LMFDB - Embedded newform 968.2.i.n.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.n.729.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

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	$0.0726944\pi$
$7$	0.844250	+	2.59833i	0.319097	+	0.982078i	−0.654939	+	0.755682i	$0.727306\pi$
$8$		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	−0.0392160	−	0.999231i	$-0.512486\pi$
$13$	−3.61153	−	2.62393i	−1.00166	−	0.727748i	−0.962443	+	0.271483i	$0.912486\pi$
$14$		0			0
$15$	−3.15078	−	9.69712i	−0.813529	−	2.50378i
$16$		0			0
$17$	−1.83481	+	1.33307i	−0.445007	+	0.323316i	−0.787621	−	0.616160i	$-0.788688\pi$
$17$	−1.83481	+	1.33307i	−0.445007	+	0.323316i	0.342614	+	0.939476i	$0.388688\pi$
$18$		0			0
$19$	1.00985	−	3.10800i	0.231676	−	0.713025i	−0.765869	−	0.642997i	$-0.777691\pi$
$19$	1.00985	−	3.10800i	0.231676	−	0.713025i	0.997545	−	0.0700286i	$-0.0223090\pi$
$20$		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	$-0.963963\pi$
$29$	−1.37948	−	4.24561i	−0.256164	−	0.788391i	0.737435	−	0.675419i	$-0.236037\pi$
$30$		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	$-0.693664\pi$
$41$	2.38934	−	7.35362i	0.373151	−	1.14844i	0.944717	−	0.327886i	$-0.106336\pi$
$42$		0			0
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		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	−0.872366	−	0.488853i	$-0.837415\pi$
$61$	−5.28765	+	3.84170i	−0.677015	+	0.491880i	0.195351	+	0.980733i	$0.437415\pi$
$62$		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	$-0.925006\pi$
$73$	−2.75897	−	8.49123i	−0.322913	−	0.993823i	0.649461	−	0.760395i	$-0.274994\pi$
$74$		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	$0.0829725\pi$
$79$	13.4203	+	9.75045i	1.50991	+	1.09701i	0.543688	+	0.839287i	$0.317027\pi$
$80$		0			0
$81$	−0.761449	−	2.34350i	−0.0846055	−	0.260389i
$82$		0			0
$83$	−1.77672	+	1.29087i	−0.195021	+	0.141691i	−0.681011	−	0.732274i	$-0.738459\pi$
$83$	−1.77672	+	1.29087i	−0.195021	+	0.141691i	0.485990	+	0.873965i	$0.338459\pi$
$84$		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	$0.0351543\pi$
$101$	14.1288	+	10.2651i	1.40586	+	1.02142i	0.411956	+	0.911204i	$0.364846\pi$
$102$		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	$0.410372\pi$
$107$	−5.29172	+	16.2862i	−0.511570	+	1.57445i	−0.789438	+	0.613830i	$0.789628\pi$
$108$		0			0
$109$	12.4641			1.19384			0.596922	−	0.802299i	$-0.296390\pi$
$109$	12.4641			1.19384			0.596922	+	0.802299i	$0.296390\pi$
$110$		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	$-0.613642\pi$
$131$	−8.00000			−0.698963			−0.349482	+	0.936943i	$0.613642\pi$
$132$		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	0.998836	−	0.0482430i	$-0.0153622\pi$
$139$	1.91472	+	5.89289i	0.162404	+	0.499829i	−0.836432	+	0.548071i	$0.815362\pi$
$140$		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	−0.389022	−	0.921229i	$-0.627187\pi$
$149$	4.47864	−	3.25392i	0.366904	−	0.266571i	0.755926	+	0.654657i	$0.227187\pi$
$150$		0			0
$151$	−3.25577	+	10.0202i	−0.264951	+	0.815435i	0.726754	+	0.686898i	$0.241028\pi$
$151$	−3.25577	+	10.0202i	−0.264951	+	0.815435i	−0.991705	+	0.128537i	$0.958972\pi$
$152$		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	0.364095	−	0.931362i	$-0.381378\pi$
$167$	−5.28765	−	3.84170i	−0.409171	−	0.297280i	−0.773266	+	0.634082i	$0.781378\pi$
$168$		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	−0.976416	−	0.215896i	$-0.930733\pi$
$173$	−0.783636	+	2.41178i	−0.0595787	+	0.183364i	0.916838	+	0.399260i	$0.130733\pi$
$174$		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	−0.955497	−	0.295001i	$-0.904680\pi$
$193$	−13.4784	+	9.79265i	−0.970199	+	0.704890i	−0.0147017	+	0.999892i	$0.504680\pi$
$194$		0			0
$195$	−14.0654	+	43.2889i	−1.00725	+	3.09998i
$196$		0			0
$197$	5.92820			0.422367			0.211183	−	0.977446i	$-0.432268\pi$
$197$	5.92820			0.422367			0.211183	+	0.977446i	$0.432268\pi$
$198$		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	−0.0336083	−	0.999435i	$-0.510700\pi$
$211$	−14.4461	−	10.4957i	−0.994513	−	0.722556i	−0.960905	+	0.276879i	$0.910700\pi$
$212$		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	0.981213	−	0.192928i	$-0.0617985\pi$
$227$	1.11484	+	3.43112i	0.0739945	+	0.227732i	−0.907218	+	0.420660i	$0.861799\pi$
$228$		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	0.619032	−	0.785366i	$-0.287525\pi$
$233$	0.967708	+	0.703081i	0.0633966	+	0.0460604i	−0.555636	+	0.831426i	$0.687525\pi$
$234$		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	$-0.682557\pi$
$239$	6.03098	−	18.5614i	0.390112	−	1.20064i	0.932704	−	0.360644i	$-0.117443\pi$
$240$		0			0
$241$	−8.92820			−0.575116			−0.287558	−	0.957763i	$-0.592843\pi$
$241$	−8.92820			−0.575116			−0.287558	+	0.957763i	$0.592843\pi$
$242$		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	$-0.522982\pi$
$263$	−2.33975			−0.144275			−0.0721375	+	0.997395i	$0.522982\pi$
$264$		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	0.870785	−	0.491665i	$-0.163611\pi$
$271$	−2.01970	−	6.21601i	−0.122688	−	0.377596i	−0.993473	+	0.114069i	$0.963611\pi$
$272$		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	0.870045	−	0.492973i	$-0.164090\pi$
$277$	11.1520	+	8.10239i	0.670058	+	0.486825i	−0.199987	+	0.979799i	$0.564090\pi$
$278$		0			0
$279$	−6.52778	−	20.0905i	−0.390808	−	1.20278i
$280$		0			0
$281$	−6.35597	+	4.61788i	−0.379165	+	0.275480i	−0.761001	−	0.648750i	$-0.775292\pi$
$281$	−6.35597	+	4.61788i	−0.379165	+	0.275480i	0.381836	+	0.924230i	$0.375292\pi$
$282$		0			0
$283$	9.55734	−	29.4145i	0.568125	−	1.74851i	−0.0903542	−	0.995910i	$-0.528800\pi$
$283$	9.55734	−	29.4145i	0.568125	−	1.74851i	0.658479	−	0.752599i	$-0.271200\pi$
$284$		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	$0.126065\pi$
$293$	6.89742	+	21.2281i	0.402951	+	1.24016i	−0.519642	+	0.854384i	$0.673935\pi$
$294$		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	$-0.876660\pi$
$307$	−32.4449			−1.85173			−0.925863	+	0.377859i	$0.876660\pi$
$308$		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	0.993177	−	0.116616i	$-0.0372048\pi$
$337$	2.22373	+	6.84395i	0.121134	+	0.372814i	−0.872043	+	0.489430i	$0.837205\pi$
$338$		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	0.0853945	−	0.996347i	$-0.472785\pi$
$347$	19.7338	−	14.3374i	1.05937	−	0.769674i	0.973971	+	0.226673i	$0.0727850\pi$
$348$		0			0
$349$	5.37452	−	16.5411i	0.287691	−	0.885423i	−0.697888	−	0.716207i	$-0.745877\pi$
$349$	5.37452	−	16.5411i	0.287691	−	0.885423i	0.985579	−	0.169216i	$-0.0541235\pi$
$350$		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	$0.132335\pi$
$359$	7.80823	+	24.0312i	0.412102	+	1.26832i	−0.502715	+	0.864452i	$0.667665\pi$
$360$		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	$-0.512068\pi$
$373$	−1.46410			−0.0758083			−0.0379042	+	0.999281i	$0.512068\pi$
$374$		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	−0.126809	−	0.991927i	$-0.540474\pi$
$409$	−22.4357	−	16.3005i	−1.10937	−	0.806007i	−0.982565	+	0.185920i	$0.940474\pi$
$410$		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	0.498905	−	0.866656i	$-0.333736\pi$
$431$	−3.55345	−	2.58173i	−0.171164	−	0.124358i	−0.670069	+	0.742299i	$0.733736\pi$
$432$		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	$-0.162083\pi$
$439$	36.5885			1.74627			0.873136	+	0.487477i	$0.162083\pi$
$440$		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	−0.517810	−	0.855496i	$-0.673253\pi$
$457$	2.90312	−	2.10924i	0.135802	−	0.0986662i	0.653612	+	0.756829i	$0.273253\pi$
$458$		0			0
$459$	2.80334	−	8.62779i	0.130849	−	0.402711i
$460$		0			0
$461$	−22.3205			−1.03957			−0.519785	−	0.854297i	$-0.673988\pi$
$461$	−22.3205			−1.03957			−0.519785	+	0.854297i	$0.673988\pi$
$462$		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	−0.802563	−	0.596568i	$-0.796531\pi$
$479$	−10.5753	+	7.68341i	−0.483198	+	0.351064i	0.319364	+	0.947632i	$0.396531\pi$
$480$		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	$-0.885447\pi$
$491$	−8.54749	−	26.3065i	−0.385743	−	1.18719i	0.550197	−	0.835035i	$-0.314553\pi$
$492$		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	$-0.756712\pi$
$503$	6.03098	−	18.5614i	0.268908	−	0.827614i	0.990767	−	0.135574i	$-0.0432878\pi$
$504$		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	−0.697360	−	0.716721i	$-0.745642\pi$
$523$	−5.28765	+	3.84170i	−0.231213	+	0.167986i	0.466147	+	0.884707i	$0.345642\pi$
$524$		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	0.900504	−	0.434847i	$-0.143197\pi$
$541$	17.7984	+	12.9313i	0.765212	+	0.555959i	−0.135293	+	0.990806i	$0.543197\pi$
$542$		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	$0.376513\pi$
$547$	−11.0359	+	33.9649i	−0.471860	+	1.45223i	−0.850147	+	0.526546i	$0.823487\pi$
$548$		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	$0.0964802\pi$
$557$	8.44250	+	25.9833i	0.357720	+	1.10095i	−0.596695	+	0.802468i	$0.703520\pi$
$558$		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	0.166210	−	0.986090i	$-0.446847\pi$
$563$	−17.0900	−	12.4166i	−0.720256	−	0.523297i	−0.886466	+	0.462794i	$0.846847\pi$
$564$		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	−0.920623	−	0.390453i	$-0.872319\pi$
$569$	1.28044	−	3.94079i	0.0536789	−	0.165207i	0.974302	+	0.225246i	$0.0723186\pi$
$570$		0			0
$571$	−8.05256			−0.336989			−0.168495	−	0.985703i	$-0.553891\pi$
$571$	−8.05256			−0.336989			−0.168495	+	0.985703i	$0.553891\pi$
$572$		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	$-0.714345\pi$
$593$	−30.3731			−1.24727			−0.623636	+	0.781715i	$0.714345\pi$
$594$		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	$-0.896967\pi$
$601$	−9.02211	−	27.7672i	−0.368019	−	1.13265i	0.580049	−	0.814581i	$-0.303033\pi$
$602$		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	−0.195460	−	0.980712i	$-0.562620\pi$
$607$	−29.2833	−	21.2756i	−1.18857	−	0.863549i	−0.993113	+	0.117163i	$0.962620\pi$
$608$		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	$-0.768160\pi$
$613$	6.15815	−	18.9528i	0.248725	−	0.765498i	0.995001	−	0.0998615i	$-0.0318400\pi$
$614$		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	$-0.481509\pi$
$659$	2.98076			0.116114			0.0580570	+	0.998313i	$0.481509\pi$
$660$		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	0.939014	−	0.343880i	$-0.111741\pi$
$673$	23.4034	+	17.0036i	0.902135	+	0.655440i	−0.0368784	+	0.999320i	$0.511741\pi$
$674$		0			0
$675$	11.0359	+	33.9649i	0.424771	+	1.30731i
$676$		0			0
$677$	13.6371	−	9.90795i	0.524117	−	0.380793i	−0.294036	−	0.955794i	$-0.594998\pi$
$677$	13.6371	−	9.90795i	0.524117	−	0.380793i	0.818153	+	0.575001i	$0.194998\pi$
$678$		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	−0.997281	−	0.0736905i	$-0.976522\pi$
$701$	−3.89599	+	11.9906i	−0.147150	+	0.452880i	0.850132	+	0.526570i	$0.176522\pi$
$702$		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	$0.108606\pi$
$733$	10.1976	+	31.3849i	0.376656	+	1.15923i	−0.565699	+	0.824612i	$0.691394\pi$
$734$		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	0.310284	−	0.950644i	$-0.399576\pi$
$739$	−13.5365	−	9.83485i	−0.497949	−	0.361781i	−0.808233	+	0.588863i	$0.799576\pi$
$740$		0			0
$741$	12.3163	+	37.9057i	0.452451	+	1.39250i
$742$		0			0
$743$	−33.4715	+	24.3185i	−1.22795	+	0.892158i	−0.996735	−	0.0807440i	$-0.974270\pi$
$743$	−33.4715	+	24.3185i	−1.22795	+	0.892158i	−0.231216	+	0.972902i	$0.574270\pi$
$744$		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	0.873447	−	0.486919i	$-0.161879\pi$
$761$	18.7661	+	13.6344i	0.680270	+	0.494245i	−0.193177	+	0.981164i	$0.561879\pi$
$762$		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	$-0.417181\pi$
$769$	14.2679			0.514515			0.257258	+	0.966343i	$0.417181\pi$
$770$		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	−0.654634	−	0.755946i	$-0.727177\pi$
$787$	−3.87083	+	2.81232i	−0.137980	+	0.100248i	0.516654	+	0.856194i	$0.327177\pi$
$788$		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	−0.765472	−	0.643469i	$-0.777495\pi$
$809$	−11.0939	+	8.06019i	−0.390041	+	0.283381i	0.375431	+	0.926850i	$0.377495\pi$
$810$		0			0
$811$	−5.27548	+	16.2362i	−0.185247	+	0.570132i	−0.999953	−	0.00974326i	$-0.996899\pi$
$811$	−5.27548	+	16.2362i	−0.185247	+	0.570132i	0.814706	+	0.579875i	$0.196899\pi$
$812$		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	0.996628	−	0.0820522i	$-0.0261474\pi$
$821$	4.07189	+	12.5320i	0.142110	+	0.437369i	−0.854518	+	0.519422i	$0.826147\pi$
$822$		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	0.889208	−	0.457502i	$-0.151256\pi$
$827$	20.9608	+	15.2289i	0.728878	+	0.529561i	−0.160330	+	0.987063i	$0.551256\pi$
$828$		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	−0.369151	−	0.929370i	$-0.620351\pi$
$853$	11.7017	−	8.50179i	0.400659	−	0.291096i	0.769809	+	0.638274i	$0.220351\pi$
$854$		0			0
$855$	−16.8244	+	51.7801i	−0.575382	+	1.77084i
$856$		0			0
$857$	−26.1436			−0.893048			−0.446524	−	0.894772i	$-0.647338\pi$
$857$	−26.1436			−0.893048			−0.446524	+	0.894772i	$0.647338\pi$
$858$		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	−0.834306	−	0.551302i	$-0.814131\pi$
$877$	4.87771	−	15.0121i	0.164709	−	0.506921i	0.999015	+	0.0443805i	$0.0141314\pi$
$878$		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	$-0.841492\pi$
$887$	−13.3586	−	41.1137i	−0.448539	−	1.38046i	0.430016	−	0.902821i	$-0.358508\pi$
$888$		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	−0.416036	−	0.909348i	$-0.636581\pi$
$919$	9.70820	−	7.05342i	0.320244	−	0.232671i	0.736280	+	0.676677i	$0.236581\pi$
$920$		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	−0.00572982	−	0.999984i	$-0.501824\pi$
$937$	−29.3414	−	21.3178i	−0.958541	−	0.696421i	−0.952812	+	0.303563i	$0.901824\pi$
$938$		0			0
$939$	−5.90975	−	18.1883i	−0.192857	−	0.593554i
$940$		0			0
$941$	−16.9894	+	12.3435i	−0.553837	+	0.402386i	−0.829198	−	0.558955i	$-0.811203\pi$
$941$	−16.9894	+	12.3435i	−0.553837	+	0.402386i	0.275361	+	0.961341i	$0.411203\pi$
$942$		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	0.827357	−	0.561677i	$-0.189844\pi$
$953$	−5.31390	−	16.3545i	−0.172134	−	0.529775i	−0.999491	+	0.0319021i	$0.989844\pi$
$954$		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	$-0.597384\pi$
$967$	−18.7321			−0.602382			−0.301191	+	0.953564i	$0.597384\pi$
$968$		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	$0.269638\pi$
$997$	17.9008	+	55.0930i	0.566924	+	1.74481i	−0.0952406	+	0.995454i	$0.530362\pi$
$998$		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.n.81.2		8
11.2	odd	10		968.2.i.o.753.1		8
11.3	even	5	inner	968.2.i.n.729.2		8
11.4	even	5	inner	968.2.i.n.9.1		8
11.5	even	5		968.2.a.l.1.2	yes	2
11.6	odd	10		968.2.a.k.1.2	✓	2
11.7	odd	10		968.2.i.o.9.1		8
11.8	odd	10		968.2.i.o.729.2		8
11.9	even	5	inner	968.2.i.n.753.1		8
11.10	odd	2		968.2.i.o.81.2		8
33.5	odd	10		8712.2.a.bs.1.2		2
33.17	even	10		8712.2.a.br.1.2		2
44.27	odd	10		1936.2.a.p.1.1		2
44.39	even	10		1936.2.a.q.1.1		2
88.5	even	10		7744.2.a.bv.1.1		2
88.27	odd	10		7744.2.a.cw.1.2		2
88.61	odd	10		7744.2.a.bu.1.1		2
88.83	even	10		7744.2.a.cx.1.2		2

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

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

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