LMFDB - Embedded newform 1332.2.bt.b.145.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1332,2,Mod(145,1332)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1332.145"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1332, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1332 = 2^{2} \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1332.bt (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$10.6360735492$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 9x^{10} - 14x^{9} + 69x^{8} - 72x^{7} + 151x^{6} - 78x^{5} + 180x^{4} - 66x^{3} + 117x^{2} + 27x + 9 $ x^12 + 9x^10 - 14x^9 + 69x^8 - 72x^7 + 151x^6 - 78x^5 + 180x^4 - 66x^3 + 117x^2 + 27x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 444)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			145.1
Root			$-0.130479 + 0.225997i$ of defining polynomial
Character	$\chi$	$=$	1332.145
Dual form			1332.2.bt.b.937.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68491 - 0.613258i) q^{5} +(2.82666 + 1.02882i) q^{7} +(1.22691 - 2.12507i) q^{11} +(-0.123126 - 0.698284i) q^{13} +(0.266790 - 1.51304i) q^{17} +(-0.404849 + 0.339709i) q^{19} +(0.594663 + 1.02999i) q^{23} +(-1.36737 - 1.14736i) q^{25} +(0.173527 - 0.300558i) q^{29} +7.53270 q^{31} +(-4.13174 - 3.46694i) q^{35} +(-0.665428 - 6.04626i) q^{37} +(1.20977 + 6.86095i) q^{41} +3.76729 q^{43} +(-1.56067 - 2.70316i) q^{47} +(1.56922 + 1.31673i) q^{49} +(9.80095 - 3.56725i) q^{53} +(-3.37045 + 2.82814i) q^{55} +(10.8220 - 3.93888i) q^{59} +(-1.34742 - 7.64158i) q^{61} +(-0.220771 + 1.25206i) q^{65} +(5.01641 + 1.82582i) q^{67} +(4.62237 - 3.87863i) q^{71} +6.37193 q^{73} +(5.65436 - 4.74457i) q^{77} +(-11.3107 - 4.11675i) q^{79} +(1.94652 - 11.0392i) q^{83} +(-1.37740 + 2.38573i) q^{85} +(2.57240 - 0.936276i) q^{89} +(0.370372 - 2.10049i) q^{91} +(0.890465 - 0.324103i) q^{95} +(-1.94047 - 3.36099i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{5} - 6 q^{11} - 6 q^{13} - 12 q^{17} + 12 q^{19} - 15 q^{25} + 3 q^{29} - 36 q^{35} + 27 q^{37} - 18 q^{41} - 12 q^{43} - 9 q^{47} - 18 q^{49} + 36 q^{53} - 3 q^{55} + 6 q^{59} - 9 q^{61} - 30 q^{65}+ \cdots - 24 q^{97}+O(q^{100}) $ 12 * q - 3 * q^5 - 6 * q^11 - 6 * q^13 - 12 * q^17 + 12 * q^19 - 15 * q^25 + 3 * q^29 - 36 * q^35 + 27 * q^37 - 18 * q^41 - 12 * q^43 - 9 * q^47 - 18 * q^49 + 36 * q^53 - 3 * q^55 + 6 * q^59 - 9 * q^61 - 30 * q^65 + 6 * q^67 - 3 * q^71 - 42 * q^73 + 51 * q^77 + 12 * q^79 - 9 * q^83 - 27 * q^85 + 27 * q^89 + 9 * q^91 + 6 * q^95 - 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1332\mathbb{Z}\right)^\times$.

$n$	$667$	$1037$	$1297$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{9}\right)$

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
$5$	−1.68491	−	0.613258i	−0.753516	−	0.274257i	−0.0634316	−	0.997986i	$-0.520204\pi$
$5$	−1.68491	−	0.613258i	−0.753516	−	0.274257i	−0.690085	+	0.723729i	$0.742427\pi$
$6$		0			0
$7$	2.82666	+	1.02882i	1.06838	+	0.388857i	0.815569	−	0.578660i	$-0.196424\pi$
$7$	2.82666	+	1.02882i	1.06838	+	0.388857i	0.252807	+	0.967517i	$0.418646\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.22691	−	2.12507i	0.369927	−	0.640732i	−0.619627	−	0.784897i	$-0.712716\pi$
$11$	1.22691	−	2.12507i	0.369927	−	0.640732i	0.989554	+	0.144164i	$0.0460494\pi$
$12$		0			0
$13$	−0.123126	−	0.698284i	−0.0341491	−	0.193669i	0.962961	−	0.269641i	$-0.0869051\pi$
$13$	−0.123126	−	0.698284i	−0.0341491	−	0.193669i	−0.997110	+	0.0759720i	$0.975794\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.266790	−	1.51304i	0.0647060	−	0.366966i	−0.935211	−	0.354091i	$-0.884790\pi$
$17$	0.266790	−	1.51304i	0.0647060	−	0.366966i	0.999917	−	0.0128754i	$-0.00409848\pi$
$18$		0			0
$19$	−0.404849	+	0.339709i	−0.0928788	+	0.0779346i	−0.688045	−	0.725668i	$-0.741531\pi$
$19$	−0.404849	+	0.339709i	−0.0928788	+	0.0779346i	0.595166	+	0.803603i	$0.297086\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.594663	+	1.02999i	0.123996	+	0.214767i	0.921340	−	0.388758i	$-0.127096\pi$
$23$	0.594663	+	1.02999i	0.123996	+	0.214767i	−0.797344	+	0.603525i	$0.793762\pi$
$24$		0			0
$25$	−1.36737	−	1.14736i	−0.273475	−	0.229473i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.173527	−	0.300558i	0.0322232	−	0.0558122i	−0.849464	−	0.527646i	$-0.823075\pi$
$29$	0.173527	−	0.300558i	0.0322232	−	0.0558122i	0.881687	+	0.471834i	$0.156408\pi$
$30$		0			0
$31$	7.53270			1.35291			0.676457	−	0.736483i	$-0.263515\pi$
$31$	7.53270			1.35291			0.676457	+	0.736483i	$0.263515\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.13174	−	3.46694i	−0.698392	−	0.586020i
$36$		0			0
$37$	−0.665428	−	6.04626i	−0.109396	−	0.993998i
$37$	−0.665428	−	6.04626i	−0.109396	−	0.993998i
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.20977	+	6.86095i	0.188934	+	1.07150i	0.920795	+	0.390046i	$0.127541\pi$
$41$	1.20977	+	6.86095i	0.188934	+	1.07150i	−0.731861	+	0.681454i	$0.761348\pi$
$42$		0			0
$43$	3.76729			0.574507			0.287253	−	0.957855i	$-0.407258\pi$
$43$	3.76729			0.574507			0.287253	+	0.957855i	$0.407258\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.56067	−	2.70316i	−0.227648	−	0.394297i	0.729463	−	0.684020i	$-0.239770\pi$
$47$	−1.56067	−	2.70316i	−0.227648	−	0.394297i	−0.957110	+	0.289723i	$0.906437\pi$
$48$		0			0
$49$	1.56922	+	1.31673i	0.224174	+	0.188104i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	9.80095	−	3.56725i	1.34626	−	0.490000i	0.434484	−	0.900679i	$-0.356931\pi$
$53$	9.80095	−	3.56725i	1.34626	−	0.490000i	0.911780	+	0.410679i	$0.134708\pi$
$54$		0			0
$55$	−3.37045	+	2.82814i	−0.454472	+	0.381347i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	10.8220	−	3.93888i	1.40890	−	0.512798i	0.478094	−	0.878309i	$-0.341328\pi$
$59$	10.8220	−	3.93888i	1.40890	−	0.512798i	0.930807	+	0.365511i	$0.119106\pi$
$60$		0			0
$61$	−1.34742	−	7.64158i	−0.172519	−	0.978404i	−0.940969	−	0.338494i	$-0.890083\pi$
$61$	−1.34742	−	7.64158i	−0.172519	−	0.978404i	0.768449	−	0.639910i	$-0.221029\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.220771	+	1.25206i	−0.0273833	+	0.155299i
$66$		0			0
$67$	5.01641	+	1.82582i	0.612852	+	0.223060i	0.629751	−	0.776797i	$-0.283157\pi$
$67$	5.01641	+	1.82582i	0.612852	+	0.223060i	−0.0168987	+	0.999857i	$0.505379\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.62237	−	3.87863i	0.548574	−	0.460308i	−0.325884	−	0.945410i	$-0.605662\pi$
$71$	4.62237	−	3.87863i	0.548574	−	0.460308i	0.874458	+	0.485101i	$0.161217\pi$
$72$		0			0
$73$	6.37193			0.745778			0.372889	−	0.927876i	$-0.378367\pi$
$73$	6.37193			0.745778			0.372889	+	0.927876i	$0.378367\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.65436	−	4.74457i	0.644375	−	0.540694i
$78$		0			0
$79$	−11.3107	−	4.11675i	−1.27255	−	0.463170i	−0.384588	−	0.923088i	$-0.625656\pi$
$79$	−11.3107	−	4.11675i	−1.27255	−	0.463170i	−0.887961	+	0.459918i	$0.847879\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.94652	−	11.0392i	0.213658	−	1.21171i	−0.669562	−	0.742756i	$-0.733518\pi$
$83$	1.94652	−	11.0392i	0.213658	−	1.21171i	0.883220	−	0.468959i	$-0.155371\pi$
$84$		0			0
$85$	−1.37740	+	2.38573i	−0.149400	+	0.258769i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.57240	−	0.936276i	0.272674	−	0.0992451i	−0.202064	−	0.979372i	$-0.564765\pi$
$89$	2.57240	−	0.936276i	0.272674	−	0.0992451i	0.474738	+	0.880127i	$0.342543\pi$
$90$		0			0
$91$	0.370372	−	2.10049i	0.0388256	−	0.220191i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.890465	−	0.324103i	0.0913598	−	0.0332523i
$96$		0			0
$97$	−1.94047	−	3.36099i	−0.197025	−	0.341257i	0.750538	−	0.660828i	$-0.229795\pi$
$97$	−1.94047	−	3.36099i	−0.197025	−	0.341257i	−0.947562	+	0.319571i	$0.896461\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.0151777	+	0.0262885i	0.00151024	+	0.00261581i	0.866780	−	0.498692i	$-0.166186\pi$
$101$	0.0151777	+	0.0262885i	0.00151024	+	0.00261581i	−0.865269	+	0.501307i	$0.832853\pi$
$102$		0			0
$103$	−1.99947	+	3.46319i	−0.197014	+	0.341238i	−0.947559	−	0.319581i	$-0.896458\pi$
$103$	−1.99947	+	3.46319i	−0.197014	+	0.341238i	0.750545	+	0.660819i	$0.229791\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.491977	−	2.79014i	−0.0475612	−	0.269733i	0.951749	−	0.306879i	$-0.0992846\pi$
$107$	−0.491977	−	2.79014i	−0.0475612	−	0.269733i	−0.999310	+	0.0371456i	$0.988173\pi$
$108$		0			0
$109$	−5.09645	−	4.27643i	−0.488152	−	0.409608i	0.365212	−	0.930924i	$-0.380997\pi$
$109$	−5.09645	−	4.27643i	−0.488152	−	0.409608i	−0.853363	+	0.521317i	$0.825441\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	9.85604	+	8.27020i	0.927178	+	0.777995i	0.975309	−	0.220846i	$-0.0708819\pi$
$113$	9.85604	+	8.27020i	0.927178	+	0.777995i	−0.0481304	+	0.998841i	$0.515326\pi$
$114$		0			0
$115$	−0.370308	−	2.10012i	−0.0345314	−	0.195837i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.31077	−	4.00237i	0.211828	−	0.366896i
$120$		0			0
$121$	2.48939	+	4.31175i	0.226308	+	0.391977i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	6.08290	+	10.5359i	0.544071	+	0.942358i
$126$		0			0
$127$	−11.5097	+	4.18921i	−1.02132	+	0.371732i	−0.797772	−	0.602960i	$-0.793988\pi$
$127$	−11.5097	+	4.18921i	−1.02132	+	0.371732i	−0.223553	+	0.974692i	$0.571766\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.28321	−	7.27747i	0.112115	−	0.635835i	−0.876023	−	0.482269i	$-0.839813\pi$
$131$	1.28321	−	7.27747i	0.112115	−	0.635835i	0.988138	−	0.153567i	$-0.0490760\pi$
$132$		0			0
$133$	−1.49387	+	0.543724i	−0.129535	+	0.0471469i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.65213	+	4.59362i	−0.226587	+	0.392459i	−0.956794	−	0.290766i	$-0.906090\pi$
$137$	−2.65213	+	4.59362i	−0.226587	+	0.392459i	0.730208	+	0.683225i	$0.239423\pi$
$138$		0			0
$139$	1.17114	−	6.64186i	0.0993347	−	0.563355i	−0.893998	−	0.448071i	$-0.852111\pi$
$139$	1.17114	−	6.64186i	0.0993347	−	0.563355i	0.993333	−	0.115284i	$-0.0367777\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.63497	−	0.595079i	−0.136723	−	0.0497630i
$144$		0			0
$145$	−0.476698	+	0.399997i	−0.0395876	+	0.0332180i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.218804			−0.0179251			−0.00896255	−	0.999960i	$-0.502853\pi$
$149$	−0.218804			−0.0179251			−0.00896255	+	0.999960i	$0.502853\pi$
$150$		0			0
$151$	−2.59809	+	2.18006i	−0.211430	+	0.177411i	−0.742352	−	0.670010i	$-0.766290\pi$
$151$	−2.59809	+	2.18006i	−0.211430	+	0.177411i	0.530923	+	0.847420i	$0.321845\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−12.6919	−	4.61949i	−1.01944	−	0.371047i
$156$		0			0
$157$	−3.07491	+	17.4387i	−0.245404	+	1.39176i	0.574147	+	0.818752i	$0.305334\pi$
$157$	−3.07491	+	17.4387i	−0.245404	+	1.39176i	−0.819552	+	0.573005i	$0.805777\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.621239	+	3.52322i	0.0489605	+	0.277669i
$162$		0			0
$163$	−1.76962	+	0.644088i	−0.138607	+	0.0504489i	−0.410392	−	0.911909i	$-0.634608\pi$
$163$	−1.76962	+	0.644088i	−0.138607	+	0.0504489i	0.271785	+	0.962358i	$0.412386\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−16.4877	+	13.8348i	−1.27586	+	1.07057i	−0.282056	+	0.959398i	$0.591016\pi$
$167$	−16.4877	+	13.8348i	−1.27586	+	1.07057i	−0.993801	+	0.111174i	$0.964539\pi$
$168$		0			0
$169$	11.7436	−	4.27431i	0.903351	−	0.328793i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	17.9244	+	15.0404i	1.36277	+	1.14350i	0.975117	+	0.221693i	$0.0711581\pi$
$173$	17.9244	+	15.0404i	1.36277	+	1.14350i	0.387652	+	0.921806i	$0.373286\pi$
$174$		0			0
$175$	−2.68467	−	4.64999i	−0.202942	−	0.351506i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−17.5543			−1.31207			−0.656036	−	0.754730i	$-0.727768\pi$
$179$	−17.5543			−1.31207			−0.656036	+	0.754730i	$0.727768\pi$
$180$		0			0
$181$	2.74388	+	15.5613i	0.203951	+	1.15666i	0.899082	+	0.437780i	$0.144235\pi$
$181$	2.74388	+	15.5613i	0.203951	+	1.15666i	−0.695131	+	0.718883i	$0.744654\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.58673	+	10.5955i	−0.190180	+	0.778996i
$186$		0			0
$187$	−2.88799	−	2.42331i	−0.211191	−	0.177210i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−9.03091			−0.653454			−0.326727	−	0.945119i	$-0.605946\pi$
$191$	−9.03091			−0.653454			−0.326727	+	0.945119i	$0.605946\pi$
$192$		0			0
$193$	4.60423	−	7.97475i	0.331419	−	0.574035i	−0.651371	−	0.758759i	$-0.725806\pi$
$193$	4.60423	−	7.97475i	0.331419	−	0.574035i	0.982790	+	0.184724i	$0.0591391\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.50243	−	7.13438i	−0.605773	−	0.508304i	0.287523	−	0.957774i	$-0.407168\pi$
$197$	−8.50243	−	7.13438i	−0.605773	−	0.508304i	−0.893295	+	0.449470i	$0.851613\pi$
$198$		0			0
$199$	8.08719	+	14.0074i	0.573286	+	0.992960i	0.996226	+	0.0868020i	$0.0276648\pi$
$199$	8.08719	+	14.0074i	0.573286	+	0.992960i	−0.422940	+	0.906158i	$0.639002\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.799722	−	0.671046i	0.0561295	−	0.0470982i
$204$		0			0
$205$	2.16918	−	12.3020i	0.151502	−	0.859209i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.225191	+	1.27712i	0.0155768	+	0.0883405i
$210$		0			0
$211$	0.0803109	−	0.139102i	0.00552883	−	0.00957621i	−0.863248	−	0.504780i	$-0.831573\pi$
$211$	0.0803109	−	0.139102i	0.00552883	−	0.00957621i	0.868777	+	0.495204i	$0.164907\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−6.34756	−	2.31032i	−0.432900	−	0.157563i
$216$		0			0
$217$	21.2924	+	7.74979i	1.44542	+	0.526090i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.08938			−0.0732797
$222$		0			0
$223$	−12.4549			−0.834041			−0.417020	−	0.908897i	$-0.636926\pi$
$223$	−12.4549			−0.834041			−0.417020	+	0.908897i	$0.636926\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−23.3567	−	8.50113i	−1.55024	−	0.564240i	−0.581763	−	0.813359i	$-0.697637\pi$
$227$	−23.3567	−	8.50113i	−1.55024	−	0.564240i	−0.968473	+	0.249119i	$0.919859\pi$
$228$		0			0
$229$	0.403499	+	0.146862i	0.0266640	+	0.00970490i	0.355318	−	0.934746i	$-0.384373\pi$
$229$	0.403499	+	0.146862i	0.0266640	+	0.00970490i	−0.328654	+	0.944450i	$0.606595\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−8.09978	+	14.0292i	−0.530634	+	0.919085i	0.468727	+	0.883343i	$0.344713\pi$
$233$	−8.09978	+	14.0292i	−0.530634	+	0.919085i	−0.999361	+	0.0357420i	$0.988621\pi$
$234$		0			0
$235$	0.971860	+	5.51169i	0.0633972	+	0.359543i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.38062	−	13.5012i	0.153990	−	0.873318i	−0.805714	−	0.592305i	$-0.798218\pi$
$239$	2.38062	−	13.5012i	0.153990	−	0.873318i	0.959704	−	0.281014i	$-0.0906707\pi$
$240$		0			0
$241$	8.81814	−	7.39930i	0.568026	−	0.476631i	−0.312964	−	0.949765i	$-0.601322\pi$
$241$	8.81814	−	7.39930i	0.568026	−	0.476631i	0.880990	+	0.473134i	$0.156877\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.83650	−	3.18091i	−0.117330	−	0.203221i
$246$		0			0
$247$	0.287061	+	0.240873i	0.0182653	+	0.0153264i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−0.284939	+	0.493528i	−0.0179852	+	0.0311512i	−0.874878	−	0.484344i	$-0.839059\pi$
$251$	−0.284939	+	0.493528i	−0.0179852	+	0.0311512i	0.856893	+	0.515495i	$0.172392\pi$
$252$		0			0
$253$	2.91839			0.183478
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.57738	−	8.03638i	−0.597420	−	0.501295i	0.293195	−	0.956053i	$-0.405282\pi$
$257$	−9.57738	−	8.03638i	−0.597420	−	0.501295i	−0.890615	+	0.454757i	$0.849726\pi$
$258$		0			0
$259$	4.33957	−	17.7753i	0.269648	−	1.10450i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.82609	+	16.0276i	0.174264	+	0.988302i	0.938990	+	0.343946i	$0.111764\pi$
$263$	2.82609	+	16.0276i	0.174264	+	0.988302i	−0.764725	+	0.644357i	$0.777125\pi$
$264$		0			0
$265$	−18.7014			−1.14882
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2.89239	−	5.00976i	−0.176352	−	0.305451i	0.764276	−	0.644889i	$-0.223096\pi$
$269$	−2.89239	−	5.00976i	−0.176352	−	0.305451i	−0.940628	+	0.339438i	$0.889763\pi$
$270$		0			0
$271$	21.1687	+	17.7626i	1.28591	+	1.07900i	0.992401	+	0.123046i	$0.0392663\pi$
$271$	21.1687	+	17.7626i	1.28591	+	1.07900i	0.293505	+	0.955957i	$0.405178\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.11587	+	1.49805i	−0.248196	+	0.0903361i
$276$		0			0
$277$	−14.9108	+	12.5117i	−0.895904	+	0.751752i	−0.969385	−	0.245544i	$-0.921033\pi$
$277$	−14.9108	+	12.5117i	−0.895904	+	0.751752i	0.0734818	+	0.997297i	$0.476589\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−21.9568	+	7.99163i	−1.30983	+	0.476741i	−0.900187	−	0.435503i	$-0.856570\pi$
$281$	−21.9568	+	7.99163i	−1.30983	+	0.476741i	−0.409647	+	0.912244i	$0.634348\pi$
$282$		0			0
$283$	−4.84293	−	27.4656i	−0.287882	−	1.63266i	−0.694804	−	0.719199i	$-0.744509\pi$
$283$	−4.84293	−	27.4656i	−0.287882	−	1.63266i	0.406922	−	0.913463i	$-0.366602\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.63907	+	20.6382i	−0.214808	+	1.21823i
$288$		0			0
$289$	13.7567	+	5.00702i	0.809215	+	0.294530i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	12.8959	−	10.8209i	0.753384	−	0.632164i	−0.183012	−	0.983111i	$-0.558585\pi$
$293$	12.8959	−	10.8209i	0.753384	−	0.632164i	0.936395	+	0.350947i	$0.114140\pi$
$294$		0			0
$295$	−20.6496			−1.20227
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.646005	−	0.542063i	0.0373594	−	0.0313483i
$300$		0			0
$301$	10.6488	+	3.87586i	0.613789	+	0.223401i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.41598	+	13.7017i	−0.138339	+	0.784558i
$306$		0			0
$307$	4.10550	−	7.11094i	0.234313	−	0.405843i	−0.724760	−	0.689002i	$-0.758049\pi$
$307$	4.10550	−	7.11094i	0.234313	−	0.405843i	0.959073	+	0.283159i	$0.0913825\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−14.8630	+	5.40970i	−0.842806	+	0.306756i	−0.727104	−	0.686528i	$-0.759134\pi$
$311$	−14.8630	+	5.40970i	−0.842806	+	0.306756i	−0.115702	+	0.993284i	$0.536912\pi$
$312$		0			0
$313$	1.53053	−	8.68008i	0.0865108	−	0.490627i	−0.910510	−	0.413488i	$-0.864310\pi$
$313$	1.53053	−	8.68008i	0.0865108	−	0.490627i	0.997020	−	0.0771389i	$-0.0245785\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	26.8737	−	9.78123i	1.50938	−	0.549368i	0.550908	−	0.834566i	$-0.314281\pi$
$317$	26.8737	−	9.78123i	1.50938	−	0.549368i	0.958469	+	0.285197i	$0.0920591\pi$
$318$		0			0
$319$	−0.425804	−	0.737515i	−0.0238405	−	0.0412929i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	0.405983	+	0.703184i	0.0225895	+	0.0391262i
$324$		0			0
$325$	−0.632826	+	1.09609i	−0.0351029	+	0.0608000i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.63042	−	9.24657i	−0.0898880	−	0.509780i
$330$		0			0
$331$	−21.3690	−	17.9307i	−1.17455	−	0.985561i	−1.00000		0.000911657i	$-0.999710\pi$
$331$	−21.3690	−	17.9307i	−1.17455	−	0.985561i	−0.174546	−	0.984649i	$-0.555846\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−7.33251	−	6.15271i	−0.400618	−	0.336158i
$336$		0			0
$337$	4.73144	+	26.8333i	0.257738	+	1.46171i	0.788945	+	0.614463i	$0.210627\pi$
$337$	4.73144	+	26.8333i	0.257738	+	1.46171i	−0.531207	+	0.847242i	$0.678262\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	9.24194	−	16.0075i	0.500479	−	0.866855i
$342$		0			0
$343$	−7.44727	−	12.8991i	−0.402115	−	0.696484i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.0455	+	19.1313i	0.592952	+	1.02702i	0.993832	+	0.110893i	$0.0353710\pi$
$347$	11.0455	+	19.1313i	0.592952	+	1.02702i	−0.400880	+	0.916130i	$0.631296\pi$
$348$		0			0
$349$	−8.86863	+	3.22792i	−0.474727	+	0.172787i	−0.568293	−	0.822827i	$-0.692396\pi$
$349$	−8.86863	+	3.22792i	−0.474727	+	0.172787i	0.0935654	+	0.995613i	$0.470174\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.36431	+	7.73741i	−0.0726151	+	0.411821i	0.926733	+	0.375720i	$0.122605\pi$
$353$	−1.36431	+	7.73741i	−0.0726151	+	0.411821i	−0.999348	+	0.0361002i	$0.988506\pi$
$354$		0			0
$355$	−10.1669	+	3.70045i	−0.539603	+	0.196399i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−10.6695	+	18.4801i	−0.563115	+	0.975343i	0.434108	+	0.900861i	$0.357064\pi$
$359$	−10.6695	+	18.4801i	−0.563115	+	0.975343i	−0.997222	+	0.0744820i	$0.976270\pi$
$360$		0			0
$361$	−3.25081	+	18.4363i	−0.171096	+	0.970331i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−10.7362	−	3.90764i	−0.561956	−	0.204535i
$366$		0			0
$367$	6.65321	−	5.58271i	0.347295	−	0.291415i	−0.452408	−	0.891811i	$-0.649435\pi$
$367$	6.65321	−	5.58271i	0.347295	−	0.291415i	0.799703	+	0.600396i	$0.204990\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	31.3740			1.62886
$372$		0			0
$373$	−27.4480	+	23.0316i	−1.42120	+	1.19253i	−0.470511	+	0.882394i	$0.655930\pi$
$373$	−27.4480	+	23.0316i	−1.42120	+	1.19253i	−0.950692	+	0.310137i	$0.899625\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.231241	−	0.0841648i	−0.0119095	−	0.00433471i
$378$		0			0
$379$	−5.28513	+	29.9735i	−0.271479	+	1.53963i	0.478449	+	0.878115i	$0.341199\pi$
$379$	−5.28513	+	29.9735i	−0.271479	+	1.53963i	−0.749928	+	0.661519i	$0.769912\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	3.86968	+	21.9461i	0.197732	+	1.12139i	0.908475	+	0.417940i	$0.137248\pi$
$383$	3.86968	+	21.9461i	0.197732	+	1.12139i	−0.710743	+	0.703452i	$0.751641\pi$
$384$		0			0
$385$	−12.4368	+	4.52661i	−0.633836	+	0.230697i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−15.6564	+	13.1373i	−0.793813	+	0.666089i	−0.946686	−	0.322157i	$-0.895592\pi$
$389$	−15.6564	+	13.1373i	−0.793813	+	0.666089i	0.152873	+	0.988246i	$0.451148\pi$
$390$		0			0
$391$	1.71706	−	0.624959i	0.0868355	−	0.0316056i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	16.5329	+	13.8727i	0.831859	+	0.698012i
$396$		0			0
$397$	5.89114	+	10.2038i	0.295668	+	0.512112i	0.975140	−	0.221589i	$-0.0711244\pi$
$397$	5.89114	+	10.2038i	0.295668	+	0.512112i	−0.679472	+	0.733701i	$0.737791\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−18.7932			−0.938488			−0.469244	−	0.883069i	$-0.655473\pi$
$401$	−18.7932			−0.938488			−0.469244	+	0.883069i	$0.655473\pi$
$402$		0			0
$403$	−0.927474	−	5.25997i	−0.0462008	−	0.262018i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−13.6651	−	6.00412i	−0.677355	−	0.297613i
$408$		0			0
$409$	8.33254	+	6.99183i	0.412018	+	0.345724i	0.825117	−	0.564962i	$-0.191109\pi$
$409$	8.33254	+	6.99183i	0.412018	+	0.345724i	−0.413099	+	0.910686i	$0.635554\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	34.6424			1.70464
$414$		0			0
$415$	−10.0496	+	17.4065i	−0.493317	+	0.854449i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−9.10697	−	7.64165i	−0.444904	−	0.373319i	0.392636	−	0.919694i	$-0.371563\pi$
$419$	−9.10697	−	7.64165i	−0.444904	−	0.373319i	−0.837541	+	0.546375i	$0.816008\pi$
$420$		0			0
$421$	−13.4119	−	23.2302i	−0.653658	−	1.13217i	−0.982228	−	0.187690i	$-0.939900\pi$
$421$	−13.4119	−	23.2302i	−0.653658	−	1.13217i	0.328570	−	0.944480i	$-0.393433\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.10081	+	1.76279i	−0.101904	+	0.0855078i
$426$		0			0
$427$	4.05312	−	22.9864i	0.196144	−	1.11239i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.449728	−	2.55053i	−0.0216626	−	0.122855i	0.972059	−	0.234737i	$-0.0754230\pi$
$431$	−0.449728	−	2.55053i	−0.0216626	−	0.122855i	−0.993721	+	0.111883i	$0.964312\pi$
$432$		0			0
$433$	−4.10143	+	7.10389i	−0.197102	+	0.341391i	−0.947588	−	0.319496i	$-0.896486\pi$
$433$	−4.10143	+	7.10389i	−0.197102	+	0.341391i	0.750485	+	0.660887i	$0.229820\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.590645	−	0.214977i	−0.0282544	−	0.0102837i
$438$		0			0
$439$	−23.6388	−	8.60384i	−1.12822	−	0.410639i	−0.290575	−	0.956852i	$-0.593846\pi$
$439$	−23.6388	−	8.60384i	−1.12822	−	0.410639i	−0.837646	+	0.546214i	$0.816069\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	24.6947			1.17328			0.586641	−	0.809847i	$-0.300450\pi$
$443$	24.6947			1.17328			0.586641	+	0.809847i	$0.300450\pi$
$444$		0			0
$445$	−4.90845			−0.232683
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−32.3629	−	11.7791i	−1.52730	−	0.555892i	−0.564343	−	0.825540i	$-0.690870\pi$
$449$	−32.3629	−	11.7791i	−1.52730	−	0.555892i	−0.962959	+	0.269648i	$0.913093\pi$
$450$		0			0
$451$	16.0643	+	5.84691i	0.756437	+	0.275320i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.91219	+	3.31200i	−0.0896447	+	0.155269i
$456$		0			0
$457$	−2.66585	−	15.1188i	−0.124703	−	0.707228i	−0.981484	−	0.191546i	$-0.938650\pi$
$457$	−2.66585	−	15.1188i	−0.124703	−	0.707228i	0.856780	−	0.515682i	$-0.172461\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.69694	+	15.2951i	−0.125609	+	0.712363i	0.855336	+	0.518074i	$0.173351\pi$
$461$	−2.69694	+	15.2951i	−0.125609	+	0.712363i	−0.980944	+	0.194289i	$0.937760\pi$
$462$		0			0
$463$	16.2316	−	13.6199i	0.754345	−	0.632970i	−0.182303	−	0.983242i	$-0.558355\pi$
$463$	16.2316	−	13.6199i	0.754345	−	0.632970i	0.936648	+	0.350272i	$0.113911\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−14.2621	−	24.7026i	−0.659970	−	1.14310i	−0.980623	−	0.195904i	$-0.937236\pi$
$467$	−14.2621	−	24.7026i	−0.659970	−	1.14310i	0.320653	−	0.947197i	$-0.396098\pi$
$468$		0			0
$469$	12.3012	+	10.3220i	0.568018	+	0.476624i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.62212	−	8.00575i	0.212525	−	0.368105i
$474$		0			0
$475$	0.943350			0.0432839
$476$		0			0
$477$		0			0
$478$		0			0
$479$	12.0822	+	10.1382i	0.552050	+	0.463225i	0.875635	−	0.482974i	$-0.160443\pi$
$479$	12.0822	+	10.1382i	0.552050	+	0.463225i	−0.323584	+	0.946199i	$0.604888\pi$
$480$		0			0
$481$	−4.14007	+	1.20911i	−0.188771	+	0.0551307i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.20837	+	6.85299i	0.0548691	+	0.311178i
$486$		0			0
$487$	−5.56555			−0.252199			−0.126100	−	0.992018i	$-0.540246\pi$
$487$	−5.56555			−0.252199			−0.126100	+	0.992018i	$0.540246\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−7.38035	−	12.7831i	−0.333071	−	0.576895i	0.650042	−	0.759899i	$-0.274751\pi$
$491$	−7.38035	−	12.7831i	−0.333071	−	0.576895i	−0.983112	+	0.183003i	$0.941418\pi$
$492$		0			0
$493$	−0.408461	−	0.342739i	−0.0183962	−	0.0154362i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	17.0563	−	6.20797i	0.765078	−	0.278466i
$498$		0			0
$499$	−10.8013	+	9.06337i	−0.483533	+	0.405732i	−0.851702	−	0.524027i	$-0.824429\pi$
$499$	−10.8013	+	9.06337i	−0.483533	+	0.405732i	0.368169	+	0.929759i	$0.379985\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	6.86538	−	2.49880i	0.306112	−	0.111416i	−0.184397	−	0.982852i	$-0.559033\pi$
$503$	6.86538	−	2.49880i	0.306112	−	0.111416i	0.490509	+	0.871436i	$0.336811\pi$
$504$		0			0
$505$	−0.00945143	−	0.0536017i	−0.000420583	−	0.00238525i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−4.28944	+	24.3266i	−0.190126	+	1.07826i	0.729064	+	0.684445i	$0.239956\pi$
$509$	−4.28944	+	24.3266i	−0.190126	+	1.07826i	−0.919190	+	0.393814i	$0.871156\pi$
$510$		0			0
$511$	18.0113	+	6.55557i	0.796772	+	0.290001i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	5.49276	−	4.60898i	0.242040	−	0.203096i
$516$		0			0
$517$	−7.65921			−0.336852
$518$		0			0
$519$		0			0
$520$		0			0
$521$	28.4446	−	23.8678i	1.24618	−	1.04567i	0.249164	−	0.968461i	$-0.419844\pi$
$521$	28.4446	−	23.8678i	1.24618	−	1.04567i	0.997015	−	0.0772075i	$-0.0246004\pi$
$522$		0			0
$523$	−4.81378	−	1.75207i	−0.210492	−	0.0766128i	0.234622	−	0.972087i	$-0.424615\pi$
$523$	−4.81378	−	1.75207i	−0.210492	−	0.0766128i	−0.445114	+	0.895474i	$0.646837\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.00965	−	11.3973i	0.0875416	−	0.496473i
$528$		0			0
$529$	10.7928	−	18.6936i	0.469250	−	0.812765i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	4.64194	−	1.68953i	0.201065	−	0.0731816i
$534$		0			0
$535$	−0.882138	+	5.00285i	−0.0381382	+	0.216292i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	4.72342	−	1.71918i	0.203452	−	0.0740505i
$540$		0			0
$541$	9.82067	+	17.0099i	0.422223	+	0.731313i	0.996157	−	0.0875896i	$-0.0279164\pi$
$541$	9.82067	+	17.0099i	0.422223	+	0.731313i	−0.573933	+	0.818902i	$0.694583\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	5.96452	+	10.3309i	0.255492	+	0.442525i
$546$		0			0
$547$	−0.414046	+	0.717149i	−0.0177033	+	0.0306631i	−0.874741	−	0.484590i	$-0.838969\pi$
$547$	−0.414046	+	0.717149i	−0.0177033	+	0.0306631i	0.857038	+	0.515253i	$0.172302\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.0318498	+	0.180629i	0.00135685	+	0.00769507i
$552$		0			0
$553$	−27.7360	−	23.2733i	−1.17945	−	0.989680i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−11.2998	−	9.48170i	−0.478790	−	0.401752i	0.371199	−	0.928553i	$-0.378947\pi$
$557$	−11.2998	−	9.48170i	−0.478790	−	0.401752i	−0.849989	+	0.526801i	$0.823391\pi$
$558$		0			0
$559$	−0.463853	−	2.63064i	−0.0196189	−	0.111264i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	19.5267	−	33.8213i	0.822953	−	1.42540i	−0.0805206	−	0.996753i	$-0.525658\pi$
$563$	19.5267	−	33.8213i	0.822953	−	1.42540i	0.903474	−	0.428644i	$-0.141008\pi$
$564$		0			0
$565$	−11.5348	−	19.9789i	−0.485273	−	0.840517i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	0.559415	+	0.968936i	0.0234519	+	0.0406199i	0.877513	−	0.479553i	$-0.159201\pi$
$569$	0.559415	+	0.968936i	0.0234519	+	0.0406199i	−0.854061	+	0.520172i	$0.825868\pi$
$570$		0			0
$571$	39.9105	−	14.5262i	1.67020	−	0.607903i	0.678285	−	0.734799i	$-0.262723\pi$
$571$	39.9105	−	14.5262i	1.67020	−	0.607903i	0.991916	+	0.126895i	$0.0405013\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.368642	−	2.09067i	0.0153734	−	0.0871871i
$576$		0			0
$577$	22.6372	−	8.23925i	0.942397	−	0.343005i	0.175285	−	0.984518i	$-0.443915\pi$
$577$	22.6372	−	8.23925i	0.942397	−	0.343005i	0.767112	+	0.641513i	$0.221693\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	16.8595	−	29.2016i	0.699451	−	1.21148i
$582$		0			0
$583$	4.44421	−	25.2044i	0.184061	−	1.04386i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	40.9026	+	14.8873i	1.68823	+	0.614465i	0.994401	−	0.105674i	$-0.0337000\pi$
$587$	40.9026	+	14.8873i	1.68823	+	0.614465i	0.693829	+	0.720140i	$0.255922\pi$
$588$		0			0
$589$	−3.04961	+	2.55893i	−0.125657	+	0.105439i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	30.5529			1.25466			0.627330	−	0.778754i	$-0.284148\pi$
$593$	30.5529			1.25466			0.627330	+	0.778754i	$0.284148\pi$
$594$		0			0
$595$	−6.34793	+	5.32655i	−0.260240	+	0.218367i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−26.4184	−	9.61553i	−1.07943	−	0.392880i	−0.259734	−	0.965680i	$-0.583635\pi$
$599$	−26.4184	−	9.61553i	−1.07943	−	0.392880i	−0.819695	+	0.572800i	$0.805857\pi$
$600$		0			0
$601$	2.86505	−	16.2485i	0.116868	−	0.662790i	−0.868941	−	0.494916i	$-0.835199\pi$
$601$	2.86505	−	16.2485i	0.116868	−	0.662790i	0.985808	−	0.167874i	$-0.0536902\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.55019	−	8.79156i	−0.0630242	−	0.357428i
$606$		0			0
$607$	24.2441	−	8.82412i	0.984036	−	0.358160i	0.200628	−	0.979667i	$-0.435702\pi$
$607$	24.2441	−	8.82412i	0.984036	−	0.358160i	0.783408	+	0.621508i	$0.213479\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.69542	+	1.42262i	−0.0685893	+	0.0575532i
$612$		0			0
$613$	30.0677	−	10.9437i	1.21442	−	0.442013i	0.346186	−	0.938166i	$-0.387477\pi$
$613$	30.0677	−	10.9437i	1.21442	−	0.442013i	0.868235	+	0.496153i	$0.165254\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−12.6996	−	10.6562i	−0.511266	−	0.429003i	0.350308	−	0.936634i	$-0.386077\pi$
$617$	−12.6996	−	10.6562i	−0.511266	−	0.429003i	−0.861575	+	0.507631i	$0.830521\pi$
$618$		0			0
$619$	7.23206	+	12.5263i	0.290681	+	0.503474i	0.973971	−	0.226673i	$-0.0727848\pi$
$619$	7.23206	+	12.5263i	0.290681	+	0.503474i	−0.683290	+	0.730147i	$0.739451\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	8.23455			0.329910
$624$		0			0
$625$	−2.23814	−	12.6931i	−0.0895256	−	0.507725i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−9.32576	−	0.606260i	−0.371842	−	0.0241732i
$630$		0			0
$631$	32.0071	+	26.8571i	1.27418	+	1.06917i	0.994018	+	0.109213i	$0.0348330\pi$
$631$	32.0071	+	26.8571i	1.27418	+	1.06917i	0.280163	+	0.959952i	$0.409611\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	21.9620			0.871535
$636$		0			0
$637$	0.726239	−	1.25788i	0.0287746	−	0.0498391i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−32.6066	−	27.3602i	−1.28788	−	1.08066i	−0.992105	−	0.125406i	$-0.959977\pi$
$641$	−32.6066	−	27.3602i	−1.28788	−	1.08066i	−0.295778	−	0.955257i	$-0.595579\pi$
$642$		0			0
$643$	11.4258	+	19.7901i	0.450590	+	0.780444i	0.998423	−	0.0561436i	$-0.0178805\pi$
$643$	11.4258	+	19.7901i	0.450590	+	0.780444i	−0.547833	+	0.836588i	$0.684547\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−16.2000	+	13.5934i	−0.636887	+	0.534411i	−0.903060	−	0.429514i	$-0.858685\pi$
$647$	−16.2000	+	13.5934i	−0.636887	+	0.534411i	0.266174	+	0.963925i	$0.414241\pi$
$648$		0			0
$649$	4.90719	−	27.8301i	0.192624	−	1.09243i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	5.15523	+	29.2368i	0.201740	+	1.14412i	0.902488	+	0.430715i	$0.141738\pi$
$653$	5.15523	+	29.2368i	0.201740	+	1.14412i	−0.700748	+	0.713408i	$0.747150\pi$
$654$		0			0
$655$	−6.62507	+	11.4750i	−0.258863	+	0.448364i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−38.3953	−	13.9747i	−1.49567	−	0.544379i	−0.540734	−	0.841194i	$-0.681853\pi$
$659$	−38.3953	−	13.9747i	−1.49567	−	0.544379i	−0.954935	+	0.296815i	$0.904076\pi$
$660$		0			0
$661$	21.0650	+	7.66703i	0.819333	+	0.298213i	0.717474	−	0.696586i	$-0.245298\pi$
$661$	21.0650	+	7.66703i	0.819333	+	0.298213i	0.101860	+	0.994799i	$0.467521\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.85048			0.110537
$666$		0			0
$667$	0.412761			0.0159822
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−17.8920	−	6.51217i	−0.690715	−	0.251400i
$672$		0			0
$673$	37.8469	+	13.7751i	1.45889	+	0.530992i	0.945059	−	0.326900i	$-0.106004\pi$
$673$	37.8469	+	13.7751i	1.45889	+	0.530992i	0.513830	+	0.857892i	$0.328226\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16.2975	+	28.2281i	−0.626365	+	1.08490i	0.361911	+	0.932213i	$0.382124\pi$
$677$	−16.2975	+	28.2281i	−0.626365	+	1.08490i	−0.988275	+	0.152682i	$0.951209\pi$
$678$		0			0
$679$	−2.02719	−	11.4968i	−0.0777964	−	0.441205i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	3.77462	−	21.4069i	0.144432	−	0.819114i	−0.823390	−	0.567476i	$-0.807920\pi$
$683$	3.77462	−	21.4069i	0.144432	−	0.819114i	0.967822	−	0.251637i	$-0.0809690\pi$
$684$		0			0
$685$	7.28568	−	6.11341i	0.278372	−	0.233581i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−3.69771	−	6.40463i	−0.140872	−	0.243997i
$690$		0			0
$691$	−9.32192	−	7.82202i	−0.354623	−	0.297564i	0.448021	−	0.894023i	$-0.352129\pi$
$691$	−9.32192	−	7.82202i	−0.354623	−	0.297564i	−0.802643	+	0.596460i	$0.796574\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−6.04644	+	10.4727i	−0.229355	+	0.397254i
$696$		0			0
$697$	10.7036			0.405429
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−7.47744	−	6.27432i	−0.282419	−	0.236978i	0.490563	−	0.871406i	$-0.336791\pi$
$701$	−7.47744	−	6.27432i	−0.282419	−	0.236978i	−0.772982	+	0.634428i	$0.781236\pi$
$702$		0			0
$703$	2.32336	+	2.22177i	0.0876274	+	0.0837957i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.0158560	+	0.0899238i	0.000596326	+	0.00338193i
$708$		0			0
$709$	−35.1920			−1.32166			−0.660831	−	0.750534i	$-0.729796\pi$
$709$	−35.1920			−1.32166			−0.660831	+	0.750534i	$0.729796\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	4.47942	+	7.75858i	0.167756	+	0.290561i
$714$		0			0
$715$	2.38984	+	2.00531i	0.0893750	+	0.0749945i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	30.9679	−	11.2714i	1.15491	−	0.420352i	0.307633	−	0.951505i	$-0.400463\pi$
$719$	30.9679	−	11.2714i	1.15491	−	0.420352i	0.847276	+	0.531153i	$0.178241\pi$
$720$		0			0
$721$	−9.21482	+	7.73215i	−0.343178	+	0.287960i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.582126	+	0.211877i	−0.0216196	+	0.00786890i
$726$		0			0
$727$	−3.59910	−	20.4115i	−0.133483	−	0.757021i	−0.975904	−	0.218200i	$-0.929981\pi$
$727$	−3.59910	−	20.4115i	−0.133483	−	0.757021i	0.842421	−	0.538820i	$-0.181130\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1.00507	−	5.70006i	0.0371740	−	0.210824i
$732$		0			0
$733$	19.0627	+	6.93827i	0.704098	+	0.256271i	0.669160	−	0.743119i	$-0.266654\pi$
$733$	19.0627	+	6.93827i	0.704098	+	0.256271i	0.0349386	+	0.999389i	$0.488876\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	10.0347	−	8.42009i	0.369632	−	0.310158i
$738$		0			0
$739$	0.643082			0.0236562			0.0118281	−	0.999930i	$-0.496235\pi$
$739$	0.643082			0.0236562			0.0118281	+	0.999930i	$0.496235\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−28.1199	+	23.5954i	−1.03162	+	0.865631i	−0.991043	−	0.133545i	$-0.957364\pi$
$743$	−28.1199	+	23.5954i	−1.03162	+	0.865631i	−0.0405767	+	0.999176i	$0.512919\pi$
$744$		0			0
$745$	0.368665	+	0.134183i	0.0135069	+	0.00491609i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.47990	−	8.39293i	0.0540744	−	0.306671i
$750$		0			0
$751$	−9.18509	+	15.9090i	−0.335169	+	0.580529i	−0.983517	−	0.180815i	$-0.942127\pi$
$751$	−9.18509	+	15.9090i	−0.335169	+	0.580529i	0.648349	+	0.761344i	$0.275460\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	5.71450	−	2.07991i	0.207972	−	0.0756955i
$756$		0			0
$757$	−5.23164	+	29.6701i	−0.190147	+	1.07838i	0.729014	+	0.684498i	$0.239979\pi$
$757$	−5.23164	+	29.6701i	−0.190147	+	1.07838i	−0.919162	+	0.393880i	$0.871132\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	14.9183	−	5.42983i	0.540789	−	0.196831i	−0.0571601	−	0.998365i	$-0.518205\pi$
$761$	14.9183	−	5.42983i	0.540789	−	0.196831i	0.597950	+	0.801534i	$0.295982\pi$
$762$		0			0
$763$	−10.0063	−	17.3313i	−0.362251	−	0.627437i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.08293	−	7.07184i	−0.147426	−	0.255349i
$768$		0			0
$769$	−12.9117	+	22.3637i	−0.465607	+	0.806456i	−0.999229	−	0.0392677i	$-0.987497\pi$
$769$	−12.9117	+	22.3637i	−0.465607	+	0.806456i	0.533621	+	0.845724i	$0.320831\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.55406	+	8.81349i	0.0558955	+	0.316999i	0.999917	−	0.0128848i	$-0.00410146\pi$
$773$	1.55406	+	8.81349i	0.0558955	+	0.316999i	−0.944021	+	0.329884i	$0.892990\pi$
$774$		0			0
$775$	−10.3000	−	8.64275i	−0.369988	−	0.310457i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.82050	−	2.36668i	−0.101055	−	0.0847951i
$780$		0			0
$781$	−2.57113	−	14.5816i	−0.0920021	−	0.521770i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	15.8754	−	27.4969i	0.566616	−	0.981408i
$786$		0			0
$787$	4.92255	+	8.52610i	0.175470	+	0.303923i	0.940324	−	0.340281i	$-0.110522\pi$
$787$	4.92255	+	8.52610i	0.175470	+	0.303923i	−0.764854	+	0.644204i	$0.777189\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	19.3511	+	33.5171i	0.688046	+	1.19173i
$792$		0			0
$793$	−5.17010	+	1.88176i	−0.183595	+	0.0668233i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.358173	−	2.03130i	0.0126871	−	0.0719523i	−0.977807	−	0.209508i	$-0.932814\pi$
$797$	0.358173	−	2.03130i	0.0126871	−	0.0719523i	0.990494	+	0.137556i	$0.0439247\pi$
$798$		0			0
$799$	−4.50637	+	1.64018i	−0.159424	+	0.0580255i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	7.81778	−	13.5408i	0.275883	−	0.477844i
$804$		0			0
$805$	1.11391	−	6.31730i	0.0392602	−	0.222656i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	2.17683	+	0.792303i	0.0765334	+	0.0278559i	0.380003	−	0.924985i	$-0.375923\pi$
$809$	2.17683	+	0.792303i	0.0765334	+	0.0278559i	−0.303470	+	0.952841i	$0.598145\pi$
$810$		0			0
$811$	−26.8917	+	22.5648i	−0.944294	+	0.792356i	−0.978327	−	0.207064i	$-0.933609\pi$
$811$	−26.8917	+	22.5648i	−0.944294	+	0.792356i	0.0340337	+	0.999421i	$0.489165\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	3.37665			0.118279
$816$		0			0
$817$	−1.52519	+	1.27978i	−0.0533595	+	0.0447739i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.52316	+	2.73821i	0.262560	+	0.0955641i	0.469946	−	0.882695i	$-0.344273\pi$
$821$	7.52316	+	2.73821i	0.262560	+	0.0955641i	−0.207386	+	0.978259i	$0.566496\pi$
$822$		0			0
$823$	−6.77578	+	38.4274i	−0.236189	+	1.33949i	0.603907	+	0.797055i	$0.293610\pi$
$823$	−6.77578	+	38.4274i	−0.236189	+	1.33949i	−0.840095	+	0.542439i	$0.817501\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.28293	−	7.27583i	−0.0446117	−	0.253005i	0.954343	−	0.298712i	$-0.0965571\pi$
$827$	−1.28293	−	7.27583i	−0.0446117	−	0.253005i	−0.998955	+	0.0457069i	$0.985446\pi$
$828$		0			0
$829$	32.3653	−	11.7800i	1.12409	−	0.409136i	0.287949	−	0.957646i	$-0.407027\pi$
$829$	32.3653	−	11.7800i	1.12409	−	0.409136i	0.836144	+	0.548509i	$0.184805\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	2.41091	−	2.02300i	0.0835332	−	0.0700927i
$834$		0			0
$835$	36.2647	−	13.1993i	1.25499	−	0.456779i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	7.50313	+	6.29587i	0.259037	+	0.217358i	0.763052	−	0.646337i	$-0.223700\pi$
$839$	7.50313	+	6.29587i	0.259037	+	0.217358i	−0.504015	+	0.863695i	$0.668144\pi$
$840$		0			0
$841$	14.4398	+	25.0104i	0.497923	+	0.862429i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−22.4081			−0.770864
$846$		0			0
$847$	2.60064	+	14.7490i	0.0893591	+	0.506781i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	5.83186	−	4.28087i	0.199914	−	0.146746i
$852$		0			0
$853$	−21.6990	−	18.2076i	−0.742958	−	0.623416i	0.190672	−	0.981654i	$-0.438933\pi$
$853$	−21.6990	−	18.2076i	−0.742958	−	0.623416i	−0.933630	+	0.358238i	$0.883378\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	41.1121			1.40436			0.702181	−	0.711998i	$-0.252210\pi$
$857$	41.1121			1.40436			0.702181	+	0.711998i	$0.252210\pi$
$858$		0			0
$859$	2.31018	−	4.00135i	0.0788223	−	0.136524i	−0.823920	−	0.566706i	$-0.808217\pi$
$859$	2.31018	−	4.00135i	0.0788223	−	0.136524i	0.902742	+	0.430182i	$0.141551\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	7.55539	+	6.33973i	0.257188	+	0.215807i	0.762260	−	0.647271i	$-0.224090\pi$
$863$	7.55539	+	6.33973i	0.257188	+	0.215807i	−0.505072	+	0.863077i	$0.668534\pi$
$864$		0			0
$865$	−20.9775	−	36.3340i	−0.713255	−	1.23539i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−22.6255	+	18.9851i	−0.767518	+	0.644024i
$870$		0			0
$871$	0.657292	−	3.72769i	0.0222715	−	0.126308i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	6.35474	+	36.0395i	0.214830	+	1.21836i
$876$		0			0
$877$	11.5143	−	19.9433i	0.388810	−	0.673439i	−0.603480	−	0.797378i	$-0.706220\pi$
$877$	11.5143	−	19.9433i	0.388810	−	0.673439i	0.992290	+	0.123940i	$0.0395529\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−29.8184	−	10.8530i	−1.00461	−	0.365648i	−0.213248	−	0.976998i	$-0.568404\pi$
$881$	−29.8184	−	10.8530i	−1.00461	−	0.365648i	−0.791360	+	0.611350i	$0.790627\pi$
$882$		0			0
$883$	−13.6475	−	4.96728i	−0.459274	−	0.167162i	0.102013	−	0.994783i	$-0.467472\pi$
$883$	−13.6475	−	4.96728i	−0.459274	−	0.167162i	−0.561288	+	0.827621i	$0.689694\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	43.8229			1.47143			0.735714	−	0.677292i	$-0.236847\pi$
$887$	43.8229			1.47143			0.735714	+	0.677292i	$0.236847\pi$
$888$		0			0
$889$	−36.8441			−1.23571
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.55013	+	0.564200i	0.0518730	+	0.0188802i
$894$		0			0
$895$	29.5775	+	10.7653i	0.988667	+	0.359845i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.30713	−	2.26401i	0.0435952	−	0.0755091i
$900$		0			0
$901$	−2.78261	−	15.7809i	−0.0927020	−	0.525739i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4.91990	−	27.9022i	0.163543	−	0.927499i
$906$		0			0
$907$	18.1963	−	15.2685i	0.604199	−	0.506983i	−0.288594	−	0.957452i	$-0.593188\pi$
$907$	18.1963	−	15.2685i	0.604199	−	0.506983i	0.892792	+	0.450469i	$0.148743\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−21.8829	−	37.9023i	−0.725013	−	1.25576i	−0.958969	−	0.283512i	$-0.908501\pi$
$911$	−21.8829	−	37.9023i	−0.725013	−	1.25576i	0.233956	−	0.972247i	$-0.424833\pi$
$912$		0			0
$913$	−21.0710	−	17.6806i	−0.697347	−	0.585144i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	11.1144	−	19.2507i	0.367030	−	0.635715i
$918$		0			0
$919$	−48.3191			−1.59390			−0.796950	−	0.604045i	$-0.793555\pi$
$919$	−48.3191			−1.59390			−0.796950	+	0.604045i	$0.793555\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−3.27752	−	2.75017i	−0.107881	−	0.0905229i
$924$		0			0
$925$	−6.02736	+	9.03098i	−0.198178	+	0.296937i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	3.86220	+	21.9036i	0.126715	+	0.718635i	0.980275	+	0.197640i	$0.0633279\pi$
$929$	3.86220	+	21.9036i	0.126715	+	0.718635i	−0.853560	+	0.520995i	$0.825561\pi$
$930$		0			0
$931$	−1.08260			−0.0354808
$932$		0			0
$933$		0			0
$934$		0			0
$935$	3.37989	+	5.85415i	0.110534	+	0.191451i
$936$		0			0
$937$	−2.38149	−	1.99831i	−0.0777999	−	0.0652819i	0.603058	−	0.797697i	$-0.293949\pi$
$937$	−2.38149	−	1.99831i	−0.0777999	−	0.0652819i	−0.680858	+	0.732415i	$0.738393\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	52.2774	−	19.0274i	1.70419	−	0.620276i	0.707903	−	0.706310i	$-0.249642\pi$
$941$	52.2774	−	19.0274i	1.70419	−	0.620276i	0.996292	+	0.0860339i	$0.0274194\pi$
$942$		0			0
$943$	−6.34728	+	5.32600i	−0.206696	+	0.173438i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	17.0620	−	6.21006i	0.554440	−	0.201800i	−0.0495778	−	0.998770i	$-0.515788\pi$
$947$	17.0620	−	6.21006i	0.554440	−	0.201800i	0.604018	+	0.796970i	$0.293565\pi$
$948$		0			0
$949$	−0.784553	−	4.44942i	−0.0254677	−	0.144434i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−6.29166	+	35.6818i	−0.203807	+	1.15585i	0.695500	+	0.718526i	$0.255183\pi$
$953$	−6.29166	+	35.6818i	−0.203807	+	1.15585i	−0.899306	+	0.437319i	$0.855928\pi$
$954$		0			0
$955$	15.2163	+	5.53828i	0.492388	+	0.179215i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−12.2227	+	10.2560i	−0.394690	+	0.331184i
$960$		0			0
$961$	25.7416			0.830374
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−12.6483	+	10.6132i	−0.407163	+	0.341651i
$966$		0			0
$967$	17.1528	+	6.24311i	0.551597	+	0.200765i	0.602756	−	0.797926i	$-0.294069\pi$
$967$	17.1528	+	6.24311i	0.551597	+	0.200765i	−0.0511589	+	0.998691i	$0.516291\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.39038	−	7.88522i	0.0446193	−	0.253049i	−0.954337	−	0.298733i	$-0.903436\pi$
$971$	1.39038	−	7.88522i	0.0446193	−	0.253049i	0.998956	+	0.0456847i	$0.0145470\pi$
$972$		0			0
$973$	10.1437	−	17.5694i	0.325191	−	0.563248i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	9.03802	−	3.28957i	0.289152	−	0.105243i	−0.193372	−	0.981126i	$-0.561942\pi$
$977$	9.03802	−	3.28957i	0.289152	−	0.105243i	0.482524	+	0.875883i	$0.339720\pi$
$978$		0			0
$979$	1.16645	−	6.61525i	0.0372798	−	0.211424i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	36.6070	−	13.3239i	1.16758	−	0.424965i	0.315781	−	0.948832i	$-0.397733\pi$
$983$	36.6070	−	13.3239i	1.16758	−	0.424965i	0.851800	+	0.523867i	$0.175511\pi$
$984$		0			0
$985$	9.95063	+	17.2350i	0.317054	+	0.549153i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.24027	+	3.88026i	0.0712364	+	0.123385i
$990$		0			0
$991$	−12.5272	+	21.6978i	−0.397940	+	0.689253i	−0.993472	−	0.114079i	$-0.963608\pi$
$991$	−12.5272	+	21.6978i	−0.397940	+	0.689253i	0.595531	+	0.803332i	$0.296942\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−5.03604	−	28.5608i	−0.159653	−	0.905439i
$996$		0			0
$997$	−25.2320	−	21.1722i	−0.799106	−	0.670529i	0.148875	−	0.988856i	$-0.452435\pi$
$997$	−25.2320	−	21.1722i	−0.799106	−	0.670529i	−0.947981	+	0.318327i	$0.896879\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1332.2.bt.b.145.1		12
3.2	odd	2		444.2.u.a.145.2	yes	12
37.12	even	9	inner	1332.2.bt.b.937.1		12
111.86	odd	18		444.2.u.a.49.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
444.2.u.a.49.2	✓	12	111.86	odd	18
444.2.u.a.145.2	yes	12	3.2	odd	2
1332.2.bt.b.145.1		12	1.1	even	1	trivial
1332.2.bt.b.937.1		12	37.12	even	9	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1332 = 2^{2} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1332.bt (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.68491 - 0.613258i) q^{5} +(2.82666 + 1.02882i) q^{7} +(1.22691 - 2.12507i) q^{11} +(-0.123126 - 0.698284i) q^{13} +(0.266790 - 1.51304i) q^{17} +(-0.404849 + 0.339709i) q^{19} +(0.594663 + 1.02999i) q^{23} +(-1.36737 - 1.14736i) q^{25} +(0.173527 - 0.300558i) q^{29} +7.53270 q^{31} +(-4.13174 - 3.46694i) q^{35} +(-0.665428 - 6.04626i) q^{37} +(1.20977 + 6.86095i) q^{41} +3.76729 q^{43} +(-1.56067 - 2.70316i) q^{47} +(1.56922 + 1.31673i) q^{49} +(9.80095 - 3.56725i) q^{53} +(-3.37045 + 2.82814i) q^{55} +(10.8220 - 3.93888i) q^{59} +(-1.34742 - 7.64158i) q^{61} +(-0.220771 + 1.25206i) q^{65} +(5.01641 + 1.82582i) q^{67} +(4.62237 - 3.87863i) q^{71} +6.37193 q^{73} +(5.65436 - 4.74457i) q^{77} +(-11.3107 - 4.11675i) q^{79} +(1.94652 - 11.0392i) q^{83} +(-1.37740 + 2.38573i) q^{85} +(2.57240 - 0.936276i) q^{89} +(0.370372 - 2.10049i) q^{91} +(0.890465 - 0.324103i) q^{95} +(-1.94047 - 3.36099i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{5} - 6 q^{11} - 6 q^{13} - 12 q^{17} + 12 q^{19} - 15 q^{25} + 3 q^{29} - 36 q^{35} + 27 q^{37} - 18 q^{41} - 12 q^{43} - 9 q^{47} - 18 q^{49} + 36 q^{53} - 3 q^{55} + 6 q^{59} - 9 q^{61} - 30 q^{65}+ \cdots - 24 q^{97}+O(q^{100}) \) 12 * q - 3 * q^5 - 6 * q^11 - 6 * q^13 - 12 * q^17 + 12 * q^19 - 15 * q^25 + 3 * q^29 - 36 * q^35 + 27 * q^37 - 18 * q^41 - 12 * q^43 - 9 * q^47 - 18 * q^49 + 36 * q^53 - 3 * q^55 + 6 * q^59 - 9 * q^61 - 30 * q^65 + 6 * q^67 - 3 * q^71 - 42 * q^73 + 51 * q^77 + 12 * q^79 - 9 * q^83 - 27 * q^85 + 27 * q^89 + 9 * q^91 + 6 * q^95 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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