328$		0			0
$329$	−24.3771	−	17.7110i	−1.34395	−	0.976439i
$330$		0			0
$331$	6.91086	−	5.02103i	0.379855	−	0.275981i	−0.381431	−	0.924397i	$-0.624568\pi$
$331$	6.91086	−	5.02103i	0.379855	−	0.275981i	0.761286	+	0.648417i	$0.224568\pi$
$332$		0			0
$333$	6.95903	+	28.0253i	0.381352	+	1.53578i
$334$		0			0
$335$	−8.20139	+	3.23618i	−0.448090	+	0.176811i
$336$		0			0
$337$	−3.29999	−	1.68143i	−0.179762	−	0.0915932i	0.361794	−	0.932258i	$-0.382164\pi$
$337$	−3.29999	−	1.68143i	−0.179762	−	0.0915932i	−0.541556	+	0.840665i	$0.682164\pi$
$338$		0			0
$339$	6.99396	−	5.55779i	0.379860	−	0.301858i
$340$		0			0
$341$	21.1372	−	6.86788i	1.14464	−	0.371917i
$342$		0			0
$343$	−12.3760	−	12.3760i	−0.668240	−	0.668240i
$344$		0			0
$345$	−11.7012	−	18.0139i	−0.629969	−	0.969836i
$346$		0			0
$347$	1.58515	+	10.0082i	0.0850953	+	0.537270i	0.993002	+	0.118098i	$0.0376797\pi$
$347$	1.58515	+	10.0082i	0.0850953	+	0.537270i	−0.907907	+	0.419172i	$0.862320\pi$
$348$		0			0
$349$		−	10.8302i		−	0.579729i	−0.957068	−	0.289864i	$-0.906390\pi$
$349$		−	10.8302i		−	0.579729i	0.957068	−	0.289864i	$-0.0936102\pi$
$350$		0			0
$351$	0.850874	−	4.55443i	0.0454163	−	0.243097i
$352$		0			0
$353$	−13.1776	+	2.08713i	−0.701375	+	0.111087i	−0.496929	−	0.867791i	$-0.665539\pi$
$353$	−13.1776	+	2.08713i	−0.701375	+	0.111087i	−0.204445	+	0.978878i	$0.565539\pi$
$354$		0			0
$355$	1.00700	+	0.0963659i	0.0534459	+	0.00511457i
$356$		0			0
$357$	4.74031	+	23.3565i	0.250884	+	1.23616i
$358$		0			0
$359$	10.0379	+	30.8935i	0.529781	+	1.63050i	0.754663	+	0.656113i	$0.227800\pi$
$359$	10.0379	+	30.8935i	0.529781	+	1.63050i	−0.224882	+	0.974386i	$0.572200\pi$
$360$		0			0
$361$	5.44028	−	16.7434i	0.286330	−	0.881234i
$362$		0			0
$363$	3.87269	−	2.18862i	0.203264	−	0.114873i
$364$		0			0
$365$	5.69051	+	3.62056i	0.297855	+	0.189509i
$366$		0			0
$367$	−1.65984	+	10.4798i	−0.0866430	+	0.547042i	0.905738	+	0.423837i	$0.139317\pi$
$367$	−1.65984	+	10.4798i	−0.0866430	+	0.547042i	−0.992381	+	0.123205i	$0.960683\pi$
$368$		0			0
$369$	23.6021	+	14.2123i	1.22867	+	0.739863i
$370$		0			0
$371$	6.49216	−	8.93569i	0.337056	−	0.463918i
$372$		0			0
$373$	14.2945	−	7.28340i	0.740140	−	0.377120i	−0.0429097	−	0.999079i	$-0.513663\pi$
$373$	14.2945	−	7.28340i	0.740140	−	0.377120i	0.783050	+	0.621959i	$0.213663\pi$
$374$		0			0
$375$	−7.54358	+	17.8352i	−0.389549	+	0.921006i
$376$		0			0
$377$	6.65759	−	3.39221i	0.342883	−	0.174708i
$378$		0			0
$379$	18.2024	−	25.0535i	0.934995	−	1.28691i	−0.0228835	−	0.999738i	$-0.507285\pi$
$379$	18.2024	−	25.0535i	0.934995	−	1.28691i	0.957879	−	0.287173i	$-0.0927153\pi$
$380$		0			0
$381$	−24.0274	+	1.03754i	−1.23096	+	0.0531550i
$382$		0			0
$383$	4.80077	−	30.3108i	0.245308	−	1.54881i	−0.490391	−	0.871503i	$-0.663146\pi$
$383$	4.80077	−	30.3108i	0.245308	−	1.54881i	0.735698	−	0.677309i	$-0.236854\pi$
$384$		0			0
$385$	−23.3144	−	14.8337i	−1.18821	−	0.755994i
$386$		0			0
$387$	−0.436841	+	6.16240i	−0.0222059	+	0.313252i
$388$		0			0
$389$	7.88532	−	24.2685i	0.399802	−	1.23046i	−0.525357	−	0.850882i	$-0.676068\pi$
$389$	7.88532	−	24.2685i	0.399802	−	1.23046i	0.925159	−	0.379581i	$-0.123932\pi$
$390$		0			0
$391$	−5.54125	−	17.0542i	−0.280233	−	0.862468i
$392$		0			0
$393$	17.9428	−	3.64157i	0.905094	−	0.183693i
$394$		0			0
$395$	−7.85016	−	0.751231i	−0.394984	−	0.0377985i
$396$		0			0
$397$	8.20587	−	1.29968i	0.411841	−	0.0652292i	0.0529236	−	0.998599i	$-0.483146\pi$
$397$	8.20587	−	1.29968i	0.411841	−	0.0652292i	0.358917	+	0.933369i	$0.383146\pi$
$398$		0			0
$399$	−4.80866	+	7.25755i	−0.240734	+	0.363332i
$400$		0			0
$401$		−	17.6021i		−	0.879008i	−0.898241	−	0.439504i	$-0.855154\pi$
$401$		−	17.6021i		−	0.879008i	0.898241	−	0.439504i	$-0.144846\pi$
$402$		0			0
$403$	−1.06762	−	6.74067i	−0.0531818	−	0.335777i
$404$		0			0
$405$	18.6029	−	7.67670i	0.924386	−	0.381458i
$406$		0			0
$407$	−19.7636	−	19.7636i	−0.979644	−	0.979644i
$408$		0			0
$409$	−14.6004	+	4.74394i	−0.721941	+	0.234573i	−0.646865	−	0.762605i	$-0.723920\pi$
$409$	−14.6004	+	4.74394i	−0.721941	+	0.234573i	−0.0750765	+	0.997178i	$0.523920\pi$
$410$		0			0
$411$	23.5697	+	29.6603i	1.16261	+	1.46303i
$412$		0			0
$413$	42.2846	+	21.5451i	2.08069	+	1.06016i
$414$		0			0
$415$	29.3660	−	11.5875i	1.44152	−	0.568807i
$416$		0			0
$417$	−16.8378	+	18.3576i	−0.824552	+	0.898977i
$418$		0			0
$419$	−7.27149	+	5.28305i	−0.355236	+	0.258094i	−0.751062	−	0.660232i	$-0.770458\pi$
$419$	−7.27149	+	5.28305i	−0.355236	+	0.258094i	0.395827	+	0.918325i	$0.370458\pi$
$420$		0			0
$421$	22.8808	+	16.6239i	1.11514	+	0.810199i	0.983466	−	0.181093i	$-0.0579636\pi$
$421$	22.8808	+	16.6239i	1.11514	+	0.810199i	0.131678	+	0.991293i	$0.457964\pi$
$422$		0			0
$423$	−13.6684	+	16.2578i	−0.664582	+	0.790481i
$424$		0			0
$425$	−9.93760	+	12.7504i	−0.482045	+	0.618485i
$426$		0			0
$427$	16.8535	+	33.0769i	0.815599	+	1.60070i
$428$		0			0
$429$	1.56852	+	4.20132i	0.0757289	+	0.202842i
$430$		0			0
$431$	−18.6234	−	25.6329i	−0.897059	−	1.23470i	−0.971397	−	0.237462i	$-0.923684\pi$
$431$	−18.6234	−	25.6329i	−0.897059	−	1.23470i	0.0743381	−	0.997233i	$-0.476316\pi$
$432$		0			0
$433$	8.79670	+	1.39326i	0.422743	+	0.0669559i	0.364182	−	0.931328i	$-0.381349\pi$
$433$	8.79670	+	1.39326i	0.422743	+	0.0669559i	0.0585611	+	0.998284i	$0.481349\pi$
$434$		0			0
$435$	28.1085	+	16.2244i	1.34770	+	0.777899i
$436$		0			0
$437$	2.97385	−	5.83651i	0.142259	−	0.279198i
$438$		0			0
$439$	35.2858	+	11.4651i	1.68410	+	0.547198i	0.985700	−	0.168509i	$-0.0538953\pi$
$439$	35.2858	+	11.4651i	1.68410	+	0.547198i	0.698401	+	0.715707i	$0.253895\pi$
$440$		0			0
$441$	−25.1810	+	21.8473i	−1.19910	+	1.04035i
$442$		0			0
$443$	−0.101009	+	0.101009i	−0.00479907	+	0.00479907i	−0.709502	−	0.704703i	$-0.751080\pi$
$443$	−0.101009	+	0.101009i	−0.00479907	+	0.00479907i	0.704703	+	0.709502i	$0.251080\pi$
$444$		0			0
$445$	17.0917	−	3.79968i	0.810225	−	0.180122i
$446$		0			0
$447$	14.1149	−	30.9332i	0.667614	−	1.46309i
$448$		0			0
$449$	−5.09561			−0.240477			−0.120238	−	0.992745i	$-0.538366\pi$
$449$	−5.09561			−0.240477			−0.120238	+	0.992745i	$0.538366\pi$
$450$		0			0
$451$	−26.6669			−1.25569
$452$		0			0
$453$	−5.07222	+	11.1159i	−0.238314	+	0.522270i
$454$		0			0
$455$	−5.61891	+	6.35854i	−0.263418	+	0.298093i
$456$		0			0
$457$	9.17964	−	9.17964i	0.429406	−	0.429406i	−0.459020	−	0.888426i	$-0.651799\pi$
$457$	9.17964	−	9.17964i	0.429406	−	0.429406i	0.888426	+	0.459020i	$0.151799\pi$
$458$		0			0
$459$	16.6593	−	2.16892i	0.777587	−	0.101236i
$460$		0			0
$461$	2.89432	+	0.940423i	0.134802	+	0.0437999i	0.375641	−	0.926765i	$-0.377423\pi$
$461$	2.89432	+	0.940423i	0.134802	+	0.0437999i	−0.240839	+	0.970565i	$0.577423\pi$
$462$		0			0
$463$	3.81952	−	7.49623i	0.177508	−	0.348380i	−0.785060	−	0.619420i	$-0.787368\pi$
$463$	3.81952	−	7.49623i	0.177508	−	0.348380i	0.962568	+	0.271041i	$0.0873678\pi$
$464$		0			0
$465$	22.0271	−	19.8377i	1.02148	−	0.919951i
$466$		0			0
$467$	−3.67547	−	0.582137i	−0.170080	−	0.0269381i	0.0708133	−	0.997490i	$-0.477441\pi$
$467$	−3.67547	−	0.582137i	−0.170080	−	0.0269381i	−0.240894	+	0.970551i	$0.577441\pi$
$468$		0			0
$469$	−9.86354	−	13.5760i	−0.455456	−	0.626882i
$470$		0			0
$471$	−10.6878	−	28.6275i	−0.492468	−	1.31909i
$472$		0			0
$473$	−2.71470	−	5.32791i	−0.124822	−	0.244977i
$474$		0			0
$475$	−5.86042	+	0.726559i	−0.268895	+	0.0333368i
$476$		0			0
$477$	−5.95947	−	5.01031i	−0.272865	−	0.229406i
$478$		0			0
$479$	19.2357	+	13.9755i	0.878900	+	0.638558i	0.932960	−	0.359980i	$-0.117216\pi$
$479$	19.2357	+	13.9755i	0.878900	+	0.638558i	−0.0540606	+	0.998538i	$0.517216\pi$
$480$		0			0
$481$	−6.94354	+	5.04478i	−0.316598	+	0.230022i
$482$		0			0
$483$	27.6351	−	30.1295i	1.25744	−	1.37094i
$484$		0			0
$485$	2.18247	+	2.64439i	0.0991010	+	0.120075i
$486$		0			0
$487$	−36.1675	−	18.4282i	−1.63890	−	0.835063i	−0.997707	−	0.0676872i	$-0.978438\pi$
$487$	−36.1675	−	18.4282i	−1.63890	−	0.835063i	−0.641197	−	0.767376i	$-0.721562\pi$
$488$		0			0
$489$	11.1753	+	14.0631i	0.505364	+	0.635953i
$490$		0			0
$491$	−22.0112	+	7.15186i	−0.993350	+	0.322759i	−0.760205	−	0.649683i	$-0.774902\pi$
$491$	−22.0112	+	7.15186i	−0.993350	+	0.322759i	−0.233145	+	0.972442i	$0.574902\pi$
$492$		0			0
$493$	19.1577	+	19.1577i	0.862818	+	0.862818i
$494$		0			0
$495$	−11.5923	+	15.6540i	−0.521035	+	0.703594i
$496$		0			0
$497$	0.301193	+	1.90166i	0.0135103	+	0.0853010i
$498$		0			0
$499$		−	35.2669i		−	1.57876i	−0.613904	−	0.789381i	$-0.710402\pi$
$499$		−	35.2669i		−	1.57876i	0.613904	−	0.789381i	$-0.289598\pi$
$500$		0			0
$501$	4.49560	−	6.78505i	0.200848	−	0.303134i
$502$		0			0
$503$	−25.0737	+	3.97129i	−1.11798	+	0.177071i	−0.687961	−	0.725748i	$-0.741494\pi$
$503$	−25.0737	+	3.97129i	−1.11798	+	0.177071i	−0.430021	+	0.902819i	$0.641494\pi$
$504$		0			0
$505$	8.07995	−	4.76585i	0.359553	−	0.212078i
$506$		0			0
$507$	−20.7172	+	4.20464i	−0.920083	+	0.186735i
$508$		0			0
$509$	1.80435	+	5.55322i	0.0799765	+	0.246142i	0.983048	−	0.183348i	$-0.0586934\pi$
$509$	1.80435	+	5.55322i	0.0799765	+	0.246142i	−0.903072	+	0.429490i	$0.858693\pi$
$510$		0			0
$511$	−3.96685	+	12.2087i	−0.175483	+	0.540082i
$512$		0			0
$513$	4.86341	+	3.74292i	0.214725	+	0.165254i
$514$		0			0
$515$	32.4281	−	26.7637i	1.42895	−	1.17935i
$516$		0			0
$517$	3.21608	−	20.3055i	0.141443	−	0.893035i
$518$		0			0
$519$	−22.4660	+	0.970121i	−0.986148	+	0.0425836i
$520$		0			0
$521$	−5.69171	+	7.83396i	−0.249358	+	0.343212i	−0.915286	−	0.402804i	$-0.868036\pi$
$521$	−5.69171	+	7.83396i	−0.249358	+	0.343212i	0.665928	+	0.746016i	$0.268036\pi$
$522$		0			0
$523$	−0.993315	+	0.506119i	−0.0434346	+	0.0221310i	−0.475573	−	0.879676i	$-0.657759\pi$
$523$	−0.993315	+	0.506119i	−0.0434346	+	0.0221310i	0.432138	+	0.901807i	$0.357759\pi$
$524$		0			0
$525$	−36.4559	−	5.42242i	−1.59107	−	0.236654i
$526$		0			0
$527$	22.0489	−	11.2345i	0.960464	−	0.489381i
$528$		0			0
$529$	−4.56191	+	6.27893i	−0.198344	+	0.272997i
$530$		0			0
$531$	17.2569	−	28.6582i	0.748886	−	1.24366i
$532$		0			0
$533$	−1.28099	+	8.08788i	−0.0554860	+	0.350325i
$534$		0			0
$535$	1.28335	−	4.97439i	0.0554840	−	0.215062i
$536$		0			0
$537$	−17.9709	+	10.1561i	−0.775502	+	0.438268i
$538$		0			0
$539$	9.97132	−	30.6886i	0.429495	−	1.32185i
$540$		0			0
$541$	−9.75500	−	30.0228i	−0.419400	−	1.29078i	−0.908255	−	0.418417i	$-0.862585\pi$
$541$	−9.75500	−	30.0228i	−0.419400	−	1.29078i	0.488855	−	0.872365i	$-0.337415\pi$
$542$		0			0
$543$	0.864828	+	4.26120i	0.0371133	+	0.182865i
$544$		0			0
$545$	4.30170	+	3.80132i	0.184265	+	0.162831i
$546$		0			0
$547$	−30.7784	+	4.87482i	−1.31599	+	0.208432i	−0.774660	−	0.632378i	$-0.782079\pi$
$547$	−30.7784	+	4.87482i	−1.31599	+	0.208432i	−0.541330	+	0.840810i	$0.682079\pi$
$548$		0			0
$549$	24.0978	−	10.2017i	1.02847	−	0.435399i
$550$		0			0
$551$			9.89704i			0.421628i
$552$		0			0
$553$	−2.34798	−	14.8246i	−0.0998463	−	0.630405i
$554$		0			0
$555$	−34.8046	−	13.3559i	−1.47738	−	0.566926i
$556$		0			0
$557$	−11.9164	−	11.9164i	−0.504915	−	0.504915i	0.408046	−	0.912961i	$-0.366210\pi$
$557$	−11.9164	−	11.9164i	−0.504915	−	0.504915i	−0.912961	+	0.408046i	$0.866210\pi$
$558$		0			0
$559$	−1.74632	+	0.567415i	−0.0738616	+	0.0239991i
$560$		0			0
$561$	−12.7307	+	10.1165i	−0.537491	+	0.427120i
$562$		0			0
$563$	−16.5294	−	8.42215i	−0.696631	−	0.354951i	0.0695477	−	0.997579i	$-0.477844\pi$
$563$	−16.5294	−	8.42215i	−0.696631	−	0.354951i	−0.766179	+	0.642627i	$0.777844\pi$
$564$		0			0
$565$	0.710828	+	11.5110i	0.0299047	+	0.484270i
$566$		0			0
$567$	22.9927	+	30.6341i	0.965602	+	1.28651i
$568$		0			0
$569$	−1.23297	+	0.895803i	−0.0516887	+	0.0375540i	−0.613330	−	0.789827i	$-0.710170\pi$
$569$	−1.23297	+	0.895803i	−0.0516887	+	0.0375540i	0.561641	+	0.827381i	$0.310170\pi$
$570$		0			0
$571$	24.3901	+	17.7205i	1.02070	+	0.741579i	0.966425	−	0.256948i	$-0.0827168\pi$
$571$	24.3901	+	17.7205i	1.02070	+	0.741579i	0.0542700	+	0.998526i	$0.482717\pi$
$572$		0			0
$573$	−0.901447	+	7.87839i	−0.0376585	+	0.329125i
$574$		0			0
$575$	27.7156	+	0.935252i	1.15582	+	0.0390027i
$576$		0			0
$577$	16.3743	+	32.1363i	0.681669	+	1.33785i	0.929419	+	0.369027i	$0.120309\pi$
$577$	16.3743	+	32.1363i	0.681669	+	1.33785i	−0.247749	+	0.968824i	$0.579691\pi$
$578$		0			0
$579$	1.91557	−	0.715159i	0.0796085	−	0.0297210i
$580$		0			0
$581$	35.3175	+	48.6103i	1.46522	+	2.01670i
$582$		0			0
$583$	7.44321	+	1.17889i	0.308266	+	0.0488245i
$584$		0			0
$585$	4.19089	+	4.26783i	0.173272	+	0.176453i
$586$		0			0
$587$	−7.58856	+	14.8934i	−0.313213	+	0.614716i	−0.992922	−	0.118766i	$-0.962106\pi$
$587$	−7.58856	+	14.8934i	−0.313213	+	0.614716i	0.679709	+	0.733482i	$0.262106\pi$
$588$		0			0
$589$	8.59724	+	2.79341i	0.354243	+	0.115101i
$590$		0			0
$591$	35.3184	+	9.81285i	1.45280	+	0.403647i
$592$		0			0
$593$	−17.3573	+	17.3573i	−0.712780	+	0.712780i	−0.967116	−	0.254336i	$-0.918143\pi$
$593$	−17.3573	+	17.3573i	−0.712780	+	0.712780i	0.254336	+	0.967116i	$0.418143\pi$
$594$		0			0
$595$	−28.2232	−	12.2521i	−1.15704	−	0.502287i
$596$		0			0
$597$	19.0682	+	8.70088i	0.780408	+	0.356103i
$598$		0			0
$599$	−14.4303			−0.589605			−0.294802	−	0.955558i	$-0.595254\pi$
$599$	−14.4303			−0.589605			−0.294802	+	0.955558i	$0.595254\pi$
$600$		0			0
$601$	−40.6930			−1.65990			−0.829951	−	0.557837i	$-0.811632\pi$
$601$	−40.6930			−1.65990			−0.829951	+	0.557837i	$0.811632\pi$
$602$		0			0
$603$	−10.0375	+	6.25879i	−0.408759	+	0.254878i
$604$		0			0
$605$	−0.547065	+	5.71668i	−0.0222413	+	0.232416i
$606$		0			0
$607$	31.1483	−	31.1483i	1.26427	−	1.26427i	0.315266	−	0.949003i	$-0.397906\pi$
$607$	31.1483	−	31.1483i	1.26427	−	1.26427i	0.949003	−	0.315266i	$-0.102094\pi$
$608$		0			0
$609$	−16.5360	+	59.5164i	−0.670074	+	2.41173i
$610$		0			0
$611$	−6.00403	−	1.95083i	−0.242897	−	0.0789221i
$612$		0			0
$613$	−16.5958	+	32.5711i	−0.670299	+	1.31554i	0.265878	+	0.964007i	$0.414338\pi$
$613$	−16.5958	+	32.5711i	−0.670299	+	1.31554i	−0.936177	+	0.351529i	$0.885662\pi$
$614$		0			0
$615$	−32.4913	+	14.4703i	−1.31018	+	0.583500i
$616$		0			0
$617$	34.4877	+	5.46232i	1.38842	+	0.219905i	0.805487	−	0.592613i	$-0.201904\pi$
$617$	34.4877	+	5.46232i	1.38842	+	0.219905i	0.582936	+	0.812518i	$0.301904\pi$
$618$		0			0
$619$	3.48931	+	4.80263i	0.140247	+	0.193034i	0.873363	−	0.487070i	$-0.161934\pi$
$619$	3.48931	+	4.80263i	0.140247	+	0.193034i	−0.733115	+	0.680104i	$0.761934\pi$
$620$		0			0
$621$	−19.8079	−	20.9332i	−0.794863	−	0.840021i
$622$		0			0
$623$	15.1291	+	29.6924i	0.606133	+	1.18960i
$624$		0			0
$625$	−13.2978	−	21.1700i	−0.531910	−	0.846801i
$626$		0			0
$627$	−5.90155	−	0.675256i	−0.235685	−	0.0269671i
$628$		0			0
$629$	−25.1769	−	18.2921i	−1.00387	−	0.729354i
$630$		0			0
$631$	21.9450	−	15.9440i	0.873616	−	0.634719i	−0.0579392	−	0.998320i	$-0.518453\pi$
$631$	21.9450	−	15.9440i	0.873616	−	0.634719i	0.931555	+	0.363601i	$0.118453\pi$
$632$		0			0
$633$	−25.2762	−	23.1836i	−1.00464	−	0.921464i
$634$		0			0
$635$	16.6667	−	26.1955i	0.661400	−	1.03954i
$636$		0			0
$637$	−8.82864	−	4.49842i	−0.349804	−	0.178234i
$638$		0			0
$639$	1.35215	−	0.116995i	0.0534902	−	0.00462823i
$640$		0			0
$641$	−6.43772	+	2.09174i	−0.254275	+	0.0826188i	−0.433381	−	0.901211i	$-0.642679\pi$
$641$	−6.43772	+	2.09174i	−0.254275	+	0.0826188i	0.179106	+	0.983830i	$0.442679\pi$
$642$		0			0
$643$	−1.88726	−	1.88726i	−0.0744264	−	0.0744264i	0.668914	−	0.743340i	$-0.266760\pi$
$643$	−1.88726	−	1.88726i	−0.0744264	−	0.0744264i	−0.743340	+	0.668914i	$0.766760\pi$
$644$		0			0
$645$	−6.19874	−	5.01852i	−0.244075	−	0.197604i
$646$		0			0
$647$	1.80177	+	11.3759i	0.0708349	+	0.447234i	0.997459	+	0.0712445i	$0.0226971\pi$
$647$	1.80177	+	11.3759i	0.0708349	+	0.447234i	−0.926624	+	0.375989i	$0.877303\pi$
$648$		0			0
$649$			32.3795i			1.27101i
$650$		0			0
$651$	47.0328	+	31.1627i	1.84336	+	1.22136i
$652$		0			0
$653$	−41.2088	+	6.52683i	−1.61262	+	0.255414i	−0.896659	−	0.442722i	$-0.854013\pi$
$653$	−41.2088	+	6.52683i	−1.61262	+	0.255414i	−0.715965	+	0.698136i	$0.754013\pi$
$654$		0			0
$655$	−9.41222	+	21.6814i	−0.367766	+	0.847164i
$656$		0			0
$657$	8.38675	+	3.39780i	0.327198	+	0.132561i
$658$		0			0
$659$	0.104879	+	0.322784i	0.00408550	+	0.0125739i	0.953078	−	0.302723i	$-0.0978958\pi$
$659$	0.104879	+	0.322784i	0.00408550	+	0.0125739i	−0.948993	+	0.315297i	$0.897896\pi$
$660$		0			0
$661$	4.25007	−	13.0804i	0.165308	−	0.508767i	−0.833750	−	0.552141i	$-0.813811\pi$
$661$	4.25007	−	13.0804i	0.165308	−	0.508767i	0.999059	+	0.0433745i	$0.0138109\pi$
$662$		0			0
$663$	2.45673	+	4.34710i	0.0954115	+	0.168828i
$664$		0			0
$665$	−4.12542	−	10.4550i	−0.159977	−	0.405426i
$666$		0			0
$667$	7.27057	−	45.9045i	0.281517	−	1.77743i
$668$		0			0
$669$	−0.541303	−	12.5355i	−0.0209280	−	0.484649i
$670$		0			0
$671$	−14.8879	+	20.4914i	−0.574739	+	0.791061i
$672$		0			0
$673$	−8.28693	+	4.22240i	−0.319438	+	0.162762i	−0.606356	−	0.795193i	$-0.707369\pi$
$673$	−8.28693	+	4.22240i	−0.319438	+	0.162762i	0.286918	+	0.957955i	$0.407369\pi$
$674$		0			0
$675$	−5.62986	+	25.3635i	−0.216694	+	0.976240i
$676$		0			0
$677$	3.29687	−	1.67984i	0.126709	−	0.0645615i	−0.389487	−	0.921032i	$-0.627348\pi$
$677$	3.29687	−	1.67984i	0.126709	−	0.0645615i	0.516196	+	0.856470i	$0.327348\pi$
$678$		0			0
$679$	−3.83576	+	5.27948i	−0.147203	+	0.202608i
$680$		0			0
$681$	−0.138650	−	3.21084i	−0.00531307	−	0.123040i
$682$		0			0
$683$	−1.53600	+	9.69792i	−0.0587734	+	0.371081i	0.940718	+	0.339190i	$0.110153\pi$
$683$	−1.53600	+	9.69792i	−0.0587734	+	0.371081i	−0.999491	+	0.0318908i	$0.989847\pi$
$684$		0			0
$685$	−48.8161	+	3.01451i	−1.86517	+	0.115178i
$686$		0			0
$687$	−20.2810	−	35.8865i	−0.773767	−	1.36916i
$688$		0			0
$689$	0.715098	−	2.20084i	0.0272430	−	0.0838455i
$690$		0			0
$691$	−5.28572	−	16.2678i	−0.201078	−	0.618855i	−0.999852	−	0.0172234i	$-0.994517\pi$
$691$	−5.28572	−	16.2678i	−0.201078	−	0.618855i	0.798773	−	0.601632i	$-0.205483\pi$
$692$		0			0
$693$	−34.3611	−	13.9210i	−1.30527	−	0.528816i
$694$		0			0
$695$	−6.97889	−	31.3925i	−0.264725	−	1.19078i
$696$		0			0
$697$	−29.3262	+	4.64482i	−1.11081	+	0.175935i
$698$		0			0
$699$	7.47844	+	4.95501i	0.282860	+	0.187416i
$700$		0			0
$701$			33.4650i			1.26396i	0.774986	+	0.631979i	$0.217757\pi$
$701$			33.4650i			1.26396i	−0.774986	+	0.631979i	$0.782243\pi$
$702$		0			0
$703$	−1.77838	−	11.2283i	−0.0670730	−	0.423482i
$704$		0			0
$705$	−7.09993	−	26.4857i	−0.267399	−	0.997510i
$706$		0			0
$707$	12.6249	+	12.6249i	0.474808	+	0.474808i
$708$		0			0
$709$	12.9358	−	4.20308i	0.485813	−	0.157850i	−0.0558616	−	0.998439i	$-0.517791\pi$
$709$	12.9358	−	4.20308i	0.485813	−	0.157850i	0.541674	+	0.840588i	$0.317791\pi$
$710$		0			0
$711$	−10.5408	+	0.912043i	−0.395312	+	0.0342043i
$712$		0			0
$713$	−37.8237	−	19.2721i	−1.41651	−	0.721748i
$714$		0			0
$715$	−5.60600	−	1.44630i	−0.209652	−	0.0540884i
$716$		0			0
$717$	−6.26467	−	5.74603i	−0.233958	−	0.214589i
$718$		0			0
$719$	29.7221	−	21.5944i	1.10845	−	0.805335i	0.126030	−	0.992026i	$-0.459777\pi$
$719$	29.7221	−	21.5944i	1.10845	−	0.805335i	0.982419	+	0.186692i	$0.0597766\pi$
$720$		0			0
$721$	64.7423	+	47.0380i	2.41113	+	1.75179i
$722$		0			0
$723$	−9.85050	−	1.12710i	−0.366344	−	0.0419171i
$724$		0			0
$725$	−37.9526	+	17.7519i	−1.40952	+	0.659289i
$726$		0			0
$727$	−4.12344	−	8.09270i	−0.152930	−	0.300142i	0.801813	−	0.597576i	$-0.203869\pi$
$727$	−4.12344	−	8.09270i	−0.152930	−	0.300142i	−0.954742	+	0.297434i	$0.903869\pi$
$728$		0			0
$729$	22.6862	−	14.6402i	0.840230	−	0.542230i
$730$		0			0
$731$	−3.91344	−	5.38639i	−0.144744	−	0.199223i
$732$		0			0
$733$	−9.91162	−	1.56985i	−0.366094	−	0.0579836i	−0.0293225	−	0.999570i	$-0.509335\pi$
$733$	−9.91162	−	1.56985i	−0.366094	−	0.0579836i	−0.336771	+	0.941586i	$0.609335\pi$
$734$		0			0
$735$	−4.50342	−	42.8022i	−0.166111	−	1.57878i
$736$		0			0
$737$	5.19793	−	10.2015i	0.191468	−	0.375778i
$738$		0			0
$739$	−47.6656	−	15.4875i	−1.75341	−	0.569717i	−0.756924	−	0.653503i	$-0.773299\pi$
$739$	−47.6656	−	15.4875i	−1.75341	−	0.569717i	−0.996484	+	0.0837861i	$0.973299\pi$
$740$		0			0
$741$	−0.488293	+	1.75746i	−0.0179379	+	0.0645620i
$742$		0			0
$743$	0.668282	−	0.668282i	0.0245169	−	0.0245169i	−0.694742	−	0.719259i	$-0.744481\pi$
$743$	0.668282	−	0.668282i	0.0245169	−	0.0245169i	0.719259	+	0.694742i	$0.244481\pi$
$744$		0			0
$745$	22.3009	+	37.8087i	0.817043	+	1.38520i
$746$		0			0
$747$	35.9404	−	22.4103i	1.31499	−	0.819949i
$748$		0			0
$749$	9.77769			0.357269
$750$		0			0
$751$	16.7359			0.610702			0.305351	−	0.952240i	$-0.401226\pi$
$751$	16.7359			0.610702			0.305351	+	0.952240i	$0.401226\pi$
$752$		0			0
$753$	32.0527	+	14.6258i	1.16806	+	0.532992i
$754$		0			0
$755$	−8.01386	−	13.5866i	−0.291654	−	0.494466i
$756$		0			0
$757$	−14.6049	+	14.6049i	−0.530826	+	0.530826i	−0.920818	−	0.389992i	$-0.872478\pi$
$757$	−14.6049	+	14.6049i	−0.530826	+	0.530826i	0.389992	+	0.920818i	$0.372478\pi$
$758$		0			0
$759$	26.8766	+	7.46738i	0.975557	+	0.271049i
$760$		0			0
$761$	21.2600	+	6.90779i	0.770674	+	0.250407i	0.667854	−	0.744293i	$-0.267213\pi$
$761$	21.2600	+	6.90779i	0.770674	+	0.250407i	0.102821	+	0.994700i	$0.467213\pi$
$762$		0			0
$763$	−4.96032	+	9.73517i	−0.179575	+	0.352437i
$764$		0			0
$765$	−10.0217	+	19.2342i	−0.362337	+	0.695416i
$766$		0			0
$767$	9.82050	+	1.55541i	0.354598	+	0.0561627i
$768$		0			0
$769$	−2.03314	−	2.79838i	−0.0733169	−	0.100912i	0.770784	−	0.637097i	$-0.219865\pi$
$769$	−2.03314	−	2.79838i	−0.0733169	−	0.100912i	−0.844101	+	0.536185i	$0.819865\pi$
$770$		0			0
$771$	−38.7959	+	14.4840i	−1.39720	+	0.521630i
$772$		0			0
$773$	−15.1556	−	29.7445i	−0.545109	−	1.06984i	−0.985124	−	0.171846i	$-0.945027\pi$
$773$	−15.1556	−	29.7445i	−0.545109	−	1.06984i	0.440015	−	0.897990i	$-0.354973\pi$
$774$		0			0
$775$	4.70849	+	37.9787i	0.169134	+	1.36423i
$776$		0			0
$777$	8.06584	−	70.4932i	0.289360	−	2.52893i
$778$		0			0
$779$	−8.77489	−	6.37533i	−0.314393	−	0.228420i
$780$		0			0
$781$	−1.06277	+	0.772148i	−0.0380289	+	0.0276296i
$782$		0			0
$783$	41.0243	+	14.5938i	1.46609	+	0.521538i
$784$		0			0
$785$	38.1989	+	9.85497i	1.36338	+	0.351739i
$786$		0			0
$787$	18.0985	+	9.22165i	0.645142	+	0.328716i	0.745766	−	0.666208i	$-0.232084\pi$
$787$	18.0985	+	9.22165i	0.645142	+	0.328716i	−0.100624	+	0.994925i	$0.532084\pi$
$788$		0			0
$789$	−14.2908	+	11.3563i	−0.508767	+	0.404294i
$790$		0			0
$791$	−20.8761	+	6.78304i	−0.742267	+	0.241177i
$792$		0			0
$793$	5.49973	+	5.49973i	0.195301	+	0.195301i
$794$		0			0
$795$	9.70863	−	2.60256i	0.344330	−	0.0923031i
$796$		0			0
$797$	−5.53887	−	34.9710i

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)

\(f(q)\)	\(=\)	\(q+(-0.719024 + 1.57576i) q^{3} +(-1.13602 - 1.92599i) q^{5} +(3.00936 - 3.00936i) q^{7} +(-1.96601 - 2.26601i) q^{9} +O(q^{10})\)	\(q+(-0.719024 + 1.57576i) q^{3} +(-1.13602 - 1.92599i) q^{5} +(3.00936 - 3.00936i) q^{7} +(-1.96601 - 2.26601i) q^{9} +(2.76163 + 0.897307i) q^{11} +(0.404807 - 0.794479i) q^{13} +(3.85172 - 0.405257i) q^{15} +(3.19333 + 0.505773i) q^{17} +(0.694208 + 0.955496i) q^{19} +(2.57821 + 6.90582i) q^{21} +(-2.51796 - 4.94177i) q^{23} +(-2.41891 + 4.37594i) q^{25} +(4.98429 - 1.46864i) q^{27} +(6.77941 + 4.92553i) q^{29} +(6.19212 - 4.49884i) q^{31} +(-3.39961 + 3.70646i) q^{33} +(-9.21471 - 2.37731i) q^{35} +(-8.57635 - 4.36987i) q^{37} +(0.960839 + 1.20913i) q^{39} +(-8.73412 + 2.83789i) q^{41} +(-1.45614 - 1.45614i) q^{43} +(-2.13089 + 6.36076i) q^{45} +(-1.10756 - 6.99286i) q^{47} -11.1125i q^{49} +(-3.09305 + 4.66824i) q^{51} +(2.56331 - 0.405989i) q^{53} +(-1.40906 - 6.33824i) q^{55} +(-2.00478 + 0.406879i) q^{57} +(3.44583 + 10.6052i) q^{59} +(-2.69549 + 8.29586i) q^{61} +(-12.7357 - 0.902808i) q^{63} +(-1.99003 + 0.122889i) q^{65} +(0.616819 - 3.89444i) q^{67} +(9.59749 - 0.414436i) q^{69} +(-0.265914 + 0.366000i) q^{71} +(-2.68754 + 1.36937i) q^{73} +(-5.15616 - 6.95802i) q^{75} +(11.0110 - 5.61041i) q^{77} +(2.07296 - 2.85319i) q^{79} +(-1.26961 + 8.91000i) q^{81} +(-2.20859 + 13.9445i) q^{83} +(-2.65357 - 6.72490i) q^{85} +(-12.6360 + 7.14112i) q^{87} +(-2.41968 + 7.44701i) q^{89} +(-1.17266 - 3.60908i) q^{91} +(2.63679 + 12.9920i) q^{93} +(1.05164 - 2.42251i) q^{95} +(-1.51448 + 0.239870i) q^{97} +(-3.39608 - 8.02199i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \)	\( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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