LMFDB - Embedded newform 297.2.f.d.190.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(82,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("297.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 8 x^{14} - 22 x^{13} + 62 x^{12} - 24 x^{11} + 152 x^{10} - 161 x^{9} + 552 x^{8} + \cdots + 25 $ x^16 - 2x^15 + 8x^14 - 22x^13 + 62x^12 - 24x^11 + 152x^10 - 161x^9 + 552x^8 - 609x^7 + 1150x^6 - 862x^5 + 1346x^4 - 235x^3 + 340x^2 + 150*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.1
Root			$2.13024 + 1.54771i$ of defining polynomial
Character	$\chi$	$=$	297.190
Dual form			297.2.f.d.136.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32122 + 0.959922i) q^{2} +(0.206136 - 0.634423i) q^{4} +(-2.42257 - 1.76010i) q^{5} +(-0.469421 + 1.44473i) q^{7} +(-0.672677 - 2.07029i) q^{8} +O(q^{10})$	\(q+(-1.32122 + 0.959922i) q^{2} +(0.206136 - 0.634423i) q^{4} +(-2.42257 - 1.76010i) q^{5} +(-0.469421 + 1.44473i) q^{7} +(-0.672677 - 2.07029i) q^{8} +4.89031 q^{10} +(3.29968 + 0.334795i) q^{11} +(3.32385 - 2.41492i) q^{13} +(-0.766620 - 2.35941i) q^{14} +(3.95541 + 2.87378i) q^{16} +(2.16991 + 1.57653i) q^{17} +(-2.64733 - 8.14763i) q^{19} +(-1.61603 + 1.17411i) q^{20} +(-4.68098 + 2.72510i) q^{22} +4.20312 q^{23} +(1.22581 + 3.77266i) q^{25} +(-2.07340 + 6.38127i) q^{26} +(0.819805 + 0.595623i) q^{28} +(-0.598754 + 1.84278i) q^{29} +(5.57164 - 4.04803i) q^{31} -3.63091 q^{32} -4.38027 q^{34} +(3.68008 - 2.67373i) q^{35} +(-0.208931 + 0.643023i) q^{37} +(11.3188 + 8.22358i) q^{38} +(-2.01431 + 6.19940i) q^{40} +(-2.04606 - 6.29713i) q^{41} +0.0153422 q^{43} +(0.892586 - 2.02438i) q^{44} +(-5.55325 + 4.03467i) q^{46} +(1.19533 + 3.67886i) q^{47} +(3.79623 + 2.75812i) q^{49} +(-5.24102 - 3.80783i) q^{50} +(-0.846911 - 2.60653i) q^{52} +(-0.0180109 + 0.0130857i) q^{53} +(-7.40445 - 6.61884i) q^{55} +3.30677 q^{56} +(-0.977836 - 3.00947i) q^{58} +(4.17174 - 12.8393i) q^{59} +(-9.51176 - 6.91070i) q^{61} +(-3.47556 + 10.6967i) q^{62} +(-3.11359 + 2.26216i) q^{64} -12.3028 q^{65} -7.15005 q^{67} +(1.44748 - 1.05166i) q^{68} +(-2.29561 + 7.06518i) q^{70} +(-2.70704 - 1.96678i) q^{71} +(-2.56581 + 7.89675i) q^{73} +(-0.341208 - 1.05013i) q^{74} -5.71475 q^{76} +(-2.03263 + 4.60999i) q^{77} +(4.38320 - 3.18458i) q^{79} +(-4.52413 - 13.9239i) q^{80} +(8.74805 + 6.35583i) q^{82} +(-8.82754 - 6.41359i) q^{83} +(-2.48190 - 7.63852i) q^{85} +(-0.0202703 + 0.0147273i) q^{86} +(-1.52650 - 7.05650i) q^{88} +9.84351 q^{89} +(1.92862 + 5.93567i) q^{91} +(0.866417 - 2.66656i) q^{92} +(-5.11072 - 3.71316i) q^{94} +(-7.92732 + 24.3978i) q^{95} +(12.7294 - 9.24845i) q^{97} -7.66324 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} - 4 q^{4} + q^{5} - 2 q^{7}+O(q^{10}) $ 16 * q + 2 * q^2 - 4 * q^4 + q^5 - 2 * q^7	$ 16 q + 2 q^{2} - 4 q^{4} + q^{5} - 2 q^{7} + 6 q^{10} + 13 q^{11} - 2 q^{13} - 22 q^{14} - 24 q^{16} - 2 q^{17} - 2 q^{19} + 15 q^{22} + 14 q^{23} - 19 q^{25} + 21 q^{26} + 15 q^{28} + q^{29} + 14 q^{31} - 48 q^{32} + 10 q^{34} - 18 q^{35} + 9 q^{37} + 11 q^{38} + 33 q^{40} + 25 q^{41} + 14 q^{43} + 14 q^{44} + 4 q^{46} - 28 q^{47} - 4 q^{49} - 63 q^{50} + 10 q^{52} + q^{53} - 40 q^{55} + 96 q^{56} - 20 q^{58} + 41 q^{59} - 5 q^{62} - 92 q^{64} - 60 q^{65} - 48 q^{67} + 25 q^{68} - 31 q^{70} + 3 q^{71} - 13 q^{73} + 29 q^{74} - 58 q^{76} - 2 q^{77} - 83 q^{80} + 41 q^{82} - 14 q^{83} - 10 q^{85} - 56 q^{86} + 86 q^{88} + 82 q^{89} + 14 q^{91} + 74 q^{92} - 2 q^{94} - 56 q^{95} + 12 q^{97} + 26 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 - 4 * q^4 + q^5 - 2 * q^7 + 6 * q^10 + 13 * q^11 - 2 * q^13 - 22 * q^14 - 24 * q^16 - 2 * q^17 - 2 * q^19 + 15 * q^22 + 14 * q^23 - 19 * q^25 + 21 * q^26 + 15 * q^28 + q^29 + 14 * q^31 - 48 * q^32 + 10 * q^34 - 18 * q^35 + 9 * q^37 + 11 * q^38 + 33 * q^40 + 25 * q^41 + 14 * q^43 + 14 * q^44 + 4 * q^46 - 28 * q^47 - 4 * q^49 - 63 * q^50 + 10 * q^52 + q^53 - 40 * q^55 + 96 * q^56 - 20 * q^58 + 41 * q^59 - 5 * q^62 - 92 * q^64 - 60 * q^65 - 48 * q^67 + 25 * q^68 - 31 * q^70 + 3 * q^71 - 13 * q^73 + 29 * q^74 - 58 * q^76 - 2 * q^77 - 83 * q^80 + 41 * q^82 - 14 * q^83 - 10 * q^85 - 56 * q^86 + 86 * q^88 + 82 * q^89 + 14 * q^91 + 74 * q^92 - 2 * q^94 - 56 * q^95 + 12 * q^97 + 26 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.32122	+	0.959922i	−0.934243	+	0.678767i	−0.947028	−	0.321151i	$-0.895930\pi$
$2$	−1.32122	+	0.959922i	−0.934243	+	0.678767i	0.0127848	+	0.999918i	$0.495930\pi$
$3$		0			0
$3$		0			0
$4$	0.206136	−	0.634423i	0.103068	−	0.317211i
$5$	−2.42257	−	1.76010i	−1.08341	−	0.787141i	−0.105133	−	0.994458i	$-0.533527\pi$
$5$	−2.42257	−	1.76010i	−1.08341	−	0.787141i	−0.978274	+	0.207317i	$0.933527\pi$
$6$		0			0
$7$	−0.469421	+	1.44473i	−0.177425	+	0.546057i	−0.999736	−	0.0229812i	$-0.992684\pi$
$7$	−0.469421	+	1.44473i	−0.177425	+	0.546057i	0.822311	+	0.569038i	$0.192684\pi$
$8$	−0.672677	−	2.07029i	−0.237827	−	0.731957i
$9$		0			0
$10$	4.89031			1.54645
$11$	3.29968	+	0.334795i	0.994892	+	0.100944i
$11$	3.29968	+	0.334795i	0.994892	+	0.100944i
$12$		0			0
$13$	3.32385	−	2.41492i	0.921869	−	0.669777i	−0.0221193	−	0.999755i	$-0.507041\pi$
$13$	3.32385	−	2.41492i	0.921869	−	0.669777i	0.943989	+	0.329978i	$0.107041\pi$
$14$	−0.766620	−	2.35941i	−0.204888	−	0.630580i
$15$		0			0
$16$	3.95541	+	2.87378i	0.988853	+	0.718444i
$17$	2.16991	+	1.57653i	0.526280	+	0.382365i	0.818964	−	0.573844i	$-0.194549\pi$
$17$	2.16991	+	1.57653i	0.526280	+	0.382365i	−0.292684	+	0.956209i	$0.594549\pi$
$18$		0			0
$19$	−2.64733	−	8.14763i	−0.607338	−	1.86919i	−0.479840	−	0.877356i	$-0.659305\pi$
$19$	−2.64733	−	8.14763i	−0.607338	−	1.86919i	−0.127498	−	0.991839i	$-0.540695\pi$
$20$	−1.61603	+	1.17411i	−0.361355	+	0.262540i
$21$		0			0
$22$	−4.68098	+	2.72510i	−0.997989	+	0.580994i
$23$	4.20312			0.876412			0.438206	−	0.898875i	$-0.355614\pi$
$23$	4.20312			0.876412			0.438206	+	0.898875i	$0.355614\pi$
$24$		0			0
$25$	1.22581	+	3.77266i	0.245162	+	0.754532i
$26$	−2.07340	+	6.38127i	−0.406627	+	1.25147i
$27$		0			0
$28$	0.819805	+	0.595623i	0.154928	+	0.112562i
$29$	−0.598754	+	1.84278i	−0.111186	+	0.342195i	−0.991132	−	0.132878i	$-0.957578\pi$
$29$	−0.598754	+	1.84278i	−0.111186	+	0.342195i	0.879947	+	0.475073i	$0.157578\pi$
$30$		0			0
$31$	5.57164	−	4.04803i	1.00070	−	0.727048i	0.0384581	−	0.999260i	$-0.487755\pi$
$31$	5.57164	−	4.04803i	1.00070	−	0.727048i	0.962237	+	0.272213i	$0.0877554\pi$
$32$	−3.63091			−0.641860
$33$		0			0
$34$	−4.38027			−0.751210
$35$	3.68008	−	2.67373i	0.622047	−	0.451943i
$36$		0			0
$37$	−0.208931	+	0.643023i	−0.0343480	+	0.105712i	−0.966761	−	0.255683i	$-0.917700\pi$
$37$	−0.208931	+	0.643023i	−0.0343480	+	0.105712i	0.932413	+	0.361396i	$0.117700\pi$
$38$	11.3188	+	8.22358i	1.83615	+	1.33404i
$39$		0			0
$40$	−2.01431	+	6.19940i	−0.318490	+	0.980211i
$41$	−2.04606	−	6.29713i	−0.319541	−	0.983447i	−0.973845	−	0.227215i	$-0.927038\pi$
$41$	−2.04606	−	6.29713i	−0.319541	−	0.983447i	0.654304	−	0.756232i	$-0.272962\pi$
$42$		0			0
$43$	0.0153422			0.00233966			0.00116983	−	0.999999i	$-0.499628\pi$
$43$	0.0153422			0.00233966			0.00116983	+	0.999999i	$0.499628\pi$
$44$	0.892586	−	2.02438i	0.134562	−	0.305187i
$45$		0			0
$46$	−5.55325	+	4.03467i	−0.818782	+	0.594880i
$47$	1.19533	+	3.67886i	0.174357	+	0.536617i	0.999604	−	0.0281562i	$-0.00896359\pi$
$47$	1.19533	+	3.67886i	0.174357	+	0.536617i	−0.825246	+	0.564773i	$0.808964\pi$
$48$		0			0
$49$	3.79623	+	2.75812i	0.542319	+	0.394018i
$50$	−5.24102	−	3.80783i	−0.741193	−	0.538508i
$51$		0			0
$52$	−0.846911	−	2.60653i	−0.117445	−	0.361460i
$53$	−0.0180109	+	0.0130857i	−0.00247399	+	0.00179746i	−0.589022	−	0.808117i	$-0.700487\pi$
$53$	−0.0180109	+	0.0130857i	−0.00247399	+	0.00179746i	0.586548	+	0.809915i	$0.300487\pi$
$54$		0			0
$55$	−7.40445	−	6.61884i	−0.998415	−	0.892484i
$56$	3.30677			0.441886
$57$		0			0
$58$	−0.977836	−	3.00947i	−0.128396	−	0.395163i
$59$	4.17174	−	12.8393i	0.543115	−	1.67153i	−0.182317	−	0.983240i	$-0.558360\pi$
$59$	4.17174	−	12.8393i	0.543115	−	1.67153i	0.725431	−	0.688295i	$-0.241640\pi$
$60$		0			0
$61$	−9.51176	−	6.91070i	−1.21786	−	0.884824i	−0.221935	−	0.975061i	$-0.571237\pi$
$61$	−9.51176	−	6.91070i	−1.21786	−	0.884824i	−0.995920	+	0.0902374i	$0.971237\pi$
$62$	−3.47556	+	10.6967i	−0.441396	+	1.35848i
$63$		0			0
$64$	−3.11359	+	2.26216i	−0.389199	+	0.282770i
$65$	−12.3028			−1.52597
$66$		0			0
$67$	−7.15005			−0.873517			−0.436759	−	0.899579i	$-0.643874\pi$
$67$	−7.15005			−0.873517			−0.436759	+	0.899579i	$0.643874\pi$
$68$	1.44748	−	1.05166i	0.175533	−	0.127532i
$69$		0			0
$70$	−2.29561	+	7.06518i	−0.274378	+	0.844450i
$71$	−2.70704	−	1.96678i	−0.321266	−	0.233414i	0.415449	−	0.909616i	$-0.363624\pi$
$71$	−2.70704	−	1.96678i	−0.321266	−	0.233414i	−0.736716	+	0.676203i	$0.763624\pi$
$72$		0			0
$73$	−2.56581	+	7.89675i	−0.300305	+	0.924245i	0.681082	+	0.732207i	$0.261510\pi$
$73$	−2.56581	+	7.89675i	−0.300305	+	0.924245i	−0.981388	+	0.192038i	$0.938490\pi$
$74$	−0.341208	−	1.05013i	−0.0396647	−	0.122075i
$75$		0			0
$76$	−5.71475			−0.655527
$77$	−2.03263	+	4.60999i	−0.231640	+	0.525357i
$78$		0			0
$79$	4.38320	−	3.18458i	0.493148	−	0.358293i	−0.313246	−	0.949672i	$-0.601416\pi$
$79$	4.38320	−	3.18458i	0.493148	−	0.358293i	0.806394	+	0.591379i	$0.201416\pi$
$80$	−4.52413	−	13.9239i	−0.505814	−	1.55673i
$81$		0			0
$82$	8.74805	+	6.35583i	0.966061	+	0.701884i
$83$	−8.82754	−	6.41359i	−0.968949	−	0.703982i	−0.0137369	−	0.999906i	$-0.504373\pi$
$83$	−8.82754	−	6.41359i	−0.968949	−	0.703982i	−0.955212	+	0.295923i	$0.904373\pi$
$84$		0			0
$85$	−2.48190	−	7.63852i	−0.269200	−	0.828513i
$86$	−0.0202703	+	0.0147273i	−0.00218581	+	0.00158808i
$87$		0			0
$88$	−1.52650	−	7.05650i	−0.162725	−	0.752226i
$89$	9.84351			1.04341			0.521705	−	0.853126i	$-0.325296\pi$
$89$	9.84351			1.04341			0.521705	+	0.853126i	$0.325296\pi$
$90$		0			0
$91$	1.92862	+	5.93567i	0.202174	+	0.622228i
$92$	0.866417	−	2.66656i	0.0903302	−	0.278008i
$93$		0			0
$94$	−5.11072	−	3.71316i	−0.527131	−	0.382983i
$95$	−7.92732	+	24.3978i	−0.813326	+	2.50316i
$96$		0			0
$97$	12.7294	−	9.24845i	1.29248	−	0.939038i	0.292623	−	0.956228i	$-0.405472\pi$
$97$	12.7294	−	9.24845i	1.29248	−	0.939038i	0.999852	+	0.0171897i	$0.00547191\pi$
$98$	−7.66324			−0.774104
$99$		0			0
$100$	2.64614			0.264614
$101$	−3.83423	+	2.78573i	−0.381520	+	0.277190i	−0.761972	−	0.647610i	$-0.775768\pi$
$101$	−3.83423	+	2.78573i	−0.381520	+	0.277190i	0.380452	+	0.924801i	$0.375768\pi$
$102$		0			0
$103$	−5.21588	+	16.0528i	−0.513936	+	1.58173i	0.271273	+	0.962502i	$0.412555\pi$
$103$	−5.21588	+	16.0528i	−0.513936	+	1.58173i	−0.785209	+	0.619230i	$0.787445\pi$
$104$	−7.23545	−	5.25686i	−0.709494	−	0.515477i
$105$		0			0
$106$	0.0112351	−	0.0345782i	0.00109125	−	0.00335853i
$107$	1.65447	+	5.09193i	0.159943	+	0.492255i	0.998628	−	0.0523620i	$-0.0166750\pi$
$107$	1.65447	+	5.09193i	0.159943	+	0.492255i	−0.838685	+	0.544617i	$0.816675\pi$
$108$		0			0
$109$	5.80919			0.556420			0.278210	−	0.960520i	$-0.410259\pi$
$109$	5.80919			0.556420			0.278210	+	0.960520i	$0.410259\pi$
$110$	16.1365	+	1.63725i	1.53855	+	0.156106i
$111$		0			0
$112$	−6.00858	+	4.36549i	−0.567758	+	0.412500i
$113$	−1.96180	−	6.03781i	−0.184551	−	0.567989i	0.815389	−	0.578913i	$-0.196523\pi$
$113$	−1.96180	−	6.03781i	−0.184551	−	0.567989i	−0.999940	+	0.0109235i	$0.996523\pi$
$114$		0			0
$115$	−10.1824	−	7.39792i	−0.949510	−	0.689860i
$116$	1.04567	+	0.759726i	0.0970883	+	0.0705388i
$117$		0			0
$118$	6.81294	+	20.9681i	0.627182	+	1.93027i
$119$	−3.29626	+	2.39487i	−0.302168	+	0.219538i
$120$		0			0
$121$	10.7758	+	2.20943i	0.979620	+	0.200858i
$122$	19.2008			1.73836
$123$		0			0
$124$	−1.41964	−	4.36922i	−0.127488	−	0.392367i
$125$	−0.956054	+	2.94243i	−0.0855120	+	0.263179i
$126$		0			0
$127$	−12.2611	−	8.90818i	−1.08799	−	0.790473i	−0.108933	−	0.994049i	$-0.534744\pi$
$127$	−12.2611	−	8.90818i	−1.08799	−	0.790473i	−0.979059	+	0.203576i	$0.934744\pi$
$128$	4.18627	−	12.8840i	0.370018	−	1.13880i
$129$		0			0
$130$	16.2546	−	11.8097i	1.42563	−	1.03578i
$131$	8.28605			0.723955			0.361978	−	0.932187i	$-0.382102\pi$
$131$	8.28605			0.723955			0.361978	+	0.932187i	$0.382102\pi$
$132$		0			0
$133$	13.0138			1.12844
$134$	9.44678	−	6.86349i	0.816078	−	0.592915i
$135$		0			0
$136$	1.80422	−	5.55283i	0.154711	−	0.476151i
$137$	18.7947	+	13.6551i	1.60574	+	1.16664i	0.875191	+	0.483777i	$0.160736\pi$
$137$	18.7947	+	13.6551i	1.60574	+	1.16664i	0.730549	+	0.682861i	$0.239264\pi$
$138$		0			0
$139$	4.14579	−	12.7594i	0.351642	−	1.08224i	−0.606290	−	0.795244i	$-0.707343\pi$
$139$	4.14579	−	12.7594i	0.351642	−	1.08224i	0.957931	−	0.286998i	$-0.0926573\pi$
$140$	−0.937678	−	2.88588i	−0.0792483	−	0.243901i
$141$		0			0
$142$	5.46454			0.458574
$143$	11.7761	−	6.85565i	0.984771	−	0.573299i
$144$		0			0
$145$	4.69400	−	3.41039i	0.389815	−	0.283217i
$146$	−4.19027	−	12.8963i	−0.346789	−	1.06731i
$147$		0			0
$148$	0.364880	+	0.265101i	0.0299929	+	0.0217911i
$149$	12.6511	+	9.19155i	1.03642	+	0.753001i	0.969583	−	0.244763i	$-0.0787101\pi$
$149$	12.6511	+	9.19155i	1.03642	+	0.753001i	0.0668344	+	0.997764i	$0.478710\pi$
$150$		0			0
$151$	2.04040	+	6.27972i	0.166046	+	0.511036i	0.999112	−	0.0421374i	$-0.0134167\pi$
$151$	2.04040	+	6.27972i	0.166046	+	0.511036i	−0.833066	+	0.553173i	$0.813417\pi$
$152$	−15.0871	+	10.9614i	−1.22373	+	0.889091i
$153$		0			0
$154$	−1.73968	−	8.04198i	−0.140188	−	0.648041i
$155$	−20.6226			−1.65645
$156$		0			0
$157$	6.93527	+	21.3446i	0.553494	+	1.70348i	0.699886	+	0.714254i	$0.253234\pi$
$157$	6.93527	+	21.3446i	0.553494	+	1.70348i	−0.146392	+	0.989227i	$0.546766\pi$
$158$	−2.73422	+	8.41505i	−0.217523	+	0.669466i
$159$		0			0
$160$	8.79614	+	6.39077i	0.695396	+	0.505235i
$161$	−1.97304	+	6.07238i	−0.155497	+	0.478570i
$162$		0			0
$163$	−0.644560	+	0.468300i	−0.0504858	+	0.0366801i	−0.612742	−	0.790283i	$-0.709934\pi$
$163$	−0.644560	+	0.468300i	−0.0504858	+	0.0366801i	0.562256	+	0.826963i	$0.309934\pi$
$164$	−4.41681			−0.344895
$165$		0			0
$166$	17.8197			1.38307
$167$	−11.1160	+	8.07623i	−0.860180	+	0.624957i	−0.927934	−	0.372745i	$-0.878417\pi$
$167$	−11.1160	+	8.07623i	−0.860180	+	0.624957i	0.0677539	+	0.997702i	$0.478417\pi$
$168$		0			0
$169$	1.19892	−	3.68989i	0.0922244	−	0.283838i
$170$	10.6115	+	7.70972i	0.813867	+	0.591309i
$171$		0			0
$172$	0.00316258	−	0.00973341i	0.000241144	−	0.000742165i
$173$	−3.34543	−	10.2962i	−0.254349	−	0.782805i	−0.993957	−	0.109768i	$-0.964989\pi$
$173$	−3.34543	−	10.2962i	−0.254349	−	0.782805i	0.739609	−	0.673037i	$-0.235011\pi$
$174$		0			0
$175$	−6.02590			−0.455515
$176$	12.0895	+	10.8068i	0.911279	+	0.814593i
$177$		0			0
$178$	−13.0054	+	9.44900i	−0.974799	+	0.708233i
$179$	−3.32099	−	10.2210i	−0.248223	−	0.763951i	−0.995090	−	0.0989776i	$-0.968443\pi$
$179$	−3.32099	−	10.2210i	−0.248223	−	0.763951i	0.746867	−	0.664974i	$-0.231557\pi$
$180$		0			0
$181$	6.26489	+	4.55171i	0.465665	+	0.338326i	0.795750	−	0.605626i	$-0.207077\pi$
$181$	6.26489	+	4.55171i	0.465665	+	0.338326i	−0.330084	+	0.943951i	$0.607077\pi$
$182$	−8.24591	−	5.99101i	−0.611228	−	0.444083i
$183$		0			0
$184$	−2.82734	−	8.70167i	−0.208435	−	0.641496i
$185$	1.63793	−	1.19003i	0.120423	−	0.0874927i
$186$		0			0
$187$	6.63220	+	5.92853i	0.484994	+	0.433537i
$188$	2.58035			0.188192
$189$		0			0
$190$	−12.9462	−	39.8444i	−0.939219	−	2.89062i
$191$	−1.73647	+	5.34432i	−0.125647	+	0.386701i	−0.994018	−	0.109213i	$-0.965167\pi$
$191$	−1.73647	+	5.34432i	−0.125647	+	0.386701i	0.868371	+	0.495914i	$0.165167\pi$
$192$		0			0
$193$	6.03292	+	4.38318i	0.434259	+	0.315508i	0.783350	−	0.621581i	$-0.213509\pi$
$193$	6.03292	+	4.38318i	0.434259	+	0.315508i	−0.349090	+	0.937089i	$0.613509\pi$
$194$	−7.94054	+	24.4385i	−0.570098	+	1.75458i
$195$		0			0
$196$	2.53236	−	1.83986i	0.180883	−	0.131419i
$197$	−13.1566			−0.937366			−0.468683	−	0.883366i	$-0.655271\pi$
$197$	−13.1566			−0.937366			−0.468683	+	0.883366i	$0.655271\pi$
$198$		0			0
$199$	−15.9297			−1.12922			−0.564612	−	0.825357i	$-0.690974\pi$
$199$	−15.9297			−1.12922			−0.564612	+	0.825357i	$0.690974\pi$
$200$	6.98591	−	5.07556i	0.493979	−	0.358896i
$201$		0			0
$202$	2.39177	−	7.36111i	0.168284	−	0.517926i
$203$	−2.38125	−	1.73008i	−0.167131	−	0.121428i
$204$		0			0
$205$	−6.12686	+	18.8565i	−0.427918	+	1.31700i
$206$	−8.51815	−	26.2162i	−0.593487	−	1.82657i
$207$		0			0
$208$	20.0871			1.39279
$209$	−6.00755	−	27.7709i	−0.415551	−	1.92095i
$210$		0			0
$211$	3.96643	−	2.88178i	0.273061	−	0.198390i	−0.442824	−	0.896608i	$-0.646023\pi$
$211$	3.96643	−	2.88178i	0.273061	−	0.198390i	0.715885	+	0.698218i	$0.246023\pi$
$212$	0.00458916	+	0.0141240i	0.000315185	+	0.000970038i
$213$		0			0
$214$	−7.07377	−	5.13939i	−0.483553	−	0.351322i
$215$	−0.0371675	−	0.0270037i	−0.00253480	−	0.00184164i
$216$		0			0
$217$	3.23287	+	9.94974i	0.219461	+	0.675432i
$218$	−7.67522	+	5.57637i	−0.519831	+	0.377679i
$219$		0			0
$220$	−5.72547	+	3.33316i	−0.386011	+	0.224722i
$221$	11.0196			0.741261
$222$		0			0
$223$	4.35613	+	13.4068i	0.291708	+	0.897784i	0.984307	+	0.176462i	$0.0564653\pi$
$223$	4.35613	+	13.4068i	0.291708	+	0.897784i	−0.692600	+	0.721322i	$0.743535\pi$
$224$	1.70443	−	5.24569i	0.113882	−	0.350492i
$225$		0			0
$226$	8.38780	+	6.09409i	0.557948	+	0.405373i
$227$	−1.64737	+	5.07007i	−0.109340	+	0.336513i	−0.990724	−	0.135886i	$-0.956612\pi$
$227$	−1.64737	+	5.07007i	−0.109340	+	0.336513i	0.881385	+	0.472399i	$0.156612\pi$
$228$		0			0
$229$	−14.2264	+	10.3361i	−0.940109	+	0.683029i	−0.948447	−	0.316936i	$-0.897346\pi$
$229$	−14.2264	+	10.3361i	−0.940109	+	0.683029i	0.00833756	+	0.999965i	$0.497346\pi$
$230$	20.5546			1.35533
$231$		0			0
$232$	4.21784			0.276915
$233$	−3.77769	+	2.74465i	−0.247484	+	0.179808i	−0.704611	−	0.709594i	$-0.748879\pi$
$233$	−3.77769	+	2.74465i	−0.247484	+	0.179808i	0.457127	+	0.889402i	$0.348879\pi$
$234$		0			0
$235$	3.57939	−	11.0162i	0.233493	−	0.718619i
$236$	−7.28559	−	5.29329i	−0.474252	−	0.344564i
$237$		0			0
$238$	2.05619	−	6.32831i	0.133283	−	0.410203i
$239$	−3.91997	−	12.0644i	−0.253562	−	0.780384i	−0.994110	−	0.108380i	$-0.965434\pi$
$239$	−3.91997	−	12.0644i	−0.253562	−	0.780384i	0.740548	−	0.672004i	$-0.234566\pi$
$240$		0			0
$241$	−19.3920			−1.24915			−0.624573	−	0.780966i	$-0.714727\pi$
$241$	−19.3920			−1.24915			−0.624573	+	0.780966i	$0.714727\pi$
$242$	−16.3581	+	7.42481i	−1.05154	+	0.477285i
$243$		0			0
$244$	−6.34502	+	4.60993i	−0.406198	+	0.295120i
$245$	−4.34206	−	13.3635i	−0.277404	−	0.853763i
$246$		0			0
$247$	−28.4752	−	20.6884i	−1.81183	−	1.31637i
$248$	−12.1285	−	8.81187i	−0.770160	−	0.559554i
$249$		0			0
$250$	−1.56135	−	4.80533i	−0.0987483	−	0.303916i
$251$	10.7133	−	7.78364i	0.676215	−	0.491299i	−0.195885	−	0.980627i	$-0.562758\pi$
$251$	10.7133	−	7.78364i	0.676215	−	0.491299i	0.872100	+	0.489328i	$0.162758\pi$
$252$		0			0
$253$	13.8690	+	1.40718i	0.871935	+	0.0884689i
$254$	24.7507			1.55300
$255$		0			0
$256$	4.45810	+	13.7206i	0.278631	+	0.857538i
$257$	4.17508	−	12.8496i	0.260435	−	0.801535i	−0.732275	−	0.681009i	$-0.761542\pi$
$257$	4.17508	−	12.8496i	0.260435	−	0.801535i	0.992710	−	0.120527i	$-0.0384584\pi$
$258$		0			0
$259$	−0.830918	−	0.603697i	−0.0516307	−	0.0375119i
$260$	−2.53604	+	7.80514i	−0.157279	+	0.484054i
$261$		0			0
$262$	−10.9477	+	7.95396i	−0.676350	+	0.491397i
$263$	−20.4271			−1.25959			−0.629796	−	0.776761i	$-0.716861\pi$
$263$	−20.4271			−1.25959			−0.629796	+	0.776761i	$0.716861\pi$
$264$		0			0
$265$	0.0666649			0.00409519
$266$	−17.1941	+	12.4923i	−1.05424	+	0.765950i
$267$		0			0
$268$	−1.47388	+	4.53615i	−0.0900318	+	0.277090i
$269$	3.53722	+	2.56994i	0.215668	+	0.156692i	0.690375	−	0.723452i	$-0.257446\pi$
$269$	3.53722	+	2.56994i	0.215668	+	0.156692i	−0.474706	+	0.880144i	$0.657446\pi$
$270$		0			0
$271$	−0.888544	+	2.73466i	−0.0539752	+	0.166119i	−0.974410	−	0.224777i	$-0.927835\pi$
$271$	−0.888544	+	2.73466i	−0.0539752	+	0.166119i	0.920435	+	0.390896i	$0.127835\pi$
$272$	4.05229	+	12.4717i	0.245706	+	0.756205i
$273$		0			0
$274$	−37.9398			−2.29203
$275$	2.78172	+	12.8590i	0.167744	+	0.775425i
$276$		0			0
$277$	4.19065	−	3.04469i	0.251792	−	0.182937i	−0.454729	−	0.890630i	$-0.650264\pi$
$277$	4.19065	−	3.04469i	0.251792	−	0.182937i	0.706521	+	0.707693i	$0.250264\pi$
$278$	6.77057	+	20.8377i	0.406072	+	1.24976i
$279$		0			0
$280$	−8.01090	−	5.82026i	−0.478743	−	0.347827i
$281$	9.39280	+	6.82427i	0.560328	+	0.407102i	0.831579	−	0.555407i	$-0.187437\pi$
$281$	9.39280	+	6.82427i	0.560328	+	0.407102i	−0.271251	+	0.962509i	$0.587437\pi$
$282$		0			0
$283$	−2.31288	−	7.11831i	−0.137486	−	0.423139i	0.858482	−	0.512843i	$-0.171408\pi$
$283$	−2.31288	−	7.11831i	−0.137486	−	0.423139i	−0.995968	+	0.0897040i	$0.971408\pi$
$284$	−1.80579	+	1.31198i	−0.107154	+	0.0778517i
$285$		0			0
$286$	−8.97798	+	20.3620i	−0.530879	+	1.20403i
$287$	10.0581			0.593712
$288$		0			0
$289$	−3.03024	−	9.32611i	−0.178249	−	0.548594i
$290$	−2.92809	+	9.01174i	−0.171944	+	0.529188i
$291$		0			0
$292$	4.48097	+	3.25562i	0.262229	+	0.190520i
$293$	0.838542	−	2.58077i	0.0489881	−	0.150770i	−0.923570	−	0.383430i	$-0.874743\pi$
$293$	0.838542	−	2.58077i	0.0489881	−	0.150770i	0.972558	+	0.232660i	$0.0747428\pi$
$294$		0			0
$295$	−32.7048	+	23.7614i	−1.90415	+	1.38344i
$296$	1.47178			0.0855457
$297$		0			0
$298$	−25.5380			−1.47938
$299$	13.9705	−	10.1502i	0.807937	−	0.587001i
$300$		0			0
$301$	−0.00720193	+	0.0221653i	−0.000415112	+	0.00127758i
$302$	−8.72386	−	6.33825i	−0.502002	−	0.364726i
$303$		0			0
$304$	12.9432	−	39.8351i	0.742343	−	2.28470i
$305$	10.8794	+	33.4833i	0.622952	+	1.91725i
$306$		0			0
$307$	26.7702			1.52785			0.763927	−	0.645303i	$-0.223269\pi$
$307$	26.7702			1.52785			0.763927	+	0.645303i	$0.223269\pi$
$308$	2.50568	+	2.23983i	0.142775	+	0.127626i
$309$		0			0
$310$	27.2470	−	19.7961i	1.54753	−	1.12434i
$311$	4.22812	+	13.0128i	0.239755	+	0.737890i	0.996455	+	0.0841276i	$0.0268103\pi$
$311$	4.22812	+	13.0128i	0.239755	+	0.737890i	−0.756700	+	0.653762i	$0.773190\pi$
$312$		0			0
$313$	16.8780	+	12.2626i	0.953999	+	0.693121i	0.951749	−	0.306877i	$-0.0992839\pi$
$313$	16.8780	+	12.2626i	0.953999	+	0.693121i	0.00224964	+	0.999997i	$0.499284\pi$
$314$	−29.6521	−	21.5435i	−1.67337	−	1.21577i
$315$		0			0
$316$	−1.11683	−	3.43725i	−0.0628267	−	0.193361i
$317$	−0.322640	+	0.234412i	−0.0181213	+	0.0131659i	−0.596809	−	0.802383i	$-0.703565\pi$
$317$	−0.322640	+	0.234412i	−0.0181213	+	0.0131659i	0.578688	+	0.815549i	$0.303565\pi$
$318$		0			0
$319$	−2.59265	+	5.88012i	−0.145161	+	0.329223i
$320$	11.5245			0.644241
$321$		0			0
$322$	−3.22220	−	9.91690i	−0.179566	−	0.552647i
$323$	7.10054	−	21.8532i	0.395084	−	1.21594i
$324$		0			0
$325$	13.1851	+	9.57951i	0.731376	+	0.531376i
$326$	0.402074	−	1.23746i	0.0222688	−	0.0685363i
$327$		0			0
$328$	−11.6605	+	8.47187i	−0.643845	+	0.467781i
$329$	−5.87608			−0.323959
$330$		0			0
$331$	−20.0958			−1.10456			−0.552282	−	0.833658i	$-0.686243\pi$
$331$	−20.0958			−1.10456			−0.552282	+	0.833658i	$0.686243\pi$
$332$	−5.88860	+	4.27832i	−0.323179	+	0.234803i
$333$		0			0
$334$	6.93409	−	21.3409i	0.379417	−	1.16772i
$335$	17.3215	+	12.5848i	0.946375	+	0.687581i
$336$		0			0
$337$	−0.0818447	+	0.251892i	−0.00445836	+	0.0137214i	−0.953261	−	0.302148i	$-0.902296\pi$
$337$	−0.0818447	+	0.251892i	−0.00445836	+	0.0137214i	0.948803	+	0.315870i	$0.102296\pi$
$338$	1.95797	+	6.02602i	0.106500	+	0.327772i
$339$		0			0
$340$	−5.35766			−0.290560
$341$	19.7399	−	11.4919i	1.06898	−	0.622319i
$342$		0			0
$343$	−14.3695	+	10.4401i	−0.775880	+	0.563710i
$344$	−0.0103203	−	0.0317627i	−0.000556434	−	0.00171253i
$345$		0			0
$346$	14.3036	+	10.3922i	0.768966	+	0.558686i
$347$	19.1915	+	13.9434i	1.03025	+	0.748522i	0.968359	−	0.249561i	$-0.0802864\pi$
$347$	19.1915	+	13.9434i	1.03025	+	0.748522i	0.0618927	+	0.998083i	$0.480286\pi$
$348$		0			0
$349$	−0.820677	−	2.52578i	−0.0439298	−	0.135202i	0.926686	−	0.375836i	$-0.122645\pi$
$349$	−0.820677	−	2.52578i	−0.0439298	−	0.135202i	−0.970616	+	0.240634i	$0.922645\pi$
$350$	7.96153	−	5.78439i	0.425562	−	0.309189i
$351$		0			0
$352$	−11.9809	−	1.21561i	−0.638582	−	0.0647922i
$353$	−12.3315			−0.656341			−0.328171	−	0.944618i	$-0.606432\pi$
$353$	−12.3315			−0.656341			−0.328171	+	0.944618i	$0.606432\pi$
$354$		0			0
$355$	3.09626	+	9.52932i	0.164333	+	0.505764i
$356$	2.02911	−	6.24494i	0.107542	−	0.330981i
$357$		0			0
$358$	14.1991	+	10.3162i	0.750446	+	0.545231i
$359$	8.04885	−	24.7718i	0.424802	−	1.30741i	−0.478382	−	0.878152i	$-0.658776\pi$
$359$	8.04885	−	24.7718i	0.424802	−	1.30741i	0.903184	−	0.429254i	$-0.141224\pi$
$360$		0			0
$361$	−44.0042	+	31.9709i	−2.31601	+	1.68268i
$362$	−12.6466			−0.664689
$363$		0			0
$364$	4.16328			0.218215
$365$	20.1149	−	14.6144i	1.05286	−	0.764951i
$366$		0			0
$367$	5.11201	−	15.7331i	0.266845	−	0.821263i	−0.724418	−	0.689361i	$-0.757891\pi$
$367$	5.11201	−	15.7331i	0.266845	−	0.821263i	0.991263	−	0.131902i	$-0.0421085\pi$
$368$	16.6251	+	12.0788i	0.866642	+	0.629653i
$369$		0			0
$370$	−1.02174	+	3.14458i	−0.0531175	+	0.163479i
$371$	−0.0104506	−	0.0321636i	−0.000542568	−	0.00166985i
$372$		0			0
$373$	4.77235			0.247103			0.123551	−	0.992338i	$-0.460572\pi$
$373$	4.77235			0.247103			0.123551	+	0.992338i	$0.460572\pi$
$374$	−14.4535	−	1.46649i	−0.747373	−	0.0758305i
$375$		0			0
$376$	6.81223	−	4.94937i	0.351314	−	0.255244i
$377$	2.45998	+	7.57105i	0.126696	+	0.389929i
$378$		0			0
$379$	2.55461	+	1.85603i	0.131221	+	0.0953379i	0.651460	−	0.758683i	$-0.274157\pi$
$379$	2.55461	+	1.85603i	0.131221	+	0.0953379i	−0.520238	+	0.854021i	$0.674157\pi$
$380$	13.8444	+	10.0585i	0.710202	+	0.515992i
$381$		0			0
$382$	−2.83587	−	8.72790i	−0.145096	−	0.446558i
$383$	−3.78557	+	2.75038i	−0.193434	+	0.140538i	−0.680287	−	0.732946i	$-0.738145\pi$
$383$	−3.78557	+	2.75038i	−0.193434	+	0.140538i	0.486853	+	0.873484i	$0.338145\pi$
$384$		0			0
$385$	13.0382	−	7.59040i	0.664490	−	0.386843i
$386$	−12.1783			−0.619860
$387$		0			0
$388$	−3.24343	−	9.98226i	−0.164660	−	0.506773i
$389$	−8.27312	+	25.4620i	−0.419464	+	1.29098i	0.488733	+	0.872433i	$0.337459\pi$
$389$	−8.27312	+	25.4620i	−0.419464	+	1.29098i	−0.908197	+	0.418543i	$0.862541\pi$
$390$		0			0
$391$	9.12039	+	6.62635i	0.461238	+	0.335109i
$392$	3.15647	−	9.71461i	0.159426	−	0.490662i
$393$		0			0
$394$	17.3827	−	12.6293i	0.875728	−	0.636253i
$395$	−16.2238			−0.816307
$396$		0			0
$397$	37.3140			1.87273			0.936367	−	0.351022i	$-0.114166\pi$
$397$	37.3140			1.87273			0.936367	+	0.351022i	$0.114166\pi$
$398$	21.0466	−	15.2912i	1.05497	−	0.766480i
$399$		0			0
$400$	−5.99318	+	18.4451i	−0.299659	+	0.922256i
$401$	−26.1661	−	19.0108i	−1.30667	−	0.949352i	−0.306674	−	0.951815i	$-0.599216\pi$
$401$	−26.1661	−	19.0108i	−1.30667	−	0.949352i	−0.999997	+	0.00246252i	$0.999216\pi$
$402$		0			0
$403$	8.74361	−	26.9101i	0.435550	−	1.34049i
$404$	0.976955	+	3.00676i	0.0486053	+	0.149592i
$405$		0			0
$406$	4.80689			0.238562
$407$	−0.904686	+	2.05182i	−0.0448436	+	0.101705i
$408$		0			0
$409$	19.2274	−	13.9695i	0.950734	−	0.690749i	−0.000246505	−	1.00000i	$-0.500078\pi$
$409$	19.2274	−	13.9695i	0.950734	−	0.690749i	0.950980	+	0.309251i	$0.100078\pi$
$410$	−10.0059	−	30.7949i	−0.494155	−	1.52085i
$411$		0			0
$412$	9.10910	+	6.61815i	0.448773	+	0.326053i
$413$	16.5910	+	12.0541i	0.816391	+	0.593143i
$414$		0			0
$415$	10.0968	+	31.0747i	0.495632	+	1.52540i
$416$	−12.0686	+	8.76835i	−0.591711	+	0.429904i
$417$		0			0
$418$	34.5952	+	30.9247i	1.69211	+	1.51258i
$419$	−38.0549			−1.85910			−0.929552	−	0.368690i	$-0.879806\pi$
$419$	−38.0549			−1.85910			−0.929552	+	0.368690i	$0.879806\pi$
$420$		0			0
$421$	−6.25068	−	19.2376i	−0.304639	−	0.937584i	−0.979812	−	0.199923i	$-0.935931\pi$
$421$	−6.25068	−	19.2376i	−0.304639	−	0.937584i	0.675172	−	0.737660i	$-0.264069\pi$
$422$	−2.47424	+	7.61493i	−0.120444	+	0.370689i
$423$		0			0
$424$	0.0392067	+	0.0284853i	0.00190404	+	0.00138337i
$425$	−3.28781	+	10.1189i	−0.159482	+	0.490836i
$426$		0			0
$427$	14.4491	−	10.4979i	0.699242	−	0.508029i
$428$	3.57148			0.172634
$429$		0			0
$430$	0.0750278			0.00361816
$431$	−20.9744	+	15.2388i	−1.01030	+	0.734026i	−0.964272	−	0.264914i	$-0.914656\pi$
$431$	−20.9744	+	15.2388i	−1.01030	+	0.734026i	−0.0460278	+	0.998940i	$0.514656\pi$
$432$		0			0
$433$	2.65390	−	8.16787i	0.127538	−	0.392523i	−0.866817	−	0.498627i	$-0.833838\pi$
$433$	2.65390	−	8.16787i	0.127538	−	0.392523i	0.994355	+	0.106104i	$0.0338377\pi$
$434$	−13.8223	−	10.0425i	−0.663492	−	0.482055i
$435$		0			0
$436$	1.19749	−	3.68548i	0.0573492	−	0.176503i
$437$	−11.1270	−	34.2455i	−0.532278	−	1.63818i
$438$		0			0
$439$	−4.25196			−0.202935			−0.101468	−	0.994839i	$-0.532354\pi$
$439$	−4.25196			−0.202935			−0.101468	+	0.994839i	$0.532354\pi$
$440$	−8.72210	+	19.7817i	−0.415810	+	0.943054i
$441$		0			0
$442$	−14.5594	+	10.5780i	−0.692518	+	0.503144i
$443$	4.52493	+	13.9263i	0.214986	+	0.661659i	0.999155	+	0.0411108i	$0.0130897\pi$
$443$	4.52493	+	13.9263i	0.214986	+	0.661659i	−0.784169	+	0.620548i	$0.786910\pi$
$444$		0			0
$445$	−23.8466	−	17.3256i	−1.13044	−	0.821311i
$446$	−18.6249	−	13.5318i	−0.881913	−	0.640747i
$447$		0			0
$448$	−1.80662	−	5.56021i	−0.0853548	−	0.262695i
$449$	−13.9856	+	10.1612i	−0.660023	+	0.479535i	−0.866671	−	0.498881i	$-0.833745\pi$
$449$	−13.9856	+	10.1612i	−0.660023	+	0.479535i	0.206648	+	0.978415i	$0.433745\pi$
$450$		0			0
$451$	−4.64311	−	21.4635i	−0.218636	−	1.01068i
$452$	−4.23492			−0.199194
$453$		0			0
$454$	−2.69034	−	8.28003i	−0.126264	−	0.388601i
$455$	5.77517	−	17.7742i	0.270744	−	0.833265i
$456$		0			0
$457$	13.2767	+	9.64607i	0.621057	+	0.451224i	0.853290	−	0.521436i	$-0.174603\pi$
$457$	13.2767	+	9.64607i	0.621057	+	0.451224i	−0.232234	+	0.972660i	$0.574603\pi$
$458$	8.87438	−	27.3125i	0.414673	−	1.27623i
$459$		0			0
$460$	−6.79236	+	4.93494i	−0.316696	+	0.230093i
$461$	19.4785			0.907206			0.453603	−	0.891204i	$-0.350138\pi$
$461$	19.4785			0.907206			0.453603	+	0.891204i	$0.350138\pi$
$462$		0			0
$463$	−21.4251			−0.995711			−0.497855	−	0.867260i	$-0.665879\pi$
$463$	−21.4251			−0.995711			−0.497855	+	0.867260i	$0.665879\pi$
$464$	−7.66404	+	5.56825i	−0.355794	+	0.258500i
$465$		0			0
$466$	2.35650	−	7.25257i	0.109163	−	0.335969i
$467$	−11.7496	−	8.53662i	−0.543709	−	0.395028i	0.281752	−	0.959487i	$-0.409085\pi$
$467$	−11.7496	−	8.53662i	−0.543709	−	0.395028i	−0.825461	+	0.564460i	$0.809085\pi$
$468$		0			0
$469$	3.35638	−	10.3299i	0.154983	−	0.476990i
$470$	5.84556	+	17.9908i	0.269635	+	0.829852i
$471$		0			0
$472$	−29.3873			−1.35266
$473$	0.0506242	+	0.00513647i	0.00232771	+	0.000236175i
$474$		0			0
$475$	27.4931	−	19.9749i	1.26147	−	0.916512i
$476$	0.839883	+	2.58489i	0.0384960	+	0.118478i
$477$		0			0
$478$	16.7601	+	12.1769i	0.766588	+	0.556959i
$479$	7.79497	+	5.66338i	0.356161	+	0.258766i	0.751449	−	0.659791i	$-0.229355\pi$
$479$	7.79497	+	5.66338i	0.356161	+	0.258766i	−0.395288	+	0.918557i	$0.629355\pi$
$480$		0			0
$481$	0.858392	+	2.64186i	0.0391393	+	0.120458i
$482$	25.6210	−	18.6148i	1.16701	−	0.847880i
$483$		0			0
$484$	3.62300	−	6.38098i	0.164682	−	0.290045i
$485$	−47.1161			−2.13943
$486$		0			0
$487$	3.73528	+	11.4960i	0.169262	+	0.520935i	0.999325	−	0.0367349i	$-0.0116957\pi$
$487$	3.73528	+	11.4960i	0.169262	+	0.520935i	−0.830063	+	0.557669i	$0.811696\pi$
$488$	−7.90878	+	24.3407i	−0.358014	+	1.10185i
$489$		0			0
$490$	18.5647	+	13.4881i	0.838669	+	0.609329i
$491$	−1.19151	+	3.66710i	−0.0537722	+	0.165494i	−0.974336	−	0.225098i	$-0.927730\pi$
$491$	−1.19151	+	3.66710i	−0.0537722	+	0.165494i	0.920564	+	0.390592i	$0.127730\pi$
$492$		0			0
$493$	−4.20443	+	3.05470i	−0.189358	+	0.137577i
$494$	57.4812			2.58620
$495$		0			0
$496$	33.6712			1.51188
$497$	4.11220	−	2.98769i	0.184458	−	0.134016i
$498$		0			0
$499$	3.31149	−	10.1917i	0.148243	−	0.456245i	−0.849171	−	0.528118i	$-0.822898\pi$
$499$	3.31149	−	10.1917i	0.148243	−	0.456245i	0.997414	+	0.0718736i	$0.0228978\pi$
$500$	1.66967	+	1.21308i	0.0746698	+	0.0542508i
$501$		0			0
$502$	−6.68288	+	20.5678i	−0.298271	+	0.917985i
$503$	−9.79318	−	30.1403i	−0.436657	−	1.34389i	−0.891380	−	0.453258i	$-0.850262\pi$
$503$	−9.79318	−	30.1403i	−0.436657	−	1.34389i	0.454723	−	0.890633i	$-0.349738\pi$
$504$		0			0
$505$	14.1918			0.631529
$506$	−19.6747	+	11.4539i	−0.874649	+	0.509190i
$507$		0			0
$508$	−8.17900	+	5.94239i	−0.362884	+	0.263651i
$509$	6.74877	+	20.7706i	0.299134	+	0.920639i	0.981801	+	0.189910i	$0.0608197\pi$
$509$	6.74877	+	20.7706i	0.299134	+	0.920639i	−0.682668	+	0.730729i	$0.739180\pi$
$510$		0			0
$511$	−10.2042	−	7.41381i	−0.451409	−	0.327967i
$512$	2.85876	+	2.07701i	0.126340	+	0.0917917i
$513$		0			0
$514$	6.81840	+	20.9849i	0.300747	+	0.925603i
$515$	40.8905	−	29.7087i	1.80185	−	1.30912i
$516$		0			0
$517$	2.71256	+	12.5393i	0.119298	+	0.551477i
$518$	1.67733			0.0736975
$519$		0			0
$520$	8.27578	+	25.4702i	0.362917	+	1.11694i
$521$	−2.28065	+	7.01911i	−0.0999169	+	0.307513i	−0.988504	−	0.151196i	$-0.951688\pi$
$521$	−2.28065	+	7.01911i	−0.0999169	+	0.307513i	0.888587	+	0.458708i	$0.151688\pi$
$522$		0			0
$523$	−1.13512	−	0.824713i	−0.0496353	−	0.0360622i	0.562691	−	0.826667i	$-0.309766\pi$
$523$	−1.13512	−	0.824713i	−0.0496353	−	0.0360622i	−0.612326	+	0.790605i	$0.709766\pi$
$524$	1.70806	−	5.25686i	0.0746168	−	0.229647i
$525$		0			0
$526$	26.9887	−	19.6085i	1.17677	−	0.854970i
$527$	18.4718			0.804643
$528$		0			0
$529$	−5.33376			−0.231902
$530$	−0.0880789	+	0.0639931i	−0.00382590	+	0.00277968i
$531$		0			0
$532$	2.68263	−	8.25627i	0.116307	−	0.357955i
$533$	−22.0078	−	15.9896i	−0.953265	−	0.692588i
$534$		0			0
$535$	4.95424	−	15.2476i	0.214191	−	0.659211i
$536$	4.80967	+	14.8027i	0.207746	+	0.639377i
$537$		0			0
$538$	−7.14039			−0.307844
$539$	11.6030	+	10.3719i	0.499775	+	0.446749i
$540$		0			0
$541$	−8.66968	+	6.29889i	−0.372739	+	0.270810i	−0.758346	−	0.651853i	$-0.773992\pi$
$541$	−8.66968	+	6.29889i	−0.372739	+	0.270810i	0.385607	+	0.922663i	$0.373992\pi$
$542$	−1.45110	−	4.46602i	−0.0623299	−	0.191832i
$543$		0			0
$544$	−7.87874	−	5.72424i	−0.337798	−	0.245425i
$545$	−14.0732	−	10.2248i	−0.602829	−	0.437981i
$546$		0			0
$547$	−2.20975	−	6.80090i	−0.0944819	−	0.290785i	0.892636	−	0.450777i	$-0.148853\pi$
$547$	−2.20975	−	6.80090i	−0.0944819	−	0.290785i	−0.987118	+	0.159992i	$0.948853\pi$
$548$	12.5374	−	9.10896i	0.535571	−	0.389115i
$549$		0			0
$550$	−16.0189	−	14.3193i	−0.683047	−	0.610577i
$551$	16.5994			0.707156
$552$		0			0
$553$	2.54329	+	7.82744i	0.108152	+	0.332857i
$554$	−2.61411	+	8.04540i	−0.111063	+	0.341816i
$555$		0			0
$556$	−7.24028	−	5.26037i	−0.307056	−	0.223089i
$557$	−5.95114	+	18.3157i	−0.252158	+	0.776062i	0.742219	+	0.670158i	$0.233774\pi$
$557$	−5.95114	+	18.3157i	−0.252158	+	0.776062i	−0.994376	+	0.105904i	$0.966226\pi$
$558$		0			0
$559$	0.0509950	−	0.0370500i	0.00215686	−	0.00156705i
$560$	22.2399			0.939809
$561$		0			0
$562$	−18.9607			−0.799810
$563$	−27.6770	+	20.1085i	−1.16645	+	0.847472i	−0.990579	−	0.136942i	$-0.956273\pi$
$563$	−27.6770	+	20.1085i	−1.16645	+	0.847472i	−0.175866	+	0.984414i	$0.556273\pi$
$564$		0			0
$565$	−5.87455	+	18.0800i	−0.247144	+	0.760631i
$566$	9.88884	+	7.18466i	0.415659	+	0.301994i
$567$		0			0
$568$	−2.25083	+	6.92735i	−0.0944428	+	0.290665i
$569$	8.40206	+	25.8589i	0.352233	+	1.08406i	0.957597	+	0.288112i	$0.0930276\pi$
$569$	8.40206	+	25.8589i	0.352233	+	1.08406i	−0.605364	+	0.795949i	$0.706972\pi$
$570$		0			0
$571$	18.0461			0.755207			0.377603	−	0.925967i	$-0.376748\pi$
$571$	18.0461			0.755207			0.377603	+	0.925967i	$0.376748\pi$
$572$	−1.92189	−	8.88425i	−0.0803582	−	0.371469i
$573$		0			0
$574$	−13.2890	+	9.65501i	−0.554671	+	0.402992i
$575$	5.15223	+	15.8569i	0.214863	+	0.661280i
$576$		0			0
$577$	−22.3864	−	16.2647i	−0.931959	−	0.677108i	0.0145129	−	0.999895i	$-0.495380\pi$
$577$	−22.3864	−	16.2647i	−0.931959	−	0.677108i	−0.946472	+	0.322787i	$0.895380\pi$
$578$	12.9559	+	9.41304i	0.538896	+	0.391531i
$579$		0			0
$580$	−1.19602	−	3.68098i	−0.0496622	−	0.152844i
$581$	13.4097	−	9.74274i	0.556330	−	0.404197i
$582$		0			0
$583$	−0.0638114	+	0.0371487i	−0.00264280	+	0.00153854i
$584$	18.0745			0.747928
$585$		0			0
$586$	1.36944	+	4.21469i	0.0565709	+	0.174107i
$587$	1.19648	−	3.68237i	0.0493838	−	0.151988i	−0.923324	−	0.384023i	$-0.874538\pi$
$587$	1.19648	−	3.68237i	0.0493838	−	0.151988i	0.972707	+	0.232035i	$0.0745384\pi$
$588$		0			0
$589$	−47.7318	−	34.6792i	−1.96675	−	1.42893i
$590$	20.4011	−	62.7881i	0.839900	−	2.58495i
$591$		0			0
$592$	−2.67431	+	1.94300i	−0.109913	+	0.0798568i
$593$	−8.07907			−0.331768			−0.165884	−	0.986145i	$-0.553048\pi$
$593$	−8.07907			−0.331768			−0.165884	+	0.986145i	$0.553048\pi$
$594$		0			0
$595$	12.2007			0.500178
$596$	8.43918	−	6.13142i	0.345682	−	0.251153i
$597$		0			0
$598$	−8.71475	+	26.8213i	−0.356373	+	1.09680i
$599$	19.3999	+	14.0949i	0.792659	+	0.575900i	0.908751	−	0.417338i	$-0.137037\pi$
$599$	19.3999	+	14.0949i	0.792659	+	0.575900i	−0.116092	+	0.993238i	$0.537037\pi$
$600$		0			0
$601$	−13.7380	+	42.2813i	−0.560386	+	1.72469i	0.120892	+	0.992666i	$0.461425\pi$
$601$	−13.7380	+	42.2813i	−0.560386	+	1.72469i	−0.681278	+	0.732025i	$0.738575\pi$
$602$	−0.0117616	−	0.0361985i	−0.000479367	−	0.00147534i
$603$		0			0
$604$	4.40459			0.179220
$605$	−22.2164	−	24.3191i	−0.903224	−	0.988710i
$606$		0			0
$607$	−30.9660	+	22.4981i	−1.25687	+	0.913170i	−0.998600	−	0.0529019i	$-0.983153\pi$
$607$	−30.9660	+	22.4981i	−1.25687	+	0.913170i	−0.258272	+	0.966072i	$0.583153\pi$
$608$	9.61220	+	29.5833i	0.389826	+	1.19976i
$609$		0			0
$610$	−46.5154	−	33.7954i	−1.88335	−	1.36834i
$611$	12.8573	+	9.34134i	0.520149	+	0.377910i
$612$		0			0
$613$	0.200788	+	0.617961i	0.00810974	+	0.0249592i	0.955030	−	0.296511i	$-0.0958231\pi$
$613$	0.200788	+	0.617961i	0.00810974	+	0.0249592i	−0.946920	+	0.321470i	$0.895823\pi$
$614$	−35.3693	+	25.6973i	−1.42739	+	1.03706i
$615$		0			0
$616$	10.9113	+	1.10709i	0.439629	+	0.0446060i
$617$	−8.87579			−0.357326			−0.178663	−	0.983910i	$-0.557177\pi$
$617$	−8.87579			−0.357326			−0.178663	+	0.983910i	$0.557177\pi$
$618$		0			0
$619$	−4.73781	−	14.5815i	−0.190429	−	0.586079i	0.809571	−	0.587022i	$-0.199700\pi$
$619$	−4.73781	−	14.5815i	−0.190429	−	0.586079i	−1.00000		0.000943025i	$0.999700\pi$
$620$	−4.25107	+	13.0835i	−0.170727	+	0.525444i
$621$		0			0
$622$	−18.0776	−	13.1341i	−0.724845	−	0.526631i
$623$	−4.62075	+	14.2212i	−0.185127	+	0.569761i
$624$		0			0
$625$	23.5412	−	17.1037i	0.941646	−	0.684146i
$626$	−34.0706			−1.36173
$627$		0			0
$628$	14.9711			0.597411
$629$	−1.46711	+	1.06591i	−0.0584973	+	0.0425008i
$630$		0			0
$631$	3.08138	−	9.48350i	0.122668	−	0.377532i	−0.870801	−	0.491635i	$-0.836399\pi$
$631$	3.08138	−	9.48350i	0.122668	−	0.377532i	0.993469	+	0.114103i	$0.0363994\pi$
$632$	−9.54146	−	6.93228i	−0.379539	−	0.275751i
$633$		0			0
$634$	0.201261	−	0.619419i	0.00799311	−	0.0246003i
$635$	14.0240	+	43.1614i	0.556525	+	1.71281i
$636$		0			0
$637$	19.2787			0.763851
$638$	−2.21899	−	10.2577i	−0.0878508	−	0.406105i
$639$		0			0
$640$	−32.8187	+	23.8442i	−1.29727	+	0.942525i
$641$	9.70981	+	29.8837i	0.383514	+	1.18034i	0.937552	+	0.347845i	$0.113086\pi$
$641$	9.70981	+	29.8837i	0.383514	+	1.18034i	−0.554038	+	0.832492i	$0.686914\pi$
$642$		0			0
$643$	17.8766	+	12.9881i	0.704983	+	0.512200i	0.881551	−	0.472088i	$-0.156500\pi$
$643$	17.8766	+	12.9881i	0.704983	+	0.512200i	−0.176568	+	0.984288i	$0.556500\pi$
$644$	3.44574	+	2.50348i	0.135781	+	0.0986508i
$645$		0			0
$646$	11.5960	+	35.6888i	0.456239	+	1.40416i
$647$	8.87521	−	6.44822i	0.348920	−	0.253506i	−0.399496	−	0.916735i	$-0.630815\pi$
$647$	8.87521	−	6.44822i	0.348920	−	0.253506i	0.748416	+	0.663230i	$0.230815\pi$
$648$		0			0
$649$	18.0640	−	40.9690i	0.709072	−	1.60817i
$650$	−26.6159			−1.04396
$651$		0			0
$652$	0.164233	+	0.505457i	0.00643186	+	0.0197952i
$653$	−1.84766	+	5.68651i	−0.0723045	+	0.222530i	−0.980678	−	0.195630i	$-0.937325\pi$
$653$	−1.84766	+	5.68651i	−0.0723045	+	0.222530i	0.908373	+	0.418160i	$0.137325\pi$
$654$		0			0
$655$	−20.0735	−	14.5843i	−0.784338	−	0.569855i
$656$	10.0035	−	30.7877i	0.390572	−	1.20206i
$657$		0			0
$658$	7.76359	−	5.64058i	0.302656	−	0.219893i
$659$	19.2686			0.750598			0.375299	−	0.926904i	$-0.377540\pi$
$659$	19.2686			0.750598			0.375299	+	0.926904i	$0.377540\pi$
$660$		0			0
$661$	1.98684			0.0772793			0.0386396	−	0.999253i	$-0.487698\pi$
$661$	1.98684			0.0772793			0.0386396	+	0.999253i	$0.487698\pi$
$662$	26.5509	−	19.2904i	1.03193	−	0.749742i
$663$		0			0
$664$	−7.33988	+	22.5898i	−0.284842	+	0.876655i
$665$	−31.5270	−	22.9057i	−1.22256	−	0.888244i
$666$		0			0
$667$	−2.51664	+	7.74541i	−0.0974446	+	0.299904i
$668$	2.83233	+	8.71703i	0.109586	+	0.337272i
$669$		0			0
$670$	−34.9659			−1.35085
$671$	−29.0721	−	25.9876i	−1.12232	−	1.00324i
$672$		0			0
$673$	−11.0889	+	8.05653i	−0.427444	+	0.310557i	−0.780626	−	0.624998i	$-0.785100\pi$
$673$	−11.0889	+	8.05653i	−0.427444	+	0.310557i	0.353182	+	0.935555i	$0.385100\pi$
$674$	−0.133662	−	0.411369i	−0.00514847	−	0.0158453i
$675$		0			0
$676$	−2.09381	−	1.52124i	−0.0805311	−	0.0585093i
$677$	4.27886	+	3.10877i	0.164450	+	0.119480i	0.666966	−	0.745088i	$-0.267592\pi$
$677$	4.27886	+	3.10877i	0.164450	+	0.119480i	−0.502517	+	0.864568i	$0.667592\pi$
$678$		0			0
$679$	7.38607	+	22.7320i	0.283451	+	0.872373i
$680$	−14.1444	+	10.2765i	−0.542413	+	0.394086i
$681$		0			0
$682$	−15.0494	+	34.1320i	−0.576273	+	1.30698i
$683$	−7.66223			−0.293187			−0.146594	−	0.989197i	$-0.546831\pi$
$683$	−7.66223			−0.293187			−0.146594	+	0.989197i	$0.546831\pi$
$684$		0			0
$685$	−21.4971	−	66.1611i	−0.821360	−	2.52789i
$686$	8.96363	−	27.5872i	0.342233	−	1.05328i
$687$		0			0
$688$	0.0606845	+	0.0440899i	0.00231358	+	0.00168091i
$689$	−0.0282647	+	0.0869897i	−0.00107680	+	0.00331404i
$690$		0			0
$691$	6.46496	−	4.69707i	0.245939	−	0.178685i	−0.457986	−	0.888959i	$-0.651429\pi$
$691$	6.46496	−	4.69707i	0.245939	−	0.178685i	0.703925	+	0.710274i	$0.251429\pi$
$692$	−7.22175			−0.274530
$693$		0			0
$694$	−38.7407			−1.47058
$695$	−32.5014	+	23.6136i	−1.23285	+	0.895717i
$696$		0			0
$697$	5.48785	−	16.8899i	0.207867	−	0.639750i
$698$	3.50885	+	2.54933i	0.132812	+	0.0964935i
$699$		0			0
$700$	−1.24216	+	3.82296i	−0.0469491	+	0.144494i
$701$	11.2526	+	34.6318i	0.425003	+	1.30803i	0.902991	+	0.429660i	$0.141366\pi$
$701$	11.2526	+	34.6318i	0.425003	+	1.30803i	−0.477988	+	0.878367i	$0.658634\pi$
$702$		0			0
$703$	5.79222			0.218458
$704$	−11.0312	+	6.42199i	−0.415755	+	0.242038i
$705$		0			0
$706$	16.2927	−	11.8373i	0.613182	−	0.445503i
$707$	−2.22476	−	6.84710i	−0.0836706	−	0.257512i
$708$		0			0
$709$	31.0645	+	22.5697i	1.16665	+	0.847623i	0.990604	−	0.136758i	$-0.0436684\pi$
$709$	31.0645	+	22.5697i	1.16665	+	0.847623i	0.176049	+	0.984381i	$0.443668\pi$
$710$	−13.2382	−	9.61815i	−0.496822	−	0.360963i
$711$		0			0
$712$	−6.62150	−	20.3789i	−0.248151	−	0.763731i
$713$	23.4183	−	17.0144i	0.877021	−	0.637193i
$714$		0			0
$715$	−40.5952	−	4.11890i	−1.51817	−	0.154038i
$716$	−7.16899			−0.267918
$717$		0			0
$718$	13.1447	+	40.4553i	0.490556	+	1.50978i
$719$	11.2349	−	34.5776i	0.418993	−	1.28953i	−0.489638	−	0.871926i	$-0.662871\pi$
$719$	11.2349	−	34.5776i	0.418993	−	1.28953i	0.908630	−	0.417601i	$-0.137129\pi$
$720$		0			0
$721$	−20.7436	−	15.0711i	−0.772531	−	0.561276i
$722$	27.4496	−	84.4813i	1.02157	−	3.14407i
$723$		0			0
$724$	4.17913	−	3.03631i	0.155316	−	0.112844i
$725$	−7.68612			−0.285455
$726$		0			0
$727$	26.3651			0.977827			0.488914	−	0.872332i	$-0.337393\pi$
$727$	26.3651			0.977827			0.488914	+	0.872332i	$0.337393\pi$
$728$	10.9912	−	7.98558i	0.407361	−	0.295965i
$729$		0			0
$730$	−12.5476	+	38.6176i	−0.464408	+	1.42930i
$731$	0.0332911	+	0.0241874i	0.00123131	+	0.000894602i
$732$		0			0
$733$	−3.79198	+	11.6705i	−0.140060	+	0.431060i	−0.996343	−	0.0854472i	$-0.972768\pi$
$733$	−3.79198	+	11.6705i	−0.140060	+	0.431060i	0.856283	+	0.516507i	$0.172768\pi$
$734$	8.34851	+	25.6941i	0.308149	+	0.948385i
$735$		0			0
$736$	−15.2612			−0.562534
$737$	−23.5929	−	2.39380i	−0.869055	−	0.0881767i
$738$		0			0
$739$	8.61932	−	6.26231i	0.317067	−	0.230363i	−0.417856	−	0.908513i	$-0.637218\pi$
$739$	8.61932	−	6.26231i	0.317067	−	0.230363i	0.734923	+	0.678151i	$0.237218\pi$
$740$	−0.417343	−	1.28445i	−0.0153418	−	0.0472174i
$741$		0			0
$742$	0.0446821	+	0.0324634i	0.00164033	+	0.00119177i
$743$	11.2636	+	8.18347i	0.413221	+	0.300222i	0.774904	−	0.632078i	$-0.217798\pi$
$743$	11.2636	+	8.18347i	0.413221	+	0.300222i	−0.361684	+	0.932301i	$0.617798\pi$
$744$		0			0
$745$	−14.4701	−	44.5344i	−0.530143	−	1.63161i
$746$	−6.30532	+	4.58108i	−0.230854	+	0.167725i
$747$		0			0
$748$	5.12833	−	2.98553i	0.187510	−	0.109162i
$749$	−8.13310			−0.297177
$750$		0			0
$751$	9.10149	+	28.0115i	0.332118	+	1.02215i	0.968124	+	0.250471i	$0.0805854\pi$
$751$	9.10149	+	28.0115i	0.332118	+	1.02215i	−0.636006	+	0.771684i	$0.719415\pi$
$752$	−5.84418	+	17.9865i	−0.213115	+	0.655902i
$753$		0			0
$754$	−10.5178	−	7.64162i	−0.383035	−	0.278291i
$755$	6.10991	−	18.8044i	0.222362	−	0.684361i
$756$		0			0
$757$	13.1092	−	9.52440i	0.476463	−	0.346170i	−0.323492	−	0.946231i	$-0.604857\pi$
$757$	13.1092	−	9.52440i	0.476463	−	0.346170i	0.799955	+	0.600061i	$0.204857\pi$
$758$	−5.15684			−0.187305
$759$		0			0
$760$	55.8429			2.02564
$761$	37.6581	−	27.3602i	1.36511	−	0.991807i	0.367004	−	0.930219i	$-0.380383\pi$
$761$	37.6581	−	27.3602i	1.36511	−	0.991807i	0.998102	−	0.0615882i	$-0.0196165\pi$
$762$		0			0
$763$	−2.72696	+	8.39271i	−0.0987225	+	0.303837i
$764$	3.03261	+	2.20332i	0.109716	+	0.0797132i
$765$		0			0
$766$	2.36142	−	7.26770i	0.0853216	−	0.262593i
$767$	−17.1396	−	52.7503i	−0.618875	−	1.90470i
$768$		0			0
$769$	−31.2406			−1.12657			−0.563283	−	0.826264i	$-0.690462\pi$
$769$	−31.2406			−1.12657			−0.563283	+	0.826264i	$0.690462\pi$
$770$	−9.94019	+	22.5443i	−0.358219	+	0.812440i
$771$		0			0
$772$	4.02439	−	2.92389i	0.144841	−	0.105233i
$773$	0.672766	+	2.07056i	0.0241977	+	0.0744729i	0.962426	−	0.271544i	$-0.0875341\pi$
$773$	0.672766	+	2.07056i	0.0241977	+	0.0744729i	−0.938228	+	0.346016i	$0.887534\pi$
$774$		0			0
$775$	22.1016	+	16.0578i	0.793913	+	0.576812i
$776$	−27.7097	−	20.1323i	−0.994721	−	0.722707i
$777$		0			0
$778$	−13.5110	−	41.5825i	−0.484392	−	1.49080i
$779$	−45.8901	+	33.3411i	−1.64418	+	1.19457i
$780$		0			0
$781$	−8.27390	−	7.39604i	−0.296063	−	0.264651i
$782$	−18.4108			−0.658370
$783$		0			0
$784$	7.08943	+	21.8190i	0.253194	+	0.779251i
$785$	20.7674	−	63.9155i	0.741220	−	2.28124i
$786$		0			0
$787$	21.9379	+	15.9388i	0.782003	+	0.568159i	0.905580	−	0.424176i	$-0.139436\pi$
$787$	21.9379	+	15.9388i	0.782003	+	0.568159i	−0.123576	+	0.992335i	$0.539436\pi$
$788$	−2.71205	+	8.34682i	−0.0966126	+	0.297343i
$789$		0			0
$790$	21.4352	−	15.5736i	0.762629	−	0.554083i
$791$	9.64392			0.342898
$792$		0			0
$793$	−48.3044			−1.71534
$794$	−49.2999	+	35.8185i	−1.74959	+	1.27115i
$795$		0			0
$796$	−3.28368	+	10.1061i	−0.116387	+	0.358202i
$797$	17.7764	+	12.9153i	0.629674	+	0.457485i	0.856287	−	0.516500i	$-0.172765\pi$
$797$	17.7764	+	12.9153i	0.629674	+	0.457485i	−0.226613	+	0.973985i	$0.572765\pi$
$798$		0			0
$799$	−3.20607	+	9.86728i	−0.113423	+	0.349079i
$800$	−4.45081	−	13.6982i	−0.157360	−	0.484304i
$801$		0			0
$802$	52.8200			1.86514
$803$	−11.1102	+	25.1978i	−0.392069	+	0.889210i
$804$		0			0
$805$	15.4678	−	11.2380i	0.545169	−	0.396088i
$806$	14.2793	+	43.9473i	0.502968	+	1.54798i
$807$		0			0
$808$	8.34645	+	6.06405i	0.293627	+	0.213333i
$809$	21.6405	+	15.7228i	0.760840	+	0.552783i	0.899168	−	0.437604i	$-0.144173\pi$
$809$	21.6405	+	15.7228i	0.760840	+	0.552783i	−0.138328	+	0.990386i	$0.544173\pi$
$810$		0			0
$811$	3.89926	+	12.0007i	0.136922	+	0.421401i	0.995884	−	0.0906373i	$-0.0288904\pi$
$811$	3.89926	+	12.0007i	0.136922	+	0.421401i	−0.858962	+	0.512039i	$0.828890\pi$
$812$	−1.58846	+	1.15408i	−0.0557440	+	0.0405004i
$813$		0			0
$814$	−0.774301	−	3.57934i	−0.0271392	−	0.125456i
$815$	2.38575			0.0835691
$816$		0			0
$817$	−0.0406157	−	0.125002i	−0.00142096	−	0.00437327i
$818$	−11.9940	+	36.9136i	−0.419359	+	1.29065i
$819$		0			0
$820$	10.7000	+	7.77403i	0.373661	+	0.271481i
$821$	−6.28672	+	19.3485i	−0.219408	+	0.675269i	0.779403	+	0.626523i	$0.215522\pi$
$821$	−6.28672	+	19.3485i	−0.219408	+	0.675269i	−0.998811	+	0.0487460i	$0.984478\pi$
$822$		0			0
$823$	29.8928	−	21.7184i	1.04200	−	0.757056i	0.0713233	−	0.997453i	$-0.477278\pi$
$823$	29.8928	−	21.7184i	1.04200	−	0.757056i	0.970675	+	0.240397i	$0.0772778\pi$
$824$	36.7426			1.27999
$825$		0			0
$826$	−33.4914			−1.16531
$827$	−22.3256	+	16.2205i	−0.776337	+	0.564042i	−0.903877	−	0.427792i	$-0.859292\pi$
$827$	−22.3256	+	16.2205i	−0.776337	+	0.564042i	0.127541	+	0.991833i	$0.459292\pi$
$828$		0			0
$829$	−4.81545	+	14.8204i	−0.167247	+	0.514735i	−0.999195	−	0.0401197i	$-0.987226\pi$
$829$	−4.81545	+	14.8204i	−0.167247	+	0.514735i	0.831947	+	0.554854i	$0.187226\pi$
$830$	−43.1694	−	31.3644i	−1.49843	−	1.08867i
$831$		0			0
$832$	−4.88619	+	15.0381i	−0.169398	+	0.521354i
$833$	3.88921	+	11.9697i	0.134753	+	0.414727i
$834$		0			0
$835$	41.1442			1.42385
$836$	−18.8569	−	1.91327i	−0.652178	−	0.0661718i
$837$		0			0
$838$	50.2789	−	36.5298i	1.73686	−	1.26190i
$839$	4.13275	+	12.7193i	0.142678	+	0.439118i	0.996705	−	0.0811104i	$-0.0258466\pi$
$839$	4.13275	+	12.7193i	0.142678	+	0.439118i	−0.854027	+	0.520229i	$0.825847\pi$
$840$		0			0
$841$	20.4242	+	14.8390i	0.704282	+	0.511691i
$842$	26.7251	+	19.4169i	0.921009	+	0.669152i
$843$		0			0
$844$	−1.01064	−	3.11044i	−0.0347877	−	0.107066i
$845$	−9.39904	+	6.82880i	−0.323337	+	0.234918i
$846$		0			0
$847$	−8.25044	+	14.5310i	−0.283488	+	0.499291i
$848$	−0.108846			−0.00373779
$849$		0			0
$850$	−5.36939	−	16.5253i	−0.184168	−	0.566812i
$851$	−0.878162	+	2.70270i	−0.0301030	+	0.0926475i
$852$		0			0
$853$	−6.41238	−	4.65887i	−0.219556	−	0.159517i	0.472571	−	0.881293i	$-0.343326\pi$
$853$	−6.41238	−	4.65887i	−0.219556	−	0.159517i	−0.692127	+	0.721776i	$0.743326\pi$
$854$	−9.01329	+	27.7400i	−0.308428	+	0.949245i
$855$		0			0
$856$	9.42883	−	6.85044i	0.322271	−	0.234143i
$857$	53.6860			1.83388			0.916939	−	0.399027i	$-0.130652\pi$
$857$	53.6860			1.83388			0.916939	+	0.399027i	$0.130652\pi$
$858$		0			0
$859$	16.8510			0.574947			0.287474	−	0.957789i	$-0.407185\pi$
$859$	16.8510			0.574947			0.287474	+	0.957789i	$0.407185\pi$
$860$	−0.0247933	+	0.0180134i	−0.000845446	+	0.000614252i
$861$		0			0
$862$	13.0837	−	40.2675i	0.445633	−	1.37152i
$863$	−30.3055	−	22.0183i	−1.03161	−	0.749510i	−0.0629816	−	0.998015i	$-0.520061\pi$
$863$	−30.3055	−	22.0183i	−1.03161	−	0.749510i	−0.968631	+	0.248504i	$0.920061\pi$
$864$		0			0
$865$	−10.0178	+	30.8316i	−0.340615	+	1.04830i
$866$	4.33413	+	13.3391i	0.147280	+	0.453281i
$867$		0			0
$868$	6.97875			0.236874
$869$	15.5293	−	9.04063i	0.526797	−	0.306682i
$870$		0			0
$871$	−23.7657	+	17.2668i	−0.805269	+	0.585062i
$872$	−3.90771	−	12.0267i	−0.132332	−	0.407275i
$873$		0			0
$874$	47.5743	+	34.5647i	1.60922	+	1.16917i
$875$	−3.80223	−	2.76248i	−0.128539	−	0.0933888i
$876$		0			0
$877$	−0.968381	−	2.98037i	−0.0326999	−	0.100640i	0.933374	−	0.358904i	$-0.116850\pi$
$877$	−0.968381	−	2.98037i	−0.0326999	−	0.100640i	−0.966074	+	0.258264i	$0.916850\pi$
$878$	5.61778	−	4.08155i	0.189591	−	0.137746i
$879$		0			0
$880$	−10.2666	−	47.4590i	−0.346086	−	1.59984i
$881$	26.3658			0.888286			0.444143	−	0.895956i	$-0.353508\pi$
$881$	26.3658			0.888286			0.444143	+	0.895956i	$0.353508\pi$
$882$		0			0
$883$	−0.0272129	−	0.0837526i	−0.000915786	−	0.00281850i	0.950598	−	0.310426i	$-0.100472\pi$
$883$	−0.0272129	−	0.0837526i	−0.000915786	−	0.00281850i	−0.951513	+	0.307607i	$0.900472\pi$
$884$	2.27155	−	6.99110i	0.0764004	−	0.235136i
$885$		0			0
$886$	−19.3466	−	14.0561i	−0.649961	−	0.472225i
$887$	14.7402	−	45.3656i	0.494926	−	1.52323i	−0.322145	−	0.946690i	$-0.604404\pi$
$887$	14.7402	−	45.3656i	0.494926	−	1.52323i	0.817072	−	0.576536i	$-0.195596\pi$
$888$		0			0
$889$	18.6255	−	13.5322i	0.624680	−	0.453856i
$890$	48.1378			1.61358
$891$		0			0
$892$	9.40352			0.314853
$893$	26.8096	−	19.4783i	0.897148	−	0.651816i
$894$		0			0
$895$	−9.94459	+	30.6063i	−0.332411	+	1.02306i
$896$	16.6488	+	12.0961i	0.556198	+	0.404101i
$897$		0			0
$898$	8.72418	−	26.8503i	0.291130	−	0.896004i
$899$	4.12357	+	12.6910i	0.137529	+	0.423270i
$900$		0			0
$901$	−0.0597120			−0.00198930
$902$	26.7379	+	23.9010i	0.890275	+	0.795817i
$903$		0			0
$904$	−11.1803	+	8.12299i	−0.371853	+	0.270167i
$905$	−7.16567	−	22.0537i	−0.238195	−	0.733089i
$906$		0			0
$907$	7.73823	+	5.62216i	0.256944	+	0.186681i	0.708799	−	0.705411i	$-0.249237\pi$
$907$	7.73823	+	5.62216i	0.256944	+	0.186681i	−0.451855	+	0.892092i	$0.649237\pi$
$908$	2.87699	+	2.09025i	0.0954762	+	0.0693675i
$909$		0			0
$910$	9.43154	+	29.0273i	0.312652	+	0.962245i
$911$	45.5137	−	33.0677i	1.50794	−	1.09558i	0.540856	−	0.841115i	$-0.318100\pi$
$911$	45.5137	−	33.0677i	1.50794	−	1.09558i	0.967082	−	0.254466i	$-0.0818996\pi$
$912$		0			0
$913$	−26.9809	−	24.1182i	−0.892936	−	0.798196i
$914$	−26.8009			−0.886494
$915$		0			0
$916$	3.62488	+	11.1562i	0.119769	+	0.368612i
$917$	−3.88965	+	11.9711i	−0.128447	+	0.395321i
$918$		0			0
$919$	11.9478	+	8.68058i	0.394121	+	0.286346i	0.767142	−	0.641477i	$-0.221678\pi$
$919$	11.9478	+	8.68058i	0.394121	+	0.286346i	−0.373021	+	0.927823i	$0.621678\pi$
$920$	−8.46638	+	26.0568i	−0.279128	+	0.859068i
$921$		0			0
$922$	−25.7354	+	18.6979i	−0.847551	+	0.615782i
$923$	−13.7474			−0.452500
$924$		0			0
$925$	−2.68201			−0.0881841
$926$	28.3073	−	20.5665i	0.930236	−	0.675856i
$927$		0			0
$928$	2.17402	−	6.69095i	0.0713658	−	0.219641i
$929$	1.36433	+	0.991240i	0.0447621	+	0.0325215i	0.609941	−	0.792447i	$-0.291193\pi$
$929$	1.36433	+	0.991240i	0.0447621	+	0.0325215i	−0.565179	+	0.824968i	$0.691193\pi$
$930$		0			0
$931$	12.4223	−	38.2319i	0.407125	−	1.25300i
$932$	0.962549	+	2.96242i	0.0315293	+	0.0970373i
$933$		0			0
$934$	23.7183			0.776088
$935$	−5.63216	−	26.0356i	−0.184191	−	0.851456i
$936$		0			0
$937$	−19.4568	+	14.1362i	−0.635625	+	0.461809i	−0.858344	−	0.513074i	$-0.828507\pi$
$937$	−19.4568	+	14.1362i	−0.635625	+	0.461809i	0.222719	+	0.974883i	$0.428507\pi$
$938$	5.48137	+	16.8699i	0.178973	+	0.550822i
$939$		0			0
$940$	−6.25109	−	4.54169i	−0.203888	−	0.148133i
$941$	36.8226	+	26.7532i	1.20038	+	0.872130i	0.994322	−	0.106409i	$-0.0339353\pi$
$941$	36.8226	+	26.7532i	1.20038	+	0.872130i	0.206062	+	0.978539i	$0.433935\pi$
$942$		0			0
$943$	−8.59985	−	26.4676i	−0.280050	−	0.861904i
$944$	53.3982	−	38.7961i	1.73796	−	1.26270i
$945$		0			0
$946$	−0.0718163	+	0.0418089i	−0.00233495	+	0.00135933i
$947$	−22.7486			−0.739229			−0.369615	−	0.929185i	$-0.620510\pi$
$947$	−22.7486			−0.739229			−0.369615	+	0.929185i	$0.620510\pi$
$948$		0			0
$949$	10.5416	+	32.4438i	0.342196	+	1.05317i
$950$	−17.1501	+	52.7825i	−0.556422	+	1.71249i
$951$		0			0
$952$	7.17540	+	5.21323i	0.232556	+	0.168962i
$953$	−2.86907	+	8.83009i	−0.0929383	+	0.286035i	−0.986711	−	0.162486i	$-0.948049\pi$
$953$	−2.86907	+	8.83009i	−0.0929383	+	0.286035i	0.893773	+	0.448520i	$0.148049\pi$
$954$		0			0
$955$	13.6133	−	9.89063i	0.440515	−	0.320053i
$956$	−8.46200			−0.273681
$957$		0			0
$958$	−15.7353			−0.508383
$959$	−28.5506	+	20.7433i	−0.921948	+	0.669835i
$960$		0			0
$961$	5.07705	−	15.6255i	0.163776	−	0.504050i
$962$	−3.67010	−	2.66649i	−0.118329	−	0.0859710i
$963$		0			0
$964$	−3.99739	+	12.3027i	−0.128747	+	0.396243i
$965$	−6.90036	−	21.2371i	−0.222130	−	0.683647i
$966$		0			0
$967$	13.0299			0.419013			0.209506	−	0.977807i	$-0.432814\pi$
$967$	13.0299			0.419013			0.209506	+	0.977807i	$0.432814\pi$
$968$	−2.67449	−	23.7953i	−0.0859613	−	0.764809i
$969$		0			0
$970$	62.2507	−	45.2278i	1.99875	−	1.45218i
$971$	−3.52662	−	10.8538i	−0.113175	−	0.348316i	0.878387	−	0.477950i	$-0.158620\pi$
$971$	−3.52662	−	10.8538i	−0.113175	−	0.348316i	−0.991562	+	0.129634i	$0.958620\pi$
$972$		0			0
$973$	16.4878	+	11.9791i	0.528575	+	0.384033i
$974$	−15.9704	−	11.6032i	−0.511725	−	0.371790i
$975$		0			0
$976$	−17.7631	−	54.6693i	−0.568584	−	1.74992i
$977$	32.3081	−	23.4732i	1.03363	−	0.750973i	0.0645951	−	0.997912i	$-0.479424\pi$
$977$	32.3081	−	23.4732i	1.03363	−	0.750973i	0.969031	+	0.246938i	$0.0794244\pi$
$978$		0			0
$979$	32.4805	+	3.29556i	1.03808	+	0.105326i
$980$	−9.37316			−0.299415
$981$		0			0
$982$	−1.94588	−	5.98880i	−0.0620955	−	0.191110i
$983$	−0.973201	+	2.99521i	−0.0310403	+	0.0955322i	−0.965376	−	0.260861i	$-0.915994\pi$
$983$	−0.973201	+	2.99521i	−0.0310403	+	0.0955322i	0.934336	+	0.356393i	$0.115994\pi$
$984$		0			0
$985$	31.8727	+	23.1569i	1.01555	+	0.737839i
$986$	2.62271	−	8.07186i	0.0835240	−	0.257060i
$987$		0			0
$988$	−18.9950	+	13.8006i	−0.604310	+	0.439057i
$989$	0.0644849			0.00205050
$990$		0			0
$991$	−34.8622			−1.10743			−0.553717	−	0.832705i	$-0.686791\pi$
$991$	−34.8622			−1.10743			−0.553717	+	0.832705i	$0.686791\pi$
$992$	−20.2301	+	14.6980i	−0.642307	+	0.466663i
$993$		0			0
$994$	−2.56517	+	7.89479i	−0.0813623	+	0.250408i
$995$	38.5907	+	28.0378i	1.22341	+	0.888858i
$996$		0			0
$997$	−3.51185	+	10.8083i	−0.111221	+	0.342304i	−0.991140	−	0.132820i	$-0.957597\pi$
$997$	−3.51185	+	10.8083i	−0.111221	+	0.342304i	0.879919	+	0.475124i	$0.157597\pi$
$998$	5.40806	+	16.6443i	0.171189	+	0.526866i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.f.d.190.1	yes	16
3.2	odd	2		297.2.f.a.190.4	yes	16
9.2	odd	6		891.2.n.i.190.1		32
9.4	even	3		891.2.n.f.784.1		32
9.5	odd	6		891.2.n.i.784.4		32
9.7	even	3		891.2.n.f.190.4		32
11.2	odd	10		3267.2.a.bl.1.2		8
11.4	even	5	inner	297.2.f.d.136.1	yes	16
11.9	even	5		3267.2.a.be.1.7		8
33.2	even	10		3267.2.a.bf.1.7		8
33.20	odd	10		3267.2.a.bm.1.2		8
33.26	odd	10		297.2.f.a.136.4	✓	16
99.4	even	15		891.2.n.f.136.4		32
99.59	odd	30		891.2.n.i.136.1		32
99.70	even	15		891.2.n.f.433.1		32
99.92	odd	30		891.2.n.i.433.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.a.136.4	✓	16	33.26	odd	10
297.2.f.a.190.4	yes	16	3.2	odd	2
297.2.f.d.136.1	yes	16	11.4	even	5	inner
297.2.f.d.190.1	yes	16	1.1	even	1	trivial
891.2.n.f.136.4		32	99.4	even	15
891.2.n.f.190.4		32	9.7	even	3
891.2.n.f.433.1		32	99.70	even	15
891.2.n.f.784.1		32	9.4	even	3
891.2.n.i.136.1		32	99.59	odd	30
891.2.n.i.190.1		32	9.2	odd	6
891.2.n.i.433.4		32	99.92	odd	30
891.2.n.i.784.4		32	9.5	odd	6
3267.2.a.be.1.7		8	11.9	even	5
3267.2.a.bf.1.7		8	33.2	even	10
3267.2.a.bl.1.2		8	11.2	odd	10
3267.2.a.bm.1.2		8	33.20	odd	10

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32122 + 0.959922i) q^{2} +(0.206136 - 0.634423i) q^{4} +(-2.42257 - 1.76010i) q^{5} +(-0.469421 + 1.44473i) q^{7} +(-0.672677 - 2.07029i) q^{8} +O(q^{10})\)	\(q+(-1.32122 + 0.959922i) q^{2} +(0.206136 - 0.634423i) q^{4} +(-2.42257 - 1.76010i) q^{5} +(-0.469421 + 1.44473i) q^{7} +(-0.672677 - 2.07029i) q^{8} +4.89031 q^{10} +(3.29968 + 0.334795i) q^{11} +(3.32385 - 2.41492i) q^{13} +(-0.766620 - 2.35941i) q^{14} +(3.95541 + 2.87378i) q^{16} +(2.16991 + 1.57653i) q^{17} +(-2.64733 - 8.14763i) q^{19} +(-1.61603 + 1.17411i) q^{20} +(-4.68098 + 2.72510i) q^{22} +4.20312 q^{23} +(1.22581 + 3.77266i) q^{25} +(-2.07340 + 6.38127i) q^{26} +(0.819805 + 0.595623i) q^{28} +(-0.598754 + 1.84278i) q^{29} +(5.57164 - 4.04803i) q^{31} -3.63091 q^{32} -4.38027 q^{34} +(3.68008 - 2.67373i) q^{35} +(-0.208931 + 0.643023i) q^{37} +(11.3188 + 8.22358i) q^{38} +(-2.01431 + 6.19940i) q^{40} +(-2.04606 - 6.29713i) q^{41} +0.0153422 q^{43} +(0.892586 - 2.02438i) q^{44} +(-5.55325 + 4.03467i) q^{46} +(1.19533 + 3.67886i) q^{47} +(3.79623 + 2.75812i) q^{49} +(-5.24102 - 3.80783i) q^{50} +(-0.846911 - 2.60653i) q^{52} +(-0.0180109 + 0.0130857i) q^{53} +(-7.40445 - 6.61884i) q^{55} +3.30677 q^{56} +(-0.977836 - 3.00947i) q^{58} +(4.17174 - 12.8393i) q^{59} +(-9.51176 - 6.91070i) q^{61} +(-3.47556 + 10.6967i) q^{62} +(-3.11359 + 2.26216i) q^{64} -12.3028 q^{65} -7.15005 q^{67} +(1.44748 - 1.05166i) q^{68} +(-2.29561 + 7.06518i) q^{70} +(-2.70704 - 1.96678i) q^{71} +(-2.56581 + 7.89675i) q^{73} +(-0.341208 - 1.05013i) q^{74} -5.71475 q^{76} +(-2.03263 + 4.60999i) q^{77} +(4.38320 - 3.18458i) q^{79} +(-4.52413 - 13.9239i) q^{80} +(8.74805 + 6.35583i) q^{82} +(-8.82754 - 6.41359i) q^{83} +(-2.48190 - 7.63852i) q^{85} +(-0.0202703 + 0.0147273i) q^{86} +(-1.52650 - 7.05650i) q^{88} +9.84351 q^{89} +(1.92862 + 5.93567i) q^{91} +(0.866417 - 2.66656i) q^{92} +(-5.11072 - 3.71316i) q^{94} +(-7.92732 + 24.3978i) q^{95} +(12.7294 - 9.24845i) q^{97} -7.66324 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} - 4 q^{4} + q^{5} - 2 q^{7}+O(q^{10}) \) 16 * q + 2 * q^2 - 4 * q^4 + q^5 - 2 * q^7	\( 16 q + 2 q^{2} - 4 q^{4} + q^{5} - 2 q^{7} + 6 q^{10} + 13 q^{11} - 2 q^{13} - 22 q^{14} - 24 q^{16} - 2 q^{17} - 2 q^{19} + 15 q^{22} + 14 q^{23} - 19 q^{25} + 21 q^{26} + 15 q^{28} + q^{29} + 14 q^{31} - 48 q^{32} + 10 q^{34} - 18 q^{35} + 9 q^{37} + 11 q^{38} + 33 q^{40} + 25 q^{41} + 14 q^{43} + 14 q^{44} + 4 q^{46} - 28 q^{47} - 4 q^{49} - 63 q^{50} + 10 q^{52} + q^{53} - 40 q^{55} + 96 q^{56} - 20 q^{58} + 41 q^{59} - 5 q^{62} - 92 q^{64} - 60 q^{65} - 48 q^{67} + 25 q^{68} - 31 q^{70} + 3 q^{71} - 13 q^{73} + 29 q^{74} - 58 q^{76} - 2 q^{77} - 83 q^{80} + 41 q^{82} - 14 q^{83} - 10 q^{85} - 56 q^{86} + 86 q^{88} + 82 q^{89} + 14 q^{91} + 74 q^{92} - 2 q^{94} - 56 q^{95} + 12 q^{97} + 26 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 - 4 * q^4 + q^5 - 2 * q^7 + 6 * q^10 + 13 * q^11 - 2 * q^13 - 22 * q^14 - 24 * q^16 - 2 * q^17 - 2 * q^19 + 15 * q^22 + 14 * q^23 - 19 * q^25 + 21 * q^26 + 15 * q^28 + q^29 + 14 * q^31 - 48 * q^32 + 10 * q^34 - 18 * q^35 + 9 * q^37 + 11 * q^38 + 33 * q^40 + 25 * q^41 + 14 * q^43 + 14 * q^44 + 4 * q^46 - 28 * q^47 - 4 * q^49 - 63 * q^50 + 10 * q^52 + q^53 - 40 * q^55 + 96 * q^56 - 20 * q^58 + 41 * q^59 - 5 * q^62 - 92 * q^64 - 60 * q^65 - 48 * q^67 + 25 * q^68 - 31 * q^70 + 3 * q^71 - 13 * q^73 + 29 * q^74 - 58 * q^76 - 2 * q^77 - 83 * q^80 + 41 * q^82 - 14 * q^83 - 10 * q^85 - 56 * q^86 + 86 * q^88 + 82 * q^89 + 14 * q^91 + 74 * q^92 - 2 * q^94 - 56 * q^95 + 12 * q^97 + 26 * q^98

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