LMFDB - Embedded newform 960.2.bb.a.593.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(497,960)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("960.497");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.bb (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			593.21
Character	$\chi$	$=$	960.593
Dual form			960.2.bb.a.497.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.117548 - 1.72806i) q^{3} +(-1.15738 + 1.91324i) q^{5} +(-0.912923 - 0.912923i) q^{7} +(-2.97237 + 0.406258i) q^{9} +(1.03554 + 1.03554i) q^{11} +2.08132i q^{13} +(3.44223 + 1.77512i) q^{15} +(1.49126 + 1.49126i) q^{17} +(2.35078 - 2.35078i) q^{19} +(-1.47027 + 1.68489i) q^{21} +(4.27105 + 4.27105i) q^{23} +(-2.32095 - 4.42868i) q^{25} +(1.05143 + 5.08866i) q^{27} +(2.58251 + 2.58251i) q^{29} +5.18620 q^{31} +(1.66774 - 1.91119i) q^{33} +(2.80323 - 0.690039i) q^{35} +10.8954i q^{37} +(3.59664 - 0.244654i) q^{39} +9.82802 q^{41} -0.814988 q^{43} +(2.66289 - 6.15703i) q^{45} +(-6.63331 - 6.63331i) q^{47} -5.33314i q^{49} +(2.40169 - 2.75228i) q^{51} +7.26025i q^{53} +(-3.17974 + 0.782718i) q^{55} +(-4.33861 - 3.78596i) q^{57} +(-6.09835 + 6.09835i) q^{59} +(9.87198 + 9.87198i) q^{61} +(3.08442 + 2.34266i) q^{63} +(-3.98205 - 2.40887i) q^{65} -10.8038 q^{67} +(6.87857 - 7.88268i) q^{69} +2.57569 q^{71} +(7.40366 - 7.40366i) q^{73} +(-7.38019 + 4.53131i) q^{75} -1.89073i q^{77} -8.54920i q^{79} +(8.66991 - 2.41509i) q^{81} +11.5636 q^{83} +(-4.57909 + 1.12718i) q^{85} +(4.15916 - 4.76629i) q^{87} +9.67152i q^{89} +(1.90008 - 1.90008i) q^{91} +(-0.609625 - 8.96205i) q^{93} +(1.77685 + 7.21834i) q^{95} +(-6.58488 + 6.58488i) q^{97} +(-3.49869 - 2.65730i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{15} + 8 q^{19} - 4 q^{21} + 16 q^{31} - 4 q^{33} - 24 q^{39} + 40 q^{43} + 8 q^{45} + 4 q^{51} + 12 q^{57} - 24 q^{61} + 32 q^{63} + 8 q^{67} - 12 q^{69} + 24 q^{75} - 8 q^{81} - 24 q^{85} + 12 q^{87}+ \cdots + 32 q^{99}+O(q^{100}) $ 88 * q + 4 * q^15 + 8 * q^19 - 4 * q^21 + 16 * q^31 - 4 * q^33 - 24 * q^39 + 40 * q^43 + 8 * q^45 + 4 * q^51 + 12 * q^57 - 24 * q^61 + 32 * q^63 + 8 * q^67 - 12 * q^69 + 24 * q^75 - 8 * q^81 - 24 * q^85 + 12 * q^87 + 8 * q^91 - 8 * q^97 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.117548	−	1.72806i	−0.0678662	−	0.997694i
$3$	−0.117548	−	1.72806i	−0.0678662	−	0.997694i
$4$		0			0
$5$	−1.15738	+	1.91324i	−0.517596	+	0.855625i
$5$	−1.15738	+	1.91324i	−0.517596	+	0.855625i
$6$		0			0
$7$	−0.912923	−	0.912923i	−0.345052	−	0.345052i	0.513210	−	0.858263i	$-0.328456\pi$
$7$	−0.912923	−	0.912923i	−0.345052	−	0.345052i	−0.858263	+	0.513210i	$0.828456\pi$
$8$		0			0
$9$	−2.97237	+	0.406258i	−0.990788	+	0.135419i
$10$		0			0
$11$	1.03554	+	1.03554i	0.312226	+	0.312226i	0.845771	−	0.533545i	$-0.179141\pi$
$11$	1.03554	+	1.03554i	0.312226	+	0.312226i	−0.533545	+	0.845771i	$0.679141\pi$
$12$		0			0
$13$			2.08132i			0.577254i	0.957442	+	0.288627i	$0.0931987\pi$
$13$			2.08132i			0.577254i	−0.957442	+	0.288627i	$0.906801\pi$
$14$		0			0
$15$	3.44223	+	1.77512i	0.888780	+	0.458334i
$16$		0			0
$17$	1.49126	+	1.49126i	0.361684	+	0.361684i	0.864433	−	0.502749i	$-0.167678\pi$
$17$	1.49126	+	1.49126i	0.361684	+	0.361684i	−0.502749	+	0.864433i	$0.667678\pi$
$18$		0			0
$19$	2.35078	−	2.35078i	0.539306	−	0.539306i	−0.384019	−	0.923325i	$-0.625460\pi$
$19$	2.35078	−	2.35078i	0.539306	−	0.539306i	0.923325	+	0.384019i	$0.125460\pi$
$20$		0			0
$21$	−1.47027	+	1.68489i	−0.320839	+	0.367674i
$22$		0			0
$23$	4.27105	+	4.27105i	0.890576	+	0.890576i	0.994577	−	0.104001i	$-0.0331645\pi$
$23$	4.27105	+	4.27105i	0.890576	+	0.890576i	−0.104001	+	0.994577i	$0.533165\pi$
$24$		0			0
$25$	−2.32095	−	4.42868i	−0.464189	−	0.885736i
$26$		0			0
$27$	1.05143	+	5.08866i	0.202348	+	0.979314i
$28$		0			0
$29$	2.58251	+	2.58251i	0.479560	+	0.479560i	0.904991	−	0.425431i	$-0.139878\pi$
$29$	2.58251	+	2.58251i	0.479560	+	0.479560i	−0.425431	+	0.904991i	$0.639878\pi$
$30$		0			0
$31$	5.18620			0.931469			0.465734	−	0.884925i	$-0.345790\pi$
$31$	5.18620			0.931469			0.465734	+	0.884925i	$0.345790\pi$
$32$		0			0
$33$	1.66774	−	1.91119i	0.290317	−	0.332696i
$34$		0			0
$35$	2.80323	−	0.690039i	0.473833	−	0.116638i
$36$		0			0
$37$			10.8954i			1.79120i	0.444863	+	0.895599i	$0.353253\pi$
$37$			10.8954i			1.79120i	−0.444863	+	0.895599i	$0.646747\pi$
$38$		0			0
$39$	3.59664	−	0.244654i	0.575923	−	0.0391760i
$40$		0			0
$41$	9.82802			1.53488			0.767439	−	0.641122i	$-0.221531\pi$
$41$	9.82802			1.53488			0.767439	+	0.641122i	$0.221531\pi$
$42$		0			0
$43$	−0.814988			−0.124284			−0.0621422	−	0.998067i	$-0.519793\pi$
$43$	−0.814988			−0.124284			−0.0621422	+	0.998067i	$0.519793\pi$
$44$		0			0
$45$	2.66289	−	6.15703i	0.396960	−	0.917836i
$46$		0			0
$47$	−6.63331	−	6.63331i	−0.967568	−	0.967568i	0.0319224	−	0.999490i	$-0.489837\pi$
$47$	−6.63331	−	6.63331i	−0.967568	−	0.967568i	−0.999490	+	0.0319224i	$0.989837\pi$
$48$		0			0
$49$		−	5.33314i		−	0.761878i
$50$		0			0
$51$	2.40169	−	2.75228i	0.336304	−	0.385396i
$52$		0			0
$53$			7.26025i			0.997273i	0.866811	+	0.498636i	$0.166166\pi$
$53$			7.26025i			0.997273i	−0.866811	+	0.498636i	$0.833834\pi$
$54$		0			0
$55$	−3.17974	+	0.782718i	−0.428756	+	0.105542i
$56$		0			0
$57$	−4.33861	−	3.78596i	−0.574663	−	0.501462i
$58$		0			0
$59$	−6.09835	+	6.09835i	−0.793938	+	0.793938i	−0.982132	−	0.188194i	$-0.939737\pi$
$59$	−6.09835	+	6.09835i	−0.793938	+	0.793938i	0.188194	+	0.982132i	$0.439737\pi$
$60$		0			0
$61$	9.87198	+	9.87198i	1.26398	+	1.26398i	0.949148	+	0.314829i	$0.101947\pi$
$61$	9.87198	+	9.87198i	1.26398	+	1.26398i	0.314829	+	0.949148i	$0.398053\pi$
$62$		0			0
$63$	3.08442	+	2.34266i	0.388601	+	0.295147i
$64$		0			0
$65$	−3.98205	−	2.40887i	−0.493913	−	0.298784i
$66$		0			0
$67$	−10.8038			−1.31990			−0.659949	−	0.751310i	$-0.729422\pi$
$67$	−10.8038			−1.31990			−0.659949	+	0.751310i	$0.729422\pi$
$68$		0			0
$69$	6.87857	−	7.88268i	0.828083	−	0.948963i
$70$		0			0
$71$	2.57569			0.305678			0.152839	−	0.988251i	$-0.451158\pi$
$71$	2.57569			0.305678			0.152839	+	0.988251i	$0.451158\pi$
$72$		0			0
$73$	7.40366	−	7.40366i	0.866533	−	0.866533i	−0.125554	−	0.992087i	$-0.540071\pi$
$73$	7.40366	−	7.40366i	0.866533	−	0.866533i	0.992087	+	0.125554i	$0.0400708\pi$
$74$		0			0
$75$	−7.38019	+	4.53131i	−0.852191	+	0.523231i
$76$		0			0
$77$		−	1.89073i		−	0.215469i
$78$		0			0
$79$		−	8.54920i		−	0.961861i	−0.876759	−	0.480930i	$-0.840299\pi$
$79$		−	8.54920i		−	0.961861i	0.876759	−	0.480930i	$-0.159701\pi$
$80$		0			0
$81$	8.66991	−	2.41509i	0.963323	−	0.268344i
$82$		0			0
$83$	11.5636			1.26927			0.634635	−	0.772812i	$-0.281151\pi$
$83$	11.5636			1.26927			0.634635	+	0.772812i	$0.281151\pi$
$84$		0			0
$85$	−4.57909	+	1.12718i	−0.496672	+	0.122260i
$86$		0			0
$87$	4.15916	−	4.76629i	0.445908	−	0.511000i
$88$		0			0
$89$			9.67152i			1.02518i	0.858634	+	0.512590i	$0.171314\pi$
$89$			9.67152i			1.02518i	−0.858634	+	0.512590i	$0.828686\pi$
$90$		0			0
$91$	1.90008	−	1.90008i	0.199183	−	0.199183i
$92$		0			0
$93$	−0.609625	−	8.96205i	−0.0632152	−	0.929321i
$94$		0			0
$95$	1.77685	+	7.21834i	0.182301	+	0.740586i
$96$		0			0
$97$	−6.58488	+	6.58488i	−0.668593	+	0.668593i	−0.957390	−	0.288797i	$-0.906745\pi$
$97$	−6.58488	+	6.58488i	−0.668593	+	0.668593i	0.288797	+	0.957390i	$0.406745\pi$
$98$		0			0
$99$	−3.49869	−	2.65730i	−0.351632	−	0.267069i
$100$		0			0
$101$	−4.86989	−	4.86989i	−0.484572	−	0.484572i	0.422016	−	0.906588i	$-0.361322\pi$
$101$	−4.86989	−	4.86989i	−0.484572	−	0.484572i	−0.906588	+	0.422016i	$0.861322\pi$
$102$		0			0
$103$	−4.41364	+	4.41364i	−0.434888	+	0.434888i	−0.890287	−	0.455399i	$-0.849497\pi$
$103$	−4.41364	+	4.41364i	−0.434888	+	0.434888i	0.455399	+	0.890287i	$0.349497\pi$
$104$		0			0
$105$	−1.52194	−	4.76304i	−0.148526	−	0.464825i
$106$		0			0
$107$	8.76918			0.847748			0.423874	−	0.905721i	$-0.360670\pi$
$107$	8.76918			0.847748			0.423874	+	0.905721i	$0.360670\pi$
$108$		0			0
$109$	5.82689	−	5.82689i	0.558115	−	0.558115i	−0.370656	−	0.928770i	$-0.620867\pi$
$109$	5.82689	−	5.82689i	0.558115	−	0.558115i	0.928770	+	0.370656i	$0.120867\pi$
$110$		0			0
$111$	18.8279	−	1.28073i	1.78707	−	0.121562i
$112$		0			0
$113$	−6.67807	+	6.67807i	−0.628220	+	0.628220i	−0.947620	−	0.319400i	$-0.896519\pi$
$113$	−6.67807	+	6.67807i	−0.628220	+	0.628220i	0.319400	+	0.947620i	$0.396519\pi$
$114$		0			0
$115$	−13.1148	+	3.22831i	−1.22296	+	0.301041i
$116$		0			0
$117$	−0.845552	−	6.18644i	−0.0781713	−	0.571936i
$118$		0			0
$119$		−	2.72281i		−	0.249600i
$120$		0			0
$121$		−	8.85533i		−	0.805030i
$122$		0			0
$123$	−1.15526	−	16.9834i	−0.104166	−	1.53134i
$124$		0			0
$125$	11.1593	+	0.685142i	0.998121	+	0.0612810i
$126$		0			0
$127$	4.03563	−	4.03563i	0.358105	−	0.358105i	−0.505009	−	0.863114i	$-0.668511\pi$
$127$	4.03563	−	4.03563i	0.358105	−	0.358105i	0.863114	+	0.505009i	$0.168511\pi$
$128$		0			0
$129$	0.0957999	+	1.40835i	0.00843471	+	0.123998i
$130$		0			0
$131$	−12.4730	+	12.4730i	−1.08977	+	1.08977i	−0.0942236	+	0.995551i	$0.530037\pi$
$131$	−12.4730	+	12.4730i	−1.08977	+	1.08977i	−0.995551	+	0.0942236i	$0.969963\pi$
$132$		0			0
$133$	−4.29216			−0.372178
$134$		0			0
$135$	−10.9527	−	3.87787i	−0.942660	−	0.333754i
$136$		0			0
$137$	−2.68828	+	2.68828i	−0.229675	+	0.229675i	−0.812557	−	0.582882i	$-0.801925\pi$
$137$	−2.68828	+	2.68828i	−0.229675	+	0.229675i	0.582882	+	0.812557i	$0.301925\pi$
$138$		0			0
$139$	4.14179	+	4.14179i	0.351302	+	0.351302i	0.860594	−	0.509292i	$-0.170093\pi$
$139$	4.14179	+	4.14179i	0.351302	+	0.351302i	−0.509292	+	0.860594i	$0.670093\pi$
$140$		0			0
$141$	−10.6830	+	12.2425i	−0.899672	+	1.03100i
$142$		0			0
$143$	−2.15528	+	2.15528i	−0.180234	+	0.180234i
$144$		0			0
$145$	−7.92989	+	1.95201i	−0.658542	+	0.162105i
$146$		0			0
$147$	−9.21598	+	0.626898i	−0.760121	+	0.0517057i
$148$		0			0
$149$	−3.27529	+	3.27529i	−0.268322	+	0.268322i	−0.828424	−	0.560102i	$-0.810762\pi$
$149$	−3.27529	+	3.27529i	−0.268322	+	0.268322i	0.560102	+	0.828424i	$0.310762\pi$
$150$		0			0
$151$			11.4102i			0.928548i	0.885692	+	0.464274i	$0.153685\pi$
$151$			11.4102i			0.928548i	−0.885692	+	0.464274i	$0.846315\pi$
$152$		0			0
$153$	−5.03841	−	3.82674i	−0.407332	−	0.309373i
$154$		0			0
$155$	−6.00240	+	9.92242i	−0.482124	+	0.796988i
$156$		0			0
$157$	3.40961			0.272116			0.136058	−	0.990701i	$-0.456557\pi$
$157$	3.40961			0.272116			0.136058	+	0.990701i	$0.456557\pi$
$158$		0			0
$159$	12.5461	−	0.853426i	0.994973	−	0.0676811i
$160$		0			0
$161$		−	7.79828i		−	0.614591i
$162$		0			0
$163$		−	4.71686i		−	0.369453i	−0.982790	−	0.184727i	$-0.940860\pi$
$163$		−	4.71686i		−	0.369453i	0.982790	−	0.184727i	$-0.0591400\pi$
$164$		0			0
$165$	1.72635	+	5.40276i	0.134396	+	0.420604i
$166$		0			0
$167$	−14.7875	+	14.7875i	−1.14429	+	1.14429i	−0.156635	+	0.987657i	$0.550065\pi$
$167$	−14.7875	+	14.7875i	−1.14429	+	1.14429i	−0.987657	+	0.156635i	$0.949935\pi$
$168$		0			0
$169$	8.66811			0.666778
$170$		0			0
$171$	−6.03236	+	7.94240i	−0.461306	+	0.607371i
$172$		0			0
$173$	−20.6855			−1.57269			−0.786343	−	0.617790i	$-0.788028\pi$
$173$	−20.6855			−1.57269			−0.786343	+	0.617790i	$0.788028\pi$
$174$		0			0
$175$	−1.92420	+	6.16189i	−0.145456	+	0.465795i
$176$		0			0
$177$	11.2552	+	9.82146i	0.845989	+	0.738226i
$178$		0			0
$179$	−15.0062	−	15.0062i	−1.12162	−	1.12162i	−0.991499	−	0.130118i	$-0.958464\pi$
$179$	−15.0062	−	15.0062i	−1.12162	−	1.12162i	−0.130118	−	0.991499i	$-0.541536\pi$
$180$		0			0
$181$	2.48233	−	2.48233i	0.184510	−	0.184510i	−0.608808	−	0.793318i	$-0.708352\pi$
$181$	2.48233	−	2.48233i	0.184510	−	0.184510i	0.793318	+	0.608808i	$0.208352\pi$
$182$		0			0
$183$	15.8989	−	18.2198i	1.17528	−	1.34684i
$184$		0			0
$185$	−20.8455	−	12.6101i	−1.53259	−	0.927116i
$186$		0			0
$187$			3.08851i			0.225855i
$188$		0			0
$189$	3.68568	−	5.60543i	0.268094	−	0.407735i
$190$		0			0
$191$			14.6164i			1.05761i	0.848744	+	0.528804i	$0.177359\pi$
$191$			14.6164i			1.05761i	−0.848744	+	0.528804i	$0.822641\pi$
$192$		0			0
$193$	−5.06820	−	5.06820i	−0.364817	−	0.364817i	0.500766	−	0.865583i	$-0.333052\pi$
$193$	−5.06820	−	5.06820i	−0.364817	−	0.364817i	−0.865583	+	0.500766i	$0.833052\pi$
$194$		0			0
$195$	−3.69459	+	7.16437i	−0.264575	+	0.513052i
$196$		0			0
$197$	−4.73103			−0.337072			−0.168536	−	0.985696i	$-0.553904\pi$
$197$	−4.73103			−0.337072			−0.168536	+	0.985696i	$0.553904\pi$
$198$		0			0
$199$	7.61133			0.539553			0.269776	−	0.962923i	$-0.413050\pi$
$199$	7.61133			0.539553			0.269776	+	0.962923i	$0.413050\pi$
$200$		0			0
$201$	1.26997	+	18.6696i	0.0895764	+	1.31686i
$202$		0			0
$203$		−	4.71526i		−	0.330946i
$204$		0			0
$205$	−11.3747	+	18.8033i	−0.794447	+	1.31328i
$206$		0			0
$207$	−14.4303	−	10.9600i	−1.00297	−	0.761771i
$208$		0			0
$209$	4.86864			0.336771
$210$		0			0
$211$	7.48648	+	7.48648i	0.515391	+	0.515391i	0.916173	−	0.400783i	$-0.131262\pi$
$211$	7.48648	+	7.48648i	0.515391	+	0.515391i	−0.400783	+	0.916173i	$0.631262\pi$
$212$		0			0
$213$	−0.302766	−	4.45094i	−0.0207452	−	0.304973i
$214$		0			0
$215$	0.943250	−	1.55926i	0.0643291	−	0.106341i
$216$		0			0
$217$	−4.73460	−	4.73460i	−0.321405	−	0.321405i
$218$		0			0
$219$	−13.6642	−	11.9237i	−0.923343	−	0.805727i
$220$		0			0
$221$	−3.10379	+	3.10379i	−0.208784	+	0.208784i
$222$		0			0
$223$	−14.9484	−	14.9484i	−1.00102	−	1.00102i	−0.999999	−	0.00101699i	$-0.999676\pi$
$223$	−14.9484	−	14.9484i	−1.00102	−	1.00102i	−0.00101699	−	0.999999i	$-0.500324\pi$
$224$		0			0
$225$	8.69789	+	12.2208i	0.579859	+	0.814717i
$226$		0			0
$227$			5.12514i			0.340167i	0.985430	+	0.170084i	$0.0544038\pi$
$227$			5.12514i			0.340167i	−0.985430	+	0.170084i	$0.945596\pi$
$228$		0			0
$229$	−1.86356	−	1.86356i	−0.123148	−	0.123148i	0.642847	−	0.765995i	$-0.277753\pi$
$229$	−1.86356	−	1.86356i	−0.123148	−	0.123148i	−0.765995	+	0.642847i	$0.777753\pi$
$230$		0			0
$231$	−3.26729	+	0.222251i	−0.214972	+	0.0146230i
$232$		0			0
$233$	5.48648	+	5.48648i	0.359431	+	0.359431i	0.863603	−	0.504172i	$-0.168202\pi$
$233$	5.48648	+	5.48648i	0.359431	+	0.359431i	−0.504172	+	0.863603i	$0.668202\pi$
$234$		0			0
$235$	20.3684	−	5.01384i	1.32868	−	0.327067i
$236$		0			0
$237$	−14.7735	+	1.00494i	−0.959643	+	0.0652778i
$238$		0			0
$239$	9.45252			0.611433			0.305716	−	0.952123i	$-0.401104\pi$
$239$	9.45252			0.611433			0.305716	+	0.952123i	$0.401104\pi$
$240$		0			0
$241$	10.3530			0.666894			0.333447	−	0.942769i	$-0.391788\pi$
$241$	10.3530			0.666894			0.333447	+	0.942769i	$0.391788\pi$
$242$		0			0
$243$	−5.19255	−	14.6982i	−0.333102	−	0.942891i
$244$		0			0
$245$	10.2036	+	6.17247i	0.651882	+	0.394345i
$246$		0			0
$247$	4.89272	+	4.89272i	0.311316	+	0.311316i
$248$		0			0
$249$	−1.35927	−	19.9826i	−0.0861404	−	1.26634i
$250$		0			0
$251$	−18.5502	−	18.5502i	−1.17088	−	1.17088i	−0.982001	−	0.188874i	$-0.939516\pi$
$251$	−18.5502	−	18.5502i	−1.17088	−	1.17088i	−0.188874	−	0.982001i	$-0.560484\pi$
$252$		0			0
$253$			8.84567i			0.556122i
$254$		0			0
$255$	2.48610	+	7.78044i	0.155685	+	0.487230i
$256$		0			0
$257$	5.32881	+	5.32881i	0.332402	+	0.332402i	0.853498	−	0.521096i	$-0.174477\pi$
$257$	5.32881	+	5.32881i	0.332402	+	0.332402i	−0.521096	+	0.853498i	$0.674477\pi$
$258$		0			0
$259$	9.94669	−	9.94669i	0.618057	−	0.618057i
$260$		0			0
$261$	−8.72532	−	6.62699i	−0.540084	−	0.410201i
$262$		0			0
$263$	−6.84521	−	6.84521i	−0.422094	−	0.422094i	0.463830	−	0.885924i	$-0.346475\pi$
$263$	−6.84521	−	6.84521i	−0.422094	−	0.422094i	−0.885924	+	0.463830i	$0.846475\pi$
$264$		0			0
$265$	−13.8906	−	8.40287i	−0.853292	−	0.516184i
$266$		0			0
$267$	16.7129	−	1.13686i	1.02282	−	0.0695750i
$268$		0			0
$269$	−0.0586414	−	0.0586414i	−0.00357543	−	0.00357543i	0.705317	−	0.708892i	$-0.250805\pi$
$269$	−0.0586414	−	0.0586414i	−0.00357543	−	0.00357543i	−0.708892	+	0.705317i	$0.750805\pi$
$270$		0			0
$271$	−14.7531			−0.896185			−0.448093	−	0.893987i	$-0.647897\pi$
$271$	−14.7531			−0.896185			−0.448093	+	0.893987i	$0.647897\pi$
$272$		0			0
$273$	−3.50680	−	3.06010i	−0.212241	−	0.185206i
$274$		0			0
$275$	2.18264	−	6.98949i	0.131618	−	0.421482i
$276$		0			0
$277$		−	12.2040i		−	0.733266i	−0.930366	−	0.366633i	$-0.880510\pi$
$277$		−	12.2040i		−	0.733266i	0.930366	−	0.366633i	$-0.119490\pi$
$278$		0			0
$279$	−15.4153	+	2.10693i	−0.922888	+	0.126139i
$280$		0			0
$281$	2.18598			0.130404			0.0652022	−	0.997872i	$-0.479231\pi$
$281$	2.18598			0.130404			0.0652022	+	0.997872i	$0.479231\pi$
$282$		0			0
$283$	10.8232			0.643373			0.321686	−	0.946846i	$-0.395750\pi$
$283$	10.8232			0.643373			0.321686	+	0.946846i	$0.395750\pi$
$284$		0			0
$285$	12.2648	−	3.91901i	0.726507	−	0.232142i
$286$		0			0
$287$	−8.97222	−	8.97222i	−0.529614	−	0.529614i
$288$		0			0
$289$		−	12.5523i		−	0.738369i
$290$		0			0
$291$	12.1531	+	10.6050i	0.712427	+	0.621677i
$292$		0			0
$293$		−	13.0105i		−	0.760084i	−0.924969	−	0.380042i	$-0.875910\pi$
$293$		−	13.0105i		−	0.760084i	0.924969	−	0.380042i	$-0.124090\pi$
$294$		0			0
$295$	−4.60948	−	18.7257i	−0.268375	−	1.09025i
$296$		0			0
$297$	−4.18070	+	6.35830i	−0.242589	+	0.368946i
$298$		0			0
$299$	−8.88942	+	8.88942i	−0.514088	+	0.514088i
$300$		0			0
$301$	0.744021	+	0.744021i	0.0428846	+	0.0428846i
$302$		0			0
$303$	−7.84300	+	8.98789i	−0.450568	+	0.516341i
$304$		0			0
$305$	−30.3131	+	7.46181i	−1.73572	+	0.427262i
$306$		0			0
$307$	34.3297			1.95930			0.979649	−	0.200718i	$-0.0643275\pi$
$307$	34.3297			1.95930			0.979649	+	0.200718i	$0.0643275\pi$
$308$		0			0
$309$	8.14583	+	7.10820i	0.463400	+	0.404372i
$310$		0			0
$311$	19.7120			1.11777			0.558883	−	0.829247i	$-0.311230\pi$
$311$	19.7120			1.11777			0.558883	+	0.829247i	$0.311230\pi$
$312$		0			0
$313$	−8.82647	+	8.82647i	−0.498902	+	0.498902i	−0.911096	−	0.412194i	$-0.864763\pi$
$313$	−8.82647	+	8.82647i	−0.498902	+	0.498902i	0.412194	+	0.911096i	$0.364763\pi$
$314$		0			0
$315$	−8.05190	+	3.18989i	−0.453673	+	0.179730i
$316$		0			0
$317$		−	27.9576i		−	1.57026i	−0.619334	−	0.785128i	$-0.712597\pi$
$317$		−	27.9576i		−	1.57026i	0.619334	−	0.785128i	$-0.287403\pi$
$318$		0			0
$319$			5.34857i			0.299462i
$320$		0			0
$321$	−1.03080	−	15.1536i	−0.0575334	−	0.845794i
$322$		0			0
$323$	7.01126			0.390117
$324$		0			0
$325$	9.21749	−	4.83063i	0.511294	−	0.267955i
$326$		0			0
$327$	−10.7541	−	9.38426i	−0.594705	−	0.518951i
$328$		0			0
$329$			12.1114i			0.667723i
$330$		0			0
$331$	11.7945	−	11.7945i	0.648285	−	0.648285i	−0.304293	−	0.952578i	$-0.598420\pi$
$331$	11.7945	−	11.7945i	0.648285	−	0.648285i	0.952578	+	0.304293i	$0.0984203\pi$
$332$		0			0
$333$	−4.42636	−	32.3852i	−0.242563	−	1.77470i
$334$		0			0
$335$	12.5041	−	20.6703i	0.683174	−	1.12934i
$336$		0			0
$337$	1.70964	−	1.70964i	0.0931298	−	0.0931298i	−0.659007	−	0.752137i	$-0.729023\pi$
$337$	1.70964	−	1.70964i	0.0931298	−	0.0931298i	0.752137	+	0.659007i	$0.229023\pi$
$338$		0			0
$339$	12.3251	+	10.7551i	0.669407	+	0.584137i
$340$		0			0
$341$	5.37050	+	5.37050i	0.290829	+	0.290829i
$342$		0			0
$343$	−11.2592	+	11.2592i	−0.607940	+	0.607940i
$344$		0			0
$345$	7.12031	+	22.2836i	0.383344	+	1.19971i
$346$		0			0
$347$	19.6676			1.05581			0.527905	−	0.849304i	$-0.322978\pi$
$347$	19.6676			1.05581			0.527905	+	0.849304i	$0.322978\pi$
$348$		0			0
$349$	−5.38375	+	5.38375i	−0.288186	+	0.288186i	−0.836362	−	0.548177i	$-0.815322\pi$
$349$	−5.38375	+	5.38375i	−0.288186	+	0.288186i	0.548177	+	0.836362i	$0.315322\pi$
$350$		0			0
$351$	−10.5911	+	2.18836i	−0.565313	+	0.116806i
$352$		0			0
$353$	25.3482	−	25.3482i	1.34915	−	1.34915i	0.462556	−	0.886590i	$-0.346933\pi$
$353$	25.3482	−	25.3482i	1.34915	−	1.34915i	0.886590	−	0.462556i	$-0.153067\pi$
$354$		0			0
$355$	−2.98105	+	4.92790i	−0.158218	+	0.261546i
$356$		0			0
$357$	−4.70518	+	0.320060i	−0.249025	+	0.0169394i
$358$		0			0
$359$		−	22.5488i		−	1.19008i	−0.803696	−	0.595040i	$-0.797136\pi$
$359$		−	22.5488i		−	1.19008i	0.803696	−	0.595040i	$-0.202864\pi$
$360$		0			0
$361$			7.94766i			0.418298i
$362$		0			0
$363$	−15.3025	+	1.04092i	−0.803174	+	0.0546343i
$364$		0			0
$365$	5.59611	+	22.7338i	0.292914	+	1.18994i
$366$		0			0
$367$	−16.5406	+	16.5406i	−0.863411	+	0.863411i	−0.991733	−	0.128322i	$-0.959041\pi$
$367$	−16.5406	+	16.5406i	−0.863411	+	0.863411i	0.128322	+	0.991733i	$0.459041\pi$
$368$		0			0
$369$	−29.2125	+	3.99271i	−1.52074	+	0.207852i
$370$		0			0
$371$	6.62805	−	6.62805i	0.344111	−	0.344111i
$372$		0			0
$373$	−7.24873			−0.375325			−0.187663	−	0.982234i	$-0.560091\pi$
$373$	−7.24873			−0.375325			−0.187663	+	0.982234i	$0.560091\pi$
$374$		0			0
$375$	−0.127788	−	19.3645i	−0.00659892	−	0.999978i
$376$		0			0
$377$	−5.37502	+	5.37502i	−0.276828	+	0.276828i
$378$		0			0
$379$	6.48173	+	6.48173i	0.332944	+	0.332944i	0.853703	−	0.520759i	$-0.174351\pi$
$379$	6.48173	+	6.48173i	0.332944	+	0.332944i	−0.520759	+	0.853703i	$0.674351\pi$
$380$		0			0
$381$	−7.44819	−	6.49943i	−0.381582	−	0.332976i
$382$		0			0
$383$	−13.1911	+	13.1911i	−0.674035	+	0.674035i	−0.958644	−	0.284609i	$-0.908136\pi$
$383$	−13.1911	+	13.1911i	−0.674035	+	0.674035i	0.284609	+	0.958644i	$0.408136\pi$
$384$		0			0
$385$	3.61741	+	2.18829i	0.184361	+	0.111526i
$386$		0			0
$387$	2.42244	−	0.331095i	0.123140	−	0.0168305i
$388$		0			0
$389$	−1.04217	+	1.04217i	−0.0528401	+	0.0528401i	−0.733033	−	0.680193i	$-0.761896\pi$
$389$	−1.04217	+	1.04217i	−0.0528401	+	0.0528401i	0.680193	+	0.733033i	$0.261896\pi$
$390$		0			0
$391$			12.7385i			0.644215i
$392$		0			0
$393$	23.0203	+	20.0880i	1.16122	+	1.01330i
$394$		0			0
$395$	16.3566	+	9.89467i	0.822992	+	0.497855i
$396$		0			0
$397$	0.837780			0.0420470			0.0210235	−	0.999779i	$-0.493308\pi$
$397$	0.837780			0.0420470			0.0210235	+	0.999779i	$0.493308\pi$
$398$		0			0
$399$	0.504534	+	7.41710i	0.0252583	+	0.371320i
$400$		0			0
$401$			23.6742i			1.18223i	0.806587	+	0.591116i	$0.201312\pi$
$401$			23.6742i			1.18223i	−0.806587	+	0.591116i	$0.798688\pi$
$402$		0			0
$403$			10.7941i			0.537694i
$404$		0			0
$405$	−5.41372	+	19.3828i	−0.269010	+	0.963137i
$406$		0			0
$407$	−11.2826	+	11.2826i	−0.559259	+	0.559259i
$408$		0			0
$409$	25.7330			1.27242			0.636208	−	0.771517i	$-0.280502\pi$
$409$	25.7330			1.27242			0.636208	+	0.771517i	$0.280502\pi$
$410$		0			0
$411$	4.96151	+	4.32950i	0.244733	+	0.213559i
$412$		0			0
$413$	11.1347			0.547900
$414$		0			0
$415$	−13.3835	+	22.1239i	−0.656968	+	1.08602i
$416$		0			0
$417$	6.67040	−	7.64411i	0.326651	−	0.374334i
$418$		0			0
$419$	13.8036	+	13.8036i	0.674351	+	0.674351i	0.958716	−	0.284365i	$-0.0917829\pi$
$419$	13.8036	+	13.8036i	0.674351	+	0.674351i	−0.284365	+	0.958716i	$0.591783\pi$
$420$		0			0
$421$	13.7845	−	13.7845i	0.671817	−	0.671817i	−0.286318	−	0.958135i	$-0.592431\pi$
$421$	13.7845	−	13.7845i	0.671817	−	0.671817i	0.958135	+	0.286318i	$0.0924314\pi$
$422$		0			0
$423$	22.4115	+	17.0218i	1.08968	+	0.827628i
$424$		0			0
$425$	3.14318	−	10.0655i	0.152467	−	0.488247i
$426$		0			0
$427$		−	18.0247i		−	0.872277i
$428$		0			0
$429$	3.97780	+	3.47110i	0.192050	+	0.167586i
$430$		0			0
$431$		−	2.16037i		−	0.104061i	−0.998645	−	0.0520307i	$-0.983431\pi$
$431$		−	2.16037i		−	0.104061i	0.998645	−	0.0520307i	$-0.0165694\pi$
$432$		0			0
$433$	−17.6860	−	17.6860i	−0.849935	−	0.849935i	0.140189	−	0.990125i	$-0.455229\pi$
$433$	−17.6860	−	17.6860i	−0.849935	−	0.849935i	−0.990125	+	0.140189i	$0.955229\pi$
$434$		0			0
$435$	4.30532	+	13.4739i	0.206424	+	0.646022i
$436$		0			0
$437$	20.0806			0.960586
$438$		0			0
$439$	11.2105			0.535049			0.267525	−	0.963551i	$-0.413794\pi$
$439$	11.2105			0.535049			0.267525	+	0.963551i	$0.413794\pi$
$440$		0			0
$441$	2.16663	+	15.8521i	0.103173	+	0.754860i
$442$		0			0
$443$			5.63824i			0.267881i	0.990989	+	0.133940i	$0.0427631\pi$
$443$			5.63824i			0.267881i	−0.990989	+	0.133940i	$0.957237\pi$
$444$		0			0
$445$	−18.5039	−	11.1936i	−0.877170	−	0.530629i
$446$		0			0
$447$	6.04489	+	5.27488i	0.285913	+	0.249493i
$448$		0			0
$449$	9.38457			0.442885			0.221443	−	0.975173i	$-0.428923\pi$
$449$	9.38457			0.442885			0.221443	+	0.975173i	$0.428923\pi$
$450$		0			0
$451$	10.1773	+	10.1773i	0.479229	+	0.479229i
$452$		0			0
$453$	19.7175	−	1.34124i	0.926407	−	0.0630170i
$454$		0			0
$455$	1.43619	+	5.83442i	0.0673297	+	0.273522i
$456$		0			0
$457$	16.2317	+	16.2317i	0.759289	+	0.759289i	0.976193	−	0.216904i	$-0.0695959\pi$
$457$	16.2317	+	16.2317i	0.759289	+	0.759289i	−0.216904	+	0.976193i	$0.569596\pi$
$458$		0			0
$459$	−6.02057	+	9.15649i	−0.281016	+	0.427388i
$460$		0			0
$461$	−7.62591	+	7.62591i	−0.355174	+	0.355174i	−0.862030	−	0.506857i	$-0.830807\pi$
$461$	−7.62591	+	7.62591i	−0.355174	+	0.355174i	0.506857	+	0.862030i	$0.330807\pi$
$462$		0			0
$463$	−10.9986	−	10.9986i	−0.511149	−	0.511149i	0.403730	−	0.914878i	$-0.367714\pi$
$463$	−10.9986	−	10.9986i	−0.511149	−	0.511149i	−0.914878	+	0.403730i	$0.867714\pi$
$464$		0			0
$465$	17.8521	+	9.20613i	0.827870	+	0.426924i
$466$		0			0
$467$			9.64270i			0.446211i	0.974794	+	0.223105i	$0.0716194\pi$
$467$			9.64270i			0.446211i	−0.974794	+	0.223105i	$0.928381\pi$
$468$		0			0
$469$	9.86307	+	9.86307i	0.455434	+	0.455434i
$470$		0			0
$471$	−0.400791	−	5.89200i	−0.0184675	−	0.271489i
$472$		0			0
$473$	−0.843950	−	0.843950i	−0.0388049	−	0.0388049i
$474$		0			0
$475$	−15.8669	−	4.95482i	−0.728023	−	0.227343i
$476$		0			0
$477$	−2.94954	−	21.5801i	−0.135050	−	0.988086i
$478$		0			0
$479$	−0.350518			−0.0160156			−0.00800779	−	0.999968i	$-0.502549\pi$
$479$	−0.350518			−0.0160156			−0.00800779	+	0.999968i	$0.502549\pi$
$480$		0			0
$481$	−22.6769			−1.03398
$482$		0			0
$483$	−13.4759	+	0.916670i	−0.613174	+	0.0417099i
$484$		0			0
$485$	−4.97723	−	20.2196i	−0.226004	−	0.918126i
$486$		0			0
$487$	−3.32822	−	3.32822i	−0.150816	−	0.150816i	0.627666	−	0.778482i	$-0.284010\pi$
$487$	−3.32822	−	3.32822i	−0.150816	−	0.150816i	−0.778482	+	0.627666i	$0.784010\pi$
$488$		0			0
$489$	−8.15101	+	0.554456i	−0.368601	+	0.0250734i
$490$		0			0
$491$	−20.7903	−	20.7903i	−0.938255	−	0.938255i	0.0599467	−	0.998202i	$-0.480907\pi$
$491$	−20.7903	−	20.7903i	−0.938255	−	0.938255i	−0.998202	+	0.0599467i	$0.980907\pi$
$492$		0			0
$493$			7.70239i			0.346898i
$494$		0			0
$495$	9.13335	−	3.61832i	0.410514	−	0.162631i
$496$		0			0
$497$	−2.35140	−	2.35140i	−0.105475	−	0.105475i
$498$		0			0
$499$	−2.98889	+	2.98889i	−0.133801	+	0.133801i	−0.770835	−	0.637034i	$-0.780161\pi$
$499$	−2.98889	+	2.98889i	−0.133801	+	0.133801i	0.637034	+	0.770835i	$0.280161\pi$
$500$		0			0
$501$	27.2919	+	23.8154i	1.21931	+	1.06399i
$502$		0			0
$503$	11.0899	+	11.0899i	0.494475	+	0.494475i	0.909713	−	0.415238i	$-0.136302\pi$
$503$	11.0899	+	11.0899i	0.494475	+	0.494475i	−0.415238	+	0.909713i	$0.636302\pi$
$504$		0			0
$505$	14.9535	−	3.68094i	0.665424	−	0.163800i
$506$		0			0
$507$	−1.01892	−	14.9790i	−0.0452517	−	0.665241i
$508$		0			0
$509$	16.8263	+	16.8263i	0.745811	+	0.745811i	0.973690	−	0.227879i	$-0.0731789\pi$
$509$	16.8263	+	16.8263i	0.745811	+	0.745811i	−0.227879	+	0.973690i	$0.573179\pi$
$510$		0			0
$511$	−13.5179			−0.597998
$512$		0			0
$513$	14.4340	+	9.49065i	0.637277	+	0.419022i
$514$		0			0
$515$	−3.33608	−	13.5526i	−0.147005	−	0.597198i
$516$		0			0
$517$		−	13.7381i		−	0.604200i
$518$		0			0
$519$	2.43153	+	35.7457i	0.106732	+	1.56906i
$520$		0			0
$521$	30.3997			1.33184			0.665918	−	0.746025i	$-0.268040\pi$
$521$	30.3997			1.33184			0.665918	+	0.746025i	$0.268040\pi$
$522$		0			0
$523$	−8.45346			−0.369644			−0.184822	−	0.982772i	$-0.559171\pi$
$523$	−8.45346			−0.369644			−0.184822	+	0.982772i	$0.559171\pi$
$524$		0			0
$525$	10.8743	+	2.60081i	0.474593	+	0.113509i
$526$		0			0
$527$	7.73398	+	7.73398i	0.336897	+	0.336897i
$528$		0			0
$529$			13.4838i			0.586252i
$530$		0			0
$531$	15.6490	−	20.6040i	0.679110	−	0.894139i
$532$		0			0
$533$			20.4552i			0.886015i
$534$		0			0
$535$	−10.1493	+	16.7775i	−0.438791	+	0.725355i
$536$		0			0
$537$	−24.1676	+	27.6955i	−1.04291	+	1.19515i
$538$		0			0
$539$	5.52267	−	5.52267i	0.237878	−	0.237878i
$540$		0			0
$541$	−7.99141	−	7.99141i	−0.343578	−	0.343578i	0.514133	−	0.857710i	$-0.328114\pi$
$541$	−7.99141	−	7.99141i	−0.343578	−	0.343578i	−0.857710	+	0.514133i	$0.828114\pi$
$542$		0			0
$543$	−4.58140	−	3.99781i	−0.196607	−	0.171563i
$544$		0			0
$545$	4.40430	+	17.8921i	0.188659	+	0.766415i
$546$		0			0
$547$	−19.6579			−0.840511			−0.420255	−	0.907406i	$-0.638060\pi$
$547$	−19.6579			−0.840511			−0.420255	+	0.907406i	$0.638060\pi$
$548$		0			0
$549$	−33.3537	−	25.3326i	−1.42350	−	1.08117i
$550$		0			0
$551$	12.1418			0.517259
$552$		0			0
$553$	−7.80476	+	7.80476i	−0.331892	+	0.331892i
$554$		0			0
$555$	−19.3407	+	37.5046i	−0.820967	+	1.59198i
$556$		0			0
$557$		−	32.6270i		−	1.38245i	−0.722640	−	0.691225i	$-0.757072\pi$
$557$		−	32.6270i		−	1.38245i	0.722640	−	0.691225i	$-0.242928\pi$
$558$		0			0
$559$		−	1.69625i		−	0.0717437i
$560$		0			0
$561$	5.33713	−	0.363048i	0.225334	−	0.0153279i
$562$		0			0
$563$	−22.9635			−0.967798			−0.483899	−	0.875124i	$-0.660780\pi$
$563$	−22.9635			−0.967798			−0.483899	+	0.875124i	$0.660780\pi$
$564$		0			0
$565$	−5.04767	−	20.5058i	−0.212357	−	0.862685i
$566$		0			0
$567$	−10.1198	−	5.71016i	−0.424990	−	0.239804i
$568$		0			0
$569$		−	42.0779i		−	1.76400i	−0.471254	−	0.881998i	$-0.656198\pi$
$569$		−	42.0779i		−	1.76400i	0.471254	−	0.881998i	$-0.343802\pi$
$570$		0			0
$571$	12.9520	−	12.9520i	0.542026	−	0.542026i	−0.382096	−	0.924122i	$-0.624798\pi$
$571$	12.9520	−	12.9520i	0.542026	−	0.542026i	0.924122	+	0.382096i	$0.124798\pi$
$572$		0			0
$573$	25.2580	−	1.71813i	1.05517	−	0.0717758i
$574$		0			0
$575$	9.00224	−	28.8280i	0.375419	−	1.20221i
$576$		0			0
$577$	6.79698	−	6.79698i	0.282962	−	0.282962i	−0.551327	−	0.834289i	$-0.685878\pi$
$577$	6.79698	−	6.79698i	0.282962	−	0.282962i	0.834289	+	0.551327i	$0.185878\pi$
$578$		0			0
$579$	−8.16238	+	9.35389i	−0.339217	+	0.388734i
$580$		0			0
$581$	−10.5567	−	10.5567i	−0.437964	−	0.437964i
$582$		0			0
$583$	−7.51826	+	7.51826i	−0.311375	+	0.311375i
$584$		0			0
$585$	12.8147	+	5.54231i	0.529824	+	0.229146i
$586$		0			0
$587$	37.8077			1.56049			0.780245	−	0.625474i	$-0.215094\pi$
$587$	37.8077			1.56049			0.780245	+	0.625474i	$0.215094\pi$
$588$		0			0
$589$	12.1916	−	12.1916i	0.502347	−	0.502347i
$590$		0			0
$591$	0.556121	+	8.17549i	0.0228758	+	0.336295i
$592$		0			0
$593$	21.2191	−	21.2191i	0.871365	−	0.871365i	−0.121256	−	0.992621i	$-0.538692\pi$
$593$	21.2191	−	21.2191i	0.871365	−	0.871365i	0.992621	+	0.121256i	$0.0386923\pi$
$594$		0			0
$595$	5.20939	+	3.15133i	0.213564	+	0.129192i
$596$		0			0
$597$	−0.894694	−	13.1528i	−0.0366174	−	0.538309i
$598$		0			0
$599$		−	17.6257i		−	0.720165i	−0.932920	−	0.360083i	$-0.882749\pi$
$599$		−	17.6257i		−	0.720165i	0.932920	−	0.360083i	$-0.117251\pi$
$600$		0			0
$601$			1.46847i			0.0599003i	0.999551	+	0.0299501i	$0.00953485\pi$
$601$			1.46847i			0.0599003i	−0.999551	+	0.0299501i	$0.990465\pi$
$602$		0			0
$603$	32.1129	−	4.38915i	1.30774	−	0.178740i
$604$		0			0
$605$	16.9423	+	10.2490i	0.688804	+	0.416680i
$606$		0			0
$607$	12.7986	−	12.7986i	0.519479	−	0.519479i	−0.397935	−	0.917414i	$-0.630273\pi$
$607$	12.7986	−	12.7986i	0.519479	−	0.519479i	0.917414	+	0.397935i	$0.130273\pi$
$608$		0			0
$609$	−8.14824	+	0.554268i	−0.330183	+	0.0224601i
$610$		0			0
$611$	13.8060	−	13.8060i	0.558532	−	0.558532i
$612$		0			0
$613$	−8.91389			−0.360029			−0.180014	−	0.983664i	$-0.557614\pi$
$613$	−8.91389			−0.360029			−0.180014	+	0.983664i	$0.557614\pi$
$614$		0			0
$615$	33.8303	+	17.4459i	1.36417	+	0.703488i
$616$		0			0
$617$	−1.81921	+	1.81921i	−0.0732388	+	0.0732388i	−0.742777	−	0.669539i	$-0.766492\pi$
$617$	−1.81921	+	1.81921i	−0.0732388	+	0.0732388i	0.669539	+	0.742777i	$0.266492\pi$
$618$		0			0
$619$	0.786785	+	0.786785i	0.0316236	+	0.0316236i	0.722742	−	0.691118i	$-0.242882\pi$
$619$	0.786785	+	0.786785i	0.0316236	+	0.0316236i	−0.691118	+	0.722742i	$0.742882\pi$
$620$		0			0
$621$	−17.2432	+	26.2247i	−0.691947	+	1.05236i
$622$		0			0
$623$	8.82935	−	8.82935i	0.353741	−	0.353741i
$624$		0			0
$625$	−14.2264	+	20.5575i	−0.569056	+	0.822298i
$626$		0			0
$627$	−0.572297	−	8.41329i	−0.0228554	−	0.335995i
$628$		0			0
$629$	−16.2479	+	16.2479i	−0.647848	+	0.647848i
$630$		0			0
$631$		−	39.2718i		−	1.56339i	−0.623663	−	0.781693i	$-0.714356\pi$
$631$		−	39.2718i		−	1.56339i	0.623663	−	0.781693i	$-0.285644\pi$
$632$		0			0
$633$	12.0571	−	13.8171i	0.479225	−	0.549180i
$634$		0			0
$635$	3.05036	+	12.3919i	0.121050	+	0.491757i
$636$		0			0
$637$	11.1000			0.439797
$638$		0			0
$639$	−7.65589	+	1.04639i	−0.302862	+	0.0413947i
$640$		0			0
$641$		−	26.9846i		−	1.06583i	−0.846170	−	0.532914i	$-0.821097\pi$
$641$		−	26.9846i		−	1.06583i	0.846170	−	0.532914i	$-0.178903\pi$
$642$		0			0
$643$			18.7886i			0.740949i	0.928843	+	0.370474i	$0.120805\pi$
$643$			18.7886i			0.740949i	−0.928843	+	0.370474i	$0.879195\pi$
$644$		0			0
$645$	−2.80537	−	1.44670i	−0.110462	−	0.0569638i
$646$		0			0
$647$	4.74385	−	4.74385i	0.186500	−	0.186500i	−0.607681	−	0.794181i	$-0.707900\pi$
$647$	4.74385	−	4.74385i	0.186500	−	0.186500i	0.794181	+	0.607681i	$0.207900\pi$
$648$		0			0
$649$	−12.6301			−0.495776
$650$		0			0
$651$	−7.62512	+	8.73820i	−0.298852	+	0.342477i
$652$		0			0
$653$	−37.7676			−1.47796			−0.738981	−	0.673726i	$-0.764693\pi$
$653$	−37.7676			−1.47796			−0.738981	+	0.673726i	$0.764693\pi$
$654$		0			0
$655$	−9.42784	−	38.2999i	−0.368376	−	1.49650i
$656$		0			0
$657$	−18.9986	+	25.0142i	−0.741205	+	0.975896i
$658$		0			0
$659$	13.5538	+	13.5538i	0.527980	+	0.527980i	0.919970	−	0.391990i	$-0.128213\pi$
$659$	13.5538	+	13.5538i	0.527980	+	0.527980i	−0.391990	+	0.919970i	$0.628213\pi$
$660$		0			0
$661$	−16.9462	+	16.9462i	−0.659132	+	0.659132i	−0.955175	−	0.296043i	$-0.904333\pi$
$661$	−16.9462	+	16.9462i	−0.659132	+	0.659132i	0.296043	+	0.955175i	$0.404333\pi$
$662$		0			0
$663$	5.72837	+	4.99869i	0.222472	+	0.194133i
$664$		0			0
$665$	4.96766	−	8.21192i	0.192638	−	0.318445i
$666$		0			0
$667$			22.0601i			0.854169i
$668$		0			0
$669$	−24.0745	+	27.5888i	−0.930773	+	1.06664i
$670$		0			0
$671$			20.4456i			0.789294i
$672$		0			0
$673$	26.0839	+	26.0839i	1.00546	+	1.00546i	0.999985	+	0.00547515i	$0.00174280\pi$
$673$	26.0839	+	26.0839i	1.00546	+	1.00546i	0.00547515	+	0.999985i	$0.498257\pi$
$674$		0			0
$675$	20.0957	−	16.4670i	0.773485	−	0.633814i
$676$		0			0
$677$	6.41910			0.246706			0.123353	−	0.992363i	$-0.460635\pi$
$677$	6.41910			0.246706			0.123353	+	0.992363i	$0.460635\pi$
$678$		0			0
$679$	12.0230			0.461399
$680$		0			0
$681$	8.85653	−	0.602448i	0.339383	−	0.0230858i
$682$		0			0
$683$		−	14.6529i		−	0.560679i	−0.959901	−	0.280340i	$-0.909553\pi$
$683$		−	14.6529i		−	0.560679i	0.959901	−	0.280340i	$-0.0904471\pi$
$684$		0			0
$685$	−2.03196	−	8.25468i	−0.0776371	−	0.315395i
$686$		0			0
$687$	−3.00129	+	3.43940i	−0.114506	+	0.131221i
$688$		0			0
$689$	−15.1109			−0.575679
$690$		0			0
$691$	−28.3072	−	28.3072i	−1.07686	−	1.07686i	−0.996789	−	0.0800692i	$-0.974486\pi$
$691$	−28.3072	−	28.3072i	−1.07686	−	1.07686i	−0.0800692	−	0.996789i	$-0.525514\pi$
$692$		0			0
$693$	0.768125	+	5.61994i	0.0291786	+	0.213484i
$694$		0			0
$695$	−12.7179	+	3.13060i	−0.482416	+	0.118751i
$696$		0			0
$697$	14.6562	+	14.6562i	0.555141	+	0.555141i
$698$		0			0
$699$	8.83603	−	10.1259i	0.334209	−	0.382996i
$700$		0			0
$701$	23.7655	−	23.7655i	0.897612	−	0.897612i	−0.0976124	−	0.995225i	$-0.531121\pi$
$701$	23.7655	−	23.7655i	0.897612	−	0.897612i	0.995225	+	0.0976124i	$0.0311205\pi$
$702$		0			0
$703$	25.6128	+	25.6128i	0.966004	+	0.966004i
$704$		0			0
$705$	−11.0584	−	34.6083i	−0.416485	−	1.30342i
$706$		0			0
$707$			8.89166i			0.334405i
$708$		0			0
$709$	−5.81334	−	5.81334i	−0.218325	−	0.218325i	0.589468	−	0.807792i	$-0.299338\pi$
$709$	−5.81334	−	5.81334i	−0.218325	−	0.218325i	−0.807792	+	0.589468i	$0.799338\pi$
$710$		0			0
$711$	3.47318	+	25.4114i	0.130255	+	0.953000i
$712$		0			0
$713$	22.1505	+	22.1505i	0.829544	+	0.829544i
$714$		0			0
$715$	−1.62909	−	6.61804i	−0.0609243	−	0.247501i
$716$		0			0
$717$	−1.11112	−	16.3345i	−0.0414956	−	0.610023i
$718$		0			0
$719$	−2.88200			−0.107480			−0.0537402	−	0.998555i	$-0.517114\pi$
$719$	−2.88200			−0.107480			−0.0537402	+	0.998555i	$0.517114\pi$
$720$		0			0
$721$	8.05862			0.300119
$722$		0			0
$723$	−1.21697	−	17.8905i	−0.0452595	−	0.665356i
$724$		0			0
$725$	5.44324	−	17.4310i	0.202157	−	0.647370i
$726$		0			0
$727$	24.4474	+	24.4474i	0.906704	+	0.906704i	0.996005	−	0.0893004i	$-0.0284631\pi$
$727$	24.4474	+	24.4474i	0.906704	+	0.906704i	−0.0893004	+	0.996005i	$0.528463\pi$
$728$		0			0
$729$	−24.7890	+	10.7008i	−0.918110	+	0.396325i
$730$		0			0
$731$	−1.21536	−	1.21536i	−0.0449517	−	0.0449517i
$732$		0			0
$733$			17.2734i			0.638007i	0.947754	+	0.319003i	$0.103348\pi$
$733$			17.2734i			0.638007i	−0.947754	+	0.319003i	$0.896652\pi$
$734$		0			0
$735$	9.46698	−	18.3579i	0.349195	−	0.677142i
$736$		0			0
$737$	−11.1878	−	11.1878i	−0.412107	−	0.412107i
$738$		0			0
$739$	7.62856	−	7.62856i	0.280621	−	0.280621i	−0.552736	−	0.833357i	$-0.686416\pi$
$739$	7.62856	−	7.62856i	0.280621	−	0.280621i	0.833357	+	0.552736i	$0.186416\pi$
$740$		0			0
$741$	7.87978	−	9.03003i	0.289471	−	0.331727i
$742$		0			0
$743$	−21.3182	−	21.3182i	−0.782090	−	0.782090i	0.198093	−	0.980183i	$-0.436525\pi$
$743$	−21.3182	−	21.3182i	−0.782090	−	0.782090i	−0.980183	+	0.198093i	$0.936525\pi$
$744$		0			0
$745$	−2.47565	−	10.0571i	−0.0907008	−	0.368465i
$746$		0			0
$747$	−34.3712	+	4.69780i	−1.25758	+	0.171884i
$748$		0			0
$749$	−8.00558	−	8.00558i	−0.292518	−	0.292518i
$750$		0			0
$751$	26.1007			0.952430			0.476215	−	0.879329i	$-0.342008\pi$
$751$	26.1007			0.952430			0.476215	+	0.879329i	$0.342008\pi$
$752$		0			0
$753$	−29.8752	+	34.2363i	−1.08871	+	1.24764i
$754$		0			0
$755$	−21.8304	−	13.2059i	−0.794489	−	0.480612i
$756$		0			0
$757$			42.5694i			1.54721i	0.633668	+	0.773605i	$0.281548\pi$
$757$			42.5694i			1.54721i	−0.633668	+	0.773605i	$0.718452\pi$
$758$		0			0
$759$	15.2858	−	1.03979i	0.554840	−	0.0377419i
$760$		0			0
$761$	−51.8643			−1.88008			−0.940040	−	0.341065i	$-0.889212\pi$
$761$	−51.8643			−1.88008			−0.940040	+	0.341065i	$0.889212\pi$
$762$		0			0
$763$	−10.6390			−0.385158
$764$		0			0
$765$	13.1528	−	5.21069i	0.475541	−	0.188393i
$766$		0			0
$767$	−12.6926	−	12.6926i	−0.458304	−	0.458304i
$768$		0			0
$769$			4.33991i			0.156501i	0.996934	+	0.0782506i	$0.0249334\pi$
$769$			4.33991i			0.156501i	−0.996934	+	0.0782506i	$0.975067\pi$
$770$		0			0
$771$	8.58210	−	9.83487i	0.309077	−	0.354194i
$772$		0			0
$773$		−	39.7001i		−	1.42791i	−0.700190	−	0.713957i	$-0.746901\pi$
$773$		−	39.7001i		−	1.42791i	0.700190	−	0.713957i	$-0.253099\pi$
$774$		0			0
$775$	−12.0369	−	22.9680i	−0.432378	−	0.825035i
$776$		0			0
$777$	−18.3577	−	16.0192i	−0.658577	−	0.574687i
$778$		0			0
$779$	23.1035	−	23.1035i	0.827769	−	0.827769i
$780$		0			0
$781$	2.66722	+	2.66722i	0.0954407	+	0.0954407i
$782$		0			0
$783$	−10.4262	+	15.8568i	−0.372601	+	0.566677i
$784$		0			0
$785$	−3.94621	+	6.52339i	−0.140846	+	0.232830i
$786$		0			0
$787$	5.30056			0.188945			0.0944723	−	0.995527i	$-0.469884\pi$
$787$	5.30056			0.188945			0.0944723	+	0.995527i	$0.469884\pi$
$788$		0			0
$789$	−11.0243	+	12.6336i	−0.392475	+	0.449767i
$790$		0			0
$791$	12.1931			0.433538
$792$		0			0
$793$	−20.5467	+	20.5467i	−0.729636	+	0.729636i
$794$		0			0
$795$	−12.8878	+	24.9915i	−0.457084	+	0.886356i
$796$		0			0
$797$			17.4862i			0.619394i	0.950835	+	0.309697i	$0.100228\pi$
$797$			17.4862i			0.619394i	−0.950835	+	0.309697i	$0.899772\pi$
$798$		0			0
$799$		−	19.7840i		−	0.699908i
$800$		0			0
$801$	−3.92914	−	28.7473i	−0.138829	−	1.01574i
$802$		0			0
$803$	15.3335			0.541108
$804$		0			0
$805$	14.9200	+	9.02557i	0.525859	+	0.318110i
$806$		0			0
$807$	−0.0944426	+	0.108229i	−0.00332454	+	0.00380984i
$808$		0			0
$809$		−	37.4327i		−	1.31606i	−0.752991	−	0.658031i	$-0.771389\pi$
$809$		−	37.4327i		−	1.31606i	0.752991	−	0.658031i	$-0.228611\pi$
$810$		0			0
$811$	−7.78970	+	7.78970i	−0.273533	+	0.273533i	−0.830521	−	0.556987i	$-0.811957\pi$
$811$	−7.78970	+	7.78970i	−0.273533	+	0.273533i	0.556987	+	0.830521i	$0.311957\pi$
$812$		0			0
$813$	1.73419	+	25.4942i	0.0608206	+	0.894119i
$814$		0			0
$815$	9.02447	+	5.45920i	0.316113	+	0.191227i
$816$		0			0
$817$	−1.91586	+	1.91586i	−0.0670274	+	0.0670274i
$818$		0			0
$819$	−4.87582	+	6.41966i	−0.170375	+	0.224321i
$820$		0			0
$821$	−12.3460	−	12.3460i	−0.430879	−	0.430879i	0.458049	−	0.888927i	$-0.348549\pi$
$821$	−12.3460	−	12.3460i	−0.430879	−	0.430879i	−0.888927	+	0.458049i	$0.848549\pi$
$822$		0			0
$823$	10.6014	−	10.6014i	0.369542	−	0.369542i	−0.497768	−	0.867310i	$-0.665847\pi$
$823$	10.6014	−	10.6014i	0.369542	−	0.369542i	0.867310	+	0.497768i	$0.165847\pi$
$824$		0			0
$825$	−12.3348	−	2.95012i	−0.429443	−	0.102710i
$826$		0			0
$827$	−18.5764			−0.645966			−0.322983	−	0.946405i	$-0.604686\pi$
$827$	−18.5764			−0.645966			−0.322983	+	0.946405i	$0.604686\pi$
$828$		0			0
$829$	−14.7854	+	14.7854i	−0.513517	+	0.513517i	−0.915602	−	0.402085i	$-0.868286\pi$
$829$	−14.7854	+	14.7854i	−0.513517	+	0.513517i	0.402085	+	0.915602i	$0.368286\pi$
$830$		0			0
$831$	−21.0892	+	1.43455i	−0.731575	+	0.0497640i
$832$		0			0
$833$	7.95312	−	7.95312i	0.275559	−	0.275559i
$834$		0			0
$835$	−11.1772	−	45.4067i	−0.386804	−	1.57137i
$836$		0			0
$837$	5.45293	+	26.3908i	0.188481	+	0.912200i
$838$		0			0
$839$		−	33.8653i		−	1.16916i	−0.811336	−	0.584580i	$-0.801259\pi$
$839$		−	33.8653i		−	1.16916i	0.811336	−	0.584580i	$-0.198741\pi$
$840$		0			0
$841$		−	15.6613i		−	0.540045i
$842$		0			0
$843$	−0.256956	−	3.77749i	−0.00885004	−	0.130104i
$844$		0			0
$845$	−10.0323	+	16.5842i	−0.345121	+	0.570512i
$846$		0			0
$847$	−8.08423	+	8.08423i	−0.277777	+	0.277777i
$848$		0			0
$849$	−1.27224	−	18.7031i	−0.0436632	−	0.641889i
$850$		0			0
$851$	−46.5350	+	46.5350i	−1.59520	+	1.59520i
$852$		0			0
$853$	27.4595			0.940194			0.470097	−	0.882615i	$-0.344219\pi$
$853$	27.4595			0.940194			0.470097	+	0.882615i	$0.344219\pi$
$854$		0			0
$855$	−8.21397	−	20.7337i	−0.280912	−	0.709077i
$856$		0			0
$857$	−17.7906	+	17.7906i	−0.607715	+	0.607715i	−0.942348	−	0.334634i	$-0.891387\pi$
$857$	−17.7906	+	17.7906i	−0.607715	+	0.607715i	0.334634	+	0.942348i	$0.391387\pi$
$858$		0			0
$859$	−4.90738	−	4.90738i	−0.167438	−	0.167438i	0.618414	−	0.785852i	$-0.287775\pi$
$859$	−4.90738	−	4.90738i	−0.167438	−	0.167438i	−0.785852	+	0.618414i	$0.787775\pi$
$860$		0			0
$861$	−14.4499	+	16.5592i	−0.492450	+	0.564335i
$862$		0			0
$863$	−4.91101	+	4.91101i	−0.167173	+	0.167173i	−0.785735	−	0.618563i	$-0.787715\pi$
$863$	−4.91101	+	4.91101i	−0.167173	+	0.167173i	0.618563	+	0.785735i	$0.287715\pi$
$864$		0			0
$865$	23.9409	−	39.5762i	0.814016	−	1.34563i
$866$		0			0
$867$	−21.6911	+	1.47549i	−0.736667	+	0.0501103i
$868$		0			0
$869$	8.85302	−	8.85302i	0.300318	−	0.300318i
$870$		0			0
$871$		−	22.4862i		−	0.761916i
$872$		0			0
$873$	16.8975	−	22.2478i	0.571894	−	0.752975i
$874$		0			0
$875$	−9.56212	−	10.8131i	−0.323259	−	0.365549i
$876$		0			0
$877$	20.1399			0.680076			0.340038	−	0.940412i	$-0.389560\pi$
$877$	20.1399			0.680076			0.340038	+	0.940412i	$0.389560\pi$
$878$		0			0
$879$	−22.4830	+	1.52936i	−0.758331	+	0.0515840i
$880$		0			0
$881$			36.5232i			1.23050i	0.788333	+	0.615249i	$0.210944\pi$
$881$			36.5232i			1.23050i	−0.788333	+	0.615249i	$0.789056\pi$
$882$		0			0
$883$			28.7937i			0.968985i	0.874795	+	0.484493i	$0.160996\pi$
$883$			28.7937i			0.968985i	−0.874795	+	0.484493i	$0.839004\pi$
$884$		0			0
$885$	−31.8173	+	10.1666i	−1.06953	+	0.341747i
$886$		0			0
$887$	−28.4788	+	28.4788i	−0.956224	+	0.956224i	−0.999081	−	0.0428570i	$-0.986354\pi$
$887$	−28.4788	+	28.4788i	−0.956224	+	0.956224i	0.0428570	+	0.999081i	$0.486354\pi$
$888$		0			0
$889$	−7.36844			−0.247130
$890$		0			0
$891$	11.4789	+	6.47709i	0.384559	+	0.216991i
$892$		0			0
$893$	−31.1869			−1.04363
$894$		0			0
$895$	46.0783	−	11.3425i	1.54023	−	0.379139i
$896$		0			0
$897$	16.4064	+	14.3165i	0.547792	+	0.478014i
$898$		0			0
$899$	13.3934	+	13.3934i	0.446695	+	0.446695i
$900$		0			0
$901$	−10.8269	+	10.8269i	−0.360698	+	0.360698i
$902$		0			0
$903$	1.19825	−	1.37317i	0.0398754	−	0.0456962i
$904$		0			0
$905$	1.87629	+	7.62227i	0.0623698	+	0.253373i
$906$		0			0
$907$			21.8599i			0.725846i	0.931819	+	0.362923i	$0.118221\pi$
$907$			21.8599i			0.725846i	−0.931819	+	0.362923i	$0.881779\pi$
$908$		0			0
$909$	16.4535	+	12.4966i	0.545728	+	0.414488i
$910$		0			0
$911$			26.5894i			0.880945i	0.897766	+	0.440473i	$0.145189\pi$
$911$			26.5894i			0.880945i	−0.897766	+	0.440473i	$0.854811\pi$
$912$		0			0
$913$	11.9745	+	11.9745i	0.396299	+	0.396299i
$914$		0			0
$915$	16.4577	+	51.5056i	0.544073	+	1.70272i
$916$		0			0
$917$	22.7738			0.752059
$918$		0			0
$919$	−46.8512			−1.54548			−0.772739	−	0.634723i	$-0.781114\pi$
$919$	−46.8512			−1.54548			−0.772739	+	0.634723i	$0.781114\pi$
$920$		0			0
$921$	−4.03537	−	59.3237i	−0.132970	−	1.95478i
$922$		0			0
$923$			5.36083i			0.176454i
$924$		0			0
$925$	48.2524	−	25.2877i	1.58653	−	0.831455i
$926$		0			0
$927$	11.3259	−	14.9120i	0.371990	−	0.489775i
$928$		0			0
$929$	20.5659			0.674747			0.337373	−	0.941371i	$-0.390462\pi$
$929$	20.5659			0.674747			0.337373	+	0.941371i	$0.390462\pi$
$930$		0			0
$931$	−12.5371	−	12.5371i	−0.410885	−	0.410885i
$932$		0			0
$933$	−2.31710	−	34.0635i	−0.0758585	−	1.11519i
$934$		0			0
$935$	−5.90906	−	3.57458i	−0.193247	−	0.116901i
$936$		0			0
$937$	−34.0136	−	34.0136i	−1.11118	−	1.11118i	−0.992992	−	0.118184i	$-0.962293\pi$
$937$	−34.0136	−	34.0136i	−1.11118	−	1.11118i	−0.118184	−	0.992992i	$-0.537707\pi$
$938$		0			0
$939$	16.2902	+	14.2151i	0.531610	+	0.463893i
$940$		0			0
$941$	−12.2462	+	12.2462i	−0.399216	+	0.399216i	−0.877956	−	0.478741i	$-0.841093\pi$
$941$	−12.2462	+	12.2462i	−0.399216	+	0.399216i	0.478741	+	0.877956i	$0.341093\pi$
$942$		0			0
$943$	41.9760	+	41.9760i	1.36693	+	1.36693i
$944$		0			0
$945$	6.45879	+	13.5392i	0.210104	+	0.440430i
$946$		0			0
$947$		−	47.5663i		−	1.54570i	−0.634592	−	0.772848i	$-0.718832\pi$
$947$		−	47.5663i		−	1.54570i	0.634592	−	0.772848i	$-0.281168\pi$
$948$		0			0
$949$	15.4094	+	15.4094i	0.500209	+	0.500209i
$950$		0			0
$951$	−48.3124	+	3.28635i	−1.56664	+	0.106567i
$952$		0			0
$953$	−22.3066	−	22.3066i	−0.722582	−	0.722582i	0.246548	−	0.969131i	$-0.420704\pi$
$953$	−22.3066	−	22.3066i	−0.722582	−	0.722582i	−0.969131	+	0.246548i	$0.920704\pi$
$954$		0			0
$955$	−27.9647	−	16.9167i	−0.904916	−	0.547413i
$956$		0			0
$957$	9.24263	−	0.628711i	0.298772	−	0.0203233i
$958$		0			0
$959$	4.90839			0.158500
$960$		0			0
$961$	−4.10336			−0.132366
$962$		0			0
$963$	−26.0652	+	3.56255i	−0.839939	+	0.114802i
$964$		0			0
$965$	15.5625	−	3.83083i	0.500974	−	0.123319i
$966$		0			0
$967$	−9.83196	−	9.83196i	−0.316175	−	0.316175i	0.531121	−	0.847296i	$-0.321771\pi$
$967$	−9.83196	−	9.83196i	−0.316175	−	0.316175i	−0.847296	+	0.531121i	$0.821771\pi$
$968$		0			0
$969$	−0.824157	−	12.1159i	−0.0264757	−	0.389218i
$970$		0			0
$971$	−27.1430	−	27.1430i	−0.871059	−	0.871059i	0.121529	−	0.992588i	$-0.461220\pi$
$971$	−27.1430	−	27.1430i	−0.871059	−	0.871059i	−0.992588	+	0.121529i	$0.961220\pi$
$972$		0			0
$973$		−	7.56227i		−	0.242435i
$974$		0			0
$975$	−9.43110	−	15.3605i	−0.302037	−	0.491931i
$976$		0			0
$977$	27.0368	+	27.0368i	0.864984	+	0.864984i	0.991912	−	0.126928i	$-0.0405116\pi$
$977$	27.0368	+	27.0368i	0.864984	+	0.864984i	−0.126928	+	0.991912i	$0.540512\pi$
$978$		0			0
$979$	−10.0152	+	10.0152i	−0.320088	+	0.320088i
$980$		0			0
$981$	−14.9524	+	19.6869i	−0.477394	+	0.628553i
$982$		0			0
$983$	−15.4408	−	15.4408i	−0.492484	−	0.492484i	0.416604	−	0.909088i	$-0.363220\pi$
$983$	−15.4408	−	15.4408i	−0.492484	−	0.492484i	−0.909088	+	0.416604i	$0.863220\pi$
$984$		0			0
$985$	5.47559	−	9.05158i	0.174467	−	0.288407i
$986$		0			0
$987$	20.9292	−	1.42367i	0.666184	−	0.0453158i
$988$		0			0
$989$	−3.48086	−	3.48086i	−0.110685	−	0.110685i
$990$		0			0
$991$	9.30144			0.295470			0.147735	−	0.989027i	$-0.452802\pi$
$991$	9.30144			0.295470			0.147735	+	0.989027i	$0.452802\pi$
$992$		0			0
$993$	−21.7680	−	18.9952i	−0.690787	−	0.602794i
$994$		0			0
$995$	−8.80919	+	14.5623i	−0.279270	+	0.461655i
$996$		0			0
$997$			14.4349i			0.457158i	0.973525	+	0.228579i	$0.0734080\pi$
$997$			14.4349i			0.457158i	−0.973525	+	0.228579i	$0.926592\pi$
$998$		0			0
$999$	−55.4432	+	11.4558i	−1.75414	+	0.362446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.bb.a.593.21		88
3.2	odd	2	inner	960.2.bb.a.593.24		88
4.3	odd	2		240.2.bb.a.173.8	✓	88
5.2	odd	4		960.2.bf.a.17.4		88
12.11	even	2		240.2.bb.a.173.37	yes	88
15.2	even	4		960.2.bf.a.17.3		88
16.5	even	4		960.2.bf.a.113.4		88
16.11	odd	4		240.2.bf.a.53.30	yes	88
20.7	even	4		240.2.bf.a.77.15	yes	88
48.5	odd	4		960.2.bf.a.113.3		88
48.11	even	4		240.2.bf.a.53.15	yes	88
60.47	odd	4		240.2.bf.a.77.30	yes	88
80.27	even	4		240.2.bb.a.197.37	yes	88
80.37	odd	4	inner	960.2.bb.a.497.24		88
240.107	odd	4		240.2.bb.a.197.8	yes	88
240.197	even	4	inner	960.2.bb.a.497.21		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bb.a.173.8	✓	88	4.3	odd	2
240.2.bb.a.173.37	yes	88	12.11	even	2
240.2.bb.a.197.8	yes	88	240.107	odd	4
240.2.bb.a.197.37	yes	88	80.27	even	4
240.2.bf.a.53.15	yes	88	48.11	even	4
240.2.bf.a.53.30	yes	88	16.11	odd	4
240.2.bf.a.77.15	yes	88	20.7	even	4
240.2.bf.a.77.30	yes	88	60.47	odd	4
960.2.bb.a.497.21		88	240.197	even	4	inner
960.2.bb.a.497.24		88	80.37	odd	4	inner
960.2.bb.a.593.21		88	1.1	even	1	trivial
960.2.bb.a.593.24		88	3.2	odd	2	inner
960.2.bf.a.17.3		88	15.2	even	4
960.2.bf.a.17.4		88	5.2	odd	4
960.2.bf.a.113.3		88	48.5	odd	4
960.2.bf.a.113.4		88	16.5	even	4

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.bb (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.117548 - 1.72806i) q^{3} +(-1.15738 + 1.91324i) q^{5} +(-0.912923 - 0.912923i) q^{7} +(-2.97237 + 0.406258i) q^{9} +(1.03554 + 1.03554i) q^{11} +2.08132i q^{13} +(3.44223 + 1.77512i) q^{15} +(1.49126 + 1.49126i) q^{17} +(2.35078 - 2.35078i) q^{19} +(-1.47027 + 1.68489i) q^{21} +(4.27105 + 4.27105i) q^{23} +(-2.32095 - 4.42868i) q^{25} +(1.05143 + 5.08866i) q^{27} +(2.58251 + 2.58251i) q^{29} +5.18620 q^{31} +(1.66774 - 1.91119i) q^{33} +(2.80323 - 0.690039i) q^{35} +10.8954i q^{37} +(3.59664 - 0.244654i) q^{39} +9.82802 q^{41} -0.814988 q^{43} +(2.66289 - 6.15703i) q^{45} +(-6.63331 - 6.63331i) q^{47} -5.33314i q^{49} +(2.40169 - 2.75228i) q^{51} +7.26025i q^{53} +(-3.17974 + 0.782718i) q^{55} +(-4.33861 - 3.78596i) q^{57} +(-6.09835 + 6.09835i) q^{59} +(9.87198 + 9.87198i) q^{61} +(3.08442 + 2.34266i) q^{63} +(-3.98205 - 2.40887i) q^{65} -10.8038 q^{67} +(6.87857 - 7.88268i) q^{69} +2.57569 q^{71} +(7.40366 - 7.40366i) q^{73} +(-7.38019 + 4.53131i) q^{75} -1.89073i q^{77} -8.54920i q^{79} +(8.66991 - 2.41509i) q^{81} +11.5636 q^{83} +(-4.57909 + 1.12718i) q^{85} +(4.15916 - 4.76629i) q^{87} +9.67152i q^{89} +(1.90008 - 1.90008i) q^{91} +(-0.609625 - 8.96205i) q^{93} +(1.77685 + 7.21834i) q^{95} +(-6.58488 + 6.58488i) q^{97} +(-3.49869 - 2.65730i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{15} + 8 q^{19} - 4 q^{21} + 16 q^{31} - 4 q^{33} - 24 q^{39} + 40 q^{43} + 8 q^{45} + 4 q^{51} + 12 q^{57} - 24 q^{61} + 32 q^{63} + 8 q^{67} - 12 q^{69} + 24 q^{75} - 8 q^{81} - 24 q^{85} + 12 q^{87}+ \cdots + 32 q^{99}+O(q^{100}) \) 88 * q + 4 * q^15 + 8 * q^19 - 4 * q^21 + 16 * q^31 - 4 * q^33 - 24 * q^39 + 40 * q^43 + 8 * q^45 + 4 * q^51 + 12 * q^57 - 24 * q^61 + 32 * q^63 + 8 * q^67 - 12 * q^69 + 24 * q^75 - 8 * q^81 - 24 * q^85 + 12 * q^87 + 8 * q^91 - 8 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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