LMFDB - Embedded newform 432.2.u.f.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, not 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.4
Character	$\chi$	$=$	432.49
Dual form			432.2.u.f.97.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.968921 + 1.43569i) q^{3} +(-2.72954 + 0.993471i) q^{5} +(0.186943 + 1.06021i) q^{7} +(-1.12238 + 2.78213i) q^{9} +O(q^{10})$	\(q+(0.968921 + 1.43569i) q^{3} +(-2.72954 + 0.993471i) q^{5} +(0.186943 + 1.06021i) q^{7} +(-1.12238 + 2.78213i) q^{9} +(3.28397 + 1.19527i) q^{11} +(-3.77837 - 3.17043i) q^{13} +(-4.07102 - 2.95616i) q^{15} +(-3.54041 + 6.13217i) q^{17} +(-1.08712 - 1.88294i) q^{19} +(-1.34099 + 1.29565i) q^{21} +(-1.11177 + 6.30518i) q^{23} +(2.63317 - 2.20949i) q^{25} +(-5.08177 + 1.08428i) q^{27} +(2.20769 - 1.85247i) q^{29} +(-0.481312 + 2.72965i) q^{31} +(1.46588 + 5.87286i) q^{33} +(-1.56355 - 2.70815i) q^{35} +(4.40997 - 7.63829i) q^{37} +(0.890795 - 8.49644i) q^{39} +(-0.953592 - 0.800158i) q^{41} +(7.05867 + 2.56915i) q^{43} +(0.299623 - 8.70899i) q^{45} +(0.575841 + 3.26576i) q^{47} +(5.48876 - 1.99775i) q^{49} +(-12.2342 + 0.858675i) q^{51} -1.88716 q^{53} -10.1512 q^{55} +(1.64998 - 3.38518i) q^{57} +(13.0776 - 4.75985i) q^{59} +(2.65444 + 15.0541i) q^{61} +(-3.15945 - 0.669858i) q^{63} +(13.4629 + 4.90011i) q^{65} +(1.47352 + 1.23643i) q^{67} +(-10.1295 + 4.51307i) q^{69} +(-0.650072 + 1.12596i) q^{71} +(2.86037 + 4.95431i) q^{73} +(5.72347 + 1.63958i) q^{75} +(-0.653313 + 3.70512i) q^{77} +(7.35069 - 6.16796i) q^{79} +(-6.48051 - 6.24524i) q^{81} +(-1.95760 + 1.64262i) q^{83} +(3.57155 - 20.2553i) q^{85} +(4.79865 + 1.37465i) q^{87} +(1.77803 + 3.07963i) q^{89} +(2.65497 - 4.59853i) q^{91} +(-4.38528 + 1.95381i) q^{93} +(4.83797 + 4.05954i) q^{95} +(-6.41676 - 2.33551i) q^{97} +(-7.01126 + 7.79488i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{9}\right)$

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	$0.00966015\pi$
$7$	0.186943	+	1.06021i	0.0706577	+	0.400720i	−0.928882	+	0.370376i	$0.879229\pi$
$8$		0			0
$9$	−1.12238	+	2.78213i	−0.374128	+	0.927377i
$10$		0			0
$11$	3.28397	+	1.19527i	0.990153	+	0.360386i	0.785779	−	0.618507i	$-0.212262\pi$
$11$	3.28397	+	1.19527i	0.990153	+	0.360386i	0.204373	+	0.978893i	$0.434484\pi$
$12$		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	0.713958	−	0.700188i	$-0.246901\pi$
$19$	−1.08712	−	1.88294i	−0.249402	−	0.431976i	−0.963360	+	0.268212i	$0.913567\pi$
$20$		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	$0.288192\pi$
$23$	−1.11177	+	6.30518i	−0.231821	+	1.31472i	−0.849206	+	0.528061i	$0.822919\pi$
$24$		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	$0.135628\pi$
$31$	−0.481312	+	2.72965i	−0.0864461	+	0.490260i	−0.997035	+	0.0769473i	$0.975483\pi$
$32$		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	0.818580	−	0.574392i	$-0.194762\pi$
$43$	7.05867	+	2.56915i	1.07644	+	0.391791i	0.257857	+	0.966183i	$0.416984\pi$
$44$		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	$0.0222000\pi$
$47$	0.575841	+	3.26576i	0.0839951	+	0.476360i	−0.913574	+	0.406673i	$0.866689\pi$
$48$		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	0.706443	−	0.707770i	$-0.250299\pi$
$59$	13.0776	−	4.75985i	1.70256	−	0.619679i	0.996112	+	0.0880908i	$0.0280766\pi$
$60$		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	0.728345	−	0.685211i	$-0.240290\pi$
$67$	1.47352	+	1.23643i	0.180019	+	0.151054i	−0.548325	+	0.836265i	$0.684734\pi$
$68$		0			0
$69$	−10.1295	+	4.51307i	−1.21945	+	0.543310i
$70$		0			0
$71$	−0.650072	+	1.12596i	−0.0771494	+	0.133627i	−0.902019	−	0.431696i	$-0.857915\pi$
$71$	−0.650072	+	1.12596i	−0.0771494	+	0.133627i	0.824870	+	0.565323i	$0.191248\pi$
$72$		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	−0.127587	−	0.991827i	$-0.540723\pi$
$79$	7.35069	−	6.16796i	0.827017	−	0.693950i	0.954604	+	0.297877i	$0.0962787\pi$
$80$		0			0
$81$	−6.48051	−	6.24524i	−0.720057	−	0.693915i
$82$		0			0
$83$	−1.95760	+	1.64262i	−0.214875	+	0.180301i	−0.743872	−	0.668322i	$-0.767013\pi$
$83$	−1.95760	+	1.64262i	−0.214875	+	0.180301i	0.528997	+	0.848624i	$0.322568\pi$
$84$		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	0.333683	−	0.942685i	$-0.391708\pi$
$103$	12.1304	−	4.41511i	1.19525	−	0.435034i	0.861563	+	0.507651i	$0.169486\pi$
$104$		0			0
$105$	2.37309	−	4.86875i	0.231590	−	0.475141i
$106$		0			0
$107$	−3.84595			−0.371803			−0.185901	−	0.982568i	$-0.559520\pi$
$107$	−3.84595			−0.371803			−0.185901	+	0.982568i	$0.559520\pi$
$108$		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	0.977031	−	0.213098i	$-0.0683552\pi$
$127$	3.42554	+	5.93321i	0.303968	+	0.526487i	−0.673063	+	0.739585i	$0.735022\pi$
$128$		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	$0.446072\pi$
$131$	−3.74217	+	21.2229i	−0.326955	+	1.85425i	−0.495565	+	0.868571i	$0.665039\pi$
$132$		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	$-0.628304\pi$
$139$	3.43030	−	19.4542i	0.290954	−	1.65008i	0.683207	−	0.730225i	$-0.260585\pi$
$140$		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	0.972018	−	0.234907i	$-0.0754784\pi$
$151$	19.2388	+	7.00235i	1.56563	+	0.569843i	0.593614	+	0.804750i	$0.297701\pi$
$152$		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	$-0.933337\pi$
$163$	−24.9764			−1.95630			−0.978150	+	0.207899i	$0.933337\pi$
$164$		0			0
$165$	−9.83568	−	14.5739i	−0.765707	−	1.13458i
$166$		0			0
$167$	−14.7375	+	5.36402i	−1.14042	+	0.415081i	−0.842067	−	0.539373i	$-0.818661\pi$
$167$	−14.7375	+	5.36402i	−1.14042	+	0.415081i	−0.298358	+	0.954454i	$0.596439\pi$
$168$		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	$-0.647219\pi$
$179$	7.38452	−	12.7904i	0.551945	−	0.955997i	0.998134	−	0.0610585i	$-0.0194476\pi$
$180$		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	−0.699714	−	0.714423i	$-0.746689\pi$
$191$	−1.62594	+	1.36432i	−0.117649	+	0.0987190i	0.582065	+	0.813142i	$0.302245\pi$
$192$		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	−0.991916	−	0.126897i	$-0.959498\pi$
$199$	−5.44607	+	9.43287i	−0.386062	+	0.668678i	0.605854	+	0.795576i	$0.292831\pi$
$200$		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	−0.722261	−	0.691620i	$-0.756897\pi$
$211$	−12.0707	+	4.39337i	−0.830980	+	0.302452i	−0.108719	+	0.994073i	$0.534675\pi$
$212$		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	$0.0326318\pi$
$223$	1.41853	+	8.04489i	0.0949919	+	0.538726i	−0.899758	+	0.436389i	$0.856257\pi$
$224$		0			0
$225$	3.19167	+	9.80573i	0.212778	+	0.653715i
$226$		0			0
$227$	12.0494	+	4.38563i	0.799749	+	0.291085i	0.709382	−	0.704824i	$-0.248974\pi$
$227$	12.0494	+	4.38563i	0.799749	+	0.291085i	0.0903664	+	0.995909i	$0.471196\pi$
$228$		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	−0.959673	−	0.281120i	$-0.909294\pi$
$239$	0.591690	−	3.35564i	0.0382732	−	0.217058i	0.997946	+	0.0640613i	$0.0204053\pi$
$240$		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	0.962457	−	0.271434i	$-0.0874980\pi$
$251$	3.89990	+	6.75483i	0.246160	+	0.426361i	−0.716297	+	0.697795i	$0.754165\pi$
$252$		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	$-0.997875\pi$
$263$	−1.01502	−	5.75649i	−0.0625891	−	0.354960i	0.937389	−	0.348285i	$-0.113236\pi$
$264$		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	$-0.367042\pi$
$271$	13.3560			0.811321			0.405660	+	0.914024i	$0.367042\pi$
$272$		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	0.669668	−	0.742660i	$-0.266436\pi$
$283$	0.918128	+	0.770401i	0.0545771	+	0.0457956i	−0.615091	+	0.788456i	$0.710881\pi$
$284$		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	$0.341280\pi$
$307$	−9.13677	+	15.8253i	−0.521463	+	0.903200i	−0.999688	+	0.0249632i	$0.992053\pi$
$308$		0			0
$309$	18.0921	+	13.1376i	1.02923	+	0.747370i
$310$		0			0
$311$	−17.9485	−	15.0605i	−1.01776	−	0.854005i	−0.0284189	−	0.999596i	$-0.509047\pi$
$311$	−17.9485	−	15.0605i	−1.01776	−	0.854005i	−0.989345	+	0.145591i	$0.953492\pi$
$312$		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	$-0.993939\pi$
$331$	−1.21547	−	6.89327i	−0.0668083	−	0.378889i	0.933010	−	0.359849i	$-0.117172\pi$
$332$		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	−0.943921	−	0.330171i	$-0.892893\pi$
$347$	1.04316	−	5.91606i	0.0559999	−	0.317591i	0.999921	+	0.0125804i	$0.00400457\pi$
$348$		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	0.988480	−	0.151351i	$-0.0483624\pi$
$359$	6.88101	+	11.9183i	0.363166	+	0.629022i	−0.625314	+	0.780373i	$0.715029\pi$
$360$		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	0.596576	−	0.802556i	$-0.296527\pi$
$367$	10.3010	+	3.74925i	0.537707	+	0.195709i	−0.0588694	+	0.998266i	$0.518750\pi$
$368$		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	$-0.339132\pi$
$379$	18.8505			0.968285			0.484142	+	0.874989i	$0.339132\pi$
$380$		0			0
$381$	−5.19914	+	10.6668i	−0.266360	+	0.546477i
$382$		0			0
$383$	18.3285	−	6.67102i	0.936542	−	0.340873i	0.171742	−	0.985142i	$-0.445060\pi$
$383$	18.3285	−	6.67102i	0.936542	−	0.340873i	0.764799	+	0.644269i	$0.222838\pi$
$384$		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	$-0.989219\pi$
$419$	−24.6928	−	20.7198i	−1.20632	−	1.01223i	−0.206898	−	0.978363i	$-0.566337\pi$
$420$		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	$-0.535688\pi$
$431$	−4.64545			−0.223764			−0.111882	+	0.993722i	$0.535688\pi$
$432$		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	0.998722	−	0.0505338i	$-0.0160923\pi$
$439$	0.899835	+	5.10322i	0.0429468	+	0.243563i	−0.955776	+	0.294097i	$0.904981\pi$
$440$		0			0
$441$	−0.602505	+	17.5127i	−0.0286907	+	0.833938i
$442$		0			0
$443$	17.7897	+	6.47493i	0.845216	+	0.307633i	0.728088	−	0.685483i	$-0.240409\pi$
$443$	17.7897	+	6.47493i	0.845216	+	0.307633i	0.117128	+	0.993117i	$0.462631\pi$
$444$		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	$0.186665\pi$
$463$	−2.99174	+	16.9670i	−0.139038	+	0.788525i	−0.971962	+	0.235137i	$0.924446\pi$
$464$		0			0
$465$	10.0287	−	9.68963i	0.465071	−	0.449346i
$466$		0			0
$467$	−8.84287	−	15.3163i	−0.409199	−	0.708754i	0.585601	−	0.810600i	$-0.300859\pi$
$467$	−8.84287	−	15.3163i	−0.409199	−	0.708754i	−0.994800	+	0.101846i	$0.967525\pi$
$468$		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	$0.0648618\pi$
$479$	2.80736	+	15.9213i	0.128272	+	0.727464i	−0.851039	+	0.525102i	$0.824027\pi$
$480$		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	$-0.279725\pi$
$487$	28.1628			1.27618			0.638088	+	0.769963i	$0.279725\pi$
$488$		0			0
$489$	−24.2001	−	35.8582i	−1.09437	−	1.62156i
$490$		0			0
$491$	−3.64776	+	1.32768i	−0.164621	+	0.0599172i	−0.423016	−	0.906122i	$-0.639029\pi$
$491$	−3.64776	+	1.32768i	−0.164621	+	0.0599172i	0.258395	+	0.966039i	$0.416806\pi$
$492$		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	0.550320	−	0.834954i	$-0.314506\pi$
$499$	−3.94018	−	3.30620i	−0.176387	−	0.148006i	−0.726707	+	0.686948i	$0.758950\pi$
$500$		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	$0.389981\pi$
$503$	−14.4751	+	25.0716i	−0.645412	+	1.11789i	−0.984206	+	0.177026i	$0.943352\pi$
$504$		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	−0.582441	−	0.812873i	$-0.697902\pi$
$523$	9.43922	−	16.3492i	0.412748	−	0.714901i	0.995189	+	0.0979723i	$0.0312356\pi$
$524$		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	$0.187254\pi$
$547$	5.61233	+	31.8291i	0.239966	+	1.36091i	−0.591934	+	0.805987i	$0.701635\pi$
$548$		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	−0.999849	−	0.0173588i	$-0.994474\pi$
$563$	−1.28986	+	7.31517i	−0.0543612	+	0.308298i	0.945488	+	0.325657i	$0.105585\pi$
$564$		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	$-0.565093\pi$
$571$	7.70985	−	43.7247i	0.322647	−	1.82982i	0.525719	−	0.850658i	$-0.323796\pi$
$572$		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	$-0.784433\pi$
$587$	−6.33127	−	35.9064i	−0.261319	−	1.48202i	0.517996	−	0.855383i	$-0.326678\pi$
$588$		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	−0.0992019	−	0.995067i	$-0.531629\pi$
$599$	11.3665	−	4.13706i	0.464422	−	0.169036i	0.563624	+	0.826032i	$0.309407\pi$
$600$		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	0.999841	−	0.0178336i	$-0.00567691\pi$
$607$	28.4783	+	23.8961i	1.15590	+	0.969914i	0.156058	+	0.987748i	$0.450121\pi$
$608$		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	−0.644301	−	0.764772i	$-0.722852\pi$
$619$	−0.0753697	+	0.0632427i	−0.00302936	+	0.00254194i	0.641272	+	0.767314i	$0.278407\pi$
$620$		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	−0.881389	−	0.472391i	$-0.843391\pi$
$631$	−0.793583	+	1.37453i	−0.0315921	+	0.0547190i	0.849797	+	0.527110i	$0.176724\pi$
$632$		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	−0.340827	−	0.940126i	$-0.610707\pi$
$643$	0.0605107	−	0.0220241i	0.00238631	−	0.000868545i	0.343213	+	0.939258i	$0.388485\pi$
$644$		0			0
$645$	−21.1412	−	31.3256i	−0.832432	−	1.23344i
$646$		0			0
$647$	33.2653			1.30780			0.653898	−	0.756583i	$-0.273133\pi$
$647$	33.2653			1.30780			0.653898	+	0.756583i	$0.273133\pi$
$648$		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	0.497533	−	0.867445i	$-0.334240\pi$
$659$	8.24248	+	3.00002i	0.321081	+	0.116864i	−0.176451	+	0.984309i	$0.556462\pi$
$660$		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	$0.0287109\pi$
$683$	15.0527	+	26.0720i	0.575975	+	0.997619i	−0.419960	+	0.907543i	$0.637956\pi$
$684$		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	−0.228696	−	0.973498i	$-0.573446\pi$
$691$	−27.0660	−	9.85122i	−1.02964	−	0.374758i	−0.800944	+	0.598740i	$0.795668\pi$
$692$		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	−0.766461	−	0.642290i	$-0.777984\pi$
$719$	4.63910	−	8.03516i	0.173009	−	0.299661i	0.939471	+	0.342630i	$0.111318\pi$
$720$		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	−0.159500	−	0.987198i	$-0.550988\pi$
$727$	21.1660	−	17.7604i	0.785004	−	0.658696i	0.944503	+	0.328502i	$0.106544\pi$
$728$		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	−0.884329	−	0.466864i	$-0.845384\pi$
$739$	−1.02889	+	1.78209i	−0.0378484	+	0.0655553i	0.846481	+	0.532419i	$0.178717\pi$
$740$		0			0
$741$	−16.9667	+	7.55931i	−0.623287	+	0.277698i
$742$		0			0
$743$	−22.2183	−	18.6434i	−0.815111	−	0.683959i	0.136711	−	0.990611i	$-0.456347\pi$
$743$	−22.2183	−	18.6434i	−0.815111	−	0.683959i	−0.951822	+	0.306652i	$0.900791\pi$
$744$		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	−0.386243	−	0.922397i	$-0.626227\pi$
$751$	−2.44493	+	0.889882i	−0.0892168	+	0.0324723i	0.297026	+	0.954869i	$0.404005\pi$
$752$		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	$0.182983\pi$
$787$	−3.79697	+	21.5337i	−0.135347	+	0.767592i	−0.974617	+	0.223878i	$0.928128\pi$
$788$		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	$-0.325017\pi$
$811$	29.7570			1.04491			0.522454	+	0.852667i	$0.325017\pi$
$812$		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	0.146300	−	0.989240i	$-0.453264\pi$
$823$	−23.0223	−	19.3180i	−0.802507	−	0.673383i	−0.948807	+	0.315857i	$0.897708\pi$
$824$		0			0
$825$	16.8360	+	12.2254i	0.586153	+	0.425634i
$826$		0			0
$827$	5.21104	−	9.02579i	0.181206	−	0.313857i	−0.761086	−	0.648651i	$-0.775333\pi$
$827$	5.21104	−	9.02579i	0.181206	−	0.313857i	0.942291	+	0.334794i	$0.108667\pi$
$828$		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	−0.622490	−	0.782627i	$-0.713879\pi$
$839$	1.16305	−	0.975911i	0.0401528	−	0.0336922i	0.662643	+	0.748935i	$0.269435\pi$
$840$		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	−0.560749	−	0.827986i	$-0.689487\pi$
$859$	−13.4260	+	4.88666i	−0.458089	+	0.166731i	0.102660	+	0.994716i	$0.467265\pi$
$860$		0			0
$861$	2.31548	−	0.162515i	0.0789113	−	0.00553848i
$862$		0			0
$863$	26.2533			0.893672			0.446836	−	0.894616i	$-0.352551\pi$
$863$	26.2533			0.893672			0.446836	+	0.894616i	$0.352551\pi$
$864$		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	0.894328	−	0.447411i	$-0.147654\pi$
$883$	1.77384	+	3.07239i	0.0596946	+	0.103394i	−0.834634	+	0.550805i	$0.814321\pi$
$884$		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	$-0.732456\pi$
$887$	6.39045	−	36.2420i	0.214570	−	1.21689i	0.881651	−	0.471903i	$-0.156433\pi$
$888$		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	0.0476090	−	0.998866i	$-0.484840\pi$
$907$	−16.8043	−	6.11628i	−0.557979	−	0.203088i	−0.605588	+	0.795778i	$0.707062\pi$
$908$		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	$-0.804840\pi$
$911$	−7.42880	−	42.1308i	−0.246127	−	1.39586i	0.571733	−	0.820440i	$-0.306271\pi$
$912$		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	$-0.530987\pi$
$919$	−5.89290			−0.194389			−0.0971944	+	0.995265i	$0.530987\pi$
$920$		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	−0.955172	−	0.296053i	$-0.904330\pi$
$947$	−25.5259	+	21.4188i	−0.829481	+	0.696017i	0.125691	+	0.992069i	$0.459885\pi$
$948$		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	−0.452724	−	0.891651i	$-0.649548\pi$
$967$	−7.03992	+	2.56232i	−0.226389	+	0.0823987i	0.226335	+	0.974049i	$0.427325\pi$
$968$		0			0
$969$	14.9169	+	22.1029i	0.479199	+	0.710046i
$970$		0			0
$971$	25.9164			0.831698			0.415849	−	0.909434i	$-0.363485\pi$
$971$	25.9164			0.831698			0.415849	+	0.909434i	$0.363485\pi$
$972$		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	0.938655	−	0.344857i	$-0.112073\pi$
$983$	45.0238	+	16.3873i	1.43604	+	0.522675i	0.497382	+	0.867532i	$0.334295\pi$
$984$		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	0.973587	−	0.228317i	$-0.0733223\pi$
$991$	9.09981	+	15.7613i	0.289065	+	0.500675i	−0.684522	+	0.728992i	$0.739989\pi$
$992$		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	432.2.u.f.49.4		30
4.3	odd	2		216.2.q.b.49.2	✓	30
12.11	even	2		648.2.q.b.361.4		30
27.16	even	9	inner	432.2.u.f.97.4		30
108.11	even	18		648.2.q.b.289.4		30
108.23	even	18		5832.2.a.l.1.3		15
108.31	odd	18		5832.2.a.k.1.13		15
108.43	odd	18		216.2.q.b.97.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.b.49.2	✓	30	4.3	odd	2
216.2.q.b.97.2	yes	30	108.43	odd	18
432.2.u.f.49.4		30	1.1	even	1	trivial
432.2.u.f.97.4		30	27.16	even	9	inner
648.2.q.b.289.4		30	108.11	even	18
648.2.q.b.361.4		30	12.11	even	2
5832.2.a.k.1.13		15	108.31	odd	18
5832.2.a.l.1.3		15	108.23	even	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.u (of order \(9\), degree \(6\), not 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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