LMFDB - Embedded newform 784.2.m.j.589.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(197,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("784.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.m (of order $4$, degree $2$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			589.6
Character	$\chi$	$=$	784.589
Dual form			784.2.m.j.197.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.350694 - 1.37004i) q^{2} +(1.17747 + 1.17747i) q^{3} +(-1.75403 - 0.960931i) q^{4} +(-1.42676 + 1.42676i) q^{5} +(2.02612 - 1.20025i) q^{6} +(-1.93164 + 2.06610i) q^{8} -0.227125i q^{9} +(1.45437 + 2.45508i) q^{10} +(4.46446 - 4.46446i) q^{11} +(-0.933847 - 3.19678i) q^{12} +(1.13388 + 1.13388i) q^{13} -3.35995 q^{15} +(2.15322 + 3.37100i) q^{16} +1.92158 q^{17} +(-0.311171 - 0.0796515i) q^{18} +(4.46208 + 4.46208i) q^{19} +(3.87361 - 1.13156i) q^{20} +(-4.55083 - 7.68215i) q^{22} -1.06764i q^{23} +(-4.70722 + 0.158316i) q^{24} +0.928685i q^{25} +(1.95110 - 1.15581i) q^{26} +(3.79985 - 3.79985i) q^{27} +(5.08936 + 5.08936i) q^{29} +(-1.17831 + 4.60327i) q^{30} +0.396586 q^{31} +(5.37353 - 1.76781i) q^{32} +10.5135 q^{33} +(0.673887 - 2.63264i) q^{34} +(-0.218252 + 0.398384i) q^{36} +(-0.239603 + 0.239603i) q^{37} +(7.67806 - 4.54841i) q^{38} +2.67021i q^{39} +(-0.191834 - 5.70383i) q^{40} -7.26189i q^{41} +(1.75565 - 1.75565i) q^{43} +(-12.1208 + 3.54074i) q^{44} +(0.324054 + 0.324054i) q^{45} +(-1.46271 - 0.374416i) q^{46} +2.16235 q^{47} +(-1.43390 + 6.50461i) q^{48} +(1.27234 + 0.325684i) q^{50} +(2.26260 + 2.26260i) q^{51} +(-0.899272 - 3.07842i) q^{52} +(0.304333 - 0.304333i) q^{53} +(-3.87336 - 6.53853i) q^{54} +12.7395i q^{55} +10.5079i q^{57} +(8.75744 - 5.18782i) q^{58} +(-6.35074 + 6.35074i) q^{59} +(5.89344 + 3.22868i) q^{60} +(-7.44956 - 7.44956i) q^{61} +(0.139080 - 0.543339i) q^{62} +(-0.537512 - 7.98192i) q^{64} -3.23555 q^{65} +(3.68704 - 14.4040i) q^{66} +(-5.76447 - 5.76447i) q^{67} +(-3.37050 - 1.84651i) q^{68} +(1.25712 - 1.25712i) q^{69} +2.78982i q^{71} +(0.469263 + 0.438725i) q^{72} -2.37557i q^{73} +(0.244238 + 0.412293i) q^{74} +(-1.09350 + 1.09350i) q^{75} +(-3.53886 - 12.1144i) q^{76} +(3.65830 + 0.936427i) q^{78} -10.2166 q^{79} +(-7.88176 - 1.73748i) q^{80} +8.26704 q^{81} +(-9.94909 - 2.54670i) q^{82} +(1.17951 + 1.17951i) q^{83} +(-2.74164 + 2.74164i) q^{85} +(-1.78962 - 3.02101i) q^{86} +11.9851i q^{87} +(0.600264 + 17.8477i) q^{88} +12.7560i q^{89} +(0.557612 - 0.330324i) q^{90} +(-1.02593 + 1.87267i) q^{92} +(0.466968 + 0.466968i) q^{93} +(0.758325 - 2.96252i) q^{94} -12.7327 q^{95} +(8.40872 + 4.24563i) q^{96} -2.21148 q^{97} +(-1.01399 - 1.01399i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 4 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{10} + 4 q^{11} - 2 q^{12} - 12 q^{13} - 20 q^{15} - 16 q^{16} - 8 q^{17} - 18 q^{18} + 4 q^{19} - 8 q^{20} - 18 q^{24} + 10 q^{26} - 12 q^{27}+ \cdots - 12 q^{99}+O(q^{100}) $ 24 * q + 4 * q^2 + 4 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^10 + 4 * q^11 - 2 * q^12 - 12 * q^13 - 20 * q^15 - 16 * q^16 - 8 * q^17 - 18 * q^18 + 4 * q^19 - 8 * q^20 - 18 * q^24 + 10 * q^26 - 12 * q^27 + 12 * q^29 + 4 * q^30 - 28 * q^31 - 16 * q^32 - 16 * q^33 - 22 * q^34 - 36 * q^36 + 24 * q^37 - 20 * q^38 - 26 * q^40 - 20 * q^43 - 6 * q^44 + 28 * q^45 + 14 * q^46 + 20 * q^47 + 28 * q^48 + 28 * q^50 - 24 * q^51 + 16 * q^52 + 16 * q^53 - 64 * q^54 + 6 * q^58 + 20 * q^59 - 46 * q^60 - 8 * q^61 + 12 * q^62 + 40 * q^64 - 8 * q^65 + 20 * q^66 - 48 * q^67 - 20 * q^69 + 32 * q^72 + 8 * q^74 + 4 * q^75 - 18 * q^76 + 58 * q^78 + 36 * q^79 + 28 * q^80 - 2 * q^82 - 4 * q^83 + 20 * q^86 + 42 * q^88 - 10 * q^90 + 38 * q^92 - 8 * q^93 + 72 * q^94 + 4 * q^95 + 120 * q^96 - 24 * q^97 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.350694	−	1.37004i	0.247978	−	0.968766i
$2$	0.350694	−	1.37004i	0.247978	−	0.968766i
$3$	1.17747	+	1.17747i	0.679813	+	0.679813i	0.959958	−	0.280145i	$-0.0903825\pi$
$3$	1.17747	+	1.17747i	0.679813	+	0.679813i	−0.280145	+	0.959958i	$0.590382\pi$
$4$	−1.75403	−	0.960931i	−0.877014	−	0.480466i
$5$	−1.42676	+	1.42676i	−0.638069	+	0.638069i	−0.950079	−	0.312010i	$-0.898998\pi$
$5$	−1.42676	+	1.42676i	−0.638069	+	0.638069i	0.312010	+	0.950079i	$0.398998\pi$
$6$	2.02612	−	1.20025i	0.827158	−	0.490001i
$7$		0			0
$7$		0			0
$8$	−1.93164	+	2.06610i	−0.682939	+	0.730476i
$9$		−	0.227125i		−	0.0757084i
$10$	1.45437	+	2.45508i	0.459912	+	0.776366i
$11$	4.46446	−	4.46446i	1.34608	−	1.34608i	0.456216	−	0.889869i	$-0.349205\pi$
$11$	4.46446	−	4.46446i	1.34608	−	1.34608i	0.889869	−	0.456216i	$-0.150795\pi$
$12$	−0.933847	−	3.19678i	−0.269578	−	0.922832i
$13$	1.13388	+	1.13388i	0.314480	+	0.314480i	0.846642	−	0.532162i	$-0.178620\pi$
$13$	1.13388	+	1.13388i	0.314480	+	0.314480i	−0.532162	+	0.846642i	$0.678620\pi$
$14$		0			0
$15$	−3.35995			−0.867535
$16$	2.15322	+	3.37100i	0.538306	+	0.842750i
$17$	1.92158			0.466051			0.233026	−	0.972471i	$-0.425137\pi$
$17$	1.92158			0.466051			0.233026	+	0.972471i	$0.425137\pi$
$18$	−0.311171	−	0.0796515i	−0.0733437	−	0.0187740i
$19$	4.46208	+	4.46208i	1.02367	+	1.02367i	0.999713	+	0.0239589i	$0.00762708\pi$
$19$	4.46208	+	4.46208i	1.02367	+	1.02367i	0.0239589	+	0.999713i	$0.492373\pi$
$20$	3.87361	−	1.13156i	0.866165	−	0.253025i
$21$		0			0
$22$	−4.55083	−	7.68215i	−0.970241	−	1.63784i
$23$		−	1.06764i		−	0.222619i	−0.993786	−	0.111309i	$-0.964496\pi$
$23$		−	1.06764i		−	0.222619i	0.993786	−	0.111309i	$-0.0355045\pi$
$24$	−4.70722	+	0.158316i	−0.960858	+	0.0323160i
$25$			0.928685i			0.185737i
$26$	1.95110	−	1.15581i	0.382642	−	0.226673i
$27$	3.79985	−	3.79985i	0.731281	−	0.731281i
$28$		0			0
$29$	5.08936	+	5.08936i	0.945070	+	0.945070i	0.998568	−	0.0534979i	$-0.0170370\pi$
$29$	5.08936	+	5.08936i	0.945070	+	0.945070i	−0.0534979	+	0.998568i	$0.517037\pi$
$30$	−1.17831	+	4.60327i	−0.215130	+	0.840438i
$31$	0.396586			0.0712290			0.0356145	−	0.999366i	$-0.488661\pi$
$31$	0.396586			0.0712290			0.0356145	+	0.999366i	$0.488661\pi$
$32$	5.37353	−	1.76781i	0.949915	−	0.312508i
$33$	10.5135			1.83017
$34$	0.673887	−	2.63264i	0.115571	−	0.451494i
$35$		0			0
$36$	−0.218252	+	0.398384i	−0.0363753	+	0.0663973i
$37$	−0.239603	+	0.239603i	−0.0393904	+	0.0393904i	−0.726528	−	0.687137i	$-0.758867\pi$
$37$	−0.239603	+	0.239603i	−0.0393904	+	0.0393904i	0.687137	+	0.726528i	$0.258867\pi$
$38$	7.67806	−	4.54841i	1.24555	−	0.737850i
$39$			2.67021i			0.427576i
$40$	−0.191834	−	5.70383i	−0.0303316	−	0.901855i
$41$		−	7.26189i		−	1.13412i	−0.823678	−	0.567058i	$-0.808081\pi$
$41$		−	7.26189i		−	1.13412i	0.823678	−	0.567058i	$-0.191919\pi$
$42$		0			0
$43$	1.75565	−	1.75565i	0.267734	−	0.267734i	−0.560452	−	0.828187i	$-0.689373\pi$
$43$	1.75565	−	1.75565i	0.267734	−	0.267734i	0.828187	+	0.560452i	$0.189373\pi$
$44$	−12.1208	+	3.54074i	−1.82728	+	0.533787i
$45$	0.324054	+	0.324054i	0.0483072	+	0.0483072i
$46$	−1.46271	−	0.374416i	−0.215666	−	0.0552047i
$47$	2.16235			0.315412			0.157706	−	0.987486i	$-0.449590\pi$
$47$	2.16235			0.315412			0.157706	+	0.987486i	$0.449590\pi$
$48$	−1.43390	+	6.50461i	−0.206965	+	0.938859i
$49$		0			0
$50$	1.27234	+	0.325684i	0.179936	+	0.0460587i
$51$	2.26260	+	2.26260i	0.316828	+	0.316828i
$52$	−0.899272	−	3.07842i	−0.124707	−	0.426901i
$53$	0.304333	−	0.304333i	0.0418034	−	0.0418034i	−0.685896	−	0.727699i	$-0.740590\pi$
$53$	0.304333	−	0.304333i	0.0418034	−	0.0418034i	0.727699	+	0.685896i	$0.240590\pi$
$54$	−3.87336	−	6.53853i	−0.527098	−	0.889781i
$55$			12.7395i			1.71779i
$56$		0			0
$57$			10.5079i			1.39181i
$58$	8.75744	−	5.18782i	1.14991	−	0.681195i
$59$	−6.35074	+	6.35074i	−0.826795	+	0.826795i	−0.987072	−	0.160277i	$-0.948761\pi$
$59$	−6.35074	+	6.35074i	−0.826795	+	0.826795i	0.160277	+	0.987072i	$0.448761\pi$
$60$	5.89344	+	3.22868i	0.760840	+	0.416821i
$61$	−7.44956	−	7.44956i	−0.953818	−	0.953818i	0.0451612	−	0.998980i	$-0.485620\pi$
$61$	−7.44956	−	7.44956i	−0.953818	−	0.953818i	−0.998980	+	0.0451612i	$0.985620\pi$
$62$	0.139080	−	0.543339i	0.0176632	−	0.0690042i
$63$		0			0
$64$	−0.537512	−	7.98192i	−0.0671890	−	0.997740i
$65$	−3.23555			−0.401320
$66$	3.68704	−	14.4040i	0.453843	−	1.77301i
$67$	−5.76447	−	5.76447i	−0.704242	−	0.704242i	0.261076	−	0.965318i	$-0.415923\pi$
$67$	−5.76447	−	5.76447i	−0.704242	−	0.704242i	−0.965318	+	0.261076i	$0.915923\pi$
$68$	−3.37050	−	1.84651i	−0.408733	−	0.223922i
$69$	1.25712	−	1.25712i	0.151339	−	0.151339i
$70$		0			0
$71$			2.78982i			0.331090i	0.986202	+	0.165545i	$0.0529384\pi$
$71$			2.78982i			0.331090i	−0.986202	+	0.165545i	$0.947062\pi$
$72$	0.469263	+	0.438725i	0.0553031	+	0.0517042i
$73$		−	2.37557i		−	0.278040i	−0.990290	−	0.139020i	$-0.955605\pi$
$73$		−	2.37557i		−	0.278040i	0.990290	−	0.139020i	$-0.0443952\pi$
$74$	0.244238	+	0.412293i	0.0283921	+	0.0479281i
$75$	−1.09350	+	1.09350i	−0.126266	+	0.126266i
$76$	−3.53886	−	12.1144i	−0.405935	−	1.38961i
$77$		0			0
$78$	3.65830	+	0.936427i	0.414221	+	0.106029i
$79$	−10.2166			−1.14945			−0.574727	−	0.818345i	$-0.694892\pi$
$79$	−10.2166			−1.14945			−0.574727	+	0.818345i	$0.694892\pi$
$80$	−7.88176	−	1.73748i	−0.881208	−	0.194256i
$81$	8.26704			0.918560
$82$	−9.94909	−	2.54670i	−1.09869	−	0.281236i
$83$	1.17951	+	1.17951i	0.129468	+	0.129468i	0.768871	−	0.639404i	$-0.220819\pi$
$83$	1.17951	+	1.17951i	0.129468	+	0.129468i	−0.639404	+	0.768871i	$0.720819\pi$
$84$		0			0
$85$	−2.74164	+	2.74164i	−0.297373	+	0.297373i
$86$	−1.78962	−	3.02101i	−0.192980	−	0.325764i
$87$			11.9851i			1.28494i
$88$	0.600264	+	17.8477i	0.0639884	+	1.90258i
$89$			12.7560i			1.35213i	0.736841	+	0.676066i	$0.236317\pi$
$89$			12.7560i			1.35213i	−0.736841	+	0.676066i	$0.763683\pi$
$90$	0.557612	−	0.330324i	0.0587774	−	0.0348192i
$91$		0			0
$92$	−1.02593	+	1.87267i	−0.106961	+	0.195240i
$93$	0.466968	+	0.466968i	0.0484224	+	0.0484224i
$94$	0.758325	−	2.96252i	0.0782153	−	0.305560i
$95$	−12.7327			−1.30635
$96$	8.40872	+	4.24563i	0.858212	+	0.433317i
$97$	−2.21148			−0.224542			−0.112271	−	0.993678i	$-0.535813\pi$
$97$	−2.21148			−0.224542			−0.112271	+	0.993678i	$0.535813\pi$
$98$		0			0
$99$	−1.01399	−	1.01399i	−0.101910	−	0.101910i
$100$	0.892402	−	1.62894i	0.0892402	−	0.162894i
$101$	5.08793	−	5.08793i	0.506268	−	0.506268i	−0.407111	−	0.913379i	$-0.633464\pi$
$101$	5.08793	−	5.08793i	0.506268	−	0.506268i	0.913379	+	0.407111i	$0.133464\pi$
$102$	3.89334	−	2.30638i	0.385498	−	0.228365i
$103$			17.4888i			1.72322i	0.507572	+	0.861609i	$0.330543\pi$
$103$			17.4888i			1.72322i	−0.507572	+	0.861609i	$0.669457\pi$
$104$	−4.53294	+	0.152454i	−0.444491	+	0.0149493i
$105$		0			0
$106$	−0.310221	−	0.523677i	−0.0301314	−	0.0508640i
$107$	−2.12921	+	2.12921i	−0.205838	+	0.205838i	−0.802496	−	0.596658i	$-0.796495\pi$
$107$	−2.12921	+	2.12921i	−0.205838	+	0.205838i	0.596658	+	0.802496i	$0.296495\pi$
$108$	−10.3164	+	3.01364i	−0.992698	+	0.289988i
$109$	−5.02579	−	5.02579i	−0.481384	−	0.481384i	0.424190	−	0.905573i	$-0.360559\pi$
$109$	−5.02579	−	5.02579i	−0.481384	−	0.481384i	−0.905573	+	0.424190i	$0.860559\pi$
$110$	17.4536	+	4.46766i	1.66413	+	0.425974i
$111$	−0.564250			−0.0535562
$112$		0			0
$113$	−5.96535			−0.561173			−0.280586	−	0.959829i	$-0.590529\pi$
$113$	−5.96535			−0.561173			−0.280586	+	0.959829i	$0.590529\pi$
$114$	14.3963	+	3.68507i	1.34834	+	0.345139i
$115$	1.52328	+	1.52328i	0.142046	+	0.142046i
$116$	−4.03635	−	13.8174i	−0.374766	−	1.28291i
$117$	0.257532	−	0.257532i	0.0238088	−	0.0238088i
$118$	6.47360	+	10.9279i	0.595944	+	1.00600i
$119$		0			0
$120$	6.49022	−	6.94198i	0.592473	−	0.633713i
$121$		−	28.8628i		−	2.62389i
$122$	−12.8187	+	7.59369i	−1.16055	+	0.687500i
$123$	8.55066	−	8.55066i	0.770987	−	0.770987i
$124$	−0.695623	−	0.381092i	−0.0624688	−	0.0342231i
$125$	−8.45884	−	8.45884i	−0.756582	−	0.756582i
$126$		0			0
$127$	6.41296			0.569058			0.284529	−	0.958667i	$-0.408163\pi$
$127$	6.41296			0.569058			0.284529	+	0.958667i	$0.408163\pi$
$128$	−11.1241	−	2.06280i	−0.983238	−	0.182328i
$129$	4.13446			0.364019
$130$	−1.13469	+	4.43283i	−0.0995187	+	0.388785i
$131$	−10.5812	−	10.5812i	−0.924482	−	0.924482i	0.0728597	−	0.997342i	$-0.476787\pi$
$131$	−10.5812	−	10.5812i	−0.924482	−	0.924482i	−0.997342	+	0.0728597i	$0.976787\pi$
$132$	−18.4410	−	10.1028i	−1.60509	−	0.879335i
$133$		0			0
$134$	−9.91913	+	5.87600i	−0.856882	+	0.507609i
$135$			10.8430i			0.933214i
$136$	−3.71180	+	3.97017i	−0.318285	+	0.340439i
$137$		−	1.74276i		−	0.148894i	−0.997225	−	0.0744472i	$-0.976281\pi$
$137$		−	1.74276i		−	0.148894i	0.997225	−	0.0744472i	$-0.0237192\pi$
$138$	−1.28144	−	2.16317i	−0.109083	−	0.184141i
$139$	2.84436	−	2.84436i	0.241256	−	0.241256i	−0.576114	−	0.817370i	$-0.695431\pi$
$139$	2.84436	−	2.84436i	0.241256	−	0.241256i	0.817370	+	0.576114i	$0.195431\pi$
$140$		0			0
$141$	2.54611	+	2.54611i	0.214421	+	0.214421i
$142$	3.82217	+	0.978373i	0.320749	+	0.0821032i
$143$	10.1243			0.846634
$144$	0.765639	−	0.489051i	0.0638033	−	0.0407543i
$145$	−14.5226			−1.20604
$146$	−3.25463	−	0.833099i	−0.269355	−	0.0689478i
$147$		0			0
$148$	0.650511	−	0.190028i	0.0534717	−	0.0156202i
$149$	13.0194	−	13.0194i	1.06659	−	1.06659i	0.0689725	−	0.997619i	$-0.478028\pi$
$149$	13.0194	−	13.0194i	1.06659	−	1.06659i	0.997619	−	0.0689725i	$-0.0219721\pi$
$150$	1.11466	+	1.88162i	0.0910112	+	0.153634i
$151$			6.37899i			0.519115i	0.965728	+	0.259557i	$0.0835767\pi$
$151$			6.37899i			0.519115i	−0.965728	+	0.259557i	$0.916423\pi$
$152$	−17.8382	+	0.599944i	−1.44687	+	0.0486619i
$153$		−	0.436439i		−	0.0352840i
$154$		0			0
$155$	−0.565835	+	0.565835i	−0.0454490	+	0.0454490i
$156$	2.56589	−	4.68362i	0.205435	−	0.374990i
$157$	−12.8971	−	12.8971i	−1.02930	−	1.02930i	−0.999558	−	0.0297395i	$-0.990532\pi$
$157$	−12.8971	−	12.8971i	−1.02930	−	1.02930i	−0.0297395	−	0.999558i	$-0.509468\pi$
$158$	−3.58290	+	13.9971i	−0.285040	+	1.11355i
$159$	0.716687			0.0568370
$160$	−5.14451	+	10.1890i	−0.406709	+	0.805513i
$161$		0			0
$162$	2.89920	−	11.3262i	0.227783	−	0.889869i
$163$	8.12343	+	8.12343i	0.636276	+	0.636276i	0.949635	−	0.313359i	$-0.101454\pi$
$163$	8.12343	+	8.12343i	0.636276	+	0.636276i	−0.313359	+	0.949635i	$0.601454\pi$
$164$	−6.97818	+	12.7376i	−0.544904	+	0.994636i
$165$	−15.0003	+	15.0003i	−1.16778	+	1.16778i
$166$	2.02962	−	1.20233i	0.157529	−	0.0933186i
$167$			21.6693i			1.67682i	0.545040	+	0.838410i	$0.316514\pi$
$167$			21.6693i			1.67682i	−0.545040	+	0.838410i	$0.683486\pi$
$168$		0			0
$169$		−	10.4287i		−	0.802204i
$170$	2.79468	+	4.71764i	0.214342	+	0.361826i
$171$	1.01345	−	1.01345i	0.0775006	−	0.0775006i
$172$	−4.76652	+	1.39240i	−0.363444	+	0.106170i
$173$	9.04787	+	9.04787i	0.687897	+	0.687897i	0.961767	−	0.273870i	$-0.0883038\pi$
$173$	9.04787	+	9.04787i	0.687897	+	0.687897i	−0.273870	+	0.961767i	$0.588304\pi$
$174$	16.4201	+	4.20312i	1.24481	+	0.318638i
$175$		0			0
$176$	24.6627	+	5.43671i	1.85902	+	0.409808i
$177$	−14.9556			−1.12413
$178$	17.4762	+	4.47345i	1.30990	+	0.335300i
$179$	−2.23963	−	2.23963i	−0.167398	−	0.167398i	0.618437	−	0.785835i	$-0.287766\pi$
$179$	−2.23963	−	2.23963i	−0.167398	−	0.167398i	−0.785835	+	0.618437i	$0.787766\pi$
$180$	−0.257006	−	0.879794i	−0.0191561	−	0.0655760i
$181$	−14.3765	+	14.3765i	−1.06860	+	1.06860i	−0.0711279	+	0.997467i	$0.522660\pi$
$181$	−14.3765	+	14.3765i	−1.06860	+	1.06860i	−0.997467	+	0.0711279i	$0.977340\pi$
$182$		0			0
$183$		−	17.5433i		−	1.29684i
$184$	2.20585	+	2.06230i	0.162618	+	0.152035i
$185$		−	0.683713i		−	0.0502676i
$186$	0.803529	−	0.476003i	0.0589176	−	0.0349022i
$187$	8.57881	−	8.57881i	0.627345	−	0.627345i
$188$	−3.79283	−	2.07787i	−0.276620	−	0.151545i
$189$		0			0
$190$	−4.46528	+	17.4443i	−0.323945	+	1.26554i
$191$	12.2418			0.885784			0.442892	−	0.896575i	$-0.353953\pi$
$191$	12.2418			0.885784			0.442892	+	0.896575i	$0.353953\pi$
$192$	8.76558	−	10.0314i	0.632601	−	0.723953i
$193$	−2.17799			−0.156775			−0.0783877	−	0.996923i	$-0.524977\pi$
$193$	−2.17799			−0.156775			−0.0783877	+	0.996923i	$0.524977\pi$
$194$	−0.775555	+	3.02983i	−0.0556816	+	0.217529i
$195$	−3.80976	−	3.80976i	−0.272823	−	0.272823i
$196$		0			0
$197$	9.97878	−	9.97878i	0.710959	−	0.710959i	−0.255777	−	0.966736i	$-0.582331\pi$
$197$	9.97878	−	9.97878i	0.710959	−	0.710959i	0.966736	+	0.255777i	$0.0823313\pi$
$198$	−1.74481	+	1.03361i	−0.123998	+	0.0734554i
$199$			10.5571i			0.748372i	0.927354	+	0.374186i	$0.122078\pi$
$199$			10.5571i			0.748372i	−0.927354	+	0.374186i	$0.877922\pi$
$200$	−1.91875	−	1.79389i	−0.135676	−	0.126847i
$201$		−	13.5750i		−	0.957506i
$202$	−5.18637	−	8.75499i	−0.364912	−	0.615999i
$203$		0			0
$204$	−1.79446	−	6.14287i	−0.125637	−	0.430087i
$205$	10.3610	+	10.3610i	0.723644	+	0.723644i
$206$	23.9603	+	6.13321i	1.66940	+	0.427321i
$207$	−0.242489			−0.0168541
$208$	−1.38081	+	6.26378i	−0.0957417	+	0.434315i
$209$	39.8416			2.75590
$210$		0			0
$211$	5.20378	+	5.20378i	0.358243	+	0.358243i	0.863165	−	0.504922i	$-0.168479\pi$
$211$	5.20378	+	5.20378i	0.358243	+	0.358243i	−0.504922	+	0.863165i	$0.668479\pi$
$212$	−0.826252	+	0.241366i	−0.0567472	+	0.0165771i
$213$	−3.28493	+	3.28493i	−0.225080	+	0.225080i
$214$	2.17040	+	3.66380i	0.148366	+	0.250452i
$215$			5.00981i			0.341666i
$216$	0.510904	+	15.1908i	0.0347626	+	1.03360i
$217$		0			0
$218$	−8.64806	+	5.12303i	−0.585721	+	0.346975i
$219$	2.79717	−	2.79717i	0.189015	−	0.189015i
$220$	12.2417	−	22.3454i	0.825339	−	1.50652i
$221$	2.17883	+	2.17883i	0.146564	+	0.146564i
$222$	−0.197879	+	0.773046i	−0.0132808	+	0.0518835i
$223$	−22.3888			−1.49926			−0.749632	−	0.661855i	$-0.769770\pi$
$223$	−22.3888			−1.49926			−0.749632	+	0.661855i	$0.769770\pi$
$224$		0			0
$225$	0.210928			0.0140619
$226$	−2.09201	+	8.17277i	−0.139159	+	0.543645i
$227$	13.1588	+	13.1588i	0.873383	+	0.873383i	0.992839	−	0.119456i	$-0.0381152\pi$
$227$	13.1588	+	13.1588i	0.873383	+	0.873383i	−0.119456	+	0.992839i	$0.538115\pi$
$228$	10.0974	−	18.4312i	0.668717	−	1.22064i
$229$	−5.94737	+	5.94737i	−0.393014	+	0.393014i	−0.875760	−	0.482747i	$-0.839639\pi$
$229$	−5.94737	+	5.94737i	−0.393014	+	0.393014i	0.482747	+	0.875760i	$0.339639\pi$
$230$	2.62115	−	1.55275i	0.172834	−	0.102385i
$231$		0			0
$232$	−20.3459	+	0.684284i	−1.33578	+	0.0449255i
$233$			17.2372i			1.12925i	0.825349	+	0.564623i	$0.190978\pi$
$233$			17.2372i			1.12925i	−0.825349	+	0.564623i	$0.809022\pi$
$234$	−0.262514	−	0.443144i	−0.0171611	−	0.0289692i
$235$	−3.08517	+	3.08517i	−0.201254	+	0.201254i
$236$	17.2420	−	5.03674i	1.12236	−	0.327864i
$237$	−12.0297	−	12.0297i	−0.781414	−	0.781414i
$238$		0			0
$239$	−0.572679			−0.0370435			−0.0185218	−	0.999828i	$-0.505896\pi$
$239$	−0.572679			−0.0370435			−0.0185218	+	0.999828i	$0.505896\pi$
$240$	−7.23471	−	11.3264i	−0.466999	−	0.731115i
$241$	−11.7864			−0.759227			−0.379613	−	0.925145i	$-0.623943\pi$
$241$	−11.7864			−0.759227			−0.379613	+	0.925145i	$0.623943\pi$
$242$	−39.5432	−	10.1220i	−2.54193	−	0.650667i
$243$	−1.66534	−	1.66534i	−0.106832	−	0.106832i
$244$	5.90822	+	20.2252i	0.378235	+	1.29479i
$245$		0			0
$246$	−8.71610	−	14.7134i	−0.555718	−	0.938094i
$247$			10.1189i			0.643849i
$248$	−0.766063	+	0.819385i	−0.0486450	+	0.0520310i
$249$			2.77767i			0.176027i
$250$	−14.5554	+	8.62249i	−0.920566	+	0.545334i
$251$	−5.57539	+	5.57539i	−0.351916	+	0.351916i	−0.860822	−	0.508906i	$-0.830050\pi$
$251$	−5.57539	+	5.57539i	−0.351916	+	0.351916i	0.508906	+	0.860822i	$0.330050\pi$
$252$		0			0
$253$	−4.76645	−	4.76645i	−0.299664	−	0.299664i
$254$	2.24899	−	8.78602i	0.141114	−	0.551284i
$255$	−6.45640			−0.404316
$256$	−6.72727	+	14.5170i	−0.420454	+	0.907314i
$257$	29.0655			1.81306			0.906528	−	0.422146i	$-0.138723\pi$
$257$	29.0655			1.81306			0.906528	+	0.422146i	$0.138723\pi$
$258$	1.44993	−	5.66438i	0.0902688	−	0.352649i
$259$		0			0
$260$	5.67523	+	3.10914i	0.351963	+	0.192820i
$261$	1.15592	−	1.15592i	0.0715498	−	0.0715498i
$262$	−18.2074	+	10.7859i	−1.12486	+	0.666355i
$263$			17.6833i			1.09040i	0.838307	+	0.545198i	$0.183546\pi$
$263$			17.6833i			1.09040i	−0.838307	+	0.545198i	$0.816454\pi$
$264$	−20.3084	+	21.7220i	−1.24990	+	1.33690i
$265$			0.868424i			0.0533469i
$266$		0			0
$267$	−15.0198	+	15.0198i	−0.919198	+	0.919198i
$268$	4.57178	+	15.6503i	0.279266	+	0.955994i
$269$	−10.5612	−	10.5612i	−0.643927	−	0.643927i	0.307592	−	0.951518i	$-0.400477\pi$
$269$	−10.5612	−	10.5612i	−0.643927	−	0.643927i	−0.951518	+	0.307592i	$0.900477\pi$
$270$	14.8553	+	3.80257i	0.904066	+	0.231417i
$271$	−13.8634			−0.842145			−0.421072	−	0.907027i	$-0.638346\pi$
$271$	−13.8634			−0.842145			−0.421072	+	0.907027i	$0.638346\pi$
$272$	4.13759	+	6.47764i	0.250878	+	0.392765i
$273$		0			0
$274$	−2.38766	−	0.611177i	−0.144244	−	0.0369226i
$275$	4.14607	+	4.14607i	0.250018	+	0.250018i
$276$	−3.41302	+	0.997015i	−0.205440	+	0.0600133i
$277$	−1.63232	+	1.63232i	−0.0980768	+	0.0980768i	−0.754443	−	0.656366i	$-0.772093\pi$
$277$	−1.63232	+	1.63232i	−0.0980768	+	0.0980768i	0.656366	+	0.754443i	$0.272093\pi$
$278$	−2.89939	−	4.89440i	−0.173894	−	0.293546i
$279$		−	0.0900747i		−	0.00539263i
$280$		0			0
$281$			0.680351i			0.0405863i	0.999794	+	0.0202932i	$0.00645996\pi$
$281$			0.680351i			0.0405863i	−0.999794	+	0.0202932i	$0.993540\pi$
$282$	4.38118	−	2.59537i	0.260896	−	0.154552i
$283$	0.269140	−	0.269140i	0.0159987	−	0.0159987i	−0.699062	−	0.715061i	$-0.746399\pi$
$283$	0.269140	−	0.269140i	0.0159987	−	0.0159987i	0.715061	+	0.699062i	$0.246399\pi$
$284$	2.68082	−	4.89342i	0.159078	−	0.290371i
$285$	−14.9924	−	14.9924i	−0.888071	−	0.888071i
$286$	3.55053	−	13.8707i	0.209947	−	0.820190i
$287$		0			0
$288$	−0.401515	−	1.22046i	−0.0236595	−	0.0719166i
$289$	−13.3075			−0.782796
$290$	−5.09300	+	19.8966i	−0.299071	+	1.16837i
$291$	−2.60396	−	2.60396i	−0.152647	−	0.152647i
$292$	−2.28276	+	4.16682i	−0.133588	+	0.243844i
$293$	7.49220	−	7.49220i	0.437699	−	0.437699i	−0.453538	−	0.891237i	$-0.649838\pi$
$293$	7.49220	−	7.49220i	0.437699	−	0.437699i	0.891237	+	0.453538i	$0.149838\pi$
$294$		0			0
$295$		−	18.1220i		−	1.05510i
$296$	−0.0322155	−	0.957869i	−0.00187249	−	0.0556750i
$297$		−	33.9285i		−	1.96873i
$298$	−13.2713	−	22.4030i	−0.768785	−	1.29777i
$299$	1.21057	−	1.21057i	0.0700093	−	0.0700093i
$300$	2.96880	−	0.867250i	0.171404	−	0.0500707i
$301$		0			0
$302$	8.73948	+	2.23707i	0.502901	+	0.128729i
$303$	11.9818			0.688335
$304$	−5.43382	+	24.6495i	−0.311651	+	1.41375i
$305$	21.2575			1.21720
$306$	−0.597940	−	0.153057i	−0.0341819	−	0.00874967i
$307$	−6.27988	−	6.27988i	−0.358412	−	0.358412i	0.504816	−	0.863227i	$-0.331561\pi$
$307$	−6.27988	−	6.27988i	−0.358412	−	0.358412i	−0.863227	+	0.504816i	$0.831561\pi$
$308$		0			0
$309$	−20.5925	+	20.5925i	−1.17147	+	1.17147i
$310$	0.576782	+	0.973652i	0.0327590	+	0.0552997i
$311$		−	9.88060i		−	0.560278i	−0.959960	−	0.280139i	$-0.909620\pi$
$311$		−	9.88060i		−	0.560278i	0.959960	−	0.280139i	$-0.0903805\pi$
$312$	−5.51691	−	5.15789i	−0.312334	−	0.292008i
$313$		−	17.1743i		−	0.970747i	−0.874307	−	0.485374i	$-0.838684\pi$
$313$		−	17.1743i		−	0.970747i	0.874307	−	0.485374i	$-0.161316\pi$
$314$	−22.1924	+	13.1466i	−1.25239	+	0.741904i
$315$		0			0
$316$	17.9202	+	9.81743i	1.00809	+	0.552274i
$317$	−15.0227	−	15.0227i	−0.843760	−	0.843760i	0.145585	−	0.989346i	$-0.453493\pi$
$317$	−15.0227	−	15.0227i	−0.843760	−	0.843760i	−0.989346	+	0.145585i	$0.953493\pi$
$318$	0.251338	−	0.981891i	0.0140943	−	0.0550617i
$319$	45.4425			2.54429
$320$	12.1552	+	10.6214i	0.679498	+	0.593756i
$321$	−5.01416			−0.279863
$322$		0			0
$323$	8.57424	+	8.57424i	0.477084	+	0.477084i
$324$	−14.5006	−	7.94406i	−0.805589	−	0.441336i
$325$	−1.05301	+	1.05301i	−0.0584106	+	0.0584106i
$326$	13.9783	−	8.28060i	0.774185	−	0.458620i
$327$		−	11.8355i		−	0.654502i
$328$	15.0038	+	14.0274i	0.828445	+	0.774532i
$329$		0			0
$330$	15.2906	+	25.8116i	0.841718	+	1.42088i
$331$	−17.1115	+	17.1115i	−0.940535	+	0.940535i	−0.998329	−	0.0577937i	$-0.981593\pi$
$331$	−17.1115	+	17.1115i	−0.940535	+	0.940535i	0.0577937	+	0.998329i	$0.481593\pi$
$332$	−0.935461	−	3.20231i	−0.0513401	−	0.175750i
$333$	0.0544198	+	0.0544198i	0.00298219	+	0.00298219i
$334$	29.6878	+	7.59929i	1.62445	+	0.415815i
$335$	16.4491			0.898709
$336$		0			0
$337$	−4.26739			−0.232460			−0.116230	−	0.993222i	$-0.537081\pi$
$337$	−4.26739			−0.232460			−0.116230	+	0.993222i	$0.537081\pi$
$338$	−14.2877	−	3.65727i	−0.777148	−	0.198929i
$339$	−7.02402	−	7.02402i	−0.381493	−	0.381493i
$340$	7.44344	−	2.17438i	0.403677	−	0.117923i
$341$	1.77054	−	1.77054i	0.0958802	−	0.0958802i
$342$	−1.03306	−	1.74388i	−0.0558614	−	0.0942983i
$343$		0			0
$344$	0.236054	+	7.01864i	0.0127272	+	0.378420i
$345$			3.58722i			0.193130i
$346$	15.5690	−	9.22292i	0.836994	−	0.495827i
$347$	−0.0382032	+	0.0382032i	−0.00205085	+	0.00205085i	−0.708131	−	0.706081i	$-0.750462\pi$
$347$	−0.0382032	+	0.0382032i	−0.00205085	+	0.00205085i	0.706081	+	0.708131i	$0.250462\pi$
$348$	11.5169	−	21.0223i	0.617370	−	1.12691i
$349$	−15.4928	−	15.4928i	−0.829309	−	0.829309i	0.158112	−	0.987421i	$-0.449459\pi$
$349$	−15.4928	−	15.4928i	−0.829309	−	0.829309i	−0.987421	+	0.158112i	$0.949459\pi$
$350$		0			0
$351$	8.61710			0.459947
$352$	16.0976	−	31.8822i	0.858004	−	1.69933i
$353$	16.7632			0.892217			0.446108	−	0.894979i	$-0.352810\pi$
$353$	16.7632			0.892217			0.446108	+	0.894979i	$0.352810\pi$
$354$	−5.24485	+	20.4898i	−0.278760	+	1.08902i
$355$	−3.98041	−	3.98041i	−0.211258	−	0.211258i
$356$	12.2576	−	22.3744i	0.649653	−	1.18584i
$357$		0			0
$358$	−3.85381	+	2.28296i	−0.203680	+	0.120658i
$359$		−	34.4998i		−	1.82083i	−0.413696	−	0.910415i	$-0.635762\pi$
$359$		−	34.4998i		−	1.82083i	0.413696	−	0.910415i	$-0.364238\pi$
$360$	−1.29548	+	0.0435704i	−0.0682780	+	0.00229636i
$361$			20.8204i			1.09581i
$362$	14.6546	+	24.7381i	0.770230	+	1.30021i
$363$	33.9851	−	33.9851i	1.78375	−	1.78375i
$364$		0			0
$365$	3.38938	+	3.38938i	0.177408	+	0.177408i
$366$	−24.0350	−	6.15233i	−1.25633	−	0.321587i
$367$	−20.5289			−1.07160			−0.535799	−	0.844345i	$-0.679990\pi$
$367$	−20.5289			−1.07160			−0.535799	+	0.844345i	$0.679990\pi$
$368$	3.59902	−	2.29887i	0.187612	−	0.119837i
$369$	−1.64936			−0.0858622
$370$	−0.936715	−	0.239774i	−0.0486975	−	0.0124653i
$371$		0			0
$372$	−0.370351	−	1.26780i	−0.0192018	−	0.0657324i
$373$	−11.1837	+	11.1837i	−0.579072	+	0.579072i	−0.934647	−	0.355576i	$-0.884285\pi$
$373$	−11.1837	+	11.1837i	−0.579072	+	0.579072i	0.355576	+	0.934647i	$0.384285\pi$
$374$	−8.74478	−	14.7619i	−0.452182	−	0.763318i
$375$		−	19.9201i		−	1.02867i
$376$	−4.17690	+	4.46763i	−0.215407	+	0.230401i
$377$			11.5414i			0.594412i
$378$		0			0
$379$	11.2717	−	11.2717i	0.578987	−	0.578987i	−0.355637	−	0.934624i	$-0.615736\pi$
$379$	11.2717	−	11.2717i	0.578987	−	0.578987i	0.934624	+	0.355637i	$0.115736\pi$
$380$	22.3335	+	12.2352i	1.14568	+	0.627654i
$381$	7.55107	+	7.55107i	0.386853	+	0.386853i
$382$	4.29312	−	16.7717i	0.219655	−	0.858117i
$383$	10.2919			0.525890			0.262945	−	0.964811i	$-0.415306\pi$
$383$	10.2919			0.525890			0.262945	+	0.964811i	$0.415306\pi$
$384$	−10.6694	−	15.5272i	−0.544469	−	0.792367i
$385$		0			0
$386$	−0.763809	+	2.98394i	−0.0388769	+	0.151879i
$387$	−0.398753	−	0.398753i	−0.0202698	−	0.0202698i
$388$	3.87900	+	2.12508i	0.196927	+	0.107885i
$389$	14.4939	−	14.4939i	0.734869	−	0.734869i	−0.236711	−	0.971580i	$-0.576069\pi$
$389$	14.4939	−	14.4939i	0.734869	−	0.734869i	0.971580	+	0.236711i	$0.0760695\pi$
$390$	−6.55559	+	3.88347i	−0.331955	+	0.196647i
$391$		−	2.05156i		−	0.103752i
$392$		0			0
$393$		−	24.9181i		−	1.25695i
$394$	−10.1718	−	17.1708i	−0.512450	−	0.865055i
$395$	14.5767	−	14.5767i	0.733431	−	0.733431i
$396$	0.804192	+	2.75294i	0.0404122	+	0.138341i
$397$	−5.53600	−	5.53600i	−0.277844	−	0.277844i	0.554404	−	0.832248i	$-0.312946\pi$
$397$	−5.53600	−	5.53600i	−0.277844	−	0.277844i	−0.832248	+	0.554404i	$0.812946\pi$
$398$	14.4636	+	3.70231i	0.724997	+	0.185580i
$399$		0			0
$400$	−3.13060	+	1.99966i	−0.156530	+	0.0999832i
$401$	14.1997			0.709099			0.354549	−	0.935037i	$-0.384634\pi$
$401$	14.1997			0.709099			0.354549	+	0.935037i	$0.384634\pi$
$402$	−18.5983	−	4.76067i	−0.927599	−	0.237441i
$403$	0.449679	+	0.449679i	0.0224001	+	0.0224001i
$404$	−13.8135	+	4.03522i	−0.687248	+	0.200760i
$405$	−11.7951	+	11.7951i	−0.586104	+	0.586104i
$406$		0			0
$407$			2.13939i			0.106046i
$408$	−9.04530	+	0.304216i	−0.447809	+	0.0150609i
$409$			26.4149i			1.30613i	0.757302	+	0.653065i	$0.226517\pi$
$409$			26.4149i			1.30613i	−0.757302	+	0.653065i	$0.773483\pi$
$410$	17.8286	−	10.5615i	0.880490	−	0.521594i
$411$	2.05205	−	2.05205i	0.101220	−	0.101220i
$412$	16.8055	−	30.6758i	0.827947	−	1.51129i
$413$		0			0
$414$	−0.0850394	+	0.332220i	−0.00417946	+	0.0163277i
$415$	−3.36575			−0.165218
$416$	8.09739	+	4.08843i	0.397007	+	0.200452i
$417$	6.69831			0.328018
$418$	13.9722	−	54.5846i	0.683403	−	2.66982i
$419$	−15.6893	−	15.6893i	−0.766471	−	0.766471i	0.211012	−	0.977483i	$-0.432324\pi$
$419$	−15.6893	−	15.6893i	−0.766471	−	0.766471i	−0.977483	+	0.211012i	$0.932324\pi$
$420$		0			0
$421$	25.7068	−	25.7068i	1.25287	−	1.25287i	0.298444	−	0.954427i	$-0.403532\pi$
$421$	25.7068	−	25.7068i	1.25287	−	1.25287i	0.954427	−	0.298444i	$-0.0964675\pi$
$422$	8.95433	−	5.30446i	0.435890	−	0.258217i
$423$		−	0.491125i		−	0.0238793i
$424$	0.0409188	+	1.21665i	0.00198719	+	0.0590855i
$425$			1.78454i			0.0865630i
$426$	3.34848	+	5.65249i	0.162235	+	0.273864i
$427$		0			0
$428$	5.78071	−	1.68867i	0.279421	−	0.0816247i
$429$	11.9210	+	11.9210i	0.575553	+	0.575553i
$430$	6.86364	+	1.75691i	0.330994	+	0.0847257i
$431$	−24.7961			−1.19439			−0.597194	−	0.802097i	$-0.703718\pi$
$431$	−24.7961			−1.19439			−0.597194	+	0.802097i	$0.703718\pi$
$432$	20.9912	+	4.62736i	1.00994	+	0.222634i
$433$	5.22863			0.251272			0.125636	−	0.992076i	$-0.459903\pi$
$433$	5.22863			0.251272			0.125636	+	0.992076i	$0.459903\pi$
$434$		0			0
$435$	−17.1000	−	17.1000i	−0.819881	−	0.819881i
$436$	3.98594	+	13.6448i	0.190892	+	0.653469i
$437$	4.76391	−	4.76391i	0.227889	−	0.227889i
$438$	−2.85128	−	4.81318i	−0.136240	−	0.229983i
$439$		−	22.1438i		−	1.05687i	−0.848975	−	0.528433i	$-0.822780\pi$
$439$		−	22.1438i		−	1.05687i	0.848975	−	0.528433i	$-0.177220\pi$
$440$	−26.3210	−	24.6081i	−1.25480	−	1.17314i
$441$		0			0
$442$	3.74919	−	2.22098i	0.178331	−	0.105641i
$443$	−15.9636	+	15.9636i	−0.758455	+	0.758455i	−0.976041	−	0.217586i	$-0.930182\pi$
$443$	−15.9636	+	15.9636i	−0.758455	+	0.758455i	0.217586	+	0.976041i	$0.430182\pi$
$444$	0.989710	+	0.542206i	0.0469696	+	0.0257319i
$445$	−18.1998	−	18.1998i	−0.862754	−	0.862754i
$446$	−7.85162	+	30.6736i	−0.371785	+	1.45244i
$447$	30.6599			1.45017
$448$		0			0
$449$	−36.3678			−1.71630			−0.858152	−	0.513396i	$-0.828387\pi$
$449$	−36.3678			−1.71630			−0.858152	+	0.513396i	$0.828387\pi$
$450$	0.0739712	−	0.288980i	0.00348703	−	0.0136226i
$451$	−32.4204	−	32.4204i	−1.52662	−	1.52662i
$452$	10.4634	+	5.73229i	0.492156	+	0.269624i
$453$	−7.51107	+	7.51107i	−0.352901	+	0.352901i
$454$	22.6429	−	13.4134i	1.06268	−	0.629523i
$455$		0			0
$456$	−21.7104	−	20.2976i	−1.01668	−	0.950522i
$457$			24.9193i			1.16567i	0.812589	+	0.582837i	$0.198057\pi$
$457$			24.9193i			1.16567i	−0.812589	+	0.582837i	$0.801943\pi$
$458$	6.06244	+	10.2339i	0.283279	+	0.478197i
$459$	7.30170	−	7.30170i	0.340814	−	0.340814i
$460$	−1.20810	−	4.13563i	−0.0563281	−	0.192825i
$461$	−1.60588	−	1.60588i	−0.0747933	−	0.0747933i	0.668721	−	0.743514i	$-0.266842\pi$
$461$	−1.60588	−	1.60588i	−0.0747933	−	0.0747933i	−0.743514	+	0.668721i	$0.766842\pi$
$462$		0			0
$463$	−14.8176			−0.688634			−0.344317	−	0.938853i	$-0.611890\pi$
$463$	−14.8176			−0.688634			−0.344317	+	0.938853i	$0.611890\pi$
$464$	−6.19770	+	28.1147i	−0.287721	+	1.30519i
$465$	−1.33251			−0.0617936
$466$	23.6157	+	6.04498i	1.09397	+	0.280028i
$467$	−8.77849	−	8.77849i	−0.406220	−	0.406220i	0.474198	−	0.880418i	$-0.342738\pi$
$467$	−8.77849	−	8.77849i	−0.406220	−	0.406220i	−0.880418	+	0.474198i	$0.842738\pi$
$468$	−0.699188	+	0.204247i	−0.0323200	+	0.00944133i
$469$		0			0
$470$	3.14486	+	5.30876i	0.145062	+	0.244875i
$471$		−	30.3718i		−	1.39946i
$472$	−0.853881	−	25.3886i	−0.0393031	−	1.16860i
$473$		−	15.6761i		−	0.720787i
$474$	−20.7000	+	12.2625i	−0.950781	+	0.563234i
$475$	−4.14387	+	4.14387i	−0.190134	+	0.190134i
$476$		0			0
$477$	−0.0691218	−	0.0691218i	−0.00316487	−	0.00316487i
$478$	−0.200835	+	0.784594i	−0.00918599	+	0.0358865i
$479$	−2.05417			−0.0938576			−0.0469288	−	0.998898i	$-0.514943\pi$
$479$	−2.05417			−0.0938576			−0.0469288	+	0.998898i	$0.514943\pi$
$480$	−18.0548	+	5.93976i	−0.824084	+	0.271112i
$481$	−0.543359			−0.0247750
$482$	−4.13341	+	16.1478i	−0.188272	+	0.735513i
$483$		0			0
$484$	−27.7351	+	50.6261i	−1.26069	+	2.30119i
$485$	3.15527	−	3.15527i	0.143273	−	0.143273i
$486$	−2.86561	+	1.69756i	−0.129987	+	0.0770029i
$487$			40.8816i			1.85252i	0.376883	+	0.926261i	$0.376996\pi$
$487$			40.8816i			1.85252i	−0.376883	+	0.926261i	$0.623004\pi$
$488$	29.7814	−	1.00162i	1.34814	−	0.0453413i
$489$			19.1302i			0.865098i
$490$		0			0
$491$	−0.278015	+	0.278015i	−0.0125466	+	0.0125466i	−0.713352	−	0.700806i	$-0.752824\pi$
$491$	−0.278015	+	0.278015i	−0.0125466	+	0.0125466i	0.700806	+	0.713352i	$0.252824\pi$
$492$	−23.2147	+	6.78150i	−1.04660	+	0.305733i
$493$	9.77960	+	9.77960i	0.440451	+	0.440451i
$494$	13.8633	+	3.54864i	0.623739	+	0.159661i
$495$	2.89345			0.130051
$496$	0.853938	+	1.33689i	0.0383429	+	0.0600282i
$497$		0			0
$498$	3.80552	+	0.974112i	0.170529	+	0.0436510i
$499$	−8.71632	−	8.71632i	−0.390196	−	0.390196i	0.484561	−	0.874757i	$-0.338979\pi$
$499$	−8.71632	−	8.71632i	−0.390196	−	0.390196i	−0.874757	+	0.484561i	$0.838979\pi$
$500$	6.70867	+	22.9654i	0.300021	+	1.02704i
$501$	−25.5150	+	25.5150i	−1.13992	+	1.13992i
$502$	5.68326	+	9.59378i	0.253656	+	0.428191i
$503$			0.367839i			0.0164011i	0.999966	+	0.00820057i	$0.00261035\pi$
$503$			0.367839i			0.0164011i	−0.999966	+	0.00820057i	$0.997390\pi$
$504$		0			0
$505$			14.5186i			0.646068i
$506$	−8.20180	+	4.85866i	−0.364614	+	0.215994i
$507$	12.2794	−	12.2794i	0.545349	−	0.545349i
$508$	−11.2485	−	6.16241i	−0.499071	−	0.273413i
$509$	−5.73240	−	5.73240i	−0.254084	−	0.254084i	0.568559	−	0.822643i	$-0.307501\pi$
$509$	−5.73240	−	5.73240i	−0.254084	−	0.254084i	−0.822643	+	0.568559i	$0.807501\pi$
$510$	−2.26422	+	8.84554i	−0.100262	+	0.391687i
$511$		0			0
$512$	17.5297	+	14.3077i	0.774711	+	0.632316i
$513$	33.9104			1.49718
$514$	10.1931	−	39.8209i	0.449599	−	1.75643i
$515$	−24.9523	−	24.9523i	−1.09953	−	1.09953i
$516$	−7.25195	−	3.97293i	−0.319249	−	0.174899i
$517$	9.65374	−	9.65374i	0.424571	−	0.424571i
$518$		0			0
$519$			21.3072i			0.935282i
$520$	6.24992	−	6.68495i	0.274077	−	0.293154i
$521$			13.3039i			0.582853i	0.956593	+	0.291427i	$0.0941299\pi$
$521$			13.3039i			0.582853i	−0.956593	+	0.291427i	$0.905870\pi$
$522$	−1.17829	−	1.98904i	−0.0515722	−	0.0870577i
$523$	20.0974	−	20.0974i	0.878798	−	0.878798i	−0.114612	−	0.993410i	$-0.536562\pi$
$523$	20.0974	−	20.0974i	0.878798	−	0.878798i	0.993410	+	0.114612i	$0.0365625\pi$
$524$	8.39189	+	28.7275i	0.366602	+	1.25497i
$525$		0			0
$526$	24.2268	+	6.20142i	1.05634	+	0.270395i
$527$	0.762071			0.0331964
$528$	22.6380	+	35.4411i	0.985192	+	1.54238i
$529$	21.8601			0.950441
$530$	1.18978	+	0.304551i	0.0516806	+	0.0132289i
$531$	1.44241	+	1.44241i	0.0625954	+	0.0625954i
$532$		0			0
$533$	8.23408	−	8.23408i	0.356657	−	0.356657i
$534$	15.3104	+	25.8451i	0.662546	+	1.11843i
$535$		−	6.07576i		−	0.262678i
$536$	23.0448	−	0.775056i	0.995386	−	0.0334773i
$537$		−	5.27420i		−	0.227599i
$538$	−18.1730	+	10.7655i	−0.783494	+	0.464134i
$539$		0			0
$540$	10.4194	−	19.0189i	0.448377	−	0.818442i
$541$	−12.9992	−	12.9992i	−0.558878	−	0.558878i	0.370110	−	0.928988i	$-0.379320\pi$
$541$	−12.9992	−	12.9992i	−0.558878	−	0.558878i	−0.928988	+	0.370110i	$0.879320\pi$
$542$	−4.86183	+	18.9935i	−0.208834	+	0.815841i
$543$	−33.8558			−1.45289
$544$	10.3257	−	3.39699i	0.442709	−	0.145645i
$545$	14.3413			0.614312
$546$		0			0
$547$	−22.9801	−	22.9801i	−0.982558	−	0.982558i	0.0172930	−	0.999850i	$-0.494495\pi$
$547$	−22.9801	−	22.9801i	−0.982558	−	0.982558i	−0.999850	+	0.0172930i	$0.994495\pi$
$548$	−1.67468	+	3.05685i	−0.0715386	+	0.130582i
$549$	−1.69198	+	1.69198i	−0.0722121	+	0.0722121i
$550$	7.13430	−	4.22629i	0.304208	−	0.180210i
$551$			45.4183i			1.93488i
$552$	0.169024	+	5.02563i	0.00719416	+	0.213905i
$553$		0			0
$554$	1.66390	+	2.80880i	0.0706925	+	0.119334i
$555$	0.805052	−	0.805052i	0.0341726	−	0.0341726i
$556$	−7.72233	+	2.25585i	−0.327500	+	0.0956695i
$557$	−3.29662	−	3.29662i	−0.139682	−	0.139682i	0.633808	−	0.773490i	$-0.281491\pi$
$557$	−3.29662	−	3.29662i	−0.139682	−	0.139682i	−0.773490	+	0.633808i	$0.781491\pi$
$558$	−0.123406	−	0.0315887i	−0.00522420	−	0.00133726i
$559$	3.98138			0.168394
$560$		0			0
$561$	20.2026			0.852954
$562$	0.932108	+	0.238595i	0.0393186	+	0.0100645i
$563$	2.95969	+	2.95969i	0.124736	+	0.124736i	0.766719	−	0.641983i	$-0.221888\pi$
$563$	2.95969	+	2.95969i	0.124736	+	0.124736i	−0.641983	+	0.766719i	$0.721888\pi$
$564$	−2.01931	−	6.91258i	−0.0850282	−	0.291072i
$565$	8.51115	−	8.51115i	0.358067	−	0.358067i
$566$	−0.274347	−	0.463118i	−0.0115317	−	0.0194663i
$567$		0			0
$568$	−5.76403	−	5.38893i	−0.241853	−	0.226115i
$569$			4.48223i			0.187905i	0.995577	+	0.0939524i	$0.0299502\pi$
$569$			4.48223i			0.187905i	−0.995577	+	0.0939524i	$0.970050\pi$
$570$	−25.7979	+	15.2824i	−1.08055	+	0.640110i
$571$	−0.344719	+	0.344719i	−0.0144261	+	0.0144261i	−0.714283	−	0.699857i	$-0.753247\pi$
$571$	−0.344719	+	0.344719i	−0.0144261	+	0.0144261i	0.699857	+	0.714283i	$0.253247\pi$
$572$	−17.7583	−	9.72873i	−0.742510	−	0.406779i
$573$	14.4143	+	14.4143i	0.602167	+	0.602167i
$574$		0			0
$575$	0.991504			0.0413486
$576$	−1.81290	+	0.122083i	−0.0755373	+	0.00508677i
$577$	−10.6396			−0.442934			−0.221467	−	0.975168i	$-0.571085\pi$
$577$	−10.6396			−0.442934			−0.221467	+	0.975168i	$0.571085\pi$
$578$	−4.66688	+	18.2319i	−0.194116	+	0.758346i
$579$	−2.56452	−	2.56452i	−0.106578	−	0.106578i
$580$	25.4731	+	13.9553i	1.05771	+	0.579460i
$581$		0			0
$582$	−4.48072	+	2.65434i	−0.185732	+	0.110026i
$583$		−	2.71737i		−	0.112542i
$584$	4.90816	+	4.58875i	0.203101	+	0.189884i
$585$			0.734874i			0.0303833i
$586$	−7.63716	−	12.8921i	−0.315488	−	0.532568i
$587$	−13.2861	+	13.2861i	−0.548376	+	0.548376i	−0.925971	−	0.377595i	$-0.876751\pi$
$587$	−13.2861	+	13.2861i	−0.548376	+	0.548376i	0.377595	+	0.925971i	$0.376751\pi$
$588$		0			0
$589$	1.76960	+	1.76960i	0.0729151	+	0.0729151i
$590$	−24.8279	−	6.35528i	−1.02215	−	0.261643i
$591$	23.4994			0.966638
$592$	−1.32362	−	0.291782i	−0.0544004	−	0.0119922i
$593$	−0.396993			−0.0163026			−0.00815128	−	0.999967i	$-0.502595\pi$
$593$	−0.396993			−0.0163026			−0.00815128	+	0.999967i	$0.502595\pi$
$594$	−46.4835	−	11.8985i	−1.90724	−	0.488203i
$595$		0			0
$596$	−35.3471	+	10.3256i	−1.44788	+	0.422954i
$597$	−12.4307	+	12.4307i	−0.508753	+	0.508753i
$598$	−1.23399	−	2.08308i	−0.0504618	−	0.0851834i
$599$		−	13.8238i		−	0.564825i	−0.959293	−	0.282412i	$-0.908865\pi$
$599$		−	13.8238i		−	0.564825i	0.959293	−	0.282412i	$-0.0911346\pi$
$600$	−0.147025	−	4.37152i	−0.00600228	−	0.178467i
$601$		−	8.73396i		−	0.356266i	−0.984006	−	0.178133i	$-0.942994\pi$
$601$		−	8.73396i		−	0.356266i	0.984006	−	0.178133i	$-0.0570057\pi$
$602$		0			0
$603$	−1.30926	+	1.30926i	−0.0533170	+	0.0533170i
$604$	6.12977	−	11.1889i	0.249417	−	0.455271i
$605$	41.1804	+	41.1804i	1.67422	+	1.67422i
$606$	4.20194	−	16.4155i	0.170692	−	0.666836i
$607$	−28.7873			−1.16844			−0.584220	−	0.811595i	$-0.698600\pi$
$607$	−28.7873			−1.16844			−0.584220	+	0.811595i	$0.698600\pi$
$608$	31.8653	+	16.0890i	1.29231	+	0.652495i
$609$		0			0
$610$	7.45490	−	29.1237i	0.301840	−	1.17918i
$611$	2.45184	+	2.45184i	0.0991908	+	0.0991908i
$612$	−0.419388	+	0.765526i	−0.0169528	+	0.0309446i
$613$	24.9569	−	24.9569i	1.00800	−	1.00800i	0.00803222	−	0.999968i	$-0.497443\pi$
$613$	24.9569	−	24.9569i	1.00800	−	1.00800i	0.999968	−	0.00803222i	$-0.00255676\pi$
$614$	−10.8060	+	6.40138i	−0.436095	+	0.258339i
$615$			24.3996i			0.983886i
$616$		0			0
$617$			33.4612i			1.34710i	0.739143	+	0.673548i	$0.235231\pi$
$617$			33.4612i			1.34710i	−0.739143	+	0.673548i	$0.764769\pi$
$618$	20.9909	+	35.4343i	0.844378	+	1.42537i
$619$	−6.59415	+	6.59415i	−0.265041	+	0.265041i	−0.827098	−	0.562057i	$-0.810010\pi$
$619$	−6.59415	+	6.59415i	−0.265041	+	0.265041i	0.562057	+	0.827098i	$0.310010\pi$
$620$	1.53622	−	0.448761i	0.0616960	−	0.0180227i
$621$	−4.05688	−	4.05688i	−0.162797	−	0.162797i
$622$	−13.5368	−	3.46507i	−0.542778	−	0.138937i
$623$		0			0
$624$	−9.00127	+	5.74955i	−0.360339	+	0.230166i
$625$	19.4941			0.779765
$626$	−23.5295	−	6.02292i	−0.940427	−	0.240724i
$627$	46.9123	+	46.9123i	1.87350	+	1.87350i
$628$	10.2286	+	35.0150i	0.408166	+	1.39725i
$629$	−0.460415	+	0.460415i	−0.0183580	+	0.0183580i
$630$		0			0
$631$			22.2587i			0.886105i	0.896496	+	0.443053i	$0.146104\pi$
$631$			22.2587i			0.886105i	−0.896496	+	0.443053i	$0.853896\pi$
$632$	19.7348	−	21.1084i	0.785007	−	0.839649i
$633$			12.2546i			0.487077i
$634$	−25.8501	+	15.3134i	−1.02664	+	0.608172i
$635$	−9.14978	+	9.14978i	−0.363098	+	0.363098i
$636$	−1.25709	−	0.688687i	−0.0498468	−	0.0273082i
$637$		0			0
$638$	15.9364	−	62.2580i	0.630928	−	2.46482i
$639$	0.633638			0.0250663
$640$	18.8146	−	12.9283i	0.743711	−	0.511036i
$641$	−8.27515			−0.326849			−0.163424	−	0.986556i	$-0.552254\pi$
$641$	−8.27515			−0.326849			−0.163424	+	0.986556i	$0.552254\pi$
$642$	−1.75844	+	6.86961i	−0.0694000	+	0.271122i
$643$	4.19175	+	4.19175i	0.165307	+	0.165307i	0.784913	−	0.619606i	$-0.212708\pi$
$643$	4.19175	+	4.19175i	0.165307	+	0.165307i	−0.619606	+	0.784913i	$0.712708\pi$
$644$		0			0
$645$	−5.89890	+	5.89890i	−0.232269	+	0.232269i
$646$	14.7540	−	8.74013i	0.580489	−	0.343876i
$647$		−	21.0650i		−	0.828150i	−0.910243	−	0.414075i	$-0.864105\pi$
$647$		−	21.0650i		−	0.828150i	0.910243	−	0.414075i	$-0.135895\pi$
$648$	−15.9690	+	17.0805i	−0.627320	+	0.670985i
$649$			56.7052i			2.22587i
$650$	1.07339	+	1.81196i	0.0421016	+	0.0710708i
$651$		0			0
$652$	−6.44266	−	22.0548i	−0.252314	−	0.863732i
$653$	12.1077	+	12.1077i	0.473811	+	0.473811i	0.903146	−	0.429334i	$-0.141252\pi$
$653$	12.1077	+	12.1077i	0.473811	+	0.473811i	−0.429334	+	0.903146i	$0.641252\pi$
$654$	−16.2151	−	4.15062i	−0.634059	−	0.162302i
$655$	30.1937			1.17977
$656$	24.4798	−	15.6365i	0.955777	−	0.610501i
$657$	−0.539552			−0.0210499
$658$		0			0
$659$	19.9513	+	19.9513i	0.777192	+	0.777192i	0.979352	−	0.202161i	$-0.0647964\pi$
$659$	19.9513	+	19.9513i	0.777192	+	0.777192i	−0.202161	+	0.979352i	$0.564796\pi$
$660$	40.7253	−	11.8967i	1.58523	−	0.463079i
$661$	−15.1853	+	15.1853i	−0.590642	+	0.590642i	−0.937805	−	0.347163i	$-0.887145\pi$
$661$	−15.1853	+	15.1853i	−0.590642	+	0.590642i	0.347163	+	0.937805i	$0.387145\pi$
$662$	17.4426	+	29.4444i	0.677926	+	1.14439i
$663$			5.13102i			0.199272i
$664$	−4.71536	+	0.158589i	−0.182991	+	0.00615445i
$665$		0			0
$666$	0.0936421	−	0.0554727i	0.00362856	−	0.00214952i
$667$	5.43362	−	5.43362i	0.210390	−	0.210390i
$668$	20.8227	−	38.0085i	0.805654	−	1.47059i
$669$	−26.3621	−	26.3621i	−1.01922	−	1.01922i
$670$	5.76860	−	22.5359i	0.222860	−	0.870639i
$671$	−66.5165			−2.56784
$672$		0			0
$673$	21.0339			0.810796			0.405398	−	0.914140i	$-0.367133\pi$
$673$	21.0339			0.810796			0.405398	+	0.914140i	$0.367133\pi$
$674$	−1.49655	+	5.84651i	−0.0576450	+	0.225199i
$675$	3.52886	+	3.52886i	0.135826	+	0.135826i
$676$	−10.0212	+	18.2921i	−0.385432	+	0.703544i
$677$	−4.40719	+	4.40719i	−0.169382	+	0.169382i	−0.786708	−	0.617326i	$-0.788216\pi$
$677$	−4.40719	+	4.40719i	−0.169382	+	0.169382i	0.617326	+	0.786708i	$0.288216\pi$
$678$	−12.0865	+	7.15992i	−0.464179	+	0.274975i
$679$		0			0
$680$	−0.368624	−	10.9604i	−0.0141361	−	0.420311i
$681$			30.9883i			1.18747i
$682$	−1.80480	−	3.04663i	−0.0691093	−	0.116662i
$683$	−15.7913	+	15.7913i	−0.604236	+	0.604236i	−0.941434	−	0.337198i	$-0.890521\pi$
$683$	−15.7913	+	15.7913i	−0.604236	+	0.604236i	0.337198	+	0.941434i	$0.390521\pi$
$684$	−2.75148	+	0.803764i	−0.105205	+	0.0307327i
$685$	2.48651	+	2.48651i	0.0950048	+	0.0950048i
$686$		0			0
$687$	−14.0057			−0.534351
$688$	9.69861	+	2.13799i	0.369756	+	0.0815102i
$689$	0.690152			0.0262927
$690$	4.91465	+	1.25802i	0.187097	+	0.0478920i
$691$	27.1679	+	27.1679i	1.03351	+	1.03351i	0.999419	+	0.0340957i	$0.0108551\pi$
$691$	27.1679	+	27.1679i	1.03351	+	1.03351i	0.0340957	+	0.999419i	$0.489145\pi$
$692$	−7.17583	−	24.5646i	−0.272784	−	0.933805i
$693$		0			0
$694$	0.0389423	+	0.0657375i	0.00147823	+	0.00249536i
$695$			8.11647i			0.307875i
$696$	−24.7625	−	23.1510i	−0.938619	−	0.877537i
$697$		−	13.9543i		−	0.528557i
$698$	−26.6590	+	15.7925i	−1.00906	+	0.597756i
$699$	−20.2963	+	20.2963i	−0.767676	+	0.767676i
$700$		0			0
$701$	1.40129	+	1.40129i	0.0529259	+	0.0529259i	0.733074	−	0.680148i	$-0.238085\pi$
$701$	1.40129	+	1.40129i	0.0529259	+	0.0529259i	−0.680148	+	0.733074i	$0.738085\pi$
$702$	3.02197	−	11.8058i	0.114057	−	0.445581i
$703$	−2.13825			−0.0806457
$704$	−38.0347	−	33.2353i	−1.43349	−	1.25260i
$705$	−7.26540			−0.273631
$706$	5.87877	−	22.9663i	0.221250	−	0.864349i
$707$		0			0
$708$	26.2325	+	14.3713i	0.985879	+	0.540107i
$709$	6.16411	−	6.16411i	0.231498	−	0.231498i	−0.581820	−	0.813318i	$-0.697659\pi$
$709$	6.16411	−	6.16411i	0.231498	−	0.231498i	0.813318	+	0.581820i	$0.197659\pi$
$710$	−6.84924	+	4.05742i	−0.257047	+	0.152272i
$711$			2.32044i			0.0870234i
$712$	−26.3551	−	24.6400i	−0.987700	−	0.923424i
$713$		−	0.423412i		−	0.0158569i
$714$		0			0
$715$	−14.4450	+	14.4450i	−0.540211	+	0.540211i
$716$	1.77624	+	6.08051i	0.0663813	+	0.227239i
$717$	−0.674313	−	0.674313i	−0.0251827	−	0.0251827i
$718$	−47.2662	−	12.0989i	−1.76396	−	0.451526i
$719$	26.6660			0.994473			0.497236	−	0.867615i	$-0.334348\pi$
$719$	26.6660			0.994473			0.497236	+	0.867615i	$0.334348\pi$
$720$	−0.394626	+	1.79015i	−0.0147068	+	0.0667149i
$721$		0			0
$722$	28.5247	+	7.30158i	1.06158	+	0.271737i
$723$	−13.8781	−	13.8781i	−0.516132	−	0.516132i
$724$	39.0315	−	11.4019i	1.45060	−	0.423749i
$725$	−4.72641	+	4.72641i	−0.175534	+	0.175534i
$726$	−34.6426	−	58.4793i	−1.28571	−	2.17037i
$727$		−	37.7224i		−	1.39905i	−0.714610	−	0.699523i	$-0.753396\pi$
$727$		−	37.7224i		−	1.39905i	0.714610	−	0.699523i	$-0.246604\pi$
$728$		0			0
$729$		−	28.7229i		−	1.06381i
$730$	5.83223	−	3.45496i	0.215860	−	0.127874i
$731$	3.37362	−	3.37362i	0.124778	−	0.124778i
$732$	−16.8579	+	30.7714i	−0.623085	+	1.13734i
$733$	16.0658	+	16.0658i	0.593405	+	0.593405i	0.938549	−	0.345145i	$-0.112170\pi$
$733$	16.0658	+	16.0658i	0.593405	+	0.593405i	−0.345145	+	0.938549i	$0.612170\pi$
$734$	−7.19936	+	28.1254i	−0.265733	+	1.03813i
$735$		0			0
$736$	−1.88739	−	5.73701i	−0.0695703	−	0.211469i
$737$	−51.4705			−1.89594
$738$	−0.578421	+	2.25969i	−0.0212920	+	0.0831803i
$739$	−18.5432	−	18.5432i	−0.682121	−	0.682121i	0.278357	−	0.960478i	$-0.410210\pi$
$739$	−18.5432	−	18.5432i	−0.682121	−	0.682121i	−0.960478	+	0.278357i	$0.910210\pi$
$740$	−0.657001	+	1.19925i	−0.0241518	+	0.0440854i
$741$	−11.9147	+	11.9147i	−0.437697	+	0.437697i
$742$		0			0
$743$		−	20.7110i		−	0.759812i	−0.925025	−	0.379906i	$-0.875956\pi$
$743$		−	20.7110i		−	0.759812i	0.925025	−	0.379906i	$-0.124044\pi$
$744$	−1.86682	+	0.0627858i	−0.0684409	+	0.00230184i
$745$			37.1513i			1.36112i
$746$	11.4001	+	19.2442i	0.417387	+	0.704582i
$747$	0.267896	−	0.267896i	0.00980179	−	0.00980179i
$748$	−23.2911	+	6.80382i	−0.851607	+	0.248772i
$749$		0			0
$750$	−27.2913	−	6.98585i	−0.996538	−	0.255087i
$751$	−15.4773			−0.564775			−0.282387	−	0.959300i	$-0.591126\pi$
$751$	−15.4773			−0.564775			−0.282387	+	0.959300i	$0.591126\pi$
$752$	4.65603	+	7.28930i	0.169788	+	0.265813i
$753$	−13.1297			−0.478474
$754$	15.8122	+	4.04750i	0.575846	+	0.147401i
$755$	−9.10132	−	9.10132i	−0.331231	−	0.331231i
$756$		0			0
$757$	18.4631	−	18.4631i	0.671051	−	0.671051i	−0.286907	−	0.957958i	$-0.592627\pi$
$757$	18.4631	−	18.4631i	0.671051	−	0.671051i	0.957958	+	0.286907i	$0.0926272\pi$
$758$	−11.4898	−	19.3956i	−0.417327	−	0.704479i
$759$		−	11.2247i		−	0.407431i
$760$	24.5950	−	26.3070i	0.892154	−	0.954254i
$761$		−	12.8657i		−	0.466380i	−0.972431	−	0.233190i	$-0.925084\pi$
$761$		−	12.8657i		−	0.466380i	0.972431	−	0.233190i	$-0.0749164\pi$
$762$	12.9934	−	7.69716i	0.470701	−	0.278839i
$763$		0			0
$764$	−21.4724	−	11.7635i	−0.776844	−	0.425589i
$765$	0.622696	+	0.622696i	0.0225136	+	0.0225136i
$766$	3.60930	−	14.1003i	0.130409	−	0.509464i
$767$	−14.4019			−0.520022
$768$	−25.0145	+	9.17220i	−0.902634	+	0.330973i
$769$	−16.5676			−0.597443			−0.298722	−	0.954340i	$-0.596560\pi$
$769$	−16.5676			−0.597443			−0.298722	+	0.954340i	$0.596560\pi$
$770$		0			0
$771$	34.2238	+	34.2238i	1.23254	+	1.23254i
$772$	3.82026	+	2.09290i	0.137494	+	0.0753252i
$773$	−34.6443	+	34.6443i	−1.24607	+	1.24607i	−0.288626	+	0.957442i	$0.593198\pi$
$773$	−34.6443	+	34.6443i	−1.24607	+	1.24607i	−0.957442	+	0.288626i	$0.906802\pi$
$774$	−0.686149	+	0.406468i	−0.0246631	+	0.0146102i
$775$			0.368303i			0.0132298i
$776$	4.27180	−	4.56914i	0.153349	−	0.164023i
$777$		0			0
$778$	−14.7743	−	24.9401i	−0.529684	−	0.894147i
$779$	32.4032	−	32.4032i	1.16096	−	1.16096i
$780$	3.02151	+	10.3433i	0.108187	+	0.370351i
$781$	12.4550	+	12.4550i	0.445676	+	0.445676i
$782$	−2.81072	−	0.719470i	−0.100511	−	0.0257282i
$783$	38.6776			1.38222
$784$		0			0
$785$	36.8021			1.31352
$786$	−34.1388	−	8.73862i	−1.21769	−	0.311696i
$787$	3.70417	+	3.70417i	0.132039	+	0.132039i	0.770038	−	0.637998i	$-0.220237\pi$
$787$	3.70417	+	3.70417i	0.132039	+	0.132039i	−0.637998	+	0.770038i	$0.720237\pi$
$788$	−27.0920	+	7.91413i	−0.965112	+	0.281929i
$789$	−20.8215	+	20.8215i	−0.741266	+	0.741266i
$790$	−14.8587	−	25.0826i	−0.528648	−	0.892398i
$791$		0			0
$792$	4.05367	−	0.136335i	0.144041	−	0.00484446i
$793$		−	16.8937i		−	0.599914i
$794$	−9.52599	+	5.64310i	−0.338065	+	0.200266i
$795$	−1.02254	+	1.02254i	−0.0362659	+	0.0362659i
$796$	10.1446	−	18.5174i	0.359567	−	0.656332i
$797$	20.4204	+	20.4204i	0.723329	+	0.723329i	0.969282	−	0.245953i	$-0.0791009\pi$
$797$	20.4204	+	20.4204i	0.723329	+	0.723329i	−0.245953	+	0.969282i	$0.579101\pi$
$798$		0			0
$799$	4.15514			0.146998
$800$	1.64174	+	4.99032i	0.0580443	+	0.176434i
$801$	2.89721			0.102368
$802$	4.97975	−	19.4542i	0.175841	−	0.686951i
$803$	−10.6056	−	10.6056i	−0.374265	−	0.374265i
$804$	−13.0446	+	23.8109i	−0.460049	+	0.839746i
$805$		0			0
$806$	0.773779	−	0.458379i	0.0272552	−	0.0161457i
$807$		−	24.8710i		−	0.875499i
$808$	0.684092	+	20.3402i	0.0240663	+	0.715567i
$809$			38.8827i			1.36704i	0.729931	+	0.683521i	$0.239552\pi$
$809$			38.8827i			1.36704i	−0.729931	+	0.683521i	$0.760448\pi$
$810$	12.0233	+	20.2963i	0.422456	+	0.713139i
$811$	12.4718	−	12.4718i	0.437945	−	0.437945i	−0.453375	−	0.891320i	$-0.649780\pi$
$811$	12.4718	−	12.4718i	0.437945	−	0.437945i	0.891320	+	0.453375i	$0.149780\pi$
$812$		0			0
$813$	−16.3238	−	16.3238i	−0.572501	−	0.572501i
$814$	2.93106	+	0.750272i	0.102733	+	0.0262970i
$815$	−23.1805			−0.811976
$816$	−2.75535	+	12.4991i	−0.0964564	+	0.437557i
$817$	15.6677			0.548145
$818$	36.1894	+	9.26354i	1.26533	+	0.323892i
$819$		0			0
$820$	−8.21727	−	28.1297i	−0.286960	−	0.982332i
$821$	13.5414	−	13.5414i	0.472598	−	0.472598i	−0.430156	−	0.902754i	$-0.641542\pi$
$821$	13.5414	−	13.5414i	0.472598	−	0.472598i	0.902754	+	0.430156i	$0.141542\pi$
$822$	−2.09175	−	3.53104i	−0.0729583	−	0.123159i
$823$		−	10.3548i		−	0.360944i	−0.983580	−	0.180472i	$-0.942237\pi$
$823$		−	10.3548i		−	0.360944i	0.983580	−	0.180472i	$-0.0577625\pi$
$824$	−36.1335	−	33.7820i	−1.25877	−	1.17685i
$825$			9.76376i			0.339931i
$826$		0			0
$827$	−9.65786	+	9.65786i	−0.335837	+	0.335837i	−0.854798	−	0.518961i	$-0.826319\pi$
$827$	−9.65786	+	9.65786i	−0.335837	+	0.335837i	0.518961	+	0.854798i	$0.326319\pi$
$828$	0.425332	+	0.233015i	0.0147813	+	0.00809783i
$829$	−18.8124	−	18.8124i	−0.653383	−	0.653383i	0.300423	−	0.953806i	$-0.402872\pi$
$829$	−18.8124	−	18.8124i	−0.653383	−	0.653383i	−0.953806	+	0.300423i	$0.902872\pi$
$830$	−1.18035	+	4.61122i	−0.0409706	+	0.160058i
$831$	−3.84403			−0.133348
$832$	8.44103	−	9.65997i	0.292640	−	0.334899i
$833$		0			0
$834$	2.34906	−	9.17696i	0.0813412	−	0.317772i
$835$	−30.9170	−	30.9170i	−1.06993	−	1.06993i
$836$	−69.8832	−	38.2850i	−2.41696	−	1.32411i
$837$	1.50697	−	1.50697i	0.0520884	−	0.0520884i
$838$	−26.9971	+	15.9928i	−0.932599	+	0.552463i
$839$		−	46.4429i		−	1.60339i	−0.597736	−	0.801693i	$-0.703933\pi$
$839$		−	46.4429i		−	1.60339i	0.597736	−	0.801693i	$-0.296067\pi$
$840$		0			0
$841$			22.8031i			0.786315i
$842$	−26.2041	−	44.2345i	−0.903054	−	1.52442i
$843$	−0.801093	+	0.801093i	−0.0275911	+	0.0275911i
$844$	−4.12710	−	14.1281i	−0.142061	−	0.486308i
$845$	14.8792	+	14.8792i	0.511861	+	0.511861i
$846$	−0.672862	−	0.172235i	−0.0231335	−	0.00592156i
$847$		0			0
$848$	1.68120	+	0.370610i	0.0577328	+	0.0127268i
$849$	0.633809			0.0217523
$850$	2.44490	+	0.625828i	0.0838592	+	0.0214657i
$851$	0.255810	+	0.255810i	0.00876905	+	0.00876905i
$852$	8.91845	−	2.60526i	0.305541	−	0.0892549i
$853$	−31.3013	+	31.3013i	−1.07174	+	1.07174i	−0.0745177	+	0.997220i	$0.523742\pi$
$853$	−31.3013	+	31.3013i	−1.07174	+	1.07174i	−0.997220	+	0.0745177i	$0.976258\pi$
$854$		0			0
$855$			2.89191i			0.0989014i
$856$	−0.286280	−	8.51202i	−0.00978486	−	0.290935i
$857$		−	26.3725i		−	0.900869i	−0.892810	−	0.450434i	$-0.851269\pi$
$857$		−	26.3725i		−	0.900869i	0.892810	−	0.450434i	$-0.148731\pi$
$858$	20.5130	−	12.1517i	0.700301	−	0.414851i
$859$	2.13661	−	2.13661i	0.0729004	−	0.0729004i	−0.669717	−	0.742617i	$-0.733584\pi$
$859$	2.13661	−	2.13661i	0.0729004	−	0.0729004i	0.742617	+	0.669717i	$0.233584\pi$
$860$	4.81408	−	8.78734i	0.164159	−	0.299646i
$861$		0			0
$862$	−8.69586	+	33.9717i	−0.296182	+	1.15708i
$863$	7.00913			0.238593			0.119297	−	0.992859i	$-0.461936\pi$
$863$	7.00913			0.238593			0.119297	+	0.992859i	$0.461936\pi$
$864$	13.7012	−	27.1360i	0.466123	−	0.923186i
$865$	−25.8184			−0.877851
$866$	1.83365	−	7.16344i	0.0623100	−	0.243424i
$867$	−15.6692	−	15.6692i	−0.532155	−	0.532155i
$868$		0			0
$869$	−45.6115	+	45.6115i	−1.54726	+	1.54726i
$870$	−29.4245	+	17.4308i	−0.997585	+	0.590960i
$871$		−	13.0724i		−	0.442941i
$872$	20.0918	−	0.675738i	0.680395	−	0.0228834i
$873$			0.502284i			0.0169997i
$874$	−4.85608	−	8.19743i	−0.164259	−	0.277282i
$875$		0			0
$876$	−7.59419	+	2.21842i	−0.256584	+	0.0749535i
$877$	29.0327	+	29.0327i	0.980363	+	0.980363i	0.999811	−	0.0194475i	$-0.00619074\pi$
$877$	29.0327	+	29.0327i	0.980363	+	0.980363i	−0.0194475	+	0.999811i	$0.506191\pi$
$878$	−30.3379	−	7.76571i	−1.02386	−	0.262080i
$879$	17.6437			0.595107
$880$	−42.9447	+	27.4309i	−1.44767	+	0.924695i
$881$	−13.6166			−0.458755			−0.229377	−	0.973338i	$-0.573669\pi$
$881$	−13.6166			−0.458755			−0.229377	+	0.973338i	$0.573669\pi$
$882$		0			0
$883$	35.2238	+	35.2238i	1.18537	+	1.18537i	0.978332	+	0.207042i	$0.0663836\pi$
$883$	35.2238	+	35.2238i	1.18537	+	1.18537i	0.207042	+	0.978332i	$0.433616\pi$
$884$	−1.72802	−	5.91543i	−0.0581196	−	0.198958i
$885$	21.3381	−	21.3381i	0.717274	−	0.717274i
$886$	16.2725	+	27.4692i	0.546685	+	0.922845i
$887$		−	6.29208i		−	0.211268i	−0.994405	−	0.105634i	$-0.966313\pi$
$887$		−	6.29208i		−	0.211268i	0.994405	−	0.105634i	$-0.0336871\pi$
$888$	1.08993	−	1.16580i	0.0365756	−	0.0391215i
$889$		0			0
$890$	−31.3171	+	18.5519i	−1.04975	+	0.621862i
$891$	36.9078	−	36.9078i	1.23646	−	1.23646i
$892$	39.2706	+	21.5141i	1.31488	+	0.720345i
$893$	9.64860	+	9.64860i	0.322878	+	0.322878i
$894$	10.7523	−	42.0054i	0.359609	−	1.40487i
$895$	6.39085			0.213623
$896$		0			0
$897$	2.85083			0.0951864
$898$	−12.7540	+	49.8254i	−0.425606	+	1.66270i
$899$	2.01837	+	2.01837i	0.0673164	+	0.0673164i
$900$	−0.369973	−	0.202687i	−0.0123324	−	0.00675624i
$901$	0.584800	−	0.584800i	0.0194825	−	0.0194825i
$902$	−55.7870	+	33.0477i	−1.85750	+	1.10037i
$903$		0			0
$904$	11.5229	−	12.3250i	0.383247	−	0.409923i
$905$		−	41.0237i		−	1.36367i
$906$	7.65639	+	12.9246i	0.254367	+	0.429390i
$907$	31.7014	−	31.7014i	1.05263	−	1.05263i	0.0540924	−	0.998536i	$-0.482773\pi$
$907$	31.7014	−	31.7014i	1.05263	−	1.05263i	0.998536	−	0.0540924i	$-0.0172266\pi$
$908$	−10.4362	−	35.7257i	−0.346338	−	1.18560i
$909$	−1.15560	−	1.15560i	−0.0383288	−	0.0383288i
$910$		0			0
$911$	42.8973			1.42125			0.710625	−	0.703571i	$-0.248412\pi$
$911$	42.8973			1.42125			0.710625	+	0.703571i	$0.248412\pi$
$912$	−35.4223	+	22.6259i	−1.17295	+	0.749220i
$913$	10.5317			0.348549
$914$	34.1404	+	8.73904i	1.12926	+	0.289062i
$915$	25.0301	+	25.0301i	0.827471	+	0.827471i
$916$	16.1469	−	4.71684i	0.533508	−	0.155849i
$917$		0			0
$918$	−7.44297	−	12.5643i	−0.245655	−	0.414684i
$919$			30.2811i			0.998880i	0.866348	+	0.499440i	$0.166461\pi$
$919$			30.2811i			0.998880i	−0.866348	+	0.499440i	$0.833539\pi$
$920$	−6.08966	+	0.204810i	−0.200770	+	0.00675240i
$921$		−	14.7888i		−	0.487306i
$922$	−2.76330	+	1.63695i	−0.0910043	+	0.0539101i
$923$	−3.16330	+	3.16330i	−0.104121	+	0.104121i
$924$		0			0
$925$	−0.222515	−	0.222515i	−0.00731626	−	0.00731626i
$926$	−5.19646	+	20.3008i	−0.170766	+	0.667125i
$927$	3.97214			0.130462
$928$	36.3449	+	18.3508i	1.19308	+	0.602394i
$929$	−13.8667			−0.454951			−0.227475	−	0.973784i	$-0.573047\pi$
$929$	−13.8667			−0.454951			−0.227475	+	0.973784i	$0.573047\pi$
$930$	−0.467303	+	1.82559i	−0.0153235	+	0.0598635i
$931$		0			0
$932$	16.5638	−	30.2345i	0.542564	−	0.990364i
$933$	11.6341	−	11.6341i	0.380884	−	0.380884i
$934$	−15.1055	+	8.94833i	−0.494266	+	0.292798i
$935$			24.4799i			0.800578i
$936$	0.0346261	+	1.02954i	0.00113179	+	0.0336517i
$937$			46.7544i			1.52740i	0.645572	+	0.763699i	$0.276619\pi$
$937$			46.7544i			1.52740i	−0.645572	+	0.763699i	$0.723381\pi$
$938$		0			0
$939$	20.2222	−	20.2222i	0.659927	−	0.659927i
$940$	8.37611	−	2.44684i	0.273199	−	0.0798070i
$941$	−5.88867	−	5.88867i	−0.191965	−	0.191965i	0.604580	−	0.796545i	$-0.293341\pi$
$941$	−5.88867	−	5.88867i	−0.191965	−	0.191965i	−0.796545	+	0.604580i	$0.793341\pi$
$942$	−41.6106	−	10.6512i	−1.35575	−	0.347036i
$943$	−7.75311			−0.252476
$944$	−35.0829	−	7.73378i	−1.14185	−	0.251713i
$945$		0			0
$946$	−21.4769	−	5.49751i	−0.698273	−	0.178739i
$947$	5.19057	+	5.19057i	0.168671	+	0.168671i	0.786395	−	0.617724i	$-0.211945\pi$
$947$	5.19057	+	5.19057i	0.168671	+	0.168671i	−0.617724	+	0.786395i	$0.711945\pi$
$948$	9.54072	+	32.6602i	0.309868	+	1.06075i
$949$	2.69360	−	2.69360i	0.0874380	−	0.0874380i
$950$	4.22404	+	7.13050i	0.137046	+	0.231344i
$951$		−	35.3776i		−	1.14720i
$952$		0			0
$953$		−	41.3553i		−	1.33963i	−0.742528	−	0.669815i	$-0.766373\pi$
$953$		−	41.3553i		−	1.33963i	0.742528	−	0.669815i	$-0.233627\pi$
$954$	−0.118940	+	0.0704591i	−0.00385084	+	0.00228120i
$955$	−17.4661	+	17.4661i	−0.565191	+	0.565191i
$956$	1.00449	+	0.550305i	0.0324877	+	0.0177981i
$957$	53.5072	+	53.5072i	1.72964	+	1.72964i
$958$	−0.720387	+	2.81430i	−0.0232746	+	0.0909260i
$959$		0			0
$960$	1.80601	+	26.8188i	0.0582888	+	0.865574i
$961$	−30.8427			−0.994926
$962$	−0.190553	+	0.744424i	−0.00614367	+	0.0240012i
$963$	0.483597	+	0.483597i	0.0155837	+	0.0155837i
$964$	20.6736	+	11.3259i	0.665852	+	0.364782i
$965$	3.10748	−	3.10748i	0.100033	−	0.100033i
$966$		0			0
$967$			40.5984i			1.30556i	0.757549	+	0.652778i	$0.226397\pi$
$967$			40.5984i			1.30556i	−0.757549	+	0.652778i	$0.773603\pi$
$968$	59.6333	+	55.7526i	1.91669	+	1.79196i
$969$			20.1918i			0.648655i
$970$	−3.21631	−	5.42938i	−0.103270	−	0.174327i
$971$	−22.9960	+	22.9960i	−0.737978	+	0.737978i	−0.972186	−	0.234208i	$-0.924750\pi$
$971$	−22.9960	+	22.9960i	−0.737978	+	0.737978i	0.234208	+	0.972186i	$0.424750\pi$
$972$	1.32077	+	4.52133i	0.0423639	+	0.145022i
$973$		0			0
$974$	56.0095	+	14.3369i	1.79466	+	0.459385i
$975$	−2.47978			−0.0794166
$976$	9.07190	−	41.1530i	0.290385	−	1.31728i
$977$	−16.6857			−0.533823			−0.266912	−	0.963721i	$-0.586003\pi$
$977$	−16.6857			−0.533823			−0.266912	+	0.963721i	$0.586003\pi$
$978$	26.2092	+	6.70885i	0.838077	+	0.214525i
$979$	56.9486	+	56.9486i	1.82009	+	1.82009i
$980$		0			0
$981$	−1.14148	+	1.14148i	−0.0364448	+	0.0364448i
$982$	0.283393	+	0.478389i	0.00904344	+	0.0152660i
$983$			11.7778i			0.375655i	0.982202	+	0.187827i	$0.0601445\pi$
$983$			11.7778i			0.375655i	−0.982202	+	0.187827i	$0.939855\pi$
$984$	1.14967	+	34.1833i	0.0366502	+	1.08972i
$985$			28.4747i			0.907281i
$986$	16.8281	−	9.96881i	0.535916	−	0.317472i
$987$		0			0
$988$	9.72355	−	17.7488i	0.309347	−	0.564665i
$989$	−1.87441	−	1.87441i	−0.0596028	−	0.0596028i
$990$	1.01472	−	3.96415i	0.0322498	−	0.125989i
$991$	−31.7745			−1.00935			−0.504675	−	0.863310i	$-0.668387\pi$
$991$	−31.7745			−1.00935			−0.504675	+	0.863310i	$0.668387\pi$
$992$	2.13107	−	0.701090i	0.0676615	−	0.0222596i
$993$	−40.2967			−1.27878
$994$		0			0
$995$	−15.0625	−	15.0625i	−0.477513	−	0.477513i
$996$	2.66915	−	4.87210i	0.0845752	−	0.154379i
$997$	−0.845464	+	0.845464i	−0.0267761	+	0.0267761i	−0.720368	−	0.693592i	$-0.756027\pi$
$997$	−0.845464	+	0.845464i	−0.0267761	+	0.0267761i	0.693592	+	0.720368i	$0.256027\pi$
$998$	−14.9985	+	8.88496i	−0.474769	+	0.281248i
$999$			1.82091i			0.0576109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.m.j.589.6		24
7.2	even	3		112.2.w.c.109.2	yes	48
7.3	odd	6		784.2.x.o.765.10		48
7.4	even	3		112.2.w.c.93.10	yes	48
7.5	odd	6		784.2.x.o.557.2		48
7.6	odd	2		784.2.m.k.589.6		24
16.5	even	4	inner	784.2.m.j.197.6		24
28.11	odd	6		448.2.ba.c.401.4		48
28.23	odd	6		448.2.ba.c.81.9		48
56.11	odd	6		896.2.ba.e.289.9		48
56.37	even	6		896.2.ba.f.417.9		48
56.51	odd	6		896.2.ba.e.417.4		48
56.53	even	6		896.2.ba.f.289.4		48
112.5	odd	12		784.2.x.o.165.10		48
112.11	odd	12		448.2.ba.c.177.9		48
112.37	even	12		112.2.w.c.53.10	yes	48
112.51	odd	12		896.2.ba.e.865.9		48
112.53	even	12		112.2.w.c.37.2	✓	48
112.67	odd	12		896.2.ba.e.737.4		48
112.69	odd	4		784.2.m.k.197.6		24
112.93	even	12		896.2.ba.f.865.4		48
112.101	odd	12		784.2.x.o.373.2		48
112.107	odd	12		448.2.ba.c.305.4		48
112.109	even	12		896.2.ba.f.737.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.2	✓	48	112.53	even	12
112.2.w.c.53.10	yes	48	112.37	even	12
112.2.w.c.93.10	yes	48	7.4	even	3
112.2.w.c.109.2	yes	48	7.2	even	3
448.2.ba.c.81.9		48	28.23	odd	6
448.2.ba.c.177.9		48	112.11	odd	12
448.2.ba.c.305.4		48	112.107	odd	12
448.2.ba.c.401.4		48	28.11	odd	6
784.2.m.j.197.6		24	16.5	even	4	inner
784.2.m.j.589.6		24	1.1	even	1	trivial
784.2.m.k.197.6		24	112.69	odd	4
784.2.m.k.589.6		24	7.6	odd	2
784.2.x.o.165.10		48	112.5	odd	12
784.2.x.o.373.2		48	112.101	odd	12
784.2.x.o.557.2		48	7.5	odd	6
784.2.x.o.765.10		48	7.3	odd	6
896.2.ba.e.289.9		48	56.11	odd	6
896.2.ba.e.417.4		48	56.51	odd	6
896.2.ba.e.737.4		48	112.67	odd	12
896.2.ba.e.865.9		48	112.51	odd	12
896.2.ba.f.289.4		48	56.53	even	6
896.2.ba.f.417.9		48	56.37	even	6
896.2.ba.f.737.9		48	112.109	even	12
896.2.ba.f.865.4		48	112.93	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.350694 - 1.37004i) q^{2} +(1.17747 + 1.17747i) q^{3} +(-1.75403 - 0.960931i) q^{4} +(-1.42676 + 1.42676i) q^{5} +(2.02612 - 1.20025i) q^{6} +(-1.93164 + 2.06610i) q^{8} -0.227125i q^{9} +(1.45437 + 2.45508i) q^{10} +(4.46446 - 4.46446i) q^{11} +(-0.933847 - 3.19678i) q^{12} +(1.13388 + 1.13388i) q^{13} -3.35995 q^{15} +(2.15322 + 3.37100i) q^{16} +1.92158 q^{17} +(-0.311171 - 0.0796515i) q^{18} +(4.46208 + 4.46208i) q^{19} +(3.87361 - 1.13156i) q^{20} +(-4.55083 - 7.68215i) q^{22} -1.06764i q^{23} +(-4.70722 + 0.158316i) q^{24} +0.928685i q^{25} +(1.95110 - 1.15581i) q^{26} +(3.79985 - 3.79985i) q^{27} +(5.08936 + 5.08936i) q^{29} +(-1.17831 + 4.60327i) q^{30} +0.396586 q^{31} +(5.37353 - 1.76781i) q^{32} +10.5135 q^{33} +(0.673887 - 2.63264i) q^{34} +(-0.218252 + 0.398384i) q^{36} +(-0.239603 + 0.239603i) q^{37} +(7.67806 - 4.54841i) q^{38} +2.67021i q^{39} +(-0.191834 - 5.70383i) q^{40} -7.26189i q^{41} +(1.75565 - 1.75565i) q^{43} +(-12.1208 + 3.54074i) q^{44} +(0.324054 + 0.324054i) q^{45} +(-1.46271 - 0.374416i) q^{46} +2.16235 q^{47} +(-1.43390 + 6.50461i) q^{48} +(1.27234 + 0.325684i) q^{50} +(2.26260 + 2.26260i) q^{51} +(-0.899272 - 3.07842i) q^{52} +(0.304333 - 0.304333i) q^{53} +(-3.87336 - 6.53853i) q^{54} +12.7395i q^{55} +10.5079i q^{57} +(8.75744 - 5.18782i) q^{58} +(-6.35074 + 6.35074i) q^{59} +(5.89344 + 3.22868i) q^{60} +(-7.44956 - 7.44956i) q^{61} +(0.139080 - 0.543339i) q^{62} +(-0.537512 - 7.98192i) q^{64} -3.23555 q^{65} +(3.68704 - 14.4040i) q^{66} +(-5.76447 - 5.76447i) q^{67} +(-3.37050 - 1.84651i) q^{68} +(1.25712 - 1.25712i) q^{69} +2.78982i q^{71} +(0.469263 + 0.438725i) q^{72} -2.37557i q^{73} +(0.244238 + 0.412293i) q^{74} +(-1.09350 + 1.09350i) q^{75} +(-3.53886 - 12.1144i) q^{76} +(3.65830 + 0.936427i) q^{78} -10.2166 q^{79} +(-7.88176 - 1.73748i) q^{80} +8.26704 q^{81} +(-9.94909 - 2.54670i) q^{82} +(1.17951 + 1.17951i) q^{83} +(-2.74164 + 2.74164i) q^{85} +(-1.78962 - 3.02101i) q^{86} +11.9851i q^{87} +(0.600264 + 17.8477i) q^{88} +12.7560i q^{89} +(0.557612 - 0.330324i) q^{90} +(-1.02593 + 1.87267i) q^{92} +(0.466968 + 0.466968i) q^{93} +(0.758325 - 2.96252i) q^{94} -12.7327 q^{95} +(8.40872 + 4.24563i) q^{96} -2.21148 q^{97} +(-1.01399 - 1.01399i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 4 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{10} + 4 q^{11} - 2 q^{12} - 12 q^{13} - 20 q^{15} - 16 q^{16} - 8 q^{17} - 18 q^{18} + 4 q^{19} - 8 q^{20} - 18 q^{24} + 10 q^{26} - 12 q^{27}+ \cdots - 12 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 4 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^10 + 4 * q^11 - 2 * q^12 - 12 * q^13 - 20 * q^15 - 16 * q^16 - 8 * q^17 - 18 * q^18 + 4 * q^19 - 8 * q^20 - 18 * q^24 + 10 * q^26 - 12 * q^27 + 12 * q^29 + 4 * q^30 - 28 * q^31 - 16 * q^32 - 16 * q^33 - 22 * q^34 - 36 * q^36 + 24 * q^37 - 20 * q^38 - 26 * q^40 - 20 * q^43 - 6 * q^44 + 28 * q^45 + 14 * q^46 + 20 * q^47 + 28 * q^48 + 28 * q^50 - 24 * q^51 + 16 * q^52 + 16 * q^53 - 64 * q^54 + 6 * q^58 + 20 * q^59 - 46 * q^60 - 8 * q^61 + 12 * q^62 + 40 * q^64 - 8 * q^65 + 20 * q^66 - 48 * q^67 - 20 * q^69 + 32 * q^72 + 8 * q^74 + 4 * q^75 - 18 * q^76 + 58 * q^78 + 36 * q^79 + 28 * q^80 - 2 * q^82 - 4 * q^83 + 20 * q^86 + 42 * q^88 - 10 * q^90 + 38 * q^92 - 8 * q^93 + 72 * q^94 + 4 * q^95 + 120 * q^96 - 24 * q^97 - 12 * q^99

Introduction

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