LMFDB - Embedded newform 300.2.m.a.241.2

Newspace parameters

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.m (of order $5$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\Q(\zeta_{15})$
Defining polynomial:	$x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1$
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			241.2
Root			$-0.104528 + 0.994522i$ of defining polynomial
Character	$\chi$	$=$	300.241
Dual form			300.2.m.a.61.2

$q$-expansion

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{3} +(2.18720 + 0.464905i) q^{5} +0.547318 q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{3} +(2.18720 + 0.464905i) q^{5} +0.547318 q^{7} +(-0.809017 + 0.587785i) q^{9} +(1.08268 + 0.786610i) q^{11} +(-0.244415 + 0.177578i) q^{13} +(0.233733 + 2.22382i) q^{15} +(1.24898 - 3.84398i) q^{17} +(-1.74064 + 5.35713i) q^{19} +(0.169131 + 0.520530i) q^{21} +(-0.198375 - 0.144128i) q^{23} +(4.56773 + 2.03368i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(-0.423273 - 1.30270i) q^{29} +(-1.09336 + 3.36501i) q^{31} +(-0.413545 + 1.27276i) q^{33} +(1.19710 + 0.254451i) q^{35} +(1.76988 - 1.28589i) q^{37} +(-0.244415 - 0.177578i) q^{39} +(7.93066 - 5.76196i) q^{41} -8.35963 q^{43} +(-2.04275 + 0.909491i) q^{45} +(-3.23656 - 9.96110i) q^{47} -6.70044 q^{49} +4.04179 q^{51} +(-2.37819 - 7.31931i) q^{53} +(2.00234 + 2.22382i) q^{55} -5.63282 q^{57} +(-3.35916 + 2.44057i) q^{59} +(-1.67981 - 1.22046i) q^{61} +(-0.442790 + 0.321706i) q^{63} +(-0.617142 + 0.274769i) q^{65} +(2.62230 - 8.07061i) q^{67} +(0.0757724 - 0.233204i) q^{69} +(-2.83777 - 8.73377i) q^{71} +(-8.86356 - 6.43975i) q^{73} +(-0.522642 + 4.97261i) q^{75} +(0.592568 + 0.430526i) q^{77} +(4.69177 + 14.4398i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-2.05626 + 6.32850i) q^{83} +(4.51886 - 7.82690i) q^{85} +(1.10814 - 0.805112i) q^{87} +(-4.02780 - 2.92637i) q^{89} +(-0.133773 + 0.0971915i) q^{91} -3.53818 q^{93} +(-6.29768 + 10.9079i) q^{95} +(1.25499 + 3.86248i) q^{97} -1.33826 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8q - 2q^{3} + 5q^{5} - 8q^{7} - 2q^{9} + O(q^{10}) $	$ 8q - 2q^{3} + 5q^{5} - 8q^{7} - 2q^{9} - 2q^{11} - 5q^{15} + 7q^{17} + 5q^{19} - 3q^{21} + 7q^{23} + 5q^{25} - 2q^{27} + 27q^{29} - 3q^{31} + 3q^{33} + 20q^{35} - 9q^{37} + 20q^{41} - 68q^{43} - 5q^{45} - 7q^{47} - 8q^{49} - 8q^{51} - 11q^{53} + 5q^{55} - 10q^{57} + 2q^{59} - 14q^{61} + 7q^{63} - 35q^{65} + 28q^{67} + 2q^{69} - 15q^{71} + 6q^{73} + 5q^{75} + 17q^{77} + 24q^{79} - 2q^{81} + 2q^{83} + 10q^{85} - 23q^{87} + 5q^{91} - 18q^{93} + 5q^{95} + 34q^{97} - 2q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$		0			0
$5$	2.18720	+	0.464905i	0.978148	+	0.207912i
$5$	2.18720	+	0.464905i	0.978148	+	0.207912i
$6$		0			0
$7$	0.547318			0.206867			0.103433	−	0.994636i	$-0.467017\pi$
$7$	0.547318			0.206867			0.103433	+	0.994636i	$0.467017\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	1.08268	+	0.786610i	0.326439	+	0.237172i	0.738918	−	0.673795i	$-0.235337\pi$
$11$	1.08268	+	0.786610i	0.326439	+	0.237172i	−0.412479	+	0.910967i	$0.635337\pi$
$12$		0			0
$13$	−0.244415	+	0.177578i	−0.0677885	+	0.0492512i	−0.621163	−	0.783681i	$-0.713340\pi$
$13$	−0.244415	+	0.177578i	−0.0677885	+	0.0492512i	0.553375	+	0.832932i	$0.313340\pi$
$14$		0			0
$15$	0.233733	+	2.22382i	0.0603495	+	0.574187i
$16$		0			0
$17$	1.24898	−	3.84398i	0.302923	−	0.932301i	−0.677521	−	0.735503i	$-0.736946\pi$
$17$	1.24898	−	3.84398i	0.302923	−	0.932301i	0.980444	−	0.196798i	$-0.0630542\pi$
$18$		0			0
$19$	−1.74064	+	5.35713i	−0.399329	+	1.22901i	0.526209	+	0.850355i	$0.323613\pi$
$19$	−1.74064	+	5.35713i	−0.399329	+	1.22901i	−0.925538	+	0.378654i	$0.876387\pi$
$20$		0			0
$21$	0.169131	+	0.520530i	0.0369073	+	0.113589i
$22$		0			0
$23$	−0.198375	−	0.144128i	−0.0413640	−	0.0300527i	0.566911	−	0.823779i	$-0.308138\pi$
$23$	−0.198375	−	0.144128i	−0.0413640	−	0.0300527i	−0.608275	+	0.793726i	$0.708138\pi$
$24$		0			0
$25$	4.56773	+	2.03368i	0.913545	+	0.406737i
$26$		0			0
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$		0			0
$29$	−0.423273	−	1.30270i	−0.0785997	−	0.241905i	0.904034	−	0.427460i	$-0.140592\pi$
$29$	−0.423273	−	1.30270i	−0.0785997	−	0.241905i	−0.982634	+	0.185555i	$0.940592\pi$
$30$		0			0
$31$	−1.09336	+	3.36501i	−0.196373	+	0.604374i	0.803585	+	0.595190i	$0.202923\pi$
$31$	−1.09336	+	3.36501i	−0.196373	+	0.604374i	−0.999958	+	0.00918358i	$0.997077\pi$
$32$		0			0
$33$	−0.413545	+	1.27276i	−0.0719890	+	0.221559i
$34$		0			0
$35$	1.19710	+	0.254451i	0.202346	+	0.0430100i
$36$		0			0
$37$	1.76988	−	1.28589i	0.290967	−	0.211400i	−0.432720	−	0.901528i	$-0.642446\pi$
$37$	1.76988	−	1.28589i	0.290967	−	0.211400i	0.723687	+	0.690129i	$0.242446\pi$
$38$		0			0
$39$	−0.244415	−	0.177578i	−0.0391377	−	0.0284352i
$40$		0			0
$41$	7.93066	−	5.76196i	1.23856	−	0.899868i	0.241060	−	0.970510i	$-0.422505\pi$
$41$	7.93066	−	5.76196i	1.23856	−	0.899868i	0.997502	+	0.0706425i	$0.0225049\pi$
$42$		0			0
$43$	−8.35963			−1.27483			−0.637415	−	0.770520i	$-0.719996\pi$
$43$	−8.35963			−1.27483			−0.637415	+	0.770520i	$0.719996\pi$
$44$		0			0
$45$	−2.04275	+	0.909491i	−0.304515	+	0.135579i
$46$		0			0
$47$	−3.23656	−	9.96110i	−0.472100	−	1.45298i	−0.849829	−	0.527059i	$-0.823295\pi$
$47$	−3.23656	−	9.96110i	−0.472100	−	1.45298i	0.377729	−	0.925916i	$-0.376705\pi$
$48$		0			0
$49$	−6.70044			−0.957206
$50$		0			0
$51$	4.04179			0.565964
$52$		0			0
$53$	−2.37819	−	7.31931i	−0.326669	−	1.00538i	−0.970682	−	0.240369i	$-0.922731\pi$
$53$	−2.37819	−	7.31931i	−0.326669	−	1.00538i	0.644012	−	0.765015i	$-0.277269\pi$
$54$		0			0
$55$	2.00234	+	2.22382i	0.269995	+	0.299860i
$56$		0			0
$57$	−5.63282			−0.746085
$58$		0			0
$59$	−3.35916	+	2.44057i	−0.437325	+	0.317735i	−0.784571	−	0.620039i	$-0.787117\pi$
$59$	−3.35916	+	2.44057i	−0.437325	+	0.317735i	0.347246	+	0.937774i	$0.387117\pi$
$60$		0			0
$61$	−1.67981	−	1.22046i	−0.215078	−	0.156263i	0.475030	−	0.879969i	$-0.342437\pi$
$61$	−1.67981	−	1.22046i	−0.215078	−	0.156263i	−0.690108	+	0.723706i	$0.742437\pi$
$62$		0			0
$63$	−0.442790	+	0.321706i	−0.0557863	+	0.0405311i
$64$		0			0
$65$	−0.617142	+	0.274769i	−0.0765470	+	0.0340809i
$66$		0			0
$67$	2.62230	−	8.07061i	0.320365	−	0.985982i	−0.653125	−	0.757251i	$-0.726542\pi$
$67$	2.62230	−	8.07061i	0.320365	−	0.985982i	0.973490	−	0.228732i	$-0.0734578\pi$
$68$		0			0
$69$	0.0757724	−	0.233204i	0.00912193	−	0.0280744i
$70$		0			0
$71$	−2.83777	−	8.73377i	−0.336782	−	1.03651i	−0.965838	−	0.259148i	$-0.916558\pi$
$71$	−2.83777	−	8.73377i	−0.336782	−	1.03651i	0.629056	−	0.777360i	$-0.283442\pi$
$72$		0			0
$73$	−8.86356	−	6.43975i	−1.03740	−	0.753716i	−0.0676248	−	0.997711i	$-0.521542\pi$
$73$	−8.86356	−	6.43975i	−1.03740	−	0.753716i	−0.969777	+	0.243995i	$0.921542\pi$
$74$		0			0
$75$	−0.522642	+	4.97261i	−0.0603495	+	0.574187i
$76$		0			0
$77$	0.592568	+	0.430526i	0.0675294	+	0.0490630i
$78$		0			0
$79$	4.69177	+	14.4398i	0.527866	+	1.62460i	0.758578	+	0.651582i	$0.225894\pi$
$79$	4.69177	+	14.4398i	0.527866	+	1.62460i	−0.230713	+	0.973022i	$0.574106\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	−2.05626	+	6.32850i	−0.225703	+	0.694643i	0.772516	+	0.634995i	$0.218998\pi$
$83$	−2.05626	+	6.32850i	−0.225703	+	0.694643i	−0.998219	+	0.0596483i	$0.981002\pi$
$84$		0			0
$85$	4.51886	−	7.82690i	0.490140	−	0.848947i
$86$		0			0
$87$	1.10814	−	0.805112i	0.118805	−	0.0863171i
$88$		0			0
$89$	−4.02780	−	2.92637i	−0.426946	−	0.310194i	0.353481	−	0.935442i	$-0.384998\pi$
$89$	−4.02780	−	2.92637i	−0.426946	−	0.310194i	−0.780427	+	0.625247i	$0.784998\pi$
$90$		0			0
$91$	−0.133773	+	0.0971915i	−0.0140232	+	0.0101884i
$92$		0			0
$93$	−3.53818			−0.366892
$94$		0			0
$95$	−6.29768	+	10.9079i	−0.646128	+	1.11913i
$96$		0			0
$97$	1.25499	+	3.86248i	0.127425	+	0.392175i	0.994335	−	0.106290i	$-0.0338972\pi$
$97$	1.25499	+	3.86248i	0.127425	+	0.392175i	−0.866910	+	0.498465i	$0.833897\pi$
$98$		0			0
$99$	−1.33826			−0.134500
$100$		0			0
$101$	18.4489			1.83573			0.917865	−	0.396892i	$-0.129911\pi$
$101$	18.4489			1.83573			0.917865	+	0.396892i	$0.129911\pi$
$102$		0			0
$103$	−4.54762	−	13.9961i	−0.448090	−	1.37908i	−0.879059	−	0.476713i	$-0.841828\pi$
$103$	−4.54762	−	13.9961i	−0.448090	−	1.37908i	0.430969	−	0.902367i	$-0.358172\pi$
$104$		0			0
$105$	0.127926	+	1.21714i	0.0124843	+	0.118780i
$106$		0			0
$107$	−5.10528			−0.493546			−0.246773	−	0.969073i	$-0.579370\pi$
$107$	−5.10528			−0.493546			−0.246773	+	0.969073i	$0.579370\pi$
$108$		0			0
$109$	−3.82331	+	2.77780i	−0.366207	+	0.266065i	−0.755636	−	0.654991i	$-0.772672\pi$
$109$	−3.82331	+	2.77780i	−0.366207	+	0.266065i	0.389429	+	0.921056i	$0.372672\pi$
$110$		0			0
$111$	1.76988	+	1.28589i	0.167990	+	0.122052i
$112$		0			0
$113$	−3.34799	+	2.43246i	−0.314952	+	0.228826i	−0.734019	−	0.679129i	$-0.762357\pi$
$113$	−3.34799	+	2.43246i	−0.314952	+	0.228826i	0.419066	+	0.907956i	$0.362357\pi$
$114$		0			0
$115$	−0.366881	−	0.407462i	−0.0342118	−	0.0379961i
$116$		0			0
$117$	0.0933582	−	0.287327i	0.00863097	−	0.0265634i
$118$		0			0
$119$	0.683591	−	2.10388i	0.0626647	−	0.192862i
$120$		0			0
$121$	−2.84576	−	8.75833i	−0.258705	−	0.796212i
$122$		0			0
$123$	7.93066	+	5.76196i	0.715084	+	0.519539i
$124$		0			0
$125$	9.04508	+	6.57164i	0.809017	+	0.587785i
$126$		0			0
$127$	10.2568	+	7.45200i	0.910144	+	0.661258i	0.941051	−	0.338264i	$-0.109840\pi$
$127$	10.2568	+	7.45200i	0.910144	+	0.661258i	−0.0309074	+	0.999522i	$0.509840\pi$
$128$		0			0
$129$	−2.58327	−	7.95048i	−0.227444	−	0.700000i
$130$		0			0
$131$	−3.81046	+	11.7274i	−0.332921	+	1.02463i	0.634815	+	0.772664i	$0.281076\pi$
$131$	−3.81046	+	11.7274i	−0.332921	+	1.02463i	−0.967737	+	0.251963i	$0.918924\pi$
$132$		0			0
$133$	−0.952682	+	2.93205i	−0.0826080	+	0.254241i
$134$		0			0
$135$	−1.49622	−	1.66172i	−0.128774	−	0.143018i
$136$		0			0
$137$	−8.67508	+	6.30281i	−0.741162	+	0.538486i	−0.893075	−	0.449908i	$-0.851457\pi$
$137$	−8.67508	+	6.30281i	−0.741162	+	0.538486i	0.151913	+	0.988394i	$0.451457\pi$
$138$		0			0
$139$	11.0632	+	8.03786i	0.938365	+	0.681762i	0.948027	−	0.318191i	$-0.103075\pi$
$139$	11.0632	+	8.03786i	0.938365	+	0.681762i	−0.00966163	+	0.999953i	$0.503075\pi$
$140$		0			0
$141$	8.47341	−	6.15630i	0.713590	−	0.518454i
$142$		0			0
$143$	−0.404307			−0.0338098
$144$		0			0
$145$	−0.320153	−	3.04605i	−0.0265872	−	0.252961i
$146$		0			0
$147$	−2.07055	−	6.37250i	−0.170776	−	0.525595i
$148$		0			0
$149$	8.88176			0.727622			0.363811	−	0.931473i	$-0.381475\pi$
$149$	8.88176			0.727622			0.363811	+	0.931473i	$0.381475\pi$
$150$		0			0
$151$	2.68310			0.218348			0.109174	−	0.994023i	$-0.465179\pi$
$151$	2.68310			0.218348			0.109174	+	0.994023i	$0.465179\pi$
$152$		0			0
$153$	1.24898	+	3.84398i	0.100974	+	0.310767i
$154$		0			0
$155$	−3.95581	+	6.85166i	−0.317738	+	0.550338i
$156$		0			0
$157$	11.7576			0.938355			0.469178	−	0.883104i	$-0.344550\pi$
$157$	11.7576			0.938355			0.469178	+	0.883104i	$0.344550\pi$
$158$		0			0
$159$	6.22618	−	4.52358i	0.493768	−	0.358743i
$160$		0			0
$161$	−0.108574	−	0.0788837i	−0.00855684	−	0.00621691i
$162$		0			0
$163$	14.8153	−	10.7639i	1.16042	−	0.843097i	0.170592	−	0.985342i	$-0.445432\pi$
$163$	14.8153	−	10.7639i	1.16042	−	0.843097i	0.989831	+	0.142245i	$0.0454322\pi$
$164$		0			0
$165$	−1.49622	+	2.59153i	−0.116481	+	0.201750i
$166$		0			0
$167$	1.36097	−	4.18862i	0.105315	−	0.324125i	−0.884489	−	0.466560i	$-0.845493\pi$
$167$	1.36097	−	4.18862i	0.105315	−	0.324125i	0.989804	+	0.142435i	$0.0454931\pi$
$168$		0			0
$169$	−3.98902	+	12.2769i	−0.306847	+	0.944379i
$170$		0			0
$171$	−1.74064	−	5.35713i	−0.133110	−	0.409670i
$172$		0			0
$173$	12.8882	+	9.36385i	0.979875	+	0.711921i	0.957681	−	0.287833i	$-0.0929349\pi$
$173$	12.8882	+	9.36385i	0.979875	+	0.711921i	0.0221940	+	0.999754i	$0.492935\pi$
$174$		0			0
$175$	2.50000	+	1.11307i	0.188982	+	0.0841403i
$176$		0			0
$177$	−3.35916	−	2.44057i	−0.252490	−	0.183445i
$178$		0			0
$179$	1.16493	+	3.58528i	0.0870707	+	0.267976i	0.985106	−	0.171947i	$-0.0550057\pi$
$179$	1.16493	+	3.58528i	0.0870707	+	0.267976i	−0.898035	+	0.439923i	$0.855006\pi$
$180$		0			0
$181$	−8.24669	+	25.3807i	−0.612971	+	1.88653i	−0.185004	+	0.982738i	$0.559230\pi$
$181$	−8.24669	+	25.3807i	−0.612971	+	1.88653i	−0.427967	+	0.903794i	$0.640770\pi$
$182$		0			0
$183$	0.641631	−	1.97474i	0.0474308	−	0.145977i
$184$		0			0
$185$	4.46891	−	1.98969i	0.328561	−	0.146285i
$186$		0			0
$187$	4.37595	−	3.17932i	0.320001	−	0.232495i
$188$		0			0
$189$	−0.442790	−	0.321706i	−0.0322082	−	0.0234006i
$190$		0			0
$191$	−3.74803	+	2.72310i	−0.271198	+	0.197037i	−0.715069	−	0.699054i	$-0.753605\pi$
$191$	−3.74803	+	2.72310i	−0.271198	+	0.197037i	0.443871	+	0.896091i	$0.353605\pi$
$192$		0			0
$193$	−20.7440			−1.49319			−0.746594	−	0.665280i	$-0.768312\pi$
$193$	−20.7440			−1.49319			−0.746594	+	0.665280i	$0.768312\pi$
$194$		0			0
$195$	−0.452029	−	0.502029i	−0.0323704	−	0.0359510i
$196$		0			0
$197$	6.34529	+	19.5288i	0.452083	+	1.39137i	0.874526	+	0.484979i	$0.161173\pi$
$197$	6.34529	+	19.5288i	0.452083	+	1.39137i	−0.422443	+	0.906390i	$0.638827\pi$
$198$		0			0
$199$	5.91437			0.419259			0.209629	−	0.977781i	$-0.432774\pi$
$199$	5.91437			0.419259			0.209629	+	0.977781i	$0.432774\pi$
$200$		0			0
$201$	8.48594			0.598552
$202$		0			0
$203$	−0.231665	−	0.712991i	−0.0162597	−	0.0500421i
$204$		0			0
$205$	20.0247	−	8.91559i	1.39859	−	0.622692i
$206$		0			0
$207$	0.245205			0.0170429
$208$		0			0
$209$	−6.09852	+	4.43083i	−0.421843	+	0.306487i
$210$		0			0
$211$	−18.5512	−	13.4782i	−1.27712	−	0.927880i	−0.277655	−	0.960681i	$-0.589557\pi$
$211$	−18.5512	−	13.4782i	−1.27712	−	0.927880i	−0.999462	+	0.0328013i	$0.989557\pi$
$212$		0			0
$213$	7.42939	−	5.39777i	0.509053	−	0.369849i
$214$		0			0
$215$	−18.2842	−	3.88643i	−1.24697	−	0.265052i
$216$		0			0
$217$	−0.598415	+	1.84173i	−0.0406230	+	0.125025i
$218$		0			0
$219$	3.38558	−	10.4197i	0.228776	−	0.704101i
$220$		0			0
$221$	0.377335	+	1.16132i	0.0253823	+	0.0781186i
$222$		0			0
$223$	10.3148	+	7.49414i	0.690730	+	0.501845i	0.876900	−	0.480673i	$-0.159607\pi$
$223$	10.3148	+	7.49414i	0.690730	+	0.501845i	−0.186170	+	0.982518i	$0.559607\pi$
$224$		0			0
$225$	−4.89074	+	1.03956i	−0.326049	+	0.0693039i
$226$		0			0
$227$	−8.92301	−	6.48294i	−0.592241	−	0.430288i	0.250876	−	0.968019i	$-0.419281\pi$
$227$	−8.92301	−	6.48294i	−0.592241	−	0.430288i	−0.843116	+	0.537731i	$0.819281\pi$
$228$		0			0
$229$	−7.13214	−	21.9505i	−0.471305	−	1.45053i	−0.850876	−	0.525366i	$-0.823928\pi$
$229$	−7.13214	−	21.9505i	−0.471305	−	1.45053i	0.379571	−	0.925163i	$-0.376072\pi$
$230$		0			0
$231$	−0.226341	+	0.696606i	−0.0148921	+	0.0458333i
$232$		0			0
$233$	−9.05055	+	27.8547i	−0.592921	+	1.82482i	−0.0281067	+	0.999605i	$0.508948\pi$
$233$	−9.05055	+	27.8547i	−0.592921	+	1.82482i	−0.564814	+	0.825218i	$0.691052\pi$
$234$		0			0
$235$	−2.44805	−	23.2916i	−0.159693	−	1.51938i
$236$		0			0
$237$	−12.2832	+	8.92428i	−0.797881	+	0.579694i
$238$		0			0
$239$	−8.57443	−	6.22969i	−0.554634	−	0.402965i	0.274857	−	0.961485i	$-0.411369\pi$
$239$	−8.57443	−	6.22969i	−0.554634	−	0.402965i	−0.829491	+	0.558520i	$0.811369\pi$
$240$		0			0
$241$	−15.3888	+	11.1806i	−0.991282	+	0.720208i	−0.960201	−	0.279309i	$-0.909895\pi$
$241$	−15.3888	+	11.1806i	−0.991282	+	0.720208i	−0.0310802	+	0.999517i	$0.509895\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−14.6552	−	3.11507i	−0.936289	−	0.199014i
$246$		0			0
$247$	−0.525870	−	1.61846i	−0.0334603	−	0.102980i
$248$		0			0
$249$	−6.65418			−0.421692
$250$		0			0
$251$	0.0370816			0.00234057			0.00117028	−	0.999999i	$-0.499627\pi$
$251$	0.0370816			0.00234057			0.00117028	+	0.999999i	$0.499627\pi$
$252$		0			0
$253$	−0.101403	−	0.312087i	−0.00637517	−	0.0196208i
$254$		0			0
$255$	8.84023	+	1.87905i	0.553597	+	0.117671i
$256$		0			0
$257$	−10.0237			−0.625262			−0.312631	−	0.949875i	$-0.601210\pi$
$257$	−10.0237			−0.625262			−0.312631	+	0.949875i	$0.601210\pi$
$258$		0			0
$259$	0.968688	−	0.703793i	0.0601913	−	0.0437316i
$260$		0			0
$261$	1.10814	+	0.805112i	0.0685923	+	0.0498352i
$262$		0			0
$263$	10.3407	−	7.51296i	0.637635	−	0.463269i	−0.221402	−	0.975183i	$-0.571063\pi$
$263$	10.3407	−	7.51296i	0.637635	−	0.463269i	0.859037	+	0.511914i	$0.171063\pi$
$264$		0			0
$265$	−1.79880	−	17.1145i	−0.110500	−	1.05133i
$266$		0			0
$267$	1.53848	−	4.73496i	0.0941536	−	0.289775i
$268$		0			0
$269$	6.58562	−	20.2685i	0.401533	−	1.23579i	−0.522224	−	0.852809i	$-0.674897\pi$
$269$	6.58562	−	20.2685i	0.401533	−	1.23579i	0.923756	−	0.382981i	$-0.125103\pi$
$270$		0			0
$271$	−4.14194	−	12.7476i	−0.251605	−	0.774361i	−0.994480	−	0.104930i	$-0.966538\pi$
$271$	−4.14194	−	12.7476i	−0.251605	−	0.774361i	0.742875	−	0.669431i	$-0.233462\pi$
$272$		0			0
$273$	−0.133773	−	0.0971915i	−0.00809629	−	0.00588230i
$274$		0			0
$275$	3.34565	+	5.79484i	0.201750	+	0.349442i
$276$		0			0
$277$	15.2678	+	11.0927i	0.917354	+	0.666496i	0.942864	−	0.333178i	$-0.108121\pi$
$277$	15.2678	+	11.0927i	0.917354	+	0.666496i	−0.0255104	+	0.999675i	$0.508121\pi$
$278$		0			0
$279$	−1.09336	−	3.36501i	−0.0654576	−	0.201458i
$280$		0			0
$281$	−5.37674	+	16.5479i	−0.320750	+	0.987166i	0.652573	+	0.757726i	$0.273690\pi$
$281$	−5.37674	+	16.5479i	−0.320750	+	0.987166i	−0.973323	+	0.229440i	$0.926310\pi$
$282$		0			0
$283$	7.31371	−	22.5093i	0.434755	−	1.33804i	−0.458583	−	0.888652i	$-0.651643\pi$
$283$	7.31371	−	22.5093i	0.434755	−	1.33804i	0.893338	−	0.449386i	$-0.148357\pi$
$284$		0			0
$285$	−12.3201	−	2.61872i	−0.729781	−	0.155120i
$286$		0			0
$287$	4.34060	−	3.15363i	0.256217	−	0.186153i
$288$		0			0
$289$	0.537103	+	0.390228i	0.0315943	+	0.0229546i
$290$		0			0
$291$	−3.28562	+	2.38714i	−0.192606	+	0.139937i
$292$		0			0
$293$	19.0317			1.11184			0.555921	−	0.831235i	$-0.312366\pi$
$293$	19.0317			1.11184			0.555921	+	0.831235i	$0.312366\pi$
$294$		0			0
$295$	−8.48180	+	3.77634i	−0.493829	+	0.219867i
$296$		0			0
$297$	−0.413545	−	1.27276i	−0.0239963	−	0.0738531i
$298$		0			0
$299$	0.0740796			0.00428414
$300$		0			0
$301$	−4.57537			−0.263720
$302$		0			0
$303$	5.70101	+	17.5459i	0.327515	+	1.00799i
$304$		0			0
$305$	−3.10670	−	3.45034i	−0.177889	−	0.197566i
$306$		0			0
$307$	−0.669899			−0.0382332			−0.0191166	−	0.999817i	$-0.506085\pi$
$307$	−0.669899			−0.0382332			−0.0191166	+	0.999817i	$0.506085\pi$
$308$		0			0
$309$	11.9058	−	8.65009i	0.677299	−	0.492086i
$310$		0			0
$311$	−25.5534	−	18.5656i	−1.44900	−	1.05276i	−0.986064	−	0.166366i	$-0.946797\pi$
$311$	−25.5534	−	18.5656i	−1.44900	−	1.05276i	−0.462934	−	0.886393i	$-0.653203\pi$
$312$		0			0
$313$	1.17726	−	0.855327i	0.0665425	−	0.0483459i	−0.554017	−	0.832506i	$-0.686906\pi$
$313$	1.17726	−	0.855327i	0.0665425	−	0.0483459i	0.620559	+	0.784160i	$0.286906\pi$
$314$		0			0
$315$	−1.11803	+	0.497781i	−0.0629941	+	0.0280468i
$316$		0			0
$317$	−4.95857	+	15.2609i	−0.278501	+	0.857138i	0.709771	+	0.704433i	$0.248798\pi$
$317$	−4.95857	+	15.2609i	−0.278501	+	0.857138i	−0.988272	+	0.152705i	$0.951202\pi$
$318$		0			0
$319$	0.566449	−	1.74335i	0.0317151	−	0.0976089i
$320$		0			0
$321$	−1.57762	−	4.85541i	−0.0880541	−	0.271003i
$322$		0			0
$323$	18.4186	+	13.3819i	1.02484	+	0.744590i
$324$		0			0
$325$	−1.47756	+	0.314065i	−0.0819601	+	0.0174212i
$326$		0			0
$327$	−3.82331	−	2.77780i	−0.211430	−	0.153613i
$328$		0			0
$329$	−1.77143	−	5.45189i	−0.0976619	−	0.300572i
$330$		0			0
$331$	−8.31262	+	25.5836i	−0.456903	+	1.40620i	0.411984	+	0.911191i	$0.364836\pi$
$331$	−8.31262	+	25.5836i	−0.456903	+	1.40620i	−0.868887	+	0.495011i	$0.835164\pi$
$332$		0			0
$333$	−0.676034	+	2.08062i	−0.0370464	+	0.114017i
$334$		0			0
$335$	9.48757	−	16.4330i	0.518361	−	0.897828i
$336$		0			0
$337$	−1.10171	+	0.800436i	−0.0600137	+	0.0436025i	−0.617388	−	0.786659i	$-0.711809\pi$
$337$	−1.10171	+	0.800436i	−0.0600137	+	0.0436025i	0.557374	+	0.830262i	$0.311809\pi$
$338$		0			0
$339$	−3.34799	−	2.43246i	−0.181838	−	0.132113i
$340$		0			0
$341$	−3.83070	+	2.78317i	−0.207444	+	0.150717i
$342$		0			0
$343$	−7.49850			−0.404881
$344$		0			0
$345$	0.274147	−	0.474837i	0.0147596	−	0.0255644i
$346$		0			0
$347$	−0.712835	−	2.19388i	−0.0382670	−	0.117774i	0.930098	−	0.367311i	$-0.119722\pi$
$347$	−0.712835	−	2.19388i	−0.0382670	−	0.117774i	−0.968365	+	0.249537i	$0.919722\pi$
$348$		0			0
$349$	2.35292			0.125949			0.0629744	−	0.998015i	$-0.479941\pi$
$349$	2.35292			0.125949			0.0629744	+	0.998015i	$0.479941\pi$
$350$		0			0
$351$	0.302113			0.0161256
$352$		0			0
$353$	−9.55559	−	29.4091i	−0.508593	−	1.56529i	−0.794646	−	0.607073i	$-0.792343\pi$
$353$	−9.55559	−	29.4091i	−0.508593	−	1.56529i	0.286053	−	0.958214i	$-0.407657\pi$
$354$		0			0
$355$	−2.14642	−	20.4218i	−0.113920	−	1.08388i
$356$		0			0
$357$	2.21215			0.117079
$358$		0			0
$359$	15.8812	−	11.5383i	0.838176	−	0.608971i	−0.0836845	−	0.996492i	$-0.526669\pi$
$359$	15.8812	−	11.5383i	0.838176	−	0.608971i	0.921861	+	0.387522i	$0.126669\pi$
$360$		0			0
$361$	−10.2977	−	7.48170i	−0.541983	−	0.393774i
$362$		0			0
$363$	7.45028	−	5.41295i	0.391038	−	0.284106i
$364$		0			0
$365$	−16.3926	−	18.2058i	−0.858025	−	0.952934i
$366$		0			0
$367$	−9.94076	+	30.5945i	−0.518903	+	1.59702i	0.257163	+	0.966368i	$0.417212\pi$
$367$	−9.94076	+	30.5945i	−0.518903	+	1.59702i	−0.776066	+	0.630652i	$0.782788\pi$
$368$		0			0
$369$	−3.02924	+	9.32306i	−0.157696	+	0.485339i
$370$		0			0
$371$	−1.30163	−	4.00599i	−0.0675770	−	0.207981i
$372$		0			0
$373$	11.0291	+	8.01309i	0.571064	+	0.414902i	0.835492	−	0.549503i	$-0.185183\pi$
$373$	11.0291	+	8.01309i	0.571064	+	0.414902i	−0.264428	+	0.964406i	$0.585183\pi$
$374$		0			0
$375$	−3.45492	+	10.6331i	−0.178411	+	0.549093i
$376$		0			0
$377$	0.334784	+	0.243235i	0.0172423	+	0.0125272i
$378$		0			0
$379$	7.62106	+	23.4552i	0.391467	+	1.20481i	0.931679	+	0.363283i	$0.118344\pi$
$379$	7.62106	+	23.4552i	0.391467	+	1.20481i	−0.540211	+	0.841529i	$0.681656\pi$
$380$		0			0
$381$	−3.91775	+	12.0576i	−0.200712	+	0.617729i
$382$		0			0
$383$	−3.79232	+	11.6716i	−0.193779	+	0.596389i	0.806210	+	0.591629i	$0.201515\pi$
$383$	−3.79232	+	11.6716i	−0.193779	+	0.596389i	−0.999989	+	0.00475994i	$0.998485\pi$
$384$		0			0
$385$	1.09591	+	1.21714i	0.0558530	+	0.0620310i
$386$		0			0
$387$	6.76308	−	4.91366i	0.343787	−	0.249776i
$388$		0			0
$389$	−9.39823	−	6.82822i	−0.476509	−	0.346204i	0.323463	−	0.946241i	$-0.395153\pi$
$389$	−9.39823	−	6.82822i	−0.476509	−	0.346204i	−0.799973	+	0.600036i	$0.795153\pi$
$390$		0			0
$391$	−0.801790	+	0.582535i	−0.0405483	+	0.0294600i
$392$		0			0
$393$	−12.3309			−0.622012
$394$		0			0
$395$	3.54874	+	33.7640i	0.178556	+	1.69885i
$396$		0			0
$397$	5.26383	+	16.2004i	0.264184	+	0.813075i	0.991880	+	0.127175i	$0.0405911\pi$
$397$	5.26383	+	16.2004i	0.264184	+	0.813075i	−0.727696	+	0.685900i	$0.759409\pi$
$398$		0			0
$399$	−3.08294			−0.154340
$400$		0			0
$401$	32.2134			1.60866			0.804330	−	0.594183i	$-0.202524\pi$
$401$	32.2134			1.60866			0.804330	+	0.594183i	$0.202524\pi$
$402$		0			0
$403$	−0.330318	−	1.01661i	−0.0164543	−	0.0506412i
$404$		0			0
$405$	1.11803	−	1.93649i	0.0555556	−	0.0962250i
$406$		0			0
$407$	2.92770			0.145121
$408$		0			0
$409$	5.64632	−	4.10229i	0.279193	−	0.202845i	−0.439373	−	0.898305i	$-0.644799\pi$
$409$	5.64632	−	4.10229i	0.279193	−	0.202845i	0.718565	+	0.695460i	$0.244799\pi$
$410$		0			0
$411$	−8.67508	−	6.30281i	−0.427910	−	0.310895i
$412$		0			0
$413$	−1.83853	+	1.33577i	−0.0904681	+	0.0657289i
$414$		0			0
$415$	−7.43960	+	12.8858i	−0.365196	+	0.632537i
$416$		0			0
$417$	−4.22575	+	13.0055i	−0.206936	+	0.636883i
$418$		0			0
$419$	8.60796	−	26.4926i	0.420526	−	1.29425i	−0.486687	−	0.873576i	$-0.661795\pi$
$419$	8.60796	−	26.4926i	0.420526	−	1.29425i	0.907214	−	0.420670i	$-0.138205\pi$
$420$		0			0
$421$	2.65766	+	8.17943i	0.129526	+	0.398641i	0.994699	−	0.102834i	$-0.0327910\pi$
$421$	2.65766	+	8.17943i	0.129526	+	0.398641i	−0.865172	+	0.501475i	$0.832791\pi$
$422$		0			0
$423$	8.47341	+	6.15630i	0.411991	+	0.299329i
$424$		0			0
$425$	13.5224	−	15.0182i	0.655935	−	0.728489i
$426$		0			0
$427$	−0.919392	−	0.667977i	−0.0444925	−	0.0323257i
$428$		0			0
$429$	−0.124938	−	0.384518i	−0.00603204	−	0.0185647i
$430$		0			0
$431$	0.0559037	−	0.172054i	0.00269278	−	0.00828754i	−0.949701	−	0.313158i	$-0.898613\pi$
$431$	0.0559037	−	0.172054i	0.00269278	−	0.00828754i	0.952394	+	0.304870i	$0.0986131\pi$
$432$		0			0
$433$	−9.71549	+	29.9012i	−0.466897	+	1.43696i	0.389684	+	0.920948i	$0.372584\pi$
$433$	−9.71549	+	29.9012i	−0.466897	+	1.43696i	−0.856581	+	0.516012i	$0.827416\pi$
$434$		0			0
$435$	2.79803	−	1.24576i	0.134155	−	0.0597298i
$436$		0			0
$437$	1.11741	−	0.811845i	0.0534529	−	0.0388358i
$438$		0			0
$439$	13.6019	+	9.88233i	0.649181	+	0.471658i	0.862992	−	0.505217i	$-0.168588\pi$
$439$	13.6019	+	9.88233i	0.649181	+	0.471658i	−0.213811	+	0.976875i	$0.568588\pi$
$440$		0			0
$441$	5.42077	−	3.93842i	0.258132	−	0.187544i
$442$		0			0
$443$	36.1952			1.71969			0.859843	−	0.510559i	$-0.170561\pi$
$443$	36.1952			1.71969			0.859843	+	0.510559i	$0.170561\pi$
$444$		0			0
$445$	−7.44914	−	8.27311i	−0.353123	−	0.392183i
$446$		0			0
$447$	2.74461	+	8.44705i	0.129816	+	0.399532i
$448$		0			0
$449$	28.3299			1.33697			0.668486	−	0.743725i	$-0.266943\pi$
$449$	28.3299			1.33697			0.668486	+	0.743725i	$0.266943\pi$
$450$		0			0
$451$	13.1188			0.617738
$452$		0			0
$453$	0.829124	+	2.55178i	0.0389557	+	0.119893i
$454$		0			0
$455$	−0.337773	+	0.150386i	−0.0158350	+	0.00705022i
$456$		0			0
$457$	16.5396			0.773691			0.386846	−	0.922144i	$-0.373565\pi$
$457$	16.5396			0.773691			0.386846	+	0.922144i	$0.373565\pi$
$458$		0			0
$459$	−3.26988	+	2.37571i	−0.152625	+	0.110889i
$460$		0			0
$461$	−0.351142	−	0.255120i	−0.0163543	−	0.0118821i	0.579578	−	0.814917i	$-0.303217\pi$
$461$	−0.351142	−	0.255120i	−0.0163543	−	0.0118821i	−0.595932	+	0.803035i	$0.703217\pi$
$462$		0			0
$463$	16.1500	−	11.7337i	0.750556	−	0.545311i	−0.145443	−	0.989367i	$-0.546461\pi$
$463$	16.1500	−	11.7337i	0.750556	−	0.545311i	0.895999	+	0.444056i	$0.146461\pi$
$464$		0			0
$465$	−7.73873	−	1.64492i	−0.358875	−	0.0762812i
$466$		0			0
$467$	−1.91815	+	5.90347i	−0.0887615	+	0.273180i	−0.985578	−	0.169223i	$-0.945874\pi$
$467$	−1.91815	+	5.90347i	−0.0887615	+	0.273180i	0.896816	+	0.442403i	$0.145874\pi$
$468$		0			0
$469$	1.43523	−	4.41719i	0.0662729	−	0.203967i
$470$		0			0
$471$	3.63328	+	11.1821i	0.167413	+	0.515244i
$472$		0			0
$473$	−9.05077	−	6.57577i	−0.416155	−	0.302354i
$474$		0			0
$475$	−18.8455	+	20.9300i	−0.864689	+	0.960334i
$476$		0			0
$477$	6.22618	+	4.52358i	0.285077	+	0.207121i
$478$		0			0
$479$	7.25191	+	22.3191i	0.331348	+	1.01978i	0.968493	+	0.249041i	$0.0801153\pi$
$479$	7.25191	+	22.3191i	0.331348	+	1.01978i	−0.637145	+	0.770744i	$0.719885\pi$
$480$		0			0
$481$	−0.204239	+	0.628583i	−0.00931250	+	0.0286609i
$482$		0			0
$483$	0.0414716	−	0.127637i	0.00188702	−	0.00580766i
$484$		0			0
$485$	0.949247	+	9.03148i	0.0431031	+	0.410098i
$486$		0			0
$487$	2.70709	−	1.96682i	0.122670	−	0.0891250i	−0.524759	−	0.851251i	$-0.675844\pi$
$487$	2.70709	−	1.96682i	0.122670	−	0.0891250i	0.647429	+	0.762126i	$0.275844\pi$
$488$		0			0
$489$	14.8153	+	10.7639i	0.669971	+	0.486762i
$490$		0			0
$491$	0.442522	−	0.321511i	0.0199708	−	0.0145096i	−0.577755	−	0.816210i	$-0.696071\pi$
$491$	0.442522	−	0.321511i	0.0199708	−	0.0145096i	0.597726	+	0.801701i	$0.296071\pi$
$492$		0			0
$493$	−5.53620			−0.249338
$494$		0			0
$495$	−2.92705	−	0.622164i	−0.131561	−	0.0279642i
$496$		0			0
$497$	−1.55316	−	4.78015i	−0.0696690	−	0.214419i
$498$		0			0
$499$	−8.08164			−0.361784			−0.180892	−	0.983503i	$-0.557898\pi$
$499$	−8.08164			−0.361784			−0.180892	+	0.983503i	$0.557898\pi$
$500$		0			0
$501$	4.40418			0.196764
$502$		0			0
$503$	−8.74922	−	26.9273i	−0.390109	−	1.20063i	−0.932706	−	0.360638i	$-0.882559\pi$
$503$	−8.74922	−	26.9273i	−0.390109	−	1.20063i	0.542597	−	0.839993i	$-0.317441\pi$
$504$		0			0
$505$	40.3514	+	8.57696i	1.79562	+	0.381670i
$506$		0			0
$507$	−12.9087			−0.573297
$508$		0			0
$509$	−4.61968	+	3.35639i	−0.204764	+	0.148770i	−0.685441	−	0.728128i	$-0.740391\pi$
$509$	−4.61968	+	3.35639i	−0.204764	+	0.148770i	0.480678	+	0.876897i	$0.340391\pi$
$510$		0			0
$511$	−4.85119	−	3.52459i	−0.214604	−	0.155919i
$512$		0			0
$513$	4.55705	−	3.31089i	0.201198	−	0.146179i
$514$		0			0
$515$	−3.43971	−	32.7266i	−0.151572	−	1.44211i
$516$		0			0
$517$	4.33136	−	13.3305i	0.190493	−	0.586277i
$518$		0			0
$519$	−4.92287	+	15.1510i	−0.216090	+	0.665056i
$520$		0			0
$521$	−7.87683	−	24.2424i	−0.345090	−	1.06208i	−0.961536	−	0.274681i	$-0.911428\pi$
$521$	−7.87683	−	24.2424i	−0.345090	−	1.06208i	0.616445	−	0.787398i	$-0.288572\pi$
$522$		0			0
$523$	−2.29098	−	1.66449i	−0.100177	−	0.0727832i	0.536569	−	0.843857i	$-0.319720\pi$
$523$	−2.29098	−	1.66449i	−0.100177	−	0.0727832i	−0.636746	+	0.771073i	$0.719720\pi$
$524$		0			0
$525$	−0.286052	+	2.72160i	−0.0124843	+	0.118780i
$526$		0			0
$527$	11.5694	+	8.40568i	0.503972	+	0.366157i
$528$		0			0
$529$	−7.08881	−	21.8171i	−0.308209	−	0.948570i
$530$		0			0
$531$	1.28308	−	3.94893i	0.0556811	−	0.171369i
$532$		0			0
$533$	−0.915175	+	2.81662i	−0.0396406	+	0.122001i
$534$		0			0
$535$	−11.1663	−	2.37347i	−0.482761	−	0.102614i
$536$		0			0
$537$	−3.04982	+	2.21582i	−0.131609	+	0.0956198i
$538$		0			0
$539$	−7.25441	−	5.27064i	−0.312470	−	0.227022i
$540$		0			0
$541$	−3.64130	+	2.64556i	−0.156552	+	0.113742i	−0.663303	−	0.748351i	$-0.730846\pi$
$541$	−3.64130	+	2.64556i	−0.156552	+	0.113742i	0.506752	+	0.862092i	$0.330846\pi$
$542$		0			0
$543$	−26.6868			−1.14524
$544$		0			0
$545$	−9.65378	+	4.29814i	−0.413522	+	0.184112i
$546$		0			0
$547$	2.94045	+	9.04979i	0.125725	+	0.386941i	0.994032	−	0.109085i	$-0.0347921\pi$
$547$	2.94045	+	9.04979i	0.125725	+	0.386941i	−0.868308	+	0.496026i	$0.834792\pi$
$548$		0			0
$549$	2.07636			0.0886170
$550$		0			0
$551$	7.71549			0.328691
$552$		0			0
$553$	2.56789	+	7.90316i	0.109198	+	0.336077i
$554$		0			0
$555$	3.27327	+	3.63534i	0.138943	+	0.154311i
$556$		0			0
$557$	25.5173			1.08120			0.540601	−	0.841279i	$-0.318197\pi$
$557$	25.5173			1.08120			0.540601	+	0.841279i	$0.318197\pi$
$558$		0			0
$559$	2.04322	−	1.48448i	0.0864189	−	0.0627870i
$560$		0			0
$561$	4.37595	+	3.17932i	0.184753	+	0.134231i
$562$		0			0
$563$	−11.1180	+	8.07772i	−0.468569	+	0.340435i	−0.796883	−	0.604133i	$-0.793520\pi$
$563$	−11.1180	+	8.07772i	−0.468569	+	0.340435i	0.328314	+	0.944569i	$0.393520\pi$
$564$		0			0
$565$	−8.45360	+	3.76378i	−0.355645	+	0.158344i
$566$		0			0
$567$	0.169131	−	0.520530i	0.00710282	−	0.0218602i
$568$		0			0
$569$	−8.75873	+	26.9566i	−0.367185	+	1.13008i	0.581416	+	0.813606i	$0.302499\pi$
$569$	−8.75873	+	26.9566i	−0.367185	+	1.13008i	−0.948601	+	0.316473i	$0.897501\pi$
$570$		0			0
$571$	−0.603552	−	1.85754i	−0.0252579	−	0.0777357i	0.937633	−	0.347627i	$-0.113012\pi$
$571$	−0.603552	−	1.85754i	−0.0252579	−	0.0777357i	−0.962891	+	0.269891i	$0.913012\pi$
$572$		0			0
$573$	−3.74803	−	2.72310i	−0.156576	−	0.113759i
$574$		0			0
$575$	−0.613012	−	1.06177i	−0.0255644	−	0.0442788i
$576$		0			0
$577$	−34.6572	−	25.1799i	−1.44280	−	1.04825i	−0.987448	−	0.157942i	$-0.949514\pi$
$577$	−34.6572	−	25.1799i	−1.44280	−	1.04825i	−0.455350	−	0.890313i	$-0.650486\pi$
$578$		0			0
$579$	−6.41026	−	19.7287i	−0.266401	−	0.819898i
$580$		0			0
$581$	−1.12543	+	3.46370i	−0.0466905	+	0.143699i
$582$		0			0
$583$	3.18264	−	9.79515i	0.131811	−	0.405674i
$584$		0			0
$585$	0.337773	−	0.585040i	0.0139652	−	0.0241884i
$586$		0			0
$587$	1.59845	−	1.16134i	0.0659751	−	0.0479337i	−0.554309	−	0.832311i	$-0.687017\pi$
$587$	1.59845	−	1.16134i	0.0659751	−	0.0479337i	0.620284	+	0.784377i	$0.287017\pi$
$588$		0			0
$589$	−16.1237	−	11.7145i	−0.664364	−	0.482688i
$590$		0			0
$591$	−16.6122	+	12.0695i	−0.683334	+	0.496471i
$592$		0			0
$593$	−17.3986			−0.714475			−0.357237	−	0.934014i	$-0.616281\pi$
$593$	−17.3986			−0.714475			−0.357237	+	0.934014i	$0.616281\pi$
$594$		0			0
$595$	2.47326	−	4.28381i	0.101394	−	0.175619i
$596$		0			0
$597$	1.82764	+	5.62490i	0.0748004	+	0.230212i
$598$		0			0
$599$	−3.17298			−0.129644			−0.0648222	−	0.997897i	$-0.520648\pi$
$599$	−3.17298			−0.129644			−0.0648222	+	0.997897i	$0.520648\pi$
$600$		0			0
$601$	32.1659			1.31207			0.656037	−	0.754729i	$-0.272232\pi$
$601$	32.1659			1.31207			0.656037	+	0.754729i	$0.272232\pi$
$602$		0			0
$603$	2.62230	+	8.07061i	0.106788	+	0.328661i
$604$		0			0
$605$	−2.15246	−	20.4793i	−0.0875099	−	0.832601i
$606$		0			0
$607$	−28.4215			−1.15359			−0.576797	−	0.816888i	$-0.695698\pi$
$607$	−28.4215			−1.15359			−0.576797	+	0.816888i	$0.695698\pi$
$608$		0			0
$609$	0.606506	−	0.440652i	0.0245769	−	0.0178561i
$610$		0			0
$611$	2.55993	+	1.85990i	0.103564	+	0.0752435i
$612$		0			0
$613$	2.00920	−	1.45977i	0.0811510	−	0.0589597i	−0.546470	−	0.837479i	$-0.684029\pi$
$613$	2.00920	−	1.45977i	0.0811510	−	0.0589597i	0.627621	+	0.778519i	$0.284029\pi$
$614$		0			0
$615$	14.6672	+	16.2896i	0.591439	+	0.656860i
$616$		0			0
$617$	3.03970	−	9.35524i	0.122374	−	0.376628i	−0.871040	−	0.491213i	$-0.836554\pi$
$617$	3.03970	−	9.35524i	0.122374	−	0.376628i	0.993413	+	0.114585i	$0.0365538\pi$
$618$		0			0
$619$	−4.22997	+	13.0185i	−0.170017	+	0.523258i	−0.999371	−	0.0354655i	$-0.988709\pi$
$619$	−4.22997	+	13.0185i	−0.170017	+	0.523258i	0.829354	+	0.558723i	$0.188709\pi$
$620$		0			0
$621$	0.0757724	+	0.233204i	0.00304064	+	0.00935814i
$622$		0			0
$623$	−2.20449	−	1.60165i	−0.0883210	−	0.0641689i
$624$		0			0
$625$	16.7283	+	18.5786i	0.669131	+	0.743145i
$626$		0			0
$627$	−6.09852	−	4.43083i	−0.243551	−	0.176950i
$628$		0			0
$629$	−2.73239	−	8.40944i	−0.108948	−	0.335306i
$630$		0			0
$631$	6.15441	−	18.9413i	0.245003	−	0.754042i	−0.750633	−	0.660720i	$-0.770251\pi$
$631$	6.15441	−	18.9413i	0.245003	−	0.754042i	0.995636	−	0.0933224i	$-0.0297487\pi$
$632$		0			0
$633$	7.08592	−	21.8082i	0.281640	−	0.866799i
$634$		0			0
$635$	18.9692	+	21.0675i	0.752772	+	0.836038i
$636$		0			0
$637$	1.63769	−	1.18985i	0.0648876	−	0.0471436i
$638$		0			0
$639$	7.42939	+	5.39777i	0.293902	+	0.213532i
$640$		0			0
$641$	10.6407	−	7.73090i	0.420281	−	0.305352i	−0.357470	−	0.933925i	$-0.616360\pi$
$641$	10.6407	−	7.73090i	0.420281	−	0.305352i	0.777751	+	0.628572i	$0.216360\pi$
$642$		0			0
$643$	−34.4841			−1.35992			−0.679960	−	0.733249i	$-0.738003\pi$
$643$	−34.4841			−1.35992			−0.679960	+	0.733249i	$0.738003\pi$
$644$		0			0
$645$	−1.95392	−	18.5903i	−0.0769355	−	0.731992i
$646$		0			0
$647$	−11.7895	−	36.2842i	−0.463492	−	1.42648i	−0.860870	−	0.508825i	$-0.830080\pi$
$647$	−11.7895	−	36.2842i	−0.463492	−	1.42648i	0.397378	−	0.917655i	$-0.369920\pi$
$648$		0			0
$649$	−5.55666			−0.218118
$650$		0			0
$651$	−1.93651			−0.0758978
$652$		0			0
$653$	−10.7056	−	32.9484i	−0.418942	−	1.28937i	−0.908677	−	0.417499i	$-0.862907\pi$
$653$	−10.7056	−	32.9484i	−0.418942	−	1.28937i	0.489736	−	0.871871i	$-0.337093\pi$
$654$		0			0
$655$	−13.7864	+	23.8787i	−0.538678	+	0.933018i
$656$		0			0
$657$	10.9560			0.427433
$658$		0			0
$659$	−40.6525	+	29.5358i	−1.58360	+	1.15055i	−0.671178	+	0.741297i	$0.734211\pi$
$659$	−40.6525	+	29.5358i	−1.58360	+	1.15055i	−0.912420	+	0.409254i	$0.865789\pi$
$660$		0			0
$661$	−8.72436	−	6.33862i	−0.339338	−	0.246544i	0.405044	−	0.914297i	$-0.367256\pi$
$661$	−8.72436	−	6.33862i	−0.339338	−	0.246544i	−0.744383	+	0.667753i	$0.767256\pi$
$662$		0			0
$663$	−0.987875	+	0.717733i	−0.0383659	+	0.0278744i
$664$		0			0
$665$	−3.44684	+	5.97009i	−0.133663	+	0.231510i
$666$		0			0
$667$	−0.103788	+	0.319428i	−0.00401870	+	0.0123683i
$668$		0			0
$669$	−3.93990	+	12.1258i	−0.152325	+	0.468810i
$670$		0			0
$671$	−0.858670	−	2.64272i	−0.0331486	−	0.102021i
$672$		0			0
$673$	13.6011	+	9.88179i	0.524285	+	0.380915i	0.818216	−	0.574912i	$-0.194964\pi$
$673$	13.6011	+	9.88179i	0.524285	+	0.380915i	−0.293931	+	0.955827i	$0.594964\pi$
$674$		0			0
$675$	−2.50000	−	4.33013i	−0.0962250	−	0.166667i
$676$		0			0
$677$	−30.1258	−	21.8877i	−1.15783	−	0.841211i	−0.168325	−	0.985731i	$-0.553836\pi$
$677$	−30.1258	−	21.8877i	−1.15783	−	0.841211i	−0.989502	+	0.144521i	$0.953836\pi$
$678$		0			0
$679$	0.686881	+	2.11400i	0.0263601	+	0.0811280i
$680$		0			0
$681$	3.40828	−	10.4896i	0.130606	−	0.401963i
$682$		0			0
$683$	−9.83629	+	30.2730i	−0.376375	+	1.15836i	0.566171	+	0.824288i	$0.308424\pi$
$683$	−9.83629	+	30.2730i	−0.376375	+	1.15836i	−0.942546	+	0.334076i	$0.891576\pi$
$684$		0			0
$685$	−21.9044	+	9.75246i	−0.836923	+	0.372622i
$686$		0			0
$687$	18.6722	−	13.5661i	0.712389	−	0.517581i
$688$		0			0
$689$	1.88101	+	1.36663i	0.0716608	+	0.0520646i
$690$		0			0
$691$	15.3436	−	11.1478i	0.583699	−	0.424082i	−0.256357	−	0.966582i	$-0.582522\pi$
$691$	15.3436	−	11.1478i	0.583699	−	0.424082i	0.840056	+	0.542500i	$0.182522\pi$
$692$		0			0
$693$	−0.732455			−0.0278237
$694$		0			0
$695$	20.4606	+	22.7237i	0.776113	+	0.861961i
$696$		0			0
$697$	−12.2436	−	37.6819i	−0.463759	−	1.42730i
$698$		0			0
$699$	−29.2882			−1.10778
$700$		0			0
$701$	−19.2027			−0.725275			−0.362638	−	0.931930i	$-0.618124\pi$
$701$	−19.2027			−0.725275			−0.362638	+	0.931930i	$0.618124\pi$
$702$		0			0
$703$	3.80798	+	11.7197i	0.143621	+	0.442019i
$704$		0			0
$705$	21.3952	−	9.52575i	0.805789	−	0.358760i
$706$		0			0
$707$	10.0974			0.379752
$708$		0			0
$709$	8.91896	−	6.48000i	0.334959	−	0.243362i	−0.407573	−	0.913173i	$-0.633625\pi$
$709$	8.91896	−	6.48000i	0.334959	−	0.243362i	0.742532	+	0.669811i	$0.233625\pi$
$710$		0			0
$711$	−12.2832	−	8.92428i	−0.460657	−	0.334687i
$712$		0			0
$713$	0.701886	−	0.509950i	0.0262858	−	0.0190978i
$714$		0			0
$715$	−0.884301	−	0.187964i	−0.0330710	−	0.00702946i
$716$		0			0
$717$	3.27514	−	10.0798i	0.122312	−	0.376439i
$718$		0			0
$719$	8.20996	−	25.2676i	0.306180	−	0.942324i	−0.673055	−	0.739593i	$-0.735018\pi$
$719$	8.20996	−	25.2676i	0.306180	−	0.942324i	0.979234	−	0.202732i	$-0.0649819\pi$
$720$		0			0
$721$	−2.48899	−	7.66034i	−0.0926950	−	0.285286i
$722$		0			0
$723$	−15.3888	−	11.1806i	−0.572317	−	0.415812i
$724$		0			0
$725$	0.715883	−	6.81118i	0.0265872	−	0.252961i
$726$		0			0
$727$	−22.1224	−	16.0729i	−0.820474	−	0.596109i	0.0963741	−	0.995345i	$-0.469275\pi$
$727$	−22.1224	−	16.0729i	−0.820474	−	0.596109i	−0.916848	+	0.399236i	$0.869275\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−10.4410	+	32.1342i	−0.386176	+	1.18853i
$732$		0			0
$733$	2.56626	−	7.89814i	0.0947871	−	0.291725i	−0.892411	−	0.451223i	$-0.850988\pi$
$733$	2.56626	−	7.89814i	0.0947871	−	0.291725i	0.987198	+	0.159499i	$0.0509878\pi$
$734$		0			0
$735$	−1.56611	−	14.9006i	−0.0577669	−	0.549616i
$736$		0			0
$737$	9.18753	−	6.67513i	0.338427	−	0.245882i
$738$		0			0
$739$	−1.30623	−	0.949030i	−0.0480504	−	0.0349106i	0.563501	−	0.826116i	$-0.309454\pi$
$739$	−1.30623	−	0.949030i	−0.0480504	−	0.0349106i	−0.611551	+	0.791205i	$0.709454\pi$
$740$		0			0
$741$	1.37674	−	1.00026i	0.0505760	−	0.0367456i
$742$		0			0
$743$	−3.77367			−0.138443			−0.0692213	−	0.997601i	$-0.522051\pi$
$743$	−3.77367			−0.138443			−0.0692213	+	0.997601i	$0.522051\pi$
$744$		0			0
$745$	19.4262	+	4.12917i	0.711722	+	0.151281i
$746$		0			0
$747$	−2.05626	−	6.32850i	−0.0752344	−	0.231548i
$748$		0			0
$749$	−2.79421			−0.102098
$750$		0			0
$751$	53.4032			1.94871			0.974355	−	0.225016i	$-0.0722435\pi$
$751$	53.4032			1.94871			0.974355	+	0.225016i	$0.0722435\pi$
$752$		0			0
$753$	0.0114588	+	0.0352667i	0.000417583	+	0.00128519i
$754$		0			0
$755$	5.86850	+	1.24739i	0.213576	+	0.0453971i
$756$		0			0
$757$	11.6322			0.422781			0.211390	−	0.977402i	$-0.432201\pi$
$757$	11.6322			0.422781			0.211390	+	0.977402i	$0.432201\pi$
$758$		0			0
$759$	0.265477	−	0.192881i	0.00963622	−	0.00700112i
$760$		0			0
$761$	−3.77626	−	2.74361i	−0.136889	−	0.0994560i	0.517233	−	0.855844i	$-0.326962\pi$
$761$	−3.77626	−	2.74361i	−0.136889	−	0.0994560i	−0.654123	+	0.756389i	$0.726962\pi$
$762$		0			0
$763$	−2.09257	+	1.52034i	−0.0757561	+	0.0550400i
$764$		0			0
$765$	0.944700	+	8.98822i	0.0341557	+	0.324970i
$766$		0			0
$767$	0.387637	−	1.19302i	0.0139968	−	0.0430776i
$768$		0			0
$769$	−6.98515	+	21.4981i	−0.251891	+	0.775241i	0.742535	+	0.669807i	$0.233623\pi$
$769$	−6.98515	+	21.4981i	−0.251891	+	0.775241i	−0.994426	+	0.105434i	$0.966377\pi$
$770$		0			0
$771$	−3.09750	−	9.53312i	−0.111554	−	0.343327i
$772$		0			0
$773$	−32.1006	−	23.3225i	−1.15458	−	0.838851i	−0.165497	−	0.986210i	$-0.552923\pi$
$773$	−32.1006	−	23.3225i	−1.15458	−	0.838851i	−0.989083	+	0.147359i	$0.952923\pi$
$774$		0			0
$775$	−11.8375	+	13.1469i	−0.425217	+	0.472251i
$776$		0			0
$777$	0.968688	+	0.703793i	0.0347515	+	0.0252484i
$778$		0			0
$779$	17.0632	+	52.5151i	0.611352	+	1.88155i
$780$		0			0
$781$	3.79768	−	11.6881i	0.135892	−	0.418232i
$782$		0			0
$783$	−0.423273	+	1.30270i	−0.0151265	+	0.0465547i
$784$		0			0
$785$	25.7162	+	5.46614i	0.917850	+	0.195095i
$786$		0			0
$787$	−3.83261	+	2.78456i	−0.136618	+	0.0992587i	−0.653995	−	0.756499i	$-0.726908\pi$
$787$	−3.83261	+	2.78456i	−0.136618	+	0.0992587i	0.517377	+	0.855757i	$0.326908\pi$
$788$		0			0
$789$	10.3407	+	7.51296i	0.368139	+	0.267468i
$790$		0			0
$791$	−1.83241	+	1.33133i	−0.0651532	+	0.0473365i
$792$		0			0
$793$	0.627297			0.0222760
$794$		0			0

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.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{3} +(2.18720 + 0.464905i) q^{5} +0.547318 q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{3} +(2.18720 + 0.464905i) q^{5} +0.547318 q^{7} +(-0.809017 + 0.587785i) q^{9} +(1.08268 + 0.786610i) q^{11} +(-0.244415 + 0.177578i) q^{13} +(0.233733 + 2.22382i) q^{15} +(1.24898 - 3.84398i) q^{17} +(-1.74064 + 5.35713i) q^{19} +(0.169131 + 0.520530i) q^{21} +(-0.198375 - 0.144128i) q^{23} +(4.56773 + 2.03368i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(-0.423273 - 1.30270i) q^{29} +(-1.09336 + 3.36501i) q^{31} +(-0.413545 + 1.27276i) q^{33} +(1.19710 + 0.254451i) q^{35} +(1.76988 - 1.28589i) q^{37} +(-0.244415 - 0.177578i) q^{39} +(7.93066 - 5.76196i) q^{41} -8.35963 q^{43} +(-2.04275 + 0.909491i) q^{45} +(-3.23656 - 9.96110i) q^{47} -6.70044 q^{49} +4.04179 q^{51} +(-2.37819 - 7.31931i) q^{53} +(2.00234 + 2.22382i) q^{55} -5.63282 q^{57} +(-3.35916 + 2.44057i) q^{59} +(-1.67981 - 1.22046i) q^{61} +(-0.442790 + 0.321706i) q^{63} +(-0.617142 + 0.274769i) q^{65} +(2.62230 - 8.07061i) q^{67} +(0.0757724 - 0.233204i) q^{69} +(-2.83777 - 8.73377i) q^{71} +(-8.86356 - 6.43975i) q^{73} +(-0.522642 + 4.97261i) q^{75} +(0.592568 + 0.430526i) q^{77} +(4.69177 + 14.4398i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-2.05626 + 6.32850i) q^{83} +(4.51886 - 7.82690i) q^{85} +(1.10814 - 0.805112i) q^{87} +(-4.02780 - 2.92637i) q^{89} +(-0.133773 + 0.0971915i) q^{91} -3.53818 q^{93} +(-6.29768 + 10.9079i) q^{95} +(1.25499 + 3.86248i) q^{97} -1.33826 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8q - 2q^{3} + 5q^{5} - 8q^{7} - 2q^{9} + O(q^{10}) \)	\( 8q - 2q^{3} + 5q^{5} - 8q^{7} - 2q^{9} - 2q^{11} - 5q^{15} + 7q^{17} + 5q^{19} - 3q^{21} + 7q^{23} + 5q^{25} - 2q^{27} + 27q^{29} - 3q^{31} + 3q^{33} + 20q^{35} - 9q^{37} + 20q^{41} - 68q^{43} - 5q^{45} - 7q^{47} - 8q^{49} - 8q^{51} - 11q^{53} + 5q^{55} - 10q^{57} + 2q^{59} - 14q^{61} + 7q^{63} - 35q^{65} + 28q^{67} + 2q^{69} - 15q^{71} + 6q^{73} + 5q^{75} + 17q^{77} + 24q^{79} - 2q^{81} + 2q^{83} + 10q^{85} - 23q^{87} + 5q^{91} - 18q^{93} + 5q^{95} + 34q^{97} - 2q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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