LMFDB - Embedded newform 810.2.k.e.451.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(91,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("810.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.k (of order $9$, degree $6$, 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:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			451.4
Character	$\chi$	$=$	810.451
Dual form			810.2.k.e.361.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(0.781269 - 4.43080i) q^{7} +(-0.500000 + 0.866025i) q^{8} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(0.781269 - 4.43080i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.500000 - 0.866025i) q^{10} +(-0.978505 + 0.356147i) q^{11} +(2.22799 - 1.86951i) q^{13} +(3.44655 - 2.89200i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-3.16530 - 5.48247i) q^{17} +(-0.956131 + 1.65607i) q^{19} +(0.173648 - 0.984808i) q^{20} +(-0.978505 - 0.356147i) q^{22} +(-0.953104 - 5.40532i) q^{23} +(0.766044 + 0.642788i) q^{25} +2.90844 q^{26} +4.49915 q^{28} +(5.97572 + 5.01422i) q^{29} +(-1.09858 - 6.23038i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(1.09930 - 6.23443i) q^{34} +(-2.24958 + 3.89638i) q^{35} +(-1.09572 - 1.89784i) q^{37} +(-1.79694 + 0.654032i) q^{38} +(0.766044 - 0.642788i) q^{40} +(6.63474 - 5.56721i) q^{41} +(7.48957 - 2.72598i) q^{43} +(-0.520652 - 0.901795i) q^{44} +(2.74435 - 4.75336i) q^{46} +(-1.46717 + 8.32074i) q^{47} +(-12.4437 - 4.52915i) q^{49} +(0.173648 + 0.984808i) q^{50} +(2.22799 + 1.86951i) q^{52} +7.94437 q^{53} +1.04130 q^{55} +(3.44655 + 2.89200i) q^{56} +(1.35458 + 7.68223i) q^{58} +(0.00700732 + 0.00255046i) q^{59} +(-2.63861 + 14.9643i) q^{61} +(3.16325 - 5.47890i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-2.73304 + 0.994745i) q^{65} +(-8.46057 + 7.09926i) q^{67} +(4.84953 - 4.06924i) q^{68} +(-4.22782 + 1.53880i) q^{70} +(3.83372 + 6.64020i) q^{71} +(4.26097 - 7.38021i) q^{73} +(0.380538 - 2.15814i) q^{74} +(-1.79694 - 0.654032i) q^{76} +(0.813538 + 4.61381i) q^{77} +(-2.91155 - 2.44308i) q^{79} +1.00000 q^{80} +8.66104 q^{82} +(-0.910253 - 0.763793i) q^{83} +(1.09930 + 6.23443i) q^{85} +(7.48957 + 2.72598i) q^{86} +(0.180820 - 1.02548i) q^{88} +(-1.75776 + 3.04453i) q^{89} +(-6.54276 - 11.3324i) q^{91} +(5.15770 - 1.87725i) q^{92} +(-6.47239 + 5.43098i) q^{94} +(1.46488 - 1.22918i) q^{95} +(-2.30205 + 0.837879i) q^{97} +(-6.62118 - 11.4682i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{7} - 12 q^{8}+O(q^{10}) $ 24 * q + 3 * q^7 - 12 * q^8	$ 24 q + 3 q^{7} - 12 q^{8} - 12 q^{10} + 9 q^{13} + 3 q^{14} - 15 q^{17} - 9 q^{19} + 12 q^{23} + 12 q^{26} + 6 q^{28} + 33 q^{29} - 21 q^{31} - 15 q^{34} - 3 q^{35} - 12 q^{37} - 12 q^{38} - 21 q^{41} + 12 q^{43} - 9 q^{44} - 15 q^{46} + 21 q^{47} + 27 q^{49} + 9 q^{52} + 60 q^{53} + 18 q^{55} + 3 q^{56} - 21 q^{58} - 36 q^{59} + 33 q^{61} - 18 q^{62} - 12 q^{64} - 12 q^{67} + 3 q^{68} - 6 q^{70} - 12 q^{71} - 6 q^{74} - 12 q^{76} + 60 q^{77} - 15 q^{79} + 24 q^{80} + 6 q^{82} + 27 q^{83} - 15 q^{85} + 12 q^{86} - 9 q^{88} - 30 q^{89} - 9 q^{91} - 6 q^{92} + 12 q^{94} + 15 q^{95} + 3 q^{97} - 27 q^{98}+O(q^{100}) $ 24 * q + 3 * q^7 - 12 * q^8 - 12 * q^10 + 9 * q^13 + 3 * q^14 - 15 * q^17 - 9 * q^19 + 12 * q^23 + 12 * q^26 + 6 * q^28 + 33 * q^29 - 21 * q^31 - 15 * q^34 - 3 * q^35 - 12 * q^37 - 12 * q^38 - 21 * q^41 + 12 * q^43 - 9 * q^44 - 15 * q^46 + 21 * q^47 + 27 * q^49 + 9 * q^52 + 60 * q^53 + 18 * q^55 + 3 * q^56 - 21 * q^58 - 36 * q^59 + 33 * q^61 - 18 * q^62 - 12 * q^64 - 12 * q^67 + 3 * q^68 - 6 * q^70 - 12 * q^71 - 6 * q^74 - 12 * q^76 + 60 * q^77 - 15 * q^79 + 24 * q^80 + 6 * q^82 + 27 * q^83 - 15 * q^85 + 12 * q^86 - 9 * q^88 - 30 * q^89 - 9 * q^91 - 6 * q^92 + 12 * q^94 + 15 * q^95 + 3 * q^97 - 27 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$		0			0
$3$		0			0
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.939693	−	0.342020i	−0.420243	−	0.152956i
$5$	−0.939693	−	0.342020i	−0.420243	−	0.152956i
$6$		0			0
$7$	0.781269	−	4.43080i	0.295292	−	1.67468i	−0.370721	−	0.928744i	$-0.620889\pi$
$7$	0.781269	−	4.43080i	0.295292	−	1.67468i	0.666013	−	0.745940i	$-0.268000\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$		0			0
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−0.978505	+	0.356147i	−0.295030	+	0.107382i	−0.485295	−	0.874351i	$-0.661288\pi$
$11$	−0.978505	+	0.356147i	−0.295030	+	0.107382i	0.190264	+	0.981733i	$0.439065\pi$
$12$		0			0
$13$	2.22799	−	1.86951i	0.617935	−	0.518509i	−0.279219	−	0.960227i	$-0.590076\pi$
$13$	2.22799	−	1.86951i	0.617935	−	0.518509i	0.897154	+	0.441719i	$0.145631\pi$
$14$	3.44655	−	2.89200i	0.921129	−	0.772919i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−3.16530	−	5.48247i	−0.767699	−	1.32969i	−0.938808	−	0.344441i	$-0.888068\pi$
$17$	−3.16530	−	5.48247i	−0.767699	−	1.32969i	0.171109	−	0.985252i	$-0.445265\pi$
$18$		0			0
$19$	−0.956131	+	1.65607i	−0.219351	+	0.379928i	−0.954610	−	0.297859i	$-0.903727\pi$
$19$	−0.956131	+	1.65607i	−0.219351	+	0.379928i	0.735258	+	0.677787i	$0.237061\pi$
$20$	0.173648	−	0.984808i	0.0388289	−	0.220210i
$21$		0			0
$22$	−0.978505	−	0.356147i	−0.208618	−	0.0759307i
$23$	−0.953104	−	5.40532i	−0.198736	−	1.12709i	−0.906997	−	0.421137i	$-0.861631\pi$
$23$	−0.953104	−	5.40532i	−0.198736	−	1.12709i	0.708261	−	0.705951i	$-0.249480\pi$
$24$		0			0
$25$	0.766044	+	0.642788i	0.153209	+	0.128558i
$26$	2.90844			0.570392
$27$		0			0
$28$	4.49915			0.850260
$29$	5.97572	+	5.01422i	1.10966	+	0.931117i	0.998037	−	0.0626329i	$-0.0199497\pi$
$29$	5.97572	+	5.01422i	1.10966	+	0.931117i	0.111626	+	0.993750i	$0.464394\pi$
$30$		0			0
$31$	−1.09858	−	6.23038i	−0.197312	−	1.11901i	−0.909088	−	0.416604i	$-0.863220\pi$
$31$	−1.09858	−	6.23038i	−0.197312	−	1.11901i	0.711777	−	0.702406i	$-0.247891\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$		0			0
$34$	1.09930	−	6.23443i	0.188528	−	1.06920i
$35$	−2.24958	+	3.89638i	−0.380248	+	0.658608i
$36$		0			0
$37$	−1.09572	−	1.89784i	−0.180135	−	0.312002i	0.761792	−	0.647822i	$-0.224320\pi$
$37$	−1.09572	−	1.89784i	−0.180135	−	0.312002i	−0.941926	+	0.335820i	$0.890987\pi$
$38$	−1.79694	+	0.654032i	−0.291502	+	0.106098i
$39$		0			0
$40$	0.766044	−	0.642788i	0.121122	−	0.101634i
$41$	6.63474	−	5.56721i	1.03617	−	0.869452i	0.0446003	−	0.999005i	$-0.485799\pi$
$41$	6.63474	−	5.56721i	1.03617	−	0.869452i	0.991573	+	0.129553i	$0.0413541\pi$
$42$		0			0
$43$	7.48957	−	2.72598i	1.14215	−	0.415708i	0.299460	−	0.954109i	$-0.403194\pi$
$43$	7.48957	−	2.72598i	1.14215	−	0.415708i	0.842689	+	0.538401i	$0.180971\pi$
$44$	−0.520652	−	0.901795i	−0.0784912	−	0.135951i
$45$		0			0
$46$	2.74435	−	4.75336i	0.404633	−	0.700845i
$47$	−1.46717	+	8.32074i	−0.214009	+	1.21370i	0.668609	+	0.743614i	$0.266890\pi$
$47$	−1.46717	+	8.32074i	−0.214009	+	1.21370i	−0.882618	+	0.470091i	$0.844221\pi$
$48$		0			0
$49$	−12.4437	−	4.52915i	−1.77768	−	0.647022i
$50$	0.173648	+	0.984808i	0.0245576	+	0.139273i
$51$		0			0
$52$	2.22799	+	1.86951i	0.308967	+	0.259254i
$53$	7.94437			1.09124			0.545622	−	0.838032i	$-0.316294\pi$
$53$	7.94437			1.09124			0.545622	+	0.838032i	$0.316294\pi$
$54$		0			0
$55$	1.04130			0.140409
$56$	3.44655	+	2.89200i	0.460565	+	0.386460i
$57$		0			0
$58$	1.35458	+	7.68223i	0.177866	+	1.00873i
$59$	0.00700732	+	0.00255046i	0.000912275	+	0.000332041i	0.342476	−	0.939526i	$-0.388734\pi$
$59$	0.00700732	+	0.00255046i	0.000912275	+	0.000332041i	−0.341564	+	0.939859i	$0.610957\pi$
$60$		0			0
$61$	−2.63861	+	14.9643i	−0.337839	+	1.91598i	0.0593401	+	0.998238i	$0.481100\pi$
$61$	−2.63861	+	14.9643i	−0.337839	+	1.91598i	−0.397179	+	0.917741i	$0.630011\pi$
$62$	3.16325	−	5.47890i	0.401733	−	0.695822i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−2.73304	+	0.994745i	−0.338992	+	0.123383i
$66$		0			0
$67$	−8.46057	+	7.09926i	−1.03362	+	0.867313i	−0.991278	−	0.131790i	$-0.957927\pi$
$67$	−8.46057	+	7.09926i	−1.03362	+	0.867313i	−0.0423456	+	0.999103i	$0.513483\pi$
$68$	4.84953	−	4.06924i	0.588091	−	0.493467i
$69$		0			0
$70$	−4.22782	+	1.53880i	−0.505321	+	0.183922i
$71$	3.83372	+	6.64020i	0.454979	+	0.788047i	0.998687	−	0.0512274i	$-0.0163133\pi$
$71$	3.83372	+	6.64020i	0.454979	+	0.788047i	−0.543708	+	0.839275i	$0.682980\pi$
$72$		0			0
$73$	4.26097	−	7.38021i	0.498708	−	0.863788i	−0.501291	−	0.865279i	$-0.667141\pi$
$73$	4.26097	−	7.38021i	0.498708	−	0.863788i	0.999999	+	0.00149084i	$0.000474548\pi$
$74$	0.380538	−	2.15814i	0.0442367	−	0.250879i
$75$		0			0
$76$	−1.79694	−	0.654032i	−0.206123	−	0.0750226i
$77$	0.813538	+	4.61381i	0.0927113	+	0.525792i
$78$		0			0
$79$	−2.91155	−	2.44308i	−0.327575	−	0.274868i	0.464136	−	0.885764i	$-0.346365\pi$
$79$	−2.91155	−	2.44308i	−0.327575	−	0.274868i	−0.791711	+	0.610896i	$0.790809\pi$
$80$	1.00000			0.111803
$81$		0			0
$82$	8.66104			0.956452
$83$	−0.910253	−	0.763793i	−0.0999132	−	0.0838372i	0.591463	−	0.806332i	$-0.298551\pi$
$83$	−0.910253	−	0.763793i	−0.0999132	−	0.0838372i	−0.691376	+	0.722495i	$0.742995\pi$
$84$		0			0
$85$	1.09930	+	6.23443i	0.119236	+	0.676219i
$86$	7.48957	+	2.72598i	0.807621	+	0.293950i
$87$		0			0
$88$	0.180820	−	1.02548i	0.0192755	−	0.109317i
$89$	−1.75776	+	3.04453i	−0.186322	+	0.322720i	−0.944021	−	0.329885i	$-0.892990\pi$
$89$	−1.75776	+	3.04453i	−0.186322	+	0.322720i	0.757699	+	0.652604i	$0.226324\pi$
$90$		0			0
$91$	−6.54276	−	11.3324i	−0.685867	−	1.18796i
$92$	5.15770	−	1.87725i	0.537727	−	0.195717i
$93$		0			0
$94$	−6.47239	+	5.43098i	−0.667576	+	0.560162i
$95$	1.46488	−	1.22918i	0.150293	−	0.126111i
$96$		0			0
$97$	−2.30205	+	0.837879i	−0.233738	+	0.0850738i	−0.456234	−	0.889860i	$-0.650802\pi$
$97$	−2.30205	+	0.837879i	−0.233738	+	0.0850738i	0.222496	+	0.974934i	$0.428580\pi$
$98$	−6.62118	−	11.4682i	−0.668840	−	1.15847i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	1.10705	−	6.27840i	0.110156	−	0.624724i	−0.878879	−	0.477044i	$-0.841708\pi$
$101$	1.10705	−	6.27840i	0.110156	−	0.624724i	0.989035	−	0.147680i	$-0.0471807\pi$
$102$		0			0
$103$	−5.07667	−	1.84776i	−0.500219	−	0.182065i	0.0795735	−	0.996829i	$-0.474644\pi$
$103$	−5.07667	−	1.84776i	−0.500219	−	0.182065i	−0.579792	+	0.814764i	$0.696866\pi$
$104$	0.505045	+	2.86426i	0.0495238	+	0.280863i
$105$		0			0
$106$	6.08574	+	5.10654i	0.591100	+	0.495991i
$107$	−6.10435			−0.590130			−0.295065	−	0.955477i	$-0.595341\pi$
$107$	−6.10435			−0.590130			−0.295065	+	0.955477i	$0.595341\pi$
$108$		0			0
$109$	−1.48807			−0.142531			−0.0712654	−	0.997457i	$-0.522704\pi$
$109$	−1.48807			−0.142531			−0.0712654	+	0.997457i	$0.522704\pi$
$110$	0.797685	+	0.669337i	0.0760562	+	0.0638188i
$111$		0			0
$112$	0.781269	+	4.43080i	0.0738230	+	0.418671i
$113$	−3.38041	−	1.23037i	−0.318002	−	0.115743i	0.178087	−	0.984015i	$-0.443009\pi$
$113$	−3.38041	−	1.23037i	−0.318002	−	0.115743i	−0.496090	+	0.868271i	$0.665231\pi$
$114$		0			0
$115$	−0.953104	+	5.40532i	−0.0888774	+	0.504049i
$116$	−3.90037	+	6.75564i	−0.362140	+	0.627246i
$117$		0			0
$118$	0.00372852	+	0.00645798i	0.000343238	+	0.000594505i
$119$	−26.7647	+	9.74154i	−2.45351	+	0.893005i
$120$		0			0
$121$	−7.59586	+	6.37368i	−0.690532	+	0.579426i
$122$	−11.6401	+	9.76724i	−1.05385	+	0.884284i
$123$		0			0
$124$	5.94496	−	2.16379i	0.533873	−	0.194314i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$		0			0
$127$	−1.43709	+	2.48911i	−0.127521	+	0.220873i	−0.922715	−	0.385482i	$-0.874035\pi$
$127$	−1.43709	+	2.48911i	−0.127521	+	0.220873i	0.795195	+	0.606354i	$0.207369\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$		0			0
$130$	−2.73304	−	0.994745i	−0.239703	−	0.0872449i
$131$	−3.09405	−	17.5473i	−0.270329	−	1.53311i	−0.753419	−	0.657540i	$-0.771597\pi$
$131$	−3.09405	−	17.5473i	−0.270329	−	1.53311i	0.483091	−	0.875570i	$-0.339514\pi$
$132$		0			0
$133$	6.59071	+	5.53026i	0.571487	+	0.479534i
$134$	−11.0445			−0.954099
$135$		0			0
$136$	6.33061			0.542845
$137$	13.3223	+	11.1787i	1.13820	+	0.955064i	0.999378	−	0.0352536i	$-0.0112239\pi$
$137$	13.3223	+	11.1787i	1.13820	+	0.955064i	0.138822	+	0.990317i	$0.455668\pi$
$138$		0			0
$139$	−3.09916	−	17.5762i	−0.262867	−	1.49079i	−0.775040	−	0.631912i	$-0.782270\pi$
$139$	−3.09916	−	17.5762i	−0.262867	−	1.49079i	0.512173	−	0.858882i	$-0.328841\pi$
$140$	−4.22782	−	1.53880i	−0.357316	−	0.130052i
$141$		0			0
$142$	−1.33144	+	7.55096i	−0.111732	+	0.633663i
$143$	−1.51428	+	2.62282i	−0.126631	+	0.219331i
$144$		0			0
$145$	−3.90037	−	6.75564i	−0.323908	−	0.561025i
$146$	8.00800	−	2.91467i	0.662747	−	0.241220i
$147$		0			0
$148$	1.67873	−	1.40863i	0.137991	−	0.115788i
$149$	−3.04070	+	2.55145i	−0.249104	+	0.209023i	−0.758786	−	0.651340i	$-0.774207\pi$
$149$	−3.04070	+	2.55145i	−0.249104	+	0.209023i	0.509683	+	0.860363i	$0.329763\pi$
$150$		0			0
$151$	11.1025	−	4.04096i	0.903505	−	0.328849i	0.151848	−	0.988404i	$-0.451477\pi$
$151$	11.1025	−	4.04096i	0.903505	−	0.328849i	0.751656	+	0.659555i	$0.229255\pi$
$152$	−0.956131	−	1.65607i	−0.0775525	−	0.134325i
$153$		0			0
$154$	−2.34249	+	4.05731i	−0.188763	+	0.326948i
$155$	−1.09858	+	6.23038i	−0.0882404	+	0.500436i
$156$		0			0
$157$	17.8295	+	6.48942i	1.42295	+	0.517912i	0.934902	−	0.354905i	$-0.115487\pi$
$157$	17.8295	+	6.48942i	1.42295	+	0.517912i	0.488048	+	0.872817i	$0.337709\pi$
$158$	−0.659995	−	3.74302i	−0.0525064	−	0.297778i
$159$		0			0
$160$	0.766044	+	0.642788i	0.0605611	+	0.0508168i
$161$	−24.6945			−1.94620
$162$		0			0
$163$	12.7000			0.994741			0.497371	−	0.867538i	$-0.334299\pi$
$163$	12.7000			0.994741			0.497371	+	0.867538i	$0.334299\pi$
$164$	6.63474	+	5.56721i	0.518086	+	0.434726i
$165$		0			0
$166$	−0.206338	−	1.17020i	−0.0160149	−	0.0908250i
$167$	2.79174	+	1.01611i	0.216032	+	0.0786291i	0.447769	−	0.894149i	$-0.352219\pi$
$167$	2.79174	+	1.01611i	0.216032	+	0.0786291i	−0.231737	+	0.972778i	$0.574441\pi$
$168$		0			0
$169$	−0.788531	+	4.47198i	−0.0606563	+	0.343999i
$170$	−3.16530	+	5.48247i	−0.242768	+	0.420486i
$171$		0			0
$172$	3.98512	+	6.90243i	0.303862	+	0.526305i
$173$	−2.45299	+	0.892817i	−0.186498	+	0.0678796i	−0.433581	−	0.901115i	$-0.642750\pi$
$173$	−2.45299	+	0.892817i	−0.186498	+	0.0678796i	0.247083	+	0.968994i	$0.420528\pi$
$174$		0			0
$175$	3.44655	−	2.89200i	0.260535	−	0.218615i
$176$	0.797685	−	0.669337i	0.0601277	−	0.0504532i
$177$		0			0
$178$	−3.30351	+	1.20238i	−0.247609	+	0.0901221i
$179$	6.62823	+	11.4804i	0.495418	+	0.858088i	0.999986	−	0.00528334i	$-0.00168175\pi$
$179$	6.62823	+	11.4804i	0.495418	+	0.858088i	−0.504569	+	0.863372i	$0.668348\pi$
$180$		0			0
$181$	−8.00291	+	13.8615i	−0.594852	+	1.03031i	0.398716	+	0.917074i	$0.369456\pi$
$181$	−8.00291	+	13.8615i	−0.594852	+	1.03031i	−0.993568	+	0.113239i	$0.963877\pi$
$182$	2.27228	−	12.8867i	0.168432	−	0.955227i
$183$		0			0
$184$	5.15770	+	1.87725i	0.380231	+	0.138393i
$185$	0.380538	+	2.15814i	0.0279777	+	0.158670i
$186$		0			0
$187$	5.04983	+	4.23731i	0.369280	+	0.309863i
$188$	−8.44910			−0.616214
$189$		0			0
$190$	1.91226			0.138730
$191$	1.61241	+	1.35297i	0.116670	+	0.0978974i	0.699256	−	0.714871i	$-0.253515\pi$
$191$	1.61241	+	1.35297i	0.116670	+	0.0978974i	−0.582586	+	0.812769i	$0.697959\pi$
$192$		0			0
$193$	1.72731	+	9.79605i	0.124334	+	0.705135i	0.981701	+	0.190429i	$0.0609879\pi$
$193$	1.72731	+	9.79605i	0.124334	+	0.705135i	−0.857367	+	0.514706i	$0.827901\pi$
$194$	−2.30205	−	0.837879i	−0.165278	−	0.0601562i
$195$		0			0
$196$	2.29951	−	13.0412i	0.164251	−	0.931513i
$197$	4.11536	−	7.12801i	0.293207	−	0.507850i	−0.681359	−	0.731949i	$-0.738611\pi$
$197$	4.11536	−	7.12801i	0.293207	−	0.507850i	0.974566	+	0.224100i	$0.0719441\pi$
$198$		0			0
$199$	−2.80269	−	4.85439i	−0.198677	−	0.344119i	0.749423	−	0.662092i	$-0.230331\pi$
$199$	−2.80269	−	4.85439i	−0.198677	−	0.344119i	−0.948100	+	0.317973i	$0.896998\pi$
$200$	−0.939693	+	0.342020i	−0.0664463	+	0.0241845i
$201$		0			0
$202$	4.88373	−	4.09794i	0.343618	−	0.288330i
$203$	26.8856	−	22.5597i	1.88700	−	1.58338i
$204$		0			0
$205$	−8.13872	+	2.96225i	−0.568433	+	0.206893i
$206$	−2.70124	−	4.67868i	−0.188204	−	0.325979i
$207$		0			0
$208$	−1.45422	+	2.51878i	−0.100832	+	0.174646i
$209$	0.345776	−	1.96099i	0.0239178	−	0.135645i
$210$		0			0
$211$	10.6547	+	3.87798i	0.733497	+	0.266971i	0.681644	−	0.731684i	$-0.261265\pi$
$211$	10.6547	+	3.87798i	0.733497	+	0.266971i	0.0518525	+	0.998655i	$0.483487\pi$
$212$	1.37953	+	7.82368i	0.0947462	+	0.537332i
$213$		0			0
$214$	−4.67620	−	3.92380i	−0.319659	−	0.268225i
$215$	−7.97023			−0.543565
$216$		0			0
$217$	−28.4639			−1.93225
$218$	−1.13992	−	0.956510i	−0.0772054	−	0.0647830i
$219$		0			0
$220$	0.180820	+	1.02548i	0.0121909	+	0.0691381i
$221$	−17.3018	−	6.29734i	−1.16385	−	0.423605i
$222$		0			0
$223$	−1.22919	+	6.97110i	−0.0823128	+	0.466819i	0.915591	+	0.402110i	$0.131723\pi$
$223$	−1.22919	+	6.97110i	−0.0823128	+	0.466819i	−0.997904	+	0.0647091i	$0.979388\pi$
$224$	−2.24958	+	3.89638i	−0.150306	+	0.260338i
$225$		0			0
$226$	−1.79868	−	3.11540i	−0.119646	−	0.207233i
$227$	−12.4488	+	4.53101i	−0.826259	+	0.300734i	−0.720323	−	0.693639i	$-0.756006\pi$
$227$	−12.4488	+	4.53101i	−0.826259	+	0.300734i	−0.105936	+	0.994373i	$0.533784\pi$
$228$		0			0
$229$	−13.3335	+	11.1881i	−0.881101	+	0.739332i	−0.966405	−	0.257023i	$-0.917258\pi$
$229$	−13.3335	+	11.1881i	−0.881101	+	0.739332i	0.0853038	+	0.996355i	$0.472814\pi$
$230$	−4.20459	+	3.52807i	−0.277243	+	0.232634i
$231$		0			0
$232$	−7.33030	+	2.66801i	−0.481258	+	0.175164i
$233$	10.8413	+	18.7776i	0.710236	+	1.23016i	0.964768	+	0.263101i	$0.0847451\pi$
$233$	10.8413	+	18.7776i	0.710236	+	1.23016i	−0.254532	+	0.967064i	$0.581922\pi$
$234$		0			0
$235$	4.22455	−	7.31713i	0.275579	−	0.477317i
$236$	−0.00129490	+	0.00734375i	−8.42908e−5	+	0.000478037i
$237$		0			0
$238$	−26.7647	−	9.74154i	−1.73490	−	0.631450i
$239$	−1.66281	−	9.43027i	−0.107558	−	0.609994i	−0.990168	−	0.139886i	$-0.955326\pi$
$239$	−1.66281	−	9.43027i	−0.107558	−	0.609994i	0.882609	−	0.470107i	$-0.155785\pi$
$240$		0			0
$241$	12.8166	+	10.7544i	0.825590	+	0.692752i	0.954274	−	0.298933i	$-0.0966308\pi$
$241$	12.8166	+	10.7544i	0.825590	+	0.692752i	−0.128684	+	0.991686i	$0.541075\pi$
$242$	−9.91569			−0.637405
$243$		0			0
$244$	−15.1951			−0.972768
$245$	10.1442	+	8.51203i	0.648092	+	0.543813i
$246$		0			0
$247$	0.965779	+	5.47721i	0.0614511	+	0.348506i
$248$	5.94496	+	2.16379i	0.377505	+	0.137401i
$249$		0			0
$250$	0.173648	−	0.984808i	0.0109825	−	0.0622847i
$251$	6.58047	−	11.3977i	0.415355	−	0.719417i	−0.580110	−	0.814538i	$-0.696991\pi$
$251$	6.58047	−	11.3977i	0.415355	−	0.719417i	0.995466	+	0.0951213i	$0.0303239\pi$
$252$		0			0
$253$	2.85771	+	4.94969i	0.179662	+	0.311184i
$254$	−2.70084	+	0.983025i	−0.169466	+	0.0616805i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−5.71894	+	4.79876i	−0.356737	+	0.299338i	−0.803489	−	0.595320i	$-0.797025\pi$
$257$	−5.71894	+	4.79876i	−0.356737	+	0.299338i	0.446751	+	0.894658i	$0.352581\pi$
$258$		0			0
$259$	−9.26498	+	3.37218i	−0.575698	+	0.209537i
$260$	−1.45422	−	2.51878i	−0.0901869	−	0.156208i
$261$		0			0
$262$	8.90897	−	15.4308i	0.550398	−	0.953318i
$263$	2.42282	−	13.7405i	0.149397	−	0.847274i	−0.814333	−	0.580397i	$-0.802897\pi$
$263$	2.42282	−	13.7405i	0.149397	−	0.847274i	0.963731	−	0.266877i	$-0.0859917\pi$
$264$		0			0
$265$	−7.46527	−	2.71714i	−0.458588	−	0.166912i
$266$	1.49399	+	8.47285i	0.0916025	+	0.519504i
$267$		0			0
$268$	−8.46057	−	7.09926i	−0.516812	−	0.433656i
$269$	5.79747			0.353478			0.176739	−	0.984258i	$-0.443445\pi$
$269$	5.79747			0.353478			0.176739	+	0.984258i	$0.443445\pi$
$270$		0			0
$271$	27.1766			1.65086			0.825431	−	0.564504i	$-0.190932\pi$
$271$	27.1766			1.65086			0.825431	+	0.564504i	$0.190932\pi$
$272$	4.84953	+	4.06924i	0.294046	+	0.246734i
$273$		0			0
$274$	3.01992	+	17.1268i	0.182440	+	1.03467i
$275$	−0.978505	−	0.356147i	−0.0590061	−	0.0214765i
$276$		0			0
$277$	−1.17705	+	6.67539i	−0.0707221	+	0.401085i	0.928812	+	0.370552i	$0.120832\pi$
$277$	−1.17705	+	6.67539i	−0.0707221	+	0.401085i	−0.999534	+	0.0305329i	$0.990280\pi$
$278$	8.92367	−	15.4563i	0.535206	−	0.927004i
$279$		0			0
$280$	−2.24958	−	3.89638i	−0.134438	−	0.232853i
$281$	−0.113162	+	0.0411874i	−0.00675065	+	0.00245704i	−0.345393	−	0.938458i	$-0.612254\pi$
$281$	−0.113162	+	0.0411874i	−0.00675065	+	0.00245704i	0.338643	+	0.940915i	$0.390032\pi$
$282$		0			0
$283$	23.4636	−	19.6883i	1.39477	−	1.17035i	0.431398	−	0.902162i	$-0.358021\pi$
$283$	23.4636	−	19.6883i	1.39477	−	1.17035i	0.963367	−	0.268185i	$-0.0864239\pi$
$284$	−5.87361	+	4.92854i	−0.348534	+	0.292455i
$285$		0			0
$286$	−2.84592	+	1.03583i	−0.168283	+	0.0612500i
$287$	−19.4837	−	33.7467i	−1.15008	−	1.99201i
$288$		0			0
$289$	−11.5383	+	19.9849i	−0.678723	+	1.17558i
$290$	1.35458	−	7.68223i	0.0795440	−	0.451116i
$291$		0			0
$292$	8.00800	+	2.91467i	0.468633	+	0.170568i
$293$	4.37636	+	24.8195i	0.255669	+	1.44997i	0.794348	+	0.607462i	$0.207812\pi$
$293$	4.37636	+	24.8195i	0.255669	+	1.44997i	−0.538679	+	0.842511i	$0.681076\pi$
$294$		0			0
$295$	−0.00571242	−	0.00479329i	−0.000332590	−	0.000279076i
$296$	2.19143			0.127374
$297$		0			0
$298$	−3.96935			−0.229938
$299$	−12.2288	−	10.2612i	−0.707211	−	0.593420i
$300$		0			0
$301$	−6.22690	−	35.3145i	−0.358913	−	2.03549i
$302$	11.1025	+	4.04096i	0.638874	+	0.232531i
$303$		0			0
$304$	0.332061	−	1.88321i	0.0190450	−	0.108010i
$305$	7.59756	−	13.1594i	0.435035	−	0.753503i
$306$		0			0
$307$	−13.3766	−	23.1690i	−0.763445	−	1.32233i	−0.941065	−	0.338227i	$-0.890173\pi$
$307$	−13.3766	−	23.1690i	−0.763445	−	1.32233i	0.177619	−	0.984099i	$-0.443160\pi$
$308$	−4.40244	+	1.60236i	−0.250852	+	0.0913028i
$309$		0			0
$310$	−4.84638	+	4.06659i	−0.275256	+	0.230967i
$311$	−21.4267	+	17.9791i	−1.21500	+	1.01950i	−0.215925	+	0.976410i	$0.569277\pi$
$311$	−21.4267	+	17.9791i	−1.21500	+	1.01950i	−0.999071	+	0.0430925i	$0.986279\pi$
$312$		0			0
$313$	29.3074	−	10.6670i	1.65655	−	0.602936i	0.666737	−	0.745293i	$-0.267690\pi$
$313$	29.3074	−	10.6670i	1.65655	−	0.602936i	0.989815	+	0.142357i	$0.0454683\pi$
$314$	9.48689	+	16.4318i	0.535376	+	0.927299i
$315$		0			0
$316$	1.90038	−	3.29155i	0.106905	−	0.185164i
$317$	3.17333	−	17.9968i	0.178232	−	1.01080i	−0.756115	−	0.654438i	$-0.772905\pi$
$317$	3.17333	−	17.9968i	0.178232	−	1.01080i	0.934347	−	0.356364i	$-0.115984\pi$
$318$		0			0
$319$	−7.63307	−	2.77821i	−0.427370	−	0.155550i
$320$	0.173648	+	0.984808i	0.00970723	+	0.0550524i
$321$		0			0
$322$	−18.9171	−	15.8733i	−1.05421	−	0.884587i
$323$	12.1058			0.673583
$324$		0			0
$325$	2.90844			0.161331
$326$	9.72877	+	8.16341i	0.538827	+	0.452129i
$327$		0			0
$328$	1.50397	+	8.52946i	0.0830431	+	0.470961i
$329$	35.7213	+	13.0015i	1.96938	+	0.716795i
$330$		0			0
$331$	−0.544913	+	3.09036i	−0.0299511	+	0.169861i	−0.996114	−	0.0880705i	$-0.971930\pi$
$331$	−0.544913	+	3.09036i	−0.0299511	+	0.169861i	0.966163	+	0.257932i	$0.0830410\pi$
$332$	0.594125	−	1.02906i	0.0326069	−	0.0564767i
$333$		0			0
$334$	1.48546	+	2.57288i	0.0812805	+	0.140782i
$335$	10.3784	−	3.77744i	0.567034	−	0.206384i
$336$		0			0
$337$	22.3508	−	18.7546i	1.21753	−	1.02163i	0.218578	−	0.975820i	$-0.429858\pi$
$337$	22.3508	−	18.7546i	1.21753	−	1.02163i	0.998950	−	0.0458079i	$-0.0145862\pi$
$338$	−3.47859	+	2.91888i	−0.189210	+	0.158766i
$339$		0			0
$340$	−5.94882	+	2.16520i	−0.322620	+	0.117424i
$341$	3.29390	+	5.70520i	0.178375	+	0.308954i
$342$		0			0
$343$	−14.0427	+	24.3226i	−0.758233	+	1.31330i
$344$	−1.38402	+	7.84915i	−0.0746212	+	0.423198i
$345$		0			0
$346$	−2.45299	−	0.892817i	−0.131874	−	0.0479981i
$347$	−0.859502	−	4.87448i	−0.0461405	−	0.261676i	0.953007	−	0.302947i	$-0.0979704\pi$
$347$	−0.859502	−	4.87448i	−0.0461405	−	0.261676i	−0.999148	+	0.0412710i	$0.986859\pi$
$348$		0			0
$349$	26.2542	+	22.0299i	1.40535	+	1.17923i	0.958664	+	0.284541i	$0.0918413\pi$
$349$	26.2542	+	22.0299i	1.40535	+	1.17923i	0.446689	+	0.894689i	$0.352603\pi$
$350$	4.49915			0.240490
$351$		0			0
$352$	1.04130			0.0555017
$353$	12.0053	+	10.0736i	0.638978	+	0.536166i	0.903704	−	0.428158i	$-0.140837\pi$
$353$	12.0053	+	10.0736i	0.638978	+	0.536166i	−0.264726	+	0.964324i	$0.585282\pi$
$354$		0			0
$355$	−1.33144	−	7.55096i	−0.0706654	−	0.400763i
$356$	−3.30351	−	1.20238i	−0.175086	−	0.0637260i
$357$		0			0
$358$	−2.30196	+	13.0551i	−0.121662	+	0.689982i
$359$	−4.84257	+	8.38757i	−0.255581	+	0.442679i	−0.965053	−	0.262054i	$-0.915600\pi$
$359$	−4.84257	+	8.38757i	−0.255581	+	0.442679i	0.709472	+	0.704733i	$0.248933\pi$
$360$		0			0
$361$	7.67163	+	13.2876i	0.403770	+	0.699350i
$362$	−15.0406	+	5.47432i	−0.790514	+	0.287724i
$363$		0			0
$364$	10.0241	−	8.41121i	0.525405	−	0.440867i
$365$	−6.52818	+	5.47779i	−0.341700	+	0.286721i
$366$		0			0
$367$	−18.8775	+	6.87086i	−0.985398	+	0.358656i	−0.783937	−	0.620841i	$-0.786791\pi$
$367$	−18.8775	+	6.87086i	−0.985398	+	0.358656i	−0.201462	+	0.979496i	$0.564569\pi$
$368$	2.74435	+	4.75336i	0.143059	+	0.247786i
$369$		0			0
$370$	−1.09572	+	1.89784i	−0.0569636	+	0.0986638i
$371$	6.20669	−	35.1999i	0.322236	−	1.82749i
$372$		0			0
$373$	20.7651	+	7.55789i	1.07518	+	0.391333i	0.818111	−	0.575061i	$-0.195022\pi$
$373$	20.7651	+	7.55789i	1.07518	+	0.391333i	0.257067	+	0.966394i	$0.417244\pi$
$374$	1.14470	+	6.49193i	0.0591912	+	0.335690i
$375$		0			0
$376$	−6.47239	−	5.43098i	−0.333788	−	0.280081i
$377$	22.6880			1.16849
$378$		0			0
$379$	−4.24995			−0.218305			−0.109153	−	0.994025i	$-0.534814\pi$
$379$	−4.24995			−0.218305			−0.109153	+	0.994025i	$0.534814\pi$
$380$	1.46488	+	1.22918i	0.0751466	+	0.0630555i
$381$		0			0
$382$	0.365503	+	2.07287i	0.0187007	+	0.106057i
$383$	−4.88582	−	1.77829i	−0.249654	−	0.0908666i	0.214162	−	0.976798i	$-0.431298\pi$
$383$	−4.88582	−	1.77829i	−0.249654	−	0.0908666i	−0.463816	+	0.885932i	$0.653520\pi$
$384$		0			0
$385$	0.813538	−	4.61381i	0.0414618	−	0.235141i
$386$	−4.97358	+	8.61450i	−0.253149	+	0.438467i
$387$		0			0
$388$	−1.22490	−	2.12159i	−0.0621848	−	0.107707i
$389$	−27.3531	+	9.95573i	−1.38686	+	0.504776i	−0.924250	−	0.381787i	$-0.875309\pi$
$389$	−27.3531	+	9.95573i	−1.38686	+	0.504776i	−0.462609	+	0.886562i	$0.653087\pi$
$390$		0			0
$391$	−26.6176	+	22.3348i	−1.34611	+	1.12952i
$392$	10.1442	−	8.51203i	0.512361	−	0.429922i
$393$		0			0
$394$	7.73435	−	2.81507i	0.389651	−	0.141821i
$395$	1.90038	+	3.29155i	0.0956185	+	0.165616i
$396$		0			0
$397$	15.5080	−	26.8607i	0.778326	−	1.34810i	−0.154581	−	0.987980i	$-0.549403\pi$
$397$	15.5080	−	26.8607i	0.778326	−	1.34810i	0.932906	−	0.360119i	$-0.117264\pi$
$398$	0.973363	−	5.52021i	0.0487903	−	0.276703i
$399$		0			0
$400$	−0.939693	−	0.342020i	−0.0469846	−	0.0171010i
$401$	−2.70680	−	15.3510i	−0.135171	−	0.766592i	−0.974741	−	0.223340i	$-0.928304\pi$
$401$	−2.70680	−	15.3510i	−0.135171	−	0.766592i	0.839570	−	0.543252i	$-0.182807\pi$
$402$		0			0
$403$	−14.0954	−	11.8274i	−0.702142	−	0.589167i
$404$	6.37526			0.317181
$405$		0			0
$406$	35.0967			1.74182
$407$	1.74807	+	1.46681i	0.0866487	+	0.0727069i
$408$		0			0
$409$	−4.70504	−	26.6836i	−0.232649	−	1.31942i	−0.847508	−	0.530783i	$-0.821898\pi$
$409$	−4.70504	−	26.6836i	−0.232649	−	1.31942i	0.614859	−	0.788637i	$-0.289213\pi$
$410$	−8.13872	−	2.96225i	−0.401943	−	0.146295i
$411$		0			0
$412$	0.938130	−	5.32040i	0.0462184	−	0.262117i
$413$	0.0167752	−	0.0290554i	0.000825452	−	0.00142972i
$414$		0			0
$415$	0.594125	+	1.02906i	0.0291645	+	0.0505143i
$416$	−2.73304	+	0.994745i	−0.133998	+	0.0487714i
$417$		0			0
$418$	1.52538	−	1.27995i	0.0746089	−	0.0626043i
$419$	17.8678	−	14.9928i	0.872897	−	0.732447i	−0.0918092	−	0.995777i	$-0.529265\pi$
$419$	17.8678	−	14.9928i	0.872897	−	0.732447i	0.964706	+	0.263329i	$0.0848205\pi$
$420$		0			0
$421$	−1.57077	+	0.571715i	−0.0765548	+	0.0278637i	−0.380014	−	0.924981i	$-0.624081\pi$
$421$	−1.57077	+	0.571715i	−0.0765548	+	0.0278637i	0.303459	+	0.952845i	$0.401859\pi$
$422$	5.66922	+	9.81938i	0.275973	+	0.478000i
$423$		0			0
$424$	−3.97219	+	6.88003i	−0.192906	+	0.334124i
$425$	1.09930	−	6.23443i	0.0533238	−	0.302414i
$426$		0			0
$427$	64.2422	+	23.3823i	3.10890	+	1.13155i
$428$	−1.06001	−	6.01161i	−0.0512375	−	0.290582i
$429$		0			0
$430$	−6.10555	−	5.12317i	−0.294436	−	0.247061i
$431$	30.5125			1.46974			0.734868	−	0.678210i	$-0.237244\pi$
$431$	30.5125			1.46974			0.734868	+	0.678210i	$0.237244\pi$
$432$		0			0
$433$	−20.6724			−0.993453			−0.496727	−	0.867907i	$-0.665465\pi$
$433$	−20.6724			−0.993453			−0.496727	+	0.867907i	$0.665465\pi$
$434$	−21.8046	−	18.2962i	−1.04665	−	0.878246i
$435$		0			0
$436$	−0.258400	−	1.46546i	−0.0123751	−	0.0701827i
$437$	9.86287	+	3.58979i	0.471805	+	0.171723i
$438$		0			0
$439$	5.59606	−	31.7368i	0.267085	−	1.51472i	−0.495945	−	0.868354i	$-0.665178\pi$
$439$	5.59606	−	31.7368i	0.267085	−	1.51472i	0.763030	−	0.646363i	$-0.223711\pi$
$440$	−0.520652	+	0.901795i	−0.0248211	+	0.0429914i
$441$		0			0
$442$	−9.20610	−	15.9454i	−0.437889	−	0.758447i
$443$	−7.90098	+	2.87572i	−0.375387	+	0.136630i	−0.522822	−	0.852442i	$-0.675121\pi$
$443$	−7.90098	+	2.87572i	−0.375387	+	0.136630i	0.147435	+	0.989072i	$0.452898\pi$
$444$		0			0
$445$	2.69305	−	2.25973i	0.127663	−	0.107122i
$446$	−5.42255	+	4.55006i	−0.256765	+	0.215452i
$447$		0			0
$448$	−4.22782	+	1.53880i	−0.199746	+	0.0727015i
$449$	0.268245	+	0.464614i	0.0126593	+	0.0219265i	0.872286	−	0.488997i	$-0.162637\pi$
$449$	0.268245	+	0.464614i	0.0126593	+	0.0219265i	−0.859626	+	0.510923i	$0.829304\pi$
$450$		0			0
$451$	−4.50939	+	7.81049i	−0.212339	+	0.367781i
$452$	0.624674	−	3.54270i	0.0293822	−	0.166635i
$453$		0			0
$454$	−12.4488	−	4.53101i	−0.584253	−	0.212651i
$455$	2.27228	+	12.8867i	0.106526	+	0.604139i
$456$		0			0
$457$	−13.3703	−	11.2190i	−0.625434	−	0.524802i	0.274072	−	0.961709i	$-0.411629\pi$
$457$	−13.3703	−	11.2190i	−0.625434	−	0.524802i	−0.899507	+	0.436907i	$0.856074\pi$
$458$	−17.4056			−0.813312
$459$		0			0
$460$	−5.48871			−0.255912
$461$	25.3547	+	21.2751i	1.18088	+	0.990879i	0.999973	+	0.00737974i	$0.00234906\pi$
$461$	25.3547	+	21.2751i	1.18088	+	0.990879i	0.180911	+	0.983499i	$0.442095\pi$
$462$		0			0
$463$	−0.530377	−	3.00792i	−0.0246487	−	0.139790i	0.970000	−	0.243105i	$-0.0781660\pi$
$463$	−0.530377	−	3.00792i	−0.0246487	−	0.139790i	−0.994649	+	0.103315i	$0.967055\pi$
$464$	−7.33030	−	2.66801i	−0.340301	−	0.123859i
$465$		0			0
$466$	−3.76514	+	21.3532i	−0.174417	+	0.989166i
$467$	−2.05999	+	3.56800i	−0.0953248	+	0.165107i	−0.909744	−	0.415169i	$-0.863722\pi$
$467$	−2.05999	+	3.56800i	−0.0953248	+	0.165107i	0.814419	+	0.580277i	$0.197056\pi$
$468$		0			0
$469$	24.8454	+	43.0335i	1.14725	+	1.98710i
$470$	7.93956	−	2.88976i	0.366224	−	0.133295i
$471$		0			0
$472$	−0.00571242	+	0.00479329i	−0.000262935	+	0.000220629i
$473$	−6.35773	+	5.33477i	−0.292329	+	0.245293i
$474$		0			0
$475$	−1.79694	+	0.654032i	−0.0824492	+	0.0300090i
$476$	−14.2412	−	24.6664i	−0.652743	−	1.13058i
$477$		0			0
$478$	4.78787	−	8.29284i	0.218992	−	0.379306i
$479$	0.869952	−	4.93374i	0.0397491	−	0.225428i	−0.958462	−	0.285221i	$-0.907933\pi$
$479$	0.869952	−	4.93374i	0.0397491	−	0.225428i	0.998211	+	0.0597929i	$0.0190440\pi$
$480$		0			0
$481$	−5.98927	−	2.17992i	−0.273087	−	0.0993957i
$482$	2.90529	+	16.4767i	0.132332	+	0.750493i
$483$		0			0
$484$	−7.59586	−	6.37368i	−0.345266	−	0.289713i
$485$	2.44980			0.111239
$486$		0			0
$487$	−17.8452			−0.808642			−0.404321	−	0.914617i	$-0.632492\pi$
$487$	−17.8452			−0.808642			−0.404321	+	0.914617i	$0.632492\pi$
$488$	−11.6401	−	9.76724i	−0.526924	−	0.442142i
$489$		0			0
$490$	2.29951	+	13.0412i	0.103881	+	0.589140i
$491$	8.81678	+	3.20904i	0.397896	+	0.144822i	0.533215	−	0.845980i	$-0.320984\pi$
$491$	8.81678	+	3.20904i	0.397896	+	0.144822i	−0.135319	+	0.990802i	$0.543206\pi$
$492$		0			0
$493$	8.57534	−	48.6332i	0.386214	−	2.19033i
$494$	−2.78085	+	4.81657i	−0.125116	+	0.216708i
$495$		0			0
$496$	3.16325	+	5.47890i	0.142034	+	0.246010i
$497$	32.4166	−	11.7987i	1.45408	−	0.529243i
$498$		0			0
$499$	4.72528	−	3.96498i	0.211532	−	0.177497i	−0.530865	−	0.847456i	$-0.678133\pi$
$499$	4.72528	−	3.96498i	0.211532	−	0.177497i	0.742398	+	0.669959i	$0.233689\pi$
$500$	0.766044	−	0.642788i	0.0342585	−	0.0287463i
$501$		0			0
$502$	12.3672	−	4.50130i	0.551977	−	0.200903i
$503$	13.7665	+	23.8443i	0.613818	+	1.06316i	0.990591	+	0.136858i	$0.0437005\pi$
$503$	13.7665	+	23.8443i	0.613818	+	1.06316i	−0.376773	+	0.926306i	$0.622966\pi$
$504$		0			0
$505$	−3.18763	+	5.52113i	−0.141848	+	0.245687i
$506$	−0.992471	+	5.62858i	−0.0441207	+	0.250221i
$507$		0			0
$508$	−2.70084	−	0.983025i	−0.119830	−	0.0436147i
$509$	−1.18154	−	6.70086i	−0.0523710	−	0.297011i	0.947361	−	0.320168i	$-0.103739\pi$
$509$	−1.18154	−	6.70086i	−0.0523710	−	0.297011i	−0.999732	+	0.0231572i	$0.992628\pi$
$510$		0			0
$511$	−29.3713	−	24.6454i	−1.29931	−	1.09025i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−7.46554			−0.329291
$515$	4.13854	+	3.47265i	0.182366	+	0.153023i
$516$		0			0
$517$	−1.52777	−	8.66441i	−0.0671912	−	0.381060i
$518$	−9.26498	−	3.37218i	−0.407080	−	0.148165i
$519$		0			0
$520$	0.505045	−	2.86426i	0.0221477	−	0.125606i
$521$	−6.67365	+	11.5591i	−0.292378	+	0.506414i	−0.974372	−	0.224945i	$-0.927780\pi$
$521$	−6.67365	+	11.5591i	−0.292378	+	0.506414i	0.681994	+	0.731358i	$0.261113\pi$
$522$		0			0
$523$	−1.06763	−	1.84919i	−0.0466843	−	0.0808596i	0.841739	−	0.539885i	$-0.181532\pi$
$523$	−1.06763	−	1.84919i	−0.0466843	−	0.0808596i	−0.888423	+	0.459025i	$0.848199\pi$
$524$	16.7434	−	6.09410i	0.731439	−	0.266222i
$525$		0			0
$526$	10.6882	−	8.96846i	0.466027	−	0.391043i
$527$	−30.6805	+	25.7440i	−1.33646	+	1.12143i
$528$		0			0
$529$	−6.69618	+	2.43721i	−0.291138	+	0.105966i
$530$	−3.97219	−	6.88003i	−0.172541	−	0.298849i
$531$		0			0
$532$	−4.30178	+	7.45090i	−0.186506	+	0.323037i
$533$	4.37422	−	24.8074i	0.189469	−	1.07453i
$534$		0			0
$535$	5.73621	+	2.08781i	0.247998	+	0.0902639i
$536$	−1.91786	−	10.8767i	−0.0828387	−	0.469802i
$537$		0			0
$538$	4.44112	+	3.72654i	0.191470	+	0.160663i
$539$	13.7893			0.593948
$540$		0			0
$541$	−15.8254			−0.680386			−0.340193	−	0.940356i	$-0.610492\pi$
$541$	−15.8254			−0.680386			−0.340193	+	0.940356i	$0.610492\pi$
$542$	20.8185	+	17.4688i	0.894231	+	0.750348i
$543$		0			0
$544$	1.09930	+	6.23443i	0.0471320	+	0.267299i
$545$	1.39832	+	0.508948i	0.0598976	+	0.0218009i
$546$		0			0
$547$	−2.23559	+	12.6787i	−0.0955870	+	0.542101i	0.898979	+	0.437992i	$0.144310\pi$
$547$	−2.23559	+	12.6787i	−0.0955870	+	0.542101i	−0.994566	+	0.104109i	$0.966801\pi$
$548$	−8.69551	+	15.0611i	−0.371454	+	0.643377i
$549$		0			0
$550$	−0.520652	−	0.901795i	−0.0222007	−	0.0384527i
$551$	−14.0175	+	5.10194i	−0.597164	+	0.217350i
$552$		0			0
$553$	−13.0995	+	10.9918i	−0.557048	+	0.467418i
$554$	−5.19253	+	4.35705i	−0.220609	+	0.185113i
$555$		0			0
$556$	16.7710	−	6.10415i	0.711250	−	0.258874i
$557$	−8.05089	−	13.9445i	−0.341127	−	0.590849i	0.643515	−	0.765433i	$-0.277475\pi$
$557$	−8.05089	−	13.9445i	−0.341127	−	0.590849i	−0.984642	+	0.174584i	$0.944142\pi$
$558$		0			0
$559$	11.5905	−	20.0753i	0.490225	−	0.849095i
$560$	0.781269	−	4.43080i	0.0330147	−	0.187235i
$561$		0			0
$562$	−0.113162	−	0.0411874i	−0.00477343	−	0.00173739i
$563$	−4.32216	−	24.5122i	−0.182157	−	1.03307i	−0.929554	−	0.368687i	$-0.879807\pi$
$563$	−4.32216	−	24.5122i	−0.182157	−	1.03307i	0.747396	−	0.664379i	$-0.231304\pi$
$564$		0			0
$565$	2.75573	+	2.31234i	0.115935	+	0.0972807i
$566$	30.6295			1.28746
$567$		0			0
$568$	−7.66745			−0.321719
$569$	−21.5829	−	18.1102i	−0.904804	−	0.759220i	0.0663197	−	0.997798i	$-0.478874\pi$
$569$	−21.5829	−	18.1102i	−0.904804	−	0.759220i	−0.971123	+	0.238578i	$0.923319\pi$
$570$		0			0
$571$	3.70345	+	21.0033i	0.154985	+	0.878961i	0.958800	+	0.284082i	$0.0916888\pi$
$571$	3.70345	+	21.0033i	0.154985	+	0.878961i	−0.803815	+	0.594879i	$0.797200\pi$
$572$	−2.84592	−	1.03583i	−0.118994	−	0.0433103i
$573$		0			0
$574$	6.76661	−	38.3753i	0.282433	−	1.60176i
$575$	2.74435	−	4.75336i	0.114447	−	0.198229i
$576$		0			0
$577$	18.0221	+	31.2151i	0.750269	+	1.29950i	0.947692	+	0.319185i	$0.103409\pi$
$577$	18.0221	+	31.2151i	0.750269	+	1.29950i	−0.197424	+	0.980318i	$0.563257\pi$
$578$	−21.6849	+	7.89266i	−0.901973	+	0.328291i
$579$		0			0
$580$	5.97572	−	5.01422i	0.248128	−	0.208204i
$581$	−4.09537	+	3.43642i	−0.169904	+	0.142567i
$582$		0			0
$583$	−7.77361	+	2.82936i	−0.321950	+	0.117180i
$584$	4.26097	+	7.38021i	0.176320	+	0.305395i
$585$		0			0
$586$	−12.6012	+	21.8259i	−0.520551	+	0.901621i
$587$	2.88975	−	16.3886i	0.119273	−	0.676429i	−0.865273	−	0.501301i	$-0.832855\pi$
$587$	2.88975	−	16.3886i	0.119273	−	0.676429i	0.984546	−	0.175128i	$-0.0560339\pi$
$588$		0			0
$589$	11.3683	+	4.13773i	0.468423	+	0.170492i
$590$	−0.00129490	−	0.00734375i	−5.33102e−5	−	0.000302337i
$591$		0			0
$592$	1.67873	+	1.40863i	0.0689956	+	0.0578942i
$593$	17.9818			0.738423			0.369211	−	0.929345i	$-0.379628\pi$
$593$	17.9818			0.738423			0.369211	+	0.929345i	$0.379628\pi$
$594$		0			0
$595$	28.4824			1.16766
$596$	−3.04070	−	2.55145i	−0.124552	−	0.104511i
$597$		0			0
$598$	−2.77205	−	15.7211i	−0.113357	−	0.642882i
$599$	−17.1440	−	6.23989i	−0.700484	−	0.254955i	−0.0328662	−	0.999460i	$-0.510464\pi$
$599$	−17.1440	−	6.23989i	−0.700484	−	0.254955i	−0.667617	+	0.744505i	$0.732686\pi$
$600$		0			0
$601$	7.02934	−	39.8654i	0.286733	−	1.62614i	−0.412297	−	0.911049i	$-0.635273\pi$
$601$	7.02934	−	39.8654i	0.286733	−	1.62614i	0.699030	−	0.715092i	$-0.253615\pi$
$602$	17.9296	−	31.0551i	0.730758	−	1.26571i
$603$		0			0
$604$	5.90749	+	10.2321i	0.240372	+	0.416337i
$605$	9.31770	−	3.39136i	0.378818	−	0.137879i
$606$		0			0
$607$	−12.7734	+	10.7182i	−0.518457	+	0.435037i	−0.864093	−	0.503332i	$-0.832107\pi$
$607$	−12.7734	+	10.7182i	−0.518457	+	0.435037i	0.345637	+	0.938368i	$0.387663\pi$
$608$	1.46488	−	1.22918i	0.0594086	−	0.0498498i
$609$		0			0
$610$	14.2787	−	5.19704i	0.578129	−	0.210422i
$611$	12.2869	+	21.2815i	0.497073	+	0.860955i
$612$		0			0
$613$	−7.23109	+	12.5246i	−0.292061	+	0.505864i	−0.974297	−	0.225268i	$-0.927674\pi$
$613$	−7.23109	+	12.5246i	−0.292061	+	0.505864i	0.682236	+	0.731132i	$0.261008\pi$
$614$	4.64566	−	26.3468i	0.187484	−	1.06327i
$615$		0			0
$616$	−4.40244	−	1.60236i	−0.177379	−	0.0645608i
$617$	1.25002	+	7.08922i	0.0503239	+	0.285401i	0.999576	−	0.0291148i	$-0.00926885\pi$
$617$	1.25002	+	7.08922i	0.0503239	+	0.285401i	−0.949252	+	0.314516i	$0.898158\pi$
$618$		0			0
$619$	0.656586	+	0.550941i	0.0263904	+	0.0221442i	0.655887	−	0.754859i	$-0.272295\pi$
$619$	0.656586	+	0.550941i	0.0263904	+	0.0221442i	−0.629497	+	0.777003i	$0.716739\pi$
$620$	−6.32649			−0.254078
$621$		0			0
$622$	−27.9706			−1.12152
$623$	12.1164	+	10.1669i	0.485434	+	0.407328i
$624$		0			0
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	29.3074	+	10.6670i	1.17136	+	0.426340i
$627$		0			0
$628$	−3.29476	+	18.6855i	−0.131475	+	0.745634i
$629$	−6.93655	+	12.0145i	−0.276578	+	0.479048i
$630$		0			0
$631$	−20.8032	−	36.0322i	−0.828162	−	1.43442i	−0.899479	−	0.436965i	$-0.856053\pi$
$631$	−20.8032	−	36.0322i	−0.828162	−	1.43442i	0.0713167	−	0.997454i	$-0.477280\pi$
$632$	3.57154	−	1.29994i	0.142068	−	0.0517087i
$633$		0			0
$634$	13.9990	−	11.7466i	0.555973	−	0.466517i
$635$	2.20174	−	1.84748i	0.0873736	−	0.0733151i
$636$		0			0
$637$	−36.1919	+	13.1728i	−1.43398	+	0.521924i
$638$	−4.06147	−	7.03467i	−0.160795	−	0.278505i
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−3.28567	+	18.6340i	−0.129776	+	0.735998i	0.848580	+	0.529068i	$0.177458\pi$
$641$	−3.28567	+	18.6340i	−0.129776	+	0.735998i	−0.978356	+	0.206930i	$0.933653\pi$
$642$		0			0
$643$	−1.56943	−	0.571224i	−0.0618921	−	0.0225269i	0.310889	−	0.950446i	$-0.399373\pi$
$643$	−1.56943	−	0.571224i	−0.0618921	−	0.0225269i	−0.372781	+	0.927919i	$0.621596\pi$
$644$	−4.28816	−	24.3194i	−0.168977	−	0.958317i
$645$		0			0
$646$	9.27356	+	7.78144i	0.364863	+	0.306157i
$647$	41.9906			1.65082			0.825410	−	0.564533i	$-0.190944\pi$
$647$	41.9906			1.65082			0.825410	+	0.564533i	$0.190944\pi$
$648$		0			0
$649$	−0.00776504			−0.000304804
$650$	2.22799	+	1.86951i	0.0873892	+	0.0733282i
$651$		0			0
$652$	2.20533	+	12.5071i	0.0863675	+	0.489814i
$653$	−44.3845	−	16.1546i	−1.73690	−	0.632179i	−0.737816	−	0.675002i	$-0.764143\pi$
$653$	−44.3845	−	16.1546i	−1.73690	−	0.632179i	−0.999083	+	0.0428222i	$0.986365\pi$
$654$		0			0
$655$	−3.09405	+	17.5473i	−0.120895	+	0.685628i
$656$	−4.33052	+	7.50068i	−0.169078	+	0.292852i
$657$		0			0
$658$	19.0069	+	32.9209i	0.740966	+	1.28339i
$659$	−27.5273	+	10.0191i	−1.07231	+	0.390289i	−0.817040	−	0.576581i	$-0.804387\pi$
$659$	−27.5273	+	10.0191i	−1.07231	+	0.390289i	−0.255270	+	0.966870i	$0.582164\pi$
$660$		0			0
$661$	6.81275	−	5.71658i	0.264985	−	0.222349i	−0.500608	−	0.865674i	$-0.666890\pi$
$661$	6.81275	−	5.71658i	0.264985	−	0.222349i	0.765593	+	0.643325i	$0.222446\pi$
$662$	−2.40387	+	2.01709i	−0.0934291	+	0.0783963i
$663$		0			0
$664$	1.11659	−	0.406406i	0.0433321	−	0.0157716i
$665$	−4.30178	−	7.45090i	−0.166816	−	0.288933i
$666$		0			0
$667$	21.4080	−	37.0797i	0.828921	−	1.43573i
$668$	−0.515893	+	2.92578i	−0.0199605	+	0.113202i
$669$		0			0
$670$	10.3784	+	3.77744i	0.400954	+	0.145935i
$671$	−2.74759	−	15.5823i	−0.106069	−	0.601550i
$672$		0			0
$673$	19.3051	+	16.1989i	0.744157	+	0.624422i	0.933951	−	0.357402i	$-0.116338\pi$
$673$	19.3051	+	16.1989i	0.744157	+	0.624422i	−0.189794	+	0.981824i	$0.560782\pi$
$674$	29.1770			1.12385
$675$		0			0
$676$	−4.54097			−0.174653
$677$	−29.9879	−	25.1629i	−1.15253	−	0.967088i	−0.152754	−	0.988264i	$-0.548814\pi$
$677$	−29.9879	−	25.1629i	−1.15253	−	0.967088i	−0.999776	+	0.0211766i	$0.993259\pi$
$678$		0			0
$679$	1.91395	+	10.8546i	0.0734507	+	0.416559i
$680$	−5.94882	−	2.16520i	−0.228127	−	0.0830314i
$681$		0			0
$682$	−1.14396	+	6.48772i	−0.0438045	+	0.248427i
$683$	−4.97083	+	8.60974i	−0.190204	+	0.329442i	−0.945318	−	0.326151i	$-0.894248\pi$
$683$	−4.97083	+	8.60974i	−0.190204	+	0.329442i	0.755114	+	0.655594i	$0.227582\pi$
$684$		0			0
$685$	−8.69551	−	15.0611i	−0.332238	−	0.575454i
$686$	−26.3916	+	9.60575i	−1.00763	+	0.366749i
$687$		0			0
$688$	−6.10555	+	5.12317i	−0.232772	+	0.195319i
$689$	17.7000	−	14.8521i	0.674317	−	0.565819i
$690$		0			0
$691$	−30.8004	+	11.2104i	−1.17170	+	0.426464i	−0.853264	−	0.521480i	$-0.825380\pi$
$691$	−30.8004	+	11.2104i	−1.17170	+	0.426464i	−0.318437	+	0.947944i	$0.603158\pi$
$692$	−1.30521	−	2.26069i	−0.0496167	−	0.0859386i
$693$		0			0
$694$	2.47484	−	4.28655i	0.0939436	−	0.162715i
$695$	−3.09916	+	17.5762i	−0.117558	+	0.666703i
$696$		0			0
$697$	−51.5230	−	18.7528i	−1.95157	−	0.710315i
$698$	5.95133	+	33.7517i	0.225261	+	1.27752i
$699$		0			0
$700$	3.44655	+	2.89200i	0.130267	+	0.109307i
$701$	−13.4334			−0.507373			−0.253687	−	0.967286i	$-0.581643\pi$
$701$	−13.4334			−0.507373			−0.253687	+	0.967286i	$0.581643\pi$
$702$		0			0
$703$	4.19059			0.158051
$704$	0.797685	+	0.669337i	0.0300639	+	0.0252266i
$705$		0			0
$706$	2.72138	+	15.4337i	0.102421	+	0.580856i
$707$	−26.9534	−	9.81025i	−1.01369	−	0.368952i
$708$		0			0
$709$	−1.52552	+	8.65166i	−0.0572922	+	0.324920i	−0.999961	−	0.00880904i	$-0.997196\pi$
$709$	−1.52552	+	8.65166i	−0.0572922	+	0.324920i	0.942669	+	0.333729i	$0.108307\pi$
$710$	3.83372	−	6.64020i	0.143877	−	0.249202i
$711$		0			0
$712$	−1.75776	−	3.04453i	−0.0658749	−	0.114099i
$713$	−32.6302	+	11.8764i	−1.22201	+	0.444775i
$714$		0			0
$715$	2.32002	−	1.94673i	0.0867638	−	0.0728035i
$716$	−10.1550	+	8.52109i	−0.379512	+	0.318448i
$717$		0			0
$718$	−9.10105	+	3.31251i	−0.339648	+	0.123622i
$719$	−13.7650	−	23.8417i	−0.513349	−	0.889147i	−0.999880	−	0.0154833i	$-0.995071\pi$
$719$	−13.7650	−	23.8417i	−0.513349	−	0.889147i	0.486531	−	0.873663i	$-0.338262\pi$
$720$		0			0
$721$	−12.1533	+	21.0501i	−0.452612	+	0.783947i
$722$	−2.66433	+	15.1102i	−0.0991560	+	0.562342i
$723$		0			0
$724$	−15.0406	−	5.47432i	−0.558978	−	0.203451i
$725$	1.35458	+	7.68223i	0.0503080	+	0.285311i
$726$		0			0
$727$	−30.1042	−	25.2604i	−1.11650	−	0.936856i	−0.118079	−	0.993004i	$-0.537674\pi$
$727$	−30.1042	−	25.2604i	−1.11650	−	0.936856i	−0.998422	+	0.0561481i	$0.982118\pi$
$728$	13.0855			0.484981
$729$		0			0
$730$	−8.52193			−0.315411
$731$	−38.6519	−	32.4328i	−1.42959	−	1.19957i
$732$		0			0
$733$	−3.37643	−	19.1487i	−0.124711	−	0.707273i	−0.981479	−	0.191570i	$-0.938642\pi$
$733$	−3.37643	−	19.1487i	−0.124711	−	0.707273i	0.856768	−	0.515703i	$-0.172469\pi$
$734$	−18.8775	−	6.87086i	−0.696782	−	0.253608i
$735$		0			0
$736$	−0.953104	+	5.40532i	−0.0351319	+	0.199243i
$737$	5.75033	−	9.95987i	0.211816	−	0.366876i
$738$		0			0
$739$	25.3396	+	43.8894i	0.932132	+	1.61450i	0.779671	+	0.626190i	$0.215386\pi$
$739$	25.3396	+	43.8894i	0.932132	+	1.61450i	0.152461	+	0.988310i	$0.451280\pi$
$740$	−2.05927	+	0.749514i	−0.0757004	+	0.0275527i
$741$		0			0
$742$	27.3807	−	22.9751i	1.00518	−	0.843443i
$743$	−16.4209	+	13.7788i	−0.602426	+	0.505495i	−0.892224	−	0.451592i	$-0.850856\pi$
$743$	−16.4209	+	13.7788i	−0.602426	+	0.505495i	0.289798	+	0.957088i	$0.406412\pi$
$744$		0			0
$745$	3.72997	−	1.35760i	0.136655	−	0.0497385i
$746$	11.0489	+	19.1373i	0.404529	+	0.700665i
$747$		0			0
$748$	−3.29604	+	5.70891i	−0.120515	+	0.208738i
$749$	−4.76914	+	27.0471i	−0.174261	+	0.988281i
$750$		0			0
$751$	0.0575145	+	0.0209336i	0.00209873	+	0.000763877i	0.343069	−	0.939310i	$-0.388533\pi$
$751$	0.0575145	+	0.0209336i	0.00209873	+	0.000763877i	−0.340971	+	0.940074i	$0.610756\pi$
$752$	−1.46717	−	8.32074i	−0.0535022	−	0.303426i
$753$		0			0
$754$	17.3800	+	14.5836i	0.632943	+	0.531102i
$755$	−11.8150			−0.429991
$756$		0			0
$757$	7.63063			0.277340			0.138670	−	0.990339i	$-0.455717\pi$
$757$	7.63063			0.277340			0.138670	+	0.990339i	$0.455717\pi$
$758$	−3.25565	−	2.73182i	−0.118251	−	0.0992241i
$759$		0			0
$760$	0.332061	+	1.88321i	0.0120451	+	0.0683112i
$761$	25.0005	+	9.09944i	0.906268	+	0.329854i	0.752762	−	0.658293i	$-0.228721\pi$
$761$	25.0005	+	9.09944i	0.906268	+	0.329854i	0.153506	+	0.988148i	$0.450944\pi$
$762$		0			0
$763$	−1.16258	+	6.59332i	−0.0420882	+	0.238694i
$764$	−1.05242	+	1.82285i	−0.0380753	+	0.0659484i
$765$		0			0
$766$	−2.59969	−	4.50280i	−0.0939307	−	0.162693i
$767$	0.0203804	−	0.00741785i	0.000735893	−	0.000267843i
$768$		0			0
$769$	−13.0099	+	10.9166i	−0.469150	+	0.393663i	−0.846484	−	0.532414i	$-0.821285\pi$
$769$	−13.0099	+	10.9166i	−0.469150	+	0.393663i	0.377335	+	0.926077i	$0.376841\pi$
$770$	3.58890	−	3.01145i	0.129335	−	0.108525i
$771$		0			0
$772$	−9.34728	+	3.40213i	−0.336416	+	0.122445i
$773$	−10.2787	−	17.8032i	−0.369698	−	0.640335i	0.619820	−	0.784744i	$-0.287205\pi$
$773$	−10.2787	−	17.8032i	−0.369698	−	0.640335i	−0.989518	+	0.144408i	$0.953872\pi$
$774$		0			0
$775$	3.16325	−	5.47890i	0.113627	−	0.196808i
$776$	0.425403	−	2.41258i	0.0152711	−	0.0866065i
$777$		0			0
$778$	−27.3531	−	9.95573i	−0.980658	−	0.356930i
$779$	2.87599	+	16.3106i	0.103043	+	0.584387i
$780$		0			0
$781$	−6.11620	−	5.13211i	−0.218855	−	0.183641i
$782$	−34.7469			−1.24255
$783$		0			0
$784$	13.2424			0.472941
$785$	−14.5348	−	12.1961i	−0.518768	−	0.435298i
$786$		0			0
$787$	8.44956	+	47.9199i	0.301194	+	1.70816i	0.640898	+	0.767626i	$0.278562\pi$
$787$	8.44956	+	47.9199i	0.301194	+	1.70816i	−0.339704	+	0.940533i	$0.610327\pi$
$788$	7.73435	+	2.81507i	0.275525	+	0.100283i
$789$		0			0
$790$	−0.659995	+	3.74302i	−0.0234816	+	0.133171i
$791$	−8.09252	+	14.0167i	−0.287737	+	0.498375i
$792$		0			0
$793$	22.0971	+	38.2732i	0.784690	+	1.35912i
$794$	29.1456	−	10.6081i	1.03434	−	0.376468i
$795$		0			0
$796$	4.29396	−	3.60306i	0.152196	−	0.127707i
$797$	−31.7229	+	26.6187i	−1.12368	+	0.942882i	−0.998785	−	0.0492878i	$-0.984305\pi$
$797$	−31.7229	+	26.6187i	−1.12368	+	0.942882i	−0.124898	+	0.992170i	$0.539860\pi$
$798$		0			0
$799$	50.2622	−	18.2939i	1.77815	−	0.647193i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	7.79391	−	13.4994i	0.275212	−	0.476682i
$803$	−1.54094	+	8.73910i	−0.0543786	+	0.308396i
$804$		0			0
$805$	23.2053	+	8.44603i	0.817878	+	0.297683i
$806$	−3.19517	−	18.1207i	−0.112545	−	0.638274i
$807$		0			0
$808$	4.88373	+	4.09794i	0.171809	+	0.144165i
$809$	−6.03595			−0.212213			−0.106106	−	0.994355i	$-0.533838\pi$
$809$	−6.03595			−0.212213			−0.106106	+	0.994355i	$0.533838\pi$
$810$		0			0
$811$	−10.8481			−0.380927			−0.190463	−	0.981694i	$-0.560999\pi$
$811$	−10.8481			−0.380927			−0.190463	+	0.981694i	$0.560999\pi$
$812$	26.8856	+	22.5597i	0.943501	+	0.791692i
$813$		0			0
$814$	0.396256	+	2.24728i	0.0138888	+	0.0787671i
$815$	−11.9341	−	4.34366i	−0.418033	−	0.152152i
$816$		0			0
$817$	−2.64660	+	15.0096i	−0.0925929	+	0.525120i
$818$	13.5476	−	23.4652i	0.473682	−	0.820441i
$819$		0			0
$820$	−4.33052	−	7.50068i	−0.151228	−	0.261935i
$821$	−0.405758	+	0.147684i	−0.0141611	+	0.00515420i	−0.349091	−	0.937089i	$-0.613510\pi$
$821$	−0.405758	+	0.147684i	−0.0141611	+	0.00515420i	0.334930	+	0.942243i	$0.391287\pi$
$822$		0			0
$823$	−27.4766	+	23.0556i	−0.957773	+	0.803667i	−0.980589	−	0.196073i	$-0.937181\pi$
$823$	−27.4766	+	23.0556i	−0.957773	+	0.803667i	0.0228166	+	0.999740i	$0.492737\pi$
$824$	4.13854	−	3.47265i	0.144173	−	0.120975i
$825$		0			0
$826$	0.0315270	−	0.0114749i	0.00109696	−	0.000399262i
$827$	11.0212	+	19.0893i	0.383245	+	0.663800i	0.991524	−	0.129923i	$-0.0414730\pi$
$827$	11.0212	+	19.0893i	0.383245	+	0.663800i	−0.608279	+	0.793724i	$0.708140\pi$
$828$		0			0
$829$	−4.69740	+	8.13614i	−0.163148	+	0.282580i	−0.935996	−	0.352011i	$-0.885498\pi$
$829$	−4.69740	+	8.13614i	−0.163148	+	0.282580i	0.772848	+	0.634591i	$0.218831\pi$
$830$	−0.206338	+	1.17020i	−0.00716208	+	0.0406182i
$831$		0			0
$832$	−2.73304	−	0.994745i	−0.0947511	−	0.0344866i
$833$	14.5573	+	82.5586i	0.504381	+	2.86049i
$834$		0			0
$835$	−2.27585	−	1.90967i	−0.0787591	−	0.0660867i
$836$	1.99124			0.0688686
$837$		0			0
$838$	23.3247			0.805738
$839$	32.3444	+	27.1401i	1.11665	+	0.936982i	0.998430	−	0.0560056i	$-0.0178365\pi$
$839$	32.3444	+	27.1401i	1.11665	+	0.936982i	0.118221	+	0.992987i	$0.462281\pi$
$840$		0			0
$841$	5.53097	+	31.3677i	0.190723	+	1.08164i
$842$	−1.57077	−	0.571715i	−0.0541324	−	0.0197026i
$843$		0			0
$844$	−1.96890	+	11.1662i	−0.0677724	+	0.384356i
$845$	2.27049	−	3.93260i	0.0781071	−	0.135285i
$846$		0			0
$847$	22.3061	+	38.6353i	0.766446	+	1.32752i
$848$	−7.46527	+	2.71714i	−0.256358	+	0.0933068i
$849$		0			0
$850$	4.84953	−	4.06924i	0.166337	−	0.139574i
$851$	−9.21409	+	7.73154i	−0.315855	+	0.265034i
$852$		0			0
$853$	22.5933	−	8.22328i	0.773579	−	0.281560i	0.0750865	−	0.997177i	$-0.476077\pi$
$853$	22.5933	−	8.22328i	0.773579	−	0.281560i	0.698493	+	0.715617i	$0.253854\pi$
$854$	34.1826	+	59.2060i	1.16970	+	2.02599i
$855$		0			0
$856$	3.05217	−	5.28652i	0.104321	−	0.180690i
$857$	−2.81752	+	15.9789i	−0.0962446	+	0.545830i	0.898114	+	0.439762i	$0.144937\pi$
$857$	−2.81752	+	15.9789i	−0.0962446	+	0.545830i	−0.994359	+	0.106068i	$0.966174\pi$
$858$		0			0
$859$	−3.42952	−	1.24824i	−0.117014	−	0.0425895i	0.282850	−	0.959164i	$-0.408720\pi$
$859$	−3.42952	−	1.24824i	−0.117014	−	0.0425895i	−0.399863	+	0.916575i	$0.630942\pi$
$860$	−1.38402	−	7.84915i	−0.0471946	−	0.267654i
$861$		0			0
$862$	23.3739	+	19.6131i	0.796120	+	0.668024i
$863$	−55.7759			−1.89863			−0.949317	−	0.314319i	$-0.898224\pi$
$863$	−55.7759			−1.89863			−0.949317	+	0.314319i	$0.898224\pi$
$864$		0			0
$865$	2.61042			0.0887570
$866$	−15.8360	−	13.2880i	−0.538129	−	0.451544i
$867$		0			0
$868$	−4.94270	−	28.0314i	−0.167766	−	0.951448i
$869$	3.71906	+	1.35363i	0.126161	+	0.0459187i
$870$		0			0
$871$	−5.57797	+	31.6342i	−0.189002	+	1.07189i
$872$	0.744033	−	1.28870i	0.0251961	−	0.0436410i
$873$		0			0
$874$	5.24792	+	9.08967i	0.177514	+	0.307463i
$875$	−4.22782	+	1.53880i	−0.142926	+	0.0520209i
$876$		0			0
$877$	−12.4065	+	10.4103i	−0.418938	+	0.351531i	−0.827759	−	0.561084i	$-0.810384\pi$
$877$	−12.4065	+	10.4103i	−0.418938	+	0.351531i	0.408821	+	0.912615i	$0.365940\pi$
$878$	24.6869	−	20.7147i	0.833142	−	0.699089i
$879$		0			0
$880$	−0.978505	+	0.356147i	−0.0329854	+	0.0120057i
$881$	8.24703	+	14.2843i	0.277849	+	0.481249i	0.970850	−	0.239688i	$-0.0770450\pi$
$881$	8.24703	+	14.2843i	0.277849	+	0.481249i	−0.693001	+	0.720937i	$0.743712\pi$
$882$		0			0
$883$	8.85612	−	15.3393i	0.298032	−	0.516207i	−0.677653	−	0.735381i	$-0.737003\pi$
$883$	8.85612	−	15.3393i	0.298032	−	0.516207i	0.975686	+	0.219174i	$0.0703363\pi$
$884$	3.19724	−	18.1325i	0.107535	−	0.609861i
$885$		0			0
$886$	−7.90098	−	2.87572i	−0.265439	−	0.0966118i
$887$	5.54900	+	31.4699i	0.186317	+	1.05666i	0.924251	+	0.381784i	$0.124690\pi$
$887$	5.54900	+	31.4699i	0.186317	+	1.05666i	−0.737934	+	0.674873i	$0.764199\pi$
$888$		0			0
$889$	9.90598	+	8.31211i	0.332236	+	0.278779i
$890$	3.51552			0.117841
$891$		0			0
$892$	−7.07864			−0.237010
$893$	−12.3769	−	10.3854i	−0.414177	−	0.347536i
$894$		0			0
$895$	−2.30196	−	13.0551i	−0.0769461	−	0.436383i
$896$	−4.22782	−	1.53880i	−0.141242	−	0.0514077i
$897$		0			0
$898$	−0.0931605	+	0.528340i	−0.00310881	+	0.0176309i
$899$	24.6757	−	42.7395i	0.822980	−	1.42544i
$900$		0			0
$901$	−25.1463	−	43.5548i	−0.837746	−	1.45102i
$902$	−8.47487	+	3.08460i	−0.282182	+	0.102706i
$903$		0			0
$904$	2.75573	−	2.31234i	0.0916544	−	0.0769071i
$905$	12.2612	−	10.2883i	0.407575	−	0.341996i
$906$		0			0
$907$	25.9562	−	9.44729i	0.861862	−	0.313692i	0.126995	−	0.991903i	$-0.459467\pi$
$907$	25.9562	−	9.44729i	0.861862	−	0.313692i	0.734867	+	0.678211i	$0.237244\pi$
$908$	−6.62389	−	11.4729i	−0.219822	−	0.380742i
$909$		0			0
$910$	−6.54276	+	11.3324i	−0.216890	+	0.375665i
$911$	−0.673457	+	3.81936i	−0.0223126	+	0.126541i	−0.993929	−	0.110019i	$-0.964909\pi$
$911$	−0.673457	+	3.81936i	−0.0223126	+	0.126541i	0.971617	+	0.236560i	$0.0760200\pi$
$912$		0			0
$913$	1.16271	+	0.423192i	0.0384801	+	0.0140056i
$914$	−3.03079	−	17.1885i	−0.100250	−	0.568544i
$915$		0			0
$916$	−13.3335	−	11.1881i	−0.440551	−	0.369666i
$917$	−80.1656			−2.64730
$918$		0			0
$919$	−1.19751			−0.0395023			−0.0197512	−	0.999805i	$-0.506287\pi$
$919$	−1.19751			−0.0395023			−0.0197512	+	0.999805i	$0.506287\pi$
$920$	−4.20459	−	3.52807i	−0.138621	−	0.116317i
$921$		0			0
$922$	5.74743	+	32.5953i	0.189282	+	1.07347i
$923$	20.9554	+	7.62716i	0.689757	+	0.251051i
$924$		0			0
$925$	0.380538	−	2.15814i	0.0125120	−	0.0709592i
$926$	1.52716	−	2.64512i	0.0501856	−	0.0869240i
$927$		0			0
$928$	−3.90037	−	6.75564i	−0.128036	−	0.221765i
$929$	22.0336	−	8.01959i	0.722900	−	0.263114i	0.0457436	−	0.998953i	$-0.485434\pi$
$929$	22.0336	−	8.01959i	0.722900	−	0.263114i	0.677156	+	0.735839i	$0.263212\pi$
$930$		0			0
$931$	19.3984	−	16.2772i	0.635758	−	0.533464i
$932$	−16.6098	+	13.9373i	−0.544072	+	0.456531i
$933$		0			0
$934$	−3.87151	+	1.40911i	−0.126680	+	0.0461076i
$935$	−3.29604	−	5.70891i	−0.107792	−	0.186701i
$936$		0			0
$937$	8.83997	−	15.3113i	0.288789	−	0.500198i	−0.684732	−	0.728795i	$-0.740081\pi$
$937$	8.83997	−	15.3113i	0.288789	−	0.500198i	0.973521	+	0.228598i	$0.0734140\pi$
$938$	−8.62872	+	48.9359i	−0.281738	+	1.59781i
$939$		0			0
$940$	7.93956	+	2.88976i	0.258960	+	0.0942536i
$941$	3.32971	+	18.8837i	0.108546	+	0.615592i	0.989745	+	0.142847i	$0.0456257\pi$
$941$	3.32971	+	18.8837i	0.108546	+	0.615592i	−0.881199	+	0.472745i	$0.843263\pi$
$942$		0			0
$943$	−36.4162	−	30.5568i	−1.18587	−	0.995066i
$944$	−0.00745704			−0.000242706
$945$		0			0
$946$	−8.29943			−0.269838
$947$	34.1827	+	28.6827i	1.11079	+	0.932063i	0.998103	−	0.0615673i	$-0.0196099\pi$
$947$	34.1827	+	28.6827i	1.11079	+	0.932063i	0.112687	+	0.993631i	$0.464054\pi$
$948$		0			0
$949$	−4.30396	−	24.4090i	−0.139713	−	0.792349i
$950$	−1.79694	−	0.654032i	−0.0583004	−	0.0212196i
$951$		0			0
$952$	4.94591	−	28.0496i	0.160298	−	0.909094i
$953$	−23.9555	+	41.4921i	−0.775994	+	1.34406i	0.158240	+	0.987401i	$0.449418\pi$
$953$	−23.9555	+	41.4921i	−0.775994	+	1.34406i	−0.934234	+	0.356661i	$0.883915\pi$
$954$		0			0
$955$	−1.05242	−	1.82285i	−0.0340556	−	0.0589860i
$956$	8.99826	−	3.27510i	0.291025	−	0.105924i
$957$		0			0
$958$	3.83777	−	3.22027i	0.123993	−	0.104042i
$959$	59.9390	−	50.2948i	1.93553	−	1.62410i
$960$		0			0
$961$	−8.48028	+	3.08657i	−0.273557	+	0.0995667i
$962$	−3.18683	−	5.51974i	−0.102747	−	0.177964i
$963$		0			0
$964$	−8.36544	+	14.4894i	−0.269433	+	0.466671i
$965$	1.72731	−	9.79605i	0.0556040	−	0.315346i
$966$		0			0
$967$	3.10518	+	1.13019i	0.0998559	+	0.0363446i	0.391465	−	0.920193i	$-0.371968\pi$
$967$	3.10518	+	1.13019i	0.0998559	+	0.0363446i	−0.291609	+	0.956538i	$0.594191\pi$
$968$	−1.72184	−	9.76505i	−0.0553421	−	0.313860i
$969$		0			0
$970$	1.87665	+	1.57470i	0.0602557	+	0.0505605i
$971$	−24.3377			−0.781034			−0.390517	−	0.920596i	$-0.627704\pi$
$971$	−24.3377			−0.781034			−0.390517	+	0.920596i	$0.627704\pi$
$972$		0			0
$973$	−80.2979			−2.57423
$974$	−13.6702	−	11.4707i	−0.438022	−	0.367544i
$975$		0			0
$976$	−2.63861	−	14.9643i	−0.0844597	−	0.478995i
$977$	−39.7660	−	14.4737i	−1.27223	−	0.463053i	−0.384374	−	0.923177i	$-0.625583\pi$
$977$	−39.7660	−	14.4737i	−1.27223	−	0.463053i	−0.887855	+	0.460124i	$0.847805\pi$
$978$		0			0
$979$	0.635678	−	3.60511i	0.0203164	−	0.115220i
$980$	−6.62118	+	11.4682i	−0.211506	+	0.366339i
$981$		0			0
$982$	4.69131	+	8.12559i	0.149706	+	0.259298i
$983$	24.1406	−	8.78647i	0.769967	−	0.280245i	0.0729842	−	0.997333i	$-0.476748\pi$
$983$	24.1406	−	8.78647i	0.769967	−	0.280245i	0.696982	+	0.717088i	$0.254526\pi$
$984$		0			0
$985$	−6.30510	+	5.29060i	−0.200897	+	0.168573i
$986$	37.8299	−	31.7431i	1.20475	−	1.01090i
$987$		0			0
$988$	−5.22629	+	1.90221i	−0.166270	+	0.0605175i
$989$	−21.8731	−	37.8854i	−0.695526	−	1.20469i
$990$		0			0
$991$	−21.6574	+	37.5118i	−0.687971	+	1.19160i	0.284523	+	0.958669i	$0.408165\pi$
$991$	−21.6574	+	37.5118i	−0.687971	+	1.19160i	−0.972493	+	0.232931i	$0.925168\pi$
$992$	−1.09858	+	6.23038i	−0.0348801	+	0.197815i
$993$		0			0
$994$	32.4166	+	11.7987i	1.02819	+	0.374231i
$995$	0.973363	+	5.52021i	0.0308577	+	0.175003i
$996$		0			0
$997$	−20.6110	−	17.2947i	−0.652758	−	0.547729i	0.255148	−	0.966902i	$-0.417876\pi$
$997$	−20.6110	−	17.2947i	−0.652758	−	0.547729i	−0.907907	+	0.419173i	$0.862320\pi$
$998$	6.16841			0.195258
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.k.e.451.4		24
3.2	odd	2		270.2.k.e.151.4	✓	24
27.5	odd	18		270.2.k.e.211.4	yes	24
27.7	even	9		7290.2.a.v.1.12		12
27.20	odd	18		7290.2.a.s.1.12		12
27.22	even	9	inner	810.2.k.e.361.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.k.e.151.4	✓	24	3.2	odd	2
270.2.k.e.211.4	yes	24	27.5	odd	18
810.2.k.e.361.4		24	27.22	even	9	inner
810.2.k.e.451.4		24	1.1	even	1	trivial
7290.2.a.s.1.12		12	27.20	odd	18
7290.2.a.v.1.12		12	27.7	even	9

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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.k (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(0.781269 - 4.43080i) q^{7} +(-0.500000 + 0.866025i) q^{8} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(0.781269 - 4.43080i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.500000 - 0.866025i) q^{10} +(-0.978505 + 0.356147i) q^{11} +(2.22799 - 1.86951i) q^{13} +(3.44655 - 2.89200i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-3.16530 - 5.48247i) q^{17} +(-0.956131 + 1.65607i) q^{19} +(0.173648 - 0.984808i) q^{20} +(-0.978505 - 0.356147i) q^{22} +(-0.953104 - 5.40532i) q^{23} +(0.766044 + 0.642788i) q^{25} +2.90844 q^{26} +4.49915 q^{28} +(5.97572 + 5.01422i) q^{29} +(-1.09858 - 6.23038i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(1.09930 - 6.23443i) q^{34} +(-2.24958 + 3.89638i) q^{35} +(-1.09572 - 1.89784i) q^{37} +(-1.79694 + 0.654032i) q^{38} +(0.766044 - 0.642788i) q^{40} +(6.63474 - 5.56721i) q^{41} +(7.48957 - 2.72598i) q^{43} +(-0.520652 - 0.901795i) q^{44} +(2.74435 - 4.75336i) q^{46} +(-1.46717 + 8.32074i) q^{47} +(-12.4437 - 4.52915i) q^{49} +(0.173648 + 0.984808i) q^{50} +(2.22799 + 1.86951i) q^{52} +7.94437 q^{53} +1.04130 q^{55} +(3.44655 + 2.89200i) q^{56} +(1.35458 + 7.68223i) q^{58} +(0.00700732 + 0.00255046i) q^{59} +(-2.63861 + 14.9643i) q^{61} +(3.16325 - 5.47890i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-2.73304 + 0.994745i) q^{65} +(-8.46057 + 7.09926i) q^{67} +(4.84953 - 4.06924i) q^{68} +(-4.22782 + 1.53880i) q^{70} +(3.83372 + 6.64020i) q^{71} +(4.26097 - 7.38021i) q^{73} +(0.380538 - 2.15814i) q^{74} +(-1.79694 - 0.654032i) q^{76} +(0.813538 + 4.61381i) q^{77} +(-2.91155 - 2.44308i) q^{79} +1.00000 q^{80} +8.66104 q^{82} +(-0.910253 - 0.763793i) q^{83} +(1.09930 + 6.23443i) q^{85} +(7.48957 + 2.72598i) q^{86} +(0.180820 - 1.02548i) q^{88} +(-1.75776 + 3.04453i) q^{89} +(-6.54276 - 11.3324i) q^{91} +(5.15770 - 1.87725i) q^{92} +(-6.47239 + 5.43098i) q^{94} +(1.46488 - 1.22918i) q^{95} +(-2.30205 + 0.837879i) q^{97} +(-6.62118 - 11.4682i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{7} - 12 q^{8}+O(q^{10}) \) 24 * q + 3 * q^7 - 12 * q^8	\( 24 q + 3 q^{7} - 12 q^{8} - 12 q^{10} + 9 q^{13} + 3 q^{14} - 15 q^{17} - 9 q^{19} + 12 q^{23} + 12 q^{26} + 6 q^{28} + 33 q^{29} - 21 q^{31} - 15 q^{34} - 3 q^{35} - 12 q^{37} - 12 q^{38} - 21 q^{41} + 12 q^{43} - 9 q^{44} - 15 q^{46} + 21 q^{47} + 27 q^{49} + 9 q^{52} + 60 q^{53} + 18 q^{55} + 3 q^{56} - 21 q^{58} - 36 q^{59} + 33 q^{61} - 18 q^{62} - 12 q^{64} - 12 q^{67} + 3 q^{68} - 6 q^{70} - 12 q^{71} - 6 q^{74} - 12 q^{76} + 60 q^{77} - 15 q^{79} + 24 q^{80} + 6 q^{82} + 27 q^{83} - 15 q^{85} + 12 q^{86} - 9 q^{88} - 30 q^{89} - 9 q^{91} - 6 q^{92} + 12 q^{94} + 15 q^{95} + 3 q^{97} - 27 q^{98}+O(q^{100}) \) 24 * q + 3 * q^7 - 12 * q^8 - 12 * q^10 + 9 * q^13 + 3 * q^14 - 15 * q^17 - 9 * q^19 + 12 * q^23 + 12 * q^26 + 6 * q^28 + 33 * q^29 - 21 * q^31 - 15 * q^34 - 3 * q^35 - 12 * q^37 - 12 * q^38 - 21 * q^41 + 12 * q^43 - 9 * q^44 - 15 * q^46 + 21 * q^47 + 27 * q^49 + 9 * q^52 + 60 * q^53 + 18 * q^55 + 3 * q^56 - 21 * q^58 - 36 * q^59 + 33 * q^61 - 18 * q^62 - 12 * q^64 - 12 * q^67 + 3 * q^68 - 6 * q^70 - 12 * q^71 - 6 * q^74 - 12 * q^76 + 60 * q^77 - 15 * q^79 + 24 * q^80 + 6 * q^82 + 27 * q^83 - 15 * q^85 + 12 * q^86 - 9 * q^88 - 30 * q^89 - 9 * q^91 - 6 * q^92 + 12 * q^94 + 15 * q^95 + 3 * q^97 - 27 * q^98

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