LMFDB - Embedded newform 756.2.ck.a.605.8

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			605.8
Character	$\chi$	$=$	756.605
Dual form			756.2.ck.a.5.8

$q$-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 $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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	−0.997117	−	0.0758781i	$-0.975824\pi$
$5$	−0.192493	−	1.09168i	−0.0860854	−	0.488214i	0.911032	−	0.412336i	$-0.135287\pi$
$6$		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	0.545855	−	0.837880i	$-0.316205\pi$
$11$	2.56116	+	0.451601i	0.772219	+	0.136163i	0.226364	+	0.974043i	$0.427316\pi$
$12$		0			0
$13$	2.84782	+	3.39390i	0.789843	+	0.941298i	0.999333	−	0.0365127i	$-0.0116249\pi$
$13$	2.84782	+	3.39390i	0.789843	+	0.941298i	−0.209490	+	0.977811i	$0.567180\pi$
$14$		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	$0.0728582\pi$
$19$			1.97804i			0.453794i	−0.973919	+	0.226897i	$0.927142\pi$
$20$		0			0
$21$	4.17766	−	1.88339i	0.911640	−	0.410989i
$22$		0			0
$23$	−0.918430	−	1.09454i	−0.191506	−	0.228228i	0.661744	−	0.749730i	$-0.269816\pi$
$23$	−0.918430	−	1.09454i	−0.191506	−	0.228228i	−0.853250	+	0.521502i	$0.825372\pi$
$24$		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	−0.891502	−	0.453016i	$-0.850348\pi$
$29$	−1.56472	+	1.86476i	−0.290561	+	0.346277i	0.600942	+	0.799293i	$0.294792\pi$
$30$		0			0
$31$	0.482623	−	1.32600i	0.0866817	−	0.238156i	−0.888776	−	0.458341i	$-0.848444\pi$
$31$	0.482623	−	1.32600i	0.0866817	−	0.238156i	0.975458	+	0.220185i	$0.0706661\pi$
$32$		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	−0.717644	−	0.696410i	$-0.754780\pi$
$37$	1.48594	−	2.57372i	0.244287	−	0.423117i	0.961931	+	0.273293i	$0.0881129\pi$
$38$		0			0
$39$	2.96799	−	7.07650i	0.475259	−	1.13315i
$40$		0			0
$41$	7.49508	−	6.28912i	1.17054	−	0.982196i	0.170540	−	0.985351i	$-0.445449\pi$
$41$	7.49508	−	6.28912i	1.17054	−	0.982196i	0.999995	+	0.00315517i	$0.00100432\pi$
$42$		0			0
$43$	−10.5897	+	3.85434i	−1.61492	+	0.587782i	−0.982404	−	0.186768i	$-0.940199\pi$
$43$	−10.5897	+	3.85434i	−1.61492	+	0.587782i	−0.632513	+	0.774550i	$0.717977\pi$
$44$		0			0
$45$	3.00141	+	1.43210i	0.447424	+	0.213485i
$46$		0			0
$47$	9.93706	−	3.61679i	1.44947	−	0.527564i	0.507026	−	0.861931i	$-0.330745\pi$
$47$	9.93706	−	3.61679i	1.44947	−	0.527564i	0.942443	+	0.334367i	$0.108522\pi$
$48$		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	0.747470	−	0.664296i	$-0.231269\pi$
$53$	3.97427	+	2.29454i	0.545907	+	0.315180i	−0.201562	+	0.979476i	$0.564602\pi$
$54$		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	−0.712549	−	0.701622i	$-0.752460\pi$
$59$	−1.11622	+	0.936622i	−0.145320	+	0.121938i	0.567230	+	0.823560i	$0.308015\pi$
$60$		0			0
$61$	2.84554	+	7.81804i	0.364333	+	1.00100i	0.977480	+	0.211029i	$0.0676813\pi$
$61$	2.84554	+	7.81804i	0.364333	+	1.00100i	−0.613146	+	0.789969i	$0.710096\pi$
$62$		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	0.989417	−	0.145098i	$-0.0463499\pi$
$67$	0.0822020	+	0.466191i	0.0100426	+	0.0569543i	−0.979375	+	0.202053i	$0.935239\pi$
$68$		0			0
$69$	−0.957186	+	2.28219i	−0.115232	+	0.274744i
$70$		0			0
$71$	−8.36281	+	4.82827i	−0.992483	+	0.573010i	−0.906016	−	0.423244i	$-0.860891\pi$
$71$	−8.36281	+	4.82827i	−0.992483	+	0.573010i	−0.0864676	+	0.996255i	$0.527558\pi$
$72$		0			0
$73$	12.9594	−	7.48209i	1.51678	−	0.875713i	0.516973	−	0.856002i	$-0.327059\pi$
$73$	12.9594	−	7.48209i	1.51678	−	0.875713i	0.999806	−	0.0197110i	$-0.00627461\pi$
$74$		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	0.844529	+	0.535509i	$0.179880\pi$
$79$	−1.17523	+	6.66506i	−0.132224	+	0.749877i	−0.976753	+	0.214368i	$0.931231\pi$
$80$		0			0
$81$	−2.92780	−	8.51046i	−0.325311	−	0.945607i
$82$		0			0
$83$	0.735605	+	0.617246i	0.0807431	+	0.0677515i	0.682266	−	0.731104i	$-0.260995\pi$
$83$	0.735605	+	0.617246i	0.0807431	+	0.0677515i	−0.601523	+	0.798856i	$0.705439\pi$
$84$		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	0.907744	+	0.419525i	$0.137803\pi$
$97$	4.74751	+	13.0437i	0.482037	+	1.32439i	−0.425707	+	0.904861i	$0.639974\pi$
$98$		0			0
$99$	−5.56553	+	5.46774i	−0.559357	+	0.549529i
$100$		0			0
$101$	7.96739	+	6.68543i	0.792785	+	0.665226i	0.946433	−	0.322900i	$-0.104658\pi$
$101$	7.96739	+	6.68543i	0.792785	+	0.665226i	−0.153648	+	0.988126i	$0.549102\pi$
$102$		0			0
$103$	−11.6309	+	2.05085i	−1.14603	+	0.202076i	−0.714241	−	0.699899i	$-0.753228\pi$
$103$	−11.6309	+	2.05085i	−1.14603	+	0.202076i	−0.431788	+	0.901975i	$0.642117\pi$
$104$		0			0
$105$	−2.86023	−	4.19813i	−0.279130	−	0.409696i
$106$		0			0
$107$	7.14243	−	4.12369i	0.690485	−	0.398652i	−0.113309	−	0.993560i	$-0.536145\pi$
$107$	7.14243	−	4.12369i	0.690485	−	0.398652i	0.803794	+	0.594908i	$0.202812\pi$
$108$		0			0
$109$	−0.0911298	+	0.157841i	−0.00872865	+	0.0151185i	−0.870357	−	0.492422i	$-0.836112\pi$
$109$	−0.0911298	+	0.157841i	−0.00872865	+	0.0151185i	0.861628	+	0.507540i	$0.169445\pi$
$110$		0			0
$111$	−5.14150	−	0.247315i	−0.488009	−	0.0234741i
$112$		0			0
$113$	−2.98486	+	8.20082i	−0.280792	+	0.771469i	0.716477	+	0.697611i	$0.245753\pi$
$113$	−2.98486	+	8.20082i	−0.280792	+	0.771469i	−0.997269	+	0.0738581i	$0.976469\pi$
$114$		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	−0.938335	−	0.345727i	$-0.887632\pi$
$127$	−1.91309	+	3.31356i	−0.169759	+	0.294031i	0.768576	+	0.639758i	$0.220966\pi$
$128$		0			0
$129$	14.3324	+	13.2505i	1.26190	+	1.16665i
$130$		0			0
$131$	−5.32055	+	4.46447i	−0.464859	+	0.390063i	−0.844915	−	0.534901i	$-0.820349\pi$
$131$	−5.32055	+	4.46447i	−0.464859	+	0.390063i	0.380056	+	0.924963i	$0.375905\pi$
$132$		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	−0.677828	−	0.735220i	$-0.737079\pi$
$137$	−7.38768	−	20.2975i	−0.631172	−	1.73413i	0.0466563	−	0.998911i	$-0.485143\pi$
$138$		0			0
$139$	−12.3574	+	2.17894i	−1.04814	+	0.184815i	−0.671088	−	0.741378i	$-0.734173\pi$
$139$	−12.3574	+	2.17894i	−1.04814	+	0.184815i	−0.377050	+	0.926193i	$0.623062\pi$
$140$		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	0.725005	+	0.688744i	$0.241838\pi$
$149$	−3.33358	+	9.15893i	−0.273097	+	0.750328i	−0.998102	+	0.0615845i	$0.980385\pi$
$150$		0			0
$151$	0.556841	−	3.15800i	0.0453150	−	0.256994i	−0.953731	−	0.300661i	$-0.902793\pi$
$151$	0.556841	−	3.15800i	0.0453150	−	0.256994i	0.999046	+	0.0436665i	$0.0139039\pi$
$152$		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	0.657507	−	0.753449i	$-0.271611\pi$
$157$	−2.48933	−	2.96666i	−0.198670	−	0.236766i	−0.856177	+	0.516683i	$0.827167\pi$
$158$		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	0.923697	−	0.383124i	$-0.125152\pi$
$163$	1.66040	+	2.87591i	0.130053	+	0.225258i	−0.793644	+	0.608383i	$0.791819\pi$
$164$		0			0
$165$	−4.43931	+	2.28601i	−0.345600	+	0.177966i
$166$		0			0
$167$	−7.24079	−	2.63543i	−0.560309	−	0.203936i	0.0463118	−	0.998927i	$-0.485253\pi$
$167$	−7.24079	−	2.63543i	−0.560309	−	0.203936i	−0.606621	+	0.794991i	$0.707475\pi$
$168$		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	−0.929671	−	0.368390i	$-0.879909\pi$
$173$	−19.1231	−	16.0462i	−1.45390	−	1.21997i	−0.524229	−	0.851577i	$-0.675646\pi$
$174$		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	$-0.874525\pi$
$179$		−	10.2768i		−	0.768121i	0.923308	−	0.384060i	$-0.125475\pi$
$180$		0			0
$181$	−0.236613	−	0.136609i	−0.0175873	−	0.0101540i	0.491181	−	0.871058i	$-0.336566\pi$
$181$	−0.236613	−	0.136609i	−0.0175873	−	0.0101540i	−0.508768	+	0.860904i	$0.669899\pi$
$182$		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	0.532674	−	0.846321i	$-0.321187\pi$
$191$	10.2790	+	1.81247i	0.743765	+	0.131146i	0.211091	+	0.977466i	$0.432298\pi$
$192$		0			0
$193$	3.65214	+	1.32927i	0.262887	+	0.0956831i	0.470101	−	0.882613i	$-0.344217\pi$
$193$	3.65214	+	1.32927i	0.262887	+	0.0956831i	−0.207214	+	0.978296i	$0.566440\pi$
$194$		0			0
$195$	−8.29660	−	1.87792i	−0.594132	−	0.134481i
$196$		0			0
$197$	15.4374	+	8.91279i	1.09987	+	0.635010i	0.936187	−	0.351503i	$-0.114329\pi$
$197$	15.4374	+	8.91279i	1.09987	+	0.635010i	0.163683	+	0.986513i	$0.447663\pi$
$198$		0			0
$199$		−	1.02772i		−	0.0728533i	−0.999336	−	0.0364266i	$-0.988402\pi$
$199$		−	1.02772i		−	0.0728533i	0.999336	−	0.0364266i	$-0.0115975\pi$
$200$		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	−0.115857	−	0.993266i	$-0.536962\pi$
$211$	−12.2463	−	4.45728i	−0.843068	−	0.306852i	−0.727211	+	0.686414i	$0.759184\pi$
$212$		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	0.451719	−	0.892160i	$-0.350811\pi$
$223$	8.52773	+	1.50367i	0.571059	+	0.100693i	0.119340	+	0.992853i	$0.461922\pi$
$224$		0			0
$225$	−3.02490	+	10.9017i	−0.201660	+	0.726777i
$226$		0			0
$227$	5.20218	−	29.5031i	0.345281	−	1.95819i	0.0667035	−	0.997773i	$-0.478752\pi$
$227$	5.20218	−	29.5031i	0.345281	−	1.95819i	0.278578	−	0.960414i	$-0.410137\pi$
$228$		0			0
$229$	−5.43169	+	14.9234i	−0.358936	+	0.986169i	0.620463	+	0.784236i	$0.286945\pi$
$229$	−5.43169	+	14.9234i	−0.358936	+	0.986169i	−0.979399	+	0.201933i	$0.935278\pi$
$230$		0			0
$231$	11.5502	−	2.93702i	0.759947	−	0.193242i
$232$		0			0
$233$	−3.53816	−	2.04276i	−0.231793	−	0.133826i	0.379606	−	0.925148i	$-0.376060\pi$
$233$	−3.53816	−	2.04276i	−0.231793	−	0.133826i	−0.611399	+	0.791323i	$0.709393\pi$
$234$		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	−0.847903	−	0.530152i	$-0.822135\pi$
$239$	−22.6228	+	3.98901i	−1.46335	+	0.258028i	−0.615445	+	0.788180i	$0.711024\pi$
$240$		0			0
$241$	1.77041	+	4.86416i	0.114042	+	0.313328i	0.983562	−	0.180569i	$-0.0577940\pi$
$241$	1.77041	+	4.86416i	0.114042	+	0.313328i	−0.869520	+	0.493897i	$0.835572\pi$
$242$		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	−0.930544	−	0.366180i	$-0.880665\pi$
$251$	−2.34715	+	4.06538i	−0.148151	+	0.256604i	0.782393	+	0.622785i	$0.213999\pi$
$252$		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	−0.261010	−	0.965336i	$-0.584056\pi$
$257$	−17.3371	−	6.31020i	−1.08146	−	0.393620i	−0.820451	+	0.571716i	$0.806278\pi$
$258$		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	0.0545106	−	0.998513i	$-0.482640\pi$
$263$	16.6777	−	19.8757i	1.02839	−	1.22559i	0.973878	−	0.227072i	$-0.0729154\pi$
$264$		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	0.0709484	+	0.997480i	$0.477397\pi$
$269$	−13.5863	+	23.5321i	−0.828369	+	1.43478i	−0.899317	+	0.437297i	$0.855936\pi$
$270$		0			0
$271$	8.32385	−	4.80578i	0.505638	−	0.291930i	−0.225401	−	0.974266i	$-0.572369\pi$
$271$	8.32385	−	4.80578i	0.505638	−	0.291930i	0.731039	+	0.682336i	$0.239036\pi$
$272$		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	0.831039	−	0.556214i	$-0.187747\pi$
$277$	7.11640	+	5.97137i	0.427583	+	0.358785i	−0.403456	+	0.914999i	$0.632191\pi$
$278$		0			0
$279$	2.39729	+	3.48909i	0.143522	+	0.208886i
$280$		0			0
$281$	−5.95969	−	16.3741i	−0.355526	−	0.976798i	−0.980563	−	0.196204i	$-0.937139\pi$
$281$	−5.95969	−	16.3741i	−0.355526	−	0.976798i	0.625038	−	0.780595i	$-0.285084\pi$
$282$		0			0
$283$	9.35523	−	1.64958i	0.556111	−	0.0980573i	0.111472	−	0.993768i	$-0.464443\pi$
$283$	9.35523	−	1.64958i	0.556111	−	0.0980573i	0.444638	+	0.895710i	$0.353332\pi$
$284$		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	−0.885509	−	0.464623i	$-0.846190\pi$
$293$	−3.63421	−	20.6107i	−0.212313	−	1.20409i	0.673196	−	0.739464i	$-0.264921\pi$
$294$		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	−0.386813	−	0.922158i	$-0.626424\pi$
$307$	3.82657	−	2.20927i	0.218394	−	0.126090i	0.605206	+	0.796069i	$0.293091\pi$
$308$		0			0
$309$	12.3809	+	16.2840i	0.704323	+	0.926362i
$310$		0			0
$311$	0.494496	+	2.80443i	0.0280403	+	0.159024i	0.995613	−	0.0935690i	$-0.0298276\pi$
$311$	0.494496	+	2.80443i	0.0280403	+	0.159024i	−0.967572	+	0.252594i	$0.918716\pi$
$312$		0			0
$313$	7.42776	−	8.85206i	0.419842	−	0.500348i	−0.514121	−	0.857718i	$-0.671882\pi$
$313$	7.42776	−	8.85206i	0.419842	−	0.500348i	0.933963	+	0.357370i	$0.116326\pi$
$314$		0			0
$315$	−4.19657	+	7.73333i	−0.236450	+	0.435724i
$316$		0			0
$317$	6.33865	+	17.4153i	0.356014	+	0.978141i	0.980399	+	0.197024i	$0.0631277\pi$
$317$	6.33865	+	17.4153i	0.356014	+	0.978141i	−0.624384	+	0.781117i	$0.714650\pi$
$318$		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	−0.956133	−	0.292934i	$-0.905368\pi$
$331$	−27.2952	+	9.93463i	−1.50028	+	0.546057i	−0.544146	+	0.838991i	$0.683146\pi$
$332$		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	−0.305204	−	0.952287i	$-0.598725\pi$
$337$	10.6404	−	8.92833i	0.579618	−	0.486357i	0.884822	+	0.465930i	$0.154280\pi$
$338$		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	−0.995318	−	0.0966539i	$-0.969186\pi$
$347$	−3.18039	+	8.73805i	−0.170732	+	0.469083i	0.824586	+	0.565737i	$0.191408\pi$
$348$		0			0
$349$	18.3394	−	21.8561i	0.981686	−	1.16993i	−0.00376869	−	0.999993i	$-0.501200\pi$
$349$	18.3394	−	21.8561i	0.981686	−	1.16993i	0.985455	−	0.169936i	$-0.0543559\pi$
$350$		0			0
$351$	12.1100	+	19.5785i	0.646386	+	1.04503i
$352$		0			0
$353$	−23.9298	+	8.70972i	−1.27365	+	0.463572i	−0.888328	−	0.459209i	$-0.848133\pi$
$353$	−23.9298	+	8.70972i	−1.27365	+	0.463572i	−0.385325	+	0.922781i	$0.625911\pi$
$354$		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	$0.0583206\pi$
$359$			6.90425i			0.364392i	−0.983262	+	0.182196i	$0.941679\pi$
$360$		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	0.122758	−	0.992437i	$-0.460826\pi$
$367$	−1.94103	−	0.342257i	−0.101321	−	0.0178657i	−0.224079	+	0.974571i	$0.571937\pi$
$368$		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	−0.966725	−	0.255819i	$-0.917655\pi$
$373$	−2.81578	−	15.9691i	−0.145796	−	0.826849i	0.820929	−	0.571030i	$-0.193456\pi$
$374$		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	0.962152	−	0.272514i	$-0.0878550\pi$
$383$	−0.688493	−	3.90464i	−0.0351804	−	0.199518i	−0.997332	+	0.0729961i	$0.976744\pi$
$384$		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	−0.424016	−	0.905655i	$-0.639380\pi$
$389$	−22.3307	−	3.93751i	−1.13221	−	0.199640i	−0.708197	+	0.706015i	$0.750491\pi$
$390$		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	$-0.950189\pi$
$397$		−	6.21045i		−	0.311694i	0.987781	−	0.155847i	$-0.0498106\pi$
$398$		0			0
$399$	3.72542	+	8.26360i	0.186504	+	0.413697i
$400$		0			0
$401$	9.61370	+	11.4572i	0.480085	+	0.572143i	0.950667	−	0.310213i	$-0.100400\pi$
$401$	9.61370	+	11.4572i	0.480085	+	0.572143i	−0.470582	+	0.882356i	$0.655956\pi$
$402$		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	−0.841999	−	0.539478i	$-0.818621\pi$
$409$	3.02910	−	8.32239i	0.149780	−	0.411516i	0.991779	+	0.127962i	$0.0408437\pi$
$410$		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	−0.682506	−	0.730880i	$-0.739110\pi$
$419$	−1.66306	+	1.39547i	−0.0812457	+	0.0681732i	0.601260	+	0.799053i	$0.294665\pi$
$420$		0			0
$421$	−12.3900	+	4.50961i	−0.603854	+	0.219785i	−0.625812	−	0.779974i	$-0.715232\pi$
$421$	−12.3900	+	4.50961i	−0.603854	+	0.219785i	0.0219579	+	0.999759i	$0.493010\pi$
$422$		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	0.870576	−	0.492035i	$-0.163747\pi$
$431$	18.2641	+	10.5448i	0.879749	+	0.507923i	0.00917317	+	0.999958i	$0.497080\pi$
$432$		0			0
$433$		−	24.5525i		−	1.17992i	−0.807433	−	0.589959i	$-0.799144\pi$
$433$		−	24.5525i		−	1.17992i	0.807433	−	0.589959i	$-0.200856\pi$
$434$		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	0.745099	+	0.666954i	$0.232402\pi$
$439$	12.6349	+	34.7140i	0.603030	+	1.65681i	−0.142069	+	0.989857i	$0.545375\pi$
$440$		0			0
$441$	13.9057	−	15.7363i	0.662176	−	0.749348i
$442$		0			0
$443$	14.6233	−	17.4273i	0.694772	−	0.827997i	−0.297152	−	0.954830i	$-0.596037\pi$
$443$	14.6233	−	17.4273i	0.694772	−	0.827997i	0.991924	+	0.126833i	$0.0404812\pi$
$444$		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	−0.936395	−	0.350948i	$-0.885859\pi$
$449$	−23.3226	+	13.4653i	−1.10066	+	0.635468i	−0.164268	+	0.986416i	$0.552526\pi$
$450$		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	0.890495	+	0.454993i	$0.150358\pi$
$457$	−2.17866	+	12.3558i	−0.101913	+	0.577979i	−0.992408	+	0.122986i	$0.960753\pi$
$458$		0			0
$459$	11.1798	+	1.62333i	0.521829	+	0.0757704i
$460$		0			0
$461$	−12.3292	−	10.3454i	−0.574229	−	0.481835i	0.308817	−	0.951121i	$-0.400067\pi$
$461$	−12.3292	−	10.3454i	−0.574229	−	0.481835i	−0.883046	+	0.469286i	$0.844511\pi$
$462$		0			0
$463$	−0.398483	−	2.25991i	−0.0185191	−	0.105027i	0.974147	−	0.225915i	$-0.0725370\pi$
$463$	−0.398483	−	2.25991i	−0.0185191	−	0.105027i	−0.992666	+	0.120888i	$0.961426\pi$
$464$		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	0.785365	−	0.619033i	$-0.212475\pi$
$479$	6.83095	+	5.73185i	0.312114	+	0.261895i	−0.473251	+	0.880928i	$0.656920\pi$
$480$		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	−0.164618	−	0.986357i	$-0.552639\pi$
$487$	17.0344	−	29.5044i	0.771901	−	1.33697i	0.936520	−	0.350615i	$-0.114027\pi$
$488$		0			0
$489$	3.11191	−	4.83729i	0.140726	−	0.218750i
$490$		0			0
$491$	6.27488	−	17.2401i	0.283181	−	0.778034i	−0.713797	−	0.700353i	$-0.753026\pi$
$491$	6.27488	−	17.2401i	0.283181	−	0.778034i	0.996978	−	0.0776816i	$-0.0247518\pi$
$492$		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	−0.172798	−	0.984957i	$-0.555281\pi$
$499$	−20.9598	−	7.62873i	−0.938287	−	0.341509i	−0.765489	+	0.643449i	$0.777503\pi$
$500$		0			0
$501$	1.68339	+	13.2397i	0.0752082	+	0.591506i
$502$		0			0
$503$	−3.88720	−	6.73283i	−0.173322	−	0.300202i	0.766257	−	0.642534i	$-0.222117\pi$
$503$	−3.88720	−	6.73283i	−0.173322	−	0.300202i	−0.939579	+	0.342331i	$0.888783\pi$
$504$		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	−0.652363	−	0.757907i	$-0.726222\pi$
$509$	−0.434346	+	0.364459i	−0.0192520	+	0.0161544i	0.633111	+	0.774061i	$0.281778\pi$
$510$		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	−0.738535	−	0.674216i	$-0.764482\pi$
$521$	−21.7562	−	37.6828i	−0.953155	−	1.65091i	−0.214621	−	0.976697i	$-0.568851\pi$
$522$		0			0
$523$	26.5254	+	15.3144i	1.15987	+	0.669654i	0.951274	−	0.308347i	$-0.0997758\pi$
$523$	26.5254	+	15.3144i	1.15987	+	0.669654i	0.208600	+	0.978001i	$0.433109\pi$
$524$		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	0.892456	+	0.451134i	$0.148980\pi$
$541$	19.4663	+	33.7166i	0.836921	+	1.44959i	−0.0555351	+	0.998457i	$0.517686\pi$
$542$		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	−0.168562	−	0.985691i	$-0.553912\pi$
$547$	7.64697	−	43.3681i	0.326961	−	1.85429i	0.495523	−	0.868595i	$-0.334977\pi$
$548$		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	$-0.865003\pi$
$557$		−	19.4237i		−	0.823010i	0.911407	−	0.411505i	$-0.134997\pi$
$558$		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	−0.237479	−	0.971393i	$-0.576321\pi$
$563$	−24.7668	−	9.01439i	−1.04380	−	0.379911i	−0.806319	+	0.591481i	$0.798543\pi$
$564$		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	−0.683558	−	0.729896i	$-0.739568\pi$
$569$	−37.5823	−	6.62677i	−1.57553	−	0.277809i	−0.891974	+	0.452087i	$0.850680\pi$
$570$		0			0
$571$	−33.6216	−	12.2373i	−1.40702	−	0.512114i	−0.476767	−	0.879030i	$-0.658191\pi$
$571$	−33.6216	−	12.2373i	−1.40702	−	0.512114i	−0.930254	+	0.366916i	$0.880414\pi$
$572$		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	$-0.757274\pi$
$577$		−	33.1855i		−	1.38153i	0.723079	−	0.690765i	$-0.242726\pi$
$578$		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	0.493262	+	0.869881i	$0.335804\pi$
$587$	−6.48754	+	36.7927i	−0.267769	+	1.51860i	−0.761032	+	0.648715i	$0.775307\pi$
$588$		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	−0.987534	−	0.157406i	$-0.949687\pi$
$593$	−15.3436	−	26.5758i	−0.630084	−	1.09134i	0.357450	−	0.933932i	$-0.383646\pi$
$594$		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	0.527343	−	0.849653i	$-0.323188\pi$
$599$	−9.81363	−	11.6954i	−0.400974	−	0.477862i	−0.928317	+	0.371790i	$0.878744\pi$
$600$		0			0
$601$	4.22303	+	0.744633i	0.172261	+	0.0303742i	0.259113	−	0.965847i	$-0.416570\pi$
$601$	4.22303	+	0.744633i	0.172261	+	0.0303742i	−0.0868524	+	0.996221i	$0.527681\pi$
$602$		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	−0.852313	−	0.523032i	$-0.824801\pi$
$607$	3.37027	−	9.25974i	0.136795	−	0.375841i	0.989108	+	0.147191i	$0.0470231\pi$
$608$		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	0.935313	+	0.353820i	$0.115118\pi$
$613$	19.1652	+	33.1951i	0.774074	+	1.34074i	−0.161239	+	0.986915i	$0.551549\pi$
$614$		0			0
$615$	−4.14720	+	18.3222i	−0.167231	+	0.738822i
$616$		0			0
$617$	−26.7808	+	4.72218i	−1.07816	+	0.190108i	−0.684399	−	0.729107i	$-0.739936\pi$
$617$	−26.7808	+	4.72218i	−1.07816	+	0.190108i	−0.393756	+	0.919215i	$0.628824\pi$
$618$		0			0
$619$	−4.97533	−	13.6696i	−0.199976	−	0.549428i	0.798653	−	0.601792i	$-0.205547\pi$
$619$	−4.97533	−	13.6696i	−0.199976	−	0.549428i	−0.998628	+	0.0523642i	$0.983324\pi$
$620$		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	0.885092	−	0.465415i	$-0.154095\pi$
$631$	0.991846	+	1.71793i	0.0394847	+	0.0683896i	−0.845608	+	0.533805i	$0.820762\pi$
$632$		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	−0.712777	−	0.701391i	$-0.752563\pi$
$641$	2.57561	−	3.06949i	0.101730	−	0.121238i	0.814507	+	0.580153i	$0.197007\pi$
$642$		0			0
$643$	−6.23306	+	17.1252i	−0.245808	+	0.675351i	0.754021	+	0.656850i	$0.228112\pi$
$643$	−6.23306	+	17.1252i	−0.245808	+	0.675351i	−0.999829	+	0.0185010i	$0.994111\pi$
$644$		0			0
$645$	11.7065	−	18.1970i	0.460942	−	0.716507i
$646$		0			0
$647$	−13.6102	+	23.5735i	−0.535072	+	0.926771i	0.464088	+	0.885789i	$0.346382\pi$
$647$	−13.6102	+	23.5735i	−0.535072	+	0.926771i	−0.999160	+	0.0409821i	$0.986951\pi$
$648$		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	−0.470871	−	0.882202i	$-0.656060\pi$
$653$	−15.6291	+	2.75583i	−0.611614	+	0.107844i	−0.140743	+	0.990046i	$0.544949\pi$
$654$		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	−0.769620	−	0.638502i	$-0.779554\pi$
$659$	−15.1582	−	41.6467i	−0.590478	−	1.62232i	0.179142	−	0.983823i	$-0.442668\pi$
$660$		0			0
$661$	−1.36845	+	0.241294i	−0.0532263	+	0.00938524i	−0.200198	−	0.979755i	$-0.564159\pi$
$661$	−1.36845	+	0.241294i	−0.0532263	+	0.00938524i	0.146972	+	0.989141i	$0.453047\pi$
$662$		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	0.501860	−	0.864949i	$-0.332649\pi$
$673$	−6.81767	−	5.72071i	−0.262802	−	0.220517i	−0.764662	+	0.644432i	$0.777094\pi$
$674$		0			0
$675$	19.1858	−	3.98657i	0.738463	−	0.153443i
$676$		0			0
$677$	2.10373	−	11.9308i	0.0808527	−	0.458539i	−0.917322	−	0.398146i	$-0.869654\pi$
$677$	2.10373	−	11.9308i	0.0808527	−	0.458539i	0.998175	−	0.0603925i	$-0.0192352\pi$
$678$		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	−0.754426	+	0.656385i	$0.772085\pi$
$683$	−44.4305	+	25.6519i	−1.70009	+	0.981545i	−0.945659	+	0.325159i	$0.894582\pi$
$684$		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	−0.118867	+	0.992910i	$0.537926\pi$
$691$	−28.2860	+	33.7100i	−1.07605	+	1.28239i	−0.957185	+	0.289478i	$0.906518\pi$
$692$		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	$0.330049\pi$
$701$			45.5828i			1.72164i	−0.508909	+	0.860820i	$0.669951\pi$
$702$		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	−0.986710	−	0.162494i	$-0.948046\pi$
$709$	−43.6184	+	15.8758i	−1.63812	+	0.596228i	−0.651415	+	0.758722i	$0.725824\pi$
$710$		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	−0.434478	−	0.900682i	$-0.643067\pi$
$719$	15.0903	−	26.1372i	0.562775	−	0.974754i	0.997253	−	0.0740719i	$-0.0235994\pi$
$720$		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	−0.450235	−	0.892910i	$-0.648660\pi$
$727$	13.6781	−	16.3009i	0.507293	−	0.604568i	0.957527	+	0.288342i	$0.0931041\pi$
$728$		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	0.870834	−	0.491577i	$-0.163580\pi$
$733$	6.37608	+	7.59872i	0.235506	+	0.280665i	−0.635328	+	0.772242i	$0.719135\pi$
$734$		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	0.415928	−	0.909397i	$-0.363457\pi$
$743$	−15.0431	−	17.9277i	−0.551879	−	0.657703i	−0.967807	+	0.251694i	$0.919012\pi$
$744$		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	0.884664	+	0.466230i	$0.154388\pi$
$751$	5.83197	+	33.0748i	0.212812	+	1.20691i	−0.671852	+	0.740685i	$0.734501\pi$
$752$		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	−0.881705	−	0.471801i	$-0.843604\pi$
$761$	−5.91832	−	33.5645i	−0.214539	−	1.21671i	0.667166	−	0.744909i	$-0.267507\pi$
$762$		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	0.915789	+	0.401659i	$0.131566\pi$
$769$	31.9548	+	38.0823i	1.15232	+	1.37328i	0.236531	+	0.971624i	$0.423989\pi$
$770$		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	−0.474326	−	0.880349i	$-0.657308\pi$
$787$	12.7617	−	35.0625i	0.454906	−	1.24984i	0.929232	−	0.369496i	$-0.120470\pi$
$788$		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	0.0118051	−	0.999930i	$-0.496242\pi$
$797$	28.1915	−	23.6555i	0.998594	−	0.837920i	0.986789	+	0.162010i	$0.0517978\pi$
$798$		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	0.293804	−	0.955866i	$-0.405079\pi$
$809$	−11.0102	−	6.35674i	−0.387098	−	0.223491i	−0.680902	+	0.732375i	$0.738412\pi$
$810$		0			0
$811$		−	9.81361i		−	0.344603i	−0.985044	−	0.172301i	$-0.944880\pi$
$811$		−	9.81361i		−	0.344603i	0.985044	−	0.172301i	$-0.0551203\pi$
$812$		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	−0.630682	−	0.776041i	$-0.717225\pi$
$821$	6.96515	−	8.30075i	0.243086	−	0.289698i	0.873768	+	0.486343i	$0.161669\pi$
$822$		0			0
$823$	4.08642	+	23.1753i	0.142444	+	0.807838i	0.969384	+	0.245549i	$0.0789682\pi$
$823$	4.08642	+	23.1753i	0.142444	+	0.807838i	−0.826940	+	0.562289i	$0.809921\pi$
$824$		0			0
$825$	−10.2814	−	13.5226i	−0.357951	−	0.470796i
$826$		0			0
$827$	4.95821	−	2.86262i	0.172414	−	0.0995432i	−0.411310	−	0.911496i	$-0.634929\pi$
$827$	4.95821	−	2.86262i	0.172414	−	0.0995432i	0.583724	+	0.811952i	$0.301595\pi$
$828$		0			0
$829$	−18.1311	+	10.4680i	−0.629719	+	0.363569i	−0.780643	−	0.624977i	$-0.785108\pi$
$829$	−18.1311	+	10.4680i	−0.629719	+	0.363569i	0.150924	+	0.988545i	$0.451775\pi$
$830$		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	0.793005	−	0.609215i	$-0.208515\pi$
$839$	9.58032	+	8.03885i	0.330750	+	0.277532i	−0.462256	+	0.886747i	$0.652960\pi$
$840$		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	−0.978942	−	0.204137i	$-0.934561\pi$
$853$	−10.5214	−	28.9073i	−0.360246	−	0.989768i	0.618696	−	0.785630i	$-0.287661\pi$
$854$		0			0
$855$	−2.83276	+	5.93692i	−0.0968783	+	0.203038i
$856$		0			0
$857$	−30.0674	−	25.2296i	−1.02708	−	0.861826i	−0.0365829	−	0.999331i	$-0.511647\pi$
$857$	−30.0674	−	25.2296i	−1.02708	−	0.861826i	−0.990501	+	0.137505i	$0.956092\pi$
$858$		0			0
$859$	36.4758	−	6.43167i	1.24454	−	0.219446i	0.487679	−	0.873023i	$-0.337844\pi$
$859$	36.4758	−	6.43167i	1.24454	−	0.219446i	0.756859	+	0.653578i	$0.226733\pi$
$860$		0			0
$861$	19.4671	−	40.3900i	0.663436	−	1.37649i
$862$		0			0
$863$	34.1803	−	19.7340i	1.16351	−	0.671754i	0.211369	−	0.977406i	$-0.432208\pi$
$863$	34.1803	−	19.7340i	1.16351	−	0.671754i	0.952143	+	0.305652i	$0.0988744\pi$
$864$		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	−0.106223	−	0.994342i	$-0.533876\pi$
$877$	−24.4834	−	8.91122i	−0.826745	−	0.300911i	−0.720522	+	0.693432i	$0.756098\pi$
$878$		0			0
$879$	−28.8561	+	21.9396i	−0.973292	+	0.740004i
$880$		0			0
$881$	−2.38743	−	4.13514i	−0.0804345	−	0.139317i	0.823002	−	0.568038i	$-0.192297\pi$
$881$	−2.38743	−	4.13514i	−0.0804345	−	0.139317i	−0.903437	+	0.428722i	$0.858964\pi$
$882$		0			0
$883$	−13.0553	+	22.6124i	−0.439345	+	0.760969i	−0.997639	−	0.0686748i	$-0.978123\pi$
$883$	−13.0553	+	22.6124i	−0.439345	+	0.760969i	0.558294	+	0.829643i	$0.311456\pi$
$884$		0			0
$885$	0.617631	−	2.72867i	0.0207615	−	0.0917234i
$886$		0			0
$887$	36.9868	−	31.0356i	1.24190	−	1.04207i	0.244523	−	0.969644i	$-0.421369\pi$
$887$	36.9868	−	31.0356i	1.24190	−	1.04207i	0.997373	−	0.0724311i	$-0.0230757\pi$
$888$		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	0.898799	+	0.438362i	$0.144441\pi$
$907$	−2.88288	+	16.3496i	−0.0957244	+	0.542880i	−0.994523	+	0.104518i	$0.966670\pi$
$908$		0			0
$909$	−30.2093	+	7.80826i	−1.00198	+	0.258984i
$910$		0			0
$911$	39.9656	+	7.04701i	1.32412	+	0.233478i	0.790612	−	0.612317i	$-0.209762\pi$
$911$	39.9656	+	7.04701i	1.32412	+	0.233478i	0.533508	+	0.845795i	$0.320874\pi$
$912$		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	0.628975	−	0.777426i	$-0.283475\pi$
$919$	−10.8765	−	18.8387i	−0.358783	−	0.621431i	−0.987758	+	0.155995i	$0.950142\pi$
$920$		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	0.137714	−	0.990472i	$-0.456024\pi$
$929$	−24.8041	−	20.8131i	−0.813796	−	0.682856i	−0.951511	+	0.307616i	$0.900469\pi$
$930$		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	0.986146	+	0.165878i	$0.0530457\pi$
$937$	49.6769	+	28.6810i	1.62287	+	0.936967i	0.636727	+	0.771089i	$0.280288\pi$
$938$		0			0
$939$	−19.5210	−	4.41854i	−0.637043	−	0.144194i
$940$		0			0
$941$	−0.0852964	−	0.0310453i	−0.00278058	−	0.00101205i	0.340629	−	0.940198i	$-0.389360\pi$
$941$	−0.0852964	−	0.0310453i	−0.00278058	−	0.00101205i	−0.343410	+	0.939186i	$0.611582\pi$
$942$		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	−0.306305	−	0.951933i	$-0.599093\pi$
$947$	−28.3028	−	4.99055i	−0.919718	−	0.162171i	−0.613413	+	0.789762i	$0.710204\pi$
$948$		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	0.978149	+	0.207905i	$0.0666646\pi$
$953$	50.8525	+	29.3597i	1.64727	+	0.951055i	0.669126	+	0.743149i	$0.266669\pi$
$954$		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	0.999819	−	0.0190105i	$-0.00605161\pi$
$967$	54.5281	+	19.8466i	1.75351	+	0.638224i	0.753686	+	0.657234i	$0.228274\pi$
$968$		0			0
$969$	6.62224	−	3.41011i	0.212737	−	0.109548i
$970$		0			0
$971$	4.34443	+	7.52477i	0.139419	+	0.241481i	0.927277	−	0.374376i	$-0.122143\pi$
$971$	4.34443	+	7.52477i	0.139419	+	0.241481i	−0.787858	+	0.615857i	$0.788810\pi$
$972$		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	0.983901	+	0.178716i	$0.0571943\pi$
$977$	30.9147	+	36.8427i	0.989049	+	1.17870i	0.00514810	+	0.999987i	$0.498361\pi$
$978$		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	−0.981441	−	0.191762i	$-0.938580\pi$
$983$	0.200604	−	1.13768i	0.00639828	−	0.0362864i	0.987840	+	0.155475i	$0.0496910\pi$
$984$		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	0.914054	+	0.405593i	$0.132935\pi$
$991$	25.4448	+	44.0717i	0.808281	+	1.39998i	−0.105773	+	0.994390i	$0.533732\pi$
$992$		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	−0.995963	−	0.0897607i	$-0.971390\pi$
$997$	−9.17920	−	25.2197i	−0.290708	−	0.798714i	0.705255	−	0.708954i	$-0.250832\pi$
$998$		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.605.8	yes	144
7.5	odd	6		756.2.ca.a.173.1	✓	144
27.5	odd	18		756.2.ca.a.437.1	yes	144
189.5	even	18	inner	756.2.ck.a.5.8	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.1	✓	144	7.5	odd	6
756.2.ca.a.437.1	yes	144	27.5	odd	18
756.2.ck.a.5.8	yes	144	189.5	even	18	inner
756.2.ck.a.605.8	yes	144	1.1	even	1	trivial

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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