LMFDB - Embedded newform 936.2.s.f.529.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(529,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.529"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.s (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,-3,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.6
Character	$\chi$	$=$	936.529
Dual form			936.2.s.f.913.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.11550 - 1.32501i) q^{3} +(-0.816777 - 1.41470i) q^{5} -0.664936 q^{7} +(-0.511312 + 2.95611i) q^{9} +(2.30132 + 3.98600i) q^{11} +(-3.59014 + 0.333001i) q^{13} +(-0.963376 + 2.66034i) q^{15} +(0.691459 + 1.19764i) q^{17} +(2.59815 + 4.50012i) q^{19} +(0.741737 + 0.881048i) q^{21} -4.31354 q^{23} +(1.16575 - 2.01914i) q^{25} +(4.48724 - 2.62005i) q^{27} +(0.173958 + 0.301305i) q^{29} +(2.78262 + 4.81965i) q^{31} +(2.71437 - 7.49567i) q^{33} +(0.543104 + 0.940684i) q^{35} +(2.78525 - 4.82419i) q^{37} +(4.44604 + 4.38552i) q^{39} +2.66959 q^{41} +12.7711 q^{43} +(4.59963 - 1.69113i) q^{45} +(-5.07938 + 8.79774i) q^{47} -6.55786 q^{49} +(0.815566 - 2.25216i) q^{51} -0.833384 q^{53} +(3.75933 - 6.51135i) q^{55} +(3.06448 - 8.46247i) q^{57} +(-3.54267 + 6.13608i) q^{59} +6.99585 q^{61} +(0.339990 - 1.96562i) q^{63} +(3.40344 + 4.80698i) q^{65} +12.3540 q^{67} +(4.81176 + 5.71549i) q^{69} +(-2.13470 - 3.69740i) q^{71} +8.70686 q^{73} +(-3.97579 + 0.707721i) q^{75} +(-1.53023 - 2.65044i) q^{77} +(-7.71985 + 13.3712i) q^{79} +(-8.47712 - 3.02298i) q^{81} +(0.471968 - 0.817473i) q^{83} +(1.12954 - 1.95641i) q^{85} +(0.205181 - 0.566602i) q^{87} +(-6.06011 + 10.4964i) q^{89} +(2.38721 - 0.221424i) q^{91} +(3.28207 - 9.06334i) q^{93} +(4.24421 - 7.35119i) q^{95} -15.0716 q^{97} +(-12.9597 + 4.76486i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{3} + q^{5} - 14 q^{7} - 9 q^{9} - 3 q^{13} + 2 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} + 2 q^{23} - 23 q^{25} - 3 q^{27} + 12 q^{29} + 8 q^{31} - 5 q^{33} - 12 q^{35} + 18 q^{37} - 6 q^{39}+ \cdots + 28 q^{99}+O(q^{100}) $ 40 * q - 3 * q^3 + q^5 - 14 * q^7 - 9 * q^9 - 3 * q^13 + 2 * q^15 - q^17 + 2 * q^19 - 30 * q^21 + 2 * q^23 - 23 * q^25 - 3 * q^27 + 12 * q^29 + 8 * q^31 - 5 * q^33 - 12 * q^35 + 18 * q^37 - 6 * q^39 + 6 * q^41 - 16 * q^43 - 3 * q^45 + 4 * q^47 + 46 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 - 4 * q^59 + 6 * q^61 - 8 * q^63 + 7 * q^65 - 54 * q^67 + 19 * q^69 + q^71 - 12 * q^73 - 28 * q^75 - 4 * q^77 + 13 * q^79 - 13 * q^81 - 15 * q^83 + 5 * q^85 + 37 * q^87 + 12 * q^89 - 57 * q^91 - 22 * q^93 + q^95 - 70 * q^97 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	−1.11550	−	1.32501i	−0.644035	−	0.764996i
$3$	−1.11550	−	1.32501i	−0.644035	−	0.764996i
$4$		0			0
$5$	−0.816777	−	1.41470i	−0.365274	−	0.632672i	0.623546	−	0.781786i	$-0.285691\pi$
$5$	−0.816777	−	1.41470i	−0.365274	−	0.632672i	−0.988820	+	0.149114i	$0.952358\pi$
$6$		0			0
$7$	−0.664936			−0.251322			−0.125661	−	0.992073i	$-0.540105\pi$
$7$	−0.664936			−0.251322			−0.125661	+	0.992073i	$0.540105\pi$
$8$		0			0
$9$	−0.511312	+	2.95611i	−0.170437	+	0.985369i
$10$		0			0
$11$	2.30132	+	3.98600i	0.693874	+	1.20183i	0.970559	+	0.240864i	$0.0774309\pi$
$11$	2.30132	+	3.98600i	0.693874	+	1.20183i	−0.276685	+	0.960961i	$0.589236\pi$
$12$		0			0
$13$	−3.59014	+	0.333001i	−0.995726	+	0.0923578i
$13$	−3.59014	+	0.333001i	−0.995726	+	0.0923578i
$14$		0			0
$15$	−0.963376	+	2.66034i	−0.248743	+	0.686896i
$16$		0			0
$17$	0.691459	+	1.19764i	0.167703	+	0.290471i	0.937612	−	0.347683i	$-0.113032\pi$
$17$	0.691459	+	1.19764i	0.167703	+	0.290471i	−0.769909	+	0.638154i	$0.779698\pi$
$18$		0			0
$19$	2.59815	+	4.50012i	0.596056	+	1.03240i	0.993397	+	0.114728i	$0.0365996\pi$
$19$	2.59815	+	4.50012i	0.596056	+	1.03240i	−0.397341	+	0.917671i	$0.630067\pi$
$20$		0			0
$21$	0.741737	+	0.881048i	0.161860	+	0.192260i
$22$		0			0
$23$	−4.31354			−0.899435			−0.449717	−	0.893171i	$-0.648475\pi$
$23$	−4.31354			−0.899435			−0.449717	+	0.893171i	$0.648475\pi$
$24$		0			0
$25$	1.16575	−	2.01914i	0.233150	−	0.403828i
$26$		0			0
$27$	4.48724	−	2.62005i	0.863570	−	0.504228i
$28$		0			0
$29$	0.173958	+	0.301305i	0.0323032	+	0.0559508i	0.881725	−	0.471764i	$-0.156382\pi$
$29$	0.173958	+	0.301305i	0.0323032	+	0.0559508i	−0.849422	+	0.527714i	$0.823049\pi$
$30$		0			0
$31$	2.78262	+	4.81965i	0.499774	+	0.865634i	1.00000		0.000260735i	$-8.29944e-5\pi$
$31$	2.78262	+	4.81965i	0.499774	+	0.865634i	−0.500226	+	0.865895i	$0.666750\pi$
$32$		0			0
$33$	2.71437	−	7.49567i	0.472512	−	1.30483i
$34$		0			0
$35$	0.543104	+	0.940684i	0.0918014	+	0.159005i
$36$		0			0
$37$	2.78525	−	4.82419i	0.457892	−	0.793092i	−0.540958	−	0.841050i	$-0.681938\pi$
$37$	2.78525	−	4.82419i	0.457892	−	0.793092i	0.998849	+	0.0479583i	$0.0152714\pi$
$38$		0			0
$39$	4.44604	+	4.38552i	0.711936	+	0.702244i
$40$		0			0
$41$	2.66959			0.416919			0.208460	−	0.978031i	$-0.433155\pi$
$41$	2.66959			0.416919			0.208460	+	0.978031i	$0.433155\pi$
$42$		0			0
$43$	12.7711			1.94757			0.973786	−	0.227467i	$-0.0730443\pi$
$43$	12.7711			1.94757			0.973786	+	0.227467i	$0.0730443\pi$
$44$		0			0
$45$	4.59963	−	1.69113i	0.685672	−	0.252098i
$46$		0			0
$47$	−5.07938	+	8.79774i	−0.740904	+	1.28328i	0.211181	+	0.977447i	$0.432269\pi$
$47$	−5.07938	+	8.79774i	−0.740904	+	1.28328i	−0.952084	+	0.305836i	$0.901064\pi$
$48$		0			0
$49$	−6.55786			−0.936837
$50$		0			0
$51$	0.815566	−	2.25216i	0.114202	−	0.315366i
$52$		0			0
$53$	−0.833384			−0.114474			−0.0572371	−	0.998361i	$-0.518229\pi$
$53$	−0.833384			−0.114474			−0.0572371	+	0.998361i	$0.518229\pi$
$54$		0			0
$55$	3.75933	−	6.51135i	0.506908	−	0.877990i
$56$		0			0
$57$	3.06448	−	8.46247i	0.405900	−	1.12088i
$58$		0			0
$59$	−3.54267	+	6.13608i	−0.461216	+	0.798850i	−0.999022	−	0.0442192i	$-0.985920\pi$
$59$	−3.54267	+	6.13608i	−0.461216	+	0.798850i	0.537806	+	0.843069i	$0.319253\pi$
$60$		0			0
$61$	6.99585			0.895727			0.447864	−	0.894102i	$-0.352185\pi$
$61$	6.99585			0.895727			0.447864	+	0.894102i	$0.352185\pi$
$62$		0			0
$63$	0.339990	−	1.96562i	0.0428347	−	0.247645i
$64$		0			0
$65$	3.40344	+	4.80698i	0.422145	+	0.596232i
$66$		0			0
$67$	12.3540			1.50928			0.754642	−	0.656136i	$-0.227810\pi$
$67$	12.3540			1.50928			0.754642	+	0.656136i	$0.227810\pi$
$68$		0			0
$69$	4.81176	+	5.71549i	0.579268	+	0.688064i
$70$		0			0
$71$	−2.13470	−	3.69740i	−0.253342	−	0.438801i	0.711102	−	0.703089i	$-0.248196\pi$
$71$	−2.13470	−	3.69740i	−0.253342	−	0.438801i	−0.964444	+	0.264288i	$0.914863\pi$
$72$		0			0
$73$	8.70686			1.01906			0.509530	−	0.860453i	$-0.329819\pi$
$73$	8.70686			1.01906			0.509530	+	0.860453i	$0.329819\pi$
$74$		0			0
$75$	−3.97579	+	0.707721i	−0.459084	+	0.0817206i
$76$		0			0
$77$	−1.53023	−	2.65044i	−0.174386	−	0.302045i
$78$		0			0
$79$	−7.71985	+	13.3712i	−0.868551	+	1.50437i	−0.00507268	+	0.999987i	$0.501615\pi$
$79$	−7.71985	+	13.3712i	−0.868551	+	1.50437i	−0.863478	+	0.504387i	$0.831719\pi$
$80$		0			0
$81$	−8.47712	−	3.02298i	−0.941902	−	0.335887i
$82$		0			0
$83$	0.471968	−	0.817473i	0.0518052	−	0.0897293i	−0.838960	−	0.544193i	$-0.816836\pi$
$83$	0.471968	−	0.817473i	0.0518052	−	0.0897293i	0.890765	+	0.454464i	$0.150169\pi$
$84$		0			0
$85$	1.12954	−	1.95641i	0.122515	−	0.212203i
$86$		0			0
$87$	0.205181	−	0.566602i	0.0219977	−	0.0607462i
$88$		0			0
$89$	−6.06011	+	10.4964i	−0.642371	+	1.11262i	0.342531	+	0.939506i	$0.388716\pi$
$89$	−6.06011	+	10.4964i	−0.642371	+	1.11262i	−0.984902	+	0.173112i	$0.944618\pi$
$90$		0			0
$91$	2.38721	−	0.221424i	0.250248	−	0.0232116i
$92$		0			0
$93$	3.28207	−	9.06334i	0.340334	−	0.939824i
$94$		0			0
$95$	4.24421	−	7.35119i	0.435447	−	0.754216i
$96$		0			0
$97$	−15.0716			−1.53028			−0.765142	−	0.643861i	$-0.777331\pi$
$97$	−15.0716			−1.53028			−0.765142	+	0.643861i	$0.777331\pi$
$98$		0			0
$99$	−12.9597	+	4.76486i	−1.30250	+	0.478886i
$100$		0			0
$101$	2.43790	+	4.22257i	0.242580	+	0.420162i	0.961449	−	0.274985i	$-0.0886729\pi$
$101$	2.43790	+	4.22257i	0.242580	+	0.420162i	−0.718868	+	0.695146i	$0.755340\pi$
$102$		0			0
$103$	4.73932	+	8.20874i	0.466979	+	0.808831i	0.999288	−	0.0377187i	$-0.0120091\pi$
$103$	4.73932	+	8.20874i	0.466979	+	0.808831i	−0.532310	+	0.846550i	$0.678676\pi$
$104$		0			0
$105$	0.640584	−	1.76895i	0.0625146	−	0.172632i
$106$		0			0
$107$	4.16685	−	7.21719i	0.402824	−	0.697712i	−0.591241	−	0.806495i	$-0.701362\pi$
$107$	4.16685	−	7.21719i	0.402824	−	0.697712i	0.994066	+	0.108782i	$0.0346952\pi$
$108$		0			0
$109$	9.70824			0.929881			0.464941	−	0.885342i	$-0.346076\pi$
$109$	9.70824			0.929881			0.464941	+	0.885342i	$0.346076\pi$
$110$		0			0
$111$	−9.49905	+	1.69091i	−0.901610	+	0.160494i
$112$		0			0
$113$	−4.54566	+	7.87331i	−0.427619	+	0.740659i	−0.996661	−	0.0816502i	$-0.973981\pi$
$113$	−4.54566	+	7.87331i	−0.427619	+	0.740659i	0.569042	+	0.822309i	$0.307314\pi$
$114$		0			0
$115$	3.52320	+	6.10236i	0.328540	+	0.569048i
$116$		0			0
$117$	0.851295	−	10.7831i	0.0787022	−	0.996898i
$118$		0			0
$119$	−0.459776	−	0.796356i	−0.0421476	−	0.0730018i
$120$		0			0
$121$	−5.09215	+	8.81986i	−0.462923	+	0.801806i
$122$		0			0
$123$	−2.97793	−	3.53723i	−0.268511	−	0.318941i
$124$		0			0
$125$	−11.9764			−1.07120
$126$		0			0
$127$	0.0953037	−	0.165071i	0.00845684	−	0.0146477i	−0.861766	−	0.507306i	$-0.830641\pi$
$127$	0.0953037	−	0.165071i	0.00845684	−	0.0146477i	0.870223	+	0.492658i	$0.163975\pi$
$128$		0			0
$129$	−14.2462	−	16.9218i	−1.25430	−	1.48988i
$130$		0			0
$131$	5.09811	+	8.83018i	0.445424	+	0.771496i	0.998082	−	0.0619118i	$-0.0197197\pi$
$131$	5.09811	+	8.83018i	0.445424	+	0.771496i	−0.552658	+	0.833408i	$0.686386\pi$
$132$		0			0
$133$	−1.72760	−	2.99229i	−0.149802	−	0.259465i
$134$		0			0
$135$	−7.37165	−	4.20810i	−0.634451	−	0.362176i
$136$		0			0
$137$	5.25697			0.449134			0.224567	−	0.974459i	$-0.427903\pi$
$137$	5.25697			0.449134			0.224567	+	0.974459i	$0.427903\pi$
$138$		0			0
$139$	−5.79676	+	10.0403i	−0.491675	+	0.851606i	−0.999954	−	0.00958627i	$-0.996949\pi$
$139$	−5.79676	+	10.0403i	−0.491675	+	0.851606i	0.508279	+	0.861192i	$0.330282\pi$
$140$		0			0
$141$	17.3232	−	3.08366i	1.45887	−	0.259691i
$142$		0			0
$143$	−9.58941	−	13.5440i	−0.801906	−	1.13260i
$144$		0			0
$145$	0.284170	−	0.492197i	0.0235990	−	0.0408747i
$146$		0			0
$147$	7.31530	+	8.68924i	0.603356	+	0.716676i
$148$		0			0
$149$	8.38434	−	14.5221i	0.686872	−	1.18970i	−0.285973	−	0.958238i	$-0.592317\pi$
$149$	8.38434	−	14.5221i	0.686872	−	1.18970i	0.972845	−	0.231459i	$-0.0743500\pi$
$150$		0			0
$151$	3.77500	−	6.53849i	0.307205	−	0.532095i	−0.670545	−	0.741869i	$-0.733940\pi$
$151$	3.77500	−	6.53849i	0.307205	−	0.532095i	0.977750	+	0.209774i	$0.0672730\pi$
$152$		0			0
$153$	−3.89391	+	1.43166i	−0.314804	+	0.115743i
$154$		0			0
$155$	4.54557	−	7.87315i	0.365109	−	0.632387i
$156$		0			0
$157$	4.76579	+	8.25459i	0.380351	+	0.658788i	0.991112	−	0.133027i	$-0.0424697\pi$
$157$	4.76579	+	8.25459i	0.380351	+	0.658788i	−0.610761	+	0.791815i	$0.709136\pi$
$158$		0			0
$159$	0.929642	+	1.10424i	0.0737254	+	0.0875722i
$160$		0			0
$161$	2.86823			0.226048
$162$		0			0
$163$	−5.75947	−	9.97569i	−0.451116	−	0.781356i	0.547339	−	0.836911i	$-0.315641\pi$
$163$	−5.75947	−	9.97569i	−0.451116	−	0.781356i	−0.998456	+	0.0555544i	$0.982307\pi$
$164$		0			0
$165$	−12.8212	+	2.28227i	−0.998125	+	0.177674i
$166$		0			0
$167$	−7.81595			−0.604817			−0.302408	−	0.953178i	$-0.597791\pi$
$167$	−7.81595			−0.604817			−0.302408	+	0.953178i	$0.597791\pi$
$168$		0			0
$169$	12.7782	−	2.39104i	0.982940	−	0.183926i
$170$		0			0
$171$	−14.6313	+	5.37943i	−1.11888	+	0.411375i
$172$		0			0
$173$	−12.7224			−0.967267			−0.483633	−	0.875271i	$-0.660683\pi$
$173$	−12.7224			−0.967267			−0.483633	+	0.875271i	$0.660683\pi$
$174$		0			0
$175$	−0.775151	+	1.34260i	−0.0585959	+	0.101491i
$176$		0			0
$177$	12.0822	−	2.15073i	0.908156	−	0.161659i
$178$		0			0
$179$	−10.3196	+	17.8741i	−0.771323	+	1.33597i	0.165515	+	0.986207i	$0.447072\pi$
$179$	−10.3196	+	17.8741i	−0.771323	+	1.33597i	−0.936838	+	0.349764i	$0.886262\pi$
$180$		0			0
$181$	1.81730			0.135079			0.0675393	−	0.997717i	$-0.478485\pi$
$181$	1.81730			0.135079			0.0675393	+	0.997717i	$0.478485\pi$
$182$		0			0
$183$	−7.80388	−	9.26958i	−0.576880	−	0.685227i
$184$		0			0
$185$	−9.09969			−0.669023
$186$		0			0
$187$	−3.18254	+	5.51232i	−0.232730	+	0.403101i
$188$		0			0
$189$	−2.98373	+	1.74216i	−0.217034	+	0.126724i
$190$		0			0
$191$	−16.0161			−1.15888			−0.579441	−	0.815014i	$-0.696729\pi$
$191$	−16.0161			−1.15888			−0.579441	+	0.815014i	$0.696729\pi$
$192$		0			0
$193$	−7.97233			−0.573861			−0.286931	−	0.957951i	$-0.592635\pi$
$193$	−7.97233			−0.573861			−0.286931	+	0.957951i	$0.592635\pi$
$194$		0			0
$195$	2.57276	−	9.87179i	0.184239	−	0.706934i
$196$		0			0
$197$	−6.65872	+	11.5332i	−0.474414	+	0.821710i	−0.999571	−	0.0292961i	$-0.990673\pi$
$197$	−6.65872	+	11.5332i	−0.474414	+	0.821710i	0.525157	+	0.851006i	$0.324007\pi$
$198$		0			0
$199$	−9.38627	−	16.2575i	−0.665375	−	1.15246i	−0.979184	−	0.202977i	$-0.934938\pi$
$199$	−9.38627	−	16.2575i	−0.665375	−	1.15246i	0.313809	−	0.949486i	$-0.398395\pi$
$200$		0			0
$201$	−13.7809	−	16.3692i	−0.972033	−	1.15460i
$202$		0			0
$203$	−0.115671	−	0.200348i	−0.00811852	−	0.0140617i
$204$		0			0
$205$	−2.18045	−	3.77666i	−0.152290	−	0.263773i
$206$		0			0
$207$	2.20556	−	12.7513i	0.153297	−	0.886275i
$208$		0			0
$209$	−11.9583	+	20.7124i	−0.827175	+	1.43271i
$210$		0			0
$211$	6.13429			0.422302			0.211151	−	0.977453i	$-0.432279\pi$
$211$	6.13429			0.422302			0.211151	+	0.977453i	$0.432279\pi$
$212$		0			0
$213$	−2.51784	+	6.95296i	−0.172520	+	0.476409i
$214$		0			0
$215$	−10.4311	−	18.0672i	−0.711396	−	1.23217i
$216$		0			0
$217$	−1.85027	−	3.20476i	−0.125604	−	0.217553i
$218$		0			0
$219$	−9.71252	−	11.5367i	−0.656311	−	0.779577i
$220$		0			0
$221$	−2.88125	−	4.06945i	−0.193814	−	0.273741i
$222$		0			0
$223$	8.71404	+	15.0932i	0.583535	+	1.01071i	0.995056	+	0.0993126i	$0.0316644\pi$
$223$	8.71404	+	15.0932i	0.583535	+	1.01071i	−0.411521	+	0.911400i	$0.635002\pi$
$224$		0			0
$225$	5.37273	+	4.47850i	0.358182	+	0.298566i
$226$		0			0
$227$	−6.26522			−0.415837			−0.207919	−	0.978146i	$-0.566669\pi$
$227$	−6.26522			−0.415837			−0.207919	+	0.978146i	$0.566669\pi$
$228$		0			0
$229$	−1.00519	−	1.74104i	−0.0664249	−	0.115051i	0.830900	−	0.556421i	$-0.187826\pi$
$229$	−1.00519	−	1.74104i	−0.0664249	−	0.115051i	−0.897325	+	0.441370i	$0.854493\pi$
$230$		0			0
$231$	−1.80489	+	4.98414i	−0.118753	+	0.327932i
$232$		0			0
$233$	9.05233			0.593038			0.296519	−	0.955027i	$-0.404174\pi$
$233$	9.05233			0.593038			0.296519	+	0.955027i	$0.404174\pi$
$234$		0			0
$235$	16.5949			1.08253
$236$		0			0
$237$	26.3285	−	4.68667i	1.71022	−	0.304432i
$238$		0			0
$239$	13.9602	+	24.1798i	0.903010	+	1.56406i	0.823567	+	0.567219i	$0.191981\pi$
$239$	13.9602	+	24.1798i	0.903010	+	1.56406i	0.0794431	+	0.996839i	$0.474686\pi$
$240$		0			0
$241$	2.57210			0.165683			0.0828417	−	0.996563i	$-0.473600\pi$
$241$	2.57210			0.165683			0.0828417	+	0.996563i	$0.473600\pi$
$242$		0			0
$243$	5.45076	+	14.6044i	0.349666	+	0.936874i
$244$		0			0
$245$	5.35631	+	9.27739i	0.342202	+	0.592711i
$246$		0			0
$247$	−10.8263	−	15.2909i	−0.688858	−	0.972936i
$248$		0			0
$249$	−1.60964	+	0.286529i	−0.102007	+	0.0181580i
$250$		0			0
$251$	−13.5098	−	23.3997i	−0.852733	−	1.47698i	−0.878732	−	0.477315i	$-0.841610\pi$
$251$	−13.5098	−	23.3997i	−0.852733	−	1.47698i	0.0259992	−	0.999662i	$-0.491723\pi$
$252$		0			0
$253$	−9.92683	−	17.1938i	−0.624095	−	1.08096i
$254$		0			0
$255$	−3.85227	+	0.685734i	−0.241238	+	0.0429423i
$256$		0			0
$257$	8.61257			0.537238			0.268619	−	0.963247i	$-0.413433\pi$
$257$	8.61257			0.537238			0.268619	+	0.963247i	$0.413433\pi$
$258$		0			0
$259$	−1.85201	+	3.20778i	−0.115078	+	0.199322i
$260$		0			0
$261$	−0.979635	+	0.360178i	−0.0606379	+	0.0222945i
$262$		0			0
$263$	−2.13343	−	3.69520i	−0.131553	−	0.227856i	0.792723	−	0.609583i	$-0.208663\pi$
$263$	−2.13343	−	3.69520i	−0.131553	−	0.227856i	−0.924275	+	0.381727i	$0.875330\pi$
$264$		0			0
$265$	0.680689	+	1.17899i	0.0418144	+	0.0724246i
$266$		0			0
$267$	20.6679	−	3.67906i	1.26486	−	0.225155i
$268$		0			0
$269$	6.63958	+	11.5001i	0.404822	+	0.701173i	0.994301	−	0.106611i	$-0.0340000\pi$
$269$	6.63958	+	11.5001i	0.404822	+	0.701173i	−0.589478	+	0.807784i	$0.700667\pi$
$270$		0			0
$271$	9.70756	−	16.8140i	0.589692	−	1.02138i	−0.404581	−	0.914502i	$-0.632582\pi$
$271$	9.70756	−	16.8140i	0.589692	−	1.02138i	0.994273	−	0.106874i	$-0.0340842\pi$
$272$		0			0
$273$	−2.95633	−	2.91609i	−0.178925	−	0.176490i
$274$		0			0
$275$	10.7311			0.647108
$276$		0			0
$277$	−16.2171			−0.974391			−0.487196	−	0.873293i	$-0.661980\pi$
$277$	−16.2171			−0.974391			−0.487196	+	0.873293i	$0.661980\pi$
$278$		0			0
$279$	−15.6702	+	5.76139i	−0.938149	+	0.344925i
$280$		0			0
$281$	−4.85826	+	8.41475i	−0.289819	+	0.501982i	−0.973766	−	0.227550i	$-0.926929\pi$
$281$	−4.85826	+	8.41475i	−0.289819	+	0.501982i	0.683947	+	0.729532i	$0.260262\pi$
$282$		0			0
$283$	−11.4304			−0.679467			−0.339734	−	0.940522i	$-0.610337\pi$
$283$	−11.4304			−0.679467			−0.339734	+	0.940522i	$0.610337\pi$
$284$		0			0
$285$	−14.4748	+	2.57664i	−0.857415	+	0.152627i
$286$		0			0
$287$	−1.77510			−0.104781
$288$		0			0
$289$	7.54377	−	13.0662i	0.443751	−	0.768599i
$290$		0			0
$291$	16.8123	+	19.9700i	0.985557	+	1.17066i
$292$		0			0
$293$	−2.99310	+	5.18421i	−0.174859	+	0.302865i	−0.940112	−	0.340864i	$-0.889280\pi$
$293$	−2.99310	+	5.18421i	−0.174859	+	0.302865i	0.765254	+	0.643729i	$0.222614\pi$
$294$		0			0
$295$	11.5743			0.673880
$296$		0			0
$297$	20.7701	+	11.8566i	1.20520	+	0.687990i
$298$		0			0
$299$	15.4862	−	1.43641i	0.895591	−	0.0830698i
$300$		0			0
$301$	−8.49195			−0.489468
$302$		0			0
$303$	2.87547	−	7.94053i	0.165191	−	0.456172i
$304$		0			0
$305$	−5.71405	−	9.89702i	−0.327185	−	0.566702i
$306$		0			0
$307$	5.39543			0.307934			0.153967	−	0.988076i	$-0.450795\pi$
$307$	5.39543			0.307934			0.153967	+	0.988076i	$0.450795\pi$
$308$		0			0
$309$	5.58996	−	15.4365i	0.318002	−	0.878153i
$310$		0			0
$311$	−9.11590	−	15.7892i	−0.516915	−	0.895323i	−0.999807	−	0.0196433i	$-0.993747\pi$
$311$	−9.11590	−	15.7892i	−0.516915	−	0.895323i	0.482892	−	0.875680i	$-0.339586\pi$
$312$		0			0
$313$	−15.9537	+	27.6326i	−0.901756	+	1.56189i	−0.0765432	+	0.997066i	$0.524388\pi$
$313$	−15.9537	+	27.6326i	−0.901756	+	1.56189i	−0.825213	+	0.564822i	$0.808945\pi$
$314$		0			0
$315$	−3.05846	+	1.12449i	−0.172325	+	0.0633579i
$316$		0			0
$317$	10.6884	−	18.5128i	0.600318	−	1.03978i	−0.392455	−	0.919771i	$-0.628374\pi$
$317$	10.6884	−	18.5128i	0.600318	−	1.03978i	0.992773	−	0.120010i	$-0.0382927\pi$
$318$		0			0
$319$	−0.800667	+	1.38680i	−0.0448288	+	0.0776457i
$320$		0			0
$321$	−14.2110	+	2.52967i	−0.793180	+	0.141192i
$322$		0			0
$323$	−3.59302	+	6.22330i	−0.199921	+	0.346274i
$324$		0			0
$325$	−3.51284	+	7.63720i	−0.194857	+	0.423636i
$326$		0			0
$327$	−10.8296	−	12.8635i	−0.598876	−	0.711355i
$328$		0			0
$329$	3.37746	−	5.84994i	0.186206	−	0.322517i
$330$		0			0
$331$	28.1723			1.54849			0.774246	−	0.632885i	$-0.218129\pi$
$331$	28.1723			1.54849			0.774246	+	0.632885i	$0.218129\pi$
$332$		0			0
$333$	12.8367	+	10.7001i	0.703446	+	0.586364i
$334$		0			0
$335$	−10.0905	−	17.4772i	−0.551302	−	0.954883i
$336$		0			0
$337$	−17.2030	−	29.7965i	−0.937107	−	1.62312i	−0.770833	−	0.637038i	$-0.780159\pi$
$337$	−17.2030	−	29.7965i	−0.937107	−	1.62312i	−0.166275	−	0.986079i	$-0.553174\pi$
$338$		0			0
$339$	15.5029	−	2.75964i	0.842003	−	0.149883i
$340$		0			0
$341$	−12.8074	+	22.1831i	−0.693561	+	1.20128i
$342$		0			0
$343$	9.01511			0.486770
$344$		0			0
$345$	4.15556	−	11.4755i	0.223728	−	0.617818i
$346$		0			0
$347$	−1.15620	+	2.00260i	−0.0620683	+	0.107505i	−0.895390	−	0.445283i	$-0.853103\pi$
$347$	−1.15620	+	2.00260i	−0.0620683	+	0.107505i	0.833321	+	0.552789i	$0.186436\pi$
$348$		0			0
$349$	−2.28054	−	3.95000i	−0.122074	−	0.211439i	0.798511	−	0.601980i	$-0.205621\pi$
$349$	−2.28054	−	3.95000i	−0.122074	−	0.211439i	−0.920586	+	0.390541i	$0.872288\pi$
$350$		0			0
$351$	−15.2374	+	10.9006i	−0.813310	+	0.581831i
$352$		0			0
$353$	−1.53379	−	2.65661i	−0.0816355	−	0.141397i	0.822317	−	0.569030i	$-0.192681\pi$
$353$	−1.53379	−	2.65661i	−0.0816355	−	0.141397i	−0.903953	+	0.427633i	$0.859348\pi$
$354$		0			0
$355$	−3.48714	+	6.03990i	−0.185078	+	0.320565i
$356$		0			0
$357$	−0.542299	+	1.49754i	−0.0287015	+	0.0792585i
$358$		0			0
$359$	32.8421			1.73334			0.866670	−	0.498881i	$-0.166256\pi$
$359$	32.8421			1.73334			0.866670	+	0.498881i	$0.166256\pi$
$360$		0			0
$361$	−4.00073	+	6.92947i	−0.210565	+	0.364709i
$362$		0			0
$363$	17.3667	−	3.09141i	0.911516	−	0.162257i
$364$		0			0
$365$	−7.11156	−	12.3176i	−0.372236	−	0.644732i
$366$		0			0
$367$	6.53536	+	11.3196i	0.341143	+	0.590877i	0.984645	−	0.174567i	$-0.0558527\pi$
$367$	6.53536	+	11.3196i	0.341143	+	0.590877i	−0.643502	+	0.765444i	$0.722519\pi$
$368$		0			0
$369$	−1.36499	+	7.89158i	−0.0710585	+	0.410819i
$370$		0			0
$371$	0.554147			0.0287699
$372$		0			0
$373$	−9.81020	+	16.9918i	−0.507953	+	0.879800i	0.492005	+	0.870592i	$0.336264\pi$
$373$	−9.81020	+	16.9918i	−0.507953	+	0.879800i	−0.999958	+	0.00920747i	$0.997069\pi$
$374$		0			0
$375$	13.3597	+	15.8689i	0.689892	+	0.819465i
$376$		0			0
$377$	−0.724869	−	1.02380i	−0.0373327	−	0.0527282i
$378$		0			0
$379$	−3.69728	+	6.40388i	−0.189917	+	0.328945i	−0.945222	−	0.326427i	$-0.894155\pi$
$379$	−3.69728	+	6.40388i	−0.189917	+	0.328945i	0.755306	+	0.655373i	$0.227488\pi$
$380$		0			0
$381$	−0.325032	+	0.0578583i	−0.0166519	+	0.00296417i
$382$		0			0
$383$	8.48425	−	14.6951i	0.433525	−	0.750887i	−0.563649	−	0.826014i	$-0.690603\pi$
$383$	8.48425	−	14.6951i	0.433525	−	0.750887i	0.997174	+	0.0751275i	$0.0239364\pi$
$384$		0			0
$385$	−2.49971	+	4.32963i	−0.127397	+	0.220658i
$386$		0			0
$387$	−6.53000	+	37.7527i	−0.331939	+	1.91908i
$388$		0			0
$389$	−14.6557	+	25.3844i	−0.743073	+	1.28704i	0.208017	+	0.978125i	$0.433299\pi$
$389$	−14.6557	+	25.3844i	−0.743073	+	1.28704i	−0.951090	+	0.308915i	$0.900034\pi$
$390$		0			0
$391$	−2.98264	−	5.16608i	−0.150838	−	0.261260i
$392$		0			0
$393$	6.01314	−	16.6051i	0.303323	−	0.837618i
$394$		0			0
$395$	25.2216			1.26903
$396$		0			0
$397$	8.31130	+	14.3956i	0.417132	+	0.722494i	0.995650	−	0.0931756i	$-0.0297018\pi$
$397$	8.31130	+	14.3956i	0.417132	+	0.722494i	−0.578517	+	0.815670i	$0.696368\pi$
$398$		0			0
$399$	−2.03768	+	5.62700i	−0.102012	+	0.281702i
$400$		0			0
$401$	31.6115			1.57860			0.789301	−	0.614007i	$-0.210443\pi$
$401$	31.6115			1.57860			0.789301	+	0.614007i	$0.210443\pi$
$402$		0			0
$403$	−11.5950	−	16.3766i	−0.577586	−	0.815776i
$404$		0			0
$405$	2.64731	+	14.4617i	0.131546	+	0.718606i
$406$		0			0
$407$	25.6390			1.27088
$408$		0			0
$409$	1.80815	−	3.13181i	0.0894074	−	0.154858i	−0.817853	−	0.575427i	$-0.804836\pi$
$409$	1.80815	−	3.13181i	0.0894074	−	0.154858i	0.907261	+	0.420568i	$0.138169\pi$
$410$		0			0
$411$	−5.86416	−	6.96555i	−0.289258	−	0.343585i
$412$		0			0
$413$	2.35565	−	4.08010i	0.115914	−	0.200769i
$414$		0			0
$415$	−1.54197			−0.0756923
$416$		0			0
$417$	19.7698	−	3.51918i	0.968131	−	0.172335i
$418$		0			0
$419$	−27.5402			−1.34542			−0.672712	−	0.739904i	$-0.734871\pi$
$419$	−27.5402			−1.34542			−0.672712	+	0.739904i	$0.734871\pi$
$420$		0			0
$421$	15.5966	−	27.0140i	0.760129	−	1.31658i	−0.182654	−	0.983177i	$-0.558469\pi$
$421$	15.5966	−	27.0140i	0.760129	−	1.31658i	0.942784	−	0.333405i	$-0.108198\pi$
$422$		0			0
$423$	−23.4099	−	19.5136i	−1.13823	−	0.948782i
$424$		0			0
$425$	3.22428			0.156401
$426$		0			0
$427$	−4.65179			−0.225116
$428$		0			0
$429$	−7.24892	+	27.8144i	−0.349981	+	1.34289i
$430$		0			0
$431$	−8.66639	+	15.0106i	−0.417445	+	0.723037i	−0.995682	−	0.0928327i	$-0.970408\pi$
$431$	−8.66639	+	15.0106i	−0.417445	+	0.723037i	0.578236	+	0.815869i	$0.303741\pi$
$432$		0			0
$433$	−2.73416	−	4.73570i	−0.131395	−	0.227583i	0.792819	−	0.609457i	$-0.208612\pi$
$433$	−2.73416	−	4.73570i	−0.131395	−	0.227583i	−0.924215	+	0.381873i	$0.875279\pi$
$434$		0			0
$435$	−0.969159	+	0.172518i	−0.0464676	+	0.00827160i
$436$		0			0
$437$	−11.2072	−	19.4114i	−0.536113	−	0.928576i
$438$		0			0
$439$	9.12053	+	15.7972i	0.435299	+	0.753960i	0.997320	−	0.0731628i	$-0.0233093\pi$
$439$	9.12053	+	15.7972i	0.435299	+	0.753960i	−0.562021	+	0.827123i	$0.689976\pi$
$440$		0			0
$441$	3.35311	−	19.3857i	0.159672	−	0.923130i
$442$		0			0
$443$	16.5689	−	28.6981i	0.787211	−	1.36349i	−0.140458	−	0.990087i	$-0.544858\pi$
$443$	16.5689	−	28.6981i	0.787211	−	1.36349i	0.927669	−	0.373403i	$-0.121809\pi$
$444$		0			0
$445$	19.7990			0.938564
$446$		0			0
$447$	−28.5947	+	5.09008i	−1.35248	+	0.240753i
$448$		0			0
$449$	13.7300	+	23.7811i	0.647959	+	1.12230i	0.983610	+	0.180312i	$0.0577106\pi$
$449$	13.7300	+	23.7811i	0.647959	+	1.12230i	−0.335650	+	0.941987i	$0.608956\pi$
$450$		0			0
$451$	6.14357	+	10.6410i	0.289289	+	0.501064i
$452$		0			0
$453$	−12.8746	+	2.29178i	−0.604901	+	0.107677i
$454$		0			0
$455$	−2.26307	−	3.19633i	−0.106094	−	0.149846i
$456$		0			0
$457$	18.1458	+	31.4294i	0.848822	+	1.47020i	0.882260	+	0.470763i	$0.156021\pi$
$457$	18.1458	+	31.4294i	0.848822	+	1.47020i	−0.0334374	+	0.999441i	$0.510645\pi$
$458$		0			0
$459$	6.24063	+	3.56246i	0.291287	+	0.166281i
$460$		0			0
$461$	6.29317			0.293102			0.146551	−	0.989203i	$-0.453183\pi$
$461$	6.29317			0.293102			0.146551	+	0.989203i	$0.453183\pi$
$462$		0			0
$463$	−8.38617	−	14.5253i	−0.389738	−	0.675047i	0.602676	−	0.797986i	$-0.294101\pi$
$463$	−8.38617	−	14.5253i	−0.389738	−	0.675047i	−0.992414	+	0.122940i	$0.960768\pi$
$464$		0			0
$465$	−15.5026	+	2.75959i	−0.718916	+	0.127973i
$466$		0			0
$467$	29.7285			1.37567			0.687836	−	0.725866i	$-0.258561\pi$
$467$	29.7285			1.37567			0.687836	+	0.725866i	$0.258561\pi$
$468$		0			0
$469$	−8.21464			−0.379317
$470$		0			0
$471$	5.62118	−	15.5227i	0.259010	−	0.715250i
$472$		0			0
$473$	29.3903	+	50.9056i	1.35137	+	2.34064i
$474$		0			0
$475$	12.1152			0.555883
$476$		0			0
$477$	0.426119	−	2.46357i	0.0195106	−	0.112799i
$478$		0			0
$479$	−13.9265	−	24.1214i	−0.636318	−	1.10213i	−0.986234	−	0.165354i	$-0.947123\pi$
$479$	−13.9265	−	24.1214i	−0.636318	−	1.10213i	0.349917	−	0.936781i	$-0.386210\pi$
$480$		0			0
$481$	−8.39297	+	18.2470i	−0.382686	+	0.831992i
$482$		0			0
$483$	−3.19951	−	3.80043i	−0.145583	−	0.172926i
$484$		0			0
$485$	12.3101	+	21.3217i	0.558972	+	0.968169i
$486$		0			0
$487$	0.285544	+	0.494577i	0.0129392	+	0.0224114i	0.872423	−	0.488752i	$-0.162548\pi$
$487$	0.285544	+	0.494577i	0.0129392	+	0.0224114i	−0.859483	+	0.511164i	$0.829215\pi$
$488$		0			0
$489$	−6.79321	+	18.7593i	−0.307200	+	0.848323i
$490$		0			0
$491$	−18.4641			−0.833272			−0.416636	−	0.909073i	$-0.636791\pi$
$491$	−18.4641			−0.833272			−0.416636	+	0.909073i	$0.636791\pi$
$492$		0			0
$493$	−0.240570	+	0.416680i	−0.0108347	+	0.0187663i
$494$		0			0
$495$	17.3260	+	14.4423i	0.778748	+	0.649133i
$496$		0			0
$497$	1.41944	+	2.45854i	0.0636704	+	0.110280i
$498$		0			0
$499$	−9.12938	−	15.8126i	−0.408687	−	0.707867i	0.586056	−	0.810271i	$-0.300680\pi$
$499$	−9.12938	−	15.8126i	−0.408687	−	0.707867i	−0.994743	+	0.102404i	$0.967347\pi$
$500$		0			0
$501$	8.71871	+	10.3562i	0.389523	+	0.462682i
$502$		0			0
$503$	0.524528	+	0.908510i	0.0233876	+	0.0405085i	0.877482	−	0.479609i	$-0.159221\pi$
$503$	0.524528	+	0.908510i	0.0233876	+	0.0405085i	−0.854095	+	0.520117i	$0.825888\pi$
$504$		0			0
$505$	3.98244	−	6.89779i	0.177216	−	0.306948i
$506$		0			0
$507$	−17.4223	−	14.2641i	−0.773751	−	0.633490i
$508$		0			0
$509$	−31.2081			−1.38327			−0.691637	−	0.722245i	$-0.743110\pi$
$509$	−31.2081			−1.38327			−0.691637	+	0.722245i	$0.743110\pi$
$510$		0			0
$511$	−5.78950			−0.256113
$512$		0			0
$513$	23.4490	+	13.3859i	1.03530	+	0.591001i
$514$		0			0
$515$	7.74193	−	13.4094i	0.341150	−	0.590889i
$516$		0			0
$517$	−46.7571			−2.05638
$518$		0			0
$519$	14.1919	+	16.8573i	0.622954	+	0.739955i
$520$		0			0
$521$	37.5709			1.64601			0.823006	−	0.568033i	$-0.192296\pi$
$521$	37.5709			1.64601			0.823006	+	0.568033i	$0.192296\pi$
$522$		0			0
$523$	−4.27086	+	7.39736i	−0.186752	+	0.323464i	−0.944165	−	0.329472i	$-0.893129\pi$
$523$	−4.27086	+	7.39736i	−0.186752	+	0.323464i	0.757414	+	0.652935i	$0.226463\pi$
$524$		0			0
$525$	2.64364	−	0.470589i	0.115378	−	0.0205382i
$526$		0			0
$527$	−3.84814	+	6.66518i	−0.167628	+	0.290340i
$528$		0			0
$529$	−4.39338			−0.191017
$530$		0			0
$531$	−16.3275	−	13.6099i	−0.708553	−	0.590621i
$532$		0			0
$533$	−9.58419	+	0.888974i	−0.415137	+	0.0385057i
$534$		0			0
$535$	−13.6135			−0.588565
$536$		0			0
$537$	35.1949	−	6.26497i	1.51877	−	0.270353i
$538$		0			0
$539$	−15.0917	−	26.1397i	−0.650047	−	1.12591i
$540$		0			0
$541$	11.3495			0.487953			0.243977	−	0.969781i	$-0.421548\pi$
$541$	11.3495			0.487953			0.243977	+	0.969781i	$0.421548\pi$
$542$		0			0
$543$	−2.02720	−	2.40794i	−0.0869954	−	0.103335i
$544$		0			0
$545$	−7.92947	−	13.7342i	−0.339661	−	0.588310i
$546$		0			0
$547$	−4.12504	+	7.14478i	−0.176374	+	0.305489i	−0.940636	−	0.339417i	$-0.889770\pi$
$547$	−4.12504	+	7.14478i	−0.176374	+	0.305489i	0.764262	+	0.644906i	$0.223103\pi$
$548$		0			0
$549$	−3.57706	+	20.6805i	−0.152665	+	0.882621i
$550$		0			0
$551$	−0.903938	+	1.56567i	−0.0385091	+	0.0666996i
$552$		0			0
$553$	5.13320	−	8.89097i	0.218286	−	0.378083i
$554$		0			0
$555$	10.1507	+	12.0572i	0.430874	+	0.511800i
$556$		0			0
$557$	14.8382	−	25.7005i	0.628715	−	1.08897i	−0.359095	−	0.933301i	$-0.616915\pi$
$557$	14.8382	−	25.7005i	0.628715	−	1.08897i	0.987810	−	0.155665i	$-0.0497520\pi$
$558$		0			0
$559$	−45.8500	+	4.25278i	−1.93925	+	0.179873i
$560$		0			0
$561$	10.8540	−	1.93210i	0.458257	−	0.0815733i
$562$		0			0
$563$	−2.59357	+	4.49219i	−0.109306	+	0.189323i	−0.915489	−	0.402342i	$-0.868196\pi$
$563$	−2.59357	+	4.49219i	−0.109306	+	0.189323i	0.806183	+	0.591666i	$0.201529\pi$
$564$		0			0
$565$	14.8511			0.624792
$566$		0			0
$567$	5.63674	+	2.01009i	0.236721	+	0.0844158i
$568$		0			0
$569$	−19.2800	−	33.3939i	−0.808260	−	1.39995i	−0.914068	−	0.405560i	$-0.867076\pi$
$569$	−19.2800	−	33.3939i	−0.808260	−	1.39995i	0.105809	−	0.994386i	$-0.466257\pi$
$570$		0			0
$571$	2.65412	+	4.59707i	0.111071	+	0.192381i	0.916202	−	0.400716i	$-0.131238\pi$
$571$	2.65412	+	4.59707i	0.111071	+	0.192381i	−0.805131	+	0.593097i	$0.797905\pi$
$572$		0			0
$573$	17.8659	+	21.2215i	0.746361	+	0.886540i
$574$		0			0
$575$	−5.02852	+	8.70965i	−0.209704	+	0.363217i
$576$		0			0
$577$	−20.1830			−0.840228			−0.420114	−	0.907471i	$-0.638010\pi$
$577$	−20.1830			−0.840228			−0.420114	+	0.907471i	$0.638010\pi$
$578$		0			0
$579$	8.89315	+	10.5634i	0.369587	+	0.439001i
$580$		0			0
$581$	−0.313829	+	0.543567i	−0.0130198	+	0.0225510i
$582$		0			0
$583$	−1.91788	−	3.32187i	−0.0794306	−	0.137578i
$584$		0			0
$585$	−15.9502	+	7.60306i	−0.659458	+	0.314348i
$586$		0			0
$587$	7.51712	+	13.0200i	0.310265	+	0.537394i	0.978420	−	0.206628i	$-0.0662490\pi$
$587$	7.51712	+	13.0200i	0.310265	+	0.537394i	−0.668155	+	0.744022i	$0.732916\pi$
$588$		0			0
$589$	−14.4593	+	25.0443i	−0.595786	+	1.03193i
$590$		0			0
$591$	22.7095	−	4.04247i	0.934144	−	0.166285i
$592$		0			0
$593$	18.9694			0.778980			0.389490	−	0.921031i	$-0.372651\pi$
$593$	18.9694			0.778980			0.389490	+	0.921031i	$0.372651\pi$
$594$		0			0
$595$	−0.751069	+	1.30089i	−0.0307908	+	0.0533313i
$596$		0			0
$597$	−11.0710	+	30.5722i	−0.453105	+	1.25124i
$598$		0			0
$599$	12.1207	+	20.9936i	0.495237	+	0.857776i	0.999985	−	0.00549092i	$-0.00174782\pi$
$599$	12.1207	+	20.9936i	0.495237	+	0.857776i	−0.504748	+	0.863267i	$0.668414\pi$
$600$		0			0
$601$	0.962996	+	1.66796i	0.0392814	+	0.0680374i	0.884998	−	0.465595i	$-0.154160\pi$
$601$	0.962996	+	1.66796i	0.0392814	+	0.0680374i	−0.845716	+	0.533633i	$0.820826\pi$
$602$		0			0
$603$	−6.31676	+	36.5198i	−0.257238	+	1.48720i
$604$		0			0
$605$	16.6366			0.676374
$606$		0			0
$607$	6.97184	−	12.0756i	0.282978	−	0.490133i	−0.689139	−	0.724630i	$-0.742011\pi$
$607$	6.97184	−	12.0756i	0.282978	−	0.490133i	0.972117	+	0.234497i	$0.0753442\pi$
$608$		0			0
$609$	−0.136432	+	0.376754i	−0.00552852	+	0.0152669i
$610$		0			0
$611$	15.3060	−	33.2766i	0.619216	−	1.34623i
$612$		0			0
$613$	10.1080	−	17.5076i	0.408260	−	0.707126i	−0.586435	−	0.809996i	$-0.699469\pi$
$613$	10.1080	−	17.5076i	0.408260	−	0.707126i	0.994695	+	0.102870i	$0.0328025\pi$
$614$		0			0
$615$	−2.57182	+	7.10200i	−0.103706	+	0.286380i
$616$		0			0
$617$	20.3557	−	35.2570i	0.819488	−	1.41940i	−0.0865717	−	0.996246i	$-0.527591\pi$
$617$	20.3557	−	35.2570i	0.819488	−	1.41940i	0.906060	−	0.423149i	$-0.139075\pi$
$618$		0			0
$619$	−5.06866	+	8.77917i	−0.203727	+	0.352865i	−0.949726	−	0.313082i	$-0.898639\pi$
$619$	−5.06866	+	8.77917i	−0.203727	+	0.352865i	0.746000	+	0.665946i	$0.231972\pi$
$620$		0			0
$621$	−19.3559	+	11.3017i	−0.776725	+	0.453521i
$622$		0			0
$623$	4.02959	−	6.97945i	0.161442	−	0.279626i
$624$		0			0
$625$	3.95328	+	6.84729i	0.158131	+	0.273892i
$626$		0			0
$627$	40.7838	−	7.25983i	1.62875	−	0.289930i
$628$		0			0
$629$	7.70354			0.307160
$630$		0			0
$631$	−24.1319	−	41.7977i	−0.960677	−	1.66394i	−0.720807	−	0.693136i	$-0.756229\pi$
$631$	−24.1319	−	41.7977i	−0.960677	−	1.66394i	−0.239870	−	0.970805i	$-0.577105\pi$
$632$		0			0
$633$	−6.84281	−	8.12801i	−0.271977	−	0.323059i
$634$		0			0
$635$	−0.311367			−0.0123562
$636$		0			0
$637$	23.5436	−	2.18377i	0.932833	−	0.0865242i
$638$		0			0
$639$	12.0214	−	4.41986i	0.475559	−	0.174847i
$640$		0			0
$641$	3.38102			0.133542			0.0667711	−	0.997768i	$-0.478730\pi$
$641$	3.38102			0.133542			0.0667711	+	0.997768i	$0.478730\pi$
$642$		0			0
$643$	15.6424	−	27.0934i	0.616875	−	1.06846i	−0.373178	−	0.927760i	$-0.621732\pi$
$643$	15.6424	−	27.0934i	0.616875	−	1.06846i	0.990053	−	0.140698i	$-0.0449348\pi$
$644$		0			0
$645$	−12.3034	+	33.9754i	−0.484444	+	1.33778i
$646$		0			0
$647$	−10.7606	+	18.6379i	−0.423044	+	0.732733i	−0.996235	−	0.0866881i	$-0.972372\pi$
$647$	−10.7606	+	18.6379i	−0.423044	+	0.732733i	0.573192	+	0.819421i	$0.305705\pi$
$648$		0			0
$649$	−32.6112			−1.28010
$650$		0			0
$651$	−2.18236	+	6.02654i	−0.0855336	+	0.236199i
$652$		0			0
$653$	26.2714			1.02808			0.514041	−	0.857766i	$-0.328148\pi$
$653$	26.2714			1.02808			0.514041	+	0.857766i	$0.328148\pi$
$654$		0			0
$655$	8.32803	−	14.4246i	0.325403	−	0.563615i
$656$		0			0
$657$	−4.45192	+	25.7384i	−0.173686	+	1.00415i
$658$		0			0
$659$	16.7286			0.651653			0.325826	−	0.945430i	$-0.394358\pi$
$659$	16.7286			0.651653			0.325826	+	0.945430i	$0.394358\pi$
$660$		0			0
$661$	10.6486			0.414183			0.207091	−	0.978322i	$-0.433600\pi$
$661$	10.6486			0.414183			0.207091	+	0.978322i	$0.433600\pi$
$662$		0			0
$663$	−2.17803	+	8.35717i	−0.0845875	+	0.324566i
$664$		0			0
$665$	−2.82213	+	4.88807i	−0.109437	+	0.189551i
$666$		0			0
$667$	−0.750376	−	1.29969i	−0.0290547	−	0.0503241i
$668$		0			0
$669$	10.2781	−	28.3827i	0.397374	−	1.09734i
$670$		0			0
$671$	16.0997	+	27.8855i	0.621522	+	1.07651i
$672$		0			0
$673$	−2.79201	−	4.83591i	−0.107624	−	0.186410i	0.807183	−	0.590301i	$-0.200991\pi$
$673$	−2.79201	−	4.83591i	−0.107624	−	0.186410i	−0.914807	+	0.403891i	$0.867658\pi$
$674$		0			0
$675$	−0.0592339	−	12.1147i	−0.00227991	−	0.466295i
$676$		0			0
$677$	16.0457	−	27.7919i	0.616684	−	1.06813i	−0.373402	−	0.927670i	$-0.621809\pi$
$677$	16.0457	−	27.7919i	0.616684	−	1.06813i	0.990086	−	0.140459i	$-0.0448579\pi$
$678$		0			0
$679$	10.0216			0.384594
$680$		0			0
$681$	6.98886	+	8.30149i	0.267814	+	0.318114i
$682$		0			0
$683$	−0.113469	−	0.196534i	−0.00434178	−	0.00752018i	0.863846	−	0.503755i	$-0.168049\pi$
$683$	−0.113469	−	0.196534i	−0.00434178	−	0.00752018i	−0.868188	+	0.496235i	$0.834715\pi$
$684$		0			0
$685$	−4.29377	−	7.43703i	−0.164057	−	0.284154i
$686$		0			0
$687$	−1.18561	+	3.27403i	−0.0452338	+	0.124912i
$688$		0			0
$689$	2.99197	−	0.277518i	0.113985	−	0.0105726i
$690$		0			0
$691$	6.77795	+	11.7398i	0.257845	+	0.446601i	0.965664	−	0.259792i	$-0.0836541\pi$
$691$	6.77795	+	11.7398i	0.257845	+	0.446601i	−0.707819	+	0.706394i	$0.750321\pi$
$692$		0			0
$693$	8.61740	−	3.16832i	0.327348	−	0.120355i
$694$		0			0
$695$	18.9386			0.718384
$696$		0			0
$697$	1.84591	+	3.19721i	0.0699188	+	0.121103i
$698$		0			0
$699$	−10.0979	−	11.9944i	−0.381937	−	0.453671i
$700$		0			0
$701$	−33.6536			−1.27108			−0.635540	−	0.772068i	$-0.719222\pi$
$701$	−33.6536			−1.27108			−0.635540	+	0.772068i	$0.719222\pi$
$702$		0			0
$703$	28.9459			1.09172
$704$		0			0
$705$	−18.5116	−	21.9884i	−0.697188	−	0.828131i
$706$		0			0
$707$	−1.62105	−	2.80774i	−0.0609658	−	0.105596i
$708$		0			0
$709$	1.35327			0.0508233			0.0254116	−	0.999677i	$-0.491910\pi$
$709$	1.35327			0.0508233			0.0254116	+	0.999677i	$0.491910\pi$
$710$		0			0
$711$	−35.5793	−	29.6575i	−1.33433	−	1.11224i
$712$		0			0
$713$	−12.0030	−	20.7897i	−0.449514	−	0.778582i
$714$		0			0
$715$	−11.3282	+	24.6285i	−0.423652	+	0.921054i
$716$		0			0
$717$	16.4658	−	45.4700i	0.614928	−	1.69811i
$718$		0			0
$719$	−16.6891	−	28.9064i	−0.622398	−	1.07803i	−0.989038	−	0.147663i	$-0.952825\pi$
$719$	−16.6891	−	28.9064i	−0.622398	−	1.07803i	0.366639	−	0.930363i	$-0.380508\pi$
$720$		0			0
$721$	−3.15134	−	5.45829i	−0.117362	−	0.203277i
$722$		0			0
$723$	−2.86918	−	3.40806i	−0.106706	−	0.126747i
$724$		0			0
$725$	0.811169			0.0301261
$726$		0			0
$727$	6.68899	−	11.5857i	0.248081	−	0.429689i	−0.714912	−	0.699214i	$-0.753533\pi$
$727$	6.68899	−	11.5857i	0.248081	−	0.429689i	0.962993	+	0.269525i	$0.0868667\pi$
$728$		0			0
$729$	13.2707	−	23.5136i	0.491508	−	0.870873i
$730$		0			0
$731$	8.83068	+	15.2952i	0.326615	+	0.565713i
$732$		0			0
$733$	−14.3874	−	24.9197i	−0.531410	−	0.920429i	−0.999328	−	0.0366568i	$-0.988329\pi$
$733$	−14.3874	−	24.9197i	−0.531410	−	0.920429i	0.467918	−	0.883772i	$-0.345004\pi$
$734$		0			0
$735$	6.31769	−	17.4461i	0.233031	−	0.643510i
$736$		0			0
$737$	28.4306	+	49.2432i	1.04725	+	1.81390i
$738$		0			0
$739$	−9.01328	+	15.6115i	−0.331559	+	0.574277i	−0.982818	−	0.184579i	$-0.940908\pi$
$739$	−9.01328	+	15.6115i	−0.331559	+	0.574277i	0.651259	+	0.758856i	$0.274241\pi$
$740$		0			0
$741$	−8.18389	+	31.4019i	−0.300643	+	1.15358i
$742$		0			0
$743$	−19.7552			−0.724747			−0.362373	−	0.932033i	$-0.618033\pi$
$743$	−19.7552			−0.724747			−0.362373	+	0.932033i	$0.618033\pi$
$744$		0			0
$745$	−27.3925			−1.00358
$746$		0			0
$747$	2.17521	+	1.81317i	0.0795869	+	0.0663405i
$748$		0			0
$749$	−2.77069	+	4.79897i	−0.101239	+	0.175351i
$750$		0			0
$751$	−39.9837			−1.45903			−0.729513	−	0.683967i	$-0.760253\pi$
$751$	−39.9837			−1.45903			−0.729513	+	0.683967i	$0.760253\pi$
$752$		0			0
$753$	−15.9347	+	44.0031i	−0.580691	+	1.60356i
$754$		0			0
$755$	−12.3333			−0.448855
$756$		0			0
$757$	1.13756	−	1.97031i	0.0413454	−	0.0716123i	−0.844612	−	0.535379i	$-0.820169\pi$
$757$	1.13756	−	1.97031i	0.0413454	−	0.0716123i	0.885958	+	0.463766i	$0.153502\pi$
$758$		0			0
$759$	−11.7086	+	32.3329i	−0.424994	+	1.17361i
$760$		0			0
$761$	8.06709	−	13.9726i	0.292432	−	0.506507i	−0.681952	−	0.731397i	$-0.738869\pi$
$761$	8.06709	−	13.9726i	0.292432	−	0.506507i	0.974384	+	0.224890i	$0.0722022\pi$
$762$		0			0
$763$	−6.45536			−0.233700
$764$		0			0
$765$	5.20582	+	4.33936i	0.188217	+	0.156890i
$766$		0			0
$767$	10.6754	−	23.2091i	0.385465	−	0.838032i
$768$		0			0
$769$	−38.5720			−1.39094			−0.695471	−	0.718554i	$-0.744804\pi$
$769$	−38.5720			−1.39094			−0.695471	+	0.718554i	$0.744804\pi$
$770$		0			0
$771$	−9.60734	−	11.4118i	−0.346000	−	0.410984i
$772$		0			0
$773$	−9.95027	−	17.2344i	−0.357886	−	0.619877i	0.629721	−	0.776821i	$-0.283169\pi$
$773$	−9.95027	−	17.2344i	−0.357886	−	0.619877i	−0.987608	+	0.156944i	$0.949836\pi$
$774$		0			0
$775$	12.9754			0.466090
$776$		0			0
$777$	6.31626	−	1.12434i	0.226595	−	0.0403356i
$778$		0			0
$779$	6.93597	+	12.0135i	0.248507	+	0.430427i
$780$		0			0
$781$	9.82524	−	17.0178i	0.351575	−	0.608945i
$782$		0			0
$783$	1.57002	+	0.896248i	0.0561081	+	0.0320293i
$784$		0			0
$785$	7.78517	−	13.4843i	0.277865	−	0.481276i
$786$		0			0
$787$	12.3659	−	21.4184i	0.440797	−	0.763483i	−0.556951	−	0.830545i	$-0.688029\pi$
$787$	12.3659	−	21.4184i	0.440797	−	0.763483i	0.997749	+	0.0670616i	$0.0213624\pi$
$788$		0			0
$789$	−2.51635	+	6.94882i	−0.0895843	+	0.247385i
$790$		0			0
$791$	3.02257	−	5.23525i	0.107470	−	0.186144i
$792$		0			0
$793$	−25.1161	+	2.32962i	−0.891899	+	0.0827274i
$794$		0			0
$795$	0.802862	−	2.21708i	0.0284746	−	0.0786318i
$796$		0			0
$797$	16.7586	−	29.0268i	0.593621	−	1.02818i	−0.400119	−	0.916463i	$-0.631031\pi$
$797$	16.7586	−	29.0268i	0.593621	−	1.02818i	0.993740	−	0.111719i	$-0.0356355\pi$
$798$		0			0
$799$	−14.0487			−0.497009
$800$		0			0
$801$	−27.9299	−	23.2813i	−0.986856	−	0.822603i
$802$		0			0
$803$	20.0373	+	34.7056i	0.707100	+	1.22473i
$804$		0			0
$805$	−2.34270	−	4.05768i	−0.0825694	−	0.143014i
$806$		0			0
$807$	7.83129	−	21.6259i	0.275674	−	0.761267i
$808$		0			0
$809$	19.8782	−	34.4301i	0.698882	−	1.21050i	−0.269973	−	0.962868i	$-0.587015\pi$
$809$	19.8782	−	34.4301i	0.698882	−	1.21050i	0.968854	−	0.247631i	$-0.0796520\pi$
$810$		0			0
$811$	−2.74775			−0.0964867			−0.0482434	−	0.998836i	$-0.515362\pi$
$811$	−2.74775			−0.0964867			−0.0482434	+	0.998836i	$0.515362\pi$
$812$		0			0
$813$	−33.1075	+	5.89340i	−1.16113	+	0.206691i
$814$		0			0
$815$	−9.40840	+	16.2958i	−0.329562	+	0.570818i
$816$		0			0
$817$	33.1811	+	57.4714i	1.16086	+	2.01067i
$818$		0			0
$819$	−0.566057	+	7.17007i	−0.0197796	+	0.250543i
$820$		0			0
$821$	−17.7476	−	30.7397i	−0.619395	−	1.07282i	−0.989596	−	0.143871i	$-0.954045\pi$
$821$	−17.7476	−	30.7397i	−0.619395	−	1.07282i	0.370202	−	0.928951i	$-0.379289\pi$
$822$		0			0
$823$	−22.8848	+	39.6376i	−0.797713	+	1.38168i	0.123390	+	0.992358i	$0.460623\pi$
$823$	−22.8848	+	39.6376i	−0.797713	+	1.38168i	−0.921102	+	0.389320i	$0.872710\pi$
$824$		0			0
$825$	−11.9705	−	14.2188i	−0.416760	−	0.495035i
$826$		0			0
$827$	−18.2377			−0.634188			−0.317094	−	0.948394i	$-0.602707\pi$
$827$	−18.2377			−0.634188			−0.317094	+	0.948394i	$0.602707\pi$
$828$		0			0
$829$	12.9490	−	22.4284i	0.449739	−	0.778971i	−0.548630	−	0.836065i	$-0.684850\pi$
$829$	12.9490	−	22.4284i	0.449739	−	0.778971i	0.998369	+	0.0570946i	$0.0181837\pi$
$830$		0			0
$831$	18.0902	+	21.4878i	0.627542	+	0.745405i
$832$		0			0
$833$	−4.53449	−	7.85397i	−0.157111	−	0.272124i
$834$		0			0
$835$	6.38389	+	11.0572i	0.220924	+	0.382651i
$836$		0			0
$837$	25.1140	+	14.3363i	0.868068	+	0.495536i
$838$		0			0
$839$	−3.59367			−0.124067			−0.0620336	−	0.998074i	$-0.519759\pi$
$839$	−3.59367			−0.124067			−0.0620336	+	0.998074i	$0.519759\pi$
$840$		0			0
$841$	14.4395	−	25.0099i	0.497913	−	0.862411i
$842$		0			0
$843$	16.5690	−	2.94942i	0.570668	−	0.101583i
$844$		0			0
$845$	−13.8196	−	16.1244i	−0.475407	−	0.554696i
$846$		0			0
$847$	3.38595	−	5.86464i	0.116343	−	0.201512i
$848$		0			0
$849$	12.7506	+	15.1454i	0.437601	+	0.519790i
$850$		0			0
$851$	−12.0143	+	20.8093i	−0.411844	+	0.713334i
$852$		0			0
$853$	17.0535	−	29.5375i	0.583901	−	1.01135i	−0.411111	−	0.911585i	$-0.634859\pi$
$853$	17.0535	−	29.5375i	0.583901	−	1.01135i	0.995011	−	0.0997604i	$-0.0318076\pi$
$854$		0			0
$855$	19.5608	+	16.3051i	0.668964	+	0.557622i
$856$		0			0
$857$	−15.7794	+	27.3308i	−0.539015	+	0.933601i	0.459943	+	0.887949i	$0.347870\pi$
$857$	−15.7794	+	27.3308i	−0.539015	+	0.933601i	−0.998957	+	0.0456525i	$0.985463\pi$
$858$		0			0
$859$	13.4662	+	23.3241i	0.459460	+	0.795807i	0.998932	−	0.0461957i	$-0.0147098\pi$
$859$	13.4662	+	23.3241i	0.459460	+	0.795807i	−0.539473	+	0.842003i	$0.681376\pi$
$860$		0			0
$861$	1.98013	+	2.35203i	0.0674827	+	0.0801571i
$862$		0			0
$863$	−38.0216			−1.29427			−0.647135	−	0.762376i	$-0.724033\pi$
$863$	−38.0216			−1.29427			−0.647135	+	0.762376i	$0.724033\pi$
$864$		0			0
$865$	10.3914	+	17.9984i	0.353317	+	0.611963i
$866$		0			0
$867$	−25.7279	+	4.57978i	−0.873767	+	0.155537i
$868$		0			0
$869$	−71.0634			−2.41066
$870$		0			0
$871$	−44.3527	+	4.11390i	−1.50283	+	0.139394i
$872$		0			0
$873$	7.70626	−	44.5531i	0.260817	−	1.50789i
$874$		0			0
$875$	7.96354			0.269217
$876$		0			0
$877$	24.5692	−	42.5550i	0.829642	−	1.43698i	−0.0686781	−	0.997639i	$-0.521878\pi$
$877$	24.5692	−	42.5550i	0.829642	−	1.43698i	0.898320	−	0.439342i	$-0.144789\pi$
$878$		0			0
$879$	10.2079	−	1.81710i	0.344305	−	0.0612891i
$880$		0			0
$881$	17.4459	−	30.2172i	0.587768	−	1.01804i	−0.406756	−	0.913537i	$-0.633340\pi$
$881$	17.4459	−	30.2172i	0.587768	−	1.01804i	0.994524	−	0.104507i	$-0.0333265\pi$
$882$		0			0
$883$	−40.3318			−1.35727			−0.678636	−	0.734475i	$-0.737429\pi$
$883$	−40.3318			−1.35727			−0.678636	+	0.734475i	$0.737429\pi$
$884$		0			0
$885$	−12.9111	−	15.3360i	−0.434003	−	0.515515i
$886$		0			0
$887$	6.74768			0.226565			0.113283	−	0.993563i	$-0.463863\pi$
$887$	6.74768			0.226565			0.113283	+	0.993563i	$0.463863\pi$
$888$		0			0
$889$	−0.0633709	+	0.109762i	−0.00212539	+	0.00368128i
$890$		0			0
$891$	−7.45895	−	40.7467i	−0.249884	−	1.36507i
$892$		0			0
$893$	−52.7879			−1.76648
$894$		0			0
$895$	33.7152			1.12698
$896$		0			0
$897$	−19.1782	−	18.9171i	−0.640340	−	0.631623i
$898$		0			0
$899$	−0.968121	+	1.67683i	−0.0322886	+	0.0559256i
$900$		0			0
$901$	−0.576251	−	0.998096i	−0.0191977	−	0.0332514i
$902$		0			0
$903$	9.47279	+	11.2519i	0.315235	+	0.374441i
$904$		0			0
$905$	−1.48433	−	2.57093i	−0.0493406	−	0.0854605i
$906$		0			0
$907$	−17.2965	−	29.9583i	−0.574319	−	0.994750i	−0.996115	−	0.0880593i	$-0.971933\pi$
$907$	−17.2965	−	29.9583i	−0.574319	−	0.994750i	0.421796	−	0.906691i	$-0.361400\pi$
$908$		0			0
$909$	−13.7289	+	5.04765i	−0.455359	+	0.167420i
$910$		0			0
$911$	−29.8143	+	51.6399i	−0.987793	+	1.71091i	−0.358994	+	0.933340i	$0.616880\pi$
$911$	−29.8143	+	51.6399i	−0.987793	+	1.71091i	−0.628799	+	0.777568i	$0.716453\pi$
$912$		0			0
$913$	4.34460			0.143785
$914$		0			0
$915$	−6.73964	+	18.6113i	−0.222806	+	0.615271i
$916$		0			0
$917$	−3.38992	−	5.87151i	−0.111945	−	0.193894i
$918$		0			0
$919$	22.3087	+	38.6399i	0.735897	+	1.27461i	0.954328	+	0.298759i	$0.0965728\pi$
$919$	22.3087	+	38.6399i	0.735897	+	1.27461i	−0.218431	+	0.975852i	$0.570094\pi$
$920$		0			0
$921$	−6.01861	−	7.14901i	−0.198320	−	0.235568i
$922$		0			0
$923$	8.89510	+	12.5633i	0.292786	+	0.413527i
$924$		0			0
$925$	−6.49381	−	11.2476i	−0.213515	−	0.369819i
$926$		0			0
$927$	−26.6892	+	9.81270i	−0.876587	+	0.322291i
$928$		0			0
$929$	−22.5988			−0.741441			−0.370721	−	0.928744i	$-0.620889\pi$
$929$	−22.5988			−0.741441			−0.370721	+	0.928744i	$0.620889\pi$
$930$		0			0
$931$	−17.0383	−	29.5112i	−0.558407	−	0.967189i
$932$		0			0
$933$	−10.7521	+	29.6915i	−0.352007	+	0.972058i
$934$		0			0
$935$	10.3977			0.340041
$936$		0			0
$937$	−50.3581			−1.64513			−0.822564	−	0.568672i	$-0.807457\pi$
$937$	−50.3581			−1.64513			−0.822564	+	0.568672i	$0.807457\pi$
$938$		0			0
$939$	54.4099	−	9.68540i	1.77560	−	0.316071i
$940$		0			0
$941$	28.8445	+	49.9601i	0.940304	+	1.62865i	0.764892	+	0.644158i	$0.222792\pi$
$941$	28.8445	+	49.9601i	0.940304	+	1.62865i	0.175412	+	0.984495i	$0.443874\pi$
$942$		0			0
$943$	−11.5154			−0.374992
$944$		0			0
$945$	4.90168	+	2.79812i	0.159452	+	0.0910228i
$946$		0			0
$947$	−1.23791	−	2.14413i	−0.0402267	−	0.0696748i	0.845211	−	0.534433i	$-0.179475\pi$
$947$	−1.23791	−	2.14413i	−0.0402267	−	0.0696748i	−0.885438	+	0.464758i	$0.846141\pi$
$948$		0			0
$949$	−31.2588	+	2.89939i	−1.01471	+	0.0941182i
$950$		0			0
$951$	−36.4525	+	6.48884i	−1.18205	+	0.210415i
$952$		0			0
$953$	−4.94384	−	8.56298i	−0.160147	−	0.277382i	0.774774	−	0.632238i	$-0.217863\pi$
$953$	−4.94384	−	8.56298i	−0.160147	−	0.277382i	−0.934921	+	0.354856i	$0.884530\pi$
$954$		0			0
$955$	13.0815	+	22.6579i	0.423309	+	0.733192i
$956$		0			0
$957$	2.73067	−	0.486080i	0.0882699	−	0.0157127i
$958$		0			0
$959$	−3.49555			−0.112877
$960$		0			0
$961$	0.0139977	−	0.0242447i	0.000451538	−	0.000782086i
$962$		0			0
$963$	19.2042	+	16.0079i	0.618848	+	0.515847i
$964$		0			0
$965$	6.51162	+	11.2784i	0.209616	+	0.363066i
$966$		0			0
$967$	−13.4158	−	23.2369i	−0.431425	−	0.747249i	0.565572	−	0.824699i	$-0.308656\pi$
$967$	−13.4158	−	23.2369i	−0.431425	−	0.747249i	−0.996996	+	0.0774499i	$0.975322\pi$
$968$		0			0
$969$	12.2540	−	2.18130i	0.393654	−	0.0700736i
$970$		0			0
$971$	21.6035	+	37.4183i	0.693289	+	1.20081i	0.970754	+	0.240076i	$0.0771722\pi$
$971$	21.6035	+	37.4183i	0.693289	+	1.20081i	−0.277466	+	0.960736i	$0.589494\pi$
$972$		0			0
$973$	3.85448	−	6.67615i	0.123569	−	0.214028i
$974$		0			0
$975$	14.0380	−	3.86476i	0.449574	−	0.123771i
$976$		0			0
$977$	−43.0153			−1.37618			−0.688090	−	0.725625i	$-0.741551\pi$
$977$	−43.0153			−1.37618			−0.688090	+	0.725625i	$0.741551\pi$
$978$		0			0
$979$	−55.7850			−1.78290
$980$		0			0
$981$	−4.96394	+	28.6986i	−0.158486	+	0.916276i
$982$		0			0
$983$	15.6828	−	27.1635i	0.500205	−	0.866380i	−0.499795	−	0.866144i	$-0.666591\pi$
$983$	15.6828	−	27.1635i	0.500205	−	0.866380i	1.00000		0.000236510i	$-7.52834e-5\pi$
$984$		0			0
$985$	21.7547			0.693164
$986$		0			0
$987$	−11.5188	+	2.05044i	−0.366647	+	0.0652662i
$988$		0			0
$989$	−55.0886			−1.75171
$990$		0			0
$991$	−3.61332	+	6.25845i	−0.114781	+	0.198806i	−0.917692	−	0.397292i	$-0.869950\pi$
$991$	−3.61332	+	6.25845i	−0.114781	+	0.198806i	0.802911	+	0.596099i	$0.203283\pi$
$992$		0			0
$993$	−31.4263	−	37.3287i	−0.997283	−	1.18459i
$994$		0			0
$995$	−15.3330	+	26.5575i	−0.486088	+	0.841929i
$996$		0			0
$997$	−0.473222			−0.0149871			−0.00749354	−	0.999972i	$-0.502385\pi$
$997$	−0.473222			−0.0149871			−0.00749354	+	0.999972i	$0.502385\pi$
$998$		0			0
$999$	−0.141523	−	28.9448i	−0.00447760	−	0.915772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.s.f.529.6	yes	40
3.2	odd	2		2808.2.s.f.1153.15		40
9.4	even	3		936.2.r.f.841.18	yes	40
9.5	odd	6		2808.2.r.f.2089.15		40
13.3	even	3		936.2.r.f.601.18	✓	40
39.29	odd	6		2808.2.r.f.289.15		40
117.68	odd	6		2808.2.s.f.1225.15		40
117.94	even	3	inner	936.2.s.f.913.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.r.f.601.18	✓	40	13.3	even	3
936.2.r.f.841.18	yes	40	9.4	even	3
936.2.s.f.529.6	yes	40	1.1	even	1	trivial
936.2.s.f.913.6	yes	40	117.94	even	3	inner
2808.2.r.f.289.15		40	39.29	odd	6
2808.2.r.f.2089.15		40	9.5	odd	6
2808.2.s.f.1153.15		40	3.2	odd	2
2808.2.s.f.1225.15		40	117.68	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11550 - 1.32501i) q^{3} +(-0.816777 - 1.41470i) q^{5} -0.664936 q^{7} +(-0.511312 + 2.95611i) q^{9} +(2.30132 + 3.98600i) q^{11} +(-3.59014 + 0.333001i) q^{13} +(-0.963376 + 2.66034i) q^{15} +(0.691459 + 1.19764i) q^{17} +(2.59815 + 4.50012i) q^{19} +(0.741737 + 0.881048i) q^{21} -4.31354 q^{23} +(1.16575 - 2.01914i) q^{25} +(4.48724 - 2.62005i) q^{27} +(0.173958 + 0.301305i) q^{29} +(2.78262 + 4.81965i) q^{31} +(2.71437 - 7.49567i) q^{33} +(0.543104 + 0.940684i) q^{35} +(2.78525 - 4.82419i) q^{37} +(4.44604 + 4.38552i) q^{39} +2.66959 q^{41} +12.7711 q^{43} +(4.59963 - 1.69113i) q^{45} +(-5.07938 + 8.79774i) q^{47} -6.55786 q^{49} +(0.815566 - 2.25216i) q^{51} -0.833384 q^{53} +(3.75933 - 6.51135i) q^{55} +(3.06448 - 8.46247i) q^{57} +(-3.54267 + 6.13608i) q^{59} +6.99585 q^{61} +(0.339990 - 1.96562i) q^{63} +(3.40344 + 4.80698i) q^{65} +12.3540 q^{67} +(4.81176 + 5.71549i) q^{69} +(-2.13470 - 3.69740i) q^{71} +8.70686 q^{73} +(-3.97579 + 0.707721i) q^{75} +(-1.53023 - 2.65044i) q^{77} +(-7.71985 + 13.3712i) q^{79} +(-8.47712 - 3.02298i) q^{81} +(0.471968 - 0.817473i) q^{83} +(1.12954 - 1.95641i) q^{85} +(0.205181 - 0.566602i) q^{87} +(-6.06011 + 10.4964i) q^{89} +(2.38721 - 0.221424i) q^{91} +(3.28207 - 9.06334i) q^{93} +(4.24421 - 7.35119i) q^{95} -15.0716 q^{97} +(-12.9597 + 4.76486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{3} + q^{5} - 14 q^{7} - 9 q^{9} - 3 q^{13} + 2 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} + 2 q^{23} - 23 q^{25} - 3 q^{27} + 12 q^{29} + 8 q^{31} - 5 q^{33} - 12 q^{35} + 18 q^{37} - 6 q^{39}+ \cdots + 28 q^{99}+O(q^{100}) \) 40 * q - 3 * q^3 + q^5 - 14 * q^7 - 9 * q^9 - 3 * q^13 + 2 * q^15 - q^17 + 2 * q^19 - 30 * q^21 + 2 * q^23 - 23 * q^25 - 3 * q^27 + 12 * q^29 + 8 * q^31 - 5 * q^33 - 12 * q^35 + 18 * q^37 - 6 * q^39 + 6 * q^41 - 16 * q^43 - 3 * q^45 + 4 * q^47 + 46 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 - 4 * q^59 + 6 * q^61 - 8 * q^63 + 7 * q^65 - 54 * q^67 + 19 * q^69 + q^71 - 12 * q^73 - 28 * q^75 - 4 * q^77 + 13 * q^79 - 13 * q^81 - 15 * q^83 + 5 * q^85 + 37 * q^87 + 12 * q^89 - 57 * q^91 - 22 * q^93 + q^95 - 70 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more