LMFDB - Embedded newform 315.2.ce.a.53.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(53,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 8]))

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

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

chi := DirichletCharacter("315.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.ce (of order $12$, degree $4$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			53.11
Character	$\chi$	$=$	315.53
Dual form			315.2.ce.a.107.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.271660 - 1.01385i) q^{2} +(0.777962 + 0.449157i) q^{4} +(-0.310035 + 2.21447i) q^{5} +(-1.26800 + 2.32211i) q^{7} +(2.15109 - 2.15109i) q^{8} +O(q^{10})$	\(q+(0.271660 - 1.01385i) q^{2} +(0.777962 + 0.449157i) q^{4} +(-0.310035 + 2.21447i) q^{5} +(-1.26800 + 2.32211i) q^{7} +(2.15109 - 2.15109i) q^{8} +(2.16091 + 0.915911i) q^{10} +(-1.52584 - 0.880947i) q^{11} +(4.98616 + 4.98616i) q^{13} +(2.00980 + 1.91638i) q^{14} +(-0.698204 - 1.20932i) q^{16} +(0.458916 - 0.122966i) q^{17} +(2.33452 - 1.34783i) q^{19} +(-1.23584 + 1.58352i) q^{20} +(-1.30766 + 1.30766i) q^{22} +(-6.30772 - 1.69015i) q^{23} +(-4.80776 - 1.37313i) q^{25} +(6.40974 - 3.70067i) q^{26} +(-2.02944 + 1.23698i) q^{28} +7.01357 q^{29} +(3.95306 - 6.84689i) q^{31} +(4.46115 - 1.19536i) q^{32} -0.498676i q^{34} +(-4.74912 - 3.52788i) q^{35} +(-6.45801 - 1.73042i) q^{37} +(-0.732304 - 2.73300i) q^{38} +(4.09662 + 5.43045i) q^{40} -6.20839i q^{41} +(-2.28209 - 2.28209i) q^{43} +(-0.791366 - 1.37069i) q^{44} +(-3.42711 + 5.93593i) q^{46} +(-0.393943 + 1.47022i) q^{47} +(-3.78437 - 5.88885i) q^{49} +(-2.69822 + 4.50131i) q^{50} +(1.63948 + 6.11861i) q^{52} +(2.26472 + 8.45204i) q^{53} +(2.42390 - 3.10581i) q^{55} +(2.26749 + 7.72265i) q^{56} +(1.90530 - 7.11069i) q^{58} +(-6.17967 + 10.7035i) q^{59} +(-2.26113 - 3.91639i) q^{61} +(-5.86782 - 5.86782i) q^{62} -7.64048i q^{64} +(-12.5876 + 9.49581i) q^{65} +(-0.530569 - 1.98011i) q^{67} +(0.412250 + 0.110462i) q^{68} +(-4.86687 + 3.85650i) q^{70} -9.79937i q^{71} +(-1.45962 + 0.391103i) q^{73} +(-3.50876 + 6.07735i) q^{74} +2.42155 q^{76} +(3.98042 - 2.42614i) q^{77} +(9.08059 - 5.24268i) q^{79} +(2.89448 - 1.17122i) q^{80} +(-6.29436 - 1.68657i) q^{82} +(-2.07156 + 2.07156i) q^{83} +(0.130025 + 1.05438i) q^{85} +(-2.93365 + 1.69374i) q^{86} +(-5.17723 + 1.38724i) q^{88} +(1.64959 + 2.85718i) q^{89} +(-17.9008 + 5.25597i) q^{91} +(-4.14803 - 4.14803i) q^{92} +(1.38356 + 0.798797i) q^{94} +(2.26095 + 5.58759i) q^{95} +(3.21237 - 3.21237i) q^{97} +(-6.99846 + 2.23701i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{7}+O(q^{10}) $ 64 * q + 8 * q^7	$ 64 q + 8 q^{7} + 8 q^{10} + 32 q^{16} - 48 q^{22} - 16 q^{25} + 88 q^{28} + 32 q^{31} - 16 q^{37} - 40 q^{40} - 16 q^{43} - 80 q^{52} - 32 q^{55} - 88 q^{58} + 48 q^{61} - 32 q^{67} - 112 q^{70} - 88 q^{73} - 320 q^{76} - 56 q^{82} + 16 q^{85} + 120 q^{88} - 128 q^{91} + 208 q^{97}+O(q^{100}) $ 64 * q + 8 * q^7 + 8 * q^10 + 32 * q^16 - 48 * q^22 - 16 * q^25 + 88 * q^28 + 32 * q^31 - 16 * q^37 - 40 * q^40 - 16 * q^43 - 80 * q^52 - 32 * q^55 - 88 * q^58 + 48 * q^61 - 32 * q^67 - 112 * q^70 - 88 * q^73 - 320 * q^76 - 56 * q^82 + 16 * q^85 + 120 * q^88 - 128 * q^91 + 208 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	0.271660	−	1.01385i	0.192092	−	0.716899i	−0.800908	−	0.598788i	$-0.795649\pi$
$2$	0.271660	−	1.01385i	0.192092	−	0.716899i	0.993000	−	0.118111i	$-0.0376840\pi$
$3$		0			0
$3$		0			0
$4$	0.777962	+	0.449157i	0.388981	+	0.224578i
$5$	−0.310035	+	2.21447i	−0.138652	+	0.990341i
$5$	−0.310035	+	2.21447i	−0.138652	+	0.990341i
$6$		0			0
$7$	−1.26800	+	2.32211i	−0.479258	+	0.877674i
$7$	−1.26800	+	2.32211i	−0.479258	+	0.877674i
$8$	2.15109	−	2.15109i	0.760527	−	0.760527i
$9$		0			0
$10$	2.16091	+	0.915911i	0.683340	+	0.289636i
$11$	−1.52584	−	0.880947i	−0.460059	−	0.265615i	0.252010	−	0.967725i	$-0.418908\pi$
$11$	−1.52584	−	0.880947i	−0.460059	−	0.265615i	−0.712069	+	0.702109i	$0.752242\pi$
$12$		0			0
$13$	4.98616	+	4.98616i	1.38291	+	1.38291i	0.839406	+	0.543506i	$0.182903\pi$
$13$	4.98616	+	4.98616i	1.38291	+	1.38291i	0.543506	+	0.839406i	$0.317097\pi$
$14$	2.00980	+	1.91638i	0.537142	+	0.512174i
$15$		0			0
$16$	−0.698204	−	1.20932i	−0.174551	−	0.302331i
$17$	0.458916	−	0.122966i	0.111303	−	0.0298237i	−0.202737	−	0.979233i	$-0.564984\pi$
$17$	0.458916	−	0.122966i	0.111303	−	0.0298237i	0.314041	+	0.949409i	$0.398317\pi$
$18$		0			0
$19$	2.33452	−	1.34783i	0.535575	−	0.309214i	−0.207709	−	0.978191i	$-0.566601\pi$
$19$	2.33452	−	1.34783i	0.535575	−	0.309214i	0.743284	+	0.668977i	$0.233267\pi$
$20$	−1.23584	+	1.58352i	−0.276342	+	0.354086i
$21$		0			0
$22$	−1.30766	+	1.30766i	−0.278793	+	0.278793i
$23$	−6.30772	−	1.69015i	−1.31525	−	0.352420i	−0.468054	−	0.883700i	$-0.655045\pi$
$23$	−6.30772	−	1.69015i	−1.31525	−	0.352420i	−0.847197	+	0.531279i	$0.821711\pi$
$24$		0			0
$25$	−4.80776	−	1.37313i	−0.961551	−	0.274625i
$26$	6.40974	−	3.70067i	1.25705	−	0.725761i
$27$		0			0
$28$	−2.02944	+	1.23698i	−0.383529	+	0.233768i
$29$	7.01357			1.30239			0.651193	−	0.758912i	$-0.274269\pi$
$29$	7.01357			1.30239			0.651193	+	0.758912i	$0.274269\pi$
$30$		0			0
$31$	3.95306	−	6.84689i	0.709990	−	1.22974i	−0.254871	−	0.966975i	$-0.582033\pi$
$31$	3.95306	−	6.84689i	0.709990	−	1.22974i	0.964860	−	0.262763i	$-0.0846338\pi$
$32$	4.46115	−	1.19536i	0.788628	−	0.211312i
$33$		0			0
$34$		−	0.498676i		−	0.0855222i
$35$	−4.74912	−	3.52788i	−0.802747	−	0.596320i
$36$		0			0
$37$	−6.45801	−	1.73042i	−1.06169	−	0.284479i	−0.314615	−	0.949219i	$-0.601875\pi$
$37$	−6.45801	−	1.73042i	−1.06169	−	0.284479i	−0.747074	+	0.664740i	$0.768542\pi$
$38$	−0.732304	−	2.73300i	−0.118795	−	0.443351i
$39$		0			0
$40$	4.09662	+	5.43045i	0.647732	+	0.858629i
$41$		−	6.20839i		−	0.969588i	−0.874628	−	0.484794i	$-0.838895\pi$
$41$		−	6.20839i		−	0.969588i	0.874628	−	0.484794i	$-0.161105\pi$
$42$		0			0
$43$	−2.28209	−	2.28209i	−0.348016	−	0.348016i	0.511354	−	0.859370i	$-0.329144\pi$
$43$	−2.28209	−	2.28209i	−0.348016	−	0.348016i	−0.859370	+	0.511354i	$0.829144\pi$
$44$	−0.791366	−	1.37069i	−0.119303	−	0.206639i
$45$		0			0
$46$	−3.42711	+	5.93593i	−0.505299	+	0.875204i
$47$	−0.393943	+	1.47022i	−0.0574625	+	0.214453i	−0.988687	−	0.149993i	$-0.952075\pi$
$47$	−0.393943	+	1.47022i	−0.0574625	+	0.214453i	0.931225	+	0.364446i	$0.118742\pi$
$48$		0			0
$49$	−3.78437	−	5.88885i	−0.540624	−	0.841264i
$50$	−2.69822	+	4.50131i	−0.381585	+	0.636582i
$51$		0			0
$52$	1.63948	+	6.11861i	0.227354	+	0.848498i
$53$	2.26472	+	8.45204i	0.311083	+	1.16098i	0.927581	+	0.373621i	$0.121884\pi$
$53$	2.26472	+	8.45204i	0.311083	+	1.16098i	−0.616499	+	0.787356i	$0.711449\pi$
$54$		0			0
$55$	2.42390	−	3.10581i	0.326838	−	0.418788i
$56$	2.26749	+	7.72265i	0.303006	+	1.03198i
$57$		0			0
$58$	1.90530	−	7.11069i	0.250179	−	0.933680i
$59$	−6.17967	+	10.7035i	−0.804525	+	1.39348i	0.112086	+	0.993698i	$0.464247\pi$
$59$	−6.17967	+	10.7035i	−0.804525	+	1.39348i	−0.916611	+	0.399780i	$0.869087\pi$
$60$		0			0
$61$	−2.26113	−	3.91639i	−0.289508	−	0.501442i	0.684185	−	0.729309i	$-0.260158\pi$
$61$	−2.26113	−	3.91639i	−0.289508	−	0.501442i	−0.973692	+	0.227867i	$0.926825\pi$
$62$	−5.86782	−	5.86782i	−0.745214	−	0.745214i
$63$		0			0
$64$		−	7.64048i		−	0.955060i
$65$	−12.5876	+	9.49581i	−1.56130	+	1.17781i
$66$		0			0
$67$	−0.530569	−	1.98011i	−0.0648193	−	0.241909i	0.925913	−	0.377736i	$-0.123297\pi$
$67$	−0.530569	−	1.98011i	−0.0648193	−	0.241909i	−0.990733	+	0.135827i	$0.956631\pi$
$68$	0.412250	+	0.110462i	0.0499927	+	0.0133955i
$69$		0			0
$70$	−4.86687	+	3.85650i	−0.581703	+	0.460940i
$71$		−	9.79937i		−	1.16297i	−0.813557	−	0.581486i	$-0.802472\pi$
$71$		−	9.79937i		−	1.16297i	0.813557	−	0.581486i	$-0.197528\pi$
$72$		0			0
$73$	−1.45962	+	0.391103i	−0.170835	+	0.0457751i	−0.343223	−	0.939254i	$-0.611519\pi$
$73$	−1.45962	+	0.391103i	−0.170835	+	0.0457751i	0.172388	+	0.985029i	$0.444852\pi$
$74$	−3.50876	+	6.07735i	−0.407885	+	0.706478i
$75$		0			0
$76$	2.42155			0.277771
$77$	3.98042	−	2.42614i	0.453611	−	0.276484i
$78$		0			0
$79$	9.08059	−	5.24268i	1.02165	−	0.589848i	0.107066	−	0.994252i	$-0.465855\pi$
$79$	9.08059	−	5.24268i	1.02165	−	0.589848i	0.914580	+	0.404404i	$0.132521\pi$
$80$	2.89448	−	1.17122i	0.323613	−	0.130946i
$81$		0			0
$82$	−6.29436	−	1.68657i	−0.695096	−	0.186250i
$83$	−2.07156	+	2.07156i	−0.227384	+	0.227384i	−0.811599	−	0.584215i	$-0.801402\pi$
$83$	−2.07156	+	2.07156i	−0.227384	+	0.227384i	0.584215	+	0.811599i	$0.301402\pi$
$84$		0			0
$85$	0.130025	+	1.05438i	0.0141032	+	0.114364i
$86$	−2.93365	+	1.69374i	−0.316343	+	0.182641i
$87$		0			0
$88$	−5.17723	+	1.38724i	−0.551895	+	0.147880i
$89$	1.64959	+	2.85718i	0.174856	+	0.302860i	0.940112	−	0.340867i	$-0.110721\pi$
$89$	1.64959	+	2.85718i	0.174856	+	0.302860i	−0.765255	+	0.643727i	$0.777387\pi$
$90$		0			0
$91$	−17.9008	+	5.25597i	−1.87652	+	0.550975i
$92$	−4.14803	−	4.14803i	−0.432462	−	0.432462i
$93$		0			0
$94$	1.38356	+	0.798797i	0.142703	+	0.0823896i
$95$	2.26095	+	5.58759i	0.231969	+	0.573275i
$96$		0			0
$97$	3.21237	−	3.21237i	0.326167	−	0.326167i	−0.524960	−	0.851127i	$-0.675920\pi$
$97$	3.21237	−	3.21237i	0.326167	−	0.326167i	0.851127	+	0.524960i	$0.175920\pi$
$98$	−6.99846	+	2.23701i	−0.706951	+	0.225972i
$99$		0			0
$100$	−3.12350	−	3.22768i	−0.312350	−	0.322768i
$101$	−0.992660	−	0.573113i	−0.0987734	−	0.0570268i	0.449800	−	0.893129i	$-0.351495\pi$
$101$	−0.992660	−	0.573113i	−0.0987734	−	0.0570268i	−0.548573	+	0.836103i	$0.684829\pi$
$102$		0			0
$103$	−2.74470	+	10.2434i	−0.270444	+	1.00931i	0.688390	+	0.725341i	$0.258318\pi$
$103$	−2.74470	+	10.2434i	−0.270444	+	1.00931i	−0.958834	+	0.283968i	$0.908349\pi$
$104$	21.4514			2.10348
$105$		0			0
$106$	9.18432			0.892060
$107$	2.55850	−	9.54845i	0.247340	−	0.923084i	−0.724854	−	0.688903i	$-0.758093\pi$
$107$	2.55850	−	9.54845i	0.247340	−	0.923084i	0.972193	−	0.234181i	$-0.0752407\pi$
$108$		0			0
$109$	4.52490	+	2.61245i	0.433407	+	0.250228i	0.700797	−	0.713361i	$-0.252828\pi$
$109$	4.52490	+	2.61245i	0.433407	+	0.250228i	−0.267390	+	0.963588i	$0.586161\pi$
$110$	−2.49035	−	3.30119i	−0.237445	−	0.314756i
$111$		0			0
$112$	3.69350	−	0.0878855i	0.349003	−	0.00830440i
$113$	−2.48328	+	2.48328i	−0.233608	+	0.233608i	−0.814197	−	0.580589i	$-0.802822\pi$
$113$	−2.48328	+	2.48328i	−0.233608	+	0.233608i	0.580589	+	0.814197i	$0.302822\pi$
$114$		0			0
$115$	5.69840	−	13.4443i	0.531378	−	1.25368i
$116$	5.45629	+	3.15019i	0.506604	+	0.292488i
$117$		0			0
$118$	9.17296	+	9.17296i	0.844440	+	0.844440i
$119$	−0.296363	+	1.22157i	−0.0271676	+	0.111981i
$120$		0			0
$121$	−3.94787	−	6.83790i	−0.358897	−	0.621628i
$122$	−4.58488	+	1.22852i	−0.415096	+	0.111225i
$123$		0			0
$124$	6.15065	−	3.55108i	0.552345	−	0.318897i
$125$	4.53132	−	10.2209i	0.405294	−	0.914187i
$126$		0			0
$127$	2.62423	−	2.62423i	0.232863	−	0.232863i	−0.581024	−	0.813887i	$-0.697348\pi$
$127$	2.62423	−	2.62423i	0.232863	−	0.232863i	0.813887	+	0.581024i	$0.197348\pi$
$128$	1.17602	+	0.315114i	0.103947	+	0.0278524i
$129$		0			0
$130$	6.20777	+	15.3415i	0.544458	+	1.34554i
$131$	−6.74520	+	3.89434i	−0.589331	+	0.340250i	−0.764833	−	0.644229i	$-0.777178\pi$
$131$	−6.74520	+	3.89434i	−0.589331	+	0.340250i	0.175502	+	0.984479i	$0.443845\pi$
$132$		0			0
$133$	0.169657	+	7.13004i	0.0147111	+	0.618253i
$134$	−2.15166			−0.185875
$135$		0			0
$136$	0.722660	−	1.25168i	0.0619675	−	0.107331i
$137$	2.28661	−	0.612694i	0.195358	−	0.0523460i	−0.159813	−	0.987147i	$-0.551089\pi$
$137$	2.28661	−	0.612694i	0.195358	−	0.0523460i	0.355171	+	0.934801i	$0.384423\pi$
$138$		0			0
$139$			0.386213i			0.0327582i	0.999866	+	0.0163791i	$0.00521386\pi$
$139$			0.386213i			0.0327582i	−0.999866	+	0.0163791i	$0.994786\pi$
$140$	−2.11006	−	4.87765i	−0.178333	−	0.412237i
$141$		0			0
$142$	−9.93507	−	2.66209i	−0.833733	−	0.223398i
$143$	−3.21556	−	12.0006i	−0.268899	−	1.00354i
$144$		0			0
$145$	−2.17445	+	15.5313i	−0.180578	+	1.28981i
$146$			1.58608i			0.131265i
$147$		0			0
$148$	−4.24685	−	4.24685i	−0.349089	−	0.349089i
$149$	0.149777	+	0.259421i	0.0122702	+	0.0212526i	0.872095	−	0.489336i	$-0.162761\pi$
$149$	0.149777	+	0.259421i	0.0122702	+	0.0212526i	−0.859825	+	0.510589i	$0.829428\pi$
$150$		0			0
$151$	−1.42265	+	2.46410i	−0.115773	+	0.200525i	−0.918089	−	0.396375i	$-0.870268\pi$
$151$	−1.42265	+	2.46410i	−0.115773	+	0.200525i	0.802315	+	0.596900i	$0.203601\pi$
$152$	2.12245	−	7.92108i	0.172153	−	0.642484i
$153$		0			0
$154$	−1.37842	−	4.69462i	−0.111076	−	0.378304i
$155$	13.9367	+	10.8767i	1.11942	+	0.873638i
$156$		0			0
$157$	−1.21853	−	4.54760i	−0.0972490	−	0.362938i	0.900102	−	0.435680i	$-0.143492\pi$
$157$	−1.21853	−	4.54760i	−0.0972490	−	0.362938i	−0.997351	+	0.0727413i	$0.976825\pi$
$158$	−2.84845	−	10.6306i	−0.226611	−	0.845722i
$159$		0			0
$160$	1.26398	+	10.2497i	0.0999264	+	0.810310i
$161$	11.9229	−	12.5041i	0.939654	−	0.985462i
$162$		0			0
$163$	5.40524	−	20.1726i	0.423371	−	1.58004i	−0.344084	−	0.938939i	$-0.611811\pi$
$163$	5.40524	−	20.1726i	0.423371	−	1.58004i	0.767455	−	0.641103i	$-0.221523\pi$
$164$	2.78854	−	4.82989i	0.217748	−	0.377151i
$165$		0			0
$166$	1.53749	+	2.66301i	0.119332	+	0.206690i
$167$	1.95679	+	1.95679i	0.151421	+	0.151421i	0.778752	−	0.627332i	$-0.215853\pi$
$167$	1.95679	+	1.95679i	0.151421	+	0.151421i	−0.627332	+	0.778752i	$0.715853\pi$
$168$		0			0
$169$			36.7235i			2.82489i
$170$	1.10430	+	0.154607i	0.0846962	+	0.0118578i
$171$		0			0
$172$	−0.750364	−	2.80040i	−0.0572147	−	0.213528i
$173$	16.4931	+	4.41932i	1.25395	+	0.335994i	0.823860	−	0.566793i	$-0.191816\pi$
$173$	16.4931	+	4.41932i	1.25395	+	0.335994i	0.430088	+	0.902787i	$0.358483\pi$
$174$		0			0
$175$	9.28477	−	9.42301i	0.701862	−	0.712313i
$176$			2.46032i			0.185454i
$177$		0			0
$178$	3.34487	−	0.896256i	0.250709	−	0.0671772i
$179$	11.3823	−	19.7148i	0.850756	−	1.47355i	−0.0297713	−	0.999557i	$-0.509478\pi$
$179$	11.3823	−	19.7148i	0.850756	−	1.47355i	0.880527	−	0.473996i	$-0.157189\pi$
$180$		0			0
$181$	13.8864			1.03217			0.516085	−	0.856537i	$-0.327389\pi$
$181$	13.8864			1.03217			0.516085	+	0.856537i	$0.327389\pi$
$182$	0.465817	+	19.5765i	0.0345286	+	1.45111i
$183$		0			0
$184$	−17.2042	+	9.93283i	−1.26831	+	0.732258i
$185$	5.83417	−	13.7646i	0.428936	−	1.01199i
$186$		0			0
$187$	−0.808561	−	0.216653i	−0.0591278	−	0.0158433i
$188$	−0.966830	+	0.966830i	−0.0705133	+	0.0705133i
$189$		0			0
$190$	6.27918	−	0.774341i	0.455539	−	0.0561766i
$191$	−7.42891	+	4.28908i	−0.537537	+	0.310347i	−0.744080	−	0.668090i	$-0.767112\pi$
$191$	−7.42891	+	4.28908i	−0.537537	+	0.310347i	0.206543	+	0.978437i	$0.433779\pi$
$192$		0			0
$193$	−9.17387	+	2.45813i	−0.660350	+	0.176940i	−0.573404	−	0.819273i	$-0.694377\pi$
$193$	−9.17387	+	2.45813i	−0.660350	+	0.176940i	−0.0869458	+	0.996213i	$0.527711\pi$
$194$	−2.38418	−	4.12953i	−0.171174	−	0.296483i
$195$		0			0
$196$	−0.299081	−	6.28107i	−0.0213629	−	0.448648i
$197$	−8.44537	−	8.44537i	−0.601708	−	0.601708i	0.339058	−	0.940765i	$-0.389892\pi$
$197$	−8.44537	−	8.44537i	−0.601708	−	0.601708i	−0.940765	+	0.339058i	$0.889892\pi$
$198$		0			0
$199$	2.01459	+	1.16312i	0.142811	+	0.0824517i	0.569703	−	0.821851i	$-0.307058\pi$
$199$	2.01459	+	1.16312i	0.142811	+	0.0824517i	−0.426892	+	0.904302i	$0.640392\pi$
$200$	−13.2957	+	7.38821i	−0.940145	+	0.522425i
$201$		0			0
$202$	−0.850715	+	0.850715i	−0.0598561	+	0.0598561i
$203$	−8.89318	+	16.2863i	−0.624179	+	1.14307i
$204$		0			0
$205$	13.7483	+	1.92482i	0.960223	+	0.134435i
$206$	9.63959	+	5.56542i	0.671622	+	0.387761i
$207$		0			0
$208$	2.54853	−	9.51123i	0.176709	−	0.659485i
$209$	−4.74948			−0.328528
$210$		0			0
$211$	−11.0268			−0.759119			−0.379560	−	0.925167i	$-0.623924\pi$
$211$	−11.0268			−0.759119			−0.379560	+	0.925167i	$0.623924\pi$
$212$	−2.03443	+	7.59258i	−0.139725	+	0.521460i
$213$		0			0
$214$	−8.98564	−	5.18786i	−0.614246	−	0.354635i
$215$	5.76116	−	4.34610i	0.392908	−	0.296401i
$216$		0			0
$217$	10.8868	+	17.8613i	0.739042	+	1.21250i
$218$	3.87786	−	3.87786i	0.262642	−	0.262642i
$219$		0			0
$220$	3.28069	−	1.32750i	0.221184	−	0.0894997i
$221$	2.90136	+	1.67510i	0.195166	+	0.112679i
$222$		0			0
$223$	−3.85605	−	3.85605i	−0.258220	−	0.258220i	0.566110	−	0.824330i	$-0.308448\pi$
$223$	−3.85605	−	3.85605i	−0.258220	−	0.258220i	−0.824330	+	0.566110i	$0.808448\pi$
$224$	−2.88097	+	11.8750i	−0.192493	+	0.793431i
$225$		0			0
$226$	1.84306	+	3.19228i	0.122599	+	0.212347i
$227$	−5.58057	+	1.49531i	−0.370395	+	0.0992471i	−0.439215	−	0.898382i	$-0.644743\pi$
$227$	−5.58057	+	1.49531i	−0.370395	+	0.0992471i	0.0688197	+	0.997629i	$0.478077\pi$
$228$		0			0
$229$	4.43105	−	2.55827i	0.292812	−	0.169055i	−0.346397	−	0.938088i	$-0.612595\pi$
$229$	4.43105	−	2.55827i	0.292812	−	0.169055i	0.639209	+	0.769033i	$0.279262\pi$
$230$	−12.0824	−	9.42957i	−0.796690	−	0.621768i
$231$		0			0
$232$	15.0868	−	15.0868i	0.990500	−	0.990500i
$233$	13.4616	+	3.60703i	0.881900	+	0.236304i	0.671227	−	0.741252i	$-0.265768\pi$
$233$	13.4616	+	3.60703i	0.881900	+	0.236304i	0.210673	+	0.977556i	$0.432434\pi$
$234$		0			0
$235$	−3.13361	−	1.32819i	−0.204414	−	0.0866418i
$236$	−9.61510	+	5.55128i	−0.625890	+	0.361358i
$237$		0			0
$238$	1.15798	+	0.632319i	0.0750607	+	0.0409872i
$239$	−13.6605			−0.883622			−0.441811	−	0.897108i	$-0.645664\pi$
$239$	−13.6605			−0.883622			−0.441811	+	0.897108i	$0.645664\pi$
$240$		0			0
$241$	−12.7159	+	22.0246i	−0.819105	+	1.41873i	0.0872381	+	0.996187i	$0.472196\pi$
$241$	−12.7159	+	22.0246i	−0.819105	+	1.41873i	−0.906343	+	0.422543i	$0.861137\pi$
$242$	−8.00507	+	2.14495i	−0.514585	+	0.137883i
$243$		0			0
$244$		−	4.06240i		−	0.260069i
$245$	14.2140	−	6.55463i	0.908097	−	0.418760i
$246$		0			0
$247$	18.3608	+	4.91975i	1.16827	+	0.313036i
$248$	−6.22492	−	23.2317i	−0.395283	−	1.47521i
$249$		0			0
$250$	−9.13148	−	7.37068i	−0.577525	−	0.466163i
$251$		−	5.24589i		−	0.331118i	−0.986200	−	0.165559i	$-0.947057\pi$
$251$		−	5.24589i		−	0.331118i	0.986200	−	0.165559i	$-0.0529428\pi$
$252$		0			0
$253$	8.13567	+	8.13567i	0.511485	+	0.511485i
$254$	−1.94768	−	3.37347i	−0.122208	−	0.211671i
$255$		0			0
$256$	8.27943	−	14.3404i	0.517465	−	0.896275i
$257$	−6.49879	+	24.2538i	−0.405383	+	1.51291i	0.397964	+	0.917401i	$0.369717\pi$
$257$	−6.49879	+	24.2538i	−0.405383	+	1.51291i	−0.803348	+	0.595510i	$0.796950\pi$
$258$		0			0
$259$	12.2069	−	12.8020i	0.758503	−	0.795479i
$260$	−14.0578	+	1.73359i	−0.871826	+	0.107513i
$261$		0			0
$262$	2.11587	+	7.89655i	0.130719	+	0.487850i
$263$	3.65342	+	13.6347i	0.225279	+	0.840754i	0.982292	+	0.187354i	$0.0599912\pi$
$263$	3.65342	+	13.6347i	0.225279	+	0.840754i	−0.757013	+	0.653400i	$0.773342\pi$
$264$		0			0
$265$	−19.4189	+	2.39472i	−1.19290	+	0.147107i
$266$	7.27487	+	1.76494i	0.446051	+	0.108215i
$267$		0			0
$268$	0.476617	−	1.77876i	0.0291140	−	0.108655i
$269$	−12.0006	+	20.7857i	−0.731690	+	1.26732i	0.224470	+	0.974481i	$0.427935\pi$
$269$	−12.0006	+	20.7857i	−0.731690	+	1.26732i	−0.956160	+	0.292844i	$0.905398\pi$
$270$		0			0
$271$	−1.45514	−	2.52038i	−0.0883935	−	0.153102i	0.818439	−	0.574594i	$-0.194840\pi$
$271$	−1.45514	−	2.52038i	−0.0883935	−	0.153102i	−0.906832	+	0.421492i	$0.861507\pi$
$272$	−0.469123	−	0.469123i	−0.0284447	−	0.0284447i
$273$		0			0
$274$		−	2.48472i		−	0.150107i
$275$	6.12624	+	6.33056i	0.369426	+	0.381747i
$276$		0			0
$277$	−3.43387	−	12.8154i	−0.206321	−	0.770002i	−0.989043	−	0.147630i	$-0.952836\pi$
$277$	−3.43387	−	12.8154i	−0.206321	−	0.770002i	0.782721	−	0.622372i	$-0.213831\pi$
$278$	0.391562	+	0.104919i	0.0234843	+	0.00629260i
$279$		0			0
$280$	−17.8046	+	2.62700i	−1.06403	+	0.156993i
$281$			14.8454i			0.885605i	0.896619	+	0.442803i	$0.146016\pi$
$281$			14.8454i			0.885605i	−0.896619	+	0.442803i	$0.853984\pi$
$282$		0			0
$283$	−27.0490	+	7.24775i	−1.60789	+	0.430834i	−0.947414	−	0.320010i	$-0.896314\pi$
$283$	−27.0490	+	7.24775i	−1.60789	+	0.430834i	−0.660480	+	0.750844i	$0.729647\pi$
$284$	4.40145	−	7.62354i	0.261178	−	0.452374i
$285$		0			0
$286$	−13.0404			−0.771093
$287$	14.4166	+	7.87222i	0.850982	+	0.464682i
$288$		0			0
$289$	−14.5269	+	8.38714i	−0.854526	+	0.493361i
$290$	15.1557	+	6.42380i	0.889974	+	0.377219i
$291$		0			0
$292$	−1.31119	−	0.351333i	−0.0767317	−	0.0205602i
$293$	−18.9121	+	18.9121i	−1.10486	+	1.10486i	−0.111040	+	0.993816i	$0.535418\pi$
$293$	−18.9121	+	18.9121i	−1.10486	+	1.10486i	−0.993816	+	0.111040i	$0.964582\pi$
$294$		0			0
$295$	−21.7867	−	17.0032i	−1.26847	−	0.989963i
$296$	−17.6141	+	10.1695i	−1.02380	+	0.591089i
$297$		0			0
$298$	0.303701	−	0.0813765i	0.0175929	−	0.00471401i
$299$	−23.0239	−	39.8786i	−1.33151	−	2.30624i
$300$		0			0
$301$	8.19295	−	2.40558i	0.472234	−	0.138655i
$302$	2.11174	+	2.11174i	0.121517	+	0.121517i
$303$		0			0
$304$	−3.25994	−	1.88212i	−0.186970	−	0.107947i
$305$	9.37375	−	3.79298i	0.536740	−	0.217186i
$306$		0			0
$307$	12.1826	−	12.1826i	0.695299	−	0.695299i	−0.268094	−	0.963393i	$-0.586394\pi$
$307$	12.1826	−	12.1826i	0.695299	−	0.695299i	0.963393	+	0.268094i	$0.0863938\pi$
$308$	4.18633	−	0.0996121i	0.238538	−	0.00567593i
$309$		0			0
$310$	14.8134	−	11.1749i	0.841342	−	0.634691i
$311$	3.94363	+	2.27686i	0.223623	+	0.129109i	0.607627	−	0.794223i	$-0.292122\pi$
$311$	3.94363	+	2.27686i	0.223623	+	0.129109i	−0.384004	+	0.923332i	$0.625455\pi$
$312$		0			0
$313$	−0.206986	+	0.772482i	−0.0116995	+	0.0436632i	−0.971529	−	0.236921i	$-0.923862\pi$
$313$	−0.206986	+	0.772482i	−0.0116995	+	0.0436632i	0.959829	+	0.280585i	$0.0905283\pi$
$314$	−4.94160			−0.278871
$315$		0			0
$316$	9.41914			0.529868
$317$	7.22831	−	26.9764i	0.405982	−	1.51515i	−0.396255	−	0.918141i	$-0.629690\pi$
$317$	7.22831	−	26.9764i	0.405982	−	1.51515i	0.802237	−	0.597006i	$-0.203643\pi$
$318$		0			0
$319$	−10.7016	−	6.17858i	−0.599175	−	0.345934i
$320$	16.9196	+	2.36882i	0.945835	+	0.132421i
$321$		0			0
$322$	−9.43830	−	15.4848i	−0.525976	−	0.862937i
$323$	0.905608	−	0.905608i	0.0503894	−	0.0503894i
$324$		0			0
$325$	−17.1256	−	30.8189i	−0.949958	−	1.70952i
$326$	−18.9836	−	10.9602i	−1.05140	−	0.607028i
$327$		0			0
$328$	−13.3548	−	13.3548i	−0.737397	−	0.737397i
$329$	−2.91448	−	2.77901i	−0.160681	−	0.153212i
$330$		0			0
$331$	14.5790	+	25.2515i	0.801333	+	1.38795i	0.918739	+	0.394866i	$0.129209\pi$
$331$	14.5790	+	25.2515i	0.801333	+	1.38795i	−0.117406	+	0.993084i	$0.537458\pi$
$332$	−2.54206	+	0.681142i	−0.139513	+	0.0373825i
$333$		0			0
$334$	2.51547	−	1.45230i	0.137640	−	0.0794666i
$335$	4.54939	−	0.561025i	0.248560	−	0.0306521i
$336$		0			0
$337$	−16.3404	+	16.3404i	−0.890118	+	0.890118i	−0.994534	−	0.104416i	$-0.966703\pi$
$337$	−16.3404	+	16.3404i	−0.890118	+	0.890118i	0.104416	+	0.994534i	$0.466703\pi$
$338$	37.2321	+	9.97630i	2.02516	+	0.542639i
$339$		0			0
$340$	−0.372427	+	0.878669i	−0.0201977	+	0.0476525i
$341$	−12.0635	+	6.96486i	−0.653275	+	0.377169i
$342$		0			0
$343$	18.4731	−	1.32068i	0.997454	−	0.0713098i
$344$	−9.81799			−0.529351
$345$		0			0
$346$	8.96103	−	15.5210i	0.481748	−	0.834412i
$347$	6.89055	−	1.84632i	0.369904	−	0.0991155i	−0.0690781	−	0.997611i	$-0.522006\pi$
$347$	6.89055	−	1.84632i	0.369904	−	0.0991155i	0.438982	+	0.898496i	$0.355339\pi$
$348$		0			0
$349$		−	7.69466i		−	0.411885i	−0.978564	−	0.205943i	$-0.933974\pi$
$349$		−	7.69466i		−	0.411885i	0.978564	−	0.205943i	$-0.0660261\pi$
$350$	−7.03120	−	11.9732i	−0.375834	−	0.639994i
$351$		0			0
$352$	−7.86008	−	2.10610i	−0.418944	−	0.112256i
$353$	−5.96070	−	22.2456i	−0.317256	−	1.18401i	−0.921871	−	0.387497i	$-0.873340\pi$
$353$	−5.96070	−	22.2456i	−0.317256	−	1.18401i	0.604615	−	0.796518i	$-0.293327\pi$
$354$		0			0
$355$	21.7004	+	3.03815i	1.15174	+	0.161248i
$356$			2.96370i			0.157076i
$357$		0			0
$358$	−16.8957	−	16.8957i	−0.892964	−	0.892964i
$359$	−10.2039	−	17.6738i	−0.538544	−	0.932785i	−0.998983	−	0.0450939i	$-0.985641\pi$
$359$	−10.2039	−	17.6738i	−0.538544	−	0.932785i	0.460439	−	0.887691i	$-0.347692\pi$
$360$		0			0
$361$	−5.86669	+	10.1614i	−0.308773	+	0.534811i
$362$	3.77238	−	14.0787i	0.198272	−	0.739962i
$363$		0			0
$364$	−16.2869	−	3.95133i	−0.853666	−	0.207106i
$365$	−0.413554	−	3.35353i	−0.0216464	−	0.175532i
$366$		0			0
$367$	5.45535	+	20.3596i	0.284767	+	1.06276i	0.949009	+	0.315248i	$0.102088\pi$
$367$	5.45535	+	20.3596i	0.284767	+	1.06276i	−0.664242	+	0.747517i	$0.731246\pi$
$368$	2.36014	+	8.80815i	0.123031	+	0.459156i
$369$		0			0
$370$	−12.3703	−	9.65424i	−0.643100	−	0.501900i
$371$	−22.4982	−	5.45824i	−1.16805	−	0.283378i
$372$		0			0
$373$	−3.12909	+	11.6779i	−0.162018	+	0.604660i	0.836384	+	0.548145i	$0.184666\pi$
$373$	−3.12909	+	11.6779i	−0.162018	+	0.604660i	−0.998402	+	0.0565154i	$0.982001\pi$
$374$	−0.439307	+	0.760902i	−0.0227160	+	0.0393453i
$375$		0			0
$376$	2.31516	+	4.00998i	0.119395	+	0.206799i
$377$	34.9708	+	34.9708i	1.80109	+	1.80109i
$378$		0			0
$379$			18.8474i			0.968125i	0.875033	+	0.484063i	$0.160839\pi$
$379$			18.8474i			0.968125i	−0.875033	+	0.484063i	$0.839161\pi$
$380$	−0.750766	+	5.36246i	−0.0385135	+	0.275088i
$381$		0			0
$382$	2.33034	+	8.69695i	0.119231	+	0.444975i
$383$	3.27595	+	0.877789i	0.167393	+	0.0448529i	0.341542	−	0.939866i	$-0.389051\pi$
$383$	3.27595	+	0.877789i	0.167393	+	0.0448529i	−0.174149	+	0.984719i	$0.555717\pi$
$384$		0			0
$385$	4.13854	+	9.56671i	0.210920	+	0.487565i
$386$			9.96869i			0.507393i
$387$		0			0
$388$	3.94196	−	1.05624i	0.200123	−	0.0536227i
$389$	−13.3892	+	23.1907i	−0.678857	+	1.17581i	0.296469	+	0.955043i	$0.404191\pi$
$389$	−13.3892	+	23.1907i	−0.678857	+	1.17581i	−0.975325	+	0.220772i	$0.929142\pi$
$390$		0			0
$391$	−3.10254			−0.156902
$392$	−20.8080	−	4.52693i	−1.05096	−	0.228645i
$393$		0			0
$394$	−10.8566	+	6.26805i	−0.546947	+	0.315780i
$395$	8.79446	+	21.7341i	0.442497	+	1.09356i
$396$		0			0
$397$	−6.98100	−	1.87055i	−0.350366	−	0.0938803i	0.0793438	−	0.996847i	$-0.474718\pi$
$397$	−6.98100	−	1.87055i	−0.350366	−	0.0938803i	−0.429710	+	0.902967i	$0.641384\pi$
$398$	1.72651	−	1.72651i	0.0865424	−	0.0865424i
$399$		0			0
$400$	1.69624	+	6.77286i	0.0848119	+	0.338643i
$401$	18.1748	−	10.4932i	0.907604	−	0.524006i	0.0279447	−	0.999609i	$-0.491104\pi$
$401$	18.1748	−	10.4932i	0.907604	−	0.524006i	0.879660	+	0.475604i	$0.157770\pi$
$402$		0			0
$403$	53.8502	−	14.4291i	2.68247	−	0.718766i
$404$	−0.514834	−	0.891719i	−0.0256140	−	0.0443647i
$405$		0			0
$406$	14.0959	+	13.4407i	0.699567	+	0.667049i
$407$	8.32951	+	8.32951i	0.412878	+	0.412878i
$408$		0			0
$409$	5.03785	+	2.90860i	0.249105	+	0.143821i	0.619355	−	0.785111i	$-0.287394\pi$
$409$	5.03785	+	2.90860i	0.249105	+	0.143821i	−0.370249	+	0.928933i	$0.620728\pi$
$410$	5.68633	−	13.4158i	0.280828	−	0.662559i
$411$		0			0
$412$	−6.73615	+	6.73615i	−0.331866	+	0.331866i
$413$	−17.0189	−	27.9219i	−0.837445	−	1.37395i
$414$		0			0
$415$	−3.94516	−	5.22968i	−0.193660	−	0.256715i
$416$	28.2043	+	16.2837i	1.38283	+	0.798376i
$417$		0			0
$418$	−1.29024	+	4.81525i	−0.0631078	+	0.235522i
$419$	1.72404			0.0842249			0.0421125	−	0.999113i	$-0.486591\pi$
$419$	1.72404			0.0842249			0.0421125	+	0.999113i	$0.486591\pi$
$420$		0			0
$421$	27.7158			1.35079			0.675393	−	0.737458i	$-0.263974\pi$
$421$	27.7158			1.35079			0.675393	+	0.737458i	$0.263974\pi$
$422$	−2.99555	+	11.1795i	−0.145821	+	0.544212i
$423$		0			0
$424$	23.0528	+	13.3095i	1.11954	+	0.646367i
$425$	−2.37520	−	0.0389584i	−0.115214	−	0.00188976i
$426$		0			0
$427$	11.9614	−	0.284616i	0.578852	−	0.0137736i
$428$	6.27917	−	6.27917i	0.303515	−	0.303515i
$429$		0			0
$430$	−2.84121	−	7.02160i	−0.137015	−	0.338611i
$431$	−29.2945	−	16.9132i	−1.41107	−	0.814681i	−0.415580	−	0.909557i	$-0.636421\pi$
$431$	−29.2945	−	16.9132i	−1.41107	−	0.814681i	−0.995489	+	0.0948760i	$0.969755\pi$
$432$		0			0
$433$	1.44725	+	1.44725i	0.0695502	+	0.0695502i	0.741026	−	0.671476i	$-0.234339\pi$
$433$	1.44725	+	1.44725i	0.0695502	+	0.0695502i	−0.671476	+	0.741026i	$0.734339\pi$
$434$	21.0661	−	6.18534i	1.01121	−	0.296906i
$435$		0			0
$436$	2.34680	+	4.06478i	0.112391	+	0.194668i
$437$	−17.0035	+	4.55608i	−0.813388	+	0.217947i
$438$		0			0
$439$	−22.2721	+	12.8588i	−1.06299	+	0.613716i	−0.926257	−	0.376892i	$-0.876993\pi$
$439$	−22.2721	+	12.8588i	−1.06299	+	0.613716i	−0.136731	+	0.990608i	$0.543660\pi$
$440$	−1.46687	−	11.8949i	−0.0699302	−	0.567068i
$441$		0			0
$442$	2.48648	−	2.48648i	0.118270	−	0.118270i
$443$	30.3245	+	8.12542i	1.44076	+	0.386050i	0.892800	−	0.450454i	$-0.148738\pi$
$443$	30.3245	+	8.12542i	1.44076	+	0.386050i	0.547960	+	0.836504i	$0.315405\pi$
$444$		0			0
$445$	−6.83857	+	2.76715i	−0.324179	+	0.131175i
$446$	−4.95698	+	2.86191i	−0.234720	+	0.135516i
$447$		0			0
$448$	17.7420	+	9.68810i	0.838231	+	0.457720i
$449$	14.9435			0.705227			0.352613	−	0.935769i	$-0.385293\pi$
$449$	14.9435			0.705227			0.352613	+	0.935769i	$0.385293\pi$
$450$		0			0
$451$	−5.46926	+	9.47304i	−0.257537	+	0.446068i
$452$	−3.04728	+	0.816517i	−0.143332	+	0.0384057i
$453$		0			0
$454$			6.06406i			0.284601i
$455$	−6.08930	−	41.2704i	−0.285471	−	1.93478i
$456$		0			0
$457$	13.3837	+	3.58616i	0.626065	+	0.167754i	0.557884	−	0.829919i	$-0.311614\pi$
$457$	13.3837	+	3.58616i	0.626065	+	0.167754i	0.0681817	+	0.997673i	$0.478280\pi$
$458$	−1.38996	−	5.18739i	−0.0649484	−	0.242391i
$459$		0			0
$460$	10.4717	−	7.89965i	0.488246	−	0.368323i
$461$		−	22.9821i		−	1.07038i	−0.844731	−	0.535191i	$-0.820240\pi$
$461$		−	22.9821i		−	1.07038i	0.844731	−	0.535191i	$-0.179760\pi$
$462$		0			0
$463$	−3.83823	−	3.83823i	−0.178378	−	0.178378i	0.612271	−	0.790648i	$-0.290256\pi$
$463$	−3.83823	−	3.83823i	−0.178378	−	0.178378i	−0.790648	+	0.612271i	$0.790256\pi$
$464$	−4.89690	−	8.48168i	−0.227333	−	0.393752i
$465$		0			0
$466$	7.31396	−	12.6682i	0.338813	−	0.586841i
$467$	−7.67888	+	28.6580i	−0.355336	+	1.32613i	0.524725	+	0.851272i	$0.324168\pi$
$467$	−7.67888	+	28.6580i	−0.355336	+	1.32613i	−0.880061	+	0.474861i	$0.842498\pi$
$468$		0			0
$469$	5.27079	+	1.27873i	0.243382	+	0.0590464i
$470$	−2.19786	+	2.81619i	−0.101380	+	0.129901i
$471$		0			0
$472$	9.73120	+	36.3173i	0.447915	+	1.67164i
$473$	1.47172	+	5.49252i	0.0676696	+	0.252546i
$474$		0			0
$475$	−13.0745	+	3.27447i	−0.599901	+	0.150243i
$476$	−0.779237	+	0.817224i	−0.0357163	+	0.0374574i
$477$		0			0
$478$	−3.71100	+	13.8496i	−0.169737	+	0.633468i
$479$	−6.46249	+	11.1934i	−0.295278	+	0.511437i	−0.975050	−	0.221987i	$-0.928746\pi$
$479$	−6.46249	+	11.1934i	−0.295278	+	0.511437i	0.679771	+	0.733424i	$0.262079\pi$
$480$		0			0
$481$	−23.5725	−	40.8288i	−1.07481	−	1.86163i
$482$	18.8752	+	18.8752i	0.859743	+	0.859743i
$483$		0			0
$484$		−	7.09284i		−	0.322402i
$485$	6.11775	+	8.10965i	0.277793	+	0.368240i
$486$		0			0
$487$	−3.33114	−	12.4320i	−0.150949	−	0.563348i	−0.999418	−	0.0341038i	$-0.989142\pi$
$487$	−3.33114	−	12.4320i	−0.150949	−	0.563348i	0.848470	−	0.529244i	$-0.177524\pi$
$488$	−13.2884	−	3.56062i	−0.601538	−	0.161182i
$489$		0			0
$490$	−2.78403	−	16.1914i	−0.125770	−	0.731454i
$491$		−	4.28020i		−	0.193163i	−0.995325	−	0.0965813i	$-0.969209\pi$
$491$		−	4.28020i		−	0.193163i	0.995325	−	0.0965813i	$-0.0307908\pi$
$492$		0			0
$493$	3.21864	−	0.862431i	0.144960	−	0.0388420i
$494$	9.97576	−	17.2785i	0.448831	−	0.777398i
$495$		0			0
$496$	−11.0402			−0.495718
$497$	22.7552	+	12.4256i	1.02071	+	0.557363i
$498$		0			0
$499$	−20.5513	+	11.8653i	−0.920001	+	0.531163i	−0.883635	−	0.468176i	$-0.844911\pi$
$499$	−20.5513	+	11.8653i	−0.920001	+	0.531163i	−0.0363657	+	0.999339i	$0.511578\pi$
$500$	8.11599	−	5.91621i	0.362958	−	0.264581i
$501$		0			0
$502$	−5.31854	−	1.42510i	−0.237378	−	0.0636053i
$503$	−19.3902	+	19.3902i	−0.864565	+	0.864565i	−0.991864	−	0.127299i	$-0.959369\pi$
$503$	−19.3902	+	19.3902i	−0.864565	+	0.864565i	0.127299	+	0.991864i	$0.459369\pi$
$504$		0			0
$505$	1.57690	−	2.02053i	0.0701711	−	0.0899124i
$506$	10.4585	−	6.03820i	0.464936	−	0.268431i
$507$		0			0
$508$	3.22025	−	0.862862i	0.142875	−	0.0382833i
$509$	9.31969	+	16.1422i	0.413088	+	0.715489i	0.995226	−	0.0976008i	$-0.0311168\pi$
$509$	9.31969	+	16.1422i	0.413088	+	0.715489i	−0.582138	+	0.813090i	$0.697784\pi$
$510$		0			0
$511$	0.942605	−	3.88530i	0.0416984	−	0.171876i
$512$	−10.5680	−	10.5680i	−0.467043	−	0.467043i
$513$		0			0
$514$	22.8242	+	13.1776i	1.00673	+	0.581238i
$515$	−21.8327	−	9.25386i	−0.962063	−	0.407774i
$516$		0			0
$517$	1.89628	−	1.89628i	0.0833982	−	0.0833982i
$518$	−9.66317	−	15.8538i	−0.424575	−	0.696575i
$519$		0			0
$520$	−6.65068	+	47.5035i	−0.291652	+	2.08316i
$521$	4.84586	+	2.79776i	0.212301	+	0.122572i	0.602380	−	0.798209i	$-0.294219\pi$
$521$	4.84586	+	2.79776i	0.212301	+	0.122572i	−0.390079	+	0.920781i	$0.627552\pi$
$522$		0			0
$523$	3.13335	−	11.6938i	0.137012	−	0.511335i	−0.862970	−	0.505256i	$-0.831398\pi$
$523$	3.13335	−	11.6938i	0.137012	−	0.511335i	0.999982	−	0.00607937i	$-0.00193514\pi$
$524$	−6.99668			−0.305651
$525$		0			0
$526$	14.8160			0.646010
$527$	0.972184	−	3.62824i	0.0423490	−	0.158049i
$528$		0			0
$529$	17.0122	+	9.82197i	0.739659	+	0.427042i
$530$	−2.84746	+	20.3384i	−0.123686	+	0.883444i
$531$		0			0
$532$	−3.07052	+	5.62311i	−0.133124	+	0.243793i
$533$	30.9560	−	30.9560i	1.34085	−	1.34085i
$534$		0			0
$535$	20.3515	+	8.62608i	0.879874	+	0.372938i
$536$	−5.40070	−	3.11810i	−0.233275	−	0.134681i
$537$		0			0
$538$	17.8134	+	17.8134i	0.767991	+	0.767991i
$539$	0.586598	+	12.3193i	0.0252666	+	0.530630i
$540$		0			0
$541$	13.3293	+	23.0870i	0.573070	+	0.992586i	0.996248	+	0.0865397i	$0.0275809\pi$
$541$	13.3293	+	23.0870i	0.573070	+	0.992586i	−0.423179	+	0.906046i	$0.639086\pi$
$542$	−2.95058	+	0.790606i	−0.126738	+	0.0339594i
$543$		0			0
$544$	1.90031	−	1.09714i	0.0814749	−	0.0470396i
$545$	−7.18808	+	9.21030i	−0.307903	+	0.394526i
$546$		0			0
$547$	−14.2107	+	14.2107i	−0.607604	+	0.607604i	−0.942319	−	0.334715i	$-0.891360\pi$
$547$	−14.2107	+	14.2107i	−0.607604	+	0.607604i	0.334715	+	0.942319i	$0.391360\pi$
$548$	2.05409	+	0.550391i	0.0877463	+	0.0235116i
$549$		0			0
$550$	8.08247	−	4.49132i	0.344638	−	0.191510i
$551$	16.3733	−	9.45312i	0.697525	−	0.402716i
$552$		0			0
$553$	0.659915	+	27.7338i	0.0280625	+	1.17936i
$554$	−13.9257			−0.591646
$555$		0			0
$556$	−0.173470	+	0.300459i	−0.00735678	+	0.0127423i
$557$	6.83156	−	1.83051i	0.289463	−	0.0775613i	−0.111166	−	0.993802i	$-0.535458\pi$
$557$	6.83156	−	1.83051i	0.289463	−	0.0775613i	0.400628	+	0.916241i	$0.368792\pi$
$558$		0			0
$559$		−	22.7577i		−	0.962550i
$560$	−0.950495	+	8.20640i	−0.0401658	+	0.346784i
$561$		0			0
$562$	15.0510	+	4.03291i	0.634889	+	0.170118i
$563$	4.80399	+	17.9287i	0.202464	+	0.755606i	0.990208	+	0.139603i	$0.0445825\pi$
$563$	4.80399	+	17.9287i	0.202464	+	0.755606i	−0.787744	+	0.616003i	$0.788751\pi$
$564$		0			0
$565$	−4.72925	−	6.26906i	−0.198961	−	0.263741i
$566$			29.3925i			1.23546i
$567$		0			0
$568$	−21.0794	−	21.0794i	−0.884470	−	0.884470i
$569$	−11.1362	−	19.2885i	−0.466854	−	0.808615i	0.532429	−	0.846475i	$-0.321279\pi$
$569$	−11.1362	−	19.2885i	−0.466854	−	0.808615i	−0.999283	+	0.0378597i	$0.987946\pi$
$570$		0			0
$571$	15.3879	−	26.6526i	0.643962	−	1.11538i	−0.340578	−	0.940216i	$-0.610623\pi$
$571$	15.3879	−	26.6526i	0.643962	−	1.11538i	0.984540	−	0.175159i	$-0.0560440\pi$
$572$	2.88858	−	10.7803i	0.120778	−	0.450748i
$573$		0			0
$574$	11.8976	−	12.4776i	0.496597	−	0.520806i
$575$	28.0052	+	16.7871i	1.16790	+	0.700071i
$576$		0			0
$577$	−8.40573	−	31.3706i	−0.349935	−	1.30598i	−0.886740	−	0.462269i	$-0.847035\pi$
$577$	−8.40573	−	31.3706i	−0.349935	−	1.30598i	0.536804	−	0.843707i	$-0.319631\pi$
$578$	4.55690	+	17.0066i	0.189542	+	0.707380i
$579$		0			0
$580$	−8.66764	+	11.1061i	−0.359904	+	0.461157i
$581$	−2.18366	−	7.43713i	−0.0905935	−	0.308544i
$582$		0			0
$583$	3.99019	−	14.8916i	0.165257	−	0.616747i
$584$	−2.29847	+	3.98107i	−0.0951115	+	0.164738i
$585$		0			0
$586$	14.0363	+	24.3116i	0.579835	+	1.00430i
$587$	−31.6777	−	31.6777i	−1.30748	−	1.30748i	−0.923229	−	0.384250i	$-0.874460\pi$
$587$	−31.6777	−	31.6777i	−1.30748	−	1.30748i	−0.384250	−	0.923229i	$-0.625540\pi$
$588$		0			0
$589$		−	21.3122i		−	0.878156i
$590$	−23.1572	+	17.4693i	−0.953367	+	0.719200i
$591$		0			0
$592$	2.41637	+	9.01801i	0.0993121	+	0.370638i
$593$	8.31765	+	2.22871i	0.341565	+	0.0915221i	0.425524	−	0.904947i	$-0.360090\pi$
$593$	8.31765	+	2.22871i	0.341565	+	0.0915221i	−0.0839589	+	0.996469i	$0.526756\pi$
$594$		0			0
$595$	−2.61325	−	1.03502i	−0.107133	−	0.0424316i
$596$			0.269092i			0.0110225i
$597$		0			0
$598$	−46.6856	+	12.5094i	−1.90911	+	0.511546i
$599$	18.5292	−	32.0935i	0.757083	−	1.31131i	−0.187249	−	0.982312i	$-0.559957\pi$
$599$	18.5292	−	32.0935i	0.757083	−	1.31131i	0.944332	−	0.328993i	$-0.106709\pi$
$600$		0			0
$601$	−43.1404			−1.75973			−0.879866	−	0.475222i	$-0.842368\pi$
$601$	−43.1404			−1.75973			−0.879866	+	0.475222i	$0.842368\pi$
$602$	−0.213198	−	8.95991i	−0.00868928	−	0.365179i
$603$		0			0
$604$	−2.21353	+	1.27798i	−0.0900672	+	0.0520003i
$605$	16.3663	−	6.62244i	0.665385	−	0.269240i
$606$		0			0
$607$	−11.0226	−	2.95350i	−0.447394	−	0.119879i	0.0280858	−	0.999606i	$-0.491059\pi$
$607$	−11.0226	−	2.95350i	−0.447394	−	0.119879i	−0.475480	+	0.879727i	$0.657725\pi$
$608$	8.80348	−	8.80348i	0.357028	−	0.357028i
$609$		0			0
$610$	−1.29904	−	10.5340i	−0.0525964	−	0.426508i
$611$	−9.29499	+	5.36646i	−0.376035	+	0.217104i
$612$		0			0
$613$	−9.00403	+	2.41262i	−0.363669	+	0.0974449i	−0.436026	−	0.899934i	$-0.643615\pi$
$613$	−9.00403	+	2.41262i	−0.363669	+	0.0974449i	0.0723570	+	0.997379i	$0.476948\pi$
$614$	−9.04180	−	15.6608i	−0.364897	−	0.632020i
$615$		0			0
$616$	3.34340	−	13.7811i	0.134710	−	0.555257i
$617$	−19.0964	−	19.0964i	−0.768792	−	0.768792i	0.209102	−	0.977894i	$-0.432946\pi$
$617$	−19.0964	−	19.0964i	−0.768792	−	0.768792i	−0.977894	+	0.209102i	$0.932946\pi$
$618$		0			0
$619$	−27.3794	−	15.8075i	−1.10047	−	0.635357i	−0.164126	−	0.986439i	$-0.552480\pi$
$619$	−27.3794	−	15.8075i	−1.10047	−	0.635357i	−0.936345	+	0.351083i	$0.885814\pi$
$620$	5.95685	+	14.7214i	0.239233	+	0.591226i
$621$		0			0
$622$	3.37971	−	3.37971i	0.135514	−	0.135514i
$623$	−8.72635	+	0.207640i	−0.349614	+	0.00831893i
$624$		0			0
$625$	21.2290	+	13.2033i	0.849162	+	0.528133i
$626$	0.726949	+	0.419704i	0.0290547	+	0.0167748i
$627$		0			0
$628$	1.09462	−	4.08517i	0.0436800	−	0.163016i
$629$	−3.17646			−0.126654
$630$		0			0
$631$	−42.3073			−1.68423			−0.842114	−	0.539300i	$-0.818689\pi$
$631$	−42.3073			−1.68423			−0.842114	+	0.539300i	$0.818689\pi$
$632$	8.25570	−	30.8107i	0.328394	−	1.22558i
$633$		0			0
$634$	−25.3863	−	14.6568i	−1.00822	−	0.582096i
$635$	4.99768	+	6.62489i	0.198327	+	0.262901i
$636$		0			0
$637$	10.4933	−	48.2322i	0.415758	−	1.91103i
$638$	−9.17134	+	9.17134i	−0.363097	+	0.363097i
$639$		0			0
$640$	−1.06242	+	2.50657i	−0.0419958	+	0.0990809i
$641$	29.3871	+	16.9667i	1.16072	+	0.670143i	0.951477	−	0.307720i	$-0.0995660\pi$
$641$	29.3871	+	16.9667i	1.16072	+	0.670143i	0.209245	+	0.977863i	$0.432899\pi$
$642$		0			0
$643$	4.11153	+	4.11153i	0.162143	+	0.162143i	0.783515	−	0.621372i	$-0.213425\pi$
$643$	4.11153	+	4.11153i	0.162143	+	0.162143i	−0.621372	+	0.783515i	$0.713425\pi$
$644$	14.8918	−	4.37248i	0.586821	−	0.172300i
$645$		0			0
$646$	−0.672132	−	1.16417i	−0.0264447	−	0.0458035i
$647$	−26.0716	+	6.98587i	−1.02498	+	0.274643i	−0.731877	−	0.681437i	$-0.761355\pi$
$647$	−26.0716	+	6.98587i	−1.02498	+	0.274643i	−0.293105	+	0.956080i	$0.594689\pi$
$648$		0			0
$649$	18.8584	−	10.8879i	0.740259	−	0.427389i
$650$	−35.8980	+	8.99052i	−1.40803	+	0.352637i
$651$		0			0
$652$	13.2657	−	13.2657i	0.519526	−	0.519526i
$653$	−32.3816	−	8.67662i	−1.26719	−	0.339542i	−0.438236	−	0.898860i	$-0.644397\pi$
$653$	−32.3816	−	8.67662i	−1.26719	−	0.339542i	−0.828953	+	0.559318i	$0.811063\pi$
$654$		0			0
$655$	−6.53266	−	16.1444i	−0.255252	−	0.630815i
$656$	−7.50796	+	4.33472i	−0.293137	+	0.169242i
$657$		0			0
$658$	−3.60924	+	2.19990i	−0.140703	+	0.0857609i
$659$	27.0855			1.05510			0.527551	−	0.849523i	$-0.323110\pi$
$659$	27.0855			1.05510			0.527551	+	0.849523i	$0.323110\pi$
$660$		0			0
$661$	18.5720	−	32.1676i	0.722365	−	1.25117i	−0.237684	−	0.971343i	$-0.576388\pi$
$661$	18.5720	−	32.1676i	0.722365	−	1.25117i	0.960049	−	0.279831i	$-0.0902785\pi$
$662$	29.5617	−	7.92104i	1.14895	−	0.307860i
$663$		0			0
$664$			8.91226i			0.345863i
$665$	−15.8419	−	1.83486i	−0.614321	−	0.0711530i
$666$		0			0
$667$	−44.2396	−	11.8540i	−1.71297	−	0.458988i
$668$	0.643402	+	2.40121i	0.0248940	+	0.0929056i
$669$		0			0
$670$	0.667091	−	4.76480i	0.0257720	−	0.184080i
$671$			7.96773i			0.307591i
$672$		0			0
$673$	−9.99850	−	9.99850i	−0.385414	−	0.385414i	0.487634	−	0.873048i	$-0.337860\pi$
$673$	−9.99850	−	9.99850i	−0.385414	−	0.385414i	−0.873048	+	0.487634i	$0.837860\pi$
$674$	12.1277	+	21.0057i	0.467140	+	0.809110i
$675$		0			0
$676$	−16.4946	+	28.5695i	−0.634408	+	1.09883i
$677$	10.3350	−	38.5707i	0.397206	−	1.48239i	−0.420784	−	0.907161i	$-0.638245\pi$
$677$	10.3350	−	38.5707i	0.397206	−	1.48239i	0.817990	−	0.575232i	$-0.195088\pi$
$678$		0			0
$679$	3.38620	+	11.5327i	0.129950	+	0.442586i
$680$	2.54776	+	1.98837i	0.0977023	+	0.0762506i
$681$		0			0
$682$	3.78415	+	14.1226i	0.144902	+	0.540783i
$683$	−6.81805	−	25.4453i	−0.260886	−	0.973638i	−0.964721	−	0.263275i	$-0.915197\pi$
$683$	−6.81805	−	25.4453i	−0.260886	−	0.973638i	0.703835	−	0.710363i	$-0.251469\pi$
$684$		0			0
$685$	0.647865	+	5.25358i	0.0247537	+	0.200729i
$686$	3.67944	−	19.0877i	0.140482	−	0.728772i
$687$		0			0
$688$	−1.16642	+	4.35316i	−0.0444695	+	0.165963i
$689$	−30.8510	+	53.4354i	−1.17533	+	2.03573i
$690$		0			0
$691$	9.23344	+	15.9928i	0.351256	+	0.608394i	0.986470	−	0.163943i	$-0.0524212\pi$
$691$	9.23344	+	15.9928i	0.351256	+	0.608394i	−0.635213	+	0.772337i	$0.719088\pi$
$692$	10.8461	+	10.8461i	0.412305	+	0.412305i
$693$		0			0
$694$		−	7.48754i		−	0.284223i
$695$	−0.855258	−	0.119740i	−0.0324418	−	0.00454198i
$696$		0			0
$697$	−0.763422	−	2.84913i	−0.0289167	−	0.107918i
$698$	−7.80121	−	2.09033i	−0.295280	−	0.0791201i
$699$		0			0
$700$	11.4556	−	3.16043i	0.432981	−	0.119453i
$701$			19.8045i			0.748007i	0.927427	+	0.374003i	$0.122015\pi$
$701$			19.8045i			0.748007i	−0.927427	+	0.374003i	$0.877985\pi$
$702$		0			0
$703$	−17.4086	+	4.66463i	−0.656579	+	0.175930i
$704$	−6.73085	+	11.6582i	−0.253679	+	0.439384i
$705$		0			0
$706$	−24.1730			−0.909761
$707$	2.58952	−	1.57836i	0.0973889	−	0.0593603i
$708$		0			0
$709$	11.5459	−	6.66605i	0.433617	−	0.250349i	−0.267270	−	0.963622i	$-0.586121\pi$
$709$	11.5459	−	6.66605i	0.433617	−	0.250349i	0.700886	+	0.713273i	$0.252788\pi$
$710$	8.97535	−	21.1756i	0.336839	−	0.794705i
$711$		0			0
$712$	9.69449	+	2.59763i	0.363316	+	0.0973503i
$713$	−36.5070	+	36.5070i	−1.36720	+	1.36720i
$714$		0			0
$715$	27.5720	−	3.40015i	1.03113	−	0.127158i
$716$	17.7101	−	10.2249i	0.661856	−	0.382123i
$717$		0			0
$718$	−20.6905	+	5.54401i	−0.772163	+	0.206900i
$719$	25.6917	+	44.4994i	0.958140	+	1.65955i	0.727013	+	0.686624i	$0.240908\pi$
$719$	25.6917	+	44.4994i	0.958140	+	1.65955i	0.231128	+	0.972923i	$0.425759\pi$
$720$		0			0
$721$	−20.3059	−	19.3620i	−0.756232	−	0.721080i
$722$	8.70838	+	8.70838i	0.324092	+	0.324092i
$723$		0			0
$724$	10.8031	+	6.23718i	0.401495	+	0.231803i
$725$	−33.7195	−	9.63052i	−1.25231	−	0.357668i
$726$		0			0
$727$	0.303997	−	0.303997i	0.0112746	−	0.0112746i	−0.701447	−	0.712722i	$-0.747462\pi$
$727$	0.303997	−	0.303997i	0.0112746	−	0.0112746i	0.712722	+	0.701447i	$0.247462\pi$
$728$	−27.2003	+	49.8124i	−1.00811	+	1.84617i
$729$		0			0
$730$	−3.51232	−	0.491739i	−0.129997	−	0.0182001i
$731$	−1.32791	−	0.766668i	−0.0491145	−	0.0283563i
$732$		0			0
$733$	7.13083	−	26.6126i	0.263383	−	0.982960i	−0.699849	−	0.714291i	$-0.746750\pi$
$733$	7.13083	−	26.6126i	0.263383	−	0.982960i	0.963233	−	0.268669i	$-0.0865838\pi$
$734$	22.1236			0.816597
$735$		0			0
$736$	−30.1600			−1.11171
$737$	−0.934806	+	3.48874i	−0.0344340	+	0.128509i
$738$		0			0
$739$	−6.55301	−	3.78338i	−0.241056	−	0.139174i	0.374606	−	0.927184i	$-0.377778\pi$
$739$	−6.55301	−	3.78338i	−0.241056	−	0.139174i	−0.615662	+	0.788010i	$0.711111\pi$
$740$	10.7212	−	8.08786i	0.394119	−	0.297316i
$741$		0			0
$742$	−11.6457	+	21.3270i	−0.427526	+	0.782938i
$743$	−26.7436	+	26.7436i	−0.981127	+	0.981127i	−0.999825	−	0.0186980i	$-0.994048\pi$
$743$	−26.7436	+	26.7436i	−0.981127	+	0.981127i	0.0186980	+	0.999825i	$0.494048\pi$
$744$		0			0
$745$	−0.620915	+	0.251246i	−0.0227486	+	0.00920495i
$746$	10.9896	+	6.34485i	0.402358	+	0.232301i
$747$		0			0
$748$	−0.531718	−	0.531718i	−0.0194416	−	0.0194416i
$749$	18.9284	+	18.0485i	0.691627	+	0.659478i
$750$		0			0
$751$	11.8157	+	20.4654i	0.431161	+	0.746793i	0.996974	−	0.0777411i	$-0.0247707\pi$
$751$	11.8157	+	20.4654i	0.431161	+	0.746793i	−0.565813	+	0.824534i	$0.691437\pi$
$752$	2.05302	−	0.550105i	0.0748659	−	0.0200603i
$753$		0			0
$754$	44.9552	−	25.9549i	1.63717	−	0.945221i
$755$	−5.01560	−	3.91436i	−0.182536	−	0.142458i
$756$		0			0
$757$	2.26721	−	2.26721i	0.0824032	−	0.0824032i	−0.664704	−	0.747107i	$-0.731442\pi$
$757$	2.26721	−	2.26721i	0.0824032	−	0.0824032i	0.747107	+	0.664704i	$0.231442\pi$
$758$	19.1084	+	5.12008i	0.694048	+	0.185970i
$759$		0			0
$760$	16.8830	+	7.15591i	0.612409	+	0.259572i
$761$	−2.27730	+	1.31480i	−0.0825522	+	0.0476615i	−0.540708	−	0.841210i	$-0.681844\pi$
$761$	−2.27730	+	1.31480i	−0.0825522	+	0.0476615i	0.458156	+	0.888872i	$0.348510\pi$
$762$		0			0
$763$	−11.8040	+	7.19473i	−0.427332	+	0.260467i
$764$	−7.70588			−0.278789
$765$		0			0
$766$	1.77989	−	3.08286i	0.0643100	−	0.111388i
$767$	−84.1822	+	22.5566i	−3.03964	+	0.814470i
$768$		0			0
$769$		−	21.3373i		−	0.769444i	−0.923032	−	0.384722i	$-0.874297\pi$
$769$		−	21.3373i		−	0.769444i	0.923032	−	0.384722i	$-0.125703\pi$
$770$	10.8235	−	1.59696i	0.390051	−	0.0575506i
$771$		0			0
$772$	−8.24101	−	2.20817i	−0.296600	−	0.0794738i
$773$	−9.47820	−	35.3731i	−0.340907	−	1.27228i	−0.897321	−	0.441378i	$-0.854490\pi$
$773$	−9.47820	−	35.3731i	−0.340907	−	1.27228i	0.556414	−	0.830905i	$-0.312177\pi$
$774$		0			0
$775$	−28.4070	+	27.4902i	−1.02041	+	0.987475i
$776$		−	13.8202i		−	0.496117i
$777$		0			0
$778$	19.8745	+	19.8745i	0.712537	+	0.712537i
$779$	−8.36787	−	14.4936i	−0.299810	−	0.519287i
$780$		0			0
$781$	−8.63272	+	14.9523i	−0.308903	+	0.535036i
$782$	−0.842837	+	3.14551i	−0.0301398	+	0.112483i
$783$		0			0
$784$	−4.47927	+	8.68815i	−0.159974	+	0.310291i
$785$	10.4483	−	1.28847i	0.372916	−	0.0459876i
$786$		0			0
$787$	2.88368	+	10.7620i	0.102792	+	0.383625i	0.998085	−	0.0618519i	$-0.0197007\pi$
$787$	2.88368	+	10.7620i	0.102792	+	0.383625i	−0.895293	+	0.445477i	$0.853034\pi$
$788$	−2.77688	−	10.3635i	−0.0989223	−	0.369183i
$789$		0			0
$790$	24.4242	−	3.01196i	0.868973	−	0.107161i
$791$	−2.61766	−	8.91524i	−0.0930732	−	0.316990i
$792$		0			0
$793$	8.25339	−	30.8021i	0.293086	−	1.09381i
$794$	−3.79291	+	6.56952i	−0.134605	+	0.233143i
$795$		0			0
$796$	1.04485	+	1.80973i	0.0370337	+	0.0641443i
$797$	−18.6220	−	18.6220i	−0.659625	−	0.659625i	0.295666	−	0.955291i	$-0.404458\pi$
$797$	−18.6220	−	18.6220i	−0.659625	−	0.659625i	−0.955291	+	0.295666i	$0.904458\pi$
$798$		0			0
$799$			0.723147i			0.0255831i
$800$	−23.0895	−	0.378718i	−0.816338	−	0.0133897i
$801$		0			0
$802$	−5.70116	−	21.2770i	−0.201315	−	0.751318i
$803$	2.57169	+	0.689082i	0.0907529	+	0.0243172i
$804$		0			0
$805$	23.9935	+	30.2796i	0.845658	+	1.06721i
$806$		−	58.5158i		−	2.06113i
$807$		0			0
$808$	−3.36812	+	0.902486i	−0.118490	+	0.0317493i
$809$	−5.59782	+	9.69571i	−0.196809	+	0.340883i	−0.947492	−	0.319779i	$-0.896391\pi$
$809$	−5.59782	+	9.69571i	−0.196809	+	0.340883i	0.750683	+	0.660662i	$0.229725\pi$
$810$		0			0
$811$	29.8505			1.04819			0.524096	−	0.851659i	$-0.324403\pi$
$811$	29.8505			1.04819			0.524096	+	0.851659i	$0.324403\pi$
$812$	−14.2336	+	8.67566i	−0.499503	+	0.304456i
$813$		0			0
$814$	10.7076	−	6.18206i	0.375303	−	0.216681i
$815$	42.9959	+	18.2240i	1.50608	+	0.638357i
$816$		0			0
$817$	−8.40346	−	2.25170i	−0.294000	−	0.0787770i
$818$	4.31746	−	4.31746i	0.150956	−	0.150956i
$819$		0			0
$820$	9.83111	+	7.67257i	0.343317	+	0.267938i
$821$	−9.47172	+	5.46850i	−0.330565	+	0.190852i	−0.656092	−	0.754681i	$-0.727792\pi$
$821$	−9.47172	+	5.46850i	−0.330565	+	0.190852i	0.325527	+	0.945533i	$0.394458\pi$
$822$		0			0
$823$	12.5748	−	3.36941i	0.438331	−	0.117450i	−0.0329033	−	0.999459i	$-0.510475\pi$
$823$	12.5748	−	3.36941i	0.438331	−	0.117450i	0.471234	+	0.882008i	$0.343809\pi$
$824$	16.1303	+	27.9386i	0.561927	+	0.973286i
$825$		0			0
$826$	−32.9319	+	9.66933i	−1.14585	+	0.336439i
$827$	−1.42655	−	1.42655i	−0.0496061	−	0.0496061i	0.681869	−	0.731475i	$-0.261168\pi$
$827$	−1.42655	−	1.42655i	−0.0496061	−	0.0496061i	−0.731475	+	0.681869i	$0.761168\pi$
$828$		0			0
$829$	31.9139	+	18.4255i	1.10842	+	0.639944i	0.938419	−	0.345500i	$-0.112291\pi$
$829$	31.9139	+	18.4255i	1.10842	+	0.639944i	0.169997	+	0.985444i	$0.445624\pi$
$830$	−6.37384	+	2.57910i	−0.221239	+	0.0895219i
$831$		0			0
$832$	38.0966	−	38.0966i	1.32076	−	1.32076i
$833$	−2.46084	−	2.23714i	−0.0852629	−	0.0775122i
$834$		0			0
$835$	−4.93992	+	3.72657i	−0.170953	+	0.128963i
$836$	−3.69491	−	2.13326i	−0.127791	−	0.0737803i
$837$		0			0
$838$	0.468353	−	1.74792i	0.0161790	−	0.0603808i
$839$	48.4327			1.67208			0.836041	−	0.548667i	$-0.184864\pi$
$839$	48.4327			1.67208			0.836041	+	0.548667i	$0.184864\pi$
$840$		0			0
$841$	20.1901			0.696212
$842$	7.52927	−	28.0996i	0.259476	−	0.968376i
$843$		0			0
$844$	−8.57846	−	4.95278i	−0.295283	−	0.170482i
$845$	−81.3231	−	11.3856i	−2.79760	−	0.391676i
$846$		0			0
$847$	20.8842	−	0.496932i	0.717591	−	0.0170748i
$848$	8.64002	−	8.64002i	0.296700	−	0.296700i
$849$		0			0
$850$	−0.684745	+	2.39751i	−0.0234866	+	0.0822340i
$851$	37.8106	+	21.8300i	1.29613	+	0.748322i
$852$		0			0
$853$	−14.2865	−	14.2865i	−0.489161	−	0.489161i	0.418881	−	0.908041i	$-0.362423\pi$
$853$	−14.2865	−	14.2865i	−0.489161	−	0.489161i	−0.908041	+	0.418881i	$0.862423\pi$
$854$	2.96087	−	12.2043i	0.101319	−	0.417624i
$855$		0			0
$856$	−15.0360	−	26.0432i	−0.513921	−	0.890138i
$857$	47.9864	−	12.8579i	1.63918	−	0.439218i	0.682627	−	0.730767i	$-0.260837\pi$
$857$	47.9864	−	12.8579i	1.63918	−	0.439218i	0.956556	+	0.291549i	$0.0941707\pi$
$858$		0			0
$859$	−35.4574	+	20.4713i	−1.20979	+	0.698473i	−0.962714	−	0.270523i	$-0.912803\pi$
$859$	−35.4574	+	20.4713i	−1.20979	+	0.698473i	−0.247077	+	0.968996i	$0.579470\pi$
$860$	6.43404	−	0.793438i	0.219399	−	0.0270560i
$861$		0			0
$862$	−25.1056	+	25.1056i	−0.855099	+	0.855099i
$863$	41.3772	+	11.0870i	1.40850	+	0.377405i	0.881388	−	0.472393i	$-0.156610\pi$
$863$	41.3772	+	11.0870i	1.40850	+	0.377405i	0.527107	+	0.849799i	$0.323277\pi$
$864$		0			0
$865$	−14.8999	+	35.1534i	−0.506611	+	1.19525i
$866$	1.86045	−	1.07413i	0.0632205	−	0.0365004i
$867$		0			0
$868$	0.446988	+	18.7852i	0.0151718	+	0.637613i
$869$	−18.4741			−0.626690
$870$		0			0
$871$	7.22764	−	12.5186i	0.244899	−	0.424178i
$872$	15.3531	−	4.11386i	0.519922	−	0.139313i
$873$		0			0
$874$			18.4767i			0.624983i
$875$	17.9884	+	23.4823i	0.608118	+	0.793847i
$876$		0			0
$877$	−23.3170	−	6.24778i	−0.787361	−	0.210973i	−0.157333	−	0.987546i	$-0.550290\pi$
$877$	−23.3170	−	6.24778i	−0.787361	−	0.210973i	−0.630027	+	0.776573i	$0.716956\pi$
$878$	6.98643	+	26.0737i	0.235781	+	0.879945i
$879$		0			0
$880$	−5.44831	−	0.762786i	−0.183662	−	0.0257135i
$881$		−	21.9086i		−	0.738118i	−0.929406	−	0.369059i	$-0.879680\pi$
$881$		−	21.9086i		−	0.738118i	0.929406	−	0.369059i	$-0.120320\pi$
$882$		0			0
$883$	22.5079	+	22.5079i	0.757450	+	0.757450i	0.975858	−	0.218408i	$-0.0700863\pi$
$883$	22.5079	+	22.5079i	0.757450	+	0.757450i	−0.218408	+	0.975858i	$0.570086\pi$
$884$	1.50476	+	2.60633i	0.0506106	+	0.0876602i
$885$		0			0
$886$	16.4759	−	28.5371i	0.553518	−	0.958722i
$887$	5.09973	−	19.0325i	0.171232	−	0.639047i	−0.825931	−	0.563772i	$-0.809350\pi$
$887$	5.09973	−	19.0325i	0.171232	−	0.639047i	0.997163	−	0.0752754i	$-0.0239836\pi$
$888$		0			0
$889$	2.76623	+	9.42127i	0.0927765	+	0.315979i
$890$	0.947704	+	7.68499i	0.0317671	+	0.257601i
$891$		0			0
$892$	−1.26789	−	4.73183i	−0.0424521	−	0.158433i
$893$	1.06194	+	3.96321i	0.0355364	+	0.132624i
$894$		0			0
$895$	40.1289	+	31.3181i	1.34136	+	1.04685i
$896$	−2.22292	+	2.33129i	−0.0742626	+	0.0778828i
$897$		0			0
$898$	4.05954	−	15.1504i	0.135469	−	0.505576i
$899$	27.7250	−	48.0212i	0.924681	−	1.60160i
$900$		0			0
$901$	2.07863	+	3.60029i	0.0692492	+	0.119943i
$902$	8.11844	+	8.11844i	0.270315	+	0.270315i
$903$		0			0
$904$			10.6836i			0.355330i
$905$	−4.30528	+	30.7511i	−0.143112	+	1.02220i
$906$		0			0
$907$	3.78809	+	14.1374i	0.125782	+	0.469423i	0.999866	−	0.0163502i	$-0.00520467\pi$
$907$	3.78809	+	14.1374i	0.125782	+	0.469423i	−0.874085	+	0.485773i	$0.838538\pi$
$908$	−5.01310	−	1.34325i	−0.166365	−	0.0445775i
$909$		0			0
$910$	−43.4961	−	5.03788i	−1.44188	−	0.167004i
$911$			26.6668i			0.883510i	0.897136	+	0.441755i	$0.145644\pi$
$911$			26.6668i			0.883510i	−0.897136	+	0.441755i	$0.854356\pi$
$912$		0			0
$913$	4.98582	−	1.33595i	0.165007	−	0.0442134i
$914$	7.27165	−	12.5949i	0.240525	−	0.416601i
$915$		0			0
$916$	4.59625			0.151864
$917$	−0.490195	−	20.6011i	−0.0161877	−	0.680308i
$918$		0			0
$919$	30.7779	−	17.7696i	1.01527	−	0.586167i	0.102540	−	0.994729i	$-0.467303\pi$
$919$	30.7779	−	17.7696i	1.01527	−	0.586167i	0.912730	+	0.408562i	$0.133970\pi$
$920$	−16.6621	−	41.1776i	−0.549332	−	1.35759i
$921$		0			0
$922$	−23.3003	−	6.24330i	−0.767355	−	0.205612i
$923$	48.8612	−	48.8612i	1.60829	−	1.60829i
$924$		0			0
$925$	28.6724	+	17.1871i	0.942744	+	0.565108i
$926$	−4.93408	+	2.84869i	−0.162144	+	0.0936138i
$927$		0			0
$928$	31.2886	−	8.38376i	1.02710	−	0.275210i
$929$	−7.12543	−	12.3416i	−0.233778	−	0.404915i	0.725139	−	0.688602i	$-0.241775\pi$
$929$	−7.12543	−	12.3416i	−0.233778	−	0.404915i	−0.958917	+	0.283688i	$0.908442\pi$
$930$		0			0
$931$	−16.7719	−	8.64691i	−0.549675	−	0.283391i
$932$	8.85251	+	8.85251i	0.289974	+	0.289974i
$933$		0			0
$934$	26.9688	+	15.5704i	0.882446	+	0.509480i
$935$	0.730454	−	1.72336i	0.0238884	−	0.0563600i
$936$		0			0
$937$	−32.0420	+	32.0420i	−1.04677	+	1.04677i	−0.0479143	+	0.998851i	$0.515257\pi$
$937$	−32.0420	+	32.0420i	−1.04677	+	1.04677i	−0.998851	+	0.0479143i	$0.984743\pi$
$938$	2.72830	−	4.99640i	0.0890822	−	0.163138i
$939$		0			0
$940$	−1.84126	−	2.44077i	−0.0600554	−	0.0796090i
$941$	−33.0877	−	19.1032i	−1.07863	−	0.622746i	−0.148102	−	0.988972i	$-0.547316\pi$
$941$	−33.0877	−	19.1032i	−1.07863	−	0.622746i	−0.930526	+	0.366226i	$0.880650\pi$
$942$		0			0
$943$	−10.4931	+	39.1608i	−0.341702	+	1.27525i
$944$	17.2587			0.561722
$945$		0			0
$946$	5.96839			0.194049
$947$	−4.40587	+	16.4429i	−0.143172	+	0.534324i	0.856658	+	0.515884i	$0.172537\pi$
$947$	−4.40587	+	16.4429i	−0.143172	+	0.534324i	−0.999830	+	0.0184397i	$0.994130\pi$
$948$		0			0
$949$	−9.22798	−	5.32777i	−0.299553	−	0.172947i
$950$	−0.232010	+	14.1451i	−0.00752741	+	0.458929i
$951$		0			0
$952$	1.99021	+	3.26522i	0.0645032	+	0.105826i
$953$	−4.61295	+	4.61295i	−0.149428	+	0.149428i	−0.777862	−	0.628435i	$-0.783696\pi$
$953$	−4.61295	+	4.61295i	−0.149428	+	0.149428i	0.628435	+	0.777862i	$0.283696\pi$
$954$		0			0
$955$	−7.19482	−	17.7809i	−0.232819	−	0.575375i
$956$	−10.6273	−	6.13569i	−0.343712	−	0.198442i
$957$		0			0
$958$	9.59276	+	9.59276i	0.309928	+	0.309928i
$959$	−1.47667	+	6.08664i	−0.0476841	+	0.196548i
$960$		0			0
$961$	−15.7533	−	27.2855i	−0.508171	−	0.880178i
$962$	−47.7979	+	12.8074i	−1.54107	+	0.412927i
$963$		0			0
$964$	−19.7850	+	11.4229i	−0.637232	+	0.367906i
$965$	−2.59924	−	21.0774i	−0.0836724	−	0.678504i
$966$		0			0
$967$	−11.7981	+	11.7981i	−0.379401	+	0.379401i	−0.870886	−	0.491485i	$-0.836454\pi$
$967$	−11.7981	+	11.7981i	−0.379401	+	0.379401i	0.491485	+	0.870886i	$0.336454\pi$
$968$	−23.2012	−	6.21674i	−0.745715	−	0.199814i
$969$		0			0
$970$	9.88390	−	3.99941i	0.317353	−	0.128413i
$971$	32.5038	−	18.7661i	1.04310	−	0.602233i	0.122389	−	0.992482i	$-0.460945\pi$
$971$	32.5038	−	18.7661i	1.04310	−	0.602233i	0.920709	+	0.390249i	$0.127611\pi$
$972$		0			0
$973$	−0.896829	−	0.489717i	−0.0287510	−	0.0156996i
$974$	−13.5091			−0.432859
$975$		0			0
$976$	−3.15746	+	5.46887i	−0.101068	+	0.175054i
$977$	37.6298	−	10.0829i	1.20388	−	0.322580i	0.399524	−	0.916723i	$-0.369175\pi$
$977$	37.6298	−	10.0829i	1.20388	−	0.322580i	0.804360	+	0.594143i	$0.202509\pi$
$978$		0			0
$979$		−	5.81281i		−	0.185778i
$980$	14.0020	+	1.28505i	0.447277	+	0.0410493i
$981$		0			0
$982$	−4.33947	−	1.16276i	−0.138478	−	0.0371051i
$983$	−12.9764	−	48.4288i	−0.413884	−	1.54464i	−0.787060	−	0.616877i	$-0.788398\pi$
$983$	−12.9764	−	48.4288i	−0.413884	−	1.54464i	0.373175	−	0.927761i	$-0.378269\pi$
$984$		0			0
$985$	21.3204	−	16.0837i	0.679324	−	0.512468i
$986$		−	3.49750i		−	0.111383i
$987$		0			0
$988$	12.0742	+	12.0742i	0.384133	+	0.384133i
$989$	10.5377	+	18.2519i	0.335080	+	0.580376i
$990$		0			0
$991$	−17.8816	+	30.9718i	−0.568028	+	0.983853i	0.428733	+	0.903431i	$0.358960\pi$
$991$	−17.8816	+	30.9718i	−0.568028	+	0.983853i	−0.996761	+	0.0804219i	$0.974373\pi$
$992$	9.45067	−	35.2704i	0.300059	−	1.11984i
$993$		0			0
$994$	18.7793	−	19.6948i	0.595643	−	0.624681i
$995$	−3.20030	+	4.10064i	−0.101456	+	0.129999i
$996$		0			0
$997$	−7.48842	−	27.9472i	−0.237161	−	0.885096i	−0.977163	−	0.212491i	$-0.931842\pi$
$997$	−7.48842	−	27.9472i	−0.237161	−	0.885096i	0.740002	−	0.672604i	$-0.234824\pi$
$998$	6.44664	+	24.0592i	0.204065	+	0.761580i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.ce.a.53.11	yes	64
3.2	odd	2	inner	315.2.ce.a.53.6	✓	64
5.2	odd	4	inner	315.2.ce.a.242.11	yes	64
7.2	even	3	inner	315.2.ce.a.233.6	yes	64
15.2	even	4	inner	315.2.ce.a.242.6	yes	64
21.2	odd	6	inner	315.2.ce.a.233.11	yes	64
35.2	odd	12	inner	315.2.ce.a.107.6	yes	64
105.2	even	12	inner	315.2.ce.a.107.11	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.ce.a.53.6	✓	64	3.2	odd	2	inner
315.2.ce.a.53.11	yes	64	1.1	even	1	trivial
315.2.ce.a.107.6	yes	64	35.2	odd	12	inner
315.2.ce.a.107.11	yes	64	105.2	even	12	inner
315.2.ce.a.233.6	yes	64	7.2	even	3	inner
315.2.ce.a.233.11	yes	64	21.2	odd	6	inner
315.2.ce.a.242.6	yes	64	15.2	even	4	inner
315.2.ce.a.242.11	yes	64	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.271660 - 1.01385i) q^{2} +(0.777962 + 0.449157i) q^{4} +(-0.310035 + 2.21447i) q^{5} +(-1.26800 + 2.32211i) q^{7} +(2.15109 - 2.15109i) q^{8} +O(q^{10})\)	\(q+(0.271660 - 1.01385i) q^{2} +(0.777962 + 0.449157i) q^{4} +(-0.310035 + 2.21447i) q^{5} +(-1.26800 + 2.32211i) q^{7} +(2.15109 - 2.15109i) q^{8} +(2.16091 + 0.915911i) q^{10} +(-1.52584 - 0.880947i) q^{11} +(4.98616 + 4.98616i) q^{13} +(2.00980 + 1.91638i) q^{14} +(-0.698204 - 1.20932i) q^{16} +(0.458916 - 0.122966i) q^{17} +(2.33452 - 1.34783i) q^{19} +(-1.23584 + 1.58352i) q^{20} +(-1.30766 + 1.30766i) q^{22} +(-6.30772 - 1.69015i) q^{23} +(-4.80776 - 1.37313i) q^{25} +(6.40974 - 3.70067i) q^{26} +(-2.02944 + 1.23698i) q^{28} +7.01357 q^{29} +(3.95306 - 6.84689i) q^{31} +(4.46115 - 1.19536i) q^{32} -0.498676i q^{34} +(-4.74912 - 3.52788i) q^{35} +(-6.45801 - 1.73042i) q^{37} +(-0.732304 - 2.73300i) q^{38} +(4.09662 + 5.43045i) q^{40} -6.20839i q^{41} +(-2.28209 - 2.28209i) q^{43} +(-0.791366 - 1.37069i) q^{44} +(-3.42711 + 5.93593i) q^{46} +(-0.393943 + 1.47022i) q^{47} +(-3.78437 - 5.88885i) q^{49} +(-2.69822 + 4.50131i) q^{50} +(1.63948 + 6.11861i) q^{52} +(2.26472 + 8.45204i) q^{53} +(2.42390 - 3.10581i) q^{55} +(2.26749 + 7.72265i) q^{56} +(1.90530 - 7.11069i) q^{58} +(-6.17967 + 10.7035i) q^{59} +(-2.26113 - 3.91639i) q^{61} +(-5.86782 - 5.86782i) q^{62} -7.64048i q^{64} +(-12.5876 + 9.49581i) q^{65} +(-0.530569 - 1.98011i) q^{67} +(0.412250 + 0.110462i) q^{68} +(-4.86687 + 3.85650i) q^{70} -9.79937i q^{71} +(-1.45962 + 0.391103i) q^{73} +(-3.50876 + 6.07735i) q^{74} +2.42155 q^{76} +(3.98042 - 2.42614i) q^{77} +(9.08059 - 5.24268i) q^{79} +(2.89448 - 1.17122i) q^{80} +(-6.29436 - 1.68657i) q^{82} +(-2.07156 + 2.07156i) q^{83} +(0.130025 + 1.05438i) q^{85} +(-2.93365 + 1.69374i) q^{86} +(-5.17723 + 1.38724i) q^{88} +(1.64959 + 2.85718i) q^{89} +(-17.9008 + 5.25597i) q^{91} +(-4.14803 - 4.14803i) q^{92} +(1.38356 + 0.798797i) q^{94} +(2.26095 + 5.58759i) q^{95} +(3.21237 - 3.21237i) q^{97} +(-6.99846 + 2.23701i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{7}+O(q^{10}) \) 64 * q + 8 * q^7	\( 64 q + 8 q^{7} + 8 q^{10} + 32 q^{16} - 48 q^{22} - 16 q^{25} + 88 q^{28} + 32 q^{31} - 16 q^{37} - 40 q^{40} - 16 q^{43} - 80 q^{52} - 32 q^{55} - 88 q^{58} + 48 q^{61} - 32 q^{67} - 112 q^{70} - 88 q^{73} - 320 q^{76} - 56 q^{82} + 16 q^{85} + 120 q^{88} - 128 q^{91} + 208 q^{97}+O(q^{100}) \) 64 * q + 8 * q^7 + 8 * q^10 + 32 * q^16 - 48 * q^22 - 16 * q^25 + 88 * q^28 + 32 * q^31 - 16 * q^37 - 40 * q^40 - 16 * q^43 - 80 * q^52 - 32 * q^55 - 88 * q^58 + 48 * q^61 - 32 * q^67 - 112 * q^70 - 88 * q^73 - 320 * q^76 - 56 * q^82 + 16 * q^85 + 120 * q^88 - 128 * q^91 + 208 * q^97

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