LMFDB - Embedded newform 952.2.cw.b.129.14

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			129.14
Character	$\chi$	$=$	952.129
Dual form			952.2.cw.b.369.14

$q$-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 $\left(\mathbb{Z}/952\mathbb{Z}\right)^\times$.

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

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
$3$	0.676224	+	1.37125i	0.390418	+	0.791689i	0.999999	−	0.00103421i	$-0.000329200\pi$
$3$	0.676224	+	1.37125i	0.390418	+	0.791689i	−0.609582	+	0.792723i	$0.708663\pi$
$4$		0			0
$5$	−1.51754	+	1.33085i	−0.678665	+	0.595173i	−0.927702	−	0.373321i	$-0.878219\pi$
$5$	−1.51754	+	1.33085i	−0.678665	+	0.595173i	0.249038	+	0.968494i	$0.419886\pi$
$6$		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	−0.0427321	−	0.999087i	$-0.513606\pi$
$11$	0.150271	−	0.00984927i	0.0453083	−	0.00296967i	0.0880404	+	0.996117i	$0.471940\pi$
$12$		0			0
$13$	−3.08120	−	3.08120i	−0.854571	−	0.854571i	0.136121	−	0.990692i	$-0.456536\pi$
$13$	−3.08120	−	3.08120i	−0.854571	−	0.854571i	−0.990692	+	0.136121i	$0.956536\pi$
$14$		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	−0.999992	−	0.00389530i	$-0.998760\pi$
$19$	−0.152919	−	1.16154i	−0.0350821	−	0.266475i	0.964910	−	0.262580i	$-0.0845732\pi$
$20$		0			0
$21$	1.33160	−	3.81969i	0.290579	−	0.833524i
$22$		0			0
$23$	−5.01931	−	2.47525i	−1.04660	−	0.516125i	−0.164102	−	0.986443i	$-0.552472\pi$
$23$	−5.01931	−	2.47525i	−1.04660	−	0.516125i	−0.882497	+	0.470318i	$0.844139\pi$
$24$		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	0.998539	+	0.0540348i	$0.0172082\pi$
$29$	0.520678	+	2.61762i	0.0966875	+	0.486081i	−0.901852	+	0.432046i	$0.857792\pi$
$30$		0			0
$31$	−3.05391	+	1.50602i	−0.548499	+	0.270490i	−0.695353	−	0.718668i	$-0.744752\pi$
$31$	−3.05391	+	1.50602i	−0.548499	+	0.270490i	0.146854	+	0.989158i	$0.453085\pi$
$32$		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	−0.380133	−	0.924932i	$-0.624122\pi$
$37$	0.714577	−	10.9023i	0.117476	−	1.79233i	0.497609	−	0.867401i	$-0.334211\pi$
$38$		0			0
$39$	2.14150	−	6.30866i	0.342915	−	1.01019i
$40$		0			0
$41$	2.03703	−	10.2408i	0.318130	−	1.59935i	−0.408791	−	0.912628i	$-0.634050\pi$
$41$	2.03703	−	10.2408i	0.318130	−	1.59935i	0.726922	−	0.686721i	$-0.240950\pi$
$42$		0			0
$43$	−2.49747	−	6.02944i	−0.380861	−	0.919481i	−0.991800	−	0.127802i	$-0.959208\pi$
$43$	−2.49747	−	6.02944i	−0.380861	−	0.919481i	0.610938	−	0.791678i	$-0.290792\pi$
$44$		0			0
$45$	0.0874456	+	1.33416i	0.0130356	+	0.198885i
$46$		0			0
$47$	−3.19006	+	11.9055i	−0.465318	+	1.73659i	0.190513	+	0.981685i	$0.438985\pi$
$47$	−3.19006	+	11.9055i	−0.465318	+	1.73659i	−0.655831	+	0.754907i	$0.727682\pi$
$48$		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	0.546696	−	0.837331i	$-0.315885\pi$
$53$	−2.93824	−	3.82919i	−0.403599	−	0.525980i	−0.950295	+	0.311351i	$0.899219\pi$
$54$		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	0.152086	−	0.988367i	$-0.451401\pi$
$59$	0.331680	+	0.0436665i	0.0431810	+	0.00568489i	−0.108905	+	0.994052i	$0.534734\pi$
$60$		0			0
$61$	−3.80806	−	11.2182i	−0.487573	−	1.43634i	−0.860963	−	0.508668i	$-0.830138\pi$
$61$	−3.80806	−	11.2182i	−0.487573	−	1.43634i	0.373390	−	0.927674i	$-0.378195\pi$
$62$		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	0.644293	−	0.764779i	$-0.277152\pi$
$67$	2.48934	+	1.43722i	0.304122	+	0.175585i	−0.340171	+	0.940364i	$0.610485\pi$
$68$		0			0
$69$		−	8.55653i		−	1.03009i
$70$		0			0
$71$	8.90077	+	5.94731i	1.05633	+	0.705815i	0.957249	−	0.289264i	$-0.0934106\pi$
$71$	8.90077	+	5.94731i	1.05633	+	0.705815i	0.0990781	+	0.995080i	$0.468411\pi$
$72$		0			0
$73$	13.7879	+	4.68037i	1.61375	+	0.547796i	0.975113	−	0.221709i	$-0.0711634\pi$
$73$	13.7879	+	4.68037i	1.61375	+	0.547796i	0.638641	+	0.769504i	$0.279497\pi$
$74$		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	−0.631497	−	0.775378i	$-0.717559\pi$
$79$	3.27159	−	6.63413i	0.368083	−	0.746398i	0.999580	+	0.0289803i	$0.00922600\pi$
$80$		0			0
$81$	1.70148	+	6.34999i	0.189053	+	0.705555i
$82$		0			0
$83$	−3.21226	+	7.75508i	−0.352591	+	0.851230i	0.643708	+	0.765272i	$0.277395\pi$
$83$	−3.21226	+	7.75508i	−0.352591	+	0.851230i	−0.996299	+	0.0859587i	$0.972605\pi$
$84$		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	−0.164120	−	0.986440i	$-0.552478\pi$
$89$	−7.54220	−	2.02093i	−0.799472	−	0.214218i	−0.635352	+	0.772223i	$0.719145\pi$
$90$		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	−0.959159	+	0.282868i	$0.908714\pi$
$97$	−19.2403	+	3.82713i	−1.95355	+	0.388586i	−0.994396	+	0.105718i	$0.966286\pi$
$98$		0			0
$99$	0.0554203	−	0.0829424i	0.00556995	−	0.00833602i
$100$		0			0
$101$	−5.59722	+	9.69467i	−0.556944	+	0.964656i	0.440805	+	0.897603i	$0.354693\pi$
$101$	−5.59722	+	9.69467i	−0.556944	+	0.964656i	−0.997749	+	0.0670528i	$0.978640\pi$
$102$		0			0
$103$	−15.9890	+	9.23128i	−1.57545	+	0.909585i	−0.579964	+	0.814642i	$0.696934\pi$
$103$	−15.9890	+	9.23128i	−1.57545	+	0.909585i	−0.995483	+	0.0949429i	$0.969733\pi$
$104$		0			0
$105$	3.06266	+	7.56868i	0.298885	+	0.738628i
$106$		0			0
$107$	3.87670	+	4.42053i	0.374775	+	0.427349i	0.908225	−	0.418483i	$-0.137438\pi$
$107$	3.87670	+	4.42053i	0.374775	+	0.427349i	−0.533450	+	0.845832i	$0.679105\pi$
$108$		0			0
$109$	10.0205	−	11.4262i	0.959788	−	1.09443i	−0.0356830	−	0.999363i	$-0.511361\pi$
$109$	10.0205	−	11.4262i	0.959788	−	1.09443i	0.995471	−	0.0950653i	$-0.0303060\pi$
$110$		0			0
$111$	15.4330	−	6.39256i	1.46484	−	0.606755i
$112$		0			0
$113$	−6.09088	−	9.11565i	−0.572982	−	0.857528i	0.425901	−	0.904770i	$-0.359957\pi$
$113$	−6.09088	−	9.11565i	−0.572982	−	0.857528i	−0.998884	+	0.0472413i	$0.984957\pi$
$114$		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	−0.658042	−	0.752981i	$-0.728615\pi$
$127$	−6.65922	+	2.75834i	−0.590910	+	0.244763i	0.0671322	+	0.997744i	$0.478615\pi$
$128$		0			0
$129$	6.57899	−	7.50190i	0.579248	−	0.660505i
$130$		0			0
$131$	4.44636	+	5.07010i	0.388480	+	0.442977i	0.912715	−	0.408597i	$-0.133982\pi$
$131$	4.44636	+	5.07010i	0.388480	+	0.442977i	−0.524235	+	0.851574i	$0.675648\pi$
$132$		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	−0.833736	−	0.552163i	$-0.813803\pi$
$137$	0.717716	−	1.24312i	0.0613187	−	0.106207i	0.895055	+	0.445956i	$0.147136\pi$
$138$		0			0
$139$	3.20809	−	4.80124i	0.272106	−	0.407236i	−0.670099	−	0.742272i	$-0.733748\pi$
$139$	3.20809	−	4.80124i	0.272106	−	0.407236i	0.942205	+	0.335036i	$0.108748\pi$
$140$		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	0.171254	−	0.985227i	$-0.445218\pi$
$149$	−2.11234	−	0.566000i	−0.173050	−	0.0463686i	−0.344303	+	0.938858i	$0.611885\pi$
$150$		0			0
$151$	−10.5042	+	8.06018i	−0.854822	+	0.655928i	−0.940276	−	0.340414i	$-0.889433\pi$
$151$	−10.5042	+	8.06018i	−0.854822	+	0.655928i	0.0854534	+	0.996342i	$0.472766\pi$
$152$		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	0.889301	−	0.457323i	$-0.151192\pi$
$157$	−1.37225	−	5.12132i	−0.109518	−	0.408726i	−0.998818	+	0.0485972i	$0.984525\pi$
$158$		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	−0.620972	−	0.783833i	$-0.713262\pi$
$163$	−8.12571	+	2.75831i	−0.636455	+	0.216047i	−0.0154830	+	0.999880i	$0.504929\pi$
$164$		0			0
$165$	−0.440071	−	0.149384i	−0.0342595	−	0.0116295i
$166$		0			0
$167$	4.59233	+	3.06849i	0.355365	+	0.237447i	0.720419	−	0.693539i	$-0.243950\pi$
$167$	4.59233	+	3.06849i	0.355365	+	0.237447i	−0.365054	+	0.930986i	$0.618950\pi$
$168$		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	0.144959	−	0.989438i	$-0.453695\pi$
$173$	2.09830	+	0.137530i	0.159530	+	0.0104562i	0.0145714	+	0.999894i	$0.495362\pi$
$174$		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	0.863263	−	0.504755i	$-0.168417\pi$
$179$	20.9579	+	2.75917i	1.56647	+	0.206230i	0.703208	+	0.710984i	$0.251750\pi$
$180$		0			0
$181$	−7.43847	+	4.97023i	−0.552897	+	0.369434i	−0.800412	−	0.599450i	$-0.795386\pi$
$181$	−7.43847	+	4.97023i	−0.552897	+	0.369434i	0.247515	+	0.968884i	$0.420386\pi$
$182$		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	−0.618939	−	0.785439i	$-0.712437\pi$
$191$	4.28149	−	15.9787i	0.309798	−	1.15618i	0.928736	−	0.370741i	$-0.120896\pi$
$192$		0			0
$193$	−0.544167	−	8.30239i	−0.0391700	−	0.597619i	−0.971654	−	0.236408i	$-0.924030\pi$
$193$	−0.544167	−	8.30239i	−0.0391700	−	0.597619i	0.932484	−	0.361211i	$-0.117637\pi$
$194$		0			0
$195$	5.14605	+	12.4237i	0.368516	+	0.889677i
$196$		0			0
$197$	−1.59412	+	8.01421i	−0.113577	+	0.570989i	0.881525	+	0.472137i	$0.156517\pi$
$197$	−1.59412	+	8.01421i	−0.113577	+	0.570989i	−0.995102	+	0.0988521i	$0.968483\pi$
$198$		0			0
$199$	−5.15241	+	15.1785i	−0.365244	+	1.07598i	0.596638	+	0.802511i	$0.296503\pi$
$199$	−5.15241	+	15.1785i	−0.365244	+	1.07598i	−0.961882	+	0.273465i	$0.911830\pi$
$200$		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	−0.462982	−	0.886368i	$-0.653221\pi$
$211$	−17.8656	−	3.55369i	−1.22992	−	0.244646i	−0.766938	+	0.641721i	$0.778221\pi$
$212$		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	0.234868	−	0.972027i	$-0.424534\pi$
$223$	−4.27659	−	1.77142i	−0.286382	−	0.118623i	−0.521250	+	0.853404i	$0.674534\pi$
$224$		0			0
$225$	0.433693	+	0.433693i	0.0289129	+	0.0289129i
$226$		0			0
$227$	−11.1238	+	0.729092i	−0.738312	+	0.0483915i	−0.429919	−	0.902868i	$-0.641458\pi$
$227$	−11.1238	+	0.729092i	−0.738312	+	0.0483915i	−0.308393	+	0.951259i	$0.599791\pi$
$228$		0			0
$229$	3.05683	−	3.98374i	0.202001	−	0.263253i	−0.681357	−	0.731951i	$-0.738610\pi$
$229$	3.05683	−	3.98374i	0.202001	−	0.263253i	0.883359	+	0.468698i	$0.155277\pi$
$230$		0			0
$231$	0.162479	−	0.587102i	0.0106904	−	0.0386285i
$232$		0			0
$233$	18.4542	−	16.1839i	1.20897	−	1.06024i	0.212429	−	0.977176i	$-0.431862\pi$
$233$	18.4542	−	16.1839i	1.20897	−	1.06024i	0.996544	−	0.0830650i	$-0.0264709\pi$
$234$		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	0.998738	+	0.0502170i	$0.0159913\pi$
$241$	6.68447	+	13.5548i	0.430585	+	0.873140i	−0.568154	+	0.822923i	$0.692342\pi$
$242$		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	0.717763	−	0.696287i	$-0.245166\pi$
$251$	0.340239	+	0.340239i	0.0214757	+	0.0214757i	−0.696287	+	0.717763i	$0.745166\pi$
$252$		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	0.984429	+	0.175783i	$0.0562456\pi$
$257$	1.26710	+	9.62458i	0.0790395	+	0.600365i	−0.905389	+	0.424582i	$0.860421\pi$
$258$		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	−0.990442	−	0.137928i	$-0.955956\pi$
$263$	0.0316220	−	0.240193i	0.00194990	−	0.0148109i	0.992392	+	0.123117i	$0.0392891\pi$
$264$		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	−0.00347936	−	0.999994i	$-0.501108\pi$
$269$	12.9201	−	6.37148i	0.787751	−	0.388476i	0.791230	+	0.611518i	$0.209441\pi$
$270$		0			0
$271$	−8.96543	−	15.5286i	−0.544611	−	0.943294i	−0.998631	−	0.0523024i	$-0.983344\pi$
$271$	−8.96543	−	15.5286i	−0.544611	−	0.943294i	0.454020	−	0.890991i	$-0.349989\pi$
$272$		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	−0.998522	−	0.0543557i	$-0.982690\pi$
$277$	−2.88348	+	8.49446i	−0.173252	+	0.510382i	0.825270	+	0.564738i	$0.191023\pi$
$278$		0			0
$279$	−0.440034	+	2.21220i	−0.0263442	+	0.132441i
$280$		0			0
$281$	1.49391	+	3.60662i	0.0891193	+	0.215153i	0.962155	−	0.272504i	$-0.0878517\pi$
$281$	1.49391	+	3.60662i	0.0891193	+	0.215153i	−0.873035	+	0.487657i	$0.837852\pi$
$282$		0			0
$283$	−0.0768909	−	1.17313i	−0.00457069	−	0.0697352i	0.994964	−	0.100231i	$-0.0319581\pi$
$283$	−0.0768909	−	1.17313i	−0.00457069	−	0.0697352i	−0.999535	+	0.0304956i	$0.990291\pi$
$284$		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	−0.629615	−	0.776908i	$-0.716787\pi$
$293$	2.52125	−	2.52125i	0.147293	−	0.147293i	0.776908	+	0.629615i	$0.216787\pi$
$294$		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	$0.0497708\pi$
$307$			5.45699i			0.311447i	−0.987801	+	0.155723i	$0.950229\pi$
$308$		0			0
$309$	−23.4705	−	15.6825i	−1.33519	−	0.892146i
$310$		0			0
$311$	26.7027	+	9.06436i	1.51417	+	0.513992i	0.950157	−	0.311772i	$-0.100922\pi$
$311$	26.7027	+	9.06436i	1.51417	+	0.513992i	0.564016	+	0.825764i	$0.309256\pi$
$312$		0			0
$313$	16.6856	−	5.66399i	0.943124	−	0.320148i	0.192816	−	0.981235i	$-0.438238\pi$
$313$	16.6856	−	5.66399i	0.943124	−	0.320148i	0.750309	+	0.661087i	$0.229905\pi$
$314$		0			0
$315$	2.35410	−	2.64039i	0.132639	−	0.148769i
$316$		0			0
$317$	2.77367	−	5.62444i	0.155785	−	0.315900i	−0.804962	−	0.593326i	$-0.797815\pi$
$317$	2.77367	−	5.62444i	0.155785	−	0.315900i	0.960747	+	0.277426i	$0.0894813\pi$
$318$		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	0.496617	−	0.867970i	$-0.334575\pi$
$331$	−3.87963	−	2.97695i	−0.213244	−	0.163628i	−0.709861	+	0.704342i	$0.751242\pi$
$332$		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	−0.921997	−	0.387198i	$-0.873443\pi$
$337$	−3.88152	+	5.80910i	−0.211440	+	0.316442i	0.710557	+	0.703640i	$0.248443\pi$
$338$		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	−0.0473119	−	0.998880i	$-0.515065\pi$
$347$	17.6816	−	20.1620i	0.949198	−	1.08235i	0.996510	−	0.0834729i	$-0.0266012\pi$
$348$		0			0
$349$	11.2136	−	4.64482i	0.600250	−	0.248632i	−0.0618036	−	0.998088i	$-0.519685\pi$
$349$	11.2136	−	4.64482i	0.600250	−	0.248632i	0.662053	+	0.749457i	$0.269685\pi$
$350$		0			0
$351$	−13.5558	−	20.2877i	−0.723555	−	1.08288i
$352$		0			0
$353$	−16.4320	+	4.40293i	−0.874585	+	0.234344i	−0.668070	−	0.744099i	$-0.732879\pi$
$353$	−16.4320	+	4.40293i	−0.874585	+	0.234344i	−0.206516	+	0.978443i	$0.566212\pi$
$354$		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	−0.830898	−	0.556425i	$-0.812173\pi$
$359$	−28.2214	+	3.71542i	−1.48947	+	0.196092i	−0.658572	+	0.752518i	$0.728839\pi$
$360$		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	−0.595819	−	0.803119i	$-0.703173\pi$
$367$	5.32951	−	6.07715i	0.278198	−	0.317224i	0.874018	+	0.485894i	$0.161506\pi$
$368$		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	0.116033	−	0.993245i	$-0.462982\pi$
$373$	19.9742	−	11.5321i	1.03422	−	0.597110i	0.918192	+	0.396135i	$0.129649\pi$
$374$		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	−0.105692	−	0.994399i	$-0.533706\pi$
$379$	3.44973	−	0.686195i	0.177201	−	0.0352475i	0.282893	+	0.959151i	$0.408706\pi$
$380$		0			0
$381$	−8.28548	−	7.26617i	−0.424478	−	0.372257i
$382$		0			0
$383$	−20.7537	−	15.9248i	−1.06046	−	0.813721i	−0.0774013	−	0.997000i	$-0.524662\pi$
$383$	−20.7537	−	15.9248i	−1.06046	−	0.813721i	−0.983061	+	0.183279i	$0.941329\pi$
$384$		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	0.304078	−	0.952647i	$-0.401652\pi$
$389$	25.6985	−	19.7192i	1.30297	−	0.999801i	0.998888	−	0.0471539i	$-0.0150151\pi$
$390$		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	−0.566587	−	0.824002i	$-0.691737\pi$
$397$	8.60861	−	17.4565i	0.432054	−	0.876118i	0.998641	−	0.0521166i	$-0.0165967\pi$
$398$		0			0
$399$	−4.64033	−	0.962599i	−0.232307	−	0.0481902i
$400$		0			0
$401$	−6.09357	+	2.06849i	−0.304298	+	0.103295i	−0.469412	−	0.882979i	$-0.655534\pi$
$401$	−6.09357	+	2.06849i	−0.304298	+	0.103295i	0.165114	+	0.986275i	$0.447201\pi$
$402$		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	0.547532	−	0.836785i	$-0.315567\pi$
$409$	1.95406	+	1.12817i	0.0966218	+	0.0557846i	−0.450910	+	0.892569i	$0.648901\pi$
$410$		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	−0.170262	−	0.985399i	$-0.554461\pi$
$419$	13.8163	−	9.23178i	0.674972	−	0.451002i	0.845234	+	0.534397i	$0.179461\pi$
$420$		0			0
$421$	−22.2012	+	22.2012i	−1.08202	+	1.08202i	−0.0857016	+	0.996321i	$0.527313\pi$
$421$	−22.2012	+	22.2012i	−1.08202	+	1.08202i	−0.996321	+	0.0857016i	$0.972687\pi$
$422$		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	0.914564	+	0.404440i	$0.132534\pi$
$431$	1.25839	+	19.1993i	0.0606143	+	0.924796i	−0.853950	+	0.520355i	$0.825800\pi$
$432$		0			0
$433$	−5.73803	−	13.8528i	−0.275752	−	0.665724i	0.723957	−	0.689845i	$-0.242321\pi$
$433$	−5.73803	−	13.8528i	−0.275752	−	0.665724i	−0.999709	+	0.0241207i	$0.992321\pi$
$434$		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	−0.791236	−	0.611511i	$-0.790562\pi$
$439$	1.53055	−	23.3517i	0.0730491	−	1.11451i	0.864285	−	0.503003i	$-0.167771\pi$
$440$		0			0
$441$	3.63192	+	2.88262i	0.172949	+	0.137268i
$442$		0			0
$443$	−14.3352	−	24.8294i	−0.681088	−	1.17968i	−0.974649	−	0.223739i	$-0.928174\pi$
$443$	−14.3352	−	24.8294i	−0.681088	−	1.17968i	0.293561	−	0.955940i	$-0.405160\pi$
$444$		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	0.130693	−	0.991423i	$-0.458280\pi$
$449$	−2.71151	−	0.539353i	−0.127964	−	0.0254537i	−0.258657	+	0.965969i	$0.583280\pi$
$450$		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	0.999814	+	0.0192918i	$0.00614116\pi$
$457$	0.835027	+	6.34266i	0.0390609	+	0.296697i	−0.960753	+	0.277405i	$0.910526\pi$
$458$		0			0
$459$	−20.4430	−	10.7291i	−0.954197	−	0.500791i
$460$		0			0
$461$	−18.9108	−	7.83313i	−0.880766	−	0.364825i	−0.103972	−	0.994580i	$-0.533155\pi$
$461$	−18.9108	−	7.83313i	−0.880766	−	0.364825i	−0.776794	+	0.629755i	$0.783155\pi$
$462$		0			0
$463$	−3.60403	−	3.60403i	−0.167493	−	0.167493i	0.618383	−	0.785877i	$-0.287788\pi$
$463$	−3.60403	−	3.60403i	−0.167493	−	0.167493i	−0.785877	+	0.618383i	$0.787788\pi$
$464$		0			0
$465$	10.4856	−	0.687264i	0.486259	−	0.0318711i
$466$		0			0
$467$	7.47719	−	9.74446i	0.346003	−	0.450920i	−0.587641	−	0.809122i	$-0.699943\pi$
$467$	7.47719	−	9.74446i	0.346003	−	0.450920i	0.933644	+	0.358202i	$0.116610\pi$
$468$		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	−0.999568	−	0.0293745i	$-0.990648\pi$
$479$	−9.06902	−	18.3902i	−0.414374	−	0.840268i	0.585194	−	0.810893i	$-0.301018\pi$
$480$		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	0.158723	−	0.987323i	$-0.449262\pi$
$487$	9.81941	−	0.643598i	0.444960	−	0.0291642i	0.286237	+	0.958159i	$0.407596\pi$
$488$		0			0
$489$	−9.27712	−	9.27712i	−0.419526	−	0.419526i
$490$		0			0
$491$	−12.2643	−	5.08005i	−0.553481	−	0.229259i	0.0883712	−	0.996088i	$-0.471834\pi$
$491$	−12.2643	−	5.08005i	−0.553481	−	0.229259i	−0.641852	+	0.766828i	$0.721834\pi$
$492$		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	−0.478045	−	0.878336i	$-0.658654\pi$
$499$	−32.7455	−	16.1483i	−1.46589	−	0.722897i	−0.987846	+	0.155438i	$0.950321\pi$
$500$		0			0
$501$	−1.10222	+	8.37219i	−0.0492436	+	0.374042i
$502$		0			0
$503$	31.8541	+	6.33618i	1.42031	+	0.282516i	0.844713	−	0.535220i	$-0.179771\pi$
$503$	31.8541	+	6.33618i	1.42031	+	0.282516i	0.575593	+	0.817736i	$0.304771\pi$
$504$		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	0.693018	+	0.720920i	$0.256281\pi$
$509$	21.9032	+	37.9375i	0.970844	+	1.68155i	0.277826	+	0.960631i	$0.410386\pi$
$510$		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	0.869065	+	0.494697i	$0.164721\pi$
$521$	1.64357	+	25.0760i	0.0720059	+	1.09860i	−0.797059	+	0.603901i	$0.793612\pi$
$522$		0			0
$523$	10.0589	−	37.5405i	0.439847	−	1.64153i	−0.289347	−	0.957224i	$-0.593438\pi$
$523$	10.0589	−	37.5405i	0.439847	−	1.64153i	0.729194	−	0.684307i	$-0.239895\pi$
$524$		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	−0.834984	−	0.550275i	$-0.814523\pi$
$541$	−40.3469	−	2.64448i	−1.73465	−	0.113695i	−0.899666	+	0.436580i	$0.856190\pi$
$542$		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	0.135076	−	0.990835i	$-0.456872\pi$
$547$	−17.0416	−	11.3868i	−0.728645	−	0.486865i	−0.863721	+	0.503970i	$0.831872\pi$
$548$		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	−0.939514	−	0.342509i	$-0.888723\pi$
$557$	−7.01242	−	26.1707i	−0.297126	−	1.10889i	0.642389	−	0.766379i	$-0.277943\pi$
$558$		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	−0.562536	−	0.826773i	$-0.690174\pi$
$563$	2.14666	−	1.64719i	0.0904707	−	0.0694206i	0.653006	+	0.757352i	$0.273507\pi$
$564$		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	0.977291	−	0.211900i	$-0.0679653\pi$
$569$	24.4632	+	18.7713i	1.02555	+	0.786934i	0.0482614	+	0.998835i	$0.484632\pi$
$570$		0			0
$571$	29.2415	+	25.6441i	1.22372	+	1.07317i	0.995020	+	0.0996756i	$0.0317805\pi$
$571$	29.2415	+	25.6441i	1.22372	+	1.07317i	0.228699	+	0.973497i	$0.426553\pi$
$572$		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	−0.773443	−	0.633866i	$-0.781467\pi$
$577$	3.89672	−	6.74931i	0.162223	−	0.280978i	0.935665	+	0.352888i	$0.114800\pi$
$578$		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	−0.541634	−	0.840615i	$-0.682194\pi$
$587$	−8.00066	+	3.31398i	−0.330223	+	0.136783i	0.211411	+	0.977397i	$0.432194\pi$
$588$		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	−0.667779	−	0.744360i	$-0.732755\pi$
$593$	−27.2774	+	3.59114i	−1.12015	+	0.147470i	−0.452370	+	0.891830i	$0.649421\pi$
$594$		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	0.00745047	−	0.999972i	$-0.497628\pi$
$599$	12.5772	−	3.37004i	0.513889	−	0.137696i	0.506438	+	0.862276i	$0.330962\pi$
$600$		0			0
$601$	−20.5102	−	30.6957i	−0.836629	−	1.25210i	−0.965490	−	0.260441i	$-0.916132\pi$
$601$	−20.5102	−	30.6957i	−0.836629	−	1.25210i	0.128861	−	0.991663i	$-0.458868\pi$
$602$		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	0.851176	−	0.524881i	$-0.175890\pi$
$607$	5.41245	+	6.17172i	0.219685	+	0.250502i	−0.631491	+	0.775383i	$0.717557\pi$
$608$		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	−0.930450	−	0.366420i	$-0.880583\pi$
$613$	−3.66172	+	6.34229i	−0.147896	+	0.256163i	0.782554	+	0.622583i	$0.213917\pi$
$614$		0			0
$615$	−17.9019	+	26.7921i	−0.721875	+	1.08036i
$616$		0			0
$617$	−12.2532	+	2.43731i	−0.493295	+	0.0981225i	−0.435468	−	0.900204i	$-0.643417\pi$
$617$	−12.2532	+	2.43731i	−0.493295	+	0.0981225i	−0.0578268	+	0.998327i	$0.518417\pi$
$618$		0			0
$619$	36.0802	+	31.6415i	1.45019	+	1.27178i	0.899396	+	0.437134i	$0.144007\pi$
$619$	36.0802	+	31.6415i	1.45019	+	1.27178i	0.550789	+	0.834644i	$0.314327\pi$
$620$		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	−0.135940	−	0.990717i	$-0.543406\pi$
$631$	16.5973	−	40.0693i	0.660727	−	1.59514i	0.796667	−	0.604418i	$-0.206594\pi$
$632$		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	−0.0729859	−	0.997333i	$-0.523253\pi$
$641$	−18.6854	−	6.34282i	−0.738027	−	0.250527i	−0.665041	+	0.746806i	$0.731586\pi$
$642$		0			0
$643$	−13.8431	−	9.24968i	−0.545920	−	0.364772i	0.251820	−	0.967774i	$-0.418971\pi$
$643$	−13.8431	−	9.24968i	−0.545920	−	0.364772i	−0.797739	+	0.603002i	$0.793971\pi$
$644$		0			0
$645$			20.1401i			0.793014i
$646$		0			0
$647$	2.58347	+	1.49157i	0.101567	+	0.0586395i	0.549923	−	0.835215i	$-0.314657\pi$
$647$	2.58347	+	1.49157i	0.101567	+	0.0586395i	−0.448356	+	0.893855i	$0.647990\pi$
$648$		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	0.909372	−	0.415984i	$-0.136563\pi$
$653$	−1.66909	−	4.91697i	−0.0653165	−	0.192416i	−0.974688	+	0.223568i	$0.928229\pi$
$654$		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	−0.770406	−	0.637553i	$-0.779946\pi$
$659$	−3.41046	+	3.41046i	−0.132853	+	0.132853i	0.637553	+	0.770406i	$0.279946\pi$
$660$		0			0
$661$	9.72128	+	12.6690i	0.378114	+	0.492768i	0.943182	−	0.332277i	$-0.107817\pi$
$661$	9.72128	+	12.6690i	0.378114	+	0.492768i	−0.565068	+	0.825044i	$0.691150\pi$
$662$		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	−0.935606	−	0.353046i	$-0.885146\pi$
$673$	1.65735	−	8.33204i	0.0638860	−	0.321177i	0.999492	+	0.0318692i	$0.0101460\pi$
$674$		0			0
$675$	−1.66657	+	4.90955i	−0.0641462	+	0.188969i
$676$		0			0
$677$	1.85697	−	28.3318i	0.0713690	−	1.08888i	−0.800561	−	0.599251i	$-0.795465\pi$
$677$	1.85697	−	28.3318i	0.0713690	−	1.08888i	0.871930	−	0.489630i	$-0.162868\pi$
$678$		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	−0.929696	−	0.368328i	$-0.879930\pi$
$683$	−31.4512	+	15.5100i	−1.20345	+	0.593473i	−0.273749	+	0.961801i	$0.588264\pi$
$684$		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	0.302124	−	0.953269i	$-0.402304\pi$
$691$	−7.10358	−	3.50310i	−0.270233	−	0.133264i	−0.572357	+	0.820004i	$0.693971\pi$
$692$		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	0.956246	−	0.292565i	$-0.0945089\pi$
$701$	17.5719	+	17.5719i	0.663680	+	0.663680i	−0.292565	+	0.956246i	$0.594509\pi$
$702$		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	−0.0583421	−	0.998297i	$-0.518581\pi$
$709$	24.5980	−	21.5719i	0.923799	−	0.810150i	0.982141	+	0.188147i	$0.0602481\pi$
$710$		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	−0.245510	−	0.969394i	$-0.578955\pi$
$719$	18.3287	−	16.0739i	0.683546	−	0.599453i	0.929055	+	0.369941i	$0.120622\pi$
$720$		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	0.482822	−	0.875719i	$-0.339612\pi$
$727$	−10.5936	−	10.5936i	−0.392896	−	0.392896i	−0.875719	+	0.482822i	$0.839612\pi$
$728$		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	0.997015	+	0.0772054i	$0.0245997\pi$
$733$	1.46077	+	11.0956i	0.0539547	+	0.409827i	−0.943061	+	0.332621i	$0.892067\pi$
$734$		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	0.965213	+	0.261464i	$0.0842052\pi$
$739$	−0.945559	+	7.18223i	−0.0347830	+	0.264203i	−0.999996	+	0.00273900i	$0.999128\pi$
$740$		0			0
$741$	−7.65522	−	1.52272i	−0.281222	−	0.0559385i
$742$		0			0
$743$	8.45984	+	42.5305i	0.310361	+	1.56029i	0.749581	+	0.661912i	$0.230255\pi$
$743$	8.45984	+	42.5305i	0.310361	+	1.56029i	−0.439220	+	0.898380i	$0.644745\pi$
$744$		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	−0.719088	−	0.694919i	$-0.755440\pi$
$751$	2.31713	−	35.3526i	0.0845533	−	1.29003i	0.803641	−	0.595114i	$-0.202893\pi$
$752$		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	−0.985460	−	0.169910i	$-0.945652\pi$
$757$	−11.2470	−	27.1527i	−0.408779	−	0.986880i	0.576680	−	0.816970i	$-0.304348\pi$
$758$		0			0
$759$	−0.0842755	−	1.28580i	−0.00305901	−	0.0466715i
$760$		0			0
$761$	−4.52207	+	16.8766i	−0.163925	+	0.611775i	0.834250	+	0.551386i	$0.185901\pi$
$761$	−4.52207	+	16.8766i	−0.163925	+	0.611775i	−0.998175	+	0.0603893i	$0.980766\pi$
$762$		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	−0.821205	−	0.570634i	$-0.806698\pi$
$769$	−6.94855	+	6.94855i	−0.250571	+	0.250571i	0.570634	+	0.821205i	$0.306698\pi$
$770$		0			0
$771$	−12.3408	+	8.24588i	−0.444444	+	0.296968i
$772$		0			0
$773$	18.0760	+	2.37975i	0.650148	+	0.0855936i	0.448385	−	0.893841i	$-0.352000\pi$
$773$	18.0760	+	2.37975i	0.650148	+	0.0855936i	0.201763	+	0.979434i	$0.435333\pi$
$774$		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	0.270548	−	0.962707i	$-0.412795\pi$
$787$	−2.82978	−	0.960582i	−0.100871	−	0.0342411i	−0.371419	+	0.928465i	$0.621129\pi$
$788$		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	−0.842448	−	0.538778i	$-0.818886\pi$
$797$	3.78937	−	9.14835i	0.134226	−	0.324051i	0.976674	+	0.214727i	$0.0688862\pi$
$798$		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	0.809685	−	0.586865i	$-0.199638\pi$
$809$	9.48643	+	8.31937i	0.333525	+	0.292494i	−0.476160	+	0.879359i	$0.657972\pi$
$810$		0			0
$811$	33.9297	−	6.74904i	1.19143	−	0.236991i	0.440736	−	0.897637i	$-0.354718\pi$
$811$	33.9297	−	6.74904i	1.19143	−	0.236991i	0.750698	+	0.660646i	$0.229718\pi$
$812$		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	0.786112	−	0.618084i	$-0.212091\pi$
$821$	2.02599	+	2.31020i	0.0707076	+	0.0806266i	−0.715404	+	0.698711i	$0.753758\pi$
$822$		0			0
$823$	−4.57859	+	5.22088i	−0.159600	+	0.181988i	−0.826113	−	0.563505i	$-0.809453\pi$
$823$	−4.57859	+	5.22088i	−0.159600	+	0.181988i	0.666513	+	0.745493i	$0.267786\pi$
$824$		0			0
$825$	−0.196960	+	0.0815834i	−0.00685726	+	0.00284037i
$826$		0			0
$827$	27.6963	+	41.4504i	0.963095	+	1.44137i	0.896219	+	0.443612i	$0.146303\pi$
$827$	27.6963	+	41.4504i	0.963095	+	1.44137i	0.0668758	+	0.997761i	$0.478697\pi$
$828$		0			0
$829$	−3.21405	+	0.861202i	−0.111629	+	0.0299108i	−0.314201	−	0.949357i	$-0.601737\pi$
$829$	−3.21405	+	0.861202i	−0.111629	+	0.0299108i	0.202572	+	0.979267i	$0.435070\pi$
$830$		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	0.962384	−	0.271694i	$-0.0875840\pi$
$839$	9.93755	+	14.8726i	0.343082	+	0.513459i	−0.619301	+	0.785153i	$0.712584\pi$
$840$		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	−0.703506	−	0.710689i	$-0.748383\pi$
$853$	6.49269	−	9.71700i	0.222306	−	0.332704i	0.925811	+	0.377986i	$0.123383\pi$
$854$		0			0
$855$	1.53631	−	0.305591i	0.0525406	−	0.0104510i
$856$		0			0
$857$	−23.4655	−	20.5787i	−0.801567	−	0.702955i	0.157070	−	0.987587i	$-0.449795\pi$
$857$	−23.4655	−	20.5787i	−0.801567	−	0.702955i	−0.958637	+	0.284632i	$0.908128\pi$
$858$		0			0
$859$	−7.89827	−	6.06055i	−0.269485	−	0.206783i	0.465175	−	0.885219i	$-0.345992\pi$
$859$	−7.89827	−	6.06055i	−0.269485	−	0.206783i	−0.734660	+	0.678436i	$0.762658\pi$
$860$		0			0
$861$	−36.4042	−	21.4175i	−1.24065	−	0.729906i
$862$		0			0
$863$	10.6310	+	2.84857i	0.361884	+	0.0969665i	0.435179	−	0.900344i	$-0.356685\pi$
$863$	10.6310	+	2.84857i	0.361884	+	0.0969665i	−0.0732955	+	0.997310i	$0.523352\pi$
$864$		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	−0.653357	−	0.757050i	$-0.726640\pi$
$877$	−21.0509	+	7.14581i	−0.710838	+	0.241297i	−0.0574805	+	0.998347i	$0.518307\pi$
$878$		0			0
$879$	5.16218	+	1.75232i	0.174116	+	0.0591044i
$880$		0			0
$881$	−36.1875	−	24.1797i	−1.21919	−	0.814636i	−0.231772	−	0.972770i	$-0.574452\pi$
$881$	−36.1875	−	24.1797i	−1.21919	−	0.814636i	−0.987418	+	0.158134i	$0.949452\pi$
$882$		0			0
$883$		−	2.75706i		−	0.0927826i	−0.998923	−	0.0463913i	$-0.985228\pi$
$883$		−	2.75706i		−	0.0927826i	0.998923	−	0.0463913i	$-0.0147721\pi$
$884$		0			0
$885$	−0.894088	−	0.516202i	−0.0300545	−	0.0173519i
$886$		0			0
$887$	−44.6321	−	2.92534i	−1.49860	−	0.0982233i	−0.706107	−	0.708106i	$-0.749550\pi$
$887$	−44.6321	−	2.92534i	−1.49860	−	0.0982233i	−0.792492	+	0.609882i	$0.791217\pi$
$888$		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	−0.422709	−	0.906266i	$-0.638921\pi$
$907$	−3.67143	−	56.0151i	−0.121908	−	1.85995i	0.300801	−	0.953687i	$-0.402746\pi$
$908$		0			0
$909$	2.83770	+	6.85082i	0.0941206	+	0.227227i
$910$		0			0
$911$	−9.38431	+	47.1781i	−0.310916	+	1.56308i	0.437108	+	0.899409i	$0.356003\pi$
$911$	−9.38431	+	47.1781i	−0.310916	+	1.56308i	−0.748024	+	0.663671i	$0.768997\pi$
$912$		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	0.867504	+	0.497431i	$0.165723\pi$
$919$	26.2085	+	45.3945i	0.864540	+	1.49743i	−0.00296381	+	0.999996i	$0.500943\pi$
$920$		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	0.126560	−	0.991959i	$-0.459607\pi$
$929$	−17.7808	−	8.76853i	−0.583370	−	0.287686i	−0.709929	+	0.704273i	$0.751273\pi$
$930$		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	0.836736	−	0.547606i	$-0.184461\pi$
$937$	31.8711	+	13.2014i	1.04118	+	0.431272i	0.204446	+	0.978878i	$0.434461\pi$
$938$		0			0
$939$	19.0499	+	19.0499i	0.621670	+	0.621670i
$940$		0			0
$941$	2.33431	−	0.152999i	0.0760964	−	0.00498762i	−0.0273074	−	0.999627i	$-0.508693\pi$
$941$	2.33431	−	0.152999i	0.0760964	−	0.00498762i	0.103404	+	0.994639i	$0.467027\pi$
$942$		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	−0.486595	−	0.873627i	$-0.661761\pi$
$947$	9.72575	−	8.52925i	0.316044	−	0.277164i	0.802640	+	0.596464i	$0.203428\pi$
$948$		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	0.610086	−	0.792335i	$-0.291135\pi$
$967$	14.9642	+	6.19838i	0.481217	+	0.199326i	−0.128870	+	0.991662i	$0.541135\pi$
$968$		0			0
$969$	−7.05097	+	2.19724i	−0.226510	+	0.0705854i
$970$		0			0
$971$	−1.35195	−	10.2691i	−0.0433860	−	0.329550i	−0.999349	−	0.0360639i	$-0.988518\pi$
$971$	−1.35195	−	10.2691i	−0.0433860	−	0.329550i	0.955963	−	0.293486i	$-0.0948153\pi$
$972$		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	0.960510	+	0.278247i	$0.0897534\pi$
$977$	−1.22800	+	9.32756i	−0.0392871	+	0.298415i	−0.999797	+	0.0201679i	$0.993580\pi$
$978$		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	−0.866671	−	0.498881i	$-0.833745\pi$
$983$	−31.3051	+	15.4380i	−0.998478	+	0.492395i	−0.131807	+	0.991275i	$0.542078\pi$
$984$		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	0.635127	+	0.772408i	$0.280948\pi$
$991$	−10.6707	+	31.4348i	−0.338965	+	0.998560i	−0.974092	+	0.226152i	$0.927385\pi$
$992$		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	−0.920685	−	0.390308i	$-0.872369\pi$
$997$	−1.85732	−	28.3372i	−0.0588219	−	0.897449i	0.861863	−	0.507142i	$-0.169298\pi$
$998$		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.129.14	✓	288
7.5	odd	6	inner	952.2.cw.b.537.14	yes	288
17.12	odd	16	inner	952.2.cw.b.913.14	yes	288
119.12	even	48	inner	952.2.cw.b.369.14	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
952.2.cw.b.129.14	✓	288	1.1	even	1	trivial
952.2.cw.b.369.14	yes	288	119.12	even	48	inner
952.2.cw.b.537.14	yes	288	7.5	odd	6	inner
952.2.cw.b.913.14	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)

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