LMFDB - Embedded newform 297.2.f.a.190.4

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			190.4
Root			$2.13024 + 1.54771i$ of defining polynomial
Character	$\chi$	$=$	297.190
Dual form			297.2.f.a.136.4

$q$-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	−0.0127848	−	0.999918i	$-0.504070\pi$
$2$	1.32122	−	0.959922i	0.934243	−	0.678767i	0.947028	+	0.321151i	$0.104070\pi$
$3$		0			0
$3$		0			0
$4$	0.206136	−	0.634423i	0.103068	−	0.317211i
$5$	2.42257	+	1.76010i	1.08341	+	0.787141i	0.978274	−	0.207317i	$-0.0664732\pi$
$5$	2.42257	+	1.76010i	1.08341	+	0.787141i	0.105133	+	0.994458i	$0.466473\pi$
$6$		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	0.292684	−	0.956209i	$-0.405451\pi$
$17$	−2.16991	−	1.57653i	−0.526280	−	0.382365i	−0.818964	+	0.573844i	$0.805451\pi$
$18$		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	$-0.644386\pi$
$23$	−4.20312			−0.876412			−0.438206	+	0.898875i	$0.644386\pi$
$24$		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	−0.879947	−	0.475073i	$-0.842422\pi$
$29$	0.598754	−	1.84278i	0.111186	−	0.342195i	0.991132	+	0.132878i	$0.0424218\pi$
$30$		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	$0.0729619\pi$
$41$	2.04606	+	6.29713i	0.319541	+	0.983447i	−0.654304	+	0.756232i	$0.727038\pi$
$42$		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	0.825246	−	0.564773i	$-0.191036\pi$
$47$	−1.19533	−	3.67886i	−0.174357	−	0.536617i	−0.999604	+	0.0281562i	$0.991036\pi$
$48$		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	−0.586548	−	0.809915i	$-0.699513\pi$
$53$	0.0180109	−	0.0130857i	0.00247399	−	0.00179746i	0.589022	+	0.808117i	$0.299513\pi$
$54$		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	$0.441640\pi$
$59$	−4.17174	+	12.8393i	−0.543115	+	1.67153i	−0.725431	+	0.688295i	$0.758360\pi$
$60$		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	0.736716	−	0.676203i	$-0.236376\pi$
$71$	2.70704	+	1.96678i	0.321266	+	0.233414i	−0.415449	+	0.909616i	$0.636376\pi$
$72$		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	0.955212	−	0.295923i	$-0.0956273\pi$
$83$	8.82754	+	6.41359i	0.968949	+	0.703982i	0.0137369	+	0.999906i	$0.495627\pi$
$84$		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	$-0.674704\pi$
$89$	−9.84351			−1.04341			−0.521705	+	0.853126i	$0.674704\pi$
$90$		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	−0.380452	−	0.924801i	$-0.624232\pi$
$101$	3.83423	−	2.78573i	0.381520	−	0.277190i	0.761972	+	0.647610i	$0.224232\pi$
$102$		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	0.838685	−	0.544617i	$-0.183325\pi$
$107$	−1.65447	−	5.09193i	−0.159943	−	0.492255i	−0.998628	+	0.0523620i	$0.983325\pi$
$108$		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	0.999940	−	0.0109235i	$-0.00347713\pi$
$113$	1.96180	+	6.03781i	0.184551	+	0.567989i	−0.815389	+	0.578913i	$0.803477\pi$
$114$		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	$-0.617898\pi$
$131$	−8.28605			−0.723955			−0.361978	+	0.932187i	$0.617898\pi$
$132$		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	$-0.839264\pi$
$137$	−18.7947	−	13.6551i	−1.60574	−	1.16664i	−0.730549	−	0.682861i	$-0.760736\pi$
$138$		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	−0.0668344	−	0.997764i	$-0.521290\pi$
$149$	−12.6511	−	9.19155i	−1.03642	−	0.753001i	−0.969583	+	0.244763i	$0.921290\pi$
$150$		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	−0.0677539	−	0.997702i	$-0.521583\pi$
$167$	11.1160	−	8.07623i	0.860180	−	0.624957i	0.927934	+	0.372745i	$0.121583\pi$
$168$		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	$0.0350106\pi$
$173$	3.34543	+	10.2962i	0.254349	+	0.782805i	−0.739609	+	0.673037i	$0.764989\pi$
$174$		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	$0.0315572\pi$
$179$	3.32099	+	10.2210i	0.248223	+	0.763951i	−0.746867	+	0.664974i	$0.768443\pi$
$180$		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	−0.868371	−	0.495914i	$-0.834833\pi$
$191$	1.73647	−	5.34432i	0.125647	−	0.386701i	0.994018	+	0.109213i	$0.0348330\pi$
$192$		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	$-0.344729\pi$
$197$	13.1566			0.937366			0.468683	+	0.883366i	$0.344729\pi$
$198$		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	−0.881385	−	0.472399i	$-0.843388\pi$
$227$	1.64737	−	5.07007i	0.109340	−	0.336513i	0.990724	+	0.135886i	$0.0433882\pi$
$228$		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	−0.457127	−	0.889402i	$-0.651121\pi$
$233$	3.77769	−	2.74465i	0.247484	−	0.179808i	0.704611	+	0.709594i	$0.251121\pi$
$234$		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	$0.0345662\pi$
$239$	3.91997	+	12.0644i	0.253562	+	0.780384i	−0.740548	+	0.672004i	$0.765434\pi$
$240$		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	−0.872100	−	0.489328i	$-0.837242\pi$
$251$	−10.7133	+	7.78364i	−0.676215	+	0.491299i	0.195885	+	0.980627i	$0.437242\pi$
$252$		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	$0.238458\pi$
$257$	−4.17508	+	12.8496i	−0.260435	+	0.801535i	−0.992710	+	0.120527i	$0.961542\pi$
$258$		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	$-0.283139\pi$
$263$	20.4271			1.25959			0.629796	+	0.776761i	$0.283139\pi$
$264$		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	0.474706	−	0.880144i	$-0.342554\pi$
$269$	−3.53722	−	2.56994i	−0.215668	−	0.156692i	−0.690375	+	0.723452i	$0.742554\pi$
$270$		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	0.271251	−	0.962509i	$-0.412563\pi$
$281$	−9.39280	−	6.82427i	−0.560328	−	0.407102i	−0.831579	+	0.555407i	$0.812563\pi$
$282$		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	−0.972558	−	0.232660i	$-0.925257\pi$
$293$	−0.838542	+	2.58077i	−0.0489881	+	0.150770i	0.923570	+	0.383430i	$0.125257\pi$
$294$		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	$-0.973190\pi$
$311$	−4.22812	−	13.0128i	−0.239755	−	0.737890i	0.756700	−	0.653762i	$-0.226810\pi$
$312$		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	−0.578688	−	0.815549i	$-0.696435\pi$
$317$	0.322640	−	0.234412i	0.0181213	−	0.0131659i	0.596809	+	0.802383i	$0.296435\pi$
$318$		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	−0.0618927	−	0.998083i	$-0.519714\pi$
$347$	−19.1915	−	13.9434i	−1.03025	−	0.748522i	−0.968359	+	0.249561i	$0.919714\pi$
$348$		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	$-0.393568\pi$
$353$	12.3315			0.656341			0.328171	+	0.944618i	$0.393568\pi$
$354$		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	$0.341224\pi$
$359$	−8.04885	+	24.7718i	−0.424802	+	1.30741i	−0.903184	+	0.429254i	$0.858776\pi$
$360$		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	−0.486853	−	0.873484i	$-0.661855\pi$
$383$	3.78557	−	2.75038i	0.193434	−	0.140538i	0.680287	+	0.732946i	$0.261855\pi$
$384$		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	$-0.662541\pi$
$389$	8.27312	−	25.4620i	0.419464	−	1.29098i	0.908197	−	0.418543i	$-0.137459\pi$
$390$		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	0.999997	−	0.00246252i	$-0.000783847\pi$
$401$	26.1661	+	19.0108i	1.30667	+	0.949352i	0.306674	+	0.951815i	$0.400784\pi$
$402$		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	$-0.120194\pi$
$419$	38.0549			1.85910			0.929552	+	0.368690i	$0.120194\pi$
$420$		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	0.0460278	−	0.998940i	$-0.485344\pi$
$431$	20.9744	−	15.2388i	1.01030	−	0.734026i	0.964272	+	0.264914i	$0.0853437\pi$
$432$		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	$-0.986910\pi$
$443$	−4.52493	−	13.9263i	−0.214986	−	0.661659i	0.784169	−	0.620548i	$-0.213090\pi$
$444$		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	−0.206648	−	0.978415i	$-0.566255\pi$
$449$	13.9856	−	10.1612i	0.660023	−	0.479535i	0.866671	+	0.498881i	$0.166255\pi$
$450$		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	$-0.649862\pi$
$461$	−19.4785			−0.907206			−0.453603	+	0.891204i	$0.649862\pi$
$462$		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	0.825461	−	0.564460i	$-0.190915\pi$
$467$	11.7496	+	8.53662i	0.543709	+	0.395028i	−0.281752	+	0.959487i	$0.590915\pi$
$468$		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	0.395288	−	0.918557i	$-0.370645\pi$
$479$	−7.79497	−	5.66338i	−0.356161	−	0.258766i	−0.751449	+	0.659791i	$0.770645\pi$
$480$		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	−0.920564	−	0.390592i	$-0.872270\pi$
$491$	1.19151	−	3.66710i	0.0537722	−	0.165494i	0.974336	+	0.225098i	$0.0722703\pi$
$492$		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	$0.149738\pi$
$503$	9.79318	+	30.1403i	0.436657	+	1.34389i	−0.454723	+	0.890633i	$0.650262\pi$
$504$		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	$-0.939180\pi$
$509$	−6.74877	−	20.7706i	−0.299134	−	0.920639i	0.682668	−	0.730729i	$-0.260820\pi$
$510$		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	−0.888587	−	0.458708i	$-0.848312\pi$
$521$	2.28065	−	7.01911i	0.0999169	−	0.307513i	0.988504	+	0.151196i	$0.0483123\pi$
$522$		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	$-0.766226\pi$
$557$	5.95114	−	18.3157i	0.252158	−	0.776062i	0.994376	−	0.105904i	$-0.0337736\pi$
$558$		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	0.175866	−	0.984414i	$-0.443727\pi$
$563$	27.6770	−	20.1085i	1.16645	−	0.847472i	0.990579	+	0.136942i	$0.0437274\pi$
$564$		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	$-0.906972\pi$
$569$	−8.40206	−	25.8589i	−0.352233	−	1.08406i	0.605364	−	0.795949i	$-0.293028\pi$
$570$		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	−0.972707	−	0.232035i	$-0.925462\pi$
$587$	−1.19648	+	3.68237i	−0.0493838	+	0.151988i	0.923324	+	0.384023i	$0.125462\pi$
$588$		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	$-0.446952\pi$
$593$	8.07907			0.331768			0.165884	+	0.986145i	$0.446952\pi$
$594$		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	0.116092	−	0.993238i	$-0.462963\pi$
$599$	−19.3999	−	14.0949i	−0.792659	−	0.575900i	−0.908751	+	0.417338i	$0.862963\pi$
$600$		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	$-0.442823\pi$
$617$	8.87579			0.357326			0.178663	+	0.983910i	$0.442823\pi$
$618$		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	$-0.886914\pi$
$641$	−9.70981	−	29.8837i	−0.383514	−	1.18034i	0.554038	−	0.832492i	$-0.313086\pi$
$642$		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	−0.748416	−	0.663230i	$-0.769185\pi$
$647$	−8.87521	+	6.44822i	−0.348920	+	0.253506i	0.399496	+	0.916735i	$0.369185\pi$
$648$		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	−0.908373	−	0.418160i	$-0.862675\pi$
$653$	1.84766	−	5.68651i	0.0723045	−	0.222530i	0.980678	+	0.195630i	$0.0626751\pi$
$654$		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	$-0.622460\pi$
$659$	−19.2686			−0.750598			−0.375299	+	0.926904i	$0.622460\pi$
$660$		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	0.502517	−	0.864568i	$-0.332408\pi$
$677$	−4.27886	−	3.10877i	−0.164450	−	0.119480i	−0.666966	+	0.745088i	$0.732408\pi$
$678$		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	$-0.453169\pi$
$683$	7.66223			0.293187			0.146594	+	0.989197i	$0.453169\pi$
$684$		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	$-0.858634\pi$
$701$	−11.2526	−	34.6318i	−0.425003	−	1.30803i	0.477988	−	0.878367i	$-0.341366\pi$
$702$		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	$0.337129\pi$
$719$	−11.2349	+	34.5776i	−0.418993	+	1.28953i	−0.908630	+	0.417601i	$0.862871\pi$
$720$		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	0.361684	−	0.932301i	$-0.382202\pi$
$743$	−11.2636	−	8.18347i	−0.413221	−	0.300222i	−0.774904	+	0.632078i	$0.782202\pi$
$744$		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	$0.619617\pi$
$761$	−37.6581	+	27.3602i	−1.36511	+	0.991807i	−0.998102	+	0.0615882i	$0.980383\pi$
$762$		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	0.938228	−	0.346016i	$-0.112466\pi$
$773$	−0.672766	−	2.07056i	−0.0241977	−	0.0744729i	−0.962426	+	0.271544i	$0.912466\pi$
$774$		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	0.226613	−	0.973985i	$-0.427235\pi$
$797$	−17.7764	−	12.9153i	−0.629674	−	0.457485i	−0.856287	+	0.516500i	$0.827235\pi$
$798$		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	0.138328	−	0.990386i	$-0.455827\pi$
$809$	−21.6405	−	15.7228i	−0.760840	−	0.552783i	−0.899168	+	0.437604i	$0.855827\pi$
$810$		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	$-0.784478\pi$
$821$	6.28672	−	19.3485i	0.219408	−	0.675269i	0.998811	−	0.0487460i	$-0.0155225\pi$
$822$		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	−0.127541	−	0.991833i	$-0.540708\pi$
$827$	22.3256	−	16.2205i	0.776337	−	0.564042i	0.903877	+	0.427792i	$0.140708\pi$
$828$		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	0.854027	−	0.520229i	$-0.174153\pi$
$839$	−4.13275	−	12.7193i	−0.142678	−	0.439118i	−0.996705	+	0.0811104i	$0.974153\pi$
$840$		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	$-0.869348\pi$
$857$	−53.6860			−1.83388			−0.916939	+	0.399027i	$0.869348\pi$
$858$		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	0.968631	−	0.248504i	$-0.0799391\pi$
$863$	30.3055	+	22.0183i	1.03161	+	0.749510i	0.0629816	+	0.998015i	$0.479939\pi$
$864$		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	$-0.646492\pi$
$881$	−26.3658			−0.888286			−0.444143	+	0.895956i	$0.646492\pi$
$882$		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	$0.395596\pi$
$887$	−14.7402	+	45.3656i	−0.494926	+	1.52323i	−0.817072	+	0.576536i	$0.804404\pi$
$888$		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	$0.681900\pi$
$911$	−45.5137	+	33.0677i	−1.50794	+	1.09558i	−0.967082	+	0.254466i	$0.918100\pi$
$912$		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	0.565179	−	0.824968i	$-0.308807\pi$
$929$	−1.36433	−	0.991240i	−0.0447621	−	0.0325215i	−0.609941	+	0.792447i	$0.708807\pi$
$930$		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	−0.206062	−	0.978539i	$-0.566065\pi$
$941$	−36.8226	−	26.7532i	−1.20038	−	0.872130i	−0.994322	+	0.106409i	$0.966065\pi$
$942$		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	$-0.379490\pi$
$947$	22.7486			0.739229			0.369615	+	0.929185i	$0.379490\pi$
$948$		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	−0.893773	−	0.448520i	$-0.851951\pi$
$953$	2.86907	−	8.83009i	0.0929383	−	0.286035i	0.986711	+	0.162486i	$0.0519511\pi$
$954$		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	0.991562	−	0.129634i	$-0.0413802\pi$
$971$	3.52662	+	10.8538i	0.113175	+	0.348316i	−0.878387	+	0.477950i	$0.841380\pi$
$972$		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	−0.969031	−	0.246938i	$-0.920576\pi$
$977$	−32.3081	+	23.4732i	−1.03363	+	0.750973i	−0.0645951	+	0.997912i	$0.520576\pi$
$978$		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	−0.934336	−	0.356393i	$-0.884006\pi$
$983$	0.973201	−	2.99521i	0.0310403	−	0.0955322i	0.965376	+	0.260861i	$0.0840064\pi$
$984$		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.a.190.4	yes	16
3.2	odd	2		297.2.f.d.190.1	yes	16
9.2	odd	6		891.2.n.f.190.4		32
9.4	even	3		891.2.n.i.784.4		32
9.5	odd	6		891.2.n.f.784.1		32
9.7	even	3		891.2.n.i.190.1		32
11.2	odd	10		3267.2.a.bf.1.7		8
11.4	even	5	inner	297.2.f.a.136.4	✓	16
11.9	even	5		3267.2.a.bm.1.2		8
33.2	even	10		3267.2.a.bl.1.2		8
33.20	odd	10		3267.2.a.be.1.7		8
33.26	odd	10		297.2.f.d.136.1	yes	16
99.4	even	15		891.2.n.i.136.1		32
99.59	odd	30		891.2.n.f.136.4		32
99.70	even	15		891.2.n.i.433.4		32
99.92	odd	30		891.2.n.f.433.1		32

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

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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