LMFDB - Embedded newform 693.2.i.i.100.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(100,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("693.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.i (of order $3$, degree $2$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.10423593216.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 8x^{6} + 21x^{4} - 4x^{3} + 28x^{2} + 12x + 9 $ x^8 - 2x^7 + 8x^6 + 21x^4 - 4x^3 + 28x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.4
Root			$1.39083 - 2.40898i$ of defining polynomial
Character	$\chi$	$=$	693.100
Dual form			693.2.i.i.298.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39083 - 2.40898i) q^{2} +(-2.86880 - 4.96890i) q^{4} +(0.412855 - 0.715087i) q^{5} +(2.63323 - 0.257073i) q^{7} -10.3967 q^{8} +O(q^{10})$	\(q+(1.39083 - 2.40898i) q^{2} +(-2.86880 - 4.96890i) q^{4} +(0.412855 - 0.715087i) q^{5} +(2.63323 - 0.257073i) q^{7} -10.3967 q^{8} +(-1.14842 - 1.98912i) q^{10} +(-0.500000 - 0.866025i) q^{11} -0.296842 q^{13} +(3.04309 - 6.70095i) q^{14} +(-8.72241 + 15.1077i) q^{16} +(-3.34677 - 5.79677i) q^{17} +(1.41669 - 2.45379i) q^{19} -4.73760 q^{20} -2.78165 q^{22} +(-1.98481 + 3.43779i) q^{23} +(2.15910 + 3.73967i) q^{25} +(-0.412855 + 0.715087i) q^{26} +(-8.83158 - 12.3468i) q^{28} +0.484812 q^{29} +(3.66564 + 6.34907i) q^{31} +(13.8660 + 24.0166i) q^{32} -18.6191 q^{34} +(0.903315 - 1.98912i) q^{35} +(2.86880 - 4.96890i) q^{37} +(-3.94075 - 6.82559i) q^{38} +(-4.29233 + 7.43454i) q^{40} -0.645420 q^{41} +6.43308 q^{43} +(-2.86880 + 4.96890i) q^{44} +(5.52106 + 9.56275i) q^{46} +(3.86880 - 6.70095i) q^{47} +(6.86783 - 1.35386i) q^{49} +12.0117 q^{50} +(0.851579 + 1.47498i) q^{52} +(3.55677 + 6.16050i) q^{53} -0.825711 q^{55} +(-27.3769 + 2.67271i) q^{56} +(0.674289 - 1.16790i) q^{58} +(-0.578495 - 1.00198i) q^{59} +(-2.63323 + 4.56089i) q^{61} +20.3931 q^{62} +42.2513 q^{64} +(-0.122553 + 0.212268i) q^{65} +(-1.50865 - 2.61306i) q^{67} +(-19.2024 + 33.2595i) q^{68} +(-3.53541 - 4.94260i) q^{70} -3.58061 q^{71} +(-8.01625 - 13.8845i) q^{73} +(-7.98000 - 13.8218i) q^{74} -16.2568 q^{76} +(-1.53925 - 2.15191i) q^{77} +(2.16210 - 3.74487i) q^{79} +(7.20219 + 12.4746i) q^{80} +(-0.897667 + 1.55481i) q^{82} -2.37594 q^{83} -5.52693 q^{85} +(8.94729 - 15.4972i) q^{86} +(5.19835 + 9.00380i) q^{88} +(6.08617 - 10.5416i) q^{89} +(-0.781653 + 0.0763099i) q^{91} +22.7761 q^{92} +(-10.7617 - 18.6397i) q^{94} +(-1.16978 - 2.02612i) q^{95} -10.7680 q^{97} +(6.29052 - 18.4275i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} - 24 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 - 24 * q^8	$ 8 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} - 24 q^{8} - 10 q^{10} - 4 q^{11} - 4 q^{13} + 4 q^{14} - 12 q^{16} + 2 q^{17} - 4 q^{22} + 4 q^{23} - 4 q^{25} - 4 q^{26} - 22 q^{28} - 16 q^{29} + 12 q^{31} + 26 q^{32} - 32 q^{34} + 2 q^{35} + 4 q^{37} + 8 q^{38} + 6 q^{40} - 4 q^{41} + 36 q^{43} - 4 q^{44} + 14 q^{46} + 12 q^{47} - 4 q^{49} - 4 q^{50} + 6 q^{52} - 12 q^{53} - 8 q^{55} - 48 q^{56} + 4 q^{58} + 12 q^{59} - 2 q^{61} + 52 q^{62} + 112 q^{64} - 4 q^{65} - 28 q^{67} - 48 q^{68} - 32 q^{70} - 24 q^{71} - 6 q^{73} - 16 q^{74} - 36 q^{76} - 4 q^{77} - 2 q^{79} + 16 q^{80} + 12 q^{82} + 24 q^{83} + 36 q^{85} + 36 q^{86} + 12 q^{88} + 8 q^{89} + 12 q^{91} + 32 q^{92} - 20 q^{94} + 34 q^{95} - 88 q^{97} - 16 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 - 24 * q^8 - 10 * q^10 - 4 * q^11 - 4 * q^13 + 4 * q^14 - 12 * q^16 + 2 * q^17 - 4 * q^22 + 4 * q^23 - 4 * q^25 - 4 * q^26 - 22 * q^28 - 16 * q^29 + 12 * q^31 + 26 * q^32 - 32 * q^34 + 2 * q^35 + 4 * q^37 + 8 * q^38 + 6 * q^40 - 4 * q^41 + 36 * q^43 - 4 * q^44 + 14 * q^46 + 12 * q^47 - 4 * q^49 - 4 * q^50 + 6 * q^52 - 12 * q^53 - 8 * q^55 - 48 * q^56 + 4 * q^58 + 12 * q^59 - 2 * q^61 + 52 * q^62 + 112 * q^64 - 4 * q^65 - 28 * q^67 - 48 * q^68 - 32 * q^70 - 24 * q^71 - 6 * q^73 - 16 * q^74 - 36 * q^76 - 4 * q^77 - 2 * q^79 + 16 * q^80 + 12 * q^82 + 24 * q^83 + 36 * q^85 + 36 * q^86 + 12 * q^88 + 8 * q^89 + 12 * q^91 + 32 * q^92 - 20 * q^94 + 34 * q^95 - 88 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.39083	−	2.40898i	0.983463	−	1.70341i	0.334886	−	0.942259i	$-0.391302\pi$
$2$	1.39083	−	2.40898i	0.983463	−	1.70341i	0.648577	−	0.761149i	$-0.275365\pi$
$3$		0			0
$3$		0			0
$4$	−2.86880	−	4.96890i	−1.43440	−	2.48445i
$5$	0.412855	−	0.715087i	0.184635	−	0.319796i	−0.758819	−	0.651302i	$-0.774223\pi$
$5$	0.412855	−	0.715087i	0.184635	−	0.319796i	0.943453	+	0.331505i	$0.107557\pi$
$6$		0			0
$7$	2.63323	−	0.257073i	0.995268	−	0.0971643i
$7$	2.63323	−	0.257073i	0.995268	−	0.0971643i
$8$	−10.3967			−3.67579
$9$		0			0
$10$	−1.14842	−	1.98912i	−0.363163	−	0.629016i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	−0.296842			−0.0823291			−0.0411645	−	0.999152i	$-0.513107\pi$
$13$	−0.296842			−0.0823291			−0.0411645	+	0.999152i	$0.513107\pi$
$14$	3.04309	−	6.70095i	0.813299	−	1.79091i
$15$		0			0
$16$	−8.72241	+	15.1077i	−2.18060	+	3.77691i
$17$	−3.34677	−	5.79677i	−0.811711	−	1.40592i	−0.911666	−	0.410932i	$-0.865203\pi$
$17$	−3.34677	−	5.79677i	−0.811711	−	1.40592i	0.0999551	−	0.994992i	$-0.468130\pi$
$18$		0			0
$19$	1.41669	−	2.45379i	0.325012	−	0.562937i	−0.656503	−	0.754324i	$-0.727965\pi$
$19$	1.41669	−	2.45379i	0.325012	−	0.562937i	0.981515	+	0.191386i	$0.0612983\pi$
$20$	−4.73760			−1.05936
$21$		0			0
$22$	−2.78165			−0.593051
$23$	−1.98481	+	3.43779i	−0.413862	+	0.716830i	−0.995308	−	0.0967550i	$-0.969154\pi$
$23$	−1.98481	+	3.43779i	−0.413862	+	0.716830i	0.581446	+	0.813585i	$0.302487\pi$
$24$		0			0
$25$	2.15910	+	3.73967i	0.431820	+	0.747934i
$26$	−0.412855	+	0.715087i	−0.0809676	+	0.140240i
$27$		0			0
$28$	−8.83158	−	12.3468i	−1.66901	−	2.33332i
$29$	0.484812			0.0900273			0.0450136	−	0.998986i	$-0.485667\pi$
$29$	0.484812			0.0900273			0.0450136	+	0.998986i	$0.485667\pi$
$30$		0			0
$31$	3.66564	+	6.34907i	0.658368	+	1.14033i	0.981038	+	0.193816i	$0.0620864\pi$
$31$	3.66564	+	6.34907i	0.658368	+	1.14033i	−0.322670	+	0.946512i	$0.604580\pi$
$32$	13.8660	+	24.0166i	2.45119	+	4.24558i
$33$		0			0
$34$	−18.6191			−3.19315
$35$	0.903315	−	1.98912i	0.152688	−	0.336223i
$36$		0			0
$37$	2.86880	−	4.96890i	0.471627	−	0.816883i	−0.527846	−	0.849340i	$-0.677000\pi$
$37$	2.86880	−	4.96890i	0.471627	−	0.816883i	0.999473	+	0.0324576i	$0.0103334\pi$
$38$	−3.94075	−	6.82559i	−0.639275	−	1.10726i
$39$		0			0
$40$	−4.29233	+	7.43454i	−0.678677	+	1.17550i
$41$	−0.645420			−0.100798			−0.0503988	−	0.998729i	$-0.516049\pi$
$41$	−0.645420			−0.100798			−0.0503988	+	0.998729i	$0.516049\pi$
$42$		0			0
$43$	6.43308			0.981035			0.490517	−	0.871431i	$-0.336808\pi$
$43$	6.43308			0.981035			0.490517	+	0.871431i	$0.336808\pi$
$44$	−2.86880	+	4.96890i	−0.432488	+	0.749090i
$45$		0			0
$46$	5.52106	+	9.56275i	0.814036	+	1.40995i
$47$	3.86880	−	6.70095i	0.564322	−	0.977435i	−0.432790	−	0.901495i	$-0.642471\pi$
$47$	3.86880	−	6.70095i	0.564322	−	0.977435i	0.997112	−	0.0759400i	$-0.0241958\pi$
$48$		0			0
$49$	6.86783	−	1.35386i	0.981118	−	0.193409i
$50$	12.0117			1.69872
$51$		0			0
$52$	0.851579	+	1.47498i	0.118093	+	0.204543i
$53$	3.55677	+	6.16050i	0.488560	+	0.846210i	0.999913	−	0.0131602i	$-0.00418914\pi$
$53$	3.55677	+	6.16050i	0.488560	+	0.846210i	−0.511354	+	0.859370i	$0.670856\pi$
$54$		0			0
$55$	−0.825711			−0.111339
$56$	−27.3769	+	2.67271i	−3.65839	+	0.357155i
$57$		0			0
$58$	0.674289	−	1.16790i	0.0885385	−	0.153353i
$59$	−0.578495	−	1.00198i	−0.0753137	−	0.130447i	0.825909	−	0.563803i	$-0.190662\pi$
$59$	−0.578495	−	1.00198i	−0.0753137	−	0.130447i	−0.901223	+	0.433356i	$0.857329\pi$
$60$		0			0
$61$	−2.63323	+	4.56089i	−0.337151	+	0.583962i	−0.983896	−	0.178744i	$-0.942797\pi$
$61$	−2.63323	+	4.56089i	−0.337151	+	0.583962i	0.646745	+	0.762707i	$0.276130\pi$
$62$	20.3931			2.58992
$63$		0			0
$64$	42.2513			5.28141
$65$	−0.122553	+	0.212268i	−0.0152008	+	0.0263286i
$66$		0			0
$67$	−1.50865	−	2.61306i	−0.184311	−	0.319236i	0.759033	−	0.651052i	$-0.225672\pi$
$67$	−1.50865	−	2.61306i	−0.184311	−	0.319236i	−0.943344	+	0.331816i	$0.892339\pi$
$68$	−19.2024	+	33.2595i	−2.32863	+	4.03331i
$69$		0			0
$70$	−3.53541	−	4.94260i	−0.422562	−	0.590753i
$71$	−3.58061			−0.424940			−0.212470	−	0.977168i	$-0.568151\pi$
$71$	−3.58061			−0.424940			−0.212470	+	0.977168i	$0.568151\pi$
$72$		0			0
$73$	−8.01625	−	13.8845i	−0.938231	−	1.62506i	−0.768769	−	0.639527i	$-0.779130\pi$
$73$	−8.01625	−	13.8845i	−0.938231	−	1.62506i	−0.169462	−	0.985537i	$-0.554203\pi$
$74$	−7.98000	−	13.8218i	−0.927656	−	1.60675i
$75$		0			0
$76$	−16.2568			−1.86479
$77$	−1.53925	−	2.15191i	−0.175414	−	0.245233i
$78$		0			0
$79$	2.16210	−	3.74487i	0.243255	−	0.421331i	−0.718384	−	0.695647i	$-0.755118\pi$
$79$	2.16210	−	3.74487i	0.243255	−	0.421331i	0.961640	+	0.274316i	$0.0884513\pi$
$80$	7.20219	+	12.4746i	0.805229	+	1.39470i
$81$		0			0
$82$	−0.897667	+	1.55481i	−0.0991308	+	0.171700i
$83$	−2.37594			−0.260793			−0.130397	−	0.991462i	$-0.541625\pi$
$83$	−2.37594			−0.260793			−0.130397	+	0.991462i	$0.541625\pi$
$84$		0			0
$85$	−5.52693			−0.599480
$86$	8.94729	−	15.4972i	0.964811	−	1.67110i
$87$		0			0
$88$	5.19835	+	9.00380i	0.554146	+	0.959809i
$89$	6.08617	−	10.5416i	0.645133	−	1.11740i	−0.339138	−	0.940737i	$-0.610135\pi$
$89$	6.08617	−	10.5416i	0.645133	−	1.11740i	0.984271	−	0.176667i	$-0.0565314\pi$
$90$		0			0
$91$	−0.781653	+	0.0763099i	−0.0819395	+	0.00799945i
$92$	22.7761			2.37457
$93$		0			0
$94$	−10.7617	−	18.6397i	−1.10998	−	1.92254i
$95$	−1.16978	−	2.02612i	−0.120017	−	0.207875i
$96$		0			0
$97$	−10.7680			−1.09332			−0.546661	−	0.837354i	$-0.684101\pi$
$97$	−10.7680			−1.09332			−0.546661	+	0.837354i	$0.684101\pi$
$98$	6.29052	−	18.4275i	0.635439	−	1.86146i
$99$		0			0
$100$	12.3880	−	21.4567i	1.23880	−	2.14567i
$101$	7.49519	+	12.9821i	0.745799	+	1.29176i	0.949820	+	0.312796i	$0.101266\pi$
$101$	7.49519	+	12.9821i	0.745799	+	1.29176i	−0.204021	+	0.978966i	$0.565401\pi$
$102$		0			0
$103$	1.23203	−	2.13393i	0.121395	−	0.210263i	−0.798923	−	0.601434i	$-0.794596\pi$
$103$	1.23203	−	2.13393i	0.121395	−	0.210263i	0.920318	+	0.391171i	$0.127930\pi$
$104$	3.08617			0.302624
$105$		0			0
$106$	19.7874			1.92192
$107$	−5.79022	+	10.0290i	−0.559762	+	0.969536i	0.437754	+	0.899095i	$0.355774\pi$
$107$	−5.79022	+	10.0290i	−0.559762	+	0.969536i	−0.997516	+	0.0704414i	$0.977559\pi$
$108$		0			0
$109$	2.71173	+	4.69685i	0.259736	+	0.449877i	0.966171	−	0.257901i	$-0.0830310\pi$
$109$	2.71173	+	4.69685i	0.259736	+	0.449877i	−0.706435	+	0.707778i	$0.749698\pi$
$110$	−1.14842	+	1.98912i	−0.109498	+	0.189655i
$111$		0			0
$112$	−19.0844	+	42.0243i	−1.80330	+	3.97092i
$113$	17.5156			1.64773			0.823866	−	0.566785i	$-0.191813\pi$
$113$	17.5156			1.64773			0.823866	+	0.566785i	$0.191813\pi$
$114$		0			0
$115$	1.63888	+	2.83862i	0.152826	+	0.264703i
$116$	−1.39083	−	2.40898i	−0.129135	−	0.223668i
$117$		0			0
$118$	−3.21835			−0.296273
$119$	−10.3030	−	14.4039i	−0.944476	−	1.32040i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	7.32474	+	12.6868i	0.663151	+	1.14861i
$123$		0			0
$124$	21.0320	−	36.4284i	1.88873	−	3.27137i
$125$	7.69414			0.688185
$126$		0			0
$127$	5.97924			0.530572			0.265286	−	0.964170i	$-0.414534\pi$
$127$	5.97924			0.530572			0.265286	+	0.964170i	$0.414534\pi$
$128$	31.0322	−	53.7493i	2.74288	−	4.75081i
$129$		0			0
$130$	0.340899	+	0.590455i	0.0298988	+	0.0517863i
$131$	8.82120	−	15.2788i	0.770712	−	1.33491i	−0.166461	−	0.986048i	$-0.553234\pi$
$131$	8.82120	−	15.2788i	0.770712	−	1.33491i	0.937173	−	0.348864i	$-0.113433\pi$
$132$		0			0
$133$	3.09969	−	6.82559i	0.268777	−	0.591853i
$134$	−8.39308			−0.725052
$135$		0			0
$136$	34.7953	+	60.2673i	2.98368	+	5.16788i
$137$	4.67986	+	8.10575i	0.399827	+	0.692521i	0.993704	−	0.112035i	$-0.0357368\pi$
$137$	4.67986	+	8.10575i	0.399827	+	0.692521i	−0.593877	+	0.804556i	$0.702403\pi$
$138$		0			0
$139$	7.40270			0.627889			0.313944	−	0.949441i	$-0.398349\pi$
$139$	7.40270			0.627889			0.313944	+	0.949441i	$0.398349\pi$
$140$	−12.4752	+	1.21791i	−1.05435	+	0.102932i
$141$		0			0
$142$	−4.98000	+	8.62562i	−0.417912	+	0.723846i
$143$	0.148421	+	0.257073i	0.0124116	+	0.0214975i
$144$		0			0
$145$	0.200157	−	0.346682i	0.0166221	−	0.0287904i
$146$	−44.5968			−3.69086
$147$		0			0
$148$	−32.9200			−2.70601
$149$	−6.00587	+	10.4025i	−0.492020	+	0.852204i	−0.999958	−	0.00919009i	$-0.997075\pi$
$149$	−6.00587	+	10.4025i	−0.492020	+	0.852204i	0.507938	+	0.861394i	$0.330408\pi$
$150$		0			0
$151$	−4.66091	−	8.07293i	−0.379299	−	0.656966i	0.611661	−	0.791120i	$-0.290502\pi$
$151$	−4.66091	−	8.07293i	−0.379299	−	0.656966i	−0.990960	+	0.134154i	$0.957168\pi$
$152$	−14.7289	+	25.5113i	−1.19468	+	2.06924i
$153$		0			0
$154$	−7.32474	+	0.715087i	−0.590244	+	0.0576233i
$155$	6.05352			0.486230
$156$		0			0
$157$	2.55174	+	4.41974i	0.203651	+	0.352733i	0.949702	−	0.313155i	$-0.101386\pi$
$157$	2.55174	+	4.41974i	0.203651	+	0.352733i	−0.746051	+	0.665889i	$0.768053\pi$
$158$	−6.01422	−	10.4169i	−0.478465	−	0.828727i
$159$		0			0
$160$	22.8986			1.81030
$161$	−4.34271	+	9.56275i	−0.342253	+	0.753651i
$162$		0			0
$163$	−4.74413	+	8.21708i	−0.371589	+	0.643612i	−0.989810	−	0.142393i	$-0.954520\pi$
$163$	−4.74413	+	8.21708i	−0.371589	+	0.643612i	0.618221	+	0.786004i	$0.287854\pi$
$164$	1.85158	+	3.20703i	0.144584	+	0.250427i
$165$		0			0
$166$	−3.30452	+	5.72360i	−0.256481	+	0.444237i
$167$	3.03850			0.235126			0.117563	−	0.993065i	$-0.462492\pi$
$167$	3.03850			0.235126			0.117563	+	0.993065i	$0.462492\pi$
$168$		0			0
$169$	−12.9119			−0.993222
$170$	−7.68700	+	13.3143i	−0.589566	+	1.02116i
$171$		0			0
$172$	−18.4552	−	31.9653i	−1.40720	−	2.43733i
$173$	−2.88602	+	4.99873i	−0.219420	+	0.380046i	−0.954631	−	0.297792i	$-0.903750\pi$
$173$	−2.88602	+	4.99873i	−0.219420	+	0.380046i	0.735211	+	0.677838i	$0.237083\pi$
$174$		0			0
$175$	6.64678	+	9.29238i	0.502449	+	0.702438i
$176$	17.4448			1.31495
$177$		0			0
$178$	−16.9296	−	29.3230i	−1.26893	−	2.19785i
$179$	−1.51422	−	2.62270i	−0.113178	−	0.196030i	0.803872	−	0.594802i	$-0.202770\pi$
$179$	−1.51422	−	2.62270i	−0.113178	−	0.196030i	−0.917050	+	0.398772i	$0.869436\pi$
$180$		0			0
$181$	−9.67878			−0.719418			−0.359709	−	0.933064i	$-0.617124\pi$
$181$	−9.67878			−0.719418			−0.359709	+	0.933064i	$0.617124\pi$
$182$	−0.903315	+	1.98912i	−0.0669582	+	0.147444i
$183$		0			0
$184$	20.6355	−	35.7417i	1.52127	−	2.63491i
$185$	−2.36880	−	4.10288i	−0.174157	−	0.301650i
$186$		0			0
$187$	−3.34677	+	5.79677i	−0.244740	+	0.423902i
$188$	−44.3952			−3.23785
$189$		0			0
$190$	−6.50785			−0.472129
$191$	−0.645420	+	1.11790i	−0.0467009	+	0.0808884i	−0.888431	−	0.459010i	$-0.848204\pi$
$191$	−0.645420	+	1.11790i	−0.0467009	+	0.0808884i	0.841730	+	0.539899i	$0.181537\pi$
$192$		0			0
$193$	10.4889	+	18.1673i	0.755006	+	1.30771i	0.945372	+	0.325995i	$0.105699\pi$
$193$	10.4889	+	18.1673i	0.755006	+	1.30771i	−0.190366	+	0.981713i	$0.560967\pi$
$194$	−14.9764	+	25.9399i	−1.07524	+	1.86237i
$195$		0			0
$196$	−26.4296	−	30.2416i	−1.88783	−	2.16012i
$197$	−15.0836			−1.07466			−0.537332	−	0.843371i	$-0.680568\pi$
$197$	−15.0836			−1.07466			−0.537332	+	0.843371i	$0.680568\pi$
$198$		0			0
$199$	12.8601	+	22.2744i	0.911632	+	1.57899i	0.811759	+	0.583992i	$0.198510\pi$
$199$	12.8601	+	22.2744i	0.911632	+	1.57899i	0.0998726	+	0.995000i	$0.468156\pi$
$200$	−22.4475	−	38.8802i	−1.58728	−	2.74925i
$201$		0			0
$202$	41.6980			2.93386
$203$	1.27662	−	0.124632i	0.0896013	−	0.00874743i
$204$		0			0
$205$	−0.266465	+	0.461531i	−0.0186107	+	0.0322347i
$206$	−3.42707	−	5.93587i	−0.238776	−	0.413571i
$207$		0			0
$208$	2.58918	−	4.48458i	0.179527	−	0.310950i
$209$	−2.83339			−0.195990
$210$		0			0
$211$	1.84814			0.127232			0.0636158	−	0.997974i	$-0.479737\pi$
$211$	1.84814			0.127232			0.0636158	+	0.997974i	$0.479737\pi$
$212$	20.4073	−	35.3465i	1.40158	−	2.42761i
$213$		0			0
$214$	16.1064	+	27.8971i	1.10101	+	1.90701i
$215$	2.65593	−	4.60021i	0.181133	−	0.313731i
$216$		0			0
$217$	11.2847	+	15.7763i	0.766052	+	1.07096i
$218$	15.0862			1.02176
$219$		0			0
$220$	2.36880	+	4.10288i	0.159704	+	0.276616i
$221$	0.993461	+	1.72072i	0.0668274	+	0.115748i
$222$		0			0
$223$	−6.17851			−0.413744			−0.206872	−	0.978368i	$-0.566328\pi$
$223$	−6.17851			−0.413744			−0.206872	+	0.978368i	$0.566328\pi$
$224$	42.6865	+	59.6768i	2.85211	+	3.98733i
$225$		0			0
$226$	24.3612	−	42.1949i	1.62048	−	2.80676i
$227$	2.50557	+	4.33977i	0.166300	+	0.288041i	0.937116	−	0.349017i	$-0.113485\pi$
$227$	2.50557	+	4.33977i	0.166300	+	0.288041i	−0.770816	+	0.637058i	$0.780151\pi$
$228$		0			0
$229$	−11.2164	+	19.4274i	−0.741201	+	1.28380i	0.210748	+	0.977540i	$0.432410\pi$
$229$	−11.2164	+	19.4274i	−0.741201	+	1.28380i	−0.951949	+	0.306257i	$0.900923\pi$
$230$	9.11760			0.601197
$231$		0			0
$232$	−5.04044			−0.330921
$233$	2.41669	−	4.18584i	0.158323	−	0.274223i	−0.775941	−	0.630805i	$-0.782725\pi$
$233$	2.41669	−	4.18584i	0.158323	−	0.274223i	0.934264	+	0.356582i	$0.116058\pi$
$234$		0			0
$235$	−3.19451	−	5.53305i	−0.208387	−	0.360937i
$236$	−3.31917	+	5.74897i	−0.216060	+	0.374226i
$237$		0			0
$238$	−49.0284	+	4.78646i	−3.17804	+	0.310260i
$239$	2.58467			0.167188			0.0835941	−	0.996500i	$-0.473360\pi$
$239$	2.58467			0.167188			0.0835941	+	0.996500i	$0.473360\pi$
$240$		0			0
$241$	−1.38902	−	2.40585i	−0.0894745	−	0.154974i	0.817815	−	0.575482i	$-0.195185\pi$
$241$	−1.38902	−	2.40585i	−0.0894745	−	0.154974i	−0.907289	+	0.420507i	$0.861852\pi$
$242$	1.39083	+	2.40898i	0.0894057	+	0.154855i
$243$		0			0
$244$	30.2168			1.93444
$245$	1.86729	−	5.47004i	0.119297	−	0.349468i
$246$		0			0
$247$	−0.420534	+	0.728387i	−0.0267580	+	0.0463461i
$248$	−38.1105	−	66.0094i	−2.42002	−	4.19160i
$249$		0			0
$250$	10.7012	−	18.5351i	0.676804	−	1.17226i
$251$	−0.936967			−0.0591409			−0.0295704	−	0.999563i	$-0.509414\pi$
$251$	−0.936967			−0.0591409			−0.0295704	+	0.999563i	$0.509414\pi$
$252$		0			0
$253$	3.96962			0.249568
$254$	8.31609	−	14.4039i	0.521798	−	0.903781i
$255$		0			0
$256$	−44.0695	−	76.3306i	−2.75434	−	4.77066i
$257$	−9.01714	+	15.6181i	−0.562474	+	0.974233i	0.434806	+	0.900524i	$0.356817\pi$
$257$	−9.01714	+	15.6181i	−0.562474	+	0.974233i	−0.997280	+	0.0737089i	$0.976516\pi$
$258$		0			0
$259$	6.27684	−	13.8218i	0.390024	−	0.858843i
$260$	1.40632			0.0872160
$261$		0			0
$262$	−24.5375	−	42.5002i	−1.51593	−	2.62567i
$263$	3.94826	+	6.83859i	0.243460	+	0.421686i	0.961698	−	0.274113i	$-0.0883841\pi$
$263$	3.94826	+	6.83859i	0.243460	+	0.421686i	−0.718237	+	0.695798i	$0.755051\pi$
$264$		0			0
$265$	5.87372			0.360820
$266$	−12.1316	−	16.9603i	−0.743836	−	1.03990i
$267$		0			0
$268$	−8.65602	+	14.9927i	−0.528751	+	0.915823i
$269$	8.60850	+	14.9104i	0.524870	+	0.909101i	0.999581	+	0.0289593i	$0.00921931\pi$
$269$	8.60850	+	14.9104i	0.524870	+	0.909101i	−0.474711	+	0.880142i	$0.657447\pi$
$270$		0			0
$271$	4.66767	−	8.08464i	0.283541	−	0.491107i	−0.688713	−	0.725034i	$-0.741824\pi$
$271$	4.66767	−	8.08464i	0.283541	−	0.491107i	0.972254	+	0.233927i	$0.0751575\pi$
$272$	116.768			7.08007
$273$		0			0
$274$	26.0355			1.57286
$275$	2.15910	−	3.73967i	0.130199	−	0.225511i
$276$		0			0
$277$	−2.73760	−	4.74166i	−0.164486	−	0.284898i	0.771987	−	0.635639i	$-0.219263\pi$
$277$	−2.73760	−	4.74166i	−0.164486	−	0.284898i	−0.936473	+	0.350740i	$0.885930\pi$
$278$	10.2959	−	17.8330i	0.617505	−	1.06955i
$279$		0			0
$280$	−9.39150	+	20.6803i	−0.561249	+	1.23589i
$281$	18.3501			1.09467			0.547337	−	0.836912i	$-0.315641\pi$
$281$	18.3501			1.09467			0.547337	+	0.836912i	$0.315641\pi$
$282$		0			0
$283$	−13.0203	−	22.5518i	−0.773977	−	1.34057i	−0.935368	−	0.353677i	$-0.884931\pi$
$283$	−13.0203	−	22.5518i	−0.773977	−	1.34057i	0.161391	−	0.986891i	$-0.448402\pi$
$284$	10.2720	+	17.7917i	0.609533	+	1.05574i
$285$		0			0
$286$	0.825711			0.0488253
$287$	−1.69954	+	0.165920i	−0.100321	+	0.00979393i
$288$		0			0
$289$	−13.9017	+	24.0785i	−0.817749	+	1.41638i
$290$	−0.556768	−	0.964350i	−0.0326945	−	0.0566286i
$291$		0			0
$292$	−45.9940	+	79.6639i	−2.69159	+	4.66198i
$293$	−21.3317			−1.24621			−0.623106	−	0.782137i	$-0.714130\pi$
$293$	−21.3317			−1.24621			−0.623106	+	0.782137i	$0.714130\pi$
$294$		0			0
$295$	−0.955340			−0.0556220
$296$	−29.8260	+	51.6602i	−1.73360	+	3.00269i
$297$		0			0
$298$	16.7062	+	28.9361i	0.967767	+	1.67622i
$299$	0.589175	−	1.02048i	0.0340729	−	0.0590159i
$300$		0			0
$301$	16.9398	−	1.65377i	0.976393	−	0.0953215i
$302$	−25.9301			−1.49211
$303$		0			0
$304$	24.7140	+	42.8059i	1.41744	+	2.45508i
$305$	2.17429	+	3.76598i	0.124499	+	0.215639i
$306$		0			0
$307$	−6.88329			−0.392850			−0.196425	−	0.980519i	$-0.562933\pi$
$307$	−6.88329			−0.392850			−0.196425	+	0.980519i	$0.562933\pi$
$308$	−6.27684	+	13.8218i	−0.357656	+	0.787568i
$309$		0			0
$310$	8.41939	−	14.5828i	0.478189	−	0.828248i
$311$	−1.89864	−	3.28854i	−0.107662	−	0.186476i	0.807161	−	0.590332i	$-0.201003\pi$
$311$	−1.89864	−	3.28854i	−0.107662	−	0.186476i	−0.914823	+	0.403856i	$0.867670\pi$
$312$		0			0
$313$	−1.30955	+	2.26821i	−0.0740203	+	0.128207i	−0.900660	−	0.434525i	$-0.856916\pi$
$313$	−1.30955	+	2.26821i	−0.0740203	+	0.128207i	0.826640	+	0.562732i	$0.190250\pi$
$314$	14.1961			0.801132
$315$		0			0
$316$	−24.8105			−1.39570
$317$	−13.9321	+	24.1311i	−0.782505	+	1.35534i	0.147973	+	0.988991i	$0.452725\pi$
$317$	−13.9321	+	24.1311i	−0.782505	+	1.35534i	−0.930478	+	0.366347i	$0.880608\pi$
$318$		0			0
$319$	−0.242406	−	0.419859i	−0.0135721	−	0.0235076i
$320$	17.4437	−	30.2133i	0.975131	−	1.68898i
$321$		0			0
$322$	16.9966	+	23.7616i	0.947181	+	1.32418i
$323$	−18.9654			−1.05526
$324$		0			0
$325$	−0.640911	−	1.11009i	−0.0355514	−	0.0615768i
$326$	13.1965	+	22.8571i	0.730889	+	1.26594i
$327$		0			0
$328$	6.71023			0.370511
$329$	8.46481	−	18.6397i	0.466680	−	1.02764i
$330$		0			0
$331$	4.02076	−	6.96416i	0.221001	−	0.382785i	−0.734111	−	0.679029i	$-0.762401\pi$
$331$	4.02076	−	6.96416i	0.221001	−	0.382785i	0.955112	+	0.296245i	$0.0957343\pi$
$332$	6.81609	+	11.8058i	0.374082	+	0.647928i
$333$		0			0
$334$	4.22603	−	7.31969i	0.231238	−	0.400516i
$335$	−2.49142			−0.136121
$336$		0			0
$337$	26.2686			1.43094			0.715471	−	0.698643i	$-0.246212\pi$
$337$	26.2686			1.43094			0.715471	+	0.698643i	$0.246212\pi$
$338$	−17.9582	+	31.1045i	−0.976797	+	1.69186i
$339$		0			0
$340$	15.8556	+	27.4628i	0.859893	+	1.48938i
$341$	3.66564	−	6.34907i	0.198506	−	0.343822i
$342$		0			0
$343$	17.7365	−	5.33057i	0.957683	−	0.287824i
$344$	−66.8827			−3.60608
$345$		0			0
$346$	8.02790	+	13.9047i	0.431583	+	0.747523i
$347$	4.24421	+	7.35120i	0.227841	+	0.394633i	0.957168	−	0.289533i	$-0.0934999\pi$
$347$	4.24421	+	7.35120i	0.227841	+	0.394633i	−0.729327	+	0.684166i	$0.760167\pi$
$348$		0			0
$349$	−31.9290			−1.70912			−0.854561	−	0.519351i	$-0.826174\pi$
$349$	−31.9290			−1.70912			−0.854561	+	0.519351i	$0.826174\pi$
$350$	31.6297	−	3.08789i	1.69068	−	0.165055i
$351$		0			0
$352$	13.8660	−	24.0166i	0.739061	−	1.28009i
$353$	0.0719562	+	0.124632i	0.00382984	+	0.00663348i	0.867934	−	0.496680i	$-0.165448\pi$
$353$	0.0719562	+	0.124632i	0.00382984	+	0.00663348i	−0.864104	+	0.503313i	$0.832114\pi$
$354$		0			0
$355$	−1.47827	+	2.56044i	−0.0784586	+	0.135894i
$356$	−69.8400			−3.70151
$357$		0			0
$358$	−8.42406			−0.445225
$359$	4.11744	−	7.13162i	0.217310	−	0.376392i	−0.736675	−	0.676247i	$-0.763605\pi$
$359$	4.11744	−	7.13162i	0.217310	−	0.376392i	0.953985	+	0.299855i	$0.0969383\pi$
$360$		0			0
$361$	5.48595	+	9.50195i	0.288734	+	0.500102i
$362$	−13.4615	+	23.3160i	−0.707521	+	1.22546i
$363$		0			0
$364$	2.62158	+	3.66504i	0.137408	+	0.192100i
$365$	−13.2382			−0.692919
$366$		0			0
$367$	−8.31512	−	14.4022i	−0.434046	−	0.751789i	0.563171	−	0.826340i	$-0.309581\pi$
$367$	−8.31512	−	14.4022i	−0.434046	−	0.751789i	−0.997217	+	0.0745508i	$0.976248\pi$
$368$	−34.6247	−	59.9717i	−1.80494	−	3.12624i
$369$		0			0
$370$	−13.1784			−0.685110
$371$	10.9495	+	15.3077i	0.568469	+	0.794736i
$372$		0			0
$373$	2.56242	−	4.43823i	0.132677	−	0.229803i	−0.792031	−	0.610481i	$-0.790976\pi$
$373$	2.56242	−	4.43823i	0.132677	−	0.229803i	0.924708	+	0.380678i	$0.124309\pi$
$374$	9.30955	+	16.1246i	0.481385	+	0.833784i
$375$		0			0
$376$	−40.2227	+	69.6678i	−2.07433	+	3.59284i
$377$	−0.143912			−0.00741186
$378$		0			0
$379$	−19.6383			−1.00875			−0.504377	−	0.863484i	$-0.668278\pi$
$379$	−19.6383			−1.00875			−0.504377	+	0.863484i	$0.668278\pi$
$380$	−6.71173	+	11.6251i	−0.344304	+	0.596353i
$381$		0			0
$382$	1.79533	+	3.10961i	0.0918573	+	0.159102i
$383$	−5.38513	+	9.32731i	−0.275167	+	0.476603i	−0.970177	−	0.242397i	$-0.922067\pi$
$383$	−5.38513	+	9.32731i	−0.275167	+	0.476603i	0.695010	+	0.719000i	$0.255400\pi$
$384$		0			0
$385$	−2.17429	+	0.212268i	−0.110812	+	0.0108182i
$386$	58.3528			2.97008
$387$		0			0
$388$	30.8911	+	53.5050i	1.56826	+	2.71631i
$389$	16.3394	+	28.3007i	0.828441	+	1.43490i	0.899261	+	0.437412i	$0.144105\pi$
$389$	16.3394	+	28.3007i	0.828441	+	1.43490i	−0.0708206	+	0.997489i	$0.522562\pi$
$390$		0			0
$391$	26.5708			1.34374
$392$	−71.4027	+	14.0757i	−3.60638	+	0.710931i
$393$		0			0
$394$	−20.9787	+	36.3362i	−1.05689	+	1.83059i
$395$	−1.78527	−	3.09218i	−0.0898267	−	0.155584i
$396$		0			0
$397$	16.4742	−	28.5342i	0.826817	−	1.43209i	−0.0737049	−	0.997280i	$-0.523482\pi$
$397$	16.4742	−	28.5342i	0.826817	−	1.43209i	0.900522	−	0.434810i	$-0.143184\pi$
$398$	71.5450			3.58622
$399$		0			0
$400$	−75.3302			−3.76651
$401$	−9.67932	+	16.7651i	−0.483362	+	0.837208i	−0.999817	−	0.0191063i	$-0.993918\pi$
$401$	−9.67932	+	16.7651i	−0.483362	+	0.837208i	0.516455	+	0.856314i	$0.327251\pi$
$402$		0			0
$403$	−1.08812	−	1.88467i	−0.0542029	−	0.0938821i
$404$	43.0044	−	74.4858i	2.13955	−	3.70580i
$405$		0			0
$406$	1.47532	−	3.24870i	0.0732191	−	0.161230i
$407$	−5.73760			−0.284402
$408$		0			0
$409$	15.0573	+	26.0800i	0.744535	+	1.28957i	0.950412	+	0.310995i	$0.100662\pi$
$409$	15.0573	+	26.0800i	0.744535	+	1.28957i	−0.205877	+	0.978578i	$0.566005\pi$
$410$	0.741214	+	1.28382i	0.0366059	+	0.0634033i
$411$		0			0
$412$	−14.1378			−0.696517
$413$	−1.78089	−	2.48974i	−0.0876321	−	0.122512i
$414$		0			0
$415$	−0.980920	+	1.69900i	−0.0481515	+	0.0834008i
$416$	−4.11601	−	7.12914i	−0.201804	−	0.349535i
$417$		0			0
$418$	−3.94075	+	6.82559i	−0.192749	+	0.333850i
$419$	2.70722			0.132256			0.0661282	−	0.997811i	$-0.478935\pi$
$419$	2.70722			0.132256			0.0661282	+	0.997811i	$0.478935\pi$
$420$		0			0
$421$	−30.1501			−1.46943			−0.734713	−	0.678378i	$-0.762683\pi$
$421$	−30.1501			−1.46943			−0.734713	+	0.678378i	$0.762683\pi$
$422$	2.57045	−	4.45215i	0.125127	−	0.216727i
$423$		0			0
$424$	−36.9786	−	64.0489i	−1.79584	−	3.11049i
$425$	14.4520	−	25.0316i	0.701026	−	1.21421i
$426$		0			0
$427$	−5.76143	+	12.6868i	−0.278815	+	0.613958i
$428$	66.4439			3.21169
$429$		0			0
$430$	−7.38788	−	12.7962i	−0.356275	−	0.617087i
$431$	16.3405	+	28.3025i	0.787092	+	1.36328i	0.927741	+	0.373224i	$0.121748\pi$
$431$	16.3405	+	28.3025i	0.787092	+	1.36328i	−0.140650	+	0.990059i	$0.544919\pi$
$432$		0			0
$433$	−26.2432			−1.26117			−0.630583	−	0.776122i	$-0.717184\pi$
$433$	−26.2432			−1.26117			−0.630583	+	0.776122i	$0.717184\pi$
$434$	53.6997	−	5.24250i	2.57767	−	0.251648i
$435$		0			0
$436$	15.5588	−	26.9486i	0.745131	−	1.29061i
$437$	5.62374	+	9.74061i	0.269020	+	0.465957i
$438$		0			0
$439$	13.8453	−	23.9807i	0.660798	−	1.14454i	−0.319608	−	0.947550i	$-0.603551\pi$
$439$	13.8453	−	23.9807i	0.660798	−	1.14454i	0.980406	−	0.196986i	$-0.0631155\pi$
$440$	8.58467			0.409258
$441$		0			0
$442$	5.52693			0.262889
$443$	−10.4469	+	18.0946i	−0.496348	+	0.859701i	−0.999991	−	0.00421138i	$-0.998659\pi$
$443$	−10.4469	+	18.0946i	−0.496348	+	0.859701i	0.503643	+	0.863912i	$0.331993\pi$
$444$		0			0
$445$	−5.02542	−	8.70428i	−0.238228	−	0.412623i
$446$	−8.59324	+	14.8839i	−0.406902	+	0.704774i
$447$		0			0
$448$	111.257	−	10.8616i	5.25642	−	0.513164i
$449$	−23.9615			−1.13081			−0.565407	−	0.824812i	$-0.691281\pi$
$449$	−23.9615			−1.13081			−0.565407	+	0.824812i	$0.691281\pi$
$450$		0			0
$451$	0.322710	+	0.558950i	0.0151958	+	0.0263199i
$452$	−50.2488	−	87.0335i	−2.36351	−	4.09371i
$453$		0			0
$454$	13.9392			0.654201
$455$	−0.268142	+	0.590455i	−0.0125707	+	0.0276810i
$456$		0			0
$457$	−9.30541	+	16.1174i	−0.435289	+	0.753942i	−0.997319	−	0.0731743i	$-0.976687\pi$
$457$	−9.30541	+	16.1174i	−0.435289	+	0.753942i	0.562030	+	0.827117i	$0.310020\pi$
$458$	31.2002	+	54.0403i	1.45789	+	2.52514i
$459$		0			0
$460$	9.40324	−	16.2869i	0.438428	−	0.759380i
$461$	6.88513			0.320672			0.160336	−	0.987062i	$-0.448742\pi$
$461$	6.88513			0.320672			0.160336	+	0.987062i	$0.448742\pi$
$462$		0			0
$463$	2.73532			0.127121			0.0635605	−	0.997978i	$-0.479754\pi$
$463$	2.73532			0.127121			0.0635605	+	0.997978i	$0.479754\pi$
$464$	−4.22872	+	7.32437i	−0.196314	+	0.340025i
$465$		0			0
$466$	−6.72241	−	11.6436i	−0.311410	−	0.539377i
$467$	17.8180	−	30.8618i	0.824521	−	1.42811i	−0.0777644	−	0.996972i	$-0.524778\pi$
$467$	17.8180	−	30.8618i	0.824521	−	1.42811i	0.902285	−	0.431140i	$-0.141888\pi$
$468$		0			0
$469$	−4.64437	−	6.49296i	−0.214457	−	0.299817i
$470$	−17.7720			−0.819763
$471$		0			0
$472$	6.01444	+	10.4173i	0.276837	+	0.479496i
$473$	−3.21654	−	5.57121i	−0.147897	−	0.256164i
$474$		0			0
$475$	12.2351			0.561387
$476$	−42.0143	+	92.5165i	−1.92572	+	4.24049i
$477$		0			0
$478$	3.59482	−	6.22642i	0.164423	−	0.284790i
$479$	−13.6899	−	23.7116i	−0.625508	−	1.08341i	−0.988442	−	0.151598i	$-0.951558\pi$
$479$	−13.6899	−	23.7116i	−0.625508	−	1.08341i	0.362934	−	0.931815i	$-0.381775\pi$
$480$		0			0
$481$	−0.851579	+	1.47498i	−0.0388287	+	0.0672532i
$482$	−7.72753			−0.351979
$483$		0			0
$484$	5.73760			0.260800
$485$	−4.44562	+	7.70003i	−0.201865	+	0.349641i
$486$		0			0
$487$	−14.6853	−	25.4357i	−0.665455	−	1.15260i	−0.979162	−	0.203083i	$-0.934904\pi$
$487$	−14.6853	−	25.4357i	−0.665455	−	1.15260i	0.313706	−	0.949520i	$-0.398429\pi$
$488$	27.3769	−	47.4182i	1.23929	−	2.14652i
$489$		0			0
$490$	−10.5802	−	12.1062i	−0.477963	−	0.546900i
$491$	1.69115			0.0763207			0.0381604	−	0.999272i	$-0.487850\pi$
$491$	1.69115			0.0763207			0.0381604	+	0.999272i	$0.487850\pi$
$492$		0			0
$493$	−1.62255	−	2.81034i	−0.0730761	−	0.126572i
$494$	1.16978	+	2.02612i	0.0526309	+	0.0911594i
$495$		0			0
$496$	−127.893			−5.74256
$497$	−9.42857	+	0.920475i	−0.422929	+	0.0412890i
$498$		0			0
$499$	−14.7983	+	25.6313i	−0.662461	+	1.14742i	0.317506	+	0.948256i	$0.397155\pi$
$499$	−14.7983	+	25.6313i	−0.662461	+	1.14742i	−0.979967	+	0.199160i	$0.936179\pi$
$500$	−22.0729	−	38.2314i	−0.987132	−	1.70976i
$501$		0			0
$502$	−1.30316	+	2.25714i	−0.0581628	+	0.100741i
$503$	−28.2737			−1.26066			−0.630331	−	0.776326i	$-0.717081\pi$
$503$	−28.2737			−1.26066			−0.630331	+	0.776326i	$0.717081\pi$
$504$		0			0
$505$	12.3777			0.550801
$506$	5.52106	−	9.56275i	0.245441	−	0.425116i
$507$		0			0
$508$	−17.1532	−	29.7103i	−0.761052	−	1.31818i
$509$	5.45037	−	9.44032i	0.241584	−	0.418435i	−0.719582	−	0.694408i	$-0.755667\pi$
$509$	5.45037	−	9.44032i	0.241584	−	0.418435i	0.961166	+	0.275972i	$0.0889999\pi$
$510$		0			0
$511$	−24.6780	−	34.5005i	−1.09169	−	1.52621i
$512$	−121.043			−5.34941
$513$		0			0
$514$	25.0826	+	43.4443i	1.10634	+	1.91624i
$515$	−1.01730	−	1.76201i	−0.0448275	−	0.0776436i
$516$		0			0
$517$	−7.73760			−0.340299
$518$	−24.5664	−	34.3445i	−1.07939	−	1.50901i
$519$		0			0
$520$	1.27414	−	2.20688i	0.0558749	−	0.0967782i
$521$	2.81803	+	4.88098i	0.123460	+	0.213839i	0.921130	−	0.389255i	$-0.127268\pi$
$521$	2.81803	+	4.88098i	0.123460	+	0.213839i	−0.797670	+	0.603094i	$0.793934\pi$
$522$		0			0
$523$	13.4113	−	23.2290i	0.586434	−	1.01573i	−0.408261	−	0.912865i	$-0.633865\pi$
$523$	13.4113	−	23.2290i	0.586434	−	1.01573i	0.994695	−	0.102868i	$-0.0328019\pi$
$524$	−101.225			−4.42203
$525$		0			0
$526$	21.9654			0.957737
$527$	24.5361	−	42.4978i	1.06881	−	1.85123i
$528$		0			0
$529$	3.62105	+	6.27183i	0.157437	+	0.272688i
$530$	8.16933	−	14.1497i	0.354853	−	0.614624i
$531$		0			0
$532$	−42.8081	+	4.17919i	−1.85596	+	0.181191i
$533$	0.191588			0.00829858
$534$		0			0
$535$	4.78105	+	8.28102i	0.206703	+	0.358020i
$536$	15.6850	+	27.1672i	0.677487	+	1.17344i
$537$		0			0
$538$	47.8918			2.06476
$539$	−4.60639	−	5.27078i	−0.198411	−	0.227029i
$540$		0			0
$541$	−3.03355	+	5.25426i	−0.130422	+	0.225898i	−0.923839	−	0.382780i	$-0.874967\pi$
$541$	−3.03355	+	5.25426i	−0.130422	+	0.225898i	0.793417	+	0.608678i	$0.208300\pi$
$542$	−12.9838	−	22.4887i	−0.557704	−	0.965971i
$543$		0			0
$544$	92.8127	−	160.756i	3.97931	−	6.89237i
$545$	4.47821			0.191825
$546$		0			0
$547$	−13.7115			−0.586263			−0.293132	−	0.956072i	$-0.594697\pi$
$547$	−13.7115			−0.586263			−0.293132	+	0.956072i	$0.594697\pi$
$548$	26.8511	−	46.5075i	1.14702	−	1.98670i
$549$		0			0
$550$	−6.00587	−	10.4025i	−0.256091	−	0.443563i
$551$	0.686830	−	1.18962i	0.0292600	−	0.0506797i
$552$		0			0
$553$	4.73061	−	10.4169i	0.201166	−	0.442973i
$554$	−15.2301			−0.647064
$555$		0			0
$556$	−21.2368	−	36.7833i	−0.900643	−	1.55996i
$557$	−5.54782	−	9.60910i	−0.235069	−	0.407151i	0.724224	−	0.689565i	$-0.242198\pi$
$557$	−5.54782	−	9.60910i	−0.235069	−	0.407151i	−0.959293	+	0.282414i	$0.908865\pi$
$558$		0			0
$559$	−1.90961			−0.0807677
$560$	22.1719	+	30.9969i	0.936934	+	1.30986i
$561$		0			0
$562$	25.5218	−	44.2051i	1.07657	−	1.86468i
$563$	2.17578	+	3.76857i	0.0916983	+	0.158826i	0.908226	−	0.418480i	$-0.137437\pi$
$563$	2.17578	+	3.76857i	0.0916983	+	0.158826i	−0.816528	+	0.577306i	$0.804104\pi$
$564$		0			0
$565$	7.23142	−	12.5252i	0.304228	−	0.526939i
$566$	−72.4360			−3.04471
$567$		0			0
$568$	37.2265			1.56199
$569$	4.57112	−	7.91741i	0.191631	−	0.331915i	−0.754160	−	0.656691i	$-0.771956\pi$
$569$	4.57112	−	7.91741i	0.191631	−	0.331915i	0.945791	+	0.324776i	$0.105289\pi$
$570$		0			0
$571$	−2.38226	−	4.12619i	−0.0996944	−	0.172676i	0.811864	−	0.583847i	$-0.198453\pi$
$571$	−2.38226	−	4.12619i	−0.0996944	−	0.172676i	−0.911558	+	0.411171i	$0.865120\pi$
$572$	0.851579	−	1.47498i	0.0356063	−	0.0616719i
$573$		0			0
$574$	−1.96407	+	4.32493i	−0.0819786	+	0.180519i
$575$	−17.1416			−0.714856
$576$		0			0
$577$	8.80479	+	15.2504i	0.366548	+	0.634880i	0.989023	−	0.147759i	$-0.0472061\pi$
$577$	8.80479	+	15.2504i	0.366548	+	0.634880i	−0.622475	+	0.782640i	$0.713873\pi$
$578$	38.6698	+	66.9780i	1.60845	+	2.78592i
$579$		0			0
$580$	−2.29684			−0.0953712
$581$	−6.25640	+	0.610789i	−0.259559	+	0.0253398i
$582$		0			0
$583$	3.55677	−	6.16050i	0.147306	−	0.255142i
$584$	83.3425	+	144.353i	3.44874	+	5.97339i
$585$		0			0
$586$	−29.6687	+	51.3877i	−1.22560	+	2.12281i
$587$	−33.3405			−1.37611			−0.688054	−	0.725659i	$-0.741535\pi$
$587$	−33.3405			−1.37611			−0.688054	+	0.725659i	$0.741535\pi$
$588$		0			0
$589$	20.7724			0.855911
$590$	−1.32871	+	2.30140i	−0.0547022	+	0.0947470i
$591$		0			0
$592$	50.0457	+	86.6816i	2.05686	+	3.56259i
$593$	−1.86707	+	3.23386i	−0.0766713	+	0.132799i	−0.901812	−	0.432129i	$-0.857763\pi$
$593$	−1.86707	+	3.23386i	−0.0766713	+	0.132799i	0.825141	+	0.564928i	$0.191096\pi$
$594$		0			0
$595$	−14.5537	+	1.42082i	−0.596643	+	0.0582480i
$596$	68.9185			2.82301
$597$		0			0
$598$	−1.63888	−	2.83862i	−0.0670188	−	0.116080i
$599$	7.08256	+	12.2673i	0.289385	+	0.501230i	0.973663	−	0.227991i	$-0.0732158\pi$
$599$	7.08256	+	12.2673i	0.289385	+	0.501230i	−0.684278	+	0.729221i	$0.739882\pi$
$600$		0			0
$601$	−18.3032			−0.746602			−0.373301	−	0.927710i	$-0.621774\pi$
$601$	−18.3032			−0.746602			−0.373301	+	0.927710i	$0.621774\pi$
$602$	19.5764	−	43.1077i	0.797875	−	1.75694i
$603$		0			0
$604$	−26.7424	+	46.3192i	−1.08813	+	1.88470i
$605$	0.412855	+	0.715087i	0.0167850	+	0.0290724i
$606$		0			0
$607$	22.6313	−	39.1985i	0.918576	−	1.59102i	0.116996	−	0.993132i	$-0.462674\pi$
$607$	22.6313	−	39.1985i	0.918576	−	1.59102i	0.801580	−	0.597888i	$-0.203993\pi$
$608$	78.5757			3.18666
$609$		0			0
$610$	12.0962			0.489762
$611$	−1.14842	+	1.98912i	−0.0464601	+	0.0804713i
$612$		0			0
$613$	7.28722	+	12.6218i	0.294328	+	0.509791i	0.974828	−	0.222957i	$-0.0715708\pi$
$613$	7.28722	+	12.6218i	0.294328	+	0.509791i	−0.680500	+	0.732748i	$0.738237\pi$
$614$	−9.57346	+	16.5817i	−0.386354	+	0.669184i
$615$		0			0
$616$	16.0031	+	22.3728i	0.644783	+	0.901424i
$617$	39.8257			1.60332			0.801662	−	0.597778i	$-0.203950\pi$
$617$	39.8257			1.60332			0.801662	+	0.597778i	$0.203950\pi$
$618$		0			0
$619$	0.218883	+	0.379117i	0.00879767	+	0.0152380i	0.870391	−	0.492362i	$-0.163866\pi$
$619$	0.218883	+	0.379117i	0.00879767	+	0.0152380i	−0.861593	+	0.507600i	$0.830533\pi$
$620$	−17.3663	−	30.0793i	−0.697448	−	1.20802i
$621$		0			0
$622$	−10.5627			−0.423526
$623$	13.3164	−	29.3230i	0.533509	−	1.17480i
$624$		0			0
$625$	−7.61894	+	13.1964i	−0.304757	+	0.527855i
$626$	3.64272	+	6.30938i	0.145592	+	0.252173i
$627$		0			0
$628$	14.6408	−	25.3587i	0.584233	−	1.01192i
$629$	−38.4048			−1.53130
$630$		0			0
$631$	29.1632			1.16097			0.580484	−	0.814272i	$-0.302863\pi$
$631$	29.1632			1.16097			0.580484	+	0.814272i	$0.302863\pi$
$632$	−22.4787	+	38.9343i	−0.894155	+	1.54872i
$633$		0			0
$634$	38.7543	+	67.1244i	1.53913	+	2.66585i
$635$	2.46856	−	4.27568i	0.0979619	−	0.169675i
$636$		0			0
$637$	−2.03866	+	0.401883i	−0.0807746	+	0.0159232i
$638$	−1.34858			−0.0533907
$639$		0			0
$640$	−25.6236	−	44.3814i	−1.01286	−	1.75433i
$641$	−2.69300	−	4.66442i	−0.106367	−	0.184233i	0.807929	−	0.589280i	$-0.200589\pi$
$641$	−2.69300	−	4.66442i	−0.106367	−	0.184233i	−0.914296	+	0.405047i	$0.867255\pi$
$642$		0			0
$643$	−2.19971			−0.0867481			−0.0433740	−	0.999059i	$-0.513811\pi$
$643$	−2.19971			−0.0867481			−0.0433740	+	0.999059i	$0.513811\pi$
$644$	59.9748	−	5.85511i	2.36334	−	0.230724i
$645$		0			0
$646$	−26.3776	+	45.6873i	−1.03781	+	1.79754i
$647$	−8.62105	−	14.9321i	−0.338928	−	0.587041i	0.645303	−	0.763927i	$-0.276731\pi$
$647$	−8.62105	−	14.9321i	−0.338928	−	0.587041i	−0.984231	+	0.176886i	$0.943398\pi$
$648$		0			0
$649$	−0.578495	+	1.00198i	−0.0227079	+	0.0393313i
$650$	−3.56559			−0.139854
$651$		0			0
$652$	54.4399			2.13203
$653$	20.3835	−	35.3052i	0.797666	−	1.38160i	−0.123466	−	0.992349i	$-0.539401\pi$
$653$	20.3835	−	35.3052i	0.797666	−	1.38160i	0.921132	−	0.389250i	$-0.127266\pi$
$654$		0			0
$655$	−7.28376	−	12.6158i	−0.284600	−	0.492942i
$656$	5.62961	−	9.75078i	0.219800	−	0.380704i
$657$		0			0
$658$	−33.1297	−	46.3162i	−1.29153	−	1.80559i
$659$	−33.9747			−1.32347			−0.661734	−	0.749739i	$-0.730179\pi$
$659$	−33.9747			−1.32347			−0.661734	+	0.749739i	$0.730179\pi$
$660$		0			0
$661$	14.9579	+	25.9078i	0.581795	+	1.00770i	0.995267	+	0.0971811i	$0.0309826\pi$
$661$	14.9579	+	25.9078i	0.581795	+	1.00770i	−0.413472	+	0.910517i	$0.635684\pi$
$662$	−11.1844	−	19.3719i	−0.434692	−	0.752909i
$663$		0			0
$664$	24.7019			0.958621
$665$	−3.60116	−	5.03452i	−0.139647	−	0.195230i
$666$		0			0
$667$	−0.962260	+	1.66668i	−0.0372589	+	0.0645342i
$668$	−8.71684	−	15.0980i	−0.337265	−	0.584159i
$669$		0			0
$670$	−3.46513	+	6.00178i	−0.133870	+	0.231869i
$671$	5.26647			0.203310
$672$		0			0
$673$	11.3711			0.438325			0.219163	−	0.975688i	$-0.429667\pi$
$673$	11.3711			0.438325			0.219163	+	0.975688i	$0.429667\pi$
$674$	36.5351	−	63.2806i	1.40728	−	2.43748i
$675$		0			0
$676$	37.0416	+	64.1579i	1.42468	+	2.46761i
$677$	4.85596	−	8.41076i	0.186630	−	0.323252i	−0.757495	−	0.652841i	$-0.773577\pi$
$677$	4.85596	−	8.41076i	0.186630	−	0.323252i	0.944124	+	0.329589i	$0.106910\pi$
$678$		0			0
$679$	−28.3546	+	2.76815i	−1.08815	+	0.106232i
$680$	57.4618			2.20356
$681$		0			0
$682$	−10.1965	−	17.6609i	−0.390446	−	0.676272i
$683$	4.85512	+	8.40931i	0.185776	+	0.321773i	0.943838	−	0.330409i	$-0.107187\pi$
$683$	4.85512	+	8.40931i	0.185776	+	0.321773i	−0.758062	+	0.652183i	$0.773853\pi$
$684$		0			0
$685$	7.72842			0.295288
$686$	11.8272	−	50.1409i	0.451565	−	1.91439i
$687$		0			0
$688$	−56.1119	+	97.1887i	−2.13925	+	3.70528i
$689$	−1.05580	−	1.82869i	−0.0402227	−	0.0696677i
$690$		0			0
$691$	1.96902	−	3.41044i	0.0749051	−	0.129739i	−0.826140	−	0.563465i	$-0.809468\pi$
$691$	1.96902	−	3.41044i	0.0749051	−	0.129739i	0.901045	+	0.433726i	$0.142801\pi$
$692$	33.1176			1.25894
$693$		0			0
$694$	23.6119			0.896294
$695$	3.05624	−	5.29357i	0.115930	−	0.200797i
$696$		0			0
$697$	2.16007	+	3.74135i	0.0818185	+	0.141714i
$698$	−44.4077	+	76.9165i	−1.68086	+	2.91133i
$699$		0			0
$700$	27.1047	−	59.6852i	1.02446	−	2.25589i
$701$	−11.7432			−0.443533			−0.221766	−	0.975100i	$-0.571182\pi$
$701$	−11.7432			−0.443533			−0.221766	+	0.975100i	$0.571182\pi$
$702$		0			0
$703$	−8.12842	−	14.0788i	−0.306569	−	0.530994i
$704$	−21.1256	−	36.5907i	−0.796203	−	1.37906i
$705$		0			0
$706$	0.400314			0.0150660
$707$	23.0739	+	32.2579i	0.867784	+	1.21319i
$708$		0			0
$709$	3.26744	−	5.65936i	0.122711	−	0.212542i	−0.798125	−	0.602492i	$-0.794174\pi$
$709$	3.26744	−	5.65936i	0.122711	−	0.212542i	0.920836	+	0.389950i	$0.127508\pi$
$710$	4.11204	+	7.12227i	0.154322	+	0.267294i
$711$		0			0
$712$	−63.2761	+	109.597i	−2.37137	+	4.10734i
$713$	−29.1024			−1.08989
$714$		0			0
$715$	0.245106			0.00916643
$716$	−8.68797	+	15.0480i	−0.324685	+	0.562370i
$717$		0			0
$718$	−11.4533	−	19.8377i	−0.427433	−	0.740336i
$719$	−1.84382	+	3.19359i	−0.0687629	+	0.119101i	−0.898357	−	0.439266i	$-0.855239\pi$
$719$	−1.84382	+	3.19359i	−0.0687629	+	0.119101i	0.829594	+	0.558367i	$0.188572\pi$
$720$		0			0
$721$	2.69564	−	5.93587i	0.100391	−	0.221063i
$722$	30.5200			1.13584
$723$		0			0
$724$	27.7665	+	48.0929i	1.03193	+	1.78736i
$725$	1.04676	+	1.81304i	0.0388756	+	0.0673345i
$726$		0			0
$727$	−0.674563			−0.0250182			−0.0125091	−	0.999922i	$-0.503982\pi$
$727$	−0.674563			−0.0250182			−0.0125091	+	0.999922i	$0.503982\pi$
$728$	8.12661	−	0.793371i	0.301192	−	0.0294043i
$729$		0			0
$730$	−18.4121	+	31.8906i	−0.681461	+	1.18032i
$731$	−21.5300	−	37.2911i	−0.796317	−	1.37926i
$732$		0			0
$733$	−8.66961	+	15.0162i	−0.320219	+	0.554636i	−0.980533	−	0.196354i	$-0.937090\pi$
$733$	−8.66961	+	15.0162i	−0.320219	+	0.554636i	0.660314	+	0.750990i	$0.270423\pi$
$734$	−46.2596			−1.70747
$735$		0			0
$736$	−110.086			−4.05781
$737$	−1.50865	+	2.61306i	−0.0555718	+	0.0962532i
$738$		0			0
$739$	−18.2695	−	31.6437i	−0.672054	−	1.16403i	−0.977321	−	0.211764i	$-0.932079\pi$
$739$	−18.2695	−	31.6437i	−0.672054	−	1.16403i	0.305267	−	0.952267i	$-0.401254\pi$
$740$	−13.5912	+	23.5407i	−0.499623	+	0.865372i
$741$		0			0
$742$	52.1048	−	5.08679i	1.91283	−	0.186742i
$743$	−9.83489			−0.360807			−0.180404	−	0.983593i	$-0.557740\pi$
$743$	−9.83489			−0.360807			−0.180404	+	0.983593i	$0.557740\pi$
$744$		0			0
$745$	4.95911	+	8.58944i	0.181688	+	0.314693i
$746$	−7.12775	−	12.3456i	−0.260966	−	0.452006i
$747$		0			0
$748$	38.4048			1.40422
$749$	−12.6688	+	27.8971i	−0.462909	+	1.01934i
$750$		0			0
$751$	14.3484	−	24.8522i	0.523581	−	0.906869i	−0.476042	−	0.879423i	$-0.657929\pi$
$751$	14.3484	−	24.8522i	0.523581	−	0.906869i	0.999623	−	0.0274468i	$-0.00873768\pi$
$752$	67.4905	+	116.897i	2.46112	+	4.26279i
$753$		0			0
$754$	−0.200157	+	0.346682i	−0.00728929	+	0.0126254i
$755$	−7.69713			−0.280127
$756$		0			0
$757$	−50.9435			−1.85157			−0.925786	−	0.378047i	$-0.876596\pi$
$757$	−50.9435			−1.85157			−0.925786	+	0.378047i	$0.876596\pi$
$758$	−27.3135	+	47.3084i	−0.992072	+	1.71832i
$759$		0			0
$760$	12.1619	+	21.0649i	0.441157	+	0.764106i
$761$	21.9590	−	38.0340i	0.796011	−	1.37873i	−0.126184	−	0.992007i	$-0.540273\pi$
$761$	21.9590	−	38.0340i	0.796011	−	1.37873i	0.922195	−	0.386725i	$-0.126394\pi$
$762$		0			0
$763$	8.34804	+	11.6708i	0.302219	+	0.422511i
$764$	7.40632			0.267951
$765$		0			0
$766$	14.9796	+	25.9453i	0.541233	+	0.937444i
$767$	0.171722	+	0.297430i	0.00620051	+	0.0107396i
$768$		0			0
$769$	4.82343			0.173937			0.0869687	−	0.996211i	$-0.472282\pi$
$769$	4.82343			0.173937			0.0869687	+	0.996211i	$0.472282\pi$
$770$	−2.51271	+	5.53305i	−0.0905518	+	0.199397i
$771$		0			0
$772$	60.1809	−	104.236i	2.16596	−	3.75155i
$773$	3.64542	+	6.31405i	0.131117	+	0.227101i	0.924107	−	0.382133i	$-0.124810\pi$
$773$	3.64542	+	6.31405i	0.131117	+	0.227101i	−0.792991	+	0.609234i	$0.791477\pi$
$774$		0			0
$775$	−15.8290	+	27.4166i	−0.568593	+	0.984833i
$776$	111.951			4.01882
$777$		0			0
$778$	90.9011			3.25896
$779$	−0.914363	+	1.58372i	−0.0327605	+	0.0567428i
$780$		0			0
$781$	1.79030	+	3.10090i	0.0640621	+	0.110959i
$782$	36.9554	−	64.0087i	1.32152	−	2.28894i

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39083 - 2.40898i) q^{2} +(-2.86880 - 4.96890i) q^{4} +(0.412855 - 0.715087i) q^{5} +(2.63323 - 0.257073i) q^{7} -10.3967 q^{8} +O(q^{10})\)	\(q+(1.39083 - 2.40898i) q^{2} +(-2.86880 - 4.96890i) q^{4} +(0.412855 - 0.715087i) q^{5} +(2.63323 - 0.257073i) q^{7} -10.3967 q^{8} +(-1.14842 - 1.98912i) q^{10} +(-0.500000 - 0.866025i) q^{11} -0.296842 q^{13} +(3.04309 - 6.70095i) q^{14} +(-8.72241 + 15.1077i) q^{16} +(-3.34677 - 5.79677i) q^{17} +(1.41669 - 2.45379i) q^{19} -4.73760 q^{20} -2.78165 q^{22} +(-1.98481 + 3.43779i) q^{23} +(2.15910 + 3.73967i) q^{25} +(-0.412855 + 0.715087i) q^{26} +(-8.83158 - 12.3468i) q^{28} +0.484812 q^{29} +(3.66564 + 6.34907i) q^{31} +(13.8660 + 24.0166i) q^{32} -18.6191 q^{34} +(0.903315 - 1.98912i) q^{35} +(2.86880 - 4.96890i) q^{37} +(-3.94075 - 6.82559i) q^{38} +(-4.29233 + 7.43454i) q^{40} -0.645420 q^{41} +6.43308 q^{43} +(-2.86880 + 4.96890i) q^{44} +(5.52106 + 9.56275i) q^{46} +(3.86880 - 6.70095i) q^{47} +(6.86783 - 1.35386i) q^{49} +12.0117 q^{50} +(0.851579 + 1.47498i) q^{52} +(3.55677 + 6.16050i) q^{53} -0.825711 q^{55} +(-27.3769 + 2.67271i) q^{56} +(0.674289 - 1.16790i) q^{58} +(-0.578495 - 1.00198i) q^{59} +(-2.63323 + 4.56089i) q^{61} +20.3931 q^{62} +42.2513 q^{64} +(-0.122553 + 0.212268i) q^{65} +(-1.50865 - 2.61306i) q^{67} +(-19.2024 + 33.2595i) q^{68} +(-3.53541 - 4.94260i) q^{70} -3.58061 q^{71} +(-8.01625 - 13.8845i) q^{73} +(-7.98000 - 13.8218i) q^{74} -16.2568 q^{76} +(-1.53925 - 2.15191i) q^{77} +(2.16210 - 3.74487i) q^{79} +(7.20219 + 12.4746i) q^{80} +(-0.897667 + 1.55481i) q^{82} -2.37594 q^{83} -5.52693 q^{85} +(8.94729 - 15.4972i) q^{86} +(5.19835 + 9.00380i) q^{88} +(6.08617 - 10.5416i) q^{89} +(-0.781653 + 0.0763099i) q^{91} +22.7761 q^{92} +(-10.7617 - 18.6397i) q^{94} +(-1.16978 - 2.02612i) q^{95} -10.7680 q^{97} +(6.29052 - 18.4275i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} - 24 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 - 24 * q^8	\( 8 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} - 24 q^{8} - 10 q^{10} - 4 q^{11} - 4 q^{13} + 4 q^{14} - 12 q^{16} + 2 q^{17} - 4 q^{22} + 4 q^{23} - 4 q^{25} - 4 q^{26} - 22 q^{28} - 16 q^{29} + 12 q^{31} + 26 q^{32} - 32 q^{34} + 2 q^{35} + 4 q^{37} + 8 q^{38} + 6 q^{40} - 4 q^{41} + 36 q^{43} - 4 q^{44} + 14 q^{46} + 12 q^{47} - 4 q^{49} - 4 q^{50} + 6 q^{52} - 12 q^{53} - 8 q^{55} - 48 q^{56} + 4 q^{58} + 12 q^{59} - 2 q^{61} + 52 q^{62} + 112 q^{64} - 4 q^{65} - 28 q^{67} - 48 q^{68} - 32 q^{70} - 24 q^{71} - 6 q^{73} - 16 q^{74} - 36 q^{76} - 4 q^{77} - 2 q^{79} + 16 q^{80} + 12 q^{82} + 24 q^{83} + 36 q^{85} + 36 q^{86} + 12 q^{88} + 8 q^{89} + 12 q^{91} + 32 q^{92} - 20 q^{94} + 34 q^{95} - 88 q^{97} - 16 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 - 24 * q^8 - 10 * q^10 - 4 * q^11 - 4 * q^13 + 4 * q^14 - 12 * q^16 + 2 * q^17 - 4 * q^22 + 4 * q^23 - 4 * q^25 - 4 * q^26 - 22 * q^28 - 16 * q^29 + 12 * q^31 + 26 * q^32 - 32 * q^34 + 2 * q^35 + 4 * q^37 + 8 * q^38 + 6 * q^40 - 4 * q^41 + 36 * q^43 - 4 * q^44 + 14 * q^46 + 12 * q^47 - 4 * q^49 - 4 * q^50 + 6 * q^52 - 12 * q^53 - 8 * q^55 - 48 * q^56 + 4 * q^58 + 12 * q^59 - 2 * q^61 + 52 * q^62 + 112 * q^64 - 4 * q^65 - 28 * q^67 - 48 * q^68 - 32 * q^70 - 24 * q^71 - 6 * q^73 - 16 * q^74 - 36 * q^76 - 4 * q^77 - 2 * q^79 + 16 * q^80 + 12 * q^82 + 24 * q^83 + 36 * q^85 + 36 * q^86 + 12 * q^88 + 8 * q^89 + 12 * q^91 + 32 * q^92 - 20 * q^94 + 34 * q^95 - 88 * q^97 - 16 * q^98

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