LMFDB - Embedded newform 927.2.ba.e.298.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [927,2,Mod(19,927)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(927, base_ring=CyclotomicField(102))

chi = DirichletCharacter(H, H._module([0, 80]))

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

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

chi := DirichletCharacter("927.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 927 = 3^{2} \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	927.ba (of order $51$, degree $32$, 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:	$7.40213226737$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$16$ over $\Q(\zeta_{51})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{51}]$

Embedding invariants

Embedding label			298.16
Character	$\chi$	$=$	927.298
Dual form			927.2.ba.e.28.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.49514 + 2.25639i) q^{2} +(-2.07629 + 4.90543i) q^{4} +(3.86801 + 1.23050i) q^{5} +(-0.664684 - 1.88624i) q^{7} +(-8.85150 + 1.65463i) q^{8} +O(q^{10})$	\(q+(1.49514 + 2.25639i) q^{2} +(-2.07629 + 4.90543i) q^{4} +(3.86801 + 1.23050i) q^{5} +(-0.664684 - 1.88624i) q^{7} +(-8.85150 + 1.65463i) q^{8} +(3.00672 + 10.5675i) q^{10} +(-4.48388 + 0.276556i) q^{11} +(5.97230 + 1.11642i) q^{13} +(3.26229 - 4.31997i) q^{14} +(-9.55146 - 9.85027i) q^{16} +(-4.11509 + 1.89324i) q^{17} +(-4.30415 + 2.31128i) q^{19} +(-14.0673 + 16.4194i) q^{20} +(-7.32804 - 9.70389i) q^{22} +(1.49238 + 2.99710i) q^{23} +(9.36639 + 6.63033i) q^{25} +(6.41034 + 15.1450i) q^{26} +(10.6329 + 0.655813i) q^{28} +(-0.0384363 - 0.175506i) q^{29} +(1.14950 - 4.04009i) q^{31} +(4.09245 - 18.6867i) q^{32} +(-10.4245 - 6.45460i) q^{34} +(-0.249986 - 8.11388i) q^{35} +(6.81802 + 2.64132i) q^{37} +(-11.6505 - 6.25616i) q^{38} +(-36.2737 - 4.49166i) q^{40} +(6.60095 - 2.09991i) q^{41} +(0.447616 - 2.88359i) q^{43} +(7.95320 - 22.5695i) q^{44} +(-4.53132 + 7.84847i) q^{46} +(3.22026 + 5.57765i) q^{47} +(2.33748 - 1.88096i) q^{49} +(-0.956563 + 31.0475i) q^{50} +(-17.8767 + 26.9787i) q^{52} +(0.107627 - 3.49327i) q^{53} +(-17.6840 - 4.44770i) q^{55} +(9.00447 + 15.5962i) q^{56} +(0.338542 - 0.349133i) q^{58} +(2.00212 - 5.68159i) q^{59} +(1.25166 - 13.5075i) q^{61} +(10.8347 - 3.44676i) q^{62} +(22.6948 - 8.79203i) q^{64} +(21.7272 + 11.6672i) q^{65} +(1.54148 + 1.79922i) q^{67} +(-0.743043 - 24.1172i) q^{68} +(17.9343 - 12.6954i) q^{70} +(-0.592198 + 2.70406i) q^{71} +(-5.54736 - 5.05709i) q^{73} +(4.23405 + 19.3333i) q^{74} +(-2.40115 - 25.9126i) q^{76} +(3.50201 + 8.27383i) q^{77} +(3.21422 - 2.93015i) q^{79} +(-24.8244 - 49.8541i) q^{80} +(14.6076 + 11.7547i) q^{82} +(6.44757 - 7.52564i) q^{83} +(-18.2469 + 2.25945i) q^{85} +(7.17575 - 3.30137i) q^{86} +(39.2314 - 9.86710i) q^{88} +(0.235936 - 0.312429i) q^{89} +(-1.86387 - 12.0072i) q^{91} +(-17.8007 + 1.09791i) q^{92} +(-7.77062 + 15.6055i) q^{94} +(-19.4925 + 3.64379i) q^{95} +(-4.12515 - 1.89787i) q^{97} +(7.73905 + 2.46197i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q + 18 q^{4} - 8 q^{7}+O(q^{10}) $ 512 * q + 18 * q^4 - 8 * q^7	$ 512 q + 18 q^{4} - 8 q^{7} - 36 q^{10} + 4 q^{13} + 18 q^{16} + 30 q^{19} + 40 q^{22} - 42 q^{25} - 110 q^{28} - 32 q^{31} - 110 q^{34} + 48 q^{37} - 22 q^{40} - 2 q^{43} + 152 q^{46} + 76 q^{49} + 68 q^{52} + 32 q^{55} - 44 q^{58} + 20 q^{61} - 170 q^{64} - 8 q^{67} - 38 q^{70} - 4 q^{73} + 188 q^{76} + 20 q^{79} + 212 q^{82} + 60 q^{85} + 164 q^{88} - 310 q^{91} + 228 q^{94} - 100 q^{97}+O(q^{100}) $ 512 * q + 18 * q^4 - 8 * q^7 - 36 * q^10 + 4 * q^13 + 18 * q^16 + 30 * q^19 + 40 * q^22 - 42 * q^25 - 110 * q^28 - 32 * q^31 - 110 * q^34 + 48 * q^37 - 22 * q^40 - 2 * q^43 + 152 * q^46 + 76 * q^49 + 68 * q^52 + 32 * q^55 - 44 * q^58 + 20 * q^61 - 170 * q^64 - 8 * q^67 - 38 * q^70 - 4 * q^73 + 188 * q^76 + 20 * q^79 + 212 * q^82 + 60 * q^85 + 164 * q^88 - 310 * q^91 + 228 * q^94 - 100 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/927\mathbb{Z}\right)^\times$.

$n$	$722$	$829$
$\chi(n)$	$1$	$e\left(\frac{5}{51}\right)$

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 $

$2$	1.49514	+	2.25639i	1.05722	+	1.59551i	0.770438	+	0.637515i	$0.220038\pi$
$2$	1.49514	+	2.25639i	1.05722	+	1.59551i	0.286785	+	0.957995i	$0.407413\pi$
$3$		0			0
$3$		0			0
$4$	−2.07629	+	4.90543i	−1.03814	+	2.45271i
$5$	3.86801	+	1.23050i	1.72983	+	0.550298i	0.992172	−	0.124880i	$-0.0398546\pi$
$5$	3.86801	+	1.23050i	1.72983	+	0.550298i	0.737655	+	0.675178i	$0.235933\pi$
$6$		0			0
$7$	−0.664684	−	1.88624i	−0.251227	−	0.712930i	−0.998810	−	0.0487625i	$-0.984472\pi$
$7$	−0.664684	−	1.88624i	−0.251227	−	0.712930i	0.747583	−	0.664168i	$-0.231214\pi$
$8$	−8.85150	+	1.65463i	−3.12948	+	0.585001i
$9$		0			0
$10$	3.00672	+	10.5675i	0.950808	+	3.34174i
$11$	−4.48388	+	0.276556i	−1.35194	+	0.0833848i	−0.721263	−	0.692661i	$-0.756438\pi$
$11$	−4.48388	+	0.276556i	−1.35194	+	0.0833848i	−0.630676	+	0.776046i	$0.717222\pi$
$12$		0			0
$13$	5.97230	+	1.11642i	1.65642	+	0.309638i	0.927178	−	0.374621i	$-0.122227\pi$
$13$	5.97230	+	1.11642i	1.65642	+	0.309638i	0.729239	+	0.684259i	$0.239874\pi$
$14$	3.26229	−	4.31997i	0.871884	−	1.15456i
$15$		0			0
$16$	−9.55146	−	9.85027i	−2.38787	−	2.46257i
$17$	−4.11509	+	1.89324i	−0.998056	+	0.459179i	−0.848284	−	0.529542i	$-0.822364\pi$
$17$	−4.11509	+	1.89324i	−0.998056	+	0.459179i	−0.149772	+	0.988720i	$0.547854\pi$
$18$		0			0
$19$	−4.30415	+	2.31128i	−0.987439	+	0.530244i	−0.885546	−	0.464552i	$-0.846216\pi$
$19$	−4.30415	+	2.31128i	−0.987439	+	0.530244i	−0.101893	+	0.994795i	$0.532490\pi$
$20$	−14.0673	+	16.4194i	−3.14553	+	3.67148i
$21$		0			0
$22$	−7.32804	−	9.70389i	−1.56234	−	2.06888i
$23$	1.49238	+	2.99710i	0.311182	+	0.624938i	0.994448	−	0.105232i	$-0.0335584\pi$
$23$	1.49238	+	2.99710i	0.311182	+	0.624938i	−0.683265	+	0.730170i	$0.739441\pi$
$24$		0			0
$25$	9.36639	+	6.63033i	1.87328	+	1.32607i
$26$	6.41034	+	15.1450i	1.25717	+	2.97019i
$27$		0			0
$28$	10.6329	+	0.655813i	2.00942	+	0.123937i
$29$	−0.0384363	−	0.175506i	−0.00713745	−	0.0325906i	0.973144	−	0.230199i	$-0.0739376\pi$
$29$	−0.0384363	−	0.175506i	−0.00713745	−	0.0325906i	−0.980281	+	0.197608i	$0.936683\pi$
$30$		0			0
$31$	1.14950	−	4.04009i	0.206457	−	0.725621i	−0.787545	−	0.616258i	$-0.788648\pi$
$31$	1.14950	−	4.04009i	0.206457	−	0.725621i	0.994002	−	0.109364i	$-0.0348814\pi$
$32$	4.09245	−	18.6867i	0.723449	−	3.30337i
$33$		0			0
$34$	−10.4245	−	6.45460i	−1.78779	−	1.10695i
$35$	−0.249986	−	8.11388i	−0.0422553	−	1.37150i
$36$		0			0
$37$	6.81802	+	2.64132i	1.12088	+	0.434230i	0.849154	−	0.528146i	$-0.177113\pi$
$37$	6.81802	+	2.64132i	1.12088	+	0.434230i	0.271722	+	0.962376i	$0.412407\pi$
$38$	−11.6505	−	6.25616i	−1.88995	−	1.01488i
$39$		0			0
$40$	−36.2737	−	4.49166i	−5.73538	−	0.710194i
$41$	6.60095	−	2.09991i	1.03090	−	0.327951i	0.260470	−	0.965482i	$-0.416122\pi$
$41$	6.60095	−	2.09991i	1.03090	−	0.327951i	0.770425	+	0.637530i	$0.220044\pi$
$42$		0			0
$43$	0.447616	−	2.88359i	0.0682607	−	0.439743i	−0.929263	−	0.369418i	$-0.879557\pi$
$43$	0.447616	−	2.88359i	0.0682607	−	0.439743i	0.997524	−	0.0703251i	$-0.0224037\pi$
$44$	7.95320	−	22.5695i	1.19899	−	3.40249i
$45$		0			0
$46$	−4.53132	+	7.84847i	−0.668106	+	1.15719i
$47$	3.22026	+	5.57765i	0.469723	+	0.813583i	0.999401	−	0.0346154i	$-0.0110206\pi$
$47$	3.22026	+	5.57765i	0.469723	+	0.813583i	−0.529678	+	0.848199i	$0.677687\pi$
$48$		0			0
$49$	2.33748	−	1.88096i	0.333926	−	0.268709i
$50$	−0.956563	+	31.0475i	−0.135278	+	4.39078i
$51$		0			0
$52$	−17.8767	+	26.9787i	−2.47905	+	3.74127i
$53$	0.107627	−	3.49327i	0.0147837	−	0.479838i	−0.962912	−	0.269814i	$-0.913038\pi$
$53$	0.107627	−	3.49327i	0.0147837	−	0.479838i	0.977696	−	0.210024i	$-0.0673543\pi$
$54$		0			0
$55$	−17.6840	−	4.44770i	−2.38451	−	0.599728i
$56$	9.00447	+	15.5962i	1.20327	+	2.08413i
$57$		0			0
$58$	0.338542	−	0.349133i	0.0444527	−	0.0458434i
$59$	2.00212	−	5.68159i	0.260653	−	0.739681i	−0.737290	−	0.675577i	$-0.763895\pi$
$59$	2.00212	−	5.68159i	0.260653	−	0.739681i	0.997943	−	0.0641040i	$-0.0204189\pi$
$60$		0			0
$61$	1.25166	−	13.5075i	0.160258	−	1.72946i	−0.413556	−	0.910479i	$-0.635713\pi$
$61$	1.25166	−	13.5075i	0.160258	−	1.72946i	0.573815	−	0.818985i	$-0.305463\pi$
$62$	10.8347	−	3.44676i	1.37601	−	0.437739i
$63$		0			0
$64$	22.6948	−	8.79203i	2.83686	−	1.09900i
$65$	21.7272	+	11.6672i	2.69492	+	1.44714i
$66$		0			0
$67$	1.54148	+	1.79922i	0.188322	+	0.219810i	0.845571	−	0.533863i	$-0.179260\pi$
$67$	1.54148	+	1.79922i	0.188322	+	0.219810i	−0.657249	+	0.753674i	$0.728280\pi$
$68$	−0.743043	−	24.1172i	−0.0901072	−	2.92464i
$69$		0			0
$70$	17.9343	−	12.6954i	2.14356	−	1.51740i
$71$	−0.592198	+	2.70406i	−0.0702809	+	0.320912i	−0.998720	−	0.0505710i	$-0.983896\pi$
$71$	−0.592198	+	2.70406i	−0.0702809	+	0.320912i	0.928440	+	0.371484i	$0.121151\pi$
$72$		0			0
$73$	−5.54736	−	5.05709i	−0.649270	−	0.591888i	0.280578	−	0.959831i	$-0.409474\pi$
$73$	−5.54736	−	5.05709i	−0.649270	−	0.591888i	−0.929848	+	0.367943i	$0.880062\pi$
$74$	4.23405	+	19.3333i	0.492198	+	2.24745i
$75$		0			0
$76$	−2.40115	−	25.9126i	−0.275431	−	2.97238i
$77$	3.50201	+	8.27383i	0.399091	+	0.942890i
$78$		0			0
$79$	3.21422	−	2.93015i	0.361628	−	0.329668i	−0.472405	−	0.881381i	$-0.656614\pi$
$79$	3.21422	−	2.93015i	0.361628	−	0.329668i	0.834034	+	0.551714i	$0.186026\pi$
$80$	−24.8244	−	49.8541i	−2.77545	−	5.57385i
$81$		0			0
$82$	14.6076	+	11.7547i	1.61314	+	1.29809i
$83$	6.44757	−	7.52564i	0.707713	−	0.826046i	−0.283409	−	0.958999i	$-0.591465\pi$
$83$	6.44757	−	7.52564i	0.707713	−	0.826046i	0.991122	+	0.132953i	$0.0424459\pi$
$84$		0			0
$85$	−18.2469	+	2.25945i	−1.97915	+	0.245072i
$86$	7.17575	−	3.30137i	0.773781	−	0.355996i
$87$		0			0
$88$	39.2314	−	9.86710i	4.18208	−	1.05184i
$89$	0.235936	−	0.312429i	0.0250091	−	0.0331174i	−0.785341	−	0.619064i	$-0.787512\pi$
$89$	0.235936	−	0.312429i	0.0250091	−	0.0331174i	0.810350	+	0.585946i	$0.199277\pi$
$90$		0			0
$91$	−1.86387	−	12.0072i	−0.195386	−	1.25870i
$92$	−17.8007	+	1.09791i	−1.85585	+	0.114465i
$93$		0			0
$94$	−7.77062	+	15.6055i	−0.801479	+	1.60959i
$95$	−19.4925	+	3.64379i	−1.99989	+	0.373844i
$96$		0			0
$97$	−4.12515	−	1.89787i	−0.418845	−	0.192699i	0.197281	−	0.980347i	$-0.436789\pi$
$97$	−4.12515	−	1.89787i	−0.418845	−	0.192699i	−0.616126	+	0.787648i	$0.711299\pi$
$98$	7.73905	+	2.46197i	0.781762	+	0.248696i
$99$		0			0
$100$	−51.9719	+	32.1797i	−5.19719	+	3.21797i
$101$	−1.46222	−	2.20671i	−0.145496	−	0.219576i	0.753593	−	0.657341i	$-0.228319\pi$
$101$	−1.46222	−	2.20671i	−0.145496	−	0.219576i	−0.899089	+	0.437765i	$0.855770\pi$
$102$		0			0
$103$	8.74264	−	5.15425i	0.861438	−	0.507863i
$103$	8.74264	−	5.15425i	0.861438	−	0.507863i
$104$	−54.7110			−5.36486
$105$		0			0
$106$	8.04311	−	4.98008i	0.781216	−	0.483709i
$107$	−2.44147	+	5.76819i	−0.236025	+	0.557632i	−0.995696	−	0.0926756i	$-0.970458\pi$
$107$	−2.44147	+	5.76819i	−0.236025	+	0.557632i	0.759671	+	0.650308i	$0.225360\pi$
$108$		0			0
$109$	−0.945270	−	0.434893i	−0.0905405	−	0.0416552i	0.372171	−	0.928164i	$-0.378614\pi$
$109$	−0.945270	−	0.434893i	−0.0905405	−	0.0416552i	−0.462711	+	0.886509i	$0.653123\pi$
$110$	−16.4043	−	46.5519i	−1.56409	−	4.43855i
$111$		0			0
$112$	−12.2312	+	24.5636i	−1.15574	+	2.32104i
$113$	0.336471	+	1.18257i	0.0316525	+	0.111247i	0.976042	−	0.217581i	$-0.0698168\pi$
$113$	0.336471	+	1.18257i	0.0316525	+	0.111247i	−0.944390	+	0.328828i	$0.893346\pi$
$114$		0			0
$115$	2.08460	+	13.4292i	0.194390	+	1.25228i
$116$	0.940736	+	0.175854i	0.0873451	+	0.0163276i
$117$		0			0
$118$	15.8133	−	3.97722i	1.45574	−	0.366132i
$119$	6.30634	+	6.50363i	0.578101	+	0.596187i
$120$		0			0
$121$	9.11203	−	1.12831i	0.828367	−	0.102574i
$122$	32.3497	−	17.3714i	2.92881	−	1.57274i
$123$		0			0
$124$	17.4317	+	14.0272i	1.56541	+	1.25968i
$125$	15.8401	+	20.9757i	1.41678	+	1.87612i
$126$		0			0
$127$	1.64336	−	1.49812i	0.145824	−	0.132936i	−0.597497	−	0.801871i	$-0.703838\pi$
$127$	1.64336	−	1.49812i	0.145824	−	0.132936i	0.743321	+	0.668935i	$0.233250\pi$
$128$	22.5433	+	15.9580i	1.99256	+	1.41051i
$129$		0			0
$130$	6.15927	+	66.4691i	0.540204	+	5.82973i
$131$	−8.23957	−	0.508199i	−0.719894	−	0.0444016i	−0.302529	−	0.953140i	$-0.597831\pi$
$131$	−8.23957	−	0.508199i	−0.719894	−	0.0444016i	−0.417365	+	0.908739i	$0.637047\pi$
$132$		0			0
$133$	7.22052	+	6.58237i	0.626098	+	0.570764i
$134$	−1.75503	+	6.16827i	−0.151611	+	0.532858i
$135$		0			0
$136$	33.2921	−	23.5670i	2.85477	−	2.02085i
$137$	2.66110	+	1.64769i	0.227354	+	0.140771i	0.635382	−	0.772198i	$-0.280843\pi$
$137$	2.66110	+	1.64769i	0.227354	+	0.140771i	−0.408029	+	0.912969i	$0.633784\pi$
$138$		0			0
$139$	−4.55564	−	5.31736i	−0.386404	−	0.451013i	0.531948	−	0.846777i	$-0.321460\pi$
$139$	−4.55564	−	5.31736i	−0.386404	−	0.451013i	−0.918352	+	0.395764i	$0.870480\pi$
$140$	40.3211	+	15.6205i	3.40775	+	1.32017i
$141$		0			0
$142$	−6.98683	+	2.70671i	−0.586322	+	0.227142i
$143$	−27.0878	−	3.35419i	−2.26519	−	0.280492i
$144$		0			0
$145$	0.0672881	−	0.726154i	0.00558797	−	0.0603038i
$146$	3.11669	−	20.0781i	0.257939	−	1.66167i
$147$		0			0
$148$	−27.1130	+	27.9612i	−2.22867	+	2.29840i
$149$	−1.02009	+	1.76685i	−0.0835693	+	0.144746i	−0.904781	−	0.425878i	$-0.859965\pi$
$149$	−1.02009	+	1.76685i	−0.0835693	+	0.144746i	0.821211	+	0.570624i	$0.193299\pi$
$150$		0			0
$151$	−10.8616	−	2.73180i	−0.883904	−	0.222311i	−0.224838	−	0.974396i	$-0.572185\pi$
$151$	−10.8616	−	2.73180i	−0.883904	−	0.222311i	−0.659066	+	0.752085i	$0.729048\pi$
$152$	34.2738	−	27.5801i	2.77998	−	2.23704i
$153$		0			0
$154$	−13.4330	+	20.2724i	−1.08246	+	1.63360i
$155$	9.41764	−	14.2126i	0.756443	−	1.14159i
$156$		0			0
$157$	3.27480	−	2.63522i	0.261357	−	0.210313i	−0.487363	−	0.873199i	$-0.662041\pi$
$157$	3.27480	−	2.63522i	0.261357	−	0.210313i	0.748720	+	0.662886i	$0.230669\pi$
$158$	11.4173	+	2.87156i	0.908310	+	0.228449i
$159$		0			0
$160$	38.8236	−	67.2445i	3.06928	−	5.31614i
$161$	4.66128	−	4.80710i	0.367360	−	0.378853i
$162$		0			0
$163$	−0.425167	+	2.73897i	−0.0333017	+	0.214533i	−0.998977	−	0.0452188i	$-0.985601\pi$
$163$	−0.425167	+	2.73897i	−0.0333017	+	0.214533i	0.965675	+	0.259752i	$0.0836407\pi$
$164$	−3.40451	+	36.7405i	−0.265848	+	2.86895i
$165$		0			0
$166$	26.6208	+	3.29637i	2.06618	+	0.255848i
$167$	−12.6401	+	4.89681i	−0.978121	+	0.378926i	−0.796631	−	0.604466i	$-0.793386\pi$
$167$	−12.6401	+	4.89681i	−0.978121	+	0.378926i	−0.181491	+	0.983393i	$0.558092\pi$
$168$		0			0
$169$	22.2998	+	8.63899i	1.71537	+	0.664537i
$170$	−32.3798	−	37.7939i	−2.48342	−	2.89866i
$171$		0			0
$172$	13.2159	+	8.18291i	1.00770	+	0.623941i
$173$	−13.8179	+	9.78152i	−1.05056	+	0.743675i	−0.967500	−	0.252870i	$-0.918626\pi$
$173$	−13.8179	+	9.78152i	−1.05056	+	0.743675i	−0.0830581	+	0.996545i	$0.526469\pi$
$174$		0			0
$175$	6.28068	−	22.0743i	0.474775	−	1.66866i
$176$	45.5517	+	41.5259i	3.43359	+	3.13013i
$177$		0			0
$178$	1.05772	+	0.0652379i	0.0792794	+	0.00488979i
$179$	2.00371	+	21.6234i	0.149764	+	1.61621i	0.656648	+	0.754198i	$0.271974\pi$
$179$	2.00371	+	21.6234i	0.149764	+	1.61621i	−0.506883	+	0.862015i	$0.669203\pi$
$180$		0			0
$181$	−10.2828	−	7.27907i	−0.764318	−	0.541049i	0.128369	−	0.991726i	$-0.459026\pi$
$181$	−10.2828	−	7.27907i	−0.764318	−	0.541049i	−0.892687	+	0.450677i	$0.851183\pi$
$182$	24.3063	−	22.1581i	1.80170	−	1.64247i
$183$		0			0
$184$	−18.1689	−	24.0595i	−1.33943	−	1.77369i
$185$	23.1220	+	18.6062i	1.69997	+	1.36796i
$186$		0			0
$187$	17.9280	−	9.62712i	1.31102	−	0.704005i
$188$	−34.0469	+	4.21592i	−2.48313	+	0.307478i
$189$		0			0
$190$	−37.3659	−	38.5348i	−2.71080	−	2.79561i
$191$	17.1350	−	4.30962i	1.23984	−	0.311833i	0.432348	−	0.901707i	$-0.357685\pi$
$191$	17.1350	−	4.30962i	1.23984	−	0.311833i	0.807496	+	0.589874i	$0.200822\pi$
$192$		0			0
$193$	−7.55707	−	1.41266i	−0.543970	−	0.101686i	−0.0954093	−	0.995438i	$-0.530416\pi$
$193$	−7.55707	−	1.41266i	−0.543970	−	0.101686i	−0.448560	+	0.893753i	$0.648063\pi$
$194$	−1.88534	−	12.1455i	−0.135359	−	0.871998i
$195$		0			0
$196$	4.37365	+	15.3718i	0.312403	+	1.09798i
$197$	−10.0547	+	20.1925i	−0.716366	+	1.43866i	0.174625	+	0.984635i	$0.444129\pi$
$197$	−10.0547	+	20.1925i	−0.716366	+	1.43866i	−0.890991	+	0.454021i	$0.849989\pi$
$198$		0			0
$199$	3.65752	+	10.3793i	0.259275	+	0.735768i	0.998085	+	0.0618550i	$0.0197016\pi$
$199$	3.65752	+	10.3793i	0.259275	+	0.735768i	−0.738810	+	0.673913i	$0.764612\pi$
$200$	−93.8773	−	43.1904i	−6.63813	−	3.05402i
$201$		0			0
$202$	2.79298	−	6.59868i	0.196514	−	0.464282i
$203$	−0.305497	+	0.189156i	−0.0214417	+	0.0132761i
$204$		0			0
$205$	28.1165			1.96374
$206$	24.7015	+	12.0205i	1.72103	+	0.837508i
$207$		0			0
$208$	−46.0472	−	69.4921i	−3.19280	−	4.81841i
$209$	18.6601	−	11.5538i	1.29074	−	0.799195i
$210$		0			0
$211$	12.7266	+	4.04864i	0.876138	+	0.278720i	0.707291	−	0.706923i	$-0.249917\pi$
$211$	12.7266	+	4.04864i	0.876138	+	0.278720i	0.168847	+	0.985642i	$0.445996\pi$
$212$	16.9125	+	7.78101i	1.16156	+	0.534402i
$213$		0			0
$214$	−16.6656	+	3.11535i	−1.13924	+	0.212961i
$215$	5.27964	−	10.6030i	0.360069	−	0.723116i
$216$		0			0
$217$	−8.38462	+	0.517146i	−0.569185	+	0.0351061i
$218$	−0.432021	−	2.78313i	−0.0292602	−	0.188497i
$219$		0			0
$220$	58.5350	−	77.5128i	3.94643	−	5.22591i
$221$	−26.6902	+	6.71285i	−1.79538	+	0.451555i
$222$		0			0
$223$	−25.3147	+	11.6466i	−1.69520	+	0.779915i	−0.697187	+	0.716889i	$0.745565\pi$
$223$	−25.3147	+	11.6466i	−1.69520	+	0.779915i	−0.998012	+	0.0630264i	$0.979925\pi$
$224$	−37.9677	+	4.70142i	−2.53682	+	0.314127i
$225$		0			0
$226$	−2.16527	+	2.52732i	−0.144032	+	0.168115i
$227$	19.3651	+	15.5830i	1.28530	+	1.03428i	0.997052	+	0.0767263i	$0.0244468\pi$
$227$	19.3651	+	15.5830i	1.28530	+	1.03428i	0.288252	+	0.957554i	$0.406926\pi$
$228$		0			0
$229$	−5.40158	−	10.8478i	−0.356947	−	0.716846i	0.641801	−	0.766871i	$-0.278187\pi$
$229$	−5.40158	−	10.8478i	−0.356947	−	0.716846i	−0.998748	+	0.0500253i	$0.984070\pi$
$230$	−27.1848	+	24.7822i	−1.79251	+	1.63409i
$231$		0			0
$232$	0.630616	+	1.48989i	0.0414020	+	0.0978161i
$233$	−2.02375	−	21.8398i	−0.132580	−	1.43077i	−0.758901	−	0.651205i	$-0.774264\pi$
$233$	−2.02375	−	21.8398i	−0.132580	−	1.43077i	0.626321	−	0.779565i	$-0.284560\pi$
$234$		0			0
$235$	5.59267	+	25.5369i	0.364826	+	1.66585i
$236$	23.7137	+	21.6179i	1.54363	+	1.40720i
$237$		0			0
$238$	−5.24588	+	23.9534i	−0.340040	+	1.55267i
$239$	−21.1378	+	14.9631i	−1.36729	+	0.967885i	−0.368015	+	0.929820i	$0.619962\pi$
$239$	−21.1378	+	14.9631i	−1.36729	+	0.967885i	−0.999275	+	0.0380646i	$0.987881\pi$
$240$		0			0
$241$	−0.677622	−	21.9938i	−0.0436495	−	1.41675i	−0.726991	−	0.686647i	$-0.759082\pi$
$241$	−0.677622	−	21.9938i	−0.0436495	−	1.41675i	0.683341	−	0.730099i	$-0.260526\pi$
$242$	16.1697	+	18.8733i	1.03943	+	1.21322i
$243$		0			0
$244$	63.6615	+	34.1855i	4.07551	+	2.18850i
$245$	11.3559	−	4.39931i	0.725504	−	0.281062i
$246$		0			0
$247$	−28.2860	+	8.99842i	−1.79979	+	0.572556i
$248$	−3.48998	+	37.6628i	−0.221614	+	2.39159i
$249$		0			0
$250$	−23.6462	+	67.1031i	−1.49552	+	4.24397i
$251$	6.83965	−	7.05363i	0.431715	−	0.445221i	−0.466669	−	0.884432i	$-0.654546\pi$
$251$	6.83965	−	7.05363i	0.431715	−	0.445221i	0.898384	+	0.439211i	$0.144742\pi$
$252$		0			0
$253$	−7.52050	−	13.0259i	−0.472810	−	0.818931i
$254$	5.83738	+	1.46816i	0.366270	+	0.0921206i
$255$		0			0
$256$	−0.803278	+	26.0723i	−0.0502049	+	1.62952i
$257$	8.15329	−	12.3046i	0.508588	−	0.767537i	−0.485716	−	0.874117i	$-0.661441\pi$
$257$	8.15329	−	12.3046i	0.508588	−	0.767537i	0.994304	+	0.106580i	$0.0339900\pi$
$258$		0			0
$259$	0.450315	−	14.6160i	0.0279812	−	0.908197i
$260$	−102.345	+	82.3564i	−6.34715	+	5.10753i
$261$		0			0
$262$	−11.1726	−	19.3515i	−0.690246	−	1.19554i
$263$	8.52800	−	14.7709i	0.525859	−	0.910815i	−0.473687	−	0.880693i	$-0.657077\pi$
$263$	8.52800	−	14.7709i	0.525859	−	0.910815i	0.999546	−	0.0301217i	$-0.00958947\pi$
$264$		0			0
$265$	4.71479	−	13.3796i	0.289627	−	0.821902i
$266$	−4.05673	+	26.1339i	−0.248734	+	1.60237i
$267$		0			0
$268$	−12.0265	+	3.82591i	−0.734637	+	0.233705i
$269$	−17.8449	−	2.20968i	−1.08803	−	0.134727i	−0.441233	−	0.897393i	$-0.645459\pi$
$269$	−17.8449	−	2.20968i	−1.08803	−	0.134727i	−0.646792	+	0.762666i	$0.723890\pi$
$270$		0			0
$271$	5.61183	+	3.01349i	0.340894	+	0.183056i	0.634602	−	0.772839i	$-0.281164\pi$
$271$	5.61183	+	3.01349i	0.340894	+	0.183056i	−0.293708	+	0.955895i	$0.594889\pi$
$272$	57.9541	+	22.4515i	3.51398	+	1.36132i
$273$		0			0
$274$	0.260897	+	8.46802i	0.0157614	+	0.511572i
$275$	−43.8314	−	27.1392i	−2.64313	−	1.63656i
$276$		0			0
$277$	−4.22262	+	19.2811i	−0.253713	+	1.15849i	0.659724	+	0.751508i	$0.270673\pi$
$277$	−4.22262	+	19.2811i	−0.253713	+	1.15849i	−0.913437	+	0.406980i	$0.866582\pi$
$278$	5.18674	−	18.2295i	0.311080	−	1.09333i
$279$		0			0
$280$	15.6382	+	71.4063i	0.934563	+	4.26734i
$281$	−10.8842	−	0.671314i	−0.649297	−	0.0400473i	−0.266435	−	0.963853i	$-0.585846\pi$
$281$	−10.8842	−	0.671314i	−0.649297	−	0.0400473i	−0.382862	+	0.923806i	$0.625061\pi$
$282$		0			0
$283$	0.941822	+	2.22514i	0.0559855	+	0.132271i	0.946520	−	0.322644i	$-0.104572\pi$
$283$	0.941822	+	2.22514i	0.0559855	+	0.132271i	−0.890535	+	0.454915i	$0.849670\pi$
$284$	−12.0350	−	8.51939i	−0.714145	−	0.505533i
$285$		0			0
$286$	−32.9316	−	66.1356i	−1.94729	−	3.91068i
$287$	−8.34848	−	11.0552i	−0.492795	−	0.652566i
$288$		0			0
$289$	2.28910	−	2.67185i	0.134653	−	0.157168i
$290$	1.73909	−	0.933873i	0.102123	−	0.0548389i
$291$		0			0
$292$	36.3251	−	16.7122i	2.12577	−	0.978008i
$293$	−9.78259	−	10.0886i	−0.571505	−	0.589384i	0.368888	−	0.929474i	$-0.379739\pi$
$293$	−9.78259	−	10.0886i	−0.571505	−	0.589384i	−0.940393	+	0.340090i	$0.889543\pi$
$294$		0			0
$295$	14.7354	−	19.5129i	0.857930	−	1.13608i
$296$	−64.7201	−	12.0983i	−3.76178	−	0.703199i
$297$		0			0
$298$	−5.51189	+	0.339962i	−0.319295	+	0.0196935i
$299$	5.56692	+	19.5657i	0.321943	+	1.13151i
$300$		0			0
$301$	−5.73665	+	1.07237i	−0.330655	+	0.0618101i
$302$	−10.0756	−	28.5924i	−0.579785	−	1.64531i
$303$		0			0
$304$	63.8776	+	20.3209i	3.66363	+	1.16549i
$305$	21.4625	−	50.7072i	1.22894	−	2.90348i
$306$		0			0
$307$	−7.03200	−	10.6124i	−0.401338	−	0.605679i	0.575979	−	0.817465i	$-0.304621\pi$
$307$	−7.03200	−	10.6124i	−0.401338	−	0.605679i	−0.977316	+	0.211786i	$0.932072\pi$
$308$	−47.8579			−2.72695
$309$		0			0
$310$	46.1500			2.62114
$311$	−2.21584	−	3.34403i	−0.125649	−	0.189623i	0.765369	−	0.643592i	$-0.222557\pi$
$311$	−2.21584	−	3.34403i	−0.125649	−	0.189623i	−0.891017	+	0.453969i	$0.850008\pi$
$312$		0			0
$313$	−10.6847	+	25.2436i	−0.603935	+	1.42685i	0.280346	+	0.959899i	$0.409551\pi$
$313$	−10.6847	+	25.2436i	−0.603935	+	1.42685i	−0.884281	+	0.466955i	$0.845351\pi$
$314$	10.8424	+	3.44921i	0.611870	+	0.194650i
$315$		0			0
$316$	7.69999	+	21.8510i	0.433158	+	1.22921i
$317$	−12.5214	+	2.34065i	−0.703271	+	0.131464i	−0.523226	−	0.852194i	$-0.675272\pi$
$317$	−12.5214	+	2.34065i	−0.703271	+	0.131464i	−0.180045	+	0.983658i	$0.557624\pi$
$318$		0			0
$319$	0.220881	+	0.776316i	0.0123670	+	0.0434653i
$320$	98.6025	−	6.08160i	5.51205	−	0.339972i
$321$		0			0
$322$	17.8160	+	3.33038i	0.992845	+	0.185595i
$323$	13.3362	−	17.6599i	0.742044	−	0.982624i
$324$		0			0
$325$	48.5366	+	50.0551i	2.69233	+	2.77655i
$326$	−6.81588	+	3.13580i	−0.377497	+	0.173676i
$327$		0			0
$328$	−54.9537	+	29.5095i	−3.03431	+	1.62939i
$329$	8.38031	−	9.78154i	0.462021	−	0.539274i
$330$		0			0
$331$	−15.5221	−	20.5546i	−0.853171	−	1.12978i	−0.990261	−	0.139223i	$-0.955540\pi$
$331$	−15.5221	−	20.5546i	−0.853171	−	1.12978i	0.137090	−	0.990559i	$-0.456225\pi$
$332$	23.5295	+	47.2535i	1.29135	+	2.59337i
$333$		0			0
$334$	−29.9478	−	21.1996i	−1.63867	−	1.15999i
$335$	3.74851	+	8.85621i	0.204803	+	0.483867i
$336$		0			0
$337$	−8.72914	−	0.538395i	−0.475507	−	0.0293282i	−0.177964	−	0.984037i	$-0.556951\pi$
$337$	−8.72914	−	0.538395i	−0.475507	−	0.0293282i	−0.297542	+	0.954709i	$0.596167\pi$
$338$	13.8484	+	63.2336i	0.753252	+	3.43945i
$339$		0			0
$340$	26.8022	−	94.2000i	1.45355	−	5.10871i
$341$	−4.03692	+	18.4332i	−0.218612	+	0.998212i
$342$		0			0
$343$	−17.0042	−	10.5286i	−0.918141	−	0.568489i
$344$	0.809207	+	26.2647i	0.0436295	+	1.41610i
$345$		0			0
$346$	−42.7307	−	16.5540i	−2.29722	−	0.889946i
$347$	22.7843	+	12.2349i	1.22312	+	0.656804i	0.952105	−	0.305770i	$-0.0989138\pi$
$347$	22.7843	+	12.2349i	1.22312	+	0.656804i	0.271019	+	0.962574i	$0.412639\pi$
$348$		0			0
$349$	−34.2274	−	4.23827i	−1.83215	−	0.226869i	−0.868809	−	0.495147i	$-0.835114\pi$
$349$	−34.2274	−	4.23827i	−1.83215	−	0.226869i	−0.963342	+	0.268277i	$0.913546\pi$
$350$	59.1987	−	18.8325i	3.16431	−	1.00664i
$351$		0			0
$352$	−13.1821	+	84.9205i	−0.702608	+	4.52628i
$353$	−2.51918	+	7.14892i	−0.134083	+	0.380499i	−0.990808	−	0.135274i	$-0.956809\pi$
$353$	−2.51918	+	7.14892i	−0.134083	+	0.380499i	0.856726	+	0.515772i	$0.172495\pi$
$354$		0			0
$355$	−5.61798	+	9.73062i	−0.298171	+	0.516448i
$356$	1.04273	+	1.80606i	0.0552645	+	0.0957210i
$357$		0			0
$358$	−45.7951	+	36.8512i	−2.42035	+	1.94765i
$359$	0.105243	−	3.41592i	0.00555453	−	0.180285i	−0.992675	−	0.120812i	$-0.961450\pi$
$359$	0.105243	−	3.41592i	0.00555453	−	0.180285i	0.998230	−	0.0594730i	$-0.0189420\pi$
$360$		0			0
$361$	2.68875	−	4.05773i	0.141513	−	0.213565i
$362$	1.05016	−	34.0853i	0.0551951	−	1.79149i
$363$		0			0
$364$	62.7705	+	15.7874i	3.29007	+	0.827486i
$365$	−15.2345	−	26.3869i	−0.797410	−	1.38115i
$366$		0			0
$367$	−3.54620	+	3.65714i	−0.185110	+	0.190901i	−0.804093	−	0.594503i	$-0.797349\pi$
$367$	−3.54620	+	3.65714i	−0.185110	+	0.190901i	0.618983	+	0.785404i	$0.287545\pi$
$368$	15.2678	−	43.3270i	0.795892	−	2.25858i
$369$		0			0
$370$	−7.41228	+	79.9913i	−0.385346	+	4.15855i
$371$	−6.66068	+	2.11891i	−0.345805	+	0.110009i
$372$		0			0
$373$	11.7640	−	4.55740i	0.609117	−	0.235973i	−0.0368719	−	0.999320i	$-0.511739\pi$
$373$	11.7640	−	4.55740i	0.609117	−	0.235973i	0.645989	+	0.763347i	$0.276445\pi$
$374$	48.5274	+	26.0586i	2.50929	+	1.34746i
$375$		0			0
$376$	−37.7330	−	44.0422i	−1.94593	−	2.27130i
$377$	−0.0336159	−	1.09108i	−0.00173131	−	0.0561936i
$378$		0			0
$379$	17.6629	−	12.5033i	0.907282	−	0.642251i	−0.0266726	−	0.999644i	$-0.508491\pi$
$379$	17.6629	−	12.5033i	0.907282	−	0.642251i	0.933954	+	0.357393i	$0.116334\pi$
$380$	22.5978	−	103.185i	1.15924	−	5.29327i
$381$		0			0
$382$	35.3434	+	32.2197i	1.80832	+	1.64851i
$383$	−0.0480053	−	0.219199i	−0.00245296	−	0.0112005i	0.975606	−	0.219530i	$-0.0704523\pi$
$383$	−0.0480053	−	0.219199i	−0.00245296	−	0.0112005i	−0.978059	+	0.208329i	$0.933197\pi$
$384$		0			0
$385$	3.36485	+	36.3125i	0.171489	+	1.85066i
$386$	−8.11135	−	19.1638i	−0.412857	−	0.975413i
$387$		0			0
$388$	17.8749	−	16.2951i	0.907459	−	0.827258i
$389$	−5.90134	−	11.8515i	−0.299210	−	0.600895i	0.693632	−	0.720330i	$-0.256009\pi$
$389$	−5.90134	−	11.8515i	−0.299210	−	0.600895i	−0.992842	+	0.119435i	$0.961892\pi$
$390$		0			0
$391$	−11.8155	−	9.50791i	−0.597536	−	0.480835i
$392$	−17.5779	+	20.5170i	−0.887818	+	1.03627i
$393$		0			0
$394$	−60.5953	+	7.50333i	−3.05275	+	0.378012i
$395$	16.0382	−	7.37875i	0.806970	−	0.371265i
$396$		0			0
$397$	11.4289	−	2.87447i	0.573598	−	0.144266i	0.0537952	−	0.998552i	$-0.482868\pi$
$397$	11.4289	−	2.87447i	0.573598	−	0.144266i	0.519803	+	0.854286i	$0.326005\pi$
$398$	−17.9512	+	23.7713i	−0.899814	+	1.19155i
$399$		0			0
$400$	−24.1521	−	155.591i	−1.20761	−	7.77954i
$401$	0.178866	−	0.0110320i	0.00893212	−	0.000550914i	−0.0570942	−	0.998369i	$-0.518184\pi$
$401$	0.178866	−	0.0110320i	0.00893212	−	0.000550914i	0.0660263	+	0.997818i	$0.478968\pi$
$402$		0			0
$403$	11.3756	−	22.8453i	0.566659	−	1.13800i
$404$	13.8609	−	2.59104i	0.689603	−	0.128909i
$405$		0			0
$406$	−0.883571	−	0.406507i	−0.0438509	−	0.0201746i
$407$	−31.3016	−	9.95777i	−1.55156	−	0.493588i
$408$		0			0
$409$	25.2030	−	15.6050i	1.24621	−	0.771619i	0.264940	−	0.964265i	$-0.414648\pi$
$409$	25.2030	−	15.6050i	1.24621	−	0.771619i	0.981268	+	0.192646i	$0.0617068\pi$
$410$	42.0381	+	63.4418i	2.07611	+	3.13317i
$411$		0			0
$412$	7.13154	+	53.5881i	0.351346	+	2.64010i
$413$	−12.0476			−0.592824
$414$		0			0
$415$	34.1996	−	21.1755i	1.67879	−	1.03946i
$416$	45.3034	−	107.033i	2.22118	−	5.24775i
$417$		0			0
$418$	53.9694	+	24.8298i	2.63973	+	1.21447i
$419$	1.30934	+	3.71563i	0.0639653	+	0.181520i	0.970760	−	0.240052i	$-0.0771646\pi$
$419$	1.30934	+	3.71563i	0.0639653	+	0.181520i	−0.906795	+	0.421573i	$0.861478\pi$
$420$		0			0
$421$	−5.36486	+	10.7741i	−0.261467	+	0.525097i	−0.986529	−	0.163587i	$-0.947694\pi$
$421$	−5.36486	+	10.7741i	−0.261467	+	0.525097i	0.725062	+	0.688684i	$0.241811\pi$
$422$	9.89279	+	34.7696i	0.481574	+	1.69256i
$423$		0			0
$424$	4.82743	+	31.0988i	0.234441	+	1.51029i
$425$	−51.0964	−	9.55156i	−2.47854	−	0.463319i
$426$		0			0
$427$	−26.3104	+	6.61733i	−1.27325	+	0.320235i
$428$	−23.2263	−	23.9529i	−1.12268	−	1.15781i
$429$		0			0
$430$	31.8182	−	3.93995i	1.53441	−	0.190001i
$431$	28.6881	−	15.4052i	1.38186	−	0.742043i	0.397398	−	0.917646i	$-0.369913\pi$
$431$	28.6881	−	15.4052i	1.38186	−	0.742043i	0.984461	+	0.175603i	$0.0561876\pi$
$432$		0			0
$433$	−5.36428	−	4.31662i	−0.257791	−	0.207443i	0.489389	−	0.872066i	$-0.337220\pi$
$433$	−5.36428	−	4.31662i	−0.257791	−	0.207443i	−0.747180	+	0.664622i	$0.768592\pi$
$434$	−13.7031	−	18.1458i	−0.657768	−	0.871025i
$435$		0			0
$436$	4.09599	−	3.73399i	0.196163	−	0.178826i
$437$	−13.3506	−	9.45066i	−0.638643	−	0.452086i
$438$		0			0
$439$	−3.44894	−	37.2200i	−0.164609	−	1.77641i	−0.532387	−	0.846501i	$-0.678705\pi$
$439$	−3.44894	−	37.2200i	−0.164609	−	1.77641i	0.367778	−	0.929914i	$-0.380119\pi$
$440$	163.889	+	10.1083i	7.81310	+	0.481896i
$441$		0			0
$442$	−55.0524	−	50.1869i	−2.61857	−	2.38715i
$443$	−2.99777	+	10.5361i	−0.142428	+	0.500584i	−0.999903	−	0.0139429i	$-0.995562\pi$
$443$	−2.99777	+	10.5361i	−0.142428	+	0.500584i	0.857474	+	0.514527i	$0.172032\pi$
$444$		0			0
$445$	1.29705	−	0.918160i	0.0614859	−	0.0435250i
$446$	−64.1284	−	39.7066i	−3.03657	−	1.88016i
$447$		0			0
$448$	−31.6688	−	36.9639i	−1.49621	−	1.74638i
$449$	−36.1927	−	14.0211i	−1.70804	−	0.661698i	−0.708988	−	0.705221i	$-0.750848\pi$
$449$	−36.1927	−	14.0211i	−1.70804	−	0.661698i	−0.999052	+	0.0435223i	$0.986142\pi$
$450$		0			0
$451$	−29.0171	+	11.2413i	−1.36636	+	0.529331i
$452$	−6.49963	−	0.804829i	−0.305717	−	0.0378560i
$453$		0			0
$454$	−6.20790	+	66.9939i	−0.291351	+	3.14418i
$455$	7.56547	−	48.7376i	0.354675	−	2.28485i
$456$		0			0
$457$	−14.1285	+	14.5705i	−0.660903	+	0.681579i	−0.962322	−	0.271913i	$-0.912344\pi$
$457$	−14.1285	+	14.5705i	−0.660903	+	0.681579i	0.301419	+	0.953492i	$0.402540\pi$
$458$	16.4009	−	28.4071i	0.766362	−	1.32738i
$459$		0			0
$460$	−70.2042	−	17.6571i	−3.27329	−	0.823264i
$461$	1.45065	−	1.16734i	0.0675636	−	0.0543682i	−0.592552	−	0.805532i	$-0.701880\pi$
$461$	1.45065	−	1.16734i	0.0675636	−	0.0543682i	0.660116	+	0.751164i	$0.270507\pi$
$462$		0			0
$463$	12.3052	−	18.5704i	0.571870	−	0.863039i	−0.427286	−	0.904117i	$-0.640530\pi$
$463$	12.3052	−	18.5704i	0.571870	−	0.863039i	0.999156	+	0.0410779i	$0.0130792\pi$
$464$	−1.36166	+	2.05494i	−0.0632133	+	0.0953984i
$465$		0			0
$466$	46.2533	−	37.2199i	2.14264	−	1.72418i
$467$	−10.0670	−	2.53194i	−0.465844	−	0.117164i	0.00385242	−	0.999993i	$-0.498774\pi$
$467$	−10.0670	−	2.53194i	−0.465844	−	0.117164i	−0.469696	+	0.882828i	$0.655636\pi$
$468$		0			0
$469$	2.36916	−	4.10351i	0.109398	−	0.189483i
$470$	−49.2595	+	50.8005i	−2.27217	+	2.34325i
$471$		0			0
$472$	−8.32078	+	53.6034i	−0.382995	+	2.46730i
$473$	−1.20958	+	13.0534i	−0.0556165	+	0.600198i
$474$		0			0
$475$	−55.6389	−	6.88958i	−2.55289	−	0.316116i
$476$	−44.9969	+	17.4319i	−2.06243	+	0.798989i
$477$		0			0
$478$	−65.3666	−	25.3232i	−2.98980	−	1.15825i
$479$	26.1080	+	30.4733i	1.19290	+	1.39236i	0.899812	+	0.436278i	$0.143703\pi$
$479$	26.1080	+	30.4733i	1.19290	+	1.39236i	0.293091	+	0.956085i	$0.405316\pi$
$480$		0			0
$481$	37.7704	+	23.3865i	1.72218	+	1.06633i
$482$	48.6135	−	34.4128i	2.21429	−	1.56746i
$483$		0			0
$484$	−13.3844	+	47.0411i	−0.608380	+	2.13823i
$485$	−13.6208	−	12.4170i	−0.618488	−	0.563826i
$486$		0			0
$487$	27.0650	+	1.66931i	1.22643	+	0.0756438i	0.661789	−	0.749690i	$-0.269798\pi$
$487$	27.0650	+	1.66931i	1.22643	+	0.0756438i	0.564645	+	0.825334i	$0.309013\pi$
$488$	11.2710	+	121.633i	0.510212	+	5.50607i
$489$		0			0
$490$	26.9053	+	19.0458i	1.21546	+	0.860404i
$491$	3.29942	−	3.00782i	0.148901	−	0.135741i	−0.595818	−	0.803120i	$-0.703172\pi$
$491$	3.29942	−	3.00782i	0.148901	−	0.135741i	0.744719	+	0.667379i	$0.232584\pi$
$492$		0			0
$493$	0.490444	+	0.649453i	0.0220885	+	0.0292499i
$494$	−62.5955	−	50.3704i	−2.81630	−	2.26627i
$495$		0			0
$496$	−50.7754	+	27.2658i	−2.27988	+	1.22427i
$497$	5.49411	−	0.680319i	0.246445	−	0.0305165i
$498$		0			0
$499$	−0.383359	−	0.395352i	−0.0171615	−	0.0176984i	0.709277	−	0.704930i	$-0.249022\pi$
$499$	−0.383359	−	0.395352i	−0.0171615	−	0.0176984i	−0.726438	+	0.687232i	$0.758826\pi$
$500$	−135.783	+	34.1509i	−6.07242	+	1.52728i
$501$		0			0
$502$	26.1420	+	4.88678i	1.16677	+	0.218108i
$503$	−1.24670	−	8.03138i	−0.0555876	−	0.358101i	−0.999602	−	0.0281982i	$-0.991023\pi$
$503$	−1.24670	−	8.03138i	−0.0555876	−	0.358101i	0.944015	−	0.329903i	$-0.107016\pi$
$504$		0			0
$505$	−2.94052	−	10.3348i	−0.130851	−	0.459895i
$506$	18.1473	−	36.4447i	0.806747	−	1.62017i
$507$		0			0
$508$	3.93682	+	11.1719i	0.174668	+	0.495672i
$509$	−2.27666	−	1.04743i	−0.100911	−	0.0464265i	0.366860	−	0.930276i	$-0.380433\pi$
$509$	−2.27666	−	1.04743i	−0.100911	−	0.0464265i	−0.467771	+	0.883850i	$0.654943\pi$
$510$		0			0
$511$	−5.85162	+	13.8250i	−0.258861	+	0.611582i
$512$	−13.0645	+	8.08919i	−0.577374	+	0.357495i
$513$		0			0
$514$	39.9542			1.76230
$515$	40.1589	−	9.17884i	1.76961	−	0.404468i
$516$		0			0
$517$	−15.9818	−	24.1189i	−0.702877	−	1.06075i
$518$	33.6528	−	20.8369i	1.47862	−	0.915522i
$519$		0			0
$520$	−211.623	−	67.3220i	−9.28027	−	2.95227i
$521$	8.54828	+	3.93283i	0.374507	+	0.172301i	0.596239	−	0.802807i	$-0.296661\pi$
$521$	8.54828	+	3.93283i	0.374507	+	0.172301i	−0.221732	+	0.975108i	$0.571171\pi$
$522$		0			0
$523$	26.8814	−	5.02501i	1.17544	−	0.219728i	0.440434	−	0.897785i	$-0.354825\pi$
$523$	26.8814	−	5.02501i	1.17544	−	0.219728i	0.735009	+	0.678057i	$0.237178\pi$
$524$	19.6007	−	39.3634i	0.856259	−	1.71960i
$525$		0			0
$526$	46.0796	−	2.84209i	2.00916	−	0.123921i
$527$	2.91855	+	18.8016i	0.127134	+	0.819012i
$528$		0			0
$529$	7.10518	−	9.40878i	0.308921	−	0.409078i
$530$	37.2389	−	9.36595i	1.61755	−	0.406831i
$531$		0			0
$532$	−47.2812	+	21.7528i	−2.04990	+	0.943105i
$533$	41.7672	−	5.17190i	1.80914	−	0.224020i
$534$		0			0
$535$	−16.5414	+	19.3072i	−0.715147	+	0.834723i
$536$	−16.6215	−	13.3752i	−0.717938	−	0.577722i
$537$		0			0
$538$	−21.6948	−	43.5690i	−0.935328	−	1.87839i
$539$	−9.96078	+	9.08045i	−0.429041	+	0.391123i
$540$		0			0
$541$	15.8412	+	37.4262i	0.681064	+	1.60908i	0.788621	+	0.614879i	$0.210795\pi$
$541$	15.8412	+	37.4262i	0.681064	+	1.60908i	−0.107557	+	0.994199i	$0.534303\pi$
$542$	1.59085	+	17.1681i	0.0683331	+	0.737431i
$543$		0			0
$544$	18.5376	+	84.6454i	0.794794	+	3.62914i
$545$	−3.12118	−	2.84533i	−0.133697	−	0.121881i
$546$		0			0
$547$	−1.96819	+	8.98703i	−0.0841538	+	0.384258i	−0.999845	−	0.0176255i	$-0.994389\pi$
$547$	−1.96819	+	8.98703i	−0.0841538	+	0.384258i	0.915691	+	0.401883i	$0.131644\pi$
$548$	−13.6078	+	9.63279i	−0.581298	+	0.411492i
$549$		0			0
$550$	−4.29726	−	139.478i	−0.183236	−	5.94735i
$551$	0.571078	+	0.666565i	0.0243288	+	0.0283966i
$552$		0			0
$553$	−7.66340	−	4.11516i	−0.325881	−	0.174994i
$554$	−49.8191	+	19.3000i	−2.11661	+	0.819979i
$555$		0			0
$556$	35.5428	−	11.3070i	1.50735	−	0.479522i
$557$	0.599507	−	6.46972i	0.0254019	−	0.274131i	−0.973554	−	0.228455i	$-0.926633\pi$
$557$	0.599507	−	6.46972i	0.0254019	−	0.274131i	0.998956	−	0.0456753i	$-0.0145440\pi$
$558$		0			0
$559$	5.89257	−	16.7219i	0.249229	−	0.707261i
$560$	−77.5362	+	79.9618i	−3.27650	+	3.37900i
$561$		0			0
$562$	−14.7586	−	25.5627i	−0.622556	−	1.07830i
$563$	−41.5012	−	10.4380i	−1.74907	−	0.439908i	−0.769108	−	0.639118i	$-0.779299\pi$
$563$	−41.5012	−	10.4380i	−1.74907	−	0.439908i	−0.979957	+	0.199211i	$0.936162\pi$
$564$		0			0
$565$	−0.153686	+	4.98823i	−0.00646561	+	0.209856i
$566$	−3.61264	+	5.45202i	−0.151850	+	0.229165i
$567$		0			0
$568$	0.767617	−	24.9148i	0.0322085	−	1.04540i
$569$	16.2076	−	13.0422i	0.679459	−	0.546758i	−0.224449	−	0.974486i	$-0.572058\pi$
$569$	16.2076	−	13.0422i	0.679459	−	0.546758i	0.903908	+	0.427728i	$0.140686\pi$
$570$		0			0
$571$	1.19371	+	2.06756i	0.0499551	+	0.0865247i	0.889922	−	0.456113i	$-0.150759\pi$
$571$	1.19371	+	2.06756i	0.0499551	+	0.0865247i	−0.839967	+	0.542638i	$0.817426\pi$
$572$	72.6959	−	125.913i	3.03957	−	5.26468i
$573$		0			0
$574$	12.4627	−	35.3665i	0.520182	−	1.47617i
$575$	−5.89356	+	37.9669i	−0.245778	+	1.58333i
$576$		0			0
$577$	−17.0910	+	5.43704i	−0.711508	+	0.226347i	−0.636989	−	0.770873i	$-0.719820\pi$
$577$	−17.0910	+	5.43704i	−0.711508	+	0.226347i	−0.0745184	+	0.997220i	$0.523742\pi$
$578$	9.45127	+	1.17032i	0.393121	+	0.0486789i
$579$		0			0
$580$	3.42239	+	1.83778i	0.142107	+	0.0763098i
$581$	−18.4807	−	7.15947i	−0.766710	−	0.297025i
$582$		0			0
$583$	0.483502	+	15.6932i	0.0200246	+	0.649945i
$584$	57.4701	+	35.5840i	2.37813	+	1.47248i
$585$		0			0
$586$	8.13757	−	37.1573i	0.336160	−	1.53495i
$587$	2.67974	−	9.41831i	0.110605	−	0.388735i	−0.886679	−	0.462385i	$-0.846994\pi$
$587$	2.67974	−	9.41831i	0.110605	−	0.388735i	0.997284	+	0.0736493i	$0.0234646\pi$
$588$		0			0
$589$	4.39014	+	20.0460i	0.180892	+	0.825980i
$590$	66.0602	+	4.07445i	2.71965	+	0.167743i
$591$		0			0
$592$	−39.1044	−	92.3878i	−1.60718	−	3.79711i
$593$	4.11299	+	2.91153i	0.168900	+	0.119562i	0.659123	−	0.752035i	$-0.270928\pi$
$593$	4.11299	+	2.91153i	0.168900	+	0.119562i	−0.490223	+	0.871597i	$0.663085\pi$
$594$		0			0
$595$	16.3903	+	32.9161i	0.671935	+	1.34943i
$596$	−6.54916	−	8.67249i	−0.268264	−	0.355239i
$597$		0			0
$598$	−35.8245	+	41.8146i	−1.46497	+	1.70992i
$599$	−15.8249	+	8.49777i	−0.646586	+	0.347209i	−0.763383	−	0.645946i	$-0.776463\pi$
$599$	−15.8249	+	8.49777i	−0.646586	+	0.347209i	0.116797	+	0.993156i	$0.462737\pi$
$600$		0			0
$601$	−5.61453	+	2.58309i	−0.229021	+	0.105367i	−0.529137	−	0.848536i	$-0.677484\pi$
$601$	−5.61453	+	2.58309i	−0.229021	+	0.105367i	0.300116	+	0.953903i	$0.402975\pi$
$602$	−10.9968	−	11.3408i	−0.448195	−	0.462216i
$603$		0			0
$604$	35.9525	−	47.6088i	1.46289	−	1.93717i
$605$	36.6338	+	6.84805i	1.48938	+	0.278413i
$606$		0			0
$607$	37.3532	−	2.30387i	1.51612	−	0.0935111i	0.718015	−	0.696028i	$-0.245051\pi$
$607$	37.3532	−	2.30387i	1.51612	−	0.0935111i	0.798106	+	0.602517i	$0.205835\pi$
$608$	25.5756	+	89.8890i	1.03723	+	3.64548i
$609$		0			0
$610$	146.505	−	27.3865i	5.93180	−	1.10885i
$611$	13.0053	+	36.9065i	0.526140	+	1.49308i
$612$		0			0
$613$	32.7927	+	10.4321i	1.32448	+	0.421349i	0.880228	−	0.474552i	$-0.157390\pi$
$613$	32.7927	+	10.4321i	1.32448	+	0.421349i	0.444256	+	0.895900i	$0.353468\pi$
$614$	13.4318	−	31.7339i	0.542064	−	1.28068i
$615$		0			0
$616$	−44.6882	−	67.4412i	−1.80054	−	2.71728i
$617$	2.83453			0.114114			0.0570570	−	0.998371i	$-0.481828\pi$
$617$	2.83453			0.114114			0.0570570	+	0.998371i	$0.481828\pi$
$618$		0			0
$619$	−36.4012			−1.46309			−0.731544	−	0.681795i	$-0.761200\pi$
$619$	−36.4012			−1.46309			−0.731544	+	0.681795i	$0.761200\pi$
$620$	50.1654	+	75.7071i	2.01469	+	3.04047i
$621$		0			0
$622$	4.23246	−	9.99959i	0.169706	−	0.400947i
$623$	−0.746138	−	0.237364i	−0.0298934	−	0.00950977i
$624$		0			0
$625$	16.3891	+	46.5090i	0.655566	+	1.86036i
$626$	−72.9346	+	13.6338i	−2.91505	+	0.544918i
$627$		0			0
$628$	6.12745	+	21.5358i	0.244512	+	0.859371i
$629$	−33.0574	+	2.03891i	−1.31809	+	0.0812968i
$630$		0			0
$631$	14.4704	+	2.70498i	0.576057	+	0.107684i	0.463713	−	0.885986i	$-0.346517\pi$
$631$	14.4704	+	2.70498i	0.576057	+	0.107684i	0.112344	+	0.993669i	$0.464164\pi$
$632$	−23.6024	+	31.2546i	−0.938851	+	1.24324i
$633$		0			0
$634$	−24.0026	−	24.7535i	−0.953267	−	0.983089i
$635$	8.19995	−	3.77258i	0.325405	−	0.149710i
$636$		0			0
$637$	16.0601	−	8.62407i	0.636323	−	0.341698i
$638$	−1.42142	+	1.65909i	−0.0562748	+	0.0656842i
$639$		0			0
$640$	67.5612	+	89.4654i	2.67059	+	3.53643i
$641$	−13.2055	−	26.5203i	−0.521587	−	1.04749i	−0.986748	−	0.162261i	$-0.948121\pi$
$641$	−13.2055	−	26.5203i	−0.521587	−	1.04749i	0.465161	−	0.885226i	$-0.345996\pi$
$642$		0			0
$643$	30.2276	+	21.3977i	1.19206	+	0.843842i	0.990752	−	0.135685i	$-0.0433237\pi$
$643$	30.2276	+	21.3977i	1.19206	+	0.843842i	0.201309	+	0.979528i	$0.435481\pi$
$644$	13.9027	+	32.8465i	0.547845	+	1.29433i
$645$		0			0
$646$	59.7871	+	3.68754i	2.35229	+	0.145084i
$647$	−8.15768	−	37.2491i	−0.320712	−	1.46441i	−0.806967	−	0.590597i	$-0.798892\pi$
$647$	−8.15768	−	37.2491i	−0.320712	−	1.46441i	0.486255	−	0.873817i	$-0.338363\pi$
$648$		0			0
$649$	−7.40596	+	26.0293i	−0.290709	+	1.02174i
$650$	−40.3748	+	184.357i	−1.58363	+	7.23107i
$651$		0			0
$652$	−12.5531	−	7.77253i	−0.491616	−	0.304396i
$653$	1.30648	+	42.4049i	0.0511266	+	1.65943i	0.582898	+	0.812546i	$0.301919\pi$
$653$	1.30648	+	42.4049i	0.0511266	+	1.65943i	−0.531771	+	0.846888i	$0.678473\pi$
$654$		0			0
$655$	−31.2454	−	12.1045i	−1.22086	−	0.472963i
$656$	−83.7334	−	44.9639i	−3.26924	−	1.75555i
$657$		0			0
$658$	34.6007	+	4.28450i	1.34888	+	0.167027i
$659$	12.9507	−	4.11990i	0.504486	−	0.160489i	−0.0400964	−	0.999196i	$-0.512767\pi$
$659$	12.9507	−	4.11990i	0.504486	−	0.160489i	0.544583	+	0.838707i	$0.316688\pi$
$660$		0			0
$661$	−6.14210	+	39.5681i	−0.238900	+	1.53902i	0.500490	+	0.865742i	$0.333153\pi$
$661$	−6.14210	+	39.5681i	−0.238900	+	1.53902i	−0.739390	+	0.673277i	$0.764886\pi$
$662$	23.1715	−	65.7559i	0.900585	−	2.55567i
$663$		0			0
$664$	−44.6185	+	77.2815i	−1.73153	+	2.99910i
$665$	19.8294	+	34.3456i	0.768952	+	1.33186i
$666$		0			0
$667$	0.468646	−	0.377118i	0.0181461	−	0.0146021i
$668$	2.22361	−	72.1724i	0.0860339	−	2.79243i
$669$		0			0
$670$	−14.3785	+	21.6994i	−0.555491	+	0.838320i
$671$	−1.87669	+	60.9123i	−0.0724487	+	2.35149i
$672$		0			0
$673$	13.9348	+	3.50476i	0.537149	+	0.135098i	0.502948	−	0.864317i	$-0.332249\pi$
$673$	13.9348	+	3.50476i	0.537149	+	0.135098i	0.0342008	+	0.999415i	$0.489111\pi$
$674$	−11.8365	−	20.5013i	−0.455923	−	0.789682i
$675$		0			0
$676$	−88.6788	+	91.4530i	−3.41072	+	3.51742i
$677$	−13.3117	+	37.7758i	−0.511610	+	1.45184i	0.346340	+	0.938109i	$0.387424\pi$
$677$	−13.3117	+	37.7758i	−0.511610	+	1.45184i	−0.857949	+	0.513734i	$0.828262\pi$
$678$		0			0
$679$	−0.837910	+	9.04249i	−0.0321560	+	0.347019i
$680$	157.773	−	50.1914i	6.05034	−	1.92475i
$681$		0			0
$682$	−47.6282	+	18.4513i	−1.82378	+	0.706535i
$683$	−9.47930	−	5.09028i	−0.362715	−	0.194774i	0.281604	−	0.959531i	$-0.409134\pi$
$683$	−9.47930	−	5.09028i	−0.362715	−	0.194774i	−0.644319	+	0.764757i	$0.722859\pi$
$684$		0			0
$685$	8.26570	+	9.64777i	0.315816	+	0.368622i
$686$	−1.66711	−	54.1098i	−0.0636504	−	2.06592i
$687$		0			0
$688$	−32.6795	+	23.1333i	−1.24589	+	0.881950i
$689$	4.54272	−	20.7427i	0.173064	−	0.790234i
$690$		0			0
$691$	31.1645	+	28.4102i	1.18555	+	1.08077i	0.995079	+	0.0990807i	$0.0315902\pi$
$691$	31.1645	+	28.4102i	1.18555	+	1.08077i	0.190472	+	0.981693i	$0.438998\pi$
$692$	−19.2925	−	88.0922i	−0.733390	−	3.34876i
$693$		0			0
$694$	6.45895	+	69.7032i	0.245178	+	2.64590i
$695$	−11.0782	−	26.1733i	−0.420221	−	0.992811i
$696$		0			0
$697$	−23.1879	+	21.1385i	−0.878303	+	0.800679i
$698$	−41.6115	−	83.5672i	−1.57502	−	3.16307i
$699$		0			0
$700$	95.2434	+	76.6420i	3.59986	+	2.89680i
$701$	−31.3091	+	36.5442i	−1.18253	+	1.38025i	−0.274372	+	0.961624i	$0.588470\pi$
$701$	−31.3091	+	36.5442i	−1.18253	+	1.38025i	−0.908157	+	0.418630i	$0.862510\pi$
$702$		0			0
$703$	−35.4506	+	4.38974i	−1.33704	+	0.165562i
$704$	−99.3294	+	45.6988i	−3.74362	+	1.72234i
$705$		0			0
$706$	−19.8973	+	5.00437i	−0.748844	+	0.188342i
$707$	−3.19046	+	4.22486i	−0.119990	+	0.158892i
$708$		0			0
$709$	4.40480	+	28.3762i	0.165426	+	1.06569i	0.914907	+	0.403665i	$0.132264\pi$
$709$	4.40480	+	28.3762i	0.165426	+	1.06569i	−0.749481	+	0.662026i	$0.769697\pi$
$710$	−30.3557	+	1.87228i	−1.13923	+	0.0702654i
$711$		0			0
$712$	−1.57143	+	3.15585i	−0.0588918	+	0.118271i
$713$	13.8240	−	2.58416i	0.517715	−	0.0967776i
$714$		0			0
$715$	−100.648	−	46.3057i	−3.76404	−	1.73173i
$716$	−110.233	−	35.0675i	−4.11958	−	1.31053i
$717$		0			0
$718$	7.86500	−	4.86980i	0.293519	−	0.181739i
$719$	14.3413	+	21.6432i	0.534839	+	0.807153i	0.996816	−	0.0797388i	$-0.0254086\pi$
$719$	14.3413	+	21.6432i	0.534839	+	0.807153i	−0.461977	+	0.886892i	$0.652860\pi$
$720$		0			0
$721$	−15.5332	−	13.0647i	−0.578487	−	0.486556i
$722$	13.1759			0.490356
$723$		0			0
$724$	57.0571	−	35.3283i	2.12051	−	1.31297i
$725$	0.803650	−	1.89870i	0.0298468	−	0.0705159i
$726$		0			0
$727$	19.6366	+	9.03428i	0.728282	+	0.335063i	0.747056	−	0.664761i	$-0.231466\pi$
$727$	19.6366	+	9.03428i	0.728282	+	0.335063i	−0.0187740	+	0.999824i	$0.505976\pi$
$728$	36.3655	+	103.198i	1.34780	+	3.82477i
$729$		0			0
$730$	36.7615	−	73.8271i	1.36061	−	2.73246i
$731$	3.61735	+	12.7137i	0.133793	+	0.470232i
$732$		0			0
$733$	−7.17728	−	46.2368i	−0.265099	−	1.70780i	−0.629871	−	0.776700i	$-0.716892\pi$
$733$	−7.17728	−	46.2368i	−0.265099	−	1.70780i	0.364772	−	0.931097i	$-0.381147\pi$
$734$	−13.5540	−	2.53368i	−0.500287	−	0.0935199i
$735$		0			0
$736$	62.1133	−	15.6221i	2.28953	−	0.575839i
$737$	−7.40939	−	7.64119i	−0.272929	−	0.281467i
$738$		0			0
$739$	−19.4634	+	2.41009i	−0.715973	+	0.0886566i	−0.472601	−	0.881277i	$-0.656685\pi$
$739$	−19.4634	+	2.41009i	−0.715973	+	0.0886566i	−0.243372	+	0.969933i	$0.578253\pi$
$740$	−139.280	+	74.7916i	−5.12002	+	2.74939i
$741$		0			0
$742$	−14.7397	−	11.8610i	−0.541113	−	0.435432i
$743$	17.4300	+	23.0811i	0.639446	+	0.846763i	0.996169	−	0.0874472i	$-0.0278709\pi$
$743$	17.4300	+	23.0811i	0.639446	+	0.846763i	−0.356724	+	0.934210i	$0.616106\pi$
$744$		0			0
$745$	−6.11985	+	5.57898i	−0.224214	+	0.204398i
$746$	27.8721	+	19.7303i	1.02047	+	0.722376i
$747$		0			0
$748$	10.0015	+	107.933i	0.365690	+	3.94642i
$749$	12.5030	+	0.771157i	0.456849	+	0.0281775i
$750$		0			0
$751$	−25.5089	−	23.2544i	−0.930832	−	0.848565i	0.0578909	−	0.998323i	$-0.481562\pi$
$751$	−25.5089	−	23.2544i	−0.930832	−	0.848565i	−0.988723	+	0.149758i	$0.952151\pi$
$752$	24.1832	−	84.9951i	0.881870	−	3.09945i
$753$		0			0
$754$	2.41165	−	1.70717i	0.0878271	−	0.0621715i
$755$	−38.6513	−	23.9319i	−1.40666	−	0.870970i
$756$		0			0
$757$	11.8660	+	13.8500i	0.431277	+	0.503388i	0.932120	−	0.362150i	$-0.117957\pi$
$757$	11.8660	+	13.8500i	0.431277	+	0.503388i	−0.500843	+	0.865538i	$0.666977\pi$
$758$	54.6208	+	21.1602i	1.98392	+	0.768574i
$759$		0			0
$760$	166.509	−	64.5059i	6.03991	−	2.33987i
$761$	53.0763	+	6.57227i	1.92401	+	0.238245i	0.992197	−	0.124682i	$-0.0397911\pi$
$761$	53.0763	+	6.57227i	1.92401	+	0.238245i	0.931818	+	0.362927i	$0.118222\pi$
$762$		0			0
$763$	−0.192006	+	2.07207i	−0.00695107	+	0.0750140i
$764$	−14.4366	+	93.0024i	−0.522300	+	3.36471i
$765$		0			0
$766$	0.422824	−	0.436052i	0.0152772	−	0.0157552i
$767$	18.3003	−	31.6970i	0.660784	−	1.14451i
$768$		0			0
$769$	−6.62982	−	1.66747i	−0.239078	−	0.0601304i	0.122515	−	0.992467i	$-0.460904\pi$
$769$	−6.62982	−	1.66747i	−0.239078	−	0.0601304i	−0.361592	+	0.932336i	$0.617767\pi$
$770$	−76.9043	+	61.8846i	−2.77144	+	2.23017i
$771$		0			0
$772$	22.6204	−	34.1376i	0.814125	−	1.22864i
$773$	5.78896	−	8.73641i	0.208214	−	0.314227i	−0.714555	−	0.699579i	$-0.753371\pi$
$773$	5.78896	−	8.73641i	0.208214	−	0.314227i	0.922770	+	0.385352i	$0.125920\pi$
$774$		0			0
$775$	37.5538	−	30.2194i	1.34897	−	1.08551i
$776$	39.6540	+	9.97338i	1.42350	+	0.358024i
$777$		0			0
$778$	17.9183	−	31.0354i	0.642402	−	1.11267i
$779$	−23.5580	+	24.2950i	−0.844053	+	0.870458i
$780$		0			0
$781$	1.90752	−	12.2884i	0.0682563	−	0.439715i
$782$	3.78773	−	40.8761i	0.135449	−	1.46173i
$783$		0			0
$784$	−40.8544	−	5.05887i	−1.45908	−	0.180674i
$785$	15.9096	−	6.16341i	0.567838	−	0.219982i
$786$		0			0
$787$	0.821129	+	0.318107i	0.0292701	+	0.0113393i	0.375832	−	0.926688i	$-0.377357\pi$
$787$	0.821129	+	0.318107i	0.0292701	+	0.0113393i	−0.346562	+	0.938027i	$0.612651\pi$
$788$	−78.1765	−	91.2480i	−2.78492	−	3.25057i
$789$		0			0
$790$	40.6287	+	25.1562i	1.44550	+	0.895018i
$791$	2.00696	−	1.42070i	0.0713594	−	0.0505143i
$792$		0			0
$793$	22.5553	−	79.2737i	0.800962	−	2.81509i
$794$	23.5737	+	21.4902i	0.836598	+	0.762660i
$795$		0			0
$796$	−58.5089	−	3.60871i	−2.07379	−	0.127907i
$797$	−2.38490	−	25.7372i	−0.0844776	−	0.911658i	−0.927511	−	0.373796i	$-0.878056\pi$
$797$	−2.38490	−	25.7372i	−0.0844776	−	0.911658i	0.843033	−	0.537862i	$-0.180768\pi$
$798$		0			0
$799$	−23.8115	−	16.8558i	−0.842390	−	0.596315i
$800$	162.230	−	147.892i	5.73570	−	5.22878i
$801$		0			0
$802$	0.292322	+	0.387096i	0.0103222	+	0.0136688i
$803$	26.2723	+	21.1412i	0.927128	+	0.746057i
$804$		0			0
$805$	23.9450	−	12.8582i	0.843951	−	0.453192i
$806$	68.5560	−	8.48907i	2.41478	−	0.299015i
$807$		0			0
$808$	16.5941	+	17.1133i	0.583779	+	0.602042i
$809$	−41.0851	+	10.3333i	−1.44448	+	0.363300i	−0.885017	−	0.465558i	$-0.845854\pi$
$809$	−41.0851	+	10.3333i	−1.44448	+	0.363300i	−0.559458	+	0.828858i	$0.688991\pi$
$810$		0			0
$811$	−25.9654	−	4.85377i	−0.911768	−	0.170439i	−0.293091	−	0.956085i	$-0.594684\pi$
$811$	−25.9654	−	4.85377i	−0.911768	−	0.170439i	−0.618677	+	0.785646i	$0.712331\pi$
$812$	−0.293590	−	1.89134i	−0.0103030	−	0.0663729i
$813$		0			0
$814$	−24.3317	−	85.5170i	−0.852825	−	2.99737i
$815$	−5.01486	+	10.0712i	−0.175663	+	0.352779i
$816$		0			0
$817$	4.73817	+	13.4460i	0.165768	+	0.470414i
$818$	72.8931	+	33.5361i	2.54865	+	1.17256i
$819$		0			0
$820$	−58.3780	+	137.923i	−2.03865	+	4.81650i
$821$	−32.0069	+	19.8179i	−1.11705	+	0.691648i	−0.955434	−	0.295205i	$-0.904612\pi$
$821$	−32.0069	+	19.8179i	−1.11705	+	0.691648i	−0.161616	+	0.986854i	$0.551671\pi$
$822$		0			0
$823$	−17.4754			−0.609155			−0.304577	−	0.952488i	$-0.598515\pi$
$823$	−17.4754			−0.609155			−0.304577	+	0.952488i	$0.598515\pi$
$824$	−68.8571	+	60.0886i	−2.39875	+	2.09329i
$825$		0			0
$826$	−18.0128	−	27.1841i	−0.626747	−	0.945856i
$827$	31.8859	−	19.7429i	1.10878	−	0.686528i	0.155266	−	0.987873i	$-0.450377\pi$
$827$	31.8859	−	19.7429i	1.10878	−	0.686528i	0.953515	+	0.301344i	$0.0974354\pi$
$828$		0			0
$829$	35.9027	+	11.4215i	1.24695	+	0.396684i	0.852740	−	0.522336i	$-0.174939\pi$
$829$	35.9027	+	11.4215i	1.24695	+	0.396684i	0.394212	+	0.919020i	$0.371018\pi$
$830$	98.9134	+	45.5074i	3.43333	+	1.57958i
$831$		0			0
$832$	145.356	−	27.1717i	5.03931	−	0.942010i
$833$	−6.05783	+	12.1658i	−0.209891	+	0.421519i
$834$		0			0
$835$	−54.9176	+	3.38720i	−1.90050	+	0.117219i
$836$	17.9328	+	115.525i	0.620217	+	3.99551i
$837$		0			0
$838$	−6.42627	+	8.50976i	−0.221992	+	0.293965i
$839$	−7.79695	+	1.96101i	−0.269181	+	0.0677017i	−0.376144	−	0.926561i	$-0.622750\pi$
$839$	−7.79695	+	1.96101i	−0.269181	+	0.0677017i	0.106963	+	0.994263i	$0.465887\pi$
$840$		0			0
$841$	26.3162	−	12.1074i	0.907454	−	0.417495i
$842$	−32.3318	+	4.00354i	−1.11423	+	0.137971i
$843$		0			0
$844$	−46.2845	+	54.0235i	−1.59318	+	1.85956i
$845$	75.6255	+	60.8556i	2.60160	+	2.09350i
$846$		0			0
$847$	−8.18489	−	16.4375i	−0.281236	−	0.564798i
$848$	−35.4377	+	32.3057i	−1.21694	+	1.10938i
$849$		0			0
$850$	−54.8441	−	129.574i	−1.88114	−	4.44436i
$851$	2.25878	+	24.3761i	0.0774300	+	0.835603i
$852$		0			0
$853$	−11.6738	−	53.3041i	−0.399702	−	1.82510i	−0.548402	−	0.836215i	$-0.684764\pi$
$853$	−11.6738	−	53.3041i	−0.399702	−	1.82510i	0.148699	−	0.988882i	$-0.452491\pi$
$854$	−54.2690	−	49.4727i	−1.85705	−	1.69292i
$855$		0			0
$856$	12.0664	−	55.0968i	0.412421	−	1.88317i
$857$	−31.7103	+	22.4473i	−1.08320	+	0.766785i	−0.973844	−	0.227217i	$-0.927037\pi$
$857$	−31.7103	+	22.4473i	−1.08320	+	0.766785i	−0.109361	+	0.994002i	$0.534880\pi$
$858$		0			0
$859$	−0.834012	−	27.0698i	−0.0284561	−	0.923610i	−0.900675	−	0.434494i	$-0.856927\pi$
$859$	−0.834012	−	27.0698i	−0.0284561	−	0.923610i	0.872219	−	0.489116i	$-0.162681\pi$
$860$	41.0500	+	47.9137i	1.39979	+	1.63384i
$861$		0			0
$862$	77.6530	+	41.6988i	2.64487	+	1.42027i
$863$	31.2282	−	12.0979i	1.06302	−	0.411817i	0.234699	−	0.972068i	$-0.424590\pi$
$863$	31.2282	−	12.0979i	1.06302	−	0.411817i	0.828322	+	0.560252i	$0.189296\pi$
$864$		0			0
$865$	−65.4841	+	20.8320i	−2.22653	+	0.708309i
$866$	1.71964	−	18.5579i	0.0584357	−	0.630622i
$867$		0			0
$868$	14.8721	−	42.2039i	0.504791	−	1.43249i
$869$	−13.6018	+	14.0273i	−0.461410	+	0.475845i
$870$		0			0
$871$	7.19750	+	12.4664i	0.243878	+	0.422409i
$872$	9.08665	+	2.28538i	0.307713	+	0.0773928i
$873$		0			0
$874$	1.36346	−	44.2541i	0.0461196	−	1.49692i
$875$	29.0365	−	43.8204i	0.981611	−	1.48140i
$876$		0			0
$877$	0.879986	−	28.5620i	0.0297150	−	0.964471i	−0.860643	−	0.509209i	$-0.829938\pi$
$877$	0.879986	−	28.5620i	0.0297150	−	0.964471i	0.890358	−	0.455261i	$-0.150454\pi$
$878$	78.8263	−	63.4313i	2.66026	−	2.14070i
$879$		0			0
$880$	125.097	+	216.674i	4.21701	+	7.30408i
$881$	−1.71136	+	2.96416i	−0.0576571	+	0.0998651i	−0.893413	−	0.449236i	$-0.851696\pi$
$881$	−1.71136	+	2.96416i	−0.0576571	+	0.0998651i	0.835756	+	0.549101i	$0.185030\pi$
$882$		0			0
$883$	1.97506	−	5.60480i	0.0664659	−	0.188617i	−0.905195	−	0.424997i	$-0.860275\pi$
$883$	1.97506	−	5.60480i	0.0664659	−	0.188617i	0.971660	+	0.236381i	$0.0759613\pi$
$884$	22.4872	−	144.865i	0.756325	−	4.87233i
$885$		0			0
$886$	−28.2556	+	8.98875i	−0.949265	+	0.301983i
$887$	−10.9459	−	1.35540i	−0.367527	−	0.0455098i	−0.0630005	−	0.998013i	$-0.520067\pi$
$887$	−10.9459	−	1.35540i	−0.367527	−	0.0455098i	−0.304527	+	0.952504i	$0.598498\pi$
$888$		0			0
$889$	−3.91811	−	2.10398i	−0.131409	−	0.0705653i
$890$	4.01100	+	1.55387i	0.134449	+	0.0520858i
$891$		0			0
$892$	−4.57096	−	148.361i	−0.153047	−	4.96750i
$893$	−26.7520	−	16.5641i	−0.895220	−	0.554297i
$894$		0			0
$895$	−18.8573	+	86.1053i	−0.630332	+	2.87818i
$896$	15.1165	−	53.1290i	0.505007	−	1.77491i
$897$		0			0
$898$	−22.4760	−	102.629i	−0.750034	−	3.42476i
$899$	−0.753241	−	0.0464583i	−0.0251220	−	0.00154947i
$900$		0			0
$901$	6.17072	+	14.5789i	0.205577	+	0.485694i
$902$	−68.7494	−	48.6667i	−2.28910	−	1.62042i
$903$		0			0
$904$	−4.93499	−	9.91080i	−0.164135	−	0.329628i
$905$	−30.8172	−	40.8086i	−1.02440	−	1.35652i
$906$		0			0
$907$	19.2076	−	22.4192i	0.637778	−	0.744418i	−0.343045	−	0.939319i	$-0.611458\pi$
$907$	19.2076	−	22.4192i	0.637778	−	0.744418i	0.980823	+	0.194901i	$0.0624386\pi$
$908$	−116.649	+	62.6391i	−3.87113	+	2.07875i
$909$		0			0
$910$	121.282	−	55.7988i	4.02047	−	1.84971i
$911$	27.1233	+	27.9719i	0.898637	+	0.926750i	0.997662	−	0.0683352i	$-0.0217687\pi$
$911$	27.1233	+	27.9719i	0.898637	+	0.926750i	−0.0990259	+	0.995085i	$0.531573\pi$
$912$		0			0
$913$	−26.8289	+	35.5271i	−0.887905	+	1.17578i
$914$	−54.0008	−	10.0945i	−1.78619	−	0.333896i
$915$		0			0
$916$	64.4286	−	3.97382i	2.12878	−	0.131299i
$917$	4.51812	+	15.8796i	0.149202	+	0.524389i
$918$		0			0
$919$	−46.9624	+	8.77879i	−1.54915	+	0.289586i	−0.887706	−	0.460412i	$-0.847702\pi$
$919$	−46.9624	+	8.77879i	−1.54915	+	0.289586i	−0.661441	+	0.749997i	$0.730055\pi$
$920$	−40.6722	−	115.419i	−1.34092	−	3.80526i
$921$		0			0
$922$	4.80289	+	1.52791i	0.158175	+	0.0503190i
$923$	−6.55563	+	15.4883i	−0.215781	+	0.509803i
$924$		0			0
$925$	46.3474	+	69.9453i	1.52389	+	2.29979i
$926$	60.3000			1.98158
$927$		0			0
$928$	−3.43692			−0.112822
$929$	−0.961033	−	1.45034i	−0.0315305	−	0.0475843i	0.817498	−	0.575932i	$-0.195361\pi$
$929$	−0.961033	−	1.45034i	−0.0315305	−	0.0475843i	−0.849028	+	0.528348i	$0.822812\pi$
$930$		0			0
$931$	−5.71343	+	13.4985i	−0.187250	+	0.442396i
$932$	111.335	+	35.4183i	3.64691	+	1.16017i
$933$		0			0
$934$	−9.33846	−	26.5006i	−0.305564	−	0.867127i
$935$	81.1918	−	15.1774i	2.65526	−	0.496353i
$936$		0			0
$937$	10.1940	+	35.8280i	0.333022	+	1.17045i	0.929806	+	0.368049i	$0.119974\pi$
$937$	10.1940	+	35.8280i	0.333022	+	1.17045i	−0.596784	+	0.802402i	$0.703555\pi$
$938$	12.8014	−	0.789561i	0.417979	−	0.0257801i
$939$		0			0
$940$	−136.882	−	25.5876i	−4.46459	−	0.834576i
$941$	−1.42301	+	1.88436i	−0.0463887	+	0.0614285i	−0.820620	−	0.571474i	$-0.806372\pi$
$941$	−1.42301	+	1.88436i	−0.0463887	+	0.0614285i	0.774232	+	0.632902i	$0.218137\pi$
$942$		0			0
$943$	16.1448	+	16.6498i	0.525746	+	0.542194i
$944$	−75.0884	+	34.5461i	−2.44392	+	1.12438i
$945$		0			0
$946$	−31.2622	+	16.7874i	−1.01642	+	0.545806i
$947$	11.1649	−	13.0318i	0.362812	−	0.423476i	−0.547883	−	0.836555i	$-0.684566\pi$
$947$	11.1649	−	13.0318i	0.362812	−	0.423476i	0.910695	+	0.413079i	$0.135547\pi$
$948$		0			0
$949$	−27.4847	−	36.3956i	−0.892191	−	1.18145i
$950$	−67.6422	−	135.844i	−2.19460	−	4.40736i
$951$		0			0
$952$	−66.5816	−	47.1322i	−2.15792	−	1.52756i
$953$	−23.3981	−	55.2801i	−0.757937	−	1.79070i	−0.594415	−	0.804158i	$-0.702616\pi$
$953$	−23.3981	−	55.2801i	−0.757937	−	1.79070i	−0.163522	−	0.986540i	$-0.552286\pi$
$954$		0			0
$955$	71.5813	+	4.41498i	2.31632	+	0.142865i
$956$	−29.5124	−	134.758i	−0.954499	−	4.35838i
$957$		0			0
$958$	−29.7248	+	104.472i	−0.960363	+	3.37533i
$959$	1.33913	−	6.11466i	0.0432428	−	0.197453i
$960$		0			0
$961$	11.3558	+	7.03120i	0.366315	+	0.226813i
$962$	3.70304	+	120.191i	0.119391	+	3.87511i
$963$		0			0
$964$	109.296	+	42.3415i	3.52019	+	1.36373i
$965$	−27.4925	−	14.7632i	−0.885016	−	0.475244i
$966$		0			0
$967$	−40.6471	−	5.03320i	−1.30712	−	0.161857i	−0.561084	−	0.827759i	$-0.689615\pi$
$967$	−40.6471	−	5.03320i	−1.30712	−	0.161857i	−0.746039	+	0.665902i	$0.768047\pi$
$968$	−78.7882	+	25.0643i	−2.53235	+	0.805598i
$969$		0			0
$970$	7.65261	−	49.2990i	0.245711	−	1.58289i
$971$	−6.35088	+	18.0225i	−0.203809	+	0.578369i	−0.999631	−	0.0271619i	$-0.991353\pi$
$971$	−6.35088	+	18.0225i	−0.203809	+	0.578369i	0.795822	+	0.605531i	$0.207039\pi$
$972$		0			0
$973$	−7.00174	+	12.1274i	−0.224466	+	0.388786i
$974$	36.6994	+	63.5652i	1.17592	+	2.03676i
$975$		0			0
$976$	−145.008	+	116.688i	−4.64160	+	3.73508i
$977$	0.217903	−	7.07256i	0.00697134	−	0.226271i	−0.989617	−	0.143733i	$-0.954089\pi$
$977$	0.217903	−	7.07256i	0.00697134	−	0.226271i	0.996588	−	0.0825384i	$-0.0263027\pi$
$978$		0			0
$979$	−0.971502	+	1.46614i	−0.0310493	+	0.0468582i
$980$	−1.99770	+	64.8400i	−0.0638141	+	2.07124i
$981$		0			0
$982$	11.7199	+	2.94767i	0.373997	+	0.0940641i
$983$	−21.8443	−	37.8354i	−0.696724	−	1.20676i	−0.969596	−	0.244711i	$-0.921307\pi$
$983$	−21.8443	−	37.8354i	−0.696724	−	1.20676i	0.272872	−	0.962050i	$-0.412026\pi$
$984$		0			0
$985$	−63.7385	+	65.7325i	−2.03088	+	2.09441i
$986$	−0.732138	+	2.07766i	−0.0233160	+	0.0661660i
$987$		0			0
$988$	14.5888	−	157.438i	0.464132	−	5.00878i
$989$	9.31041	−	2.96185i	0.296054	−	0.0941815i
$990$		0			0
$991$	−47.1576	+	18.2689i	−1.49801	+	0.580332i	−0.964177	−	0.265258i	$-0.914543\pi$
$991$	−47.1576	+	18.2689i	−1.49801	+	0.580332i	−0.533832	+	0.845590i	$0.679249\pi$
$992$	−70.7916	−	38.0143i	−2.24763	−	1.20695i
$993$		0			0
$994$	9.74953	+	11.3797i	0.309236	+	0.360942i
$995$	1.37558	+	44.6478i	0.0436089	+	1.41543i
$996$		0			0
$997$	23.5687	−	16.6839i	0.746427	−	0.528385i	−0.140620	−	0.990064i	$-0.544910\pi$
$997$	23.5687	−	16.6839i	0.746427	−	0.528385i	0.887047	+	0.461679i	$0.152753\pi$
$998$	0.318894	−	1.45612i	0.0100944	−	0.0460925i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	927.2.ba.e.298.16	yes	512
3.2	odd	2	inner	927.2.ba.e.298.1	yes	512
103.28	even	51	inner	927.2.ba.e.28.16	yes	512
309.131	odd	102	inner	927.2.ba.e.28.1	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
927.2.ba.e.28.1	✓	512	309.131	odd	102	inner
927.2.ba.e.28.16	yes	512	103.28	even	51	inner
927.2.ba.e.298.1	yes	512	3.2	odd	2	inner
927.2.ba.e.298.16	yes	512	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 927 = 3^{2} \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	927.ba (of order \(51\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(1.49514 + 2.25639i) q^{2} +(-2.07629 + 4.90543i) q^{4} +(3.86801 + 1.23050i) q^{5} +(-0.664684 - 1.88624i) q^{7} +(-8.85150 + 1.65463i) q^{8} +O(q^{10})\)	\(q+(1.49514 + 2.25639i) q^{2} +(-2.07629 + 4.90543i) q^{4} +(3.86801 + 1.23050i) q^{5} +(-0.664684 - 1.88624i) q^{7} +(-8.85150 + 1.65463i) q^{8} +(3.00672 + 10.5675i) q^{10} +(-4.48388 + 0.276556i) q^{11} +(5.97230 + 1.11642i) q^{13} +(3.26229 - 4.31997i) q^{14} +(-9.55146 - 9.85027i) q^{16} +(-4.11509 + 1.89324i) q^{17} +(-4.30415 + 2.31128i) q^{19} +(-14.0673 + 16.4194i) q^{20} +(-7.32804 - 9.70389i) q^{22} +(1.49238 + 2.99710i) q^{23} +(9.36639 + 6.63033i) q^{25} +(6.41034 + 15.1450i) q^{26} +(10.6329 + 0.655813i) q^{28} +(-0.0384363 - 0.175506i) q^{29} +(1.14950 - 4.04009i) q^{31} +(4.09245 - 18.6867i) q^{32} +(-10.4245 - 6.45460i) q^{34} +(-0.249986 - 8.11388i) q^{35} +(6.81802 + 2.64132i) q^{37} +(-11.6505 - 6.25616i) q^{38} +(-36.2737 - 4.49166i) q^{40} +(6.60095 - 2.09991i) q^{41} +(0.447616 - 2.88359i) q^{43} +(7.95320 - 22.5695i) q^{44} +(-4.53132 + 7.84847i) q^{46} +(3.22026 + 5.57765i) q^{47} +(2.33748 - 1.88096i) q^{49} +(-0.956563 + 31.0475i) q^{50} +(-17.8767 + 26.9787i) q^{52} +(0.107627 - 3.49327i) q^{53} +(-17.6840 - 4.44770i) q^{55} +(9.00447 + 15.5962i) q^{56} +(0.338542 - 0.349133i) q^{58} +(2.00212 - 5.68159i) q^{59} +(1.25166 - 13.5075i) q^{61} +(10.8347 - 3.44676i) q^{62} +(22.6948 - 8.79203i) q^{64} +(21.7272 + 11.6672i) q^{65} +(1.54148 + 1.79922i) q^{67} +(-0.743043 - 24.1172i) q^{68} +(17.9343 - 12.6954i) q^{70} +(-0.592198 + 2.70406i) q^{71} +(-5.54736 - 5.05709i) q^{73} +(4.23405 + 19.3333i) q^{74} +(-2.40115 - 25.9126i) q^{76} +(3.50201 + 8.27383i) q^{77} +(3.21422 - 2.93015i) q^{79} +(-24.8244 - 49.8541i) q^{80} +(14.6076 + 11.7547i) q^{82} +(6.44757 - 7.52564i) q^{83} +(-18.2469 + 2.25945i) q^{85} +(7.17575 - 3.30137i) q^{86} +(39.2314 - 9.86710i) q^{88} +(0.235936 - 0.312429i) q^{89} +(-1.86387 - 12.0072i) q^{91} +(-17.8007 + 1.09791i) q^{92} +(-7.77062 + 15.6055i) q^{94} +(-19.4925 + 3.64379i) q^{95} +(-4.12515 - 1.89787i) q^{97} +(7.73905 + 2.46197i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q + 18 q^{4} - 8 q^{7}+O(q^{10}) \) 512 * q + 18 * q^4 - 8 * q^7	\( 512 q + 18 q^{4} - 8 q^{7} - 36 q^{10} + 4 q^{13} + 18 q^{16} + 30 q^{19} + 40 q^{22} - 42 q^{25} - 110 q^{28} - 32 q^{31} - 110 q^{34} + 48 q^{37} - 22 q^{40} - 2 q^{43} + 152 q^{46} + 76 q^{49} + 68 q^{52} + 32 q^{55} - 44 q^{58} + 20 q^{61} - 170 q^{64} - 8 q^{67} - 38 q^{70} - 4 q^{73} + 188 q^{76} + 20 q^{79} + 212 q^{82} + 60 q^{85} + 164 q^{88} - 310 q^{91} + 228 q^{94} - 100 q^{97}+O(q^{100}) \) 512 * q + 18 * q^4 - 8 * q^7 - 36 * q^10 + 4 * q^13 + 18 * q^16 + 30 * q^19 + 40 * q^22 - 42 * q^25 - 110 * q^28 - 32 * q^31 - 110 * q^34 + 48 * q^37 - 22 * q^40 - 2 * q^43 + 152 * q^46 + 76 * q^49 + 68 * q^52 + 32 * q^55 - 44 * q^58 + 20 * q^61 - 170 * q^64 - 8 * q^67 - 38 * q^70 - 4 * q^73 + 188 * q^76 + 20 * q^79 + 212 * q^82 + 60 * q^85 + 164 * q^88 - 310 * q^91 + 228 * q^94 - 100 * q^97

Introduction

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