LMFDB - Embedded newform 441.2.bb.e.109.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			109.5
Character	$\chi$	$=$	441.109
Dual form			441.2.bb.e.352.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.02691 - 1.88070i) q^{2} +(0.421883 - 5.62963i) q^{4} +(-0.259960 + 0.662367i) q^{5} +(2.63989 + 0.175969i) q^{7} +(-6.28460 - 7.88063i) q^{8} +O(q^{10})$	\(q+(2.02691 - 1.88070i) q^{2} +(0.421883 - 5.62963i) q^{4} +(-0.259960 + 0.662367i) q^{5} +(2.63989 + 0.175969i) q^{7} +(-6.28460 - 7.88063i) q^{8} +(0.718799 + 1.83147i) q^{10} +(1.00245 + 0.309214i) q^{11} +(-0.0833615 - 0.365231i) q^{13} +(5.68178 - 4.60818i) q^{14} +(-16.3947 - 2.47111i) q^{16} +(-4.77730 + 3.25711i) q^{17} +(2.35070 + 4.07154i) q^{19} +(3.61921 + 1.74292i) q^{20} +(2.61341 - 1.25855i) q^{22} +(-5.75822 - 3.92589i) q^{23} +(3.29411 + 3.05649i) q^{25} +(-0.855856 - 0.583513i) q^{26} +(2.10436 - 14.7874i) q^{28} +(2.01190 + 0.968882i) q^{29} +(2.36528 - 4.09679i) q^{31} +(-21.2216 + 14.4687i) q^{32} +(-3.55753 + 15.5866i) q^{34} +(-0.802823 + 1.70283i) q^{35} +(-0.0212227 - 0.283197i) q^{37} +(12.4220 + 3.83168i) q^{38} +(6.85362 - 2.11406i) q^{40} +(7.79407 + 9.77345i) q^{41} +(-0.0228637 + 0.0286702i) q^{43} +(2.16368 - 5.51296i) q^{44} +(-19.0548 + 2.87205i) q^{46} +(-0.395549 + 0.367016i) q^{47} +(6.93807 + 0.929078i) q^{49} +12.4252 q^{50} +(-2.09128 + 0.315210i) q^{52} +(0.231873 - 3.09413i) q^{53} +(-0.465409 + 0.583605i) q^{55} +(-15.2039 - 21.9099i) q^{56} +(5.90013 - 1.81995i) q^{58} +(0.412627 + 1.05136i) q^{59} +(-0.591318 - 7.89059i) q^{61} +(-2.91061 - 12.7522i) q^{62} +(-8.42443 + 36.9099i) q^{64} +(0.263587 + 0.0397294i) q^{65} +(-5.41480 + 9.37871i) q^{67} +(16.3209 + 28.2686i) q^{68} +(1.57527 + 4.96137i) q^{70} +(6.78165 - 3.26587i) q^{71} +(-6.60507 - 6.12861i) q^{73} +(-0.575625 - 0.534102i) q^{74} +(23.9130 - 11.5159i) q^{76} +(2.59194 + 0.992691i) q^{77} +(2.98149 + 5.16409i) q^{79} +(5.89876 - 10.2169i) q^{80} +(34.1788 + 5.15163i) q^{82} +(1.20057 - 5.26005i) q^{83} +(-0.915495 - 4.01104i) q^{85} +(0.00757729 + 0.101112i) q^{86} +(-3.86317 - 9.84320i) q^{88} +(-6.11722 + 1.88691i) q^{89} +(-0.155796 - 0.978839i) q^{91} +(-24.5306 + 30.7604i) q^{92} +(-0.111497 + 1.48782i) q^{94} +(-3.30794 + 0.498592i) q^{95} -12.8457 q^{97} +(15.8102 - 11.1653i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) $ 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8	$ 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) $ 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8 - 34 * q^10 + 11 * q^11 - 2 * q^13 - 40 * q^14 - 31 * q^16 + 9 * q^17 - 29 * q^19 + 43 * q^20 + 9 * q^22 + 4 * q^23 + 55 * q^25 - 36 * q^26 - 57 * q^28 - 4 * q^29 - 39 * q^31 + 92 * q^32 - 36 * q^34 + 33 * q^35 - 24 * q^37 - 118 * q^38 - 35 * q^41 + 2 * q^43 - 40 * q^44 - 40 * q^46 + 5 * q^47 + 129 * q^49 + 176 * q^50 - 6 * q^52 - 26 * q^53 + 2 * q^55 - 63 * q^56 + 11 * q^58 + 41 * q^59 + 6 * q^61 - 36 * q^62 + 74 * q^64 + 51 * q^65 - 55 * q^67 + 22 * q^68 - 68 * q^70 + 66 * q^71 + 24 * q^73 - 28 * q^74 + 3 * q^76 + 34 * q^77 - 51 * q^79 + 5 * q^80 - 41 * q^82 - 30 * q^83 + 68 * q^85 - 110 * q^86 + 129 * q^88 - 75 * q^89 + 5 * q^91 + 38 * q^94 - 36 * q^95 - 168 * q^97 - 227 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{20}{21}\right)$	$1$

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 $

$2$	2.02691	−	1.88070i	1.43324	−	1.32986i	0.573426	−	0.819257i	$-0.305614\pi$
$2$	2.02691	−	1.88070i	1.43324	−	1.32986i	0.859819	−	0.510599i	$-0.170576\pi$
$3$		0			0
$3$		0			0
$4$	0.421883	−	5.62963i	0.210941	−	2.81482i
$5$	−0.259960	+	0.662367i	−0.116258	+	0.296220i	−0.977144	−	0.212577i	$-0.931814\pi$
$5$	−0.259960	+	0.662367i	−0.116258	+	0.296220i	0.860887	+	0.508797i	$0.169910\pi$
$6$		0			0
$7$	2.63989	+	0.175969i	0.997786	+	0.0665100i
$7$	2.63989	+	0.175969i	0.997786	+	0.0665100i
$8$	−6.28460	−	7.88063i	−2.22194	−	2.78623i
$9$		0			0
$10$	0.718799	+	1.83147i	0.227304	+	0.579161i
$11$	1.00245	+	0.309214i	0.302249	+	0.0932315i	0.442170	−	0.896931i	$-0.354209\pi$
$11$	1.00245	+	0.309214i	0.302249	+	0.0932315i	−0.139921	+	0.990163i	$0.544685\pi$
$12$		0			0
$13$	−0.0833615	−	0.365231i	−0.0231203	−	0.101297i	0.962051	−	0.272869i	$-0.0879725\pi$
$13$	−0.0833615	−	0.365231i	−0.0231203	−	0.101297i	−0.985172	+	0.171572i	$0.945115\pi$
$14$	5.68178	−	4.60818i	1.51852	−	1.23159i
$15$		0			0
$16$	−16.3947	−	2.47111i	−4.09868	−	0.617777i
$17$	−4.77730	+	3.25711i	−1.15867	+	0.789965i	−0.980977	−	0.194122i	$-0.937814\pi$
$17$	−4.77730	+	3.25711i	−1.15867	+	0.789965i	−0.177688	+	0.984087i	$0.556862\pi$
$18$		0			0
$19$	2.35070	+	4.07154i	0.539288	+	0.934074i	0.998943	+	0.0459765i	$0.0146399\pi$
$19$	2.35070	+	4.07154i	0.539288	+	0.934074i	−0.459654	+	0.888098i	$0.652027\pi$
$20$	3.61921	+	1.74292i	0.809280	+	0.389729i
$21$		0			0
$22$	2.61341	−	1.25855i	0.557181	−	0.268324i
$23$	−5.75822	−	3.92589i	−1.20067	−	0.818604i	−0.213294	−	0.976988i	$-0.568419\pi$
$23$	−5.75822	−	3.92589i	−1.20067	−	0.818604i	−0.987378	+	0.158384i	$0.949372\pi$
$24$		0			0
$25$	3.29411	+	3.05649i	0.658822	+	0.611297i
$26$	−0.855856	−	0.583513i	−0.167847	−	0.114436i
$27$		0			0
$28$	2.10436	−	14.7874i	0.397688	−	2.79455i
$29$	2.01190	+	0.968882i	0.373601	+	0.179917i	0.611256	−	0.791433i	$-0.290665\pi$
$29$	2.01190	+	0.968882i	0.373601	+	0.179917i	−0.237655	+	0.971350i	$0.576379\pi$
$30$		0			0
$31$	2.36528	−	4.09679i	0.424817	−	0.735804i	−0.571586	−	0.820542i	$-0.693672\pi$
$31$	2.36528	−	4.09679i	0.424817	−	0.735804i	0.996403	+	0.0847374i	$0.0270051\pi$
$32$	−21.2216	+	14.4687i	−3.75149	+	2.55772i
$33$		0			0
$34$	−3.55753	+	15.5866i	−0.610111	+	2.67307i
$35$	−0.802823	+	1.70283i	−0.135702	+	0.287831i
$36$		0			0
$37$	−0.0212227	−	0.283197i	−0.00348899	−	0.0465573i	0.995188	−	0.0979884i	$-0.0312408\pi$
$37$	−0.0212227	−	0.283197i	−0.00348899	−	0.0465573i	−0.998677	+	0.0514311i	$0.983622\pi$
$38$	12.4220	+	3.83168i	2.01512	+	0.621581i
$39$		0			0
$40$	6.85362	−	2.11406i	1.08365	−	0.334262i
$41$	7.79407	+	9.77345i	1.21723	+	1.52636i	0.778378	+	0.627796i	$0.216043\pi$
$41$	7.79407	+	9.77345i	1.21723	+	1.52636i	0.438851	+	0.898560i	$0.355386\pi$
$42$		0			0
$43$	−0.0228637	+	0.0286702i	−0.00348668	+	0.00437216i	−0.783572	−	0.621301i	$-0.786604\pi$
$43$	−0.0228637	+	0.0286702i	−0.00348668	+	0.00437216i	0.780085	+	0.625673i	$0.215176\pi$
$44$	2.16368	−	5.51296i	0.326186	−	0.831109i
$45$		0			0
$46$	−19.0548	+	2.87205i	−2.80948	+	0.423461i
$47$	−0.395549	+	0.367016i	−0.0576967	+	0.0535347i	−0.708494	−	0.705717i	$-0.750625\pi$
$47$	−0.395549	+	0.367016i	−0.0576967	+	0.0535347i	0.650797	+	0.759251i	$0.274435\pi$
$48$		0			0
$49$	6.93807	+	0.929078i	0.991153	+	0.132725i
$50$	12.4252			1.75719
$51$		0			0
$52$	−2.09128	+	0.315210i	−0.290009	+	0.0437118i
$53$	0.231873	−	3.09413i	0.0318502	−	0.425012i	−0.958373	−	0.285520i	$-0.907834\pi$
$53$	0.231873	−	3.09413i	0.0318502	−	0.425012i	0.990223	−	0.139492i	$-0.0445471\pi$
$54$		0			0
$55$	−0.465409	+	0.583605i	−0.0627558	+	0.0786932i
$56$	−15.2039	−	21.9099i	−2.03171	−	2.92784i
$57$		0			0
$58$	5.90013	−	1.81995i	0.774725	−	0.238971i
$59$	0.412627	+	1.05136i	0.0537194	+	0.136875i	0.955214	−	0.295915i	$-0.0956245\pi$
$59$	0.412627	+	1.05136i	0.0537194	+	0.136875i	−0.901495	+	0.432790i	$0.857529\pi$
$60$		0			0
$61$	−0.591318	−	7.89059i	−0.0757105	−	1.01029i	−0.897649	−	0.440711i	$-0.854726\pi$
$61$	−0.591318	−	7.89059i	−0.0757105	−	1.01029i	0.821939	−	0.569576i	$-0.192893\pi$
$62$	−2.91061	−	12.7522i	−0.369648	−	1.61953i
$63$		0			0
$64$	−8.42443	+	36.9099i	−1.05305	+	4.61373i
$65$	0.263587	+	0.0397294i	0.0326940	+	0.00492783i
$66$		0			0
$67$	−5.41480	+	9.37871i	−0.661523	+	1.14579i	0.318692	+	0.947858i	$0.396756\pi$
$67$	−5.41480	+	9.37871i	−0.661523	+	1.14579i	−0.980215	+	0.197934i	$0.936577\pi$
$68$	16.3209	+	28.2686i	1.97920	+	3.42807i
$69$		0			0
$70$	1.57527	+	4.96137i	0.188281	+	0.592997i
$71$	6.78165	−	3.26587i	0.804833	−	0.387587i	0.0142167	−	0.999899i	$-0.495475\pi$
$71$	6.78165	−	3.26587i	0.804833	−	0.387587i	0.790616	+	0.612312i	$0.209760\pi$
$72$		0			0
$73$	−6.60507	−	6.12861i	−0.773065	−	0.717300i	0.191399	−	0.981512i	$-0.438698\pi$
$73$	−6.60507	−	6.12861i	−0.773065	−	0.717300i	−0.964465	+	0.264212i	$0.914888\pi$
$74$	−0.575625	−	0.534102i	−0.0669151	−	0.0620881i
$75$		0			0
$76$	23.9130	−	11.5159i	2.74301	−	1.32096i
$77$	2.59194	+	0.992691i	0.295379	+	0.113128i
$78$		0			0
$79$	2.98149	+	5.16409i	0.335443	+	0.581005i	0.983570	−	0.180528i	$-0.0577805\pi$
$79$	2.98149	+	5.16409i	0.335443	+	0.581005i	−0.648126	+	0.761533i	$0.724447\pi$
$80$	5.89876	−	10.2169i	0.659501	−	1.14229i
$81$		0			0
$82$	34.1788	+	5.15163i	3.77442	+	0.568902i
$83$	1.20057	−	5.26005i	0.131780	−	0.577366i	−0.865317	−	0.501225i	$-0.832883\pi$
$83$	1.20057	−	5.26005i	0.131780	−	0.577366i	0.997097	−	0.0761409i	$-0.0242599\pi$
$84$		0			0
$85$	−0.915495	−	4.01104i	−0.0992994	−	0.435059i
$86$	0.00757729	+	0.101112i	0.000817080	+	0.0109032i
$87$		0			0
$88$	−3.86317	−	9.84320i	−0.411816	−	1.04929i
$89$	−6.11722	+	1.88691i	−0.648424	+	0.200012i	−0.601484	−	0.798885i	$-0.705423\pi$
$89$	−6.11722	+	1.88691i	−0.648424	+	0.200012i	−0.0469409	+	0.998898i	$0.514947\pi$
$90$		0			0
$91$	−0.155796	−	0.978839i	−0.0163319	−	0.102610i
$92$	−24.5306	+	30.7604i	−2.55749	+	3.20699i
$93$		0			0
$94$	−0.111497	+	1.48782i	−0.0115000	+	0.153457i
$95$	−3.30794	+	0.498592i	−0.339388	+	0.0511544i
$96$		0			0
$97$	−12.8457			−1.30428			−0.652142	−	0.758097i	$-0.726129\pi$
$97$	−12.8457			−1.30428			−0.652142	+	0.758097i	$0.726129\pi$
$98$	15.8102	−	11.1653i	1.59707	−	1.12786i
$99$		0			0
$100$	18.5966	−	17.2551i	1.85966	−	1.72551i
$101$	−8.53012	+	1.28571i	−0.848779	+	0.127933i	−0.559007	−	0.829163i	$-0.688818\pi$
$101$	−8.53012	+	1.28571i	−0.848779	+	0.127933i	−0.289772	+	0.957096i	$0.593579\pi$
$102$		0			0
$103$	−3.59921	+	9.17063i	−0.354640	+	0.903609i	0.636559	+	0.771228i	$0.280357\pi$
$103$	−3.59921	+	9.17063i	−0.354640	+	0.903609i	−0.991199	+	0.132381i	$0.957738\pi$
$104$	−2.35436	+	2.95227i	−0.230864	+	0.289494i
$105$		0			0
$106$	−5.34915	−	6.70763i	−0.519556	−	0.651502i
$107$	2.56618	−	0.791563i	0.248082	−	0.0765233i	−0.168220	−	0.985749i	$-0.553802\pi$
$107$	2.56618	−	0.791563i	0.248082	−	0.0765233i	0.416303	+	0.909226i	$0.363326\pi$
$108$		0			0
$109$	−12.5076	−	3.85809i	−1.19801	−	0.369538i	−0.369352	−	0.929290i	$-0.620420\pi$
$109$	−12.5076	−	3.85809i	−1.19801	−	0.369538i	−0.828660	+	0.559752i	$0.810896\pi$
$110$	0.154242	+	2.05821i	0.0147064	+	0.196243i
$111$		0			0
$112$	−42.8455	−	9.40842i	−4.04852	−	0.889012i
$113$	1.02513	−	4.49138i	0.0964360	−	0.422514i	−0.903546	−	0.428491i	$-0.859045\pi$
$113$	1.02513	−	4.49138i	0.0964360	−	0.422514i	0.999982	+	0.00597719i	$0.00190261\pi$
$114$		0			0
$115$	4.09729	−	2.79348i	0.382074	−	0.260494i
$116$	6.30324	−	10.9175i	0.585241	−	1.01367i
$117$		0			0
$118$	2.81364	+	1.35498i	0.259017	+	0.124736i
$119$	−13.1847	+	7.75776i	−1.20864	+	0.711153i
$120$		0			0
$121$	−8.17934	−	5.57658i	−0.743576	−	0.506962i
$122$	−16.0384	−	14.8815i	−1.45205	−	1.34730i
$123$		0			0
$124$	−22.0655	−	15.0440i	−1.98154	−	1.35099i
$125$	−6.08629	+	2.93100i	−0.544375	+	0.262157i
$126$		0			0
$127$	3.53246	+	1.70114i	0.313455	+	0.150952i	0.583996	−	0.811756i	$-0.301488\pi$
$127$	3.53246	+	1.70114i	0.313455	+	0.150952i	−0.270541	+	0.962708i	$0.587203\pi$
$128$	26.6562	+	46.1699i	2.35610	+	4.08088i
$129$		0			0
$130$	0.608988	−	0.415201i	0.0534118	−	0.0364156i
$131$	−0.412351	−	0.0621519i	−0.0360272	−	0.00543023i	0.131004	−	0.991382i	$-0.458180\pi$
$131$	−0.412351	−	0.0621519i	−0.0360272	−	0.00543023i	−0.167031	+	0.985952i	$0.553418\pi$
$132$		0			0
$133$	5.48914	+	11.1621i	0.475969	+	0.967874i
$134$	6.66322	+	29.1935i	0.575614	+	2.52193i
$135$		0			0
$136$	55.6915	+	17.1785i	4.77550	+	1.47305i
$137$	−1.63871	−	4.17536i	−0.140004	−	0.356725i	0.843624	−	0.536934i	$-0.180418\pi$
$137$	−1.63871	−	4.17536i	−0.140004	−	0.356725i	−0.983628	+	0.180209i	$0.942323\pi$
$138$		0			0
$139$	1.64660	+	2.06478i	0.139663	+	0.175132i	0.846744	−	0.532001i	$-0.178560\pi$
$139$	1.64660	+	2.06478i	0.139663	+	0.175132i	−0.707081	+	0.707133i	$0.749988\pi$
$140$	9.24763	+	5.23799i	0.781568	+	0.442691i
$141$		0			0
$142$	7.60369	−	19.3739i	0.638087	−	1.62582i
$143$	0.0293689	−	0.391901i	0.00245595	−	0.0327724i
$144$		0			0
$145$	−1.16477	+	1.08075i	−0.0967289	+	0.0897513i
$146$	−24.9140			−2.06190
$147$		0			0
$148$	−1.60325			−0.131786
$149$	10.1588	−	9.42598i	0.832241	−	0.772207i	−0.143843	−	0.989601i	$-0.545946\pi$
$149$	10.1588	−	9.42598i	0.832241	−	0.772207i	0.976084	+	0.217394i	$0.0697556\pi$
$150$		0			0
$151$	−0.0762120	+	1.01698i	−0.00620204	+	0.0827605i	−0.999446	−	0.0332855i	$-0.989403\pi$
$151$	−0.0762120	+	1.01698i	−0.00620204	+	0.0827605i	0.993244	+	0.116046i	$0.0370220\pi$
$152$	17.3131	−	44.1130i	1.40428	−	3.57804i
$153$		0			0
$154$	7.12060	−	2.86257i	0.573794	−	0.230672i
$155$	2.09870	+	2.63168i	0.168572	+	0.211382i
$156$		0			0
$157$	−3.59272	−	9.15411i	−0.286731	−	0.730578i	−0.999572	−	0.0292524i	$-0.990687\pi$
$157$	−3.59272	−	9.15411i	−0.286731	−	0.730578i	0.712842	−	0.701325i	$-0.247408\pi$
$158$	15.7553	+	4.85987i	1.25343	+	0.386631i
$159$		0			0
$160$	−4.06679	−	17.8178i	−0.321508	−	1.40862i
$161$	−14.5102	−	11.3772i	−1.14357	−	0.896648i
$162$		0			0
$163$	−9.07831	−	1.36834i	−0.711068	−	0.107176i	−0.216459	−	0.976292i	$-0.569451\pi$
$163$	−9.07831	−	1.36834i	−0.711068	−	0.107176i	−0.494609	+	0.869115i	$0.664689\pi$
$164$	58.3091	−	39.7545i	4.55318	−	3.10430i
$165$		0			0
$166$	−7.45913	−	12.9196i	−0.578941	−	1.00275i
$167$	12.9836	+	6.25255i	1.00470	+	0.483837i	0.862530	−	0.506005i	$-0.168878\pi$
$167$	12.9836	+	6.25255i	1.00470	+	0.483837i	0.142168	+	0.989843i	$0.454593\pi$
$168$		0			0
$169$	11.5862	−	5.57960i	0.891242	−	0.429200i
$170$	−9.39921	−	6.40827i	−0.720886	−	0.491492i
$171$		0			0
$172$	0.151757	+	0.140810i	0.0115714	+	0.0107366i
$173$	−12.9889	−	8.85570i	−0.987530	−	0.673286i	−0.0421002	−	0.999113i	$-0.513405\pi$
$173$	−12.9889	−	8.85570i	−0.987530	−	0.673286i	−0.945429	+	0.325827i	$0.894357\pi$
$174$		0			0
$175$	8.15825	+	8.64846i	0.616705	+	0.653762i
$176$	−15.6707	−	7.54663i	−1.18123	−	0.568849i
$177$		0			0
$178$	−8.85037	+	15.3293i	−0.663363	+	1.14898i
$179$	−2.89334	+	1.97265i	−0.216259	+	0.147443i	−0.666605	−	0.745411i	$-0.732253\pi$
$179$	−2.89334	+	1.97265i	−0.216259	+	0.147443i	0.450346	+	0.892854i	$0.351301\pi$
$180$		0			0
$181$	−3.95495	+	17.3278i	−0.293969	+	1.28796i	0.584980	+	0.811048i	$0.301102\pi$
$181$	−3.95495	+	17.3278i	−0.293969	+	1.28796i	−0.878949	+	0.476915i	$0.841755\pi$
$182$	−2.15669	−	1.69102i	−0.159864	−	0.125346i
$183$		0			0
$184$	5.24960	+	70.0510i	0.387006	+	5.16423i
$185$	0.193097	+	0.0595627i	0.0141968	+	0.00437913i
$186$		0			0
$187$	−5.79613	+	1.78787i	−0.423855	+	0.130742i
$188$	1.89929	+	2.38163i	0.138520	+	0.173698i
$189$		0			0
$190$	−5.76721	+	7.23185i	−0.418397	+	0.524654i
$191$	−5.85852	+	14.9273i	−0.423908	+	1.08010i	0.546249	+	0.837623i	$0.316055\pi$
$191$	−5.85852	+	14.9273i	−0.423908	+	1.08010i	−0.970157	+	0.242477i	$0.922040\pi$
$192$		0			0
$193$	11.7225	−	1.76689i	0.843806	−	0.127183i	0.287108	−	0.957898i	$-0.407306\pi$
$193$	11.7225	−	1.76689i	0.843806	−	0.127183i	0.556698	+	0.830715i	$0.312068\pi$
$194$	−26.0371	+	24.1589i	−1.86936	+	1.73451i
$195$		0			0
$196$	8.15742	−	38.6668i	0.582673	−	2.76192i
$197$	4.94090			0.352025			0.176012	−	0.984388i	$-0.443680\pi$
$197$	4.94090			0.352025			0.176012	+	0.984388i	$0.443680\pi$
$198$		0			0
$199$	−14.3260	+	2.15929i	−1.01554	+	0.153068i	−0.635661	−	0.771968i	$-0.719272\pi$
$199$	−14.3260	+	2.15929i	−1.01554	+	0.153068i	−0.379879	+	0.925036i	$0.624034\pi$
$200$	3.38491	−	45.1684i	0.239349	−	3.19389i
$201$		0			0
$202$	−14.8718	+	18.6486i	−1.04638	+	1.31211i
$203$	5.14072	+	2.91178i	0.360808	+	0.204367i
$204$		0			0
$205$	−8.49976	+	2.62183i	−0.593649	+	0.183116i
$206$	9.95193	+	25.3571i	0.693384	+	1.76671i
$207$		0			0
$208$	0.464165	+	6.19385i	0.0321841	+	0.429466i
$209$	1.09748	+	4.80837i	0.0759142	+	0.332602i
$210$		0			0
$211$	0.900333	−	3.94462i	0.0619815	−	0.271559i	−0.934436	−	0.356132i	$-0.884095\pi$
$211$	0.900333	−	3.94462i	0.0619815	−	0.271559i	0.996417	+	0.0845730i	$0.0269526\pi$
$212$	−17.3210	−	2.61072i	−1.18961	−	0.179305i
$213$		0			0
$214$	3.71274	−	6.43066i	0.253798	−	0.439591i
$215$	−0.0130465	−	0.0225973i	−0.000889767	−	0.00154112i
$216$		0			0
$217$	6.96499	−	10.3989i	0.472815	−	0.705921i
$218$	−32.6078	+	15.7031i	−2.20848	+	1.06355i
$219$		0			0
$220$	3.08913	+	2.86630i	0.208269	+	0.193246i
$221$	1.58784	+	1.47330i	0.106810	+	0.0991048i
$222$		0			0
$223$	12.3075	−	5.92699i	0.824173	−	0.396901i	0.0262466	−	0.999655i	$-0.491644\pi$
$223$	12.3075	−	5.92699i	0.824173	−	0.396901i	0.797927	+	0.602755i	$0.205930\pi$
$224$	−58.5689	+	34.4614i	−3.91330	+	2.30255i
$225$		0			0
$226$	−6.36910	−	11.0316i	−0.423666	−	0.733811i
$227$	−7.58682	+	13.1407i	−0.503555	+	0.872182i	0.496437	+	0.868073i	$0.334641\pi$
$227$	−7.58682	+	13.1407i	−0.503555	+	0.872182i	−0.999992	+	0.00410941i	$0.998692\pi$
$228$		0			0
$229$	−22.1751	−	3.34236i	−1.46537	−	0.220869i	−0.632597	−	0.774481i	$-0.718011\pi$
$229$	−22.1751	−	3.34236i	−1.46537	−	0.220869i	−0.832775	+	0.553612i	$0.813249\pi$
$230$	3.05114	−	13.3679i	0.201186	−	0.881455i
$231$		0			0
$232$	−5.00860	−	21.9441i	−0.328831	−	1.44070i
$233$	−0.777482	−	10.3748i	−0.0509345	−	0.679674i	−0.962978	−	0.269580i	$-0.913115\pi$
$233$	−0.777482	−	10.3748i	−0.0509345	−	0.679674i	0.912043	−	0.410094i	$-0.134504\pi$
$234$		0			0
$235$	−0.140272	−	0.357408i	−0.00915036	−	0.0233147i
$236$	6.09283	−	1.87939i	0.396609	−	0.122338i
$237$		0			0
$238$	−12.1342	+	40.5208i	−0.786546	+	2.62657i
$239$	15.2930	−	19.1768i	0.989221	−	1.24044i	0.0186006	−	0.999827i	$-0.494079\pi$
$239$	15.2930	−	19.1768i	0.989221	−	1.24044i	0.970620	−	0.240617i	$-0.0773497\pi$
$240$		0			0
$241$	1.08139	−	14.4302i	0.0696586	−	0.929529i	−0.847446	−	0.530882i	$-0.821861\pi$
$241$	1.08139	−	14.4302i	0.0696586	−	0.929529i	0.917104	−	0.398647i	$-0.130520\pi$
$242$	−27.0667	+	4.07965i	−1.73991	+	0.262250i
$243$		0			0
$244$	−44.6706			−2.85974
$245$	−2.41901	+	4.35403i	−0.154545	+	0.278169i
$246$		0			0
$247$	1.29109	−	1.19796i	0.0821502	−	0.0762242i
$248$	−47.1501	+	7.10674i	−2.99403	+	0.451278i
$249$		0			0
$250$	−6.82405	+	17.3874i	−0.431591	+	1.09968i
$251$	−3.52065	+	4.41475i	−0.222221	+	0.278657i	−0.880427	−	0.474181i	$-0.842744\pi$
$251$	−3.52065	+	4.41475i	−0.222221	+	0.278657i	0.658206	+	0.752838i	$0.271316\pi$
$252$		0			0
$253$	−4.55837	−	5.71601i	−0.286582	−	0.359363i
$254$	10.3593	−	3.19543i	0.650002	−	0.200499i
$255$		0			0
$256$	68.5074	+	21.1317i	4.28171	+	1.32073i
$257$	−0.129214	−	1.72424i	−0.00806016	−	0.107555i	0.991723	−	0.128399i	$-0.0409838\pi$
$257$	−0.129214	−	1.72424i	−0.00806016	−	0.107555i	−0.999783	+	0.0208436i	$0.993365\pi$
$258$		0			0
$259$	−0.00619177	−	0.751344i	−0.000384738	−	0.0466862i
$260$	0.334865	−	1.46714i	0.0207674	−	0.0909881i
$261$		0			0
$262$	−0.952688	+	0.649532i	−0.0588573	+	0.0401282i
$263$	1.30333	−	2.25743i	0.0803666	−	0.139199i	−0.823041	−	0.567982i	$-0.807724\pi$
$263$	1.30333	−	2.25743i	0.0803666	−	0.139199i	0.903407	+	0.428783i	$0.141058\pi$
$264$		0			0
$265$	1.98918	+	0.957936i	0.122194	+	0.0588456i
$266$	32.1185	+	12.3011i	1.96931	+	0.754230i
$267$		0			0
$268$	50.5143	+	34.4401i	3.08565	+	2.10376i
$269$	0.179455	+	0.166510i	0.0109416	+	0.0101523i	0.685625	−	0.727955i	$-0.259529\pi$
$269$	0.179455	+	0.166510i	0.0109416	+	0.0101523i	−0.674683	+	0.738108i	$0.735720\pi$
$270$		0			0
$271$	−6.22393	−	4.24340i	−0.378077	−	0.257768i	0.359339	−	0.933207i	$-0.383002\pi$
$271$	−6.22393	−	4.24340i	−0.378077	−	0.257768i	−0.737416	+	0.675438i	$0.763954\pi$
$272$	86.3712	−	41.5942i	5.23702	−	2.52202i
$273$		0			0
$274$	−11.1741	−	5.38118i	−0.675054	−	0.325089i
$275$	2.35706	+	4.08255i	0.142136	+	0.246187i
$276$		0			0
$277$	−15.0646	+	10.2709i	−0.905147	+	0.617119i	−0.923870	−	0.382706i	$-0.874992\pi$
$277$	−15.0646	+	10.2709i	−0.905147	+	0.617119i	0.0187235	+	0.999825i	$0.494040\pi$
$278$	7.22075	+	1.08835i	0.433072	+	0.0652751i
$279$		0			0
$280$	18.4648	−	4.37487i	1.10348	−	0.261449i
$281$	−3.53281	−	15.4782i	−0.210750	−	0.923354i	−0.964059	−	0.265688i	$-0.914401\pi$
$281$	−3.53281	−	15.4782i	−0.210750	−	0.923354i	0.753309	−	0.657666i	$-0.228456\pi$
$282$		0			0
$283$	−15.1740	−	4.68057i	−0.902002	−	0.278231i	−0.191140	−	0.981563i	$-0.561219\pi$
$283$	−15.1740	−	4.68057i	−0.902002	−	0.278231i	−0.710862	+	0.703332i	$0.751695\pi$
$284$	−15.5246	−	39.5560i	−0.921214	−	2.34722i
$285$		0			0
$286$	−0.677520	−	0.849583i	−0.0400626	−	0.0502369i
$287$	18.8557	+	27.1724i	1.11302	+	1.60393i
$288$		0			0
$289$	6.00304	−	15.2955i	0.353120	−	0.899736i
$290$	−0.328323	+	4.38117i	−0.0192798	+	0.257271i
$291$		0			0
$292$	−37.2884	+	34.5986i	−2.18214	+	2.02473i
$293$	14.1021			0.823854			0.411927	−	0.911217i	$-0.364856\pi$
$293$	14.1021			0.823854			0.411927	+	0.911217i	$0.364856\pi$
$294$		0			0
$295$	−0.803650			−0.0467903
$296$	−2.09840	+	1.94703i	−0.121967	+	0.113169i
$297$		0			0
$298$	2.86354	−	38.2113i	0.165881	−	2.21352i
$299$	−0.953840	+	2.43035i	−0.0551620	+	0.140551i
$300$		0			0
$301$	−0.0654028	+	0.0716629i	−0.00376976	+	0.00413058i
$302$	1.75816	+	2.20466i	0.101171	+	0.126864i
$303$		0			0
$304$	−28.4779	−	72.5606i	−1.63332	−	4.16163i
$305$	5.38019	+	1.65957i	0.308069	+	0.0950266i
$306$		0			0
$307$	4.79297	+	20.9994i	0.273549	+	1.19850i	0.905791	+	0.423726i	$0.139278\pi$
$307$	4.79297	+	20.9994i	0.273549	+	1.19850i	−0.632241	+	0.774771i	$0.717865\pi$
$308$	6.68198	−	14.1729i	0.380741	−	0.807574i
$309$		0			0
$310$	9.20330	+	1.38717i	0.522712	+	0.0787862i
$311$	14.5965	−	9.95171i	0.827690	−	0.564309i	−0.0737186	−	0.997279i	$-0.523487\pi$
$311$	14.5965	−	9.95171i	0.827690	−	0.564309i	0.901409	+	0.432970i	$0.142534\pi$
$312$		0			0
$313$	17.1207	+	29.6540i	0.967722	+	1.67614i	0.702117	+	0.712061i	$0.252238\pi$
$313$	17.1207	+	29.6540i	0.967722	+	1.67614i	0.265605	+	0.964082i	$0.414428\pi$
$314$	−24.4983	−	11.7978i	−1.38252	−	0.665786i
$315$		0			0
$316$	30.3297	−	14.6060i	1.70618	−	0.821654i
$317$	6.84955	+	4.66994i	0.384709	+	0.262290i	0.740196	−	0.672391i	$-0.234733\pi$
$317$	6.84955	+	4.66994i	0.384709	+	0.262290i	−0.355487	+	0.934681i	$0.615685\pi$
$318$		0			0
$319$	1.71723	+	1.59336i	0.0961467	+	0.0892111i
$320$	−22.2579	−	15.1752i	−1.24425	−	0.848317i
$321$		0			0
$322$	−50.8081	+	4.22886i	−2.83143	+	0.235665i
$323$	−24.4914	−	11.7945i	−1.36274	−	0.656261i
$324$		0			0
$325$	0.841720	−	1.45790i	0.0466902	−	0.0808699i
$326$	−20.9744	+	14.3001i	−1.16166	+	0.792009i
$327$		0			0
$328$	28.0384	−	122.844i	1.54816	−	6.78295i
$329$	−1.10879	+	0.899278i	−0.0611296	+	0.0495788i
$330$		0			0
$331$	−1.83481	−	24.4838i	−0.100850	−	1.34575i	−0.786396	−	0.617723i	$-0.788055\pi$
$331$	−1.83481	−	24.4838i	−0.100850	−	1.34575i	0.685546	−	0.728029i	$-0.259564\pi$
$332$	−29.1057	−	8.97791i	−1.59738	−	0.492727i
$333$		0			0
$334$	38.0758	−	11.7448i	2.08341	−	0.642648i
$335$	−4.80452	−	6.02468i	−0.262499	−	0.329163i
$336$		0			0
$337$	11.8438	−	14.8517i	0.645175	−	0.809024i	−0.346465	−	0.938063i	$-0.612618\pi$
$337$	11.8438	−	14.8517i	0.645175	−	0.809024i	0.991639	+	0.129039i	$0.0411893\pi$
$338$	12.9906	−	33.0995i	0.706594	−	1.80037i
$339$		0			0
$340$	−22.9669	+	3.46171i	−1.24556	+	0.187738i
$341$	3.63785	−	3.37543i	0.197001	−	0.182790i
$342$		0			0
$343$	18.1523	+	3.67355i	0.980131	+	0.198353i
$344$	0.369629			0.0199290
$345$		0			0
$346$	−42.9824	+	6.47855i	−2.31075	+	0.348289i
$347$	−2.02287	+	26.9933i	−0.108593	+	1.44907i	0.630876	+	0.775884i	$0.282696\pi$
$347$	−2.02287	+	26.9933i	−0.108593	+	1.44907i	−0.739469	+	0.673191i	$0.764923\pi$
$348$		0			0
$349$	21.8683	−	27.4219i	1.17058	−	1.46786i	0.315837	−	0.948813i	$-0.397715\pi$
$349$	21.8683	−	27.4219i	1.17058	−	1.46786i	0.854744	−	0.519049i	$-0.173714\pi$
$350$	32.8012	+	2.18645i	1.75330	+	0.116871i
$351$		0			0
$352$	−25.7475	+	7.94204i	−1.37234	+	0.423312i
$353$	−12.5466	−	31.9681i	−0.667786	−	1.70149i	−0.711726	−	0.702457i	$-0.752086\pi$
$353$	−12.5466	−	31.9681i	−0.667786	−	1.70149i	0.0439405	−	0.999034i	$-0.486009\pi$
$354$		0			0
$355$	0.400248	+	5.34094i	0.0212429	+	0.283467i
$356$	8.04188	+	35.2338i	0.426219	+	1.86739i
$357$		0			0
$358$	−2.15460	+	9.43991i	−0.113874	+	0.498915i
$359$	12.1672	+	1.83391i	0.642161	+	0.0967902i	0.462047	−	0.886856i	$-0.347115\pi$
$359$	12.1672	+	1.83391i	0.642161	+	0.0967902i	0.180114	+	0.983646i	$0.442353\pi$
$360$		0			0
$361$	−1.55160	+	2.68745i	−0.0816633	+	0.141445i
$362$	24.5720	+	42.5600i	1.29148	+	2.23690i
$363$		0			0
$364$	−5.57623	+	0.464121i	−0.292274	+	0.0243265i
$365$	5.77645	−	2.78179i	0.302353	−	0.145606i
$366$		0			0
$367$	−4.55087	−	4.22259i	−0.237554	−	0.220418i	0.552408	−	0.833574i	$-0.313709\pi$
$367$	−4.55087	−	4.22259i	−0.237554	−	0.220418i	−0.789962	+	0.613156i	$0.789900\pi$
$368$	84.7032	+	78.5930i	4.41546	+	4.09695i
$369$		0			0
$370$	0.503411	−	0.242430i	0.0261711	−	0.0126033i
$371$	1.15659	−	8.12738i	0.0600472	−	0.421952i
$372$		0			0
$373$	−5.35077	−	9.26780i	−0.277052	−	0.479869i	0.693599	−	0.720362i	$-0.256024\pi$
$373$	−5.35077	−	9.26780i	−0.277052	−	0.479869i	−0.970651	+	0.240493i	$0.922691\pi$
$374$	−8.38581	+	14.5247i	−0.433620	+	0.751052i
$375$		0			0
$376$	5.37818	+	0.810631i	0.277359	+	0.0418051i
$377$	0.186150	−	0.815576i	0.00958721	−	0.0420043i
$378$		0			0
$379$	6.17457	+	27.0526i	0.317167	+	1.38960i	0.842498	+	0.538700i	$0.181084\pi$
$379$	6.17457	+	27.0526i	0.317167	+	1.38960i	−0.525331	+	0.850898i	$0.676059\pi$
$380$	1.41133	+	18.8328i	0.0723995	+	0.966104i
$381$		0			0
$382$	16.1990	+	41.2744i	0.828814	+	2.11178i
$383$	30.9781	−	9.55546i	1.58290	−	0.488261i	0.626283	−	0.779596i	$-0.284575\pi$
$383$	30.9781	−	9.55546i	1.58290	−	0.488261i	0.956621	+	0.291334i	$0.0940991\pi$
$384$		0			0
$385$	−1.33133	+	1.45876i	−0.0678507	+	0.0743451i
$386$	20.4376	−	25.6279i	1.04024	−	1.30443i
$387$		0			0
$388$	−5.41938	+	72.3166i	−0.275127	+	3.67132i
$389$	−22.1412	+	3.33725i	−1.12261	+	0.169205i	−0.684005	−	0.729477i	$-0.739764\pi$
$389$	−22.1412	+	3.33725i	−1.12261	+	0.169205i	−0.438600	+	0.898683i	$0.644525\pi$
$390$		0			0
$391$	40.2958			2.03784
$392$	−36.2812	−	60.5153i	−1.83248	−	3.05648i
$393$		0			0
$394$	10.0148	−	9.29236i	0.504538	−	0.468143i
$395$	−4.19559	+	0.632383i	−0.211103	+	0.0318187i
$396$		0			0
$397$	−5.16466	+	13.1593i	−0.259207	+	0.660448i	−0.999936	−	0.0113561i	$-0.996385\pi$
$397$	−5.16466	+	13.1593i	−0.259207	+	0.660448i	0.740729	+	0.671804i	$0.234480\pi$
$398$	−24.9765	+	31.3195i	−1.25196	+	1.56991i
$399$		0			0
$400$	−46.4531	−	58.2504i	−2.32266	−	2.91252i
$401$	−12.4682	+	3.84593i	−0.622632	+	0.192057i	−0.589990	−	0.807411i	$-0.700868\pi$
$401$	−12.4682	+	3.84593i	−0.622632	+	0.192057i	−0.0326420	+	0.999467i	$0.510392\pi$
$402$		0			0
$403$	−1.69345	−	0.522359i	−0.0843565	−	0.0260205i
$404$	3.63936	+	48.5639i	0.181065	+	2.41614i
$405$		0			0
$406$	15.8960	−	3.76623i	0.788904	−	0.186915i
$407$	0.0662938	−	0.290452i	0.00328606	−	0.0143972i
$408$		0			0
$409$	15.3168	−	10.4428i	0.757368	−	0.516365i	−0.121987	−	0.992532i	$-0.538926\pi$
$409$	15.3168	−	10.4428i	0.757368	−	0.516365i	0.879355	+	0.476167i	$0.157974\pi$
$410$	−12.2974	+	21.2997i	−0.607325	+	1.05192i
$411$		0			0
$412$	50.1088	+	24.1311i	2.46868	+	1.18886i
$413$	0.904284	+	2.84808i	0.0444969	+	0.140145i
$414$		0			0
$415$	3.17199	+	2.16262i	0.155707	+	0.106159i
$416$	7.05347	+	6.54466i	0.345825	+	0.320878i
$417$		0			0
$418$	11.2676	+	7.68212i	0.551116	+	0.375745i
$419$	−10.9357	+	5.26634i	−0.534243	+	0.257278i	−0.681497	−	0.731821i	$-0.738671\pi$
$419$	−10.9357	+	5.26634i	−0.534243	+	0.257278i	0.147254	+	0.989099i	$0.452956\pi$
$420$		0			0
$421$	28.7632	+	13.8516i	1.40183	+	0.675088i	0.973533	−	0.228548i	$-0.0733976\pi$
$421$	28.7632	+	13.8516i	1.40183	+	0.675088i	0.428302	+	0.903636i	$0.359112\pi$
$422$	−5.59375	−	9.68866i	−0.272299	−	0.471637i
$423$		0			0
$424$	−25.8410	+	17.6181i	−1.25495	+	0.855609i
$425$	−25.6922	−	3.87248i	−1.24626	−	0.187843i
$426$		0			0
$427$	−0.172519	−	20.9344i	−0.00834876	−	1.01309i
$428$	−3.37358	−	14.7806i	−0.163068	−	0.714448i
$429$		0			0
$430$	−0.0689430	−	0.0212661i	−0.00332473	−	0.00102554i
$431$	5.63746	+	14.3640i	0.271547	+	0.691890i	0.999977	+	0.00677023i	$0.00215505\pi$
$431$	5.63746	+	14.3640i	0.271547	+	0.691890i	−0.728430	+	0.685120i	$0.759750\pi$
$432$		0			0
$433$	−8.91403	−	11.1778i	−0.428381	−	0.537173i	0.520059	−	0.854131i	$-0.325910\pi$
$433$	−8.91403	−	11.1778i	−0.428381	−	0.537173i	−0.948440	+	0.316958i	$0.897339\pi$
$434$	−5.43971	−	34.1767i	−0.261114	−	1.64053i
$435$		0			0
$436$	−26.9964	+	68.7856i	−1.29289	+	3.29423i
$437$	2.44853	−	32.6734i	0.117129	−	1.56298i
$438$		0			0
$439$	−13.6429	+	12.6588i	−0.651142	+	0.604171i	−0.934980	−	0.354701i	$-0.884583\pi$
$439$	−13.6429	+	12.6588i	−0.651142	+	0.604171i	0.283838	+	0.958872i	$0.408392\pi$
$440$	7.52409			0.358697
$441$		0			0
$442$	5.98925			0.284879
$443$	−11.7543	+	10.9064i	−0.558465	+	0.518180i	−0.908126	−	0.418696i	$-0.862487\pi$
$443$	−11.7543	+	10.9064i	−0.558465	+	0.518180i	0.349661	+	0.936876i	$0.386297\pi$
$444$		0			0
$445$	0.340404	−	4.54237i	0.0161367	−	0.215329i
$446$	13.7994	−	35.1603i	0.653421	−	1.66489i
$447$		0			0
$448$	−28.7346	+	95.9556i	−1.35758	+	4.53348i
$449$	5.12316	+	6.42424i	0.241777	+	0.303179i	0.887883	−	0.460069i	$-0.152175\pi$
$449$	5.12316	+	6.42424i	0.241777	+	0.303179i	−0.646106	+	0.763247i	$0.723604\pi$
$450$		0			0
$451$	4.79105	+	12.2074i	0.225602	+	0.574824i
$452$	−24.8523	−	7.66593i	−1.16896	−	0.360575i
$453$		0			0
$454$	9.33600	+	40.9037i	0.438160	+	1.91971i
$455$	0.688852	+	0.151265i	0.0322939	+	0.00709139i
$456$		0			0
$457$	10.7276	+	1.61692i	0.501816	+	0.0756365i	0.395072	−	0.918650i	$-0.370720\pi$
$457$	10.7276	+	1.61692i	0.501816	+	0.0756365i	0.106743	+	0.994287i	$0.465958\pi$
$458$	−51.2330	+	34.9301i	−2.39396	+	1.63217i
$459$		0			0
$460$	−13.9977	−	24.2447i	−0.652646	−	1.13042i
$461$	23.3275	+	11.2339i	1.08647	+	0.523216i	0.889380	−	0.457169i	$-0.151137\pi$
$461$	23.3275	+	11.2339i	1.08647	+	0.523216i	0.197090	+	0.980385i	$0.436851\pi$
$462$		0			0
$463$	17.5107	−	8.43269i	0.813790	−	0.391900i	0.0197791	−	0.999804i	$-0.493704\pi$
$463$	17.5107	−	8.43269i	0.813790	−	0.391900i	0.794011	+	0.607904i	$0.207989\pi$
$464$	−30.5904	−	20.8562i	−1.42012	−	0.968224i
$465$		0			0
$466$	−21.0877	−	19.5666i	−0.976871	−	0.906404i
$467$	7.17461	+	4.89157i	0.332001	+	0.226355i	0.717834	−	0.696214i	$-0.245134\pi$
$467$	7.17461	+	4.89157i	0.332001	+	0.226355i	−0.385833	+	0.922569i	$0.626086\pi$
$468$		0			0
$469$	−15.9449	+	23.8060i	−0.736265	+	1.09926i
$470$	−0.956498	−	0.460625i	−0.0441200	−	0.0212471i
$471$		0			0
$472$	5.69216	−	9.85911i	0.262003	−	0.453802i
$473$	−0.0317849	+	0.0216706i	−0.00146147	+	0.000996414i
$474$		0			0
$475$	−4.70112	+	20.5970i	−0.215702	+	0.945054i
$476$	38.1109	+	77.4979i	1.74681	+	3.55211i
$477$		0			0
$478$	−5.06826	−	67.6312i	−0.231817	−	3.09338i
$479$	6.55888	+	2.02315i	0.299683	+	0.0924399i	0.440950	−	0.897532i	$-0.354642\pi$
$479$	6.55888	+	2.02315i	0.299683	+	0.0924399i	−0.141267	+	0.989971i	$0.545118\pi$
$480$		0			0
$481$	−0.101663	+	0.0313589i	−0.00463543	+	0.00142984i
$482$	−24.9470	−	31.2825i	−1.13630	−	1.42488i
$483$		0			0
$484$	−34.8448	+	43.6940i	−1.58386	+	1.98609i
$485$	3.33937	−	8.50857i	0.151633	−	0.386354i
$486$		0			0
$487$	15.4858	−	2.33411i	0.701729	−	0.105769i	0.211520	−	0.977374i	$-0.432159\pi$
$487$	15.4858	−	2.33411i	0.701729	−	0.105769i	0.490209	+	0.871605i	$0.336920\pi$
$488$	−58.4667	+	54.2492i	−2.64666	+	2.45574i
$489$		0			0
$490$	3.28550	+	13.3747i	0.148424	+	0.604206i
$491$	26.4361			1.19304			0.596522	−	0.802597i	$-0.296549\pi$
$491$	26.4361			1.19304			0.596522	+	0.802597i	$0.296549\pi$
$492$		0			0
$493$	−12.7672	+	1.92435i	−0.575007	+	0.0866683i
$494$	0.363931	−	4.85632i	0.0163740	−	0.218496i
$495$		0			0
$496$	−48.9017	+	61.3208i	−2.19575	+	2.75339i
$497$	18.4775	−	7.42818i	0.828830	−	0.333200i
$498$		0			0
$499$	33.0104	−	10.1824i	1.47775	−	0.455825i	0.551962	−	0.833869i	$-0.313879\pi$
$499$	33.0104	−	10.1824i	1.47775	−	0.455825i	0.925788	+	0.378044i	$0.123403\pi$
$500$	13.9328	+	35.5001i	0.623093	+	1.58761i
$501$		0			0
$502$	1.16678	+	15.5696i	0.0520760	+	0.694905i
$503$	−1.44947	−	6.35054i	−0.0646286	−	0.283156i	0.932279	−	0.361740i	$-0.117817\pi$
$503$	−1.44947	−	6.35054i	−0.0646286	−	0.283156i	−0.996908	+	0.0785839i	$0.974960\pi$
$504$		0			0
$505$	1.36588	−	5.98431i	0.0607808	−	0.266298i
$506$	−19.9895	−	3.01294i	−0.888643	−	0.133941i
$507$		0			0
$508$	11.0671	−	19.1688i	0.491023	−	0.850476i
$509$	−6.54966	−	11.3443i	−0.290309	−	0.502829i	0.683574	−	0.729881i	$-0.260425\pi$
$509$	−6.54966	−	11.3443i	−0.290309	−	0.502829i	−0.973883	+	0.227052i	$0.927091\pi$
$510$		0			0
$511$	−16.3582	−	17.3412i	−0.723646	−	0.767128i
$512$	82.5354	−	39.7470i	3.64759	−	1.75658i
$513$		0			0
$514$	−3.50469	−	3.25188i	−0.154585	−	0.143434i
$515$	−5.13867	−	4.76799i	−0.226437	−	0.210103i
$516$		0			0
$517$	−0.510003	+	0.245605i	−0.0224299	+	0.0108017i
$518$	−1.42560	−	1.51126i	−0.0626374	−	0.0664012i
$519$		0			0
$520$	−1.34345	−	2.32692i	−0.0589141	−	0.102042i
$521$	7.87206	−	13.6348i	0.344881	−	0.597352i	−0.640451	−	0.767999i	$-0.721253\pi$
$521$	7.87206	−	13.6348i	0.344881	−	0.597352i	0.985332	+	0.170647i	$0.0545859\pi$
$522$		0			0
$523$	−31.6407	−	4.76906i	−1.38355	−	0.208537i	−0.585277	−	0.810833i	$-0.699014\pi$
$523$	−31.6407	−	4.76906i	−1.38355	−	0.208537i	−0.798272	+	0.602297i	$0.794252\pi$
$524$	−0.523856	+	2.29516i	−0.0228847	+	0.100265i
$525$		0			0
$526$	−1.60382	−	7.02679i	−0.0699298	−	0.306382i
$527$	2.04402	+	27.2755i	0.0890389	+	1.18814i
$528$		0			0
$529$	9.34165	+	23.8021i	0.406159	+	1.03488i
$530$	5.83348	−	1.79939i	0.253390	−	0.0781605i
$531$		0			0
$532$	65.1541	−	26.1928i	2.82479	−	1.13560i
$533$	2.91984	−	3.66136i	0.126472	−	0.158591i
$534$		0			0
$535$	−0.142800	+	1.90553i	−0.00617378	+	0.0823833i
$536$	107.940	−	16.2693i	4.66230	−	0.702729i
$537$		0			0
$538$	0.676897			0.0291831
$539$	6.66776	+	3.07670i	0.287201	+	0.132523i
$540$		0			0
$541$	−22.1517	+	20.5537i	−0.952374	+	0.883674i	−0.993309	−	0.115487i	$-0.963157\pi$
$541$	−22.1517	+	20.5537i	−0.952374	+	0.883674i	0.0409344	+	0.999162i	$0.486967\pi$
$542$	−20.5959	+	3.10434i	−0.884672	+	0.133343i
$543$		0			0
$544$	54.2561	−	138.242i	2.32621	−	5.92709i
$545$	5.80695	−	7.28168i	0.248742	−	0.311913i
$546$		0			0
$547$	−26.2095	−	32.8657i	−1.12064	−	1.40524i	−0.903231	−	0.429154i	$-0.858812\pi$
$547$	−26.2095	−	32.8657i	−1.12064	−	1.40524i	−0.217406	−	0.976081i	$-0.569760\pi$
$548$	−24.1971	+	7.46382i	−1.03365	+	0.318838i
$549$		0			0
$550$	12.4556	+	3.84205i	0.531109	+	0.163825i
$551$	0.784550	+	10.4691i	0.0334229	+	0.445998i
$552$		0			0
$553$	6.96209	+	14.1573i	0.296058	+	0.602029i
$554$	−11.2182	+	49.1503i	−0.476617	+	2.08820i
$555$		0			0
$556$	12.3186	−	8.39868i	0.522425	−	0.356183i
$557$	20.1049	−	34.8227i	0.851872	−	1.47549i	−0.0276443	−	0.999618i	$-0.508801\pi$
$557$	20.1049	−	34.8227i	0.851872	−	1.47549i	0.879517	−	0.475868i	$-0.157866\pi$
$558$		0			0
$559$	0.0123772	+	0.00596054i	0.000523499	+	0.000252104i
$560$	17.3699	−	25.9336i	0.734014	−	1.09590i
$561$		0			0
$562$	−36.2706	−	24.7289i	−1.52999	−	1.04313i
$563$	−7.47065	−	6.93175i	−0.314850	−	0.292139i	0.506878	−	0.862018i	$-0.330799\pi$
$563$	−7.47065	−	6.93175i	−0.314850	−	0.292139i	−0.821728	+	0.569879i	$0.806990\pi$
$564$		0			0
$565$	2.70845	+	1.84659i	0.113945	+	0.0776867i
$566$	−39.5592	+	19.0507i	−1.66280	+	0.800761i
$567$		0			0
$568$	−68.3570	−	32.9190i	−2.86820	−	1.38125i
$569$	2.69322	+	4.66479i	0.112905	+	0.195558i	0.916941	−	0.399024i	$-0.130651\pi$
$569$	2.69322	+	4.66479i	0.112905	+	0.195558i	−0.804035	+	0.594582i	$0.797318\pi$
$570$		0			0
$571$	35.4153	−	24.1457i	1.48208	−	1.01047i	0.491907	−	0.870648i	$-0.336300\pi$
$571$	35.4153	−	24.1457i	1.48208	−	1.01047i	0.990177	−	0.139820i	$-0.0446525\pi$
$572$	−2.19387	−	0.330672i	−0.0917302	−	0.0138261i
$573$		0			0
$574$	89.3220	+	19.6142i	3.72823	+	0.818679i
$575$	−6.96878	−	30.5322i	−0.290618	−	1.27328i
$576$		0			0
$577$	31.0213	+	9.56881i	1.29143	+	0.398355i	0.862993	−	0.505215i	$-0.168587\pi$
$577$	31.0213	+	9.56881i	1.29143	+	0.398355i	0.428441	+	0.903570i	$0.359063\pi$
$578$	−16.5986	−	42.2926i	−0.690412	−	1.75914i
$579$		0			0
$580$	5.59282	+	7.01318i	0.232229	+	0.291206i
$581$	4.09499	−	13.6747i	0.169889	−	0.567323i
$582$		0			0
$583$	1.18919	−	3.03001i	0.0492512	−	0.125490i
$584$	−6.78714	+	90.5680i	−0.280854	+	3.74773i
$585$		0			0
$586$	28.5838	−	26.5219i	1.18078	−	1.09561i
$587$	25.9804			1.07233			0.536163	−	0.844115i	$-0.319873\pi$
$587$	25.9804			1.07233			0.536163	+	0.844115i	$0.319873\pi$
$588$		0			0
$589$	22.2403			0.916395
$590$	−1.62893	+	1.51143i	−0.0670620	+	0.0622244i
$591$		0			0
$592$	−0.351870	+	4.69538i	−0.0144618	+	0.192979i
$593$	−10.5443	+	26.8666i	−0.433004	+	1.10328i	0.533312	+	0.845919i	$0.320947\pi$
$593$	−10.5443	+	26.8666i	−0.433004	+	1.10328i	−0.966316	+	0.257358i	$0.917148\pi$
$594$		0			0
$595$	−1.71099	−	10.7498i	−0.0701437	−	0.440700i
$596$	−48.7790	−	61.1669i	−1.99807	−	2.50550i
$597$		0			0
$598$	2.63740	+	6.71999i	0.107851	+	0.274801i
$599$	33.2637	+	10.2605i	1.35912	+	0.419233i	0.886783	−	0.462186i	$-0.152935\pi$
$599$	33.2637	+	10.2605i	1.35912	+	0.419233i	0.472336	+	0.881419i	$0.343411\pi$
$600$		0			0
$601$	3.98739	+	17.4699i	0.162649	+	0.712611i	0.988810	+	0.149178i	$0.0476627\pi$
$601$	3.98739	+	17.4699i	0.162649	+	0.712611i	−0.826162	+	0.563433i	$0.809480\pi$
$602$	0.00221069	+	0.268258i	9.01011e−5	+	0.0109334i
$603$		0			0
$604$	5.69306	+	0.858091i	0.231647	+	0.0349152i
$605$	5.82005	−	3.96804i	0.236618	−	0.161324i
$606$		0			0
$607$	−10.3693	−	17.9601i	−0.420877	−	0.728980i	0.575149	−	0.818049i	$-0.304944\pi$
$607$	−10.3693	−	17.9601i	−0.420877	−	0.728980i	−0.996025	+	0.0890691i	$0.971611\pi$
$608$	−108.795	−	52.3931i	−4.41224	−	2.12482i
$609$		0			0
$610$	14.0263	−	6.75473i	0.567910	−	0.273491i
$611$	0.167019	+	0.113872i	0.00675686	+	0.00460675i
$612$		0			0
$613$	−15.3954	−	14.2848i	−0.621814	−	0.576959i	0.305059	−	0.952333i	$-0.401324\pi$
$613$	−15.3954	−	14.2848i	−0.621814	−	0.576959i	−0.926873	+	0.375374i	$0.877514\pi$
$614$	49.2085	+	33.5498i	1.98589	+	1.35396i
$615$		0			0
$616$	−8.46626	−	26.6648i	−0.341116	−	1.07436i
$617$	6.90692	+	3.32620i	0.278062	+	0.133908i	0.567718	−	0.823223i	$-0.307827\pi$
$617$	6.90692	+	3.32620i	0.278062	+	0.133908i	−0.289656	+	0.957131i	$0.593541\pi$
$618$		0			0
$619$	−18.5284	+	32.0922i	−0.744721	+	1.28989i	0.205605	+	0.978635i	$0.434084\pi$
$619$	−18.5284	+	32.0922i	−0.744721	+	1.28989i	−0.950325	+	0.311259i	$0.899249\pi$
$620$	15.7008	−	10.7046i	0.630560	−	0.429909i
$621$		0			0
$622$	10.8696	−	47.6229i	0.435832	−	1.90950i
$623$	−16.4809	+	3.90481i	−0.660291	+	0.156443i
$624$		0			0
$625$	1.31986	+	17.6123i	0.0527944	+	0.704493i
$626$	90.4726	+	27.9071i	3.61601	+	1.11539i
$627$		0			0
$628$	−53.0500	+	16.3638i	−2.11693	+	0.652985i
$629$	1.02379	+	1.28379i	0.0408212	+	0.0511881i
$630$		0			0
$631$	−8.86726	+	11.1192i	−0.353000	+	0.442648i	−0.926351	−	0.376662i	$-0.877072\pi$
$631$	−8.86726	+	11.1192i	−0.353000	+	0.442648i	0.573351	+	0.819310i	$0.305643\pi$
$632$	21.9588	−	55.9502i	0.873476	−	2.22558i
$633$		0			0
$634$	22.6662	−	3.41638i	0.900190	−	0.135682i
$635$	−2.04508	+	1.89756i	−0.0811565	+	0.0753022i
$636$		0			0
$637$	−0.239040	−	2.61145i	−0.00947112	−	0.103469i
$638$	6.47732			0.256440
$639$		0			0
$640$	−37.5110	+	5.65387i	−1.48275	+	0.223489i
$641$	−2.87592	+	38.3765i	−0.113592	+	1.51578i	0.591293	+	0.806457i	$0.298618\pi$
$641$	−2.87592	+	38.3765i	−0.113592	+	1.51578i	−0.704885	+	0.709322i	$0.749001\pi$
$642$		0			0
$643$	−18.5483	+	23.2589i	−0.731475	+	0.917241i	−0.998926	−	0.0463309i	$-0.985247\pi$
$643$	−18.5483	+	23.2589i	−0.731475	+	0.917241i	0.267451	+	0.963571i	$0.413819\pi$
$644$	−70.1710	+	76.8875i	−2.76513	+	3.02979i
$645$		0			0
$646$	−71.8239	+	22.1547i	−2.82587	+	0.871667i
$647$	0.317193	+	0.808195i	0.0124702	+	0.0317734i	0.936973	−	0.349401i	$-0.113615\pi$
$647$	0.317193	+	0.808195i	0.0124702	+	0.0317734i	−0.924503	+	0.381175i	$0.875520\pi$
$648$		0			0
$649$	0.0885425	+	1.18152i	0.00347560	+	0.0463786i
$650$	−1.03578	−	4.53807i	−0.0406268	−	0.177998i
$651$		0			0
$652$	−11.5332	+	50.5303i	−0.451675	+	1.97892i
$653$	32.6764	+	4.92518i	1.27873	+	0.192737i	0.753059	−	0.657953i	$-0.228577\pi$
$653$	32.6764	+	4.92518i	1.27873	+	0.192737i	0.525668	+	0.850690i	$0.323815\pi$
$654$		0			0
$655$	0.148362	−	0.256971i	0.00579698	−	0.0100407i
$656$	−103.630	−	179.493i	−4.04609	−	7.00803i
$657$		0			0
$658$	−0.556149	+	3.90806i	−0.0216809	+	0.152352i
$659$	2.65504	−	1.27860i	0.103426	−	0.0498071i	−0.381456	−	0.924387i	$-0.624577\pi$
$659$	2.65504	−	1.27860i	0.103426	−	0.0498071i	0.484881	+	0.874580i	$0.338863\pi$
$660$		0			0
$661$	−18.7663	−	17.4126i	−0.729924	−	0.677271i	0.224920	−	0.974377i	$-0.427788\pi$
$661$	−18.7663	−	17.4126i	−0.729924	−	0.677271i	−0.954844	+	0.297106i	$0.903978\pi$
$662$	−49.7657	−	46.1759i	−1.93420	−	1.79468i
$663$		0			0
$664$	−48.9977	+	23.5960i	−1.90148	+	0.915704i
$665$	−8.82035	+	0.734135i	−0.342038	+	0.0284685i
$666$		0			0
$667$	−7.78126	−	13.4775i	−0.301292	−	0.521852i
$668$	40.6771	−	70.4548i	1.57385	−	2.72598i
$669$		0			0
$670$	−21.0690	−	3.17564i	−0.813965	−	0.122686i
$671$	1.84712	−	8.09274i	0.0713071	−	0.312417i
$672$		0			0
$673$	−1.71878	−	7.53046i	−0.0662540	−	0.290278i	0.930937	−	0.365180i	$-0.118993\pi$
$673$	−1.71878	−	7.53046i	−0.0662540	−	0.290278i	−0.997191	+	0.0749024i	$0.976135\pi$
$674$	−3.92518	−	52.3778i	−0.151192	−	2.01752i
$675$		0			0
$676$	−26.5231	−	67.5797i	−1.02012	−	2.59922i
$677$	−0.819275	+	0.252713i	−0.0314873	+	0.00971254i	−0.310459	−	0.950587i	$-0.600483\pi$
$677$	−0.819275	+	0.252713i	−0.0314873	+	0.00971254i	0.278972	+	0.960299i	$0.410006\pi$
$678$		0			0
$679$	−33.9113	−	2.26044i	−1.30140	−	0.0867478i
$680$	−25.8561	+	32.4225i	−0.991535	+	1.24335i
$681$		0			0
$682$	1.02543	−	13.6834i	0.0392658	−	0.523965i
$683$	−35.8816	+	5.40829i	−1.37297	+	0.206942i	−0.793758	−	0.608233i	$-0.791879\pi$
$683$	−35.8816	+	5.40829i	−1.37297	+	0.206942i	−0.579214	+	0.815176i	$0.696640\pi$
$684$		0			0
$685$	3.19162			0.121946
$686$	43.7019	−	26.6930i	1.66855	−	1.01914i
$687$		0			0
$688$	0.445692	−	0.413541i	0.0169918	−	0.0157661i
$689$	−1.14940	+	0.173244i	−0.0437887	+	0.00660009i
$690$		0			0
$691$	10.5048	−	26.7658i	0.399621	−	1.01822i	−0.579506	−	0.814968i	$-0.696754\pi$
$691$	10.5048	−	26.7658i	0.399621	−	1.01822i	0.979127	−	0.203250i	$-0.0651504\pi$
$692$	−55.3341	+	69.3868i	−2.10349	+	2.63769i
$693$		0			0
$694$	46.6661	+	58.5174i	1.77142	+	2.22129i
$695$	−1.79569	+	0.553897i	−0.0681145	+	0.0210105i
$696$		0			0
$697$	−69.0678	−	21.3046i	−2.61613	−	0.806969i
$698$	−7.24738	−	96.7096i	−0.274317	−	3.66051i
$699$		0			0
$700$	52.1295	−	42.2793i	1.97031	−	1.59801i
$701$	−10.3945	+	45.5411i	−0.392593	+	1.72006i	0.262866	+	0.964832i	$0.415332\pi$
$701$	−10.3945	+	45.5411i	−0.392593	+	1.72006i	−0.655459	+	0.755230i	$0.727525\pi$
$702$		0			0
$703$	1.10316	−	0.752120i	0.0416064	−	0.0283668i
$704$	−19.8581	+	34.3952i	−0.748430	+	1.29632i
$705$		0			0
$706$	−85.5533	−	41.2003i	−3.21984	−	1.55059i
$707$	−22.7449	+	1.89310i	−0.855408	+	0.0711973i
$708$		0			0
$709$	11.3310	+	7.72534i	0.425545	+	0.290131i	0.757093	−	0.653307i	$-0.226619\pi$
$709$	11.3310	+	7.72534i	0.425545	+	0.290131i	−0.331549	+	0.943438i	$0.607571\pi$
$710$	10.8560	+	10.0729i	0.407417	+	0.378028i
$711$		0			0
$712$	53.3144	+	36.3491i	1.99804	+	1.36224i
$713$	−29.7033	+	14.3044i	−1.11240	+	0.535703i
$714$		0			0
$715$	0.251948	+	0.121332i	0.00942230	+	0.00453754i
$716$	9.88464	+	17.1207i	0.369406	+	0.639830i
$717$		0			0
$718$	28.1109	−	19.1657i	1.04909	−	0.715258i
$719$	31.5896	+	4.76137i	1.17809	+	0.177569i	0.708759	−	0.705451i	$-0.249255\pi$
$719$	31.5896	+	4.76137i	1.17809	+	0.177569i	0.469335	+	0.883020i	$0.344494\pi$
$720$		0			0
$721$	−11.1153	+	23.5761i	−0.413954	+	0.878021i
$722$	1.90933	+	8.36534i	0.0710581	+	0.311326i
$723$		0			0
$724$	95.8804	+	29.5752i	3.56337	+	1.09915i
$725$	3.66605	+	9.34096i	0.136154	+	0.346914i
$726$		0			0
$727$	−8.03317	−	10.0733i	−0.297934	−	0.373597i	0.610221	−	0.792231i	$-0.291080\pi$
$727$	−8.03317	−	10.0733i	−0.297934	−	0.373597i	−0.908155	+	0.418634i	$0.862509\pi$
$728$	−6.73475	+	7.37938i	−0.249607	+	0.273498i
$729$		0			0
$730$	6.47665	−	16.5022i	0.239711	−	0.610775i
$731$	0.0158449	−	0.211436i	0.000586045	−	0.00782023i
$732$		0			0
$733$	10.9031	−	10.1166i	0.402717	−	0.373666i	−0.452651	−	0.891688i	$-0.649522\pi$
$733$	10.9031	−	10.1166i	0.402717	−	0.373666i	0.855368	+	0.518021i	$0.173331\pi$
$734$	−17.1657			−0.633596
$735$		0			0
$736$	179.001			6.59807
$737$	−8.32808	+	7.72733i	−0.306769	+	0.284640i
$738$		0			0
$739$	−2.16228	+	28.8537i	−0.0795409	+	1.06140i	0.804488	+	0.593968i	$0.202440\pi$
$739$	−2.16228	+	28.8537i	−0.0795409	+	1.06140i	−0.884029	+	0.467431i	$0.845179\pi$
$740$	0.416780	−	1.06194i	0.0153211	−	0.0390377i
$741$		0			0
$742$	−12.9409	−	18.6487i	−0.475074	−	0.684615i
$743$	−2.53079	−	3.17351i	−0.0928457	−	0.116425i	0.733238	−	0.679972i	$-0.238008\pi$
$743$	−2.53079	−	3.17351i	−0.0928457	−	0.116425i	−0.826084	+	0.563547i	$0.809436\pi$
$744$		0			0
$745$	3.60258	+	9.17923i	0.131988	+	0.336301i
$746$	−28.2755	−	8.72184i	−1.03524	−	0.319329i
$747$		0			0
$748$	7.61976	+	33.3844i	0.278606	+	1.22065i
$749$	6.91374	−	1.63807i	0.252623	−	0.0598539i
$750$		0			0
$751$	15.1578	+	2.28467i	0.553115	+	0.0833686i	0.419652	−	0.907685i	$-0.362152\pi$
$751$	15.1578	+	2.28467i	0.553115	+	0.0833686i	0.133463	+	0.991054i	$0.457390\pi$
$752$	7.39185	−	5.03968i	0.269553	−	0.183778i
$753$		0			0
$754$	−1.15655	−	2.00320i	−0.0421189	−	0.0729521i
$755$	−0.653801	−	0.314854i	−0.0237943	−	0.0114587i
$756$		0			0
$757$	−15.6910	+	7.55641i	−0.570301	+	0.274642i	−0.696730	−	0.717333i	$-0.745363\pi$
$757$	−15.6910	+	7.55641i	−0.570301	+	0.274642i	0.126429	+	0.991976i	$0.459648\pi$
$758$	63.3931	+	43.2207i	2.30254	+	1.56985i
$759$		0			0
$760$	24.7183	+	22.9352i	0.896627	+	0.831948i
$761$	−38.6046	−	26.3202i	−1.39941	−	0.954105i	−0.999291	−	0.0376437i	$-0.988015\pi$
$761$	−38.6046	−	26.3202i	−1.39941	−	0.954105i	−0.400124	−	0.916461i	$-0.631033\pi$
$762$		0			0
$763$	−32.3399	−	12.3859i	−1.17078	−	0.448399i
$764$	81.5635	+	39.2789i	2.95086	+	1.42106i
$765$		0			0
$766$	44.8189	−	77.6286i	1.61937	−	2.80483i
$767$	0.349590	−	0.238346i	0.0126230	−	0.00860619i
$768$		0			0
$769$	0.168995	−	0.740414i	0.00609410	−	0.0267000i	−0.971789	−	0.235850i	$-0.924213\pi$
$769$	0.168995	−	0.740414i	0.00609410	−	0.0267000i	0.977884	+	0.209150i	$0.0670697\pi$
$770$	0.0450004	+	5.46060i	0.00162170	+	0.196786i
$771$		0			0
$772$	−5.00139	−	66.7389i	−0.180004	−	2.40199i
$773$	−22.6961	−	7.00083i	−0.816323	−	0.251802i	−0.141648	−	0.989917i	$-0.545240\pi$
$773$	−22.6961	−	7.00083i	−0.816323	−	0.251802i	−0.674675	+	0.738115i	$0.735716\pi$
$774$		0			0
$775$	20.3133	−	6.26581i	0.729674	−	0.225075i
$776$	80.7300	+	101.232i	2.89804	+	3.63403i
$777$		0			0
$778$	−38.6020	+	48.4054i	−1.38395	+	1.73542i
$779$	−21.4714	+	54.7083i	−0.769293	+	1.96013i
$780$		0			0
$781$	7.80809	−	1.17688i	0.279395	−	0.0421121i
$782$	81.6761	−	75.7843i	2.92073	−	2.71004i
$783$		0			0
$784$	−111.452	−	32.3767i	−3.98043	−	1.15631i
$785$	6.99735			0.249746
$786$		0			0
$787$	−3.58242	+	0.539962i	−0.127699	+	0.0192476i	−0.212581	−	0.977143i	$-0.568187\pi$
$787$	−3.58242	+	0.539962i	−0.127699	+	0.0192476i	0.0848816	+	0.996391i	$0.472949\pi$
$788$	2.08448	−	27.8155i	0.0742566	−	0.990885i
$789$		0			0
$790$	−7.31477	+	9.17244i	−0.260248	+	0.326341i
$791$	3.49657	−	11.6764i	0.124324	−	0.415164i
$792$		0			0
$793$	−2.83259	+	0.873739i	−0.100588	+	0.0310274i
$794$	14.2805	+	36.3860i	0.506795	+	1.29129i
$795$		0			0
$796$	6.11214	+	81.5608i	0.216639	+	2.89085i
$797$	−6.88695	−	30.1737i	−0.243948	−	1.06881i	−0.937386	−	0.348291i	$-0.886762\pi$
$797$	−6.88695	−	30.1737i	−0.243948	−	1.06881i	0.693438	−	0.720516i	$-0.256095\pi$
$798$		0			0
$799$	0.694246	−	3.04169i	0.0245607	−	0.107607i
$800$	−114.130	−	17.2023i	−4.03509	−	0.608192i
$801$		0			0
$802$	−18.0389	+	31.2443i	−0.636976	+	1.10328i
$803$	−4.72618	−	8.18599i	−0.166783	−	0.288877i
$804$		0			0
$805$	11.3080	−	6.65350i	0.398553	−	0.234505i
$806$	−4.41487	+	2.12609i	−0.155507	+	0.0748883i
$807$		0			0
$808$	63.7406	+	59.1426i	2.24239	+	2.08063i
$809$	−9.61442	−	8.92088i	−0.338025	−	0.313641i	0.492835	−	0.870123i	$-0.335961\pi$
$809$	−9.61442	−	8.92088i	−0.338025	−	0.313641i	−0.830860	+	0.556481i	$0.812151\pi$
$810$		0			0
$811$	29.4519	−	14.1833i	1.03420	−	0.498043i	0.161791	−	0.986825i	$-0.448273\pi$
$811$	29.4519	−	14.1833i	1.03420	−	0.498043i	0.872406	+	0.488782i	$0.162559\pi$
$812$	18.5610	−	27.7119i	0.651364	−	0.972498i
$813$		0			0
$814$	−0.411882	−	0.713400i	−0.0144365	−	0.0250047i
$815$	3.26634	−	5.65747i	0.114415	−	0.198172i
$816$		0			0
$817$	−0.170478	−	0.0256954i	−0.00596425	−	0.000898967i
$818$	11.4060	−	49.9731i	0.398803	−	1.74727i
$819$		0			0
$820$	11.1740	+	48.9566i	0.390214	+	1.70964i
$821$	−2.84979	−	38.0278i	−0.0994584	−	1.32718i	−0.794084	−	0.607808i	$-0.792049\pi$
$821$	−2.84979	−	38.0278i	−0.0994584	−	1.32718i	0.694625	−	0.719372i	$-0.255570\pi$
$822$		0			0
$823$	4.44281	+	11.3201i	0.154867	+	0.394594i	0.987159	−	0.159744i	$-0.0510668\pi$
$823$	4.44281	+	11.3201i	0.154867	+	0.394594i	−0.832292	+	0.554338i	$0.812972\pi$
$824$	94.8899	−	29.2697i	3.30565	−	1.01966i
$825$		0			0
$826$	7.18929	+	4.07212i	0.250147	+	0.141687i
$827$	−23.5467	+	29.5266i	−0.818798	+	1.02674i	0.180271	+	0.983617i	$0.442302\pi$
$827$	−23.5467	+	29.5266i	−0.818798	+	1.02674i	−0.999070	+	0.0431238i	$0.986269\pi$
$828$		0			0
$829$	1.05554	−	14.0852i	0.0366603	−	0.489198i	−0.948410	−	0.317046i	$-0.897309\pi$
$829$	1.05554	−	14.0852i	0.0366603	−	0.489198i	0.985070	−	0.172152i	$-0.0550720\pi$
$830$	10.4966	−	1.58211i	0.364342	−	0.0549157i
$831$		0			0
$832$	14.1829			0.491703
$833$	−36.1713	+	18.1596i	−1.25326	+	0.629191i
$834$		0			0
$835$	−7.51669	+	6.97447i	−0.260126	+	0.241362i
$836$	27.5324	−	4.14983i	0.952226	−	0.143525i
$837$		0			0
$838$	−12.2613	+	31.2412i	−0.423558	+	1.07921i
$839$	19.5644	−	24.5330i	0.675439	−	0.846973i	−0.319487	−	0.947591i	$-0.603510\pi$
$839$	19.5644	−	24.5330i	0.675439	−	0.846973i	0.994925	+	0.100618i	$0.0320819\pi$
$840$		0			0
$841$	−14.9722	−	18.7745i	−0.516282	−	0.647397i
$842$	84.3514	−	26.0190i	2.90694	−	0.896673i
$843$		0			0
$844$	−21.8269	−	6.73271i	−0.751313	−	0.231749i
$845$	0.683806	+	9.12476i	0.0235236	+	0.313901i
$846$		0			0
$847$	−20.6113	−	16.1609i	−0.708212	−	0.555294i
$848$	−11.4474	+	50.1545i	−0.393107	+	1.72231i
$849$		0			0
$850$	−59.3590	+	40.4703i	−2.03600	+	1.38812i
$851$	−0.989594	+	1.71403i	−0.0339228	+	0.0587561i
$852$		0			0
$853$	−41.0408	−	19.7642i	−1.40521	−	0.676713i	−0.430998	−	0.902353i	$-0.641839\pi$
$853$	−41.0408	−	19.7642i	−1.40521	−	0.676713i	−0.974211	+	0.225640i	$0.927553\pi$
$854$	−39.7210	−	42.1077i	−1.35922	−	1.44090i
$855$		0			0
$856$	−22.3655	−	15.2485i	−0.764436	−	0.521183i
$857$	−19.8874	−	18.4528i	−0.679342	−	0.630337i	0.263076	−	0.964775i	$-0.415263\pi$
$857$	−19.8874	−	18.4528i	−0.679342	−	0.630337i	−0.942418	+	0.334438i	$0.891453\pi$
$858$		0			0
$859$	42.1118	+	28.7113i	1.43684	+	0.979618i	0.996656	+	0.0817084i	$0.0260376\pi$
$859$	42.1118	+	28.7113i	1.43684	+	0.979618i	0.440180	+	0.897910i	$0.354915\pi$
$860$	−0.132719	+	0.0639139i	−0.00452566	+	0.00217944i
$861$		0			0
$862$	38.4411	+	18.5122i	1.30931	+	0.630530i
$863$	−17.2043	−	29.7988i	−0.585642	−	1.01436i	−0.994795	−	0.101896i	$-0.967509\pi$
$863$	−17.2043	−	29.7988i	−0.585642	−	1.01436i	0.409153	−	0.912466i	$-0.365824\pi$
$864$		0			0
$865$	9.24233	−	6.30131i	0.314248	−	0.214251i
$866$	−39.0902	−	5.89189i	−1.32834	−	0.200215i
$867$		0			0
$868$	−55.6034	−	43.5975i	−1.88730	−	1.47979i
$869$	1.39197	+	6.09864i	0.0472195	+	0.206882i
$870$		0			0
$871$	3.87678	+	1.19583i	0.131360	+	0.0405191i
$872$	48.2011	+	122.814i	1.63230	+	4.15902i
$873$		0			0
$874$	−56.4859	−	70.8311i	−1.91066	−	2.39590i
$875$	−16.5829	+	6.66654i	−0.560605	+	0.225370i
$876$		0			0
$877$	−7.45686	+	18.9998i	−0.251800	+	0.641577i	−0.999754	−	0.0221741i	$-0.992941\pi$
$877$	−7.45686	+	18.9998i	−0.251800	+	0.641577i	0.747954	+	0.663751i	$0.231036\pi$
$878$	−3.84564	+	51.3166i	−0.129784	+	1.73185i
$879$		0			0
$880$	9.07241	−	8.41797i	0.305831	−	0.283770i
$881$	−38.1342			−1.28477			−0.642386	−	0.766381i	$-0.722056\pi$
$881$	−38.1342			−1.28477			−0.642386	+	0.766381i	$0.722056\pi$
$882$		0			0
$883$	−11.6157			−0.390899			−0.195449	−	0.980714i	$-0.562617\pi$
$883$	−11.6157			−0.390899			−0.195449	+	0.980714i	$0.562617\pi$
$884$	8.96401	−	8.31739i	0.301492	−	0.279744i
$885$		0			0
$886$	−3.31329	+	44.2128i	−0.111312	+	1.48536i
$887$	−16.2258	+	41.3426i	−0.544808	+	1.38815i	0.347908	+	0.937529i	$0.386892\pi$
$887$	−16.2258	+	41.3426i	−0.544808	+	1.38815i	−0.892716	+	0.450619i	$0.851203\pi$
$888$		0			0
$889$	9.02596	+	5.11243i	0.302721	+	0.171466i
$890$	−7.85288	−	9.84719i	−0.263229	−	0.330079i
$891$		0			0
$892$	−28.1745	−	71.7874i	−0.943351	−	2.40362i
$893$	−2.42414	−	0.747747i	−0.0811206	−	0.0250224i
$894$		0			0
$895$	−0.554464	−	2.42927i	−0.0185337	−	0.0812014i
$896$	62.2450	+	126.574i	2.07946	+	4.22855i
$897$		0			0
$898$	22.4663	+	3.38625i	0.749710	+	0.113001i
$899$	8.72802	−	5.95066i	0.291096	−	0.198466i
$900$		0			0
$901$	8.97020	+	15.5368i	0.298841	+	0.517607i
$902$	32.6695	+	15.7328i	1.08778	+	0.523845i
$903$		0			0
$904$	−41.8374	+	20.1479i	−1.39149	+	0.670108i
$905$	−10.4492	−	7.12416i	−0.347344	−	0.236815i
$906$		0			0
$907$	20.5119	+	19.0323i	0.681088	+	0.631957i	0.942867	−	0.333171i	$-0.108119\pi$
$907$	20.5119	+	19.0323i	0.681088	+	0.631957i	−0.261779	+	0.965128i	$0.584309\pi$
$908$	70.7769	+	48.2548i	2.34881	+	1.60139i
$909$		0			0
$910$	1.68073	−	0.988924i	0.0557155	−	0.0327825i
$911$	−33.8029	−	16.2786i	−1.11994	−	0.539334i	−0.220066	−	0.975485i	$-0.570627\pi$
$911$	−33.8029	−	16.2786i	−1.11994	−	0.539334i	−0.899874	+	0.436151i	$0.856341\pi$
$912$		0			0
$913$	2.82999	−	4.90169i	0.0936591	−	0.162222i
$914$	24.7849	−	16.8980i	0.819810	−	0.558937i
$915$		0			0
$916$	−28.1715	+	123.428i	−0.930814	+	4.07816i
$917$	−1.07762	−	0.236635i	−0.0355863	−	0.00781438i
$918$		0			0
$919$	4.09011	+	54.5787i	0.134920	+	1.80039i	0.496492	+	0.868041i	$0.334621\pi$
$919$	4.09011	+	54.5787i	0.134920	+	1.80039i	−0.361572	+	0.932344i	$0.617760\pi$
$920$	−47.7642	−	14.7333i	−1.57474	−	0.485743i
$921$		0			0
$922$	68.4105	−	21.1019i	2.25298	−	0.694952i
$923$	−1.75812	−	2.20462i	−0.0578693	−	0.0725658i
$924$		0			0
$925$	0.795677	−	0.997748i	0.0261617	−	0.0328057i
$926$	19.6332	−	50.0247i	0.645188	−	1.64391i
$927$		0			0
$928$	−56.7143	+	8.54831i	−1.86174	+	0.280612i
$929$	−11.8388	+	10.9848i	−0.388417	+	0.360398i	−0.850077	−	0.526659i	$-0.823445\pi$
$929$	−11.8388	+	10.9848i	−0.388417	+	0.360398i	0.461660	+	0.887057i	$0.347254\pi$
$930$		0			0
$931$	12.5266	+	30.4326i	0.410542	+	0.997388i
$932$	−58.7342			−1.92390
$933$		0			0
$934$	23.7419	−	3.57851i	0.776858	−	0.117093i
$935$	0.322536	−	4.30394i	0.0105481	−	0.140754i
$936$		0			0
$937$	6.66410	−	8.35652i	0.217707	−	0.272995i	−0.660971	−	0.750412i	$-0.729855\pi$
$937$	6.66410	−	8.35652i	0.217707	−	0.272995i	0.878677	+	0.477416i	$0.158427\pi$
$938$	12.4530	+	78.2401i	0.406606	+	2.55463i
$939$		0			0
$940$	−2.07125	+	0.638897i	−0.0675569	+	0.0208385i
$941$	3.51386	+	8.95318i	0.114549	+	0.291865i	0.976638	−	0.214891i	$-0.0689396\pi$
$941$	3.51386	+	8.95318i	0.114549	+	0.291865i	−0.862089	+	0.506756i	$0.830844\pi$
$942$		0			0
$943$	−6.51048	−	86.8763i	−0.212010	−	2.82908i
$944$	−4.16689	−	18.2563i	−0.135621	−	0.594193i
$945$		0			0
$946$	−0.0236694	+	0.103702i	−0.000769557	+	0.00337165i
$947$	−32.7450	−	4.93552i	−1.06407	−	0.160383i	−0.406405	−	0.913693i	$-0.633218\pi$
$947$	−32.7450	−	4.93552i	−1.06407	−	0.160383i	−0.657665	+	0.753311i	$0.728456\pi$
$948$		0			0
$949$	−1.68775	+	2.92327i	−0.0547866	+	0.0948932i
$950$	29.2080	+	50.5897i	0.947632	+	1.64135i
$951$		0			0
$952$	143.997	+	55.1495i	4.66696	+	1.78741i
$953$	14.8800	−	7.16583i	0.482011	−	0.232124i	−0.177067	−	0.984199i	$-0.556661\pi$
$953$	14.8800	−	7.16583i	0.482011	−	0.232124i	0.659078	+	0.752075i	$0.270947\pi$
$954$		0			0
$955$	−8.36436	−	7.76099i	−0.270664	−	0.251140i
$956$	−101.506	−	94.1842i	−3.28295	−	3.04614i
$957$		0			0
$958$	17.0992	−	8.23455i	0.552451	−	0.266046i
$959$	−3.59128	−	11.3109i	−0.115969	−	0.365247i
$960$		0			0
$961$	4.31090	+	7.46669i	0.139061	+	0.240861i
$962$	−0.147085	+	0.254760i	−0.00474223	+	0.00821378i
$963$		0			0
$964$	−80.7803	−	12.1757i	−2.60176	−	0.392152i
$965$	−1.87706	+	8.22393i	−0.0604247	+	0.264738i
$966$		0			0
$967$	8.58042	+	37.5933i	0.275928	+	1.20892i	0.902891	+	0.429870i	$0.141441\pi$
$967$	8.58042	+	37.5933i	0.275928	+	1.20892i	−0.626963	+	0.779049i	$0.715702\pi$
$968$	7.45686	+	99.5049i	0.239673	+	3.19821i
$969$		0			0
$970$	−9.23347	−	23.5265i	−0.296469	−	0.755390i
$971$	−32.9357	+	10.1593i	−1.05696	+	0.326028i	−0.774053	−	0.633121i	$-0.781774\pi$
$971$	−32.9357	+	10.1593i	−1.05696	+	0.326028i	−0.282903	+	0.959149i	$0.591297\pi$
$972$		0			0
$973$	3.98352	+	5.74054i	0.127706	+	0.184033i
$974$	26.9987	−	33.8552i	0.865093	−	1.08479i
$975$		0			0
$976$	−9.80401	+	130.825i	−0.313819	+	4.18762i
$977$	34.7758	−	5.24161i	1.11258	−	0.167694i	0.433068	−	0.901361i	$-0.357431\pi$
$977$	34.7758	−	5.24161i	1.11258	−	0.167694i	0.679509	+	0.733668i	$0.262193\pi$
$978$		0			0
$979$	−6.71565			−0.214633
$980$	23.4910	+	15.4550i	0.750394	+	0.493693i
$981$		0			0
$982$	53.5837	−	49.7184i	1.70992	−	1.58658i
$983$	34.3093	−	5.17129i	1.09430	−	0.164939i	0.423002	−	0.906129i	$-0.360976\pi$
$983$	34.3093	−	5.17129i	1.09430	−	0.164939i	0.671295	+	0.741190i	$0.265738\pi$
$984$		0			0
$985$	−1.28444	+	3.27269i	−0.0409256	+	0.104277i
$986$	−22.2589	+	27.9118i	−0.708869	+	0.888893i
$987$		0			0
$988$	−6.19937	−	7.77377i	−0.197228	−	0.247317i
$989$	0.244210	−	0.0753289i	0.00776543	−	0.00239532i
$990$		0			0
$991$	−36.4795	−	11.2524i	−1.15881	−	0.357445i	−0.345015	−	0.938597i	$-0.612126\pi$
$991$	−36.4795	−	11.2524i	−1.15881	−	0.357445i	−0.813795	+	0.581152i	$0.802602\pi$
$992$	9.07991	+	121.163i	0.288287	+	3.84693i
$993$		0			0
$994$	23.4821	−	49.8070i	0.744808	−	1.57978i
$995$	2.29393	−	10.0504i	0.0727225	−	0.318618i
$996$		0			0
$997$	28.0837	−	19.1472i	0.889421	−	0.606397i	−0.0300527	−	0.999548i	$-0.509567\pi$
$997$	28.0837	−	19.1472i	0.889421	−	0.606397i	0.919474	+	0.393151i	$0.128615\pi$
$998$	47.7593	−	82.7215i	1.51179	−	2.61850i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.e.109.5		60
3.2	odd	2		147.2.m.b.109.1	yes	60
49.9	even	21	inner	441.2.bb.e.352.5		60
147.95	odd	42		7203.2.a.n.1.29		30
147.101	even	42		7203.2.a.m.1.29		30
147.107	odd	42		147.2.m.b.58.1	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.b.58.1	✓	60	147.107	odd	42
147.2.m.b.109.1	yes	60	3.2	odd	2
441.2.bb.e.109.5		60	1.1	even	1	trivial
441.2.bb.e.352.5		60	49.9	even	21	inner
7203.2.a.m.1.29		30	147.101	even	42
7203.2.a.n.1.29		30	147.95	odd	42

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.02691 - 1.88070i) q^{2} +(0.421883 - 5.62963i) q^{4} +(-0.259960 + 0.662367i) q^{5} +(2.63989 + 0.175969i) q^{7} +(-6.28460 - 7.88063i) q^{8} +O(q^{10})\)	\(q+(2.02691 - 1.88070i) q^{2} +(0.421883 - 5.62963i) q^{4} +(-0.259960 + 0.662367i) q^{5} +(2.63989 + 0.175969i) q^{7} +(-6.28460 - 7.88063i) q^{8} +(0.718799 + 1.83147i) q^{10} +(1.00245 + 0.309214i) q^{11} +(-0.0833615 - 0.365231i) q^{13} +(5.68178 - 4.60818i) q^{14} +(-16.3947 - 2.47111i) q^{16} +(-4.77730 + 3.25711i) q^{17} +(2.35070 + 4.07154i) q^{19} +(3.61921 + 1.74292i) q^{20} +(2.61341 - 1.25855i) q^{22} +(-5.75822 - 3.92589i) q^{23} +(3.29411 + 3.05649i) q^{25} +(-0.855856 - 0.583513i) q^{26} +(2.10436 - 14.7874i) q^{28} +(2.01190 + 0.968882i) q^{29} +(2.36528 - 4.09679i) q^{31} +(-21.2216 + 14.4687i) q^{32} +(-3.55753 + 15.5866i) q^{34} +(-0.802823 + 1.70283i) q^{35} +(-0.0212227 - 0.283197i) q^{37} +(12.4220 + 3.83168i) q^{38} +(6.85362 - 2.11406i) q^{40} +(7.79407 + 9.77345i) q^{41} +(-0.0228637 + 0.0286702i) q^{43} +(2.16368 - 5.51296i) q^{44} +(-19.0548 + 2.87205i) q^{46} +(-0.395549 + 0.367016i) q^{47} +(6.93807 + 0.929078i) q^{49} +12.4252 q^{50} +(-2.09128 + 0.315210i) q^{52} +(0.231873 - 3.09413i) q^{53} +(-0.465409 + 0.583605i) q^{55} +(-15.2039 - 21.9099i) q^{56} +(5.90013 - 1.81995i) q^{58} +(0.412627 + 1.05136i) q^{59} +(-0.591318 - 7.89059i) q^{61} +(-2.91061 - 12.7522i) q^{62} +(-8.42443 + 36.9099i) q^{64} +(0.263587 + 0.0397294i) q^{65} +(-5.41480 + 9.37871i) q^{67} +(16.3209 + 28.2686i) q^{68} +(1.57527 + 4.96137i) q^{70} +(6.78165 - 3.26587i) q^{71} +(-6.60507 - 6.12861i) q^{73} +(-0.575625 - 0.534102i) q^{74} +(23.9130 - 11.5159i) q^{76} +(2.59194 + 0.992691i) q^{77} +(2.98149 + 5.16409i) q^{79} +(5.89876 - 10.2169i) q^{80} +(34.1788 + 5.15163i) q^{82} +(1.20057 - 5.26005i) q^{83} +(-0.915495 - 4.01104i) q^{85} +(0.00757729 + 0.101112i) q^{86} +(-3.86317 - 9.84320i) q^{88} +(-6.11722 + 1.88691i) q^{89} +(-0.155796 - 0.978839i) q^{91} +(-24.5306 + 30.7604i) q^{92} +(-0.111497 + 1.48782i) q^{94} +(-3.30794 + 0.498592i) q^{95} -12.8457 q^{97} +(15.8102 - 11.1653i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) \) 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) \) 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8 - 34 * q^10 + 11 * q^11 - 2 * q^13 - 40 * q^14 - 31 * q^16 + 9 * q^17 - 29 * q^19 + 43 * q^20 + 9 * q^22 + 4 * q^23 + 55 * q^25 - 36 * q^26 - 57 * q^28 - 4 * q^29 - 39 * q^31 + 92 * q^32 - 36 * q^34 + 33 * q^35 - 24 * q^37 - 118 * q^38 - 35 * q^41 + 2 * q^43 - 40 * q^44 - 40 * q^46 + 5 * q^47 + 129 * q^49 + 176 * q^50 - 6 * q^52 - 26 * q^53 + 2 * q^55 - 63 * q^56 + 11 * q^58 + 41 * q^59 + 6 * q^61 - 36 * q^62 + 74 * q^64 + 51 * q^65 - 55 * q^67 + 22 * q^68 - 68 * q^70 + 66 * q^71 + 24 * q^73 - 28 * q^74 + 3 * q^76 + 34 * q^77 - 51 * q^79 + 5 * q^80 - 41 * q^82 - 30 * q^83 + 68 * q^85 - 110 * q^86 + 129 * q^88 - 75 * q^89 + 5 * q^91 + 38 * q^94 - 36 * q^95 - 168 * q^97 - 227 * q^98

Introduction

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