LMFDB - Embedded newform 1008.2.r.h.337.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(337,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("1008.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.r (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
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:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			337.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	1008.337
Dual form			1008.2.r.h.673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70574 + 0.300767i) q^{3} +(-1.26604 + 2.19285i) q^{5} +(0.500000 + 0.866025i) q^{7} +(2.81908 - 1.02606i) q^{9} +O(q^{10})$	\(q+(-1.70574 + 0.300767i) q^{3} +(-1.26604 + 2.19285i) q^{5} +(0.500000 + 0.866025i) q^{7} +(2.81908 - 1.02606i) q^{9} +(0.233956 + 0.405223i) q^{11} +(-2.91147 + 5.04282i) q^{13} +(1.50000 - 4.12122i) q^{15} +3.87939 q^{17} +2.18479 q^{19} +(-1.11334 - 1.32683i) q^{21} +(-0.0530334 + 0.0918566i) q^{23} +(-0.705737 - 1.22237i) q^{25} +(-4.50000 + 2.59808i) q^{27} +(-4.39053 - 7.60462i) q^{29} +(-3.84002 + 6.65111i) q^{31} +(-0.520945 - 0.620838i) q^{33} -2.53209 q^{35} -7.68004 q^{37} +(3.44949 - 9.47740i) q^{39} +(1.11334 - 1.92836i) q^{41} +(0.613341 + 1.06234i) q^{43} +(-1.31908 + 7.48086i) q^{45} +(-2.66637 - 4.61830i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-6.61721 + 1.16679i) q^{51} -0.716881 q^{53} -1.18479 q^{55} +(-3.72668 + 0.657115i) q^{57} +(0.368241 - 0.637812i) q^{59} +(-0.479055 - 0.829748i) q^{61} +(2.29813 + 1.92836i) q^{63} +(-7.37211 - 12.7689i) q^{65} +(-4.81908 + 8.34689i) q^{67} +(0.0628336 - 0.172634i) q^{69} -13.2344 q^{71} -10.2686 q^{73} +(1.57145 + 1.87278i) q^{75} +(-0.233956 + 0.405223i) q^{77} +(-6.31908 - 10.9450i) q^{79} +(6.89440 - 5.78509i) q^{81} +(-1.36571 - 2.36549i) q^{83} +(-4.91147 + 8.50692i) q^{85} +(9.77631 + 11.6510i) q^{87} -8.11381 q^{89} -5.82295 q^{91} +(4.54963 - 12.5000i) q^{93} +(-2.76604 + 4.79093i) q^{95} +(6.80200 + 11.7814i) q^{97} +(1.07532 + 0.902302i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} + 3 q^{7}+O(q^{10}) $ 6 * q - 3 * q^5 + 3 * q^7	$ 6 q - 3 q^{5} + 3 q^{7} + 6 q^{11} + 3 q^{13} + 9 q^{15} + 12 q^{17} + 6 q^{19} + 12 q^{23} + 6 q^{25} - 27 q^{27} - 9 q^{29} - 3 q^{31} - 6 q^{35} - 6 q^{37} + 18 q^{39} - 3 q^{43} + 9 q^{45} + 3 q^{47} - 3 q^{49} - 9 q^{51} + 12 q^{53} - 9 q^{57} - 3 q^{59} - 6 q^{61} - 15 q^{65} - 12 q^{67} - 9 q^{69} - 18 q^{71} - 42 q^{73} + 9 q^{75} - 6 q^{77} - 21 q^{79} - 18 q^{83} - 9 q^{85} - 9 q^{87} + 24 q^{89} + 6 q^{91} - 27 q^{93} - 12 q^{95} + 3 q^{97} - 18 q^{99}+O(q^{100}) $ 6 * q - 3 * q^5 + 3 * q^7 + 6 * q^11 + 3 * q^13 + 9 * q^15 + 12 * q^17 + 6 * q^19 + 12 * q^23 + 6 * q^25 - 27 * q^27 - 9 * q^29 - 3 * q^31 - 6 * q^35 - 6 * q^37 + 18 * q^39 - 3 * q^43 + 9 * q^45 + 3 * q^47 - 3 * q^49 - 9 * q^51 + 12 * q^53 - 9 * q^57 - 3 * q^59 - 6 * q^61 - 15 * q^65 - 12 * q^67 - 9 * q^69 - 18 * q^71 - 42 * q^73 + 9 * q^75 - 6 * q^77 - 21 * q^79 - 18 * q^83 - 9 * q^85 - 9 * q^87 + 24 * q^89 + 6 * q^91 - 27 * q^93 - 12 * q^95 + 3 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.70574	+	0.300767i	−0.984808	+	0.173648i
$3$	−1.70574	+	0.300767i	−0.984808	+	0.173648i
$4$		0			0
$5$	−1.26604	+	2.19285i	−0.566192	+	0.980674i	0.430745	+	0.902473i	$0.358251\pi$
$5$	−1.26604	+	2.19285i	−0.566192	+	0.980674i	−0.996938	+	0.0782003i	$0.975083\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$		0			0
$9$	2.81908	−	1.02606i	0.939693	−	0.342020i
$10$		0			0
$11$	0.233956	+	0.405223i	0.0705403	+	0.122179i	0.899138	−	0.437665i	$-0.144194\pi$
$11$	0.233956	+	0.405223i	0.0705403	+	0.122179i	−0.828598	+	0.559844i	$0.810861\pi$
$12$		0			0
$13$	−2.91147	+	5.04282i	−0.807498	+	1.39863i	0.107094	+	0.994249i	$0.465845\pi$
$13$	−2.91147	+	5.04282i	−0.807498	+	1.39863i	−0.914592	+	0.404378i	$0.867488\pi$
$14$		0			0
$15$	1.50000	−	4.12122i	0.387298	−	1.06409i
$16$		0			0
$17$	3.87939			0.940889			0.470445	−	0.882430i	$-0.344094\pi$
$17$	3.87939			0.940889			0.470445	+	0.882430i	$0.344094\pi$
$18$		0			0
$19$	2.18479			0.501226			0.250613	−	0.968087i	$-0.419368\pi$
$19$	2.18479			0.501226			0.250613	+	0.968087i	$0.419368\pi$
$20$		0			0
$21$	−1.11334	−	1.32683i	−0.242951	−	0.289538i
$22$		0			0
$23$	−0.0530334	+	0.0918566i	−0.0110582	+	0.0191534i	−0.871502	−	0.490393i	$-0.836853\pi$
$23$	−0.0530334	+	0.0918566i	−0.0110582	+	0.0191534i	0.860443	+	0.509546i	$0.170187\pi$
$24$		0			0
$25$	−0.705737	−	1.22237i	−0.141147	−	0.244474i
$26$		0			0
$27$	−4.50000	+	2.59808i	−0.866025	+	0.500000i
$28$		0			0
$29$	−4.39053	−	7.60462i	−0.815301	−	1.41214i	−0.909112	−	0.416552i	$-0.863238\pi$
$29$	−4.39053	−	7.60462i	−0.815301	−	1.41214i	0.0938108	−	0.995590i	$-0.470095\pi$
$30$		0			0
$31$	−3.84002	+	6.65111i	−0.689688	+	1.19458i	0.282250	+	0.959341i	$0.408919\pi$
$31$	−3.84002	+	6.65111i	−0.689688	+	1.19458i	−0.971939	+	0.235235i	$0.924414\pi$
$32$		0			0
$33$	−0.520945	−	0.620838i	−0.0906848	−	0.108074i
$34$		0			0
$35$	−2.53209			−0.428001
$36$		0			0
$37$	−7.68004			−1.26259			−0.631296	−	0.775542i	$-0.717477\pi$
$37$	−7.68004			−1.26259			−0.631296	+	0.775542i	$0.717477\pi$
$38$		0			0
$39$	3.44949	−	9.47740i	0.552361	−	1.51760i
$40$		0			0
$41$	1.11334	−	1.92836i	0.173875	−	0.301160i	−0.765897	−	0.642964i	$-0.777705\pi$
$41$	1.11334	−	1.92836i	0.173875	−	0.301160i	0.939771	+	0.341804i	$0.111038\pi$
$42$		0			0
$43$	0.613341	+	1.06234i	0.0935336	+	0.162005i	0.908996	−	0.416806i	$-0.136850\pi$
$43$	0.613341	+	1.06234i	0.0935336	+	0.162005i	−0.815462	+	0.578811i	$0.803517\pi$
$44$		0			0
$45$	−1.31908	+	7.48086i	−0.196637	+	1.11518i
$46$		0			0
$47$	−2.66637	−	4.61830i	−0.388931	−	0.673648i	0.603375	−	0.797457i	$-0.293822\pi$
$47$	−2.66637	−	4.61830i	−0.388931	−	0.673648i	−0.992306	+	0.123810i	$0.960489\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$	−6.61721	+	1.16679i	−0.926595	+	0.163384i
$52$		0			0
$53$	−0.716881			−0.0984712			−0.0492356	−	0.998787i	$-0.515679\pi$
$53$	−0.716881			−0.0984712			−0.0492356	+	0.998787i	$0.515679\pi$
$54$		0			0
$55$	−1.18479			−0.159757
$56$		0			0
$57$	−3.72668	+	0.657115i	−0.493611	+	0.0870369i
$58$		0			0
$59$	0.368241	−	0.637812i	0.0479409	−	0.0830360i	−0.841059	−	0.540943i	$-0.818067\pi$
$59$	0.368241	−	0.637812i	0.0479409	−	0.0830360i	0.889000	+	0.457907i	$0.151401\pi$
$60$		0			0
$61$	−0.479055	−	0.829748i	−0.0613368	−	0.106238i	0.833726	−	0.552178i	$-0.186203\pi$
$61$	−0.479055	−	0.829748i	−0.0613368	−	0.106238i	−0.895063	+	0.445939i	$0.852870\pi$
$62$		0			0
$63$	2.29813	+	1.92836i	0.289538	+	0.242951i
$64$		0			0
$65$	−7.37211	−	12.7689i	−0.914398	−	1.58378i
$66$		0			0
$67$	−4.81908	+	8.34689i	−0.588744	+	1.01973i	0.405653	+	0.914027i	$0.367044\pi$
$67$	−4.81908	+	8.34689i	−0.588744	+	1.01973i	−0.994397	+	0.105708i	$0.966289\pi$
$68$		0			0
$69$	0.0628336	−	0.172634i	0.00756428	−	0.0207827i
$70$		0			0
$71$	−13.2344			−1.57064			−0.785318	−	0.619092i	$-0.787501\pi$
$71$	−13.2344			−1.57064			−0.785318	+	0.619092i	$0.787501\pi$
$72$		0			0
$73$	−10.2686			−1.20185			−0.600923	−	0.799307i	$-0.705200\pi$
$73$	−10.2686			−1.20185			−0.600923	+	0.799307i	$0.705200\pi$
$74$		0			0
$75$	1.57145	+	1.87278i	0.181456	+	0.216250i
$76$		0			0
$77$	−0.233956	+	0.405223i	−0.0266617	+	0.0461794i
$78$		0			0
$79$	−6.31908	−	10.9450i	−0.710952	−	1.23140i	−0.964500	−	0.264082i	$-0.914931\pi$
$79$	−6.31908	−	10.9450i	−0.710952	−	1.23140i	0.253548	−	0.967323i	$-0.418402\pi$
$80$		0			0
$81$	6.89440	−	5.78509i	0.766044	−	0.642788i
$82$		0			0
$83$	−1.36571	−	2.36549i	−0.149907	−	0.259646i	0.781286	−	0.624173i	$-0.214564\pi$
$83$	−1.36571	−	2.36549i	−0.149907	−	0.259646i	−0.931193	+	0.364527i	$0.881231\pi$
$84$		0			0
$85$	−4.91147	+	8.50692i	−0.532724	+	0.922705i
$86$		0			0
$87$	9.77631	+	11.6510i	1.04813	+	1.24911i
$88$		0			0
$89$	−8.11381			−0.860062			−0.430031	−	0.902814i	$-0.641497\pi$
$89$	−8.11381			−0.860062			−0.430031	+	0.902814i	$0.641497\pi$
$90$		0			0
$91$	−5.82295			−0.610411
$92$		0			0
$93$	4.54963	−	12.5000i	0.471775	−	1.29619i
$94$		0			0
$95$	−2.76604	+	4.79093i	−0.283790	+	0.491539i
$96$		0			0
$97$	6.80200	+	11.7814i	0.690639	+	1.19622i	0.971629	+	0.236511i	$0.0760039\pi$
$97$	6.80200	+	11.7814i	0.690639	+	1.19622i	−0.280990	+	0.959711i	$0.590663\pi$
$98$		0			0
$99$	1.07532	+	0.902302i	0.108074	+	0.0906848i
$100$		0			0
$101$	4.78699	+	8.29131i	0.476323	+	0.825016i	0.999632	−	0.0271271i	$-0.00863590\pi$
$101$	4.78699	+	8.29131i	0.476323	+	0.825016i	−0.523309	+	0.852143i	$0.675303\pi$
$102$		0			0
$103$	1.52094	−	2.63435i	0.149863	−	0.259571i	−0.781314	−	0.624139i	$-0.785450\pi$
$103$	1.52094	−	2.63435i	0.149863	−	0.259571i	0.931177	+	0.364568i	$0.118783\pi$
$104$		0			0
$105$	4.31908	−	0.761570i	0.421499	−	0.0743216i
$106$		0			0
$107$	6.51754			0.630074			0.315037	−	0.949079i	$-0.397983\pi$
$107$	6.51754			0.630074			0.315037	+	0.949079i	$0.397983\pi$
$108$		0			0
$109$	10.6382			1.01895			0.509475	−	0.860485i	$-0.329840\pi$
$109$	10.6382			1.01895			0.509475	+	0.860485i	$0.329840\pi$
$110$		0			0
$111$	13.1001	−	2.30991i	1.24341	−	0.219247i
$112$		0			0
$113$	−2.58853	+	4.48346i	−0.243508	+	0.421768i	−0.961711	−	0.274065i	$-0.911632\pi$
$113$	−2.58853	+	4.48346i	−0.243508	+	0.421768i	0.718203	+	0.695834i	$0.244965\pi$
$114$		0			0
$115$	−0.134285	−	0.232589i	−0.0125222	−	0.0216890i
$116$		0			0
$117$	−3.03343	+	17.2035i	−0.280441	+	1.59046i
$118$		0			0
$119$	1.93969	+	3.35965i	0.177811	+	0.307978i
$120$		0			0
$121$	5.39053	−	9.33667i	0.490048	−	0.848788i
$122$		0			0
$123$	−1.31908	+	3.62414i	−0.118937	+	0.326777i
$124$		0			0
$125$	−9.08647			−0.812718
$126$		0			0
$127$	8.88207			0.788157			0.394078	−	0.919077i	$-0.371064\pi$
$127$	8.88207			0.788157			0.394078	+	0.919077i	$0.371064\pi$
$128$		0			0
$129$	−1.36571	−	1.62760i	−0.120244	−	0.143302i
$130$		0			0
$131$	5.68139	−	9.84045i	0.496385	−	0.859764i	−0.503606	−	0.863933i	$-0.667994\pi$
$131$	5.68139	−	9.84045i	0.496385	−	0.859764i	0.999991	+	0.00416893i	$0.00132701\pi$
$132$		0			0
$133$	1.09240	+	1.89209i	0.0947228	+	0.164065i
$134$		0			0
$135$		−	13.1571i		−	1.13238i
$136$		0			0
$137$	2.86231	+	4.95767i	0.244544	+	0.423562i	0.962003	−	0.273038i	$-0.0880285\pi$
$137$	2.86231	+	4.95767i	0.244544	+	0.423562i	−0.717459	+	0.696600i	$0.754695\pi$
$138$		0			0
$139$	−0.461981	+	0.800175i	−0.0391847	+	0.0678700i	−0.884953	−	0.465681i	$-0.845809\pi$
$139$	−0.461981	+	0.800175i	−0.0391847	+	0.0678700i	0.845768	+	0.533551i	$0.179143\pi$
$140$		0			0
$141$	5.93717	+	7.07564i	0.500000	+	0.595876i
$142$		0			0
$143$	−2.72462			−0.227844
$144$		0			0
$145$	22.2344			1.84647
$146$		0			0
$147$	0.592396	−	1.62760i	0.0488600	−	0.134242i
$148$		0			0
$149$	−4.36231	+	7.55574i	−0.357374	+	0.618991i	−0.987521	−	0.157485i	$-0.949661\pi$
$149$	−4.36231	+	7.55574i	−0.357374	+	0.618991i	0.630147	+	0.776476i	$0.282995\pi$
$150$		0			0
$151$	9.21348	+	15.9582i	0.749782	+	1.29866i	0.947927	+	0.318488i	$0.103175\pi$
$151$	9.21348	+	15.9582i	0.749782	+	1.29866i	−0.198145	+	0.980173i	$0.563492\pi$
$152$		0			0
$153$	10.9363	−	3.98048i	0.884147	−	0.321803i
$154$		0			0
$155$	−9.72328	−	16.8412i	−0.780992	−	1.35272i
$156$		0			0
$157$	−2.46198	+	4.26428i	−0.196488	+	0.340326i	−0.947387	−	0.320090i	$-0.896287\pi$
$157$	−2.46198	+	4.26428i	−0.196488	+	0.340326i	0.750900	+	0.660416i	$0.229620\pi$
$158$		0			0
$159$	1.22281	−	0.215615i	0.0969752	−	0.0170994i
$160$		0			0
$161$	−0.106067			−0.00835924
$162$		0			0
$163$	−7.63816			−0.598267			−0.299133	−	0.954211i	$-0.596698\pi$
$163$	−7.63816			−0.598267			−0.299133	+	0.954211i	$0.596698\pi$
$164$		0			0
$165$	2.02094	−	0.356347i	0.157330	−	0.0277416i
$166$		0			0
$167$	−2.82770	+	4.89771i	−0.218814	+	0.378996i	−0.954446	−	0.298385i	$-0.903552\pi$
$167$	−2.82770	+	4.89771i	−0.218814	+	0.378996i	0.735632	+	0.677382i	$0.236885\pi$
$168$		0			0
$169$	−10.4534	−	18.1058i	−0.804105	−	1.39275i
$170$		0			0
$171$	6.15910	−	2.24173i	0.470998	−	0.171429i
$172$		0			0
$173$	−10.5346	−	18.2465i	−0.800932	−	1.38725i	−0.919003	−	0.394250i	$-0.871005\pi$
$173$	−10.5346	−	18.2465i	−0.800932	−	1.38725i	0.118071	−	0.993005i	$-0.462329\pi$
$174$		0			0
$175$	0.705737	−	1.22237i	0.0533487	−	0.0924027i
$176$		0			0
$177$	−0.436289	+	1.19869i	−0.0327935	+	0.0900994i
$178$		0			0
$179$	5.12061			0.382733			0.191366	−	0.981519i	$-0.438708\pi$
$179$	5.12061			0.382733			0.191366	+	0.981519i	$0.438708\pi$
$180$		0			0
$181$	−0.319955			−0.0237821			−0.0118910	−	0.999929i	$-0.503785\pi$
$181$	−0.319955			−0.0237821			−0.0118910	+	0.999929i	$0.503785\pi$
$182$		0			0
$183$	1.06670	+	1.27125i	0.0788530	+	0.0939734i
$184$		0			0
$185$	9.72328	−	16.8412i	0.714870	−	1.23819i
$186$		0			0
$187$	0.907604	+	1.57202i	0.0663706	+	0.114957i
$188$		0			0
$189$	−4.50000	−	2.59808i	−0.327327	−	0.188982i
$190$		0			0
$191$	−7.78359	−	13.4816i	−0.563200	−	0.975492i	−0.997215	−	0.0745858i	$-0.976237\pi$
$191$	−7.78359	−	13.4816i	−0.563200	−	0.975492i	0.434014	−	0.900906i	$-0.357097\pi$
$192$		0			0
$193$	−3.02094	+	5.23243i	−0.217452	+	0.376639i	−0.954028	−	0.299716i	$-0.903108\pi$
$193$	−3.02094	+	5.23243i	−0.217452	+	0.376639i	0.736576	+	0.676355i	$0.236441\pi$
$194$		0			0
$195$	16.4153	+	19.5630i	1.17553	+	1.40094i
$196$		0			0
$197$	25.2344			1.79788			0.898939	−	0.438074i	$-0.144339\pi$
$197$	25.2344			1.79788			0.898939	+	0.438074i	$0.144339\pi$
$198$		0			0
$199$	−3.04189			−0.215634			−0.107817	−	0.994171i	$-0.534386\pi$
$199$	−3.04189			−0.215634			−0.107817	+	0.994171i	$0.534386\pi$
$200$		0			0
$201$	5.70961	−	15.6870i	0.402725	−	1.10648i
$202$		0			0
$203$	4.39053	−	7.60462i	0.308155	−	0.533740i
$204$		0			0
$205$	2.81908	+	4.88279i	0.196893	+	0.341029i
$206$		0			0
$207$	−0.0552549	+	0.313366i	−0.00384048	+	0.0217805i
$208$		0			0
$209$	0.511144	+	0.885328i	0.0353566	+	0.0612394i
$210$		0			0
$211$	−2.72668	+	4.72275i	−0.187713	+	0.325128i	−0.944487	−	0.328548i	$-0.893441\pi$
$211$	−2.72668	+	4.72275i	−0.187713	+	0.325128i	0.756775	+	0.653676i	$0.226774\pi$
$212$		0			0
$213$	22.5744	−	3.98048i	1.54678	−	0.272738i
$214$		0			0
$215$	−3.10607			−0.211832
$216$		0			0
$217$	−7.68004			−0.521355
$218$		0			0
$219$	17.5155	−	3.08845i	1.18359	−	0.208698i
$220$		0			0
$221$	−11.2947	+	19.5630i	−0.759766	+	1.31595i
$222$		0			0
$223$	7.09627	+	12.2911i	0.475201	+	0.823073i	0.999597	−	0.0284023i	$-0.00904195\pi$
$223$	7.09627	+	12.2911i	0.475201	+	0.823073i	−0.524395	+	0.851475i	$0.675709\pi$
$224$		0			0
$225$	−3.24376	−	2.72183i	−0.216250	−	0.181456i
$226$		0			0
$227$	−1.44697	−	2.50622i	−0.0960385	−	0.166344i	0.814003	−	0.580861i	$-0.197284\pi$
$227$	−1.44697	−	2.50622i	−0.0960385	−	0.166344i	−0.910042	+	0.414517i	$0.863951\pi$
$228$		0			0
$229$	−4.58378	+	7.93934i	−0.302905	+	0.524646i	−0.976793	−	0.214187i	$-0.931290\pi$
$229$	−4.58378	+	7.93934i	−0.302905	+	0.524646i	0.673888	+	0.738834i	$0.264623\pi$
$230$		0			0
$231$	0.277189	−	0.761570i	0.0182377	−	0.0501076i
$232$		0			0
$233$	13.2713			0.869429			0.434715	−	0.900568i	$-0.356849\pi$
$233$	13.2713			0.869429			0.434715	+	0.900568i	$0.356849\pi$
$234$		0			0
$235$	13.5030			0.880838
$236$		0			0
$237$	14.0706	+	16.7687i	0.913982	+	1.08924i
$238$		0			0
$239$	4.76857	−	8.25941i	0.308453	−	0.534257i	−0.669571	−	0.742748i	$-0.733522\pi$
$239$	4.76857	−	8.25941i	0.308453	−	0.534257i	0.978024	+	0.208491i	$0.0668553\pi$
$240$		0			0
$241$	4.47906	+	7.75795i	0.288521	+	0.499734i	0.973457	−	0.228870i	$-0.0735031\pi$
$241$	4.47906	+	7.75795i	0.288521	+	0.499734i	−0.684936	+	0.728604i	$0.740170\pi$
$242$		0			0
$243$	−10.0201	+	11.9415i	−0.642788	+	0.766044i
$244$		0			0
$245$	−1.26604	−	2.19285i	−0.0808846	−	0.140096i
$246$		0			0
$247$	−6.36097	+	11.0175i	−0.404739	+	0.701028i
$248$		0			0
$249$	3.04101	+	3.62414i	0.192716	+	0.229670i
$250$		0			0
$251$	24.9982			1.57788			0.788938	−	0.614473i	$-0.210631\pi$
$251$	24.9982			1.57788			0.788938	+	0.614473i	$0.210631\pi$
$252$		0			0
$253$	−0.0496299			−0.00312020
$254$		0			0
$255$	5.81908	−	15.9878i	0.364405	−	1.00119i
$256$		0			0
$257$	−5.42602	+	9.39815i	−0.338466	+	0.586240i	−0.984144	−	0.177369i	$-0.943241\pi$
$257$	−5.42602	+	9.39815i	−0.338466	+	0.586240i	0.645678	+	0.763609i	$0.276575\pi$
$258$		0			0
$259$	−3.84002	−	6.65111i	−0.238607	−	0.413280i
$260$		0			0
$261$	−20.1800	−	16.9331i	−1.24911	−	1.04813i
$262$		0			0
$263$	13.0437	+	22.5924i	0.804309	+	1.39310i	0.916757	+	0.399446i	$0.130798\pi$
$263$	13.0437	+	22.5924i	0.804309	+	1.39310i	−0.112448	+	0.993658i	$0.535869\pi$
$264$		0			0
$265$	0.907604	−	1.57202i	0.0557537	−	0.0965682i
$266$		0			0
$267$	13.8400	−	2.44037i	0.846996	−	0.149348i
$268$		0			0
$269$	−7.63310			−0.465399			−0.232699	−	0.972549i	$-0.574756\pi$
$269$	−7.63310			−0.465399			−0.232699	+	0.972549i	$0.574756\pi$
$270$		0			0
$271$	−3.40373			−0.206762			−0.103381	−	0.994642i	$-0.532966\pi$
$271$	−3.40373			−0.206762			−0.103381	+	0.994642i	$0.532966\pi$
$272$		0			0
$273$	9.93242	−	1.75135i	0.601137	−	0.105997i
$274$		0			0
$275$	0.330222	−	0.571962i	0.0199131	−	0.0344906i
$276$		0			0
$277$	2.86097	+	4.95534i	0.171899	+	0.297738i	0.939084	−	0.343689i	$-0.111676\pi$
$277$	2.86097	+	4.95534i	0.171899	+	0.297738i	−0.767185	+	0.641426i	$0.778343\pi$
$278$		0			0
$279$	−4.00088	+	22.6901i	−0.239526	+	1.35842i
$280$		0			0
$281$	−14.1887	−	24.5755i	−0.846425	−	1.46605i	−0.884378	−	0.466771i	$-0.845417\pi$
$281$	−14.1887	−	24.5755i	−0.846425	−	1.46605i	0.0379535	−	0.999280i	$-0.487916\pi$
$282$		0			0
$283$	2.28564	−	3.95885i	0.135867	−	0.235329i	−0.790061	−	0.613028i	$-0.789951\pi$
$283$	2.28564	−	3.95885i	0.135867	−	0.235329i	0.925929	+	0.377699i	$0.123285\pi$
$284$		0			0
$285$	3.27719	−	9.00400i	0.194124	−	0.533351i
$286$		0			0
$287$	2.22668			0.131437
$288$		0			0
$289$	−1.95037			−0.114728
$290$		0			0
$291$	−15.1459	−	18.0502i	−0.887868	−	1.05812i
$292$		0			0
$293$	−2.16385	+	3.74789i	−0.126413	+	0.218954i	−0.922285	−	0.386512i	$-0.873680\pi$
$293$	−2.16385	+	3.74789i	−0.126413	+	0.218954i	0.795871	+	0.605466i	$0.207013\pi$
$294$		0			0
$295$	0.932419	+	1.61500i	0.0542875	+	0.0940287i
$296$		0			0
$297$	−2.10560	−	1.21567i	−0.122179	−	0.0705403i
$298$		0			0
$299$	−0.308811	−	0.534876i	−0.0178590	−	0.0309327i
$300$		0			0
$301$	−0.613341	+	1.06234i	−0.0353524	+	0.0612321i
$302$		0			0
$303$	−10.6591	−	12.7030i	−0.612349	−	0.729769i
$304$		0			0
$305$	2.42602			0.138914
$306$		0			0
$307$	−12.3773			−0.706411			−0.353206	−	0.935546i	$-0.614908\pi$
$307$	−12.3773			−0.706411			−0.353206	+	0.935546i	$0.614908\pi$
$308$		0			0
$309$	−1.80200	+	4.95096i	−0.102512	+	0.281651i
$310$		0			0
$311$	−10.9927	+	19.0400i	−0.623340	+	1.07966i	0.365519	+	0.930804i	$0.380892\pi$
$311$	−10.9927	+	19.0400i	−0.623340	+	1.07966i	−0.988859	+	0.148853i	$0.952442\pi$
$312$		0			0
$313$	6.94491	+	12.0289i	0.392549	+	0.679915i	0.992785	−	0.119908i	$-0.0382599\pi$
$313$	6.94491	+	12.0289i	0.392549	+	0.679915i	−0.600236	+	0.799823i	$0.704927\pi$
$314$		0			0
$315$	−7.13816	+	2.59808i	−0.402190	+	0.146385i
$316$		0			0
$317$	3.09105	+	5.35386i	0.173611	+	0.300703i	0.939680	−	0.342056i	$-0.111123\pi$
$317$	3.09105	+	5.35386i	0.173611	+	0.300703i	−0.766069	+	0.642759i	$0.777790\pi$
$318$		0			0
$319$	2.05438	−	3.55829i	0.115023	−	0.199226i
$320$		0			0
$321$	−11.1172	+	1.96026i	−0.620502	+	0.109411i
$322$		0			0
$323$	8.47565			0.471598
$324$		0			0
$325$	8.21894			0.455905
$326$		0			0
$327$	−18.1459	+	3.19961i	−1.00347	+	0.176939i
$328$		0			0
$329$	2.66637	−	4.61830i	0.147002	−	0.254615i
$330$		0			0
$331$	5.36571	+	9.29369i	0.294926	+	0.510827i	0.974968	−	0.222346i	$-0.0713715\pi$
$331$	5.36571	+	9.29369i	0.294926	+	0.510827i	−0.680041	+	0.733174i	$0.738038\pi$
$332$		0			0
$333$	−21.6506	+	7.88019i	−1.18645	+	0.431832i
$334$		0			0
$335$	−12.2023	−	21.1351i	−0.666685	−	1.15473i
$336$		0			0
$337$	9.29726	−	16.1033i	0.506454	−	0.877204i	−0.493518	−	0.869735i	$-0.664289\pi$
$337$	9.29726	−	16.1033i	0.506454	−	0.877204i	0.999972	−	0.00746831i	$-0.00237726\pi$
$338$		0			0
$339$	3.06687	−	8.42615i	0.166569	−	0.457645i
$340$		0			0
$341$	−3.59358			−0.194603
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	0.299011	+	0.356347i	0.0160982	+	0.0191851i
$346$		0			0
$347$	−10.2062	+	17.6777i	−0.547898	+	0.948987i	0.450521	+	0.892766i	$0.351238\pi$
$347$	−10.2062	+	17.6777i	−0.547898	+	0.948987i	−0.998418	+	0.0562207i	$0.982095\pi$
$348$		0			0
$349$	1.78106	+	3.08489i	0.0953379	+	0.165130i	0.909750	−	0.415157i	$-0.136274\pi$
$349$	1.78106	+	3.08489i	0.0953379	+	0.165130i	−0.814412	+	0.580288i	$0.802940\pi$
$350$		0			0
$351$		−	30.2569i		−	1.61500i
$352$		0			0
$353$	−5.01114	−	8.67956i	−0.266716	−	0.461966i	0.701296	−	0.712871i	$-0.252605\pi$
$353$	−5.01114	−	8.67956i	−0.266716	−	0.461966i	−0.968012	+	0.250904i	$0.919272\pi$
$354$		0			0
$355$	16.7554	−	29.0211i	0.889283	−	1.54028i
$356$		0			0
$357$	−4.31908	−	5.14728i	−0.228590	−	0.272423i
$358$		0			0
$359$	−9.48070			−0.500372			−0.250186	−	0.968198i	$-0.580492\pi$
$359$	−9.48070			−0.500372			−0.250186	+	0.968198i	$0.580492\pi$
$360$		0			0
$361$	−14.2267			−0.748773
$362$		0			0
$363$	−6.38666	+	17.5472i	−0.335213	+	0.920989i
$364$		0			0
$365$	13.0005	−	22.5175i	0.680476	−	1.17862i
$366$		0			0
$367$	8.06670	+	13.9719i	0.421079	+	0.729329i	0.996045	−	0.0888474i	$-0.0283183\pi$
$367$	8.06670	+	13.9719i	0.421079	+	0.729329i	−0.574967	+	0.818177i	$0.694985\pi$
$368$		0			0
$369$	1.15998	−	6.57856i	0.0603860	−	0.342466i
$370$		0			0
$371$	−0.358441	−	0.620838i	−0.0186093	−	0.0322323i
$372$		0			0
$373$	−7.02481	+	12.1673i	−0.363731	+	0.630001i	−0.988572	−	0.150752i	$-0.951831\pi$
$373$	−7.02481	+	12.1673i	−0.363731	+	0.630001i	0.624841	+	0.780752i	$0.285164\pi$
$374$		0			0
$375$	15.4991	−	2.73291i	0.800371	−	0.141127i
$376$		0			0
$377$	51.1317			2.63341
$378$		0			0
$379$	−16.0574			−0.824812			−0.412406	−	0.911000i	$-0.635311\pi$
$379$	−16.0574			−0.824812			−0.412406	+	0.911000i	$0.635311\pi$
$380$		0			0
$381$	−15.1505	+	2.67144i	−0.776183	+	0.136862i
$382$		0			0
$383$	−16.0103	+	27.7306i	−0.818086	+	1.41697i	0.0890039	+	0.996031i	$0.471632\pi$
$383$	−16.0103	+	27.7306i	−0.818086	+	1.41697i	−0.907090	+	0.420936i	$0.861702\pi$
$384$		0			0
$385$	−0.592396	−	1.02606i	−0.0301913	−	0.0522929i
$386$		0			0
$387$	2.81908	+	2.36549i	0.143302	+	0.120244i
$388$		0			0
$389$	15.0214	+	26.0178i	0.761616	+	1.31916i	0.942017	+	0.335564i	$0.108927\pi$
$389$	15.0214	+	26.0178i	0.761616	+	1.31916i	−0.180402	+	0.983593i	$0.557740\pi$
$390$		0			0
$391$	−0.205737	+	0.356347i	−0.0104046	+	0.0180212i
$392$		0			0
$393$	−6.73127	+	18.4940i	−0.339548	+	0.932899i
$394$		0			0
$395$	32.0009			1.61014
$396$		0			0
$397$	−12.3200			−0.618321			−0.309160	−	0.951010i	$-0.600048\pi$
$397$	−12.3200			−0.618321			−0.309160	+	0.951010i	$0.600048\pi$
$398$		0			0
$399$	−2.43242	−	2.89884i	−0.121773	−	0.145124i
$400$		0			0
$401$	−10.4880	+	18.1657i	−0.523745	+	0.907152i	0.475873	+	0.879514i	$0.342132\pi$
$401$	−10.4880	+	18.1657i	−0.523745	+	0.907152i	−0.999618	+	0.0276385i	$0.991201\pi$
$402$		0			0
$403$	−22.3603	−	38.7291i	−1.11384	−	1.92923i
$404$		0			0
$405$	3.95723	+	22.4426i	0.196637	+	1.11518i
$406$		0			0
$407$	−1.79679	−	3.11213i	−0.0890635	−	0.154263i
$408$		0			0
$409$	−12.8307	+	22.2234i	−0.634437	+	1.09888i	0.352197	+	0.935926i	$0.385435\pi$
$409$	−12.8307	+	22.2234i	−0.634437	+	1.09888i	−0.986634	+	0.162951i	$0.947899\pi$
$410$		0			0
$411$	−6.37346	−	7.59559i	−0.314379	−	0.374663i
$412$		0			0
$413$	0.736482			0.0362399
$414$		0			0
$415$	6.91622			0.339504
$416$		0			0
$417$	0.547352	−	1.50384i	0.0268039	−	0.0736432i
$418$		0			0
$419$	−0.739885	+	1.28152i	−0.0361458	+	0.0626063i	−0.883532	−	0.468370i	$-0.844841\pi$
$419$	−0.739885	+	1.28152i	−0.0361458	+	0.0626063i	0.847387	+	0.530976i	$0.178175\pi$
$420$		0			0
$421$	−6.55350	−	11.3510i	−0.319398	−	0.553214i	0.660965	−	0.750417i	$-0.270147\pi$
$421$	−6.55350	−	11.3510i	−0.319398	−	0.553214i	−0.980363	+	0.197203i	$0.936814\pi$
$422$		0			0
$423$	−12.2554	−	10.2835i	−0.595876	−	0.500000i
$424$		0			0
$425$	−2.73783	−	4.74205i	−0.132804	−	0.230023i
$426$		0			0
$427$	0.479055	−	0.829748i	0.0231831	−	0.0401543i
$428$		0			0
$429$	4.64749	−	0.819478i	0.224383	−	0.0395648i
$430$		0			0
$431$	−17.7270			−0.853879			−0.426939	−	0.904280i	$-0.640408\pi$
$431$	−17.7270			−0.853879			−0.426939	+	0.904280i	$0.640408\pi$
$432$		0			0
$433$	−5.83843			−0.280577			−0.140289	−	0.990111i	$-0.544803\pi$
$433$	−5.83843			−0.280577			−0.140289	+	0.990111i	$0.544803\pi$
$434$		0			0
$435$	−37.9261	+	6.68739i	−1.81842	+	0.320636i
$436$		0			0
$437$	−0.115867	+	0.200688i	−0.00554267	+	0.00960019i
$438$		0			0
$439$	14.9277	+	25.8555i	0.712459	+	1.23401i	0.963931	+	0.266151i	$0.0857518\pi$
$439$	14.9277	+	25.8555i	0.712459	+	1.23401i	−0.251473	+	0.967864i	$0.580915\pi$
$440$		0			0
$441$	−0.520945	+	2.95442i	−0.0248069	+	0.140687i
$442$		0			0
$443$	5.33275	+	9.23659i	0.253367	+	0.438844i	0.964451	−	0.264263i	$-0.0851288\pi$
$443$	5.33275	+	9.23659i	0.253367	+	0.438844i	−0.711084	+	0.703107i	$0.751795\pi$
$444$		0			0
$445$	10.2724	−	17.7924i	0.486960	−	0.843440i
$446$		0			0
$447$	5.16843	−	14.2002i	0.244459	−	0.671644i
$448$		0			0
$449$	3.55438			0.167741			0.0838707	−	0.996477i	$-0.473272\pi$
$449$	3.55438			0.167741			0.0838707	+	0.996477i	$0.473272\pi$
$450$		0			0
$451$	1.04189			0.0490606
$452$		0			0
$453$	−20.5155	−	24.4494i	−0.963901	−	1.14873i
$454$		0			0
$455$	7.37211	−	12.7689i	0.345610	−	0.598614i
$456$		0			0
$457$	−2.51161	−	4.35024i	−0.117488	−	0.203496i	0.801283	−	0.598285i	$-0.204151\pi$
$457$	−2.51161	−	4.35024i	−0.117488	−	0.203496i	−0.918772	+	0.394789i	$0.870818\pi$
$458$		0			0
$459$	−17.4572	+	10.0789i	−0.814834	+	0.470445i
$460$		0			0
$461$	−9.23055	−	15.9878i	−0.429910	−	0.744625i	0.566955	−	0.823749i	$-0.308121\pi$
$461$	−9.23055	−	15.9878i	−0.429910	−	0.744625i	−0.996865	+	0.0791233i	$0.974788\pi$
$462$		0			0
$463$	−7.11721	+	12.3274i	−0.330765	+	0.572902i	−0.982662	−	0.185406i	$-0.940640\pi$
$463$	−7.11721	+	12.3274i	−0.330765	+	0.572902i	0.651897	+	0.758307i	$0.273973\pi$
$464$		0			0
$465$	21.6506	+	25.8022i	1.00402	+	1.19655i
$466$		0			0
$467$	3.36865			0.155883			0.0779413	−	0.996958i	$-0.475165\pi$
$467$	3.36865			0.155883			0.0779413	+	0.996958i	$0.475165\pi$
$468$		0			0
$469$	−9.63816			−0.445049
$470$		0			0
$471$	2.91694	−	8.01422i	0.134405	−	0.369276i
$472$		0			0
$473$	−0.286989	+	0.497079i	−0.0131958	+	0.0228557i
$474$		0			0
$475$	−1.54189	−	2.67063i	−0.0707467	−	0.122537i
$476$		0			0
$477$	−2.02094	+	0.735564i	−0.0925327	+	0.0336791i
$478$		0			0
$479$	−18.3833	−	31.8407i	−0.839952	−	1.45484i	−0.889934	−	0.456090i	$-0.849249\pi$
$479$	−18.3833	−	31.8407i	−0.839952	−	1.45484i	0.0499812	−	0.998750i	$-0.484084\pi$
$480$		0			0
$481$	22.3603	−	38.7291i	1.01954	−	1.76589i
$482$		0			0
$483$	0.180922	−	0.0319015i	0.00823224	−	0.00145157i
$484$		0			0
$485$	−34.4466			−1.56414
$486$		0			0
$487$	37.4175			1.69555			0.847773	−	0.530358i	$-0.177943\pi$
$487$	37.4175			1.69555			0.847773	+	0.530358i	$0.177943\pi$
$488$		0			0
$489$	13.0287	−	2.29731i	0.589178	−	0.103888i
$490$		0			0
$491$	−13.3353	+	23.0974i	−0.601813	+	1.04237i	0.390734	+	0.920504i	$0.372221\pi$
$491$	−13.3353	+	23.0974i	−0.601813	+	1.04237i	−0.992547	+	0.121866i	$0.961112\pi$
$492$		0			0
$493$	−17.0326	−	29.5013i	−0.767108	−	1.32867i
$494$		0			0
$495$	−3.34002	+	1.21567i	−0.150123	+	0.0546402i
$496$		0			0
$497$	−6.61721	−	11.4613i	−0.296822	−	0.514112i
$498$		0			0
$499$	16.8726	−	29.2242i	0.755320	−	1.30825i	−0.189895	−	0.981804i	$-0.560815\pi$
$499$	16.8726	−	29.2242i	0.755320	−	1.30825i	0.945215	−	0.326449i	$-0.105852\pi$
$500$		0			0
$501$	3.35023	−	9.20469i	0.149677	−	0.411235i
$502$		0			0
$503$	32.0401			1.42860			0.714299	−	0.699840i	$-0.246745\pi$
$503$	32.0401			1.42860			0.714299	+	0.699840i	$0.246745\pi$
$504$		0			0
$505$	−24.2422			−1.07876
$506$		0			0
$507$	23.2763	+	27.7396i	1.03374	+	1.23196i
$508$		0			0
$509$	3.96926	−	6.87495i	0.175934	−	0.304727i	−0.764550	−	0.644564i	$-0.777039\pi$
$509$	3.96926	−	6.87495i	0.175934	−	0.304727i	0.940484	+	0.339838i	$0.110372\pi$
$510$		0			0
$511$	−5.13429	−	8.89284i	−0.227127	−	0.393396i
$512$		0			0
$513$	−9.83157	+	5.67626i	−0.434074	+	0.250613i
$514$		0			0
$515$	3.85117	+	6.67042i	0.169703	+	0.293934i
$516$		0			0
$517$	1.24763	−	2.16095i	0.0548705	−	0.0950386i
$518$		0			0
$519$	23.4572	+	27.9552i	1.02966	+	1.22710i
$520$		0			0
$521$	−14.6750			−0.642923			−0.321462	−	0.946923i	$-0.604174\pi$
$521$	−14.6750			−0.642923			−0.321462	+	0.946923i	$0.604174\pi$
$522$		0			0
$523$	−28.3432			−1.23936			−0.619680	−	0.784854i	$-0.712738\pi$
$523$	−28.3432			−1.23936			−0.619680	+	0.784854i	$0.712738\pi$
$524$		0			0
$525$	−0.836152	+	2.29731i	−0.0364927	+	0.100263i
$526$		0			0
$527$	−14.8969	+	25.8022i	−0.648920	+	1.12396i
$528$		0			0
$529$	11.4944	+	19.9088i	0.499755	+	0.865602i
$530$		0			0
$531$	0.383666	−	2.17588i	0.0166497	−	0.0944251i
$532$		0			0
$533$	6.48293	+	11.2288i	0.280807	+	0.486371i
$534$		0			0
$535$	−8.25150	+	14.2920i	−0.356743	+	0.617898i
$536$		0			0
$537$	−8.73442	+	1.54011i	−0.376918	+	0.0664608i
$538$		0			0
$539$	−0.467911			−0.0201544
$540$		0			0
$541$	11.2858			0.485215			0.242607	−	0.970125i	$-0.421997\pi$
$541$	11.2858			0.485215			0.242607	+	0.970125i	$0.421997\pi$
$542$		0			0
$543$	0.545759	−	0.0962321i	0.0234208	−	0.00412972i
$544$		0			0
$545$	−13.4684	+	23.3279i	−0.576922	+	0.999258i
$546$		0			0
$547$	−14.6202	−	25.3229i	−0.625115	−	1.08273i	−0.988519	−	0.151099i	$-0.951719\pi$
$547$	−14.6202	−	25.3229i	−0.625115	−	1.08273i	0.363404	−	0.931632i	$-0.381615\pi$
$548$		0			0
$549$	−2.20187	−	1.84759i	−0.0939734	−	0.0788530i
$550$		0			0
$551$	−9.59240	−	16.6145i	−0.408650	−	0.707802i
$552$		0			0
$553$	6.31908	−	10.9450i	0.268715	−	0.465427i
$554$		0			0
$555$	−11.5201	+	31.6511i	−0.489000	+	1.34352i
$556$		0			0
$557$	−0.775682			−0.0328667			−0.0164334	−	0.999865i	$-0.505231\pi$
$557$	−0.775682			−0.0328667			−0.0164334	+	0.999865i	$0.505231\pi$
$558$		0			0
$559$	−7.14290			−0.302113
$560$		0			0
$561$	−2.02094	−	2.40847i	−0.0853243	−	0.101686i
$562$		0			0
$563$	12.4761	−	21.6093i	0.525806	−	0.910722i	−0.473742	−	0.880663i	$-0.657097\pi$
$563$	12.4761	−	21.6093i	0.525806	−	0.910722i	0.999548	−	0.0300588i	$-0.00956944\pi$
$564$		0			0
$565$	−6.55438	−	11.3525i	−0.275745	−	0.477604i
$566$		0			0
$567$	8.45723	+	3.07818i	0.355170	+	0.129271i
$568$		0			0
$569$	12.4017	+	21.4803i	0.519905	+	0.900502i	0.999732	+	0.0231391i	$0.00736608\pi$
$569$	12.4017	+	21.4803i	0.519905	+	0.900502i	−0.479827	+	0.877363i	$0.659301\pi$
$570$		0			0
$571$	4.39827	−	7.61803i	0.184062	−	0.318805i	−0.759198	−	0.650860i	$-0.774409\pi$
$571$	4.39827	−	7.61803i	0.184062	−	0.318805i	0.943260	+	0.332055i	$0.107742\pi$
$572$		0			0
$573$	17.3316	+	20.6550i	0.724037	+	0.862873i
$574$		0			0
$575$	0.149711			0.00624336
$576$		0			0
$577$	−12.8743			−0.535965			−0.267983	−	0.963424i	$-0.586357\pi$
$577$	−12.8743			−0.535965			−0.267983	+	0.963424i	$0.586357\pi$
$578$		0			0
$579$	3.57919	−	9.83375i	0.148746	−	0.408677i
$580$		0			0
$581$	1.36571	−	2.36549i	0.0566594	−	0.0981369i
$582$		0			0
$583$	−0.167718	−	0.290497i	−0.00694619	−	0.0120311i
$584$		0			0
$585$	−33.8842	−	28.4322i	−1.40094	−	1.17553i
$586$		0			0
$587$	22.4315	+	38.8526i	0.925849	+	1.60362i	0.790190	+	0.612861i	$0.209982\pi$
$587$	22.4315	+	38.8526i	0.925849	+	1.60362i	0.135658	+	0.990756i	$0.456685\pi$
$588$		0			0
$589$	−8.38965	+	14.5313i	−0.345690	+	0.598752i
$590$		0			0
$591$	−43.0433	+	7.58969i	−1.77056	+	0.312198i
$592$		0			0
$593$	3.76053			0.154426			0.0772131	−	0.997015i	$-0.475398\pi$
$593$	3.76053			0.154426			0.0772131	+	0.997015i	$0.475398\pi$
$594$		0			0
$595$	−9.82295			−0.402702
$596$		0			0
$597$	5.18866	−	0.914901i	0.212358	−	0.0374444i
$598$		0			0
$599$	−1.84524	+	3.19604i	−0.0753943	+	0.130587i	−0.901258	−	0.433283i	$-0.857355\pi$
$599$	−1.84524	+	3.19604i	−0.0753943	+	0.130587i	0.825863	+	0.563870i	$0.190688\pi$
$600$		0			0
$601$	10.9285	+	18.9288i	0.445785	+	0.772122i	0.998107	−	0.0615091i	$-0.0195913\pi$
$601$	10.9285	+	18.9288i	0.445785	+	0.772122i	−0.552322	+	0.833631i	$0.686258\pi$
$602$		0			0
$603$	−5.02094	+	28.4752i	−0.204469	+	1.15960i
$604$		0			0
$605$	13.6493	+	23.6413i	0.554923	+	0.961155i
$606$		0			0
$607$	12.1973	−	21.1263i	0.495072	−	0.857490i	−0.504911	−	0.863171i	$-0.668475\pi$
$607$	12.1973	−	21.1263i	0.495072	−	0.857490i	0.999984	+	0.00568063i	$0.00180821\pi$
$608$		0			0
$609$	−5.20187	+	14.2920i	−0.210790	+	0.579142i
$610$		0			0
$611$	31.0523			1.25624
$612$		0			0
$613$	42.0215			1.69723			0.848616	−	0.529010i	$-0.177437\pi$
$613$	42.0215			1.69723			0.848616	+	0.529010i	$0.177437\pi$
$614$		0			0
$615$	−6.27719	−	7.48086i	−0.253121	−	0.301657i
$616$		0			0
$617$	−23.2049	+	40.1920i	−0.934192	+	1.61807i	−0.158125	+	0.987419i	$0.550545\pi$
$617$	−23.2049	+	40.1920i	−0.934192	+	1.61807i	−0.776068	+	0.630650i	$0.782788\pi$
$618$		0			0
$619$	−13.6047	−	23.5641i	−0.546820	−	0.947120i	−0.998490	−	0.0549349i	$-0.982505\pi$
$619$	−13.6047	−	23.5641i	−0.546820	−	0.947120i	0.451670	−	0.892185i	$-0.350828\pi$
$620$		0			0
$621$		−	0.551139i		−	0.0221165i
$622$		0			0
$623$	−4.05690	−	7.02676i	−0.162536	−	0.281521i
$624$		0			0
$625$	15.0326	−	26.0372i	0.601302	−	1.04149i
$626$		0			0
$627$	−1.13816	−	1.35640i	−0.0454536	−	0.0541694i
$628$		0			0
$629$	−29.7939			−1.18796
$630$		0			0
$631$	29.6023			1.17845			0.589224	−	0.807970i	$-0.299434\pi$
$631$	29.6023			1.17845			0.589224	+	0.807970i	$0.299434\pi$
$632$		0			0
$633$	3.23055	−	8.87587i	0.128403	−	0.352784i
$634$		0			0
$635$	−11.2451	+	19.4771i	−0.446248	+	0.772925i
$636$		0			0
$637$	−2.91147	−	5.04282i	−0.115357	−	0.199804i
$638$		0			0
$639$	−37.3089	+	13.5793i	−1.47592	+	0.537189i
$640$		0			0
$641$	0.139500	+	0.241621i	0.00550991	+	0.00954345i	0.868767	−	0.495221i	$-0.164913\pi$
$641$	0.139500	+	0.241621i	0.00550991	+	0.00954345i	−0.863257	+	0.504764i	$0.831579\pi$
$642$		0			0
$643$	−9.12196	+	15.7997i	−0.359735	+	0.623079i	−0.987916	−	0.154988i	$-0.950466\pi$
$643$	−9.12196	+	15.7997i	−0.359735	+	0.623079i	0.628181	+	0.778067i	$0.283800\pi$
$644$		0			0
$645$	5.29813	−	0.934204i	0.208614	−	0.0367842i
$646$		0			0
$647$	−22.4570			−0.882875			−0.441438	−	0.897292i	$-0.645531\pi$
$647$	−22.4570			−0.882875			−0.441438	+	0.897292i	$0.645531\pi$
$648$		0			0
$649$	0.344608			0.0135270
$650$		0			0
$651$	13.1001	−	2.30991i	0.513435	−	0.0905324i
$652$		0			0
$653$	25.2656	−	43.7614i	0.988721	−	1.71251i	0.364655	−	0.931143i	$-0.381187\pi$
$653$	25.2656	−	43.7614i	0.988721	−	1.71251i	0.624066	−	0.781372i	$-0.285480\pi$
$654$		0			0
$655$	14.3858	+	24.9169i	0.562099	+	0.973584i
$656$		0			0
$657$	−28.9479	+	10.5362i	−1.12937	+	0.411055i
$658$		0			0
$659$	−1.33631	−	2.31456i	−0.0520554	−	0.0901626i	0.838824	−	0.544403i	$-0.183244\pi$
$659$	−1.33631	−	2.31456i	−0.0520554	−	0.0901626i	−0.890879	+	0.454241i	$0.849911\pi$
$660$		0			0
$661$	17.3050	−	29.9731i	0.673086	−	1.16582i	−0.303938	−	0.952692i	$-0.598302\pi$
$661$	17.3050	−	29.9731i	0.673086	−	1.16582i	0.977024	−	0.213128i	$-0.0683651\pi$
$662$		0			0
$663$	13.3819	−	36.7665i	0.519710	−	1.42789i
$664$		0			0
$665$	−5.53209			−0.214525
$666$		0			0
$667$	0.931379			0.0360631
$668$		0			0
$669$	−15.8011	−	18.8310i	−0.610907	−	0.728050i
$670$		0			0
$671$	0.224155	−	0.388249i	0.00865342	−	0.0149882i
$672$		0			0
$673$	−8.25624	−	14.3002i	−0.318255	−	0.551234i	0.661869	−	0.749619i	$-0.269763\pi$
$673$	−8.25624	−	14.3002i	−0.318255	−	0.551234i	−0.980124	+	0.198386i	$0.936430\pi$
$674$		0			0
$675$	6.35163	+	3.66712i	0.244474	+	0.141147i
$676$		0			0
$677$	21.8790	+	37.8955i	0.840877	+	1.45644i	0.889154	+	0.457608i	$0.151294\pi$
$677$	21.8790	+	37.8955i	0.840877	+	1.45644i	−0.0482766	+	0.998834i	$0.515373\pi$
$678$		0			0
$679$	−6.80200	+	11.7814i	−0.261037	+	0.452129i
$680$		0			0
$681$	3.22193	+	3.83975i	0.123465	+	0.147140i
$682$		0			0
$683$	−28.2412			−1.08062			−0.540310	−	0.841466i	$-0.681693\pi$
$683$	−28.2412			−1.08062			−0.540310	+	0.841466i	$0.681693\pi$
$684$		0			0
$685$	−14.4953			−0.553835
$686$		0			0
$687$	5.43083	−	14.9211i	0.207199	−	0.569274i
$688$		0			0
$689$	2.08718	−	3.61510i	0.0795153	−	0.137725i
$690$		0			0
$691$	−14.5326	−	25.1711i	−0.552844	−	0.957555i	−0.998068	−	0.0621351i	$-0.980209\pi$
$691$	−14.5326	−	25.1711i	−0.552844	−	0.957555i	0.445223	−	0.895420i	$-0.353124\pi$
$692$		0			0
$693$	−0.243756	+	1.38241i	−0.00925951	+	0.0525133i
$694$		0			0
$695$	−1.16978	−	2.02611i	−0.0443722	−	0.0768549i
$696$		0			0
$697$	4.31908	−	7.48086i	0.163597	−	0.283358i
$698$		0			0
$699$	−22.6373	+	3.99156i	−0.856221	+	0.150975i
$700$		0			0
$701$	−1.10876			−0.0418771			−0.0209386	−	0.999781i	$-0.506665\pi$
$701$	−1.10876			−0.0418771			−0.0209386	+	0.999781i	$0.506665\pi$
$702$		0			0
$703$	−16.7793			−0.632843
$704$		0			0
$705$	−23.0326	+	4.06126i	−0.867456	+	0.152956i
$706$		0			0
$707$	−4.78699	+	8.29131i	−0.180033	+	0.311827i
$708$		0			0
$709$	9.23442	+	15.9945i	0.346806	+	0.600686i	0.985680	−	0.168626i	$-0.0539329\pi$
$709$	9.23442	+	15.9945i	0.346806	+	0.600686i	−0.638874	+	0.769311i	$0.720600\pi$
$710$		0			0
$711$	−29.0442	−	24.3709i	−1.08924	−	0.913982i
$712$		0			0
$713$	−0.407299	−	0.705463i	−0.0152535	−	0.0264198i
$714$		0			0
$715$	3.44949	−	5.97470i	0.129004	−	0.223441i
$716$		0			0
$717$	−5.64977	+	15.5226i	−0.210994	+	0.579702i
$718$		0			0
$719$	33.7769			1.25967			0.629834	−	0.776730i	$-0.283123\pi$
$719$	33.7769			1.25967			0.629834	+	0.776730i	$0.283123\pi$
$720$		0			0
$721$	3.04189			0.113286
$722$		0			0
$723$	−9.97343	−	11.8859i	−0.370916	−	0.442040i
$724$		0			0
$725$	−6.19712	+	10.7337i	−0.230155	+	0.398641i
$726$		0			0
$727$	8.40214	+	14.5529i	0.311618	+	0.539738i	0.978713	−	0.205234i	$-0.0657957\pi$
$727$	8.40214	+	14.5529i	0.311618	+	0.539738i	−0.667095	+	0.744973i	$0.732462\pi$
$728$		0			0
$729$	13.5000	−	23.3827i	0.500000	−	0.866025i
$730$		0			0
$731$	2.37939	+	4.12122i	0.0880047	+	0.152429i
$732$		0			0
$733$	6.81820	−	11.8095i	0.251836	−	0.436193i	−0.712195	−	0.701981i	$-0.752299\pi$
$733$	6.81820	−	11.8095i	0.251836	−	0.436193i	0.964031	+	0.265789i	$0.0856323\pi$
$734$		0			0
$735$	2.81908	+	3.35965i	0.103983	+	0.123922i
$736$		0			0
$737$	−4.50980			−0.166121
$738$		0			0
$739$	32.0419			1.17868			0.589340	−	0.807885i	$-0.299388\pi$
$739$	32.0419			1.17868			0.589340	+	0.807885i	$0.299388\pi$
$740$		0			0
$741$	7.53643	−	20.7062i	0.276858	−	0.760660i
$742$		0			0
$743$	16.8764	−	29.2309i	0.619137	−	1.07238i	−0.370507	−	0.928830i	$-0.620816\pi$
$743$	16.8764	−	29.2309i	0.619137	−	1.07238i	0.989644	−	0.143547i	$-0.0458507\pi$
$744$		0			0
$745$	−11.0458	−	19.1318i	−0.404685	−	0.700936i
$746$		0			0
$747$	−6.27719	−	5.26719i	−0.229670	−	0.192716i
$748$		0			0
$749$	3.25877	+	5.64436i	0.119073	+	0.206240i
$750$		0			0
$751$	13.0582	−	22.6175i	0.476502	−	0.825326i	−0.523135	−	0.852250i	$-0.675238\pi$
$751$	13.0582	−	22.6175i	0.476502	−	0.825326i	0.999637	+	0.0269236i	$0.00857108\pi$
$752$		0			0
$753$	−42.6404	+	7.51866i	−1.55390	+	0.273995i
$754$		0			0
$755$	−46.6587			−1.69808
$756$		0			0
$757$	35.6536			1.29585			0.647927	−	0.761703i	$-0.275636\pi$
$757$	35.6536			1.29585			0.647927	+	0.761703i	$0.275636\pi$
$758$		0			0
$759$	0.0846555	−	0.0149270i	0.00307280	−	0.000541817i
$760$		0			0
$761$	−20.3824	+	35.3033i	−0.738861	+	1.27974i	0.214148	+	0.976801i	$0.431302\pi$
$761$	−20.3824	+	35.3033i	−0.738861	+	1.27974i	−0.953009	+	0.302943i	$0.902031\pi$
$762$		0			0
$763$	5.31908	+	9.21291i	0.192564	+	0.333530i
$764$		0			0
$765$	−5.11721	+	29.0211i	−0.185013	+	1.04926i
$766$		0			0
$767$	2.14425	+	3.71395i	0.0774243	+	0.134103i
$768$		0			0
$769$	−19.7135	+	34.1447i	−0.710886	+	1.23129i	0.253639	+	0.967299i	$0.418373\pi$
$769$	−19.7135	+	34.1447i	−0.710886	+	1.23129i	−0.964525	+	0.263992i	$0.914961\pi$
$770$		0			0
$771$	6.42871	−	17.6627i	0.231524	−	0.636108i
$772$		0			0
$773$	24.9026			0.895685			0.447842	−	0.894113i	$-0.352193\pi$
$773$	24.9026			0.895685			0.447842	+	0.894113i	$0.352193\pi$
$774$		0			0
$775$	10.8402			0.389391
$776$		0			0
$777$	8.55051	+	10.1901i	0.306748	+	0.365568i
$778$		0			0
$779$	2.43242	−	4.21307i	0.0871504	−	0.150949i
$780$		0			0
$781$	−3.09627	−	5.36289i	−0.110793	−	0.191899i
$782$		0			0
$783$	39.5148	+	22.8139i	1.41214	+	0.815301i
$784$		0			0
$785$	−6.23396	−	10.7975i	−0.222499	−	0.385380i
$786$		0			0
$787$	−15.3525	+	26.5913i	−0.547258	+	0.947879i	0.451203	+	0.892421i	$0.350995\pi$
$787$	−15.3525	+	26.5913i	−0.547258	+	0.947879i	−0.998461	+	0.0554572i	$0.982338\pi$
$788$		0			0
$789$	−29.0442	−	34.6135i	−1.03400	−	1.23227i
$790$		0			0
$791$	−5.17705			−0.184075
$792$		0			0
$793$	5.57903			0.198117
$794$		0			0
$795$	−1.07532	+	2.95442i	−0.0381377	+	0.104783i
$796$		0			0
$797$	5.50686	−	9.53817i	0.195063	−	0.337859i	−0.751858	−	0.659325i	$-0.770842\pi$
$797$	5.50686	−	9.53817i	0.195063	−	0.337859i	0.946921	+	0.321466i	$0.104175\pi$
$798$		0			0
$799$	−10.3439	−	17.9161i	−0.365941	−	0.633828i
$800$		0			0
$801$	−22.8735	+	8.32526i	−0.808194	+	0.294158i
$802$		0			0
$803$	−2.40239	−	4.16106i	−0.0847785	−	0.146841i
$804$		0			0
$805$	0.134285	−	0.232589i	0.00473294	−	0.00819769i
$806$		0			0
$807$	13.0201	−	2.29579i	0.458328	−	0.0808156i
$808$		0			0
$809$	16.9881			0.597271			0.298636	−	0.954367i	$-0.403468\pi$
$809$	16.9881			0.597271			0.298636	+	0.954367i	$0.403468\pi$
$810$		0			0
$811$	−37.9796			−1.33364			−0.666822	−	0.745217i	$-0.732346\pi$
$811$	−37.9796			−1.33364			−0.666822	+	0.745217i	$0.732346\pi$
$812$		0			0
$813$	5.80587	−	1.02373i	0.203621	−	0.0359039i
$814$		0			0
$815$	9.67024	−	16.7494i	0.338734	−	0.586704i
$816$		0			0
$817$	1.34002	+	2.32099i	0.0468814	+	0.0812011i
$818$		0			0
$819$	−16.4153	+	5.97470i	−0.573599	+	0.208773i
$820$		0			0
$821$	−4.13934	−	7.16954i	−0.144464	−	0.250219i	0.784709	−	0.619864i	$-0.212812\pi$
$821$	−4.13934	−	7.16954i	−0.144464	−	0.250219i	−0.929173	+	0.369646i	$0.879479\pi$
$822$		0			0
$823$	27.2763	−	47.2440i	0.950792	−	1.64682i	0.207077	−	0.978325i	$-0.433605\pi$
$823$	27.2763	−	47.2440i	0.950792	−	1.64682i	0.743716	−	0.668496i	$-0.233062\pi$
$824$		0			0
$825$	−0.391245	+	1.07494i	−0.0136214	+	0.0374245i
$826$		0			0
$827$	31.8708			1.10826			0.554129	−	0.832431i	$-0.313052\pi$
$827$	31.8708			1.10826			0.554129	+	0.832431i	$0.313052\pi$
$828$		0			0
$829$	−0.352349			−0.0122376			−0.00611879	−	0.999981i	$-0.501948\pi$
$829$	−0.352349			−0.0122376			−0.00611879	+	0.999981i	$0.501948\pi$
$830$		0			0
$831$	−6.37046	−	7.59202i	−0.220989	−	0.263364i
$832$		0			0
$833$	−1.93969	+	3.35965i	−0.0672064	+	0.116405i
$834$		0			0
$835$	−7.15998	−	12.4014i	−0.247781	−	0.429170i
$836$		0			0
$837$		−	39.9067i		−	1.37938i
$838$		0			0
$839$	12.5077	+	21.6640i	0.431815	+	0.747926i	0.997030	−	0.0770182i	$-0.0245399\pi$
$839$	12.5077	+	21.6640i	0.431815	+	0.747926i	−0.565215	+	0.824944i	$0.691207\pi$
$840$		0			0
$841$	−24.0535	+	41.6619i	−0.829431	+	1.43662i
$842$		0			0
$843$	31.5936	+	37.6518i	1.08814	+	1.29680i
$844$		0			0
$845$	52.9377			1.82111
$846$		0			0
$847$	10.7811			0.370442
$848$		0			0
$849$	−2.70801	+	7.44021i	−0.0929388	+	0.255347i
$850$		0			0
$851$	0.407299	−	0.705463i	0.0139620	−	0.0241829i
$852$		0			0
$853$	−19.5954	−	33.9402i	−0.670933	−	1.16209i	−0.977640	−	0.210286i	$-0.932560\pi$
$853$	−19.5954	−	33.9402i	−0.670933	−	1.16209i	0.306706	−	0.951804i	$-0.400773\pi$
$854$		0			0
$855$	−2.88191	+	16.3441i	−0.0985593	+	0.558958i
$856$		0			0
$857$	−8.20368	−	14.2092i	−0.280232	−	0.485377i	0.691210	−	0.722654i	$-0.257078\pi$
$857$	−8.20368	−	14.2092i	−0.280232	−	0.485377i	−0.971442	+	0.237278i	$0.923745\pi$
$858$		0			0
$859$	−13.4162	+	23.2376i	−0.457756	+	0.792856i	−0.998842	−	0.0481111i	$-0.984680\pi$
$859$	−13.4162	+	23.2376i	−0.457756	+	0.792856i	0.541086	+	0.840967i	$0.318013\pi$
$860$		0			0
$861$	−3.79813	+	0.669713i	−0.129440	+	0.0228238i
$862$		0			0
$863$	−14.5057			−0.493779			−0.246890	−	0.969044i	$-0.579408\pi$
$863$	−14.5057			−0.493779			−0.246890	+	0.969044i	$0.579408\pi$
$864$		0			0
$865$	53.3492			1.81393
$866$		0			0
$867$	3.32682	−	0.586608i	0.112985	−	0.0199222i
$868$		0			0
$869$	2.95677	−	5.12127i	0.100301	−	0.173727i
$870$		0			0
$871$	−28.0612	−	48.6035i	−0.950819	−	1.64687i
$872$		0			0
$873$	31.2638	+	26.2335i	1.05812	+	0.887868i
$874$		0			0
$875$	−4.54323	−	7.86911i	−0.153589	−	0.266024i
$876$		0			0
$877$	−9.45723	+	16.3804i	−0.319348	+	0.553127i	−0.980352	−	0.197255i	$-0.936797\pi$
$877$	−9.45723	+	16.3804i	−0.319348	+	0.553127i	0.661004	+	0.750382i	$0.270131\pi$
$878$		0			0
$879$	2.56371	−	7.04374i	0.0864718	−	0.237579i
$880$		0			0
$881$	53.8976			1.81585			0.907927	−	0.419128i	$-0.137664\pi$
$881$	53.8976			1.81585			0.907927	+	0.419128i	$0.137664\pi$
$882$		0			0
$883$	−43.4252			−1.46137			−0.730687	−	0.682712i	$-0.760800\pi$
$883$	−43.4252			−1.46137			−0.730687	+	0.682712i	$0.760800\pi$
$884$		0			0
$885$	−2.07620	−	2.47432i	−0.0697907	−	0.0831733i
$886$		0			0
$887$	−19.4800	+	33.7403i	−0.654074	+	1.13289i	0.328051	+	0.944660i	$0.393608\pi$
$887$	−19.4800	+	33.7403i	−0.654074	+	1.13289i	−0.982125	+	0.188229i	$0.939725\pi$
$888$		0			0
$889$	4.44104	+	7.69210i	0.148948	+	0.257985i
$890$		0			0
$891$	3.95723	+	1.44032i	0.132572	+	0.0482524i
$892$		0			0
$893$	−5.82547	−	10.0900i	−0.194942	−	0.337650i
$894$		0			0
$895$	−6.48293	+	11.2288i	−0.216700	+	0.375336i
$896$		0			0
$897$	0.687623	+	0.819478i	0.0229591	+	0.0273616i
$898$		0			0
$899$	67.4389			2.24921
$900$		0			0
$901$	−2.78106			−0.0926505
$902$		0			0
$903$	0.726682	−	1.99654i	0.0241824	−	0.0664407i
$904$		0			0
$905$	0.405078	−	0.701615i	0.0134652	−	0.0233225i
$906$		0			0
$907$	17.2638	+	29.9018i	0.573236	+	0.992874i	0.996231	+	0.0867416i	$0.0276454\pi$
$907$	17.2638	+	29.9018i	0.573236	+	0.992874i	−0.422995	+	0.906132i	$0.639021\pi$
$908$		0			0
$909$	22.0023	+	18.4621i	0.729769	+	0.612349i
$910$		0			0
$911$	23.2631	+	40.2929i	0.770741	+	1.33496i	0.937157	+	0.348907i	$0.113447\pi$
$911$	23.2631	+	40.2929i	0.770741	+	1.33496i	−0.166416	+	0.986056i	$0.553220\pi$
$912$		0			0
$913$	0.639033	−	1.10684i	0.0211489	−	0.0366310i
$914$		0			0
$915$	−4.13816	+	0.729669i	−0.136803	+	0.0241221i
$916$		0			0
$917$	11.3628			0.375232
$918$		0			0
$919$	9.95636			0.328430			0.164215	−	0.986425i	$-0.447491\pi$
$919$	9.95636			0.328430			0.164215	+	0.986425i	$0.447491\pi$
$920$		0			0
$921$	21.1125	−	3.72270i	0.695679	−	0.122667i
$922$		0			0
$923$	38.5317	−	66.7388i	1.26829	−	2.19674i
$924$		0			0
$925$	5.42009	+	9.38788i	0.178212	+	0.308671i
$926$		0			0
$927$	1.58466	−	8.98703i	0.0520469	−	0.295173i
$928$		0			0
$929$	−4.52300	−	7.83407i	−0.148395	−	0.257028i	0.782239	−	0.622978i	$-0.214077\pi$
$929$	−4.52300	−	7.83407i	−0.148395	−	0.257028i	−0.930634	+	0.365950i	$0.880744\pi$
$930$		0			0
$931$	−1.09240	+	1.89209i	−0.0358018	+	0.0620106i
$932$		0			0
$933$	13.0241	−	35.7834i	0.426390	−	1.17150i
$934$		0			0
$935$	−4.59627			−0.150314
$936$		0			0
$937$	−24.3928			−0.796878			−0.398439	−	0.917195i	$-0.630448\pi$
$937$	−24.3928			−0.796878			−0.398439	+	0.917195i	$0.630448\pi$
$938$		0			0
$939$	−15.4641	−	18.4294i	−0.504652	−	0.601421i
$940$		0			0
$941$	29.7690	−	51.5615i	0.970443	−	1.68086i	0.276223	−	0.961094i	$-0.410917\pi$
$941$	29.7690	−	51.5615i	0.970443	−	1.68086i	0.694220	−	0.719763i	$-0.255749\pi$
$942$		0			0
$943$	0.118089	+	0.204535i	0.00384549	+	0.00666059i
$944$		0			0
$945$	11.3944	−	6.57856i	0.370660	−	0.214001i
$946$		0			0
$947$	4.32429	+	7.48989i	0.140521	+	0.243389i	0.927693	−	0.373344i	$-0.121789\pi$
$947$	4.32429	+	7.48989i	0.140521	+	0.243389i	−0.787172	+	0.616733i	$0.788456\pi$
$948$		0			0
$949$	29.8967	−	51.7826i	0.970487	−	1.68093i
$950$		0			0
$951$	−6.88279	−	8.20259i	−0.223190	−	0.265987i
$952$		0			0
$953$	3.78249			0.122527			0.0612634	−	0.998122i	$-0.480487\pi$
$953$	3.78249			0.122527			0.0612634	+	0.998122i	$0.480487\pi$
$954$		0			0
$955$	39.4175			1.27552
$956$		0			0
$957$	−2.43401	+	6.68739i	−0.0786804	+	0.216173i
$958$		0			0
$959$	−2.86231	+	4.95767i	−0.0924288	+	0.160091i
$960$		0			0
$961$	−13.9915	−	24.2341i	−0.451340	−	0.781744i
$962$		0			0
$963$	18.3735	−	6.68739i	0.592076	−	0.215498i
$964$		0			0
$965$	−7.64930	−	13.2490i	−0.246240	−	0.426500i
$966$		0			0
$967$	−16.4745	+	28.5346i	−0.529783	+	0.917611i	0.469613	+	0.882872i	$0.344393\pi$
$967$	−16.4745	+	28.5346i	−0.529783	+	0.917611i	−0.999396	+	0.0347392i	$0.988940\pi$
$968$		0			0
$969$	−14.4572	+	2.54920i	−0.464433	+	0.0818921i
$970$		0			0
$971$	55.4570			1.77970			0.889850	−	0.456254i	$-0.150809\pi$
$971$	55.4570			1.77970			0.889850	+	0.456254i	$0.150809\pi$
$972$		0			0
$973$	−0.923963			−0.0296209
$974$		0			0
$975$	−14.0194	+	2.47199i	−0.448979	+	0.0791670i
$976$		0			0
$977$	−28.2743	+	48.9724i	−0.904573	+	1.56677i	−0.0830847	+	0.996542i	$0.526477\pi$
$977$	−28.2743	+	48.9724i	−0.904573	+	1.56677i	−0.821489	+	0.570225i	$0.806856\pi$
$978$		0			0
$979$	−1.89827	−	3.28790i	−0.0606690	−	0.105082i
$980$		0			0
$981$	29.9898	−	10.9154i	0.957500	−	0.348502i
$982$		0			0
$983$	14.4987	+	25.1124i	0.462435	+	0.800961i	0.999082	−	0.0428458i	$-0.0136424\pi$
$983$	14.4987	+	25.1124i	0.462435	+	0.800961i	−0.536646	+	0.843807i	$0.680309\pi$
$984$		0			0
$985$	−31.9479	+	55.3354i	−1.01794	+	1.76313i
$986$		0			0
$987$	−3.15910	+	8.67956i	−0.100555	+	0.276273i
$988$		0			0
$989$	−0.130110			−0.00413726
$990$		0			0
$991$	−6.80922			−0.216302			−0.108151	−	0.994134i	$-0.534493\pi$
$991$	−6.80922			−0.216302			−0.108151	+	0.994134i	$0.534493\pi$
$992$		0			0
$993$	−11.9477	−	14.2388i	−0.379150	−	0.451853i
$994$		0			0
$995$	3.85117	−	6.67042i	0.122090	−	0.211466i
$996$		0			0
$997$	19.4688	+	33.7210i	0.616585	+	1.06796i	0.990104	+	0.140333i	$0.0448175\pi$
$997$	19.4688	+	33.7210i	0.616585	+	1.06796i	−0.373520	+	0.927622i	$0.621849\pi$
$998$		0			0
$999$	34.5602	−	19.9533i	1.09344	−	0.631296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.r.h.337.1		6
3.2	odd	2		3024.2.r.k.1009.3		6
4.3	odd	2		63.2.f.a.22.2	✓	6
9.2	odd	6		3024.2.r.k.2017.3		6
9.4	even	3		9072.2.a.ca.1.3		3
9.5	odd	6		9072.2.a.bs.1.1		3
9.7	even	3	inner	1008.2.r.h.673.1		6
12.11	even	2		189.2.f.b.64.2		6
28.3	even	6		441.2.h.e.373.2		6
28.11	odd	6		441.2.h.d.373.2		6
28.19	even	6		441.2.g.b.67.2		6
28.23	odd	6		441.2.g.c.67.2		6
28.27	even	2		441.2.f.c.148.2		6
36.7	odd	6		63.2.f.a.43.2	yes	6
36.11	even	6		189.2.f.b.127.2		6
36.23	even	6		567.2.a.c.1.2		3
36.31	odd	6		567.2.a.h.1.2		3
84.11	even	6		1323.2.h.c.226.2		6
84.23	even	6		1323.2.g.d.361.2		6
84.47	odd	6		1323.2.g.e.361.2		6
84.59	odd	6		1323.2.h.b.226.2		6
84.83	odd	2		1323.2.f.d.442.2		6
252.11	even	6		1323.2.g.d.667.2		6
252.47	odd	6		1323.2.h.b.802.2		6
252.79	odd	6		441.2.h.d.214.2		6
252.83	odd	6		1323.2.f.d.883.2		6
252.115	even	6		441.2.g.b.79.2		6
252.139	even	6		3969.2.a.q.1.2		3
252.151	odd	6		441.2.g.c.79.2		6
252.167	odd	6		3969.2.a.l.1.2		3
252.187	even	6		441.2.h.e.214.2		6
252.191	even	6		1323.2.h.c.802.2		6
252.223	even	6		441.2.f.c.295.2		6
252.227	odd	6		1323.2.g.e.667.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.2	✓	6	4.3	odd	2
63.2.f.a.43.2	yes	6	36.7	odd	6
189.2.f.b.64.2		6	12.11	even	2
189.2.f.b.127.2		6	36.11	even	6
441.2.f.c.148.2		6	28.27	even	2
441.2.f.c.295.2		6	252.223	even	6
441.2.g.b.67.2		6	28.19	even	6
441.2.g.b.79.2		6	252.115	even	6
441.2.g.c.67.2		6	28.23	odd	6
441.2.g.c.79.2		6	252.151	odd	6
441.2.h.d.214.2		6	252.79	odd	6
441.2.h.d.373.2		6	28.11	odd	6
441.2.h.e.214.2		6	252.187	even	6
441.2.h.e.373.2		6	28.3	even	6
567.2.a.c.1.2		3	36.23	even	6
567.2.a.h.1.2		3	36.31	odd	6
1008.2.r.h.337.1		6	1.1	even	1	trivial
1008.2.r.h.673.1		6	9.7	even	3	inner
1323.2.f.d.442.2		6	84.83	odd	2
1323.2.f.d.883.2		6	252.83	odd	6
1323.2.g.d.361.2		6	84.23	even	6
1323.2.g.d.667.2		6	252.11	even	6
1323.2.g.e.361.2		6	84.47	odd	6
1323.2.g.e.667.2		6	252.227	odd	6
1323.2.h.b.226.2		6	84.59	odd	6
1323.2.h.b.802.2		6	252.47	odd	6
1323.2.h.c.226.2		6	84.11	even	6
1323.2.h.c.802.2		6	252.191	even	6
3024.2.r.k.1009.3		6	3.2	odd	2
3024.2.r.k.2017.3		6	9.2	odd	6
3969.2.a.l.1.2		3	252.167	odd	6
3969.2.a.q.1.2		3	252.139	even	6
9072.2.a.bs.1.1		3	9.5	odd	6
9072.2.a.ca.1.3		3	9.4	even	3

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.70574 + 0.300767i) q^{3} +(-1.26604 + 2.19285i) q^{5} +(0.500000 + 0.866025i) q^{7} +(2.81908 - 1.02606i) q^{9} +O(q^{10})\)	\(q+(-1.70574 + 0.300767i) q^{3} +(-1.26604 + 2.19285i) q^{5} +(0.500000 + 0.866025i) q^{7} +(2.81908 - 1.02606i) q^{9} +(0.233956 + 0.405223i) q^{11} +(-2.91147 + 5.04282i) q^{13} +(1.50000 - 4.12122i) q^{15} +3.87939 q^{17} +2.18479 q^{19} +(-1.11334 - 1.32683i) q^{21} +(-0.0530334 + 0.0918566i) q^{23} +(-0.705737 - 1.22237i) q^{25} +(-4.50000 + 2.59808i) q^{27} +(-4.39053 - 7.60462i) q^{29} +(-3.84002 + 6.65111i) q^{31} +(-0.520945 - 0.620838i) q^{33} -2.53209 q^{35} -7.68004 q^{37} +(3.44949 - 9.47740i) q^{39} +(1.11334 - 1.92836i) q^{41} +(0.613341 + 1.06234i) q^{43} +(-1.31908 + 7.48086i) q^{45} +(-2.66637 - 4.61830i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-6.61721 + 1.16679i) q^{51} -0.716881 q^{53} -1.18479 q^{55} +(-3.72668 + 0.657115i) q^{57} +(0.368241 - 0.637812i) q^{59} +(-0.479055 - 0.829748i) q^{61} +(2.29813 + 1.92836i) q^{63} +(-7.37211 - 12.7689i) q^{65} +(-4.81908 + 8.34689i) q^{67} +(0.0628336 - 0.172634i) q^{69} -13.2344 q^{71} -10.2686 q^{73} +(1.57145 + 1.87278i) q^{75} +(-0.233956 + 0.405223i) q^{77} +(-6.31908 - 10.9450i) q^{79} +(6.89440 - 5.78509i) q^{81} +(-1.36571 - 2.36549i) q^{83} +(-4.91147 + 8.50692i) q^{85} +(9.77631 + 11.6510i) q^{87} -8.11381 q^{89} -5.82295 q^{91} +(4.54963 - 12.5000i) q^{93} +(-2.76604 + 4.79093i) q^{95} +(6.80200 + 11.7814i) q^{97} +(1.07532 + 0.902302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} + 3 q^{7}+O(q^{10}) \) 6 * q - 3 * q^5 + 3 * q^7	\( 6 q - 3 q^{5} + 3 q^{7} + 6 q^{11} + 3 q^{13} + 9 q^{15} + 12 q^{17} + 6 q^{19} + 12 q^{23} + 6 q^{25} - 27 q^{27} - 9 q^{29} - 3 q^{31} - 6 q^{35} - 6 q^{37} + 18 q^{39} - 3 q^{43} + 9 q^{45} + 3 q^{47} - 3 q^{49} - 9 q^{51} + 12 q^{53} - 9 q^{57} - 3 q^{59} - 6 q^{61} - 15 q^{65} - 12 q^{67} - 9 q^{69} - 18 q^{71} - 42 q^{73} + 9 q^{75} - 6 q^{77} - 21 q^{79} - 18 q^{83} - 9 q^{85} - 9 q^{87} + 24 q^{89} + 6 q^{91} - 27 q^{93} - 12 q^{95} + 3 q^{97} - 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^5 + 3 * q^7 + 6 * q^11 + 3 * q^13 + 9 * q^15 + 12 * q^17 + 6 * q^19 + 12 * q^23 + 6 * q^25 - 27 * q^27 - 9 * q^29 - 3 * q^31 - 6 * q^35 - 6 * q^37 + 18 * q^39 - 3 * q^43 + 9 * q^45 + 3 * q^47 - 3 * q^49 - 9 * q^51 + 12 * q^53 - 9 * q^57 - 3 * q^59 - 6 * q^61 - 15 * q^65 - 12 * q^67 - 9 * q^69 - 18 * q^71 - 42 * q^73 + 9 * q^75 - 6 * q^77 - 21 * q^79 - 18 * q^83 - 9 * q^85 - 9 * q^87 + 24 * q^89 + 6 * q^91 - 27 * q^93 - 12 * q^95 + 3 * q^97 - 18 * q^99

Introduction

L-functions

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