LMFDB - Embedded newform 361.2.e.d.234.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,2,Mod(28,361)] 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("361.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [6,0,0,0,0,0,3,0,0,0,-9,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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			234.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	361.234
Dual form			361.2.e.d.54.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.87939 + 0.684040i) q^{3} +(-0.347296 + 1.96962i) q^{4} +(0.520945 + 2.95442i) q^{5} +(0.500000 - 0.866025i) q^{7} +(0.766044 + 0.642788i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-2.00000 + 3.46410i) q^{12} +(3.75877 - 1.36808i) q^{13} +(-1.04189 + 5.90885i) q^{15} +(-3.75877 - 1.36808i) q^{16} +(-2.29813 + 1.92836i) q^{17} -6.00000 q^{20} +(1.53209 - 1.28558i) q^{21} +(-3.75877 + 1.36808i) q^{25} +(-2.00000 - 3.46410i) q^{27} +(1.53209 + 1.28558i) q^{28} +(4.59627 + 3.85673i) q^{29} +(2.00000 - 3.46410i) q^{31} +(-1.04189 - 5.90885i) q^{33} +(2.81908 + 1.02606i) q^{35} +(-1.53209 + 1.28558i) q^{36} +2.00000 q^{37} +8.00000 q^{39} +(5.63816 + 2.05212i) q^{41} +(-0.173648 - 0.984808i) q^{43} +(5.63816 - 2.05212i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(-2.29813 - 1.92836i) q^{47} +(-6.12836 - 5.14230i) q^{48} +(3.00000 + 5.19615i) q^{49} +(-5.63816 + 2.05212i) q^{51} +(1.38919 + 7.87846i) q^{52} +(2.08378 - 11.8177i) q^{53} +(6.89440 - 5.78509i) q^{55} +(-4.59627 + 3.85673i) q^{59} +(-11.2763 - 4.10424i) q^{60} +(-0.173648 + 0.984808i) q^{61} +(0.939693 - 0.342020i) q^{63} +(4.00000 - 6.92820i) q^{64} +(6.00000 + 10.3923i) q^{65} +(-3.06418 - 2.57115i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(1.04189 + 5.90885i) q^{71} +(6.57785 + 2.39414i) q^{73} -8.00000 q^{75} -3.00000 q^{77} +(-7.51754 - 2.73616i) q^{79} +(2.08378 - 11.8177i) q^{80} +(-1.91013 - 10.8329i) q^{81} +(-6.00000 + 10.3923i) q^{83} +(2.00000 + 3.46410i) q^{84} +(-6.89440 - 5.78509i) q^{85} +(6.00000 + 10.3923i) q^{87} +(-11.2763 + 4.10424i) q^{89} +(0.694593 - 3.93923i) q^{91} +(6.12836 - 5.14230i) q^{93} +(6.12836 - 5.14230i) q^{97} +(0.520945 - 2.95442i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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		−0.642788	−	0.766044i	$-0.722222\pi$
$2$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$3$	1.87939	+	0.684040i	1.08506	+	0.394931i	0.821790	−	0.569790i	$-0.192976\pi$
$3$	1.87939	+	0.684040i	1.08506	+	0.394931i	0.263274	+	0.964721i	$0.415198\pi$
$4$	−0.347296	+	1.96962i	−0.173648	+	0.984808i
$5$	0.520945	+	2.95442i	0.232973	+	1.32126i	0.846840	+	0.531848i	$0.178502\pi$
$5$	0.520945	+	2.95442i	0.232973	+	1.32126i	−0.613866	+	0.789410i	$0.710387\pi$
$6$		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
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$		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
$13$	3.75877	−	1.36808i	1.04250	−	0.379437i	0.236670	−	0.971590i	$-0.423944\pi$
$13$	3.75877	−	1.36808i	1.04250	−	0.379437i	0.805826	+	0.592153i	$0.201722\pi$
$14$		0			0
$15$	−1.04189	+	5.90885i	−0.269015	+	1.52566i
$16$	−3.75877	−	1.36808i	−0.939693	−	0.342020i
$17$	−2.29813	+	1.92836i	−0.557379	+	0.467697i	−0.877431	−	0.479703i	$-0.840744\pi$
$17$	−2.29813	+	1.92836i	−0.557379	+	0.467697i	0.320051	+	0.947400i	$0.396300\pi$
$18$		0			0
$19$		0			0
$19$		0			0
$20$	−6.00000			−1.34164
$21$	1.53209	−	1.28558i	0.334329	−	0.280536i
$22$		0			0
$23$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$23$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$24$		0			0
$25$	−3.75877	+	1.36808i	−0.751754	+	0.273616i
$26$		0			0
$27$	−2.00000	−	3.46410i	−0.384900	−	0.666667i
$28$	1.53209	+	1.28558i	0.289538	+	0.242951i
$29$	4.59627	+	3.85673i	0.853505	+	0.716176i	0.960559	−	0.278077i	$-0.0896971\pi$
$29$	4.59627	+	3.85673i	0.853505	+	0.716176i	−0.107053	+	0.994253i	$0.534142\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$		0			0
$33$	−1.04189	−	5.90885i	−0.181370	−	1.02860i
$34$		0			0
$35$	2.81908	+	1.02606i	0.476511	+	0.173436i
$36$	−1.53209	+	1.28558i	−0.255348	+	0.214263i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$	8.00000			1.28103
$40$		0			0
$41$	5.63816	+	2.05212i	0.880532	+	0.320487i	0.742424	−	0.669930i	$-0.233676\pi$
$41$	5.63816	+	2.05212i	0.880532	+	0.320487i	0.138108	+	0.990417i	$0.455898\pi$
$42$		0			0
$43$	−0.173648	−	0.984808i	−0.0264811	−	0.150182i	0.968700	−	0.248234i	$-0.0798500\pi$
$43$	−0.173648	−	0.984808i	−0.0264811	−	0.150182i	−0.995181	+	0.0980518i	$0.968739\pi$
$44$	5.63816	−	2.05212i	0.849984	−	0.309369i
$45$	−1.50000	+	2.59808i	−0.223607	+	0.387298i
$46$		0			0
$47$	−2.29813	−	1.92836i	−0.335217	−	0.281281i	0.459604	−	0.888124i	$-0.347991\pi$
$47$	−2.29813	−	1.92836i	−0.335217	−	0.281281i	−0.794822	+	0.606843i	$0.792436\pi$
$48$	−6.12836	−	5.14230i	−0.884552	−	0.742227i
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$		0			0
$51$	−5.63816	+	2.05212i	−0.789500	+	0.287354i
$52$	1.38919	+	7.87846i	0.192645	+	1.09255i
$53$	2.08378	−	11.8177i	0.286229	−	1.62328i	−0.414633	−	0.909989i	$-0.636090\pi$
$53$	2.08378	−	11.8177i	0.286229	−	1.62328i	0.700862	−	0.713296i	$-0.252799\pi$
$54$		0			0
$55$	6.89440	−	5.78509i	0.929641	−	0.780061i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.59627	+	3.85673i	−0.598383	+	0.502103i	−0.890925	−	0.454150i	$-0.849943\pi$
$59$	−4.59627	+	3.85673i	−0.598383	+	0.502103i	0.292542	+	0.956253i	$0.405499\pi$
$60$	−11.2763	−	4.10424i	−1.45577	−	0.529855i
$61$	−0.173648	+	0.984808i	−0.0222334	+	0.126092i	−0.993904	−	0.110246i	$-0.964836\pi$
$61$	−0.173648	+	0.984808i	−0.0222334	+	0.126092i	0.971671	+	0.236338i	$0.0759472\pi$
$62$		0			0
$63$	0.939693	−	0.342020i	0.118390	−	0.0430905i
$64$	4.00000	−	6.92820i	0.500000	−	0.866025i
$65$	6.00000	+	10.3923i	0.744208	+	1.28901i
$66$		0			0
$67$	−3.06418	−	2.57115i	−0.374349	−	0.314116i	0.436130	−	0.899884i	$-0.356349\pi$
$67$	−3.06418	−	2.57115i	−0.374349	−	0.314116i	−0.810479	+	0.585768i	$0.800793\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$		0			0
$70$		0			0
$71$	1.04189	+	5.90885i	0.123649	+	0.701251i	0.982101	+	0.188356i	$0.0603159\pi$
$71$	1.04189	+	5.90885i	0.123649	+	0.701251i	−0.858451	+	0.512895i	$0.828573\pi$
$72$		0			0
$73$	6.57785	+	2.39414i	0.769879	+	0.280213i	0.696946	−	0.717124i	$-0.254542\pi$
$73$	6.57785	+	2.39414i	0.769879	+	0.280213i	0.0729331	+	0.997337i	$0.476764\pi$
$74$		0			0
$75$	−8.00000			−0.923760
$76$		0			0
$77$	−3.00000			−0.341882
$78$		0			0
$79$	−7.51754	−	2.73616i	−0.845789	−	0.307842i	−0.117467	−	0.993077i	$-0.537477\pi$
$79$	−7.51754	−	2.73616i	−0.845789	−	0.307842i	−0.728322	+	0.685235i	$0.759700\pi$
$80$	2.08378	−	11.8177i	0.232973	−	1.32126i
$81$	−1.91013	−	10.8329i	−0.212237	−	1.20365i
$82$		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
$85$	−6.89440	−	5.78509i	−0.747803	−	0.627481i
$86$		0			0
$87$	6.00000	+	10.3923i	0.643268	+	1.11417i
$88$		0			0
$89$	−11.2763	+	4.10424i	−1.19529	+	0.435049i	−0.861577	−	0.507627i	$-0.830523\pi$
$89$	−11.2763	+	4.10424i	−1.19529	+	0.435049i	−0.333710	+	0.942676i	$0.608301\pi$
$90$		0			0
$91$	0.694593	−	3.93923i	0.0728131	−	0.412944i
$92$		0			0
$93$	6.12836	−	5.14230i	0.635481	−	0.533232i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	6.12836	−	5.14230i	0.622240	−	0.522122i	−0.276267	−	0.961081i	$-0.589097\pi$
$97$	6.12836	−	5.14230i	0.622240	−	0.522122i	0.898507	+	0.438959i	$0.144653\pi$
$98$		0			0
$99$	0.520945	−	2.95442i	0.0523569	−	0.296931i
$100$	−1.38919	−	7.87846i	−0.138919	−	0.787846i
$101$	−5.63816	+	2.05212i	−0.561017	+	0.204194i	−0.606935	−	0.794752i	$-0.707601\pi$
$101$	−5.63816	+	2.05212i	−0.561017	+	0.204194i	0.0459174	+	0.998945i	$0.485379\pi$
$102$		0			0
$103$	−7.00000	−	12.1244i	−0.689730	−	1.19465i	−0.971925	−	0.235291i	$-0.924396\pi$
$103$	−7.00000	−	12.1244i	−0.689730	−	1.19465i	0.282194	−	0.959357i	$-0.408938\pi$
$104$		0			0
$105$	4.59627	+	3.85673i	0.448550	+	0.376378i
$106$		0			0
$107$	9.00000	−	15.5885i	0.870063	−	1.50699i	0.00813215	−	0.999967i	$-0.497411\pi$
$107$	9.00000	−	15.5885i	0.870063	−	1.50699i	0.861931	−	0.507026i	$-0.169255\pi$
$108$	7.51754	−	2.73616i	0.723376	−	0.263287i
$109$	−2.77837	−	15.7569i	−0.266120	−	1.50924i	−0.765828	−	0.643046i	$-0.777671\pi$
$109$	−2.77837	−	15.7569i	−0.266120	−	1.50924i	0.499708	−	0.866194i	$-0.333441\pi$
$110$		0			0
$111$	3.75877	+	1.36808i	0.356767	+	0.129852i
$112$	−3.06418	+	2.57115i	−0.289538	+	0.242951i
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$		0			0
$116$	−9.19253	+	7.71345i	−0.853505	+	0.716176i
$117$	3.75877	+	1.36808i	0.347498	+	0.126479i
$118$		0			0
$119$	0.520945	+	2.95442i	0.0477549	+	0.270832i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$	9.19253	+	7.71345i	0.828863	+	0.695498i
$124$	6.12836	+	5.14230i	0.550343	+	0.461792i
$125$	1.50000	+	2.59808i	0.134164	+	0.232379i
$126$		0			0
$127$	−1.87939	+	0.684040i	−0.166768	+	0.0606988i	−0.424055	−	0.905636i	$-0.639394\pi$
$127$	−1.87939	+	0.684040i	−0.166768	+	0.0606988i	0.257287	+	0.966335i	$0.417172\pi$
$128$		0			0
$129$	0.347296	−	1.96962i	0.0305777	−	0.173415i
$130$		0			0
$131$	−11.4907	+	9.64181i	−1.00394	+	0.842409i	−0.987526	−	0.157456i	$-0.949671\pi$
$131$	−11.4907	+	9.64181i	−1.00394	+	0.842409i	−0.0164182	+	0.999865i	$0.505226\pi$
$132$	12.0000			1.04447
$133$		0			0
$134$		0			0
$135$	9.19253	−	7.71345i	0.791167	−	0.663868i
$136$		0			0
$137$	−0.520945	+	2.95442i	−0.0445073	+	0.252413i	−0.998941	−	0.0460096i	$-0.985350\pi$
$137$	−0.520945	+	2.95442i	−0.0445073	+	0.252413i	0.954434	+	0.298423i	$0.0964606\pi$
$138$		0			0
$139$	12.2160	−	4.44626i	1.03615	−	0.377127i	0.232729	−	0.972542i	$-0.425234\pi$
$139$	12.2160	−	4.44626i	1.03615	−	0.377127i	0.803419	+	0.595415i	$0.203012\pi$
$140$	−3.00000	+	5.19615i	−0.253546	+	0.439155i
$141$	−3.00000	−	5.19615i	−0.252646	−	0.437595i
$142$		0			0
$143$	−9.19253	−	7.71345i	−0.768718	−	0.645031i
$144$	−2.00000	−	3.46410i	−0.166667	−	0.288675i
$145$	−9.00000	+	15.5885i	−0.747409	+	1.29455i
$146$		0			0
$147$	2.08378	+	11.8177i	0.171867	+	0.974707i
$148$	−0.694593	+	3.93923i	−0.0570952	+	0.323803i
$149$	−19.7335	−	7.18242i	−1.61663	−	0.588407i	−0.633898	−	0.773416i	$-0.718546\pi$
$149$	−19.7335	−	7.18242i	−1.61663	−	0.588407i	−0.982737	+	0.185009i	$0.940768\pi$
$150$		0			0
$151$	−10.0000			−0.813788			−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000			−0.813788			−0.406894	+	0.913475i	$0.633388\pi$
$152$		0			0
$153$	−3.00000			−0.242536
$154$		0			0
$155$	11.2763	+	4.10424i	0.905735	+	0.329661i
$156$	−2.77837	+	15.7569i	−0.222448	+	1.26156i
$157$	2.43107	+	13.7873i	0.194021	+	1.10035i	0.913806	+	0.406150i	$0.133129\pi$
$157$	2.43107	+	13.7873i	0.194021	+	1.10035i	−0.719785	+	0.694197i	$0.755760\pi$
$158$		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
$165$	16.9145	−	6.15636i	1.31679	−	0.479272i
$166$		0			0
$167$	−3.12567	+	17.7265i	−0.241871	+	1.37172i	0.585776	+	0.810473i	$0.300790\pi$
$167$	−3.12567	+	17.7265i	−0.241871	+	1.37172i	−0.827648	+	0.561248i	$0.810321\pi$
$168$		0			0
$169$	2.29813	−	1.92836i	0.176779	−	0.148336i
$170$		0			0
$171$		0			0
$172$	2.00000			0.152499
$173$	−13.7888	+	11.5702i	−1.04834	+	0.879664i	−0.992918	−	0.118799i	$-0.962096\pi$
$173$	−13.7888	+	11.5702i	−1.04834	+	0.879664i	−0.0554247	+	0.998463i	$0.517651\pi$
$174$		0			0
$175$	−0.694593	+	3.93923i	−0.0525063	+	0.297778i
$176$	2.08378	+	11.8177i	0.157071	+	0.890792i
$177$	−11.2763	+	4.10424i	−0.847579	+	0.308494i
$178$		0			0
$179$	9.00000	+	15.5885i	0.672692	+	1.16514i	0.977138	+	0.212607i	$0.0681952\pi$
$179$	9.00000	+	15.5885i	0.672692	+	1.16514i	−0.304446	+	0.952529i	$0.598471\pi$
$180$	−4.59627	−	3.85673i	−0.342585	−	0.287463i
$181$	1.53209	+	1.28558i	0.113879	+	0.0955561i	0.697949	−	0.716147i	$-0.254096\pi$
$181$	1.53209	+	1.28558i	0.113879	+	0.0955561i	−0.584070	+	0.811703i	$0.698541\pi$
$182$		0			0
$183$	−1.00000	+	1.73205i	−0.0739221	+	0.128037i
$184$		0			0
$185$	1.04189	+	5.90885i	0.0766012	+	0.434427i
$186$		0			0
$187$	8.45723	+	3.07818i	0.618454	+	0.225099i
$188$	4.59627	−	3.85673i	0.335217	−	0.281281i
$189$	−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	$0.465384\pi$
$192$	12.2567	−	10.2846i	0.884552	−	0.742227i
$193$	3.75877	+	1.36808i	0.270562	+	0.0984766i	0.473738	−	0.880666i	$-0.342904\pi$
$193$	3.75877	+	1.36808i	0.270562	+	0.0984766i	−0.203176	+	0.979142i	$0.565126\pi$
$194$		0			0
$195$	4.16756	+	23.6354i	0.298445	+	1.69257i
$196$	−11.2763	+	4.10424i	−0.805451	+	0.293160i
$197$	−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
$199$	8.42649	+	7.07066i	0.597338	+	0.501226i	0.890589	−	0.454809i	$-0.150293\pi$
$199$	8.42649	+	7.07066i	0.597338	+	0.501226i	−0.293251	+	0.956036i	$0.594737\pi$
$200$		0			0
$201$	−4.00000	−	6.92820i	−0.282138	−	0.488678i
$202$		0			0
$203$	5.63816	−	2.05212i	0.395721	−	0.144031i
$204$	−2.08378	−	11.8177i	−0.145894	−	0.827404i
$205$	−3.12567	+	17.7265i	−0.218306	+	1.23808i
$206$		0			0
$207$		0			0
$208$	−16.0000			−1.10940
$209$		0			0
$210$		0			0
$211$	10.7246	−	8.99903i	0.738313	−	0.619519i	−0.194071	−	0.980988i	$-0.562169\pi$
$211$	10.7246	−	8.99903i	0.738313	−	0.619519i	0.932384	+	0.361469i	$0.117725\pi$
$212$	22.5526	+	8.20848i	1.54892	+	0.563761i
$213$	−2.08378	+	11.8177i	−0.142778	+	0.809735i
$214$		0			0
$215$	2.81908	−	1.02606i	0.192260	−	0.0699767i
$216$		0			0
$217$	−2.00000	−	3.46410i	−0.135769	−	0.235159i
$218$		0			0
$219$	10.7246	+	8.99903i	0.724703	+	0.608098i
$220$	9.00000	+	15.5885i	0.606780	+	1.05097i
$221$	−6.00000	+	10.3923i	−0.403604	+	0.699062i
$222$		0			0
$223$	−1.73648	−	9.84808i	−0.116283	−	0.659476i	−0.986107	−	0.166113i	$-0.946878\pi$
$223$	−1.73648	−	9.84808i	−0.116283	−	0.659476i	0.869823	−	0.493363i	$-0.164233\pi$
$224$		0			0
$225$	−3.75877	−	1.36808i	−0.250585	−	0.0912054i
$226$		0			0
$227$	12.0000			0.796468			0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000			0.796468			0.398234	+	0.917284i	$0.369623\pi$
$228$		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
$231$	−5.63816	−	2.05212i	−0.370963	−	0.135020i
$232$		0			0
$233$	−3.64661	−	20.6810i	−0.238897	−	1.35485i	−0.834248	−	0.551389i	$-0.814098\pi$
$233$	−3.64661	−	20.6810i	−0.238897	−	1.35485i	0.595351	−	0.803466i	$-0.297013\pi$
$234$		0			0
$235$	4.50000	−	7.79423i	0.293548	−	0.508439i
$236$	−6.00000	−	10.3923i	−0.390567	−	0.676481i
$237$	−12.2567	−	10.2846i	−0.796159	−	0.668057i
$238$		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
$241$	9.39693	−	3.42020i	0.605309	−	0.220315i	−0.0211403	−	0.999777i	$-0.506730\pi$
$241$	9.39693	−	3.42020i	0.605309	−	0.220315i	0.626450	+	0.779462i	$0.284507\pi$
$242$		0			0
$243$	1.73648	−	9.84808i	0.111395	−	0.631754i
$244$	−1.87939	−	0.684040i	−0.120315	−	0.0437912i
$245$	−13.7888	+	11.5702i	−0.880934	+	0.739191i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−18.3851	+	15.4269i	−1.16511	+	0.977640i
$250$		0			0
$251$	3.64661	−	20.6810i	0.230172	−	1.30537i	−0.622375	−	0.782720i	$-0.713832\pi$
$251$	3.64661	−	20.6810i	0.230172	−	1.30537i	0.852547	−	0.522651i	$-0.175057\pi$
$252$	0.347296	+	1.96962i	0.0218776	+	0.124074i
$253$		0			0
$254$		0			0
$255$	−9.00000	−	15.5885i	−0.563602	−	0.976187i
$256$	12.2567	+	10.2846i	0.766044	+	0.642788i
$257$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$257$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$258$		0			0
$259$	1.00000	−	1.73205i	0.0621370	−	0.107624i
$260$	−22.5526	+	8.20848i	−1.39865	+	0.509069i
$261$	1.04189	+	5.90885i	0.0644913	+	0.365748i
$262$		0			0
$263$	−8.45723	−	3.07818i	−0.521495	−	0.189809i	0.0678416	−	0.997696i	$-0.478389\pi$
$263$	−8.45723	−	3.07818i	−0.521495	−	0.189809i	−0.589337	+	0.807887i	$0.700611\pi$
$264$		0			0
$265$	36.0000			2.21146
$266$		0			0
$267$	−24.0000			−1.46878
$268$	6.12836	−	5.14230i	0.374349	−	0.314116i
$269$	−22.5526	−	8.20848i	−1.37506	−	0.500480i	−0.454381	−	0.890807i	$-0.650140\pi$
$269$	−22.5526	−	8.20848i	−1.37506	−	0.500480i	−0.920676	+	0.390327i	$0.872362\pi$
$270$		0			0
$271$	−2.77837	−	15.7569i	−0.168774	−	0.957165i	−0.945087	−	0.326818i	$-0.894024\pi$
$271$	−2.77837	−	15.7569i	−0.168774	−	0.957165i	0.776313	−	0.630347i	$-0.217087\pi$
$272$	11.2763	−	4.10424i	0.683727	−	0.248856i
$273$	4.00000	−	6.92820i	0.242091	−	0.419314i
$274$		0			0
$275$	9.19253	+	7.71345i	0.554331	+	0.465139i
$276$		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
$279$	3.75877	−	1.36808i	0.225032	−	0.0819048i
$280$		0			0
$281$	1.04189	−	5.90885i	0.0621539	−	0.352492i	−0.937832	−	0.347091i	$-0.887170\pi$
$281$	1.04189	−	5.90885i	0.0621539	−	0.352492i	0.999985	−	0.00540141i	$-0.00171933\pi$
$282$		0			0
$283$	−9.95858	+	8.35624i	−0.591976	+	0.496727i	−0.888855	−	0.458188i	$-0.848499\pi$
$283$	−9.95858	+	8.35624i	−0.591976	+	0.496727i	0.296879	+	0.954915i	$0.404054\pi$
$284$	−12.0000			−0.712069
$285$		0			0
$286$		0			0
$287$	4.59627	−	3.85673i	0.271309	−	0.227655i
$288$		0			0
$289$	−1.38919	+	7.87846i	−0.0817168	+	0.463439i
$290$		0			0
$291$	15.0351	−	5.47232i	0.881372	−	0.320793i
$292$	−7.00000	+	12.1244i	−0.409644	+	0.709524i
$293$	6.00000	+	10.3923i	0.350524	+	0.607125i	0.986341	−	0.164714i	$-0.0526703\pi$
$293$	6.00000	+	10.3923i	0.350524	+	0.607125i	−0.635818	+	0.771839i	$0.719337\pi$
$294$		0			0
$295$	−13.7888	−	11.5702i	−0.802815	−	0.673642i
$296$		0			0
$297$	−6.00000	+	10.3923i	−0.348155	+	0.603023i
$298$		0			0
$299$		0			0
$300$	2.77837	−	15.7569i	0.160409	−	0.909726i
$301$	−0.939693	−	0.342020i	−0.0541630	−	0.0197137i
$302$		0			0
$303$	−12.0000			−0.689382
$304$		0			0
$305$	−3.00000			−0.171780
$306$		0			0
$307$	−18.7939	−	6.84040i	−1.07262	−	0.390402i	−0.255465	−	0.966818i	$-0.582229\pi$
$307$	−18.7939	−	6.84040i	−1.07262	−	0.390402i	−0.817157	+	0.576416i	$0.804451\pi$
$308$	1.04189	−	5.90885i	0.0593671	−	0.336688i
$309$	−4.86215	−	27.5746i	−0.276598	−	1.56867i
$310$		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
$313$	−7.66044	−	6.42788i	−0.432994	−	0.363325i	0.400086	−	0.916478i	$-0.368980\pi$
$313$	−7.66044	−	6.42788i	−0.432994	−	0.363325i	−0.833080	+	0.553153i	$0.813425\pi$
$314$		0			0
$315$	1.50000	+	2.59808i	0.0845154	+	0.146385i
$316$	8.00000	−	13.8564i	0.450035	−	0.779484i
$317$	−5.63816	+	2.05212i	−0.316670	+	0.115259i	−0.495465	−	0.868628i	$-0.665002\pi$
$317$	−5.63816	+	2.05212i	−0.316670	+	0.115259i	0.178795	+	0.983886i	$0.442780\pi$
$318$		0			0
$319$	3.12567	−	17.7265i	0.175004	−	0.992496i
$320$	22.5526	+	8.20848i	1.26073	+	0.458868i
$321$	27.5776	−	23.1404i	1.53923	−	1.29157i
$322$		0			0
$323$		0			0
$324$	22.0000			1.22222
$325$	−12.2567	+	10.2846i	−0.679880	+	0.570487i
$326$		0			0
$327$	5.55674	−	31.5138i	0.307289	−	1.74272i
$328$		0			0
$329$	−2.81908	+	1.02606i	−0.155421	+	0.0565685i
$330$		0			0
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	0.937829	+	0.347097i	$0.112833\pi$
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	−0.168320	+	0.985732i	$0.553834\pi$
$332$	−18.3851	−	15.4269i	−1.00901	−	0.846661i
$333$	1.53209	+	1.28558i	0.0839580	+	0.0704491i
$334$		0			0
$335$	6.00000	−	10.3923i	0.327815	−	0.567792i
$336$	−7.51754	+	2.73616i	−0.410115	+	0.149270i
$337$	5.55674	+	31.5138i	0.302695	+	1.71667i	0.634161	+	0.773201i	$0.281346\pi$
$337$	5.55674	+	31.5138i	0.302695	+	1.71667i	−0.331466	+	0.943467i	$0.607543\pi$
$338$		0			0
$339$	11.2763	+	4.10424i	0.612445	+	0.222912i
$340$	13.7888	−	11.5702i	0.747803	−	0.627481i
$341$	−12.0000			−0.649836
$342$		0			0
$343$	13.0000			0.701934
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3.64661	+	20.6810i	0.195760	+	1.11021i	0.911332	+	0.411673i	$0.135055\pi$
$347$	3.64661	+	20.6810i	0.195760	+	1.11021i	−0.715571	+	0.698540i	$0.753834\pi$
$348$	−22.5526	+	8.20848i	−1.20895	+	0.440021i
$349$	−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
$351$	−12.2567	−	10.2846i	−0.654215	−	0.548951i
$352$		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
$355$	−16.9145	+	6.15636i	−0.897727	+	0.326746i
$356$	−4.16756	−	23.6354i	−0.220880	−	1.25267i
$357$	−1.04189	+	5.90885i	−0.0551426	+	0.312729i
$358$		0			0
$359$	11.4907	−	9.64181i	0.606454	−	0.508875i	−0.287059	−	0.957913i	$-0.592677\pi$
$359$	11.4907	−	9.64181i	0.606454	−	0.508875i	0.893513	+	0.449037i	$0.148233\pi$
$360$		0			0
$361$		0			0
$362$		0			0
$363$	3.06418	−	2.57115i	0.160828	−	0.134950i
$364$	7.51754	+	2.73616i	0.394026	+	0.143414i
$365$	−3.64661	+	20.6810i	−0.190872	+	1.08249i
$366$		0			0
$367$	−7.51754	+	2.73616i	−0.392412	+	0.142826i	−0.530688	−	0.847567i	$-0.678066\pi$
$367$	−7.51754	+	2.73616i	−0.392412	+	0.142826i	0.138275	+	0.990394i	$0.455844\pi$
$368$		0			0
$369$	3.00000	+	5.19615i	0.156174	+	0.270501i
$370$		0			0
$371$	−9.19253	−	7.71345i	−0.477253	−	0.400462i
$372$	8.00000	+	13.8564i	0.414781	+	0.718421i
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	−0.809591	−	0.586994i	$-0.800311\pi$
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	0.913147	+	0.407630i	$0.133645\pi$
$374$		0			0
$375$	1.04189	+	5.90885i	0.0538029	+	0.305132i
$376$		0			0
$377$	22.5526	+	8.20848i	1.16152	+	0.422758i
$378$		0			0
$379$	−34.0000			−1.74646			−0.873231	−	0.487306i	$-0.837980\pi$
$379$	−34.0000			−1.74646			−0.873231	+	0.487306i	$0.837980\pi$
$380$		0			0
$381$	−4.00000			−0.204926
$382$		0			0
$383$	−11.2763	−	4.10424i	−0.576193	−	0.209717i	0.0374532	−	0.999298i	$-0.488075\pi$
$383$	−11.2763	−	4.10424i	−0.576193	−	0.209717i	−0.613646	+	0.789581i	$0.710298\pi$
$384$		0			0
$385$	−1.56283	−	8.86327i	−0.0796494	−	0.451714i
$386$		0			0
$387$	0.500000	−	0.866025i	0.0254164	−	0.0440225i
$388$	8.00000	+	13.8564i	0.406138	+	0.703452i
$389$	11.4907	+	9.64181i	0.582600	+	0.488859i	0.885800	−	0.464068i	$-0.153611\pi$
$389$	11.4907	+	9.64181i	0.582600	+	0.488859i	−0.303200	+	0.952927i	$0.598055\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−28.1908	+	10.2606i	−1.42204	+	0.517579i
$394$		0			0
$395$	4.16756	−	23.6354i	0.209693	−	1.18923i
$396$	5.63816	+	2.05212i	0.283328	+	0.103123i
$397$	−5.36231	+	4.49951i	−0.269127	+	0.225824i	−0.767356	−	0.641221i	$-0.778428\pi$
$397$	−5.36231	+	4.49951i	−0.269127	+	0.225824i	0.498230	+	0.867045i	$0.333984\pi$
$398$		0			0
$399$		0			0
$400$	16.0000			0.800000
$401$	9.19253	−	7.71345i	0.459053	−	0.385191i	−0.383729	−	0.923446i	$-0.625360\pi$
$401$	9.19253	−	7.71345i	0.459053	−	0.385191i	0.842783	+	0.538254i	$0.180916\pi$
$402$		0			0
$403$	2.77837	−	15.7569i	0.138401	−	0.784908i
$404$	−2.08378	−	11.8177i	−0.103672	−	0.587952i
$405$	31.0099	−	11.2867i	1.54089	−	0.560839i
$406$		0			0
$407$	−3.00000	−	5.19615i	−0.148704	−	0.257564i
$408$		0			0
$409$	−3.06418	−	2.57115i	−0.151514	−	0.127135i	0.563880	−	0.825857i	$-0.309308\pi$
$409$	−3.06418	−	2.57115i	−0.151514	−	0.127135i	−0.715394	+	0.698722i	$0.753753\pi$
$410$		0			0
$411$	−3.00000	+	5.19615i	−0.147979	+	0.256307i
$412$	26.3114	−	9.57656i	1.29627	−	0.471803i
$413$	1.04189	+	5.90885i	0.0512680	+	0.290755i
$414$		0			0
$415$	−33.8289	−	12.3127i	−1.66060	−	0.604408i
$416$		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	$0.594693\pi$
$420$	−9.19253	+	7.71345i	−0.448550	+	0.376378i
$421$	−7.51754	−	2.73616i	−0.366383	−	0.133352i	0.152267	−	0.988339i	$-0.451343\pi$
$421$	−7.51754	−	2.73616i	−0.366383	−	0.133352i	−0.518649	+	0.854987i	$0.673565\pi$
$422$		0			0
$423$	−0.520945	−	2.95442i	−0.0253292	−	0.143649i
$424$		0			0
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		0			0
$427$	0.766044	+	0.642788i	0.0370715	+	0.0311067i
$428$	27.5776	+	23.1404i	1.33301	+	1.11853i
$429$	−12.0000	−	20.7846i	−0.579365	−	1.00349i
$430$		0			0
$431$	22.5526	−	8.20848i	1.08632	−	0.395389i	0.264065	−	0.964505i	$-0.414937\pi$
$431$	22.5526	−	8.20848i	1.08632	−	0.395389i	0.822257	+	0.569116i	$0.192715\pi$
$432$	2.77837	+	15.7569i	0.133674	+	0.758105i
$433$	0.347296	−	1.96962i	0.0166900	−	0.0946537i	−0.975325	−	0.220774i	$-0.929142\pi$
$433$	0.347296	−	1.96962i	0.0166900	−	0.0946537i	0.992015	+	0.126121i	$0.0402527\pi$
$434$		0			0
$435$	−27.5776	+	23.1404i	−1.32224	+	1.10950i
$436$	32.0000			1.53252
$437$		0			0
$438$		0			0
$439$	−7.66044	+	6.42788i	−0.365613	+	0.306786i	−0.807023	−	0.590520i	$-0.798923\pi$
$439$	−7.66044	+	6.42788i	−0.365613	+	0.306786i	0.441410	+	0.897305i	$0.354478\pi$
$440$		0			0
$441$	−1.04189	+	5.90885i	−0.0496138	+	0.281374i
$442$		0			0
$443$	2.81908	−	1.02606i	0.133938	−	0.0487496i	−0.274181	−	0.961678i	$-0.588407\pi$
$443$	2.81908	−	1.02606i	0.133938	−	0.0487496i	0.408120	+	0.912928i	$0.366185\pi$
$444$	−4.00000	+	6.92820i	−0.189832	+	0.328798i
$445$	−18.0000	−	31.1769i	−0.853282	−	1.47793i
$446$		0			0
$447$	−32.1739	−	26.9971i	−1.52177	−	1.27692i
$448$	−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
$451$	−3.12567	−	17.7265i	−0.147182	−	0.834710i
$452$	−2.08378	+	11.8177i	−0.0980127	+	0.555858i
$453$	−18.7939	−	6.84040i	−0.883012	−	0.321390i
$454$		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
$459$	11.2763	+	4.10424i	0.526333	+	0.191570i
$460$		0			0
$461$	1.56283	+	8.86327i	0.0727884	+	0.412804i	0.999330	+	0.0366103i	$0.0116560\pi$
$461$	1.56283	+	8.86327i	0.0727884	+	0.412804i	−0.926541	+	0.376193i	$0.877233\pi$
$462$		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
$465$	18.3851	+	15.4269i	0.852587	+	0.715405i
$466$		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
$469$	−3.75877	+	1.36808i	−0.173564	+	0.0631721i
$470$		0			0
$471$	−4.86215	+	27.5746i	−0.224036	+	1.27057i
$472$		0			0
$473$	−2.29813	+	1.92836i	−0.105668	+	0.0886662i
$474$		0			0
$475$		0			0
$476$	−6.00000			−0.275010
$477$	9.19253	−	7.71345i	0.420897	−	0.353175i
$478$		0			0
$479$	−2.08378	+	11.8177i	−0.0952103	+	0.539964i	0.899472	+	0.436977i	$0.143951\pi$
$479$	−2.08378	+	11.8177i	−0.0952103	+	0.539964i	−0.994683	+	0.102987i	$0.967160\pi$
$480$		0			0
$481$	7.51754	−	2.73616i	0.342770	−	0.124758i
$482$		0			0
$483$		0			0
$484$	3.06418	+	2.57115i	0.139281	+	0.116870i
$485$	18.3851	+	15.4269i	0.834823	+	0.700500i
$486$		0			0
$487$	−1.00000	+	1.73205i	−0.0453143	+	0.0784867i	−0.887793	−	0.460243i	$-0.847762\pi$
$487$	−1.00000	+	1.73205i	−0.0453143	+	0.0784867i	0.842479	+	0.538730i	$0.181096\pi$
$488$		0			0
$489$	−6.94593	−	39.3923i	−0.314106	−	1.78138i
$490$		0			0
$491$	−11.2763	−	4.10424i	−0.508893	−	0.185222i	0.0747967	−	0.997199i	$-0.476169\pi$
$491$	−11.2763	−	4.10424i	−0.508893	−	0.185222i	−0.583689	+	0.811977i	$0.698391\pi$
$492$	−18.3851	+	15.4269i	−0.828863	+	0.695498i
$493$	−18.0000			−0.810679
$494$		0			0
$495$	9.00000			0.404520
$496$	−12.2567	+	10.2846i	−0.550343	+	0.461792i
$497$	5.63816	+	2.05212i	0.252906	+	0.0920502i
$498$		0			0
$499$	0.868241	+	4.92404i	0.0388678	+	0.220430i	0.998055	−	0.0623422i	$-0.0198570\pi$
$499$	0.868241	+	4.92404i	0.0388678	+	0.220430i	−0.959187	+	0.282772i	$0.908746\pi$
$500$	−5.63816	+	2.05212i	−0.252146	+	0.0917736i
$501$	−18.0000	+	31.1769i	−0.804181	+	1.39288i
$502$		0			0
$503$	9.19253	+	7.71345i	0.409875	+	0.343926i	0.824296	−	0.566160i	$-0.191571\pi$
$503$	9.19253	+	7.71345i	0.409875	+	0.343926i	−0.414421	+	0.910085i	$0.636016\pi$
$504$		0			0
$505$	−9.00000	−	15.5885i	−0.400495	−	0.693677i
$506$		0			0
$507$	5.63816	−	2.05212i	0.250399	−	0.0911379i
$508$	−0.694593	−	3.93923i	−0.0308176	−	0.174775i
$509$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$509$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$510$		0			0
$511$	5.36231	−	4.49951i	0.237215	−	0.199047i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	32.1739	−	26.9971i	1.41775	−	1.18963i
$516$	3.75877	+	1.36808i	0.165471	+	0.0602264i
$517$	−1.56283	+	8.86327i	−0.0687333	+	0.389806i
$518$		0			0
$519$	−33.8289	+	12.3127i	−1.48493	+	0.540469i
$520$		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
$523$	29.1097	+	24.4259i	1.27288	+	1.06807i	0.994184	+	0.107691i	$0.0343458\pi$
$523$	29.1097	+	24.4259i	1.27288	+	1.06807i	0.278693	+	0.960380i	$0.410099\pi$
$524$	−15.0000	−	25.9808i	−0.655278	−	1.13497i
$525$	−4.00000	+	6.92820i	−0.174574	+	0.302372i
$526$		0			0
$527$	2.08378	+	11.8177i	0.0907708	+	0.514787i
$528$	−4.16756	+	23.6354i	−0.181370	+	1.02860i
$529$	21.6129	+	7.86646i	0.939693	+	0.342020i
$530$		0			0
$531$	−6.00000			−0.260378
$532$		0			0
$533$	24.0000			1.03956
$534$		0			0
$535$	50.7434	+	18.4691i	2.19383	+	0.798488i
$536$		0			0
$537$	6.25133	+	35.4531i	0.269765	+	1.52991i
$538$		0			0
$539$	9.00000	−	15.5885i	0.387657	−	0.671442i
$540$	12.0000	+	20.7846i	0.516398	+	0.894427i
$541$	−19.1511	−	16.0697i	−0.823371	−	0.690890i	0.130388	−	0.991463i	$-0.458378\pi$
$541$	−19.1511	−	16.0697i	−0.823371	−	0.690890i	−0.953759	+	0.300573i	$0.902822\pi$
$542$		0			0
$543$	2.00000	+	3.46410i	0.0858282	+	0.148659i
$544$		0			0
$545$	45.1052	−	16.4170i	1.93210	−	0.703226i
$546$		0			0
$547$	−4.86215	+	27.5746i	−0.207890	+	1.17901i	0.684936	+	0.728604i	$0.259830\pi$
$547$	−4.86215	+	27.5746i	−0.207890	+	1.17901i	−0.892826	+	0.450402i	$0.851281\pi$
$548$	−5.63816	−	2.05212i	−0.240850	−	0.0876623i
$549$	−0.766044	+	0.642788i	−0.0326940	+	0.0274335i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−6.12836	+	5.14230i	−0.260604	+	0.218673i
$554$		0			0
$555$	−2.08378	+	11.8177i	−0.0884515	+	0.501633i
$556$	4.51485	+	25.6050i	0.191472	+	1.08589i
$557$	−19.7335	+	7.18242i	−0.836137	+	0.304329i	−0.724375	−	0.689406i	$-0.757872\pi$
$557$	−19.7335	+	7.18242i	−0.836137	+	0.304329i	−0.111762	+	0.993735i	$0.535649\pi$
$558$		0			0
$559$	−2.00000	−	3.46410i	−0.0845910	−	0.146516i
$560$	−9.19253	−	7.71345i	−0.388455	−	0.325953i
$561$	13.7888	+	11.5702i	0.582164	+	0.488493i
$562$		0			0
$563$	−3.00000	+	5.19615i	−0.126435	+	0.218992i	−0.922293	−	0.386492i	$-0.873687\pi$
$563$	−3.00000	+	5.19615i	−0.126435	+	0.218992i	0.795858	+	0.605483i	$0.207020\pi$
$564$	11.2763	−	4.10424i	0.474818	−	0.172820i
$565$	3.12567	+	17.7265i	0.131498	+	0.745761i
$566$		0			0
$567$	−10.3366	−	3.76222i	−0.434097	−	0.157998i
$568$		0			0
$569$	−24.0000			−1.00613			−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000			−1.00613			−0.503066	+	0.864248i	$0.667795\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$	18.3851	−	15.4269i	0.768718	−	0.645031i
$573$	5.63816	+	2.05212i	0.235537	+	0.0857286i
$574$		0			0
$575$		0			0
$576$	7.51754	−	2.73616i	0.313231	−	0.114007i
$577$	−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
$579$	6.12836	+	5.14230i	0.254686	+	0.213707i
$580$	−27.5776	−	23.1404i	−1.14510	−	0.960851i
$581$	6.00000	+	10.3923i	0.248922	+	0.431145i
$582$		0			0
$583$	−33.8289	+	12.3127i	−1.40105	+	0.509941i
$584$		0			0
$585$	−2.08378	+	11.8177i	−0.0861536	+	0.488601i
$586$		0			0
$587$	34.4720	−	28.9254i	1.42281	−	1.19388i	0.472998	−	0.881063i	$-0.343172\pi$
$587$	34.4720	−	28.9254i	1.42281	−	1.19388i	0.949813	−	0.312818i	$-0.101273\pi$
$588$	−24.0000			−0.989743
$589$		0			0
$590$		0			0
$591$	−27.5776	+	23.1404i	−1.13439	+	0.951867i
$592$	−7.51754	−	2.73616i	−0.308969	−	0.112456i
$593$	−7.29322	+	41.3619i	−0.299497	+	1.69853i	0.348844	+	0.937181i	$0.386574\pi$
$593$	−7.29322	+	41.3619i	−0.299497	+	1.69853i	−0.648341	+	0.761350i	$0.724537\pi$
$594$		0			0
$595$	−8.45723	+	3.07818i	−0.346713	+	0.126193i
$596$	21.0000	−	36.3731i	0.860194	−	1.48990i
$597$	11.0000	+	19.0526i	0.450200	+	0.779769i
$598$		0			0
$599$	−27.5776	−	23.1404i	−1.12679	−	0.945489i	−0.127863	−	0.991792i	$-0.540812\pi$
$599$	−27.5776	−	23.1404i	−1.12679	−	0.945489i	−0.998927	+	0.0463026i	$0.985256\pi$
$600$		0			0
$601$	−13.0000	+	22.5167i	−0.530281	+	0.918474i	0.469095	+	0.883148i	$0.344580\pi$
$601$	−13.0000	+	22.5167i	−0.530281	+	0.918474i	−0.999376	+	0.0353259i	$0.988753\pi$
$602$		0			0
$603$	−0.694593	−	3.93923i	−0.0282860	−	0.160418i
$604$	3.47296	−	19.6962i	0.141313	−	0.801425i
$605$	5.63816	+	2.05212i	0.229224	+	0.0834306i
$606$		0			0
$607$	32.0000			1.29884			0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000			1.29884			0.649420	+	0.760430i	$0.275012\pi$
$608$		0			0
$609$	12.0000			0.486265
$610$		0			0
$611$	−11.2763	−	4.10424i	−0.456191	−	0.166040i
$612$	1.04189	−	5.90885i	0.0421159	−	0.238851i
$613$	5.03580	+	28.5594i	0.203394	+	1.15350i	0.899947	+	0.435999i	$0.143605\pi$
$613$	5.03580	+	28.5594i	0.203394	+	1.15350i	−0.696553	+	0.717505i	$0.745284\pi$
$614$		0			0
$615$	−18.0000	+	31.1769i	−0.725830	+	1.25717i
$616$		0			0
$617$	6.89440	+	5.78509i	0.277558	+	0.232899i	0.770930	−	0.636919i	$-0.219792\pi$
$617$	6.89440	+	5.78509i	0.277558	+	0.232899i	−0.493372	+	0.869818i	$0.664236\pi$
$618$		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
$623$	−2.08378	+	11.8177i	−0.0834848	+	0.473466i
$624$	−30.0702	−	10.9446i	−1.20377	−	0.438136i
$625$	−22.2153	+	18.6408i	−0.888612	+	0.745634i
$626$		0			0
$627$		0			0
$628$	−28.0000			−1.11732
$629$	−4.59627	+	3.85673i	−0.183265	+	0.153778i
$630$		0			0
$631$	1.91013	−	10.8329i	0.0760411	−	0.431250i	−0.922892	−	0.385060i	$-0.874181\pi$
$631$	1.91013	−	10.8329i	0.0760411	−	0.431250i	0.998933	−	0.0461904i	$-0.0147081\pi$
$632$		0			0
$633$	26.3114	−	9.57656i	1.04578	−	0.380634i
$634$		0			0
$635$	−3.00000	−	5.19615i	−0.119051	−	0.206203i
$636$	36.7701	+	30.8538i	1.45803	+	1.22343i
$637$	18.3851	+	15.4269i	0.728443	+	0.611236i
$638$		0			0
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$		0			0
$641$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$641$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$642$		0			0
$643$	12.2160	+	4.44626i	0.481752	+	0.175343i	0.571469	−	0.820624i	$-0.306374\pi$
$643$	12.2160	+	4.44626i	0.481752	+	0.175343i	−0.0897165	+	0.995967i	$0.528596\pi$
$644$		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
$649$	16.9145	+	6.15636i	0.663951	+	0.241658i
$650$		0			0
$651$	−1.38919	−	7.87846i	−0.0544465	−	0.308781i
$652$	37.5877	−	13.6808i	1.47205	−	0.535782i
$653$	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
$655$	−34.4720	−	28.9254i	−1.34693	−	1.13021i
$656$	−18.3851	−	15.4269i	−0.717816	−	0.602319i
$657$	3.50000	+	6.06218i	0.136548	+	0.236508i
$658$		0			0
$659$	28.1908	−	10.2606i	1.09816	−	0.399696i	0.271520	−	0.962433i	$-0.412474\pi$
$659$	28.1908	−	10.2606i	1.09816	−	0.399696i	0.826636	+	0.562736i	$0.190251\pi$
$660$	6.25133	+	35.4531i	0.243333	+	1.38001i
$661$	5.55674	−	31.5138i	0.216132	−	1.22575i	−0.662799	−	0.748798i	$-0.730632\pi$
$661$	5.55674	−	31.5138i	0.216132	−	1.22575i	0.878931	−	0.476949i	$-0.158257\pi$
$662$		0			0
$663$	−18.3851	+	15.4269i	−0.714017	+	0.599131i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−33.8289	−	12.3127i	−1.30888	−	0.476394i
$669$	3.47296	−	19.6962i	0.134273	−	0.761497i
$670$		0			0
$671$	2.81908	−	1.02606i	0.108829	−	0.0396106i
$672$		0			0
$673$	5.00000	+	8.66025i	0.192736	+	0.333828i	0.946156	−	0.323711i	$-0.104931\pi$
$673$	5.00000	+	8.66025i	0.192736	+	0.333828i	−0.753420	+	0.657539i	$0.771597\pi$
$674$		0			0
$675$	12.2567	+	10.2846i	0.471761	+	0.395855i
$676$	3.00000	+	5.19615i	0.115385	+	0.199852i
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	−0.107772	−	0.994176i	$-0.534372\pi$
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	0.914867	−	0.403755i	$-0.132295\pi$
$678$		0			0
$679$	−1.38919	−	7.87846i	−0.0533120	−	0.302348i
$680$		0			0
$681$	22.5526	+	8.20848i	0.864218	+	0.314550i
$682$		0			0
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$		0			0
$685$	−9.00000			−0.343872
$686$		0			0
$687$	9.39693	+	3.42020i	0.358515	+	0.130489i
$688$	−0.694593	+	3.93923i	−0.0264811	+	0.150182i
$689$	−8.33511	−	47.2708i	−0.317542	−	1.80087i
$690$		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
$693$	−2.29813	−	1.92836i	−0.0872989	−	0.0732524i
$694$		0			0
$695$	19.5000	+	33.7750i	0.739677	+	1.28116i
$696$		0			0
$697$	−16.9145	+	6.15636i	−0.640681	+	0.233189i
$698$		0			0
$699$	7.29322	−	41.3619i	0.275855	−	1.56445i
$700$	−7.51754	−	2.73616i	−0.284136	−	0.103417i
$701$	4.59627	−	3.85673i	0.173599	−	0.145667i	−0.551849	−	0.833944i	$-0.686077\pi$
$701$	4.59627	−	3.85673i	0.173599	−	0.145667i	0.725447	+	0.688278i	$0.241633\pi$
$702$		0			0
$703$		0			0
$704$	−24.0000			−0.904534
$705$	13.7888	−	11.5702i	0.519316	−	0.435758i
$706$		0			0
$707$	−1.04189	+	5.90885i	−0.0391843	+	0.222225i
$708$	−4.16756	−	23.6354i	−0.156626	−	0.888272i
$709$	−24.4320	+	8.89252i	−0.917563	+	0.333966i	−0.757269	−	0.653103i	$-0.773467\pi$
$709$	−24.4320	+	8.89252i	−0.917563	+	0.333966i	−0.160295	+	0.987069i	$0.551244\pi$
$710$		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
$716$	−33.8289	+	12.3127i	−1.26425	+	0.460148i
$717$	−5.20945	−	29.5442i	−0.194550	−	1.10335i
$718$		0			0
$719$	−14.0954	−	5.13030i	−0.525669	−	0.191328i	0.0655343	−	0.997850i	$-0.479125\pi$
$719$	−14.0954	−	5.13030i	−0.525669	−	0.191328i	−0.591204	+	0.806522i	$0.701347\pi$
$720$	9.19253	−	7.71345i	0.342585	−	0.287463i
$721$	−14.0000			−0.521387
$722$		0			0
$723$	20.0000			0.743808
$724$	−3.06418	+	2.57115i	−0.113879	+	0.0955561i
$725$	−22.5526	−	8.20848i	−0.837583	−	0.304855i
$726$		0			0
$727$	−3.29932	−	18.7113i	−0.122365	−	0.693965i	−0.982838	−	0.184470i	$-0.940943\pi$
$727$	−3.29932	−	18.7113i	−0.122365	−	0.693965i	0.860473	−	0.509496i	$-0.170168\pi$
$728$		0			0
$729$	−6.50000	+	11.2583i	−0.240741	+	0.416975i
$730$		0			0
$731$	2.29813	+	1.92836i	0.0849995	+	0.0713231i
$732$	−3.06418	−	2.57115i	−0.113255	−	0.0950325i
$733$	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
$735$	−33.8289	+	12.3127i	−1.24780	+	0.454162i
$736$		0			0
$737$	−2.08378	+	11.8177i	−0.0767570	+	0.435310i
$738$		0			0
$739$	8.42649	−	7.07066i	0.309973	−	0.260099i	−0.474508	−	0.880251i	$-0.657374\pi$
$739$	8.42649	−	7.07066i	0.309973	−	0.260099i	0.784481	+	0.620153i	$0.212929\pi$
$740$	−12.0000			−0.441129
$741$		0			0
$742$		0			0
$743$	−18.3851	+	15.4269i	−0.674483	+	0.565958i	−0.914388	−	0.404838i	$-0.867328\pi$
$743$	−18.3851	+	15.4269i	−0.674483	+	0.565958i	0.239906	+	0.970796i	$0.422883\pi$
$744$		0			0
$745$	10.9398	−	62.0429i	0.400805	−	2.27308i
$746$		0			0
$747$	−11.2763	+	4.10424i	−0.412579	+	0.150166i
$748$	−9.00000	+	15.5885i	−0.329073	+	0.569970i
$749$	−9.00000	−	15.5885i	−0.328853	−	0.569590i
$750$		0			0
$751$	24.5134	+	20.5692i	0.894507	+	0.750581i	0.969109	−	0.246633i	$-0.0793241\pi$
$751$	24.5134	+	20.5692i	0.894507	+	0.750581i	−0.0746016	+	0.997213i	$0.523769\pi$
$752$	6.00000	+	10.3923i	0.218797	+	0.378968i
$753$	21.0000	−	36.3731i	0.765283	−	1.32551i
$754$		0			0
$755$	−5.20945	−	29.5442i	−0.189591	−	1.07522i
$756$	1.38919	−	7.87846i	0.0505242	−	0.286537i
$757$	23.4923	+	8.55050i	0.853843	+	0.310773i	0.731606	−	0.681728i	$-0.238771\pi$
$757$	23.4923	+	8.55050i	0.853843	+	0.310773i	0.122237	+	0.992501i	$0.460993\pi$
$758$		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
$763$	−15.0351	−	5.47232i	−0.544307	−	0.198111i
$764$	−1.04189	+	5.90885i	−0.0376942	+	0.213775i
$765$	−1.56283	−	8.86327i	−0.0565044	−	0.320452i
$766$		0			0
$767$	−12.0000	+	20.7846i	−0.433295	+	0.750489i
$768$	16.0000	+	27.7128i	0.577350	+	1.00000i
$769$	17.6190	+	14.7841i	0.635358	+	0.533129i	0.902589	−	0.430504i	$-0.141664\pi$
$769$	17.6190	+	14.7841i	0.635358	+	0.533129i	−0.267231	+	0.963633i	$0.586109\pi$
$770$		0			0
$771$		0			0
$772$	−4.00000	+	6.92820i	−0.143963	+	0.249351i
$773$	5.63816	−	2.05212i	0.202790	−	0.0738097i	−0.238628	−	0.971111i	$-0.576698\pi$
$773$	5.63816	−	2.05212i	0.202790	−	0.0738097i	0.441418	+	0.897301i	$0.354475\pi$
$774$		0			0
$775$	−2.77837	+	15.7569i	−0.0998020	+	0.566005i
$776$		0			0
$777$	3.06418	−	2.57115i	0.109927	−	0.0922395i
$778$		0			0
$779$		0			0
$780$	−48.0000			−1.71868
$781$	13.7888	−	11.5702i	0.493402	−	0.414013i
$782$		0			0
$783$	4.16756	−	23.6354i	0.148936	−	0.844660i
$784$	−4.16756	−	23.6354i	−0.148841	−	0.844121i
$785$	−39.4671	+	14.3648i	−1.40864	+	0.512703i
$786$		0			0
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	0.899468	−	0.436987i	$-0.143954\pi$
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	−0.828176	+	0.560469i	$0.810621\pi$
$788$	−27.5776	−	23.1404i	−0.982411	−	0.824341i
$789$	−13.7888	−	11.5702i	−0.490894	−	0.411909i
$790$		0			0
$791$	3.00000	−	5.19615i	0.106668	−	0.184754i
$792$		0			0
$793$	0.694593	+	3.93923i	0.0246657	+	0.139886i
$794$		0			0
$795$	67.6579	+	24.6255i	2.39958	+	0.873375i
$796$	−16.8530	+	14.1413i	−0.597338	+	0.501226i
$797$	−12.0000			−0.425062			−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000			−0.425062			−0.212531	+	0.977154i	$0.568171\pi$
$798$		0			0
$799$	9.00000			0.318397
$800$		0			0
$801$	−11.2763	−	4.10424i	−0.398429	−	0.145016i
$802$		0			0
$803$	−3.64661	−	20.6810i	−0.128686	−	0.729815i
$804$	15.0351	−	5.47232i	0.530246	−	0.192994i
$805$		0			0
$806$		0			0
$807$	−36.7701	−	30.8538i	−1.29437	−	1.08611i
$808$		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
$811$	15.0351	−	5.47232i	0.527953	−	0.192159i	−0.0642710	−	0.997932i	$-0.520472\pi$
$811$	15.0351	−	5.47232i	0.527953	−	0.192159i	0.592224	+	0.805773i	$0.298250\pi$
$812$	2.08378	+	11.8177i	0.0731263	+	0.414720i
$813$	5.55674	−	31.5138i	0.194883	−	1.10524i
$814$		0			0
$815$	45.9627	−	38.5673i	1.61000	−	1.35095i
$816$	24.0000			0.840168
$817$		0			0
$818$		0			0
$819$	3.06418	−	2.57115i	0.107071	−	0.0898433i
$820$	−33.8289	−	12.3127i	−1.18136	−	0.429979i
$821$	5.73039	−	32.4987i	0.199992	−	1.13421i	−0.705136	−	0.709072i	$-0.749114\pi$
$821$	5.73039	−	32.4987i	0.199992	−	1.13421i	0.905128	−	0.425139i	$-0.139775\pi$
$822$		0			0
$823$	46.0449	−	16.7590i	1.60503	−	0.584182i	0.624578	−	0.780962i	$-0.285271\pi$
$823$	46.0449	−	16.7590i	1.60503	−	0.584182i	0.980448	+	0.196781i	$0.0630487\pi$
$824$		0			0
$825$	12.0000	+	20.7846i	0.417786	+	0.723627i
$826$		0			0
$827$	9.19253	+	7.71345i	0.319656	+	0.268223i	0.788469	−	0.615074i	$-0.210874\pi$
$827$	9.19253	+	7.71345i	0.319656	+	0.268223i	−0.468814	+	0.883297i	$0.655318\pi$
$828$		0			0
$829$	8.00000	−	13.8564i	0.277851	−	0.481253i	−0.692999	−	0.720938i	$-0.743711\pi$
$829$	8.00000	−	13.8564i	0.277851	−	0.481253i	0.970851	+	0.239686i	$0.0770444\pi$
$830$		0			0
$831$	6.59863	+	37.4227i	0.228904	+	1.29818i
$832$	5.55674	−	31.5138i	0.192645	−	1.09255i
$833$	−16.9145	−	6.15636i	−0.586052	−	0.213305i
$834$		0			0
$835$	−54.0000			−1.86875
$836$		0			0
$837$	−16.0000			−0.553041
$838$		0			0
$839$	−16.9145	−	6.15636i	−0.583952	−	0.212541i	0.0331151	−	0.999452i	$-0.489457\pi$
$839$	−16.9145	−	6.15636i	−0.583952	−	0.212541i	−0.617067	+	0.786910i	$0.711679\pi$
$840$		0			0
$841$	1.21554	+	6.89365i	0.0419151	+	0.237712i
$842$		0			0
$843$	6.00000	−	10.3923i	0.206651	−	0.357930i
$844$	14.0000	+	24.2487i	0.481900	+	0.834675i
$845$	6.89440	+	5.78509i	0.237175	+	0.199013i
$846$		0			0
$847$	−1.00000	−	1.73205i	−0.0343604	−	0.0595140i
$848$	−24.0000	+	41.5692i	−0.824163	+	1.42749i
$849$	−24.4320	+	8.89252i	−0.838504	+	0.305191i
$850$		0			0
$851$		0			0
$852$	−22.5526	−	8.20848i	−0.772640	−	0.281218i
$853$	19.9172	−	16.7125i	0.681950	−	0.572224i	−0.234625	−	0.972086i	$-0.575386\pi$
$853$	19.9172	−	16.7125i	0.681950	−	0.572224i	0.916576	+	0.399862i	$0.130942\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	13.7888	−	11.5702i	0.471016	−	0.395230i	−0.376149	−	0.926559i	$-0.622752\pi$
$857$	13.7888	−	11.5702i	0.471016	−	0.395230i	0.847165	+	0.531330i	$0.178307\pi$
$858$		0			0
$859$	−8.50876	+	48.2556i	−0.290315	+	1.64646i	0.395342	+	0.918534i	$0.370626\pi$
$859$	−8.50876	+	48.2556i	−0.290315	+	1.64646i	−0.685657	+	0.727925i	$0.740485\pi$
$860$	1.04189	+	5.90885i	0.0355281	+	0.201490i
$861$	11.2763	−	4.10424i	0.384296	−	0.139872i
$862$		0			0
$863$	−9.00000	−	15.5885i	−0.306364	−	0.530637i	0.671200	−	0.741276i	$-0.265779\pi$
$863$	−9.00000	−	15.5885i	−0.306364	−	0.530637i	−0.977564	+	0.210639i	$0.932446\pi$
$864$		0			0
$865$	−41.3664	−	34.7105i	−1.40650	−	1.18019i
$866$		0			0
$867$	−8.00000	+	13.8564i	−0.271694	+	0.470588i
$868$	7.51754	−	2.73616i	0.255162	−	0.0928714i
$869$	4.16756	+	23.6354i	0.141375	+	0.801776i
$870$		0			0
$871$	−15.0351	−	5.47232i	−0.509444	−	0.185423i
$872$		0			0
$873$	8.00000			0.270759
$874$		0			0
$875$	3.00000			0.101419
$876$	−21.4492	+	17.9981i	−0.724703	+	0.608098i
$877$	20.6732	+	7.52444i	0.698086	+	0.254082i	0.666593	−	0.745422i	$-0.267752\pi$
$877$	20.6732	+	7.52444i	0.698086	+	0.254082i	0.0314923	+	0.999504i	$0.489974\pi$
$878$		0			0
$879$	4.16756	+	23.6354i	0.140568	+	0.797202i
$880$	−33.8289	+	12.3127i	−1.14037	+	0.415062i
$881$	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
$883$	36.0041	+	30.2110i	1.21163	+	1.01668i	0.999219	+	0.0395021i	$0.0125772\pi$
$883$	36.0041	+	30.2110i	1.21163	+	1.01668i	0.212415	+	0.977180i	$0.431867\pi$
$884$	−18.3851	−	15.4269i	−0.618357	−	0.518863i
$885$	−18.0000	−	31.1769i	−0.605063	−	1.04800i
$886$		0			0
$887$	−16.9145	+	6.15636i	−0.567932	+	0.206710i	−0.609996	−	0.792405i	$-0.708829\pi$
$887$	−16.9145	+	6.15636i	−0.567932	+	0.206710i	0.0420638	+	0.999115i	$0.486607\pi$
$888$		0			0
$889$	−0.347296	+	1.96962i	−0.0116479	+	0.0660588i
$890$		0			0
$891$	−25.2795	+	21.2120i	−0.846894	+	0.710628i
$892$	20.0000			0.669650
$893$		0			0
$894$		0			0
$895$	−41.3664	+	34.7105i	−1.38273	+	1.16025i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	22.5526	−	8.20848i	0.752172	−	0.273768i
$900$	4.00000	−	6.92820i	0.133333	−	0.230940i
$901$	18.0000	+	31.1769i	0.599667	+	1.03865i
$902$		0			0
$903$	−1.53209	−	1.28558i	−0.0509847	−	0.0427813i
$904$		0			0
$905$	−3.00000	+	5.19615i	−0.0997234	+	0.172726i
$906$		0			0
$907$	1.38919	+	7.87846i	0.0461271	+	0.261600i	0.999146	−	0.0413097i	$-0.0131530\pi$
$907$	1.38919	+	7.87846i	0.0461271	+	0.261600i	−0.953019	+	0.302910i	$0.902042\pi$
$908$	−4.16756	+	23.6354i	−0.138305	+	0.784368i
$909$	−5.63816	−	2.05212i	−0.187006	−	0.0680646i
$910$		0			0
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$		0			0
$913$	36.0000			1.19143
$914$		0			0
$915$	−5.63816	−	2.05212i	−0.186392	−	0.0678410i
$916$	−1.73648	+	9.84808i	−0.0573750	+	0.325390i
$917$	2.60472	+	14.7721i	0.0860155	+	0.487818i
$918$		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
$921$	−30.6418	−	25.7115i	−1.00968	−	0.847223i
$922$		0			0
$923$	12.0000	+	20.7846i	0.394985	+	0.684134i
$924$	6.00000	−	10.3923i	0.197386	−	0.341882i
$925$	−7.51754	+	2.73616i	−0.247175	+	0.0899644i
$926$		0			0
$927$	2.43107	−	13.7873i	0.0798470	−	0.452835i
$928$		0			0
$929$	−13.7888	+	11.5702i	−0.452396	+	0.379605i	−0.840324	−	0.542084i	$-0.817635\pi$
$929$	−13.7888	+	11.5702i	−0.452396	+	0.379605i	0.387928	+	0.921690i	$0.373191\pi$
$930$		0			0
$931$		0			0
$932$	42.0000			1.37576
$933$	4.59627	−	3.85673i	0.150475	−	0.126264i
$934$		0			0
$935$	−4.68850	+	26.5898i	−0.153330	+	0.869580i
$936$		0			0
$937$	6.57785	−	2.39414i	0.214889	−	0.0782132i	−0.232333	−	0.972636i	$-0.574636\pi$
$937$	6.57785	−	2.39414i	0.214889	−	0.0782132i	0.447222	+	0.894423i	$0.352414\pi$
$938$		0			0
$939$	−10.0000	−	17.3205i	−0.326338	−	0.565233i
$940$	13.7888	+	11.5702i	0.449741	+	0.377378i
$941$	−13.7888	−	11.5702i	−0.449502	−	0.377177i	0.389749	−	0.920921i	$-0.372562\pi$
$941$	−13.7888	−	11.5702i	−0.449502	−	0.377177i	−0.839251	+	0.543744i	$0.817006\pi$
$942$		0			0
$943$		0			0
$944$	22.5526	−	8.20848i	0.734025	−	0.267163i
$945$	−2.08378	−	11.8177i	−0.0677853	−	0.384430i
$946$		0			0
$947$	33.8289	+	12.3127i	1.09929	+	0.400110i	0.827055	−	0.562120i	$-0.190014\pi$
$947$	33.8289	+	12.3127i	1.09929	+	0.400110i	0.272237	+	0.962230i	$0.412236\pi$
$948$	24.5134	−	20.5692i	0.796159	−	0.668057i
$949$	28.0000			0.908918
$950$		0			0
$951$	−12.0000			−0.389127
$952$		0			0
$953$	45.1052	+	16.4170i	1.46110	+	0.531798i	0.945669	−	0.325132i	$-0.105409\pi$
$953$	45.1052	+	16.4170i	1.46110	+	0.531798i	0.515434	+	0.856930i	$0.327631\pi$
$954$		0			0
$955$	1.56283	+	8.86327i	0.0505721	+	0.286809i
$956$	28.1908	−	10.2606i	0.911755	−	0.331852i
$957$	18.0000	−	31.1769i	0.581857	−	1.00781i
$958$		0			0
$959$	2.29813	+	1.92836i	0.0742106	+	0.0622701i
$960$	36.7701	+	30.8538i	1.18675	+	0.995802i
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$	16.9145	−	6.15636i	0.545061	−	0.198386i
$964$	3.47296	+	19.6962i	0.111857	+	0.634370i
$965$	−2.08378	+	11.8177i	−0.0670792	+	0.380425i
$966$		0			0
$967$	−30.6418	+	25.7115i	−0.985373	+	0.826826i	−0.984891	−	0.173174i	$-0.944598\pi$
$967$	−30.6418	+	25.7115i	−0.985373	+	0.826826i	−0.000481834		1.00000i	$0.500153\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	45.9627	−	38.5673i	1.47501	−	1.23768i	0.563691	−	0.825986i	$-0.309381\pi$
$971$	45.9627	−	38.5673i	1.47501	−	1.23768i	0.911321	−	0.411697i	$-0.135064\pi$
$972$	18.7939	+	6.84040i	0.602813	+	0.219406i
$973$	2.25743	−	12.8025i	0.0723698	−	0.410429i
$974$		0			0
$975$	−30.0702	+	10.9446i	−0.963016	+	0.350509i
$976$	2.00000	−	3.46410i	0.0640184	−	0.110883i
$977$	−12.0000	−	20.7846i	−0.383914	−	0.664959i	0.607704	−	0.794164i	$-0.292091\pi$
$977$	−12.0000	−	20.7846i	−0.383914	−	0.664959i	−0.991618	+	0.129205i	$0.958757\pi$
$978$		0			0
$979$	27.5776	+	23.1404i	0.881384	+	0.739569i
$980$	−18.0000	−	31.1769i	−0.574989	−	0.995910i
$981$	8.00000	−	13.8564i	0.255420	−	0.442401i
$982$		0			0
$983$	−6.25133	−	35.4531i	−0.199387	−	1.13078i	−0.906032	−	0.423210i	$-0.860903\pi$
$983$	−6.25133	−	35.4531i	−0.199387	−	1.13078i	0.706645	−	0.707568i	$-0.250208\pi$
$984$		0			0
$985$	−50.7434	−	18.4691i	−1.61682	−	0.588474i
$986$		0			0
$987$	−6.00000			−0.190982
$988$		0			0
$989$		0			0
$990$		0			0
$991$	31.9495	+	11.6287i	1.01491	+	0.369397i	0.795317	−	0.606194i	$-0.207304\pi$
$991$	31.9495	+	11.6287i	1.01491	+	0.369397i	0.219594	+	0.975591i	$0.429527\pi$
$992$		0			0
$993$	9.72430	+	55.1492i	0.308591	+	1.75011i
$994$		0			0
$995$	−16.5000	+	28.5788i	−0.523085	+	0.906010i
$996$	−24.0000	−	41.5692i	−0.760469	−	1.31717i
$997$	13.0228	+	10.9274i	0.412435	+	0.346074i	0.825276	−	0.564729i	$-0.191019\pi$
$997$	13.0228	+	10.9274i	0.412435	+	0.346074i	−0.412842	+	0.910803i	$0.635464\pi$
$998$		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.d.234.1		6
19.2	odd	18		361.2.e.e.62.1		6
19.3	odd	18		361.2.e.e.54.1		6
19.4	even	9		19.2.a.a.1.1	✓	1
19.5	even	9	inner	361.2.e.d.245.1		6
19.6	even	9		361.2.c.c.292.1		2
19.7	even	3	inner	361.2.e.d.28.1		6
19.8	odd	6		361.2.e.e.99.1		6
19.9	even	9		361.2.c.c.68.1		2
19.10	odd	18		361.2.c.a.68.1		2
19.11	even	3	inner	361.2.e.d.99.1		6
19.12	odd	6		361.2.e.e.28.1		6
19.13	odd	18		361.2.c.a.292.1		2
19.14	odd	18		361.2.e.e.245.1		6
19.15	odd	18		361.2.a.b.1.1		1
19.16	even	9	inner	361.2.e.d.54.1		6
19.17	even	9	inner	361.2.e.d.62.1		6
19.18	odd	2		361.2.e.e.234.1		6
57.23	odd	18		171.2.a.b.1.1		1
57.53	even	18		3249.2.a.d.1.1		1
76.15	even	18		5776.2.a.c.1.1		1
76.23	odd	18		304.2.a.f.1.1		1
95.4	even	18		475.2.a.b.1.1		1
95.23	odd	36		475.2.b.a.324.1		2
95.34	odd	18		9025.2.a.d.1.1		1
95.42	odd	36		475.2.b.a.324.2		2
133.4	even	9		931.2.f.c.324.1		2
133.23	even	9		931.2.f.c.704.1		2
133.61	odd	18		931.2.f.b.704.1		2
133.80	odd	18		931.2.f.b.324.1		2
133.118	odd	18		931.2.a.a.1.1		1
152.61	even	18		1216.2.a.o.1.1		1
152.99	odd	18		1216.2.a.b.1.1		1
209.175	odd	18		2299.2.a.b.1.1		1
228.23	even	18		2736.2.a.c.1.1		1
247.194	even	18		3211.2.a.a.1.1		1
285.194	odd	18		4275.2.a.i.1.1		1
323.118	even	18		5491.2.a.b.1.1		1
380.99	odd	18		7600.2.a.c.1.1		1
399.251	even	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	19.4	even	9
171.2.a.b.1.1		1	57.23	odd	18
304.2.a.f.1.1		1	76.23	odd	18
361.2.a.b.1.1		1	19.15	odd	18
361.2.c.a.68.1		2	19.10	odd	18
361.2.c.a.292.1		2	19.13	odd	18
361.2.c.c.68.1		2	19.9	even	9
361.2.c.c.292.1		2	19.6	even	9
361.2.e.d.28.1		6	19.7	even	3	inner
361.2.e.d.54.1		6	19.16	even	9	inner
361.2.e.d.62.1		6	19.17	even	9	inner
361.2.e.d.99.1		6	19.11	even	3	inner
361.2.e.d.234.1		6	1.1	even	1	trivial
361.2.e.d.245.1		6	19.5	even	9	inner
361.2.e.e.28.1		6	19.12	odd	6
361.2.e.e.54.1		6	19.3	odd	18
361.2.e.e.62.1		6	19.2	odd	18
361.2.e.e.99.1		6	19.8	odd	6
361.2.e.e.234.1		6	19.18	odd	2
361.2.e.e.245.1		6	19.14	odd	18
475.2.a.b.1.1		1	95.4	even	18
475.2.b.a.324.1		2	95.23	odd	36
475.2.b.a.324.2		2	95.42	odd	36
931.2.a.a.1.1		1	133.118	odd	18
931.2.f.b.324.1		2	133.80	odd	18
931.2.f.b.704.1		2	133.61	odd	18
931.2.f.c.324.1		2	133.4	even	9
931.2.f.c.704.1		2	133.23	even	9
1216.2.a.b.1.1		1	152.99	odd	18
1216.2.a.o.1.1		1	152.61	even	18
2299.2.a.b.1.1		1	209.175	odd	18
2736.2.a.c.1.1		1	228.23	even	18
3211.2.a.a.1.1		1	247.194	even	18
3249.2.a.d.1.1		1	57.53	even	18
4275.2.a.i.1.1		1	285.194	odd	18
5491.2.a.b.1.1		1	323.118	even	18
5776.2.a.c.1.1		1	76.15	even	18
7600.2.a.c.1.1		1	380.99	odd	18
8379.2.a.j.1.1		1	399.251	even	18
9025.2.a.d.1.1		1	95.34	odd	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.87939 + 0.684040i) q^{3} +(-0.347296 + 1.96962i) q^{4} +(0.520945 + 2.95442i) q^{5} +(0.500000 - 0.866025i) q^{7} +(0.766044 + 0.642788i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-2.00000 + 3.46410i) q^{12} +(3.75877 - 1.36808i) q^{13} +(-1.04189 + 5.90885i) q^{15} +(-3.75877 - 1.36808i) q^{16} +(-2.29813 + 1.92836i) q^{17} -6.00000 q^{20} +(1.53209 - 1.28558i) q^{21} +(-3.75877 + 1.36808i) q^{25} +(-2.00000 - 3.46410i) q^{27} +(1.53209 + 1.28558i) q^{28} +(4.59627 + 3.85673i) q^{29} +(2.00000 - 3.46410i) q^{31} +(-1.04189 - 5.90885i) q^{33} +(2.81908 + 1.02606i) q^{35} +(-1.53209 + 1.28558i) q^{36} +2.00000 q^{37} +8.00000 q^{39} +(5.63816 + 2.05212i) q^{41} +(-0.173648 - 0.984808i) q^{43} +(5.63816 - 2.05212i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(-2.29813 - 1.92836i) q^{47} +(-6.12836 - 5.14230i) q^{48} +(3.00000 + 5.19615i) q^{49} +(-5.63816 + 2.05212i) q^{51} +(1.38919 + 7.87846i) q^{52} +(2.08378 - 11.8177i) q^{53} +(6.89440 - 5.78509i) q^{55} +(-4.59627 + 3.85673i) q^{59} +(-11.2763 - 4.10424i) q^{60} +(-0.173648 + 0.984808i) q^{61} +(0.939693 - 0.342020i) q^{63} +(4.00000 - 6.92820i) q^{64} +(6.00000 + 10.3923i) q^{65} +(-3.06418 - 2.57115i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(1.04189 + 5.90885i) q^{71} +(6.57785 + 2.39414i) q^{73} -8.00000 q^{75} -3.00000 q^{77} +(-7.51754 - 2.73616i) q^{79} +(2.08378 - 11.8177i) q^{80} +(-1.91013 - 10.8329i) q^{81} +(-6.00000 + 10.3923i) q^{83} +(2.00000 + 3.46410i) q^{84} +(-6.89440 - 5.78509i) q^{85} +(6.00000 + 10.3923i) q^{87} +(-11.2763 + 4.10424i) q^{89} +(0.694593 - 3.93923i) q^{91} +(6.12836 - 5.14230i) q^{93} +(6.12836 - 5.14230i) q^{97} +(0.520945 - 2.95442i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{7} - 9 q^{11} - 12 q^{12} - 36 q^{20} - 12 q^{27} + 12 q^{31} + 12 q^{37} + 48 q^{39} - 9 q^{45} + 18 q^{49} + 24 q^{64} + 36 q^{65} - 18 q^{68} - 48 q^{75} - 18 q^{77} - 36 q^{83} + 12 q^{84}+ \cdots + 36 q^{87}+O(q^{100}) \) 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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