LMFDB - Embedded newform 952.2.cw.b.369.14

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			369.14
Character	$\chi$	$=$	952.369
Dual form			952.2.cw.b.129.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.676224 - 1.37125i) q^{3} +(-1.51754 - 1.33085i) q^{5} +(-1.85544 + 1.88609i) q^{7} +(0.403248 + 0.525523i) q^{9} +(0.150271 + 0.00984927i) q^{11} +(-3.08120 + 3.08120i) q^{13} +(-2.85111 + 1.18097i) q^{15} +(-3.95450 + 1.16701i) q^{17} +(-0.152919 + 1.16154i) q^{19} +(1.33160 + 3.81969i) q^{21} +(-5.01931 + 2.47525i) q^{23} +(-0.120857 - 0.917997i) q^{25} +(5.49193 - 1.09241i) q^{27} +(0.520678 - 2.61762i) q^{29} +(-3.05391 - 1.50602i) q^{31} +(0.115122 - 0.199398i) q^{33} +(5.32580 - 0.392909i) q^{35} +(0.714577 + 10.9023i) q^{37} +(2.14150 + 6.30866i) q^{39} +(2.03703 + 10.2408i) q^{41} +(-2.49747 + 6.02944i) q^{43} +(0.0874456 - 1.33416i) q^{45} +(-3.19006 - 11.9055i) q^{47} +(-0.114672 - 6.99906i) q^{49} +(-1.07387 + 6.21175i) q^{51} +(-2.93824 + 3.82919i) q^{53} +(-0.214934 - 0.214934i) q^{55} +(1.48935 + 0.995149i) q^{57} +(0.331680 - 0.0436665i) q^{59} +(-3.80806 + 11.2182i) q^{61} +(-1.73939 - 0.214515i) q^{63} +(8.77645 - 0.575239i) q^{65} +(2.48934 - 1.43722i) q^{67} +8.55653i q^{69} +(8.90077 - 5.94731i) q^{71} +(13.7879 - 4.68037i) q^{73} +(-1.34053 - 0.455047i) q^{75} +(-0.297395 + 0.265150i) q^{77} +(3.27159 + 6.63413i) q^{79} +(1.70148 - 6.34999i) q^{81} +(-3.21226 - 7.75508i) q^{83} +(7.55423 + 3.49185i) q^{85} +(-3.23731 - 2.48408i) q^{87} +(-7.54220 + 2.02093i) q^{89} +(-0.0944340 - 11.5284i) q^{91} +(-4.13026 + 3.16926i) q^{93} +(1.77789 - 1.55917i) q^{95} +(-19.2403 - 3.82713i) q^{97} +(0.0554203 + 0.0829424i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 32 q^{15} + 48 q^{21} - 32 q^{29} - 72 q^{31} - 16 q^{37} - 32 q^{39} + 32 q^{43} + 24 q^{47} - 48 q^{49} - 16 q^{53} - 128 q^{57} - 72 q^{61} - 40 q^{63} + 32 q^{65} + 80 q^{71} + 96 q^{73} - 216 q^{75}+ \cdots + 192 q^{99}+O(q^{100}) $ 288 * q + 32 * q^15 + 48 * q^21 - 32 * q^29 - 72 * q^31 - 16 * q^37 - 32 * q^39 + 32 * q^43 + 24 * q^47 - 48 * q^49 - 16 * q^53 - 128 * q^57 - 72 * q^61 - 40 * q^63 + 32 * q^65 + 80 * q^71 + 96 * q^73 - 216 * q^75 - 8 * q^77 + 32 * q^79 + 64 * q^81 - 96 * q^85 + 144 * q^87 - 144 * q^89 + 64 * q^91 - 32 * q^93 + 64 * q^95 + 192 * q^99

Character values

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

$n$	$239$	$409$	$477$	$785$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{13}{16}\right)$

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
$3$	0.676224	−	1.37125i	0.390418	−	0.791689i	−0.609582	−	0.792723i	$-0.708663\pi$
$3$	0.676224	−	1.37125i	0.390418	−	0.791689i	0.999999	+	0.00103421i	$0.000329200\pi$
$4$		0			0
$5$	−1.51754	−	1.33085i	−0.678665	−	0.595173i	0.249038	−	0.968494i	$-0.419886\pi$
$5$	−1.51754	−	1.33085i	−0.678665	−	0.595173i	−0.927702	+	0.373321i	$0.878219\pi$
$6$		0			0
$7$	−1.85544	+	1.88609i	−0.701291	+	0.712875i
$7$	−1.85544	+	1.88609i	−0.701291	+	0.712875i
$8$		0			0
$9$	0.403248	+	0.525523i	0.134416	+	0.175174i
$10$		0			0
$11$	0.150271	+	0.00984927i	0.0453083	+	0.00296967i	0.0880404	−	0.996117i	$-0.471940\pi$
$11$	0.150271	+	0.00984927i	0.0453083	+	0.00296967i	−0.0427321	+	0.999087i	$0.513606\pi$
$12$		0			0
$13$	−3.08120	+	3.08120i	−0.854571	+	0.854571i	−0.990692	−	0.136121i	$-0.956536\pi$
$13$	−3.08120	+	3.08120i	−0.854571	+	0.854571i	0.136121	+	0.990692i	$0.456536\pi$
$14$		0			0
$15$	−2.85111	+	1.18097i	−0.736155	+	0.304925i
$16$		0			0
$17$	−3.95450	+	1.16701i	−0.959108	+	0.283042i
$17$	−3.95450	+	1.16701i	−0.959108	+	0.283042i
$18$		0			0
$19$	−0.152919	+	1.16154i	−0.0350821	+	0.266475i	0.964910	+	0.262580i	$0.0845732\pi$
$19$	−0.152919	+	1.16154i	−0.0350821	+	0.266475i	−0.999992	+	0.00389530i	$0.998760\pi$
$20$		0			0
$21$	1.33160	+	3.81969i	0.290579	+	0.833524i
$22$		0			0
$23$	−5.01931	+	2.47525i	−1.04660	+	0.516125i	−0.882497	−	0.470318i	$-0.844139\pi$
$23$	−5.01931	+	2.47525i	−1.04660	+	0.516125i	−0.164102	+	0.986443i	$0.552472\pi$
$24$		0			0
$25$	−0.120857	−	0.917997i	−0.0241713	−	0.183599i
$26$		0			0
$27$	5.49193	−	1.09241i	1.05692	−	0.210235i
$28$		0			0
$29$	0.520678	−	2.61762i	0.0966875	−	0.486081i	−0.901852	−	0.432046i	$-0.857792\pi$
$29$	0.520678	−	2.61762i	0.0966875	−	0.486081i	0.998539	−	0.0540348i	$-0.0172082\pi$
$30$		0			0
$31$	−3.05391	−	1.50602i	−0.548499	−	0.270490i	0.146854	−	0.989158i	$-0.453085\pi$
$31$	−3.05391	−	1.50602i	−0.548499	−	0.270490i	−0.695353	+	0.718668i	$0.744752\pi$
$32$		0			0
$33$	0.115122	−	0.199398i	0.0200402	−	0.0347107i
$34$		0			0
$35$	5.32580	−	0.392909i	0.900225	−	0.0664137i
$36$		0			0
$37$	0.714577	+	10.9023i	0.117476	+	1.79233i	0.497609	+	0.867401i	$0.334211\pi$
$37$	0.714577	+	10.9023i	0.117476	+	1.79233i	−0.380133	+	0.924932i	$0.624122\pi$
$38$		0			0
$39$	2.14150	+	6.30866i	0.342915	+	1.01019i
$40$		0			0
$41$	2.03703	+	10.2408i	0.318130	+	1.59935i	0.726922	+	0.686721i	$0.240950\pi$
$41$	2.03703	+	10.2408i	0.318130	+	1.59935i	−0.408791	+	0.912628i	$0.634050\pi$
$42$		0			0
$43$	−2.49747	+	6.02944i	−0.380861	+	0.919481i	0.610938	+	0.791678i	$0.290792\pi$
$43$	−2.49747	+	6.02944i	−0.380861	+	0.919481i	−0.991800	+	0.127802i	$0.959208\pi$
$44$		0			0
$45$	0.0874456	−	1.33416i	0.0130356	−	0.198885i
$46$		0			0
$47$	−3.19006	−	11.9055i	−0.465318	−	1.73659i	−0.655831	−	0.754907i	$-0.727682\pi$
$47$	−3.19006	−	11.9055i	−0.465318	−	1.73659i	0.190513	−	0.981685i	$-0.438985\pi$
$48$		0			0
$49$	−0.114672	−	6.99906i	−0.0163817	−	0.999866i
$50$		0			0
$51$	−1.07387	+	6.21175i	−0.150372	+	0.869820i
$52$		0			0
$53$	−2.93824	+	3.82919i	−0.403599	+	0.525980i	−0.950295	−	0.311351i	$-0.899219\pi$
$53$	−2.93824	+	3.82919i	−0.403599	+	0.525980i	0.546696	+	0.837331i	$0.315885\pi$
$54$		0			0
$55$	−0.214934	−	0.214934i	−0.0289817	−	0.0289817i
$56$		0			0
$57$	1.48935	+	0.995149i	0.197269	+	0.131811i
$58$		0			0
$59$	0.331680	−	0.0436665i	0.0431810	−	0.00568489i	−0.108905	−	0.994052i	$-0.534734\pi$
$59$	0.331680	−	0.0436665i	0.0431810	−	0.00568489i	0.152086	+	0.988367i	$0.451401\pi$
$60$		0			0
$61$	−3.80806	+	11.2182i	−0.487573	+	1.43634i	0.373390	+	0.927674i	$0.378195\pi$
$61$	−3.80806	+	11.2182i	−0.487573	+	1.43634i	−0.860963	+	0.508668i	$0.830138\pi$
$62$		0			0
$63$	−1.73939	−	0.214515i	−0.219142	−	0.0270264i
$64$		0			0
$65$	8.77645	−	0.575239i	1.08858	−	0.0713496i
$66$		0			0
$67$	2.48934	−	1.43722i	0.304122	−	0.175585i	−0.340171	−	0.940364i	$-0.610485\pi$
$67$	2.48934	−	1.43722i	0.304122	−	0.175585i	0.644293	+	0.764779i	$0.277152\pi$
$68$		0			0
$69$			8.55653i			1.03009i
$70$		0			0
$71$	8.90077	−	5.94731i	1.05633	−	0.705815i	0.0990781	−	0.995080i	$-0.468411\pi$
$71$	8.90077	−	5.94731i	1.05633	−	0.705815i	0.957249	+	0.289264i	$0.0934106\pi$
$72$		0			0
$73$	13.7879	−	4.68037i	1.61375	−	0.547796i	0.638641	−	0.769504i	$-0.279497\pi$
$73$	13.7879	−	4.68037i	1.61375	−	0.547796i	0.975113	+	0.221709i	$0.0711634\pi$
$74$		0			0
$75$	−1.34053	−	0.455047i	−0.154791	−	0.0525443i
$76$		0			0
$77$	−0.297395	+	0.265150i	−0.0338913	+	0.0302166i
$78$		0			0
$79$	3.27159	+	6.63413i	0.368083	+	0.746398i	0.999580	−	0.0289803i	$-0.00922600\pi$
$79$	3.27159	+	6.63413i	0.368083	+	0.746398i	−0.631497	+	0.775378i	$0.717559\pi$
$80$		0			0
$81$	1.70148	−	6.34999i	0.189053	−	0.705555i
$82$		0			0
$83$	−3.21226	−	7.75508i	−0.352591	−	0.851230i	−0.996299	−	0.0859587i	$-0.972605\pi$
$83$	−3.21226	−	7.75508i	−0.352591	−	0.851230i	0.643708	−	0.765272i	$-0.277395\pi$
$84$		0			0
$85$	7.55423	+	3.49185i	0.819371	+	0.378745i
$86$		0			0
$87$	−3.23731	−	2.48408i	−0.347076	−	0.266321i
$88$		0			0
$89$	−7.54220	+	2.02093i	−0.799472	+	0.214218i	−0.635352	−	0.772223i	$-0.719145\pi$
$89$	−7.54220	+	2.02093i	−0.799472	+	0.214218i	−0.164120	+	0.986440i	$0.552478\pi$
$90$		0			0
$91$	−0.0944340	−	11.5284i	−0.00989938	−	1.20851i
$92$		0			0
$93$	−4.13026	+	3.16926i	−0.428288	+	0.328637i
$94$		0			0
$95$	1.77789	−	1.55917i	0.182408	−	0.159967i
$96$		0			0
$97$	−19.2403	−	3.82713i	−1.95355	−	0.388586i	−0.994396	−	0.105718i	$-0.966286\pi$
$97$	−19.2403	−	3.82713i	−1.95355	−	0.388586i	−0.959159	−	0.282868i	$-0.908714\pi$
$98$		0			0
$99$	0.0554203	+	0.0829424i	0.00556995	+	0.00833602i
$100$		0			0
$101$	−5.59722	−	9.69467i	−0.556944	−	0.964656i	−0.997749	−	0.0670528i	$-0.978640\pi$
$101$	−5.59722	−	9.69467i	−0.556944	−	0.964656i	0.440805	−	0.897603i	$-0.354693\pi$
$102$		0			0
$103$	−15.9890	−	9.23128i	−1.57545	−	0.909585i	−0.995483	−	0.0949429i	$-0.969733\pi$
$103$	−15.9890	−	9.23128i	−1.57545	−	0.909585i	−0.579964	−	0.814642i	$-0.696934\pi$
$104$		0			0
$105$	3.06266	−	7.56868i	0.298885	−	0.738628i
$106$		0			0
$107$	3.87670	−	4.42053i	0.374775	−	0.427349i	−0.533450	−	0.845832i	$-0.679105\pi$
$107$	3.87670	−	4.42053i	0.374775	−	0.427349i	0.908225	+	0.418483i	$0.137438\pi$
$108$		0			0
$109$	10.0205	+	11.4262i	0.959788	+	1.09443i	0.995471	+	0.0950653i	$0.0303060\pi$
$109$	10.0205	+	11.4262i	0.959788	+	1.09443i	−0.0356830	+	0.999363i	$0.511361\pi$
$110$		0			0
$111$	15.4330	+	6.39256i	1.46484	+	0.606755i
$112$		0			0
$113$	−6.09088	+	9.11565i	−0.572982	+	0.857528i	−0.998884	−	0.0472413i	$-0.984957\pi$
$113$	−6.09088	+	9.11565i	−0.572982	+	0.857528i	0.425901	+	0.904770i	$0.359957\pi$
$114$		0			0
$115$	10.9112	+	2.92364i	1.01747	+	0.272631i
$116$		0			0
$117$	−2.86173	−	0.376753i	−0.264567	−	0.0348309i
$118$		0			0
$119$	5.13626	−	9.62387i	0.470840	−	0.882218i
$120$		0			0
$121$	−10.8834	−	1.43283i	−0.989401	−	0.130257i
$122$		0			0
$123$	15.4202	+	4.13182i	1.39039	+	0.372554i
$124$		0			0
$125$	−6.64522	+	9.94528i	−0.594367	+	0.889533i
$126$		0			0
$127$	−6.65922	−	2.75834i	−0.590910	−	0.244763i	0.0671322	−	0.997744i	$-0.478615\pi$
$127$	−6.65922	−	2.75834i	−0.590910	−	0.244763i	−0.658042	+	0.752981i	$0.728615\pi$
$128$		0			0
$129$	6.57899	+	7.50190i	0.579248	+	0.660505i
$130$		0			0
$131$	4.44636	−	5.07010i	0.388480	−	0.442977i	−0.524235	−	0.851574i	$-0.675648\pi$
$131$	4.44636	−	5.07010i	0.388480	−	0.442977i	0.912715	+	0.408597i	$0.133982\pi$
$132$		0			0
$133$	−1.90703	−	2.44358i	−0.165361	−	0.211886i
$134$		0			0
$135$	−9.78806	−	5.65114i	−0.842422	−	0.486373i
$136$		0			0
$137$	0.717716	+	1.24312i	0.0613187	+	0.106207i	0.895055	−	0.445956i	$-0.147136\pi$
$137$	0.717716	+	1.24312i	0.0613187	+	0.106207i	−0.833736	+	0.552163i	$0.813803\pi$
$138$		0			0
$139$	3.20809	+	4.80124i	0.272106	+	0.407236i	0.942205	−	0.335036i	$-0.108748\pi$
$139$	3.20809	+	4.80124i	0.272106	+	0.407236i	−0.670099	+	0.742272i	$0.733748\pi$
$140$		0			0
$141$	−18.4825	−	3.67640i	−1.55651	−	0.309609i
$142$		0			0
$143$	−0.493362	+	0.432667i	−0.0412570	+	0.0361814i
$144$		0			0
$145$	−4.27381	+	3.27941i	−0.354920	+	0.272340i
$146$		0			0
$147$	−9.67498	−	4.57569i	−0.797979	−	0.377396i
$148$		0			0
$149$	−2.11234	+	0.566000i	−0.173050	+	0.0463686i	−0.344303	−	0.938858i	$-0.611885\pi$
$149$	−2.11234	+	0.566000i	−0.173050	+	0.0463686i	0.171254	+	0.985227i	$0.445218\pi$
$150$		0			0
$151$	−10.5042	−	8.06018i	−0.854822	−	0.655928i	0.0854534	−	0.996342i	$-0.472766\pi$
$151$	−10.5042	−	8.06018i	−0.854822	−	0.655928i	−0.940276	+	0.340414i	$0.889433\pi$
$152$		0			0
$153$	−2.20793	−	1.60759i	−0.178501	−	0.129966i
$154$		0			0
$155$	2.63015	+	6.34974i	0.211259	+	0.510024i
$156$		0			0
$157$	−1.37225	+	5.12132i	−0.109518	+	0.408726i	−0.998818	−	0.0485972i	$-0.984525\pi$
$157$	−1.37225	+	5.12132i	−0.109518	+	0.408726i	0.889301	+	0.457323i	$0.151192\pi$
$158$		0			0
$159$	3.26385	+	6.61844i	0.258840	+	0.524876i
$160$		0			0
$161$	4.64449	−	14.0596i	0.366037	−	1.10805i
$162$		0			0
$163$	−8.12571	−	2.75831i	−0.636455	−	0.216047i	−0.0154830	−	0.999880i	$-0.504929\pi$
$163$	−8.12571	−	2.75831i	−0.636455	−	0.216047i	−0.620972	+	0.783833i	$0.713262\pi$
$164$		0			0
$165$	−0.440071	+	0.149384i	−0.0342595	+	0.0116295i
$166$		0			0
$167$	4.59233	−	3.06849i	0.355365	−	0.237447i	−0.365054	−	0.930986i	$-0.618950\pi$
$167$	4.59233	−	3.06849i	0.355365	−	0.237447i	0.720419	+	0.693539i	$0.243950\pi$
$168$		0			0
$169$		−	5.98759i		−	0.460583i
$170$		0			0
$171$	−0.672078	+	0.388025i	−0.0513951	+	0.0296730i
$172$		0			0
$173$	2.09830	−	0.137530i	0.159530	−	0.0104562i	0.0145714	−	0.999894i	$-0.495362\pi$
$173$	2.09830	−	0.137530i	0.159530	−	0.0104562i	0.144959	+	0.989438i	$0.453695\pi$
$174$		0			0
$175$	1.95567	+	1.47534i	0.147835	+	0.111525i
$176$		0			0
$177$	0.164412	−	0.484343i	0.0123580	−	0.0364054i
$178$		0			0
$179$	20.9579	−	2.75917i	1.56647	−	0.206230i	0.703208	−	0.710984i	$-0.251750\pi$
$179$	20.9579	−	2.75917i	1.56647	−	0.206230i	0.863263	+	0.504755i	$0.168417\pi$
$180$		0			0
$181$	−7.43847	−	4.97023i	−0.552897	−	0.369434i	0.247515	−	0.968884i	$-0.420386\pi$
$181$	−7.43847	−	4.97023i	−0.552897	−	0.369434i	−0.800412	+	0.599450i	$0.795386\pi$
$182$		0			0
$183$	12.8078	+	12.8078i	0.946780	+	0.946780i
$184$		0			0
$185$	13.4249	−	17.4957i	0.987021	−	1.28631i
$186$		0			0
$187$	−0.605740	+	0.136419i	−0.0442961	+	0.00997591i
$188$		0			0
$189$	−8.12957	+	12.3852i	−0.591339	+	0.900890i
$190$		0			0
$191$	4.28149	+	15.9787i	0.309798	+	1.15618i	0.928736	+	0.370741i	$0.120896\pi$
$191$	4.28149	+	15.9787i	0.309798	+	1.15618i	−0.618939	+	0.785439i	$0.712437\pi$
$192$		0			0
$193$	−0.544167	+	8.30239i	−0.0391700	+	0.597619i	0.932484	+	0.361211i	$0.117637\pi$
$193$	−0.544167	+	8.30239i	−0.0391700	+	0.597619i	−0.971654	+	0.236408i	$0.924030\pi$
$194$		0			0
$195$	5.14605	−	12.4237i	0.368516	−	0.889677i
$196$		0			0
$197$	−1.59412	−	8.01421i	−0.113577	−	0.570989i	−0.995102	−	0.0988521i	$-0.968483\pi$
$197$	−1.59412	−	8.01421i	−0.113577	−	0.570989i	0.881525	−	0.472137i	$-0.156517\pi$
$198$		0			0
$199$	−5.15241	−	15.1785i	−0.365244	−	1.07598i	−0.961882	−	0.273465i	$-0.911830\pi$
$199$	−5.15241	−	15.1785i	−0.365244	−	1.07598i	0.596638	−	0.802511i	$-0.296503\pi$
$200$		0			0
$201$	−0.287433	−	4.38539i	−0.0202740	−	0.309321i
$202$		0			0
$203$	3.97099	+	5.83890i	0.278709	+	0.409810i
$204$		0			0
$205$	10.5377	−	18.2518i	0.735985	−	1.27476i
$206$		0			0
$207$	−3.32482	−	1.63962i	−0.231091	−	0.113962i
$208$		0			0
$209$	−0.0344196	+	0.173039i	−0.00238085	+	0.0119694i
$210$		0			0
$211$	−17.8656	+	3.55369i	−1.22992	+	0.244646i	−0.766938	−	0.641721i	$-0.778221\pi$
$211$	−17.8656	+	3.55369i	−1.22992	+	0.244646i	−0.462982	+	0.886368i	$0.653221\pi$
$212$		0			0
$213$	−2.13631	−	16.2269i	−0.146377	−	1.11185i
$214$		0			0
$215$	11.8143	−	5.82616i	0.805727	−	0.397341i
$216$		0			0
$217$	8.50685	−	2.96562i	0.577483	−	0.201319i
$218$		0			0
$219$	2.90578	−	22.0716i	0.196355	−	1.49146i
$220$		0			0
$221$	8.58882	−	15.7804i	0.577747	−	1.06150i
$222$		0			0
$223$	−4.27659	+	1.77142i	−0.286382	+	0.118623i	−0.521250	−	0.853404i	$-0.674534\pi$
$223$	−4.27659	+	1.77142i	−0.286382	+	0.118623i	0.234868	+	0.972027i	$0.424534\pi$
$224$		0			0
$225$	0.433693	−	0.433693i	0.0289129	−	0.0289129i
$226$		0			0
$227$	−11.1238	−	0.729092i	−0.738312	−	0.0483915i	−0.308393	−	0.951259i	$-0.599791\pi$
$227$	−11.1238	−	0.729092i	−0.738312	−	0.0483915i	−0.429919	+	0.902868i	$0.641458\pi$
$228$		0			0
$229$	3.05683	+	3.98374i	0.202001	+	0.263253i	0.883359	−	0.468698i	$-0.155277\pi$
$229$	3.05683	+	3.98374i	0.202001	+	0.263253i	−0.681357	+	0.731951i	$0.738610\pi$
$230$		0			0
$231$	0.162479	+	0.587102i	0.0106904	+	0.0386285i
$232$		0			0
$233$	18.4542	+	16.1839i	1.20897	+	1.06024i	0.996544	+	0.0830650i	$0.0264709\pi$
$233$	18.4542	+	16.1839i	1.20897	+	1.06024i	0.212429	+	0.977176i	$0.431862\pi$
$234$		0			0
$235$	−11.0033	+	22.3125i	−0.717777	+	1.45551i
$236$		0			0
$237$	11.3093			0.734621
$238$		0			0
$239$	14.2607			0.922450			0.461225	−	0.887283i	$-0.347410\pi$
$239$	14.2607			0.922450			0.461225	+	0.887283i	$0.347410\pi$
$240$		0			0
$241$	6.68447	−	13.5548i	0.430585	−	0.873140i	−0.568154	−	0.822923i	$-0.692342\pi$
$241$	6.68447	−	13.5548i	0.430585	−	0.873140i	0.998738	−	0.0502170i	$-0.0159913\pi$
$242$		0			0
$243$	5.07301	+	4.44891i	0.325434	+	0.285398i
$244$		0			0
$245$	−9.14066	+	10.7740i	−0.583975	+	0.688324i
$246$		0			0
$247$	−3.10775	−	4.05010i	−0.197742	−	0.257702i
$248$		0			0
$249$	−12.8063	−	0.839371i	−0.811568	−	0.0531930i
$250$		0			0
$251$	0.340239	−	0.340239i	0.0214757	−	0.0214757i	−0.696287	−	0.717763i	$-0.745166\pi$
$251$	0.340239	−	0.340239i	0.0214757	−	0.0214757i	0.717763	+	0.696287i	$0.245166\pi$
$252$		0			0
$253$	−0.778635	+	0.322521i	−0.0489524	+	0.0202767i
$254$		0			0
$255$	9.89654	−	7.99743i	0.619745	−	0.500818i
$256$		0			0
$257$	1.26710	−	9.62458i	0.0790395	−	0.600365i	−0.905389	−	0.424582i	$-0.860421\pi$
$257$	1.26710	−	9.62458i	0.0790395	−	0.600365i	0.984429	−	0.175783i	$-0.0562456\pi$
$258$		0			0
$259$	−21.8886	−	18.8809i	−1.36009	−	1.17320i
$260$		0			0
$261$	1.58558	−	0.781923i	0.0981451	−	0.0483998i
$262$		0			0
$263$	0.0316220	+	0.240193i	0.00194990	+	0.0148109i	0.992392	−	0.123117i	$-0.0392891\pi$
$263$	0.0316220	+	0.240193i	0.00194990	+	0.0148109i	−0.990442	+	0.137928i	$0.955956\pi$
$264$		0			0
$265$	9.55497	−	1.90060i	0.586957	−	0.116753i
$266$		0			0
$267$	−2.32903	+	11.7088i	−0.142534	+	0.716567i
$268$		0			0
$269$	12.9201	+	6.37148i	0.787751	+	0.388476i	0.791230	−	0.611518i	$-0.209441\pi$
$269$	12.9201	+	6.37148i	0.787751	+	0.388476i	−0.00347936	+	0.999994i	$0.501108\pi$
$270$		0			0
$271$	−8.96543	+	15.5286i	−0.544611	+	0.943294i	0.454020	+	0.890991i	$0.349989\pi$
$271$	−8.96543	+	15.5286i	−0.544611	+	0.943294i	−0.998631	+	0.0523024i	$0.983344\pi$
$272$		0			0
$273$	−15.8721	−	7.66629i	−0.960626	−	0.463985i
$274$		0			0
$275$	−0.00911961	−	0.139138i	−0.000549933	−	0.00839036i
$276$		0			0
$277$	−2.88348	−	8.49446i	−0.173252	−	0.510382i	0.825270	−	0.564738i	$-0.191023\pi$
$277$	−2.88348	−	8.49446i	−0.173252	−	0.510382i	−0.998522	+	0.0543557i	$0.982690\pi$
$278$		0			0
$279$	−0.440034	−	2.21220i	−0.0263442	−	0.132441i
$280$		0			0
$281$	1.49391	−	3.60662i	0.0891193	−	0.215153i	−0.873035	−	0.487657i	$-0.837852\pi$
$281$	1.49391	−	3.60662i	0.0891193	−	0.215153i	0.962155	+	0.272504i	$0.0878517\pi$
$282$		0			0
$283$	−0.0768909	+	1.17313i	−0.00457069	+	0.0697352i	−0.999535	−	0.0304956i	$-0.990291\pi$
$283$	−0.0768909	+	1.17313i	−0.00457069	+	0.0697352i	0.994964	+	0.100231i	$0.0319581\pi$
$284$		0			0
$285$	−0.935751	−	3.49227i	−0.0554291	−	0.206864i
$286$		0			0
$287$	−23.0947	−	15.1592i	−1.36324	−	0.894822i
$288$		0			0
$289$	14.2762	−	9.22989i	0.839775	−	0.542935i
$290$		0			0
$291$	−18.2587	+	23.7952i	−1.07034	+	1.39490i
$292$		0			0
$293$	2.52125	+	2.52125i	0.147293	+	0.147293i	0.776908	−	0.629615i	$-0.216787\pi$
$293$	2.52125	+	2.52125i	0.147293	+	0.147293i	−0.629615	+	0.776908i	$0.716787\pi$
$294$		0			0
$295$	−0.561451	−	0.375149i	−0.0326889	−	0.0218420i
$296$		0			0
$297$	0.836036	−	0.110066i	0.0485117	−	0.00638669i
$298$		0			0
$299$	7.83876	−	23.0922i	0.453327	−	1.33546i
$300$		0			0
$301$	−6.73814	−	15.8977i	−0.388380	−	0.916330i
$302$		0			0
$303$	−17.0787	+	1.11940i	−0.981148	+	0.0643079i
$304$		0			0
$305$	20.7086	−	11.9561i	1.18577	−	0.684605i
$306$		0			0
$307$		−	5.45699i		−	0.311447i	−0.987801	−	0.155723i	$-0.950229\pi$
$307$		−	5.45699i		−	0.311447i	0.987801	−	0.155723i	$-0.0497708\pi$
$308$		0			0
$309$	−23.4705	+	15.6825i	−1.33519	+	0.892146i
$310$		0			0
$311$	26.7027	−	9.06436i	1.51417	−	0.513992i	0.564016	−	0.825764i	$-0.309256\pi$
$311$	26.7027	−	9.06436i	1.51417	−	0.513992i	0.950157	+	0.311772i	$0.100922\pi$
$312$		0			0
$313$	16.6856	+	5.66399i	0.943124	+	0.320148i	0.750309	−	0.661087i	$-0.229905\pi$
$313$	16.6856	+	5.66399i	0.943124	+	0.320148i	0.192816	+	0.981235i	$0.438238\pi$
$314$		0			0
$315$	2.35410	+	2.64039i	0.132639	+	0.148769i
$316$		0			0
$317$	2.77367	+	5.62444i	0.155785	+	0.315900i	0.960747	−	0.277426i	$-0.0894813\pi$
$317$	2.77367	+	5.62444i	0.155785	+	0.315900i	−0.804962	+	0.593326i	$0.797815\pi$
$318$		0			0
$319$	0.104024	−	0.388224i	0.00582425	−	0.0217364i
$320$		0			0
$321$	−3.44012	−	8.30517i	−0.192009	−	0.463550i
$322$		0			0
$323$	−0.750806	−	4.77176i	−0.0417760	−	0.265508i
$324$		0			0
$325$	3.20091	+	2.45615i	0.177555	+	0.136243i
$326$		0			0
$327$	22.4442	−	6.01390i	1.24117	−	0.332569i
$328$		0			0
$329$	28.3738	+	16.0732i	1.56430	+	0.886143i
$330$		0			0
$331$	−3.87963	+	2.97695i	−0.213244	+	0.163628i	−0.709861	−	0.704342i	$-0.751242\pi$
$331$	−3.87963	+	2.97695i	−0.213244	+	0.163628i	0.496617	+	0.867970i	$0.334575\pi$
$332$		0			0
$333$	−5.44127	+	4.77187i	−0.298180	+	0.261497i
$334$		0			0
$335$	−5.69040	−	1.13189i	−0.310900	−	0.0618419i
$336$		0			0
$337$	−3.88152	−	5.80910i	−0.211440	−	0.316442i	0.710557	−	0.703640i	$-0.248443\pi$
$337$	−3.88152	−	5.80910i	−0.211440	−	0.316442i	−0.921997	+	0.387198i	$0.873443\pi$
$338$		0			0
$339$	8.38100	+	14.5163i	0.455193	+	0.788418i
$340$		0			0
$341$	−0.444081	−	0.256390i	−0.0240483	−	0.0138843i
$342$		0			0
$343$	13.4136	+	12.7701i	0.724268	+	0.689519i
$344$		0			0
$345$	11.3874	−	12.9849i	0.613079	−	0.699082i
$346$		0			0
$347$	17.6816	+	20.1620i	0.949198	+	1.08235i	0.996510	+	0.0834729i	$0.0266012\pi$
$347$	17.6816	+	20.1620i	0.949198	+	1.08235i	−0.0473119	+	0.998880i	$0.515065\pi$
$348$		0			0
$349$	11.2136	+	4.64482i	0.600250	+	0.248632i	0.662053	−	0.749457i	$-0.269685\pi$
$349$	11.2136	+	4.64482i	0.600250	+	0.248632i	−0.0618036	+	0.998088i	$0.519685\pi$
$350$		0			0
$351$	−13.5558	+	20.2877i	−0.723555	+	1.08288i
$352$		0			0
$353$	−16.4320	−	4.40293i	−0.874585	−	0.234344i	−0.206516	−	0.978443i	$-0.566212\pi$
$353$	−16.4320	−	4.40293i	−0.874585	−	0.234344i	−0.668070	+	0.744099i	$0.732879\pi$
$354$		0			0
$355$	−21.4222	−	2.82029i	−1.13697	−	0.149685i
$356$		0			0
$357$	−9.72342	−	13.5510i	−0.514618	−	0.717193i
$358$		0			0
$359$	−28.2214	−	3.71542i	−1.48947	−	0.196092i	−0.658572	−	0.752518i	$-0.728839\pi$
$359$	−28.2214	−	3.71542i	−1.48947	−	0.196092i	−0.830898	+	0.556425i	$0.812173\pi$
$360$		0			0
$361$	17.0268	+	4.56232i	0.896148	+	0.240122i
$362$		0			0
$363$	−9.32438	+	13.9549i	−0.489403	+	0.732443i
$364$		0			0
$365$	−27.1526	−	11.2470i	−1.42123	−	0.588693i
$366$		0			0
$367$	5.32951	+	6.07715i	0.278198	+	0.317224i	0.874018	−	0.485894i	$-0.161506\pi$
$367$	5.32951	+	6.07715i	0.278198	+	0.317224i	−0.595819	+	0.803119i	$0.703173\pi$
$368$		0			0
$369$	−4.56036	+	5.20009i	−0.237403	+	0.270706i
$370$		0			0
$371$	−1.77046	−	12.6466i	−0.0919179	−	0.656580i
$372$		0			0
$373$	19.9742	+	11.5321i	1.03422	+	0.597110i	0.918192	−	0.396135i	$-0.129649\pi$
$373$	19.9742	+	11.5321i	1.03422	+	0.597110i	0.116033	+	0.993245i	$0.462982\pi$
$374$		0			0
$375$	9.14376	+	15.8375i	0.472182	+	0.817843i
$376$		0			0
$377$	6.46111	+	9.66974i	0.332764	+	0.498017i
$378$		0			0
$379$	3.44973	+	0.686195i	0.177201	+	0.0352475i	0.282893	−	0.959151i	$-0.408706\pi$
$379$	3.44973	+	0.686195i	0.177201	+	0.0352475i	−0.105692	+	0.994399i	$0.533706\pi$
$380$		0			0
$381$	−8.28548	+	7.26617i	−0.424478	+	0.372257i
$382$		0			0
$383$	−20.7537	+	15.9248i	−1.06046	+	0.813721i	−0.983061	−	0.183279i	$-0.941329\pi$
$383$	−20.7537	+	15.9248i	−1.06046	+	0.813721i	−0.0774013	+	0.997000i	$0.524662\pi$
$384$		0			0
$385$	0.804183	−	0.00658740i	0.0409849	−	0.000335725i
$386$		0			0
$387$	−4.17571	+	1.11888i	−0.212263	+	0.0568757i
$388$		0			0
$389$	25.6985	+	19.7192i	1.30297	+	0.999801i	0.998888	+	0.0471539i	$0.0150151\pi$
$389$	25.6985	+	19.7192i	1.30297	+	0.999801i	0.304078	+	0.952647i	$0.401652\pi$
$390$		0			0
$391$	16.9602	−	15.6460i	0.857716	−	0.791250i
$392$		0			0
$393$	−3.94562	−	9.52558i	−0.199030	−	0.480502i
$394$		0			0
$395$	3.86424	−	14.4215i	0.194431	−	0.725627i
$396$		0			0
$397$	8.60861	+	17.4565i	0.432054	+	0.876118i	0.998641	+	0.0521166i	$0.0165967\pi$
$397$	8.60861	+	17.4565i	0.432054	+	0.876118i	−0.566587	+	0.824002i	$0.691737\pi$
$398$		0			0
$399$	−4.64033	+	0.962599i	−0.232307	+	0.0481902i
$400$		0			0
$401$	−6.09357	−	2.06849i	−0.304298	−	0.103295i	0.165114	−	0.986275i	$-0.447201\pi$
$401$	−6.09357	−	2.06849i	−0.304298	−	0.103295i	−0.469412	+	0.882979i	$0.655534\pi$
$402$		0			0
$403$	14.0501	−	4.76936i	0.699884	−	0.237579i
$404$		0			0
$405$	−11.0329	+	7.37197i	−0.548231	+	0.366316i
$406$		0			0
$407$			1.64534i			0.0815565i
$408$		0			0
$409$	1.95406	−	1.12817i	0.0966218	−	0.0557846i	−0.450910	−	0.892569i	$-0.648901\pi$
$409$	1.95406	−	1.12817i	0.0966218	−	0.0557846i	0.547532	+	0.836785i	$0.315567\pi$
$410$		0			0
$411$	2.18996	−	0.143538i	0.108023	−	0.00708019i
$412$		0			0
$413$	−0.533054	+	0.706599i	−0.0262299	+	0.0347694i
$414$		0			0
$415$	−5.44609	+	16.0437i	−0.267338	+	0.787553i
$416$		0			0
$417$	8.75307	−	1.15236i	0.428639	−	0.0564315i
$418$		0			0
$419$	13.8163	+	9.23178i	0.674972	+	0.451002i	0.845234	−	0.534397i	$-0.179461\pi$
$419$	13.8163	+	9.23178i	0.674972	+	0.451002i	−0.170262	+	0.985399i	$0.554461\pi$
$420$		0			0
$421$	−22.2012	−	22.2012i	−1.08202	−	1.08202i	−0.996321	−	0.0857016i	$-0.972687\pi$
$421$	−22.2012	−	22.2012i	−1.08202	−	1.08202i	−0.0857016	−	0.996321i	$-0.527313\pi$
$422$		0			0
$423$	4.97021	−	6.47730i	0.241660	−	0.314937i
$424$		0			0
$425$	1.54924	+	3.48918i	0.0751491	+	0.169250i
$426$		0			0
$427$	−14.0929	−	27.9971i	−0.682002	−	1.35487i
$428$		0			0
$429$	0.259670	+	0.969100i	0.0125370	+	0.0467886i
$430$		0			0
$431$	1.25839	−	19.1993i	0.0606143	−	0.924796i	−0.853950	−	0.520355i	$-0.825800\pi$
$431$	1.25839	−	19.1993i	0.0606143	−	0.924796i	0.914564	−	0.404440i	$-0.132534\pi$
$432$		0			0
$433$	−5.73803	+	13.8528i	−0.275752	+	0.665724i	−0.999709	−	0.0241207i	$-0.992321\pi$
$433$	−5.73803	+	13.8528i	−0.275752	+	0.665724i	0.723957	+	0.689845i	$0.242321\pi$
$434$		0			0
$435$	1.60682	+	8.07805i	0.0770414	+	0.387313i
$436$		0			0
$437$	−2.10755	−	6.20863i	−0.100818	−	0.296999i
$438$		0			0
$439$	1.53055	+	23.3517i	0.0730491	+	1.11451i	0.864285	+	0.503003i	$0.167771\pi$
$439$	1.53055	+	23.3517i	0.0730491	+	1.11451i	−0.791236	+	0.611511i	$0.790562\pi$
$440$		0			0
$441$	3.63192	−	2.88262i	0.172949	−	0.137268i
$442$		0			0
$443$	−14.3352	+	24.8294i	−0.681088	+	1.17968i	0.293561	+	0.955940i	$0.405160\pi$
$443$	−14.3352	+	24.8294i	−0.681088	+	1.17968i	−0.974649	+	0.223739i	$0.928174\pi$
$444$		0			0
$445$	14.1351	+	6.97068i	0.670070	+	0.330442i
$446$		0			0
$447$	−0.652290	+	3.27928i	−0.0308523	+	0.155105i
$448$		0			0
$449$	−2.71151	+	0.539353i	−0.127964	+	0.0254537i	−0.258657	−	0.965969i	$-0.583280\pi$
$449$	−2.71151	+	0.539353i	−0.127964	+	0.0254537i	0.130693	+	0.991423i	$0.458280\pi$
$450$		0			0
$451$	0.205241	+	1.55896i	0.00966442	+	0.0734086i
$452$		0			0
$453$	−18.1557	+	8.95340i	−0.853029	+	0.420667i
$454$		0			0
$455$	−15.1992	+	17.6205i	−0.712551	+	0.826062i
$456$		0			0
$457$	0.835027	−	6.34266i	0.0390609	−	0.296697i	−0.960753	−	0.277405i	$-0.910526\pi$
$457$	0.835027	−	6.34266i	0.0390609	−	0.296697i	0.999814	−	0.0192918i	$-0.00614116\pi$
$458$		0			0
$459$	−20.4430	+	10.7291i	−0.954197	+	0.500791i
$460$		0			0
$461$	−18.9108	+	7.83313i	−0.880766	+	0.364825i	−0.776794	−	0.629755i	$-0.783155\pi$
$461$	−18.9108	+	7.83313i	−0.880766	+	0.364825i	−0.103972	+	0.994580i	$0.533155\pi$
$462$		0			0
$463$	−3.60403	+	3.60403i	−0.167493	+	0.167493i	−0.785877	−	0.618383i	$-0.787788\pi$
$463$	−3.60403	+	3.60403i	−0.167493	+	0.167493i	0.618383	+	0.785877i	$0.287788\pi$
$464$		0			0
$465$	10.4856	+	0.687264i	0.486259	+	0.0318711i
$466$		0			0
$467$	7.47719	+	9.74446i	0.346003	+	0.450920i	0.933644	−	0.358202i	$-0.116610\pi$
$467$	7.47719	+	9.74446i	0.346003	+	0.450920i	−0.587641	+	0.809122i	$0.699943\pi$
$468$		0			0
$469$	−1.90810	+	7.36181i	−0.0881079	+	0.339937i
$470$		0			0
$471$	6.09464	+	5.34485i	0.280826	+	0.246278i
$472$		0			0
$473$	−0.434683	+	0.881450i	−0.0199867	+	0.0405291i
$474$		0			0
$475$	1.08477			0.0497726
$476$		0			0
$477$	−3.19717			−0.146388
$478$		0			0
$479$	−9.06902	+	18.3902i	−0.414374	+	0.840268i	0.585194	+	0.810893i	$0.301018\pi$
$479$	−9.06902	+	18.3902i	−0.414374	+	0.840268i	−0.999568	+	0.0293745i	$0.990648\pi$
$480$		0			0
$481$	−35.7940	−	31.3905i	−1.63207	−	1.43128i
$482$		0			0
$483$	−16.1384	−	15.8761i	−0.734322	−	0.722389i
$484$		0			0
$485$	24.1046	+	31.4137i	1.09453	+	1.42642i
$486$		0			0
$487$	9.81941	+	0.643598i	0.444960	+	0.0291642i	0.286237	−	0.958159i	$-0.407596\pi$
$487$	9.81941	+	0.643598i	0.444960	+	0.0291642i	0.158723	+	0.987323i	$0.449262\pi$
$488$		0			0
$489$	−9.27712	+	9.27712i	−0.419526	+	0.419526i
$490$		0			0
$491$	−12.2643	+	5.08005i	−0.553481	+	0.229259i	−0.641852	−	0.766828i	$-0.721834\pi$
$491$	−12.2643	+	5.08005i	−0.553481	+	0.229259i	0.0883712	+	0.996088i	$0.471834\pi$
$492$		0			0
$493$	0.995772	+	10.9590i	0.0448473	+	0.493570i
$494$		0			0
$495$	0.0262810	−	0.199624i	0.00118125	−	0.00897245i
$496$		0			0
$497$	−5.29771	+	27.8225i	−0.237635	+	1.24801i
$498$		0			0
$499$	−32.7455	+	16.1483i	−1.46589	+	0.722897i	−0.987846	−	0.155438i	$-0.950321\pi$
$499$	−32.7455	+	16.1483i	−1.46589	+	0.722897i	−0.478045	+	0.878336i	$0.658654\pi$
$500$		0			0
$501$	−1.10222	−	8.37219i	−0.0492436	−	0.374042i
$502$		0			0
$503$	31.8541	−	6.33618i	1.42031	−	0.282516i	0.575593	−	0.817736i	$-0.304771\pi$
$503$	31.8541	−	6.33618i	1.42031	−	0.282516i	0.844713	+	0.535220i	$0.179771\pi$
$504$		0			0
$505$	−4.40812	+	22.1611i	−0.196159	+	0.986156i
$506$		0			0
$507$	−8.21045	−	4.04895i	−0.364639	−	0.179820i
$508$		0			0
$509$	21.9032	−	37.9375i	0.970844	−	1.68155i	0.277826	−	0.960631i	$-0.410386\pi$
$509$	21.9032	−	37.9375i	0.970844	−	1.68155i	0.693018	−	0.720920i	$-0.256281\pi$
$510$		0			0
$511$	−16.7551	+	34.6894i	−0.741202	+	1.53457i
$512$		0			0
$513$	0.429056	+	6.54613i	0.0189433	+	0.289019i
$514$		0			0
$515$	11.9786	+	35.2878i	0.527840	+	1.55497i
$516$		0			0
$517$	−0.362113	−	1.82046i	−0.0159257	−	0.0800640i
$518$		0			0
$519$	1.23033	−	2.97028i	0.0540055	−	0.130381i
$520$		0			0
$521$	1.64357	−	25.0760i	0.0720059	−	1.09860i	−0.797059	−	0.603901i	$-0.793612\pi$
$521$	1.64357	−	25.0760i	0.0720059	−	1.09860i	0.869065	−	0.494697i	$-0.164721\pi$
$522$		0			0
$523$	10.0589	+	37.5405i	0.439847	+	1.64153i	0.729194	+	0.684307i	$0.239895\pi$
$523$	10.0589	+	37.5405i	0.439847	+	1.64153i	−0.289347	+	0.957224i	$0.593438\pi$
$524$		0			0
$525$	3.34553	−	1.68404i	0.146011	−	0.0734974i
$526$		0			0
$527$	13.8343	+	2.39163i	0.602629	+	0.104181i
$528$		0			0
$529$	5.06510	−	6.60096i	0.220222	−	0.286998i
$530$		0			0
$531$	0.156697	+	0.156697i	0.00680006	+	0.00680006i
$532$		0			0
$533$	−37.8305	−	25.2775i	−1.63862	−	1.09489i
$534$		0			0
$535$	−11.7661	+	1.54904i	−0.508693	+	0.0669706i
$536$		0			0
$537$	10.3888	−	30.6043i	0.448308	−	1.32067i
$538$		0			0
$539$	0.0517037	−	1.05288i	0.00222704	−	0.0453509i
$540$		0			0
$541$	−40.3469	+	2.64448i	−1.73465	+	0.113695i	−0.899666	−	0.436580i	$-0.856190\pi$
$541$	−40.3469	+	2.64448i	−1.73465	+	0.113695i	−0.834984	+	0.550275i	$0.814523\pi$
$542$		0			0
$543$	−11.8455	+	6.83898i	−0.508338	+	0.293489i
$544$		0			0
$545$		−	30.6754i		−	1.31399i
$546$		0			0
$547$	−17.0416	+	11.3868i	−0.728645	+	0.486865i	−0.863721	−	0.503970i	$-0.831872\pi$
$547$	−17.0416	+	11.3868i	−0.728645	+	0.486865i	0.135076	+	0.990835i	$0.456872\pi$
$548$		0			0
$549$	−7.43101	+	2.52249i	−0.317148	+	0.107657i
$550$		0			0
$551$	2.96085	+	1.00507i	0.126136	+	0.0428175i
$552$		0			0
$553$	−18.5828	−	6.13872i	−0.790221	−	0.261045i
$554$		0			0
$555$	−14.9127	−	30.2399i	−0.633008	−	1.28361i
$556$		0			0
$557$	−7.01242	+	26.1707i	−0.297126	+	1.10889i	0.642389	+	0.766379i	$0.277943\pi$
$557$	−7.01242	+	26.1707i	−0.297126	+	1.10889i	−0.939514	+	0.342509i	$0.888723\pi$
$558$		0			0
$559$	−10.8827	−	26.2731i	−0.460288	−	1.11123i
$560$		0			0
$561$	−0.222553	+	0.922868i	−0.00939618	+	0.0389635i
$562$		0			0
$563$	2.14666	+	1.64719i	0.0904707	+	0.0694206i	0.653006	−	0.757352i	$-0.273507\pi$
$563$	2.14666	+	1.64719i	0.0904707	+	0.0694206i	−0.562536	+	0.826773i	$0.690174\pi$
$564$		0			0
$565$	21.3747	−	5.72733i	0.899240	−	0.240951i
$566$		0			0
$567$	8.81967	+	14.9912i	0.370391	+	0.629570i
$568$		0			0
$569$	24.4632	−	18.7713i	1.02555	−	0.786934i	0.0482614	−	0.998835i	$-0.484632\pi$
$569$	24.4632	−	18.7713i	1.02555	−	0.786934i	0.977291	+	0.211900i	$0.0679653\pi$
$570$		0			0
$571$	29.2415	−	25.6441i	1.22372	−	1.07317i	0.228699	−	0.973497i	$-0.426553\pi$
$571$	29.2415	−	25.6441i	1.22372	−	1.07317i	0.995020	−	0.0996756i	$-0.0317805\pi$
$572$		0			0
$573$	24.8060	+	4.93422i	1.03629	+	0.206130i
$574$		0			0
$575$	2.87889	+	4.30856i	0.120058	+	0.179679i
$576$		0			0
$577$	3.89672	+	6.74931i	0.162223	+	0.280978i	0.935665	−	0.352888i	$-0.114800\pi$
$577$	3.89672	+	6.74931i	0.162223	+	0.280978i	−0.773443	+	0.633866i	$0.781467\pi$
$578$		0			0
$579$	11.0166	+	6.36046i	0.457836	+	0.264332i
$580$		0			0
$581$	20.5869	+	8.33048i	0.854090	+	0.345607i
$582$		0			0
$583$	−0.479247	+	0.546476i	−0.0198484	+	0.0226327i
$584$		0			0
$585$	3.84138	+	4.38026i	0.158822	+	0.181101i
$586$		0			0
$587$	−8.00066	−	3.31398i	−0.330223	−	0.136783i	0.211411	−	0.977397i	$-0.432194\pi$
$587$	−8.00066	−	3.31398i	−0.330223	−	0.136783i	−0.541634	+	0.840615i	$0.682194\pi$
$588$		0			0
$589$	2.21630	−	3.31693i	0.0913212	−	0.136672i
$590$		0			0
$591$	−12.0674	−	3.23346i	−0.496388	−	0.133007i
$592$		0			0
$593$	−27.2774	−	3.59114i	−1.12015	−	0.147470i	−0.452370	−	0.891830i	$-0.649421\pi$
$593$	−27.2774	−	3.59114i	−1.12015	−	0.147470i	−0.667779	+	0.744360i	$0.732755\pi$
$594$		0			0
$595$	−20.6024	+	7.76903i	−0.844615	+	0.318499i
$596$		0			0
$597$	−24.2976	−	3.19884i	−0.994436	−	0.130920i
$598$		0			0
$599$	12.5772	+	3.37004i	0.513889	+	0.137696i	0.506438	−	0.862276i	$-0.330962\pi$
$599$	12.5772	+	3.37004i	0.513889	+	0.137696i	0.00745047	+	0.999972i	$0.497628\pi$
$600$		0			0
$601$	−20.5102	+	30.6957i	−0.836629	+	1.25210i	0.128861	+	0.991663i	$0.458868\pi$
$601$	−20.5102	+	30.6957i	−0.836629	+	1.25210i	−0.965490	+	0.260441i	$0.916132\pi$
$602$		0			0
$603$	1.75912	+	0.728650i	0.0716367	+	0.0296729i
$604$		0			0
$605$	14.6091	+	16.6585i	0.593946	+	0.677265i
$606$		0			0
$607$	5.41245	−	6.17172i	0.219685	−	0.250502i	−0.631491	−	0.775383i	$-0.717557\pi$
$607$	5.41245	−	6.17172i	0.219685	−	0.250502i	0.851176	+	0.524881i	$0.175890\pi$
$608$		0			0
$609$	10.6918	−	1.49680i	0.433255	−	0.0606535i
$610$		0			0
$611$	46.5124	+	26.8539i	1.88169	+	1.08639i
$612$		0			0
$613$	−3.66172	−	6.34229i	−0.147896	−	0.256163i	0.782554	−	0.622583i	$-0.213917\pi$
$613$	−3.66172	−	6.34229i	−0.147896	−	0.256163i	−0.930450	+	0.366420i	$0.880583\pi$
$614$		0			0
$615$	−17.9019	−	26.7921i	−0.721875	−	1.08036i
$616$		0			0
$617$	−12.2532	−	2.43731i	−0.493295	−	0.0981225i	−0.0578268	−	0.998327i	$-0.518417\pi$
$617$	−12.2532	−	2.43731i	−0.493295	−	0.0981225i	−0.435468	+	0.900204i	$0.643417\pi$
$618$		0			0
$619$	36.0802	−	31.6415i	1.45019	−	1.27178i	0.550789	−	0.834644i	$-0.314327\pi$
$619$	36.0802	−	31.6415i	1.45019	−	1.27178i	0.899396	−	0.437134i	$-0.144007\pi$
$620$		0			0
$621$	−24.8617	+	19.0771i	−0.997666	+	0.765536i
$622$		0			0
$623$	10.1825	−	17.9750i	0.407952	−	0.720152i
$624$		0			0
$625$	18.8482	−	5.05036i	0.753928	−	0.202014i
$626$		0			0
$627$	0.214004	+	0.164211i	0.00854648	+	0.00655795i
$628$		0			0
$629$	−15.5489	−	42.2794i	−0.619977	−	1.68579i
$630$		0			0
$631$	16.5973	+	40.0693i	0.660727	+	1.59514i	0.796667	+	0.604418i	$0.206594\pi$
$631$	16.5973	+	40.0693i	0.660727	+	1.59514i	−0.135940	+	0.990717i	$0.543406\pi$
$632$		0			0
$633$	−7.20817	+	26.9012i	−0.286499	+	1.06923i
$634$		0			0
$635$	6.43470	+	13.0483i	0.255353	+	0.517805i
$636$		0			0
$637$	21.9188	+	21.2122i	0.868456	+	0.840457i
$638$		0			0
$639$	6.71466	+	2.27932i	0.265628	+	0.0901685i
$640$		0			0
$641$	−18.6854	+	6.34282i	−0.738027	+	0.250527i	−0.665041	−	0.746806i	$-0.731586\pi$
$641$	−18.6854	+	6.34282i	−0.738027	+	0.250527i	−0.0729859	+	0.997333i	$0.523253\pi$
$642$		0			0
$643$	−13.8431	+	9.24968i	−0.545920	+	0.364772i	−0.797739	−	0.603002i	$-0.793971\pi$
$643$	−13.8431	+	9.24968i	−0.545920	+	0.364772i	0.251820	+	0.967774i	$0.418971\pi$
$644$		0			0
$645$		−	20.1401i		−	0.793014i
$646$		0			0
$647$	2.58347	−	1.49157i	0.101567	−	0.0586395i	−0.448356	−	0.893855i	$-0.647990\pi$
$647$	2.58347	−	1.49157i	0.101567	−	0.0586395i	0.549923	+	0.835215i	$0.314657\pi$
$648$		0			0
$649$	0.0502719	−	0.00329499i	0.00197334	−	0.000129340i
$650$		0			0
$651$	1.68595	−	13.6704i	0.0660774	−	0.535786i
$652$		0			0
$653$	−1.66909	+	4.91697i	−0.0653165	+	0.192416i	−0.974688	−	0.223568i	$-0.928229\pi$
$653$	−1.66909	+	4.91697i	−0.0653165	+	0.192416i	0.909372	+	0.415984i	$0.136563\pi$
$654$		0			0
$655$	−13.4951	+	1.77666i	−0.527296	+	0.0694198i
$656$		0			0
$657$	8.01959	+	5.35852i	0.312874	+	0.209056i
$658$		0			0
$659$	−3.41046	−	3.41046i	−0.132853	−	0.132853i	0.637553	−	0.770406i	$-0.279946\pi$
$659$	−3.41046	−	3.41046i	−0.132853	−	0.132853i	−0.770406	+	0.637553i	$0.779946\pi$
$660$		0			0
$661$	9.72128	−	12.6690i	0.378114	−	0.492768i	−0.565068	−	0.825044i	$-0.691150\pi$
$661$	9.72128	−	12.6690i	0.378114	−	0.492768i	0.943182	+	0.332277i	$0.107817\pi$
$662$		0			0
$663$	−15.8308	−	22.4485i	−0.614819	−	0.871826i
$664$		0			0
$665$	−0.358040	+	6.24620i	−0.0138842	+	0.242217i
$666$		0			0
$667$	3.86583	+	14.4275i	0.149686	+	0.558634i
$668$		0			0
$669$	−0.462877	+	7.06214i	−0.0178959	+	0.273038i
$670$		0			0
$671$	−0.682732	+	1.64826i	−0.0263566	+	0.0636304i
$672$		0			0
$673$	1.65735	+	8.33204i	0.0638860	+	0.321177i	0.999492	−	0.0318692i	$-0.0101460\pi$
$673$	1.65735	+	8.33204i	0.0638860	+	0.321177i	−0.935606	+	0.353046i	$0.885146\pi$
$674$		0			0
$675$	−1.66657	−	4.90955i	−0.0641462	−	0.188969i
$676$		0			0
$677$	1.85697	+	28.3318i	0.0713690	+	1.08888i	0.871930	+	0.489630i	$0.162868\pi$
$677$	1.85697	+	28.3318i	0.0713690	+	1.08888i	−0.800561	+	0.599251i	$0.795465\pi$
$678$		0			0
$679$	42.9175	−	29.1879i	1.64702	−	1.12013i
$680$		0			0
$681$	−8.52193	+	14.7604i	−0.326561	+	0.565621i
$682$		0			0
$683$	−31.4512	−	15.5100i	−1.20345	−	0.593473i	−0.273749	−	0.961801i	$-0.588264\pi$
$683$	−31.4512	−	15.5100i	−1.20345	−	0.593473i	−0.929696	+	0.368328i	$0.879930\pi$
$684$		0			0
$685$	0.565241	−	2.84166i	0.0215967	−	0.108574i
$686$		0			0
$687$	7.52979	−	1.49777i	0.287280	−	0.0571435i
$688$		0			0
$689$	−2.74519	−	20.8518i	−0.104584	−	0.794391i
$690$		0			0
$691$	−7.10358	+	3.50310i	−0.270233	+	0.133264i	−0.572357	−	0.820004i	$-0.693971\pi$
$691$	−7.10358	+	3.50310i	−0.270233	+	0.133264i	0.302124	+	0.953269i	$0.402304\pi$
$692$		0			0
$693$	−0.259266	−	0.0493670i	−0.00984870	−	0.00187530i
$694$		0			0
$695$	1.52132	−	11.5555i	0.0577068	−	0.438327i
$696$		0			0
$697$	−20.0066	−	38.1201i	−0.757803	−	1.44390i
$698$		0			0
$699$	34.6712	−	14.3613i	1.31139	−	0.543194i
$700$		0			0
$701$	17.5719	−	17.5719i	0.663680	−	0.663680i	−0.292565	−	0.956246i	$-0.594509\pi$
$701$	17.5719	−	17.5719i	0.663680	−	0.663680i	0.956246	+	0.292565i	$0.0945089\pi$
$702$		0			0
$703$	−12.7727	−	0.837170i	−0.481733	−	0.0315745i
$704$		0			0
$705$	23.1552	+	30.1765i	0.872077	+	1.13651i
$706$		0			0
$707$	28.6703	+	7.43103i	1.07826	+	0.279473i
$708$		0			0
$709$	24.5980	+	21.5719i	0.923799	+	0.810150i	0.982141	−	0.188147i	$-0.0602481\pi$
$709$	24.5980	+	21.5719i	0.923799	+	0.810150i	−0.0583421	+	0.998297i	$0.518581\pi$
$710$		0			0
$711$	−2.16712	+	4.39449i	−0.0812735	+	0.164806i
$712$		0			0
$713$	19.0563			0.713665
$714$		0			0
$715$	1.32451			0.0495339
$716$		0			0
$717$	9.64344	−	19.5550i	0.360141	−	0.730294i
$718$		0			0
$719$	18.3287	+	16.0739i	0.683546	+	0.599453i	0.929055	−	0.369941i	$-0.120622\pi$
$719$	18.3287	+	16.0739i	0.683546	+	0.599453i	−0.245510	+	0.969394i	$0.578955\pi$
$720$		0			0
$721$	47.0778	−	13.0287i	1.75327	−	0.485213i
$722$		0			0
$723$	−14.0667	−	18.3321i	−0.523147	−	0.681779i
$724$		0			0
$725$	−2.46590	−	0.161624i	−0.0915812	−	0.00600255i
$726$		0			0
$727$	−10.5936	+	10.5936i	−0.392896	+	0.392896i	−0.875719	−	0.482822i	$-0.839612\pi$
$727$	−10.5936	+	10.5936i	−0.392896	+	0.392896i	0.482822	+	0.875719i	$0.339612\pi$
$728$		0			0
$729$	27.7518	−	11.4952i	1.02784	−	0.425747i
$730$		0			0
$731$	2.83986	−	26.7580i	0.105036	−	0.989680i
$732$		0			0
$733$	1.46077	−	11.0956i	0.0539547	−	0.409827i	−0.943061	−	0.332621i	$-0.892067\pi$
$733$	1.46077	−	11.0956i	0.0539547	−	0.409827i	0.997015	−	0.0772054i	$-0.0245997\pi$
$734$		0			0
$735$	8.59263	+	19.8197i	0.316944	+	0.731061i
$736$		0			0
$737$	0.388231	−	0.191455i	0.0143007	−	0.00705232i
$738$		0			0
$739$	−0.945559	−	7.18223i	−0.0347830	−	0.264203i	−0.999996	−	0.00273900i	$-0.999128\pi$
$739$	−0.945559	−	7.18223i	−0.0347830	−	0.264203i	0.965213	−	0.261464i	$-0.0842052\pi$
$740$		0			0
$741$	−7.65522	+	1.52272i	−0.281222	+	0.0559385i
$742$		0			0
$743$	8.45984	−	42.5305i	0.310361	−	1.56029i	−0.439220	−	0.898380i	$-0.644745\pi$
$743$	8.45984	−	42.5305i	0.310361	−	1.56029i	0.749581	−	0.661912i	$-0.230255\pi$
$744$		0			0
$745$	3.95882	+	1.95228i	0.145040	+	0.0715259i
$746$		0			0
$747$	2.78013	−	4.81533i	0.101720	−	0.176184i
$748$		0			0
$749$	1.14453	+	15.5138i	0.0418200	+	0.566863i
$750$		0			0
$751$	2.31713	+	35.3526i	0.0845533	+	1.29003i	0.803641	+	0.595114i	$0.202893\pi$
$751$	2.31713	+	35.3526i	0.0845533	+	1.29003i	−0.719088	+	0.694919i	$0.755440\pi$
$752$		0			0
$753$	−0.236474	−	0.696630i	−0.00861759	−	0.0253866i
$754$		0			0
$755$	5.21373	+	26.2112i	0.189747	+	0.953922i
$756$		0			0
$757$	−11.2470	+	27.1527i	−0.408779	+	0.986880i	0.576680	+	0.816970i	$0.304348\pi$
$757$	−11.2470	+	27.1527i	−0.408779	+	0.986880i	−0.985460	+	0.169910i	$0.945652\pi$
$758$		0			0
$759$	−0.0842755	+	1.28580i	−0.00305901	+	0.0466715i
$760$		0			0
$761$	−4.52207	−	16.8766i	−0.163925	−	0.611775i	−0.998175	−	0.0603893i	$-0.980766\pi$
$761$	−4.52207	−	16.8766i	−0.163925	−	0.611775i	0.834250	−	0.551386i	$-0.185901\pi$
$762$		0			0
$763$	−40.1432	−	2.30106i	−1.45328	−	0.0833039i
$764$		0			0
$765$	1.21118	+	5.37800i	0.0437902	+	0.194442i
$766$		0			0
$767$	−0.887427	+	1.15652i	−0.0320431	+	0.0417594i
$768$		0			0
$769$	−6.94855	−	6.94855i	−0.250571	−	0.250571i	0.570634	−	0.821205i	$-0.306698\pi$
$769$	−6.94855	−	6.94855i	−0.250571	−	0.250571i	−0.821205	+	0.570634i	$0.806698\pi$
$770$		0			0
$771$	−12.3408	−	8.24588i	−0.444444	−	0.296968i
$772$		0			0
$773$	18.0760	−	2.37975i	0.650148	−	0.0855936i	0.201763	−	0.979434i	$-0.435333\pi$
$773$	18.0760	−	2.37975i	0.650148	−	0.0855936i	0.448385	+	0.893841i	$0.352000\pi$
$774$		0			0
$775$	−1.01344	+	2.98549i	−0.0364038	+	0.107242i
$776$		0			0
$777$	−40.6920	+	17.2470i	−1.45982	+	0.618733i
$778$		0			0
$779$	−12.2066	+	0.800063i	−0.437347	+	0.0286652i
$780$		0			0
$781$	1.39610	−	0.806040i	0.0499565	−	0.0288424i
$782$		0			0
$783$		−	14.9446i		−	0.534077i
$784$		0			0
$785$	8.89814	−	5.94555i	0.317588	−	0.212206i
$786$		0			0
$787$	−2.82978	+	0.960582i	−0.100871	+	0.0342411i	−0.371419	−	0.928465i	$-0.621129\pi$
$787$	−2.82978	+	0.960582i	−0.100871	+	0.0342411i	0.270548	+	0.962707i	$0.412795\pi$
$788$		0			0
$789$	0.350747	+	0.119063i	0.0124869	+	0.00423874i
$790$		0			0
$791$	−5.89166	−	28.4015i	−0.209483	−	1.00984i
$792$		0			0
$793$	−22.8321	−	46.2989i	−0.810791	−	1.64412i
$794$		0			0
$795$	3.85510	−	14.3874i	0.136726	−	0.510270i
$796$		0			0
$797$	3.78937	+	9.14835i	0.134226	+	0.324051i	0.976674	−	0.214727i	$-0.0688862\pi$
$797$	3.78937	+	9.14835i	0.134226	+	0.324051i	−0.842448	+	0.538778i	$0.818886\pi$
$798$		0			0
$799$	26.5089	+	43.3574i	0.937818	+	1.53387i
$800$		0			0
$801$	−4.10342	−	3.14866i	−0.144987	−	0.111253i
$802$		0			0
$803$	2.11802	−	0.567522i	0.0747433	−	0.0200274i
$804$		0			0
$805$	−25.7593	+	15.1548i	−0.907897	+	0.534137i
$806$		0			0
$807$	17.4737	−	13.4081i	0.615104	−	0.471986i
$808$		0			0
$809$	9.48643	−	8.31937i	0.333525	−	0.292494i	−0.476160	−	0.879359i	$-0.657972\pi$
$809$	9.48643	−	8.31937i	0.333525	−	0.292494i	0.809685	+	0.586865i	$0.199638\pi$
$810$		0			0
$811$	33.9297	+	6.74904i	1.19143	+	0.236991i	0.750698	−	0.660646i	$-0.229718\pi$
$811$	33.9297	+	6.74904i	1.19143	+	0.236991i	0.440736	+	0.897637i	$0.354718\pi$
$812$		0			0
$813$	15.2309	+	22.7946i	0.534170	+	0.799441i
$814$		0			0
$815$	8.66021	+	14.9999i	0.303354	+	0.525424i
$816$		0			0
$817$	−6.62151	−	3.82293i	−0.231657	−	0.133747i
$818$		0			0
$819$	6.02036	−	4.69843i	0.210368	−	0.164176i
$820$		0			0
$821$	2.02599	−	2.31020i	0.0707076	−	0.0806266i	−0.715404	−	0.698711i	$-0.753758\pi$
$821$	2.02599	−	2.31020i	0.0707076	−	0.0806266i	0.786112	+	0.618084i	$0.212091\pi$
$822$		0			0
$823$	−4.57859	−	5.22088i	−0.159600	−	0.181988i	0.666513	−	0.745493i	$-0.267786\pi$
$823$	−4.57859	−	5.22088i	−0.159600	−	0.181988i	−0.826113	+	0.563505i	$0.809453\pi$
$824$		0			0
$825$	−0.196960	−	0.0815834i	−0.00685726	−	0.00284037i
$826$		0			0
$827$	27.6963	−	41.4504i	0.963095	−	1.44137i	0.0668758	−	0.997761i	$-0.478697\pi$
$827$	27.6963	−	41.4504i	0.963095	−	1.44137i	0.896219	−	0.443612i	$-0.146303\pi$
$828$		0			0
$829$	−3.21405	−	0.861202i	−0.111629	−	0.0299108i	0.202572	−	0.979267i	$-0.435070\pi$
$829$	−3.21405	−	0.861202i	−0.111629	−	0.0299108i	−0.314201	+	0.949357i	$0.601737\pi$
$830$		0			0
$831$	−13.5979	−	1.79019i	−0.471705	−	0.0621011i
$832$		0			0
$833$	8.62145	+	27.5440i	0.298715	+	0.954342i
$834$		0			0
$835$	−11.0527	−	1.45512i	−0.382496	−	0.0503565i
$836$		0			0
$837$	−18.4171	−	4.93484i	−0.636587	−	0.170573i
$838$		0			0
$839$	9.93755	−	14.8726i	0.343082	−	0.513459i	−0.619301	−	0.785153i	$-0.712584\pi$
$839$	9.93755	−	14.8726i	0.343082	−	0.513459i	0.962384	+	0.271694i	$0.0875840\pi$
$840$		0			0
$841$	20.2117	+	8.37194i	0.696954	+	0.288688i
$842$		0			0
$843$	−3.93535	−	4.48740i	−0.135541	−	0.154554i
$844$		0			0
$845$	−7.96856	+	9.08640i	−0.274127	+	0.312582i
$846$		0			0
$847$	22.8960	−	17.8686i	0.786715	−	0.613971i
$848$		0			0
$849$	1.55665	+	0.898733i	0.0534241	+	0.0308444i
$850$		0			0
$851$	−30.5727	−	52.9535i	−1.04802	−	1.81522i
$852$		0			0
$853$	6.49269	+	9.71700i	0.222306	+	0.332704i	0.925811	−	0.377986i	$-0.123383\pi$
$853$	6.49269	+	9.71700i	0.222306	+	0.332704i	−0.703506	+	0.710689i	$0.748383\pi$
$854$		0			0
$855$	1.53631	+	0.305591i	0.0525406	+	0.0104510i
$856$		0			0
$857$	−23.4655	+	20.5787i	−0.801567	+	0.702955i	−0.958637	−	0.284632i	$-0.908128\pi$
$857$	−23.4655	+	20.5787i	−0.801567	+	0.702955i	0.157070	+	0.987587i	$0.449795\pi$
$858$		0			0
$859$	−7.89827	+	6.06055i	−0.269485	+	0.206783i	−0.734660	−	0.678436i	$-0.762658\pi$
$859$	−7.89827	+	6.06055i	−0.269485	+	0.206783i	0.465175	+	0.885219i	$0.345992\pi$
$860$		0			0
$861$	−36.4042	+	21.4175i	−1.24065	+	0.729906i
$862$		0			0
$863$	10.6310	−	2.84857i	0.361884	−	0.0969665i	−0.0732955	−	0.997310i	$-0.523352\pi$
$863$	10.6310	−	2.84857i	0.361884	−	0.0969665i	0.435179	+	0.900344i	$0.356685\pi$
$864$		0			0
$865$	−3.36728	−	2.58380i	−0.114491	−	0.0878519i
$866$		0			0
$867$	−3.00256	−	25.8176i	−0.101972	−	0.876812i
$868$		0			0
$869$	0.426283	+	1.02914i	0.0144607	+	0.0349111i
$870$		0			0
$871$	−3.24179	+	12.0985i	−0.109844	+	0.409943i
$872$		0			0
$873$	−5.74736	−	11.6545i	−0.194519	−	0.394445i
$874$		0			0
$875$	−6.42787	−	30.9864i	−0.217302	−	1.04753i
$876$		0			0
$877$	−21.0509	−	7.14581i	−0.710838	−	0.241297i	−0.0574805	−	0.998347i	$-0.518307\pi$
$877$	−21.0509	−	7.14581i	−0.710838	−	0.241297i	−0.653357	+	0.757050i	$0.726640\pi$
$878$		0			0
$879$	5.16218	−	1.75232i	0.174116	−	0.0591044i
$880$		0			0
$881$	−36.1875	+	24.1797i	−1.21919	+	0.814636i	−0.987418	−	0.158134i	$-0.949452\pi$
$881$	−36.1875	+	24.1797i	−1.21919	+	0.814636i	−0.231772	+	0.972770i	$0.574452\pi$
$882$		0			0
$883$			2.75706i			0.0927826i	0.998923	+	0.0463913i	$0.0147721\pi$
$883$			2.75706i			0.0927826i	−0.998923	+	0.0463913i	$0.985228\pi$
$884$		0			0
$885$	−0.894088	+	0.516202i	−0.0300545	+	0.0173519i
$886$		0			0
$887$	−44.6321	+	2.92534i	−1.49860	+	0.0982233i	−0.792492	−	0.609882i	$-0.791217\pi$
$887$	−44.6321	+	2.92534i	−1.49860	+	0.0982233i	−0.706107	+	0.708106i	$0.749550\pi$
$888$		0			0
$889$	17.5583	−	7.44195i	0.588885	−	0.249595i
$890$		0			0
$891$	0.318225	−	0.937460i	0.0106609	−	0.0314061i
$892$		0			0
$893$	14.3165	−	1.88480i	0.479083	−	0.0630724i
$894$		0			0
$895$	−35.4766	−	23.7047i	−1.18585	−	0.792360i
$896$		0			0
$897$	−26.3644	−	26.3644i	−0.880281	−	0.880281i
$898$		0			0
$899$	−5.53231	+	7.20985i	−0.184513	+	0.240462i
$900$		0			0
$901$	7.15058	−	18.5715i	0.238220	−	0.618706i
$902$		0			0
$903$	−26.3562	−	1.51077i	−0.877079	−	0.0502753i
$904$		0			0
$905$	4.67356	+	17.4420i	0.155355	+	0.579791i
$906$		0			0
$907$	−3.67143	+	56.0151i	−0.121908	+	1.85995i	0.300801	+	0.953687i	$0.402746\pi$
$907$	−3.67143	+	56.0151i	−0.121908	+	1.85995i	−0.422709	+	0.906266i	$0.638921\pi$
$908$		0			0
$909$	2.83770	−	6.85082i	0.0941206	−	0.227227i
$910$		0			0
$911$	−9.38431	−	47.1781i	−0.310916	−	1.56308i	−0.748024	−	0.663671i	$-0.768997\pi$
$911$	−9.38431	−	47.1781i	−0.310916	−	1.56308i	0.437108	−	0.899409i	$-0.356003\pi$
$912$		0			0
$913$	−0.406327	−	1.19700i	−0.0134475	−	0.0396149i
$914$		0			0
$915$	−2.39113	−	36.4816i	−0.0790483	−	1.20604i
$916$		0			0
$917$	1.31271	+	17.7935i	0.0433494	+	0.587594i
$918$		0			0
$919$	26.2085	−	45.3945i	0.864540	−	1.49743i	−0.00296381	−	0.999996i	$-0.500943\pi$
$919$	26.2085	−	45.3945i	0.864540	−	1.49743i	0.867504	−	0.497431i	$-0.165723\pi$
$920$		0			0
$921$	−7.48287	−	3.69014i	−0.246569	−	0.121594i
$922$		0			0
$923$	−9.10022	+	45.7499i	−0.299537	+	1.50588i
$924$		0			0
$925$	9.92195	−	1.97360i	0.326232	−	0.0648915i
$926$		0			0
$927$	−1.59630	−	12.1251i	−0.0524293	−	0.398240i
$928$		0			0
$929$	−17.7808	+	8.76853i	−0.583370	+	0.287686i	−0.709929	−	0.704273i	$-0.751273\pi$
$929$	−17.7808	+	8.76853i	−0.583370	+	0.287686i	0.126560	+	0.991959i	$0.459607\pi$
$930$		0			0
$931$	8.14721	+	0.937095i	0.267014	+	0.0307121i
$932$		0			0
$933$	5.62756	−	42.7455i	0.184238	−	1.39943i
$934$		0			0
$935$	1.10079	+	0.599127i	0.0359996	+	0.0195936i
$936$		0			0
$937$	31.8711	−	13.2014i	1.04118	−	0.431272i	0.204446	−	0.978878i	$-0.434461\pi$
$937$	31.8711	−	13.2014i	1.04118	−	0.431272i	0.836736	+	0.547606i	$0.184461\pi$
$938$		0			0
$939$	19.0499	−	19.0499i	0.621670	−	0.621670i
$940$		0			0
$941$	2.33431	+	0.152999i	0.0760964	+	0.00498762i	0.103404	−	0.994639i	$-0.467027\pi$
$941$	2.33431	+	0.152999i	0.0760964	+	0.00498762i	−0.0273074	+	0.999627i	$0.508693\pi$
$942$		0			0
$943$	−35.5731	−	46.3597i	−1.15842	−	1.50968i
$944$		0			0
$945$	28.8197	−	7.97580i	0.937506	−	0.259453i
$946$		0			0
$947$	9.72575	+	8.52925i	0.316044	+	0.277164i	0.802640	−	0.596464i	$-0.203428\pi$
$947$	9.72575	+	8.52925i	0.316044	+	0.277164i	−0.486595	+	0.873627i	$0.661761\pi$
$948$		0			0
$949$	−28.0622	+	56.9045i	−0.910937	+	1.84720i
$950$		0			0
$951$	9.58811			0.310916
$952$		0			0
$953$	32.3766			1.04878			0.524391	−	0.851478i	$-0.324293\pi$
$953$	32.3766			1.04878			0.524391	+	0.851478i	$0.324293\pi$
$954$		0			0
$955$	14.7679	−	29.9464i	0.477879	−	0.969042i
$956$		0			0
$957$	−0.462007	−	0.405169i	−0.0149346	−	0.0130973i
$958$		0			0
$959$	−3.67632	−	0.952861i	−0.118715	−	0.0307695i
$960$		0			0
$961$	−11.8133	−	15.3954i	−0.381075	−	0.496627i
$962$		0			0
$963$	3.88636	+	0.254725i	0.125236	+	0.00820841i
$964$		0			0
$965$	11.8750	−	11.8750i	0.382270	−	0.382270i
$966$		0			0
$967$	14.9642	−	6.19838i	0.481217	−	0.199326i	−0.128870	−	0.991662i	$-0.541135\pi$
$967$	14.9642	−	6.19838i	0.481217	−	0.199326i	0.610086	+	0.792335i	$0.291135\pi$
$968$		0			0
$969$	−7.05097	−	2.19724i	−0.226510	−	0.0705854i
$970$		0			0
$971$	−1.35195	+	10.2691i	−0.0433860	+	0.329550i	0.955963	+	0.293486i	$0.0948153\pi$
$971$	−1.35195	+	10.2691i	−0.0433860	+	0.329550i	−0.999349	+	0.0360639i	$0.988518\pi$
$972$		0			0
$973$	−15.0080	−	2.85768i	−0.481134	−	0.0916131i
$974$		0			0
$975$	5.53252	−	2.72834i	0.177182	−	0.0873767i
$976$		0			0
$977$	−1.22800	−	9.32756i	−0.0392871	−	0.298415i	−0.999797	−	0.0201679i	$-0.993580\pi$
$977$	−1.22800	−	9.32756i	−0.0392871	−	0.298415i	0.960510	−	0.278247i	$-0.0897534\pi$
$978$		0			0
$979$	−1.15328	+	0.229401i	−0.0368589	+	0.00733169i
$980$		0			0
$981$	−1.96397	+	9.87356i	−0.0627049	+	0.315239i
$982$		0			0
$983$	−31.3051	−	15.4380i	−0.998478	−	0.492395i	−0.131807	−	0.991275i	$-0.542078\pi$
$983$	−31.3051	−	15.4380i	−0.998478	−	0.492395i	−0.866671	+	0.498881i	$0.833745\pi$
$984$		0			0
$985$	−8.24653	+	14.2834i	−0.262756	+	0.455108i
$986$		0			0
$987$	41.2273	−	28.0384i	1.31228	−	0.892471i
$988$		0			0
$989$	−2.38876	−	36.4455i	−0.0759583	−	1.15890i
$990$		0			0
$991$	−10.6707	−	31.4348i	−0.338965	−	0.998560i	−0.974092	−	0.226152i	$-0.927385\pi$
$991$	−10.6707	−	31.4348i	−0.338965	−	0.998560i	0.635127	−	0.772408i	$-0.280948\pi$
$992$		0			0
$993$	1.45863	+	7.33301i	0.0462881	+	0.232706i
$994$		0			0
$995$	−12.3813	+	29.8911i	−0.392513	+	0.947610i
$996$		0			0
$997$	−1.85732	+	28.3372i	−0.0588219	+	0.897449i	0.861863	+	0.507142i	$0.169298\pi$
$997$	−1.85732	+	28.3372i	−0.0588219	+	0.897449i	−0.920685	+	0.390308i	$0.872369\pi$
$998$		0			0
$999$	15.8343	+	59.0943i	0.500974	+	1.86966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	952.2.cw.b.369.14	yes	288
7.3	odd	6	inner	952.2.cw.b.913.14	yes	288
17.10	odd	16	inner	952.2.cw.b.537.14	yes	288
119.10	even	48	inner	952.2.cw.b.129.14	✓	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
952.2.cw.b.129.14	✓	288	119.10	even	48	inner
952.2.cw.b.369.14	yes	288	1.1	even	1	trivial
952.2.cw.b.537.14	yes	288	17.10	odd	16	inner
952.2.cw.b.913.14	yes	288	7.3	odd	6	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)

\(f(q)\)	\(=\)	\(q+(0.676224 - 1.37125i) q^{3} +(-1.51754 - 1.33085i) q^{5} +(-1.85544 + 1.88609i) q^{7} +(0.403248 + 0.525523i) q^{9} +(0.150271 + 0.00984927i) q^{11} +(-3.08120 + 3.08120i) q^{13} +(-2.85111 + 1.18097i) q^{15} +(-3.95450 + 1.16701i) q^{17} +(-0.152919 + 1.16154i) q^{19} +(1.33160 + 3.81969i) q^{21} +(-5.01931 + 2.47525i) q^{23} +(-0.120857 - 0.917997i) q^{25} +(5.49193 - 1.09241i) q^{27} +(0.520678 - 2.61762i) q^{29} +(-3.05391 - 1.50602i) q^{31} +(0.115122 - 0.199398i) q^{33} +(5.32580 - 0.392909i) q^{35} +(0.714577 + 10.9023i) q^{37} +(2.14150 + 6.30866i) q^{39} +(2.03703 + 10.2408i) q^{41} +(-2.49747 + 6.02944i) q^{43} +(0.0874456 - 1.33416i) q^{45} +(-3.19006 - 11.9055i) q^{47} +(-0.114672 - 6.99906i) q^{49} +(-1.07387 + 6.21175i) q^{51} +(-2.93824 + 3.82919i) q^{53} +(-0.214934 - 0.214934i) q^{55} +(1.48935 + 0.995149i) q^{57} +(0.331680 - 0.0436665i) q^{59} +(-3.80806 + 11.2182i) q^{61} +(-1.73939 - 0.214515i) q^{63} +(8.77645 - 0.575239i) q^{65} +(2.48934 - 1.43722i) q^{67} +8.55653i q^{69} +(8.90077 - 5.94731i) q^{71} +(13.7879 - 4.68037i) q^{73} +(-1.34053 - 0.455047i) q^{75} +(-0.297395 + 0.265150i) q^{77} +(3.27159 + 6.63413i) q^{79} +(1.70148 - 6.34999i) q^{81} +(-3.21226 - 7.75508i) q^{83} +(7.55423 + 3.49185i) q^{85} +(-3.23731 - 2.48408i) q^{87} +(-7.54220 + 2.02093i) q^{89} +(-0.0944340 - 11.5284i) q^{91} +(-4.13026 + 3.16926i) q^{93} +(1.77789 - 1.55917i) q^{95} +(-19.2403 - 3.82713i) q^{97} +(0.0554203 + 0.0829424i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 32 q^{15} + 48 q^{21} - 32 q^{29} - 72 q^{31} - 16 q^{37} - 32 q^{39} + 32 q^{43} + 24 q^{47} - 48 q^{49} - 16 q^{53} - 128 q^{57} - 72 q^{61} - 40 q^{63} + 32 q^{65} + 80 q^{71} + 96 q^{73} - 216 q^{75}+ \cdots + 192 q^{99}+O(q^{100}) \) 288 * q + 32 * q^15 + 48 * q^21 - 32 * q^29 - 72 * q^31 - 16 * q^37 - 32 * q^39 + 32 * q^43 + 24 * q^47 - 48 * q^49 - 16 * q^53 - 128 * q^57 - 72 * q^61 - 40 * q^63 + 32 * q^65 + 80 * q^71 + 96 * q^73 - 216 * q^75 - 8 * q^77 + 32 * q^79 + 64 * q^81 - 96 * q^85 + 144 * q^87 - 144 * q^89 + 64 * q^91 - 32 * q^93 + 64 * q^95 + 192 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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