LMFDB - Embedded newform 968.2.i.r.81.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [968,2,Mod(9,968)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [8,0,-1,0,-3,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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:	8.0.1305015625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 5x^{6} - 9x^{5} + 29x^{4} + 36x^{3} + 80x^{2} + 64x + 256 $ x^8 - x^7 + 5x^6 - 9x^5 + 29x^4 + 36x^3 + 80x^2 + 64x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$-1.26332 - 0.917858i$ of defining polynomial
Character	$\chi$	$=$	968.81
Dual form			968.2.i.r.729.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.482546 + 1.48512i) q^{3} +(-2.88136 + 2.09343i) q^{5} +(0.965093 + 2.97025i) q^{7} +(0.454306 + 0.330072i) q^{9} +(4.14468 + 3.01129i) q^{13} +(-1.71861 - 5.28935i) q^{15} +(-1.61803 + 1.17557i) q^{17} +(-1.23607 + 3.80423i) q^{19} -4.87689 q^{21} +2.43845 q^{23} +(2.37469 - 7.30854i) q^{25} +(-4.49939 + 3.26900i) q^{27} +(-1.58313 - 4.87236i) q^{29} +(4.49939 + 3.26900i) q^{31} +(-8.99878 - 6.53800i) q^{35} +(-2.33665 - 7.19146i) q^{37} +(-6.47214 + 4.70228i) q^{39} +(-0.347059 + 1.06814i) q^{41} -7.12311 q^{43} -2.00000 q^{45} +(2.47214 - 7.60845i) q^{47} +(-2.22786 + 1.61864i) q^{49} +(-0.965093 - 2.97025i) q^{51} +(-9.90739 - 7.19814i) q^{53} +(-5.05329 - 3.67143i) q^{57} +(2.41273 + 7.42562i) q^{59} +(-0.908612 + 0.660145i) q^{61} +(-0.541951 + 1.66795i) q^{63} -18.2462 q^{65} +9.56155 q^{67} +(-1.17666 + 3.62140i) q^{69} +(7.02604 - 5.10471i) q^{71} +(1.58313 + 4.87236i) q^{73} +(9.70820 + 7.05342i) q^{75} +(8.99878 + 6.53800i) q^{79} +(-2.16312 - 6.65740i) q^{81} +(-0.709422 + 0.515426i) q^{83} +(2.20116 - 6.77448i) q^{85} +8.00000 q^{87} +2.68466 q^{89} +(-4.94427 + 15.2169i) q^{91} +(-7.02604 + 5.10471i) q^{93} +(-4.40232 - 13.5490i) q^{95} +(-12.5896 - 9.14685i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{3} - 3 q^{5} + 2 q^{7} - 3 q^{9} + 2 q^{13} + 7 q^{15} - 4 q^{17} + 8 q^{19} - 72 q^{21} + 36 q^{23} - 3 q^{25} - 7 q^{27} + 2 q^{29} + 7 q^{31} - 14 q^{35} + 11 q^{37} - 16 q^{39} - 6 q^{41}+ \cdots - 27 q^{97}+O(q^{100}) $ 8 * q - q^3 - 3 * q^5 + 2 * q^7 - 3 * q^9 + 2 * q^13 + 7 * q^15 - 4 * q^17 + 8 * q^19 - 72 * q^21 + 36 * q^23 - 3 * q^25 - 7 * q^27 + 2 * q^29 + 7 * q^31 - 14 * q^35 + 11 * q^37 - 16 * q^39 - 6 * q^41 - 24 * q^43 - 16 * q^45 - 16 * q^47 - 22 * q^49 - 2 * q^51 - 8 * q^53 + 4 * q^57 + 5 * q^59 + 6 * q^61 + 20 * q^63 - 80 * q^65 + 60 * q^67 - 13 * q^69 + 5 * q^71 - 2 * q^73 + 24 * q^75 + 14 * q^79 + 14 * q^81 - 10 * q^83 - 6 * q^85 + 64 * q^87 - 28 * q^89 + 32 * q^91 - 5 * q^93 + 12 * q^95 - 27 * 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
$3$	−0.482546	+	1.48512i	−0.278598	+	0.857437i	0.709647	+	0.704558i	$0.248855\pi$
$3$	−0.482546	+	1.48512i	−0.278598	+	0.857437i	−0.988245	+	0.152879i	$0.951145\pi$
$4$		0			0
$5$	−2.88136	+	2.09343i	−1.28858	+	0.936210i	−0.999776	−	0.0211780i	$-0.993258\pi$
$5$	−2.88136	+	2.09343i	−1.28858	+	0.936210i	−0.288806	+	0.957388i	$0.593258\pi$
$6$		0			0
$7$	0.965093	+	2.97025i	0.364771	+	1.12265i	0.950124	+	0.311871i	$0.100956\pi$
$7$	0.965093	+	2.97025i	0.364771	+	1.12265i	−0.585354	+	0.810778i	$0.699044\pi$
$8$		0			0
$9$	0.454306	+	0.330072i	0.151435	+	0.110024i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	4.14468	+	3.01129i	1.14953	+	0.835180i	0.988418	−	0.151756i	$-0.0484928\pi$
$13$	4.14468	+	3.01129i	1.14953	+	0.835180i	0.161109	+	0.986937i	$0.448493\pi$
$14$		0			0
$15$	−1.71861	−	5.28935i	−0.443744	−	1.36570i
$16$		0			0
$17$	−1.61803	+	1.17557i	−0.392431	+	0.285118i	−0.766451	−	0.642303i	$-0.777979\pi$
$17$	−1.61803	+	1.17557i	−0.392431	+	0.285118i	0.374020	+	0.927421i	$0.377979\pi$
$18$		0			0
$19$	−1.23607	+	3.80423i	−0.283573	+	0.872749i	0.703249	+	0.710943i	$0.251732\pi$
$19$	−1.23607	+	3.80423i	−0.283573	+	0.872749i	−0.986823	+	0.161806i	$0.948268\pi$
$20$		0			0
$21$	−4.87689			−1.06423
$22$		0			0
$23$	2.43845			0.508451			0.254226	−	0.967145i	$-0.418179\pi$
$23$	2.43845			0.508451			0.254226	+	0.967145i	$0.418179\pi$
$24$		0			0
$25$	2.37469	−	7.30854i	0.474938	−	1.46171i
$26$		0			0
$27$	−4.49939	+	3.26900i	−0.865908	+	0.629119i
$28$		0			0
$29$	−1.58313	−	4.87236i	−0.293979	−	0.904775i	−0.983562	−	0.180569i	$-0.942206\pi$
$29$	−1.58313	−	4.87236i	−0.293979	−	0.904775i	0.689583	−	0.724207i	$-0.257794\pi$
$30$		0			0
$31$	4.49939	+	3.26900i	0.808114	+	0.587130i	0.913283	−	0.407325i	$-0.133538\pi$
$31$	4.49939	+	3.26900i	0.808114	+	0.587130i	−0.105169	+	0.994454i	$0.533538\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−8.99878	−	6.53800i	−1.52107	−	1.10512i
$36$		0			0
$37$	−2.33665	−	7.19146i	−0.384143	−	1.18227i	−0.937100	−	0.349060i	$-0.886501\pi$
$37$	−2.33665	−	7.19146i	−0.384143	−	1.18227i	0.552958	−	0.833209i	$-0.313499\pi$
$38$		0			0
$39$	−6.47214	+	4.70228i	−1.03637	+	0.752968i
$40$		0			0
$41$	−0.347059	+	1.06814i	−0.0542015	+	0.166815i	−0.974493	−	0.224419i	$-0.927952\pi$
$41$	−0.347059	+	1.06814i	−0.0542015	+	0.166815i	0.920291	+	0.391234i	$0.127952\pi$
$42$		0			0
$43$	−7.12311			−1.08626			−0.543132	−	0.839648i	$-0.682762\pi$
$43$	−7.12311			−1.08626			−0.543132	+	0.839648i	$0.682762\pi$
$44$		0			0
$45$	−2.00000			−0.298142
$46$		0			0
$47$	2.47214	−	7.60845i	0.360598	−	1.10981i	−0.592094	−	0.805869i	$-0.701699\pi$
$47$	2.47214	−	7.60845i	0.360598	−	1.10981i	0.952692	−	0.303938i	$-0.0983015\pi$
$48$		0			0
$49$	−2.22786	+	1.61864i	−0.318266	+	0.231234i
$50$		0			0
$51$	−0.965093	−	2.97025i	−0.135140	−	0.415918i
$52$		0			0
$53$	−9.90739	−	7.19814i	−1.36089	−	0.988741i	−0.998388	−	0.0567560i	$-0.981924\pi$
$53$	−9.90739	−	7.19814i	−1.36089	−	0.988741i	−0.362497	−	0.931985i	$-0.618076\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−5.05329	−	3.67143i	−0.669325	−	0.486293i
$58$		0			0
$59$	2.41273	+	7.42562i	0.314111	+	0.966734i	0.976119	+	0.217237i	$0.0697045\pi$
$59$	2.41273	+	7.42562i	0.314111	+	0.966734i	−0.662008	+	0.749497i	$0.730295\pi$
$60$		0			0
$61$	−0.908612	+	0.660145i	−0.116336	+	0.0845229i	−0.644432	−	0.764662i	$-0.722906\pi$
$61$	−0.908612	+	0.660145i	−0.116336	+	0.0845229i	0.528096	+	0.849185i	$0.322906\pi$
$62$		0			0
$63$	−0.541951	+	1.66795i	−0.0682793	+	0.210142i
$64$		0			0
$65$	−18.2462			−2.26316
$66$		0			0
$67$	9.56155			1.16813			0.584065	−	0.811707i	$-0.301461\pi$
$67$	9.56155			1.16813			0.584065	+	0.811707i	$0.301461\pi$
$68$		0			0
$69$	−1.17666	+	3.62140i	−0.141654	+	0.435965i
$70$		0			0
$71$	7.02604	−	5.10471i	0.833837	−	0.605818i	−0.0868052	−	0.996225i	$-0.527666\pi$
$71$	7.02604	−	5.10471i	0.833837	−	0.605818i	0.920642	+	0.390407i	$0.127666\pi$
$72$		0			0
$73$	1.58313	+	4.87236i	0.185291	+	0.570267i	0.999953	−	0.00966869i	$-0.00307769\pi$
$73$	1.58313	+	4.87236i	0.185291	+	0.570267i	−0.814662	+	0.579936i	$0.803078\pi$
$74$		0			0
$75$	9.70820	+	7.05342i	1.12101	+	0.814459i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	8.99878	+	6.53800i	1.01244	+	0.735582i	0.964720	−	0.263278i	$-0.0848038\pi$
$79$	8.99878	+	6.53800i	1.01244	+	0.735582i	0.0477221	+	0.998861i	$0.484804\pi$
$80$		0			0
$81$	−2.16312	−	6.65740i	−0.240347	−	0.739711i
$82$		0			0
$83$	−0.709422	+	0.515426i	−0.0778692	+	0.0565753i	−0.626039	−	0.779792i	$-0.715325\pi$
$83$	−0.709422	+	0.515426i	−0.0778692	+	0.0565753i	0.548170	+	0.836367i	$0.315325\pi$
$84$		0			0
$85$	2.20116	−	6.77448i	0.238749	−	0.734795i
$86$		0			0
$87$	8.00000			0.857690
$88$		0			0
$89$	2.68466			0.284573			0.142287	−	0.989825i	$-0.454555\pi$
$89$	2.68466			0.284573			0.142287	+	0.989825i	$0.454555\pi$
$90$		0			0
$91$	−4.94427	+	15.2169i	−0.518301	+	1.59516i
$92$		0			0
$93$	−7.02604	+	5.10471i	−0.728566	+	0.529334i
$94$		0			0
$95$	−4.40232	−	13.5490i	−0.451669	−	1.39009i
$96$		0			0
$97$	−12.5896	−	9.14685i	−1.27828	−	0.928722i	−0.278777	−	0.960356i	$-0.589929\pi$
$97$	−12.5896	−	9.14685i	−1.27828	−	0.928722i	−0.999500	+	0.0316339i	$0.989929\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.61803	+	1.17557i	0.161000	+	0.116974i	0.665368	−	0.746515i	$-0.268274\pi$
$101$	1.61803	+	1.17557i	0.161000	+	0.116974i	−0.504368	+	0.863489i	$0.668274\pi$
$102$		0			0
$103$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$103$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$104$		0			0
$105$	14.0521	−	10.2094i	1.37134	−	0.996338i
$106$		0			0
$107$	−4.13135	+	12.7150i	−0.399392	+	1.22920i	0.526095	+	0.850426i	$0.323655\pi$
$107$	−4.13135	+	12.7150i	−0.399392	+	1.22920i	−0.925488	+	0.378778i	$0.876345\pi$
$108$		0			0
$109$	12.2462			1.17297			0.586487	−	0.809959i	$-0.300510\pi$
$109$	12.2462			1.17297			0.586487	+	0.809959i	$0.300510\pi$
$110$		0			0
$111$	11.8078			1.12074
$112$		0			0
$113$	−0.135488	+	0.416988i	−0.0127456	+	0.0392269i	−0.957227	−	0.289338i	$-0.906565\pi$
$113$	−0.135488	+	0.416988i	−0.0127456	+	0.0392269i	0.944481	+	0.328565i	$0.106565\pi$
$114$		0			0
$115$	−7.02604	+	5.10471i	−0.655181	+	0.476017i
$116$		0			0
$117$	0.889009	+	2.73609i	0.0821889	+	0.252952i
$118$		0			0
$119$	−5.05329	−	3.67143i	−0.463234	−	0.336560i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	−1.41884	−	1.03085i	−0.127933	−	0.0929487i
$124$		0			0
$125$	2.95468	+	9.09358i	0.264275	+	0.813354i
$126$		0			0
$127$	−5.05329	+	3.67143i	−0.448407	+	0.325787i	−0.788967	−	0.614436i	$-0.789384\pi$
$127$	−5.05329	+	3.67143i	−0.448407	+	0.325787i	0.340559	+	0.940223i	$0.389384\pi$
$128$		0			0
$129$	3.43723	−	10.5787i	0.302631	−	0.931403i
$130$		0			0
$131$	13.3693			1.16808			0.584041	−	0.811724i	$-0.301471\pi$
$131$	13.3693			1.16808			0.584041	+	0.811724i	$0.301471\pi$
$132$		0			0
$133$	−12.4924			−1.08323
$134$		0			0
$135$	6.12094	−	18.8383i	0.526806	−	1.62134i
$136$		0			0
$137$	6.82685	−	4.95999i	0.583257	−	0.423761i	−0.256640	−	0.966507i	$-0.582615\pi$
$137$	6.82685	−	4.95999i	0.583257	−	0.423761i	0.839897	+	0.542746i	$0.182615\pi$
$138$		0			0
$139$	4.67330	+	14.3829i	0.396384	+	1.21994i	0.927879	+	0.372882i	$0.121631\pi$
$139$	4.67330	+	14.3829i	0.396384	+	1.21994i	−0.531495	+	0.847062i	$0.678369\pi$
$140$		0			0
$141$	10.1066	+	7.34286i	0.851128	+	0.618381i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	14.7615	+	10.7249i	1.22588	+	0.890651i
$146$		0			0
$147$	−1.32883	−	4.08972i	−0.109600	−	0.337314i
$148$		0			0
$149$	−3.43526	+	2.49586i	−0.281427	+	0.204469i	−0.719540	−	0.694451i	$-0.755647\pi$
$149$	−3.43526	+	2.49586i	−0.281427	+	0.204469i	0.438112	+	0.898920i	$0.355647\pi$
$150$		0			0
$151$	−2.89528	+	8.91075i	−0.235614	+	0.725147i	0.761425	+	0.648253i	$0.224500\pi$
$151$	−2.89528	+	8.91075i	−0.235614	+	0.725147i	−0.997039	+	0.0768934i	$0.975500\pi$
$152$		0			0
$153$	−1.12311			−0.0907977
$154$		0			0
$155$	−19.8078			−1.59100
$156$		0			0
$157$	−1.37156	+	4.22121i	−0.109462	+	0.336890i	−0.990752	−	0.135687i	$-0.956676\pi$
$157$	−1.37156	+	4.22121i	−0.109462	+	0.336890i	0.881290	+	0.472576i	$0.156676\pi$
$158$		0			0
$159$	15.4709	−	11.2403i	1.22692	−	0.891412i
$160$		0			0
$161$	2.35333	+	7.24280i	0.185468	+	0.570812i
$162$		0			0
$163$	3.23607	+	2.35114i	0.253468	+	0.184156i	0.707263	−	0.706951i	$-0.249930\pi$
$163$	3.23607	+	2.35114i	0.253468	+	0.184156i	−0.453794	+	0.891107i	$0.649930\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.47214	−	4.70228i	−0.500829	−	0.363874i	0.308505	−	0.951223i	$-0.400171\pi$
$167$	−6.47214	−	4.70228i	−0.500829	−	0.363874i	−0.809334	+	0.587349i	$0.800171\pi$
$168$		0			0
$169$	4.09330	+	12.5979i	0.314870	+	0.969069i
$170$		0			0
$171$	−1.81722	+	1.32029i	−0.138967	+	0.100965i
$172$		0			0
$173$	3.78429	−	11.6468i	0.287714	−	0.885493i	−0.697858	−	0.716236i	$-0.745863\pi$
$173$	3.78429	−	11.6468i	0.287714	−	0.885493i	0.985572	−	0.169257i	$-0.0541367\pi$
$174$		0			0
$175$	24.0000			1.81423
$176$		0			0
$177$	−12.1922			−0.916425
$178$		0			0
$179$	−1.98959	+	6.12333i	−0.148709	+	0.457679i	−0.997469	−	0.0710987i	$-0.977349\pi$
$179$	−1.98959	+	6.12333i	−0.148709	+	0.457679i	0.848760	+	0.528778i	$0.177349\pi$
$180$		0			0
$181$	1.06413	−	0.773138i	0.0790964	−	0.0574669i	−0.547534	−	0.836783i	$-0.684433\pi$
$181$	1.06413	−	0.773138i	0.0790964	−	0.0574669i	0.626631	+	0.779316i	$0.284433\pi$
$182$		0			0
$183$	−0.541951	−	1.66795i	−0.0400621	−	0.123299i
$184$		0			0
$185$	21.7875	+	15.8296i	1.60185	+	1.16381i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−14.0521	−	10.2094i	−1.02214	−	0.742627i
$190$		0			0
$191$	−3.22566	−	9.92755i	−0.233400	−	0.718333i	−0.997330	−	0.0730324i	$-0.976732\pi$
$191$	−3.22566	−	9.92755i	−0.233400	−	0.718333i	0.763929	−	0.645300i	$-0.223268\pi$
$192$		0			0
$193$	7.38075	−	5.36243i	0.531278	−	0.385996i	−0.289558	−	0.957161i	$-0.593508\pi$
$193$	7.38075	−	5.36243i	0.531278	−	0.385996i	0.820836	+	0.571165i	$0.193508\pi$
$194$		0			0
$195$	8.80464	−	27.0979i	0.630514	−	1.94052i
$196$		0			0
$197$	−14.4924			−1.03254			−0.516271	−	0.856425i	$-0.672680\pi$
$197$	−14.4924			−1.03254			−0.516271	+	0.856425i	$0.672680\pi$
$198$		0			0
$199$	−12.4924			−0.885564			−0.442782	−	0.896629i	$-0.646009\pi$
$199$	−12.4924			−0.885564			−0.442782	+	0.896629i	$0.646009\pi$
$200$		0			0
$201$	−4.61389	+	14.2001i	−0.325439	+	1.00160i
$202$		0			0
$203$	12.9443	−	9.40456i	0.908510	−	0.660071i
$204$		0			0
$205$	−1.23607	−	3.80423i	−0.0863307	−	0.265699i
$206$		0			0
$207$	1.10780	+	0.804864i	0.0769975	+	0.0559419i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−6.87051	−	4.99172i	−0.472986	−	0.343644i	0.325618	−	0.945501i	$-0.394428\pi$
$211$	−6.87051	−	4.99172i	−0.472986	−	0.343644i	−0.798604	+	0.601857i	$0.794428\pi$
$212$		0			0
$213$	4.19075	+	12.8978i	0.287145	+	0.883743i
$214$		0			0
$215$	20.5242	−	14.9117i	1.39974	−	1.01697i
$216$		0			0
$217$	−5.36741	+	16.5192i	−0.364364	+	1.12140i
$218$		0			0
$219$	−8.00000			−0.540590
$220$		0			0
$221$	−10.2462			−0.689235
$222$		0			0
$223$	−3.64880	+	11.2299i	−0.244342	+	0.752006i	0.751402	+	0.659844i	$0.229378\pi$
$223$	−3.64880	+	11.2299i	−0.244342	+	0.752006i	−0.995744	+	0.0921621i	$0.970622\pi$
$224$		0			0
$225$	3.49118	−	2.53649i	0.232746	−	0.169100i
$226$		0			0
$227$	7.14543	+	21.9914i	0.474259	+	1.45962i	0.846954	+	0.531665i	$0.178434\pi$
$227$	7.14543	+	21.9914i	0.474259	+	1.45962i	−0.372695	+	0.927954i	$0.621566\pi$
$228$		0			0
$229$	−11.8801	−	8.63143i	−0.785062	−	0.570381i	0.121432	−	0.992600i	$-0.461251\pi$
$229$	−11.8801	−	8.63143i	−0.785062	−	0.570381i	−0.906494	+	0.422219i	$0.861251\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.96190	+	4.33158i	0.390577	+	0.283771i	0.765692	−	0.643207i	$-0.222397\pi$
$233$	5.96190	+	4.33158i	0.390577	+	0.283771i	−0.375115	+	0.926978i	$0.622397\pi$
$234$		0			0
$235$	8.80464	+	27.0979i	0.574352	+	1.76767i
$236$		0			0
$237$	−14.0521	+	10.2094i	−0.912780	+	0.663174i
$238$		0			0
$239$	−1.50704	+	4.63820i	−0.0974825	+	0.300020i	−0.987893	−	0.155139i	$-0.950418\pi$
$239$	−1.50704	+	4.63820i	−0.0974825	+	0.300020i	0.890410	+	0.455159i	$0.150418\pi$
$240$		0			0
$241$	29.1231			1.87598			0.937992	−	0.346657i	$-0.112683\pi$
$241$	29.1231			1.87598			0.937992	+	0.346657i	$0.112683\pi$
$242$		0			0
$243$	−5.75379			−0.369106
$244$		0			0
$245$	3.03077	−	9.32774i	0.193629	−	0.595927i
$246$		0			0
$247$	−16.5787	+	12.0451i	−1.05488	+	0.766414i
$248$		0			0
$249$	−0.423142	−	1.30230i	−0.0268155	−	0.0825298i
$250$		0			0
$251$	−1.26332	−	0.917858i	−0.0797402	−	0.0579347i	0.547201	−	0.837001i	$-0.315693\pi$
$251$	−1.26332	−	0.917858i	−0.0797402	−	0.0579347i	−0.626941	+	0.779067i	$0.715693\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	8.99878	+	6.53800i	0.563526	+	0.409425i
$256$		0			0
$257$	3.63212	+	11.1785i	0.226565	+	0.697297i	0.998129	+	0.0611444i	$0.0194750\pi$
$257$	3.63212	+	11.1785i	0.226565	+	0.697297i	−0.771563	+	0.636152i	$0.780525\pi$
$258$		0			0
$259$	19.1054	−	13.8809i	1.18715	−	0.862515i
$260$		0			0
$261$	0.889009	−	2.73609i	0.0550283	−	0.169360i
$262$		0			0
$263$	19.1231			1.17918			0.589591	−	0.807702i	$-0.299289\pi$
$263$	19.1231			1.17918			0.589591	+	0.807702i	$0.299289\pi$
$264$		0			0
$265$	43.6155			2.67928
$266$		0			0
$267$	−1.29547	+	3.98705i	−0.0792816	+	0.244004i
$268$		0			0
$269$	16.7779	−	12.1899i	1.02297	−	0.743229i	0.0560781	−	0.998426i	$-0.482140\pi$
$269$	16.7779	−	12.1899i	1.02297	−	0.743229i	0.966889	+	0.255197i	$0.0821404\pi$
$270$		0			0
$271$	−8.80464	−	27.0979i	−0.534844	−	1.64608i	−0.743986	−	0.668195i	$-0.767067\pi$
$271$	−8.80464	−	27.0979i	−0.534844	−	1.64608i	0.209142	−	0.977885i	$-0.432933\pi$
$272$		0			0
$273$	−20.2132	−	14.6857i	−1.22336	−	0.888820i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	14.5623	+	10.5801i	0.874964	+	0.635699i	0.931914	−	0.362678i	$-0.118138\pi$
$277$	14.5623	+	10.5801i	0.874964	+	0.635699i	−0.0569502	+	0.998377i	$0.518138\pi$
$278$		0			0
$279$	0.965093	+	2.97025i	0.0577786	+	0.177824i
$280$		0			0
$281$	−13.1435	+	9.54928i	−0.784073	+	0.569662i	−0.906199	−	0.422852i	$-0.861029\pi$
$281$	−13.1435	+	9.54928i	−0.784073	+	0.569662i	0.122126	+	0.992515i	$0.461029\pi$
$282$		0			0
$283$	6.18034	−	19.0211i	0.367383	−	1.13069i	−0.581092	−	0.813838i	$-0.697374\pi$
$283$	6.18034	−	19.0211i	0.367383	−	1.13069i	0.948475	−	0.316851i	$-0.102626\pi$
$284$		0			0
$285$	22.2462			1.31775
$286$		0			0
$287$	−3.50758			−0.207046
$288$		0			0
$289$	−4.01722	+	12.3637i	−0.236307	+	0.727279i
$290$		0			0
$291$	19.6593	−	14.2833i	1.15245	−	0.837301i
$292$		0			0
$293$	−1.04118	−	3.20441i	−0.0608262	−	0.187204i	0.916026	−	0.401119i	$-0.131378\pi$
$293$	−1.04118	−	3.20441i	−0.0608262	−	0.187204i	−0.976852	+	0.213915i	$0.931378\pi$
$294$		0			0
$295$	−22.4970	−	16.3450i	−1.30982	−	0.951642i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	10.1066	+	7.34286i	0.584479	+	0.424649i
$300$		0			0
$301$	−6.87446	−	21.1574i	−0.396237	−	1.21949i
$302$		0			0
$303$	−2.52665	+	1.83572i	−0.145152	+	0.105459i
$304$		0			0
$305$	1.23607	−	3.80423i	0.0707770	−	0.217829i
$306$		0			0
$307$	−32.4924			−1.85444			−0.927220	−	0.374516i	$-0.877809\pi$
$307$	−32.4924			−1.85444			−0.927220	+	0.374516i	$0.877809\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3.01409	−	9.27640i	0.170913	−	0.526017i	−0.828510	−	0.559974i	$-0.810811\pi$
$311$	3.01409	−	9.27640i	0.170913	−	0.526017i	0.999423	+	0.0339575i	$0.0108111\pi$
$312$		0			0
$313$	7.93465	−	5.76486i	0.448493	−	0.325849i	−0.340508	−	0.940242i	$-0.610599\pi$
$313$	7.93465	−	5.76486i	0.448493	−	0.325849i	0.789000	+	0.614393i	$0.210599\pi$
$314$		0			0
$315$	−1.93019	−	5.94050i	−0.108754	−	0.334709i
$316$		0			0
$317$	11.4818	+	8.34199i	0.644880	+	0.468533i	0.861523	−	0.507718i	$-0.169511\pi$
$317$	11.4818	+	8.34199i	0.644880	+	0.468533i	−0.216643	+	0.976251i	$0.569511\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−16.8898	−	12.2711i	−0.942695	−	0.684908i
$322$		0			0
$323$	−2.47214	−	7.60845i	−0.137553	−	0.423346i
$324$		0			0
$325$	31.8504	−	23.1407i	1.76674	−	1.28362i
$326$		0			0
$327$	−5.90936	+	18.1872i	−0.326789	+	1.00575i
$328$		0			0
$329$	24.9848			1.37746
$330$		0			0
$331$	34.9309			1.91997			0.959987	−	0.280044i	$-0.0903491\pi$
$331$	34.9309			1.91997			0.959987	+	0.280044i	$0.0903491\pi$
$332$		0			0
$333$	1.31215	−	4.03839i	0.0719055	−	0.221302i
$334$		0			0
$335$	−27.5502	+	20.0164i	−1.50523	+	1.09361i
$336$		0			0
$337$	−5.17252	−	15.9194i	−0.281765	−	0.867184i	−0.987350	−	0.158558i	$-0.949315\pi$
$337$	−5.17252	−	15.9194i	−0.281765	−	0.867184i	0.705584	−	0.708626i	$-0.250685\pi$
$338$		0			0
$339$	−0.553900	−	0.402432i	−0.0300837	−	0.0218571i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	10.7287	+	7.79484i	0.579294	+	0.420882i
$344$		0			0
$345$	−4.19075	−	12.8978i	−0.225622	−	0.694394i
$346$		0			0
$347$	−18.3959	+	13.3654i	−0.987546	+	0.717494i	−0.959382	−	0.282109i	$-0.908966\pi$
$347$	−18.3959	+	13.3654i	−0.987546	+	0.717494i	−0.0281636	+	0.999603i	$0.508966\pi$
$348$		0			0
$349$	−9.96463	+	30.6680i	−0.533394	+	1.64162i	0.213699	+	0.976900i	$0.431449\pi$
$349$	−9.96463	+	30.6680i	−0.533394	+	1.64162i	−0.747093	+	0.664719i	$0.768551\pi$
$350$		0			0
$351$	−28.4924			−1.52081
$352$		0			0
$353$	−24.0540			−1.28026			−0.640132	−	0.768265i	$-0.721120\pi$
$353$	−24.0540			−1.28026			−0.640132	+	0.768265i	$0.721120\pi$
$354$		0			0
$355$	−9.55816	+	29.4170i	−0.507295	+	1.56129i
$356$		0			0
$357$	7.89098	−	5.73313i	0.417635	−	0.303430i
$358$		0			0
$359$	1.38823	+	4.27255i	0.0732682	+	0.225496i	0.980984	−	0.194090i	$-0.0621753\pi$
$359$	1.38823	+	4.27255i	0.0732682	+	0.225496i	−0.907716	+	0.419586i	$0.862175\pi$
$360$		0			0
$361$	2.42705	+	1.76336i	0.127740	+	0.0928082i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−14.7615	−	10.7249i	−0.772652	−	0.561365i
$366$		0			0
$367$	7.08603	+	21.8086i	0.369888	+	1.13840i	0.946863	+	0.321636i	$0.104233\pi$
$367$	7.08603	+	21.8086i	0.369888	+	1.13840i	−0.576976	+	0.816761i	$0.695767\pi$
$368$		0			0
$369$	−0.510233	+	0.370706i	−0.0265617	+	0.0192982i
$370$		0			0
$371$	11.8187	−	36.3743i	0.613598	−	1.88846i
$372$		0			0
$373$	−8.24621			−0.426973			−0.213486	−	0.976946i	$-0.568482\pi$
$373$	−8.24621			−0.426973			−0.213486	+	0.976946i	$0.568482\pi$
$374$		0			0
$375$	−14.9309			−0.771027
$376$		0			0
$377$	8.11053	−	24.9616i	0.417713	−	1.28559i
$378$		0			0
$379$	−0.155522	+	0.112993i	−0.00798864	+	0.00580408i	−0.591772	−	0.806105i	$-0.701572\pi$
$379$	−0.155522	+	0.112993i	−0.00798864	+	0.00580408i	0.583784	+	0.811909i	$0.301572\pi$
$380$		0			0
$381$	−3.01409	−	9.27640i	−0.154416	−	0.475245i
$382$		0			0
$383$	1.66170	+	1.20730i	0.0849090	+	0.0616900i	0.629430	−	0.777057i	$-0.283288\pi$
$383$	1.66170	+	1.20730i	0.0849090	+	0.0616900i	−0.544521	+	0.838747i	$0.683288\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.23607	−	2.35114i	−0.164499	−	0.119515i
$388$		0			0
$389$	1.10058	+	3.38724i	0.0558016	+	0.171740i	0.975073	−	0.221885i	$-0.0712209\pi$
$389$	1.10058	+	3.38724i	0.0558016	+	0.171740i	−0.919271	+	0.393625i	$0.871221\pi$
$390$		0			0
$391$	−3.94549	+	2.86657i	−0.199532	+	0.144969i
$392$		0			0
$393$	−6.45132	+	19.8551i	−0.325426	+	1.00156i
$394$		0			0
$395$	−39.6155			−1.99327
$396$		0			0
$397$	10.4924			0.526600			0.263300	−	0.964714i	$-0.415189\pi$
$397$	10.4924			0.526600			0.263300	+	0.964714i	$0.415189\pi$
$398$		0			0
$399$	6.02817	−	18.5528i	0.301786	−	0.928802i
$400$		0			0
$401$	−24.6689	+	17.9230i	−1.23191	+	0.895032i	−0.997032	−	0.0769941i	$-0.975468\pi$
$401$	−24.6689	+	17.9230i	−1.23191	+	0.895032i	−0.234874	+	0.972026i	$0.575468\pi$
$402$		0			0
$403$	8.80464	+	27.0979i	0.438590	+	1.34984i
$404$		0			0
$405$	20.1695	+	14.6540i	1.00223	+	0.728163i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−18.1968	−	13.2207i	−0.899771	−	0.653722i	0.0386358	−	0.999253i	$-0.487699\pi$
$409$	−18.1968	−	13.2207i	−0.899771	−	0.653722i	−0.938407	+	0.345531i	$0.887699\pi$
$410$		0			0
$411$	4.07194	+	12.5321i	0.200854	+	0.618165i
$412$		0			0
$413$	−19.7275	+	14.3328i	−0.970724	+	0.705273i
$414$		0			0
$415$	0.965093	−	2.97025i	0.0473745	−	0.145804i
$416$		0			0
$417$	−23.6155			−1.15646
$418$		0			0
$419$	−32.4924			−1.58736			−0.793679	−	0.608336i	$-0.791837\pi$
$419$	−32.4924			−1.58736			−0.793679	+	0.608336i	$0.791837\pi$
$420$		0			0
$421$	0.770201	−	2.37043i	0.0375373	−	0.115528i	−0.930532	−	0.366210i	$-0.880655\pi$
$421$	0.770201	−	2.37043i	0.0375373	−	0.115528i	0.968069	+	0.250683i	$0.0806550\pi$
$422$		0			0
$423$	3.63445	−	2.64058i	0.176713	−	0.128389i
$424$		0			0
$425$	4.74938	+	14.6171i	0.230379	+	0.709033i
$426$		0			0
$427$	−2.83769	−	2.06170i	−0.137325	−	0.0997728i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−21.9431	−	15.9426i	−1.05696	−	0.767926i	−0.0834362	−	0.996513i	$-0.526589\pi$
$431$	−21.9431	−	15.9426i	−1.05696	−	0.767926i	−0.973523	+	0.228587i	$0.926589\pi$
$432$		0			0
$433$	−7.00994	−	21.5744i	−0.336876	−	1.03680i	−0.965790	−	0.259324i	$-0.916500\pi$
$433$	−7.00994	−	21.5744i	−0.336876	−	1.03680i	0.628914	−	0.777475i	$-0.283500\pi$
$434$		0			0
$435$	−23.0509	+	16.7474i	−1.10520	+	0.802978i
$436$		0			0
$437$	−3.01409	+	9.27640i	−0.144183	+	0.443751i
$438$		0			0
$439$	4.49242			0.214412			0.107206	−	0.994237i	$-0.465810\pi$
$439$	4.49242			0.214412			0.107206	+	0.994237i	$0.465810\pi$
$440$		0			0
$441$	−1.54640			−0.0736380
$442$		0			0
$443$	3.49663	−	10.7615i	0.166130	−	0.511296i	−0.832988	−	0.553291i	$-0.813372\pi$
$443$	3.49663	−	10.7615i	0.166130	−	0.511296i	0.999118	+	0.0419957i	$0.0133716\pi$
$444$		0			0
$445$	−7.73546	+	5.62014i	−0.366696	+	0.266420i
$446$		0			0
$447$	−2.04899	−	6.30615i	−0.0969141	−	0.298271i
$448$		0			0
$449$	29.5667	+	21.4814i	1.39534	+	1.01377i	0.995256	+	0.0972917i	$0.0310180\pi$
$449$	29.5667	+	21.4814i	1.39534	+	1.01377i	0.400081	+	0.916480i	$0.368982\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−11.8365	−	8.59970i	−0.556126	−	0.404049i
$454$		0			0
$455$	−17.6093	−	54.1958i	−0.825536	−	2.54074i
$456$		0			0
$457$	−19.3046	+	14.0256i	−0.903029	+	0.656089i	−0.939242	−	0.343255i	$-0.888470\pi$
$457$	−19.3046	+	14.0256i	−0.903029	+	0.656089i	0.0362133	+	0.999344i	$0.488470\pi$
$458$		0			0
$459$	3.43723	−	10.5787i	0.160436	−	0.493772i
$460$		0			0
$461$	1.12311			0.0523082			0.0261541	−	0.999658i	$-0.491674\pi$
$461$	1.12311			0.0523082			0.0261541	+	0.999658i	$0.491674\pi$
$462$		0			0
$463$	15.3153			0.711764			0.355882	−	0.934531i	$-0.384180\pi$
$463$	15.3153			0.711764			0.355882	+	0.934531i	$0.384180\pi$
$464$		0			0
$465$	9.55816	−	29.4170i	0.443249	−	1.36418i
$466$		0			0
$467$	−22.8953	+	16.6344i	−1.05947	+	0.769750i	−0.973990	−	0.226590i	$-0.927242\pi$
$467$	−22.8953	+	16.6344i	−1.05947	+	0.769750i	−0.0854794	+	0.996340i	$0.527242\pi$
$468$		0			0
$469$	9.22778	+	28.4002i	0.426100	+	1.31140i
$470$		0			0
$471$	−5.60719	−	4.07386i	−0.258366	−	0.187714i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	24.8681	+	18.0677i	1.14103	+	0.829004i
$476$		0			0
$477$	−2.12508	−	6.54032i	−0.0973006	−	0.299460i
$478$		0			0
$479$	12.9443	−	9.40456i	0.591439	−	0.429705i	−0.251391	−	0.967886i	$-0.580888\pi$
$479$	12.9443	−	9.40456i	0.591439	−	0.429705i	0.842830	+	0.538180i	$0.180888\pi$
$480$		0			0
$481$	11.9709	−	36.8426i	0.545826	−	1.67988i
$482$		0			0
$483$	−11.8920			−0.541107
$484$		0			0
$485$	55.4233			2.51664
$486$		0			0
$487$	4.61389	−	14.2001i	0.209075	−	0.643468i	−0.790446	−	0.612532i	$-0.790151\pi$
$487$	4.61389	−	14.2001i	0.209075	−	0.643468i	0.999521	−	0.0309362i	$-0.00984886\pi$
$488$		0			0
$489$	−5.05329	+	3.67143i	−0.228518	+	0.166028i
$490$		0			0
$491$	4.25015	+	13.0806i	0.191807	+	0.590321i	0.999999	+	0.00140182i	$0.000446213\pi$
$491$	4.25015	+	13.0806i	0.191807	+	0.590321i	−0.808192	+	0.588919i	$0.799554\pi$
$492$		0			0
$493$	8.28936	+	6.02257i	0.373334	+	0.271243i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	21.9431	+	15.9426i	0.984280	+	0.715122i
$498$		0			0
$499$	−8.95681	−	27.5662i	−0.400962	−	1.23403i	−0.924220	−	0.381860i	$-0.875284\pi$
$499$	−8.95681	−	27.5662i	−0.400962	−	1.23403i	0.523258	−	0.852174i	$-0.324716\pi$
$500$		0			0
$501$	10.1066	−	7.34286i	0.451529	−	0.328055i
$502$		0			0
$503$	−9.76974	+	30.0682i	−0.435611	+	1.34067i	0.456848	+	0.889545i	$0.348978\pi$
$503$	−9.76974	+	30.0682i	−0.435611	+	1.34067i	−0.892459	+	0.451128i	$0.851022\pi$
$504$		0			0
$505$	−7.12311			−0.316974
$506$		0			0
$507$	−20.6847			−0.918638
$508$		0			0
$509$	−5.65507	+	17.4045i	−0.250657	+	0.771441i	0.743998	+	0.668182i	$0.232927\pi$
$509$	−5.65507	+	17.4045i	−0.250657	+	0.771441i	−0.994654	+	0.103260i	$0.967073\pi$
$510$		0			0
$511$	−12.9443	+	9.40456i	−0.572621	+	0.416033i
$512$		0			0
$513$	−6.87446	−	21.1574i	−0.303515	−	0.934122i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	15.4709	+	11.2403i	0.679098	+	0.493394i
$520$		0			0
$521$	0.406463	+	1.25096i	0.0178075	+	0.0548057i	0.959565	−	0.281486i	$-0.0908272\pi$
$521$	0.406463	+	1.25096i	0.0178075	+	0.0548057i	−0.941758	+	0.336292i	$0.890827\pi$
$522$		0			0
$523$	9.70820	−	7.05342i	0.424510	−	0.308425i	−0.354940	−	0.934889i	$-0.615499\pi$
$523$	9.70820	−	7.05342i	0.424510	−	0.308425i	0.779450	+	0.626464i	$0.215499\pi$
$524$		0			0
$525$	−11.5811	+	35.6430i	−0.505441	+	1.55559i
$526$		0			0
$527$	−11.1231			−0.484530
$528$		0			0
$529$	−17.0540			−0.741477
$530$		0			0
$531$	−1.35488	+	4.16988i	−0.0587966	+	0.180957i
$532$		0			0
$533$	−4.65491	+	3.38199i	−0.201627	+	0.146490i
$534$		0			0
$535$	−14.7140	−	45.2851i	−0.636142	−	1.95784i
$536$		0			0
$537$	−8.13384	−	5.90958i	−0.351001	−	0.255017i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	19.3046	+	14.0256i	0.829968	+	0.603007i	0.919550	−	0.392973i	$-0.128553\pi$
$541$	19.3046	+	14.0256i	0.829968	+	0.603007i	−0.0895826	+	0.995979i	$0.528553\pi$
$542$		0			0
$543$	0.634713	+	1.95345i	0.0272382	+	0.0838304i
$544$		0			0
$545$	−35.2857	+	25.6366i	−1.51147	+	1.09815i
$546$		0			0
$547$	−13.0548	+	40.1785i	−0.558183	+	1.71791i	0.129203	+	0.991618i	$0.458758\pi$
$547$	−13.0548	+	40.1785i	−0.558183	+	1.71791i	−0.687386	+	0.726292i	$0.741242\pi$
$548$		0			0
$549$	−0.630683			−0.0269169
$550$		0			0
$551$	20.4924			0.873007
$552$		0			0
$553$	−10.7348	+	33.0384i	−0.456491	+	1.40494i
$554$		0			0
$555$	−34.0224	+	24.7187i	−1.44417	+	1.04925i
$556$		0			0
$557$	−1.15998	−	3.57007i	−0.0491501	−	0.151269i	0.923469	−	0.383673i	$-0.125341\pi$
$557$	−1.15998	−	3.57007i	−0.0491501	−	0.151269i	−0.972619	+	0.232404i	$0.925341\pi$
$558$		0			0
$559$	−29.5230	−	21.4497i	−1.24869	−	0.907226i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−19.8148	−	14.3963i	−0.835094	−	0.606731i	0.0859021	−	0.996304i	$-0.472623\pi$
$563$	−19.8148	−	14.3963i	−0.835094	−	0.606731i	−0.920996	+	0.389573i	$0.872623\pi$
$564$		0			0
$565$	−0.482546	−	1.48512i	−0.0203009	−	0.0624797i
$566$		0			0
$567$	17.6865	−	12.8500i	0.742764	−	0.539650i
$568$		0			0
$569$	−8.30542	+	25.5614i	−0.348181	+	1.07159i	0.611677	+	0.791107i	$0.290495\pi$
$569$	−8.30542	+	25.5614i	−0.348181	+	1.07159i	−0.959859	+	0.280484i	$0.909505\pi$
$570$		0			0
$571$	16.4924			0.690186			0.345093	−	0.938568i	$-0.387847\pi$
$571$	16.4924			0.690186			0.345093	+	0.938568i	$0.387847\pi$
$572$		0			0
$573$	16.3002			0.680950
$574$		0			0
$575$	5.79056	−	17.8215i	0.241483	−	0.743208i
$576$		0			0
$577$	−12.5896	+	9.14685i	−0.524110	+	0.380788i	−0.818150	−	0.575005i	$-0.805000\pi$
$577$	−12.5896	+	9.14685i	−0.524110	+	0.380788i	0.294040	+	0.955793i	$0.405000\pi$
$578$		0			0
$579$	4.40232	+	13.5490i	0.182954	+	0.563075i
$580$		0			0
$581$	−2.21560	−	1.60973i	−0.0919186	−	0.0667828i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−8.28936	−	6.02257i	−0.342723	−	0.249003i
$586$		0			0
$587$	−7.56857	−	23.2937i	−0.312389	−	0.961433i	−0.976816	−	0.214080i	$-0.931325\pi$
$587$	−7.56857	−	23.2937i	−0.312389	−	0.961433i	0.664428	−	0.747353i	$-0.268675\pi$
$588$		0			0
$589$	−17.9976	+	13.0760i	−0.741577	+	0.538787i
$590$		0			0
$591$	6.99327	−	21.5231i	0.287665	−	0.885340i
$592$		0			0
$593$	3.36932			0.138361			0.0691806	−	0.997604i	$-0.477962\pi$
$593$	3.36932			0.138361			0.0691806	+	0.997604i	$0.477962\pi$
$594$		0			0
$595$	22.2462			0.912006
$596$		0			0
$597$	6.02817	−	18.5528i	0.246717	−	0.759316i
$598$		0			0
$599$	12.9443	−	9.40456i	0.528889	−	0.384260i	−0.291053	−	0.956707i	$-0.594006\pi$
$599$	12.9443	−	9.40456i	0.528889	−	0.384260i	0.819942	+	0.572447i	$0.194006\pi$
$600$		0			0
$601$	1.15998	+	3.57007i	0.0473168	+	0.145626i	0.971924	−	0.235297i	$-0.0756063\pi$
$601$	1.15998	+	3.57007i	0.0473168	+	0.145626i	−0.924607	+	0.380923i	$0.875606\pi$
$602$		0			0
$603$	4.34387	+	3.15601i	0.176896	+	0.128522i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	37.1029	+	26.9569i	1.50596	+	1.09414i	0.967930	+	0.251220i	$0.0808318\pi$
$607$	37.1029	+	26.9569i	1.50596	+	1.09414i	0.538031	+	0.842925i	$0.319168\pi$
$608$		0			0
$609$	7.72074	+	23.7620i	0.312860	+	0.962885i
$610$		0			0
$611$	33.1574	−	24.0903i	1.34141	−	0.974589i
$612$		0			0
$613$	3.66548	−	11.2812i	0.148047	−	0.455643i	−0.849343	−	0.527841i	$-0.823002\pi$
$613$	3.66548	−	11.2812i	0.148047	−	0.455643i	0.997390	+	0.0721986i	$0.0230015\pi$
$614$		0			0
$615$	6.24621			0.251872
$616$		0			0
$617$	−2.49242			−0.100341			−0.0501706	−	0.998741i	$-0.515976\pi$
$617$	−2.49242			−0.100341			−0.0501706	+	0.998741i	$0.515976\pi$
$618$		0			0
$619$	5.84996	−	18.0043i	0.235130	−	0.723655i	−0.761974	−	0.647607i	$-0.775770\pi$
$619$	5.84996	−	18.0043i	0.235130	−	0.723655i	0.997104	−	0.0760479i	$-0.0242302\pi$
$620$		0			0
$621$	−10.9715	+	7.97128i	−0.440272	+	0.319876i
$622$		0			0
$623$	2.59094	+	7.97411i	0.103804	+	0.319476i
$624$		0			0
$625$	3.53485	+	2.56822i	0.141394	+	0.102729i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	12.2348	+	8.88914i	0.487835	+	0.354433i
$630$		0			0
$631$	−12.9954	−	39.9957i	−0.517338	−	1.59220i	−0.778987	−	0.627041i	$-0.784266\pi$
$631$	−12.9954	−	39.9957i	−0.517338	−	1.59220i	0.261648	−	0.965163i	$-0.415734\pi$
$632$		0			0
$633$	10.7287	−	7.79484i	0.426426	−	0.309817i
$634$		0			0
$635$	6.87446	−	21.1574i	0.272805	−	0.839606i
$636$		0			0
$637$	−14.1080			−0.558977
$638$		0			0
$639$	4.87689			0.192927
$640$		0			0
$641$	−14.3075	+	44.0341i	−0.565114	+	1.73924i	0.102498	+	0.994733i	$0.467316\pi$
$641$	−14.3075	+	44.0341i	−0.565114	+	1.73924i	−0.667612	+	0.744509i	$0.732684\pi$
$642$		0			0
$643$	7.42441	−	5.39415i	0.292790	−	0.212725i	−0.431687	−	0.902024i	$-0.642081\pi$
$643$	7.42441	−	5.39415i	0.292790	−	0.212725i	0.724477	+	0.689299i	$0.242081\pi$
$644$		0			0
$645$	12.2419	+	37.6766i	0.482023	+	1.48351i
$646$		0			0
$647$	−10.9715	−	7.97128i	−0.431335	−	0.313383i	0.350847	−	0.936433i	$-0.385894\pi$
$647$	−10.9715	−	7.97128i	−0.431335	−	0.313383i	−0.782183	+	0.623049i	$0.785894\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−21.9431	−	15.9426i	−0.860016	−	0.624838i
$652$		0			0
$653$	10.8703	+	33.4554i	0.425388	+	1.30921i	0.902622	+	0.430434i	$0.141640\pi$
$653$	10.8703	+	33.4554i	0.425388	+	1.30921i	−0.477234	+	0.878776i	$0.658360\pi$
$654$		0			0
$655$	−38.5218	+	27.9877i	−1.50517	+	1.09357i
$656$		0			0
$657$	−0.889009	+	2.73609i	−0.0346836	+	0.106745i
$658$		0			0
$659$	−11.6155			−0.452477			−0.226238	−	0.974072i	$-0.572643\pi$
$659$	−11.6155			−0.452477			−0.226238	+	0.974072i	$0.572643\pi$
$660$		0			0
$661$	41.8078			1.62613			0.813067	−	0.582170i	$-0.197796\pi$
$661$	41.8078			1.62613			0.813067	+	0.582170i	$0.197796\pi$
$662$		0			0
$663$	4.94427	−	15.2169i	0.192020	−	0.590976i
$664$		0			0
$665$	35.9951	−	26.1520i	1.39583	−	1.01413i
$666$		0			0
$667$	−3.86037	−	11.8810i	−0.149474	−	0.460034i
$668$		0			0
$669$	−14.9170	−	10.8378i	−0.576725	−	0.419015i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−26.8845	−	19.5327i	−1.03632	−	0.752931i	−0.0667569	−	0.997769i	$-0.521265\pi$
$673$	−26.8845	−	19.5327i	−1.03632	−	0.752931i	−0.969564	+	0.244838i	$0.921265\pi$
$674$		0			0
$675$	13.2070	+	40.6469i	0.508336	+	1.56450i
$676$		0			0
$677$	16.7779	−	12.1899i	0.644827	−	0.468494i	−0.216678	−	0.976243i	$-0.569522\pi$
$677$	16.7779	−	12.1899i	0.644827	−	0.468494i	0.861505	+	0.507749i	$0.169522\pi$
$678$		0			0
$679$	15.0183	−	46.2217i	0.576351	−	1.77383i
$680$		0			0
$681$	−36.1080			−1.38366
$682$		0			0
$683$	6.73863			0.257847			0.128923	−	0.991655i	$-0.458848\pi$
$683$	6.73863			0.257847			0.128923	+	0.991655i	$0.458848\pi$
$684$		0			0
$685$	−9.28719	+	28.5830i	−0.354845	+	1.09210i
$686$		0			0
$687$	18.5515	−	13.4784i	0.707782	−	0.514234i
$688$		0			0
$689$	−19.3873	−	59.6680i	−0.738597	−	2.27317i
$690$		0			0
$691$	8.04650	+	5.84613i	0.306103	+	0.222397i	0.730223	−	0.683209i	$-0.239416\pi$
$691$	8.04650	+	5.84613i	0.306103	+	0.222397i	−0.424119	+	0.905606i	$0.639416\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−43.5751	−	31.6591i	−1.65290	−	1.20090i
$696$		0			0
$697$	−0.694117	−	2.13627i	−0.0262916	−	0.0809171i
$698$		0			0
$699$	−9.30983	+	6.76398i	−0.352130	+	0.255837i
$700$		0			0
$701$	15.6030	−	48.0211i	0.589318	−	1.81373i	0.00812617	−	0.999967i	$-0.497413\pi$
$701$	15.6030	−	48.0211i	0.589318	−	1.81373i	0.581192	−	0.813767i	$-0.302587\pi$
$702$		0			0
$703$	30.2462			1.14076
$704$		0			0
$705$	−44.4924			−1.67568
$706$		0			0
$707$	−1.93019	+	5.94050i	−0.0725921	+	0.223415i
$708$		0			0
$709$	−1.77356	+	1.28856i	−0.0666073	+	0.0483930i	−0.620591	−	0.784135i	$-0.713107\pi$
$709$	−1.77356	+	1.28856i	−0.0666073	+	0.0483930i	0.553983	+	0.832528i	$0.313107\pi$
$710$		0			0
$711$	1.93019	+	5.94050i	0.0723876	+	0.222786i
$712$		0			0
$713$	10.9715	+	7.97128i	0.410887	+	0.298527i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−6.16109	−	4.47630i	−0.230090	−	0.167170i
$718$		0			0
$719$	10.9464	+	33.6896i	0.408232	+	1.25641i	0.918166	+	0.396195i	$0.129670\pi$
$719$	10.9464	+	33.6896i	0.408232	+	1.25641i	−0.509935	+	0.860213i	$0.670330\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−14.0532	+	43.2515i	−0.522646	+	1.60854i
$724$		0			0
$725$	−39.3693			−1.46214
$726$		0			0
$727$	−23.3153			−0.864718			−0.432359	−	0.901702i	$-0.642319\pi$
$727$	−23.3153			−0.864718			−0.432359	+	0.901702i	$0.642319\pi$
$728$		0			0
$729$	9.26583	−	28.5173i	0.343179	−	1.05620i
$730$		0			0
$731$	11.5254	−	8.37371i	0.426283	−	0.309713i
$732$		0			0
$733$	0.347059	+	1.06814i	0.0128189	+	0.0394525i	0.957261	−	0.289224i	$-0.0933973\pi$
$733$	0.347059	+	1.06814i	0.0128189	+	0.0394525i	−0.944442	+	0.328677i	$0.893397\pi$
$734$		0			0
$735$	12.3904	+	9.00213i	0.457026	+	0.332049i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	2.12827	+	1.54628i	0.0782896	+	0.0568807i	0.626242	−	0.779629i	$-0.284592\pi$
$739$	2.12827	+	1.54628i	0.0782896	+	0.0568807i	−0.547952	+	0.836510i	$0.684592\pi$
$740$		0			0
$741$	−9.88854	−	30.4338i	−0.363265	−	1.11801i
$742$		0			0
$743$	−8.68774	+	6.31201i	−0.318722	+	0.231565i	−0.735630	−	0.677384i	$-0.763114\pi$
$743$	−8.68774	+	6.31201i	−0.318722	+	0.231565i	0.416908	+	0.908949i	$0.363114\pi$
$744$		0			0
$745$	4.67330	−	14.3829i	0.171216	−	0.526950i
$746$		0			0
$747$	−0.492423			−0.0180168
$748$		0			0
$749$	−41.7538			−1.52565
$750$		0			0
$751$	1.71861	−	5.28935i	0.0627131	−	0.193011i	−0.914791	−	0.403928i	$-0.867645\pi$
$751$	1.71861	−	5.28935i	0.0627131	−	0.193011i	0.977504	+	0.210916i	$0.0676448\pi$
$752$		0			0
$753$	1.97275	−	1.43328i	0.0718908	−	0.0522317i
$754$		0			0
$755$	−10.3117	−	31.7361i	−0.375281	−	1.15500i
$756$		0			0
$757$	−12.7451	−	9.25984i	−0.463228	−	0.336555i	0.331568	−	0.943431i	$-0.392422\pi$
$757$	−12.7451	−	9.25984i	−0.463228	−	0.336555i	−0.794796	+	0.606876i	$0.792422\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−4.14468	−	3.01129i	−0.150245	−	0.109159i	0.510123	−	0.860101i	$-0.329600\pi$
$761$	−4.14468	−	3.01129i	−0.150245	−	0.109159i	−0.660368	+	0.750942i	$0.729600\pi$
$762$		0			0
$763$	11.8187	+	36.3743i	0.427867	+	1.31684i
$764$		0			0
$765$	3.23607	−	2.35114i	0.117000	−	0.0850057i
$766$		0			0
$767$	−12.3607	+	38.0423i	−0.446318	+	1.37363i
$768$		0			0
$769$	25.6155			0.923720			0.461860	−	0.886953i	$-0.347182\pi$
$769$	25.6155			0.923720			0.461860	+	0.886953i	$0.347182\pi$
$770$		0			0
$771$	−18.3542			−0.661009
$772$		0			0
$773$	12.5889	−	38.7447i	0.452792	−	1.39355i	−0.420915	−	0.907100i	$-0.638291\pi$
$773$	12.5889	−	38.7447i	0.452792	−	1.39355i	0.873708	−	0.486452i	$-0.161709\pi$
$774$		0			0
$775$	34.5763	−	25.1211i	1.24202	−	0.902378i
$776$		0			0
$777$	11.3956	+	35.0720i	0.408814	+	1.25820i
$778$		0			0
$779$	−3.63445	−	2.64058i	−0.130218	−	0.0946086i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	23.0509	+	16.7474i	0.823770	+	0.598504i
$784$		0			0
$785$	−4.88487	−	15.0341i	−0.174348	−	0.536589i
$786$		0			0
$787$	24.0713	−	17.4888i	0.858050	−	0.623410i	−0.0693038	−	0.997596i	$-0.522078\pi$
$787$	24.0713	−	17.4888i	0.858050	−	0.623410i	0.927354	+	0.374186i	$0.122078\pi$
$788$		0			0
$789$	−9.22778	+	28.4002i	−0.328518	+	1.01107i
$790$		0			0
$791$	−1.36932			−0.0486873
$792$		0			0
$793$	−5.75379			−0.204323
$794$		0			0
$795$	−21.0465	+	64.7745i	−0.746443	+	2.29732i
$796$		0			0
$797$	11.4818	−	8.34199i	0.406705	−	0.295488i	−0.365562	−	0.930787i	$-0.619123\pi$
$797$	11.4818	−	8.34199i	0.406705	−	0.295488i	0.772266	+	0.635299i	$0.219123\pi$
$798$		0			0
$799$	4.94427	+	15.2169i	0.174916	+	0.538335i
$800$		0			0
$801$	1.21966	+	0.886132i	0.0430944	+	0.0313099i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−21.9431	−	15.9426i	−0.773391	−	0.561901i
$806$		0			0
$807$	10.0074	+	30.7995i	0.352275	+	1.08419i
$808$		0			0
$809$	36.9037	−	26.8121i	1.29747	−	0.942664i	0.297539	−	0.954710i	$-0.403834\pi$
$809$	36.9037	−	26.8121i	1.29747	−	0.942664i	0.999927	+	0.0120453i	$0.00383422\pi$
$810$		0			0
$811$	−2.20116	+	6.77448i	−0.0772932	+	0.237884i	−0.982236	−	0.187649i	$-0.939913\pi$
$811$	−2.20116	+	6.77448i	−0.0772932	+	0.237884i	0.904943	+	0.425533i	$0.139913\pi$
$812$		0			0
$813$	44.4924			1.56042
$814$		0			0
$815$	−14.2462			−0.499023
$816$		0			0
$817$	8.80464	−	27.0979i	0.308035	−	0.948036i
$818$		0			0
$819$	−7.26889	+	5.28116i	−0.253996	+	0.184539i
$820$		0			0
$821$	−13.2830	−	40.8810i	−0.463582	−	1.42676i	−0.860758	−	0.509015i	$-0.830010\pi$
$821$	−13.2830	−	40.8810i	−0.463582	−	1.42676i	0.397176	−	0.917742i	$-0.369990\pi$
$822$		0			0
$823$	44.1290	+	32.0616i	1.53824	+	1.11760i	0.951428	+	0.307872i	$0.0996169\pi$
$823$	44.1290	+	32.0616i	1.53824	+	1.11760i	0.586811	+	0.809724i	$0.300383\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−31.3402	−	22.7700i	−1.08981	−	0.791790i	−0.110440	−	0.993883i	$-0.535226\pi$
$827$	−31.3402	−	22.7700i	−1.08981	−	0.791790i	−0.979366	+	0.202092i	$0.935226\pi$
$828$		0			0
$829$	4.65662	+	14.3316i	0.161731	+	0.497757i	0.998781	−	0.0493702i	$-0.0157214\pi$
$829$	4.65662	+	14.3316i	0.161731	+	0.497757i	−0.837050	+	0.547127i	$0.815721\pi$
$830$		0			0
$831$	−22.7398	+	16.5214i	−0.788835	+	0.573122i
$832$		0			0
$833$	1.70194	−	5.23802i	0.0589686	−	0.181487i
$834$		0			0
$835$	28.4924			0.986021
$836$		0			0
$837$	−30.9309			−1.06913
$838$		0			0
$839$	−6.12094	+	18.8383i	−0.211318	+	0.650370i	0.788076	+	0.615577i	$0.211077\pi$
$839$	−6.12094	+	18.8383i	−0.211318	+	0.650370i	−0.999395	+	0.0347930i	$0.988923\pi$
$840$		0			0
$841$	2.22786	−	1.61864i	0.0768228	−	0.0558150i
$842$		0			0
$843$	−7.83955	−	24.1277i	−0.270008	−	0.831001i
$844$		0			0
$845$	−38.1671	−	27.7300i	−1.31299	−	0.953941i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	25.2665	+	18.3572i	0.867142	+	0.630016i
$850$		0			0
$851$	−5.69779	−	17.5360i	−0.195318	−	0.601127i
$852$		0			0
$853$	37.6132	−	27.3276i	1.28785	−	0.935678i	0.288090	−	0.957603i	$-0.406980\pi$
$853$	37.6132	−	27.3276i	1.28785	−	0.935678i	0.999760	+	0.0219254i	$0.00697962\pi$
$854$		0			0
$855$	2.47214	−	7.60845i	0.0845453	−	0.260204i
$856$		0			0
$857$	30.1080			1.02847			0.514234	−	0.857650i	$-0.328076\pi$
$857$	30.1080			1.02847			0.514234	+	0.857650i	$0.328076\pi$
$858$		0			0
$859$	30.0540			1.02543			0.512714	−	0.858559i	$-0.328640\pi$
$859$	30.0540			1.02543			0.512714	+	0.858559i	$0.328640\pi$
$860$		0			0
$861$	1.69257	−	5.20919i	0.0576826	−	0.177529i
$862$		0			0
$863$	29.5230	−	21.4497i	1.00497	−	0.730157i	0.0418253	−	0.999125i	$-0.486683\pi$
$863$	29.5230	−	21.4497i	1.00497	−	0.730157i	0.963149	+	0.268968i	$0.0866827\pi$
$864$		0			0
$865$	13.4779	+	41.4808i	0.458264	+	1.41039i
$866$		0			0
$867$	−16.4232	−	11.9322i	−0.557761	−	0.405237i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	39.6296	+	28.7926i	1.34280	+	0.975599i
$872$		0			0
$873$	−2.70039	−	8.31093i	−0.0913942	−	0.281283i
$874$		0			0
$875$	−24.1587	+	17.5523i	−0.816712	+	0.593376i
$876$		0			0
$877$	17.1101	−	52.6593i	0.577766	−	1.77818i	−0.0487968	−	0.998809i	$-0.515539\pi$
$877$	17.1101	−	52.6593i	0.577766	−	1.77818i	0.626563	−	0.779371i	$-0.284461\pi$
$878$		0			0
$879$	5.26137			0.177461
$880$		0			0
$881$	34.3002			1.15560			0.577801	−	0.816177i	$-0.303911\pi$
$881$	34.3002			1.15560			0.577801	+	0.816177i	$0.303911\pi$
$882$		0			0
$883$	2.62430	−	8.07677i	0.0883148	−	0.271805i	−0.897139	−	0.441748i	$-0.854358\pi$
$883$	2.62430	−	8.07677i	0.0883148	−	0.271805i	0.985454	+	0.169943i	$0.0543584\pi$
$884$		0			0
$885$	35.1302	−	25.5236i	1.18089	−	0.857965i
$886$		0			0
$887$	9.76974	+	30.0682i	0.328036	+	1.00959i	0.970052	+	0.242899i	$0.0780982\pi$
$887$	9.76974	+	30.0682i	0.328036	+	1.00959i	−0.642016	+	0.766691i	$0.721902\pi$
$888$		0			0
$889$	−15.7820	−	11.4663i	−0.529310	−	0.384566i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	25.8885	+	18.8091i	0.866327	+	0.629423i
$894$		0			0
$895$	−7.08603	−	21.8086i	−0.236860	−	0.728980i
$896$		0			0
$897$	−15.7820	+	11.4663i	−0.526944	+	0.382847i
$898$		0			0
$899$	8.80464	−	27.0979i	0.293651	−	0.903766i
$900$		0			0
$901$	24.4924			0.815961
$902$		0			0
$903$	34.7386			1.15603
$904$		0			0
$905$	−1.44764	+	4.45537i	−0.0481212	+	0.148102i
$906$		0			0
$907$	−13.3427	+	9.69400i	−0.443035	+	0.321884i	−0.786840	−	0.617157i	$-0.788284\pi$
$907$	−13.3427	+	9.69400i	−0.443035	+	0.321884i	0.343804	+	0.939041i	$0.388284\pi$
$908$		0			0
$909$	0.347059	+	1.06814i	0.0115112	+	0.0354279i
$910$		0			0
$911$	21.6320	+	15.7166i	0.716700	+	0.520713i	0.885328	−	0.464966i	$-0.153934\pi$
$911$	21.6320	+	15.7166i	0.716700	+	0.520713i	−0.168628	+	0.985680i	$0.553934\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	5.05329	+	3.67143i	0.167057	+	0.121374i
$916$		0			0
$917$	12.9026	+	39.7102i	0.426082	+	1.31135i
$918$		0			0
$919$	−5.36434	+	3.89742i	−0.176953	+	0.128564i	−0.672736	−	0.739882i	$-0.734881\pi$
$919$	−5.36434	+	3.89742i	−0.176953	+	0.128564i	0.495783	+	0.868446i	$0.334881\pi$
$920$		0			0
$921$	15.6791	−	48.2553i	0.516644	−	1.59007i
$922$		0			0
$923$	44.4924			1.46449
$924$		0			0
$925$	−58.1080			−1.91058
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−37.6132	+	27.3276i	−1.23405	+	0.896588i	−0.997187	−	0.0749554i	$-0.976119\pi$
$929$	−37.6132	+	27.3276i	−1.23405	+	0.896588i	−0.236861	+	0.971544i	$0.576119\pi$
$930$		0			0
$931$	−3.40387	−	10.4760i	−0.111557	−	0.343338i
$932$		0			0
$933$	12.3222	+	8.95259i	0.403410	+	0.293095i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	34.0660	+	24.7504i	1.11289	+	0.808561i	0.983116	−	0.182982i	$-0.0585751\pi$
$937$	34.0660	+	24.7504i	1.11289	+	0.808561i	0.129773	+	0.991544i	$0.458575\pi$
$938$		0			0
$939$	4.73270	+	14.5658i	0.154446	+	0.475335i
$940$		0			0
$941$	26.0877	−	18.9538i	0.850436	−	0.617878i	−0.0748304	−	0.997196i	$-0.523842\pi$
$941$	26.0877	−	18.9538i	0.850436	−	0.617878i	0.925266	+	0.379319i	$0.123842\pi$
$942$		0			0
$943$	−0.846284	+	2.60460i	−0.0275588	+	0.0848173i
$944$		0			0
$945$	61.8617			2.01236
$946$		0			0
$947$	−12.6847			−0.412196			−0.206098	−	0.978531i	$-0.566077\pi$
$947$	−12.6847			−0.412196			−0.206098	+	0.978531i	$0.566077\pi$
$948$		0			0
$949$	−8.11053	+	24.9616i	−0.263279	+	0.810289i
$950$		0			0
$951$	−17.9294	+	13.0265i	−0.581400	+	0.422412i
$952$		0			0
$953$	0.0760835	+	0.234161i	0.00246459	+	0.00758521i	0.952281	−	0.305222i	$-0.0987306\pi$
$953$	0.0760835	+	0.234161i	0.00246459	+	0.00758521i	−0.949817	+	0.312807i	$0.898731\pi$
$954$		0			0
$955$	30.0769	+	21.8521i	0.973265	+	0.707119i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	21.3210	+	15.4906i	0.688490	+	0.500217i
$960$		0			0
$961$	−0.0213624	−	0.0657468i	−0.000689111	−	0.00212087i
$962$		0			0
$963$	−6.07376	+	4.41284i	−0.195724	+	0.142202i
$964$		0			0
$965$	−10.0407	+	30.9021i	−0.323222	+	0.994775i
$966$		0			0
$967$	8.00000			0.257263			0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000			0.257263			0.128631	+	0.991692i	$0.458942\pi$
$968$		0			0
$969$	12.4924			0.401314
$970$		0			0
$971$	−10.6754	+	32.8556i	−0.342591	+	1.05439i	0.620270	+	0.784388i	$0.287023\pi$
$971$	−10.6754	+	32.8556i	−0.342591	+	1.05439i	−0.962861	+	0.269998i	$0.912977\pi$
$972$		0			0
$973$	−38.2107	+	27.7617i	−1.22498	+	0.890000i
$974$		0			0
$975$	18.9975	+	58.4684i	0.608408	+	1.87249i
$976$		0			0
$977$	−43.5314	−	31.6274i	−1.39269	−	1.01185i	−0.995564	−	0.0940876i	$-0.970007\pi$
$977$	−43.5314	−	31.6274i	−1.39269	−	1.01185i	−0.397129	−	0.917763i	$-0.629993\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	5.56352	+	4.04214i	0.177630	+	0.129056i
$982$		0			0
$983$	9.55816	+	29.4170i	0.304858	+	0.938257i	0.979730	+	0.200322i	$0.0641988\pi$
$983$	9.55816	+	29.4170i	0.304858	+	0.938257i	−0.674872	+	0.737935i	$0.735801\pi$
$984$		0			0
$985$	41.7578	−	30.3388i	1.33052	−	0.966676i
$986$		0			0
$987$	−12.0563	+	37.1056i	−0.383758	+	1.18108i
$988$		0			0
$989$	−17.3693			−0.552312
$990$		0			0
$991$	−4.49242			−0.142707			−0.0713533	−	0.997451i	$-0.522732\pi$
$991$	−4.49242			−0.142707			−0.0713533	+	0.997451i	$0.522732\pi$
$992$		0			0
$993$	−16.8558	+	51.8767i	−0.534901	+	1.64626i
$994$		0			0
$995$	35.9951	−	26.1520i	1.14112	−	0.829074i
$996$		0			0
$997$	16.1450	+	49.6891i	0.511316	+	1.57367i	0.789886	+	0.613254i	$0.210140\pi$
$997$	16.1450	+	49.6891i	0.511316	+	1.57367i	−0.278570	+	0.960416i	$0.589860\pi$
$998$		0			0
$999$	34.0224	+	24.7187i	1.07642	+	0.782065i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.i.r.81.1		8
11.2	odd	10		968.2.i.q.753.2		8
11.3	even	5	inner	968.2.i.r.729.1		8
11.4	even	5	inner	968.2.i.r.9.2		8
11.5	even	5		88.2.a.b.1.1	✓	2
11.6	odd	10		968.2.a.j.1.1		2
11.7	odd	10		968.2.i.q.9.2		8
11.8	odd	10		968.2.i.q.729.1		8
11.9	even	5	inner	968.2.i.r.753.2		8
11.10	odd	2		968.2.i.q.81.1		8
33.5	odd	10		792.2.a.h.1.1		2
33.17	even	10		8712.2.a.bb.1.1		2
44.27	odd	10		176.2.a.d.1.2		2
44.39	even	10		1936.2.a.r.1.2		2
55.27	odd	20		2200.2.b.g.1849.3		4
55.38	odd	20		2200.2.b.g.1849.2		4
55.49	even	10		2200.2.a.o.1.2		2
77.27	odd	10		4312.2.a.n.1.2		2
88.5	even	10		704.2.a.m.1.2		2
88.27	odd	10		704.2.a.p.1.1		2
88.61	odd	10		7744.2.a.by.1.2		2
88.83	even	10		7744.2.a.cl.1.1		2
132.71	even	10		1584.2.a.t.1.1		2
176.5	even	20		2816.2.c.w.1409.3		4
176.27	odd	20		2816.2.c.p.1409.2		4
176.93	even	20		2816.2.c.w.1409.2		4
176.115	odd	20		2816.2.c.p.1409.3		4
220.27	even	20		4400.2.b.v.4049.2		4
220.159	odd	10		4400.2.a.bp.1.1		2
220.203	even	20		4400.2.b.v.4049.3		4
264.5	odd	10		6336.2.a.cu.1.2		2
264.203	even	10		6336.2.a.cx.1.2		2
308.27	even	10		8624.2.a.cb.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.a.b.1.1	✓	2	11.5	even	5
176.2.a.d.1.2		2	44.27	odd	10
704.2.a.m.1.2		2	88.5	even	10
704.2.a.p.1.1		2	88.27	odd	10
792.2.a.h.1.1		2	33.5	odd	10
968.2.a.j.1.1		2	11.6	odd	10
968.2.i.q.9.2		8	11.7	odd	10
968.2.i.q.81.1		8	11.10	odd	2
968.2.i.q.729.1		8	11.8	odd	10
968.2.i.q.753.2		8	11.2	odd	10
968.2.i.r.9.2		8	11.4	even	5	inner
968.2.i.r.81.1		8	1.1	even	1	trivial
968.2.i.r.729.1		8	11.3	even	5	inner
968.2.i.r.753.2		8	11.9	even	5	inner
1584.2.a.t.1.1		2	132.71	even	10
1936.2.a.r.1.2		2	44.39	even	10
2200.2.a.o.1.2		2	55.49	even	10
2200.2.b.g.1849.2		4	55.38	odd	20
2200.2.b.g.1849.3		4	55.27	odd	20
2816.2.c.p.1409.2		4	176.27	odd	20
2816.2.c.p.1409.3		4	176.115	odd	20
2816.2.c.w.1409.2		4	176.93	even	20
2816.2.c.w.1409.3		4	176.5	even	20
4312.2.a.n.1.2		2	77.27	odd	10
4400.2.a.bp.1.1		2	220.159	odd	10
4400.2.b.v.4049.2		4	220.27	even	20
4400.2.b.v.4049.3		4	220.203	even	20
6336.2.a.cu.1.2		2	264.5	odd	10
6336.2.a.cx.1.2		2	264.203	even	10
7744.2.a.by.1.2		2	88.61	odd	10
7744.2.a.cl.1.1		2	88.83	even	10
8624.2.a.cb.1.1		2	308.27	even	10
8712.2.a.bb.1.1		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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.482546 + 1.48512i) q^{3} +(-2.88136 + 2.09343i) q^{5} +(0.965093 + 2.97025i) q^{7} +(0.454306 + 0.330072i) q^{9} +(4.14468 + 3.01129i) q^{13} +(-1.71861 - 5.28935i) q^{15} +(-1.61803 + 1.17557i) q^{17} +(-1.23607 + 3.80423i) q^{19} -4.87689 q^{21} +2.43845 q^{23} +(2.37469 - 7.30854i) q^{25} +(-4.49939 + 3.26900i) q^{27} +(-1.58313 - 4.87236i) q^{29} +(4.49939 + 3.26900i) q^{31} +(-8.99878 - 6.53800i) q^{35} +(-2.33665 - 7.19146i) q^{37} +(-6.47214 + 4.70228i) q^{39} +(-0.347059 + 1.06814i) q^{41} -7.12311 q^{43} -2.00000 q^{45} +(2.47214 - 7.60845i) q^{47} +(-2.22786 + 1.61864i) q^{49} +(-0.965093 - 2.97025i) q^{51} +(-9.90739 - 7.19814i) q^{53} +(-5.05329 - 3.67143i) q^{57} +(2.41273 + 7.42562i) q^{59} +(-0.908612 + 0.660145i) q^{61} +(-0.541951 + 1.66795i) q^{63} -18.2462 q^{65} +9.56155 q^{67} +(-1.17666 + 3.62140i) q^{69} +(7.02604 - 5.10471i) q^{71} +(1.58313 + 4.87236i) q^{73} +(9.70820 + 7.05342i) q^{75} +(8.99878 + 6.53800i) q^{79} +(-2.16312 - 6.65740i) q^{81} +(-0.709422 + 0.515426i) q^{83} +(2.20116 - 6.77448i) q^{85} +8.00000 q^{87} +2.68466 q^{89} +(-4.94427 + 15.2169i) q^{91} +(-7.02604 + 5.10471i) q^{93} +(-4.40232 - 13.5490i) q^{95} +(-12.5896 - 9.14685i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{3} - 3 q^{5} + 2 q^{7} - 3 q^{9} + 2 q^{13} + 7 q^{15} - 4 q^{17} + 8 q^{19} - 72 q^{21} + 36 q^{23} - 3 q^{25} - 7 q^{27} + 2 q^{29} + 7 q^{31} - 14 q^{35} + 11 q^{37} - 16 q^{39} - 6 q^{41}+ \cdots - 27 q^{97}+O(q^{100}) \) 8 * q - q^3 - 3 * q^5 + 2 * q^7 - 3 * q^9 + 2 * q^13 + 7 * q^15 - 4 * q^17 + 8 * q^19 - 72 * q^21 + 36 * q^23 - 3 * q^25 - 7 * q^27 + 2 * q^29 + 7 * q^31 - 14 * q^35 + 11 * q^37 - 16 * q^39 - 6 * q^41 - 24 * q^43 - 16 * q^45 - 16 * q^47 - 22 * q^49 - 2 * q^51 - 8 * q^53 + 4 * q^57 + 5 * q^59 + 6 * q^61 + 20 * q^63 - 80 * q^65 + 60 * q^67 - 13 * q^69 + 5 * q^71 - 2 * q^73 + 24 * q^75 + 14 * q^79 + 14 * q^81 - 10 * q^83 - 6 * q^85 + 64 * q^87 - 28 * q^89 + 32 * q^91 - 5 * q^93 + 12 * q^95 - 27 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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