LMFDB - Embedded newform 117.2.ba.a.71.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(71,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 5]))

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

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

chi := DirichletCharacter("117.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.ba (of order $12$, degree $4$, 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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			71.2
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	117.71
Dual form			117.2.ba.a.89.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.93185 - 0.517638i) q^{2} +(1.73205 - 1.00000i) q^{4} +(-0.517638 - 0.517638i) q^{5} +(-0.500000 + 1.86603i) q^{7} +(-1.26795 - 0.732051i) q^{10} +(-1.60368 - 5.98502i) q^{11} +(-1.59808 + 3.23205i) q^{13} +3.86370i q^{14} +(-2.00000 + 3.46410i) q^{16} +(0.896575 + 1.55291i) q^{17} +(3.36603 + 0.901924i) q^{19} +(-1.41421 - 0.378937i) q^{20} +(-6.19615 - 10.7321i) q^{22} +(-1.22474 + 2.12132i) q^{23} -4.46410i q^{25} +(-1.41421 + 7.07107i) q^{26} +(1.00000 + 3.73205i) q^{28} +(-1.22474 - 0.707107i) q^{29} +(6.36603 - 6.36603i) q^{31} +(-2.07055 + 7.72741i) q^{32} +(2.53590 + 2.53590i) q^{34} +(1.22474 - 0.707107i) q^{35} +(-7.83013 + 2.09808i) q^{37} +6.96953 q^{38} +(5.27792 - 1.41421i) q^{41} +(3.69615 - 2.13397i) q^{43} +(-8.76268 - 8.76268i) q^{44} +(-1.26795 + 4.73205i) q^{46} +(4.76028 - 4.76028i) q^{47} +(2.83013 + 1.63397i) q^{49} +(-2.31079 - 8.62398i) q^{50} +(0.464102 + 7.19615i) q^{52} +8.76268i q^{53} +(-2.26795 + 3.92820i) q^{55} +(-2.73205 - 0.732051i) q^{58} +(-9.84873 - 2.63896i) q^{59} +(-1.40192 - 2.42820i) q^{61} +(9.00292 - 15.5935i) q^{62} +8.00000i q^{64} +(2.50026 - 0.845807i) q^{65} +(-2.40192 - 8.96410i) q^{67} +(3.10583 + 1.79315i) q^{68} +(2.00000 - 2.00000i) q^{70} +(-0.429705 + 1.60368i) q^{71} +(8.09808 + 8.09808i) q^{73} +(-14.0406 + 8.10634i) q^{74} +(6.73205 - 1.80385i) q^{76} +11.9700 q^{77} -3.19615 q^{79} +(2.82843 - 0.757875i) q^{80} +(9.46410 - 5.46410i) q^{82} +(0.378937 + 0.378937i) q^{83} +(0.339746 - 1.26795i) q^{85} +(6.03579 - 6.03579i) q^{86} +(2.96713 + 11.0735i) q^{89} +(-5.23205 - 4.59808i) q^{91} +4.89898i q^{92} +(6.73205 - 11.6603i) q^{94} +(-1.27551 - 2.20925i) q^{95} +(-11.6962 - 3.13397i) q^{97} +(6.31319 + 1.69161i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{7} - 24 q^{10} + 8 q^{13} - 16 q^{16} + 20 q^{19} - 8 q^{22} + 8 q^{28} + 44 q^{31} + 48 q^{34} - 28 q^{37} - 12 q^{43} - 24 q^{46} - 12 q^{49} - 24 q^{52} - 32 q^{55} - 8 q^{58} - 32 q^{61}+ \cdots - 52 q^{97}+O(q^{100}) $ 8 * q - 4 * q^7 - 24 * q^10 + 8 * q^13 - 16 * q^16 + 20 * q^19 - 8 * q^22 + 8 * q^28 + 44 * q^31 + 48 * q^34 - 28 * q^37 - 12 * q^43 - 24 * q^46 - 12 * q^49 - 24 * q^52 - 32 * q^55 - 8 * q^58 - 32 * q^61 - 40 * q^67 + 16 * q^70 + 44 * q^73 + 40 * q^76 + 16 * q^79 + 48 * q^82 + 72 * q^85 - 28 * q^91 + 40 * q^94 - 52 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.93185	−	0.517638i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$2$	1.93185	−	0.517638i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$3$		0			0
$3$		0			0
$4$	1.73205	−	1.00000i	0.866025	−	0.500000i
$5$	−0.517638	−	0.517638i	−0.231495	−	0.231495i	0.581822	−	0.813316i	$-0.302340\pi$
$5$	−0.517638	−	0.517638i	−0.231495	−	0.231495i	−0.813316	+	0.581822i	$0.802340\pi$
$6$		0			0
$7$	−0.500000	+	1.86603i	−0.188982	+	0.705291i	0.804761	+	0.593599i	$0.202294\pi$
$7$	−0.500000	+	1.86603i	−0.188982	+	0.705291i	−0.993743	+	0.111692i	$0.964373\pi$
$8$		0			0
$9$		0			0
$10$	−1.26795	−	0.732051i	−0.400961	−	0.231495i
$11$	−1.60368	−	5.98502i	−0.483528	−	1.80455i	−0.586598	−	0.809878i	$-0.699533\pi$
$11$	−1.60368	−	5.98502i	−0.483528	−	1.80455i	0.103069	−	0.994674i	$-0.467134\pi$
$12$		0			0
$13$	−1.59808	+	3.23205i	−0.443227	+	0.896410i
$13$	−1.59808	+	3.23205i	−0.443227	+	0.896410i
$14$			3.86370i			1.03262i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	0.896575	+	1.55291i	0.217451	+	0.376637i	0.954028	−	0.299717i	$-0.0968923\pi$
$17$	0.896575	+	1.55291i	0.217451	+	0.376637i	−0.736577	+	0.676354i	$0.763559\pi$
$18$		0			0
$19$	3.36603	+	0.901924i	0.772219	+	0.206916i	0.623352	−	0.781942i	$-0.285771\pi$
$19$	3.36603	+	0.901924i	0.772219	+	0.206916i	0.148868	+	0.988857i	$0.452437\pi$
$20$	−1.41421	−	0.378937i	−0.316228	−	0.0847330i
$21$		0			0
$22$	−6.19615	−	10.7321i	−1.32102	−	2.28808i
$23$	−1.22474	+	2.12132i	−0.255377	+	0.442326i	−0.964998	−	0.262258i	$-0.915533\pi$
$23$	−1.22474	+	2.12132i	−0.255377	+	0.442326i	0.709621	+	0.704584i	$0.248866\pi$
$24$		0			0
$25$		−	4.46410i		−	0.892820i
$26$	−1.41421	+	7.07107i	−0.277350	+	1.38675i
$27$		0			0
$28$	1.00000	+	3.73205i	0.188982	+	0.705291i
$29$	−1.22474	−	0.707107i	−0.227429	−	0.131306i	0.381956	−	0.924180i	$-0.375251\pi$
$29$	−1.22474	−	0.707107i	−0.227429	−	0.131306i	−0.609386	+	0.792874i	$0.708584\pi$
$30$		0			0
$31$	6.36603	−	6.36603i	1.14337	−	1.14337i	0.155543	−	0.987829i	$-0.450287\pi$
$31$	6.36603	−	6.36603i	1.14337	−	1.14337i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$	−2.07055	+	7.72741i	−0.366025	+	1.36603i
$33$		0			0
$34$	2.53590	+	2.53590i	0.434903	+	0.434903i
$35$	1.22474	−	0.707107i	0.207020	−	0.119523i
$36$		0			0
$37$	−7.83013	+	2.09808i	−1.28726	+	0.344922i	−0.836621	−	0.547782i	$-0.815472\pi$
$37$	−7.83013	+	2.09808i	−1.28726	+	0.344922i	−0.450644	+	0.892704i	$0.648806\pi$
$38$	6.96953			1.13061
$39$		0			0
$40$		0			0
$41$	5.27792	−	1.41421i	0.824272	−	0.220863i	0.178059	−	0.984020i	$-0.443018\pi$
$41$	5.27792	−	1.41421i	0.824272	−	0.220863i	0.646213	+	0.763157i	$0.276352\pi$
$42$		0			0
$43$	3.69615	−	2.13397i	0.563658	−	0.325428i	−0.190954	−	0.981599i	$-0.561158\pi$
$43$	3.69615	−	2.13397i	0.563658	−	0.325428i	0.754612	+	0.656171i	$0.227825\pi$
$44$	−8.76268	−	8.76268i	−1.32102	−	1.32102i
$45$		0			0
$46$	−1.26795	+	4.73205i	−0.186949	+	0.697703i
$47$	4.76028	−	4.76028i	0.694358	−	0.694358i	−0.268830	−	0.963188i	$-0.586637\pi$
$47$	4.76028	−	4.76028i	0.694358	−	0.694358i	0.963188	+	0.268830i	$0.0866369\pi$
$48$		0			0
$49$	2.83013	+	1.63397i	0.404304	+	0.233425i
$50$	−2.31079	−	8.62398i	−0.326795	−	1.21962i
$51$		0			0
$52$	0.464102	+	7.19615i	0.0643593	+	0.997927i
$53$			8.76268i			1.20365i	0.798629	+	0.601824i	$0.205559\pi$
$53$			8.76268i			1.20365i	−0.798629	+	0.601824i	$0.794441\pi$
$54$		0			0
$55$	−2.26795	+	3.92820i	−0.305810	+	0.529679i
$56$		0			0
$57$		0			0
$58$	−2.73205	−	0.732051i	−0.358736	−	0.0961230i
$59$	−9.84873	−	2.63896i	−1.28220	−	0.343563i	−0.447504	−	0.894282i	$-0.647687\pi$
$59$	−9.84873	−	2.63896i	−1.28220	−	0.343563i	−0.834691	+	0.550719i	$0.814354\pi$
$60$		0			0
$61$	−1.40192	−	2.42820i	−0.179498	−	0.310900i	0.762211	−	0.647329i	$-0.224114\pi$
$61$	−1.40192	−	2.42820i	−0.179498	−	0.310900i	−0.941709	+	0.336429i	$0.890781\pi$
$62$	9.00292	−	15.5935i	1.14337	−	1.98038i
$63$		0			0
$64$			8.00000i			1.00000i
$65$	2.50026	−	0.845807i	0.310119	−	0.104910i
$66$		0			0
$67$	−2.40192	−	8.96410i	−0.293442	−	1.09514i	−0.942447	−	0.334355i	$-0.891481\pi$
$67$	−2.40192	−	8.96410i	−0.293442	−	1.09514i	0.649005	−	0.760784i	$-0.275185\pi$
$68$	3.10583	+	1.79315i	0.376637	+	0.217451i
$69$		0			0
$70$	2.00000	−	2.00000i	0.239046	−	0.239046i
$71$	−0.429705	+	1.60368i	−0.0509966	+	0.190322i	−0.986725	−	0.162399i	$-0.948077\pi$
$71$	−0.429705	+	1.60368i	−0.0509966	+	0.190322i	0.935729	+	0.352721i	$0.114744\pi$
$72$		0			0
$73$	8.09808	+	8.09808i	0.947808	+	0.947808i	0.998704	−	0.0508958i	$-0.0162077\pi$
$73$	8.09808	+	8.09808i	0.947808	+	0.947808i	−0.0508958	+	0.998704i	$0.516208\pi$
$74$	−14.0406	+	8.10634i	−1.63219	+	0.942343i
$75$		0			0
$76$	6.73205	−	1.80385i	0.772219	−	0.206916i
$77$	11.9700			1.36411
$78$		0			0
$79$	−3.19615			−0.359595			−0.179798	−	0.983704i	$-0.557544\pi$
$79$	−3.19615			−0.359595			−0.179798	+	0.983704i	$0.557544\pi$
$80$	2.82843	−	0.757875i	0.316228	−	0.0847330i
$81$		0			0
$82$	9.46410	−	5.46410i	1.04514	−	0.603409i
$83$	0.378937	+	0.378937i	0.0415938	+	0.0415938i	0.727598	−	0.686004i	$-0.240637\pi$
$83$	0.378937	+	0.378937i	0.0415938	+	0.0415938i	−0.686004	+	0.727598i	$0.740637\pi$
$84$		0			0
$85$	0.339746	−	1.26795i	0.0368506	−	0.137528i
$86$	6.03579	−	6.03579i	0.650856	−	0.650856i
$87$		0			0
$88$		0			0
$89$	2.96713	+	11.0735i	0.314515	+	1.17379i	0.924440	+	0.381327i	$0.124533\pi$
$89$	2.96713	+	11.0735i	0.314515	+	1.17379i	−0.609925	+	0.792459i	$0.708801\pi$
$90$		0			0
$91$	−5.23205	−	4.59808i	−0.548468	−	0.482009i
$92$			4.89898i			0.510754i
$93$		0			0
$94$	6.73205	−	11.6603i	0.694358	−	1.20266i
$95$	−1.27551	−	2.20925i	−0.130865	−	0.226665i
$96$		0			0
$97$	−11.6962	−	3.13397i	−1.18756	−	0.318207i	−0.389642	−	0.920967i	$-0.627401\pi$
$97$	−11.6962	−	3.13397i	−1.18756	−	0.318207i	−0.797923	+	0.602760i	$0.794068\pi$
$98$	6.31319	+	1.69161i	0.637729	+	0.170879i
$99$		0			0
$100$	−4.46410	−	7.73205i	−0.446410	−	0.773205i
$101$	−7.91688	+	13.7124i	−0.787759	+	1.36444i	0.139579	+	0.990211i	$0.455425\pi$
$101$	−7.91688	+	13.7124i	−0.787759	+	1.36444i	−0.927337	+	0.374227i	$0.877908\pi$
$102$		0			0
$103$			8.66025i			0.853320i	0.904412	+	0.426660i	$0.140310\pi$
$103$			8.66025i			0.853320i	−0.904412	+	0.426660i	$0.859690\pi$
$104$		0			0
$105$		0			0
$106$	4.53590	+	16.9282i	0.440565	+	1.64421i
$107$	−11.2629	−	6.50266i	−1.08883	−	0.628636i	−0.155565	−	0.987826i	$-0.549720\pi$
$107$	−11.2629	−	6.50266i	−1.08883	−	0.628636i	−0.933265	+	0.359190i	$0.883053\pi$
$108$		0			0
$109$	4.29423	−	4.29423i	0.411313	−	0.411313i	−0.470883	−	0.882196i	$-0.656065\pi$
$109$	4.29423	−	4.29423i	0.411313	−	0.411313i	0.882196	+	0.470883i	$0.156065\pi$
$110$	−2.34795	+	8.76268i	−0.223869	+	0.835489i
$111$		0			0
$112$	−5.46410	−	5.46410i	−0.516309	−	0.516309i
$113$	−8.81345	+	5.08845i	−0.829100	+	0.478681i	−0.853544	−	0.521020i	$-0.825552\pi$
$113$	−8.81345	+	5.08845i	−0.829100	+	0.478681i	0.0244446	+	0.999701i	$0.492218\pi$
$114$		0			0
$115$	1.73205	−	0.464102i	0.161515	−	0.0432777i
$116$	−2.82843			−0.262613
$117$		0			0
$118$	−20.3923			−1.87726
$119$	−3.34607	+	0.896575i	−0.306733	+	0.0821889i
$120$		0			0
$121$	−23.7224	+	13.6962i	−2.15658	+	1.24510i
$122$	−3.96524	−	3.96524i	−0.358996	−	0.358996i
$123$		0			0
$124$	4.66025	−	17.3923i	0.418503	−	1.56188i
$125$	−4.89898	+	4.89898i	−0.438178	+	0.438178i
$126$		0			0
$127$	3.40192	+	1.96410i	0.301872	+	0.174286i	0.643284	−	0.765628i	$-0.277572\pi$
$127$	3.40192	+	1.96410i	0.301872	+	0.174286i	−0.341412	+	0.939914i	$0.610905\pi$
$128$		0			0
$129$		0			0
$130$	4.39230	−	2.92820i	0.385231	−	0.256820i
$131$		−	7.07107i		−	0.617802i	−0.951094	−	0.308901i	$-0.900039\pi$
$131$		−	7.07107i		−	0.617802i	0.951094	−	0.308901i	$-0.0999612\pi$
$132$		0			0
$133$	−3.36603	+	5.83013i	−0.291871	+	0.505536i
$134$	−9.28032	−	16.0740i	−0.801698	−	1.38858i
$135$		0			0
$136$		0			0
$137$	−1.03528	−	0.277401i	−0.0884496	−	0.0237000i	0.214323	−	0.976763i	$-0.431246\pi$
$137$	−1.03528	−	0.277401i	−0.0884496	−	0.0237000i	−0.302772	+	0.953063i	$0.597912\pi$
$138$		0			0
$139$	8.69615	+	15.0622i	0.737598	+	1.27756i	0.953574	+	0.301159i	$0.0973734\pi$
$139$	8.69615	+	15.0622i	0.737598	+	1.27756i	−0.215976	+	0.976399i	$0.569293\pi$
$140$	1.41421	−	2.44949i	0.119523	−	0.207020i
$141$		0			0
$142$			3.32051i			0.278651i
$143$	21.9067	+	4.38134i	1.83193	+	0.366386i
$144$		0			0
$145$	0.267949	+	1.00000i	0.0222520	+	0.0830455i
$146$	19.8362	+	11.4524i	1.64165	+	0.947808i
$147$		0			0
$148$	−11.4641	+	11.4641i	−0.942343	+	0.942343i
$149$	3.72500	−	13.9019i	0.305164	−	1.13889i	−0.627640	−	0.778504i	$-0.715979\pi$
$149$	3.72500	−	13.9019i	0.305164	−	1.13889i	0.932804	−	0.360384i	$-0.117354\pi$
$150$		0			0
$151$	−1.53590	−	1.53590i	−0.124990	−	0.124990i	0.641845	−	0.766835i	$-0.278169\pi$
$151$	−1.53590	−	1.53590i	−0.124990	−	0.124990i	−0.766835	+	0.641845i	$0.778169\pi$
$152$		0			0
$153$		0			0
$154$	23.1244	−	6.19615i	1.86341	−	0.499300i
$155$	−6.59059			−0.529369
$156$		0			0
$157$	9.39230			0.749588			0.374794	−	0.927108i	$-0.377714\pi$
$157$	9.39230			0.749588			0.374794	+	0.927108i	$0.377714\pi$
$158$	−6.17449	+	1.65445i	−0.491216	+	0.131621i
$159$		0			0
$160$	5.07180	−	2.92820i	0.400961	−	0.231495i
$161$	−3.34607	−	3.34607i	−0.263707	−	0.263707i
$162$		0			0
$163$	3.93782	−	14.6962i	0.308434	−	1.15109i	−0.621515	−	0.783402i	$-0.713482\pi$
$163$	3.93782	−	14.6962i	0.308434	−	1.15109i	0.929949	−	0.367689i	$-0.119851\pi$
$164$	7.72741	−	7.72741i	0.603409	−	0.603409i
$165$		0			0
$166$	0.928203	+	0.535898i	0.0720425	+	0.0415938i
$167$	−0.378937	−	1.41421i	−0.0293231	−	0.109435i	0.949713	−	0.313121i	$-0.101375\pi$
$167$	−0.378937	−	1.41421i	−0.0293231	−	0.109435i	−0.979036	+	0.203686i	$0.934708\pi$
$168$		0			0
$169$	−7.89230	−	10.3301i	−0.607100	−	0.794625i
$170$		−	2.62536i		−	0.201356i
$171$		0			0
$172$	4.26795	−	7.39230i	0.325428	−	0.563658i
$173$	2.77766	+	4.81105i	0.211182	+	0.365777i	0.952085	−	0.305835i	$-0.0989356\pi$
$173$	2.77766	+	4.81105i	0.211182	+	0.365777i	−0.740903	+	0.671612i	$0.765602\pi$
$174$		0			0
$175$	8.33013	+	2.23205i	0.629698	+	0.168727i
$176$	23.9401	+	6.41473i	1.80455	+	0.483528i
$177$		0			0
$178$	11.4641	+	19.8564i	0.859271	+	1.48830i
$179$	−4.00240	+	6.93237i	−0.299154	+	0.518149i	−0.975943	−	0.218028i	$-0.930038\pi$
$179$	−4.00240	+	6.93237i	−0.299154	+	0.518149i	0.676789	+	0.736177i	$0.263371\pi$
$180$		0			0
$181$		−	6.00000i		−	0.445976i	−0.974821	−	0.222988i	$-0.928419\pi$
$181$		−	6.00000i		−	0.445976i	0.974821	−	0.222988i	$-0.0715812\pi$
$182$	−12.4877	−	6.17449i	−0.925649	−	0.457684i
$183$		0			0
$184$		0			0
$185$	5.13922	+	2.96713i	0.377843	+	0.218148i
$186$		0			0
$187$	7.85641	−	7.85641i	0.574517	−	0.574517i
$188$	3.48477	−	13.0053i	0.254153	−	0.948511i
$189$		0			0
$190$	−3.60770	−	3.60770i	−0.261730	−	0.261730i
$191$	−1.46498	+	0.845807i	−0.106002	+	0.0612005i	−0.552064	−	0.833802i	$-0.686160\pi$
$191$	−1.46498	+	0.845807i	−0.106002	+	0.0612005i	0.446062	+	0.895002i	$0.352826\pi$
$192$		0			0
$193$	10.6962	−	2.86603i	0.769926	−	0.206301i	0.147587	−	0.989049i	$-0.452849\pi$
$193$	10.6962	−	2.86603i	0.769926	−	0.206301i	0.622339	+	0.782748i	$0.286183\pi$
$194$	−24.2175			−1.73871
$195$		0			0
$196$	6.53590			0.466850
$197$	20.2151	−	5.41662i	1.44027	−	0.385918i	0.547639	−	0.836715i	$-0.315527\pi$
$197$	20.2151	−	5.41662i	1.44027	−	0.385918i	0.892627	+	0.450797i	$0.148860\pi$
$198$		0			0
$199$	−5.59808	+	3.23205i	−0.396837	+	0.229114i	−0.685118	−	0.728432i	$-0.740250\pi$
$199$	−5.59808	+	3.23205i	−0.396837	+	0.229114i	0.288281	+	0.957546i	$0.406916\pi$
$200$		0			0
$201$		0			0
$202$	−8.19615	+	30.5885i	−0.576679	+	2.15220i
$203$	1.93185	−	1.93185i	0.135589	−	0.135589i
$204$		0			0
$205$	−3.46410	−	2.00000i	−0.241943	−	0.139686i
$206$	4.48288	+	16.7303i	0.312337	+	1.16566i
$207$		0			0
$208$	−8.00000	−	12.0000i	−0.554700	−	0.832050i
$209$		−	21.5921i		−	1.49356i
$210$		0			0
$211$	2.40192	−	4.16025i	0.165355	−	0.286404i	−0.771426	−	0.636319i	$-0.780456\pi$
$211$	2.40192	−	4.16025i	0.165355	−	0.286404i	0.936781	+	0.349915i	$0.113790\pi$
$212$	8.76268	+	15.1774i	0.601824	+	1.04239i
$213$		0			0
$214$	−25.1244	−	6.73205i	−1.71747	−	0.460194i
$215$	−3.01790	−	0.808643i	−0.205819	−	0.0551490i
$216$		0			0
$217$	8.69615	+	15.0622i	0.590333	+	1.02249i
$218$	6.07296	−	10.5187i	0.411313	−	0.712414i
$219$		0			0
$220$			9.07180i			0.611620i
$221$	−6.45189	+	0.416102i	−0.434001	+	0.0279901i
$222$		0			0
$223$	−1.24167	−	4.63397i	−0.0831484	−	0.310314i	0.911809	−	0.410615i	$-0.134686\pi$
$223$	−1.24167	−	4.63397i	−0.0831484	−	0.310314i	−0.994957	+	0.100301i	$0.968019\pi$
$224$	−13.3843	−	7.72741i	−0.894274	−	0.516309i
$225$		0			0
$226$	−14.3923	+	14.3923i	−0.957362	+	0.957362i
$227$	3.48477	−	13.0053i	0.231292	−	0.863194i	−0.748493	−	0.663142i	$-0.769222\pi$
$227$	3.48477	−	13.0053i	0.231292	−	0.863194i	0.979785	−	0.200051i	$-0.0641109\pi$
$228$		0			0
$229$	−0.267949	−	0.267949i	−0.0177066	−	0.0177066i	0.698198	−	0.715905i	$-0.253985\pi$
$229$	−0.267949	−	0.267949i	−0.0177066	−	0.0177066i	−0.715905	+	0.698198i	$0.753985\pi$
$230$	3.10583	−	1.79315i	0.204792	−	0.118237i
$231$		0			0
$232$		0			0
$233$	−10.4543			−0.684884			−0.342442	−	0.939539i	$-0.611254\pi$
$233$	−10.4543			−0.684884			−0.342442	+	0.939539i	$0.611254\pi$
$234$		0			0
$235$	−4.92820			−0.321481
$236$	−19.6975	+	5.27792i	−1.28220	+	0.343563i
$237$		0			0
$238$	−6.00000	+	3.46410i	−0.388922	+	0.224544i
$239$	9.52056	+	9.52056i	0.615834	+	0.615834i	0.944460	−	0.328626i	$-0.106586\pi$
$239$	9.52056	+	9.52056i	0.615834	+	0.615834i	−0.328626	+	0.944460i	$0.606586\pi$
$240$		0			0
$241$	4.29423	−	16.0263i	0.276616	−	1.03234i	−0.678135	−	0.734937i	$-0.737212\pi$
$241$	4.29423	−	16.0263i	0.276616	−	1.03234i	0.954751	−	0.297406i	$-0.0961216\pi$
$242$	−38.7386	+	38.7386i	−2.49021	+	2.49021i
$243$		0			0
$244$	−4.85641	−	2.80385i	−0.310900	−	0.179498i
$245$	−0.619174	−	2.31079i	−0.0395576	−	0.147631i
$246$		0			0
$247$	−8.29423	+	9.43782i	−0.527749	+	0.600514i
$248$		0			0
$249$		0			0
$250$	−6.92820	+	12.0000i	−0.438178	+	0.758947i
$251$	−6.45189	−	11.1750i	−0.407240	−	0.705360i	0.587339	−	0.809341i	$-0.300175\pi$
$251$	−6.45189	−	11.1750i	−0.407240	−	0.705360i	−0.994579	+	0.103980i	$0.966842\pi$
$252$		0			0
$253$	14.6603	+	3.92820i	0.921682	+	0.246964i
$254$	7.58871	+	2.03339i	0.476158	+	0.127586i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−9.14162	+	15.8338i	−0.570239	+	0.987682i	0.426302	+	0.904581i	$0.359816\pi$
$257$	−9.14162	+	15.8338i	−0.570239	+	0.987682i	−0.996541	+	0.0831016i	$0.973517\pi$
$258$		0			0
$259$		−	15.6603i		−	0.973081i
$260$	3.48477	−	3.96524i	0.216116	−	0.245914i
$261$		0			0
$262$	−3.66025	−	13.6603i	−0.226131	−	0.843933i
$263$	17.8671	+	10.3156i	1.10173	+	0.636087i	0.936676	−	0.350197i	$-0.113885\pi$
$263$	17.8671	+	10.3156i	1.10173	+	0.636087i	0.165059	+	0.986284i	$0.447219\pi$
$264$		0			0
$265$	4.53590	−	4.53590i	0.278638	−	0.278638i
$266$	−3.48477	+	13.0053i	−0.213665	+	0.797408i
$267$		0			0
$268$	−13.1244	−	13.1244i	−0.801698	−	0.801698i
$269$	20.3166	−	11.7298i	1.23873	−	0.715179i	0.269893	−	0.962890i	$-0.413012\pi$
$269$	20.3166	−	11.7298i	1.23873	−	0.715179i	0.968834	+	0.247711i	$0.0796784\pi$
$270$		0			0
$271$	−21.6244	+	5.79423i	−1.31359	+	0.351974i	−0.846571	−	0.532275i	$-0.821337\pi$
$271$	−21.6244	+	5.79423i	−1.31359	+	0.351974i	−0.467015	+	0.884250i	$0.654670\pi$
$272$	−7.17260			−0.434903
$273$		0			0
$274$	−2.14359			−0.129499
$275$	−26.7178	+	7.15900i	−1.61114	+	0.431704i
$276$		0			0
$277$	6.80385	−	3.92820i	0.408804	−	0.236023i	−0.281472	−	0.959569i	$-0.590823\pi$
$277$	6.80385	−	3.92820i	0.408804	−	0.236023i	0.690276	+	0.723547i	$0.257489\pi$
$278$	24.5964	+	24.5964i	1.47520	+	1.47520i
$279$		0			0
$280$		0			0
$281$	15.2146	−	15.2146i	0.907626	−	0.907626i	−0.0884547	−	0.996080i	$-0.528193\pi$
$281$	15.2146	−	15.2146i	0.907626	−	0.907626i	0.996080	+	0.0884547i	$0.0281928\pi$
$282$		0			0
$283$	4.20577	+	2.42820i	0.250007	+	0.144342i	0.619768	−	0.784785i	$-0.287227\pi$
$283$	4.20577	+	2.42820i	0.250007	+	0.144342i	−0.369760	+	0.929127i	$0.620560\pi$
$284$	0.859411	+	3.20736i	0.0509966	+	0.190322i
$285$		0			0
$286$	44.5885	−	2.87564i	2.63657	−	0.170040i
$287$			10.5558i			0.623091i
$288$		0			0
$289$	6.89230	−	11.9378i	0.405430	−	0.702225i
$290$	1.03528	+	1.79315i	0.0607935	+	0.105297i
$291$		0			0
$292$	22.1244	+	5.92820i	1.29473	+	0.346922i
$293$	−21.4398	−	5.74479i	−1.25253	−	0.335614i	−0.429216	−	0.903202i	$-0.641210\pi$
$293$	−21.4398	−	5.74479i	−1.25253	−	0.335614i	−0.823313	+	0.567588i	$0.807877\pi$
$294$		0			0
$295$	3.73205	+	6.46410i	0.217288	+	0.376355i
$296$		0			0
$297$		0			0
$298$		−	28.7846i		−	1.66745i
$299$	−4.89898	−	7.34847i	−0.283315	−	0.424973i
$300$		0			0
$301$	2.13397	+	7.96410i	0.123000	+	0.459043i
$302$	−3.76217	−	2.17209i	−0.216488	−	0.124990i
$303$		0			0
$304$	−9.85641	+	9.85641i	−0.565304	+	0.565304i
$305$	−0.531241	+	1.98262i	−0.0304188	+	0.113524i
$306$		0			0
$307$	3.70577	+	3.70577i	0.211500	+	0.211500i	0.804904	−	0.593405i	$-0.202217\pi$
$307$	3.70577	+	3.70577i	0.211500	+	0.211500i	−0.593405	+	0.804904i	$0.702217\pi$
$308$	20.7327	−	11.9700i	1.18136	−	0.682057i
$309$		0			0
$310$	−12.7321	+	3.41154i	−0.723132	+	0.193763i
$311$	28.0812			1.59234			0.796169	−	0.605074i	$-0.206856\pi$
$311$	28.0812			1.59234			0.796169	+	0.605074i	$0.206856\pi$
$312$		0			0
$313$	7.19615			0.406751			0.203375	−	0.979101i	$-0.434809\pi$
$313$	7.19615			0.406751			0.203375	+	0.979101i	$0.434809\pi$
$314$	18.1445	−	4.86181i	1.02396	−	0.274368i
$315$		0			0
$316$	−5.53590	+	3.19615i	−0.311419	+	0.179798i
$317$	−0.757875	−	0.757875i	−0.0425665	−	0.0425665i	0.685503	−	0.728070i	$-0.259582\pi$
$317$	−0.757875	−	0.757875i	−0.0425665	−	0.0425665i	−0.728070	+	0.685503i	$0.759582\pi$
$318$		0			0
$319$	−2.26795	+	8.46410i	−0.126981	+	0.473899i
$320$	4.14110	−	4.14110i	0.231495	−	0.231495i
$321$		0			0
$322$	−8.19615	−	4.73205i	−0.456754	−	0.263707i
$323$	1.61729	+	6.03579i	0.0899882	+	0.335840i
$324$		0			0
$325$	14.4282	+	7.13397i	0.800333	+	0.395722i
$326$		−	30.4292i		−	1.68531i
$327$		0			0
$328$		0			0
$329$	6.50266	+	11.2629i	0.358503	+	0.620946i
$330$		0			0
$331$	6.59808	+	1.76795i	0.362663	+	0.0971753i	0.435549	−	0.900165i	$-0.356554\pi$
$331$	6.59808	+	1.76795i	0.362663	+	0.0971753i	−0.0728860	+	0.997340i	$0.523221\pi$
$332$	1.03528	+	0.277401i	0.0568182	+	0.0152244i
$333$		0			0
$334$	−1.46410	−	2.53590i	−0.0801121	−	0.138758i
$335$	−3.39683	+	5.88349i	−0.185589	+	0.321449i
$336$		0			0
$337$			14.0718i			0.766540i	0.923636	+	0.383270i	$0.125202\pi$
$337$			14.0718i			0.766540i	−0.923636	+	0.383270i	$0.874798\pi$
$338$	−20.5940	−	15.8709i	−1.12017	−	0.863264i
$339$		0			0
$340$	−0.679492	−	2.53590i	−0.0368506	−	0.137528i
$341$	−48.3099	−	27.8917i	−2.61613	−	1.51042i
$342$		0			0
$343$	−14.0263	+	14.0263i	−0.757348	+	0.757348i
$344$		0			0
$345$		0			0
$346$	7.85641	+	7.85641i	0.422363	+	0.422363i
$347$	12.9682	−	7.48717i	0.696167	−	0.401932i	−0.109751	−	0.993959i	$-0.535005\pi$
$347$	12.9682	−	7.48717i	0.696167	−	0.401932i	0.805918	+	0.592027i	$0.201672\pi$
$348$		0			0
$349$	−33.4545	+	8.96410i	−1.79078	+	0.479837i	−0.992478	−	0.122423i	$-0.960933\pi$
$349$	−33.4545	+	8.96410i	−1.79078	+	0.479837i	−0.798299	+	0.602261i	$0.794267\pi$
$350$	17.2480			0.921942
$351$		0			0
$352$	49.5692			2.64205
$353$	−11.7806	+	3.15660i	−0.627017	+	0.168009i	−0.558316	−	0.829629i	$-0.688552\pi$
$353$	−11.7806	+	3.15660i	−0.627017	+	0.168009i	−0.0687013	+	0.997637i	$0.521886\pi$
$354$		0			0
$355$	1.05256	−	0.607695i	0.0558640	−	0.0322531i
$356$	16.2127	+	16.2127i	0.859271	+	0.859271i
$357$		0			0
$358$	−4.14359	+	15.4641i	−0.218996	+	0.817303i
$359$	−7.07107	+	7.07107i	−0.373197	+	0.373197i	−0.868640	−	0.495443i	$-0.835006\pi$
$359$	−7.07107	+	7.07107i	−0.373197	+	0.373197i	0.495443	+	0.868640i	$0.335006\pi$
$360$		0			0
$361$	−5.93782	−	3.42820i	−0.312517	−	0.180432i
$362$	−3.10583	−	11.5911i	−0.163239	−	0.609215i
$363$		0			0
$364$	−13.6603	−	2.73205i	−0.715992	−	0.143198i
$365$		−	8.38375i		−	0.438825i
$366$		0			0
$367$	−7.69615	+	13.3301i	−0.401736	+	0.695827i	−0.993936	−	0.109964i	$-0.964926\pi$
$367$	−7.69615	+	13.3301i	−0.401736	+	0.695827i	0.592200	+	0.805791i	$0.298260\pi$
$368$	−4.89898	−	8.48528i	−0.255377	−	0.442326i
$369$		0			0
$370$	11.4641	+	3.07180i	0.595990	+	0.159695i
$371$	−16.3514	−	4.38134i	−0.848922	−	0.227468i
$372$		0			0
$373$	−11.7942	−	20.4282i	−0.610682	−	1.05773i	−0.991126	−	0.132928i	$-0.957562\pi$
$373$	−11.7942	−	20.4282i	−0.610682	−	1.05773i	0.380444	−	0.924804i	$-0.375771\pi$
$374$	11.1106	−	19.2442i	0.574517	−	0.995093i
$375$		0			0
$376$		0			0
$377$	4.24264	−	2.82843i	0.218507	−	0.145671i
$378$		0			0
$379$	−5.35641	−	19.9904i	−0.275140	−	1.02684i	−0.955747	−	0.294188i	$-0.904951\pi$
$379$	−5.35641	−	19.9904i	−0.275140	−	1.02684i	0.680607	−	0.732648i	$-0.261716\pi$
$380$	−4.41851	−	2.55103i	−0.226665	−	0.130865i
$381$		0			0
$382$	−2.39230	+	2.39230i	−0.122401	+	0.122401i
$383$	2.58819	−	9.65926i	0.132250	−	0.493565i	−0.867744	−	0.497012i	$-0.834431\pi$
$383$	2.58819	−	9.65926i	0.132250	−	0.493565i	0.999994	+	0.00344689i	$0.00109718\pi$
$384$		0			0
$385$	−6.19615	−	6.19615i	−0.315785	−	0.315785i
$386$	19.1798	−	11.0735i	0.976227	−	0.563625i
$387$		0			0
$388$	−23.3923	+	6.26795i	−1.18756	+	0.318207i
$389$	−1.79315			−0.0909164			−0.0454582	−	0.998966i	$-0.514475\pi$
$389$	−1.79315			−0.0909164			−0.0454582	+	0.998966i	$0.514475\pi$
$390$		0			0
$391$	−4.39230			−0.222128
$392$		0			0
$393$		0			0
$394$	36.2487	−	20.9282i	1.82618	−	1.05435i
$395$	1.65445	+	1.65445i	0.0832444	+	0.0832444i
$396$		0			0
$397$	−6.66987	+	24.8923i	−0.334751	+	1.24931i	0.569387	+	0.822069i	$0.307181\pi$
$397$	−6.66987	+	24.8923i	−0.334751	+	1.24931i	−0.904139	+	0.427239i	$0.859486\pi$
$398$	−9.14162	+	9.14162i	−0.458228	+	0.458228i
$399$		0			0
$400$	15.4641	+	8.92820i	0.773205	+	0.446410i
$401$	3.14299	+	11.7298i	0.156954	+	0.585759i	0.998930	+	0.0462447i	$0.0147254\pi$
$401$	3.14299	+	11.7298i	0.156954	+	0.585759i	−0.841977	+	0.539514i	$0.818608\pi$
$402$		0			0
$403$	10.4019	+	30.7487i	0.518157	+	1.53170i
$404$			31.6675i			1.57552i
$405$		0			0
$406$	2.73205	−	4.73205i	0.135589	−	0.234848i
$407$	25.1141	+	43.4988i	1.24486	+	2.15616i
$408$		0			0
$409$	9.42820	+	2.52628i	0.466195	+	0.124916i	0.484267	−	0.874920i	$-0.339086\pi$
$409$	9.42820	+	2.52628i	0.466195	+	0.124916i	−0.0180725	+	0.999837i	$0.505753\pi$
$410$	−7.72741	−	2.07055i	−0.381629	−	0.102257i
$411$		0			0
$412$	8.66025	+	15.0000i	0.426660	+	0.738997i
$413$	9.84873	−	17.0585i	0.484624	−	0.839394i
$414$		0			0
$415$		−	0.392305i		−	0.0192575i
$416$	−21.6665	−	19.0411i	−1.06229	−	0.933567i
$417$		0			0
$418$	−11.1769	−	41.7128i	−0.546681	−	2.04024i
$419$	22.5259	+	13.0053i	1.10046	+	0.635352i	0.936342	−	0.351089i	$-0.114189\pi$
$419$	22.5259	+	13.0053i	1.10046	+	0.635352i	0.164119	+	0.986441i	$0.447522\pi$
$420$		0			0
$421$	13.6340	−	13.6340i	0.664479	−	0.664479i	−0.291953	−	0.956433i	$-0.594305\pi$
$421$	13.6340	−	13.6340i	0.664479	−	0.664479i	0.956433	+	0.291953i	$0.0943052\pi$
$422$	2.48665	−	9.28032i	0.121048	−	0.451759i
$423$		0			0
$424$		0			0
$425$	6.93237	−	4.00240i	0.336269	−	0.194145i
$426$		0			0
$427$	5.23205	−	1.40192i	0.253197	−	0.0678438i
$428$	−26.0106			−1.25727
$429$		0			0
$430$	−6.24871			−0.301340
$431$	−11.4524	+	3.06866i	−0.551643	+	0.147812i	−0.523864	−	0.851802i	$-0.675510\pi$
$431$	−11.4524	+	3.06866i	−0.551643	+	0.147812i	−0.0277789	+	0.999614i	$0.508843\pi$
$432$		0			0
$433$	9.99038	−	5.76795i	0.480107	−	0.277190i	−0.240354	−	0.970685i	$-0.577264\pi$
$433$	9.99038	−	5.76795i	0.480107	−	0.277190i	0.720461	+	0.693495i	$0.243930\pi$
$434$	24.5964	+	24.5964i	1.18067	+	1.18067i
$435$		0			0
$436$	3.14359	−	11.7321i	0.150551	−	0.561863i
$437$	−6.03579	+	6.03579i	−0.288731	+	0.288731i
$438$		0			0
$439$	−18.6962	−	10.7942i	−0.892319	−	0.515180i	−0.0176185	−	0.999845i	$-0.505608\pi$
$439$	−18.6962	−	10.7942i	−0.892319	−	0.515180i	−0.874700	+	0.484664i	$0.838942\pi$
$440$		0			0
$441$		0			0
$442$	−12.2487	+	4.14359i	−0.582612	+	0.197091i
$443$			35.0507i			1.66531i	0.553792	+	0.832655i	$0.313180\pi$
$443$			35.0507i			1.66531i	−0.553792	+	0.832655i	$0.686820\pi$
$444$		0			0
$445$	4.19615	−	7.26795i	0.198917	−	0.344534i
$446$	−4.79744	−	8.30942i	−0.227166	−	0.393462i
$447$		0			0
$448$	−14.9282	−	4.00000i	−0.705291	−	0.188982i
$449$	5.08845	+	1.36345i	0.240139	+	0.0643450i	0.376881	−	0.926262i	$-0.376997\pi$
$449$	5.08845	+	1.36345i	0.240139	+	0.0643450i	−0.136742	+	0.990607i	$0.543663\pi$
$450$		0			0
$451$	−16.9282	−	29.3205i	−0.797118	−	1.38065i
$452$	−10.1769	+	17.6269i	−0.478681	+	0.829100i
$453$		0			0
$454$		−	26.9282i		−	1.26380i
$455$	0.328169	+	5.08845i	0.0153848	+	0.238550i
$456$		0			0
$457$	1.06218	+	3.96410i	0.0496866	+	0.185433i	0.986309	−	0.164908i	$-0.0527326\pi$
$457$	1.06218	+	3.96410i	0.0496866	+	0.185433i	−0.936622	+	0.350340i	$0.886066\pi$
$458$	−0.656339	−	0.378937i	−0.0306687	−	0.0177066i
$459$		0			0
$460$	2.53590	−	2.53590i	0.118237	−	0.118237i
$461$	−9.65926	+	36.0488i	−0.449877	+	1.67896i	0.252853	+	0.967505i	$0.418631\pi$
$461$	−9.65926	+	36.0488i	−0.449877	+	1.67896i	−0.702729	+	0.711457i	$0.748036\pi$
$462$		0			0
$463$	3.83013	+	3.83013i	0.178001	+	0.178001i	0.790484	−	0.612483i	$-0.209829\pi$
$463$	3.83013	+	3.83013i	0.178001	+	0.178001i	−0.612483	+	0.790484i	$0.709829\pi$
$464$	4.89898	−	2.82843i	0.227429	−	0.131306i
$465$		0			0
$466$	−20.1962	+	5.41154i	−0.935569	+	0.250685i
$467$	−22.0454			−1.02014			−0.510070	−	0.860133i	$-0.670380\pi$
$467$	−22.0454			−1.02014			−0.510070	+	0.860133i	$0.670380\pi$
$468$		0			0
$469$	17.9282			0.827848
$470$	−9.52056	+	2.55103i	−0.439151	+	0.117670i
$471$		0			0
$472$		0			0
$473$	−18.6993	−	18.6993i	−0.859797	−	0.859797i
$474$		0			0
$475$	4.02628	−	15.0263i	0.184738	−	0.689453i
$476$	−4.89898	+	4.89898i	−0.224544	+	0.224544i
$477$		0			0
$478$	23.3205	+	13.4641i	1.06666	+	0.615834i
$479$	−1.03528	−	3.86370i	−0.0473030	−	0.176537i	0.938233	−	0.346005i	$-0.112462\pi$
$479$	−1.03528	−	3.86370i	−0.0473030	−	0.176537i	−0.985536	+	0.169468i	$0.945795\pi$
$480$		0			0
$481$	5.73205	−	28.6603i	0.261359	−	1.30680i
$482$		−	33.1833i		−	1.51146i
$483$		0			0
$484$	−27.3923	+	47.4449i	−1.24510	+	2.15658i
$485$	4.43211	+	7.67664i	0.201252	+	0.348578i
$486$		0			0
$487$	−13.8301	−	3.70577i	−0.626703	−	0.167925i	−0.0685298	−	0.997649i	$-0.521831\pi$
$487$	−13.8301	−	3.70577i	−0.626703	−	0.167925i	−0.558173	+	0.829725i	$0.688497\pi$
$488$		0			0
$489$		0			0
$490$	−2.39230	−	4.14359i	−0.108073	−	0.187188i
$491$	−8.15711	+	14.1285i	−0.368125	+	0.637612i	−0.989272	−	0.146082i	$-0.953334\pi$
$491$	−8.15711	+	14.1285i	−0.368125	+	0.637612i	0.621147	+	0.783694i	$0.286667\pi$
$492$		0			0
$493$		−	2.53590i		−	0.114211i
$494$	−11.1378	+	22.5259i	−0.501115	+	1.01349i
$495$		0			0
$496$	9.32051	+	34.7846i	0.418503	+	1.56188i
$497$	−2.77766	−	1.60368i	−0.124595	−	0.0719350i
$498$		0			0
$499$	−27.7321	+	27.7321i	−1.24146	+	1.24146i	−0.282060	+	0.959397i	$0.591018\pi$
$499$	−27.7321	+	27.7321i	−1.24146	+	1.24146i	−0.959397	+	0.282060i	$0.908982\pi$
$500$	−3.58630	+	13.3843i	−0.160384	+	0.598562i
$501$		0			0
$502$	−18.2487	−	18.2487i	−0.814480	−	0.814480i
$503$	23.2702	−	13.4350i	1.03756	−	0.599038i	0.118422	−	0.992963i	$-0.462216\pi$
$503$	23.2702	−	13.4350i	1.03756	−	0.599038i	0.919143	+	0.393925i	$0.128883\pi$
$504$		0			0
$505$	11.1962	−	3.00000i	0.498222	−	0.133498i
$506$	30.3548			1.34944
$507$		0			0
$508$	7.85641			0.348572
$509$	24.7859	−	6.64136i	1.09862	−	0.294373i	0.336415	−	0.941714i	$-0.390786\pi$
$509$	24.7859	−	6.64136i	1.09862	−	0.294373i	0.762201	+	0.647341i	$0.224119\pi$
$510$		0			0
$511$	−19.1603	+	11.0622i	−0.847600	+	0.489362i
$512$	−22.6274	−	22.6274i	−1.00000	−	1.00000i
$513$		0			0
$514$	−9.46410	+	35.3205i	−0.417444	+	1.55792i
$515$	4.48288	−	4.48288i	0.197539	−	0.197539i
$516$		0			0
$517$	−36.1244	−	20.8564i	−1.58875	−	0.917264i
$518$	−8.10634	−	30.2533i	−0.356172	−	1.32925i
$519$		0			0
$520$		0			0
$521$		−	32.2223i		−	1.41168i	−0.708369	−	0.705842i	$-0.750569\pi$
$521$		−	32.2223i		−	1.41168i	0.708369	−	0.705842i	$-0.249431\pi$
$522$		0			0
$523$	0.607695	−	1.05256i	0.0265727	−	0.0460252i	−0.852433	−	0.522836i	$-0.824874\pi$
$523$	0.607695	−	1.05256i	0.0265727	−	0.0460252i	0.879006	+	0.476811i	$0.158207\pi$
$524$	−7.07107	−	12.2474i	−0.308901	−	0.535032i
$525$		0			0
$526$	39.8564	+	10.6795i	1.73782	+	0.465648i
$527$	15.5935	+	4.17827i	0.679264	+	0.182008i
$528$		0			0
$529$	8.50000	+	14.7224i	0.369565	+	0.640106i
$530$	6.41473	−	11.1106i	0.278638	−	0.482615i
$531$		0			0
$532$			13.4641i			0.583743i
$533$	−3.86370	+	19.3185i	−0.167356	+	0.836778i
$534$		0			0
$535$	2.46410	+	9.19615i	0.106532	+	0.397584i
$536$		0			0
$537$		0			0
$538$	33.1769	−	33.1769i	1.43036	−	1.43036i
$539$	5.24075	−	19.5588i	0.225735	−	0.842455i
$540$		0			0
$541$	5.68653	+	5.68653i	0.244483	+	0.244483i	0.818702	−	0.574219i	$-0.194694\pi$
$541$	5.68653	+	5.68653i	0.244483	+	0.244483i	−0.574219	+	0.818702i	$0.694694\pi$
$542$	−38.7757	+	22.3872i	−1.66556	+	0.961612i
$543$		0			0
$544$	−13.8564	+	3.71281i	−0.594089	+	0.159186i
$545$	−4.44571			−0.190433
$546$		0			0
$547$	3.39230			0.145044			0.0725222	−	0.997367i	$-0.476895\pi$
$547$	3.39230			0.145044			0.0725222	+	0.997367i	$0.476895\pi$
$548$	−2.07055	+	0.554803i	−0.0884496	+	0.0237000i
$549$		0			0
$550$	−47.9090	+	27.6603i	−2.04285	+	1.17944i
$551$	−3.48477	−	3.48477i	−0.148456	−	0.148456i
$552$		0			0
$553$	1.59808	−	5.96410i	0.0679571	−	0.253619i
$554$	11.1106	−	11.1106i	0.472046	−	0.472046i
$555$		0			0
$556$	30.1244	+	17.3923i	1.27756	+	0.737598i
$557$	2.96713	+	11.0735i	0.125721	+	0.469198i	0.999864	−	0.0164704i	$-0.00524292\pi$
$557$	2.96713	+	11.0735i	0.125721	+	0.469198i	−0.874143	+	0.485668i	$0.838576\pi$
$558$		0			0
$559$	0.990381	+	15.3564i	0.0418887	+	0.649507i
$560$			5.65685i			0.239046i
$561$		0			0
$562$	21.5167	−	37.2679i	0.907626	−	1.57205i
$563$	−14.8492	−	25.7196i	−0.625821	−	1.08395i	−0.988381	−	0.151993i	$-0.951431\pi$
$563$	−14.8492	−	25.7196i	−0.625821	−	1.08395i	0.362561	−	0.931960i	$-0.381903\pi$
$564$		0			0
$565$	7.19615	+	1.92820i	0.302744	+	0.0811201i
$566$	9.38186	+	2.51386i	0.394349	+	0.105665i
$567$		0			0
$568$		0			0
$569$	−3.67423	+	6.36396i	−0.154032	+	0.266791i	−0.932706	−	0.360637i	$-0.882559\pi$
$569$	−3.67423	+	6.36396i	−0.154032	+	0.266791i	0.778674	+	0.627428i	$0.215893\pi$
$570$		0			0
$571$		−	33.7128i		−	1.41084i	−0.708791	−	0.705419i	$-0.750759\pi$
$571$		−	33.7128i		−	1.41084i	0.708791	−	0.705419i	$-0.249241\pi$
$572$	42.3249	−	14.3180i	1.76969	−	0.598666i
$573$		0			0
$574$	5.46410	+	20.3923i	0.228067	+	0.851158i
$575$	9.46979	+	5.46739i	0.394918	+	0.228006i
$576$		0			0
$577$	−1.19615	+	1.19615i	−0.0497965	+	0.0497965i	−0.731567	−	0.681770i	$-0.761210\pi$
$577$	−1.19615	+	1.19615i	−0.0497965	+	0.0497965i	0.681770	+	0.731567i	$0.261210\pi$
$578$	7.13544	−	26.6298i	0.296795	−	1.10765i
$579$		0			0
$580$	1.46410	+	1.46410i	0.0607935	+	0.0607935i
$581$	−0.896575	+	0.517638i	−0.0371962	+	0.0214752i
$582$		0			0
$583$	52.4449	−	14.0526i	2.17204	−	0.581998i
$584$		0			0
$585$		0			0
$586$	−44.3923			−1.83383
$587$	7.15900	−	1.91825i	0.295484	−	0.0791746i	−0.108032	−	0.994147i	$-0.534455\pi$
$587$	7.15900	−	1.91825i	0.295484	−	0.0791746i	0.403515	+	0.914973i	$0.367788\pi$
$588$		0			0
$589$	27.1699	−	15.6865i	1.11952	−	0.646352i
$590$	10.5558	+	10.5558i	0.434577	+	0.434577i
$591$		0			0
$592$	8.39230	−	31.3205i	0.344922	−	1.28726i
$593$	11.4524	−	11.4524i	0.470294	−	0.470294i	−0.431716	−	0.902010i	$-0.642092\pi$
$593$	11.4524	−	11.4524i	0.470294	−	0.470294i	0.902010	+	0.431716i	$0.142092\pi$
$594$		0			0
$595$	2.19615	+	1.26795i	0.0900335	+	0.0519808i
$596$	−7.45001	−	27.8038i	−0.305164	−	1.13889i
$597$		0			0
$598$	−13.2679	−	11.6603i	−0.542567	−	0.476823i
$599$			29.9759i			1.22478i	0.790555	+	0.612391i	$0.209792\pi$
$599$			29.9759i			1.22478i	−0.790555	+	0.612391i	$0.790208\pi$
$600$		0			0
$601$	−2.39230	+	4.14359i	−0.0975842	+	0.169021i	−0.910684	−	0.413103i	$-0.864445\pi$
$601$	−2.39230	+	4.14359i	−0.0975842	+	0.169021i	0.813100	+	0.582124i	$0.197778\pi$
$602$	8.24504	+	14.2808i	0.336043	+	0.582043i
$603$		0			0
$604$	−4.19615	−	1.12436i	−0.170739	−	0.0457494i
$605$	19.3693	+	5.18998i	0.787473	+	0.211003i
$606$		0			0
$607$	8.80385	+	15.2487i	0.357337	+	0.618926i	0.987515	−	0.157525i	$-0.0503514\pi$
$607$	8.80385	+	15.2487i	0.357337	+	0.618926i	−0.630178	+	0.776451i	$0.717018\pi$
$608$	−13.9391	+	24.1432i	−0.565304	+	0.979135i
$609$		0			0
$610$			4.10512i			0.166211i
$611$	7.77817	+	22.9928i	0.314671	+	0.930187i
$612$		0			0
$613$	2.33013	+	8.69615i	0.0941129	+	0.351234i	0.996883	−	0.0788882i	$-0.0251370\pi$
$613$	2.33013	+	8.69615i	0.0941129	+	0.351234i	−0.902771	+	0.430123i	$0.858470\pi$
$614$	9.07725	+	5.24075i	0.366328	+	0.211500i
$615$		0			0
$616$		0			0
$617$	5.43022	−	20.2659i	0.218612	−	0.815873i	−0.766251	−	0.642541i	$-0.777880\pi$
$617$	5.43022	−	20.2659i	0.218612	−	0.815873i	0.984864	−	0.173332i	$-0.0554532\pi$
$618$		0			0
$619$	4.16987	+	4.16987i	0.167601	+	0.167601i	0.785924	−	0.618323i	$-0.212188\pi$
$619$	4.16987	+	4.16987i	0.167601	+	0.167601i	−0.618323	+	0.785924i	$0.712188\pi$
$620$	−11.4152	+	6.59059i	−0.458447	+	0.264685i
$621$		0			0
$622$	54.2487	−	14.5359i	2.17518	−	0.582836i
$623$	−22.1469			−0.887299
$624$		0			0
$625$	−17.2487			−0.689948
$626$	13.9019	−	3.72500i	0.555632	−	0.148881i
$627$		0			0
$628$	16.2679	−	9.39230i	0.649162	−	0.374794i
$629$	−10.2784	−	10.2784i	−0.409828	−	0.409828i
$630$		0			0
$631$	5.54552	−	20.6962i	0.220764	−	0.823901i	−0.763294	−	0.646051i	$-0.776419\pi$
$631$	5.54552	−	20.6962i	0.220764	−	0.823901i	0.984058	−	0.177850i	$-0.0569141\pi$
$632$		0			0
$633$		0			0
$634$	−1.85641	−	1.07180i	−0.0737273	−	0.0425665i
$635$	−0.744272	−	2.77766i	−0.0295355	−	0.110228i
$636$		0			0
$637$	−9.80385	+	6.53590i	−0.388443	+	0.258962i
$638$			17.5254i			0.693836i
$639$		0			0
$640$		0			0
$641$	−13.4722	−	23.3345i	−0.532120	−	0.921658i	−0.999297	−	0.0374946i	$-0.988062\pi$
$641$	−13.4722	−	23.3345i	−0.532120	−	0.921658i	0.467177	−	0.884164i	$-0.345271\pi$
$642$		0			0
$643$	−0.964102	−	0.258330i	−0.0380205	−	0.0101876i	0.239759	−	0.970833i	$-0.422932\pi$
$643$	−0.964102	−	0.258330i	−0.0380205	−	0.0101876i	−0.277779	+	0.960645i	$0.589598\pi$
$644$	−9.14162	−	2.44949i	−0.360230	−	0.0965234i
$645$		0			0
$646$	6.24871	+	10.8231i	0.245852	+	0.425829i
$647$	23.9909	−	41.5534i	0.943178	−	1.63363i	0.183820	−	0.982960i	$-0.441154\pi$
$647$	23.9909	−	41.5534i	0.943178	−	1.63363i	0.759359	−	0.650672i	$-0.225513\pi$
$648$		0			0
$649$			63.1769i			2.47991i
$650$	31.5660	+	6.31319i	1.23812	+	0.247624i
$651$		0			0
$652$	−7.87564	−	29.3923i	−0.308434	−	1.15109i
$653$	9.79796	+	5.65685i	0.383424	+	0.221370i	0.679307	−	0.733854i	$-0.262281\pi$
$653$	9.79796	+	5.65685i	0.383424	+	0.221370i	−0.295883	+	0.955224i	$0.595614\pi$
$654$		0			0
$655$	−3.66025	+	3.66025i	−0.143018	+	0.143018i
$656$	−5.65685	+	21.1117i	−0.220863	+	0.824272i
$657$		0			0
$658$	18.3923	+	18.3923i	0.717007	+	0.717007i
$659$	−23.2466	+	13.4214i	−0.905559	+	0.522825i	−0.878999	−	0.476823i	$-0.841788\pi$
$659$	−23.2466	+	13.4214i	−0.905559	+	0.522825i	−0.0265591	+	0.999647i	$0.508455\pi$
$660$		0			0
$661$	4.40192	−	1.17949i	0.171215	−	0.0458769i	−0.172193	−	0.985063i	$-0.555085\pi$
$661$	4.40192	−	1.17949i	0.171215	−	0.0458769i	0.343408	+	0.939186i	$0.388419\pi$
$662$	13.6617			0.530976
$663$		0			0
$664$		0			0
$665$	4.76028	−	1.27551i	0.184596	−	0.0494623i
$666$		0			0
$667$	3.00000	−	1.73205i	0.116160	−	0.0670653i
$668$	−2.07055	−	2.07055i	−0.0801121	−	0.0801121i
$669$		0			0
$670$	−3.51666	+	13.1244i	−0.135860	+	0.507038i
$671$	−12.2846	+	12.2846i	−0.474242	+	0.474242i
$672$		0			0
$673$	−34.2846	−	19.7942i	−1.32157	−	0.763011i	−0.337595	−	0.941292i	$-0.609613\pi$
$673$	−34.2846	−	19.7942i	−1.32157	−	0.763011i	−0.983980	+	0.178280i	$0.942947\pi$
$674$	7.28410	+	27.1846i	0.280573	+	1.04711i
$675$		0			0
$676$	−24.0000	−	10.0000i	−0.923077	−	0.384615i
$677$		−	42.9812i		−	1.65190i	−0.563742	−	0.825951i	$-0.690639\pi$
$677$		−	42.9812i		−	1.65190i	0.563742	−	0.825951i	$-0.309361\pi$
$678$		0			0
$679$	11.6962	−	20.2583i	0.448857	−	0.777443i
$680$		0			0
$681$		0			0
$682$	−107.765	−	28.8756i	−4.12655	−	1.10571i
$683$	−26.5791	−	7.12184i	−1.01702	−	0.272509i	−0.288460	−	0.957492i	$-0.593143\pi$
$683$	−26.5791	−	7.12184i	−1.01702	−	0.272509i	−0.728559	+	0.684983i	$0.759810\pi$
$684$		0			0
$685$	0.392305	+	0.679492i	0.0149892	+	0.0259621i
$686$	−19.8362	+	34.3572i	−0.757348	+	1.31177i
$687$		0			0
$688$			17.0718i			0.650856i
$689$	−28.3214	−	14.0034i	−1.07896	−	0.533488i
$690$		0			0
$691$	10.5718	+	39.4545i	0.402170	+	1.50092i	0.809216	+	0.587511i	$0.199892\pi$
$691$	10.5718	+	39.4545i	0.402170	+	1.50092i	−0.407046	+	0.913408i	$0.633441\pi$
$692$	9.62209	+	5.55532i	0.365777	+	0.211182i
$693$		0			0
$694$	21.1769	−	21.1769i	0.803865	−	0.803865i
$695$	3.29530	−	12.2982i	0.124998	−	0.466498i
$696$		0			0
$697$	6.92820	+	6.92820i	0.262424	+	0.262424i
$698$	−59.9889	+	34.6346i	−2.27061	+	1.31094i
$699$		0			0
$700$	16.6603	−	4.46410i	0.629698	−	0.168727i
$701$	−6.21166			−0.234611			−0.117306	−	0.993096i	$-0.537426\pi$
$701$	−6.21166			−0.234611			−0.117306	+	0.993096i	$0.537426\pi$
$702$		0			0
$703$	−28.2487			−1.06542
$704$	47.8802	−	12.8295i	1.80455	−	0.483528i
$705$		0			0
$706$	−21.1244	+	12.1962i	−0.795026	+	0.459008i
$707$	−21.6293	−	21.6293i	−0.813454	−	0.813454i
$708$		0			0
$709$	−1.30385	+	4.86603i	−0.0489670	+	0.182747i	−0.986078	−	0.166285i	$-0.946823\pi$
$709$	−1.30385	+	4.86603i	−0.0489670	+	0.182747i	0.937111	+	0.349032i	$0.113490\pi$
$710$	1.71882	−	1.71882i	0.0645062	−	0.0645062i
$711$		0			0
$712$		0			0
$713$	5.70762	+	21.3011i	0.213752	+	0.797734i
$714$		0			0
$715$	−9.07180	−	13.6077i	−0.339266	−	0.508899i
$716$			16.0096i			0.598307i
$717$		0			0
$718$	−10.0000	+	17.3205i	−0.373197	+	0.646396i
$719$	4.98691	+	8.63759i	0.185980	+	0.322128i	0.943906	−	0.330213i	$-0.107121\pi$
$719$	4.98691	+	8.63759i	0.185980	+	0.322128i	−0.757926	+	0.652341i	$0.773787\pi$
$720$		0			0
$721$	−16.1603	−	4.33013i	−0.601839	−	0.161262i
$722$	−13.2456	−	3.54914i	−0.492949	−	0.132085i
$723$		0			0
$724$	−6.00000	−	10.3923i	−0.222988	−	0.386227i
$725$	−3.15660	+	5.46739i	−0.117233	+	0.203054i
$726$		0			0
$727$			41.1051i			1.52450i	0.647280	+	0.762252i	$0.275906\pi$
$727$			41.1051i			1.52450i	−0.647280	+	0.762252i	$0.724094\pi$
$728$		0			0
$729$		0			0
$730$	−4.33975	−	16.1962i	−0.160621	−	0.599446i
$731$	6.62776	+	3.82654i	0.245137	+	0.141530i
$732$		0			0
$733$	−10.2417	+	10.2417i	−0.378285	+	0.378285i	−0.870483	−	0.492198i	$-0.836193\pi$
$733$	−10.2417	+	10.2417i	−0.378285	+	0.378285i	0.492198	+	0.870483i	$0.336193\pi$
$734$	−7.96764	+	29.7356i	−0.294091	+	1.09756i
$735$		0			0
$736$	−13.8564	−	13.8564i	−0.510754	−	0.510754i
$737$	−49.7984	+	28.7511i	−1.83435	+	1.05906i
$738$		0			0
$739$	11.5622	−	3.09808i	0.425322	−	0.113965i	−0.0398077	−	0.999207i	$-0.512675\pi$
$739$	11.5622	−	3.09808i	0.425322	−	0.113965i	0.465129	+	0.885243i	$0.346008\pi$
$740$	11.8685			0.436295
$741$		0			0
$742$	−33.8564			−1.24291
$743$	−30.0638	+	8.05558i	−1.10293	+	0.295530i	−0.763959	−	0.645265i	$-0.776747\pi$
$743$	−30.0638	+	8.05558i	−1.10293	+	0.295530i	−0.338976	+	0.940795i	$0.610080\pi$
$744$		0			0
$745$	−9.12436	+	5.26795i	−0.334291	+	0.193003i
$746$	−33.3591	−	33.3591i	−1.22136	−	1.22136i
$747$		0			0
$748$	5.75129	−	21.4641i	0.210288	−	0.784805i
$749$	17.7656	−	17.7656i	0.649141	−	0.649141i
$750$		0			0
$751$	32.7846	+	18.9282i	1.19633	+	0.690700i	0.959734	−	0.280909i	$-0.0906359\pi$
$751$	32.7846	+	18.9282i	1.19633	+	0.690700i	0.236593	+	0.971609i	$0.423969\pi$
$752$	6.96953	+	26.0106i	0.254153	+	0.948511i
$753$		0			0
$754$	6.73205	−	7.66025i	0.245167	−	0.278970i
$755$			1.59008i			0.0578689i
$756$		0			0
$757$	25.1962	−	43.6410i	0.915770	−	1.58616i	0.109999	−	0.993932i	$-0.464915\pi$
$757$	25.1962	−	43.6410i	0.915770	−	1.58616i	0.805770	−	0.592228i	$-0.201752\pi$
$758$	−20.6956	−	35.8458i	−0.751697	−	1.30198i
$759$		0			0
$760$		0			0
$761$	41.3268	+	11.0735i	1.49809	+	0.401413i	0.912461	−	0.409163i	$-0.134179\pi$
$761$	41.3268	+	11.0735i	1.49809	+	0.401413i	0.585633	+	0.810577i	$0.300846\pi$
$762$		0			0
$763$	5.86603	+	10.1603i	0.212364	+	0.367826i
$764$	−1.69161	+	2.92996i	−0.0612005	+	0.106002i
$765$		0			0
$766$		−	20.0000i		−	0.722629i
$767$	24.2683	−	27.6143i	0.876276	−	0.997096i
$768$		0			0
$769$	7.50962	+	28.0263i	0.270804	+	1.01065i	0.958601	+	0.284751i	$0.0919109\pi$
$769$	7.50962	+	28.0263i	0.270804	+	1.01065i	−0.687798	+	0.725902i	$0.741422\pi$
$770$	−15.1774	−	8.76268i	−0.546956	−	0.315785i
$771$		0			0
$772$	15.6603	−	15.6603i	0.563625	−	0.563625i
$773$	−10.8840	+	40.6197i	−0.391470	+	1.46099i	0.436239	+	0.899831i	$0.356310\pi$
$773$	−10.8840	+	40.6197i	−0.391470	+	1.46099i	−0.827710	+	0.561157i	$0.810357\pi$
$774$		0			0
$775$	−28.4186	−	28.4186i	−1.02083	−	1.02083i
$776$		0			0
$777$		0			0
$778$	−3.46410	+	0.928203i	−0.124194	+	0.0332777i
$779$	19.0411			0.682219
$780$		0			0
$781$	10.2872			0.368104
$782$	−8.48528	+	2.27362i	−0.303433	+	0.0813046i
$783$		0			0
$784$	−11.3205	+	6.53590i	−0.404304	+	0.233425i
$785$	−4.86181	−	4.86181i	−0.173526	−	0.173526i
$786$		0			0
$787$	5.16025	−	19.2583i	0.183943	−	0.686485i	−0.810911	−	0.585169i	$-0.801028\pi$
$787$	5.16025	−	19.2583i	0.183943	−	0.686485i	0.994854	−	0.101316i	$-0.0323053\pi$
$788$	29.5969	−	29.5969i	1.05435	−	1.05435i
$789$		0			0
$790$	4.05256	+	2.33975i	0.144184	+	0.0832444i
$791$	−5.08845	−	18.9903i	−0.180924	−	0.675219i
$792$		0			0
$793$	10.0885	−	0.650635i	0.358252	−	0.0231047i
$794$			51.5408i			1.82912i
$795$		0			0
$796$	−6.46410	+	11.1962i	−0.229114	+	0.396837i
$797$	6.93237	+	12.0072i	0.245557	+	0.425317i	0.962288	−	0.272032i	$-0.0876958\pi$
$797$	6.93237	+	12.0072i	0.245557	+	0.425317i	−0.716731	+	0.697350i	$0.754362\pi$
$798$		0			0
$799$	11.6603	+	3.12436i	0.412510	+	0.110532i
$800$	34.4959	+	9.24316i	1.21962	+	0.326795i
$801$		0			0
$802$	12.1436	+	21.0333i	0.428805	+	0.742712i
$803$	35.4804	−	61.4539i	1.25208	−	2.16866i
$804$		0			0
$805$			3.46410i			0.122094i
$806$	36.0117	+	54.0175i	1.26846	+	1.90269i
$807$		0			0
$808$		0			0
$809$	29.1536	+	16.8319i	1.02499	+	0.591777i	0.915545	−	0.402216i	$-0.131760\pi$
$809$	29.1536	+	16.8319i	1.02499	+	0.591777i	0.109443	+	0.993993i	$0.465093\pi$
$810$		0			0
$811$	2.90192	−	2.90192i	0.101900	−	0.101900i	−0.654319	−	0.756219i	$-0.727044\pi$
$811$	2.90192	−	2.90192i	0.101900	−	0.101900i	0.756219	+	0.654319i	$0.227044\pi$
$812$	1.41421	−	5.27792i	0.0496292	−	0.185219i
$813$		0			0
$814$	71.0333	+	71.0333i	2.48972	+	2.48972i
$815$	−9.64566	+	5.56892i	−0.337873	+	0.195071i
$816$		0			0
$817$	14.3660	−	3.84936i	0.502604	−	0.134672i
$818$	19.5216			0.682556
$819$		0			0
$820$	−8.00000			−0.279372
$821$	−20.6820	+	5.54172i	−0.721805	+	0.193407i	−0.600977	−	0.799266i	$-0.705222\pi$
$821$	−20.6820	+	5.54172i	−0.721805	+	0.193407i	−0.120828	+	0.992673i	$0.538555\pi$
$822$		0			0
$823$	14.1962	−	8.19615i	0.494847	−	0.285700i	−0.231736	−	0.972779i	$-0.574441\pi$
$823$	14.1962	−	8.19615i	0.494847	−	0.285700i	0.726583	+	0.687079i	$0.241107\pi$
$824$		0			0
$825$		0			0
$826$	10.1962	−	38.0526i	0.354770	−	1.32402i
$827$	11.8685	−	11.8685i	0.412709	−	0.412709i	−0.469972	−	0.882681i	$-0.655736\pi$
$827$	11.8685	−	11.8685i	0.412709	−	0.412709i	0.882681	+	0.469972i	$0.155736\pi$
$828$		0			0
$829$	31.7942	+	18.3564i	1.10426	+	0.637544i	0.937336	−	0.348426i	$-0.113284\pi$
$829$	31.7942	+	18.3564i	1.10426	+	0.637544i	0.166923	+	0.985970i	$0.446617\pi$
$830$	−0.203072	−	0.757875i	−0.00704873	−	0.0263062i
$831$		0			0
$832$	−25.8564	−	12.7846i	−0.896410	−	0.443227i
$833$			5.85993i			0.203034i
$834$		0			0
$835$	−0.535898	+	0.928203i	−0.0185455	+	0.0321218i
$836$	−21.5921	−	37.3987i	−0.746780	−	1.29346i
$837$		0			0
$838$	50.2487	+	13.4641i	1.73581	+	0.465110i
$839$	−30.5815	−	8.19428i	−1.05579	−	0.282898i	−0.311147	−	0.950362i	$-0.600713\pi$
$839$	−30.5815	−	8.19428i	−1.05579	−	0.282898i	−0.744642	+	0.667464i	$0.767380\pi$
$840$		0			0
$841$	−13.5000	−	23.3827i	−0.465517	−	0.806300i
$842$	19.2814	−	33.3963i	0.664479	−	1.15091i
$843$		0			0
$844$		−	9.60770i		−	0.330711i
$845$	−1.26191	+	9.43262i	−0.0434110	+	0.324492i
$846$		0			0
$847$	−13.6962	−	51.1147i	−0.470605	−	1.75632i
$848$	−30.3548	−	17.5254i	−1.04239	−	0.601824i
$849$		0			0
$850$	11.3205	−	11.3205i	0.388290	−	0.388290i
$851$	5.13922	−	19.1798i	0.176170	−	0.657476i
$852$		0			0
$853$	−18.2224	−	18.2224i	−0.623924	−	0.623924i	0.322608	−	0.946533i	$-0.395440\pi$
$853$	−18.2224	−	18.2224i	−0.623924	−	0.623924i	−0.946533	+	0.322608i	$0.895440\pi$
$854$	9.38186	−	5.41662i	0.321041	−	0.185353i
$855$		0			0
$856$		0			0
$857$	45.7081			1.56136			0.780679	−	0.624932i	$-0.214873\pi$
$857$	45.7081			1.56136			0.780679	+	0.624932i	$0.214873\pi$
$858$		0			0
$859$	−40.8038			−1.39221			−0.696105	−	0.717940i	$-0.745085\pi$
$859$	−40.8038			−1.39221			−0.696105	+	0.717940i	$0.745085\pi$
$860$	−6.03579	+	1.61729i	−0.205819	+	0.0551490i
$861$		0			0
$862$	−20.5359	+	11.8564i	−0.699455	+	0.403831i
$863$	11.7298	+	11.7298i	0.399287	+	0.399287i	0.877982	−	0.478694i	$-0.158890\pi$
$863$	11.7298	+	11.7298i	0.399287	+	0.399287i	−0.478694	+	0.877982i	$0.658890\pi$
$864$		0			0
$865$	1.05256	−	3.92820i	0.0357881	−	0.133563i
$866$	16.3142	−	16.3142i	0.554380	−	0.554380i
$867$		0			0
$868$	30.1244	+	17.3923i	1.02249	+	0.590333i
$869$	5.12561	+	19.1290i	0.173875	+	0.648909i
$870$		0			0
$871$	32.8109	+	6.56218i	1.11175	+	0.222351i
$872$		0			0
$873$		0			0
$874$	−8.53590	+	14.7846i	−0.288731	+	0.500097i
$875$	−6.69213	−	11.5911i	−0.226235	−	0.391851i
$876$		0			0
$877$	−37.1506	−	9.95448i	−1.25449	−	0.336139i	−0.430419	−	0.902629i	$-0.641634\pi$
$877$	−37.1506	−	9.95448i	−1.25449	−	0.336139i	−0.824069	+	0.566490i	$0.808301\pi$
$878$	−41.7057	−	11.1750i	−1.40750	−	0.377138i
$879$		0			0
$880$	−9.07180	−	15.7128i	−0.305810	−	0.529679i
$881$	−12.4877	+	21.6293i	−0.420721	+	0.728710i	−0.996010	−	0.0892402i	$-0.971556\pi$
$881$	−12.4877	+	21.6293i	−0.420721	+	0.728710i	0.575289	+	0.817950i	$0.304889\pi$
$882$		0			0
$883$			17.7846i			0.598500i	0.954175	+	0.299250i	$0.0967364\pi$
$883$			17.7846i			0.598500i	−0.954175	+	0.299250i	$0.903264\pi$
$884$	−10.7589	+	7.17260i	−0.361861	+	0.241241i
$885$		0			0
$886$	18.1436	+	67.7128i	0.609546	+	2.27486i
$887$	−0.504035	−	0.291005i	−0.0169238	−	0.00977098i	0.491514	−	0.870870i	$-0.336444\pi$
$887$	−0.504035	−	0.291005i	−0.0169238	−	0.00977098i	−0.508438	+	0.861099i	$0.669777\pi$
$888$		0			0
$889$	−5.36603	+	5.36603i	−0.179971	+	0.179971i
$890$	4.34418	−	16.2127i	0.145617	−	0.543451i
$891$		0			0
$892$	−6.78461	−	6.78461i	−0.227166	−	0.227166i
$893$	20.3166	−	11.7298i	0.679870	−	0.392523i
$894$		0			0
$895$	5.66025	−	1.51666i	0.189201	−	0.0506964i
$896$		0			0
$897$		0			0
$898$	10.5359			0.351587
$899$	−12.2982	+	3.29530i	−0.410168	+	0.109904i
$900$		0			0
$901$	−13.6077	+	7.85641i	−0.453338	+	0.261735i
$902$	−47.8802	−	47.8802i	−1.59424	−	1.59424i
$903$		0			0
$904$		0			0
$905$	−3.10583	+	3.10583i	−0.103241	+	0.103241i
$906$		0			0
$907$	15.5885	+	9.00000i	0.517606	+	0.298840i	0.735955	−	0.677031i	$-0.236734\pi$
$907$	15.5885	+	9.00000i	0.517606	+	0.298840i	−0.218348	+	0.975871i	$0.570067\pi$
$908$	−6.96953	−	26.0106i	−0.231292	−	0.863194i
$909$		0			0
$910$	3.26795	+	9.66025i	0.108331	+	0.320234i
$911$		−	6.76646i		−	0.224183i	−0.993698	−	0.112091i	$-0.964245\pi$
$911$		−	6.76646i		−	0.224183i	0.993698	−	0.112091i	$-0.0357549\pi$
$912$		0			0
$913$	1.66025	−	2.87564i	0.0549464	−	0.0951699i
$914$	4.10394	+	7.10823i	0.135746	+	0.235119i
$915$		0			0
$916$	−0.732051	−	0.196152i	−0.0241876	−	0.00648106i
$917$	13.1948	+	3.53553i	0.435730	+	0.116754i
$918$		0			0
$919$	−16.5885	−	28.7321i	−0.547203	−	0.947783i	−0.998465	−	0.0553914i	$-0.982359\pi$
$919$	−16.5885	−	28.7321i	−0.547203	−	0.947783i	0.451262	−	0.892392i	$-0.350974\pi$
$920$		0			0
$921$		0			0
$922$			74.6410i			2.45817i
$923$	−4.49648	−	3.95164i	−0.148003	−	0.130070i
$924$		0			0
$925$	9.36603	+	34.9545i	0.307953	+	1.14930i
$926$	9.38186	+	5.41662i	0.308307	+	0.178001i
$927$		0			0
$928$	8.00000	−	8.00000i	0.262613	−	0.262613i
$929$	−11.2122	+	41.8444i	−0.367859	+	1.37287i	0.495643	+	0.868526i	$0.334932\pi$
$929$	−11.2122	+	41.8444i	−0.367859	+	1.37287i	−0.863503	+	0.504344i	$0.831734\pi$
$930$		0			0
$931$	8.05256	+	8.05256i	0.263912	+	0.263912i
$932$	−18.1074	+	10.4543i	−0.593127	+	0.342442i
$933$		0			0
$934$	−42.5885	+	11.4115i	−1.39354	+	0.373397i
$935$	−8.13355			−0.265996
$936$		0			0
$937$	31.5692			1.03132			0.515661	−	0.856793i	$-0.327547\pi$
$937$	31.5692			1.03132			0.515661	+	0.856793i	$0.327547\pi$
$938$	34.6346	−	9.28032i	1.13086	−	0.303013i
$939$		0			0
$940$	−8.53590	+	4.92820i	−0.278410	+	0.160740i
$941$	−9.00292	−	9.00292i	−0.293487	−	0.293487i	0.544969	−	0.838456i	$-0.316541\pi$
$941$	−9.00292	−	9.00292i	−0.293487	−	0.293487i	−0.838456	+	0.544969i	$0.816541\pi$
$942$		0			0
$943$	−3.46410	+	12.9282i	−0.112807	+	0.421000i
$944$	28.8391	−	28.8391i	0.938632	−	0.938632i
$945$		0			0
$946$	−45.8038	−	26.4449i	−1.48921	−	0.859797i
$947$	−1.03528	−	3.86370i	−0.0336420	−	0.125553i	0.947063	−	0.321049i	$-0.104035\pi$
$947$	−1.03528	−	3.86370i	−0.0336420	−	0.125553i	−0.980705	+	0.195495i	$0.937369\pi$
$948$		0			0
$949$	−39.1147	+	13.2321i	−1.26972	+	0.429531i
$950$		−	31.1127i		−	1.00943i
$951$		0			0
$952$		0			0
$953$	12.6400	+	21.8931i	0.409449	+	0.709187i	0.994828	−	0.101573i	$-0.0323875\pi$
$953$	12.6400	+	21.8931i	0.409449	+	0.709187i	−0.585379	+	0.810760i	$0.699054\pi$
$954$		0			0
$955$	1.19615	+	0.320508i	0.0387066	+	0.0103714i
$956$	26.0106	+	6.96953i	0.841244	+	0.225411i
$957$		0			0
$958$	−4.00000	−	6.92820i	−0.129234	−	0.223840i
$959$	1.03528	−	1.79315i	0.0334308	−	0.0579039i
$960$		0			0
$961$		−	50.0526i		−	1.61460i
$962$	−3.76217	−	58.3345i	−0.121297	−	1.88078i
$963$		0			0
$964$	−8.58846	−	32.0526i	−0.276616	−	1.03234i
$965$	−7.02030	−	4.05317i	−0.225991	−	0.130476i
$966$		0			0
$967$	2.26795	−	2.26795i	0.0729323	−	0.0729323i	−0.669700	−	0.742632i	$-0.733577\pi$
$967$	2.26795	−	2.26795i	0.0729323	−	0.0729323i	0.742632	+	0.669700i	$0.233577\pi$
$968$		0			0
$969$		0			0
$970$	12.5359	+	12.5359i	0.402503	+	0.402503i
$971$	−5.85993	+	3.38323i	−0.188054	+	0.108573i	−0.591071	−	0.806619i	$-0.701295\pi$
$971$	−5.85993	+	3.38323i	−0.188054	+	0.108573i	0.403017	+	0.915192i	$0.367961\pi$
$972$		0			0
$973$	−32.4545	+	8.69615i	−1.04044	+	0.278786i
$974$	−28.6360			−0.917557
$975$		0			0
$976$	11.2154			0.358996
$977$	36.9454	−	9.89949i	1.18199	−	0.316713i	0.386274	−	0.922384i	$-0.373762\pi$
$977$	36.9454	−	9.89949i	1.18199	−	0.316713i	0.795715	+	0.605671i	$0.207095\pi$
$978$		0			0
$979$	61.5167	−	35.5167i	1.96608	−	1.13512i
$980$	−3.38323	−	3.38323i	−0.108073	−	0.108073i
$981$		0			0
$982$	−8.44486	+	31.5167i	−0.269486	+	1.00574i
$983$	−22.6646	+	22.6646i	−0.722888	+	0.722888i	−0.969192	−	0.246305i	$-0.920784\pi$
$983$	−22.6646	+	22.6646i	−0.722888	+	0.722888i	0.246305	+	0.969192i	$0.420784\pi$
$984$		0			0
$985$	−13.2679	−	7.66025i	−0.422752	−	0.244076i
$986$	−1.31268	−	4.89898i	−0.0418042	−	0.156015i
$987$		0			0
$988$	−4.92820	+	24.6410i	−0.156787	+	0.783935i
$989$			10.4543i			0.332427i
$990$		0			0
$991$	−15.1962	+	26.3205i	−0.482722	+	0.836098i	−0.999803	−	0.0198377i	$-0.993685\pi$
$991$	−15.1962	+	26.3205i	−0.482722	+	0.836098i	0.517082	+	0.855936i	$0.327018\pi$
$992$	36.0117	+	62.3741i	1.14337	+	1.98038i
$993$		0			0
$994$	−6.19615	−	1.66025i	−0.196530	−	0.0526601i
$995$	4.57081	+	1.22474i	0.144904	+	0.0388270i
$996$		0			0
$997$	−0.892305	−	1.54552i	−0.0282596	−	0.0489470i	0.851550	−	0.524274i	$-0.175663\pi$
$997$	−0.892305	−	1.54552i	−0.0282596	−	0.0489470i	−0.879809	+	0.475327i	$0.842330\pi$
$998$	−39.2190	+	67.9294i	−1.24146	+	2.15027i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.ba.a.71.2	yes	8
3.2	odd	2	inner	117.2.ba.a.71.1	✓	8
13.4	even	6		1521.2.i.e.746.4		8
13.6	odd	12		1521.2.i.e.944.1		8
13.7	odd	12		1521.2.i.d.944.4		8
13.9	even	3		1521.2.i.d.746.1		8
13.11	odd	12	inner	117.2.ba.a.89.1	yes	8
39.11	even	12	inner	117.2.ba.a.89.2	yes	8
39.17	odd	6		1521.2.i.e.746.1		8
39.20	even	12		1521.2.i.d.944.1		8
39.32	even	12		1521.2.i.e.944.4		8
39.35	odd	6		1521.2.i.d.746.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.ba.a.71.1	✓	8	3.2	odd	2	inner
117.2.ba.a.71.2	yes	8	1.1	even	1	trivial
117.2.ba.a.89.1	yes	8	13.11	odd	12	inner
117.2.ba.a.89.2	yes	8	39.11	even	12	inner
1521.2.i.d.746.1		8	13.9	even	3
1521.2.i.d.746.4		8	39.35	odd	6
1521.2.i.d.944.1		8	39.20	even	12
1521.2.i.d.944.4		8	13.7	odd	12
1521.2.i.e.746.1		8	39.17	odd	6
1521.2.i.e.746.4		8	13.4	even	6
1521.2.i.e.944.1		8	13.6	odd	12
1521.2.i.e.944.4		8	39.32	even	12

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.ba (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.93185 - 0.517638i) q^{2} +(1.73205 - 1.00000i) q^{4} +(-0.517638 - 0.517638i) q^{5} +(-0.500000 + 1.86603i) q^{7} +(-1.26795 - 0.732051i) q^{10} +(-1.60368 - 5.98502i) q^{11} +(-1.59808 + 3.23205i) q^{13} +3.86370i q^{14} +(-2.00000 + 3.46410i) q^{16} +(0.896575 + 1.55291i) q^{17} +(3.36603 + 0.901924i) q^{19} +(-1.41421 - 0.378937i) q^{20} +(-6.19615 - 10.7321i) q^{22} +(-1.22474 + 2.12132i) q^{23} -4.46410i q^{25} +(-1.41421 + 7.07107i) q^{26} +(1.00000 + 3.73205i) q^{28} +(-1.22474 - 0.707107i) q^{29} +(6.36603 - 6.36603i) q^{31} +(-2.07055 + 7.72741i) q^{32} +(2.53590 + 2.53590i) q^{34} +(1.22474 - 0.707107i) q^{35} +(-7.83013 + 2.09808i) q^{37} +6.96953 q^{38} +(5.27792 - 1.41421i) q^{41} +(3.69615 - 2.13397i) q^{43} +(-8.76268 - 8.76268i) q^{44} +(-1.26795 + 4.73205i) q^{46} +(4.76028 - 4.76028i) q^{47} +(2.83013 + 1.63397i) q^{49} +(-2.31079 - 8.62398i) q^{50} +(0.464102 + 7.19615i) q^{52} +8.76268i q^{53} +(-2.26795 + 3.92820i) q^{55} +(-2.73205 - 0.732051i) q^{58} +(-9.84873 - 2.63896i) q^{59} +(-1.40192 - 2.42820i) q^{61} +(9.00292 - 15.5935i) q^{62} +8.00000i q^{64} +(2.50026 - 0.845807i) q^{65} +(-2.40192 - 8.96410i) q^{67} +(3.10583 + 1.79315i) q^{68} +(2.00000 - 2.00000i) q^{70} +(-0.429705 + 1.60368i) q^{71} +(8.09808 + 8.09808i) q^{73} +(-14.0406 + 8.10634i) q^{74} +(6.73205 - 1.80385i) q^{76} +11.9700 q^{77} -3.19615 q^{79} +(2.82843 - 0.757875i) q^{80} +(9.46410 - 5.46410i) q^{82} +(0.378937 + 0.378937i) q^{83} +(0.339746 - 1.26795i) q^{85} +(6.03579 - 6.03579i) q^{86} +(2.96713 + 11.0735i) q^{89} +(-5.23205 - 4.59808i) q^{91} +4.89898i q^{92} +(6.73205 - 11.6603i) q^{94} +(-1.27551 - 2.20925i) q^{95} +(-11.6962 - 3.13397i) q^{97} +(6.31319 + 1.69161i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{7} - 24 q^{10} + 8 q^{13} - 16 q^{16} + 20 q^{19} - 8 q^{22} + 8 q^{28} + 44 q^{31} + 48 q^{34} - 28 q^{37} - 12 q^{43} - 24 q^{46} - 12 q^{49} - 24 q^{52} - 32 q^{55} - 8 q^{58} - 32 q^{61}+ \cdots - 52 q^{97}+O(q^{100}) \) 8 * q - 4 * q^7 - 24 * q^10 + 8 * q^13 - 16 * q^16 + 20 * q^19 - 8 * q^22 + 8 * q^28 + 44 * q^31 + 48 * q^34 - 28 * q^37 - 12 * q^43 - 24 * q^46 - 12 * q^49 - 24 * q^52 - 32 * q^55 - 8 * q^58 - 32 * q^61 - 40 * q^67 + 16 * q^70 + 44 * q^73 + 40 * q^76 + 16 * q^79 + 48 * q^82 + 72 * q^85 - 28 * q^91 + 40 * q^94 - 52 * q^97

Introduction

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