LMFDB - Embedded newform 324.2.l.a.35.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(35,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("324.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.l (of order $18$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			35.4
Character	$\chi$	$=$	324.35
Dual form			324.2.l.a.287.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09968 - 0.889210i) q^{2} +(0.418610 + 1.95570i) q^{4} +(-0.605021 + 1.66228i) q^{5} +(-0.748045 - 0.131901i) q^{7} +(1.27869 - 2.52289i) q^{8} +O(q^{10})$	\(q+(-1.09968 - 0.889210i) q^{2} +(0.418610 + 1.95570i) q^{4} +(-0.605021 + 1.66228i) q^{5} +(-0.748045 - 0.131901i) q^{7} +(1.27869 - 2.52289i) q^{8} +(2.14345 - 1.28999i) q^{10} +(-3.01780 + 1.09839i) q^{11} +(-1.07167 + 0.899234i) q^{13} +(0.705326 + 0.810218i) q^{14} +(-3.64953 + 1.63735i) q^{16} +(-5.55887 + 3.20941i) q^{17} +(-2.51793 - 1.45373i) q^{19} +(-3.50420 - 0.487393i) q^{20} +(4.29533 + 1.47558i) q^{22} +(1.06877 + 6.06131i) q^{23} +(1.43309 + 1.20251i) q^{25} +(1.97810 - 0.0359374i) q^{26} +(-0.0551813 - 1.51817i) q^{28} +(4.87432 - 5.80899i) q^{29} +(-9.30557 + 1.64082i) q^{31} +(5.46928 + 1.44463i) q^{32} +(8.96684 + 1.41366i) q^{34} +(0.671839 - 1.16366i) q^{35} +(1.62042 + 2.80666i) q^{37} +(1.47626 + 3.83761i) q^{38} +(3.42011 + 3.65194i) q^{40} +(4.14810 + 4.94351i) q^{41} +(2.50294 + 6.87676i) q^{43} +(-3.41140 - 5.44212i) q^{44} +(4.21447 - 7.61589i) q^{46} +(-0.737485 + 4.18249i) q^{47} +(-6.03567 - 2.19681i) q^{49} +(-0.506666 - 2.59669i) q^{50} +(-2.20724 - 1.71943i) q^{52} -9.63986i q^{53} -5.68099i q^{55} +(-1.28929 + 1.71857i) q^{56} +(-10.5256 + 2.05376i) q^{58} +(-0.397395 - 0.144640i) q^{59} +(1.38430 - 7.85077i) q^{61} +(11.6922 + 6.47022i) q^{62} +(-4.72990 - 6.45198i) q^{64} +(-0.846401 - 2.32547i) q^{65} +(3.65540 + 4.35634i) q^{67} +(-8.60365 - 9.52798i) q^{68} +(-1.77355 + 0.682252i) q^{70} +(-1.88825 - 3.27054i) q^{71} +(-5.59853 + 9.69694i) q^{73} +(0.713753 - 4.52733i) q^{74} +(1.78903 - 5.53287i) q^{76} +(2.40233 - 0.423595i) q^{77} +(6.53113 - 7.78350i) q^{79} +(-0.513698 - 7.05719i) q^{80} +(-0.165777 - 9.12484i) q^{82} +(-3.80396 - 3.19190i) q^{83} +(-1.97172 - 11.1822i) q^{85} +(3.36245 - 9.78790i) q^{86} +(-1.08772 + 9.01807i) q^{88} +(0.509288 + 0.294037i) q^{89} +(0.920264 - 0.531314i) q^{91} +(-11.4067 + 4.62752i) q^{92} +(4.53011 - 3.94364i) q^{94} +(3.93991 - 3.30598i) q^{95} +(15.8811 - 5.78024i) q^{97} +(4.68391 + 7.78278i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−1.09968	−	0.889210i	−0.777594	−	0.628767i
$2$	−1.09968	−	0.889210i	−0.777594	−	0.628767i
$3$		0			0
$3$		0			0
$4$	0.418610	+	1.95570i	0.209305	+	0.977850i
$5$	−0.605021	+	1.66228i	−0.270574	+	0.743395i	0.727768	+	0.685824i	$0.240558\pi$
$5$	−0.605021	+	1.66228i	−0.270574	+	0.743395i	−0.998341	+	0.0575715i	$0.981664\pi$
$6$		0			0
$7$	−0.748045	−	0.131901i	−0.282734	−	0.0498537i	0.0304825	−	0.999535i	$-0.490296\pi$
$7$	−0.748045	−	0.131901i	−0.282734	−	0.0498537i	−0.313217	+	0.949682i	$0.601407\pi$
$8$	1.27869	−	2.52289i	0.452085	−	0.891975i
$9$		0			0
$10$	2.14345	−	1.28999i	0.677819	−	0.407932i
$11$	−3.01780	+	1.09839i	−0.909901	+	0.331177i	−0.754213	−	0.656629i	$-0.771982\pi$
$11$	−3.01780	+	1.09839i	−0.909901	+	0.331177i	−0.155688	+	0.987806i	$0.549759\pi$
$12$		0			0
$13$	−1.07167	+	0.899234i	−0.297227	+	0.249403i	−0.779189	−	0.626789i	$-0.784369\pi$
$13$	−1.07167	+	0.899234i	−0.297227	+	0.249403i	0.481962	+	0.876192i	$0.339924\pi$
$14$	0.705326	+	0.810218i	0.188506	+	0.216540i
$15$		0			0
$16$	−3.64953	+	1.63735i	−0.912383	+	0.409338i
$17$	−5.55887	+	3.20941i	−1.34822	+	0.778397i	−0.987998	−	0.154469i	$-0.950633\pi$
$17$	−5.55887	+	3.20941i	−1.34822	+	0.778397i	−0.360225	+	0.932865i	$0.617300\pi$
$18$		0			0
$19$	−2.51793	−	1.45373i	−0.577653	−	0.333508i	0.182547	−	0.983197i	$-0.441566\pi$
$19$	−2.51793	−	1.45373i	−0.577653	−	0.333508i	−0.760200	+	0.649689i	$0.774899\pi$
$20$	−3.50420	−	0.487393i	−0.783562	−	0.108984i
$21$		0			0
$22$	4.29533	+	1.47558i	0.915767	+	0.314594i
$23$	1.06877	+	6.06131i	0.222854	+	1.26387i	0.866744	+	0.498752i	$0.166208\pi$
$23$	1.06877	+	6.06131i	0.222854	+	1.26387i	−0.643890	+	0.765118i	$0.722681\pi$
$24$		0			0
$25$	1.43309	+	1.20251i	0.286618	+	0.240501i
$26$	1.97810	−	0.0359374i	0.387938	−	0.00704791i
$27$		0			0
$28$	−0.0551813	−	1.51817i	−0.0104283	−	0.286907i
$29$	4.87432	−	5.80899i	0.905138	−	1.07870i	−0.0914207	−	0.995812i	$-0.529141\pi$
$29$	4.87432	−	5.80899i	0.905138	−	1.07870i	0.996559	−	0.0828892i	$-0.0264148\pi$
$30$		0			0
$31$	−9.30557	+	1.64082i	−1.67133	+	0.294701i	−0.927543	−	0.373716i	$-0.878084\pi$
$31$	−9.30557	+	1.64082i	−1.67133	+	0.294701i	−0.743787	+	0.668417i	$0.766972\pi$
$32$	5.46928	+	1.44463i	0.966842	+	0.255377i
$33$		0			0
$34$	8.96684	+	1.41366i	1.53780	+	0.242441i
$35$	0.671839	−	1.16366i	0.113562	−	0.196694i
$36$		0			0
$37$	1.62042	+	2.80666i	0.266396	+	0.461411i	0.967928	−	0.251226i	$-0.0808338\pi$
$37$	1.62042	+	2.80666i	0.266396	+	0.461411i	−0.701532	+	0.712638i	$0.747500\pi$
$38$	1.47626	+	3.83761i	0.239481	+	0.622543i
$39$		0			0
$40$	3.42011	+	3.65194i	0.540767	+	0.577423i
$41$	4.14810	+	4.94351i	0.647824	+	0.772047i	0.985584	−	0.169185i	$-0.0541136\pi$
$41$	4.14810	+	4.94351i	0.647824	+	0.772047i	−0.337760	+	0.941232i	$0.609669\pi$
$42$		0			0
$43$	2.50294	+	6.87676i	0.381694	+	1.04870i	0.970643	+	0.240526i	$0.0773199\pi$
$43$	2.50294	+	6.87676i	0.381694	+	1.04870i	−0.588949	+	0.808171i	$0.700458\pi$
$44$	−3.41140	−	5.44212i	−0.514288	−	0.820430i
$45$		0			0
$46$	4.21447	−	7.61589i	0.621389	−	1.12290i
$47$	−0.737485	+	4.18249i	−0.107573	+	0.610079i	0.882588	+	0.470147i	$0.155799\pi$
$47$	−0.737485	+	4.18249i	−0.107573	+	0.610079i	−0.990161	+	0.139931i	$0.955312\pi$
$48$		0			0
$49$	−6.03567	−	2.19681i	−0.862239	−	0.313829i
$50$	−0.506666	−	2.59669i	−0.0716534	−	0.367228i
$51$		0			0
$52$	−2.20724	−	1.71943i	−0.306090	−	0.238442i
$53$		−	9.63986i		−	1.32414i	−0.749444	−	0.662068i	$-0.769679\pi$
$53$		−	9.63986i		−	1.32414i	0.749444	−	0.662068i	$-0.230321\pi$
$54$		0			0
$55$		−	5.68099i		−	0.766024i
$56$	−1.28929	+	1.71857i	−0.172288	+	0.229654i
$57$		0			0
$58$	−10.5256	+	2.05376i	−1.38208	+	0.269671i
$59$	−0.397395	−	0.144640i	−0.0517364	−	0.0188305i	0.316022	−	0.948752i	$-0.397653\pi$
$59$	−0.397395	−	0.144640i	−0.0517364	−	0.0188305i	−0.367759	+	0.929921i	$0.619875\pi$
$60$		0			0
$61$	1.38430	−	7.85077i	0.177242	−	1.00519i	−0.758283	−	0.651926i	$-0.773961\pi$
$61$	1.38430	−	7.85077i	0.177242	−	1.00519i	0.935524	−	0.353262i	$-0.114928\pi$
$62$	11.6922	+	6.47022i	1.48491	+	0.821719i
$63$		0			0
$64$	−4.72990	−	6.45198i	−0.591238	−	0.806497i
$65$	−0.846401	−	2.32547i	−0.104983	−	0.288439i
$66$		0			0
$67$	3.65540	+	4.35634i	0.446579	+	0.532212i	0.941629	−	0.336653i	$-0.109295\pi$
$67$	3.65540	+	4.35634i	0.446579	+	0.532212i	−0.495050	+	0.868864i	$0.664850\pi$
$68$	−8.60365	−	9.52798i	−1.04335	−	1.15544i
$69$		0			0
$70$	−1.77355	+	0.682252i	−0.211980	+	0.0815447i
$71$	−1.88825	−	3.27054i	−0.224094	−	0.388142i	0.731953	−	0.681355i	$-0.238609\pi$
$71$	−1.88825	−	3.27054i	−0.224094	−	0.388142i	−0.956047	+	0.293213i	$0.905276\pi$
$72$		0			0
$73$	−5.59853	+	9.69694i	−0.655258	+	1.13494i	0.326571	+	0.945173i	$0.394107\pi$
$73$	−5.59853	+	9.69694i	−0.655258	+	1.13494i	−0.981829	+	0.189768i	$0.939226\pi$
$74$	0.713753	−	4.52733i	0.0829721	−	0.526292i
$75$		0			0
$76$	1.78903	−	5.53287i	0.205215	−	0.634663i
$77$	2.40233	−	0.423595i	0.273771	−	0.0482732i
$78$		0			0
$79$	6.53113	−	7.78350i	0.734810	−	0.875712i	−0.261170	−	0.965293i	$-0.584108\pi$
$79$	6.53113	−	7.78350i	0.734810	−	0.875712i	0.995980	+	0.0895809i	$0.0285528\pi$
$80$	−0.513698	−	7.05719i	−0.0574331	−	0.789017i
$81$		0			0
$82$	−0.165777	−	9.12484i	−0.0183070	−	1.00767i
$83$	−3.80396	−	3.19190i	−0.417538	−	0.350356i	0.409687	−	0.912226i	$-0.365638\pi$
$83$	−3.80396	−	3.19190i	−0.417538	−	0.350356i	−0.827226	+	0.561870i	$0.810082\pi$
$84$		0			0
$85$	−1.97172	−	11.1822i	−0.213863	−	1.21288i
$86$	3.36245	−	9.78790i	0.362582	−	1.05546i
$87$		0			0
$88$	−1.08772	+	9.01807i	−0.115952	+	0.961329i
$89$	0.509288	+	0.294037i	0.0539844	+	0.0311679i	0.526749	−	0.850021i	$-0.323411\pi$
$89$	0.509288	+	0.294037i	0.0539844	+	0.0311679i	−0.472765	+	0.881189i	$0.656744\pi$
$90$		0			0
$91$	0.920264	−	0.531314i	0.0964698	−	0.0556969i
$92$	−11.4067	+	4.62752i	−1.18923	+	0.482453i
$93$		0			0
$94$	4.53011	−	3.94364i	0.467245	−	0.406755i
$95$	3.93991	−	3.30598i	0.404226	−	0.339186i
$96$		0			0
$97$	15.8811	−	5.78024i	1.61248	−	0.586895i	0.630552	−	0.776147i	$-0.282829\pi$
$97$	15.8811	−	5.78024i	1.61248	−	0.586895i	0.981928	+	0.189252i	$0.0606065\pi$
$98$	4.68391	+	7.78278i	0.473147	+	0.786179i
$99$		0			0
$100$	−1.75183	+	3.30608i	−0.175183	+	0.330608i
$101$	5.39858	+	0.951915i	0.537178	+	0.0947191i	0.435654	−	0.900114i	$-0.356517\pi$
$101$	5.39858	+	0.951915i	0.537178	+	0.0947191i	0.101524	+	0.994833i	$0.467628\pi$
$102$		0			0
$103$	2.06594	−	5.67611i	0.203563	−	0.559284i	−0.795338	−	0.606167i	$-0.792706\pi$
$103$	2.06594	−	5.67611i	0.203563	−	0.559284i	0.998900	+	0.0468827i	$0.0149287\pi$
$104$	0.898336	+	3.85353i	0.0880891	+	0.377870i
$105$		0			0
$106$	−8.57186	+	10.6008i	−0.832573	+	1.02964i
$107$	4.28762			0.414500			0.207250	−	0.978288i	$-0.433549\pi$
$107$	4.28762			0.414500			0.207250	+	0.978288i	$0.433549\pi$
$108$		0			0
$109$	−4.75148			−0.455109			−0.227554	−	0.973765i	$-0.573073\pi$
$109$	−4.75148			−0.455109			−0.227554	+	0.973765i	$0.573073\pi$
$110$	−5.05159	+	6.24729i	−0.481650	+	0.595656i
$111$		0			0
$112$	2.94598	−	0.743438i	0.278369	−	0.0702483i
$113$	−3.11256	+	8.55169i	−0.292805	+	0.804475i	0.702848	+	0.711340i	$0.251911\pi$
$113$	−3.11256	+	8.55169i	−0.292805	+	0.804475i	−0.995653	+	0.0931357i	$0.970311\pi$
$114$		0			0
$115$	−10.7222	−	1.89062i	−0.999854	−	0.176301i
$116$	13.4011	+	7.10101i	1.24426	+	0.659312i
$117$		0			0
$118$	0.308394	+	0.512426i	0.0283899	+	0.0471726i
$119$	4.58161	−	1.66757i	0.419995	−	0.152866i
$120$		0			0
$121$	−0.525827	+	0.441221i	−0.0478025	+	0.0401110i
$122$	−8.50328	+	7.40243i	−0.769851	+	0.670185i
$123$		0			0
$124$	−7.10437	−	17.5121i	−0.637991	−	1.57263i
$125$	−10.5258	+	6.07707i	−0.941456	+	0.543550i
$126$		0			0
$127$	7.58333	+	4.37824i	0.672911	+	0.388506i	0.797179	−	0.603743i	$-0.206325\pi$
$127$	7.58333	+	4.37824i	0.672911	+	0.388506i	−0.124267	+	0.992249i	$0.539658\pi$
$128$	−0.535768	+	11.3010i	−0.0473557	+	0.998878i
$129$		0			0
$130$	−1.13706	+	3.30991i	−0.0997264	+	0.290298i
$131$	−1.28295	−	7.27595i	−0.112092	−	0.635703i	−0.988149	−	0.153496i	$-0.950947\pi$
$131$	−1.28295	−	7.27595i	−0.112092	−	0.635703i	0.876058	−	0.482206i	$-0.160164\pi$
$132$		0			0
$133$	1.69178	+	1.41957i	0.146696	+	0.123092i
$134$	−0.146086	−	8.04102i	−0.0126199	−	0.694639i
$135$		0			0
$136$	0.988912	+	18.1282i	0.0847985	+	1.55448i
$137$	−3.47834	+	4.14532i	−0.297174	+	0.354158i	−0.893884	−	0.448299i	$-0.852030\pi$
$137$	−3.47834	+	4.14532i	−0.297174	+	0.354158i	0.596709	+	0.802457i	$0.296474\pi$
$138$		0			0
$139$	14.3790	−	2.53541i	1.21961	−	0.215050i	0.473453	−	0.880819i	$-0.343007\pi$
$139$	14.3790	−	2.53541i	1.21961	−	0.215050i	0.746158	+	0.665769i	$0.231896\pi$
$140$	2.55701	+	0.826797i	0.216107	+	0.0698771i
$141$		0			0
$142$	−0.831723	+	5.27561i	−0.0697966	+	0.442720i
$143$	2.24636	−	3.89082i	0.187850	−	0.325366i
$144$		0			0
$145$	6.70711	+	11.6171i	0.556995	+	0.964744i
$146$	14.7792	−	5.68530i	1.22314	−	0.470519i
$147$		0			0
$148$	−4.81065	+	4.34396i	−0.395433	+	0.357071i
$149$	0.667920	+	0.795997i	0.0547182	+	0.0652106i	0.792709	−	0.609600i	$-0.208670\pi$
$149$	0.667920	+	0.795997i	0.0547182	+	0.0652106i	−0.737991	+	0.674810i	$0.764225\pi$
$150$		0			0
$151$	5.18707	+	14.2513i	0.422117	+	1.15976i	0.950493	+	0.310747i	$0.100579\pi$
$151$	5.18707	+	14.2513i	0.422117	+	1.15976i	−0.528375	+	0.849011i	$0.677199\pi$
$152$	−6.88724	+	4.49358i	−0.558629	+	0.364478i
$153$		0			0
$154$	−3.01847	−	1.67035i	−0.243235	−	0.134601i
$155$	2.90256	−	16.4612i	0.233139	−	1.32220i
$156$		0			0
$157$	−7.35933	−	2.67858i	−0.587338	−	0.213774i	0.0312200	−	0.999513i	$-0.490061\pi$
$157$	−7.35933	−	2.67858i	−0.587338	−	0.213774i	−0.618558	+	0.785739i	$0.712283\pi$
$158$	−14.1033	+	2.75184i	−1.12200	+	0.218925i
$159$		0			0
$160$	−5.71042	+	8.21746i	−0.451448	+	0.649647i
$161$		−	4.67510i		−	0.368450i
$162$		0			0
$163$			14.8714i			1.16482i	0.812897	+	0.582408i	$0.197889\pi$
$163$			14.8714i			1.16482i	−0.812897	+	0.582408i	$0.802111\pi$
$164$	−7.93160	+	10.1818i	−0.619354	+	0.795069i
$165$		0			0
$166$	1.34488	+	6.89260i	0.104383	+	0.534969i
$167$	−0.956267	−	0.348053i	−0.0739981	−	0.0269331i	0.304756	−	0.952431i	$-0.401425\pi$
$167$	−0.956267	−	0.348053i	−0.0739981	−	0.0269331i	−0.378754	+	0.925497i	$0.623647\pi$
$168$		0			0
$169$	−1.91758	+	10.8751i	−0.147506	+	0.836550i
$170$	−7.77503	+	14.0501i	−0.596318	+	1.07760i
$171$		0			0
$172$	−12.4011	+	7.77368i	−0.945578	+	0.592737i
$173$	−2.67234	−	7.34218i	−0.203174	−	0.558216i	0.795698	−	0.605693i	$-0.207104\pi$
$173$	−2.67234	−	7.34218i	−0.203174	−	0.558216i	−0.998872	+	0.0474772i	$0.984882\pi$
$174$		0			0
$175$	−0.913405	−	1.08855i	−0.0690469	−	0.0822869i
$176$	9.21511	−	8.94981i	0.694615	−	0.674617i
$177$		0			0
$178$	−0.298594	−	0.776212i	−0.0223806	−	0.0581795i
$179$	3.90388	+	6.76172i	0.291790	+	0.505395i	0.974233	−	0.225544i	$-0.0724159\pi$
$179$	3.90388	+	6.76172i	0.291790	+	0.505395i	−0.682443	+	0.730939i	$0.739083\pi$
$180$		0			0
$181$	1.45395	−	2.51831i	0.108071	−	0.187184i	−0.806918	−	0.590664i	$-0.798866\pi$
$181$	1.45395	−	2.51831i	0.108071	−	0.187184i	0.914989	+	0.403479i	$0.132199\pi$
$182$	−1.48445	−	0.234030i	−0.110035	−	0.0173474i
$183$		0			0
$184$	16.6586	+	5.05415i	1.22809	+	0.372597i
$185$	−5.64585	+	0.995515i	−0.415091	+	0.0731917i
$186$		0			0
$187$	13.2504	−	15.7912i	0.968963	−	1.15476i
$188$	−8.48841	+	0.308531i	−0.619081	+	0.0225019i
$189$		0			0
$190$	−7.27236	+	0.132122i	−0.527593	+	0.00958512i
$191$	12.1323	+	10.1802i	0.877859	+	0.736611i	0.965738	−	0.259520i	$-0.0835643\pi$
$191$	12.1323	+	10.1802i	0.877859	+	0.736611i	−0.0878785	+	0.996131i	$0.528009\pi$
$192$		0			0
$193$	2.21465	+	12.5599i	0.159414	+	0.904083i	0.954638	+	0.297767i	$0.0962420\pi$
$193$	2.21465	+	12.5599i	0.159414	+	0.904083i	−0.795224	+	0.606315i	$0.792647\pi$
$194$	−22.6040	−	7.76519i	−1.62287	−	0.557508i
$195$		0			0
$196$	1.76970	−	12.7236i	0.126407	−	0.908827i
$197$	6.84336	+	3.95102i	0.487570	+	0.281498i	0.723566	−	0.690256i	$-0.242502\pi$
$197$	6.84336	+	3.95102i	0.487570	+	0.281498i	−0.235996	+	0.971754i	$0.575835\pi$
$198$		0			0
$199$	3.36883	−	1.94499i	0.238810	−	0.137877i	−0.375820	−	0.926693i	$-0.622639\pi$
$199$	3.36883	−	1.94499i	0.238810	−	0.137877i	0.614630	+	0.788816i	$0.289306\pi$
$200$	4.86626	−	2.07789i	0.344097	−	0.146929i
$201$		0			0
$202$	−5.09028	−	5.84728i	−0.358151	−	0.411413i
$203$	−4.41242	+	3.70246i	−0.309691	+	0.259862i
$204$		0			0
$205$	−10.7272	+	3.90438i	−0.749220	+	0.272694i
$206$	−7.31913	+	4.40488i	−0.509948	+	0.306902i
$207$		0			0
$208$	2.43871	−	5.03648i	0.169094	−	0.349217i
$209$	9.19538	+	1.62139i	0.636057	+	0.112154i
$210$		0			0
$211$	1.32215	−	3.63257i	0.0910203	−	0.250076i	−0.885826	−	0.464017i	$-0.846408\pi$
$211$	1.32215	−	3.63257i	0.0910203	−	0.250076i	0.976847	+	0.213941i	$0.0686299\pi$
$212$	18.8527	−	4.03534i	1.29481	−	0.277148i
$213$		0			0
$214$	−4.71502	−	3.81259i	−0.322312	−	0.260623i
$215$	−12.9455			−0.882872
$216$		0			0
$217$	7.17741			0.487235
$218$	5.22512	+	4.22506i	0.353890	+	0.286157i
$219$		0			0
$220$	11.1103	−	2.37812i	0.749057	−	0.160333i
$221$	3.07123	−	8.43814i	0.206593	−	0.567611i
$222$		0			0
$223$	−23.0164	−	4.05841i	−1.54129	−	0.271771i	−0.662531	−	0.749035i	$-0.730518\pi$
$223$	−23.0164	−	4.05841i	−1.54129	−	0.271771i	−0.878760	+	0.477264i	$0.841629\pi$
$224$	−3.90072	−	1.80205i	−0.260628	−	0.120405i
$225$		0			0
$226$	11.0271	−	6.63644i	0.733511	−	0.441449i
$227$	9.97504	−	3.63062i	0.662067	−	0.240973i	0.0109383	−	0.999940i	$-0.496518\pi$
$227$	9.97504	−	3.63062i	0.662067	−	0.240973i	0.651128	+	0.758968i	$0.274296\pi$
$228$		0			0
$229$	−5.32931	+	4.47182i	−0.352171	+	0.295506i	−0.801661	−	0.597779i	$-0.796050\pi$
$229$	−5.32931	+	4.47182i	−0.352171	+	0.295506i	0.449490	+	0.893285i	$0.351606\pi$
$230$	10.1099	+	11.6134i	0.666628	+	0.765766i
$231$		0			0
$232$	−8.42266	−	19.7252i	−0.552975	−	1.29503i
$233$	−13.9988	+	8.08221i	−0.917091	+	0.529483i	−0.882706	−	0.469926i	$-0.844281\pi$
$233$	−13.9988	+	8.08221i	−0.917091	+	0.529483i	−0.0343854	+	0.999409i	$0.510947\pi$
$234$		0			0
$235$	−6.50628	−	3.75640i	−0.424423	−	0.245041i
$236$	0.116519	−	0.837734i	0.00758474	−	0.0545318i
$237$		0			0
$238$	−6.52114	−	2.24021i	−0.422703	−	0.145211i
$239$	−3.92960	−	22.2858i	−0.254184	−	1.44155i	−0.798157	−	0.602449i	$-0.794192\pi$
$239$	−3.92960	−	22.2858i	−0.254184	−	1.44155i	0.543973	−	0.839103i	$-0.316919\pi$
$240$		0			0
$241$	−0.165024	−	0.138471i	−0.0106301	−	0.00891972i	0.637457	−	0.770486i	$-0.279986\pi$
$241$	−0.165024	−	0.138471i	−0.0106301	−	0.00891972i	−0.648087	+	0.761566i	$0.724431\pi$
$242$	0.970582	−	0.0176332i	0.0623914	−	0.00113350i
$243$		0			0
$244$	15.9332	−	0.579130i	1.02002	−	0.0370750i
$245$	7.30342	−	8.70388i	0.466599	−	0.556071i
$246$		0			0
$247$	4.00562	−	0.706299i	0.254872	−	0.0449407i
$248$	−7.75934	+	25.5750i	−0.492718	+	1.62401i
$249$		0			0
$250$	16.9788	+	2.67679i	1.07384	+	0.169295i
$251$	−11.9282	+	20.6602i	−0.752899	+	1.30406i	0.193513	+	0.981098i	$0.438012\pi$
$251$	−11.9282	+	20.6602i	−0.752899	+	1.30406i	−0.946412	+	0.322961i	$0.895322\pi$
$252$		0			0
$253$	−9.88302	−	17.1179i	−0.621340	−	1.07619i
$254$	−4.44609	−	11.5578i	−0.278973	−	0.725204i
$255$		0			0
$256$	10.6382	−	11.9511i	0.664885	−	0.746946i
$257$	0.876576	+	1.04466i	0.0546793	+	0.0651642i	0.792691	−	0.609624i	$-0.208679\pi$
$257$	0.876576	+	1.04466i	0.0546793	+	0.0651642i	−0.738012	+	0.674788i	$0.764235\pi$
$258$		0			0
$259$	−0.841951	−	2.31324i	−0.0523163	−	0.143738i
$260$	4.19361	−	2.62877i	0.260076	−	0.163029i
$261$		0			0
$262$	−5.05901	+	9.14205i	−0.312547	+	0.564798i
$263$	−2.98147	+	16.9087i	−0.183845	+	1.04264i	0.743585	+	0.668641i	$0.233124\pi$
$263$	−2.98147	+	16.9087i	−0.183845	+	1.04264i	−0.927430	+	0.373996i	$0.877987\pi$
$264$		0			0
$265$	16.0242	+	5.83232i	0.984357	+	0.358277i
$266$	−0.598125	−	3.06543i	−0.0366734	−	0.187953i
$267$		0			0
$268$	−6.98951	+	8.97249i	−0.426952	+	0.548082i
$269$		−	8.79633i		−	0.536322i	−0.963374	−	0.268161i	$-0.913584\pi$
$269$		−	8.79633i		−	0.536322i	0.963374	−	0.268161i	$-0.0864159\pi$
$270$		0			0
$271$		−	3.18958i		−	0.193753i	−0.995296	−	0.0968765i	$-0.969115\pi$
$271$		−	3.18958i		−	0.193753i	0.995296	−	0.0968765i	$-0.0308852\pi$
$272$	15.0323	−	20.8147i	0.911468	−	1.26207i
$273$		0			0
$274$	7.51113	−	1.46557i	0.453764	−	0.0885383i
$275$	−5.64560	−	2.05483i	−0.340442	−	0.123911i
$276$		0			0
$277$	2.42778	−	13.7686i	0.145871	−	0.827276i	−0.820793	−	0.571226i	$-0.806468\pi$
$277$	2.42778	−	13.7686i	0.145871	−	0.827276i	0.966664	−	0.256049i	$-0.0824210\pi$
$278$	−18.0669	−	9.99782i	−1.08358	−	0.599629i
$279$		0			0
$280$	−2.07671	−	3.18293i	−0.124107	−	0.190217i
$281$	1.60512	+	4.41002i	0.0957532	+	0.263080i	0.978317	−	0.207113i	$-0.0664067\pi$
$281$	1.60512	+	4.41002i	0.0957532	+	0.263080i	−0.882564	+	0.470192i	$0.844184\pi$
$282$		0			0
$283$	−2.77680	−	3.30926i	−0.165063	−	0.196715i	0.677172	−	0.735825i	$-0.263205\pi$
$283$	−2.77680	−	3.30926i	−0.165063	−	0.196715i	−0.842236	+	0.539110i	$0.818761\pi$
$284$	5.60576	−	5.06193i	0.332641	−	0.300370i
$285$		0			0
$286$	−5.93004	+	2.28118i	−0.350651	+	0.134889i
$287$	−2.45091	−	4.24511i	−0.144673	−	0.250581i
$288$		0			0
$289$	12.1007	−	20.9590i	0.711803	−	1.23288i
$290$	2.95430	−	18.7391i	0.173483	−	1.10040i
$291$		0			0
$292$	−21.3079	−	6.88981i	−1.24695	−	0.403196i
$293$	11.2158	−	1.97765i	0.655235	−	0.115536i	0.163860	−	0.986484i	$-0.447605\pi$
$293$	11.2158	−	1.97765i	0.655235	−	0.115536i	0.491375	+	0.870948i	$0.336494\pi$
$294$		0			0
$295$	0.480865	−	0.573073i	0.0279970	−	0.0333656i
$296$	9.15289	−	0.499299i	0.532001	−	0.0290212i
$297$		0			0
$298$	−0.0266931	−	1.46927i	−0.00154629	−	0.0851123i
$299$	−6.59590	−	5.53462i	−0.381451	−	0.320075i
$300$		0			0
$301$	−0.965261	−	5.47427i	−0.0556367	−	0.315531i
$302$	6.96831	−	20.2844i	0.400981	−	1.16723i
$303$		0			0
$304$	11.5695	+	1.18269i	0.663558	+	0.0678317i
$305$	12.2127	+	7.05099i	0.699295	+	0.403738i
$306$		0			0
$307$	−18.5894	+	10.7326i	−1.06095	+	0.612541i	−0.925696	−	0.378269i	$-0.876519\pi$
$307$	−18.5894	+	10.7326i	−1.06095	+	0.612541i	−0.135257	+	0.990811i	$0.543186\pi$
$308$	1.83407	+	4.52092i	0.104506	+	0.257603i
$309$		0			0
$310$	−17.8294	+	15.5212i	−1.01264	+	0.881543i
$311$	−8.69917	+	7.29947i	−0.493285	+	0.413915i	−0.855202	−	0.518295i	$-0.826567\pi$
$311$	−8.69917	+	7.29947i	−0.493285	+	0.413915i	0.361917	+	0.932210i	$0.382122\pi$
$312$		0			0
$313$	−24.1218	+	8.77962i	−1.36345	+	0.496254i	−0.917118	−	0.398616i	$-0.869491\pi$
$313$	−24.1218	+	8.77962i	−1.36345	+	0.496254i	−0.446328	+	0.894870i	$0.647268\pi$
$314$	5.71112	+	9.48958i	0.322297	+	0.535528i
$315$		0			0
$316$	17.9562	+	9.51468i	1.01011	+	0.535243i
$317$	−24.5290	−	4.32513i	−1.37769	−	0.242923i	−0.564743	−	0.825267i	$-0.691025\pi$
$317$	−24.5290	−	4.32513i	−1.37769	−	0.242923i	−0.812943	+	0.582343i	$0.802136\pi$
$318$		0			0
$319$	−8.32919	+	22.8843i	−0.466345	+	1.28127i
$320$	13.5867	−	3.95885i	0.759520	−	0.221306i
$321$		0			0
$322$	−4.15715	+	5.14114i	−0.231669	+	0.286504i
$323$	18.6625			1.03841
$324$		0			0
$325$	−2.61713			−0.145172
$326$	13.2238	−	16.3538i	0.732397	−	0.905754i
$327$		0			0
$328$	17.7761	−	4.14396i	0.981518	−	0.228812i
$329$	1.10334	−	3.03141i	0.0608294	−	0.167127i
$330$		0			0
$331$	−31.0724	−	5.47891i	−1.70790	−	0.301148i	−0.767454	−	0.641103i	$-0.778477\pi$
$331$	−31.0724	−	5.47891i	−1.70790	−	0.301148i	−0.940442	+	0.339955i	$0.889588\pi$
$332$	4.65002	−	8.77556i	0.255203	−	0.481621i
$333$		0			0
$334$	0.742099	+	1.23307i	0.0406059	+	0.0674706i
$335$	−9.45307	+	3.44064i	−0.516476	+	0.187982i
$336$		0			0
$337$	15.8413	−	13.2924i	0.862929	−	0.724083i	−0.0996680	−	0.995021i	$-0.531778\pi$
$337$	15.8413	−	13.2924i	0.862929	−	0.724083i	0.962597	+	0.270937i	$0.0873336\pi$
$338$	11.7790	−	10.2541i	0.640694	−	0.557749i
$339$		0			0
$340$	21.0436	−	8.53706i	1.14125	−	0.462987i
$341$	26.2801	−	15.1728i	1.42315	−	0.821655i
$342$		0			0
$343$	8.82994	+	5.09797i	0.476772	+	0.275264i
$344$	20.5498	+	2.47863i	1.10797	+	0.133639i
$345$		0			0
$346$	−3.59002	+	10.4504i	−0.193001	+	0.561814i
$347$	4.96431	+	28.1540i	0.266498	+	1.51139i	0.764734	+	0.644346i	$0.222870\pi$
$347$	4.96431	+	28.1540i	0.266498	+	1.51139i	−0.498236	+	0.867041i	$0.666019\pi$
$348$		0			0
$349$	−11.0490	−	9.27121i	−0.591439	−	0.496276i	0.297242	−	0.954802i	$-0.403933\pi$
$349$	−11.0490	−	9.27121i	−0.591439	−	0.496276i	−0.888681	+	0.458526i	$0.848378\pi$
$350$	0.0365038	+	2.00927i	0.00195121	+	0.107400i
$351$		0			0
$352$	−18.0920	+	1.64780i	−0.964305	+	0.0878278i
$353$	−16.3175	+	19.4465i	−0.868496	+	1.03503i	0.130554	+	0.991441i	$0.458324\pi$
$353$	−16.3175	+	19.4465i	−0.868496	+	1.03503i	−0.999049	+	0.0435915i	$0.986120\pi$
$354$		0			0
$355$	6.57900	−	1.16005i	0.349177	−	0.0615693i
$356$	−0.361856	+	1.11910i	−0.0191783	+	0.0593122i
$357$		0			0
$358$	1.71956	−	10.9071i	0.0908813	−	0.576460i
$359$	2.61678	−	4.53239i	0.138108	−	0.239211i	−0.788672	−	0.614814i	$-0.789231\pi$
$359$	2.61678	−	4.53239i	0.138108	−	0.239211i	0.926781	+	0.375603i	$0.122564\pi$
$360$		0			0
$361$	−5.27335	−	9.13371i	−0.277545	−	0.480721i
$362$	−3.83819	+	1.47648i	−0.201731	+	0.0776021i
$363$		0			0
$364$	1.42432	+	1.57735i	0.0746548	+	0.0826754i
$365$	−12.7318	−	15.1732i	−0.666414	−	0.794201i
$366$		0			0
$367$	11.0968	+	30.4882i	0.579247	+	1.59147i	0.789452	+	0.613812i	$0.210365\pi$
$367$	11.0968	+	30.4882i	0.579247	+	1.59147i	−0.210205	+	0.977657i	$0.567413\pi$
$368$	−13.8250	−	20.3710i	−0.720679	−	1.06191i
$369$		0			0
$370$	7.09387	+	3.92559i	0.368793	+	0.204082i
$371$	−1.27150	+	7.21105i	−0.0660131	+	0.374379i
$372$		0			0
$373$	13.8536	+	5.04230i	0.717312	+	0.261080i	0.674784	−	0.738015i	$-0.264237\pi$
$373$	13.8536	+	5.04230i	0.717312	+	0.261080i	0.0425278	+	0.999095i	$0.486459\pi$
$374$	−28.6129	+	5.58294i	−1.47954	+	0.288687i
$375$		0			0
$376$	9.60892	+	7.20870i	0.495542	+	0.371760i
$377$			10.6084i			0.546363i
$378$		0			0
$379$		−	2.17390i		−	0.111666i	−0.998440	−	0.0558329i	$-0.982219\pi$
$379$		−	2.17390i		−	0.111666i	0.998440	−	0.0558329i	$-0.0177814\pi$
$380$	8.11479	+	6.32137i	0.416280	+	0.324279i
$381$		0			0
$382$	−4.28934	−	21.9831i	−0.219461	−	1.12475i
$383$	25.4781	+	9.27327i	1.30187	+	0.473842i	0.897605	−	0.440800i	$-0.145305\pi$
$383$	25.4781	+	9.27327i	1.30187	+	0.473842i	0.404265	+	0.914642i	$0.367527\pi$
$384$		0			0
$385$	−0.749325	+	4.24963i	−0.0381891	+	0.216581i
$386$	8.73299	−	15.7812i	0.444498	−	0.803244i
$387$		0			0
$388$	17.9524	+	28.6390i	0.911396	+	1.45392i
$389$	9.29522	+	25.5384i	0.471286	+	1.29485i	0.916719	+	0.399533i	$0.130828\pi$
$389$	9.29522	+	25.5384i	0.471286	+	1.29485i	−0.445432	+	0.895316i	$0.646950\pi$
$390$		0			0
$391$	−25.3944	−	30.2639i	−1.28425	−	1.53051i
$392$	−13.2600	+	12.4183i	−0.669734	+	0.627218i
$393$		0			0
$394$	−4.01225	−	10.4301i	−0.202134	−	0.525459i
$395$	8.98690	+	15.5658i	0.452180	+	0.783199i
$396$		0			0
$397$	−4.91342	+	8.51029i	−0.246597	+	0.427119i	−0.962579	−	0.271000i	$-0.912646\pi$
$397$	−4.91342	+	8.51029i	−0.246597	+	0.427119i	0.715982	+	0.698119i	$0.245979\pi$
$398$	−5.43415	−	0.856717i	−0.272389	−	0.0429434i
$399$		0			0
$400$	−7.19903	−	2.04211i	−0.359951	−	0.102105i
$401$	−8.92802	+	1.57425i	−0.445844	+	0.0786143i	−0.392063	−	0.919938i	$-0.628238\pi$
$401$	−8.92802	+	1.57425i	−0.445844	+	0.0786143i	−0.0537811	+	0.998553i	$0.517127\pi$
$402$		0			0
$403$	8.49698	−	10.1263i	0.423265	−	0.504427i
$404$	0.398238	+	10.9565i	0.0198131	+	0.545105i
$405$		0			0
$406$	8.14453	−	0.147967i	0.404206	−	0.00734348i
$407$	−7.97292	−	6.69007i	−0.395203	−	0.331615i
$408$		0			0
$409$	4.97696	+	28.2258i	0.246095	+	1.39567i	0.817936	+	0.575309i	$0.195118\pi$
$409$	4.97696	+	28.2258i	0.246095	+	1.39567i	−0.571841	+	0.820364i	$0.693771\pi$
$410$	15.2684	+	5.24515i	0.754050	+	0.259040i
$411$		0			0
$412$	11.9656	+	1.66427i	0.589503	+	0.0819929i
$413$	0.278191	+	0.160614i	0.0136889	+	0.00790329i
$414$		0			0
$415$	7.60731	−	4.39208i	0.373428	−	0.215599i
$416$	−7.16030	+	3.37000i	−0.351063	+	0.165228i
$417$		0			0
$418$	−8.67025	−	9.95964i	−0.424076	−	0.487142i
$419$	−12.8762	+	10.8044i	−0.629046	+	0.527832i	−0.900632	−	0.434582i	$-0.856896\pi$
$419$	−12.8762	+	10.8044i	−0.629046	+	0.527832i	0.271587	+	0.962414i	$0.412452\pi$
$420$		0			0
$421$	9.49415	−	3.45559i	0.462716	−	0.168415i	−0.100134	−	0.994974i	$-0.531927\pi$
$421$	9.49415	−	3.45559i	0.462716	−	0.168415i	0.562850	+	0.826559i	$0.309705\pi$
$422$	−4.68406	+	2.81901i	−0.228016	+	0.137227i
$423$		0			0
$424$	−24.3203	−	12.3264i	−1.18110	−	0.598623i
$425$	−11.8257	−	2.08519i	−0.573630	−	0.101146i
$426$		0			0
$427$	−2.07104	+	5.69014i	−0.100225	+	0.275365i
$428$	1.79484	+	8.38529i	0.0867568	+	0.405319i
$429$		0			0
$430$	14.2359	+	11.5112i	0.686516	+	0.555121i
$431$	−27.3550			−1.31764			−0.658822	−	0.752299i	$-0.728945\pi$
$431$	−27.3550			−1.31764			−0.658822	+	0.752299i	$0.728945\pi$
$432$		0			0
$433$	−8.86214			−0.425887			−0.212944	−	0.977065i	$-0.568305\pi$
$433$	−8.86214			−0.425887			−0.212944	+	0.977065i	$0.568305\pi$
$434$	−7.89289	−	6.38223i	−0.378871	−	0.306357i
$435$		0			0
$436$	−1.98902	−	9.29247i	−0.0952566	−	0.445028i
$437$	6.12040	−	16.8157i	0.292779	−	0.804402i
$438$		0			0
$439$	24.2876	+	4.28256i	1.15918	+	0.204395i	0.719982	−	0.693993i	$-0.244150\pi$
$439$	24.2876	+	4.28256i	1.15918	+	0.204395i	0.439202	+	0.898388i	$0.355261\pi$
$440$	−14.3325	−	7.26422i	−0.683274	−	0.346308i
$441$		0			0
$442$	−10.8807	+	6.54832i	−0.517540	+	0.311472i
$443$	−11.7116	+	4.26266i	−0.556433	+	0.202525i	−0.604902	−	0.796300i	$-0.706788\pi$
$443$	−11.7116	+	4.26266i	−0.556433	+	0.202525i	0.0484697	+	0.998825i	$0.484566\pi$
$444$		0			0
$445$	−0.796903	+	0.668681i	−0.0377768	+	0.0316985i
$446$	21.7020	+	24.9294i	1.02762	+	1.18044i
$447$		0			0
$448$	2.68716	+	5.45025i	0.126956	+	0.257500i
$449$	30.7560	−	17.7570i	1.45146	−	0.838003i	0.452899	−	0.891562i	$-0.350390\pi$
$449$	30.7560	−	17.7570i	1.45146	−	0.838003i	0.998565	+	0.0535589i	$0.0170565\pi$
$450$		0			0
$451$	−17.9480	−	10.3623i	−0.845140	−	0.487942i
$452$	−18.0275	−	2.50741i	−0.847942	−	0.117939i
$453$		0			0
$454$	−14.1978	−	4.87738i	−0.666335	−	0.228907i
$455$	0.326416	+	1.85119i	0.0153026	+	0.0867853i
$456$		0			0
$457$	12.8012	+	10.7415i	0.598816	+	0.502467i	0.891065	−	0.453876i	$-0.149959\pi$
$457$	12.8012	+	10.7415i	0.598816	+	0.502467i	−0.292249	+	0.956342i	$0.594403\pi$
$458$	9.83695	−	0.178714i	0.459651	−	0.00835077i
$459$		0			0
$460$	−0.790951	−	21.7609i	−0.0368783	−	1.01461i
$461$	−4.70721	+	5.60984i	−0.219237	+	0.261276i	−0.864441	−	0.502734i	$-0.832328\pi$
$461$	−4.70721	+	5.60984i	−0.219237	+	0.261276i	0.645205	+	0.764010i	$0.276772\pi$
$462$		0			0
$463$	−14.7017	+	2.59231i	−0.683246	+	0.120475i	−0.504489	−	0.863418i	$-0.668319\pi$
$463$	−14.7017	+	2.59231i	−0.683246	+	0.120475i	−0.178758	+	0.983893i	$0.557208\pi$
$464$	−8.27762	+	29.1811i	−0.384279	+	1.35470i
$465$		0			0
$466$	22.5810	+	3.56000i	1.04605	+	0.164914i
$467$	15.8668	−	27.4821i	0.734227	−	1.27172i	−0.220834	−	0.975311i	$-0.570878\pi$
$467$	15.8668	−	27.4821i	0.734227	−	1.27172i	0.955062	−	0.296408i	$-0.0957887\pi$
$468$		0			0
$469$	−2.15980	−	3.74089i	−0.0997305	−	0.172738i
$470$	3.81462	+	9.91631i	0.175955	+	0.457405i
$471$		0			0
$472$	−0.873055	+	0.817632i	−0.0401856	+	0.0376346i
$473$	−15.1067	−	18.0035i	−0.694608	−	0.827802i
$474$		0			0
$475$	−1.86031	−	5.11115i	−0.0853567	−	0.234516i
$476$	5.17917	+	8.26219i	0.237387	+	0.378697i
$477$		0			0
$478$	−15.4955	+	28.0016i	−0.708747	+	1.28076i
$479$	2.34547	−	13.3018i	0.107167	−	0.607775i	−0.883165	−	0.469062i	$-0.844592\pi$
$479$	2.34547	−	13.3018i	0.107167	−	0.607775i	0.990333	−	0.138713i	$-0.0442967\pi$
$480$		0			0
$481$	−4.26039	−	1.55066i	−0.194257	−	0.0707038i
$482$	0.0583438	+	0.299015i	0.00265749	+	0.0136198i
$483$		0			0
$484$	−1.08301	−	0.843661i	−0.0492279	−	0.0383482i
$485$			29.8960i			1.35751i
$486$		0			0
$487$		−	21.1864i		−	0.960045i	−0.877256	−	0.480023i	$-0.840628\pi$
$487$		−	21.1864i		−	0.960045i	0.877256	−	0.480023i	$-0.159372\pi$
$488$	−18.0365	−	13.5311i	−0.816474	−	0.612526i
$489$		0			0
$490$	−15.7710	+	3.07724i	−0.712463	+	0.139016i
$491$	−18.5924	−	6.76707i	−0.839062	−	0.305394i	−0.113490	−	0.993539i	$-0.536203\pi$
$491$	−18.5924	−	6.76707i	−0.839062	−	0.305394i	−0.725573	+	0.688145i	$0.758425\pi$
$492$		0			0
$493$	−8.45225	+	47.9351i	−0.380670	+	2.15889i
$494$	−5.03297	−	2.78513i	−0.226444	−	0.125309i
$495$		0			0
$496$	31.2744	−	21.2247i	1.40426	−	0.953019i
$497$	0.981109	+	2.69557i	0.0440087	+	0.120913i
$498$		0			0
$499$	18.9238	+	22.5525i	0.847146	+	1.00959i	0.999773	+	0.0213055i	$0.00678228\pi$
$499$	18.9238	+	22.5525i	0.847146	+	1.00959i	−0.152627	+	0.988284i	$0.548773\pi$
$500$	−16.2911	−	18.0414i	−0.728562	−	0.806835i
$501$		0			0
$502$	31.4884	−	12.1130i	1.40540	−	0.540631i
$503$	−15.3565	−	26.5983i	−0.684714	−	1.18596i	−0.973527	−	0.228574i	$-0.926594\pi$
$503$	−15.3565	−	26.5983i	−0.684714	−	1.18596i	0.288812	−	0.957386i	$-0.406740\pi$
$504$		0			0
$505$	−4.84861	+	8.39803i	−0.215760	+	0.373707i
$506$	−4.35321	+	27.6124i	−0.193524	+	1.22752i
$507$		0			0
$508$	−5.38806	+	16.6635i	−0.239057	+	0.739323i
$509$	−13.2428	+	2.33506i	−0.586977	+	0.103500i	−0.459246	−	0.888309i	$-0.651880\pi$
$509$	−13.2428	+	2.33506i	−0.586977	+	0.103500i	−0.127731	+	0.991809i	$0.540769\pi$
$510$		0			0
$511$	5.46698	−	6.51530i	0.241845	−	0.288220i
$512$	−22.3257	+	3.68292i	−0.986665	+	0.162763i
$513$		0			0
$514$	−0.0350319	−	1.92826i	−0.00154519	−	0.0850518i
$515$	8.18537	+	6.86834i	0.360690	+	0.302655i
$516$		0			0
$517$	−2.36842	−	13.4320i	−0.104163	−	0.590737i
$518$	−1.13108	+	3.29250i	−0.0496967	+	0.144664i
$519$		0			0
$520$	−6.94917	−	0.838180i	−0.304741	−	0.0367566i
$521$	−9.44955	−	5.45570i	−0.413992	−	0.239018i	0.278511	−	0.960433i	$-0.410159\pi$
$521$	−9.44955	−	5.45570i	−0.413992	−	0.239018i	−0.692504	+	0.721414i	$0.743492\pi$
$522$		0			0
$523$	16.1086	−	9.30028i	0.704378	−	0.406673i	−0.104598	−	0.994515i	$-0.533356\pi$
$523$	16.1086	−	9.30028i	0.704378	−	0.406673i	0.808976	+	0.587842i	$0.200022\pi$
$524$	13.6925	−	5.55484i	0.598161	−	0.242665i
$525$		0			0
$526$	18.3141	−	15.9431i	0.798532	−	0.695153i
$527$	46.4624	−	38.9865i	2.02393	−	1.69828i
$528$		0			0
$529$	−13.9843	+	5.08986i	−0.608012	+	0.221298i
$530$	−12.4354	−	20.6626i	−0.540158	−	0.897525i
$531$		0			0
$532$	−2.06806	+	3.90286i	−0.0896618	+	0.169210i
$533$	−8.89075	−	1.56768i	−0.385101	−	0.0679037i
$534$		0			0
$535$	−2.59410	+	7.12723i	−0.112153	+	0.308137i
$536$	15.6647	−	3.65176i	0.676611	−	0.157732i
$537$		0			0
$538$	−7.82179	+	9.67319i	−0.337221	+	0.417041i
$539$	20.6274			0.888486
$540$		0			0
$541$	16.5311			0.710730			0.355365	−	0.934728i	$-0.384357\pi$
$541$	16.5311			0.710730			0.355365	+	0.934728i	$0.384357\pi$
$542$	−2.83620	+	3.50753i	−0.121825	+	0.150661i
$543$		0			0
$544$	−35.0394	+	9.52267i	−1.50230	+	0.408281i
$545$	2.87475	−	7.89830i	0.123141	−	0.338326i
$546$		0			0
$547$	9.59158	+	1.69125i	0.410106	+	0.0723128i	0.374895	−	0.927067i	$-0.377679\pi$
$547$	9.59158	+	1.69125i	0.410106	+	0.0723128i	0.0352109	+	0.999380i	$0.488790\pi$
$548$	−9.56307	−	5.06731i	−0.408514	−	0.216465i
$549$		0			0
$550$	4.38120	+	7.27979i	0.186815	+	0.310411i
$551$	−20.7179	+	7.54069i	−0.882612	+	0.321244i
$552$		0			0
$553$	−5.91223	+	4.96095i	−0.251413	+	0.210961i
$554$	−14.9130	+	12.9823i	−0.633592	+	0.551566i
$555$		0			0
$556$	10.9777	+	27.0597i	0.465558	+	1.14759i
$557$	16.9093	−	9.76261i	0.716471	−	0.413655i	−0.0969812	−	0.995286i	$-0.530919\pi$
$557$	16.9093	−	9.76261i	0.716471	−	0.413655i	0.813453	+	0.581631i	$0.197585\pi$
$558$		0			0
$559$	−8.86613	−	5.11886i	−0.374997	−	0.216505i
$560$	−0.546577	+	5.34685i	−0.0230971	+	0.225946i
$561$		0			0
$562$	2.15631	−	6.27691i	0.0909586	−	0.264776i
$563$	0.00844444	+	0.0478908i	0.000355891	+	0.00201836i	0.984985	−	0.172639i	$-0.0552294\pi$
$563$	0.00844444	+	0.0478908i	0.000355891	+	0.00201836i	−0.984629	+	0.174657i	$0.944118\pi$
$564$		0			0
$565$	−12.3322	−	10.3479i	−0.518818	−	0.435340i
$566$	0.110973	+	6.10829i	0.00466456	+	0.256751i
$567$		0			0
$568$	−10.6657	+	0.581823i	−0.447522	+	0.0244128i
$569$	−14.3594	+	17.1129i	−0.601978	+	0.717409i	−0.977860	−	0.209258i	$-0.932895\pi$
$569$	−14.3594	+	17.1129i	−0.601978	+	0.717409i	0.375883	+	0.926667i	$0.377340\pi$
$570$		0			0
$571$	−7.54185	+	1.32983i	−0.315617	+	0.0556518i	−0.329213	−	0.944256i	$-0.606783\pi$
$571$	−7.54185	+	1.32983i	−0.315617	+	0.0556518i	0.0135958	+	0.999908i	$0.495672\pi$
$572$	8.54962	+	2.76448i	0.357478	+	0.115589i
$573$		0			0
$574$	−1.07956	+	6.84765i	−0.0450601	+	0.285816i
$575$	−5.75711	+	9.97161i	−0.240088	+	0.415845i
$576$		0			0
$577$	−0.594755	−	1.03015i	−0.0247600	−	0.0428855i	0.853380	−	0.521289i	$-0.174549\pi$
$577$	−0.594755	−	1.03015i	−0.0247600	−	0.0428855i	−0.878140	+	0.478404i	$0.841215\pi$
$578$	−31.9438	+	12.2882i	−1.32869	+	0.511122i
$579$		0			0
$580$	−19.9118	+	17.9801i	−0.826793	+	0.746584i
$581$	2.42452	+	2.88943i	0.100586	+	0.119874i
$582$		0			0
$583$	10.5883	+	29.0912i	0.438524	+	1.20483i
$584$	17.3055	+	26.5238i	0.716106	+	1.09756i
$585$		0			0
$586$	−14.0924	−	7.79843i	−0.582152	−	0.322150i
$587$	2.07929	−	11.7922i	0.0858214	−	0.486717i	−0.911355	−	0.411621i	$-0.864963\pi$
$587$	2.07929	−	11.7922i	0.0858214	−	0.486717i	0.997176	−	0.0750959i	$-0.0239263\pi$
$588$		0			0
$589$	25.8161	+	9.39629i	1.06373	+	0.387168i
$590$	−1.03838	+	0.202609i	−0.0427495	+	0.00834127i
$591$		0			0
$592$	−10.5093	−	7.58977i	−0.431928	−	0.311938i
$593$			33.8346i			1.38942i	0.719290	+	0.694710i	$0.244467\pi$
$593$			33.8346i			1.38942i	−0.719290	+	0.694710i	$0.755533\pi$
$594$		0			0
$595$			8.62484i			0.353584i
$596$	−1.27713	+	1.63946i	−0.0523134	+	0.0671551i
$597$		0			0
$598$	2.33197	+	11.9515i	0.0953613	+	0.488732i
$599$	4.43045	+	1.61255i	0.181023	+	0.0658871i	0.430942	−	0.902380i	$-0.358182\pi$
$599$	4.43045	+	1.61255i	0.181023	+	0.0658871i	−0.249918	+	0.968267i	$0.580404\pi$
$600$		0			0
$601$	2.90395	−	16.4691i	0.118455	−	0.671790i	−0.866527	−	0.499131i	$-0.833653\pi$
$601$	2.90395	−	16.4691i	0.118455	−	0.671790i	0.984982	−	0.172660i	$-0.0552361\pi$
$602$	−3.80629	+	6.87828i	−0.155133	+	0.280338i
$603$		0			0
$604$	−25.7000	+	16.1101i	−1.04572	+	0.655511i
$605$	−0.415298	−	1.14102i	−0.0168843	−	0.0463891i
$606$		0			0
$607$	16.3490	+	19.4839i	0.663584	+	0.790828i	0.987895	−	0.155122i	$-0.0495770\pi$
$607$	16.3490	+	19.4839i	0.663584	+	0.790828i	−0.324311	+	0.945950i	$0.605133\pi$
$608$	−11.6712	−	11.5883i	−0.473329	−	0.469969i
$609$		0			0
$610$	−7.16026	−	18.6135i	−0.289911	−	0.753638i
$611$	−2.97070	−	5.14540i	−0.120182	−	0.208161i
$612$		0			0
$613$	23.0173	−	39.8671i	0.929658	−	1.61022i	0.145765	−	0.989319i	$-0.453436\pi$
$613$	23.0173	−	39.8671i	0.929658	−	1.61022i	0.783893	−	0.620896i	$-0.213231\pi$
$614$	29.9860	+	4.72742i	1.21014	+	0.190783i
$615$		0			0
$616$	2.00315	−	6.60245i	0.0807093	−	0.266020i
$617$	0.162348	−	0.0286264i	0.00653590	−	0.00115246i	−0.170379	−	0.985379i	$-0.554499\pi$
$617$	0.162348	−	0.0286264i	0.00653590	−	0.00115246i	0.176915	+	0.984226i	$0.443388\pi$
$618$		0			0
$619$	8.86726	−	10.5676i	0.356405	−	0.424747i	−0.557815	−	0.829965i	$-0.688360\pi$
$619$	8.86726	−	10.5676i	0.356405	−	0.424747i	0.914220	+	0.405218i	$0.132805\pi$
$620$	33.4083	−	1.21430i	1.34171	−	0.0487675i
$621$		0			0
$622$	16.0571	−	0.291720i	0.643831	−	0.0116969i
$623$	−0.342186	−	0.287129i	−0.0137094	−	0.0115036i
$624$		0			0
$625$	−2.10920	−	11.9619i	−0.0843681	−	0.478475i
$626$	34.3333	+	11.7946i	1.37224	+	0.471405i
$627$		0			0
$628$	2.15780	−	15.5139i	0.0861058	−	0.619073i
$629$	−18.0154	−	10.4012i	−0.718322	−	0.414724i
$630$		0			0
$631$	28.8999	−	16.6854i	1.15049	−	0.664234i	0.201481	−	0.979492i	$-0.435425\pi$
$631$	28.8999	−	16.6854i	1.15049	−	0.664234i	0.949006	+	0.315259i	$0.102091\pi$
$632$	−11.2856	−	26.4300i	−0.448916	−	1.05133i
$633$		0			0
$634$	23.1282	+	26.5677i	0.918539	+	1.05514i
$635$	−11.8659	+	9.95671i	−0.470885	+	0.395120i
$636$		0			0
$637$	8.44367	−	3.07324i	0.334550	−	0.121766i
$638$	29.5084	−	17.7591i	1.16825	−	0.703088i
$639$		0			0
$640$	−18.4613	−	7.72795i	−0.729748	−	0.305474i
$641$	44.1736	+	7.78900i	1.74475	+	0.307647i	0.952949	−	0.303129i	$-0.0980313\pi$
$641$	44.1736	+	7.78900i	1.74475	+	0.307647i	0.791803	+	0.610776i	$0.209142\pi$
$642$		0			0
$643$	9.50479	−	26.1142i	0.374832	−	1.02984i	−0.598636	−	0.801021i	$-0.704290\pi$
$643$	9.50479	−	26.1142i	0.374832	−	1.02984i	0.973468	−	0.228822i	$-0.0734874\pi$
$644$	9.14311	−	1.95705i	0.360289	−	0.0771184i
$645$		0			0
$646$	−20.5228	−	16.5948i	−0.807459	−	0.652916i
$647$	29.6395			1.16525			0.582624	−	0.812742i	$-0.302026\pi$
$647$	29.6395			1.16525			0.582624	+	0.812742i	$0.302026\pi$
$648$		0			0
$649$	1.35813			0.0533113
$650$	2.87801	+	2.32718i	0.112885	+	0.0912793i
$651$		0			0
$652$	−29.0839	+	6.22531i	−1.13902	+	0.243802i
$653$	−3.24289	+	8.90976i	−0.126904	+	0.348666i	−0.986832	−	0.161750i	$-0.948286\pi$
$653$	−3.24289	+	8.90976i	−0.126904	+	0.348666i	0.859928	+	0.510416i	$0.170508\pi$
$654$		0			0
$655$	12.8709	+	2.26949i	0.502907	+	0.0886762i
$656$	−23.2329	−	11.2496i	−0.907092	−	0.439223i
$657$		0			0
$658$	−3.90890	+	2.35249i	−0.152385	+	0.0917097i
$659$	39.0039	−	14.1963i	1.51938	−	0.553008i	0.558385	−	0.829582i	$-0.311421\pi$
$659$	39.0039	−	14.1963i	1.51938	−	0.553008i	0.960993	+	0.276573i	$0.0891989\pi$
$660$		0			0
$661$	−1.13289	+	0.950604i	−0.0440642	+	0.0369742i	−0.664554	−	0.747240i	$-0.731378\pi$
$661$	−1.13289	+	0.950604i	−0.0440642	+	0.0369742i	0.620490	+	0.784215i	$0.286934\pi$
$662$	29.2980	+	33.6550i	1.13870	+	1.30804i
$663$		0			0
$664$	−12.9169	+	5.51550i	−0.501272	+	0.214043i
$665$	−3.38329	+	1.95334i	−0.131198	+	0.0757474i
$666$		0			0
$667$	40.4196	+	23.3363i	1.56505	+	0.903584i
$668$	0.280384	−	2.01587i	0.0108484	−	0.0779963i
$669$		0			0
$670$	13.4548	+	4.62215i	0.519806	+	0.178569i
$671$	4.44566	+	25.2126i	0.171623	+	0.973320i
$672$		0			0
$673$	−6.61457	−	5.55028i	−0.254973	−	0.213948i	0.506337	−	0.862335i	$-0.330999\pi$
$673$	−6.61457	−	5.55028i	−0.254973	−	0.213948i	−0.761310	+	0.648388i	$0.775444\pi$
$674$	−29.2401	+	0.531224i	−1.12629	+	0.0204620i
$675$		0			0
$676$	−22.0712	+	0.802230i	−0.848894	+	0.0308550i
$677$	16.1671	−	19.2672i	0.621353	−	0.740499i	−0.359950	−	0.932972i	$-0.617206\pi$
$677$	16.1671	−	19.2672i	0.621353	−	0.740499i	0.981302	+	0.192472i	$0.0616506\pi$
$678$		0			0
$679$	−12.6422	+	2.22916i	−0.485163	+	0.0855473i
$680$	−30.7325	−	9.32411i	−1.17854	−	0.357563i
$681$		0			0
$682$	−42.3916	−	6.68323i	−1.62326	−	0.255914i
$683$	10.1910	−	17.6513i	0.389948	−	0.675409i	−0.602494	−	0.798123i	$-0.705826\pi$
$683$	10.1910	−	17.6513i	0.389948	−	0.675409i	0.992442	+	0.122714i	$0.0391597\pi$
$684$		0			0
$685$	−4.78622	−	8.28998i	−0.182872	−	0.316744i
$686$	−5.17698	−	13.4578i	−0.197658	−	0.513822i
$687$		0			0
$688$	−20.3942	−	20.9988i	−0.777523	−	0.800571i
$689$	8.66849	+	10.3307i	0.330243	+	0.393569i
$690$		0			0
$691$	−10.6380	−	29.2276i	−0.404688	−	1.11187i	−0.959944	−	0.280192i	$-0.909602\pi$
$691$	−10.6380	−	29.2276i	−0.404688	−	1.11187i	0.555256	−	0.831679i	$-0.312620\pi$
$692$	13.2404	−	8.29980i	0.503326	−	0.315511i
$693$		0			0
$694$	19.5757	−	35.3748i	0.743082	−	1.34281i
$695$	−4.48504	+	25.4360i	−0.170127	+	0.964841i
$696$		0			0
$697$	−38.9245	−	14.1674i	−1.47437	−	0.536627i
$698$	3.90635	+	20.0203i	0.147858	+	0.757779i
$699$		0			0
$700$	1.74652	−	2.24203i	0.0660124	−	0.0847406i
$701$		−	6.46847i		−	0.244311i	−0.992511	−	0.122155i	$-0.961019\pi$
$701$		−	6.46847i		−	0.244311i	0.992511	−	0.122155i	$-0.0389806\pi$
$702$		0			0
$703$		−	9.42262i		−	0.355381i
$704$	21.3607	+	14.2755i	0.805061	+	0.538029i
$705$		0			0
$706$	35.2362	−	6.87527i	1.32613	−	0.258754i
$707$	−3.91282	−	1.42415i	−0.147157	−	0.0535607i
$708$		0			0
$709$	3.74684	−	21.2494i	0.140715	−	0.798036i	−0.829993	−	0.557774i	$-0.811655\pi$
$709$	3.74684	−	21.2494i	0.140715	−	0.798036i	0.970708	−	0.240262i	$-0.0772334\pi$
$710$	−8.26635	−	4.57442i	−0.310231	−	0.171675i
$711$		0			0
$712$	1.39304	−	0.908892i	0.0522065	−	0.0340622i
$713$	−19.8911	−	54.6503i	−0.744927	−	2.04667i
$714$		0			0
$715$	5.10854	+	6.08812i	0.191048	+	0.227683i
$716$	−11.5897	+	10.4653i	−0.433127	+	0.391108i
$717$		0			0
$718$	−6.90788	+	2.65733i	−0.257800	+	0.0991708i
$719$	4.48435	+	7.76713i	0.167238	+	0.289665i	0.937448	−	0.348126i	$-0.113182\pi$
$719$	4.48435	+	7.76713i	0.167238	+	0.289665i	−0.770210	+	0.637791i	$0.779848\pi$
$720$		0			0
$721$	−2.29410	+	3.97349i	−0.0854366	+	0.147980i
$722$	−2.32277	+	14.7333i	−0.0864445	+	0.548317i
$723$		0			0
$724$	5.53370	+	1.78929i	0.205658	+	0.0664986i
$725$	13.9707	−	2.46341i	0.518858	−	0.0914886i
$726$		0			0
$727$	−25.5804	+	30.4856i	−0.948726	+	1.13065i	0.0425829	+	0.999093i	$0.486441\pi$
$727$	−25.5804	+	30.4856i	−0.948726	+	1.13065i	−0.991309	+	0.131555i	$0.958003\pi$
$728$	−0.163713	−	3.00111i	−0.00606762	−	0.111228i
$729$		0			0
$730$	0.508821	+	28.0070i	0.0188323	+	1.03658i
$731$	−35.9839	−	30.1940i	−1.33091	−	1.11677i
$732$		0			0
$733$	5.60310	+	31.7768i	0.206955	+	1.17370i	0.894333	+	0.447402i	$0.147651\pi$
$733$	5.60310	+	31.7768i	0.206955	+	1.17370i	−0.687378	+	0.726300i	$0.741238\pi$
$734$	14.9074	−	43.3947i	0.550243	−	1.60173i
$735$		0			0
$736$	−2.91094	+	34.6950i	−0.107299	+	1.27887i
$737$	−15.8162	−	9.13151i	−0.582599	−	0.336364i
$738$		0			0
$739$	−45.5964	+	26.3251i	−1.67729	+	0.968384i	−0.713912	+	0.700235i	$0.753078\pi$
$739$	−45.5964	+	26.3251i	−1.67729	+	0.968384i	−0.963378	+	0.268148i	$0.913588\pi$
$740$	−4.31034	−	10.6249i	−0.158451	−	0.390577i
$741$		0			0
$742$	7.81039	−	6.79924i	0.286728	−	0.249608i
$743$	5.64333	−	4.73531i	0.207034	−	0.173722i	−0.533375	−	0.845879i	$-0.679077\pi$
$743$	5.64333	−	4.73531i	0.207034	−	0.173722i	0.740409	+	0.672157i	$0.234632\pi$
$744$		0			0
$745$	−1.72728	+	0.628678i	−0.0632825	+	0.0230330i
$746$	−10.7509	−	17.8637i	−0.393619	−	0.654036i
$747$		0			0
$748$	36.4295	+	19.3034i	1.33200	+	0.705802i
$749$	−3.20733	−	0.565539i	−0.117193	−	0.0206643i
$750$		0			0
$751$	14.4395	−	39.6722i	0.526905	−	1.44766i	−0.335792	−	0.941936i	$-0.609004\pi$
$751$	14.4395	−	39.6722i	0.526905	−	1.44766i	0.862696	−	0.505722i	$-0.168774\pi$
$752$	−4.15673	−	16.4716i	−0.151580	−	0.600659i
$753$		0			0
$754$	9.43314	−	11.6659i	0.343535	−	0.424848i
$755$	−26.8280			−0.976373
$756$		0			0
$757$	−18.7376			−0.681028			−0.340514	−	0.940239i	$-0.610601\pi$
$757$	−18.7376			−0.681028			−0.340514	+	0.940239i	$0.610601\pi$
$758$	−1.93306	+	2.39060i	−0.0702117	+	0.0868307i
$759$		0			0
$760$	−3.30268	−	14.1673i	−0.119801	−	0.513901i
$761$	−2.99398	+	8.22589i	−0.108532	+	0.298188i	−0.982055	−	0.188594i	$-0.939607\pi$
$761$	−2.99398	+	8.22589i	−0.108532	+	0.298188i	0.873524	+	0.486782i	$0.161829\pi$
$762$		0			0
$763$	3.55432	+	0.626722i	0.128675	+	0.0226889i
$764$	−14.8307	+	27.9886i	−0.536555	+	1.01259i
$765$		0			0
$766$	−19.7720	−	32.8531i	−0.714390	−	1.18703i
$767$	0.555940	−	0.202346i	0.0200738	−	0.00730627i
$768$		0			0
$769$	18.0034	−	15.1066i	0.649219	−	0.544759i	−0.257615	−	0.966248i	$-0.582937\pi$
$769$	18.0034	−	15.1066i	0.649219	−	0.544759i	0.906834	+	0.421489i	$0.138492\pi$
$770$	4.60284	−	4.00695i	0.165875	−	0.144400i
$771$		0			0
$772$	−23.6364	+	9.58891i	−0.850692	+	0.345112i
$773$	−13.5604	+	7.82910i	−0.487733	+	0.281593i	−0.723634	−	0.690184i	$-0.757529\pi$
$773$	−13.5604	+	7.82910i	−0.487733	+	0.281593i	0.235900	+	0.971777i	$0.424196\pi$
$774$		0			0
$775$	−15.3088	−	8.83855i	−0.549909	−	0.317490i
$776$	5.72410	−	47.4573i	0.205483	−	1.70362i
$777$		0			0
$778$	12.4872	−	36.3496i	0.447688	−	1.30320i
$779$	−3.25811	−	18.4776i	−0.116734	−	0.662030i
$780$		0			0
$781$	9.29069	+	7.79581i	0.332447	+	0.278956i
$782$	1.01487	+	55.8617i	0.0362919	+	1.99761i
$783$		0			0
$784$	25.6243	−	1.86521i	0.915155	−	0.0666148i
$785$	8.90510	−	10.6127i	0.317837	−	0.378783i
$786$		0			0
$787$	15.9427	−	2.81113i	0.568296	−	0.100206i	0.117885	−	0.993027i	$-0.462388\pi$
$787$	15.9427	−	2.81113i	0.568296	−	0.100206i	0.450411	+	0.892821i	$0.351277\pi$
$788$	−4.86231	+	15.0375i	−0.173213	+	0.535689i
$789$		0			0
$790$	3.95849	−	25.1087i	0.140837	−	0.893326i
$791$	3.45631	−	5.98650i	0.122892	−	0.212856i
$792$		0			0
$793$	5.57617	+	9.65821i	0.198016	+	0.342973i
$794$	12.9706	−	4.98957i	0.460311	−	0.177073i
$795$		0			0
$796$	5.21405	+	5.77422i	0.184807	+	0.204662i
$797$	19.0625	+	22.7178i	0.675229	+	0.804707i	0.989486	−	0.144631i	$-0.0461996\pi$
$797$	19.0625	+	22.7178i	0.675229	+	0.804707i	−0.314256	+	0.949338i	$0.601755\pi$
$798$		0			0
$799$	−9.32375	−	25.6168i	−0.329850	−	0.906257i
$800$	6.10080	+	8.64712i	0.215696	+	0.305722i
$801$		0			0
$802$	11.2178	+	6.20771i	0.396116	+	0.219202i
$803$	6.24423	−	35.4128i	0.220354	−	1.24969i
$804$		0			0
$805$	7.77135	+	2.82854i	0.273904	+	0.0996929i
$806$	−18.3484	+	3.58013i	−0.646295	+	0.126105i
$807$		0			0
$808$	9.30468	−	12.4028i	0.327337	−	0.436328i
$809$		−	28.2066i		−	0.991690i	−0.868411	−	0.495845i	$-0.834858\pi$
$809$		−	28.2066i		−	0.991690i	0.868411	−	0.495845i	$-0.165142\pi$
$810$		0			0
$811$			28.0396i			0.984605i	0.870424	+	0.492302i	$0.163845\pi$
$811$			28.0396i			0.984605i	−0.870424	+	0.492302i	$0.836155\pi$
$812$	−9.08798	−	7.07948i	−0.318926	−	0.248441i
$813$		0			0
$814$	2.81881	+	14.4466i	0.0987992	+	0.506352i
$815$	−24.7204	−	8.99750i	−0.865918	−	0.315169i
$816$		0			0
$817$	3.69472	−	20.9538i	0.129262	−	0.733081i
$818$	19.6255	−	35.4650i	0.686191	−	1.24000i
$819$		0			0
$820$	−12.1263	−	19.3448i	−0.423470	−	0.675549i
$821$	10.1420	+	27.8650i	0.353960	+	0.972496i	0.981085	+	0.193578i	$0.0620092\pi$
$821$	10.1420	+	27.8650i	0.353960	+	0.972496i	−0.627125	+	0.778918i	$0.715769\pi$
$822$		0			0
$823$	−7.87250	−	9.38208i	−0.274418	−	0.327039i	0.611180	−	0.791492i	$-0.290695\pi$
$823$	−7.87250	−	9.38208i	−0.274418	−	0.327039i	−0.885598	+	0.464453i	$0.846251\pi$
$824$	−11.6785	−	12.4701i	−0.406839	−	0.434417i
$825$		0			0
$826$	−0.163103	−	0.423995i	−0.00567508	−	0.0147527i
$827$	5.15219	+	8.92386i	0.179159	+	0.310313i	0.941593	−	0.336754i	$-0.109329\pi$
$827$	5.15219	+	8.92386i	0.179159	+	0.310313i	−0.762434	+	0.647067i	$0.775996\pi$
$828$		0			0
$829$	−20.0735	+	34.7684i	−0.697183	+	1.20756i	0.272256	+	0.962225i	$0.412230\pi$
$829$	−20.0735	+	34.7684i	−0.697183	+	1.20756i	−0.969439	+	0.245332i	$0.921103\pi$
$830$	−12.2711	−	1.93460i	−0.425937	−	0.0671508i
$831$		0			0
$832$	10.8707	+	2.66107i	0.376874	+	0.0922561i
$833$	40.6020	−	7.15922i	1.40677	−	0.248052i
$834$		0			0
$835$	1.15712	−	1.37901i	0.0400439	−	0.0477225i
$836$	0.678318	+	18.6621i	0.0234601	+	0.645443i
$837$		0			0
$838$	23.7672	−	0.431795i	0.821025	−	0.0149161i
$839$	37.1850	+	31.2019i	1.28377	+	1.07721i	0.992713	+	0.120502i	$0.0384506\pi$
$839$	37.1850	+	31.2019i	1.28377	+	1.07721i	0.291055	+	0.956706i	$0.405994\pi$
$840$		0			0
$841$	−4.94954	−	28.0703i	−0.170674	−	0.967940i
$842$	−13.5133	−	4.64224i	−0.465699	−	0.159982i
$843$		0			0
$844$	7.65768	+	1.06509i	0.263588	+	0.0366620i
$845$	−16.9174	−	9.76726i	−0.581976	−	0.336004i
$846$		0			0
$847$	0.451540	−	0.260697i	0.0155151	−	0.00895764i
$848$	15.7838	+	35.1810i	0.542020	+	1.20812i
$849$		0			0
$850$	11.1503	+	12.8086i	0.382454	+	0.439330i
$851$	−15.2801	+	12.8216i	−0.523797	+	0.439518i
$852$		0			0
$853$	−10.1083	+	3.67913i	−0.346102	+	0.125971i	−0.509222	−	0.860635i	$-0.670067\pi$
$853$	−10.1083	+	3.67913i	−0.346102	+	0.125971i	0.163119	+	0.986606i	$0.447844\pi$
$854$	7.33722	−	4.41576i	0.251075	−	0.151104i
$855$		0			0
$856$	5.48253	−	10.8172i	0.187389	−	0.369723i
$857$	3.33877	+	0.588716i	0.114050	+	0.0201102i	0.230382	−	0.973100i	$-0.426002\pi$
$857$	3.33877	+	0.588716i	0.114050	+	0.0201102i	−0.116332	+	0.993210i	$0.537114\pi$
$858$		0			0
$859$	−6.70377	+	18.4184i	−0.228730	+	0.628429i	−0.999967	−	0.00811819i	$-0.997416\pi$
$859$	−6.70377	+	18.4184i	−0.228730	+	0.628429i	0.771237	+	0.636548i	$0.219638\pi$
$860$	−5.41910	−	25.3174i	−0.184790	−	0.863317i
$861$		0			0
$862$	30.0819	+	24.3244i	1.02459	+	0.828491i
$863$	−48.0692			−1.63629			−0.818147	−	0.575009i	$-0.804999\pi$
$863$	−48.0692			−1.63629			−0.818147	+	0.575009i	$0.804999\pi$
$864$		0			0
$865$	13.8216			0.469949
$866$	9.74555	+	7.88030i	0.331167	+	0.267784i
$867$		0			0
$868$	3.00454	+	14.0369i	0.101981	+	0.476443i
$869$	−11.1603	+	30.6628i	−0.378588	+	1.04016i
$870$		0			0
$871$	−7.83474	−	1.38148i	−0.265470	−	0.0468095i
$872$	−6.07567	+	11.9874i	−0.205748	+	0.405946i
$873$		0			0
$874$	−21.6832	+	13.0496i	−0.733444	+	0.441409i
$875$	8.67534	−	3.15756i	0.293280	−	0.106745i
$876$		0			0
$877$	−36.3911	+	30.5358i	−1.22884	+	1.03112i	−0.230527	+	0.973066i	$0.574045\pi$
$877$	−36.3911	+	30.5358i	−1.22884	+	1.03112i	−0.998313	+	0.0580531i	$0.981511\pi$
$878$	−22.9006	−	26.3062i	−0.772857	−	0.887792i
$879$		0			0
$880$	9.30178	+	20.7329i	0.313563	+	0.698907i
$881$	9.71356	−	5.60813i	0.327258	−	0.188943i	−0.327365	−	0.944898i	$-0.606161\pi$
$881$	9.71356	−	5.60813i	0.327258	−	0.188943i	0.654623	+	0.755955i	$0.272827\pi$
$882$		0			0
$883$	7.49573	+	4.32766i	0.252251	+	0.145637i	0.620795	−	0.783973i	$-0.286810\pi$
$883$	7.49573	+	4.32766i	0.252251	+	0.145637i	−0.368543	+	0.929611i	$0.620143\pi$
$884$	17.7881	+	2.47412i	0.598279	+	0.0832136i
$885$		0			0
$886$	16.6694	+	5.72646i	0.560020	+	0.192384i
$887$	−5.65003	−	32.0429i	−0.189710	−	1.07590i	−0.919754	−	0.392496i	$-0.871612\pi$
$887$	−5.65003	−	32.0429i	−0.189710	−	1.07590i	0.730044	−	0.683400i	$-0.239500\pi$
$888$		0			0
$889$	−5.09518	−	4.27536i	−0.170887	−	0.143391i
$890$	1.47094	−	0.0267235i	0.0493060	−	0.000895774i
$891$		0			0
$892$	−1.69786	−	46.7120i	−0.0568484	−	1.56404i
$893$	7.93714	−	9.45911i	0.265606	−	0.316537i
$894$		0			0
$895$	−13.6018	+	2.39837i	−0.454659	+	0.0801686i
$896$	1.89139	−	8.38300i	0.0631869	−	0.280056i
$897$		0			0
$898$	−49.6115	−	7.82147i	−1.65556	−	0.261006i
$899$	−35.8268	+	62.0538i	−1.19489	+	2.06961i
$900$		0			0
$901$	30.9383	+	53.5867i	1.03070	+	1.78523i
$902$	10.5229	+	27.3548i	0.350374	+	0.910817i
$903$		0			0
$904$	17.5949	+	18.7876i	0.585199	+	0.624866i
$905$	3.30647	+	3.94050i	0.109911	+	0.130987i
$906$		0			0
$907$	−13.7943	−	37.8996i	−0.458033	−	1.25843i	−0.926947	−	0.375191i	$-0.877577\pi$
$907$	−13.7943	−	37.8996i	−0.458033	−	1.25843i	0.468915	−	0.883243i	$-0.344645\pi$
$908$	11.2761	+	17.9884i	0.374209	+	0.596965i
$909$		0			0
$910$	1.28715	−	2.32598i	0.0426685	−	0.0771055i
$911$	−8.02183	+	45.4941i	−0.265775	+	1.50729i	0.501044	+	0.865422i	$0.332949\pi$
$911$	−8.02183	+	45.4941i	−0.265775	+	1.50729i	−0.766819	+	0.641863i	$0.778162\pi$
$912$		0			0
$913$	14.9855	+	5.45429i	0.495949	+	0.180511i
$914$	−4.52585	−	23.1953i	−0.149702	−	0.767231i
$915$		0			0
$916$	−10.9765	−	8.55059i	−0.362672	−	0.282519i
$917$			5.61196i			0.185323i
$918$		0			0
$919$		−	1.23662i		−	0.0407922i	−0.999792	−	0.0203961i	$-0.993507\pi$
$919$		−	1.23662i		−	0.0407922i	0.999792	−	0.0203961i	$-0.00649274\pi$
$920$	−18.4802	+	24.6335i	−0.609276	+	0.812141i
$921$		0			0
$922$	10.1648	−	1.98335i	0.334759	−	0.0653181i
$923$	4.96455	+	1.80695i	0.163410	+	0.0594765i
$924$		0			0
$925$	−1.05281	+	5.97076i	−0.0346160	+	0.196317i
$926$	18.4723	+	10.2222i	0.607039	+	0.335922i
$927$		0			0
$928$	35.0509	−	24.7294i	1.15060	−	0.811782i
$929$	−8.79850	−	24.1737i	−0.288669	−	0.793112i	−0.996253	−	0.0864831i	$-0.972437\pi$
$929$	−8.79850	−	24.1737i	−0.288669	−	0.793112i	0.707584	−	0.706629i	$-0.249785\pi$
$930$		0			0
$931$	12.0039	+	14.3056i	0.393410	+	0.468848i
$932$	−21.6664	−	23.9942i	−0.709707	−	0.785955i
$933$		0			0
$934$	−41.8858	+	16.1127i	−1.37055	+	0.527223i
$935$	18.2326	+	31.5798i	0.596271	+	1.03277i
$936$		0			0
$937$	−13.9758	+	24.2068i	−0.456569	+	0.790801i	−0.998777	−	0.0494437i	$-0.984255\pi$
$937$	−13.9758	+	24.2068i	−0.456569	+	0.790801i	0.542208	+	0.840244i	$0.317588\pi$
$938$	−0.951336	+	6.03432i	−0.0310622	+	0.197027i
$939$		0			0
$940$	4.62281	−	14.2968i	0.150779	−	0.466311i
$941$	−48.5322	+	8.55753i	−1.58210	+	0.278968i	−0.894483	−	0.447103i	$-0.852456\pi$
$941$	−48.5322	+	8.55753i	−1.58210	+	0.278968i	−0.687621	+	0.726070i	$0.741345\pi$
$942$		0			0
$943$	−25.5308	+	30.4264i	−0.831397	+	0.990820i
$944$	1.68713	−	0.122808i	0.0549115	−	0.00399705i
$945$		0			0
$946$	0.603733	+	33.2312i	0.0196291	+	1.08044i
$947$	21.6693	+	18.1827i	0.704158	+	0.590858i	0.922953	−	0.384912i	$-0.125768\pi$
$947$	21.6693	+	18.1827i	0.704158	+	0.590858i	−0.218796	+	0.975771i	$0.570213\pi$
$948$		0			0
$949$	−2.72007	−	15.4263i	−0.0882971	−	0.500758i
$950$	−2.49914	+	7.27485i	−0.0810827	+	0.236027i
$951$		0			0
$952$	1.65137	−	13.6912i	0.0535213	−	0.443733i
$953$	−18.2626	−	10.5439i	−0.591583	−	0.341551i	0.174140	−	0.984721i	$-0.444285\pi$
$953$	−18.2626	−	10.5439i	−0.591583	−	0.341551i	−0.765723	+	0.643170i	$0.777619\pi$
$954$		0			0
$955$	−24.2626	+	14.0080i	−0.785119	+	0.453289i
$956$	41.9395	−	17.0142i	1.35642	−	0.550278i
$957$		0			0
$958$	−14.4074	+	12.5422i	−0.465481	+	0.405219i
$959$	3.14872	−	2.64209i	0.101678	−	0.0853176i
$960$		0			0
$961$	54.7709	−	19.9350i	1.76680	−	0.643064i
$962$	3.30623	+	5.49362i	0.106597	+	0.177121i
$963$		0			0
$964$	0.201728	−	0.380702i	0.00649721	−	0.0122616i
$965$	−22.2180	−	3.91764i	−0.715224	−	0.126113i
$966$		0			0
$967$	3.43633	−	9.44123i	0.110505	−	0.303610i	−0.872097	−	0.489333i	$-0.837240\pi$
$967$	3.43633	−	9.44123i	0.110505	−	0.303610i	0.982602	+	0.185723i	$0.0594627\pi$
$968$	0.440781	+	1.89079i	0.0141672	+	0.0607722i
$969$		0			0
$970$	26.5839	−	32.8762i	0.853556	−	1.05559i
$971$	38.1342			1.22378			0.611892	−	0.790942i	$-0.290409\pi$
$971$	38.1342			1.22378			0.611892	+	0.790942i	$0.290409\pi$
$972$		0			0
$973$	−11.0906			−0.355547
$974$	−18.8391	+	23.2983i	−0.603645	+	0.746526i
$975$		0			0
$976$	7.80242	+	30.9182i	0.249749	+	0.989668i
$977$	2.05993	−	5.65962i	0.0659031	−	0.181067i	−0.902370	−	0.430963i	$-0.858174\pi$
$977$	2.05993	−	5.65962i	0.0659031	−	0.181067i	0.968273	+	0.249895i	$0.0803962\pi$
$978$		0			0
$979$	−1.85990	−	0.327950i	−0.0594425	−	0.0104813i
$980$	20.0795	+	10.6398i	0.641415	+	0.339875i
$981$		0			0
$982$	14.4284	+	23.9742i	0.460429	+	0.765047i
$983$	−2.09396	+	0.762140i	−0.0667870	+	0.0243085i	−0.375198	−	0.926945i	$-0.622425\pi$
$983$	−2.09396	+	0.762140i	−0.0667870	+	0.0243085i	0.308411	+	0.951253i	$0.400203\pi$
$984$		0			0
$985$	−10.7081	+	8.98515i	−0.341188	+	0.286291i
$986$	51.9192	−	45.1976i	1.65344	−	1.43938i
$987$		0			0
$988$	3.05810	+	7.53813i	0.0972912	+	0.239820i
$989$	−39.0071	+	22.5208i	−1.24035	+	0.716119i
$990$		0			0
$991$	−29.4685	−	17.0137i	−0.936098	−	0.540457i	−0.0473631	−	0.998878i	$-0.515082\pi$
$991$	−29.4685	−	17.0137i	−0.936098	−	0.540457i	−0.888735	+	0.458421i	$0.848415\pi$
$992$	−53.2652	−	4.46899i	−1.69117	−	0.141891i
$993$		0			0
$994$	1.31802	−	3.83669i	0.0418051	−	0.121692i
$995$	1.19492	+	6.77670i	0.0378814	+	0.214836i
$996$		0			0
$997$	36.1230	+	30.3108i	1.14403	+	0.959953i	0.999563	−	0.0295568i	$-0.00940960\pi$
$997$	36.1230	+	30.3108i	1.14403	+	0.959953i	0.144465	+	0.989510i	$0.453854\pi$
$998$	−0.756281	−	41.6279i	−0.0239396	−	1.31771i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.l.a.35.4		96
3.2	odd	2		108.2.l.a.11.13	yes	96
4.3	odd	2	inner	324.2.l.a.35.13		96
9.2	odd	6		972.2.l.d.755.8		96
9.4	even	3		972.2.l.b.431.14		96
9.5	odd	6		972.2.l.c.431.3		96
9.7	even	3		972.2.l.a.755.9		96
12.11	even	2		108.2.l.a.11.4	✓	96
27.4	even	9		972.2.l.d.215.7		96
27.5	odd	18	inner	324.2.l.a.287.13		96
27.13	even	9		972.2.l.c.539.15		96
27.14	odd	18		972.2.l.b.539.2		96
27.22	even	9		108.2.l.a.59.4	yes	96
27.23	odd	18		972.2.l.a.215.10		96
36.7	odd	6		972.2.l.a.755.10		96
36.11	even	6		972.2.l.d.755.7		96
36.23	even	6		972.2.l.c.431.15		96
36.31	odd	6		972.2.l.b.431.2		96
108.23	even	18		972.2.l.a.215.9		96
108.31	odd	18		972.2.l.d.215.8		96
108.59	even	18	inner	324.2.l.a.287.4		96
108.67	odd	18		972.2.l.c.539.3		96
108.95	even	18		972.2.l.b.539.14		96
108.103	odd	18		108.2.l.a.59.13	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.11.4	✓	96	12.11	even	2
108.2.l.a.11.13	yes	96	3.2	odd	2
108.2.l.a.59.4	yes	96	27.22	even	9
108.2.l.a.59.13	yes	96	108.103	odd	18
324.2.l.a.35.4		96	1.1	even	1	trivial
324.2.l.a.35.13		96	4.3	odd	2	inner
324.2.l.a.287.4		96	108.59	even	18	inner
324.2.l.a.287.13		96	27.5	odd	18	inner
972.2.l.a.215.9		96	108.23	even	18
972.2.l.a.215.10		96	27.23	odd	18
972.2.l.a.755.9		96	9.7	even	3
972.2.l.a.755.10		96	36.7	odd	6
972.2.l.b.431.2		96	36.31	odd	6
972.2.l.b.431.14		96	9.4	even	3
972.2.l.b.539.2		96	27.14	odd	18
972.2.l.b.539.14		96	108.95	even	18
972.2.l.c.431.3		96	9.5	odd	6
972.2.l.c.431.15		96	36.23	even	6
972.2.l.c.539.3		96	108.67	odd	18
972.2.l.c.539.15		96	27.13	even	9
972.2.l.d.215.7		96	27.4	even	9
972.2.l.d.215.8		96	108.31	odd	18
972.2.l.d.755.7		96	36.11	even	6
972.2.l.d.755.8		96	9.2	odd	6

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.09968 - 0.889210i) q^{2} +(0.418610 + 1.95570i) q^{4} +(-0.605021 + 1.66228i) q^{5} +(-0.748045 - 0.131901i) q^{7} +(1.27869 - 2.52289i) q^{8} +O(q^{10})\)	\(q+(-1.09968 - 0.889210i) q^{2} +(0.418610 + 1.95570i) q^{4} +(-0.605021 + 1.66228i) q^{5} +(-0.748045 - 0.131901i) q^{7} +(1.27869 - 2.52289i) q^{8} +(2.14345 - 1.28999i) q^{10} +(-3.01780 + 1.09839i) q^{11} +(-1.07167 + 0.899234i) q^{13} +(0.705326 + 0.810218i) q^{14} +(-3.64953 + 1.63735i) q^{16} +(-5.55887 + 3.20941i) q^{17} +(-2.51793 - 1.45373i) q^{19} +(-3.50420 - 0.487393i) q^{20} +(4.29533 + 1.47558i) q^{22} +(1.06877 + 6.06131i) q^{23} +(1.43309 + 1.20251i) q^{25} +(1.97810 - 0.0359374i) q^{26} +(-0.0551813 - 1.51817i) q^{28} +(4.87432 - 5.80899i) q^{29} +(-9.30557 + 1.64082i) q^{31} +(5.46928 + 1.44463i) q^{32} +(8.96684 + 1.41366i) q^{34} +(0.671839 - 1.16366i) q^{35} +(1.62042 + 2.80666i) q^{37} +(1.47626 + 3.83761i) q^{38} +(3.42011 + 3.65194i) q^{40} +(4.14810 + 4.94351i) q^{41} +(2.50294 + 6.87676i) q^{43} +(-3.41140 - 5.44212i) q^{44} +(4.21447 - 7.61589i) q^{46} +(-0.737485 + 4.18249i) q^{47} +(-6.03567 - 2.19681i) q^{49} +(-0.506666 - 2.59669i) q^{50} +(-2.20724 - 1.71943i) q^{52} -9.63986i q^{53} -5.68099i q^{55} +(-1.28929 + 1.71857i) q^{56} +(-10.5256 + 2.05376i) q^{58} +(-0.397395 - 0.144640i) q^{59} +(1.38430 - 7.85077i) q^{61} +(11.6922 + 6.47022i) q^{62} +(-4.72990 - 6.45198i) q^{64} +(-0.846401 - 2.32547i) q^{65} +(3.65540 + 4.35634i) q^{67} +(-8.60365 - 9.52798i) q^{68} +(-1.77355 + 0.682252i) q^{70} +(-1.88825 - 3.27054i) q^{71} +(-5.59853 + 9.69694i) q^{73} +(0.713753 - 4.52733i) q^{74} +(1.78903 - 5.53287i) q^{76} +(2.40233 - 0.423595i) q^{77} +(6.53113 - 7.78350i) q^{79} +(-0.513698 - 7.05719i) q^{80} +(-0.165777 - 9.12484i) q^{82} +(-3.80396 - 3.19190i) q^{83} +(-1.97172 - 11.1822i) q^{85} +(3.36245 - 9.78790i) q^{86} +(-1.08772 + 9.01807i) q^{88} +(0.509288 + 0.294037i) q^{89} +(0.920264 - 0.531314i) q^{91} +(-11.4067 + 4.62752i) q^{92} +(4.53011 - 3.94364i) q^{94} +(3.93991 - 3.30598i) q^{95} +(15.8811 - 5.78024i) q^{97} +(4.68391 + 7.78278i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Introduction

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