LMFDB - Embedded newform 968.2.i.o.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(9,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("968.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.i (of order $5$, degree $4$, 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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.324000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 $ x^8 + 3x^6 + 9x^4 + 27*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.2
Root			$-1.40126 + 1.01807i$ of defining polynomial
Character	$\chi$	$=$	968.81
Dual form			968.2.i.o.729.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.844250 - 2.59833i) q^{3} +(3.01929 - 2.19364i) q^{5} +(-0.844250 - 2.59833i) q^{7} +(-3.61153 - 2.62393i) q^{9} +O(q^{10})$	\(q+(0.844250 - 2.59833i) q^{3} +(3.01929 - 2.19364i) q^{5} +(-0.844250 - 2.59833i) q^{7} +(-3.61153 - 2.62393i) q^{9} +(3.61153 + 2.62393i) q^{13} +(-3.15078 - 9.69712i) q^{15} +(1.83481 - 1.33307i) q^{17} +(-1.00985 + 3.10800i) q^{19} -7.46410 q^{21} -2.19615 q^{23} +(2.75897 - 8.49123i) q^{25} +(-3.23607 + 2.35114i) q^{27} +(1.37948 + 4.24561i) q^{29} +(3.82831 + 2.78143i) q^{31} +(-8.24886 - 5.99315i) q^{35} +(1.77130 + 5.45150i) q^{37} +(9.86689 - 7.16872i) q^{39} +(-2.38934 + 7.35362i) q^{41} -8.00000 q^{43} -16.6603 q^{45} +(-1.00985 + 3.10800i) q^{47} +(-0.375466 + 0.272792i) q^{49} +(-1.91472 - 5.89289i) q^{51} +(-0.967708 - 0.703081i) q^{53} +(7.22307 + 5.24787i) q^{57} +(4.16064 + 12.8051i) q^{59} +(5.28765 - 3.84170i) q^{61} +(-3.76882 + 11.5992i) q^{63} +16.6603 q^{65} -0.196152 q^{67} +(-1.85410 + 5.70634i) q^{69} +(-2.05158 + 1.49056i) q^{71} +(2.75897 + 8.49123i) q^{73} +(-19.7338 - 14.3374i) q^{75} +(-13.4203 - 9.75045i) q^{79} +(-0.761449 - 2.34350i) q^{81} +(1.77672 - 1.29087i) q^{83} +(2.61555 - 8.04984i) q^{85} +12.1962 q^{87} -16.4641 q^{89} +(3.76882 - 11.5992i) q^{91} +(10.4591 - 7.59901i) q^{93} +(3.76882 + 11.5992i) q^{95} +(9.65012 + 7.01122i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 4 q^{5} + 2 q^{7} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 4 * q^5 + 2 * q^7 - 2 * q^9	$ 8 q - 2 q^{3} + 4 q^{5} + 2 q^{7} - 2 q^{9} + 2 q^{13} + 10 q^{15} + 8 q^{17} + 10 q^{19} - 32 q^{21} + 24 q^{23} - 4 q^{25} - 8 q^{27} - 2 q^{29} + 6 q^{31} - 10 q^{35} - 8 q^{37} + 14 q^{39} + 12 q^{41} - 64 q^{43} - 64 q^{45} + 10 q^{47} + 6 q^{49} + 2 q^{51} + 8 q^{53} + 4 q^{57} - 20 q^{59} + 20 q^{61} + 14 q^{63} + 64 q^{65} + 40 q^{67} + 12 q^{69} - 12 q^{71} - 4 q^{73} - 28 q^{75} - 2 q^{79} - 2 q^{81} - 6 q^{83} - 10 q^{85} + 56 q^{87} - 104 q^{89} - 14 q^{91} + 12 q^{93} - 14 q^{95} + 10 q^{97}+O(q^{100}) $ 8 * q - 2 * q^3 + 4 * q^5 + 2 * q^7 - 2 * q^9 + 2 * q^13 + 10 * q^15 + 8 * q^17 + 10 * q^19 - 32 * q^21 + 24 * q^23 - 4 * q^25 - 8 * q^27 - 2 * q^29 + 6 * q^31 - 10 * q^35 - 8 * q^37 + 14 * q^39 + 12 * q^41 - 64 * q^43 - 64 * q^45 + 10 * q^47 + 6 * q^49 + 2 * q^51 + 8 * q^53 + 4 * q^57 - 20 * q^59 + 20 * q^61 + 14 * q^63 + 64 * q^65 + 40 * q^67 + 12 * q^69 - 12 * q^71 - 4 * q^73 - 28 * q^75 - 2 * q^79 - 2 * q^81 - 6 * q^83 - 10 * q^85 + 56 * q^87 - 104 * q^89 - 14 * q^91 + 12 * q^93 - 14 * q^95 + 10 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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
$3$	0.844250	−	2.59833i	0.487428	−	1.50015i	−0.341005	−	0.940061i	$-0.610767\pi$
$3$	0.844250	−	2.59833i	0.487428	−	1.50015i	0.828433	−	0.560088i	$-0.189233\pi$
$4$		0			0
$5$	3.01929	−	2.19364i	1.35027	−	0.981028i	0.351271	−	0.936274i	$-0.385750\pi$
$5$	3.01929	−	2.19364i	1.35027	−	0.981028i	0.998998	−	0.0447536i	$-0.0142503\pi$
$6$		0			0
$7$	−0.844250	−	2.59833i	−0.319097	−	0.982078i	−0.974035	−	0.226396i	$-0.927306\pi$
$7$	−0.844250	−	2.59833i	−0.319097	−	0.982078i	0.654939	−	0.755682i	$-0.272694\pi$
$8$		0			0
$9$	−3.61153	−	2.62393i	−1.20384	−	0.874644i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	3.61153	+	2.62393i	1.00166	+	0.727748i	0.962443	−	0.271483i	$-0.0875140\pi$
$13$	3.61153	+	2.62393i	1.00166	+	0.727748i	0.0392160	+	0.999231i	$0.487514\pi$
$14$		0			0
$15$	−3.15078	−	9.69712i	−0.813529	−	2.50378i
$16$		0			0
$17$	1.83481	−	1.33307i	0.445007	−	0.323316i	−0.342614	−	0.939476i	$-0.611312\pi$
$17$	1.83481	−	1.33307i	0.445007	−	0.323316i	0.787621	+	0.616160i	$0.211312\pi$
$18$		0			0
$19$	−1.00985	+	3.10800i	−0.231676	+	0.713025i	0.765869	+	0.642997i	$0.222309\pi$
$19$	−1.00985	+	3.10800i	−0.231676	+	0.713025i	−0.997545	+	0.0700286i	$0.977691\pi$
$20$		0			0
$21$	−7.46410			−1.62880
$22$		0			0
$23$	−2.19615			−0.457929			−0.228965	−	0.973435i	$-0.573534\pi$
$23$	−2.19615			−0.457929			−0.228965	+	0.973435i	$0.573534\pi$
$24$		0			0
$25$	2.75897	−	8.49123i	0.551793	−	1.69825i
$26$		0			0
$27$	−3.23607	+	2.35114i	−0.622782	+	0.452477i
$28$		0			0
$29$	1.37948	+	4.24561i	0.256164	+	0.788391i	0.993598	+	0.112972i	$0.0360370\pi$
$29$	1.37948	+	4.24561i	0.256164	+	0.788391i	−0.737435	+	0.675419i	$0.763963\pi$
$30$		0			0
$31$	3.82831	+	2.78143i	0.687585	+	0.499560i	0.875865	−	0.482556i	$-0.160291\pi$
$31$	3.82831	+	2.78143i	0.687585	+	0.499560i	−0.188281	+	0.982115i	$0.560291\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−8.24886	−	5.99315i	−1.39431	−	1.01303i
$36$		0			0
$37$	1.77130	+	5.45150i	0.291200	+	0.896222i	0.984471	+	0.175545i	$0.0561688\pi$
$37$	1.77130	+	5.45150i	0.291200	+	0.896222i	−0.693271	+	0.720677i	$0.743831\pi$
$38$		0			0
$39$	9.86689	−	7.16872i	1.57997	−	1.14791i
$40$		0			0
$41$	−2.38934	+	7.35362i	−0.373151	+	1.14844i	0.571566	+	0.820556i	$0.306336\pi$
$41$	−2.38934	+	7.35362i	−0.373151	+	1.14844i	−0.944717	+	0.327886i	$0.893664\pi$
$42$		0			0
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$		0			0
$45$	−16.6603			−2.48356
$46$		0			0
$47$	−1.00985	+	3.10800i	−0.147302	+	0.453349i	−0.997300	−	0.0734372i	$-0.976603\pi$
$47$	−1.00985	+	3.10800i	−0.147302	+	0.453349i	0.849998	+	0.526786i	$0.176603\pi$
$48$		0			0
$49$	−0.375466	+	0.272792i	−0.0536380	+	0.0389703i
$50$		0			0
$51$	−1.91472	−	5.89289i	−0.268114	−	0.825170i
$52$		0			0
$53$	−0.967708	−	0.703081i	−0.132925	−	0.0965756i	0.519336	−	0.854570i	$-0.326179\pi$
$53$	−0.967708	−	0.703081i	−0.132925	−	0.0965756i	−0.652261	+	0.757995i	$0.726179\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	7.22307	+	5.24787i	0.956719	+	0.695097i
$58$		0			0
$59$	4.16064	+	12.8051i	0.541669	+	1.66708i	0.728781	+	0.684746i	$0.240087\pi$
$59$	4.16064	+	12.8051i	0.541669	+	1.66708i	−0.187113	+	0.982338i	$0.559913\pi$
$60$		0			0
$61$	5.28765	−	3.84170i	0.677015	−	0.491880i	−0.195351	−	0.980733i	$-0.562585\pi$
$61$	5.28765	−	3.84170i	0.677015	−	0.491880i	0.872366	+	0.488853i	$0.162585\pi$
$62$		0			0
$63$	−3.76882	+	11.5992i	−0.474826	+	1.46137i
$64$		0			0
$65$	16.6603			2.06645
$66$		0			0
$67$	−0.196152			−0.0239638			−0.0119819	−	0.999928i	$-0.503814\pi$
$67$	−0.196152			−0.0239638			−0.0119819	+	0.999928i	$0.503814\pi$
$68$		0			0
$69$	−1.85410	+	5.70634i	−0.223208	+	0.686963i
$70$		0			0
$71$	−2.05158	+	1.49056i	−0.243478	+	0.176897i	−0.702832	−	0.711356i	$-0.748081\pi$
$71$	−2.05158	+	1.49056i	−0.243478	+	0.176897i	0.459353	+	0.888254i	$0.348081\pi$
$72$		0			0
$73$	2.75897	+	8.49123i	0.322913	+	0.993823i	0.972374	+	0.233428i	$0.0749944\pi$
$73$	2.75897	+	8.49123i	0.322913	+	0.993823i	−0.649461	+	0.760395i	$0.725006\pi$
$74$		0			0
$75$	−19.7338	−	14.3374i	−2.27866	−	1.65554i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−13.4203	−	9.75045i	−1.50991	−	1.09701i	−0.966219	−	0.257724i	$-0.917027\pi$
$79$	−13.4203	−	9.75045i	−1.50991	−	1.09701i	−0.543688	−	0.839287i	$-0.682973\pi$
$80$		0			0
$81$	−0.761449	−	2.34350i	−0.0846055	−	0.260389i
$82$		0			0
$83$	1.77672	−	1.29087i	0.195021	−	0.141691i	−0.485990	−	0.873965i	$-0.661541\pi$
$83$	1.77672	−	1.29087i	0.195021	−	0.141691i	0.681011	+	0.732274i	$0.261541\pi$
$84$		0			0
$85$	2.61555	−	8.04984i	0.283696	−	0.873128i
$86$		0			0
$87$	12.1962			1.30756
$88$		0			0
$89$	−16.4641			−1.74519			−0.872596	−	0.488443i	$-0.837565\pi$
$89$	−16.4641			−1.74519			−0.872596	+	0.488443i	$0.837565\pi$
$90$		0			0
$91$	3.76882	−	11.5992i	0.395080	−	1.21593i
$92$		0			0
$93$	10.4591	−	7.59901i	1.08456	−	0.787980i
$94$		0			0
$95$	3.76882	+	11.5992i	0.386673	+	1.19006i
$96$		0			0
$97$	9.65012	+	7.01122i	0.979821	+	0.711882i	0.957669	−	0.287873i	$-0.0929481\pi$
$97$	9.65012	+	7.01122i	0.979821	+	0.711882i	0.0221525	+	0.999755i	$0.492948\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−14.1288	−	10.2651i	−1.40586	−	1.02142i	−0.993908	−	0.110216i	$-0.964846\pi$
$101$	−14.1288	−	10.2651i	−1.40586	−	1.02142i	−0.411956	−	0.911204i	$-0.635154\pi$
$102$		0			0
$103$	−2.01970	−	6.21601i	−0.199007	−	0.612482i	−0.999906	−	0.0136822i	$-0.995645\pi$
$103$	−2.01970	−	6.21601i	−0.199007	−	0.612482i	0.800899	−	0.598799i	$-0.204355\pi$
$104$		0			0
$105$	−22.5363	+	16.3736i	−2.19932	+	1.59790i
$106$		0			0
$107$	5.29172	−	16.2862i	0.511570	−	1.57445i	−0.277869	−	0.960619i	$-0.589628\pi$
$107$	5.29172	−	16.2862i	0.511570	−	1.57445i	0.789438	−	0.613830i	$-0.210372\pi$
$108$		0			0
$109$	−12.4641			−1.19384			−0.596922	−	0.802299i	$-0.703610\pi$
$109$	−12.4641			−1.19384			−0.596922	+	0.802299i	$0.703610\pi$
$110$		0			0
$111$	15.6603			1.48641
$112$		0			0
$113$	1.54508	−	4.75528i	0.145349	−	0.447339i	−0.851706	−	0.524019i	$-0.824432\pi$
$113$	1.54508	−	4.75528i	0.145349	−	0.447339i	0.997056	+	0.0766799i	$0.0244320\pi$
$114$		0			0
$115$	−6.63083	+	4.81758i	−0.618328	+	0.449241i
$116$		0			0
$117$	−6.15815	−	18.9528i	−0.569321	−	1.75219i
$118$		0			0
$119$	−5.01279	−	3.64201i	−0.459522	−	0.333862i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	17.0900	+	12.4166i	1.54095	+	1.11957i
$124$		0			0
$125$	−4.53027	−	13.9427i	−0.405199	−	1.24708i
$126$		0			0
$127$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$127$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$128$		0			0
$129$	−6.75400	+	20.7867i	−0.594657	+	1.83016i
$130$		0			0
$131$	8.00000			0.698963			0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000			0.698963			0.349482	+	0.936943i	$0.386358\pi$
$132$		0			0
$133$	8.92820			0.774173
$134$		0			0
$135$	−4.61307	+	14.1976i	−0.397030	+	1.22193i
$136$		0			0
$137$	2.05158	−	1.49056i	0.175279	−	0.127347i	−0.496687	−	0.867930i	$-0.665450\pi$
$137$	2.05158	−	1.49056i	0.175279	−	0.127347i	0.671966	+	0.740582i	$0.265450\pi$
$138$		0			0
$139$	−1.91472	−	5.89289i	−0.162404	−	0.499829i	0.836432	−	0.548071i	$-0.184638\pi$
$139$	−1.91472	−	5.89289i	−0.162404	−	0.499829i	−0.998836	+	0.0482430i	$0.984638\pi$
$140$		0			0
$141$	7.22307	+	5.24787i	0.608292	+	0.441950i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	13.4784	+	9.79265i	1.11932	+	0.813235i
$146$		0			0
$147$	0.391818	+	1.20589i	0.0323166	+	0.0994602i
$148$		0			0
$149$	−4.47864	+	3.25392i	−0.366904	+	0.266571i	−0.755926	−	0.654657i	$-0.772813\pi$
$149$	−4.47864	+	3.25392i	−0.366904	+	0.266571i	0.389022	+	0.921229i	$0.372813\pi$
$150$		0			0
$151$	3.25577	−	10.0202i	0.264951	−	0.815435i	−0.726754	−	0.686898i	$-0.758972\pi$
$151$	3.25577	−	10.0202i	0.264951	−	0.815435i	0.991705	−	0.128537i	$-0.0410281\pi$
$152$		0			0
$153$	−10.1244			−0.818506
$154$		0			0
$155$	17.6603			1.41851
$156$		0			0
$157$	−6.42280	+	19.7673i	−0.512595	+	1.57761i	0.275020	+	0.961438i	$0.411315\pi$
$157$	−6.42280	+	19.7673i	−0.512595	+	1.57761i	−0.787616	+	0.616167i	$0.788685\pi$
$158$		0			0
$159$	−2.64383	+	1.92085i	−0.209669	+	0.152333i
$160$		0			0
$161$	1.85410	+	5.70634i	0.146124	+	0.449723i
$162$		0			0
$163$	19.0254	+	13.8227i	1.49018	+	1.08268i	0.974093	+	0.226146i	$0.0726127\pi$
$163$	19.0254	+	13.8227i	1.49018	+	1.08268i	0.516089	+	0.856535i	$0.327387\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.28765	+	3.84170i	0.409171	+	0.297280i	0.773266	−	0.634082i	$-0.218622\pi$
$167$	5.28765	+	3.84170i	0.409171	+	0.297280i	−0.364095	+	0.931362i	$0.618622\pi$
$168$		0			0
$169$	2.14093	+	6.58911i	0.164687	+	0.506855i
$170$		0			0
$171$	11.8023	−	8.57488i	0.902545	−	0.655737i
$172$		0			0
$173$	0.783636	−	2.41178i	0.0595787	−	0.183364i	−0.916838	−	0.399260i	$-0.869267\pi$
$173$	0.783636	−	2.41178i	0.0595787	−	0.183364i	0.976416	+	0.215896i	$0.0692671\pi$
$174$		0			0
$175$	−24.3923			−1.84388
$176$		0			0
$177$	36.7846			2.76490
$178$		0			0
$179$	4.94427	−	15.2169i	0.369552	−	1.13736i	−0.577529	−	0.816370i	$-0.695983\pi$
$179$	4.94427	−	15.2169i	0.369552	−	1.13736i	0.947081	−	0.320995i	$-0.104017\pi$
$180$		0			0
$181$	2.26836	−	1.64806i	0.168606	−	0.122499i	−0.500282	−	0.865862i	$-0.666770\pi$
$181$	2.26836	−	1.64806i	0.168606	−	0.122499i	0.668888	+	0.743363i	$0.266770\pi$
$182$		0			0
$183$	−5.51793	−	16.9825i	−0.407897	−	1.25538i
$184$		0			0
$185$	17.3067	+	12.5741i	1.27242	+	0.924465i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	8.84110	+	6.42344i	0.643096	+	0.467236i
$190$		0			0
$191$	1.35730	+	4.17733i	0.0982106	+	0.302261i	0.988077	−	0.153960i	$-0.0492027\pi$
$191$	1.35730	+	4.17733i	0.0982106	+	0.302261i	−0.889867	+	0.456221i	$0.849203\pi$
$192$		0			0
$193$	13.4784	−	9.79265i	0.970199	−	0.704890i	0.0147017	−	0.999892i	$-0.495320\pi$
$193$	13.4784	−	9.79265i	0.970199	−	0.704890i	0.955497	+	0.295001i	$0.0953201\pi$
$194$		0			0
$195$	14.0654	−	43.2889i	1.00725	−	3.09998i
$196$		0			0
$197$	−5.92820			−0.422367			−0.211183	−	0.977446i	$-0.567732\pi$
$197$	−5.92820			−0.422367			−0.211183	+	0.977446i	$0.567732\pi$
$198$		0			0
$199$	−6.53590			−0.463318			−0.231659	−	0.972797i	$-0.574415\pi$
$199$	−6.53590			−0.463318			−0.231659	+	0.972797i	$0.574415\pi$
$200$		0			0
$201$	−0.165602	+	0.509670i	−0.0116806	+	0.0359493i
$202$		0			0
$203$	9.86689	−	7.16872i	0.692520	−	0.503145i
$204$		0			0
$205$	8.91712	+	27.4441i	0.622799	+	1.91678i
$206$		0			0
$207$	7.93148	+	5.76256i	0.551276	+	0.400525i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	14.4461	+	10.4957i	0.994513	+	0.722556i	0.960905	−	0.276879i	$-0.0893001\pi$
$211$	14.4461	+	10.4957i	0.994513	+	0.722556i	0.0336083	+	0.999435i	$0.489300\pi$
$212$		0			0
$213$	2.14093	+	6.58911i	0.146694	+	0.451479i
$214$		0			0
$215$	−24.1543	+	17.5492i	−1.64731	+	1.19684i
$216$		0			0
$217$	3.99503	−	12.2955i	0.271201	−	0.834670i
$218$		0			0
$219$	24.3923			1.64828
$220$		0			0
$221$	10.1244			0.681038
$222$		0			0
$223$	−2.59336	+	7.98156i	−0.173665	+	0.534485i	−0.999570	−	0.0293242i	$-0.990664\pi$
$223$	−2.59336	+	7.98156i	−0.173665	+	0.534485i	0.825905	+	0.563809i	$0.190664\pi$
$224$		0			0
$225$	−32.2445	+	23.4270i	−2.14963	+	1.56180i
$226$		0			0
$227$	−1.11484	−	3.43112i	−0.0739945	−	0.227732i	0.907218	−	0.420660i	$-0.138201\pi$
$227$	−1.11484	−	3.43112i	−0.0739945	−	0.227732i	−0.981213	+	0.192928i	$0.938201\pi$
$228$		0			0
$229$	−10.3585	−	7.52591i	−0.684511	−	0.497326i	0.190340	−	0.981718i	$-0.439041\pi$
$229$	−10.3585	−	7.52591i	−0.684511	−	0.497326i	−0.874851	+	0.484392i	$0.839041\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.967708	−	0.703081i	−0.0633966	−	0.0460604i	0.555636	−	0.831426i	$-0.312475\pi$
$233$	−0.967708	−	0.703081i	−0.0633966	−	0.0460604i	−0.619032	+	0.785366i	$0.712475\pi$
$234$		0			0
$235$	3.76882	+	11.5992i	0.245851	+	0.756650i
$236$		0			0
$237$	−36.6651	+	26.6387i	−2.38165	+	1.73037i
$238$		0			0
$239$	−6.03098	+	18.5614i	−0.390112	+	1.20064i	0.542592	+	0.839996i	$0.317443\pi$
$239$	−6.03098	+	18.5614i	−0.390112	+	1.20064i	−0.932704	+	0.360644i	$0.882557\pi$
$240$		0			0
$241$	8.92820			0.575116			0.287558	−	0.957763i	$-0.407157\pi$
$241$	8.92820			0.575116			0.287558	+	0.957763i	$0.407157\pi$
$242$		0			0
$243$	−18.7321			−1.20166
$244$		0			0
$245$	−0.535233	+	1.64728i	−0.0341948	+	0.105241i
$246$		0			0
$247$	−11.8023	+	8.57488i	−0.750963	+	0.545607i
$248$		0			0
$249$	−1.85410	−	5.70634i	−0.117499	−	0.361625i
$250$		0			0
$251$	−13.9701	−	10.1498i	−0.881783	−	0.640653i	0.0519399	−	0.998650i	$-0.483460\pi$
$251$	−13.9701	−	10.1498i	−0.881783	−	0.640653i	−0.933722	+	0.357998i	$0.883460\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−18.7080	−	13.5922i	−1.17154	−	0.851174i
$256$		0			0
$257$	−1.37948	−	4.24561i	−0.0860498	−	0.264834i	0.898768	−	0.438424i	$-0.144463\pi$
$257$	−1.37948	−	4.24561i	−0.0860498	−	0.264834i	−0.984818	+	0.173590i	$0.944463\pi$
$258$		0			0
$259$	12.6694	−	9.20487i	0.787239	−	0.571963i
$260$		0			0
$261$	6.15815	−	18.9528i	0.381180	−	1.17315i
$262$		0			0
$263$	2.33975			0.144275			0.0721375	−	0.997395i	$-0.477018\pi$
$263$	2.33975			0.144275			0.0721375	+	0.997395i	$0.477018\pi$
$264$		0			0
$265$	−4.46410			−0.274228
$266$		0			0
$267$	−13.8998	+	42.7792i	−0.850655	+	2.61805i
$268$		0			0
$269$	15.4138	−	11.1988i	0.939799	−	0.682804i	−0.00857354	−	0.999963i	$-0.502729\pi$
$269$	15.4138	−	11.1988i	0.939799	−	0.682804i	0.948372	+	0.317160i	$0.102729\pi$
$270$		0			0
$271$	2.01970	+	6.21601i	0.122688	+	0.377596i	0.993473	−	0.114069i	$-0.0363885\pi$
$271$	2.01970	+	6.21601i	0.122688	+	0.377596i	−0.870785	+	0.491665i	$0.836389\pi$
$272$		0			0
$273$	−26.9569	−	19.5853i	−1.63150	−	1.18536i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−11.1520	−	8.10239i	−0.670058	−	0.486825i	0.199987	−	0.979799i	$-0.435910\pi$
$277$	−11.1520	−	8.10239i	−0.670058	−	0.486825i	−0.870045	+	0.492973i	$0.835910\pi$
$278$		0			0
$279$	−6.52778	−	20.0905i	−0.390808	−	1.20278i
$280$		0			0
$281$	6.35597	−	4.61788i	0.379165	−	0.275480i	−0.381836	−	0.924230i	$-0.624708\pi$
$281$	6.35597	−	4.61788i	0.379165	−	0.275480i	0.761001	+	0.648750i	$0.224708\pi$
$282$		0			0
$283$	−9.55734	+	29.4145i	−0.568125	+	1.74851i	0.0903542	+	0.995910i	$0.471200\pi$
$283$	−9.55734	+	29.4145i	−0.568125	+	1.74851i	−0.658479	+	0.752599i	$0.728800\pi$
$284$		0			0
$285$	33.3205			1.97374
$286$		0			0
$287$	21.1244			1.24693
$288$		0			0
$289$	−3.66383	+	11.2761i	−0.215519	+	0.663301i
$290$		0			0
$291$	26.3646	−	19.1550i	1.54552	−	1.12289i
$292$		0			0
$293$	−6.89742	−	21.2281i	−0.402951	−	1.24016i	−0.922594	−	0.385773i	$-0.873935\pi$
$293$	−6.89742	−	21.2281i	−0.402951	−	1.24016i	0.519642	−	0.854384i	$-0.326065\pi$
$294$		0			0
$295$	40.6521	+	29.5355i	2.36685	+	1.71962i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−7.93148	−	5.76256i	−0.458689	−	0.333257i
$300$		0			0
$301$	6.75400	+	20.7867i	0.389294	+	1.19812i
$302$		0			0
$303$	−38.6005	+	28.0449i	−2.21754	+	1.61114i
$304$		0			0
$305$	7.53764	−	23.1985i	0.431604	−	1.32834i
$306$		0			0
$307$	32.4449			1.85173			0.925863	−	0.377859i	$-0.123340\pi$
$307$	32.4449			1.85173			0.925863	+	0.377859i	$0.123340\pi$
$308$		0			0
$309$	−17.8564			−1.01582
$310$		0			0
$311$	5.18673	−	15.9631i	0.294112	−	0.905185i	−0.689406	−	0.724375i	$-0.742128\pi$
$311$	5.18673	−	15.9631i	0.294112	−	0.905185i	0.983518	−	0.180810i	$-0.0578718\pi$
$312$		0			0
$313$	5.66312	−	4.11450i	0.320098	−	0.232565i	−0.416119	−	0.909310i	$-0.636610\pi$
$313$	5.66312	−	4.11450i	0.320098	−	0.232565i	0.736217	+	0.676745i	$0.236610\pi$
$314$		0			0
$315$	14.0654	+	43.2889i	0.792497	+	2.43905i
$316$		0			0
$317$	−3.11990	−	2.26674i	−0.175231	−	0.127313i	0.496713	−	0.867915i	$-0.334540\pi$
$317$	−3.11990	−	2.26674i	−0.175231	−	0.127313i	−0.671944	+	0.740602i	$0.734540\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−37.8495	−	27.4993i	−2.11256	−	1.53486i
$322$		0			0
$323$	2.29029	+	7.04880i	0.127435	+	0.392206i
$324$		0			0
$325$	32.2445	−	23.4270i	1.78860	−	1.29950i
$326$		0			0
$327$	−10.5228	+	32.3859i	−0.581913	+	1.79094i
$328$		0			0
$329$	8.92820			0.492228
$330$		0			0
$331$	−1.07180			−0.0589113			−0.0294556	−	0.999566i	$-0.509377\pi$
$331$	−1.07180			−0.0589113			−0.0294556	+	0.999566i	$0.509377\pi$
$332$		0			0
$333$	7.90727	−	24.3361i	0.433316	−	1.33361i
$334$		0			0
$335$	−0.592242	+	0.430289i	−0.0323576	+	0.0235092i
$336$		0			0
$337$	−2.22373	−	6.84395i	−0.121134	−	0.372814i	0.872043	−	0.489430i	$-0.162795\pi$
$337$	−2.22373	−	6.84395i	−0.121134	−	0.372814i	−0.993177	+	0.116616i	$0.962795\pi$
$338$		0			0
$339$	−11.0514	−	8.02930i	−0.600228	−	0.436091i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−14.4461	−	10.4957i	−0.780018	−	0.566716i
$344$		0			0
$345$	6.91960	+	21.2963i	0.372539	+	1.14656i
$346$		0			0
$347$	−19.7338	+	14.3374i	−1.05937	+	0.769674i	−0.973971	−	0.226673i	$-0.927215\pi$
$347$	−19.7338	+	14.3374i	−1.05937	+	0.769674i	−0.0853945	+	0.996347i	$0.527215\pi$
$348$		0			0
$349$	−5.37452	+	16.5411i	−0.287691	+	0.885423i	0.697888	+	0.716207i	$0.254123\pi$
$349$	−5.37452	+	16.5411i	−0.287691	+	0.885423i	−0.985579	+	0.169216i	$0.945877\pi$
$350$		0			0
$351$	−17.8564			−0.953104
$352$		0			0
$353$	−7.92820			−0.421976			−0.210988	−	0.977489i	$-0.567668\pi$
$353$	−7.92820			−0.421976			−0.210988	+	0.977489i	$0.567668\pi$
$354$		0			0
$355$	−2.92457	+	9.00090i	−0.155220	+	0.477718i
$356$		0			0
$357$	−13.6952	+	9.95015i	−0.724827	+	0.526618i
$358$		0			0
$359$	−7.80823	−	24.0312i	−0.412102	−	1.26832i	−0.914817	−	0.403868i	$-0.867665\pi$
$359$	−7.80823	−	24.0312i	−0.412102	−	1.26832i	0.502715	−	0.864452i	$-0.332335\pi$
$360$		0			0
$361$	6.73143	+	4.89067i	0.354286	+	0.257404i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	26.9569	+	19.5853i	1.41099	+	1.02514i
$366$		0			0
$367$	6.64901	+	20.4636i	0.347076	+	1.06819i	0.960463	+	0.278407i	$0.0898064\pi$
$367$	6.64901	+	20.4636i	0.347076	+	1.06819i	−0.613387	+	0.789782i	$0.710194\pi$
$368$		0			0
$369$	27.9246	−	20.2884i	1.45369	−	1.05617i
$370$		0			0
$371$	−1.00985	+	3.10800i	−0.0524289	+	0.161360i
$372$		0			0
$373$	1.46410			0.0758083			0.0379042	−	0.999281i	$-0.487932\pi$
$373$	1.46410			0.0758083			0.0379042	+	0.999281i	$0.487932\pi$
$374$		0			0
$375$	−40.0526			−2.06831
$376$		0			0
$377$	−6.15815	+	18.9528i	−0.317161	+	0.976121i
$378$		0			0
$379$	−26.8407	+	19.5009i	−1.37871	+	1.00169i	−0.381714	+	0.924280i	$0.624666\pi$
$379$	−26.8407	+	19.5009i	−1.37871	+	1.00169i	−0.996999	+	0.0774137i	$0.975334\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−15.6306	−	11.3563i	−0.798687	−	0.580280i	0.111841	−	0.993726i	$-0.464325\pi$
$383$	−15.6306	−	11.3563i	−0.798687	−	0.580280i	−0.910529	+	0.413446i	$0.864325\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	28.8923	+	20.9915i	1.46868	+	1.06706i
$388$		0			0
$389$	−9.30894	−	28.6500i	−0.471982	−	1.45261i	−0.849985	−	0.526807i	$-0.823389\pi$
$389$	−9.30894	−	28.6500i	−0.471982	−	1.45261i	0.378003	−	0.925804i	$-0.376611\pi$
$390$		0			0
$391$	−4.02952	+	2.92762i	−0.203782	+	0.148056i
$392$		0			0
$393$	6.75400	−	20.7867i	0.340694	−	1.04855i
$394$		0			0
$395$	−61.9090			−3.11498
$396$		0			0
$397$	11.8756			0.596022			0.298011	−	0.954563i	$-0.403677\pi$
$397$	11.8756			0.596022			0.298011	+	0.954563i	$0.403677\pi$
$398$		0			0
$399$	7.53764	−	23.1985i	0.377354	−	1.16138i
$400$		0			0
$401$	7.48236	−	5.43626i	0.373651	−	0.271474i	−0.385072	−	0.922887i	$-0.625823\pi$
$401$	7.48236	−	5.43626i	0.373651	−	0.271474i	0.758723	+	0.651413i	$0.225823\pi$
$402$		0			0
$403$	6.52778	+	20.0905i	0.325172	+	1.00078i
$404$		0			0
$405$	−7.43984	−	5.40536i	−0.369689	−	0.268595i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	22.4357	+	16.3005i	1.10937	+	0.806007i	0.982565	−	0.185920i	$-0.0595265\pi$
$409$	22.4357	+	16.3005i	1.10937	+	0.806007i	0.126809	+	0.991927i	$0.459526\pi$
$410$		0			0
$411$	−2.14093	−	6.58911i	−0.105604	−	0.325017i
$412$		0			0
$413$	29.7594	−	21.6215i	1.46436	−	1.06392i
$414$		0			0
$415$	2.53275	−	7.79500i	0.124328	−	0.382642i
$416$		0			0
$417$	−16.9282			−0.828978
$418$		0			0
$419$	−5.66025			−0.276522			−0.138261	−	0.990396i	$-0.544151\pi$
$419$	−5.66025			−0.276522			−0.138261	+	0.990396i	$0.544151\pi$
$420$		0			0
$421$	3.86786	−	11.9041i	0.188508	−	0.580168i	−0.811483	−	0.584376i	$-0.801339\pi$
$421$	3.86786	−	11.9041i	0.188508	−	0.580168i	0.999991	+	0.00420785i	$0.00133940\pi$
$422$		0			0
$423$	11.8023	−	8.57488i	0.573848	−	0.416925i
$424$		0			0
$425$	−6.25720	−	19.2577i	−0.303519	−	0.934134i
$426$		0			0
$427$	−14.4461	−	10.4957i	−0.699098	−	0.507924i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	3.55345	+	2.58173i	0.171164	+	0.124358i	0.670069	−	0.742299i	$-0.266264\pi$
$431$	3.55345	+	2.58173i	0.171164	+	0.124358i	−0.498905	+	0.866656i	$0.666264\pi$
$432$		0			0
$433$	−2.78115	−	8.55951i	−0.133654	−	0.411344i	0.861724	−	0.507376i	$-0.169385\pi$
$433$	−2.78115	−	8.55951i	−0.133654	−	0.411344i	−0.995378	+	0.0960328i	$0.969385\pi$
$434$		0			0
$435$	36.8238	−	26.7540i	1.76556	−	1.28276i
$436$		0			0
$437$	2.21779	−	6.82565i	0.106091	−	0.326515i
$438$		0			0
$439$	−36.5885			−1.74627			−0.873136	−	0.487477i	$-0.837917\pi$
$439$	−36.5885			−1.74627			−0.873136	+	0.487477i	$0.837917\pi$
$440$		0			0
$441$	2.07180			0.0986570
$442$		0			0
$443$	4.61307	−	14.1976i	0.219173	−	0.674547i	−0.779657	−	0.626206i	$-0.784607\pi$
$443$	4.61307	−	14.1976i	0.219173	−	0.674547i	0.998831	−	0.0483404i	$-0.0153932\pi$
$444$		0			0
$445$	−49.7099	+	36.1164i	−2.35648	+	1.71208i
$446$		0			0
$447$	4.67368	+	14.3841i	0.221058	+	0.680345i
$448$		0			0
$449$	0.925187	+	0.672187i	0.0436623	+	0.0317225i	0.609402	−	0.792861i	$-0.291409\pi$
$449$	0.925187	+	0.672187i	0.0436623	+	0.0317225i	−0.565740	+	0.824584i	$0.691409\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−23.2872	−	16.9192i	−1.09413	−	0.794932i
$454$		0			0
$455$	−14.0654	−	43.2889i	−0.659397	−	2.02942i
$456$		0			0
$457$	−2.90312	+	2.10924i	−0.135802	+	0.0986662i	−0.653612	−	0.756829i	$-0.726747\pi$
$457$	−2.90312	+	2.10924i	−0.135802	+	0.0986662i	0.517810	+	0.855496i	$0.326747\pi$
$458$		0			0
$459$	−2.80334	+	8.62779i	−0.130849	+	0.402711i
$460$		0			0
$461$	22.3205			1.03957			0.519785	−	0.854297i	$-0.326012\pi$
$461$	22.3205			1.03957			0.519785	+	0.854297i	$0.326012\pi$
$462$		0			0
$463$	−36.7846			−1.70953			−0.854763	−	0.519019i	$-0.826298\pi$
$463$	−36.7846			−1.70953			−0.854763	+	0.519019i	$0.826298\pi$
$464$		0			0
$465$	14.9097	−	45.8873i	0.691419	−	2.12797i
$466$		0			0
$467$	22.9699	−	16.6886i	1.06292	−	0.772255i	0.0882922	−	0.996095i	$-0.471859\pi$
$467$	22.9699	−	16.6886i	1.06292	−	0.772255i	0.974626	+	0.223839i	$0.0718591\pi$
$468$		0			0
$469$	0.165602	+	0.509670i	0.00764678	+	0.0235344i
$470$		0			0
$471$	45.9397	+	33.3772i	2.11679	+	1.53794i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	23.6046	+	17.1498i	1.08305	+	0.786885i
$476$		0			0
$477$	1.65007	+	5.07840i	0.0755516	+	0.232524i
$478$		0			0
$479$	10.5753	−	7.68341i	0.483198	−	0.351064i	−0.319364	−	0.947632i	$-0.603469\pi$
$479$	10.5753	−	7.68341i	0.483198	−	0.351064i	0.802563	+	0.596568i	$0.203469\pi$
$480$		0			0
$481$	−7.90727	+	24.3361i	−0.360540	+	1.10963i
$482$		0			0
$483$	16.3923			0.745876
$484$		0			0
$485$	44.5167			2.02140
$486$		0			0
$487$	−5.62292	+	17.3056i	−0.254799	+	0.784190i	0.739070	+	0.673628i	$0.235265\pi$
$487$	−5.62292	+	17.3056i	−0.254799	+	0.784190i	−0.993869	+	0.110562i	$0.964735\pi$
$488$		0			0
$489$	51.9783	−	37.7644i	2.35054	−	1.70777i
$490$		0			0
$491$	8.54749	+	26.3065i	0.385743	+	1.18719i	0.935940	+	0.352159i	$0.114553\pi$
$491$	8.54749	+	26.3065i	0.385743	+	1.18719i	−0.550197	+	0.835035i	$0.685447\pi$
$492$		0			0
$493$	8.19078	+	5.95095i	0.368894	+	0.268017i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	5.60503	+	4.07230i	0.251420	+	0.182667i
$498$		0			0
$499$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$499$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$500$		0			0
$501$	14.4461	−	10.4957i	0.645406	−	0.468915i
$502$		0			0
$503$	−6.03098	+	18.5614i	−0.268908	+	0.827614i	0.721859	+	0.692040i	$0.243288\pi$
$503$	−6.03098	+	18.5614i	−0.268908	+	0.827614i	−0.990767	+	0.135574i	$0.956712\pi$
$504$		0			0
$505$	−65.1769			−2.90033
$506$		0			0
$507$	18.9282			0.840631
$508$		0			0
$509$	13.2212	−	40.6906i	0.586018	−	1.80358i	−0.00912468	−	0.999958i	$-0.502905\pi$
$509$	13.2212	−	40.6906i	0.586018	−	1.80358i	0.595143	−	0.803620i	$-0.297095\pi$
$510$		0			0
$511$	19.7338	−	14.3374i	0.872971	−	0.634251i
$512$		0			0
$513$	−4.03941	−	12.4320i	−0.178344	−	0.548887i
$514$		0			0
$515$	−19.7338	−	14.3374i	−0.869575	−	0.631783i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−5.60503	−	4.07230i	−0.246034	−	0.178754i
$520$		0			0
$521$	−10.9146	−	33.5918i	−0.478179	−	1.47168i	−0.841622	−	0.540067i	$-0.818399\pi$
$521$	−10.9146	−	33.5918i	−0.478179	−	1.47168i	0.363443	−	0.931616i	$-0.381601\pi$
$522$		0			0
$523$	5.28765	−	3.84170i	0.231213	−	0.167986i	−0.466147	−	0.884707i	$-0.654358\pi$
$523$	5.28765	−	3.84170i	0.231213	−	0.167986i	0.697360	+	0.716721i	$0.254358\pi$
$524$		0			0
$525$	−20.5932	+	63.3794i	−0.898761	+	2.76610i
$526$		0			0
$527$	10.7321			0.467495
$528$		0			0
$529$	−18.1769			−0.790301
$530$		0			0
$531$	18.5735	−	57.1634i	0.806021	−	2.48068i
$532$		0			0
$533$	−27.9246	+	20.2884i	−1.20955	+	0.878787i
$534$		0			0
$535$	−19.7490	−	60.7810i	−0.853822	−	2.62779i
$536$		0			0
$537$	−35.3644	−	25.6937i	−1.52609	−	1.10877i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−17.7984	−	12.9313i	−0.765212	−	0.555959i	0.135293	−	0.990806i	$-0.456803\pi$
$541$	−17.7984	−	12.9313i	−0.765212	−	0.555959i	−0.900504	+	0.434847i	$0.856803\pi$
$542$		0			0
$543$	−2.36715	−	7.28533i	−0.101584	−	0.312644i
$544$		0			0
$545$	−37.6328	+	27.3418i	−1.61201	+	1.17119i
$546$		0			0
$547$	11.0359	−	33.9649i	0.471860	−	1.45223i	−0.378287	−	0.925688i	$-0.623487\pi$
$547$	11.0359	−	33.9649i	0.471860	−	1.45223i	0.850147	−	0.526546i	$-0.176513\pi$
$548$		0			0
$549$	−29.1769			−1.24524
$550$		0			0
$551$	−14.5885			−0.621489
$552$		0			0
$553$	−14.0048	+	43.1024i	−0.595545	+	1.83290i
$554$		0			0
$555$	47.2829	−	34.3530i	2.00705	−	1.45820i
$556$		0			0
$557$	−8.44250	−	25.9833i	−0.357720	−	1.10095i	−0.954415	−	0.298482i	$-0.903520\pi$
$557$	−8.44250	−	25.9833i	−0.357720	−	1.10095i	0.596695	−	0.802468i	$-0.296480\pi$
$558$		0			0
$559$	−28.8923	−	20.9915i	−1.22201	−	0.887844i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	17.0900	+	12.4166i	0.720256	+	0.523297i	0.886466	−	0.462794i	$-0.153153\pi$
$563$	17.0900	+	12.4166i	0.720256	+	0.523297i	−0.166210	+	0.986090i	$0.553153\pi$
$564$		0			0
$565$	−5.76634	−	17.7470i	−0.242592	−	0.746620i
$566$		0			0
$567$	−5.44634	+	3.95700i	−0.228725	+	0.166178i
$568$		0			0
$569$	−1.28044	+	3.94079i	−0.0536789	+	0.165207i	−0.974302	−	0.225246i	$-0.927681\pi$
$569$	−1.28044	+	3.94079i	−0.0536789	+	0.165207i	0.920623	+	0.390453i	$0.127681\pi$
$570$		0			0
$571$	8.05256			0.336989			0.168495	−	0.985703i	$-0.446109\pi$
$571$	8.05256			0.336989			0.168495	+	0.985703i	$0.446109\pi$
$572$		0			0
$573$	12.0000			0.501307
$574$		0			0
$575$	−6.05911	+	18.6480i	−0.252682	+	0.777676i
$576$		0			0
$577$	−10.9508	+	7.95620i	−0.455887	+	0.331221i	−0.791916	−	0.610631i	$-0.790916\pi$
$577$	−10.9508	+	7.95620i	−0.455887	+	0.331221i	0.336029	+	0.941852i	$0.390916\pi$
$578$		0			0
$579$	−14.0654	−	43.2889i	−0.584539	−	1.79903i
$580$		0			0
$581$	−4.85410	−	3.52671i	−0.201382	−	0.146313i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−60.1691	−	43.7154i	−2.48769	−	1.80741i
$586$		0			0
$587$	5.78852	+	17.8152i	0.238918	+	0.735314i	0.996577	+	0.0826637i	$0.0263427\pi$
$587$	5.78852	+	17.8152i	0.238918	+	0.735314i	−0.757660	+	0.652650i	$0.773657\pi$
$588$		0			0
$589$	−12.5107	+	9.08957i	−0.515495	+	0.374529i
$590$		0			0
$591$	−5.00489	+	15.4035i	−0.205874	+	0.633614i
$592$		0			0
$593$	30.3731			1.24727			0.623636	−	0.781715i	$-0.285655\pi$
$593$	30.3731			1.24727			0.623636	+	0.781715i	$0.285655\pi$
$594$		0			0
$595$	−23.1244			−0.948006
$596$		0			0
$597$	−5.51793	+	16.9825i	−0.225834	+	0.695045i
$598$		0			0
$599$	−17.0900	+	12.4166i	−0.698277	+	0.507328i	−0.879371	−	0.476138i	$-0.842036\pi$
$599$	−17.0900	+	12.4166i	−0.698277	+	0.507328i	0.181094	+	0.983466i	$0.442036\pi$
$600$		0			0
$601$	9.02211	+	27.7672i	0.368019	+	1.13265i	0.948069	+	0.318066i	$0.103033\pi$
$601$	9.02211	+	27.7672i	0.368019	+	1.13265i	−0.580049	+	0.814581i	$0.696967\pi$
$602$		0			0
$603$	0.708411	+	0.514691i	0.0288487	+	0.0209598i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	29.2833	+	21.2756i	1.18857	+	0.863549i	0.993113	−	0.117163i	$-0.0373800\pi$
$607$	29.2833	+	21.2756i	1.18857	+	0.863549i	0.195460	+	0.980712i	$0.437380\pi$
$608$		0			0
$609$	−10.2966	−	31.6897i	−0.417239	−	1.28413i
$610$		0			0
$611$	−11.8023	+	8.57488i	−0.477470	+	0.346903i
$612$		0			0
$613$	−6.15815	+	18.9528i	−0.248725	+	0.765498i	0.746276	+	0.665637i	$0.231840\pi$
$613$	−6.15815	+	18.9528i	−0.248725	+	0.765498i	−0.995001	+	0.0998615i	$0.968160\pi$
$614$		0			0
$615$	78.8372			3.17902
$616$		0			0
$617$	−44.3205			−1.78428			−0.892138	−	0.451763i	$-0.850795\pi$
$617$	−44.3205			−1.78428			−0.892138	+	0.451763i	$0.850795\pi$
$618$		0			0
$619$	10.4016	−	32.0128i	0.418075	−	1.28670i	−0.491396	−	0.870936i	$-0.663513\pi$
$619$	10.4016	−	32.0128i	0.418075	−	1.28670i	0.909471	−	0.415767i	$-0.136487\pi$
$620$		0			0
$621$	7.10690	−	5.16346i	0.285190	−	0.207203i
$622$		0			0
$623$	13.8998	+	42.7792i	0.556885	+	1.71391i
$624$		0			0
$625$	−8.14825	−	5.92005i	−0.325930	−	0.236802i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	10.5172	+	7.64121i	0.419349	+	0.304675i
$630$		0			0
$631$	9.90479	+	30.4838i	0.394303	+	1.21354i	0.929503	+	0.368815i	$0.120236\pi$
$631$	9.90479	+	30.4838i	0.394303	+	1.21354i	−0.535200	+	0.844726i	$0.679764\pi$
$632$		0			0
$633$	39.4676	−	28.6749i	1.56870	−	1.13972i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−2.07180			−0.0820876
$638$		0			0
$639$	11.3205			0.447832
$640$		0			0
$641$	−3.23359	+	9.95195i	−0.127719	+	0.393078i	−0.994387	−	0.105807i	$-0.966257\pi$
$641$	−3.23359	+	9.95195i	−0.127719	+	0.393078i	0.866668	+	0.498886i	$0.166257\pi$
$642$		0			0
$643$	−27.5491	+	20.0156i	−1.08643	+	0.789338i	−0.978793	−	0.204852i	$-0.934329\pi$
$643$	−27.5491	+	20.0156i	−1.08643	+	0.789338i	−0.107638	+	0.994190i	$0.534329\pi$
$644$		0			0
$645$	25.2063	+	77.5769i	0.992496	+	3.05459i
$646$		0			0
$647$	−13.2617	−	9.63516i	−0.521369	−	0.378797i	0.295750	−	0.955265i	$-0.404430\pi$
$647$	−13.2617	−	9.63516i	−0.521369	−	0.378797i	−0.817120	+	0.576468i	$0.804430\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−28.5749	−	20.7609i	−1.11994	−	0.813683i
$652$		0			0
$653$	2.14093	+	6.58911i	0.0837812	+	0.257852i	0.984168	−	0.177239i	$-0.0567164\pi$
$653$	2.14093	+	6.58911i	0.0837812	+	0.257852i	−0.900387	+	0.435090i	$0.856716\pi$
$654$		0			0
$655$	24.1543	−	17.5492i	0.943788	−	0.685702i
$656$		0			0
$657$	12.3163	−	37.9057i	0.480505	−	1.47884i
$658$		0			0
$659$	−2.98076			−0.116114			−0.0580570	−	0.998313i	$-0.518491\pi$
$659$	−2.98076			−0.116114			−0.0580570	+	0.998313i	$0.518491\pi$
$660$		0			0
$661$	−17.3397			−0.674438			−0.337219	−	0.941426i	$-0.609486\pi$
$661$	−17.3397			−0.674438			−0.337219	+	0.941426i	$0.609486\pi$
$662$		0			0
$663$	8.54749	−	26.3065i	0.331957	−	1.02166i
$664$		0			0
$665$	26.9569	−	19.5853i	1.04534	−	0.759485i
$666$		0			0
$667$	−3.02956	−	9.32401i	−0.117305	−	0.361027i
$668$		0			0
$669$	18.5493	+	13.4769i	0.717158	+	0.521045i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−23.4034	−	17.0036i	−0.902135	−	0.655440i	0.0368784	−	0.999320i	$-0.488259\pi$
$673$	−23.4034	−	17.0036i	−0.902135	−	0.655440i	−0.939014	+	0.343880i	$0.888259\pi$
$674$		0			0
$675$	11.0359	+	33.9649i	0.424771	+	1.30731i
$676$		0			0
$677$	−13.6371	+	9.90795i	−0.524117	+	0.380793i	−0.818153	−	0.575001i	$-0.805002\pi$
$677$	−13.6371	+	9.90795i	−0.524117	+	0.380793i	0.294036	+	0.955794i	$0.405002\pi$
$678$		0			0
$679$	10.0704	−	30.9935i	0.386466	−	1.18942i
$680$		0			0
$681$	−9.85641			−0.377698
$682$		0			0
$683$	−23.1244			−0.884829			−0.442414	−	0.896811i	$-0.645878\pi$
$683$	−23.1244			−0.884829			−0.442414	+	0.896811i	$0.645878\pi$
$684$		0			0
$685$	2.92457	−	9.00090i	0.111742	−	0.343907i
$686$		0			0
$687$	−28.3000	+	20.5612i	−1.07971	+	0.784458i
$688$		0			0
$689$	−1.65007	−	5.07840i	−0.0628627	−	0.193472i
$690$		0			0
$691$	17.1325	+	12.4475i	0.651750	+	0.473524i	0.863867	−	0.503720i	$-0.168036\pi$
$691$	17.1325	+	12.4475i	0.651750	+	0.473524i	−0.212117	+	0.977244i	$0.568036\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−18.7080	−	13.5922i	−0.709635	−	0.515580i
$696$		0			0
$697$	5.41889	+	16.6776i	0.205255	+	0.631710i
$698$		0			0
$699$	−2.64383	+	1.92085i	−0.0999987	+	0.0726533i
$700$		0			0
$701$	3.89599	−	11.9906i	0.147150	−	0.452880i	−0.850132	−	0.526570i	$-0.823478\pi$
$701$	3.89599	−	11.9906i	0.147150	−	0.452880i	0.997281	+	0.0736905i	$0.0234777\pi$
$702$		0			0
$703$	−18.7321			−0.706493
$704$		0			0
$705$	33.3205			1.25492
$706$		0			0
$707$	−14.7441	+	45.3776i	−0.554508	+	1.70660i
$708$		0			0
$709$	0.116170	−	0.0844022i	0.00436284	−	0.00316979i	−0.585602	−	0.810599i	$-0.699142\pi$
$709$	0.116170	−	0.0844022i	0.00436284	−	0.00316979i	0.589965	+	0.807429i	$0.299142\pi$
$710$		0			0
$711$	22.8835	+	70.4282i	0.858198	+	2.64126i
$712$		0			0
$713$	−8.40755	−	6.10844i	−0.314865	−	0.228763i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	43.1372	+	31.3410i	1.61099	+	1.17045i
$718$		0			0
$719$	3.15078	+	9.69712i	0.117504	+	0.361641i	0.992461	−	0.122560i	$-0.0391103\pi$
$719$	3.15078	+	9.69712i	0.117504	+	0.361641i	−0.874957	+	0.484201i	$0.839110\pi$
$720$		0			0
$721$	−14.4461	+	10.4957i	−0.538002	+	0.390881i
$722$		0			0
$723$	7.53764	−	23.1985i	0.280328	−	0.862760i
$724$		0			0
$725$	39.8564			1.48023
$726$		0			0
$727$	−2.19615			−0.0814508			−0.0407254	−	0.999170i	$-0.512967\pi$
$727$	−2.19615			−0.0814508			−0.0407254	+	0.999170i	$0.512967\pi$
$728$		0			0
$729$	−13.5302	+	41.6416i	−0.501118	+	1.54228i
$730$		0			0
$731$	−14.6785	+	10.6645i	−0.542903	+	0.394442i
$732$		0			0
$733$	−10.1976	−	31.3849i	−0.376656	−	1.15923i	−0.942355	−	0.334615i	$-0.891394\pi$
$733$	−10.1976	−	31.3849i	−0.376656	−	1.15923i	0.565699	−	0.824612i	$-0.308606\pi$
$734$		0			0
$735$	3.82831	+	2.78143i	0.141209	+	0.102595i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	13.5365	+	9.83485i	0.497949	+	0.361781i	0.808233	−	0.588863i	$-0.200424\pi$
$739$	13.5365	+	9.83485i	0.497949	+	0.361781i	−0.310284	+	0.950644i	$0.600424\pi$
$740$		0			0
$741$	12.3163	+	37.9057i	0.452451	+	1.39250i
$742$		0			0
$743$	33.4715	−	24.3185i	1.22795	−	0.892158i	0.231216	−	0.972902i	$-0.425730\pi$
$743$	33.4715	−	24.3185i	1.22795	−	0.892158i	0.996735	+	0.0807440i	$0.0257296\pi$
$744$		0			0
$745$	−6.38437	+	19.6491i	−0.233905	+	0.719886i
$746$		0			0
$747$	−9.80385			−0.358704
$748$		0			0
$749$	−46.7846			−1.70947
$750$		0			0
$751$	−10.4622	+	32.1994i	−0.381771	+	1.17497i	0.557024	+	0.830496i	$0.311943\pi$
$751$	−10.4622	+	32.1994i	−0.381771	+	1.17497i	−0.938796	+	0.344475i	$0.888057\pi$
$752$		0			0
$753$	−38.1669	+	27.7299i	−1.39088	+	1.01053i
$754$		0			0
$755$	−12.1507	−	37.3960i	−0.442209	−	1.36098i
$756$		0			0
$757$	30.8433	+	22.4089i	1.12102	+	0.814467i	0.984363	−	0.176152i	$-0.0563651\pi$
$757$	30.8433	+	22.4089i	1.12102	+	0.814467i	0.136654	+	0.990619i	$0.456365\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−18.7661	−	13.6344i	−0.680270	−	0.494245i	0.193177	−	0.981164i	$-0.438121\pi$
$761$	−18.7661	−	13.6344i	−0.680270	−	0.494245i	−0.873447	+	0.486919i	$0.838121\pi$
$762$		0			0
$763$	10.5228	+	32.3859i	0.380952	+	1.17245i
$764$		0			0
$765$	−30.5684	+	22.2092i	−1.10520	+	0.802977i
$766$		0			0
$767$	−18.5735	+	57.1634i	−0.670650	+	2.06405i
$768$		0			0
$769$	−14.2679			−0.514515			−0.257258	−	0.966343i	$-0.582819\pi$
$769$	−14.2679			−0.514515			−0.257258	+	0.966343i	$0.582819\pi$
$770$		0			0
$771$	−12.1962			−0.439234
$772$		0			0
$773$	−12.3163	+	37.9057i	−0.442987	+	1.36337i	0.441690	+	0.897168i	$0.354379\pi$
$773$	−12.3163	+	37.9057i	−0.442987	+	1.36337i	−0.884677	+	0.466205i	$0.845621\pi$
$774$		0			0
$775$	34.1799	−	24.8332i	1.22778	−	0.892034i
$776$		0			0
$777$	−13.2212	−	40.6906i	−0.474307	−	1.45977i
$778$		0			0
$779$	−20.4422	−	14.8521i	−0.732418	−	0.532133i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−14.4461	−	10.4957i	−0.516263	−	0.375087i
$784$		0			0
$785$	23.9702	+	73.7727i	0.855533	+	2.63306i
$786$		0			0
$787$	3.87083	−	2.81232i	0.137980	−	0.100248i	−0.516654	−	0.856194i	$-0.672823\pi$
$787$	3.87083	−	2.81232i	0.137980	−	0.100248i	0.654634	+	0.755946i	$0.272823\pi$
$788$		0			0
$789$	1.97533	−	6.07944i	0.0703236	−	0.216434i
$790$		0			0
$791$	−13.6603			−0.485703
$792$		0			0
$793$	29.1769			1.03610
$794$		0			0
$795$	−3.76882	+	11.5992i	−0.133666	+	0.411382i
$796$		0			0
$797$	−32.8793	+	23.8882i	−1.16464	+	0.846163i	−0.990358	−	0.138532i	$-0.955762\pi$
$797$	−32.8793	+	23.8882i	−1.16464	+	0.846163i	−0.174286	+	0.984695i	$0.555762\pi$
$798$		0			0
$799$	2.29029	+	7.04880i	0.0810247	+	0.249368i
$800$		0			0
$801$	59.4607	+	43.2007i	2.10094	+	1.52642i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	18.1158	+	13.1619i	0.638496	+	0.463895i
$806$		0			0
$807$	−16.0851	−	49.5049i	−0.566223	−	1.74266i
$808$		0			0
$809$	11.0939	−	8.06019i	0.390041	−	0.283381i	−0.375431	−	0.926850i	$-0.622505\pi$
$809$	11.0939	−	8.06019i	0.390041	−	0.283381i	0.765472	+	0.643469i	$0.222505\pi$
$810$		0			0
$811$	5.27548	−	16.2362i	0.185247	−	0.570132i	−0.814706	−	0.579875i	$-0.803101\pi$
$811$	5.27548	−	16.2362i	0.185247	−	0.570132i	0.999953	+	0.00974326i	$0.00310143\pi$
$812$		0			0
$813$	17.8564			0.626252
$814$		0			0
$815$	87.7654			3.07429
$816$		0			0
$817$	8.07881	−	24.8640i	0.282642	−	0.869882i
$818$		0			0
$819$	−44.0468	+	32.0019i	−1.53912	+	1.11824i
$820$		0			0
$821$	−4.07189	−	12.5320i	−0.142110	−	0.437369i	0.854518	−	0.519422i	$-0.173853\pi$
$821$	−4.07189	−	12.5320i	−0.142110	−	0.437369i	−0.996628	+	0.0820522i	$0.973853\pi$
$822$		0			0
$823$	−6.47214	−	4.70228i	−0.225604	−	0.163911i	0.469241	−	0.883070i	$-0.344527\pi$
$823$	−6.47214	−	4.70228i	−0.225604	−	0.163911i	−0.694846	+	0.719159i	$0.744527\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−20.9608	−	15.2289i	−0.728878	−	0.529561i	0.160330	−	0.987063i	$-0.448744\pi$
$827$	−20.9608	−	15.2289i	−0.728878	−	0.529561i	−0.889208	+	0.457502i	$0.848744\pi$
$828$		0			0
$829$	0.490860	+	1.51071i	0.0170483	+	0.0524692i	0.959219	−	0.282665i	$-0.0912184\pi$
$829$	0.490860	+	1.51071i	0.0170483	+	0.0524692i	−0.942170	+	0.335134i	$0.891218\pi$
$830$		0			0
$831$	−30.4678	+	22.1361i	−1.05692	+	0.767894i
$832$		0			0
$833$	−0.325259	+	1.00104i	−0.0112695	+	0.0346841i
$834$		0			0
$835$	24.3923			0.844131
$836$		0			0
$837$	−18.9282			−0.654254
$838$		0			0
$839$	−16.4488	+	50.6242i	−0.567876	+	1.74774i	0.0913716	+	0.995817i	$0.470875\pi$
$839$	−16.4488	+	50.6242i	−0.567876	+	1.74774i	−0.659248	+	0.751926i	$0.729125\pi$
$840$		0			0
$841$	7.33924	−	5.33227i	0.253077	−	0.183871i
$842$		0			0
$843$	−6.63277	−	20.4136i	−0.228445	−	0.703081i
$844$		0			0
$845$	20.9183	+	15.1980i	0.719610	+	0.522828i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	68.3599	+	49.6663i	2.34610	+	1.70454i
$850$		0			0
$851$	−3.89005	−	11.9723i	−0.133349	−	0.410406i
$852$		0			0
$853$	−11.7017	+	8.50179i	−0.400659	+	0.291096i	−0.769809	−	0.638274i	$-0.779649\pi$
$853$	−11.7017	+	8.50179i	−0.400659	+	0.291096i	0.369151	+	0.929370i	$0.379649\pi$
$854$		0			0
$855$	16.8244	−	51.7801i	0.575382	−	1.77084i
$856$		0			0
$857$	26.1436			0.893048			0.446524	−	0.894772i	$-0.352662\pi$
$857$	26.1436			0.893048			0.446524	+	0.894772i	$0.352662\pi$
$858$		0			0
$859$	54.6410			1.86433			0.932164	−	0.362037i	$-0.117919\pi$
$859$	54.6410			1.86433			0.932164	+	0.362037i	$0.117919\pi$
$860$		0			0
$861$	17.8342	−	54.8881i	0.607789	−	1.87058i
$862$		0			0
$863$	11.8023	−	8.57488i	0.401755	−	0.291892i	−0.368500	−	0.929628i	$-0.620129\pi$
$863$	11.8023	−	8.57488i	0.401755	−	0.291892i	0.770256	+	0.637735i	$0.220129\pi$
$864$		0			0
$865$	−2.92457	−	9.00090i	−0.0994383	−	0.306040i
$866$		0			0
$867$	26.2059	+	19.0397i	0.890000	+	0.646623i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−0.708411	−	0.514691i	−0.0240036	−	0.0174396i
$872$		0			0
$873$	−16.4548	−	50.6425i	−0.556909	−	1.71399i
$874$		0			0
$875$	−32.4032	+	23.5423i	−1.09543	+	0.795875i
$876$		0			0
$877$	−4.87771	+	15.0121i	−0.164709	+	0.506921i	−0.999015	−	0.0443805i	$-0.985869\pi$
$877$	−4.87771	+	15.0121i	−0.164709	+	0.506921i	0.834306	+	0.551302i	$0.185869\pi$
$878$		0			0
$879$	−60.9808			−2.05683
$880$		0			0
$881$	−9.67949			−0.326110			−0.163055	−	0.986617i	$-0.552135\pi$
$881$	−9.67949			−0.326110			−0.163055	+	0.986617i	$0.552135\pi$
$882$		0			0
$883$	2.01970	−	6.21601i	0.0679684	−	0.209185i	−0.911303	−	0.411735i	$-0.864923\pi$
$883$	2.01970	−	6.21601i	0.0679684	−	0.209185i	0.979272	+	0.202550i	$0.0649228\pi$
$884$		0			0
$885$	111.063	−	80.6924i	3.73336	−	2.71244i
$886$		0			0
$887$	13.3586	+	41.1137i	0.448539	+	1.38046i	0.878555	+	0.477641i	$0.158508\pi$
$887$	13.3586	+	41.1137i	0.448539	+	1.38046i	−0.430016	+	0.902821i	$0.641492\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−8.63989	−	6.27725i	−0.289123	−	0.210060i
$894$		0			0
$895$	−18.4523	−	56.7903i	−0.616791	−	1.89829i
$896$		0			0
$897$	−21.6692	+	15.7436i	−0.723514	+	0.525663i
$898$		0			0
$899$	−6.52778	+	20.0905i	−0.217714	+	0.670054i
$900$		0			0
$901$	−2.71281			−0.0903769
$902$		0			0
$903$	59.7128			1.98712
$904$		0			0
$905$	3.23359	−	9.95195i	0.107488	−	0.330814i
$906$		0			0
$907$	−14.4461	+	10.4957i	−0.479676	+	0.348505i	−0.801200	−	0.598396i	$-0.795805\pi$
$907$	−14.4461	+	10.4957i	−0.479676	+	0.348505i	0.321524	+	0.946901i	$0.395805\pi$
$908$		0			0
$909$	24.0914	+	74.1458i	0.799062	+	2.45926i
$910$		0			0
$911$	10.6603	+	7.74520i	0.353193	+	0.256610i	0.750207	−	0.661203i	$-0.229954\pi$
$911$	10.6603	+	7.74520i	0.353193	+	0.256610i	−0.397014	+	0.917812i	$0.629954\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−53.9137	−	39.1706i	−1.78233	−	1.29494i
$916$		0			0
$917$	−6.75400	−	20.7867i	−0.223037	−	0.686437i
$918$		0			0
$919$	−9.70820	+	7.05342i	−0.320244	+	0.232671i	−0.736280	−	0.676677i	$-0.763419\pi$
$919$	−9.70820	+	7.05342i	−0.320244	+	0.232671i	0.416036	+	0.909348i	$0.363419\pi$
$920$		0			0
$921$	27.3916	−	84.3026i	0.902583	−	2.77787i
$922$		0			0
$923$	−11.3205			−0.372619
$924$		0			0
$925$	51.1769			1.68269
$926$		0			0
$927$	−9.01616	+	27.7489i	−0.296130	+	0.911393i
$928$		0			0
$929$	16.1223	−	11.7135i	0.528954	−	0.384308i	−0.291012	−	0.956719i	$-0.593992\pi$
$929$	16.1223	−	11.7135i	0.528954	−	0.384308i	0.819966	+	0.572412i	$0.193992\pi$
$930$		0			0
$931$	−0.468674	−	1.44243i	−0.0153602	−	0.0472737i
$932$		0			0
$933$	−37.0986	−	26.9537i	−1.21455	−	0.882425i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	29.3414	+	21.3178i	0.958541	+	0.696421i	0.952812	−	0.303563i	$-0.0981761\pi$
$937$	29.3414	+	21.3178i	0.958541	+	0.696421i	0.00572982	+	0.999984i	$0.498176\pi$
$938$		0			0
$939$	−5.90975	−	18.1883i	−0.192857	−	0.593554i
$940$		0			0
$941$	16.9894	−	12.3435i	0.553837	−	0.402386i	−0.275361	−	0.961341i	$-0.588797\pi$
$941$	16.9894	−	12.3435i	0.553837	−	0.402386i	0.829198	+	0.558955i	$0.188797\pi$
$942$		0			0
$943$	5.24734	−	16.1497i	0.170877	−	0.525905i
$944$		0			0
$945$	40.7846			1.32672
$946$		0			0
$947$	−11.5167			−0.374241			−0.187121	−	0.982337i	$-0.559916\pi$
$947$	−11.5167			−0.374241			−0.187121	+	0.982337i	$0.559916\pi$
$948$		0			0
$949$	−12.3163	+	37.9057i	−0.399804	+	1.23047i
$950$		0			0
$951$	−8.52372	+	6.19285i	−0.276401	+	0.200817i
$952$		0			0
$953$	5.31390	+	16.3545i	0.172134	+	0.529775i	0.999491	−	0.0319021i	$-0.0101565\pi$
$953$	5.31390	+	16.3545i	0.172134	+	0.529775i	−0.827357	+	0.561677i	$0.810156\pi$
$954$		0			0
$955$	13.2617	+	9.63516i	0.429137	+	0.311786i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−5.60503	−	4.07230i	−0.180996	−	0.131501i
$960$		0			0
$961$	−2.65992	−	8.18640i	−0.0858040	−	0.264078i
$962$		0			0
$963$	−61.8452	+	44.9332i	−1.99293	+	1.44795i
$964$		0			0
$965$	19.2137	−	59.1338i	0.618512	−	1.90358i
$966$		0			0
$967$	18.7321			0.602382			0.301191	−	0.953564i	$-0.402616\pi$
$967$	18.7321			0.602382			0.301191	+	0.953564i	$0.402616\pi$
$968$		0			0
$969$	20.2487			0.650482
$970$		0			0
$971$	12.2113	−	37.5826i	0.391880	−	1.20608i	−0.539485	−	0.841995i	$-0.681381\pi$
$971$	12.2113	−	37.5826i	0.391880	−	1.20608i	0.931365	−	0.364087i	$-0.118619\pi$
$972$		0			0
$973$	−13.6952	+	9.95015i	−0.439048	+	0.318987i
$974$		0			0
$975$	−33.6488	−	103.560i	−1.07762	−	3.31658i
$976$		0			0
$977$	−21.1776	−	15.3864i	−0.677530	−	0.492255i	0.195007	−	0.980802i	$-0.437527\pi$
$977$	−21.1776	−	15.3864i	−0.677530	−	0.492255i	−0.872537	+	0.488547i	$0.837527\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	45.0145	+	32.7050i	1.43720	+	1.04419i
$982$		0			0
$983$	11.1571	+	34.3380i	0.355856	+	1.09521i	0.955511	+	0.294954i	$0.0953043\pi$
$983$	11.1571	+	34.3380i	0.355856	+	1.09521i	−0.599655	+	0.800258i	$0.704696\pi$
$984$		0			0
$985$	−17.8990	+	13.0044i	−0.570309	+	0.414354i
$986$		0			0
$987$	7.53764	−	23.1985i	0.239926	−	0.738415i
$988$		0			0
$989$	17.5692			0.558669
$990$		0			0
$991$	17.8564			0.567227			0.283614	−	0.958939i	$-0.408467\pi$
$991$	17.8564			0.567227			0.283614	+	0.958939i	$0.408467\pi$
$992$		0			0
$993$	−0.904865	+	2.78489i	−0.0287150	+	0.0883757i
$994$		0			0
$995$	−19.7338	+	14.3374i	−0.625603	+	0.454527i
$996$		0			0
$997$	−17.9008	−	55.0930i	−0.566924	−	1.74481i	−0.662165	−	0.749358i	$-0.730362\pi$
$997$	−17.9008	−	55.0930i	−0.566924	−	1.74481i	0.0952406	−	0.995454i	$-0.469638\pi$
$998$		0			0
$999$	−18.5493	−	13.4769i	−0.586874	−	0.426389i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.i.o.81.2		8
11.2	odd	10		968.2.i.n.753.1		8
11.3	even	5	inner	968.2.i.o.729.2		8
11.4	even	5	inner	968.2.i.o.9.1		8
11.5	even	5		968.2.a.k.1.2	✓	2
11.6	odd	10		968.2.a.l.1.2	yes	2
11.7	odd	10		968.2.i.n.9.1		8
11.8	odd	10		968.2.i.n.729.2		8
11.9	even	5	inner	968.2.i.o.753.1		8
11.10	odd	2		968.2.i.n.81.2		8
33.5	odd	10		8712.2.a.br.1.2		2
33.17	even	10		8712.2.a.bs.1.2		2
44.27	odd	10		1936.2.a.q.1.1		2
44.39	even	10		1936.2.a.p.1.1		2
88.5	even	10		7744.2.a.bu.1.1		2
88.27	odd	10		7744.2.a.cx.1.2		2
88.61	odd	10		7744.2.a.bv.1.1		2
88.83	even	10		7744.2.a.cw.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
968.2.a.k.1.2	✓	2	11.5	even	5
968.2.a.l.1.2	yes	2	11.6	odd	10
968.2.i.n.9.1		8	11.7	odd	10
968.2.i.n.81.2		8	11.10	odd	2
968.2.i.n.729.2		8	11.8	odd	10
968.2.i.n.753.1		8	11.2	odd	10
968.2.i.o.9.1		8	11.4	even	5	inner
968.2.i.o.81.2		8	1.1	even	1	trivial
968.2.i.o.729.2		8	11.3	even	5	inner
968.2.i.o.753.1		8	11.9	even	5	inner
1936.2.a.p.1.1		2	44.39	even	10
1936.2.a.q.1.1		2	44.27	odd	10
7744.2.a.bu.1.1		2	88.5	even	10
7744.2.a.bv.1.1		2	88.61	odd	10
7744.2.a.cw.1.2		2	88.83	even	10
7744.2.a.cx.1.2		2	88.27	odd	10
8712.2.a.br.1.2		2	33.5	odd	10
8712.2.a.bs.1.2		2	33.17	even	10

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.i (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.844250 - 2.59833i) q^{3} +(3.01929 - 2.19364i) q^{5} +(-0.844250 - 2.59833i) q^{7} +(-3.61153 - 2.62393i) q^{9} +O(q^{10})\)	\(q+(0.844250 - 2.59833i) q^{3} +(3.01929 - 2.19364i) q^{5} +(-0.844250 - 2.59833i) q^{7} +(-3.61153 - 2.62393i) q^{9} +(3.61153 + 2.62393i) q^{13} +(-3.15078 - 9.69712i) q^{15} +(1.83481 - 1.33307i) q^{17} +(-1.00985 + 3.10800i) q^{19} -7.46410 q^{21} -2.19615 q^{23} +(2.75897 - 8.49123i) q^{25} +(-3.23607 + 2.35114i) q^{27} +(1.37948 + 4.24561i) q^{29} +(3.82831 + 2.78143i) q^{31} +(-8.24886 - 5.99315i) q^{35} +(1.77130 + 5.45150i) q^{37} +(9.86689 - 7.16872i) q^{39} +(-2.38934 + 7.35362i) q^{41} -8.00000 q^{43} -16.6603 q^{45} +(-1.00985 + 3.10800i) q^{47} +(-0.375466 + 0.272792i) q^{49} +(-1.91472 - 5.89289i) q^{51} +(-0.967708 - 0.703081i) q^{53} +(7.22307 + 5.24787i) q^{57} +(4.16064 + 12.8051i) q^{59} +(5.28765 - 3.84170i) q^{61} +(-3.76882 + 11.5992i) q^{63} +16.6603 q^{65} -0.196152 q^{67} +(-1.85410 + 5.70634i) q^{69} +(-2.05158 + 1.49056i) q^{71} +(2.75897 + 8.49123i) q^{73} +(-19.7338 - 14.3374i) q^{75} +(-13.4203 - 9.75045i) q^{79} +(-0.761449 - 2.34350i) q^{81} +(1.77672 - 1.29087i) q^{83} +(2.61555 - 8.04984i) q^{85} +12.1962 q^{87} -16.4641 q^{89} +(3.76882 - 11.5992i) q^{91} +(10.4591 - 7.59901i) q^{93} +(3.76882 + 11.5992i) q^{95} +(9.65012 + 7.01122i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 4 q^{5} + 2 q^{7} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 4 * q^5 + 2 * q^7 - 2 * q^9	\( 8 q - 2 q^{3} + 4 q^{5} + 2 q^{7} - 2 q^{9} + 2 q^{13} + 10 q^{15} + 8 q^{17} + 10 q^{19} - 32 q^{21} + 24 q^{23} - 4 q^{25} - 8 q^{27} - 2 q^{29} + 6 q^{31} - 10 q^{35} - 8 q^{37} + 14 q^{39} + 12 q^{41} - 64 q^{43} - 64 q^{45} + 10 q^{47} + 6 q^{49} + 2 q^{51} + 8 q^{53} + 4 q^{57} - 20 q^{59} + 20 q^{61} + 14 q^{63} + 64 q^{65} + 40 q^{67} + 12 q^{69} - 12 q^{71} - 4 q^{73} - 28 q^{75} - 2 q^{79} - 2 q^{81} - 6 q^{83} - 10 q^{85} + 56 q^{87} - 104 q^{89} - 14 q^{91} + 12 q^{93} - 14 q^{95} + 10 q^{97}+O(q^{100}) \) 8 * q - 2 * q^3 + 4 * q^5 + 2 * q^7 - 2 * q^9 + 2 * q^13 + 10 * q^15 + 8 * q^17 + 10 * q^19 - 32 * q^21 + 24 * q^23 - 4 * q^25 - 8 * q^27 - 2 * q^29 + 6 * q^31 - 10 * q^35 - 8 * q^37 + 14 * q^39 + 12 * q^41 - 64 * q^43 - 64 * q^45 + 10 * q^47 + 6 * q^49 + 2 * q^51 + 8 * q^53 + 4 * q^57 - 20 * q^59 + 20 * q^61 + 14 * q^63 + 64 * q^65 + 40 * q^67 + 12 * q^69 - 12 * q^71 - 4 * q^73 - 28 * q^75 - 2 * q^79 - 2 * q^81 - 6 * q^83 - 10 * q^85 + 56 * q^87 - 104 * q^89 - 14 * q^91 + 12 * q^93 - 14 * q^95 + 10 * q^97

Introduction

L-functions

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