LMFDB - Embedded newform 252.2.j.a.169.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(85,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("252.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.j (of order $3$, degree $2$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			169.2
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	252.169
Dual form			252.2.j.a.85.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.933463 - 1.45899i) q^{3} +(-1.23025 - 2.13086i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-1.25729 + 2.72382i) q^{9} +(-2.32383 + 4.02499i) q^{11} +(-3.55408 - 6.15585i) q^{13} +(-1.96050 + 3.78400i) q^{15} -4.51459 q^{17} +4.32743 q^{19} +(-1.73025 + 0.0789082i) q^{21} +(-2.93346 - 5.08091i) q^{23} +(-0.527042 + 0.912864i) q^{25} +(5.14766 - 0.708209i) q^{27} +(3.48755 - 6.04061i) q^{29} +(3.69076 + 6.39258i) q^{31} +(8.04163 - 0.366739i) q^{33} -2.46050 q^{35} -0.726654 q^{37} +(-5.66372 + 10.9316i) q^{39} +(-0.136673 - 0.236725i) q^{41} +(2.41741 - 4.18708i) q^{43} +(7.35087 - 0.671871i) q^{45} +(-1.83628 + 3.18054i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(4.21420 + 6.58673i) q^{51} +5.05408 q^{53} +11.4356 q^{55} +(-4.03950 - 6.31367i) q^{57} +(-4.56654 - 7.90947i) q^{59} +(6.90856 - 11.9660i) q^{61} +(1.73025 + 2.45076i) q^{63} +(-8.74484 + 15.1465i) q^{65} +(0.663715 + 1.14959i) q^{67} +(-4.67471 + 9.02273i) q^{69} +13.5218 q^{71} -4.32743 q^{73} +(1.82383 - 0.0831759i) q^{75} +(2.32383 + 4.02499i) q^{77} +(-3.21780 + 5.57339i) q^{79} +(-5.83842 - 6.84929i) q^{81} +(-0.742705 + 1.28640i) q^{83} +(5.55408 + 9.61996i) q^{85} +(-12.0687 + 0.550392i) q^{87} +9.83482 q^{89} -7.10817 q^{91} +(5.88151 - 11.3520i) q^{93} +(-5.32383 - 9.22115i) q^{95} +(0.246304 - 0.426611i) q^{97} +(-8.04163 - 11.3903i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{3} - q^{5} + 3 q^{7} + 8 q^{9} - 2 q^{11} - 3 q^{13} + q^{15} + 4 q^{17} + 6 q^{19} - 4 q^{21} - 14 q^{23} + 6 q^{25} + 7 q^{27} - q^{29} + 3 q^{31} + 8 q^{33} - 2 q^{35} - 6 q^{37} - 24 q^{39}+ \cdots - 8 q^{99}+O(q^{100}) $ 6 * q - 2 * q^3 - q^5 + 3 * q^7 + 8 * q^9 - 2 * q^11 - 3 * q^13 + q^15 + 4 * q^17 + 6 * q^19 - 4 * q^21 - 14 * q^23 + 6 * q^25 + 7 * q^27 - q^29 + 3 * q^31 + 8 * q^33 - 2 * q^35 - 6 * q^37 - 24 * q^39 - 3 * q^43 + 23 * q^45 - 21 * q^47 - 3 * q^49 + 5 * q^51 + 12 * q^53 + 12 * q^55 - 37 * q^57 - 31 * q^59 - 6 * q^61 + 4 * q^63 - 15 * q^65 - 6 * q^67 + 5 * q^69 + 34 * q^71 - 6 * q^73 - q^75 + 2 * q^77 + 9 * q^79 + 8 * q^81 - 20 * q^83 + 15 * q^85 - 23 * q^87 + 24 * q^89 - 6 * q^91 - 3 * q^93 - 20 * q^95 + 9 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.933463	−	1.45899i	−0.538935	−	0.842347i
$3$	−0.933463	−	1.45899i	−0.538935	−	0.842347i
$4$		0			0
$5$	−1.23025	−	2.13086i	−0.550186	−	0.952949i	−0.998261	−	0.0589535i	$-0.981224\pi$
$5$	−1.23025	−	2.13086i	−0.550186	−	0.952949i	0.448075	−	0.893996i	$-0.352110\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$		0			0
$9$	−1.25729	+	2.72382i	−0.419098	+	0.907941i
$10$		0			0
$11$	−2.32383	+	4.02499i	−0.700662	+	1.21358i	0.267573	+	0.963538i	$0.413778\pi$
$11$	−2.32383	+	4.02499i	−0.700662	+	1.21358i	−0.968234	+	0.250044i	$0.919555\pi$
$12$		0			0
$13$	−3.55408	−	6.15585i	−0.985726	−	1.70733i	−0.638667	−	0.769484i	$-0.720514\pi$
$13$	−3.55408	−	6.15585i	−0.985726	−	1.70733i	−0.347059	−	0.937843i	$-0.612820\pi$
$14$		0			0
$15$	−1.96050	+	3.78400i	−0.506200	+	0.977025i
$16$		0			0
$17$	−4.51459			−1.09495			−0.547474	−	0.836822i	$-0.684411\pi$
$17$	−4.51459			−1.09495			−0.547474	+	0.836822i	$0.684411\pi$
$18$		0			0
$19$	4.32743			0.992781			0.496390	−	0.868099i	$-0.334658\pi$
$19$	4.32743			0.992781			0.496390	+	0.868099i	$0.334658\pi$
$20$		0			0
$21$	−1.73025	+	0.0789082i	−0.377572	+	0.0172192i
$22$		0			0
$23$	−2.93346	−	5.08091i	−0.611669	−	1.05944i	−0.990959	−	0.134164i	$-0.957165\pi$
$23$	−2.93346	−	5.08091i	−0.611669	−	1.05944i	0.379290	−	0.925278i	$-0.376168\pi$
$24$		0			0
$25$	−0.527042	+	0.912864i	−0.105408	+	0.182573i
$26$		0			0
$27$	5.14766	−	0.708209i	0.990668	−	0.136295i
$28$		0			0
$29$	3.48755	−	6.04061i	0.647621	−	1.12171i	−0.336068	−	0.941838i	$-0.609097\pi$
$29$	3.48755	−	6.04061i	0.647621	−	1.12171i	0.983689	−	0.179875i	$-0.0575694\pi$
$30$		0			0
$31$	3.69076	+	6.39258i	0.662880	+	1.14814i	0.979856	+	0.199708i	$0.0639992\pi$
$31$	3.69076	+	6.39258i	0.662880	+	1.14814i	−0.316976	+	0.948434i	$0.602667\pi$
$32$		0			0
$33$	8.04163	−	0.366739i	1.39987	−	0.0638411i
$34$		0			0
$35$	−2.46050			−0.415901
$36$		0			0
$37$	−0.726654			−0.119461			−0.0597306	−	0.998215i	$-0.519024\pi$
$37$	−0.726654			−0.119461			−0.0597306	+	0.998215i	$0.519024\pi$
$38$		0			0
$39$	−5.66372	+	10.9316i	−0.906920	+	1.75046i
$40$		0			0
$41$	−0.136673	−	0.236725i	−0.0213448	−	0.0369702i	0.855156	−	0.518371i	$-0.173461\pi$
$41$	−0.136673	−	0.236725i	−0.0213448	−	0.0369702i	−0.876500	+	0.481401i	$0.840128\pi$
$42$		0			0
$43$	2.41741	−	4.18708i	0.368652	−	0.638524i	−0.620703	−	0.784046i	$-0.713153\pi$
$43$	2.41741	−	4.18708i	0.368652	−	0.638524i	0.989355	+	0.145522i	$0.0464862\pi$
$44$		0			0
$45$	7.35087	−	0.671871i	1.09580	−	0.100157i
$46$		0			0
$47$	−1.83628	+	3.18054i	−0.267850	+	0.463929i	−0.968306	−	0.249766i	$-0.919646\pi$
$47$	−1.83628	+	3.18054i	−0.267850	+	0.463929i	0.700457	+	0.713695i	$0.252980\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$	4.21420	+	6.58673i	0.590106	+	0.922327i
$52$		0			0
$53$	5.05408			0.694232			0.347116	−	0.937822i	$-0.387161\pi$
$53$	5.05408			0.694232			0.347116	+	0.937822i	$0.387161\pi$
$54$		0			0
$55$	11.4356			1.54198
$56$		0			0
$57$	−4.03950	−	6.31367i	−0.535044	−	0.836266i
$58$		0			0
$59$	−4.56654	−	7.90947i	−0.594513	−	1.02973i	−0.993615	−	0.112820i	$-0.964012\pi$
$59$	−4.56654	−	7.90947i	−0.594513	−	1.02973i	0.399103	−	0.916906i	$-0.369322\pi$
$60$		0			0
$61$	6.90856	−	11.9660i	0.884550	−	1.53209i	0.0383215	−	0.999265i	$-0.487799\pi$
$61$	6.90856	−	11.9660i	0.884550	−	1.53209i	0.846228	−	0.532820i	$-0.178868\pi$
$62$		0			0
$63$	1.73025	+	2.45076i	0.217991	+	0.308767i
$64$		0			0
$65$	−8.74484	+	15.1465i	−1.08466	+	1.87869i
$66$		0			0
$67$	0.663715	+	1.14959i	0.0810857	+	0.140445i	0.903717	−	0.428131i	$-0.140828\pi$
$67$	0.663715	+	1.14959i	0.0810857	+	0.140445i	−0.822631	+	0.568576i	$0.807495\pi$
$68$		0			0
$69$	−4.67471	+	9.02273i	−0.562768	+	1.08621i
$70$		0			0
$71$	13.5218			1.60474			0.802370	−	0.596826i	$-0.203572\pi$
$71$	13.5218			1.60474			0.802370	+	0.596826i	$0.203572\pi$
$72$		0			0
$73$	−4.32743			−0.506487			−0.253244	−	0.967403i	$-0.581497\pi$
$73$	−4.32743			−0.506487			−0.253244	+	0.967403i	$0.581497\pi$
$74$		0			0
$75$	1.82383	−	0.0831759i	0.210598	−	0.00960433i
$76$		0			0
$77$	2.32383	+	4.02499i	0.264825	+	0.458691i
$78$		0			0
$79$	−3.21780	+	5.57339i	−0.362031	+	0.627056i	−0.988295	−	0.152555i	$-0.951250\pi$
$79$	−3.21780	+	5.57339i	−0.362031	+	0.627056i	0.626264	+	0.779611i	$0.284583\pi$
$80$		0			0
$81$	−5.83842	−	6.84929i	−0.648713	−	0.761033i
$82$		0			0
$83$	−0.742705	+	1.28640i	−0.0815225	+	0.141201i	−0.903904	−	0.427735i	$-0.859312\pi$
$83$	−0.742705	+	1.28640i	−0.0815225	+	0.141201i	0.822382	+	0.568936i	$0.192645\pi$
$84$		0			0
$85$	5.55408	+	9.61996i	0.602425	+	1.04343i
$86$		0			0
$87$	−12.0687	+	0.550392i	−1.29390	+	0.0590083i
$88$		0			0
$89$	9.83482			1.04249			0.521245	−	0.853407i	$-0.325468\pi$
$89$	9.83482			1.04249			0.521245	+	0.853407i	$0.325468\pi$
$90$		0			0
$91$	−7.10817			−0.745139
$92$		0			0
$93$	5.88151	−	11.3520i	0.609885	−	1.17715i
$94$		0			0
$95$	−5.32383	−	9.22115i	−0.546214	−	0.946070i
$96$		0			0
$97$	0.246304	−	0.426611i	0.0250084	−	0.0433158i	−0.853250	−	0.521502i	$-0.825372\pi$
$97$	0.246304	−	0.426611i	0.0250084	−	0.0433158i	0.878259	+	0.478186i	$0.158705\pi$
$98$		0			0
$99$	−8.04163	−	11.3903i	−0.808214	−	1.14477i
$100$		0			0
$101$	−1.70321	+	2.95005i	−0.169476	+	0.293541i	−0.938236	−	0.345997i	$-0.887541\pi$
$101$	−1.70321	+	2.95005i	−0.169476	+	0.293541i	0.768760	+	0.639537i	$0.220874\pi$
$102$		0			0
$103$	−2.58113	−	4.47064i	−0.254326	−	0.440505i	0.710386	−	0.703812i	$-0.248520\pi$
$103$	−2.58113	−	4.47064i	−0.254326	−	0.440505i	−0.964712	+	0.263307i	$0.915187\pi$
$104$		0			0
$105$	2.29679	+	3.58985i	0.224144	+	0.350333i
$106$		0			0
$107$	−5.76303			−0.557133			−0.278567	−	0.960417i	$-0.589859\pi$
$107$	−5.76303			−0.557133			−0.278567	+	0.960417i	$0.589859\pi$
$108$		0			0
$109$	−8.98229			−0.860347			−0.430174	−	0.902746i	$-0.641548\pi$
$109$	−8.98229			−0.860347			−0.430174	+	0.902746i	$0.641548\pi$
$110$		0			0
$111$	0.678304	+	1.06018i	0.0643818	+	0.100628i
$112$		0			0
$113$	0.679767	+	1.17739i	0.0639471	+	0.110760i	0.896226	−	0.443597i	$-0.146298\pi$
$113$	0.679767	+	1.17739i	0.0639471	+	0.110760i	−0.832279	+	0.554356i	$0.812964\pi$
$114$		0			0
$115$	−7.21780	+	12.5016i	−0.673063	+	1.16578i
$116$		0			0
$117$	21.2360	−	1.94097i	1.96327	−	0.179443i
$118$		0			0
$119$	−2.25729	+	3.90975i	−0.206926	+	0.358406i
$120$		0			0
$121$	−5.30039	−	9.18054i	−0.481853	−	0.834595i
$122$		0			0
$123$	−0.217799	+	0.420378i	−0.0196383	+	0.0379042i
$124$		0			0
$125$	−9.70895			−0.868394
$126$		0			0
$127$	−0.820039			−0.0727667			−0.0363833	−	0.999338i	$-0.511584\pi$
$127$	−0.820039			−0.0727667			−0.0363833	+	0.999338i	$0.511584\pi$
$128$		0			0
$129$	−8.36546	+	0.381507i	−0.736538	+	0.0335898i
$130$		0			0
$131$	−3.89397	−	6.74455i	−0.340218	−	0.589274i	0.644255	−	0.764810i	$-0.277167\pi$
$131$	−3.89397	−	6.74455i	−0.340218	−	0.589274i	−0.984473	+	0.175536i	$0.943834\pi$
$132$		0			0
$133$	2.16372	−	3.74766i	0.187618	−	0.324964i
$134$		0			0
$135$	−7.84202	−	10.0977i	−0.674934	−	0.869069i
$136$		0			0
$137$	1.49640	−	2.59184i	0.127846	−	0.221436i	−0.794996	−	0.606615i	$-0.792527\pi$
$137$	1.49640	−	2.59184i	0.127846	−	0.221436i	0.922842	+	0.385179i	$0.125860\pi$
$138$		0			0
$139$	−3.16372	−	5.47972i	−0.268343	−	0.464783i	0.700091	−	0.714053i	$-0.253143\pi$
$139$	−3.16372	−	5.47972i	−0.268343	−	0.464783i	−0.968434	+	0.249270i	$0.919809\pi$
$140$		0			0
$141$	6.35447	−	0.289796i	0.535143	−	0.0244052i
$142$		0			0
$143$	33.0364			2.76264
$144$		0			0
$145$	−17.1623			−1.42525
$146$		0			0
$147$	−0.796790	+	1.53790i	−0.0657181	+	0.126844i
$148$		0			0
$149$	2.19076	+	3.79450i	0.179474	+	0.310858i	0.941700	−	0.336452i	$-0.109227\pi$
$149$	2.19076	+	3.79450i	0.179474	+	0.310858i	−0.762227	+	0.647310i	$0.775894\pi$
$150$		0			0
$151$	−3.30039	+	5.71644i	−0.268582	+	0.465197i	−0.968496	−	0.249030i	$-0.919888\pi$
$151$	−3.30039	+	5.71644i	−0.268582	+	0.465197i	0.699914	+	0.714227i	$0.253222\pi$
$152$		0			0
$153$	5.67617	−	12.2969i	0.458891	−	0.994149i
$154$		0			0
$155$	9.08113	−	15.7290i	0.729414	−	1.26338i
$156$		0			0
$157$	2.89037	+	5.00627i	0.230677	+	0.399544i	0.958007	−	0.286743i	$-0.0925727\pi$
$157$	2.89037	+	5.00627i	0.230677	+	0.399544i	−0.727331	+	0.686287i	$0.759239\pi$
$158$		0			0
$159$	−4.71780	−	7.37385i	−0.374146	−	0.584784i
$160$		0			0
$161$	−5.86693			−0.462379
$162$		0			0
$163$	7.32743			0.573929			0.286964	−	0.957941i	$-0.407354\pi$
$163$	7.32743			0.573929			0.286964	+	0.957941i	$0.407354\pi$
$164$		0			0
$165$	−10.6747	−	16.6844i	−0.831025	−	1.29888i
$166$		0			0
$167$	6.01459	+	10.4176i	0.465423	+	0.806136i	0.999221	−	0.0394762i	$-0.0125689\pi$
$167$	6.01459	+	10.4176i	0.465423	+	0.806136i	−0.533798	+	0.845612i	$0.679236\pi$
$168$		0			0
$169$	−18.7630	+	32.4985i	−1.44331	+	2.49989i
$170$		0			0
$171$	−5.44085	+	11.7872i	−0.416073	+	0.901386i
$172$		0			0
$173$	−2.44951	+	4.24268i	−0.186233	+	0.322565i	−0.943991	−	0.329970i	$-0.892961\pi$
$173$	−2.44951	+	4.24268i	−0.186233	+	0.322565i	0.757758	+	0.652535i	$0.226295\pi$
$174$		0			0
$175$	0.527042	+	0.912864i	0.0398406	+	0.0690060i
$176$		0			0
$177$	−7.27714	+	14.0457i	−0.546983	+	1.05574i
$178$		0			0
$179$	−1.78074			−0.133099			−0.0665493	−	0.997783i	$-0.521199\pi$
$179$	−1.78074			−0.133099			−0.0665493	+	0.997783i	$0.521199\pi$
$180$		0			0
$181$	−16.9430			−1.25936			−0.629681	−	0.776854i	$-0.716815\pi$
$181$	−16.9430			−1.25936			−0.629681	+	0.776854i	$0.716815\pi$
$182$		0			0
$183$	−23.9071	+	1.09028i	−1.76726	+	0.0805961i
$184$		0			0
$185$	0.893968	+	1.54840i	0.0657258	+	0.113840i
$186$		0			0
$187$	10.4911	−	18.1712i	0.767189	−	1.32881i
$188$		0			0
$189$	1.96050	−	4.81211i	0.142606	−	0.350030i
$190$		0			0
$191$	2.74484	−	4.75420i	0.198610	−	0.344002i	−0.749468	−	0.662040i	$-0.769691\pi$
$191$	2.74484	−	4.75420i	0.198610	−	0.344002i	0.948078	+	0.318038i	$0.103024\pi$
$192$		0			0
$193$	2.75370	+	4.76954i	0.198215	+	0.343319i	0.947950	−	0.318420i	$-0.103152\pi$
$193$	2.75370	+	4.76954i	0.198215	+	0.343319i	−0.749734	+	0.661739i	$0.769819\pi$
$194$		0			0
$195$	30.2616	−	1.38008i	2.16708	−	0.0988296i
$196$		0			0
$197$	11.6300			0.828600			0.414300	−	0.910140i	$-0.364026\pi$
$197$	11.6300			0.828600			0.414300	+	0.910140i	$0.364026\pi$
$198$		0			0
$199$	−4.14747			−0.294006			−0.147003	−	0.989136i	$-0.546963\pi$
$199$	−4.14747			−0.294006			−0.147003	+	0.989136i	$0.546963\pi$
$200$		0			0
$201$	1.05768	−	2.04145i	0.0746032	−	0.143993i
$202$		0			0
$203$	−3.48755	−	6.04061i	−0.244778	−	0.423968i
$204$		0			0
$205$	−0.336285	+	0.582462i	−0.0234871	+	0.0406809i
$206$		0			0
$207$	17.5277	−	1.60204i	1.21826	−	0.111349i
$208$		0			0
$209$	−10.0562	+	17.4179i	−0.695603	+	1.20482i
$210$		0			0
$211$	13.6082	+	23.5700i	0.936825	+	1.62263i	0.771347	+	0.636415i	$0.219583\pi$
$211$	13.6082	+	23.5700i	0.936825	+	1.62263i	0.165478	+	0.986213i	$0.447083\pi$
$212$		0			0
$213$	−12.6221	−	19.7281i	−0.864851	−	1.35175i
$214$		0			0
$215$	−11.8961			−0.811308
$216$		0			0
$217$	7.38151			0.501090
$218$		0			0
$219$	4.03950	+	6.31367i	0.272964	+	0.426638i
$220$		0			0
$221$	16.0452	+	27.7912i	1.07932	+	1.86944i
$222$		0			0
$223$	1.60817	−	2.78543i	0.107691	−	0.186526i	−0.807144	−	0.590355i	$-0.798988\pi$
$223$	1.60817	−	2.78543i	0.107691	−	0.186526i	0.914834	+	0.403829i	$0.132321\pi$
$224$		0			0
$225$	−1.82383	−	2.58331i	−0.121589	−	0.172221i
$226$		0			0
$227$	−7.97296	+	13.8096i	−0.529184	+	0.916573i	0.470237	+	0.882540i	$0.344168\pi$
$227$	−7.97296	+	13.8096i	−0.529184	+	0.916573i	−0.999421	+	0.0340330i	$0.989165\pi$
$228$		0			0
$229$	0.608168	+	1.05338i	0.0401889	+	0.0696092i	0.885420	−	0.464791i	$-0.153871\pi$
$229$	0.608168	+	1.05338i	0.0401889	+	0.0696092i	−0.845231	+	0.534401i	$0.820537\pi$
$230$		0			0
$231$	3.70321	−	7.14763i	0.243653	−	0.470279i
$232$		0			0
$233$	19.9722			1.30842			0.654210	−	0.756313i	$-0.273001\pi$
$233$	19.9722			1.30842			0.654210	+	0.756313i	$0.273001\pi$
$234$		0			0
$235$	9.03638			0.589468
$236$		0			0
$237$	11.1352	−	0.507822i	0.723310	−	0.0329866i
$238$		0			0
$239$	−3.00739	−	5.20896i	−0.194532	−	0.336939i	0.752215	−	0.658918i	$-0.228985\pi$
$239$	−3.00739	−	5.20896i	−0.194532	−	0.336939i	−0.946747	+	0.321978i	$0.895652\pi$
$240$		0			0
$241$	9.30778	−	16.1215i	0.599567	−	1.03848i	−0.393318	−	0.919402i	$-0.628673\pi$
$241$	9.30778	−	16.1215i	0.599567	−	1.03848i	0.992885	−	0.119078i	$-0.0379938\pi$
$242$		0			0
$243$	−4.54309	+	14.9118i	−0.291440	+	0.956589i
$244$		0			0
$245$	−1.23025	+	2.13086i	−0.0785979	+	0.136136i
$246$		0			0
$247$	−15.3801	−	26.6390i	−0.978609	−	1.69500i
$248$		0			0
$249$	2.57014	−	0.117211i	0.162876	−	0.00742796i
$250$		0			0
$251$	6.99707			0.441651			0.220826	−	0.975313i	$-0.429125\pi$
$251$	6.99707			0.441651			0.220826	+	0.975313i	$0.429125\pi$
$252$		0			0
$253$	27.2675			1.71429
$254$		0			0
$255$	8.85087	−	17.0832i	0.554263	−	1.06979i
$256$		0			0
$257$	8.88891	+	15.3960i	0.554475	+	0.960378i	0.997944	+	0.0640889i	$0.0204141\pi$
$257$	8.88891	+	15.3960i	0.554475	+	0.960378i	−0.443469	+	0.896289i	$0.646253\pi$
$258$		0			0
$259$	−0.363327	+	0.629301i	−0.0225760	+	0.0391028i
$260$		0			0
$261$	12.0687	+	17.0943i	0.747032	+	1.05811i
$262$		0			0
$263$	13.5993	−	23.5547i	0.838570	−	1.45245i	−0.0525210	−	0.998620i	$-0.516726\pi$
$263$	13.5993	−	23.5547i	0.838570	−	1.45245i	0.891091	−	0.453825i	$-0.149941\pi$
$264$		0			0
$265$	−6.21780	−	10.7695i	−0.381956	−	0.661568i
$266$		0			0
$267$	−9.18044	−	14.3489i	−0.561834	−	0.878138i
$268$		0			0
$269$	23.8961			1.45697			0.728486	−	0.685061i	$-0.240225\pi$
$269$	23.8961			1.45697			0.728486	+	0.685061i	$0.240225\pi$
$270$		0			0
$271$	12.2733			0.745553			0.372776	−	0.927921i	$-0.378406\pi$
$271$	12.2733			0.745553			0.372776	+	0.927921i	$0.378406\pi$
$272$		0			0
$273$	6.63521	+	10.3707i	0.401581	+	0.627665i
$274$		0			0
$275$	−2.44951	−	4.24268i	−0.147711	−	0.255843i
$276$		0			0
$277$	−6.39037	+	11.0684i	−0.383960	+	0.665038i	−0.991624	−	0.129156i	$-0.958773\pi$
$277$	−6.39037	+	11.0684i	−0.383960	+	0.665038i	0.607664	+	0.794194i	$0.292107\pi$
$278$		0			0
$279$	−22.0526	+	2.01561i	−1.32026	+	0.120672i
$280$		0			0
$281$	14.2573	−	24.6944i	0.850519	−	1.47314i	−0.0302219	−	0.999543i	$-0.509621\pi$
$281$	14.2573	−	24.6944i	0.850519	−	1.47314i	0.880741	−	0.473599i	$-0.157045\pi$
$282$		0			0
$283$	−0.363327	−	0.629301i	−0.0215975	−	0.0374080i	0.855025	−	0.518587i	$-0.173542\pi$
$283$	−0.363327	−	0.629301i	−0.0215975	−	0.0374080i	−0.876622	+	0.481179i	$0.840209\pi$
$284$		0			0
$285$	−8.48395	+	16.3750i	−0.502546	+	0.969972i
$286$		0			0
$287$	−0.273346			−0.0161351
$288$		0			0
$289$	3.38151			0.198913
$290$		0			0
$291$	−0.852336	+	0.0388708i	−0.0499648	+	0.00227865i
$292$		0			0
$293$	−12.7901	−	22.1531i	−0.747204	−	1.29420i	−0.949158	−	0.314800i	$-0.898062\pi$
$293$	−12.7901	−	22.1531i	−0.747204	−	1.29420i	0.201954	−	0.979395i	$-0.435271\pi$
$294$		0			0
$295$	−11.2360	+	19.4613i	−0.654184	+	1.13308i
$296$		0			0
$297$	−9.11177	+	22.3651i	−0.528718	+	1.29775i
$298$		0			0
$299$	−20.8515	+	36.1159i	−1.20588	+	2.08864i
$300$		0			0
$301$	−2.41741	−	4.18708i	−0.139337	−	0.241339i
$302$		0			0
$303$	5.89397	−	0.268795i	0.338600	−	0.0154419i
$304$		0			0
$305$	−33.9971			−1.94667
$306$		0			0
$307$	−6.23405			−0.355796			−0.177898	−	0.984049i	$-0.556930\pi$
$307$	−6.23405			−0.355796			−0.177898	+	0.984049i	$0.556930\pi$
$308$		0			0
$309$	−4.11323	+	7.93901i	−0.233993	+	0.451635i
$310$		0			0
$311$	−14.6192	−	25.3211i	−0.828976	−	1.43583i	−0.898842	−	0.438273i	$-0.855590\pi$
$311$	−14.6192	−	25.3211i	−0.828976	−	1.43583i	0.0698655	−	0.997556i	$-0.477743\pi$
$312$		0			0
$313$	−14.2434	+	24.6703i	−0.805083	+	1.39445i	0.111151	+	0.993803i	$0.464546\pi$
$313$	−14.2434	+	24.6703i	−0.805083	+	1.39445i	−0.916235	+	0.400642i	$0.868787\pi$
$314$		0			0
$315$	3.09358	−	6.70198i	0.174303	−	0.377614i
$316$		0			0
$317$	−0.809243	+	1.40165i	−0.0454516	+	0.0787245i	−0.887856	−	0.460121i	$-0.847806\pi$
$317$	−0.809243	+	1.40165i	−0.0454516	+	0.0787245i	0.842405	+	0.538846i	$0.181139\pi$
$318$		0			0
$319$	16.2089	+	28.0747i	0.907527	+	1.57188i
$320$		0			0
$321$	5.37957	+	8.40819i	0.300258	+	0.469300i
$322$		0			0
$323$	−19.5366			−1.08704
$324$		0			0
$325$	7.49261			0.415615
$326$		0			0
$327$	8.38463	+	13.1051i	0.463671	+	0.724711i
$328$		0			0
$329$	1.83628	+	3.18054i	0.101238	+	0.175349i
$330$		0			0
$331$	6.99115	−	12.1090i	0.384268	−	0.665572i	−0.607399	−	0.794397i	$-0.707787\pi$
$331$	6.99115	−	12.1090i	0.384268	−	0.665572i	0.991667	+	0.128825i	$0.0411205\pi$
$332$		0			0
$333$	0.913618	−	1.97928i	0.0500660	−	0.108464i
$334$		0			0
$335$	1.63307	−	2.82857i	0.0892244	−	0.154541i
$336$		0			0
$337$	−13.8619	−	24.0095i	−0.755104	−	1.30788i	−0.945323	−	0.326137i	$-0.894253\pi$
$337$	−13.8619	−	24.0095i	−0.755104	−	1.30788i	0.190219	−	0.981742i	$-0.439080\pi$
$338$		0			0
$339$	1.08326	−	2.09082i	0.0588347	−	0.113558i
$340$		0			0
$341$	−34.3068			−1.85782
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	24.9772	−	1.13909i	1.34473	−	0.0613264i
$346$		0			0
$347$	−3.76449	−	6.52029i	−0.202089	−	0.350028i	0.747113	−	0.664697i	$-0.231440\pi$
$347$	−3.76449	−	6.52029i	−0.202089	−	0.350028i	−0.949201	+	0.314670i	$0.898106\pi$
$348$		0			0
$349$	15.0541	−	26.0744i	0.805827	−	1.39573i	−0.109905	−	0.993942i	$-0.535055\pi$
$349$	15.0541	−	26.0744i	0.805827	−	1.39573i	0.915732	−	0.401791i	$-0.131612\pi$
$350$		0			0
$351$	−22.6549	−	29.1712i	−1.20923	−	1.55705i
$352$		0			0
$353$	10.1819	−	17.6356i	0.541928	−	0.938647i	−0.456865	−	0.889536i	$-0.651028\pi$
$353$	10.1819	−	17.6356i	0.541928	−	0.938647i	0.998793	−	0.0491110i	$-0.0156388\pi$
$354$		0			0
$355$	−16.6352	−	28.8130i	−0.882905	−	1.52924i
$356$		0			0
$357$	7.81138	−	0.356238i	0.413422	−	0.0188541i
$358$		0			0
$359$	−16.0263			−0.845833			−0.422917	−	0.906169i	$-0.638994\pi$
$359$	−16.0263			−0.845833			−0.422917	+	0.906169i	$0.638994\pi$
$360$		0			0
$361$	−0.273346			−0.0143866
$362$		0			0
$363$	−8.44659	+	16.3029i	−0.443331	+	0.855680i
$364$		0			0
$365$	5.32383	+	9.22115i	0.278662	+	0.482657i
$366$		0			0
$367$	6.79893	−	11.7761i	0.354901	−	0.614707i	−0.632200	−	0.774805i	$-0.717848\pi$
$367$	6.79893	−	11.7761i	0.354901	−	0.614707i	0.987101	+	0.160099i	$0.0511812\pi$
$368$		0			0
$369$	0.816635	−	0.0746406i	0.0425123	−	0.00388563i
$370$		0			0
$371$	2.52704	−	4.37697i	0.131197	−	0.227241i
$372$		0			0
$373$	10.9641	+	18.9904i	0.567700	+	0.983285i	0.996793	+	0.0800246i	$0.0254999\pi$
$373$	10.9641	+	18.9904i	0.567700	+	0.983285i	−0.429093	+	0.903260i	$0.641167\pi$
$374$		0			0
$375$	9.06294	+	14.1652i	0.468008	+	0.731490i
$376$		0			0
$377$	−49.5801			−2.55351
$378$		0			0
$379$	−29.7965			−1.53054			−0.765271	−	0.643708i	$-0.777395\pi$
$379$	−29.7965			−1.53054			−0.765271	+	0.643708i	$0.777395\pi$
$380$		0			0
$381$	0.765475	+	1.19643i	0.0392165	+	0.0612948i
$382$		0			0
$383$	0.0109905	+	0.0190361i	0.000561587	+	0.000972697i	0.866306	−	0.499514i	$-0.166488\pi$
$383$	0.0109905	+	0.0190361i	0.000561587	+	0.000972697i	−0.865744	+	0.500486i	$0.833155\pi$
$384$		0			0
$385$	5.71780	−	9.90352i	0.291406	−	0.504730i
$386$		0			0
$387$	8.36546	+	11.8490i	0.425240	+	0.602318i
$388$		0			0
$389$	17.6783	−	30.6197i	0.896326	−	1.55248i	0.0641702	−	0.997939i	$-0.479560\pi$
$389$	17.6783	−	30.6197i	0.896326	−	1.55248i	0.832155	−	0.554543i	$-0.187107\pi$
$390$		0			0
$391$	13.2434	+	22.9382i	0.669746	+	1.16003i
$392$		0			0
$393$	−6.20535	+	11.9770i	−0.313018	+	0.604162i
$394$		0			0
$395$	15.8348			0.796736
$396$		0			0
$397$	−16.9430			−0.850344			−0.425172	−	0.905112i	$-0.639786\pi$
$397$	−16.9430			−0.850344			−0.425172	+	0.905112i	$0.639786\pi$
$398$		0			0
$399$	−7.48755	+	0.341470i	−0.374846	+	0.0170949i
$400$		0			0
$401$	1.48181	+	2.56657i	0.0739982	+	0.128169i	0.900650	−	0.434545i	$-0.143091\pi$
$401$	1.48181	+	2.56657i	0.0739982	+	0.128169i	−0.826652	+	0.562713i	$0.809757\pi$
$402$		0			0
$403$	26.2345	−	45.4395i	1.30683	−	2.26350i
$404$		0			0
$405$	−7.41216	+	20.8672i	−0.368313	+	1.03690i
$406$		0			0
$407$	1.68862	−	2.92478i	0.0837018	−	0.144976i
$408$		0			0
$409$	7.32743	+	12.6915i	0.362318	+	0.627553i	0.988342	−	0.152251i	$-0.0486521\pi$
$409$	7.32743	+	12.6915i	0.362318	+	0.627553i	−0.626024	+	0.779804i	$0.715319\pi$
$410$		0			0
$411$	−5.17830	+	0.236157i	−0.255427	+	0.0116488i
$412$		0			0
$413$	−9.13307			−0.449409
$414$		0			0
$415$	3.65486			0.179410
$416$		0			0
$417$	−5.04163	+	9.73093i	−0.246890	+	0.476526i
$418$		0			0
$419$	12.6352	+	21.8848i	0.617270	+	1.06914i	0.989982	+	0.141196i	$0.0450949\pi$
$419$	12.6352	+	21.8848i	0.617270	+	1.06914i	−0.372711	+	0.927947i	$0.621572\pi$
$420$		0			0
$421$	7.99854	−	13.8539i	0.389825	−	0.675196i	−0.602601	−	0.798043i	$-0.705869\pi$
$421$	7.99854	−	13.8539i	0.389825	−	0.675196i	0.992426	+	0.122846i	$0.0392022\pi$
$422$		0			0
$423$	−6.35447	−	9.00059i	−0.308965	−	0.437624i
$424$		0			0
$425$	2.37938	−	4.12120i	0.115417	−	0.199908i
$426$		0			0
$427$	−6.90856	−	11.9660i	−0.334328	−	0.579074i
$428$		0			0
$429$	−30.8382	−	48.1997i	−1.48888	−	2.32710i
$430$		0			0
$431$	13.0335			0.627799			0.313900	−	0.949456i	$-0.398364\pi$
$431$	13.0335			0.627799			0.313900	+	0.949456i	$0.398364\pi$
$432$		0			0
$433$	23.5467			1.13158			0.565791	−	0.824549i	$-0.308571\pi$
$433$	23.5467			1.13158			0.565791	+	0.824549i	$0.308571\pi$
$434$		0			0
$435$	16.0203	+	25.0395i	0.768116	+	1.20055i
$436$		0			0
$437$	−12.6944	−	21.9873i	−0.607253	−	1.05179i
$438$		0			0
$439$	−3.35447	+	5.81012i	−0.160100	+	0.277302i	−0.934904	−	0.354900i	$-0.884515\pi$
$439$	−3.35447	+	5.81012i	−0.160100	+	0.277302i	0.774804	+	0.632201i	$0.217848\pi$
$440$		0			0
$441$	2.98755	−	0.273062i	0.142264	−	0.0130030i
$442$		0			0
$443$	−17.6228	+	30.5235i	−0.837282	+	1.45022i	0.0548760	+	0.998493i	$0.482524\pi$
$443$	−17.6228	+	30.5235i	−0.837282	+	1.45022i	−0.892158	+	0.451723i	$0.850810\pi$
$444$		0			0
$445$	−12.0993	−	20.9566i	−0.573562	−	0.993439i
$446$		0			0
$447$	3.49115	−	6.73832i	0.165126	−	0.318711i
$448$		0			0
$449$	−12.9387			−0.610616			−0.305308	−	0.952254i	$-0.598759\pi$
$449$	−12.9387			−0.610616			−0.305308	+	0.952254i	$0.598759\pi$
$450$		0			0
$451$	1.27042			0.0598218
$452$		0			0
$453$	11.4210	−	0.520856i	0.536606	−	0.0244719i
$454$		0			0
$455$	8.74484	+	15.1465i	0.409964	+	0.710079i
$456$		0			0
$457$	14.5993	−	25.2868i	0.682927	−	1.18286i	−0.291156	−	0.956675i	$-0.594040\pi$
$457$	14.5993	−	25.2868i	0.682927	−	1.18286i	0.974083	−	0.226189i	$-0.0726267\pi$
$458$		0			0
$459$	−23.2396	+	3.19727i	−1.08473	+	0.149236i
$460$		0			0
$461$	9.34348	−	16.1834i	0.435169	−	0.753735i	−0.562140	−	0.827042i	$-0.690022\pi$
$461$	9.34348	−	16.1834i	0.435169	−	0.753735i	0.997309	+	0.0733066i	$0.0233552\pi$
$462$		0			0
$463$	19.1249	+	33.1253i	0.888809	+	1.53946i	0.841285	+	0.540593i	$0.181800\pi$
$463$	19.1249	+	33.1253i	0.888809	+	1.53946i	0.0475247	+	0.998870i	$0.484867\pi$
$464$		0			0
$465$	−31.4253	+	1.43315i	−1.45731	+	0.0664608i
$466$		0			0
$467$	−15.2877			−0.707432			−0.353716	−	0.935353i	$-0.615082\pi$
$467$	−15.2877			−0.707432			−0.353716	+	0.935353i	$0.615082\pi$
$468$		0			0
$469$	1.32743			0.0612950
$470$		0			0
$471$	4.60603	−	8.89018i	0.212235	−	0.409638i
$472$		0			0
$473$	11.2353	+	19.4601i	0.516600	+	0.894778i
$474$		0			0
$475$	−2.28074	+	3.95035i	−0.104647	+	0.181255i
$476$		0			0
$477$	−6.35447	+	13.7664i	−0.290951	+	0.630322i
$478$		0			0
$479$	−5.51605	+	9.55408i	−0.252035	+	0.436537i	−0.964086	−	0.265591i	$-0.914433\pi$
$479$	−5.51605	+	9.55408i	−0.252035	+	0.436537i	0.712051	+	0.702128i	$0.247766\pi$
$480$		0			0
$481$	2.58259	+	4.47318i	0.117756	+	0.203959i
$482$		0			0
$483$	5.47656	+	8.55978i	0.249192	+	0.389483i
$484$		0			0
$485$	−1.21206			−0.0550370
$486$		0			0
$487$	16.6008			0.752253			0.376126	−	0.926568i	$-0.377256\pi$
$487$	16.6008			0.752253			0.376126	+	0.926568i	$0.377256\pi$
$488$		0			0
$489$	−6.83988	−	10.6906i	−0.309310	−	0.483447i
$490$		0			0
$491$	13.3633	+	23.1460i	0.603079	+	1.04456i	0.992352	+	0.123440i	$0.0393928\pi$
$491$	13.3633	+	23.1460i	0.603079	+	1.04456i	−0.389273	+	0.921122i	$0.627274\pi$
$492$		0			0
$493$	−15.7448	+	27.2709i	−0.709112	+	1.22822i
$494$		0			0
$495$	−14.3779	+	31.1485i	−0.646239	+	1.40002i
$496$		0			0
$497$	6.76089	−	11.7102i	0.303268	−	0.525275i
$498$		0			0
$499$	−0.618485	−	1.07125i	−0.0276872	−	0.0479557i	0.851850	−	0.523786i	$-0.175481\pi$
$499$	−0.618485	−	1.07125i	−0.0276872	−	0.0479557i	−0.879537	+	0.475830i	$0.842148\pi$
$500$		0			0
$501$	9.58472	−	18.4996i	0.428214	−	0.826503i
$502$		0			0
$503$	−1.07179			−0.0477889			−0.0238944	−	0.999714i	$-0.507607\pi$
$503$	−1.07179			−0.0477889			−0.0238944	+	0.999714i	$0.507607\pi$
$504$		0			0
$505$	8.38151			0.372973
$506$		0			0
$507$	64.9296	−	2.96112i	2.88362	−	0.131508i
$508$		0			0
$509$	−10.0344	−	17.3801i	−0.444768	−	0.770362i	0.553268	−	0.833004i	$-0.313381\pi$
$509$	−10.0344	−	17.3801i	−0.444768	−	0.770362i	−0.998036	+	0.0626420i	$0.980047\pi$
$510$		0			0
$511$	−2.16372	+	3.74766i	−0.0957171	+	0.165787i
$512$		0			0
$513$	22.2762	−	3.06472i	0.983516	−	0.135311i
$514$		0			0
$515$	−6.35087	+	11.0000i	−0.279853	+	0.484720i
$516$		0			0
$517$	−8.53443	−	14.7821i	−0.375344	−	0.650115i
$518$		0			0
$519$	8.47656	−	0.386574i	0.372080	−	0.0169687i
$520$		0			0
$521$	−30.8860			−1.35314			−0.676570	−	0.736379i	$-0.736534\pi$
$521$	−30.8860			−1.35314			−0.676570	+	0.736379i	$0.736534\pi$
$522$		0			0
$523$	−7.39922			−0.323545			−0.161773	−	0.986828i	$-0.551721\pi$
$523$	−7.39922			−0.323545			−0.161773	+	0.986828i	$0.551721\pi$
$524$		0			0
$525$	0.839883	−	1.62107i	0.0366555	−	0.0707494i
$526$		0			0
$527$	−16.6623	−	28.8599i	−0.725819	−	1.25716i
$528$		0			0
$529$	−5.71041	+	9.89072i	−0.248279	+	0.430031i
$530$		0			0
$531$	27.2855	−	2.49390i	1.18409	−	0.108226i
$532$		0			0
$533$	−0.971495	+	1.68268i	−0.0420801	+	0.0728849i
$534$		0			0
$535$	7.08998	+	12.2802i	0.306527	+	0.530920i
$536$		0			0
$537$	1.66225	+	2.59808i	0.0717315	+	0.112115i
$538$		0			0
$539$	4.64766			0.200189
$540$		0			0
$541$	22.6696			0.974644			0.487322	−	0.873222i	$-0.337974\pi$
$541$	22.6696			0.974644			0.487322	+	0.873222i	$0.337974\pi$
$542$		0			0
$543$	15.8157	+	24.7196i	0.678715	+	1.06082i
$544$		0			0
$545$	11.0505	+	19.1400i	0.473351	+	0.819868i
$546$		0			0
$547$	3.07373	−	5.32386i	0.131423	−	0.227632i	−0.792802	−	0.609479i	$-0.791379\pi$
$547$	3.07373	−	5.32386i	0.131423	−	0.227632i	0.924225	+	0.381847i	$0.124712\pi$
$548$		0			0
$549$	23.9071	+	33.8624i	1.02033	+	1.44521i
$550$		0			0
$551$	15.0921	−	26.1403i	0.642946	−	1.11361i
$552$		0			0
$553$	3.21780	+	5.57339i	0.136835	+	0.237005i
$554$		0			0
$555$	1.42461	−	2.74966i	0.0604713	−	0.116717i
$556$		0			0
$557$	29.6739			1.25732			0.628662	−	0.777679i	$-0.283603\pi$
$557$	29.6739			1.25732			0.628662	+	0.777679i	$0.283603\pi$
$558$		0			0
$559$	−34.3667			−1.45356
$560$		0			0
$561$	−36.3047	+	1.65568i	−1.53278	+	0.0699027i
$562$		0			0
$563$	14.6555	+	25.3841i	0.617657	+	1.06981i	0.989912	+	0.141683i	$0.0452514\pi$
$563$	14.6555	+	25.3841i	0.617657	+	1.06981i	−0.372255	+	0.928131i	$0.621415\pi$
$564$		0			0
$565$	1.67257	−	2.89698i	0.0703655	−	0.121877i
$566$		0			0
$567$	−8.85087	+	1.63157i	−0.371702	+	0.0685196i
$568$		0			0
$569$	18.4430	−	31.9442i	0.773170	−	1.33917i	−0.162647	−	0.986684i	$-0.552003\pi$
$569$	18.4430	−	31.9442i	0.773170	−	1.33917i	0.935817	−	0.352486i	$-0.114664\pi$
$570$		0			0
$571$	−16.1893	−	28.0407i	−0.677501	−	1.17347i	−0.975731	−	0.218972i	$-0.929730\pi$
$571$	−16.1893	−	28.0407i	−0.677501	−	1.17347i	0.298230	−	0.954494i	$-0.403604\pi$
$572$		0			0
$573$	−9.49854	+	0.433181i	−0.396807	+	0.0180964i
$574$		0			0
$575$	6.18423			0.257900
$576$		0			0
$577$	23.0187			0.958280			0.479140	−	0.877739i	$-0.340949\pi$
$577$	23.0187			0.958280			0.479140	+	0.877739i	$0.340949\pi$
$578$		0			0
$579$	4.38823	−	8.46980i	0.182369	−	0.351993i
$580$		0			0
$581$	0.742705	+	1.28640i	0.0308126	+	0.0533690i
$582$		0			0
$583$	−11.7448	+	20.3427i	−0.486422	+	0.842507i
$584$		0			0
$585$	−30.2616	−	42.8630i	−1.25116	−	1.77217i
$586$		0			0
$587$	−2.87052	+	4.97189i	−0.118479	+	0.205212i	−0.919165	−	0.393872i	$-0.871135\pi$
$587$	−2.87052	+	4.97189i	−0.118479	+	0.205212i	0.800686	+	0.599084i	$0.204469\pi$
$588$		0			0
$589$	15.9715	+	27.6634i	0.658094	+	1.13985i
$590$		0			0
$591$	−10.8561	−	16.9680i	−0.446562	−	0.697969i
$592$		0			0
$593$	27.7453			1.13936			0.569682	−	0.821865i	$-0.307066\pi$
$593$	27.7453			1.13936			0.569682	+	0.821865i	$0.307066\pi$
$594$		0			0
$595$	11.1082			0.455391
$596$		0			0
$597$	3.87151	+	6.05111i	0.158450	+	0.247655i
$598$		0			0
$599$	−2.05408	−	3.55778i	−0.0839276	−	0.145367i	0.821006	−	0.570919i	$-0.193413\pi$
$599$	−2.05408	−	3.55778i	−0.0839276	−	0.145367i	−0.904934	+	0.425552i	$0.860080\pi$
$600$		0			0
$601$	−7.80924	+	13.5260i	−0.318546	+	0.551737i	−0.980185	−	0.198085i	$-0.936528\pi$
$601$	−7.80924	+	13.5260i	−0.318546	+	0.551737i	0.661639	+	0.749822i	$0.269861\pi$
$602$		0			0
$603$	−3.96576	+	0.362471i	−0.161498	+	0.0147610i
$604$		0			0
$605$	−13.0416	+	22.5888i	−0.530218	+	0.918364i
$606$		0			0
$607$	0.280738	+	0.486253i	0.0113948	+	0.0197364i	0.871667	−	0.490099i	$-0.163040\pi$
$607$	0.280738	+	0.486253i	0.0113948	+	0.0197364i	−0.860272	+	0.509836i	$0.829706\pi$
$608$		0			0
$609$	−5.55768	+	10.7270i	−0.225209	+	0.434679i
$610$		0			0
$611$	26.1052			1.05611
$612$		0			0
$613$	−20.2016			−0.815933			−0.407967	−	0.912997i	$-0.633762\pi$
$613$	−20.2016			−0.815933			−0.407967	+	0.912997i	$0.633762\pi$
$614$		0			0
$615$	1.16372	−	0.0530713i	0.0469255	−	0.00214004i
$616$		0			0
$617$	11.4569	+	19.8439i	0.461238	+	0.798887i	0.999023	−	0.0441948i	$-0.0140722\pi$
$617$	11.4569	+	19.8439i	0.461238	+	0.798887i	−0.537785	+	0.843082i	$0.680739\pi$
$618$		0			0
$619$	−19.8515	+	34.3839i	−0.797901	+	1.38201i	0.123080	+	0.992397i	$0.460723\pi$
$619$	−19.8515	+	34.3839i	−0.797901	+	1.38201i	−0.920981	+	0.389608i	$0.872610\pi$
$620$		0			0
$621$	−18.6988	−	24.0773i	−0.750358	−	0.966188i
$622$		0			0
$623$	4.91741	−	8.51721i	0.197012	−	0.341235i
$624$		0			0
$625$	14.5797	+	25.2527i	0.583187	+	1.01011i
$626$		0			0
$627$	34.7996	−	1.58704i	1.38976	−	0.0633802i
$628$		0			0
$629$	3.28054			0.130804
$630$		0			0
$631$	−31.0364			−1.23554			−0.617769	−	0.786359i	$-0.711963\pi$
$631$	−31.0364			−1.23554			−0.617769	+	0.786359i	$0.711963\pi$
$632$		0			0
$633$	21.6857	−	41.8559i	0.861929	−	1.66362i
$634$		0			0
$635$	1.00885	+	1.74739i	0.0400352	+	0.0693429i
$636$		0			0
$637$	−3.55408	+	6.15585i	−0.140818	+	0.243904i
$638$		0			0
$639$	−17.0009	+	36.8309i	−0.672544	+	1.45701i
$640$		0			0
$641$	14.7932	−	25.6226i	0.584296	−	1.01203i	−0.410667	−	0.911785i	$-0.634704\pi$
$641$	14.7932	−	25.6226i	0.584296	−	1.01203i	0.994963	−	0.100245i	$-0.0319626\pi$
$642$		0			0
$643$	−12.8442	−	22.2467i	−0.506524	−	0.877325i	−0.999972	−	0.00754978i	$-0.997597\pi$
$643$	−12.8442	−	22.2467i	−0.506524	−	0.877325i	0.493447	−	0.869776i	$-0.335737\pi$
$644$		0			0
$645$	11.1046	+	17.3563i	0.437242	+	0.683403i
$646$		0			0
$647$	17.0177			0.669035			0.334518	−	0.942390i	$-0.391427\pi$
$647$	17.0177			0.669035			0.334518	+	0.942390i	$0.391427\pi$
$648$		0			0
$649$	42.4475			1.66621
$650$		0			0
$651$	−6.89037	−	10.7695i	−0.270055	−	0.422092i
$652$		0			0
$653$	−0.735508	−	1.27394i	−0.0287827	−	0.0498530i	0.851275	−	0.524719i	$-0.175830\pi$
$653$	−0.735508	−	1.27394i	−0.0287827	−	0.0498530i	−0.880058	+	0.474866i	$0.842496\pi$
$654$		0			0
$655$	−9.58113	+	16.5950i	−0.374366	+	0.648420i
$656$		0			0
$657$	5.44085	−	11.7872i	0.212268	−	0.459861i
$658$		0			0
$659$	20.7003	−	35.8539i	0.806369	−	1.39667i	−0.108995	−	0.994042i	$-0.534763\pi$
$659$	20.7003	−	35.8539i	0.806369	−	1.39667i	0.915363	−	0.402629i	$-0.131904\pi$
$660$		0			0
$661$	−19.1352	−	33.1432i	−0.744273	−	1.28912i	−0.950533	−	0.310622i	$-0.899463\pi$
$661$	−19.1352	−	33.1432i	−0.744273	−	1.28912i	0.206260	−	0.978497i	$-0.433871\pi$
$662$		0			0
$663$	25.5693	−	49.3518i	0.993031	−	1.91667i
$664$		0			0
$665$	−10.6477			−0.412899
$666$		0			0
$667$	−40.9224			−1.58452
$668$		0			0
$669$	−5.56507	+	0.253795i	−0.215158	+	0.00981230i
$670$		0			0
$671$	32.1086	+	55.6138i	1.23954	+	2.14695i
$672$		0			0
$673$	15.2448	−	26.4048i	0.587645	−	1.01783i	−0.406894	−	0.913475i	$-0.633388\pi$
$673$	15.2448	−	26.4048i	0.587645	−	1.01783i	0.994540	−	0.104357i	$-0.0332783\pi$
$674$		0			0
$675$	−2.06654	+	5.07237i	−0.0795411	+	0.195236i
$676$		0			0
$677$	−22.4626	+	38.9064i	−0.863309	+	1.49530i	0.00540665	+	0.999985i	$0.498279\pi$
$677$	−22.4626	+	38.9064i	−0.863309	+	1.49530i	−0.868716	+	0.495310i	$0.835054\pi$
$678$		0			0
$679$	−0.246304	−	0.426611i	−0.00945228	−	0.0163718i
$680$		0			0
$681$	27.5905	−	1.25826i	1.05727	−	0.0482168i
$682$		0			0
$683$	−48.3973			−1.85187			−0.925935	−	0.377683i	$-0.876721\pi$
$683$	−48.3973			−1.85187			−0.925935	+	0.377683i	$0.876721\pi$
$684$		0			0
$685$	−7.36381			−0.281357
$686$		0			0
$687$	0.969165	−	1.87060i	0.0369759	−	0.0713679i
$688$		0			0
$689$	−17.9626	−	31.1122i	−0.684322	−	1.18528i
$690$		0			0
$691$	−9.19076	+	15.9189i	−0.349633	+	0.605582i	−0.986184	−	0.165652i	$-0.947027\pi$
$691$	−9.19076	+	15.9189i	−0.349633	+	0.605582i	0.636551	+	0.771234i	$0.280360\pi$
$692$		0			0
$693$	−13.8851	+	1.26910i	−0.527452	+	0.0482092i
$694$		0			0
$695$	−7.78434	+	13.4829i	−0.295277	+	0.511434i
$696$		0			0
$697$	0.617023	+	1.06871i	0.0233714	+	0.0404805i
$698$		0			0
$699$	−18.6433	−	29.1392i	−0.705153	−	1.10214i
$700$		0			0
$701$	−27.0292			−1.02088			−0.510439	−	0.859914i	$-0.670517\pi$
$701$	−27.0292			−1.02088			−0.510439	+	0.859914i	$0.670517\pi$
$702$		0			0
$703$	−3.14454			−0.118599
$704$		0			0
$705$	−8.43512	−	13.1840i	−0.317685	−	0.496537i
$706$		0			0
$707$	1.70321	+	2.95005i	0.0640558	+	0.110948i
$708$		0			0
$709$	−2.49261	+	4.31732i	−0.0936119	+	0.162141i	−0.909028	−	0.416734i	$-0.863175\pi$
$709$	−2.49261	+	4.31732i	−0.0936119	+	0.162141i	0.815417	+	0.578875i	$0.196508\pi$
$710$		0			0
$711$	−11.1352	−	15.7721i	−0.417603	−	0.591500i
$712$		0			0
$713$	21.6534	−	37.5048i	0.810926	−	1.40457i
$714$		0			0
$715$	−40.6431	−	70.3959i	−1.51997	−	2.63266i
$716$		0			0
$717$	−4.79252	+	9.25012i	−0.178980	+	0.345452i
$718$		0			0
$719$	15.6942			0.585293			0.292647	−	0.956221i	$-0.405464\pi$
$719$	15.6942			0.585293			0.292647	+	0.956221i	$0.405464\pi$
$720$		0			0
$721$	−5.16225			−0.192252
$722$		0			0
$723$	−32.2096	+	1.46892i	−1.19789	+	0.0546298i
$724$		0			0
$725$	3.67617	+	6.36731i	0.136529	+	0.236476i
$726$		0			0
$727$	−10.9071	+	18.8916i	−0.404522	+	0.700652i	−0.994266	−	0.106938i	$-0.965895\pi$
$727$	−10.9071	+	18.8916i	−0.404522	+	0.700652i	0.589744	+	0.807590i	$0.299229\pi$
$728$		0			0
$729$	25.9969	−	7.29124i	0.962847	−	0.270046i
$730$		0			0
$731$	−10.9136	+	18.9029i	−0.403655	+	0.699151i
$732$		0			0
$733$	12.0074	+	20.7974i	0.443503	+	0.768170i	0.997947	−	0.0640514i	$-0.0204022\pi$
$733$	12.0074	+	20.7974i	0.443503	+	0.768170i	−0.554443	+	0.832221i	$0.687069\pi$
$734$		0			0
$735$	4.25729	−	0.194154i	0.157033	−	0.00716148i
$736$		0			0
$737$	−6.16945			−0.227255
$738$		0			0
$739$	18.7089			0.688220			0.344110	−	0.938929i	$-0.388181\pi$
$739$	18.7089			0.688220			0.344110	+	0.938929i	$0.388181\pi$
$740$		0			0
$741$	−24.5093	+	47.3059i	−0.900373	+	1.73782i
$742$		0			0
$743$	20.1534	+	34.9067i	0.739356	+	1.28060i	0.952785	+	0.303644i	$0.0982035\pi$
$743$	20.1534	+	34.9067i	0.739356	+	1.28060i	−0.213429	+	0.976959i	$0.568463\pi$
$744$		0			0
$745$	5.39037	−	9.33639i	0.197488	−	0.342059i
$746$		0			0
$747$	−2.57014	−	3.64039i	−0.0940364	−	0.133195i
$748$		0			0
$749$	−2.88151	+	4.99093i	−0.105288	+	0.182365i
$750$		0			0
$751$	10.5629	+	18.2955i	0.385447	+	0.667614i	0.991831	−	0.127558i	$-0.0407139\pi$
$751$	10.5629	+	18.2955i	0.385447	+	0.667614i	−0.606384	+	0.795172i	$0.707381\pi$
$752$		0			0
$753$	−6.53151	−	10.2087i	−0.238021	−	0.372024i
$754$		0			0
$755$	16.2412			0.591079
$756$		0			0
$757$	8.85934			0.321998			0.160999	−	0.986955i	$-0.448528\pi$
$757$	8.85934			0.321998			0.160999	+	0.986955i	$0.448528\pi$
$758$		0			0
$759$	−25.4532	−	39.7830i	−0.923892	−	1.44403i
$760$		0			0
$761$	−0.694551	−	1.20300i	−0.0251774	−	0.0436086i	0.853162	−	0.521646i	$-0.174682\pi$
$761$	−0.694551	−	1.20300i	−0.0251774	−	0.0436086i	−0.878340	+	0.478037i	$0.841348\pi$
$762$		0			0
$763$	−4.49115	+	7.77889i	−0.162590	+	0.281615i
$764$		0			0
$765$	−33.1862	+	3.03322i	−1.19985	+	0.109666i
$766$		0			0
$767$	−32.4597	+	56.2219i	−1.17205	+	2.03005i
$768$		0			0
$769$	18.9626	+	32.8443i	0.683810	+	1.18439i	0.973809	+	0.227367i	$0.0730118\pi$
$769$	18.9626	+	32.8443i	0.683810	+	1.18439i	−0.289999	+	0.957027i	$0.593655\pi$
$770$		0			0
$771$	14.1652	−	27.3404i	0.510146	−	0.984642i
$772$		0			0
$773$	1.31596			0.0473318			0.0236659	−	0.999720i	$-0.492466\pi$
$773$	1.31596			0.0473318			0.0236659	+	0.999720i	$0.492466\pi$
$774$		0			0
$775$	−7.78074			−0.279492
$776$		0			0
$777$	1.25729	−	0.0573390i	0.0451052	−	0.00205702i
$778$		0			0
$779$	−0.591443	−	1.02441i	−0.0211907	−	0.0367033i
$780$		0			0
$781$	−31.4224	+	54.4251i	−1.12438	+	1.94748i
$782$		0			0
$783$	13.6747	−	33.5649i	0.488694	−	1.19951i
$784$		0			0
$785$	7.11177	−	12.3179i	0.253830	−	0.439646i
$786$		0			0
$787$	−6.12928	−	10.6162i	−0.218485	−	0.378428i	0.735860	−	0.677134i	$-0.236778\pi$
$787$	−6.12928	−	10.6162i	−0.218485	−	0.378428i	−0.954345	+	0.298706i	$0.903445\pi$
$788$		0			0
$789$	−47.0605	+	2.14620i	−1.67540	+	0.0764066i
$790$		0			0
$791$	1.35953			0.0483395
$792$		0			0
$793$	−98.2144			−3.48769
$794$		0			0
$795$	−9.90856	+	19.1247i	−0.351420	+	0.678282i
$796$		0			0
$797$	−10.7178	−	18.5638i	−0.379644	−	0.657563i	0.611366	−	0.791348i	$-0.290620\pi$
$797$	−10.7178	−	18.5638i	−0.379644	−	0.657563i	−0.991010	+	0.133785i	$0.957287\pi$
$798$		0			0
$799$	8.29007	−	14.3588i	0.293282	−	0.507979i
$800$		0			0
$801$	−12.3653	+	26.7883i	−0.436905	+	0.946518i
$802$		0			0
$803$	10.0562	−	17.4179i	0.354876	−	0.614664i
$804$		0			0
$805$	7.21780	+	12.5016i	0.254394	+	0.440623i
$806$		0			0
$807$	−22.3061	−	34.8641i	−0.785213	−	1.22728i
$808$		0			0
$809$	26.6955			0.938564			0.469282	−	0.883048i	$-0.344513\pi$
$809$	26.6955			0.938564			0.469282	+	0.883048i	$0.344513\pi$
$810$		0			0
$811$	38.2852			1.34438			0.672188	−	0.740381i	$-0.265355\pi$
$811$	38.2852			1.34438			0.672188	+	0.740381i	$0.265355\pi$
$812$		0			0
$813$	−11.4567	−	17.9067i	−0.401804	−	0.628014i
$814$		0			0
$815$	−9.01459	−	15.6137i	−0.315767	−	0.546925i
$816$		0			0
$817$	10.4612	−	18.1193i	0.365990	−	0.633914i
$818$		0			0
$819$	8.93706	−	19.3614i	0.312286	−	0.676542i
$820$		0			0
$821$	5.24990	−	9.09310i	0.183223	−	0.317351i	−0.759753	−	0.650211i	$-0.774680\pi$
$821$	5.24990	−	9.09310i	0.183223	−	0.317351i	0.942976	+	0.332860i	$0.108014\pi$
$822$		0			0
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	0.692240	−	0.721668i	$-0.256624\pi$
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	−0.971102	+	0.238664i	$0.923291\pi$
$824$		0			0
$825$	−3.90350	+	7.53420i	−0.135902	+	0.262307i
$826$		0			0
$827$	−48.7817			−1.69631			−0.848153	−	0.529752i	$-0.822285\pi$
$827$	−48.7817			−1.69631			−0.848153	+	0.529752i	$0.822285\pi$
$828$		0			0
$829$	−6.21926			−0.216004			−0.108002	−	0.994151i	$-0.534445\pi$
$829$	−6.21926			−0.216004			−0.108002	+	0.994151i	$0.534445\pi$
$830$		0			0
$831$	22.1139	−	1.00851i	0.767123	−	0.0349847i
$832$		0			0
$833$	2.25729	+	3.90975i	0.0782106	+	0.135465i
$834$		0			0
$835$	14.7989	−	25.6325i	0.512138	−	0.887049i
$836$		0			0
$837$	23.5261	+	30.2930i	0.813180	+	1.04708i
$838$		0			0
$839$	21.0366	−	36.4364i	0.726263	−	1.25792i	−0.232189	−	0.972671i	$-0.574589\pi$
$839$	21.0366	−	36.4364i	0.726263	−	1.25792i	0.958452	−	0.285254i	$-0.0920779\pi$
$840$		0			0
$841$	−9.82597	−	17.0191i	−0.338826	−	0.586865i
$842$		0			0
$843$	−49.3374	+	2.25004i	−1.69927	+	0.0774954i
$844$		0			0
$845$	92.3330			3.17635
$846$		0			0
$847$	−10.6008			−0.364247
$848$		0			0
$849$	−0.578990	+	1.11752i	−0.0198709	+	0.0383531i
$850$		0			0
$851$	2.13161	+	3.69206i	0.0730707	+	0.126562i
$852$		0			0
$853$	6.72519	−	11.6484i	0.230266	−	0.398833i	−0.727620	−	0.685980i	$-0.759374\pi$
$853$	6.72519	−	11.6484i	0.230266	−	0.398833i	0.957886	+	0.287147i	$0.0927070\pi$
$854$		0			0
$855$	31.8104	−	2.90748i	1.08789	−	0.0994336i
$856$		0			0
$857$	−20.6893	+	35.8349i	−0.706733	+	1.22410i	0.259330	+	0.965789i	$0.416498\pi$
$857$	−20.6893	+	35.8349i	−0.706733	+	1.22410i	−0.966063	+	0.258308i	$0.916835\pi$
$858$		0			0
$859$	19.8815	+	34.4358i	0.678349	+	1.17493i	0.975478	+	0.220097i	$0.0706374\pi$
$859$	19.8815	+	34.4358i	0.678349	+	1.17493i	−0.297129	+	0.954837i	$0.596029\pi$
$860$		0			0
$861$	0.255158	+	0.398809i	0.00869578	+	0.0135914i
$862$		0			0
$863$	53.3858			1.81727			0.908637	−	0.417588i	$-0.137124\pi$
$863$	53.3858			1.81727			0.908637	+	0.417588i	$0.137124\pi$
$864$		0			0
$865$	12.0541			0.409851
$866$		0			0
$867$	−3.15652	−	4.93359i	−0.107201	−	0.167554i
$868$		0			0
$869$	−14.9552	−	25.9033i	−0.507322	−	0.878708i
$870$		0			0
$871$	4.71780	−	8.17147i	0.159857	−	0.276880i
$872$		0			0
$873$	0.852336	+	1.20726i	0.0288472	+	0.0408597i
$874$		0			0
$875$	−4.85447	+	8.40819i	−0.164111	+	0.284249i
$876$		0			0
$877$	3.42674	+	5.93530i	0.115713	+	0.200421i	0.918065	−	0.396431i	$-0.129751\pi$
$877$	3.42674	+	5.93530i	0.115713	+	0.200421i	−0.802352	+	0.596852i	$0.796418\pi$
$878$		0			0
$879$	−20.3820	+	39.3396i	−0.687468	+	1.32689i
$880$		0			0
$881$	−12.5103			−0.421483			−0.210742	−	0.977542i	$-0.567588\pi$
$881$	−12.5103			−0.421483			−0.210742	+	0.977542i	$0.567588\pi$
$882$		0			0
$883$	6.69124			0.225178			0.112589	−	0.993642i	$-0.464086\pi$
$883$	6.69124			0.225178			0.112589	+	0.993642i	$0.464086\pi$
$884$		0			0
$885$	38.8822	−	1.77322i	1.30701	−	0.0596063i
$886$		0			0
$887$	−16.0708	−	27.8355i	−0.539605	−	0.934623i	−0.998925	−	0.0463524i	$-0.985240\pi$
$887$	−16.0708	−	27.8355i	−0.539605	−	0.934623i	0.459320	−	0.888271i	$-0.348093\pi$
$888$		0			0
$889$	−0.410019	+	0.710174i	−0.0137516	+	0.0238185i
$890$		0			0
$891$	41.1359	−	7.58300i	1.37810	−	0.254040i
$892$		0			0
$893$	−7.94639	+	13.7636i	−0.265916	+	0.460580i
$894$		0			0
$895$	2.19076	+	3.79450i	0.0732289	+	0.126836i
$896$		0			0
$897$	72.1569	−	3.29072i	2.40925	−	0.109874i
$898$		0			0
$899$	51.4868			1.71718
$900$		0			0
$901$	−22.8171			−0.760148
$902$		0			0
$903$	−3.85234	+	7.43546i	−0.128198	+	0.247437i
$904$		0			0
$905$	20.8442	+	36.1031i	0.692883	+	1.20011i
$906$		0			0
$907$	15.7016	−	27.1959i	0.521362	−	0.903025i	−0.478330	−	0.878180i	$-0.658758\pi$
$907$	15.7016	−	27.1959i	0.521362	−	0.903025i	0.999691	−	0.0248444i	$-0.00790902\pi$
$908$		0			0
$909$	−5.89397	−	8.34832i	−0.195491	−	0.276896i
$910$		0			0
$911$	−22.8982	+	39.6609i	−0.758653	+	1.31402i	0.184885	+	0.982760i	$0.440809\pi$
$911$	−22.8982	+	39.6609i	−0.758653	+	1.31402i	−0.943538	+	0.331265i	$0.892525\pi$
$912$		0			0
$913$	−3.45185	−	5.97877i	−0.114239	−	0.197868i
$914$		0			0
$915$	31.7350	+	49.6013i	1.04913	+	1.63977i
$916$		0			0
$917$	−7.78794			−0.257180
$918$		0			0
$919$	27.1800			0.896584			0.448292	−	0.893887i	$-0.352032\pi$
$919$	27.1800			0.896584			0.448292	+	0.893887i	$0.352032\pi$
$920$		0			0
$921$	5.81925	+	9.09540i	0.191751	+	0.299704i
$922$		0			0
$923$	−48.0576	−	83.2381i	−1.58183	−	2.73982i
$924$		0			0
$925$	0.382977	−	0.663336i	0.0125922	−	0.0218104i
$926$		0			0
$927$	15.4225	−	1.40962i	0.506540	−	0.0462979i
$928$		0			0
$929$	20.3338	−	35.2192i	0.667132	−	1.15551i	−0.311571	−	0.950223i	$-0.600855\pi$
$929$	20.3338	−	35.2192i	0.667132	−	1.15551i	0.978703	−	0.205283i	$-0.0658115\pi$
$930$		0			0
$931$	−2.16372	−	3.74766i	−0.0709129	−	0.122825i
$932$		0			0
$933$	−23.2968	+	44.9655i	−0.762703	+	1.47210i
$934$		0			0
$935$	−51.6270			−1.68838
$936$		0			0
$937$	16.4150			0.536254			0.268127	−	0.963384i	$-0.413595\pi$
$937$	16.4150			0.536254			0.268127	+	0.963384i	$0.413595\pi$
$938$		0			0
$939$	49.2893	−	2.24784i	1.60849	−	0.0733555i
$940$		0			0
$941$	−3.66878	−	6.35451i	−0.119599	−	0.207151i	0.800010	−	0.599987i	$-0.204827\pi$
$941$	−3.66878	−	6.35451i	−0.119599	−	0.207151i	−0.919609	+	0.392836i	$0.871494\pi$
$942$		0			0
$943$	−0.801851	+	1.38885i	−0.0261119	+	0.0452271i
$944$		0			0
$945$	−12.6659	+	1.74255i	−0.412020	+	0.0566852i
$946$		0			0
$947$	−29.5562	+	51.1929i	−0.960448	+	1.66354i	−0.239071	+	0.971002i	$0.576843\pi$
$947$	−29.5562	+	51.1929i	−0.960448	+	1.66354i	−0.721377	+	0.692543i	$0.756490\pi$
$948$		0			0
$949$	15.3801	+	26.6390i	0.499258	+	0.864740i
$950$		0			0
$951$	2.80039	−	0.127712i	0.0908088	−	0.00414134i
$952$		0			0
$953$	−16.9354			−0.548592			−0.274296	−	0.961645i	$-0.588445\pi$
$953$	−16.9354			−0.548592			−0.274296	+	0.961645i	$0.588445\pi$
$954$		0			0
$955$	−13.5074			−0.437089
$956$		0			0
$957$	25.8302	−	49.8554i	0.834973	−	1.61160i
$958$		0			0
$959$	−1.49640	−	2.59184i	−0.0483213	−	0.0836950i
$960$		0			0
$961$	−11.7434	+	20.3401i	−0.378819	+	0.656133i
$962$		0			0
$963$	7.24583	−	15.6975i	0.233493	−	0.505844i
$964$		0			0
$965$	6.77548	−	11.7355i	0.218110	−	0.377778i
$966$		0			0
$967$	3.55555	+	6.15839i	0.114339	+	0.198040i	0.917515	−	0.397701i	$-0.130192\pi$
$967$	3.55555	+	6.15839i	0.114339	+	0.198040i	−0.803177	+	0.595741i	$0.796858\pi$
$968$		0			0
$969$	18.2367	+	28.5036i	0.585846	+	0.915669i
$970$		0			0
$971$	−1.47102			−0.0472072			−0.0236036	−	0.999721i	$-0.507514\pi$
$971$	−1.47102			−0.0472072			−0.0236036	+	0.999721i	$0.507514\pi$
$972$		0			0
$973$	−6.32743			−0.202848
$974$		0			0
$975$	−6.99407	−	10.9316i	−0.223990	−	0.350092i
$976$		0			0
$977$	9.71634	+	16.8292i	0.310853	+	0.538413i	0.978547	−	0.206022i	$-0.0660519\pi$
$977$	9.71634	+	16.8292i	0.310853	+	0.538413i	−0.667694	+	0.744436i	$0.732719\pi$
$978$		0			0
$979$	−22.8545	+	39.5851i	−0.730432	+	1.26515i
$980$		0			0
$981$	11.2934	−	24.4662i	0.360570	−	0.781145i
$982$		0			0
$983$	−3.87218	+	6.70681i	−0.123503	+	0.213914i	−0.921147	−	0.389215i	$-0.872746\pi$
$983$	−3.87218	+	6.70681i	−0.123503	+	0.213914i	0.797644	+	0.603129i	$0.206080\pi$
$984$		0			0
$985$	−14.3078	−	24.7818i	−0.455884	−	0.789614i
$986$		0			0
$987$	2.92627	−	5.64803i	0.0931441	−	0.179779i
$988$		0			0
$989$	−28.3655			−0.901972
$990$		0			0
$991$	−14.4710			−0.459687			−0.229843	−	0.973228i	$-0.573821\pi$
$991$	−14.4710			−0.459687			−0.229843	+	0.973228i	$0.573821\pi$
$992$		0			0
$993$	−24.1929	+	1.10332i	−0.767738	+	0.0350127i
$994$		0			0
$995$	5.10243	+	8.83767i	0.161758	+	0.280173i
$996$		0			0
$997$	27.6549	−	47.8996i	0.875838	−	1.51700i	0.0199711	−	0.999801i	$-0.493643\pi$
$997$	27.6549	−	47.8996i	0.875838	−	1.51700i	0.855867	−	0.517196i	$-0.173024\pi$
$998$		0			0
$999$	−3.74057	+	0.514623i	−0.118346	+	0.0162819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.j.a.169.2	yes	6
3.2	odd	2		756.2.j.b.505.3		6
4.3	odd	2		1008.2.r.j.673.2		6
7.2	even	3		1764.2.i.g.1537.3		6
7.3	odd	6		1764.2.l.f.961.2		6
7.4	even	3		1764.2.l.e.961.2		6
7.5	odd	6		1764.2.i.d.1537.1		6
7.6	odd	2		1764.2.j.e.1177.2		6
9.2	odd	6		2268.2.a.h.1.1		3
9.4	even	3	inner	252.2.j.a.85.2	✓	6
9.5	odd	6		756.2.j.b.253.3		6
9.7	even	3		2268.2.a.i.1.3		3
12.11	even	2		3024.2.r.j.2017.3		6
21.2	odd	6		5292.2.i.f.2125.3		6
21.5	even	6		5292.2.i.e.2125.1		6
21.11	odd	6		5292.2.l.e.3313.1		6
21.17	even	6		5292.2.l.f.3313.3		6
21.20	even	2		5292.2.j.d.3529.1		6
36.7	odd	6		9072.2.a.by.1.3		3
36.11	even	6		9072.2.a.bv.1.1		3
36.23	even	6		3024.2.r.j.1009.3		6
36.31	odd	6		1008.2.r.j.337.2		6
63.4	even	3		1764.2.i.g.373.3		6
63.5	even	6		5292.2.l.f.361.3		6
63.13	odd	6		1764.2.j.e.589.2		6
63.23	odd	6		5292.2.l.e.361.1		6
63.31	odd	6		1764.2.i.d.373.1		6
63.32	odd	6		5292.2.i.f.1549.3		6
63.40	odd	6		1764.2.l.f.949.2		6
63.41	even	6		5292.2.j.d.1765.1		6
63.58	even	3		1764.2.l.e.949.2		6
63.59	even	6		5292.2.i.e.1549.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.j.a.85.2	✓	6	9.4	even	3	inner
252.2.j.a.169.2	yes	6	1.1	even	1	trivial
756.2.j.b.253.3		6	9.5	odd	6
756.2.j.b.505.3		6	3.2	odd	2
1008.2.r.j.337.2		6	36.31	odd	6
1008.2.r.j.673.2		6	4.3	odd	2
1764.2.i.d.373.1		6	63.31	odd	6
1764.2.i.d.1537.1		6	7.5	odd	6
1764.2.i.g.373.3		6	63.4	even	3
1764.2.i.g.1537.3		6	7.2	even	3
1764.2.j.e.589.2		6	63.13	odd	6
1764.2.j.e.1177.2		6	7.6	odd	2
1764.2.l.e.949.2		6	63.58	even	3
1764.2.l.e.961.2		6	7.4	even	3
1764.2.l.f.949.2		6	63.40	odd	6
1764.2.l.f.961.2		6	7.3	odd	6
2268.2.a.h.1.1		3	9.2	odd	6
2268.2.a.i.1.3		3	9.7	even	3
3024.2.r.j.1009.3		6	36.23	even	6
3024.2.r.j.2017.3		6	12.11	even	2
5292.2.i.e.1549.1		6	63.59	even	6
5292.2.i.e.2125.1		6	21.5	even	6
5292.2.i.f.1549.3		6	63.32	odd	6
5292.2.i.f.2125.3		6	21.2	odd	6
5292.2.j.d.1765.1		6	63.41	even	6
5292.2.j.d.3529.1		6	21.20	even	2
5292.2.l.e.361.1		6	63.23	odd	6
5292.2.l.e.3313.1		6	21.11	odd	6
5292.2.l.f.361.3		6	63.5	even	6
5292.2.l.f.3313.3		6	21.17	even	6
9072.2.a.bv.1.1		3	36.11	even	6
9072.2.a.by.1.3		3	36.7	odd	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.933463 - 1.45899i) q^{3} +(-1.23025 - 2.13086i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-1.25729 + 2.72382i) q^{9} +(-2.32383 + 4.02499i) q^{11} +(-3.55408 - 6.15585i) q^{13} +(-1.96050 + 3.78400i) q^{15} -4.51459 q^{17} +4.32743 q^{19} +(-1.73025 + 0.0789082i) q^{21} +(-2.93346 - 5.08091i) q^{23} +(-0.527042 + 0.912864i) q^{25} +(5.14766 - 0.708209i) q^{27} +(3.48755 - 6.04061i) q^{29} +(3.69076 + 6.39258i) q^{31} +(8.04163 - 0.366739i) q^{33} -2.46050 q^{35} -0.726654 q^{37} +(-5.66372 + 10.9316i) q^{39} +(-0.136673 - 0.236725i) q^{41} +(2.41741 - 4.18708i) q^{43} +(7.35087 - 0.671871i) q^{45} +(-1.83628 + 3.18054i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(4.21420 + 6.58673i) q^{51} +5.05408 q^{53} +11.4356 q^{55} +(-4.03950 - 6.31367i) q^{57} +(-4.56654 - 7.90947i) q^{59} +(6.90856 - 11.9660i) q^{61} +(1.73025 + 2.45076i) q^{63} +(-8.74484 + 15.1465i) q^{65} +(0.663715 + 1.14959i) q^{67} +(-4.67471 + 9.02273i) q^{69} +13.5218 q^{71} -4.32743 q^{73} +(1.82383 - 0.0831759i) q^{75} +(2.32383 + 4.02499i) q^{77} +(-3.21780 + 5.57339i) q^{79} +(-5.83842 - 6.84929i) q^{81} +(-0.742705 + 1.28640i) q^{83} +(5.55408 + 9.61996i) q^{85} +(-12.0687 + 0.550392i) q^{87} +9.83482 q^{89} -7.10817 q^{91} +(5.88151 - 11.3520i) q^{93} +(-5.32383 - 9.22115i) q^{95} +(0.246304 - 0.426611i) q^{97} +(-8.04163 - 11.3903i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{3} - q^{5} + 3 q^{7} + 8 q^{9} - 2 q^{11} - 3 q^{13} + q^{15} + 4 q^{17} + 6 q^{19} - 4 q^{21} - 14 q^{23} + 6 q^{25} + 7 q^{27} - q^{29} + 3 q^{31} + 8 q^{33} - 2 q^{35} - 6 q^{37} - 24 q^{39}+ \cdots - 8 q^{99}+O(q^{100}) \) 6 * q - 2 * q^3 - q^5 + 3 * q^7 + 8 * q^9 - 2 * q^11 - 3 * q^13 + q^15 + 4 * q^17 + 6 * q^19 - 4 * q^21 - 14 * q^23 + 6 * q^25 + 7 * q^27 - q^29 + 3 * q^31 + 8 * q^33 - 2 * q^35 - 6 * q^37 - 24 * q^39 - 3 * q^43 + 23 * q^45 - 21 * q^47 - 3 * q^49 + 5 * q^51 + 12 * q^53 + 12 * q^55 - 37 * q^57 - 31 * q^59 - 6 * q^61 + 4 * q^63 - 15 * q^65 - 6 * q^67 + 5 * q^69 + 34 * q^71 - 6 * q^73 - q^75 + 2 * q^77 + 9 * q^79 + 8 * q^81 - 20 * q^83 + 15 * q^85 - 23 * q^87 + 24 * q^89 - 6 * q^91 - 3 * q^93 - 20 * q^95 + 9 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more