LMFDB - Embedded newform 441.2.bg.a.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(17,441)]

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([21, 25]))

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

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

chi := DirichletCharacter("441.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bg (of order $42$, 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:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			26.1
Character	$\chi$	$=$	441.26
Dual form			441.2.bg.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.68471 - 0.201191i) q^{2} +(5.18952 + 0.782194i) q^{4} +(-0.00530717 - 0.00492433i) q^{5} +(-1.62374 + 2.08889i) q^{7} +(-8.52551 - 1.94589i) q^{8} +O(q^{10})$	\(q+(-2.68471 - 0.201191i) q^{2} +(5.18952 + 0.782194i) q^{4} +(-0.00530717 - 0.00492433i) q^{5} +(-1.62374 + 2.08889i) q^{7} +(-8.52551 - 1.94589i) q^{8} +(0.0132575 + 0.0142882i) q^{10} +(1.87564 - 2.75105i) q^{11} +(-2.95636 - 6.13894i) q^{13} +(4.77955 - 5.28137i) q^{14} +(12.4671 + 3.84558i) q^{16} +(-1.89039 + 4.81664i) q^{17} +(0.904202 + 0.522041i) q^{19} +(-0.0236899 - 0.0297062i) q^{20} +(-5.58902 + 7.00841i) q^{22} +(3.40428 - 1.33608i) q^{23} +(-0.373647 - 4.98597i) q^{25} +(6.70186 + 17.0761i) q^{26} +(-10.0604 + 9.57025i) q^{28} +(0.670125 - 0.534407i) q^{29} +(-0.262107 + 0.151328i) q^{31} +(-16.4162 - 6.44288i) q^{32} +(6.04421 - 12.5509i) q^{34} +(0.0189039 - 0.00309023i) q^{35} +(5.03306 - 0.758612i) q^{37} +(-2.32249 - 1.58345i) q^{38} +(0.0356641 + 0.0523096i) q^{40} +(1.23674 - 5.41853i) q^{41} +(-1.02261 - 4.48033i) q^{43} +(11.8855 - 12.8095i) q^{44} +(-9.40831 + 2.90208i) q^{46} +(0.767589 - 10.2428i) q^{47} +(-1.72691 - 6.78364i) q^{49} +13.4610i q^{50} +(-10.5402 - 34.1706i) q^{52} +(0.784657 - 5.20586i) q^{53} +(-0.0235014 + 0.00536404i) q^{55} +(17.9080 - 14.6492i) q^{56} +(-1.90661 + 1.29990i) q^{58} +(4.69436 - 4.35573i) q^{59} +(1.33340 + 8.84651i) q^{61} +(0.734128 - 0.353537i) q^{62} +(19.2671 + 9.27855i) q^{64} +(-0.0145403 + 0.0471385i) q^{65} +(0.0388745 + 0.0673326i) q^{67} +(-13.5778 + 23.5174i) q^{68} +(-0.0513731 + 0.00449306i) q^{70} +(-11.5277 - 9.19301i) q^{71} +(-13.2312 + 0.991545i) q^{73} +(-13.6649 + 1.02404i) q^{74} +(4.28404 + 3.41641i) q^{76} +(2.70109 + 8.38500i) q^{77} +(6.84313 - 11.8526i) q^{79} +(-0.0472279 - 0.0818011i) q^{80} +(-4.41046 + 14.2983i) q^{82} +(0.491582 + 0.236733i) q^{83} +(0.0337513 - 0.0162538i) q^{85} +(1.84400 + 12.2341i) q^{86} +(-21.3440 + 19.8043i) q^{88} +(-7.67173 + 5.23050i) q^{89} +(17.6239 + 3.79257i) q^{91} +(18.7117 - 4.27081i) q^{92} +(-4.12150 + 27.3444i) q^{94} +(-0.00222805 - 0.00722315i) q^{95} +8.02999i q^{97} +(3.27144 + 18.5595i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) $ 216 * q - 16 * q^4 + 2 * q^7	$ 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) $ 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{17}{42}\right)$	$-1$

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 $

$2$	−2.68471	−	0.201191i	−1.89838	−	0.142264i	−0.926278	−	0.376840i	$-0.877010\pi$
$2$	−2.68471	−	0.201191i	−1.89838	−	0.142264i	−0.972098	+	0.234577i	$0.924630\pi$
$3$		0			0
$3$		0			0
$4$	5.18952	+	0.782194i	2.59476	+	0.391097i
$5$	−0.00530717	−	0.00492433i	−0.00237344	−	0.00220223i	0.678985	−	0.734152i	$-0.262420\pi$
$5$	−0.00530717	−	0.00492433i	−0.00237344	−	0.00220223i	−0.681359	+	0.731950i	$0.738611\pi$
$6$		0			0
$7$	−1.62374	+	2.08889i	−0.613718	+	0.789526i
$7$	−1.62374	+	2.08889i	−0.613718	+	0.789526i
$8$	−8.52551	−	1.94589i	−3.01422	−	0.687977i
$9$		0			0
$10$	0.0132575	+	0.0142882i	0.00419238	+	0.00451831i
$11$	1.87564	−	2.75105i	0.565525	−	0.829473i	−0.431845	−	0.901948i	$-0.642137\pi$
$11$	1.87564	−	2.75105i	0.565525	−	0.829473i	0.997370	+	0.0724746i	$0.0230896\pi$
$12$		0			0
$13$	−2.95636	−	6.13894i	−0.819946	−	1.70264i	−0.704935	−	0.709272i	$-0.749024\pi$
$13$	−2.95636	−	6.13894i	−0.819946	−	1.70264i	−0.115011	−	0.993364i	$-0.536690\pi$
$14$	4.77955	−	5.28137i	1.27739	−	1.41151i
$15$		0			0
$16$	12.4671	+	3.84558i	3.11676	+	0.961394i
$17$	−1.89039	+	4.81664i	−0.458487	+	1.16821i	0.495566	+	0.868570i	$0.334961\pi$
$17$	−1.89039	+	4.81664i	−0.458487	+	1.16821i	−0.954054	+	0.299636i	$0.903135\pi$
$18$		0			0
$19$	0.904202	+	0.522041i	0.207438	+	0.119764i	0.600120	−	0.799910i	$-0.295119\pi$
$19$	0.904202	+	0.522041i	0.207438	+	0.119764i	−0.392682	+	0.919674i	$0.628453\pi$
$20$	−0.0236899	−	0.0297062i	−0.00529722	−	0.00664250i
$21$		0			0
$22$	−5.58902	+	7.00841i	−1.19158	+	1.49420i
$23$	3.40428	−	1.33608i	0.709842	−	0.278592i	0.0171773	−	0.999852i	$-0.494532\pi$
$23$	3.40428	−	1.33608i	0.709842	−	0.278592i	0.692664	+	0.721260i	$0.256437\pi$
$24$		0			0
$25$	−0.373647	−	4.98597i	−0.0747293	−	0.997193i
$26$	6.70186	+	17.0761i	1.31434	+	3.34889i
$27$		0			0
$28$	−10.0604	+	9.57025i	−1.90123	+	1.80861i
$29$	0.670125	−	0.534407i	0.124439	−	0.0992368i	−0.559293	−	0.828970i	$-0.688927\pi$
$29$	0.670125	−	0.534407i	0.124439	−	0.0992368i	0.683732	+	0.729733i	$0.260356\pi$
$30$		0			0
$31$	−0.262107	+	0.151328i	−0.0470759	+	0.0271793i	−0.523353	−	0.852116i	$-0.675319\pi$
$31$	−0.262107	+	0.151328i	−0.0470759	+	0.0271793i	0.476277	+	0.879295i	$0.341986\pi$
$32$	−16.4162	−	6.44288i	−2.90200	−	1.13895i
$33$		0			0
$34$	6.04421	−	12.5509i	1.03657	−	2.15247i
$35$	0.0189039	−	0.00309023i	0.00319534	−	0.000522343i
$36$		0			0
$37$	5.03306	−	0.758612i	0.827430	−	0.124715i	0.278345	−	0.960481i	$-0.410214\pi$
$37$	5.03306	−	0.758612i	0.827430	−	0.124715i	0.549085	+	0.835766i	$0.314976\pi$
$38$	−2.32249	−	1.58345i	−0.376757	−	0.256869i
$39$		0			0
$40$	0.0356641	+	0.0523096i	0.00563899	+	0.00827088i
$41$	1.23674	−	5.41853i	0.193147	−	0.846232i	−0.781753	−	0.623588i	$-0.785674\pi$
$41$	1.23674	−	5.41853i	0.193147	−	0.846232i	0.974900	−	0.222644i	$-0.0714686\pi$
$42$		0			0
$43$	−1.02261	−	4.48033i	−0.155946	−	0.683243i	−0.991088	−	0.133209i	$-0.957472\pi$
$43$	−1.02261	−	4.48033i	−0.155946	−	0.683243i	0.835142	−	0.550034i	$-0.185385\pi$
$44$	11.8855	−	12.8095i	1.79181	−	1.93111i
$45$		0			0
$46$	−9.40831	+	2.90208i	−1.38718	+	0.427888i
$47$	0.767589	−	10.2428i	0.111964	−	1.49406i	−0.604595	−	0.796533i	$-0.706665\pi$
$47$	0.767589	−	10.2428i	0.111964	−	1.49406i	0.716559	−	0.697527i	$-0.245716\pi$
$48$		0			0
$49$	−1.72691	−	6.78364i	−0.246701	−	0.969092i
$50$			13.4610i			1.90368i
$51$		0			0
$52$	−10.5402	−	34.1706i	−1.46167	−	4.73861i
$53$	0.784657	−	5.20586i	0.107781	−	0.715080i	−0.868038	−	0.496498i	$-0.834619\pi$
$53$	0.784657	−	5.20586i	0.107781	−	0.715080i	0.975819	−	0.218582i	$-0.0701430\pi$
$54$		0			0
$55$	−0.0235014	+	0.00536404i	−0.00316893	+	0.000723287i
$56$	17.9080	−	14.6492i	2.39306	−	1.95758i
$57$		0			0
$58$	−1.90661	+	1.29990i	−0.250350	+	0.170686i
$59$	4.69436	−	4.35573i	0.611154	−	0.567068i	−0.312682	−	0.949858i	$-0.601227\pi$
$59$	4.69436	−	4.35573i	0.611154	−	0.567068i	0.923835	+	0.382790i	$0.125037\pi$
$60$		0			0
$61$	1.33340	+	8.84651i	0.170724	+	1.13268i	0.895945	+	0.444164i	$0.146499\pi$
$61$	1.33340	+	8.84651i	0.170724	+	1.13268i	−0.725221	+	0.688516i	$0.758263\pi$
$62$	0.734128	−	0.353537i	0.0932343	−	0.0448993i
$63$		0			0
$64$	19.2671	+	9.27855i	2.40839	+	1.15982i
$65$	−0.0145403	+	0.0471385i	−0.00180350	+	0.00584681i
$66$		0			0
$67$	0.0388745	+	0.0673326i	0.00474927	+	0.00822599i	0.868390	−	0.495881i	$-0.165155\pi$
$67$	0.0388745	+	0.0673326i	0.00474927	+	0.00822599i	−0.863641	+	0.504107i	$0.831822\pi$
$68$	−13.5778	+	23.5174i	−1.64655	+	2.85190i
$69$		0			0
$70$	−0.0513731	+	0.00449306i	−0.00614026	+	0.000537024i
$71$	−11.5277	−	9.19301i	−1.36808	−	1.09101i	−0.985975	−	0.166892i	$-0.946627\pi$
$71$	−11.5277	−	9.19301i	−1.36808	−	1.09101i	−0.382108	−	0.924118i	$-0.624802\pi$
$72$		0			0
$73$	−13.2312	+	0.991545i	−1.54860	+	0.116052i	−0.821392	−	0.570365i	$-0.806802\pi$
$73$	−13.2312	+	0.991545i	−1.54860	+	0.116052i	−0.727209	+	0.686416i	$0.759183\pi$
$74$	−13.6649	+	1.02404i	−1.58852	+	0.119043i
$75$		0			0
$76$	4.28404	+	3.41641i	0.491413	+	0.391889i
$77$	2.70109	+	8.38500i	0.307817	+	0.955559i
$78$		0			0
$79$	6.84313	−	11.8526i	0.769912	−	1.33353i	−0.167698	−	0.985838i	$-0.553633\pi$
$79$	6.84313	−	11.8526i	0.769912	−	1.33353i	0.937610	−	0.347689i	$-0.113033\pi$
$80$	−0.0472279	−	0.0818011i	−0.00528024	−	0.00914564i
$81$		0			0
$82$	−4.41046	+	14.2983i	−0.487053	+	1.57899i
$83$	0.491582	+	0.236733i	0.0539581	+	0.0259848i	0.460668	−	0.887572i	$-0.347610\pi$
$83$	0.491582	+	0.236733i	0.0539581	+	0.0259848i	−0.406710	+	0.913557i	$0.633324\pi$
$84$		0			0
$85$	0.0337513	−	0.0162538i	0.00366085	−	0.00176297i
$86$	1.84400	+	12.2341i	0.198843	+	1.31924i
$87$		0			0
$88$	−21.3440	+	19.8043i	−2.27528	+	2.11115i
$89$	−7.67173	+	5.23050i	−0.813202	+	0.554432i	−0.896989	−	0.442052i	$-0.854251\pi$
$89$	−7.67173	+	5.23050i	−0.813202	+	0.554432i	0.0837875	+	0.996484i	$0.473298\pi$
$90$		0			0
$91$	17.6239	+	3.79257i	1.84749	+	0.397569i
$92$	18.7117	−	4.27081i	1.95083	−	0.445263i
$93$		0			0
$94$	−4.12150	+	27.3444i	−0.425101	+	2.82036i
$95$	−0.00222805	−	0.00722315i	−0.000228593	−	0.000741080i
$96$		0			0
$97$			8.02999i			0.815322i	0.913133	+	0.407661i	$0.133656\pi$
$97$			8.02999i			0.815322i	−0.913133	+	0.407661i	$0.866344\pi$
$98$	3.27144	+	18.5595i	0.330465	+	1.87480i
$99$		0			0
$100$	1.96095	−	26.1670i	0.196095	−	2.61670i
$101$	9.82484	−	3.03056i	0.977609	−	0.301552i	0.235531	−	0.971867i	$-0.424317\pi$
$101$	9.82484	−	3.03056i	0.977609	−	0.301552i	0.742077	+	0.670314i	$0.233841\pi$
$102$		0			0
$103$	10.4748	−	11.2891i	1.03211	−	1.11235i	0.0385276	−	0.999258i	$-0.487733\pi$
$103$	10.4748	−	11.2891i	1.03211	−	1.11235i	0.993584	−	0.113095i	$-0.0360763\pi$
$104$	13.2587	+	58.0904i	1.30013	+	5.69623i
$105$		0			0
$106$	−3.15395	+	13.8184i	−0.306339	+	1.34216i
$107$	8.94057	+	13.1134i	0.864318	+	1.26772i	0.962150	+	0.272519i	$0.0878567\pi$
$107$	8.94057	+	13.1134i	0.864318	+	1.26772i	−0.0978326	+	0.995203i	$0.531191\pi$
$108$		0			0
$109$	1.07416	+	0.732353i	0.102886	+	0.0701467i	0.613670	−	0.789562i	$-0.289692\pi$
$109$	1.07416	+	0.732353i	0.102886	+	0.0701467i	−0.510784	+	0.859709i	$0.670645\pi$
$110$	0.0641736	−	0.00967262i	0.00611872	−	0.000922248i
$111$		0			0
$112$	−28.2763	+	19.7981i	−2.67186	+	1.87074i
$113$	1.46231	−	3.03651i	0.137562	−	0.285651i	−0.820795	−	0.571223i	$-0.806469\pi$
$113$	1.46231	−	3.03651i	0.137562	−	0.285651i	0.958357	+	0.285572i	$0.0921835\pi$
$114$		0			0
$115$	−0.0246464	−	0.00967300i	−0.00229829	−	0.000902012i
$116$	3.89564	−	2.24915i	0.361701	−	0.208828i
$117$		0			0
$118$	−13.4793	+	10.7494i	−1.24087	+	0.989563i
$119$	−6.99191	−	11.7698i	−0.640947	−	1.07894i
$120$		0			0
$121$	−0.0315259	−	0.0803267i	−0.00286599	−	0.00730243i
$122$	−1.79994	−	24.0186i	−0.162959	−	2.17454i
$123$		0			0
$124$	−1.47858	+	0.580300i	−0.132780	+	0.0521124i
$125$	−0.0451393	+	0.0566030i	−0.00403739	+	0.00506272i
$126$		0			0
$127$	0.947155	+	1.18770i	0.0840464	+	0.105391i	0.822077	−	0.569377i	$-0.192815\pi$
$127$	0.947155	+	1.18770i	0.0840464	+	0.105391i	−0.738030	+	0.674767i	$0.764244\pi$
$128$	−19.3147	−	11.1513i	−1.70719	−	0.985648i
$129$		0			0
$130$	0.0485203	−	0.123628i	0.00425551	−	0.0108429i
$131$	−9.45144	−	2.91538i	−0.825776	−	0.254718i	−0.147068	−	0.989126i	$-0.546984\pi$
$131$	−9.45144	−	2.91538i	−0.825776	−	0.254718i	−0.678708	+	0.734408i	$0.737460\pi$
$132$		0			0
$133$	−2.55868	+	1.04112i	−0.221866	+	0.0902761i
$134$	−0.0908200	−	0.188590i	−0.00784565	−	0.0162917i
$135$		0			0
$136$	25.4892	−	37.3858i	2.18568	−	3.20580i
$137$	1.17569	+	1.26710i	0.100446	+	0.108255i	0.781274	−	0.624188i	$-0.214570\pi$
$137$	1.17569	+	1.26710i	0.100446	+	0.108255i	−0.680828	+	0.732444i	$0.738380\pi$
$138$		0			0
$139$	−8.04117	−	1.83534i	−0.682043	−	0.155672i	−0.132558	−	0.991175i	$-0.542319\pi$
$139$	−8.04117	−	1.83534i	−0.682043	−	0.155672i	−0.549485	+	0.835503i	$0.685176\pi$
$140$	0.100519	−	0.00125029i	0.00849542	−	0.000105669i
$141$		0			0
$142$	29.0989	+	26.9998i	2.44192	+	2.26578i
$143$	−22.4336	−	3.38132i	−1.87599	−	0.282760i
$144$		0			0
$145$	−0.00618806		0.000463731i	−0.000513891		3.85108e-5i
$146$	35.7215			2.95634
$147$		0			0
$148$	26.7126			2.19576
$149$	−20.2332	−	1.51627i	−1.65757	−	0.124218i	−0.787228	−	0.616662i	$-0.788484\pi$
$149$	−20.2332	−	1.51627i	−1.65757	−	0.124218i	−0.870344	+	0.492445i	$0.836103\pi$
$150$		0			0
$151$	−1.08401	−	0.163388i	−0.0882153	−	0.0132963i	0.104786	−	0.994495i	$-0.466584\pi$
$151$	−1.08401	−	0.163388i	−0.0882153	−	0.0132963i	−0.193002	+	0.981198i	$0.561822\pi$
$152$	−6.69295	−	6.21015i	−0.542870	−	0.503709i
$153$		0			0
$154$	−5.56465	−	23.0547i	−0.448412	−	1.85780i
$155$	0.00213624		0.000487582i	0.000171587		3.91635e-5i
$156$		0			0
$157$	8.94657	+	9.64211i	0.714014	+	0.769524i	0.980965	−	0.194186i	$-0.0622065\pi$
$157$	8.94657	+	9.64211i	0.714014	+	0.769524i	−0.266950	+	0.963710i	$0.586016\pi$
$158$	−20.7565	+	30.4441i	−1.65129	+	2.42200i
$159$		0			0
$160$	0.0553966	+	0.115032i	0.00437948	+	0.00909409i
$161$	−2.73676	+	9.28062i	−0.215687	+	0.731415i
$162$		0			0
$163$	−6.54013	−	2.01736i	−0.512263	−	0.158012i	0.0278381	−	0.999612i	$-0.491138\pi$
$163$	−6.54013	−	2.01736i	−0.512263	−	0.158012i	−0.540101	+	0.841600i	$0.681614\pi$
$164$	10.6564	−	27.1522i	0.832129	−	2.12023i
$165$		0			0
$166$	−1.27212	−	0.734462i	−0.0987360	−	0.0570053i
$167$	−4.50561	−	5.64986i	−0.348655	−	0.437199i	0.576322	−	0.817223i	$-0.304487\pi$
$167$	−4.50561	−	5.64986i	−0.348655	−	0.437199i	−0.924977	+	0.380023i	$0.875916\pi$
$168$		0			0
$169$	−20.8412	+	26.1340i	−1.60317	+	2.01031i
$170$	−0.0938827	+	0.0368462i	−0.00720047	+	0.00282598i
$171$		0			0
$172$	−1.80235	−	24.0506i	−0.137428	−	1.83384i
$173$	5.14607	+	13.1120i	0.391248	+	0.996884i	0.981806	+	0.189889i	$0.0608127\pi$
$173$	5.14607	+	13.1120i	0.391248	+	0.996884i	−0.590557	+	0.806996i	$0.701092\pi$
$174$		0			0
$175$	11.0218	+	7.31543i	0.833172	+	0.552994i
$176$	33.9630	−	27.0846i	2.56006	−	2.04158i
$177$		0			0
$178$	21.6487	−	12.4989i	1.62264	−	0.936831i
$179$	9.63083	+	3.77982i	0.719842	+	0.282517i	0.696848	−	0.717219i	$-0.254585\pi$
$179$	9.63083	+	3.77982i	0.719842	+	0.282517i	0.0229935	+	0.999736i	$0.492680\pi$
$180$		0			0
$181$	6.77836	−	14.0754i	0.503832	−	1.04622i	−0.481639	−	0.876370i	$-0.659958\pi$
$181$	6.77836	−	14.0754i	0.503832	−	1.04622i	0.985470	−	0.169848i	$-0.0543275\pi$
$182$	−46.5521	−	13.7277i	−3.45067	−	1.01757i
$183$		0			0
$184$	−31.6231	+	4.76641i	−2.33129	+	0.351385i
$185$	−0.0304470	−	0.0207584i	−0.00223850	−	0.00152619i
$186$		0			0
$187$	9.70513	+	14.2348i	0.709710	+	1.04095i
$188$	11.9952	−	52.5546i	0.874843	−	3.83294i
$189$		0			0
$190$	0.00452842	+	0.0198403i	0.000328526	+	0.00143937i
$191$	−4.15346	+	4.47636i	−0.300534	+	0.323898i	−0.865206	−	0.501417i	$-0.832812\pi$
$191$	−4.15346	+	4.47636i	−0.300534	+	0.323898i	0.564672	+	0.825315i	$0.309003\pi$
$192$		0			0
$193$	13.2675	−	4.09247i	0.955013	−	0.294582i	0.222191	−	0.975003i	$-0.428679\pi$
$193$	13.2675	−	4.09247i	0.955013	−	0.294582i	0.732822	+	0.680421i	$0.238203\pi$
$194$	1.61556	−	21.5582i	0.115991	−	1.54779i
$195$		0			0
$196$	−3.65570	−	36.5546i	−0.261122	−	2.61104i
$197$		−	7.41614i		−	0.528378i	−0.964471	−	0.264189i	$-0.914896\pi$
$197$		−	7.41614i		−	0.528378i	0.964471	−	0.264189i	$-0.0851043\pi$
$198$		0			0
$199$	6.59202	+	21.3708i	0.467296	+	1.51494i	0.816195	+	0.577776i	$0.196079\pi$
$199$	6.59202	+	21.3708i	0.467296	+	1.51494i	−0.348899	+	0.937160i	$0.613444\pi$
$200$	−6.51662	+	43.2350i	−0.460795	+	3.05717i
$201$		0			0
$202$	−26.9866	+	6.15951i	−1.89877	+	0.433381i
$203$	0.0282045	+	2.26756i	0.00197957	+	0.159151i
$204$		0			0
$205$	−0.0332462	+	0.0226669i	−0.00232202	+	0.00158313i
$206$	−30.3930	+	28.2006i	−2.11758	+	1.96483i
$207$		0			0
$208$	−13.2493	−	87.9034i	−0.918674	−	6.09501i
$209$	3.13212	−	1.50835i	0.216653	−	0.104335i
$210$		0			0
$211$	−1.26934	−	0.611281i	−0.0873849	−	0.0420823i	0.389681	−	0.920950i	$-0.372585\pi$
$211$	−1.26934	−	0.611281i	−0.0873849	−	0.0420823i	−0.477066	+	0.878868i	$0.658300\pi$
$212$	8.14399	−	26.4022i	0.559332	−	1.81331i
$213$		0			0
$214$	−21.3645	−	37.0045i	−1.46045	−	2.52957i
$215$	−0.0166355	+	0.0288135i	−0.00113453	+	0.00196506i
$216$		0			0
$217$	0.109489	−	0.793231i	0.00743257	−	0.0538480i
$218$	−2.73647	−	2.18227i	−0.185337	−	0.147802i
$219$		0			0
$220$	−0.126157	+	0.00945414i	−0.00850549	+	0.000637398i
$221$	35.1577	−	2.63471i	2.36496	−	0.177230i
$222$		0			0
$223$	−13.9984	−	11.1634i	−0.937403	−	0.747554i	0.0303277	−	0.999540i	$-0.490345\pi$
$223$	−13.9984	−	11.1634i	−0.937403	−	0.747554i	−0.967731	+	0.251986i	$0.918916\pi$
$224$	40.1141	−	23.8300i	2.68024	−	1.59221i
$225$		0			0
$226$	−4.53679	+	7.85795i	−0.301783	+	0.522703i
$227$	−3.86805	−	6.69966i	−0.256731	−	0.444672i	0.708633	−	0.705577i	$-0.249312\pi$
$227$	−3.86805	−	6.69966i	−0.256731	−	0.444672i	−0.965364	+	0.260905i	$0.915979\pi$
$228$		0			0
$229$	−4.17778	+	13.5440i	−0.276075	+	0.895014i	0.706271	+	0.707942i	$0.250376\pi$
$229$	−4.17778	+	13.5440i	−0.276075	+	0.895014i	−0.982346	+	0.187072i	$0.940100\pi$
$230$	0.0642223	+	0.0309278i	0.00423469	+	0.00203932i
$231$		0			0
$232$	−6.75305	+	3.25210i	−0.443360	+	0.213511i
$233$	3.21363	+	21.3210i	0.210532	+	1.39679i	0.805290	+	0.592881i	$0.202010\pi$
$233$	3.21363	+	21.3210i	0.210532	+	1.39679i	−0.594758	+	0.803905i	$0.702752\pi$
$234$		0			0
$235$	−0.0545125	+	0.0505802i	−0.00355600	+	0.00329949i
$236$	27.7685	−	18.9323i	1.80758	−	1.23238i
$237$		0			0
$238$	16.4033	+	33.0052i	1.06326	+	2.13941i
$239$	14.3458	−	3.27434i	0.927954	−	0.211799i	0.268271	−	0.963343i	$-0.413548\pi$
$239$	14.3458	−	3.27434i	0.927954	−	0.211799i	0.659683	+	0.751544i	$0.270691\pi$
$240$		0			0
$241$	−0.217821	+	1.44515i	−0.0140311	+	0.0930903i	−0.994750	−	0.102332i	$-0.967370\pi$
$241$	−0.217821	+	1.44515i	−0.0140311	+	0.0930903i	0.980719	+	0.195422i	$0.0626077\pi$
$242$	0.0684769	+	0.221997i	0.00440186	+	0.0142705i
$243$		0			0
$244$			46.9521i			3.00580i
$245$	−0.0242399	+	0.0445058i	−0.00154863	+	0.00284337i
$246$		0			0
$247$	0.531636	−	7.09418i	0.0338272	−	0.451392i
$248$	2.52907	−	0.780114i	0.160596	−	0.0495373i
$249$		0			0
$250$	0.132574	−	0.142881i	0.00838472	−	0.00903658i
$251$	2.96961	+	13.0107i	0.187440	+	0.821229i	0.977960	+	0.208793i	$0.0669534\pi$
$251$	2.96961	+	13.0107i	0.187440	+	0.821229i	−0.790520	+	0.612437i	$0.790189\pi$
$252$		0			0
$253$	2.70956	−	11.8714i	0.170349	−	0.746346i
$254$	−2.30388	−	3.37917i	−0.144558	−	0.212028i
$255$		0			0
$256$	14.2727	+	9.73098i	0.892045	+	0.608186i
$257$	−27.6732	+	4.17106i	−1.72621	+	0.260184i	−0.935833	−	0.352444i	$-0.885351\pi$
$257$	−27.6732	+	4.17106i	−1.72621	+	0.260184i	−0.790372	+	0.612627i	$0.790113\pi$
$258$		0			0
$259$	−6.58775	+	11.7453i	−0.409343	+	0.729817i
$260$	−0.112329	+	0.233253i	−0.00696633	+	0.0144657i
$261$		0			0
$262$	24.7878	+	9.72850i	1.53140	+	0.601029i
$263$	7.42313	−	4.28574i	0.457730	−	0.264270i	−0.253360	−	0.967372i	$-0.581536\pi$
$263$	7.42313	−	4.28574i	0.457730	−	0.264270i	0.711089	+	0.703102i	$0.248202\pi$
$264$		0			0
$265$	−0.0297997	+	0.0237645i	−0.00183058	+	0.00145984i
$266$	7.07877	−	2.28031i	0.434027	−	0.139815i
$267$		0			0
$268$	0.149073	+	0.379831i	0.00910607	+	0.0232019i
$269$	2.21406	+	29.5445i	0.134993	+	1.80136i	0.495503	+	0.868606i	$0.334984\pi$
$269$	2.21406	+	29.5445i	0.134993	+	1.80136i	−0.360510	+	0.932756i	$0.617397\pi$
$270$		0			0
$271$	15.0846	−	5.92025i	0.916322	−	0.359630i	0.140135	−	0.990132i	$-0.455246\pi$
$271$	15.0846	−	5.92025i	0.916322	−	0.359630i	0.776187	+	0.630503i	$0.217151\pi$
$272$	−42.0904	+	52.7796i	−2.55210	+	3.20024i
$273$		0			0
$274$	−2.90146	−	3.63832i	−0.175284	−	0.219799i
$275$	−14.4175	−	8.32393i	−0.869407	−	0.501952i
$276$		0			0
$277$	−0.971748	+	2.47597i	−0.0583867	+	0.148767i	−0.957090	−	0.289789i	$-0.906415\pi$
$277$	−0.971748	+	2.47597i	−0.0583867	+	0.148767i	0.898704	+	0.438556i	$0.144510\pi$
$278$	21.2189	+	6.54518i	1.27263	+	0.392554i
$279$		0			0
$280$	−0.167178	−	0.0104391i	−0.00999082	−	0.000623858i
$281$	−5.89574	−	12.2426i	−0.351710	−	0.730334i	0.647794	−	0.761815i	$-0.275692\pi$
$281$	−5.89574	−	12.2426i	−0.351710	−	0.730334i	−0.999504	+	0.0314817i	$0.989977\pi$
$282$		0			0
$283$	−9.62222	+	14.1132i	−0.571982	+	0.838943i	−0.997829	−	0.0658517i	$-0.979024\pi$
$283$	−9.62222	+	14.1132i	−0.571982	+	0.838943i	0.425848	+	0.904795i	$0.359976\pi$
$284$	−52.6324	−	56.7242i	−3.12316	−	3.36596i
$285$		0			0
$286$	59.5474	+	13.5913i	3.52111	+	0.803670i
$287$	9.31054	+	11.3817i	0.549584	+	0.671842i
$288$		0			0
$289$	−7.16454	−	6.64772i	−0.421443	−	0.391042i
$290$	0.0165198	+	0.00248997i	0.000970079	+	0.000146216i
$291$		0			0
$292$	−69.4394	−	5.20377i	−4.06364	−	0.304527i
$293$	−6.94400			−0.405673			−0.202836	−	0.979213i	$-0.565016\pi$
$293$	−6.94400			−0.405673			−0.202836	+	0.979213i	$0.565016\pi$
$294$		0			0
$295$	−0.0463628			−0.00269935
$296$	−44.3856	−	3.32624i	−2.57986	−	0.193334i
$297$		0			0
$298$	54.0153	+	8.14149i	3.12902	+	0.471624i
$299$	−18.2664	−	16.9487i	−1.05637	−	0.980171i
$300$		0			0
$301$	11.0193	+	5.13880i	0.635145	+	0.296195i
$302$	2.87737	+	0.656742i	0.165574	+	0.0377912i
$303$		0			0
$304$	9.26518	+	9.98549i	0.531395	+	0.572707i
$305$	0.0364866	−	0.0535160i	0.00208922	−	0.00306432i
$306$		0			0
$307$	−11.8874	−	24.6843i	−0.678447	−	1.40881i	−0.900970	−	0.433882i	$-0.857143\pi$
$307$	−11.8874	−	24.6843i	−0.678447	−	1.40881i	0.222523	−	0.974927i	$-0.428571\pi$
$308$	7.45865	+	45.6269i	0.424996	+	2.59983i
$309$		0			0
$310$	−0.00563707	−	0.00173881i	−0.000320164	−	9.87576e-5i
$311$	1.52915	−	3.89622i	0.0867103	−	0.220934i	−0.880941	−	0.473227i	$-0.843089\pi$
$311$	1.52915	−	3.89622i	0.0867103	−	0.220934i	0.967651	+	0.252292i	$0.0811844\pi$
$312$		0			0
$313$	7.98091	+	4.60778i	0.451108	+	0.260447i	0.708298	−	0.705914i	$-0.249463\pi$
$313$	7.98091	+	4.60778i	0.451108	+	0.260447i	−0.257190	+	0.966361i	$0.582797\pi$
$314$	−22.0790	−	27.6862i	−1.24599	−	1.56242i
$315$		0			0
$316$	44.7836	−	56.1569i	2.51928	−	3.15907i
$317$	7.81535	−	3.06730i	0.438954	−	0.172277i	−0.135564	−	0.990769i	$-0.543285\pi$
$317$	7.81535	−	3.06730i	0.438954	−	0.172277i	0.574518	+	0.818492i	$0.305190\pi$
$318$		0			0
$319$	−0.213271	−	2.84590i	−0.0119409	−	0.159340i
$320$	−0.0565631	−	0.144121i	−0.00316198	−	0.00805658i
$321$		0			0
$322$	9.21457	−	24.3651i	0.513508	−	1.35782i
$323$	−4.22378	+	3.36835i	−0.235017	+	0.187420i
$324$		0			0
$325$	−29.5039	+	17.0341i	−1.63658	+	0.944882i
$326$	17.1525	+	6.73185i	0.949988	+	0.372843i
$327$		0			0
$328$	−21.0877	+	43.7891i	−1.16438	+	2.41785i
$329$	20.1496	+	18.2350i	1.11088	+	1.00533i
$330$		0			0
$331$	11.3373	−	1.70883i	0.623156	−	0.0939257i	0.170128	−	0.985422i	$-0.445582\pi$
$331$	11.3373	−	1.70883i	0.623156	−	0.0939257i	0.453028	+	0.891496i	$0.350344\pi$
$332$	2.36590	+	1.61304i	0.129846	+	0.0885273i
$333$		0			0
$334$	10.9596	+	16.0747i	0.599680	+	0.879569i
$335$	0.000125255	0	0.000548776i	6.84339e−6	0	2.99829e-5i
$336$		0			0
$337$	−2.17085	−	9.51110i	−0.118254	−	0.518103i	−0.999008	−	0.0445297i	$-0.985821\pi$
$337$	−2.17085	−	9.51110i	−0.118254	−	0.518103i	0.880754	−	0.473573i	$-0.157036\pi$
$338$	61.2104	−	65.9692i	3.32941	−	3.58825i
$339$		0			0
$340$	0.187867	−	0.0579493i	0.0101885	−	0.00314274i
$341$	−0.0753073	+	1.00491i	−0.00407812	+	0.0544187i
$342$		0			0
$343$	16.9743	+	7.40758i	0.916527	+	0.399972i
$344$			40.1869i			2.16673i
$345$		0			0
$346$	−11.1777	−	36.2372i	−0.600916	−	1.94812i
$347$	−1.62712	+	10.7952i	−0.0873484	+	0.579519i	0.901749	+	0.432259i	$0.142283\pi$
$347$	−1.62712	+	10.7952i	−0.0873484	+	0.579519i	−0.989098	+	0.147260i	$0.952955\pi$
$348$		0			0
$349$	−27.5890	+	6.29701i	−1.47681	+	0.337071i	−0.883700	−	0.468054i	$-0.844955\pi$
$349$	−27.5890	+	6.29701i	−1.47681	+	0.337071i	−0.593105	+	0.805125i	$0.702098\pi$
$350$	−28.1186	−	21.8573i	−1.50300	−	1.16832i
$351$		0			0
$352$	−48.5155	+	33.0773i	−2.58588	+	1.76302i
$353$	−13.2524	+	12.2965i	−0.705357	+	0.654475i	−0.948959	−	0.315400i	$-0.897861\pi$
$353$	−13.2524	+	12.2965i	−0.705357	+	0.654475i	0.243602	+	0.969875i	$0.421671\pi$
$354$		0			0
$355$	0.0159099	+	0.105555i	0.000844407	+	0.00560228i
$356$	−43.9039	+	21.1430i	−2.32690	+	1.12058i
$357$		0			0
$358$	−25.0955	−	12.0854i	−1.32634	−	0.638731i
$359$	4.99805	−	16.2033i	0.263787	−	0.855176i	−0.722675	−	0.691188i	$-0.757088\pi$
$359$	4.99805	−	16.2033i	0.263787	−	0.855176i	0.986462	−	0.163988i	$-0.0524360\pi$
$360$		0			0
$361$	−8.95495	−	15.5104i	−0.471313	−	0.816338i
$362$	−21.0298	+	36.4246i	−1.10530	+	1.91444i
$363$		0			0
$364$	88.4933	+	33.4670i	4.63831	+	1.75415i
$365$	0.0751032	+	0.0598928i	0.00393108	+	0.00313493i
$366$		0			0
$367$	7.81435	−	0.585605i	0.407906	−	0.0305683i	0.130803	−	0.991408i	$-0.458245\pi$
$367$	7.81435	−	0.585605i	0.407906	−	0.0305683i	0.277103	+	0.960840i	$0.410626\pi$
$368$	47.5794	−	3.56558i	2.48025	−	0.185869i
$369$		0			0
$370$	0.0775648	+	0.0618559i	0.00403240	+	0.00321573i
$371$	9.60038	+	10.0920i	0.498427	+	0.523953i
$372$		0			0
$373$	11.7942	−	20.4281i	0.610680	−	1.05773i	−0.380447	−	0.924803i	$-0.624230\pi$
$373$	11.7942	−	20.4281i	0.610680	−	1.05773i	0.991126	−	0.132925i	$-0.0424370\pi$
$374$	−23.1915	−	40.1689i	−1.19921	−	2.07709i
$375$		0			0
$376$	−26.4754	+	85.8311i	−1.36536	+	4.42640i
$377$	−5.26182	−	2.53396i	−0.270998	−	0.130506i
$378$		0			0
$379$	−11.9634	+	5.76129i	−0.614520	+	0.295937i	−0.715133	−	0.698988i	$-0.753634\pi$
$379$	−11.9634	+	5.76129i	−0.614520	+	0.295937i	0.100613	+	0.994926i	$0.467920\pi$
$380$	−0.00591259	−	0.0392275i	−0.000303309	−	0.00201233i
$381$		0			0
$382$	12.0514	−	11.1821i	0.616604	−	0.572125i
$383$	8.67424	−	5.91400i	0.443233	−	0.302191i	−0.321062	−	0.947058i	$-0.604040\pi$
$383$	8.67424	−	5.91400i	0.443233	−	0.302191i	0.764295	+	0.644867i	$0.223087\pi$
$384$		0			0
$385$	0.0269554	−	0.0578016i	0.00137377	−	0.00294584i
$386$	−36.4426	+	8.31780i	−1.85488	+	0.423365i
$387$		0			0
$388$	−6.28102	+	41.6718i	−0.318870	+	2.11557i
$389$	−5.79775	−	18.7958i	−0.293957	−	0.952986i	−0.975274	−	0.220998i	$-0.929069\pi$
$389$	−5.79775	−	18.7958i	−0.293957	−	0.952986i	0.681317	−	0.731989i	$-0.261408\pi$
$390$		0			0
$391$			18.9229i			0.956972i
$392$	1.52254	+	61.1944i	0.0769001	+	3.09078i
$393$		0			0
$394$	−1.49206	+	19.9102i	−0.0751690	+	1.00306i
$395$	−0.0946840	+	0.0292062i	−0.00476407	+	0.00146952i
$396$		0			0
$397$	−11.6083	+	12.5108i	−0.582603	+	0.627897i	−0.953722	−	0.300688i	$-0.902784\pi$
$397$	−11.6083	+	12.5108i	−0.582603	+	0.627897i	0.371119	+	0.928585i	$0.378974\pi$
$398$	−13.3980	−	58.7007i	−0.671583	−	2.94240i
$399$		0			0
$400$	14.5156	−	63.5972i	0.725782	−	3.17986i
$401$	13.4122	+	19.6722i	0.669776	+	0.982380i	0.999269	+	0.0382225i	$0.0121696\pi$
$401$	13.4122	+	19.6722i	0.669776	+	0.982380i	−0.329494	+	0.944158i	$0.606878\pi$
$402$		0			0
$403$	1.70388	+	1.16168i	0.0848761	+	0.0578675i
$404$	53.3567	−	8.04223i	2.65460	−	0.400116i
$405$		0			0
$406$	0.380491	−	6.09340i	0.0188835	−	0.302410i
$407$	7.35320	−	15.2691i	0.364485	−	0.756861i
$408$		0			0
$409$	−22.3506	−	8.77198i	−1.10517	−	0.433747i	−0.258577	−	0.965991i	$-0.583254\pi$
$409$	−22.3506	−	8.77198i	−1.10517	−	0.433747i	−0.846591	+	0.532244i	$0.821349\pi$
$410$	0.0938168	−	0.0541652i	0.00463328	−	0.00267503i
$411$		0			0
$412$	63.1895	−	50.3919i	3.11312	−	2.48263i
$413$	1.47619	+	16.8786i	0.0726387	+	0.830541i
$414$		0			0
$415$	−0.00144315	−	0.00367710i	−7.08416e−5	−	0.000180502i
$416$	8.97968	+	119.825i	0.440265	+	5.87493i
$417$		0			0
$418$	−8.71228	+	3.41932i	−0.426132	+	0.167244i
$419$	7.48671	−	9.38803i	0.365750	−	0.458635i	−0.564570	−	0.825385i	$-0.690958\pi$
$419$	7.48671	−	9.38803i	0.365750	−	0.458635i	0.930320	+	0.366750i	$0.119529\pi$
$420$		0			0
$421$	−6.75745	−	8.47357i	−0.329338	−	0.412977i	0.589402	−	0.807840i	$-0.299363\pi$
$421$	−6.75745	−	8.47357i	−0.329338	−	0.412977i	−0.918740	+	0.394863i	$0.870792\pi$
$422$	3.28482	+	1.89649i	0.159903	+	0.0923198i
$423$		0			0
$424$	−16.8196	+	42.8557i	−0.816834	+	2.08126i
$425$	24.7219	+	7.62571i	1.19919	+	0.369901i
$426$		0			0
$427$	−20.6445	−	11.5792i	−0.999056	−	0.560355i
$428$	36.1401	+	75.0456i	1.74690	+	3.62747i
$429$		0			0
$430$	0.0504584	−	0.0740089i	0.00243332	−	0.00356903i
$431$	4.41112	+	4.75405i	0.212476	+	0.228995i	0.830293	−	0.557327i	$-0.188173\pi$
$431$	4.41112	+	4.75405i	0.212476	+	0.228995i	−0.617817	+	0.786322i	$0.711983\pi$
$432$		0			0
$433$	6.86075	+	1.56592i	0.329707	+	0.0752534i	0.384170	−	0.923262i	$-0.374488\pi$
$433$	6.86075	+	1.56592i	0.329707	+	0.0752534i	−0.0544634	+	0.998516i	$0.517345\pi$
$434$	−0.453536	+	2.10756i	−0.0217704	+	0.101166i
$435$		0			0
$436$	5.00156	+	4.64077i	0.239531	+	0.222252i
$437$	3.77565	+	0.569087i	0.180614	+	0.0272231i
$438$		0			0
$439$	−11.4425	−	0.857496i	−0.546120	−	0.0409260i	−0.201186	−	0.979553i	$-0.564480\pi$
$439$	−11.4425	−	0.857496i	−0.546120	−	0.0409260i	−0.344934	+	0.938627i	$0.612099\pi$
$440$	0.210799			0.0100495
$441$		0			0
$442$	−94.9183			−4.51480
$443$	7.19956	+	0.539533i	0.342061	+	0.0256340i	0.244654	−	0.969611i	$-0.421326\pi$
$443$	7.19956	+	0.539533i	0.342061	+	0.0256340i	0.0974080	+	0.995245i	$0.468945\pi$
$444$		0			0
$445$	0.0664719	+	0.0100190i	0.00315107	+	0.000474947i
$446$	35.3357	+	32.7867i	1.67319	+	1.55250i
$447$		0			0
$448$	−50.6667	+	25.1808i	−2.39378	+	1.18968i
$449$	4.70170	+	1.07313i	0.221887	+	0.0506442i	0.332019	−	0.943273i	$-0.392270\pi$
$449$	4.70170	+	1.07313i	0.221887	+	0.0506442i	−0.110132	+	0.993917i	$0.535127\pi$
$450$		0			0
$451$	−12.5870	−	13.5655i	−0.592697	−	0.638776i
$452$	9.96382	−	14.6142i	0.468659	−	0.687396i
$453$		0			0
$454$	9.03667	+	18.7648i	0.424112	+	0.880678i
$455$	−0.0748573	−	0.106914i	−0.00350937	−	0.00501220i
$456$		0			0
$457$	8.83743	+	2.72599i	0.413397	+	0.127516i	0.494476	−	0.869192i	$-0.335360\pi$
$457$	8.83743	+	2.72599i	0.413397	+	0.127516i	−0.0810782	+	0.996708i	$0.525836\pi$
$458$	13.9411	−	35.5212i	0.651423	−	1.65980i
$459$		0			0
$460$	−0.120337	−	0.0694765i	−0.00561074	−	0.00323936i
$461$	12.3337	+	15.4660i	0.574437	+	0.720322i	0.981153	−	0.193233i	$-0.0618974\pi$
$461$	12.3337	+	15.4660i	0.574437	+	0.720322i	−0.406715	+	0.913555i	$0.633326\pi$
$462$		0			0
$463$	15.7738	−	19.7797i	0.733069	−	0.919239i	−0.265929	−	0.963993i	$-0.585679\pi$
$463$	15.7738	−	19.7797i	0.733069	−	0.919239i	0.998998	+	0.0447534i	$0.0142502\pi$
$464$	10.4096	−	4.08546i	0.483253	−	0.189663i
$465$		0			0
$466$	−4.33805	−	57.8873i	−0.200956	−	2.68158i
$467$	−0.995317	−	2.53603i	−0.0460578	−	0.117353i	0.905994	−	0.423291i	$-0.139125\pi$
$467$	−0.995317	−	2.53603i	−0.0460578	−	0.117353i	−0.952051	+	0.305938i	$0.901030\pi$
$468$		0			0
$469$	−0.203772	−	0.0281264i	−0.00940934	−	0.00129876i
$470$	0.156526	−	0.124826i	0.00722003	−	0.00575778i
$471$		0			0
$472$	−48.4976	+	28.0001i	−2.23228	+	1.28881i
$473$	−14.2436	−	5.59022i	−0.654923	−	0.257038i
$474$		0			0
$475$	2.26503	−	4.70338i	0.103927	−	0.215806i
$476$	−27.0784	−	66.5487i	−1.24114	−	3.05025i
$477$		0			0
$478$	−39.1731	+	5.90440i	−1.79174	+	0.270061i
$479$	8.48606	+	5.78569i	0.387738	+	0.264355i	0.741462	−	0.670994i	$-0.234133\pi$
$479$	8.48606	+	5.78569i	0.387738	+	0.264355i	−0.353725	+	0.935350i	$0.615085\pi$
$480$		0			0
$481$	−19.5366	−	28.6549i	−0.890792	−	1.30655i
$482$	0.875538	−	3.83598i	0.0398797	−	0.174724i
$483$		0			0
$484$	−0.100773	−	0.441517i	−0.00458060	−	0.0200689i
$485$	0.0395424	−	0.0426165i	0.00179553	−	0.00193512i
$486$		0			0
$487$	11.0682	−	3.41408i	0.501546	−	0.154707i	−0.0336510	−	0.999434i	$-0.510713\pi$
$487$	11.0682	−	3.41408i	0.501546	−	0.154707i	0.535197	+	0.844727i	$0.320237\pi$
$488$	5.84647	−	78.0157i	0.264657	−	3.53160i
$489$		0			0
$490$	0.0740313	−	0.114608i	0.00334439	−	0.00517747i
$491$		−	34.9733i		−	1.57832i	−0.614186	−	0.789161i	$-0.710516\pi$
$491$		−	34.9733i		−	1.57832i	0.614186	−	0.789161i	$-0.289484\pi$
$492$		0			0
$493$	1.30725	+	4.23799i	0.0588754	+	0.190869i
$494$	−2.85457	+	18.9389i	−0.128433	+	0.852099i
$495$		0			0
$496$	−3.84965	+	0.878657i	−0.172854	+	0.0394529i
$497$	37.9212	−	9.15292i	1.70100	−	0.410565i
$498$		0			0
$499$	18.2652	−	12.4530i	0.817663	−	0.557473i	−0.0806940	−	0.996739i	$-0.525714\pi$
$499$	18.2652	−	12.4530i	0.817663	−	0.557473i	0.898357	+	0.439266i	$0.144761\pi$
$500$	−0.278526	+	0.258434i	−0.0124561	+	0.0115575i
$501$		0			0
$502$	−5.35490	−	35.5275i	−0.239001	−	1.58567i
$503$	−9.00251	+	4.33538i	−0.401402	+	0.193305i	−0.623683	−	0.781678i	$-0.714364\pi$
$503$	−9.00251	+	4.33538i	−0.401402	+	0.193305i	0.222281	+	0.974983i	$0.428650\pi$
$504$		0			0
$505$	−0.0670656	−	0.0322971i	−0.00298438	−	0.00143720i
$506$	−9.66279	+	31.3260i	−0.429563	+	1.39261i
$507$		0			0
$508$	3.98627	+	6.90443i	0.176862	+	0.306334i
$509$	−3.47997	+	6.02749i	−0.154247	+	0.267164i	−0.932785	−	0.360434i	$-0.882629\pi$
$509$	−3.47997	+	6.02749i	−0.154247	+	0.267164i	0.778538	+	0.627598i	$0.215962\pi$
$510$		0			0
$511$	19.4129	−	29.2486i	0.858778	−	1.29388i
$512$	−1.48644	−	1.18540i	−0.0656920	−	0.0523876i
$513$		0			0
$514$	75.1336	−	5.63048i	3.31400	−	0.248350i
$515$	−0.111183	+	0.00833201i	−0.00489931	+	0.000367152i
$516$		0			0
$517$	−26.7386	−	21.3234i	−1.17596	−	0.937800i
$518$	20.0492	−	30.2073i	0.880913	−	1.32723i
$519$		0			0
$520$	0.215690	−	0.373586i	0.00945863	−	0.0163828i
$521$	6.22953	+	10.7899i	0.272921	+	0.472712i	0.969608	−	0.244662i	$-0.0786770\pi$
$521$	6.22953	+	10.7899i	0.272921	+	0.472712i	−0.696688	+	0.717374i	$0.745344\pi$
$522$		0			0
$523$	4.20588	−	13.6351i	0.183910	−	0.596222i	−0.815927	−	0.578155i	$-0.803773\pi$
$523$	4.20588	−	13.6351i	0.183910	−	0.596222i	0.999837	−	0.0180666i	$-0.00575109\pi$
$524$	−46.7680	−	22.5223i	−2.04307	−	0.983891i
$525$		0			0
$526$	−20.7912	+	10.0125i	−0.906539	+	0.436566i
$527$	−0.233406	−	1.54854i	−0.0101673	−	0.0674557i
$528$		0			0
$529$	−7.05618	+	6.54718i	−0.306790	+	0.284660i
$530$	0.0847847	−	0.0578052i	0.00368281	−	0.00251090i
$531$		0			0
$532$	−14.0927	+	3.40151i	−0.610995	+	0.147474i
$533$	−36.9203	+	8.42681i	−1.59919	+	0.365006i
$534$		0			0
$535$	0.0171257	−	0.113621i	0.000740408	−	0.00491228i
$536$	−0.200403	−	0.649690i	−0.00865609	−	0.0280623i
$537$		0			0
$538$		−	79.7639i		−	3.43887i
$539$	−21.9012	−	7.97282i	−0.943351	−	0.343414i
$540$		0			0
$541$	−0.985725	+	13.1536i	−0.0423796	+	0.565517i	0.935086	+	0.354421i	$0.115322\pi$
$541$	−0.985725	+	13.1536i	−0.0423796	+	0.565517i	−0.977465	+	0.211095i	$0.932297\pi$
$542$	−41.6887	+	12.8593i	−1.79069	+	0.552353i
$543$		0			0
$544$	62.0660	−	66.8912i	2.66106	−	2.86794i
$545$	−0.00209442	−	0.00917626i	−8.97152e−5	−	0.000393068i
$546$		0			0
$547$	−4.09280	+	17.9317i	−0.174996	+	0.766706i	0.808898	+	0.587949i	$0.200065\pi$
$547$	−4.09280	+	17.9317i	−0.174996	+	0.766706i	−0.983893	+	0.178756i	$0.942793\pi$
$548$	5.11017	+	7.49524i	0.218296	+	0.320181i
$549$		0			0
$550$	37.0320	+	25.2480i	1.57905	+	1.07658i
$551$	0.884910	−	0.133379i	0.0376984	−	0.00568213i
$552$		0			0
$553$	13.6474	+	33.5402i	0.580345	+	1.42627i
$554$	3.10700	−	6.45176i	0.132004	−	0.274109i
$555$		0			0
$556$	−40.2942	−	15.8143i	−1.70886	−	0.670676i
$557$	20.2779	−	11.7075i	0.859204	−	0.496062i	−0.00454163	−	0.999990i	$-0.501446\pi$
$557$	20.2779	−	11.7075i	0.859204	−	0.496062i	0.863746	+	0.503928i	$0.168112\pi$
$558$		0			0
$559$	−24.4813	+	19.5232i	−1.03545	+	0.825742i
$560$	0.247559	+	0.0341703i	0.0104613	+	0.00144396i
$561$		0			0
$562$	13.3652	+	34.0541i	0.563778	+	1.43648i
$563$	0.635522	+	8.48046i	0.0267841	+	0.357409i	0.994453	+	0.105184i	$0.0335431\pi$
$563$	0.635522	+	8.48046i	0.0267841	+	0.357409i	−0.967669	+	0.252225i	$0.918838\pi$
$564$		0			0
$565$	−0.0227135	+	0.00891440i	−0.000955564	+	0.000375031i
$566$	28.6723	−	35.9539i	1.20519	−	1.51126i
$567$		0			0
$568$	80.3907	+	100.807i	3.37312	+	4.22976i
$569$	18.2642	+	10.5448i	0.765676	+	0.442063i	0.831330	−	0.555779i	$-0.187580\pi$
$569$	18.2642	+	10.5448i	0.765676	+	0.442063i	−0.0656542	+	0.997842i	$0.520913\pi$
$570$		0			0
$571$	10.6238	−	27.0691i	0.444594	−	1.13281i	−0.516427	−	0.856331i	$-0.672738\pi$
$571$	10.6238	−	27.0691i	0.444594	−	1.13281i	0.961021	−	0.276476i	$-0.0891666\pi$
$572$	−113.775	−	35.0949i	−4.75716	−	1.46739i
$573$		0			0
$574$	−22.7062	−	32.4298i	−0.947738	−	1.35359i
$575$	−7.93366	−	16.4744i	−0.330856	−	0.687030i
$576$		0			0
$577$	2.39248	−	3.50912i	0.0996003	−	0.146087i	−0.773204	−	0.634158i	$-0.781347\pi$
$577$	2.39248	−	3.50912i	0.0996003	−	0.146087i	0.872804	+	0.488071i	$0.162299\pi$
$578$	17.8972	+	19.2886i	0.744427	+	0.802301i
$579$		0			0
$580$	−0.0317504	−	0.00724681i	−0.00131836	−	0.000300907i
$581$	−1.29271	+	0.642465i	−0.0536307	+	0.0266539i
$582$		0			0
$583$	−12.8499	−	11.9229i	−0.532187	−	0.493797i
$584$	114.733	+	17.2932i	4.74767	+	0.715596i
$585$		0			0
$586$	18.6426	+	1.39707i	0.770119	+	0.0577124i
$587$	8.45390			0.348930			0.174465	−	0.984663i	$-0.444180\pi$
$587$	8.45390			0.348930			0.174465	+	0.984663i	$0.444180\pi$
$588$		0			0
$589$	−0.315997			−0.0130204
$590$	0.124471	+	0.00932779i	0.00512438	+	0.000384019i
$591$		0			0
$592$	65.6647	+	9.89737i	2.69880	+	0.406779i
$593$	−12.8551	−	11.9278i	−0.527896	−	0.489816i	0.370603	−	0.928791i	$-0.379151\pi$
$593$	−12.8551	−	11.9278i	−0.527896	−	0.489816i	−0.898499	+	0.438975i	$0.855342\pi$
$594$		0			0
$595$	−0.0208512	+	0.0968948i	−0.000854816	+	0.00397230i
$596$	−103.815	−	23.6951i	−4.25242	−	0.970587i
$597$		0			0
$598$	45.6300	+	49.1775i	1.86595	+	2.01102i
$599$	20.7072	−	30.3719i	0.846075	−	1.24096i	−0.122557	−	0.992462i	$-0.539109\pi$
$599$	20.7072	−	30.3719i	0.846075	−	1.24096i	0.968631	−	0.248502i	$-0.0799383\pi$
$600$		0			0
$601$	3.77567	+	7.84026i	0.154013	+	0.319811i	0.963672	−	0.267090i	$-0.0860621\pi$
$601$	3.77567	+	7.84026i	0.154013	+	0.319811i	−0.809659	+	0.586901i	$0.800348\pi$
$602$	−28.5499	−	16.0132i	−1.16361	−	0.652648i
$603$		0			0
$604$	−5.49768	−	1.69581i	−0.223698	−	0.0690016i
$605$	−0.000228242	0	0.000581552i	−9.27936e−6	0	2.36434e-5i
$606$		0			0
$607$	38.8048	+	22.4040i	1.57504	+	0.909348i	0.995537	+	0.0943771i	$0.0300860\pi$
$607$	38.8048	+	22.4040i	1.57504	+	0.909348i	0.579501	+	0.814971i	$0.303247\pi$
$608$	−11.4801	−	14.3956i	−0.465579	−	0.583818i
$609$		0			0
$610$	−0.108723	+	0.136334i	−0.00440206	+	0.00552001i
$611$	−65.1490	+	25.5691i	−2.63565	+	1.03441i
$612$		0			0
$613$	−0.532033	−	7.09949i	−0.0214886	−	0.286746i	−0.997588	−	0.0694191i	$-0.977885\pi$
$613$	−0.532033	−	7.09949i	−0.0214886	−	0.286746i	0.976099	−	0.217326i	$-0.0697336\pi$
$614$	26.9478	+	68.6619i	1.08752	+	2.77097i
$615$		0			0
$616$	−6.71185	−	76.7424i	−0.270428	−	3.09204i
$617$	18.5954	−	14.8293i	0.748623	−	0.597007i	−0.173078	−	0.984908i	$-0.555371\pi$
$617$	18.5954	−	14.8293i	0.748623	−	0.597007i	0.921701	+	0.387901i	$0.126800\pi$
$618$		0			0
$619$	−6.01699	+	3.47391i	−0.241843	+	0.139628i	−0.616024	−	0.787728i	$-0.711257\pi$
$619$	−6.01699	+	3.47391i	−0.241843	+	0.139628i	0.374180	+	0.927356i	$0.377924\pi$
$620$	0.0107047	+	0.00420127i	0.000429909	+	0.000168727i
$621$		0			0
$622$	−4.88921	+	10.1526i	−0.196040	+	0.407080i
$623$	1.53100	−	24.5184i	0.0613384	−	0.982308i
$624$		0			0
$625$	−24.7200	+	3.72594i	−0.988800	+	0.149038i
$626$	−20.4994	−	13.9762i	−0.819319	−	0.558603i
$627$		0			0
$628$	38.8864	+	57.0359i	1.55174	+	2.27598i
$629$	−5.86049	+	25.6765i	−0.233673	+	1.02379i
$630$		0			0
$631$	10.3653	+	45.4134i	0.412637	+	1.80788i	0.571528	+	0.820583i	$0.306351\pi$
$631$	10.3653	+	45.4134i	0.412637	+	1.80788i	−0.158891	+	0.987296i	$0.550792\pi$
$632$	−81.4051	+	87.7339i	−3.23812	+	3.48987i
$633$		0			0
$634$	−21.5990	+	6.66242i	−0.857808	+	0.264599i
$635$	0.000821893	−	0.0109674i	3.26158e−5	−	0.000435228i
$636$		0			0
$637$	−36.5390	+	30.6563i	−1.44773	+	1.21465i
$638$			7.68332i			0.304186i
$639$		0			0
$640$	0.0475934	+	0.154294i	0.00188129	+	0.00609901i
$641$	−2.18198	+	14.4765i	−0.0861829	+	0.571786i	0.903509	+	0.428570i	$0.140982\pi$
$641$	−2.18198	+	14.4765i	−0.0861829	+	0.571786i	−0.989691	+	0.143216i	$0.954256\pi$
$642$		0			0
$643$	−1.68439	+	0.384452i	−0.0664260	+	0.0151613i	−0.255605	−	0.966781i	$-0.582275\pi$
$643$	−1.68439	+	0.384452i	−0.0664260	+	0.0151613i	0.189179	+	0.981943i	$0.439417\pi$
$644$	−21.4617	+	46.0213i	−0.845710	+	1.81349i
$645$		0			0
$646$	12.0173	−	8.19325i	0.472814	−	0.322359i
$647$	22.2801	−	20.6729i	0.875919	−	0.812734i	−0.107477	−	0.994208i	$-0.534277\pi$
$647$	22.2801	−	20.6729i	0.875919	−	0.812734i	0.983396	+	0.181473i	$0.0580866\pi$
$648$		0			0
$649$	−3.17793	−	21.0842i	−0.124745	−	0.827627i
$650$	82.6366	−	39.7957i	3.24127	−	1.56091i
$651$		0			0
$652$	−32.3622	−	15.5848i	−1.26740	−	0.610348i
$653$	8.03665	−	26.0542i	0.314498	−	1.01958i	−0.650980	−	0.759095i	$-0.725642\pi$
$653$	8.03665	−	26.0542i	0.314498	−	1.01958i	0.965478	−	0.260484i	$-0.0838820\pi$
$654$		0			0
$655$	0.0358041	+	0.0620144i	0.00139898	+	0.00242310i
$656$	36.2559	−	62.7971i	1.41556	−	2.45181i
$657$		0			0
$658$	−50.4271	−	53.0097i	−1.96585	−	2.06653i
$659$	14.5758	+	11.6238i	0.567793	+	0.452800i	0.864829	−	0.502067i	$-0.167427\pi$
$659$	14.5758	+	11.6238i	0.567793	+	0.452800i	−0.297036	+	0.954866i	$0.595998\pi$
$660$		0			0
$661$	24.5940	−	1.84307i	0.956598	−	0.0716871i	0.412726	−	0.910855i	$-0.364577\pi$
$661$	24.5940	−	1.84307i	0.956598	−	0.0716871i	0.543872	+	0.839168i	$0.316958\pi$
$662$	−30.7812	+	2.30673i	−1.19635	+	0.0896538i
$663$		0			0
$664$	−3.73033	−	2.97484i	−0.144765	−	0.115446i
$665$	0.0187061	+	0.00707441i	0.000725393	+	0.000274334i
$666$		0			0
$667$	1.56728	−	2.71461i	0.0606854	−	0.105110i
$668$	−18.9627	−	32.8443i	−0.733688	−	1.27078i
$669$		0			0
$670$	−0.000446681		0.00144810i	−1.72568e−5		5.59452e-5i
$671$	26.8382	+	12.9246i	1.03608	+	0.498948i
$672$		0			0
$673$	15.9259	−	7.66951i	0.613898	−	0.295638i	−0.100978	−	0.994889i	$-0.532197\pi$
$673$	15.9259	−	7.66951i	0.613898	−	0.295638i	0.714876	+	0.699251i	$0.246483\pi$
$674$	3.91454	+	25.9713i	0.150783	+	1.00038i
$675$		0			0
$676$	−128.598	+	119.321i	−4.94606	+	4.58928i
$677$	−8.29062	+	5.65245i	−0.318634	+	0.217241i	−0.712066	−	0.702113i	$-0.752240\pi$
$677$	−8.29062	+	5.65245i	−0.318634	+	0.217241i	0.393431	+	0.919354i	$0.371288\pi$
$678$		0			0
$679$	−16.7738	−	13.0387i	−0.643718	−	0.500378i
$680$	−0.319376	+	0.0728954i	−0.0122475	+	0.00279541i
$681$		0			0
$682$	0.404356	−	2.68273i	0.0154836	−	0.102727i
$683$	13.2458	+	42.9419i	0.506838	+	1.64313i	0.741427	+	0.671033i	$0.234149\pi$
$683$	13.2458	+	42.9419i	0.506838	+	1.64313i	−0.234589	+	0.972095i	$0.575374\pi$
$684$		0			0
$685$		−	0.0125142i		−	0.000478143i
$686$	−44.0808	−	23.3023i	−1.68301	−	0.889685i
$687$		0			0
$688$	4.48056	−	59.7890i	0.170820	−	2.27943i
$689$	−34.2782	+	10.5734i	−1.30590	+	0.402815i
$690$		0			0
$691$	−10.7456	+	11.5810i	−0.408782	+	0.440562i	−0.903563	−	0.428456i	$-0.859058\pi$
$691$	−10.7456	+	11.5810i	−0.408782	+	0.440562i	0.494781	+	0.869018i	$0.335248\pi$
$692$	16.4495	+	72.0700i	0.625317	+	2.73969i
$693$		0			0
$694$	6.54025	−	28.6547i	0.248265	−	1.08772i
$695$	0.0336380	+	0.0493379i	0.00127596	+	0.00187149i
$696$		0			0
$697$	23.7611	+	16.2001i	0.900018	+	0.613622i
$698$	75.3353	−	11.3550i	2.85148	−	0.429792i
$699$		0			0
$700$	51.4760	+	46.5848i	1.94561	+	1.76074i
$701$	−11.5358	+	23.9544i	−0.435703	+	0.904746i	0.561317	+	0.827601i	$0.310295\pi$
$701$	−11.5358	+	23.9544i	−0.435703	+	0.904746i	−0.997020	+	0.0771451i	$0.975420\pi$
$702$		0			0
$703$	4.94693	+	1.94153i	0.186577	+	0.0732261i
$704$	61.6638	−	35.6016i	2.32404	−	1.34179i
$705$		0			0
$706$	38.0529	−	30.3462i	1.43214	−	1.14209i
$707$	−9.62253	+	25.4439i	−0.361892	+	0.956915i
$708$		0			0
$709$	7.32779	+	18.6709i	0.275201	+	0.701201i	0.999926	+	0.0121625i	$0.00387155\pi$
$709$	7.32779	+	18.6709i	0.275201	+	0.701201i	−0.724725	+	0.689038i	$0.758033\pi$
$710$	−0.0214766	−	0.286585i	−0.000806002	−	0.0107554i
$711$		0			0
$712$	75.5834	−	29.6643i	2.83261	−	1.11172i
$713$	−0.690101	+	0.865359i	−0.0258445	+	0.0324079i
$714$		0			0
$715$	0.102408	+	0.128416i	0.00382985	+	0.00480248i
$716$	47.0228	+	27.1486i	1.75733	+	1.01459i
$717$		0			0
$718$	−16.6783	+	42.4955i	−0.622427	+	1.58592i
$719$	−31.9409	−	9.85246i	−1.19119	−	0.367435i	−0.365101	−	0.930968i	$-0.618966\pi$
$719$	−31.9409	−	9.85246i	−1.19119	−	0.367435i	−0.826094	+	0.563533i	$0.809442\pi$
$720$		0			0
$721$	6.57337	+	40.2113i	0.244805	+	1.49755i
$722$	20.9209	+	43.4426i	0.778594	+	1.61677i
$723$		0			0
$724$	46.1862	−	67.7427i	1.71650	−	2.51764i
$725$	−2.91492	−	3.14154i	−0.108258	−	0.116674i
$726$		0			0
$727$	21.4950	+	4.90609i	0.797204	+	0.181957i	0.601675	−	0.798741i	$-0.294500\pi$
$727$	21.4950	+	4.90609i	0.797204	+	0.181957i	0.195529	+	0.980698i	$0.437357\pi$
$728$	−142.873	−	66.6279i	−5.29523	−	2.46939i
$729$		0			0
$730$	−0.189580	−	0.175905i	−0.00701668	−	0.00651053i
$731$	23.5132	+	3.54405i	0.869668	+	0.131081i
$732$		0			0
$733$	17.0506	+	1.27776i	0.629777	+	0.0471952i	0.385795	−	0.922585i	$-0.373927\pi$
$733$	17.0506	+	1.27776i	0.629777	+	0.0471952i	0.243982	+	0.969780i	$0.421546\pi$
$734$	−21.0971			−0.778707
$735$		0			0
$736$	−64.4935			−2.37726
$737$	0.258150	+	0.0193457i	0.00950907	+	0.000712606i
$738$		0			0
$739$	−15.7099	−	2.36788i	−0.577897	−	0.0871040i	−0.146411	−	0.989224i	$-0.546772\pi$
$739$	−15.7099	−	2.36788i	−0.577897	−	0.0871040i	−0.431486	+	0.902120i	$0.642010\pi$
$740$	−0.141768	−	0.131542i	−0.00521150	−	0.00483556i
$741$		0			0
$742$	−23.7438	−	29.0257i	−0.871662	−	1.06557i
$743$	27.7459	+	6.33282i	1.01790	+	0.232329i	0.698742	−	0.715373i	$-0.253743\pi$
$743$	27.7459	+	6.33282i	1.01790	+	0.232329i	0.319156	+	0.947702i	$0.396601\pi$
$744$		0			0
$745$	0.0999146	+	0.107682i	0.00366059	+	0.00394517i
$746$	−35.7739	+	52.4707i	−1.30978	+	1.92109i
$747$		0			0
$748$	39.2306	+	81.4632i	1.43441	+	2.97859i
$749$	−41.9097	−	2.61697i	−1.53135	−	0.0956220i
$750$		0			0
$751$	−38.4637	−	11.8645i	−1.40356	−	0.432941i	−0.501727	−	0.865026i	$-0.667302\pi$
$751$	−38.4637	−	11.8645i	−1.40356	−	0.432941i	−0.901833	+	0.432085i	$0.857778\pi$
$752$	48.9589	−	124.745i	1.78535	−	4.54899i
$753$		0			0
$754$	13.6166	+	7.86157i	0.495889	+	0.286302i
$755$	0.00494844	+	0.00620515i	0.000180092	+	0.000225828i
$756$		0			0
$757$	26.2687	−	32.9400i	0.954754	−	1.19722i	−0.0255389	−	0.999674i	$-0.508130\pi$
$757$	26.2687	−	32.9400i	0.954754	−	1.19722i	0.980293	−	0.197550i	$-0.0632984\pi$
$758$	33.2775	−	13.0604i	1.20869	−	0.474376i
$759$		0			0
$760$	0.00493977	+	0.0659166i	0.000179184	+	0.00239105i
$761$	−10.8489	−	27.6426i	−0.393272	−	1.00204i	−0.981177	−	0.193111i	$-0.938142\pi$
$761$	−10.8489	−	27.6426i	−0.393272	−	1.00204i	0.587904	−	0.808930i	$-0.299953\pi$
$762$		0			0
$763$	−3.27397	+	1.05466i	−0.118526	+	0.0381811i
$764$	−25.0558	+	19.9814i	−0.906488	+	0.722900i
$765$		0			0
$766$	−24.4776	+	14.1322i	−0.884413	+	0.510616i
$767$	−40.6178	−	15.9413i	−1.46662	−	0.575607i
$768$		0			0
$769$	14.1472	−	29.3769i	0.510160	−	1.05936i	−0.473745	−	0.880662i	$-0.657098\pi$
$769$	14.1472	−	29.3769i	0.510160	−	1.05936i	0.983904	−	0.178695i	$-0.0571876\pi$
$770$	−0.0839965	+	0.149757i	−0.00302703	+	0.00539688i
$771$		0			0
$772$	72.0529	−	10.8602i	2.59324	−	0.390868i
$773$	2.14974	+	1.46567i	0.0773207	+	0.0527164i	0.601363	−	0.798976i	$-0.294624\pi$
$773$	2.14974	+	1.46567i	0.0773207	+	0.0527164i	−0.524043	+	0.851692i	$0.675577\pi$
$774$		0			0
$775$	0.852451	+	1.25032i	0.0306209	+	0.0449127i
$776$	15.6255	−	68.4598i	0.560923	−	2.45756i
$777$		0			0
$778$	11.7837	+	51.6278i	0.422466	+	1.85095i
$779$	3.94696	−	4.25381i	0.141415	−	0.152409i
$780$		0			0
$781$	−46.9122	+	14.4705i	−1.67865	+	0.517795i
$782$	3.80712	−	50.8025i	0.136142	−	1.81669i
$783$		0			0
$784$	4.55755	−	91.2130i	0.162770	−	3.25761i
$785$		−	0.0952282i		−	0.00339884i
$786$		0			0
$787$	1.80420	+	5.84906i	0.0643127	+	0.208497i	0.982026	−	0.188748i	$-0.0604428\pi$
$787$	1.80420	+	5.84906i	0.0643127	+	0.208497i	−0.917713	+	0.397244i	$0.869967\pi$
$788$	5.80086	−	38.4862i	0.206647	−	1.37101i
$789$		0			0
$790$	0.260075	−	0.0593604i	0.00925305	−	0.00211195i
$791$	3.96852	+	7.98512i	0.141104	+	0.283918i
$792$		0			0
$793$	50.3662	−	34.3391i	1.78856	−	1.21942i
$794$	33.6819	−	31.2522i	1.19533	−	1.10910i
$795$		0			0
$796$	17.4933	+	116.061i	0.620034	+	4.11366i
$797$	−24.7901	+	11.9383i	−0.878110	+	0.422875i	−0.817934	−	0.575312i	$-0.804881\pi$
$797$	−24.7901	+	11.9383i	−0.878110	+	0.422875i	−0.0601761	+	0.998188i	$0.519166\pi$
$798$		0			0
$799$	47.8846	+	23.0600i	1.69404	+	0.815805i
$800$	−25.9901	+	84.2579i	−0.918890	+	2.97897i
$801$		0			0
$802$	−32.0501	−	55.5124i	−1.13173	−	1.96021i
$803$	−22.0892	+	38.2596i	−0.779511	+	1.35015i
$804$		0			0
$805$	0.0602253	−	0.0357771i	0.00212266	−	0.00126098i
$806$	−4.34069	−	3.46158i	−0.152894	−	0.121929i
$807$		0			0
$808$	−89.6589	+	6.71901i	−3.15419	+	0.236374i
$809$	−6.42373	+	0.481392i	−0.225846	+	0.0169249i	−0.187173	−	0.982327i	$-0.559932\pi$
$809$	−6.42373	+	0.481392i	−0.225846	+	0.0169249i	−0.0386738	+	0.999252i	$0.512313\pi$
$810$		0			0
$811$	9.62294	+	7.67403i	0.337907	+	0.269472i	0.777711	−	0.628622i	$-0.216381\pi$
$811$	9.62294	+	7.67403i	0.337907	+	0.269472i	−0.439804	+	0.898094i	$0.644952\pi$
$812$	−1.62730	+	11.7896i	−0.0571071	+	0.413733i
$813$		0			0
$814$	−22.8132	+	39.5137i	−0.799603	+	1.38495i
$815$	0.0247754	+	0.0429123i	0.000867845	+	0.00150315i
$816$		0			0
$817$	1.41427	−	4.58496i	0.0494792	−	0.160407i
$818$	58.2401	+	28.0470i	2.03632	+	0.980639i
$819$		0			0
$820$	−0.190262	+	0.0916253i	−0.00664424	+	0.00319970i
$821$	−5.31006	−	35.2299i	−0.185322	−	1.22953i	−0.867160	−	0.498029i	$-0.834057\pi$
$821$	−5.31006	−	35.2299i	−0.185322	−	1.22953i	0.681838	−	0.731503i	$-0.261181\pi$
$822$		0			0
$823$	−7.14778	+	6.63217i	−0.249156	+	0.231183i	−0.794857	−	0.606797i	$-0.792454\pi$
$823$	−7.14778	+	6.63217i	−0.249156	+	0.231183i	0.545701	+	0.837980i	$0.316264\pi$
$824$	−111.270	+	75.8629i	−3.87629	+	2.64281i
$825$		0			0
$826$	−0.567324	−	45.6111i	−0.0197397	−	1.58701i
$827$	39.7119	−	9.06397i	1.38092	−	0.315185i	0.533359	−	0.845889i	$-0.320929\pi$
$827$	39.7119	−	9.06397i	1.38092	−	0.315185i	0.847557	+	0.530704i	$0.178072\pi$
$828$		0			0
$829$	4.26287	−	28.2823i	0.148055	−	0.982284i	−0.784207	−	0.620500i	$-0.786930\pi$
$829$	4.26287	−	28.2823i	0.148055	−	0.982284i	0.932262	−	0.361784i	$-0.117832\pi$
$830$	0.00313465	+	0.0101623i	0.000108805	+	0.000352738i
$831$		0			0
$832$		−	145.710i		−	5.05160i
$833$	35.9389	+	4.50584i	1.24521	+	0.156118i
$834$		0			0
$835$	−0.00390974	+	0.0521719i	−0.000135302	+	0.00180548i
$836$	17.4340	−	5.37768i	0.602967	−	0.185991i
$837$		0			0
$838$	−21.9884	+	23.6979i	−0.759577	+	0.818630i
$839$	−10.4254	−	45.6768i	−0.359926	−	1.57694i	−0.753375	−	0.657592i	$-0.771575\pi$
$839$	−10.4254	−	45.6768i	−0.359926	−	1.57694i	0.393449	−	0.919347i	$-0.371282\pi$
$840$		0			0
$841$	−6.28963	+	27.5567i	−0.216884	+	0.950230i
$842$	16.4370	+	24.1086i	0.566456	+	0.830838i
$843$		0			0
$844$	−6.10912	−	4.16513i	−0.210285	−	0.143370i
$845$	0.239300	−	0.0360687i	0.00823218	−	0.00124080i
$846$		0			0
$847$	0.218984	+	0.0645759i	0.00752436	+	0.00221886i
$848$	29.8019	−	61.8843i	1.02340	−	2.12512i
$849$		0			0
$850$	−64.8370	−	25.4466i	−2.22389	−	0.872812i
$851$	16.1204	−	9.30711i	0.552600	−	0.319044i
$852$		0			0
$853$	1.23443	−	0.984422i	0.0422660	−	0.0337060i	−0.602129	−	0.798399i	$-0.705681\pi$
$853$	1.23443	−	0.984422i	0.0422660	−	0.0337060i	0.644395	+	0.764693i	$0.277109\pi$
$854$	53.0948	+	35.2401i	1.81687	+	1.20589i
$855$		0			0
$856$	−50.7057	−	129.196i	−1.73308	−	4.41583i
$857$	−3.18216	−	42.4630i	−0.108700	−	1.45051i	−0.738764	−	0.673964i	$-0.764590\pi$
$857$	−3.18216	−	42.4630i	−0.108700	−	1.45051i	0.630064	−	0.776543i	$-0.283029\pi$
$858$		0			0
$859$	24.6931	−	9.69133i	0.842518	−	0.330664i	0.0954688	−	0.995432i	$-0.469565\pi$
$859$	24.6931	−	9.69133i	0.842518	−	0.330664i	0.747050	+	0.664768i	$0.231470\pi$
$860$	−0.108868	+	0.136516i	−0.00371237	+	0.00465516i
$861$		0			0
$862$	−10.8861	−	13.6507i	−0.370782	−	0.464946i
$863$	−44.4001	−	25.6344i	−1.51140	−	0.872605i	−0.999911	−	0.0133118i	$-0.995763\pi$
$863$	−44.4001	−	25.6344i	−1.51140	−	0.872605i	−0.511484	−	0.859293i	$-0.670904\pi$
$864$		0			0
$865$	0.0372566	−	0.0949284i	0.00126676	−	0.00322766i
$866$	−18.1041	−	5.58436i	−0.615201	−	0.189764i
$867$		0			0
$868$	1.18865	−	4.03085i	0.0403455	−	0.136816i
$869$	−19.7720	−	41.0570i	−0.670720	−	1.39276i
$870$		0			0
$871$	0.298424	−	0.437708i	0.0101117	−	0.0148312i
$872$	−7.73272	−	8.33389i	−0.261863	−	0.282221i
$873$		0			0
$874$	−10.0220	−	2.28746i	−0.339000	−	0.0773745i
$875$	−0.0449425	−	0.186200i	−0.00151933	−	0.00629470i
$876$		0			0
$877$	−17.8275	−	16.5415i	−0.601991	−	0.558566i	0.319195	−	0.947689i	$-0.396588\pi$
$877$	−17.8275	−	16.5415i	−0.601991	−	0.558566i	−0.921186	+	0.389123i	$0.872778\pi$
$878$	30.5472	+	4.60425i	1.03092	+	0.155386i
$879$		0			0
$880$	−0.313621	−	0.0235027i	−0.0105722	−	0.000792274i
$881$	−26.7873			−0.902489			−0.451244	−	0.892400i	$-0.649020\pi$
$881$	−26.7873			−0.902489			−0.451244	+	0.892400i	$0.649020\pi$
$882$		0			0
$883$	−1.97057			−0.0663149			−0.0331575	−	0.999450i	$-0.510556\pi$
$883$	−1.97057			−0.0663149			−0.0331575	+	0.999450i	$0.510556\pi$
$884$	184.513	+	13.8273i	6.20583	+	0.465063i
$885$		0			0
$886$	−19.2202	−	2.89698i	−0.645714	−	0.0973258i
$887$	−25.5953	−	23.7490i	−0.859406	−	0.797413i	0.121358	−	0.992609i	$-0.461275\pi$
$887$	−25.5953	−	23.7490i	−0.859406	−	0.797413i	−0.980764	+	0.195196i	$0.937466\pi$
$888$		0			0
$889$	−4.01890	+	0.0499883i	−0.134790	+	0.00167655i
$890$	−0.176442	−	0.0402717i	−0.00591435	−	0.00134991i
$891$		0			0
$892$	−63.9132	−	68.8820i	−2.13997	−	2.30634i
$893$	6.04120	−	8.86081i	0.202161	−	0.296516i
$894$		0			0
$895$	−0.0324993	−	0.0674856i	−0.00108633	−	0.00225579i
$896$	54.6560	−	22.2393i	1.82593	−	0.742963i
$897$		0			0
$898$	−12.4068	−	3.82699i	−0.414020	−	0.127708i
$899$	−0.0947741	+	0.241480i	−0.00316089	+	0.00805382i
$900$		0			0
$901$	23.5914	+	13.6205i	0.785945	+	0.453765i
$902$	31.0631	+	38.9519i	1.03429	+	1.29696i
$903$		0			0
$904$	−18.3756	+	23.0423i	−0.611165	+	0.766376i
$905$	−0.105286	+	0.0413217i	−0.00349982	+	0.00137358i
$906$		0			0
$907$	2.75165	+	36.7182i	0.0913670	+	1.21921i	0.834860	+	0.550463i	$0.185549\pi$
$907$	2.75165	+	36.7182i	0.0913670	+	1.21921i	−0.743493	+	0.668744i	$0.766832\pi$
$908$	−14.8329	−	37.7936i	−0.492247	−	1.25422i
$909$		0			0
$910$	0.179460	+	0.302093i	0.00594904	+	0.0100143i
$911$	−22.9167	+	18.2754i	−0.759263	+	0.605492i	−0.924686	−	0.380731i	$-0.875672\pi$
$911$	−22.9167	+	18.2754i	−0.759263	+	0.605492i	0.165423	+	0.986223i	$0.447101\pi$
$912$		0			0
$913$	1.57329	−	0.908341i	0.0520684	−	0.0300617i
$914$	−23.1775	−	9.09649i	−0.766643	−	0.300885i
$915$		0			0
$916$	−32.2747	+	67.0192i	−1.06639	+	2.21438i
$917$	21.4366	−	15.0092i	0.707900	−	0.495646i
$918$		0			0
$919$	18.4898	−	2.78689i	0.609923	−	0.0919311i	0.163184	−	0.986596i	$-0.447823\pi$
$919$	18.4898	−	2.78689i	0.609923	−	0.0919311i	0.446739	+	0.894665i	$0.352585\pi$
$920$	0.191301	+	0.130426i	0.00630699	+	0.00430003i
$921$		0			0
$922$	−30.0008	−	44.0030i	−0.988022	−	1.44916i
$923$	−22.3554	+	97.9456i	−0.735838	+	3.22392i
$924$		0			0
$925$	−5.66300	−	24.8112i	−0.186198	−	0.815788i
$926$	−46.3274	+	49.9291i	−1.52241	+	1.64077i
$927$		0			0
$928$	−14.4440	+	4.45539i	−0.474148	+	0.146255i
$929$	−0.274088	+	3.65745i	−0.00899254	+	0.119997i	−0.999893	−	0.0145961i	$-0.995354\pi$
$929$	−0.274088	+	3.65745i	−0.00899254	+	0.119997i	0.990901	+	0.134593i	$0.0429728\pi$
$930$		0			0
$931$	1.97987	−	7.03530i	0.0648875	−	0.230573i
$932$			113.160i			3.70666i
$933$		0			0
$934$	2.16191	+	7.00874i	0.0707399	+	0.229333i
$935$	0.0185902	−	0.123338i	0.000607964	−	0.00403358i
$936$		0			0
$937$	2.46011	−	0.561503i	0.0803682	−	0.0183435i	−0.182148	−	0.983271i	$-0.558305\pi$
$937$	2.46011	−	0.561503i	0.0803682	−	0.0183435i	0.262516	+	0.964928i	$0.415448\pi$
$938$	0.541411	+	0.116509i	0.0176777	+	0.00380414i
$939$		0			0
$940$	−0.322457	+	0.219848i	−0.0105174	+	0.00717064i
$941$	−29.9394	+	27.7797i	−0.975995	+	0.905591i	−0.995552	−	0.0942177i	$-0.969965\pi$
$941$	−29.9394	+	27.7797i	−0.975995	+	0.905591i	0.0195566	+	0.999809i	$0.493775\pi$
$942$		0			0
$943$	−3.02937	−	20.0986i	−0.0986500	−	0.654500i
$944$	75.2752	−	36.2506i	2.45000	−	1.17986i
$945$		0			0
$946$	37.1153	+	17.8738i	1.20672	+	0.581127i
$947$	−16.8544	+	54.6405i	−0.547693	+	1.77558i	0.0796360	+	0.996824i	$0.474624\pi$
$947$	−16.8544	+	54.6405i	−0.547693	+	1.77558i	−0.627329	+	0.778754i	$0.715852\pi$
$948$		0			0
$949$	45.2034	+	78.2945i	1.46736	+	2.54155i
$950$	−7.02722	+	12.1715i	−0.227993	+	0.394896i
$951$		0			0
$952$	36.7068	+	113.949i	1.18967	+	3.69311i
$953$	9.84277	+	7.84935i	0.318839	+	0.254265i	0.769810	−	0.638273i	$-0.220351\pi$
$953$	9.84277	+	7.84935i	0.318839	+	0.254265i	−0.450971	+	0.892538i	$0.648922\pi$
$954$		0			0
$955$	0.0440862	−	0.00330380i	0.00142660	−	0.000106909i
$956$	77.0091	−	5.77104i	2.49065	−	0.186649i
$957$		0			0
$958$	−21.6186	−	17.2402i	−0.698464	−	0.557006i
$959$	−4.55584	+	0.398452i	−0.147116	+	0.0128667i
$960$		0			0
$961$	−15.4542	+	26.7675i	−0.498523	+	0.863466i
$962$	46.6850	+	80.8607i	1.50518	+	2.60706i
$963$		0			0
$964$	−2.26078	+	7.32926i	−0.0728147	+	0.236060i
$965$	−0.0905654	−	0.0436140i	−0.00291540	−	0.00140398i
$966$		0			0
$967$	−6.84699	+	3.29733i	−0.220184	+	0.106035i	−0.540724	−	0.841200i	$-0.681850\pi$
$967$	−6.84699	+	3.29733i	−0.220184	+	0.106035i	0.320540	+	0.947235i	$0.396136\pi$
$968$	0.112467	+	0.746172i	0.00361484	+	0.0239829i
$969$		0			0
$970$	−0.114734	+	0.106457i	−0.00368388	+	0.00341814i
$971$	36.1048	−	24.6159i	1.15866	−	0.789961i	0.177683	−	0.984088i	$-0.443140\pi$
$971$	36.1048	−	24.6159i	1.15866	−	0.789961i	0.980976	+	0.194127i	$0.0621874\pi$
$972$		0			0
$973$	16.8906	−	13.8170i	0.541489	−	0.442952i
$974$	−30.4017	+	6.93898i	−0.974132	+	0.222339i
$975$		0			0
$976$	−17.3964	+	115.418i	−0.556846	+	3.69443i
$977$	−2.66094	−	8.62654i	−0.0851309	−	0.275988i	0.902991	−	0.429659i	$-0.141366\pi$
$977$	−2.66094	−	8.62654i	−0.0851309	−	0.275988i	−0.988122	+	0.153672i	$0.950890\pi$
$978$		0			0
$979$			30.9158i			0.988074i
$980$	−0.160606	+	0.212003i	−0.00513036	+	0.00677220i
$981$		0			0
$982$	−7.03631	+	93.8931i	−0.224538	+	2.99625i
$983$	40.0381	−	12.3501i	1.27702	−	0.393907i	0.419214	−	0.907887i	$-0.362306\pi$
$983$	40.0381	−	12.3501i	1.27702	−	0.393907i	0.857802	+	0.513980i	$0.171830\pi$
$984$		0			0
$985$	−0.0365195	+	0.0393587i	−0.00116361	+	0.00125407i
$986$	−2.65693	−	11.6408i	−0.0846138	−	0.370717i
$987$		0			0
$988$	8.30797	−	36.3996i	0.264312	−	1.15802i
$989$	−9.46732	−	13.8860i	−0.301043	−	0.441549i
$990$		0			0
$991$	9.51097	+	6.48447i	0.302126	+	0.205986i	0.704888	−	0.709319i	$-0.250997\pi$
$991$	9.51097	+	6.48447i	0.302126	+	0.205986i	−0.402762	+	0.915305i	$0.631950\pi$
$992$	5.27779	−	0.795499i	0.167570	−	0.0252571i
$993$		0			0
$994$	−103.649	+	16.9435i	−3.28754	+	0.537416i
$995$	0.0702520	−	0.145880i	0.00222714	−	0.00462470i
$996$		0			0
$997$	−2.85966	−	1.12233i	−0.0905662	−	0.0355446i	0.319625	−	0.947544i	$-0.396443\pi$
$997$	−2.85966	−	1.12233i	−0.0905662	−	0.0355446i	−0.410192	+	0.911999i	$0.634538\pi$
$998$	−51.5422	+	29.7579i	−1.63154	+	0.941970i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bg.a.26.1	yes	216
3.2	odd	2	inner	441.2.bg.a.26.18	yes	216
49.17	odd	42	inner	441.2.bg.a.17.18	yes	216
147.17	even	42	inner	441.2.bg.a.17.1	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bg.a.17.1	✓	216	147.17	even	42	inner
441.2.bg.a.17.18	yes	216	49.17	odd	42	inner
441.2.bg.a.26.1	yes	216	1.1	even	1	trivial
441.2.bg.a.26.18	yes	216	3.2	odd	2	inner

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.bg (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.68471 - 0.201191i) q^{2} +(5.18952 + 0.782194i) q^{4} +(-0.00530717 - 0.00492433i) q^{5} +(-1.62374 + 2.08889i) q^{7} +(-8.52551 - 1.94589i) q^{8} +O(q^{10})\)	\(q+(-2.68471 - 0.201191i) q^{2} +(5.18952 + 0.782194i) q^{4} +(-0.00530717 - 0.00492433i) q^{5} +(-1.62374 + 2.08889i) q^{7} +(-8.52551 - 1.94589i) q^{8} +(0.0132575 + 0.0142882i) q^{10} +(1.87564 - 2.75105i) q^{11} +(-2.95636 - 6.13894i) q^{13} +(4.77955 - 5.28137i) q^{14} +(12.4671 + 3.84558i) q^{16} +(-1.89039 + 4.81664i) q^{17} +(0.904202 + 0.522041i) q^{19} +(-0.0236899 - 0.0297062i) q^{20} +(-5.58902 + 7.00841i) q^{22} +(3.40428 - 1.33608i) q^{23} +(-0.373647 - 4.98597i) q^{25} +(6.70186 + 17.0761i) q^{26} +(-10.0604 + 9.57025i) q^{28} +(0.670125 - 0.534407i) q^{29} +(-0.262107 + 0.151328i) q^{31} +(-16.4162 - 6.44288i) q^{32} +(6.04421 - 12.5509i) q^{34} +(0.0189039 - 0.00309023i) q^{35} +(5.03306 - 0.758612i) q^{37} +(-2.32249 - 1.58345i) q^{38} +(0.0356641 + 0.0523096i) q^{40} +(1.23674 - 5.41853i) q^{41} +(-1.02261 - 4.48033i) q^{43} +(11.8855 - 12.8095i) q^{44} +(-9.40831 + 2.90208i) q^{46} +(0.767589 - 10.2428i) q^{47} +(-1.72691 - 6.78364i) q^{49} +13.4610i q^{50} +(-10.5402 - 34.1706i) q^{52} +(0.784657 - 5.20586i) q^{53} +(-0.0235014 + 0.00536404i) q^{55} +(17.9080 - 14.6492i) q^{56} +(-1.90661 + 1.29990i) q^{58} +(4.69436 - 4.35573i) q^{59} +(1.33340 + 8.84651i) q^{61} +(0.734128 - 0.353537i) q^{62} +(19.2671 + 9.27855i) q^{64} +(-0.0145403 + 0.0471385i) q^{65} +(0.0388745 + 0.0673326i) q^{67} +(-13.5778 + 23.5174i) q^{68} +(-0.0513731 + 0.00449306i) q^{70} +(-11.5277 - 9.19301i) q^{71} +(-13.2312 + 0.991545i) q^{73} +(-13.6649 + 1.02404i) q^{74} +(4.28404 + 3.41641i) q^{76} +(2.70109 + 8.38500i) q^{77} +(6.84313 - 11.8526i) q^{79} +(-0.0472279 - 0.0818011i) q^{80} +(-4.41046 + 14.2983i) q^{82} +(0.491582 + 0.236733i) q^{83} +(0.0337513 - 0.0162538i) q^{85} +(1.84400 + 12.2341i) q^{86} +(-21.3440 + 19.8043i) q^{88} +(-7.67173 + 5.23050i) q^{89} +(17.6239 + 3.79257i) q^{91} +(18.7117 - 4.27081i) q^{92} +(-4.12150 + 27.3444i) q^{94} +(-0.00222805 - 0.00722315i) q^{95} +8.02999i q^{97} +(3.27144 + 18.5595i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 216 * q - 16 * q^4 + 2 * q^7	\( 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) \) 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Introduction

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