LMFDB - Embedded newform 288.2.w.b.35.6

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			35.6
Character	$\chi$	$=$	288.35
Dual form			288.2.w.b.107.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19734 - 0.752583i) q^{2} +(0.867238 - 1.80219i) q^{4} +(0.0913223 - 0.0378270i) q^{5} +(-3.05457 - 3.05457i) q^{7} +(-0.317923 - 2.81050i) q^{8} +O(q^{10})$	\(q+(1.19734 - 0.752583i) q^{2} +(0.867238 - 1.80219i) q^{4} +(0.0913223 - 0.0378270i) q^{5} +(-3.05457 - 3.05457i) q^{7} +(-0.317923 - 2.81050i) q^{8} +(0.0808758 - 0.114019i) q^{10} +(5.25649 - 2.17731i) q^{11} +(-1.57202 + 3.79519i) q^{13} +(-5.95618 - 1.35854i) q^{14} +(-2.49580 - 3.12586i) q^{16} +2.56471 q^{17} +(2.64058 + 1.09376i) q^{19} +(0.0110267 - 0.197385i) q^{20} +(4.65519 - 6.56292i) q^{22} +(4.03079 + 4.03079i) q^{23} +(-3.52863 + 3.52863i) q^{25} +(0.973958 + 5.72721i) q^{26} +(-8.15397 + 2.85589i) q^{28} +(-2.06984 + 4.99704i) q^{29} +1.44203i q^{31} +(-5.34078 - 1.86442i) q^{32} +(3.07083 - 1.93016i) q^{34} +(-0.394496 - 0.163406i) q^{35} +(-2.07758 - 5.01573i) q^{37} +(3.98482 - 0.677651i) q^{38} +(-0.135346 - 0.244636i) q^{40} +(-0.296726 + 0.296726i) q^{41} +(-2.72382 - 6.57588i) q^{43} +(0.634695 - 11.3615i) q^{44} +(7.85972 + 1.79271i) q^{46} +7.42367i q^{47} +11.6608i q^{49} +(-1.56937 + 6.88054i) q^{50} +(5.47636 + 6.12442i) q^{52} +(-1.53235 - 3.69941i) q^{53} +(0.397674 - 0.397674i) q^{55} +(-7.61376 + 9.55600i) q^{56} +(1.28239 + 7.54087i) q^{58} +(-0.988255 - 2.38586i) q^{59} +(10.4346 + 4.32215i) q^{61} +(1.08525 + 1.72660i) q^{62} +(-7.79785 + 1.78705i) q^{64} +0.406051i q^{65} +(-0.690522 + 1.66707i) q^{67} +(2.22421 - 4.62211i) q^{68} +(-0.595321 + 0.101239i) q^{70} +(2.97957 - 2.97957i) q^{71} +(9.22401 + 9.22401i) q^{73} +(-6.26232 - 4.44197i) q^{74} +(4.26119 - 3.81028i) q^{76} +(-22.7071 - 9.40558i) q^{77} -1.12181 q^{79} +(-0.346164 - 0.191052i) q^{80} +(-0.131971 + 0.578593i) q^{82} +(4.13529 - 9.98348i) q^{83} +(0.234216 - 0.0970152i) q^{85} +(-8.21022 - 5.82365i) q^{86} +(-7.79049 - 14.0812i) q^{88} +(12.0590 + 12.0590i) q^{89} +(16.3945 - 6.79084i) q^{91} +(10.7599 - 3.76861i) q^{92} +(5.58693 + 8.88865i) q^{94} +0.282518 q^{95} -18.5545 q^{97} +(8.77574 + 13.9619i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$

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 $

$2$	1.19734	−	0.752583i	0.846646	−	0.532157i
$2$	1.19734	−	0.752583i	0.846646	−	0.532157i
$3$		0			0
$3$		0			0
$4$	0.867238	−	1.80219i	0.433619	−	0.901096i
$5$	0.0913223	−	0.0378270i	0.0408406	−	0.0169167i	−0.362170	−	0.932112i	$-0.617964\pi$
$5$	0.0913223	−	0.0378270i	0.0408406	−	0.0169167i	0.403010	+	0.915195i	$0.367964\pi$
$6$		0			0
$7$	−3.05457	−	3.05457i	−1.15452	−	1.15452i	−0.985636	−	0.168884i	$-0.945984\pi$
$7$	−3.05457	−	3.05457i	−1.15452	−	1.15452i	−0.168884	−	0.985636i	$-0.554016\pi$
$8$	−0.317923	−	2.81050i	−0.112403	−	0.993663i
$9$		0			0
$10$	0.0808758	−	0.114019i	0.0255752	−	0.0360561i
$11$	5.25649	−	2.17731i	1.58489	−	0.656483i	0.595712	−	0.803198i	$-0.296870\pi$
$11$	5.25649	−	2.17731i	1.58489	−	0.656483i	0.989179	+	0.146715i	$0.0468699\pi$
$12$		0			0
$13$	−1.57202	+	3.79519i	−0.436000	+	1.05260i	0.541317	+	0.840818i	$0.317926\pi$
$13$	−1.57202	+	3.79519i	−0.436000	+	1.05260i	−0.977318	+	0.211779i	$0.932074\pi$
$14$	−5.95618	−	1.35854i	−1.59185	−	0.363084i
$15$		0			0
$16$	−2.49580	−	3.12586i	−0.623949	−	0.781465i
$17$	2.56471			0.622034			0.311017	−	0.950404i	$-0.399330\pi$
$17$	2.56471			0.622034			0.311017	+	0.950404i	$0.399330\pi$
$18$		0			0
$19$	2.64058	+	1.09376i	0.605791	+	0.250927i	0.664428	−	0.747353i	$-0.268675\pi$
$19$	2.64058	+	1.09376i	0.605791	+	0.250927i	−0.0586367	+	0.998279i	$0.518675\pi$
$20$	0.0110267	−	0.197385i	0.00246565	−	0.0441367i
$21$		0			0
$22$	4.65519	−	6.56292i	0.992490	−	1.39922i
$23$	4.03079	+	4.03079i	0.840477	+	0.840477i	0.988921	−	0.148443i	$-0.0474263\pi$
$23$	4.03079	+	4.03079i	0.840477	+	0.840477i	−0.148443	+	0.988921i	$0.547426\pi$
$24$		0			0
$25$	−3.52863	+	3.52863i	−0.705725	+	0.705725i
$26$	0.973958	+	5.72721i	0.191009	+	1.12320i
$27$		0			0
$28$	−8.15397	+	2.85589i	−1.54096	+	0.539712i
$29$	−2.06984	+	4.99704i	−0.384360	+	0.927927i	0.606752	+	0.794892i	$0.292472\pi$
$29$	−2.06984	+	4.99704i	−0.384360	+	0.927927i	−0.991111	+	0.133035i	$0.957528\pi$
$30$		0			0
$31$			1.44203i			0.258996i	0.991580	+	0.129498i	$0.0413366\pi$
$31$			1.44203i			0.258996i	−0.991580	+	0.129498i	$0.958663\pi$
$32$	−5.34078	−	1.86442i	−0.944126	−	0.329585i
$33$		0			0
$34$	3.07083	−	1.93016i	0.526643	−	0.331019i
$35$	−0.394496	−	0.163406i	−0.0666820	−	0.0276206i
$36$		0			0
$37$	−2.07758	−	5.01573i	−0.341552	−	0.824581i	−0.997559	−	0.0698256i	$-0.977756\pi$
$37$	−2.07758	−	5.01573i	−0.341552	−	0.824581i	0.656007	−	0.754755i	$-0.272244\pi$
$38$	3.98482	−	0.677651i	0.646423	−	0.109929i
$39$		0			0
$40$	−0.135346	−	0.244636i	−0.0214001	−	0.0386803i
$41$	−0.296726	+	0.296726i	−0.0463409	+	0.0463409i	−0.729897	−	0.683557i	$-0.760432\pi$
$41$	−0.296726	+	0.296726i	−0.0463409	+	0.0463409i	0.683557	+	0.729897i	$0.260432\pi$
$42$		0			0
$43$	−2.72382	−	6.57588i	−0.415378	−	1.00281i	−0.983669	−	0.179984i	$-0.942395\pi$
$43$	−2.72382	−	6.57588i	−0.415378	−	1.00281i	0.568291	−	0.822828i	$-0.307605\pi$
$44$	0.634695	−	11.3615i	0.0956838	−	1.71280i
$45$		0			0
$46$	7.85972	+	1.79271i	1.15885	+	0.264321i
$47$			7.42367i			1.08285i	0.840748	+	0.541427i	$0.182116\pi$
$47$			7.42367i			1.08285i	−0.840748	+	0.541427i	$0.817884\pi$
$48$		0			0
$49$			11.6608i			1.66583i
$50$	−1.56937	+	6.88054i	−0.221943	+	0.973055i
$51$		0			0
$52$	5.47636	+	6.12442i	0.759434	+	0.849304i
$53$	−1.53235	−	3.69941i	−0.210484	−	0.508153i	0.783014	−	0.622004i	$-0.213681\pi$
$53$	−1.53235	−	3.69941i	−0.210484	−	0.508153i	−0.993498	+	0.113851i	$0.963681\pi$
$54$		0			0
$55$	0.397674	−	0.397674i	0.0536223	−	0.0536223i
$56$	−7.61376	+	9.55600i	−1.01743	+	1.27697i
$57$		0			0
$58$	1.28239	+	7.54087i	0.168386	+	0.990165i
$59$	−0.988255	−	2.38586i	−0.128660	−	0.310612i	0.846402	−	0.532544i	$-0.178764\pi$
$59$	−0.988255	−	2.38586i	−0.128660	−	0.310612i	−0.975062	+	0.221931i	$0.928764\pi$
$60$		0			0
$61$	10.4346	+	4.32215i	1.33601	+	0.553395i	0.932365	−	0.361519i	$-0.117742\pi$
$61$	10.4346	+	4.32215i	1.33601	+	0.553395i	0.403649	+	0.914914i	$0.367742\pi$
$62$	1.08525	+	1.72660i	0.137827	+	0.219278i
$63$		0			0
$64$	−7.79785	+	1.78705i	−0.974731	+	0.223381i
$65$			0.406051i			0.0503644i
$66$		0			0
$67$	−0.690522	+	1.66707i	−0.0843606	+	0.203665i	−0.960431	−	0.278519i	$-0.910156\pi$
$67$	−0.690522	+	1.66707i	−0.0843606	+	0.203665i	0.876070	+	0.482184i	$0.160156\pi$
$68$	2.22421	−	4.62211i	0.269726	−	0.560513i
$69$		0			0
$70$	−0.595321	+	0.101239i	−0.0711545	+	0.0121004i
$71$	2.97957	−	2.97957i	0.353610	−	0.353610i	−0.507841	−	0.861451i	$-0.669556\pi$
$71$	2.97957	−	2.97957i	0.353610	−	0.353610i	0.861451	+	0.507841i	$0.169556\pi$
$72$		0			0
$73$	9.22401	+	9.22401i	1.07959	+	1.07959i	0.996546	+	0.0830429i	$0.0264638\pi$
$73$	9.22401	+	9.22401i	1.07959	+	1.07959i	0.0830429	+	0.996546i	$0.473536\pi$
$74$	−6.26232	−	4.44197i	−0.727980	−	0.516368i
$75$		0			0
$76$	4.26119	−	3.81028i	0.488792	−	0.437070i
$77$	−22.7071	−	9.40558i	−2.58771	−	1.07187i
$78$		0			0
$79$	−1.12181			−0.126213			−0.0631065	−	0.998007i	$-0.520101\pi$
$79$	−1.12181			−0.126213			−0.0631065	+	0.998007i	$0.520101\pi$
$80$	−0.346164	−	0.191052i	−0.0387023	−	0.0213603i
$81$		0			0
$82$	−0.131971	+	0.578593i	−0.0145737	+	0.0638949i
$83$	4.13529	−	9.98348i	0.453907	−	1.09583i	−0.516916	−	0.856036i	$-0.672920\pi$
$83$	4.13529	−	9.98348i	0.453907	−	1.09583i	0.970824	−	0.239794i	$-0.0770798\pi$
$84$		0			0
$85$	0.234216	−	0.0970152i	0.0254042	−	0.0105228i
$86$	−8.21022	−	5.82365i	−0.885331	−	0.627980i
$87$		0			0
$88$	−7.79049	−	14.0812i	−0.830469	−	1.50106i
$89$	12.0590	+	12.0590i	1.27825	+	1.27825i	0.941644	+	0.336609i	$0.109280\pi$
$89$	12.0590	+	12.0590i	1.27825	+	1.27825i	0.336609	+	0.941644i	$0.390720\pi$
$90$		0			0
$91$	16.3945	−	6.79084i	1.71862	−	0.711874i
$92$	10.7599	−	3.76861i	1.12180	−	0.392904i
$93$		0			0
$94$	5.58693	+	8.88865i	0.576248	+	0.916794i
$95$	0.282518			0.0289857
$96$		0			0
$97$	−18.5545			−1.88393			−0.941963	−	0.335717i	$-0.891022\pi$
$97$	−18.5545			−1.88393			−0.941963	+	0.335717i	$0.891022\pi$
$98$	8.77574	+	13.9619i	0.886483	+	1.41037i
$99$		0			0
$100$	3.29911	+	9.41942i	0.329911	+	0.941942i
$101$	−5.24603	+	2.17298i	−0.521999	+	0.216219i	−0.628095	−	0.778137i	$-0.716165\pi$
$101$	−5.24603	+	2.17298i	−0.521999	+	0.216219i	0.106096	+	0.994356i	$0.466165\pi$
$102$		0			0
$103$	−11.0095	−	11.0095i	−1.08479	−	1.08479i	−0.996055	−	0.0887398i	$-0.971716\pi$
$103$	−11.0095	−	11.0095i	−1.08479	−	1.08479i	−0.0887398	−	0.996055i	$-0.528284\pi$
$104$	11.1662	+	3.21159i	1.09493	+	0.314922i
$105$		0			0
$106$	−4.61885	−	3.27623i	−0.448622	−	0.318215i
$107$	−0.182628	+	0.0756468i	−0.0176553	+	0.00731305i	−0.391494	−	0.920181i	$-0.628041\pi$
$107$	−0.182628	+	0.0756468i	−0.0176553	+	0.00731305i	0.373838	+	0.927494i	$0.378041\pi$
$108$		0			0
$109$	2.10265	−	5.07626i	0.201398	−	0.486217i	−0.790621	−	0.612305i	$-0.790242\pi$
$109$	2.10265	−	5.07626i	0.201398	−	0.486217i	0.992019	+	0.126088i	$0.0402423\pi$
$110$	0.176868	−	0.775433i	0.0168637	−	0.0739346i
$111$		0			0
$112$	−1.92457	+	17.1718i	−0.181855	+	1.62258i
$113$	−5.91777			−0.556697			−0.278348	−	0.960480i	$-0.589787\pi$
$113$	−5.91777			−0.556697			−0.278348	+	0.960480i	$0.589787\pi$
$114$		0			0
$115$	0.520573	+	0.215629i	0.0485437	+	0.0201075i
$116$	7.21058	+	8.06387i	0.669486	+	0.748712i
$117$		0			0
$118$	−2.97883	−	2.11294i	−0.274224	−	0.194512i
$119$	−7.83410	−	7.83410i	−0.718151	−	0.718151i
$120$		0			0
$121$	15.1118	−	15.1118i	1.37380	−	1.37380i
$122$	15.7465	−	2.67782i	1.42562	−	0.242439i
$123$		0			0
$124$	2.59882	+	1.25058i	0.233381	+	0.112306i
$125$	−0.377900	+	0.912331i	−0.0338004	+	0.0816014i
$126$		0			0
$127$		−	9.70061i		−	0.860790i	−0.902641	−	0.430395i	$-0.858374\pi$
$127$		−	9.70061i		−	0.860790i	0.902641	−	0.430395i	$-0.141626\pi$
$128$	−7.99176	+	8.00823i	−0.706379	+	0.707834i
$129$		0			0
$130$	0.305587	+	0.486180i	0.0268017	+	0.0426408i
$131$	−12.7327	−	5.27407i	−1.11246	−	0.460798i	−0.250678	−	0.968070i	$-0.580654\pi$
$131$	−12.7327	−	5.27407i	−1.11246	−	0.460798i	−0.861786	+	0.507273i	$0.830654\pi$
$132$		0			0
$133$	−4.72486	−	11.4068i	−0.409698	−	0.989098i
$134$	0.427818	+	2.51572i	0.0369579	+	0.217325i
$135$		0			0
$136$	−0.815381	−	7.20813i	−0.0699183	−	0.618092i
$137$	5.62861	−	5.62861i	0.480884	−	0.480884i	−0.424530	−	0.905414i	$-0.639561\pi$
$137$	5.62861	−	5.62861i	0.480884	−	0.480884i	0.905414	+	0.424530i	$0.139561\pi$
$138$		0			0
$139$	0.202389	+	0.488610i	0.0171664	+	0.0414434i	0.932230	−	0.361865i	$-0.117860\pi$
$139$	0.202389	+	0.488610i	0.0171664	+	0.0414434i	−0.915064	+	0.403309i	$0.867860\pi$
$140$	−0.636610	+	0.569246i	−0.0538034	+	0.0481101i
$141$		0			0
$142$	1.32518	−	5.80993i	0.111207	−	0.487559i
$143$			23.3722i			1.95448i
$144$		0			0
$145$			0.534637i			0.0443992i
$146$	17.9861	+	4.10243i	1.48854	+	0.339519i
$147$		0			0
$148$	−10.8411	−	0.605624i	−0.891130	−	0.0497820i
$149$	−1.35052	−	3.26046i	−0.110639	−	0.267107i	0.858856	−	0.512217i	$-0.171176\pi$
$149$	−1.35052	−	3.26046i	−0.110639	−	0.267107i	−0.969495	+	0.245110i	$0.921176\pi$
$150$		0			0
$151$	−13.6492	+	13.6492i	−1.11076	+	1.11076i	−0.117709	+	0.993048i	$0.537555\pi$
$151$	−13.6492	+	13.6492i	−1.11076	+	1.11076i	−0.993048	+	0.117709i	$0.962445\pi$
$152$	2.23453	−	7.76910i	0.181244	−	0.630157i
$153$		0			0
$154$	−34.2665	+	5.82730i	−2.76128	+	0.469577i
$155$	0.0545476	+	0.131690i	0.00438137	+	0.0105776i
$156$		0			0
$157$	−15.4587	−	6.40321i	−1.23374	−	0.511032i	−0.331987	−	0.943284i	$-0.607719\pi$
$157$	−15.4587	−	6.40321i	−1.23374	−	0.511032i	−0.901753	+	0.432252i	$0.857719\pi$
$158$	−1.34318	+	0.844252i	−0.106858	+	0.0671651i
$159$		0			0
$160$	−0.558258	+	0.0317627i	−0.0441342	+	0.00251106i
$161$		−	24.6247i		−	1.94070i
$162$		0			0
$163$	−6.04288	+	14.5888i	−0.473315	+	1.14268i	0.489374	+	0.872074i	$0.337225\pi$
$163$	−6.04288	+	14.5888i	−0.473315	+	1.14268i	−0.962689	+	0.270609i	$0.912775\pi$
$164$	0.277426	+	0.792090i	0.0216633	+	0.0618519i
$165$		0			0
$166$	−2.56205	−	15.0658i	−0.198854	−	1.16933i
$167$	−6.58872	+	6.58872i	−0.509850	+	0.509850i	−0.914480	−	0.404630i	$-0.867400\pi$
$167$	−6.58872	+	6.58872i	−0.509850	+	0.509850i	0.404630	+	0.914480i	$0.367400\pi$
$168$		0			0
$169$	−2.73986	−	2.73986i	−0.210759	−	0.210759i
$170$	0.207423	−	0.292427i	0.0159086	−	0.0224281i
$171$		0			0
$172$	−14.2132	−	0.794004i	−1.08375	−	0.0605422i
$173$	17.8204	+	7.38143i	1.35486	+	0.561200i	0.937640	−	0.347608i	$-0.113006\pi$
$173$	17.8204	+	7.38143i	1.35486	+	0.561200i	0.417216	+	0.908807i	$0.363006\pi$
$174$		0			0
$175$	21.5569			1.62955
$176$	−19.9251	−	10.9969i	−1.50191	−	0.828924i
$177$		0			0
$178$	23.5141	+	5.36331i	1.76246	+	0.401997i
$179$	4.07369	−	9.83475i	0.304482	−	0.735084i	−0.695383	−	0.718639i	$-0.744765\pi$
$179$	4.07369	−	9.83475i	0.304482	−	0.735084i	0.999865	−	0.0164446i	$-0.00523471\pi$
$180$		0			0
$181$	8.06280	−	3.33972i	0.599303	−	0.248239i	−0.0623442	−	0.998055i	$-0.519858\pi$
$181$	8.06280	−	3.33972i	0.599303	−	0.248239i	0.661647	+	0.749815i	$0.269858\pi$
$182$	14.5191	−	20.4692i	1.07623	−	1.51728i
$183$		0			0
$184$	10.0471	−	12.6100i	0.740679	−	0.929623i
$185$	−0.379459	−	0.379459i	−0.0278984	−	0.0278984i
$186$		0			0
$187$	13.4814	−	5.58417i	0.985856	−	0.408355i
$188$	13.3789	+	6.43809i	0.975756	+	0.469546i
$189$		0			0
$190$	0.338270	−	0.212618i	0.0245406	−	0.0154249i
$191$	−13.0520			−0.944411			−0.472205	−	0.881489i	$-0.656542\pi$
$191$	−13.0520			−0.944411			−0.472205	+	0.881489i	$0.656542\pi$
$192$		0			0
$193$	−3.05926			−0.220210			−0.110105	−	0.993920i	$-0.535119\pi$
$193$	−3.05926			−0.220210			−0.110105	+	0.993920i	$0.535119\pi$
$194$	−22.2160	+	13.9638i	−1.59502	+	1.00254i
$195$		0			0
$196$	21.0151	+	10.1127i	1.50108	+	0.722336i
$197$	5.46774	−	2.26481i	0.389560	−	0.161361i	−0.179302	−	0.983794i	$-0.557384\pi$
$197$	5.46774	−	2.26481i	0.389560	−	0.161361i	0.568862	+	0.822433i	$0.307384\pi$
$198$		0			0
$199$	−4.48835	−	4.48835i	−0.318170	−	0.318170i	0.529894	−	0.848064i	$-0.322232\pi$
$199$	−4.48835	−	4.48835i	−0.318170	−	0.318170i	−0.848064	+	0.529894i	$0.822232\pi$
$200$	11.0390	+	8.79538i	0.780578	+	0.621927i
$201$		0			0
$202$	−4.64593	+	6.54986i	−0.326886	+	0.460846i
$203$	21.5863	−	8.94133i	1.51506	−	0.627559i
$204$		0			0
$205$	−0.0158735	+	0.0383220i	−0.00110865	+	0.00267652i
$206$	−21.4676	−	4.89652i	−1.49572	−	0.341156i
$207$		0			0
$208$	15.7867	−	4.55812i	1.09461	−	0.316049i
$209$	16.2617			1.12484
$210$		0			0
$211$	0.322439	+	0.133558i	0.0221976	+	0.00919454i	0.393755	−	0.919216i	$-0.371176\pi$
$211$	0.322439	+	0.133558i	0.0221976	+	0.00919454i	−0.371557	+	0.928410i	$0.621176\pi$
$212$	−7.99596	−	0.446685i	−0.549165	−	0.0306785i
$213$		0			0
$214$	−0.161736	+	0.228017i	−0.0110561	+	0.0155869i
$215$	−0.497491	−	0.497491i	−0.0339286	−	0.0339286i
$216$		0			0
$217$	4.40478	−	4.40478i	0.299016	−	0.299016i
$218$	−1.30272	−	7.66042i	−0.0882311	−	0.518829i
$219$		0			0
$220$	−0.371807	−	1.06156i	−0.0250672	−	0.0715706i
$221$	−4.03178	+	9.73358i	−0.271207	+	0.654752i
$222$		0			0
$223$			19.1612i			1.28313i	0.767068	+	0.641566i	$0.221715\pi$
$223$			19.1612i			1.28313i	−0.767068	+	0.641566i	$0.778285\pi$
$224$	10.6188	+	22.0088i	0.709499	+	1.47052i
$225$		0			0
$226$	−7.08557	+	4.45361i	−0.471325	+	0.296250i
$227$	−19.4451	−	8.05441i	−1.29061	−	0.534590i	−0.371446	−	0.928455i	$-0.621138\pi$
$227$	−19.4451	−	8.05441i	−1.29061	−	0.534590i	−0.919169	+	0.393864i	$0.871138\pi$
$228$		0			0
$229$	−6.97193	−	16.8317i	−0.460718	−	1.11227i	−0.968103	−	0.250552i	$-0.919388\pi$
$229$	−6.97193	−	16.8317i	−0.460718	−	1.11227i	0.507385	−	0.861719i	$-0.330612\pi$
$230$	0.785581	−	0.133594i	0.0517997	−	0.00880895i
$231$		0			0
$232$	14.7022	+	4.22862i	0.965249	+	0.277623i
$233$	−16.7768	+	16.7768i	−1.09909	+	1.09909i	−0.104569	+	0.994518i	$0.533346\pi$
$233$	−16.7768	+	16.7768i	−1.09909	+	1.09909i	−0.994518	+	0.104569i	$0.966654\pi$
$234$		0			0
$235$	0.280815	+	0.677947i	0.0183183	+	0.0442244i
$236$	−5.15683	−	0.288080i	−0.335681	−	0.0187524i
$237$		0			0
$238$	−15.2759	−	3.48426i	−0.990188	−	0.225851i
$239$		−	9.10976i		−	0.589261i	−0.955611	−	0.294631i	$-0.904803\pi$
$239$		−	9.10976i		−	0.589261i	0.955611	−	0.294631i	$-0.0951966\pi$
$240$		0			0
$241$			7.39995i			0.476673i	0.971183	+	0.238336i	$0.0766020\pi$
$241$			7.39995i			0.476673i	−0.971183	+	0.238336i	$0.923398\pi$
$242$	6.72106	−	29.4669i	0.432046	−	1.89420i
$243$		0			0
$244$	16.8386	−	15.0568i	1.07798	−	0.963914i
$245$	0.441093	+	1.06489i	0.0281804	+	0.0680336i
$246$		0			0
$247$	−8.30210	+	8.30210i	−0.528250	+	0.528250i
$248$	4.05283	−	0.458454i	0.257355	−	0.0291119i
$249$		0			0
$250$	0.234131	+	1.37677i	0.0148077	+	0.0870746i
$251$	4.84250	+	11.6908i	0.305656	+	0.737919i	0.999836	+	0.0181174i	$0.00576726\pi$
$251$	4.84250	+	11.6908i	0.305656	+	0.737919i	−0.694180	+	0.719802i	$0.744233\pi$
$252$		0			0
$253$	29.9641	+	12.4115i	1.88382	+	0.780306i
$254$	−7.30051	−	11.6149i	−0.458075	−	0.728784i
$255$		0			0
$256$	−3.54199	+	15.6030i	−0.221374	+	0.975189i
$257$			6.02571i			0.375873i	0.982181	+	0.187937i	$0.0601800\pi$
$257$			6.02571i			0.375873i	−0.982181	+	0.187937i	$0.939820\pi$
$258$		0			0
$259$	−8.97478	+	21.6670i	−0.557666	+	1.34632i
$260$	0.731782	+	0.352143i	0.0453832	+	0.0218390i
$261$		0			0
$262$	−19.2146	+	3.26759i	−1.18708	+	0.201872i
$263$	6.79218	−	6.79218i	0.418824	−	0.418824i	−0.465974	−	0.884798i	$-0.654296\pi$
$263$	6.79218	−	6.79218i	0.418824	−	0.418824i	0.884798	+	0.465974i	$0.154296\pi$
$264$		0			0
$265$	−0.279875	−	0.279875i	−0.0171926	−	0.0171926i
$266$	−14.2418	−	10.1020i	−0.873224	−	0.619392i
$267$		0			0
$268$	2.40553	+	2.69020i	0.146941	+	0.164330i
$269$	−13.8548	−	5.73883i	−0.844740	−	0.349903i	−0.0820193	−	0.996631i	$-0.526137\pi$
$269$	−13.8548	−	5.73883i	−0.844740	−	0.349903i	−0.762721	+	0.646728i	$0.776137\pi$
$270$		0			0
$271$	5.62497			0.341692			0.170846	−	0.985298i	$-0.445350\pi$
$271$	5.62497			0.341692			0.170846	+	0.985298i	$0.445350\pi$
$272$	−6.40100	−	8.01693i	−0.388118	−	0.486098i
$273$		0			0
$274$	2.50335	−	10.9753i	0.151233	−	0.663045i
$275$	−10.8653	+	26.2311i	−0.655201	+	1.58179i
$276$		0			0
$277$	−1.00843	+	0.417706i	−0.0605908	+	0.0250975i	−0.412773	−	0.910834i	$-0.635440\pi$
$277$	−1.00843	+	0.417706i	−0.0605908	+	0.0250975i	0.352182	+	0.935931i	$0.385440\pi$
$278$	0.610048	+	0.432717i	0.0365883	+	0.0259527i
$279$		0			0
$280$	−0.333832	+	1.16068i	−0.0199503	+	0.0693640i
$281$	21.7589	+	21.7589i	1.29803	+	1.29803i	0.929693	+	0.368335i	$0.120072\pi$
$281$	21.7589	+	21.7589i	1.29803	+	1.29803i	0.368335	+	0.929693i	$0.379928\pi$
$282$		0			0
$283$	−22.3614	+	9.26239i	−1.32925	+	0.550592i	−0.930441	−	0.366443i	$-0.880576\pi$
$283$	−22.3614	+	9.26239i	−1.32925	+	0.550592i	−0.398807	+	0.917035i	$0.630576\pi$
$284$	−2.78577	−	7.95376i	−0.165305	−	0.471969i
$285$		0			0
$286$	17.5895	+	27.9844i	1.04009	+	1.65475i
$287$	1.81274			0.107003
$288$		0			0
$289$	−10.4223			−0.613074
$290$	0.402359	+	0.640141i	0.0236273	+	0.0375904i
$291$		0			0
$292$	24.6229	−	8.62404i	1.44094	−	0.504684i
$293$	29.2423	−	12.1126i	1.70835	−	0.707623i	0.708355	−	0.705856i	$-0.249438\pi$
$293$	29.2423	−	12.1126i	1.70835	−	0.707623i	0.999998	−	0.00176683i	$-0.000562400\pi$
$294$		0			0
$295$	−0.180500	−	0.180500i	−0.0105091	−	0.0105091i
$296$	−13.4362	+	7.43367i	−0.780964	+	0.432073i
$297$		0			0
$298$	−4.07080	−	2.88749i	−0.235815	−	0.167268i
$299$	−21.6341	+	8.96114i	−1.25113	+	0.518236i
$300$		0			0
$301$	−11.7664	+	28.4066i	−0.678204	+	1.63733i
$302$	−6.07056	+	26.6149i	−0.349322	+	1.53152i
$303$		0			0
$304$	−3.17140	−	10.9839i	−0.181892	−	0.629970i
$305$	1.11641			0.0639252
$306$		0			0
$307$	13.7854	+	5.71009i	0.786773	+	0.325892i	0.739645	−	0.672997i	$-0.234993\pi$
$307$	13.7854	+	5.71009i	0.786773	+	0.325892i	0.0471275	+	0.998889i	$0.484993\pi$
$308$	−36.6431	+	32.7657i	−2.08793	+	1.86700i
$309$		0			0
$310$	0.164419	+	0.116625i	0.00933838	+	0.00662387i
$311$	11.4220	+	11.4220i	0.647684	+	0.647684i	0.952433	−	0.304749i	$-0.0985725\pi$
$311$	11.4220	+	11.4220i	0.647684	+	0.647684i	−0.304749	+	0.952433i	$0.598573\pi$
$312$		0			0
$313$	2.24707	−	2.24707i	0.127012	−	0.127012i	−0.640743	−	0.767755i	$-0.721374\pi$
$313$	2.24707	−	2.24707i	0.127012	−	0.127012i	0.767755	+	0.640743i	$0.221374\pi$
$314$	−23.3283	+	3.96716i	−1.31649	+	0.223880i
$315$		0			0
$316$	−0.972872	+	2.02171i	−0.0547283	+	0.113730i
$317$	1.05906	−	2.55679i	0.0594826	−	0.143604i	−0.891344	−	0.453328i	$-0.850237\pi$
$317$	1.05906	−	2.55679i	0.0594826	−	0.143604i	0.950826	+	0.309724i	$0.100237\pi$
$318$		0			0
$319$			30.7736i			1.72299i
$320$	−0.644519	+	0.458166i	−0.0360297	+	0.0256123i
$321$		0			0
$322$	−18.5321	−	29.4841i	−1.03275	−	1.64308i
$323$	6.77233	+	2.80519i	0.376823	+	0.156085i
$324$		0			0
$325$	−7.84475	−	18.9389i	−0.435148	−	1.05054i
$326$	3.74391	+	22.0155i	0.207356	+	1.21933i
$327$		0			0
$328$	0.928286	+	0.739614i	0.0512560	+	0.0408384i
$329$	22.6761	−	22.6761i	1.25018	−	1.25018i
$330$		0			0
$331$	−0.123439	−	0.298008i	−0.00678481	−	0.0163800i	0.920451	−	0.390858i	$-0.127822\pi$
$331$	−0.123439	−	0.298008i	−0.00678481	−	0.0163800i	−0.927236	+	0.374478i	$0.877822\pi$
$332$	−14.4059	−	16.1106i	−0.790625	−	0.884187i
$333$		0			0
$334$	−2.93037	+	12.8475i	−0.160343	+	0.702983i
$335$			0.178361i			0.00974489i
$336$		0			0
$337$		−	16.5067i		−	0.899179i	−0.893235	−	0.449590i	$-0.851570\pi$
$337$		−	16.5067i		−	0.899179i	0.893235	−	0.449590i	$-0.148430\pi$
$338$	−5.34252	−	1.21857i	−0.290595	−	0.0662814i
$339$		0			0
$340$	0.0282803	−	0.506237i	0.00153372	−	0.0274545i
$341$	3.13974	+	7.58001i	0.170027	+	0.410481i
$342$		0			0
$343$	14.2368	−	14.2368i	0.768716	−	0.768716i
$344$	−17.6156	+	9.74592i	−0.949767	+	0.525465i
$345$		0			0
$346$	26.8921	−	4.57322i	1.44573	−	0.245858i
$347$	5.96248	+	14.3947i	0.320083	+	0.772748i	0.999248	+	0.0387633i	$0.0123418\pi$
$347$	5.96248	+	14.3947i	0.320083	+	0.772748i	−0.679166	+	0.733985i	$0.737658\pi$
$348$		0			0
$349$	1.57618	+	0.652873i	0.0843707	+	0.0349475i	0.424470	−	0.905442i	$-0.360461\pi$
$349$	1.57618	+	0.652873i	0.0843707	+	0.0349475i	−0.340099	+	0.940390i	$0.610461\pi$
$350$	25.8109	−	16.2233i	1.37965	−	0.867174i
$351$		0			0
$352$	−32.1332	+	1.82825i	−1.71270	+	0.0974463i
$353$			18.7091i			0.995786i	0.867239	+	0.497893i	$0.165893\pi$
$353$			18.7091i			0.995786i	−0.867239	+	0.497893i	$0.834107\pi$
$354$		0			0
$355$	0.159393	−	0.384810i	0.00845972	−	0.0204236i
$356$	32.1907	−	11.2746i	1.70610	−	0.597555i
$357$		0			0
$358$	−2.52388	−	14.8413i	−0.133391	−	0.784388i
$359$	23.5065	−	23.5065i	1.24062	−	1.24062i	0.280882	−	0.959742i	$-0.409373\pi$
$359$	23.5065	−	23.5065i	1.24062	−	1.24062i	0.959742	−	0.280882i	$-0.0906270\pi$
$360$		0			0
$361$	−7.65868	−	7.65868i	−0.403088	−	0.403088i
$362$	7.14048	−	10.0667i	0.375295	−	0.529094i
$363$		0			0
$364$	1.97956	−	35.4354i	0.103757	−	1.85732i
$365$	1.19127	+	0.493442i	0.0623542	+	0.0258279i
$366$		0			0
$367$	−2.95190			−0.154088			−0.0770440	−	0.997028i	$-0.524548\pi$
$367$	−2.95190			−0.154088			−0.0770440	+	0.997028i	$0.524548\pi$
$368$	2.53964	−	22.6597i	0.132388	−	1.18122i
$369$		0			0
$370$	−0.739916	−	0.168767i	−0.0384664	−	0.00877376i
$371$	−6.61945	+	15.9808i	−0.343665	+	0.829680i
$372$		0			0
$373$	−19.7552	+	8.18287i	−1.02289	+	0.423693i	−0.830140	−	0.557556i	$-0.811739\pi$
$373$	−19.7552	+	8.18287i	−1.02289	+	0.423693i	−0.192746	+	0.981249i	$0.561739\pi$
$374$	11.9392	−	16.8320i	0.617362	−	0.870362i
$375$		0			0
$376$	20.8643	−	2.36016i	1.07599	−	0.121716i
$377$	−15.7109	−	15.7109i	−0.809152	−	0.809152i
$378$		0			0
$379$	4.26476	−	1.76652i	0.219066	−	0.0907402i	−0.270451	−	0.962734i	$-0.587173\pi$
$379$	4.26476	−	1.76652i	0.219066	−	0.0907402i	0.489518	+	0.871993i	$0.337173\pi$
$380$	0.245010	−	0.509152i	0.0125688	−	0.0261189i
$381$		0			0
$382$	−15.6277	+	9.82273i	−0.799582	+	0.502574i
$383$	−9.45328			−0.483040			−0.241520	−	0.970396i	$-0.577646\pi$
$383$	−9.45328			−0.483040			−0.241520	+	0.970396i	$0.577646\pi$
$384$		0			0
$385$	−2.42945			−0.123816
$386$	−3.66296	+	2.30234i	−0.186440	+	0.117186i
$387$		0			0
$388$	−16.0912	+	33.4388i	−0.816906	+	1.69760i
$389$	20.8554	−	8.63860i	1.05741	−	0.437994i	0.214880	−	0.976640i	$-0.431064\pi$
$389$	20.8554	−	8.63860i	1.05741	−	0.437994i	0.842532	+	0.538646i	$0.181064\pi$
$390$		0			0
$391$	10.3378	+	10.3378i	0.522806	+	0.522806i
$392$	32.7728	−	3.70724i	1.65527	−	0.187244i
$393$		0			0
$394$	4.84228	−	6.82667i	0.243950	−	0.343923i
$395$	−0.102446	+	0.0424345i	−0.00515461	+	0.00213511i
$396$		0			0
$397$	3.29268	−	7.94922i	0.165255	−	0.398960i	−0.819460	−	0.573137i	$-0.805726\pi$
$397$	3.29268	−	7.94922i	0.165255	−	0.398960i	0.984714	+	0.174177i	$0.0557264\pi$
$398$	−8.75192	−	1.99622i	−0.438694	−	0.100061i
$399$		0			0
$400$	19.8367	+	2.22325i	0.991836	+	0.111162i
$401$	−32.5903			−1.62748			−0.813740	−	0.581229i	$-0.802572\pi$
$401$	−32.5903			−1.62748			−0.813740	+	0.581229i	$0.802572\pi$
$402$		0			0
$403$	−5.47278	−	2.26690i	−0.272619	−	0.112922i
$404$	−0.633431	+	11.3388i	−0.0315144	+	0.564128i
$405$		0			0
$406$	19.1170	−	26.9513i	0.948760	−	1.33757i
$407$	−21.8416	−	21.8416i	−1.08265	−	1.08265i
$408$		0			0
$409$	5.41708	−	5.41708i	0.267858	−	0.267858i	−0.560379	−	0.828236i	$-0.689344\pi$
$409$	5.41708	−	5.41708i	0.267858	−	0.267858i	0.828236	+	0.560379i	$0.189344\pi$
$410$	0.00983455	+	0.0578305i	0.000485694	+	0.00285605i
$411$		0			0
$412$	−29.3890	+	10.2934i	−1.44789	+	0.507117i
$413$	−4.26908	+	10.3065i	−0.210068	+	0.507149i
$414$		0			0
$415$		−	1.06814i		−	0.0524329i
$416$	15.4716	−	17.3384i	0.758560	−	0.850085i
$417$		0			0
$418$	19.4707	−	12.2382i	0.952343	−	0.598592i
$419$	22.0298	+	9.12504i	1.07623	+	0.445787i	0.849184	−	0.528097i	$-0.177094\pi$
$419$	22.0298	+	9.12504i	1.07623	+	0.445787i	0.227042	+	0.973885i	$0.427094\pi$
$420$		0			0
$421$	2.82553	+	6.82144i	0.137708	+	0.332457i	0.977656	−	0.210210i	$-0.0674147\pi$
$421$	2.82553	+	6.82144i	0.137708	+	0.332457i	−0.839948	+	0.542667i	$0.817415\pi$
$422$	0.486582	−	0.0827472i	0.0236864	−	0.00402807i
$423$		0			0
$424$	−9.91003	+	5.48279i	−0.481274	+	0.266268i
$425$	−9.04991	+	9.04991i	−0.438985	+	0.438985i
$426$		0			0
$427$	−18.6709	−	45.0756i	−0.903549	−	2.18136i
$428$	−0.0220514	+	0.394734i	−0.00106589	+	0.0190802i
$429$		0			0
$430$	−0.970068	−	0.221262i	−0.0467808	−	0.0106702i
$431$		−	6.73112i		−	0.324226i	−0.986772	−	0.162113i	$-0.948169\pi$
$431$		−	6.73112i		−	0.324226i	0.986772	−	0.162113i	$-0.0518310\pi$
$432$		0			0
$433$		−	12.1160i		−	0.582257i	−0.956684	−	0.291129i	$-0.905969\pi$
$433$		−	12.1160i		−	0.582257i	0.956684	−	0.291129i	$-0.0940308\pi$
$434$	1.95905	−	8.58898i	0.0940374	−	0.412284i
$435$		0			0
$436$	−7.32489	−	8.19171i	−0.350799	−	0.392312i
$437$	6.23489	+	15.0524i	0.298255	+	0.720052i
$438$		0			0
$439$	14.0767	−	14.0767i	0.671843	−	0.671843i	−0.286298	−	0.958141i	$-0.592425\pi$
$439$	14.0767	−	14.0767i	0.671843	−	0.671843i	0.958141	+	0.286298i	$0.0924246\pi$
$440$	−1.24409	−	0.991234i	−0.0593098	−	0.0472552i
$441$		0			0
$442$	2.49792	+	14.6886i	0.118814	+	0.698667i
$443$	−14.5313	−	35.0817i	−0.690404	−	1.66678i	−0.743965	−	0.668218i	$-0.767057\pi$
$443$	−14.5313	−	35.0817i	−0.690404	−	1.66678i	0.0535615	−	0.998565i	$-0.482943\pi$
$444$		0			0
$445$	1.55741	+	0.645102i	0.0738285	+	0.0305808i
$446$	14.4204	+	22.9425i	0.682827	+	1.08636i
$447$		0			0
$448$	29.2778	+	18.3604i	1.38324	+	0.867449i
$449$		−	25.9809i		−	1.22611i	−0.790039	−	0.613056i	$-0.789940\pi$
$449$		−	25.9809i		−	1.22611i	0.790039	−	0.613056i	$-0.210060\pi$
$450$		0			0
$451$	−0.913674	+	2.20580i	−0.0430232	+	0.103867i
$452$	−5.13211	+	10.6650i	−0.241394	+	0.501638i
$453$		0			0
$454$	−29.3439	+	4.99017i	−1.37718	+	0.234200i
$455$	1.24031	−	1.24031i	0.0581467	−	0.0581467i
$456$		0			0
$457$	6.23785	+	6.23785i	0.291794	+	0.291794i	0.837789	−	0.545994i	$-0.183848\pi$
$457$	6.23785	+	6.23785i	0.291794	+	0.291794i	−0.545994	+	0.837789i	$0.683848\pi$
$458$	−21.0150	−	14.9063i	−0.981968	−	0.696526i
$459$		0			0
$460$	0.840065	−	0.751172i	0.0391682	−	0.0350236i
$461$	23.3278	+	9.66269i	1.08648	+	0.450036i	0.852779	−	0.522271i	$-0.174915\pi$
$461$	23.3278	+	9.66269i	1.08648	+	0.450036i	0.233704	+	0.972308i	$0.424915\pi$
$462$		0			0
$463$	3.99595			0.185707			0.0928537	−	0.995680i	$-0.470401\pi$
$463$	3.99595			0.185707			0.0928537	+	0.995680i	$0.470401\pi$
$464$	20.7859	−	6.00156i	0.964963	−	0.278616i
$465$		0			0
$466$	−7.46158	+	32.7135i	−0.345651	+	1.51542i
$467$	7.26272	−	17.5338i	0.336079	−	0.811366i	−0.662006	−	0.749499i	$-0.730294\pi$
$467$	7.26272	−	17.5338i	0.336079	−	0.811366i	0.998084	−	0.0618671i	$-0.0197055\pi$
$468$		0			0
$469$	7.20142	−	2.98293i	0.332531	−	0.137739i
$470$	0.846442	+	0.600396i	0.0390435	+	0.0276942i
$471$		0			0
$472$	−6.39127	+	3.53601i	−0.294182	+	0.162758i
$473$	−28.6354	−	28.6354i	−1.31666	−	1.31666i
$474$		0			0
$475$	−13.1771	+	5.45814i	−0.604607	+	0.250437i
$476$	−20.9126	+	7.32453i	−0.958527	+	0.335719i
$477$		0			0
$478$	−6.85585	−	10.9075i	−0.313579	−	0.498896i
$479$	21.7665			0.994537			0.497268	−	0.867597i	$-0.334336\pi$
$479$	21.7665			0.994537			0.497268	+	0.867597i	$0.334336\pi$
$480$		0			0
$481$	22.3017			1.01687
$482$	5.56908	+	8.86024i	0.253664	+	0.403573i
$483$		0			0
$484$	−14.1289	−	40.3400i	−0.642222	−	1.83364i
$485$	−1.69444	+	0.701861i	−0.0769407	+	0.0318699i
$486$		0			0
$487$	−9.10128	−	9.10128i	−0.412419	−	0.412419i	0.470162	−	0.882580i	$-0.344196\pi$
$487$	−9.10128	−	9.10128i	−0.412419	−	0.412419i	−0.882580	+	0.470162i	$0.844196\pi$
$488$	8.83002	−	30.7006i	0.399716	−	1.38975i
$489$		0			0
$490$	1.32956	+	0.943078i	0.0600633	+	0.0426039i
$491$	15.2645	−	6.32276i	0.688876	−	0.285342i	−0.0106556	−	0.999943i	$-0.503392\pi$
$491$	15.2645	−	6.32276i	0.688876	−	0.285342i	0.699532	+	0.714601i	$0.253392\pi$
$492$		0			0
$493$	−5.30855	+	12.8160i	−0.239085	+	0.577202i
$494$	−3.69240	+	16.1884i	−0.166129	+	0.728352i
$495$		0			0
$496$	4.50758	−	3.59901i	0.202396	−	0.161601i
$497$	−18.2026			−0.816500
$498$		0			0
$499$	−32.2595	−	13.3623i	−1.44413	−	0.598180i	−0.483337	−	0.875434i	$-0.660575\pi$
$499$	−32.2595	−	13.3623i	−1.44413	−	0.598180i	−0.960796	+	0.277255i	$0.910575\pi$
$500$	1.31647	+	1.47226i	0.0588742	+	0.0658413i
$501$		0			0
$502$	14.5964	+	10.3535i	0.651471	+	0.462099i
$503$	−7.34111	−	7.34111i	−0.327324	−	0.327324i	0.524244	−	0.851568i	$-0.324348\pi$
$503$	−7.34111	−	7.34111i	−0.327324	−	0.327324i	−0.851568	+	0.524244i	$0.824348\pi$
$504$		0			0
$505$	−0.396882	+	0.396882i	−0.0176610	+	0.0176610i
$506$	45.2178	−	7.68966i	2.01018	−	0.341847i
$507$		0			0
$508$	−17.4824	−	8.41273i	−0.775654	−	0.373255i
$509$	7.55299	−	18.2345i	0.334780	−	0.808231i	−0.663419	−	0.748248i	$-0.730895\pi$
$509$	7.55299	−	18.2345i	0.334780	−	0.808231i	0.998199	−	0.0599832i	$-0.0191047\pi$
$510$		0			0
$511$		−	56.3508i		−	2.49281i
$512$	7.50161	+	21.3477i	0.331528	+	0.943446i
$513$		0			0
$514$	4.53485	+	7.21481i	0.200024	+	0.318232i
$515$	−1.42186	−	0.588955i	−0.0626548	−	0.0259525i
$516$		0			0
$517$	16.1636	+	39.0225i	0.710876	+	1.71621i
$518$	5.56039	+	32.6970i	0.244310	+	1.43662i
$519$		0			0
$520$	1.14121	−	0.129093i	0.0500452	−	0.00566109i
$521$	−26.3209	+	26.3209i	−1.15314	+	1.15314i	−0.167218	+	0.985920i	$0.553478\pi$
$521$	−26.3209	+	26.3209i	−1.15314	+	1.15314i	−0.985920	+	0.167218i	$0.946522\pi$
$522$		0			0
$523$	5.50275	+	13.2848i	0.240619	+	0.580905i	0.997345	−	0.0728276i	$-0.0232023\pi$
$523$	5.50275	+	13.2848i	0.240619	+	0.580905i	−0.756726	+	0.653732i	$0.773202\pi$
$524$	−20.5472	+	18.3730i	−0.897608	+	0.802627i
$525$		0			0
$526$	3.02086	−	13.2442i	0.131716	−	0.577475i
$527$			3.69839i			0.161104i
$528$		0			0
$529$			9.49450i			0.412805i
$530$	−0.545734	−	0.124476i	−0.0237052	−	0.00540688i
$531$		0			0
$532$	−24.6549	−	1.37732i	−1.06893	−	0.0597143i
$533$	−0.659674	−	1.59259i	−0.0285737	−	0.0689829i
$534$		0			0
$535$	−0.0138165	+	0.0138165i	−0.000597339	+	0.000597339i
$536$	4.90483	+	1.41071i	0.211856	+	0.0609336i
$537$		0			0
$538$	−20.9078	+	3.55554i	−0.901399	+	0.153290i
$539$	25.3892	+	61.2950i	1.09359	+	2.64016i
$540$		0			0
$541$	1.34772	+	0.558245i	0.0579431	+	0.0240008i	0.411467	−	0.911425i	$-0.365017\pi$
$541$	1.34772	+	0.558245i	0.0579431	+	0.0240008i	−0.353524	+	0.935426i	$0.615017\pi$
$542$	6.73499	−	4.23325i	0.289292	−	0.181834i
$543$		0			0
$544$	−13.6976	−	4.78169i	−0.587278	−	0.205013i
$545$		−	0.543113i		−	0.0232644i
$546$		0			0
$547$	3.11417	−	7.51828i	0.133152	−	0.321458i	−0.843215	−	0.537577i	$-0.819340\pi$
$547$	3.11417	−	7.51828i	0.133152	−	0.321458i	0.976367	+	0.216119i	$0.0693398\pi$
$548$	−5.26250	−	15.0252i	−0.224803	−	0.641844i
$549$		0			0
$550$	6.73166	+	39.5845i	0.287039	+	1.68789i
$551$	−10.9312	+	10.9312i	−0.465683	+	0.465683i
$552$		0			0
$553$	3.42664	+	3.42664i	0.145715	+	0.145715i
$554$	−0.893076	+	1.25906i	−0.0379431	+	0.0534925i
$555$		0			0
$556$	1.05609	+	0.0589973i	0.0447882	+	0.00250204i
$557$	−10.3810	−	4.29993i	−0.439855	−	0.182194i	0.151755	−	0.988418i	$-0.451508\pi$
$557$	−10.3810	−	4.29993i	−0.439855	−	0.182194i	−0.591610	+	0.806224i	$0.701508\pi$
$558$		0			0
$559$	29.2386			1.23666
$560$	0.473799	+	1.64097i	0.0200217	+	0.0693434i
$561$		0			0
$562$	42.4282	+	9.67739i	1.78972	+	0.408216i
$563$	−1.95005	+	4.70784i	−0.0821848	+	0.198412i	−0.959630	−	0.281265i	$-0.909246\pi$
$563$	−1.95005	+	4.70784i	−0.0821848	+	0.198412i	0.877445	+	0.479677i	$0.159246\pi$
$564$		0			0
$565$	−0.540424	+	0.223851i	−0.0227358	+	0.00941749i
$566$	−19.8034	+	27.9190i	−0.832400	+	1.17352i
$567$		0			0
$568$	−9.32137	−	7.42682i	−0.391116	−	0.311623i
$569$	−3.12423	−	3.12423i	−0.130974	−	0.130974i	0.638581	−	0.769555i	$-0.279522\pi$
$569$	−3.12423	−	3.12423i	−0.130974	−	0.130974i	−0.769555	+	0.638581i	$0.779522\pi$
$570$		0			0
$571$	33.4029	−	13.8360i	1.39787	−	0.579017i	0.448672	−	0.893697i	$-0.351897\pi$
$571$	33.4029	−	13.8360i	1.39787	−	0.579017i	0.949198	+	0.314680i	$0.101897\pi$
$572$	42.1212	+	20.2692i	1.76117	+	0.847499i
$573$		0			0
$574$	2.17047	−	1.36424i	0.0905936	−	0.0569423i
$575$	−28.4463			−1.18629
$576$		0			0
$577$	−14.0315			−0.584141			−0.292070	−	0.956397i	$-0.594344\pi$
$577$	−14.0315			−0.584141			−0.292070	+	0.956397i	$0.594344\pi$
$578$	−12.4790	+	7.84361i	−0.519056	+	0.326251i
$579$		0			0
$580$	0.963519	+	0.463657i	0.0400079	+	0.0192523i
$581$	−43.1268	+	17.8637i	−1.78920	+	0.741112i
$582$		0			0
$583$	−16.1095	−	16.1095i	−0.667188	−	0.667188i
$584$	22.9916	−	28.8566i	0.951398	−	1.19410i
$585$		0			0
$586$	25.8972	−	36.5101i	1.06980	−	1.50822i
$587$	−12.0165	+	4.97740i	−0.495975	+	0.205439i	−0.616627	−	0.787255i	$-0.711501\pi$
$587$	−12.0165	+	4.97740i	−0.495975	+	0.205439i	0.120652	+	0.992695i	$0.461501\pi$
$588$		0			0
$589$	−1.57724	+	3.80780i	−0.0649891	+	0.156898i
$590$	−0.351960	−	0.0802781i	−0.0144900	−	0.00330500i
$591$		0			0
$592$	−10.4932	+	19.0125i	−0.431269	+	0.781408i
$593$	−17.6528			−0.724914			−0.362457	−	0.932000i	$-0.618062\pi$
$593$	−17.6528			−0.724914			−0.362457	+	0.932000i	$0.618062\pi$
$594$		0			0
$595$	−1.01177	−	0.419088i	−0.0414785	−	0.0171809i
$596$	−7.04719	−	0.393684i	−0.288664	−	0.0161259i
$597$		0			0
$598$	−19.1593	+	27.0110i	−0.783484	+	1.10456i
$599$	5.25995	+	5.25995i	0.214916	+	0.214916i	0.806352	−	0.591436i	$-0.201439\pi$
$599$	5.25995	+	5.25995i	0.214916	+	0.214916i	−0.591436	+	0.806352i	$0.701439\pi$
$600$		0			0
$601$	6.54574	−	6.54574i	0.267006	−	0.267006i	−0.560886	−	0.827893i	$-0.689540\pi$
$601$	6.54574	−	6.54574i	0.267006	−	0.267006i	0.827893	+	0.560886i	$0.189540\pi$
$602$	7.28996	+	42.8675i	0.297117	+	1.74715i
$603$		0			0
$604$	12.7614	+	36.4356i	0.519254	+	1.48255i
$605$	0.808413	−	1.95168i	0.0328667	−	0.0793472i
$606$		0			0
$607$		−	1.72276i		−	0.0699248i	−0.999389	−	0.0349624i	$-0.988869\pi$
$607$		−	1.72276i		−	0.0699248i	0.999389	−	0.0349624i	$-0.0111311\pi$
$608$	−12.0635	−	10.7647i	−0.489241	−	0.436566i
$609$		0			0
$610$	1.33672	−	0.840188i	0.0541220	−	0.0340182i
$611$	−28.1743	−	11.6702i	−1.13981	−	0.472125i
$612$		0			0
$613$	16.6267	+	40.1405i	0.671547	+	1.62126i	0.778982	+	0.627046i	$0.215736\pi$
$613$	16.6267	+	40.1405i	0.671547	+	1.62126i	−0.107435	+	0.994212i	$0.534264\pi$
$614$	20.8031	−	3.53773i	0.839544	−	0.142771i
$615$		0			0
$616$	−19.2153	+	66.8085i	−0.774207	+	2.69179i
$617$	−7.78933	+	7.78933i	−0.313587	+	0.313587i	−0.846297	−	0.532711i	$-0.821173\pi$
$617$	−7.78933	+	7.78933i	−0.313587	+	0.313587i	0.532711	+	0.846297i	$0.321173\pi$
$618$		0			0
$619$	11.0171	+	26.5976i	0.442814	+	1.06905i	0.974957	+	0.222394i	$0.0713871\pi$
$619$	11.0171	+	26.5976i	0.442814	+	1.06905i	−0.532143	+	0.846655i	$0.678613\pi$
$620$	0.284636	+	0.0159008i	0.0114312	+	0.000638593i
$621$		0			0
$622$	22.2721	+	5.08001i	0.893028	+	0.203690i
$623$		−	73.6703i		−	2.95154i
$624$		0			0
$625$		−	24.8535i		−	0.994141i
$626$	0.999396	−	4.38161i	0.0399439	−	0.175124i
$627$		0			0
$628$	−24.9462	+	22.3065i	−0.995461	+	0.890125i
$629$	−5.32840	−	12.8639i	−0.212457	−	0.512917i
$630$		0			0
$631$	−21.0548	+	21.0548i	−0.838177	+	0.838177i	−0.988619	−	0.150442i	$-0.951930\pi$
$631$	−21.0548	+	21.0548i	−0.838177	+	0.838177i	0.150442	+	0.988619i	$0.451930\pi$
$632$	0.356648	+	3.15284i	0.0141867	+	0.125413i
$633$		0			0
$634$	−0.656147	−	3.85837i	−0.0260589	−	0.153235i
$635$	−0.366944	−	0.885882i	−0.0145617	−	0.0351552i
$636$		0			0
$637$	−44.2551	−	18.3311i	−1.75345	−	0.726303i
$638$	23.1597	+	36.8464i	0.916900	+	1.45876i
$639$		0			0
$640$	−0.426900	+	1.03363i	−0.0168747	+	0.0408580i
$641$		−	5.65123i		−	0.223210i	−0.993753	−	0.111605i	$-0.964401\pi$
$641$		−	5.65123i		−	0.223210i	0.993753	−	0.111605i	$-0.0355992\pi$
$642$		0			0
$643$	17.0022	−	41.0470i	0.670502	−	1.61874i	−0.110256	−	0.993903i	$-0.535167\pi$
$643$	17.0022	−	41.0470i	0.670502	−	1.61874i	0.780759	−	0.624833i	$-0.214833\pi$
$644$	−44.3784	−	21.3554i	−1.74875	−	0.841522i
$645$		0			0
$646$	10.2199	−	1.73798i	0.402097	−	0.0683799i
$647$	−0.0151270	+	0.0151270i	−0.000594703	+	0.000594703i	−0.707404	−	0.706809i	$-0.750134\pi$
$647$	−0.0151270	+	0.0151270i	−0.000594703	+	0.000594703i	0.706809	+	0.707404i	$0.250134\pi$
$648$		0			0
$649$	−10.3895	−	10.3895i	−0.407824	−	0.407824i
$650$	−23.6459	−	16.7724i	−0.927469	−	0.657869i
$651$		0			0
$652$	21.0512	+	23.5424i	0.824429	+	0.921991i
$653$	28.8575	+	11.9531i	1.12928	+	0.467763i	0.867536	−	0.497375i	$-0.165703\pi$
$653$	28.8575	+	11.9531i	1.12928	+	0.467763i	0.261744	+	0.965137i	$0.415703\pi$
$654$		0			0
$655$	−1.36228			−0.0532289
$656$	1.66809	+	0.186956i	0.0651281	+	0.00729940i
$657$		0			0
$658$	10.0853	−	44.2167i	0.393167	−	1.72375i
$659$	−7.25678	+	17.5194i	−0.282684	+	0.682459i	−0.999896	−	0.0143952i	$-0.995418\pi$
$659$	−7.25678	+	17.5194i	−0.282684	+	0.682459i	0.717212	+	0.696855i	$0.245418\pi$
$660$		0			0
$661$	−15.6310	+	6.47456i	−0.607974	+	0.251831i	−0.665362	−	0.746521i	$-0.731723\pi$
$661$	−15.6310	+	6.47456i	−0.607974	+	0.251831i	0.0573877	+	0.998352i	$0.481723\pi$
$662$	−0.372074	−	0.263918i	−0.0144611	−	0.0102575i
$663$		0			0
$664$	−29.3733	−	8.44828i	−1.13991	−	0.327857i
$665$	−0.862971	−	0.862971i	−0.0334646	−	0.0334646i
$666$		0			0
$667$	−28.4851	+	11.7989i	−1.10295	+	0.456856i
$668$	6.16016	+	17.5881i	0.238344	+	0.680505i
$669$		0			0
$670$	0.134231	+	0.213558i	0.00518581	+	0.00825047i
$671$	64.2600			2.48073
$672$		0			0
$673$	26.5987			1.02530			0.512652	−	0.858596i	$-0.328663\pi$
$673$	26.5987			1.02530			0.512652	+	0.858596i	$0.328663\pi$
$674$	−12.4227	−	19.7641i	−0.478504	−	0.761287i
$675$		0			0
$676$	−7.31387	+	2.56165i	−0.281303	+	0.0985249i
$677$	−26.3000	+	10.8938i	−1.01079	+	0.418683i	−0.825743	−	0.564047i	$-0.809244\pi$
$677$	−26.3000	+	10.8938i	−1.01079	+	0.418683i	−0.185047	+	0.982730i	$0.559244\pi$
$678$		0			0
$679$	56.6761	+	56.6761i	2.17503	+	2.17503i
$680$	−0.347124	−	0.627420i	−0.0133116	−	0.0240605i
$681$		0			0
$682$	9.46392	+	6.71292i	0.362392	+	0.257051i
$683$	−29.9528	+	12.4069i	−1.14611	+	0.474735i	−0.873228	−	0.487312i	$-0.837978\pi$
$683$	−29.9528	+	12.4069i	−1.14611	+	0.474735i	−0.272884	+	0.962047i	$0.587978\pi$
$684$		0			0
$685$	0.301105	−	0.726931i	0.0115046	−	0.0277746i
$686$	6.33190	−	27.7607i	0.241753	−	1.05991i
$687$		0			0
$688$	−13.7572	+	24.9263i	−0.524487	+	0.950307i
$689$	16.4489			0.626652
$690$		0			0
$691$	−9.94272	−	4.11841i	−0.378239	−	0.156672i	0.185460	−	0.982652i	$-0.440622\pi$
$691$	−9.94272	−	4.11841i	−0.378239	−	0.156672i	−0.563699	+	0.825980i	$0.690622\pi$
$692$	28.7572	−	25.7143i	1.09319	−	0.977509i
$693$		0			0
$694$	17.9723	+	12.7481i	0.682220	+	0.483910i
$695$	0.0369653	+	0.0369653i	0.00140217	+	0.00140217i
$696$		0			0
$697$	−0.761018	+	0.761018i	−0.0288256	+	0.0288256i
$698$	2.37856	−	0.404493i	0.0900297	−	0.0153103i
$699$		0			0
$700$	18.6949	−	38.8497i	0.706602	−	1.46838i
$701$	5.59430	−	13.5058i	0.211294	−	0.510108i	−0.782329	−	0.622866i	$-0.785968\pi$
$701$	5.59430	−	13.5058i	0.211294	−	0.510108i	0.993623	+	0.112757i	$0.0359683\pi$
$702$		0			0
$703$		−	15.5168i		−	0.585228i
$704$	−37.0984	+	26.3719i	−1.39820	+	0.993929i
$705$		0			0
$706$	14.0802	+	22.4011i	0.529914	+	0.843078i
$707$	22.6619	+	9.38686i	0.852288	+	0.353029i
$708$		0			0
$709$	4.92207	+	11.8829i	0.184852	+	0.446273i	0.988955	−	0.148218i	$-0.0473537\pi$
$709$	4.92207	+	11.8829i	0.184852	+	0.446273i	−0.804102	+	0.594491i	$0.797354\pi$
$710$	−0.0987534	−	0.580704i	−0.00370615	−	0.0217934i
$711$		0			0
$712$	30.0581	−	37.7258i	1.12647	−	1.41383i
$713$	−5.81252	+	5.81252i	−0.217680	+	0.217680i
$714$		0			0
$715$	0.884098	+	2.13440i	0.0330634	+	0.0798221i
$716$	−14.1913	−	15.8706i	−0.530352	−	0.593114i
$717$		0			0
$718$	10.4546	−	45.8358i	0.390163	−	1.71058i
$719$			16.1029i			0.600537i	0.953855	+	0.300268i	$0.0970762\pi$
$719$			16.1029i			0.600537i	−0.953855	+	0.300268i	$0.902924\pi$
$720$		0			0
$721$			67.2584i			2.50483i
$722$	−14.9338	−	3.40624i	−0.555779	−	0.126767i
$723$		0			0
$724$	0.973542	−	17.4270i	0.0361814	−	0.647671i
$725$	−10.3290	−	24.9364i	−0.383609	−	0.926113i
$726$		0			0
$727$	21.0560	−	21.0560i	0.780923	−	0.780923i	−0.199064	−	0.979987i	$-0.563790\pi$
$727$	21.0560	−	21.0560i	0.780923	−	0.780923i	0.979987	+	0.199064i	$0.0637900\pi$
$728$	−24.2979	−	43.9180i	−0.900540	−	1.62771i
$729$		0			0
$730$	1.79771	−	0.305716i	0.0665364	−	0.0113151i
$731$	−6.98581	−	16.8652i	−0.258379	−	0.623783i
$732$		0			0
$733$	41.2426	+	17.0832i	1.52333	+	0.630984i	0.978255	−	0.207404i	$-0.0665015\pi$
$733$	41.2426	+	17.0832i	1.52333	+	0.630984i	0.545074	+	0.838388i	$0.316501\pi$
$734$	−3.53443	+	2.22155i	−0.130458	+	0.0819990i
$735$		0			0
$736$	−14.0125	−	29.0426i	−0.516508	−	1.07053i
$737$			10.2664i			0.378168i
$738$		0			0
$739$	11.2262	−	27.1024i	0.412962	−	0.996977i	−0.571377	−	0.820688i	$-0.693591\pi$
$739$	11.2262	−	27.1024i	0.412962	−	0.996977i	0.984338	−	0.176290i	$-0.0564095\pi$
$740$	−1.01294	+	0.354778i	−0.0372364	+	0.0130419i
$741$		0			0
$742$	4.10113	+	24.1161i	0.150557	+	0.885329i
$743$	15.8059	−	15.8059i	0.579863	−	0.579863i	−0.355003	−	0.934865i	$-0.615520\pi$
$743$	15.8059	−	15.8059i	0.579863	−	0.579863i	0.934865	+	0.355003i	$0.115520\pi$
$744$		0			0
$745$	−0.246666	−	0.246666i	−0.00903715	−	0.00903715i
$746$	−17.4954	+	24.6651i	−0.640551	+	0.903053i
$747$		0			0
$748$	1.62781	−	29.1389i	0.0595186	−	1.06542i
$749$	0.788918	+	0.326780i	0.0288264	+	0.0119403i
$750$		0			0
$751$	−12.4955			−0.455969			−0.227984	−	0.973665i	$-0.573213\pi$
$751$	−12.4955			−0.455969			−0.227984	+	0.973665i	$0.573213\pi$
$752$	23.2054	−	18.5280i	0.846212	−	0.675646i
$753$		0			0
$754$	−30.6350	−	6.98750i	−1.11566	−	0.254470i
$755$	−0.730170	+	1.76279i	−0.0265736	+	0.0641544i
$756$		0			0
$757$	30.0398	−	12.4429i	1.09182	−	0.452245i	0.237176	−	0.971467i	$-0.423778\pi$
$757$	30.0398	−	12.4429i	1.09182	−	0.452245i	0.854639	+	0.519222i	$0.173778\pi$
$758$	3.77691	−	5.32471i	0.137184	−	0.193402i
$759$		0			0
$760$	−0.0898189	−	0.794017i	−0.00325807	−	0.0288020i
$761$	15.5032	+	15.5032i	0.561992	+	0.561992i	0.929873	−	0.367881i	$-0.119917\pi$
$761$	15.5032	+	15.5032i	0.561992	+	0.561992i	−0.367881	+	0.929873i	$0.619917\pi$
$762$		0			0
$763$	−21.9285	+	9.08308i	−0.793865	+	0.328830i
$764$	−11.3192	+	23.5223i	−0.409514	+	0.851005i
$765$		0			0
$766$	−11.3188	+	7.11438i	−0.408964	+	0.257053i
$767$	10.6084			0.383046
$768$		0			0
$769$	−7.08253			−0.255403			−0.127701	−	0.991813i	$-0.540760\pi$
$769$	−7.08253			−0.255403			−0.127701	+	0.991813i	$0.540760\pi$
$770$	−2.90887	+	1.82836i	−0.104828	+	0.0658896i
$771$		0			0
$772$	−2.65310	+	5.51337i	−0.0954872	+	0.198430i
$773$	30.3534	−	12.5728i	1.09173	−	0.452211i	0.237123	−	0.971480i	$-0.423796\pi$
$773$	30.3534	−	12.5728i	1.09173	−	0.452211i	0.854611	+	0.519268i	$0.173796\pi$
$774$		0			0
$775$	−5.08838	−	5.08838i	−0.182780	−	0.182780i
$776$	5.89891	+	52.1475i	0.211758	+	1.87199i
$777$		0			0
$778$	18.4697	−	26.0388i	0.662172	−	0.933535i
$779$	−1.10808	+	0.458981i	−0.0397011	+	0.0164447i
$780$		0			0
$781$	9.17464	−	22.1495i	0.328294	−	0.792573i
$782$	20.1579	+	4.59780i	0.720846	+	0.164417i
$783$		0			0
$784$	36.4501	−	29.1031i	1.30179	−	1.03939i
$785$	−1.65394			−0.0590316
$786$		0			0
$787$	−37.1276	−	15.3788i	−1.32346	−	0.548194i	−0.394675	−	0.918821i	$-0.629143\pi$
$787$	−37.1276	−	15.3788i	−1.32346	−	0.548194i	−0.928782	+	0.370627i	$0.879143\pi$
$788$	0.660202	−	11.8181i	0.0235187	−	0.421001i
$789$		0			0
$790$	−0.0907270	+	0.127908i	−0.00322792	+	0.00455074i
$791$	18.0763	+	18.0763i	0.642718	+	0.642718i
$792$		0			0
$793$	−32.8068	+	32.8068i	−1.16500	+	1.16500i
$794$	−2.04000	−	11.9959i	−0.0723970	−	0.425719i
$795$		0			0
$796$	−11.9813	+	4.19640i	−0.424667	+	0.148738i
$797$	1.87919	−	4.53677i	0.0665644	−	0.160701i	−0.887097	−	0.461584i	$-0.847281\pi$
$797$	1.87919	−	4.53677i	0.0665644	−	0.160701i	0.953661	+	0.300883i	$0.0972814\pi$
$798$		0			0
$799$			19.0396i			0.673572i
$800$	25.4244	−	12.2668i	0.898890	−	0.433697i
$801$		0			0
$802$	−39.0216	+	24.5269i	−1.37790	+	0.866074i
$803$	68.5694	+	28.4024i	2.41976	+	1.00230i
$804$		0			0
$805$	−0.931476	−	2.24878i	−0.0328302	−	0.0792592i
$806$	−8.25880	+	1.40448i	−0.290904	+	0.0494706i
$807$		0			0
$808$	7.77499	+	14.0531i	0.273523	+	0.494388i
$809$	30.6738	−	30.6738i	1.07843	−	1.07843i	0.0817820	−	0.996650i	$-0.473939\pi$
$809$	30.6738	−	30.6738i	1.07843	−	1.07843i	0.996650	−	0.0817820i	$-0.0260611\pi$
$810$		0			0
$811$	−2.57082	−	6.20650i	−0.0902736	−	0.217940i	0.872294	−	0.488982i	$-0.162632\pi$
$811$	−2.57082	−	6.20650i	−0.0902736	−	0.217940i	−0.962567	+	0.271042i	$0.912632\pi$
$812$	2.60644	−	46.6569i	0.0914680	−	1.63734i
$813$		0			0
$814$	−42.5894	−	9.71416i	−1.49276	−	0.340481i
$815$			1.56087i			0.0546748i
$816$		0			0
$817$		−	20.3434i		−	0.711724i
$818$	2.40928	−	10.5629i	0.0842384	−	0.369323i
$819$		0			0
$820$	0.0552975	+	0.0618414i	0.00193107	+	0.00215959i
$821$	8.97965	+	21.6788i	0.313392	+	0.756595i	0.999575	+	0.0291659i	$0.00928510\pi$
$821$	8.97965	+	21.6788i	0.313392	+	0.756595i	−0.686183	+	0.727429i	$0.740715\pi$
$822$		0			0
$823$	17.8793	−	17.8793i	0.623234	−	0.623234i	−0.323123	−	0.946357i	$-0.604733\pi$
$823$	17.8793	−	17.8793i	0.623234	−	0.623234i	0.946357	+	0.323123i	$0.104733\pi$
$824$	−27.4420	+	34.4423i	−0.955986	+	1.19985i
$825$		0			0
$826$	2.64494	+	15.5532i	0.0920293	+	0.541164i
$827$	−15.5945	−	37.6486i	−0.542275	−	1.30917i	−0.923114	−	0.384527i	$-0.874365\pi$
$827$	−15.5945	−	37.6486i	−0.542275	−	1.30917i	0.380838	−	0.924642i	$-0.375635\pi$
$828$		0			0
$829$	−46.3584	−	19.2023i	−1.61009	−	0.666922i	−0.617296	−	0.786731i	$-0.711772\pi$
$829$	−46.3584	−	19.2023i	−1.61009	−	0.666922i	−0.992797	+	0.119808i	$0.961772\pi$
$830$	−0.803864	−	1.27893i	−0.0279025	−	0.0443921i
$831$		0			0
$832$	5.47620	−	32.4036i	0.189853	−	1.12339i
$833$			29.9067i			1.03620i
$834$		0			0
$835$	−0.352466	+	0.850928i	−0.0121976	+	0.0294476i
$836$	14.1027	−	29.3066i	0.487753	−	1.01359i
$837$		0			0
$838$	33.2445	−	5.65349i	1.14841	−	0.195297i
$839$	−33.5966	+	33.5966i	−1.15988	+	1.15988i	−0.175383	+	0.984500i	$0.556116\pi$
$839$	−33.5966	+	33.5966i	−1.15988	+	1.15988i	−0.984500	+	0.175383i	$0.943884\pi$
$840$		0			0
$841$	−0.180047	−	0.180047i	−0.00620852	−	0.00620852i
$842$	8.51682	+	6.04112i	0.293509	+	0.208191i
$843$		0			0
$844$	0.520329	−	0.465270i	0.0179105	−	0.0160152i
$845$	−0.353851	−	0.146570i	−0.0121729	−	0.00504216i
$846$		0			0
$847$	−92.3203			−3.17216
$848$	−7.73941	+	14.0229i	−0.265772	+	0.481547i
$849$		0			0
$850$	−4.02499	+	17.6466i	−0.138056	+	0.605274i
$851$	11.8430	−	28.5916i	0.405974	−	0.980108i
$852$		0			0
$853$	−0.0647873	+	0.0268358i	−0.00221827	+	0.000918839i	−0.383792	−	0.923419i	$-0.625382\pi$
$853$	−0.0647873	+	0.0268358i	−0.00221827	+	0.000918839i	0.381574	+	0.924338i	$0.375382\pi$
$854$	−56.2785	−	39.9193i	−1.92581	−	1.36601i
$855$		0			0
$856$	0.270667	+	0.489225i	0.00925121	+	0.0167214i
$857$	−22.9971	−	22.9971i	−0.785567	−	0.785567i	0.195197	−	0.980764i	$-0.437465\pi$
$857$	−22.9971	−	22.9971i	−0.785567	−	0.785567i	−0.980764	+	0.195197i	$0.937465\pi$
$858$		0			0
$859$	−14.9596	+	6.19647i	−0.510415	+	0.211421i	−0.623001	−	0.782221i	$-0.714087\pi$
$859$	−14.9596	+	6.19647i	−0.510415	+	0.211421i	0.112586	+	0.993642i	$0.464087\pi$
$860$	−1.32802	+	0.465132i	−0.0452850	+	0.0158609i
$861$		0			0
$862$	−5.06572	−	8.05942i	−0.172539	−	0.274505i
$863$	−20.2047			−0.687775			−0.343888	−	0.939011i	$-0.611744\pi$
$863$	−20.2047			−0.687775			−0.343888	+	0.939011i	$0.611744\pi$
$864$		0			0
$865$	1.90661			0.0648268
$866$	−9.11829	−	14.5069i	−0.309852	−	0.492966i
$867$		0			0
$868$	−4.11827	−	11.7583i	−0.139783	−	0.399101i
$869$	−5.89676	+	2.44252i	−0.200034	+	0.0828567i
$870$		0			0
$871$	−5.24133	−	5.24133i	−0.177596	−	0.177596i
$872$	−14.9353	−	4.29566i	−0.505774	−	0.145469i
$873$		0			0
$874$	18.7934	+	13.3305i	0.635697	+	0.450911i
$875$	3.94110	−	1.63246i	0.133234	−	0.0551872i
$876$		0			0
$877$	8.55444	−	20.6523i	0.288863	−	0.697377i	−0.711121	−	0.703070i	$-0.751812\pi$
$877$	8.55444	−	20.6523i	0.288863	−	0.697377i	0.999984	+	0.00569289i	$0.00181211\pi$
$878$	6.26067	−	27.4484i	0.211288	−	0.926339i
$879$		0			0
$880$	−2.23559	−	0.250559i	−0.0753616	−	0.00844634i
$881$	29.9972			1.01063			0.505315	−	0.862935i	$-0.331376\pi$
$881$	29.9972			1.01063			0.505315	+	0.862935i	$0.331376\pi$
$882$		0			0
$883$	28.2360	+	11.6957i	0.950217	+	0.393593i	0.803312	−	0.595558i	$-0.203069\pi$
$883$	28.2360	+	11.6957i	0.950217	+	0.393593i	0.146905	+	0.989151i	$0.453069\pi$
$884$	14.0453	+	15.7074i	0.472394	+	0.528296i
$885$		0			0
$886$	−43.8008	−	31.0687i	−1.47152	−	1.04377i
$887$	4.07846	+	4.07846i	0.136941	+	0.136941i	0.772254	−	0.635313i	$-0.219129\pi$
$887$	4.07846	+	4.07846i	0.136941	+	0.136941i	−0.635313	+	0.772254i	$0.719129\pi$
$888$		0			0
$889$	−29.6312	+	29.6312i	−0.993799	+	0.993799i
$890$	2.35024	−	0.399678i	0.0787804	−	0.0133972i
$891$		0			0
$892$	34.5322	+	16.6173i	1.15623	+	0.556390i
$893$	−8.11975	+	19.6028i	−0.271717	+	0.655983i
$894$		0			0
$895$		−	1.05223i		−	0.0351721i
$896$	48.8731	−	0.0502912i	1.63274	−	0.00168011i
$897$		0			0
$898$	−19.5527	−	31.1079i	−0.652484	−	1.03808i
$899$	−7.20588	−	2.98477i	−0.240329	−	0.0995477i
$900$		0			0
$901$	−3.93003	−	9.48792i	−0.130928	−	0.316088i
$902$	0.566074	+	3.32871i	0.0188482	+	0.110834i
$903$		0			0
$904$	1.88139	+	16.6319i	0.0625742	+	0.553169i
$905$	0.609982	−	0.609982i	0.0202765	−	0.0202765i
$906$		0			0
$907$	13.3711	+	32.2808i	0.443981	+	1.07187i	0.974539	+	0.224217i	$0.0719824\pi$
$907$	13.3711	+	32.2808i	0.443981	+	1.07187i	−0.530558	+	0.847649i	$0.678018\pi$
$908$	−31.3791	+	28.0587i	−1.04135	+	0.931160i
$909$		0			0
$910$	0.551635	−	2.41851i	0.0182865	−	0.0801728i
$911$			30.1517i			0.998971i	0.866322	+	0.499486i	$0.166478\pi$
$911$			30.1517i			0.998971i	−0.866322	+	0.499486i	$0.833522\pi$
$912$		0			0
$913$		−	61.4819i		−	2.03475i
$914$	12.1633	+	2.77432i	0.402327	+	0.0917662i
$915$		0			0
$916$	−36.3803	−	2.03235i	−1.20204	−	0.0671506i
$917$	22.7830	+	55.0031i	0.752362	+	1.81636i
$918$		0			0
$919$	−1.45081	+	1.45081i	−0.0478579	+	0.0478579i	−0.730631	−	0.682773i	$-0.760774\pi$
$919$	−1.45081	+	1.45081i	−0.0478579	+	0.0478579i	0.682773	+	0.730631i	$0.260774\pi$
$920$	0.440522	−	1.53163i	0.0145236	−	0.0504962i
$921$		0			0
$922$	35.2032	−	5.98659i	1.15936	−	0.197158i
$923$	6.62411	+	15.9920i	0.218035	+	0.526383i
$924$		0			0
$925$	25.0296	+	10.3676i	0.822969	+	0.340885i
$926$	4.78450	−	3.00728i	0.157228	−	0.0988254i
$927$		0			0
$928$	20.3711	−	22.8290i	0.668715	−	0.749400i
$929$			52.1840i			1.71210i	0.516890	+	0.856052i	$0.327089\pi$
$929$			52.1840i			1.71210i	−0.516890	+	0.856052i	$0.672911\pi$
$930$		0			0
$931$	−12.7542	+	30.7914i	−0.418002	+	1.00915i
$932$	15.6856	+	44.7846i	0.513798	+	1.46697i
$933$		0			0
$934$	−4.49968	−	26.4597i	−0.147234	−	0.865786i
$935$	1.01992	−	1.01992i	0.0333549	−	0.0333549i
$936$		0			0
$937$	1.45171	+	1.45171i	0.0474253	+	0.0474253i	0.730422	−	0.682996i	$-0.239324\pi$
$937$	1.45171	+	1.45171i	0.0474253	+	0.0474253i	−0.682996	+	0.730422i	$0.739324\pi$
$938$	6.37764	−	8.99124i	0.208237	−	0.293574i
$939$		0			0
$940$	1.46532	+	0.0818587i	0.0477936	+	0.00266994i
$941$	−3.19665	−	1.32409i	−0.104208	−	0.0431642i	0.329971	−	0.943991i	$-0.392961\pi$
$941$	−3.19665	−	1.32409i	−0.104208	−	0.0431642i	−0.434178	+	0.900827i	$0.642961\pi$
$942$		0			0
$943$	−2.39208			−0.0778969
$944$	−4.99137	+	9.04377i	−0.162455	+	0.294350i
$945$		0			0
$946$	−55.8368	−	12.7358i	−1.81541	−	0.414075i
$947$	4.34992	−	10.5016i	0.141353	−	0.341257i	−0.837310	−	0.546729i	$-0.815873\pi$
$947$	4.34992	−	10.5016i	0.141353	−	0.341257i	0.978663	+	0.205472i	$0.0658728\pi$
$948$		0			0
$949$	−49.5073	+	20.5066i	−1.60707	+	0.665672i
$950$	−11.6698	+	16.4521i	−0.378617	+	0.533777i
$951$		0			0
$952$	−19.5271	+	24.5084i	−0.632877	+	0.794322i
$953$	8.74508	+	8.74508i	0.283281	+	0.283281i	0.834416	−	0.551135i	$-0.185805\pi$
$953$	8.74508	+	8.74508i	0.283281	+	0.283281i	−0.551135	+	0.834416i	$0.685805\pi$
$954$		0			0
$955$	−1.19194	+	0.493718i	−0.0385703	+	0.0159763i
$956$	−16.4175	−	7.90033i	−0.530981	−	0.255515i
$957$		0			0
$958$	26.0619	−	16.3811i	0.842020	−	0.529249i
$959$	−34.3860			−1.11038
$960$		0			0
$961$	28.9206			0.932921
$962$	26.7026	−	16.7839i	0.860928	−	0.541133i
$963$		0			0
$964$	13.3361	+	6.41751i	0.429528	+	0.206694i
$965$	−0.279378	+	0.115722i	−0.00899351	+	0.00372523i
$966$		0			0
$967$	30.3193	+	30.3193i	0.975003	+	0.975003i	0.999695	−	0.0246926i	$-0.00786069\pi$
$967$	30.3193	+	30.3193i	0.975003	+	0.975003i	−0.0246926	+	0.999695i	$0.507861\pi$
$968$	−47.2762	−	37.6674i	−1.51952	−	1.21068i
$969$		0			0
$970$	−1.50061	+	2.11557i	−0.0481817	+	0.0679270i
$971$	50.2589	−	20.8179i	1.61288	−	0.668078i	0.619722	−	0.784822i	$-0.287246\pi$
$971$	50.2589	−	20.8179i	1.61288	−	0.668078i	0.993162	+	0.116743i	$0.0372455\pi$
$972$		0			0
$973$	0.874284	−	2.11071i	0.0280283	−	0.0676662i
$974$	−17.7468	−	4.04784i	−0.568644	−	0.129701i
$975$		0			0
$976$	−12.5322	−	43.4043i	−0.401146	−	1.38934i
$977$	28.6269			0.915857			0.457928	−	0.888989i	$-0.348592\pi$
$977$	28.6269			0.915857			0.457928	+	0.888989i	$0.348592\pi$
$978$		0			0
$979$	89.6443	+	37.1319i	2.86505	+	1.18674i
$980$	2.30168	+	0.128581i	0.0735244	+	0.00410735i
$981$		0			0
$982$	13.5183	−	19.0583i	0.431388	−	0.608174i
$983$	3.81670	+	3.81670i	0.121734	+	0.121734i	0.765349	−	0.643615i	$-0.222566\pi$
$983$	3.81670	+	3.81670i	0.121734	+	0.121734i	−0.643615	+	0.765349i	$0.722566\pi$
$984$		0			0
$985$	0.413656	−	0.413656i	0.0131802	−	0.0131802i
$986$	3.28895	+	19.3402i	0.104742	+	0.615916i
$987$		0			0
$988$	7.76209	+	22.1619i	0.246945	+	0.705063i
$989$	15.5268	−	37.4851i	0.493725	−	1.19196i
$990$		0			0
$991$			27.6845i			0.879426i	0.898138	+	0.439713i	$0.144920\pi$
$991$			27.6845i			0.879426i	−0.898138	+	0.439713i	$0.855080\pi$
$992$	2.68854	−	7.70157i	0.0853613	−	0.244525i
$993$		0			0
$994$	−21.7947	+	13.6990i	−0.691286	+	0.434506i
$995$	−0.579667	−	0.240106i	−0.0183767	−	0.00761187i
$996$		0			0
$997$	−5.51070	−	13.3040i	−0.174526	−	0.421342i	0.812277	−	0.583273i	$-0.198228\pi$
$997$	−5.51070	−	13.3040i	−0.174526	−	0.421342i	−0.986802	+	0.161930i	$0.948228\pi$
$998$	−48.6818	+	8.27873i	−1.54099	+	0.262059i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.w.b.35.6	yes	32
3.2	odd	2		288.2.w.a.35.3	✓	32
4.3	odd	2		1152.2.w.a.431.5		32
12.11	even	2		1152.2.w.b.431.4		32
32.11	odd	8		288.2.w.a.107.3	yes	32
32.21	even	8		1152.2.w.b.719.4		32
96.11	even	8	inner	288.2.w.b.107.6	yes	32
96.53	odd	8		1152.2.w.a.719.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.35.3	✓	32	3.2	odd	2
288.2.w.a.107.3	yes	32	32.11	odd	8
288.2.w.b.35.6	yes	32	1.1	even	1	trivial
288.2.w.b.107.6	yes	32	96.11	even	8	inner
1152.2.w.a.431.5		32	4.3	odd	2
1152.2.w.a.719.5		32	96.53	odd	8
1152.2.w.b.431.4		32	12.11	even	2
1152.2.w.b.719.4		32	32.21	even	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)

\(f(q)\)	\(=\)	\(q+(1.19734 - 0.752583i) q^{2} +(0.867238 - 1.80219i) q^{4} +(0.0913223 - 0.0378270i) q^{5} +(-3.05457 - 3.05457i) q^{7} +(-0.317923 - 2.81050i) q^{8} +O(q^{10})\)	\(q+(1.19734 - 0.752583i) q^{2} +(0.867238 - 1.80219i) q^{4} +(0.0913223 - 0.0378270i) q^{5} +(-3.05457 - 3.05457i) q^{7} +(-0.317923 - 2.81050i) q^{8} +(0.0808758 - 0.114019i) q^{10} +(5.25649 - 2.17731i) q^{11} +(-1.57202 + 3.79519i) q^{13} +(-5.95618 - 1.35854i) q^{14} +(-2.49580 - 3.12586i) q^{16} +2.56471 q^{17} +(2.64058 + 1.09376i) q^{19} +(0.0110267 - 0.197385i) q^{20} +(4.65519 - 6.56292i) q^{22} +(4.03079 + 4.03079i) q^{23} +(-3.52863 + 3.52863i) q^{25} +(0.973958 + 5.72721i) q^{26} +(-8.15397 + 2.85589i) q^{28} +(-2.06984 + 4.99704i) q^{29} +1.44203i q^{31} +(-5.34078 - 1.86442i) q^{32} +(3.07083 - 1.93016i) q^{34} +(-0.394496 - 0.163406i) q^{35} +(-2.07758 - 5.01573i) q^{37} +(3.98482 - 0.677651i) q^{38} +(-0.135346 - 0.244636i) q^{40} +(-0.296726 + 0.296726i) q^{41} +(-2.72382 - 6.57588i) q^{43} +(0.634695 - 11.3615i) q^{44} +(7.85972 + 1.79271i) q^{46} +7.42367i q^{47} +11.6608i q^{49} +(-1.56937 + 6.88054i) q^{50} +(5.47636 + 6.12442i) q^{52} +(-1.53235 - 3.69941i) q^{53} +(0.397674 - 0.397674i) q^{55} +(-7.61376 + 9.55600i) q^{56} +(1.28239 + 7.54087i) q^{58} +(-0.988255 - 2.38586i) q^{59} +(10.4346 + 4.32215i) q^{61} +(1.08525 + 1.72660i) q^{62} +(-7.79785 + 1.78705i) q^{64} +0.406051i q^{65} +(-0.690522 + 1.66707i) q^{67} +(2.22421 - 4.62211i) q^{68} +(-0.595321 + 0.101239i) q^{70} +(2.97957 - 2.97957i) q^{71} +(9.22401 + 9.22401i) q^{73} +(-6.26232 - 4.44197i) q^{74} +(4.26119 - 3.81028i) q^{76} +(-22.7071 - 9.40558i) q^{77} -1.12181 q^{79} +(-0.346164 - 0.191052i) q^{80} +(-0.131971 + 0.578593i) q^{82} +(4.13529 - 9.98348i) q^{83} +(0.234216 - 0.0970152i) q^{85} +(-8.21022 - 5.82365i) q^{86} +(-7.79049 - 14.0812i) q^{88} +(12.0590 + 12.0590i) q^{89} +(16.3945 - 6.79084i) q^{91} +(10.7599 - 3.76861i) q^{92} +(5.58693 + 8.88865i) q^{94} +0.282518 q^{95} -18.5545 q^{97} +(8.77574 + 13.9619i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 4 q^{8}+O(q^{10}) \) 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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