LMFDB - Embedded newform 900.2.n.a.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(181,900)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("900.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.1
Root			$-0.104528 - 0.994522i$ of defining polynomial
Character	$\chi$	$=$	900.361
Dual form			900.2.n.a.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.18720 + 0.464905i) q^{5} +0.547318 q^{7} +O(q^{10})$	$q+(-2.18720 + 0.464905i) q^{5} +0.547318 q^{7} +(-1.08268 + 0.786610i) q^{11} +(-0.244415 - 0.177578i) q^{13} +(-1.24898 - 3.84398i) q^{17} +(-1.74064 - 5.35713i) q^{19} +(0.198375 - 0.144128i) q^{23} +(4.56773 - 2.03368i) q^{25} +(0.423273 - 1.30270i) q^{29} +(-1.09336 - 3.36501i) q^{31} +(-1.19710 + 0.254451i) q^{35} +(1.76988 + 1.28589i) q^{37} +(-7.93066 - 5.76196i) q^{41} -8.35963 q^{43} +(3.23656 - 9.96110i) q^{47} -6.70044 q^{49} +(2.37819 - 7.31931i) q^{53} +(2.00234 - 2.22382i) q^{55} +(3.35916 + 2.44057i) q^{59} +(-1.67981 + 1.22046i) q^{61} +(0.617142 + 0.274769i) q^{65} +(2.62230 + 8.07061i) q^{67} +(2.83777 - 8.73377i) q^{71} +(-8.86356 + 6.43975i) q^{73} +(-0.592568 + 0.430526i) q^{77} +(4.69177 - 14.4398i) q^{79} +(2.05626 + 6.32850i) q^{83} +(4.51886 + 7.82690i) q^{85} +(4.02780 - 2.92637i) q^{89} +(-0.133773 - 0.0971915i) q^{91} +(6.29768 + 10.9079i) q^{95} +(1.25499 - 3.86248i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{5} - 8 q^{7}+O(q^{10}) $ 8 * q - 5 * q^5 - 8 * q^7	$ 8 q - 5 q^{5} - 8 q^{7} + 2 q^{11} - 7 q^{17} + 5 q^{19} - 7 q^{23} + 5 q^{25} - 27 q^{29} - 3 q^{31} - 20 q^{35} - 9 q^{37} - 20 q^{41} - 68 q^{43} + 7 q^{47} - 8 q^{49} + 11 q^{53} + 5 q^{55} - 2 q^{59} - 14 q^{61} + 35 q^{65} + 28 q^{67} + 15 q^{71} + 6 q^{73} - 17 q^{77} + 24 q^{79} - 2 q^{83} + 10 q^{85} + 5 q^{91} - 5 q^{95} + 34 q^{97}+O(q^{100}) $ 8 * q - 5 * q^5 - 8 * q^7 + 2 * q^11 - 7 * q^17 + 5 * q^19 - 7 * q^23 + 5 * q^25 - 27 * q^29 - 3 * q^31 - 20 * q^35 - 9 * q^37 - 20 * q^41 - 68 * q^43 + 7 * q^47 - 8 * q^49 + 11 * q^53 + 5 * q^55 - 2 * q^59 - 14 * q^61 + 35 * q^65 + 28 * q^67 + 15 * q^71 + 6 * q^73 - 17 * q^77 + 24 * q^79 - 2 * q^83 + 10 * q^85 + 5 * q^91 - 5 * q^95 + 34 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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			0
$3$		0			0
$4$		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			0
$10$		0			0
$11$	−1.08268	+	0.786610i	−0.326439	+	0.237172i	−0.738918	−	0.673795i	$-0.764663\pi$
$11$	−1.08268	+	0.786610i	−0.326439	+	0.237172i	0.412479	+	0.910967i	$0.364663\pi$
$12$		0			0
$13$	−0.244415	−	0.177578i	−0.0677885	−	0.0492512i	0.553375	−	0.832932i	$-0.313340\pi$
$13$	−0.244415	−	0.177578i	−0.0677885	−	0.0492512i	−0.621163	+	0.783681i	$0.713340\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.24898	−	3.84398i	−0.302923	−	0.932301i	−0.980444	−	0.196798i	$-0.936946\pi$
$17$	−1.24898	−	3.84398i	−0.302923	−	0.932301i	0.677521	−	0.735503i	$-0.263054\pi$
$18$		0			0
$19$	−1.74064	−	5.35713i	−0.399329	−	1.22901i	−0.925538	−	0.378654i	$-0.876387\pi$
$19$	−1.74064	−	5.35713i	−0.399329	−	1.22901i	0.526209	−	0.850355i	$-0.323613\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.198375	−	0.144128i	0.0413640	−	0.0300527i	−0.566911	−	0.823779i	$-0.691862\pi$
$23$	0.198375	−	0.144128i	0.0413640	−	0.0300527i	0.608275	+	0.793726i	$0.291862\pi$
$24$		0			0
$25$	4.56773	−	2.03368i	0.913545	−	0.406737i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.423273	−	1.30270i	0.0785997	−	0.241905i	−0.904034	−	0.427460i	$-0.859408\pi$
$29$	0.423273	−	1.30270i	0.0785997	−	0.241905i	0.982634	+	0.185555i	$0.0594084\pi$
$30$		0			0
$31$	−1.09336	−	3.36501i	−0.196373	−	0.604374i	−0.999958	−	0.00918358i	$-0.997077\pi$
$31$	−1.09336	−	3.36501i	−0.196373	−	0.604374i	0.803585	−	0.595190i	$-0.202923\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.19710	+	0.254451i	−0.202346	+	0.0430100i
$36$		0			0
$37$	1.76988	+	1.28589i	0.290967	+	0.211400i	0.723687	−	0.690129i	$-0.242446\pi$
$37$	1.76988	+	1.28589i	0.290967	+	0.211400i	−0.432720	+	0.901528i	$0.642446\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−7.93066	−	5.76196i	−1.23856	−	0.899868i	−0.241060	−	0.970510i	$-0.577495\pi$
$41$	−7.93066	−	5.76196i	−1.23856	−	0.899868i	−0.997502	+	0.0706425i	$0.977495\pi$
$42$		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
$45$		0			0
$46$		0			0
$47$	3.23656	−	9.96110i	0.472100	−	1.45298i	−0.377729	−	0.925916i	$-0.623295\pi$
$47$	3.23656	−	9.96110i	0.472100	−	1.45298i	0.849829	−	0.527059i	$-0.176705\pi$
$48$		0			0
$49$	−6.70044			−0.957206
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.37819	−	7.31931i	0.326669	−	1.00538i	−0.644012	−	0.765015i	$-0.722731\pi$
$53$	2.37819	−	7.31931i	0.326669	−	1.00538i	0.970682	−	0.240369i	$-0.0772685\pi$
$54$		0			0
$55$	2.00234	−	2.22382i	0.269995	−	0.299860i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.35916	+	2.44057i	0.437325	+	0.317735i	0.784571	−	0.620039i	$-0.212883\pi$
$59$	3.35916	+	2.44057i	0.437325	+	0.317735i	−0.347246	+	0.937774i	$0.612883\pi$
$60$		0			0
$61$	−1.67981	+	1.22046i	−0.215078	+	0.156263i	−0.690108	−	0.723706i	$-0.742437\pi$
$61$	−1.67981	+	1.22046i	−0.215078	+	0.156263i	0.475030	+	0.879969i	$0.342437\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.617142	+	0.274769i	0.0765470	+	0.0340809i
$66$		0			0
$67$	2.62230	+	8.07061i	0.320365	+	0.985982i	0.973490	+	0.228732i	$0.0734578\pi$
$67$	2.62230	+	8.07061i	0.320365	+	0.985982i	−0.653125	+	0.757251i	$0.726542\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.83777	−	8.73377i	0.336782	−	1.03651i	−0.629056	−	0.777360i	$-0.716558\pi$
$71$	2.83777	−	8.73377i	0.336782	−	1.03651i	0.965838	−	0.259148i	$-0.0834416\pi$
$72$		0			0
$73$	−8.86356	+	6.43975i	−1.03740	+	0.753716i	−0.969777	−	0.243995i	$-0.921542\pi$
$73$	−8.86356	+	6.43975i	−1.03740	+	0.753716i	−0.0676248	+	0.997711i	$0.521542\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.592568	+	0.430526i	−0.0675294	+	0.0490630i
$78$		0			0
$79$	4.69177	−	14.4398i	0.527866	−	1.62460i	−0.230713	−	0.973022i	$-0.574106\pi$
$79$	4.69177	−	14.4398i	0.527866	−	1.62460i	0.758578	−	0.651582i	$-0.225894\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.05626	+	6.32850i	0.225703	+	0.694643i	0.998219	+	0.0596483i	$0.0189979\pi$
$83$	2.05626	+	6.32850i	0.225703	+	0.694643i	−0.772516	+	0.634995i	$0.781002\pi$
$84$		0			0
$85$	4.51886	+	7.82690i	0.490140	+	0.848947i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.02780	−	2.92637i	0.426946	−	0.310194i	−0.353481	−	0.935442i	$-0.615002\pi$
$89$	4.02780	−	2.92637i	0.426946	−	0.310194i	0.780427	+	0.625247i	$0.215002\pi$
$90$		0			0
$91$	−0.133773	−	0.0971915i	−0.0140232	−	0.0101884i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	6.29768	+	10.9079i	0.646128	+	1.11913i
$96$		0			0
$97$	1.25499	−	3.86248i	0.127425	−	0.392175i	−0.866910	−	0.498465i	$-0.833897\pi$
$97$	1.25499	−	3.86248i	0.127425	−	0.392175i	0.994335	+	0.106290i	$0.0338972\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−18.4489			−1.83573			−0.917865	−	0.396892i	$-0.870089\pi$
$101$	−18.4489			−1.83573			−0.917865	+	0.396892i	$0.870089\pi$
$102$		0			0
$103$	−4.54762	+	13.9961i	−0.448090	+	1.37908i	0.430969	+	0.902367i	$0.358172\pi$
$103$	−4.54762	+	13.9961i	−0.448090	+	1.37908i	−0.879059	+	0.476713i	$0.841828\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.10528			0.493546			0.246773	−	0.969073i	$-0.420630\pi$
$107$	5.10528			0.493546			0.246773	+	0.969073i	$0.420630\pi$
$108$		0			0
$109$	−3.82331	−	2.77780i	−0.366207	−	0.266065i	0.389429	−	0.921056i	$-0.372672\pi$
$109$	−3.82331	−	2.77780i	−0.366207	−	0.266065i	−0.755636	+	0.654991i	$0.772672\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.34799	+	2.43246i	0.314952	+	0.228826i	0.734019	−	0.679129i	$-0.237643\pi$
$113$	3.34799	+	2.43246i	0.314952	+	0.228826i	−0.419066	+	0.907956i	$0.637643\pi$
$114$		0			0
$115$	−0.366881	+	0.407462i	−0.0342118	+	0.0379961i
$116$		0			0
$117$		0			0
$118$		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
$123$		0			0
$124$		0			0
$125$	−9.04508	+	6.57164i	−0.809017	+	0.587785i
$126$		0			0
$127$	10.2568	−	7.45200i	0.910144	−	0.661258i	−0.0309074	−	0.999522i	$-0.509840\pi$
$127$	10.2568	−	7.45200i	0.910144	−	0.661258i	0.941051	+	0.338264i	$0.109840\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.81046	+	11.7274i	0.332921	+	1.02463i	0.967737	+	0.251963i	$0.0810761\pi$
$131$	3.81046	+	11.7274i	0.332921	+	1.02463i	−0.634815	+	0.772664i	$0.718924\pi$
$132$		0			0
$133$	−0.952682	−	2.93205i	−0.0826080	−	0.254241i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.67508	+	6.30281i	0.741162	+	0.538486i	0.893075	−	0.449908i	$-0.148543\pi$
$137$	8.67508	+	6.30281i	0.741162	+	0.538486i	−0.151913	+	0.988394i	$0.548543\pi$
$138$		0			0
$139$	11.0632	−	8.03786i	0.938365	−	0.681762i	−0.00966163	−	0.999953i	$-0.503075\pi$
$139$	11.0632	−	8.03786i	0.938365	−	0.681762i	0.948027	+	0.318191i	$0.103075\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.404307			0.0338098
$144$		0			0
$145$	−0.320153	+	3.04605i	−0.0265872	+	0.252961i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−8.88176			−0.727622			−0.363811	−	0.931473i	$-0.618525\pi$
$149$	−8.88176			−0.727622			−0.363811	+	0.931473i	$0.618525\pi$
$150$		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
$153$		0			0
$154$		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
$159$		0			0
$160$		0			0
$161$	0.108574	−	0.0788837i	0.00855684	−	0.00621691i
$162$		0			0
$163$	14.8153	+	10.7639i	1.16042	+	0.843097i	0.989831	−	0.142245i	$-0.0454322\pi$
$163$	14.8153	+	10.7639i	1.16042	+	0.843097i	0.170592	+	0.985342i	$0.445432\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.36097	−	4.18862i	−0.105315	−	0.324125i	0.884489	−	0.466560i	$-0.154507\pi$
$167$	−1.36097	−	4.18862i	−0.105315	−	0.324125i	−0.989804	+	0.142435i	$0.954507\pi$
$168$		0			0
$169$	−3.98902	−	12.2769i	−0.306847	−	0.944379i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−12.8882	+	9.36385i	−0.979875	+	0.711921i	−0.957681	−	0.287833i	$-0.907065\pi$
$173$	−12.8882	+	9.36385i	−0.979875	+	0.711921i	−0.0221940	+	0.999754i	$0.507065\pi$
$174$		0			0
$175$	2.50000	−	1.11307i	0.188982	−	0.0841403i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.16493	+	3.58528i	−0.0870707	+	0.267976i	−0.985106	−	0.171947i	$-0.944994\pi$
$179$	−1.16493	+	3.58528i	−0.0870707	+	0.267976i	0.898035	+	0.439923i	$0.144994\pi$
$180$		0			0
$181$	−8.24669	−	25.3807i	−0.612971	−	1.88653i	−0.427967	−	0.903794i	$-0.640770\pi$
$181$	−8.24669	−	25.3807i	−0.612971	−	1.88653i	−0.185004	−	0.982738i	$-0.559230\pi$
$182$		0			0
$183$		0			0
$184$		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			0
$190$		0			0
$191$	3.74803	+	2.72310i	0.271198	+	0.197037i	0.715069	−	0.699054i	$-0.246395\pi$
$191$	3.74803	+	2.72310i	0.271198	+	0.197037i	−0.443871	+	0.896091i	$0.646395\pi$
$192$		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			0
$196$		0			0
$197$	−6.34529	+	19.5288i	−0.452083	+	1.39137i	0.422443	+	0.906390i	$0.361173\pi$
$197$	−6.34529	+	19.5288i	−0.452083	+	1.39137i	−0.874526	+	0.484979i	$0.838827\pi$
$198$		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
$201$		0			0
$202$		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			0
$208$		0			0
$209$	6.09852	+	4.43083i	0.421843	+	0.306487i
$210$		0			0
$211$	−18.5512	+	13.4782i	−1.27712	+	0.927880i	−0.999462	−	0.0328013i	$-0.989557\pi$
$211$	−18.5512	+	13.4782i	−1.27712	+	0.927880i	−0.277655	+	0.960681i	$0.589557\pi$
$212$		0			0
$213$		0			0
$214$		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
$219$		0			0
$220$		0			0
$221$	−0.377335	+	1.16132i	−0.0253823	+	0.0781186i
$222$		0			0
$223$	10.3148	−	7.49414i	0.690730	−	0.501845i	−0.186170	−	0.982518i	$-0.559607\pi$
$223$	10.3148	−	7.49414i	0.690730	−	0.501845i	0.876900	+	0.480673i	$0.159607\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.92301	−	6.48294i	0.592241	−	0.430288i	−0.250876	−	0.968019i	$-0.580719\pi$
$227$	8.92301	−	6.48294i	0.592241	−	0.430288i	0.843116	+	0.537731i	$0.180719\pi$
$228$		0			0
$229$	−7.13214	+	21.9505i	−0.471305	+	1.45053i	0.379571	+	0.925163i	$0.376072\pi$
$229$	−7.13214	+	21.9505i	−0.471305	+	1.45053i	−0.850876	+	0.525366i	$0.823928\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	9.05055	+	27.8547i	0.592921	+	1.82482i	0.564814	+	0.825218i	$0.308948\pi$
$233$	9.05055	+	27.8547i	0.592921	+	1.82482i	0.0281067	+	0.999605i	$0.491052\pi$
$234$		0			0
$235$	−2.44805	+	23.2916i	−0.159693	+	1.51938i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	8.57443	−	6.22969i	0.554634	−	0.402965i	−0.274857	−	0.961485i	$-0.588631\pi$
$239$	8.57443	−	6.22969i	0.554634	−	0.402965i	0.829491	+	0.558520i	$0.188631\pi$
$240$		0			0
$241$	−15.3888	−	11.1806i	−0.991282	−	0.720208i	−0.0310802	−	0.999517i	$-0.509895\pi$
$241$	−15.3888	−	11.1806i	−0.991282	−	0.720208i	−0.960201	+	0.279309i	$0.909895\pi$
$242$		0			0
$243$		0			0
$244$		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
$249$		0			0
$250$		0			0
$251$	−0.0370816			−0.00234057			−0.00117028	−	0.999999i	$-0.500373\pi$
$251$	−0.0370816			−0.00234057			−0.00117028	+	0.999999i	$0.500373\pi$
$252$		0			0
$253$	−0.101403	+	0.312087i	−0.00637517	+	0.0196208i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.0237			0.625262			0.312631	−	0.949875i	$-0.398790\pi$
$257$	10.0237			0.625262			0.312631	+	0.949875i	$0.398790\pi$
$258$		0			0
$259$	0.968688	+	0.703793i	0.0601913	+	0.0437316i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−10.3407	−	7.51296i	−0.637635	−	0.463269i	0.221402	−	0.975183i	$-0.428937\pi$
$263$	−10.3407	−	7.51296i	−0.637635	−	0.463269i	−0.859037	+	0.511914i	$0.828937\pi$
$264$		0			0
$265$	−1.79880	+	17.1145i	−0.110500	+	1.05133i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−6.58562	−	20.2685i	−0.401533	−	1.23579i	−0.923756	−	0.382981i	$-0.874897\pi$
$269$	−6.58562	−	20.2685i	−0.401533	−	1.23579i	0.522224	−	0.852809i	$-0.325103\pi$
$270$		0			0
$271$	−4.14194	+	12.7476i	−0.251605	+	0.774361i	0.742875	+	0.669431i	$0.233462\pi$
$271$	−4.14194	+	12.7476i	−0.251605	+	0.774361i	−0.994480	+	0.104930i	$0.966538\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.34565	+	5.79484i	−0.201750	+	0.349442i
$276$		0			0
$277$	15.2678	−	11.0927i	0.917354	−	0.666496i	−0.0255104	−	0.999675i	$-0.508121\pi$
$277$	15.2678	−	11.0927i	0.917354	−	0.666496i	0.942864	+	0.333178i	$0.108121\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	5.37674	+	16.5479i	0.320750	+	0.987166i	0.973323	+	0.229440i	$0.0736895\pi$
$281$	5.37674	+	16.5479i	0.320750	+	0.987166i	−0.652573	+	0.757726i	$0.726310\pi$
$282$		0			0
$283$	7.31371	+	22.5093i	0.434755	+	1.33804i	0.893338	+	0.449386i	$0.148357\pi$
$283$	7.31371	+	22.5093i	0.434755	+	1.33804i	−0.458583	+	0.888652i	$0.651643\pi$
$284$		0			0
$285$		0			0
$286$		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
$291$		0			0
$292$		0			0
$293$	−19.0317			−1.11184			−0.555921	−	0.831235i	$-0.687634\pi$
$293$	−19.0317			−1.11184			−0.555921	+	0.831235i	$0.687634\pi$
$294$		0			0
$295$	−8.48180	−	3.77634i	−0.493829	−	0.219867i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.0740796			−0.00428414
$300$		0			0
$301$	−4.57537			−0.263720
$302$		0			0
$303$		0			0
$304$		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
$309$		0			0
$310$		0			0
$311$	25.5534	−	18.5656i	1.44900	−	1.05276i	0.462934	−	0.886393i	$-0.346797\pi$
$311$	25.5534	−	18.5656i	1.44900	−	1.05276i	0.986064	−	0.166366i	$-0.0532034\pi$
$312$		0			0
$313$	1.17726	+	0.855327i	0.0665425	+	0.0483459i	0.620559	−	0.784160i	$-0.286906\pi$
$313$	1.17726	+	0.855327i	0.0665425	+	0.0483459i	−0.554017	+	0.832506i	$0.686906\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.95857	+	15.2609i	0.278501	+	0.857138i	0.988272	+	0.152705i	$0.0487984\pi$
$317$	4.95857	+	15.2609i	0.278501	+	0.857138i	−0.709771	+	0.704433i	$0.751202\pi$
$318$		0			0
$319$	0.566449	+	1.74335i	0.0317151	+	0.0976089i
$320$		0			0
$321$		0			0
$322$		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
$327$		0			0
$328$		0			0
$329$	1.77143	−	5.45189i	0.0976619	−	0.300572i
$330$		0			0
$331$	−8.31262	−	25.5836i	−0.456903	−	1.40620i	−0.868887	−	0.495011i	$-0.835164\pi$
$331$	−8.31262	−	25.5836i	−0.456903	−	1.40620i	0.411984	−	0.911191i	$-0.364836\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−9.48757	−	16.4330i	−0.518361	−	0.897828i
$336$		0			0
$337$	−1.10171	−	0.800436i	−0.0600137	−	0.0436025i	0.557374	−	0.830262i	$-0.311809\pi$
$337$	−1.10171	−	0.800436i	−0.0600137	−	0.0436025i	−0.617388	+	0.786659i	$0.711809\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	3.83070	+	2.78317i	0.207444	+	0.150717i
$342$		0			0
$343$	−7.49850			−0.404881
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.712835	−	2.19388i	0.0382670	−	0.117774i	−0.930098	−	0.367311i	$-0.880278\pi$
$347$	0.712835	−	2.19388i	0.0382670	−	0.117774i	0.968365	+	0.249537i	$0.0802785\pi$
$348$		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			0
$352$		0			0
$353$	9.55559	−	29.4091i	0.508593	−	1.56529i	−0.286053	−	0.958214i	$-0.592343\pi$
$353$	9.55559	−	29.4091i	0.508593	−	1.56529i	0.794646	−	0.607073i	$-0.207657\pi$
$354$		0			0
$355$	−2.14642	+	20.4218i	−0.113920	+	1.08388i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−15.8812	−	11.5383i	−0.838176	−	0.608971i	0.0836845	−	0.996492i	$-0.473331\pi$
$359$	−15.8812	−	11.5383i	−0.838176	−	0.608971i	−0.921861	+	0.387522i	$0.873331\pi$
$360$		0			0
$361$	−10.2977	+	7.48170i	−0.541983	+	0.393774i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	16.3926	−	18.2058i	0.858025	−	0.952934i
$366$		0			0
$367$	−9.94076	−	30.5945i	−0.518903	−	1.59702i	−0.776066	−	0.630652i	$-0.782788\pi$
$367$	−9.94076	−	30.5945i	−0.518903	−	1.59702i	0.257163	−	0.966368i	$-0.417212\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.30163	−	4.00599i	0.0675770	−	0.207981i
$372$		0			0
$373$	11.0291	−	8.01309i	0.571064	−	0.414902i	−0.264428	−	0.964406i	$-0.585183\pi$
$373$	11.0291	−	8.01309i	0.571064	−	0.414902i	0.835492	+	0.549503i	$0.185183\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.334784	+	0.243235i	−0.0172423	+	0.0125272i
$378$		0			0
$379$	7.62106	−	23.4552i	0.391467	−	1.20481i	−0.540211	−	0.841529i	$-0.681656\pi$
$379$	7.62106	−	23.4552i	0.391467	−	1.20481i	0.931679	−	0.363283i	$-0.118344\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	3.79232	+	11.6716i	0.193779	+	0.596389i	0.999989	+	0.00475994i	$0.00151514\pi$
$383$	3.79232	+	11.6716i	0.193779	+	0.596389i	−0.806210	+	0.591629i	$0.798485\pi$
$384$		0			0
$385$	1.09591	−	1.21714i	0.0558530	−	0.0620310i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	9.39823	−	6.82822i	0.476509	−	0.346204i	−0.323463	−	0.946241i	$-0.604847\pi$
$389$	9.39823	−	6.82822i	0.476509	−	0.346204i	0.799973	+	0.600036i	$0.204847\pi$
$390$		0			0
$391$	−0.801790	−	0.582535i	−0.0405483	−	0.0294600i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.54874	+	33.7640i	−0.178556	+	1.69885i
$396$		0			0
$397$	5.26383	−	16.2004i	0.264184	−	0.813075i	−0.727696	−	0.685900i	$-0.759409\pi$
$397$	5.26383	−	16.2004i	0.264184	−	0.813075i	0.991880	−	0.127175i	$-0.0405911\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−32.2134			−1.60866			−0.804330	−	0.594183i	$-0.797476\pi$
$401$	−32.2134			−1.60866			−0.804330	+	0.594183i	$0.797476\pi$
$402$		0			0
$403$	−0.330318	+	1.01661i	−0.0164543	+	0.0506412i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.92770			−0.145121
$408$		0			0
$409$	5.64632	+	4.10229i	0.279193	+	0.202845i	0.718565	−	0.695460i	$-0.244799\pi$
$409$	5.64632	+	4.10229i	0.279193	+	0.202845i	−0.439373	+	0.898305i	$0.644799\pi$
$410$		0			0
$411$		0			0
$412$		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
$417$		0			0
$418$		0			0
$419$	−8.60796	−	26.4926i	−0.420526	−	1.29425i	−0.907214	−	0.420670i	$-0.861795\pi$
$419$	−8.60796	−	26.4926i	−0.420526	−	1.29425i	0.486687	−	0.873576i	$-0.338205\pi$
$420$		0			0
$421$	2.65766	−	8.17943i	0.129526	−	0.398641i	−0.865172	−	0.501475i	$-0.832791\pi$
$421$	2.65766	−	8.17943i	0.129526	−	0.398641i	0.994699	+	0.102834i	$0.0327910\pi$
$422$		0			0
$423$		0			0
$424$		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			0
$430$		0			0
$431$	−0.0559037	−	0.172054i	−0.00269278	−	0.00828754i	0.949701	−	0.313158i	$-0.101387\pi$
$431$	−0.0559037	−	0.172054i	−0.00269278	−	0.00828754i	−0.952394	+	0.304870i	$0.901387\pi$
$432$		0			0
$433$	−9.71549	−	29.9012i	−0.466897	−	1.43696i	−0.856581	−	0.516012i	$-0.827416\pi$
$433$	−9.71549	−	29.9012i	−0.466897	−	1.43696i	0.389684	−	0.920948i	$-0.372584\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.11741	−	0.811845i	−0.0534529	−	0.0388358i
$438$		0			0
$439$	13.6019	−	9.88233i	0.649181	−	0.471658i	−0.213811	−	0.976875i	$-0.568588\pi$
$439$	13.6019	−	9.88233i	0.649181	−	0.471658i	0.862992	+	0.505217i	$0.168588\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−36.1952			−1.71969			−0.859843	−	0.510559i	$-0.829439\pi$
$443$	−36.1952			−1.71969			−0.859843	+	0.510559i	$0.829439\pi$
$444$		0			0
$445$	−7.44914	+	8.27311i	−0.353123	+	0.392183i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−28.3299			−1.33697			−0.668486	−	0.743725i	$-0.733057\pi$
$449$	−28.3299			−1.33697			−0.668486	+	0.743725i	$0.733057\pi$
$450$		0			0
$451$	13.1188			0.617738
$452$		0			0
$453$		0			0
$454$		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
$459$		0			0
$460$		0			0
$461$	0.351142	−	0.255120i	0.0163543	−	0.0118821i	−0.579578	−	0.814917i	$-0.696783\pi$
$461$	0.351142	−	0.255120i	0.0163543	−	0.0118821i	0.595932	+	0.803035i	$0.296783\pi$
$462$		0			0
$463$	16.1500	+	11.7337i	0.750556	+	0.545311i	0.895999	−	0.444056i	$-0.146461\pi$
$463$	16.1500	+	11.7337i	0.750556	+	0.545311i	−0.145443	+	0.989367i	$0.546461\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.91815	+	5.90347i	0.0887615	+	0.273180i	0.985578	−	0.169223i	$-0.0541260\pi$
$467$	1.91815	+	5.90347i	0.0887615	+	0.273180i	−0.896816	+	0.442403i	$0.854126\pi$
$468$		0			0
$469$	1.43523	+	4.41719i	0.0662729	+	0.203967i
$470$		0			0
$471$		0			0
$472$		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
$477$		0			0
$478$		0			0
$479$	−7.25191	+	22.3191i	−0.331348	+	1.01978i	0.637145	+	0.770744i	$0.280115\pi$
$479$	−7.25191	+	22.3191i	−0.331348	+	1.01978i	−0.968493	+	0.249041i	$0.919885\pi$
$480$		0			0
$481$	−0.204239	−	0.628583i	−0.00931250	−	0.0286609i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.949247	+	9.03148i	−0.0431031	+	0.410098i
$486$		0			0
$487$	2.70709	+	1.96682i	0.122670	+	0.0891250i	0.647429	−	0.762126i	$-0.275844\pi$
$487$	2.70709	+	1.96682i	0.122670	+	0.0891250i	−0.524759	+	0.851251i	$0.675844\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.442522	−	0.321511i	−0.0199708	−	0.0145096i	0.577755	−	0.816210i	$-0.303929\pi$
$491$	−0.442522	−	0.321511i	−0.0199708	−	0.0145096i	−0.597726	+	0.801701i	$0.703929\pi$
$492$		0			0
$493$	−5.53620			−0.249338
$494$		0			0
$495$		0			0
$496$		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
$501$		0			0
$502$		0			0
$503$	8.74922	−	26.9273i	0.390109	−	1.20063i	−0.542597	−	0.839993i	$-0.682559\pi$
$503$	8.74922	−	26.9273i	0.390109	−	1.20063i	0.932706	−	0.360638i	$-0.117441\pi$
$504$		0			0
$505$	40.3514	−	8.57696i	1.79562	−	0.381670i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.61968	+	3.35639i	0.204764	+	0.148770i	0.685441	−	0.728128i	$-0.259609\pi$
$509$	4.61968	+	3.35639i	0.204764	+	0.148770i	−0.480678	+	0.876897i	$0.659609\pi$
$510$		0			0
$511$	−4.85119	+	3.52459i	−0.214604	+	0.155919i
$512$		0			0
$513$		0			0
$514$		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
$519$		0			0
$520$		0			0
$521$	7.87683	−	24.2424i	0.345090	−	1.06208i	−0.616445	−	0.787398i	$-0.711428\pi$
$521$	7.87683	−	24.2424i	0.345090	−	1.06208i	0.961536	−	0.274681i	$-0.0885721\pi$
$522$		0			0
$523$	−2.29098	+	1.66449i	−0.100177	+	0.0727832i	−0.636746	−	0.771073i	$-0.719720\pi$
$523$	−2.29098	+	1.66449i	−0.100177	+	0.0727832i	0.536569	+	0.843857i	$0.319720\pi$
$524$		0			0
$525$		0			0
$526$		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
$531$		0			0
$532$		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
$537$		0			0
$538$		0			0
$539$	7.25441	−	5.27064i	0.312470	−	0.227022i
$540$		0			0
$541$	−3.64130	−	2.64556i	−0.156552	−	0.113742i	0.506752	−	0.862092i	$-0.330846\pi$
$541$	−3.64130	−	2.64556i	−0.156552	−	0.113742i	−0.663303	+	0.748351i	$0.730846\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	9.65378	+	4.29814i	0.413522	+	0.184112i
$546$		0			0
$547$	2.94045	−	9.04979i	0.125725	−	0.386941i	−0.868308	−	0.496026i	$-0.834792\pi$
$547$	2.94045	−	9.04979i	0.125725	−	0.386941i	0.994032	+	0.109085i	$0.0347921\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−7.71549			−0.328691
$552$		0			0
$553$	2.56789	−	7.90316i	0.109198	−	0.336077i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−25.5173			−1.08120			−0.540601	−	0.841279i	$-0.681803\pi$
$557$	−25.5173			−1.08120			−0.540601	+	0.841279i	$0.681803\pi$
$558$		0			0
$559$	2.04322	+	1.48448i	0.0864189	+	0.0627870i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	11.1180	+	8.07772i	0.468569	+	0.340435i	0.796883	−	0.604133i	$-0.206480\pi$
$563$	11.1180	+	8.07772i	0.468569	+	0.340435i	−0.328314	+	0.944569i	$0.606480\pi$
$564$		0			0
$565$	−8.45360	−	3.76378i	−0.355645	−	0.158344i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.75873	+	26.9566i	0.367185	+	1.13008i	0.948601	+	0.316473i	$0.102499\pi$
$569$	8.75873	+	26.9566i	0.367185	+	1.13008i	−0.581416	+	0.813606i	$0.697501\pi$
$570$		0			0
$571$	−0.603552	+	1.85754i	−0.0252579	+	0.0777357i	−0.962891	−	0.269891i	$-0.913012\pi$
$571$	−0.603552	+	1.85754i	−0.0252579	+	0.0777357i	0.937633	+	0.347627i	$0.113012\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.613012	−	1.06177i	0.0255644	−	0.0442788i
$576$		0			0
$577$	−34.6572	+	25.1799i	−1.44280	+	1.04825i	−0.455350	+	0.890313i	$0.650486\pi$
$577$	−34.6572	+	25.1799i	−1.44280	+	1.04825i	−0.987448	+	0.157942i	$0.949514\pi$
$578$		0			0
$579$		0			0
$580$		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			0
$586$		0			0
$587$	−1.59845	−	1.16134i	−0.0659751	−	0.0479337i	0.554309	−	0.832311i	$-0.312983\pi$
$587$	−1.59845	−	1.16134i	−0.0659751	−	0.0479337i	−0.620284	+	0.784377i	$0.712983\pi$
$588$		0			0
$589$	−16.1237	+	11.7145i	−0.664364	+	0.482688i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	17.3986			0.714475			0.357237	−	0.934014i	$-0.383719\pi$
$593$	17.3986			0.714475			0.357237	+	0.934014i	$0.383719\pi$
$594$		0			0
$595$	2.47326	+	4.28381i	0.101394	+	0.175619i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3.17298			0.129644			0.0648222	−	0.997897i	$-0.479352\pi$
$599$	3.17298			0.129644			0.0648222	+	0.997897i	$0.479352\pi$
$600$		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
$603$		0			0
$604$		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			0
$610$		0			0
$611$	−2.55993	+	1.85990i	−0.103564	+	0.0752435i
$612$		0			0
$613$	2.00920	+	1.45977i	0.0811510	+	0.0589597i	0.627621	−	0.778519i	$-0.284029\pi$
$613$	2.00920	+	1.45977i	0.0811510	+	0.0589597i	−0.546470	+	0.837479i	$0.684029\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−3.03970	−	9.35524i	−0.122374	−	0.376628i	0.871040	−	0.491213i	$-0.163446\pi$
$617$	−3.03970	−	9.35524i	−0.122374	−	0.376628i	−0.993413	+	0.114585i	$0.963446\pi$
$618$		0			0
$619$	−4.22997	−	13.0185i	−0.170017	−	0.523258i	0.829354	−	0.558723i	$-0.188709\pi$
$619$	−4.22997	−	13.0185i	−0.170017	−	0.523258i	−0.999371	+	0.0354655i	$0.988709\pi$
$620$		0			0
$621$		0			0
$622$		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
$627$		0			0
$628$		0			0
$629$	2.73239	−	8.40944i	0.108948	−	0.335306i
$630$		0			0
$631$	6.15441	+	18.9413i	0.245003	+	0.754042i	0.995636	+	0.0933224i	$0.0297487\pi$
$631$	6.15441	+	18.9413i	0.245003	+	0.754042i	−0.750633	+	0.660720i	$0.770251\pi$
$632$		0			0
$633$		0			0
$634$		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
$639$		0			0
$640$		0			0
$641$	−10.6407	−	7.73090i	−0.420281	−	0.305352i	0.357470	−	0.933925i	$-0.383640\pi$
$641$	−10.6407	−	7.73090i	−0.420281	−	0.305352i	−0.777751	+	0.628572i	$0.783640\pi$
$642$		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
$645$		0			0
$646$		0			0
$647$	11.7895	−	36.2842i	0.463492	−	1.42648i	−0.397378	−	0.917655i	$-0.630080\pi$
$647$	11.7895	−	36.2842i	0.463492	−	1.42648i	0.860870	−	0.508825i	$-0.169920\pi$
$648$		0			0
$649$	−5.55666			−0.218118
$650$		0			0
$651$		0			0
$652$		0			0
$653$	10.7056	−	32.9484i	0.418942	−	1.28937i	−0.489736	−	0.871871i	$-0.662907\pi$
$653$	10.7056	−	32.9484i	0.418942	−	1.28937i	0.908677	−	0.417499i	$-0.137093\pi$
$654$		0			0
$655$	−13.7864	−	23.8787i	−0.538678	−	0.933018i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	40.6525	+	29.5358i	1.58360	+	1.15055i	0.912420	+	0.409254i	$0.134211\pi$
$659$	40.6525	+	29.5358i	1.58360	+	1.15055i	0.671178	+	0.741297i	$0.265789\pi$
$660$		0			0
$661$	−8.72436	+	6.33862i	−0.339338	+	0.246544i	−0.744383	−	0.667753i	$-0.767256\pi$
$661$	−8.72436	+	6.33862i	−0.339338	+	0.246544i	0.405044	+	0.914297i	$0.367256\pi$
$662$		0			0
$663$		0			0
$664$		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
$669$		0			0
$670$		0			0
$671$	0.858670	−	2.64272i	0.0331486	−	0.102021i
$672$		0			0
$673$	13.6011	−	9.88179i	0.524285	−	0.380915i	−0.293931	−	0.955827i	$-0.594964\pi$
$673$	13.6011	−	9.88179i	0.524285	−	0.380915i	0.818216	+	0.574912i	$0.194964\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	30.1258	−	21.8877i	1.15783	−	0.841211i	0.168325	−	0.985731i	$-0.446164\pi$
$677$	30.1258	−	21.8877i	1.15783	−	0.841211i	0.989502	+	0.144521i	$0.0461640\pi$
$678$		0			0
$679$	0.686881	−	2.11400i	0.0263601	−	0.0811280i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	9.83629	+	30.2730i	0.376375	+	1.15836i	0.942546	+	0.334076i	$0.108424\pi$
$683$	9.83629	+	30.2730i	0.376375	+	1.15836i	−0.566171	+	0.824288i	$0.691576\pi$
$684$		0			0
$685$	−21.9044	−	9.75246i	−0.836923	−	0.372622i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.88101	+	1.36663i	−0.0716608	+	0.0520646i
$690$		0			0
$691$	15.3436	+	11.1478i	0.583699	+	0.424082i	0.840056	−	0.542500i	$-0.182522\pi$
$691$	15.3436	+	11.1478i	0.583699	+	0.424082i	−0.256357	+	0.966582i	$0.582522\pi$
$692$		0			0
$693$		0			0
$694$		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
$699$		0			0
$700$		0			0
$701$	19.2027			0.725275			0.362638	−	0.931930i	$-0.381876\pi$
$701$	19.2027			0.725275			0.362638	+	0.931930i	$0.381876\pi$
$702$		0			0
$703$	3.80798	−	11.7197i	0.143621	−	0.442019i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−10.0974			−0.379752
$708$		0			0
$709$	8.91896	+	6.48000i	0.334959	+	0.243362i	0.742532	−	0.669811i	$-0.233625\pi$
$709$	8.91896	+	6.48000i	0.334959	+	0.243362i	−0.407573	+	0.913173i	$0.633625\pi$
$710$		0			0
$711$		0			0
$712$		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
$717$		0			0
$718$		0			0
$719$	−8.20996	−	25.2676i	−0.306180	−	0.942324i	−0.979234	−	0.202732i	$-0.935018\pi$
$719$	−8.20996	−	25.2676i	−0.306180	−	0.942324i	0.673055	−	0.739593i	$-0.264982\pi$
$720$		0			0
$721$	−2.48899	+	7.66034i	−0.0926950	+	0.285286i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.715883	−	6.81118i	−0.0265872	−	0.252961i
$726$		0			0
$727$	−22.1224	+	16.0729i	−0.820474	+	0.596109i	−0.916848	−	0.399236i	$-0.869275\pi$
$727$	−22.1224	+	16.0729i	−0.820474	+	0.596109i	0.0963741	+	0.995345i	$0.469275\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	10.4410	+	32.1342i	0.386176	+	1.18853i
$732$		0			0
$733$	2.56626	+	7.89814i	0.0947871	+	0.291725i	0.987198	−	0.159499i	$-0.0509878\pi$
$733$	2.56626	+	7.89814i	0.0947871	+	0.291725i	−0.892411	+	0.451223i	$0.850988\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−9.18753	−	6.67513i	−0.338427	−	0.245882i
$738$		0			0
$739$	−1.30623	+	0.949030i	−0.0480504	+	0.0349106i	−0.611551	−	0.791205i	$-0.709454\pi$
$739$	−1.30623	+	0.949030i	−0.0480504	+	0.0349106i	0.563501	+	0.826116i	$0.309454\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	3.77367			0.138443			0.0692213	−	0.997601i	$-0.477949\pi$
$743$	3.77367			0.138443			0.0692213	+	0.997601i	$0.477949\pi$
$744$		0			0
$745$	19.4262	−	4.12917i	0.711722	−	0.151281i
$746$		0			0
$747$		0			0
$748$		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			0
$754$		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			0
$760$		0			0
$761$	3.77626	−	2.74361i	0.136889	−	0.0994560i	−0.517233	−	0.855844i	$-0.673038\pi$
$761$	3.77626	−	2.74361i	0.136889	−	0.0994560i	0.654123	+	0.756389i	$0.273038\pi$
$762$		0			0
$763$	−2.09257	−	1.52034i	−0.0757561	−	0.0550400i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.387637	−	1.19302i	−0.0139968	−	0.0430776i
$768$		0			0
$769$	−6.98515	−	21.4981i	−0.251891	−	0.775241i	−0.994426	−	0.105434i	$-0.966377\pi$
$769$	−6.98515	−	21.4981i	−0.251891	−	0.775241i	0.742535	−	0.669807i	$-0.233623\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	32.1006	−	23.3225i	1.15458	−	0.838851i	0.165497	−	0.986210i	$-0.447077\pi$
$773$	32.1006	−	23.3225i	1.15458	−	0.838851i	0.989083	+	0.147359i	$0.0470772\pi$
$774$		0			0
$775$	−11.8375	−	13.1469i	−0.425217	−	0.472251i
$776$		0			0
$777$		0			0
$778$		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			0
$784$		0			0
$785$	−25.7162	+	5.46614i	−0.917850	+	0.195095i
$786$		0			0
$787$	−3.83261	−	2.78456i	−0.136618	−	0.0992587i	0.517377	−	0.855757i	$-0.326908\pi$
$787$	−3.83261	−	2.78456i	−0.136618	−	0.0992587i	−0.653995	+	0.756499i	$0.726908\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.83241	+	1.33133i	0.0651532	+	0.0473365i
$792$		0			0
$793$	0.627297			0.0222760
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.93088	+	27.4864i	−0.316348	+	0.973619i	0.658848	+	0.752276i	$0.271044\pi$
$797$	−8.93088	+	27.4864i	−0.316348	+	0.973619i	−0.975196	+	0.221343i	$0.928956\pi$
$798$		0			0
$799$	−42.3326			−1.49762
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.53079	−	13.9443i	0.159888	−	0.492085i
$804$		0			0
$805$	−0.200800	+	0.223011i	−0.00707729	+	0.00786012i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	36.1225	+	26.2445i	1.27000	+	0.922709i	0.999203	−	0.0399280i	$-0.0127128\pi$
$809$	36.1225	+	26.2445i	1.27000	+	0.922709i	0.270797	+	0.962637i	$0.412713\pi$
$810$		0			0
$811$	36.5354	−	26.5445i	1.28293	−	0.932105i	0.283295	−	0.959033i	$-0.408572\pi$
$811$	36.5354	−	26.5445i	1.28293	−	0.932105i	0.999637	+	0.0269280i	$0.00857248\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−37.4083	−	16.6552i	−1.31035	−	0.583407i
$816$		0			0
$817$	14.5511	+	44.7836i	0.509077	+	1.56678i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−14.7519	+	45.4016i	−0.514844	+	1.58453i	0.268722	+	0.963218i	$0.413399\pi$
$821$	−14.7519	+	45.4016i	−0.514844	+	1.58453i	−0.783566	+	0.621308i	$0.786601\pi$
$822$		0			0
$823$	5.22903	−	3.79912i	0.182273	−	0.132429i	−0.492907	−	0.870082i	$-0.664066\pi$
$823$	5.22903	−	3.79912i	0.182273	−	0.132429i	0.675180	+	0.737653i	$0.264066\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−40.6005	+	29.4980i	−1.41182	+	1.02575i	−0.418763	+	0.908095i	$0.637536\pi$
$827$	−40.6005	+	29.4980i	−1.41182	+	1.02575i	−0.993055	+	0.117650i	$0.962464\pi$
$828$		0			0
$829$	−11.5098	+	35.4234i	−0.399751	+	1.23031i	0.525449	+	0.850825i	$0.323897\pi$
$829$	−11.5098	+	35.4234i	−0.399751	+	1.23031i	−0.925200	+	0.379481i	$0.876103\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	8.36874	+	25.7563i	0.289960	+	0.892404i
$834$		0			0
$835$	4.92402	+	8.52866i	0.170403	+	0.295146i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	10.7171	−	7.78643i	0.369995	−	0.268817i	−0.387214	−	0.921990i	$-0.626562\pi$
$839$	10.7171	−	7.78643i	0.369995	−	0.268817i	0.757209	+	0.653173i	$0.226562\pi$
$840$		0			0
$841$	21.9436	+	15.9430i	0.756677	+	0.549758i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	14.4324	+	24.9976i	0.496490	+	0.859945i
$846$		0			0
$847$	−1.55753	+	4.79359i	−0.0535175	+	0.164710i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	0.536433			0.0183887
$852$		0			0
$853$	13.8064	−	42.4917i	0.472722	−	1.45489i	−0.376284	−	0.926504i	$-0.622798\pi$
$853$	13.8064	−	42.4917i	0.472722	−	1.45489i	0.849006	−	0.528384i	$-0.177202\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	41.6798			1.42375			0.711877	−	0.702304i	$-0.247845\pi$
$857$	41.6798			1.42375			0.711877	+	0.702304i	$0.247845\pi$
$858$		0			0
$859$	30.4001	+	22.0870i	1.03724	+	0.753597i	0.969744	−	0.244123i	$-0.0785000\pi$
$859$	30.4001	+	22.0870i	1.03724	+	0.753597i	0.0674930	+	0.997720i	$0.478500\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	45.4724	+	33.0376i	1.54790	+	1.12461i	0.945129	+	0.326697i	$0.105936\pi$
$863$	45.4724	+	33.0376i	1.54790	+	1.12461i	0.602768	+	0.797916i	$0.294064\pi$
$864$		0			0
$865$	23.8359	−	26.4725i	0.810445	−	0.900091i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	6.27882	+	19.3242i	0.212994	+	0.655529i
$870$		0			0
$871$	0.792232	−	2.43824i	0.0268438	−	0.0826166i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−4.95054	+	3.59678i	−0.167359	+	0.121593i
$876$		0			0
$877$	−1.91115	+	1.38853i	−0.0645349	+	0.0468873i	−0.619585	−	0.784930i	$-0.712699\pi$
$877$	−1.91115	+	1.38853i	−0.0645349	+	0.0468873i	0.555050	+	0.831817i	$0.312699\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−14.7309	−	45.3372i	−0.496298	−	1.52745i	−0.814924	−	0.579568i	$-0.803221\pi$
$881$	−14.7309	−	45.3372i	−0.496298	−	1.52745i	0.318626	−	0.947881i	$-0.396779\pi$
$882$		0			0
$883$	3.07555	+	9.46556i	0.103500	+	0.318541i	0.989376	−	0.145382i	$-0.0464412\pi$
$883$	3.07555	+	9.46556i	0.103500	+	0.318541i	−0.885875	+	0.463924i	$0.846441\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−10.8114	−	7.85495i	−0.363012	−	0.263743i	0.391296	−	0.920265i	$-0.372027\pi$
$887$	−10.8114	−	7.85495i	−0.363012	−	0.263743i	−0.754307	+	0.656522i	$0.772027\pi$
$888$		0			0
$889$	5.61373	−	4.07862i	0.188279	−	0.136792i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−58.9965			−1.97424
$894$		0			0
$895$	0.881122	−	8.38331i	0.0294527	−	0.280223i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−4.84638			−0.161636
$900$		0			0
$901$	−31.1056			−1.03628
$902$		0			0
$903$		0			0
$904$		0			0
$905$	29.8368	+	51.6788i	0.991809	+	1.71786i
$906$		0			0
$907$	−32.4136			−1.07627			−0.538137	−	0.842857i	$-0.680872\pi$
$907$	−32.4136			−1.07627			−0.538137	+	0.842857i	$0.680872\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−32.4946	+	23.6087i	−1.07659	+	0.782191i	−0.977086	−	0.212846i	$-0.931727\pi$
$911$	−32.4946	+	23.6087i	−1.07659	+	0.782191i	−0.0995074	+	0.995037i	$0.531727\pi$
$912$		0			0
$913$	−7.20432	−	5.23425i	−0.238428	−	0.173228i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.08553	+	6.41861i	0.0688704	+	0.211961i
$918$		0			0
$919$	9.99204	+	30.7523i	0.329607	+	1.01443i	0.969318	+	0.245810i	$0.0790540\pi$
$919$	9.99204	+	30.7523i	0.329607	+	1.01443i	−0.639711	+	0.768616i	$0.720946\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.24452	+	1.63074i	−0.0738792	+	0.0536764i
$924$		0			0
$925$	10.6994	+	2.27423i	0.351795	+	0.0747764i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−16.4945	+	50.7648i	−0.541167	+	1.66554i	0.188767	+	0.982022i	$0.439551\pi$
$929$	−16.4945	+	50.7648i	−0.541167	+	1.66554i	−0.729934	+	0.683518i	$0.760449\pi$
$930$		0			0
$931$	11.6630	+	35.8951i	0.382241	+	1.17642i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−11.0492	−	4.91941i	−0.361347	−	0.160882i
$936$		0			0
$937$	6.92518	+	5.03143i	0.226236	+	0.164370i	0.695129	−	0.718885i	$-0.255347\pi$
$937$	6.92518	+	5.03143i	0.226236	+	0.164370i	−0.468893	+	0.883255i	$0.655347\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	27.3583	+	19.8770i	0.891856	+	0.647971i	0.936361	−	0.351038i	$-0.114171\pi$
$941$	27.3583	+	19.8770i	0.891856	+	0.647971i	−0.0445052	+	0.999009i	$0.514171\pi$
$942$		0			0
$943$	−2.40370			−0.0782753
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.26850	−	16.2148i	0.171203	−	0.526909i	−0.828236	−	0.560379i	$-0.810656\pi$
$947$	5.26850	−	16.2148i	0.171203	−	0.526909i	0.999440	+	0.0334693i	$0.0106556\pi$
$948$		0			0
$949$	3.30994			0.107445
$950$		0			0
$951$		0			0
$952$		0			0
$953$	11.6221	−	35.7692i	0.376478	−	1.15868i	−0.565999	−	0.824406i	$-0.691509\pi$
$953$	11.6221	−	35.7692i	0.376478	−	1.15868i	0.942476	−	0.334273i	$-0.108491\pi$
$954$		0			0
$955$	−9.46369	−	4.21350i	−0.306238	−	0.136346i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	4.74803	+	3.44964i	0.153322	+	0.111395i
$960$		0			0
$961$	14.9517	−	10.8630i	0.482312	−	0.350420i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	45.3714	−	9.64399i	1.46056	−	0.310451i
$966$		0			0
$967$	−5.17395	−	15.9238i	−0.166383	−	0.512074i	0.832753	−	0.553645i	$-0.186764\pi$
$967$	−5.17395	−	15.9238i	−0.166383	−	0.512074i	−0.999136	+	0.0415712i	$0.986764\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.90916	−	5.87580i	0.0612680	−	0.188563i	−0.915738	−	0.401777i	$-0.868393\pi$
$971$	1.90916	−	5.87580i	0.0612680	−	0.188563i	0.977006	+	0.213213i	$0.0683929\pi$
$972$		0			0
$973$	6.05507	−	4.39926i	0.194117	−	0.141034i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	10.6508	−	7.73829i	0.340750	−	0.247570i	−0.404228	−	0.914658i	$-0.632460\pi$
$977$	10.6508	−	7.73829i	0.340750	−	0.247570i	0.744978	+	0.667089i	$0.232460\pi$
$978$		0			0
$979$	−2.05889	+	6.33662i	−0.0658025	+	0.202519i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−4.24039	−	13.0506i	−0.135248	−	0.416249i	0.860381	−	0.509652i	$-0.170226\pi$
$983$	−4.24039	−	13.0506i	−0.135248	−	0.416249i	−0.995628	+	0.0934024i	$0.970226\pi$
$984$		0			0
$985$	4.79942	−	45.6634i	0.152922	−	1.45496i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.65834	+	1.20485i	−0.0527321	+	0.0383121i
$990$		0			0
$991$	38.5515	+	28.0093i	1.22463	+	0.889744i	0.996476	−	0.0838819i	$-0.0267318\pi$
$991$	38.5515	+	28.0093i	1.22463	+	0.889744i	0.228152	+	0.973626i	$0.426732\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−12.9359	+	2.74962i	−0.410097	+	0.0871688i
$996$		0			0
$997$	−6.13379	+	18.8779i	−0.194259	+	0.597868i	0.805725	+	0.592289i	$0.201776\pi$
$997$	−6.13379	+	18.8779i	−0.194259	+	0.597868i	−0.999984	+	0.00557886i	$0.998224\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.n.a.361.1		8
3.2	odd	2		300.2.m.a.61.2	✓	8
15.2	even	4		1500.2.o.a.949.2		16
15.8	even	4		1500.2.o.a.949.3		16
15.14	odd	2		1500.2.m.b.301.1		8
25.16	even	5	inner	900.2.n.a.541.1		8
75.29	odd	10		7500.2.a.d.1.2		4
75.38	even	20		1500.2.o.a.49.1		16
75.41	odd	10		300.2.m.a.241.2	yes	8
75.47	even	20		7500.2.d.d.1249.3		8
75.53	even	20		7500.2.d.d.1249.6		8
75.59	odd	10		1500.2.m.b.1201.1		8
75.62	even	20		1500.2.o.a.49.4		16
75.71	odd	10		7500.2.a.g.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.m.a.61.2	✓	8	3.2	odd	2
300.2.m.a.241.2	yes	8	75.41	odd	10
900.2.n.a.361.1		8	1.1	even	1	trivial
900.2.n.a.541.1		8	25.16	even	5	inner
1500.2.m.b.301.1		8	15.14	odd	2
1500.2.m.b.1201.1		8	75.59	odd	10
1500.2.o.a.49.1		16	75.38	even	20
1500.2.o.a.49.4		16	75.62	even	20
1500.2.o.a.949.2		16	15.2	even	4
1500.2.o.a.949.3		16	15.8	even	4
7500.2.a.d.1.2		4	75.29	odd	10
7500.2.a.g.1.3		4	75.71	odd	10
7500.2.d.d.1249.3		8	75.47	even	20
7500.2.d.d.1249.6		8	75.53	even	20

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.18720 + 0.464905i) q^{5} +0.547318 q^{7} +O(q^{10})\)	\(q+(-2.18720 + 0.464905i) q^{5} +0.547318 q^{7} +(-1.08268 + 0.786610i) q^{11} +(-0.244415 - 0.177578i) q^{13} +(-1.24898 - 3.84398i) q^{17} +(-1.74064 - 5.35713i) q^{19} +(0.198375 - 0.144128i) q^{23} +(4.56773 - 2.03368i) q^{25} +(0.423273 - 1.30270i) q^{29} +(-1.09336 - 3.36501i) q^{31} +(-1.19710 + 0.254451i) q^{35} +(1.76988 + 1.28589i) q^{37} +(-7.93066 - 5.76196i) q^{41} -8.35963 q^{43} +(3.23656 - 9.96110i) q^{47} -6.70044 q^{49} +(2.37819 - 7.31931i) q^{53} +(2.00234 - 2.22382i) q^{55} +(3.35916 + 2.44057i) q^{59} +(-1.67981 + 1.22046i) q^{61} +(0.617142 + 0.274769i) q^{65} +(2.62230 + 8.07061i) q^{67} +(2.83777 - 8.73377i) q^{71} +(-8.86356 + 6.43975i) q^{73} +(-0.592568 + 0.430526i) q^{77} +(4.69177 - 14.4398i) q^{79} +(2.05626 + 6.32850i) q^{83} +(4.51886 + 7.82690i) q^{85} +(4.02780 - 2.92637i) q^{89} +(-0.133773 - 0.0971915i) q^{91} +(6.29768 + 10.9079i) q^{95} +(1.25499 - 3.86248i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{5} - 8 q^{7}+O(q^{10}) \) 8 * q - 5 * q^5 - 8 * q^7	\( 8 q - 5 q^{5} - 8 q^{7} + 2 q^{11} - 7 q^{17} + 5 q^{19} - 7 q^{23} + 5 q^{25} - 27 q^{29} - 3 q^{31} - 20 q^{35} - 9 q^{37} - 20 q^{41} - 68 q^{43} + 7 q^{47} - 8 q^{49} + 11 q^{53} + 5 q^{55} - 2 q^{59} - 14 q^{61} + 35 q^{65} + 28 q^{67} + 15 q^{71} + 6 q^{73} - 17 q^{77} + 24 q^{79} - 2 q^{83} + 10 q^{85} + 5 q^{91} - 5 q^{95} + 34 q^{97}+O(q^{100}) \) 8 * q - 5 * q^5 - 8 * q^7 + 2 * q^11 - 7 * q^17 + 5 * q^19 - 7 * q^23 + 5 * q^25 - 27 * q^29 - 3 * q^31 - 20 * q^35 - 9 * q^37 - 20 * q^41 - 68 * q^43 + 7 * q^47 - 8 * q^49 + 11 * q^53 + 5 * q^55 - 2 * q^59 - 14 * q^61 + 35 * q^65 + 28 * q^67 + 15 * q^71 + 6 * q^73 - 17 * q^77 + 24 * q^79 - 2 * q^83 + 10 * q^85 + 5 * q^91 - 5 * q^95 + 34 * q^97

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