LMFDB - Embedded newform 288.2.w.a.251.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(35,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3, 4]))

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

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

chi := DirichletCharacter("288.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.w (of order $8$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			251.7
Character	$\chi$	$=$	288.251
Dual form			288.2.w.a.179.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24152 - 0.677214i) q^{2} +(1.08276 - 1.68155i) q^{4} +(0.0963530 - 0.232617i) q^{5} +(0.617536 - 0.617536i) q^{7} +(0.205502 - 2.82095i) q^{8} +O(q^{10})$	\(q+(1.24152 - 0.677214i) q^{2} +(1.08276 - 1.68155i) q^{4} +(0.0963530 - 0.232617i) q^{5} +(0.617536 - 0.617536i) q^{7} +(0.205502 - 2.82095i) q^{8} +(-0.0379068 - 0.354051i) q^{10} +(-0.505112 + 1.21945i) q^{11} +(3.41575 - 1.41485i) q^{13} +(0.348482 - 1.18489i) q^{14} +(-1.65525 - 3.64145i) q^{16} -2.76109 q^{17} +(0.189895 + 0.458448i) q^{19} +(-0.286830 - 0.413891i) q^{20} +(0.198719 + 1.85604i) q^{22} +(-4.46959 + 4.46959i) q^{23} +(3.49071 + 3.49071i) q^{25} +(3.28257 - 4.06976i) q^{26} +(-0.369776 - 1.70707i) q^{28} +(0.0101033 - 0.00418494i) q^{29} +4.03370i q^{31} +(-4.52107 - 3.39998i) q^{32} +(-3.42796 + 1.86985i) q^{34} +(-0.0841477 - 0.203151i) q^{35} +(6.30586 + 2.61197i) q^{37} +(0.546227 + 0.440574i) q^{38} +(-0.636400 - 0.319610i) q^{40} +(-5.34633 - 5.34633i) q^{41} +(-10.1719 - 4.21336i) q^{43} +(1.50365 + 2.16975i) q^{44} +(-2.52223 + 8.57598i) q^{46} +11.5870i q^{47} +6.23730i q^{49} +(6.69775 + 1.96984i) q^{50} +(1.31930 - 7.27571i) q^{52} +(9.04956 + 3.74845i) q^{53} +(0.234995 + 0.234995i) q^{55} +(-1.61513 - 1.86894i) q^{56} +(0.00970943 - 0.0120378i) q^{58} +(-0.939369 - 0.389099i) q^{59} +(-2.97084 - 7.17223i) q^{61} +(2.73168 + 5.00793i) q^{62} +(-7.91554 - 1.15942i) q^{64} -0.930884i q^{65} +(-7.40244 + 3.06619i) q^{67} +(-2.98960 + 4.64292i) q^{68} +(-0.242048 - 0.195230i) q^{70} +(1.20890 + 1.20890i) q^{71} +(3.73875 - 3.73875i) q^{73} +(9.59774 - 1.02759i) q^{74} +(0.976516 + 0.177071i) q^{76} +(0.441128 + 1.06498i) q^{77} -7.22016 q^{79} +(-1.00655 + 0.0341749i) q^{80} +(-10.2582 - 3.01699i) q^{82} +(11.2970 - 4.67935i) q^{83} +(-0.266039 + 0.642275i) q^{85} +(-15.4820 + 1.65760i) q^{86} +(3.33620 + 1.67550i) q^{88} +(3.70197 - 3.70197i) q^{89} +(1.23563 - 2.98307i) q^{91} +(2.67636 + 12.3554i) q^{92} +(7.84687 + 14.3855i) q^{94} +0.124940 q^{95} -14.0257 q^{97} +(4.22399 + 7.74375i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} - 4 q^{8}+O(q^{10}) $ 32 * q - 4 * q^2 - 4 * q^8	$ 32 q - 4 q^{2} - 4 q^{8} + 8 q^{10} - 8 q^{11} + 12 q^{14} + 8 q^{16} + 32 q^{20} + 16 q^{22} - 36 q^{26} - 16 q^{29} - 24 q^{32} + 24 q^{35} + 32 q^{38} - 32 q^{40} + 8 q^{44} - 32 q^{46} + 8 q^{50} - 56 q^{52} - 16 q^{53} - 32 q^{55} + 40 q^{56} - 32 q^{58} + 32 q^{59} + 32 q^{61} - 68 q^{62} - 48 q^{64} - 16 q^{67} - 72 q^{68} - 48 q^{70} + 16 q^{71} + 60 q^{74} - 8 q^{76} - 16 q^{77} - 32 q^{79} + 96 q^{80} + 40 q^{82} - 40 q^{83} - 40 q^{86} + 40 q^{88} - 48 q^{91} - 16 q^{92} + 72 q^{94} - 80 q^{95} - 44 q^{98}+O(q^{100}) $ 32 * q - 4 * q^2 - 4 * q^8 + 8 * q^10 - 8 * q^11 + 12 * q^14 + 8 * q^16 + 32 * q^20 + 16 * q^22 - 36 * q^26 - 16 * q^29 - 24 * q^32 + 24 * q^35 + 32 * q^38 - 32 * q^40 + 8 * q^44 - 32 * q^46 + 8 * q^50 - 56 * q^52 - 16 * q^53 - 32 * q^55 + 40 * q^56 - 32 * q^58 + 32 * q^59 + 32 * q^61 - 68 * q^62 - 48 * q^64 - 16 * q^67 - 72 * q^68 - 48 * q^70 + 16 * q^71 + 60 * q^74 - 8 * q^76 - 16 * q^77 - 32 * q^79 + 96 * q^80 + 40 * q^82 - 40 * q^83 - 40 * q^86 + 40 * q^88 - 48 * q^91 - 16 * q^92 + 72 * q^94 - 80 * q^95 - 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.24152	−	0.677214i	0.877890	−	0.478863i
$2$	1.24152	−	0.677214i	0.877890	−	0.478863i
$3$		0			0
$3$		0			0
$4$	1.08276	−	1.68155i	0.541381	−	0.840777i
$5$	0.0963530	−	0.232617i	0.0430904	−	0.104029i	−0.900869	−	0.434091i	$-0.857070\pi$
$5$	0.0963530	−	0.232617i	0.0430904	−	0.104029i	0.943959	+	0.330062i	$0.107070\pi$
$6$		0			0
$7$	0.617536	−	0.617536i	0.233407	−	0.233407i	−0.580706	−	0.814113i	$-0.697224\pi$
$7$	0.617536	−	0.617536i	0.233407	−	0.233407i	0.814113	+	0.580706i	$0.197224\pi$
$8$	0.205502	−	2.82095i	0.0726560	−	0.997357i
$9$		0			0
$10$	−0.0379068	−	0.354051i	−0.0119872	−	0.111961i
$11$	−0.505112	+	1.21945i	−0.152297	+	0.367677i	−0.981553	−	0.191192i	$-0.938765\pi$
$11$	−0.505112	+	1.21945i	−0.152297	+	0.367677i	0.829256	+	0.558869i	$0.188765\pi$
$12$		0			0
$13$	3.41575	−	1.41485i	0.947358	−	0.392408i	0.145121	−	0.989414i	$-0.453643\pi$
$13$	3.41575	−	1.41485i	0.947358	−	0.392408i	0.802237	+	0.597006i	$0.203643\pi$
$14$	0.348482	−	1.18489i	0.0931356	−	0.316675i
$15$		0			0
$16$	−1.65525	−	3.64145i	−0.413813	−	0.910362i
$17$	−2.76109			−0.669662			−0.334831	−	0.942278i	$-0.608679\pi$
$17$	−2.76109			−0.669662			−0.334831	+	0.942278i	$0.608679\pi$
$18$		0			0
$19$	0.189895	+	0.458448i	0.0435650	+	0.105175i	0.944164	−	0.329475i	$-0.106872\pi$
$19$	0.189895	+	0.458448i	0.0435650	+	0.105175i	−0.900599	+	0.434651i	$0.856872\pi$
$20$	−0.286830	−	0.413891i	−0.0641372	−	0.0925489i
$21$		0			0
$22$	0.198719	+	1.85604i	0.0423670	+	0.395710i
$23$	−4.46959	+	4.46959i	−0.931975	+	0.931975i	−0.997829	−	0.0658547i	$-0.979023\pi$
$23$	−4.46959	+	4.46959i	−0.931975	+	0.931975i	0.0658547	+	0.997829i	$0.479023\pi$
$24$		0			0
$25$	3.49071	+	3.49071i	0.698141	+	0.698141i
$26$	3.28257	−	4.06976i	0.643766	−	0.798146i
$27$		0			0
$28$	−0.369776	−	1.70707i	−0.0698811	−	0.322605i
$29$	0.0101033	−	0.00418494i	0.00187614	−	0.000777123i	−0.381745	−	0.924268i	$-0.624677\pi$
$29$	0.0101033	−	0.00418494i	0.00187614	−	0.000777123i	0.383621	+	0.923490i	$0.374677\pi$
$30$		0			0
$31$			4.03370i			0.724474i	0.932086	+	0.362237i	$0.117987\pi$
$31$			4.03370i			0.724474i	−0.932086	+	0.362237i	$0.882013\pi$
$32$	−4.52107	−	3.39998i	−0.799221	−	0.601038i
$33$		0			0
$34$	−3.42796	+	1.86985i	−0.587890	+	0.320676i
$35$	−0.0841477	−	0.203151i	−0.0142236	−	0.0343387i
$36$		0			0
$37$	6.30586	+	2.61197i	1.03668	+	0.429406i	0.835118	−	0.550071i	$-0.185399\pi$
$37$	6.30586	+	2.61197i	1.03668	+	0.429406i	0.201559	+	0.979476i	$0.435399\pi$
$38$	0.546227	+	0.440574i	0.0886097	+	0.0714705i
$39$		0			0
$40$	−0.636400	−	0.319610i	−0.100624	−	0.0505348i
$41$	−5.34633	−	5.34633i	−0.834957	−	0.834957i	0.153233	−	0.988190i	$-0.451031\pi$
$41$	−5.34633	−	5.34633i	−0.834957	−	0.834957i	−0.988190	+	0.153233i	$0.951031\pi$
$42$		0			0
$43$	−10.1719	−	4.21336i	−1.55121	−	0.642531i	−0.567673	−	0.823254i	$-0.692156\pi$
$43$	−10.1719	−	4.21336i	−1.55121	−	0.642531i	−0.983534	+	0.180724i	$0.942156\pi$
$44$	1.50365	+	2.16975i	0.226684	+	0.327101i
$45$		0			0
$46$	−2.52223	+	8.57598i	−0.371883	+	1.26446i
$47$			11.5870i			1.69013i	0.534660	+	0.845067i	$0.320440\pi$
$47$			11.5870i			1.69013i	−0.534660	+	0.845067i	$0.679560\pi$
$48$		0			0
$49$			6.23730i			0.891043i
$50$	6.69775	+	1.96984i	0.947205	+	0.278577i
$51$		0			0
$52$	1.31930	−	7.27571i	0.182953	−	1.00896i
$53$	9.04956	+	3.74845i	1.24305	+	0.514889i	0.904667	−	0.426119i	$-0.140119\pi$
$53$	9.04956	+	3.74845i	1.24305	+	0.514889i	0.338385	+	0.941008i	$0.390119\pi$
$54$		0			0
$55$	0.234995	+	0.234995i	0.0316867	+	0.0316867i
$56$	−1.61513	−	1.86894i	−0.215831	−	0.249748i
$57$		0			0
$58$	0.00970943	−	0.0120378i	0.00127491	−	0.00158064i
$59$	−0.939369	−	0.389099i	−0.122295	−	0.0506564i	0.320697	−	0.947182i	$-0.396083\pi$
$59$	−0.939369	−	0.389099i	−0.122295	−	0.0506564i	−0.442992	+	0.896526i	$0.646083\pi$
$60$		0			0
$61$	−2.97084	−	7.17223i	−0.380377	−	0.918311i	−0.991893	−	0.127078i	$-0.959440\pi$
$61$	−2.97084	−	7.17223i	−0.380377	−	0.918311i	0.611516	−	0.791232i	$-0.290560\pi$
$62$	2.73168	+	5.00793i	0.346924	+	0.636008i
$63$		0			0
$64$	−7.91554	−	1.15942i	−0.989442	−	0.144928i
$65$		−	0.930884i		−	0.115462i
$66$		0			0
$67$	−7.40244	+	3.06619i	−0.904352	+	0.374595i	−0.785892	−	0.618364i	$-0.787796\pi$
$67$	−7.40244	+	3.06619i	−0.904352	+	0.374595i	−0.118460	+	0.992959i	$0.537796\pi$
$68$	−2.98960	+	4.64292i	−0.362542	+	0.563037i
$69$		0			0
$70$	−0.242048	−	0.195230i	−0.0289303	−	0.0233345i
$71$	1.20890	+	1.20890i	0.143470	+	0.143470i	0.775194	−	0.631724i	$-0.217652\pi$
$71$	1.20890	+	1.20890i	0.143470	+	0.143470i	−0.631724	+	0.775194i	$0.717652\pi$
$72$		0			0
$73$	3.73875	−	3.73875i	0.437588	−	0.437588i	−0.453612	−	0.891199i	$-0.649865\pi$
$73$	3.73875	−	3.73875i	0.437588	−	0.437588i	0.891199	+	0.453612i	$0.149865\pi$
$74$	9.59774	−	1.02759i	1.11571	−	0.119455i
$75$		0			0
$76$	0.976516	+	0.177071i	0.112014	+	0.0203114i
$77$	0.441128	+	1.06498i	0.0502712	+	0.121366i
$78$		0			0
$79$	−7.22016			−0.812331			−0.406166	−	0.913800i	$-0.633134\pi$
$79$	−7.22016			−0.812331			−0.406166	+	0.913800i	$0.633134\pi$
$80$	−1.00655	+	0.0341749i	−0.112536	+	0.00382088i
$81$		0			0
$82$	−10.2582	−	3.01699i	−1.13283	−	0.333170i
$83$	11.2970	−	4.67935i	1.24000	−	0.513626i	0.336287	−	0.941760i	$-0.390829\pi$
$83$	11.2970	−	4.67935i	1.24000	−	0.513626i	0.903715	+	0.428134i	$0.140829\pi$
$84$		0			0
$85$	−0.266039	+	0.642275i	−0.0288560	+	0.0696645i
$86$	−15.4820	+	1.65760i	−1.66947	+	0.178744i
$87$		0			0
$88$	3.33620	+	1.67550i	0.355640	+	0.178608i
$89$	3.70197	−	3.70197i	0.392408	−	0.392408i	−0.483137	−	0.875545i	$-0.660503\pi$
$89$	3.70197	−	3.70197i	0.392408	−	0.392408i	0.875545	+	0.483137i	$0.160503\pi$
$90$		0			0
$91$	1.23563	−	2.98307i	0.129529	−	0.312710i
$92$	2.67636	+	12.3554i	0.279030	+	1.28814i
$93$		0			0
$94$	7.84687	+	14.3855i	0.809342	+	1.48375i
$95$	0.124940			0.0128185
$96$		0			0
$97$	−14.0257			−1.42409			−0.712046	−	0.702133i	$-0.752231\pi$
$97$	−14.0257			−1.42409			−0.712046	+	0.702133i	$0.752231\pi$
$98$	4.22399	+	7.74375i	0.426687	+	0.782237i
$99$		0			0
$100$	9.64942	−	2.09021i	0.964942	−	0.209021i
$101$	4.26734	−	10.3023i	0.424616	−	1.02511i	−0.556352	−	0.830947i	$-0.687799\pi$
$101$	4.26734	−	10.3023i	0.424616	−	1.02511i	0.980968	−	0.194168i	$-0.0622006\pi$
$102$		0			0
$103$	8.34273	−	8.34273i	0.822034	−	0.822034i	−0.164366	−	0.986399i	$-0.552558\pi$
$103$	8.34273	−	8.34273i	0.822034	−	0.822034i	0.986399	+	0.164366i	$0.0525577\pi$
$104$	−3.28928	−	9.92641i	−0.322540	−	0.973365i
$105$		0			0
$106$	13.7737	−	1.47470i	1.33782	−	0.143235i
$107$	1.28476	−	3.10168i	0.124202	−	0.299850i	−0.849533	−	0.527536i	$-0.823116\pi$
$107$	1.28476	−	3.10168i	0.124202	−	0.299850i	0.973735	+	0.227686i	$0.0731159\pi$
$108$		0			0
$109$	8.00684	−	3.31654i	0.766916	−	0.317667i	0.0352935	−	0.999377i	$-0.488763\pi$
$109$	8.00684	−	3.31654i	0.766916	−	0.317667i	0.731623	+	0.681710i	$0.238763\pi$
$110$	0.450894	+	0.132610i	0.0429910	+	0.0126439i
$111$		0			0
$112$	−3.27090	−	1.22655i	−0.309071	−	0.115898i
$113$	−5.12115			−0.481757			−0.240879	−	0.970555i	$-0.577436\pi$
$113$	−5.12115			−0.481757			−0.240879	+	0.970555i	$0.577436\pi$
$114$		0			0
$115$	0.609043	+	1.47036i	0.0567936	+	0.137112i
$116$	0.00390230	−	0.0215206i	0.000362320	−	0.00199814i
$117$		0			0
$118$	−1.42975	+	0.153078i	−0.131619	+	0.0140920i
$119$	−1.70507	+	1.70507i	−0.156304	+	0.156304i
$120$		0			0
$121$	6.54626	+	6.54626i	0.595114	+	0.595114i
$122$	−8.54550	−	6.89261i	−0.773673	−	0.624027i
$123$		0			0
$124$	6.78289	+	4.36754i	0.609121	+	0.392217i
$125$	2.31142	−	0.957421i	0.206740	−	0.0856344i
$126$		0			0
$127$			8.28564i			0.735232i	0.929978	+	0.367616i	$0.119826\pi$
$127$			8.28564i			0.735232i	−0.929978	+	0.367616i	$0.880174\pi$
$128$	−10.6125	+	3.92106i	−0.938022	+	0.346576i
$129$		0			0
$130$	−0.630408	−	1.15571i	−0.0552904	−	0.101363i
$131$	−7.82244	−	18.8850i	−0.683450	−	1.64999i	−0.757578	−	0.652745i	$-0.773617\pi$
$131$	−7.82244	−	18.8850i	−0.683450	−	1.64999i	0.0741279	−	0.997249i	$-0.476383\pi$
$132$		0			0
$133$	0.400375	+	0.165841i	0.0347169	+	0.0143802i
$134$	−7.11384	+	8.81978i	−0.614542	+	0.761913i
$135$		0			0
$136$	−0.567410	+	7.78890i	−0.0486550	+	0.667892i
$137$	−13.3963	−	13.3963i	−1.14452	−	1.14452i	−0.987613	−	0.156906i	$-0.949848\pi$
$137$	−13.3963	−	13.3963i	−1.14452	−	1.14452i	−0.156906	−	0.987613i	$-0.550152\pi$
$138$		0			0
$139$	−18.0954	−	7.49538i	−1.53484	−	0.635750i	−0.554340	−	0.832290i	$-0.687029\pi$
$139$	−18.0954	−	7.49538i	−1.53484	−	0.635750i	−0.980496	+	0.196540i	$0.937029\pi$
$140$	−0.432721	−	0.0784648i	−0.0365716	−	0.00663148i
$141$		0			0
$142$	2.31956	+	0.682193i	0.194653	+	0.0572484i
$143$			4.87998i			0.408085i
$144$		0			0
$145$		−	0.00275343i		−	0.000228660i
$146$	2.10981	−	7.17369i	0.174609	−	0.593698i
$147$		0			0
$148$	11.2199	−	7.77550i	0.922272	−	0.639142i
$149$	14.0938	+	5.83786i	1.15461	+	0.478256i	0.876078	−	0.482170i	$-0.160151\pi$
$149$	14.0938	+	5.83786i	1.15461	+	0.478256i	0.278535	+	0.960426i	$0.410151\pi$
$150$		0			0
$151$	3.91247	+	3.91247i	0.318392	+	0.318392i	0.848149	−	0.529757i	$-0.177717\pi$
$151$	3.91247	+	3.91247i	0.318392	+	0.318392i	−0.529757	+	0.848149i	$0.677717\pi$
$152$	1.33228	−	0.441473i	0.108062	−	0.0358082i
$153$		0			0
$154$	1.26889	+	1.02346i	0.102250	+	0.0824725i
$155$	0.938306	+	0.388659i	0.0753665	+	0.0312178i
$156$		0			0
$157$	−7.38756	−	17.8351i	−0.589591	−	1.42340i	−0.883894	−	0.467687i	$-0.845088\pi$
$157$	−7.38756	−	17.8351i	−0.589591	−	1.42340i	0.294303	−	0.955712i	$-0.404912\pi$
$158$	−8.96400	+	4.88959i	−0.713137	+	0.388995i
$159$		0			0
$160$	−1.22651	+	0.724079i	−0.0969643	+	0.0572434i
$161$			5.52027i			0.435058i
$162$		0			0
$163$	17.9611	−	7.43971i	1.40682	−	0.582723i	0.455307	−	0.890335i	$-0.349530\pi$
$163$	17.9611	−	7.43971i	1.40682	−	0.582723i	0.951512	+	0.307611i	$0.0995296\pi$
$164$	−14.7790	+	3.20134i	−1.15404	+	0.249983i
$165$		0			0
$166$	10.8565	−	13.4600i	0.842629	−	1.04470i
$167$	−13.9383	−	13.9383i	−1.07858	−	1.07858i	−0.996637	−	0.0819391i	$-0.973889\pi$
$167$	−13.9383	−	13.9383i	−1.07858	−	1.07858i	−0.0819391	−	0.996637i	$-0.526111\pi$
$168$		0			0
$169$	0.473139	−	0.473139i	0.0363953	−	0.0363953i
$170$	0.104664	+	0.977565i	0.00802736	+	0.0749758i
$171$		0			0
$172$	−18.0988	+	12.5426i	−1.38002	+	0.956365i
$173$	1.06460	+	2.57018i	0.0809402	+	0.195407i	0.959169	−	0.282834i	$-0.0912746\pi$
$173$	1.06460	+	2.57018i	0.0809402	+	0.195407i	−0.878229	+	0.478241i	$0.841275\pi$
$174$		0			0
$175$	4.31128			0.325902
$176$	5.27664	−	0.179156i	0.397742	−	0.0135044i
$177$		0			0
$178$	2.08906	−	7.10312i	0.156582	−	0.532401i
$179$	14.3931	−	5.96183i	1.07579	−	0.445608i	0.226761	−	0.973950i	$-0.427186\pi$
$179$	14.3931	−	5.96183i	1.07579	−	0.445608i	0.849031	+	0.528342i	$0.177186\pi$
$180$		0			0
$181$	−2.56470	+	6.19174i	−0.190633	+	0.460229i	−0.990079	−	0.140509i	$-0.955126\pi$
$181$	−2.56470	+	6.19174i	−0.190633	+	0.460229i	0.799446	+	0.600737i	$0.205126\pi$
$182$	−0.486115	−	4.54033i	−0.0360332	−	0.336552i
$183$		0			0
$184$	11.6900	+	13.5270i	0.861798	+	0.997225i
$185$	1.21518	−	1.21518i	0.0893415	−	0.0893415i
$186$		0			0
$187$	1.39466	−	3.36700i	0.101988	−	0.246220i
$188$	19.4841	+	12.5459i	1.42103	+	0.915007i
$189$		0			0
$190$	0.155115	−	0.0846108i	0.0112533	−	0.00613831i
$191$	15.0419			1.08840			0.544198	−	0.838957i	$-0.316834\pi$
$191$	15.0419			1.08840			0.544198	+	0.838957i	$0.316834\pi$
$192$		0			0
$193$	−19.6537			−1.41470			−0.707352	−	0.706861i	$-0.750111\pi$
$193$	−19.6537			−1.41470			−0.707352	+	0.706861i	$0.750111\pi$
$194$	−17.4132	+	9.49838i	−1.25020	+	0.681944i
$195$		0			0
$196$	10.4884	+	6.75351i	0.749168	+	0.482394i
$197$	−3.28693	+	7.93534i	−0.234184	+	0.565370i	−0.996661	−	0.0816448i	$-0.973983\pi$
$197$	−3.28693	+	7.93534i	−0.234184	+	0.565370i	0.762478	+	0.647015i	$0.223983\pi$
$198$		0			0
$199$	14.6374	−	14.6374i	1.03761	−	1.03761i	0.0383500	−	0.999264i	$-0.487790\pi$
$199$	14.6374	−	14.6374i	1.03761	−	1.03761i	0.999264	−	0.0383500i	$-0.0122102\pi$
$200$	10.5645	−	9.12977i	0.747021	−	0.645572i
$201$		0			0
$202$	−1.67884	−	15.6804i	−0.118123	−	1.10327i
$203$	0.00365482	−	0.00882352i	0.000256518	−	0.000619290i
$204$		0			0
$205$	−1.75878	+	0.728511i	−0.122839	+	0.0508814i
$206$	4.70788	−	16.0075i	0.328014	−	1.11530i
$207$		0			0
$208$	−10.8060	−	10.0963i	−0.749263	−	0.700055i
$209$	−0.654971			−0.0453053
$210$		0			0
$211$	6.76173	+	16.3243i	0.465497	+	1.12381i	0.966108	+	0.258137i	$0.0831085\pi$
$211$	6.76173	+	16.3243i	0.465497	+	1.12381i	−0.500612	+	0.865672i	$0.666891\pi$
$212$	16.1017	−	11.1586i	1.10587	−	0.766379i
$213$		0			0
$214$	−0.505443	−	4.72086i	−0.0345514	−	0.322711i
$215$	−1.96019	+	1.96019i	−0.133684	+	0.133684i
$216$		0			0
$217$	2.49096	+	2.49096i	0.169097	+	0.169097i
$218$	7.69467	−	9.53991i	0.521149	−	0.646124i
$219$		0			0
$220$	0.649600	−	0.140713i	0.0437960	−	0.00948688i
$221$	−9.43118	+	3.90652i	−0.634410	+	0.262781i
$222$		0			0
$223$			15.8618i			1.06219i	0.847313	+	0.531093i	$0.178219\pi$
$223$			15.8618i			1.06219i	−0.847313	+	0.531093i	$0.821781\pi$
$224$	−4.89154	+	0.692314i	−0.326830	+	0.0462572i
$225$		0			0
$226$	−6.35803	+	3.46812i	−0.422930	+	0.230696i
$227$	2.50806	+	6.05500i	0.166466	+	0.401884i	0.984995	−	0.172580i	$-0.0552104\pi$
$227$	2.50806	+	6.05500i	0.166466	+	0.401884i	−0.818530	+	0.574464i	$0.805210\pi$
$228$		0			0
$229$	−7.60466	−	3.14995i	−0.502530	−	0.208155i	0.116994	−	0.993133i	$-0.462674\pi$
$229$	−7.60466	−	3.14995i	−0.502530	−	0.208155i	−0.619524	+	0.784978i	$0.712674\pi$
$230$	1.75189	+	1.41303i	0.115516	+	0.0931727i
$231$		0			0
$232$	−0.00972925	−	0.0293610i	−0.000638756	−	0.00192765i
$233$	5.99464	+	5.99464i	0.392722	+	0.392722i	0.875656	−	0.482935i	$-0.160429\pi$
$233$	5.99464	+	5.99464i	0.392722	+	0.392722i	−0.482935	+	0.875656i	$0.660429\pi$
$234$		0			0
$235$	2.69532	+	1.11644i	0.175824	+	0.0728285i
$236$	−1.67140	+	1.15830i	−0.108799	+	0.0753988i
$237$		0			0
$238$	−0.962188	+	3.27159i	−0.0623694	+	0.212065i
$239$			1.11236i			0.0719527i	0.999353	+	0.0359763i	$0.0114541\pi$
$239$			1.11236i			0.0719527i	−0.999353	+	0.0359763i	$0.988546\pi$
$240$		0			0
$241$			0.709331i			0.0456920i	0.999739	+	0.0228460i	$0.00727274\pi$
$241$			0.709331i			0.0456920i	−0.999739	+	0.0228460i	$0.992727\pi$
$242$	12.5606	+	3.69412i	0.807423	+	0.237467i
$243$		0			0
$244$	−15.2772	−	2.77020i	−0.978023	−	0.177344i
$245$	1.45090	+	0.600982i	0.0926946	+	0.0383953i
$246$		0			0
$247$	1.29727	+	1.29727i	0.0825432	+	0.0825432i
$248$	11.3789	+	0.828935i	0.722559	+	0.0526374i
$249$		0			0
$250$	2.22130	−	2.75399i	0.140488	−	0.174177i
$251$	−10.3657	−	4.29361i	−0.654276	−	0.271010i	0.0307514	−	0.999527i	$-0.490210\pi$
$251$	−10.3657	−	4.29361i	−0.654276	−	0.271010i	−0.685028	+	0.728517i	$0.740210\pi$
$252$		0			0
$253$	−3.19279	−	7.70808i	−0.200729	−	0.484603i
$254$	5.61115	+	10.2868i	0.352075	+	0.645452i
$255$		0			0
$256$	−10.5203	+	12.0550i	−0.657517	+	0.753439i
$257$			29.1264i			1.81686i	0.418042	+	0.908428i	$0.362716\pi$
$257$			29.1264i			1.81686i	−0.418042	+	0.908428i	$0.637284\pi$
$258$		0			0
$259$	5.50708	−	2.28111i	0.342194	−	0.141741i
$260$	−1.56533	−	1.00793i	−0.0970778	−	0.0625089i
$261$		0			0
$262$	−22.5010	−	18.1488i	−1.39011	−	1.12123i
$263$	1.87052	+	1.87052i	0.115341	+	0.115341i	0.762422	−	0.647080i	$-0.224010\pi$
$263$	1.87052	+	1.87052i	0.115341	+	0.115341i	−0.647080	+	0.762422i	$0.724010\pi$
$264$		0			0
$265$	1.74390	−	1.74390i	0.107127	−	0.107127i
$266$	0.609385	−	0.0652444i	0.0373638	−	0.00400039i
$267$		0			0
$268$	−2.85911	+	15.7676i	−0.174648	+	0.963157i
$269$	1.63828	+	3.95517i	0.0998879	+	0.241151i	0.965922	−	0.258835i	$-0.0833386\pi$
$269$	1.63828	+	3.95517i	0.0998879	+	0.241151i	−0.866034	+	0.499986i	$0.833339\pi$
$270$		0			0
$271$	0.865193			0.0525567			0.0262784	−	0.999655i	$-0.491634\pi$
$271$	0.865193			0.0525567			0.0262784	+	0.999655i	$0.491634\pi$
$272$	4.57030	+	10.0544i	0.277115	+	0.609635i
$273$		0			0
$274$	−25.7039	−	7.55964i	−1.55283	−	0.456695i
$275$	−6.01993	+	2.49354i	−0.363016	+	0.150366i
$276$		0			0
$277$	−10.8442	+	26.1801i	−0.651563	+	1.57301i	0.158948	+	0.987287i	$0.449190\pi$
$277$	−10.8442	+	26.1801i	−0.651563	+	1.57301i	−0.810510	+	0.585724i	$0.800810\pi$
$278$	−27.5419	+	2.94880i	−1.65185	+	0.176857i
$279$		0			0
$280$	−0.590371	+	0.195629i	−0.0352814	+	0.0116911i
$281$	−3.20552	+	3.20552i	−0.191225	+	0.191225i	−0.796225	−	0.605000i	$-0.793173\pi$
$281$	−3.20552	+	3.20552i	−0.191225	+	0.191225i	0.605000	+	0.796225i	$0.293173\pi$
$282$		0			0
$283$	−0.808604	+	1.95214i	−0.0480665	+	0.116043i	−0.946089	−	0.323907i	$-0.895004\pi$
$283$	−0.808604	+	1.95214i	−0.0480665	+	0.116043i	0.898023	+	0.439949i	$0.145004\pi$
$284$	3.34178	−	0.723879i	0.198298	−	0.0429543i
$285$		0			0
$286$	3.30479	+	6.05861i	0.195416	+	0.358253i
$287$	−6.60311			−0.389769
$288$		0			0
$289$	−9.37639			−0.551552
$290$	−0.00186466	−	0.00341845i	−0.000109497	−	0.000200738i
$291$		0			0
$292$	−2.23874	−	10.3351i	−0.131012	−	0.604816i
$293$	−2.84084	+	6.85839i	−0.165964	+	0.400671i	−0.984879	−	0.173242i	$-0.944576\pi$
$293$	−2.84084	+	6.85839i	−0.165964	+	0.400671i	0.818916	+	0.573914i	$0.194576\pi$
$294$		0			0
$295$	−0.181022	+	0.181022i	−0.0105395	+	0.0105395i
$296$	8.66412	−	17.2518i	0.503592	−	1.00274i
$297$		0			0
$298$	21.4513	−	2.29671i	1.24264	−	0.133045i
$299$	−8.94320	+	21.5908i	−0.517199	+	1.24863i
$300$		0			0
$301$	−8.88344	+	3.67964i	−0.512033	+	0.212091i
$302$	7.50701	+	2.20784i	0.431980	+	0.127047i
$303$		0			0
$304$	1.35509	−	1.45034i	0.0777197	−	0.0831827i
$305$	−1.95463			−0.111922
$306$		0			0
$307$	5.75328	+	13.8897i	0.328357	+	0.792724i	0.998715	+	0.0506860i	$0.0161408\pi$
$307$	5.75328	+	13.8897i	0.328357	+	0.792724i	−0.670357	+	0.742038i	$0.733859\pi$
$308$	2.26846	+	0.411336i	0.129257	+	0.0234381i
$309$		0			0
$310$	1.42813	−	0.152905i	0.0811126	−	0.00868440i
$311$	9.92757	−	9.92757i	0.562941	−	0.562941i	−0.367201	−	0.930142i	$-0.619684\pi$
$311$	9.92757	−	9.92757i	0.562941	−	0.562941i	0.930142	+	0.367201i	$0.119684\pi$
$312$		0			0
$313$	−6.07029	−	6.07029i	−0.343113	−	0.343113i	0.514423	−	0.857536i	$-0.328006\pi$
$313$	−6.07029	−	6.07029i	−0.343113	−	0.343113i	−0.857536	+	0.514423i	$0.828006\pi$
$314$	−21.2500	−	17.1398i	−1.19921	−	0.967254i
$315$		0			0
$316$	−7.81771	+	12.1411i	−0.439781	+	0.682990i
$317$	−28.8754	+	11.9606i	−1.62180	+	0.671773i	−0.994278	−	0.106823i	$-0.965932\pi$
$317$	−28.8754	+	11.9606i	−1.62180	+	0.671773i	−0.627525	+	0.778596i	$0.715932\pi$
$318$		0			0
$319$			0.0144343i			0.000808168i
$320$	−1.03239	+	1.72957i	−0.0577122	+	0.0966860i
$321$		0			0
$322$	3.73841	+	6.85355i	0.208333	+	0.381933i
$323$	−0.524318	−	1.26581i	−0.0291738	−	0.0704318i
$324$		0			0
$325$	16.8622	+	6.98455i	0.935346	+	0.387433i
$326$	17.2608	−	21.4001i	0.955987	−	1.18524i
$327$		0			0
$328$	−16.1804	+	13.9831i	−0.893415	+	0.772085i
$329$	7.15538	+	7.15538i	0.394489	+	0.394489i
$330$		0			0
$331$	13.5735	+	5.62233i	0.746067	+	0.309031i	0.723136	−	0.690706i	$-0.242700\pi$
$331$	13.5735	+	5.62233i	0.746067	+	0.309031i	0.0229312	+	0.999737i	$0.492700\pi$
$332$	4.36333	−	24.0631i	0.239469	−	1.32063i
$333$		0			0
$334$	−26.7439	−	7.86551i	−1.46336	−	0.430381i
$335$			2.01737i			0.110221i
$336$		0			0
$337$			7.22397i			0.393515i	0.980452	+	0.196757i	$0.0630411\pi$
$337$			7.22397i			0.393515i	−0.980452	+	0.196757i	$0.936959\pi$
$338$	0.266997	−	0.907830i	0.0145227	−	0.0493795i
$339$		0			0
$340$	0.791964	+	1.14279i	0.0429503	+	0.0619765i
$341$	−4.91889	−	2.03747i	−0.266373	−	0.110335i
$342$		0			0
$343$	8.17451	+	8.17451i	0.441382	+	0.441382i
$344$	−13.9760	+	27.8287i	−0.753537	+	1.50042i
$345$		0			0
$346$	3.06229	+	2.46997i	0.164630	+	0.132787i
$347$	−6.78836	−	2.81183i	−0.364418	−	0.150947i	0.192958	−	0.981207i	$-0.438192\pi$
$347$	−6.78836	−	2.81183i	−0.364418	−	0.150947i	−0.557376	+	0.830260i	$0.688192\pi$
$348$		0			0
$349$	0.0989263	+	0.238829i	0.00529540	+	0.0127842i	0.926505	−	0.376282i	$-0.122798\pi$
$349$	0.0989263	+	0.238829i	0.00529540	+	0.0127842i	−0.921210	+	0.389066i	$0.872798\pi$
$350$	5.35255	−	2.91966i	0.286106	−	0.156062i
$351$		0			0
$352$	6.42975	−	3.79584i	0.342707	−	0.202319i
$353$			1.04908i			0.0558369i	0.999610	+	0.0279184i	$0.00888787\pi$
$353$			1.04908i			0.0558369i	−0.999610	+	0.0279184i	$0.991112\pi$
$354$		0			0
$355$	0.397691	−	0.164729i	0.0211072	−	0.00874290i
$356$	−2.21671	−	10.2334i	−0.117486	−	0.542371i
$357$		0			0
$358$	13.8320	−	17.1490i	0.731043	−	0.906352i
$359$	−10.9586	−	10.9586i	−0.578375	−	0.578375i	0.356080	−	0.934455i	$-0.384113\pi$
$359$	−10.9586	−	10.9586i	−0.578375	−	0.578375i	−0.934455	+	0.356080i	$0.884113\pi$
$360$		0			0
$361$	13.2609	−	13.2609i	0.697943	−	0.697943i
$362$	1.00900	+	9.42405i	0.0530316	+	0.495317i
$363$		0			0
$364$	−3.67830	−	5.30773i	−0.192795	−	0.278200i
$365$	−0.509456	−	1.22994i	−0.0266662	−	0.0643778i
$366$		0			0
$367$	−14.0919			−0.735589			−0.367795	−	0.929907i	$-0.619887\pi$
$367$	−14.0919			−0.735589			−0.367795	+	0.929907i	$0.619887\pi$
$368$	23.6741	+	8.87748i	1.23410	+	0.462771i
$369$		0			0
$370$	0.685736	−	2.33160i	0.0356497	−	0.121214i
$371$	7.90323	−	3.27363i	0.410315	−	0.169958i
$372$		0			0
$373$	0.973904	−	2.35121i	0.0504268	−	0.121741i	−0.896659	−	0.442723i	$-0.854013\pi$
$373$	0.973904	−	2.35121i	0.0504268	−	0.121741i	0.947086	+	0.320981i	$0.104013\pi$
$374$	−0.548681	−	5.12470i	−0.0283716	−	0.264992i
$375$		0			0
$376$	32.6863	+	2.38115i	1.68567	+	0.122798i
$377$	0.0285894	−	0.0285894i	0.00147243	−	0.00147243i
$378$		0			0
$379$	7.22577	−	17.4446i	0.371163	−	0.896067i	−0.622391	−	0.782707i	$-0.713839\pi$
$379$	7.22577	−	17.4446i	0.371163	−	0.896067i	0.993554	−	0.113360i	$-0.0361615\pi$
$380$	0.135280	−	0.210093i	0.00693971	−	0.0107775i
$381$		0			0
$382$	18.6749	−	10.1866i	0.955491	−	0.521192i
$383$	4.91841			0.251319			0.125660	−	0.992073i	$-0.459895\pi$
$383$	4.91841			0.251319			0.125660	+	0.992073i	$0.459895\pi$
$384$		0			0
$385$	0.290236			0.0147918
$386$	−24.4005	+	13.3098i	−1.24196	+	0.677449i
$387$		0			0
$388$	−15.1865	+	23.5849i	−0.770976	+	1.19734i
$389$	6.57039	−	15.8623i	0.333132	−	0.804252i	−0.665208	−	0.746658i	$-0.731657\pi$
$389$	6.57039	−	15.8623i	0.333132	−	0.804252i	0.998340	−	0.0575939i	$-0.0183429\pi$
$390$		0			0
$391$	12.3409	−	12.3409i	0.624108	−	0.624108i
$392$	17.5951	+	1.28178i	0.888688	+	0.0647396i
$393$		0			0
$394$	1.29313	+	12.0779i	0.0651469	+	0.608474i
$395$	−0.695683	+	1.67953i	−0.0350036	+	0.0845062i
$396$		0			0
$397$	1.49381	−	0.618757i	0.0749723	−	0.0310545i	−0.344882	−	0.938646i	$-0.612081\pi$
$397$	1.49381	−	0.618757i	0.0749723	−	0.0310545i	0.419854	+	0.907591i	$0.362081\pi$
$398$	8.26000	−	28.0852i	0.414036	−	1.40779i
$399$		0			0
$400$	6.93323	−	18.4892i	0.346661	−	0.924461i
$401$	29.8271			1.48949			0.744747	−	0.667347i	$-0.232570\pi$
$401$	29.8271			1.48949			0.744747	+	0.667347i	$0.232570\pi$
$402$		0			0
$403$	5.70708	+	13.7781i	0.284290	+	0.686336i
$404$	−12.7033	−	18.3307i	−0.632014	−	0.911985i
$405$		0			0
$406$	−0.00143786	−	0.0134297i	−7.13600e−5	−	0.000666505i
$407$	−6.37033	+	6.37033i	−0.315765	+	0.315765i
$408$		0			0
$409$	9.09883	+	9.09883i	0.449908	+	0.449908i	0.895324	−	0.445416i	$-0.146944\pi$
$409$	9.09883	+	9.09883i	0.449908	+	0.449908i	−0.445416	+	0.895324i	$0.646944\pi$
$410$	−1.69021	+	2.09553i	−0.0834735	+	0.103491i
$411$		0			0
$412$	−4.99557	−	23.0620i	−0.246114	−	1.13618i
$413$	−0.820377	+	0.339811i	−0.0403681	+	0.0167210i
$414$		0			0
$415$		−	3.07873i		−	0.151129i
$416$	−20.2533	−	5.21684i	−0.993000	−	0.255777i
$417$		0			0
$418$	−0.813163	+	0.443556i	−0.0397731	+	0.0216950i
$419$	3.94681	+	9.52845i	0.192814	+	0.465495i	0.990489	−	0.137593i	$-0.0439366\pi$
$419$	3.94681	+	9.52845i	0.192814	+	0.465495i	−0.797674	+	0.603088i	$0.793937\pi$
$420$		0			0
$421$	2.91334	+	1.20674i	0.141987	+	0.0588131i	0.452546	−	0.891741i	$-0.350516\pi$
$421$	2.91334	+	1.20674i	0.141987	+	0.0588131i	−0.310558	+	0.950554i	$0.600516\pi$
$422$	19.4499	+	15.6878i	0.946805	+	0.763671i
$423$		0			0
$424$	12.4339	−	24.7580i	0.603843	−	1.20236i
$425$	−9.63815	−	9.63815i	−0.467519	−	0.467519i
$426$		0			0
$427$	−6.26371	−	2.59451i	−0.303122	−	0.125557i
$428$	−3.82455	−	5.51877i	−0.184867	−	0.266760i
$429$		0			0
$430$	−1.10616	+	3.76110i	−0.0533436	+	0.181376i
$431$		−	23.1792i		−	1.11650i	−0.829672	−	0.558252i	$-0.811472\pi$
$431$		−	23.1792i		−	1.11650i	0.829672	−	0.558252i	$-0.188528\pi$
$432$		0			0
$433$		−	25.2987i		−	1.21578i	−0.794023	−	0.607888i	$-0.792017\pi$
$433$		−	25.2987i		−	1.21578i	0.794023	−	0.607888i	$-0.207983\pi$
$434$	4.77949	+	1.40567i	0.229423	+	0.0674743i
$435$		0			0
$436$	3.09256	−	17.0550i	0.148107	−	0.816785i
$437$	−2.89783	−	1.20032i	−0.138622	−	0.0574191i
$438$		0			0
$439$	−28.3833	−	28.3833i	−1.35466	−	1.35466i	−0.880365	−	0.474297i	$-0.842702\pi$
$439$	−28.3833	−	28.3833i	−1.35466	−	1.35466i	−0.474297	−	0.880365i	$-0.657298\pi$
$440$	0.711201	−	0.614617i	0.0339052	−	0.0293007i
$441$		0			0
$442$	−9.06348	+	11.2370i	−0.431106	+	0.534488i
$443$	19.8722	+	8.23132i	0.944155	+	0.391082i	0.801031	−	0.598623i	$-0.204285\pi$
$443$	19.8722	+	8.23132i	0.944155	+	0.391082i	0.143124	+	0.989705i	$0.454285\pi$
$444$		0			0
$445$	−0.504444	−	1.21784i	−0.0239130	−	0.0577310i
$446$	10.7419	+	19.6928i	0.508642	+	0.932483i
$447$		0			0
$448$	−5.60412	+	4.17214i	−0.264770	+	0.197115i
$449$		−	12.5843i		−	0.593889i	−0.954895	−	0.296944i	$-0.904032\pi$
$449$		−	12.5843i		−	0.593889i	0.954895	−	0.296944i	$-0.0959676\pi$
$450$		0			0
$451$	9.22007	−	3.81908i	0.434156	−	0.179833i
$452$	−5.54499	+	8.61150i	−0.260814	+	0.405051i
$453$		0			0
$454$	7.21435	+	5.81893i	0.338586	+	0.273096i
$455$	−0.574855	−	0.574855i	−0.0269496	−	0.0269496i
$456$		0			0
$457$	8.93449	−	8.93449i	0.417938	−	0.417938i	−0.466554	−	0.884492i	$-0.654505\pi$
$457$	8.93449	−	8.93449i	0.417938	−	0.417938i	0.884492	+	0.466554i	$0.154505\pi$
$458$	−11.5746	+	1.23924i	−0.540844	+	0.0579060i
$459$		0			0
$460$	3.13194	+	0.567911i	0.146027	+	0.0264790i
$461$	−12.9213	−	31.1949i	−0.601807	−	1.45289i	−0.871720	−	0.490005i	$-0.836995\pi$
$461$	−12.9213	−	31.1949i	−0.601807	−	1.45289i	0.269913	−	0.962885i	$-0.413005\pi$
$462$		0			0
$463$	−1.78637			−0.0830196			−0.0415098	−	0.999138i	$-0.513217\pi$
$463$	−1.78637			−0.0830196			−0.0415098	+	0.999138i	$0.513217\pi$
$464$	−0.0319628	−	0.0298636i	−0.00148384	−	0.00138638i
$465$		0			0
$466$	11.5021	+	3.38283i	0.532826	+	0.156707i
$467$	−37.9374	+	15.7142i	−1.75553	+	0.727166i	−0.758376	+	0.651818i	$0.774007\pi$
$467$	−37.9374	+	15.7142i	−1.75553	+	0.727166i	−0.997157	+	0.0753479i	$0.975993\pi$
$468$		0			0
$469$	−2.67779	+	6.46476i	−0.123649	+	0.298515i
$470$	4.10238	−	0.439225i	0.189229	−	0.0202599i
$471$		0			0
$472$	−1.29067	+	2.56995i	−0.0594080	+	0.118292i
$473$	10.2759	−	10.2759i	0.472488	−	0.472488i
$474$		0			0
$475$	−0.937438	+	2.26318i	−0.0430126	+	0.103842i
$476$	1.02098	+	4.71336i	0.0467967	+	0.216036i
$477$		0			0
$478$	0.753307	+	1.38102i	0.0344555	+	0.0631665i
$479$	30.3196			1.38534			0.692669	−	0.721256i	$-0.256435\pi$
$479$	30.3196			1.38534			0.692669	+	0.721256i	$0.256435\pi$
$480$		0			0
$481$	25.2348			1.15061
$482$	0.480369	+	0.880651i	0.0218802	+	0.0401126i
$483$		0			0
$484$	18.0959	−	3.91985i	0.822542	−	0.178175i
$485$	−1.35142	+	3.26260i	−0.0613646	+	0.148147i
$486$		0			0
$487$	−23.2907	+	23.2907i	−1.05540	+	1.05540i	−0.0570287	+	0.998373i	$0.518163\pi$
$487$	−23.2907	+	23.2907i	−1.05540	+	1.05540i	−0.998373	+	0.0570287i	$0.981837\pi$
$488$	−20.8430	+	6.90668i	−0.943520	+	0.312651i
$489$		0			0
$490$	2.20832	−	0.236436i	0.0997617	−	0.0106811i
$491$	−4.68275	+	11.3052i	−0.211330	+	0.510195i	−0.993628	−	0.112709i	$-0.964047\pi$
$491$	−4.68275	+	11.3052i	−0.211330	+	0.510195i	0.782298	+	0.622904i	$0.214047\pi$
$492$		0			0
$493$	−0.0278962	+	0.0115550i	−0.00125638	+	0.000520410i
$494$	2.48912	+	0.732061i	0.111991	+	0.0329370i
$495$		0			0
$496$	14.6885	−	6.67679i	0.659533	−	0.299797i
$497$	1.49308			0.0669736
$498$		0			0
$499$	−8.69892	−	21.0011i	−0.389417	−	0.940136i	−0.990063	−	0.140621i	$-0.955090\pi$
$499$	−8.69892	−	21.0011i	−0.389417	−	0.940136i	0.600646	−	0.799515i	$-0.294910\pi$
$500$	0.892761	−	4.92344i	0.0399255	−	0.220183i
$501$		0			0
$502$	−15.7769	+	1.68917i	−0.704159	+	0.0753915i
$503$	27.4548	−	27.4548i	1.22415	−	1.22415i	0.258004	−	0.966144i	$-0.416935\pi$
$503$	27.4548	−	27.4548i	1.22415	−	1.22415i	0.966144	−	0.258004i	$-0.0830649\pi$
$504$		0			0
$505$	−1.98531	−	1.98531i	−0.0883451	−	0.0883451i
$506$	−9.18395	−	7.40756i	−0.408276	−	0.329306i
$507$		0			0
$508$	13.9328	+	8.97138i	0.618166	+	0.398041i
$509$	16.5641	−	6.86109i	0.734193	−	0.304113i	0.0159191	−	0.999873i	$-0.494933\pi$
$509$	16.5641	−	6.86109i	0.734193	−	0.304113i	0.718274	+	0.695761i	$0.244933\pi$
$510$		0			0
$511$		−	4.61763i		−	0.204272i
$512$	−4.89734	+	22.0911i	−0.216434	+	0.976297i
$513$		0			0
$514$	19.7248	+	36.1611i	0.870024	+	1.59500i
$515$	−1.13681	−	2.74451i	−0.0500939	−	0.120937i
$516$		0			0
$517$	−14.1297	−	5.85272i	−0.621424	−	0.257402i
$518$	5.29238	−	6.56152i	0.232534	−	0.288297i
$519$		0			0
$520$	−2.62598	−	0.191299i	−0.115157	−	0.00838901i
$521$	24.2903	+	24.2903i	1.06418	+	1.06418i	0.997794	+	0.0663854i	$0.0211467\pi$
$521$	24.2903	+	24.2903i	1.06418	+	1.06418i	0.0663854	+	0.997794i	$0.478853\pi$
$522$		0			0
$523$	3.09598	+	1.28240i	0.135378	+	0.0560753i	0.449344	−	0.893359i	$-0.351658\pi$
$523$	3.09598	+	1.28240i	0.135378	+	0.0560753i	−0.313966	+	0.949434i	$0.601658\pi$
$524$	−40.2261	−	7.29415i	−1.75728	−	0.318646i
$525$		0			0
$526$	3.58904	+	1.05555i	0.156490	+	0.0460243i
$527$		−	11.1374i		−	0.485153i
$528$		0			0
$529$		−	16.9545i		−	0.737153i
$530$	0.984101	−	3.34609i	0.0427466	−	0.145345i
$531$		0			0
$532$	0.712382	−	0.493687i	0.0308857	−	0.0214040i
$533$	−25.8260	−	10.6975i	−1.11865	−	0.463359i
$534$		0			0
$535$	−0.597711	−	0.597711i	−0.0258413	−	0.0258413i
$536$	7.12836	+	21.5120i	0.307898	+	0.929178i
$537$		0			0
$538$	4.71246	+	3.80096i	0.203169	+	0.163871i
$539$	−7.60606	−	3.15053i	−0.327616	−	0.135703i
$540$		0			0
$541$	12.7340	+	30.7426i	0.547477	+	1.32173i	0.919349	+	0.393443i	$0.128716\pi$
$541$	12.7340	+	30.7426i	0.547477	+	1.32173i	−0.371872	+	0.928284i	$0.621284\pi$
$542$	1.07416	−	0.585921i	0.0461390	−	0.0251675i
$543$		0			0
$544$	12.4831	+	9.38765i	0.535208	+	0.402492i
$545$		−	2.18208i		−	0.0934701i
$546$		0			0
$547$	1.08569	−	0.449709i	0.0464209	−	0.0192282i	−0.359352	−	0.933202i	$-0.617002\pi$
$547$	1.08569	−	0.449709i	0.0464209	−	0.0192282i	0.405773	+	0.913974i	$0.367002\pi$
$548$	−37.0315	+	8.02158i	−1.58191	+	0.342665i
$549$		0			0
$550$	−5.78523	+	7.17257i	−0.246683	+	0.305839i
$551$	0.00383715	+	0.00383715i	0.000163468	+	0.000163468i
$552$		0			0
$553$	−4.45871	+	4.45871i	−0.189604	+	0.189604i
$554$	4.26626	+	39.8471i	0.181256	+	1.69294i
$555$		0			0
$556$	−32.1970	+	22.3128i	−1.36546	+	0.946272i
$557$	−9.36569	−	22.6108i	−0.396837	−	0.958049i	−0.988411	−	0.151799i	$-0.951493\pi$
$557$	−9.36569	−	22.6108i	−0.396837	−	0.958049i	0.591574	−	0.806250i	$-0.298507\pi$
$558$		0			0
$559$	−40.7060			−1.72168
$560$	−0.600477	+	0.642685i	−0.0253748	+	0.0271584i
$561$		0			0
$562$	−1.80890	+	6.15055i	−0.0763040	+	0.259445i
$563$	25.1131	−	10.4022i	1.05839	−	0.438400i	0.215511	−	0.976501i	$-0.430858\pi$
$563$	25.1131	−	10.4022i	1.05839	−	0.438400i	0.842880	+	0.538101i	$0.180858\pi$
$564$		0			0
$565$	−0.493438	+	1.19126i	−0.0207591	+	0.0501169i
$566$	0.318118	+	2.97123i	0.0133715	+	0.124890i
$567$		0			0
$568$	3.65867	−	3.16181i	0.153515	−	0.132667i
$569$	21.7622	−	21.7622i	0.912319	−	0.912319i	−0.0841358	−	0.996454i	$-0.526813\pi$
$569$	21.7622	−	21.7622i	0.912319	−	0.912319i	0.996454	+	0.0841358i	$0.0268129\pi$
$570$		0			0
$571$	−12.7421	+	30.7622i	−0.533241	+	1.28736i	0.396124	+	0.918197i	$0.370355\pi$
$571$	−12.7421	+	30.7622i	−0.533241	+	1.28736i	−0.929365	+	0.369161i	$0.879645\pi$
$572$	8.20596	+	5.28386i	0.343108	+	0.220929i
$573$		0			0
$574$	−8.19791	+	4.47172i	−0.342174	+	0.186646i
$575$	−31.2041			−1.30130
$576$		0			0
$577$	9.17163			0.381820			0.190910	−	0.981608i	$-0.438856\pi$
$577$	9.17163			0.381820			0.190910	+	0.981608i	$0.438856\pi$
$578$	−11.6410	+	6.34982i	−0.484202	+	0.264118i
$579$		0			0
$580$	−0.00463005	−	0.00298131i	−0.000192252	−	0.000123792i
$581$	4.08661	−	9.86595i	0.169541	−	0.409308i
$582$		0			0
$583$	−9.14208	+	9.14208i	−0.378626	+	0.378626i
$584$	−9.77852	−	11.3152i	−0.404638	−	0.468225i
$585$		0			0
$586$	1.11763	+	10.4387i	0.0461689	+	0.431219i
$587$	−10.6350	+	25.6751i	−0.438953	+	1.05973i	0.537359	+	0.843354i	$0.319422\pi$
$587$	−10.6350	+	25.6751i	−0.438953	+	1.05973i	−0.976311	+	0.216371i	$0.930578\pi$
$588$		0			0
$589$	−1.84924	+	0.765981i	−0.0761966	+	0.0315617i
$590$	−0.102152	+	0.347334i	−0.00420555	+	0.0142995i
$591$		0			0
$592$	−0.926427	−	27.2859i	−0.0380759	−	1.12144i
$593$	−10.8973			−0.447497			−0.223748	−	0.974647i	$-0.571829\pi$
$593$	−10.8973			−0.447497			−0.223748	+	0.974647i	$0.571829\pi$
$594$		0			0
$595$	0.232339	+	0.560917i	0.00952498	+	0.0229953i
$596$	25.0770	−	17.3786i	1.02719	−	0.711853i
$597$		0			0
$598$	3.51840	+	32.8619i	0.143878	+	1.34382i
$599$	−7.15470	+	7.15470i	−0.292333	+	0.292333i	−0.838001	−	0.545668i	$-0.816276\pi$
$599$	−7.15470	+	7.15470i	−0.292333	+	0.292333i	0.545668	+	0.838001i	$0.316276\pi$
$600$		0			0
$601$	−16.0354	−	16.0354i	−0.654098	−	0.654098i	0.299879	−	0.953977i	$-0.403054\pi$
$601$	−16.0354	−	16.0354i	−0.654098	−	0.654098i	−0.953977	+	0.299879i	$0.903054\pi$
$602$	−8.53710	+	10.5844i	−0.347946	+	0.431386i
$603$		0			0
$604$	10.8153	−	2.34276i	0.440069	−	0.0953255i
$605$	2.15352	−	0.892017i	0.0875530	−	0.0362657i
$606$		0			0
$607$		−	26.1378i		−	1.06090i	−0.847716	−	0.530450i	$-0.822023\pi$
$607$		−	26.1378i		−	1.06090i	0.847716	−	0.530450i	$-0.177977\pi$
$608$	0.700184	−	2.71832i	0.0283962	−	0.110242i
$609$		0			0
$610$	−2.42672	+	1.32370i	−0.0982550	+	0.0535952i
$611$	16.3938	+	39.5782i	0.663223	+	1.60116i
$612$		0			0
$613$	−0.264513	−	0.109565i	−0.0106836	−	0.00442529i	0.377335	−	0.926077i	$-0.376840\pi$
$613$	−0.264513	−	0.109565i	−0.0106836	−	0.00442529i	−0.388019	+	0.921651i	$0.626840\pi$
$614$	16.5491	+	13.3481i	0.667867	+	0.538687i
$615$		0			0
$616$	3.09490	−	1.02555i	0.124697	−	0.0413204i
$617$	9.11322	+	9.11322i	0.366884	+	0.366884i	0.866340	−	0.499455i	$-0.166467\pi$
$617$	9.11322	+	9.11322i	0.366884	+	0.366884i	−0.499455	+	0.866340i	$0.666467\pi$
$618$		0			0
$619$	−4.31772	−	1.78846i	−0.173544	−	0.0718842i	0.294220	−	0.955738i	$-0.404940\pi$
$619$	−4.31772	−	1.78846i	−0.173544	−	0.0718842i	−0.467764	+	0.883854i	$0.654940\pi$
$620$	1.66951	−	1.15699i	0.0670493	−	0.0464657i
$621$		0			0
$622$	5.60223	−	19.0484i	0.224629	−	0.763772i
$623$		−	4.57221i		−	0.183182i
$624$		0			0
$625$			24.0531i			0.962124i
$626$	−11.6473	−	3.42552i	−0.465519	−	0.136911i
$627$		0			0
$628$	−37.9897	−	6.88863i	−1.51595	−	0.274886i
$629$	−17.4110	−	7.21189i	−0.694223	−	0.287557i
$630$		0			0
$631$	−24.3839	−	24.3839i	−0.970707	−	0.970707i	0.0288764	−	0.999583i	$-0.490807\pi$
$631$	−24.3839	−	24.3839i	−0.970707	−	0.970707i	−0.999583	+	0.0288764i	$0.990807\pi$
$632$	−1.48376	+	20.3677i	−0.0590208	+	0.810184i
$633$		0			0
$634$	−27.7496	+	34.4042i	−1.10208	+	1.36636i
$635$	1.92738	+	0.798346i	0.0764856	+	0.0316814i
$636$		0			0
$637$	8.82483	+	21.3050i	0.349653	+	0.844136i
$638$	0.00977514	+	0.0179206i	0.000387002	+	0.000709483i
$639$		0			0
$640$	−0.110442	+	2.84645i	−0.00436562	+	0.112516i
$641$		−	8.45729i		−	0.334043i	−0.985953	−	0.167022i	$-0.946585\pi$
$641$		−	8.45729i		−	0.334043i	0.985953	−	0.167022i	$-0.0534149\pi$
$642$		0			0
$643$	−34.7117	+	14.3781i	−1.36890	+	0.567015i	−0.941489	−	0.337044i	$-0.890573\pi$
$643$	−34.7117	+	14.3781i	−1.36890	+	0.567015i	−0.427407	+	0.904059i	$0.640573\pi$
$644$	9.28264	+	5.97714i	0.365787	+	0.235532i
$645$		0			0
$646$	−1.50818	−	1.21646i	−0.0593385	−	0.0478611i
$647$	26.4083	+	26.4083i	1.03822	+	1.03822i	0.999240	+	0.0389780i	$0.0124102\pi$
$647$	26.4083	+	26.4083i	1.03822	+	1.03822i	0.0389780	+	0.999240i	$0.487590\pi$
$648$		0			0
$649$	0.948973	−	0.948973i	0.0372504	−	0.0372504i
$650$	25.6648	−	2.74783i	1.00666	−	0.107779i
$651$		0			0
$652$	6.93727	−	38.2579i	0.271684	−	1.49830i
$653$	11.3223	+	27.3345i	0.443076	+	1.06968i	0.974864	+	0.222802i	$0.0715205\pi$
$653$	11.3223	+	27.3345i	0.443076	+	1.06968i	−0.531788	+	0.846878i	$0.678480\pi$
$654$		0			0
$655$	−5.14669			−0.201098
$656$	−10.6189	+	28.3179i	−0.414597	+	1.10563i
$657$		0			0
$658$	13.7293	+	4.03785i	0.535224	+	0.157412i
$659$	−35.5774	+	14.7366i	−1.38590	+	0.574058i	−0.946052	−	0.324015i	$-0.894967\pi$
$659$	−35.5774	+	14.7366i	−1.38590	+	0.574058i	−0.439847	+	0.898073i	$0.644967\pi$
$660$		0			0
$661$	11.9242	−	28.7874i	0.463796	−	1.11970i	−0.503031	−	0.864268i	$-0.667782\pi$
$661$	11.9242	−	28.7874i	0.463796	−	1.11970i	0.966827	−	0.255434i	$-0.0822182\pi$
$662$	20.6593	−	2.21191i	0.802948	−	0.0859684i
$663$		0			0
$664$	−10.8787	−	32.8298i	−0.422174	−	1.27404i
$665$	0.0771547	−	0.0771547i	0.00299193	−	0.00299193i
$666$		0			0
$667$	−0.0264528	+	0.0638627i	−0.00102426	+	0.00247278i
$668$	−38.5298	+	8.34614i	−1.49076	+	0.322922i
$669$		0			0
$670$	1.36619	+	2.50461i	0.0527805	+	0.0967615i
$671$	10.2468			0.395572
$672$		0			0
$673$	4.89312			0.188616			0.0943080	−	0.995543i	$-0.469936\pi$
$673$	4.89312			0.188616			0.0943080	+	0.995543i	$0.469936\pi$
$674$	4.89217	+	8.96873i	0.188439	+	0.345463i
$675$		0			0
$676$	−0.283312	−	1.30791i	−0.0108966	−	0.0503041i
$677$	3.36496	−	8.12372i	0.129326	−	0.312220i	−0.845932	−	0.533291i	$-0.820955\pi$
$677$	3.36496	−	8.12372i	0.129326	−	0.312220i	0.975258	+	0.221071i	$0.0709552\pi$
$678$		0			0
$679$	−8.66136	+	8.66136i	−0.332392	+	0.332392i
$680$	1.75716	+	0.882472i	0.0673838	+	0.0338413i
$681$		0			0
$682$	−7.48672	+	0.801573i	−0.286681	+	0.0306938i
$683$	13.0545	−	31.5165i	0.499518	−	1.20594i	−0.450225	−	0.892915i	$-0.648656\pi$
$683$	13.0545	−	31.5165i	0.499518	−	1.20594i	0.949744	−	0.313029i	$-0.101344\pi$
$684$		0			0
$685$	−4.40696	+	1.82542i	−0.168381	+	0.0697459i
$686$	15.6847	+	4.61295i	0.598846	+	0.176123i
$687$		0			0
$688$	1.49441	+	44.0148i	0.0569740	+	1.67805i
$689$	36.2145			1.37966
$690$		0			0
$691$	−13.7784	−	33.2640i	−0.524155	−	1.26542i	−0.935301	−	0.353853i	$-0.884871\pi$
$691$	−13.7784	−	33.2640i	−0.524155	−	1.26542i	0.411146	−	0.911569i	$-0.365129\pi$
$692$	5.47460	+	0.992703i	0.208113	+	0.0377369i
$693$		0			0
$694$	−10.3321	+	1.10622i	−0.392202	+	0.0419915i
$695$	−3.48710	+	3.48710i	−0.132273	+	0.132273i
$696$		0			0
$697$	14.7617	+	14.7617i	0.559139	+	0.559139i
$698$	0.284558	+	0.229518i	0.0107707	+	0.00868738i
$699$		0			0
$700$	4.66809	−	7.24965i	0.176437	−	0.274011i
$701$	19.9772	−	8.27483i	0.754529	−	0.312536i	0.0279411	−	0.999610i	$-0.491105\pi$
$701$	19.9772	−	8.27483i	0.754529	−	0.312536i	0.726588	+	0.687073i	$0.241105\pi$
$702$		0			0
$703$			3.38691i			0.127740i
$704$	5.41209	−	9.06695i	0.203976	−	0.341723i
$705$		0			0
$706$	0.710452	+	1.30246i	0.0267382	+	0.0490186i
$707$	−3.72679	−	8.99726i	−0.140160	−	0.338377i
$708$		0			0
$709$	16.4355	+	6.80779i	0.617246	+	0.255672i	0.669323	−	0.742971i	$-0.266584\pi$
$709$	16.4355	+	6.80779i	0.617246	+	0.255672i	−0.0520769	+	0.998643i	$0.516584\pi$
$710$	0.382186	−	0.473837i	0.0143432	−	0.0177828i
$711$		0			0
$712$	−9.68232	−	11.2039i	−0.362860	−	0.419882i
$713$	−18.0290	−	18.0290i	−0.675191	−	0.675191i
$714$		0			0
$715$	1.13516	+	0.470201i	0.0424528	+	0.0175845i
$716$	5.55919	−	30.6581i	0.207757	−	1.14575i
$717$		0			0
$718$	−21.0268	−	6.18407i	−0.784712	−	0.230787i
$719$			13.9143i			0.518917i	0.965754	+	0.259458i	$0.0835440\pi$
$719$			13.9143i			0.518917i	−0.965754	+	0.259458i	$0.916456\pi$
$720$		0			0
$721$		−	10.3039i		−	0.383736i
$722$	7.48326	−	25.4442i	0.278498	−	0.946936i
$723$		0			0
$724$	7.63479	+	11.0169i	0.283745	+	0.409439i
$725$	0.0498762	+	0.0206594i	0.00185235	+	0.000767270i
$726$		0			0
$727$	21.4548	+	21.4548i	0.795713	+	0.795713i	0.982416	−	0.186703i	$-0.0597803\pi$
$727$	21.4548	+	21.4548i	0.795713	+	0.795713i	−0.186703	+	0.982416i	$0.559780\pi$
$728$	−8.16116	−	4.09867i	−0.302473	−	0.151907i
$729$		0			0
$730$	−1.46543	−	1.18198i	−0.0542381	−	0.0437472i
$731$	28.0856	+	11.6334i	1.03878	+	0.430279i
$732$		0			0
$733$	−6.82805	−	16.4844i	−0.252200	−	0.608864i	0.746181	−	0.665743i	$-0.231885\pi$
$733$	−6.82805	−	16.4844i	−0.252200	−	0.608864i	−0.998381	+	0.0568787i	$0.981885\pi$
$734$	−17.4954	+	9.54320i	−0.645766	+	0.352246i
$735$		0			0
$736$	35.4039	−	5.01082i	1.30501	−	0.184701i
$737$		−	10.5757i		−	0.389559i
$738$		0			0
$739$	6.45405	−	2.67336i	0.237416	−	0.0983410i	−0.260803	−	0.965392i	$-0.583987\pi$
$739$	6.45405	−	2.67336i	0.237416	−	0.0983410i	0.498219	+	0.867051i	$0.333987\pi$
$740$	−0.727639	−	3.35913i	−0.0267485	−	0.123484i
$741$		0			0
$742$	7.59510	−	9.41646i	0.278825	−	0.345689i
$743$	−15.5864	−	15.5864i	−0.571811	−	0.571811i	0.360823	−	0.932634i	$-0.382496\pi$
$743$	−15.5864	−	15.5864i	−0.571811	−	0.571811i	−0.932634	+	0.360823i	$0.882496\pi$
$744$		0			0
$745$	2.71597	−	2.71597i	0.0995053	−	0.0995053i
$746$	−0.383149	−	3.57863i	−0.0140281	−	0.131023i
$747$		0			0
$748$	−4.15172	−	5.99086i	−0.151802	−	0.219047i
$749$	−1.12201	−	2.70878i	−0.0409975	−	0.0989767i
$750$		0			0
$751$	42.0270			1.53359			0.766793	−	0.641894i	$-0.221851\pi$
$751$	42.0270			1.53359			0.766793	+	0.641894i	$0.221851\pi$
$752$	42.1934	−	19.1794i	1.53863	−	0.699400i
$753$		0			0
$754$	0.0161333	−	0.0548555i	0.000587538	−	0.00199772i
$755$	1.28708	−	0.533128i	0.0468418	−	0.0194025i
$756$		0			0
$757$	−7.05779	+	17.0390i	−0.256520	+	0.619294i	−0.998704	−	0.0509027i	$-0.983790\pi$
$757$	−7.05779	+	17.0390i	−0.256520	+	0.619294i	0.742184	+	0.670196i	$0.233790\pi$
$758$	−2.84273	−	26.5512i	−0.103253	−	0.964384i
$759$		0			0
$760$	0.0256754	−	0.352448i	0.000931343	−	0.0127846i
$761$	−26.7062	+	26.7062i	−0.968098	+	0.968098i	−0.999507	−	0.0314086i	$-0.990001\pi$
$761$	−26.7062	+	26.7062i	−0.968098	+	0.968098i	0.0314086	+	0.999507i	$0.490001\pi$
$762$		0			0
$763$	2.89643	−	6.99260i	0.104858	−	0.253149i
$764$	16.2868	−	25.2938i	0.589237	−	0.915098i
$765$		0			0
$766$	6.10632	−	3.33082i	0.220630	−	0.120347i
$767$	−3.75916			−0.135735
$768$		0			0
$769$	44.3834			1.60051			0.800253	−	0.599662i	$-0.204698\pi$
$769$	44.3834			1.60051			0.800253	+	0.599662i	$0.204698\pi$
$770$	0.360334	−	0.196552i	0.0129856	−	0.00708323i
$771$		0			0
$772$	−21.2803	+	33.0488i	−0.765894	+	1.18945i
$773$	−14.1152	+	34.0770i	−0.507687	+	1.22566i	0.437525	+	0.899206i	$0.355855\pi$
$773$	−14.1152	+	34.0770i	−0.507687	+	1.22566i	−0.945212	+	0.326458i	$0.894145\pi$
$774$		0			0
$775$	−14.0805	+	14.0805i	−0.505785	+	0.505785i
$776$	−2.88231	+	39.5657i	−0.103469	+	1.42033i
$777$		0			0
$778$	−2.58490	−	24.1430i	−0.0926730	−	0.865569i
$779$	1.43577	−	3.46626i	0.0514418	−	0.124191i
$780$		0			0
$781$	−2.08482	+	0.863560i	−0.0746006	+	0.0309006i
$782$	6.96411	−	23.6790i	0.249036	−	0.846760i
$783$		0			0
$784$	22.7128	−	10.3243i	0.811171	−	0.368725i
$785$	−4.86056			−0.173481
$786$		0			0
$787$	5.82978	+	14.0743i	0.207809	+	0.501696i	0.993078	−	0.117460i	$-0.0374751\pi$
$787$	5.82978	+	14.0743i	0.207809	+	0.501696i	−0.785269	+	0.619155i	$0.787475\pi$
$788$	9.78475	+	14.1192i	0.348567	+	0.502977i
$789$		0			0
$790$	0.273693	+	2.55630i	0.00973755	+	0.0909491i
$791$	−3.16250	+	3.16250i	−0.112445	+	0.112445i
$792$		0			0
$793$	−20.2953	−	20.2953i	−0.720705	−	0.720705i
$794$	1.43557	−	1.77983i	0.0509466	−	0.0631639i
$795$		0			0
$796$	−8.76474	−	40.4623i	−0.310658	−	1.43415i
$797$	−17.7102	+	7.33581i	−0.627328	+	0.259848i	−0.673617	−	0.739080i	$-0.735260\pi$
$797$	−17.7102	+	7.33581i	−0.627328	+	0.259848i	0.0462892	+	0.998928i	$0.485260\pi$
$798$		0			0
$799$		−	31.9927i		−	1.13182i
$800$	−3.91340	−	27.6501i	−0.138360	−	0.977578i
$801$		0			0
$802$	37.0311	−	20.1993i	1.30761	−	0.713263i
$803$	2.67073	+	6.44770i	0.0942479	+	0.227535i
$804$		0			0
$805$	1.28411	+	0.531894i	0.0452588	+	0.0187468i
$806$	16.4162	+	13.2409i	0.578236	+	0.466392i
$807$		0			0
$808$	−28.1853	−	14.1551i	−0.991554	−	0.497975i
$809$	15.6456	+	15.6456i	0.550069	+	0.550069i	0.926461	−	0.376391i	$-0.122835\pi$
$809$	15.6456	+	15.6456i	0.550069	+	0.550069i	−0.376391	+	0.926461i	$0.622835\pi$
$810$		0			0
$811$	44.2382	+	18.3241i	1.55341	+	0.643445i	0.983929	−	0.178558i	$-0.0571432\pi$
$811$	44.2382	+	18.3241i	1.55341	+	0.643445i	0.569484	+	0.822003i	$0.307143\pi$
$812$	−0.0108799	−	0.0156996i	−0.000381811	−	0.000550946i
$813$		0			0
$814$	−3.59484	+	12.2230i	−0.125999	+	0.428416i
$815$		−	4.89488i		−	0.171460i
$816$		0			0
$817$		−	5.46340i		−	0.191140i
$818$	17.4583	+	5.13456i	0.610414	+	0.179526i
$819$		0			0
$820$	−0.679310	+	3.74629i	−0.0237225	+	0.130826i
$821$	−9.06690	−	3.75563i	−0.316437	−	0.131072i	0.218812	−	0.975767i	$-0.429782\pi$
$821$	−9.06690	−	3.75563i	−0.316437	−	0.131072i	−0.535248	+	0.844695i	$0.679782\pi$
$822$		0			0
$823$	21.6440	+	21.6440i	0.754461	+	0.754461i	0.975308	−	0.220847i	$-0.0708823\pi$
$823$	21.6440	+	21.6440i	0.754461	+	0.754461i	−0.220847	+	0.975308i	$0.570882\pi$
$824$	−21.8200	−	25.2489i	−0.760135	−	0.879587i
$825$		0			0
$826$	−0.788393	+	0.977455i	−0.0274317	+	0.0340100i
$827$	−38.2211	−	15.8317i	−1.32908	−	0.550522i	−0.398685	−	0.917088i	$-0.630533\pi$
$827$	−38.2211	−	15.8317i	−1.32908	−	0.550522i	−0.930392	+	0.366566i	$0.880533\pi$
$828$		0			0
$829$	14.2172	+	34.3234i	0.493784	+	1.19210i	0.952780	+	0.303661i	$0.0982091\pi$
$829$	14.2172	+	34.3234i	0.493784	+	1.19210i	−0.458996	+	0.888438i	$0.651791\pi$
$830$	−2.08496	−	3.82231i	−0.0723700	−	0.132674i
$831$		0			0
$832$	−28.6779	+	7.23899i	−0.994227	+	0.250967i
$833$		−	17.2217i		−	0.596698i
$834$		0			0
$835$	−4.58527	+	1.89928i	−0.158680	+	0.0657273i
$836$	−0.709178	+	1.10137i	−0.0245274	+	0.0380917i
$837$		0			0
$838$	11.3529	+	9.15696i	0.392178	+	0.316322i
$839$	25.0743	+	25.0743i	0.865660	+	0.865660i	0.991988	−	0.126329i	$-0.0403194\pi$
$839$	25.0743	+	25.0743i	0.865660	+	0.865660i	−0.126329	+	0.991988i	$0.540319\pi$
$840$		0			0
$841$	−20.5060	+	20.5060i	−0.707104	+	0.707104i
$842$	4.43420	−	0.474752i	0.152813	−	0.0163610i
$843$		0			0
$844$	34.7715	+	6.30507i	1.19688	+	0.217030i
$845$	−0.0644717	−	0.155648i	−0.00221789	−	0.00535447i
$846$		0			0
$847$	8.08510			0.277807
$848$	−1.32952	−	39.1581i	−0.0456559	−	1.34470i
$849$		0			0
$850$	−18.4931	−	5.43890i	−0.634308	−	0.186553i
$851$	−39.8591	+	16.5102i	−1.36635	+	0.565961i
$852$		0			0
$853$	19.6749	−	47.4993i	0.673655	−	1.62635i	−0.101696	−	0.994816i	$-0.532427\pi$
$853$	19.6749	−	47.4993i	0.673655	−	1.62635i	0.775351	−	0.631531i	$-0.217573\pi$
$854$	−9.53359	+	1.02072i	−0.326233	+	0.0349284i
$855$		0			0
$856$	−8.48566	−	4.26164i	−0.290034	−	0.145660i
$857$	−21.0148	+	21.0148i	−0.717851	+	0.717851i	−0.968165	−	0.250314i	$-0.919466\pi$
$857$	−21.0148	+	21.0148i	−0.717851	+	0.717851i	0.250314	+	0.968165i	$0.419466\pi$
$858$		0			0
$859$	0.592319	−	1.42998i	0.0202097	−	0.0487905i	−0.913453	−	0.406945i	$-0.866594\pi$
$859$	0.592319	−	1.42998i	0.0202097	−	0.0487905i	0.933662	+	0.358155i	$0.116594\pi$
$860$	1.17375	+	5.41860i	0.0400245	+	0.184773i
$861$		0			0
$862$	−15.6973	−	28.7775i	−0.534652	−	0.980167i
$863$	−46.0354			−1.56706			−0.783531	−	0.621352i	$-0.786584\pi$
$863$	−46.0354			−1.56706			−0.783531	+	0.621352i	$0.786584\pi$
$864$		0			0
$865$	0.700443			0.0238158
$866$	−17.1326	−	31.4089i	−0.582190	−	1.06732i
$867$		0			0
$868$	6.88579	−	1.49157i	0.233719	−	0.0506270i
$869$	3.64699	−	8.80461i	0.123716	−	0.298676i
$870$		0			0
$871$	−20.9467	+	20.9467i	−0.709750	+	0.709750i
$872$	−7.71038	−	23.2685i	−0.261106	−	0.787970i
$873$		0			0
$874$	−4.41060	+	0.472225i	−0.149191	+	0.0159732i
$875$	0.836143	−	2.01863i	0.0282668	−	0.0682421i
$876$		0			0
$877$	5.47725	−	2.26875i	0.184954	−	0.0766103i	−0.288285	−	0.957545i	$-0.593085\pi$
$877$	5.47725	−	2.26875i	0.184954	−	0.0766103i	0.473238	+	0.880934i	$0.343085\pi$
$878$	−54.4601	−	16.0170i	−1.83794	−	0.540547i
$879$		0			0
$880$	0.466746	−	1.24470i	0.0157340	−	0.0419587i
$881$	−27.4957			−0.926355			−0.463178	−	0.886265i	$-0.653291\pi$
$881$	−27.4957			−0.926355			−0.463178	+	0.886265i	$0.653291\pi$
$882$		0			0
$883$	−10.6048	−	25.6023i	−0.356880	−	0.861585i	−0.995735	−	0.0922578i	$-0.970592\pi$
$883$	−10.6048	−	25.6023i	−0.356880	−	0.861585i	0.638855	−	0.769327i	$-0.279408\pi$
$884$	−3.64269	+	20.0889i	−0.122517	+	0.675662i
$885$		0			0
$886$	30.2461	−	3.23833i	1.01614	−	0.108794i
$887$	10.2715	−	10.2715i	0.344883	−	0.344883i	−0.513316	−	0.858199i	$-0.671583\pi$
$887$	10.2715	−	10.2715i	0.344883	−	0.344883i	0.858199	+	0.513316i	$0.171583\pi$
$888$		0			0
$889$	5.11668	+	5.11668i	0.171608	+	0.171608i
$890$	−1.45102	−	1.17036i	−0.0486382	−	0.0392304i
$891$		0			0
$892$	26.6725	+	17.1746i	0.893062	+	0.575048i
$893$	−5.31202	+	2.20031i	−0.177760	+	0.0736306i
$894$		0			0
$895$		−	3.92252i		−	0.131115i
$896$	−4.13221	+	8.97500i	−0.138047	+	0.299834i
$897$		0			0
$898$	−8.52225	−	15.6237i	−0.284391	−	0.521369i
$899$	0.0168808	+	0.0407538i	0.000563006	+	0.00135922i
$900$		0			0
$901$	−24.9866	−	10.3498i	−0.832425	−	0.344802i
$902$	8.86060	−	10.9854i	0.295026	−	0.365775i
$903$		0			0
$904$	−1.05241	+	14.4465i	−0.0350026	+	0.480484i
$905$	1.19319	+	1.19319i	0.0396628	+	0.0396628i
$906$		0			0
$907$	39.7977	+	16.4847i	1.32146	+	0.547367i	0.928207	−	0.372064i	$-0.121350\pi$
$907$	39.7977	+	16.4847i	1.32146	+	0.547367i	0.393253	+	0.919430i	$0.371350\pi$
$908$	12.8974	+	2.33868i	0.428017	+	0.0776118i
$909$		0			0
$910$	−1.10300	−	0.324396i	−0.0365639	−	0.0107536i
$911$		−	12.4103i		−	0.411171i	−0.978639	−	0.205585i	$-0.934090\pi$
$911$		−	12.4103i		−	0.411171i	0.978639	−	0.205585i	$-0.0659098\pi$
$912$		0			0
$913$			16.1396i			0.534144i
$914$	5.04182	−	17.1429i	0.166769	−	0.567038i
$915$		0			0
$916$	−13.5309	+	9.37700i	−0.447072	+	0.309825i
$917$	−16.4928	−	6.83156i	−0.544641	−	0.225598i
$918$		0			0
$919$	−1.07058	−	1.07058i	−0.0353151	−	0.0353151i	0.689229	−	0.724544i	$-0.257950\pi$
$919$	−1.07058	−	1.07058i	−0.0353151	−	0.0353151i	−0.724544	+	0.689229i	$0.757950\pi$
$920$	4.27297	−	1.41592i	0.140876	−	0.0466815i
$921$		0			0
$922$	−37.1678	−	29.9787i	−1.22405	−	0.987294i
$923$	5.83970	+	2.41888i	0.192216	+	0.0796185i
$924$		0			0
$925$	12.8943	+	31.1295i	0.423961	+	1.02353i
$926$	−2.21782	+	1.20975i	−0.0728821	+	0.0397550i
$927$		0			0
$928$	−0.0599066	−	0.0154307i	−0.00196653	−	0.000506539i
$929$			7.00180i			0.229722i	0.993382	+	0.114861i	$0.0366422\pi$
$929$			7.00180i			0.229722i	−0.993382	+	0.114861i	$0.963358\pi$
$930$		0			0
$931$	−2.85947	+	1.18443i	−0.0937155	+	0.0388182i
$932$	16.5711	−	3.58955i	0.542804	−	0.117579i
$933$		0			0
$934$	−36.4583	+	45.2013i	−1.19295	+	1.47903i
$935$	−0.648842	−	0.648842i	−0.0212194	−	0.0212194i
$936$		0			0
$937$	−18.5015	+	18.5015i	−0.604417	+	0.604417i	−0.941481	−	0.337065i	$-0.890566\pi$
$937$	−18.5015	+	18.5015i	−0.604417	+	0.604417i	0.337065	+	0.941481i	$0.390566\pi$
$938$	1.05348	+	9.83959i	0.0343975	+	0.321274i
$939$		0			0
$940$	4.79575	−	3.32350i	0.156420	−	0.108400i
$941$	14.8709	+	35.9014i	0.484776	+	1.17035i	0.957316	+	0.289044i	$0.0933373\pi$
$941$	14.8709	+	35.9014i	0.484776	+	1.17035i	−0.472540	+	0.881309i	$0.656663\pi$
$942$		0			0
$943$	47.7918			1.55632
$944$	0.138008	+	4.06472i	0.00449177	+	0.132295i
$945$		0			0
$946$	5.79881	−	19.7168i	0.188536	−	0.641049i
$947$	26.6795	−	11.0510i	0.866969	−	0.359110i	0.0955398	−	0.995426i	$-0.469542\pi$
$947$	26.6795	−	11.0510i	0.866969	−	0.359110i	0.771429	+	0.636315i	$0.219542\pi$
$948$		0			0
$949$	7.48086	−	18.0604i	0.242839	−	0.586265i
$950$	0.368803	+	3.44463i	0.0119655	+	0.111759i
$951$		0			0
$952$	4.45953	+	5.16032i	0.144534	+	0.167247i
$953$	−12.5517	+	12.5517i	−0.406591	+	0.406591i	−0.880548	−	0.473957i	$-0.842825\pi$
$953$	−12.5517	+	12.5517i	−0.406591	+	0.406591i	0.473957	+	0.880548i	$0.342825\pi$
$954$		0			0
$955$	1.44933	−	3.49900i	0.0468993	−	0.113225i
$956$	1.87050	+	1.20442i	0.0604962	+	0.0389538i
$957$		0			0
$958$	37.6425	−	20.5328i	1.21617	−	0.663386i
$959$	−16.5454			−0.534277
$960$		0			0
$961$	14.7293			0.475137
$962$	31.3296	−	17.0893i	1.01011	−	0.550982i
$963$		0			0
$964$	1.19278	+	0.768037i	0.0384168	+	0.0247368i
$965$	−1.89369	+	4.57178i	−0.0609601	+	0.147171i
$966$		0			0
$967$	33.7248	−	33.7248i	1.08452	−	1.08452i	0.0884351	−	0.996082i	$-0.471813\pi$
$967$	33.7248	−	33.7248i	1.08452	−	1.08452i	0.996082	−	0.0884351i	$-0.0281866\pi$
$968$	19.8120	−	17.1214i	0.636780	−	0.550303i
$969$		0			0
$970$	0.531668	+	4.96580i	0.0170708	+	0.159442i
$971$	18.5211	−	44.7139i	0.594371	−	1.43494i	−0.284873	−	0.958565i	$-0.591951\pi$
$971$	18.5211	−	44.7139i	0.594371	−	1.43494i	0.879243	−	0.476373i	$-0.158049\pi$
$972$		0			0
$973$	−15.8033	+	6.54593i	−0.506629	+	0.209853i
$974$	−13.1432	+	44.6887i	−0.421134	+	1.43192i
$975$		0			0
$976$	−21.1998	+	22.6900i	−0.678590	+	0.726289i
$977$	−40.3998			−1.29250			−0.646252	−	0.763124i	$-0.723664\pi$
$977$	−40.3998			−1.29250			−0.646252	+	0.763124i	$0.723664\pi$
$978$		0			0
$979$	2.64445	+	6.38428i	0.0845171	+	0.204042i
$980$	2.58156	−	1.78905i	0.0824650	−	0.0571490i
$981$		0			0
$982$	1.84227	+	17.2068i	0.0587891	+	0.549093i
$983$	−39.1712	+	39.1712i	−1.24937	+	1.24937i	−0.293369	+	0.955999i	$0.594776\pi$
$983$	−39.1712	+	39.1712i	−1.24937	+	1.24937i	−0.955999	+	0.293369i	$0.905224\pi$
$984$		0			0
$985$	1.52919	+	1.52919i	0.0487240	+	0.0487240i
$986$	−0.0268086	+	0.0332375i	−0.000853759	+	0.00105850i
$987$		0			0
$988$	3.58606	−	0.776794i	0.114088	−	0.0247131i
$989$	64.2964	−	26.6325i	2.04451	−	0.846863i
$990$		0			0
$991$			16.6218i			0.528007i	0.964522	+	0.264004i	$0.0850431\pi$
$991$			16.6218i			0.528007i	−0.964522	+	0.264004i	$0.914957\pi$
$992$	13.7145	−	18.2367i	0.435436	−	0.579015i
$993$		0			0
$994$	1.85369	−	1.01113i	0.0587955	−	0.0320712i
$995$	−1.99454	−	4.81524i	−0.0632311	−	0.152653i
$996$		0			0
$997$	−17.9978	−	7.45495i	−0.569997	−	0.236101i	0.0790217	−	0.996873i	$-0.474820\pi$
$997$	−17.9978	−	7.45495i	−0.569997	−	0.236101i	−0.649019	+	0.760772i	$0.724820\pi$
$998$	−25.0221	−	20.1823i	−0.792062	−	0.638859i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.w.a.251.7	yes	32
3.2	odd	2		288.2.w.b.251.2	yes	32
4.3	odd	2		1152.2.w.b.143.4		32
12.11	even	2		1152.2.w.a.143.5		32
32.13	even	8		1152.2.w.a.1007.5		32
32.19	odd	8		288.2.w.b.179.2	yes	32
96.77	odd	8		1152.2.w.b.1007.4		32
96.83	even	8	inner	288.2.w.a.179.7	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.179.7	✓	32	96.83	even	8	inner
288.2.w.a.251.7	yes	32	1.1	even	1	trivial
288.2.w.b.179.2	yes	32	32.19	odd	8
288.2.w.b.251.2	yes	32	3.2	odd	2
1152.2.w.a.143.5		32	12.11	even	2
1152.2.w.a.1007.5		32	32.13	even	8
1152.2.w.b.143.4		32	4.3	odd	2
1152.2.w.b.1007.4		32	96.77	odd	8

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.24152 - 0.677214i) q^{2} +(1.08276 - 1.68155i) q^{4} +(0.0963530 - 0.232617i) q^{5} +(0.617536 - 0.617536i) q^{7} +(0.205502 - 2.82095i) q^{8} +O(q^{10})\)	\(q+(1.24152 - 0.677214i) q^{2} +(1.08276 - 1.68155i) q^{4} +(0.0963530 - 0.232617i) q^{5} +(0.617536 - 0.617536i) q^{7} +(0.205502 - 2.82095i) q^{8} +(-0.0379068 - 0.354051i) q^{10} +(-0.505112 + 1.21945i) q^{11} +(3.41575 - 1.41485i) q^{13} +(0.348482 - 1.18489i) q^{14} +(-1.65525 - 3.64145i) q^{16} -2.76109 q^{17} +(0.189895 + 0.458448i) q^{19} +(-0.286830 - 0.413891i) q^{20} +(0.198719 + 1.85604i) q^{22} +(-4.46959 + 4.46959i) q^{23} +(3.49071 + 3.49071i) q^{25} +(3.28257 - 4.06976i) q^{26} +(-0.369776 - 1.70707i) q^{28} +(0.0101033 - 0.00418494i) q^{29} +4.03370i q^{31} +(-4.52107 - 3.39998i) q^{32} +(-3.42796 + 1.86985i) q^{34} +(-0.0841477 - 0.203151i) q^{35} +(6.30586 + 2.61197i) q^{37} +(0.546227 + 0.440574i) q^{38} +(-0.636400 - 0.319610i) q^{40} +(-5.34633 - 5.34633i) q^{41} +(-10.1719 - 4.21336i) q^{43} +(1.50365 + 2.16975i) q^{44} +(-2.52223 + 8.57598i) q^{46} +11.5870i q^{47} +6.23730i q^{49} +(6.69775 + 1.96984i) q^{50} +(1.31930 - 7.27571i) q^{52} +(9.04956 + 3.74845i) q^{53} +(0.234995 + 0.234995i) q^{55} +(-1.61513 - 1.86894i) q^{56} +(0.00970943 - 0.0120378i) q^{58} +(-0.939369 - 0.389099i) q^{59} +(-2.97084 - 7.17223i) q^{61} +(2.73168 + 5.00793i) q^{62} +(-7.91554 - 1.15942i) q^{64} -0.930884i q^{65} +(-7.40244 + 3.06619i) q^{67} +(-2.98960 + 4.64292i) q^{68} +(-0.242048 - 0.195230i) q^{70} +(1.20890 + 1.20890i) q^{71} +(3.73875 - 3.73875i) q^{73} +(9.59774 - 1.02759i) q^{74} +(0.976516 + 0.177071i) q^{76} +(0.441128 + 1.06498i) q^{77} -7.22016 q^{79} +(-1.00655 + 0.0341749i) q^{80} +(-10.2582 - 3.01699i) q^{82} +(11.2970 - 4.67935i) q^{83} +(-0.266039 + 0.642275i) q^{85} +(-15.4820 + 1.65760i) q^{86} +(3.33620 + 1.67550i) q^{88} +(3.70197 - 3.70197i) q^{89} +(1.23563 - 2.98307i) q^{91} +(2.67636 + 12.3554i) q^{92} +(7.84687 + 14.3855i) q^{94} +0.124940 q^{95} -14.0257 q^{97} +(4.22399 + 7.74375i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} - 4 q^{8}+O(q^{10}) \) 32 * q - 4 * q^2 - 4 * q^8	\( 32 q - 4 q^{2} - 4 q^{8} + 8 q^{10} - 8 q^{11} + 12 q^{14} + 8 q^{16} + 32 q^{20} + 16 q^{22} - 36 q^{26} - 16 q^{29} - 24 q^{32} + 24 q^{35} + 32 q^{38} - 32 q^{40} + 8 q^{44} - 32 q^{46} + 8 q^{50} - 56 q^{52} - 16 q^{53} - 32 q^{55} + 40 q^{56} - 32 q^{58} + 32 q^{59} + 32 q^{61} - 68 q^{62} - 48 q^{64} - 16 q^{67} - 72 q^{68} - 48 q^{70} + 16 q^{71} + 60 q^{74} - 8 q^{76} - 16 q^{77} - 32 q^{79} + 96 q^{80} + 40 q^{82} - 40 q^{83} - 40 q^{86} + 40 q^{88} - 48 q^{91} - 16 q^{92} + 72 q^{94} - 80 q^{95} - 44 q^{98}+O(q^{100}) \) 32 * q - 4 * q^2 - 4 * q^8 + 8 * q^10 - 8 * q^11 + 12 * q^14 + 8 * q^16 + 32 * q^20 + 16 * q^22 - 36 * q^26 - 16 * q^29 - 24 * q^32 + 24 * q^35 + 32 * q^38 - 32 * q^40 + 8 * q^44 - 32 * q^46 + 8 * q^50 - 56 * q^52 - 16 * q^53 - 32 * q^55 + 40 * q^56 - 32 * q^58 + 32 * q^59 + 32 * q^61 - 68 * q^62 - 48 * q^64 - 16 * q^67 - 72 * q^68 - 48 * q^70 + 16 * q^71 + 60 * q^74 - 8 * q^76 - 16 * q^77 - 32 * q^79 + 96 * q^80 + 40 * q^82 - 40 * q^83 - 40 * q^86 + 40 * q^88 - 48 * q^91 - 16 * q^92 + 72 * q^94 - 80 * q^95 - 44 * q^98

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