LMFDB - Embedded newform 756.2.ck.a.5.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(5,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5, 15]))

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

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

chi := DirichletCharacter("756.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ck (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.8
Character	$\chi$	$=$	756.5
Dual form			756.2.ck.a.605.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.792956 + 1.53988i) q^{3} +(-0.192493 + 1.09168i) q^{5} +(-0.137506 - 2.64218i) q^{7} +(-1.74244 - 2.44211i) q^{9} +O(q^{10})$	\(q+(-0.792956 + 1.53988i) q^{3} +(-0.192493 + 1.09168i) q^{5} +(-0.137506 - 2.64218i) q^{7} +(-1.74244 - 2.44211i) q^{9} +(2.56116 - 0.451601i) q^{11} +(2.84782 - 3.39390i) q^{13} +(-1.52842 - 1.16207i) q^{15} +2.17412 q^{17} -1.97804i q^{19} +(4.17766 + 1.88339i) q^{21} +(-0.918430 + 1.09454i) q^{23} +(3.54375 + 1.28982i) q^{25} +(5.14223 - 0.746660i) q^{27} +(-1.56472 - 1.86476i) q^{29} +(0.482623 + 1.32600i) q^{31} +(-1.33548 + 4.30197i) q^{33} +(2.91088 + 0.358487i) q^{35} +(1.48594 + 2.57372i) q^{37} +(2.96799 + 7.07650i) q^{39} +(7.49508 + 6.28912i) q^{41} +(-10.5897 - 3.85434i) q^{43} +(3.00141 - 1.43210i) q^{45} +(9.93706 + 3.61679i) q^{47} +(-6.96218 + 0.726628i) q^{49} +(-1.72398 + 3.34787i) q^{51} +(3.97427 - 2.29454i) q^{53} +2.88290i q^{55} +(3.04594 + 1.56850i) q^{57} +(-1.11622 - 0.936622i) q^{59} +(2.84554 - 7.81804i) q^{61} +(-6.21289 + 4.93964i) q^{63} +(3.15687 + 3.76221i) q^{65} +(0.0822020 - 0.466191i) q^{67} +(-0.957186 - 2.28219i) q^{69} +(-8.36281 - 4.82827i) q^{71} +(12.9594 + 7.48209i) q^{73} +(-4.79620 + 4.43417i) q^{75} +(-1.54538 - 6.70493i) q^{77} +(-1.17523 - 6.66506i) q^{79} +(-2.92780 + 8.51046i) q^{81} +(0.735605 - 0.617246i) q^{83} +(-0.418502 + 2.37344i) q^{85} +(4.11225 - 0.930801i) q^{87} +16.3867 q^{89} +(-9.35887 - 7.05776i) q^{91} +(-2.42457 - 0.308277i) q^{93} +(2.15939 + 0.380759i) q^{95} +(4.74751 - 13.0437i) q^{97} +(-5.56553 - 5.46774i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.792956	+	1.53988i	−0.457813	+	0.889048i
$3$	−0.792956	+	1.53988i	−0.457813	+	0.889048i
$4$		0			0
$5$	−0.192493	+	1.09168i	−0.0860854	+	0.488214i	0.911032	+	0.412336i	$0.135287\pi$
$5$	−0.192493	+	1.09168i	−0.0860854	+	0.488214i	−0.997117	+	0.0758781i	$0.975824\pi$
$6$		0			0
$7$	−0.137506	−	2.64218i	−0.0519722	−	0.998649i
$7$	−0.137506	−	2.64218i	−0.0519722	−	0.998649i
$8$		0			0
$9$	−1.74244	−	2.44211i	−0.580814	−	0.814036i
$10$		0			0
$11$	2.56116	−	0.451601i	0.772219	−	0.136163i	0.226364	−	0.974043i	$-0.427316\pi$
$11$	2.56116	−	0.451601i	0.772219	−	0.136163i	0.545855	+	0.837880i	$0.316205\pi$
$12$		0			0
$13$	2.84782	−	3.39390i	0.789843	−	0.941298i	−0.209490	−	0.977811i	$-0.567180\pi$
$13$	2.84782	−	3.39390i	0.789843	−	0.941298i	0.999333	+	0.0365127i	$0.0116249\pi$
$14$		0			0
$15$	−1.52842	−	1.16207i	−0.394635	−	0.300045i
$16$		0			0
$17$	2.17412			0.527301			0.263650	−	0.964618i	$-0.415073\pi$
$17$	2.17412			0.527301			0.263650	+	0.964618i	$0.415073\pi$
$18$		0			0
$19$		−	1.97804i		−	0.453794i	−0.973919	−	0.226897i	$-0.927142\pi$
$19$		−	1.97804i		−	0.453794i	0.973919	−	0.226897i	$-0.0728582\pi$
$20$		0			0
$21$	4.17766	+	1.88339i	0.911640	+	0.410989i
$22$		0			0
$23$	−0.918430	+	1.09454i	−0.191506	+	0.228228i	−0.853250	−	0.521502i	$-0.825372\pi$
$23$	−0.918430	+	1.09454i	−0.191506	+	0.228228i	0.661744	+	0.749730i	$0.269816\pi$
$24$		0			0
$25$	3.54375	+	1.28982i	0.708750	+	0.257964i
$26$		0			0
$27$	5.14223	−	0.746660i	0.989622	−	0.143695i
$28$		0			0
$29$	−1.56472	−	1.86476i	−0.290561	−	0.346277i	0.600942	−	0.799293i	$-0.294792\pi$
$29$	−1.56472	−	1.86476i	−0.290561	−	0.346277i	−0.891502	+	0.453016i	$0.850348\pi$
$30$		0			0
$31$	0.482623	+	1.32600i	0.0866817	+	0.238156i	0.975458	−	0.220185i	$-0.0706661\pi$
$31$	0.482623	+	1.32600i	0.0866817	+	0.238156i	−0.888776	+	0.458341i	$0.848444\pi$
$32$		0			0
$33$	−1.33548	+	4.30197i	−0.232477	+	0.748877i
$34$		0			0
$35$	2.91088	+	0.358487i	0.492029	+	0.0605954i
$36$		0			0
$37$	1.48594	+	2.57372i	0.244287	+	0.423117i	0.961931	−	0.273293i	$-0.0881129\pi$
$37$	1.48594	+	2.57372i	0.244287	+	0.423117i	−0.717644	+	0.696410i	$0.754780\pi$
$38$		0			0
$39$	2.96799	+	7.07650i	0.475259	+	1.13315i
$40$		0			0
$41$	7.49508	+	6.28912i	1.17054	+	0.982196i	0.999995	−	0.00315517i	$-0.00100432\pi$
$41$	7.49508	+	6.28912i	1.17054	+	0.982196i	0.170540	+	0.985351i	$0.445449\pi$
$42$		0			0
$43$	−10.5897	−	3.85434i	−1.61492	−	0.587782i	−0.632513	−	0.774550i	$-0.717977\pi$
$43$	−10.5897	−	3.85434i	−1.61492	−	0.587782i	−0.982404	+	0.186768i	$0.940199\pi$
$44$		0			0
$45$	3.00141	−	1.43210i	0.447424	−	0.213485i
$46$		0			0
$47$	9.93706	+	3.61679i	1.44947	+	0.527564i	0.942443	−	0.334367i	$-0.108522\pi$
$47$	9.93706	+	3.61679i	1.44947	+	0.527564i	0.507026	+	0.861931i	$0.330745\pi$
$48$		0			0
$49$	−6.96218	+	0.726628i	−0.994598	+	0.103804i
$50$		0			0
$51$	−1.72398	+	3.34787i	−0.241405	+	0.468796i
$52$		0			0
$53$	3.97427	−	2.29454i	0.545907	−	0.315180i	−0.201562	−	0.979476i	$-0.564602\pi$
$53$	3.97427	−	2.29454i	0.545907	−	0.315180i	0.747470	+	0.664296i	$0.231269\pi$
$54$		0			0
$55$			2.88290i			0.388730i
$56$		0			0
$57$	3.04594	+	1.56850i	0.403445	+	0.207753i
$58$		0			0
$59$	−1.11622	−	0.936622i	−0.145320	−	0.121938i	0.567230	−	0.823560i	$-0.308015\pi$
$59$	−1.11622	−	0.936622i	−0.145320	−	0.121938i	−0.712549	+	0.701622i	$0.752460\pi$
$60$		0			0
$61$	2.84554	−	7.81804i	0.364333	−	1.00100i	−0.613146	−	0.789969i	$-0.710096\pi$
$61$	2.84554	−	7.81804i	0.364333	−	1.00100i	0.977480	−	0.211029i	$-0.0676813\pi$
$62$		0			0
$63$	−6.21289	+	4.93964i	−0.782750	+	0.622336i
$64$		0			0
$65$	3.15687	+	3.76221i	0.391561	+	0.466645i
$66$		0			0
$67$	0.0822020	−	0.466191i	0.0100426	−	0.0569543i	−0.979375	−	0.202053i	$-0.935239\pi$
$67$	0.0822020	−	0.466191i	0.0100426	−	0.0569543i	0.989417	+	0.145098i	$0.0463499\pi$
$68$		0			0
$69$	−0.957186	−	2.28219i	−0.115232	−	0.274744i
$70$		0			0
$71$	−8.36281	−	4.82827i	−0.992483	−	0.573010i	−0.0864676	−	0.996255i	$-0.527558\pi$
$71$	−8.36281	−	4.82827i	−0.992483	−	0.573010i	−0.906016	+	0.423244i	$0.860891\pi$
$72$		0			0
$73$	12.9594	+	7.48209i	1.51678	+	0.875713i	0.999806	+	0.0197110i	$0.00627461\pi$
$73$	12.9594	+	7.48209i	1.51678	+	0.875713i	0.516973	+	0.856002i	$0.327059\pi$
$74$		0			0
$75$	−4.79620	+	4.43417i	−0.553818	+	0.512014i
$76$		0			0
$77$	−1.54538	−	6.70493i	−0.176113	−	0.764098i
$78$		0			0
$79$	−1.17523	−	6.66506i	−0.132224	−	0.749877i	−0.976753	−	0.214368i	$-0.931231\pi$
$79$	−1.17523	−	6.66506i	−0.132224	−	0.749877i	0.844529	−	0.535509i	$-0.179880\pi$
$80$		0			0
$81$	−2.92780	+	8.51046i	−0.325311	+	0.945607i
$82$		0			0
$83$	0.735605	−	0.617246i	0.0807431	−	0.0677515i	−0.601523	−	0.798856i	$-0.705439\pi$
$83$	0.735605	−	0.617246i	0.0807431	−	0.0677515i	0.682266	+	0.731104i	$0.260995\pi$
$84$		0			0
$85$	−0.418502	+	2.37344i	−0.0453929	+	0.257436i
$86$		0			0
$87$	4.11225	−	0.930801i	0.440879	−	0.0997924i
$88$		0			0
$89$	16.3867			1.73699			0.868493	−	0.495702i	$-0.165089\pi$
$89$	16.3867			1.73699			0.868493	+	0.495702i	$0.165089\pi$
$90$		0			0
$91$	−9.35887	−	7.05776i	−0.981076	−	0.739854i
$92$		0			0
$93$	−2.42457	−	0.308277i	−0.251416	−	0.0319668i
$94$		0			0
$95$	2.15939	+	0.380759i	0.221549	+	0.0390651i
$96$		0			0
$97$	4.74751	−	13.0437i	0.482037	−	1.32439i	−0.425707	−	0.904861i	$-0.639974\pi$
$97$	4.74751	−	13.0437i	0.482037	−	1.32439i	0.907744	−	0.419525i	$-0.137803\pi$
$98$		0			0
$99$	−5.56553	−	5.46774i	−0.559357	−	0.549529i
$100$		0			0
$101$	7.96739	−	6.68543i	0.792785	−	0.665226i	−0.153648	−	0.988126i	$-0.549102\pi$
$101$	7.96739	−	6.68543i	0.792785	−	0.665226i	0.946433	+	0.322900i	$0.104658\pi$
$102$		0			0
$103$	−11.6309	−	2.05085i	−1.14603	−	0.202076i	−0.431788	−	0.901975i	$-0.642117\pi$
$103$	−11.6309	−	2.05085i	−1.14603	−	0.202076i	−0.714241	+	0.699899i	$0.753228\pi$
$104$		0			0
$105$	−2.86023	+	4.19813i	−0.279130	+	0.409696i
$106$		0			0
$107$	7.14243	+	4.12369i	0.690485	+	0.398652i	0.803794	−	0.594908i	$-0.202812\pi$
$107$	7.14243	+	4.12369i	0.690485	+	0.398652i	−0.113309	+	0.993560i	$0.536145\pi$
$108$		0			0
$109$	−0.0911298	−	0.157841i	−0.00872865	−	0.0151185i	0.861628	−	0.507540i	$-0.169445\pi$
$109$	−0.0911298	−	0.157841i	−0.00872865	−	0.0151185i	−0.870357	+	0.492422i	$0.836112\pi$
$110$		0			0
$111$	−5.14150	+	0.247315i	−0.488009	+	0.0234741i
$112$		0			0
$113$	−2.98486	−	8.20082i	−0.280792	−	0.771469i	−0.997269	−	0.0738581i	$-0.976469\pi$
$113$	−2.98486	−	8.20082i	−0.280792	−	0.771469i	0.716477	−	0.697611i	$-0.245753\pi$
$114$		0			0
$115$	−1.01810	−	1.21332i	−0.0949383	−	0.113143i
$116$		0			0
$117$	−13.2504	−	1.04102i	−1.22500	−	0.0962419i
$118$		0			0
$119$	−0.298953	−	5.74440i	−0.0274050	−	0.526588i
$120$		0			0
$121$	−3.98103	+	1.44898i	−0.361911	+	0.131725i
$122$		0			0
$123$	−15.6277	+	6.55451i	−1.40911	+	0.591000i
$124$		0			0
$125$	−4.86152	+	8.42040i	−0.434828	+	0.753144i
$126$		0			0
$127$	−1.91309	−	3.31356i	−0.169759	−	0.294031i	0.768576	−	0.639758i	$-0.220966\pi$
$127$	−1.91309	−	3.31356i	−0.169759	−	0.294031i	−0.938335	+	0.345727i	$0.887632\pi$
$128$		0			0
$129$	14.3324	−	13.2505i	1.26190	−	1.16665i
$130$		0			0
$131$	−5.32055	−	4.46447i	−0.464859	−	0.390063i	0.380056	−	0.924963i	$-0.375905\pi$
$131$	−5.32055	−	4.46447i	−0.464859	−	0.390063i	−0.844915	+	0.534901i	$0.820349\pi$
$132$		0			0
$133$	−5.22634	+	0.271992i	−0.453181	+	0.0235847i
$134$		0			0
$135$	−0.174727	+	5.75740i	−0.0150381	+	0.495518i
$136$		0			0
$137$	−7.38768	+	20.2975i	−0.631172	+	1.73413i	0.0466563	+	0.998911i	$0.485143\pi$
$137$	−7.38768	+	20.2975i	−0.631172	+	1.73413i	−0.677828	+	0.735220i	$0.737079\pi$
$138$		0			0
$139$	−12.3574	−	2.17894i	−1.04814	−	0.184815i	−0.377050	−	0.926193i	$-0.623062\pi$
$139$	−12.3574	−	2.17894i	−1.04814	−	0.184815i	−0.671088	+	0.741378i	$0.734173\pi$
$140$		0			0
$141$	−13.4491	+	12.4339i	−1.13262	+	1.04712i
$142$		0			0
$143$	5.76103	−	9.97839i	0.481761	−	0.834435i
$144$		0			0
$145$	2.33692	−	1.34922i	0.194070	−	0.112047i
$146$		0			0
$147$	4.40179	−	11.2971i	0.363053	−	0.931768i
$148$		0			0
$149$	−3.33358	−	9.15893i	−0.273097	−	0.750328i	−0.998102	−	0.0615845i	$-0.980385\pi$
$149$	−3.33358	−	9.15893i	−0.273097	−	0.750328i	0.725005	−	0.688744i	$-0.241838\pi$
$150$		0			0
$151$	0.556841	+	3.15800i	0.0453150	+	0.256994i	0.999046	−	0.0436665i	$-0.0139039\pi$
$151$	0.556841	+	3.15800i	0.0453150	+	0.256994i	−0.953731	+	0.300661i	$0.902793\pi$
$152$		0			0
$153$	−3.78827	−	5.30943i	−0.306264	−	0.429242i
$154$		0			0
$155$	−1.54047	+	0.271626i	−0.123733	+	0.0218175i
$156$		0			0
$157$	−2.48933	+	2.96666i	−0.198670	+	0.236766i	−0.856177	−	0.516683i	$-0.827167\pi$
$157$	−2.48933	+	2.96666i	−0.198670	+	0.236766i	0.657507	+	0.753449i	$0.271611\pi$
$158$		0			0
$159$	0.381896	+	7.93935i	0.0302863	+	0.629632i
$160$		0			0
$161$	3.01826	+	2.27615i	0.237872	+	0.179386i
$162$		0			0
$163$	1.66040	−	2.87591i	0.130053	−	0.225258i	−0.793644	−	0.608383i	$-0.791819\pi$
$163$	1.66040	−	2.87591i	0.130053	−	0.225258i	0.923697	+	0.383124i	$0.125152\pi$
$164$		0			0
$165$	−4.43931	−	2.28601i	−0.345600	−	0.177966i
$166$		0			0
$167$	−7.24079	+	2.63543i	−0.560309	+	0.203936i	−0.606621	−	0.794991i	$-0.707475\pi$
$167$	−7.24079	+	2.63543i	−0.560309	+	0.203936i	0.0463118	+	0.998927i	$0.485253\pi$
$168$		0			0
$169$	−1.15105	−	6.52791i	−0.0885421	−	0.502147i
$170$		0			0
$171$	−4.83060	+	3.44663i	−0.369405	+	0.263570i
$172$		0			0
$173$	−19.1231	+	16.0462i	−1.45390	+	1.21997i	−0.524229	+	0.851577i	$0.675646\pi$
$173$	−19.1231	+	16.0462i	−1.45390	+	1.21997i	−0.929671	+	0.368390i	$0.879909\pi$
$174$		0			0
$175$	2.92064	−	9.54057i	0.220780	−	0.721199i
$176$		0			0
$177$	2.32740	−	0.976145i	0.174938	−	0.0733715i
$178$		0			0
$179$			10.2768i			0.768121i	0.923308	+	0.384060i	$0.125475\pi$
$179$			10.2768i			0.768121i	−0.923308	+	0.384060i	$0.874525\pi$
$180$		0			0
$181$	−0.236613	+	0.136609i	−0.0175873	+	0.0101540i	−0.508768	−	0.860904i	$-0.669899\pi$
$181$	−0.236613	+	0.136609i	−0.0175873	+	0.0101540i	0.491181	+	0.871058i	$0.336566\pi$
$182$		0			0
$183$	9.78244	+	10.5811i	0.723139	+	0.782180i
$184$		0			0
$185$	−3.09571	+	1.12675i	−0.227601	+	0.0828401i
$186$		0			0
$187$	5.56826	−	0.981835i	0.407192	−	0.0717989i
$188$		0			0
$189$	−2.67989	−	13.4840i	−0.194933	−	0.980816i
$190$		0			0
$191$	10.2790	−	1.81247i	0.743765	−	0.131146i	0.211091	−	0.977466i	$-0.432298\pi$
$191$	10.2790	−	1.81247i	0.743765	−	0.131146i	0.532674	+	0.846321i	$0.321187\pi$
$192$		0			0
$193$	3.65214	−	1.32927i	0.262887	−	0.0956831i	−0.207214	−	0.978296i	$-0.566440\pi$
$193$	3.65214	−	1.32927i	0.262887	−	0.0956831i	0.470101	+	0.882613i	$0.344217\pi$
$194$		0			0
$195$	−8.29660	+	1.87792i	−0.594132	+	0.134481i
$196$		0			0
$197$	15.4374	−	8.91279i	1.09987	−	0.635010i	0.163683	−	0.986513i	$-0.447663\pi$
$197$	15.4374	−	8.91279i	1.09987	−	0.635010i	0.936187	+	0.351503i	$0.114329\pi$
$198$		0			0
$199$			1.02772i			0.0728533i	0.999336	+	0.0364266i	$0.0115975\pi$
$199$			1.02772i			0.0728533i	−0.999336	+	0.0364266i	$0.988402\pi$
$200$		0			0
$201$	0.652694	+	0.496250i	0.0460375	+	0.0350027i
$202$		0			0
$203$	−4.71186	+	4.39067i	−0.330708	+	0.308165i
$204$		0			0
$205$	−8.30846	+	6.97163i	−0.580288	+	0.486919i
$206$		0			0
$207$	4.27330	+	0.335731i	0.297015	+	0.0233349i
$208$		0			0
$209$	−0.893288	−	5.06609i	−0.0617900	−	0.350429i
$210$		0			0
$211$	−12.2463	+	4.45728i	−0.843068	+	0.306852i	−0.727211	−	0.686414i	$-0.759184\pi$
$211$	−12.2463	+	4.45728i	−0.843068	+	0.306852i	−0.115857	+	0.993266i	$0.536962\pi$
$212$		0			0
$213$	14.0663	−	9.04909i	0.963806	−	0.620034i
$214$		0			0
$215$	6.24616	−	10.8187i	0.425984	−	0.737827i
$216$		0			0
$217$	3.43715	−	1.45751i	0.233329	−	0.0989420i
$218$		0			0
$219$	−21.7977	+	14.0229i	−1.47295	+	0.947577i
$220$		0			0
$221$	6.19149	−	7.37873i	0.416485	−	0.496347i
$222$		0			0
$223$	8.52773	−	1.50367i	0.571059	−	0.100693i	0.119340	−	0.992853i	$-0.461922\pi$
$223$	8.52773	−	1.50367i	0.571059	−	0.100693i	0.451719	+	0.892160i	$0.350811\pi$
$224$		0			0
$225$	−3.02490	−	10.9017i	−0.201660	−	0.726777i
$226$		0			0
$227$	5.20218	+	29.5031i	0.345281	+	1.95819i	0.278578	+	0.960414i	$0.410137\pi$
$227$	5.20218	+	29.5031i	0.345281	+	1.95819i	0.0667035	+	0.997773i	$0.478752\pi$
$228$		0			0
$229$	−5.43169	−	14.9234i	−0.358936	−	0.986169i	−0.979399	−	0.201933i	$-0.935278\pi$
$229$	−5.43169	−	14.9234i	−0.358936	−	0.986169i	0.620463	−	0.784236i	$-0.286945\pi$
$230$		0			0
$231$	11.5502	+	2.93702i	0.759947	+	0.193242i
$232$		0			0
$233$	−3.53816	+	2.04276i	−0.231793	+	0.133826i	−0.611399	−	0.791323i	$-0.709393\pi$
$233$	−3.53816	+	2.04276i	−0.231793	+	0.133826i	0.379606	+	0.925148i	$0.376060\pi$
$234$		0			0
$235$	−5.86120	+	10.1519i	−0.382342	+	0.662236i
$236$		0			0
$237$	11.1953	+	3.47539i	0.727211	+	0.225751i
$238$		0			0
$239$	−22.6228	−	3.98901i	−1.46335	−	0.258028i	−0.615445	−	0.788180i	$-0.711024\pi$
$239$	−22.6228	−	3.98901i	−1.46335	−	0.258028i	−0.847903	+	0.530152i	$0.822135\pi$
$240$		0			0
$241$	1.77041	−	4.86416i	0.114042	−	0.313328i	−0.869520	−	0.493897i	$-0.835572\pi$
$241$	1.77041	−	4.86416i	0.114042	−	0.313328i	0.983562	+	0.180569i	$0.0577940\pi$
$242$		0			0
$243$	−10.7835	−	11.2569i	−0.691759	−	0.722129i
$244$		0			0
$245$	0.546925	−	7.74035i	0.0349417	−	0.494513i
$246$		0			0
$247$	−6.71328	−	5.63311i	−0.427156	−	0.358426i
$248$		0			0
$249$	0.367180	+	1.62219i	0.0232691	+	0.102802i
$250$		0			0
$251$	−2.34715	−	4.06538i	−0.148151	−	0.256604i	0.782393	−	0.622785i	$-0.213999\pi$
$251$	−2.34715	−	4.06538i	−0.148151	−	0.256604i	−0.930544	+	0.366180i	$0.880665\pi$
$252$		0			0
$253$	−1.85795	+	3.21806i	−0.116808	+	0.202318i
$254$		0			0
$255$	−3.32295	−	2.52648i	−0.208091	−	0.158214i
$256$		0			0
$257$	−17.3371	+	6.31020i	−1.08146	+	0.393620i	−0.820451	−	0.571716i	$-0.806278\pi$
$257$	−17.3371	+	6.31020i	−1.08146	+	0.393620i	−0.261010	+	0.965336i	$0.584056\pi$
$258$		0			0
$259$	6.59590	−	4.28001i	0.409849	−	0.265947i
$260$		0			0
$261$	−1.82751	+	7.07044i	−0.113120	+	0.437649i
$262$		0			0
$263$	16.6777	+	19.8757i	1.02839	+	1.22559i	0.973878	+	0.227072i	$0.0729154\pi$
$263$	16.6777	+	19.8757i	1.02839	+	1.22559i	0.0545106	+	0.998513i	$0.482640\pi$
$264$		0			0
$265$	1.73989	+	4.78031i	0.106881	+	0.293652i
$266$		0			0
$267$	−12.9939	+	25.2335i	−0.795215	+	1.54426i
$268$		0			0
$269$	−13.5863	−	23.5321i	−0.828369	−	1.43478i	−0.899317	−	0.437297i	$-0.855936\pi$
$269$	−13.5863	−	23.5321i	−0.828369	−	1.43478i	0.0709484	−	0.997480i	$-0.477397\pi$
$270$		0			0
$271$	8.32385	+	4.80578i	0.505638	+	0.291930i	0.731039	−	0.682336i	$-0.239036\pi$
$271$	8.32385	+	4.80578i	0.505638	+	0.291930i	−0.225401	+	0.974266i	$0.572369\pi$
$272$		0			0
$273$	18.2892	−	8.81501i	1.10692	−	0.533509i
$274$		0			0
$275$	9.65859	+	1.70307i	0.582435	+	0.102699i
$276$		0			0
$277$	7.11640	−	5.97137i	0.427583	−	0.358785i	−0.403456	−	0.914999i	$-0.632191\pi$
$277$	7.11640	−	5.97137i	0.427583	−	0.358785i	0.831039	+	0.556214i	$0.187747\pi$
$278$		0			0
$279$	2.39729	−	3.48909i	0.143522	−	0.208886i
$280$		0			0
$281$	−5.95969	+	16.3741i	−0.355526	+	0.976798i	0.625038	+	0.780595i	$0.285084\pi$
$281$	−5.95969	+	16.3741i	−0.355526	+	0.976798i	−0.980563	+	0.196204i	$0.937139\pi$
$282$		0			0
$283$	9.35523	+	1.64958i	0.556111	+	0.0980573i	0.444638	−	0.895710i	$-0.353332\pi$
$283$	9.35523	+	1.64958i	0.556111	+	0.0980573i	0.111472	+	0.993768i	$0.464443\pi$
$284$		0			0
$285$	−2.29863	+	3.02327i	−0.136159	+	0.179083i
$286$		0			0
$287$	15.5863	−	20.6681i	0.920033	−	1.22000i
$288$		0			0
$289$	−12.2732			−0.721954
$290$		0			0
$291$	16.3211	+	17.6537i	0.956760	+	1.03488i
$292$		0			0
$293$	−3.63421	+	20.6107i	−0.212313	+	1.20409i	0.673196	+	0.739464i	$0.264921\pi$
$293$	−3.63421	+	20.6107i	−0.212313	+	1.20409i	−0.885509	+	0.464623i	$0.846190\pi$
$294$		0			0
$295$	1.23736	−	1.03827i	0.0720417	−	0.0604501i
$296$		0			0
$297$	12.8329	−	4.23455i	0.744639	−	0.245714i
$298$		0			0
$299$	1.09924	+	6.23412i	0.0635709	+	0.360528i
$300$		0			0
$301$	−8.72771	+	28.5099i	−0.503057	+	1.64328i
$302$		0			0
$303$	3.97695	+	17.5701i	0.228470	+	1.00937i
$304$		0			0
$305$	7.98706	+	4.61133i	0.457338	+	0.264044i
$306$		0			0
$307$	3.82657	+	2.20927i	0.218394	+	0.126090i	0.605206	−	0.796069i	$-0.293091\pi$
$307$	3.82657	+	2.20927i	0.218394	+	0.126090i	−0.386813	+	0.922158i	$0.626424\pi$
$308$		0			0
$309$	12.3809	−	16.2840i	0.704323	−	0.926362i
$310$		0			0
$311$	0.494496	−	2.80443i	0.0280403	−	0.159024i	−0.967572	−	0.252594i	$-0.918716\pi$
$311$	0.494496	−	2.80443i	0.0280403	−	0.159024i	0.995613	+	0.0935690i	$0.0298276\pi$
$312$		0			0
$313$	7.42776	+	8.85206i	0.419842	+	0.500348i	0.933963	−	0.357370i	$-0.116326\pi$
$313$	7.42776	+	8.85206i	0.419842	+	0.500348i	−0.514121	+	0.857718i	$0.671882\pi$
$314$		0			0
$315$	−4.19657	−	7.73333i	−0.236450	−	0.435724i
$316$		0			0
$317$	6.33865	−	17.4153i	0.356014	−	0.978141i	−0.624384	−	0.781117i	$-0.714650\pi$
$317$	6.33865	−	17.4153i	0.356014	−	0.978141i	0.980399	−	0.197024i	$-0.0631277\pi$
$318$		0			0
$319$	−4.84962	−	4.06931i	−0.271526	−	0.227838i
$320$		0			0
$321$	−12.0136	+	7.72857i	−0.670534	+	0.431367i
$322$		0			0
$323$		−	4.30050i		−	0.239286i
$324$		0			0
$325$	14.4695	−	8.35395i	0.802622	−	0.463394i
$326$		0			0
$327$	0.315318	−	0.0151673i	0.0174371	−	0.000838756i
$328$		0			0
$329$	8.18981	−	26.7528i	0.451519	−	1.47493i
$330$		0			0
$331$	−27.2952	−	9.93463i	−1.50028	−	0.546057i	−0.544146	−	0.838991i	$-0.683146\pi$
$331$	−27.2952	−	9.93463i	−1.50028	−	0.546057i	−0.956133	+	0.292934i	$0.905368\pi$
$332$		0			0
$333$	3.69615	−	8.11338i	0.202548	−	0.444610i
$334$		0			0
$335$	0.493108	+	0.179477i	0.0269414	+	0.00980586i
$336$		0			0
$337$	10.6404	+	8.92833i	0.579618	+	0.486357i	0.884822	−	0.465930i	$-0.154280\pi$
$337$	10.6404	+	8.92833i	0.579618	+	0.486357i	−0.305204	+	0.952287i	$0.598725\pi$
$338$		0			0
$339$	14.9951	+	1.90658i	0.814423	+	0.103551i
$340$		0			0
$341$	1.83490	+	3.17813i	0.0993652	+	0.172106i
$342$		0			0
$343$	2.87722	+	18.2954i	0.155355	+	0.987859i
$344$		0			0
$345$	2.67568	−	0.605636i	0.144054	−	0.0326063i
$346$		0			0
$347$	−3.18039	−	8.73805i	−0.170732	−	0.469083i	0.824586	−	0.565737i	$-0.191408\pi$
$347$	−3.18039	−	8.73805i	−0.170732	−	0.469083i	−0.995318	+	0.0966539i	$0.969186\pi$
$348$		0			0
$349$	18.3394	+	21.8561i	0.981686	+	1.16993i	0.985455	+	0.169936i	$0.0543559\pi$
$349$	18.3394	+	21.8561i	0.981686	+	1.16993i	−0.00376869	+	0.999993i	$0.501200\pi$
$350$		0			0
$351$	12.1100	−	19.5785i	0.646386	−	1.04503i
$352$		0			0
$353$	−23.9298	−	8.70972i	−1.27365	−	0.463572i	−0.385325	−	0.922781i	$-0.625911\pi$
$353$	−23.9298	−	8.70972i	−1.27365	−	0.463572i	−0.888328	+	0.459209i	$0.848133\pi$
$354$		0			0
$355$	6.88071	−	8.20011i	0.365190	−	0.435217i
$356$		0			0
$357$	9.08273	+	4.09471i	0.480709	+	0.216715i
$358$		0			0
$359$		−	6.90425i		−	0.364392i	−0.983262	−	0.182196i	$-0.941679\pi$
$359$		−	6.90425i		−	0.364392i	0.983262	−	0.182196i	$-0.0583206\pi$
$360$		0			0
$361$	15.0873			0.794071
$362$		0			0
$363$	0.925536	−	7.27926i	0.0485780	−	0.382062i
$364$		0			0
$365$	−10.6626	+	12.7072i	−0.558108	+	0.665127i
$366$		0			0
$367$	−1.94103	+	0.342257i	−0.101321	+	0.0178657i	−0.224079	−	0.974571i	$-0.571937\pi$
$367$	−1.94103	+	0.342257i	−0.101321	+	0.0178657i	0.122758	+	0.992437i	$0.460826\pi$
$368$		0			0
$369$	2.29898	−	29.2622i	0.119680	−	1.52333i
$370$		0			0
$371$	−6.60907	−	10.1852i	−0.343126	−	0.528789i
$372$		0			0
$373$	−2.81578	+	15.9691i	−0.145796	+	0.826849i	0.820929	+	0.571030i	$0.193456\pi$
$373$	−2.81578	+	15.9691i	−0.145796	+	0.826849i	−0.966725	+	0.255819i	$0.917655\pi$
$374$		0			0
$375$	−9.11141	−	14.1632i	−0.470511	−	0.731382i
$376$		0			0
$377$	−10.7848			−0.555447
$378$		0			0
$379$	18.2120			0.935489			0.467744	−	0.883864i	$-0.345067\pi$
$379$	18.2120			0.935489			0.467744	+	0.883864i	$0.345067\pi$
$380$		0			0
$381$	6.61947	−	0.318408i	0.339126	−	0.0163125i
$382$		0			0
$383$	−0.688493	+	3.90464i	−0.0351804	+	0.199518i	−0.997332	−	0.0729961i	$-0.976744\pi$
$383$	−0.688493	+	3.90464i	−0.0351804	+	0.199518i	0.962152	+	0.272514i	$0.0878550\pi$
$384$		0			0
$385$	7.61712	−	0.396414i	0.388205	−	0.0202032i
$386$		0			0
$387$	9.03924	+	32.5772i	0.459490	+	1.65599i
$388$		0			0
$389$	−22.3307	+	3.93751i	−1.13221	+	0.199640i	−0.708197	−	0.706015i	$-0.750491\pi$
$389$	−22.3307	+	3.93751i	−1.13221	+	0.199640i	−0.424016	+	0.905655i	$0.639380\pi$
$390$		0			0
$391$	−1.99678	+	2.37966i	−0.100981	+	0.120345i
$392$		0			0
$393$	11.0937	−	4.65286i	0.559603	−	0.234706i
$394$		0			0
$395$	7.50234			0.377483
$396$		0			0
$397$			6.21045i			0.311694i	0.987781	+	0.155847i	$0.0498106\pi$
$397$			6.21045i			0.311694i	−0.987781	+	0.155847i	$0.950189\pi$
$398$		0			0
$399$	3.72542	−	8.26360i	0.186504	−	0.413697i
$400$		0			0
$401$	9.61370	−	11.4572i	0.480085	−	0.572143i	−0.470582	−	0.882356i	$-0.655956\pi$
$401$	9.61370	−	11.4572i	0.480085	−	0.572143i	0.950667	+	0.310213i	$0.100400\pi$
$402$		0			0
$403$	5.87472	+	2.13822i	0.292641	+	0.106512i
$404$		0			0
$405$	−8.72713	−	4.83442i	−0.433655	−	0.240224i
$406$		0			0
$407$	4.96802	+	5.92065i	0.246256	+	0.293476i
$408$		0			0
$409$	3.02910	+	8.32239i	0.149780	+	0.411516i	0.991779	−	0.127962i	$-0.0408437\pi$
$409$	3.02910	+	8.32239i	0.149780	+	0.411516i	−0.841999	+	0.539478i	$0.818621\pi$
$410$		0			0
$411$	−25.3975	−	27.4711i	−1.25277	−	1.35505i
$412$		0			0
$413$	−2.32123	+	3.07805i	−0.114220	+	0.151461i
$414$		0			0
$415$	0.532237	+	0.921861i	0.0261265	+	0.0452524i
$416$		0			0
$417$	13.1541	−	17.3010i	0.644161	−	0.847235i
$418$		0			0
$419$	−1.66306	−	1.39547i	−0.0812457	−	0.0681732i	0.601260	−	0.799053i	$-0.294665\pi$
$419$	−1.66306	−	1.39547i	−0.0812457	−	0.0681732i	−0.682506	+	0.730880i	$0.739110\pi$
$420$		0			0
$421$	−12.3900	−	4.50961i	−0.603854	−	0.219785i	0.0219579	−	0.999759i	$-0.493010\pi$
$421$	−12.3900	−	4.50961i	−0.603854	−	0.219785i	−0.625812	+	0.779974i	$0.715232\pi$
$422$		0			0
$423$	−8.48214	−	30.5694i	−0.412416	−	1.48634i
$424$		0			0
$425$	7.70453	+	2.80422i	0.373725	+	0.136025i
$426$		0			0
$427$	−21.0479	−	6.44338i	−1.01858	−	0.311817i
$428$		0			0
$429$	10.7973	+	16.7837i	0.521296	+	0.810325i
$430$		0			0
$431$	18.2641	−	10.5448i	0.879749	−	0.507923i	0.00917317	−	0.999958i	$-0.497080\pi$
$431$	18.2641	−	10.5448i	0.879749	−	0.507923i	0.870576	+	0.492035i	$0.163747\pi$
$432$		0			0
$433$			24.5525i			1.17992i	0.807433	+	0.589959i	$0.200856\pi$
$433$			24.5525i			1.17992i	−0.807433	+	0.589959i	$0.799144\pi$
$434$		0			0
$435$	0.224560	+	4.66843i	0.0107668	+	0.223834i
$436$		0			0
$437$	2.16505	+	1.81670i	0.103569	+	0.0869044i
$438$		0			0
$439$	12.6349	−	34.7140i	0.603030	−	1.65681i	−0.142069	−	0.989857i	$-0.545375\pi$
$439$	12.6349	−	34.7140i	0.603030	−	1.65681i	0.745099	−	0.666954i	$-0.232402\pi$
$440$		0			0
$441$	13.9057	+	15.7363i	0.662176	+	0.749348i
$442$		0			0
$443$	14.6233	+	17.4273i	0.694772	+	0.827997i	0.991924	−	0.126833i	$-0.0404812\pi$
$443$	14.6233	+	17.4273i	0.694772	+	0.827997i	−0.297152	+	0.954830i	$0.596037\pi$
$444$		0			0
$445$	−3.15432	+	17.8890i	−0.149529	+	0.848021i
$446$		0			0
$447$	16.7470	+	2.12933i	0.792106	+	0.100714i
$448$		0			0
$449$	−23.3226	−	13.4653i	−1.10066	−	0.635468i	−0.164268	−	0.986416i	$-0.552526\pi$
$449$	−23.3226	−	13.4653i	−1.10066	−	0.635468i	−0.936395	+	0.350948i	$0.885859\pi$
$450$		0			0
$451$	22.0363	+	12.7226i	1.03765	+	0.599086i
$452$		0			0
$453$	−5.30448	−	1.64669i	−0.249226	−	0.0773682i
$454$		0			0
$455$	9.50633	−	8.85833i	0.445664	−	0.415285i
$456$		0			0
$457$	−2.17866	−	12.3558i	−0.101913	−	0.577979i	−0.992408	−	0.122986i	$-0.960753\pi$
$457$	−2.17866	−	12.3558i	−0.101913	−	0.577979i	0.890495	−	0.454993i	$-0.150358\pi$
$458$		0			0
$459$	11.1798	−	1.62333i	0.521829	−	0.0757704i
$460$		0			0
$461$	−12.3292	+	10.3454i	−0.574229	+	0.481835i	−0.883046	−	0.469286i	$-0.844511\pi$
$461$	−12.3292	+	10.3454i	−0.574229	+	0.481835i	0.308817	+	0.951121i	$0.400067\pi$
$462$		0			0
$463$	−0.398483	+	2.25991i	−0.0185191	+	0.105027i	−0.992666	−	0.120888i	$-0.961426\pi$
$463$	−0.398483	+	2.25991i	−0.0185191	+	0.105027i	0.974147	+	0.225915i	$0.0725370\pi$
$464$		0			0
$465$	0.803252	−	2.58752i	0.0372499	−	0.119993i
$466$		0			0
$467$	3.76536			0.174240			0.0871201	−	0.996198i	$-0.472234\pi$
$467$	3.76536			0.174240			0.0871201	+	0.996198i	$0.472234\pi$
$468$		0			0
$469$	−1.24306	−	0.153088i	−0.0573992	−	0.00706896i
$470$		0			0
$471$	−2.59437	−	6.18569i	−0.119542	−	0.285022i
$472$		0			0
$473$	−28.8626	−	5.08925i	−1.32710	−	0.234004i
$474$		0			0
$475$	2.55132	−	7.00969i	0.117063	−	0.321627i
$476$		0			0
$477$	−12.5285	−	5.70748i	−0.573638	−	0.261328i
$478$		0			0
$479$	6.83095	−	5.73185i	0.312114	−	0.261895i	−0.473251	−	0.880928i	$-0.656920\pi$
$479$	6.83095	−	5.73185i	0.312114	−	0.261895i	0.785365	+	0.619033i	$0.212475\pi$
$480$		0			0
$481$	12.9666	+	2.28637i	0.591227	+	0.104249i
$482$		0			0
$483$	−5.89834	+	2.84287i	−0.268384	+	0.129355i
$484$		0			0
$485$	13.3257	+	7.69359i	0.605088	+	0.349348i
$486$		0			0
$487$	17.0344	+	29.5044i	0.771901	+	1.33697i	0.936520	+	0.350615i	$0.114027\pi$
$487$	17.0344	+	29.5044i	0.771901	+	1.33697i	−0.164618	+	0.986357i	$0.552639\pi$
$488$		0			0
$489$	3.11191	+	4.83729i	0.140726	+	0.218750i
$490$		0			0
$491$	6.27488	+	17.2401i	0.283181	+	0.778034i	0.996978	+	0.0776816i	$0.0247518\pi$
$491$	6.27488	+	17.2401i	0.283181	+	0.778034i	−0.713797	+	0.700353i	$0.753026\pi$
$492$		0			0
$493$	−3.40188	−	4.05420i	−0.153213	−	0.182592i
$494$		0			0
$495$	7.04035	−	5.02328i	0.316440	−	0.225780i
$496$		0			0
$497$	−11.6072	+	22.7599i	−0.520655	+	1.02092i
$498$		0			0
$499$	−20.9598	+	7.62873i	−0.938287	+	0.341509i	−0.765489	−	0.643449i	$-0.777503\pi$
$499$	−20.9598	+	7.62873i	−0.938287	+	0.341509i	−0.172798	+	0.984957i	$0.555281\pi$
$500$		0			0
$501$	1.68339	−	13.2397i	0.0752082	−	0.591506i
$502$		0			0
$503$	−3.88720	+	6.73283i	−0.173322	+	0.300202i	−0.939579	−	0.342331i	$-0.888783\pi$
$503$	−3.88720	+	6.73283i	−0.173322	+	0.300202i	0.766257	+	0.642534i	$0.222117\pi$
$504$		0			0
$505$	5.76469	+	9.98474i	0.256526	+	0.444315i
$506$		0			0
$507$	10.9649	+	3.40388i	0.486969	+	0.151172i
$508$		0			0
$509$	−0.434346	−	0.364459i	−0.0192520	−	0.0161544i	0.633111	−	0.774061i	$-0.281778\pi$
$509$	−0.434346	−	0.364459i	−0.0192520	−	0.0161544i	−0.652363	+	0.757907i	$0.726222\pi$
$510$		0			0
$511$	17.9870	−	35.2697i	0.795699	−	1.56024i
$512$		0			0
$513$	−1.47693	−	10.1716i	−0.0652079	−	0.449085i
$514$		0			0
$515$	4.47774	−	12.3025i	0.197313	−	0.542112i
$516$		0			0
$517$	27.0837	+	4.77560i	1.19114	+	0.210030i
$518$		0			0
$519$	−9.54536	−	42.1711i	−0.418995	−	1.85111i
$520$		0			0
$521$	−21.7562	+	37.6828i	−0.953155	+	1.65091i	−0.214621	+	0.976697i	$0.568851\pi$
$521$	−21.7562	+	37.6828i	−0.953155	+	1.65091i	−0.738535	+	0.674216i	$0.764482\pi$
$522$		0			0
$523$	26.5254	−	15.3144i	1.15987	−	0.669654i	0.208600	−	0.978001i	$-0.433109\pi$
$523$	26.5254	−	15.3144i	1.15987	−	0.669654i	0.951274	+	0.308347i	$0.0997758\pi$
$524$		0			0
$525$	12.3754	+	12.0627i	0.540105	+	0.526459i
$526$		0			0
$527$	1.04928	+	2.88287i	0.0457073	+	0.125580i
$528$		0			0
$529$	3.63940	+	20.6401i	0.158235	+	0.897394i
$530$		0			0
$531$	−0.342381	+	4.35794i	−0.0148581	+	0.189119i
$532$		0			0
$533$	42.6893	−	7.52727i	1.84908	−	0.326042i
$534$		0			0
$535$	−5.87662	+	7.00348i	−0.254068	+	0.302787i
$536$		0			0
$537$	−15.8249	−	8.14901i	−0.682896	−	0.351656i
$538$		0			0
$539$	−17.5031	+	5.00514i	−0.753913	+	0.215587i
$540$		0			0
$541$	19.4663	−	33.7166i	0.836921	−	1.44959i	−0.0555351	−	0.998457i	$-0.517686\pi$
$541$	19.4663	−	33.7166i	0.836921	−	1.44959i	0.892456	−	0.451134i	$-0.148980\pi$
$542$		0			0
$543$	−0.0227367	−	0.472679i	−0.000975724	−	0.0202846i
$544$		0			0
$545$	0.189854	−	0.0691013i	0.00813246	−	0.00295997i
$546$		0			0
$547$	7.64697	+	43.3681i	0.326961	+	1.85429i	0.495523	+	0.868595i	$0.334977\pi$
$547$	7.64697	+	43.3681i	0.326961	+	1.85429i	−0.168562	+	0.985691i	$0.553912\pi$
$548$		0			0
$549$	−24.0507	+	6.67338i	−1.02646	+	0.284813i
$550$		0			0
$551$	−3.68857	+	3.09508i	−0.157138	+	0.131855i
$552$		0			0
$553$	−17.4486	+	4.02164i	−0.741992	+	0.171018i
$554$		0			0
$555$	0.719712	−	5.66048i	0.0305501	−	0.240274i
$556$		0			0
$557$			19.4237i			0.823010i	0.911407	+	0.411505i	$0.134997\pi$
$557$			19.4237i			0.823010i	−0.911407	+	0.411505i	$0.865003\pi$
$558$		0			0
$559$	−43.2389	+	24.9640i	−1.82881	+	1.05586i
$560$		0			0
$561$	−2.90348	+	9.35299i	−0.122585	+	0.394883i
$562$		0			0
$563$	−24.7668	+	9.01439i	−1.04380	+	0.379911i	−0.806319	−	0.591481i	$-0.798543\pi$
$563$	−24.7668	+	9.01439i	−1.04380	+	0.379911i	−0.237479	+	0.971393i	$0.576321\pi$
$564$		0			0
$565$	9.52724	−	1.67991i	0.400814	−	0.0706744i
$566$		0			0
$567$	22.8887	+	6.56551i	0.961236	+	0.275726i
$568$		0			0
$569$	−37.5823	+	6.62677i	−1.57553	+	0.277809i	−0.891974	−	0.452087i	$-0.850680\pi$
$569$	−37.5823	+	6.62677i	−1.57553	+	0.277809i	−0.683558	+	0.729896i	$0.739568\pi$
$570$		0			0
$571$	−33.6216	+	12.2373i	−1.40702	+	0.512114i	−0.930254	−	0.366916i	$-0.880414\pi$
$571$	−33.6216	+	12.2373i	−1.40702	+	0.512114i	−0.476767	+	0.879030i	$0.658191\pi$
$572$		0			0
$573$	−5.35984	+	17.2657i	−0.223911	+	0.721283i
$574$		0			0
$575$	−4.66645	+	2.69418i	−0.194604	+	0.112355i
$576$		0			0
$577$			33.1855i			1.38153i	0.723079	+	0.690765i	$0.242726\pi$
$577$			33.1855i			1.38153i	−0.723079	+	0.690765i	$0.757274\pi$
$578$		0			0
$579$	−0.849075	+	6.67791i	−0.0352864	+	0.277524i
$580$		0			0
$581$	−1.73202	−	1.85872i	−0.0718564	−	0.0771128i
$582$		0			0
$583$	9.14251	−	7.67147i	0.378644	−	0.317720i
$584$		0			0
$585$	3.68707	−	14.2648i	0.152442	−	0.589779i
$586$		0			0
$587$	−6.48754	−	36.7927i	−0.267769	−	1.51860i	−0.761032	−	0.648715i	$-0.775307\pi$
$587$	−6.48754	−	36.7927i	−0.267769	−	1.51860i	0.493262	−	0.869881i	$-0.335804\pi$
$588$		0			0
$589$	2.62288	−	0.954650i	0.108074	−	0.0393357i
$590$		0			0
$591$	1.48342	+	30.8392i	0.0610196	+	1.26855i
$592$		0			0
$593$	−15.3436	+	26.5758i	−0.630084	+	1.09134i	0.357450	+	0.933932i	$0.383646\pi$
$593$	−15.3436	+	26.5758i	−0.630084	+	1.09134i	−0.987534	+	0.157406i	$0.949687\pi$
$594$		0			0
$595$	6.32860	+	0.779394i	0.259447	+	0.0319520i
$596$		0			0
$597$	−1.58257	−	0.814938i	−0.0647701	−	0.0333532i
$598$		0			0
$599$	−9.81363	+	11.6954i	−0.400974	+	0.477862i	−0.928317	−	0.371790i	$-0.878744\pi$
$599$	−9.81363	+	11.6954i	−0.400974	+	0.477862i	0.527343	+	0.849653i	$0.323188\pi$
$600$		0			0
$601$	4.22303	−	0.744633i	0.172261	−	0.0303742i	−0.0868524	−	0.996221i	$-0.527681\pi$
$601$	4.22303	−	0.744633i	0.172261	−	0.0303742i	0.259113	+	0.965847i	$0.416570\pi$
$602$		0			0
$603$	−1.28172	+	0.611564i	−0.0521957	+	0.0249048i
$604$		0			0
$605$	−0.815499	−	4.62493i	−0.0331548	−	0.188030i
$606$		0			0
$607$	3.37027	+	9.25974i	0.136795	+	0.375841i	0.989108	−	0.147191i	$-0.0470231\pi$
$607$	3.37027	+	9.25974i	0.136795	+	0.375841i	−0.852313	+	0.523032i	$0.824801\pi$
$608$		0			0
$609$	−3.02480	−	10.7373i	−0.122571	−	0.435097i
$610$		0			0
$611$	40.5740	−	23.4254i	1.64145	−	0.947690i
$612$		0			0
$613$	19.1652	−	33.1951i	0.774074	−	1.34074i	−0.161239	−	0.986915i	$-0.551549\pi$
$613$	19.1652	−	33.1951i	0.774074	−	1.34074i	0.935313	−	0.353820i	$-0.115118\pi$
$614$		0			0
$615$	−4.14720	−	18.3222i	−0.167231	−	0.738822i
$616$		0			0
$617$	−26.7808	−	4.72218i	−1.07816	−	0.190108i	−0.393756	−	0.919215i	$-0.628824\pi$
$617$	−26.7808	−	4.72218i	−1.07816	−	0.190108i	−0.684399	+	0.729107i	$0.739936\pi$
$618$		0			0
$619$	−4.97533	+	13.6696i	−0.199976	+	0.549428i	−0.998628	−	0.0523642i	$-0.983324\pi$
$619$	−4.97533	+	13.6696i	−0.199976	+	0.549428i	0.798653	+	0.601792i	$0.205547\pi$
$620$		0			0
$621$	−3.90553	+	6.31414i	−0.156723	+	0.253378i
$622$		0			0
$623$	−2.25326	−	43.2965i	−0.0902750	−	1.73464i
$624$		0			0
$625$	6.18788	+	5.19224i	0.247515	+	0.207690i
$626$		0			0
$627$	8.50949	+	2.64163i	0.339836	+	0.105497i
$628$		0			0
$629$	3.23060	+	5.59557i	0.128813	+	0.223110i
$630$		0			0
$631$	0.991846	−	1.71793i	0.0394847	−	0.0683896i	−0.845608	−	0.533805i	$-0.820762\pi$
$631$	0.991846	−	1.71793i	0.0394847	−	0.0683896i	0.885092	+	0.465415i	$0.154095\pi$
$632$		0			0
$633$	2.84710	−	22.3922i	0.113162	−	0.890009i
$634$		0			0
$635$	3.98561	−	1.45064i	0.158164	−	0.0575670i
$636$		0			0
$637$	−17.3609	+	25.6983i	−0.687865	+	1.01820i
$638$		0			0
$639$	2.78054	+	28.8359i	0.109997	+	1.14073i
$640$		0			0
$641$	2.57561	+	3.06949i	0.101730	+	0.121238i	0.814507	−	0.580153i	$-0.197007\pi$
$641$	2.57561	+	3.06949i	0.101730	+	0.121238i	−0.712777	+	0.701391i	$0.752563\pi$
$642$		0			0
$643$	−6.23306	−	17.1252i	−0.245808	−	0.675351i	−0.999829	−	0.0185010i	$-0.994111\pi$
$643$	−6.23306	−	17.1252i	−0.245808	−	0.675351i	0.754021	−	0.656850i	$-0.228112\pi$
$644$		0			0
$645$	11.7065	+	18.1970i	0.460942	+	0.716507i
$646$		0			0
$647$	−13.6102	−	23.5735i	−0.535072	−	0.926771i	−0.999160	−	0.0409821i	$-0.986951\pi$
$647$	−13.6102	−	23.5735i	−0.535072	−	0.926771i	0.464088	−	0.885789i	$-0.346382\pi$
$648$		0			0
$649$	−3.28180	−	1.89475i	−0.128822	−	0.0743754i
$650$		0			0
$651$	−0.481129	+	6.44853i	−0.0188569	+	0.252738i
$652$		0			0
$653$	−15.6291	−	2.75583i	−0.611614	−	0.107844i	−0.140743	−	0.990046i	$-0.544949\pi$
$653$	−15.6291	−	2.75583i	−0.611614	−	0.107844i	−0.470871	+	0.882202i	$0.656060\pi$
$654$		0			0
$655$	5.89794	−	4.94896i	0.230452	−	0.193372i
$656$		0			0
$657$	−4.30885	−	44.6853i	−0.168104	−	1.74334i
$658$		0			0
$659$	−15.1582	+	41.6467i	−0.590478	+	1.62232i	0.179142	+	0.983823i	$0.442668\pi$
$659$	−15.1582	+	41.6467i	−0.590478	+	1.62232i	−0.769620	+	0.638502i	$0.779554\pi$
$660$		0			0
$661$	−1.36845	−	0.241294i	−0.0532263	−	0.00938524i	0.146972	−	0.989141i	$-0.453047\pi$
$661$	−1.36845	−	0.241294i	−0.0532263	−	0.00938524i	−0.200198	+	0.979755i	$0.564159\pi$
$662$		0			0
$663$	6.45276	+	15.3851i	0.250604	+	0.597510i
$664$		0			0
$665$	0.709104	−	5.75785i	0.0274979	−	0.223280i
$666$		0			0
$667$	3.47814			0.134674
$668$		0			0
$669$	−4.44665	+	14.3240i	−0.171917	+	0.553798i
$670$		0			0
$671$	3.75723	−	21.3083i	0.145046	−	0.822598i
$672$		0			0
$673$	−6.81767	+	5.72071i	−0.262802	+	0.220517i	−0.764662	−	0.644432i	$-0.777094\pi$
$673$	−6.81767	+	5.72071i	−0.262802	+	0.220517i	0.501860	+	0.864949i	$0.332649\pi$
$674$		0			0
$675$	19.1858	+	3.98657i	0.738463	+	0.153443i
$676$		0			0
$677$	2.10373	+	11.9308i	0.0808527	+	0.458539i	0.998175	+	0.0603925i	$0.0192352\pi$
$677$	2.10373	+	11.9308i	0.0808527	+	0.458539i	−0.917322	+	0.398146i	$0.869654\pi$
$678$		0			0
$679$	−35.1165	−	10.7502i	−1.34765	−	0.412554i
$680$		0			0
$681$	−49.5562	−	15.3839i	−1.89900	−	0.589512i
$682$		0			0
$683$	−44.4305	−	25.6519i	−1.70009	−	0.981545i	−0.945659	−	0.325159i	$-0.894582\pi$
$683$	−44.4305	−	25.6519i	−1.70009	−	0.981545i	−0.754426	−	0.656385i	$-0.772085\pi$
$684$		0			0
$685$	−20.7363	−	11.9721i	−0.792293	−	0.457431i
$686$		0			0
$687$	27.2874	+	3.46950i	1.04108	+	0.132370i
$688$		0			0
$689$	3.53054	−	20.0227i	0.134503	−	0.762804i
$690$		0			0
$691$	−28.2860	−	33.7100i	−1.07605	−	1.28239i	−0.957185	−	0.289478i	$-0.906518\pi$
$691$	−28.2860	−	33.7100i	−1.07605	−	1.28239i	−0.118867	−	0.992910i	$-0.537926\pi$
$692$		0			0
$693$	−13.6814	+	15.4570i	−0.519715	+	0.587161i
$694$		0			0
$695$	4.75741	−	13.0709i	0.180459	−	0.495806i
$696$		0			0
$697$	16.2952	+	13.6733i	0.617224	+	0.517913i
$698$		0			0
$699$	−0.339990	−	7.06815i	−0.0128596	−	0.267342i
$700$		0			0
$701$		−	45.5828i		−	1.72164i	−0.508909	−	0.860820i	$-0.669951\pi$
$701$		−	45.5828i		−	1.72164i	0.508909	−	0.860820i	$-0.330049\pi$
$702$		0			0
$703$	5.09093	−	2.93925i	0.192008	−	0.110856i
$704$		0			0
$705$	−10.9850	−	17.0755i	−0.413719	−	0.643101i
$706$		0			0
$707$	−18.7597	−	20.1320i	−0.705529	−	0.757140i
$708$		0			0
$709$	−43.6184	−	15.8758i	−1.63812	−	0.596228i	−0.651415	−	0.758722i	$-0.725824\pi$
$709$	−43.6184	−	15.8758i	−1.63812	−	0.596228i	−0.986710	+	0.162494i	$0.948046\pi$
$710$		0			0
$711$	−14.2290	+	14.4835i	−0.533630	+	0.543174i
$712$		0			0
$713$	−1.89462	−	0.689584i	−0.0709539	−	0.0258251i
$714$		0			0
$715$	9.78426	+	8.20997i	0.365911	+	0.307036i
$716$		0			0
$717$	24.0815	−	31.6732i	0.899339	−	1.18286i
$718$		0			0
$719$	15.0903	+	26.1372i	0.562775	+	0.974754i	0.997253	+	0.0740719i	$0.0235994\pi$
$719$	15.0903	+	26.1372i	0.562775	+	0.974754i	−0.434478	+	0.900682i	$0.643067\pi$
$720$		0			0
$721$	−3.81938	+	31.0129i	−0.142241	+	1.15498i
$722$		0			0
$723$	6.08635	+	6.58328i	0.226354	+	0.244835i
$724$		0			0
$725$	−3.13977	−	8.62644i	−0.116608	−	0.320378i
$726$		0			0
$727$	13.6781	+	16.3009i	0.507293	+	0.604568i	0.957527	−	0.288342i	$-0.0931041\pi$
$727$	13.6781	+	16.3009i	0.507293	+	0.604568i	−0.450235	+	0.892910i	$0.648660\pi$
$728$		0			0
$729$	25.8850	−	7.67899i	0.958704	−	0.284407i
$730$		0			0
$731$	−23.0233	−	8.37980i	−0.851547	−	0.309938i
$732$		0			0
$733$	6.37608	−	7.59872i	0.235506	−	0.280665i	−0.635328	−	0.772242i	$-0.719135\pi$
$733$	6.37608	−	7.59872i	0.235506	−	0.280665i	0.870834	+	0.491577i	$0.163580\pi$
$734$		0			0
$735$	11.4855	+	6.97996i	0.423649	+	0.257460i
$736$		0			0
$737$		−	1.23111i		−	0.0453486i
$738$		0			0
$739$	−29.4812			−1.08449			−0.542243	−	0.840222i	$-0.682425\pi$
$739$	−29.4812			−1.08449			−0.542243	+	0.840222i	$0.682425\pi$
$740$		0			0
$741$	13.9976	−	5.87082i	0.514216	−	0.215670i
$742$		0			0
$743$	−15.0431	+	17.9277i	−0.551879	+	0.657703i	−0.967807	−	0.251694i	$-0.919012\pi$
$743$	−15.0431	+	17.9277i	−0.551879	+	0.657703i	0.415928	+	0.909397i	$0.363457\pi$
$744$		0			0
$745$	10.6403	−	1.87617i	0.389831	−	0.0687377i
$746$		0			0
$747$	−2.78913	−	0.720913i	−0.102049	−	0.0263768i
$748$		0			0
$749$	9.91338	−	19.4386i	0.362227	−	0.710271i
$750$		0			0
$751$	5.83197	−	33.0748i	0.212812	−	1.20691i	−0.671852	−	0.740685i	$-0.734501\pi$
$751$	5.83197	−	33.0748i	0.212812	−	1.20691i	0.884664	−	0.466230i	$-0.154388\pi$
$752$		0			0
$753$	8.12136	−	0.390651i	0.295959	−	0.0142361i
$754$		0			0
$755$	−3.55471			−0.129369
$756$		0			0
$757$	−52.5640			−1.91047			−0.955235	−	0.295847i	$-0.904398\pi$
$757$	−52.5640			−1.91047			−0.955235	+	0.295847i	$0.904398\pi$
$758$		0			0
$759$	−3.48215	−	5.41280i	−0.126394	−	0.196472i
$760$		0			0
$761$	−5.91832	+	33.5645i	−0.214539	+	1.21671i	0.667166	+	0.744909i	$0.267507\pi$
$761$	−5.91832	+	33.5645i	−0.214539	+	1.21671i	−0.881705	+	0.471801i	$0.843604\pi$
$762$		0			0
$763$	−0.404514	+	0.262485i	−0.0146444	+	0.00950259i
$764$		0			0
$765$	6.52542	−	3.11356i	0.235927	−	0.112571i
$766$		0			0
$767$	−6.35760	+	1.12102i	−0.229560	+	0.0404775i
$768$		0			0
$769$	31.9548	−	38.0823i	1.15232	−	1.37328i	0.236531	−	0.971624i	$-0.423989\pi$
$769$	31.9548	−	38.0823i	1.15232	−	1.37328i	0.915789	−	0.401659i	$-0.131566\pi$
$770$		0			0
$771$	4.03065	−	31.7008i	0.145160	−	1.14168i
$772$		0			0
$773$	3.99081			0.143539			0.0717697	−	0.997421i	$-0.477135\pi$
$773$	3.99081			0.143539			0.0717697	+	0.997421i	$0.477135\pi$
$774$		0			0
$775$			5.32150i			0.191154i
$776$		0			0
$777$	1.36043	+	13.5507i	0.0488053	+	0.486130i
$778$		0			0
$779$	12.4402	−	14.8256i	0.445715	−	0.531182i
$780$		0			0
$781$	−23.5989	−	8.58932i	−0.844437	−	0.307350i
$782$		0			0
$783$	−9.43847	−	8.42069i	−0.337303	−	0.300931i
$784$		0			0
$785$	−2.75947	−	3.28861i	−0.0984898	−	0.117376i
$786$		0			0
$787$	12.7617	+	35.0625i	0.454906	+	1.24984i	0.929232	+	0.369496i	$0.120470\pi$
$787$	12.7617	+	35.0625i	0.454906	+	1.24984i	−0.474326	+	0.880349i	$0.657308\pi$
$788$		0			0
$789$	−43.8307	+	9.92102i	−1.56041	+	0.353198i
$790$		0			0
$791$	−21.2576	+	9.01417i	−0.755833	+	0.320507i
$792$		0			0
$793$	−18.4301	−	31.9218i	−0.654471	−	1.13358i
$794$		0			0
$795$	−8.74075	−	1.11136i	−0.310002	−	0.0394158i
$796$		0			0
$797$	28.1915	+	23.6555i	0.998594	+	0.837920i	0.986789	−	0.162010i	$-0.0517978\pi$
$797$	28.1915	+	23.6555i	0.998594	+	0.837920i	0.0118051	+	0.999930i	$0.496242\pi$
$798$		0			0
$799$	21.6043	+	7.86334i	0.764307	+	0.278185i
$800$		0			0
$801$	−28.5528	−	40.0181i	−1.00887	−	1.41397i
$802$		0			0
$803$	36.5699	+	13.3104i	1.29052	+	0.469712i
$804$		0			0
$805$	−3.06582	+	2.85684i	−0.108056	+	0.100690i
$806$		0			0
$807$	47.0098	−	2.26125i	1.65482	−	0.0795998i
$808$		0			0
$809$	−11.0102	+	6.35674i	−0.387098	+	0.223491i	−0.680902	−	0.732375i	$-0.738412\pi$
$809$	−11.0102	+	6.35674i	−0.387098	+	0.223491i	0.293804	+	0.955866i	$0.405079\pi$
$810$		0			0
$811$			9.81361i			0.344603i	0.985044	+	0.172301i	$0.0551203\pi$
$811$			9.81361i			0.344603i	−0.985044	+	0.172301i	$0.944880\pi$
$812$		0			0
$813$	−14.0008	+	9.00693i	−0.491028	+	0.315887i
$814$		0			0
$815$	2.81995	+	2.36622i	0.0987787	+	0.0828852i
$816$		0			0
$817$	−7.62406	+	20.9469i	−0.266732	+	0.732841i
$818$		0			0
$819$	−0.928539	+	35.1531i	−0.0324458	+	1.22835i
$820$		0			0
$821$	6.96515	+	8.30075i	0.243086	+	0.289698i	0.873768	−	0.486343i	$-0.161669\pi$
$821$	6.96515	+	8.30075i	0.243086	+	0.289698i	−0.630682	+	0.776041i	$0.717225\pi$
$822$		0			0
$823$	4.08642	−	23.1753i	0.142444	−	0.807838i	−0.826940	−	0.562289i	$-0.809921\pi$
$823$	4.08642	−	23.1753i	0.142444	−	0.807838i	0.969384	−	0.245549i	$-0.0789682\pi$
$824$		0			0
$825$	−10.2814	+	13.5226i	−0.357951	+	0.470796i
$826$		0			0
$827$	4.95821	+	2.86262i	0.172414	+	0.0995432i	0.583724	−	0.811952i	$-0.301595\pi$
$827$	4.95821	+	2.86262i	0.172414	+	0.0995432i	−0.411310	+	0.911496i	$0.634929\pi$
$828$		0			0
$829$	−18.1311	−	10.4680i	−0.629719	−	0.363569i	0.150924	−	0.988545i	$-0.451775\pi$
$829$	−18.1311	−	10.4680i	−0.629719	−	0.363569i	−0.780643	+	0.624977i	$0.785108\pi$
$830$		0			0
$831$	3.55218	+	15.6934i	0.123224	+	0.544398i
$832$		0			0
$833$	−15.1366	+	1.57977i	−0.524452	+	0.0547359i
$834$		0			0
$835$	−1.48325	−	8.41193i	−0.0513300	−	0.291107i
$836$		0			0
$837$	3.47183	+	6.45822i	0.120004	+	0.223229i
$838$		0			0
$839$	9.58032	−	8.03885i	0.330750	−	0.277532i	−0.462256	−	0.886747i	$-0.652960\pi$
$839$	9.58032	−	8.03885i	0.330750	−	0.277532i	0.793005	+	0.609215i	$0.208515\pi$
$840$		0			0
$841$	4.00682	−	22.7238i	0.138166	−	0.783579i
$842$		0			0
$843$	−20.4884	−	22.1612i	−0.705657	−	0.763271i
$844$		0			0
$845$	7.34797			0.252778
$846$		0			0
$847$	4.37586	+	10.3193i	0.150356	+	0.354576i
$848$		0			0
$849$	−9.95844	+	13.0979i	−0.341773	+	0.449517i
$850$		0			0
$851$	−4.18178	−	0.737360i	−0.143349	−	0.0252764i
$852$		0			0
$853$	−10.5214	+	28.9073i	−0.360246	+	0.989768i	0.618696	+	0.785630i	$0.287661\pi$
$853$	−10.5214	+	28.9073i	−0.360246	+	0.989768i	−0.978942	+	0.204137i	$0.934561\pi$
$854$		0			0
$855$	−2.83276	−	5.93692i	−0.0968783	−	0.203038i
$856$		0			0
$857$	−30.0674	+	25.2296i	−1.02708	+	0.861826i	−0.990501	−	0.137505i	$-0.956092\pi$
$857$	−30.0674	+	25.2296i	−1.02708	+	0.861826i	−0.0365829	+	0.999331i	$0.511647\pi$
$858$		0			0
$859$	36.4758	+	6.43167i	1.24454	+	0.219446i	0.756859	−	0.653578i	$-0.226733\pi$
$859$	36.4758	+	6.43167i	1.24454	+	0.219446i	0.487679	+	0.873023i	$0.337844\pi$
$860$		0			0
$861$	19.4671	+	40.3900i	0.663436	+	1.37649i
$862$		0			0
$863$	34.1803	+	19.7340i	1.16351	+	0.671754i	0.952143	−	0.305652i	$-0.0988744\pi$
$863$	34.1803	+	19.7340i	1.16351	+	0.671754i	0.211369	+	0.977406i	$0.432208\pi$
$864$		0			0
$865$	−13.8362	−	23.9651i	−0.470446	−	0.814837i
$866$		0			0
$867$	9.73212	−	18.8992i	0.330520	−	0.641852i
$868$		0			0
$869$	−6.01990	−	16.5395i	−0.204211	−	0.561065i
$870$		0			0
$871$	−1.34811	−	1.60661i	−0.0456789	−	0.0544380i
$872$		0			0
$873$	−40.1264	+	11.1339i	−1.35807	+	0.376826i
$874$		0			0
$875$	22.9167	+	11.6871i	0.774725	+	0.395097i
$876$		0			0
$877$	−24.4834	+	8.91122i	−0.826745	+	0.300911i	−0.720522	−	0.693432i	$-0.756098\pi$
$877$	−24.4834	+	8.91122i	−0.826745	+	0.300911i	−0.106223	+	0.994342i	$0.533876\pi$
$878$		0			0
$879$	−28.8561	−	21.9396i	−0.973292	−	0.740004i
$880$		0			0
$881$	−2.38743	+	4.13514i	−0.0804345	+	0.139317i	−0.903437	−	0.428722i	$-0.858964\pi$
$881$	−2.38743	+	4.13514i	−0.0804345	+	0.139317i	0.823002	+	0.568038i	$0.192297\pi$
$882$		0			0
$883$	−13.0553	−	22.6124i	−0.439345	−	0.760969i	0.558294	−	0.829643i	$-0.311456\pi$
$883$	−13.0553	−	22.6124i	−0.439345	−	0.760969i	−0.997639	+	0.0686748i	$0.978123\pi$
$884$		0			0
$885$	0.617631	+	2.72867i	0.0207615	+	0.0917234i
$886$		0			0
$887$	36.9868	+	31.0356i	1.24190	+	1.04207i	0.997373	+	0.0724311i	$0.0230757\pi$
$887$	36.9868	+	31.0356i	1.24190	+	1.04207i	0.244523	+	0.969644i	$0.421369\pi$
$888$		0			0
$889$	−8.49196	+	5.51035i	−0.284811	+	0.184811i
$890$		0			0
$891$	−3.65521	+	23.1189i	−0.122454	+	0.774511i
$892$		0			0
$893$	7.15418	−	19.6559i	0.239405	−	0.657761i
$894$		0			0
$895$	−11.2189	−	1.97820i	−0.375008	−	0.0661240i
$896$		0			0
$897$	−10.4714	−	3.25068i	−0.349631	−	0.108537i
$898$		0			0
$899$	1.71749	−	2.97478i	0.0572816	−	0.0992146i
$900$		0			0
$901$	8.64052	−	4.98861i	0.287857	−	0.166195i
$902$		0			0
$903$	−36.9810	−	36.0467i	−1.23065	−	1.19956i
$904$		0			0
$905$	−0.103587	−	0.284602i	−0.00344334	−	0.00946049i
$906$		0			0
$907$	−2.88288	−	16.3496i	−0.0957244	−	0.542880i	−0.994523	−	0.104518i	$-0.966670\pi$
$907$	−2.88288	−	16.3496i	−0.0957244	−	0.542880i	0.898799	−	0.438362i	$-0.144441\pi$
$908$		0			0
$909$	−30.2093	−	7.80826i	−1.00198	−	0.258984i
$910$		0			0
$911$	39.9656	−	7.04701i	1.32412	−	0.233478i	0.533508	−	0.845795i	$-0.320874\pi$
$911$	39.9656	−	7.04701i	1.32412	−	0.233478i	0.790612	+	0.612317i	$0.209762\pi$
$912$		0			0
$913$	1.60525	−	1.91306i	0.0531261	−	0.0633132i
$914$		0			0
$915$	−13.4343	+	8.64251i	−0.444123	+	0.285712i
$916$		0			0
$917$	−11.0643	+	14.6717i	−0.365376	+	0.484503i
$918$		0			0
$919$	−10.8765	+	18.8387i	−0.358783	+	0.621431i	−0.987758	−	0.155995i	$-0.950142\pi$
$919$	−10.8765	+	18.8387i	−0.358783	+	0.621431i	0.628975	+	0.777426i	$0.283475\pi$
$920$		0			0
$921$	−6.43630	+	4.14059i	−0.212083	+	0.136437i
$922$		0			0
$923$	−40.2024	+	14.6325i	−1.32328	+	0.481634i
$924$		0			0
$925$	1.94616	+	11.0372i	0.0639893	+	0.362901i
$926$		0			0
$927$	15.2578	+	31.9775i	0.501132	+	1.05028i
$928$		0			0
$929$	−24.8041	+	20.8131i	−0.813796	+	0.682856i	−0.951511	−	0.307616i	$-0.900469\pi$
$929$	−24.8041	+	20.8131i	−0.813796	+	0.682856i	0.137714	+	0.990472i	$0.456024\pi$
$930$		0			0
$931$	1.43730	+	13.7715i	0.0471057	+	0.451343i
$932$		0			0
$933$	3.92636	+	2.98525i	0.128543	+	0.0977327i
$934$		0			0
$935$			6.26776i			0.204978i
$936$		0			0
$937$	49.6769	−	28.6810i	1.62287	−	0.936967i	0.636727	−	0.771089i	$-0.280288\pi$
$937$	49.6769	−	28.6810i	1.62287	−	0.936967i	0.986146	−	0.165878i	$-0.0530457\pi$
$938$		0			0
$939$	−19.5210	+	4.41854i	−0.637043	+	0.144194i
$940$		0			0
$941$	−0.0852964	+	0.0310453i	−0.00278058	+	0.00101205i	−0.343410	−	0.939186i	$-0.611582\pi$
$941$	−0.0852964	+	0.0310453i	−0.00278058	+	0.00101205i	0.340629	+	0.940198i	$0.389360\pi$
$942$		0			0
$943$	−13.7674	+	2.42757i	−0.448329	+	0.0790525i
$944$		0			0
$945$	15.2361	−	0.330014i	0.495630	−	0.0107354i
$946$		0			0
$947$	−28.3028	+	4.99055i	−0.919718	+	0.162171i	−0.613413	−	0.789762i	$-0.710204\pi$
$947$	−28.3028	+	4.99055i	−0.919718	+	0.162171i	−0.306305	+	0.951933i	$0.599093\pi$
$948$		0			0
$949$	62.2994	−	22.6751i	2.02232	−	0.736066i
$950$		0			0
$951$	21.7912	+	23.5703i	0.706627	+	0.764320i
$952$		0			0
$953$	50.8525	−	29.3597i	1.64727	−	0.951055i	0.669126	−	0.743149i	$-0.266669\pi$
$953$	50.8525	−	29.3597i	1.64727	−	0.951055i	0.978149	−	0.207905i	$-0.0666646\pi$
$954$		0			0
$955$			11.5703i			0.374406i
$956$		0			0
$957$	10.1118	−	4.24103i	0.326867	−	0.137093i
$958$		0			0
$959$	54.6454	+	16.7285i	1.76459	+	0.540192i
$960$		0			0
$961$	22.2220	−	18.6465i	0.716840	−	0.601500i
$962$		0			0
$963$	−2.37478	−	24.6279i	−0.0765262	−	0.793623i
$964$		0			0
$965$	0.748129	+	4.24285i	0.0240831	+	0.136582i
$966$		0			0
$967$	54.5281	−	19.8466i	1.75351	−	0.638224i	0.753686	−	0.657234i	$-0.228274\pi$
$967$	54.5281	−	19.8466i	1.75351	−	0.638224i	0.999819	+	0.0190105i	$0.00605161\pi$
$968$		0			0
$969$	6.62224	+	3.41011i	0.212737	+	0.109548i
$970$		0			0
$971$	4.34443	−	7.52477i	0.139419	−	0.241481i	−0.787858	−	0.615857i	$-0.788810\pi$
$971$	4.34443	−	7.52477i	0.139419	−	0.241481i	0.927277	+	0.374376i	$0.122143\pi$
$972$		0			0
$973$	−4.05793	+	32.9500i	−0.130091	+	1.05633i
$974$		0			0
$975$	1.39040	+	28.9055i	0.0445286	+	0.925718i
$976$		0			0
$977$	30.9147	−	36.8427i	0.989049	−	1.17870i	0.00514810	−	0.999987i	$-0.498361\pi$
$977$	30.9147	−	36.8427i	0.989049	−	1.17870i	0.983901	−	0.178716i	$-0.0571943\pi$
$978$		0			0
$979$	41.9689	−	7.40025i	1.34133	−	0.236513i
$980$		0			0
$981$	−0.226678	+	0.497578i	−0.00723726	+	0.0158864i
$982$		0			0
$983$	0.200604	+	1.13768i	0.00639828	+	0.0362864i	0.987840	−	0.155475i	$-0.0496910\pi$
$983$	0.200604	+	1.13768i	0.00639828	+	0.0362864i	−0.981441	+	0.191762i	$0.938580\pi$
$984$		0			0
$985$	6.75833	+	18.5684i	0.215338	+	0.591637i
$986$		0			0
$987$	34.7018	+	33.8251i	1.10457	+	1.07666i
$988$		0			0
$989$	13.9447	−	8.05096i	0.443415	−	0.256006i
$990$		0			0
$991$	25.4448	−	44.0717i	0.808281	−	1.39998i	−0.105773	−	0.994390i	$-0.533732\pi$
$991$	25.4448	−	44.0717i	0.808281	−	1.39998i	0.914054	−	0.405593i	$-0.132935\pi$
$992$		0			0
$993$	36.9420	−	34.1535i	1.17232	−	1.08383i
$994$		0			0
$995$	−1.12194	−	0.197829i	−0.0355680	−	0.00627160i
$996$		0			0
$997$	−9.17920	+	25.2197i	−0.290708	+	0.798714i	0.705255	+	0.708954i	$0.250832\pi$
$997$	−9.17920	+	25.2197i	−0.290708	+	0.798714i	−0.995963	+	0.0897607i	$0.971390\pi$
$998$		0			0
$999$	9.56272	+	12.1252i	0.302551	+	0.383623i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ck.a.5.8	yes	144
7.3	odd	6		756.2.ca.a.437.1	yes	144
27.11	odd	18		756.2.ca.a.173.1	✓	144
189.38	even	18	inner	756.2.ck.a.605.8	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.1	✓	144	27.11	odd	18
756.2.ca.a.437.1	yes	144	7.3	odd	6
756.2.ck.a.5.8	yes	144	1.1	even	1	trivial
756.2.ck.a.605.8	yes	144	189.38	even	18	inner

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ck (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.792956 + 1.53988i) q^{3} +(-0.192493 + 1.09168i) q^{5} +(-0.137506 - 2.64218i) q^{7} +(-1.74244 - 2.44211i) q^{9} +O(q^{10})\)	\(q+(-0.792956 + 1.53988i) q^{3} +(-0.192493 + 1.09168i) q^{5} +(-0.137506 - 2.64218i) q^{7} +(-1.74244 - 2.44211i) q^{9} +(2.56116 - 0.451601i) q^{11} +(2.84782 - 3.39390i) q^{13} +(-1.52842 - 1.16207i) q^{15} +2.17412 q^{17} -1.97804i q^{19} +(4.17766 + 1.88339i) q^{21} +(-0.918430 + 1.09454i) q^{23} +(3.54375 + 1.28982i) q^{25} +(5.14223 - 0.746660i) q^{27} +(-1.56472 - 1.86476i) q^{29} +(0.482623 + 1.32600i) q^{31} +(-1.33548 + 4.30197i) q^{33} +(2.91088 + 0.358487i) q^{35} +(1.48594 + 2.57372i) q^{37} +(2.96799 + 7.07650i) q^{39} +(7.49508 + 6.28912i) q^{41} +(-10.5897 - 3.85434i) q^{43} +(3.00141 - 1.43210i) q^{45} +(9.93706 + 3.61679i) q^{47} +(-6.96218 + 0.726628i) q^{49} +(-1.72398 + 3.34787i) q^{51} +(3.97427 - 2.29454i) q^{53} +2.88290i q^{55} +(3.04594 + 1.56850i) q^{57} +(-1.11622 - 0.936622i) q^{59} +(2.84554 - 7.81804i) q^{61} +(-6.21289 + 4.93964i) q^{63} +(3.15687 + 3.76221i) q^{65} +(0.0822020 - 0.466191i) q^{67} +(-0.957186 - 2.28219i) q^{69} +(-8.36281 - 4.82827i) q^{71} +(12.9594 + 7.48209i) q^{73} +(-4.79620 + 4.43417i) q^{75} +(-1.54538 - 6.70493i) q^{77} +(-1.17523 - 6.66506i) q^{79} +(-2.92780 + 8.51046i) q^{81} +(0.735605 - 0.617246i) q^{83} +(-0.418502 + 2.37344i) q^{85} +(4.11225 - 0.930801i) q^{87} +16.3867 q^{89} +(-9.35887 - 7.05776i) q^{91} +(-2.42457 - 0.308277i) q^{93} +(2.15939 + 0.380759i) q^{95} +(4.74751 - 13.0437i) q^{97} +(-5.56553 - 5.46774i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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