LMFDB - Embedded newform 441.2.u.d.64.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(64,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("441.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.u (of order $7$, degree $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			64.5
Character	$\chi$	$=$	441.64
Dual form			441.2.u.d.379.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.441918 - 1.93617i) q^{2} +(-1.75153 - 0.843490i) q^{4} +(-2.19876 + 2.75716i) q^{5} +(1.51600 + 2.16835i) q^{7} +(0.0692834 - 0.0868787i) q^{8} +O(q^{10})$	\(q+(0.441918 - 1.93617i) q^{2} +(-1.75153 - 0.843490i) q^{4} +(-2.19876 + 2.75716i) q^{5} +(1.51600 + 2.16835i) q^{7} +(0.0692834 - 0.0868787i) q^{8} +(4.36666 + 5.47561i) q^{10} +(-0.927537 + 4.06381i) q^{11} +(-1.27228 + 5.57421i) q^{13} +(4.86825 - 1.97699i) q^{14} +(-2.56178 - 3.21237i) q^{16} +(2.79877 - 1.34782i) q^{17} -2.60172 q^{19} +(6.17682 - 2.97460i) q^{20} +(7.45833 + 3.59174i) q^{22} +(-0.106638 - 0.0513542i) q^{23} +(-1.65477 - 7.25003i) q^{25} +(10.2304 + 4.92669i) q^{26} +(-0.826321 - 5.07665i) q^{28} +(4.91110 - 2.36506i) q^{29} +8.12903 q^{31} +(-7.15156 + 3.44401i) q^{32} +(-1.37277 - 6.01452i) q^{34} +(-9.31181 - 0.587847i) q^{35} +(-2.18282 + 1.05119i) q^{37} +(-1.14975 + 5.03736i) q^{38} +(0.0872006 + 0.382051i) q^{40} +(-2.52983 + 3.17230i) q^{41} +(-6.43734 - 8.07217i) q^{43} +(5.05239 - 6.33549i) q^{44} +(-0.146556 + 0.183775i) q^{46} +(0.896159 - 3.92633i) q^{47} +(-2.40351 + 6.57443i) q^{49} -14.7686 q^{50} +(6.93022 - 8.69022i) q^{52} +(4.38388 + 2.11117i) q^{53} +(-9.16513 - 11.4927i) q^{55} +(0.293417 + 0.0185232i) q^{56} +(-2.40886 - 10.5539i) q^{58} +(5.79088 + 7.26153i) q^{59} +(-5.49421 + 2.64587i) q^{61} +(3.59237 - 15.7392i) q^{62} +(1.67921 + 7.35708i) q^{64} +(-12.5716 - 15.7642i) q^{65} +2.57419 q^{67} -6.03898 q^{68} +(-5.25323 + 17.7695i) q^{70} +(1.85784 + 0.894690i) q^{71} +(2.14468 + 9.39646i) q^{73} +(1.07066 + 4.69086i) q^{74} +(4.55697 + 2.19452i) q^{76} +(-10.2179 + 4.14949i) q^{77} +8.80338 q^{79} +14.4898 q^{80} +(5.02414 + 6.30007i) q^{82} +(-0.504736 - 2.21139i) q^{83} +(-2.43768 + 10.6802i) q^{85} +(-18.4739 + 8.89655i) q^{86} +(0.288795 + 0.362138i) q^{88} +(-2.16500 - 9.48548i) q^{89} +(-14.0156 + 5.69174i) q^{91} +(0.143462 + 0.179896i) q^{92} +(-7.20601 - 3.47023i) q^{94} +(5.72055 - 7.17334i) q^{95} +10.8774 q^{97} +(11.6671 + 7.55897i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) $ 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8	$ 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8} + 10 q^{10} + 7 q^{11} - 12 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} + 6 q^{19} - 25 q^{20} - 21 q^{22} + 20 q^{23} - 2 q^{25} - 6 q^{26} - q^{28} + 22 q^{29} + 16 q^{31} - 26 q^{32} + 6 q^{34} + 9 q^{35} + 32 q^{37} - 17 q^{38} - 21 q^{40} + 5 q^{41} - 34 q^{43} - 2 q^{44} - 32 q^{46} + 7 q^{47} + 20 q^{49} - 236 q^{50} + 20 q^{52} + 32 q^{53} - 17 q^{55} + 39 q^{56} - 53 q^{58} + q^{59} + 14 q^{61} + 60 q^{62} - 21 q^{64} + 39 q^{65} - 22 q^{67} + 110 q^{68} - 40 q^{70} - 36 q^{71} - 11 q^{73} + 46 q^{74} - 101 q^{76} + 17 q^{77} - 14 q^{79} + 112 q^{80} + 2 q^{82} - 12 q^{83} - 44 q^{85} - 184 q^{86} + 204 q^{88} - 12 q^{89} - 16 q^{91} + 105 q^{92} - 5 q^{94} - 18 q^{95} + 172 q^{97} - q^{98}+O(q^{100}) $ 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8 + 10 * q^10 + 7 * q^11 - 12 * q^13 + q^14 - 3 * q^16 + 3 * q^17 + 6 * q^19 - 25 * q^20 - 21 * q^22 + 20 * q^23 - 2 * q^25 - 6 * q^26 - q^28 + 22 * q^29 + 16 * q^31 - 26 * q^32 + 6 * q^34 + 9 * q^35 + 32 * q^37 - 17 * q^38 - 21 * q^40 + 5 * q^41 - 34 * q^43 - 2 * q^44 - 32 * q^46 + 7 * q^47 + 20 * q^49 - 236 * q^50 + 20 * q^52 + 32 * q^53 - 17 * q^55 + 39 * q^56 - 53 * q^58 + q^59 + 14 * q^61 + 60 * q^62 - 21 * q^64 + 39 * q^65 - 22 * q^67 + 110 * q^68 - 40 * q^70 - 36 * q^71 - 11 * q^73 + 46 * q^74 - 101 * q^76 + 17 * q^77 - 14 * q^79 + 112 * q^80 + 2 * q^82 - 12 * q^83 - 44 * q^85 - 184 * q^86 + 204 * q^88 - 12 * q^89 - 16 * q^91 + 105 * q^92 - 5 * q^94 - 18 * q^95 + 172 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	0.441918	−	1.93617i	0.312483	−	1.36908i	−0.537941	−	0.842982i	$-0.680798\pi$
$2$	0.441918	−	1.93617i	0.312483	−	1.36908i	0.850425	−	0.526097i	$-0.176345\pi$
$3$		0			0
$3$		0			0
$4$	−1.75153	−	0.843490i	−0.875763	−	0.421745i
$5$	−2.19876	+	2.75716i	−0.983316	+	1.23304i	−0.0108626	+	0.999941i	$0.503458\pi$
$5$	−2.19876	+	2.75716i	−0.983316	+	1.23304i	−0.972453	+	0.233098i	$0.925114\pi$
$6$		0			0
$7$	1.51600	+	2.16835i	0.572993	+	0.819560i
$7$	1.51600	+	2.16835i	0.572993	+	0.819560i
$8$	0.0692834	−	0.0868787i	0.0244954	−	0.0307163i
$9$		0			0
$10$	4.36666	+	5.47561i	1.38086	+	1.73154i
$11$	−0.927537	+	4.06381i	−0.279663	+	1.22528i	0.618558	+	0.785739i	$0.287717\pi$
$11$	−0.927537	+	4.06381i	−0.279663	+	1.22528i	−0.898221	+	0.439545i	$0.855140\pi$
$12$		0			0
$13$	−1.27228	+	5.57421i	−0.352866	+	1.54601i	0.417662	+	0.908603i	$0.362850\pi$
$13$	−1.27228	+	5.57421i	−0.352866	+	1.54601i	−0.770528	+	0.637406i	$0.780007\pi$
$14$	4.86825	−	1.97699i	1.30109	−	0.528373i
$15$		0			0
$16$	−2.56178	−	3.21237i	−0.640445	−	0.803093i
$17$	2.79877	−	1.34782i	0.678801	−	0.326893i	−0.0625202	−	0.998044i	$-0.519914\pi$
$17$	2.79877	−	1.34782i	0.678801	−	0.326893i	0.741321	+	0.671150i	$0.234199\pi$
$18$		0			0
$19$	−2.60172			−0.596874			−0.298437	−	0.954429i	$-0.596465\pi$
$19$	−2.60172			−0.596874			−0.298437	+	0.954429i	$0.596465\pi$
$20$	6.17682	−	2.97460i	1.38118	−	0.665141i
$21$		0			0
$22$	7.45833	+	3.59174i	1.59012	+	0.765762i
$23$	−0.106638	−	0.0513542i	−0.0222356	−	0.0107081i	0.422733	−	0.906254i	$-0.361071\pi$
$23$	−0.106638	−	0.0513542i	−0.0222356	−	0.0107081i	−0.444968	+	0.895546i	$0.646785\pi$
$24$		0			0
$25$	−1.65477	−	7.25003i	−0.330954	−	1.45001i
$26$	10.2304	+	4.92669i	2.00634	+	0.966204i
$27$		0			0
$28$	−0.826321	−	5.07665i	−0.156160	−	0.959397i
$29$	4.91110	−	2.36506i	0.911969	−	0.439181i	0.0817717	−	0.996651i	$-0.473942\pi$
$29$	4.91110	−	2.36506i	0.911969	−	0.439181i	0.830197	+	0.557470i	$0.188228\pi$
$30$		0			0
$31$	8.12903			1.46002			0.730008	−	0.683438i	$-0.239516\pi$
$31$	8.12903			1.46002			0.730008	+	0.683438i	$0.239516\pi$
$32$	−7.15156	+	3.44401i	−1.26423	+	0.608821i
$33$		0			0
$34$	−1.37277	−	6.01452i	−0.235429	−	1.03148i
$35$	−9.31181	−	0.587847i	−1.57398	−	0.0993643i
$36$		0			0
$37$	−2.18282	+	1.05119i	−0.358854	+	0.172815i	−0.604620	−	0.796514i	$-0.706675\pi$
$37$	−2.18282	+	1.05119i	−0.358854	+	0.172815i	0.245766	+	0.969329i	$0.420961\pi$
$38$	−1.14975	+	5.03736i	−0.186513	+	0.817168i
$39$		0			0
$40$	0.0872006	+	0.382051i	0.0137876	+	0.0604076i
$41$	−2.52983	+	3.17230i	−0.395093	+	0.495430i	−0.939097	−	0.343652i	$-0.888336\pi$
$41$	−2.52983	+	3.17230i	−0.395093	+	0.495430i	0.544005	+	0.839082i	$0.316907\pi$
$42$		0			0
$43$	−6.43734	−	8.07217i	−0.981686	−	1.23100i	−0.972946	−	0.231033i	$-0.925789\pi$
$43$	−6.43734	−	8.07217i	−0.981686	−	1.23100i	−0.00873990	−	0.999962i	$-0.502782\pi$
$44$	5.05239	−	6.33549i	0.761676	−	0.955111i
$45$		0			0
$46$	−0.146556	+	0.183775i	−0.0216085	+	0.0270962i
$47$	0.896159	−	3.92633i	0.130718	−	0.572714i	−0.866566	−	0.499063i	$-0.833678\pi$
$47$	0.896159	−	3.92633i	0.130718	−	0.572714i	0.997284	−	0.0736512i	$-0.0234652\pi$
$48$		0			0
$49$	−2.40351	+	6.57443i	−0.343359	+	0.939204i
$50$	−14.7686			−2.08859
$51$		0			0
$52$	6.93022	−	8.69022i	0.961049	−	1.20512i
$53$	4.38388	+	2.11117i	0.602173	+	0.289991i	0.710026	−	0.704176i	$-0.248683\pi$
$53$	4.38388	+	2.11117i	0.602173	+	0.289991i	−0.107853	+	0.994167i	$0.534398\pi$
$54$		0			0
$55$	−9.16513	−	11.4927i	−1.23583	−	1.54968i
$56$	0.293417	+	0.0185232i	0.0392095	+	0.00247527i
$57$		0			0
$58$	−2.40886	−	10.5539i	−0.316298	−	1.38579i
$59$	5.79088	+	7.26153i	0.753908	+	0.945371i	0.999713	−	0.0239483i	$-0.00762373\pi$
$59$	5.79088	+	7.26153i	0.753908	+	0.945371i	−0.245805	+	0.969319i	$0.579052\pi$
$60$		0			0
$61$	−5.49421	+	2.64587i	−0.703462	+	0.338769i	−0.751185	−	0.660091i	$-0.770518\pi$
$61$	−5.49421	+	2.64587i	−0.703462	+	0.338769i	0.0477236	+	0.998861i	$0.484803\pi$
$62$	3.59237	−	15.7392i	0.456231	−	1.99888i
$63$		0			0
$64$	1.67921	+	7.35708i	0.209901	+	0.919635i
$65$	−12.5716	−	15.7642i	−1.55931	−	1.95531i
$66$		0			0
$67$	2.57419			0.314488			0.157244	−	0.987560i	$-0.449739\pi$
$67$	2.57419			0.314488			0.157244	+	0.987560i	$0.449739\pi$
$68$	−6.03898			−0.732334
$69$		0			0
$70$	−5.25323	+	17.7695i	−0.627881	+	2.12386i
$71$	1.85784	+	0.894690i	0.220485	+	0.106180i	0.540866	−	0.841109i	$-0.318097\pi$
$71$	1.85784	+	0.894690i	0.220485	+	0.106180i	−0.320381	+	0.947289i	$0.603811\pi$
$72$		0			0
$73$	2.14468	+	9.39646i	0.251016	+	1.09977i	0.930560	+	0.366138i	$0.119320\pi$
$73$	2.14468	+	9.39646i	0.251016	+	1.09977i	−0.679545	+	0.733634i	$0.737823\pi$
$74$	1.07066	+	4.69086i	0.124461	+	0.545301i
$75$		0			0
$76$	4.55697	+	2.19452i	0.522720	+	0.251729i
$77$	−10.2179	+	4.14949i	−1.16444	+	0.472878i
$78$		0			0
$79$	8.80338			0.990458			0.495229	−	0.868763i	$-0.335084\pi$
$79$	8.80338			0.990458			0.495229	+	0.868763i	$0.335084\pi$
$80$	14.4898			1.62000
$81$		0			0
$82$	5.02414	+	6.30007i	0.554823	+	0.695727i
$83$	−0.504736	−	2.21139i	−0.0554019	−	0.242732i	0.939643	−	0.342156i	$-0.111157\pi$
$83$	−0.504736	−	2.21139i	−0.0554019	−	0.242732i	−0.995045	+	0.0994241i	$0.968300\pi$
$84$		0			0
$85$	−2.43768	+	10.6802i	−0.264404	+	1.15843i
$86$	−18.4739	+	8.89655i	−1.99209	+	0.959340i
$87$		0			0
$88$	0.288795	+	0.362138i	0.0307857	+	0.0386040i
$89$	−2.16500	−	9.48548i	−0.229490	−	1.00546i	−0.950057	−	0.312075i	$-0.898976\pi$
$89$	−2.16500	−	9.48548i	−0.229490	−	1.00546i	0.720568	−	0.693384i	$-0.243881\pi$
$90$		0			0
$91$	−14.0156	+	5.69174i	−1.46924	+	0.596656i
$92$	0.143462	+	0.179896i	0.0149570	+	0.0187555i
$93$		0			0
$94$	−7.20601	−	3.47023i	−0.743244	−	0.357927i
$95$	5.72055	−	7.17334i	0.586916	−	0.735970i
$96$		0			0
$97$	10.8774			1.10443			0.552217	−	0.833701i	$-0.313782\pi$
$97$	10.8774			1.10443			0.552217	+	0.833701i	$0.313782\pi$
$98$	11.6671	+	7.55897i	1.17855	+	0.763571i
$99$		0			0
$100$	−3.21695	+	14.0944i	−0.321695	+	1.40944i
$101$	−0.439326	+	0.550898i	−0.0437146	+	0.0548164i	−0.803208	−	0.595698i	$-0.796875\pi$
$101$	−0.439326	+	0.550898i	−0.0437146	+	0.0548164i	0.759494	+	0.650515i	$0.225447\pi$
$102$		0			0
$103$	4.56824	−	5.72839i	0.450122	−	0.564435i	−0.504058	−	0.863670i	$-0.668160\pi$
$103$	4.56824	−	5.72839i	0.450122	−	0.564435i	0.954179	+	0.299235i	$0.0967315\pi$
$104$	0.396133	+	0.496734i	0.0388440	+	0.0487088i
$105$		0			0
$106$	6.02490	−	7.55498i	0.585190	−	0.733805i
$107$	2.58742	+	11.3362i	0.250136	+	1.09592i	0.931434	+	0.363910i	$0.118558\pi$
$107$	2.58742	+	11.3362i	0.250136	+	1.09592i	−0.681298	+	0.732006i	$0.738584\pi$
$108$		0			0
$109$	2.79240	−	12.2343i	0.267464	−	1.17184i	−0.645489	−	0.763770i	$-0.723346\pi$
$109$	2.79240	−	12.2343i	0.267464	−	1.17184i	0.912952	−	0.408066i	$-0.133797\pi$
$110$	−26.3021	+	12.6664i	−2.50780	+	1.20770i
$111$		0			0
$112$	3.08190	−	10.4248i	0.291213	−	0.985050i
$113$	−2.55078	−	11.1757i	−0.239957	−	1.05132i	−0.941055	−	0.338254i	$-0.890164\pi$
$113$	−2.55078	−	11.1757i	−0.239957	−	1.05132i	0.701098	−	0.713065i	$-0.252694\pi$
$114$		0			0
$115$	0.376063	−	0.181103i	0.0350681	−	0.0168879i
$116$	−10.5968			−0.983890
$117$		0			0
$118$	16.6187	−	8.00312i	1.52987	−	0.736747i
$119$	7.16546	+	4.02543i	0.656857	+	0.369011i
$120$		0			0
$121$	−5.74354	−	2.76595i	−0.522140	−	0.251450i
$122$	2.69487	+	11.8070i	0.243982	+	1.06895i
$123$		0			0
$124$	−14.2382	−	6.85675i	−1.27863	−	0.615755i
$125$	7.74142	+	3.72807i	0.692414	+	0.333449i
$126$		0			0
$127$	5.39167	−	2.59649i	0.478434	−	0.230402i	−0.179094	−	0.983832i	$-0.557317\pi$
$127$	5.39167	−	2.59649i	0.478434	−	0.230402i	0.657528	+	0.753430i	$0.271602\pi$
$128$	−0.888628			−0.0785444
$129$		0			0
$130$	−36.0778	+	17.3742i	−3.16424	+	1.52382i
$131$	−4.36874	−	5.47822i	−0.381698	−	0.478635i	0.553454	−	0.832880i	$-0.313309\pi$
$131$	−4.36874	−	5.47822i	−0.381698	−	0.478635i	−0.935153	+	0.354245i	$0.884738\pi$
$132$		0			0
$133$	−3.94419	−	5.64144i	−0.342005	−	0.489175i
$134$	1.13758	−	4.98408i	0.0982723	−	0.430559i
$135$		0			0
$136$	0.0768118	−	0.336535i	0.00658656	−	0.0288576i
$137$	2.79635	+	3.50652i	0.238909	+	0.299582i	0.886802	−	0.462149i	$-0.152921\pi$
$137$	2.79635	+	3.50652i	0.238909	+	0.299582i	−0.647894	+	0.761731i	$0.724350\pi$
$138$		0			0
$139$	−2.94896	+	3.69787i	−0.250127	+	0.313650i	−0.891005	−	0.453993i	$-0.849999\pi$
$139$	−2.94896	+	3.69787i	−0.250127	+	0.313650i	0.640878	+	0.767643i	$0.278570\pi$
$140$	15.8140	+	8.88405i	1.33653	+	0.750839i
$141$		0			0
$142$	2.55329	−	3.20172i	0.214267	−	0.268682i
$143$	−21.4724	−	10.3406i	−1.79562	−	0.864723i
$144$		0			0
$145$	−4.27749	+	18.7409i	−0.355226	+	1.55635i
$146$	19.1409			1.58411
$147$		0			0
$148$	4.70994			0.387155
$149$	3.40225	−	14.9062i	0.278723	−	1.22117i	−0.620686	−	0.784059i	$-0.713146\pi$
$149$	3.40225	−	14.9062i	0.278723	−	1.22117i	0.899410	−	0.437107i	$-0.143997\pi$
$150$		0			0
$151$	5.55915	+	2.67714i	0.452397	+	0.217863i	0.646185	−	0.763180i	$-0.276363\pi$
$151$	5.55915	+	2.67714i	0.452397	+	0.217863i	−0.193789	+	0.981043i	$0.562078\pi$
$152$	−0.180256	+	0.226034i	−0.0146207	+	0.0183337i
$153$		0			0
$154$	3.51863	+	21.6173i	0.283540	+	1.74198i
$155$	−17.8738	+	22.4130i	−1.43566	+	1.80026i
$156$		0			0
$157$	−0.522154	−	0.654760i	−0.0416724	−	0.0522556i	0.760559	−	0.649269i	$-0.224925\pi$
$157$	−0.522154	−	0.654760i	−0.0416724	−	0.0522556i	−0.802231	+	0.597014i	$0.796354\pi$
$158$	3.89037	−	17.0448i	0.309502	−	1.35601i
$159$		0			0
$160$	6.22889	−	27.2905i	0.492437	−	2.15751i
$161$	−0.0503089	−	0.309082i	−0.00396490	−	0.0243590i
$162$		0			0
$163$	2.55485	+	3.20368i	0.200111	+	0.250932i	0.871754	−	0.489943i	$-0.162982\pi$
$163$	2.55485	+	3.20368i	0.200111	+	0.250932i	−0.671643	+	0.740875i	$0.734411\pi$
$164$	7.10686	−	3.42248i	0.554953	−	0.267251i
$165$		0			0
$166$	−4.50468			−0.349631
$167$	−4.22213	+	2.03327i	−0.326718	+	0.157339i	−0.590051	−	0.807366i	$-0.700893\pi$
$167$	−4.22213	+	2.03327i	−0.326718	+	0.157339i	0.263333	+	0.964705i	$0.415178\pi$
$168$		0			0
$169$	−17.7406	−	8.54341i	−1.36466	−	0.657185i
$170$	19.6014	+	9.43953i	1.50336	+	0.723979i
$171$		0			0
$172$	4.46637	+	19.5685i	0.340558	+	1.49208i
$173$	−14.3578	−	6.91435i	−1.09160	−	0.525688i	−0.200594	−	0.979674i	$-0.564287\pi$
$173$	−14.3578	−	6.91435i	−1.09160	−	0.525688i	−0.891009	+	0.453986i	$0.850002\pi$
$174$		0			0
$175$	13.2120	−	14.5791i	0.998733	−	1.10208i
$176$	15.4306	−	7.43099i	1.16313	−	0.560132i
$177$		0			0
$178$	−19.3223			−1.44826
$179$	−18.0408	+	8.68800i	−1.34843	+	0.649372i	−0.962026	−	0.272956i	$-0.911999\pi$
$179$	−18.0408	+	8.68800i	−1.34843	+	0.649372i	−0.386408	+	0.922328i	$0.626284\pi$
$180$		0			0
$181$	1.24503	+	5.45482i	0.0925421	+	0.405453i	0.999889	−	0.0149303i	$-0.00475265\pi$
$181$	1.24503	+	5.45482i	0.0925421	+	0.405453i	−0.907346	+	0.420384i	$0.861896\pi$
$182$	4.82641	+	29.6519i	0.357758	+	2.19795i
$183$		0			0
$184$	−0.0118498	+	0.00570658i	−0.000873581	+	0.000420695i
$185$	1.90120	−	8.32972i	0.139779	−	0.612413i
$186$		0			0
$187$	2.88130	+	12.6238i	0.210702	+	0.923144i
$188$	−4.88147	+	6.12116i	−0.356017	+	0.446432i
$189$		0			0
$190$	−11.3608	−	14.2460i	−0.824199	−	1.03351i
$191$	2.92909	−	3.67296i	0.211941	−	0.265766i	−0.664485	−	0.747301i	$-0.731349\pi$
$191$	2.92909	−	3.67296i	0.211941	−	0.265766i	0.876427	+	0.481535i	$0.159921\pi$
$192$		0			0
$193$	12.4181	−	15.5718i	0.893874	−	1.12088i	−0.0981928	−	0.995167i	$-0.531306\pi$
$193$	12.4181	−	15.5718i	0.893874	−	1.12088i	0.992066	−	0.125715i	$-0.0401224\pi$
$194$	4.80693	−	21.0605i	0.345117	−	1.51206i
$195$		0			0
$196$	9.75528	−	9.48794i	0.696805	−	0.677710i
$197$	2.76013			0.196651			0.0983257	−	0.995154i	$-0.468651\pi$
$197$	2.76013			0.196651			0.0983257	+	0.995154i	$0.468651\pi$
$198$		0			0
$199$	10.4483	−	13.1017i	0.740658	−	0.928756i	−0.258649	−	0.965971i	$-0.583277\pi$
$199$	10.4483	−	13.1017i	0.740658	−	0.928756i	0.999307	+	0.0372154i	$0.0118488\pi$
$200$	−0.744521	−	0.358543i	−0.0526456	−	0.0253528i
$201$		0			0
$202$	0.872485	+	1.09406i	0.0613879	+	0.0769779i
$203$	12.5735	+	7.06358i	0.882487	+	0.495766i
$204$		0			0
$205$	−3.18406	−	13.9503i	−0.222384	−	0.974329i
$206$	−9.07235	−	11.3764i	−0.632100	−	0.792629i
$207$		0			0
$208$	21.1657	−	10.1929i	1.46758	−	0.706749i
$209$	2.41319	−	10.5729i	0.166924	−	0.731341i
$210$		0			0
$211$	3.69639	+	16.1949i	0.254470	+	1.11491i	0.927067	+	0.374896i	$0.122322\pi$
$211$	3.69639	+	16.1949i	0.254470	+	1.11491i	−0.672597	+	0.740009i	$0.734821\pi$
$212$	−5.89773	−	7.39552i	−0.405058	−	0.507927i
$213$		0			0
$214$	23.0923			1.57856
$215$	36.4105			2.48317
$216$		0			0
$217$	12.3236	+	17.6266i	0.836579	+	1.19657i
$218$	−22.4537	−	10.8131i	−1.52076	−	0.732358i
$219$		0			0
$220$	6.35897	+	27.8605i	0.428722	+	1.87835i
$221$	3.95220	+	17.3157i	0.265854	+	1.16478i
$222$		0			0
$223$	13.1953	+	6.35454i	0.883625	+	0.425532i	0.819947	−	0.572439i	$-0.194003\pi$
$223$	13.1953	+	6.35454i	0.883625	+	0.425532i	0.0636780	+	0.997970i	$0.479717\pi$
$224$	−18.3096	−	10.2860i	−1.22336	−	0.687262i
$225$		0			0
$226$	−22.7653			−1.51432
$227$	29.8391			1.98049			0.990246	−	0.139330i	$-0.0444950\pi$
$227$	29.8391			1.98049			0.990246	+	0.139330i	$0.0444950\pi$
$228$		0			0
$229$	−16.6171	−	20.8372i	−1.09809	−	1.37696i	−0.919524	−	0.393033i	$-0.871426\pi$
$229$	−16.6171	−	20.8372i	−1.09809	−	1.37696i	−0.178566	−	0.983928i	$-0.557146\pi$
$230$	−0.184456	−	0.808155i	−0.0121627	−	0.0532882i
$231$		0			0
$232$	0.134785	−	0.590530i	0.00884904	−	0.0387702i
$233$	12.3340	−	5.93973i	0.808026	−	0.389125i	0.0161979	−	0.999869i	$-0.494844\pi$
$233$	12.3340	−	5.93973i	0.808026	−	0.389125i	0.791828	+	0.610744i	$0.209130\pi$
$234$		0			0
$235$	8.85508	+	11.1039i	0.577642	+	0.724340i
$236$	−4.01784	−	17.6033i	−0.261539	−	1.14588i
$237$		0			0
$238$	10.9605	−	12.0946i	0.710462	−	0.783979i
$239$	15.4936	+	19.4284i	1.00220	+	1.25672i	0.966315	+	0.257361i	$0.0828530\pi$
$239$	15.4936	+	19.4284i	1.00220	+	1.25672i	0.0358831	+	0.999356i	$0.488576\pi$
$240$		0			0
$241$	−14.8752	−	7.16350i	−0.958193	−	0.461441i	−0.111642	−	0.993749i	$-0.535611\pi$
$241$	−14.8752	−	7.16350i	−0.958193	−	0.461441i	−0.846551	+	0.532307i	$0.821325\pi$
$242$	−7.89352	+	9.89816i	−0.507415	+	0.636278i
$243$		0			0
$244$	11.8550			0.758940
$245$	−12.8420	−	21.0825i	−0.820446	−	1.34691i
$246$		0			0
$247$	3.31011	−	14.5025i	0.210617	−	0.922773i
$248$	0.563207	−	0.706239i	0.0357637	−	0.0448462i
$249$		0			0
$250$	10.6393	−	13.3412i	0.672886	−	0.843772i
$251$	−6.57580	−	8.24579i	−0.415061	−	0.520469i	0.529720	−	0.848172i	$-0.322297\pi$
$251$	−6.57580	−	8.24579i	−0.415061	−	0.520469i	−0.944781	+	0.327703i	$0.893725\pi$
$252$		0			0
$253$	0.307604	−	0.385724i	0.0193389	−	0.0242502i
$254$	−2.64457	−	11.5866i	−0.165935	−	0.727010i
$255$		0			0
$256$	−3.75111	+	16.4347i	−0.234445	+	1.02717i
$257$	−1.89733	+	0.913707i	−0.118352	+	0.0569955i	−0.492123	−	0.870526i	$-0.663779\pi$
$257$	−1.89733	+	0.913707i	−0.118352	+	0.0569955i	0.373771	+	0.927521i	$0.378065\pi$
$258$		0			0
$259$	−5.58851	−	3.13953i	−0.347253	−	0.195081i
$260$	8.72243	+	38.2154i	0.540942	+	2.37002i
$261$		0			0
$262$	−12.5374	+	6.03769i	−0.774563	+	0.373010i
$263$	6.22719			0.383985			0.191993	−	0.981396i	$-0.438505\pi$
$263$	6.22719			0.383985			0.191993	+	0.981396i	$0.438505\pi$
$264$		0			0
$265$	−15.4599	+	7.44511i	−0.949696	+	0.457350i
$266$	−12.6658	+	5.14357i	−0.776590	+	0.315373i
$267$		0			0
$268$	−4.50877	−	2.17131i	−0.275417	−	0.132634i
$269$	−4.42457	−	19.3853i	−0.269771	−	1.18194i	−0.910280	−	0.413993i	$-0.864134\pi$
$269$	−4.42457	−	19.3853i	−0.269771	−	1.18194i	0.640509	−	0.767951i	$-0.278723\pi$
$270$		0			0
$271$	−5.21878	−	2.51323i	−0.317018	−	0.152668i	0.268607	−	0.963250i	$-0.413437\pi$
$271$	−5.21878	−	2.51323i	−0.317018	−	0.152668i	−0.585625	+	0.810582i	$0.699151\pi$
$272$	−11.4995	−	5.53787i	−0.697261	−	0.335783i
$273$		0			0
$274$	8.02497	−	3.86462i	0.484806	−	0.233470i
$275$	30.9976			1.86922
$276$		0			0
$277$	5.72157	−	2.75536i	0.343776	−	0.165554i	−0.254026	−	0.967197i	$-0.581755\pi$
$277$	5.72157	−	2.75536i	0.343776	−	0.165554i	0.597802	+	0.801644i	$0.296041\pi$
$278$	5.85652	+	7.34384i	0.351251	+	0.440454i
$279$		0			0
$280$	−0.696225	+	0.768270i	−0.0416074	+	0.0459129i
$281$	−6.76430	+	29.6363i	−0.403524	+	1.76796i	0.209416	+	0.977827i	$0.432844\pi$
$281$	−6.76430	+	29.6363i	−0.403524	+	1.76796i	−0.612941	+	0.790129i	$0.710014\pi$
$282$		0			0
$283$	3.65799	−	16.0267i	0.217445	−	0.952689i	−0.741913	−	0.670497i	$-0.766081\pi$
$283$	3.65799	−	16.0267i	0.217445	−	0.952689i	0.959358	−	0.282193i	$-0.0910618\pi$
$284$	−2.49940	−	3.13414i	−0.148312	−	0.185977i
$285$		0			0
$286$	−29.5102	+	37.0046i	−1.74497	+	2.18813i
$287$	−10.7139	−	0.676359i	−0.632420	−	0.0399242i
$288$		0			0
$289$	−4.58283	+	5.74668i	−0.269578	+	0.338040i
$290$	34.3953	+	16.5639i	2.01976	+	0.972665i
$291$		0			0
$292$	4.16936	−	18.2672i	0.243993	−	1.06900i
$293$	1.83585			0.107251			0.0536256	−	0.998561i	$-0.482922\pi$
$293$	1.83585			0.107251			0.0536256	+	0.998561i	$0.482922\pi$
$294$		0			0
$295$	−32.7540			−1.90701
$296$	−0.0599073	+	0.262471i	−0.00348204	+	0.0152558i
$297$		0			0
$298$	−27.3575	−	13.1747i	−1.58478	−	0.763188i
$299$	0.421932	−	0.529086i	0.0244010	−	0.0305979i
$300$		0			0
$301$	7.74433	−	26.1958i	0.446376	−	1.50990i
$302$	7.64009	−	9.58037i	0.439638	−	0.551289i
$303$		0			0
$304$	6.66502	+	8.35768i	0.382265	+	0.479346i
$305$	4.78537	−	20.9661i	0.274009	−	1.20051i
$306$		0			0
$307$	−4.73003	+	20.7236i	−0.269957	+	1.18276i	0.640105	+	0.768287i	$0.278891\pi$
$307$	−4.73003	+	20.7236i	−0.269957	+	1.18276i	−0.910062	+	0.414472i	$0.863966\pi$
$308$	21.3970	+	1.35077i	1.21921	+	0.0769675i
$309$		0			0
$310$	35.4967	+	44.5114i	2.01608	+	2.52808i
$311$	−23.7359	+	11.4306i	−1.34594	+	0.648170i	−0.961455	−	0.274962i	$-0.911335\pi$
$311$	−23.7359	+	11.4306i	−1.34594	+	0.648170i	−0.384484	+	0.923132i	$0.625620\pi$
$312$		0			0
$313$	24.4409			1.38148			0.690740	−	0.723103i	$-0.257285\pi$
$313$	24.4409			1.38148			0.690740	+	0.723103i	$0.257285\pi$
$314$	−1.49848	+	0.721628i	−0.0845639	+	0.0407239i
$315$		0			0
$316$	−15.4193	−	7.42556i	−0.867406	−	0.417721i
$317$	15.5760	+	7.50101i	0.874836	+	0.421299i	0.816736	−	0.577012i	$-0.195781\pi$
$317$	15.5760	+	7.50101i	0.874836	+	0.421299i	0.0581005	+	0.998311i	$0.481496\pi$
$318$		0			0
$319$	5.05592	+	22.1515i	0.283077	+	1.24024i
$320$	−23.9768	−	11.5466i	−1.34035	−	0.645476i
$321$		0			0
$322$	−0.620667	−	0.0391822i	−0.0345884	−	0.00218354i
$323$	−7.28160	+	3.50663i	−0.405159	+	0.195114i
$324$		0			0
$325$	42.5185			2.35850
$326$	7.33191	−	3.53086i	0.406077	−	0.195556i
$327$		0			0
$328$	0.100330	+	0.439576i	0.00553982	+	0.0242715i
$329$	9.87224	−	4.00911i	0.544274	−	0.221030i
$330$		0			0
$331$	6.59765	−	3.17726i	0.362640	−	0.174638i	−0.243687	−	0.969854i	$-0.578357\pi$
$331$	6.59765	−	3.17726i	0.362640	−	0.174638i	0.606326	+	0.795216i	$0.292643\pi$
$332$	−0.981229	+	4.29905i	−0.0538520	+	0.235941i
$333$		0			0
$334$	2.07092	+	9.07330i	0.113316	+	0.496469i
$335$	−5.66004	+	7.09747i	−0.309241	+	0.387776i
$336$		0			0
$337$	−21.1275	−	26.4930i	−1.15089	−	1.44317i	−0.876406	−	0.481573i	$-0.840066\pi$
$337$	−21.1275	−	26.4930i	−1.15089	−	1.44317i	−0.274480	−	0.961593i	$-0.588506\pi$
$338$	−24.3814	+	30.5733i	−1.32617	+	1.66297i
$339$		0			0
$340$	13.2783	−	16.6504i	0.720116	−	0.902997i
$341$	−7.53998	+	33.0348i	−0.408313	+	1.78893i
$342$		0			0
$343$	−17.8994	+	4.75515i	−0.966477	+	0.256754i
$344$	−1.14730			−0.0618583
$345$		0			0
$346$	−19.7323	+	24.7436i	−1.06082	+	1.33022i
$347$	28.3881	+	13.6710i	1.52395	+	0.733898i	0.993502	−	0.113817i	$-0.0363079\pi$
$347$	28.3881	+	13.6710i	1.52395	+	0.733898i	0.530452	+	0.847715i	$0.322022\pi$
$348$		0			0
$349$	5.43785	+	6.81885i	0.291082	+	0.365005i	0.905773	−	0.423763i	$-0.139291\pi$
$349$	5.43785	+	6.81885i	0.291082	+	0.365005i	−0.614692	+	0.788768i	$0.710720\pi$
$350$	−22.3891	−	32.0235i	−1.19675	−	1.71173i
$351$		0			0
$352$	−7.36245	−	32.2570i	−0.392420	−	1.71930i
$353$	−6.61307	−	8.29253i	−0.351978	−	0.441367i	0.574050	−	0.818820i	$-0.305371\pi$
$353$	−6.61307	−	8.29253i	−0.351978	−	0.441367i	−0.926029	+	0.377453i	$0.876800\pi$
$354$		0			0
$355$	−6.55176	+	3.15516i	−0.347731	+	0.167458i
$356$	−4.20886	+	18.4402i	−0.223069	+	0.977330i
$357$		0			0
$358$	8.84888	+	38.7695i	0.467678	+	2.04903i
$359$	−8.97101	−	11.2493i	−0.473472	−	0.593715i	0.486546	−	0.873655i	$-0.338257\pi$
$359$	−8.97101	−	11.2493i	−0.473472	−	0.593715i	−0.960017	+	0.279940i	$0.909685\pi$
$360$		0			0
$361$	−12.2311			−0.643741
$362$	11.1117			0.584015
$363$		0			0
$364$	29.3497	+	1.85282i	1.53834	+	0.0971142i
$365$	−30.6232	−	14.7473i	−1.60289	−	0.771911i
$366$		0			0
$367$	2.59287	+	11.3601i	0.135347	+	0.592993i	0.996422	+	0.0845157i	$0.0269343\pi$
$367$	2.59287	+	11.3601i	0.135347	+	0.592993i	−0.861075	+	0.508477i	$0.830209\pi$
$368$	0.108215	+	0.474119i	0.00564108	+	0.0247152i
$369$		0			0
$370$	−15.2876	−	7.36211i	−0.794763	−	0.382738i
$371$	2.06820	+	12.7063i	0.107375	+	0.659680i
$372$		0			0
$373$	14.7340			0.762898			0.381449	−	0.924390i	$-0.375425\pi$
$373$	14.7340			0.762898			0.381449	+	0.924390i	$0.375425\pi$
$374$	25.7151			1.32970
$375$		0			0
$376$	−0.279025	−	0.349887i	−0.0143896	−	0.0180440i
$377$	6.93507	+	30.3845i	0.357175	+	1.56488i
$378$		0			0
$379$	−3.12767	+	13.7032i	−0.160658	+	0.703887i	0.828858	+	0.559460i	$0.188991\pi$
$379$	−3.12767	+	13.7032i	−0.160658	+	0.703887i	−0.989515	+	0.144428i	$0.953866\pi$
$380$	−16.0703	+	7.73906i	−0.824391	+	0.397006i
$381$		0			0
$382$	−5.81706	−	7.29436i	−0.297626	−	0.373212i
$383$	5.14979	+	22.5627i	0.263142	+	1.15290i	0.917821	+	0.396994i	$0.129947\pi$
$383$	5.14979	+	22.5627i	0.263142	+	1.15290i	−0.654679	+	0.755907i	$0.727196\pi$
$384$		0			0
$385$	11.0259	−	37.2961i	0.561934	−	1.90079i
$386$	−24.6619	−	30.9250i	−1.25526	−	1.57404i
$387$		0			0
$388$	−19.0521	−	9.17499i	−0.967222	−	0.465789i
$389$	−12.2108	+	15.3118i	−0.619110	+	0.776340i	−0.988219	−	0.153046i	$-0.951092\pi$
$389$	−12.2108	+	15.3118i	−0.619110	+	0.776340i	0.369109	+	0.929386i	$0.379663\pi$
$390$		0			0
$391$	−0.367671			−0.0185939
$392$	0.404654	+	0.664313i	0.0204381	+	0.0335529i
$393$		0			0
$394$	1.21975	−	5.34409i	0.0614503	−	0.269231i
$395$	−19.3565	+	24.2723i	−0.973933	+	1.22127i
$396$		0			0
$397$	−2.31203	+	2.89919i	−0.116037	+	0.145506i	−0.836458	−	0.548031i	$-0.815377\pi$
$397$	−2.31203	+	2.89919i	−0.116037	+	0.145506i	0.720420	+	0.693538i	$0.243949\pi$
$398$	−20.7499	−	26.0195i	−1.04010	−	1.30424i
$399$		0			0
$400$	−19.0506	+	23.8887i	−0.952531	+	1.19444i
$401$	−1.09854	−	4.81302i	−0.0548585	−	0.240351i	0.940064	−	0.340999i	$-0.110765\pi$
$401$	−1.09854	−	4.81302i	−0.0548585	−	0.240351i	−0.994922	+	0.100649i	$0.967908\pi$
$402$		0			0
$403$	−10.3424	+	45.3129i	−0.515191	+	2.25720i
$404$	1.23417	−	0.594344i	0.0614021	−	0.0295697i
$405$		0			0
$406$	19.2327	−	21.2229i	0.954505	−	1.05328i
$407$	−2.24719	−	9.84560i	−0.111389	−	0.488028i
$408$		0			0
$409$	−24.7201	+	11.9046i	−1.22233	+	0.588643i	−0.929959	−	0.367662i	$-0.880158\pi$
$409$	−24.7201	+	11.9046i	−1.22233	+	0.588643i	−0.292370	+	0.956305i	$0.594444\pi$
$410$	−28.4172			−1.40342
$411$		0			0
$412$	−12.8332	+	6.18015i	−0.632248	+	0.304474i
$413$	−6.96661	+	23.5651i	−0.342805	+	1.15956i
$414$		0			0
$415$	7.20695	+	3.47068i	0.353775	+	0.170369i
$416$	−10.0989	−	44.2461i	−0.495138	−	2.16934i
$417$		0			0
$418$	−19.4044	−	9.34469i	−0.949102	−	0.457064i
$419$	−1.37199	−	0.660714i	−0.0670259	−	0.0322780i	0.400071	−	0.916484i	$-0.368986\pi$
$419$	−1.37199	−	0.660714i	−0.0670259	−	0.0322780i	−0.467096	+	0.884206i	$0.654700\pi$
$420$		0			0
$421$	23.4685	−	11.3019i	1.14379	−	0.550819i	0.236625	−	0.971601i	$-0.423959\pi$
$421$	23.4685	−	11.3019i	1.14379	−	0.550819i	0.907162	+	0.420782i	$0.138244\pi$
$422$	32.9897			1.60591
$423$		0			0
$424$	0.487146	−	0.234597i	0.0236579	−	0.0113930i
$425$	−14.4030	−	18.0608i	−0.698650	−	0.876079i
$426$		0			0
$427$	−14.0664	−	7.90226i	−0.680721	−	0.382417i
$428$	5.03007	−	22.0382i	0.243138	−	1.06526i
$429$		0			0
$430$	16.0904	−	70.4968i	0.775950	−	3.39966i
$431$	−5.28809	−	6.63105i	−0.254718	−	0.319407i	0.637987	−	0.770047i	$-0.279767\pi$
$431$	−5.28809	−	6.63105i	−0.254718	−	0.319407i	−0.892706	+	0.450640i	$0.851196\pi$
$432$		0			0
$433$	−21.7759	+	27.3061i	−1.04648	+	1.31225i	−0.0980814	+	0.995178i	$0.531271\pi$
$433$	−21.7759	+	27.3061i	−1.04648	+	1.31225i	−0.948402	+	0.317070i	$0.897301\pi$
$434$	39.5741	−	16.0710i	1.89962	−	0.771434i
$435$		0			0
$436$	−15.2105	+	19.0734i	−0.728451	+	0.913448i
$437$	0.277442	+	0.133609i	0.0132718	+	0.00639138i
$438$		0			0
$439$	2.61945	−	11.4765i	0.125019	−	0.547746i	−0.873160	−	0.487433i	$-0.837933\pi$
$439$	2.61945	−	11.4765i	0.125019	−	0.547746i	0.998180	−	0.0603122i	$-0.0192096\pi$
$440$	−1.63346			−0.0778723
$441$		0			0
$442$	35.2728			1.67775
$443$	6.37268	−	27.9205i	0.302775	−	1.32655i	−0.563143	−	0.826360i	$-0.690408\pi$
$443$	6.37268	−	27.9205i	0.302775	−	1.32655i	0.865918	−	0.500186i	$-0.166735\pi$
$444$		0			0
$445$	30.9133	+	14.8871i	1.46543	+	0.705715i
$446$	18.1347	−	22.7402i	0.858704	−	1.07678i
$447$		0			0
$448$	−13.4071	+	14.7944i	−0.633425	+	0.698971i
$449$	23.4032	−	29.3467i	1.10447	−	1.38496i	0.189282	−	0.981923i	$-0.439384\pi$
$449$	23.4032	−	29.3467i	1.10447	−	1.38496i	0.915185	−	0.403035i	$-0.132045\pi$
$450$		0			0
$451$	−10.5451	−	13.2232i	−0.496550	−	0.622654i
$452$	−4.95883	+	21.7260i	−0.233244	+	1.02191i
$453$		0			0
$454$	13.1864	−	57.7736i	0.618871	−	2.71145i
$455$	15.1240	−	51.1581i	0.709024	−	2.39833i
$456$		0			0
$457$	−10.2745	−	12.8838i	−0.480620	−	0.602679i	0.481115	−	0.876657i	$-0.340232\pi$
$457$	−10.2745	−	12.8838i	−0.480620	−	0.602679i	−0.961736	+	0.273978i	$0.911660\pi$
$458$	−47.6878	+	22.9652i	−2.22830	+	1.07309i
$459$		0			0
$460$	−0.811442			−0.0378337
$461$	5.91615	−	2.84907i	0.275542	−	0.132694i	−0.291010	−	0.956720i	$-0.593991\pi$
$461$	5.91615	−	2.84907i	0.275542	−	0.132694i	0.566552	+	0.824026i	$0.308277\pi$
$462$		0			0
$463$	15.5161	+	7.47215i	0.721094	+	0.347260i	0.758174	−	0.652052i	$-0.226092\pi$
$463$	15.5161	+	7.47215i	0.721094	+	0.347260i	−0.0370807	+	0.999312i	$0.511806\pi$
$464$	−20.1786	−	9.71751i	−0.936769	−	0.451124i
$465$		0			0
$466$	−6.04972	−	26.5056i	−0.280248	−	1.22785i
$467$	−8.78218	−	4.22927i	−0.406391	−	0.195707i	0.219510	−	0.975610i	$-0.429554\pi$
$467$	−8.78218	−	4.22927i	−0.406391	−	0.195707i	−0.625901	+	0.779903i	$0.715268\pi$
$468$		0			0
$469$	3.90247	+	5.58176i	0.180199	+	0.257742i
$470$	25.4123	−	12.2379i	1.17218	−	0.564493i
$471$		0			0
$472$	1.03208			0.0475055
$473$	38.7746	−	18.6729i	1.78286	−	0.858580i
$474$		0			0
$475$	4.30525	+	18.8625i	0.197538	+	0.865472i
$476$	−9.15508	−	13.0946i	−0.419622	−	0.600192i
$477$		0			0
$478$	44.4635	−	21.4125i	2.03372	−	0.979386i
$479$	−3.26025	+	14.2841i	−0.148964	+	0.652656i	0.844209	+	0.536013i	$0.180070\pi$
$479$	−3.26025	+	14.2841i	−0.148964	+	0.652656i	−0.993174	+	0.116643i	$0.962787\pi$
$480$		0			0
$481$	−3.08241	−	13.5049i	−0.140546	−	0.615772i
$482$	−20.4434	+	25.6352i	−0.931169	+	1.16765i
$483$		0			0
$484$	7.72692	+	9.68925i	0.351223	+	0.440420i
$485$	−23.9168	+	29.9908i	−1.08601	+	1.36181i
$486$		0			0
$487$	−19.7112	+	24.7170i	−0.893198	+	1.12003i	0.0989661	+	0.995091i	$0.468446\pi$
$487$	−19.7112	+	24.7170i	−0.893198	+	1.12003i	−0.992164	+	0.124944i	$0.960125\pi$
$488$	−0.150788	+	0.660645i	−0.00682585	+	0.0299060i
$489$		0			0
$490$	−46.4944	+	15.5476i	−2.10040	+	0.702368i
$491$	16.2732			0.734399			0.367200	−	0.930142i	$-0.380317\pi$
$491$	16.2732			0.734399			0.367200	+	0.930142i	$0.380317\pi$
$492$		0			0
$493$	10.5574	−	13.2385i	0.475480	−	0.596233i
$494$	−26.6165	−	12.8179i	−1.19754	−	0.576702i
$495$		0			0
$496$	−20.8248	−	26.1135i	−0.935060	−	1.17253i
$497$	0.876479	+	5.38481i	0.0393155	+	0.241542i
$498$		0			0
$499$	4.01744	+	17.6016i	0.179845	+	0.787954i	0.981700	+	0.190435i	$0.0609898\pi$
$499$	4.01744	+	17.6016i	0.179845	+	0.787954i	−0.801854	+	0.597520i	$0.796153\pi$
$500$	−10.4147	−	13.0596i	−0.465760	−	0.584044i
$501$		0			0
$502$	−18.8712	+	9.08790i	−0.842263	+	0.405613i
$503$	−2.74929	+	12.0454i	−0.122585	+	0.537079i	0.875922	+	0.482453i	$0.160254\pi$
$503$	−2.74929	+	12.0454i	−0.122585	+	0.537079i	−0.998507	+	0.0546267i	$0.982603\pi$
$504$		0			0
$505$	−0.552939	−	2.42258i	−0.0246055	−	0.107804i
$506$	−0.610890	−	0.766032i	−0.0271574	−	0.0340543i
$507$		0			0
$508$	−11.6338			−0.516165
$509$	−5.12371			−0.227104			−0.113552	−	0.993532i	$-0.536223\pi$
$509$	−5.12371			−0.227104			−0.113552	+	0.993532i	$0.536223\pi$
$510$		0			0
$511$	−17.1235	+	18.8954i	−0.757500	+	0.835884i
$512$	28.5614	+	13.7545i	1.26225	+	0.607867i
$513$		0			0
$514$	0.930626	+	4.07734i	0.0410482	+	0.179844i
$515$	5.74962	+	25.1907i	0.253358	+	1.11004i
$516$		0			0
$517$	15.1246	+	7.28364i	0.665180	+	0.320334i
$518$	−8.54833	+	9.43289i	−0.375592	+	0.414457i
$519$		0			0
$520$	−2.24058			−0.0982558
$521$	−22.7067			−0.994799			−0.497399	−	0.867522i	$-0.665712\pi$
$521$	−22.7067			−0.994799			−0.497399	+	0.867522i	$0.665712\pi$
$522$		0			0
$523$	13.3291	+	16.7142i	0.582842	+	0.730860i	0.982595	−	0.185763i	$-0.0594755\pi$
$523$	13.3291	+	16.7142i	0.582842	+	0.730860i	−0.399753	+	0.916623i	$0.630904\pi$
$524$	3.03113	+	13.2802i	0.132415	+	0.580150i
$525$		0			0
$526$	2.75191	−	12.0569i	0.119989	−	0.525706i
$527$	22.7513	−	10.9564i	0.991061	−	0.477270i
$528$		0			0
$529$	−14.3315	−	17.9712i	−0.623110	−	0.781355i
$530$	7.58298	+	33.2232i	0.329384	+	1.44312i
$531$		0			0
$532$	2.14985	+	13.2080i	0.0932080	+	0.572640i
$533$	−14.4644	−	18.1378i	−0.626525	−	0.785637i
$534$		0			0
$535$	−36.9450	−	17.7918i	−1.59727	−	0.769204i
$536$	0.178349	−	0.223643i	0.00770351	−	0.00965989i
$537$		0			0
$538$	−39.4886			−1.70247
$539$	−24.4879	−	15.8654i	−1.05477	−	0.683373i
$540$		0			0
$541$	−0.281892	+	1.23505i	−0.0121195	+	0.0530989i	−0.980626	−	0.195889i	$-0.937241\pi$
$541$	−0.281892	+	1.23505i	−0.0121195	+	0.0530989i	0.968507	+	0.248988i	$0.0800979\pi$
$542$	−7.17232	+	8.99381i	−0.308078	+	0.386317i
$543$		0			0
$544$	−15.3737	+	19.2780i	−0.659141	+	0.826536i
$545$	27.5922	+	34.5995i	1.18192	+	1.48208i
$546$		0			0
$547$	14.9626	−	18.7625i	0.639755	−	0.802228i	−0.351217	−	0.936294i	$-0.614232\pi$
$547$	14.9626	−	18.7625i	0.639755	−	0.802228i	0.990972	+	0.134066i	$0.0428035\pi$
$548$	−1.94017	−	8.50045i	−0.0828800	−	0.363121i
$549$		0			0
$550$	13.6984	−	60.0166i	0.584102	−	2.55912i
$551$	−12.7773	+	6.15322i	−0.544331	+	0.262136i
$552$		0			0
$553$	13.3459	+	19.0888i	0.567525	+	0.811740i
$554$	−2.80639	−	12.2956i	−0.119232	−	0.522389i
$555$		0			0
$556$	8.28429	−	3.98950i	0.351332	−	0.169193i
$557$	12.9557			0.548950			0.274475	−	0.961594i	$-0.411496\pi$
$557$	12.9557			0.548950			0.274475	+	0.961594i	$0.411496\pi$
$558$		0			0
$559$	53.1861	−	25.6131i	2.24953	−	1.08332i
$560$	21.9664	+	31.4189i	0.928251	+	1.32769i
$561$		0			0
$562$	54.3917	+	26.1937i	2.29438	+	1.10491i
$563$	7.12035	+	31.1963i	0.300087	+	1.31477i	0.869996	+	0.493059i	$0.164121\pi$
$563$	7.12035	+	31.1963i	0.300087	+	1.31477i	−0.569909	+	0.821708i	$0.693021\pi$
$564$		0			0
$565$	36.4217	+	17.5398i	1.53227	+	0.737903i
$566$	−29.4139	−	14.1650i	−1.23636	−	0.595399i
$567$		0			0
$568$	0.206447	−	0.0994197i	0.00866233	−	0.00417156i
$569$	−43.0360			−1.80416			−0.902081	−	0.431566i	$-0.857961\pi$
$569$	−43.0360			−1.80416			−0.902081	+	0.431566i	$0.857961\pi$
$570$		0			0
$571$	33.7460	−	16.2512i	1.41223	−	0.680093i	0.436627	−	0.899643i	$-0.356173\pi$
$571$	33.7460	−	16.2512i	1.41223	−	0.680093i	0.975601	+	0.219549i	$0.0704587\pi$
$572$	28.8873	+	36.2236i	1.20784	+	1.51458i
$573$		0			0
$574$	−6.04420	+	20.4450i	−0.252280	+	0.853358i
$575$	−0.195858	+	0.858108i	−0.00816783	+	0.0357856i
$576$		0			0
$577$	−2.56894	+	11.2553i	−0.106946	+	0.468563i	0.892886	+	0.450282i	$0.148676\pi$
$577$	−2.56894	+	11.2553i	−0.106946	+	0.468563i	−0.999833	+	0.0182810i	$0.994181\pi$
$578$	9.10132	+	11.4127i	0.378565	+	0.474706i
$579$		0			0
$580$	23.2999	−	29.2171i	0.967475	−	1.21318i
$581$	4.02990	−	4.44691i	0.167188	−	0.184489i
$582$		0			0
$583$	−12.6456	+	15.8571i	−0.523727	+	0.656733i
$584$	0.964943	+	0.464692i	0.0399296	+	0.0192291i
$585$		0			0
$586$	0.811294	−	3.55451i	0.0335142	−	0.146835i
$587$	7.80179			0.322014			0.161007	−	0.986953i	$-0.448526\pi$
$587$	7.80179			0.322014			0.161007	+	0.986953i	$0.448526\pi$
$588$		0			0
$589$	−21.1494			−0.871447
$590$	−14.4746	+	63.4172i	−0.595909	+	2.61085i
$591$		0			0
$592$	8.96874	+	4.31912i	0.368613	+	0.177515i
$593$	17.6724	−	22.1605i	0.725719	−	0.910023i	−0.272928	−	0.962035i	$-0.587992\pi$
$593$	17.6724	−	22.1605i	0.725719	−	0.910023i	0.998646	+	0.0520118i	$0.0165634\pi$
$594$		0			0
$595$	−26.8539	+	10.9054i	−1.10090	+	0.447076i
$596$	−18.5324	+	23.2389i	−0.759116	+	0.951901i
$597$		0			0
$598$	−0.837942	−	1.05075i	−0.0342660	−	0.0429682i
$599$	6.66950	−	29.2210i	0.272508	−	1.19394i	−0.634533	−	0.772895i	$-0.718808\pi$
$599$	6.66950	−	29.2210i	0.272508	−	1.19394i	0.907042	−	0.421041i	$-0.138335\pi$
$600$		0			0
$601$	−5.08242	+	22.2675i	−0.207316	+	0.908311i	0.759028	+	0.651058i	$0.225675\pi$
$601$	−5.08242	+	22.2675i	−0.207316	+	0.908311i	−0.966344	+	0.257253i	$0.917183\pi$
$602$	−47.2972	−	26.5708i	−1.92769	−	1.08294i
$603$		0			0
$604$	−7.47884	−	9.37817i	−0.304310	−	0.381592i
$605$	20.2548	−	9.75421i	0.823476	−	0.396565i
$606$		0			0
$607$	−16.6281			−0.674915			−0.337457	−	0.941341i	$-0.609567\pi$
$607$	−16.6281			−0.674915			−0.337457	+	0.941341i	$0.609567\pi$
$608$	18.6063	−	8.96033i	0.754586	−	0.363389i
$609$		0			0
$610$	−38.4791	−	18.5306i	−1.55797	−	0.750281i
$611$	20.7460	+	9.99077i	0.839295	+	0.404183i
$612$		0			0
$613$	−7.12607	−	31.2213i	−0.287819	−	1.26102i	−0.887511	−	0.460787i	$-0.847567\pi$
$613$	−7.12607	−	31.2213i	−0.287819	−	1.26102i	0.599692	−	0.800231i	$-0.295290\pi$
$614$	38.0342	+	18.3163i	1.53493	+	0.739185i
$615$		0			0
$616$	−0.347430	+	1.17521i	−0.0139984	+	0.0473505i
$617$	−17.0389	+	8.20551i	−0.685961	+	0.330342i	−0.744196	−	0.667961i	$-0.767167\pi$
$617$	−17.0389	+	8.20551i	−0.685961	+	0.330342i	0.0582346	+	0.998303i	$0.481453\pi$
$618$		0			0
$619$	−31.6066			−1.27038			−0.635189	−	0.772357i	$-0.719078\pi$
$619$	−31.6066			−1.27038			−0.635189	+	0.772357i	$0.719078\pi$
$620$	50.2116	−	24.1806i	2.01654	−	0.971117i
$621$		0			0
$622$	11.6423	+	51.0081i	0.466812	+	2.04524i
$623$	17.2857	−	19.0744i	0.692539	−	0.764201i
$624$		0			0
$625$	6.19974	−	2.98564i	0.247990	−	0.119425i
$626$	10.8009	−	47.3217i	0.431689	−	1.89135i
$627$		0			0
$628$	0.362282	+	1.58726i	0.0144566	+	0.0633386i
$629$	−4.69241	+	5.88409i	−0.187098	+	0.234614i
$630$		0			0
$631$	24.1773	+	30.3174i	0.962484	+	1.20692i	0.978332	+	0.207042i	$0.0663836\pi$
$631$	24.1773	+	30.3174i	0.962484	+	1.20692i	−0.0158486	+	0.999874i	$0.505045\pi$
$632$	0.609928	−	0.764826i	0.0242616	−	0.0304231i
$633$		0			0
$634$	21.4066	−	26.8430i	0.850163	−	1.06607i
$635$	−4.69606	+	20.5748i	−0.186357	+	0.816485i
$636$		0			0
$637$	−33.5893	−	21.7622i	−1.33086	−	0.862249i
$638$	45.1233			1.78645
$639$		0			0
$640$	1.95388	−	2.45009i	0.0772339	−	0.0968483i
$641$	28.2006	+	13.5807i	1.11386	+	0.536404i	0.897989	−	0.440018i	$-0.145028\pi$
$641$	28.2006	+	13.5807i	1.11386	+	0.536404i	0.215867	+	0.976423i	$0.430742\pi$
$642$		0			0
$643$	−7.58740	−	9.51430i	−0.299218	−	0.375207i	0.609381	−	0.792878i	$-0.291418\pi$
$643$	−7.58740	−	9.51430i	−0.299218	−	0.375207i	−0.908599	+	0.417670i	$0.862847\pi$
$644$	−0.172590	+	0.583799i	−0.00680100	+	0.0230049i
$645$		0			0
$646$	3.57157	+	15.6481i	0.140521	+	0.615665i
$647$	0.477042	+	0.598192i	0.0187545	+	0.0235174i	0.791120	−	0.611661i	$-0.209498\pi$
$647$	0.477042	+	0.598192i	0.0187545	+	0.0235174i	−0.772366	+	0.635178i	$0.780927\pi$
$648$		0			0
$649$	−34.8807	+	16.7977i	−1.36919	+	0.659366i
$650$	18.7897	−	82.3231i	0.736993	−	3.22898i
$651$		0			0
$652$	−1.77261	−	7.76633i	−0.0694209	−	0.304153i
$653$	12.2584	+	15.3715i	0.479708	+	0.601535i	0.961518	−	0.274741i	$-0.0885920\pi$
$653$	12.2584	+	15.3715i	0.479708	+	0.601535i	−0.481810	+	0.876275i	$0.660021\pi$
$654$		0			0
$655$	24.7102			0.965505
$656$	16.6715			0.650912
$657$		0			0
$658$	−3.39960	−	20.8860i	−0.132530	−	0.814223i
$659$	−5.03782	−	2.42609i	−0.196246	−	0.0945069i	0.333180	−	0.942863i	$-0.391878\pi$
$659$	−5.03782	−	2.42609i	−0.196246	−	0.0945069i	−0.529426	+	0.848356i	$0.677593\pi$
$660$		0			0
$661$	3.80825	+	16.6851i	0.148124	+	0.648973i	0.993406	+	0.114652i	$0.0365754\pi$
$661$	3.80825	+	16.6851i	0.148124	+	0.648973i	−0.845282	+	0.534321i	$0.820567\pi$
$662$	−3.23610	−	14.1783i	−0.125774	−	0.551054i
$663$		0			0
$664$	−0.227093	−	0.109362i	−0.00881290	−	0.00424407i
$665$	24.2267	+	1.52941i	0.939470	+	0.0593080i
$666$		0			0
$667$	−0.645166			−0.0249809
$668$	9.11021			0.352485
$669$		0			0
$670$	11.2406	+	14.0953i	0.434263	+	0.544549i
$671$	−5.65623	−	24.7816i	−0.218356	−	0.956682i
$672$		0			0
$673$	−9.91818	+	43.4544i	−0.382318	+	1.67504i	0.307883	+	0.951424i	$0.400380\pi$
$673$	−9.91818	+	43.4544i	−0.382318	+	1.67504i	−0.690200	+	0.723619i	$0.742478\pi$
$674$	−60.6316	+	29.1986i	−2.33544	+	1.12469i
$675$		0			0
$676$	23.8668	+	29.9280i	0.917953	+	1.15108i
$677$	−5.79336	−	25.3824i	−0.222657	−	0.975523i	−0.955469	−	0.295092i	$-0.904650\pi$
$677$	−5.79336	−	25.3824i	−0.222657	−	0.975523i	0.732812	−	0.680431i	$-0.238207\pi$
$678$		0			0
$679$	16.4901	+	23.5861i	0.632833	+	0.905150i
$680$	0.758989	+	0.951742i	0.0291059	+	0.0364976i
$681$		0			0
$682$	60.6289	+	29.1974i	2.32160	+	1.11802i
$683$	10.6088	−	13.3031i	0.405936	−	0.509027i	−0.536277	−	0.844042i	$-0.680170\pi$
$683$	10.6088	−	13.3031i	0.405936	−	0.509027i	0.942213	+	0.335015i	$0.108741\pi$
$684$		0			0
$685$	−15.8165			−0.604319
$686$	1.29672	+	36.7577i	0.0495089	+	1.40341i
$687$		0			0
$688$	−9.43976	+	41.3583i	−0.359887	+	1.57677i
$689$	−17.3456	+	21.7507i	−0.660815	+	0.828636i
$690$		0			0
$691$	6.23015	−	7.81236i	0.237006	−	0.297196i	−0.649077	−	0.760723i	$-0.724845\pi$
$691$	6.23015	−	7.81236i	0.237006	−	0.297196i	0.886083	+	0.463527i	$0.153416\pi$
$692$	19.3159	+	24.2213i	0.734279	+	0.920757i
$693$		0			0
$694$	39.0146	−	48.9228i	1.48097	−	1.85708i
$695$	−3.71158	−	16.2615i	−0.140788	−	0.616833i
$696$		0			0
$697$	−2.80472	+	12.2883i	−0.106236	+	0.465452i
$698$	15.6055	−	7.51523i	0.590679	−	0.284456i
$699$		0			0
$700$	−35.4385	+	14.3916i	−1.33945	+	0.543950i
$701$	5.88202	+	25.7708i	0.222161	+	0.973350i	0.955848	+	0.293862i	$0.0949408\pi$
$701$	5.88202	+	25.7708i	0.222161	+	0.973350i	−0.733687	+	0.679488i	$0.762202\pi$
$702$		0			0
$703$	5.67909	−	2.73490i	0.214191	−	0.103149i
$704$	−31.4553			−1.18552
$705$		0			0
$706$	−18.9782	+	9.13941i	−0.714253	+	0.343966i
$707$	−1.86056	−	0.117456i	−0.0699735	−	0.00441737i
$708$		0			0
$709$	−31.8390	−	15.3329i	−1.19574	−	0.575838i	−0.273281	−	0.961934i	$-0.588109\pi$
$709$	−31.8390	−	15.3329i	−1.19574	−	0.575838i	−0.922458	+	0.386096i	$0.873823\pi$
$710$	3.21358	+	14.0796i	0.120604	+	0.528399i
$711$		0			0
$712$	−0.974085	−	0.469095i	−0.0365054	−	0.0175801i
$713$	−0.866864	−	0.417460i	−0.0324643	−	0.0156340i
$714$		0			0
$715$	75.7234	−	36.4665i	2.83189	−	1.36377i
$716$	38.9272			1.45478
$717$		0			0
$718$	−25.7450	+	12.3981i	−0.960794	+	0.462694i
$719$	4.08839	+	5.12668i	0.152471	+	0.191193i	0.852201	−	0.523215i	$-0.175268\pi$
$719$	4.08839	+	5.12668i	0.152471	+	0.191193i	−0.699730	+	0.714408i	$0.746696\pi$
$720$		0			0
$721$	19.3466	+	1.22134i	0.720505	+	0.0454849i
$722$	−5.40513	+	23.6814i	−0.201158	+	0.881332i
$723$		0			0
$724$	2.42039	−	10.6044i	0.0899530	−	0.394110i
$725$	−25.2735	−	31.6920i	−0.938635	−	1.17701i
$726$		0			0
$727$	6.83741	−	8.57384i	0.253586	−	0.317986i	−0.638702	−	0.769454i	$-0.720528\pi$
$727$	6.83741	−	8.57384i	0.253586	−	0.317986i	0.892287	+	0.451468i	$0.149100\pi$
$728$	−0.476560	+	1.61200i	−0.0176625	+	0.0597448i
$729$		0			0
$730$	−42.0863	+	52.7746i	−1.55768	+	1.95327i
$731$	−28.8964	−	13.9158i	−1.06877	−	0.514694i
$732$		0			0
$733$	2.41352	−	10.5743i	0.0891454	−	0.390572i	−0.910596	−	0.413297i	$-0.864377\pi$
$733$	2.41352	−	10.5743i	0.0891454	−	0.390572i	0.999742	+	0.0227253i	$0.00723432\pi$
$734$	23.1410			0.854148
$735$		0			0
$736$	0.939493			0.0346302
$737$	−2.38766	+	10.4610i	−0.0879507	+	0.385337i
$738$		0			0
$739$	−23.1509	−	11.1489i	−0.851621	−	0.410119i	−0.0434420	−	0.999056i	$-0.513832\pi$
$739$	−23.1509	−	11.1489i	−0.851621	−	0.410119i	−0.808179	+	0.588937i	$0.799547\pi$
$740$	−10.3560	+	12.9861i	−0.380696	+	0.477377i
$741$		0			0
$742$	25.5156	+	1.61078i	0.936707	+	0.0591336i
$743$	18.9880	−	23.8102i	0.696603	−	0.873512i	−0.300162	−	0.953888i	$-0.597041\pi$
$743$	18.9880	−	23.8102i	0.696603	−	0.873512i	0.996765	+	0.0803760i	$0.0256121\pi$
$744$		0			0
$745$	33.6181	+	42.1558i	1.23167	+	1.54447i
$746$	6.51122	−	28.5275i	0.238393	−	1.04447i
$747$		0			0
$748$	5.60138	−	24.5413i	0.204807	−	0.897317i
$749$	−20.6585	+	22.7961i	−0.754843	+	0.832953i
$750$		0			0
$751$	−18.3163	−	22.9679i	−0.668370	−	0.838109i	0.325856	−	0.945419i	$-0.394348\pi$
$751$	−18.3163	−	22.9679i	−0.668370	−	0.838109i	−0.994226	+	0.107310i	$0.965776\pi$
$752$	−14.9086	+	7.17960i	−0.543660	+	0.261813i
$753$		0			0
$754$	61.8944			2.25406
$755$	−19.6045	+	9.44105i	−0.713482	+	0.343595i
$756$		0			0
$757$	−30.9619	−	14.9105i	−1.12533	−	0.541930i	−0.223794	−	0.974636i	$-0.571844\pi$
$757$	−30.9619	−	14.9105i	−1.12533	−	0.541930i	−0.901535	+	0.432706i	$0.857559\pi$
$758$	25.1496	+	12.1114i	0.913475	+	0.439906i
$759$		0			0
$760$	−0.226871	−	0.993988i	−0.00822948	−	0.0360557i
$761$	2.56913	+	1.23723i	0.0931309	+	0.0448495i	0.479869	−	0.877340i	$-0.340684\pi$
$761$	2.56913	+	1.23723i	0.0931309	+	0.0448495i	−0.386738	+	0.922189i	$0.626398\pi$
$762$		0			0
$763$	30.7616	−	12.4923i	1.11365	−	0.452251i
$764$	−8.22847	+	3.96262i	−0.297696	+	0.143363i
$765$		0			0
$766$	45.9610			1.66064
$767$	−47.8449	+	23.0409i	−1.72758	+	0.831959i
$768$		0			0
$769$	−4.11250	−	18.0180i	−0.148300	−	0.649747i	−0.993357	−	0.115070i	$-0.963291\pi$
$769$	−4.11250	−	18.0180i	−0.148300	−	0.649747i	0.845057	−	0.534676i	$-0.179566\pi$
$770$	−67.3391	−	37.8300i	−2.42673	−	1.36330i
$771$		0			0
$772$	−34.8852	+	16.7999i	−1.25555	+	0.604640i
$773$	4.02906	−	17.6525i	0.144915	−	0.634916i	−0.849337	−	0.527851i	$-0.822998\pi$
$773$	4.02906	−	17.6525i	0.144915	−	0.634916i	0.994252	−	0.107064i	$-0.0341451\pi$
$774$		0			0
$775$	−13.4517	−	58.9357i	−0.483199	−	2.11703i
$776$	0.753624	−	0.945015i	0.0270535	−	0.0339241i
$777$		0			0
$778$	24.2501	+	30.4087i	0.869409	+	1.09020i
$779$	6.58189	−	8.25343i	0.235821	−	0.295710i
$780$		0			0
$781$	−5.35907	+	6.72006i	−0.191762	+	0.240463i
$782$	−0.162481	+	0.711874i	−0.00581029	+	0.0254566i
$783$		0			0
$784$	27.2768	−	9.12128i	0.974171	−	0.325760i
$785$	2.95337			0.105410
$786$		0			0
$787$	−16.2192	+	20.3383i	−0.578154	+	0.724982i	−0.981797	−	0.189935i	$-0.939172\pi$
$787$	−16.2192	+	20.3383i	−0.578154	+	0.724982i	0.403643	+	0.914917i	$0.367744\pi$
$788$	−4.83444	−	2.32815i	−0.172220	−	0.0829368i
$789$		0			0
$790$	38.4413	+	48.2039i	1.36768	+	1.71502i
$791$	20.3659	−	22.4733i	0.724126	−	0.799058i
$792$		0			0
$793$	−7.75850	−	33.9922i	−0.275512	−	1.20710i
$794$	4.59160	+	5.75769i	0.162950	+	0.204333i
$795$		0			0
$796$	−29.3516	+	14.1350i	−1.04034	+	0.501001i
$797$	7.41539	−	32.4889i	0.262667	−	1.15082i	−0.655680	−	0.755039i	$-0.727618\pi$
$797$	7.41539	−	32.4889i	0.262667	−	1.15082i	0.918346	−	0.395778i	$-0.129525\pi$
$798$		0			0
$799$	−2.78383	−	12.1967i	−0.0984847	−	0.431490i
$800$	36.8034	+	46.1500i	1.30120	+	1.63165i
$801$		0			0
$802$	−9.80429			−0.346202
$803$	−40.1747			−1.41773
$804$		0			0
$805$	0.962805	+	0.540887i	0.0339344	+	0.0190638i
$806$	83.1631	+	40.0492i	2.92929	+	1.41067i
$807$		0			0
$808$	0.0174232	+	0.0763362i	0.000612947	+	0.00268550i
$809$	−7.46571	−	32.7094i	−0.262481	−	1.15000i	−0.918551	−	0.395303i	$-0.870640\pi$
$809$	−7.46571	−	32.7094i	−0.262481	−	1.15000i	0.656070	−	0.754700i	$-0.272217\pi$
$810$		0			0
$811$	−26.1289	−	12.5830i	−0.917509	−	0.441849i	−0.0853280	−	0.996353i	$-0.527194\pi$
$811$	−26.1289	−	12.5830i	−0.917509	−	0.441849i	−0.832181	+	0.554504i	$0.812908\pi$
$812$	−16.0647	−	22.9777i	−0.563762	−	0.806358i
$813$		0			0
$814$	−20.0558			−0.702956
$815$	−14.4506			−0.506182
$816$		0			0
$817$	16.7481	+	21.0015i	0.585943	+	0.734750i
$818$	12.1250	+	53.1231i	0.423941	+	1.85741i
$819$		0			0
$820$	−6.18996	+	27.1200i	−0.216163	+	0.947070i
$821$	−45.1446	+	21.7405i	−1.57556	+	0.758749i	−0.998326	−	0.0578322i	$-0.981581\pi$
$821$	−45.1446	+	21.7405i	−1.57556	+	0.758749i	−0.577231	+	0.816581i	$0.695867\pi$
$822$		0			0
$823$	−33.9413	−	42.5611i	−1.18312	−	1.48359i	−0.838550	−	0.544824i	$-0.816596\pi$
$823$	−33.9413	−	42.5611i	−1.18312	−	1.48359i	−0.344569	−	0.938761i	$-0.611975\pi$
$824$	−0.181172	−	0.793765i	−0.00631141	−	0.0276521i
$825$		0			0
$826$	42.5474	+	23.9024i	1.48041	+	0.831671i
$827$	−14.8135	−	18.5755i	−0.515114	−	0.645933i	0.454449	−	0.890773i	$-0.349836\pi$
$827$	−14.8135	−	18.5755i	−0.515114	−	0.645933i	−0.969564	+	0.244840i	$0.921265\pi$
$828$		0			0
$829$	−45.3658	−	21.8470i	−1.57562	−	0.758778i	−0.577287	−	0.816541i	$-0.695889\pi$
$829$	−45.3658	−	21.8470i	−1.57562	−	0.758778i	−0.998330	+	0.0577634i	$0.981603\pi$
$830$	9.90472	−	12.4201i	0.343798	−	0.431109i
$831$		0			0
$832$	−43.1464			−1.49583
$833$	2.13425	+	21.6398i	0.0739475	+	0.749775i
$834$		0			0
$835$	3.67741	−	16.1118i	0.127262	−	0.557571i
$836$	−13.1449	+	16.4831i	−0.454625	+	0.570082i
$837$		0			0
$838$	−1.88556	+	2.36442i	−0.0651356	+	0.0816775i
$839$	8.13662	+	10.2030i	0.280907	+	0.352247i	0.902189	−	0.431341i	$-0.141959\pi$
$839$	8.13662	+	10.2030i	0.280907	+	0.352247i	−0.621282	+	0.783587i	$0.713388\pi$
$840$		0			0
$841$	0.444199	−	0.557008i	0.0153172	−	0.0192072i
$842$	−11.5111	−	50.4336i	−0.396700	−	1.73806i
$843$		0			0
$844$	7.18595	−	31.4837i	0.247351	−	1.08371i
$845$	62.5628	−	30.1287i	2.15223	−	1.03646i
$846$		0			0
$847$	−2.70965	−	16.6472i	−0.0931046	−	0.572004i
$848$	−4.44869	−	19.4910i	−0.152769	−	0.669324i
$849$		0			0
$850$	−41.3338	+	19.9053i	−1.41774	+	0.682746i
$851$	0.286755			0.00982984
$852$		0			0
$853$	11.4771	−	5.52709i	0.392969	−	0.189244i	−0.226956	−	0.973905i	$-0.572877\pi$
$853$	11.4771	−	5.52709i	0.392969	−	0.189244i	0.619925	+	0.784661i	$0.287163\pi$
$854$	−21.5163	+	23.7428i	−0.736273	+	0.812461i
$855$		0			0
$856$	1.16414	+	0.560622i	0.0397896	+	0.0191617i
$857$	−0.199653	−	0.874737i	−0.00682002	−	0.0298804i	0.971403	−	0.237435i	$-0.0763067\pi$
$857$	−0.199653	−	0.874737i	−0.00682002	−	0.0298804i	−0.978223	+	0.207555i	$0.933450\pi$
$858$		0			0
$859$	14.1622	+	6.82017i	0.483209	+	0.232701i	0.659597	−	0.751620i	$-0.270727\pi$
$859$	14.1622	+	6.82017i	0.483209	+	0.232701i	−0.176388	+	0.984321i	$0.556441\pi$
$860$	−63.7738	−	30.7119i	−2.17467	−	1.04727i
$861$		0			0
$862$	−15.1757	+	7.30825i	−0.516888	+	0.248920i
$863$	24.6747			0.839935			0.419968	−	0.907539i	$-0.362041\pi$
$863$	24.6747			0.839935			0.419968	+	0.907539i	$0.362041\pi$
$864$		0			0
$865$	50.6333	−	24.3837i	1.72159	−	0.829072i
$866$	43.2461	+	54.2289i	1.46956	+	1.84277i
$867$		0			0
$868$	−6.71719	−	41.2683i	−0.227996	−	1.40074i
$869$	−8.16546	+	35.7752i	−0.276994	+	1.21359i
$870$		0			0
$871$	−3.27509	+	14.3491i	−0.110972	+	0.486201i
$872$	−0.869435	−	1.09024i	−0.0294428	−	0.0369201i
$873$		0			0
$874$	0.381296	−	0.478130i	0.0128975	−	0.0161730i
$875$	3.65219	+	22.4379i	0.123467	+	0.758539i
$876$		0			0
$877$	8.04339	−	10.0861i	0.271606	−	0.340583i	−0.627257	−	0.778812i	$-0.715823\pi$
$877$	8.04339	−	10.0861i	0.271606	−	0.340583i	0.898863	+	0.438229i	$0.144394\pi$
$878$	−21.0630	−	10.1434i	−0.710840	−	0.342323i
$879$		0			0
$880$	−13.4398	+	58.8836i	−0.453055	+	1.98497i
$881$	−14.7712			−0.497654			−0.248827	−	0.968548i	$-0.580045\pi$
$881$	−14.7712			−0.497654			−0.248827	+	0.968548i	$0.580045\pi$
$882$		0			0
$883$	42.3259			1.42438			0.712190	−	0.701986i	$-0.247703\pi$
$883$	42.3259			1.42438			0.712190	+	0.701986i	$0.247703\pi$
$884$	7.68326	−	33.6626i	0.258416	−	1.13220i
$885$		0			0
$886$	−51.2427	−	24.6772i	−1.72153	−	0.829047i
$887$	−4.24138	+	5.31853i	−0.142412	+	0.178579i	−0.847922	−	0.530121i	$-0.822146\pi$
$887$	−4.24138	+	5.31853i	−0.142412	+	0.178579i	0.705510	+	0.708700i	$0.250718\pi$
$888$		0			0
$889$	13.8039	+	7.75478i	0.462967	+	0.260087i
$890$	42.4850	−	53.2746i	1.42410	−	1.78577i
$891$		0			0
$892$	−17.7520	−	22.2603i	−0.594380	−	0.745329i
$893$	−2.33155	+	10.2152i	−0.0780224	+	0.341838i
$894$		0			0
$895$	15.7133	−	68.8443i	0.525236	−	2.30121i
$896$	−1.34716	−	1.92686i	−0.0450054	−	0.0643719i
$897$		0			0
$898$	−46.4779	−	58.2815i	−1.55099	−	1.94488i
$899$	39.9225	−	19.2257i	1.33149	−	0.641211i
$900$		0			0
$901$	15.1149			0.503552
$902$	−30.2624	+	14.5736i	−1.00763	+	0.485247i
$903$		0			0
$904$	−1.14765	−	0.552681i	−0.0381704	−	0.0183819i
$905$	−17.7773	−	8.56110i	−0.590938	−	0.284581i
$906$		0			0
$907$	−3.11548	−	13.6498i	−0.103448	−	0.453235i	−0.999948	−	0.0101916i	$-0.996756\pi$
$907$	−3.11548	−	13.6498i	−0.103448	−	0.453235i	0.896500	−	0.443044i	$-0.146101\pi$
$908$	−52.2640	−	25.1690i	−1.73444	−	0.835263i
$909$		0			0
$910$	−92.3672	−	51.8903i	−3.06194	−	1.72015i
$911$	22.1853	−	10.6839i	0.735031	−	0.353972i	−0.0286300	−	0.999590i	$-0.509114\pi$
$911$	22.1853	−	10.6839i	0.735031	−	0.353972i	0.763660	+	0.645618i	$0.223400\pi$
$912$		0			0
$913$	9.45483			0.312909
$914$	−29.4857	+	14.1996i	−0.975301	+	0.469680i
$915$		0			0
$916$	11.5293	+	50.5133i	0.380940	+	1.66901i
$917$	5.25573	−	17.7779i	0.173560	−	0.587079i
$918$		0			0
$919$	−40.4481	+	19.4788i	−1.33426	+	0.642546i	−0.958744	−	0.284270i	$-0.908249\pi$
$919$	−40.4481	+	19.4788i	−1.33426	+	0.642546i	−0.375516	+	0.926816i	$0.622535\pi$
$920$	0.0103210	−	0.0452193i	0.000340273	−	0.00149084i
$921$		0			0
$922$	−2.90182	−	12.7137i	−0.0955665	−	0.418704i
$923$	−7.35089	+	9.21772i	−0.241957	+	0.303405i
$924$		0			0
$925$	11.2333	+	14.0861i	0.369347	+	0.463147i
$926$	21.3242	−	26.7397i	0.700757	−	0.878721i
$927$		0			0
$928$	−26.9767	+	33.8278i	−0.885555	+	1.11045i
$929$	−6.89259	+	30.1984i	−0.226139	+	0.990778i	0.726618	+	0.687042i	$0.241091\pi$
$929$	−6.89259	+	30.1984i	−0.226139	+	0.990778i	−0.952756	+	0.303736i	$0.901766\pi$
$930$		0			0
$931$	6.25325	−	17.1048i	0.204942	−	0.560587i
$932$	−26.6134			−0.871750
$933$		0			0
$934$	−12.0696	+	15.1348i	−0.394929	+	0.495226i
$935$	−41.1411	−	19.8125i	−1.34546	−	0.647939i
$936$		0			0
$937$	−28.8759	−	36.2092i	−0.943334	−	1.18290i	−0.982984	−	0.183690i	$-0.941196\pi$
$937$	−28.8759	−	36.2092i	−0.943334	−	1.18290i	0.0396500	−	0.999214i	$-0.487376\pi$
$938$	12.5318	−	5.08916i	0.409178	−	0.166167i
$939$		0			0
$940$	−6.14385	−	26.9180i	−0.200390	−	0.877967i
$941$	−15.6589	−	19.6357i	−0.510466	−	0.640105i	0.458088	−	0.888907i	$-0.348534\pi$
$941$	−15.6589	−	19.6357i	−0.510466	−	0.640105i	−0.968554	+	0.248802i	$0.919963\pi$
$942$		0			0
$943$	0.432687	−	0.208371i	0.0140902	−	0.00678549i
$944$	8.49178	−	37.2049i	0.276384	−	1.21092i
$945$		0			0
$946$	−19.0187	−	83.3262i	−0.618350	−	2.70917i
$947$	−10.7257	−	13.4496i	−0.348537	−	0.437052i	0.576402	−	0.817166i	$-0.304456\pi$
$947$	−10.7257	−	13.4496i	−0.348537	−	0.437052i	−0.924940	+	0.380114i	$0.875885\pi$
$948$		0			0
$949$	−55.1065			−1.78883
$950$	38.4236			1.24663
$951$		0			0
$952$	0.846172	−	0.343630i	0.0274246	−	0.0111371i
$953$	−14.3205	−	6.89638i	−0.463886	−	0.223396i	0.187317	−	0.982300i	$-0.440021\pi$
$953$	−14.3205	−	6.89638i	−0.463886	−	0.223396i	−0.651203	+	0.758904i	$0.725735\pi$
$954$		0			0
$955$	3.68657	+	16.1519i	0.119295	+	0.522664i
$956$	−10.7498	−	47.0980i	−0.347674	−	1.52326i
$957$		0			0
$958$	26.2156	+	12.6248i	0.846989	+	0.407888i
$959$	−3.36410	+	11.3793i	−0.108633	+	0.367458i
$960$		0			0
$961$	35.0811			1.13165
$962$	−27.5100			−0.886959
$963$		0			0
$964$	20.0119	+	25.0941i	0.644539	+	0.808226i
$965$	15.6295	+	68.4773i	0.503131	+	2.20436i
$966$		0			0
$967$	3.24544	−	14.2192i	0.104366	−	0.457258i	−0.895558	−	0.444945i	$-0.853223\pi$
$967$	3.24544	−	14.2192i	0.104366	−	0.457258i	0.999924	−	0.0123134i	$-0.00391958\pi$
$968$	−0.638234	+	0.307357i	−0.0205136	+	0.00987884i
$969$		0			0
$970$	47.4979	+	59.5605i	1.52507	+	1.91237i
$971$	4.12290	+	18.0636i	0.132310	+	0.579688i	0.997001	+	0.0773846i	$0.0246569\pi$
$971$	4.12290	+	18.0636i	0.132310	+	0.579688i	−0.864691	+	0.502304i	$0.832486\pi$
$972$		0			0
$973$	−12.4889	−	0.788415i	−0.400376	−	0.0252754i
$974$	39.1456	+	49.0870i	1.25431	+	1.57285i
$975$		0			0
$976$	22.5745	+	10.8713i	0.722592	+	0.347982i
$977$	−4.87649	+	6.11492i	−0.156013	+	0.195634i	−0.853695	−	0.520774i	$-0.825643\pi$
$977$	−4.87649	+	6.11492i	−0.156013	+	0.195634i	0.697682	+	0.716408i	$0.254215\pi$
$978$		0			0
$979$	40.5553			1.29615
$980$	4.71025	+	47.7586i	0.150463	+	1.52559i
$981$		0			0
$982$	7.19142	−	31.5077i	0.229488	−	1.00545i
$983$	32.6245	−	40.9098i	1.04056	−	1.30482i	0.0894403	−	0.995992i	$-0.471492\pi$
$983$	32.6245	−	40.9098i	1.04056	−	1.30482i	0.951118	−	0.308827i	$-0.0999364\pi$
$984$		0			0
$985$	−6.06888	+	7.61013i	−0.193370	+	0.242479i
$986$	−20.9665	−	26.2912i	−0.667711	−	0.837283i
$987$		0			0
$988$	−18.0305	+	22.6095i	−0.573625	+	0.719304i
$989$	0.271926	+	1.19139i	0.00864674	+	0.0378839i
$990$		0			0
$991$	1.23771	−	5.42278i	0.0393173	−	0.172260i	−0.951457	−	0.307781i	$-0.900414\pi$
$991$	1.23771	−	5.42278i	0.0393173	−	0.172260i	0.990775	+	0.135521i	$0.0432707\pi$
$992$	−58.1352	+	27.9964i	−1.84580	+	0.888888i
$993$		0			0
$994$	10.8132	+	0.682631i	0.342975	+	0.0216517i
$995$	13.1503	+	57.6151i	0.416891	+	1.82652i
$996$		0			0
$997$	21.8538	−	10.5242i	0.692117	−	0.333306i	−0.0545433	−	0.998511i	$-0.517370\pi$
$997$	21.8538	−	10.5242i	0.692117	−	0.333306i	0.746660	+	0.665205i	$0.231656\pi$
$998$	35.8550			1.13497
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.d.64.5		36
3.2	odd	2		147.2.i.b.64.2	✓	36
49.36	even	7	inner	441.2.u.d.379.5		36
147.92	odd	14		7203.2.a.h.1.14		18
147.104	even	14		7203.2.a.g.1.14		18
147.134	odd	14		147.2.i.b.85.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.b.64.2	✓	36	3.2	odd	2
147.2.i.b.85.2	yes	36	147.134	odd	14
441.2.u.d.64.5		36	1.1	even	1	trivial
441.2.u.d.379.5		36	49.36	even	7	inner
7203.2.a.g.1.14		18	147.104	even	14
7203.2.a.h.1.14		18	147.92	odd	14

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.441918 - 1.93617i) q^{2} +(-1.75153 - 0.843490i) q^{4} +(-2.19876 + 2.75716i) q^{5} +(1.51600 + 2.16835i) q^{7} +(0.0692834 - 0.0868787i) q^{8} +O(q^{10})\)	\(q+(0.441918 - 1.93617i) q^{2} +(-1.75153 - 0.843490i) q^{4} +(-2.19876 + 2.75716i) q^{5} +(1.51600 + 2.16835i) q^{7} +(0.0692834 - 0.0868787i) q^{8} +(4.36666 + 5.47561i) q^{10} +(-0.927537 + 4.06381i) q^{11} +(-1.27228 + 5.57421i) q^{13} +(4.86825 - 1.97699i) q^{14} +(-2.56178 - 3.21237i) q^{16} +(2.79877 - 1.34782i) q^{17} -2.60172 q^{19} +(6.17682 - 2.97460i) q^{20} +(7.45833 + 3.59174i) q^{22} +(-0.106638 - 0.0513542i) q^{23} +(-1.65477 - 7.25003i) q^{25} +(10.2304 + 4.92669i) q^{26} +(-0.826321 - 5.07665i) q^{28} +(4.91110 - 2.36506i) q^{29} +8.12903 q^{31} +(-7.15156 + 3.44401i) q^{32} +(-1.37277 - 6.01452i) q^{34} +(-9.31181 - 0.587847i) q^{35} +(-2.18282 + 1.05119i) q^{37} +(-1.14975 + 5.03736i) q^{38} +(0.0872006 + 0.382051i) q^{40} +(-2.52983 + 3.17230i) q^{41} +(-6.43734 - 8.07217i) q^{43} +(5.05239 - 6.33549i) q^{44} +(-0.146556 + 0.183775i) q^{46} +(0.896159 - 3.92633i) q^{47} +(-2.40351 + 6.57443i) q^{49} -14.7686 q^{50} +(6.93022 - 8.69022i) q^{52} +(4.38388 + 2.11117i) q^{53} +(-9.16513 - 11.4927i) q^{55} +(0.293417 + 0.0185232i) q^{56} +(-2.40886 - 10.5539i) q^{58} +(5.79088 + 7.26153i) q^{59} +(-5.49421 + 2.64587i) q^{61} +(3.59237 - 15.7392i) q^{62} +(1.67921 + 7.35708i) q^{64} +(-12.5716 - 15.7642i) q^{65} +2.57419 q^{67} -6.03898 q^{68} +(-5.25323 + 17.7695i) q^{70} +(1.85784 + 0.894690i) q^{71} +(2.14468 + 9.39646i) q^{73} +(1.07066 + 4.69086i) q^{74} +(4.55697 + 2.19452i) q^{76} +(-10.2179 + 4.14949i) q^{77} +8.80338 q^{79} +14.4898 q^{80} +(5.02414 + 6.30007i) q^{82} +(-0.504736 - 2.21139i) q^{83} +(-2.43768 + 10.6802i) q^{85} +(-18.4739 + 8.89655i) q^{86} +(0.288795 + 0.362138i) q^{88} +(-2.16500 - 9.48548i) q^{89} +(-14.0156 + 5.69174i) q^{91} +(0.143462 + 0.179896i) q^{92} +(-7.20601 - 3.47023i) q^{94} +(5.72055 - 7.17334i) q^{95} +10.8774 q^{97} +(11.6671 + 7.55897i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) \) 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8	\( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8} + 10 q^{10} + 7 q^{11} - 12 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} + 6 q^{19} - 25 q^{20} - 21 q^{22} + 20 q^{23} - 2 q^{25} - 6 q^{26} - q^{28} + 22 q^{29} + 16 q^{31} - 26 q^{32} + 6 q^{34} + 9 q^{35} + 32 q^{37} - 17 q^{38} - 21 q^{40} + 5 q^{41} - 34 q^{43} - 2 q^{44} - 32 q^{46} + 7 q^{47} + 20 q^{49} - 236 q^{50} + 20 q^{52} + 32 q^{53} - 17 q^{55} + 39 q^{56} - 53 q^{58} + q^{59} + 14 q^{61} + 60 q^{62} - 21 q^{64} + 39 q^{65} - 22 q^{67} + 110 q^{68} - 40 q^{70} - 36 q^{71} - 11 q^{73} + 46 q^{74} - 101 q^{76} + 17 q^{77} - 14 q^{79} + 112 q^{80} + 2 q^{82} - 12 q^{83} - 44 q^{85} - 184 q^{86} + 204 q^{88} - 12 q^{89} - 16 q^{91} + 105 q^{92} - 5 q^{94} - 18 q^{95} + 172 q^{97} - q^{98}+O(q^{100}) \) 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8 + 10 * q^10 + 7 * q^11 - 12 * q^13 + q^14 - 3 * q^16 + 3 * q^17 + 6 * q^19 - 25 * q^20 - 21 * q^22 + 20 * q^23 - 2 * q^25 - 6 * q^26 - q^28 + 22 * q^29 + 16 * q^31 - 26 * q^32 + 6 * q^34 + 9 * q^35 + 32 * q^37 - 17 * q^38 - 21 * q^40 + 5 * q^41 - 34 * q^43 - 2 * q^44 - 32 * q^46 + 7 * q^47 + 20 * q^49 - 236 * q^50 + 20 * q^52 + 32 * q^53 - 17 * q^55 + 39 * q^56 - 53 * q^58 + q^59 + 14 * q^61 + 60 * q^62 - 21 * q^64 + 39 * q^65 - 22 * q^67 + 110 * q^68 - 40 * q^70 - 36 * q^71 - 11 * q^73 + 46 * q^74 - 101 * q^76 + 17 * q^77 - 14 * q^79 + 112 * q^80 + 2 * q^82 - 12 * q^83 - 44 * q^85 - 184 * q^86 + 204 * q^88 - 12 * q^89 - 16 * q^91 + 105 * q^92 - 5 * q^94 - 18 * q^95 + 172 * q^97 - q^98

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