LMFDB - Embedded newform 432.2.v.a.35.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(35,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("432.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.v (of order $12$, degree $4$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			35.10
Character	$\chi$	$=$	432.35
Dual form			432.2.v.a.395.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.254908 + 1.39105i) q^{2} +(-1.87004 - 0.709181i) q^{4} +(0.0458174 - 0.170993i) q^{5} +(1.17432 - 2.03397i) q^{7} +(1.46320 - 2.42055i) q^{8} +O(q^{10})$	\(q+(-0.254908 + 1.39105i) q^{2} +(-1.87004 - 0.709181i) q^{4} +(0.0458174 - 0.170993i) q^{5} +(1.17432 - 2.03397i) q^{7} +(1.46320 - 2.42055i) q^{8} +(0.226181 + 0.107322i) q^{10} +(0.0913188 + 0.340806i) q^{11} +(0.399362 - 1.49044i) q^{13} +(2.53002 + 2.15201i) q^{14} +(2.99413 + 2.65240i) q^{16} -3.58081i q^{17} +(5.36462 - 5.36462i) q^{19} +(-0.206946 + 0.287272i) q^{20} +(-0.497357 + 0.0401547i) q^{22} +(-0.165085 + 0.0953117i) q^{23} +(4.30299 + 2.48433i) q^{25} +(1.97148 + 0.935459i) q^{26} +(-3.63847 + 2.97082i) q^{28} +(2.43879 + 9.10169i) q^{29} +(3.43903 - 1.98552i) q^{31} +(-4.45285 + 3.48886i) q^{32} +(4.98108 + 0.912777i) q^{34} +(-0.293991 - 0.293991i) q^{35} +(-3.28315 + 3.28315i) q^{37} +(6.09498 + 8.82995i) q^{38} +(-0.346857 - 0.361100i) q^{40} +(-4.25538 - 7.37054i) q^{41} +(-4.09402 + 1.09699i) q^{43} +(0.0709232 - 0.702084i) q^{44} +(-0.0905019 - 0.253937i) q^{46} +(4.93030 - 8.53953i) q^{47} +(0.741968 + 1.28513i) q^{49} +(-4.55270 + 5.35240i) q^{50} +(-1.80382 + 2.50397i) q^{52} +(-4.83735 - 4.83735i) q^{53} +0.0624595 q^{55} +(-3.20508 - 5.81859i) q^{56} +(-13.2826 + 1.07238i) q^{58} +(2.68985 + 0.720744i) q^{59} +(-7.97394 + 2.13661i) q^{61} +(1.88533 + 5.28999i) q^{62} +(-3.71812 - 7.08347i) q^{64} +(-0.236557 - 0.136576i) q^{65} +(11.4543 + 3.06917i) q^{67} +(-2.53944 + 6.69626i) q^{68} +(0.483897 - 0.334016i) q^{70} -1.13635i q^{71} +5.67961i q^{73} +(-3.73012 - 5.40392i) q^{74} +(-13.8366 + 6.22759i) q^{76} +(0.800428 + 0.214474i) q^{77} +(-12.8621 - 7.42593i) q^{79} +(0.590725 - 0.390449i) q^{80} +(11.3375 - 4.04064i) q^{82} +(12.3635 - 3.31278i) q^{83} +(-0.612293 - 0.164063i) q^{85} +(-0.482368 - 5.97461i) q^{86} +(0.958556 + 0.277625i) q^{88} +3.05719 q^{89} +(-2.56254 - 2.56254i) q^{91} +(0.376309 - 0.0611622i) q^{92} +(10.6221 + 9.03509i) q^{94} +(-0.671520 - 1.16311i) q^{95} +(-0.996701 + 1.72634i) q^{97} +(-1.97681 + 0.704526i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7}+O(q^{10}) $ 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7	$ 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 40 q^{46} - 24 q^{49} - 72 q^{50} - 2 q^{52} - 16 q^{55} - 36 q^{56} + 16 q^{58} + 42 q^{59} - 2 q^{61} - 44 q^{64} + 12 q^{65} - 2 q^{67} - 96 q^{68} - 16 q^{70} - 78 q^{74} - 14 q^{76} + 6 q^{77} - 36 q^{82} - 54 q^{83} + 8 q^{85} - 54 q^{86} + 22 q^{88} + 20 q^{91} - 108 q^{92} + 6 q^{94} - 4 q^{97}+O(q^{100}) $ 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.254908	+	1.39105i	−0.180247	+	0.983621i
$2$	−0.254908	+	1.39105i	−0.180247	+	0.983621i
$3$		0			0
$3$		0			0
$4$	−1.87004	−	0.709181i	−0.935022	−	0.354590i
$5$	0.0458174	−	0.170993i	0.0204902	−	0.0764704i	−0.954924	−	0.296851i	$-0.904063\pi$
$5$	0.0458174	−	0.170993i	0.0204902	−	0.0764704i	0.975414	+	0.220381i	$0.0707301\pi$
$6$		0			0
$7$	1.17432	−	2.03397i	0.443849	−	0.768770i	−0.554122	−	0.832436i	$-0.686946\pi$
$7$	1.17432	−	2.03397i	0.443849	−	0.768770i	0.997971	+	0.0636659i	$0.0202792\pi$
$8$	1.46320	−	2.42055i	0.517318	−	0.855793i
$9$		0			0
$10$	0.226181	+	0.107322i	0.0715246	+	0.0339382i
$11$	0.0913188	+	0.340806i	0.0275337	+	0.102757i	0.978325	−	0.207074i	$-0.0663941\pi$
$11$	0.0913188	+	0.340806i	0.0275337	+	0.102757i	−0.950792	+	0.309831i	$0.899727\pi$
$12$		0			0
$13$	0.399362	−	1.49044i	0.110763	−	0.413374i	−0.888172	−	0.459511i	$-0.848025\pi$
$13$	0.399362	−	1.49044i	0.110763	−	0.413374i	0.998935	+	0.0461375i	$0.0146912\pi$
$14$	2.53002	+	2.15201i	0.676176	+	0.575148i
$15$		0			0
$16$	2.99413	+	2.65240i	0.748531	+	0.663099i
$17$		−	3.58081i		−	0.868473i	−0.900799	−	0.434236i	$-0.857018\pi$
$17$		−	3.58081i		−	0.868473i	0.900799	−	0.434236i	$-0.142982\pi$
$18$		0			0
$19$	5.36462	−	5.36462i	1.23073	−	1.23073i	0.267045	−	0.963684i	$-0.413953\pi$
$19$	5.36462	−	5.36462i	1.23073	−	1.23073i	0.963684	−	0.267045i	$-0.0860473\pi$
$20$	−0.206946	+	0.287272i	−0.0462744	+	0.0642359i
$21$		0			0
$22$	−0.497357	+	0.0401547i	−0.106037	+	0.00856101i
$23$	−0.165085	+	0.0953117i	−0.0344225	+	0.0198739i	−0.517113	−	0.855917i	$-0.672993\pi$
$23$	−0.165085	+	0.0953117i	−0.0344225	+	0.0198739i	0.482690	+	0.875791i	$0.339660\pi$
$24$		0			0
$25$	4.30299	+	2.48433i	0.860598	+	0.496866i
$26$	1.97148	+	0.935459i	0.386638	+	0.183459i
$27$		0			0
$28$	−3.63847	+	2.97082i	−0.687607	+	0.561432i
$29$	2.43879	+	9.10169i	0.452872	+	1.69014i	0.694270	+	0.719714i	$0.255727\pi$
$29$	2.43879	+	9.10169i	0.452872	+	1.69014i	−0.241398	+	0.970426i	$0.577606\pi$
$30$		0			0
$31$	3.43903	−	1.98552i	0.617668	−	0.356611i	−0.158293	−	0.987392i	$-0.550599\pi$
$31$	3.43903	−	1.98552i	0.617668	−	0.356611i	0.775960	+	0.630782i	$0.217266\pi$
$32$	−4.45285	+	3.48886i	−0.787159	+	0.616750i
$33$		0			0
$34$	4.98108	+	0.912777i	0.854248	+	0.156540i
$35$	−0.293991	−	0.293991i	−0.0496936	−	0.0496936i
$36$		0			0
$37$	−3.28315	+	3.28315i	−0.539746	+	0.539746i	−0.923454	−	0.383709i	$-0.874647\pi$
$37$	−3.28315	+	3.28315i	−0.539746	+	0.539746i	0.383709	+	0.923454i	$0.374647\pi$
$38$	6.09498	+	8.82995i	0.988736	+	1.43241i
$39$		0			0
$40$	−0.346857	−	0.361100i	−0.0548429	−	0.0570949i
$41$	−4.25538	−	7.37054i	−0.664579	−	1.15109i	−0.979399	−	0.201934i	$-0.935277\pi$
$41$	−4.25538	−	7.37054i	−0.664579	−	1.15109i	0.314820	−	0.949151i	$-0.398056\pi$
$42$		0			0
$43$	−4.09402	+	1.09699i	−0.624332	+	0.167289i	−0.557096	−	0.830448i	$-0.688085\pi$
$43$	−4.09402	+	1.09699i	−0.624332	+	0.167289i	−0.0672354	+	0.997737i	$0.521418\pi$
$44$	0.0709232	−	0.702084i	0.0106921	−	0.105843i
$45$		0			0
$46$	−0.0905019	−	0.253937i	−0.0133438	−	0.0374409i
$47$	4.93030	−	8.53953i	0.719158	−	1.24562i	−0.242176	−	0.970232i	$-0.577861\pi$
$47$	4.93030	−	8.53953i	0.719158	−	1.24562i	0.961334	−	0.275386i	$-0.0888057\pi$
$48$		0			0
$49$	0.741968	+	1.28513i	0.105995	+	0.183590i
$50$	−4.55270	+	5.35240i	−0.643849	+	0.756943i
$51$		0			0
$52$	−1.80382	+	2.50397i	−0.250144	+	0.347238i
$53$	−4.83735	−	4.83735i	−0.664461	−	0.664461i	0.291967	−	0.956428i	$-0.405690\pi$
$53$	−4.83735	−	4.83735i	−0.664461	−	0.664461i	−0.956428	+	0.291967i	$0.905690\pi$
$54$		0			0
$55$	0.0624595			0.00842204
$56$	−3.20508	−	5.81859i	−0.428297	−	0.777542i
$57$		0			0
$58$	−13.2826	+	1.07238i	−1.74409	+	0.140811i
$59$	2.68985	+	0.720744i	0.350189	+	0.0938328i	0.429626	−	0.903007i	$-0.358646\pi$
$59$	2.68985	+	0.720744i	0.350189	+	0.0938328i	−0.0794368	+	0.996840i	$0.525312\pi$
$60$		0			0
$61$	−7.97394	+	2.13661i	−1.02096	+	0.273565i	−0.730201	−	0.683232i	$-0.760574\pi$
$61$	−7.97394	+	2.13661i	−1.02096	+	0.273565i	−0.290757	+	0.956797i	$0.593907\pi$
$62$	1.88533	+	5.28999i	0.239437	+	0.671829i
$63$		0			0
$64$	−3.71812	−	7.08347i	−0.464765	−	0.885434i
$65$	−0.236557	−	0.136576i	−0.0293413	−	0.0169402i
$66$		0			0
$67$	11.4543	+	3.06917i	1.39936	+	0.374959i	0.878117	−	0.478446i	$-0.158800\pi$
$67$	11.4543	+	3.06917i	1.39936	+	0.374959i	0.521248	+	0.853405i	$0.325467\pi$
$68$	−2.53944	+	6.69626i	−0.307952	+	0.812041i
$69$		0			0
$70$	0.483897	−	0.334016i	0.0578368	−	0.0399225i
$71$		−	1.13635i		−	0.134860i	−0.997724	−	0.0674300i	$-0.978520\pi$
$71$		−	1.13635i		−	0.134860i	0.997724	−	0.0674300i	$-0.0214799\pi$
$72$		0			0
$73$			5.67961i			0.664748i	0.943148	+	0.332374i	$0.107850\pi$
$73$			5.67961i			0.664748i	−0.943148	+	0.332374i	$0.892150\pi$
$74$	−3.73012	−	5.40392i	−0.433618	−	0.628193i
$75$		0			0
$76$	−13.8366	+	6.22759i	−1.58716	+	0.714354i
$77$	0.800428	+	0.214474i	0.0912173	+	0.0244416i
$78$		0			0
$79$	−12.8621	−	7.42593i	−1.44710	−	0.835482i	−0.448790	−	0.893637i	$-0.648145\pi$
$79$	−12.8621	−	7.42593i	−1.44710	−	0.835482i	−0.998308	+	0.0581546i	$0.981478\pi$
$80$	0.590725	−	0.390449i	0.0660450	−	0.0436535i
$81$		0			0
$82$	11.3375	−	4.04064i	1.25202	−	0.446214i
$83$	12.3635	−	3.31278i	1.35707	−	0.363625i	0.494329	−	0.869275i	$-0.335414\pi$
$83$	12.3635	−	3.31278i	1.35707	−	0.363625i	0.862739	+	0.505649i	$0.168747\pi$
$84$		0			0
$85$	−0.612293	−	0.164063i	−0.0664125	−	0.0177952i
$86$	−0.482368	−	5.97461i	−0.0520150	−	0.644259i
$87$		0			0
$88$	0.958556	+	0.277625i	0.102182	+	0.0295949i
$89$	3.05719			0.324061			0.162031	−	0.986786i	$-0.448196\pi$
$89$	3.05719			0.324061			0.162031	+	0.986786i	$0.448196\pi$
$90$		0			0
$91$	−2.56254	−	2.56254i	−0.268627	−	0.268627i
$92$	0.376309	−	0.0611622i	0.0392329	−	0.00637660i
$93$		0			0
$94$	10.6221	+	9.03509i	1.09559	+	0.931899i
$95$	−0.671520	−	1.16311i	−0.0688965	−	0.119332i
$96$		0			0
$97$	−0.996701	+	1.72634i	−0.101200	+	0.175283i	−0.912179	−	0.409792i	$-0.865601\pi$
$97$	−0.996701	+	1.72634i	−0.101200	+	0.175283i	0.810980	+	0.585075i	$0.198935\pi$
$98$	−1.97681	+	0.704526i	−0.199688	+	0.0711679i
$99$		0			0
$100$	−6.28494	−	7.69740i	−0.628494	−	0.769740i
$101$	−15.4663	+	4.14419i	−1.53896	+	0.412362i	−0.925928	−	0.377700i	$-0.876715\pi$
$101$	−15.4663	+	4.14419i	−1.53896	+	0.412362i	−0.613027	+	0.790062i	$0.710048\pi$
$102$		0			0
$103$	−8.12150	−	14.0668i	−0.800235	−	1.38605i	−0.919461	−	0.393181i	$-0.871375\pi$
$103$	−8.12150	−	14.0668i	−0.800235	−	1.38605i	0.119226	−	0.992867i	$-0.461959\pi$
$104$	−3.02334	−	3.14748i	−0.296463	−	0.308636i
$105$		0			0
$106$	7.96208	−	5.49592i	0.773346	−	0.533811i
$107$	−2.08262	+	2.08262i	−0.201334	+	0.201334i	−0.800571	−	0.599237i	$-0.795471\pi$
$107$	−2.08262	+	2.08262i	−0.201334	+	0.201334i	0.599237	+	0.800571i	$0.295471\pi$
$108$		0			0
$109$	7.70191	+	7.70191i	0.737709	+	0.737709i	0.972134	−	0.234425i	$-0.0753207\pi$
$109$	7.70191	+	7.70191i	0.737709	+	0.737709i	−0.234425	+	0.972134i	$0.575321\pi$
$110$	−0.0159214	+	0.0868843i	−0.00151805	+	0.00828410i
$111$		0			0
$112$	8.91095	−	2.97522i	0.842006	−	0.281132i
$113$	−10.3137	+	5.95461i	−0.970230	+	0.560162i	−0.899306	−	0.437319i	$-0.855928\pi$
$113$	−10.3137	+	5.95461i	−0.970230	+	0.560162i	−0.0709236	+	0.997482i	$0.522595\pi$
$114$		0			0
$115$	0.00873387	+	0.0325953i	0.000814438	+	0.00303952i
$116$	1.89410	−	18.7501i	0.175862	−	1.74090i
$117$		0			0
$118$	−1.68826	+	3.55800i	−0.155417	+	0.327540i
$119$	−7.28326	−	4.20499i	−0.667656	−	0.385471i
$120$		0			0
$121$	9.41847	−	5.43776i	0.856225	−	0.494341i
$122$	−0.939511	−	11.6368i	−0.0850593	−	1.05355i
$123$		0			0
$124$	−7.83923	+	1.27412i	−0.703984	+	0.114420i
$125$	1.24783	−	1.24783i	0.111610	−	0.111610i
$126$		0			0
$127$			8.43197i			0.748216i	0.927385	+	0.374108i	$0.122051\pi$
$127$			8.43197i			0.748216i	−0.927385	+	0.374108i	$0.877949\pi$
$128$	10.8012	−	3.36645i	0.954705	−	0.297555i
$129$		0			0
$130$	0.250285	−	0.294248i	0.0219514	−	0.0258073i
$131$	1.40833	−	5.25596i	0.123046	−	0.459215i	−0.876716	−	0.481008i	$-0.840271\pi$
$131$	1.40833	−	5.25596i	0.123046	−	0.459215i	0.999763	+	0.0217928i	$0.00693742\pi$
$132$		0			0
$133$	−4.61174	−	17.2113i	−0.399889	−	1.49241i
$134$	−7.18916	+	15.1511i	−0.621049	+	1.30886i
$135$		0			0
$136$	−8.66752	−	5.23942i	−0.743233	−	0.449276i
$137$	1.62151	−	2.80854i	0.138535	−	0.239950i	−0.788407	−	0.615154i	$-0.789094\pi$
$137$	1.62151	−	2.80854i	0.138535	−	0.239950i	0.926942	+	0.375204i	$0.122427\pi$
$138$		0			0
$139$	−3.54037	+	13.2129i	−0.300291	+	1.12070i	0.636633	+	0.771167i	$0.280326\pi$
$139$	−3.54037	+	13.2129i	−0.300291	+	1.12070i	−0.936924	+	0.349533i	$0.886340\pi$
$140$	0.341283	+	0.758269i	0.0288437	+	0.0640854i
$141$		0			0
$142$	1.58072	+	0.289665i	0.132651	+	0.0243082i
$143$	0.544421			0.0455268
$144$		0			0
$145$	1.66806			0.138525
$146$	−7.90063	−	1.44778i	−0.653861	−	0.119819i
$147$		0			0
$148$	8.46797	−	3.81128i	0.696063	−	0.313285i
$149$	−3.28089	+	12.2444i	−0.268781	+	1.00310i	0.691115	+	0.722745i	$0.257120\pi$
$149$	−3.28089	+	12.2444i	−0.268781	+	1.00310i	−0.959895	+	0.280358i	$0.909547\pi$
$150$		0			0
$151$	0.791297	−	1.37057i	0.0643948	−	0.111535i	−0.832031	−	0.554730i	$-0.812822\pi$
$151$	0.791297	−	1.37057i	0.0643948	−	0.111535i	0.896425	+	0.443195i	$0.146155\pi$
$152$	−5.13584	−	20.8348i	−0.416572	−	1.68993i
$153$		0			0
$154$	−0.502380	+	1.05877i	−0.0404829	+	0.0853177i
$155$	−0.181943	−	0.679022i	−0.0146140	−	0.0545403i
$156$		0			0
$157$	−2.07187	+	7.73231i	−0.165353	+	0.617106i	0.832642	+	0.553812i	$0.186827\pi$
$157$	−2.07187	+	7.73231i	−0.165353	+	0.617106i	−0.997995	+	0.0632940i	$0.979839\pi$
$158$	13.6085	−	15.9989i	1.08263	−	1.27280i
$159$		0			0
$160$	0.392553	+	0.921256i	0.0310341	+	0.0728317i
$161$			0.447704i			0.0352840i
$162$		0			0
$163$	−10.2400	+	10.2400i	−0.802055	+	0.802055i	−0.983416	−	0.181362i	$-0.941950\pi$
$163$	−10.2400	+	10.2400i	−0.802055	+	0.802055i	0.181362	+	0.983416i	$0.441950\pi$
$164$	2.73071	+	16.8011i	0.213233	+	1.31194i
$165$		0			0
$166$	1.45670	+	18.0427i	0.113062	+	1.40038i
$167$	−10.1700	+	5.87166i	−0.786979	+	0.454362i	−0.838898	−	0.544289i	$-0.816800\pi$
$167$	−10.1700	+	5.87166i	−0.786979	+	0.454362i	0.0519191	+	0.998651i	$0.483466\pi$
$168$		0			0
$169$	9.19641	+	5.30955i	0.707416	+	0.408427i
$170$	0.384299	−	0.809909i	0.0294744	−	0.0621172i
$171$		0			0
$172$	8.43395	+	0.851981i	0.643083	+	0.0649629i
$173$	3.84530	+	14.3509i	0.292353	+	1.09108i	0.943297	+	0.331950i	$0.107707\pi$
$173$	3.84530	+	14.3509i	0.292353	+	1.09108i	−0.650944	+	0.759126i	$0.725627\pi$
$174$		0			0
$175$	10.1061	−	5.83477i	0.763951	−	0.441068i
$176$	−0.630534	+	1.26263i	−0.0475283	+	0.0951744i
$177$		0			0
$178$	−0.779302	+	4.25270i	−0.0584112	+	0.318753i
$179$	10.4051	+	10.4051i	0.777712	+	0.777712i	0.979441	−	0.201730i	$-0.0646563\pi$
$179$	10.4051	+	10.4051i	0.777712	+	0.777712i	−0.201730	+	0.979441i	$0.564656\pi$
$180$		0			0
$181$	−16.0569	+	16.0569i	−1.19350	+	1.19350i	−0.217424	+	0.976077i	$0.569765\pi$
$181$	−16.0569	+	16.0569i	−1.19350	+	1.19350i	−0.976077	+	0.217424i	$0.930235\pi$
$182$	4.21783	−	2.91141i	0.312647	−	0.215808i
$183$		0			0
$184$	−0.0108445	+	0.539055i	−0.000799471	+	0.0397397i
$185$	0.410970	+	0.711820i	0.0302151	+	0.0523341i
$186$		0			0
$187$	1.22036	−	0.326995i	0.0892417	−	0.0239122i
$188$	−15.2759	+	12.4728i	−1.11411	+	0.909674i
$189$		0			0
$190$	1.78912	−	0.637633i	0.129796	−	0.0462587i
$191$	−3.45557	+	5.98522i	−0.250036	+	0.433075i	−0.963535	−	0.267581i	$-0.913776\pi$
$191$	−3.45557	+	5.98522i	−0.250036	+	0.433075i	0.713499	+	0.700656i	$0.247109\pi$
$192$		0			0
$193$	−7.82918	−	13.5605i	−0.563557	−	0.976109i	−0.997182	−	0.0750156i	$-0.976099\pi$
$193$	−7.82918	−	13.5605i	−0.563557	−	0.976109i	0.433626	−	0.901093i	$-0.357234\pi$
$194$	−2.14735	−	1.82652i	−0.154171	−	0.131136i
$195$		0			0
$196$	−0.476126	−	2.92943i	−0.0340090	−	0.209245i
$197$	8.24778	+	8.24778i	0.587630	+	0.587630i	0.936989	−	0.349359i	$-0.113601\pi$
$197$	8.24778	+	8.24778i	0.587630	+	0.587630i	−0.349359	+	0.936989i	$0.613601\pi$
$198$		0			0
$199$	5.52708			0.391804			0.195902	−	0.980623i	$-0.437237\pi$
$199$	5.52708			0.391804			0.195902	+	0.980623i	$0.437237\pi$
$200$	12.3096	−	6.78053i	0.870417	−	0.479456i
$201$		0			0
$202$	−1.82228	−	22.5708i	−0.128215	−	1.58808i
$203$	21.3765	+	5.72781i	1.50034	+	0.402014i
$204$		0			0
$205$	−1.45528	+	0.389942i	−0.101641	+	0.0272347i
$206$	21.6379	−	7.71166i	1.50759	−	0.537297i
$207$		0			0
$208$	5.14898	−	3.40330i	0.357018	−	0.235976i
$209$	2.31819	+	1.33841i	0.160353	+	0.0925796i
$210$		0			0
$211$	−4.08372	−	1.09423i	−0.281135	−	0.0753299i	0.115496	−	0.993308i	$-0.463154\pi$
$211$	−4.08372	−	1.09423i	−0.281135	−	0.0753299i	−0.396631	+	0.917978i	$0.629821\pi$
$212$	5.61550	+	12.4766i	0.385674	+	0.856897i
$213$		0			0
$214$	−2.36615	−	3.42790i	−0.161747	−	0.234327i
$215$			0.750309i			0.0511707i
$216$		0			0
$217$		−	9.32653i		−	0.633126i
$218$	−12.6770	+	8.75047i	−0.858597	+	0.592657i
$219$		0			0
$220$	−0.116802	−	0.0442951i	−0.00787479	−	0.00298637i
$221$	−5.33698	−	1.43004i	−0.359004	−	0.0961948i
$222$		0			0
$223$	6.50548	+	3.75594i	0.435639	+	0.251517i	0.701746	−	0.712427i	$-0.252404\pi$
$223$	6.50548	+	3.75594i	0.435639	+	0.251517i	−0.266107	+	0.963944i	$0.585737\pi$
$224$	1.86721	+	13.1540i	0.124758	+	0.878888i
$225$		0			0
$226$	−5.65412	−	15.8647i	−0.376106	−	1.05531i
$227$	6.31276	−	1.69150i	0.418993	−	0.112269i	−0.0431619	−	0.999068i	$-0.513743\pi$
$227$	6.31276	−	1.69150i	0.418993	−	0.112269i	0.462155	+	0.886799i	$0.347076\pi$
$228$		0			0
$229$	1.08810	+	0.291556i	0.0719037	+	0.0192665i	0.294592	−	0.955623i	$-0.404816\pi$
$229$	1.08810	+	0.291556i	0.0719037	+	0.0192665i	−0.222688	+	0.974890i	$0.571483\pi$
$230$	−0.0475680	+	0.00384046i	−0.00313654	+	0.000253232i
$231$		0			0
$232$	25.5995	+	7.41434i	1.68069	+	0.486775i
$233$	13.9406			0.913280			0.456640	−	0.889652i	$-0.349053\pi$
$233$	13.9406			0.913280			0.456640	+	0.889652i	$0.349053\pi$
$234$		0			0
$235$	−1.23431	−	1.23431i	−0.0805173	−	0.0805173i
$236$	−4.51900	−	3.25541i	−0.294162	−	0.211909i
$237$		0			0
$238$	7.70592	−	9.05950i	0.499501	−	0.587240i
$239$	14.8075	+	25.6474i	0.957820	+	1.65899i	0.727780	+	0.685811i	$0.240552\pi$
$239$	14.8075	+	25.6474i	0.957820	+	1.65899i	0.230040	+	0.973181i	$0.426114\pi$
$240$		0			0
$241$	−6.03200	+	10.4477i	−0.388555	+	0.672997i	−0.992255	−	0.124214i	$-0.960359\pi$
$241$	−6.03200	+	10.4477i	−0.388555	+	0.672997i	0.603700	+	0.797211i	$0.293692\pi$
$242$	5.16335	+	14.4877i	0.331913	+	0.931304i
$243$		0			0
$244$	16.4269	+	1.65941i	1.05162	+	0.106233i
$245$	0.253743	−	0.0679902i	0.0162110	−	0.00434373i
$246$		0			0
$247$	−5.85322	−	10.1381i	−0.372432	−	0.645071i
$248$	0.225913	−	11.2296i	0.0143455	−	0.713077i
$249$		0			0
$250$	1.41772	+	2.05388i	0.0896642	+	0.129899i
$251$	−13.9356	+	13.9356i	−0.879610	+	0.879610i	−0.993494	−	0.113884i	$-0.963671\pi$
$251$	−13.9356	+	13.9356i	−0.879610	+	0.879610i	0.113884	+	0.993494i	$0.463671\pi$
$252$		0			0
$253$	−0.0475582	−	0.0475582i	−0.00298996	−	0.00298996i
$254$	−11.7293	−	2.14938i	−0.735961	−	0.134864i
$255$		0			0
$256$	1.92958	+	15.8832i	0.120599	+	0.992701i
$257$	21.0025	−	12.1258i	1.31010	−	0.756387i	0.327988	−	0.944682i	$-0.393630\pi$
$257$	21.0025	−	12.1258i	1.31010	−	0.756387i	0.982112	+	0.188295i	$0.0602963\pi$
$258$		0			0
$259$	2.82238	+	10.5333i	0.175374	+	0.654506i
$260$	0.345515	+	0.423165i	0.0214279	+	0.0262436i
$261$		0			0
$262$	6.95231	+	3.29885i	0.429515	+	0.203803i
$263$	−26.7072	−	15.4194i	−1.64683	−	0.950800i	−0.978319	−	0.207102i	$-0.933597\pi$
$263$	−26.7072	−	15.4194i	−1.64683	−	0.950800i	−0.668515	−	0.743699i	$-0.733070\pi$
$264$		0			0
$265$	−1.04879	+	0.605518i	−0.0644265	+	0.0371967i
$266$	25.1173	−	2.02788i	1.54004	−	0.124337i
$267$		0			0
$268$	−19.2434	−	13.8626i	−1.17548	−	0.846796i
$269$	5.24359	−	5.24359i	0.319707	−	0.319707i	−0.528947	−	0.848655i	$-0.677413\pi$
$269$	5.24359	−	5.24359i	0.319707	−	0.319707i	0.848655	+	0.528947i	$0.177413\pi$
$270$		0			0
$271$			6.82794i			0.414768i	0.978260	+	0.207384i	$0.0664949\pi$
$271$			6.82794i			0.414768i	−0.978260	+	0.207384i	$0.933505\pi$
$272$	9.49772	−	10.7214i	0.575884	−	0.650079i
$273$		0			0
$274$	3.49349	+	2.97153i	0.211049	+	0.179517i
$275$	−0.453732	+	1.69335i	−0.0273611	+	0.102113i
$276$		0			0
$277$	−1.70011	−	6.34489i	−0.102150	−	0.381228i	0.895857	−	0.444343i	$-0.146563\pi$
$277$	−1.70011	−	6.34489i	−0.102150	−	0.381228i	−0.998006	+	0.0631157i	$0.979896\pi$
$278$	−17.4773	−	8.29291i	−1.04822	−	0.497375i
$279$		0			0
$280$	−1.14179	+	0.281453i	−0.0682348	+	0.0168201i
$281$	−2.29891	+	3.98183i	−0.137141	+	0.237536i	−0.926413	−	0.376508i	$-0.877125\pi$
$281$	−2.29891	+	3.98183i	−0.137141	+	0.237536i	0.789272	+	0.614044i	$0.210458\pi$
$282$		0			0
$283$	−2.26861	+	8.46655i	−0.134855	+	0.503284i	0.865144	+	0.501524i	$0.167227\pi$
$283$	−2.26861	+	8.46655i	−0.134855	+	0.503284i	−0.999998	+	0.00176039i	$0.999440\pi$
$284$	−0.805878	+	2.12503i	−0.0478200	+	0.126097i
$285$		0			0
$286$	−0.138777	+	0.757317i	−0.00820608	+	0.0447811i
$287$	−19.9886			−1.17989
$288$		0			0
$289$	4.17783			0.245755
$290$	−0.425203	+	2.32036i	−0.0249688	+	0.136256i
$291$		0			0
$292$	4.02787	−	10.6211i	0.235713	−	0.621554i
$293$	4.46706	−	16.6713i	0.260969	−	0.973948i	−0.703703	−	0.710494i	$-0.748472\pi$
$293$	4.46706	−	16.6713i	0.260969	−	0.973948i	0.964672	−	0.263454i	$-0.0848617\pi$
$294$		0			0
$295$	0.246484	−	0.426923i	0.0143509	−	0.0248564i
$296$	3.14313	+	12.7509i	0.182691	+	0.741131i
$297$		0			0
$298$	−16.1963	−	7.68509i	−0.938227	−	0.445185i
$299$	0.0761278	+	0.284113i	0.00440258	+	0.0164307i
$300$		0			0
$301$	−2.57642	+	9.61533i	−0.148502	+	0.554218i
$302$	1.70482	+	1.45010i	0.0981013	+	0.0834440i
$303$		0			0
$304$	30.2915	−	1.83325i	1.73734	−	0.105144i
$305$			1.46138i			0.0836785i
$306$		0			0
$307$	−3.08820	+	3.08820i	−0.176253	+	0.176253i	−0.789720	−	0.613467i	$-0.789774\pi$
$307$	−3.08820	+	3.08820i	−0.176253	+	0.176253i	0.613467	+	0.789720i	$0.289774\pi$
$308$	−1.34473	−	0.968724i	−0.0766234	−	0.0551982i
$309$		0			0
$310$	0.990932	−	0.0800041i	0.0562812	−	0.00454393i
$311$	11.7879	−	6.80577i	0.668433	−	0.385920i	−0.127050	−	0.991896i	$-0.540551\pi$
$311$	11.7879	−	6.80577i	0.668433	−	0.385920i	0.795483	+	0.605976i	$0.207217\pi$
$312$		0			0
$313$	9.11117	+	5.26034i	0.514994	+	0.297332i	0.734884	−	0.678193i	$-0.237237\pi$
$313$	9.11117	+	5.26034i	0.514994	+	0.297332i	−0.219890	+	0.975525i	$0.570570\pi$
$314$	−10.2279	−	4.85310i	−0.577194	−	0.273876i
$315$		0			0
$316$	18.7863	+	23.0084i	1.05681	+	1.29432i
$317$	−5.02863	−	18.7671i	−0.282436	−	1.05406i	−0.950693	−	0.310134i	$-0.899626\pi$
$317$	−5.02863	−	18.7671i	−0.282436	−	1.05406i	0.668257	−	0.743931i	$-0.267041\pi$
$318$		0			0
$319$	−2.87921	+	1.66231i	−0.161205	+	0.0930715i
$320$	−1.38158	+	0.311225i	−0.0772326	+	0.0173980i
$321$		0			0
$322$	−0.622779	−	0.114123i	−0.0347061	−	0.00635985i
$323$	−19.2097	−	19.2097i	−1.06885	−	1.06885i
$324$		0			0
$325$	5.42120	−	5.42120i	0.300714	−	0.300714i
$326$	−11.6340	−	16.8545i	−0.644350	−	0.933486i
$327$		0			0
$328$	−24.0672	−	0.484177i	−1.32889	−	0.0267342i
$329$	−11.5795	−	20.0562i	−0.638396	−	1.10573i
$330$		0			0
$331$	12.3204	−	3.30125i	0.677192	−	0.181453i	0.0961997	−	0.995362i	$-0.469331\pi$
$331$	12.3204	−	3.30125i	0.677192	−	0.181453i	0.580992	+	0.813909i	$0.302665\pi$
$332$	−25.4696	−	2.57289i	−1.39783	−	0.141206i
$333$		0			0
$334$	−5.57535	−	15.6437i	−0.305070	−	0.855987i
$335$	1.04961	−	1.81798i	0.0573465	−	0.0993270i
$336$		0			0
$337$	−5.77771	−	10.0073i	−0.314732	−	0.545132i	0.664648	−	0.747156i	$-0.268581\pi$
$337$	−5.77771	−	10.0073i	−0.314732	−	0.545132i	−0.979381	+	0.202024i	$0.935248\pi$
$338$	−9.73009	+	11.4392i	−0.529247	+	0.622212i
$339$		0			0
$340$	1.02866	+	0.741032i	0.0557871	+	0.0401881i
$341$	0.990728	+	0.990728i	0.0536509	+	0.0536509i
$342$		0			0
$343$	19.9256			1.07588
$344$	−3.33503	+	11.5149i	−0.179813	+	0.620840i
$345$		0			0
$346$	−20.9430	+	1.69086i	−1.12590	+	0.0909010i
$347$	−6.49207	−	1.73954i	−0.348512	−	0.0933836i	0.0803163	−	0.996769i	$-0.474407\pi$
$347$	−6.49207	−	1.73954i	−0.348512	−	0.0933836i	−0.428829	+	0.903386i	$0.641074\pi$
$348$		0			0
$349$	−8.76397	+	2.34830i	−0.469125	+	0.125702i	−0.485634	−	0.874162i	$-0.661411\pi$
$349$	−8.76397	+	2.34830i	−0.469125	+	0.125702i	0.0165095	+	0.999864i	$0.494745\pi$
$350$	5.54033	+	15.5455i	0.296143	+	0.830940i
$351$		0			0
$352$	−1.59566	−	1.19896i	−0.0850487	−	0.0639048i
$353$	10.8100	+	6.24115i	0.575357	+	0.332183i	0.759286	−	0.650757i	$-0.225548\pi$
$353$	10.8100	+	6.24115i	0.575357	+	0.332183i	−0.183929	+	0.982940i	$0.558882\pi$
$354$		0			0
$355$	−0.194308	−	0.0520647i	−0.0103128	−	0.00276331i
$356$	−5.71707	−	2.16810i	−0.303004	−	0.114909i
$357$		0			0
$358$	−17.1263	+	11.8216i	−0.905154	+	0.624793i
$359$			13.9088i			0.734079i	0.930205	+	0.367040i	$0.119629\pi$
$359$			13.9088i			0.734079i	−0.930205	+	0.367040i	$0.880371\pi$
$360$		0			0
$361$		−	38.5584i		−	2.02939i
$362$	−18.2429	−	26.4290i	−0.958828	−	1.38908i
$363$		0			0
$364$	2.97476	+	6.60936i	0.155920	+	0.346425i
$365$	0.971174	+	0.260225i	0.0508336	+	0.0136208i
$366$		0			0
$367$	−5.69950	−	3.29061i	−0.297512	−	0.171768i	0.343813	−	0.939038i	$-0.388281\pi$
$367$	−5.69950	−	3.29061i	−0.297512	−	0.171768i	−0.641325	+	0.767270i	$0.721615\pi$
$368$	−0.747089	−	0.152495i	−0.0389447	−	0.00794935i
$369$		0			0
$370$	−1.09494	+	0.390231i	−0.0569231	+	0.0202871i
$371$	−15.5196	+	4.15847i	−0.805738	+	0.215897i
$372$		0			0
$373$	25.3268	+	6.78631i	1.31137	+	0.351382i	0.845740	−	0.533595i	$-0.179159\pi$
$373$	25.3268	+	6.78631i	1.31137	+	0.351382i	0.465635	+	0.884977i	$0.345826\pi$
$374$	0.143786	+	1.78094i	0.00743501	+	0.0920901i
$375$		0			0
$376$	−13.4564	−	24.4290i	−0.693959	−	1.25983i
$377$	14.5395			0.748821
$378$		0			0
$379$	−5.68301	−	5.68301i	−0.291917	−	0.291917i	0.545920	−	0.837837i	$-0.316180\pi$
$379$	−5.68301	−	5.68301i	−0.291917	−	0.291917i	−0.837837	+	0.545920i	$0.816180\pi$
$380$	0.430919	+	2.65129i	0.0221057	+	0.136008i
$381$		0			0
$382$	−7.44489	−	6.33255i	−0.380914	−	0.324001i
$383$	−6.91570	−	11.9783i	−0.353376	−	0.612065i	0.633463	−	0.773773i	$-0.281633\pi$
$383$	−6.91570	−	11.9783i	−0.353376	−	0.612065i	−0.986839	+	0.161708i	$0.948300\pi$
$384$		0			0
$385$	0.0733472	−	0.127041i	0.00373812	−	0.00647461i
$386$	20.8591	−	7.43409i	1.06170	−	0.378385i
$387$		0			0
$388$	3.08816	−	2.52148i	0.156777	−	0.128009i
$389$	21.4044	−	5.73529i	1.08525	−	0.290791i	0.328503	−	0.944503i	$-0.393456\pi$
$389$	21.4044	−	5.73529i	1.08525	−	0.290791i	0.756743	+	0.653712i	$0.226789\pi$
$390$		0			0
$391$	0.341293	+	0.591136i	0.0172599	+	0.0298950i
$392$	4.19636	+	0.0844210i	0.211948	+	0.00426390i
$393$		0			0
$394$	−13.5755	+	9.37065i	−0.683924	+	0.472086i
$395$	−1.85909	+	1.85909i	−0.0935410	+	0.0935410i
$396$		0			0
$397$	−11.5684	−	11.5684i	−0.580603	−	0.580603i	0.354466	−	0.935069i	$-0.384663\pi$
$397$	−11.5684	−	11.5684i	−0.580603	−	0.580603i	−0.935069	+	0.354466i	$0.884663\pi$
$398$	−1.40890	+	7.68844i	−0.0706216	+	0.385387i
$399$		0			0
$400$	6.29425	+	18.8516i	0.314713	+	0.942582i
$401$	−19.4681	+	11.2399i	−0.972191	+	0.561295i	−0.899904	−	0.436089i	$-0.856363\pi$
$401$	−19.4681	+	11.2399i	−0.972191	+	0.561295i	−0.0722876	+	0.997384i	$0.523030\pi$
$402$		0			0
$403$	−1.58589	−	5.91861i	−0.0789987	−	0.294827i
$404$	31.8616	+	3.21860i	1.58518	+	0.160131i
$405$		0			0
$406$	−13.4167	+	28.2757i	−0.665861	+	1.40330i
$407$	−1.41873	−	0.819104i	−0.0703238	−	0.0406015i
$408$		0			0
$409$	−6.68684	+	3.86065i	−0.330643	+	0.190897i	−0.656127	−	0.754651i	$-0.727806\pi$
$409$	−6.68684	+	3.86065i	−0.330643	+	0.190897i	0.325484	+	0.945548i	$0.394473\pi$
$410$	−0.171465	−	2.12377i	−0.00846806	−	0.104886i
$411$		0			0
$412$	5.21162	+	32.0652i	0.256758	+	1.57974i
$413$	4.62471	−	4.62471i	0.227567	−	0.227567i
$414$		0			0
$415$		−	2.26585i		−	0.111226i
$416$	3.42164	+	8.03002i	0.167760	+	0.393704i
$417$		0			0
$418$	−2.45272	+	2.88355i	−0.119966	+	0.141039i
$419$	0.801918	−	2.99280i	0.0391763	−	0.146208i	−0.943567	−	0.331181i	$-0.892553\pi$
$419$	0.801918	−	2.99280i	0.0391763	−	0.146208i	0.982744	+	0.184973i	$0.0592197\pi$
$420$		0			0
$421$	−4.47770	−	16.7110i	−0.218230	−	0.814445i	−0.985005	−	0.172528i	$-0.944806\pi$
$421$	−4.47770	−	16.7110i	−0.218230	−	0.814445i	0.766775	−	0.641916i	$-0.221860\pi$
$422$	2.56310	−	5.40173i	0.124770	−	0.262952i
$423$		0			0
$424$	−18.7870	+	4.63106i	−0.912379	+	0.224904i
$425$	8.89591	−	15.4082i	0.431515	−	0.747406i
$426$		0			0
$427$	−5.01811	+	18.7278i	−0.242843	+	0.906303i
$428$	5.37154	−	2.41763i	0.259643	−	0.116861i
$429$		0			0
$430$	−1.04372	−	0.191260i	−0.0503326	−	0.00922338i
$431$	−12.1601			−0.585730			−0.292865	−	0.956154i	$-0.594609\pi$
$431$	−12.1601			−0.585730			−0.292865	+	0.956154i	$0.594609\pi$
$432$		0			0
$433$	18.6952			0.898436			0.449218	−	0.893422i	$-0.351703\pi$
$433$	18.6952			0.898436			0.449218	+	0.893422i	$0.351703\pi$
$434$	12.9737	+	2.37741i	0.622756	+	0.114119i
$435$		0			0
$436$	−8.94086	−	19.8650i	−0.428190	−	0.951359i
$437$	−0.374306	+	1.39693i	−0.0179055	+	0.0668241i
$438$		0			0
$439$	−18.2383	+	31.5896i	−0.870466	+	1.50769i	−0.00895100	+	0.999960i	$0.502849\pi$
$439$	−18.2383	+	31.5896i	−0.870466	+	1.50769i	−0.861515	+	0.507732i	$0.830484\pi$
$440$	0.0913905	−	0.151186i	0.00435687	−	0.00720753i
$441$		0			0
$442$	3.34970	−	7.05948i	0.159329	−	0.335785i
$443$	−3.53871	−	13.2067i	−0.168129	−	0.627467i	−0.997620	−	0.0689472i	$-0.978036\pi$
$443$	−3.53871	−	13.2067i	−0.168129	−	0.627467i	0.829491	−	0.558520i	$-0.188631\pi$
$444$		0			0
$445$	0.140072	−	0.522757i	0.00664007	−	0.0247811i
$446$	−6.88301	+	8.09204i	−0.325920	+	0.383169i
$447$		0			0
$448$	−18.7738	−	0.755678i	−0.886981	−	0.0357024i
$449$			8.41249i			0.397010i	0.980100	+	0.198505i	$0.0636086\pi$
$449$			8.41249i			0.397010i	−0.980100	+	0.198505i	$0.936391\pi$
$450$		0			0
$451$	2.12333	−	2.12333i	0.0999838	−	0.0999838i
$452$	23.5099	−	3.82111i	1.10581	−	0.179730i
$453$		0			0
$454$	0.743786	+	9.21255i	0.0349076	+	0.432366i
$455$	−0.555585	+	0.320767i	−0.0260462	+	0.0150378i
$456$		0			0
$457$	−22.1026	−	12.7609i	−1.03392	−	0.596932i	−0.115812	−	0.993271i	$-0.536947\pi$
$457$	−22.1026	−	12.7609i	−1.03392	−	0.596932i	−0.918104	+	0.396339i	$0.870280\pi$
$458$	−0.682935	+	1.43928i	−0.0319114	+	0.0672533i
$459$		0			0
$460$	0.00678320	−	0.0671485i	0.000316268	−	0.00313081i
$461$	2.23068	+	8.32500i	0.103893	+	0.387734i	0.998217	−	0.0596856i	$-0.0190098\pi$
$461$	2.23068	+	8.32500i	0.103893	+	0.387734i	−0.894324	+	0.447419i	$0.852343\pi$
$462$		0			0
$463$	−13.7328	+	7.92866i	−0.638219	+	0.368476i	−0.783928	−	0.620852i	$-0.786787\pi$
$463$	−13.7328	+	7.92866i	−0.638219	+	0.368476i	0.145709	+	0.989327i	$0.453454\pi$
$464$	−16.8392	+	33.7202i	−0.781742	+	1.56542i
$465$		0			0
$466$	−3.55358	+	19.3921i	−0.164616	+	0.898322i
$467$	3.55396	+	3.55396i	0.164458	+	0.164458i	0.784538	−	0.620081i	$-0.212900\pi$
$467$	3.55396	+	3.55396i	0.164458	+	0.164458i	−0.620081	+	0.784538i	$0.712900\pi$
$468$		0			0
$469$	19.6936	−	19.6936i	0.909364	−	0.909364i
$470$	2.03162	−	1.40235i	0.0937115	−	0.0646855i
$471$		0			0
$472$	5.68038	−	5.45633i	0.261460	−	0.251148i
$473$	−0.747721	−	1.29509i	−0.0343803	−	0.0595484i
$474$		0			0
$475$	36.4114	−	9.75641i	1.67067	−	0.447655i
$476$	10.6379	+	13.0287i	0.487588	+	0.597168i
$477$		0			0
$478$	−39.4514	+	14.0603i	−1.80446	+	0.643103i
$479$	−1.39132	+	2.40984i	−0.0635712	+	0.110109i	−0.896059	−	0.443934i	$-0.853582\pi$
$479$	−1.39132	+	2.40984i	−0.0635712	+	0.110109i	0.832488	+	0.554043i	$0.186916\pi$
$480$		0			0
$481$	3.58217	+	6.20450i	0.163333	+	0.282901i
$482$	−12.9957	−	11.0540i	−0.591938	−	0.503497i
$483$		0			0
$484$	−21.4693	+	3.48945i	−0.975877	+	0.158611i
$485$	0.249525	+	0.249525i	0.0113304	+	0.0113304i
$486$		0			0
$487$	−4.42582			−0.200553			−0.100277	−	0.994960i	$-0.531973\pi$
$487$	−4.42582			−0.200553			−0.100277	+	0.994960i	$0.531973\pi$
$488$	−6.49566	+	22.4276i	−0.294045	+	1.01525i
$489$		0			0
$490$	0.0298966	+	0.370300i	0.00135059	+	0.0167285i
$491$	1.57973	+	0.423288i	0.0712923	+	0.0191027i	0.294289	−	0.955717i	$-0.404917\pi$
$491$	1.57973	+	0.423288i	0.0712923	+	0.0191027i	−0.222997	+	0.974819i	$0.571584\pi$
$492$		0			0
$493$	32.5914	−	8.73283i	1.46784	−	0.393307i
$494$	15.5946	−	5.55785i	0.701635	−	0.250059i
$495$		0			0
$496$	15.5633	+	3.17676i	0.698812	+	0.142641i
$497$	−2.31131	−	1.33443i	−0.103676	−	0.0598575i
$498$		0			0
$499$	4.51417	+	1.20957i	0.202082	+	0.0541478i	0.358440	−	0.933553i	$-0.383309\pi$
$499$	4.51417	+	1.20957i	0.202082	+	0.0541478i	−0.156358	+	0.987700i	$0.549975\pi$
$500$	−3.21844	+	1.44856i	−0.143933	+	0.0647817i
$501$		0			0
$502$	−15.8329	−	22.9375i	−0.706656	−	1.02375i
$503$		−	18.8954i		−	0.842506i	−0.906943	−	0.421253i	$-0.861590\pi$
$503$		−	18.8954i		−	0.842506i	0.906943	−	0.421253i	$-0.138410\pi$
$504$		0			0
$505$			2.83451i			0.126134i
$506$	0.0782788	−	0.0540329i	0.00347992	−	0.00240205i
$507$		0			0
$508$	5.97979	−	15.7681i	0.265310	−	0.699598i
$509$	−28.2383	−	7.56644i	−1.25164	−	0.335377i	−0.428672	−	0.903460i	$-0.641018\pi$
$509$	−28.2383	−	7.56644i	−1.25164	−	0.335377i	−0.822971	+	0.568084i	$0.807685\pi$
$510$		0			0
$511$	11.5522	+	6.66965i	0.511038	+	0.295048i
$512$	−22.5862	−	1.36462i	−0.998180	−	0.0603083i
$513$		0			0
$514$	11.5139	+	32.3065i	0.507856	+	1.42498i
$515$	−2.77744	+	0.744213i	−0.122389	+	0.0327939i
$516$		0			0
$517$	3.36056	+	0.900458i	0.147797	+	0.0396021i
$518$	−15.3718	+	1.24106i	−0.675397	+	0.0545290i
$519$		0			0
$520$	−0.676719	+	0.372760i	−0.0296761	+	0.0163466i
$521$	−18.9291			−0.829299			−0.414649	−	0.909981i	$-0.636096\pi$
$521$	−18.9291			−0.829299			−0.414649	+	0.909981i	$0.636096\pi$
$522$		0			0
$523$	−22.0490	−	22.0490i	−0.964137	−	0.964137i	0.0352421	−	0.999379i	$-0.488780\pi$
$523$	−22.0490	−	22.0490i	−0.964137	−	0.964137i	−0.999379	+	0.0352421i	$0.988780\pi$
$524$	−6.36106	+	8.83011i	−0.277884	+	0.385745i
$525$		0			0
$526$	28.2570	−	33.2205i	1.23207	−	1.44848i
$527$	−7.10978	−	12.3145i	−0.309707	−	0.536428i
$528$		0			0
$529$	−11.4818	+	19.8871i	−0.499210	+	0.864657i
$530$	−0.574962	−	1.61327i	−0.0249747	−	0.0700759i
$531$		0			0
$532$	−3.58173	+	35.4564i	−0.155288	+	1.53723i
$533$	−12.6848	+	3.39888i	−0.549439	+	0.147222i
$534$		0			0
$535$	0.260693	+	0.451533i	0.0112707	+	0.0195215i
$536$	24.1889	−	23.2349i	1.04480	−	1.00359i
$537$		0			0
$538$	5.95746	+	8.63073i	0.256845	+	0.372097i
$539$	−0.370224	+	0.370224i	−0.0159467	+	0.0159467i
$540$		0			0
$541$	−16.0780	−	16.0780i	−0.691246	−	0.691246i	0.271260	−	0.962506i	$-0.412560\pi$
$541$	−16.0780	−	16.0780i	−0.691246	−	0.691246i	−0.962506	+	0.271260i	$0.912560\pi$
$542$	−9.49801	−	1.74050i	−0.407975	−	0.0747608i
$543$		0			0
$544$	12.4929	+	15.9448i	0.535630	+	0.683627i
$545$	1.66986	−	0.964091i	0.0715287	−	0.0412971i
$546$		0			0
$547$	2.61213	+	9.74859i	0.111686	+	0.416819i	0.999018	−	0.0443131i	$-0.0141099\pi$
$547$	2.61213	+	9.74859i	0.111686	+	0.416819i	−0.887331	+	0.461133i	$0.847443\pi$
$548$	−5.02407	+	4.10215i	−0.214617	+	0.175235i
$549$		0			0
$550$	−2.23988	−	1.06281i	−0.0955087	−	0.0453185i
$551$	61.9103	+	35.7439i	2.63747	+	1.52274i
$552$		0			0
$553$	−30.2083	+	17.4408i	−1.28459	+	0.741657i
$554$	9.25944	−	0.747572i	0.393396	−	0.0317613i
$555$		0			0
$556$	15.9910	−	22.1979i	0.678168	−	0.941399i
$557$	9.47553	−	9.47553i	0.401491	−	0.401491i	−0.477267	−	0.878758i	$-0.658373\pi$
$557$	9.47553	−	9.47553i	0.401491	−	0.401491i	0.878758	+	0.477267i	$0.158373\pi$
$558$		0			0
$559$			6.53998i			0.276612i
$560$	−0.100465	−	1.66003i	−0.00424543	−	0.0701490i
$561$		0			0
$562$	−4.95291	−	4.21290i	−0.208926	−	0.177710i
$563$	−1.51015	+	5.63595i	−0.0636451	+	0.237527i	−0.990419	−	0.138092i	$-0.955903\pi$
$563$	−1.51015	+	5.63595i	−0.0636451	+	0.237527i	0.926774	+	0.375619i	$0.122570\pi$
$564$		0			0
$565$	0.545650	+	2.03639i	0.0229557	+	0.0856717i
$566$	−11.1991	−	5.31394i	−0.470734	−	0.223361i
$567$		0			0
$568$	−2.75059	−	1.66270i	−0.115412	−	0.0697655i
$569$	−13.1217	+	22.7275i	−0.550090	+	0.952784i	0.448177	+	0.893945i	$0.352073\pi$
$569$	−13.1217	+	22.7275i	−0.550090	+	0.952784i	−0.998267	+	0.0588397i	$0.981260\pi$
$570$		0			0
$571$	0.417246	−	1.55718i	0.0174612	−	0.0651661i	−0.956646	−	0.291255i	$-0.905927\pi$
$571$	0.417246	−	1.55718i	0.0174612	−	0.0651661i	0.974107	+	0.226089i	$0.0725939\pi$
$572$	−1.01809	−	0.386093i	−0.0425685	−	0.0161433i
$573$		0			0
$574$	5.09527	−	27.8052i	0.212673	−	1.16057i
$575$	−0.947143			−0.0394986
$576$		0			0
$577$	29.9562			1.24709			0.623546	−	0.781787i	$-0.285691\pi$
$577$	29.9562			1.24709			0.623546	+	0.781787i	$0.285691\pi$
$578$	−1.06496	+	5.81158i	−0.0442967	+	0.241730i
$579$		0			0
$580$	−3.11935	−	1.18296i	−0.129524	−	0.0491197i
$581$	7.78051	−	29.0372i	0.322790	−	1.20467i
$582$		0			0
$583$	1.20686	−	2.09034i	0.0499830	−	0.0865731i
$584$	13.7478	+	8.31038i	0.568887	+	0.343886i
$585$		0			0
$586$	22.0519	+	10.4636i	0.910957	+	0.432246i
$587$	−1.00931	−	3.76680i	−0.0416587	−	0.155473i	0.941963	−	0.335716i	$-0.108978\pi$
$587$	−1.00931	−	3.76680i	−0.0416587	−	0.155473i	−0.983622	+	0.180243i	$0.942312\pi$
$588$		0			0
$589$	7.79751	−	29.1007i	0.321291	−	1.19907i
$590$	0.531041	+	0.451698i	0.0218626	+	0.0185961i
$591$		0			0
$592$	−18.5384	+	1.12195i	−0.761922	+	0.0461117i
$593$		−	33.7168i		−	1.38459i	−0.721617	−	0.692293i	$-0.756601\pi$
$593$		−	33.7168i		−	1.38459i	0.721617	−	0.692293i	$-0.243399\pi$
$594$		0			0
$595$	−1.05272	+	1.05272i	−0.0431575	+	0.0431575i
$596$	14.8189	−	20.5709i	0.607007	−	0.842617i
$597$		0			0
$598$	−0.414621	+	0.0334749i	−0.0169551	+	0.00136889i
$599$	23.4461	−	13.5366i	0.957981	−	0.553091i	0.0624300	−	0.998049i	$-0.480115\pi$
$599$	23.4461	−	13.5366i	0.957981	−	0.553091i	0.895551	+	0.444959i	$0.146782\pi$
$600$		0			0
$601$	25.7087	+	14.8429i	1.04868	+	0.605455i	0.922279	−	0.386524i	$-0.126324\pi$
$601$	25.7087	+	14.8429i	1.04868	+	0.605455i	0.126400	+	0.991979i	$0.459658\pi$
$602$	−12.7187	−	6.03496i	−0.518374	−	0.245966i
$603$		0			0
$604$	−2.45174	+	2.00185i	−0.0997598	+	0.0814540i
$605$	−0.498288	−	1.85964i	−0.0202583	−	0.0756050i
$606$		0			0
$607$	28.8436	−	16.6529i	1.17073	−	0.675918i	0.216874	−	0.976200i	$-0.430414\pi$
$607$	28.8436	−	16.6529i	1.17073	−	0.675918i	0.953851	+	0.300281i	$0.0970805\pi$
$608$	−5.17141	+	42.6043i	−0.209728	+	1.72783i
$609$		0			0
$610$	−2.03286	−	0.372518i	−0.0823079	−	0.0150828i
$611$	−10.7587	−	10.7587i	−0.435250	−	0.435250i
$612$		0			0
$613$	−16.1448	+	16.1448i	−0.652082	+	0.652082i	−0.953494	−	0.301412i	$-0.902542\pi$
$613$	−16.1448	+	16.1448i	−0.652082	+	0.652082i	0.301412	+	0.953494i	$0.402542\pi$
$614$	−3.50863	−	5.08304i	−0.141597	−	0.205135i
$615$		0			0
$616$	1.69033	−	1.62366i	0.0681053	−	0.0654191i
$617$	18.3244	+	31.7389i	0.737714	+	1.27776i	0.953522	+	0.301323i	$0.0974282\pi$
$617$	18.3244	+	31.7389i	0.737714	+	1.27776i	−0.215808	+	0.976436i	$0.569238\pi$
$618$		0			0
$619$	3.40743	−	0.913019i	0.136956	−	0.0366973i	−0.189690	−	0.981844i	$-0.560748\pi$
$619$	3.40743	−	0.913019i	0.136956	−	0.0366973i	0.326646	+	0.945147i	$0.394082\pi$
$620$	−0.141307	+	1.39883i	−0.00567503	+	0.0561784i
$621$		0			0
$622$	6.46233	+	18.1325i	0.259116	+	0.727046i
$623$	3.59010	−	6.21824i	0.143834	−	0.249128i
$624$		0			0
$625$	12.2655	+	21.2444i	0.490618	+	0.849776i
$626$	−9.63991	+	11.3332i	−0.385288	+	0.452966i
$627$		0			0
$628$	9.35809	−	12.9904i	0.373428	−	0.518375i
$629$	11.7563	+	11.7563i	0.468754	+	0.468754i
$630$		0			0
$631$	−10.2367			−0.407515			−0.203758	−	0.979021i	$-0.565315\pi$
$631$	−10.2367			−0.407515			−0.203758	+	0.979021i	$0.565315\pi$
$632$	−36.7946	+	20.2677i	−1.46361	+	0.806207i
$633$		0			0
$634$	27.3878	−	2.21119i	1.08771	−	0.0878175i
$635$	1.44181	+	0.386331i	0.0572164	+	0.0153311i
$636$		0			0
$637$	2.21172	−	0.592628i	0.0876315	−	0.0234808i
$638$	−1.57842	−	4.42886i	−0.0624904	−	0.175340i
$639$		0			0
$640$	−0.0807544	−	2.00118i	−0.00319210	−	0.0791036i
$641$	−13.3541	−	7.70998i	−0.527454	−	0.304526i	0.212525	−	0.977156i	$-0.431831\pi$
$641$	−13.3541	−	7.70998i	−0.527454	−	0.304526i	−0.739979	+	0.672630i	$0.765165\pi$
$642$		0			0
$643$	−18.4511	−	4.94396i	−0.727641	−	0.194971i	−0.124063	−	0.992274i	$-0.539592\pi$
$643$	−18.4511	−	4.94396i	−0.727641	−	0.194971i	−0.603579	+	0.797303i	$0.706259\pi$
$644$	0.317503	−	0.837226i	0.0125114	−	0.0329913i
$645$		0			0
$646$	31.6183	−	21.8249i	1.24401	−	0.858690i
$647$		−	0.502526i		−	0.0197563i	−0.999951	−	0.00987817i	$-0.996856\pi$
$647$		−	0.502526i		−	0.0197563i	0.999951	−	0.00987817i	$-0.00314437\pi$
$648$		0			0
$649$			0.982536i			0.0385679i
$650$	6.15925	+	8.92307i	0.241586	+	0.349992i
$651$		0			0
$652$	26.4111	−	11.8872i	1.03434	−	0.465538i
$653$	29.9343	+	8.02087i	1.17142	+	0.313881i	0.791518	−	0.611146i	$-0.209291\pi$
$653$	29.9343	+	8.02087i	1.17142	+	0.313881i	0.379902	+	0.925027i	$0.375958\pi$
$654$		0			0
$655$	−0.834206	−	0.481629i	−0.0325951	−	0.0188188i
$656$	6.80845	−	33.3553i	0.265825	−	1.30231i
$657$		0			0
$658$	30.8509	−	10.9951i	1.20269	−	0.428634i
$659$	−28.4091	+	7.61220i	−1.10666	+	0.296529i	−0.765475	−	0.643466i	$-0.777496\pi$
$659$	−28.4091	+	7.61220i	−1.10666	+	0.296529i	−0.341188	+	0.939995i	$0.610829\pi$
$660$		0			0
$661$	22.3717	+	5.99448i	0.870159	+	0.233158i	0.666156	−	0.745812i	$-0.267938\pi$
$661$	22.3717	+	5.99448i	0.870159	+	0.233158i	0.204002	+	0.978970i	$0.434605\pi$
$662$	1.45163	+	17.9799i	0.0564190	+	0.698807i
$663$		0			0
$664$	10.0714	−	34.7737i	0.390847	−	1.34948i
$665$	−3.15430			−0.122319
$666$		0			0
$667$	−1.27010	−	1.27010i	−0.0491786	−	0.0491786i
$668$	23.1824	−	3.76788i	0.896955	−	0.145784i
$669$		0			0
$670$	2.26135	+	1.92348i	0.0873636	+	0.0743107i
$671$	−1.45634	−	2.52246i	−0.0562214	−	0.0973784i
$672$		0			0
$673$	20.8639	−	36.1374i	0.804246	−	1.39300i	−0.112553	−	0.993646i	$-0.535903\pi$
$673$	20.8639	−	36.1374i	0.804246	−	1.39300i	0.916799	−	0.399349i	$-0.130764\pi$
$674$	15.3934	−	5.48615i	0.592933	−	0.211319i
$675$		0			0
$676$	−13.4323	−	16.4510i	−0.516625	−	0.632731i
$677$	26.8914	−	7.20552i	1.03352	−	0.276931i	0.298094	−	0.954537i	$-0.403649\pi$
$677$	26.8914	−	7.20552i	1.03352	−	0.276931i	0.735425	+	0.677606i	$0.236983\pi$
$678$		0			0
$679$	2.34088	+	4.05452i	0.0898348	+	0.155598i
$680$	−1.29303	+	1.24203i	−0.0495853	+	0.0476296i
$681$		0			0
$682$	−1.63070	+	1.12561i	−0.0624426	+	0.0431017i
$683$	31.1964	−	31.1964i	1.19370	−	1.19370i	0.217674	−	0.976022i	$-0.430153\pi$
$683$	31.1964	−	31.1964i	1.19370	−	1.19370i	0.976022	−	0.217674i	$-0.0698470\pi$
$684$		0			0
$685$	−0.405948	−	0.405948i	−0.0155105	−	0.0155105i
$686$	−5.07921	+	27.7176i	−0.193925	+	1.05826i
$687$		0			0
$688$	−15.1676	−	7.57443i	−0.578261	−	0.288773i
$689$	−9.14164	+	5.27793i	−0.348269	+	0.201073i
$690$		0			0
$691$	−8.56164	−	31.9525i	−0.325700	−	1.21553i	−0.913606	−	0.406600i	$-0.866714\pi$
$691$	−8.56164	−	31.9525i	−0.325700	−	1.21553i	0.587906	−	0.808929i	$-0.299953\pi$
$692$	2.98647	−	29.5637i	0.113529	−	1.12384i
$693$		0			0
$694$	4.07468	−	8.58737i	0.154673	−	0.325972i
$695$	2.09710	+	1.21076i	0.0795474	+	0.0459267i
$696$		0			0
$697$	−26.3925	+	15.2377i	−0.999686	+	0.577169i
$698$	−1.03259	−	12.7897i	−0.0390843	−	0.484099i
$699$		0			0
$700$	−23.0368	+	3.74421i	−0.870709	+	0.141518i
$701$	−22.9365	+	22.9365i	−0.866299	+	0.866299i	−0.992061	−	0.125761i	$-0.959863\pi$
$701$	−22.9365	+	22.9365i	−0.866299	+	0.866299i	0.125761	+	0.992061i	$0.459863\pi$
$702$		0			0
$703$			35.2257i			1.32856i
$704$	2.07456	−	1.91401i	0.0781879	−	0.0721371i
$705$		0			0
$706$	−11.4373	+	13.4463i	−0.430449	+	0.506059i
$707$	−9.73316	+	36.3246i	−0.366053	+	1.36613i
$708$		0			0
$709$	2.89716	+	10.8123i	0.108805	+	0.406066i	0.998749	−	0.0500039i	$-0.0159234\pi$
$709$	2.89716	+	10.8123i	0.108805	+	0.406066i	−0.889944	+	0.456070i	$0.849257\pi$
$710$	0.121955	−	0.257021i	0.00457690	−	0.00964581i
$711$		0			0
$712$	4.47326	−	7.40007i	0.167643	−	0.277329i
$713$	−0.378487	+	0.655559i	−0.0141745	+	0.0245509i
$714$		0			0
$715$	0.0249440	−	0.0930922i	0.000932852	−	0.00348145i
$716$	−12.0789	−	26.8370i	−0.451408	−	1.00295i
$717$		0			0
$718$	−19.3479	−	3.54547i	−0.722056	−	0.132316i
$719$	45.6552			1.70265			0.851325	−	0.524639i	$-0.175800\pi$
$719$	45.6552			1.70265			0.851325	+	0.524639i	$0.175800\pi$
$720$		0			0
$721$	−38.1488			−1.42074
$722$	53.6367	+	9.82885i	1.99615	+	0.365792i
$723$		0			0
$724$	41.4144	−	18.6399i	1.53915	−	0.692746i
$725$	−12.1175	+	45.2232i	−0.450033	+	1.67955i
$726$		0			0
$727$	−14.6537	+	25.3810i	−0.543477	+	0.941331i	0.455224	+	0.890377i	$0.349559\pi$
$727$	−14.6537	+	25.3810i	−0.543477	+	0.941331i	−0.998701	+	0.0509534i	$0.983774\pi$
$728$	−9.95225	+	2.45326i	−0.368855	+	0.0909237i
$729$		0			0
$730$	−0.609547	+	1.28462i	−0.0225603	+	0.0475459i
$731$	3.92810	+	14.6599i	0.145286	+	0.542215i
$732$		0			0
$733$	1.38877	−	5.18294i	0.0512952	−	0.191436i	−0.935524	−	0.353263i	$-0.885072\pi$
$733$	1.38877	−	5.18294i	0.0512952	−	0.191436i	0.986819	+	0.161827i	$0.0517386\pi$
$734$	6.03026	−	7.08949i	0.222581	−	0.261678i
$735$		0			0
$736$	0.402567	−	1.00037i	0.0148388	−	0.0368740i
$737$			4.18397i			0.154119i
$738$		0			0
$739$	25.3597	−	25.3597i	0.932873	−	0.932873i	−0.0650119	−	0.997884i	$-0.520709\pi$
$739$	25.3597	−	25.3597i	0.932873	−	0.932873i	0.997884	+	0.0650119i	$0.0207085\pi$
$740$	−0.263722	−	1.62259i	−0.00969461	−	0.0596475i
$741$		0			0
$742$	−1.82856	−	22.6486i	−0.0671286	−	0.831456i
$743$	−2.86105	+	1.65183i	−0.104962	+	0.0605998i	−0.551562	−	0.834134i	$-0.685968\pi$
$743$	−2.86105	+	1.65183i	−0.104962	+	0.0605998i	0.446600	+	0.894734i	$0.352635\pi$
$744$		0			0
$745$	1.94339	+	1.12202i	0.0712004	+	0.0411075i
$746$	−15.8961	+	33.5010i	−0.581998	+	1.22656i
$747$		0			0
$748$	−2.51403	−	0.253962i	−0.0919220	−	0.00928577i
$749$	1.79034	+	6.68164i	0.0654176	+	0.244142i
$750$		0			0
$751$	−15.0045	+	8.66287i	−0.547523	+	0.316112i	−0.748122	−	0.663561i	$-0.769044\pi$
$751$	−15.0045	+	8.66287i	−0.547523	+	0.316112i	0.200599	+	0.979673i	$0.435711\pi$
$752$	37.4122	−	12.4913i	1.36428	−	0.455511i
$753$		0			0
$754$	−3.70623	+	20.2252i	−0.134973	+	0.736557i
$755$	−0.198102	−	0.198102i	−0.00720967	−	0.00720967i
$756$		0			0
$757$	−29.0206	+	29.0206i	−1.05477	+	1.05477i	−0.0563619	+	0.998410i	$0.517950\pi$
$757$	−29.0206	+	29.0206i	−1.05477	+	1.05477i	−0.998410	+	0.0563619i	$0.982050\pi$
$758$	9.35401	−	6.45671i	0.339753	−	0.234518i
$759$		0			0
$760$	−3.79792	−	0.0764054i	−0.137765	−	0.00277152i
$761$	9.85285	+	17.0656i	0.357166	+	0.618629i	0.987486	−	0.157706i	$-0.0504098\pi$
$761$	9.85285	+	17.0656i	0.357166	+	0.618629i	−0.630320	+	0.776335i	$0.717076\pi$
$762$		0			0
$763$	24.7100	−	6.62101i	0.894560	−	0.239697i
$764$	10.7067	−	8.74200i	0.387353	−	0.316274i
$765$		0			0
$766$	18.4253	−	6.56671i	0.665735	−	0.237265i
$767$	2.14845	−	3.72123i	0.0775761	−	0.134366i
$768$		0			0
$769$	−20.5479	−	35.5899i	−0.740974	−	1.28341i	−0.952052	−	0.305936i	$-0.901031\pi$
$769$	−20.5479	−	35.5899i	−0.740974	−	1.28341i	0.211078	−	0.977469i	$-0.432303\pi$
$770$	0.158024	+	0.134413i	0.00569478	+	0.00484392i
$771$		0			0
$772$	5.02404	+	30.9111i	0.180819	+	1.11251i
$773$	−18.7350	−	18.7350i	−0.673853	−	0.673853i	0.284749	−	0.958602i	$-0.408090\pi$
$773$	−18.7350	−	18.7350i	−0.673853	−	0.673853i	−0.958602	+	0.284749i	$0.908090\pi$
$774$		0			0
$775$	19.7308			0.708751
$776$	2.72031	+	4.93853i	0.0976536	+	0.177283i
$777$		0			0
$778$	2.52192	+	31.2366i	0.0904153	+	1.11989i
$779$	−62.3687	−	16.7116i	−2.23459	−	0.598757i
$780$		0			0
$781$	0.387276	−	0.103770i	0.0138578	−	0.00371319i
$782$	−0.909298	+	0.324070i	−0.0325164	+	0.0115887i
$783$		0			0
$784$	−1.18712	+	5.81583i	−0.0423971	+	0.207708i
$785$	1.22724	+	0.708550i	0.0438022	+	0.0252892i
$786$		0			0
$787$	−34.0663	−	9.12803i	−1.21433	−	0.325379i	−0.405872	−	0.913930i	$-0.633032\pi$
$787$	−34.0663	−	9.12803i	−1.21433	−	0.325379i	−0.808460	+	0.588551i	$0.799699\pi$
$788$	−9.57454	−	21.2729i	−0.341079	−	0.757814i
$789$		0			0
$790$	−2.11219	−	3.05999i	−0.0751484	−	0.108869i
$791$			27.9703i			0.994511i
$792$		0			0
$793$			12.7380i			0.452338i
$794$	19.0412	−	13.1434i	0.675746	−	0.466442i
$795$		0			0
$796$	−10.3359	−	3.91969i	−0.366345	−	0.138930i
$797$	11.1029	+	2.97502i	0.393286	+	0.105381i	0.450042	−	0.893007i	$-0.351409\pi$
$797$	11.1029	+	2.97502i	0.393286	+	0.105381i	−0.0567557	+	0.998388i	$0.518076\pi$
$798$		0			0
$799$	−30.5784	−	17.6544i	−1.08179	−	0.624569i
$800$	−27.8280	+	3.95019i	−0.983869	+	0.139660i
$801$		0			0
$802$	−10.6727	−	29.9463i	−0.376867	−	1.05744i
$803$	−1.93565	+	0.518655i	−0.0683076	+	0.0183030i
$804$		0			0
$805$	0.0765542	+	0.0205126i	0.00269818	+	0.000722976i
$806$	8.63734	−	0.697346i	0.304237	−	0.0245630i
$807$		0			0
$808$	−12.5990	+	43.5007i	−0.443232	+	1.53035i
$809$	−25.8320			−0.908205			−0.454102	−	0.890950i	$-0.650040\pi$
$809$	−25.8320			−0.908205			−0.454102	+	0.890950i	$0.650040\pi$
$810$		0			0
$811$	−16.1463	−	16.1463i	−0.566973	−	0.566973i	0.364306	−	0.931279i	$-0.381306\pi$
$811$	−16.1463	−	16.1463i	−0.566973	−	0.566973i	−0.931279	+	0.364306i	$0.881306\pi$
$812$	−35.9129	−	25.8711i	−1.26030	−	0.907896i
$813$		0			0
$814$	1.50106	−	1.76473i	0.0526122	−	0.0618537i
$815$	1.28179	+	2.22013i	0.0448992	+	0.0777677i
$816$		0			0
$817$	−16.0779	+	27.8478i	−0.562495	+	0.974271i
$818$	−3.66583	−	10.2858i	−0.128173	−	0.359636i
$819$		0			0
$820$	2.99798	+	0.302850i	0.104694	+	0.0105760i
$821$	7.01329	−	1.87921i	0.244766	−	0.0655848i	−0.134350	−	0.990934i	$-0.542895\pi$
$821$	7.01329	−	1.87921i	0.244766	−	0.0655848i	0.379116	+	0.925349i	$0.376228\pi$
$822$		0			0
$823$	16.1543	+	27.9801i	0.563103	+	0.975324i	0.997223	+	0.0744686i	$0.0237261\pi$
$823$	16.1543	+	27.9801i	0.563103	+	0.975324i	−0.434120	+	0.900855i	$0.642941\pi$
$824$	−45.9328	−	0.924063i	−1.60015	−	0.0321912i
$825$		0			0
$826$	5.25433	+	7.61208i	0.182821	+	0.264858i
$827$	−12.0458	+	12.0458i	−0.418875	+	0.418875i	−0.884816	−	0.465941i	$-0.845716\pi$
$827$	−12.0458	+	12.0458i	−0.418875	+	0.418875i	0.465941	+	0.884816i	$0.345716\pi$
$828$		0			0
$829$	22.8912	+	22.8912i	0.795046	+	0.795046i	0.982310	−	0.187264i	$-0.0599619\pi$
$829$	22.8912	+	22.8912i	0.795046	+	0.795046i	−0.187264	+	0.982310i	$0.559962\pi$
$830$	3.15192	+	0.577584i	0.109405	+	0.0200482i
$831$		0			0
$832$	−12.0424	+	2.71276i	−0.417494	+	0.0940480i
$833$	4.60179	−	2.65684i	0.159443	−	0.0920542i
$834$		0			0
$835$	0.538048	+	2.00802i	0.0186199	+	0.0694905i
$836$	−3.38594	−	4.14690i	−0.117105	−	0.143423i
$837$		0			0
$838$	3.95872	+	1.87840i	0.136752	+	0.0648882i
$839$	4.97011	+	2.86949i	0.171587	+	0.0990659i	0.583334	−	0.812232i	$-0.301748\pi$
$839$	4.97011	+	2.86949i	0.171587	+	0.0990659i	−0.411747	+	0.911298i	$0.635081\pi$
$840$		0			0
$841$	−51.7783	+	29.8942i	−1.78546	+	1.03083i
$842$	24.3873	−	1.96893i	0.840440	−	0.0678540i
$843$		0			0
$844$	6.86073	+	4.94235i	0.236156	+	0.170123i
$845$	1.32925	−	1.32925i	0.0457276	−	0.0457276i
$846$		0			0
$847$		−	25.5426i		−	0.877653i
$848$	−1.65306	−	27.3142i	−0.0567664	−	0.937974i
$849$		0			0
$850$	19.1659	+	16.3023i	0.657385	+	0.559165i
$851$	0.229075	−	0.854919i	0.00785258	−	0.0293062i
$852$		0			0
$853$	12.2179	+	45.5977i	0.418331	+	1.56123i	0.778068	+	0.628180i	$0.216200\pi$
$853$	12.2179	+	45.5977i	0.418331	+	1.56123i	−0.359737	+	0.933054i	$0.617133\pi$
$854$	−24.7722	−	11.7543i	−0.847687	−	0.402225i
$855$		0			0
$856$	1.99380	+	8.08836i	0.0681467	+	0.276454i
$857$	−23.4789	+	40.6666i	−0.802023	+	1.38914i	0.116260	+	0.993219i	$0.462910\pi$
$857$	−23.4789	+	40.6666i	−0.802023	+	1.38914i	−0.918283	+	0.395926i	$0.870424\pi$
$858$		0			0
$859$	4.21294	−	15.7229i	0.143744	−	0.536459i	−0.856064	−	0.516869i	$-0.827097\pi$
$859$	4.21294	−	15.7229i	0.143744	−	0.536459i	0.999808	−	0.0195896i	$-0.00623598\pi$
$860$	0.532105	−	1.40311i	0.0181446	−	0.0478457i
$861$		0			0
$862$	3.09970	−	16.9153i	0.105576	−	0.576136i
$863$	51.2010			1.74290			0.871451	−	0.490482i	$-0.163179\pi$
$863$	51.2010			1.74290			0.871451	+	0.490482i	$0.163179\pi$
$864$		0			0
$865$	2.63008			0.0894253
$866$	−4.76557	+	26.0060i	−0.161941	+	0.883720i
$867$		0			0
$868$	−6.61419	+	17.4410i	−0.224500	+	0.591986i
$869$	1.35625	−	5.06161i	0.0460078	−	0.171703i
$870$		0			0
$871$	9.14883	−	15.8462i	0.309996	−	0.536929i
$872$	29.9123	−	7.37345i	1.01296	−	0.249697i
$873$		0			0
$874$	−1.84778	−	0.876767i	−0.0625022	−	0.0296571i
$875$	−1.07271	−	4.00341i	−0.0362642	−	0.135340i
$876$		0			0
$877$	8.77699	−	32.7562i	0.296378	−	1.10610i	−0.643739	−	0.765245i	$-0.722618\pi$
$877$	8.77699	−	32.7562i	0.296378	−	1.10610i	0.940117	−	0.340852i	$-0.110716\pi$
$878$	−39.2937	−	33.4229i	−1.32610	−	1.12797i
$879$		0			0
$880$	0.187012	+	0.165667i	0.00630416	+	0.00558465i
$881$			54.6465i			1.84109i	0.390639	+	0.920544i	$0.372254\pi$
$881$			54.6465i			1.84109i	−0.390639	+	0.920544i	$0.627746\pi$
$882$		0			0
$883$	6.31259	−	6.31259i	0.212436	−	0.212436i	−0.592866	−	0.805301i	$-0.702004\pi$
$883$	6.31259	−	6.31259i	0.212436	−	0.212436i	0.805301	+	0.592866i	$0.202004\pi$
$884$	8.96622	+	6.45911i	0.301567	+	0.217244i
$885$		0			0
$886$	19.2732	−	1.55604i	0.647495	−	0.0522763i
$887$	−33.1288	+	19.1269i	−1.11236	+	0.642219i	−0.939438	−	0.342718i	$-0.888652\pi$
$887$	−33.1288	+	19.1269i	−1.11236	+	0.642219i	−0.172917	+	0.984936i	$0.555319\pi$
$888$		0			0
$889$	17.1504	+	9.90179i	0.575206	+	0.332095i
$890$	0.691476	+	0.328103i	0.0231783	+	0.0109980i
$891$		0			0
$892$	−9.50190	−	11.6373i	−0.318147	−	0.389647i
$893$	−19.3622	−	72.2606i	−0.647930	−	2.41811i
$894$		0			0
$895$	2.25593	−	1.30246i	0.0754074	−	0.0435365i
$896$	5.83679	−	25.9227i	0.194994	−	0.866018i
$897$		0			0
$898$	−11.7022	−	2.14441i	−0.390508	−	0.0715600i
$899$	26.4587	+	26.4587i	0.882447	+	0.882447i
$900$		0			0
$901$	−17.3216	+	17.3216i	−0.577066	+	0.577066i
$902$	2.41241	+	3.49492i	0.0803244	+	0.116368i
$903$		0			0
$904$	−0.677514	+	33.6775i	−0.0225338	+	1.12010i
$905$	2.00993	+	3.48131i	0.0668124	+	0.115723i
$906$		0			0
$907$	−10.5600	+	2.82954i	−0.350639	+	0.0939534i	−0.429840	−	0.902905i	$-0.641430\pi$
$907$	−10.5600	+	2.82954i	−0.350639	+	0.0939534i	0.0792006	+	0.996859i	$0.474763\pi$
$908$	−13.0047	−	1.31371i	−0.431577	−	0.0435970i
$909$		0			0
$910$	−0.304580	−	0.854613i	−0.0100967	−	0.0283302i
$911$	−4.41606	+	7.64884i	−0.146311	+	0.253417i	−0.929861	−	0.367911i	$-0.880073\pi$
$911$	−4.41606	+	7.64884i	−0.146311	+	0.253417i	0.783551	+	0.621328i	$0.213407\pi$
$912$		0			0
$913$	2.25804	+	3.91103i	0.0747301	+	0.129436i
$914$	23.3853	−	27.4930i	0.773516	−	0.909387i
$915$		0			0
$916$	−1.82803	−	1.31688i	−0.0603998	−	0.0435110i
$917$	−9.03666	−	9.03666i	−0.298417	−	0.298417i
$918$		0			0
$919$	−5.12206			−0.168961			−0.0844806	−	0.996425i	$-0.526923\pi$
$919$	−5.12206			−0.168961			−0.0844806	+	0.996425i	$0.526923\pi$
$920$	0.0916778	+	0.0265525i	0.00302253	+	0.000875409i
$921$		0			0
$922$	−12.1491	+	0.980873i	−0.400110	+	0.0323033i
$923$	−1.69366	−	0.453816i	−0.0557476	−	0.0149375i
$924$		0			0
$925$	−22.2838	+	5.97091i	−0.732685	+	0.196322i
$926$	−7.52855	−	21.1242i	−0.247404	−	0.694183i
$927$		0			0
$928$	−42.6141	−	32.0198i	−1.39888	−	1.05110i
$929$	7.86161	+	4.53890i	0.257931	+	0.148916i	0.623390	−	0.781911i	$-0.285755\pi$
$929$	7.86161	+	4.53890i	0.257931	+	0.148916i	−0.365459	+	0.930827i	$0.619088\pi$
$930$		0			0
$931$	10.8746	+	2.91384i	0.356401	+	0.0954973i
$932$	−26.0696	−	9.88641i	−0.853937	−	0.323840i
$933$		0			0
$934$	−5.84967	+	4.03780i	−0.191407	+	0.132121i
$935$		−	0.223655i		−	0.00731431i
$936$		0			0
$937$			8.98159i			0.293416i	0.989180	+	0.146708i	$0.0468677\pi$
$937$			8.98159i			0.293416i	−0.989180	+	0.146708i	$0.953132\pi$
$938$	22.3747	+	32.4148i	0.730559	+	1.05838i
$939$		0			0
$940$	1.43286	+	3.18355i	0.0467348	+	0.103836i
$941$	−38.5789	−	10.3372i	−1.25764	−	0.336982i	−0.432354	−	0.901704i	$-0.642317\pi$
$941$	−38.5789	−	10.3372i	−1.25764	−	0.336982i	−0.825282	+	0.564721i	$0.808984\pi$
$942$		0			0
$943$	1.40500	+	0.811176i	0.0457530	+	0.0264155i
$944$	6.14206	+	9.29255i	0.199907	+	0.302447i
$945$		0			0
$946$	1.99214	−	0.709989i	0.0647700	−	0.0230837i
$947$	7.36412	−	1.97321i	0.239302	−	0.0641207i	−0.137175	−	0.990547i	$-0.543802\pi$
$947$	7.36412	−	1.97321i	0.239302	−	0.0641207i	0.376476	+	0.926426i	$0.377136\pi$
$948$		0			0
$949$	8.46512	+	2.26822i	0.274789	+	0.0736296i
$950$	4.29009	+	53.1371i	0.139189	+	1.72400i
$951$		0			0
$952$	−20.8352	+	11.4768i	−0.675274	+	0.371964i
$953$	−9.35277			−0.302966			−0.151483	−	0.988460i	$-0.548405\pi$
$953$	−9.35277			−0.302966			−0.151483	+	0.988460i	$0.548405\pi$
$954$		0			0
$955$	0.865105	+	0.865105i	0.0279941	+	0.0279941i
$956$	−9.50209	−	58.4630i	−0.307320	−	1.89083i
$957$		0			0
$958$	−2.99756	−	2.54969i	−0.0968466	−	0.0823768i
$959$	−3.80834	−	6.59623i	−0.122978	−	0.213003i
$960$		0			0
$961$	−7.61538	+	13.1902i	−0.245658	+	0.425491i
$962$	−9.54389	+	3.40140i	−0.307707	+	0.109665i
$963$		0			0
$964$	18.6894	−	15.2599i	0.601946	−	0.491489i
$965$	−2.67747	+	0.717426i	−0.0861908	+	0.0230948i
$966$		0			0
$967$	5.00369	+	8.66664i	0.160908	+	0.278700i	0.935194	−	0.354135i	$-0.115225\pi$
$967$	5.00369	+	8.66664i	0.160908	+	0.278700i	−0.774287	+	0.632835i	$0.781891\pi$
$968$	0.618707	−	30.7544i	0.0198860	−	0.988483i
$969$		0			0
$970$	−0.410708	+	0.283496i	−0.0131870	+	0.00910251i
$971$	35.7927	−	35.7927i	1.14864	−	1.14864i	0.161822	−	0.986820i	$-0.448263\pi$
$971$	35.7927	−	35.7927i	1.14864	−	1.14864i	0.986820	−	0.161822i	$-0.0517370\pi$
$972$		0			0
$973$	22.7171	+	22.7171i	0.728276	+	0.728276i
$974$	1.12818	−	6.15654i	0.0361492	−	0.197268i
$975$		0			0
$976$	−29.5421	−	14.7528i	−0.945620	−	0.472225i
$977$	18.9576	−	10.9452i	0.606506	−	0.350167i	−0.165091	−	0.986278i	$-0.552792\pi$
$977$	18.9576	−	10.9452i	0.606506	−	0.350167i	0.771597	+	0.636112i	$0.219458\pi$
$978$		0			0
$979$	0.279179	+	1.04191i	0.00892259	+	0.0332996i
$980$	−0.522727	−	0.0528049i	−0.0166979	−	0.00168679i
$981$		0			0
$982$	−0.991502	+	2.08959i	−0.0316401	+	0.0666814i
$983$	11.0681	+	6.39017i	0.353018	+	0.203815i	0.666014	−	0.745940i	$-0.267999\pi$
$983$	11.0681	+	6.39017i	0.353018	+	0.203815i	−0.312996	+	0.949754i	$0.601333\pi$
$984$		0			0
$985$	1.78820	−	1.03242i	0.0569769	−	0.0328956i
$986$	3.84000	+	47.5623i	0.122291	+	1.51469i
$987$		0			0
$988$	3.75605	+	23.1096i	0.119496	+	0.735216i
$989$	0.571303	−	0.571303i	0.0181664	−	0.0181664i
$990$		0			0
$991$		−	51.8246i		−	1.64626i	−0.567852	−	0.823131i	$-0.692225\pi$
$991$		−	51.8246i		−	1.64626i	0.567852	−	0.823131i	$-0.307775\pi$
$992$	−8.38625	+	20.8395i	−0.266264	+	0.661656i
$993$		0			0
$994$	2.44544	−	2.87499i	0.0775645	−	0.0911890i
$995$	0.253236	−	0.945091i	0.00802813	−	0.0299614i
$996$		0			0
$997$	−12.2448	−	45.6984i	−0.387798	−	1.44728i	−0.833709	−	0.552204i	$-0.813787\pi$
$997$	−12.2448	−	45.6984i	−0.387798	−	1.44728i	0.445911	−	0.895077i	$-0.352880\pi$
$998$	−2.83327	+	5.97112i	−0.0896857	+	0.189012i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.v.a.35.10		88
3.2	odd	2		144.2.u.a.83.13	yes	88
4.3	odd	2		1728.2.z.a.1007.12		88
9.4	even	3		144.2.u.a.131.6	yes	88
9.5	odd	6	inner	432.2.v.a.179.17		88
12.11	even	2		576.2.y.a.47.14		88
16.5	even	4		1728.2.z.a.143.12		88
16.11	odd	4	inner	432.2.v.a.251.17		88
36.23	even	6		1728.2.z.a.1583.12		88
36.31	odd	6		576.2.y.a.239.2		88
48.5	odd	4		576.2.y.a.335.2		88
48.11	even	4		144.2.u.a.11.6	✓	88
144.5	odd	12		1728.2.z.a.719.12		88
144.59	even	12	inner	432.2.v.a.395.10		88
144.85	even	12		576.2.y.a.527.14		88
144.139	odd	12		144.2.u.a.59.13	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.6	✓	88	48.11	even	4
144.2.u.a.59.13	yes	88	144.139	odd	12
144.2.u.a.83.13	yes	88	3.2	odd	2
144.2.u.a.131.6	yes	88	9.4	even	3
432.2.v.a.35.10		88	1.1	even	1	trivial
432.2.v.a.179.17		88	9.5	odd	6	inner
432.2.v.a.251.17		88	16.11	odd	4	inner
432.2.v.a.395.10		88	144.59	even	12	inner
576.2.y.a.47.14		88	12.11	even	2
576.2.y.a.239.2		88	36.31	odd	6
576.2.y.a.335.2		88	48.5	odd	4
576.2.y.a.527.14		88	144.85	even	12
1728.2.z.a.143.12		88	16.5	even	4
1728.2.z.a.719.12		88	144.5	odd	12
1728.2.z.a.1007.12		88	4.3	odd	2
1728.2.z.a.1583.12		88	36.23	even	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.v (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.254908 + 1.39105i) q^{2} +(-1.87004 - 0.709181i) q^{4} +(0.0458174 - 0.170993i) q^{5} +(1.17432 - 2.03397i) q^{7} +(1.46320 - 2.42055i) q^{8} +O(q^{10})\)	\(q+(-0.254908 + 1.39105i) q^{2} +(-1.87004 - 0.709181i) q^{4} +(0.0458174 - 0.170993i) q^{5} +(1.17432 - 2.03397i) q^{7} +(1.46320 - 2.42055i) q^{8} +(0.226181 + 0.107322i) q^{10} +(0.0913188 + 0.340806i) q^{11} +(0.399362 - 1.49044i) q^{13} +(2.53002 + 2.15201i) q^{14} +(2.99413 + 2.65240i) q^{16} -3.58081i q^{17} +(5.36462 - 5.36462i) q^{19} +(-0.206946 + 0.287272i) q^{20} +(-0.497357 + 0.0401547i) q^{22} +(-0.165085 + 0.0953117i) q^{23} +(4.30299 + 2.48433i) q^{25} +(1.97148 + 0.935459i) q^{26} +(-3.63847 + 2.97082i) q^{28} +(2.43879 + 9.10169i) q^{29} +(3.43903 - 1.98552i) q^{31} +(-4.45285 + 3.48886i) q^{32} +(4.98108 + 0.912777i) q^{34} +(-0.293991 - 0.293991i) q^{35} +(-3.28315 + 3.28315i) q^{37} +(6.09498 + 8.82995i) q^{38} +(-0.346857 - 0.361100i) q^{40} +(-4.25538 - 7.37054i) q^{41} +(-4.09402 + 1.09699i) q^{43} +(0.0709232 - 0.702084i) q^{44} +(-0.0905019 - 0.253937i) q^{46} +(4.93030 - 8.53953i) q^{47} +(0.741968 + 1.28513i) q^{49} +(-4.55270 + 5.35240i) q^{50} +(-1.80382 + 2.50397i) q^{52} +(-4.83735 - 4.83735i) q^{53} +0.0624595 q^{55} +(-3.20508 - 5.81859i) q^{56} +(-13.2826 + 1.07238i) q^{58} +(2.68985 + 0.720744i) q^{59} +(-7.97394 + 2.13661i) q^{61} +(1.88533 + 5.28999i) q^{62} +(-3.71812 - 7.08347i) q^{64} +(-0.236557 - 0.136576i) q^{65} +(11.4543 + 3.06917i) q^{67} +(-2.53944 + 6.69626i) q^{68} +(0.483897 - 0.334016i) q^{70} -1.13635i q^{71} +5.67961i q^{73} +(-3.73012 - 5.40392i) q^{74} +(-13.8366 + 6.22759i) q^{76} +(0.800428 + 0.214474i) q^{77} +(-12.8621 - 7.42593i) q^{79} +(0.590725 - 0.390449i) q^{80} +(11.3375 - 4.04064i) q^{82} +(12.3635 - 3.31278i) q^{83} +(-0.612293 - 0.164063i) q^{85} +(-0.482368 - 5.97461i) q^{86} +(0.958556 + 0.277625i) q^{88} +3.05719 q^{89} +(-2.56254 - 2.56254i) q^{91} +(0.376309 - 0.0611622i) q^{92} +(10.6221 + 9.03509i) q^{94} +(-0.671520 - 1.16311i) q^{95} +(-0.996701 + 1.72634i) q^{97} +(-1.97681 + 0.704526i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7}+O(q^{10}) \) 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 40 q^{46} - 24 q^{49} - 72 q^{50} - 2 q^{52} - 16 q^{55} - 36 q^{56} + 16 q^{58} + 42 q^{59} - 2 q^{61} - 44 q^{64} + 12 q^{65} - 2 q^{67} - 96 q^{68} - 16 q^{70} - 78 q^{74} - 14 q^{76} + 6 q^{77} - 36 q^{82} - 54 q^{83} + 8 q^{85} - 54 q^{86} + 22 q^{88} + 20 q^{91} - 108 q^{92} + 6 q^{94} - 4 q^{97}+O(q^{100}) \) 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

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