LMFDB - Embedded newform 729.2.g.d.190.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			190.5
Character	$\chi$	$=$	729.190
Dual form			729.2.g.d.541.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.197225 - 0.264919i) q^{2} +(0.542322 + 1.81148i) q^{4} +(-2.51951 - 1.65711i) q^{5} +(-0.00631548 - 0.00669402i) q^{7} +(1.20756 + 0.439517i) q^{8} +(-0.935909 + 0.340643i) q^{10} +(-3.18003 - 1.59707i) q^{11} +(1.40228 - 3.25085i) q^{13} +(-0.00301894 + 0.000352863i) q^{14} +(-2.80509 + 1.84493i) q^{16} +(-3.09319 - 2.59549i) q^{17} +(5.54096 - 4.64941i) q^{19} +(1.63544 - 5.46274i) q^{20} +(-1.05027 + 0.527467i) q^{22} +(3.52849 - 3.73998i) q^{23} +(1.62154 + 3.75915i) q^{25} +(-0.584647 - 1.01264i) q^{26} +(0.00870107 - 0.0150707i) q^{28} +(4.72215 + 0.551940i) q^{29} +(-8.79465 - 2.08437i) q^{31} +(-0.213914 + 3.67276i) q^{32} +(-1.29765 + 0.307548i) q^{34} +(0.00481921 + 0.0273311i) q^{35} +(0.0241986 - 0.137237i) q^{37} +(-0.138903 - 2.38488i) q^{38} +(-2.31414 - 3.10843i) q^{40} +(-2.15318 - 2.89222i) q^{41} +(-0.0714431 - 1.22663i) q^{43} +(1.16847 - 6.62670i) q^{44} +(-0.294886 - 1.67238i) q^{46} +(-1.01434 + 0.240402i) q^{47} +(0.407009 - 6.98807i) q^{49} +(1.31568 + 0.311821i) q^{50} +(6.64935 + 0.777197i) q^{52} +(1.88778 - 3.26973i) q^{53} +(5.36561 + 9.29351i) q^{55} +(-0.00468420 - 0.0108592i) q^{56} +(1.07754 - 1.14213i) q^{58} +(4.63792 - 2.32925i) q^{59} +(-1.96546 + 6.56510i) q^{61} +(-2.28671 + 1.91878i) q^{62} +(-4.21308 - 3.53519i) q^{64} +(-8.92009 + 5.86684i) q^{65} +(-8.26821 + 0.966415i) q^{67} +(3.02419 - 7.01085i) q^{68} +(0.00819099 + 0.00411367i) q^{70} +(-2.49894 + 0.909541i) q^{71} +(2.10657 + 0.766729i) q^{73} +(-0.0315840 - 0.0334771i) q^{74} +(11.4273 + 7.51586i) q^{76} +(0.00939260 + 0.0313735i) q^{77} +(-2.46941 + 3.31699i) q^{79} +10.1247 q^{80} -1.19086 q^{82} +(-7.70358 + 10.3477i) q^{83} +(3.49231 + 11.6651i) q^{85} +(-0.339047 - 0.222995i) q^{86} +(-3.13814 - 3.32624i) q^{88} +(-9.21313 - 3.35330i) q^{89} +(-0.0306173 + 0.0111438i) q^{91} +(8.68850 + 4.36353i) q^{92} +(-0.136365 + 0.316129i) q^{94} +(-21.6651 + 2.53229i) q^{95} +(13.1887 - 8.67437i) q^{97} +(-1.77100 - 1.48604i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{19}{27}\right)$

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 $

$2$	0.197225	−	0.264919i	0.139459	−	0.187326i	−0.726907	−	0.686736i	$-0.759043\pi$
$2$	0.197225	−	0.264919i	0.139459	−	0.187326i	0.866365	+	0.499411i	$0.166450\pi$
$3$		0			0
$3$		0			0
$4$	0.542322	+	1.81148i	0.271161	+	0.905741i
$5$	−2.51951	−	1.65711i	−1.12676	−	0.741082i	−0.157598	−	0.987503i	$-0.550375\pi$
$5$	−2.51951	−	1.65711i	−1.12676	−	0.741082i	−0.969163	+	0.246421i	$0.920745\pi$
$6$		0			0
$7$	−0.00631548	−	0.00669402i	−0.00238703	−	0.00253010i	0.726179	−	0.687506i	$-0.241294\pi$
$7$	−0.00631548	−	0.00669402i	−0.00238703	−	0.00253010i	−0.728566	+	0.684976i	$0.759813\pi$
$8$	1.20756	+	0.439517i	0.426938	+	0.155393i
$9$		0			0
$10$	−0.935909	+	0.340643i	−0.295961	+	0.107721i
$11$	−3.18003	−	1.59707i	−0.958815	−	0.481535i	−0.100658	−	0.994921i	$-0.532095\pi$
$11$	−3.18003	−	1.59707i	−0.958815	−	0.481535i	−0.858158	+	0.513386i	$0.828391\pi$
$12$		0			0
$13$	1.40228	−	3.25085i	0.388923	−	0.901624i	−0.605469	−	0.795869i	$-0.707015\pi$
$13$	1.40228	−	3.25085i	0.388923	−	0.901624i	0.994392	−	0.105756i	$-0.0337261\pi$
$14$	−0.00301894		0.000352863i	−0.000806845		9.43066e-5i
$15$		0			0
$16$	−2.80509	+	1.84493i	−0.701271	+	0.461233i
$17$	−3.09319	−	2.59549i	−0.750208	−	0.629500i	0.185350	−	0.982673i	$-0.440658\pi$
$17$	−3.09319	−	2.59549i	−0.750208	−	0.629500i	−0.935558	+	0.353173i	$0.885103\pi$
$18$		0			0
$19$	5.54096	−	4.64941i	1.27118	−	1.06665i	0.276786	−	0.960931i	$-0.410731\pi$
$19$	5.54096	−	4.64941i	1.27118	−	1.06665i	0.994396	−	0.105717i	$-0.0337139\pi$
$20$	1.63544	−	5.46274i	0.365695	−	1.22151i
$21$		0			0
$22$	−1.05027	+	0.527467i	−0.223919	+	0.112456i
$23$	3.52849	−	3.73998i	0.735742	−	0.779841i	−0.246160	−	0.969229i	$-0.579169\pi$
$23$	3.52849	−	3.73998i	0.735742	−	0.779841i	0.981902	+	0.189388i	$0.0606505\pi$
$24$		0			0
$25$	1.62154	+	3.75915i	0.324308	+	0.751830i
$26$	−0.584647	−	1.01264i	−0.114659	−	0.198595i
$27$		0			0
$28$	0.00870107	−	0.0150707i	0.00164435	−	0.00284809i
$29$	4.72215	+	0.551940i	0.876882	+	0.102493i	0.542611	−	0.839984i	$-0.317436\pi$
$29$	4.72215	+	0.551940i	0.876882	+	0.102493i	0.334271	+	0.942477i	$0.391510\pi$
$30$		0			0
$31$	−8.79465	−	2.08437i	−1.57957	−	0.374364i	−0.655074	−	0.755565i	$-0.727362\pi$
$31$	−8.79465	−	2.08437i	−1.57957	−	0.374364i	−0.924492	+	0.381201i	$0.875511\pi$
$32$	−0.213914	+	3.67276i	−0.0378150	+	0.649258i
$33$		0			0
$34$	−1.29765	+	0.307548i	−0.222545	+	0.0527440i
$35$	0.00481921	+	0.0273311i	0.000814596	+	0.00461980i
$36$		0			0
$37$	0.0241986	−	0.137237i	0.00397822	−	0.0225616i	−0.982754	−	0.184918i	$-0.940798\pi$
$37$	0.0241986	−	0.137237i	0.00397822	−	0.0225616i	0.986732	+	0.162356i	$0.0519093\pi$
$38$	−0.138903	−	2.38488i	−0.0225331	−	0.386879i
$39$		0			0
$40$	−2.31414	−	3.10843i	−0.365898	−	0.491486i
$41$	−2.15318	−	2.89222i	−0.336270	−	0.451689i	0.601538	−	0.798844i	$-0.294555\pi$
$41$	−2.15318	−	2.89222i	−0.336270	−	0.451689i	−0.937808	+	0.347156i	$0.887148\pi$
$42$		0			0
$43$	−0.0714431	−	1.22663i	−0.0108950	−	0.187059i	−0.999365	−	0.0356406i	$-0.988653\pi$
$43$	−0.0714431	−	1.22663i	−0.0108950	−	0.187059i	0.988470	−	0.151419i	$-0.0483842\pi$
$44$	1.16847	−	6.62670i	0.176153	−	0.999012i
$45$		0			0
$46$	−0.294886	−	1.67238i	−0.0434785	−	0.246579i
$47$	−1.01434	+	0.240402i	−0.147956	+	0.0350662i	−0.303926	−	0.952696i	$-0.598298\pi$
$47$	−1.01434	+	0.240402i	−0.147956	+	0.0350662i	0.155970	+	0.987762i	$0.450150\pi$
$48$		0			0
$49$	0.407009	−	6.98807i	0.0581441	−	0.998296i
$50$	1.31568	+	0.311821i	0.186065	+	0.0440981i
$51$		0			0
$52$	6.64935	+	0.777197i	0.922099	+	0.107778i
$53$	1.88778	−	3.26973i	0.259307	−	0.449133i	−0.706750	−	0.707464i	$-0.749839\pi$
$53$	1.88778	−	3.26973i	0.259307	−	0.449133i	0.966056	+	0.258331i	$0.0831726\pi$
$54$		0			0
$55$	5.36561	+	9.29351i	0.723499	+	1.25314i
$56$	−0.00468420	−	0.0108592i	−0.000625953	−	0.00145112i
$57$		0			0
$58$	1.07754	−	1.14213i	0.141488	−	0.149969i
$59$	4.63792	−	2.32925i	0.603806	−	0.303243i	−0.120509	−	0.992712i	$-0.538453\pi$
$59$	4.63792	−	2.32925i	0.603806	−	0.303243i	0.724315	+	0.689470i	$0.242156\pi$
$60$		0			0
$61$	−1.96546	+	6.56510i	−0.251652	+	0.840575i	0.735047	+	0.678016i	$0.237160\pi$
$61$	−1.96546	+	6.56510i	−0.251652	+	0.840575i	−0.986699	+	0.162559i	$0.948025\pi$
$62$	−2.28671	+	1.91878i	−0.290412	+	0.243685i
$63$		0			0
$64$	−4.21308	−	3.53519i	−0.526635	−	0.441899i
$65$	−8.92009	+	5.86684i	−1.10640	+	0.727691i
$66$		0			0
$67$	−8.26821	+	0.966415i	−1.01012	+	0.118066i	−0.605024	−	0.796207i	$-0.706837\pi$
$67$	−8.26821	+	0.966415i	−1.01012	+	0.118066i	−0.405098	+	0.914273i	$0.632763\pi$
$68$	3.02419	−	7.01085i	0.366736	−	0.850190i
$69$		0			0
$70$	0.00819099	+	0.00411367i	0.000979010	+	0.000491677i
$71$	−2.49894	+	0.909541i	−0.296570	+	0.107943i	−0.486020	−	0.873948i	$-0.661552\pi$
$71$	−2.49894	+	0.909541i	−0.296570	+	0.107943i	0.189450	+	0.981890i	$0.439330\pi$
$72$		0			0
$73$	2.10657	+	0.766729i	0.246555	+	0.0897388i	0.462342	−	0.886702i	$-0.347009\pi$
$73$	2.10657	+	0.766729i	0.246555	+	0.0897388i	−0.215786	+	0.976441i	$0.569232\pi$
$74$	−0.0315840	−	0.0334771i	−0.00367157	−	0.00389164i
$75$		0			0
$76$	11.4273	+	7.51586i	1.31080	+	0.862129i
$77$	0.00939260	+	0.0313735i	0.00107039	+	0.00357534i
$78$		0			0
$79$	−2.46941	+	3.31699i	−0.277830	+	0.373190i	−0.919033	−	0.394181i	$-0.871028\pi$
$79$	−2.46941	+	3.31699i	−0.277830	+	0.373190i	0.641203	+	0.767371i	$0.278436\pi$
$80$	10.1247			1.13198
$81$		0			0
$82$	−1.19086			−0.131509
$83$	−7.70358	+	10.3477i	−0.845578	+	1.13581i	0.143679	+	0.989624i	$0.454107\pi$
$83$	−7.70358	+	10.3477i	−0.845578	+	1.13581i	−0.989257	+	0.146184i	$0.953301\pi$
$84$		0			0
$85$	3.49231	+	11.6651i	0.378795	+	1.26526i
$86$	−0.339047	−	0.222995i	−0.0365604	−	0.0240462i
$87$		0			0
$88$	−3.13814	−	3.32624i	−0.334527	−	0.354578i
$89$	−9.21313	−	3.35330i	−0.976590	−	0.355450i	−0.196076	−	0.980589i	$-0.562820\pi$
$89$	−9.21313	−	3.35330i	−0.976590	−	0.355450i	−0.780513	+	0.625139i	$0.785042\pi$
$90$		0			0
$91$	−0.0306173	+	0.0111438i	−0.00320957	+	0.00116819i
$92$	8.68850	+	4.36353i	0.905838	+	0.454929i
$93$		0			0
$94$	−0.136365	+	0.316129i	−0.0140650	+	0.0326062i
$95$	−21.6651	+	2.53229i	−2.22279	+	0.259807i
$96$		0			0
$97$	13.1887	−	8.67437i	1.33911	−	0.880749i	0.340876	−	0.940108i	$-0.389276\pi$
$97$	13.1887	−	8.67437i	1.33911	−	0.880749i	0.998237	+	0.0593596i	$0.0189059\pi$
$98$	−1.77100	−	1.48604i	−0.178898	−	0.150113i
$99$		0			0
$100$	−5.93024	+	4.97606i	−0.593024	+	0.497606i
$101$	5.52059	−	18.4401i	0.549319	−	1.83485i	−0.00115077	−	0.999999i	$-0.500366\pi$
$101$	5.52059	−	18.4401i	0.549319	−	1.83485i	0.550470	−	0.834855i	$-0.314449\pi$
$102$		0			0
$103$	7.80287	−	3.91875i	0.768840	−	0.386126i	−0.0207311	−	0.999785i	$-0.506599\pi$
$103$	7.80287	−	3.91875i	0.768840	−	0.386126i	0.789571	+	0.613659i	$0.210303\pi$
$104$	3.12214	−	3.30928i	0.306151	−	0.324502i
$105$		0			0
$106$	−0.493896	−	1.14498i	−0.0479715	−	0.111210i
$107$	7.06211	+	12.2319i	0.682720	+	1.18251i	0.974147	+	0.225913i	$0.0725365\pi$
$107$	7.06211	+	12.2319i	0.682720	+	1.18251i	−0.291427	+	0.956593i	$0.594130\pi$
$108$		0			0
$109$	−3.80056	+	6.58277i	−0.364028	+	0.630515i	−0.988620	−	0.150437i	$-0.951932\pi$
$109$	−3.80056	+	6.58277i	−0.364028	+	0.630515i	0.624592	+	0.780951i	$0.285265\pi$
$110$	3.52025	+	0.411458i	0.335643	+	0.0392310i
$111$		0			0
$112$	0.0300655	+	0.00712565i	0.00284092	+	0.000673311i
$113$	−1.12179	+	19.2605i	−0.105529	+	1.81187i	0.366639	+	0.930363i	$0.380508\pi$
$113$	−1.12179	+	19.2605i	−0.105529	+	1.81187i	−0.472169	+	0.881508i	$0.656529\pi$
$114$		0			0
$115$	−15.0877	+	3.57584i	−1.40693	+	0.333449i
$116$	1.56110	+	8.85342i	0.144944	+	0.822020i
$117$		0			0
$118$	0.297650	−	1.68806i	0.0274009	−	0.155398i
$119$	0.00216069	+	0.0370976i	0.000198070	+	0.00340074i
$120$		0			0
$121$	0.993214	+	1.33412i	0.0902922	+	0.121283i
$122$	1.35158	+	1.81549i	0.122366	+	0.164366i
$123$		0			0
$124$	−0.993734	−	17.0618i	−0.0892400	−	1.53219i
$125$	−0.474449	+	2.69073i	−0.0424360	+	0.240667i
$126$		0			0
$127$	−1.36077	−	7.71730i	−0.120749	−	0.684800i	−0.983742	−	0.179585i	$-0.942524\pi$
$127$	−1.36077	−	7.71730i	−0.120749	−	0.684800i	0.862994	−	0.505214i	$-0.168587\pi$
$128$	−8.92709	+	2.11576i	−0.789051	+	0.187008i
$129$		0			0
$130$	−0.205027	+	3.52018i	−0.0179821	+	0.308740i
$131$	4.20527	+	0.996668i	0.367417	+	0.0870793i	0.410177	−	0.912006i	$-0.365467\pi$
$131$	4.20527	+	0.996668i	0.367417	+	0.0870793i	−0.0427602	+	0.999085i	$0.513615\pi$
$132$		0			0
$133$	−0.0661171	−	0.00772798i	−0.00573308	−	0.000670101i
$134$	−1.37467	+	2.38100i	−0.118754	+	0.205687i
$135$		0			0
$136$	−2.59445	−	4.49373i	−0.222473	−	0.385334i
$137$	0.0466346	+	0.108111i	0.00398426	+	0.00923656i	0.920197	−	0.391456i	$-0.128029\pi$
$137$	0.0466346	+	0.108111i	0.00398426	+	0.00923656i	−0.916212	+	0.400693i	$0.868769\pi$
$138$		0			0
$139$	−0.893528	+	0.947084i	−0.0757881	+	0.0803307i	−0.764158	−	0.645029i	$-0.776845\pi$
$139$	−0.893528	+	0.947084i	−0.0757881	+	0.0803307i	0.688370	+	0.725360i	$0.258327\pi$
$140$	−0.0468963	+	0.0235522i	−0.00396346	+	0.00199052i
$141$		0			0
$142$	−0.251899	+	0.841400i	−0.0211389	+	0.0706087i
$143$	−9.65114	+	8.09827i	−0.807069	+	0.677211i
$144$		0			0
$145$	−10.9829	−	9.21575i	−0.912081	−	0.765326i
$146$	0.618588	−	0.406852i	0.0511947	−	0.0336713i
$147$		0			0
$148$	0.261726	−	0.0305913i	0.0215137	−	0.00251459i
$149$	−2.74784	+	6.37022i	−0.225112	+	0.521869i	−0.992916	−	0.118816i	$-0.962090\pi$
$149$	−2.74784	+	6.37022i	−0.225112	+	0.521869i	0.767804	+	0.640685i	$0.221349\pi$
$150$		0			0
$151$	−8.43639	−	4.23692i	−0.686544	−	0.344795i	0.0710946	−	0.997470i	$-0.477351\pi$
$151$	−8.43639	−	4.23692i	−0.686544	−	0.344795i	−0.757639	+	0.652674i	$0.773647\pi$
$152$	8.73454	−	3.17911i	0.708465	−	0.257860i
$153$		0			0
$154$	0.0101639	+	0.00369934i	0.000819027	+	0.000298102i
$155$	18.7042	+	19.8253i	1.50236	+	1.59241i
$156$		0			0
$157$	−5.12881	−	3.37327i	−0.409323	−	0.269216i	0.328105	−	0.944641i	$-0.393590\pi$
$157$	−5.12881	−	3.37327i	−0.409323	−	0.269216i	−0.737429	+	0.675425i	$0.763960\pi$
$158$	0.391704	+	1.30838i	0.0311623	+	0.104089i
$159$		0			0
$160$	6.62513	−	8.89909i	0.523762	−	0.703535i
$161$	−0.0473197			−0.00372931
$162$		0			0
$163$	1.40640			0.110158			0.0550788	−	0.998482i	$-0.482459\pi$
$163$	1.40640			0.110158			0.0550788	+	0.998482i	$0.482459\pi$
$164$	4.07149	−	5.46896i	0.317930	−	0.427054i
$165$		0			0
$166$	1.22196	+	4.08164i	0.0948428	+	0.316797i
$167$	12.2870	+	8.08129i	0.950797	+	0.625349i	0.927278	−	0.374374i	$-0.122143\pi$
$167$	12.2870	+	8.08129i	0.950797	+	0.625349i	0.0235192	+	0.999723i	$0.492513\pi$
$168$		0			0
$169$	0.319491	+	0.338641i	0.0245762	+	0.0260493i
$170$	3.77908	+	1.37547i	0.289842	+	0.105494i
$171$		0			0
$172$	2.18327	−	0.794647i	0.166473	−	0.0605912i
$173$	−6.85105	−	3.44072i	−0.520875	−	0.261593i	0.168879	−	0.985637i	$-0.445985\pi$
$173$	−6.85105	−	3.44072i	−0.520875	−	0.261593i	−0.689754	+	0.724043i	$0.742282\pi$
$174$		0			0
$175$	0.0149230	−	0.0345954i	0.00112807	−	0.00261517i
$176$	11.8667	−	1.38702i	0.894490	−	0.104551i
$177$		0			0
$178$	−2.70541	+	1.77937i	−0.202779	+	0.133370i
$179$	4.59366	+	3.85454i	0.343347	+	0.288102i	0.798112	−	0.602509i	$-0.205832\pi$
$179$	4.59366	+	3.85454i	0.343347	+	0.288102i	−0.454765	+	0.890611i	$0.650277\pi$
$180$		0			0
$181$	7.92436	−	6.64933i	0.589013	−	0.494241i	−0.298880	−	0.954291i	$-0.596613\pi$
$181$	7.92436	−	6.64933i	0.589013	−	0.494241i	0.887893	+	0.460050i	$0.152169\pi$
$182$	−0.00308629	+	0.0103089i	−0.000228771	+	0.000764149i
$183$		0			0
$184$	5.90466	−	2.96543i	0.435297	−	0.218615i
$185$	−0.288385	+	0.305671i	−0.0212025	+	0.0224734i
$186$		0			0
$187$	5.69125	+	13.1938i	0.416185	+	0.964826i
$188$	−0.985580	−	1.70707i	−0.0718808	−	0.124501i
$189$		0			0
$190$	−3.60204	+	6.23892i	−0.261320	+	0.452619i
$191$	15.7686	+	1.84308i	1.14097	+	0.133361i	0.665520	−	0.746380i	$-0.268210\pi$
$191$	15.7686	+	1.84308i	1.14097	+	0.133361i	0.475454	+	0.879741i	$0.342284\pi$
$192$		0			0
$193$	19.1266	+	4.53308i	1.37676	+	0.326298i	0.851371	−	0.524564i	$-0.175772\pi$
$193$	19.1266	+	4.53308i	1.37676	+	0.326298i	0.525389	+	0.850862i	$0.323920\pi$
$194$	0.303141	−	5.20474i	0.0217643	−	0.373678i
$195$		0			0
$196$	12.8795	−	3.05250i	0.919964	−	0.218036i
$197$	−0.0147762	−	0.0837998i	−0.00105276	−	0.00597049i	0.984277	−	0.176633i	$-0.0565204\pi$
$197$	−0.0147762	−	0.0837998i	−0.00105276	−	0.00597049i	−0.985330	+	0.170662i	$0.945409\pi$
$198$		0			0
$199$	−3.10186	+	17.5915i	−0.219885	+	1.24703i	0.652340	+	0.757927i	$0.273788\pi$
$199$	−3.10186	+	17.5915i	−0.219885	+	1.24703i	−0.872225	+	0.489105i	$0.837324\pi$
$200$	0.305900	+	5.25210i	0.0216304	+	0.371379i
$201$		0			0
$202$	−3.79632	−	5.09934i	−0.267108	−	0.358788i
$203$	−0.0261280	−	0.0350959i	−0.00183382	−	0.00246325i
$204$		0			0
$205$	0.632234	+	10.8550i	0.0441571	+	0.758149i
$206$	0.500769	−	2.84000i	0.0348902	−	0.197872i
$207$		0			0
$208$	2.06409	+	11.7060i	0.143119	+	0.811667i
$209$	−25.0459	+	5.93598i	−1.73246	+	0.410600i
$210$		0			0
$211$	−0.453749	+	7.79057i	−0.0312374	+	0.536325i	0.945999	+	0.324170i	$0.105085\pi$
$211$	−0.453749	+	7.79057i	−0.0312374	+	0.536325i	−0.977236	+	0.212154i	$0.931952\pi$
$212$	6.94685	+	1.64643i	0.477112	+	0.113078i
$213$		0			0
$214$	4.63329	+	0.541554i	0.316725	+	0.0370199i
$215$	−1.85266	+	3.20890i	−0.126350	+	0.218845i
$216$		0			0
$217$	0.0415896	+	0.0720354i	0.00282329	+	0.00489008i
$218$	0.994333	+	2.30512i	0.0673447	+	0.156123i
$219$		0			0
$220$	−13.9251	+	14.7598i	−0.938832	+	0.995104i
$221$	−12.7751	+	6.41589i	−0.859345	+	0.431579i
$222$		0			0
$223$	6.44347	−	21.5227i	0.431486	−	1.44126i	−0.415472	−	0.909606i	$-0.636384\pi$
$223$	6.44347	−	21.5227i	0.431486	−	1.44126i	0.846959	−	0.531659i	$-0.178431\pi$
$224$	0.0259365	−	0.0217633i	0.00173295	−	0.00145412i
$225$		0			0
$226$	4.88121	+	4.09582i	0.324693	+	0.272450i
$227$	−13.5423	+	8.90691i	−0.898834	+	0.591172i	−0.912654	−	0.408732i	$-0.865971\pi$
$227$	−13.5423	+	8.90691i	−0.898834	+	0.591172i	0.0138207	+	0.999904i	$0.495601\pi$
$228$		0			0
$229$	14.4985	−	1.69463i	0.958088	−	0.111984i	0.377346	−	0.926072i	$-0.376837\pi$
$229$	14.4985	−	1.69463i	0.958088	−	0.111984i	0.580742	+	0.814088i	$0.302763\pi$
$230$	−2.02835	+	4.70224i	−0.133745	+	0.310057i
$231$		0			0
$232$	5.45970	+	2.74197i	0.358447	+	0.180019i
$233$	−9.97733	+	3.63145i	−0.653637	+	0.237904i	−0.647487	−	0.762077i	$-0.724180\pi$
$233$	−9.97733	+	3.63145i	−0.653637	+	0.237904i	−0.00615012	+	0.999981i	$0.501958\pi$
$234$		0			0
$235$	2.95400	+	1.07517i	0.192698	+	0.0701363i
$236$	6.73464	+	7.13830i	0.438388	+	0.464664i
$237$		0			0
$238$	0.0102540	+	0.00674416i	0.000664668	+	0.000437159i
$239$	−1.45377	−	4.85595i	−0.0940369	−	0.314105i	0.898010	−	0.439975i	$-0.145013\pi$
$239$	−1.45377	−	4.85595i	−0.0940369	−	0.314105i	−0.992047	+	0.125870i	$0.959828\pi$
$240$		0			0
$241$	−0.212191	+	0.285023i	−0.0136685	+	0.0183599i	−0.808905	−	0.587940i	$-0.799939\pi$
$241$	−0.212191	+	0.285023i	−0.0136685	+	0.0183599i	0.795236	+	0.606299i	$0.207347\pi$
$242$	0.549319			0.0353116
$243$		0			0
$244$	−12.9585			−0.829581
$245$	−12.6055	+	16.9321i	−0.805334	+	1.08175i
$246$		0			0
$247$	−7.34458	−	24.5326i	−0.467325	−	1.56097i
$248$	−9.70397	−	6.38240i	−0.616203	−	0.405283i
$249$		0			0
$250$	0.619252	+	0.656369i	0.0391650	+	0.0415124i
$251$	20.8143	+	7.57577i	1.31378	+	0.478179i	0.901462	−	0.432859i	$-0.142495\pi$
$251$	20.8143	+	7.57577i	1.31378	+	0.478179i	0.412323	+	0.911038i	$0.364717\pi$
$252$		0			0
$253$	−17.1937	+	6.25801i	−1.08096	+	0.393438i
$254$	−2.31283	−	1.16155i	−0.145120	−	0.0728820i
$255$		0			0
$256$	3.15657	−	7.31774i	0.197285	−	0.457359i
$257$	20.3852	−	2.38269i	1.27159	−	0.148628i	0.546606	−	0.837390i	$-0.315919\pi$
$257$	20.3852	−	2.38269i	1.27159	−	0.148628i	0.724988	+	0.688762i	$0.241845\pi$
$258$		0			0
$259$	−0.00107149		0.000704731i	−6.65793e−5		4.37899e-5i
$260$	−15.4652	−	12.9769i	−0.959113	−	0.804791i
$261$		0			0
$262$	1.09342	−	0.917488i	0.0675517	−	0.0566826i
$263$	6.36750	−	21.2689i	0.392637	−	1.31150i	−0.502064	−	0.864831i	$-0.667426\pi$
$263$	6.36750	−	21.2689i	0.392637	−	1.31150i	0.894700	−	0.446667i	$-0.147389\pi$
$264$		0			0
$265$	−10.1746	+	5.10988i	−0.625021	+	0.313897i
$266$	−0.0150872	+	0.0159915i	−0.000925055	+	0.000980501i
$267$		0			0
$268$	−6.23468	−	14.4536i	−0.380843	−	0.882894i
$269$	−8.77459	−	15.1980i	−0.534996	−	0.926641i	−0.999164	−	0.0408933i	$-0.986980\pi$
$269$	−8.77459	−	15.1980i	−0.534996	−	0.926641i	0.464167	−	0.885748i	$-0.346354\pi$
$270$		0			0
$271$	11.7223	−	20.3037i	0.712082	−	1.23336i	−0.251992	−	0.967729i	$-0.581086\pi$
$271$	11.7223	−	20.3037i	0.712082	−	1.23336i	0.964074	−	0.265633i	$-0.0855809\pi$
$272$	13.4652	+	1.57385i	0.816446	+	0.0954288i
$273$		0			0
$274$	0.0378381	+	0.00896780i	0.00228589	+	0.000541765i
$275$	0.847087	−	14.5439i	0.0510813	−	0.877032i
$276$		0			0
$277$	0.335217	−	0.0794478i	0.0201412	−	0.00477356i	−0.220533	−	0.975380i	$-0.570780\pi$
$277$	0.335217	−	0.0794478i	0.0201412	−	0.00477356i	0.240674	+	0.970606i	$0.422631\pi$
$278$	0.0746746	+	0.423500i	0.00447868	+	0.0253999i
$279$		0			0
$280$	−0.00619298	+	0.0351222i	−0.000370102	+	0.00209895i
$281$	−1.75863	−	30.1945i	−0.104911	−	1.80125i	−0.483145	−	0.875540i	$-0.660506\pi$
$281$	−1.75863	−	30.1945i	−0.104911	−	1.80125i	0.378234	−	0.925710i	$-0.376531\pi$
$282$		0			0
$283$	−3.30186	−	4.43517i	−0.196275	−	0.263643i	0.693080	−	0.720861i	$-0.256253\pi$
$283$	−3.30186	−	4.43517i	−0.196275	−	0.263643i	−0.889355	+	0.457218i	$0.848846\pi$
$284$	−3.00285	−	4.03353i	−0.178186	−	0.239346i
$285$		0			0
$286$	0.241940	+	4.15394i	0.0143062	+	0.245628i
$287$	−0.00576222	+	0.0326792i	−0.000340133	+	0.00192899i
$288$		0			0
$289$	−0.120790	−	0.685032i	−0.00710527	−	0.0402960i
$290$	−4.60752	+	1.09200i	−0.270563	+	0.0641246i
$291$		0			0
$292$	−0.246476	+	4.23183i	−0.0144239	+	0.247649i
$293$	−19.4630	−	4.61281i	−1.13704	−	0.269483i	−0.381361	−	0.924426i	$-0.624544\pi$
$293$	−19.4630	−	4.61281i	−1.13704	−	0.269483i	−0.755678	+	0.654943i	$0.772693\pi$
$294$		0			0
$295$	−15.5451	−	1.81697i	−0.905072	−	0.105788i
$296$	0.0895392	−	0.155086i	0.00520436	−	0.00901421i
$297$		0			0
$298$	1.14565	+	1.98432i	0.0663655	+	0.114948i
$299$	−7.21020	−	16.7151i	−0.416977	−	0.966660i
$300$		0			0
$301$	−0.00775989	+	0.00822500i	−0.000447272	+	0.000474081i
$302$	−2.78630	+	1.39933i	−0.160334	+	0.0805226i
$303$		0			0
$304$	−6.96499	+	23.2647i	−0.399470	+	1.33432i
$305$	15.8311	−	13.2839i	0.906487	−	0.760632i
$306$		0			0
$307$	0.858198	+	0.720114i	0.0489799	+	0.0410991i	0.666949	−	0.745103i	$-0.267600\pi$
$307$	0.858198	+	0.720114i	0.0489799	+	0.0410991i	−0.617969	+	0.786202i	$0.712044\pi$
$308$	−0.0517386	+	0.0340290i	−0.00294808	+	0.00193898i
$309$		0			0
$310$	8.94102	−	1.04506i	0.507816	−	0.0593552i
$311$	−0.326814	+	0.757641i	−0.0185319	+	0.0429619i	−0.927231	−	0.374490i	$-0.877818\pi$
$311$	−0.326814	+	0.757641i	−0.0185319	+	0.0429619i	0.908699	+	0.417452i	$0.137077\pi$
$312$		0			0
$313$	1.04206	+	0.523341i	0.0589006	+	0.0295810i	0.478006	−	0.878357i	$-0.341360\pi$
$313$	1.04206	+	0.523341i	0.0589006	+	0.0295810i	−0.419105	+	0.907938i	$0.637656\pi$
$314$	−1.90517	+	0.693424i	−0.107515	+	0.0391322i
$315$		0			0
$316$	−7.34788	−	2.67441i	−0.413351	−	0.150447i
$317$	3.18438	+	3.37524i	0.178853	+	0.189573i	0.810598	−	0.585604i	$-0.199142\pi$
$317$	3.18438	+	3.37524i	0.178853	+	0.189573i	−0.631745	+	0.775176i	$0.717661\pi$
$318$		0			0
$319$	−14.1351	−	9.29680i	−0.791414	−	0.520521i
$320$	4.75670	+	15.8885i	0.265908	+	0.888194i
$321$		0			0
$322$	−0.00933260	+	0.0125359i	−0.000520085	+	0.000698596i
$323$	−29.2067			−1.62511
$324$		0			0
$325$	14.4943			0.803999
$326$	0.277376	−	0.372581i	0.0153624	−	0.0206353i
$327$		0			0
$328$	−1.32892	−	4.43889i	−0.0733771	−	0.245097i
$329$	0.00801527	+	0.00527172i	0.000441896	+	0.000290640i
$330$		0			0
$331$	4.56840	+	4.84222i	0.251102	+	0.266152i	0.840648	−	0.541583i	$-0.182175\pi$
$331$	4.56840	+	4.84222i	0.251102	+	0.266152i	−0.589546	+	0.807735i	$0.700693\pi$
$332$	−22.9225	−	8.34311i	−1.25804	−	0.457888i
$333$		0			0
$334$	4.56418	−	1.66123i	0.249741	−	0.0908982i
$335$	22.4333	+	11.2664i	1.22566	+	0.615551i
$336$		0			0
$337$	−6.57079	+	15.2328i	−0.357934	+	0.829784i	0.640170	+	0.768233i	$0.278864\pi$
$337$	−6.57079	+	15.2328i	−0.357934	+	0.829784i	−0.998104	+	0.0615509i	$0.980395\pi$
$338$	0.152724	−	0.0178508i	0.00830707	−	0.000970958i
$339$		0			0
$340$	−19.2372	+	12.6525i	−1.04329	+	0.686180i
$341$	24.6384	+	20.6741i	1.33424	+	1.11956i
$342$		0			0
$343$	−0.0986981	+	0.0828175i	−0.00532920	+	0.00447173i
$344$	0.452852	−	1.51263i	0.0244162	−	0.0815557i
$345$		0			0
$346$	−2.26271	+	1.13637i	−0.121644	+	0.0610918i
$347$	−9.41754	+	9.98201i	−0.505560	+	0.535862i	−0.929009	−	0.370058i	$-0.879338\pi$
$347$	−9.41754	+	9.98201i	−0.505560	+	0.535862i	0.423449	+	0.905920i	$0.360819\pi$
$348$		0			0
$349$	−5.59590	−	12.9727i	−0.299542	−	0.694415i	0.700269	−	0.713879i	$-0.253063\pi$
$349$	−5.59590	−	12.9727i	−0.299542	−	0.694415i	−0.999811	+	0.0194637i	$0.993804\pi$
$350$	−0.00622179	−	0.0107765i	−0.000332569	−	0.000576026i
$351$		0			0
$352$	6.54591	−	11.3378i	0.348898	−	0.604309i
$353$	−9.19481	−	1.07472i	−0.489390	−	0.0572015i	−0.132181	−	0.991226i	$-0.542198\pi$
$353$	−9.19481	−	1.07472i	−0.489390	−	0.0572015i	−0.357210	+	0.934024i	$0.616272\pi$
$354$		0			0
$355$	7.80333	+	1.84942i	0.414158	+	0.0981572i
$356$	1.07797	−	18.5080i	0.0571322	−	0.980921i
$357$		0			0
$358$	1.92712	−	0.456736i	0.101852	−	0.0241393i
$359$	−3.82037	−	21.6664i	−0.201631	−	1.14351i	−0.902653	−	0.430368i	$-0.858384\pi$
$359$	−3.82037	−	21.6664i	−0.201631	−	1.14351i	0.701022	−	0.713140i	$-0.252727\pi$
$360$		0			0
$361$	5.78583	−	32.8131i	0.304517	−	1.72700i
$362$	−0.198652	−	3.41072i	−0.0104409	−	0.179264i
$363$		0			0
$364$	−0.0367913	−	0.0494192i	−0.00192839	−	0.00259027i
$365$	−4.03698	−	5.42260i	−0.211305	−	0.283832i
$366$		0			0
$367$	1.14897	+	19.7270i	0.0599757	+	1.02974i	0.885281	+	0.465056i	$0.153966\pi$
$367$	1.14897	+	19.7270i	0.0599757	+	1.02974i	−0.825305	+	0.564687i	$0.808997\pi$
$368$	−2.99770	+	17.0008i	−0.156266	+	0.886229i
$369$		0			0
$370$	0.0241011	+	0.136684i	0.00125296	+	0.00710588i
$371$	−0.0338099	+	0.00801310i	−0.00175532	+	0.000416019i
$372$		0			0
$373$	−0.431505	+	7.40865i	−0.0223425	+	0.383605i	0.968538	+	0.248864i	$0.0800573\pi$
$373$	−0.431505	+	7.40865i	−0.0223425	+	0.383605i	−0.990881	+	0.134741i	$0.956980\pi$
$374$	4.61773	+	1.09442i	0.238777	+	0.0565913i
$375$		0			0
$376$	−1.33053	−	0.155517i	−0.0686170	−	0.00802018i
$377$	8.41606	−	14.5770i	0.433449	−	0.750756i
$378$		0			0
$379$	4.80243	+	8.31805i	0.246684	+	0.427269i	0.962604	−	0.270913i	$-0.0873257\pi$
$379$	4.80243	+	8.31805i	0.246684	+	0.427269i	−0.715920	+	0.698183i	$0.753992\pi$
$380$	−16.3367	−	37.8727i	−0.838053	−	1.94283i
$381$		0			0
$382$	3.59822	−	3.81389i	0.184101	−	0.195135i
$383$	8.16588	−	4.10106i	0.417257	−	0.209554i	−0.227769	−	0.973715i	$-0.573143\pi$
$383$	8.16588	−	4.10106i	0.417257	−	0.209554i	0.645026	+	0.764161i	$0.276847\pi$
$384$		0			0
$385$	0.0283245	−	0.0946105i	0.00144355	−	0.00482180i
$386$	4.97312	−	4.17295i	0.253125	−	0.212397i
$387$		0			0
$388$	22.8660	+	19.1869i	1.16085	+	0.974065i
$389$	13.3115	−	8.75510i	0.674919	−	0.443901i	−0.165231	−	0.986255i	$-0.552837\pi$
$389$	13.3115	−	8.75510i	0.674919	−	0.443901i	0.840150	+	0.542353i	$0.182467\pi$
$390$		0			0
$391$	−20.6214	+	2.41030i	−1.04287	+	0.121894i
$392$	3.56286	−	8.25964i	0.179952	−	0.417175i
$393$		0			0
$394$	−0.0251143	−	0.0126129i	−0.00126524	−	0.000635428i
$395$	11.7183	−	4.26512i	0.589613	−	0.214602i
$396$		0			0
$397$	−5.92327	−	2.15589i	−0.297280	−	0.108201i	0.189074	−	0.981963i	$-0.439451\pi$
$397$	−5.92327	−	2.15589i	−0.297280	−	0.108201i	−0.486354	+	0.873762i	$0.661674\pi$
$398$	4.04856	+	4.29122i	0.202936	+	0.215100i
$399$		0			0
$400$	−11.4839	−	7.55310i	−0.574197	−	0.377655i
$401$	−9.17353	−	30.6417i	−0.458104	−	1.53017i	−0.805581	−	0.592485i	$-0.798147\pi$
$401$	−9.17353	−	30.6417i	−0.458104	−	1.53017i	0.347477	−	0.937688i	$-0.387038\pi$
$402$		0			0
$403$	−19.1086	+	25.6672i	−0.951865	+	1.27858i
$404$	36.3978			1.81086
$405$		0			0
$406$	−0.0144506			−0.000717173
$407$	−0.296129	+	0.397771i	−0.0146786	+	0.0197168i
$408$		0			0
$409$	−10.2848	−	34.3537i	−0.508552	−	1.69868i	−0.697405	−	0.716677i	$-0.745662\pi$
$409$	−10.2848	−	34.3537i	−0.508552	−	1.69868i	0.188853	−	0.982005i	$-0.439523\pi$
$410$	3.00039	+	1.97339i	0.148179	+	0.0974588i
$411$		0			0
$412$	11.3304	+	12.0095i	0.558210	+	0.591668i
$413$	−0.0448827	−	0.0163360i	−0.00220853	−	0.000803841i
$414$		0			0
$415$	36.5566	−	13.3055i	1.79449	−	0.653142i
$416$	11.6396	+	5.84564i	0.570680	+	0.286606i
$417$		0			0
$418$	−3.36711	+	7.80583i	−0.164691	+	0.381796i
$419$	7.19967	−	0.841521i	0.351727	−	0.0411110i	0.0616049	−	0.998101i	$-0.480378\pi$
$419$	7.19967	−	0.841521i	0.351727	−	0.0411110i	0.290122	+	0.956990i	$0.406304\pi$
$420$		0			0
$421$	2.42843	−	1.59720i	0.118354	−	0.0778428i	−0.488952	−	0.872311i	$-0.662621\pi$
$421$	2.42843	−	1.59720i	0.118354	−	0.0778428i	0.607306	+	0.794468i	$0.292250\pi$
$422$	1.97437	+	1.65670i	0.0961111	+	0.0806467i
$423$		0			0
$424$	3.71672	−	3.11870i	0.180500	−	0.151457i
$425$	4.74112	−	15.8364i	0.229978	−	0.768181i
$426$		0			0
$427$	0.0563597	−	0.0283049i	0.00272744	−	0.00136977i
$428$	−18.3280	+	19.4265i	−0.885917	+	0.939017i
$429$		0			0
$430$	0.484707	+	1.12368i	0.0233747	+	0.0541886i
$431$	−0.349866	−	0.605986i	−0.0168525	−	0.0291893i	0.857476	−	0.514524i	$-0.172031\pi$
$431$	−0.349866	−	0.605986i	−0.0168525	−	0.0291893i	−0.874329	+	0.485334i	$0.838698\pi$
$432$		0			0
$433$	−8.81031	+	15.2599i	−0.423397	+	0.733344i	−0.996269	−	0.0863000i	$-0.972496\pi$
$433$	−8.81031	+	15.2599i	−0.423397	+	0.733344i	0.572873	+	0.819644i	$0.305829\pi$
$434$	0.0272860	+	0.00318928i	0.00130977	+	0.000153090i
$435$		0			0
$436$	−13.9857	−	3.31467i	−0.669793	−	0.158744i
$437$	2.16249	−	37.1285i	0.103446	−	1.77610i
$438$		0			0
$439$	23.4934	−	5.56804i	1.12128	−	0.265748i	0.372151	−	0.928172i	$-0.378620\pi$
$439$	23.4934	−	5.56804i	1.12128	−	0.265748i	0.749129	+	0.662424i	$0.230472\pi$
$440$	2.39465	+	13.5808i	0.114161	+	0.647437i
$441$		0			0
$442$	−0.819872	+	4.64973i	−0.0389974	+	0.221165i
$443$	0.397074	+	6.81750i	0.0188656	+	0.323909i	0.994516	+	0.104580i	$0.0333498\pi$
$443$	0.397074	+	6.81750i	0.0188656	+	0.323909i	−0.975651	+	0.219329i	$0.929613\pi$
$444$		0			0
$445$	17.6558	+	23.7159i	0.836966	+	1.12424i
$446$	−4.43095	−	5.95179i	−0.209811	−	0.281826i
$447$		0			0
$448$	0.00294297	+	0.0505288i	0.000139042	+	0.00238726i
$449$	0.451728	−	2.56188i	0.0213184	−	0.120902i	−0.972291	−	0.233772i	$-0.924893\pi$
$449$	0.451728	−	2.56188i	0.0213184	−	0.120902i	0.993610	+	0.112870i	$0.0360042\pi$
$450$		0			0
$451$	2.22809	+	12.6361i	0.104917	+	0.595012i
$452$	−35.4983	+	8.41326i	−1.66970	+	0.395727i
$453$		0			0
$454$	−0.311268	+	5.34427i	−0.0146085	+	0.250819i
$455$	0.0956074	+	0.0226594i	0.00448214	+	0.00106229i
$456$		0			0
$457$	−7.71397	−	0.901634i	−0.360844	−	0.0421767i	−0.0662607	−	0.997802i	$-0.521107\pi$
$457$	−7.71397	−	0.901634i	−0.360844	−	0.0421767i	−0.294584	+	0.955626i	$0.595181\pi$
$458$	2.41052	−	4.17515i	0.112636	−	0.195092i
$459$		0			0
$460$	−14.6599	−	25.3918i	−0.683523	−	1.18390i
$461$	0.268889	+	0.623356i	0.0125234	+	0.0290326i	0.924363	−	0.381514i	$-0.124597\pi$
$461$	0.268889	+	0.623356i	0.0125234	+	0.0290326i	−0.911840	+	0.410547i	$0.865338\pi$
$462$		0			0
$463$	13.8822	−	14.7142i	0.645159	−	0.683829i	−0.319423	−	0.947612i	$-0.603489\pi$
$463$	13.8822	−	14.7142i	0.645159	−	0.683829i	0.964582	+	0.263783i	$0.0849704\pi$
$464$	−14.2643	+	7.16382i	−0.662205	+	0.332572i
$465$		0			0
$466$	−1.00574	+	3.35939i	−0.0465898	+	0.155621i
$467$	6.20374	−	5.20555i	0.287075	−	0.240884i	−0.487866	−	0.872919i	$-0.662224\pi$
$467$	6.20374	−	5.20555i	0.287075	−	0.240884i	0.774940	+	0.632035i	$0.217780\pi$
$468$		0			0
$469$	0.0586869	+	0.0492442i	0.00270991	+	0.00227388i
$470$	0.867435	−	0.570521i	0.0400118	−	0.0263162i
$471$		0			0
$472$	6.62432	−	0.774272i	0.304909	−	0.0356387i
$473$	−1.73182	+	4.01482i	−0.0796294	+	0.184602i
$474$		0			0
$475$	26.4627	+	13.2901i	1.21419	+	0.609791i
$476$	−0.0660299	+	0.0240329i	−0.00302648	+	0.00110155i
$477$		0			0
$478$	−1.57315	−	0.572580i	−0.0719542	−	0.0261892i
$479$	19.9734	+	21.1705i	0.912606	+	0.967306i	0.999582	−	0.0289044i	$-0.00920184\pi$
$479$	19.9734	+	21.1705i	0.912606	+	0.967306i	−0.0869760	+	0.996210i	$0.527720\pi$
$480$		0			0
$481$	−0.412204	−	0.271111i	−0.0187949	−	0.0123616i
$482$	0.0336584	+	0.112427i	0.00153310	+	0.00512090i
$483$		0			0
$484$	−1.87809	+	2.52271i	−0.0853677	+	0.114669i
$485$	−47.6036			−2.16157
$486$		0			0
$487$	3.59484			0.162898			0.0814489	−	0.996678i	$-0.474045\pi$
$487$	3.59484			0.162898			0.0814489	+	0.996678i	$0.474045\pi$
$488$	−5.25889	+	7.06391i	−0.238059	+	0.319768i
$489$		0			0
$490$	1.99952	+	6.67885i	0.0903289	+	0.301720i
$491$	28.0965	+	18.4794i	1.26798	+	0.833963i	0.991881	−	0.127167i	$-0.0405883\pi$
$491$	28.0965	+	18.4794i	1.26798	+	0.833963i	0.276098	+	0.961130i	$0.410959\pi$
$492$		0			0
$493$	−13.1739	−	13.9636i	−0.593325	−	0.628888i
$494$	−7.94768	−	2.89272i	−0.357583	−	0.130150i
$495$		0			0
$496$	28.5153	−	10.3787i	1.28037	−	0.466018i
$497$	0.0218705	+	0.0109838i	0.000981026	+	0.000492690i
$498$		0			0
$499$	−5.43495	+	12.5996i	−0.243302	+	0.564037i	−0.995485	−	0.0949171i	$-0.969741\pi$
$499$	−5.43495	+	12.5996i	−0.243302	+	0.564037i	0.752184	+	0.658954i	$0.229001\pi$
$500$	−5.13152	+	0.599789i	−0.229489	+	0.0268234i
$501$		0			0
$502$	6.11205	−	4.01996i	0.272794	−	0.179419i
$503$	−2.12583	−	1.78378i	−0.0947859	−	0.0795348i	0.594163	−	0.804344i	$-0.297483\pi$
$503$	−2.12583	−	1.78378i	−0.0947859	−	0.0795348i	−0.688949	+	0.724810i	$0.741928\pi$
$504$		0			0
$505$	−44.4664	+	37.3118i	−1.97873	+	1.66035i
$506$	−1.73316	+	5.78917i	−0.0770486	+	0.257360i
$507$		0			0
$508$	13.2418	−	6.65027i	0.587509	−	0.295058i
$509$	5.02620	−	5.32746i	0.222783	−	0.236136i	−0.606336	−	0.795209i	$-0.707361\pi$
$509$	5.02620	−	5.32746i	0.222783	−	0.236136i	0.829119	+	0.559073i	$0.188843\pi$
$510$		0			0
$511$	−0.00817150	−	0.0189437i	−0.000361486	−	0.000838019i
$512$	−10.4904	−	18.1700i	−0.463616	−	0.803007i
$513$		0			0
$514$	3.38924	−	5.87034i	0.149493	−	0.258930i
$515$	−26.1533	−	3.05688i	−1.15245	−	0.134702i
$516$		0			0
$517$	3.60956	+	0.855481i	0.158748	+	0.0376240i
$518$	−2.46281e−5	0	0.000422848i	−1.08210e−6	0	1.85789e-5i
$519$		0			0
$520$	−13.3501	+	3.16404i	−0.585442	+	0.138752i
$521$	−6.17963	−	35.0464i	−0.270734	−	1.53541i	−0.752193	−	0.658942i	$-0.771004\pi$
$521$	−6.17963	−	35.0464i	−0.270734	−	1.53541i	0.481459	−	0.876469i	$-0.340107\pi$
$522$		0			0
$523$	−5.30847	+	30.1059i	−0.232123	+	1.31644i	0.616465	+	0.787383i	$0.288564\pi$
$523$	−5.30847	+	30.1059i	−0.232123	+	1.31644i	−0.848588	+	0.529054i	$0.822547\pi$
$524$	0.475167	+	8.15829i	0.0207577	+	0.356397i
$525$		0			0
$526$	−4.37870	−	5.88162i	−0.190921	−	0.256451i
$527$	21.7935	+	29.2738i	0.949342	+	1.27519i
$528$		0			0
$529$	−0.199888	−	3.43194i	−0.00869077	−	0.149215i
$530$	−0.652980	+	3.70324i	−0.0283637	+	0.160858i
$531$		0			0
$532$	−0.0218577	−	0.123961i	−0.000947650	−	0.00537439i
$533$	−12.4215	+	2.94396i	−0.538036	+	0.127517i
$534$		0			0
$535$	2.47658	−	42.5212i	0.107072	−	1.83835i
$536$	−10.4091	−	2.46701i	−0.449606	−	0.106559i
$537$		0			0
$538$	−5.75681	−	0.672874i	−0.248194	−	0.0290097i
$539$	−12.4548	+	21.5723i	−0.536464	+	0.929183i
$540$		0			0
$541$	−14.2816	−	24.7364i	−0.614012	−	1.06350i	−0.990557	−	0.137102i	$-0.956221\pi$
$541$	−14.2816	−	24.7364i	−0.614012	−	1.06350i	0.376545	−	0.926398i	$-0.377112\pi$
$542$	−3.06689	−	7.10986i	−0.131734	−	0.305394i
$543$		0			0
$544$	10.1943	−	10.8053i	0.437077	−	0.463274i
$545$	20.4840	−	10.2874i	0.877436	−	0.440665i
$546$		0			0
$547$	8.57611	−	28.6462i	0.366688	−	1.22482i	−0.553335	−	0.832959i	$-0.686645\pi$
$547$	8.57611	−	28.6462i	0.366688	−	1.22482i	0.920023	−	0.391864i	$-0.128170\pi$
$548$	−0.170550	+	0.143109i	−0.00728555	+	0.00611331i
$549$		0			0
$550$	−3.68589	−	3.09283i	−0.157167	−	0.131879i
$551$	28.7314	−	18.8970i	1.22400	−	0.805038i
$552$		0			0
$553$	0.0377995	−	0.00441812i	0.00160740	−	0.000187878i
$554$	0.0450658	−	0.104474i	0.00191466	−	0.00443868i
$555$		0			0
$556$	−2.20021	−	1.10499i	−0.0933095	−	0.0468618i
$557$	−11.4069	+	4.15178i	−0.483327	+	0.175917i	−0.572180	−	0.820128i	$-0.693902\pi$
$557$	−11.4069	+	4.15178i	−0.483327	+	0.175917i	0.0888529	+	0.996045i	$0.471680\pi$
$558$		0			0
$559$	−4.08778	−	1.48783i	−0.172895	−	0.0629285i
$560$	−0.0639424	−	0.0677750i	−0.00270206	−	0.00286402i
$561$		0			0
$562$	−8.34591	−	5.48919i	−0.352051	−	0.231548i
$563$	5.27258	+	17.6116i	0.222213	+	0.742242i	0.994290	+	0.106713i	$0.0340327\pi$
$563$	5.27258	+	17.6116i	0.222213	+	0.742242i	−0.772077	+	0.635529i	$0.780782\pi$
$564$		0			0
$565$	34.7431	−	46.6681i	1.46165	−	1.96334i
$566$	−1.82617			−0.0767595
$567$		0			0
$568$	−3.41739			−0.143390
$569$	5.09492	−	6.84367i	0.213590	−	0.286901i	−0.682397	−	0.730982i	$-0.739062\pi$
$569$	5.09492	−	6.84367i	0.213590	−	0.286901i	0.895987	+	0.444081i	$0.146470\pi$
$570$		0			0
$571$	11.8721	+	39.6555i	0.496830	+	1.65953i	0.727200	+	0.686426i	$0.240821\pi$
$571$	11.8721	+	39.6555i	0.496830	+	1.65953i	−0.230370	+	0.973103i	$0.573994\pi$
$572$	−19.9039	−	13.0910i	−0.832224	−	0.547362i
$573$		0			0
$574$	0.00752086	+	0.00797165i	0.000313915	+	0.000332730i
$575$	19.7808	+	7.19960i	0.824914	+	0.300244i
$576$		0			0
$577$	−41.2655	+	15.0194i	−1.71791	+	0.625266i	−0.997655	−	0.0684479i	$-0.978195\pi$
$577$	−41.2655	+	15.0194i	−1.71791	+	0.625266i	−0.720250	+	0.693714i	$0.755973\pi$
$578$	−0.205300	−	0.103106i	−0.00853936	−	0.00428863i
$579$		0			0
$580$	10.7379	−	24.8932i	0.445867	−	1.03364i
$581$	0.117920	−	0.0137828i	0.00489213	−	0.000571808i
$582$		0			0
$583$	−11.2252	+	7.38293i	−0.464901	+	0.305770i
$584$	2.20682	+	1.85174i	0.0913190	+	0.0766258i
$585$		0			0
$586$	−5.06059	+	4.24634i	−0.209051	+	0.175415i
$587$	−3.77189	+	12.5990i	−0.155683	+	0.520016i	−0.999872	−	0.0160298i	$-0.994897\pi$
$587$	−3.77189	+	12.5990i	−0.155683	+	0.520016i	0.844189	+	0.536046i	$0.180083\pi$
$588$		0			0
$589$	−58.4219	+	29.3406i	−2.40723	+	1.20896i
$590$	−3.54723	+	3.75984i	−0.146037	+	0.154790i
$591$		0			0
$592$	0.185314	+	0.429606i	0.00761636	+	0.0176567i
$593$	10.7252	+	18.5766i	0.440432	+	0.762850i	0.997721	−	0.0674679i	$-0.0214920\pi$
$593$	10.7252	+	18.5766i	0.440432	+	0.762850i	−0.557290	+	0.830318i	$0.688159\pi$
$594$		0			0
$595$	0.0560310	−	0.0970486i	0.00229705	−	0.00397860i
$596$	−13.0298	−	1.52296i	−0.533719	−	0.0623829i
$597$		0			0
$598$	−5.85017	−	1.38652i	−0.239231	−	0.0566989i
$599$	−1.30398	+	22.3884i	−0.0532790	+	0.914766i	0.860727	+	0.509066i	$0.170009\pi$
$599$	−1.30398	+	22.3884i	−0.0532790	+	0.914766i	−0.914007	+	0.405700i	$0.867028\pi$
$600$		0			0
$601$	9.25757	−	2.19409i	0.377624	−	0.0894986i	−0.0374204	−	0.999300i	$-0.511914\pi$
$601$	9.25757	−	2.19409i	0.377624	−	0.0894986i	0.415045	+	0.909801i	$0.363766\pi$
$602$	0.000648515		0.00367791i	2.64315e−5		0.000149900i
$603$		0			0
$604$	3.09986	−	17.5802i	0.126131	−	0.715326i
$605$	−0.291636	−	5.00720i	−0.0118567	−	0.203572i
$606$		0			0
$607$	14.6385	+	19.6629i	0.594157	+	0.798091i	0.992898	−	0.118972i	$-0.0379600\pi$
$607$	14.6385	+	19.6629i	0.594157	+	0.798091i	−0.398741	+	0.917064i	$0.630553\pi$
$608$	15.8909	+	21.3452i	0.644461	+	0.865661i
$609$		0			0
$610$	−0.396862	−	6.81386i	−0.0160685	−	0.275885i
$611$	−0.640872	+	3.63457i	−0.0259269	+	0.147039i
$612$		0			0
$613$	−1.29645	−	7.35253i	−0.0523631	−	0.296966i	0.947368	−	0.320146i	$-0.103732\pi$
$613$	−1.29645	−	7.35253i	−0.0523631	−	0.296966i	−0.999731	+	0.0231801i	$0.992621\pi$
$614$	0.360029	−	0.0853285i	0.0145296	−	0.00344358i
$615$		0			0
$616$	−0.00244701	+	0.0420136i	−9.85930e−5	+	0.00169278i
$617$	13.9222	+	3.29962i	0.560486	+	0.132838i	0.501087	−	0.865397i	$-0.332934\pi$
$617$	13.9222	+	3.29962i	0.560486	+	0.132838i	0.0593988	+	0.998234i	$0.481082\pi$
$618$		0			0
$619$	4.14941	+	0.484997i	0.166779	+	0.0194937i	0.199073	−	0.979985i	$-0.436207\pi$
$619$	4.14941	+	0.484997i	0.166779	+	0.0194937i	−0.0322935	+	0.999478i	$0.510281\pi$
$620$	−25.7695	+	44.6341i	−1.03493	+	1.79255i
$621$		0			0
$622$	0.136257	+	0.236004i	0.00546342	+	0.00946292i
$623$	0.0357382	+	0.0828506i	0.00143182	+	0.00331934i
$624$		0			0
$625$	19.7015	−	20.8824i	0.788060	−	0.835294i
$626$	0.344162	−	0.172845i	0.0137555	−	0.00690827i
$627$		0			0
$628$	3.32915	−	11.1201i	0.132848	−	0.443742i
$629$	−0.431048	+	0.361692i	−0.0171870	+	0.0144216i
$630$		0			0
$631$	14.2403	+	11.9490i	0.566896	+	0.475683i	0.880614	−	0.473834i	$-0.157130\pi$
$631$	14.2403	+	11.9490i	0.566896	+	0.475683i	−0.313718	+	0.949516i	$0.601575\pi$
$632$	−4.43983	+	2.92012i	−0.176607	+	0.116156i
$633$		0			0
$634$	1.52220	−	0.177920i	0.0604544	−	0.00706610i
$635$	−9.35994	+	21.6988i	−0.371438	+	0.861090i
$636$		0			0
$637$	−22.1465	−	11.1224i	−0.877474	−	0.440684i
$638$	−5.25068	+	1.91109i	−0.207877	+	0.0756609i
$639$		0			0
$640$	25.9980	+	9.46249i	1.02766	+	0.374038i
$641$	11.0207	+	11.6813i	0.435293	+	0.461384i	0.907468	−	0.420121i	$-0.138012\pi$
$641$	11.0207	+	11.6813i	0.435293	+	0.461384i	−0.472175	+	0.881505i	$0.656531\pi$
$642$		0			0
$643$	22.3940	+	14.7288i	0.883133	+	0.580846i	0.908058	−	0.418844i	$-0.137564\pi$
$643$	22.3940	+	14.7288i	0.883133	+	0.580846i	−0.0249254	+	0.999689i	$0.507935\pi$
$644$	−0.0256625	−	0.0857187i	−0.00101124	−	0.00337779i
$645$		0			0
$646$	−5.76029	+	7.73741i	−0.226635	+	0.304424i
$647$	16.2621			0.639328			0.319664	−	0.947531i	$-0.396430\pi$
$647$	16.2621			0.639328			0.319664	+	0.947531i	$0.396430\pi$
$648$		0			0
$649$	−18.4687			−0.724960
$650$	2.85863	−	3.83981i	0.112125	−	0.150610i
$651$		0			0
$652$	0.762720	+	2.54766i	0.0298704	+	0.0997742i
$653$	−36.5341	−	24.0289i	−1.42969	−	0.940322i	−0.999290	−	0.0376835i	$-0.988002\pi$
$653$	−36.5341	−	24.0289i	−1.42969	−	0.940322i	−0.430400	−	0.902638i	$-0.641628\pi$
$654$		0			0
$655$	−8.94366	−	9.47973i	−0.349458	−	0.370404i
$656$	11.3758	+	4.14045i	0.444150	+	0.161657i
$657$		0			0
$658$	0.00297738	−	0.00108368i	0.000116071	−	4.22462e-5i
$659$	23.8182	+	11.9619i	0.927824	+	0.465971i	0.847498	−	0.530798i	$-0.178108\pi$
$659$	23.8182	+	11.9619i	0.927824	+	0.465971i	0.0803258	+	0.996769i	$0.474404\pi$
$660$		0			0
$661$	−6.93400	+	16.0748i	−0.269701	+	0.625238i	−0.998211	−	0.0597979i	$-0.980954\pi$
$661$	−6.93400	+	16.0748i	−0.269701	+	0.625238i	0.728509	+	0.685036i	$0.240214\pi$
$662$	2.18379	−	0.255249i	0.0848755	−	0.00992053i
$663$		0			0
$664$	−13.8505	+	9.10965i	−0.537505	+	0.353523i
$665$	0.153777	+	0.129034i	0.00596321	+	0.00500373i
$666$		0			0
$667$	18.7263	−	15.7133i	0.725086	−	0.608420i
$668$	−7.97560	+	26.6403i	−0.308585	+	1.03075i
$669$		0			0
$670$	7.40909	−	3.72098i	0.286238	−	0.143754i
$671$	16.7352	−	17.7382i	0.646054	−	0.684777i
$672$		0			0
$673$	3.17172	+	7.35287i	0.122261	+	0.283432i	0.968344	−	0.249618i	$-0.0803050\pi$
$673$	3.17172	+	7.35287i	0.122261	+	0.283432i	−0.846084	+	0.533050i	$0.821046\pi$
$674$	2.73953	+	4.74501i	0.105523	+	0.182771i
$675$		0			0
$676$	−0.440175	+	0.762405i	−0.0169298	+	0.0293233i
$677$	42.1885	+	4.93113i	1.62144	+	0.189519i	0.877787	−	0.479051i	$-0.159019\pi$
$677$	42.1885	+	4.93113i	1.62144	+	0.189519i	0.743650	+	0.668569i	$0.233093\pi$
$678$		0			0
$679$	−0.141360	−	0.0335028i	−0.00542488	−	0.00128572i
$680$	−0.909838	+	15.6213i	−0.0348907	+	0.599050i
$681$		0			0
$682$	10.3362	−	2.44973i	0.395795	−	0.0938051i
$683$	3.92505	+	22.2600i	0.150188	+	0.851757i	0.963054	+	0.269307i	$0.0867947\pi$
$683$	3.92505	+	22.2600i	0.150188	+	0.851757i	−0.812867	+	0.582450i	$0.802094\pi$
$684$		0			0
$685$	0.0616556	−	0.349666i	0.00235574	−	0.0133601i
$686$	0.00247421	+	0.0424806i	9.44659e−5	+	0.00162192i
$687$		0			0
$688$	2.46346	+	3.30899i	0.0939183	+	0.126154i
$689$	−7.98222	−	10.7220i	−0.304099	−	0.408475i
$690$		0			0
$691$	0.493311	+	8.46982i	0.0187664	+	0.322207i	0.994606	+	0.103721i	$0.0330749\pi$
$691$	0.493311	+	8.46982i	0.0187664	+	0.322207i	−0.975840	+	0.218486i	$0.929888\pi$
$692$	2.51734	−	14.2765i	0.0956948	−	0.542712i
$693$		0			0
$694$	0.787049	+	4.46358i	0.0298760	+	0.169435i
$695$	3.82068	−	0.905518i	0.144927	−	0.0343483i
$696$		0			0
$697$	−0.846552	+	14.5347i	−0.0320654	+	0.550542i
$698$	−4.54037	−	1.07609i	−0.171856	−	0.0407305i
$699$		0			0
$700$	0.0707621	+	0.00827090i	0.00267456	+	0.000312611i
$701$	18.1146	−	31.3755i	0.684181	−	1.18504i	−0.289513	−	0.957174i	$-0.593493\pi$
$701$	18.1146	−	31.3755i	0.684181	−	1.18504i	0.973694	−	0.227861i	$-0.0731733\pi$
$702$		0			0
$703$	−0.503988	−	0.872933i	−0.0190083	−	0.0329233i
$704$	7.75176	+	17.9706i	0.292155	+	0.677293i
$705$		0			0
$706$	−2.09816	+	2.22391i	−0.0789651	+	0.0836981i
$707$	−0.158303	+	0.0795029i	−0.00595361	+	0.00299001i
$708$		0			0
$709$	2.93989	−	9.81990i	0.110410	−	0.368794i	−0.884870	−	0.465837i	$-0.845753\pi$
$709$	2.93989	−	9.81990i	0.110410	−	0.368794i	0.995280	+	0.0970430i	$0.0309384\pi$
$710$	2.02896	−	1.70250i	0.0761453	−	0.0638935i
$711$		0			0
$712$	−9.65159	−	8.09865i	−0.361709	−	0.303510i
$713$	−38.8274	+	25.5372i	−1.45410	+	0.956375i
$714$		0			0
$715$	37.7359	−	4.41070i	1.41124	−	0.164951i
$716$	−4.49119	+	10.4117i	−0.167844	+	0.389105i
$717$		0			0
$718$	−6.49330	−	3.26106i	−0.242328	−	0.121702i
$719$	34.8714	−	12.6922i	1.30048	−	0.473338i	0.403330	−	0.915055i	$-0.367853\pi$
$719$	34.8714	−	12.6922i	1.30048	−	0.473338i	0.897154	+	0.441717i	$0.145630\pi$
$720$		0			0
$721$	−0.0755111	−	0.0274838i	−0.00281218	−	0.00102355i
$722$	−7.55168	−	8.00431i	−0.281044	−	0.297890i
$723$		0			0
$724$	16.3427	+	10.7488i	0.607372	+	0.399475i
$725$	5.58233	+	18.6463i	0.207322	+	0.692505i
$726$		0			0
$727$	−19.8968	+	26.7260i	−0.737930	+	0.991212i	0.261730	+	0.965141i	$0.415707\pi$
$727$	−19.8968	+	26.7260i	−0.737930	+	0.991212i	−0.999660	+	0.0260709i	$0.991700\pi$
$728$	−0.0418702			−0.00155181
$729$		0			0
$730$	−2.23274			−0.0826374
$731$	−2.96272	+	3.97963i	−0.109580	+	0.147192i
$732$		0			0
$733$	10.7746	+	35.9896i	0.397969	+	1.32931i	0.888897	+	0.458107i	$0.151473\pi$
$733$	10.7746	+	35.9896i	0.397969	+	1.32931i	−0.490928	+	0.871200i	$0.663342\pi$
$734$	5.45266	+	3.58627i	0.201261	+	0.132372i
$735$		0			0
$736$	12.9813	+	13.7593i	0.478496	+	0.507176i
$737$	27.8366	+	10.1317i	1.02537	+	0.373206i
$738$		0			0
$739$	−12.4039	+	4.51464i	−0.456283	+	0.166074i	−0.559929	−	0.828541i	$-0.689172\pi$
$739$	−12.4039	+	4.51464i	−0.456283	+	0.166074i	0.103645	+	0.994614i	$0.466949\pi$
$740$	−0.710115	−	0.356633i	−0.0261043	−	0.0131101i
$741$		0			0
$742$	−0.00454533	+	0.0105373i	−0.000166864	+	0.000386835i
$743$	6.82008	−	0.797153i	0.250204	−	0.0292447i	0.00993379	−	0.999951i	$-0.496838\pi$
$743$	6.82008	−	0.797153i	0.250204	−	0.0292447i	0.240271	+	0.970706i	$0.422764\pi$
$744$		0			0
$745$	17.4794	−	11.4964i	0.640395	−	0.421195i
$746$	1.87759	+	1.57548i	0.0687433	+	0.0576825i
$747$		0			0
$748$	−20.8138	+	17.4649i	−0.761029	+	0.638579i
$749$	0.0372802	−	0.124524i	0.00136219	−	0.00455002i
$750$		0			0
$751$	16.1685	−	8.12014i	0.589998	−	0.296308i	−0.128641	−	0.991691i	$-0.541062\pi$
$751$	16.1685	−	8.12014i	0.589998	−	0.296308i	0.718639	+	0.695383i	$0.244765\pi$
$752$	2.40177	−	2.54573i	0.0875836	−	0.0928332i
$753$		0			0
$754$	−2.20188	−	5.10452i	−0.0801876	−	0.185896i
$755$	14.2346	+	24.6550i	0.518049	+	0.897288i
$756$		0			0
$757$	−2.10262	+	3.64185i	−0.0764211	+	0.132365i	−0.901703	−	0.432355i	$-0.857683\pi$
$757$	−2.10262	+	3.64185i	−0.0764211	+	0.132365i	0.825282	+	0.564720i	$0.191016\pi$
$758$	3.15076	+	0.368271i	0.114441	+	0.0133762i
$759$		0			0
$760$	−27.2750	−	6.46428i	−0.989367	−	0.234484i
$761$	−1.13750	+	19.5301i	−0.0412344	+	0.707967i	0.912825	+	0.408350i	$0.133896\pi$
$761$	−1.13750	+	19.5301i	−0.0412344	+	0.707967i	−0.954060	+	0.299617i	$0.903141\pi$
$762$		0			0
$763$	0.0680676	−	0.0161323i	0.00246421	−	0.000584029i
$764$	5.21294	+	29.5640i	0.188597	+	1.06959i
$765$		0			0
$766$	0.524065	−	2.97212i	0.0189353	−	0.107387i
$767$	−1.06838	−	18.3435i	−0.0385771	−	0.662344i
$768$		0			0
$769$	14.1295	+	18.9792i	0.509524	+	0.684409i	0.980226	−	0.197883i	$-0.0634067\pi$
$769$	14.1295	+	18.9792i	0.509524	+	0.684409i	−0.470702	+	0.882292i	$0.655999\pi$
$770$	−0.0194778	−	0.0261632i	−0.000701930	−	0.000942856i
$771$		0			0
$772$	2.16117	+	37.1058i	0.0777821	+	1.33547i
$773$	−7.96472	+	45.1702i	−0.286471	+	1.62466i	0.413511	+	0.910499i	$0.364302\pi$
$773$	−7.96472	+	45.1702i	−0.286471	+	1.62466i	−0.699983	+	0.714160i	$0.746809\pi$
$774$		0			0
$775$	−6.42541	−	36.4403i	−0.230807	−	1.30897i
$776$	19.7387	−	4.67817i	0.708580	−	0.167936i
$777$		0			0
$778$	0.305963	−	5.25318i	0.0109693	−	0.188336i
$779$	−25.3778	−	6.01465i	−0.909254	−	0.215497i
$780$		0			0
$781$	9.39932	+	1.09862i	0.336334	+	0.0393118i
$782$	−3.42851	+	5.93836i	−0.122603	+	0.212355i
$783$		0			0
$784$	11.7508	+	20.3530i	0.419673	+	0.726894i
$785$	7.33222	+	16.9980i	0.261698	+	0.606685i
$786$		0			0
$787$	−9.21684	+	9.76928i	−0.328545	+	0.348237i	−0.870498	−	0.492171i	$-0.836203\pi$
$787$	−9.21684	+	9.76928i	−0.328545	+	0.348237i	0.541953	+	0.840408i	$0.317685\pi$
$788$	0.143788	−	0.0722132i	0.00512225	−	0.00257249i
$789$		0			0
$790$	1.18123	−	3.94559i	0.0420263	−	0.140378i
$791$	0.136015	−	0.114130i	0.00483612	−	0.00405799i
$792$		0			0
$793$	18.5860	+	15.5955i	0.660010	+	0.553814i
$794$	−1.73935	+	1.14399i	−0.0617273	+	0.0405987i
$795$		0			0
$796$	−33.5490	+	3.92131i	−1.18911	+	0.138987i
$797$	12.7849	−	29.6387i	0.452864	−	1.04986i	−0.526941	−	0.849902i	$-0.676661\pi$
$797$	12.7849	−	29.6387i	0.452864	−	1.04986i	0.979805	−	0.199955i	$-0.0640796\pi$
$798$		0			0
$799$	3.76149	+	1.88909i	0.133072	+	0.0668313i
$800$	−14.1533	+	5.15139i	−0.500395	+	0.182129i
$801$		0			0
$802$	−9.92680	−	3.61306i	−0.350527	−	0.127582i
$803$	−5.47444	−	5.80256i	−0.193189	−	0.204768i
$804$		0			0
$805$	0.119223	+	0.0784139i	0.00420204	+	0.00276373i
$806$	3.03105	+	10.1244i	0.106764	+	0.356617i
$807$		0			0
$808$	14.7712	−	19.8411i	0.519648	−	0.698008i
$809$	−17.1245			−0.602066			−0.301033	−	0.953614i	$-0.597332\pi$
$809$	−17.1245			−0.602066			−0.301033	+	0.953614i	$0.597332\pi$
$810$		0			0
$811$	−12.0048			−0.421545			−0.210772	−	0.977535i	$-0.567598\pi$
$811$	−12.0048			−0.421545			−0.210772	+	0.977535i	$0.567598\pi$
$812$	0.0494059	−	0.0663636i	0.00173381	−	0.00232891i
$813$		0			0
$814$	0.0469729	+	0.156900i	0.00164640	+	0.00549935i
$815$	−3.54344	−	2.33056i	−0.124121	−	0.0816358i
$816$		0			0
$817$	−6.09897	−	6.46454i	−0.213376	−	0.226165i
$818$	−11.1294	−	4.05076i	−0.389129	−	0.141631i
$819$		0			0
$820$	−19.3208	+	7.03221i	−0.674713	+	0.245575i
$821$	−32.3108	−	16.2271i	−1.12765	−	0.566329i	−0.215634	−	0.976474i	$-0.569182\pi$
$821$	−32.3108	−	16.2271i	−1.12765	−	0.566329i	−0.912020	+	0.410145i	$0.865478\pi$
$822$		0			0
$823$	21.0664	−	48.8374i	0.734328	−	1.70236i	0.0227664	−	0.999741i	$-0.492753\pi$
$823$	21.0664	−	48.8374i	0.734328	−	1.70236i	0.711562	−	0.702623i	$-0.247988\pi$
$824$	11.1448	−	1.30264i	0.388248	−	0.0453797i
$825$		0			0
$826$	−0.0131797	+	0.00866841i	−0.000458580	+	0.000301613i
$827$	14.2860	+	11.9874i	0.496773	+	0.416842i	0.856446	−	0.516236i	$-0.172667\pi$
$827$	14.2860	+	11.9874i	0.496773	+	0.416842i	−0.359673	+	0.933078i	$0.617112\pi$
$828$		0			0
$829$	34.9024	−	29.2866i	1.21221	−	1.01716i	0.213014	−	0.977049i	$-0.431672\pi$
$829$	34.9024	−	29.2866i	1.21221	−	1.01716i	0.999195	−	0.0401151i	$-0.0127725\pi$
$830$	3.68498	−	12.3087i	0.127908	−	0.427241i
$831$		0			0
$832$	−17.4003	+	8.73876i	−0.603247	+	0.302962i
$833$	−19.3965	+	20.5590i	−0.672047	+	0.712328i
$834$		0			0
$835$	−17.5657	−	40.7218i	−0.607886	−	1.40924i
$836$	−24.3358	−	42.1509i	−0.841673	−	1.45782i
$837$		0			0
$838$	1.19702	−	2.07330i	0.0413503	−	0.0716208i
$839$	−6.63491	−	0.775510i	−0.229062	−	0.0267736i	0.000787266	−	1.00000i	$-0.499749\pi$
$839$	−6.63491	−	0.775510i	−0.229062	−	0.0267736i	−0.229850	+	0.973226i	$0.573823\pi$
$840$		0			0
$841$	−6.22422	−	1.47517i	−0.214628	−	0.0508678i
$842$	0.0558171	−	0.958342i	0.00192358	−	0.0330266i
$843$		0			0
$844$	−14.3585	+	3.40304i	−0.494242	+	0.117137i
$845$	−0.243797	−	1.38264i	−0.00838688	−	0.0475643i
$846$		0			0
$847$	0.00265799	−	0.0150742i	9.13295e−5	−	0.000517955i
$848$	0.737053	+	12.6547i	0.0253105	+	0.434565i
$849$		0			0
$850$	−3.26030	−	4.37935i	−0.111827	−	0.150210i
$851$	−0.427879	−	0.574742i	−0.0146675	−	0.0197019i
$852$		0			0
$853$	−2.71619	−	46.6352i	−0.0930005	−	1.59676i	−0.645842	−	0.763471i	$-0.723494\pi$
$853$	−2.71619	−	46.6352i	−0.0930005	−	1.59676i	0.552842	−	0.833286i	$-0.313543\pi$
$854$	0.00361702	−	0.0205132i	0.000123772	−	0.000701946i
$855$		0			0
$856$	3.15180	+	17.8747i	0.107726	+	0.610946i
$857$	50.1724	−	11.8911i	1.71386	−	0.406192i	0.747678	−	0.664061i	$-0.231169\pi$
$857$	50.1724	−	11.8911i	1.71386	−	0.406192i	0.966180	+	0.257869i	$0.0830204\pi$
$858$		0			0
$859$	−1.19840	+	20.5757i	−0.0408888	+	0.702034i	0.914118	+	0.405449i	$0.132885\pi$
$859$	−1.19840	+	20.5757i	−0.0408888	+	0.702034i	−0.955007	+	0.296585i	$0.904152\pi$
$860$	−6.81761	−	1.61580i	−0.232478	−	0.0550984i
$861$		0			0
$862$	−0.229539	−	0.0268293i	−0.00781814	−	0.000913809i
$863$	26.9774	−	46.7263i	0.918322	−	1.59058i	0.116359	−	0.993207i	$-0.462878\pi$
$863$	26.9774	−	46.7263i	0.918322	−	1.59058i	0.801963	−	0.597373i	$-0.203789\pi$
$864$		0			0
$865$	11.5596	+	20.0219i	0.393040	+	0.680765i
$866$	2.30502	+	5.34364i	0.0783279	+	0.181584i
$867$		0			0
$868$	−0.107936	+	0.114405i	−0.00366358	+	0.00388317i
$869$	13.1503	−	6.60431i	0.446092	−	0.224036i
$870$		0			0
$871$	−8.45268	+	28.2339i	−0.286408	+	0.956669i
$872$	−7.48265	+	6.27869i	−0.253395	+	0.212623i
$873$		0			0
$874$	−9.40954	−	7.89554i	−0.318282	−	0.267071i
$875$	0.0210082	−	0.0138173i	0.000710207	−	0.000467110i
$876$		0			0
$877$	−16.1066	+	1.88260i	−0.543883	+	0.0635708i	−0.383598	−	0.923500i	$-0.625315\pi$
$877$	−16.1066	+	1.88260i	−0.543883	+	0.0635708i	−0.160285	+	0.987071i	$0.551241\pi$
$878$	3.15840	−	7.32200i	0.106591	−	0.247105i
$879$		0			0
$880$	−32.1969	−	16.1699i	−1.08536	−	0.545087i
$881$	−36.0488	+	13.1207i	−1.21451	+	0.442047i	−0.868267	−	0.496097i	$-0.834766\pi$
$881$	−36.0488	+	13.1207i	−1.21451	+	0.442047i	−0.346246	+	0.938144i	$0.612544\pi$
$882$		0			0
$883$	−51.0003	−	18.5626i	−1.71630	−	0.624681i	−0.718788	−	0.695229i	$-0.755303\pi$
$883$	−51.0003	−	18.5626i	−1.71630	−	0.624681i	−0.997508	+	0.0705487i	$0.977525\pi$
$884$	−18.5505	−	19.6624i	−0.623920	−	0.661317i
$885$		0			0
$886$	1.88439	+	1.23939i	0.0633075	+	0.0416380i
$887$	1.07207	+	3.58098i	0.0359967	+	0.120237i	0.974100	−	0.226119i	$-0.0726039\pi$
$887$	1.07207	+	3.58098i	0.0359967	+	0.120237i	−0.938103	+	0.346357i	$0.887419\pi$
$888$		0			0
$889$	−0.0430658	+	0.0578475i	−0.00144438	+	0.00194014i
$890$	9.76493			0.327321
$891$		0			0
$892$	42.4824			1.42242
$893$	−4.50266	+	6.04812i	−0.150676	+	0.202393i
$894$		0			0
$895$	−5.18640	−	17.3238i	−0.173362	−	0.579070i
$896$	0.0705418	+	0.0463961i	0.00235664	+	0.00154998i
$897$		0			0
$898$	−0.589597	−	0.624936i	−0.0196751	−	0.0208544i
$899$	−40.3792	−	14.6968i	−1.34672	−	0.490167i
$900$		0			0
$901$	−14.3258	+	5.21418i	−0.477263	+	0.173710i
$902$	3.78698	+	1.90189i	0.126093	+	0.0633261i
$903$		0			0
$904$	−9.81993	+	22.7651i	−0.326606	+	0.757158i
$905$	−30.9842	+	3.62154i	−1.02995	+	0.120384i
$906$		0			0
$907$	15.8640	−	10.4339i	0.526756	−	0.346453i	−0.258113	−	0.966115i	$-0.583101\pi$
$907$	15.8640	−	10.4339i	0.526756	−	0.346453i	0.784869	+	0.619662i	$0.212730\pi$
$908$	−23.4790	−	19.7012i	−0.779178	−	0.653808i
$909$		0			0
$910$	0.0248590	−	0.0208592i	0.000824068	−	0.000691475i
$911$	−4.20720	+	14.0530i	−0.139391	+	0.465598i	−0.998969	−	0.0454071i	$-0.985541\pi$
$911$	−4.20720	+	14.0530i	−0.139391	+	0.465598i	0.859578	+	0.511005i	$0.170727\pi$
$912$		0			0
$913$	41.0237	−	20.6029i	1.35768	−	0.681855i
$914$	−1.76024	+	1.86575i	−0.0582237	+	0.0617135i
$915$		0			0
$916$	10.9327	+	25.3447i	0.361225	+	0.837414i
$917$	−0.0198866	−	0.0344446i	−0.000656714	−	0.00113746i
$918$		0			0
$919$	−14.0757	+	24.3798i	−0.464315	+	0.804216i	−0.999170	−	0.0407270i	$-0.987033\pi$
$919$	−14.0757	+	24.3798i	−0.464315	+	0.804216i	0.534856	+	0.844943i	$0.320366\pi$
$920$	−19.7909	−	2.31323i	−0.652488	−	0.0762649i
$921$		0			0
$922$	0.218170	+	0.0517073i	0.00718505	+	0.00170289i
$923$	−0.547437	+	9.39913i	−0.0180191	+	0.309376i
$924$		0			0
$925$	0.555133	−	0.131569i	0.0182527	−	0.00432596i
$926$	−1.16017	−	6.57965i	−0.0381256	−	0.216221i
$927$		0			0
$928$	−3.03728	+	17.2253i	−0.0997035	+	0.565447i
$929$	2.19545	+	37.6944i	0.0720304	+	1.23671i	0.819758	+	0.572709i	$0.194108\pi$
$929$	2.19545	+	37.6944i	0.0720304	+	1.23671i	−0.747728	+	0.664005i	$0.768855\pi$
$930$		0			0
$931$	−30.2352	−	40.6130i	−0.990920	−	1.33104i
$932$	−11.9892	−	16.1043i	−0.392721	−	0.527515i
$933$		0			0
$934$	−0.155518	−	2.67015i	−0.00508872	−	0.0873699i
$935$	7.52440	−	42.6730i	0.246074	−	1.39556i
$936$		0			0
$937$	4.74619	+	26.9170i	0.155051	+	0.879339i	0.958739	+	0.284288i	$0.0917572\pi$
$937$	4.74619	+	26.9170i	0.155051	+	0.879339i	−0.803688	+	0.595051i	$0.797132\pi$
$938$	0.0246202	−	0.00583509i	0.000803877	−	0.000190522i
$939$		0			0
$940$	−0.345629	+	5.93422i	−0.0112732	+	0.193553i
$941$	48.2438	+	11.4340i	1.57270	+	0.372738i	0.922184	−	0.386752i	$-0.126403\pi$
$941$	48.2438	+	11.4340i	1.57270	+	0.372738i	0.650520	+	0.759489i	$0.274551\pi$
$942$		0			0
$943$	−18.4143	−	2.15233i	−0.599653	−	0.0700894i
$944$	−8.71245	+	15.0904i	−0.283566	+	0.491151i
$945$		0			0
$946$	0.722042	+	1.25061i	0.0234756	+	0.0406610i
$947$	2.62943	+	6.09569i	0.0854449	+	0.198083i	0.955581	−	0.294727i	$-0.0952288\pi$
$947$	2.62943	+	6.09569i	0.0854449	+	0.198083i	−0.870137	+	0.492811i	$0.835970\pi$
$948$		0			0
$949$	5.44652	−	5.77298i	0.176802	−	0.187399i
$950$	8.73988	−	4.38933i	0.283559	−	0.142409i
$951$		0			0
$952$	−0.0136959	+	0.0457474i	−0.000443885	+	0.00148268i
$953$	−3.58202	+	3.00567i	−0.116033	+	0.0973632i	−0.698958	−	0.715163i	$-0.746353\pi$
$953$	−3.58202	+	3.00567i	−0.116033	+	0.0973632i	0.582925	+	0.812526i	$0.301908\pi$
$954$		0			0
$955$	−36.6750	−	30.7739i	−1.18677	−	0.995822i
$956$	8.00805	−	5.26697i	0.258999	−	0.170346i
$957$		0			0
$958$	9.54770	−	1.11597i	0.308472	−	0.0360552i
$959$	0.000429178	0	0.000994947i	1.38589e−5	0	3.21285e-5i
$960$		0			0
$961$	45.2987	+	22.7499i	1.46125	+	0.733866i
$962$	−0.153119	+	0.0557307i	−0.00493675	+	0.00179683i
$963$		0			0
$964$	−0.631389	−	0.229807i	−0.0203357	−	0.00740158i
$965$	−40.6778	−	43.1160i	−1.30947	−	1.38795i
$966$		0			0
$967$	7.81249	+	5.13836i	0.251233	+	0.165238i	0.668879	−	0.743371i	$-0.266774\pi$
$967$	7.81249	+	5.13836i	0.251233	+	0.165238i	−0.417646	+	0.908610i	$0.637145\pi$
$968$	0.613001	+	2.04756i	0.0197026	+	0.0658112i
$969$		0			0
$970$	−9.38860	+	12.6111i	−0.301450	+	0.404917i
$971$	33.5606			1.07701			0.538505	−	0.842622i	$-0.318989\pi$
$971$	33.5606			1.07701			0.538505	+	0.842622i	$0.318989\pi$
$972$		0			0
$973$	0.0119829			0.000384153
$974$	0.708990	−	0.952339i	0.0227175	−	0.0305149i
$975$		0			0
$976$	−6.59888	−	22.0418i	−0.211225	−	0.705541i
$977$	−5.89799	−	3.87917i	−0.188693	−	0.124106i	0.451647	−	0.892196i	$-0.350836\pi$
$977$	−5.89799	−	3.87917i	−0.188693	−	0.124106i	−0.640341	+	0.768091i	$0.721207\pi$
$978$		0			0
$979$	23.9426	+	25.3776i	0.765208	+	0.811073i
$980$	−37.5084	−	13.6519i	−1.19816	−	0.436095i
$981$		0			0
$982$	10.4369	−	3.79871i	0.333054	−	0.121222i
$983$	−37.4968	−	18.8316i	−1.19596	−	0.600635i	−0.264469	−	0.964394i	$-0.585197\pi$
$983$	−37.4968	−	18.8316i	−1.19596	−	0.600635i	−0.931493	+	0.363759i	$0.881493\pi$
$984$		0			0
$985$	−0.101637	+	0.235621i	−0.00323842	+	0.00750749i
$986$	−6.29743	+	0.736064i	−0.200551	+	0.0234411i
$987$		0			0
$988$	40.4573	−	26.6092i	1.28712	−	0.846550i
$989$	−4.83966	−	4.06096i	−0.153892	−	0.129131i
$990$		0			0
$991$	10.7027	−	8.98062i	0.339982	−	0.285279i	−0.456770	−	0.889585i	$-0.650994\pi$
$991$	10.7027	−	8.98062i	0.339982	−	0.285279i	0.796753	+	0.604306i	$0.206549\pi$
$992$	9.53669	−	31.8548i	0.302790	−	1.01139i
$993$		0			0
$994$	0.00722321	−	0.00362763i	0.000229106	−	0.000115061i
$995$	36.9663	−	39.1820i	1.17191	−	1.24215i
$996$		0			0
$997$	6.96965	+	16.1575i	0.220731	+	0.511712i	0.992215	−	0.124537i	$-0.0397445\pi$
$997$	6.96965	+	16.1575i	0.220731	+	0.511712i	−0.771484	+	0.636249i	$0.780485\pi$
$998$	2.26597	+	3.92477i	0.0717280	+	0.124237i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.190.5		144
3.2	odd	2		729.2.g.a.190.4		144
9.2	odd	6		729.2.g.b.433.5		144
9.4	even	3		81.2.g.a.31.5	✓	144
9.5	odd	6		243.2.g.a.145.4		144
9.7	even	3		729.2.g.c.433.4		144
81.7	even	27	inner	729.2.g.d.541.5		144
81.13	even	27		6561.2.a.c.1.43		72
81.20	odd	54		243.2.g.a.181.4		144
81.34	even	27		729.2.g.c.298.4		144
81.47	odd	54		729.2.g.b.298.5		144
81.61	even	27		81.2.g.a.34.5	yes	144
81.68	odd	54		6561.2.a.d.1.30		72
81.74	odd	54		729.2.g.a.541.4		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.31.5	✓	144	9.4	even	3
81.2.g.a.34.5	yes	144	81.61	even	27
243.2.g.a.145.4		144	9.5	odd	6
243.2.g.a.181.4		144	81.20	odd	54
729.2.g.a.190.4		144	3.2	odd	2
729.2.g.a.541.4		144	81.74	odd	54
729.2.g.b.298.5		144	81.47	odd	54
729.2.g.b.433.5		144	9.2	odd	6
729.2.g.c.298.4		144	81.34	even	27
729.2.g.c.433.4		144	9.7	even	3
729.2.g.d.190.5		144	1.1	even	1	trivial
729.2.g.d.541.5		144	81.7	even	27	inner
6561.2.a.c.1.43		72	81.13	even	27
6561.2.a.d.1.30		72	81.68	odd	54

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.197225 - 0.264919i) q^{2} +(0.542322 + 1.81148i) q^{4} +(-2.51951 - 1.65711i) q^{5} +(-0.00631548 - 0.00669402i) q^{7} +(1.20756 + 0.439517i) q^{8} +(-0.935909 + 0.340643i) q^{10} +(-3.18003 - 1.59707i) q^{11} +(1.40228 - 3.25085i) q^{13} +(-0.00301894 + 0.000352863i) q^{14} +(-2.80509 + 1.84493i) q^{16} +(-3.09319 - 2.59549i) q^{17} +(5.54096 - 4.64941i) q^{19} +(1.63544 - 5.46274i) q^{20} +(-1.05027 + 0.527467i) q^{22} +(3.52849 - 3.73998i) q^{23} +(1.62154 + 3.75915i) q^{25} +(-0.584647 - 1.01264i) q^{26} +(0.00870107 - 0.0150707i) q^{28} +(4.72215 + 0.551940i) q^{29} +(-8.79465 - 2.08437i) q^{31} +(-0.213914 + 3.67276i) q^{32} +(-1.29765 + 0.307548i) q^{34} +(0.00481921 + 0.0273311i) q^{35} +(0.0241986 - 0.137237i) q^{37} +(-0.138903 - 2.38488i) q^{38} +(-2.31414 - 3.10843i) q^{40} +(-2.15318 - 2.89222i) q^{41} +(-0.0714431 - 1.22663i) q^{43} +(1.16847 - 6.62670i) q^{44} +(-0.294886 - 1.67238i) q^{46} +(-1.01434 + 0.240402i) q^{47} +(0.407009 - 6.98807i) q^{49} +(1.31568 + 0.311821i) q^{50} +(6.64935 + 0.777197i) q^{52} +(1.88778 - 3.26973i) q^{53} +(5.36561 + 9.29351i) q^{55} +(-0.00468420 - 0.0108592i) q^{56} +(1.07754 - 1.14213i) q^{58} +(4.63792 - 2.32925i) q^{59} +(-1.96546 + 6.56510i) q^{61} +(-2.28671 + 1.91878i) q^{62} +(-4.21308 - 3.53519i) q^{64} +(-8.92009 + 5.86684i) q^{65} +(-8.26821 + 0.966415i) q^{67} +(3.02419 - 7.01085i) q^{68} +(0.00819099 + 0.00411367i) q^{70} +(-2.49894 + 0.909541i) q^{71} +(2.10657 + 0.766729i) q^{73} +(-0.0315840 - 0.0334771i) q^{74} +(11.4273 + 7.51586i) q^{76} +(0.00939260 + 0.0313735i) q^{77} +(-2.46941 + 3.31699i) q^{79} +10.1247 q^{80} -1.19086 q^{82} +(-7.70358 + 10.3477i) q^{83} +(3.49231 + 11.6651i) q^{85} +(-0.339047 - 0.222995i) q^{86} +(-3.13814 - 3.32624i) q^{88} +(-9.21313 - 3.35330i) q^{89} +(-0.0306173 + 0.0111438i) q^{91} +(8.68850 + 4.36353i) q^{92} +(-0.136365 + 0.316129i) q^{94} +(-21.6651 + 2.53229i) q^{95} +(13.1887 - 8.67437i) q^{97} +(-1.77100 - 1.48604i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

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