LMFDB - Embedded newform 952.2.cw.a.129.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [952,2,Mod(73,952)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("952.73"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(952, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([0, 0, 8, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 952 = 2^{3} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	952.cw (of order $48$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [288,0,0,0,0,0,0,0,0,0,0,0,0,0,-32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(15)] == traces)

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

Self dual:	no
Analytic conductor:	$7.60175827243$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			129.10
Character	$\chi$	$=$	952.129
Dual form			952.2.cw.a.369.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0778436 + 0.157851i) q^{3} +(0.896871 - 0.786535i) q^{5} +(2.60235 - 0.477236i) q^{7} +(1.80743 - 2.35548i) q^{9} +(2.98378 - 0.195567i) q^{11} +(-2.81453 - 2.81453i) q^{13} +(0.193971 + 0.0803454i) q^{15} +(-3.93805 - 1.22136i) q^{17} +(-0.447542 - 3.39942i) q^{19} +(0.277909 + 0.373635i) q^{21} +(-3.72557 - 1.83725i) q^{23} +(-0.466890 + 3.54638i) q^{25} +(1.03037 + 0.204954i) q^{27} +(1.78975 + 8.99768i) q^{29} +(3.35258 - 1.65331i) q^{31} +(0.263138 + 0.455769i) q^{33} +(1.95861 - 2.47486i) q^{35} +(-0.119777 + 1.82744i) q^{37} +(0.225183 - 0.663369i) q^{39} +(0.438257 - 2.20327i) q^{41} +(-2.40666 - 5.81019i) q^{43} +(-0.231642 - 3.53417i) q^{45} +(2.22621 - 8.30833i) q^{47} +(6.54449 - 2.48388i) q^{49} +(-0.113758 - 0.716702i) q^{51} +(-1.15213 - 1.50148i) q^{53} +(2.52224 - 2.52224i) q^{55} +(0.501764 - 0.335268i) q^{57} +(5.13666 + 0.676254i) q^{59} +(2.08553 + 6.14378i) q^{61} +(3.57944 - 6.99237i) q^{63} +(-4.73799 - 0.310544i) q^{65} +(2.89065 + 1.66892i) q^{67} -0.731103i q^{69} +(8.77190 + 5.86120i) q^{71} +(-4.28045 - 1.45302i) q^{73} +(-0.596145 + 0.202364i) q^{75} +(7.67151 - 1.93290i) q^{77} +(-0.0797685 + 0.161754i) q^{79} +(-2.25746 - 8.42497i) q^{81} +(-3.15420 + 7.61490i) q^{83} +(-4.49257 + 2.00201i) q^{85} +(-1.28097 + 0.982925i) q^{87} +(7.42462 + 1.98942i) q^{89} +(-8.66759 - 5.98120i) q^{91} +(0.521954 + 0.400509i) q^{93} +(-3.07515 - 2.69683i) q^{95} +(2.50566 - 0.498408i) q^{97} +(4.93230 - 7.38171i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 32 q^{15} - 48 q^{21} + 32 q^{29} + 72 q^{31} + 32 q^{35} + 48 q^{37} + 32 q^{39} - 32 q^{43} - 24 q^{47} + 48 q^{49} + 16 q^{53} + 128 q^{57} - 72 q^{61} + 184 q^{63} - 32 q^{65} - 80 q^{71} - 96 q^{73}+ \cdots + 64 q^{99}+O(q^{100}) $ 288 * q - 32 * q^15 - 48 * q^21 + 32 * q^29 + 72 * q^31 + 32 * q^35 + 48 * q^37 + 32 * q^39 - 32 * q^43 - 24 * q^47 + 48 * q^49 + 16 * q^53 + 128 * q^57 - 72 * q^61 + 184 * q^63 - 32 * q^65 - 80 * q^71 - 96 * q^73 - 216 * q^75 + 56 * q^77 - 32 * q^79 - 64 * q^81 + 160 * q^85 - 144 * q^87 + 144 * q^89 - 32 * q^93 - 64 * q^95 + 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/952\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$477$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{3}{16}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.0778436	+	0.157851i	0.0449430	+	0.0911354i	0.918186	−	0.396150i	$-0.129654\pi$
$3$	0.0778436	+	0.157851i	0.0449430	+	0.0911354i	−0.873243	+	0.487285i	$0.837987\pi$
$4$		0			0
$5$	0.896871	−	0.786535i	0.401093	−	0.351749i	−0.434910	−	0.900474i	$-0.643220\pi$
$5$	0.896871	−	0.786535i	0.401093	−	0.351749i	0.836003	+	0.548725i	$0.184887\pi$
$6$		0			0
$7$	2.60235	−	0.477236i	0.983597	−	0.180378i
$7$	2.60235	−	0.477236i	0.983597	−	0.180378i
$8$		0			0
$9$	1.80743	−	2.35548i	0.602476	−	0.785162i
$10$		0			0
$11$	2.98378	−	0.195567i	0.899642	−	0.0589657i	0.391440	−	0.920204i	$-0.371977\pi$
$11$	2.98378	−	0.195567i	0.899642	−	0.0589657i	0.508202	+	0.861238i	$0.330310\pi$
$12$		0			0
$13$	−2.81453	−	2.81453i	−0.780609	−	0.780609i	0.199324	−	0.979934i	$-0.436125\pi$
$13$	−2.81453	−	2.81453i	−0.780609	−	0.780609i	−0.979934	+	0.199324i	$0.936125\pi$
$14$		0			0
$15$	0.193971	+	0.0803454i	0.0500831	+	0.0207451i
$16$		0			0
$17$	−3.93805	−	1.22136i	−0.955118	−	0.296224i
$17$	−3.93805	−	1.22136i	−0.955118	−	0.296224i
$18$		0			0
$19$	−0.447542	−	3.39942i	−0.102673	−	0.779880i	−0.962879	−	0.269933i	$-0.912998\pi$
$19$	−0.447542	−	3.39942i	−0.102673	−	0.779880i	0.860206	−	0.509947i	$-0.170335\pi$
$20$		0			0
$21$	0.277909	+	0.373635i	0.0606447	+	0.0815338i
$22$		0			0
$23$	−3.72557	−	1.83725i	−0.776834	−	0.383092i	0.0102423	−	0.999948i	$-0.496740\pi$
$23$	−3.72557	−	1.83725i	−0.776834	−	0.383092i	−0.787077	+	0.616855i	$0.788406\pi$
$24$		0			0
$25$	−0.466890	+	3.54638i	−0.0933781	+	0.709277i
$26$		0			0
$27$	1.03037	+	0.204954i	0.198295	+	0.0394434i
$28$		0			0
$29$	1.78975	+	8.99768i	0.332348	+	1.67083i	0.680007	+	0.733206i	$0.261977\pi$
$29$	1.78975	+	8.99768i	0.332348	+	1.67083i	−0.347659	+	0.937621i	$0.613023\pi$
$30$		0			0
$31$	3.35258	−	1.65331i	0.602141	−	0.296943i	−0.115553	−	0.993301i	$-0.536864\pi$
$31$	3.35258	−	1.65331i	0.602141	−	0.296943i	0.717695	+	0.696358i	$0.245197\pi$
$32$		0			0
$33$	0.263138	+	0.455769i	0.0458065	+	0.0793392i
$34$		0			0
$35$	1.95861	−	2.47486i	0.331066	−	0.418328i
$36$		0			0
$37$	−0.119777	+	1.82744i	−0.0196912	+	0.300430i	0.976642	+	0.214873i	$0.0689336\pi$
$37$	−0.119777	+	1.82744i	−0.0196912	+	0.300430i	−0.996333	+	0.0855569i	$0.972733\pi$
$38$		0			0
$39$	0.225183	−	0.663369i	0.0360582	−	0.106224i
$40$		0			0
$41$	0.438257	−	2.20327i	0.0684443	−	0.344093i	−0.931355	−	0.364112i	$-0.881373\pi$
$41$	0.438257	−	2.20327i	0.0684443	−	0.344093i	0.999800	+	0.0200189i	$0.00637264\pi$
$42$		0			0
$43$	−2.40666	−	5.81019i	−0.367012	−	0.886046i	−0.994237	−	0.107207i	$-0.965809\pi$
$43$	−2.40666	−	5.81019i	−0.367012	−	0.886046i	0.627224	−	0.778839i	$-0.284191\pi$
$44$		0			0
$45$	−0.231642	−	3.53417i	−0.0345311	−	0.526843i
$46$		0			0
$47$	2.22621	−	8.30833i	0.324726	−	1.21190i	−0.589860	−	0.807505i	$-0.700817\pi$
$47$	2.22621	−	8.30833i	0.324726	−	1.21190i	0.914587	−	0.404390i	$-0.132516\pi$
$48$		0			0
$49$	6.54449	−	2.48388i	0.934927	−	0.354839i
$50$		0			0
$51$	−0.113758	−	0.716702i	−0.0159294	−	0.100358i
$52$		0			0
$53$	−1.15213	−	1.50148i	−0.158257	−	0.206244i	0.707494	−	0.706719i	$-0.249825\pi$
$53$	−1.15213	−	1.50148i	−0.158257	−	0.206244i	−0.865751	+	0.500475i	$0.833159\pi$
$54$		0			0
$55$	2.52224	−	2.52224i	0.340099	−	0.340099i
$56$		0			0
$57$	0.501764	−	0.335268i	0.0664602	−	0.0444073i
$58$		0			0
$59$	5.13666	+	0.676254i	0.668736	+	0.0880408i	0.457247	−	0.889340i	$-0.348835\pi$
$59$	5.13666	+	0.676254i	0.668736	+	0.0880408i	0.211489	+	0.977380i	$0.432169\pi$
$60$		0			0
$61$	2.08553	+	6.14378i	0.267025	+	0.786630i	0.994895	+	0.100915i	$0.0321771\pi$
$61$	2.08553	+	6.14378i	0.267025	+	0.786630i	−0.727870	+	0.685715i	$0.759490\pi$
$62$		0			0
$63$	3.57944	−	6.99237i	0.450967	−	0.880956i
$64$		0			0
$65$	−4.73799	−	0.310544i	−0.587675	−	0.0385183i
$66$		0			0
$67$	2.89065	+	1.66892i	0.353149	+	0.203891i	0.666071	−	0.745888i	$-0.267975\pi$
$67$	2.89065	+	1.66892i	0.353149	+	0.203891i	−0.312922	+	0.949779i	$0.601308\pi$
$68$		0			0
$69$		−	0.731103i		−	0.0880144i
$70$		0			0
$71$	8.77190	+	5.86120i	1.04103	+	0.695596i	0.953754	−	0.300588i	$-0.0971828\pi$
$71$	8.77190	+	5.86120i	1.04103	+	0.695596i	0.0872790	+	0.996184i	$0.472183\pi$
$72$		0			0
$73$	−4.28045	−	1.45302i	−0.500989	−	0.170063i	0.0594944	−	0.998229i	$-0.481051\pi$
$73$	−4.28045	−	1.45302i	−0.500989	−	0.170063i	−0.560483	+	0.828166i	$0.689385\pi$
$74$		0			0
$75$	−0.596145	+	0.202364i	−0.0688369	+	0.0233670i
$76$		0			0
$77$	7.67151	−	1.93290i	0.874249	−	0.220274i
$78$		0			0
$79$	−0.0797685	+	0.161754i	−0.00897465	+	0.0181988i	−0.901314	−	0.433167i	$-0.857396\pi$
$79$	−0.0797685	+	0.161754i	−0.00897465	+	0.0181988i	0.892339	+	0.451365i	$0.149063\pi$
$80$		0			0
$81$	−2.25746	−	8.42497i	−0.250829	−	0.936108i
$82$		0			0
$83$	−3.15420	+	7.61490i	−0.346218	+	0.835844i	0.650842	+	0.759214i	$0.274416\pi$
$83$	−3.15420	+	7.61490i	−0.346218	+	0.835844i	−0.997060	+	0.0766307i	$0.975584\pi$
$84$		0			0
$85$	−4.49257	+	2.00201i	−0.487288	+	0.217149i
$86$		0			0
$87$	−1.28097	+	0.982925i	−0.137335	+	0.105381i
$88$		0			0
$89$	7.42462	+	1.98942i	0.787008	+	0.210878i	0.629872	−	0.776699i	$-0.283107\pi$
$89$	7.42462	+	1.98942i	0.787008	+	0.210878i	0.157136	+	0.987577i	$0.449774\pi$
$90$		0			0
$91$	−8.66759	−	5.98120i	−0.908610	−	0.627000i
$92$		0			0
$93$	0.521954	+	0.400509i	0.0541241	+	0.0415309i
$94$		0			0
$95$	−3.07515	−	2.69683i	−0.315504	−	0.276689i
$96$		0			0
$97$	2.50566	−	0.498408i	0.254412	−	0.0506056i	−0.0662367	−	0.997804i	$-0.521099\pi$
$97$	2.50566	−	0.498408i	0.254412	−	0.0506056i	0.320648	+	0.947198i	$0.396099\pi$
$98$		0			0
$99$	4.93230	−	7.38171i	0.495715	−	0.741890i
$100$		0			0
$101$	−4.65890	+	8.06944i	−0.463577	+	0.802940i	−0.999136	−	0.0415584i	$-0.986768\pi$
$101$	−4.65890	+	8.06944i	−0.463577	+	0.802940i	0.535559	+	0.844498i	$0.320101\pi$
$102$		0			0
$103$	4.43163	−	2.55860i	0.436661	−	0.252106i	−0.265519	−	0.964106i	$-0.585543\pi$
$103$	4.43163	−	2.55860i	0.436661	−	0.252106i	0.702180	+	0.711999i	$0.252210\pi$
$104$		0			0
$105$	0.543125	+	0.116517i	0.0530036	+	0.0113709i
$106$		0			0
$107$	2.39375	+	2.72955i	0.231412	+	0.263875i	0.855879	−	0.517176i	$-0.173017\pi$
$107$	2.39375	+	2.72955i	0.231412	+	0.263875i	−0.624466	+	0.781052i	$0.714684\pi$
$108$		0			0
$109$	−9.92087	+	11.3126i	−0.950247	+	1.08355i	0.0461662	+	0.998934i	$0.485300\pi$
$109$	−9.92087	+	11.3126i	−0.950247	+	1.08355i	−0.996414	+	0.0846157i	$0.973034\pi$
$110$		0			0
$111$	−0.297788	+	0.123348i	−0.0282647	+	0.0117076i
$112$		0			0
$113$	0.819911	+	1.22708i	0.0771308	+	0.115434i	0.868029	−	0.496513i	$-0.165386\pi$
$113$	0.819911	+	1.22708i	0.0771308	+	0.115434i	−0.790899	+	0.611947i	$0.790386\pi$
$114$		0			0
$115$	−4.78641	+	1.28251i	−0.446335	+	0.119595i
$116$		0			0
$117$	−11.7166	+	1.54252i	−1.08320	+	0.142606i
$118$		0			0
$119$	−10.8311	−	1.29904i	−0.992884	−	0.119083i
$120$		0			0
$121$	−2.04122	+	0.268732i	−0.185566	+	0.0244302i
$122$		0			0
$123$	0.381904	−	0.102331i	0.0344351	−	0.00922686i
$124$		0			0
$125$	5.68432	+	8.50718i	0.508421	+	0.760905i
$126$		0			0
$127$	14.6559	−	6.07068i	1.30050	−	0.538686i	0.378404	−	0.925641i	$-0.376473\pi$
$127$	14.6559	−	6.07068i	1.30050	−	0.538686i	0.922099	+	0.386955i	$0.126473\pi$
$128$		0			0
$129$	0.729803	−	0.832180i	0.0642555	−	0.0732694i
$130$		0			0
$131$	5.71818	+	6.52033i	0.499600	+	0.569684i	0.945593	−	0.325352i	$-0.105483\pi$
$131$	5.71818	+	6.52033i	0.499600	+	0.569684i	−0.445993	+	0.895036i	$0.647149\pi$
$132$		0			0
$133$	−2.78699	−	8.63291i	−0.241663	−	0.748568i
$134$		0			0
$135$	1.08531	−	0.626606i	0.0934090	−	0.0539297i
$136$		0			0
$137$	−6.00397	+	10.3992i	−0.512954	+	0.888463i	0.486933	+	0.873439i	$0.338116\pi$
$137$	−6.00397	+	10.3992i	−0.512954	+	0.888463i	−0.999887	+	0.0150233i	$0.995218\pi$
$138$		0			0
$139$	−0.238551	+	0.357017i	−0.0202336	+	0.0302818i	−0.841449	−	0.540337i	$-0.818297\pi$
$139$	−0.238551	+	0.357017i	−0.0202336	+	0.0302818i	0.821215	+	0.570619i	$0.193297\pi$
$140$		0			0
$141$	1.48478	−	0.295340i	0.125041	−	0.0248721i
$142$		0			0
$143$	−8.94834	−	7.84749i	−0.748298	−	0.656240i
$144$		0			0
$145$	8.68216	+	6.66206i	0.721014	+	0.553254i
$146$		0			0
$147$	0.901529	+	0.839702i	0.0743569	+	0.0692574i
$148$		0			0
$149$	18.6703	+	5.00270i	1.52953	+	0.409837i	0.922867	−	0.385119i	$-0.125840\pi$
$149$	18.6703	+	5.00270i	1.52953	+	0.409837i	0.606667	+	0.794956i	$0.292506\pi$
$150$		0			0
$151$	−15.3477	+	11.7767i	−1.24898	+	0.958375i	−0.999949	−	0.0101210i	$-0.996778\pi$
$151$	−15.3477	+	11.7767i	−1.24898	+	0.958375i	−0.249030	+	0.968496i	$0.580112\pi$
$152$		0			0
$153$	−9.99465	+	7.06850i	−0.808020	+	0.571454i
$154$		0			0
$155$	1.70645	−	4.11973i	0.137065	−	0.330904i
$156$		0			0
$157$	−3.86679	−	14.4311i	−0.308604	−	1.15172i	−0.929799	−	0.368069i	$-0.880019\pi$
$157$	−3.86679	−	14.4311i	−0.308604	−	1.15172i	0.621195	−	0.783656i	$-0.286648\pi$
$158$		0			0
$159$	0.147325	−	0.298745i	0.0116836	−	0.0236920i
$160$		0			0
$161$	−10.5720	−	3.00319i	−0.833194	−	0.236684i
$162$		0			0
$163$	5.74072	−	1.94871i	0.449648	−	0.152635i	−0.0874245	−	0.996171i	$-0.527864\pi$
$163$	5.74072	−	1.94871i	0.449648	−	0.152635i	0.537072	+	0.843536i	$0.319530\pi$
$164$		0			0
$165$	0.594479	+	0.201798i	0.0462801	+	0.0157100i
$166$		0			0
$167$	13.8912	+	9.28180i	1.07493	+	0.718247i	0.961363	−	0.275283i	$-0.0887714\pi$
$167$	13.8912	+	9.28180i	1.07493	+	0.718247i	0.113570	+	0.993530i	$0.463771\pi$
$168$		0			0
$169$			2.84312i			0.218701i
$170$		0			0
$171$	−8.81618	−	5.09002i	−0.674190	−	0.389244i
$172$		0			0
$173$	−7.49277	−	0.491102i	−0.569665	−	0.0373378i	−0.222150	−	0.975012i	$-0.571308\pi$
$173$	−7.49277	−	0.491102i	−0.569665	−	0.0373378i	−0.347514	+	0.937675i	$0.612974\pi$
$174$		0			0
$175$	0.477450	+	9.45176i	0.0360918	+	0.714486i
$176$		0			0
$177$	0.293109	+	0.863470i	0.0220314	+	0.0649024i
$178$		0			0
$179$	−16.7252	−	2.20191i	−1.25010	−	0.164579i	−0.523731	−	0.851884i	$-0.675460\pi$
$179$	−16.7252	−	2.20191i	−1.25010	−	0.164579i	−0.726369	+	0.687305i	$0.758794\pi$
$180$		0			0
$181$	−10.0083	+	6.68736i	−0.743914	+	0.497068i	−0.868837	−	0.495099i	$-0.835132\pi$
$181$	−10.0083	+	6.68736i	−0.743914	+	0.497068i	0.124922	+	0.992167i	$0.460132\pi$
$182$		0			0
$183$	−0.807457	+	0.807457i	−0.0596890	+	0.0596890i
$184$		0			0
$185$	1.32992	+	1.73319i	0.0977778	+	0.127427i
$186$		0			0
$187$	−11.9891	−	2.87412i	−0.876732	−	0.210177i
$188$		0			0
$189$	2.77920	+	0.0416311i	0.202157	+	0.00302822i
$190$		0			0
$191$	−2.90196	+	10.8303i	−0.209979	+	0.783651i	0.777895	+	0.628394i	$0.216287\pi$
$191$	−2.90196	+	10.8303i	−0.209979	+	0.783651i	−0.987874	+	0.155257i	$0.950379\pi$
$192$		0			0
$193$	−0.919813	−	14.0336i	−0.0662096	−	1.01016i	−0.893695	−	0.448676i	$-0.851896\pi$
$193$	−0.919813	−	14.0336i	−0.0662096	−	1.01016i	0.827485	−	0.561488i	$-0.189771\pi$
$194$		0			0
$195$	−0.319802	−	0.772071i	−0.0229015	−	0.0552892i
$196$		0			0
$197$	−3.72449	+	18.7243i	−0.265359	+	1.33405i	0.586361	+	0.810050i	$0.300560\pi$
$197$	−3.72449	+	18.7243i	−0.265359	+	1.33405i	−0.851719	+	0.523998i	$0.824440\pi$
$198$		0			0
$199$	2.52965	−	7.45210i	0.179322	−	0.528265i	−0.819685	−	0.572814i	$-0.805852\pi$
$199$	2.52965	−	7.45210i	0.179322	−	0.528265i	0.999007	+	0.0445488i	$0.0141850\pi$
$200$		0			0
$201$	−0.0384221	+	0.586207i	−0.00271008	+	0.0413479i
$202$		0			0
$203$	8.95158	+	22.5610i	0.628278	+	1.58347i
$204$		0			0
$205$	−1.33989	−	2.32075i	−0.0935818	−	0.162088i
$206$		0			0
$207$	−11.0613	+	5.45483i	−0.768813	+	0.379137i
$208$		0			0
$209$	−2.00018	−	10.0556i	−0.138355	−	0.695559i
$210$		0			0
$211$	7.71545	+	1.53470i	0.531154	+	0.105653i	0.453379	−	0.891318i	$-0.350218\pi$
$211$	7.71545	+	1.53470i	0.531154	+	0.105653i	0.0777749	+	0.996971i	$0.475218\pi$
$212$		0			0
$213$	−0.242361	+	1.84091i	−0.0166063	+	0.126137i
$214$		0			0
$215$	−6.72838	−	3.31807i	−0.458872	−	0.226291i
$216$		0			0
$217$	7.93558	−	5.90247i	0.538702	−	0.400686i
$218$		0			0
$219$	−0.103845	−	0.788782i	−0.00701720	−	0.0533009i
$220$		0			0
$221$	7.64620	+	14.5213i	0.514339	+	0.976810i
$222$		0			0
$223$	−5.52077	−	2.28678i	−0.369698	−	0.153134i	0.190097	−	0.981765i	$-0.439120\pi$
$223$	−5.52077	−	2.28678i	−0.369698	−	0.153134i	−0.559794	+	0.828632i	$0.689120\pi$
$224$		0			0
$225$	7.50958	+	7.50958i	0.500639	+	0.500639i
$226$		0			0
$227$	12.9602	−	0.849459i	0.860202	−	0.0563806i	0.371085	−	0.928599i	$-0.378986\pi$
$227$	12.9602	−	0.849459i	0.860202	−	0.0563806i	0.489117	+	0.872218i	$0.337319\pi$
$228$		0			0
$229$	−9.84614	+	12.8317i	−0.650651	+	0.847945i	−0.995890	−	0.0905696i	$-0.971131\pi$
$229$	−9.84614	+	12.8317i	−0.650651	+	0.847945i	0.345239	+	0.938515i	$0.387798\pi$
$230$		0			0
$231$	0.902288	+	1.06049i	0.0593662	+	0.0697753i
$232$		0			0
$233$	−15.3855	+	13.4928i	−1.00794	+	0.883940i	−0.993255	−	0.115952i	$-0.963008\pi$
$233$	−15.3855	+	13.4928i	−1.00794	+	0.883940i	−0.0146855	+	0.999892i	$0.504675\pi$
$234$		0			0
$235$	−4.53817	−	9.20250i	−0.296038	−	0.600305i
$236$		0			0
$237$	−0.0317426			−0.00206190
$238$		0			0
$239$	4.24149			0.274359			0.137180	−	0.990546i	$-0.456196\pi$
$239$	4.24149			0.274359			0.137180	+	0.990546i	$0.456196\pi$
$240$		0			0
$241$	−11.5029	−	23.3256i	−0.740967	−	1.50253i	−0.860361	−	0.509685i	$-0.829762\pi$
$241$	−11.5029	−	23.3256i	−0.740967	−	1.50253i	0.119394	−	0.992847i	$-0.461905\pi$
$242$		0			0
$243$	3.52372	−	3.09022i	0.226047	−	0.198237i
$244$		0			0
$245$	3.91591	−	7.37519i	0.250178	−	0.471183i
$246$		0			0
$247$	−8.30813	+	10.8274i	−0.528634	+	0.688929i
$248$		0			0
$249$	−1.44756	+	0.0948778i	−0.0917351	+	0.00601264i
$250$		0			0
$251$	−1.51134	−	1.51134i	−0.0953947	−	0.0953947i	0.657799	−	0.753194i	$-0.271488\pi$
$251$	−1.51134	−	1.51134i	−0.0953947	−	0.0953947i	−0.753194	+	0.657799i	$0.771488\pi$
$252$		0			0
$253$	−11.4756	−	4.75333i	−0.721462	−	0.298839i
$254$		0			0
$255$	−0.665737	−	0.553314i	−0.0416901	−	0.0346499i
$256$		0			0
$257$	−2.74018	−	20.8138i	−0.170928	−	1.29833i	−0.834830	−	0.550508i	$-0.814434\pi$
$257$	−2.74018	−	20.8138i	−0.170928	−	1.29833i	0.663902	−	0.747820i	$-0.268899\pi$
$258$		0			0
$259$	0.560420	+	4.81281i	0.0348228	+	0.299054i
$260$		0			0
$261$	24.4287	+	12.0469i	1.51210	+	0.745685i
$262$		0			0
$263$	−2.09267	+	15.8954i	−0.129040	+	0.980153i	0.797332	+	0.603541i	$0.206244\pi$
$263$	−2.09267	+	15.8954i	−0.129040	+	0.980153i	−0.926371	+	0.376612i	$0.877089\pi$
$264$		0			0
$265$	−2.21428	−	0.440447i	−0.136022	−	0.0270564i
$266$		0			0
$267$	0.263926	+	1.32685i	0.0161520	+	0.0812018i
$268$		0			0
$269$	−5.02888	+	2.47997i	−0.306616	+	0.151206i	−0.589087	−	0.808069i	$-0.700513\pi$
$269$	−5.02888	+	2.47997i	−0.306616	+	0.151206i	0.282471	+	0.959276i	$0.408846\pi$
$270$		0			0
$271$	5.72726	+	9.91990i	0.347906	+	0.602591i	0.985877	−	0.167469i	$-0.0535594\pi$
$271$	5.72726	+	9.91990i	0.347906	+	0.602591i	−0.637971	+	0.770060i	$0.720226\pi$
$272$		0			0
$273$	0.269423	−	1.83379i	0.0163062	−	0.110986i
$274$		0			0
$275$	−0.699540	+	10.6729i	−0.0421839	+	0.643601i
$276$		0			0
$277$	−7.32827	+	21.5884i	−0.440313	+	1.29712i	0.469805	+	0.882770i	$0.344324\pi$
$277$	−7.32827	+	21.5884i	−0.440313	+	1.29712i	−0.910118	+	0.414350i	$0.864009\pi$
$278$		0			0
$279$	2.16520	−	10.8852i	0.129627	−	0.651679i
$280$		0			0
$281$	−2.42106	−	5.84495i	−0.144428	−	0.348681i	0.835067	−	0.550148i	$-0.185429\pi$
$281$	−2.42106	−	5.84495i	−0.144428	−	0.348681i	−0.979495	+	0.201468i	$0.935429\pi$
$282$		0			0
$283$	−1.81143	−	27.6371i	−0.107678	−	1.64285i	−0.620391	−	0.784293i	$-0.713026\pi$
$283$	−1.81143	−	27.6371i	−0.107678	−	1.64285i	0.512713	−	0.858560i	$-0.328641\pi$
$284$		0			0
$285$	0.186318	−	0.695347i	0.0110365	−	0.0411888i
$286$		0			0
$287$	0.0890208	−	5.94284i	0.00525473	−	0.350795i
$288$		0			0
$289$	14.0165	+	9.61960i	0.824502	+	0.565859i
$290$		0			0
$291$	0.273724	+	0.356724i	0.0160460	+	0.0209115i
$292$		0			0
$293$	−1.21448	+	1.21448i	−0.0709506	+	0.0709506i	−0.741692	−	0.670741i	$-0.765976\pi$
$293$	−1.21448	+	1.21448i	−0.0709506	+	0.0709506i	0.670741	+	0.741692i	$0.265976\pi$
$294$		0			0
$295$	5.13882	−	3.43365i	0.299194	−	0.199915i
$296$		0			0
$297$	3.11448	+	0.410029i	0.180721	+	0.0237923i
$298$		0			0
$299$	5.31473	+	15.6567i	0.307359	+	0.905449i
$300$		0			0
$301$	−9.03582	−	13.9716i	−0.520816	−	0.805311i
$302$		0			0
$303$	−1.63644	−	0.107258i	−0.0940108	−	0.00616179i
$304$		0			0
$305$	6.70275	+	3.86983i	0.383798	+	0.221586i
$306$		0			0
$307$			30.5008i			1.74077i	0.492371	+	0.870386i	$0.336130\pi$
$307$			30.5008i			1.74077i	−0.492371	+	0.870386i	$0.663870\pi$
$308$		0			0
$309$	0.748851	+	0.500367i	0.0426007	+	0.0284649i
$310$		0			0
$311$	−32.2018	−	10.9311i	−1.82600	−	0.619843i	−0.998275	−	0.0587065i	$-0.981302\pi$
$311$	−32.2018	−	10.9311i	−1.82600	−	0.619843i	−0.827723	−	0.561136i	$-0.810364\pi$
$312$		0			0
$313$	17.2605	−	5.85914i	0.975619	−	0.331178i	0.212303	−	0.977204i	$-0.431903\pi$
$313$	17.2605	−	5.85914i	0.975619	−	0.331178i	0.763316	+	0.646026i	$0.223570\pi$
$314$		0			0
$315$	−2.28945	−	9.08661i	−0.128996	−	0.511973i
$316$		0			0
$317$	−9.66850	+	19.6058i	−0.543037	+	1.10117i	0.436462	+	0.899723i	$0.356231\pi$
$317$	−9.66850	+	19.6058i	−0.543037	+	1.10117i	−0.979499	+	0.201448i	$0.935435\pi$
$318$		0			0
$319$	7.09986	+	26.4970i	0.397516	+	1.48355i
$320$		0			0
$321$	−0.244524	+	0.590334i	−0.0136480	+	0.0329492i
$322$		0			0
$323$	−2.38948	+	13.9337i	−0.132954	+	0.775292i
$324$		0			0
$325$	11.2955	−	8.66732i	0.626560	−	0.480776i
$326$		0			0
$327$	−2.55798	−	0.685409i	−0.141457	−	0.0379032i
$328$		0			0
$329$	1.82835	−	22.6837i	0.100800	−	1.25059i
$330$		0			0
$331$	−13.6029	−	10.4379i	−0.747682	−	0.573717i	0.163097	−	0.986610i	$-0.447852\pi$
$331$	−13.6029	−	10.4379i	−0.747682	−	0.573717i	−0.910779	+	0.412893i	$0.864518\pi$
$332$		0			0
$333$	4.08802	+	3.58510i	0.224022	+	0.196462i
$334$		0			0
$335$	3.90520	−	0.776793i	0.213364	−	0.0424408i
$336$		0			0
$337$	7.40566	−	11.0834i	0.403412	−	0.603749i	−0.573028	−	0.819536i	$-0.694232\pi$
$337$	7.40566	−	11.0834i	0.403412	−	0.603749i	0.976441	+	0.215786i	$0.0692315\pi$
$338$		0			0
$339$	−0.129872	+	0.224945i	−0.00705367	+	0.0122173i
$340$		0			0
$341$	9.68001	−	5.58876i	0.524202	−	0.302648i
$342$		0			0
$343$	15.8457	−	9.58719i	0.855587	−	0.517660i
$344$		0			0
$345$	−0.575038	−	0.655705i	−0.0309590	−	0.0353020i
$346$		0			0
$347$	10.9882	−	12.5296i	0.589876	−	0.672625i	−0.377488	−	0.926014i	$-0.623212\pi$
$347$	10.9882	−	12.5296i	0.589876	−	0.672625i	0.967364	+	0.253389i	$0.0815454\pi$
$348$		0			0
$349$	−21.0979	+	8.73904i	−1.12935	+	0.467790i	−0.867558	−	0.497336i	$-0.834312\pi$
$349$	−21.0979	+	8.73904i	−1.12935	+	0.467790i	−0.261787	+	0.965126i	$0.584312\pi$
$350$		0			0
$351$	−2.32316	−	3.47686i	−0.124001	−	0.185581i
$352$		0			0
$353$	4.13145	−	1.10702i	0.219895	−	0.0589207i	−0.147189	−	0.989108i	$-0.547023\pi$
$353$	4.13145	−	1.10702i	0.219895	−	0.0589207i	0.367084	+	0.930188i	$0.380356\pi$
$354$		0			0
$355$	12.4773	−	1.64267i	0.662226	−	0.0871837i
$356$		0			0
$357$	−0.638076	−	1.81082i	−0.0337706	−	0.0958388i
$358$		0			0
$359$	−13.6065	+	1.79132i	−0.718121	+	0.0945425i	−0.480726	−	0.876871i	$-0.659627\pi$
$359$	−13.6065	+	1.79132i	−0.718121	+	0.0945425i	−0.237395	+	0.971413i	$0.576294\pi$
$360$		0			0
$361$	6.99684	−	1.87480i	0.368255	−	0.0986736i
$362$		0			0
$363$	−0.201316	−	0.301290i	−0.0105663	−	0.0158136i
$364$		0			0
$365$	−4.98186	+	2.06355i	−0.260762	+	0.108011i
$366$		0			0
$367$	−21.3568	+	24.3527i	−1.11481	+	1.27120i	−0.155818	+	0.987786i	$0.549801\pi$
$367$	−21.3568	+	24.3527i	−1.11481	+	1.27120i	−0.958997	+	0.283417i	$0.908532\pi$
$368$		0			0
$369$	−4.39765	−	5.01456i	−0.228932	−	0.261047i
$370$		0			0
$371$	−3.71480	−	3.35755i	−0.192863	−	0.174315i
$372$		0			0
$373$	11.8744	−	6.85572i	0.614836	−	0.354975i	−0.160020	−	0.987114i	$-0.551156\pi$
$373$	11.8744	−	6.85572i	0.614836	−	0.354975i	0.774856	+	0.632138i	$0.217823\pi$
$374$		0			0
$375$	−0.900381	+	1.55951i	−0.0464955	+	0.0805325i
$376$		0			0
$377$	20.2869	−	30.3615i	1.04483	−	1.56370i
$378$		0			0
$379$	9.74412	−	1.93823i	0.500522	−	0.0995600i	0.0616285	−	0.998099i	$-0.480371\pi$
$379$	9.74412	−	1.93823i	0.500522	−	0.0995600i	0.438893	+	0.898539i	$0.355371\pi$
$380$		0			0
$381$	2.09913	+	1.84089i	0.107542	+	0.0943117i
$382$		0			0
$383$	29.3203	+	22.4983i	1.49820	+	1.14961i	0.949576	+	0.313536i	$0.101514\pi$
$383$	29.3203	+	22.4983i	1.49820	+	1.14961i	0.548621	+	0.836071i	$0.315153\pi$
$384$		0			0
$385$	5.36006	−	7.76747i	0.273174	−	0.395867i
$386$		0			0
$387$	−18.0357	−	4.83265i	−0.916805	−	0.245657i
$388$		0			0
$389$	−29.5987	+	22.7119i	−1.50071	+	1.15154i	−0.552668	+	0.833402i	$0.686390\pi$
$389$	−29.5987	+	22.7119i	−1.50071	+	1.15154i	−0.948045	+	0.318136i	$0.896943\pi$
$390$		0			0
$391$	12.4275	+	11.7854i	0.628488	+	0.596016i
$392$		0			0
$393$	−0.584119	+	1.41019i	−0.0294649	+	0.0711345i
$394$		0			0
$395$	0.0556835	+	0.207814i	0.00280174	+	0.0104562i
$396$		0			0
$397$	10.1825	−	20.6481i	0.511046	−	1.03630i	−0.476530	−	0.879158i	$-0.658106\pi$
$397$	10.1825	−	20.6481i	0.511046	−	1.03630i	0.987576	−	0.157141i	$-0.0502278\pi$
$398$		0			0
$399$	1.14576	−	1.11195i	0.0573600	−	0.0556669i
$400$		0			0
$401$	17.2533	−	5.85670i	0.861588	−	0.292470i	0.144544	−	0.989498i	$-0.453828\pi$
$401$	17.2533	−	5.85670i	0.861588	−	0.292470i	0.717043	+	0.697029i	$0.245495\pi$
$402$		0			0
$403$	−14.0892	−	4.78264i	−0.701833	−	0.238240i
$404$		0			0
$405$	−8.65119	−	5.78054i	−0.429881	−	0.287237i
$406$		0			0
$407$			5.47610i			0.271440i
$408$		0			0
$409$	2.24259	+	1.29476i	0.110889	+	0.0640216i	0.554419	−	0.832238i	$-0.312941\pi$
$409$	2.24259	+	1.29476i	0.110889	+	0.0640216i	−0.443530	+	0.896260i	$0.646274\pi$
$410$		0			0
$411$	−2.10889	−	0.138224i	−0.104024	−	0.00681810i
$412$		0			0
$413$	13.6901	−	0.691549i	0.673648	−	0.0340289i
$414$		0			0
$415$	3.16048	+	9.31047i	0.155142	+	0.457033i
$416$		0			0
$417$	−0.0749252	−	0.00986409i	−0.00366910	−	0.000483047i
$418$		0			0
$419$	−11.5993	+	7.75043i	−0.566665	+	0.378633i	−0.805652	−	0.592389i	$-0.798185\pi$
$419$	−11.5993	+	7.75043i	−0.566665	+	0.378633i	0.238987	+	0.971023i	$0.423185\pi$
$420$		0			0
$421$	−0.0798012	+	0.0798012i	−0.00388927	+	0.00388927i	−0.709049	−	0.705159i	$-0.750875\pi$
$421$	−0.0798012	+	0.0798012i	−0.00388927	+	0.00388927i	0.705159	+	0.709049i	$0.250875\pi$
$422$		0			0
$423$	−15.5464	−	20.2605i	−0.755894	−	0.985100i
$424$		0			0
$425$	6.17007	−	13.3956i	0.299292	−	0.649782i
$426$		0			0
$427$	8.35933	+	14.9930i	0.404536	+	0.725562i
$428$		0			0
$429$	0.542164	−	2.02338i	0.0261759	−	0.0976898i
$430$		0			0
$431$	−1.52622	−	23.2856i	−0.0735153	−	1.12163i	−0.862113	−	0.506717i	$-0.830859\pi$
$431$	−1.52622	−	23.2856i	−0.0735153	−	1.12163i	0.788597	−	0.614910i	$-0.210808\pi$
$432$		0			0
$433$	−13.2005	−	31.8689i	−0.634377	−	1.53152i	−0.834068	−	0.551662i	$-0.813994\pi$
$433$	−13.2005	−	31.8689i	−0.634377	−	1.53152i	0.199691	−	0.979859i	$-0.436006\pi$
$434$		0			0
$435$	−0.375763	+	1.88909i	−0.0180164	+	0.0905748i
$436$		0			0
$437$	−4.57822	+	13.4870i	−0.219006	+	0.645171i
$438$		0			0
$439$	2.50349	−	38.1959i	0.119485	−	1.82299i	−0.346334	−	0.938111i	$-0.612573\pi$
$439$	2.50349	−	38.1959i	0.119485	−	1.82299i	0.465819	−	0.884880i	$-0.345760\pi$
$440$		0			0
$441$	5.97796	−	19.9049i	0.284665	−	0.947851i
$442$		0			0
$443$	−11.5163	−	19.9469i	−0.547157	−	0.947704i	−0.998468	−	0.0553374i	$-0.982377\pi$
$443$	−11.5163	−	19.9469i	−0.547157	−	0.947704i	0.451310	−	0.892367i	$-0.350957\pi$
$444$		0			0
$445$	8.22367	−	4.05547i	0.389839	−	0.192248i
$446$		0			0
$447$	0.663683	+	3.33656i	0.0313911	+	0.157814i
$448$		0			0
$449$	34.4969	+	6.86187i	1.62801	+	0.323832i	0.922834	−	0.385199i	$-0.125867\pi$
$449$	34.4969	+	6.86187i	1.62801	+	0.323832i	0.705178	+	0.709030i	$0.250867\pi$
$450$		0			0
$451$	0.876775	−	6.65977i	0.0412857	−	0.313596i
$452$		0			0
$453$	−3.05369	−	1.50591i	−0.143475	−	0.0707539i
$454$		0			0
$455$	−12.4781	+	1.45300i	−0.584984	+	0.0681175i
$456$		0			0
$457$	−3.61066	−	27.4257i	−0.168900	−	1.28292i	−0.840421	−	0.541934i	$-0.817692\pi$
$457$	−3.61066	−	27.4257i	−0.168900	−	1.28292i	0.671521	−	0.740985i	$-0.265641\pi$
$458$		0			0
$459$	−3.80734	−	2.06558i	−0.177711	−	0.0964130i
$460$		0			0
$461$	4.54039	+	1.88069i	0.211467	+	0.0875925i	0.485903	−	0.874013i	$-0.338491\pi$
$461$	4.54039	+	1.88069i	0.211467	+	0.0875925i	−0.274436	+	0.961605i	$0.588491\pi$
$462$		0			0
$463$	20.1790	+	20.1790i	0.937799	+	0.937799i	0.998176	−	0.0603766i	$-0.0192302\pi$
$463$	20.1790	+	20.1790i	0.937799	+	0.937799i	−0.0603766	+	0.998176i	$0.519230\pi$
$464$		0			0
$465$	0.783139	−	0.0513297i	0.0363172	−	0.00238036i
$466$		0			0
$467$	−15.1796	+	19.7824i	−0.702427	+	0.915421i	−0.999219	−	0.0395211i	$-0.987417\pi$
$467$	−15.1796	+	19.7824i	−0.702427	+	0.915421i	0.296791	+	0.954942i	$0.404083\pi$
$468$		0			0
$469$	8.31897	+	2.96359i	0.384134	+	0.136846i
$470$		0			0
$471$	1.97696	−	1.73374i	0.0910933	−	0.0798867i
$472$		0			0
$473$	−8.31722	−	16.8656i	−0.382426	−	0.775483i
$474$		0			0
$475$	12.2646			0.562738
$476$		0			0
$477$	−5.61910			−0.257281
$478$		0			0
$479$	3.57180	+	7.24289i	0.163200	+	0.330936i	0.963076	−	0.269228i	$-0.0867685\pi$
$479$	3.57180	+	7.24289i	0.163200	+	0.330936i	−0.799877	+	0.600164i	$0.795102\pi$
$480$		0			0
$481$	5.48050	−	4.80627i	0.249889	−	0.219147i
$482$		0			0
$483$	−0.348909	−	1.90259i	−0.0158759	−	0.0865708i
$484$		0			0
$485$	1.85524	−	2.41780i	0.0842422	−	0.109787i
$486$		0			0
$487$	−8.29879	+	0.543931i	−0.376054	+	0.0246479i	−0.252258	−	0.967660i	$-0.581173\pi$
$487$	−8.29879	+	0.543931i	−0.376054	+	0.0246479i	−0.123795	+	0.992308i	$0.539507\pi$
$488$		0			0
$489$	0.754484	+	0.754484i	0.0341189	+	0.0341189i
$490$		0			0
$491$	−5.83056	−	2.41510i	−0.263129	−	0.108992i	0.247219	−	0.968960i	$-0.420483\pi$
$491$	−5.83056	−	2.41510i	−0.263129	−	0.108992i	−0.510348	+	0.859968i	$0.670483\pi$
$492$		0			0
$493$	3.94131	−	37.6193i	0.177508	−	1.69429i
$494$		0			0
$495$	−1.38233	−	10.4999i	−0.0621313	−	0.471934i
$496$		0			0
$497$	25.6248	+	11.0666i	1.14943	+	0.496407i
$498$		0			0
$499$	11.3468	+	5.59564i	0.507954	+	0.250495i	0.678161	−	0.734913i	$-0.262777\pi$
$499$	11.3468	+	5.59564i	0.507954	+	0.250495i	−0.170207	+	0.985408i	$0.554444\pi$
$500$		0			0
$501$	−0.383803	+	2.91527i	−0.0171470	+	0.130245i
$502$		0			0
$503$	17.0321	+	3.38790i	0.759425	+	0.151059i	0.559589	−	0.828770i	$-0.310959\pi$
$503$	17.0321	+	3.38790i	0.759425	+	0.151059i	0.199836	+	0.979829i	$0.435959\pi$
$504$		0			0
$505$	2.16847	+	10.9016i	0.0964956	+	0.485116i
$506$		0			0
$507$	−0.448789	+	0.221318i	−0.0199314	+	0.00982909i
$508$		0			0
$509$	18.0008	+	31.1784i	0.797873	+	1.38196i	0.920999	+	0.389565i	$0.127375\pi$
$509$	18.0008	+	31.1784i	0.797873	+	1.38196i	−0.123126	+	0.992391i	$0.539292\pi$
$510$		0			0
$511$	−11.8327	−	1.73848i	−0.523447	−	0.0769057i
$512$		0			0
$513$	0.235589	−	3.59439i	0.0104015	−	0.158696i
$514$		0			0
$515$	1.96217	−	5.78036i	0.0864635	−	0.254713i
$516$		0			0
$517$	5.01768	−	25.2256i	0.220677	−	1.10942i
$518$		0			0
$519$	−0.505743	−	1.22097i	−0.0221996	−	0.0535947i
$520$		0			0
$521$	0.303579	+	4.63172i	0.0133000	+	0.202919i	0.999337	+	0.0363954i	$0.0115876\pi$
$521$	0.303579	+	4.63172i	0.0133000	+	0.202919i	−0.986037	+	0.166524i	$0.946746\pi$
$522$		0			0
$523$	−7.06283	+	26.3589i	−0.308836	+	1.15259i	0.620756	+	0.784004i	$0.286826\pi$
$523$	−7.06283	+	26.3589i	−0.308836	+	1.15259i	−0.929593	+	0.368589i	$0.879841\pi$
$524$		0			0
$525$	−1.45481	+	0.811125i	−0.0634929	+	0.0354004i
$526$		0			0
$527$	−15.2219	+	2.41610i	−0.663078	+	0.105247i
$528$		0			0
$529$	−3.49714	−	4.55756i	−0.152050	−	0.198155i
$530$		0			0
$531$	10.8770	−	10.8770i	0.472024	−	0.472024i
$532$		0			0
$533$	−7.43465	+	4.96767i	−0.322030	+	0.215174i
$534$		0			0
$535$	4.29377	+	0.565285i	0.185636	+	0.0244394i
$536$		0			0
$537$	−0.954374	−	2.81150i	−0.0411843	−	0.121325i
$538$		0			0
$539$	19.0415	−	8.69121i	0.820177	−	0.374357i
$540$		0			0
$541$	−11.2520	−	0.737494i	−0.483760	−	0.0317073i	−0.178428	−	0.983953i	$-0.557101\pi$
$541$	−11.2520	−	0.737494i	−0.483760	−	0.0317073i	−0.305333	+	0.952246i	$0.598768\pi$
$542$		0			0
$543$	−1.83469	−	1.05926i	−0.0787342	−	0.0454572i
$544$		0			0
$545$			17.9490i			0.768853i
$546$		0			0
$547$	19.3589	+	12.9352i	0.827728	+	0.553070i	0.895721	−	0.444616i	$-0.146660\pi$
$547$	19.3589	+	12.9352i	0.827728	+	0.553070i	−0.0679936	+	0.997686i	$0.521660\pi$
$548$		0			0
$549$	18.2410	+	6.19199i	0.778508	+	0.264268i
$550$		0			0
$551$	29.7859	−	10.1109i	1.26892	−	0.430741i
$552$		0			0
$553$	−0.130391	+	0.459011i	−0.00554477	+	0.0195191i
$554$		0			0
$555$	−0.170060	+	0.344847i	−0.00721864	+	0.0146379i
$556$		0			0
$557$	−0.418417	−	1.56155i	−0.0177289	−	0.0661652i	0.956495	−	0.291750i	$-0.0942375\pi$
$557$	−0.418417	−	1.56155i	−0.0177289	−	0.0661652i	−0.974224	+	0.225585i	$0.927571\pi$
$558$		0			0
$559$	−9.57933	+	23.1265i	−0.405162	+	0.978149i
$560$		0			0
$561$	−0.479593	−	2.11623i	−0.0202484	−	0.0893473i
$562$		0			0
$563$	−24.8260	+	19.0497i	−1.04629	+	0.802847i	−0.980802	−	0.195006i	$-0.937527\pi$
$563$	−24.8260	+	19.0497i	−1.04629	+	0.802847i	−0.0654889	+	0.997853i	$0.520861\pi$
$564$		0			0
$565$	1.70050	+	0.455647i	0.0715405	+	0.0191692i
$566$		0			0
$567$	−9.89542	−	20.8474i	−0.415569	−	0.875509i
$568$		0			0
$569$	19.2197	+	14.7478i	0.805733	+	0.618261i	0.927299	−	0.374323i	$-0.122125\pi$
$569$	19.2197	+	14.7478i	0.805733	+	0.618261i	−0.121565	+	0.992583i	$0.538791\pi$
$570$		0			0
$571$	−6.44536	−	5.65243i	−0.269730	−	0.236547i	0.513786	−	0.857918i	$-0.328242\pi$
$571$	−6.44536	−	5.65243i	−0.269730	−	0.236547i	−0.783516	+	0.621371i	$0.786576\pi$
$572$		0			0
$573$	−1.93547	+	0.384989i	−0.0808554	+	0.0160831i
$574$		0			0
$575$	8.25501	−	12.3545i	0.344258	−	0.515218i
$576$		0			0
$577$	−3.78321	+	6.55270i	−0.157497	+	0.272793i	−0.933965	−	0.357363i	$-0.883676\pi$
$577$	−3.78321	+	6.55270i	−0.157497	+	0.272793i	0.776469	+	0.630156i	$0.217009\pi$
$578$		0			0
$579$	2.14362	−	1.23762i	0.0890860	−	0.0514338i
$580$		0			0
$581$	−4.57423	+	21.3220i	−0.189771	+	0.884584i
$582$		0			0
$583$	−3.73133	−	4.25477i	−0.154536	−	0.176214i
$584$		0			0
$585$	−9.29505	+	10.5990i	−0.384303	+	0.438214i
$586$		0			0
$587$	35.8628	−	14.8548i	1.48021	−	0.613125i	0.511052	−	0.859550i	$-0.329256\pi$
$587$	35.8628	−	14.8548i	1.48021	−	0.613125i	0.969162	+	0.246425i	$0.0792559\pi$
$588$		0			0
$589$	−7.12071	−	10.6569i	−0.293404	−	0.439110i
$590$		0			0
$591$	−3.24557	+	0.869649i	−0.133505	+	0.0357726i
$592$		0			0
$593$	−39.6967	+	5.22617i	−1.63015	+	0.214613i	−0.889387	−	0.457156i	$-0.848868\pi$
$593$	−39.6967	+	5.22617i	−1.63015	+	0.214613i	−0.740761	+	0.671769i	$0.765535\pi$
$594$		0			0
$595$	−10.7358	+	7.35396i	−0.440126	+	0.301483i
$596$		0			0
$597$	1.37324	−	0.180790i	0.0562029	−	0.00739926i
$598$		0			0
$599$	17.0593	−	4.57103i	0.697025	−	0.186767i	0.107127	−	0.994245i	$-0.465835\pi$
$599$	17.0593	−	4.57103i	0.697025	−	0.186767i	0.589898	+	0.807478i	$0.299168\pi$
$600$		0			0
$601$	−22.9950	−	34.4145i	−0.937988	−	1.40380i	−0.914729	−	0.404068i	$-0.867596\pi$
$601$	−22.9950	−	34.4145i	−0.937988	−	1.40380i	−0.0232587	−	0.999729i	$-0.507404\pi$
$602$		0			0
$603$	9.15575	−	3.79244i	0.372851	−	0.154440i
$604$		0			0
$605$	−1.61935	+	1.84651i	−0.0658358	+	0.0750714i
$606$		0			0
$607$	−20.6952	−	23.5984i	−0.839993	−	0.957829i	0.159576	−	0.987186i	$-0.448987\pi$
$607$	−20.6952	−	23.5984i	−0.839993	−	0.957829i	−0.999569	+	0.0293567i	$0.990654\pi$
$608$		0			0
$609$	−2.86446	+	3.16925i	−0.116074	+	0.128424i
$610$		0			0
$611$	−29.6498	+	17.1183i	−1.19950	+	0.692532i
$612$		0			0
$613$	7.76220	−	13.4445i	0.313512	−	0.543019i	−0.665608	−	0.746302i	$-0.731828\pi$
$613$	7.76220	−	13.4445i	0.313512	−	0.543019i	0.979120	+	0.203283i	$0.0651610\pi$
$614$		0			0
$615$	0.262032	−	0.392158i	0.0105661	−	0.0158134i
$616$		0			0
$617$	26.1831	−	5.20815i	1.05409	−	0.209672i	0.362518	−	0.931977i	$-0.381917\pi$
$617$	26.1831	−	5.20815i	1.05409	−	0.209672i	0.691575	+	0.722305i	$0.256917\pi$
$618$		0			0
$619$	30.7910	+	27.0030i	1.23760	+	1.08534i	0.993291	+	0.115644i	$0.0368931\pi$
$619$	30.7910	+	27.0030i	1.23760	+	1.08534i	0.244305	+	0.969698i	$0.421440\pi$
$620$		0			0
$621$	−3.46217	−	2.65662i	−0.138932	−	0.106606i
$622$		0			0
$623$	20.2709	+	1.63388i	0.812137	+	0.0654599i
$624$		0			0
$625$	−5.48622	−	1.47003i	−0.219449	−	0.0588011i
$626$		0			0
$627$	1.43158	−	1.09849i	0.0571719	−	0.0438696i
$628$		0			0
$629$	2.70366	−	7.05027i	0.107802	−	0.281113i
$630$		0			0
$631$	17.5954	−	42.4791i	0.700462	−	1.69106i	−0.0220974	−	0.999756i	$-0.507034\pi$
$631$	17.5954	−	42.4791i	0.700462	−	1.69106i	0.722559	−	0.691309i	$-0.242966\pi$
$632$		0			0
$633$	0.358344	+	1.33736i	0.0142429	+	0.0531553i
$634$		0			0
$635$	8.36967	−	16.9720i	0.332140	−	0.673514i
$636$		0			0
$637$	−25.4106	−	11.4287i	−1.00680	−	0.452822i
$638$		0			0
$639$	29.6605	−	10.0684i	1.17335	−	0.398299i
$640$		0			0
$641$	15.1060	+	5.12779i	0.596650	+	0.202535i	0.603396	−	0.797442i	$-0.293814\pi$
$641$	15.1060	+	5.12779i	0.596650	+	0.202535i	−0.00674578	+	0.999977i	$0.502147\pi$
$642$		0			0
$643$	3.73879	+	2.49818i	0.147443	+	0.0985186i	0.627104	−	0.778936i	$-0.284240\pi$
$643$	3.73879	+	2.49818i	0.147443	+	0.0985186i	−0.479660	+	0.877454i	$0.659240\pi$
$644$		0			0
$645$		−	1.32037i		−	0.0519897i
$646$		0			0
$647$	−31.9856	−	18.4669i	−1.25748	−	0.726009i	−0.284899	−	0.958557i	$-0.591960\pi$
$647$	−31.9856	−	18.4669i	−1.25748	−	0.726009i	−0.972585	+	0.232549i	$0.925294\pi$
$648$		0			0
$649$	15.4589	+	1.01323i	0.606815	+	0.0397727i
$650$		0			0
$651$	1.54945	+	0.793171i	0.0607276	+	0.0310868i
$652$		0			0
$653$	1.38529	+	4.08092i	0.0542105	+	0.159699i	0.970663	−	0.240445i	$-0.0772934\pi$
$653$	1.38529	+	4.08092i	0.0542105	+	0.159699i	−0.916452	+	0.400144i	$0.868960\pi$
$654$		0			0
$655$	10.2569	+	1.35035i	0.400772	+	0.0527626i
$656$		0			0
$657$	−11.1592	+	7.45631i	−0.435360	+	0.290898i
$658$		0			0
$659$	13.0103	−	13.0103i	0.506810	−	0.506810i	−0.406736	−	0.913546i	$-0.633333\pi$
$659$	13.0103	−	13.0103i	0.506810	−	0.506810i	0.913546	+	0.406736i	$0.133333\pi$
$660$		0			0
$661$	−24.4898	−	31.9158i	−0.952545	−	1.24138i	−0.970391	−	0.241540i	$-0.922348\pi$
$661$	−24.4898	−	31.9158i	−0.952545	−	1.24138i	0.0178464	−	0.999841i	$-0.494319\pi$
$662$		0			0
$663$	−1.69700	+	2.33735i	−0.0659060	+	0.0907752i
$664$		0			0
$665$	−9.28965	−	5.55054i	−0.360237	−	0.215241i
$666$		0			0
$667$	9.86312	−	36.8097i	0.381901	−	1.42528i
$668$		0			0
$669$	−0.0687859	−	1.04947i	−0.00265942	−	0.0405749i
$670$		0			0
$671$	7.42428	+	17.9238i	0.286611	+	0.691940i
$672$		0			0
$673$	−7.68040	+	38.6120i	−0.296058	+	1.48838i	0.490813	+	0.871265i	$0.336700\pi$
$673$	−7.68040	+	38.6120i	−0.296058	+	1.48838i	−0.786871	+	0.617118i	$0.788300\pi$
$674$		0			0
$675$	−1.20792	+	3.55840i	−0.0464927	+	0.136963i
$676$		0			0
$677$	−1.85049	+	28.2330i	−0.0711200	+	1.08508i	0.801920	+	0.597432i	$0.203812\pi$
$677$	−1.85049	+	28.2330i	−0.0711200	+	1.08508i	−0.873040	+	0.487649i	$0.837854\pi$
$678$		0			0
$679$	6.28277	−	2.49283i	0.241110	−	0.0956659i
$680$		0			0
$681$	1.14296	+	1.97966i	0.0437983	+	0.0758609i
$682$		0			0
$683$	10.4339	−	5.14543i	0.399242	−	0.196884i	−0.231573	−	0.972817i	$-0.574387\pi$
$683$	10.4339	−	5.14543i	0.399242	−	0.196884i	0.630815	+	0.775933i	$0.282721\pi$
$684$		0			0
$685$	2.79453	+	14.0491i	0.106774	+	0.536787i
$686$		0			0
$687$	−2.79196	−	0.555356i	−0.106520	−	0.0211882i
$688$		0			0
$689$	−0.983267	+	7.46865i	−0.0374595	+	0.284533i
$690$		0			0
$691$	−43.6169	−	21.5095i	−1.65926	−	0.818259i	−0.997657	−	0.0684074i	$-0.978208\pi$
$691$	−43.6169	−	21.5095i	−1.65926	−	0.818259i	−0.661607	−	0.749851i	$-0.730125\pi$
$692$		0			0
$693$	9.31277	−	21.5637i	0.353763	−	0.819137i
$694$		0			0
$695$	0.0668567	+	0.507827i	0.00253602	+	0.0192630i
$696$		0			0
$697$	−4.41688	+	8.14132i	−0.167301	+	0.308374i
$698$		0			0
$699$	−3.32751	−	1.37830i	−0.125858	−	0.0521321i
$700$		0			0
$701$	30.3873	+	30.3873i	1.14771	+	1.14771i	0.987002	+	0.160709i	$0.0513781\pi$
$701$	30.3873	+	30.3873i	1.14771	+	1.14771i	0.160709	+	0.987002i	$0.448622\pi$
$702$		0			0
$703$	6.26584	−	0.410685i	0.236321	−	0.0154893i
$704$		0			0
$705$	1.09936	−	1.43271i	0.0414042	−	0.0539590i
$706$		0			0
$707$	−8.27306	+	23.2229i	−0.311141	+	0.873389i
$708$		0			0
$709$	13.4095	−	11.7598i	0.503604	−	0.441649i	−0.369466	−	0.929244i	$-0.620459\pi$
$709$	13.4095	−	11.7598i	0.503604	−	0.441649i	0.873070	+	0.487595i	$0.162126\pi$
$710$		0			0
$711$	0.236834	+	0.480253i	0.00888199	+	0.0180109i
$712$		0			0
$713$	−15.5278			−0.581521
$714$		0			0
$715$	−14.1978			−0.530969
$716$		0			0
$717$	0.330173	+	0.669524i	0.0123305	+	0.0250038i
$718$		0			0
$719$	−9.56033	+	8.38419i	−0.356540	+	0.312677i	−0.818813	−	0.574060i	$-0.805367\pi$
$719$	−9.56033	+	8.38419i	−0.356540	+	0.312677i	0.462273	+	0.886738i	$0.347034\pi$
$720$		0			0
$721$	10.3116	−	8.77332i	0.384024	−	0.326735i
$722$		0			0
$723$	2.78654	−	3.63149i	0.103633	−	0.135057i
$724$		0			0
$725$	−32.7448	+	2.14621i	−1.21611	+	0.0797082i
$726$		0			0
$727$	−17.4368	−	17.4368i	−0.646694	−	0.646694i	0.305498	−	0.952193i	$-0.401177\pi$
$727$	−17.4368	−	17.4368i	−0.646694	−	0.646694i	−0.952193	+	0.305498i	$0.901177\pi$
$728$		0			0
$729$	−23.4126	−	9.69782i	−0.867134	−	0.359179i
$730$		0			0
$731$	2.38120	+	25.8203i	0.0880718	+	0.954997i
$732$		0			0
$733$	−1.15126	−	8.74470i	−0.0425228	−	0.322993i	−0.999465	−	0.0327136i	$-0.989585\pi$
$733$	−1.15126	−	8.74470i	−0.0425228	−	0.322993i	0.956942	−	0.290279i	$-0.0937482\pi$
$734$		0			0
$735$	1.46901	+	0.0440200i	0.0541852	+	0.00162370i
$736$		0			0
$737$	8.95144	+	4.41436i	0.329731	+	0.162605i
$738$		0			0
$739$	−3.42197	+	25.9925i	−0.125879	+	0.956148i	0.805627	+	0.592423i	$0.201829\pi$
$739$	−3.42197	+	25.9925i	−0.125879	+	0.956148i	−0.931506	+	0.363725i	$0.881505\pi$
$740$		0			0
$741$	−2.35585	−	0.468607i	−0.0865442	−	0.0172147i
$742$		0			0
$743$	−4.12234	−	20.7244i	−0.151234	−	0.760304i	−0.979732	−	0.200312i	$-0.935804\pi$
$743$	−4.12234	−	20.7244i	−0.151234	−	0.760304i	0.828498	−	0.559992i	$-0.189196\pi$
$744$		0			0
$745$	20.6797	−	10.1981i	0.757645	−	0.373629i
$746$		0			0
$747$	12.2358	+	21.1930i	0.447685	+	0.775413i
$748$		0			0
$749$	7.53202	+	5.96086i	0.275214	+	0.217805i
$750$		0			0
$751$	−3.06096	+	46.7013i	−0.111696	+	1.70415i	0.463466	+	0.886115i	$0.346606\pi$
$751$	−3.06096	+	46.7013i	−0.111696	+	1.70415i	−0.575162	+	0.818039i	$0.695061\pi$
$752$		0			0
$753$	0.120918	−	0.356214i	0.00440651	−	0.0129812i
$754$		0			0
$755$	−4.50212	+	22.6337i	−0.163849	+	0.823724i
$756$		0			0
$757$	−5.43541	−	13.1222i	−0.197553	−	0.476936i	0.793796	−	0.608184i	$-0.208102\pi$
$757$	−5.43541	−	13.1222i	−0.197553	−	0.476936i	−0.991350	+	0.131248i	$0.958102\pi$
$758$		0			0
$759$	−0.142980	−	2.18145i	−0.00518983	−	0.0791815i
$760$		0			0
$761$	−12.1950	+	45.5124i	−0.442068	+	1.64982i	0.281494	+	0.959563i	$0.409170\pi$
$761$	−12.1950	+	45.5124i	−0.442068	+	1.64982i	−0.723563	+	0.690259i	$0.757497\pi$
$762$		0			0
$763$	−20.4188	+	34.1740i	−0.739212	+	1.23718i
$764$		0			0
$765$	−3.40429	+	14.2007i	−0.123082	+	0.513426i
$766$		0			0
$767$	−12.5539	−	16.3606i	−0.453296	−	0.590747i
$768$		0			0
$769$	−26.1024	+	26.1024i	−0.941278	+	0.941278i	−0.998369	−	0.0570907i	$-0.981818\pi$
$769$	−26.1024	+	26.1024i	−0.941278	+	0.941278i	0.0570907	+	0.998369i	$0.481818\pi$
$770$		0			0
$771$	3.07217	−	2.05276i	0.110642	−	0.0739283i
$772$		0			0
$773$	6.66404	+	0.877337i	0.239689	+	0.0315556i	0.249413	−	0.968397i	$-0.419762\pi$
$773$	6.66404	+	0.877337i	0.239689	+	0.0315556i	−0.00972473	+	0.999953i	$0.503096\pi$
$774$		0			0
$775$	4.29798	+	12.6615i	0.154388	+	0.454813i
$776$		0			0
$777$	−0.716083	+	0.463109i	−0.0256893	+	0.0166140i
$778$		0			0
$779$	−7.68597	−	0.503765i	−0.275378	−	0.0180493i
$780$		0			0
$781$	27.3196	+	15.7730i	0.977574	+	0.564402i
$782$		0			0
$783$			9.63777i			0.344426i
$784$		0			0
$785$	−14.8186	−	9.90144i	−0.528897	−	0.353398i
$786$		0			0
$787$	3.95668	+	1.34311i	0.141041	+	0.0478768i	0.391067	−	0.920362i	$-0.372106\pi$
$787$	3.95668	+	1.34311i	0.141041	+	0.0478768i	−0.250027	+	0.968239i	$0.580439\pi$
$788$		0			0
$789$	−2.67201	+	0.907025i	−0.0951261	+	0.0322909i
$790$		0			0
$791$	2.71931	+	2.80202i	0.0966875	+	0.0996282i
$792$		0			0
$793$	11.4220	−	23.1616i	0.405609	−	0.822493i
$794$		0			0
$795$	−0.102842	−	0.383812i	−0.00364744	−	0.0136124i
$796$		0			0
$797$	−5.77393	+	13.9395i	−0.204523	+	0.493763i	−0.992544	−	0.121886i	$-0.961106\pi$
$797$	−5.77393	+	13.9395i	−0.204523	+	0.493763i	0.788021	+	0.615648i	$0.211106\pi$
$798$		0			0
$799$	−18.9144	+	29.9997i	−0.669145	+	1.06131i
$800$		0			0
$801$	18.1055	−	13.8928i	0.639726	−	0.490879i
$802$		0			0
$803$	−13.0561	−	3.49836i	−0.460738	−	0.123454i
$804$		0			0
$805$	−11.8439	+	5.62181i	−0.417442	+	0.198143i
$806$		0			0
$807$	−0.782932	−	0.600765i	−0.0275605	−	0.0211479i
$808$		0			0
$809$	17.1861	+	15.0718i	0.604230	+	0.529895i	0.905886	−	0.423522i	$-0.139206\pi$
$809$	17.1861	+	15.0718i	0.604230	+	0.529895i	−0.301656	+	0.953417i	$0.597540\pi$
$810$		0			0
$811$	−6.22752	+	1.23873i	−0.218678	+	0.0434977i	−0.303213	−	0.952923i	$-0.598059\pi$
$811$	−6.22752	+	1.23873i	−0.218678	+	0.0434977i	0.0845353	+	0.996420i	$0.473059\pi$
$812$		0			0
$813$	−1.12004	+	1.67626i	−0.0392814	+	0.0587888i
$814$		0			0
$815$	3.61595	−	6.26302i	0.126661	−	0.219384i
$816$		0			0
$817$	−18.6742	+	10.7816i	−0.653327	+	0.377199i
$818$		0			0
$819$	−29.7547	+	9.60579i	−1.03971	+	0.335653i
$820$		0			0
$821$	6.71108	+	7.65252i	0.234218	+	0.267075i	0.856995	−	0.515325i	$-0.172329\pi$
$821$	6.71108	+	7.65252i	0.234218	+	0.267075i	−0.622777	+	0.782400i	$0.713995\pi$
$822$		0			0
$823$	8.19120	−	9.34027i	0.285527	−	0.325581i	−0.591241	−	0.806495i	$-0.701362\pi$
$823$	8.19120	−	9.34027i	0.285527	−	0.325581i	0.876768	+	0.480914i	$0.159695\pi$
$824$		0			0
$825$	−1.73919	+	0.720395i	−0.0605507	+	0.0250809i
$826$		0			0
$827$	−27.9017	−	41.7579i	−0.970239	−	1.45206i	−0.890358	−	0.455260i	$-0.849546\pi$
$827$	−27.9017	−	41.7579i	−0.970239	−	1.45206i	−0.0798801	−	0.996804i	$-0.525454\pi$
$828$		0			0
$829$	45.1493	−	12.0977i	1.56810	−	0.420171i	0.632883	−	0.774248i	$-0.281872\pi$
$829$	45.1493	−	12.0977i	1.56810	−	0.420171i	0.935216	+	0.354077i	$0.115205\pi$
$830$		0			0
$831$	−3.97821	+	0.523741i	−0.138003	+	0.0181684i
$832$		0			0
$833$	−28.8063	+	1.78843i	−0.998078	+	0.0619655i
$834$		0			0
$835$	19.7591	−	2.60133i	0.683791	−	0.0900228i
$836$		0			0
$837$	3.79326	−	1.01640i	0.131114	−	0.0351319i
$838$		0			0
$839$	17.8920	+	26.7773i	0.617702	+	0.924456i	1.00000		0.000416796i	$0.000132670\pi$
$839$	17.8920	+	26.7773i	0.617702	+	0.924456i	−0.382298	+	0.924039i	$0.624867\pi$
$840$		0			0
$841$	−50.9625	+	21.1094i	−1.75733	+	0.727909i
$842$		0			0
$843$	0.734169	−	0.837159i	0.0252861	−	0.0288333i
$844$		0			0
$845$	2.23621	+	2.54991i	0.0769279	+	0.0877195i
$846$		0			0
$847$	−5.18374	+	1.67348i	−0.178115	+	0.0575015i
$848$		0			0
$849$	4.22153	−	2.43730i	0.144883	−	0.0836480i
$850$		0			0
$851$	3.80370	−	6.58820i	0.130389	−	0.225840i
$852$		0			0
$853$	8.89340	−	13.3099i	0.304504	−	0.455723i	−0.647386	−	0.762162i	$-0.724138\pi$
$853$	8.89340	−	13.3099i	0.304504	−	0.455723i	0.951890	+	0.306440i	$0.0991377\pi$
$854$		0			0
$855$	−11.9105	+	2.36914i	−0.407329	+	0.0810228i
$856$		0			0
$857$	−2.87996	−	2.52566i	−0.0983776	−	0.0862749i	0.608744	−	0.793366i	$-0.291674\pi$
$857$	−2.87996	−	2.52566i	−0.0983776	−	0.0862749i	−0.707122	+	0.707092i	$0.750007\pi$
$858$		0			0
$859$	−9.12529	−	7.00208i	−0.311351	−	0.238908i	0.441251	−	0.897384i	$-0.354535\pi$
$859$	−9.12529	−	7.00208i	−0.311351	−	0.238908i	−0.752602	+	0.658476i	$0.771202\pi$
$860$		0			0
$861$	0.945013	−	0.448560i	0.0322060	−	0.0152869i
$862$		0			0
$863$	−41.4200	−	11.0985i	−1.40995	−	0.377796i	−0.528045	−	0.849216i	$-0.677075\pi$
$863$	−41.4200	−	11.0985i	−1.40995	−	0.377796i	−0.881909	+	0.471421i	$0.843741\pi$
$864$		0			0
$865$	−7.10631	+	5.45287i	−0.241622	+	0.185403i
$866$		0			0
$867$	−0.427367	+	2.96135i	−0.0145141	+	0.100573i
$868$		0			0
$869$	−0.206377	+	0.498239i	−0.00700087	+	0.0169016i
$870$		0			0
$871$	−3.43860	−	12.8330i	−0.116513	−	0.434831i
$872$		0			0
$873$	3.35481	−	6.80289i	0.113543	−	0.230243i
$874$		0			0
$875$	18.8525	+	19.4259i	0.637332	+	0.656716i
$876$		0			0
$877$	−0.530853	+	0.180200i	−0.0179256	+	0.00608493i	−0.330388	−	0.943845i	$-0.607180\pi$
$877$	−0.530853	+	0.180200i	−0.0179256	+	0.00608493i	0.312462	+	0.949930i	$0.398846\pi$
$878$		0			0
$879$	−0.286246	−	0.0971675i	−0.00965484	−	0.00327738i
$880$		0			0
$881$	−7.73451	−	5.16803i	−0.260582	−	0.174115i	0.418416	−	0.908256i	$-0.362585\pi$
$881$	−7.73451	−	5.16803i	−0.260582	−	0.174115i	−0.678998	+	0.734140i	$0.737585\pi$
$882$		0			0
$883$			8.67783i			0.292032i	0.989282	+	0.146016i	$0.0466452\pi$
$883$			8.67783i			0.292032i	−0.989282	+	0.146016i	$0.953355\pi$
$884$		0			0
$885$	0.942030	+	0.543881i	0.0316660	+	0.0182824i
$886$		0			0
$887$	13.3065	+	0.872155i	0.446789	+	0.0292841i	0.287138	−	0.957889i	$-0.407296\pi$
$887$	13.3065	+	0.872155i	0.446789	+	0.0292841i	0.159651	+	0.987173i	$0.448963\pi$
$888$		0			0
$889$	35.2427	−	22.7924i	1.18200	−	0.764432i
$890$		0			0
$891$	−8.38341	−	24.6967i	−0.280855	−	0.827372i
$892$		0			0
$893$	−29.2398	−	3.84950i	−0.978474	−	0.128818i
$894$		0			0
$895$	−16.7322	+	11.1801i	−0.559297	+	0.373710i
$896$		0			0
$897$	−2.05771	+	2.05771i	−0.0687049	+	0.0687049i
$898$		0			0
$899$	20.8762	+	27.2064i	0.696261	+	0.907385i
$900$		0			0
$901$	2.70328	+	7.32008i	0.0900594	+	0.243867i
$902$		0			0
$903$	1.50206	−	2.51392i	0.0499853	−	0.0836579i
$904$		0			0
$905$	−3.71635	+	13.8696i	−0.123536	+	0.461041i
$906$		0			0
$907$	−3.23107	−	49.2966i	−0.107286	−	1.63687i	−0.624510	−	0.781017i	$-0.714701\pi$
$907$	−3.23107	−	49.2966i	−0.107286	−	1.63687i	0.517224	−	0.855850i	$-0.326965\pi$
$908$		0			0
$909$	10.5868	+	25.5589i	0.351143	+	0.847735i
$910$		0			0
$911$	3.34141	−	16.7984i	0.110706	−	0.556556i	−0.885126	−	0.465351i	$-0.845928\pi$
$911$	3.34141	−	16.7984i	0.110706	−	0.556556i	0.995832	−	0.0912053i	$-0.0290719\pi$
$912$		0			0
$913$	−7.92219	+	23.3380i	−0.262186	+	0.772376i
$914$		0			0
$915$	−0.0890918	+	1.35928i	−0.00294528	+	0.0449364i
$916$		0			0
$917$	17.9925	+	14.2393i	0.594164	+	0.470223i
$918$		0			0
$919$	28.0928	+	48.6582i	0.926697	+	1.60509i	0.788810	+	0.614637i	$0.210698\pi$
$919$	28.0928	+	48.6582i	0.926697	+	1.60509i	0.137887	+	0.990448i	$0.455969\pi$
$920$		0			0
$921$	−4.81458	+	2.37429i	−0.158646	+	0.0782355i
$922$		0			0
$923$	−8.19225	−	41.1852i	−0.269651	−	1.35563i
$924$		0			0
$925$	−6.42489	−	1.27799i	−0.211249	−	0.0420200i
$926$		0			0
$927$	1.98310	−	15.0631i	0.0651334	−	0.494737i
$928$		0			0
$929$	3.32246	+	1.63845i	0.109006	+	0.0537560i	0.495974	−	0.868337i	$-0.334811\pi$
$929$	3.32246	+	1.63845i	0.109006	+	0.0537560i	−0.386968	+	0.922093i	$0.626478\pi$
$930$		0			0
$931$	−11.3727	−	21.1358i	−0.372724	−	0.692699i
$932$		0			0
$933$	−0.781227	−	5.93401i	−0.0255762	−	0.194271i
$934$		0			0
$935$	−13.0133	+	6.85215i	−0.425580	+	0.224089i
$936$		0			0
$937$	−3.13143	−	1.29708i	−0.102299	−	0.0423738i	0.330947	−	0.943649i	$-0.392632\pi$
$937$	−3.13143	−	1.29708i	−0.102299	−	0.0423738i	−0.433246	+	0.901276i	$0.642632\pi$
$938$		0			0
$939$	2.26849	+	2.26849i	0.0740293	+	0.0740293i
$940$		0			0
$941$	−20.3913	+	1.33652i	−0.664737	+	0.0435692i	−0.394037	−	0.919095i	$-0.628922\pi$
$941$	−20.3913	+	1.33652i	−0.664737	+	0.0435692i	−0.270700	+	0.962664i	$0.587255\pi$
$942$		0			0
$943$	−5.68070	+	7.40324i	−0.184989	+	0.241083i
$944$		0			0
$945$	2.52533	−	2.14860i	0.0821491	−	0.0698941i
$946$		0			0
$947$	16.8216	−	14.7521i	0.546627	−	0.479379i	−0.340922	−	0.940091i	$-0.610739\pi$
$947$	16.8216	−	14.7521i	0.546627	−	0.479379i	0.887550	+	0.460712i	$0.152406\pi$
$948$		0			0
$949$	7.95788	+	16.1370i	0.258324	+	0.523829i
$950$		0			0
$951$	−3.84742			−0.124761
$952$		0			0
$953$	−50.2015			−1.62619			−0.813094	−	0.582133i	$-0.802218\pi$
$953$	−50.2015			−1.62619			−0.813094	+	0.582133i	$0.802218\pi$
$954$		0			0
$955$	5.91570	+	11.9958i	0.191428	+	0.388177i
$956$		0			0
$957$	−3.62991	+	3.18334i	−0.117338	+	0.102903i
$958$		0			0
$959$	−10.6616	+	29.9277i	−0.344281	+	0.966415i
$960$		0			0
$961$	−10.3652	+	13.5082i	−0.334363	+	0.435750i
$962$		0			0
$963$	10.7559	−	0.704981i	0.346605	−	0.0227177i
$964$		0			0
$965$	−11.8629	−	11.8629i	−0.381880	−	0.381880i
$966$		0			0
$967$	15.3772	+	6.36943i	0.494496	+	0.204827i	0.615973	−	0.787767i	$-0.288763\pi$
$967$	15.3772	+	6.36943i	0.494496	+	0.204827i	−0.121477	+	0.992594i	$0.538763\pi$
$968$		0			0
$969$	−2.38546	+	0.707467i	−0.0766319	+	0.0227271i
$970$		0			0
$971$	−7.76495	−	58.9806i	−0.249189	−	1.89278i	−0.420078	−	0.907488i	$-0.637997\pi$
$971$	−7.76495	−	58.9806i	−0.249189	−	1.89278i	0.170889	−	0.985290i	$-0.445336\pi$
$972$		0			0
$973$	−0.450413	+	1.04293i	−0.0144396	+	0.0334348i
$974$		0			0
$975$	2.24742	+	1.10831i	0.0719752	+	0.0354942i
$976$		0			0
$977$	−2.18672	+	16.6098i	−0.0699594	+	0.531394i	0.920200	+	0.391449i	$0.128026\pi$
$977$	−2.18672	+	16.6098i	−0.0699594	+	0.531394i	−0.990159	+	0.139945i	$0.955307\pi$
$978$		0			0
$979$	22.5425	+	4.48397i	0.720460	+	0.143308i
$980$		0			0
$981$	8.71537	+	43.8151i	0.278260	+	1.39891i
$982$		0			0
$983$	11.4225	−	5.63296i	0.364322	−	0.179664i	−0.250909	−	0.968011i	$-0.580730\pi$
$983$	11.4225	−	5.63296i	0.364322	−	0.179664i	0.615231	+	0.788347i	$0.289063\pi$
$984$		0			0
$985$	11.3869	+	19.7227i	0.362817	+	0.628417i
$986$		0			0
$987$	3.72297	−	1.47717i	0.118503	−	0.0470188i
$988$		0			0
$989$	−1.70858	+	26.0679i	−0.0543297	+	0.828911i
$990$		0			0
$991$	−7.39141	+	21.7744i	−0.234796	+	0.691686i	0.764117	+	0.645077i	$0.223175\pi$
$991$	−7.39141	+	21.7744i	−0.234796	+	0.691686i	−0.998913	+	0.0466088i	$0.985159\pi$
$992$		0			0
$993$	0.588731	−	2.95975i	0.0186828	−	0.0939249i
$994$		0			0
$995$	−3.59257	−	8.67323i	−0.113892	−	0.274960i
$996$		0			0
$997$	3.89313	+	59.3977i	0.123297	+	1.88114i	0.394886	+	0.918730i	$0.370784\pi$
$997$	3.89313	+	59.3977i	0.123297	+	1.88114i	−0.271589	+	0.962413i	$0.587549\pi$
$998$		0			0
$999$	−0.497956	+	1.85840i	−0.0157546	+	0.0587971i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	952.2.cw.a.129.10	✓	288
7.5	odd	6	inner	952.2.cw.a.537.10	yes	288
17.12	odd	16	inner	952.2.cw.a.913.10	yes	288
119.12	even	48	inner	952.2.cw.a.369.10	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
952.2.cw.a.129.10	✓	288	1.1	even	1	trivial
952.2.cw.a.369.10	yes	288	119.12	even	48	inner
952.2.cw.a.537.10	yes	288	7.5	odd	6	inner
952.2.cw.a.913.10	yes	288	17.12	odd	16	inner

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:	\( N \)	\(=\)	\( 952 = 2^{3} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	952.cw (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0778436 + 0.157851i) q^{3} +(0.896871 - 0.786535i) q^{5} +(2.60235 - 0.477236i) q^{7} +(1.80743 - 2.35548i) q^{9} +(2.98378 - 0.195567i) q^{11} +(-2.81453 - 2.81453i) q^{13} +(0.193971 + 0.0803454i) q^{15} +(-3.93805 - 1.22136i) q^{17} +(-0.447542 - 3.39942i) q^{19} +(0.277909 + 0.373635i) q^{21} +(-3.72557 - 1.83725i) q^{23} +(-0.466890 + 3.54638i) q^{25} +(1.03037 + 0.204954i) q^{27} +(1.78975 + 8.99768i) q^{29} +(3.35258 - 1.65331i) q^{31} +(0.263138 + 0.455769i) q^{33} +(1.95861 - 2.47486i) q^{35} +(-0.119777 + 1.82744i) q^{37} +(0.225183 - 0.663369i) q^{39} +(0.438257 - 2.20327i) q^{41} +(-2.40666 - 5.81019i) q^{43} +(-0.231642 - 3.53417i) q^{45} +(2.22621 - 8.30833i) q^{47} +(6.54449 - 2.48388i) q^{49} +(-0.113758 - 0.716702i) q^{51} +(-1.15213 - 1.50148i) q^{53} +(2.52224 - 2.52224i) q^{55} +(0.501764 - 0.335268i) q^{57} +(5.13666 + 0.676254i) q^{59} +(2.08553 + 6.14378i) q^{61} +(3.57944 - 6.99237i) q^{63} +(-4.73799 - 0.310544i) q^{65} +(2.89065 + 1.66892i) q^{67} -0.731103i q^{69} +(8.77190 + 5.86120i) q^{71} +(-4.28045 - 1.45302i) q^{73} +(-0.596145 + 0.202364i) q^{75} +(7.67151 - 1.93290i) q^{77} +(-0.0797685 + 0.161754i) q^{79} +(-2.25746 - 8.42497i) q^{81} +(-3.15420 + 7.61490i) q^{83} +(-4.49257 + 2.00201i) q^{85} +(-1.28097 + 0.982925i) q^{87} +(7.42462 + 1.98942i) q^{89} +(-8.66759 - 5.98120i) q^{91} +(0.521954 + 0.400509i) q^{93} +(-3.07515 - 2.69683i) q^{95} +(2.50566 - 0.498408i) q^{97} +(4.93230 - 7.38171i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 32 q^{15} - 48 q^{21} + 32 q^{29} + 72 q^{31} + 32 q^{35} + 48 q^{37} + 32 q^{39} - 32 q^{43} - 24 q^{47} + 48 q^{49} + 16 q^{53} + 128 q^{57} - 72 q^{61} + 184 q^{63} - 32 q^{65} - 80 q^{71} - 96 q^{73}+ \cdots + 64 q^{99}+O(q^{100}) \) 288 * q - 32 * q^15 - 48 * q^21 + 32 * q^29 + 72 * q^31 + 32 * q^35 + 48 * q^37 + 32 * q^39 - 32 * q^43 - 24 * q^47 + 48 * q^49 + 16 * q^53 + 128 * q^57 - 72 * q^61 + 184 * q^63 - 32 * q^65 - 80 * q^71 - 96 * q^73 - 216 * q^75 + 56 * q^77 - 32 * q^79 - 64 * q^81 + 160 * q^85 - 144 * q^87 + 144 * q^89 - 32 * q^93 - 64 * q^95 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more