LMFDB - Embedded newform 361.2.e.e.28.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,2,Mod(28,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("361.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.e (of order $9$, degree $6$, not 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:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			28.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	361.28
Dual form			361.2.e.e.245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.53209 - 1.28558i) q^{3} +(1.87939 - 0.684040i) q^{4} +(-2.81908 - 1.02606i) q^{5} +(0.500000 - 0.866025i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(1.53209 - 1.28558i) q^{3} +(1.87939 - 0.684040i) q^{4} +(-2.81908 - 1.02606i) q^{5} +(0.500000 - 0.866025i) q^{7} +(0.173648 - 0.984808i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(2.00000 - 3.46410i) q^{12} +(3.06418 + 2.57115i) q^{13} +(-5.63816 + 2.05212i) q^{15} +(3.06418 - 2.57115i) q^{16} +(-0.520945 - 2.95442i) q^{17} -6.00000 q^{20} +(-0.347296 - 1.96962i) q^{21} +(3.06418 + 2.57115i) q^{25} +(2.00000 + 3.46410i) q^{27} +(0.347296 - 1.96962i) q^{28} +(-1.04189 + 5.90885i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(-5.63816 - 2.05212i) q^{33} +(-2.29813 + 1.92836i) q^{35} +(-0.347296 - 1.96962i) q^{36} -2.00000 q^{37} +8.00000 q^{39} +(4.59627 - 3.85673i) q^{41} +(0.939693 + 0.342020i) q^{43} +(-4.59627 - 3.85673i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(-0.520945 + 2.95442i) q^{47} +(1.38919 - 7.87846i) q^{48} +(3.00000 + 5.19615i) q^{49} +(-4.59627 - 3.85673i) q^{51} +(7.51754 + 2.73616i) q^{52} +(11.2763 - 4.10424i) q^{53} +(1.56283 + 8.86327i) q^{55} +(1.04189 + 5.90885i) q^{59} +(-9.19253 + 7.71345i) q^{60} +(0.939693 - 0.342020i) q^{61} +(-0.766044 - 0.642788i) q^{63} +(4.00000 - 6.92820i) q^{64} +(-6.00000 - 10.3923i) q^{65} +(0.694593 - 3.93923i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(5.63816 + 2.05212i) q^{71} +(-5.36231 + 4.49951i) q^{73} +8.00000 q^{75} -3.00000 q^{77} +(-6.12836 + 5.14230i) q^{79} +(-11.2763 + 4.10424i) q^{80} +(10.3366 + 3.76222i) q^{81} +(-6.00000 + 10.3923i) q^{83} +(-2.00000 - 3.46410i) q^{84} +(-1.56283 + 8.86327i) q^{85} +(6.00000 + 10.3923i) q^{87} +(-9.19253 - 7.71345i) q^{89} +(3.75877 - 1.36808i) q^{91} +(1.38919 + 7.87846i) q^{93} +(-1.38919 - 7.87846i) q^{97} +(-2.81908 + 1.02606i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{7}+O(q^{10}) $ 6 * q + 3 * q^7	$ 6 q + 3 q^{7} - 9 q^{11} + 12 q^{12} - 36 q^{20} + 12 q^{27} - 12 q^{31} - 12 q^{37} + 48 q^{39} - 9 q^{45} + 18 q^{49} + 24 q^{64} - 36 q^{65} - 18 q^{68} + 48 q^{75} - 18 q^{77} - 36 q^{83} - 12 q^{84} + 36 q^{87}+O(q^{100}) $ 6 * q + 3 * q^7 - 9 * q^11 + 12 * q^12 - 36 * q^20 + 12 * q^27 - 12 * q^31 - 12 * q^37 + 48 * q^39 - 9 * q^45 + 18 * q^49 + 24 * q^64 - 36 * q^65 - 18 * q^68 + 48 * q^75 - 18 * q^77 - 36 * q^83 - 12 * q^84 + 36 * q^87

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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		0.984808	−	0.173648i	$-0.0555556\pi$
$2$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$3$	1.53209	−	1.28558i	0.884552	−	0.742227i	−0.0825579	−	0.996586i	$-0.526309\pi$
$3$	1.53209	−	1.28558i	0.884552	−	0.742227i	0.967110	+	0.254359i	$0.0818645\pi$
$4$	1.87939	−	0.684040i	0.939693	−	0.342020i
$5$	−2.81908	−	1.02606i	−1.26073	−	0.458868i	−0.376716	−	0.926329i	$-0.622947\pi$
$5$	−2.81908	−	1.02606i	−1.26073	−	0.458868i	−0.884014	+	0.467461i	$0.845169\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	0.944911	+	0.327327i	$0.106148\pi$
$8$		0			0
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$	2.00000	−	3.46410i	0.577350	−	1.00000i
$13$	3.06418	+	2.57115i	0.849850	+	0.713109i	0.959757	−	0.280833i	$-0.0906107\pi$
$13$	3.06418	+	2.57115i	0.849850	+	0.713109i	−0.109907	+	0.993942i	$0.535055\pi$
$14$		0			0
$15$	−5.63816	+	2.05212i	−1.45577	+	0.529855i
$16$	3.06418	−	2.57115i	0.766044	−	0.642788i
$17$	−0.520945	−	2.95442i	−0.126348	−	0.716553i	−0.980498	−	0.196527i	$-0.937034\pi$
$17$	−0.520945	−	2.95442i	−0.126348	−	0.716553i	0.854151	−	0.520026i	$-0.174078\pi$
$18$		0			0
$19$		0			0
$19$		0			0
$20$	−6.00000			−1.34164
$21$	−0.347296	−	1.96962i	−0.0757863	−	0.429805i
$22$		0			0
$23$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$23$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$24$		0			0
$25$	3.06418	+	2.57115i	0.612836	+	0.514230i
$26$		0			0
$27$	2.00000	+	3.46410i	0.384900	+	0.666667i
$28$	0.347296	−	1.96962i	0.0656328	−	0.372222i
$29$	−1.04189	+	5.90885i	−0.193474	+	1.09725i	0.721101	+	0.692830i	$0.243636\pi$
$29$	−1.04189	+	5.90885i	−0.193474	+	1.09725i	−0.914575	+	0.404416i	$0.867475\pi$
$30$		0			0
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$		0			0
$33$	−5.63816	−	2.05212i	−0.981477	−	0.357228i
$34$		0			0
$35$	−2.29813	+	1.92836i	−0.388455	+	0.325953i
$36$	−0.347296	−	1.96962i	−0.0578827	−	0.328269i
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$		0			0
$39$	8.00000			1.28103
$40$		0			0
$41$	4.59627	−	3.85673i	0.717816	−	0.602319i	−0.208964	−	0.977923i	$-0.567009\pi$
$41$	4.59627	−	3.85673i	0.717816	−	0.602319i	0.926780	+	0.375604i	$0.122565\pi$
$42$		0			0
$43$	0.939693	+	0.342020i	0.143302	+	0.0521576i	0.412675	−	0.910878i	$-0.364594\pi$
$43$	0.939693	+	0.342020i	0.143302	+	0.0521576i	−0.269374	+	0.963036i	$0.586817\pi$
$44$	−4.59627	−	3.85673i	−0.692913	−	0.581423i
$45$	−1.50000	+	2.59808i	−0.223607	+	0.387298i
$46$		0			0
$47$	−0.520945	+	2.95442i	−0.0759876	+	0.430947i	0.922952	+	0.384914i	$0.125769\pi$
$47$	−0.520945	+	2.95442i	−0.0759876	+	0.430947i	−0.998940	+	0.0460327i	$0.985342\pi$
$48$	1.38919	−	7.87846i	0.200512	−	1.13716i
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$		0			0
$51$	−4.59627	−	3.85673i	−0.643606	−	0.540050i
$52$	7.51754	+	2.73616i	1.04250	+	0.379437i
$53$	11.2763	−	4.10424i	1.54892	−	0.563761i	0.580756	−	0.814077i	$-0.302757\pi$
$53$	11.2763	−	4.10424i	1.54892	−	0.563761i	0.968164	+	0.250316i	$0.0805347\pi$
$54$		0			0
$55$	1.56283	+	8.86327i	0.210732	+	1.19512i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.04189	+	5.90885i	0.135642	+	0.769266i	0.974410	+	0.224777i	$0.0721654\pi$
$59$	1.04189	+	5.90885i	0.135642	+	0.769266i	−0.838768	+	0.544489i	$0.816724\pi$
$60$	−9.19253	+	7.71345i	−1.18675	+	0.995802i
$61$	0.939693	−	0.342020i	0.120315	−	0.0437912i	−0.281161	−	0.959661i	$-0.590719\pi$
$61$	0.939693	−	0.342020i	0.120315	−	0.0437912i	0.401476	+	0.915869i	$0.368497\pi$
$62$		0			0
$63$	−0.766044	−	0.642788i	−0.0965125	−	0.0809836i
$64$	4.00000	−	6.92820i	0.500000	−	0.866025i
$65$	−6.00000	−	10.3923i	−0.744208	−	1.28901i
$66$		0			0
$67$	0.694593	−	3.93923i	0.0848580	−	0.481254i	−0.912529	−	0.409012i	$-0.865874\pi$
$67$	0.694593	−	3.93923i	0.0848580	−	0.481254i	0.997387	−	0.0722419i	$-0.0230154\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$		0			0
$70$		0			0
$71$	5.63816	+	2.05212i	0.669126	+	0.243542i	0.654172	−	0.756346i	$-0.273017\pi$
$71$	5.63816	+	2.05212i	0.669126	+	0.243542i	0.0149545	+	0.999888i	$0.495240\pi$
$72$		0			0
$73$	−5.36231	+	4.49951i	−0.627611	+	0.526628i	−0.900186	−	0.435506i	$-0.856569\pi$
$73$	−5.36231	+	4.49951i	−0.627611	+	0.526628i	0.272575	+	0.962135i	$0.412125\pi$
$74$		0			0
$75$	8.00000			0.923760
$76$		0			0
$77$	−3.00000			−0.341882
$78$		0			0
$79$	−6.12836	+	5.14230i	−0.689494	+	0.578554i	−0.918763	−	0.394809i	$-0.870811\pi$
$79$	−6.12836	+	5.14230i	−0.689494	+	0.578554i	0.229269	+	0.973363i	$0.426366\pi$
$80$	−11.2763	+	4.10424i	−1.26073	+	0.458868i
$81$	10.3366	+	3.76222i	1.14851	+	0.418025i
$82$		0			0
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	0.322396	+	0.946605i	$0.395512\pi$
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	−0.980982	+	0.194099i	$0.937822\pi$
$84$	−2.00000	−	3.46410i	−0.218218	−	0.377964i
$85$	−1.56283	+	8.86327i	−0.169513	+	0.961357i
$86$		0			0
$87$	6.00000	+	10.3923i	0.643268	+	1.11417i
$88$		0			0
$89$	−9.19253	−	7.71345i	−0.974407	−	0.817624i	0.00882955	−	0.999961i	$-0.497189\pi$
$89$	−9.19253	−	7.71345i	−0.974407	−	0.817624i	−0.983236	+	0.182337i	$0.941634\pi$
$90$		0			0
$91$	3.75877	−	1.36808i	0.394026	−	0.143414i
$92$		0			0
$93$	1.38919	+	7.87846i	0.144052	+	0.816958i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.38919	−	7.87846i	−0.141050	−	0.799937i	−0.970454	−	0.241287i	$-0.922431\pi$
$97$	−1.38919	−	7.87846i	−0.141050	−	0.799937i	0.829403	−	0.558650i	$-0.188680\pi$
$98$		0			0
$99$	−2.81908	+	1.02606i	−0.283328	+	0.103123i
$100$	7.51754	+	2.73616i	0.751754	+	0.273616i
$101$	4.59627	+	3.85673i	0.457346	+	0.383759i	0.842153	−	0.539238i	$-0.181288\pi$
$101$	4.59627	+	3.85673i	0.457346	+	0.383759i	−0.384808	+	0.922997i	$0.625732\pi$
$102$		0			0
$103$	7.00000	+	12.1244i	0.689730	+	1.19465i	0.971925	+	0.235291i	$0.0756043\pi$
$103$	7.00000	+	12.1244i	0.689730	+	1.19465i	−0.282194	+	0.959357i	$0.591062\pi$
$104$		0			0
$105$	−1.04189	+	5.90885i	−0.101678	+	0.576644i
$106$		0			0
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.00813215	+	0.999967i	$0.502589\pi$
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.861931	+	0.507026i	$0.830745\pi$
$108$	6.12836	+	5.14230i	0.589701	+	0.494818i
$109$	−15.0351	−	5.47232i	−1.44010	−	0.524153i	−0.500292	−	0.865857i	$-0.666774\pi$
$109$	−15.0351	−	5.47232i	−1.44010	−	0.524153i	−0.939808	+	0.341703i	$0.888996\pi$
$110$		0			0
$111$	−3.06418	+	2.57115i	−0.290839	+	0.244043i
$112$	−0.694593	−	3.93923i	−0.0656328	−	0.372222i
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$		0			0
$116$	2.08378	+	11.8177i	0.193474	+	1.09725i
$117$	3.06418	−	2.57115i	0.283283	−	0.237703i
$118$		0			0
$119$	−2.81908	−	1.02606i	−0.258424	−	0.0940588i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$	2.08378	−	11.8177i	0.187888	−	1.06557i
$124$	−1.38919	+	7.87846i	−0.124753	+	0.707507i
$125$	1.50000	+	2.59808i	0.134164	+	0.232379i
$126$		0			0
$127$	−1.53209	−	1.28558i	−0.135951	−	0.114076i	0.572276	−	0.820061i	$-0.306060\pi$
$127$	−1.53209	−	1.28558i	−0.135951	−	0.114076i	−0.708227	+	0.705984i	$0.750505\pi$
$128$		0			0
$129$	1.87939	−	0.684040i	0.165471	−	0.0602264i
$130$		0			0
$131$	−2.60472	−	14.7721i	−0.227576	−	1.29065i	−0.857700	−	0.514151i	$-0.828107\pi$
$131$	−2.60472	−	14.7721i	−0.227576	−	1.29065i	0.630124	−	0.776495i	$-0.283004\pi$
$132$	−12.0000			−1.04447
$133$		0			0
$134$		0			0
$135$	−2.08378	−	11.8177i	−0.179343	−	1.01711i
$136$		0			0
$137$	2.81908	−	1.02606i	0.240850	−	0.0876623i	−0.218775	−	0.975775i	$-0.570206\pi$
$137$	2.81908	−	1.02606i	0.240850	−	0.0876623i	0.459625	+	0.888113i	$0.347984\pi$
$138$		0			0
$139$	−9.95858	−	8.35624i	−0.844676	−	0.708767i	0.113935	−	0.993488i	$-0.463655\pi$
$139$	−9.95858	−	8.35624i	−0.844676	−	0.708767i	−0.958610	+	0.284721i	$0.908099\pi$
$140$	−3.00000	+	5.19615i	−0.253546	+	0.439155i
$141$	3.00000	+	5.19615i	0.252646	+	0.437595i
$142$		0			0
$143$	2.08378	−	11.8177i	0.174254	−	0.988245i
$144$	−2.00000	−	3.46410i	−0.166667	−	0.288675i
$145$	9.00000	−	15.5885i	0.747409	−	1.29455i
$146$		0			0
$147$	11.2763	+	4.10424i	0.930054	+	0.338512i
$148$	−3.75877	+	1.36808i	−0.308969	+	0.112456i
$149$	16.0869	−	13.4985i	1.31789	−	1.10584i	0.331146	−	0.943580i	$-0.392565\pi$
$149$	16.0869	−	13.4985i	1.31789	−	1.10584i	0.986747	−	0.162264i	$-0.0518795\pi$
$150$		0			0
$151$	10.0000			0.813788			0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000			0.813788			0.406894	+	0.913475i	$0.366612\pi$
$152$		0			0
$153$	−3.00000			−0.242536
$154$		0			0
$155$	9.19253	−	7.71345i	0.738362	−	0.619559i
$156$	15.0351	−	5.47232i	1.20377	−	0.438136i
$157$	−13.1557	−	4.78828i	−1.04994	−	0.382147i	−0.241299	−	0.970451i	$-0.577574\pi$
$157$	−13.1557	−	4.78828i	−1.04994	−	0.382147i	−0.808640	+	0.588304i	$0.799796\pi$
$158$		0			0
$159$	12.0000	−	20.7846i	0.951662	−	1.64833i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−10.0000	−	17.3205i	−0.783260	−	1.35665i	−0.930033	−	0.367477i	$-0.880222\pi$
$163$	−10.0000	−	17.3205i	−0.783260	−	1.35665i	0.146772	−	0.989170i	$-0.453112\pi$
$164$	6.00000	−	10.3923i	0.468521	−	0.811503i
$165$	13.7888	+	11.5702i	1.07346	+	0.900737i
$166$		0			0
$167$	−16.9145	+	6.15636i	−1.30888	+	0.476394i	−0.899879	−	0.436140i	$-0.856345\pi$
$167$	−16.9145	+	6.15636i	−1.30888	+	0.476394i	−0.409002	+	0.912534i	$0.634123\pi$
$168$		0			0
$169$	0.520945	+	2.95442i	0.0400727	+	0.227263i
$170$		0			0
$171$		0			0
$172$	2.00000			0.152499
$173$	3.12567	+	17.7265i	0.237640	+	1.34772i	0.836982	+	0.547231i	$0.184318\pi$
$173$	3.12567	+	17.7265i	0.237640	+	1.34772i	−0.599342	+	0.800493i	$0.704571\pi$
$174$		0			0
$175$	3.75877	−	1.36808i	0.284136	−	0.103417i
$176$	−11.2763	−	4.10424i	−0.849984	−	0.309369i
$177$	9.19253	+	7.71345i	0.690953	+	0.579779i
$178$		0			0
$179$	−9.00000	−	15.5885i	−0.672692	−	1.16514i	−0.977138	−	0.212607i	$-0.931805\pi$
$179$	−9.00000	−	15.5885i	−0.672692	−	1.16514i	0.304446	−	0.952529i	$-0.401529\pi$
$180$	−1.04189	+	5.90885i	−0.0776578	+	0.440419i
$181$	−0.347296	+	1.96962i	−0.0258143	+	0.146400i	−0.994991	−	0.0999676i	$-0.968126\pi$
$181$	−0.347296	+	1.96962i	−0.0258143	+	0.146400i	0.969176	+	0.246368i	$0.0792372\pi$
$182$		0			0
$183$	1.00000	−	1.73205i	0.0739221	−	0.128037i
$184$		0			0
$185$	5.63816	+	2.05212i	0.414525	+	0.150875i
$186$		0			0
$187$	−6.89440	+	5.78509i	−0.504168	+	0.423048i
$188$	1.04189	+	5.90885i	0.0759876	+	0.430947i
$189$	4.00000			0.290957
$190$		0			0
$191$	3.00000			0.217072			0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000			0.217072			0.108536	+	0.994092i	$0.465384\pi$
$192$	−2.77837	−	15.7569i	−0.200512	−	1.13716i
$193$	3.06418	−	2.57115i	0.220564	−	0.185075i	−0.525810	−	0.850602i	$-0.676238\pi$
$193$	3.06418	−	2.57115i	0.220564	−	0.185075i	0.746374	+	0.665527i	$0.231793\pi$
$194$		0			0
$195$	−22.5526	−	8.20848i	−1.61503	−	0.587822i
$196$	9.19253	+	7.71345i	0.656610	+	0.550961i
$197$	−9.00000	+	15.5885i	−0.641223	+	1.11063i	0.343937	+	0.938993i	$0.388239\pi$
$197$	−9.00000	+	15.5885i	−0.641223	+	1.11063i	−0.985160	+	0.171639i	$0.945094\pi$
$198$		0			0
$199$	1.91013	−	10.8329i	0.135406	−	0.767923i	−0.839171	−	0.543868i	$-0.816959\pi$
$199$	1.91013	−	10.8329i	0.135406	−	0.767923i	0.974576	−	0.224055i	$-0.0719296\pi$
$200$		0			0
$201$	−4.00000	−	6.92820i	−0.282138	−	0.488678i
$202$		0			0
$203$	4.59627	+	3.85673i	0.322595	+	0.270689i
$204$	−11.2763	−	4.10424i	−0.789500	−	0.287354i
$205$	−16.9145	+	6.15636i	−1.18136	+	0.429979i
$206$		0			0
$207$		0			0
$208$	16.0000			1.10940
$209$		0			0
$210$		0			0
$211$	−2.43107	−	13.7873i	−0.167362	−	0.949157i	−0.946595	−	0.322424i	$-0.895502\pi$
$211$	−2.43107	−	13.7873i	−0.167362	−	0.949157i	0.779233	−	0.626734i	$-0.215609\pi$
$212$	18.3851	−	15.4269i	1.26269	−	1.05952i
$213$	11.2763	−	4.10424i	0.772640	−	0.281218i
$214$		0			0
$215$	−2.29813	−	1.92836i	−0.156731	−	0.131513i
$216$		0			0
$217$	2.00000	+	3.46410i	0.135769	+	0.235159i
$218$		0			0
$219$	−2.43107	+	13.7873i	−0.164277	+	0.931660i
$220$	9.00000	+	15.5885i	0.606780	+	1.05097i
$221$	6.00000	−	10.3923i	0.403604	−	0.699062i
$222$		0			0
$223$	−9.39693	−	3.42020i	−0.629265	−	0.229034i	0.00764652	−	0.999971i	$-0.497566\pi$
$223$	−9.39693	−	3.42020i	−0.629265	−	0.229034i	−0.636911	+	0.770937i	$0.719788\pi$
$224$		0			0
$225$	3.06418	−	2.57115i	0.204279	−	0.171410i
$226$		0			0
$227$	−12.0000			−0.796468			−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000			−0.796468			−0.398234	+	0.917284i	$0.630377\pi$
$228$		0			0
$229$	5.00000			0.330409			0.165205	−	0.986259i	$-0.447172\pi$
$229$	5.00000			0.330409			0.165205	+	0.986259i	$0.447172\pi$
$230$		0			0
$231$	−4.59627	+	3.85673i	−0.302412	+	0.253754i
$232$		0			0
$233$	19.7335	+	7.18242i	1.29279	+	0.470536i	0.894641	−	0.446786i	$-0.147431\pi$
$233$	19.7335	+	7.18242i	1.29279	+	0.470536i	0.398146	+	0.917322i	$0.369654\pi$
$234$		0			0
$235$	4.50000	−	7.79423i	0.293548	−	0.508439i
$236$	6.00000	+	10.3923i	0.390567	+	0.676481i
$237$	−2.77837	+	15.7569i	−0.180475	+	1.02352i
$238$		0			0
$239$	−7.50000	−	12.9904i	−0.485135	−	0.840278i	0.514719	−	0.857359i	$-0.327896\pi$
$239$	−7.50000	−	12.9904i	−0.485135	−	0.840278i	−0.999854	+	0.0170808i	$0.994563\pi$
$240$	−12.0000	+	20.7846i	−0.774597	+	1.34164i
$241$	7.66044	+	6.42788i	0.493453	+	0.414056i	0.855262	−	0.518196i	$-0.173396\pi$
$241$	7.66044	+	6.42788i	0.493453	+	0.414056i	−0.361809	+	0.932252i	$0.617841\pi$
$242$		0			0
$243$	9.39693	−	3.42020i	0.602813	−	0.219406i
$244$	1.53209	−	1.28558i	0.0980819	−	0.0823005i
$245$	−3.12567	−	17.7265i	−0.199692	−	1.13251i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	4.16756	+	23.6354i	0.264108	+	1.49783i
$250$		0			0
$251$	−19.7335	+	7.18242i	−1.24557	+	0.453351i	−0.878903	−	0.477001i	$-0.841724\pi$
$251$	−19.7335	+	7.18242i	−1.24557	+	0.453351i	−0.366668	+	0.930352i	$0.619501\pi$
$252$	−1.87939	−	0.684040i	−0.118390	−	0.0430905i
$253$		0			0
$254$		0			0
$255$	9.00000	+	15.5885i	0.563602	+	0.976187i
$256$	2.77837	−	15.7569i	0.173648	−	0.984808i
$257$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$257$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$258$		0			0
$259$	−1.00000	+	1.73205i	−0.0621370	+	0.107624i
$260$	−18.3851	−	15.4269i	−1.14019	−	0.956736i
$261$	5.63816	+	2.05212i	0.348993	+	0.127023i
$262$		0			0
$263$	6.89440	−	5.78509i	0.425127	−	0.356724i	−0.404982	−	0.914324i	$-0.632722\pi$
$263$	6.89440	−	5.78509i	0.425127	−	0.356724i	0.830109	+	0.557601i	$0.188278\pi$
$264$		0			0
$265$	−36.0000			−2.21146
$266$		0			0
$267$	−24.0000			−1.46878
$268$	−1.38919	−	7.87846i	−0.0848580	−	0.481254i
$269$	−18.3851	+	15.4269i	−1.12096	+	0.940595i	−0.998652	−	0.0518977i	$-0.983473\pi$
$269$	−18.3851	+	15.4269i	−1.12096	+	0.940595i	−0.122305	+	0.992493i	$0.539029\pi$
$270$		0			0
$271$	15.0351	+	5.47232i	0.913316	+	0.332420i	0.755576	−	0.655061i	$-0.227357\pi$
$271$	15.0351	+	5.47232i	0.913316	+	0.332420i	0.157740	+	0.987481i	$0.449579\pi$
$272$	−9.19253	−	7.71345i	−0.557379	−	0.467697i
$273$	4.00000	−	6.92820i	0.242091	−	0.419314i
$274$		0			0
$275$	2.08378	−	11.8177i	0.125657	−	0.712634i
$276$		0			0
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	0.996484	+	0.0837823i	$0.0267000\pi$
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	−0.425684	+	0.904872i	$0.639967\pi$
$278$		0			0
$279$	3.06418	+	2.57115i	0.183448	+	0.153931i
$280$		0			0
$281$	5.63816	−	2.05212i	0.336344	−	0.122419i	−0.168326	−	0.985731i	$-0.553836\pi$
$281$	5.63816	−	2.05212i	0.336344	−	0.122419i	0.504670	+	0.863312i	$0.331614\pi$
$282$		0			0
$283$	−2.25743	−	12.8025i	−0.134190	−	0.761030i	−0.975420	−	0.220353i	$-0.929279\pi$
$283$	−2.25743	−	12.8025i	−0.134190	−	0.761030i	0.841230	−	0.540677i	$-0.181832\pi$
$284$	12.0000			0.712069
$285$		0			0
$286$		0			0
$287$	−1.04189	−	5.90885i	−0.0615008	−	0.348788i
$288$		0			0
$289$	7.51754	−	2.73616i	0.442208	−	0.160951i
$290$		0			0
$291$	−12.2567	−	10.2846i	−0.718501	−	0.602894i
$292$	−7.00000	+	12.1244i	−0.409644	+	0.709524i
$293$	−6.00000	−	10.3923i	−0.350524	−	0.607125i	0.635818	−	0.771839i	$-0.280663\pi$
$293$	−6.00000	−	10.3923i	−0.350524	−	0.607125i	−0.986341	+	0.164714i	$0.947330\pi$
$294$		0			0
$295$	3.12567	−	17.7265i	0.181983	−	1.03208i
$296$		0			0
$297$	6.00000	−	10.3923i	0.348155	−	0.603023i
$298$		0			0
$299$		0			0
$300$	15.0351	−	5.47232i	0.868051	−	0.315945i
$301$	0.766044	−	0.642788i	0.0441541	−	0.0370497i
$302$		0			0
$303$	12.0000			0.689382
$304$		0			0
$305$	−3.00000			−0.171780
$306$		0			0
$307$	−15.3209	+	12.8558i	−0.874409	+	0.733717i	−0.965022	−	0.262170i	$-0.915562\pi$
$307$	−15.3209	+	12.8558i	−0.874409	+	0.733717i	0.0906125	+	0.995886i	$0.471118\pi$
$308$	−5.63816	+	2.05212i	−0.321264	+	0.116930i
$309$	26.3114	+	9.57656i	1.49680	+	0.544792i
$310$		0			0
$311$	1.50000	−	2.59808i	0.0850572	−	0.147323i	−0.820358	−	0.571850i	$-0.806226\pi$
$311$	1.50000	−	2.59808i	0.0850572	−	0.147323i	0.905416	+	0.424526i	$0.139559\pi$
$312$		0			0
$313$	−1.73648	+	9.84808i	−0.0981518	+	0.556646i	0.895584	+	0.444892i	$0.146758\pi$
$313$	−1.73648	+	9.84808i	−0.0981518	+	0.556646i	−0.993736	+	0.111754i	$0.964353\pi$
$314$		0			0
$315$	1.50000	+	2.59808i	0.0845154	+	0.146385i
$316$	−8.00000	+	13.8564i	−0.450035	+	0.779484i
$317$	−4.59627	−	3.85673i	−0.258152	−	0.216615i	0.504521	−	0.863399i	$-0.331669\pi$
$317$	−4.59627	−	3.85673i	−0.258152	−	0.216615i	−0.762673	+	0.646784i	$0.776114\pi$
$318$		0			0
$319$	16.9145	−	6.15636i	0.947028	−	0.344690i
$320$	−18.3851	+	15.4269i	−1.02776	+	0.862390i
$321$	6.25133	+	35.4531i	0.348915	+	1.97880i
$322$		0			0
$323$		0			0
$324$	22.0000			1.22222
$325$	2.77837	+	15.7569i	0.154116	+	0.874037i
$326$		0			0
$327$	−30.0702	+	10.9446i	−1.66288	+	0.605240i
$328$		0			0
$329$	2.29813	+	1.92836i	0.126700	+	0.106314i
$330$		0			0
$331$	−14.0000	−	24.2487i	−0.769510	−	1.33283i	−0.937829	−	0.347097i	$-0.887167\pi$
$331$	−14.0000	−	24.2487i	−0.769510	−	1.33283i	0.168320	−	0.985732i	$-0.446166\pi$
$332$	−4.16756	+	23.6354i	−0.228724	+	1.29716i
$333$	−0.347296	+	1.96962i	−0.0190317	+	0.107934i
$334$		0			0
$335$	−6.00000	+	10.3923i	−0.327815	+	0.567792i
$336$	−6.12836	−	5.14230i	−0.334329	−	0.280536i
$337$	30.0702	+	10.9446i	1.63803	+	0.596193i	0.986692	−	0.162598i	$-0.0519875\pi$
$337$	30.0702	+	10.9446i	1.63803	+	0.596193i	0.651334	+	0.758791i	$0.274210\pi$
$338$		0			0
$339$	−9.19253	+	7.71345i	−0.499270	+	0.418937i
$340$	3.12567	+	17.7265i	0.169513	+	0.961357i
$341$	12.0000			0.649836
$342$		0			0
$343$	13.0000			0.701934
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−19.7335	−	7.18242i	−1.05935	−	0.385573i	−0.247167	−	0.968973i	$-0.579500\pi$
$347$	−19.7335	−	7.18242i	−1.05935	−	0.385573i	−0.812185	+	0.583400i	$0.801722\pi$
$348$	18.3851	+	15.4269i	0.985543	+	0.826969i
$349$	−8.50000	+	14.7224i	−0.454995	+	0.788074i	−0.998688	−	0.0512103i	$-0.983692\pi$
$349$	−8.50000	+	14.7224i	−0.454995	+	0.788074i	0.543693	+	0.839284i	$0.317025\pi$
$350$		0			0
$351$	−2.77837	+	15.7569i	−0.148298	+	0.841042i
$352$		0			0
$353$	3.00000	+	5.19615i	0.159674	+	0.276563i	0.934751	−	0.355303i	$-0.115622\pi$
$353$	3.00000	+	5.19615i	0.159674	+	0.276563i	−0.775077	+	0.631867i	$0.782289\pi$
$354$		0			0
$355$	−13.7888	−	11.5702i	−0.731834	−	0.614081i
$356$	−22.5526	−	8.20848i	−1.19529	−	0.435049i
$357$	−5.63816	+	2.05212i	−0.298403	+	0.108610i
$358$		0			0
$359$	2.60472	+	14.7721i	0.137472	+	0.779642i	0.973106	+	0.230356i	$0.0739892\pi$
$359$	2.60472	+	14.7721i	0.137472	+	0.779642i	−0.835634	+	0.549286i	$0.814900\pi$
$360$		0			0
$361$		0			0
$362$		0			0
$363$	−0.694593	−	3.93923i	−0.0364567	−	0.206756i
$364$	6.12836	−	5.14230i	0.321213	−	0.269530i
$365$	19.7335	−	7.18242i	1.03290	−	0.375945i
$366$		0			0
$367$	6.12836	+	5.14230i	0.319898	+	0.268426i	0.788569	−	0.614947i	$-0.210823\pi$
$367$	6.12836	+	5.14230i	0.319898	+	0.268426i	−0.468671	+	0.883373i	$0.655267\pi$
$368$		0			0
$369$	−3.00000	−	5.19615i	−0.156174	−	0.270501i
$370$		0			0
$371$	2.08378	−	11.8177i	0.108184	−	0.613544i
$372$	8.00000	+	13.8564i	0.414781	+	0.718421i
$373$	−2.00000	+	3.46410i	−0.103556	+	0.179364i	−0.913147	−	0.407630i	$-0.866355\pi$
$373$	−2.00000	+	3.46410i	−0.103556	+	0.179364i	0.809591	+	0.586994i	$0.199689\pi$
$374$		0			0
$375$	5.63816	+	2.05212i	0.291153	+	0.105971i
$376$		0			0
$377$	−18.3851	+	15.4269i	−0.946879	+	0.794526i
$378$		0			0
$379$	34.0000			1.74646			0.873231	−	0.487306i	$-0.162020\pi$
$379$	34.0000			1.74646			0.873231	+	0.487306i	$0.162020\pi$
$380$		0			0
$381$	−4.00000			−0.204926
$382$		0			0
$383$	−9.19253	+	7.71345i	−0.469717	+	0.394139i	−0.846691	−	0.532085i	$-0.821409\pi$
$383$	−9.19253	+	7.71345i	−0.469717	+	0.394139i	0.376975	+	0.926224i	$0.376964\pi$
$384$		0			0
$385$	8.45723	+	3.07818i	0.431021	+	0.156879i
$386$		0			0
$387$	0.500000	−	0.866025i	0.0254164	−	0.0440225i
$388$	−8.00000	−	13.8564i	−0.406138	−	0.703452i
$389$	2.60472	−	14.7721i	0.132065	−	0.748976i	−0.844794	−	0.535091i	$-0.820277\pi$
$389$	2.60472	−	14.7721i	0.132065	−	0.748976i	0.976859	−	0.213885i	$-0.0686117\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−22.9813	−	19.2836i	−1.15925	−	0.972730i
$394$		0			0
$395$	22.5526	−	8.20848i	1.13475	−	0.413014i
$396$	−4.59627	+	3.85673i	−0.230971	+	0.193808i
$397$	−1.21554	−	6.89365i	−0.0610061	−	0.345983i	−0.999998	−	0.00204319i	$-0.999350\pi$
$397$	−1.21554	−	6.89365i	−0.0610061	−	0.345983i	0.938992	−	0.343939i	$-0.111761\pi$
$398$		0			0
$399$		0			0
$400$	16.0000			0.800000
$401$	−2.08378	−	11.8177i	−0.104059	−	0.590147i	−0.991592	−	0.129403i	$-0.958694\pi$
$401$	−2.08378	−	11.8177i	−0.104059	−	0.590147i	0.887533	−	0.460744i	$-0.152417\pi$
$402$		0			0
$403$	−15.0351	+	5.47232i	−0.748951	+	0.272596i
$404$	11.2763	+	4.10424i	0.561017	+	0.204194i
$405$	−25.2795	−	21.2120i	−1.25615	−	1.05403i
$406$		0			0
$407$	3.00000	+	5.19615i	0.148704	+	0.257564i
$408$		0			0
$409$	0.694593	−	3.93923i	0.0343454	−	0.194782i	−0.962808	−	0.270188i	$-0.912914\pi$
$409$	0.694593	−	3.93923i	0.0343454	−	0.194782i	0.997153	+	0.0754057i	$0.0240252\pi$
$410$		0			0
$411$	3.00000	−	5.19615i	0.147979	−	0.256307i
$412$	21.4492	+	17.9981i	1.05673	+	0.886700i
$413$	5.63816	+	2.05212i	0.277436	+	0.100978i
$414$		0			0
$415$	27.5776	−	23.1404i	1.35373	−	1.13592i
$416$		0			0
$417$	−26.0000			−1.27323
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$	2.08378	+	11.8177i	0.101678	+	0.576644i
$421$	−6.12836	+	5.14230i	−0.298678	+	0.250620i	−0.779794	−	0.626037i	$-0.784676\pi$
$421$	−6.12836	+	5.14230i	−0.298678	+	0.250620i	0.481116	+	0.876657i	$0.340232\pi$
$422$		0			0
$423$	2.81908	+	1.02606i	0.137068	+	0.0498888i
$424$		0			0
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		0			0
$427$	0.173648	−	0.984808i	0.00840342	−	0.0476582i
$428$	−6.25133	+	35.4531i	−0.302170	+	1.71369i
$429$	−12.0000	−	20.7846i	−0.579365	−	1.00349i
$430$		0			0
$431$	18.3851	+	15.4269i	0.885577	+	0.743088i	0.967318	−	0.253566i	$-0.0816035\pi$
$431$	18.3851	+	15.4269i	0.885577	+	0.743088i	−0.0817406	+	0.996654i	$0.526048\pi$
$432$	15.0351	+	5.47232i	0.723376	+	0.263287i
$433$	1.87939	−	0.684040i	0.0903175	−	0.0328729i	−0.296466	−	0.955043i	$-0.595808\pi$
$433$	1.87939	−	0.684040i	0.0903175	−	0.0328729i	0.386784	+	0.922170i	$0.373586\pi$
$434$		0			0
$435$	−6.25133	−	35.4531i	−0.299729	−	1.69985i
$436$	−32.0000			−1.53252
$437$		0			0
$438$		0			0
$439$	1.73648	+	9.84808i	0.0828778	+	0.470023i	0.997794	+	0.0663803i	$0.0211450\pi$
$439$	1.73648	+	9.84808i	0.0828778	+	0.470023i	−0.914917	+	0.403643i	$0.867744\pi$
$440$		0			0
$441$	5.63816	−	2.05212i	0.268484	−	0.0977200i
$442$		0			0
$443$	−2.29813	−	1.92836i	−0.109188	−	0.0916193i	0.586559	−	0.809906i	$-0.300482\pi$
$443$	−2.29813	−	1.92836i	−0.109188	−	0.0916193i	−0.695747	+	0.718287i	$0.744927\pi$
$444$	−4.00000	+	6.92820i	−0.189832	+	0.328798i
$445$	18.0000	+	31.1769i	0.853282	+	1.47793i
$446$		0			0
$447$	7.29322	−	41.3619i	0.344958	−	1.95635i
$448$	−4.00000	−	6.92820i	−0.188982	−	0.327327i
$449$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$449$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$450$		0			0
$451$	−16.9145	−	6.15636i	−0.796471	−	0.289892i
$452$	−11.2763	+	4.10424i	−0.530393	+	0.193047i
$453$	15.3209	−	12.8558i	0.719838	−	0.604016i
$454$		0			0
$455$	−12.0000			−0.562569
$456$		0			0
$457$	−37.0000			−1.73079			−0.865393	−	0.501093i	$-0.832931\pi$
$457$	−37.0000			−1.73079			−0.865393	+	0.501093i	$0.832931\pi$
$458$		0			0
$459$	9.19253	−	7.71345i	0.429071	−	0.360033i
$460$		0			0
$461$	−8.45723	−	3.07818i	−0.393893	−	0.143365i	0.137478	−	0.990505i	$-0.456100\pi$
$461$	−8.45723	−	3.07818i	−0.393893	−	0.143365i	−0.531370	+	0.847140i	$0.678323\pi$
$462$		0			0
$463$	15.5000	−	26.8468i	0.720346	−	1.24768i	−0.240515	−	0.970645i	$-0.577316\pi$
$463$	15.5000	−	26.8468i	0.720346	−	1.24768i	0.960861	−	0.277031i	$-0.0893503\pi$
$464$	12.0000	+	20.7846i	0.557086	+	0.964901i
$465$	4.16756	−	23.6354i	0.193266	−	1.09606i
$466$		0			0
$467$	13.5000	+	23.3827i	0.624705	+	1.08202i	0.988598	+	0.150581i	$0.0481143\pi$
$467$	13.5000	+	23.3827i	0.624705	+	1.08202i	−0.363892	+	0.931441i	$0.618552\pi$
$468$	4.00000	−	6.92820i	0.184900	−	0.320256i
$469$	−3.06418	−	2.57115i	−0.141491	−	0.118725i
$470$		0			0
$471$	−26.3114	+	9.57656i	−1.21237	+	0.441265i
$472$		0			0
$473$	−0.520945	−	2.95442i	−0.0239531	−	0.135845i
$474$		0			0
$475$		0			0
$476$	−6.00000			−0.275010
$477$	−2.08378	−	11.8177i	−0.0954096	−	0.541095i
$478$		0			0
$479$	11.2763	−	4.10424i	0.515228	−	0.187528i	−0.0713027	−	0.997455i	$-0.522716\pi$
$479$	11.2763	−	4.10424i	0.515228	−	0.187528i	0.586531	+	0.809927i	$0.300493\pi$
$480$		0			0
$481$	−6.12836	−	5.14230i	−0.279429	−	0.234469i
$482$		0			0
$483$		0			0
$484$	0.694593	−	3.93923i	0.0315724	−	0.179056i
$485$	−4.16756	+	23.6354i	−0.189239	+	1.07323i
$486$		0			0
$487$	1.00000	−	1.73205i	0.0453143	−	0.0784867i	−0.842479	−	0.538730i	$-0.818904\pi$
$487$	1.00000	−	1.73205i	0.0453143	−	0.0784867i	0.887793	+	0.460243i	$0.152238\pi$
$488$		0			0
$489$	−37.5877	−	13.6808i	−1.69977	−	0.618667i
$490$		0			0
$491$	9.19253	−	7.71345i	0.414853	−	0.348103i	−0.411348	−	0.911478i	$-0.634942\pi$
$491$	9.19253	−	7.71345i	0.414853	−	0.348103i	0.826201	+	0.563375i	$0.190497\pi$
$492$	−4.16756	−	23.6354i	−0.187888	−	1.06557i
$493$	18.0000			0.810679
$494$		0			0
$495$	9.00000			0.404520
$496$	2.77837	+	15.7569i	0.124753	+	0.707507i
$497$	4.59627	−	3.85673i	0.206171	−	0.172998i
$498$		0			0
$499$	−4.69846	−	1.71010i	−0.210332	−	0.0765546i	0.234705	−	0.972067i	$-0.424587\pi$
$499$	−4.69846	−	1.71010i	−0.210332	−	0.0765546i	−0.445038	+	0.895512i	$0.646810\pi$
$500$	4.59627	+	3.85673i	0.205551	+	0.172478i
$501$	−18.0000	+	31.1769i	−0.804181	+	1.39288i
$502$		0			0
$503$	2.08378	−	11.8177i	0.0929111	−	0.526925i	−0.902456	−	0.430781i	$-0.858238\pi$
$503$	2.08378	−	11.8177i	0.0929111	−	0.526925i	0.995367	−	0.0961437i	$-0.0306508\pi$
$504$		0			0
$505$	−9.00000	−	15.5885i	−0.400495	−	0.693677i
$506$		0			0
$507$	4.59627	+	3.85673i	0.204127	+	0.171283i
$508$	−3.75877	−	1.36808i	−0.166768	−	0.0606988i
$509$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$509$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$510$		0			0
$511$	1.21554	+	6.89365i	0.0537722	+	0.304957i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−7.29322	−	41.3619i	−0.321378	−	1.82262i
$516$	3.06418	−	2.57115i	0.134893	−	0.113189i
$517$	8.45723	−	3.07818i	0.371949	−	0.135378i
$518$		0			0
$519$	27.5776	+	23.1404i	1.21052	+	1.01575i
$520$		0			0
$521$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$521$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$522$		0			0
$523$	−6.59863	+	37.4227i	−0.288538	+	1.63638i	0.403829	+	0.914835i	$0.367679\pi$
$523$	−6.59863	+	37.4227i	−0.288538	+	1.63638i	−0.692367	+	0.721546i	$0.743432\pi$
$524$	−15.0000	−	25.9808i	−0.655278	−	1.13497i
$525$	4.00000	−	6.92820i	0.174574	−	0.302372i
$526$		0			0
$527$	11.2763	+	4.10424i	0.491204	+	0.178784i
$528$	−22.5526	+	8.20848i	−0.981477	+	0.357228i
$529$	−17.6190	+	14.7841i	−0.766044	+	0.642788i
$530$		0			0
$531$	6.00000			0.260378
$532$		0			0
$533$	24.0000			1.03956
$534$		0			0
$535$	41.3664	−	34.7105i	1.78843	−	1.50067i
$536$		0			0
$537$	−33.8289	−	12.3127i	−1.45983	−	0.531333i
$538$		0			0
$539$	9.00000	−	15.5885i	0.387657	−	0.671442i
$540$	−12.0000	−	20.7846i	−0.516398	−	0.894427i
$541$	−4.34120	+	24.6202i	−0.186643	+	1.05850i	0.737183	+	0.675693i	$0.236155\pi$
$541$	−4.34120	+	24.6202i	−0.186643	+	1.05850i	−0.923826	+	0.382812i	$0.874956\pi$
$542$		0			0
$543$	2.00000	+	3.46410i	0.0858282	+	0.148659i
$544$		0			0
$545$	36.7701	+	30.8538i	1.57506	+	1.32163i
$546$		0			0
$547$	−26.3114	+	9.57656i	−1.12499	+	0.409464i	−0.836472	−	0.548009i	$-0.815386\pi$
$547$	−26.3114	+	9.57656i	−1.12499	+	0.409464i	−0.288522	+	0.957473i	$0.593164\pi$
$548$	4.59627	−	3.85673i	0.196343	−	0.164751i
$549$	−0.173648	−	0.984808i	−0.00741112	−	0.0420306i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	1.38919	+	7.87846i	0.0590742	+	0.335026i
$554$		0			0
$555$	11.2763	−	4.10424i	0.478653	−	0.174215i
$556$	−24.4320	−	8.89252i	−1.03615	−	0.377127i
$557$	16.0869	+	13.4985i	0.681625	+	0.571951i	0.916481	−	0.400079i	$-0.131017\pi$
$557$	16.0869	+	13.4985i	0.681625	+	0.571951i	−0.234856	+	0.972030i	$0.575462\pi$
$558$		0			0
$559$	2.00000	+	3.46410i	0.0845910	+	0.146516i
$560$	−2.08378	+	11.8177i	−0.0880557	+	0.499389i
$561$	−3.12567	+	17.7265i	−0.131966	+	0.748415i
$562$		0			0
$563$	3.00000	−	5.19615i	0.126435	−	0.218992i	−0.795858	−	0.605483i	$-0.792980\pi$
$563$	3.00000	−	5.19615i	0.126435	−	0.218992i	0.922293	+	0.386492i	$0.126313\pi$
$564$	9.19253	+	7.71345i	0.387075	+	0.324795i
$565$	16.9145	+	6.15636i	0.711597	+	0.259000i
$566$		0			0
$567$	8.42649	−	7.07066i	0.353879	−	0.296940i
$568$		0			0
$569$	24.0000			1.00613			0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000			1.00613			0.503066	+	0.864248i	$0.332205\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$	−4.16756	−	23.6354i	−0.174254	−	0.988245i
$573$	4.59627	−	3.85673i	0.192012	−	0.161117i
$574$		0			0
$575$		0			0
$576$	−6.12836	−	5.14230i	−0.255348	−	0.214263i
$577$	−5.50000	+	9.52628i	−0.228968	+	0.396584i	−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−5.50000	+	9.52628i	−0.228968	+	0.396584i	0.728535	+	0.685009i	$0.240202\pi$
$578$		0			0
$579$	1.38919	−	7.87846i	0.0577326	−	0.327418i
$580$	6.25133	−	35.4531i	0.259573	−	1.47211i
$581$	6.00000	+	10.3923i	0.248922	+	0.431145i
$582$		0			0
$583$	−27.5776	−	23.1404i	−1.14215	−	0.958376i
$584$		0			0
$585$	−11.2763	+	4.10424i	−0.466218	+	0.169690i
$586$		0			0
$587$	7.81417	+	44.3163i	0.322525	+	1.82913i	0.526524	+	0.850160i	$0.323495\pi$
$587$	7.81417	+	44.3163i	0.322525	+	1.82913i	−0.203999	+	0.978971i	$0.565394\pi$
$588$	24.0000			0.989743
$589$		0			0
$590$		0			0
$591$	6.25133	+	35.4531i	0.257146	+	1.45834i
$592$	−6.12836	+	5.14230i	−0.251874	+	0.211347i
$593$	39.4671	−	14.3648i	1.62072	−	0.589894i	0.637200	−	0.770698i	$-0.280092\pi$
$593$	39.4671	−	14.3648i	1.62072	−	0.589894i	0.983519	+	0.180805i	$0.0578702\pi$
$594$		0			0
$595$	6.89440	+	5.78509i	0.282643	+	0.237166i
$596$	21.0000	−	36.3731i	0.860194	−	1.48990i
$597$	−11.0000	−	19.0526i	−0.450200	−	0.779769i
$598$		0			0
$599$	6.25133	−	35.4531i	0.255423	−	1.44857i	−0.539563	−	0.841945i	$-0.681411\pi$
$599$	6.25133	−	35.4531i	0.255423	−	1.44857i	0.794986	−	0.606628i	$-0.207478\pi$
$600$		0			0
$601$	13.0000	−	22.5167i	0.530281	−	0.918474i	−0.469095	−	0.883148i	$-0.655420\pi$
$601$	13.0000	−	22.5167i	0.530281	−	0.918474i	0.999376	−	0.0353259i	$-0.0112469\pi$
$602$		0			0
$603$	−3.75877	−	1.36808i	−0.153069	−	0.0557125i
$604$	18.7939	−	6.84040i	0.764711	−	0.278332i
$605$	−4.59627	+	3.85673i	−0.186865	+	0.156798i
$606$		0			0
$607$	−32.0000			−1.29884			−0.649420	−	0.760430i	$-0.724988\pi$
$607$	−32.0000			−1.29884			−0.649420	+	0.760430i	$0.724988\pi$
$608$		0			0
$609$	12.0000			0.486265
$610$		0			0
$611$	−9.19253	+	7.71345i	−0.371890	+	0.312053i
$612$	−5.63816	+	2.05212i	−0.227909	+	0.0829521i
$613$	−27.2511	−	9.91858i	−1.10066	−	0.400608i	−0.273101	−	0.961985i	$-0.588049\pi$
$613$	−27.2511	−	9.91858i	−1.10066	−	0.400608i	−0.827560	+	0.561377i	$0.810272\pi$
$614$		0			0
$615$	−18.0000	+	31.1769i	−0.725830	+	1.25717i
$616$		0			0
$617$	1.56283	−	8.86327i	0.0629173	−	0.356822i	−0.937054	−	0.349186i	$-0.886458\pi$
$617$	1.56283	−	8.86327i	0.0629173	−	0.356822i	0.999971	−	0.00763607i	$-0.00243066\pi$
$618$		0			0
$619$	−22.0000	−	38.1051i	−0.884255	−	1.53157i	−0.846566	−	0.532284i	$-0.821334\pi$
$619$	−22.0000	−	38.1051i	−0.884255	−	1.53157i	−0.0376891	−	0.999290i	$-0.512000\pi$
$620$	12.0000	−	20.7846i	0.481932	−	0.834730i
$621$		0			0
$622$		0			0
$623$	−11.2763	+	4.10424i	−0.451776	+	0.164433i
$624$	24.5134	−	20.5692i	0.981322	−	0.823427i
$625$	−5.03580	−	28.5594i	−0.201432	−	1.14238i
$626$		0			0
$627$		0			0
$628$	−28.0000			−1.11732
$629$	1.04189	+	5.90885i	0.0415428	+	0.235601i
$630$		0			0
$631$	−10.3366	+	3.76222i	−0.411494	+	0.149772i	−0.539468	−	0.842006i	$-0.681375\pi$
$631$	−10.3366	+	3.76222i	−0.411494	+	0.149772i	0.127974	+	0.991778i	$0.459153\pi$
$632$		0			0
$633$	−21.4492	−	17.9981i	−0.852531	−	0.715358i
$634$		0			0
$635$	3.00000	+	5.19615i	0.119051	+	0.206203i
$636$	8.33511	−	47.2708i	0.330509	−	1.87441i
$637$	−4.16756	+	23.6354i	−0.165125	+	0.936468i
$638$		0			0
$639$	3.00000	−	5.19615i	0.118678	−	0.205557i
$640$		0			0
$641$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$641$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$642$		0			0
$643$	−9.95858	+	8.35624i	−0.392728	+	0.329538i	−0.817675	−	0.575680i	$-0.804737\pi$
$643$	−9.95858	+	8.35624i	−0.392728	+	0.329538i	0.424947	+	0.905218i	$0.360293\pi$
$644$		0			0
$645$	−6.00000			−0.236250
$646$		0			0
$647$	27.0000			1.06148			0.530740	−	0.847535i	$-0.321914\pi$
$647$	27.0000			1.06148			0.530740	+	0.847535i	$0.321914\pi$
$648$		0			0
$649$	13.7888	−	11.5702i	0.541258	−	0.454169i
$650$		0			0
$651$	7.51754	+	2.73616i	0.294636	+	0.107239i
$652$	−30.6418	−	25.7115i	−1.20002	−	1.00694i
$653$	19.5000	−	33.7750i	0.763094	−	1.32172i	−0.178154	−	0.984003i	$-0.557013\pi$
$653$	19.5000	−	33.7750i	0.763094	−	1.32172i	0.941248	−	0.337715i	$-0.109654\pi$
$654$		0			0
$655$	−7.81417	+	44.3163i	−0.305325	+	1.73158i
$656$	4.16756	−	23.6354i	0.162716	−	0.922807i
$657$	3.50000	+	6.06218i	0.136548	+	0.236508i
$658$		0			0
$659$	22.9813	+	19.2836i	0.895226	+	0.751184i	0.969251	−	0.246073i	$-0.0791402\pi$
$659$	22.9813	+	19.2836i	0.895226	+	0.751184i	−0.0740257	+	0.997256i	$0.523585\pi$
$660$	33.8289	+	12.3127i	1.31679	+	0.479272i
$661$	30.0702	−	10.9446i	1.16959	−	0.425697i	0.317078	−	0.948399i	$-0.397298\pi$
$661$	30.0702	−	10.9446i	1.16959	−	0.425697i	0.852515	+	0.522702i	$0.175076\pi$
$662$		0			0
$663$	−4.16756	−	23.6354i	−0.161854	−	0.917922i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−27.5776	+	23.1404i	−1.06701	+	0.895327i
$669$	−18.7939	+	6.84040i	−0.726612	+	0.264465i
$670$		0			0
$671$	−2.29813	−	1.92836i	−0.0887185	−	0.0744436i
$672$		0			0
$673$	−5.00000	−	8.66025i	−0.192736	−	0.333828i	0.753420	−	0.657539i	$-0.228403\pi$
$673$	−5.00000	−	8.66025i	−0.192736	−	0.333828i	−0.946156	+	0.323711i	$0.895069\pi$
$674$		0			0
$675$	−2.77837	+	15.7569i	−0.106940	+	0.606484i
$676$	3.00000	+	5.19615i	0.115385	+	0.199852i
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	0.107772	+	0.994176i	$0.465628\pi$
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	−0.914867	+	0.403755i	$0.867705\pi$
$678$		0			0
$679$	−7.51754	−	2.73616i	−0.288497	−	0.105004i
$680$		0			0
$681$	−18.3851	+	15.4269i	−0.704517	+	0.591160i
$682$		0			0
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$		0			0
$685$	−9.00000			−0.343872
$686$		0			0
$687$	7.66044	−	6.42788i	0.292264	−	0.245239i
$688$	3.75877	−	1.36808i	0.143302	−	0.0521576i
$689$	45.1052	+	16.4170i	1.71837	+	0.625437i
$690$		0			0
$691$	−8.50000	+	14.7224i	−0.323355	+	0.560068i	−0.981178	−	0.193105i	$-0.938144\pi$
$691$	−8.50000	+	14.7224i	−0.323355	+	0.560068i	0.657823	+	0.753173i	$0.271478\pi$
$692$	18.0000	+	31.1769i	0.684257	+	1.18517i
$693$	−0.520945	+	2.95442i	−0.0197890	+	0.112229i
$694$		0			0
$695$	19.5000	+	33.7750i	0.739677	+	1.28116i
$696$		0			0
$697$	−13.7888	−	11.5702i	−0.522288	−	0.438252i
$698$		0			0
$699$	39.4671	−	14.3648i	1.49278	−	0.543328i
$700$	6.12836	−	5.14230i	0.231630	−	0.194361i
$701$	1.04189	+	5.90885i	0.0393516	+	0.223174i	0.998141	−	0.0609428i	$-0.0194107\pi$
$701$	1.04189	+	5.90885i	0.0393516	+	0.223174i	−0.958790	+	0.284117i	$0.908300\pi$
$702$		0			0
$703$		0			0
$704$	−24.0000			−0.904534
$705$	−3.12567	−	17.7265i	−0.117719	−	0.667620i
$706$		0			0
$707$	5.63816	−	2.05212i	0.212045	−	0.0771779i
$708$	22.5526	+	8.20848i	0.847579	+	0.308494i
$709$	19.9172	+	16.7125i	0.748004	+	0.627650i	0.934974	−	0.354715i	$-0.115422\pi$
$709$	19.9172	+	16.7125i	0.748004	+	0.627650i	−0.186970	+	0.982366i	$0.559867\pi$
$710$		0			0
$711$	4.00000	+	6.92820i	0.150012	+	0.259828i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−18.0000	+	31.1769i	−0.673162	+	1.16595i
$716$	−27.5776	−	23.1404i	−1.03062	−	0.864796i
$717$	−28.1908	−	10.2606i	−1.05280	−	0.383189i
$718$		0			0
$719$	11.4907	−	9.64181i	0.428530	−	0.359579i	−0.402867	−	0.915259i	$-0.631986\pi$
$719$	11.4907	−	9.64181i	0.428530	−	0.359579i	0.831397	+	0.555680i	$0.187542\pi$
$720$	2.08378	+	11.8177i	0.0776578	+	0.440419i
$721$	14.0000			0.521387
$722$		0			0
$723$	20.0000			0.743808
$724$	0.694593	+	3.93923i	0.0258143	+	0.146400i
$725$	−18.3851	+	15.4269i	−0.682804	+	0.572941i
$726$		0			0
$727$	17.8542	+	6.49838i	0.662174	+	0.241012i	0.651175	−	0.758928i	$-0.274276\pi$
$727$	17.8542	+	6.49838i	0.662174	+	0.241012i	0.0109994	+	0.999940i	$0.496499\pi$
$728$		0			0
$729$	−6.50000	+	11.2583i	−0.240741	+	0.416975i
$730$		0			0
$731$	0.520945	−	2.95442i	0.0192678	−	0.109273i
$732$	0.694593	−	3.93923i	0.0256729	−	0.145598i
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	0.994471	−	0.105010i	$-0.0334875\pi$
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	−0.588177	+	0.808732i	$0.700154\pi$
$734$		0			0
$735$	−27.5776	−	23.1404i	−1.01722	−	0.853545i
$736$		0			0
$737$	−11.2763	+	4.10424i	−0.415368	+	0.151182i
$738$		0			0
$739$	1.91013	+	10.8329i	0.0702653	+	0.398494i	0.999574	+	0.0291901i	$0.00929280\pi$
$739$	1.91013	+	10.8329i	0.0702653	+	0.398494i	−0.929309	+	0.369304i	$0.879596\pi$
$740$	12.0000			0.441129
$741$		0			0
$742$		0			0
$743$	4.16756	+	23.6354i	0.152893	+	0.867098i	0.960687	+	0.277634i	$0.0895501\pi$
$743$	4.16756	+	23.6354i	0.152893	+	0.867098i	−0.807794	+	0.589465i	$0.799339\pi$
$744$		0			0
$745$	−59.2006	+	21.5473i	−2.16894	+	0.789431i
$746$		0			0
$747$	9.19253	+	7.71345i	0.336337	+	0.282220i
$748$	−9.00000	+	15.5885i	−0.329073	+	0.569970i
$749$	9.00000	+	15.5885i	0.328853	+	0.569590i
$750$		0			0
$751$	−5.55674	+	31.5138i	−0.202768	+	1.14996i	0.698145	+	0.715957i	$0.254009\pi$
$751$	−5.55674	+	31.5138i	−0.202768	+	1.14996i	−0.900913	+	0.434000i	$0.857102\pi$
$752$	6.00000	+	10.3923i	0.218797	+	0.378968i
$753$	−21.0000	+	36.3731i	−0.765283	+	1.32551i
$754$		0			0
$755$	−28.1908	−	10.2606i	−1.02597	−	0.373422i
$756$	7.51754	−	2.73616i	0.273410	−	0.0995132i
$757$	−19.1511	+	16.0697i	−0.696059	+	0.584063i	−0.920649	−	0.390390i	$-0.872340\pi$
$757$	−19.1511	+	16.0697i	−0.696059	+	0.584063i	0.224590	+	0.974453i	$0.427896\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	33.0000			1.19625			0.598125	−	0.801403i	$-0.295913\pi$
$761$	33.0000			1.19625			0.598125	+	0.801403i	$0.295913\pi$
$762$		0			0
$763$	−12.2567	+	10.2846i	−0.443723	+	0.372328i
$764$	5.63816	−	2.05212i	0.203981	−	0.0742431i
$765$	8.45723	+	3.07818i	0.305772	+	0.111292i
$766$		0			0
$767$	−12.0000	+	20.7846i	−0.433295	+	0.750489i
$768$	−16.0000	−	27.7128i	−0.577350	−	1.00000i
$769$	3.99391	−	22.6506i	0.144024	−	0.816801i	−0.824122	−	0.566413i	$-0.808331\pi$
$769$	3.99391	−	22.6506i	0.144024	−	0.816801i	0.968146	−	0.250388i	$-0.0805581\pi$
$770$		0			0
$771$		0			0
$772$	4.00000	−	6.92820i	0.143963	−	0.249351i
$773$	4.59627	+	3.85673i	0.165316	+	0.138717i	0.721693	−	0.692213i	$-0.243364\pi$
$773$	4.59627	+	3.85673i	0.165316	+	0.138717i	−0.556377	+	0.830930i	$0.687809\pi$
$774$		0			0
$775$	−15.0351	+	5.47232i	−0.540076	+	0.196572i
$776$		0			0
$777$	0.694593	+	3.93923i	0.0249184	+	0.141319i
$778$		0			0
$779$		0			0
$780$	−48.0000			−1.71868
$781$	−3.12567	−	17.7265i	−0.111845	−	0.634305i
$782$		0			0
$783$	−22.5526	+	8.20848i	−0.805965	+	0.293347i
$784$	22.5526	+	8.20848i	0.805451	+	0.293160i
$785$	32.1739	+	26.9971i	1.14833	+	0.963567i
$786$		0			0
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	0.828176	−	0.560469i	$-0.189379\pi$
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	−0.899468	+	0.436987i	$0.856046\pi$
$788$	−6.25133	+	35.4531i	−0.222695	+	1.26296i
$789$	3.12567	−	17.7265i	0.111277	−	0.631082i
$790$		0			0
$791$	−3.00000	+	5.19615i	−0.106668	+	0.184754i
$792$		0			0
$793$	3.75877	+	1.36808i	0.133478	+	0.0485820i
$794$		0			0
$795$	−55.1552	+	46.2807i	−1.95615	+	1.64141i
$796$	−3.82026	−	21.6658i	−0.135406	−	0.767923i
$797$	12.0000			0.425062			0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000			0.425062			0.212531	+	0.977154i	$0.431829\pi$
$798$		0			0
$799$	9.00000			0.318397
$800$		0			0
$801$	−9.19253	+	7.71345i	−0.324802	+	0.272541i
$802$		0			0
$803$	19.7335	+	7.18242i	0.696382	+	0.253462i
$804$	−12.2567	−	10.2846i	−0.432261	−	0.362710i
$805$		0			0
$806$		0			0
$807$	−8.33511	+	47.2708i	−0.293410	+	1.66401i
$808$		0			0
$809$	4.50000	+	7.79423i	0.158212	+	0.274030i	0.934224	−	0.356687i	$-0.116094\pi$
$809$	4.50000	+	7.79423i	0.158212	+	0.274030i	−0.776012	+	0.630718i	$0.782761\pi$
$810$		0			0
$811$	12.2567	+	10.2846i	0.430391	+	0.361141i	0.832099	−	0.554627i	$-0.187139\pi$
$811$	12.2567	+	10.2846i	0.430391	+	0.361141i	−0.401708	+	0.915768i	$0.631583\pi$
$812$	11.2763	+	4.10424i	0.395721	+	0.144031i
$813$	30.0702	−	10.9446i	1.05461	−	0.383845i
$814$		0			0
$815$	10.4189	+	59.0885i	0.364958	+	2.06978i
$816$	−24.0000			−0.840168
$817$		0			0
$818$		0			0
$819$	−0.694593	−	3.93923i	−0.0242710	−	0.137648i
$820$	−27.5776	+	23.1404i	−0.963052	+	0.808096i
$821$	−31.0099	+	11.2867i	−1.08225	+	0.393907i	−0.820745	−	0.571294i	$-0.806441\pi$
$821$	−31.0099	+	11.2867i	−1.08225	+	0.393907i	−0.261506	+	0.965202i	$0.584219\pi$
$822$		0			0
$823$	−37.5362	−	31.4966i	−1.30843	−	1.09790i	−0.988622	−	0.150419i	$-0.951938\pi$
$823$	−37.5362	−	31.4966i	−1.30843	−	1.09790i	−0.319807	−	0.947483i	$-0.603618\pi$
$824$		0			0
$825$	−12.0000	−	20.7846i	−0.417786	−	0.723627i
$826$		0			0
$827$	−2.08378	+	11.8177i	−0.0724601	+	0.410941i	0.926904	+	0.375297i	$0.122459\pi$
$827$	−2.08378	+	11.8177i	−0.0724601	+	0.410941i	−0.999365	+	0.0356441i	$0.988652\pi$
$828$		0			0
$829$	−8.00000	+	13.8564i	−0.277851	+	0.481253i	−0.970851	−	0.239686i	$-0.922956\pi$
$829$	−8.00000	+	13.8564i	−0.277851	+	0.481253i	0.692999	+	0.720938i	$0.256289\pi$
$830$		0			0
$831$	35.7083	+	12.9968i	1.23871	+	0.450853i
$832$	30.0702	−	10.9446i	1.04250	−	0.379437i
$833$	13.7888	−	11.5702i	0.477754	−	0.400883i
$834$		0			0
$835$	54.0000			1.86875
$836$		0			0
$837$	−16.0000			−0.553041
$838$		0			0
$839$	−13.7888	+	11.5702i	−0.476042	+	0.399447i	−0.848993	−	0.528404i	$-0.822791\pi$
$839$	−13.7888	+	11.5702i	−0.476042	+	0.399447i	0.372951	+	0.927851i	$0.378346\pi$
$840$		0			0
$841$	−6.57785	−	2.39414i	−0.226822	−	0.0825566i
$842$		0			0
$843$	6.00000	−	10.3923i	0.206651	−	0.357930i
$844$	−14.0000	−	24.2487i	−0.481900	−	0.834675i
$845$	1.56283	−	8.86327i	0.0537631	−	0.304906i
$846$		0			0
$847$	−1.00000	−	1.73205i	−0.0343604	−	0.0595140i
$848$	24.0000	−	41.5692i	0.824163	−	1.42749i
$849$	−19.9172	−	16.7125i	−0.683555	−	0.573571i
$850$		0			0
$851$		0			0
$852$	18.3851	−	15.4269i	0.629862	−	0.528517i
$853$	4.51485	+	25.6050i	0.154586	+	0.876699i	0.959164	+	0.282852i	$0.0912804\pi$
$853$	4.51485	+	25.6050i	0.154586	+	0.876699i	−0.804578	+	0.593847i	$0.797608\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−3.12567	−	17.7265i	−0.106771	−	0.605527i	−0.990498	−	0.137525i	$-0.956085\pi$
$857$	−3.12567	−	17.7265i	−0.106771	−	0.605527i	0.883728	−	0.468002i	$-0.155026\pi$
$858$		0			0
$859$	46.0449	−	16.7590i	1.57103	−	0.571809i	0.597803	−	0.801643i	$-0.296040\pi$
$859$	46.0449	−	16.7590i	1.57103	−	0.571809i	0.973230	+	0.229834i	$0.0738182\pi$
$860$	−5.63816	−	2.05212i	−0.192260	−	0.0699767i
$861$	−9.19253	−	7.71345i	−0.313281	−	0.262874i
$862$		0			0
$863$	9.00000	+	15.5885i	0.306364	+	0.530637i	0.977564	−	0.210639i	$-0.0675543\pi$
$863$	9.00000	+	15.5885i	0.306364	+	0.530637i	−0.671200	+	0.741276i	$0.734221\pi$
$864$		0			0
$865$	9.37700	−	53.1796i	0.318828	−	1.80816i
$866$		0			0
$867$	8.00000	−	13.8564i	0.271694	−	0.470588i
$868$	6.12836	+	5.14230i	0.208010	+	0.174541i
$869$	22.5526	+	8.20848i	0.765045	+	0.278454i
$870$		0			0
$871$	12.2567	−	10.2846i	0.415303	−	0.348480i
$872$		0			0
$873$	−8.00000			−0.270759
$874$		0			0
$875$	3.00000			0.101419
$876$	4.86215	+	27.5746i	0.164277	+	0.931660i
$877$	16.8530	−	14.1413i	0.569085	−	0.477519i	−0.312257	−	0.949998i	$-0.601085\pi$
$877$	16.8530	−	14.1413i	0.569085	−	0.477519i	0.881342	+	0.472479i	$0.156641\pi$
$878$		0			0
$879$	−22.5526	−	8.20848i	−0.760681	−	0.276865i
$880$	27.5776	+	23.1404i	0.929641	+	0.780061i
$881$	13.5000	−	23.3827i	0.454827	−	0.787783i	−0.543852	−	0.839181i	$-0.683035\pi$
$881$	13.5000	−	23.3827i	0.454827	−	0.787783i	0.998678	+	0.0513987i	$0.0163679\pi$
$882$		0			0
$883$	8.16146	−	46.2860i	0.274655	−	1.55765i	−0.465400	−	0.885100i	$-0.654090\pi$
$883$	8.16146	−	46.2860i	0.274655	−	1.55765i	0.740055	−	0.672546i	$-0.234799\pi$
$884$	4.16756	−	23.6354i	0.140170	−	0.794944i
$885$	−18.0000	−	31.1769i	−0.605063	−	1.04800i
$886$		0			0
$887$	−13.7888	−	11.5702i	−0.462983	−	0.388489i	0.381244	−	0.924474i	$-0.375496\pi$
$887$	−13.7888	−	11.5702i	−0.462983	−	0.388489i	−0.844227	+	0.535986i	$0.819940\pi$
$888$		0			0
$889$	−1.87939	+	0.684040i	−0.0630326	+	0.0229420i
$890$		0			0
$891$	−5.73039	−	32.4987i	−0.191975	−	1.08875i
$892$	−20.0000			−0.669650
$893$		0			0
$894$		0			0
$895$	9.37700	+	53.1796i	0.313439	+	1.77760i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−18.3851	−	15.4269i	−0.613176	−	0.514516i
$900$	4.00000	−	6.92820i	0.133333	−	0.230940i
$901$	−18.0000	−	31.1769i	−0.599667	−	1.03865i
$902$		0			0
$903$	0.347296	−	1.96962i	0.0115573	−	0.0655447i
$904$		0			0
$905$	3.00000	−	5.19615i	0.0997234	−	0.172726i
$906$		0			0
$907$	7.51754	+	2.73616i	0.249616	+	0.0908527i	0.463798	−	0.885941i	$-0.346486\pi$
$907$	7.51754	+	2.73616i	0.249616	+	0.0908527i	−0.214182	+	0.976794i	$0.568709\pi$
$908$	−22.5526	+	8.20848i	−0.748435	+	0.272408i
$909$	4.59627	−	3.85673i	0.152449	−	0.127920i
$910$		0			0
$911$	6.00000			0.198789			0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000			0.198789			0.0993944	+	0.995048i	$0.468309\pi$
$912$		0			0
$913$	36.0000			1.19143
$914$		0			0
$915$	−4.59627	+	3.85673i	−0.151948	+	0.127499i
$916$	9.39693	−	3.42020i	0.310483	−	0.113007i
$917$	−14.0954	−	5.13030i	−0.465471	−	0.169418i
$918$		0			0
$919$	−10.0000	+	17.3205i	−0.329870	+	0.571351i	−0.982486	−	0.186338i	$-0.940338\pi$
$919$	−10.0000	+	17.3205i	−0.329870	+	0.571351i	0.652616	+	0.757689i	$0.273671\pi$
$920$		0			0
$921$	−6.94593	+	39.3923i	−0.228876	+	1.29802i
$922$		0			0
$923$	12.0000	+	20.7846i	0.394985	+	0.684134i
$924$	−6.00000	+	10.3923i	−0.197386	+	0.341882i
$925$	−6.12836	−	5.14230i	−0.201499	−	0.169078i
$926$		0			0
$927$	13.1557	−	4.78828i	0.432090	−	0.157268i
$928$		0			0
$929$	−3.12567	−	17.7265i	−0.102550	−	0.581589i	−0.992171	−	0.124889i	$-0.960142\pi$
$929$	−3.12567	−	17.7265i	−0.102550	−	0.581589i	0.889621	−	0.456700i	$-0.150969\pi$
$930$		0			0
$931$		0			0
$932$	42.0000			1.37576
$933$	−1.04189	−	5.90885i	−0.0341099	−	0.193447i
$934$		0			0
$935$	25.3717	−	9.23454i	0.829743	−	0.302002i
$936$		0			0
$937$	−5.36231	−	4.49951i	−0.175179	−	0.146993i	0.550982	−	0.834517i	$-0.314253\pi$
$937$	−5.36231	−	4.49951i	−0.175179	−	0.146993i	−0.726162	+	0.687524i	$0.758698\pi$
$938$		0			0
$939$	10.0000	+	17.3205i	0.326338	+	0.565233i
$940$	3.12567	−	17.7265i	0.101948	−	0.578176i
$941$	3.12567	−	17.7265i	0.101894	−	0.577869i	−0.890522	−	0.454941i	$-0.849660\pi$
$941$	3.12567	−	17.7265i	0.101894	−	0.577869i	0.992416	−	0.122928i	$-0.0392284\pi$
$942$		0			0
$943$		0			0
$944$	18.3851	+	15.4269i	0.598383	+	0.502103i
$945$	−11.2763	−	4.10424i	−0.366818	−	0.133511i
$946$		0			0
$947$	−27.5776	+	23.1404i	−0.896152	+	0.751960i	−0.969434	−	0.245351i	$-0.921097\pi$
$947$	−27.5776	+	23.1404i	−0.896152	+	0.751960i	0.0732828	+	0.997311i	$0.476652\pi$
$948$	5.55674	+	31.5138i	0.180475	+	1.02352i
$949$	−28.0000			−0.908918
$950$		0			0
$951$	−12.0000			−0.389127
$952$		0			0
$953$	36.7701	−	30.8538i	1.19110	−	0.999453i	0.191262	−	0.981539i	$-0.438742\pi$
$953$	36.7701	−	30.8538i	1.19110	−	0.999453i	0.999840	−	0.0179138i	$-0.00570243\pi$
$954$		0			0
$955$	−8.45723	−	3.07818i	−0.273670	−	0.0996076i
$956$	−22.9813	−	19.2836i	−0.743269	−	0.623677i
$957$	18.0000	−	31.1769i	0.581857	−	1.00781i
$958$		0			0
$959$	0.520945	−	2.95442i	0.0168222	−	0.0954033i
$960$	−8.33511	+	47.2708i	−0.269015	+	1.52566i
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$	13.7888	+	11.5702i	0.444338	+	0.372844i
$964$	18.7939	+	6.84040i	0.605309	+	0.220315i
$965$	−11.2763	+	4.10424i	−0.362997	+	0.132120i
$966$		0			0
$967$	−6.94593	−	39.3923i	−0.223366	−	1.26677i	−0.865784	−	0.500417i	$-0.833180\pi$
$967$	−6.94593	−	39.3923i	−0.223366	−	1.26677i	0.642418	−	0.766354i	$-0.277931\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−10.4189	−	59.0885i	−0.334358	−	1.89624i	−0.433479	−	0.901164i	$-0.642714\pi$
$971$	−10.4189	−	59.0885i	−0.334358	−	1.89624i	0.0991209	−	0.995075i	$-0.468397\pi$
$972$	15.3209	−	12.8558i	0.491418	−	0.412348i
$973$	−12.2160	+	4.44626i	−0.391627	+	0.142541i
$974$		0			0
$975$	24.5134	+	20.5692i	0.785058	+	0.658742i
$976$	2.00000	−	3.46410i	0.0640184	−	0.110883i
$977$	12.0000	+	20.7846i	0.383914	+	0.664959i	0.991618	−	0.129205i	$-0.0412426\pi$
$977$	12.0000	+	20.7846i	0.383914	+	0.664959i	−0.607704	+	0.794164i	$0.707909\pi$
$978$		0			0
$979$	−6.25133	+	35.4531i	−0.199794	+	1.13309i
$980$	−18.0000	−	31.1769i	−0.574989	−	0.995910i
$981$	−8.00000	+	13.8564i	−0.255420	+	0.442401i
$982$		0			0
$983$	−33.8289	−	12.3127i	−1.07898	−	0.392715i	−0.259449	−	0.965757i	$-0.583541\pi$
$983$	−33.8289	−	12.3127i	−1.07898	−	0.392715i	−0.819526	+	0.573042i	$0.805763\pi$
$984$		0			0
$985$	41.3664	−	34.7105i	1.31804	−	1.10597i
$986$		0			0
$987$	6.00000			0.190982
$988$		0			0
$989$		0			0
$990$		0			0
$991$	26.0455	−	21.8548i	0.827363	−	0.694240i	−0.127321	−	0.991862i	$-0.540638\pi$
$991$	26.0455	−	21.8548i	0.827363	−	0.694240i	0.954684	+	0.297622i	$0.0961934\pi$
$992$		0			0
$993$	−52.6228	−	19.1531i	−1.66993	−	0.607806i
$994$		0			0
$995$	−16.5000	+	28.5788i	−0.523085	+	0.906010i
$996$	24.0000	+	41.5692i	0.760469	+	1.31717i
$997$	2.95202	−	16.7417i	0.0934914	−	0.530216i	−0.901708	−	0.432346i	$-0.857686\pi$
$997$	2.95202	−	16.7417i	0.0934914	−	0.530216i	0.995199	−	0.0978700i	$-0.0312029\pi$
$998$		0			0
$999$	−4.00000	−	6.92820i	−0.126554	−	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.e.e.28.1		6
19.2	odd	18		361.2.e.d.245.1		6
19.3	odd	18		361.2.e.d.62.1		6
19.4	even	9		361.2.c.a.68.1		2
19.5	even	9	inner	361.2.e.e.54.1		6
19.6	even	9		361.2.a.b.1.1		1
19.7	even	3	inner	361.2.e.e.99.1		6
19.8	odd	6		361.2.e.d.234.1		6
19.9	even	9		361.2.c.a.292.1		2
19.10	odd	18		361.2.c.c.292.1		2
19.11	even	3	inner	361.2.e.e.234.1		6
19.12	odd	6		361.2.e.d.99.1		6
19.13	odd	18		19.2.a.a.1.1	✓	1
19.14	odd	18		361.2.e.d.54.1		6
19.15	odd	18		361.2.c.c.68.1		2
19.16	even	9	inner	361.2.e.e.62.1		6
19.17	even	9	inner	361.2.e.e.245.1		6
19.18	odd	2		361.2.e.d.28.1		6
57.32	even	18		171.2.a.b.1.1		1
57.44	odd	18		3249.2.a.d.1.1		1
76.51	even	18		304.2.a.f.1.1		1
76.63	odd	18		5776.2.a.c.1.1		1
95.13	even	36		475.2.b.a.324.1		2
95.32	even	36		475.2.b.a.324.2		2
95.44	even	18		9025.2.a.d.1.1		1
95.89	odd	18		475.2.a.b.1.1		1
133.13	even	18		931.2.a.a.1.1		1
133.32	odd	18		931.2.f.c.324.1		2
133.51	odd	18		931.2.f.c.704.1		2
133.89	even	18		931.2.f.b.704.1		2
133.108	even	18		931.2.f.b.324.1		2
152.13	odd	18		1216.2.a.o.1.1		1
152.51	even	18		1216.2.a.b.1.1		1
209.32	even	18		2299.2.a.b.1.1		1
228.203	odd	18		2736.2.a.c.1.1		1
247.51	odd	18		3211.2.a.a.1.1		1
285.89	even	18		4275.2.a.i.1.1		1
323.203	odd	18		5491.2.a.b.1.1		1
380.279	even	18		7600.2.a.c.1.1		1
399.146	odd	18		8379.2.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.a.a.1.1	✓	1	19.13	odd	18
171.2.a.b.1.1		1	57.32	even	18
304.2.a.f.1.1		1	76.51	even	18
361.2.a.b.1.1		1	19.6	even	9
361.2.c.a.68.1		2	19.4	even	9
361.2.c.a.292.1		2	19.9	even	9
361.2.c.c.68.1		2	19.15	odd	18
361.2.c.c.292.1		2	19.10	odd	18
361.2.e.d.28.1		6	19.18	odd	2
361.2.e.d.54.1		6	19.14	odd	18
361.2.e.d.62.1		6	19.3	odd	18
361.2.e.d.99.1		6	19.12	odd	6
361.2.e.d.234.1		6	19.8	odd	6
361.2.e.d.245.1		6	19.2	odd	18
361.2.e.e.28.1		6	1.1	even	1	trivial
361.2.e.e.54.1		6	19.5	even	9	inner
361.2.e.e.62.1		6	19.16	even	9	inner
361.2.e.e.99.1		6	19.7	even	3	inner
361.2.e.e.234.1		6	19.11	even	3	inner
361.2.e.e.245.1		6	19.17	even	9	inner
475.2.a.b.1.1		1	95.89	odd	18
475.2.b.a.324.1		2	95.13	even	36
475.2.b.a.324.2		2	95.32	even	36
931.2.a.a.1.1		1	133.13	even	18
931.2.f.b.324.1		2	133.108	even	18
931.2.f.b.704.1		2	133.89	even	18
931.2.f.c.324.1		2	133.32	odd	18
931.2.f.c.704.1		2	133.51	odd	18
1216.2.a.b.1.1		1	152.51	even	18
1216.2.a.o.1.1		1	152.13	odd	18
2299.2.a.b.1.1		1	209.32	even	18
2736.2.a.c.1.1		1	228.203	odd	18
3211.2.a.a.1.1		1	247.51	odd	18
3249.2.a.d.1.1		1	57.44	odd	18
4275.2.a.i.1.1		1	285.89	even	18
5491.2.a.b.1.1		1	323.203	odd	18
5776.2.a.c.1.1		1	76.63	odd	18
7600.2.a.c.1.1		1	380.279	even	18
8379.2.a.j.1.1		1	399.146	odd	18
9025.2.a.d.1.1		1	95.44	even	18

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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.53209 - 1.28558i) q^{3} +(1.87939 - 0.684040i) q^{4} +(-2.81908 - 1.02606i) q^{5} +(0.500000 - 0.866025i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(1.53209 - 1.28558i) q^{3} +(1.87939 - 0.684040i) q^{4} +(-2.81908 - 1.02606i) q^{5} +(0.500000 - 0.866025i) q^{7} +(0.173648 - 0.984808i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(2.00000 - 3.46410i) q^{12} +(3.06418 + 2.57115i) q^{13} +(-5.63816 + 2.05212i) q^{15} +(3.06418 - 2.57115i) q^{16} +(-0.520945 - 2.95442i) q^{17} -6.00000 q^{20} +(-0.347296 - 1.96962i) q^{21} +(3.06418 + 2.57115i) q^{25} +(2.00000 + 3.46410i) q^{27} +(0.347296 - 1.96962i) q^{28} +(-1.04189 + 5.90885i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(-5.63816 - 2.05212i) q^{33} +(-2.29813 + 1.92836i) q^{35} +(-0.347296 - 1.96962i) q^{36} -2.00000 q^{37} +8.00000 q^{39} +(4.59627 - 3.85673i) q^{41} +(0.939693 + 0.342020i) q^{43} +(-4.59627 - 3.85673i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(-0.520945 + 2.95442i) q^{47} +(1.38919 - 7.87846i) q^{48} +(3.00000 + 5.19615i) q^{49} +(-4.59627 - 3.85673i) q^{51} +(7.51754 + 2.73616i) q^{52} +(11.2763 - 4.10424i) q^{53} +(1.56283 + 8.86327i) q^{55} +(1.04189 + 5.90885i) q^{59} +(-9.19253 + 7.71345i) q^{60} +(0.939693 - 0.342020i) q^{61} +(-0.766044 - 0.642788i) q^{63} +(4.00000 - 6.92820i) q^{64} +(-6.00000 - 10.3923i) q^{65} +(0.694593 - 3.93923i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(5.63816 + 2.05212i) q^{71} +(-5.36231 + 4.49951i) q^{73} +8.00000 q^{75} -3.00000 q^{77} +(-6.12836 + 5.14230i) q^{79} +(-11.2763 + 4.10424i) q^{80} +(10.3366 + 3.76222i) q^{81} +(-6.00000 + 10.3923i) q^{83} +(-2.00000 - 3.46410i) q^{84} +(-1.56283 + 8.86327i) q^{85} +(6.00000 + 10.3923i) q^{87} +(-9.19253 - 7.71345i) q^{89} +(3.75877 - 1.36808i) q^{91} +(1.38919 + 7.87846i) q^{93} +(-1.38919 - 7.87846i) q^{97} +(-2.81908 + 1.02606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{7}+O(q^{10}) \) 6 * q + 3 * q^7	\( 6 q + 3 q^{7} - 9 q^{11} + 12 q^{12} - 36 q^{20} + 12 q^{27} - 12 q^{31} - 12 q^{37} + 48 q^{39} - 9 q^{45} + 18 q^{49} + 24 q^{64} - 36 q^{65} - 18 q^{68} + 48 q^{75} - 18 q^{77} - 36 q^{83} - 12 q^{84} + 36 q^{87}+O(q^{100}) \) 6 * q + 3 * q^7 - 9 * q^11 + 12 * q^12 - 36 * q^20 + 12 * q^27 - 12 * q^31 - 12 * q^37 + 48 * q^39 - 9 * q^45 + 18 * q^49 + 24 * q^64 - 36 * q^65 - 18 * q^68 + 48 * q^75 - 18 * q^77 - 36 * q^83 - 12 * q^84 + 36 * q^87

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