LMFDB - Embedded newform 414.2.j.a.89.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(17,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 7]))

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

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

chi := DirichletCharacter("414.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.j (of order $22$, degree $10$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			89.1
Character	$\chi$	$=$	414.89
Dual form			414.2.j.a.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.989821 + 0.142315i) q^{2} +(0.959493 - 0.281733i) q^{4} +(-0.922790 + 1.06496i) q^{5} +(2.78807 + 4.33833i) q^{7} +(-0.909632 + 0.415415i) q^{8} +O(q^{10})$	\(q+(-0.989821 + 0.142315i) q^{2} +(0.959493 - 0.281733i) q^{4} +(-0.922790 + 1.06496i) q^{5} +(2.78807 + 4.33833i) q^{7} +(-0.909632 + 0.415415i) q^{8} +(0.761838 - 1.18544i) q^{10} +(-0.00462790 + 0.0321878i) q^{11} +(-5.09244 - 3.27271i) q^{13} +(-3.37710 - 3.89739i) q^{14} +(0.841254 - 0.540641i) q^{16} +(-3.14611 - 0.923782i) q^{17} +(0.901024 + 3.06860i) q^{19} +(-0.585378 + 1.28180i) q^{20} -0.0325188i q^{22} +(1.16457 + 4.65229i) q^{23} +(0.428983 + 2.98365i) q^{25} +(5.50636 + 2.51467i) q^{26} +(3.89739 + 3.37710i) q^{28} +(-2.24381 + 7.64172i) q^{29} +(0.137723 + 0.301571i) q^{31} +(-0.755750 + 0.654861i) q^{32} +(3.24556 + 0.466641i) q^{34} +(-7.19293 - 1.03419i) q^{35} +(3.06716 - 2.65771i) q^{37} +(-1.32856 - 2.90914i) q^{38} +(0.397000 - 1.35206i) q^{40} +(7.84292 + 6.79593i) q^{41} +(-6.61387 - 3.02045i) q^{43} +(0.00462790 + 0.0321878i) q^{44} +(-1.81480 - 4.43920i) q^{46} -9.27062i q^{47} +(-8.13982 + 17.8237i) q^{49} +(-0.849234 - 2.89223i) q^{50} +(-5.80819 - 1.70544i) q^{52} +(8.72675 - 5.60834i) q^{53} +(-0.0300080 - 0.0346311i) q^{55} +(-4.33833 - 2.78807i) q^{56} +(1.13344 - 7.88327i) q^{58} +(-3.72788 + 5.80069i) q^{59} +(-3.65105 + 1.66738i) q^{61} +(-0.179239 - 0.278901i) q^{62} +(0.654861 - 0.755750i) q^{64} +(8.18455 - 2.40320i) q^{65} +(0.0192583 - 0.00276893i) q^{67} -3.27893 q^{68} +7.26690 q^{70} +(7.16674 - 1.03042i) q^{71} +(-5.55555 + 1.63126i) q^{73} +(-2.65771 + 3.06716i) q^{74} +(1.72905 + 2.69046i) q^{76} +(-0.152544 + 0.0696645i) q^{77} +(5.27176 - 8.20303i) q^{79} +(-0.200541 + 1.39480i) q^{80} +(-8.73025 - 5.61059i) q^{82} +(2.04812 + 2.36366i) q^{83} +(3.88699 - 2.49802i) q^{85} +(6.97641 + 2.04846i) q^{86} +(-0.00916160 - 0.0312015i) q^{88} +(2.81845 - 6.17155i) q^{89} -31.2173i q^{91} +(2.42810 + 4.13574i) q^{92} +(1.31935 + 9.17626i) q^{94} +(-4.09938 - 1.87213i) q^{95} +(1.43086 + 1.23985i) q^{97} +(5.52039 - 18.8007i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 8 q^{4}+O(q^{10}) $ 80 * q + 8 * q^4	$ 80 q + 8 q^{4} - 16 q^{13} - 8 q^{16} + 24 q^{25} - 16 q^{31} + 88 q^{37} + 88 q^{43} + 8 q^{46} + 8 q^{49} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 176 q^{61} + 8 q^{64} - 88 q^{67} - 176 q^{70} - 56 q^{73} - 176 q^{79} - 88 q^{82} - 88 q^{85} + 16 q^{94}+O(q^{100}) $ 80 * q + 8 * q^4 - 16 * q^13 - 8 * q^16 + 24 * q^25 - 16 * q^31 + 88 * q^37 + 88 * q^43 + 8 * q^46 + 8 * q^49 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 176 * q^61 + 8 * q^64 - 88 * q^67 - 176 * q^70 - 56 * q^73 - 176 * q^79 - 88 * q^82 - 88 * q^85 + 16 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{5}{22}\right)$

Coefficient data

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

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

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

$2$	−0.989821	+	0.142315i	−0.699909	+	0.100632i
$2$	−0.989821	+	0.142315i	−0.699909	+	0.100632i
$3$		0			0
$3$		0			0
$4$	0.959493	−	0.281733i	0.479746	−	0.140866i
$5$	−0.922790	+	1.06496i	−0.412684	+	0.476263i	−0.923594	−	0.383371i	$-0.874763\pi$
$5$	−0.922790	+	1.06496i	−0.412684	+	0.476263i	0.510910	+	0.859634i	$0.329308\pi$
$6$		0			0
$7$	2.78807	+	4.33833i	1.05379	+	1.63973i	0.715380	+	0.698736i	$0.246254\pi$
$7$	2.78807	+	4.33833i	1.05379	+	1.63973i	0.338413	+	0.940998i	$0.390110\pi$
$8$	−0.909632	+	0.415415i	−0.321603	+	0.146871i
$9$		0			0
$10$	0.761838	−	1.18544i	0.240914	−	0.374870i
$11$	−0.00462790	+	0.0321878i	−0.00139537	+	0.00970498i	−0.990507	−	0.137461i	$-0.956106\pi$
$11$	−0.00462790	+	0.0321878i	−0.00139537	+	0.00970498i	0.989112	+	0.147166i	$0.0470150\pi$
$12$		0			0
$13$	−5.09244	−	3.27271i	−1.41239	−	0.907688i	−0.412395	−	0.911005i	$-0.635308\pi$
$13$	−5.09244	−	3.27271i	−1.41239	−	0.907688i	−0.999994	+	0.00331756i	$0.998944\pi$
$14$	−3.37710	−	3.89739i	−0.902569	−	1.04162i
$15$		0			0
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−3.14611	−	0.923782i	−0.763044	−	0.224050i	−0.123019	−	0.992404i	$-0.539258\pi$
$17$	−3.14611	−	0.923782i	−0.763044	−	0.224050i	−0.640025	+	0.768354i	$0.721076\pi$
$18$		0			0
$19$	0.901024	+	3.06860i	0.206709	+	0.703986i	0.995951	+	0.0899032i	$0.0286558\pi$
$19$	0.901024	+	3.06860i	0.206709	+	0.703986i	−0.789242	+	0.614083i	$0.789526\pi$
$20$	−0.585378	+	1.28180i	−0.130894	+	0.286619i
$21$		0			0
$22$		−	0.0325188i		−	0.00693303i
$23$	1.16457	+	4.65229i	0.242829	+	0.970069i
$23$	1.16457	+	4.65229i	0.242829	+	0.970069i
$24$		0			0
$25$	0.428983	+	2.98365i	0.0857967	+	0.596729i
$26$	5.50636	+	2.51467i	1.07989	+	0.493168i
$27$		0			0
$28$	3.89739	+	3.37710i	0.736537	+	0.638213i
$29$	−2.24381	+	7.64172i	−0.416665	+	1.41903i	0.437588	+	0.899175i	$0.355833\pi$
$29$	−2.24381	+	7.64172i	−0.416665	+	1.41903i	−0.854254	+	0.519856i	$0.825985\pi$
$30$		0			0
$31$	0.137723	+	0.301571i	0.0247357	+	0.0541637i	0.921597	−	0.388149i	$-0.126885\pi$
$31$	0.137723	+	0.301571i	0.0247357	+	0.0541637i	−0.896861	+	0.442313i	$0.854158\pi$
$32$	−0.755750	+	0.654861i	−0.133599	+	0.115764i
$33$		0			0
$34$	3.24556	+	0.466641i	0.556608	+	0.0800282i
$35$	−7.19293	−	1.03419i	−1.21583	−	0.174810i
$36$		0			0
$37$	3.06716	−	2.65771i	0.504237	−	0.436924i	−0.365228	−	0.930918i	$-0.619009\pi$
$37$	3.06716	−	2.65771i	0.504237	−	0.436924i	0.869465	+	0.493994i	$0.164463\pi$
$38$	−1.32856	−	2.90914i	−0.215521	−	0.471925i
$39$		0			0
$40$	0.397000	−	1.35206i	0.0627713	−	0.213779i
$41$	7.84292	+	6.79593i	1.22486	+	1.06135i	0.996133	+	0.0878542i	$0.0280009\pi$
$41$	7.84292	+	6.79593i	1.22486	+	1.06135i	0.228724	+	0.973491i	$0.426545\pi$
$42$		0			0
$43$	−6.61387	−	3.02045i	−1.00861	−	0.460615i	−0.158575	−	0.987347i	$-0.550690\pi$
$43$	−6.61387	−	3.02045i	−1.00861	−	0.460615i	−0.850031	+	0.526732i	$0.823417\pi$
$44$	0.00462790	+	0.0321878i	0.000697683	+	0.00485249i
$45$		0			0
$46$	−1.81480	−	4.43920i	−0.267578	−	0.654524i
$47$		−	9.27062i		−	1.35226i	−0.736783	−	0.676129i	$-0.763656\pi$
$47$		−	9.27062i		−	1.35226i	0.736783	−	0.676129i	$-0.236344\pi$
$48$		0			0
$49$	−8.13982	+	17.8237i	−1.16283	+	2.54625i
$50$	−0.849234	−	2.89223i	−0.120100	−	0.409022i
$51$		0			0
$52$	−5.80819	−	1.70544i	−0.805451	−	0.236502i
$53$	8.72675	−	5.60834i	1.19871	−	0.770365i	0.219979	−	0.975505i	$-0.429401\pi$
$53$	8.72675	−	5.60834i	1.19871	−	0.770365i	0.978733	+	0.205139i	$0.0657648\pi$
$54$		0			0
$55$	−0.0300080	−	0.0346311i	−0.00404628	−	0.00466965i
$56$	−4.33833	−	2.78807i	−0.579733	−	0.372572i
$57$		0			0
$58$	1.13344	−	7.88327i	0.148828	−	1.03512i
$59$	−3.72788	+	5.80069i	−0.485329	+	0.755186i	−0.994416	−	0.105529i	$-0.966347\pi$
$59$	−3.72788	+	5.80069i	−0.485329	+	0.755186i	0.509088	+	0.860715i	$0.329983\pi$
$60$		0			0
$61$	−3.65105	+	1.66738i	−0.467469	+	0.213486i	−0.635201	−	0.772347i	$-0.719083\pi$
$61$	−3.65105	+	1.66738i	−0.467469	+	0.213486i	0.167732	+	0.985833i	$0.446356\pi$
$62$	−0.179239	−	0.278901i	−0.0227634	−	0.0354205i
$63$		0			0
$64$	0.654861	−	0.755750i	0.0818576	−	0.0944687i
$65$	8.18455	−	2.40320i	1.01517	−	0.298080i
$66$		0			0
$67$	0.0192583	−	0.00276893i	0.00235278	−	0.000338278i	−0.141138	−	0.989990i	$-0.545076\pi$
$67$	0.0192583	−	0.00276893i	0.00235278	−	0.000338278i	0.143491	+	0.989652i	$0.454167\pi$
$68$	−3.27893			−0.397629
$69$		0			0
$70$	7.26690			0.868561
$71$	7.16674	−	1.03042i	0.850536	−	0.122289i	0.296758	−	0.954953i	$-0.404095\pi$
$71$	7.16674	−	1.03042i	0.850536	−	0.122289i	0.553778	+	0.832664i	$0.313186\pi$
$72$		0			0
$73$	−5.55555	+	1.63126i	−0.650227	+	0.190924i	−0.590180	−	0.807272i	$-0.700943\pi$
$73$	−5.55555	+	1.63126i	−0.650227	+	0.190924i	−0.0600472	+	0.998196i	$0.519125\pi$
$74$	−2.65771	+	3.06716i	−0.308952	+	0.356550i
$75$		0			0
$76$	1.72905	+	2.69046i	0.198336	+	0.308617i
$77$	−0.152544	+	0.0696645i	−0.0173840	+	0.00793901i
$78$		0			0
$79$	5.27176	−	8.20303i	0.593120	−	0.922912i	−0.406836	−	0.913501i	$-0.633368\pi$
$79$	5.27176	−	8.20303i	0.593120	−	0.922912i	0.999956	−	0.00941118i	$-0.00299572\pi$
$80$	−0.200541	+	1.39480i	−0.0224212	+	0.155943i
$81$		0			0
$82$	−8.73025	−	5.61059i	−0.964095	−	0.619586i
$83$	2.04812	+	2.36366i	0.224811	+	0.259445i	0.856938	−	0.515419i	$-0.172364\pi$
$83$	2.04812	+	2.36366i	0.224811	+	0.259445i	−0.632128	+	0.774864i	$0.717818\pi$
$84$		0			0
$85$	3.88699	−	2.49802i	0.421603	−	0.270948i
$86$	6.97641	+	2.04846i	0.752285	+	0.220891i
$87$		0			0
$88$	−0.00916160	−	0.0312015i	−0.000976630	−	0.00332610i
$89$	2.81845	−	6.17155i	0.298755	−	0.654183i	−0.699411	−	0.714720i	$-0.746554\pi$
$89$	2.81845	−	6.17155i	0.298755	−	0.654183i	0.998166	+	0.0605371i	$0.0192813\pi$
$90$		0			0
$91$		−	31.2173i		−	3.27246i
$92$	2.42810	+	4.13574i	0.253147	+	0.431181i
$93$		0			0
$94$	1.31935	+	9.17626i	0.136080	+	0.946458i
$95$	−4.09938	−	1.87213i	−0.420588	−	0.192076i
$96$		0			0
$97$	1.43086	+	1.23985i	0.145282	+	0.125888i	0.724470	−	0.689307i	$-0.242085\pi$
$97$	1.43086	+	1.23985i	0.145282	+	0.125888i	−0.579188	+	0.815194i	$0.696630\pi$
$98$	5.52039	−	18.8007i	0.557644	−	1.89916i
$99$		0			0
$100$	1.25220	+	2.74193i	0.125220	+	0.274193i
$101$	6.72368	−	5.82611i	0.669032	−	0.579719i	−0.252701	−	0.967544i	$-0.581319\pi$
$101$	6.72368	−	5.82611i	0.669032	−	0.579719i	0.921733	+	0.387825i	$0.126774\pi$
$102$		0			0
$103$	3.64199	+	0.523640i	0.358856	+	0.0515957i	0.319385	−	0.947625i	$-0.396524\pi$
$103$	3.64199	+	0.523640i	0.358856	+	0.0515957i	0.0394711	+	0.999221i	$0.487433\pi$
$104$	5.99178	+	0.861488i	0.587543	+	0.0844759i
$105$		0			0
$106$	−7.83978	+	6.79321i	−0.761466	+	0.659814i
$107$	2.11128	+	4.62307i	0.204106	+	0.446929i	0.983809	−	0.179220i	$-0.0573574\pi$
$107$	2.11128	+	4.62307i	0.204106	+	0.446929i	−0.779703	+	0.626149i	$0.784630\pi$
$108$		0			0
$109$	1.37579	−	4.68552i	0.131777	−	0.448792i	−0.866996	−	0.498315i	$-0.833952\pi$
$109$	1.37579	−	4.68552i	0.131777	−	0.448792i	0.998773	+	0.0495238i	$0.0157704\pi$
$110$	0.0346311	+	0.0300080i	0.00330194	+	0.00286115i
$111$		0			0
$112$	4.69095	+	2.14229i	0.443253	+	0.202427i
$113$	0.531718	+	3.69818i	0.0500198	+	0.347895i	0.999427	+	0.0338476i	$0.0107761\pi$
$113$	0.531718	+	3.69818i	0.0500198	+	0.347895i	−0.949407	+	0.314048i	$0.898315\pi$
$114$		0			0
$115$	−6.02913	−	3.05287i	−0.562220	−	0.284682i
$116$			7.96433i			0.739470i
$117$		0			0
$118$	2.86441	−	6.27218i	0.263690	−	0.577401i
$119$	−4.76392	−	16.2244i	−0.436708	−	1.48729i
$120$		0			0
$121$	10.5534	+	3.09876i	0.959401	+	0.281705i
$122$	3.37659	−	2.17001i	0.305702	−	0.196463i
$123$		0			0
$124$	0.217106	+	0.250554i	0.0194967	+	0.0225004i
$125$	−9.50053	−	6.10562i	−0.849753	−	0.546103i
$126$		0			0
$127$	0.563991	−	3.92264i	0.0500461	−	0.348078i	−0.949378	−	0.314137i	$-0.898285\pi$
$127$	0.563991	−	3.92264i	0.0500461	−	0.348078i	0.999424	−	0.0339415i	$-0.0108060\pi$
$128$	−0.540641	+	0.841254i	−0.0477863	+	0.0743570i
$129$		0			0
$130$	−7.75923	+	3.54352i	−0.680530	+	0.310788i
$131$	−9.86040	−	15.3431i	−0.861507	−	1.34053i	−0.939135	−	0.343548i	$-0.888371\pi$
$131$	−9.86040	−	15.3431i	−0.861507	−	1.34053i	0.0776281	−	0.996982i	$-0.475265\pi$
$132$		0			0
$133$	−10.8005	+	12.4644i	−0.936521	+	1.08080i
$134$	−0.0186682	+	0.00548148i	−0.00161269	+	0.000473528i
$135$		0			0
$136$	3.24556	−	0.466641i	0.278304	−	0.0400141i
$137$	10.8964			0.930941			0.465470	−	0.885063i	$-0.345885\pi$
$137$	10.8964			0.930941			0.465470	+	0.885063i	$0.345885\pi$
$138$		0			0
$139$	8.60693			0.730030			0.365015	−	0.931002i	$-0.381064\pi$
$139$	8.60693			0.730030			0.365015	+	0.931002i	$0.381064\pi$
$140$	−7.19293	+	1.03419i	−0.607914	+	0.0874048i
$141$		0			0
$142$	−6.94715	+	2.03987i	−0.582992	+	0.171182i
$143$	0.128909	−	0.148769i	0.0107799	−	0.0124407i
$144$		0			0
$145$	−6.06753	−	9.44126i	−0.503881	−	0.784054i
$146$	5.26685	−	2.40529i	0.435887	−	0.199063i
$147$		0			0
$148$	2.19415	−	3.41417i	0.180358	−	0.280643i
$149$	−0.672504	+	4.67737i	−0.0550937	+	0.383185i	0.943555	+	0.331216i	$0.107459\pi$
$149$	−0.672504	+	4.67737i	−0.0550937	+	0.383185i	−0.998649	+	0.0519691i	$0.983450\pi$
$150$		0			0
$151$	14.4749	+	9.30245i	1.17795	+	0.757023i	0.975008	−	0.222168i	$-0.0713134\pi$
$151$	14.4749	+	9.30245i	1.17795	+	0.757023i	0.202942	+	0.979191i	$0.434950\pi$
$152$	−2.09434	−	2.41700i	−0.169874	−	0.196045i
$153$		0			0
$154$	0.141077	−	0.0906647i	0.0113683	−	0.00730597i
$155$	−0.448249	−	0.131618i	−0.0360042	−	0.0105718i
$156$		0			0
$157$	−0.916250	−	3.12046i	−0.0731247	−	0.249040i	0.914816	−	0.403870i	$-0.132335\pi$
$157$	−0.916250	−	3.12046i	−0.0731247	−	0.249040i	−0.987941	+	0.154830i	$0.950517\pi$
$158$	−4.05069	+	8.86978i	−0.322256	+	0.705642i
$159$		0			0
$160$		−	1.40914i		−	0.111402i
$161$	−16.9362	+	18.0232i	−1.33476	+	1.42043i
$162$		0			0
$163$	−1.67154	−	11.6258i	−0.130925	−	0.910602i	−0.944352	−	0.328936i	$-0.893310\pi$
$163$	−1.67154	−	11.6258i	−0.130925	−	0.910602i	0.813427	−	0.581666i	$-0.197599\pi$
$164$	9.43986	+	4.31104i	0.737129	+	0.336636i
$165$		0			0
$166$	−2.36366	−	2.04812i	−0.183456	−	0.158965i
$167$	−0.441237	+	1.50272i	−0.0341440	+	0.116284i	−0.974802	−	0.223073i	$-0.928391\pi$
$167$	−0.441237	+	1.50272i	−0.0341440	+	0.116284i	0.940658	+	0.339357i	$0.110209\pi$
$168$		0			0
$169$	9.82192	+	21.5070i	0.755532	+	1.65438i
$170$	−3.49192	+	3.02577i	−0.267818	+	0.232066i
$171$		0			0
$172$	−7.19692	−	1.03476i	−0.548760	−	0.0788998i
$173$	−6.25921	−	0.899939i	−0.475879	−	0.0684211i	−0.0997978	−	0.995008i	$-0.531820\pi$
$173$	−6.25921	−	0.899939i	−0.475879	−	0.0684211i	−0.376081	+	0.926587i	$0.622729\pi$
$174$		0			0
$175$	−11.7480	+	10.1797i	−0.888065	+	0.769513i
$176$	0.0135088	+	0.0295801i	0.00101826	+	0.00222969i
$177$		0			0
$178$	−1.91146	+	6.50984i	−0.143270	+	0.487933i
$179$	15.4964	+	13.4277i	1.15826	+	1.00364i	0.999868	+	0.0162589i	$0.00517559\pi$
$179$	15.4964	+	13.4277i	1.15826	+	1.00364i	0.158389	+	0.987377i	$0.449370\pi$
$180$		0			0
$181$	13.7709	+	6.28898i	1.02359	+	0.467456i	0.855218	−	0.518268i	$-0.173423\pi$
$181$	13.7709	+	6.28898i	1.02359	+	0.467456i	0.168368	+	0.985724i	$0.446150\pi$
$182$	4.44268	+	30.8995i	0.329313	+	2.29042i
$183$		0			0
$184$	−2.99196	−	3.74809i	−0.220570	−	0.276313i
$185$			5.71889i			0.420461i
$186$		0			0
$187$	0.0442944	−	0.0969912i	0.00323913	−	0.00709270i
$188$	−2.61183	−	8.89509i	−0.190488	−	0.648741i
$189$		0			0
$190$	4.32409	+	1.26967i	0.313702	+	0.0921114i
$191$	−15.4625	+	9.93712i	−1.11882	+	0.719025i	−0.963198	−	0.268791i	$-0.913376\pi$
$191$	−15.4625	+	9.93712i	−1.11882	+	0.719025i	−0.155626	+	0.987816i	$0.549739\pi$
$192$		0			0
$193$	1.83102	+	2.11311i	0.131800	+	0.152105i	0.817813	−	0.575484i	$-0.195186\pi$
$193$	1.83102	+	2.11311i	0.131800	+	0.152105i	−0.686013	+	0.727589i	$0.740641\pi$
$194$	−1.59275	−	1.02360i	−0.114353	−	0.0734900i
$195$		0			0
$196$	−2.78858	+	19.3950i	−0.199184	+	1.38536i
$197$	3.74463	−	5.82676i	0.266794	−	0.415139i	−0.681847	−	0.731495i	$-0.738823\pi$
$197$	3.74463	−	5.82676i	0.266794	−	0.415139i	0.948641	+	0.316356i	$0.102459\pi$
$198$		0			0
$199$	22.8023	−	10.4135i	1.61641	−	0.738190i	0.617579	−	0.786509i	$-0.288114\pi$
$199$	22.8023	−	10.4135i	1.61641	−	0.738190i	0.998832	+	0.0483191i	$0.0153864\pi$
$200$	−1.62967	−	2.53581i	−0.115235	−	0.179309i
$201$		0			0
$202$	−5.82611	+	6.72368i	−0.409923	+	0.473077i
$203$	−39.4082	+	11.5713i	−2.76591	+	0.812145i
$204$		0			0
$205$	−14.4747	+	2.08115i	−1.01096	+	0.145354i
$206$	−3.67945			−0.256359
$207$		0			0
$208$	−6.05340			−0.419728
$209$	−0.102941	+	0.0148007i	−0.00712061	+	0.00102379i
$210$		0			0
$211$	−8.49586	+	2.49461i	−0.584879	+	0.171736i	−0.560768	−	0.827973i	$-0.689494\pi$
$211$	−8.49586	+	2.49461i	−0.584879	+	0.171736i	−0.0241115	+	0.999709i	$0.507676\pi$
$212$	6.79321	−	7.83978i	0.466559	−	0.538438i
$213$		0			0
$214$	−2.74773	−	4.27554i	−0.187831	−	0.292270i
$215$	9.31986	−	4.25624i	0.635609	−	0.290273i
$216$		0			0
$217$	−0.924331	+	1.43829i	−0.0627477	+	0.0976373i
$218$	−0.694970	+	4.83363i	−0.0470693	+	0.327374i
$219$		0			0
$220$	−0.0385492	−	0.0247740i	−0.00259898	−	0.00167027i
$221$	12.9981	+	15.0006i	0.874348	+	1.00905i
$222$		0			0
$223$	−5.76637	+	3.70582i	−0.386145	+	0.248160i	−0.719282	−	0.694718i	$-0.755529\pi$
$223$	−5.76637	+	3.70582i	−0.386145	+	0.248160i	0.333137	+	0.942878i	$0.391893\pi$
$224$	−4.94809	−	1.45289i	−0.330608	−	0.0970752i
$225$		0			0
$226$	−1.05261	−	3.58486i	−0.0700187	−	0.238462i
$227$	10.5850	−	23.1779i	0.702550	−	1.53837i	−0.134301	−	0.990941i	$-0.542879\pi$
$227$	10.5850	−	23.1779i	0.702550	−	1.53837i	0.836852	−	0.547430i	$-0.184394\pi$
$228$		0			0
$229$		−	11.5405i		−	0.762619i	−0.924448	−	0.381309i	$-0.875473\pi$
$229$		−	11.5405i		−	0.762619i	0.924448	−	0.381309i	$-0.124527\pi$
$230$	6.40224	+	2.16376i	0.422151	+	0.142674i
$231$		0			0
$232$	−1.13344	−	7.88327i	−0.0744141	−	0.517562i
$233$	−16.8693	−	7.70395i	−1.10514	−	0.504702i	−0.222589	−	0.974912i	$-0.571451\pi$
$233$	−16.8693	−	7.70395i	−1.10514	−	0.504702i	−0.882555	+	0.470210i	$0.844178\pi$
$234$		0			0
$235$	9.87280	+	8.55483i	0.644031	+	0.558056i
$236$	−1.94263	+	6.61599i	−0.126454	+	0.430664i
$237$		0			0
$238$	7.02441	+	15.3813i	0.455325	+	0.997023i
$239$	13.8677	−	12.0165i	0.897029	−	0.777280i	−0.0785541	−	0.996910i	$-0.525030\pi$
$239$	13.8677	−	12.0165i	0.897029	−	0.777280i	0.975583	+	0.219630i	$0.0704849\pi$
$240$		0			0
$241$	−21.9215	−	3.15184i	−1.41209	−	0.203028i	−0.606303	−	0.795234i	$-0.707348\pi$
$241$	−21.9215	−	3.15184i	−1.41209	−	0.203028i	−0.805787	+	0.592206i	$0.798257\pi$
$242$	−10.8870	−	1.56531i	−0.699842	−	0.100622i
$243$		0			0
$244$	−3.03340	+	2.62846i	−0.194194	+	0.168270i
$245$	−11.4701	−	25.1161i	−0.732801	−	1.60461i
$246$		0			0
$247$	5.45425	−	18.5755i	0.347046	−	1.18193i
$248$	−0.250554	−	0.217106i	−0.0159102	−	0.0137863i
$249$		0			0
$250$	10.2727	+	4.69141i	0.649706	+	0.296711i
$251$	−0.235847	−	1.64035i	−0.0148865	−	0.103538i	0.981023	−	0.193889i	$-0.0621102\pi$
$251$	−0.235847	−	1.64035i	−0.0148865	−	0.103538i	−0.995910	+	0.0903510i	$0.971201\pi$
$252$		0			0
$253$	−0.155136	+	0.0159545i	−0.00975334	+	0.00100305i
$254$			3.96298i			0.248660i
$255$		0			0
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	4.82174	+	16.4213i	0.300772	+	1.02434i	0.961750	+	0.273930i	$0.0883235\pi$
$257$	4.82174	+	16.4213i	0.300772	+	1.02434i	−0.660978	+	0.750405i	$0.729858\pi$
$258$		0			0
$259$	20.0815	+	5.89645i	1.24780	+	0.366387i
$260$	7.17596	−	4.61171i	0.445034	−	0.286006i
$261$		0			0
$262$	11.9436	+	13.7836i	0.737877	+	0.851555i
$263$	−15.3147	−	9.84218i	−0.944347	−	0.606895i	−0.0247226	−	0.999694i	$-0.507870\pi$
$263$	−15.3147	−	9.84218i	−0.944347	−	0.606895i	−0.919624	+	0.392800i	$0.871507\pi$
$264$		0			0
$265$	−2.08032	+	14.4689i	−0.127793	+	0.888819i
$266$	8.91668	−	13.8746i	0.546717	−	0.850708i
$267$		0			0
$268$	0.0176981	−	0.00808246i	0.00108108	−	0.000493715i
$269$	11.5071	+	17.9053i	0.701598	+	1.09171i	0.990917	+	0.134475i	$0.0429349\pi$
$269$	11.5071	+	17.9053i	0.701598	+	1.09171i	−0.289319	+	0.957233i	$0.593429\pi$
$270$		0			0
$271$	9.15670	−	10.5674i	0.556230	−	0.641923i	−0.406093	−	0.913832i	$-0.633109\pi$
$271$	9.15670	−	10.5674i	0.556230	−	0.641923i	0.962323	+	0.271908i	$0.0876547\pi$
$272$	−3.14611	+	0.923782i	−0.190761	+	0.0560125i
$273$		0			0
$274$	−10.7855	+	1.55072i	−0.651574	+	0.0936822i
$275$	−0.0980222			−0.00591096
$276$		0			0
$277$	25.7443			1.54683			0.773413	−	0.633903i	$-0.218548\pi$
$277$	25.7443			1.54683			0.773413	+	0.633903i	$0.218548\pi$
$278$	−8.51932	+	1.22489i	−0.510955	+	0.0734642i
$279$		0			0
$280$	6.97254	−	2.04732i	0.416689	−	0.122351i
$281$	−20.3742	+	23.5131i	−1.21542	+	1.40267i	−0.326135	+	0.945323i	$0.605746\pi$
$281$	−20.3742	+	23.5131i	−1.21542	+	1.40267i	−0.889287	+	0.457349i	$0.848799\pi$
$282$		0			0
$283$	3.91606	+	6.09350i	0.232785	+	0.362221i	0.937920	−	0.346853i	$-0.112750\pi$
$283$	3.91606	+	6.09350i	0.232785	+	0.362221i	−0.705134	+	0.709074i	$0.749113\pi$
$284$	6.58613	−	3.00779i	0.390815	−	0.178479i
$285$		0			0
$286$	−0.106425	+	0.165600i	−0.00629302	+	0.00979213i
$287$	−7.61632	+	52.9727i	−0.449577	+	3.12688i
$288$		0			0
$289$	−5.25666	−	3.37825i	−0.309215	−	0.198721i
$290$	7.34940	+	8.48166i	0.431572	+	0.498060i
$291$		0			0
$292$	−4.87093	+	3.13036i	−0.285050	+	0.183190i
$293$	−4.11537	−	1.20838i	−0.240423	−	0.0705945i	0.159301	−	0.987230i	$-0.449076\pi$
$293$	−4.11537	−	1.20838i	−0.240423	−	0.0705945i	−0.399724	+	0.916636i	$0.630894\pi$
$294$		0			0
$295$	−2.73744	−	9.32285i	−0.159380	−	0.542797i
$296$	−1.68593	+	3.69168i	−0.0979929	+	0.214574i
$297$		0			0
$298$		−	4.72547i		−	0.273739i
$299$	9.29511	−	27.5028i	0.537550	−	1.59053i
$300$		0			0
$301$	−5.33624	−	37.1144i	−0.307576	−	2.13924i
$302$	−15.6514	−	7.14777i	−0.900639	−	0.411308i
$303$		0			0
$304$	2.41700	+	2.09434i	0.138625	+	0.120119i
$305$	1.59347	−	5.42685i	0.0912416	−	0.310740i
$306$		0			0
$307$	13.3251	+	29.1778i	0.760502	+	1.66527i	0.746519	+	0.665364i	$0.231724\pi$
$307$	13.3251	+	29.1778i	0.760502	+	1.66527i	0.0139832	+	0.999902i	$0.495549\pi$
$308$	−0.126738	+	0.109819i	−0.00722158	+	0.00625753i
$309$		0			0
$310$	0.462417	+	0.0664856i	0.0262635	+	0.00377613i
$311$	0.946474	+	0.136082i	0.0536696	+	0.00771653i	0.169097	−	0.985599i	$-0.445915\pi$
$311$	0.946474	+	0.136082i	0.0536696	+	0.00771653i	−0.115428	+	0.993316i	$0.536824\pi$
$312$		0			0
$313$	−11.7741	+	10.2023i	−0.665511	+	0.576668i	−0.920723	−	0.390217i	$-0.872400\pi$
$313$	−11.7741	+	10.2023i	−0.665511	+	0.576668i	0.255212	+	0.966885i	$0.417855\pi$
$314$	1.35101	+	2.95830i	0.0762420	+	0.166947i
$315$		0			0
$316$	2.74716	−	9.35597i	0.154540	−	0.526315i
$317$	−13.6148	−	11.7973i	−0.764686	−	0.662604i	0.182530	−	0.983200i	$-0.441571\pi$
$317$	−13.6148	−	11.7973i	−0.764686	−	0.662604i	−0.947216	+	0.320596i	$0.896117\pi$
$318$		0			0
$319$	−0.235586	−	0.107588i	−0.0131903	−	0.00602380i
$320$	0.200541	+	1.39480i	0.0112106	+	0.0779715i
$321$		0			0
$322$	14.1989	−	20.2500i	0.791273	−	1.12849i
$323$		−	10.4865i		−	0.583486i
$324$		0			0
$325$	7.58005	−	16.5980i	0.420465	−	0.920691i
$326$	3.30905	+	11.2696i	0.183271	+	0.624164i
$327$		0			0
$328$	−9.95730	−	2.92373i	−0.549800	−	0.161436i
$329$	40.2190	−	25.8472i	2.21734	−	1.42500i
$330$		0			0
$331$	3.69276	+	4.26167i	0.202972	+	0.234243i	0.848105	−	0.529828i	$-0.177743\pi$
$331$	3.69276	+	4.26167i	0.202972	+	0.234243i	−0.645133	+	0.764070i	$0.723198\pi$
$332$	2.63108	+	1.69089i	0.144399	+	0.0927998i
$333$		0			0
$334$	0.222887	−	1.55022i	0.0121959	−	0.0848240i
$335$	−0.0148226	+	0.0230644i	−0.000809844	+	0.00126014i
$336$		0			0
$337$	−1.09713	+	0.501042i	−0.0597644	+	0.0272935i	−0.445073	−	0.895494i	$-0.646822\pi$
$337$	−1.09713	+	0.501042i	−0.0597644	+	0.0272935i	0.385309	+	0.922788i	$0.374095\pi$
$338$	−12.7827	−	19.8903i	−0.695288	−	1.08189i
$339$		0			0
$340$	3.02577	−	3.49192i	0.164095	−	0.189376i
$341$	−0.0103443	+	0.00303735i	−0.000560173	+	0.000164482i
$342$		0			0
$343$	−64.2882	+	9.24324i	−3.47123	+	0.499088i
$344$	7.27093			0.392022
$345$		0			0
$346$	6.32358			0.339958
$347$	−16.8773	+	2.42660i	−0.906024	+	0.130267i	−0.579547	−	0.814939i	$-0.696770\pi$
$347$	−16.8773	+	2.42660i	−0.906024	+	0.130267i	−0.326476	+	0.945205i	$0.605861\pi$
$348$		0			0
$349$	−14.2356	+	4.17995i	−0.762014	+	0.223748i	−0.639575	−	0.768728i	$-0.720890\pi$
$349$	−14.2356	+	4.17995i	−0.762014	+	0.223748i	−0.122439	+	0.992476i	$0.539072\pi$
$350$	10.1797	−	11.7480i	0.544128	−	0.627957i
$351$		0			0
$352$	−0.0175810	−	0.0273565i	−0.000937069	−	0.00145811i
$353$	17.9297	−	8.18821i	0.954300	−	0.435814i	0.123475	−	0.992348i	$-0.460596\pi$
$353$	17.9297	−	8.18821i	0.954300	−	0.435814i	0.830825	+	0.556533i	$0.187869\pi$
$354$		0			0
$355$	−5.51604	+	8.58313i	−0.292761	+	0.455545i
$356$	0.965559	−	6.71561i	0.0511745	−	0.355927i
$357$		0			0
$358$	−17.2497	−	11.0857i	−0.911673	−	0.585897i
$359$	−10.8829	−	12.5596i	−0.574379	−	0.662869i	0.392008	−	0.919962i	$-0.371781\pi$
$359$	−10.8829	−	12.5596i	−0.574379	−	0.662869i	−0.966387	+	0.257093i	$0.917235\pi$
$360$		0			0
$361$	7.37933	−	4.74241i	0.388386	−	0.249600i
$362$	−14.5258	−	4.26516i	−0.763459	−	0.224172i
$363$		0			0
$364$	−8.79492	−	29.9527i	−0.460979	−	1.56995i
$365$	3.38939	−	7.42172i	0.177409	−	0.388470i
$366$		0			0
$367$			4.54013i			0.236993i	0.992954	+	0.118497i	$0.0378074\pi$
$367$			4.54013i			0.236993i	−0.992954	+	0.118497i	$0.962193\pi$
$368$	3.49491	+	3.28414i	0.182185	+	0.171198i
$369$		0			0
$370$	−0.813883	−	5.66068i	−0.0423118	−	0.294285i
$371$	48.6617	+	22.2230i	2.52639	+	1.15376i
$372$		0			0
$373$	25.2445	+	21.8745i	1.30711	+	1.13262i	0.982397	+	0.186805i	$0.0598131\pi$
$373$	25.2445	+	21.8745i	1.30711	+	1.13262i	0.324713	+	0.945813i	$0.394732\pi$
$374$	−0.0300403	+	0.102308i	−0.00155334	+	0.00529021i
$375$		0			0
$376$	3.85115	+	8.43285i	0.198608	+	0.434891i
$377$	36.4356	−	31.5717i	1.87653	−	1.62602i
$378$		0			0
$379$	0.928280	+	0.133467i	0.0476825	+	0.00685572i	0.166115	−	0.986106i	$-0.446878\pi$
$379$	0.928280	+	0.133467i	0.0476825	+	0.00685572i	−0.118432	+	0.992962i	$0.537787\pi$
$380$	−4.46077	−	0.641362i	−0.228833	−	0.0329012i
$381$		0			0
$382$	13.8909	−	12.0365i	0.710719	−	0.615841i
$383$	−9.30017	−	20.3645i	−0.475216	−	1.04058i	−0.983751	−	0.179537i	$-0.942540\pi$
$383$	−9.30017	−	20.3645i	−0.475216	−	1.04058i	0.508535	−	0.861041i	$-0.330187\pi$
$384$		0			0
$385$	0.0665764	−	0.226739i	0.00339305	−	0.0115557i
$386$	−2.11311	−	1.83102i	−0.107554	−	0.0931964i
$387$		0			0
$388$	1.72221	+	0.786507i	0.0874320	+	0.0399288i
$389$	5.22553	+	36.3443i	0.264945	+	1.84273i	0.494180	+	0.869360i	$0.335468\pi$
$389$	5.22553	+	36.3443i	0.264945	+	1.84273i	−0.229235	+	0.973371i	$0.573623\pi$
$390$		0			0
$391$	0.633836	−	15.7124i	0.0320544	−	0.794612i
$392$		−	19.5944i		−	0.989669i
$393$		0			0
$394$	−2.87728	+	6.30036i	−0.144955	+	0.317408i
$395$	3.87113	+	13.1839i	0.194778	+	0.663352i
$396$		0			0
$397$	−21.1146	−	6.19982i	−1.05971	−	0.311160i	−0.294978	−	0.955504i	$-0.595312\pi$
$397$	−21.1146	−	6.19982i	−1.05971	−	0.311160i	−0.764736	+	0.644344i	$0.777131\pi$
$398$	−21.0882	+	13.5526i	−1.05706	+	0.679328i
$399$		0			0
$400$	1.97396	+	2.27808i	0.0986982	+	0.113904i
$401$	17.8566	+	11.4758i	0.891718	+	0.573072i	0.904323	−	0.426848i	$-0.140376\pi$
$401$	17.8566	+	11.4758i	0.891718	+	0.573072i	−0.0126054	+	0.999921i	$0.504013\pi$
$402$		0			0
$403$	0.285610	−	1.98646i	0.0142272	−	0.0989526i
$404$	4.80992	−	7.48439i	0.239303	−	0.372362i
$405$		0			0
$406$	37.3603	−	17.0619i	1.85416	−	0.846767i
$407$	0.0713512	+	0.111025i	0.00353675	+	0.00550328i
$408$		0			0
$409$	−13.5597	+	15.6487i	−0.670482	+	0.773778i	−0.984452	−	0.175655i	$-0.943796\pi$
$409$	−13.5597	+	15.6487i	−0.670482	+	0.773778i	0.313969	+	0.949433i	$0.398341\pi$
$410$	14.0312	−	4.11994i	0.692952	−	0.203469i
$411$		0			0
$412$	3.64199	−	0.523640i	0.179428	−	0.0257979i
$413$	−35.5589			−1.74974
$414$		0			0
$415$	−4.40718			−0.216340
$416$	5.99178	−	0.861488i	0.293771	−	0.0422379i
$417$		0			0
$418$	0.0997873	−	0.0293002i	0.00488075	−	0.00143312i
$419$	10.6851	−	12.3312i	0.521999	−	0.602419i	−0.432131	−	0.901811i	$-0.642238\pi$
$419$	10.6851	−	12.3312i	0.521999	−	0.602419i	0.954130	+	0.299392i	$0.0967838\pi$
$420$		0			0
$421$	−10.3225	−	16.0621i	−0.503086	−	0.782817i	0.493109	−	0.869967i	$-0.335860\pi$
$421$	−10.3225	−	16.0621i	−0.503086	−	0.782817i	−0.996195	+	0.0871505i	$0.972224\pi$
$422$	8.05436	−	3.67830i	0.392080	−	0.179057i
$423$		0			0
$424$	−5.60834	+	8.72675i	−0.272365	+	0.423809i
$425$	1.40661	−	9.78317i	0.0682305	−	0.474554i
$426$		0			0
$427$	−17.4130	−	11.1907i	−0.842675	−	0.541555i
$428$	3.32823	+	3.84098i	0.160876	+	0.185661i
$429$		0			0
$430$	−8.61928	+	5.53927i	−0.415658	+	0.267127i
$431$	21.3067	+	6.25622i	1.02631	+	0.301351i	0.751209	−	0.660064i	$-0.229471\pi$
$431$	21.3067	+	6.25622i	1.02631	+	0.301351i	0.275100	+	0.961416i	$0.411289\pi$
$432$		0			0
$433$	0.559423	+	1.90522i	0.0268842	+	0.0915590i	0.971842	−	0.235632i	$-0.0757161\pi$
$433$	0.559423	+	1.90522i	0.0268842	+	0.0915590i	−0.944958	+	0.327191i	$0.893898\pi$
$434$	0.710233	−	1.55519i	0.0340923	−	0.0746517i
$435$		0			0
$436$		−	4.88333i		−	0.233869i
$437$	−13.2267	+	7.76542i	−0.632720	+	0.371470i
$438$		0			0
$439$	−3.67293	−	25.5458i	−0.175299	−	1.21923i	−0.867466	−	0.497497i	$-0.834253\pi$
$439$	−3.67293	−	25.5458i	−0.175299	−	1.21923i	0.692166	−	0.721738i	$-0.256656\pi$
$440$	0.0416825	+	0.0190358i	0.00198714	+	0.000907494i
$441$		0			0
$442$	−15.0006	−	12.9981i	−0.713507	−	0.618258i
$443$	−1.59392	+	5.42838i	−0.0757293	+	0.257910i	−0.988652	−	0.150221i	$-0.952001\pi$
$443$	−1.59392	+	5.42838i	−0.0757293	+	0.257910i	0.912923	+	0.408132i	$0.133820\pi$
$444$		0			0
$445$	3.97159	+	8.69657i	0.188272	+	0.412257i
$446$	5.18029	−	4.48874i	0.245294	−	0.212548i
$447$		0			0
$448$	5.10449	+	0.733915i	0.241164	+	0.0346742i
$449$	−1.82066	−	0.261771i	−0.0859222	−	0.0123537i	0.0992196	−	0.995066i	$-0.468365\pi$
$449$	−1.82066	−	0.261771i	−0.0859222	−	0.0123537i	−0.185142	+	0.982712i	$0.559274\pi$
$450$		0			0
$451$	−0.255042	+	0.220995i	−0.0120095	+	0.0104063i
$452$	1.55208	+	3.39857i	0.0730035	+	0.159855i
$453$		0			0
$454$	−7.17869	+	24.4484i	−0.336913	+	1.14742i
$455$	33.2450	+	28.8070i	1.55855	+	1.35049i
$456$		0			0
$457$	23.9823	+	10.9523i	1.12184	+	0.512329i	0.887953	−	0.459934i	$-0.152127\pi$
$457$	23.9823	+	10.9523i	1.12184	+	0.512329i	0.233890	+	0.972263i	$0.424854\pi$
$458$	1.64239	+	11.4230i	0.0767437	+	0.533764i
$459$		0			0
$460$	−6.64501	−	1.23060i	−0.309825	−	0.0573772i
$461$		−	6.10583i		−	0.284377i	−0.989840	−	0.142189i	$-0.954586\pi$
$461$		−	6.10583i		−	0.284377i	0.989840	−	0.142189i	$-0.0454139\pi$
$462$		0			0
$463$	−7.28219	+	15.9458i	−0.338432	+	0.741063i	−0.999961	−	0.00885674i	$-0.997181\pi$
$463$	−7.28219	+	15.9458i	−0.338432	+	0.741063i	0.661529	+	0.749920i	$0.269908\pi$
$464$	2.24381	+	7.64172i	0.104166	+	0.354758i
$465$		0			0
$466$	17.7940	+	5.22478i	0.824290	+	0.242033i
$467$	4.62796	−	2.97421i	0.214156	−	0.137630i	−0.429165	−	0.903226i	$-0.641192\pi$
$467$	4.62796	−	2.97421i	0.214156	−	0.137630i	0.643322	+	0.765596i	$0.277556\pi$
$468$		0			0
$469$	0.0657061	+	0.0758289i	0.00303402	+	0.00350145i
$470$	−10.9898	−	7.06271i	−0.506921	−	0.325778i
$471$		0			0
$472$	0.981303	−	6.82511i	0.0451681	−	0.314151i
$473$	0.127830	−	0.198907i	0.00587763	−	0.00914578i
$474$		0			0
$475$	−8.76910	+	4.00472i	−0.402354	+	0.183749i
$476$	−9.14190	−	14.2251i	−0.419018	−	0.652005i
$477$		0			0
$478$	−12.0165	+	13.8677i	−0.549620	+	0.634295i
$479$	−35.6923	+	10.4802i	−1.63082	+	0.478853i	−0.963898	−	0.266272i	$-0.914208\pi$
$479$	−35.6923	+	10.4802i	−1.63082	+	0.478853i	−0.666925	+	0.745125i	$0.732390\pi$
$480$		0			0
$481$	−24.3172	+	3.49629i	−1.10877	+	0.159417i
$482$	22.1470			1.00877
$483$		0			0
$484$	10.9989			0.499952
$485$	−2.64077	+	0.379686i	−0.119911	+	0.0172407i
$486$		0			0
$487$	−21.0082	+	6.16856i	−0.951972	+	0.279524i	−0.720608	−	0.693343i	$-0.756137\pi$
$487$	−21.0082	+	6.16856i	−0.951972	+	0.279524i	−0.231364	+	0.972867i	$0.574319\pi$
$488$	2.62846	−	3.03340i	0.118985	−	0.137316i
$489$		0			0
$490$	14.9278	+	23.2281i	0.674369	+	1.04934i
$491$	−3.14775	+	1.43753i	−0.142056	+	0.0648748i	−0.485175	−	0.874417i	$-0.661244\pi$
$491$	−3.14775	+	1.43753i	−0.142056	+	0.0648748i	0.343119	+	0.939292i	$0.388517\pi$
$492$		0			0
$493$	14.1186	−	21.9689i	0.635868	−	0.989430i
$494$	−2.75517	+	19.1626i	−0.123961	+	0.862168i
$495$		0			0
$496$	0.278901	+	0.179239i	0.0125230	+	0.00804806i
$497$	24.4517	+	28.2188i	1.09681	+	1.26579i
$498$		0			0
$499$	9.40050	−	6.04133i	0.420824	−	0.270447i	−0.313045	−	0.949738i	$-0.601349\pi$
$499$	9.40050	−	6.04133i	0.420824	−	0.270447i	0.733869	+	0.679291i	$0.237713\pi$
$500$	−10.8358	−	3.18169i	−0.484594	−	0.142290i
$501$		0			0
$502$	0.466893	+	1.59009i	0.0208384	+	0.0709692i
$503$	−6.08768	+	13.3302i	−0.271436	+	0.594363i	−0.995435	−	0.0954383i	$-0.969575\pi$
$503$	−6.08768	+	13.3302i	−0.271436	+	0.594363i	0.723999	+	0.689801i	$0.242302\pi$
$504$		0			0
$505$			12.5367i			0.557876i
$506$	0.151287	−	0.0378703i	0.00672551	−	0.00168354i
$507$		0			0
$508$	−0.563991	−	3.92264i	−0.0250231	−	0.174039i
$509$	−9.27781	−	4.23704i	−0.411232	−	0.187803i	0.199047	−	0.979990i	$-0.436215\pi$
$509$	−9.27781	−	4.23704i	−0.411232	−	0.187803i	−0.610279	+	0.792187i	$0.708943\pi$
$510$		0			0
$511$	−22.5662	−	19.5537i	−0.998269	−	0.865005i
$512$	−0.281733	+	0.959493i	−0.0124509	+	0.0424040i
$513$		0			0
$514$	−7.10966	−	15.5680i	−0.313594	−	0.686675i
$515$	−3.91845	+	3.39535i	−0.172667	+	0.149617i
$516$		0			0
$517$	0.298401	+	0.0429035i	0.0131236	+	0.00188690i
$518$	−20.7162	−	2.97854i	−0.910218	−	0.130870i
$519$		0			0
$520$	−6.44660	+	5.58601i	−0.282702	+	0.244963i
$521$	1.42550	+	3.12140i	0.0624522	+	0.136751i	0.938285	−	0.345864i	$-0.112414\pi$
$521$	1.42550	+	3.12140i	0.0624522	+	0.136751i	−0.875832	+	0.482615i	$0.839687\pi$
$522$		0			0
$523$	−0.523368	+	1.78243i	−0.0228853	+	0.0779401i	−0.970144	−	0.242530i	$-0.922023\pi$
$523$	−0.523368	+	1.78243i	−0.0228853	+	0.0779401i	0.947259	+	0.320470i	$0.103841\pi$
$524$	−13.7836	−	11.9436i	−0.602140	−	0.521758i
$525$		0			0
$526$	16.5595	+	7.56249i	0.722030	+	0.329740i
$527$	−0.154706	−	1.07600i	−0.00673908	−	0.0468713i
$528$		0			0
$529$	−20.2876	+	10.8358i	−0.882068	+	0.471122i
$530$		−	14.6177i		−	0.634953i
$531$		0			0
$532$	−6.85136	+	15.0024i	−0.297044	+	0.650436i
$533$	−17.6985	−	60.2755i	−0.766606	−	2.61082i
$534$		0			0
$535$	−6.87164	−	2.01769i	−0.297087	−	0.0872325i
$536$	−0.0163677	+	0.0105189i	−0.000706978	+	0.000454347i
$537$		0			0
$538$	−13.9381	−	16.0855i	−0.600916	−	0.693494i
$539$	−0.536036	−	0.344489i	−0.0230887	−	0.0148382i
$540$		0			0
$541$	2.42590	−	16.8725i	0.104298	−	0.725407i	−0.868825	−	0.495120i	$-0.835124\pi$
$541$	2.42590	−	16.8725i	0.104298	−	0.725407i	0.973123	−	0.230287i	$-0.0739667\pi$
$542$	−7.55960	+	11.7630i	−0.324713	+	0.505263i
$543$		0			0
$544$	2.98262	−	1.36212i	0.127879	−	0.0584003i
$545$	3.72031	+	5.78891i	0.159360	+	0.247970i
$546$		0			0
$547$	−5.69894	+	6.57693i	−0.243669	+	0.281209i	−0.864390	−	0.502823i	$-0.832295\pi$
$547$	−5.69894	+	6.57693i	−0.243669	+	0.281209i	0.620720	+	0.784032i	$0.286840\pi$
$548$	10.4550	−	3.06987i	0.446616	−	0.131138i
$549$		0			0
$550$	0.0970245	−	0.0139500i	0.00413714	−	0.000594831i
$551$	−25.4711			−1.08511
$552$		0			0
$553$	50.2855			2.13836
$554$	−25.4823	+	3.66380i	−1.08264	+	0.155660i
$555$		0			0
$556$	8.25829	−	2.42485i	0.350229	−	0.102837i
$557$	−11.3045	+	13.0461i	−0.478989	+	0.552783i	−0.942890	−	0.333104i	$-0.891904\pi$
$557$	−11.3045	+	13.0461i	−0.478989	+	0.552783i	0.463901	+	0.885887i	$0.346449\pi$
$558$		0			0
$559$	23.7957	+	37.0268i	1.00645	+	1.56607i
$560$	−6.61021	+	3.01878i	−0.279332	+	0.127567i
$561$		0			0
$562$	16.8206	−	26.1733i	0.709532	−	1.10405i
$563$	5.70527	−	39.6810i	0.240448	−	1.67236i	−0.409448	−	0.912333i	$-0.634279\pi$
$563$	5.70527	−	39.6810i	0.240448	−	1.67236i	0.649897	−	0.760022i	$-0.274812\pi$
$564$		0			0
$565$	−4.42906	−	2.84639i	−0.186332	−	0.119748i
$566$	−4.74339	−	5.47417i	−0.199380	−	0.230096i
$567$		0			0
$568$	−6.09104	+	3.91448i	−0.255575	+	0.164248i
$569$	24.4183	+	7.16987i	1.02367	+	0.300577i	0.750135	−	0.661285i	$-0.229989\pi$
$569$	24.4183	+	7.16987i	1.02367	+	0.300577i	0.273536	+	0.961862i	$0.411807\pi$
$570$		0			0
$571$	11.9433	+	40.6753i	0.499813	+	1.70221i	0.692906	+	0.721028i	$0.256330\pi$
$571$	11.9433	+	40.6753i	0.499813	+	1.70221i	−0.193093	+	0.981181i	$0.561852\pi$
$572$	0.0817741	−	0.179060i	0.00341915	−	0.00748689i
$573$		0			0
$574$		−	53.5174i		−	2.23377i
$575$	−13.3812	+	5.47041i	−0.558034	+	0.228132i
$576$		0			0
$577$	3.35123	+	23.3083i	0.139513	+	0.970337i	0.932519	+	0.361122i	$0.117606\pi$
$577$	3.35123	+	23.3083i	0.139513	+	0.970337i	−0.793005	+	0.609215i	$0.791485\pi$
$578$	5.68393	+	2.59576i	0.236420	+	0.107970i
$579$		0			0
$580$	−8.48166	−	7.34940i	−0.352182	−	0.305167i
$581$	−4.54401	+	15.4755i	−0.188517	+	0.642031i
$582$		0			0
$583$	0.140134	+	0.306850i	0.00580374	+	0.0127084i
$584$	4.37585	−	3.79170i	0.181074	−	0.156902i
$585$		0			0
$586$	4.24546	+	0.610404i	0.175378	+	0.0252156i
$587$	28.3957	+	4.08269i	1.17202	+	0.168510i	0.700701	−	0.713455i	$-0.252870\pi$
$587$	28.3957	+	4.08269i	1.17202	+	0.168510i	0.471315	+	0.881965i	$0.343780\pi$
$588$		0			0
$589$	−0.801310	+	0.694339i	−0.0330174	+	0.0286097i
$590$	4.03635	+	8.83838i	0.166174	+	0.363870i
$591$		0			0
$592$	1.14339	−	3.89404i	0.0469931	−	0.160044i
$593$	−10.8296	−	9.38394i	−0.444720	−	0.385352i	0.403514	−	0.914973i	$-0.367789\pi$
$593$	−10.8296	−	9.38394i	−0.444720	−	0.385352i	−0.848234	+	0.529621i	$0.822334\pi$
$594$		0			0
$595$	21.6744	+	9.89837i	0.888564	+	0.405794i
$596$	0.672504	+	4.67737i	0.0275468	+	0.191592i
$597$		0			0
$598$	−5.28644	+	28.5457i	−0.216179	+	1.16732i
$599$			2.79967i			0.114391i	0.998363	+	0.0571957i	$0.0182159\pi$
$599$			2.79967i			0.114391i	−0.998363	+	0.0571957i	$0.981784\pi$
$600$		0			0
$601$	−10.8043	+	23.6581i	−0.440716	+	0.965034i	0.550750	+	0.834670i	$0.314342\pi$
$601$	−10.8043	+	23.6581i	−0.440716	+	0.965034i	−0.991466	+	0.130364i	$0.958385\pi$
$602$	10.5639	+	35.9772i	0.430551	+	1.46632i
$603$		0			0
$604$	16.5094	+	4.84759i	0.671756	+	0.197245i
$605$	−13.0386	+	8.37941i	−0.530095	+	0.340672i
$606$		0			0
$607$	21.0968	+	24.3470i	0.856293	+	0.988214i	0.999999	−	0.00140592i	$-0.000447517\pi$
$607$	21.0968	+	24.3470i	0.856293	+	0.988214i	−0.143706	+	0.989620i	$0.545902\pi$
$608$	−2.69046	−	1.72905i	−0.109112	−	0.0701223i
$609$		0			0
$610$	−0.804926	+	5.59838i	−0.0325905	+	0.226672i
$611$	−30.3401	+	47.2101i	−1.22743	+	1.90992i
$612$		0			0
$613$	−9.15327	+	4.18016i	−0.369697	+	0.168835i	−0.591596	−	0.806235i	$-0.701502\pi$
$613$	−9.15327	+	4.18016i	−0.369697	+	0.168835i	0.221899	+	0.975070i	$0.428775\pi$
$614$	−17.3419	−	26.9845i	−0.699861	−	1.08901i
$615$		0			0
$616$	0.109819	−	0.126738i	0.00442474	−	0.00510643i
$617$	−19.1920	+	5.63527i	−0.772640	+	0.226868i	−0.644208	−	0.764851i	$-0.722813\pi$
$617$	−19.1920	+	5.63527i	−0.772640	+	0.226868i	−0.128432	+	0.991718i	$0.540995\pi$
$618$		0			0
$619$	6.42948	−	0.924419i	0.258422	−	0.0371555i	−0.0118858	−	0.999929i	$-0.503783\pi$
$619$	6.42948	−	0.924419i	0.258422	−	0.0371555i	0.270308	+	0.962774i	$0.412874\pi$
$620$	−0.467173			−0.0187621
$621$		0			0
$622$	−0.956207			−0.0383404
$623$	34.6323	−	4.97937i	1.38751	−	0.199494i
$624$		0			0
$625$	0.808082	−	0.237274i	0.0323233	−	0.00949097i
$626$	10.2023	−	11.7741i	0.407766	−	0.470587i
$627$		0			0
$628$	−1.75827	−	2.73592i	−0.0701626	−	0.109175i
$629$	−12.1048	+	5.52806i	−0.482648	+	0.220418i
$630$		0			0
$631$	13.4083	−	20.8638i	0.533778	−	0.830574i	−0.464715	−	0.885460i	$-0.653843\pi$
$631$	13.4083	−	20.8638i	0.533778	−	0.830574i	0.998493	+	0.0548860i	$0.0174795\pi$
$632$	−1.38771	+	9.65170i	−0.0552000	+	0.383924i
$633$		0			0
$634$	15.1552	+	9.73965i	0.601890	+	0.386811i
$635$	3.65700	+	4.22040i	0.145124	+	0.167482i
$636$		0			0
$637$	99.7835	−	64.1270i	3.95357	−	2.54080i
$638$	0.248499	+	0.0729660i	0.00983819	+	0.00288875i
$639$		0			0
$640$	−0.397000	−	1.35206i	−0.0156928	−	0.0534448i
$641$	−0.784156	+	1.71706i	−0.0309723	+	0.0678199i	−0.924486	−	0.381216i	$-0.875505\pi$
$641$	−0.784156	+	1.71706i	−0.0309723	+	0.0678199i	0.893514	+	0.449036i	$0.148233\pi$
$642$		0			0
$643$		−	23.0430i		−	0.908726i	−0.890817	−	0.454363i	$-0.849867\pi$
$643$		−	23.0430i		−	0.908726i	0.890817	−	0.454363i	$-0.150133\pi$
$644$	−11.1725	+	22.0646i	−0.440258	+	0.869468i
$645$		0			0
$646$	1.49239	+	10.3798i	0.0587172	+	0.408387i
$647$	11.7799	+	5.37971i	0.463117	+	0.211498i	0.633288	−	0.773916i	$-0.281705\pi$
$647$	11.7799	+	5.37971i	0.463117	+	0.211498i	−0.170171	+	0.985414i	$0.554432\pi$
$648$		0			0
$649$	−0.169459	−	0.146837i	−0.00665186	−	0.00576387i
$650$	−5.14075	+	17.5078i	−0.201637	+	0.686712i
$651$		0			0
$652$	−4.87919	−	10.6839i	−0.191084	−	0.418415i
$653$	−25.9328	+	22.4709i	−1.01483	+	0.879355i	−0.992725	−	0.120400i	$-0.961582\pi$
$653$	−25.9328	+	22.4709i	−1.01483	+	0.879355i	−0.0221047	+	0.999756i	$0.507037\pi$
$654$		0			0
$655$	25.4388	+	3.65754i	0.993975	+	0.142912i
$656$	10.2720	+	1.47690i	0.401056	+	0.0576631i
$657$		0			0
$658$	−36.1312	+	31.3078i	−1.40854	+	1.22051i
$659$	−9.69547	−	21.2301i	−0.377682	−	0.827008i	−0.999054	−	0.0434922i	$-0.986152\pi$
$659$	−9.69547	−	21.2301i	−0.377682	−	0.827008i	0.621372	−	0.783516i	$-0.286576\pi$
$660$		0			0
$661$	4.79204	−	16.3202i	0.186389	−	0.634782i	−0.812283	−	0.583263i	$-0.801776\pi$
$661$	4.79204	−	16.3202i	0.186389	−	0.634782i	0.998672	−	0.0515189i	$-0.0164062\pi$
$662$	−4.26167	−	3.69276i	−0.165635	−	0.143523i
$663$		0			0
$664$	−2.84494	−	1.29924i	−0.110405	−	0.0504203i
$665$	−3.30749	−	23.0041i	−0.128259	−	0.892061i
$666$		0			0
$667$	−38.1646	−	1.53955i	−1.47774	−	0.0596116i
$668$			1.56616i			0.0605964i
$669$		0			0
$670$	0.0113893	−	0.0249391i	0.000440007	−	0.000963481i
$671$	−0.0367725	−	0.125236i	−0.00141959	−	0.00483467i
$672$		0			0
$673$	−3.95951	−	1.16262i	−0.152628	−	0.0448156i	0.204526	−	0.978861i	$-0.434435\pi$
$673$	−3.95951	−	1.16262i	−0.152628	−	0.0448156i	−0.357154	+	0.934046i	$0.616253\pi$
$674$	1.01466	−	0.652079i	0.0390831	−	0.0251172i
$675$		0			0
$676$	15.4833	+	17.8687i	0.595511	+	0.687256i
$677$	−42.9557	−	27.6059i	−1.65092	−	1.06098i	−0.929727	−	0.368248i	$-0.879958\pi$
$677$	−42.9557	−	27.6059i	−1.65092	−	1.06098i	−0.721193	−	0.692734i	$-0.756406\pi$
$678$		0			0
$679$	−1.38952	+	9.66435i	−0.0533250	+	0.370884i
$680$	−2.49802	+	3.88699i	−0.0957945	+	0.149059i
$681$		0			0
$682$	0.00980671	−	0.00447858i	0.000375518	−	0.000171494i
$683$	−6.31885	−	9.83232i	−0.241784	−	0.376223i	0.699060	−	0.715063i	$-0.253602\pi$
$683$	−6.31885	−	9.83232i	−0.241784	−	0.376223i	−0.940844	+	0.338840i	$0.889966\pi$
$684$		0			0
$685$	−10.0551	+	11.6042i	−0.384185	+	0.443373i
$686$	62.3184	−	18.2983i	2.37933	−	0.698633i
$687$		0			0
$688$	−7.19692	+	1.03476i	−0.274380	+	0.0394499i
$689$	−62.7950			−2.39230
$690$		0			0
$691$	−18.7614			−0.713719			−0.356859	−	0.934158i	$-0.616152\pi$
$691$	−18.7614			−0.713719			−0.356859	+	0.934158i	$0.616152\pi$
$692$	−6.25921	+	0.899939i	−0.237940	+	0.0342105i
$693$		0			0
$694$	16.3602	−	4.80379i	0.621025	−	0.182350i
$695$	−7.94239	+	9.16600i	−0.301272	+	0.347686i
$696$		0			0
$697$	−18.3967	−	28.6259i	−0.696826	−	1.08428i
$698$	13.4958	−	6.16334i	0.510825	−	0.233286i
$699$		0			0
$700$	−8.40417	+	13.0771i	−0.317648	+	0.494269i
$701$	5.30354	−	36.8869i	0.200312	−	1.39320i	−0.603048	−	0.797705i	$-0.706047\pi$
$701$	5.30354	−	36.8869i	0.200312	−	1.39320i	0.803360	−	0.595494i	$-0.203044\pi$
$702$		0			0
$703$	10.9190	+	7.01723i	0.411819	+	0.264660i
$704$	0.0212953	+	0.0245761i	0.000802596	+	0.000926245i
$705$		0			0
$706$	−16.5819	+	10.6565i	−0.624067	+	0.401064i
$707$	44.0217	+	12.9259i	1.65561	+	0.486130i
$708$		0			0
$709$	−10.8685	−	37.0148i	−0.408176	−	1.39012i	−0.865540	−	0.500839i	$-0.833025\pi$
$709$	−10.8685	−	37.0148i	−0.408176	−	1.39012i	0.457365	−	0.889279i	$-0.348793\pi$
$710$	4.23839	−	9.28078i	0.159064	−	0.348301i
$711$		0			0
$712$			6.78467i			0.254266i
$713$	−1.24261	+	0.991926i	−0.0465360	+	0.0371479i
$714$		0			0
$715$	0.0394764	+	0.274564i	0.00147633	+	0.0102681i
$716$	18.6517	+	8.51796i	0.697048	+	0.318331i
$717$		0			0
$718$	12.5596	+	10.8829i	0.468719	+	0.406147i
$719$	12.3650	−	42.1114i	0.461138	−	1.57049i	−0.320808	−	0.947144i	$-0.603954\pi$
$719$	12.3650	−	42.1114i	0.461138	−	1.57049i	0.781946	−	0.623347i	$-0.214227\pi$
$720$		0			0
$721$	7.88243	+	17.2601i	0.293557	+	0.642800i
$722$	−6.62930	+	5.74432i	−0.246717	+	0.213782i
$723$		0			0
$724$	14.9849	+	2.15451i	0.556911	+	0.0800717i
$725$	−23.7627	−	3.41657i	−0.882526	−	0.126888i
$726$		0			0
$727$	−25.8791	+	22.4243i	−0.959801	+	0.831673i	−0.985789	−	0.167990i	$-0.946272\pi$
$727$	−25.8791	+	22.4243i	−0.959801	+	0.831673i	0.0259874	+	0.999662i	$0.491727\pi$
$728$	12.9681	+	28.3962i	0.480630	+	1.05243i
$729$		0			0
$730$	−2.29867	+	7.82854i	−0.0850774	+	0.289747i
$731$	18.0177	+	15.6125i	0.666410	+	0.577448i
$732$		0			0
$733$	−47.2285	−	21.5686i	−1.74443	−	0.796653i	−0.990136	−	0.140112i	$-0.955254\pi$
$733$	−47.2285	−	21.5686i	−1.74443	−	0.796653i	−0.754291	−	0.656541i	$-0.772019\pi$
$734$	−0.646128	−	4.49392i	−0.0238490	−	0.165874i
$735$		0			0
$736$	−3.92672	−	2.75333i	−0.144741	−	0.101489i
$737$		0	0.000632696i		0	2.33057e-5i
$738$		0			0
$739$	−22.4697	+	49.2017i	−0.826560	+	1.80991i	−0.321174	+	0.947020i	$0.604077\pi$
$739$	−22.4697	+	49.2017i	−0.826560	+	1.80991i	−0.505386	+	0.862894i	$0.668650\pi$
$740$	1.61120	+	5.48724i	0.0592288	+	0.201715i
$741$		0			0
$742$	−51.3290	−	15.0716i	−1.88435	−	0.553294i
$743$	15.0998	−	9.70404i	0.553957	−	0.356007i	−0.233518	−	0.972352i	$-0.575024\pi$
$743$	15.0998	−	9.70404i	0.553957	−	0.356007i	0.787476	+	0.616346i	$0.211388\pi$
$744$		0			0
$745$	−4.36061	−	5.03242i	−0.159760	−	0.184373i
$746$	−28.1006	−	18.0592i	−1.02884	−	0.661193i
$747$		0			0
$748$	0.0151746	−	0.105542i	0.000554838	−	0.00385898i
$749$	−14.1700	+	22.0489i	−0.517759	+	0.805649i
$750$		0			0
$751$	4.88722	−	2.23192i	0.178337	−	0.0814439i	−0.324246	−	0.945973i	$-0.605110\pi$
$751$	4.88722	−	2.23192i	0.178337	−	0.0814439i	0.502583	+	0.864529i	$0.332383\pi$
$752$	−5.01207	−	7.79894i	−0.182772	−	0.284398i
$753$		0			0
$754$	−31.5717	+	36.4356i	−1.14977	+	1.32691i
$755$	−23.2640	+	6.83092i	−0.846663	+	0.248603i
$756$		0			0
$757$	36.9520	−	5.31289i	1.34304	−	0.193100i	0.566967	−	0.823740i	$-0.308117\pi$
$757$	36.9520	−	5.31289i	1.34304	−	0.193100i	0.776075	+	0.630640i	$0.217208\pi$
$758$	−0.937826			−0.0340634
$759$		0			0
$760$	4.50664			0.163473
$761$	−8.80528	+	1.26601i	−0.319191	+	0.0458927i	−0.300048	−	0.953924i	$-0.597003\pi$
$761$	−8.80528	+	1.26601i	−0.319191	+	0.0458927i	−0.0191428	+	0.999817i	$0.506094\pi$
$762$		0			0
$763$	24.1631	−	7.09494i	0.874764	−	0.256854i
$764$	−12.0365	+	13.8909i	−0.435466	+	0.502554i
$765$		0			0
$766$	12.1037	+	18.8337i	0.437324	+	0.680489i
$767$	37.9680	−	17.3394i	1.37095	−	0.626090i
$768$		0			0
$769$	21.2170	−	33.0143i	0.765106	−	1.19053i	−0.211895	−	0.977292i	$-0.567964\pi$
$769$	21.2170	−	33.0143i	0.765106	−	1.19053i	0.977001	−	0.213235i	$-0.0684000\pi$
$770$	−0.0336305	+	0.233905i	−0.00121196	+	0.00842937i
$771$		0			0
$772$	2.35218	+	1.51165i	0.0846568	+	0.0544056i
$773$	10.5445	+	12.1690i	0.379258	+	0.437687i	0.913000	−	0.407961i	$-0.133760\pi$
$773$	10.5445	+	12.1690i	0.379258	+	0.437687i	−0.533741	+	0.845648i	$0.679214\pi$
$774$		0			0
$775$	−0.840699	+	0.540285i	−0.0301988	+	0.0194076i
$776$	−1.81661	−	0.533406i	−0.0652126	−	0.0191481i
$777$		0			0
$778$	−10.3447	−	35.2307i	−0.370875	−	1.26308i
$779$	−13.7874	+	30.1901i	−0.493983	+	1.08167i
$780$		0			0
$781$			0.235450i			0.00842507i
$782$	1.60873	+	15.6427i	0.0575280	+	0.559382i
$783$		0			0
$784$	2.78858	+	19.3950i	0.0995921	+	0.692678i
$785$	4.16866	+	1.90376i	0.148786	+	0.0679482i
$786$		0			0
$787$	−1.10265	−	0.955449i	−0.0393051	−	0.0340581i	0.634987	−	0.772523i	$-0.281006\pi$
$787$	−1.10265	−	0.955449i	−0.0393051	−	0.0340581i	−0.674292	+	0.738465i	$0.735551\pi$
$788$	1.95136	−	6.64572i	0.0695143	−	0.236744i
$789$		0			0
$790$	−5.70799	−	12.4988i	−0.203081	−	0.444686i
$791$	−14.5614	+	12.6176i	−0.517745	+	0.448629i
$792$		0			0
$793$	24.0496	+	3.45781i	0.854027	+	0.122791i
$794$	21.7821	+	3.13179i	0.773016	+	0.111143i
$795$		0			0
$796$	18.9448	−	16.4158i	0.671481	−	0.581842i
$797$	3.08198	+	6.74859i	0.109169	+	0.239047i	0.956330	−	0.292290i	$-0.0944171\pi$
$797$	3.08198	+	6.74859i	0.109169	+	0.239047i	−0.847161	+	0.531337i	$0.821690\pi$
$798$		0			0
$799$	−8.56403	+	29.1664i	−0.302974	+	1.03183i
$800$	−2.27808	−	1.97396i	−0.0805422	−	0.0697902i
$801$		0			0
$802$	−19.3081	−	8.81769i	−0.681791	−	0.311364i
$803$	−0.0267960	−	0.186370i	−0.000945609	−	0.00657685i
$804$		0			0
$805$	−3.56533	−	34.6680i	−0.125661	−	1.22189i
$806$			2.00689i			0.0706895i
$807$		0			0
$808$	−3.69583	+	8.09273i	−0.130019	+	0.284701i
$809$	4.52778	+	15.4202i	0.159188	+	0.542145i	1.00000		0.000817269i	$0.000260145\pi$
$809$	4.52778	+	15.4202i	0.159188	+	0.542145i	−0.840811	+	0.541328i	$0.817922\pi$
$810$		0			0
$811$	5.91202	+	1.73593i	0.207599	+	0.0609566i	0.383879	−	0.923384i	$-0.374588\pi$
$811$	5.91202	+	1.73593i	0.207599	+	0.0609566i	−0.176280	+	0.984340i	$0.556406\pi$
$812$	−34.5519	+	22.2051i	−1.21253	+	0.779248i
$813$		0			0
$814$	−0.0864254	−	0.0997402i	−0.00302921	−	0.00349589i
$815$	13.9234	+	8.94805i	0.487717	+	0.313437i
$816$		0			0
$817$	3.30932	−	23.0169i	0.115779	−	0.805258i
$818$	11.1946	−	17.4192i	0.391410	−	0.609046i
$819$		0			0
$820$	−13.3021	+	6.07485i	−0.464528	+	0.212143i
$821$	23.7112	+	36.8953i	0.827525	+	1.28765i	0.955237	+	0.295843i	$0.0956005\pi$
$821$	23.7112	+	36.8953i	0.827525	+	1.28765i	−0.127712	+	0.991811i	$0.540763\pi$
$822$		0			0
$823$	18.3541	−	21.1818i	0.639784	−	0.738350i	−0.339553	−	0.940587i	$-0.610276\pi$
$823$	18.3541	−	21.1818i	0.639784	−	0.738350i	0.979337	+	0.202237i	$0.0648212\pi$
$824$	−3.53040	+	1.03662i	−0.122987	+	0.0361123i
$825$		0			0
$826$	35.1970	−	5.06056i	1.22466	−	0.176079i
$827$	6.79238			0.236194			0.118097	−	0.993002i	$-0.462321\pi$
$827$	6.79238			0.236194			0.118097	+	0.993002i	$0.462321\pi$
$828$		0			0
$829$	−24.2436			−0.842014			−0.421007	−	0.907057i	$-0.638323\pi$
$829$	−24.2436			−0.842014			−0.421007	+	0.907057i	$0.638323\pi$
$830$	4.36232	−	0.627207i	0.151418	−	0.0217707i
$831$		0			0
$832$	−5.80819	+	1.70544i	−0.201363	+	0.0591255i
$833$	42.0740	−	48.5560i	1.45778	−	1.68237i
$834$		0			0
$835$	−1.19316	−	1.85659i	−0.0412909	−	0.0642499i
$836$	−0.0946017	+	0.0432032i	−0.00327187	+	0.00149421i
$837$		0			0
$838$	−8.82138	+	13.7263i	−0.304729	+	0.474168i
$839$	4.19339	−	29.1656i	0.144772	−	1.00691i	−0.779835	−	0.625986i	$-0.784697\pi$
$839$	4.19339	−	29.1656i	0.144772	−	1.00691i	0.924606	−	0.380924i	$-0.124394\pi$
$840$		0			0
$841$	−28.9648	−	18.6146i	−0.998788	−	0.641882i
$842$	12.5033	+	14.4295i	0.430891	+	0.497274i
$843$		0			0
$844$	−7.44890	+	4.78712i	−0.256402	+	0.164779i
$845$	−31.9676	−	9.38653i	−1.09972	−	0.322906i
$846$		0			0
$847$	15.9802	+	54.4237i	0.549088	+	1.87002i
$848$	4.30931	−	9.43608i	0.147982	−	0.324036i
$849$		0			0
$850$			9.88377i			0.339011i
$851$	15.9363	+	11.1742i	0.546290	+	0.383047i
$852$		0			0
$853$	2.05203	+	14.2722i	0.0702602	+	0.488670i	0.994321	+	0.106424i	$0.0339402\pi$
$853$	2.05203	+	14.2722i	0.0702602	+	0.488670i	−0.924061	+	0.382246i	$0.875151\pi$
$854$	18.8284	+	8.59864i	0.644294	+	0.294239i
$855$		0			0
$856$	−3.84098	−	3.32823i	−0.131282	−	0.113757i
$857$	−4.24231	+	14.4480i	−0.144915	+	0.493534i	−0.999675	−	0.0254888i	$-0.991886\pi$
$857$	−4.24231	+	14.4480i	−0.144915	+	0.493534i	0.854761	+	0.519023i	$0.173704\pi$
$858$		0			0
$859$	−9.56976	−	20.9549i	−0.326516	−	0.714971i	0.673184	−	0.739475i	$-0.264926\pi$
$859$	−9.56976	−	20.9549i	−0.326516	−	0.714971i	−0.999700	+	0.0245048i	$0.992199\pi$
$860$	7.74322	−	6.70954i	0.264042	−	0.228793i
$861$		0			0
$862$	−21.9802	−	3.16028i	−0.748649	−	0.107639i
$863$	39.8840	+	5.73445i	1.35767	+	0.195203i	0.782407	−	0.622768i	$-0.213992\pi$
$863$	39.8840	+	5.73445i	1.35767	+	0.195203i	0.575260	+	0.817971i	$0.304901\pi$
$864$		0			0
$865$	6.73433	−	5.83533i	0.228974	−	0.198407i
$866$	−0.824870	−	1.80621i	−0.0280302	−	0.0613776i
$867$		0			0
$868$	−0.481677	+	1.64044i	−0.0163492	+	0.0556802i
$869$	0.239640	+	0.207649i	0.00812923	+	0.00704402i
$870$		0			0
$871$	−0.107134	−	0.0489263i	−0.00363009	−	0.00165781i
$872$	0.694970	+	4.83363i	0.0235347	+	0.163687i
$873$		0			0
$874$	11.9870	−	9.56874i	0.405465	−	0.323667i
$875$		−	58.2393i		−	1.96885i
$876$		0			0
$877$	6.51116	−	14.2575i	0.219866	−	0.481440i	−0.767269	−	0.641325i	$-0.778385\pi$
$877$	6.51116	−	14.2575i	0.219866	−	0.481440i	0.987136	+	0.159885i	$0.0511123\pi$
$878$	7.27109	+	24.7631i	0.245388	+	0.835713i
$879$		0			0
$880$	−0.0439673	−	0.0129100i	−0.00148214	−	0.000435195i
$881$	43.8700	−	28.1935i	1.47802	−	0.949864i	0.480684	−	0.876894i	$-0.340389\pi$
$881$	43.8700	−	28.1935i	1.47802	−	0.949864i	0.997334	−	0.0729703i	$-0.0232478\pi$
$882$		0			0
$883$	−6.10066	−	7.04054i	−0.205304	−	0.236933i	0.643755	−	0.765232i	$-0.277376\pi$
$883$	−6.10066	−	7.04054i	−0.205304	−	0.236933i	−0.849059	+	0.528299i	$0.822830\pi$
$884$	16.6978	+	10.7310i	0.561607	+	0.360923i
$885$		0			0
$886$	0.805154	−	5.59997i	0.0270497	−	0.188135i
$887$	5.16221	−	8.03255i	0.173330	−	0.269707i	−0.743710	−	0.668503i	$-0.766936\pi$
$887$	5.16221	−	8.03255i	0.173330	−	0.269707i	0.917040	+	0.398796i	$0.130572\pi$
$888$		0			0
$889$	18.5902	−	8.48984i	0.623494	−	0.284740i
$890$	−5.16882	−	8.04284i	−0.173259	−	0.269597i
$891$		0			0
$892$	−4.48874	+	5.18029i	−0.150294	+	0.173449i
$893$	28.4479	−	8.35304i	0.951971	−	0.279524i
$894$		0			0
$895$	−28.5999	+	4.11204i	−0.955989	+	0.137450i
$896$	−5.15698			−0.172283
$897$		0			0
$898$	1.83938			0.0613809
$899$	−2.61354	+	0.375771i	−0.0871665	+	0.0125327i
$900$		0			0
$901$	−32.6362	+	9.58286i	−1.08727	+	0.319251i
$902$	0.220995	−	0.255042i	0.00735834	−	0.00849197i
$903$		0			0
$904$	−2.01995	−	3.14310i	−0.0671824	−	0.104538i
$905$	−19.4052	+	8.86205i	−0.645050	+	0.294584i
$906$		0			0
$907$	27.3975	−	42.6313i	0.909719	−	1.41555i	0.000148297	−	1.00000i	$-0.499953\pi$
$907$	27.3975	−	42.6313i	0.909719	−	1.41555i	0.909570	−	0.415550i	$-0.136411\pi$
$908$	3.62625	−	25.2212i	0.120341	−	0.836993i
$909$		0			0
$910$	−37.0063	−	23.7825i	−1.22675	−	0.788382i
$911$	−19.7973	−	22.8473i	−0.655913	−	0.756964i	0.326191	−	0.945304i	$-0.394235\pi$
$911$	−19.7973	−	22.8473i	−0.655913	−	0.756964i	−0.982104	+	0.188340i	$0.939689\pi$
$912$		0			0
$913$	−0.0855595	+	0.0549858i	−0.00283161	+	0.00181976i
$914$	−25.2968	−	7.42782i	−0.836745	−	0.245691i
$915$		0			0
$916$	−3.25134	−	11.0730i	−0.107427	−	0.365864i
$917$	39.0718	−	85.5553i	1.29026	−	2.82528i
$918$		0			0
$919$		−	14.8595i		−	0.490170i	−0.969502	−	0.245085i	$-0.921184\pi$
$919$		−	14.8595i		−	0.490170i	0.969502	−	0.245085i	$-0.0788159\pi$
$920$	6.75250	+	0.272394i	0.222623	+	0.00898058i
$921$		0			0
$922$	0.868951	+	6.04368i	0.0286174	+	0.199038i
$923$	−39.8685	−	18.2073i	−1.31229	−	0.599302i
$924$		0			0
$925$	9.24541	+	8.01120i	0.303987	+	0.263407i
$926$	4.93875	−	16.8198i	0.162297	−	0.552734i
$927$		0			0
$928$	−3.30850	−	7.24461i	−0.108607	−	0.237816i
$929$	3.27755	−	2.84002i	0.107533	−	0.0931779i	−0.599435	−	0.800424i	$-0.704608\pi$
$929$	3.27755	−	2.84002i	0.107533	−	0.0931779i	0.706968	+	0.707246i	$0.250063\pi$
$930$		0			0
$931$	−62.0281	−	8.91830i	−2.03289	−	0.292285i
$932$	−18.3564	−	2.63925i	−0.601284	−	0.0864516i
$933$		0			0
$934$	−4.15758	+	3.60256i	−0.136040	+	0.117879i
$935$	0.0624170	+	0.136674i	0.00204125	+	0.00446972i
$936$		0			0
$937$	−0.186407	+	0.634843i	−0.00608964	+	0.0207394i	−0.962482	−	0.271346i	$-0.912531\pi$
$937$	−0.186407	+	0.634843i	−0.00608964	+	0.0207394i	0.956392	+	0.292086i	$0.0943493\pi$
$938$	−0.0758289	−	0.0657061i	−0.00247590	−	0.00214538i
$939$		0			0
$940$	11.8831	+	5.42681i	0.387583	+	0.177003i
$941$	−1.48644	−	10.3384i	−0.0484566	−	0.337023i	−0.999600	−	0.0282741i	$-0.990999\pi$
$941$	−1.48644	−	10.3384i	−0.0484566	−	0.337023i	0.951144	−	0.308749i	$-0.0999102\pi$
$942$		0			0
$943$	−22.4830	+	44.4018i	−0.732147	+	1.44592i
$944$			6.89530i			0.224423i
$945$		0			0
$946$	−0.0982215	+	0.215075i	−0.00319346	+	0.00699269i
$947$	1.58382	+	5.39398i	0.0514671	+	0.175281i	0.981216	−	0.192914i	$-0.0617940\pi$
$947$	1.58382	+	5.39398i	0.0514671	+	0.175281i	−0.929748	+	0.368195i	$0.879976\pi$
$948$		0			0
$949$	33.6299	+	9.87464i	1.09167	+	0.320544i
$950$	8.10992	−	5.21193i	0.263120	−	0.169097i
$951$		0			0
$952$	11.0733	+	12.7793i	0.358887	+	0.414178i
$953$	27.8039	+	17.8685i	0.900657	+	0.578817i	0.906985	−	0.421163i	$-0.138378\pi$
$953$	27.8039	+	17.8685i	0.900657	+	0.578817i	−0.00632805	+	0.999980i	$0.502014\pi$
$954$		0			0
$955$	3.68600	−	25.6367i	0.119276	−	0.829585i
$956$	9.92057	−	15.4367i	0.320854	−	0.499259i
$957$		0			0
$958$	33.8375	−	15.4531i	1.09324	−	0.499266i
$959$	30.3799	+	47.2721i	0.981019	+	1.52649i
$960$		0			0
$961$	20.2287	−	23.3452i	0.652539	−	0.753070i
$962$	23.5721	−	6.92141i	0.759996	−	0.223155i
$963$		0			0
$964$	−21.9215	+	3.15184i	−0.706045	+	0.101514i
$965$	−3.94001			−0.126834
$966$		0			0
$967$	0.400596			0.0128823			0.00644115	−	0.999979i	$-0.497950\pi$
$967$	0.400596			0.0128823			0.00644115	+	0.999979i	$0.497950\pi$
$968$	−10.8870	+	1.56531i	−0.349921	+	0.0503111i
$969$		0			0
$970$	2.55986	−	0.751643i	0.0821921	−	0.0241338i
$971$	−10.1273	+	11.6875i	−0.325001	+	0.375071i	−0.894612	−	0.446843i	$-0.852548\pi$
$971$	−10.1273	+	11.6875i	−0.325001	+	0.375071i	0.569611	+	0.821914i	$0.307094\pi$
$972$		0			0
$973$	23.9967	+	37.3397i	0.769300	+	1.19705i
$974$	19.9165	−	9.09555i	0.638165	−	0.291440i
$975$		0			0
$976$	−2.17001	+	3.37659i	−0.0694602	+	0.108082i
$977$	−0.516553	+	3.59271i	−0.0165260	+	0.114941i	−0.996415	−	0.0846043i	$-0.973037\pi$
$977$	−0.516553	+	3.59271i	−0.0165260	+	0.114941i	0.979889	+	0.199545i	$0.0639465\pi$
$978$		0			0
$979$	0.185605	+	0.119281i	0.00593196	+	0.00381224i
$980$	−18.0815	−	20.8672i	−0.577594	−	0.666579i
$981$		0			0
$982$	2.91113	−	1.87087i	0.0928979	−	0.0597019i
$983$	−47.4729	−	13.9393i	−1.51415	−	0.444595i	−0.583994	−	0.811758i	$-0.698511\pi$
$983$	−47.4729	−	13.9393i	−1.51415	−	0.444595i	−0.930156	+	0.367164i	$0.880329\pi$
$984$		0			0
$985$	2.74973	+	9.36474i	0.0876138	+	0.298385i
$986$	−10.8484	+	23.7546i	−0.345482	+	0.756500i
$987$		0			0
$988$		−	19.3597i		−	0.615914i
$989$	6.34971	−	34.2872i	0.201909	−	1.09027i
$990$		0			0
$991$	−8.62191	−	59.9667i	−0.273884	−	1.90491i	−0.406349	−	0.913718i	$-0.633198\pi$
$991$	−8.62191	−	59.9667i	−0.273884	−	1.90491i	0.132465	−	0.991188i	$-0.457711\pi$
$992$	−0.301571	−	0.137723i	−0.00957488	−	0.00437270i
$993$		0			0
$994$	−28.2188	−	24.4517i	−0.895045	−	0.775561i
$995$	−9.95184	+	33.8929i	−0.315495	+	1.07448i
$996$		0			0
$997$	−3.64642	−	7.98454i	−0.115483	−	0.252873i	0.843060	−	0.537819i	$-0.180752\pi$
$997$	−3.64642	−	7.98454i	−0.115483	−	0.252873i	−0.958544	+	0.284946i	$0.908024\pi$
$998$	−8.44504	+	7.31767i	−0.267323	+	0.231637i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.j.a.89.1	✓	80
3.2	odd	2	inner	414.2.j.a.89.8	yes	80
23.15	odd	22	inner	414.2.j.a.107.8	yes	80
69.38	even	22	inner	414.2.j.a.107.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.j.a.89.1	✓	80	1.1	even	1	trivial
414.2.j.a.89.8	yes	80	3.2	odd	2	inner
414.2.j.a.107.1	yes	80	69.38	even	22	inner
414.2.j.a.107.8	yes	80	23.15	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.989821 + 0.142315i) q^{2} +(0.959493 - 0.281733i) q^{4} +(-0.922790 + 1.06496i) q^{5} +(2.78807 + 4.33833i) q^{7} +(-0.909632 + 0.415415i) q^{8} +O(q^{10})\)	\(q+(-0.989821 + 0.142315i) q^{2} +(0.959493 - 0.281733i) q^{4} +(-0.922790 + 1.06496i) q^{5} +(2.78807 + 4.33833i) q^{7} +(-0.909632 + 0.415415i) q^{8} +(0.761838 - 1.18544i) q^{10} +(-0.00462790 + 0.0321878i) q^{11} +(-5.09244 - 3.27271i) q^{13} +(-3.37710 - 3.89739i) q^{14} +(0.841254 - 0.540641i) q^{16} +(-3.14611 - 0.923782i) q^{17} +(0.901024 + 3.06860i) q^{19} +(-0.585378 + 1.28180i) q^{20} -0.0325188i q^{22} +(1.16457 + 4.65229i) q^{23} +(0.428983 + 2.98365i) q^{25} +(5.50636 + 2.51467i) q^{26} +(3.89739 + 3.37710i) q^{28} +(-2.24381 + 7.64172i) q^{29} +(0.137723 + 0.301571i) q^{31} +(-0.755750 + 0.654861i) q^{32} +(3.24556 + 0.466641i) q^{34} +(-7.19293 - 1.03419i) q^{35} +(3.06716 - 2.65771i) q^{37} +(-1.32856 - 2.90914i) q^{38} +(0.397000 - 1.35206i) q^{40} +(7.84292 + 6.79593i) q^{41} +(-6.61387 - 3.02045i) q^{43} +(0.00462790 + 0.0321878i) q^{44} +(-1.81480 - 4.43920i) q^{46} -9.27062i q^{47} +(-8.13982 + 17.8237i) q^{49} +(-0.849234 - 2.89223i) q^{50} +(-5.80819 - 1.70544i) q^{52} +(8.72675 - 5.60834i) q^{53} +(-0.0300080 - 0.0346311i) q^{55} +(-4.33833 - 2.78807i) q^{56} +(1.13344 - 7.88327i) q^{58} +(-3.72788 + 5.80069i) q^{59} +(-3.65105 + 1.66738i) q^{61} +(-0.179239 - 0.278901i) q^{62} +(0.654861 - 0.755750i) q^{64} +(8.18455 - 2.40320i) q^{65} +(0.0192583 - 0.00276893i) q^{67} -3.27893 q^{68} +7.26690 q^{70} +(7.16674 - 1.03042i) q^{71} +(-5.55555 + 1.63126i) q^{73} +(-2.65771 + 3.06716i) q^{74} +(1.72905 + 2.69046i) q^{76} +(-0.152544 + 0.0696645i) q^{77} +(5.27176 - 8.20303i) q^{79} +(-0.200541 + 1.39480i) q^{80} +(-8.73025 - 5.61059i) q^{82} +(2.04812 + 2.36366i) q^{83} +(3.88699 - 2.49802i) q^{85} +(6.97641 + 2.04846i) q^{86} +(-0.00916160 - 0.0312015i) q^{88} +(2.81845 - 6.17155i) q^{89} -31.2173i q^{91} +(2.42810 + 4.13574i) q^{92} +(1.31935 + 9.17626i) q^{94} +(-4.09938 - 1.87213i) q^{95} +(1.43086 + 1.23985i) q^{97} +(5.52039 - 18.8007i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 8 q^{4}+O(q^{10}) \) 80 * q + 8 * q^4	\( 80 q + 8 q^{4} - 16 q^{13} - 8 q^{16} + 24 q^{25} - 16 q^{31} + 88 q^{37} + 88 q^{43} + 8 q^{46} + 8 q^{49} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 176 q^{61} + 8 q^{64} - 88 q^{67} - 176 q^{70} - 56 q^{73} - 176 q^{79} - 88 q^{82} - 88 q^{85} + 16 q^{94}+O(q^{100}) \) 80 * q + 8 * q^4 - 16 * q^13 - 8 * q^16 + 24 * q^25 - 16 * q^31 + 88 * q^37 + 88 * q^43 + 8 * q^46 + 8 * q^49 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 176 * q^61 + 8 * q^64 - 88 * q^67 - 176 * q^70 - 56 * q^73 - 176 * q^79 - 88 * q^82 - 88 * q^85 + 16 * q^94

Introduction

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