LMFDB - Embedded newform 216.2.q.b.49.2

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			49.2
Character	$\chi$	$=$	216.49
Dual form			216.2.q.b.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.968921 - 1.43569i) q^{3} +(-2.72954 + 0.993471i) q^{5} +(-0.186943 - 1.06021i) q^{7} +(-1.12238 + 2.78213i) q^{9} +O(q^{10})$	\(q+(-0.968921 - 1.43569i) q^{3} +(-2.72954 + 0.993471i) q^{5} +(-0.186943 - 1.06021i) q^{7} +(-1.12238 + 2.78213i) q^{9} +(-3.28397 - 1.19527i) q^{11} +(-3.77837 - 3.17043i) q^{13} +(4.07102 + 2.95616i) q^{15} +(-3.54041 + 6.13217i) q^{17} +(1.08712 + 1.88294i) q^{19} +(-1.34099 + 1.29565i) q^{21} +(1.11177 - 6.30518i) q^{23} +(2.63317 - 2.20949i) q^{25} +(5.08177 - 1.08428i) q^{27} +(2.20769 - 1.85247i) q^{29} +(0.481312 - 2.72965i) q^{31} +(1.46588 + 5.87286i) q^{33} +(1.56355 + 2.70815i) q^{35} +(4.40997 - 7.63829i) q^{37} +(-0.890795 + 8.49644i) q^{39} +(-0.953592 - 0.800158i) q^{41} +(-7.05867 - 2.56915i) q^{43} +(0.299623 - 8.70899i) q^{45} +(-0.575841 - 3.26576i) q^{47} +(5.48876 - 1.99775i) q^{49} +(12.2342 - 0.858675i) q^{51} -1.88716 q^{53} +10.1512 q^{55} +(1.64998 - 3.38518i) q^{57} +(-13.0776 + 4.75985i) q^{59} +(2.65444 + 15.0541i) q^{61} +(3.15945 + 0.669858i) q^{63} +(13.4629 + 4.90011i) q^{65} +(-1.47352 - 1.23643i) q^{67} +(-10.1295 + 4.51307i) q^{69} +(0.650072 - 1.12596i) q^{71} +(2.86037 + 4.95431i) q^{73} +(-5.72347 - 1.63958i) q^{75} +(-0.653313 + 3.70512i) q^{77} +(-7.35069 + 6.16796i) q^{79} +(-6.48051 - 6.24524i) q^{81} +(1.95760 - 1.64262i) q^{83} +(3.57155 - 20.2553i) q^{85} +(-4.79865 - 1.37465i) q^{87} +(1.77803 + 3.07963i) q^{89} +(-2.65497 + 4.59853i) q^{91} +(-4.38528 + 1.95381i) q^{93} +(-4.83797 - 4.05954i) q^{95} +(-6.41676 - 2.33551i) q^{97} +(7.01126 - 7.79488i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{9}\right)$

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
$3$	−0.968921	−	1.43569i	−0.559407	−	0.828893i
$3$	−0.968921	−	1.43569i	−0.559407	−	0.828893i
$4$		0			0
$5$	−2.72954	+	0.993471i	−1.22069	+	0.444294i	−0.870398	−	0.492348i	$-0.836139\pi$
$5$	−2.72954	+	0.993471i	−1.22069	+	0.444294i	−0.350288	+	0.936642i	$0.613916\pi$
$6$		0			0
$7$	−0.186943	−	1.06021i	−0.0706577	−	0.400720i	−0.999540	−	0.0303436i	$-0.990340\pi$
$7$	−0.186943	−	1.06021i	−0.0706577	−	0.400720i	0.928882	−	0.370376i	$-0.120771\pi$
$8$		0			0
$9$	−1.12238	+	2.78213i	−0.374128	+	0.927377i
$10$		0			0
$11$	−3.28397	−	1.19527i	−0.990153	−	0.360386i	−0.204373	−	0.978893i	$-0.565516\pi$
$11$	−3.28397	−	1.19527i	−0.990153	−	0.360386i	−0.785779	+	0.618507i	$0.787738\pi$
$12$		0			0
$13$	−3.77837	−	3.17043i	−1.04793	−	0.879319i	−0.0550565	−	0.998483i	$-0.517534\pi$
$13$	−3.77837	−	3.17043i	−1.04793	−	0.879319i	−0.992874	+	0.119165i	$0.961978\pi$
$14$		0			0
$15$	4.07102	+	2.95616i	1.05113	+	0.763278i
$16$		0			0
$17$	−3.54041	+	6.13217i	−0.858675	+	1.48727i	0.0145173	+	0.999895i	$0.495379\pi$
$17$	−3.54041	+	6.13217i	−0.858675	+	1.48727i	−0.873193	+	0.487375i	$0.837955\pi$
$18$		0			0
$19$	1.08712	+	1.88294i	0.249402	+	0.431976i	0.963360	−	0.268212i	$-0.0864328\pi$
$19$	1.08712	+	1.88294i	0.249402	+	0.431976i	−0.713958	+	0.700188i	$0.753099\pi$
$20$		0			0
$21$	−1.34099	+	1.29565i	−0.292628	+	0.282733i
$22$		0			0
$23$	1.11177	−	6.30518i	0.231821	−	1.31472i	−0.617385	−	0.786661i	$-0.711808\pi$
$23$	1.11177	−	6.30518i	0.231821	−	1.31472i	0.849206	−	0.528061i	$-0.177081\pi$
$24$		0			0
$25$	2.63317	−	2.20949i	0.526634	−	0.441899i
$26$		0			0
$27$	5.08177	−	1.08428i	0.977986	−	0.208669i
$28$		0			0
$29$	2.20769	−	1.85247i	0.409958	−	0.343996i	−0.414370	−	0.910109i	$-0.635998\pi$
$29$	2.20769	−	1.85247i	0.409958	−	0.343996i	0.824328	+	0.566113i	$0.191553\pi$
$30$		0			0
$31$	0.481312	−	2.72965i	0.0864461	−	0.490260i	−0.910589	−	0.413313i	$-0.864372\pi$
$31$	0.481312	−	2.72965i	0.0864461	−	0.490260i	0.997035	−	0.0769473i	$-0.0245173\pi$
$32$		0			0
$33$	1.46588	+	5.87286i	0.255177	+	1.02233i
$34$		0			0
$35$	1.56355	+	2.70815i	0.264288	+	0.457761i
$36$		0			0
$37$	4.40997	−	7.63829i	0.724995	−	1.25573i	−0.233982	−	0.972241i	$-0.575176\pi$
$37$	4.40997	−	7.63829i	0.724995	−	1.25573i	0.958976	−	0.283487i	$-0.0914911\pi$
$38$		0			0
$39$	−0.890795	+	8.49644i	−0.142641	+	1.36052i
$40$		0			0
$41$	−0.953592	−	0.800158i	−0.148926	−	0.124964i	0.565281	−	0.824899i	$-0.308768\pi$
$41$	−0.953592	−	0.800158i	−0.148926	−	0.124964i	−0.714207	+	0.699935i	$0.753212\pi$
$42$		0			0
$43$	−7.05867	−	2.56915i	−1.07644	−	0.391791i	−0.257857	−	0.966183i	$-0.583016\pi$
$43$	−7.05867	−	2.56915i	−1.07644	−	0.391791i	−0.818580	+	0.574392i	$0.805238\pi$
$44$		0			0
$45$	0.299623	−	8.70899i	0.0446652	−	1.29826i
$46$		0			0
$47$	−0.575841	−	3.26576i	−0.0839951	−	0.476360i	−0.997569	−	0.0696869i	$-0.977800\pi$
$47$	−0.575841	−	3.26576i	−0.0839951	−	0.476360i	0.913574	−	0.406673i	$-0.133311\pi$
$48$		0			0
$49$	5.48876	−	1.99775i	0.784109	−	0.285392i
$50$		0			0
$51$	12.2342	−	0.858675i	1.71314	−	0.120239i
$52$		0			0
$53$	−1.88716			−0.259222			−0.129611	−	0.991565i	$-0.541373\pi$
$53$	−1.88716			−0.259222			−0.129611	+	0.991565i	$0.541373\pi$
$54$		0			0
$55$	10.1512			1.36878
$56$		0			0
$57$	1.64998	−	3.38518i	0.218545	−	0.448378i
$58$		0			0
$59$	−13.0776	+	4.75985i	−1.70256	+	0.619679i	−0.996112	−	0.0880908i	$-0.971923\pi$
$59$	−13.0776	+	4.75985i	−1.70256	+	0.619679i	−0.706443	+	0.707770i	$0.749701\pi$
$60$		0			0
$61$	2.65444	+	15.0541i	0.339866	+	1.92748i	0.372556	+	0.928010i	$0.378481\pi$
$61$	2.65444	+	15.0541i	0.339866	+	1.92748i	−0.0326905	+	0.999466i	$0.510408\pi$
$62$		0			0
$63$	3.15945	+	0.669858i	0.398053	+	0.0843941i
$64$		0			0
$65$	13.4629	+	4.90011i	1.66987	+	0.607783i
$66$		0			0
$67$	−1.47352	−	1.23643i	−0.180019	−	0.151054i	0.548325	−	0.836265i	$-0.315266\pi$
$67$	−1.47352	−	1.23643i	−0.180019	−	0.151054i	−0.728345	+	0.685211i	$0.759710\pi$
$68$		0			0
$69$	−10.1295	+	4.51307i	−1.21945	+	0.543310i
$70$		0			0
$71$	0.650072	−	1.12596i	0.0771494	−	0.133627i	−0.824870	−	0.565323i	$-0.808752\pi$
$71$	0.650072	−	1.12596i	0.0771494	−	0.133627i	0.902019	+	0.431696i	$0.142085\pi$
$72$		0			0
$73$	2.86037	+	4.95431i	0.334781	+	0.579858i	0.983443	−	0.181219i	$-0.0580043\pi$
$73$	2.86037	+	4.95431i	0.334781	+	0.579858i	−0.648662	+	0.761077i	$0.724671\pi$
$74$		0			0
$75$	−5.72347	−	1.63958i	−0.660890	−	0.189323i
$76$		0			0
$77$	−0.653313	+	3.70512i	−0.0744519	+	0.422238i
$78$		0			0
$79$	−7.35069	+	6.16796i	−0.827017	+	0.693950i	−0.954604	−	0.297877i	$-0.903721\pi$
$79$	−7.35069	+	6.16796i	−0.827017	+	0.693950i	0.127587	+	0.991827i	$0.459277\pi$
$80$		0			0
$81$	−6.48051	−	6.24524i	−0.720057	−	0.693915i
$82$		0			0
$83$	1.95760	−	1.64262i	0.214875	−	0.180301i	−0.528997	−	0.848624i	$-0.677432\pi$
$83$	1.95760	−	1.64262i	0.214875	−	0.180301i	0.743872	+	0.668322i	$0.232987\pi$
$84$		0			0
$85$	3.57155	−	20.2553i	0.387389	−	2.19699i
$86$		0			0
$87$	−4.79865	−	1.37465i	−0.514469	−	0.147378i
$88$		0			0
$89$	1.77803	+	3.07963i	0.188470	+	0.326440i	0.944740	−	0.327819i	$-0.106314\pi$
$89$	1.77803	+	3.07963i	0.188470	+	0.326440i	−0.756270	+	0.654259i	$0.772980\pi$
$90$		0			0
$91$	−2.65497	+	4.59853i	−0.278316	+	0.482057i
$92$		0			0
$93$	−4.38528	+	1.95381i	−0.454732	+	0.202600i
$94$		0			0
$95$	−4.83797	−	4.05954i	−0.496365	−	0.416500i
$96$		0			0
$97$	−6.41676	−	2.33551i	−0.651523	−	0.237135i	−0.00495069	−	0.999988i	$-0.501576\pi$
$97$	−6.41676	−	2.33551i	−0.651523	−	0.237135i	−0.646572	+	0.762853i	$0.723798\pi$
$98$		0			0
$99$	7.01126	−	7.79488i	0.704658	−	0.783415i
$100$		0			0
$101$	−0.761262	−	4.31733i	−0.0757484	−	0.429590i	−0.998972	−	0.0453277i	$-0.985567\pi$
$101$	−0.761262	−	4.31733i	−0.0757484	−	0.429590i	0.923224	−	0.384263i	$-0.125544\pi$
$102$		0			0
$103$	−12.1304	+	4.41511i	−1.19525	+	0.435034i	−0.861563	−	0.507651i	$-0.830514\pi$
$103$	−12.1304	+	4.41511i	−1.19525	+	0.435034i	−0.333683	+	0.942685i	$0.608292\pi$
$104$		0			0
$105$	2.37309	−	4.86875i	0.231590	−	0.475141i
$106$		0			0
$107$	3.84595			0.371803			0.185901	−	0.982568i	$-0.440480\pi$
$107$	3.84595			0.371803			0.185901	+	0.982568i	$0.440480\pi$
$108$		0			0
$109$	−10.8768			−1.04181			−0.520906	−	0.853614i	$-0.674406\pi$
$109$	−10.8768			−1.04181			−0.520906	+	0.853614i	$0.674406\pi$
$110$		0			0
$111$	−15.2391	+	1.06957i	−1.44643	+	0.101519i
$112$		0			0
$113$	−4.82696	+	1.75687i	−0.454082	+	0.165272i	−0.558928	−	0.829216i	$-0.688787\pi$
$113$	−4.82696	+	1.75687i	−0.454082	+	0.165272i	0.104846	+	0.994488i	$0.466565\pi$
$114$		0			0
$115$	3.22939	+	18.3148i	0.301142	+	1.70786i
$116$		0			0
$117$	13.0613	−	6.95348i	1.20752	−	0.642850i
$118$		0			0
$119$	7.16321	+	2.60720i	0.656651	+	0.239001i
$120$		0			0
$121$	0.929279	+	0.779758i	0.0844799	+	0.0708871i
$122$		0			0
$123$	−0.224820	+	2.14435i	−0.0202714	+	0.193349i
$124$		0			0
$125$	2.26951	−	3.93090i	0.202991	−	0.351591i
$126$		0			0
$127$	−3.42554	−	5.93321i	−0.303968	−	0.526487i	0.673063	−	0.739585i	$-0.264978\pi$
$127$	−3.42554	−	5.93321i	−0.303968	−	0.526487i	−0.977031	+	0.213098i	$0.931645\pi$
$128$		0			0
$129$	3.15081	+	12.6233i	0.277413	+	1.11142i
$130$		0			0
$131$	3.74217	−	21.2229i	0.326955	−	1.85425i	−0.168610	−	0.985683i	$-0.553928\pi$
$131$	3.74217	−	21.2229i	0.326955	−	1.85425i	0.495565	−	0.868571i	$-0.334961\pi$
$132$		0			0
$133$	1.79307	−	1.50457i	0.155479	−	0.130463i
$134$		0			0
$135$	−12.7937	+	8.00816i	−1.10110	+	0.689233i
$136$		0			0
$137$	16.3829	−	13.7469i	1.39969	−	1.17448i	0.438446	−	0.898757i	$-0.355529\pi$
$137$	16.3829	−	13.7469i	1.39969	−	1.17448i	0.961239	−	0.275718i	$-0.0889155\pi$
$138$		0			0
$139$	−3.43030	+	19.4542i	−0.290954	+	1.65008i	0.392253	+	0.919857i	$0.371696\pi$
$139$	−3.43030	+	19.4542i	−0.290954	+	1.65008i	−0.683207	+	0.730225i	$0.739415\pi$
$140$		0			0
$141$	−4.13066	+	3.99099i	−0.347864	+	0.336102i
$142$		0			0
$143$	8.61853	+	14.9277i	0.720718	+	1.24832i
$144$		0			0
$145$	−4.18560	+	7.24967i	−0.347595	+	0.602052i
$146$		0			0
$147$	−8.18631	−	5.94447i	−0.675195	−	0.490292i
$148$		0			0
$149$	2.09436	+	1.75738i	0.171577	+	0.143970i	0.724532	−	0.689241i	$-0.242056\pi$
$149$	2.09436	+	1.75738i	0.171577	+	0.143970i	−0.552956	+	0.833211i	$0.686500\pi$
$150$		0			0
$151$	−19.2388	−	7.00235i	−1.56563	−	0.569843i	−0.593614	−	0.804750i	$-0.702299\pi$
$151$	−19.2388	−	7.00235i	−1.56563	−	0.569843i	−0.972018	+	0.234907i	$0.924522\pi$
$152$		0			0
$153$	−13.0868	−	16.7325i	−1.05801	−	1.35275i
$154$		0			0
$155$	1.39807	+	7.92886i	0.112296	+	0.636862i
$156$		0			0
$157$	−4.42835	+	1.61179i	−0.353421	+	0.128635i	−0.512629	−	0.858610i	$-0.671328\pi$
$157$	−4.42835	+	1.61179i	−0.353421	+	0.128635i	0.159208	+	0.987245i	$0.449106\pi$
$158$		0			0
$159$	1.82851	+	2.70937i	0.145011	+	0.214867i
$160$		0			0
$161$	−6.89263			−0.543215
$162$		0			0
$163$	24.9764			1.95630			0.978150	−	0.207899i	$-0.0666627\pi$
$163$	24.9764			1.95630			0.978150	+	0.207899i	$0.0666627\pi$
$164$		0			0
$165$	−9.83568	−	14.5739i	−0.765707	−	1.13458i
$166$		0			0
$167$	14.7375	−	5.36402i	1.14042	−	0.415081i	0.298358	−	0.954454i	$-0.403561\pi$
$167$	14.7375	−	5.36402i	1.14042	−	0.415081i	0.842067	+	0.539373i	$0.181339\pi$
$168$		0			0
$169$	1.96703	+	11.1556i	0.151310	+	0.858123i
$170$		0			0
$171$	−6.45875	+	0.911118i	−0.493913	+	0.0696749i
$172$		0			0
$173$	−10.6783	−	3.88659i	−0.811858	−	0.295492i	−0.0974666	−	0.995239i	$-0.531074\pi$
$173$	−10.6783	−	3.88659i	−0.811858	−	0.295492i	−0.714391	+	0.699747i	$0.753296\pi$
$174$		0			0
$175$	−2.83477	−	2.37865i	−0.214288	−	0.179809i
$176$		0			0
$177$	19.5048	+	14.1634i	1.46607	+	1.06458i
$178$		0			0
$179$	−7.38452	+	12.7904i	−0.551945	+	0.955997i	0.446189	+	0.894939i	$0.352781\pi$
$179$	−7.38452	+	12.7904i	−0.551945	+	0.955997i	−0.998134	+	0.0610585i	$0.980552\pi$
$180$		0			0
$181$	7.65465	+	13.2582i	0.568966	+	0.985478i	0.996669	+	0.0815582i	$0.0259896\pi$
$181$	7.65465	+	13.2582i	0.568966	+	0.985478i	−0.427703	+	0.903919i	$0.640677\pi$
$182$		0			0
$183$	19.0410	−	18.3971i	1.40755	−	1.35996i
$184$		0			0
$185$	−4.44876	+	25.2302i	−0.327080	+	1.85496i
$186$		0			0
$187$	18.9562	−	15.9061i	1.38621	−	1.16317i
$188$		0			0
$189$	−2.09955	−	5.18502i	−0.152720	−	0.377154i
$190$		0			0
$191$	1.62594	−	1.36432i	0.117649	−	0.0987190i	−0.582065	−	0.813142i	$-0.697755\pi$
$191$	1.62594	−	1.36432i	0.117649	−	0.0987190i	0.699714	+	0.714423i	$0.253311\pi$
$192$		0			0
$193$	−1.28004	+	7.25947i	−0.0921393	+	0.522548i	0.903447	+	0.428699i	$0.141028\pi$
$193$	−1.28004	+	7.25947i	−0.0921393	+	0.522548i	−0.995586	+	0.0938486i	$0.970083\pi$
$194$		0			0
$195$	−6.00951	−	24.0763i	−0.430350	−	1.72414i
$196$		0			0
$197$	0.546844	+	0.947161i	0.0389610	+	0.0674824i	0.884848	−	0.465879i	$-0.154262\pi$
$197$	0.546844	+	0.947161i	0.0389610	+	0.0674824i	−0.845887	+	0.533362i	$0.820929\pi$
$198$		0			0
$199$	5.44607	−	9.43287i	0.386062	−	0.668678i	−0.605854	−	0.795576i	$-0.707169\pi$
$199$	5.44607	−	9.43287i	0.386062	−	0.668678i	0.991916	+	0.126897i	$0.0405019\pi$
$200$		0			0
$201$	−0.347400	+	3.31352i	−0.0245037	+	0.233717i
$202$		0			0
$203$	−2.37671	−	1.99430i	−0.166813	−	0.139972i
$204$		0			0
$205$	3.39780	+	1.23670i	0.237313	+	0.0863747i
$206$		0			0
$207$	16.2940	+	10.1699i	1.13251	+	0.706860i
$208$		0			0
$209$	−1.31944	−	7.48290i	−0.0912674	−	0.517603i
$210$		0			0
$211$	12.0707	−	4.39337i	0.830980	−	0.302452i	0.108719	−	0.994073i	$-0.465325\pi$
$211$	12.0707	−	4.39337i	0.830980	−	0.302452i	0.722261	+	0.691620i	$0.243103\pi$
$212$		0			0
$213$	−2.24639	+	0.157665i	−0.153920	+	0.0108031i
$214$		0			0
$215$	21.8193			1.48806
$216$		0			0
$217$	−2.98397			−0.202565
$218$		0			0
$219$	4.34135	−	8.90692i	0.293361	−	0.601874i
$220$		0			0
$221$	32.8186	−	11.9450i	2.20762	−	0.803507i
$222$		0			0
$223$	−1.41853	−	8.04489i	−0.0949919	−	0.538726i	−0.994750	−	0.102336i	$-0.967368\pi$
$223$	−1.41853	−	8.04489i	−0.0949919	−	0.538726i	0.899758	−	0.436389i	$-0.143743\pi$
$224$		0			0
$225$	3.19167	+	9.80573i	0.212778	+	0.653715i
$226$		0			0
$227$	−12.0494	−	4.38563i	−0.799749	−	0.291085i	−0.0903664	−	0.995909i	$-0.528804\pi$
$227$	−12.0494	−	4.38563i	−0.799749	−	0.291085i	−0.709382	+	0.704824i	$0.751026\pi$
$228$		0			0
$229$	−8.86465	−	7.43833i	−0.585793	−	0.491538i	0.301051	−	0.953608i	$-0.402663\pi$
$229$	−8.86465	−	7.43833i	−0.585793	−	0.491538i	−0.886844	+	0.462070i	$0.847107\pi$
$230$		0			0
$231$	5.95240	−	2.65202i	0.391639	−	0.174490i
$232$		0			0
$233$	4.64371	−	8.04314i	0.304219	−	0.526923i	−0.672868	−	0.739763i	$-0.734938\pi$
$233$	4.64371	−	8.04314i	0.304219	−	0.526923i	0.977087	+	0.212839i	$0.0682711\pi$
$234$		0			0
$235$	4.81622	+	8.34193i	0.314175	+	0.544168i
$236$		0			0
$237$	15.9775	+	4.57701i	1.03785	+	0.297309i
$238$		0			0
$239$	−0.591690	+	3.35564i	−0.0382732	+	0.217058i	−0.997946	−	0.0640613i	$-0.979595\pi$
$239$	−0.591690	+	3.35564i	−0.0382732	+	0.217058i	0.959673	+	0.281120i	$0.0907058\pi$
$240$		0			0
$241$	1.24976	−	1.04867i	0.0805039	−	0.0675508i	−0.601648	−	0.798762i	$-0.705489\pi$
$241$	1.24976	−	1.04867i	0.0805039	−	0.0675508i	0.682152	+	0.731211i	$0.261044\pi$
$242$		0			0
$243$	−2.68709	+	15.3551i	−0.172377	+	0.985031i
$244$		0			0
$245$	−12.9971	+	10.9058i	−0.830353	+	0.696749i
$246$		0			0
$247$	1.86220	−	10.5611i	0.118489	−	0.671984i
$248$		0			0
$249$	−4.25505	−	1.21893i	−0.269653	−	0.0772464i
$250$		0			0
$251$	−3.89990	−	6.75483i	−0.246160	−	0.426361i	0.716297	−	0.697795i	$-0.245835\pi$
$251$	−3.89990	−	6.75483i	−0.246160	−	0.426361i	−0.962457	+	0.271434i	$0.912502\pi$
$252$		0			0
$253$	−11.1874	+	19.3771i	−0.703346	+	1.21823i
$254$		0			0
$255$	−32.5408	+	14.4981i	−2.03778	+	0.907909i
$256$		0			0
$257$	−20.7171	−	17.3837i	−1.29229	−	1.08436i	−0.991422	−	0.130699i	$-0.958278\pi$
$257$	−20.7171	−	17.3837i	−1.29229	−	1.08436i	−0.300872	−	0.953664i	$-0.597278\pi$
$258$		0			0
$259$	−8.92257	−	3.24755i	−0.554421	−	0.201793i
$260$		0			0
$261$	2.67595	+	8.22127i	0.165637	+	0.508884i
$262$		0			0
$263$	1.01502	+	5.75649i	0.0625891	+	0.354960i	0.999978	+	0.00667518i	$0.00212479\pi$
$263$	1.01502	+	5.75649i	0.0625891	+	0.354960i	−0.937389	+	0.348285i	$0.886764\pi$
$264$		0			0
$265$	5.15109	−	1.87484i	0.316429	−	0.115171i
$266$		0			0
$267$	2.69861	−	5.53660i	0.165152	−	0.338835i
$268$		0			0
$269$	−6.88970			−0.420072			−0.210036	−	0.977694i	$-0.567358\pi$
$269$	−6.88970			−0.420072			−0.210036	+	0.977694i	$0.567358\pi$
$270$		0			0
$271$	−13.3560			−0.811321			−0.405660	−	0.914024i	$-0.632958\pi$
$271$	−13.3560			−0.811321			−0.405660	+	0.914024i	$0.632958\pi$
$272$		0			0
$273$	9.17450	−	0.643923i	0.555266	−	0.0389720i
$274$		0			0
$275$	−11.2882	+	4.10856i	−0.680703	+	0.247756i
$276$		0			0
$277$	2.57154	+	14.5839i	0.154509	+	0.876265i	0.959233	+	0.282616i	$0.0912021\pi$
$277$	2.57154	+	14.5839i	0.154509	+	0.876265i	−0.804724	+	0.593649i	$0.797687\pi$
$278$		0			0
$279$	7.05404	+	4.40279i	0.422314	+	0.263588i
$280$		0			0
$281$	6.64712	+	2.41935i	0.396534	+	0.144327i	0.532588	−	0.846375i	$-0.321220\pi$
$281$	6.64712	+	2.41935i	0.396534	+	0.144327i	−0.136054	+	0.990701i	$0.543442\pi$
$282$		0			0
$283$	−0.918128	−	0.770401i	−0.0545771	−	0.0457956i	0.615091	−	0.788456i	$-0.289119\pi$
$283$	−0.918128	−	0.770401i	−0.0545771	−	0.0457956i	−0.669668	+	0.742660i	$0.733564\pi$
$284$		0			0
$285$	−1.14061	+	10.8792i	−0.0675638	+	0.644427i
$286$		0			0
$287$	−0.670065	+	1.16059i	−0.0395527	+	0.0685073i
$288$		0			0
$289$	−16.5690	−	28.6984i	−0.974647	−	1.68814i
$290$		0			0
$291$	2.86428	+	11.4754i	0.167907	+	0.672698i
$292$		0			0
$293$	−2.73358	+	15.5029i	−0.159697	+	0.905688i	0.794668	+	0.607045i	$0.207645\pi$
$293$	−2.73358	+	15.5029i	−0.159697	+	0.905688i	−0.954365	+	0.298643i	$0.903466\pi$
$294$		0			0
$295$	30.9670	−	25.9844i	1.80297	−	1.51287i
$296$		0			0
$297$	−17.9843	−	2.51334i	−1.04356	−	0.145838i
$298$		0			0
$299$	−24.1908	+	20.2985i	−1.39899	+	1.17389i
$300$		0			0
$301$	−1.40425	+	7.96392i	−0.0809399	+	0.459033i
$302$		0			0
$303$	−5.46072	+	5.27608i	−0.313710	+	0.303103i
$304$		0			0
$305$	−22.2012	−	38.4535i	−1.27123	−	2.20184i
$306$		0			0
$307$	9.13677	−	15.8253i	0.521463	−	0.903200i	−0.478225	−	0.878237i	$-0.658720\pi$
$307$	9.13677	−	15.8253i	0.521463	−	0.903200i	0.999688	−	0.0249632i	$-0.00794685\pi$
$308$		0			0
$309$	18.0921	+	13.1376i	1.02923	+	0.747370i
$310$		0			0
$311$	17.9485	+	15.0605i	1.01776	+	0.854005i	0.989345	−	0.145591i	$-0.0465083\pi$
$311$	17.9485	+	15.0605i	1.01776	+	0.854005i	0.0284189	+	0.999596i	$0.490953\pi$
$312$		0			0
$313$	−23.8400	−	8.67707i	−1.34752	−	0.490457i	−0.435346	−	0.900263i	$-0.643374\pi$
$313$	−23.8400	−	8.67707i	−1.34752	−	0.490457i	−0.912173	+	0.409806i	$0.865596\pi$
$314$		0			0
$315$	−9.28933	+	1.31042i	−0.523394	+	0.0738338i
$316$		0			0
$317$	−0.558276	−	3.16614i	−0.0313559	−	0.177828i	0.965108	−	0.261853i	$-0.0843336\pi$
$317$	−0.558276	−	3.16614i	−0.0313559	−	0.177828i	−0.996464	+	0.0840249i	$0.973222\pi$
$318$		0			0
$319$	−9.46418	+	3.44468i	−0.529892	+	0.192865i
$320$		0			0
$321$	−3.72643	−	5.52158i	−0.207989	−	0.308185i
$322$		0			0
$323$	−15.3953			−0.856620
$324$		0			0
$325$	−16.9541			−0.940446
$326$		0			0
$327$	10.5388	+	15.6157i	0.582796	+	0.863550i
$328$		0			0
$329$	−3.35472	+	1.22102i	−0.184952	+	0.0673170i
$330$		0			0
$331$	1.21547	+	6.89327i	0.0668083	+	0.378889i	0.999819	+	0.0190393i	$0.00606076\pi$
$331$	1.21547	+	6.89327i	0.0668083	+	0.378889i	−0.933010	+	0.359849i	$0.882828\pi$
$332$		0			0
$333$	16.3011	+	20.8422i	0.893292	+	1.14215i
$334$		0			0
$335$	5.25039	+	1.91098i	0.286859	+	0.104408i
$336$		0			0
$337$	16.0519	+	13.4691i	0.874402	+	0.733710i	0.965020	−	0.262176i	$-0.0844399\pi$
$337$	16.0519	+	13.4691i	0.874402	+	0.733710i	−0.0906185	+	0.995886i	$0.528884\pi$
$338$		0			0
$339$	7.19926	+	5.22773i	0.391010	+	0.283931i
$340$		0			0
$341$	−4.84327	+	8.38879i	−0.262278	+	0.454279i
$342$		0			0
$343$	−6.91207	−	11.9720i	−0.373216	−	0.646430i
$344$		0			0
$345$	23.1652	−	22.3819i	1.24717	−	1.20500i
$346$		0			0
$347$	−1.04316	+	5.91606i	−0.0559999	+	0.317591i	−0.999921	−	0.0125804i	$-0.995995\pi$
$347$	−1.04316	+	5.91606i	−0.0559999	+	0.317591i	0.943921	+	0.330171i	$0.107107\pi$
$348$		0			0
$349$	20.2988	−	17.0327i	1.08657	−	0.911738i	0.0901181	−	0.995931i	$-0.471276\pi$
$349$	20.2988	−	17.0327i	1.08657	−	0.911738i	0.996449	+	0.0841926i	$0.0268311\pi$
$350$		0			0
$351$	−22.6384	−	12.0146i	−1.20835	−	0.641291i
$352$		0			0
$353$	0.734318	−	0.616166i	0.0390838	−	0.0327952i	−0.623037	−	0.782193i	$-0.714101\pi$
$353$	0.734318	−	0.616166i	0.0390838	−	0.0327952i	0.662120	+	0.749398i	$0.269657\pi$
$354$		0			0
$355$	−0.655790	+	3.71917i	−0.0348057	+	0.197393i
$356$		0			0
$357$	−3.19747	−	12.8103i	−0.169228	−	0.677992i
$358$		0			0
$359$	−6.88101	−	11.9183i	−0.363166	−	0.629022i	0.625314	−	0.780373i	$-0.284971\pi$
$359$	−6.88101	−	11.9183i	−0.363166	−	0.629022i	−0.988480	+	0.151351i	$0.951638\pi$
$360$		0			0
$361$	7.13636	−	12.3605i	0.375598	−	0.650554i
$362$		0			0
$363$	0.219088	−	2.08968i	0.0114992	−	0.109680i
$364$		0			0
$365$	−12.7294	−	10.6813i	−0.666290	−	0.559083i
$366$		0			0
$367$	−10.3010	−	3.74925i	−0.537707	−	0.195709i	0.0588694	−	0.998266i	$-0.481250\pi$
$367$	−10.3010	−	3.74925i	−0.537707	−	0.195709i	−0.596576	+	0.802556i	$0.703473\pi$
$368$		0			0
$369$	3.29644	−	1.75493i	0.171606	−	0.0913581i
$370$		0			0
$371$	0.352792	+	2.00078i	0.0183160	+	0.103875i
$372$		0			0
$373$	18.7691	−	6.83140i	0.971828	−	0.353716i	0.193170	−	0.981165i	$-0.438123\pi$
$373$	18.7691	−	6.83140i	0.971828	−	0.353716i	0.778658	+	0.627449i	$0.215901\pi$
$374$		0			0
$375$	−7.84251	+	0.550436i	−0.404986	+	0.0284244i
$376$		0			0
$377$	−14.2146			−0.732089
$378$		0			0
$379$	−18.8505			−0.968285			−0.484142	−	0.874989i	$-0.660868\pi$
$379$	−18.8505			−0.968285			−0.484142	+	0.874989i	$0.660868\pi$
$380$		0			0
$381$	−5.19914	+	10.6668i	−0.266360	+	0.546477i
$382$		0			0
$383$	−18.3285	+	6.67102i	−0.936542	+	0.340873i	−0.764799	−	0.644269i	$-0.777162\pi$
$383$	−18.3285	+	6.67102i	−0.936542	+	0.340873i	−0.171742	+	0.985142i	$0.554940\pi$
$384$		0			0
$385$	−1.89769	−	10.7623i	−0.0967151	−	0.548499i
$386$		0			0
$387$	15.0702	−	16.7546i	0.766063	−	0.851683i
$388$		0			0
$389$	−14.4575	−	5.26210i	−0.733024	−	0.266799i	−0.0515798	−	0.998669i	$-0.516426\pi$
$389$	−14.4575	−	5.26210i	−0.733024	−	0.266799i	−0.681444	+	0.731870i	$0.738648\pi$
$390$		0			0
$391$	34.7283	+	29.1405i	1.75629	+	1.47370i
$392$		0			0
$393$	−34.0953	+	15.1907i	−1.71988	+	0.766272i
$394$		0			0
$395$	13.9363	−	24.1384i	0.701211	−	1.21453i
$396$		0			0
$397$	−7.62904	−	13.2139i	−0.382891	−	0.663186i	0.608583	−	0.793490i	$-0.291738\pi$
$397$	−7.62904	−	13.2139i	−0.382891	−	0.663186i	−0.991474	+	0.130304i	$0.958405\pi$
$398$		0			0
$399$	−3.89743	−	1.11648i	−0.195116	−	0.0558940i
$400$		0			0
$401$	−2.14588	+	12.1699i	−0.107160	+	0.607736i	0.883175	+	0.469043i	$0.155401\pi$
$401$	−2.14588	+	12.1699i	−0.107160	+	0.607736i	−0.990335	+	0.138693i	$0.955710\pi$
$402$		0			0
$403$	−10.4727	+	8.78767i	−0.521684	+	0.437745i
$404$		0			0
$405$	23.8933	+	10.6084i	1.18727	+	0.527137i
$406$		0			0
$407$	−23.6120	+	19.8128i	−1.17040	+	0.982084i
$408$		0			0
$409$	−0.255472	+	1.44885i	−0.0126323	+	0.0716412i	−0.990472	−	0.137713i	$-0.956025\pi$
$409$	−0.255472	+	1.44885i	−0.0126323	+	0.0716412i	0.977840	+	0.209354i	$0.0671361\pi$
$410$		0			0
$411$	−35.6099	−	10.2010i	−1.75651	−	0.503180i
$412$		0			0
$413$	7.49117	+	12.9751i	0.368617	+	0.638463i
$414$		0			0
$415$	−3.71145	+	6.42842i	−0.182188	+	0.315559i
$416$		0			0
$417$	31.2538	−	13.9247i	1.53050	−	0.681898i
$418$		0			0
$419$	24.6928	+	20.7198i	1.20632	+	1.01223i	0.999426	+	0.0338638i	$0.0107813\pi$
$419$	24.6928	+	20.7198i	1.20632	+	1.01223i	0.206898	+	0.978363i	$0.433663\pi$
$420$		0			0
$421$	26.6413	+	9.69665i	1.29842	+	0.472586i	0.896481	−	0.443082i	$-0.146115\pi$
$421$	26.6413	+	9.69665i	1.29842	+	0.472586i	0.401937	+	0.915667i	$0.368337\pi$
$422$		0			0
$423$	9.73208	+	2.06337i	0.473190	+	0.100324i
$424$		0			0
$425$	4.22648	+	23.9696i	0.205015	+	1.16270i
$426$		0			0
$427$	15.4642	−	5.62850i	0.748363	−	0.272382i
$428$		0			0
$429$	13.0808	−	26.8373i	0.631549	−	1.29572i
$430$		0			0
$431$	4.64545			0.223764			0.111882	−	0.993722i	$-0.464312\pi$
$431$	4.64545			0.223764			0.111882	+	0.993722i	$0.464312\pi$
$432$		0			0
$433$	13.4386			0.645818			0.322909	−	0.946430i	$-0.395339\pi$
$433$	13.4386			0.645818			0.322909	+	0.946430i	$0.395339\pi$
$434$		0			0
$435$	14.4638	−	1.01516i	0.693484	−	0.0486730i
$436$		0			0
$437$	13.0809	−	4.76106i	0.625745	−	0.227753i
$438$		0			0
$439$	−0.899835	−	5.10322i	−0.0429468	−	0.243563i	0.955776	−	0.294097i	$-0.0950189\pi$
$439$	−0.899835	−	5.10322i	−0.0429468	−	0.243563i	−0.998722	+	0.0505338i	$0.983908\pi$
$440$		0			0
$441$	−0.602505	+	17.5127i	−0.0286907	+	0.833938i
$442$		0			0
$443$	−17.7897	−	6.47493i	−0.845216	−	0.307633i	−0.117128	−	0.993117i	$-0.537369\pi$
$443$	−17.7897	−	6.47493i	−0.845216	−	0.307633i	−0.728088	+	0.685483i	$0.759591\pi$
$444$		0			0
$445$	−7.91271	−	6.63955i	−0.375098	−	0.314745i
$446$		0			0
$447$	0.493770	−	4.70960i	0.0233545	−	0.222756i
$448$		0			0
$449$	9.37884	−	16.2446i	0.442615	−	0.766631i	−0.555268	−	0.831672i	$-0.687384\pi$
$449$	9.37884	−	16.2446i	0.442615	−	0.766631i	0.997883	+	0.0650402i	$0.0207176\pi$
$450$		0			0
$451$	2.17516	+	3.76749i	0.102424	+	0.177404i
$452$		0			0
$453$	8.58771	+	34.4056i	0.403486	+	1.61652i
$454$		0			0
$455$	2.67832	−	15.1895i	0.125562	−	0.712095i
$456$		0			0
$457$	19.2001	−	16.1108i	0.898143	−	0.753631i	−0.0716839	−	0.997427i	$-0.522837\pi$
$457$	19.2001	−	16.1108i	0.898143	−	0.753631i	0.969826	+	0.243796i	$0.0783928\pi$
$458$		0			0
$459$	−11.3426	+	35.0010i	−0.529426	+	1.63371i
$460$		0			0
$461$	9.41301	−	7.89845i	0.438408	−	0.367868i	−0.396706	−	0.917946i	$-0.629847\pi$
$461$	9.41301	−	7.89845i	0.438408	−	0.367868i	0.835113	+	0.550078i	$0.185402\pi$
$462$		0			0
$463$	2.99174	−	16.9670i	0.139038	−	0.788525i	−0.832924	−	0.553387i	$-0.813335\pi$
$463$	2.99174	−	16.9670i	0.139038	−	0.788525i	0.971962	−	0.235137i	$-0.0755539\pi$
$464$		0			0
$465$	10.0287	−	9.68963i	0.465071	−	0.449346i
$466$		0			0
$467$	8.84287	+	15.3163i	0.409199	+	0.708754i	0.994800	−	0.101846i	$-0.0324747\pi$
$467$	8.84287	+	15.3163i	0.409199	+	0.708754i	−0.585601	+	0.810600i	$0.699141\pi$
$468$		0			0
$469$	−1.03541	+	1.79338i	−0.0478106	+	0.0828104i
$470$		0			0
$471$	6.60474	+	4.79602i	0.304330	+	0.220989i
$472$		0			0
$473$	20.1096	+	16.8740i	0.924641	+	0.775866i
$474$		0			0
$475$	7.02291	+	2.55613i	0.322233	+	0.117283i
$476$		0			0
$477$	2.11812	−	5.25034i	0.0969822	−	0.240397i
$478$		0			0
$479$	−2.80736	−	15.9213i	−0.128272	−	0.727464i	−0.979311	−	0.202362i	$-0.935138\pi$
$479$	−2.80736	−	15.9213i	−0.128272	−	0.727464i	0.851039	−	0.525102i	$-0.175973\pi$
$480$		0			0
$481$	−40.8792	+	14.8788i	−1.86393	+	0.678415i
$482$		0			0
$483$	6.67841	+	9.89564i	0.303878	+	0.450267i
$484$		0			0
$485$	19.8350			0.900663
$486$		0			0
$487$	−28.1628			−1.27618			−0.638088	−	0.769963i	$-0.720275\pi$
$487$	−28.1628			−1.27618			−0.638088	+	0.769963i	$0.720275\pi$
$488$		0			0
$489$	−24.2001	−	35.8582i	−1.09437	−	1.62156i
$490$		0			0
$491$	3.64776	−	1.32768i	0.164621	−	0.0599172i	−0.258395	−	0.966039i	$-0.583194\pi$
$491$	3.64776	−	1.32768i	0.164621	−	0.0599172i	0.423016	+	0.906122i	$0.360971\pi$
$492$		0			0
$493$	3.54355	+	20.0964i	0.159593	+	0.905099i
$494$		0			0
$495$	−11.3935	+	28.2419i	−0.512100	+	1.26938i
$496$		0			0
$497$	−1.31527	−	0.478720i	−0.0589980	−	0.0214735i
$498$		0			0
$499$	3.94018	+	3.30620i	0.176387	+	0.148006i	0.726707	−	0.686948i	$-0.241050\pi$
$499$	3.94018	+	3.30620i	0.176387	+	0.148006i	−0.550320	+	0.834954i	$0.685494\pi$
$500$		0			0
$501$	−21.9806	−	15.9611i	−0.982019	−	0.713091i
$502$		0			0
$503$	14.4751	−	25.0716i	0.645412	−	1.11789i	−0.338794	−	0.940861i	$-0.610019\pi$
$503$	14.4751	−	25.0716i	0.645412	−	1.11789i	0.984206	−	0.177026i	$-0.0566478\pi$
$504$		0			0
$505$	6.36703	+	11.0280i	0.283329	+	0.490741i
$506$		0			0
$507$	14.1100	−	13.6329i	0.626648	−	0.605460i
$508$		0			0
$509$	4.18488	−	23.7337i	0.185492	−	1.05198i	−0.739830	−	0.672793i	$-0.765094\pi$
$509$	4.18488	−	23.7337i	0.185492	−	1.05198i	0.925322	−	0.379182i	$-0.123795\pi$
$510$		0			0
$511$	4.71786	−	3.95875i	0.208706	−	0.175125i
$512$		0			0
$513$	7.56610	+	8.38993i	0.334051	+	0.370424i
$514$		0			0
$515$	28.7242	−	24.1024i	1.26574	−	1.06208i
$516$		0			0
$517$	−2.01241	+	11.4129i	−0.0885055	+	0.501940i
$518$		0			0
$519$	4.76653	+	19.0965i	0.209227	+	0.838243i
$520$		0			0
$521$	−8.53592	−	14.7846i	−0.373965	−	0.647727i	0.616206	−	0.787585i	$-0.288669\pi$
$521$	−8.53592	−	14.7846i	−0.373965	−	0.647727i	−0.990172	+	0.139858i	$0.955335\pi$
$522$		0			0
$523$	−9.43922	+	16.3492i	−0.412748	+	0.714901i	−0.995189	−	0.0979723i	$-0.968764\pi$
$523$	−9.43922	+	16.3492i	−0.412748	+	0.714901i	0.582441	+	0.812873i	$0.302098\pi$
$524$		0			0
$525$	−0.668330	+	6.37456i	−0.0291683	+	0.278209i
$526$		0			0
$527$	15.0347	+	12.6156i	0.654920	+	0.549543i
$528$		0			0
$529$	−16.9064	−	6.15342i	−0.735060	−	0.267540i
$530$		0			0
$531$	1.43554	−	41.7259i	0.0622969	−	1.81075i
$532$		0			0
$533$	1.06618	+	6.04659i	0.0461812	+	0.261907i
$534$		0			0
$535$	−10.4977	+	3.82084i	−0.453854	+	0.165189i
$536$		0			0
$537$	25.5180	−	1.79101i	1.10118	−	0.0772877i
$538$		0			0
$539$	−20.4127			−0.879239
$540$		0			0
$541$	−8.24128			−0.354320			−0.177160	−	0.984182i	$-0.556691\pi$
$541$	−8.24128			−0.354320			−0.177160	+	0.984182i	$0.556691\pi$
$542$		0			0
$543$	11.6179	−	23.8359i	0.498572	−	1.02289i
$544$		0			0
$545$	29.6887	−	10.8058i	1.27172	−	0.462870i
$546$		0			0
$547$	−5.61233	−	31.8291i	−0.239966	−	1.36091i	−0.831899	−	0.554927i	$-0.812746\pi$
$547$	−5.61233	−	31.8291i	−0.239966	−	1.36091i	0.591934	−	0.805987i	$-0.298365\pi$
$548$		0			0
$549$	−44.8617	−	9.51144i	−1.91465	−	0.405938i
$550$		0			0
$551$	5.88811	+	2.14310i	0.250842	+	0.0912990i
$552$		0			0
$553$	7.91346	+	6.64018i	0.336515	+	0.282369i
$554$		0			0
$555$	40.5331	−	18.0590i	1.72053	−	0.766563i
$556$		0			0
$557$	−4.10631	+	7.11234i	−0.173990	+	0.301360i	−0.939811	−	0.341694i	$-0.888999\pi$
$557$	−4.10631	+	7.11234i	−0.173990	+	0.301360i	0.765821	+	0.643053i	$0.222333\pi$
$558$		0			0
$559$	18.5250	+	32.0862i	0.783523	+	1.35710i
$560$		0			0
$561$	−41.2032	−	11.8033i	−1.73960	−	0.498336i
$562$		0			0
$563$	1.28986	−	7.31517i	0.0543612	−	0.308298i	−0.945488	−	0.325657i	$-0.894415\pi$
$563$	1.28986	−	7.31517i	0.0543612	−	0.308298i	0.999849	+	0.0173588i	$0.00552577\pi$
$564$		0			0
$565$	11.4300	−	9.59089i	0.480863	−	0.403492i
$566$		0			0
$567$	−5.40975	+	8.03817i	−0.227188	+	0.337571i
$568$		0			0
$569$	−18.8325	+	15.8024i	−0.789500	+	0.662469i	−0.945622	−	0.325268i	$-0.894545\pi$
$569$	−18.8325	+	15.8024i	−0.789500	+	0.662469i	0.156121	+	0.987738i	$0.450101\pi$
$570$		0			0
$571$	−7.70985	+	43.7247i	−0.322647	+	1.82982i	0.203072	+	0.979164i	$0.434907\pi$
$571$	−7.70985	+	43.7247i	−0.322647	+	1.82982i	−0.525719	+	0.850658i	$0.676204\pi$
$572$		0			0
$573$	−3.53415	−	1.01241i	−0.147641	−	0.0422942i
$574$		0			0
$575$	−11.0038	−	19.0591i	−0.458889	−	0.794819i
$576$		0			0
$577$	0.599153	−	1.03776i	0.0249431	−	0.0432027i	−0.853284	−	0.521446i	$-0.825393\pi$
$577$	0.599153	−	1.03776i	0.0249431	−	0.0432027i	0.878227	+	0.478243i	$0.158726\pi$
$578$		0			0
$579$	11.6626	−	5.19612i	0.484680	−	0.215943i
$580$		0			0
$581$	−2.10748	−	1.76838i	−0.0874328	−	0.0733648i
$582$		0			0
$583$	6.19738	+	2.25566i	0.256669	+	0.0934200i
$584$		0			0
$585$	−28.7433	+	31.9558i	−1.18839	+	1.32121i
$586$		0			0
$587$	6.33127	+	35.9064i	0.261319	+	1.48202i	0.779315	+	0.626632i	$0.215567\pi$
$587$	6.33127	+	35.9064i	0.261319	+	1.48202i	−0.517996	+	0.855383i	$0.673322\pi$
$588$		0			0
$589$	5.66302	−	2.06117i	0.233340	−	0.0849290i
$590$		0			0
$591$	0.829976	−	1.70282i	0.0341407	−	0.0700446i
$592$		0			0
$593$	26.8744			1.10360			0.551800	−	0.833977i	$-0.313941\pi$
$593$	26.8744			1.10360			0.551800	+	0.833977i	$0.313941\pi$
$594$		0			0
$595$	−22.1424			−0.907751
$596$		0			0
$597$	−18.8194	+	1.32086i	−0.770229	+	0.0540594i
$598$		0			0
$599$	−11.3665	+	4.13706i	−0.464422	+	0.169036i	−0.563624	−	0.826032i	$-0.690593\pi$
$599$	−11.3665	+	4.13706i	−0.464422	+	0.169036i	0.0992019	+	0.995067i	$0.468371\pi$
$600$		0			0
$601$	−2.30085	−	13.0487i	−0.0938535	−	0.532270i	−0.995093	−	0.0989476i	$-0.968452\pi$
$601$	−2.30085	−	13.0487i	−0.0938535	−	0.532270i	0.901239	−	0.433322i	$-0.142659\pi$
$602$		0			0
$603$	5.09377	−	2.71178i	0.207434	−	0.110432i
$604$		0			0
$605$	−3.31117	−	1.20517i	−0.134618	−	0.0489970i
$606$		0			0
$607$	−28.4783	−	23.8961i	−1.15590	−	0.969914i	−0.156058	−	0.987748i	$-0.549879\pi$
$607$	−28.4783	−	23.8961i	−1.15590	−	0.969914i	−0.999841	+	0.0178336i	$0.994323\pi$
$608$		0			0
$609$	−0.560338	+	5.34453i	−0.0227060	+	0.216571i
$610$		0			0
$611$	−8.17811	+	14.1649i	−0.330851	+	0.573051i
$612$		0			0
$613$	−6.12248	−	10.6044i	−0.247284	−	0.428309i	0.715487	−	0.698626i	$-0.246205\pi$
$613$	−6.12248	−	10.6044i	−0.247284	−	0.428309i	−0.962771	+	0.270317i	$0.912872\pi$
$614$		0			0
$615$	−1.51669	−	6.07643i	−0.0611589	−	0.245025i
$616$		0			0
$617$	−2.56176	+	14.5284i	−0.103132	+	0.584893i	0.888817	+	0.458261i	$0.151528\pi$
$617$	−2.56176	+	14.5284i	−0.103132	+	0.584893i	−0.991950	+	0.126631i	$0.959583\pi$
$618$		0			0
$619$	0.0753697	−	0.0632427i	0.00302936	−	0.00254194i	−0.641272	−	0.767314i	$-0.721593\pi$
$619$	0.0753697	−	0.0632427i	0.00302936	−	0.00254194i	0.644301	+	0.764772i	$0.277148\pi$
$620$		0			0
$621$	−1.18678	−	33.2469i	−0.0476240	−	1.33415i
$622$		0			0
$623$	2.93265	−	2.46079i	0.117494	−	0.0985893i
$624$		0			0
$625$	−5.27393	+	29.9099i	−0.210957	+	1.19640i
$626$		0			0
$627$	−9.46466	+	9.14464i	−0.377982	+	0.365202i
$628$		0			0
$629$	31.2262	+	54.0854i	1.24507	+	2.15652i
$630$		0			0
$631$	0.793583	−	1.37453i	0.0315921	−	0.0547190i	−0.849797	−	0.527110i	$-0.823276\pi$
$631$	0.793583	−	1.37453i	0.0315921	−	0.0547190i	0.881389	+	0.472391i	$0.156609\pi$
$632$		0			0
$633$	−18.0030	−	13.0729i	−0.715557	−	0.519600i
$634$		0			0
$635$	15.2446	+	12.7918i	0.604964	+	0.507625i
$636$		0			0
$637$	−27.0723	−	9.85350i	−1.07264	−	0.390410i
$638$		0			0
$639$	2.40293	+	3.07234i	0.0950585	+	0.121540i
$640$		0			0
$641$	−1.33921	−	7.59503i	−0.0528956	−	0.299986i	0.946870	−	0.321615i	$-0.104226\pi$
$641$	−1.33921	−	7.59503i	−0.0528956	−	0.299986i	−0.999766	+	0.0216294i	$0.993115\pi$
$642$		0			0
$643$	−0.0605107	+	0.0220241i	−0.00238631	+	0.000868545i	−0.343213	−	0.939258i	$-0.611515\pi$
$643$	−0.0605107	+	0.0220241i	−0.00238631	+	0.000868545i	0.340827	+	0.940126i	$0.389293\pi$
$644$		0			0
$645$	−21.1412	−	31.3256i	−0.832432	−	1.23344i
$646$		0			0
$647$	−33.2653			−1.30780			−0.653898	−	0.756583i	$-0.726867\pi$
$647$	−33.2653			−1.30780			−0.653898	+	0.756583i	$0.726867\pi$
$648$		0			0
$649$	48.6356			1.90911
$650$		0			0
$651$	2.89123	+	4.28404i	0.113316	+	0.167905i
$652$		0			0
$653$	−1.98055	+	0.720861i	−0.0775049	+	0.0282095i	−0.380482	−	0.924788i	$-0.624242\pi$
$653$	−1.98055	+	0.720861i	−0.0775049	+	0.0282095i	0.302977	+	0.952998i	$0.402020\pi$
$654$		0			0
$655$	10.8699	+	61.6465i	0.424724	+	2.40873i
$656$		0			0
$657$	−16.9940	+	2.39729i	−0.662998	+	0.0935273i
$658$		0			0
$659$	−8.24248	−	3.00002i	−0.321081	−	0.116864i	0.176451	−	0.984309i	$-0.443538\pi$
$659$	−8.24248	−	3.00002i	−0.321081	−	0.116864i	−0.497533	+	0.867445i	$0.665760\pi$
$660$		0			0
$661$	25.5416	+	21.4319i	0.993453	+	0.833606i	0.986064	−	0.166367i	$-0.0532035\pi$
$661$	25.5416	+	21.4319i	0.993453	+	0.833606i	0.00738903	+	0.999973i	$0.497648\pi$
$662$		0			0
$663$	−48.9478	−	35.5434i	−1.90098	−	1.38039i
$664$		0			0
$665$	−3.39952	+	5.88814i	−0.131828	+	0.228332i
$666$		0			0
$667$	−9.22573	−	15.9794i	−0.357222	−	0.618726i
$668$		0			0
$669$	−10.1755	+	9.83143i	−0.393407	+	0.380105i
$670$		0			0
$671$	9.27652	−	52.6098i	0.358116	−	2.03098i
$672$		0			0
$673$	−31.2710	+	26.2395i	−1.20541	+	1.01146i	−0.205948	+	0.978563i	$0.566028\pi$
$673$	−31.2710	+	26.2395i	−1.20541	+	1.01146i	−0.999459	+	0.0328940i	$0.989528\pi$
$674$		0			0
$675$	10.9855	−	14.0832i	0.422831	−	0.542063i
$676$		0			0
$677$	−36.8176	+	30.8936i	−1.41501	+	1.18734i	−0.461066	+	0.887366i	$0.652533\pi$
$677$	−36.8176	+	30.8936i	−1.41501	+	1.18734i	−0.953948	+	0.299972i	$0.903023\pi$
$678$		0			0
$679$	−1.27655	+	7.23968i	−0.0489896	+	0.277834i
$680$		0			0
$681$	5.37856	+	21.5485i	0.206107	+	0.825741i
$682$		0			0
$683$	−15.0527	−	26.0720i	−0.575975	−	0.997619i	−0.995935	−	0.0900758i	$-0.971289\pi$
$683$	−15.0527	−	26.0720i	−0.575975	−	0.997619i	0.419960	−	0.907543i	$-0.362044\pi$
$684$		0			0
$685$	−31.0606	+	53.7986i	−1.18676	+	2.05554i
$686$		0			0
$687$	−2.08995	+	19.9340i	−0.0797364	+	0.760530i
$688$		0			0
$689$	7.13040	+	5.98312i	0.271647	+	0.227939i
$690$		0			0
$691$	27.0660	+	9.85122i	1.02964	+	0.374758i	0.800944	−	0.598740i	$-0.204332\pi$
$691$	27.0660	+	9.85122i	1.02964	+	0.374758i	0.228696	+	0.973498i	$0.426554\pi$
$692$		0			0
$693$	−9.57487	−	5.97617i	−0.363719	−	0.227016i
$694$		0			0
$695$	−9.96403	−	56.5088i	−0.377957	−	2.14350i
$696$		0			0
$697$	8.28281	−	3.01470i	0.313734	−	0.114190i
$698$		0			0
$699$	−16.0468	+	1.12626i	−0.606946	+	0.0425992i
$700$		0			0
$701$	10.0584			0.379902			0.189951	−	0.981794i	$-0.439167\pi$
$701$	10.0584			0.379902			0.189951	+	0.981794i	$0.439167\pi$
$702$		0			0
$703$	19.1766			0.723259
$704$		0			0
$705$	7.30985	−	14.9972i	0.275305	−	0.564829i
$706$		0			0
$707$	−4.43494	+	1.61419i	−0.166793	+	0.0607078i
$708$		0			0
$709$	−6.65867	−	37.7632i	−0.250071	−	1.41823i	−0.808414	−	0.588615i	$-0.799673\pi$
$709$	−6.65867	−	37.7632i	−0.250071	−	1.41823i	0.558342	−	0.829611i	$-0.311438\pi$
$710$		0			0
$711$	−8.90978	−	27.3734i	−0.334143	−	1.02658i
$712$		0			0
$713$	−16.6759	−	6.06952i	−0.624516	−	0.227305i
$714$		0			0
$715$	−38.3549	−	32.1836i	−1.43439	−	1.20360i
$716$		0			0
$717$	5.39094	−	2.40187i	0.201328	−	0.0896995i
$718$		0			0
$719$	−4.63910	+	8.03516i	−0.173009	+	0.299661i	−0.939471	−	0.342630i	$-0.888682\pi$
$719$	−4.63910	+	8.03516i	−0.173009	+	0.299661i	0.766461	+	0.642290i	$0.222016\pi$
$720$		0			0
$721$	6.94862	+	12.0354i	0.258780	+	0.448220i
$722$		0			0
$723$	−2.71648	−	0.778178i	−0.101027	−	0.0289407i
$724$		0			0
$725$	1.72020	−	9.75576i	0.0638868	−	0.362320i
$726$		0			0
$727$	−21.1660	+	17.7604i	−0.785004	+	0.658696i	−0.944503	−	0.328502i	$-0.893456\pi$
$727$	−21.1660	+	17.7604i	−0.785004	+	0.658696i	0.159500	+	0.987198i	$0.449012\pi$
$728$		0			0
$729$	24.6487	−	11.0201i	0.912914	−	0.408151i
$730$		0			0
$731$	40.7450	−	34.1891i	1.50701	−	1.26453i
$732$		0			0
$733$	7.68032	−	43.5573i	0.283679	−	1.60882i	−0.426286	−	0.904588i	$-0.640178\pi$
$733$	7.68032	−	43.5573i	0.283679	−	1.60882i	0.709966	−	0.704236i	$-0.248710\pi$
$734$		0			0
$735$	28.2505	+	8.09281i	1.04204	+	0.298508i
$736$		0			0
$737$	3.36113	+	5.82164i	0.123809	+	0.214443i
$738$		0			0
$739$	1.02889	−	1.78209i	0.0378484	−	0.0655553i	−0.846481	−	0.532419i	$-0.821283\pi$
$739$	1.02889	−	1.78209i	0.0378484	−	0.0655553i	0.884329	+	0.466864i	$0.154616\pi$
$740$		0			0
$741$	−16.9667	+	7.55931i	−0.623287	+	0.277698i
$742$		0			0
$743$	22.2183	+	18.6434i	0.815111	+	0.683959i	0.951822	−	0.306652i	$-0.0992086\pi$
$743$	22.2183	+	18.6434i	0.815111	+	0.683959i	−0.136711	+	0.990611i	$0.543653\pi$
$744$		0			0
$745$	−7.46254	−	2.71614i	−0.273406	−	0.0995117i
$746$		0			0
$747$	2.37281	+	7.28995i	0.0868166	+	0.266725i
$748$		0			0
$749$	−0.718973	−	4.07750i	−0.0262707	−	0.148989i
$750$		0			0
$751$	2.44493	−	0.889882i	0.0892168	−	0.0324723i	−0.297026	−	0.954869i	$-0.595995\pi$
$751$	2.44493	−	0.889882i	0.0892168	−	0.0324723i	0.386243	+	0.922397i	$0.373773\pi$
$752$		0			0
$753$	−5.91911	+	12.1439i	−0.215704	+	0.442549i
$754$		0			0
$755$	59.4697			2.16432
$756$		0			0
$757$	1.54321			0.0560890			0.0280445	−	0.999607i	$-0.491072\pi$
$757$	1.54321			0.0560890			0.0280445	+	0.999607i	$0.491072\pi$
$758$		0			0
$759$	38.6592	−	2.71334i	1.40324	−	0.0984880i
$760$		0			0
$761$	−23.2016	+	8.44468i	−0.841057	+	0.306120i	−0.726388	−	0.687284i	$-0.758803\pi$
$761$	−23.2016	+	8.44468i	−0.841057	+	0.306120i	−0.114668	+	0.993404i	$0.536580\pi$
$762$		0			0
$763$	2.03334	+	11.5317i	0.0736120	+	0.417474i
$764$		0			0
$765$	52.3442	+	32.6707i	1.89251	+	1.18121i
$766$		0			0
$767$	64.5027	+	23.4770i	2.32906	+	0.847707i
$768$		0			0
$769$	−12.9729	−	10.8856i	−0.467815	−	0.392544i	0.378182	−	0.925731i	$-0.376550\pi$
$769$	−12.9729	−	10.8856i	−0.467815	−	0.392544i	−0.845997	+	0.533188i	$0.820994\pi$
$770$		0			0
$771$	−4.88429	+	46.5866i	−0.175903	+	1.67777i
$772$		0			0
$773$	−4.52442	+	7.83653i	−0.162732	+	0.281860i	−0.935848	−	0.352405i	$-0.885364\pi$
$773$	−4.52442	+	7.83653i	−0.162732	+	0.281860i	0.773116	+	0.634265i	$0.218697\pi$
$774$		0			0
$775$	−4.76378	−	8.25110i	−0.171120	−	0.296388i
$776$		0			0
$777$	3.98281	+	15.9566i	0.142882	+	0.572441i
$778$		0			0
$779$	0.469986	−	2.66542i	0.0168390	−	0.0954986i
$780$		0			0
$781$	−3.48063	+	2.92060i	−0.124547	+	0.104507i
$782$		0			0
$783$	9.21038	−	11.8076i	0.329152	−	0.421968i
$784$		0			0
$785$	10.4861	−	8.79887i	0.374264	−	0.314045i
$786$		0			0
$787$	3.79697	−	21.5337i	0.135347	−	0.767592i	−0.839270	−	0.543715i	$-0.817017\pi$
$787$	3.79697	−	21.5337i	0.135347	−	0.767592i	0.974617	−	0.223878i	$-0.0718716\pi$
$788$		0			0
$789$	7.28103	−	7.03484i	0.259211	−	0.250447i
$790$		0			0
$791$	2.76501	+	4.78914i	0.0983124	+	0.170282i
$792$		0			0
$793$	37.6984	−	65.2955i	1.33871	−	2.31871i
$794$		0			0
$795$	−7.68268	−	5.57876i	−0.272477	−	0.197858i
$796$		0			0
$797$	−21.1313	−	17.7312i	−0.748507	−	0.628072i	0.186600	−	0.982436i	$-0.440253\pi$
$797$	−21.1313	−	17.7312i	−0.748507	−	0.628072i	−0.935108	+	0.354364i	$0.884697\pi$
$798$		0			0
$799$	22.0649	+	8.03097i	0.780600	+	0.284115i
$800$		0			0
$801$	−10.5636	+	1.49017i	−0.373245	+	0.0526527i
$802$		0			0
$803$	−3.47164	−	19.6887i	−0.122512	−	0.694798i
$804$		0			0
$805$	18.8137	−	6.84762i	0.663095	−	0.241347i
$806$		0			0
$807$	6.67557	+	9.89144i	0.234991	+	0.348195i
$808$		0			0
$809$	5.52715			0.194324			0.0971621	−	0.995269i	$-0.469023\pi$
$809$	5.52715			0.194324			0.0971621	+	0.995269i	$0.469023\pi$
$810$		0			0
$811$	−29.7570			−1.04491			−0.522454	−	0.852667i	$-0.674983\pi$
$811$	−29.7570			−1.04491			−0.522454	+	0.852667i	$0.674983\pi$
$812$		0			0
$813$	12.9409	+	19.1750i	0.453858	+	0.672498i
$814$		0			0
$815$	−68.1740	+	24.8133i	−2.38803	+	0.869172i
$816$		0			0
$817$	−2.83605	−	16.0840i	−0.0992207	−	0.562708i
$818$		0			0
$819$	−9.81384	−	12.5478i	−0.342923	−	0.438455i
$820$		0			0
$821$	36.1564	+	13.1599i	1.26187	+	0.459282i	0.884395	−	0.466739i	$-0.154571\pi$
$821$	36.1564	+	13.1599i	1.26187	+	0.459282i	0.377472	+	0.926021i	$0.376793\pi$
$822$		0			0
$823$	23.0223	+	19.3180i	0.802507	+	0.673383i	0.948807	−	0.315857i	$-0.102292\pi$
$823$	23.0223	+	19.3180i	0.802507	+	0.673383i	−0.146300	+	0.989240i	$0.546736\pi$
$824$		0			0
$825$	16.8360	+	12.2254i	0.586153	+	0.425634i
$826$		0			0
$827$	−5.21104	+	9.02579i	−0.181206	+	0.313857i	−0.942291	−	0.334794i	$-0.891333\pi$
$827$	−5.21104	+	9.02579i	−0.181206	+	0.313857i	0.761086	+	0.648651i	$0.224667\pi$
$828$		0			0
$829$	−5.86269	−	10.1545i	−0.203620	−	0.352679i	0.746072	−	0.665865i	$-0.231937\pi$
$829$	−5.86269	−	10.1545i	−0.203620	−	0.352679i	−0.949692	+	0.313185i	$0.898604\pi$
$830$		0			0
$831$	18.4463	−	17.8226i	0.639896	−	0.618260i
$832$		0			0
$833$	−7.18195	+	40.7309i	−0.248840	+	1.41124i
$834$		0			0
$835$	−34.8977	+	29.2826i	−1.20768	+	1.01337i
$836$		0			0
$837$	−0.513785	−	14.3933i	−0.0177590	−	0.497506i
$838$		0			0
$839$	−1.16305	+	0.975911i	−0.0401528	+	0.0336922i	−0.662643	−	0.748935i	$-0.730565\pi$
$839$	−1.16305	+	0.975911i	−0.0401528	+	0.0336922i	0.622490	+	0.782627i	$0.286121\pi$
$840$		0			0
$841$	−3.59355	+	20.3800i	−0.123916	+	0.702760i
$842$		0			0
$843$	−2.96710	−	11.8873i	−0.102193	−	0.409422i
$844$		0			0
$845$	−16.4518	−	28.4954i	−0.565961	−	0.980273i
$846$		0			0
$847$	0.652981	−	1.13100i	0.0224367	−	0.0388615i
$848$		0			0
$849$	−0.216460	+	2.06460i	−0.00742887	+	0.0708569i
$850$		0			0
$851$	−43.2580	−	36.2977i	−1.48286	−	1.24427i
$852$		0			0
$853$	18.0903	+	6.58434i	0.619401	+	0.225444i	0.632612	−	0.774469i	$-0.281983\pi$
$853$	18.0903	+	6.58434i	0.619401	+	0.225444i	−0.0132104	+	0.999913i	$0.504205\pi$
$854$		0			0
$855$	16.7242	−	8.90351i	0.571957	−	0.304494i
$856$		0			0
$857$	5.47302	+	31.0390i	0.186955	+	1.06027i	0.923418	+	0.383796i	$0.125383\pi$
$857$	5.47302	+	31.0390i	0.186955	+	1.06027i	−0.736463	+	0.676478i	$0.763506\pi$
$858$		0			0
$859$	13.4260	−	4.88666i	0.458089	−	0.166731i	−0.102660	−	0.994716i	$-0.532735\pi$
$859$	13.4260	−	4.88666i	0.458089	−	0.166731i	0.560749	+	0.827986i	$0.310513\pi$
$860$		0			0
$861$	2.31548	−	0.162515i	0.0789113	−	0.00553848i
$862$		0			0
$863$	−26.2533			−0.893672			−0.446836	−	0.894616i	$-0.647449\pi$
$863$	−26.2533			−0.893672			−0.446836	+	0.894616i	$0.647449\pi$
$864$		0			0
$865$	33.0081			1.12231
$866$		0			0
$867$	−25.1477	+	51.5943i	−0.854062	+	1.75223i
$868$		0			0
$869$	31.5118	−	11.4693i	1.06896	−	0.389071i
$870$		0			0
$871$	1.64749	+	9.34338i	0.0558231	+	0.316588i
$872$		0			0
$873$	13.6998	−	15.2309i	0.463666	−	0.515489i
$874$		0			0
$875$	−4.59183	−	1.67129i	−0.155232	−	0.0564999i
$876$		0			0
$877$	−5.52599	−	4.63686i	−0.186599	−	0.156576i	0.544703	−	0.838629i	$-0.316643\pi$
$877$	−5.52599	−	4.63686i	−0.186599	−	0.156576i	−0.731302	+	0.682054i	$0.761087\pi$
$878$		0			0
$879$	24.9059	−	11.0965i	0.840054	−	0.374276i
$880$		0			0
$881$	25.5633	−	44.2769i	0.861249	−	1.49173i	−0.00947431	−	0.999955i	$-0.503016\pi$
$881$	25.5633	−	44.2769i	0.861249	−	1.49173i	0.870724	−	0.491773i	$-0.163651\pi$
$882$		0			0
$883$	−1.77384	−	3.07239i	−0.0596946	−	0.103394i	0.834634	−	0.550805i	$-0.185679\pi$
$883$	−1.77384	−	3.07239i	−0.0596946	−	0.103394i	−0.894328	+	0.447411i	$0.852346\pi$
$884$		0			0
$885$	−67.3099	−	19.2820i	−2.26260	−	0.648158i
$886$		0			0
$887$	−6.39045	+	36.2420i	−0.214570	+	1.21689i	0.667080	+	0.744986i	$0.267544\pi$
$887$	−6.39045	+	36.2420i	−0.214570	+	1.21689i	−0.881651	+	0.471903i	$0.843567\pi$
$888$		0			0
$889$	−5.65004	+	4.74095i	−0.189496	+	0.159006i
$890$		0			0
$891$	13.8170	+	28.2551i	0.462889	+	0.946581i
$892$		0			0
$893$	5.52322	−	4.63453i	0.184828	−	0.155089i
$894$		0			0
$895$	7.44948	−	42.2481i	0.249009	−	1.41220i
$896$		0			0
$897$	52.5813	+	15.0628i	1.75564	+	0.502931i
$898$		0			0
$899$	−3.99402	−	6.91785i	−0.133208	−	0.230723i
$900$		0			0
$901$	6.68133	−	11.5724i	0.222588	−	0.385533i
$902$		0			0
$903$	12.7943	−	5.70034i	0.425768	−	0.189696i
$904$		0			0
$905$	−34.0653	−	28.5842i	−1.13237	−	0.950171i
$906$		0			0
$907$	16.8043	+	6.11628i	0.557979	+	0.203088i	0.605588	−	0.795778i	$-0.292938\pi$
$907$	16.8043	+	6.11628i	0.557979	+	0.203088i	−0.0476090	+	0.998866i	$0.515160\pi$
$908$		0			0
$909$	12.8658	+	2.72777i	0.426732	+	0.0904744i
$910$		0			0
$911$	7.42880	+	42.1308i	0.246127	+	1.39586i	0.817860	+	0.575417i	$0.195160\pi$
$911$	7.42880	+	42.1308i	0.246127	+	1.39586i	−0.571733	+	0.820440i	$0.693729\pi$
$912$		0			0
$913$	−8.39206	+	3.05446i	−0.277737	+	0.101088i
$914$		0			0
$915$	−33.6960	+	69.1323i	−1.11396	+	2.28544i
$916$		0			0
$917$	−23.2002			−0.766138
$918$		0			0
$919$	5.89290			0.194389			0.0971944	−	0.995265i	$-0.469013\pi$
$919$	5.89290			0.194389			0.0971944	+	0.995265i	$0.469013\pi$
$920$		0			0
$921$	−31.5730	+	2.21599i	−1.04037	+	0.0730194i
$922$		0			0
$923$	−6.02598	+	2.19328i	−0.198348	+	0.0721926i
$924$		0			0
$925$	−5.26455	−	29.8567i	−0.173097	−	0.981684i
$926$		0			0
$927$	1.33157	−	38.7039i	0.0437343	−	1.27120i
$928$		0			0
$929$	35.0428	+	12.7546i	1.14972	+	0.418463i	0.845414	−	0.534112i	$-0.179354\pi$
$929$	35.0428	+	12.7546i	1.14972	+	0.418463i	0.304304	+	0.952575i	$0.401576\pi$
$930$		0			0
$931$	9.72856	+	8.16323i	0.318841	+	0.267539i
$932$		0			0
$933$	4.23156	−	40.3608i	0.138535	−	1.32135i
$934$		0			0
$935$	−35.9393	+	62.2487i	−1.17534	+	2.03575i
$936$		0			0
$937$	9.42858	+	16.3308i	0.308018	+	0.533503i	0.977929	−	0.208938i	$-0.0670008\pi$
$937$	9.42858	+	16.3308i	0.308018	+	0.533503i	−0.669910	+	0.742442i	$0.733668\pi$
$938$		0			0
$939$	10.6416	+	42.6342i	0.347275	+	1.39131i
$940$		0			0
$941$	7.26953	−	41.2276i	0.236980	−	1.34398i	−0.601424	−	0.798930i	$-0.705400\pi$
$941$	7.26953	−	41.2276i	0.236980	−	1.34398i	0.838404	−	0.545050i	$-0.183489\pi$
$942$		0			0
$943$	−6.10533	+	5.12298i	−0.198817	+	0.166827i
$944$		0			0
$945$	10.8820	+	12.0669i	0.353991	+	0.392535i
$946$		0			0
$947$	25.5259	−	21.4188i	0.829481	−	0.696017i	−0.125691	−	0.992069i	$-0.540115\pi$
$947$	25.5259	−	21.4188i	0.829481	−	0.696017i	0.955172	+	0.296053i	$0.0956704\pi$
$948$		0			0
$949$	4.89974	−	27.7878i	0.159052	−	0.902030i
$950$		0			0
$951$	−4.00465	+	3.86925i	−0.129860	+	0.125469i
$952$		0			0
$953$	22.4362	+	38.8607i	0.726781	+	1.25882i	0.958237	+	0.285976i	$0.0923177\pi$
$953$	22.4362	+	38.8607i	0.726781	+	1.25882i	−0.231456	+	0.972845i	$0.574349\pi$
$954$		0			0
$955$	−3.08264	+	5.33930i	−0.0997520	+	0.172776i
$956$		0			0
$957$	14.1155	+	10.2500i	0.456290	+	0.331334i
$958$		0			0
$959$	−17.6372	−	14.7993i	−0.569534	−	0.477896i
$960$		0			0
$961$	21.9111	+	7.97500i	0.706810	+	0.257258i
$962$		0			0
$963$	−4.31664	+	10.7000i	−0.139102	+	0.344801i
$964$		0			0
$965$	−3.71815	−	21.0867i	−0.119691	−	0.678804i
$966$		0			0
$967$	7.03992	−	2.56232i	0.226389	−	0.0823987i	−0.226335	−	0.974049i	$-0.572675\pi$
$967$	7.03992	−	2.56232i	0.226389	−	0.0823987i	0.452724	+	0.891651i	$0.350452\pi$
$968$		0			0
$969$	14.9169	+	22.1029i	0.479199	+	0.710046i
$970$		0			0
$971$	−25.9164			−0.831698			−0.415849	−	0.909434i	$-0.636515\pi$
$971$	−25.9164			−0.831698			−0.415849	+	0.909434i	$0.636515\pi$
$972$		0			0
$973$	21.2667			0.681779
$974$		0			0
$975$	16.4272	+	24.3408i	0.526092	+	0.779530i
$976$		0			0
$977$	−18.1356	+	6.60080i	−0.580208	+	0.211178i	−0.615417	−	0.788202i	$-0.711012\pi$
$977$	−18.1356	+	6.60080i	−0.580208	+	0.211178i	0.0352094	+	0.999380i	$0.488790\pi$
$978$		0			0
$979$	−2.15800	−	12.2386i	−0.0689699	−	0.391148i
$980$		0			0
$981$	12.2080	−	30.2608i	0.389771	−	0.966152i
$982$		0			0
$983$	−45.0238	−	16.3873i	−1.43604	−	0.522675i	−0.497382	−	0.867532i	$-0.665705\pi$
$983$	−45.0238	−	16.3873i	−1.43604	−	0.522675i	−0.938655	+	0.344857i	$0.887927\pi$
$984$		0			0
$985$	−2.43361	−	2.04204i	−0.0775412	−	0.0650648i
$986$		0			0
$987$	5.00346	+	3.63326i	0.159262	+	0.115648i
$988$		0			0
$989$	−24.0466	+	41.6499i	−0.764637	+	1.32439i
$990$		0			0
$991$	−9.09981	−	15.7613i	−0.289065	−	0.500675i	0.684522	−	0.728992i	$-0.260011\pi$
$991$	−9.09981	−	15.7613i	−0.289065	−	0.500675i	−0.973587	+	0.228317i	$0.926678\pi$
$992$		0			0
$993$	8.71887	−	8.42407i	0.276685	−	0.267330i
$994$		0			0
$995$	−5.49398	+	31.1579i	−0.174171	+	0.987771i
$996$		0			0
$997$	−17.7385	+	14.8844i	−0.561785	+	0.471394i	−0.878908	−	0.476990i	$-0.841728\pi$
$997$	−17.7385	+	14.8844i	−0.561785	+	0.471394i	0.317123	+	0.948384i	$0.397283\pi$
$998$		0			0
$999$	14.1284	−	43.5976i	0.447003	−	1.37937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.q.b.49.2	✓	30
3.2	odd	2		648.2.q.b.361.4		30
4.3	odd	2		432.2.u.f.49.4		30
27.4	even	9		5832.2.a.k.1.13		15
27.11	odd	18		648.2.q.b.289.4		30
27.16	even	9	inner	216.2.q.b.97.2	yes	30
27.23	odd	18		5832.2.a.l.1.3		15
108.43	odd	18		432.2.u.f.97.4		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.b.49.2	✓	30	1.1	even	1	trivial
216.2.q.b.97.2	yes	30	27.16	even	9	inner
432.2.u.f.49.4		30	4.3	odd	2
432.2.u.f.97.4		30	108.43	odd	18
648.2.q.b.289.4		30	27.11	odd	18
648.2.q.b.361.4		30	3.2	odd	2
5832.2.a.k.1.13		15	27.4	even	9
5832.2.a.l.1.3		15	27.23	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)

\(f(q)\)	\(=\)	\(q+(-0.968921 - 1.43569i) q^{3} +(-2.72954 + 0.993471i) q^{5} +(-0.186943 - 1.06021i) q^{7} +(-1.12238 + 2.78213i) q^{9} +O(q^{10})\)	\(q+(-0.968921 - 1.43569i) q^{3} +(-2.72954 + 0.993471i) q^{5} +(-0.186943 - 1.06021i) q^{7} +(-1.12238 + 2.78213i) q^{9} +(-3.28397 - 1.19527i) q^{11} +(-3.77837 - 3.17043i) q^{13} +(4.07102 + 2.95616i) q^{15} +(-3.54041 + 6.13217i) q^{17} +(1.08712 + 1.88294i) q^{19} +(-1.34099 + 1.29565i) q^{21} +(1.11177 - 6.30518i) q^{23} +(2.63317 - 2.20949i) q^{25} +(5.08177 - 1.08428i) q^{27} +(2.20769 - 1.85247i) q^{29} +(0.481312 - 2.72965i) q^{31} +(1.46588 + 5.87286i) q^{33} +(1.56355 + 2.70815i) q^{35} +(4.40997 - 7.63829i) q^{37} +(-0.890795 + 8.49644i) q^{39} +(-0.953592 - 0.800158i) q^{41} +(-7.05867 - 2.56915i) q^{43} +(0.299623 - 8.70899i) q^{45} +(-0.575841 - 3.26576i) q^{47} +(5.48876 - 1.99775i) q^{49} +(12.2342 - 0.858675i) q^{51} -1.88716 q^{53} +10.1512 q^{55} +(1.64998 - 3.38518i) q^{57} +(-13.0776 + 4.75985i) q^{59} +(2.65444 + 15.0541i) q^{61} +(3.15945 + 0.669858i) q^{63} +(13.4629 + 4.90011i) q^{65} +(-1.47352 - 1.23643i) q^{67} +(-10.1295 + 4.51307i) q^{69} +(0.650072 - 1.12596i) q^{71} +(2.86037 + 4.95431i) q^{73} +(-5.72347 - 1.63958i) q^{75} +(-0.653313 + 3.70512i) q^{77} +(-7.35069 + 6.16796i) q^{79} +(-6.48051 - 6.24524i) q^{81} +(1.95760 - 1.64262i) q^{83} +(3.57155 - 20.2553i) q^{85} +(-4.79865 - 1.37465i) q^{87} +(1.77803 + 3.07963i) q^{89} +(-2.65497 + 4.59853i) q^{91} +(-4.38528 + 1.95381i) q^{93} +(-4.83797 - 4.05954i) q^{95} +(-6.41676 - 2.33551i) q^{97} +(7.01126 - 7.79488i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{7} - 6 q^{9}+O(q^{10}) \) 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

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Database

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