LMFDB - Embedded newform 693.2.m.j.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 12 x^{18} - 3 x^{17} + 94 x^{16} - 10 x^{15} + 662 x^{14} - 153 x^{13} + 4638 x^{12} + \cdots + 121 $ x^20 + 12x^18 - 3x^17 + 94x^16 - 10x^15 + 662x^14 - 153x^13 + 4638x^12 - 1174x^11 + 15808x^10 - 3393x^9 + 26062x^8 - 15494x^7 + 11660x^6 - 33295x^5 + 67756x^4 - 43696x^3 + 13084x^2 - 1155x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			379.1
Root			$-0.864833 + 2.66168i$ of defining polynomial
Character	$\chi$	$=$	693.379
Dual form			693.2.m.j.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.864833 - 2.66168i) q^{2} +(-4.71859 + 3.42825i) q^{4} +(0.518429 - 1.59556i) q^{5} +(0.809017 - 0.587785i) q^{7} +(8.67739 + 6.30449i) q^{8} +O(q^{10})$	\(q+(-0.864833 - 2.66168i) q^{2} +(-4.71859 + 3.42825i) q^{4} +(0.518429 - 1.59556i) q^{5} +(0.809017 - 0.587785i) q^{7} +(8.67739 + 6.30449i) q^{8} -4.69523 q^{10} +(3.13215 + 1.09071i) q^{11} +(1.81428 + 5.58378i) q^{13} +(-2.26416 - 1.64501i) q^{14} +(5.67139 - 17.4547i) q^{16} +(0.0939932 - 0.289281i) q^{17} +(3.74462 + 2.72062i) q^{19} +(3.02374 + 9.30610i) q^{20} +(0.194331 - 9.28007i) q^{22} +1.38164 q^{23} +(1.76804 + 1.28455i) q^{25} +(13.2932 - 9.65808i) q^{26} +(-1.80234 + 5.54703i) q^{28} +(3.21073 - 2.33273i) q^{29} +(0.236120 + 0.726701i) q^{31} -29.9121 q^{32} -0.851264 q^{34} +(-0.518429 - 1.59556i) q^{35} +(-2.59713 + 1.88693i) q^{37} +(4.00297 - 12.3199i) q^{38} +(14.5578 - 10.5769i) q^{40} +(-6.72515 - 4.88611i) q^{41} -1.01069 q^{43} +(-18.5185 + 5.59120i) q^{44} +(-1.19489 - 3.67749i) q^{46} +(-2.09283 - 1.52053i) q^{47} +(0.309017 - 0.951057i) q^{49} +(1.89002 - 5.81688i) q^{50} +(-27.7035 - 20.1277i) q^{52} +(0.449229 + 1.38259i) q^{53} +(3.36409 - 4.43208i) q^{55} +10.7258 q^{56} +(-8.98574 - 6.52852i) q^{58} +(-2.01805 + 1.46620i) q^{59} +(1.04848 - 3.22689i) q^{61} +(1.73004 - 1.25695i) q^{62} +(14.5262 + 44.7071i) q^{64} +9.84984 q^{65} +6.16878 q^{67} +(0.548215 + 1.68723i) q^{68} +(-3.79852 + 2.75979i) q^{70} +(-2.34835 + 7.22749i) q^{71} +(10.3114 - 7.49164i) q^{73} +(7.26848 + 5.28086i) q^{74} -26.9963 q^{76} +(3.17506 - 0.958630i) q^{77} +(-1.90206 - 5.85393i) q^{79} +(-24.9099 - 18.0981i) q^{80} +(-7.18913 + 22.1259i) q^{82} +(0.621946 - 1.91415i) q^{83} +(-0.412837 - 0.299944i) q^{85} +(0.874082 + 2.69015i) q^{86} +(20.3025 + 29.2111i) q^{88} -0.0843908 q^{89} +(4.74985 + 3.45097i) q^{91} +(-6.51938 + 4.73661i) q^{92} +(-2.23722 + 6.88545i) q^{94} +(6.28224 - 4.56431i) q^{95} +(0.320682 + 0.986957i) q^{97} -2.79866 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8}+O(q^{10}) $ 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8	$ 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8} + 12 q^{10} + q^{11} + 13 q^{13} - 24 q^{16} + q^{17} + 10 q^{19} + 46 q^{20} + 26 q^{22} - 8 q^{25} + 53 q^{26} + 4 q^{28} - 3 q^{29} - 13 q^{31} - 82 q^{32} + 42 q^{34} - 5 q^{35} - 32 q^{37} - 16 q^{38} + 20 q^{40} + 3 q^{41} + 12 q^{43} - 25 q^{44} - 13 q^{46} - 20 q^{47} - 5 q^{49} + 83 q^{50} - 80 q^{52} - 3 q^{53} - 28 q^{55} + 6 q^{56} + 2 q^{58} + 9 q^{59} - 15 q^{61} + 37 q^{62} - 49 q^{64} - 58 q^{65} + 76 q^{67} - 51 q^{68} + 3 q^{70} - 37 q^{71} + 27 q^{73} + 32 q^{74} + 4 q^{76} - 6 q^{77} + 5 q^{79} - 137 q^{80} - 55 q^{82} + 42 q^{83} - 48 q^{85} - 3 q^{86} + 151 q^{88} + 18 q^{89} + 7 q^{91} - 39 q^{92} - 35 q^{94} + 96 q^{95} - 27 q^{97}+O(q^{100}) $ 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8 + 12 * q^10 + q^11 + 13 * q^13 - 24 * q^16 + q^17 + 10 * q^19 + 46 * q^20 + 26 * q^22 - 8 * q^25 + 53 * q^26 + 4 * q^28 - 3 * q^29 - 13 * q^31 - 82 * q^32 + 42 * q^34 - 5 * q^35 - 32 * q^37 - 16 * q^38 + 20 * q^40 + 3 * q^41 + 12 * q^43 - 25 * q^44 - 13 * q^46 - 20 * q^47 - 5 * q^49 + 83 * q^50 - 80 * q^52 - 3 * q^53 - 28 * q^55 + 6 * q^56 + 2 * q^58 + 9 * q^59 - 15 * q^61 + 37 * q^62 - 49 * q^64 - 58 * q^65 + 76 * q^67 - 51 * q^68 + 3 * q^70 - 37 * q^71 + 27 * q^73 + 32 * q^74 + 4 * q^76 - 6 * q^77 + 5 * q^79 - 137 * q^80 - 55 * q^82 + 42 * q^83 - 48 * q^85 - 3 * q^86 + 151 * q^88 + 18 * q^89 + 7 * q^91 - 39 * q^92 - 35 * q^94 + 96 * q^95 - 27 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.864833	−	2.66168i	−0.611530	−	1.88209i	−0.443383	−	0.896332i	$-0.646222\pi$
$2$	−0.864833	−	2.66168i	−0.611530	−	1.88209i	−0.168147	−	0.985762i	$-0.553778\pi$
$3$		0			0
$3$		0			0
$4$	−4.71859	+	3.42825i	−2.35929	+	1.71413i
$5$	0.518429	−	1.59556i	0.231849	−	0.713557i	−0.765675	−	0.643227i	$-0.777595\pi$
$5$	0.518429	−	1.59556i	0.231849	−	0.713557i	0.997524	−	0.0703294i	$-0.0224050\pi$
$6$		0			0
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$	8.67739	+	6.30449i	3.06792	+	2.22898i
$9$		0			0
$10$	−4.69523			−1.48476
$11$	3.13215	+	1.09071i	0.944378	+	0.328861i
$11$	3.13215	+	1.09071i	0.944378	+	0.328861i
$12$		0			0
$13$	1.81428	+	5.58378i	0.503191	+	1.54866i	0.803791	+	0.594912i	$0.202813\pi$
$13$	1.81428	+	5.58378i	0.503191	+	1.54866i	−0.300600	+	0.953750i	$0.597187\pi$
$14$	−2.26416	−	1.64501i	−0.605123	−	0.439648i
$15$		0			0
$16$	5.67139	−	17.4547i	1.41785	−	4.36369i
$17$	0.0939932	−	0.289281i	0.0227967	−	0.0701611i	−0.939011	−	0.343887i	$-0.888256\pi$
$17$	0.0939932	−	0.289281i	0.0227967	−	0.0701611i	0.961808	+	0.273726i	$0.0882562\pi$
$18$		0			0
$19$	3.74462	+	2.72062i	0.859074	+	0.624154i	0.927633	−	0.373494i	$-0.121840\pi$
$19$	3.74462	+	2.72062i	0.859074	+	0.624154i	−0.0685591	+	0.997647i	$0.521840\pi$
$20$	3.02374	+	9.30610i	0.676128	+	2.08091i
$21$		0			0
$22$	0.194331	−	9.28007i	0.0414316	−	1.97852i
$23$	1.38164			0.288092			0.144046	−	0.989571i	$-0.453989\pi$
$23$	1.38164			0.288092			0.144046	+	0.989571i	$0.453989\pi$
$24$		0			0
$25$	1.76804	+	1.28455i	0.353607	+	0.256911i
$26$	13.2932	−	9.65808i	2.60701	−	1.89411i
$27$		0			0
$28$	−1.80234	+	5.54703i	−0.340610	+	1.04829i
$29$	3.21073	−	2.33273i	0.596217	−	0.433177i	−0.248317	−	0.968679i	$-0.579877\pi$
$29$	3.21073	−	2.33273i	0.596217	−	0.433177i	0.844534	+	0.535502i	$0.179877\pi$
$30$		0			0
$31$	0.236120	+	0.726701i	0.0424083	+	0.130519i	0.970019	−	0.243029i	$-0.0781410\pi$
$31$	0.236120	+	0.726701i	0.0424083	+	0.130519i	−0.927611	+	0.373548i	$0.878141\pi$
$32$	−29.9121			−5.28776
$33$		0			0
$34$	−0.851264			−0.145991
$35$	−0.518429	−	1.59556i	−0.0876306	−	0.269699i
$36$		0			0
$37$	−2.59713	+	1.88693i	−0.426966	+	0.310209i	−0.780434	−	0.625238i	$-0.785002\pi$
$37$	−2.59713	+	1.88693i	−0.426966	+	0.310209i	0.353469	+	0.935446i	$0.385002\pi$
$38$	4.00297	−	12.3199i	0.649367	−	1.99855i
$39$		0			0
$40$	14.5578	−	10.5769i	2.30179	−	1.67235i
$41$	−6.72515	−	4.88611i	−1.05029	−	0.763081i	−0.0780237	−	0.996952i	$-0.524861\pi$
$41$	−6.72515	−	4.88611i	−1.05029	−	0.763081i	−0.972268	+	0.233870i	$0.924861\pi$
$42$		0			0
$43$	−1.01069			−0.154129			−0.0770647	−	0.997026i	$-0.524555\pi$
$43$	−1.01069			−0.154129			−0.0770647	+	0.997026i	$0.524555\pi$
$44$	−18.5185	+	5.59120i	−2.79178	+	0.842906i
$45$		0			0
$46$	−1.19489	−	3.67749i	−0.176177	−	0.542216i
$47$	−2.09283	−	1.52053i	−0.305271	−	0.221792i	0.424594	−	0.905384i	$-0.360417\pi$
$47$	−2.09283	−	1.52053i	−0.305271	−	0.221792i	−0.729865	+	0.683592i	$0.760417\pi$
$48$		0			0
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	1.89002	−	5.81688i	0.267289	−	0.822631i
$51$		0			0
$52$	−27.7035	−	20.1277i	−3.84178	−	2.79122i
$53$	0.449229	+	1.38259i	0.0617064	+	0.189913i	0.977157	−	0.212517i	$-0.0681659\pi$
$53$	0.449229	+	1.38259i	0.0617064	+	0.189913i	−0.915451	+	0.402429i	$0.868166\pi$
$54$		0			0
$55$	3.36409	−	4.43208i	0.453614	−	0.597622i
$56$	10.7258			1.43330
$57$		0			0
$58$	−8.98574	−	6.52852i	−1.17988	−	0.857237i
$59$	−2.01805	+	1.46620i	−0.262727	+	0.190883i	−0.711349	−	0.702839i	$-0.751915\pi$
$59$	−2.01805	+	1.46620i	−0.262727	+	0.190883i	0.448621	+	0.893722i	$0.351915\pi$
$60$		0			0
$61$	1.04848	−	3.22689i	0.134244	−	0.413161i	−0.861228	−	0.508219i	$-0.830304\pi$
$61$	1.04848	−	3.22689i	0.134244	−	0.413161i	0.995472	+	0.0950587i	$0.0303039\pi$
$62$	1.73004	−	1.25695i	0.219716	−	0.159633i
$63$		0			0
$64$	14.5262	+	44.7071i	1.81578	+	5.58839i
$65$	9.84984			1.22172
$66$		0			0
$67$	6.16878			0.753636			0.376818	−	0.926287i	$-0.377018\pi$
$67$	6.16878			0.753636			0.376818	+	0.926287i	$0.377018\pi$
$68$	0.548215	+	1.68723i	0.0664808	+	0.204607i
$69$		0			0
$70$	−3.79852	+	2.75979i	−0.454011	+	0.329858i
$71$	−2.34835	+	7.22749i	−0.278698	+	0.857745i	0.709519	+	0.704686i	$0.248912\pi$
$71$	−2.34835	+	7.22749i	−0.278698	+	0.857745i	−0.988217	+	0.153058i	$0.951088\pi$
$72$		0			0
$73$	10.3114	−	7.49164i	1.20685	−	0.876831i	0.211913	−	0.977289i	$-0.432031\pi$
$73$	10.3114	−	7.49164i	1.20685	−	0.876831i	0.994941	+	0.100458i	$0.0320308\pi$
$74$	7.26848	+	5.28086i	0.844944	+	0.613888i
$75$		0			0
$76$	−26.9963			−3.09669
$77$	3.17506	−	0.958630i	0.361832	−	0.109246i
$78$		0			0
$79$	−1.90206	−	5.85393i	−0.213998	−	0.658618i	−0.999223	−	0.0394080i	$-0.987453\pi$
$79$	−1.90206	−	5.85393i	−0.213998	−	0.658618i	0.785225	−	0.619210i	$-0.212547\pi$
$80$	−24.9099	−	18.0981i	−2.78501	−	2.02343i
$81$		0			0
$82$	−7.18913	+	22.1259i	−0.793907	+	2.44339i
$83$	0.621946	−	1.91415i	0.0682675	−	0.210106i	−0.911103	−	0.412179i	$-0.864768\pi$
$83$	0.621946	−	1.91415i	0.0682675	−	0.210106i	0.979370	+	0.202073i	$0.0647679\pi$
$84$		0			0
$85$	−0.412837	−	0.299944i	−0.0447785	−	0.0325335i
$86$	0.874082	+	2.69015i	0.0942546	+	0.290086i
$87$		0			0
$88$	20.3025	+	29.2111i	2.16426	+	3.11392i
$89$	−0.0843908			−0.00894541			−0.00447270	−	0.999990i	$-0.501424\pi$
$89$	−0.0843908			−0.00894541			−0.00447270	+	0.999990i	$0.501424\pi$
$90$		0			0
$91$	4.74985	+	3.45097i	0.497919	+	0.361760i
$92$	−6.51938	+	4.73661i	−0.679693	+	0.493826i
$93$		0			0
$94$	−2.23722	+	6.88545i	−0.230752	+	0.710180i
$95$	6.28224	−	4.56431i	0.644544	−	0.468289i
$96$		0			0
$97$	0.320682	+	0.986957i	0.0325603	+	0.100210i	0.966016	−	0.258483i	$-0.0832225\pi$
$97$	0.320682	+	0.986957i	0.0325603	+	0.100210i	−0.933456	+	0.358693i	$0.883223\pi$
$98$	−2.79866			−0.282707
$99$		0			0
$100$	−12.7464			−1.27464
$101$	6.08676	+	18.7331i	0.605656	+	1.86402i	0.492220	+	0.870471i	$0.336185\pi$
$101$	6.08676	+	18.7331i	0.605656	+	1.86402i	0.113435	+	0.993545i	$0.463815\pi$
$102$		0			0
$103$	1.95189	−	1.41813i	0.192325	−	0.139733i	−0.487455	−	0.873148i	$-0.662075\pi$
$103$	1.95189	−	1.41813i	0.192325	−	0.139733i	0.679781	+	0.733415i	$0.262075\pi$
$104$	−19.4597	+	59.8908i	−1.90818	+	5.87277i
$105$		0			0
$106$	3.29150	−	2.39141i	0.319698	−	0.232275i
$107$	−7.49357	−	5.44439i	−0.724430	−	0.526330i	0.163366	−	0.986566i	$-0.447765\pi$
$107$	−7.49357	−	5.44439i	−0.724430	−	0.526330i	−0.887797	+	0.460236i	$0.847765\pi$
$108$		0			0
$109$	−8.30530			−0.795503			−0.397752	−	0.917493i	$-0.630209\pi$
$109$	−8.30530			−0.795503			−0.397752	+	0.917493i	$0.630209\pi$
$110$	−14.7062	−	5.12113i	−1.40218	−	0.488280i
$111$		0			0
$112$	−5.67139	−	17.4547i	−0.535896	−	1.64932i
$113$	4.43310	+	3.22084i	0.417031	+	0.302991i	0.776442	−	0.630188i	$-0.217022\pi$
$113$	4.43310	+	3.22084i	0.417031	+	0.302991i	−0.359411	+	0.933179i	$0.617022\pi$
$114$		0			0
$115$	0.716282	−	2.20449i	0.0667937	−	0.205570i
$116$	−7.15291	+	22.0144i	−0.664131	+	2.04398i
$117$		0			0
$118$	5.64783	+	4.10339i	0.519925	+	0.377747i
$119$	−0.0939932	−	0.289281i	−0.00861635	−	0.0265184i
$120$		0			0
$121$	8.62071	+	6.83252i	0.783701	+	0.621138i
$122$	−9.49572			−0.859702
$123$		0			0
$124$	−3.60547	−	2.61953i	−0.323781	−	0.235240i
$125$	9.75252	−	7.08562i	0.872292	−	0.633757i
$126$		0			0
$127$	6.19815	−	19.0759i	0.549997	−	1.69272i	−0.158807	−	0.987310i	$-0.550765\pi$
$127$	6.19815	−	19.0759i	0.549997	−	1.69272i	0.708803	−	0.705406i	$-0.249235\pi$
$128$	58.0345	−	42.1646i	5.12958	−	3.72686i
$129$		0			0
$130$	−8.51847	−	26.2172i	−0.747119	−	2.29940i
$131$	−4.22096			−0.368787			−0.184394	−	0.982852i	$-0.559032\pi$
$131$	−4.22096			−0.368787			−0.184394	+	0.982852i	$0.559032\pi$
$132$		0			0
$133$	4.62860			0.401350
$134$	−5.33496	−	16.4193i	−0.460871	−	1.41841i
$135$		0			0
$136$	2.63939	−	1.91763i	0.226326	−	0.164435i
$137$	4.49191	−	13.8247i	0.383770	−	1.18112i	−0.553598	−	0.832784i	$-0.686746\pi$
$137$	4.49191	−	13.8247i	0.383770	−	1.18112i	0.937369	−	0.348339i	$-0.113254\pi$
$138$		0			0
$139$	−5.61956	+	4.08285i	−0.476645	+	0.346303i	−0.800025	−	0.599966i	$-0.795181\pi$
$139$	−5.61956	+	4.08285i	−0.476645	+	0.346303i	0.323381	+	0.946269i	$0.395181\pi$
$140$	7.91624	+	5.75149i	0.669045	+	0.486089i
$141$		0			0
$142$	21.2682			1.78479
$143$	−0.407675	+	19.4681i	−0.0340915	+	1.62800i
$144$		0			0
$145$	−2.05748	−	6.33227i	−0.170864	−	0.525866i
$146$	−28.8580	−	20.9666i	−2.38830	−	1.73521i
$147$		0			0
$148$	5.78593	−	17.8072i	0.475600	−	1.46375i
$149$	4.31512	−	13.2806i	0.353508	−	1.08799i	−0.603361	−	0.797468i	$-0.706172\pi$
$149$	4.31512	−	13.2806i	0.353508	−	1.08799i	0.956869	−	0.290519i	$-0.0938279\pi$
$150$		0			0
$151$	1.10900	+	0.805737i	0.0902492	+	0.0655699i	0.631995	−	0.774973i	$-0.282236\pi$
$151$	1.10900	+	0.805737i	0.0902492	+	0.0655699i	−0.541746	+	0.840543i	$0.682236\pi$
$152$	15.3413	+	47.2158i	1.24435	+	3.82971i
$153$		0			0
$154$	−5.29747	−	7.62196i	−0.426882	−	0.614195i
$155$	1.28191			0.102965
$156$		0			0
$157$	12.8632	+	9.34563i	1.02659	+	0.745863i	0.967624	−	0.252397i	$-0.0812190\pi$
$157$	12.8632	+	9.34563i	1.02659	+	0.745863i	0.0589681	+	0.998260i	$0.481219\pi$
$158$	−13.9363	+	10.1253i	−1.10872	+	0.805529i
$159$		0			0
$160$	−15.5073	+	47.7266i	−1.22596	+	3.77312i
$161$	1.11777	−	0.812107i	0.0880926	−	0.0640030i
$162$		0			0
$163$	3.23495	+	9.95614i	0.253381	+	0.779825i	0.994144	+	0.108060i	$0.0344637\pi$
$163$	3.23495	+	9.95614i	0.253381	+	0.779825i	−0.740764	+	0.671766i	$0.765536\pi$
$164$	48.4840			3.78596
$165$		0			0
$166$	−5.63275			−0.437186
$167$	−2.64937	−	8.15393i	−0.205015	−	0.630970i	−0.999713	−	0.0239655i	$-0.992371\pi$
$167$	−2.64937	−	8.15393i	−0.205015	−	0.630970i	0.794698	−	0.607005i	$-0.207629\pi$
$168$		0			0
$169$	−17.3698	+	12.6199i	−1.33614	+	0.970760i
$170$	−0.441320	+	1.35824i	−0.0338477	+	0.104173i
$171$		0			0
$172$	4.76905	−	3.46491i	0.363636	−	0.264197i
$173$	−11.1216	−	8.08034i	−0.845562	−	0.614337i	0.0783569	−	0.996925i	$-0.475033\pi$
$173$	−11.1216	−	8.08034i	−0.845562	−	0.614337i	−0.923919	+	0.382589i	$0.875033\pi$
$174$		0			0
$175$	2.18541			0.165202
$176$	36.8017	−	48.4850i	2.77403	−	3.65470i
$177$		0			0
$178$	0.0729840	+	0.224622i	0.00547038	+	0.0168361i
$179$	−3.11483	−	2.26306i	−0.232813	−	0.169149i	0.465262	−	0.885173i	$-0.345960\pi$
$179$	−3.11483	−	2.26306i	−0.232813	−	0.169149i	−0.698076	+	0.716024i	$0.745960\pi$
$180$		0			0
$181$	−6.04339	+	18.5996i	−0.449201	+	1.38250i	0.428608	+	0.903490i	$0.359004\pi$
$181$	−6.04339	+	18.5996i	−0.449201	+	1.38250i	−0.877810	+	0.479009i	$0.840996\pi$
$182$	5.07755	−	15.6271i	0.376373	−	1.15836i
$183$		0			0
$184$	11.9890	+	8.71054i	0.883843	+	0.642149i
$185$	1.66428	+	5.12212i	0.122360	+	0.376586i
$186$		0			0
$187$	0.609922	−	0.803553i	0.0446019	−	0.0587616i
$188$	15.0880			1.10040
$189$		0			0
$190$	−17.5818	−	12.7740i	−1.27552	−	0.926720i
$191$	−2.05896	+	1.49592i	−0.148981	+	0.108241i	−0.659779	−	0.751460i	$-0.729350\pi$
$191$	−2.05896	+	1.49592i	−0.148981	+	0.108241i	0.510798	+	0.859701i	$0.329350\pi$
$192$		0			0
$193$	6.68348	−	20.5696i	0.481087	−	1.48063i	−0.356482	−	0.934302i	$-0.616024\pi$
$193$	6.68348	−	20.5696i	0.481087	−	1.48063i	0.837569	−	0.546332i	$-0.183976\pi$
$194$	2.34963	−	1.70711i	0.168694	−	0.122563i
$195$		0			0
$196$	1.80234	+	5.54703i	0.128739	+	0.396217i
$197$	22.0693			1.57237			0.786187	−	0.617989i	$-0.212052\pi$
$197$	22.0693			1.57237			0.786187	+	0.617989i	$0.212052\pi$
$198$		0			0
$199$	−12.8315			−0.909598			−0.454799	−	0.890594i	$-0.650289\pi$
$199$	−12.8315			−0.909598			−0.454799	+	0.890594i	$0.650289\pi$
$200$	7.24349	+	22.2932i	0.512192	+	1.57636i
$201$		0			0
$202$	44.5976	−	32.4021i	3.13788	−	2.27980i
$203$	1.22639	−	3.77444i	0.0860756	−	0.264914i
$204$		0			0
$205$	−11.2826	+	8.19729i	−0.788011	+	0.572523i
$206$	−5.46268	−	3.96887i	−0.380603	−	0.276524i
$207$		0			0
$208$	107.753			7.47132
$209$	8.76129	+	12.6057i	0.606031	+	0.871953i
$210$		0			0
$211$	−5.48213	−	16.8723i	−0.377406	−	1.16154i	−0.941841	−	0.336058i	$-0.890906\pi$
$211$	−5.48213	−	16.8723i	−0.377406	−	1.16154i	0.564436	−	0.825477i	$-0.309094\pi$
$212$	−6.85958	−	4.98378i	−0.471118	−	0.342287i
$213$		0			0
$214$	−8.01057	+	24.6540i	−0.547591	+	1.68531i
$215$	−0.523973	+	1.61262i	−0.0357347	+	0.109980i
$216$		0			0
$217$	0.618169	+	0.449126i	0.0419640	+	0.0304887i
$218$	7.18270	+	22.1061i	0.486474	+	1.49721i
$219$		0			0
$220$	−0.679445	+	32.4461i	−0.0458082	+	2.18752i
$221$	1.78581			0.120127
$222$		0			0
$223$	−13.8483	−	10.0614i	−0.927349	−	0.673759i	0.0179932	−	0.999838i	$-0.494272\pi$
$223$	−13.8483	−	10.0614i	−0.927349	−	0.673759i	−0.945342	+	0.326080i	$0.894272\pi$
$224$	−24.1994	+	17.5819i	−1.61689	+	1.17474i
$225$		0			0
$226$	4.73896	−	14.5850i	0.315231	−	0.970180i
$227$	−16.5744	+	12.0420i	−1.10008	+	0.799256i	−0.981073	−	0.193637i	$-0.937971\pi$
$227$	−16.5744	+	12.0420i	−1.10008	+	0.799256i	−0.119008	+	0.992893i	$0.537971\pi$
$228$		0			0
$229$	7.55058	+	23.2383i	0.498956	+	1.53563i	0.810699	+	0.585463i	$0.199087\pi$
$229$	7.55058	+	23.2383i	0.498956	+	1.53563i	−0.311743	+	0.950167i	$0.600913\pi$
$230$	−6.48712			−0.427748
$231$		0			0
$232$	42.5674			2.79469
$233$	7.32533	+	22.5450i	0.479898	+	1.47697i	0.839236	+	0.543767i	$0.183002\pi$
$233$	7.32533	+	22.5450i	0.479898	+	1.47697i	−0.359338	+	0.933207i	$0.616998\pi$
$234$		0			0
$235$	−3.51108	+	2.55095i	−0.229038	+	0.166406i
$236$	4.49584	−	13.8368i	0.292654	−	0.900696i
$237$		0			0
$238$	−0.688687	+	0.500360i	−0.0446410	+	0.0324336i
$239$	−1.27822	−	0.928682i	−0.0826813	−	0.0600714i	0.545677	−	0.837996i	$-0.316273\pi$
$239$	−1.27822	−	0.928682i	−0.0826813	−	0.0600714i	−0.628358	+	0.777924i	$0.716273\pi$
$240$		0			0
$241$	−12.2382			−0.788333			−0.394167	−	0.919039i	$-0.628967\pi$
$241$	−12.2382			−0.788333			−0.394167	+	0.919039i	$0.628967\pi$
$242$	10.7305	−	28.8546i	0.689784	−	1.85484i
$243$		0			0
$244$	6.11525	+	18.8208i	0.391489	+	1.20488i
$245$	−1.35727	−	0.986111i	−0.0867125	−	0.0630003i
$246$		0			0
$247$	−8.39758	+	25.8451i	−0.534325	+	1.64448i
$248$	−2.53258	+	7.79449i	−0.160819	+	0.494950i
$249$		0			0
$250$	−27.2940	−	19.8302i	−1.72622	−	1.25417i
$251$	−5.99825	−	18.4607i	−0.378606	−	1.16523i	−0.941013	−	0.338370i	$-0.890125\pi$
$251$	−5.99825	−	18.4607i	−0.378606	−	1.16523i	0.562407	−	0.826861i	$-0.309875\pi$
$252$		0			0
$253$	4.32750	+	1.50696i	0.272068	+	0.0947420i
$254$	−56.1345			−3.52219
$255$		0			0
$256$	−86.3587	−	62.7432i	−5.39742	−	3.92145i
$257$	−0.218519	+	0.158763i	−0.0136308	+	0.00990337i	−0.594580	−	0.804037i	$-0.702682\pi$
$257$	−0.218519	+	0.158763i	−0.0136308	+	0.00990337i	0.580949	+	0.813940i	$0.302682\pi$
$258$		0			0
$259$	−0.992016	+	3.05311i	−0.0616408	+	0.189711i
$260$	−46.4773	+	33.7678i	−2.88240	+	2.09419i
$261$		0			0
$262$	3.65043	+	11.2349i	0.225524	+	0.694092i
$263$	−27.9927			−1.72611			−0.863053	−	0.505113i	$-0.831451\pi$
$263$	−27.9927			−1.72611			−0.863053	+	0.505113i	$0.831451\pi$
$264$		0			0
$265$	2.43889			0.149820
$266$	−4.00297	−	12.3199i	−0.245438	−	0.755379i
$267$		0			0
$268$	−29.1079	+	21.1481i	−1.77805	+	1.29183i
$269$	−0.345128	+	1.06220i	−0.0210428	+	0.0647632i	−0.961027	−	0.276456i	$-0.910840\pi$
$269$	−0.345128	+	1.06220i	−0.0210428	+	0.0647632i	0.939984	+	0.341219i	$0.110840\pi$
$270$		0			0
$271$	−20.0887	+	14.5953i	−1.22030	+	0.886600i	−0.996125	−	0.0879490i	$-0.971969\pi$
$271$	−20.0887	+	14.5953i	−1.22030	+	0.886600i	−0.224175	+	0.974549i	$0.571969\pi$
$272$	−4.51626	−	3.28126i	−0.273839	−	0.198955i
$273$		0			0
$274$	−40.6817			−2.45767
$275$	4.13668	+	5.95183i	0.249451	+	0.358909i
$276$		0			0
$277$	−3.84216	−	11.8250i	−0.230853	−	0.710493i	−0.997644	−	0.0685967i	$-0.978148\pi$
$277$	−3.84216	−	11.8250i	−0.230853	−	0.710493i	0.766791	−	0.641897i	$-0.221852\pi$
$278$	15.7272	+	11.4265i	0.943256	+	0.685316i
$279$		0			0
$280$	5.56059	−	17.1137i	0.332309	−	1.02274i
$281$	2.08141	−	6.40594i	0.124167	−	0.382146i	−0.869582	−	0.493789i	$-0.835611\pi$
$281$	2.08141	−	6.40594i	0.124167	−	0.382146i	0.993748	+	0.111643i	$0.0356114\pi$
$282$		0			0
$283$	9.02913	+	6.56005i	0.536726	+	0.389954i	0.822868	−	0.568233i	$-0.192373\pi$
$283$	9.02913	+	6.56005i	0.536726	+	0.389954i	−0.286142	+	0.958187i	$0.592373\pi$
$284$	−13.6968	−	42.1543i	−0.812753	−	2.50140i
$285$		0			0
$286$	52.1704	−	15.7515i	3.08490	−	0.931408i
$287$	−8.31274			−0.490685
$288$		0			0
$289$	13.6784	+	9.93797i	0.804614	+	0.584586i
$290$	−15.0751	+	10.9527i	−0.885242	+	0.643166i
$291$		0			0
$292$	−22.9718	+	70.7000i	−1.34432	+	4.13740i
$293$	−13.6731	+	9.93412i	−0.798794	+	0.580358i	−0.910560	−	0.413377i	$-0.864349\pi$
$293$	−13.6731	+	9.93412i	−0.798794	+	0.580358i	0.111766	+	0.993735i	$0.464349\pi$
$294$		0			0
$295$	1.29319	+	3.98004i	0.0752926	+	0.231727i
$296$	−34.4324			−2.00134
$297$		0			0
$298$	−39.0805			−2.26388
$299$	2.50668	+	7.71477i	0.144965	+	0.446157i
$300$		0			0
$301$	−0.817668	+	0.594071i	−0.0471296	+	0.0342417i
$302$	1.18551	−	3.64864i	0.0682187	−	0.209956i
$303$		0			0
$304$	68.7249	−	49.9316i	3.94165	−	2.86377i
$305$	−4.60514	−	3.34583i	−0.263689	−	0.191582i
$306$		0			0
$307$	−11.3453			−0.647511			−0.323755	−	0.946141i	$-0.604946\pi$
$307$	−11.3453			−0.647511			−0.323755	+	0.946141i	$0.604946\pi$
$308$	−11.6954	+	15.4083i	−0.666407	+	0.877970i
$309$		0			0
$310$	−1.10864	−	3.41203i	−0.0629663	−	0.193790i
$311$	19.2940	+	14.0179i	1.09406	+	0.794884i	0.980081	−	0.198599i	$-0.0636391\pi$
$311$	19.2940	+	14.0179i	1.09406	+	0.794884i	0.113983	+	0.993483i	$0.463639\pi$
$312$		0			0
$313$	9.56921	−	29.4510i	0.540884	−	1.66467i	−0.189696	−	0.981843i	$-0.560750\pi$
$313$	9.56921	−	29.4510i	0.540884	−	1.66467i	0.730580	−	0.682827i	$-0.239250\pi$
$314$	13.7506	−	42.3201i	0.775993	−	2.38826i
$315$		0			0
$316$	29.0438	+	21.1015i	1.63384	+	1.18705i
$317$	−0.991557	−	3.05170i	−0.0556914	−	0.171401i	0.919342	−	0.393460i	$-0.128722\pi$
$317$	−0.991557	−	3.05170i	−0.0556914	−	0.171401i	−0.975033	+	0.222060i	$0.928722\pi$
$318$		0			0
$319$	12.6008	−	3.80449i	0.705510	−	0.213011i
$320$	78.8637			4.40862
$321$		0			0
$322$	−3.12826	−	2.27281i	−0.174331	−	0.126659i
$323$	1.13899	−	0.827528i	0.0633753	−	0.0460449i
$324$		0			0
$325$	−3.96495	+	12.2029i	−0.219936	+	0.676894i
$326$	23.7024	−	17.2208i	1.31275	−	0.953772i
$327$		0			0
$328$	−27.5523	−	84.7973i	−1.52132	−	4.68215i
$329$	−2.58688			−0.142619
$330$		0			0
$331$	−3.98424			−0.218994			−0.109497	−	0.993987i	$-0.534924\pi$
$331$	−3.98424			−0.218994			−0.109497	+	0.993987i	$0.534924\pi$
$332$	3.62750	+	11.1643i	0.199085	+	0.612720i
$333$		0			0
$334$	−19.4119	+	14.1036i	−1.06217	+	0.771714i
$335$	3.19808	−	9.84266i	0.174730	−	0.537762i
$336$		0			0
$337$	9.14237	−	6.64232i	0.498017	−	0.361830i	−0.310242	−	0.950658i	$-0.600410\pi$
$337$	9.14237	−	6.64232i	0.498017	−	0.361830i	0.808259	+	0.588827i	$0.200410\pi$
$338$	48.6121	+	35.3187i	2.64415	+	1.92109i
$339$		0			0
$340$	2.97629			0.161412
$341$	−0.0530569	+	2.53367i	−0.00287319	+	0.137206i
$342$		0			0
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$	−8.77019	−	6.37191i	−0.472857	−	0.343550i
$345$		0			0
$346$	−11.8889	+	36.5904i	−0.639154	+	1.96711i
$347$	−2.03593	+	6.26594i	−0.109294	+	0.336373i	−0.990714	−	0.135960i	$-0.956588\pi$
$347$	−2.03593	+	6.26594i	−0.109294	+	0.336373i	0.881420	+	0.472333i	$0.156588\pi$
$348$		0			0
$349$	−16.5317	−	12.0110i	−0.884923	−	0.642934i	0.0496266	−	0.998768i	$-0.484197\pi$
$349$	−16.5317	−	12.0110i	−0.884923	−	0.642934i	−0.934549	+	0.355834i	$0.884197\pi$
$350$	−1.89002	−	5.81688i	−0.101026	−	0.310925i
$351$		0			0
$352$	−93.6892	−	32.6254i	−4.99365	−	1.73894i
$353$	−36.5457			−1.94513			−0.972565	−	0.232630i	$-0.925267\pi$
$353$	−36.5457			−1.94513			−0.972565	+	0.232630i	$0.925267\pi$
$354$		0			0
$355$	10.3144	+	7.49388i	0.547434	+	0.397734i
$356$	0.398205	−	0.289313i	0.0211048	−	0.0153336i
$357$		0			0
$358$	−3.32973	+	10.2479i	−0.175982	+	0.541616i
$359$	0.254415	−	0.184843i	0.0134275	−	0.00975564i	−0.581051	−	0.813867i	$-0.697358\pi$
$359$	0.254415	−	0.184843i	0.0134275	−	0.00975564i	0.594479	+	0.804111i	$0.297358\pi$
$360$		0			0
$361$	0.749035	+	2.30529i	0.0394229	+	0.121331i
$362$	54.7328			2.87669
$363$		0			0
$364$	−34.2434			−1.79484
$365$	−6.60767	−	20.3363i	−0.345861	−	1.06445i
$366$		0			0
$367$	−18.3608	+	13.3399i	−0.958426	+	0.696337i	−0.952785	−	0.303647i	$-0.901796\pi$
$367$	−18.3608	+	13.3399i	−0.958426	+	0.696337i	−0.00564133	+	0.999984i	$0.501796\pi$
$368$	7.83581	−	24.1162i	0.408470	−	1.25714i
$369$		0			0
$370$	12.1941	−	8.85956i	0.633943	−	0.460587i
$371$	1.17610	+	0.854485i	0.0610599	+	0.0443626i
$372$		0			0
$373$	32.8020			1.69843			0.849213	−	0.528051i	$-0.177077\pi$
$373$	32.8020			1.69843			0.849213	+	0.528051i	$0.177077\pi$
$374$	−2.66629	−	0.928480i	−0.137870	−	0.0480106i
$375$		0			0
$376$	−8.57413	−	26.3885i	−0.442177	−	1.36088i
$377$	18.8506	+	13.6958i	0.970856	+	0.705368i
$378$		0			0
$379$	7.86491	−	24.2057i	0.403993	−	1.24336i	−0.517740	−	0.855538i	$-0.673227\pi$
$379$	7.86491	−	24.2057i	0.403993	−	1.24336i	0.921733	−	0.387825i	$-0.126773\pi$
$380$	−13.9957	+	43.0742i	−0.717962	+	2.20966i
$381$		0			0
$382$	5.76234	+	4.18658i	0.294827	+	0.214204i
$383$	4.31159	+	13.2697i	0.220312	+	0.678050i	0.998734	+	0.0503087i	$0.0160205\pi$
$383$	4.31159	+	13.2697i	0.220312	+	0.678050i	−0.778422	+	0.627742i	$0.783979\pi$
$384$		0			0
$385$	0.116493	−	5.56299i	0.00593703	−	0.283516i
$386$	−60.5299			−3.08089
$387$		0			0
$388$	−4.89670	−	3.55766i	−0.248592	−	0.180613i
$389$	−7.33758	+	5.33107i	−0.372030	+	0.270296i	−0.758052	−	0.652194i	$-0.773849\pi$
$389$	−7.33758	+	5.33107i	−0.372030	+	0.270296i	0.386022	+	0.922490i	$0.373849\pi$
$390$		0			0
$391$	0.129865	−	0.399683i	0.00656754	−	0.0202128i
$392$	8.67739	−	6.30449i	0.438275	−	0.318425i
$393$		0			0
$394$	−19.0863	−	58.7415i	−0.961553	−	2.95936i
$395$	−10.3264			−0.519577
$396$		0			0
$397$	24.1849			1.21381			0.606904	−	0.794775i	$-0.292411\pi$
$397$	24.1849			1.21381			0.606904	+	0.794775i	$0.292411\pi$
$398$	11.0971	+	34.1533i	0.556246	+	1.71195i
$399$		0			0
$400$	32.4488	−	23.5754i	1.62244	−	1.17877i
$401$	−1.19394	+	3.67458i	−0.0596226	+	0.183500i	−0.976432	−	0.215826i	$-0.930756\pi$
$401$	−1.19394	+	3.67458i	−0.0596226	+	0.183500i	0.916809	+	0.399325i	$0.130756\pi$
$402$		0			0
$403$	−3.62935	+	2.63688i	−0.180791	+	0.131352i
$404$	−92.9429	−	67.5269i	−4.62408	−	3.35959i
$405$		0			0
$406$	−11.1070			−0.551230
$407$	−10.1927	+	3.07742i	−0.505233	+	0.152542i
$408$		0			0
$409$	6.21077	+	19.1148i	0.307103	+	0.945166i	0.978884	+	0.204416i	$0.0655296\pi$
$409$	6.21077	+	19.1148i	0.307103	+	0.945166i	−0.671781	+	0.740750i	$0.734470\pi$
$410$	31.5761	+	22.9414i	1.55943	+	1.13300i
$411$		0			0
$412$	−4.34845	+	13.3832i	−0.214233	+	0.659341i
$413$	−0.770825	+	2.37236i	−0.0379298	+	0.116736i
$414$		0			0
$415$	−2.73172	−	1.98471i	−0.134095	−	0.0974255i
$416$	−54.2690	−	167.023i	−2.66075	−	8.18896i
$417$		0			0
$418$	25.9753	−	34.2216i	1.27049	−	1.67383i
$419$	2.12825			0.103972			0.0519859	−	0.998648i	$-0.483445\pi$
$419$	2.12825			0.103972			0.0519859	+	0.998648i	$0.483445\pi$
$420$		0			0
$421$	3.11470	+	2.26296i	0.151801	+	0.110290i	0.661093	−	0.750304i	$-0.270093\pi$
$421$	3.11470	+	2.26296i	0.151801	+	0.110290i	−0.509292	+	0.860594i	$0.670093\pi$
$422$	−40.1675	+	29.1834i	−1.95532	+	1.42063i
$423$		0			0
$424$	−4.81837	+	14.8294i	−0.234000	+	0.720179i
$425$	0.537781	−	0.390721i	0.0260862	−	0.0189528i
$426$		0			0
$427$	−1.04848	−	3.22689i	−0.0507395	−	0.156160i
$428$	54.0238			2.61134
$429$		0			0
$430$	4.74544			0.228846
$431$	5.16151	+	15.8855i	0.248621	+	0.765177i	0.995020	+	0.0996781i	$0.0317813\pi$
$431$	5.16151	+	15.8855i	0.248621	+	0.765177i	−0.746399	+	0.665499i	$0.768219\pi$
$432$		0			0
$433$	−13.6898	+	9.94621i	−0.657889	+	0.477984i	−0.865949	−	0.500132i	$-0.833285\pi$
$433$	−13.6898	+	9.94621i	−0.657889	+	0.477984i	0.208060	+	0.978116i	$0.433285\pi$
$434$	0.660818	−	2.03379i	0.0317203	−	0.0976250i
$435$		0			0
$436$	39.1893	−	28.4727i	1.87683	−	1.36359i
$437$	5.17371	+	3.75892i	0.247492	+	0.179813i
$438$		0			0
$439$	−26.7946			−1.27883			−0.639417	−	0.768860i	$-0.720824\pi$
$439$	−26.7946			−1.27883			−0.639417	+	0.768860i	$0.720824\pi$
$440$	57.1336	−	17.2500i	2.72374	−	0.822363i
$441$		0			0
$442$	−1.54443	−	4.75327i	−0.0734611	−	0.226090i
$443$	−3.17465	−	2.30652i	−0.150832	−	0.109586i	0.509810	−	0.860287i	$-0.329716\pi$
$443$	−3.17465	−	2.30652i	−0.150832	−	0.109586i	−0.660642	+	0.750701i	$0.729716\pi$
$444$		0			0
$445$	−0.0437507	+	0.134651i	−0.00207398	+	0.00638306i
$446$	−14.8037	+	45.5611i	−0.700976	+	2.15738i
$447$		0			0
$448$	38.0301	+	27.6305i	1.79675	+	1.30542i
$449$	−6.08099	−	18.7154i	−0.286980	−	0.883233i	−0.985798	−	0.167934i	$-0.946291\pi$
$449$	−6.08099	−	18.7154i	−0.286980	−	0.883233i	0.698819	−	0.715299i	$-0.253709\pi$
$450$		0			0
$451$	−15.7349	−	22.6392i	−0.740925	−	1.06604i
$452$	−31.9598			−1.50326
$453$		0			0
$454$	46.3861	+	33.7015i	2.17701	+	1.58169i
$455$	7.96869	−	5.78959i	0.373578	−	0.271420i
$456$		0			0
$457$	6.11005	−	18.8048i	0.285816	−	0.879652i	−0.700337	−	0.713813i	$-0.746967\pi$
$457$	6.11005	−	18.8048i	0.285816	−	0.879652i	0.986153	−	0.165839i	$-0.0530332\pi$
$458$	55.3230	−	40.1945i	2.58507	−	1.87817i
$459$		0			0
$460$	4.17771	+	12.8577i	0.194787	+	0.599492i
$461$	−9.69184			−0.451394			−0.225697	−	0.974198i	$-0.572466\pi$
$461$	−9.69184			−0.451394			−0.225697	+	0.974198i	$0.572466\pi$
$462$		0			0
$463$	7.21162			0.335152			0.167576	−	0.985859i	$-0.446406\pi$
$463$	7.21162			0.335152			0.167576	+	0.985859i	$0.446406\pi$
$464$	−22.5079	−	69.2723i	−1.04490	−	3.21588i
$465$		0			0
$466$	53.6726	−	38.9954i	2.48633	−	1.80643i
$467$	−11.3013	+	34.7818i	−0.522962	+	1.60951i	0.245349	+	0.969435i	$0.421098\pi$
$467$	−11.3013	+	34.7818i	−0.522962	+	1.60951i	−0.768311	+	0.640077i	$0.778902\pi$
$468$		0			0
$469$	4.99065	−	3.62592i	0.230447	−	0.167429i
$470$	9.82633	+	7.13924i	0.453255	+	0.329309i
$471$		0			0
$472$	−26.7550			−1.23150
$473$	−3.16564	−	1.10237i	−0.145556	−	0.0506871i
$474$		0			0
$475$	3.12583	+	9.62032i	0.143423	+	0.441411i
$476$	1.43525	+	1.04277i	0.0657844	+	0.0477951i
$477$		0			0
$478$	−1.36641	+	4.20538i	−0.0624981	+	0.192349i
$479$	−12.0424	+	37.0626i	−0.550229	+	1.69343i	0.157991	+	0.987441i	$0.449498\pi$
$479$	−12.0424	+	37.0626i	−0.550229	+	1.69343i	−0.708220	+	0.705992i	$0.750502\pi$
$480$		0			0
$481$	−15.2481	−	11.0784i	−0.695254	−	0.505131i
$482$	10.5840	+	32.5743i	0.482089	+	1.48372i
$483$		0			0
$484$	−64.1012	−	2.68583i	−2.91369	−	0.122083i
$485$	1.74100			0.0790548
$486$		0			0
$487$	19.4030	+	14.0971i	0.879235	+	0.638802i	0.933049	−	0.359749i	$-0.117138\pi$
$487$	19.4030	+	14.0971i	0.879235	+	0.638802i	−0.0538139	+	0.998551i	$0.517138\pi$
$488$	29.4420	−	21.3908i	1.33278	−	0.968318i
$489$		0			0
$490$	−1.45091	+	4.46543i	−0.0655453	+	0.201728i
$491$	2.58327	−	1.87686i	0.116581	−	0.0847014i	−0.527967	−	0.849265i	$-0.677045\pi$
$491$	2.58327	−	1.87686i	0.116581	−	0.0847014i	0.644548	+	0.764564i	$0.277045\pi$
$492$		0			0
$493$	−0.373029	−	1.14807i	−0.0168004	−	0.0517063i
$494$	76.0539			3.42183
$495$		0			0
$496$	14.0235			0.629674
$497$	2.34835	+	7.22749i	0.105338	+	0.324197i
$498$		0			0
$499$	−22.2747	+	16.1835i	−0.997154	+	0.724475i	−0.961476	−	0.274889i	$-0.911359\pi$
$499$	−22.2747	+	16.1835i	−0.997154	+	0.724475i	−0.0356777	+	0.999363i	$0.511359\pi$
$500$	−21.7268	+	66.8682i	−0.971652	+	2.99044i
$501$		0			0
$502$	−43.9491	+	31.9309i	−1.96154	+	1.42515i
$503$	−26.8244	−	19.4891i	−1.19604	−	0.868976i	−0.202153	−	0.979354i	$-0.564794\pi$
$503$	−26.8244	−	19.4891i	−1.19604	−	0.868976i	−0.993890	+	0.110378i	$0.964794\pi$
$504$		0			0
$505$	33.0454			1.47050
$506$	0.268496	−	12.8217i	0.0119361	−	0.569994i
$507$		0			0
$508$	36.1507	+	111.260i	1.60393	+	4.93638i
$509$	−6.22522	−	4.52288i	−0.275928	−	0.200473i	0.441211	−	0.897403i	$-0.354549\pi$
$509$	−6.22522	−	4.52288i	−0.275928	−	0.200473i	−0.717139	+	0.696930i	$0.754549\pi$
$510$		0			0
$511$	3.93859	−	12.1217i	0.174233	−	0.536234i
$512$	−47.9823	+	147.674i	−2.12054	+	6.52635i
$513$		0			0
$514$	0.611559	+	0.444324i	0.0269747	+	0.0195983i
$515$	−1.25080	−	3.84956i	−0.0551168	−	0.169632i
$516$		0			0
$517$	−4.89660	−	7.04519i	−0.215352	−	0.309847i
$518$	8.98434			0.394749
$519$		0			0
$520$	85.4709	+	62.0983i	3.74815	+	2.72319i
$521$	−6.55164	+	4.76004i	−0.287032	+	0.208541i	−0.721979	−	0.691915i	$-0.756767\pi$
$521$	−6.55164	+	4.76004i	−0.287032	+	0.208541i	0.434946	+	0.900456i	$0.356767\pi$
$522$		0			0
$523$	5.98036	−	18.4056i	0.261503	−	0.804823i	−0.730976	−	0.682404i	$-0.760935\pi$
$523$	5.98036	−	18.4056i	0.261503	−	0.804823i	0.992478	−	0.122419i	$-0.0390653\pi$
$524$	19.9170	−	14.4705i	0.870077	−	0.632148i
$525$		0			0
$526$	24.2091	+	74.5078i	1.05557	+	3.24870i
$527$	0.232415			0.0101241
$528$		0			0
$529$	−21.0911			−0.917003
$530$	−2.10924	−	6.49156i	−0.0916194	−	0.281976i
$531$		0			0
$532$	−21.8404	+	15.8680i	−0.946904	+	0.687966i
$533$	15.0816	−	46.4165i	0.653258	−	2.01052i
$534$		0			0
$535$	−12.5718	+	9.13391i	−0.543524	+	0.394893i
$536$	53.5289	+	38.8910i	2.31210	+	1.67984i
$537$		0			0
$538$	3.12571			0.134759
$539$	2.00521	−	2.64180i	0.0863706	−	0.113791i
$540$		0			0
$541$	−8.83427	−	27.1891i	−0.379815	−	1.16895i	−0.940172	−	0.340700i	$-0.889336\pi$
$541$	−8.83427	−	27.1891i	−0.379815	−	1.16895i	0.560357	−	0.828251i	$-0.310664\pi$
$542$	56.2214	+	40.8472i	2.41491	+	1.75454i
$543$		0			0
$544$	−2.81154	+	8.65302i	−0.120544	+	0.370995i
$545$	−4.30571	+	13.2516i	−0.184436	+	0.567637i
$546$		0			0
$547$	−18.9243	−	13.7493i	−0.809143	−	0.587877i	0.104439	−	0.994531i	$-0.466695\pi$
$547$	−18.9243	−	13.7493i	−0.809143	−	0.587877i	−0.913582	+	0.406654i	$0.866695\pi$
$548$	26.1991	+	80.6324i	1.11917	+	3.44445i
$549$		0			0
$550$	12.2643	−	16.1579i	0.522953	−	0.688974i
$551$	18.3694			0.782564
$552$		0			0
$553$	−4.97965	−	3.61793i	−0.211756	−	0.153850i
$554$	−28.1515	+	20.4532i	−1.19604	+	0.868975i
$555$		0			0
$556$	12.5193	−	38.5305i	0.530938	−	1.63406i
$557$	20.5782	−	14.9510i	0.871927	−	0.633492i	−0.0591762	−	0.998248i	$-0.518847\pi$
$557$	20.5782	−	14.9510i	0.871927	−	0.633492i	0.931103	+	0.364755i	$0.118847\pi$
$558$		0			0
$559$	−1.83368	−	5.64349i	−0.0775565	−	0.238694i
$560$	−30.7903			−1.30113
$561$		0			0
$562$	−18.8506			−0.795167
$563$	−12.3233	−	37.9273i	−0.519366	−	1.59844i	−0.775195	−	0.631722i	$-0.782348\pi$
$563$	−12.3233	−	37.9273i	−0.519366	−	1.59844i	0.255829	−	0.966722i	$-0.417652\pi$
$564$		0			0
$565$	7.43730	−	5.40351i	0.312890	−	0.227328i
$566$	9.65207	−	29.7060i	0.405707	−	1.24864i
$567$		0			0
$568$	−65.9432	+	47.9106i	−2.76692	+	2.01028i
$569$	26.0897	+	18.9553i	1.09374	+	0.794648i	0.980027	−	0.198866i	$-0.0637258\pi$
$569$	26.0897	+	18.9553i	1.09374	+	0.794648i	0.113712	+	0.993514i	$0.463726\pi$
$570$		0			0
$571$	−20.6844			−0.865615			−0.432807	−	0.901486i	$-0.642477\pi$
$571$	−20.6844			−0.865615			−0.432807	+	0.901486i	$0.642477\pi$
$572$	−64.8179	−	93.2595i	−2.71017	−	3.89937i
$573$		0			0
$574$	7.18913	+	22.1259i	0.300069	+	0.923516i
$575$	2.44279	+	1.77479i	0.101871	+	0.0740139i
$576$		0			0
$577$	4.85769	−	14.9504i	0.202228	−	0.622394i	−0.797588	−	0.603203i	$-0.793891\pi$
$577$	4.85769	−	14.9504i	0.202228	−	0.622394i	0.999816	−	0.0191913i	$-0.00610914\pi$
$578$	14.6222	−	45.0024i	0.608201	−	1.87185i
$579$		0			0
$580$	31.4170	+	22.8258i	1.30452	+	0.947790i
$581$	−0.621946	−	1.91415i	−0.0258027	−	0.0794125i
$582$		0			0
$583$	−0.100943	+	4.82044i	−0.00418065	+	0.199642i
$584$	136.707			5.65697
$585$		0			0
$586$	38.2665	+	27.8022i	1.58077	+	1.14850i
$587$	16.6401	−	12.0898i	0.686812	−	0.498998i	−0.188799	−	0.982016i	$-0.560459\pi$
$587$	16.6401	−	12.0898i	0.686812	−	0.498998i	0.875611	+	0.483018i	$0.160459\pi$
$588$		0			0
$589$	−1.09290	+	3.36361i	−0.0450323	+	0.138595i
$590$	9.47521	−	6.88414i	0.390088	−	0.283416i
$591$		0			0
$592$	18.2065	+	56.0337i	0.748281	+	2.30297i
$593$	−21.1496			−0.868511			−0.434255	−	0.900790i	$-0.642988\pi$
$593$	−21.1496			−0.868511			−0.434255	+	0.900790i	$0.642988\pi$
$594$		0			0
$595$	−0.510295			−0.0209201
$596$	25.1679	+	77.4589i	1.03092	+	3.17284i
$597$		0			0
$598$	18.3664	−	13.3440i	0.751058	−	0.545676i
$599$	10.4136	−	32.0499i	0.425490	−	1.30952i	−0.477034	−	0.878885i	$-0.658288\pi$
$599$	10.4136	−	32.0499i	0.425490	−	1.30952i	0.902524	−	0.430639i	$-0.141712\pi$
$600$		0			0
$601$	29.7628	−	21.6239i	1.21405	−	0.882059i	0.218458	−	0.975846i	$-0.429897\pi$
$601$	29.7628	−	21.6239i	1.21405	−	0.882059i	0.995592	+	0.0937876i	$0.0298974\pi$
$602$	2.28838	+	1.66260i	0.0932672	+	0.0677626i
$603$		0			0
$604$	−7.99519			−0.325320
$605$	15.3709	−	10.2127i	0.624917	−	0.415205i
$606$		0			0
$607$	3.72718	+	11.4711i	0.151282	+	0.465597i	0.997765	−	0.0668177i	$-0.0212846\pi$
$607$	3.72718	+	11.4711i	0.151282	+	0.465597i	−0.846483	+	0.532415i	$0.821285\pi$
$608$	−112.009	−	81.3796i	−4.54258	−	3.30038i
$609$		0			0
$610$	−4.92286	+	15.1510i	−0.199321	+	0.613446i
$611$	4.69332	−	14.4446i	0.189872	−	0.584365i
$612$		0			0
$613$	−6.93847	−	5.04109i	−0.280242	−	0.203608i	0.438781	−	0.898594i	$-0.355410\pi$
$613$	−6.93847	−	5.04109i	−0.280242	−	0.203608i	−0.719023	+	0.694986i	$0.755410\pi$
$614$	9.81180	+	30.1976i	0.395972	+	1.21868i
$615$		0			0
$616$	33.5950	+	11.6988i	1.35358	+	0.471357i
$617$	0.0309560			0.00124624			0.000623121	−	1.00000i	$-0.499802\pi$
$617$	0.0309560			0.00124624			0.000623121		1.00000i	$0.499802\pi$
$618$		0			0
$619$	17.2270	+	12.5162i	0.692412	+	0.503067i	0.877452	−	0.479664i	$-0.159241\pi$
$619$	17.2270	+	12.5162i	0.692412	+	0.503067i	−0.185040	+	0.982731i	$0.559241\pi$
$620$	−6.04879	+	4.39471i	−0.242925	+	0.176496i
$621$		0			0
$622$	20.6252	−	63.4778i	0.826994	−	2.54523i
$623$	−0.0682736	+	0.0496037i	−0.00273532	+	0.00198733i
$624$		0			0
$625$	−2.87290	−	8.84187i	−0.114916	−	0.353675i
$626$	−86.6650			−3.46383
$627$		0			0
$628$	−92.7351			−3.70053
$629$	0.301740	+	0.928660i	0.0120312	+	0.0370281i
$630$		0			0
$631$	−17.6281	+	12.8075i	−0.701762	+	0.509860i	−0.880506	−	0.474036i	$-0.842797\pi$
$631$	−17.6281	+	12.8075i	−0.701762	+	0.509860i	0.178744	+	0.983896i	$0.442797\pi$
$632$	20.4012	−	62.7883i	0.811515	−	2.49759i
$633$		0			0
$634$	−7.26513	+	5.27842i	−0.288535	+	0.209633i
$635$	−27.2235	−	19.7791i	−1.08033	−	0.784908i
$636$		0			0
$637$	5.87113			0.232623
$638$	−21.0240	−	30.2491i	−0.832346	−	1.19757i
$639$		0			0
$640$	−37.1893	−	114.457i	−1.47004	−	4.52431i
$641$	−32.2773	−	23.4508i	−1.27487	−	0.926251i	−0.275489	−	0.961304i	$-0.588840\pi$
$641$	−32.2773	−	23.4508i	−1.27487	−	0.926251i	−0.999385	+	0.0350534i	$0.988840\pi$
$642$		0			0
$643$	2.21134	−	6.80580i	0.0872067	−	0.268395i	−0.897938	−	0.440123i	$-0.854935\pi$
$643$	2.21134	−	6.80580i	0.0872067	−	0.268395i	0.985144	+	0.171728i	$0.0549350\pi$
$644$	−2.49018	+	7.66400i	−0.0981270	+	0.302004i
$645$		0			0
$646$	−3.18766	−	2.31597i	−0.125417	−	0.0911205i
$647$	1.46751	+	4.51654i	0.0576938	+	0.177563i	0.975750	−	0.218886i	$-0.0702423\pi$
$647$	1.46751	+	4.51654i	0.0576938	+	0.177563i	−0.918057	+	0.396449i	$0.870242\pi$
$648$		0			0
$649$	−7.92002	+	2.39125i	−0.310888	+	0.0938647i
$650$	35.9092			1.40848
$651$		0			0
$652$	−49.3966	−	35.8887i	−1.93452	−	1.40551i
$653$	−4.07243	+	2.95879i	−0.159366	+	0.115786i	−0.664610	−	0.747190i	$-0.731402\pi$
$653$	−4.07243	+	2.95879i	−0.159366	+	0.115786i	0.505244	+	0.862976i	$0.331402\pi$
$654$		0			0
$655$	−2.18827	+	6.73480i	−0.0855028	+	0.263151i
$656$	−123.427	+	89.6747i	−4.81900	+	3.50121i
$657$		0			0
$658$	2.23722	+	6.88545i	0.0872159	+	0.268423i
$659$	−6.55136			−0.255205			−0.127602	−	0.991825i	$-0.540728\pi$
$659$	−6.55136			−0.255205			−0.127602	+	0.991825i	$0.540728\pi$
$660$		0			0
$661$	36.4255			1.41679			0.708394	−	0.705818i	$-0.249420\pi$
$661$	36.4255			1.41679			0.708394	+	0.705818i	$0.249420\pi$
$662$	3.44570	+	10.6048i	0.133921	+	0.412167i
$663$		0			0
$664$	17.4647	−	12.6888i	0.677760	−	0.492421i
$665$	2.39960	−	7.38521i	0.0930526	−	0.286386i
$666$		0			0
$667$	4.43607	−	3.22299i	0.171765	−	0.124795i
$668$	40.4551	+	29.3923i	1.56525	+	1.13722i
$669$		0			0
$670$	−28.9639			−1.11897
$671$	6.80359	−	8.96351i	0.262650	−	0.346033i
$672$		0			0
$673$	9.88569	+	30.4250i	0.381065	+	1.17280i	0.939295	+	0.343112i	$0.111481\pi$
$673$	9.88569	+	30.4250i	0.381065	+	1.17280i	−0.558229	+	0.829687i	$0.688519\pi$
$674$	−25.5864	−	18.5896i	−0.985551	−	0.716044i
$675$		0			0
$676$	38.6966	−	119.096i	1.48833	−	4.58062i
$677$	6.68766	−	20.5825i	0.257028	−	0.791050i	−0.736396	−	0.676551i	$-0.763474\pi$
$677$	6.68766	−	20.5825i	0.257028	−	0.791050i	0.993423	−	0.114499i	$-0.0365263\pi$
$678$		0			0
$679$	0.839556	+	0.609973i	0.0322192	+	0.0234086i
$680$	−1.69136	−	5.20546i	−0.0648606	−	0.199620i
$681$		0			0
$682$	6.78972	−	2.04998i	0.259992	−	0.0784980i
$683$	23.1587			0.886144			0.443072	−	0.896486i	$-0.353889\pi$
$683$	23.1587			0.886144			0.443072	+	0.896486i	$0.353889\pi$
$684$		0			0
$685$	−19.7294	−	14.3343i	−0.753822	−	0.547684i
$686$	−2.26416	+	1.64501i	−0.0864461	+	0.0628068i
$687$		0			0
$688$	−5.73204	+	17.6414i	−0.218532	+	0.672572i
$689$	−6.90503	+	5.01680i	−0.263061	+	0.191125i
$690$		0			0
$691$	0.833105	+	2.56403i	0.0316928	+	0.0975404i	0.965652	−	0.259840i	$-0.0836699\pi$
$691$	0.833105	+	2.56403i	0.0316928	+	0.0975404i	−0.933959	+	0.357381i	$0.883670\pi$
$692$	80.1798			3.04798
$693$		0			0
$694$	18.4387			0.699923
$695$	3.60109	+	11.0830i	0.136597	+	0.420403i
$696$		0			0
$697$	−2.04558	+	1.48620i	−0.0774818	+	0.0562938i
$698$	−17.6723	+	54.3897i	−0.668906	+	2.05868i
$699$		0			0
$700$	−10.3121	+	7.49216i	−0.389760	+	0.283177i
$701$	0.361861	+	0.262907i	0.0136673	+	0.00992987i	0.594598	−	0.804023i	$-0.297311\pi$
$701$	0.361861	+	0.262907i	0.0136673	+	0.00992987i	−0.580931	+	0.813953i	$0.697311\pi$
$702$		0			0
$703$	−14.8589			−0.560413
$704$	−3.26409	+	155.873i	−0.123020	+	5.87469i
$705$		0			0
$706$	31.6059	+	97.2731i	1.18950	+	3.66092i
$707$	15.9354	+	11.5777i	0.599311	+	0.435425i
$708$		0			0
$709$	3.46998	−	10.6795i	0.130318	−	0.401077i	−0.864515	−	0.502608i	$-0.832374\pi$
$709$	3.46998	−	10.6795i	0.130318	−	0.401077i	0.994832	+	0.101531i	$0.0323740\pi$
$710$	11.0261	−	33.9347i	0.413801	−	1.27355i
$711$		0			0
$712$	−0.732292	−	0.532041i	−0.0274438	−	0.0199391i
$713$	0.326232	+	1.00404i	0.0122175	+	0.0376015i
$714$		0			0
$715$	30.8512	+	10.7433i	1.15377	+	0.401777i
$716$	22.4559			0.839218
$717$		0			0
$718$	−0.712020	−	0.517313i	−0.0265723	−	0.0193059i
$719$	7.31641	−	5.31568i	0.272856	−	0.198241i	−0.442939	−	0.896552i	$-0.646064\pi$
$719$	7.31641	−	5.31568i	0.272856	−	0.198241i	0.715795	+	0.698310i	$0.246064\pi$
$720$		0			0
$721$	0.745556	−	2.29458i	0.0277659	−	0.0854548i
$722$	5.48817	−	3.98739i	0.204249	−	0.148395i
$723$		0			0
$724$	−35.2480	−	108.482i	−1.30998	−	4.03171i
$725$	8.67321			0.322115
$726$		0			0
$727$	−44.1368			−1.63694			−0.818471	−	0.574548i	$-0.805178\pi$
$727$	−44.1368			−1.63694			−0.818471	+	0.574548i	$0.805178\pi$
$728$	19.4597	+	59.8908i	0.721224	+	2.21970i
$729$		0			0
$730$	−48.4143	+	35.1750i	−1.79189	+	1.30189i
$731$	−0.0949984	+	0.292375i	−0.00351364	+	0.0108139i
$732$		0			0
$733$	22.6879	−	16.4837i	0.837997	−	0.608840i	−0.0838136	−	0.996481i	$-0.526710\pi$
$733$	22.6879	−	16.4837i	0.837997	−	0.608840i	0.921810	+	0.387641i	$0.126710\pi$
$734$	51.3856	+	37.3338i	1.89668	+	1.37802i
$735$		0			0
$736$	−41.3277			−1.52336
$737$	19.3215	+	6.72833i	0.711718	+	0.247841i
$738$		0			0
$739$	−13.5061	−	41.5674i	−0.496829	−	1.52908i	−0.814088	−	0.580742i	$-0.802762\pi$
$739$	−13.5061	−	41.5674i	−0.496829	−	1.52908i	0.317259	−	0.948339i	$-0.397238\pi$
$740$	−25.4130	−	18.4636i	−0.934199	−	0.678735i
$741$		0			0
$742$	1.25724	−	3.86939i	0.0461547	−	0.142050i
$743$	6.60295	−	20.3218i	0.242239	−	0.745534i	−0.753840	−	0.657058i	$-0.771801\pi$
$743$	6.60295	−	20.3218i	0.242239	−	0.745534i	0.996078	−	0.0884755i	$-0.0281995\pi$
$744$		0			0
$745$	−18.9529	−	13.7701i	−0.694380	−	0.504497i
$746$	−28.3683	−	87.3086i	−1.03864	−	3.19660i
$747$		0			0
$748$	−0.123186	+	5.88261i	−0.00450412	+	0.215089i
$749$	−9.26256			−0.338446
$750$		0			0
$751$	−1.81171	−	1.31629i	−0.0661104	−	0.0480320i	0.554239	−	0.832357i	$-0.313009\pi$
$751$	−1.81171	−	1.31629i	−0.0661104	−	0.0480320i	−0.620350	+	0.784325i	$0.713009\pi$
$752$	−38.4097	+	27.9063i	−1.40066	+	1.01764i
$753$		0			0
$754$	20.1512	−	62.0189i	0.733863	−	2.25860i
$755$	1.86054	−	1.35176i	0.0677120	−	0.0491957i
$756$		0			0
$757$	14.7429	+	45.3740i	0.535840	+	1.64915i	0.741828	+	0.670591i	$0.233959\pi$
$757$	14.7429	+	45.3740i	0.535840	+	1.64915i	−0.205988	+	0.978555i	$0.566041\pi$
$758$	−71.2297			−2.58718
$759$		0			0
$760$	83.2891			3.02121
$761$	11.0143	+	33.8985i	0.399268	+	1.22882i	0.925588	+	0.378534i	$0.123572\pi$
$761$	11.0143	+	33.8985i	0.399268	+	1.22882i	−0.526320	+	0.850287i	$0.676428\pi$
$762$		0			0
$763$	−6.71913	+	4.88173i	−0.243249	+	0.176731i
$764$	4.58699	−	14.1173i	0.165951	−	0.510746i
$765$		0			0
$766$	31.5909	−	22.9522i	1.14143	−	0.829296i
$767$	−11.8482	−	8.60824i	−0.427815	−	0.310826i
$768$		0			0
$769$	22.0645			0.795665			0.397832	−	0.917458i	$-0.369763\pi$
$769$	22.0645			0.795665			0.397832	+	0.917458i	$0.369763\pi$
$770$	−14.9077	+	4.50099i	−0.537235	+	0.162205i
$771$		0			0
$772$	38.9813	+	119.972i	1.40297	+	4.31789i
$773$	−15.2956	−	11.1129i	−0.550145	−	0.399703i	0.277694	−	0.960670i	$-0.410430\pi$
$773$	−15.2956	−	11.1129i	−0.550145	−	0.399703i	−0.827839	+	0.560966i	$0.810430\pi$
$774$		0			0
$775$	−0.516019	+	1.58814i	−0.0185360	+	0.0570478i
$776$	−3.43958	+	10.5859i	−0.123474	+	0.380013i
$777$		0			0
$778$	20.5354	+	14.9198i	0.736230	+	0.534902i
$779$	−11.8898	−	36.5932i	−0.425998	−	1.31109i
$780$		0			0
$781$	−15.2385	+	20.0762i	−0.545275	+	0.718383i
$782$	−1.17614			−0.0420587
$783$		0			0
$784$	−14.8479	−	10.7876i	−0.530282	−	0.385272i
$785$	21.5802	−	15.6789i	0.770229	−	0.559604i
$786$		0			0
$787$	2.05310	−	6.31878i	0.0731850	−	0.225240i	−0.907772	−	0.419463i	$-0.862218\pi$
$787$	2.05310	−	6.31878i	0.0731850	−	0.225240i	0.980957	+	0.194223i	$0.0622184\pi$
$788$	−104.136	+	75.6592i	−3.70969	+	2.69525i
$789$		0			0
$790$	8.93060	+	27.4856i	0.317737	+	0.977893i
$791$	5.47962			0.194833
$792$		0			0
$793$	19.9205			0.707397
$794$	−20.9159	−	64.3727i	−0.742279	−	2.28450i
$795$		0			0
$796$	60.5463	−	43.9895i	2.14601	−	1.55917i
$797$	4.72849	−	14.5528i	0.167492	−	0.515486i	−0.831720	−	0.555196i	$-0.812643\pi$
$797$	4.72849	−	14.5528i	0.167492	−	0.515486i	0.999211	+	0.0397097i	$0.0126433\pi$
$798$		0			0
$799$	−0.636573	+	0.462497i	−0.0225203	+	0.0163620i
$800$	−52.8857	−	38.4237i	−1.86979	−	1.35848i
$801$		0			0
$802$	10.8131			0.381825
$803$	40.4679	−	12.2183i	1.42808	−	0.431173i
$804$		0			0
$805$	−0.716282	−	2.20449i	−0.0252456	−	0.0776981i
$806$	10.1573	+	7.37973i	0.357776	+	0.259940i
$807$		0			0
$808$	−65.2857	+	200.929i	−2.29674	+	7.06865i
$809$	−7.63556	+	23.4998i	−0.268452	+	0.826210i	0.722426	+	0.691448i	$0.243027\pi$
$809$	−7.63556	+	23.4998i	−0.268452	+	0.826210i	−0.990878	+	0.134762i	$0.956973\pi$
$810$		0			0
$811$	−20.8629	−	15.1578i	−0.732597	−	0.532263i	0.157787	−	0.987473i	$-0.449564\pi$
$811$	−20.8629	−	15.1578i	−0.732597	−	0.532263i	−0.890384	+	0.455211i	$0.849564\pi$
$812$	7.15291	+	22.0144i	0.251018	+	0.772554i
$813$		0			0
$814$	17.0061	+	24.4682i	0.596063	+	0.857611i
$815$	17.5627			0.615195
$816$		0			0
$817$	−3.78466	−	2.74972i	−0.132408	−	0.0962004i
$818$	45.5063	−	33.0622i	1.59109	−	1.15599i
$819$		0			0
$820$	25.1355	−	77.3592i	0.877771	−	2.70150i
$821$	−14.8104	+	10.7604i	−0.516885	+	0.375539i	−0.815429	−	0.578857i	$-0.803499\pi$
$821$	−14.8104	+	10.7604i	−0.516885	+	0.375539i	0.298544	+	0.954396i	$0.403499\pi$
$822$		0			0
$823$	−1.49684	−	4.60680i	−0.0521766	−	0.160583i	0.921573	−	0.388205i	$-0.126905\pi$
$823$	−1.49684	−	4.60680i	−0.0521766	−	0.160583i	−0.973750	+	0.227622i	$0.926905\pi$
$824$	25.8779			0.901500
$825$		0			0
$826$	6.98110			0.242903
$827$	−7.99793	−	24.6151i	−0.278115	−	0.855951i	−0.988378	−	0.152014i	$-0.951424\pi$
$827$	−7.99793	−	24.6151i	−0.278115	−	0.855951i	0.710263	−	0.703936i	$-0.248576\pi$
$828$		0			0
$829$	−43.8054	+	31.8265i	−1.52142	+	1.10538i	−0.560649	+	0.828054i	$0.689448\pi$
$829$	−43.8054	+	31.8265i	−1.52142	+	1.10538i	−0.960776	+	0.277326i	$0.910552\pi$
$830$	−2.92018	+	8.98740i	−0.101361	+	0.311957i
$831$		0			0
$832$	−223.280	+	162.222i	−7.74084	+	5.62405i
$833$	−0.246078	−	0.178786i	−0.00852608	−	0.00619456i
$834$		0			0
$835$	−14.3836			−0.497766
$836$	−84.5564	−	29.4450i	−2.92444	−	1.01838i
$837$		0			0
$838$	−1.84058	−	5.66473i	−0.0635819	−	0.195685i
$839$	26.1821	+	19.0224i	0.903907	+	0.656727i	0.939467	−	0.342640i	$-0.111321\pi$
$839$	26.1821	+	19.0224i	0.903907	+	0.656727i	−0.0355593	+	0.999368i	$0.511321\pi$
$840$		0			0
$841$	−4.09435	+	12.6011i	−0.141184	+	0.434521i
$842$	3.32959	−	10.2474i	0.114745	−	0.353149i
$843$		0			0
$844$	83.7104	+	60.8191i	2.88143	+	2.09348i
$845$	11.1308	+	34.2571i	0.382911	+	1.17848i
$846$		0			0
$847$	10.9904	+	0.460494i	0.377633	+	0.0158228i
$848$	26.6804			0.916210
$849$		0			0
$850$	−1.50507	−	1.09350i	−0.0516234	−	0.0375066i
$851$	−3.58830	+	2.60705i	−0.123005	+	0.0893685i
$852$		0			0
$853$	1.89308	−	5.82631i	0.0648180	−	0.199489i	−0.913403	−	0.407057i	$-0.866555\pi$
$853$	1.89308	−	5.82631i	0.0648180	−	0.199489i	0.978221	+	0.207568i	$0.0665549\pi$
$854$	−7.68220	+	5.58144i	−0.262879	+	0.190993i
$855$		0			0
$856$	−30.7005	−	94.4863i	−1.04932	−	3.22948i
$857$	22.6396			0.773354			0.386677	−	0.922215i	$-0.373623\pi$
$857$	22.6396			0.773354			0.386677	+	0.922215i	$0.373623\pi$
$858$		0			0
$859$	−13.7204			−0.468134			−0.234067	−	0.972220i	$-0.575204\pi$
$859$	−13.7204			−0.468134			−0.234067	+	0.972220i	$0.575204\pi$
$860$	−3.05607	−	9.40562i	−0.104211	−	0.320729i
$861$		0			0
$862$	37.8183	−	27.4766i	1.28810	−	0.935857i
$863$	−13.4826	+	41.4951i	−0.458953	+	1.41251i	0.407479	+	0.913215i	$0.366408\pi$
$863$	−13.4826	+	41.4951i	−0.458953	+	1.41251i	−0.866431	+	0.499296i	$0.833592\pi$
$864$		0			0
$865$	−18.6585	+	13.5562i	−0.634407	+	0.460923i
$866$	38.3131	+	27.8361i	1.30193	+	0.945908i
$867$		0			0
$868$	−4.45660			−0.151267
$869$	0.427399	−	20.4100i	0.0144985	−	0.692361i
$870$		0			0
$871$	11.1919	+	34.4451i	0.379223	+	1.16713i
$872$	−72.0683	−	52.3607i	−2.44054	−	1.77316i
$873$		0			0
$874$	5.53065	−	17.0216i	0.187077	−	0.575764i
$875$	3.72513	−	11.4648i	0.125932	−	0.387580i
$876$		0			0
$877$	−27.4356	−	19.9331i	−0.926433	−	0.673093i	0.0186840	−	0.999825i	$-0.494052\pi$
$877$	−27.4356	−	19.9331i	−0.926433	−	0.673093i	−0.945117	+	0.326733i	$0.894052\pi$
$878$	23.1728	+	71.3186i	0.782045	+	2.40689i
$879$		0			0
$880$	−58.2818	−	83.8554i	−1.96468	−	2.82676i
$881$	−12.7514			−0.429605			−0.214803	−	0.976657i	$-0.568911\pi$
$881$	−12.7514			−0.429605			−0.214803	+	0.976657i	$0.568911\pi$
$882$		0			0
$883$	−0.713738	−	0.518561i	−0.0240192	−	0.0174510i	0.575711	−	0.817653i	$-0.304725\pi$
$883$	−0.713738	−	0.518561i	−0.0240192	−	0.0174510i	−0.599730	+	0.800202i	$0.704725\pi$
$884$	−8.42652	+	6.12223i	−0.283415	+	0.205913i
$885$		0			0
$886$	−3.39368	+	10.4447i	−0.114013	+	0.350895i
$887$	27.8500	−	20.2342i	0.935112	−	0.679399i	−0.0121270	−	0.999926i	$-0.503860\pi$
$887$	27.8500	−	20.2342i	0.935112	−	0.679399i	0.947239	+	0.320528i	$0.103860\pi$
$888$		0			0
$889$	−6.19815	−	19.0759i	−0.207879	−	0.639786i
$890$	0.396235			0.0132818
$891$		0			0
$892$	99.8372			3.34280
$893$	−3.70005	−	11.3876i	−0.123818	−	0.381071i
$894$		0			0
$895$	−5.22567	+	3.79667i	−0.174675	+	0.126909i
$896$	22.1672	−	68.2237i	0.740555	−	2.27919i
$897$		0			0
$898$	−44.5553	+	32.3713i	−1.48683	+	1.08025i
$899$	2.45331	+	1.78244i	0.0818226	+	0.0594476i
$900$		0			0
$901$	0.442181			0.0147312
$902$	−46.6503	+	61.4603i	−1.55329	+	2.04640i
$903$		0			0
$904$	18.1620	+	55.8970i	0.604060	+	1.85911i
$905$	26.5438	+	19.2852i	0.882345	+	0.641061i
$906$		0			0
$907$	11.4750	−	35.3164i	0.381021	−	1.17266i	−0.558304	−	0.829636i	$-0.688548\pi$
$907$	11.4750	−	35.3164i	0.381021	−	1.17266i	0.939326	−	0.343027i	$-0.111452\pi$
$908$	36.9247	−	113.642i	1.22539	−	3.77136i
$909$		0			0
$910$	−22.3016	−	16.2031i	−0.739292	−	0.537127i
$911$	12.0293	+	37.0223i	0.398548	+	1.22660i	0.926164	+	0.377121i	$0.123086\pi$
$911$	12.0293	+	37.0223i	0.398548	+	1.22660i	−0.527617	+	0.849483i	$0.676914\pi$
$912$		0			0
$913$	4.03581	−	5.31706i	0.133566	−	0.175969i
$914$	−55.3366			−1.83037
$915$		0			0
$916$	−115.295	−	83.7666i	−3.80945	−	2.76773i
$917$	−3.41483	+	2.48102i	−0.112768	+	0.0819305i
$918$		0			0
$919$	−9.02013	+	27.7611i	−0.297547	+	0.915754i	0.684808	+	0.728724i	$0.259886\pi$
$919$	−9.02013	+	27.7611i	−0.297547	+	0.915754i	−0.982354	+	0.187030i	$0.940114\pi$
$920$	20.1137	−	14.6134i	0.663128	−	0.481790i
$921$		0			0
$922$	8.38183	+	25.7966i	0.276041	+	0.849566i
$923$	−44.6173			−1.46860
$924$		0			0
$925$	−7.01568			−0.230674
$926$	−6.23685	−	19.1951i	−0.204956	−	0.630789i
$927$		0			0
$928$	−96.0397	+	69.7769i	−3.15266	+	2.29054i
$929$	−5.86670	+	18.0559i	−0.192480	+	0.592393i	0.807517	+	0.589845i	$0.200811\pi$
$929$	−5.86670	+	18.0559i	−0.192480	+	0.592393i	−0.999997	+	0.00254832i	$0.999189\pi$
$930$		0			0
$931$	3.74462	−	2.72062i	0.122725	−	0.0891648i
$932$	−111.855	−	81.2676i	−3.66394	−	2.66201i
$933$		0			0
$934$	102.352			3.34906
$935$	−0.965917	−	1.38975i	−0.0315889	−	0.0454498i
$936$		0			0
$937$	−6.14700	−	18.9185i	−0.200814	−	0.618041i	−0.999859	−	0.0167709i	$-0.994661\pi$
$937$	−6.14700	−	18.9185i	−0.200814	−	0.618041i	0.799046	−	0.601271i	$-0.205339\pi$
$938$	−13.9671	−	10.1477i	−0.456043	−	0.331334i
$939$		0			0
$940$	7.82204	−	24.0738i	0.255127	−	0.785200i
$941$	3.38976	−	10.4326i	0.110503	−	0.340093i	−0.880480	−	0.474084i	$-0.842779\pi$
$941$	3.38976	−	10.4326i	0.110503	−	0.340093i	0.990983	+	0.133991i	$0.0427793\pi$
$942$		0			0
$943$	−9.29173	−	6.75083i	−0.302580	−	0.219837i
$944$	14.1470	+	43.5399i	0.460444	+	1.41710i
$945$		0			0
$946$	−0.196409	+	9.37931i	−0.00638582	+	0.304948i
$947$	40.5321			1.31712			0.658558	−	0.752530i	$-0.271167\pi$
$947$	40.5321			1.31712			0.658558	+	0.752530i	$0.271167\pi$
$948$		0			0
$949$	60.5394	+	43.9845i	1.96519	+	1.42780i
$950$	22.9029	−	16.6400i	0.743069	−	0.539871i
$951$		0			0
$952$	1.00816	−	3.10279i	0.0326746	−	0.100562i
$953$	−37.7198	+	27.4051i	−1.22187	+	0.887737i	−0.996254	−	0.0864799i	$-0.972438\pi$
$953$	−37.7198	+	27.4051i	−1.22187	+	0.887737i	−0.225612	+	0.974217i	$0.572438\pi$
$954$		0			0
$955$	1.31941	+	4.06073i	0.0426952	+	0.131402i
$956$	9.21516			0.298039
$957$		0			0
$958$	109.063			3.52368
$959$	−4.49191	−	13.8247i	−0.145051	−	0.446423i
$960$		0			0
$961$	24.6072	−	17.8782i	0.793780	−	0.576715i
$962$	−16.3001	+	50.1666i	−0.525537	+	1.61744i
$963$		0			0
$964$	57.7471	−	41.9557i	1.85991	−	1.35130i
$965$	−29.3552	−	21.3278i	−0.944977	−	0.686566i
$966$		0			0
$967$	27.2512			0.876338			0.438169	−	0.898893i	$-0.355627\pi$
$967$	27.2512			0.876338			0.438169	+	0.898893i	$0.355627\pi$
$968$	31.7298	+	113.638i	1.01983	+	3.65245i
$969$		0			0
$970$	−1.50568	−	4.63399i	−0.0483443	−	0.148789i
$971$	18.7984	+	13.6579i	0.603271	+	0.438302i	0.847038	−	0.531532i	$-0.178383\pi$
$971$	18.7984	+	13.6579i	0.603271	+	0.438302i	−0.243768	+	0.969834i	$0.578383\pi$
$972$		0			0
$973$	−2.14648	+	6.60619i	−0.0688130	+	0.211785i
$974$	20.7417	−	63.8364i	0.664607	−	2.04545i
$975$		0			0
$976$	−50.3782	−	36.6019i	−1.61257	−	1.17160i
$977$	8.89186	+	27.3663i	0.284476	+	0.875527i	0.986555	+	0.163428i	$0.0522551\pi$
$977$	8.89186	+	27.3663i	0.284476	+	0.875527i	−0.702079	+	0.712099i	$0.747745\pi$
$978$		0			0
$979$	−0.264325	−	0.0920457i	−0.00844785	−	0.00294179i
$980$	9.78502			0.312571
$981$		0			0
$982$	−7.22970	−	5.25268i	−0.230709	−	0.167620i
$983$	−22.8080	+	16.5710i	−0.727462	+	0.528532i	−0.888759	−	0.458374i	$-0.848432\pi$
$983$	−22.8080	+	16.5710i	−0.727462	+	0.528532i	0.161298	+	0.986906i	$0.448432\pi$
$984$		0			0
$985$	11.4414	−	35.2130i	0.364553	−	1.12198i
$986$	−2.73318	+	1.98577i	−0.0870421	+	0.0632398i
$987$		0			0
$988$	−48.9788	−	150.741i	−1.55822	−	4.79572i
$989$	−1.39641			−0.0444034
$990$		0			0
$991$	−47.6676			−1.51421			−0.757106	−	0.653293i	$-0.773387\pi$
$991$	−47.6676			−1.51421			−0.757106	+	0.653293i	$0.773387\pi$
$992$	−7.06283	−	21.7372i	−0.224245	−	0.690156i
$993$		0			0
$994$	17.2063	−	12.5011i	0.545752	−	0.396512i
$995$	−6.65220	+	20.4734i	−0.210889	+	0.649050i
$996$		0			0
$997$	15.0982	−	10.9695i	0.478166	−	0.347408i	−0.322449	−	0.946587i	$-0.604506\pi$
$997$	15.0982	−	10.9695i	0.478166	−	0.347408i	0.800615	+	0.599179i	$0.204506\pi$
$998$	62.3394	+	45.2922i	1.97332	+	1.43370i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.j.379.1		20
3.2	odd	2		231.2.j.g.148.5	yes	20
11.3	even	5		7623.2.a.cx.1.1		10
11.8	odd	10		7623.2.a.cy.1.10		10
11.9	even	5	inner	693.2.m.j.64.1		20
33.8	even	10		2541.2.a.br.1.1		10
33.14	odd	10		2541.2.a.bq.1.10		10
33.20	odd	10		231.2.j.g.64.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.64.5	✓	20	33.20	odd	10
231.2.j.g.148.5	yes	20	3.2	odd	2
693.2.m.j.64.1		20	11.9	even	5	inner
693.2.m.j.379.1		20	1.1	even	1	trivial
2541.2.a.bq.1.10		10	33.14	odd	10
2541.2.a.br.1.1		10	33.8	even	10
7623.2.a.cx.1.1		10	11.3	even	5
7623.2.a.cy.1.10		10	11.8	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.864833 - 2.66168i) q^{2} +(-4.71859 + 3.42825i) q^{4} +(0.518429 - 1.59556i) q^{5} +(0.809017 - 0.587785i) q^{7} +(8.67739 + 6.30449i) q^{8} +O(q^{10})\)	\(q+(-0.864833 - 2.66168i) q^{2} +(-4.71859 + 3.42825i) q^{4} +(0.518429 - 1.59556i) q^{5} +(0.809017 - 0.587785i) q^{7} +(8.67739 + 6.30449i) q^{8} -4.69523 q^{10} +(3.13215 + 1.09071i) q^{11} +(1.81428 + 5.58378i) q^{13} +(-2.26416 - 1.64501i) q^{14} +(5.67139 - 17.4547i) q^{16} +(0.0939932 - 0.289281i) q^{17} +(3.74462 + 2.72062i) q^{19} +(3.02374 + 9.30610i) q^{20} +(0.194331 - 9.28007i) q^{22} +1.38164 q^{23} +(1.76804 + 1.28455i) q^{25} +(13.2932 - 9.65808i) q^{26} +(-1.80234 + 5.54703i) q^{28} +(3.21073 - 2.33273i) q^{29} +(0.236120 + 0.726701i) q^{31} -29.9121 q^{32} -0.851264 q^{34} +(-0.518429 - 1.59556i) q^{35} +(-2.59713 + 1.88693i) q^{37} +(4.00297 - 12.3199i) q^{38} +(14.5578 - 10.5769i) q^{40} +(-6.72515 - 4.88611i) q^{41} -1.01069 q^{43} +(-18.5185 + 5.59120i) q^{44} +(-1.19489 - 3.67749i) q^{46} +(-2.09283 - 1.52053i) q^{47} +(0.309017 - 0.951057i) q^{49} +(1.89002 - 5.81688i) q^{50} +(-27.7035 - 20.1277i) q^{52} +(0.449229 + 1.38259i) q^{53} +(3.36409 - 4.43208i) q^{55} +10.7258 q^{56} +(-8.98574 - 6.52852i) q^{58} +(-2.01805 + 1.46620i) q^{59} +(1.04848 - 3.22689i) q^{61} +(1.73004 - 1.25695i) q^{62} +(14.5262 + 44.7071i) q^{64} +9.84984 q^{65} +6.16878 q^{67} +(0.548215 + 1.68723i) q^{68} +(-3.79852 + 2.75979i) q^{70} +(-2.34835 + 7.22749i) q^{71} +(10.3114 - 7.49164i) q^{73} +(7.26848 + 5.28086i) q^{74} -26.9963 q^{76} +(3.17506 - 0.958630i) q^{77} +(-1.90206 - 5.85393i) q^{79} +(-24.9099 - 18.0981i) q^{80} +(-7.18913 + 22.1259i) q^{82} +(0.621946 - 1.91415i) q^{83} +(-0.412837 - 0.299944i) q^{85} +(0.874082 + 2.69015i) q^{86} +(20.3025 + 29.2111i) q^{88} -0.0843908 q^{89} +(4.74985 + 3.45097i) q^{91} +(-6.51938 + 4.73661i) q^{92} +(-2.23722 + 6.88545i) q^{94} +(6.28224 - 4.56431i) q^{95} +(0.320682 + 0.986957i) q^{97} -2.79866 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8}+O(q^{10}) \) 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8	\( 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8} + 12 q^{10} + q^{11} + 13 q^{13} - 24 q^{16} + q^{17} + 10 q^{19} + 46 q^{20} + 26 q^{22} - 8 q^{25} + 53 q^{26} + 4 q^{28} - 3 q^{29} - 13 q^{31} - 82 q^{32} + 42 q^{34} - 5 q^{35} - 32 q^{37} - 16 q^{38} + 20 q^{40} + 3 q^{41} + 12 q^{43} - 25 q^{44} - 13 q^{46} - 20 q^{47} - 5 q^{49} + 83 q^{50} - 80 q^{52} - 3 q^{53} - 28 q^{55} + 6 q^{56} + 2 q^{58} + 9 q^{59} - 15 q^{61} + 37 q^{62} - 49 q^{64} - 58 q^{65} + 76 q^{67} - 51 q^{68} + 3 q^{70} - 37 q^{71} + 27 q^{73} + 32 q^{74} + 4 q^{76} - 6 q^{77} + 5 q^{79} - 137 q^{80} - 55 q^{82} + 42 q^{83} - 48 q^{85} - 3 q^{86} + 151 q^{88} + 18 q^{89} + 7 q^{91} - 39 q^{92} - 35 q^{94} + 96 q^{95} - 27 q^{97}+O(q^{100}) \) 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8 + 12 * q^10 + q^11 + 13 * q^13 - 24 * q^16 + q^17 + 10 * q^19 + 46 * q^20 + 26 * q^22 - 8 * q^25 + 53 * q^26 + 4 * q^28 - 3 * q^29 - 13 * q^31 - 82 * q^32 + 42 * q^34 - 5 * q^35 - 32 * q^37 - 16 * q^38 + 20 * q^40 + 3 * q^41 + 12 * q^43 - 25 * q^44 - 13 * q^46 - 20 * q^47 - 5 * q^49 + 83 * q^50 - 80 * q^52 - 3 * q^53 - 28 * q^55 + 6 * q^56 + 2 * q^58 + 9 * q^59 - 15 * q^61 + 37 * q^62 - 49 * q^64 - 58 * q^65 + 76 * q^67 - 51 * q^68 + 3 * q^70 - 37 * q^71 + 27 * q^73 + 32 * q^74 + 4 * q^76 - 6 * q^77 + 5 * q^79 - 137 * q^80 - 55 * q^82 + 42 * q^83 - 48 * q^85 - 3 * q^86 + 151 * q^88 + 18 * q^89 + 7 * q^91 - 39 * q^92 - 35 * q^94 + 96 * q^95 - 27 * q^97

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