LMFDB - Embedded newform 288.2.w.b.107.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [288,2,Mod(35,288)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(288, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("288.35"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.w (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			107.3
Character	$\chi$	$=$	288.107
Dual form			288.2.w.b.35.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.430512 - 1.34709i) q^{2} +(-1.62932 + 1.15988i) q^{4} +(-1.78959 - 0.741273i) q^{5} +(-2.33709 + 2.33709i) q^{7} +(2.26391 + 1.69550i) q^{8} +(-0.228123 + 2.72987i) q^{10} +(0.683332 + 0.283045i) q^{11} +(2.43602 + 5.88107i) q^{13} +(4.15442 + 2.14213i) q^{14} +(1.30936 - 3.77963i) q^{16} -0.967834 q^{17} +(-2.52772 + 1.04702i) q^{19} +(3.77560 - 0.867939i) q^{20} +(0.0871059 - 1.04237i) q^{22} +(-5.00283 + 5.00283i) q^{23} +(-0.882385 - 0.882385i) q^{25} +(6.87361 - 5.81341i) q^{26} +(1.09712 - 6.51861i) q^{28} +(0.563403 + 1.36018i) q^{29} +7.28582i q^{31} +(-5.65520 - 0.136659i) q^{32} +(0.416664 + 1.30376i) q^{34} +(5.91486 - 2.45001i) q^{35} +(3.26572 - 7.88415i) q^{37} +(2.49864 + 2.95432i) q^{38} +(-2.79463 - 4.71243i) q^{40} +(-6.80014 - 6.80014i) q^{41} +(1.36517 - 3.29581i) q^{43} +(-1.44166 + 0.331411i) q^{44} +(8.89306 + 4.58550i) q^{46} +3.69279i q^{47} -3.92399i q^{49} +(-0.808777 + 1.56853i) q^{50} +(-10.7904 - 6.75665i) q^{52} +(-1.85469 + 4.47761i) q^{53} +(-1.01307 - 1.01307i) q^{55} +(-9.25350 + 1.32841i) q^{56} +(1.58973 - 1.34453i) q^{58} +(-4.05615 + 9.79242i) q^{59} +(10.8180 - 4.48097i) q^{61} +(9.81468 - 3.13663i) q^{62} +(2.25054 + 7.67692i) q^{64} -12.3305i q^{65} +(1.49290 + 3.60418i) q^{67} +(1.57691 - 1.12257i) q^{68} +(-5.84681 - 6.91310i) q^{70} +(-9.85675 - 9.85675i) q^{71} +(-4.81362 + 4.81362i) q^{73} +(-12.0266 - 1.00501i) q^{74} +(2.90405 - 4.63778i) q^{76} +(-2.25851 + 0.935506i) q^{77} -11.0160 q^{79} +(-5.14495 + 5.79339i) q^{80} +(-6.23288 + 12.0880i) q^{82} +(1.15064 + 2.77789i) q^{83} +(1.73203 + 0.717429i) q^{85} +(-5.02749 - 0.420125i) q^{86} +(1.06709 + 1.79938i) q^{88} +(6.82624 - 6.82624i) q^{89} +(-19.4378 - 8.05140i) q^{91} +(2.34853 - 13.9539i) q^{92} +(4.97453 - 1.58979i) q^{94} +5.29971 q^{95} +7.67976 q^{97} +(-5.28598 + 1.68932i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} + 4 q^{8} + 8 q^{10} + 8 q^{11} - 12 q^{14} + 8 q^{16} - 32 q^{20} + 16 q^{22} + 36 q^{26} + 16 q^{29} + 24 q^{32} - 24 q^{35} - 32 q^{38} - 32 q^{40} - 8 q^{44} - 32 q^{46} - 8 q^{50} - 56 q^{52}+ \cdots + 44 q^{98}+O(q^{100}) $ 32 * q + 4 * q^2 + 4 * q^8 + 8 * q^10 + 8 * q^11 - 12 * q^14 + 8 * q^16 - 32 * q^20 + 16 * q^22 + 36 * q^26 + 16 * q^29 + 24 * q^32 - 24 * q^35 - 32 * q^38 - 32 * q^40 - 8 * q^44 - 32 * q^46 - 8 * q^50 - 56 * q^52 + 16 * q^53 - 32 * q^55 - 40 * q^56 - 32 * q^58 - 32 * q^59 + 32 * q^61 + 68 * q^62 - 48 * q^64 - 16 * q^67 + 72 * q^68 - 48 * q^70 - 16 * q^71 - 60 * q^74 - 8 * q^76 + 16 * q^77 - 32 * q^79 - 96 * q^80 + 40 * q^82 + 40 * q^83 + 40 * q^86 + 40 * q^88 - 48 * q^91 + 16 * q^92 + 72 * q^94 + 80 * q^95 + 44 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$-1$

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 $

$2$	−0.430512	−	1.34709i	−0.304418	−	0.952539i
$2$	−0.430512	−	1.34709i	−0.304418	−	0.952539i
$3$		0			0
$3$		0			0
$4$	−1.62932	+	1.15988i	−0.814660	+	0.579939i
$5$	−1.78959	−	0.741273i	−0.800329	−	0.331507i	−0.0552409	−	0.998473i	$-0.517593\pi$
$5$	−1.78959	−	0.741273i	−0.800329	−	0.331507i	−0.745088	+	0.666966i	$0.767593\pi$
$6$		0			0
$7$	−2.33709	+	2.33709i	−0.883337	+	0.883337i	−0.993872	−	0.110535i	$-0.964744\pi$
$7$	−2.33709	+	2.33709i	−0.883337	+	0.883337i	0.110535	+	0.993872i	$0.464744\pi$
$8$	2.26391	+	1.69550i	0.800412	+	0.599451i
$9$		0			0
$10$	−0.228123	+	2.72987i	−0.0721389	+	0.863261i
$11$	0.683332	+	0.283045i	0.206032	+	0.0853413i	0.483313	−	0.875448i	$-0.339433\pi$
$11$	0.683332	+	0.283045i	0.206032	+	0.0853413i	−0.277281	+	0.960789i	$0.589433\pi$
$12$		0			0
$13$	2.43602	+	5.88107i	0.675630	+	1.63112i	0.771888	+	0.635759i	$0.219313\pi$
$13$	2.43602	+	5.88107i	0.675630	+	1.63112i	−0.0962579	+	0.995356i	$0.530687\pi$
$14$	4.15442	+	2.14213i	1.11032	+	0.572509i
$15$		0			0
$16$	1.30936	−	3.77963i	0.327340	−	0.944906i
$17$	−0.967834			−0.234734			−0.117367	−	0.993089i	$-0.537445\pi$
$17$	−0.967834			−0.234734			−0.117367	+	0.993089i	$0.537445\pi$
$18$		0			0
$19$	−2.52772	+	1.04702i	−0.579899	+	0.240202i	−0.653298	−	0.757100i	$-0.726615\pi$
$19$	−2.52772	+	1.04702i	−0.579899	+	0.240202i	0.0733991	+	0.997303i	$0.476615\pi$
$20$	3.77560	−	0.867939i	0.844250	−	0.194077i
$21$		0			0
$22$	0.0871059	−	1.04237i	0.0185710	−	0.222233i
$23$	−5.00283	+	5.00283i	−1.04316	+	1.04316i	−0.0441370	+	0.999025i	$0.514054\pi$
$23$	−5.00283	+	5.00283i	−1.04316	+	1.04316i	−0.999025	+	0.0441370i	$0.985946\pi$
$24$		0			0
$25$	−0.882385	−	0.882385i	−0.176477	−	0.176477i
$26$	6.87361	−	5.81341i	1.34803	−	1.14010i
$27$		0			0
$28$	1.09712	−	6.51861i	0.207337	−	1.23190i
$29$	0.563403	+	1.36018i	0.104621	+	0.252578i	0.967518	−	0.252802i	$-0.0813522\pi$
$29$	0.563403	+	1.36018i	0.104621	+	0.252578i	−0.862897	+	0.505380i	$0.831352\pi$
$30$		0			0
$31$			7.28582i			1.30857i	0.756247	+	0.654286i	$0.227031\pi$
$31$			7.28582i			1.30857i	−0.756247	+	0.654286i	$0.772969\pi$
$32$	−5.65520	−	0.136659i	−0.999708	−	0.0241581i
$33$		0			0
$34$	0.416664	+	1.30376i	0.0714573	+	0.223593i
$35$	5.91486	−	2.45001i	0.999793	−	0.414128i
$36$		0			0
$37$	3.26572	−	7.88415i	0.536881	−	1.29615i	−0.390008	−	0.920812i	$-0.627528\pi$
$37$	3.26572	−	7.88415i	0.536881	−	1.29615i	0.926889	−	0.375335i	$-0.122472\pi$
$38$	2.49864	+	2.95432i	0.405334	+	0.479255i
$39$		0			0
$40$	−2.79463	−	4.71243i	−0.441871	−	0.745100i
$41$	−6.80014	−	6.80014i	−1.06200	−	1.06200i	−0.997946	−	0.0640576i	$-0.979596\pi$
$41$	−6.80014	−	6.80014i	−1.06200	−	1.06200i	−0.0640576	−	0.997946i	$-0.520404\pi$
$42$		0			0
$43$	1.36517	−	3.29581i	0.208187	−	0.502607i	−0.784951	−	0.619558i	$-0.787312\pi$
$43$	1.36517	−	3.29581i	0.208187	−	0.502607i	0.993138	+	0.116951i	$0.0373120\pi$
$44$	−1.44166	+	0.331411i	−0.217339	+	0.0499621i
$45$		0			0
$46$	8.89306	+	4.58550i	1.31121	+	0.676095i
$47$			3.69279i			0.538649i	0.963050	+	0.269324i	$0.0868004\pi$
$47$			3.69279i			0.538649i	−0.963050	+	0.269324i	$0.913200\pi$
$48$		0			0
$49$		−	3.92399i		−	0.560570i
$50$	−0.808777	+	1.56853i	−0.114378	+	0.221824i
$51$		0			0
$52$	−10.7904	−	6.75665i	−1.49636	−	0.936979i
$53$	−1.85469	+	4.47761i	−0.254761	+	0.615047i	−0.998577	−	0.0533378i	$-0.983014\pi$
$53$	−1.85469	+	4.47761i	−0.254761	+	0.615047i	0.743816	+	0.668385i	$0.233014\pi$
$54$		0			0
$55$	−1.01307	−	1.01307i	−0.136602	−	0.136602i
$56$	−9.25350	+	1.32841i	−1.23655	+	0.177516i
$57$		0			0
$58$	1.58973	−	1.34453i	0.208742	−	0.176545i
$59$	−4.05615	+	9.79242i	−0.528066	+	1.27486i	0.404722	+	0.914440i	$0.367368\pi$
$59$	−4.05615	+	9.79242i	−0.528066	+	1.27486i	−0.932788	+	0.360425i	$0.882632\pi$
$60$		0			0
$61$	10.8180	−	4.48097i	1.38511	−	0.573730i	0.439265	−	0.898358i	$-0.355239\pi$
$61$	10.8180	−	4.48097i	1.38511	−	0.573730i	0.945842	+	0.324628i	$0.105239\pi$
$62$	9.81468	−	3.13663i	1.24647	−	0.398353i
$63$		0			0
$64$	2.25054	+	7.67692i	0.281318	+	0.959615i
$65$		−	12.3305i		−	1.52941i
$66$		0			0
$67$	1.49290	+	3.60418i	0.182387	+	0.440320i	0.988457	−	0.151499i	$-0.0484100\pi$
$67$	1.49290	+	3.60418i	0.182387	+	0.440320i	−0.806071	+	0.591819i	$0.798410\pi$
$68$	1.57691	−	1.12257i	0.191229	−	0.136132i
$69$		0			0
$70$	−5.84681	−	6.91310i	−0.698828	−	0.826274i
$71$	−9.85675	−	9.85675i	−1.16978	−	1.16978i	−0.982261	−	0.187520i	$-0.939955\pi$
$71$	−9.85675	−	9.85675i	−1.16978	−	1.16978i	−0.187520	−	0.982261i	$-0.560045\pi$
$72$		0			0
$73$	−4.81362	+	4.81362i	−0.563391	+	0.563391i	−0.930269	−	0.366878i	$-0.880427\pi$
$73$	−4.81362	+	4.81362i	−0.563391	+	0.563391i	0.366878	+	0.930269i	$0.380427\pi$
$74$	−12.0266	−	1.00501i	−1.39807	−	0.116830i
$75$		0			0
$76$	2.90405	−	4.63778i	0.333118	−	0.531990i
$77$	−2.25851	+	0.935506i	−0.257381	+	0.106611i
$78$		0			0
$79$	−11.0160			−1.23940			−0.619700	−	0.784839i	$-0.712746\pi$
$79$	−11.0160			−1.23940			−0.619700	+	0.784839i	$0.712746\pi$
$80$	−5.14495	+	5.79339i	−0.575223	+	0.647721i
$81$		0			0
$82$	−6.23288	+	12.0880i	−0.688307	+	1.33489i
$83$	1.15064	+	2.77789i	0.126299	+	0.304913i	0.974363	−	0.224981i	$-0.0722319\pi$
$83$	1.15064	+	2.77789i	0.126299	+	0.304913i	−0.848064	+	0.529894i	$0.822232\pi$
$84$		0			0
$85$	1.73203	+	0.717429i	0.187865	+	0.0778161i
$86$	−5.02749	−	0.420125i	−0.542128	−	0.0453033i
$87$		0			0
$88$	1.06709	+	1.79938i	0.113753	+	0.191814i
$89$	6.82624	−	6.82624i	0.723580	−	0.723580i	−0.245753	−	0.969333i	$-0.579035\pi$
$89$	6.82624	−	6.82624i	0.723580	−	0.723580i	0.969333	+	0.245753i	$0.0790352\pi$
$90$		0			0
$91$	−19.4378	−	8.05140i	−2.03763	−	0.844016i
$92$	2.34853	−	13.9539i	0.244851	−	1.45479i
$93$		0			0
$94$	4.97453	−	1.58979i	0.513084	−	0.163974i
$95$	5.29971			0.543739
$96$		0			0
$97$	7.67976			0.779762			0.389881	−	0.920865i	$-0.372516\pi$
$97$	7.67976			0.779762			0.389881	+	0.920865i	$0.372516\pi$
$98$	−5.28598	+	1.68932i	−0.533964	+	0.170647i
$99$		0			0
$100$	2.46115	+	0.414227i	0.246115	+	0.0414227i
$101$	1.05030	+	0.435049i	0.104509	+	0.0432890i	0.434325	−	0.900756i	$-0.356987\pi$
$101$	1.05030	+	0.435049i	0.104509	+	0.0432890i	−0.329816	+	0.944045i	$0.606987\pi$
$102$		0			0
$103$	7.06356	−	7.06356i	0.695993	−	0.695993i	−0.267551	−	0.963544i	$-0.586214\pi$
$103$	7.06356	−	7.06356i	0.695993	−	0.695993i	0.963544	+	0.267551i	$0.0862143\pi$
$104$	−4.45645	+	17.4445i	−0.436991	+	1.71057i
$105$		0			0
$106$	6.83022	+	0.570771i	0.663410	+	0.0554382i
$107$	16.1346	+	6.68316i	1.55979	+	0.646086i	0.985053	−	0.172253i	$-0.0551045\pi$
$107$	16.1346	+	6.68316i	1.55979	+	0.646086i	0.574737	+	0.818338i	$0.305105\pi$
$108$		0			0
$109$	0.771406	+	1.86234i	0.0738873	+	0.178380i	0.956508	−	0.291706i	$-0.0942230\pi$
$109$	0.771406	+	1.86234i	0.0738873	+	0.178380i	−0.882621	+	0.470086i	$0.844223\pi$
$110$	−0.928561	+	1.80084i	−0.0885348	+	0.171703i
$111$		0			0
$112$	5.77323	+	11.8934i	0.545519	+	1.12382i
$113$	0.726213			0.0683163			0.0341582	−	0.999416i	$-0.489125\pi$
$113$	0.726213			0.0683163			0.0341582	+	0.999416i	$0.489125\pi$
$114$		0			0
$115$	12.6615	−	5.24456i	1.18069	−	0.489058i
$116$	−2.49560	−	1.56268i	−0.231711	−	0.145091i
$117$		0			0
$118$	14.9375	+	1.24826i	1.37511	+	0.114912i
$119$	2.26192	−	2.26192i	0.207350	−	0.207350i
$120$		0			0
$121$	−7.39135	−	7.39135i	−0.671941	−	0.671941i
$122$	−10.6936	−	12.6438i	−0.968151	−	1.14471i
$123$		0			0
$124$	−8.45067	−	11.8709i	−0.758893	−	1.06604i
$125$	4.63138	+	11.1811i	0.414243	+	1.00007i
$126$		0			0
$127$			11.5686i			1.02654i	0.858226	+	0.513272i	$0.171567\pi$
$127$			11.5686i			1.02654i	−0.858226	+	0.513272i	$0.828433\pi$
$128$	9.37264	−	6.33669i	0.828432	−	0.560090i
$129$		0			0
$130$	−16.6103	+	5.30841i	−1.45682	+	0.465578i
$131$	17.9241	−	7.42442i	1.56604	−	0.648674i	0.579913	−	0.814678i	$-0.303087\pi$
$131$	17.9241	−	7.42442i	1.56604	−	0.648674i	0.986125	+	0.166004i	$0.0530866\pi$
$132$		0			0
$133$	3.46054	−	8.35449i	0.300067	−	0.724426i
$134$	4.21245	−	3.56271i	0.363900	−	0.307772i
$135$		0			0
$136$	−2.19109	−	1.64097i	−0.187884	−	0.140712i
$137$	15.9867	+	15.9867i	1.36584	+	1.36584i	0.866283	+	0.499553i	$0.166503\pi$
$137$	15.9867	+	15.9867i	1.36584	+	1.36584i	0.499553	+	0.866283i	$0.333497\pi$
$138$		0			0
$139$	0.0365308	−	0.0881933i	0.00309851	−	0.00748046i	−0.922323	−	0.386421i	$-0.873711\pi$
$139$	0.0365308	−	0.0881933i	0.00309851	−	0.00748046i	0.925421	+	0.378940i	$0.123711\pi$
$140$	−6.79547	+	10.8524i	−0.574322	+	0.917193i
$141$		0			0
$142$	−9.03451	+	17.5214i	−0.758159	+	1.47036i
$143$			4.70822i			0.393721i
$144$		0			0
$145$		−	2.85179i		−	0.236828i
$146$	8.55671	+	4.41207i	0.708158	+	0.365145i
$147$		0			0
$148$	3.82376	+	16.6336i	0.314311	+	1.36728i
$149$	−5.79476	+	13.9898i	−0.474725	+	1.14609i	0.487326	+	0.873220i	$0.337972\pi$
$149$	−5.79476	+	13.9898i	−0.474725	+	1.14609i	−0.962051	+	0.272868i	$0.912028\pi$
$150$		0			0
$151$	7.47087	+	7.47087i	0.607971	+	0.607971i	0.942415	−	0.334445i	$-0.108549\pi$
$151$	7.47087	+	7.47087i	0.607971	+	0.607971i	−0.334445	+	0.942415i	$0.608549\pi$
$152$	−7.49775	−	1.91541i	−0.608148	−	0.155361i
$153$		0			0
$154$	2.23253	+	2.63968i	0.179902	+	0.212711i
$155$	5.40078	−	13.0386i	0.433801	−	1.04729i
$156$		0			0
$157$	−11.0372	+	4.57177i	−0.880867	+	0.364867i	−0.776833	−	0.629707i	$-0.783175\pi$
$157$	−11.0372	+	4.57177i	−0.880867	+	0.364867i	−0.104034	+	0.994574i	$0.533175\pi$
$158$	4.74253	+	14.8396i	0.377295	+	1.18058i
$159$		0			0
$160$	10.0192	+	4.43661i	0.792087	+	0.350745i
$161$		−	23.3841i		−	1.84293i
$162$		0			0
$163$	−3.29972	−	7.96624i	−0.258454	−	0.623964i	0.740382	−	0.672186i	$-0.234644\pi$
$163$	−3.29972	−	7.96624i	−0.258454	−	0.623964i	−0.998837	+	0.0482221i	$0.984644\pi$
$164$	18.9669	+	3.19226i	1.48107	+	0.249274i
$165$		0			0
$166$	3.24671	−	2.74593i	0.251994	−	0.213126i
$167$	0.0751100	+	0.0751100i	0.00581218	+	0.00581218i	0.710007	−	0.704195i	$-0.248692\pi$
$167$	0.0751100	+	0.0751100i	0.00581218	+	0.00581218i	−0.704195	+	0.710007i	$0.748692\pi$
$168$		0			0
$169$	−19.4604	+	19.4604i	−1.49695	+	1.49695i
$170$	0.220786	−	2.64206i	0.0169335	−	0.202637i
$171$		0			0
$172$	1.59845	+	6.95337i	0.121880	+	0.530189i
$173$	21.0041	−	8.70018i	1.59691	−	0.661463i	0.605937	−	0.795512i	$-0.292798\pi$
$173$	21.0041	−	8.70018i	1.59691	−	0.661463i	0.990975	+	0.134050i	$0.0427982\pi$
$174$		0			0
$175$	4.12443			0.311777
$176$	1.96453	−	2.21213i	0.148082	−	0.166746i
$177$		0			0
$178$	−12.1344	−	6.25680i	−0.909508	−	0.468967i
$179$	−4.35530	−	10.5146i	−0.325530	−	0.785900i	−0.998913	−	0.0466061i	$-0.985159\pi$
$179$	−4.35530	−	10.5146i	−0.325530	−	0.785900i	0.673383	−	0.739294i	$-0.264841\pi$
$180$		0			0
$181$	−4.28737	−	1.77589i	−0.318677	−	0.132001i	0.217610	−	0.976036i	$-0.430174\pi$
$181$	−4.28737	−	1.77589i	−0.318677	−	0.132001i	−0.536288	+	0.844035i	$0.680174\pi$
$182$	−2.47778	+	29.6507i	−0.183665	+	2.19786i
$183$		0			0
$184$	−19.8083	+	2.84362i	−1.46028	+	0.209635i
$185$	−11.6886	+	11.6886i	−0.859364	+	0.859364i
$186$		0			0
$187$	−0.661352	−	0.273941i	−0.0483628	−	0.0200325i
$188$	−4.28319	−	6.01673i	−0.312384	−	0.438815i
$189$		0			0
$190$	−2.28159	−	7.13921i	−0.165524	−	0.517933i
$191$	−22.2718			−1.61153			−0.805766	−	0.592234i	$-0.798246\pi$
$191$	−22.2718			−1.61153			−0.805766	+	0.592234i	$0.798246\pi$
$192$		0			0
$193$	10.8858			0.783575			0.391787	−	0.920056i	$-0.371857\pi$
$193$	10.8858			0.783575			0.391787	+	0.920056i	$0.371857\pi$
$194$	−3.30623	−	10.3454i	−0.237373	−	0.742753i
$195$		0			0
$196$	4.55135	+	6.39343i	0.325096	+	0.456673i
$197$	−6.10110	−	2.52716i	−0.434686	−	0.180053i	0.154601	−	0.987977i	$-0.450591\pi$
$197$	−6.10110	−	2.52716i	−0.434686	−	0.180053i	−0.589286	+	0.807924i	$0.700591\pi$
$198$		0			0
$199$	10.1086	−	10.1086i	0.716582	−	0.716582i	−0.251322	−	0.967904i	$-0.580865\pi$
$199$	10.1086	−	10.1086i	0.716582	−	0.716582i	0.967904	+	0.251322i	$0.0808653\pi$
$200$	−0.501550	−	3.49372i	−0.0354650	−	0.247044i
$201$		0			0
$202$	0.133884	−	1.60215i	0.00942007	−	0.112727i
$203$	−4.49558	−	1.86213i	−0.315528	−	0.130696i
$204$		0			0
$205$	7.12871	+	17.2102i	0.497891	+	1.20201i
$206$	−12.5562	−	6.47432i	−0.874833	−	0.451087i
$207$		0			0
$208$	25.4179	−	1.50679i	1.76241	−	0.104477i
$209$	−2.02363			−0.139977
$210$		0			0
$211$	18.8236	−	7.79698i	1.29587	−	0.536766i	0.375139	−	0.926969i	$-0.377595\pi$
$211$	18.8236	−	7.79698i	1.29587	−	0.536766i	0.920729	+	0.390202i	$0.127595\pi$
$212$	−2.17161	−	9.44667i	−0.149147	−	0.648800i
$213$		0			0
$214$	2.05671	−	24.6120i	0.140594	−	1.68244i
$215$	−4.88619	+	4.88619i	−0.333236	+	0.333236i
$216$		0			0
$217$	−17.0276	−	17.0276i	−1.15591	−	1.15591i
$218$	2.17664	−	1.84091i	0.147421	−	0.124682i
$219$		0			0
$220$	2.82565	+	0.475576i	0.190505	+	0.0320633i
$221$	−2.35766	−	5.69190i	−0.158593	−	0.382879i
$222$		0			0
$223$			14.8162i			0.992164i	0.868276	+	0.496082i	$0.165229\pi$
$223$			14.8162i			0.992164i	−0.868276	+	0.496082i	$0.834771\pi$
$224$	13.5361	−	12.8973i	0.904419	−	0.861740i
$225$		0			0
$226$	−0.312643	−	0.978276i	−0.0207967	−	0.0650739i
$227$	−11.9755	+	4.96040i	−0.794839	+	0.329233i	−0.742887	−	0.669416i	$-0.766544\pi$
$227$	−11.9755	+	4.96040i	−0.794839	+	0.329233i	−0.0519519	+	0.998650i	$0.516544\pi$
$228$		0			0
$229$	−2.65080	+	6.39960i	−0.175170	+	0.422897i	−0.986942	−	0.161077i	$-0.948503\pi$
$229$	−2.65080	+	6.39960i	−0.175170	+	0.422897i	0.811772	+	0.583975i	$0.198503\pi$
$230$	−12.5158	−	14.7983i	−0.825269	−	0.975774i
$231$		0			0
$232$	−1.03069	+	4.03456i	−0.0676681	+	0.264882i
$233$	8.35926	+	8.35926i	0.547634	+	0.547634i	0.925756	−	0.378122i	$-0.123430\pi$
$233$	8.35926	+	8.35926i	0.547634	+	0.547634i	−0.378122	+	0.925756i	$0.623430\pi$
$234$		0			0
$235$	2.73736	−	6.60858i	0.178566	−	0.431096i
$236$	−4.74925	−	20.6596i	−0.309150	−	1.34483i
$237$		0			0
$238$	−4.02079	−	2.07323i	−0.260629	−	0.134388i
$239$		−	2.44122i		−	0.157909i	−0.996878	−	0.0789547i	$-0.974842\pi$
$239$		−	2.44122i		−	0.157909i	0.996878	−	0.0789547i	$-0.0251582\pi$
$240$		0			0
$241$			1.86406i			0.120074i	0.998196	+	0.0600372i	$0.0191219\pi$
$241$			1.86406i			0.120074i	−0.998196	+	0.0600372i	$0.980878\pi$
$242$	−6.77477	+	13.1389i	−0.435499	+	0.844600i
$243$		0			0
$244$	−12.4286	+	19.8485i	−0.795662	+	1.27067i
$245$	−2.90874	+	7.02233i	−0.185833	+	0.448640i
$246$		0			0
$247$	−12.3152	−	12.3152i	−0.783595	−	0.783595i
$248$	−12.3531	+	16.4944i	−0.784425	+	1.04740i
$249$		0			0
$250$	13.0682	−	11.0525i	0.826504	−	0.699023i
$251$	−6.30926	+	15.2319i	−0.398237	+	0.961430i	0.589847	+	0.807515i	$0.299188\pi$
$251$	−6.30926	+	15.2319i	−0.398237	+	0.961430i	−0.988084	+	0.153915i	$0.950812\pi$
$252$		0			0
$253$	−4.83462	+	2.00257i	−0.303950	+	0.125900i
$254$	15.5839	−	4.98040i	0.977822	−	0.312498i
$255$		0			0
$256$	−12.5711	−	9.89780i	−0.785696	−	0.618612i
$257$			5.84660i			0.364701i	0.983234	+	0.182350i	$0.0583705\pi$
$257$			5.84660i			0.364701i	−0.983234	+	0.182350i	$0.941629\pi$
$258$		0			0
$259$	10.7937	+	26.0583i	0.670687	+	1.61918i
$260$	14.3018	+	20.0903i	0.886962	+	1.24594i
$261$		0			0
$262$	−17.7179	−	20.9492i	−1.09462	−	1.29424i
$263$	−11.4239	−	11.4239i	−0.704427	−	0.704427i	0.260930	−	0.965358i	$-0.415971\pi$
$263$	−11.4239	−	11.4239i	−0.704427	−	0.704427i	−0.965358	+	0.260930i	$0.915971\pi$
$264$		0			0
$265$	6.63826	−	6.63826i	0.407785	−	0.407785i
$266$	−12.7441	−	1.06497i	−0.781390	−	0.0652973i
$267$		0			0
$268$	−6.61281	−	4.14077i	−0.403942	−	0.252938i
$269$	−2.42511	+	1.00451i	−0.147862	+	0.0612463i	−0.455387	−	0.890294i	$-0.650499\pi$
$269$	−2.42511	+	1.00451i	−0.147862	+	0.0612463i	0.307525	+	0.951540i	$0.400499\pi$
$270$		0			0
$271$	−10.6956			−0.649711			−0.324856	−	0.945764i	$-0.605316\pi$
$271$	−10.6956			−0.649711			−0.324856	+	0.945764i	$0.605316\pi$
$272$	−1.26725	+	3.65805i	−0.0768380	+	0.221802i
$273$		0			0
$274$	14.6531	−	28.4180i	0.885227	−	1.71680i
$275$	−0.353207	−	0.852716i	−0.0212992	−	0.0514207i
$276$		0			0
$277$	−13.7497	−	5.69533i	−0.826142	−	0.342199i	−0.0707678	−	0.997493i	$-0.522545\pi$
$277$	−13.7497	−	5.69533i	−0.826142	−	0.342199i	−0.755374	+	0.655294i	$0.772545\pi$
$278$	−0.134532	−	0.0112422i	−0.00806866	−	0.000674263i
$279$		0			0
$280$	17.5447	+	4.48206i	1.04850	+	0.267854i
$281$	−1.63475	+	1.63475i	−0.0975211	+	0.0975211i	−0.754184	−	0.656663i	$-0.771967\pi$
$281$	−1.63475	+	1.63475i	−0.0975211	+	0.0975211i	0.656663	+	0.754184i	$0.271967\pi$
$282$		0			0
$283$	−4.75108	−	1.96796i	−0.282423	−	0.116983i	0.236976	−	0.971516i	$-0.423844\pi$
$283$	−4.75108	−	1.96796i	−0.282423	−	0.116983i	−0.519398	+	0.854532i	$0.673844\pi$
$284$	27.4924	+	4.62716i	1.63138	+	0.274571i
$285$		0			0
$286$	6.34242	−	2.02695i	0.375035	−	0.119856i
$287$	31.7851			1.87622
$288$		0			0
$289$	−16.0633			−0.944900
$290$	−3.84163	+	1.22773i	−0.225588	+	0.0720948i
$291$		0			0
$292$	2.25970	−	13.4261i	0.132239	−	0.785705i
$293$	−13.0434	−	5.40274i	−0.762001	−	0.315631i	−0.0323737	−	0.999476i	$-0.510307\pi$
$293$	−13.0434	−	5.40274i	−0.762001	−	0.315631i	−0.729628	+	0.683845i	$0.760307\pi$
$294$		0			0
$295$	14.5177	−	14.5177i	0.845254	−	0.845254i
$296$	20.7609	−	12.3119i	1.20670	−	0.715617i
$297$		0			0
$298$	21.3403	+	1.78331i	1.23621	+	0.103304i
$299$	−41.6090	−	17.2350i	−2.40631	−	0.996726i
$300$		0			0
$301$	4.51209	+	10.8931i	0.260072	+	0.627870i
$302$	6.84766	−	13.2803i	0.394039	−	0.764193i
$303$		0			0
$304$	0.647629	+	10.9248i	0.0371441	+	0.626579i
$305$	−22.6815			−1.29874
$306$		0			0
$307$	13.7332	−	5.68846i	0.783793	−	0.324658i	0.0453480	−	0.998971i	$-0.485560\pi$
$307$	13.7332	−	5.68846i	0.783793	−	0.324658i	0.738445	+	0.674313i	$0.235560\pi$
$308$	2.59476	−	4.14384i	0.147850	−	0.236117i
$309$		0			0
$310$	−19.8894	−	1.66207i	−1.12964	−	0.0943990i
$311$	1.93693	−	1.93693i	0.109833	−	0.109833i	−0.650055	−	0.759888i	$-0.725254\pi$
$311$	1.93693	−	1.93693i	0.109833	−	0.109833i	0.759888	+	0.650055i	$0.225254\pi$
$312$		0			0
$313$	20.8065	+	20.8065i	1.17606	+	1.17606i	0.980741	+	0.195315i	$0.0625728\pi$
$313$	20.8065	+	20.8065i	1.17606	+	1.17606i	0.195315	+	0.980741i	$0.437427\pi$
$314$	10.9103	+	12.9000i	0.615702	+	0.727988i
$315$		0			0
$316$	17.9486	−	12.7773i	1.00969	−	0.718777i
$317$	6.99169	+	16.8794i	0.392692	+	0.948043i	0.989351	+	0.145548i	$0.0464945\pi$
$317$	6.99169	+	16.8794i	0.392692	+	0.948043i	−0.596659	+	0.802495i	$0.703505\pi$
$318$		0			0
$319$			1.08892i			0.0609678i
$320$	1.66314	−	15.4068i	0.0929726	−	0.861266i
$321$		0			0
$322$	−31.5006	+	10.0672i	−1.75546	+	0.561020i
$323$	2.44642	−	1.01334i	0.136122	−	0.0563837i
$324$		0			0
$325$	3.03986	−	7.33887i	0.168621	−	0.407087i
$326$	−9.31069	+	7.87459i	−0.515672	+	0.436133i
$327$		0			0
$328$	−3.86522	−	26.9245i	−0.213421	−	1.48666i
$329$	−8.63039	−	8.63039i	−0.475809	−	0.475809i
$330$		0			0
$331$	7.57715	−	18.2929i	0.416478	−	1.00547i	−0.566882	−	0.823799i	$-0.691850\pi$
$331$	7.57715	−	18.2929i	0.416478	−	1.00547i	0.983360	−	0.181668i	$-0.0581496\pi$
$332$	−5.09677	−	3.19146i	−0.279722	−	0.175154i
$333$		0			0
$334$	0.0688444	−	0.133516i	0.00376700	−	0.00730566i
$335$		−	7.55664i		−	0.412863i
$336$		0			0
$337$			6.73391i			0.366820i	0.983037	+	0.183410i	$0.0587135\pi$
$337$			6.73391i			0.366820i	−0.983037	+	0.183410i	$0.941286\pi$
$338$	34.5929	+	17.8370i	1.88161	+	0.970207i
$339$		0			0
$340$	−3.65415	+	0.840020i	−0.198174	+	0.0455565i
$341$	−2.06222	+	4.97863i	−0.111675	+	0.269608i
$342$		0			0
$343$	−7.18892	−	7.18892i	−0.388165	−	0.388165i
$344$	8.67868	−	5.14676i	0.467923	−	0.277495i
$345$		0			0
$346$	−20.7625	−	24.5489i	−1.11620	−	1.31976i
$347$	−2.79644	+	6.75121i	−0.150121	+	0.362424i	−0.980994	−	0.194038i	$-0.937842\pi$
$347$	−2.79644	+	6.75121i	−0.150121	+	0.362424i	0.830873	+	0.556462i	$0.187842\pi$
$348$		0			0
$349$	−3.16816	+	1.31229i	−0.169588	+	0.0702455i	−0.465862	−	0.884857i	$-0.654256\pi$
$349$	−3.16816	+	1.31229i	−0.169588	+	0.0702455i	0.296274	+	0.955103i	$0.404256\pi$
$350$	−1.77561	−	5.55599i	−0.0949106	−	0.296980i
$351$		0			0
$352$	−3.82570	−	1.69406i	−0.203910	−	0.0902938i
$353$			29.8578i			1.58917i	0.607151	+	0.794586i	$0.292312\pi$
$353$			29.8578i			1.58917i	−0.607151	+	0.794586i	$0.707688\pi$
$354$		0			0
$355$	10.3330	+	24.9461i	0.548419	+	1.32400i
$356$	−3.20451	+	19.0397i	−0.169839	+	1.00910i
$357$		0			0
$358$	−12.2892	+	10.3937i	−0.649503	+	0.549322i
$359$	−9.44266	−	9.44266i	−0.498365	−	0.498365i	0.412564	−	0.910929i	$-0.364633\pi$
$359$	−9.44266	−	9.44266i	−0.498365	−	0.498365i	−0.910929	+	0.412564i	$0.864633\pi$
$360$		0			0
$361$	−8.14189	+	8.14189i	−0.428521	+	0.428521i
$362$	−0.546521	+	6.54002i	−0.0287245	+	0.343736i
$363$		0			0
$364$	41.0090	−	9.42719i	2.14946	−	0.494119i
$365$	12.1826	−	5.04620i	0.637667	−	0.264130i
$366$		0			0
$367$	26.8327			1.40065			0.700327	−	0.713822i	$-0.253038\pi$
$367$	26.8327			1.40065			0.700327	+	0.713822i	$0.253038\pi$
$368$	12.3583	+	25.4593i	0.644222	+	1.32716i
$369$		0			0
$370$	20.7777	+	10.7136i	1.08018	+	0.556972i
$371$	−6.13001	−	14.7991i	−0.318254	−	0.768334i
$372$		0			0
$373$	−12.3312	−	5.10777i	−0.638487	−	0.264470i	0.0398670	−	0.999205i	$-0.487307\pi$
$373$	−12.3312	−	5.10777i	−0.638487	−	0.264470i	−0.678354	+	0.734735i	$0.737307\pi$
$374$	−0.0843041	+	1.00884i	−0.00435926	+	0.0521657i
$375$		0			0
$376$	−6.26114	+	8.36013i	−0.322893	+	0.431141i
$377$	−6.62683	+	6.62683i	−0.341299	+	0.341299i
$378$		0			0
$379$	−5.26078	−	2.17909i	−0.270228	−	0.111932i	0.243455	−	0.969912i	$-0.421719\pi$
$379$	−5.26078	−	2.17909i	−0.270228	−	0.111932i	−0.513683	+	0.857980i	$0.671719\pi$
$380$	−8.63493	+	6.14703i	−0.442962	+	0.315336i
$381$		0			0
$382$	9.58828	+	30.0022i	0.490579	+	1.53505i
$383$	8.14683			0.416283			0.208142	−	0.978099i	$-0.433258\pi$
$383$	8.14683			0.416283			0.208142	+	0.978099i	$0.433258\pi$
$384$		0			0
$385$	4.73527			0.241332
$386$	−4.68645	−	14.6641i	−0.238534	−	0.746385i
$387$		0			0
$388$	−12.5128	+	8.90760i	−0.635240	+	0.452215i
$389$	8.22236	+	3.40581i	0.416890	+	0.172682i	0.581261	−	0.813717i	$-0.302559\pi$
$389$	8.22236	+	3.40581i	0.416890	+	0.172682i	−0.164371	+	0.986399i	$0.552559\pi$
$390$		0			0
$391$	4.84191	−	4.84191i	0.244866	−	0.244866i
$392$	6.65313	−	8.88354i	0.336034	−	0.448686i
$393$		0			0
$394$	−0.777722	+	9.30672i	−0.0391811	+	0.468866i
$395$	19.7142	+	8.16588i	0.991927	+	0.410870i
$396$		0			0
$397$	−0.328403	−	0.792834i	−0.0164821	−	0.0397912i	0.915424	−	0.402490i	$-0.131855\pi$
$397$	−0.328403	−	0.792834i	−0.0164821	−	0.0397912i	−0.931906	+	0.362699i	$0.881855\pi$
$398$	−17.9691	−	9.26538i	−0.900712	−	0.464431i
$399$		0			0
$400$	−4.49045	+	2.17972i	−0.224522	+	0.108986i
$401$	17.3098			0.864411			0.432206	−	0.901775i	$-0.357735\pi$
$401$	17.3098			0.864411			0.432206	+	0.901775i	$0.357735\pi$
$402$		0			0
$403$	−42.8484	+	17.7484i	−2.13443	+	0.884111i
$404$	−2.21588	+	0.509388i	−0.110244	+	0.0253430i
$405$		0			0
$406$	−0.573062	+	6.85763i	−0.0284406	+	0.340338i
$407$	4.46314	−	4.46314i	0.221230	−	0.221230i
$408$		0			0
$409$	5.00972	+	5.00972i	0.247715	+	0.247715i	0.820032	−	0.572317i	$-0.193955\pi$
$409$	5.00972	+	5.00972i	0.247715	+	0.247715i	−0.572317	+	0.820032i	$0.693955\pi$
$410$	20.1148	−	17.0122i	0.993398	−	0.840175i
$411$		0			0
$412$	−3.31592	+	19.7017i	−0.163364	+	0.970631i
$413$	−13.4062	−	32.3654i	−0.659675	−	1.59260i
$414$		0			0
$415$		−	5.82422i		−	0.285900i
$416$	−12.9725	−	33.5915i	−0.636028	−	1.64696i
$417$		0			0
$418$	0.871195	+	2.72601i	0.0426115	+	0.133334i
$419$	7.01103	−	2.90406i	0.342511	−	0.141873i	−0.204796	−	0.978805i	$-0.565653\pi$
$419$	7.01103	−	2.90406i	0.342511	−	0.141873i	0.547307	+	0.836932i	$0.315653\pi$
$420$		0			0
$421$	3.94749	−	9.53009i	0.192389	−	0.464468i	−0.798021	−	0.602630i	$-0.794119\pi$
$421$	3.94749	−	9.53009i	0.192389	−	0.464468i	0.990410	+	0.138162i	$0.0441195\pi$
$422$	−18.6070	−	22.0004i	−0.905776	−	1.07096i
$423$		0			0
$424$	−11.7906	+	6.99226i	−0.572604	+	0.339574i
$425$	0.854002	+	0.854002i	0.0414252	+	0.0414252i
$426$		0			0
$427$	−14.8103	+	35.7552i	−0.716719	+	1.73031i
$428$	−34.0401	+	7.82516i	−1.64539	+	0.378243i
$429$		0			0
$430$	8.68572	+	4.47859i	0.418863	+	0.215977i
$431$			11.8098i			0.568858i	0.958697	+	0.284429i	$0.0918040\pi$
$431$			11.8098i			0.568858i	−0.958697	+	0.284429i	$0.908196\pi$
$432$		0			0
$433$			3.26662i			0.156984i	0.996915	+	0.0784919i	$0.0250105\pi$
$433$			3.26662i			0.156984i	−0.996915	+	0.0784919i	$0.974990\pi$
$434$	−15.6072	+	30.2684i	−0.749170	+	1.45293i
$435$		0			0
$436$	−3.41695	−	2.13961i	−0.163642	−	0.102469i
$437$	7.40772	−	17.8838i	0.354359	−	0.855499i
$438$		0			0
$439$	13.7003	+	13.7003i	0.653877	+	0.653877i	0.953924	−	0.300047i	$-0.0970024\pi$
$439$	13.7003	+	13.7003i	0.653877	+	0.653877i	−0.300047	+	0.953924i	$0.597002\pi$
$440$	−0.575832	−	4.01116i	−0.0274517	−	0.191224i
$441$		0			0
$442$	−6.65252	+	5.62642i	−0.316428	+	0.267621i
$443$	−7.53737	+	18.1968i	−0.358111	+	0.864557i	0.637454	+	0.770488i	$0.279988\pi$
$443$	−7.53737	+	18.1968i	−0.358111	+	0.864557i	−0.995566	+	0.0940692i	$0.970012\pi$
$444$		0			0
$445$	−17.2763	+	7.15607i	−0.818974	+	0.339230i
$446$	19.9588	−	6.37854i	0.945075	−	0.302032i
$447$		0			0
$448$	−23.2014	−	12.6819i	−1.09616	−	0.599165i
$449$			2.46488i			0.116325i	0.998307	+	0.0581625i	$0.0185241\pi$
$449$			2.46488i			0.116325i	−0.998307	+	0.0581625i	$0.981476\pi$
$450$		0			0
$451$	−2.72200	−	6.57150i	−0.128174	−	0.309440i
$452$	−1.18323	+	0.842319i	−0.0556546	+	0.0396193i
$453$		0			0
$454$	11.8377	+	13.9965i	0.555571	+	0.656891i
$455$	28.8174	+	28.8174i	1.35098	+	1.35098i
$456$		0			0
$457$	3.04617	−	3.04617i	0.142494	−	0.142494i	−0.632261	−	0.774755i	$-0.717873\pi$
$457$	3.04617	−	3.04617i	0.142494	−	0.142494i	0.774755	+	0.632261i	$0.217873\pi$
$458$	9.76206	+	0.815772i	0.456151	+	0.0381185i
$459$		0			0
$460$	−14.5465	+	23.2308i	−0.678236	+	1.08314i
$461$	−9.85993	+	4.08412i	−0.459223	+	0.190216i	−0.600288	−	0.799784i	$-0.704947\pi$
$461$	−9.85993	+	4.08412i	−0.459223	+	0.190216i	0.141065	+	0.990000i	$0.454947\pi$
$462$		0			0
$463$	−28.1511			−1.30829			−0.654147	−	0.756367i	$-0.726972\pi$
$463$	−28.1511			−1.30829			−0.654147	+	0.756367i	$0.726972\pi$
$464$	5.87865	−	0.348491i	0.272910	−	0.0161783i
$465$		0			0
$466$	7.66194	−	14.8595i	0.354933	−	0.688352i
$467$	0.133756	+	0.322916i	0.00618951	+	0.0149428i	0.926944	−	0.375200i	$-0.122426\pi$
$467$	0.133756	+	0.322916i	0.00618951	+	0.0149428i	−0.920755	+	0.390142i	$0.872426\pi$
$468$		0			0
$469$	−11.9123	−	4.93425i	−0.550060	−	0.227842i
$470$	−10.0808	−	0.842412i	−0.464995	−	0.0388576i
$471$		0			0
$472$	−25.7858	+	15.2919i	−1.18689	+	0.703867i
$473$	1.86573	−	1.86573i	0.0857863	−	0.0857863i
$474$		0			0
$475$	3.15430	+	1.30655i	0.144729	+	0.0599487i
$476$	−1.06183	+	6.30893i	−0.0486691	+	0.289169i
$477$		0			0
$478$	−3.28855	+	1.05097i	−0.150415	+	0.0480704i
$479$	25.3551			1.15850			0.579251	−	0.815149i	$-0.303345\pi$
$479$	25.3551			1.15850			0.579251	+	0.815149i	$0.303345\pi$
$480$		0			0
$481$	54.3226			2.47690
$482$	2.51106	−	0.802498i	0.114376	−	0.0365528i
$483$		0			0
$484$	20.6159	+	3.46980i	0.937088	+	0.157718i
$485$	−13.7436	−	5.69280i	−0.624066	−	0.258497i
$486$		0			0
$487$	−15.5211	+	15.5211i	−0.703327	+	0.703327i	−0.965123	−	0.261796i	$-0.915685\pi$
$487$	−15.5211	+	15.5211i	−0.703327	+	0.703327i	0.261796	+	0.965123i	$0.415685\pi$
$488$	32.0885	+	8.19749i	1.45258	+	0.371083i
$489$		0			0
$490$	10.7120	+	0.895153i	0.483918	+	0.0404389i
$491$	−7.79527	−	3.22890i	−0.351795	−	0.145718i	0.199786	−	0.979840i	$-0.435975\pi$
$491$	−7.79527	−	3.22890i	−0.351795	−	0.145718i	−0.551581	+	0.834121i	$0.685975\pi$
$492$		0			0
$493$	−0.545281	−	1.31642i	−0.0245582	−	0.0592888i
$494$	−11.2878	+	21.8915i	−0.507864	+	0.984945i
$495$		0			0
$496$	27.5377	+	9.53978i	1.23648	+	0.428349i
$497$	46.0722			2.06662
$498$		0			0
$499$	−2.14784	+	0.889664i	−0.0961504	+	0.0398268i	−0.430240	−	0.902714i	$-0.641571\pi$
$499$	−2.14784	+	0.889664i	−0.0961504	+	0.0398268i	0.334090	+	0.942541i	$0.391571\pi$
$500$	−20.5148	−	12.8458i	−0.917449	−	0.574482i
$501$		0			0
$502$	23.2350	+	1.94165i	1.03703	+	0.0866600i
$503$	−10.4975	+	10.4975i	−0.468062	+	0.468062i	−0.901286	−	0.433224i	$-0.857376\pi$
$503$	−10.4975	+	10.4975i	−0.468062	+	0.468062i	0.433224	+	0.901286i	$0.357376\pi$
$504$		0			0
$505$	−1.55712	−	1.55712i	−0.0692908	−	0.0692908i
$506$	4.77900	+	5.65056i	0.212453	+	0.251198i
$507$		0			0
$508$	−13.4181	−	18.8489i	−0.595333	−	0.836283i
$509$	−8.62373	−	20.8195i	−0.382240	−	0.922810i	−0.991532	−	0.129863i	$-0.958546\pi$
$509$	−8.62373	−	20.8195i	−0.382240	−	0.922810i	0.609292	−	0.792946i	$-0.291454\pi$
$510$		0			0
$511$		−	22.4997i		−	0.995329i
$512$	−7.92123	+	21.1956i	−0.350072	+	0.936723i
$513$		0			0
$514$	7.87592	−	2.51703i	0.347392	−	0.111021i
$515$	−17.8769	+	7.40485i	−0.787750	+	0.326297i
$516$		0			0
$517$	−1.04523	+	2.52340i	−0.0459690	+	0.110979i
$518$	30.4561	−	25.7585i	1.33816	−	1.13176i
$519$		0			0
$520$	20.9063	−	27.9150i	0.916803	−	1.22415i
$521$	23.6260	+	23.6260i	1.03508	+	1.03508i	0.999362	+	0.0357139i	$0.0113705\pi$
$521$	23.6260	+	23.6260i	1.03508	+	1.03508i	0.0357139	+	0.999362i	$0.488630\pi$
$522$		0			0
$523$	−0.967311	+	2.33529i	−0.0422975	+	0.102115i	−0.943616	−	0.331041i	$-0.892600\pi$
$523$	−0.967311	+	2.33529i	−0.0422975	+	0.102115i	0.901319	+	0.433156i	$0.142600\pi$
$524$	−20.5927	+	32.8866i	−0.899596	+	1.43666i
$525$		0			0
$526$	−10.4709	+	20.3072i	−0.456554	+	0.885434i
$527$		−	7.05147i		−	0.307167i
$528$		0			0
$529$		−	27.0566i		−	1.17638i
$530$	−11.8002	−	6.08450i	−0.512568	−	0.264294i
$531$		0			0
$532$	4.05187	+	17.6259i	0.175671	+	0.764182i
$533$	23.4268	−	56.5574i	1.01473	−	2.44977i
$534$		0			0
$535$	−23.9203	−	23.9203i	−1.03416	−	1.03416i
$536$	−2.73111	+	10.6907i	−0.117966	+	0.461769i
$537$		0			0
$538$	2.39721	+	2.83440i	0.103351	+	0.122199i
$539$	1.11067	−	2.68138i	0.0478398	−	0.115495i
$540$		0			0
$541$	13.3578	−	5.53299i	0.574298	−	0.237882i	−0.0765813	−	0.997063i	$-0.524400\pi$
$541$	13.3578	−	5.53299i	0.574298	−	0.237882i	0.650879	+	0.759181i	$0.274400\pi$
$542$	4.60458	+	14.4080i	0.197784	+	0.618875i
$543$		0			0
$544$	5.47330	+	0.132263i	0.234666	+	0.00567072i
$545$		−	3.90464i		−	0.167257i
$546$		0			0
$547$	−16.5682	−	39.9992i	−0.708406	−	1.71024i	−0.703945	−	0.710254i	$-0.748580\pi$
$547$	−16.5682	−	39.9992i	−0.708406	−	1.71024i	−0.00446097	−	0.999990i	$-0.501420\pi$
$548$	−44.5901	−	7.50480i	−1.90479	−	0.320589i
$549$		0			0
$550$	−0.996629	+	0.842907i	−0.0424964	+	0.0359417i
$551$	−2.84825	−	2.84825i	−0.121340	−	0.121340i
$552$		0			0
$553$	25.7454	−	25.7454i	1.09481	−	1.09481i
$554$	−1.75271	+	20.9741i	−0.0744656	+	0.891104i
$555$		0			0
$556$	0.0427731	+	0.186066i	0.00181398	+	0.00789097i
$557$	5.70924	−	2.36484i	0.241908	−	0.100202i	−0.258436	−	0.966029i	$-0.583207\pi$
$557$	5.70924	−	2.36484i	0.241908	−	0.100202i	0.500344	+	0.865827i	$0.333207\pi$
$558$		0			0
$559$	22.7085			0.960467
$560$	−1.51545	−	25.5639i	−0.0640394	−	1.08027i
$561$		0			0
$562$	2.90594	+	1.49838i	0.122580	+	0.0632055i
$563$	5.89410	+	14.2296i	0.248407	+	0.599707i	0.998069	−	0.0621133i	$-0.0197840\pi$
$563$	5.89410	+	14.2296i	0.248407	+	0.599707i	−0.749662	+	0.661821i	$0.769784\pi$
$564$		0			0
$565$	−1.29962	−	0.538322i	−0.0546756	−	0.0226474i
$566$	−0.605632	+	7.24738i	−0.0254566	+	0.304630i
$567$		0			0
$568$	−5.60261	−	39.0269i	−0.235080	−	1.63753i
$569$	0.242674	−	0.242674i	0.0101734	−	0.0101734i	−0.702002	−	0.712175i	$-0.747710\pi$
$569$	0.242674	−	0.242674i	0.0101734	−	0.0101734i	0.712175	+	0.702002i	$0.247710\pi$
$570$		0			0
$571$	25.8985	+	10.7275i	1.08382	+	0.448933i	0.851848	−	0.523789i	$-0.175482\pi$
$571$	25.8985	+	10.7275i	1.08382	+	0.448933i	0.231972	+	0.972722i	$0.425482\pi$
$572$	−5.46097	−	7.67120i	−0.228335	−	0.320749i
$573$		0			0
$574$	−13.6839	−	42.8175i	−0.571153	−	1.78717i
$575$	8.82885			0.368188
$576$		0			0
$577$	17.7896			0.740589			0.370294	−	0.928914i	$-0.379257\pi$
$577$	17.7896			0.740589			0.370294	+	0.928914i	$0.379257\pi$
$578$	6.91544	+	21.6388i	0.287644	+	0.900054i
$579$		0			0
$580$	3.30773	+	4.64648i	0.137346	+	0.192935i
$581$	−9.18133	−	3.80303i	−0.380906	−	0.157776i
$582$		0			0
$583$	−2.53473	+	2.53473i	−0.104978	+	0.104978i
$584$	−19.0591	+	2.73607i	−0.788670	+	0.113220i
$585$		0			0
$586$	−1.66267	+	19.8966i	−0.0686842	+	0.821920i
$587$	30.9718	+	12.8289i	1.27834	+	0.529507i	0.915490	−	0.402340i	$-0.131803\pi$
$587$	30.9718	+	12.8289i	1.27834	+	0.529507i	0.362852	+	0.931847i	$0.381803\pi$
$588$		0			0
$589$	−7.62838	−	18.4165i	−0.314322	−	0.758840i
$590$	−25.8067	−	13.3067i	−1.06245	−	0.547826i
$591$		0			0
$592$	−25.5231	−	22.6664i	−1.04899	−	0.931584i
$593$	−41.4635			−1.70270			−0.851351	−	0.524596i	$-0.824216\pi$
$593$	−41.4635			−1.70270			−0.851351	+	0.524596i	$0.824216\pi$
$594$		0			0
$595$	−5.72460	+	2.37121i	−0.234686	+	0.0972100i
$596$	−6.78495	−	29.5150i	−0.277922	−	1.20898i
$597$		0			0
$598$	−5.30400	+	63.4711i	−0.216897	+	2.59552i
$599$	32.9148	−	32.9148i	1.34486	−	1.34486i	0.453719	−	0.891145i	$-0.350097\pi$
$599$	32.9148	−	32.9148i	1.34486	−	1.34486i	0.891145	−	0.453719i	$-0.149903\pi$
$600$		0			0
$601$	−12.5748	−	12.5748i	−0.512936	−	0.512936i	0.402489	−	0.915425i	$-0.368145\pi$
$601$	−12.5748	−	12.5748i	−0.512936	−	0.512936i	−0.915425	+	0.402489i	$0.868145\pi$
$602$	12.7316	−	10.7678i	0.518900	−	0.438864i
$603$		0			0
$604$	−20.8377	−	3.50713i	−0.847875	−	0.142703i
$605$	7.74848	+	18.7065i	0.315021	+	0.760527i
$606$		0			0
$607$		−	46.0240i		−	1.86806i	−0.357198	−	0.934029i	$-0.616268\pi$
$607$		−	46.0240i		−	1.86806i	0.357198	−	0.934029i	$-0.383732\pi$
$608$	14.4379	−	5.57566i	0.585533	−	0.226123i
$609$		0			0
$610$	9.76464	+	30.5540i	0.395359	+	1.23710i
$611$	−21.7176	+	8.99570i	−0.878598	+	0.363927i
$612$		0			0
$613$	3.81762	−	9.21655i	0.154192	−	0.372253i	−0.827841	−	0.560963i	$-0.810431\pi$
$613$	3.81762	−	9.21655i	0.154192	−	0.372253i	0.982033	+	0.188711i	$0.0604308\pi$
$614$	−13.5752	−	16.0509i	−0.547850	−	0.647762i
$615$		0			0
$616$	−6.69921	−	1.71141i	−0.269919	−	0.0689548i
$617$	−9.42700	−	9.42700i	−0.379517	−	0.379517i	0.491411	−	0.870928i	$-0.336481\pi$
$617$	−9.42700	−	9.42700i	−0.379517	−	0.379517i	−0.870928	+	0.491411i	$0.836481\pi$
$618$		0			0
$619$	−10.4213	+	25.1593i	−0.418868	+	1.01124i	0.563808	+	0.825906i	$0.309336\pi$
$619$	−10.4213	+	25.1593i	−0.418868	+	1.01124i	−0.982676	+	0.185332i	$0.940664\pi$
$620$	6.32365	+	27.5084i	0.253964	+	1.10476i
$621$		0			0
$622$	−3.44309	−	1.77535i	−0.138055	−	0.0711851i
$623$			31.9071i			1.27833i
$624$		0			0
$625$		−	17.2034i		−	0.688136i
$626$	19.0709	−	36.9858i	0.762226	−	1.47825i
$627$		0			0
$628$	12.6805	−	20.2507i	0.506006	−	0.808092i
$629$	−3.16068	+	7.63055i	−0.126024	+	0.304250i
$630$		0			0
$631$	15.7973	+	15.7973i	0.628879	+	0.628879i	0.947786	−	0.318907i	$-0.103316\pi$
$631$	15.7973	+	15.7973i	0.628879	+	0.628879i	−0.318907	+	0.947786i	$0.603316\pi$
$632$	−24.9392	−	18.6777i	−0.992030	−	0.742959i
$633$		0			0
$634$	19.7282	−	16.6852i	0.783505	−	0.662656i
$635$	8.57545	−	20.7030i	0.340307	−	0.821573i
$636$		0			0
$637$	23.0772	−	9.55891i	0.914354	−	0.378738i
$638$	1.46688	−	0.468793i	0.0580742	−	0.0185597i
$639$		0			0
$640$	−21.4704	+	4.39240i	−0.848692	+	0.173625i
$641$			11.2466i			0.444215i	0.975022	+	0.222107i	$0.0712936\pi$
$641$			11.2466i			0.444215i	−0.975022	+	0.222107i	$0.928706\pi$
$642$		0			0
$643$	4.46309	+	10.7749i	0.176007	+	0.424919i	0.987122	−	0.159968i	$-0.0511390\pi$
$643$	4.46309	+	10.7749i	0.176007	+	0.424919i	−0.811115	+	0.584886i	$0.801139\pi$
$644$	27.1228	+	38.1002i	1.06879	+	1.50136i
$645$		0			0
$646$	−2.41827	−	2.85930i	−0.0951457	−	0.112497i
$647$	22.9908	+	22.9908i	0.903861	+	0.903861i	0.995768	−	0.0919063i	$-0.0292960\pi$
$647$	22.9908	+	22.9908i	0.903861	+	0.903861i	−0.0919063	+	0.995768i	$0.529296\pi$
$648$		0			0
$649$	−5.54340	+	5.54340i	−0.217597	+	0.217597i
$650$	−11.1948	−	0.935504i	−0.439098	−	0.0366935i
$651$		0			0
$652$	14.6162	+	9.15226i	0.572414	+	0.358430i
$653$	−0.731559	+	0.303022i	−0.0286281	+	0.0118582i	−0.396952	−	0.917840i	$-0.629932\pi$
$653$	−0.731559	+	0.303022i	−0.0286281	+	0.0118582i	0.368323	+	0.929698i	$0.379932\pi$
$654$		0			0
$655$	−37.5804			−1.46839
$656$	−34.6058	+	16.7981i	−1.35113	+	0.655857i
$657$		0			0
$658$	−7.91045	+	15.3414i	−0.308381	+	0.598071i
$659$	−3.48735	−	8.41921i	−0.135848	−	0.327966i	0.841286	−	0.540590i	$-0.181799\pi$
$659$	−3.48735	−	8.41921i	−0.135848	−	0.327966i	−0.977134	+	0.212624i	$0.931799\pi$
$660$		0			0
$661$	22.6551	+	9.38406i	0.881182	+	0.364998i	0.776955	−	0.629556i	$-0.216763\pi$
$661$	22.6551	+	9.38406i	0.881182	+	0.364998i	0.104227	+	0.994554i	$0.466763\pi$
$662$	−27.9042	−	2.33184i	−1.08453	−	0.0906293i
$663$		0			0
$664$	−2.10498	+	8.23979i	−0.0816890	+	0.319766i
$665$	−12.3859	+	12.3859i	−0.480305	+	0.480305i
$666$		0			0
$667$	−9.62334	−	3.98612i	−0.372617	−	0.154343i
$668$	−0.209497	−	0.0352596i	−0.00810567	−	0.00136424i
$669$		0			0
$670$	−10.1795	+	3.25322i	−0.393268	+	0.125683i
$671$	8.66062			0.334340
$672$		0			0
$673$	−17.3835			−0.670084			−0.335042	−	0.942203i	$-0.608751\pi$
$673$	−17.3835			−0.670084			−0.335042	+	0.942203i	$0.608751\pi$
$674$	9.07121	−	2.89903i	0.349410	−	0.111666i
$675$		0			0
$676$	9.13549	−	54.2789i	0.351365	−	2.08765i
$677$	39.4502	+	16.3408i	1.51620	+	0.628029i	0.976825	−	0.214040i	$-0.0686621\pi$
$677$	39.4502	+	16.3408i	1.51620	+	0.628029i	0.539371	+	0.842068i	$0.318662\pi$
$678$		0			0
$679$	−17.9483	+	17.9483i	−0.688793	+	0.688793i
$680$	2.70474	+	4.56085i	0.103722	+	0.174901i
$681$		0			0
$682$	7.59449	+	0.634638i	0.290808	+	0.0243016i
$683$	−40.6471	−	16.8366i	−1.55532	−	0.644234i	−0.571049	−	0.820916i	$-0.693464\pi$
$683$	−40.6471	−	16.8366i	−1.55532	−	0.644234i	−0.984268	+	0.176682i	$0.943464\pi$
$684$		0			0
$685$	−16.7591	−	40.4602i	−0.640334	−	1.54590i
$686$	−6.58923	+	12.7791i	−0.251578	+	0.487907i
$687$		0			0
$688$	−10.6694	−	9.47525i	−0.406769	−	0.361240i
$689$	−30.8512			−1.17534
$690$		0			0
$691$	−0.769203	+	0.318614i	−0.0292619	+	0.0121207i	−0.397266	−	0.917703i	$-0.630041\pi$
$691$	−0.769203	+	0.318614i	−0.0292619	+	0.0121207i	0.368005	+	0.929824i	$0.380041\pi$
$692$	−24.1312	+	38.5376i	−0.917331	+	1.46498i
$693$		0			0
$694$	10.2984	+	0.860593i	0.390922	+	0.0326677i
$695$	−0.130751	+	0.130751i	−0.00495965	+	0.00495965i
$696$		0			0
$697$	6.58141	+	6.58141i	0.249289	+	0.249289i
$698$	3.13171	+	3.70285i	0.118537	+	0.140155i
$699$		0			0
$700$	−6.72001	+	4.78384i	−0.253992	+	0.180812i
$701$	−10.7572	−	25.9701i	−0.406292	−	0.980876i	−0.986105	−	0.166126i	$-0.946874\pi$
$701$	−10.7572	−	25.9701i	−0.406292	−	0.980876i	0.579812	−	0.814750i	$-0.303126\pi$
$702$		0			0
$703$			23.3482i			0.880595i
$704$	−0.635050	+	5.88289i	−0.0239343	+	0.221720i
$705$		0			0
$706$	40.2213	−	12.8542i	1.51375	−	0.483773i
$707$	−3.47140	+	1.43790i	−0.130555	+	0.0540778i
$708$		0			0
$709$	−13.7081	+	33.0944i	−0.514820	+	1.24289i	0.426229	+	0.904615i	$0.359842\pi$
$709$	−13.7081	+	33.0944i	−0.514820	+	1.24289i	−0.941049	+	0.338270i	$0.890158\pi$
$710$	29.1562	−	24.6591i	1.09421	−	0.925440i
$711$		0			0
$712$	27.0279	−	3.88005i	1.01291	−	0.145411i
$713$	−36.4497	−	36.4497i	−1.36505	−	1.36505i
$714$		0			0
$715$	3.49008	−	8.42579i	0.130522	−	0.315107i
$716$	19.2919	+	12.0801i	0.720971	+	0.451453i
$717$		0			0
$718$	−8.65497	+	16.7853i	−0.323001	+	0.626423i
$719$		−	24.7319i		−	0.922345i	−0.887311	−	0.461172i	$-0.847429\pi$
$719$		−	24.7319i		−	0.922345i	0.887311	−	0.461172i	$-0.152571\pi$
$720$		0			0
$721$			33.0163i			1.22959i
$722$	14.4731	+	7.46270i	0.538632	+	0.277733i
$723$		0			0
$724$	9.04530	−	2.07934i	0.336166	−	0.0772781i
$725$	0.703060	−	1.69734i	0.0261110	−	0.0630375i
$726$		0			0
$727$	4.89101	+	4.89101i	0.181397	+	0.181397i	0.791965	−	0.610567i	$-0.209058\pi$
$727$	4.89101	+	4.89101i	0.181397	+	0.181397i	−0.610567	+	0.791965i	$0.709058\pi$
$728$	−30.3542	−	51.1844i	−1.12500	−	1.89702i
$729$		0			0
$730$	−12.0425	−	14.2386i	−0.445711	−	0.526996i
$731$	−1.32126	+	3.18980i	−0.0488685	+	0.117979i
$732$		0			0
$733$	−10.2058	+	4.22736i	−0.376958	+	0.156141i	−0.563114	−	0.826379i	$-0.690397\pi$
$733$	−10.2058	+	4.22736i	−0.376958	+	0.156141i	0.186156	+	0.982520i	$0.440397\pi$
$734$	−11.5518	−	36.1461i	−0.426384	−	1.33418i
$735$		0			0
$736$	28.9757	−	27.6083i	1.06806	−	1.01766i
$737$			2.88540i			0.106285i
$738$		0			0
$739$	1.71029	+	4.12900i	0.0629139	+	0.151888i	0.952210	−	0.305445i	$-0.0988051\pi$
$739$	1.71029	+	4.12900i	0.0629139	+	0.151888i	−0.889296	+	0.457332i	$0.848805\pi$
$740$	5.48710	−	32.6019i	0.201710	−	1.19847i
$741$		0			0
$742$	−17.2968	+	14.6289i	−0.634985	+	0.537044i
$743$	12.6977	+	12.6977i	0.465832	+	0.465832i	0.900561	−	0.434729i	$-0.143156\pi$
$743$	12.6977	+	12.6977i	0.465832	+	0.465832i	−0.434729	+	0.900561i	$0.643156\pi$
$744$		0			0
$745$	20.7405	−	20.7405i	0.759873	−	0.759873i
$746$	−1.57189	+	18.8103i	−0.0575511	+	0.688693i
$747$		0			0
$748$	1.39529	−	0.320751i	0.0510169	−	0.0117278i
$749$	−53.3272	+	22.0888i	−1.94853	+	0.807108i
$750$		0			0
$751$	−25.3864			−0.926362			−0.463181	−	0.886264i	$-0.653292\pi$
$751$	−25.3864			−0.926362			−0.463181	+	0.886264i	$0.653292\pi$
$752$	13.9574	+	4.83520i	0.508973	+	0.176322i
$753$		0			0
$754$	11.7799	+	6.07402i	0.428998	+	0.221203i
$755$	−7.83185	−	18.9078i	−0.285030	−	0.688123i
$756$		0			0
$757$	48.9351	+	20.2696i	1.77858	+	0.736711i	0.993023	+	0.117918i	$0.0376220\pi$
$757$	48.9351	+	20.2696i	1.77858	+	0.736711i	0.785554	+	0.618793i	$0.212378\pi$
$758$	−0.670604	+	8.02488i	−0.0243574	+	0.291477i
$759$		0			0
$760$	11.9981	+	8.98568i	0.435215	+	0.325945i
$761$	7.18378	−	7.18378i	0.260412	−	0.260412i	−0.564809	−	0.825221i	$-0.691050\pi$
$761$	7.18378	−	7.18378i	0.260412	−	0.260412i	0.825221	+	0.564809i	$0.191050\pi$
$762$		0			0
$763$	−6.15530	−	2.54961i	−0.222837	−	0.0923020i
$764$	36.2879	−	25.8326i	1.31285	−	0.934591i
$765$		0			0
$766$	−3.50731	−	10.9745i	−0.126724	−	0.396526i
$767$	−67.4708			−2.43623
$768$		0			0
$769$	−48.6570			−1.75462			−0.877309	−	0.479926i	$-0.840663\pi$
$769$	−48.6570			−1.75462			−0.877309	+	0.479926i	$0.840663\pi$
$770$	−2.03859	−	6.37885i	−0.0734657	−	0.229878i
$771$		0			0
$772$	−17.7364	+	12.6262i	−0.638347	+	0.454426i
$773$	7.43579	+	3.08000i	0.267447	+	0.110780i	0.512377	−	0.858761i	$-0.328765\pi$
$773$	7.43579	+	3.08000i	0.267447	+	0.110780i	−0.244930	+	0.969541i	$0.578765\pi$
$774$		0			0
$775$	6.42890	−	6.42890i	0.230933	−	0.230933i
$776$	17.3863	+	13.0211i	0.624130	+	0.467429i
$777$		0			0
$778$	1.04812	−	12.5425i	0.0375770	−	0.449671i
$779$	24.3087	+	10.0690i	0.870951	+	0.360760i
$780$		0			0
$781$	−3.94552	−	9.52534i	−0.141182	−	0.340843i
$782$	−8.60700	−	4.43800i	−0.307786	−	0.158703i
$783$		0			0
$784$	−14.8312	−	5.13792i	−0.529686	−	0.183497i
$785$	23.1411			0.825940
$786$		0			0
$787$	14.9915	−	6.20966i	0.534388	−	0.221351i	−0.0991360	−	0.995074i	$-0.531608\pi$
$787$	14.9915	−	6.20966i	0.534388	−	0.221351i	0.633524	+	0.773723i	$0.281608\pi$
$788$	12.8718	−	2.95899i	0.458540	−	0.105410i
$789$		0			0
$790$	2.51301	−	30.0723i	0.0894090	−	1.06993i
$791$	−1.69722	+	1.69722i	−0.0603464	+	0.0603464i
$792$		0			0
$793$	52.7058	+	52.7058i	1.87164	+	1.87164i
$794$	−0.926640	+	0.783713i	−0.0328852	+	0.0278129i
$795$		0			0
$796$	−4.74540	+	28.1950i	−0.168196	+	0.999344i
$797$	2.43692	+	5.88325i	0.0863202	+	0.208395i	0.961145	−	0.276044i	$-0.0890236\pi$
$797$	2.43692	+	5.88325i	0.0863202	+	0.208395i	−0.874825	+	0.484439i	$0.839024\pi$
$798$		0			0
$799$		−	3.57401i		−	0.126439i
$800$	4.86948	+	5.11065i	0.172162	+	0.180689i
$801$		0			0
$802$	−7.45208	−	23.3179i	−0.263142	−	0.823385i
$803$	−4.65177	+	1.92682i	−0.164157	+	0.0679962i
$804$		0			0
$805$	−17.3340	+	41.8480i	−0.610944	+	1.47495i
$806$	42.3555	+	50.0799i	1.49191	+	1.76399i
$807$		0			0
$808$	1.64016	+	2.76570i	0.0577005	+	0.0972969i
$809$	9.30765	+	9.30765i	0.327240	+	0.327240i	0.851536	−	0.524296i	$-0.175672\pi$
$809$	9.30765	+	9.30765i	0.327240	+	0.327240i	−0.524296	+	0.851536i	$0.675672\pi$
$810$		0			0
$811$	−8.10599	+	19.5696i	−0.284640	+	0.687181i	−0.999932	−	0.0116440i	$-0.996294\pi$
$811$	−8.10599	+	19.5696i	−0.284640	+	0.687181i	0.715292	+	0.698825i	$0.246294\pi$
$812$	9.48458	−	2.18032i	0.332843	−	0.0765143i
$813$		0			0
$814$	−7.93370	−	4.09083i	−0.278076	−	0.143384i
$815$			16.7023i			0.585056i
$816$		0			0
$817$			9.76026i			0.341468i
$818$	4.59182	−	8.90530i	0.160549	−	0.311367i
$819$		0			0
$820$	−31.5767	−	19.7725i	−1.10271	−	0.690486i
$821$	3.81353	−	9.20668i	0.133093	−	0.321315i	−0.843257	−	0.537511i	$-0.819365\pi$
$821$	3.81353	−	9.20668i	0.133093	−	0.321315i	0.976350	+	0.216195i	$0.0693648\pi$
$822$		0			0
$823$	−16.5761	−	16.5761i	−0.577808	−	0.577808i	0.356491	−	0.934299i	$-0.383973\pi$
$823$	−16.5761	−	16.5761i	−0.577808	−	0.577808i	−0.934299	+	0.356491i	$0.883973\pi$
$824$	27.9675	−	4.01495i	0.974294	−	0.139867i
$825$		0			0
$826$	−37.8277	+	31.9930i	−1.31619	+	1.11318i
$827$	−11.1677	+	26.9613i	−0.388340	+	0.937537i	0.601951	+	0.798533i	$0.294390\pi$
$827$	−11.1677	+	26.9613i	−0.388340	+	0.937537i	−0.990292	+	0.139004i	$0.955610\pi$
$828$		0			0
$829$	8.82768	−	3.65654i	0.306598	−	0.126997i	−0.224080	−	0.974571i	$-0.571938\pi$
$829$	8.82768	−	3.65654i	0.306598	−	0.126997i	0.530678	+	0.847574i	$0.321938\pi$
$830$	−7.84577	+	2.50740i	−0.272331	+	0.0870330i
$831$		0			0
$832$	−39.6661	+	31.9367i	−1.37518	+	1.10721i
$833$			3.79777i			0.131585i
$834$		0			0
$835$	−0.0787391	−	0.190093i	−0.00272488	−	0.00657844i
$836$	3.29713	−	2.34716i	0.114034	−	0.0811783i
$837$		0			0
$838$	−6.93037	−	8.19427i	−0.239406	−	0.283066i
$839$	−4.55814	−	4.55814i	−0.157364	−	0.157364i	0.624033	−	0.781398i	$-0.285493\pi$
$839$	−4.55814	−	4.55814i	−0.157364	−	0.157364i	−0.781398	+	0.624033i	$0.785493\pi$
$840$		0			0
$841$	18.9734	−	18.9734i	0.654257	−	0.654257i
$842$	−14.5374	−	1.21482i	−0.500990	−	0.0418656i
$843$		0			0
$844$	−21.6261	+	34.5368i	−0.744399	+	1.18881i
$845$	49.2516	−	20.4007i	1.69431	−	0.701805i
$846$		0			0
$847$	34.5485			1.18710
$848$	14.4952	+	12.8728i	0.497768	+	0.442055i
$849$		0			0
$850$	0.782762	−	1.51808i	0.0268485	−	0.0520697i
$851$	23.1052	+	55.7809i	0.792037	+	1.91215i
$852$		0			0
$853$	13.7268	+	5.68583i	0.469997	+	0.194679i	0.605095	−	0.796153i	$-0.293135\pi$
$853$	13.7268	+	5.68583i	0.469997	+	0.194679i	−0.135098	+	0.990832i	$0.543135\pi$
$854$	54.5415	+	4.55780i	1.86637	+	0.155965i
$855$		0			0
$856$	25.1959	+	42.4863i	0.861177	+	1.45215i
$857$	11.1744	−	11.1744i	0.381711	−	0.381711i	−0.490007	−	0.871718i	$-0.663006\pi$
$857$	11.1744	−	11.1744i	0.381711	−	0.381711i	0.871718	+	0.490007i	$0.163006\pi$
$858$		0			0
$859$	39.1836	+	16.2304i	1.33693	+	0.553773i	0.932623	−	0.360851i	$-0.117514\pi$
$859$	39.1836	+	16.2304i	1.33693	+	0.553773i	0.404304	+	0.914625i	$0.367514\pi$
$860$	2.29378	−	13.6286i	0.0782171	−	0.464730i
$861$		0			0
$862$	15.9089	−	5.08426i	0.541859	−	0.173171i
$863$	22.2298			0.756710			0.378355	−	0.925661i	$-0.376490\pi$
$863$	22.2298			0.756710			0.378355	+	0.925661i	$0.376490\pi$
$864$		0			0
$865$	−44.0379			−1.49733
$866$	4.40044	−	1.40632i	0.149533	−	0.0477887i
$867$		0			0
$868$	47.4934	+	7.99345i	1.61203	+	0.271316i
$869$	−7.52760	−	3.11803i	−0.255356	−	0.105772i
$870$		0			0
$871$	−17.5597	+	17.5597i	−0.594987	+	0.594987i
$872$	−1.41121	+	5.52408i	−0.0477896	+	0.187069i
$873$		0			0
$874$	−27.2803	−	2.27969i	−0.922769	−	0.0771118i
$875$	−36.9553	−	15.3074i	−1.24932	−	0.517484i
$876$		0			0
$877$	3.13025	+	7.55709i	0.105701	+	0.255185i	0.967877	−	0.251424i	$-0.0808989\pi$
$877$	3.13025	+	7.55709i	0.105701	+	0.255185i	−0.862176	+	0.506609i	$0.830899\pi$
$878$	12.5574	−	24.3536i	0.423792	−	0.821895i
$879$		0			0
$880$	−5.15550	+	2.50255i	−0.173792	+	0.0843610i
$881$	4.77921			0.161016			0.0805078	−	0.996754i	$-0.474346\pi$
$881$	4.77921			0.161016			0.0805078	+	0.996754i	$0.474346\pi$
$882$		0			0
$883$	−45.1752	+	18.7122i	−1.52027	+	0.629716i	−0.977645	−	0.210261i	$-0.932569\pi$
$883$	−45.1752	+	18.7122i	−1.52027	+	0.629716i	−0.542622	+	0.839977i	$0.682569\pi$
$884$	10.4433	+	6.53932i	0.351246	+	0.219941i
$885$		0			0
$886$	27.7578	+	2.31959i	0.932540	+	0.0779283i
$887$	−6.92890	+	6.92890i	−0.232650	+	0.232650i	−0.813798	−	0.581148i	$-0.802604\pi$
$887$	−6.92890	+	6.92890i	−0.232650	+	0.232650i	0.581148	+	0.813798i	$0.302604\pi$
$888$		0			0
$889$	−27.0368	−	27.0368i	−0.906784	−	0.906784i
$890$	17.0775	+	20.1920i	0.572440	+	0.676836i
$891$		0			0
$892$	−17.1850	−	24.1403i	−0.575395	−	0.808276i
$893$	−3.86641	−	9.33435i	−0.129385	−	0.312362i
$894$		0			0
$895$			22.0453i			0.736894i
$896$	−7.09529	+	36.7141i	−0.237037	+	1.22653i
$897$		0			0
$898$	3.32043	−	1.06116i	0.110804	−	0.0354114i
$899$	−9.91000	+	4.10486i	−0.330517	+	0.136905i
$900$		0			0
$901$	1.79503	−	4.33358i	0.0598011	−	0.144373i
$902$	−7.68057	+	6.49590i	−0.255735	+	0.216290i
$903$		0			0
$904$	1.64408	+	1.23130i	0.0546812	+	0.0409523i
$905$	6.35622	+	6.35622i	0.211288	+	0.211288i
$906$		0			0
$907$	14.4242	−	34.8230i	0.478946	−	1.15628i	−0.481157	−	0.876634i	$-0.659783\pi$
$907$	14.4242	−	34.8230i	0.478946	−	1.15628i	0.960104	−	0.279644i	$-0.0902166\pi$
$908$	13.7584	−	21.9722i	0.456588	−	0.729172i
$909$		0			0
$910$	26.4135	−	51.2260i	0.875599	−	1.69812i
$911$		−	44.7402i		−	1.48231i	−0.671335	−	0.741154i	$-0.734279\pi$
$911$		−	44.7402i		−	1.48231i	0.671335	−	0.741154i	$-0.265721\pi$
$912$		0			0
$913$			2.22390i			0.0736004i
$914$	−5.41488	−	2.79206i	−0.179108	−	0.0923531i
$915$		0			0
$916$	−3.10376	−	13.5016i	−0.102551	−	0.446105i
$917$	−24.5388	+	59.2418i	−0.810342	+	1.95634i
$918$		0			0
$919$	25.4709	+	25.4709i	0.840207	+	0.840207i	0.988886	−	0.148678i	$-0.0475019\pi$
$919$	25.4709	+	25.4709i	0.840207	+	0.840207i	−0.148678	+	0.988886i	$0.547502\pi$
$920$	37.5566	+	9.59439i	1.23820	+	0.316318i
$921$		0			0
$922$	9.74650	+	11.5240i	0.320984	+	0.379522i
$923$	33.9570	−	81.9795i	1.11771	−	2.69839i
$924$		0			0
$925$	−9.83848	+	4.07523i	−0.323487	+	0.133993i
$926$	12.1194	+	37.9222i	0.398268	+	1.24620i
$927$		0			0
$928$	−3.00028	−	7.76906i	−0.0984890	−	0.255032i
$929$			23.0747i			0.757058i	0.925589	+	0.378529i	$0.123570\pi$
$929$			23.0747i			0.757058i	−0.925589	+	0.378529i	$0.876430\pi$
$930$		0			0
$931$	4.10848	+	9.91875i	0.134650	+	0.325074i
$932$	−23.3156	−	3.92418i	−0.763729	−	0.128541i
$933$		0			0
$934$	0.377415	−	0.319202i	0.0123494	−	0.0104446i
$935$	0.980484	+	0.980484i	0.0320652	+	0.0320652i
$936$		0			0
$937$	6.57961	−	6.57961i	0.214947	−	0.214947i	−0.591418	−	0.806365i	$-0.701432\pi$
$937$	6.57961	−	6.57961i	0.214947	−	0.214947i	0.806365	+	0.591418i	$0.201432\pi$
$938$	−1.51849	+	18.1713i	−0.0495805	+	0.593313i
$939$		0			0
$940$	3.20511	+	13.9425i	0.104539	+	0.454754i
$941$	−40.5076	+	16.7788i	−1.32051	+	0.546973i	−0.927934	−	0.372746i	$-0.878416\pi$
$941$	−40.5076	+	16.7788i	−1.32051	+	0.546973i	−0.392577	+	0.919719i	$0.628416\pi$
$942$		0			0
$943$	68.0399			2.21569
$944$	31.7007	+	28.1526i	1.03177	+	0.916288i
$945$		0			0
$946$	−3.31653	−	1.71009i	−0.107830	−	0.0555999i
$947$	21.7966	+	52.6218i	0.708296	+	1.70998i	0.704216	+	0.709986i	$0.251299\pi$
$947$	21.7966	+	52.6218i	0.708296	+	1.70998i	0.00407986	+	0.999992i	$0.498701\pi$
$948$		0			0
$949$	−40.0353	−	16.5831i	−1.29960	−	0.538312i
$950$	0.402086	−	4.81162i	0.0130454	−	0.156109i
$951$		0			0
$952$	8.95585	−	1.28568i	0.290261	−	0.0416691i
$953$	24.5821	−	24.5821i	0.796293	−	0.796293i	−0.186216	−	0.982509i	$-0.559622\pi$
$953$	24.5821	−	24.5821i	0.796293	−	0.796293i	0.982509	+	0.186216i	$0.0596224\pi$
$954$		0			0
$955$	39.8574	+	16.5095i	1.28976	+	0.534234i
$956$	2.83152	+	3.97753i	0.0915779	+	0.128642i
$957$		0			0
$958$	−10.9157	−	34.1556i	−0.352669	−	1.10352i
$959$	−74.7248			−2.41299
$960$		0			0
$961$	−22.0832			−0.712362
$962$	−23.3865	−	73.1776i	−0.754012	−	2.35934i
$963$		0			0
$964$	−2.16208	−	3.03714i	−0.0696359	−	0.0978198i
$965$	−19.4811	−	8.06932i	−0.627118	−	0.259761i
$966$		0			0
$967$	−19.1878	+	19.1878i	−0.617037	+	0.617037i	−0.944770	−	0.327734i	$-0.893715\pi$
$967$	−19.1878	+	19.1878i	−0.617037	+	0.617037i	0.327734	+	0.944770i	$0.393715\pi$
$968$	−4.20126	−	29.2654i	−0.135034	−	0.940624i
$969$		0			0
$970$	−1.75193	+	20.9648i	−0.0562512	+	0.673138i
$971$	35.5982	+	14.7453i	1.14240	+	0.473198i	0.871979	−	0.489544i	$-0.162837\pi$
$971$	35.5982	+	14.7453i	1.14240	+	0.473198i	0.270422	+	0.962742i	$0.412837\pi$
$972$		0			0
$973$	0.120740	+	0.291492i	0.00387074	+	0.00934479i
$974$	27.5903	+	14.2263i	0.884051	+	0.455841i
$975$		0			0
$976$	−2.77169	−	46.7553i	−0.0887197	−	1.49660i
$977$	10.7488			0.343885			0.171943	−	0.985107i	$-0.444996\pi$
$977$	10.7488			0.343885			0.171943	+	0.985107i	$0.444996\pi$
$978$		0			0
$979$	6.59672	−	2.73245i	0.210832	−	0.0873295i
$980$	−3.40578	−	14.8154i	−0.108794	−	0.473261i
$981$		0			0
$982$	−0.993681	+	11.8910i	−0.0317096	+	0.379458i
$983$	−15.2745	+	15.2745i	−0.487181	+	0.487181i	−0.907416	−	0.420234i	$-0.861948\pi$
$983$	−15.2745	+	15.2745i	−0.487181	+	0.487181i	0.420234	+	0.907416i	$0.361948\pi$
$984$		0			0
$985$	9.04516	+	9.04516i	0.288203	+	0.288203i
$986$	−1.53860	+	1.30128i	−0.0489989	+	0.0414412i
$987$		0			0
$988$	34.3494	+	5.78123i	1.09280	+	0.183925i
$989$	9.65868	+	23.3181i	0.307128	+	0.741473i
$990$		0			0
$991$		−	15.5708i		−	0.494622i	−0.968936	−	0.247311i	$-0.920453\pi$
$991$		−	15.5708i		−	0.494622i	0.968936	−	0.247311i	$-0.0795469\pi$
$992$	0.995670	−	41.2028i	0.0316126	−	1.30819i
$993$		0			0
$994$	−19.8346	−	62.0636i	−0.629117	−	1.96854i
$995$	−25.5836	+	10.5971i	−0.811053	+	0.335949i
$996$		0			0
$997$	−1.71754	+	4.14652i	−0.0543951	+	0.131321i	−0.948741	−	0.316055i	$-0.897642\pi$
$997$	−1.71754	+	4.14652i	−0.0543951	+	0.131321i	0.894346	+	0.447376i	$0.147642\pi$
$998$	2.12313	+	2.51033i	0.0672065	+	0.0794630i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.w.b.107.3	yes	32
3.2	odd	2		288.2.w.a.107.6	yes	32
4.3	odd	2		1152.2.w.a.719.2		32
12.11	even	2		1152.2.w.b.719.7		32
32.3	odd	8		288.2.w.a.35.6	✓	32
32.29	even	8		1152.2.w.b.431.7		32
96.29	odd	8		1152.2.w.a.431.2		32
96.35	even	8	inner	288.2.w.b.35.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.35.6	✓	32	32.3	odd	8
288.2.w.a.107.6	yes	32	3.2	odd	2
288.2.w.b.35.3	yes	32	96.35	even	8	inner
288.2.w.b.107.3	yes	32	1.1	even	1	trivial
1152.2.w.a.431.2		32	96.29	odd	8
1152.2.w.a.719.2		32	4.3	odd	2
1152.2.w.b.431.7		32	32.29	even	8
1152.2.w.b.719.7		32	12.11	even	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.430512 - 1.34709i) q^{2} +(-1.62932 + 1.15988i) q^{4} +(-1.78959 - 0.741273i) q^{5} +(-2.33709 + 2.33709i) q^{7} +(2.26391 + 1.69550i) q^{8} +(-0.228123 + 2.72987i) q^{10} +(0.683332 + 0.283045i) q^{11} +(2.43602 + 5.88107i) q^{13} +(4.15442 + 2.14213i) q^{14} +(1.30936 - 3.77963i) q^{16} -0.967834 q^{17} +(-2.52772 + 1.04702i) q^{19} +(3.77560 - 0.867939i) q^{20} +(0.0871059 - 1.04237i) q^{22} +(-5.00283 + 5.00283i) q^{23} +(-0.882385 - 0.882385i) q^{25} +(6.87361 - 5.81341i) q^{26} +(1.09712 - 6.51861i) q^{28} +(0.563403 + 1.36018i) q^{29} +7.28582i q^{31} +(-5.65520 - 0.136659i) q^{32} +(0.416664 + 1.30376i) q^{34} +(5.91486 - 2.45001i) q^{35} +(3.26572 - 7.88415i) q^{37} +(2.49864 + 2.95432i) q^{38} +(-2.79463 - 4.71243i) q^{40} +(-6.80014 - 6.80014i) q^{41} +(1.36517 - 3.29581i) q^{43} +(-1.44166 + 0.331411i) q^{44} +(8.89306 + 4.58550i) q^{46} +3.69279i q^{47} -3.92399i q^{49} +(-0.808777 + 1.56853i) q^{50} +(-10.7904 - 6.75665i) q^{52} +(-1.85469 + 4.47761i) q^{53} +(-1.01307 - 1.01307i) q^{55} +(-9.25350 + 1.32841i) q^{56} +(1.58973 - 1.34453i) q^{58} +(-4.05615 + 9.79242i) q^{59} +(10.8180 - 4.48097i) q^{61} +(9.81468 - 3.13663i) q^{62} +(2.25054 + 7.67692i) q^{64} -12.3305i q^{65} +(1.49290 + 3.60418i) q^{67} +(1.57691 - 1.12257i) q^{68} +(-5.84681 - 6.91310i) q^{70} +(-9.85675 - 9.85675i) q^{71} +(-4.81362 + 4.81362i) q^{73} +(-12.0266 - 1.00501i) q^{74} +(2.90405 - 4.63778i) q^{76} +(-2.25851 + 0.935506i) q^{77} -11.0160 q^{79} +(-5.14495 + 5.79339i) q^{80} +(-6.23288 + 12.0880i) q^{82} +(1.15064 + 2.77789i) q^{83} +(1.73203 + 0.717429i) q^{85} +(-5.02749 - 0.420125i) q^{86} +(1.06709 + 1.79938i) q^{88} +(6.82624 - 6.82624i) q^{89} +(-19.4378 - 8.05140i) q^{91} +(2.34853 - 13.9539i) q^{92} +(4.97453 - 1.58979i) q^{94} +5.29971 q^{95} +7.67976 q^{97} +(-5.28598 + 1.68932i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 4 q^{8} + 8 q^{10} + 8 q^{11} - 12 q^{14} + 8 q^{16} - 32 q^{20} + 16 q^{22} + 36 q^{26} + 16 q^{29} + 24 q^{32} - 24 q^{35} - 32 q^{38} - 32 q^{40} - 8 q^{44} - 32 q^{46} - 8 q^{50} - 56 q^{52}+ \cdots + 44 q^{98}+O(q^{100}) \) 32 * q + 4 * q^2 + 4 * q^8 + 8 * q^10 + 8 * q^11 - 12 * q^14 + 8 * q^16 - 32 * q^20 + 16 * q^22 + 36 * q^26 + 16 * q^29 + 24 * q^32 - 24 * q^35 - 32 * q^38 - 32 * q^40 - 8 * q^44 - 32 * q^46 - 8 * q^50 - 56 * q^52 + 16 * q^53 - 32 * q^55 - 40 * q^56 - 32 * q^58 - 32 * q^59 + 32 * q^61 + 68 * q^62 - 48 * q^64 - 16 * q^67 + 72 * q^68 - 48 * q^70 - 16 * q^71 - 60 * q^74 - 8 * q^76 + 16 * q^77 - 32 * q^79 - 96 * q^80 + 40 * q^82 + 40 * q^83 + 40 * q^86 + 40 * q^88 - 48 * q^91 + 16 * q^92 + 72 * q^94 + 80 * q^95 + 44 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more