LMFDB - Embedded newform 216.2.q.b.97.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(25,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("216.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.q (of order $9$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			97.4
Character	$\chi$	$=$	216.97
Dual form			216.2.q.b.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10062 - 1.33740i) q^{3} +(3.74067 + 1.36149i) q^{5} +(-0.452652 + 2.56712i) q^{7} +(-0.577279 - 2.94393i) q^{9} +O(q^{10})$	\(q+(1.10062 - 1.33740i) q^{3} +(3.74067 + 1.36149i) q^{5} +(-0.452652 + 2.56712i) q^{7} +(-0.577279 - 2.94393i) q^{9} +(-4.99402 + 1.81767i) q^{11} +(-0.0404003 + 0.0338999i) q^{13} +(5.93792 - 3.50429i) q^{15} +(-1.69081 - 2.92857i) q^{17} +(1.23206 - 2.13399i) q^{19} +(2.93506 + 3.43079i) q^{21} +(-0.964125 - 5.46782i) q^{23} +(8.30876 + 6.97187i) q^{25} +(-4.57258 - 2.46810i) q^{27} +(-6.29991 - 5.28625i) q^{29} +(-0.115728 - 0.656323i) q^{31} +(-3.06555 + 8.67957i) q^{33} +(-5.18834 + 8.98646i) q^{35} +(2.67730 + 4.63722i) q^{37} +(0.000872395 + 0.0913423i) q^{39} +(-5.31122 + 4.45664i) q^{41} +(-0.0524095 + 0.0190755i) q^{43} +(1.84874 - 11.7983i) q^{45} +(-0.0794772 + 0.450737i) q^{47} +(0.192660 + 0.0701224i) q^{49} +(-5.77762 - 0.961949i) q^{51} +1.38667 q^{53} -21.1558 q^{55} +(-1.49797 - 3.99646i) q^{57} +(3.99339 + 1.45348i) q^{59} +(0.457339 - 2.59370i) q^{61} +(7.81873 - 0.149364i) q^{63} +(-0.197279 + 0.0718037i) q^{65} +(7.16941 - 6.01585i) q^{67} +(-8.37380 - 4.72856i) q^{69} +(7.18697 + 12.4482i) q^{71} +(-7.15357 + 12.3903i) q^{73} +(18.4690 - 3.43876i) q^{75} +(-2.40563 - 13.6430i) q^{77} +(5.93415 + 4.97935i) q^{79} +(-8.33350 + 3.39894i) q^{81} +(1.83808 + 1.54234i) q^{83} +(-2.33755 - 13.2569i) q^{85} +(-14.0036 + 2.60735i) q^{87} +(2.04047 - 3.53420i) q^{89} +(-0.0687377 - 0.119057i) q^{91} +(-1.00514 - 0.567588i) q^{93} +(7.51413 - 6.30511i) q^{95} +(-11.8711 + 4.32074i) q^{97} +(8.23406 + 13.6528i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{7} - 6 q^{9}+O(q^{10}) $ 30 * q + 3 * q^7 - 6 * q^9	$ 30 q + 3 q^{7} - 6 q^{9} - 3 q^{11} - 12 q^{13} + 15 q^{15} + 6 q^{17} - 9 q^{19} + 30 q^{21} - 12 q^{23} + 24 q^{25} - 15 q^{27} - 9 q^{29} + 27 q^{31} - 30 q^{33} - 18 q^{35} - 15 q^{37} - 21 q^{39} - 15 q^{41} - 30 q^{43} + 15 q^{45} - 18 q^{47} + 15 q^{49} - 6 q^{51} - 18 q^{53} + 54 q^{55} - 72 q^{57} - 12 q^{59} + 6 q^{61} - 54 q^{63} - 54 q^{65} - 45 q^{67} + 9 q^{69} - 36 q^{73} + 69 q^{75} + 12 q^{77} + 45 q^{79} - 30 q^{81} - 3 q^{83} + 57 q^{85} - 60 q^{87} + 36 q^{89} - 39 q^{91} + 30 q^{93} + 51 q^{95} - 84 q^{97} + 162 q^{99}+O(q^{100}) $ 30 * q + 3 * q^7 - 6 * q^9 - 3 * q^11 - 12 * q^13 + 15 * q^15 + 6 * q^17 - 9 * q^19 + 30 * q^21 - 12 * q^23 + 24 * q^25 - 15 * q^27 - 9 * q^29 + 27 * q^31 - 30 * q^33 - 18 * q^35 - 15 * q^37 - 21 * q^39 - 15 * q^41 - 30 * q^43 + 15 * q^45 - 18 * q^47 + 15 * q^49 - 6 * q^51 - 18 * q^53 + 54 * q^55 - 72 * q^57 - 12 * q^59 + 6 * q^61 - 54 * q^63 - 54 * q^65 - 45 * q^67 + 9 * q^69 - 36 * q^73 + 69 * q^75 + 12 * q^77 + 45 * q^79 - 30 * q^81 - 3 * q^83 + 57 * q^85 - 60 * q^87 + 36 * q^89 - 39 * q^91 + 30 * q^93 + 51 * q^95 - 84 * q^97 + 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.10062	−	1.33740i	0.635442	−	0.772148i
$3$	1.10062	−	1.33740i	0.635442	−	0.772148i
$4$		0			0
$5$	3.74067	+	1.36149i	1.67288	+	0.608879i	0.992307	−	0.123801i	$-0.0395085\pi$
$5$	3.74067	+	1.36149i	1.67288	+	0.608879i	0.680573	+	0.732680i	$0.261731\pi$
$6$		0			0
$7$	−0.452652	+	2.56712i	−0.171086	+	0.970278i	0.771479	+	0.636255i	$0.219517\pi$
$7$	−0.452652	+	2.56712i	−0.171086	+	0.970278i	−0.942565	+	0.334023i	$0.891594\pi$
$8$		0			0
$9$	−0.577279	−	2.94393i	−0.192426	−	0.981311i
$10$		0			0
$11$	−4.99402	+	1.81767i	−1.50575	+	0.548050i	−0.957543	−	0.288291i	$-0.906913\pi$
$11$	−4.99402	+	1.81767i	−1.50575	+	0.548050i	−0.548211	+	0.836340i	$0.684691\pi$
$12$		0			0
$13$	−0.0404003	+	0.0338999i	−0.0112050	+	0.00940214i	−0.648373	−	0.761323i	$-0.724550\pi$
$13$	−0.0404003	+	0.0338999i	−0.0112050	+	0.00940214i	0.637168	+	0.770725i	$0.280106\pi$
$14$		0			0
$15$	5.93792	−	3.50429i	1.53316	−	0.904805i
$16$		0			0
$17$	−1.69081	−	2.92857i	−0.410082	−	0.710284i	0.584816	−	0.811166i	$-0.301167\pi$
$17$	−1.69081	−	2.92857i	−0.410082	−	0.710284i	−0.994898	+	0.100882i	$0.967833\pi$
$18$		0			0
$19$	1.23206	−	2.13399i	0.282653	−	0.489570i	−0.689384	−	0.724396i	$-0.742119\pi$
$19$	1.23206	−	2.13399i	0.282653	−	0.489570i	0.972037	+	0.234826i	$0.0754521\pi$
$20$		0			0
$21$	2.93506	+	3.43079i	0.640484	+	0.748660i
$22$		0			0
$23$	−0.964125	−	5.46782i	−0.201034	−	1.14012i	−0.903560	−	0.428462i	$-0.859056\pi$
$23$	−0.964125	−	5.46782i	−0.201034	−	1.14012i	0.702526	−	0.711658i	$-0.252055\pi$
$24$		0			0
$25$	8.30876	+	6.97187i	1.66175	+	1.39437i
$26$		0			0
$27$	−4.57258	−	2.46810i	−0.879994	−	0.474985i
$28$		0			0
$29$	−6.29991	−	5.28625i	−1.16986	−	0.981632i	−0.169871	−	0.985466i	$-0.554335\pi$
$29$	−6.29991	−	5.28625i	−1.16986	−	0.981632i	−0.999993	+	0.00383417i	$0.998780\pi$
$30$		0			0
$31$	−0.115728	−	0.656323i	−0.0207853	−	0.117879i	0.972650	−	0.232276i	$-0.0746174\pi$
$31$	−0.115728	−	0.656323i	−0.0207853	−	0.117879i	−0.993435	+	0.114397i	$0.963506\pi$
$32$		0			0
$33$	−3.06555	+	8.67957i	−0.533644	+	1.51092i
$34$		0			0
$35$	−5.18834	+	8.98646i	−0.876989	+	1.51899i
$36$		0			0
$37$	2.67730	+	4.63722i	0.440145	+	0.762353i	0.997700	−	0.0677866i	$-0.0215937\pi$
$37$	2.67730	+	4.63722i	0.440145	+	0.762353i	−0.557555	+	0.830140i	$0.688260\pi$
$38$		0			0
$39$	0.000872395		0.0913423i	0.000139695		0.0146265i
$40$		0			0
$41$	−5.31122	+	4.45664i	−0.829473	+	0.696010i	−0.955170	−	0.296058i	$-0.904328\pi$
$41$	−5.31122	+	4.45664i	−0.829473	+	0.696010i	0.125697	+	0.992069i	$0.459883\pi$
$42$		0			0
$43$	−0.0524095	+	0.0190755i	−0.00799237	+	0.00290898i	−0.346013	−	0.938230i	$-0.612465\pi$
$43$	−0.0524095	+	0.0190755i	−0.00799237	+	0.00290898i	0.338021	+	0.941139i	$0.390243\pi$
$44$		0			0
$45$	1.84874	−	11.7983i	0.275593	−	1.75878i
$46$		0			0
$47$	−0.0794772	+	0.450737i	−0.0115929	+	0.0657468i	−0.990055	−	0.140678i	$-0.955072\pi$
$47$	−0.0794772	+	0.450737i	−0.0115929	+	0.0657468i	0.978462	+	0.206425i	$0.0661829\pi$
$48$		0			0
$49$	0.192660	+	0.0701224i	0.0275228	+	0.0100175i
$50$		0			0
$51$	−5.77762	−	0.961949i	−0.809028	−	0.134700i
$52$		0			0
$53$	1.38667			0.190474			0.0952370	−	0.995455i	$-0.469639\pi$
$53$	1.38667			0.190474			0.0952370	+	0.995455i	$0.469639\pi$
$54$		0			0
$55$	−21.1558			−2.85264
$56$		0			0
$57$	−1.49797	−	3.99646i	−0.198411	−	0.529344i
$58$		0			0
$59$	3.99339	+	1.45348i	0.519895	+	0.189226i	0.588621	−	0.808409i	$-0.299671\pi$
$59$	3.99339	+	1.45348i	0.519895	+	0.189226i	−0.0687257	+	0.997636i	$0.521893\pi$
$60$		0			0
$61$	0.457339	−	2.59370i	0.0585563	−	0.332089i	−0.941431	−	0.337207i	$-0.890518\pi$
$61$	0.457339	−	2.59370i	0.0585563	−	0.332089i	0.999987	+	0.00511752i	$0.00162896\pi$
$62$		0			0
$63$	7.81873	−	0.149364i	0.985067	−	0.0188181i
$64$		0			0
$65$	−0.197279	+	0.0718037i	−0.0244694	+	0.00890615i
$66$		0			0
$67$	7.16941	−	6.01585i	0.875882	−	0.734953i	−0.0894458	−	0.995992i	$-0.528510\pi$
$67$	7.16941	−	6.01585i	0.875882	−	0.734953i	0.965328	+	0.261039i	$0.0840651\pi$
$68$		0			0
$69$	−8.37380	−	4.72856i	−1.00809	−	0.569252i
$70$		0			0
$71$	7.18697	+	12.4482i	0.852937	+	1.47733i	0.878546	+	0.477658i	$0.158514\pi$
$71$	7.18697	+	12.4482i	0.852937	+	1.47733i	−0.0256094	+	0.999672i	$0.508153\pi$
$72$		0			0
$73$	−7.15357	+	12.3903i	−0.837262	+	1.45018i	0.0549141	+	0.998491i	$0.482512\pi$
$73$	−7.15357	+	12.3903i	−0.837262	+	1.45018i	−0.892176	+	0.451689i	$0.850822\pi$
$74$		0			0
$75$	18.4690	−	3.43876i	2.13261	−	0.397074i
$76$		0			0
$77$	−2.40563	−	13.6430i	−0.274147	−	1.55476i
$78$		0			0
$79$	5.93415	+	4.97935i	0.667644	+	0.560220i	0.912367	−	0.409373i	$-0.134253\pi$
$79$	5.93415	+	4.97935i	0.667644	+	0.560220i	−0.244723	+	0.969593i	$0.578697\pi$
$80$		0			0
$81$	−8.33350	+	3.39894i	−0.925944	+	0.377660i
$82$		0			0
$83$	1.83808	+	1.54234i	0.201756	+	0.169293i	0.738068	−	0.674727i	$-0.235738\pi$
$83$	1.83808	+	1.54234i	0.201756	+	0.169293i	−0.536312	+	0.844020i	$0.680183\pi$
$84$		0			0
$85$	−2.33755	−	13.2569i	−0.253542	−	1.43791i
$86$		0			0
$87$	−14.0036	+	2.60735i	−1.50135	+	0.279538i
$88$		0			0
$89$	2.04047	−	3.53420i	0.216290	−	0.374625i	−0.737381	−	0.675477i	$-0.763938\pi$
$89$	2.04047	−	3.53420i	0.216290	−	0.374625i	0.953671	+	0.300852i	$0.0972711\pi$
$90$		0			0
$91$	−0.0687377	−	0.119057i	−0.00720567	−	0.0124806i
$92$		0			0
$93$	−1.00514	−	0.567588i	−0.104228	−	0.0588561i
$94$		0			0
$95$	7.51413	−	6.30511i	0.770934	−	0.646890i
$96$		0			0
$97$	−11.8711	+	4.32074i	−1.20533	+	0.438705i	−0.865082	−	0.501630i	$-0.832734\pi$
$97$	−11.8711	+	4.32074i	−1.20533	+	0.438705i	−0.340250	+	0.940335i	$0.610512\pi$
$98$		0			0
$99$	8.23406	+	13.6528i	0.827554	+	1.37215i
$100$		0			0
$101$	1.52514	−	8.64948i	0.151757	−	0.860655i	−0.809934	−	0.586520i	$-0.800497\pi$
$101$	1.52514	−	8.64948i	0.151757	−	0.860655i	0.961691	−	0.274135i	$-0.0883915\pi$
$102$		0			0
$103$	6.59095	+	2.39891i	0.649426	+	0.236372i	0.645664	−	0.763621i	$-0.276581\pi$
$103$	6.59095	+	2.39891i	0.649426	+	0.236372i	0.00376127	+	0.999993i	$0.498803\pi$
$104$		0			0
$105$	6.30812	+	16.8295i	0.615609	+	1.64240i
$106$		0			0
$107$	−9.10320			−0.880040			−0.440020	−	0.897988i	$-0.645029\pi$
$107$	−9.10320			−0.880040			−0.440020	+	0.897988i	$0.645029\pi$
$108$		0			0
$109$	14.5496			1.39360			0.696801	−	0.717264i	$-0.254606\pi$
$109$	14.5496			1.39360			0.696801	+	0.717264i	$0.254606\pi$
$110$		0			0
$111$	9.14850	+	1.52319i	0.868337	+	0.144574i
$112$		0			0
$113$	14.0868	+	5.12716i	1.32517	+	0.482323i	0.905112	−	0.425174i	$-0.139787\pi$
$113$	14.0868	+	5.12716i	1.32517	+	0.482323i	0.420059	+	0.907497i	$0.362009\pi$
$114$		0			0
$115$	3.83793	−	21.7660i	0.357889	−	2.02969i
$116$		0			0
$117$	0.123121	+	0.0993662i	0.0113826	+	0.00918641i
$118$		0			0
$119$	8.28334	−	3.01489i	0.759332	−	0.276374i
$120$		0			0
$121$	13.2098	−	11.0843i	1.20089	−	1.00767i
$122$		0			0
$123$	0.114689	+	12.0083i	0.0103412	+	1.08275i
$124$		0			0
$125$	11.6363	+	20.1547i	1.04079	+	1.80269i
$126$		0			0
$127$	−1.00053	+	1.73296i	−0.0887824	+	0.153776i	−0.906997	−	0.421138i	$-0.861631\pi$
$127$	−1.00053	+	1.73296i	−0.0887824	+	0.153776i	0.818214	+	0.574913i	$0.194964\pi$
$128$		0			0
$129$	−0.0321713	+	0.0910872i	−0.00283252	+	0.00801978i
$130$		0			0
$131$	0.156341	+	0.886652i	0.0136595	+	0.0774671i	0.990876	−	0.134780i	$-0.0430328\pi$
$131$	0.156341	+	0.886652i	0.0136595	+	0.0774671i	−0.977216	+	0.212247i	$0.931922\pi$
$132$		0			0
$133$	4.92049	+	4.12878i	0.426661	+	0.358011i
$134$		0			0
$135$	−13.7442	−	15.4579i	−1.18292	−	1.33040i
$136$		0			0
$137$	−10.5185	−	8.82610i	−0.898659	−	0.754065i	0.0712687	−	0.997457i	$-0.477295\pi$
$137$	−10.5185	−	8.82610i	−0.898659	−	0.754065i	−0.969928	+	0.243393i	$0.921740\pi$
$138$		0			0
$139$	0.00441448	+	0.0250358i	0.000374432	+	0.00212351i	0.984994	−	0.172586i	$-0.0552124\pi$
$139$	0.00441448	+	0.0250358i	0.000374432	+	0.00212351i	−0.984620	+	0.174710i	$0.944101\pi$
$140$		0			0
$141$	0.515342	+	0.602383i	0.0433996	+	0.0507298i
$142$		0			0
$143$	0.140141	−	0.242731i	0.0117192	−	0.0202982i
$144$		0			0
$145$	−16.3687	−	28.3514i	−1.35935	−	2.35446i
$146$		0			0
$147$	0.305827	−	0.180485i	0.0252241	−	0.0148862i
$148$		0			0
$149$	9.35550	−	7.85019i	0.766432	−	0.643113i	−0.173360	−	0.984858i	$-0.555463\pi$
$149$	9.35550	−	7.85019i	0.766432	−	0.643113i	0.939793	+	0.341746i	$0.111018\pi$
$150$		0			0
$151$	2.76321	−	1.00573i	0.224867	−	0.0818448i	−0.227130	−	0.973864i	$-0.572934\pi$
$151$	2.76321	−	1.00573i	0.224867	−	0.0818448i	0.451996	+	0.892020i	$0.350712\pi$
$152$		0			0
$153$	−7.64546	+	6.66825i	−0.618099	+	0.539096i
$154$		0			0
$155$	0.460682	−	2.61265i	0.0370028	−	0.209853i
$156$		0			0
$157$	−11.3273	−	4.12280i	−0.904016	−	0.329035i	−0.152155	−	0.988357i	$-0.548621\pi$
$157$	−11.3273	−	4.12280i	−0.904016	−	0.329035i	−0.751861	+	0.659322i	$0.770844\pi$
$158$		0			0
$159$	1.52620	−	1.85453i	0.121035	−	0.147074i
$160$		0			0
$161$	14.4729			1.14063
$162$		0			0
$163$	−10.3746			−0.812605			−0.406302	−	0.913739i	$-0.633182\pi$
$163$	−10.3746			−0.812605			−0.406302	+	0.913739i	$0.633182\pi$
$164$		0			0
$165$	−23.2844	+	28.2937i	−1.81269	+	2.20266i
$166$		0			0
$167$	−4.57455	−	1.66500i	−0.353989	−	0.128842i	0.158904	−	0.987294i	$-0.449204\pi$
$167$	−4.57455	−	1.66500i	−0.353989	−	0.128842i	−0.512893	+	0.858453i	$0.671426\pi$
$168$		0			0
$169$	−2.25694	+	12.7998i	−0.173611	+	0.984597i
$170$		0			0
$171$	−6.99355	−	2.39519i	−0.534810	−	0.183165i
$172$		0			0
$173$	−14.4101	+	5.24484i	−1.09558	+	0.398758i	−0.825685	−	0.564132i	$-0.809211\pi$
$173$	−14.4101	+	5.24484i	−1.09558	+	0.398758i	−0.269894	+	0.962890i	$0.586989\pi$
$174$		0			0
$175$	−21.6586	+	18.1737i	−1.63723	+	1.37380i
$176$		0			0
$177$	6.33908	−	3.74104i	0.476474	−	0.281194i
$178$		0			0
$179$	−8.10111	−	14.0315i	−0.605505	−	1.04877i	−0.991971	−	0.126462i	$-0.959638\pi$
$179$	−8.10111	−	14.0315i	−0.605505	−	1.04877i	0.386466	−	0.922304i	$-0.373696\pi$
$180$		0			0
$181$	4.93187	−	8.54226i	0.366583	−	0.634941i	−0.622446	−	0.782663i	$-0.713861\pi$
$181$	4.93187	−	8.54226i	0.366583	−	0.634941i	0.989029	+	0.147722i	$0.0471941\pi$
$182$		0			0
$183$	−2.96546	−	3.46632i	−0.219213	−	0.256238i
$184$		0			0
$185$	3.70136	+	20.9914i	0.272129	+	1.54332i
$186$		0			0
$187$	13.7672	+	11.5520i	1.00675	+	0.844767i
$188$		0			0
$189$	8.40567	−	10.6212i	0.611423	−	0.772576i
$190$		0			0
$191$	10.4067	+	8.73226i	0.753003	+	0.631844i	0.936295	−	0.351214i	$-0.114231\pi$
$191$	10.4067	+	8.73226i	0.753003	+	0.631844i	−0.183293	+	0.983058i	$0.558676\pi$
$192$		0			0
$193$	−0.599757	−	3.40139i	−0.0431715	−	0.244838i	0.955584	−	0.294720i	$-0.0952264\pi$
$193$	−0.599757	−	3.40139i	−0.0431715	−	0.244838i	−0.998755	+	0.0498825i	$0.984115\pi$
$194$		0			0
$195$	−0.121099	+	0.342869i	−0.00867205	+	0.0245534i
$196$		0			0
$197$	−0.413665	+	0.716488i	−0.0294724	+	0.0510477i	−0.880385	−	0.474259i	$-0.842716\pi$
$197$	−0.413665	+	0.716488i	−0.0294724	+	0.0510477i	0.850913	+	0.525307i	$0.176049\pi$
$198$		0			0
$199$	1.28337	+	2.22286i	0.0909755	+	0.157574i	0.907922	−	0.419139i	$-0.137668\pi$
$199$	1.28337	+	2.22286i	0.0909755	+	0.157574i	−0.816946	+	0.576714i	$0.804335\pi$
$200$		0			0
$201$	−0.154814	−	16.2095i	−0.0109198	−	1.14333i
$202$		0			0
$203$	16.4221	−	13.7798i	1.15260	−	0.967150i
$204$		0			0
$205$	−25.9352	+	9.43965i	−1.81139	+	0.659294i
$206$		0			0
$207$	−15.5403	+	5.99478i	−1.08013	+	0.416666i
$208$		0			0
$209$	−2.27403	+	12.8966i	−0.157298	+	0.892080i
$210$		0			0
$211$	−16.6574	−	6.06281i	−1.14674	−	0.417381i	−0.302400	−	0.953181i	$-0.597788\pi$
$211$	−16.6574	−	6.06281i	−1.14674	−	0.417381i	−0.844345	+	0.535801i	$0.820010\pi$
$212$		0			0
$213$	24.5583	+	4.08886i	1.68271	+	0.280164i
$214$		0			0
$215$	−0.222018			−0.0151415
$216$		0			0
$217$	1.73724			0.117932
$218$		0			0
$219$	8.69750	+	23.2042i	0.587722	+	1.56800i
$220$		0			0
$221$	0.167588	+	0.0609970i	0.0112732	+	0.00410310i
$222$		0			0
$223$	3.62276	−	20.5457i	0.242598	−	1.37584i	−0.583407	−	0.812180i	$-0.698281\pi$
$223$	3.62276	−	20.5457i	0.242598	−	1.37584i	0.826005	−	0.563663i	$-0.190608\pi$
$224$		0			0
$225$	15.7283	−	28.4851i	1.04855	−	1.89901i
$226$		0			0
$227$	−3.39434	+	1.23544i	−0.225290	+	0.0819989i	−0.452199	−	0.891917i	$-0.649360\pi$
$227$	−3.39434	+	1.23544i	−0.225290	+	0.0819989i	0.226909	+	0.973916i	$0.427138\pi$
$228$		0			0
$229$	−3.11755	+	2.61593i	−0.206013	+	0.172866i	−0.739957	−	0.672655i	$-0.765154\pi$
$229$	−3.11755	+	2.61593i	−0.206013	+	0.172866i	0.533943	+	0.845520i	$0.320710\pi$
$230$		0			0
$231$	−20.8938	−	11.7984i	−1.37471	−	0.776281i
$232$		0			0
$233$	−12.2458	−	21.2104i	−0.802252	−	1.38954i	−0.918131	−	0.396277i	$-0.870302\pi$
$233$	−12.2458	−	21.2104i	−0.802252	−	1.38954i	0.115879	−	0.993263i	$-0.463031\pi$
$234$		0			0
$235$	−0.910974	+	1.57785i	−0.0594254	+	0.102928i
$236$		0			0
$237$	13.1906	−	2.45598i	0.856823	−	0.159533i
$238$		0			0
$239$	3.92957	+	22.2857i	0.254183	+	1.44154i	0.798161	+	0.602444i	$0.205806\pi$
$239$	3.92957	+	22.2857i	0.254183	+	1.44154i	−0.543978	+	0.839100i	$0.683082\pi$
$240$		0			0
$241$	8.75006	+	7.34218i	0.563641	+	0.472951i	0.879529	−	0.475845i	$-0.157858\pi$
$241$	8.75006	+	7.34218i	0.563641	+	0.472951i	−0.315888	+	0.948797i	$0.602302\pi$
$242$		0			0
$243$	−4.62626	+	14.8862i	−0.296774	+	0.954948i
$244$		0			0
$245$	0.625206	+	0.524610i	0.0399429	+	0.0335161i
$246$		0			0
$247$	0.0225664	+	0.127980i	0.00143586	+	0.00814319i
$248$		0			0
$249$	4.08575	−	0.760731i	0.258924	−	0.0482094i
$250$		0			0
$251$	1.27111	−	2.20163i	0.0802317	−	0.138965i	−0.823118	−	0.567871i	$-0.807767\pi$
$251$	1.27111	−	2.20163i	0.0802317	−	0.138965i	0.903349	+	0.428905i	$0.141101\pi$
$252$		0			0
$253$	14.7536	+	25.5540i	0.927550	+	1.60656i
$254$		0			0
$255$	−20.3025	−	11.4645i	−1.27139	−	0.717937i
$256$		0			0
$257$	−13.7955	+	11.5758i	−0.860539	+	0.722078i	−0.962084	−	0.272753i	$-0.912066\pi$
$257$	−13.7955	+	11.5758i	−0.860539	+	0.722078i	0.101545	+	0.994831i	$0.467621\pi$
$258$		0			0
$259$	−13.1162	+	4.77389i	−0.814998	+	0.296635i
$260$		0			0
$261$	−11.9256	+	21.5982i	−0.738174	+	1.33689i
$262$		0			0
$263$	0.130638	−	0.740886i	0.00805550	−	0.0456850i	−0.980515	−	0.196444i	$-0.937061\pi$
$263$	0.130638	−	0.740886i	0.00805550	−	0.0456850i	0.988571	+	0.150759i	$0.0481717\pi$
$264$		0			0
$265$	5.18709	+	1.88795i	0.318640	+	0.115976i
$266$		0			0
$267$	−2.48086	−	6.61874i	−0.151826	−	0.405060i
$268$		0			0
$269$	0.748703			0.0456493			0.0228246	−	0.999739i	$-0.492734\pi$
$269$	0.748703			0.0456493			0.0228246	+	0.999739i	$0.492734\pi$
$270$		0			0
$271$	28.7361			1.74559			0.872795	−	0.488086i	$-0.162305\pi$
$271$	28.7361			1.74559			0.872795	+	0.488086i	$0.162305\pi$
$272$		0			0
$273$	−0.234881	−	0.0391067i	−0.0142156	−	0.00236684i
$274$		0			0
$275$	−54.1667	−	19.7151i	−3.26638	−	1.18886i
$276$		0			0
$277$	2.02567	−	11.4881i	0.121711	−	0.690255i	−0.861497	−	0.507763i	$-0.830473\pi$
$277$	2.02567	−	11.4881i	0.121711	−	0.690255i	0.983207	−	0.182492i	$-0.0584163\pi$
$278$		0			0
$279$	−1.86537	+	0.719576i	−0.111677	+	0.0430799i
$280$		0			0
$281$	−7.59722	+	2.76516i	−0.453212	+	0.164956i	−0.558533	−	0.829483i	$-0.688635\pi$
$281$	−7.59722	+	2.76516i	−0.453212	+	0.164956i	0.105320	+	0.994438i	$0.466413\pi$
$282$		0			0
$283$	24.9217	−	20.9118i	1.48144	−	1.24308i	0.576813	−	0.816876i	$-0.304296\pi$
$283$	24.9217	−	20.9118i	1.48144	−	1.24308i	0.904628	−	0.426201i	$-0.140148\pi$
$284$		0			0
$285$	−0.162258	−	16.9889i	−0.00961136	−	1.00634i
$286$		0			0
$287$	−9.03658	−	15.6518i	−0.533412	−	0.923897i
$288$		0			0
$289$	2.78230	−	4.81909i	0.163665	−	0.283476i
$290$		0			0
$291$	−7.28704	+	20.6320i	−0.427174	+	1.20947i
$292$		0			0
$293$	0.929693	+	5.27255i	0.0543132	+	0.308026i	0.999847	−	0.0174987i	$-0.00557030\pi$
$293$	0.929693	+	5.27255i	0.0543132	+	0.308026i	−0.945534	+	0.325524i	$0.894459\pi$
$294$		0			0
$295$	12.9591	+	10.8740i	0.754506	+	0.633106i
$296$		0			0
$297$	27.3218	+	4.01425i	1.58537	+	0.232930i
$298$		0			0
$299$	0.224310	+	0.188218i	0.0129722	+	0.0108849i
$300$		0			0
$301$	−0.0252457	−	0.143176i	−0.00145514	−	0.00825251i
$302$		0			0
$303$	−9.88922	−	11.5595i	−0.568121	−	0.664076i
$304$		0			0
$305$	5.24206	−	9.07952i	0.300160	−	0.519892i
$306$		0			0
$307$	−3.29583	−	5.70854i	−0.188103	−	0.325804i	0.756515	−	0.653977i	$-0.226900\pi$
$307$	−3.29583	−	5.70854i	−0.188103	−	0.325804i	−0.944618	+	0.328173i	$0.893567\pi$
$308$		0			0
$309$	10.4624	−	6.17445i	0.595186	−	0.351252i
$310$		0			0
$311$	20.3382	−	17.0658i	1.15327	−	0.967712i	0.153483	−	0.988151i	$-0.450951\pi$
$311$	20.3382	−	17.0658i	1.15327	−	0.967712i	0.999791	+	0.0204396i	$0.00650659\pi$
$312$		0			0
$313$	17.9416	−	6.53022i	1.01412	−	0.369110i	0.219107	−	0.975701i	$-0.429686\pi$
$313$	17.9416	−	6.53022i	1.01412	−	0.369110i	0.795014	+	0.606591i	$0.207463\pi$
$314$		0			0
$315$	29.4507	+	10.0864i	1.65936	+	0.568306i
$316$		0			0
$317$	−1.36707	+	7.75306i	−0.0767825	+	0.435455i	0.922047	+	0.387079i	$0.126516\pi$
$317$	−1.36707	+	7.75306i	−0.0767825	+	0.435455i	−0.998829	+	0.0483765i	$0.984595\pi$
$318$		0			0
$319$	41.0706	+	14.9485i	2.29951	+	0.836953i
$320$		0			0
$321$	−10.0192	+	12.1746i	−0.559214	+	0.679521i
$322$		0			0
$323$	−8.33271			−0.463645
$324$		0			0
$325$	−0.572022			−0.0317301
$326$		0			0
$327$	16.0136	−	19.4587i	0.885554	−	1.07607i
$328$		0			0
$329$	−1.12112	−	0.408054i	−0.0618093	−	0.0224967i
$330$		0			0
$331$	1.21881	−	6.91220i	0.0669917	−	0.379929i	−0.932817	−	0.360351i	$-0.882657\pi$
$331$	1.21881	−	6.91220i	0.0669917	−	0.379929i	0.999808	−	0.0195775i	$-0.00623212\pi$
$332$		0			0
$333$	12.1061	−	10.5588i	0.663411	−	0.578616i
$334$		0			0
$335$	35.0090	−	12.7422i	1.91274	−	0.696182i
$336$		0			0
$337$	−27.0600	+	22.7060i	−1.47405	+	1.23688i	−0.561783	+	0.827284i	$0.689885\pi$
$337$	−27.0600	+	22.7060i	−1.47405	+	1.23688i	−0.912269	+	0.409592i	$0.865671\pi$
$338$		0			0
$339$	22.3612	−	13.1966i	1.21449	−	0.716740i
$340$		0			0
$341$	1.77093	+	3.06734i	0.0959011	+	0.166106i
$342$		0			0
$343$	−9.39073	+	16.2652i	−0.507052	+	0.878240i
$344$		0			0
$345$	−24.8857	−	29.0889i	−1.33980	−	1.56609i
$346$		0			0
$347$	−0.838421	−	4.75492i	−0.0450088	−	0.255258i	0.953998	−	0.299813i	$-0.0969241\pi$
$347$	−0.838421	−	4.75492i	−0.0450088	−	0.255258i	−0.999007	+	0.0445550i	$0.985813\pi$
$348$		0			0
$349$	−14.1473	−	11.8710i	−0.757288	−	0.635440i	0.180131	−	0.983643i	$-0.442348\pi$
$349$	−14.1473	−	11.8710i	−0.757288	−	0.635440i	−0.937419	+	0.348203i	$0.886792\pi$
$350$		0			0
$351$	0.268402	−	0.0552982i	0.0143262	−	0.00295160i
$352$		0			0
$353$	14.8590	+	12.4682i	0.790867	+	0.663616i	0.945960	−	0.324284i	$-0.105123\pi$
$353$	14.8590	+	12.4682i	0.790867	+	0.663616i	−0.155093	+	0.987900i	$0.549568\pi$
$354$		0			0
$355$	9.93597	+	56.3497i	0.527347	+	2.99073i
$356$		0			0
$357$	5.08468	−	14.3964i	0.269110	−	0.761937i
$358$		0			0
$359$	−9.99948	+	17.3196i	−0.527752	+	0.914094i	0.471724	+	0.881746i	$0.343632\pi$
$359$	−9.99948	+	17.3196i	−0.527752	+	0.914094i	−0.999477	+	0.0323477i	$0.989702\pi$
$360$		0			0
$361$	6.46407	+	11.1961i	0.340214	+	0.589268i
$362$		0			0
$363$	−0.285249	−	29.8664i	−0.0149717	−	1.56758i
$364$		0			0
$365$	−43.6285	+	36.6087i	−2.28362	+	1.91619i
$366$		0			0
$367$	−34.6495	+	12.6114i	−1.80869	+	0.658309i	−0.811421	+	0.584462i	$0.801305\pi$
$367$	−34.6495	+	12.6114i	−1.80869	+	0.658309i	−0.997270	+	0.0738470i	$0.976472\pi$
$368$		0			0
$369$	16.1861	+	13.0632i	0.842615	+	0.680041i
$370$		0			0
$371$	−0.627679	+	3.55975i	−0.0325875	+	0.184813i
$372$		0			0
$373$	−8.12357	−	2.95674i	−0.420623	−	0.153094i	0.123033	−	0.992403i	$-0.460738\pi$
$373$	−8.12357	−	2.95674i	−0.420623	−	0.153094i	−0.543655	+	0.839309i	$0.682960\pi$
$374$		0			0
$375$	39.7621	+	6.62022i	2.05331	+	0.341867i
$376$		0			0
$377$	0.433722			0.0223378
$378$		0			0
$379$	5.55752			0.285471			0.142735	−	0.989761i	$-0.454410\pi$
$379$	5.55752			0.285471			0.142735	+	0.989761i	$0.454410\pi$
$380$		0			0
$381$	1.21647	+	3.24544i	0.0623215	+	0.166269i
$382$		0			0
$383$	−6.70080	−	2.43889i	−0.342395	−	0.124622i	0.165099	−	0.986277i	$-0.447206\pi$
$383$	−6.70080	−	2.43889i	−0.342395	−	0.124622i	−0.507494	+	0.861656i	$0.669428\pi$
$384$		0			0
$385$	9.57619	−	54.3093i	0.488048	−	2.76786i
$386$		0			0
$387$	0.0864118	+	0.143278i	0.00439256	+	0.00728324i
$388$		0			0
$389$	28.6659	−	10.4335i	1.45342	−	0.529002i	0.509876	−	0.860248i	$-0.329691\pi$
$389$	28.6659	−	10.4335i	1.45342	−	0.529002i	0.943544	+	0.331246i	$0.107469\pi$
$390$		0			0
$391$	−14.3828	+	12.0686i	−0.727368	+	0.610334i
$392$		0			0
$393$	1.35788	+	0.766775i	0.0684960	+	0.0386787i
$394$		0			0
$395$	15.4184	+	26.7054i	0.775783	+	1.34370i
$396$		0			0
$397$	3.04665	−	5.27696i	0.152907	−	0.264843i	−0.779388	−	0.626542i	$-0.784470\pi$
$397$	3.04665	−	5.27696i	0.152907	−	0.264843i	0.932295	+	0.361699i	$0.117803\pi$
$398$		0			0
$399$	10.9374	−	2.03645i	0.547556	−	0.101950i
$400$		0			0
$401$	−2.45733	−	13.9362i	−0.122713	−	0.695941i	−0.982640	−	0.185523i	$-0.940602\pi$
$401$	−2.45733	−	13.9362i	−0.122713	−	0.695941i	0.859927	−	0.510418i	$-0.170509\pi$
$402$		0			0
$403$	0.0269247	+	0.0225925i	0.00134122	+	0.00112541i
$404$		0			0
$405$	−35.8005	+	1.36832i	−1.77894	+	0.0679926i
$406$		0			0
$407$	−21.7994	−	18.2919i	−1.08056	−	0.906695i
$408$		0			0
$409$	2.50869	+	14.2275i	0.124047	+	0.703503i	0.981870	+	0.189558i	$0.0607054\pi$
$409$	2.50869	+	14.2275i	0.124047	+	0.703503i	−0.857823	+	0.513945i	$0.828184\pi$
$410$		0			0
$411$	−23.3809	+	4.35333i	−1.15330	+	0.214734i
$412$		0			0
$413$	−5.53885	+	9.59358i	−0.272549	+	0.472069i
$414$		0			0
$415$	4.77579	+	8.27192i	0.234435	+	0.406053i
$416$		0			0
$417$	0.0383415	+	0.0216509i	0.00187759	+	0.00106025i
$418$		0			0
$419$	−17.6121	+	14.7783i	−0.860405	+	0.721966i	−0.962055	−	0.272855i	$-0.912032\pi$
$419$	−17.6121	+	14.7783i	−0.860405	+	0.721966i	0.101650	+	0.994820i	$0.467588\pi$
$420$		0			0
$421$	−29.3391	+	10.6785i	−1.42990	+	0.520441i	−0.936902	−	0.349591i	$-0.886321\pi$
$421$	−29.3391	+	10.6785i	−1.42990	+	0.520441i	−0.492996	+	0.870031i	$0.664098\pi$
$422$		0			0
$423$	1.37282	−	0.0262256i	0.0667489	−	0.00127513i
$424$		0			0
$425$	6.36910	−	36.1210i	0.308947	−	1.75212i
$426$		0			0
$427$	6.45131	+	2.34809i	0.312201	+	0.113632i
$428$		0			0
$429$	−0.170387	−	0.454579i	−0.00822638	−	0.0219473i
$430$		0			0
$431$	11.9923			0.577649			0.288825	−	0.957382i	$-0.406736\pi$
$431$	11.9923			0.577649			0.288825	+	0.957382i	$0.406736\pi$
$432$		0			0
$433$	−6.69798			−0.321885			−0.160942	−	0.986964i	$-0.551453\pi$
$433$	−6.69798			−0.321885			−0.160942	+	0.986964i	$0.551453\pi$
$434$		0			0
$435$	−55.9329	−	9.31259i	−2.68178	−	0.446505i
$436$		0			0
$437$	−12.8561	−	4.67924i	−0.614991	−	0.223838i
$438$		0			0
$439$	−1.65291	+	9.37410i	−0.0788889	+	0.447401i	0.919620	+	0.392810i	$0.128497\pi$
$439$	−1.65291	+	9.37410i	−0.0788889	+	0.447401i	−0.998509	+	0.0545918i	$0.982614\pi$
$440$		0			0
$441$	0.0952174	−	0.607658i	0.00453416	−	0.0289361i
$442$		0			0
$443$	−14.1355	+	5.14490i	−0.671598	+	0.244442i	−0.655236	−	0.755424i	$-0.727431\pi$
$443$	−14.1355	+	5.14490i	−0.671598	+	0.244442i	−0.0163624	+	0.999866i	$0.505209\pi$
$444$		0			0
$445$	12.4445	−	10.4422i	0.589928	−	0.495008i
$446$		0			0
$447$	−0.202020	−	21.1521i	−0.00955523	−	1.00046i
$448$		0			0
$449$	−11.1437	−	19.3014i	−0.525902	−	0.910889i	−0.999545	−	0.0301722i	$-0.990394\pi$
$449$	−11.1437	−	19.3014i	−0.525902	−	0.910889i	0.473642	−	0.880717i	$-0.342939\pi$
$450$		0			0
$451$	18.4236	−	31.9106i	0.867534	−	1.50261i
$452$		0			0
$453$	1.69618	−	4.80243i	0.0796935	−	0.225638i
$454$		0			0
$455$	−0.0950297	−	0.538940i	−0.00445506	−	0.0252659i
$456$		0			0
$457$	−14.9820	−	12.5714i	−0.700830	−	0.588066i	0.221179	−	0.975233i	$-0.429009\pi$
$457$	−14.9820	−	12.5714i	−0.700830	−	0.588066i	−0.922010	+	0.387167i	$0.873454\pi$
$458$		0			0
$459$	0.503382	+	17.5642i	0.0234959	+	0.819828i
$460$		0			0
$461$	30.9993	+	26.0115i	1.44378	+	1.21148i	0.936966	+	0.349420i	$0.113621\pi$
$461$	30.9993	+	26.0115i	1.44378	+	1.21148i	0.506814	+	0.862055i	$0.330823\pi$
$462$		0			0
$463$	−2.40694	−	13.6505i	−0.111860	−	0.634390i	−0.988257	−	0.152801i	$-0.951171\pi$
$463$	−2.40694	−	13.6505i	−0.111860	−	0.634390i	0.876397	−	0.481590i	$-0.159940\pi$
$464$		0			0
$465$	−2.98713	−	3.49165i	−0.138525	−	0.161921i
$466$		0			0
$467$	15.8137	−	27.3901i	0.731769	−	1.26746i	−0.224357	−	0.974507i	$-0.572028\pi$
$467$	15.8137	−	27.3901i	0.731769	−	1.26746i	0.956126	−	0.292955i	$-0.0946385\pi$
$468$		0			0
$469$	12.1981	+	21.1278i	0.563257	+	0.975590i
$470$		0			0
$471$	−17.9809	+	10.6115i	−0.828514	+	0.488952i
$472$		0			0
$473$	0.227061	−	0.190527i	0.0104403	−	0.00876043i
$474$		0			0
$475$	25.1147	−	9.14102i	1.15234	−	0.419419i
$476$		0			0
$477$	−0.800496	−	4.08227i	−0.0366522	−	0.186914i
$478$		0			0
$479$	−6.33650	+	35.9361i	−0.289522	+	1.64196i	0.399147	+	0.916887i	$0.369306\pi$
$479$	−6.33650	+	35.9361i	−0.289522	+	1.64196i	−0.688669	+	0.725076i	$0.741805\pi$
$480$		0			0
$481$	−0.265365	−	0.0965849i	−0.0120996	−	0.00440389i
$482$		0			0
$483$	15.9292	−	19.3561i	0.724803	−	0.880734i
$484$		0			0
$485$	−50.2887			−2.28349
$486$		0			0
$487$	0.637186			0.0288737			0.0144368	−	0.999896i	$-0.495404\pi$
$487$	0.637186			0.0288737			0.0144368	+	0.999896i	$0.495404\pi$
$488$		0			0
$489$	−11.4185	+	13.8751i	−0.516364	+	0.627452i
$490$		0			0
$491$	16.6019	+	6.04262i	0.749235	+	0.272699i	0.688284	−	0.725441i	$-0.258364\pi$
$491$	16.6019	+	6.04262i	0.749235	+	0.272699i	0.0609515	+	0.998141i	$0.480587\pi$
$492$		0			0
$493$	−4.82921	+	27.3878i	−0.217497	+	1.23349i
$494$		0			0
$495$	12.2128	+	62.2812i	0.548923	+	2.79933i
$496$		0			0
$497$	−35.2092	+	12.8151i	−1.57935	+	0.574835i
$498$		0			0
$499$	−7.39153	+	6.20223i	−0.330891	+	0.277650i	−0.793063	−	0.609140i	$-0.791515\pi$
$499$	−7.39153	+	6.20223i	−0.330891	+	0.277650i	0.462172	+	0.886790i	$0.347070\pi$
$500$		0			0
$501$	−7.26160	+	4.28547i	−0.324424	+	0.191461i
$502$		0			0
$503$	−12.0802	−	20.9235i	−0.538628	−	0.932931i	−0.998978	−	0.0451934i	$-0.985610\pi$
$503$	−12.0802	−	20.9235i	−0.538628	−	0.932931i	0.460351	−	0.887737i	$-0.347724\pi$
$504$		0			0
$505$	17.4813	−	30.2784i	0.777906	−	1.34737i
$506$		0			0
$507$	14.6344	+	17.1061i	0.649935	+	0.759708i
$508$		0			0
$509$	−3.31124	−	18.7790i	−0.146768	−	0.832362i	−0.965931	−	0.258801i	$-0.916673\pi$
$509$	−3.31124	−	18.7790i	−0.146768	−	0.832362i	0.819163	−	0.573561i	$-0.194439\pi$
$510$		0			0
$511$	−28.5694	−	23.9725i	−1.26383	−	1.06048i
$512$		0			0
$513$	−10.9006	+	6.71699i	−0.481272	+	0.296562i
$514$		0			0
$515$	21.3885	+	17.9471i	0.942490	+	0.790843i
$516$		0			0
$517$	−0.422383	−	2.39546i	−0.0185764	−	0.105352i
$518$		0			0
$519$	−8.84555	+	25.0446i	−0.388277	+	1.09934i
$520$		0			0
$521$	14.4319	−	24.9968i	0.632273	−	1.09513i	−0.354813	−	0.934937i	$-0.615456\pi$
$521$	14.4319	−	24.9968i	0.632273	−	1.09513i	0.987086	−	0.160191i	$-0.0512111\pi$
$522$		0			0
$523$	−7.76804	−	13.4546i	−0.339673	−	0.588330i	0.644698	−	0.764437i	$-0.276983\pi$
$523$	−7.76804	−	13.4546i	−0.339673	−	0.588330i	−0.984371	+	0.176107i	$0.943650\pi$
$524$		0			0
$525$	0.467690	+	48.9685i	0.0204117	+	2.13716i
$526$		0			0
$527$	−1.72642	+	1.44864i	−0.0752040	+	0.0631036i
$528$		0			0
$529$	−7.35461	+	2.67686i	−0.319766	+	0.116385i
$530$		0			0
$531$	1.97364	−	12.5953i	0.0856485	−	0.546591i
$532$		0			0
$533$	0.0634953	−	0.360100i	0.00275028	−	0.0155976i
$534$		0			0
$535$	−34.0521	−	12.3940i	−1.47220	−	0.535837i
$536$		0			0
$537$	−27.6820	−	4.60894i	−1.19457	−	0.198890i
$538$		0			0
$539$	−1.08961			−0.0469327
$540$		0			0
$541$	−6.78149			−0.291559			−0.145779	−	0.989317i	$-0.546569\pi$
$541$	−6.78149			−0.291559			−0.145779	+	0.989317i	$0.546569\pi$
$542$		0			0
$543$	−5.99631	−	15.9977i	−0.257326	−	0.686525i
$544$		0			0
$545$	54.4255	+	19.8092i	2.33133	+	0.848535i
$546$		0			0
$547$	1.14447	−	6.49059i	0.0489339	−	0.277518i	−0.950516	−	0.310675i	$-0.899445\pi$
$547$	1.14447	−	6.49059i	0.0489339	−	0.277518i	0.999450	+	0.0331570i	$0.0105561\pi$
$548$		0			0
$549$	−7.89969	+	0.150911i	−0.337151	+	0.00644073i
$550$		0			0
$551$	−19.0426	+	6.93095i	−0.811243	+	0.295268i
$552$		0			0
$553$	−15.4687	+	12.9797i	−0.657794	+	0.551955i
$554$		0			0
$555$	32.1477	+	18.1534i	1.36460	+	0.770567i
$556$		0			0
$557$	0.421123	+	0.729407i	0.0178436	+	0.0309060i	0.874809	−	0.484467i	$-0.160987\pi$
$557$	0.421123	+	0.729407i	0.0178436	+	0.0309060i	−0.856966	+	0.515373i	$0.827653\pi$
$558$		0			0
$559$	0.00147070	−	0.00254733i	6.22041e−5	−	0.000107741i
$560$		0			0
$561$	30.6020	−	5.69784i	1.29202	−	0.240563i
$562$		0			0
$563$	7.13172	+	40.4460i	0.300566	+	1.70460i	0.643674	+	0.765300i	$0.277409\pi$
$563$	7.13172	+	40.4460i	0.300566	+	1.70460i	−0.343108	+	0.939296i	$0.611480\pi$
$564$		0			0
$565$	45.7134	+	38.3581i	1.92318	+	1.61374i
$566$		0			0
$567$	−4.95330	−	22.9316i	−0.208019	−	0.963036i
$568$		0			0
$569$	−13.5383	−	11.3600i	−0.567555	−	0.476235i	0.313278	−	0.949661i	$-0.398573\pi$
$569$	−13.5383	−	11.3600i	−0.567555	−	0.476235i	−0.880834	+	0.473426i	$0.843017\pi$
$570$		0			0
$571$	−7.49724	−	42.5189i	−0.313750	−	1.77936i	−0.579147	−	0.815223i	$-0.696614\pi$
$571$	−7.49724	−	42.5189i	−0.313750	−	1.77936i	0.265397	−	0.964139i	$-0.414497\pi$
$572$		0			0
$573$	23.1323	−	4.30704i	0.966367	−	0.179929i
$574$		0			0
$575$	30.1103	−	52.1526i	1.25569	−	2.17491i
$576$		0			0
$577$	8.83839	+	15.3085i	0.367947	+	0.637303i	0.989244	−	0.146272i	$-0.0467275\pi$
$577$	8.83839	+	15.3085i	0.367947	+	0.637303i	−0.621297	+	0.783575i	$0.713394\pi$
$578$		0			0
$579$	−5.20913	−	2.94152i	−0.216484	−	0.122245i
$580$		0			0
$581$	−4.79137	+	4.02043i	−0.198779	+	0.166796i
$582$		0			0
$583$	−6.92507	+	2.52052i	−0.286807	+	0.104389i
$584$		0			0
$585$	0.325270	+	0.539326i	0.0134483	+	0.0222984i
$586$		0			0
$587$	2.91945	−	16.5570i	0.120499	−	0.683381i	−0.863381	−	0.504552i	$-0.831658\pi$
$587$	2.91945	−	16.5570i	0.120499	−	0.683381i	0.983880	−	0.178830i	$-0.0572311\pi$
$588$		0			0
$589$	−1.54317	−	0.561667i	−0.0635851	−	0.0231431i
$590$		0			0
$591$	0.502945	+	1.34182i	0.0206884	+	0.0551949i
$592$		0			0
$593$	30.6747			1.25966			0.629829	−	0.776734i	$-0.283125\pi$
$593$	30.6747			1.25966			0.629829	+	0.776734i	$0.283125\pi$
$594$		0			0
$595$	35.0900			1.43855
$596$		0			0
$597$	4.38535	+	0.730142i	0.179480	+	0.0298827i
$598$		0			0
$599$	10.8656	+	3.95476i	0.443957	+	0.161587i	0.554319	−	0.832304i	$-0.312979\pi$
$599$	10.8656	+	3.95476i	0.443957	+	0.161587i	−0.110362	+	0.993891i	$0.535201\pi$
$600$		0			0
$601$	5.36971	−	30.4531i	0.219035	−	1.24221i	−0.654731	−	0.755862i	$-0.727218\pi$
$601$	5.36971	−	30.4531i	0.219035	−	1.24221i	0.873766	−	0.486347i	$-0.161671\pi$
$602$		0			0
$603$	−21.8490	−	17.6334i	−0.889760	−	0.718089i
$604$		0			0
$605$	64.5049	−	23.4779i	2.62250	−	0.954511i
$606$		0			0
$607$	−12.3480	+	10.3612i	−0.501190	+	0.420549i	−0.858016	−	0.513622i	$-0.828303\pi$
$607$	−12.3480	+	10.3612i	−0.501190	+	0.420549i	0.356826	+	0.934171i	$0.383859\pi$
$608$		0			0
$609$	−0.354614	−	37.1292i	−0.0143697	−	1.50455i
$610$		0			0
$611$	−0.0120690	−	0.0209042i	−0.000488261	−	0.000845694i
$612$		0			0
$613$	7.76761	−	13.4539i	0.313731	−	0.543398i	−0.665436	−	0.746455i	$-0.731754\pi$
$613$	7.76761	−	13.4539i	0.313731	−	0.543398i	0.979167	+	0.203057i	$0.0650877\pi$
$614$		0			0
$615$	−15.9202	+	45.0752i	−0.641964	+	1.81761i
$616$		0			0
$617$	−5.72338	−	32.4589i	−0.230415	−	1.30675i	−0.852059	−	0.523446i	$-0.824646\pi$
$617$	−5.72338	−	32.4589i	−0.230415	−	1.30675i	0.621644	−	0.783300i	$-0.286465\pi$
$618$		0			0
$619$	−19.0195	−	15.9593i	−0.764460	−	0.641458i	0.174824	−	0.984600i	$-0.444064\pi$
$619$	−19.0195	−	15.9593i	−0.764460	−	0.641458i	−0.939284	+	0.343142i	$0.888509\pi$
$620$		0			0
$621$	−9.08657	+	27.3816i	−0.364631	+	1.09879i
$622$		0			0
$623$	8.14908	+	6.83789i	0.326486	+	0.273954i
$624$		0			0
$625$	6.66999	+	37.8274i	0.266799	+	1.51309i
$626$		0			0
$627$	14.7451	+	17.2356i	0.588864	+	0.688322i
$628$		0			0
$629$	9.05362	−	15.6813i	0.360991	−	0.625256i
$630$		0			0
$631$	−19.5573	−	33.8742i	−0.778563	−	1.34851i	−0.932770	−	0.360472i	$-0.882616\pi$
$631$	−19.5573	−	33.8742i	−0.778563	−	1.34851i	0.154207	−	0.988039i	$-0.450718\pi$
$632$		0			0
$633$	−26.4419	+	15.6048i	−1.05097	+	0.620235i
$634$		0			0
$635$	−6.10206	+	5.12024i	−0.242153	+	0.203191i
$636$		0			0
$637$	−0.0101607	+	0.00369818i	−0.000402580	+	0.000146527i
$638$		0			0
$639$	32.4978	−	28.3441i	1.28559	−	1.12127i
$640$		0			0
$641$	−8.31018	+	47.1293i	−0.328232	+	1.86150i	0.157681	+	0.987490i	$0.449598\pi$
$641$	−8.31018	+	47.1293i	−0.328232	+	1.86150i	−0.485913	+	0.874007i	$0.661513\pi$
$642$		0			0
$643$	−41.2546	−	15.0155i	−1.62692	−	0.592152i	−0.642241	−	0.766503i	$-0.721995\pi$
$643$	−41.2546	−	15.0155i	−1.62692	−	0.592152i	−0.984684	+	0.174351i	$0.944217\pi$
$644$		0			0
$645$	−0.244357	+	0.296927i	−0.00962154	+	0.0116915i
$646$		0			0
$647$	15.9642			0.627618			0.313809	−	0.949486i	$-0.398395\pi$
$647$	15.9642			0.627618			0.313809	+	0.949486i	$0.398395\pi$
$648$		0			0
$649$	−22.5850			−0.886539
$650$		0			0
$651$	1.91204	−	2.32339i	0.0749388	−	0.0910608i
$652$		0			0
$653$	13.8697	+	5.04816i	0.542763	+	0.197550i	0.598828	−	0.800877i	$-0.295633\pi$
$653$	13.8697	+	5.04816i	0.542763	+	0.197550i	−0.0560649	+	0.998427i	$0.517855\pi$
$654$		0			0
$655$	−0.622352	+	3.52953i	−0.0243173	+	0.137910i
$656$		0			0
$657$	40.6059	+	13.9069i	1.58419	+	0.542562i
$658$		0			0
$659$	9.91286	−	3.60799i	0.386150	−	0.140547i	−0.141648	−	0.989917i	$-0.545240\pi$
$659$	9.91286	−	3.60799i	0.386150	−	0.140547i	0.527798	+	0.849370i	$0.323018\pi$
$660$		0			0
$661$	25.1093	−	21.0692i	0.976640	−	0.819499i	−0.00693878	−	0.999976i	$-0.502209\pi$
$661$	25.1093	−	21.0692i	0.976640	−	0.819499i	0.983579	+	0.180477i	$0.0577643\pi$
$662$		0			0
$663$	0.266028	−	0.156998i	0.0103317	−	0.00609728i
$664$		0			0
$665$	12.7847	+	22.1437i	0.495767	+	0.858694i
$666$		0			0
$667$	−22.8304	+	39.5434i	−0.883996	+	1.53113i
$668$		0			0
$669$	−23.4906	−	27.4581i	−0.908198	−	1.06159i
$670$		0			0
$671$	2.43054	+	13.7843i	0.0938300	+	0.532136i
$672$		0			0
$673$	15.6106	+	13.0988i	0.601743	+	0.504922i	0.892005	−	0.452025i	$-0.149298\pi$
$673$	15.6106	+	13.0988i	0.601743	+	0.504922i	−0.290262	+	0.956947i	$0.593743\pi$
$674$		0			0
$675$	−20.7852	−	52.3863i	−0.800024	−	2.01635i
$676$		0			0
$677$	8.95863	+	7.51718i	0.344308	+	0.288909i	0.798500	−	0.601995i	$-0.205627\pi$
$677$	8.95863	+	7.51718i	0.344308	+	0.288909i	−0.454192	+	0.890904i	$0.650072\pi$
$678$		0			0
$679$	−5.71835	−	32.4304i	−0.219450	−	1.24456i
$680$		0			0
$681$	−2.08360	+	5.89934i	−0.0798436	+	0.226063i
$682$		0			0
$683$	−22.7585	+	39.4189i	−0.870830	+	1.50832i	−0.00968953	+	0.999953i	$0.503084\pi$
$683$	−22.7585	+	39.4189i	−0.870830	+	1.50832i	−0.861140	+	0.508368i	$0.830249\pi$
$684$		0			0
$685$	−27.3297	−	47.3365i	−1.04422	−	1.80863i
$686$		0			0
$687$	0.0673196	+	7.04855i	0.00256840	+	0.268919i
$688$		0			0
$689$	−0.0560220	+	0.0470080i	−0.00213427	+	0.00179086i
$690$		0			0
$691$	4.68876	−	1.70657i	0.178369	−	0.0649210i	−0.251292	−	0.967911i	$-0.580855\pi$
$691$	4.68876	−	1.70657i	0.178369	−	0.0649210i	0.429661	+	0.902990i	$0.358633\pi$
$692$		0			0
$693$	−38.7754	+	14.9578i	−1.47295	+	0.568201i
$694$		0			0
$695$	−0.0175729	+	0.0996610i	−0.000666579	+	0.00378036i
$696$		0			0
$697$	22.0319	+	8.01895i	0.834517	+	0.303739i
$698$		0			0
$699$	−41.8448	−	6.96698i	−1.58272	−	0.263516i
$700$		0			0
$701$	25.9484			0.980059			0.490029	−	0.871706i	$-0.336986\pi$
$701$	25.9484			0.980059			0.490029	+	0.871706i	$0.336986\pi$
$702$		0			0
$703$	13.1943			0.497634
$704$		0			0
$705$	1.10759	+	2.95495i	0.0417141	+	0.111290i
$706$		0			0
$707$	21.5139	+	7.83040i	0.809112	+	0.294493i
$708$		0			0
$709$	−1.73503	+	9.83985i	−0.0651605	+	0.369543i	0.934739	+	0.355336i	$0.115634\pi$
$709$	−1.73503	+	9.83985i	−0.0651605	+	0.369543i	−0.999899	+	0.0142073i	$0.995478\pi$
$710$		0			0
$711$	11.2332	−	20.3442i	0.421278	−	0.762968i
$712$		0			0
$713$	−3.47708	+	1.26556i	−0.130218	+	0.0473954i
$714$		0			0
$715$	0.854700	−	0.717178i	0.0319640	−	0.0268209i
$716$		0			0
$717$	34.1299	+	19.2727i	1.27460	+	0.719751i
$718$		0			0
$719$	5.41746	+	9.38332i	0.202037	+	0.349939i	0.949185	−	0.314719i	$-0.101910\pi$
$719$	5.41746	+	9.38332i	0.202037	+	0.349939i	−0.747147	+	0.664658i	$0.768577\pi$
$720$		0			0
$721$	−9.14168	+	15.8339i	−0.340454	+	0.589684i
$722$		0			0
$723$	19.4499	−	3.62141i	0.723350	−	0.134682i
$724$		0			0
$725$	−15.4893	−	87.8443i	−0.575259	−	3.26246i
$726$		0			0
$727$	13.4070	+	11.2498i	0.497237	+	0.417232i	0.856612	−	0.515962i	$-0.172565\pi$
$727$	13.4070	+	11.2498i	0.497237	+	0.417232i	−0.359374	+	0.933194i	$0.617010\pi$
$728$		0			0
$729$	14.8170	+	22.5711i	0.548778	+	0.835968i
$730$		0			0
$731$	0.144479	+	0.121232i	0.00534373	+	0.00448392i
$732$		0			0
$733$	−4.10784	−	23.2967i	−0.151727	−	0.860484i	−0.961718	−	0.274042i	$-0.911639\pi$
$733$	−4.10784	−	23.2967i	−0.151727	−	0.860484i	0.809991	−	0.586442i	$-0.199472\pi$
$734$		0			0
$735$	1.38973	−	0.258755i	0.0512609	−	0.00954433i
$736$		0			0
$737$	−24.8693	+	43.0749i	−0.916073	+	1.58668i
$738$		0			0
$739$	−1.39583	−	2.41766i	−0.0513466	−	0.0889349i	0.839210	−	0.543808i	$-0.183018\pi$
$739$	−1.39583	−	2.41766i	−0.0513466	−	0.0889349i	−0.890556	+	0.454873i	$0.849685\pi$
$740$		0			0
$741$	0.195998	+	0.110677i	0.00720016	+	0.00406583i
$742$		0			0
$743$	−28.2480	+	23.7029i	−1.03632	+	0.869576i	−0.991589	−	0.129423i	$-0.958687\pi$
$743$	−28.2480	+	23.7029i	−1.03632	+	0.869576i	−0.0447304	+	0.998999i	$0.514243\pi$
$744$		0			0
$745$	45.6839	−	16.6276i	1.67373	−	0.609187i
$746$		0			0
$747$	3.47945	−	6.30156i	0.127306	−	0.230562i
$748$		0			0
$749$	4.12058	−	23.3690i	0.150563	−	0.853884i
$750$		0			0
$751$	11.4717	+	4.17535i	0.418608	+	0.152361i	0.542732	−	0.839906i	$-0.317390\pi$
$751$	11.4717	+	4.17535i	0.418608	+	0.152361i	−0.124124	+	0.992267i	$0.539612\pi$
$752$		0			0
$753$	−1.54545	−	4.12313i	−0.0563193	−	0.150255i
$754$		0			0
$755$	11.7055			0.426009
$756$		0			0
$757$	17.4136			0.632907			0.316453	−	0.948608i	$-0.397508\pi$
$757$	17.4136			0.632907			0.316453	+	0.948608i	$0.397508\pi$
$758$		0			0
$759$	50.4139	+	8.39370i	1.82991	+	0.304672i
$760$		0			0
$761$	19.1950	+	6.98639i	0.695816	+	0.253256i	0.665624	−	0.746288i	$-0.268166\pi$
$761$	19.1950	+	6.98639i	0.695816	+	0.253256i	0.0301929	+	0.999544i	$0.490388\pi$
$762$		0			0
$763$	−6.58592	+	37.3506i	−0.238426	+	1.35218i
$764$		0			0
$765$	−37.6780	+	14.5345i	−1.36225	+	0.525496i
$766$		0			0
$767$	−0.210607	+	0.0766547i	−0.00760458	+	0.00276784i
$768$		0			0
$769$	−12.7022	+	10.6584i	−0.458052	+	0.384351i	−0.842414	−	0.538831i	$-0.818866\pi$
$769$	−12.7022	+	10.6584i	−0.458052	+	0.384351i	0.384362	+	0.923183i	$0.374422\pi$
$770$		0			0
$771$	0.297896	+	31.1906i	0.0107285	+	1.12330i
$772$		0			0
$773$	−9.24355	−	16.0103i	−0.332467	−	0.575850i	0.650528	−	0.759482i	$-0.274548\pi$
$773$	−9.24355	−	16.0103i	−0.332467	−	0.575850i	−0.982995	+	0.183632i	$0.941214\pi$
$774$		0			0
$775$	3.61425	−	6.26007i	0.129828	−	0.224868i
$776$		0			0
$777$	−8.05128	+	22.7958i	−0.288838	+	0.817794i
$778$		0			0
$779$	2.96668	+	16.8249i	0.106292	+	0.602814i
$780$		0			0
$781$	−58.5187	−	49.1030i	−2.09396	−	1.75704i
$782$		0			0
$783$	15.7599	+	39.7206i	0.563212	+	1.41950i
$784$		0			0
$785$	−36.7585	−	30.8441i	−1.31197	−	1.10087i
$786$		0			0
$787$	6.19112	+	35.1116i	0.220690	+	1.25159i	0.870756	+	0.491715i	$0.163630\pi$
$787$	6.19112	+	35.1116i	0.220690	+	1.25159i	−0.650066	+	0.759877i	$0.725259\pi$
$788$		0			0
$789$	−0.847078	−	0.990148i	−0.0301568	−	0.0352502i
$790$		0			0
$791$	−19.5384	+	33.8415i	−0.694706	+	1.20327i
$792$		0			0
$793$	0.0694495	+	0.120290i	0.00246622	+	0.00427163i
$794$		0			0
$795$	8.23394	−	4.85930i	0.292028	−	0.172342i
$796$		0			0
$797$	14.2168	−	11.9293i	0.503586	−	0.422559i	−0.355279	−	0.934760i	$-0.615614\pi$
$797$	14.2168	−	11.9293i	0.503586	−	0.422559i	0.858866	+	0.512201i	$0.171170\pi$
$798$		0			0
$799$	1.45440	−	0.529358i	0.0514529	−	0.0187273i
$800$		0			0
$801$	−11.5824	−	3.96680i	−0.409243	−	0.140160i
$802$		0			0
$803$	13.2034	−	74.8805i	0.465940	−	2.64247i
$804$		0			0
$805$	54.1386	+	19.7048i	1.90813	+	0.694504i
$806$		0			0
$807$	0.824037	−	1.00132i	0.0290075	−	0.0352480i
$808$		0			0
$809$	−11.0764			−0.389426			−0.194713	−	0.980860i	$-0.562378\pi$
$809$	−11.0764			−0.389426			−0.194713	+	0.980860i	$0.562378\pi$
$810$		0			0
$811$	−0.205736			−0.00722437			−0.00361219	−	0.999993i	$-0.501150\pi$
$811$	−0.205736			−0.00722437			−0.00361219	+	0.999993i	$0.501150\pi$
$812$		0			0
$813$	31.6274	−	38.4316i	1.10922	−	1.34786i
$814$		0			0
$815$	−38.8082	−	14.1250i	−1.35939	−	0.494778i
$816$		0			0
$817$	−0.0238646	+	0.135343i	−0.000834918	+	0.00473506i
$818$		0			0
$819$	−0.310816	+	0.271088i	−0.0108608	+	0.00947260i
$820$		0			0
$821$	−12.5004	+	4.54976i	−0.436266	+	0.158788i	−0.550810	−	0.834630i	$-0.685681\pi$
$821$	−12.5004	+	4.54976i	−0.436266	+	0.158788i	0.114545	+	0.993418i	$0.463459\pi$
$822$		0			0
$823$	38.6476	−	32.4292i	1.34717	−	1.13041i	0.367449	−	0.930044i	$-0.380231\pi$
$823$	38.6476	−	32.4292i	1.34717	−	1.13041i	0.979721	−	0.200366i	$-0.0642131\pi$
$824$		0			0
$825$	−85.9838	+	50.7438i	−2.99357	+	1.76667i
$826$		0			0
$827$	−20.1769	−	34.9473i	−0.701618	−	1.21524i	−0.967898	−	0.251342i	$-0.919128\pi$
$827$	−20.1769	−	34.9473i	−0.701618	−	1.21524i	0.266280	−	0.963896i	$-0.414205\pi$
$828$		0			0
$829$	−22.3346	+	38.6847i	−0.775713	+	1.34357i	0.158680	+	0.987330i	$0.449276\pi$
$829$	−22.3346	+	38.6847i	−0.775713	+	1.34357i	−0.934393	+	0.356244i	$0.884057\pi$
$830$		0			0
$831$	−13.1347	−	15.3532i	−0.455639	−	0.532596i
$832$		0			0
$833$	−0.120393	−	0.682782i	−0.00417137	−	0.0236570i
$834$		0			0
$835$	−14.8450	−	12.4564i	−0.513733	−	0.431073i
$836$		0			0
$837$	−1.09070	+	3.28672i	−0.0376999	+	0.113606i
$838$		0			0
$839$	−41.5143	−	34.8347i	−1.43323	−	1.20263i	−0.943770	−	0.330602i	$-0.892748\pi$
$839$	−41.5143	−	34.8347i	−1.43323	−	1.20263i	−0.489463	−	0.872024i	$-0.662807\pi$
$840$		0			0
$841$	6.70860	+	38.0464i	0.231331	+	1.31194i
$842$		0			0
$843$	−4.66351	+	13.2039i	−0.160620	+	0.454767i
$844$		0			0
$845$	−25.8693	+	44.8069i	−0.889931	+	1.54141i
$846$		0			0
$847$	22.4754	+	38.9285i	0.772262	+	1.33760i
$848$		0			0
$849$	−0.538153	−	56.3462i	−0.0184694	−	1.93380i
$850$		0			0
$851$	22.7742	−	19.1098i	0.780690	−	0.655077i
$852$		0			0
$853$	22.2184	−	8.08683i	0.760743	−	0.276888i	0.0676240	−	0.997711i	$-0.478458\pi$
$853$	22.2184	−	8.08683i	0.760743	−	0.276888i	0.693119	+	0.720823i	$0.256236\pi$
$854$		0			0
$855$	−22.8996	−	18.4813i	−0.783149	−	0.632047i
$856$		0			0
$857$	−5.20838	+	29.5382i	−0.177915	+	1.00901i	0.756810	+	0.653635i	$0.226757\pi$
$857$	−5.20838	+	29.5382i	−0.177915	+	1.00901i	−0.934725	+	0.355371i	$0.884354\pi$
$858$		0			0
$859$	−13.0283	−	4.74190i	−0.444519	−	0.161792i	0.110056	−	0.993925i	$-0.464897\pi$
$859$	−13.0283	−	4.74190i	−0.444519	−	0.161792i	−0.554575	+	0.832134i	$0.687119\pi$
$860$		0			0
$861$	−30.8786	−	5.14115i	−1.05234	−	0.175210i
$862$		0			0
$863$	−31.8027			−1.08258			−0.541288	−	0.840837i	$-0.682063\pi$
$863$	−31.8027			−1.08258			−0.541288	+	0.840837i	$0.682063\pi$
$864$		0			0
$865$	−61.0443			−2.07557
$866$		0			0
$867$	−3.38280	−	9.02502i	−0.114886	−	0.306506i
$868$		0			0
$869$	−38.6861	−	14.0806i	−1.31234	−	0.477651i
$870$		0			0
$871$	−0.0857098	+	0.486084i	−0.00290417	+	0.0164703i
$872$		0			0
$873$	19.5729	+	32.4536i	0.662444	+	1.09839i
$874$		0			0
$875$	−57.0067	+	20.7487i	−1.92718	+	0.701435i
$876$		0			0
$877$	19.2529	−	16.1551i	0.650123	−	0.545518i	−0.256985	−	0.966415i	$-0.582729\pi$
$877$	19.2529	−	16.1551i	0.650123	−	0.545518i	0.907108	+	0.420897i	$0.138285\pi$
$878$		0			0
$879$	8.07475	+	4.55969i	0.272354	+	0.153795i
$880$		0			0
$881$	13.6586	+	23.6574i	0.460170	+	0.797038i	0.998969	−	0.0453966i	$-0.0144552\pi$
$881$	13.6586	+	23.6574i	0.460170	+	0.797038i	−0.538799	+	0.842434i	$0.681122\pi$
$882$		0			0
$883$	−16.7742	+	29.0538i	−0.564498	+	0.977739i	0.432598	+	0.901587i	$0.357597\pi$
$883$	−16.7742	+	29.0538i	−0.564498	+	0.977739i	−0.997096	+	0.0761523i	$0.975736\pi$
$884$		0			0
$885$	28.8058	−	5.36340i	0.968297	−	0.180289i
$886$		0			0
$887$	1.41514	+	8.02565i	0.0475157	+	0.269475i	0.999305	−	0.0372778i	$-0.0118687\pi$
$887$	1.41514	+	8.02565i	0.0475157	+	0.269475i	−0.951789	+	0.306753i	$0.900758\pi$
$888$		0			0
$889$	−3.99583	−	3.35290i	−0.134016	−	0.112453i
$890$		0			0
$891$	35.4395	−	32.1220i	1.18727	−	1.07613i
$892$		0			0
$893$	0.863946	+	0.724937i	0.0289109	+	0.0242591i
$894$		0			0
$895$	−11.1998	−	63.5170i	−0.374367	−	2.12314i
$896$		0			0
$897$	0.498602	−	0.0928354i	0.0166478	−	0.00309968i
$898$		0			0
$899$	−2.74042	+	4.74654i	−0.0913980	+	0.158306i
$900$		0			0
$901$	−2.34460	−	4.06097i	−0.0781100	−	0.135291i
$902$		0			0
$903$	−0.219269	−	0.123818i	−0.00729682	−	0.00412041i
$904$		0			0
$905$	30.0788	−	25.2391i	0.999852	−	0.838976i
$906$		0			0
$907$	−53.9060	+	19.6202i	−1.78992	+	0.651478i	−0.790692	+	0.612215i	$0.790279\pi$
$907$	−53.9060	+	19.6202i	−1.78992	+	0.651478i	−0.999229	+	0.0392630i	$0.987499\pi$
$908$		0			0
$909$	−26.3439	+	0.503259i	−0.873773	+	0.0166920i
$910$		0			0
$911$	−5.88969	+	33.4021i	−0.195134	+	1.10666i	0.717093	+	0.696977i	$0.245472\pi$
$911$	−5.88969	+	33.4021i	−0.195134	+	1.10666i	−0.912228	+	0.409684i	$0.865639\pi$
$912$		0			0
$913$	−11.9829	−	4.36142i	−0.396576	−	0.144342i
$914$		0			0
$915$	−6.37344	−	17.0038i	−0.210700	−	0.562129i
$916$		0			0
$917$	−2.34691			−0.0775017
$918$		0			0
$919$	−21.2454			−0.700822			−0.350411	−	0.936596i	$-0.613958\pi$
$919$	−21.2454			−0.700822			−0.350411	+	0.936596i	$0.613958\pi$
$920$		0			0
$921$	−11.2621	−	1.87508i	−0.371097	−	0.0617861i
$922$		0			0
$923$	−0.712349	−	0.259274i	−0.0234472	−	0.00853410i
$924$		0			0
$925$	−10.0851	+	57.1953i	−0.331595	+	1.88057i
$926$		0			0
$927$	3.25742	−	20.7882i	0.106988	−	0.682773i
$928$		0			0
$929$	−10.5796	+	3.85065i	−0.347104	+	0.126336i	−0.509688	−	0.860359i	$-0.670239\pi$
$929$	−10.5796	+	3.85065i	−0.347104	+	0.126336i	0.162584	+	0.986695i	$0.448017\pi$
$930$		0			0
$931$	0.387008	−	0.324738i	0.0126837	−	0.0106429i
$932$		0			0
$933$	−0.439178	−	45.9832i	−0.0143781	−	1.50542i
$934$		0			0
$935$	35.7704	+	61.9562i	1.16982	+	2.02619i
$936$		0			0
$937$	−4.61998	+	8.00203i	−0.150928	+	0.261415i	−0.931569	−	0.363565i	$-0.881560\pi$
$937$	−4.61998	+	8.00203i	−0.150928	+	0.261415i	0.780641	+	0.624980i	$0.214893\pi$
$938$		0			0
$939$	11.0134	−	31.1824i	0.359408	−	1.01760i
$940$		0			0
$941$	6.71426	+	38.0785i	0.218879	+	1.24132i	0.874048	+	0.485840i	$0.161486\pi$
$941$	6.71426	+	38.0785i	0.218879	+	1.24132i	−0.655169	+	0.755483i	$0.727402\pi$
$942$		0			0
$943$	29.4888	+	24.7440i	0.960287	+	0.805777i
$944$		0			0
$945$	45.9035	−	28.2860i	1.49324	−	0.920144i
$946$		0			0
$947$	28.5183	+	23.9297i	0.926720	+	0.777610i	0.975226	−	0.221213i	$-0.0710015\pi$
$947$	28.5183	+	23.9297i	0.926720	+	0.777610i	−0.0485057	+	0.998823i	$0.515446\pi$
$948$		0			0
$949$	−0.131025	−	0.743079i	−0.00425325	−	0.0241214i
$950$		0			0
$951$	8.86432	+	10.3615i	0.287445	+	0.335994i
$952$		0			0
$953$	6.34521	−	10.9902i	0.205542	−	0.356008i	−0.744764	−	0.667328i	$-0.767438\pi$
$953$	6.34521	−	10.9902i	0.205542	−	0.356008i	0.950305	+	0.311320i	$0.100771\pi$
$954$		0			0
$955$	27.0392	+	46.8332i	0.874967	+	1.51549i
$956$		0			0
$957$	65.1951	−	38.4752i	2.10746	−	1.24373i
$958$		0			0
$959$	27.4189	−	23.0071i	0.885401	−	0.742940i
$960$		0			0
$961$	28.7131	−	10.4507i	0.926229	−	0.337120i
$962$		0			0
$963$	5.25509	+	26.7992i	0.169343	+	0.863593i
$964$		0			0
$965$	2.38748	−	13.5401i	0.0768557	−	0.435870i
$966$		0			0
$967$	32.3212	+	11.7639i	1.03938	+	0.378303i	0.804645	−	0.593757i	$-0.202356\pi$
$967$	32.3212	+	11.7639i	1.03938	+	0.378303i	0.234734	+	0.972060i	$0.424578\pi$
$968$		0			0
$969$	−9.17114	+	11.1442i	−0.294619	+	0.358002i
$970$		0			0
$971$	44.5140			1.42852			0.714261	−	0.699880i	$-0.246763\pi$
$971$	44.5140			1.42852			0.714261	+	0.699880i	$0.246763\pi$
$972$		0			0
$973$	−0.0662680			−0.00212445
$974$		0			0
$975$	−0.629578	+	0.765023i	−0.0201626	+	0.0245003i
$976$		0			0
$977$	−20.8596	−	7.59228i	−0.667359	−	0.242899i	−0.0139485	−	0.999903i	$-0.504440\pi$
$977$	−20.8596	−	7.59228i	−0.667359	−	0.242899i	−0.653410	+	0.757004i	$0.726662\pi$
$978$		0			0
$979$	−3.76613	+	21.3588i	−0.120366	+	0.682630i
$980$		0			0
$981$	−8.39920	−	42.8332i	−0.268166	−	1.36756i
$982$		0			0
$983$	21.3730	−	7.77915i	0.681694	−	0.248116i	0.0221192	−	0.999755i	$-0.492959\pi$
$983$	21.3730	−	7.77915i	0.681694	−	0.248116i	0.659575	+	0.751639i	$0.270736\pi$
$984$		0			0
$985$	−2.52288	+	2.11695i	−0.0803856	+	0.0674516i
$986$		0			0
$987$	−1.77966	+	1.05027i	−0.0566471	+	0.0334306i
$988$		0			0
$989$	0.154831	+	0.268174i	0.00492333	+	0.00852745i
$990$		0			0
$991$	19.7002	−	34.1217i	0.625798	−	1.08391i	−0.362589	−	0.931949i	$-0.618107\pi$
$991$	19.7002	−	34.1217i	0.625798	−	1.08391i	0.988386	−	0.151964i	$-0.0485597\pi$
$992$		0			0
$993$	−7.90294	−	9.23773i	−0.250792	−	0.293150i
$994$		0			0
$995$	1.77425	+	10.0623i	0.0562476	+	0.318996i
$996$		0			0
$997$	16.3941	+	13.7563i	0.519205	+	0.435665i	0.864355	−	0.502883i	$-0.167727\pi$
$997$	16.3941	+	13.7563i	0.519205	+	0.435665i	−0.345149	+	0.938548i	$0.612172\pi$
$998$		0			0
$999$	−0.797074	−	27.8119i	−0.0252183	−	0.879929i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.q.b.97.4	yes	30
3.2	odd	2		648.2.q.b.289.1		30
4.3	odd	2		432.2.u.f.97.2		30
27.5	odd	18		648.2.q.b.361.1		30
27.7	even	9		5832.2.a.k.1.1		15
27.20	odd	18		5832.2.a.l.1.15		15
27.22	even	9	inner	216.2.q.b.49.4	✓	30
108.103	odd	18		432.2.u.f.49.2		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.b.49.4	✓	30	27.22	even	9	inner
216.2.q.b.97.4	yes	30	1.1	even	1	trivial
432.2.u.f.49.2		30	108.103	odd	18
432.2.u.f.97.2		30	4.3	odd	2
648.2.q.b.289.1		30	3.2	odd	2
648.2.q.b.361.1		30	27.5	odd	18
5832.2.a.k.1.1		15	27.7	even	9
5832.2.a.l.1.15		15	27.20	odd	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10062 - 1.33740i) q^{3} +(3.74067 + 1.36149i) q^{5} +(-0.452652 + 2.56712i) q^{7} +(-0.577279 - 2.94393i) q^{9} +O(q^{10})\)	\(q+(1.10062 - 1.33740i) q^{3} +(3.74067 + 1.36149i) q^{5} +(-0.452652 + 2.56712i) q^{7} +(-0.577279 - 2.94393i) q^{9} +(-4.99402 + 1.81767i) q^{11} +(-0.0404003 + 0.0338999i) q^{13} +(5.93792 - 3.50429i) q^{15} +(-1.69081 - 2.92857i) q^{17} +(1.23206 - 2.13399i) q^{19} +(2.93506 + 3.43079i) q^{21} +(-0.964125 - 5.46782i) q^{23} +(8.30876 + 6.97187i) q^{25} +(-4.57258 - 2.46810i) q^{27} +(-6.29991 - 5.28625i) q^{29} +(-0.115728 - 0.656323i) q^{31} +(-3.06555 + 8.67957i) q^{33} +(-5.18834 + 8.98646i) q^{35} +(2.67730 + 4.63722i) q^{37} +(0.000872395 + 0.0913423i) q^{39} +(-5.31122 + 4.45664i) q^{41} +(-0.0524095 + 0.0190755i) q^{43} +(1.84874 - 11.7983i) q^{45} +(-0.0794772 + 0.450737i) q^{47} +(0.192660 + 0.0701224i) q^{49} +(-5.77762 - 0.961949i) q^{51} +1.38667 q^{53} -21.1558 q^{55} +(-1.49797 - 3.99646i) q^{57} +(3.99339 + 1.45348i) q^{59} +(0.457339 - 2.59370i) q^{61} +(7.81873 - 0.149364i) q^{63} +(-0.197279 + 0.0718037i) q^{65} +(7.16941 - 6.01585i) q^{67} +(-8.37380 - 4.72856i) q^{69} +(7.18697 + 12.4482i) q^{71} +(-7.15357 + 12.3903i) q^{73} +(18.4690 - 3.43876i) q^{75} +(-2.40563 - 13.6430i) q^{77} +(5.93415 + 4.97935i) q^{79} +(-8.33350 + 3.39894i) q^{81} +(1.83808 + 1.54234i) q^{83} +(-2.33755 - 13.2569i) q^{85} +(-14.0036 + 2.60735i) q^{87} +(2.04047 - 3.53420i) q^{89} +(-0.0687377 - 0.119057i) q^{91} +(-1.00514 - 0.567588i) q^{93} +(7.51413 - 6.30511i) q^{95} +(-11.8711 + 4.32074i) q^{97} +(8.23406 + 13.6528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{7} - 6 q^{9}+O(q^{10}) \) 30 * q + 3 * q^7 - 6 * q^9	\( 30 q + 3 q^{7} - 6 q^{9} - 3 q^{11} - 12 q^{13} + 15 q^{15} + 6 q^{17} - 9 q^{19} + 30 q^{21} - 12 q^{23} + 24 q^{25} - 15 q^{27} - 9 q^{29} + 27 q^{31} - 30 q^{33} - 18 q^{35} - 15 q^{37} - 21 q^{39} - 15 q^{41} - 30 q^{43} + 15 q^{45} - 18 q^{47} + 15 q^{49} - 6 q^{51} - 18 q^{53} + 54 q^{55} - 72 q^{57} - 12 q^{59} + 6 q^{61} - 54 q^{63} - 54 q^{65} - 45 q^{67} + 9 q^{69} - 36 q^{73} + 69 q^{75} + 12 q^{77} + 45 q^{79} - 30 q^{81} - 3 q^{83} + 57 q^{85} - 60 q^{87} + 36 q^{89} - 39 q^{91} + 30 q^{93} + 51 q^{95} - 84 q^{97} + 162 q^{99}+O(q^{100}) \) 30 * q + 3 * q^7 - 6 * q^9 - 3 * q^11 - 12 * q^13 + 15 * q^15 + 6 * q^17 - 9 * q^19 + 30 * q^21 - 12 * q^23 + 24 * q^25 - 15 * q^27 - 9 * q^29 + 27 * q^31 - 30 * q^33 - 18 * q^35 - 15 * q^37 - 21 * q^39 - 15 * q^41 - 30 * q^43 + 15 * q^45 - 18 * q^47 + 15 * q^49 - 6 * q^51 - 18 * q^53 + 54 * q^55 - 72 * q^57 - 12 * q^59 + 6 * q^61 - 54 * q^63 - 54 * q^65 - 45 * q^67 + 9 * q^69 - 36 * q^73 + 69 * q^75 + 12 * q^77 + 45 * q^79 - 30 * q^81 - 3 * q^83 + 57 * q^85 - 60 * q^87 + 36 * q^89 - 39 * q^91 + 30 * q^93 + 51 * q^95 - 84 * q^97 + 162 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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