LMFDB - Embedded newform 936.2.q.g.313.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(313,936)] 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("936.313"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22,0,0,0,-3,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			313.1
Character	$\chi$	$=$	936.313
Dual form			936.2.q.g.625.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73199 - 0.0148978i) q^{3} +(0.550001 + 0.952629i) q^{5} +(-2.20940 + 3.82679i) q^{7} +(2.99956 + 0.0516057i) q^{9} +(-0.980092 + 1.69757i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(-0.938402 - 1.65814i) q^{15} -2.75799 q^{17} +0.806396 q^{19} +(3.88366 - 6.59503i) q^{21} +(-1.05424 - 1.82600i) q^{23} +(1.89500 - 3.28223i) q^{25} +(-5.19442 - 0.134067i) q^{27} +(0.430401 - 0.745476i) q^{29} +(-0.322355 - 0.558335i) q^{31} +(1.72280 - 2.92557i) q^{33} -4.86068 q^{35} -3.81155 q^{37} +(0.853091 + 1.50739i) q^{39} +(-1.20773 - 2.09186i) q^{41} +(-4.94434 + 8.56385i) q^{43} +(1.60060 + 2.88585i) q^{45} +(1.72459 - 2.98707i) q^{47} +(-6.26287 - 10.8476i) q^{49} +(4.77679 + 0.0410880i) q^{51} -8.37048 q^{53} -2.15621 q^{55} +(-1.39667 - 0.0120136i) q^{57} +(-7.39832 - 12.8143i) q^{59} +(-6.00712 + 10.4046i) q^{61} +(-6.82470 + 11.3646i) q^{63} +(0.550001 - 0.952629i) q^{65} +(-4.62430 - 8.00953i) q^{67} +(1.79873 + 3.17832i) q^{69} +10.1222 q^{71} -3.88803 q^{73} +(-3.33101 + 5.65655i) q^{75} +(-4.33083 - 7.50121i) q^{77} +(-8.48531 + 14.6970i) q^{79} +(8.99467 + 0.309589i) q^{81} +(3.77234 - 6.53389i) q^{83} +(-1.51689 - 2.62734i) q^{85} +(-0.756555 + 1.28474i) q^{87} +4.54701 q^{89} +4.41879 q^{91} +(0.549997 + 0.971832i) q^{93} +(0.443518 + 0.768196i) q^{95} +(-1.53005 + 2.65012i) q^{97} +(-3.02745 + 5.04138i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{5} - 4 q^{7} - 4 q^{9} + 5 q^{11} - 11 q^{13} + 5 q^{15} + 8 q^{17} + 10 q^{19} + 4 q^{21} + 9 q^{23} - 24 q^{25} - 12 q^{27} - 16 q^{29} - q^{31} + 9 q^{33} + 18 q^{37} + 3 q^{39} - 6 q^{41}+ \cdots - 109 q^{99}+O(q^{100}) $ 22 * q - 3 * q^5 - 4 * q^7 - 4 * q^9 + 5 * q^11 - 11 * q^13 + 5 * q^15 + 8 * q^17 + 10 * q^19 + 4 * q^21 + 9 * q^23 - 24 * q^25 - 12 * q^27 - 16 * q^29 - q^31 + 9 * q^33 + 18 * q^37 + 3 * q^39 - 6 * q^41 - 7 * q^43 - 21 * q^45 + 21 * q^47 - 27 * q^49 - 11 * q^51 + 32 * q^53 + 34 * q^55 + 2 * q^57 + 11 * q^59 - 2 * q^61 - 27 * q^63 - 3 * q^65 - 18 * q^67 + 7 * q^69 - 30 * q^71 + 18 * q^73 + 62 * q^75 - 9 * q^77 - 30 * q^79 + 4 * q^81 - 16 * q^83 - 32 * q^85 + 33 * q^87 + 26 * q^89 + 8 * q^91 + 20 * q^95 - 10 * q^97 - 109 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.73199	−	0.0148978i	−0.999963	−	0.00860127i
$3$	−1.73199	−	0.0148978i	−0.999963	−	0.00860127i
$4$		0			0
$5$	0.550001	+	0.952629i	0.245968	+	0.426029i	0.962403	−	0.271625i	$-0.0875609\pi$
$5$	0.550001	+	0.952629i	0.245968	+	0.426029i	−0.716435	+	0.697653i	$0.754228\pi$
$6$		0			0
$7$	−2.20940	+	3.82679i	−0.835074	+	1.44639i	0.0588967	+	0.998264i	$0.481242\pi$
$7$	−2.20940	+	3.82679i	−0.835074	+	1.44639i	−0.893970	+	0.448126i	$0.852092\pi$
$8$		0			0
$9$	2.99956	+	0.0516057i	0.999852	+	0.0172019i
$10$		0			0
$11$	−0.980092	+	1.69757i	−0.295509	+	0.511837i	−0.975103	−	0.221752i	$-0.928823\pi$
$11$	−0.980092	+	1.69757i	−0.295509	+	0.511837i	0.679594	+	0.733588i	$0.262156\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$		0			0
$15$	−0.938402	−	1.65814i	−0.242294	−	0.428129i
$16$		0			0
$17$	−2.75799			−0.668910			−0.334455	−	0.942412i	$-0.608552\pi$
$17$	−2.75799			−0.668910			−0.334455	+	0.942412i	$0.608552\pi$
$18$		0			0
$19$	0.806396			0.185000			0.0924999	−	0.995713i	$-0.470514\pi$
$19$	0.806396			0.185000			0.0924999	+	0.995713i	$0.470514\pi$
$20$		0			0
$21$	3.88366	−	6.59503i	0.847484	−	1.43915i
$22$		0			0
$23$	−1.05424	−	1.82600i	−0.219825	−	0.380748i	0.734929	−	0.678144i	$-0.237215\pi$
$23$	−1.05424	−	1.82600i	−0.219825	−	0.380748i	−0.954754	+	0.297396i	$0.903882\pi$
$24$		0			0
$25$	1.89500	−	3.28223i	0.379000	−	0.656447i
$26$		0			0
$27$	−5.19442	−	0.134067i	−0.999667	−	0.0258013i
$28$		0			0
$29$	0.430401	−	0.745476i	0.0799234	−	0.138431i	−0.823293	−	0.567616i	$-0.807866\pi$
$29$	0.430401	−	0.745476i	0.0799234	−	0.138431i	0.903217	+	0.429185i	$0.141199\pi$
$30$		0			0
$31$	−0.322355	−	0.558335i	−0.0578967	−	0.100280i	0.835624	−	0.549301i	$-0.185106\pi$
$31$	−0.322355	−	0.558335i	−0.0578967	−	0.100280i	−0.893521	+	0.449021i	$0.851773\pi$
$32$		0			0
$33$	1.72280	−	2.92557i	0.299901	−	0.509276i
$34$		0			0
$35$	−4.86068			−0.821605
$36$		0			0
$37$	−3.81155			−0.626615			−0.313307	−	0.949652i	$-0.601437\pi$
$37$	−3.81155			−0.626615			−0.313307	+	0.949652i	$0.601437\pi$
$38$		0			0
$39$	0.853091	+	1.50739i	0.136604	+	0.241376i
$40$		0			0
$41$	−1.20773	−	2.09186i	−0.188616	−	0.326693i	0.756173	−	0.654372i	$-0.227067\pi$
$41$	−1.20773	−	2.09186i	−0.188616	−	0.326693i	−0.944789	+	0.327679i	$0.893734\pi$
$42$		0			0
$43$	−4.94434	+	8.56385i	−0.754005	+	1.30597i	0.191863	+	0.981422i	$0.438547\pi$
$43$	−4.94434	+	8.56385i	−0.754005	+	1.30597i	−0.945868	+	0.324553i	$0.894786\pi$
$44$		0			0
$45$	1.60060	+	2.88585i	0.238603	+	0.430197i
$46$		0			0
$47$	1.72459	−	2.98707i	0.251557	−	0.435709i	−0.712398	−	0.701776i	$-0.752391\pi$
$47$	1.72459	−	2.98707i	0.251557	−	0.435709i	0.963955	+	0.266067i	$0.0857242\pi$
$48$		0			0
$49$	−6.26287	−	10.8476i	−0.894696	−	1.54966i
$50$		0			0
$51$	4.77679	+	0.0410880i	0.668885	+	0.00575348i
$52$		0			0
$53$	−8.37048			−1.14977			−0.574887	−	0.818233i	$-0.694954\pi$
$53$	−8.37048			−1.14977			−0.574887	+	0.818233i	$0.694954\pi$
$54$		0			0
$55$	−2.15621			−0.290743
$56$		0			0
$57$	−1.39667	−	0.0120136i	−0.184993	−	0.00159123i
$58$		0			0
$59$	−7.39832	−	12.8143i	−0.963180	−	1.66828i	−0.714428	−	0.699709i	$-0.753313\pi$
$59$	−7.39832	−	12.8143i	−0.963180	−	1.66828i	−0.248751	−	0.968567i	$-0.580020\pi$
$60$		0			0
$61$	−6.00712	+	10.4046i	−0.769133	+	1.33218i	0.168901	+	0.985633i	$0.445978\pi$
$61$	−6.00712	+	10.4046i	−0.769133	+	1.33218i	−0.938034	+	0.346544i	$0.887355\pi$
$62$		0			0
$63$	−6.82470	+	11.3646i	−0.859831	+	1.43181i
$64$		0			0
$65$	0.550001	−	0.952629i	0.0682192	−	0.118159i
$66$		0			0
$67$	−4.62430	−	8.00953i	−0.564949	−	0.978520i	−0.997054	−	0.0766967i	$-0.975563\pi$
$67$	−4.62430	−	8.00953i	−0.564949	−	0.978520i	0.432106	−	0.901823i	$-0.357771\pi$
$68$		0			0
$69$	1.79873	+	3.17832i	0.216542	+	0.382625i
$70$		0			0
$71$	10.1222			1.20128			0.600639	−	0.799520i	$-0.294913\pi$
$71$	10.1222			1.20128			0.600639	+	0.799520i	$0.294913\pi$
$72$		0			0
$73$	−3.88803			−0.455059			−0.227529	−	0.973771i	$-0.573065\pi$
$73$	−3.88803			−0.455059			−0.227529	+	0.973771i	$0.573065\pi$
$74$		0			0
$75$	−3.33101	+	5.65655i	−0.384632	+	0.653162i
$76$		0			0
$77$	−4.33083	−	7.50121i	−0.493544	−	0.854843i
$78$		0			0
$79$	−8.48531	+	14.6970i	−0.954672	+	1.65354i	−0.219554	+	0.975600i	$0.570460\pi$
$79$	−8.48531	+	14.6970i	−0.954672	+	1.65354i	−0.735118	+	0.677939i	$0.762873\pi$
$80$		0			0
$81$	8.99467	+	0.309589i	0.999408	+	0.0343987i
$82$		0			0
$83$	3.77234	−	6.53389i	0.414068	−	0.717188i	−0.581262	−	0.813717i	$-0.697441\pi$
$83$	3.77234	−	6.53389i	0.414068	−	0.717188i	0.995330	+	0.0965291i	$0.0307741\pi$
$84$		0			0
$85$	−1.51689	−	2.62734i	−0.164530	−	0.284975i
$86$		0			0
$87$	−0.756555	+	1.28474i	−0.0811112	+	0.137739i
$88$		0			0
$89$	4.54701			0.481982			0.240991	−	0.970527i	$-0.422528\pi$
$89$	4.54701			0.481982			0.240991	+	0.970527i	$0.422528\pi$
$90$		0			0
$91$	4.41879			0.463216
$92$		0			0
$93$	0.549997	+	0.971832i	0.0570320	+	0.100774i
$94$		0			0
$95$	0.443518	+	0.768196i	0.0455040	+	0.0788153i
$96$		0			0
$97$	−1.53005	+	2.65012i	−0.155353	+	0.269079i	−0.933187	−	0.359390i	$-0.882985\pi$
$97$	−1.53005	+	2.65012i	−0.155353	+	0.269079i	0.777835	+	0.628469i	$0.216318\pi$
$98$		0			0
$99$	−3.02745	+	5.04138i	−0.304270	+	0.506678i
$100$		0			0
$101$	6.29565	−	10.9044i	0.626441	−	1.08503i	−0.361819	−	0.932248i	$-0.617844\pi$
$101$	6.29565	−	10.9044i	0.626441	−	1.08503i	0.988260	−	0.152779i	$-0.0488223\pi$
$102$		0			0
$103$	−0.324615	−	0.562249i	−0.0319853	−	0.0554001i	0.849590	−	0.527444i	$-0.176850\pi$
$103$	−0.324615	−	0.562249i	−0.0319853	−	0.0554001i	−0.881575	+	0.472044i	$0.843516\pi$
$104$		0			0
$105$	8.41864	+	0.0724137i	0.821575	+	0.00706685i
$106$		0			0
$107$	−18.6706			−1.80495			−0.902476	−	0.430740i	$-0.858253\pi$
$107$	−18.6706			−1.80495			−0.902476	+	0.430740i	$0.858253\pi$
$108$		0			0
$109$	−3.93071			−0.376494			−0.188247	−	0.982122i	$-0.560281\pi$
$109$	−3.93071			−0.376494			−0.188247	+	0.982122i	$0.560281\pi$
$110$		0			0
$111$	6.60155	+	0.0567839i	0.626591	+	0.00538968i
$112$		0			0
$113$	8.92632	+	15.4608i	0.839718	+	1.45443i	0.890131	+	0.455705i	$0.150613\pi$
$113$	8.92632	+	15.4608i	0.839718	+	1.45443i	−0.0504128	+	0.998728i	$0.516054\pi$
$114$		0			0
$115$	1.15967	−	2.00861i	0.108140	−	0.187304i
$116$		0			0
$117$	−1.45509	−	2.62349i	−0.134523	−	0.242542i
$118$		0			0
$119$	6.09349	−	10.5542i	0.558589	−	0.967505i
$120$		0			0
$121$	3.57884	+	6.19873i	0.325349	+	0.563521i
$122$		0			0
$123$	2.06061	+	3.64106i	0.185799	+	0.328303i
$124$		0			0
$125$	9.66901			0.864823
$126$		0			0
$127$	−6.05982			−0.537722			−0.268861	−	0.963179i	$-0.586647\pi$
$127$	−6.05982			−0.537722			−0.268861	+	0.963179i	$0.586647\pi$
$128$		0			0
$129$	8.69111	−	14.7588i	0.765210	−	1.29944i
$130$		0			0
$131$	−8.47113	−	14.6724i	−0.740126	−	1.28194i	−0.952438	−	0.304734i	$-0.901433\pi$
$131$	−8.47113	−	14.6724i	−0.740126	−	1.28194i	0.212312	−	0.977202i	$-0.431901\pi$
$132$		0			0
$133$	−1.78165	+	3.08591i	−0.154488	+	0.267582i
$134$		0			0
$135$	−2.72922	−	5.02210i	−0.234894	−	0.432233i
$136$		0			0
$137$	4.06146	−	7.03465i	0.346994	−	0.601011i	−0.638720	−	0.769439i	$-0.720536\pi$
$137$	4.06146	−	7.03465i	0.346994	−	0.601011i	0.985714	+	0.168428i	$0.0538691\pi$
$138$		0			0
$139$	−2.18590	−	3.78610i	−0.185406	−	0.321133i	0.758307	−	0.651897i	$-0.226027\pi$
$139$	−2.18590	−	3.78610i	−0.185406	−	0.321133i	−0.943713	+	0.330765i	$0.892693\pi$
$140$		0			0
$141$	−3.03146	+	5.14787i	−0.255295	+	0.433529i
$142$		0			0
$143$	1.96018			0.163919
$144$		0			0
$145$	0.946883			0.0786344
$146$		0			0
$147$	10.6856	+	18.8812i	0.881334	+	1.55730i
$148$		0			0
$149$	−2.63110	−	4.55719i	−0.215548	−	0.373340i	0.737894	−	0.674916i	$-0.235820\pi$
$149$	−2.63110	−	4.55719i	−0.215548	−	0.373340i	−0.953442	+	0.301577i	$0.902487\pi$
$150$		0			0
$151$	−1.96849	+	3.40952i	−0.160193	+	0.277463i	−0.934938	−	0.354812i	$-0.884545\pi$
$151$	−1.96849	+	3.40952i	−0.160193	+	0.277463i	0.774745	+	0.632274i	$0.217878\pi$
$152$		0			0
$153$	−8.27273	−	0.142328i	−0.668811	−	0.0115065i
$154$		0			0
$155$	0.354591	−	0.614170i	0.0284814	−	0.0493313i
$156$		0			0
$157$	4.53451	+	7.85399i	0.361893	+	0.626817i	0.988272	−	0.152701i	$-0.0487973\pi$
$157$	4.53451	+	7.85399i	0.361893	+	0.626817i	−0.626379	+	0.779518i	$0.715464\pi$
$158$		0			0
$159$	14.4976	+	0.124702i	1.14973	+	0.00988952i
$160$		0			0
$161$	9.31698			0.734281
$162$		0			0
$163$	15.6536			1.22609			0.613043	−	0.790049i	$-0.289945\pi$
$163$	15.6536			1.22609			0.613043	+	0.790049i	$0.289945\pi$
$164$		0			0
$165$	3.73452	+	0.0321228i	0.290732	+	0.00250076i
$166$		0			0
$167$	4.12571	+	7.14593i	0.319257	+	0.552969i	0.980333	−	0.197350i	$-0.0632334\pi$
$167$	4.12571	+	7.14593i	0.319257	+	0.552969i	−0.661076	+	0.750319i	$0.729900\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$		0			0
$171$	2.41883	+	0.0416146i	0.184972	+	0.00318235i
$172$		0			0
$173$	−8.87926	+	15.3793i	−0.675078	+	1.16927i	0.301368	+	0.953508i	$0.402557\pi$
$173$	−8.87926	+	15.3793i	−0.675078	+	1.16927i	−0.976446	+	0.215761i	$0.930777\pi$
$174$		0			0
$175$	8.37361	+	14.5035i	0.632985	+	1.09636i
$176$		0			0
$177$	12.6229	+	22.3044i	0.948795	+	1.67650i
$178$		0			0
$179$	3.22435			0.241000			0.120500	−	0.992713i	$-0.461550\pi$
$179$	3.22435			0.241000			0.120500	+	0.992713i	$0.461550\pi$
$180$		0			0
$181$	−3.49209			−0.259565			−0.129783	−	0.991542i	$-0.541428\pi$
$181$	−3.49209			−0.259565			−0.129783	+	0.991542i	$0.541428\pi$
$182$		0			0
$183$	10.5593	−	17.9312i	0.780563	−	1.32551i
$184$		0			0
$185$	−2.09635	−	3.63099i	−0.154127	−	0.266956i
$186$		0			0
$187$	2.70308	−	4.68187i	0.197669	−	0.342373i
$188$		0			0
$189$	11.9896	−	19.5817i	0.872114	−	1.42436i
$190$		0			0
$191$	−0.637521	+	1.10422i	−0.0461294	+	0.0798985i	−0.888168	−	0.459518i	$-0.848022\pi$
$191$	−0.637521	+	1.10422i	−0.0461294	+	0.0798985i	0.842039	+	0.539417i	$0.181355\pi$
$192$		0			0
$193$	−2.38676	−	4.13399i	−0.171803	−	0.297571i	0.767247	−	0.641351i	$-0.221626\pi$
$193$	−2.38676	−	4.13399i	−0.171803	−	0.297571i	−0.939050	+	0.343780i	$0.888293\pi$
$194$		0			0
$195$	−0.966786	+	1.64175i	−0.0692330	+	0.117568i
$196$		0			0
$197$	6.39808			0.455844			0.227922	−	0.973679i	$-0.426807\pi$
$197$	6.39808			0.455844			0.227922	+	0.973679i	$0.426807\pi$
$198$		0			0
$199$	21.0023			1.48881			0.744405	−	0.667728i	$-0.232733\pi$
$199$	21.0023			1.48881			0.744405	+	0.667728i	$0.232733\pi$
$200$		0			0
$201$	7.88991	+	13.9413i	0.556511	+	0.983343i
$202$		0			0
$203$	1.90185	+	3.29411i	0.133484	+	0.231201i
$204$		0			0
$205$	1.32851	−	2.30104i	0.0927870	−	0.160712i
$206$		0			0
$207$	−3.06803	−	5.53161i	−0.213243	−	0.384473i
$208$		0			0
$209$	−0.790342	+	1.36891i	−0.0546691	+	0.0946897i
$210$		0			0
$211$	12.9396	+	22.4120i	0.890798	+	1.54291i	0.838921	+	0.544254i	$0.183187\pi$
$211$	12.9396	+	22.4120i	0.890798	+	1.54291i	0.0518772	+	0.998653i	$0.483480\pi$
$212$		0			0
$213$	−17.5314	−	0.150798i	−1.20123	−	0.0103325i
$214$		0			0
$215$	−10.8776			−0.741844
$216$		0			0
$217$	2.84884			0.193392
$218$		0			0
$219$	6.73401	+	0.0579232i	0.455042	+	0.00391409i
$220$		0			0
$221$	1.37899	+	2.38849i	0.0927611	+	0.160667i
$222$		0			0
$223$	0.109377	−	0.189446i	0.00732440	−	0.0126862i	−0.862340	−	0.506330i	$-0.831002\pi$
$223$	0.109377	−	0.189446i	0.00732440	−	0.0126862i	0.869664	+	0.493643i	$0.164335\pi$
$224$		0			0
$225$	5.85354	−	9.74745i	0.390236	−	0.649830i
$226$		0			0
$227$	−2.99831	+	5.19322i	−0.199005	+	0.344686i	−0.948206	−	0.317656i	$-0.897104\pi$
$227$	−2.99831	+	5.19322i	−0.199005	+	0.344686i	0.749201	+	0.662342i	$0.230438\pi$
$228$		0			0
$229$	4.04613	+	7.00809i	0.267375	+	0.463108i	0.968183	−	0.250242i	$-0.0805103\pi$
$229$	4.04613	+	7.00809i	0.267375	+	0.463108i	−0.700808	+	0.713350i	$0.747177\pi$
$230$		0			0
$231$	7.38918	+	13.0565i	0.486173	+	0.859056i
$232$		0			0
$233$	−11.4650			−0.751095			−0.375547	−	0.926803i	$-0.622545\pi$
$233$	−11.4650			−0.751095			−0.375547	+	0.926803i	$0.622545\pi$
$234$		0			0
$235$	3.79409			0.247499
$236$		0			0
$237$	14.9154	−	25.3286i	0.968859	−	1.64527i
$238$		0			0
$239$	0.260007	+	0.450345i	0.0168185	+	0.0291304i	0.874312	−	0.485364i	$-0.161313\pi$
$239$	0.260007	+	0.450345i	0.0168185	+	0.0291304i	−0.857494	+	0.514494i	$0.827980\pi$
$240$		0			0
$241$	−14.6527	+	25.3793i	−0.943865	+	1.63482i	−0.185857	+	0.982577i	$0.559506\pi$
$241$	−14.6527	+	25.3793i	−0.943865	+	1.63482i	−0.758008	+	0.652245i	$0.773827\pi$
$242$		0			0
$243$	−15.5740	−	0.670205i	−0.999075	−	0.0429936i
$244$		0			0
$245$	6.88917	−	11.9324i	0.440133	−	0.762333i
$246$		0			0
$247$	−0.403198	−	0.698359i	−0.0256549	−	0.0444355i
$248$		0			0
$249$	−6.63099	+	11.2604i	−0.420222	+	0.713600i
$250$		0			0
$251$	−8.68404			−0.548132			−0.274066	−	0.961711i	$-0.588369\pi$
$251$	−8.68404			−0.548132			−0.274066	+	0.961711i	$0.588369\pi$
$252$		0			0
$253$	4.13303			0.259841
$254$		0			0
$255$	2.58810	+	4.57311i	0.162073	+	0.286379i
$256$		0			0
$257$	7.66705	+	13.2797i	0.478257	+	0.828366i	0.999689	−	0.0249267i	$-0.00793524\pi$
$257$	7.66705	+	13.2797i	0.478257	+	0.828366i	−0.521432	+	0.853293i	$0.674602\pi$
$258$		0			0
$259$	8.42122	−	14.5860i	0.523269	−	0.906329i
$260$		0			0
$261$	1.32948	−	2.21389i	0.0822929	−	0.137036i
$262$		0			0
$263$	2.56063	−	4.43514i	0.157895	−	0.273482i	−0.776214	−	0.630469i	$-0.782863\pi$
$263$	2.56063	−	4.43514i	0.157895	−	0.273482i	0.934109	+	0.356987i	$0.116196\pi$
$264$		0			0
$265$	−4.60377	−	7.97396i	−0.282807	−	0.489837i
$266$		0			0
$267$	−7.87535	−	0.0677406i	−0.481964	−	0.00414566i
$268$		0			0
$269$	11.3160			0.689947			0.344974	−	0.938612i	$-0.387888\pi$
$269$	11.3160			0.689947			0.344974	+	0.938612i	$0.387888\pi$
$270$		0			0
$271$	7.56435			0.459502			0.229751	−	0.973249i	$-0.426209\pi$
$271$	7.56435			0.459502			0.229751	+	0.973249i	$0.426209\pi$
$272$		0			0
$273$	−7.65329	−	0.0658305i	−0.463198	−	0.00398424i
$274$		0			0
$275$	3.71455	+	6.43378i	0.223996	+	0.387972i
$276$		0			0
$277$	−13.4464	+	23.2899i	−0.807918	+	1.39936i	0.106385	+	0.994325i	$0.466073\pi$
$277$	−13.4464	+	23.2899i	−0.807918	+	1.39936i	−0.914303	+	0.405031i	$0.867261\pi$
$278$		0			0
$279$	−0.938109	−	1.69139i	−0.0561631	−	0.101261i
$280$		0			0
$281$	−4.20215	+	7.27834i	−0.250679	+	0.434189i	−0.963713	−	0.266940i	$-0.913987\pi$
$281$	−4.20215	+	7.27834i	−0.250679	+	0.434189i	0.713034	+	0.701130i	$0.247321\pi$
$282$		0			0
$283$	−10.1692	−	17.6136i	−0.604498	−	1.04702i	−0.992131	−	0.125208i	$-0.960040\pi$
$283$	−10.1692	−	17.6136i	−0.604498	−	1.04702i	0.387632	−	0.921814i	$-0.373293\pi$
$284$		0			0
$285$	−0.756723	−	1.33711i	−0.0448244	−	0.0792037i
$286$		0			0
$287$	10.6734			0.630034
$288$		0			0
$289$	−9.39351			−0.552560
$290$		0			0
$291$	2.68950	−	4.56718i	0.157661	−	0.267733i
$292$		0			0
$293$	−10.0050	−	17.3291i	−0.584496	−	1.01238i	−0.994938	−	0.100490i	$-0.967959\pi$
$293$	−10.0050	−	17.3291i	−0.584496	−	1.01238i	0.410442	−	0.911887i	$-0.365374\pi$
$294$		0			0
$295$	8.13817	−	14.0957i	0.473822	−	0.820684i
$296$		0			0
$297$	5.31860	−	8.68650i	0.308617	−	0.504042i
$298$		0			0
$299$	−1.05424	+	1.82600i	−0.0609685	+	0.105601i
$300$		0			0
$301$	−21.8480	−	37.8419i	−1.25930	−	2.18117i
$302$		0			0
$303$	−11.0664	+	18.7925i	−0.635750	+	1.07960i
$304$		0			0
$305$	−13.2157			−0.756728
$306$		0			0
$307$	−31.3583			−1.78971			−0.894856	−	0.446355i	$-0.852722\pi$
$307$	−31.3583			−1.78971			−0.894856	+	0.446355i	$0.852722\pi$
$308$		0			0
$309$	0.553852	+	0.978645i	0.0315076	+	0.0556732i
$310$		0			0
$311$	−10.4791	−	18.1504i	−0.594218	−	1.02922i	−0.993657	−	0.112456i	$-0.964128\pi$
$311$	−10.4791	−	18.1504i	−0.594218	−	1.02922i	0.399439	−	0.916760i	$-0.369205\pi$
$312$		0			0
$313$	11.2371	−	19.4632i	0.635156	−	1.10012i	−0.351326	−	0.936253i	$-0.614269\pi$
$313$	11.2371	−	19.4632i	0.635156	−	1.10012i	0.986482	−	0.163869i	$-0.0523976\pi$
$314$		0			0
$315$	−14.5799	−	0.250839i	−0.821484	−	0.0141332i
$316$		0			0
$317$	−8.00550	+	13.8659i	−0.449634	+	0.778788i	−0.998362	−	0.0572123i	$-0.981779\pi$
$317$	−8.00550	+	13.8659i	−0.449634	+	0.778788i	0.548728	+	0.836001i	$0.315112\pi$
$318$		0			0
$319$	0.843665	+	1.46127i	0.0472362	+	0.0818155i
$320$		0			0
$321$	32.3372	+	0.278151i	1.80489	+	0.0155249i
$322$		0			0
$323$	−2.22403			−0.123748
$324$		0			0
$325$	−3.79000			−0.210231
$326$		0			0
$327$	6.80794	+	0.0585592i	0.376480	+	0.00323833i
$328$		0			0
$329$	7.62059	+	13.1992i	0.420137	+	0.727698i
$330$		0			0
$331$	−14.4974	+	25.1103i	−0.796851	+	1.38019i	0.124806	+	0.992181i	$0.460169\pi$
$331$	−14.4974	+	25.1103i	−0.796851	+	1.38019i	−0.921657	+	0.388005i	$0.873164\pi$
$332$		0			0
$333$	−11.4330	−	0.196698i	−0.626522	−	0.0107790i
$334$		0			0
$335$	5.08674	−	8.81049i	0.277918	−	0.481369i
$336$		0			0
$337$	−13.4112	−	23.2289i	−0.730555	−	1.26536i	−0.956646	−	0.291252i	$-0.905928\pi$
$337$	−13.4112	−	23.2289i	−0.730555	−	1.26536i	0.226092	−	0.974106i	$-0.427405\pi$
$338$		0			0
$339$	−15.2299	−	26.9110i	−0.827177	−	1.46160i
$340$		0			0
$341$	1.26375			0.0684359
$342$		0			0
$343$	24.4171			1.31840
$344$		0			0
$345$	−2.03846	+	3.46161i	−0.109747	+	0.186367i
$346$		0			0
$347$	−10.4067	−	18.0249i	−0.558658	−	0.967625i	−0.997609	−	0.0691134i	$-0.977983\pi$
$347$	−10.4067	−	18.0249i	−0.558658	−	0.967625i	0.438950	−	0.898511i	$-0.355350\pi$
$348$		0			0
$349$	7.00049	−	12.1252i	0.374728	−	0.649047i	−0.615559	−	0.788091i	$-0.711070\pi$
$349$	7.00049	−	12.1252i	0.374728	−	0.649047i	0.990286	+	0.139044i	$0.0444029\pi$
$350$		0			0
$351$	2.48111	+	4.56554i	0.132432	+	0.243690i
$352$		0			0
$353$	−8.72446	+	15.1112i	−0.464356	+	0.804288i	−0.999172	−	0.0406801i	$-0.987048\pi$
$353$	−8.72446	+	15.1112i	−0.464356	+	0.804288i	0.534816	+	0.844968i	$0.320381\pi$
$354$		0			0
$355$	5.56719	+	9.64266i	0.295476	+	0.511779i
$356$		0			0
$357$	−10.7111	+	18.1890i	−0.566890	+	0.962664i
$358$		0			0
$359$	27.6023			1.45679			0.728396	−	0.685157i	$-0.240266\pi$
$359$	27.6023			1.45679			0.728396	+	0.685157i	$0.240266\pi$
$360$		0			0
$361$	−18.3497			−0.965775
$362$		0			0
$363$	−6.10615	−	10.7894i	−0.320490	−	0.566298i
$364$		0			0
$365$	−2.13842	−	3.70385i	−0.111930	−	0.193868i
$366$		0			0
$367$	−8.13404	+	14.0886i	−0.424594	+	0.735418i	−0.996382	−	0.0849832i	$-0.972916\pi$
$367$	−8.13404	+	14.0886i	−0.424594	+	0.735418i	0.571789	+	0.820401i	$0.306250\pi$
$368$		0			0
$369$	−3.51471	−	6.33696i	−0.182969	−	0.329889i
$370$		0			0
$371$	18.4937	−	32.0320i	0.960146	−	1.66302i
$372$		0			0
$373$	15.5027	+	26.8514i	0.802699	+	1.39031i	0.917834	+	0.396965i	$0.129937\pi$
$373$	15.5027	+	26.8514i	0.802699	+	1.39031i	−0.115135	+	0.993350i	$0.536730\pi$
$374$		0			0
$375$	−16.7466	−	0.144047i	−0.864791	−	0.00743858i
$376$		0			0
$377$	−0.860802			−0.0443335
$378$		0			0
$379$	10.4947			0.539078			0.269539	−	0.962989i	$-0.413129\pi$
$379$	10.4947			0.539078			0.269539	+	0.962989i	$0.413129\pi$
$380$		0			0
$381$	10.4955	+	0.0902782i	0.537702	+	0.00462509i
$382$		0			0
$383$	18.3226	+	31.7357i	0.936241	+	1.62162i	0.772405	+	0.635130i	$0.219053\pi$
$383$	18.3226	+	31.7357i	0.936241	+	1.62162i	0.163836	+	0.986488i	$0.447613\pi$
$384$		0			0
$385$	4.76392	−	8.25135i	0.242792	−	0.420528i
$386$		0			0
$387$	−15.2728	+	25.4326i	−0.776358	+	1.29281i
$388$		0			0
$389$	−12.5593	+	21.7534i	−0.636783	+	1.10294i	0.349351	+	0.936992i	$0.386402\pi$
$389$	−12.5593	+	21.7534i	−0.636783	+	1.10294i	−0.986134	+	0.165949i	$0.946931\pi$
$390$		0			0
$391$	2.90759	+	5.03609i	0.147043	+	0.254686i
$392$		0			0
$393$	14.4533	+	25.5386i	0.729072	+	1.28825i
$394$		0			0
$395$	−18.6677			−0.939274
$396$		0			0
$397$	−14.6095			−0.733232			−0.366616	−	0.930372i	$-0.619484\pi$
$397$	−14.6095			−0.733232			−0.366616	+	0.930372i	$0.619484\pi$
$398$		0			0
$399$	3.13176	−	5.31820i	0.156784	−	0.266243i
$400$		0			0
$401$	4.73963	+	8.20928i	0.236686	+	0.409952i	0.959761	−	0.280817i	$-0.0906055\pi$
$401$	4.73963	+	8.20928i	0.236686	+	0.409952i	−0.723075	+	0.690769i	$0.757272\pi$
$402$		0			0
$403$	−0.322355	+	0.558335i	−0.0160576	+	0.0278127i
$404$		0			0
$405$	4.65215	+	8.73886i	0.231167	+	0.434238i
$406$		0			0
$407$	3.73567	−	6.47037i	0.185170	−	0.320724i
$408$		0			0
$409$	−9.12835	−	15.8108i	−0.451368	−	0.781792i	0.547104	−	0.837065i	$-0.315730\pi$
$409$	−9.12835	−	15.8108i	−0.451368	−	0.781792i	−0.998471	+	0.0552732i	$0.982397\pi$
$410$		0			0
$411$	−7.13919	+	12.1234i	−0.352150	+	0.598004i
$412$		0			0
$413$	65.3833			3.21730
$414$		0			0
$415$	8.29917			0.407390
$416$		0			0
$417$	3.72955	+	6.59003i	0.182637	+	0.322715i
$418$		0			0
$419$	1.60961	+	2.78793i	0.0786347	+	0.136199i	0.902661	−	0.430352i	$-0.141611\pi$
$419$	1.60961	+	2.78793i	0.0786347	+	0.136199i	−0.824026	+	0.566551i	$0.808277\pi$
$420$		0			0
$421$	−7.54291	+	13.0647i	−0.367619	+	0.636735i	−0.989193	−	0.146621i	$-0.953160\pi$
$421$	−7.54291	+	13.0647i	−0.367619	+	0.636735i	0.621574	+	0.783356i	$0.286494\pi$
$422$		0			0
$423$	5.32714	−	8.87089i	0.259014	−	0.431317i
$424$		0			0
$425$	−5.22638	+	9.05235i	−0.253517	+	0.439104i
$426$		0			0
$427$	−26.5442	−	45.9759i	−1.28456	−	2.22493i
$428$		0			0
$429$	−3.39501	−	0.0292025i	−0.163913	−	0.00140991i
$430$		0			0
$431$	−1.42286			−0.0685367			−0.0342683	−	0.999413i	$-0.510910\pi$
$431$	−1.42286			−0.0685367			−0.0342683	+	0.999413i	$0.510910\pi$
$432$		0			0
$433$	−3.81061			−0.183126			−0.0915632	−	0.995799i	$-0.529186\pi$
$433$	−3.81061			−0.183126			−0.0915632	+	0.995799i	$0.529186\pi$
$434$		0			0
$435$	−1.63999	−	0.0141065i	−0.0786315	−	0.000676356i
$436$		0			0
$437$	−0.850138	−	1.47248i	−0.0406676	−	0.0704384i
$438$		0			0
$439$	4.64857	−	8.05156i	0.221864	−	0.384280i	−0.733510	−	0.679679i	$-0.762119\pi$
$439$	4.64857	−	8.05156i	0.221864	−	0.384280i	0.955374	+	0.295399i	$0.0954525\pi$
$440$		0			0
$441$	−18.2260	−	32.8612i	−0.867907	−	1.56482i
$442$		0			0
$443$	2.16008	−	3.74137i	0.102628	−	0.177758i	−0.810138	−	0.586239i	$-0.800608\pi$
$443$	2.16008	−	3.74137i	0.102628	−	0.177758i	0.912767	+	0.408481i	$0.133941\pi$
$444$		0			0
$445$	2.50086	+	4.33161i	0.118552	+	0.205338i
$446$		0			0
$447$	4.48913	+	7.93219i	0.212329	+	0.375180i
$448$		0			0
$449$	−12.2966			−0.580312			−0.290156	−	0.956979i	$-0.593707\pi$
$449$	−12.2966			−0.580312			−0.290156	+	0.956979i	$0.593707\pi$
$450$		0			0
$451$	4.73476			0.222951
$452$		0			0
$453$	3.46019	−	5.87591i	0.162574	−	0.276075i
$454$		0			0
$455$	2.43034	+	4.20947i	0.113936	+	0.197343i
$456$		0			0
$457$	−1.91442	+	3.31587i	−0.0895527	+	0.155110i	−0.907322	−	0.420436i	$-0.861877\pi$
$457$	−1.91442	+	3.31587i	−0.0895527	+	0.155110i	0.817769	+	0.575546i	$0.195210\pi$
$458$		0			0
$459$	14.3261	+	0.369756i	0.668687	+	0.0172587i
$460$		0			0
$461$	−19.0643	+	33.0203i	−0.887913	+	1.53791i	−0.0455743	+	0.998961i	$0.514512\pi$
$461$	−19.0643	+	33.0203i	−0.887913	+	1.53791i	−0.842338	+	0.538949i	$0.818822\pi$
$462$		0			0
$463$	3.51635	+	6.09050i	0.163419	+	0.283050i	0.936093	−	0.351754i	$-0.114414\pi$
$463$	3.51635	+	6.09050i	0.163419	+	0.283050i	−0.772674	+	0.634803i	$0.781081\pi$
$464$		0			0
$465$	−0.623297	+	1.05845i	−0.0289047	+	0.0490845i
$466$		0			0
$467$	−3.05112			−0.141189			−0.0705945	−	0.997505i	$-0.522490\pi$
$467$	−3.05112			−0.141189			−0.0705945	+	0.997505i	$0.522490\pi$
$468$		0			0
$469$	40.8677			1.88709
$470$		0			0
$471$	−7.73670	−	13.6706i	−0.356488	−	0.629906i
$472$		0			0
$473$	−9.69182	−	16.7867i	−0.445630	−	0.771854i
$474$		0			0
$475$	1.52812	−	2.64678i	0.0701149	−	0.121443i
$476$		0			0
$477$	−25.1077	−	0.431965i	−1.14960	−	0.0197783i
$478$		0			0
$479$	15.6440	−	27.0962i	0.714792	−	1.23806i	−0.248247	−	0.968697i	$-0.579854\pi$
$479$	15.6440	−	27.0962i	0.714792	−	1.23806i	0.963040	−	0.269360i	$-0.0868122\pi$
$480$		0			0
$481$	1.90577	+	3.30090i	0.0868958	+	0.150508i
$482$		0			0
$483$	−16.1369	−	0.138803i	−0.734253	−	0.00631575i
$484$		0			0
$485$	−3.36611			−0.152847
$486$		0			0
$487$	25.0695			1.13601			0.568005	−	0.823025i	$-0.307716\pi$
$487$	25.0695			1.13601			0.568005	+	0.823025i	$0.307716\pi$
$488$		0			0
$489$	−27.1119	−	0.233205i	−1.22604	−	0.0105459i
$490$		0			0
$491$	−9.19647	−	15.9288i	−0.415031	−	0.718855i	0.580401	−	0.814331i	$-0.302896\pi$
$491$	−9.19647	−	15.9288i	−0.415031	−	0.718855i	−0.995432	+	0.0954762i	$0.969563\pi$
$492$		0			0
$493$	−1.18704	+	2.05601i	−0.0534616	+	0.0925982i
$494$		0			0
$495$	−6.46766	−	0.111273i	−0.290700	−	0.00500133i
$496$		0			0
$497$	−22.3639	+	38.7354i	−1.00316	+	1.73752i
$498$		0			0
$499$	2.85519	+	4.94534i	0.127816	+	0.221384i	0.922830	−	0.385207i	$-0.125870\pi$
$499$	2.85519	+	4.94534i	0.127816	+	0.221384i	−0.795014	+	0.606591i	$0.792537\pi$
$500$		0			0
$501$	−7.03921	−	12.4381i	−0.314489	−	0.555695i
$502$		0			0
$503$	−42.5872			−1.89887			−0.949435	−	0.313963i	$-0.898343\pi$
$503$	−42.5872			−1.89887			−0.949435	+	0.313963i	$0.898343\pi$
$504$		0			0
$505$	13.8505			0.616337
$506$		0			0
$507$	0.878895	−	1.49250i	0.0390331	−	0.0662841i
$508$		0			0
$509$	−14.4391	−	25.0093i	−0.640003	−	1.10852i	−0.985432	−	0.170072i	$-0.945600\pi$
$509$	−14.4391	−	25.0093i	−0.640003	−	1.10852i	0.345429	−	0.938445i	$-0.387733\pi$
$510$		0			0
$511$	8.59019	−	14.8787i	0.380008	−	0.658193i
$512$		0			0
$513$	−4.18876	−	0.108111i	−0.184938	−	0.00477323i
$514$		0			0
$515$	0.357077	−	0.618475i	0.0157347	−	0.0272533i
$516$		0			0
$517$	3.38051	+	5.85521i	0.148675	+	0.257512i
$518$		0			0
$519$	15.6079	−	26.5045i	0.685110	−	1.16342i
$520$		0			0
$521$	−24.9344			−1.09239			−0.546197	−	0.837657i	$-0.683925\pi$
$521$	−24.9344			−1.09239			−0.546197	+	0.837657i	$0.683925\pi$
$522$		0			0
$523$	20.1668			0.881834			0.440917	−	0.897548i	$-0.354653\pi$
$523$	20.1668			0.881834			0.440917	+	0.897548i	$0.354653\pi$
$524$		0			0
$525$	−14.2869	−	25.2446i	−0.623532	−	1.10177i
$526$		0			0
$527$	0.889051	+	1.53988i	0.0387276	+	0.0670783i
$528$		0			0
$529$	9.27714	−	16.0685i	0.403354	−	0.698629i
$530$		0			0
$531$	−21.5304	−	38.8189i	−0.934340	−	1.68460i
$532$		0			0
$533$	−1.20773	+	2.09186i	−0.0523127	+	0.0906083i
$534$		0			0
$535$	−10.2688	−	17.7861i	−0.443960	−	0.768962i
$536$		0			0
$537$	−5.58454	−	0.0480359i	−0.240991	−	0.00207290i
$538$		0			0
$539$	24.5528			1.05756
$540$		0			0
$541$	−26.9422			−1.15834			−0.579169	−	0.815208i	$-0.696623\pi$
$541$	−26.9422			−1.15834			−0.579169	+	0.815208i	$0.696623\pi$
$542$		0			0
$543$	6.04826	+	0.0520246i	0.259556	+	0.00223259i
$544$		0			0
$545$	−2.16190	−	3.74451i	−0.0926054	−	0.160397i
$546$		0			0
$547$	−16.0765	+	27.8454i	−0.687383	+	1.19058i	0.285298	+	0.958439i	$0.407907\pi$
$547$	−16.0765	+	27.8454i	−0.687383	+	1.19058i	−0.972681	+	0.232144i	$0.925426\pi$
$548$		0			0
$549$	−18.5556	+	30.8993i	−0.791935	+	1.31875i
$550$		0			0
$551$	0.347073	−	0.601149i	0.0147858	−	0.0256098i
$552$		0			0
$553$	−37.4948	−	64.9429i	−1.59444	−	2.76166i
$554$		0			0
$555$	3.57676	+	6.32006i	0.151825	+	0.268272i
$556$		0			0
$557$	19.0374			0.806639			0.403320	−	0.915059i	$-0.367856\pi$
$557$	19.0374			0.806639			0.403320	+	0.915059i	$0.367856\pi$
$558$		0			0
$559$	9.88868			0.418247
$560$		0			0
$561$	−4.75145	+	8.06867i	−0.200606	+	0.340660i
$562$		0			0
$563$	21.2659	+	36.8337i	0.896252	+	1.55235i	0.832248	+	0.554404i	$0.187054\pi$
$563$	21.2659	+	36.8337i	0.896252	+	1.55235i	0.0640044	+	0.997950i	$0.479613\pi$
$564$		0			0
$565$	−9.81897	+	17.0070i	−0.413087	+	0.715488i
$566$		0			0
$567$	−21.0575	+	33.7367i	−0.884334	+	1.41681i
$568$		0			0
$569$	−0.782584	+	1.35548i	−0.0328076	+	0.0568245i	−0.881963	−	0.471319i	$-0.843778\pi$
$569$	−0.782584	+	1.35548i	−0.0328076	+	0.0568245i	0.849155	+	0.528143i	$0.177112\pi$
$570$		0			0
$571$	5.63541	+	9.76082i	0.235835	+	0.408478i	0.959515	−	0.281658i	$-0.0908843\pi$
$571$	5.63541	+	9.76082i	0.235835	+	0.408478i	−0.723680	+	0.690135i	$0.757551\pi$
$572$		0			0
$573$	1.12063	−	1.90300i	0.0468149	−	0.0794988i
$574$		0			0
$575$	−7.99116			−0.333255
$576$		0			0
$577$	27.1341			1.12961			0.564803	−	0.825225i	$-0.308952\pi$
$577$	27.1341			1.12961			0.564803	+	0.825225i	$0.308952\pi$
$578$		0			0
$579$	4.07225	+	7.19558i	0.169237	+	0.299038i
$580$		0			0
$581$	16.6692	+	28.8719i	0.691555	+	1.19781i
$582$		0			0
$583$	8.20384	−	14.2095i	0.339768	−	0.588496i
$584$		0			0
$585$	1.69892	−	2.82908i	0.0702417	−	0.116968i
$586$		0			0
$587$	−0.709382	+	1.22869i	−0.0292793	+	0.0507133i	−0.880294	−	0.474429i	$-0.842655\pi$
$587$	−0.709382	+	1.22869i	−0.0292793	+	0.0507133i	0.851014	+	0.525142i	$0.175988\pi$
$588$		0			0
$589$	−0.259946	−	0.450239i	−0.0107109	−	0.0185518i
$590$		0			0
$591$	−11.0814	−	0.0953176i	−0.455827	−	0.00392084i
$592$		0			0
$593$	−25.2220			−1.03574			−0.517871	−	0.855459i	$-0.673275\pi$
$593$	−25.2220			−1.03574			−0.517871	+	0.855459i	$0.673275\pi$
$594$		0			0
$595$	13.4057			0.549580
$596$		0			0
$597$	−36.3756	−	0.312888i	−1.48876	−	0.0128057i
$598$		0			0
$599$	15.4427	+	26.7475i	0.630971	+	1.09287i	0.987354	+	0.158533i	$0.0506765\pi$
$599$	15.4427	+	26.7475i	0.630971	+	1.09287i	−0.356383	+	0.934340i	$0.615990\pi$
$600$		0			0
$601$	3.44059	−	5.95927i	0.140344	−	0.243084i	−0.787282	−	0.616593i	$-0.788512\pi$
$601$	3.44059	−	5.95927i	0.140344	−	0.243084i	0.927626	+	0.373510i	$0.121846\pi$
$602$		0			0
$603$	−13.4575	−	24.2637i	−0.548033	−	0.988093i
$604$		0			0
$605$	−3.93673	+	6.81861i	−0.160051	+	0.277216i
$606$		0			0
$607$	15.1515	+	26.2431i	0.614979	+	1.06518i	0.990388	+	0.138316i	$0.0441690\pi$
$607$	15.1515	+	26.2431i	0.614979	+	1.06518i	−0.375409	+	0.926859i	$0.622498\pi$
$608$		0			0
$609$	−3.24491	−	5.73368i	−0.131490	−	0.232341i
$610$		0			0
$611$	−3.44917			−0.139539
$612$		0			0
$613$	39.8512			1.60958			0.804788	−	0.593562i	$-0.202279\pi$
$613$	39.8512			1.60958			0.804788	+	0.593562i	$0.202279\pi$
$614$		0			0
$615$	−2.33524	+	3.96559i	−0.0941659	+	0.159908i
$616$		0			0
$617$	−20.9715	−	36.3237i	−0.844280	−	1.46234i	−0.886245	−	0.463217i	$-0.846695\pi$
$617$	−20.9715	−	36.3237i	−0.844280	−	1.46234i	0.0419651	−	0.999119i	$-0.486638\pi$
$618$		0			0
$619$	12.9455	−	22.4223i	0.520325	−	0.901229i	−0.479396	−	0.877599i	$-0.659144\pi$
$619$	12.9455	−	22.4223i	0.520325	−	0.901229i	0.999721	−	0.0236299i	$-0.00752235\pi$
$620$		0			0
$621$	5.23138	+	9.62638i	0.209928	+	0.386293i
$622$		0			0
$623$	−10.0461	+	17.4004i	−0.402490	+	0.697133i
$624$		0			0
$625$	−4.15703	−	7.20018i	−0.166281	−	0.288007i
$626$		0			0
$627$	1.38926	−	2.35916i	0.0554815	−	0.0942160i
$628$		0			0
$629$	10.5122			0.419149
$630$		0			0
$631$	15.5719			0.619909			0.309955	−	0.950751i	$-0.399686\pi$
$631$	15.5719			0.619909			0.309955	+	0.950751i	$0.399686\pi$
$632$		0			0
$633$	−22.0773	−	39.0101i	−0.877494	−	1.55051i
$634$		0			0
$635$	−3.33291	−	5.77276i	−0.132262	−	0.229085i
$636$		0			0
$637$	−6.26287	+	10.8476i	−0.248144	+	0.429798i
$638$		0			0
$639$	30.3620	+	0.522361i	1.20110	+	0.0206643i
$640$		0			0
$641$	−9.53448	+	16.5142i	−0.376589	+	0.652272i	−0.990564	−	0.137054i	$-0.956237\pi$
$641$	−9.53448	+	16.5142i	−0.376589	+	0.652272i	0.613974	+	0.789326i	$0.289570\pi$
$642$		0			0
$643$	−13.6289	−	23.6059i	−0.537471	−	0.930927i	−0.999039	−	0.0438224i	$-0.986046\pi$
$643$	−13.6289	−	23.6059i	−0.537471	−	0.930927i	0.461568	−	0.887105i	$-0.347287\pi$
$644$		0			0
$645$	18.8398	+	0.162052i	0.741816	+	0.00638080i
$646$		0			0
$647$	−32.4199			−1.27456			−0.637278	−	0.770634i	$-0.719940\pi$
$647$	−32.4199			−1.27456			−0.637278	+	0.770634i	$0.719940\pi$
$648$		0			0
$649$	29.0042			1.13851
$650$		0			0
$651$	−4.93416	−	0.0424416i	−0.193385	−	0.00166342i
$652$		0			0
$653$	13.1405	+	22.7600i	0.514227	+	0.890667i	0.999864	+	0.0165061i	$0.00525428\pi$
$653$	13.1405	+	22.7600i	0.514227	+	0.890667i	−0.485637	+	0.874160i	$0.661412\pi$
$654$		0			0
$655$	9.31825	−	16.1397i	0.364094	−	0.630630i
$656$		0			0
$657$	−11.6624	−	0.200644i	−0.454992	−	0.00782789i
$658$		0			0
$659$	−19.8714	+	34.4183i	−0.774081	+	1.34075i	0.161229	+	0.986917i	$0.448454\pi$
$659$	−19.8714	+	34.4183i	−0.774081	+	1.34075i	−0.935310	+	0.353830i	$0.884879\pi$
$660$		0			0
$661$	18.2288	+	31.5732i	0.709017	+	1.22805i	0.965222	+	0.261432i	$0.0841946\pi$
$661$	18.2288	+	31.5732i	0.709017	+	1.22805i	−0.256205	+	0.966623i	$0.582472\pi$
$662$		0			0
$663$	−2.35281	−	4.15737i	−0.0913757	−	0.161459i
$664$		0			0
$665$	−3.91963			−0.151997
$666$		0			0
$667$	−1.81499			−0.0702767
$668$		0			0
$669$	−0.192261	+	0.326488i	−0.00743325	+	0.0126228i
$670$		0			0
$671$	−11.7751	−	20.3950i	−0.454571	−	0.787340i
$672$		0			0
$673$	−16.1830	+	28.0298i	−0.623809	+	1.08047i	0.364961	+	0.931023i	$0.381082\pi$
$673$	−16.1830	+	28.0298i	−0.623809	+	1.08047i	−0.988770	+	0.149446i	$0.952251\pi$
$674$		0			0
$675$	−10.2835	+	16.7952i	−0.395811	+	0.646449i
$676$		0			0
$677$	−14.0626	+	24.3571i	−0.540469	+	0.936120i	0.458408	+	0.888742i	$0.348420\pi$
$677$	−14.0626	+	24.3571i	−0.540469	+	0.936120i	−0.998877	+	0.0473781i	$0.984913\pi$
$678$		0			0
$679$	−6.76096	−	11.7103i	−0.259462	−	0.449401i
$680$		0			0
$681$	5.27040	−	8.94992i	0.201962	−	0.342962i
$682$		0			0
$683$	11.6908			0.447336			0.223668	−	0.974665i	$-0.428197\pi$
$683$	11.6908			0.447336			0.223668	+	0.974665i	$0.428197\pi$
$684$		0			0
$685$	8.93522			0.341397
$686$		0			0
$687$	−6.90343	−	12.1982i	−0.263382	−	0.465391i
$688$		0			0
$689$	4.18524	+	7.24905i	0.159445	+	0.276167i
$690$		0			0
$691$	−18.7023	+	32.3934i	−0.711470	+	1.23230i	0.252835	+	0.967509i	$0.418637\pi$
$691$	−18.7023	+	32.3934i	−0.711470	+	1.23230i	−0.964305	+	0.264793i	$0.914696\pi$
$692$		0			0
$693$	−12.6035	−	22.7238i	−0.478766	−	0.863206i
$694$		0			0
$695$	2.40450	−	4.16471i	0.0912078	−	0.157977i
$696$		0			0
$697$	3.33091	+	5.76931i	0.126167	+	0.218528i
$698$		0			0
$699$	19.8572	+	0.170803i	0.751067	+	0.00646037i
$700$		0			0
$701$	−18.7049			−0.706473			−0.353236	−	0.935534i	$-0.614919\pi$
$701$	−18.7049			−0.706473			−0.353236	+	0.935534i	$0.614919\pi$
$702$		0			0
$703$	−3.07362			−0.115924
$704$		0			0
$705$	−6.57132	−	0.0565238i	−0.247490	−	0.00212881i
$706$		0			0
$707$	27.8192	+	48.1843i	1.04625	+	1.81216i
$708$		0			0
$709$	10.3589	−	17.9421i	0.389035	−	0.673829i	−0.603285	−	0.797526i	$-0.706142\pi$
$709$	10.3589	−	17.9421i	0.389035	−	0.673829i	0.992320	+	0.123697i	$0.0394750\pi$
$710$		0			0
$711$	−26.2106	+	43.6465i	−0.982974	+	1.63687i
$712$		0			0
$713$	−0.679682	+	1.17724i	−0.0254543	+	0.0440881i
$714$		0			0
$715$	1.07810	+	1.86733i	0.0403188	+	0.0698342i
$716$		0			0
$717$	−0.443619	−	0.783865i	−0.0165673	−	0.0292740i
$718$		0			0
$719$	11.2072			0.417956			0.208978	−	0.977920i	$-0.432986\pi$
$719$	11.2072			0.417956			0.208978	+	0.977920i	$0.432986\pi$
$720$		0			0
$721$	2.86881			0.106840
$722$		0			0
$723$	25.7564	−	43.7383i	0.957892	−	1.62664i
$724$		0			0
$725$	−1.63122	−	2.82535i	−0.0605819	−	0.104931i
$726$		0			0
$727$	16.1533	−	27.9783i	0.599092	−	1.03766i	−0.393864	−	0.919169i	$-0.628862\pi$
$727$	16.1533	−	27.9783i	0.599092	−	1.03766i	0.992955	−	0.118488i	$-0.0378048\pi$
$728$		0			0
$729$	26.9641	+	1.39281i	0.998669	+	0.0515854i
$730$		0			0
$731$	13.6364	−	23.6190i	0.504361	−	0.873579i
$732$		0			0
$733$	4.68022	+	8.10638i	0.172868	+	0.299416i	0.939421	−	0.342764i	$-0.111363\pi$
$733$	4.68022	+	8.10638i	0.172868	+	0.299416i	−0.766553	+	0.642181i	$0.778030\pi$
$734$		0			0
$735$	−12.1097	+	20.5641i	−0.446674	+	0.758519i
$736$		0			0
$737$	18.1290			0.667790
$738$		0			0
$739$	−48.3158			−1.77733			−0.888663	−	0.458562i	$-0.848365\pi$
$739$	−48.3158			−1.77733			−0.888663	+	0.458562i	$0.848365\pi$
$740$		0			0
$741$	0.687929	+	1.21556i	0.0252717	+	0.0446545i
$742$		0			0
$743$	25.8113	+	44.7065i	0.946924	+	1.64012i	0.751852	+	0.659332i	$0.229161\pi$
$743$	25.8113	+	44.7065i	0.946924	+	1.64012i	0.195072	+	0.980789i	$0.437506\pi$
$744$		0			0
$745$	2.89421	−	5.01292i	0.106036	−	0.183659i
$746$		0			0
$747$	11.6525	−	19.4041i	0.426344	−	0.709959i
$748$		0			0
$749$	41.2507	−	71.4483i	1.50727	−	2.61067i
$750$		0			0
$751$	−22.1753	−	38.4087i	−0.809188	−	1.40155i	−0.913427	−	0.407002i	$-0.866574\pi$
$751$	−22.1753	−	38.4087i	−0.809188	−	1.40155i	0.104239	−	0.994552i	$-0.466759\pi$
$752$		0			0
$753$	15.0406	+	0.129373i	0.548111	+	0.00471463i
$754$		0			0
$755$	−4.33068			−0.157609
$756$		0			0
$757$	10.0920			0.366802			0.183401	−	0.983038i	$-0.441289\pi$
$757$	10.0920			0.366802			0.183401	+	0.983038i	$0.441289\pi$
$758$		0			0
$759$	−7.15835	−	0.0615732i	−0.259832	−	0.00223497i
$760$		0			0
$761$	3.41216	+	5.91003i	0.123691	+	0.214238i	0.921220	−	0.389041i	$-0.127194\pi$
$761$	3.41216	+	5.91003i	0.123691	+	0.214238i	−0.797530	+	0.603280i	$0.793860\pi$
$762$		0			0
$763$	8.68451	−	15.0420i	0.314400	−	0.544557i
$764$		0			0
$765$	−4.41442	−	7.95913i	−0.159604	−	0.287763i
$766$		0			0
$767$	−7.39832	+	12.8143i	−0.267138	+	0.462696i
$768$		0			0
$769$	−7.29531	−	12.6358i	−0.263075	−	0.455660i	0.703982	−	0.710218i	$-0.251403\pi$
$769$	−7.29531	−	12.6358i	−0.263075	−	0.455660i	−0.967058	+	0.254558i	$0.918070\pi$
$770$		0			0
$771$	−13.0814	−	23.1145i	−0.471115	−	0.832449i
$772$		0			0
$773$	38.2046			1.37412			0.687062	−	0.726599i	$-0.258900\pi$
$773$	38.2046			1.37412			0.687062	+	0.726599i	$0.258900\pi$
$774$		0			0
$775$	−2.44345			−0.0877713
$776$		0			0
$777$	−14.8027	+	25.1373i	−0.531046	+	0.901795i
$778$		0			0
$779$	−0.973911	−	1.68686i	−0.0348940	−	0.0604381i
$780$		0			0
$781$	−9.92065	+	17.1831i	−0.354989	+	0.614859i
$782$		0			0
$783$	−2.33563	+	3.81462i	−0.0834685	+	0.136323i
$784$		0			0
$785$	−4.98796	+	8.63941i	−0.178028	+	0.308354i
$786$		0			0
$787$	−20.4343	−	35.3932i	−0.728404	−	1.26163i	−0.957557	−	0.288243i	$-0.906929\pi$
$787$	−20.4343	−	35.3932i	−0.728404	−	1.26163i	0.229153	−	0.973390i	$-0.426404\pi$
$788$		0			0
$789$	−4.50105	+	7.64345i	−0.160241	+	0.272114i
$790$		0			0
$791$	−78.8872			−2.80491
$792$		0			0
$793$	12.0142			0.426638
$794$		0			0
$795$	7.85487	+	13.8794i	0.278584	+	0.492251i
$796$		0			0
$797$	−4.74839	−	8.22445i	−0.168197	−	0.291325i	0.769589	−	0.638539i	$-0.220461\pi$
$797$	−4.74839	−	8.22445i	−0.168197	−	0.291325i	−0.937786	+	0.347214i	$0.887128\pi$
$798$		0			0
$799$	−4.75638	+	8.23830i	−0.168269	+	0.291450i
$800$		0			0
$801$	13.6390	+	0.234652i	0.481910	+	0.00829101i
$802$		0			0
$803$	3.81062	−	6.60020i	0.134474	−	0.232916i
$804$		0			0
$805$	5.12434	+	8.87563i	0.180609	+	0.312825i
$806$		0			0
$807$	−19.5991	−	0.168584i	−0.689922	−	0.00593442i
$808$		0			0
$809$	38.1280			1.34051			0.670255	−	0.742131i	$-0.266185\pi$
$809$	38.1280			1.34051			0.670255	+	0.742131i	$0.266185\pi$
$810$		0			0
$811$	21.3881			0.751038			0.375519	−	0.926815i	$-0.377464\pi$
$811$	21.3881			0.751038			0.375519	+	0.926815i	$0.377464\pi$
$812$		0			0
$813$	−13.1014	−	0.112693i	−0.459485	−	0.00395230i
$814$		0			0
$815$	8.60951	+	14.9121i	0.301578	+	0.522348i
$816$		0			0
$817$	−3.98709	+	6.90585i	−0.139491	+	0.241605i
$818$		0			0
$819$	13.2544	+	0.228035i	0.463147	+	0.00796819i
$820$		0			0
$821$	22.6777	−	39.2789i	0.791457	−	1.37084i	−0.133608	−	0.991034i	$-0.542656\pi$
$821$	22.6777	−	39.2789i	0.791457	−	1.37084i	0.925065	−	0.379809i	$-0.124010\pi$
$822$		0			0
$823$	−3.96158	−	6.86166i	−0.138092	−	0.239183i	0.788682	−	0.614801i	$-0.210764\pi$
$823$	−3.96158	−	6.86166i	−0.138092	−	0.239183i	−0.926774	+	0.375618i	$0.877430\pi$
$824$		0			0
$825$	−6.33770	−	11.1986i	−0.220650	−	0.389884i
$826$		0			0
$827$	49.3623			1.71650			0.858248	−	0.513234i	$-0.171553\pi$
$827$	49.3623			1.71650			0.858248	+	0.513234i	$0.171553\pi$
$828$		0			0
$829$	1.97247			0.0685066			0.0342533	−	0.999413i	$-0.489095\pi$
$829$	1.97247			0.0685066			0.0342533	+	0.999413i	$0.489095\pi$
$830$		0			0
$831$	23.6360	−	40.1375i	0.819925	−	1.39235i
$832$		0			0
$833$	17.2729	+	29.9176i	0.598471	+	1.03658i
$834$		0			0
$835$	−4.53828	+	7.86054i	−0.157054	+	0.272025i
$836$		0			0
$837$	1.59959	+	2.94345i	0.0552900	+	0.101740i
$838$		0			0
$839$	23.0859	−	39.9859i	0.797013	−	1.38047i	−0.124540	−	0.992215i	$-0.539745\pi$
$839$	23.0859	−	39.9859i	0.797013	−	1.38047i	0.921553	−	0.388253i	$-0.126921\pi$
$840$		0			0
$841$	14.1295	+	24.4730i	0.487224	+	0.843898i
$842$		0			0
$843$	7.38650	−	12.5434i	0.254405	−	0.432017i
$844$		0			0
$845$	−1.10000			−0.0378412
$846$		0			0
$847$	−31.6283			−1.08676
$848$		0			0
$849$	17.3506	+	30.6581i	0.595470	+	1.05218i
$850$		0			0
$851$	4.01830	+	6.95990i	0.137746	+	0.238582i
$852$		0			0
$853$	17.8325	−	30.8867i	0.610572	−	1.05754i	−0.380572	−	0.924751i	$-0.624273\pi$
$853$	17.8325	−	30.8867i	0.610572	−	1.05754i	0.991144	−	0.132791i	$-0.0423938\pi$
$854$		0			0
$855$	1.29071	+	2.32714i	0.0441415	+	0.0795863i
$856$		0			0
$857$	15.0095	−	25.9972i	0.512715	−	0.888048i	−0.487177	−	0.873303i	$-0.661973\pi$
$857$	15.0095	−	25.9972i	0.512715	−	0.888048i	0.999891	−	0.0147444i	$-0.00469345\pi$
$858$		0			0
$859$	6.61554	+	11.4585i	0.225719	+	0.390958i	0.956535	−	0.291617i	$-0.0941934\pi$
$859$	6.61554	+	11.4585i	0.225719	+	0.390958i	−0.730816	+	0.682575i	$0.760860\pi$
$860$		0			0
$861$	−18.4863	−	0.159011i	−0.630010	−	0.00541909i
$862$		0			0
$863$	−27.9198			−0.950400			−0.475200	−	0.879878i	$-0.657624\pi$
$863$	−27.9198			−0.950400			−0.475200	+	0.879878i	$0.657624\pi$
$864$		0			0
$865$	−19.5344			−0.664190
$866$		0			0
$867$	16.2694	+	0.139943i	0.552539	+	0.00475272i
$868$		0			0
$869$	−16.6328	−	28.8088i	−0.564228	−	0.977272i
$870$		0			0
$871$	−4.62430	+	8.00953i	−0.156689	+	0.271393i
$872$		0			0
$873$	−4.72622	+	7.87022i	−0.159958	+	0.266367i
$874$		0			0
$875$	−21.3627	+	37.0013i	−0.722191	+	1.25087i
$876$		0			0
$877$	8.58595	+	14.8713i	0.289927	+	0.502168i	0.973792	−	0.227440i	$-0.0730357\pi$
$877$	8.58595	+	14.8713i	0.289927	+	0.502168i	−0.683865	+	0.729608i	$0.739702\pi$
$878$		0			0
$879$	17.0703	+	30.1628i	0.575766	+	1.01737i
$880$		0			0
$881$	16.4467			0.554104			0.277052	−	0.960855i	$-0.410643\pi$
$881$	16.4467			0.554104			0.277052	+	0.960855i	$0.410643\pi$
$882$		0			0
$883$	21.3082			0.717079			0.358540	−	0.933515i	$-0.383275\pi$
$883$	21.3082			0.717079			0.358540	+	0.933515i	$0.383275\pi$
$884$		0			0
$885$	−14.3052	+	24.2924i	−0.480864	+	0.816579i
$886$		0			0
$887$	23.2374	+	40.2484i	0.780236	+	1.35141i	0.931804	+	0.362962i	$0.118234\pi$
$887$	23.2374	+	40.2484i	0.780236	+	1.35141i	−0.151568	+	0.988447i	$0.548432\pi$
$888$		0			0
$889$	13.3885	−	23.1896i	0.449038	−	0.777756i
$890$		0			0
$891$	−9.34116	+	14.9657i	−0.312941	+	0.501369i
$892$		0			0
$893$	1.39070	−	2.40876i	0.0465379	−	0.0806061i
$894$		0			0
$895$	1.77340	+	3.07161i	0.0592781	+	0.102673i
$896$		0			0
$897$	1.85314	−	3.14691i	0.0618746	−	0.105072i
$898$		0			0
$899$	−0.554967			−0.0185092
$900$		0			0
$901$	23.0857			0.769095
$902$		0			0
$903$	37.2767	+	65.8671i	1.24049	+	2.19192i
$904$		0			0
$905$	−1.92065	−	3.32667i	−0.0638447	−	0.110582i
$906$		0			0
$907$	−14.6731	+	25.4146i	−0.487214	+	0.843879i	−0.999892	−	0.0147018i	$-0.995320\pi$
$907$	−14.6731	+	25.4146i	−0.487214	+	0.843879i	0.512678	+	0.858581i	$0.328653\pi$
$908$		0			0
$909$	19.4469	−	32.3834i	0.645013	−	1.07409i
$910$		0			0
$911$	−6.15197	+	10.6555i	−0.203824	+	0.353033i	−0.949757	−	0.312987i	$-0.898670\pi$
$911$	−6.15197	+	10.6555i	−0.203824	+	0.353033i	0.745934	+	0.666020i	$0.232004\pi$
$912$		0			0
$913$	7.39449	+	12.8076i	0.244722	+	0.423871i
$914$		0			0
$915$	22.8894	+	0.196885i	0.756700	+	0.00650882i
$916$		0			0
$917$	74.8643			2.47224
$918$		0			0
$919$	−30.1425			−0.994309			−0.497155	−	0.867662i	$-0.665622\pi$
$919$	−30.1425			−0.994309			−0.497155	+	0.867662i	$0.665622\pi$
$920$		0			0
$921$	54.3121	+	0.467171i	1.78965	+	0.0153938i
$922$		0			0
$923$	−5.06108	−	8.76604i	−0.166587	−	0.288538i
$924$		0			0
$925$	−7.22288	+	12.5104i	−0.237487	+	0.411339i
$926$		0			0
$927$	−0.944685	−	1.70325i	−0.0310275	−	0.0559421i
$928$		0			0
$929$	−11.4567	+	19.8436i	−0.375883	+	0.651048i	−0.990459	−	0.137809i	$-0.955994\pi$
$929$	−11.4567	+	19.8436i	−0.375883	+	0.651048i	0.614576	+	0.788858i	$0.289327\pi$
$930$		0			0
$931$	−5.05035	−	8.74747i	−0.165519	−	0.286687i
$932$		0			0
$933$	17.8793	+	31.5924i	0.585343	+	1.03429i
$934$		0			0
$935$	5.94679			0.194481
$936$		0			0
$937$	37.3809			1.22118			0.610590	−	0.791947i	$-0.290932\pi$
$937$	37.3809			1.22118			0.610590	+	0.791947i	$0.290932\pi$
$938$		0			0
$939$	−19.7524	+	33.5425i	−0.644595	+	1.09462i
$940$		0			0
$941$	−24.0182	−	41.6007i	−0.782970	−	1.35614i	−0.930204	−	0.367042i	$-0.880370\pi$
$941$	−24.0182	−	41.6007i	−0.782970	−	1.35614i	0.147234	−	0.989102i	$-0.452963\pi$
$942$		0			0
$943$	−2.54649	+	4.41065i	−0.0829252	+	0.143631i
$944$		0			0
$945$	25.2484	+	0.651659i	0.821332	+	0.0211985i
$946$		0			0
$947$	−19.0587	+	33.0106i	−0.619324	+	1.07270i	0.370286	+	0.928918i	$0.379260\pi$
$947$	−19.0587	+	33.0106i	−0.619324	+	1.07270i	−0.989609	+	0.143782i	$0.954074\pi$
$948$		0			0
$949$	1.94401	+	3.36713i	0.0631053	+	0.109302i
$950$		0			0
$951$	14.0720	−	23.8963i	0.456316	−	0.774892i
$952$		0			0
$953$	−0.158875			−0.00514647			−0.00257323	−	0.999997i	$-0.500819\pi$
$953$	−0.158875			−0.00514647			−0.00257323	+	0.999997i	$0.500819\pi$
$954$		0			0
$955$	−1.40255			−0.0453854
$956$		0			0
$957$	−1.43945	−	2.54347i	−0.0465307	−	0.0822187i
$958$		0			0
$959$	17.9468	+	31.0847i	0.579531	+	1.00378i
$960$		0			0
$961$	15.2922	−	26.4868i	0.493296	−	0.854414i
$962$		0			0
$963$	−56.0034	−	0.963509i	−1.80469	−	0.0310486i
$964$		0			0
$965$	2.62544	−	4.54740i	0.0845160	−	0.146386i
$966$		0			0
$967$	10.4407	+	18.0838i	0.335749	+	0.581535i	0.983628	−	0.180208i	$-0.0576772\pi$
$967$	10.4407	+	18.0838i	0.335749	+	0.581535i	−0.647879	+	0.761743i	$0.724344\pi$
$968$		0			0
$969$	3.85199	+	0.0331332i	0.123744	+	0.00106439i
$970$		0			0
$971$	−2.57055			−0.0824929			−0.0412464	−	0.999149i	$-0.513133\pi$
$971$	−2.57055			−0.0824929			−0.0412464	+	0.999149i	$0.513133\pi$
$972$		0			0
$973$	19.3181			0.619311
$974$		0			0
$975$	6.56422	+	0.0564628i	0.210223	+	0.00180826i
$976$		0			0
$977$	19.5663	+	33.8899i	0.625982	+	1.08423i	0.988350	+	0.152198i	$0.0486350\pi$
$977$	19.5663	+	33.8899i	0.625982	+	1.08423i	−0.362368	+	0.932035i	$0.618032\pi$
$978$		0			0
$979$	−4.45649	+	7.71886i	−0.142430	+	0.246696i
$980$		0			0
$981$	−11.7904	−	0.202847i	−0.376438	−	0.00647642i
$982$		0			0
$983$	16.2941	−	28.2223i	0.519702	−	0.900151i	−0.480035	−	0.877249i	$-0.659376\pi$
$983$	16.2941	−	28.2223i	0.519702	−	0.900151i	0.999738	−	0.0229018i	$-0.00729052\pi$
$984$		0			0
$985$	3.51895	+	6.09500i	0.112123	+	0.194203i
$986$		0			0
$987$	−13.0021	−	22.9745i	−0.413862	−	0.731285i
$988$		0			0
$989$	20.8502			0.662997
$990$		0			0
$991$	3.40126			0.108045			0.0540223	−	0.998540i	$-0.482796\pi$
$991$	3.40126			0.108045			0.0540223	+	0.998540i	$0.482796\pi$
$992$		0			0
$993$	25.4834	−	43.2747i	0.808693	−	1.37328i
$994$		0			0
$995$	11.5513	+	20.0074i	0.366200	+	0.634276i
$996$		0			0
$997$	−3.02485	+	5.23920i	−0.0957981	+	0.165927i	−0.909941	−	0.414737i	$-0.863874\pi$
$997$	−3.02485	+	5.23920i	−0.0957981	+	0.165927i	0.814143	+	0.580664i	$0.197207\pi$
$998$		0			0
$999$	19.7988	+	0.511004i	0.626406	+	0.0161675i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.q.g.313.1	✓	22
3.2	odd	2		2808.2.q.g.937.5		22
9.2	odd	6		8424.2.a.be.1.7		11
9.4	even	3	inner	936.2.q.g.625.1	yes	22
9.5	odd	6		2808.2.q.g.1873.5		22
9.7	even	3		8424.2.a.bf.1.5		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.q.g.313.1	✓	22	1.1	even	1	trivial
936.2.q.g.625.1	yes	22	9.4	even	3	inner
2808.2.q.g.937.5		22	3.2	odd	2
2808.2.q.g.1873.5		22	9.5	odd	6
8424.2.a.be.1.7		11	9.2	odd	6
8424.2.a.bf.1.5		11	9.7	even	3

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73199 - 0.0148978i) q^{3} +(0.550001 + 0.952629i) q^{5} +(-2.20940 + 3.82679i) q^{7} +(2.99956 + 0.0516057i) q^{9} +(-0.980092 + 1.69757i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(-0.938402 - 1.65814i) q^{15} -2.75799 q^{17} +0.806396 q^{19} +(3.88366 - 6.59503i) q^{21} +(-1.05424 - 1.82600i) q^{23} +(1.89500 - 3.28223i) q^{25} +(-5.19442 - 0.134067i) q^{27} +(0.430401 - 0.745476i) q^{29} +(-0.322355 - 0.558335i) q^{31} +(1.72280 - 2.92557i) q^{33} -4.86068 q^{35} -3.81155 q^{37} +(0.853091 + 1.50739i) q^{39} +(-1.20773 - 2.09186i) q^{41} +(-4.94434 + 8.56385i) q^{43} +(1.60060 + 2.88585i) q^{45} +(1.72459 - 2.98707i) q^{47} +(-6.26287 - 10.8476i) q^{49} +(4.77679 + 0.0410880i) q^{51} -8.37048 q^{53} -2.15621 q^{55} +(-1.39667 - 0.0120136i) q^{57} +(-7.39832 - 12.8143i) q^{59} +(-6.00712 + 10.4046i) q^{61} +(-6.82470 + 11.3646i) q^{63} +(0.550001 - 0.952629i) q^{65} +(-4.62430 - 8.00953i) q^{67} +(1.79873 + 3.17832i) q^{69} +10.1222 q^{71} -3.88803 q^{73} +(-3.33101 + 5.65655i) q^{75} +(-4.33083 - 7.50121i) q^{77} +(-8.48531 + 14.6970i) q^{79} +(8.99467 + 0.309589i) q^{81} +(3.77234 - 6.53389i) q^{83} +(-1.51689 - 2.62734i) q^{85} +(-0.756555 + 1.28474i) q^{87} +4.54701 q^{89} +4.41879 q^{91} +(0.549997 + 0.971832i) q^{93} +(0.443518 + 0.768196i) q^{95} +(-1.53005 + 2.65012i) q^{97} +(-3.02745 + 5.04138i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{5} - 4 q^{7} - 4 q^{9} + 5 q^{11} - 11 q^{13} + 5 q^{15} + 8 q^{17} + 10 q^{19} + 4 q^{21} + 9 q^{23} - 24 q^{25} - 12 q^{27} - 16 q^{29} - q^{31} + 9 q^{33} + 18 q^{37} + 3 q^{39} - 6 q^{41}+ \cdots - 109 q^{99}+O(q^{100}) \) 22 * q - 3 * q^5 - 4 * q^7 - 4 * q^9 + 5 * q^11 - 11 * q^13 + 5 * q^15 + 8 * q^17 + 10 * q^19 + 4 * q^21 + 9 * q^23 - 24 * q^25 - 12 * q^27 - 16 * q^29 - q^31 + 9 * q^33 + 18 * q^37 + 3 * q^39 - 6 * q^41 - 7 * q^43 - 21 * q^45 + 21 * q^47 - 27 * q^49 - 11 * q^51 + 32 * q^53 + 34 * q^55 + 2 * q^57 + 11 * q^59 - 2 * q^61 - 27 * q^63 - 3 * q^65 - 18 * q^67 + 7 * q^69 - 30 * q^71 + 18 * q^73 + 62 * q^75 - 9 * q^77 - 30 * q^79 + 4 * q^81 - 16 * q^83 - 32 * q^85 + 33 * q^87 + 26 * q^89 + 8 * q^91 + 20 * q^95 - 10 * q^97 - 109 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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