LMFDB - Embedded newform 432.2.v.a.35.8

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			35.8
Character	$\chi$	$=$	432.35
Dual form			432.2.v.a.395.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.417977 - 1.35103i) q^{2} +(-1.65059 + 1.12940i) q^{4} +(-0.0776974 + 0.289971i) q^{5} +(-0.374023 + 0.647827i) q^{7} +(2.21577 + 1.75794i) q^{8} +O(q^{10})$	\(q+(-0.417977 - 1.35103i) q^{2} +(-1.65059 + 1.12940i) q^{4} +(-0.0776974 + 0.289971i) q^{5} +(-0.374023 + 0.647827i) q^{7} +(2.21577 + 1.75794i) q^{8} +(0.424236 - 0.0162292i) q^{10} +(0.599457 + 2.23720i) q^{11} +(-0.429571 + 1.60318i) q^{13} +(1.03157 + 0.234541i) q^{14} +(1.44890 - 3.72836i) q^{16} +6.74518i q^{17} +(0.621335 - 0.621335i) q^{19} +(-0.199247 - 0.566375i) q^{20} +(2.77198 - 1.74499i) q^{22} +(6.06191 - 3.49985i) q^{23} +(4.25208 + 2.45494i) q^{25} +(2.34550 - 0.0897272i) q^{26} +(-0.114299 - 1.49172i) q^{28} +(1.45829 + 5.44240i) q^{29} +(-3.13647 + 1.81084i) q^{31} +(-5.64276 - 0.399142i) q^{32} +(9.11297 - 2.81933i) q^{34} +(-0.158790 - 0.158790i) q^{35} +(6.74053 - 6.74053i) q^{37} +(-1.09915 - 0.579742i) q^{38} +(-0.681911 + 0.505921i) q^{40} +(-1.39492 - 2.41607i) q^{41} +(-7.08744 + 1.89907i) q^{43} +(-3.51616 - 3.01568i) q^{44} +(-7.26216 - 6.72700i) q^{46} +(0.307120 - 0.531947i) q^{47} +(3.22021 + 5.57757i) q^{49} +(1.53944 - 6.77082i) q^{50} +(-1.10159 - 3.13135i) q^{52} +(2.68523 + 2.68523i) q^{53} -0.695300 q^{55} +(-1.96759 + 0.777926i) q^{56} +(6.74334 - 4.24499i) q^{58} +(0.00841962 + 0.00225603i) q^{59} +(-10.1714 + 2.72542i) q^{61} +(3.75748 + 3.48059i) q^{62} +(1.81929 + 7.79039i) q^{64} +(-0.431499 - 0.249126i) q^{65} +(-8.78151 - 2.35300i) q^{67} +(-7.61803 - 11.1335i) q^{68} +(-0.148160 + 0.280902i) q^{70} -15.9645i q^{71} +8.17785i q^{73} +(-11.9241 - 6.28930i) q^{74} +(-0.323832 + 1.72731i) q^{76} +(-1.67353 - 0.448421i) q^{77} +(7.67035 + 4.42848i) q^{79} +(0.968541 + 0.709822i) q^{80} +(-2.68115 + 2.89445i) q^{82} +(1.32013 - 0.353727i) q^{83} +(-1.95590 - 0.524083i) q^{85} +(5.52810 + 8.78161i) q^{86} +(-2.60461 + 6.01094i) q^{88} +15.7852 q^{89} +(-0.877914 - 0.877914i) q^{91} +(-6.05300 + 12.6232i) q^{92} +(-0.847048 - 0.192588i) q^{94} +(0.131893 + 0.228445i) q^{95} +(-4.62075 + 8.00338i) q^{97} +(6.18952 - 6.68192i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.417977	−	1.35103i	−0.295554	−	0.955326i
$2$	−0.417977	−	1.35103i	−0.295554	−	0.955326i
$3$		0			0
$3$		0			0
$4$	−1.65059	+	1.12940i	−0.825295	+	0.564701i
$5$	−0.0776974	+	0.289971i	−0.0347473	+	0.129679i	−0.981121	−	0.193396i	$-0.938050\pi$
$5$	−0.0776974	+	0.289971i	−0.0347473	+	0.129679i	0.946373	+	0.323075i	$0.104717\pi$
$6$		0			0
$7$	−0.374023	+	0.647827i	−0.141367	+	0.244855i	−0.928012	−	0.372551i	$-0.878483\pi$
$7$	−0.374023	+	0.647827i	−0.141367	+	0.244855i	0.786644	+	0.617406i	$0.211817\pi$
$8$	2.21577	+	1.75794i	0.783394	+	0.621526i
$9$		0			0
$10$	0.424236	−	0.0162292i	0.134155	−	0.00513211i
$11$	0.599457	+	2.23720i	0.180743	+	0.674542i	0.995502	+	0.0947421i	$0.0302027\pi$
$11$	0.599457	+	2.23720i	0.180743	+	0.674542i	−0.814759	+	0.579800i	$0.803131\pi$
$12$		0			0
$13$	−0.429571	+	1.60318i	−0.119142	+	0.444642i	−0.999563	−	0.0295491i	$-0.990593\pi$
$13$	−0.429571	+	1.60318i	−0.119142	+	0.444642i	0.880422	+	0.474191i	$0.157260\pi$
$14$	1.03157	+	0.234541i	0.275699	+	0.0626838i
$15$		0			0
$16$	1.44890	−	3.72836i	0.362225	−	0.932091i
$17$			6.74518i			1.63595i	0.575256	+	0.817973i	$0.304902\pi$
$17$			6.74518i			1.63595i	−0.575256	+	0.817973i	$0.695098\pi$
$18$		0			0
$19$	0.621335	−	0.621335i	0.142544	−	0.142544i	−0.632234	−	0.774778i	$-0.717862\pi$
$19$	0.621335	−	0.621335i	0.142544	−	0.142544i	0.774778	+	0.632234i	$0.217862\pi$
$20$	−0.199247	−	0.566375i	−0.0445530	−	0.126645i
$21$		0			0
$22$	2.77198	−	1.74499i	0.590988	−	0.372032i
$23$	6.06191	−	3.49985i	1.26400	−	0.729769i	0.290151	−	0.956981i	$-0.406294\pi$
$23$	6.06191	−	3.49985i	1.26400	−	0.729769i	0.973845	+	0.227212i	$0.0729611\pi$
$24$		0			0
$25$	4.25208	+	2.45494i	0.850416	+	0.490988i
$26$	2.34550	−	0.0897272i	0.459991	−	0.0175970i
$27$		0			0
$28$	−0.114299	−	1.49172i	−0.0216004	−	0.281908i
$29$	1.45829	+	5.44240i	0.270797	+	1.01063i	0.958606	+	0.284736i	$0.0919060\pi$
$29$	1.45829	+	5.44240i	0.270797	+	1.01063i	−0.687809	+	0.725892i	$0.741427\pi$
$30$		0			0
$31$	−3.13647	+	1.81084i	−0.563326	+	0.325236i	−0.754479	−	0.656324i	$-0.772111\pi$
$31$	−3.13647	+	1.81084i	−0.563326	+	0.325236i	0.191153	+	0.981560i	$0.438777\pi$
$32$	−5.64276	−	0.399142i	−0.997508	−	0.0705590i
$33$		0			0
$34$	9.11297	−	2.81933i	1.56286	−	0.483511i
$35$	−0.158790	−	0.158790i	−0.0268404	−	0.0268404i
$36$		0			0
$37$	6.74053	−	6.74053i	1.10814	−	1.10814i	0.114740	−	0.993396i	$-0.463396\pi$
$37$	6.74053	−	6.74053i	1.10814	−	1.10814i	0.993396	−	0.114740i	$-0.0366036\pi$
$38$	−1.09915	−	0.579742i	−0.178306	−	0.0940465i
$39$		0			0
$40$	−0.681911	+	0.505921i	−0.107820	+	0.0799932i
$41$	−1.39492	−	2.41607i	−0.217850	−	0.377327i	0.736301	−	0.676655i	$-0.236571\pi$
$41$	−1.39492	−	2.41607i	−0.217850	−	0.377327i	−0.954150	+	0.299328i	$0.903238\pi$
$42$		0			0
$43$	−7.08744	+	1.89907i	−1.08082	+	0.289606i	−0.754934	−	0.655801i	$-0.772331\pi$
$43$	−7.08744	+	1.89907i	−1.08082	+	0.289606i	−0.325891	+	0.945407i	$0.605664\pi$
$44$	−3.51616	−	3.01568i	−0.530081	−	0.454631i
$45$		0			0
$46$	−7.26216	−	6.72700i	−1.07075	−	0.991842i
$47$	0.307120	−	0.531947i	0.0447980	−	0.0775924i	−0.842757	−	0.538294i	$-0.819069\pi$
$47$	0.307120	−	0.531947i	0.0447980	−	0.0775924i	0.887555	+	0.460702i	$0.152402\pi$
$48$		0			0
$49$	3.22021	+	5.57757i	0.460031	+	0.796796i
$50$	1.53944	−	6.77082i	0.217709	−	0.957538i
$51$		0			0
$52$	−1.10159	−	3.13135i	−0.152763	−	0.434241i
$53$	2.68523	+	2.68523i	0.368844	+	0.368844i	0.867056	−	0.498211i	$-0.166010\pi$
$53$	2.68523	+	2.68523i	0.368844	+	0.368844i	−0.498211	+	0.867056i	$0.666010\pi$
$54$		0			0
$55$	−0.695300			−0.0937542
$56$	−1.96759	+	0.777926i	−0.262930	+	0.103955i
$57$		0			0
$58$	6.74334	−	4.24499i	0.885444	−	0.557395i
$59$	0.00841962	+	0.00225603i	0.00109614	+	0.000293710i	0.259367	−	0.965779i	$-0.416486\pi$
$59$	0.00841962	+	0.00225603i	0.00109614	+	0.000293710i	−0.258271	+	0.966073i	$0.583153\pi$
$60$		0			0
$61$	−10.1714	+	2.72542i	−1.30232	+	0.348955i	−0.842326	−	0.538969i	$-0.818814\pi$
$61$	−10.1714	+	2.72542i	−1.30232	+	0.348955i	−0.459991	+	0.887924i	$0.652147\pi$
$62$	3.75748	+	3.48059i	0.477200	+	0.442035i
$63$		0			0
$64$	1.81929	+	7.79039i	0.227411	+	0.973799i
$65$	−0.431499	−	0.249126i	−0.0535208	−	0.0309003i
$66$		0			0
$67$	−8.78151	−	2.35300i	−1.07283	−	0.287464i	−0.321176	−	0.947020i	$-0.604078\pi$
$67$	−8.78151	−	2.35300i	−1.07283	−	0.287464i	−0.751656	+	0.659555i	$0.770745\pi$
$68$	−7.61803	−	11.1335i	−0.923821	−	1.35014i
$69$		0			0
$70$	−0.148160	+	0.280902i	−0.0177086	+	0.0335742i
$71$		−	15.9645i		−	1.89463i	−0.320297	−	0.947317i	$-0.603783\pi$
$71$		−	15.9645i		−	1.89463i	0.320297	−	0.947317i	$-0.396217\pi$
$72$		0			0
$73$			8.17785i			0.957145i	0.878048	+	0.478572i	$0.158846\pi$
$73$			8.17785i			0.957145i	−0.878048	+	0.478572i	$0.841154\pi$
$74$	−11.9241	−	6.28930i	−1.38615	−	0.731116i
$75$		0			0
$76$	−0.323832	+	1.72731i	−0.0371461	+	0.198136i
$77$	−1.67353	−	0.448421i	−0.190717	−	0.0511023i
$78$		0			0
$79$	7.67035	+	4.42848i	0.862982	+	0.498243i	0.865010	−	0.501755i	$-0.167312\pi$
$79$	7.67035	+	4.42848i	0.862982	+	0.498243i	−0.00202794	+	0.999998i	$0.500646\pi$
$80$	0.968541	+	0.709822i	0.108286	+	0.0793605i
$81$		0			0
$82$	−2.68115	+	2.89445i	−0.296084	+	0.319638i
$83$	1.32013	−	0.353727i	0.144903	−	0.0388266i	−0.185638	−	0.982618i	$-0.559435\pi$
$83$	1.32013	−	0.353727i	0.144903	−	0.0388266i	0.330541	+	0.943791i	$0.392769\pi$
$84$		0			0
$85$	−1.95590	−	0.524083i	−0.212148	−	0.0568448i
$86$	5.52810	+	8.78161i	0.596111	+	0.946946i
$87$		0			0
$88$	−2.60461	+	6.01094i	−0.277653	+	0.640768i
$89$	15.7852			1.67323			0.836613	−	0.547794i	$-0.184532\pi$
$89$	15.7852			1.67323			0.836613	+	0.547794i	$0.184532\pi$
$90$		0			0
$91$	−0.877914	−	0.877914i	−0.0920304	−	0.0920304i
$92$	−6.05300	+	12.6232i	−0.631069	+	1.31606i
$93$		0			0
$94$	−0.847048	−	0.192588i	−0.0873663	−	0.0198639i
$95$	0.131893	+	0.228445i	0.0135319	+	0.0234380i
$96$		0			0
$97$	−4.62075	+	8.00338i	−0.469166	+	0.812620i	−0.999379	−	0.0352448i	$-0.988779\pi$
$97$	−4.62075	+	8.00338i	−0.469166	+	0.812620i	0.530212	+	0.847865i	$0.322112\pi$
$98$	6.18952	−	6.68192i	0.625236	−	0.674976i
$99$		0			0
$100$	−9.79106	+	0.750212i	−0.979106	+	0.0750212i
$101$	−15.2552	+	4.08762i	−1.51795	+	0.406734i	−0.919067	−	0.394102i	$-0.871056\pi$
$101$	−15.2552	+	4.08762i	−1.51795	+	0.406734i	−0.598885	+	0.800835i	$0.704389\pi$
$102$		0			0
$103$	−5.63994	−	9.76866i	−0.555720	−	0.962535i	−0.997847	−	0.0655828i	$-0.979109\pi$
$103$	−5.63994	−	9.76866i	−0.555720	−	0.962535i	0.442127	−	0.896952i	$-0.354224\pi$
$104$	−3.77013	+	2.79712i	−0.369691	+	0.274280i
$105$		0			0
$106$	2.50547	−	4.75020i	0.243353	−	0.461380i
$107$	−9.39963	+	9.39963i	−0.908696	+	0.908696i	−0.996167	−	0.0874707i	$-0.972122\pi$
$107$	−9.39963	+	9.39963i	−0.908696	+	0.908696i	0.0874707	+	0.996167i	$0.472122\pi$
$108$		0			0
$109$	0.535130	+	0.535130i	0.0512562	+	0.0512562i	0.732270	−	0.681014i	$-0.238461\pi$
$109$	0.535130	+	0.535130i	0.0512562	+	0.0512562i	−0.681014	+	0.732270i	$0.738461\pi$
$110$	0.290619	+	0.939374i	0.0277095	+	0.0895658i
$111$		0			0
$112$	1.87341	+	2.33313i	0.177021	+	0.220460i
$113$	−3.53279	+	2.03966i	−0.332337	+	0.191875i	−0.656878	−	0.753997i	$-0.728123\pi$
$113$	−3.53279	+	2.03966i	−0.332337	+	0.191875i	0.324541	+	0.945872i	$0.394790\pi$
$114$		0			0
$115$	0.543858	+	2.02971i	0.0507150	+	0.189271i
$116$	−8.55369	−	7.33618i	−0.794191	−	0.681147i
$117$		0			0
$118$	−0.000471231	−	0.0123182i	−4.33803e−5	−	0.00113398i
$119$	−4.36971	−	2.52285i	−0.400570	−	0.231269i
$120$		0			0
$121$	4.88055	−	2.81779i	0.443686	−	0.256162i
$122$	7.93356	+	12.6028i	0.718271	+	1.14100i
$123$		0			0
$124$	3.13185	−	6.53129i	0.281249	−	0.586527i
$125$	−2.10360	+	2.10360i	−0.188152	+	0.188152i
$126$		0			0
$127$			1.78789i			0.158650i	0.996849	+	0.0793250i	$0.0252765\pi$
$127$			1.78789i			0.158650i	−0.996849	+	0.0793250i	$0.974724\pi$
$128$	9.76467	−	5.71412i	0.863083	−	0.505062i
$129$		0			0
$130$	−0.156221	+	0.687099i	−0.0137015	+	0.0602626i
$131$	−1.03741	+	3.87165i	−0.0906386	+	0.338268i	−0.996322	−	0.0856865i	$-0.972692\pi$
$131$	−1.03741	+	3.87165i	−0.0906386	+	0.338268i	0.905684	+	0.423954i	$0.139358\pi$
$132$		0			0
$133$	0.170124	+	0.634911i	0.0147516	+	0.0550538i
$134$	0.491486	+	12.8476i	0.0424579	+	1.10987i
$135$		0			0
$136$	−11.8576	+	14.9458i	−1.01678	+	1.28159i
$137$	0.396519	−	0.686792i	0.0338769	−	0.0586766i	−0.848590	−	0.529051i	$-0.822548\pi$
$137$	0.396519	−	0.686792i	0.0338769	−	0.0586766i	0.882467	+	0.470375i	$0.155881\pi$
$138$		0			0
$139$	4.74448	−	17.7067i	0.402422	−	1.50186i	−0.406340	−	0.913722i	$-0.633195\pi$
$139$	4.74448	−	17.7067i	0.402422	−	1.50186i	0.808762	−	0.588137i	$-0.200138\pi$
$140$	0.441436	+	0.0827595i	0.0373081	+	0.00699445i
$141$		0			0
$142$	−21.5686	+	6.67278i	−1.80999	+	0.559967i
$143$	−3.84415			−0.321464
$144$		0			0
$145$	−1.69144			−0.140467
$146$	11.0486	−	3.41815i	0.914385	−	0.282888i
$147$		0			0
$148$	−3.51308	+	18.7386i	−0.288773	+	1.54031i
$149$	3.38007	−	12.6146i	0.276906	−	1.03343i	−0.677647	−	0.735388i	$-0.737000\pi$
$149$	3.38007	−	12.6146i	0.276906	−	1.03343i	0.954553	−	0.298041i	$-0.0963333\pi$
$150$		0			0
$151$	9.45023	−	16.3683i	0.769049	−	1.33203i	−0.169030	−	0.985611i	$-0.554063\pi$
$151$	9.45023	−	16.3683i	0.769049	−	1.33203i	0.938079	−	0.346421i	$-0.112603\pi$
$152$	2.46901	−	0.284466i	0.200263	−	0.0230733i
$153$		0			0
$154$	0.0936646	+	2.44843i	0.00754771	+	0.197300i
$155$	−0.281395	−	1.05018i	−0.0226022	−	0.0843526i
$156$		0			0
$157$	2.46555	−	9.20155i	0.196772	−	0.734364i	−0.795029	−	0.606572i	$-0.792544\pi$
$157$	2.46555	−	9.20155i	0.196772	−	0.734364i	0.991801	−	0.127792i	$-0.0407891\pi$
$158$	2.77700	−	12.2139i	0.220926	−	0.971687i
$159$		0			0
$160$	0.554167	−	1.60522i	0.0438107	−	0.126904i
$161$			5.23609i			0.412662i
$162$		0			0
$163$	−6.24968	+	6.24968i	−0.489512	+	0.489512i	−0.908152	−	0.418640i	$-0.862507\pi$
$163$	−6.24968	+	6.24968i	−0.489512	+	0.489512i	0.418640	+	0.908152i	$0.362507\pi$
$164$	5.03116	+	2.41252i	0.392867	+	0.188386i
$165$		0			0
$166$	−1.02968	−	1.63569i	−0.0799188	−	0.126954i
$167$	−7.96426	+	4.59817i	−0.616293	+	0.355817i	−0.775424	−	0.631441i	$-0.782464\pi$
$167$	−7.96426	+	4.59817i	−0.616293	+	0.355817i	0.159132	+	0.987257i	$0.449131\pi$
$168$		0			0
$169$	8.87267	+	5.12264i	0.682513	+	0.394049i
$170$	0.109469	+	2.86155i	0.00839585	+	0.219471i
$171$		0			0
$172$	9.55364	−	11.1392i	0.728459	−	0.849354i
$173$	−2.05554	−	7.67137i	−0.156280	−	0.583243i	−0.998992	−	0.0448800i	$-0.985709\pi$
$173$	−2.05554	−	7.67137i	−0.156280	−	0.583243i	0.842713	−	0.538363i	$-0.180957\pi$
$174$		0			0
$175$	−3.18075	+	1.83641i	−0.240442	+	0.138819i
$176$	9.20966	+	1.00649i	0.694204	+	0.0758668i
$177$		0			0
$178$	−6.59784	−	21.3263i	−0.494529	−	1.59848i
$179$	−7.99447	−	7.99447i	−0.597535	−	0.597535i	0.342121	−	0.939656i	$-0.388855\pi$
$179$	−7.99447	−	7.99447i	−0.597535	−	0.597535i	−0.939656	+	0.342121i	$0.888855\pi$
$180$		0			0
$181$	14.5271	−	14.5271i	1.07979	−	1.07979i	0.0832666	−	0.996527i	$-0.473465\pi$
$181$	14.5271	−	14.5271i	1.07979	−	1.07979i	0.996527	−	0.0832666i	$-0.0265353\pi$
$182$	−0.819144	+	1.55304i	−0.0607190	+	0.115119i
$183$		0			0
$184$	19.5843	+	2.90162i	1.44378	+	0.213911i
$185$	1.43083	+	2.47828i	0.105197	+	0.182207i
$186$		0			0
$187$	−15.0903	+	4.04344i	−1.10351	+	0.295686i
$188$	0.0938535	+	1.22489i	0.00684497	+	0.0893341i
$189$		0			0
$190$	0.253509	−	0.273677i	0.0183915	−	0.0198546i
$191$	10.2382	−	17.7332i	0.740813	−	1.28313i	−0.211312	−	0.977419i	$-0.567774\pi$
$191$	10.2382	−	17.7332i	0.740813	−	1.28313i	0.952125	−	0.305708i	$-0.0988930\pi$
$192$		0			0
$193$	−2.37336	−	4.11078i	−0.170838	−	0.295901i	0.767875	−	0.640600i	$-0.221314\pi$
$193$	−2.37336	−	4.11078i	−0.170838	−	0.295901i	−0.938713	+	0.344699i	$0.887981\pi$
$194$	12.7442	+	2.89757i	0.914981	+	0.208033i
$195$		0			0
$196$	−11.6146	−	5.56937i	−0.829613	−	0.397812i
$197$	−6.65282	−	6.65282i	−0.473994	−	0.473994i	0.429210	−	0.903205i	$-0.358792\pi$
$197$	−6.65282	−	6.65282i	−0.473994	−	0.473994i	−0.903205	+	0.429210i	$0.858792\pi$
$198$		0			0
$199$	22.8401			1.61909			0.809544	−	0.587059i	$-0.199714\pi$
$199$	22.8401			1.61909			0.809544	+	0.587059i	$0.199714\pi$
$200$	5.10600	+	12.9145i	0.361049	+	0.913193i
$201$		0			0
$202$	11.8989	+	18.9018i	0.837201	+	1.32993i
$203$	−4.07116	−	1.09087i	−0.285740	−	0.0765637i
$204$		0			0
$205$	0.808971	−	0.216763i	0.0565010	−	0.0151394i
$206$	−10.8404	+	11.7028i	−0.755289	+	0.815375i
$207$		0			0
$208$	5.35483	+	3.92444i	0.371291	+	0.272111i
$209$	1.76252	+	1.01759i	0.121916	+	0.0703881i
$210$		0			0
$211$	14.8119	+	3.96884i	1.01969	+	0.273226i	0.729674	−	0.683795i	$-0.239672\pi$
$211$	14.8119	+	3.96884i	1.01969	+	0.273226i	0.290019	+	0.957021i	$0.406338\pi$
$212$	−7.46491	−	1.39951i	−0.512692	−	0.0961185i
$213$		0			0
$214$	16.6281	+	8.77040i	1.13667	+	0.599532i
$215$		−	2.20270i		−	0.150223i
$216$		0			0
$217$		−	2.70918i		−	0.183911i
$218$	0.499307	−	0.946652i	0.0338174	−	0.0641153i
$219$		0			0
$220$	1.14765	−	0.785273i	0.0773749	−	0.0529431i
$221$	−10.8137	−	2.89753i	−0.727411	−	0.194909i
$222$		0			0
$223$	6.39965	+	3.69484i	0.428552	+	0.247425i	0.698730	−	0.715386i	$-0.253749\pi$
$223$	6.39965	+	3.69484i	0.428552	+	0.247425i	−0.270178	+	0.962811i	$0.587082\pi$
$224$	2.36909	−	3.50624i	0.158292	−	0.234270i
$225$		0			0
$226$	4.23227	+	3.92039i	0.281527	+	0.260781i
$227$	20.6122	−	5.52301i	1.36808	−	0.366575i	0.501301	−	0.865273i	$-0.332855\pi$
$227$	20.6122	−	5.52301i	1.36808	−	0.366575i	0.866776	+	0.498698i	$0.166188\pi$
$228$		0			0
$229$	−17.7978	−	4.76891i	−1.17611	−	0.315138i	−0.382729	−	0.923861i	$-0.625016\pi$
$229$	−17.7978	−	4.76891i	−1.17611	−	0.315138i	−0.793383	+	0.608722i	$0.791682\pi$
$230$	2.51488	−	1.58314i	0.165827	−	0.104389i
$231$		0			0
$232$	−6.33619	+	14.6227i	−0.415991	+	0.960027i
$233$	14.3249			0.938455			0.469228	−	0.883077i	$-0.344532\pi$
$233$	14.3249			0.938455			0.469228	+	0.883077i	$0.344532\pi$
$234$		0			0
$235$	0.130387	+	0.130387i	0.00850548	+	0.00850548i
$236$	−0.0164453	+	0.00578536i	−0.00107050	+	0.000376595i
$237$		0			0
$238$	−1.58202	+	6.95812i	−0.102547	+	0.451028i
$239$	11.4921	+	19.9049i	0.743364	+	1.28754i	0.950955	+	0.309328i	$0.100104\pi$
$239$	11.4921	+	19.9049i	0.743364	+	1.28754i	−0.207592	+	0.978216i	$0.566562\pi$
$240$		0			0
$241$	10.2735	−	17.7943i	0.661777	−	1.14623i	−0.318372	−	0.947966i	$-0.603136\pi$
$241$	10.2735	−	17.7943i	0.661777	−	1.14623i	0.980148	−	0.198265i	$-0.0635306\pi$
$242$	−5.84689	−	5.41602i	−0.375852	−	0.348155i
$243$		0			0
$244$	13.7107	−	15.9862i	0.877741	−	1.02341i
$245$	−1.86754	+	0.500405i	−0.119312	+	0.0319697i
$246$		0			0
$247$	0.729205	+	1.26302i	0.0463982	+	0.0803640i
$248$	−10.1330	−	1.50132i	−0.643449	−	0.0953336i
$249$		0			0
$250$	3.72130	+	1.96278i	0.235356	+	0.124137i
$251$	−0.440838	+	0.440838i	−0.0278255	+	0.0278255i	−0.720883	−	0.693057i	$-0.756263\pi$
$251$	−0.440838	+	0.440838i	−0.0278255	+	0.0278255i	0.693057	+	0.720883i	$0.256263\pi$
$252$		0			0
$253$	11.4637	+	11.4637i	0.720718	+	0.720718i
$254$	2.41551	−	0.747298i	0.151562	−	0.0468897i
$255$		0			0
$256$	−11.8014	−	10.8040i	−0.737587	−	0.675252i
$257$	4.78636	−	2.76341i	0.298565	−	0.172377i	−0.343233	−	0.939250i	$-0.611522\pi$
$257$	4.78636	−	2.76341i	0.298565	−	0.172377i	0.641798	+	0.766874i	$0.278189\pi$
$258$		0			0
$259$	1.84558	+	6.88781i	0.114679	+	0.427987i
$260$	0.993591	−	0.0761311i	0.0616199	−	0.00472145i
$261$		0			0
$262$	5.66435	−	0.216690i	0.349945	−	0.0133871i
$263$	−4.83474	−	2.79134i	−0.298123	−	0.172121i	0.343477	−	0.939161i	$-0.388395\pi$
$263$	−4.83474	−	2.79134i	−0.298123	−	0.172121i	−0.641599	+	0.767040i	$0.721729\pi$
$264$		0			0
$265$	−0.987272	+	0.570002i	−0.0606476	+	0.0350149i
$266$	0.786679	−	0.495222i	0.0482344	−	0.0303640i
$267$		0			0
$268$	17.1522	−	6.03402i	1.04773	−	0.368587i
$269$	−1.66733	+	1.66733i	−0.101659	+	0.101659i	−0.756107	−	0.654448i	$-0.772901\pi$
$269$	−1.66733	+	1.66733i	−0.101659	+	0.101659i	0.654448	+	0.756107i	$0.272901\pi$
$270$		0			0
$271$		−	23.2740i		−	1.41379i	−0.707317	−	0.706897i	$-0.750095\pi$
$271$		−	23.2740i		−	1.41379i	0.707317	−	0.706897i	$-0.249905\pi$
$272$	25.1485	+	9.77308i	1.52485	+	0.592580i
$273$		0			0
$274$	−1.09362	−	0.248648i	−0.0660677	−	0.0150214i
$275$	−2.94326	+	10.9844i	−0.177485	+	0.662384i
$276$		0			0
$277$	0.183461	+	0.684687i	0.0110231	+	0.0411389i	0.971218	−	0.238191i	$-0.0765544\pi$
$277$	0.183461	+	0.684687i	0.0110231	+	0.0411389i	−0.960195	+	0.279330i	$0.909888\pi$
$278$	−25.9054	+	0.991010i	−1.55370	+	0.0594368i
$279$		0			0
$280$	−0.0726990	−	0.630986i	−0.00434460	−	0.0377087i
$281$	2.29162	−	3.96921i	0.136707	−	0.236783i	−0.789541	−	0.613697i	$-0.789682\pi$
$281$	2.29162	−	3.96921i	0.136707	−	0.236783i	0.926248	+	0.376914i	$0.123015\pi$
$282$		0			0
$283$	−3.75850	+	14.0269i	−0.223420	+	0.833814i	0.759612	+	0.650377i	$0.225389\pi$
$283$	−3.75850	+	14.0269i	−0.223420	+	0.833814i	−0.983031	+	0.183437i	$0.941278\pi$
$284$	18.0303	+	26.3508i	1.06990	+	1.56363i
$285$		0			0
$286$	1.60677	+	5.19358i	0.0950101	+	0.307103i
$287$	2.08693			0.123187
$288$		0			0
$289$	−28.4974			−1.67632
$290$	0.706983	+	2.28520i	0.0415155	+	0.134191i
$291$		0			0
$292$	−9.23608	−	13.4983i	−0.540501	−	0.789927i
$293$	1.61879	−	6.04141i	0.0945708	−	0.352943i	−0.902383	−	0.430934i	$-0.858184\pi$
$293$	1.61879	−	6.04141i	0.0945708	−	0.352943i	0.996954	+	0.0779914i	$0.0248507\pi$
$294$		0			0
$295$	−0.00130836	+	0.00226615i	−7.61760e−5	+	0.000131941i
$296$	26.7849	−	3.08602i	1.55684	−	0.179371i
$297$		0			0
$298$	−18.4556	+	0.706017i	−1.06910	+	0.0408985i
$299$	3.00687	+	11.2218i	0.173892	+	0.648972i
$300$		0			0
$301$	1.42059	−	5.30173i	0.0818817	−	0.305587i
$302$	−26.0641	−	5.92603i	−1.49982	−	0.341005i
$303$		0			0
$304$	−1.41631	−	3.21681i	−0.0812311	−	0.184497i
$305$		−	3.16117i		−	0.181008i
$306$		0			0
$307$	−4.52060	+	4.52060i	−0.258004	+	0.258004i	−0.824242	−	0.566238i	$-0.808398\pi$
$307$	−4.52060	+	4.52060i	−0.258004	+	0.258004i	0.566238	+	0.824242i	$0.308398\pi$
$308$	3.26876	−	1.14993i	0.186255	−	0.0655234i
$309$		0			0
$310$	−1.30121	+	0.819126i	−0.0739040	+	0.0465232i
$311$	−10.9637	+	6.32992i	−0.621697	+	0.358937i	−0.777529	−	0.628847i	$-0.783527\pi$
$311$	−10.9637	+	6.32992i	−0.621697	+	0.358937i	0.155832	+	0.987784i	$0.450194\pi$
$312$		0			0
$313$	−16.6282	−	9.60027i	−0.939879	−	0.542640i	−0.0499568	−	0.998751i	$-0.515908\pi$
$313$	−16.6282	−	9.60027i	−0.939879	−	0.542640i	−0.889922	+	0.456112i	$0.849242\pi$
$314$	−13.4622	+	0.514995i	−0.759714	+	0.0290628i
$315$		0			0
$316$	−17.6621	+	1.35331i	−0.993573	+	0.0761297i
$317$	2.96978	+	11.0834i	0.166800	+	0.622504i	0.997804	+	0.0662384i	$0.0210998\pi$
$317$	2.96978	+	11.0834i	0.166800	+	0.622504i	−0.831004	+	0.556266i	$0.812234\pi$
$318$		0			0
$319$	−11.3016	+	6.52497i	−0.632767	+	0.365328i
$320$	−2.40034	−	0.0777534i	−0.134183	−	0.00434655i
$321$		0			0
$322$	7.07414	−	2.18857i	0.394227	−	0.121964i
$323$	4.19102	+	4.19102i	0.233194	+	0.233194i
$324$		0			0
$325$	−5.76228	+	5.76228i	−0.319634	+	0.319634i
$326$	11.0557	+	5.83131i	0.612321	+	0.322966i
$327$		0			0
$328$	1.15649	−	7.80564i	0.0638563	−	0.430995i
$329$	0.229740	+	0.397921i	0.0126660	+	0.0219381i
$330$		0			0
$331$	−18.9865	+	5.08741i	−1.04359	+	0.279630i	−0.739601	−	0.673045i	$-0.764986\pi$
$331$	−18.9865	+	5.08741i	−1.04359	+	0.279630i	−0.303991	+	0.952675i	$0.598319\pi$
$332$	−1.77949	+	2.07482i	−0.0976623	+	0.113870i
$333$		0			0
$334$	9.54116	+	8.83806i	0.522069	+	0.483597i
$335$	1.36460	−	2.36356i	0.0745561	−	0.129135i
$336$		0			0
$337$	4.99010	+	8.64310i	0.271828	+	0.470820i	0.969330	−	0.245763i	$-0.0790385\pi$
$337$	4.99010	+	8.64310i	0.271828	+	0.470820i	−0.697502	+	0.716583i	$0.745705\pi$
$338$	3.21229	−	14.1284i	0.174726	−	0.768486i
$339$		0			0
$340$	3.82030	−	1.34396i	0.207185	−	0.0728863i
$341$	−5.93139	−	5.93139i	−0.321203	−	0.321203i
$342$		0			0
$343$	−10.0541			−0.542868
$344$	−19.0426	−	8.25139i	−1.02671	−	0.444885i
$345$		0			0
$346$	−9.50512	+	5.98356i	−0.510998	+	0.321678i
$347$	6.76074	+	1.81153i	0.362935	+	0.0972483i	0.435678	−	0.900102i	$-0.356509\pi$
$347$	6.76074	+	1.81153i	0.362935	+	0.0972483i	−0.0727428	+	0.997351i	$0.523175\pi$
$348$		0			0
$349$	19.5231	−	5.23119i	1.04505	−	0.280019i	0.304843	−	0.952403i	$-0.401396\pi$
$349$	19.5231	−	5.23119i	1.04505	−	0.280019i	0.740203	+	0.672383i	$0.234729\pi$
$350$	3.81053	+	3.52973i	0.203682	+	0.188672i
$351$		0			0
$352$	−2.48963	−	12.8633i	−0.132698	−	0.685614i
$353$	−8.37682	−	4.83636i	−0.445853	−	0.257414i	0.260224	−	0.965548i	$-0.416204\pi$
$353$	−8.37682	−	4.83636i	−0.445853	−	0.257414i	−0.706077	+	0.708135i	$0.749537\pi$
$354$		0			0
$355$	4.62923	+	1.24040i	0.245694	+	0.0658335i
$356$	−26.0549	+	17.8278i	−1.38091	+	0.944873i
$357$		0			0
$358$	−7.45930	+	14.1423i	−0.394236	+	0.747444i
$359$		−	0.846908i		−	0.0446981i	−0.999750	−	0.0223491i	$-0.992885\pi$
$359$		−	0.846908i		−	0.0446981i	0.999750	−	0.0223491i	$-0.00711452\pi$
$360$		0			0
$361$			18.2279i			0.959362i
$362$	−25.6987	−	13.5547i	−1.35069	−	0.712417i
$363$		0			0
$364$	2.44059	+	0.457558i	0.127922	+	0.0239825i
$365$	−2.37134	−	0.635398i	−0.124121	−	0.0332582i
$366$		0			0
$367$	15.5960	+	9.00434i	0.814103	+	0.470023i	0.848379	−	0.529390i	$-0.177579\pi$
$367$	15.5960	+	9.00434i	0.814103	+	0.470023i	−0.0342756	+	0.999412i	$0.510912\pi$
$368$	−4.26561	−	27.6719i	−0.222360	−	1.44250i
$369$		0			0
$370$	2.75018	−	2.96897i	0.142975	−	0.154349i
$371$	−2.74390	+	0.735225i	−0.142456	+	0.0381710i
$372$		0			0
$373$	−18.7086	−	5.01296i	−0.968696	−	0.259561i	−0.260419	−	0.965496i	$-0.583861\pi$
$373$	−18.7086	−	5.01296i	−0.968696	−	0.259561i	−0.708277	+	0.705934i	$0.750527\pi$
$374$	11.7702	+	18.6975i	0.608625	+	0.966825i
$375$		0			0
$376$	1.61564	−	0.638774i	0.0833202	−	0.0329423i
$377$	−9.35158			−0.481631
$378$		0			0
$379$	7.14922	+	7.14922i	0.367231	+	0.367231i	0.866466	−	0.499235i	$-0.166386\pi$
$379$	7.14922	+	7.14922i	0.367231	+	0.367231i	−0.499235	+	0.866466i	$0.666386\pi$
$380$	−0.475708	−	0.228109i	−0.0244033	−	0.0117018i
$381$		0			0
$382$	−28.2375	−	6.42017i	−1.44475	−	0.328485i
$383$	3.80911	+	6.59757i	0.194636	+	0.337120i	0.946781	−	0.321878i	$-0.104314\pi$
$383$	3.80911	+	6.59757i	0.194636	+	0.337120i	−0.752145	+	0.658998i	$0.770981\pi$
$384$		0			0
$385$	0.260058	−	0.450434i	0.0132538	−	0.0229562i
$386$	−4.56180	+	4.92471i	−0.232190	+	0.250661i
$387$		0			0
$388$	−1.41207	−	18.4290i	−0.0716869	−	0.935591i
$389$	1.55794	−	0.417448i	0.0789905	−	0.0211654i	−0.219107	−	0.975701i	$-0.570314\pi$
$389$	1.55794	−	0.417448i	0.0789905	−	0.0211654i	0.298098	+	0.954535i	$0.403648\pi$
$390$		0			0
$391$	23.6071	+	40.8887i	1.19386	+	2.06783i
$392$	−2.66979	+	18.0196i	−0.134845	+	0.910126i
$393$		0			0
$394$	−6.20747	+	11.7689i	−0.312728	+	0.592910i
$395$	−1.88010	+	1.88010i	−0.0945979	+	0.0945979i
$396$		0			0
$397$	−20.8968	−	20.8968i	−1.04878	−	1.04878i	−0.998748	−	0.0500326i	$-0.984067\pi$
$397$	−20.8968	−	20.8968i	−1.04878	−	1.04878i	−0.0500326	−	0.998748i	$-0.515933\pi$
$398$	−9.54662	−	30.8577i	−0.478529	−	1.54676i
$399$		0			0
$400$	15.3137	−	12.2963i	0.765687	−	0.614817i
$401$	16.6619	−	9.61977i	0.832057	−	0.480388i	−0.0224993	−	0.999747i	$-0.507162\pi$
$401$	16.6619	−	9.61977i	0.832057	−	0.480388i	0.854557	+	0.519358i	$0.173829\pi$
$402$		0			0
$403$	−1.55577	−	5.80621i	−0.0774983	−	0.289228i
$404$	20.5636	−	23.9763i	1.02307	−	1.19286i
$405$		0			0
$406$	0.227856	+	5.95624i	0.0113083	+	0.295603i
$407$	19.1206	+	11.0393i	0.947772	+	0.547196i
$408$		0			0
$409$	4.69044	−	2.70803i	0.231928	−	0.133903i	−0.379533	−	0.925178i	$-0.623915\pi$
$409$	4.69044	−	2.70803i	0.231928	−	0.133903i	0.611461	+	0.791275i	$0.290582\pi$
$410$	−0.630986	−	1.00235i	−0.0311622	−	0.0495024i
$411$		0			0
$412$	20.3420	+	9.75430i	1.00218	+	0.480560i
$413$	−0.00461065	+	0.00461065i	−0.000226875	+	0.000226875i
$414$		0			0
$415$			0.410282i			0.0201400i
$416$	3.06386	−	8.87489i	0.150218	−	0.435128i
$417$		0			0
$418$	0.638108	−	2.80655i	0.0312109	−	0.137273i
$419$	−1.74346	+	6.50669i	−0.0851738	+	0.317873i	−0.995347	−	0.0963549i	$-0.969282\pi$
$419$	−1.74346	+	6.50669i	−0.0851738	+	0.317873i	0.910173	+	0.414228i	$0.135948\pi$
$420$		0			0
$421$	5.09689	+	19.0218i	0.248407	+	0.927068i	0.971640	+	0.236464i	$0.0759886\pi$
$421$	5.09689	+	19.0218i	0.248407	+	0.927068i	−0.723233	+	0.690604i	$0.757345\pi$
$422$	−0.828996	−	21.6703i	−0.0403549	−	1.05489i
$423$		0			0
$424$	1.22938	+	10.6703i	0.0597039	+	0.518196i
$425$	−16.5590	+	28.6810i	−0.803230	+	1.39124i
$426$		0			0
$427$	2.03874	−	7.60869i	0.0986616	−	0.368210i
$428$	4.89897	−	26.1309i	0.236801	−	1.26308i
$429$		0			0
$430$	−2.97593	+	0.920679i	−0.143512	+	0.0443991i
$431$	−22.9770			−1.10676			−0.553380	−	0.832929i	$-0.686662\pi$
$431$	−22.9770			−1.10676			−0.553380	+	0.832929i	$0.686662\pi$
$432$		0			0
$433$	−9.38876			−0.451195			−0.225598	−	0.974221i	$-0.572433\pi$
$433$	−9.38876			−0.451195			−0.225598	+	0.974221i	$0.572433\pi$
$434$	−3.66020	+	1.13238i	−0.175695	+	0.0543558i
$435$		0			0
$436$	−1.48766	−	0.278903i	−0.0712459	−	0.0133570i
$437$	1.59190	−	5.94106i	0.0761510	−	0.284199i
$438$		0			0
$439$	−2.64587	+	4.58278i	−0.126281	+	0.218724i	−0.922233	−	0.386635i	$-0.873637\pi$
$439$	−2.64587	+	4.58278i	−0.126281	+	0.218724i	0.795952	+	0.605359i	$0.206971\pi$
$440$	−1.54063	−	1.22230i	−0.0734464	−	0.0582707i
$441$		0			0
$442$	0.605226	+	15.8208i	0.0287877	+	0.752521i
$443$	−5.57188	−	20.7945i	−0.264728	−	0.987978i	−0.962417	−	0.271577i	$-0.912455\pi$
$443$	−5.57188	−	20.7945i	−0.264728	−	0.987978i	0.697689	−	0.716401i	$-0.254212\pi$
$444$		0			0
$445$	−1.22647	+	4.57724i	−0.0581402	+	0.216982i
$446$	2.31695	−	10.1905i	0.109711	−	0.482534i
$447$		0			0
$448$	−5.72728	−	1.73520i	−0.270588	−	0.0819806i
$449$		−	22.9162i		−	1.08148i	−0.841189	−	0.540742i	$-0.818144\pi$
$449$		−	22.9162i		−	1.08148i	0.841189	−	0.540742i	$-0.181856\pi$
$450$		0			0
$451$	4.56905	−	4.56905i	0.215148	−	0.215148i
$452$	3.52759	−	7.35658i	0.165924	−	0.346024i
$453$		0			0
$454$	−16.0772	−	25.5393i	−0.754540	−	1.19862i
$455$	0.322781	−	0.186358i	0.0151322	−	0.00873658i
$456$		0			0
$457$	−2.67987	−	1.54723i	−0.125359	−	0.0723761i	0.436009	−	0.899942i	$-0.356392\pi$
$457$	−2.67987	−	1.54723i	−0.125359	−	0.0723761i	−0.561368	+	0.827566i	$0.689725\pi$
$458$	0.996112	+	26.0388i	0.0465453	+	1.21671i
$459$		0			0
$460$	−3.19004	−	2.73598i	−0.148737	−	0.127566i
$461$	−0.410957	−	1.53371i	−0.0191402	−	0.0714320i	0.955695	−	0.294358i	$-0.0951058\pi$
$461$	−0.410957	−	1.53371i	−0.0191402	−	0.0714320i	−0.974835	+	0.222926i	$0.928439\pi$
$462$		0			0
$463$	0.0991508	−	0.0572447i	0.00460793	−	0.00266039i	−0.497694	−	0.867353i	$-0.665820\pi$
$463$	0.0991508	−	0.0572447i	0.00460793	−	0.00266039i	0.502302	+	0.864692i	$0.332487\pi$
$464$	22.4041	+	2.44846i	1.04009	+	0.113667i
$465$		0			0
$466$	−5.98748	−	19.3534i	−0.277365	−	0.896531i
$467$	0.325359	+	0.325359i	0.0150558	+	0.0150558i	0.714595	−	0.699539i	$-0.246611\pi$
$467$	0.325359	+	0.325359i	0.0150558	+	0.0150558i	−0.699539	+	0.714595i	$0.746611\pi$
$468$		0			0
$469$	4.80882	−	4.80882i	0.222051	−	0.222051i
$470$	0.121658	−	0.230655i	0.00561168	−	0.0106393i
$471$		0			0
$472$	0.0146900	+	0.0198000i	0.000676161	+	0.000911371i
$473$	−8.49723	−	14.7176i	−0.390703	−	0.676718i
$474$		0			0
$475$	4.16731	−	1.11663i	0.191209	−	0.0512344i
$476$	10.0619	−	0.770965i	0.461187	−	0.0353371i
$477$		0			0
$478$	22.0888	−	23.8461i	1.01032	−	1.09069i
$479$	−9.17908	+	15.8986i	−0.419403	+	0.726427i	−0.995879	−	0.0906864i	$-0.971094\pi$
$479$	−9.17908	+	15.8986i	−0.419403	+	0.726427i	0.576476	+	0.817114i	$0.304427\pi$
$480$		0			0
$481$	7.91075	+	13.7018i	0.360699	+	0.624749i
$482$	−28.3348	−	6.44230i	−1.29061	−	0.293439i
$483$		0			0
$484$	−4.87337	+	10.1631i	−0.221517	+	0.461960i
$485$	−1.96173	−	1.96173i	−0.0890774	−	0.0890774i
$486$		0			0
$487$	−24.8691			−1.12693			−0.563464	−	0.826140i	$-0.690532\pi$
$487$	−24.8691			−1.12693			−0.563464	+	0.826140i	$0.690532\pi$
$488$	−27.3287	−	11.8418i	−1.23711	−	0.536055i
$489$		0			0
$490$	1.45665	+	2.31395i	0.0658048	+	0.104534i
$491$	−0.201003	−	0.0538587i	−0.00907115	−	0.00243061i	0.254281	−	0.967130i	$-0.418161\pi$
$491$	−0.201003	−	0.0538587i	−0.00907115	−	0.00243061i	−0.263352	+	0.964700i	$0.584828\pi$
$492$		0			0
$493$	−36.7100	+	9.83640i	−1.65333	+	0.443009i
$494$	1.40159	−	1.51309i	0.0630607	−	0.0680773i
$495$		0			0
$496$	2.20705	+	14.3176i	0.0990994	+	0.642880i
$497$	10.3422	+	5.97108i	0.463912	+	0.267840i
$498$		0			0
$499$	34.2394	+	9.17443i	1.53277	+	0.410704i	0.923921	−	0.382584i	$-0.124966\pi$
$499$	34.2394	+	9.17443i	1.53277	+	0.410704i	0.608847	+	0.793288i	$0.291632\pi$
$500$	1.09637	−	5.84800i	0.0490312	−	0.261531i
$501$		0			0
$502$	0.779848	+	0.411328i	0.0348063	+	0.0183584i
$503$			39.4177i			1.75755i	0.477239	+	0.878773i	$0.341638\pi$
$503$			39.4177i			1.75755i	−0.477239	+	0.878773i	$0.658362\pi$
$504$		0			0
$505$		−	4.74117i		−	0.210979i
$506$	10.6963	−	20.2795i	0.475509	−	0.901532i
$507$		0			0
$508$	−2.01925	−	2.95108i	−0.0895898	−	0.130933i
$509$	38.2137	+	10.2393i	1.69379	+	0.453850i	0.971364	−	0.237598i	$-0.0763600\pi$
$509$	38.2137	+	10.2393i	1.69379	+	0.453850i	0.722427	+	0.691447i	$0.243027\pi$
$510$		0			0
$511$	−5.29783	−	3.05870i	−0.234362	−	0.135309i
$512$	−9.66392	+	20.4599i	−0.427089	+	0.904210i
$513$		0			0
$514$	−5.73405	−	5.31150i	−0.252918	−	0.234280i
$515$	3.27084	−	0.876418i	0.144130	−	0.0386196i
$516$		0			0
$517$	1.37418	+	0.368210i	0.0604363	+	0.0161939i
$518$	8.53425	−	5.37239i	0.374974	−	0.236049i
$519$		0			0
$520$	−0.518154	−	1.31056i	−0.0227226	−	0.0574717i
$521$	−21.5152			−0.942596			−0.471298	−	0.881974i	$-0.656214\pi$
$521$	−21.5152			−0.942596			−0.471298	+	0.881974i	$0.656214\pi$
$522$		0			0
$523$	18.8248	+	18.8248i	0.823149	+	0.823149i	0.986558	−	0.163409i	$-0.0522490\pi$
$523$	18.8248	+	18.8248i	0.823149	+	0.823149i	−0.163409	+	0.986558i	$0.552249\pi$
$524$	−2.66032	−	7.56216i	−0.116217	−	0.330355i
$525$		0			0
$526$	−1.75038	+	7.69861i	−0.0763204	+	0.335675i
$527$	−12.2144	−	21.1560i	−0.532069	−	0.921571i
$528$		0			0
$529$	12.9979	−	22.5130i	0.565125	−	0.978825i
$530$	1.18275	+	1.09559i	0.0513753	+	0.0475894i
$531$		0			0
$532$	−0.997876	−	0.855840i	−0.0432634	−	0.0371054i
$533$	4.47261	−	1.19843i	0.193730	−	0.0519099i
$534$		0			0
$535$	−1.99529	−	3.45594i	−0.0862639	−	0.149413i
$536$	−15.3214	−	20.6511i	−0.661783	−	0.891991i
$537$		0			0
$538$	2.94953	+	1.55572i	0.127163	+	0.0670717i
$539$	−10.5478	+	10.5478i	−0.454325	+	0.454325i
$540$		0			0
$541$	17.5988	+	17.5988i	0.756630	+	0.756630i	0.975707	−	0.219078i	$-0.0703048\pi$
$541$	17.5988	+	17.5988i	0.756630	+	0.756630i	−0.219078	+	0.975707i	$0.570305\pi$
$542$	−31.4440	+	9.72799i	−1.35063	+	0.417853i
$543$		0			0
$544$	2.69228	−	38.0614i	0.115431	−	1.63187i
$545$	−0.196750	+	0.113594i	−0.00842786	+	0.00486583i
$546$		0			0
$547$	−7.80612	−	29.1328i	−0.333765	−	1.24563i	−0.905201	−	0.424983i	$-0.860280\pi$
$547$	−7.80612	−	29.1328i	−0.333765	−	1.24563i	0.571436	−	0.820647i	$-0.306387\pi$
$548$	0.121173	+	1.58144i	0.00517627	+	0.0675559i
$549$		0			0
$550$	16.0705	−	0.614778i	0.685249	−	0.0262142i
$551$	4.28764	+	2.47547i	0.182660	+	0.105459i
$552$		0			0
$553$	−5.73777	+	3.31270i	−0.243995	+	0.140871i
$554$	0.848354	−	0.534046i	0.0360431	−	0.0226895i
$555$		0			0
$556$	12.1667	+	34.5849i	0.515985	+	1.46673i
$557$	25.0618	−	25.0618i	1.06190	−	1.06190i	0.0639497	−	0.997953i	$-0.479630\pi$
$557$	25.0618	−	25.0618i	1.06190	−	1.06190i	0.997953	−	0.0639497i	$-0.0203697\pi$
$558$		0			0
$559$		−	12.1782i		−	0.515084i
$560$	−0.822098	+	0.361957i	−0.0347400	+	0.0152955i
$561$		0			0
$562$	−6.32039	−	1.43703i	−0.266609	−	0.0606173i
$563$	−3.71859	+	13.8780i	−0.156720	+	0.584886i	0.842232	+	0.539115i	$0.181241\pi$
$563$	−3.71859	+	13.8780i	−0.156720	+	0.584886i	−0.998952	+	0.0457710i	$0.985426\pi$
$564$		0			0
$565$	−0.316952	−	1.18288i	−0.0133343	−	0.0497642i
$566$	20.5218	−	0.785063i	0.862597	−	0.0329986i
$567$		0			0
$568$	28.0646	−	35.3736i	1.17756	−	1.48424i
$569$	14.1987	−	24.5928i	0.595239	−	1.03098i	−0.398274	−	0.917267i	$-0.630391\pi$
$569$	14.1987	−	24.5928i	0.595239	−	1.03098i	0.993513	−	0.113718i	$-0.0362761\pi$
$570$		0			0
$571$	4.64190	−	17.3238i	0.194257	−	0.724978i	−0.798201	−	0.602392i	$-0.794214\pi$
$571$	4.64190	−	17.3238i	0.194257	−	0.724978i	0.992458	−	0.122586i	$-0.0391188\pi$
$572$	6.34512	−	4.34159i	0.265303	−	0.181531i
$573$		0			0
$574$	−0.872287	−	2.81951i	−0.0364086	−	0.117684i
$575$	34.3677			1.43323
$576$		0			0
$577$	−10.1199			−0.421295			−0.210648	−	0.977562i	$-0.567557\pi$
$577$	−10.1199			−0.421295			−0.210648	+	0.977562i	$0.567557\pi$
$578$	11.9113	+	38.5010i	0.495444	+	1.60143i
$579$		0			0
$580$	2.79188	−	1.91032i	0.115926	−	0.0793217i
$581$	−0.264604	+	0.987517i	−0.0109776	+	0.0409691i
$582$		0			0
$583$	−4.39772	+	7.61707i	−0.182135	+	0.315467i
$584$	−14.3762	+	18.1202i	−0.594890	+	0.749821i
$585$		0			0
$586$	−8.83878	+	0.338127i	−0.365127	+	0.0139679i
$587$	5.60833	+	20.9306i	0.231480	+	0.863897i	0.979704	+	0.200450i	$0.0642404\pi$
$587$	5.60833	+	20.9306i	0.231480	+	0.863897i	−0.748224	+	0.663447i	$0.769093\pi$
$588$		0			0
$589$	−0.823658	+	3.07394i	−0.0339383	+	0.126659i
$590$	0.00360852		0.000820446i	0.000148560		3.37772e-5i
$591$		0			0
$592$	−15.3648	−	34.8975i	−0.631489	−	1.43428i
$593$			20.8755i			0.857256i	0.903481	+	0.428628i	$0.141003\pi$
$593$			20.8755i			0.857256i	−0.903481	+	0.428628i	$0.858997\pi$
$594$		0			0
$595$	1.07107	−	1.07107i	0.0439095	−	0.0439095i
$596$	8.66786	+	24.6390i	0.355049	+	1.00925i
$597$		0			0
$598$	13.9042	−	8.75282i	0.568585	−	0.357930i
$599$	9.64766	−	5.57008i	0.394193	−	0.227587i	−0.289782	−	0.957093i	$-0.593583\pi$
$599$	9.64766	−	5.57008i	0.394193	−	0.227587i	0.683975	+	0.729505i	$0.260250\pi$
$600$		0			0
$601$	−21.0323	−	12.1430i	−0.857927	−	0.495324i	0.00539080	−	0.999985i	$-0.498284\pi$
$601$	−21.0323	−	12.1430i	−0.857927	−	0.495324i	−0.863317	+	0.504661i	$0.831617\pi$
$602$	−7.75660	+	0.296729i	−0.316135	+	0.0120938i
$603$		0			0
$604$	2.88792	+	37.6905i	0.117508	+	1.53360i
$605$	0.437870	+	1.63415i	0.0178019	+	0.0664377i
$606$		0			0
$607$	−23.4924	+	13.5633i	−0.953525	+	0.550518i	−0.894174	−	0.447719i	$-0.852236\pi$
$607$	−23.4924	+	13.5633i	−0.953525	+	0.550518i	−0.0593510	+	0.998237i	$0.518903\pi$
$608$	−3.75404	+	3.25804i	−0.152247	+	0.132131i
$609$		0			0
$610$	−4.27085	+	1.32130i	−0.172922	+	0.0534977i
$611$	0.720877	+	0.720877i	0.0291636	+	0.0291636i
$612$		0			0
$613$	−25.5272	+	25.5272i	−1.03103	+	1.03103i	−0.0315305	+	0.999503i	$0.510038\pi$
$613$	−25.5272	+	25.5272i	−1.03103	+	1.03103i	−0.999503	+	0.0315305i	$0.989962\pi$
$614$	7.99700	+	4.21798i	0.322733	+	0.170224i
$615$		0			0
$616$	−2.91986	−	3.93557i	−0.117645	−	0.158569i
$617$	−3.82807	−	6.63041i	−0.154112	−	0.266930i	0.778623	−	0.627492i	$-0.215918\pi$
$617$	−3.82807	−	6.63041i	−0.154112	−	0.266930i	−0.932735	+	0.360562i	$0.882585\pi$
$618$		0			0
$619$	31.4778	−	8.43446i	1.26520	−	0.339009i	0.437010	−	0.899457i	$-0.356037\pi$
$619$	31.4778	−	8.43446i	1.26520	−	0.339009i	0.828190	+	0.560447i	$0.189371\pi$
$620$	1.65055	+	1.41561i	0.0662875	+	0.0568523i
$621$		0			0
$622$	13.1345	+	12.1666i	0.526647	+	0.487838i
$623$	−5.90402	+	10.2261i	−0.236540	+	0.409699i
$624$		0			0
$625$	11.8282	+	20.4870i	0.473126	+	0.819479i
$626$	−6.02012	+	26.4779i	−0.240612	+	1.05827i
$627$		0			0
$628$	6.32265	+	17.9726i	0.252301	+	0.717185i
$629$	45.4661	+	45.4661i	1.81285	+	1.81285i
$630$		0			0
$631$	−20.5675			−0.818781			−0.409390	−	0.912359i	$-0.634259\pi$
$631$	−20.5675			−0.818781			−0.409390	+	0.912359i	$0.634259\pi$
$632$	9.21074	+	23.2965i	0.366383	+	0.926686i
$633$		0			0
$634$	13.7327	−	8.64488i	0.545396	−	0.343332i
$635$	−0.518437	−	0.138915i	−0.0205735	−	0.00551266i
$636$		0			0
$637$	−10.3252	+	2.76662i	−0.409098	+	0.109617i
$638$	13.5393	+	12.5415i	0.536024	+	0.496524i
$639$		0			0
$640$	0.898239	+	3.27544i	0.0355060	+	0.129473i
$641$	−12.3382	−	7.12347i	−0.487330	−	0.281360i	0.236136	−	0.971720i	$-0.424119\pi$
$641$	−12.3382	−	7.12347i	−0.487330	−	0.281360i	−0.723466	+	0.690360i	$0.757452\pi$
$642$		0			0
$643$	−11.5700	−	3.10018i	−0.456277	−	0.122259i	0.0233581	−	0.999727i	$-0.492564\pi$
$643$	−11.5700	−	3.10018i	−0.456277	−	0.122259i	−0.479635	+	0.877468i	$0.659231\pi$
$644$	−5.91366	−	8.64265i	−0.233031	−	0.340568i
$645$		0			0
$646$	3.91046	−	7.41396i	0.153855	−	0.291698i
$647$		−	3.24662i		−	0.127638i	−0.997961	−	0.0638189i	$-0.979672\pi$
$647$		−	3.24662i		−	0.127638i	0.997961	−	0.0638189i	$-0.0203280\pi$
$648$		0			0
$649$			0.0201888i			0.000792479i
$650$	10.1935	+	5.37654i	0.399824	+	0.210885i
$651$		0			0
$652$	3.25725	−	17.3741i	0.127564	−	0.680421i
$653$	0.0969809	+	0.0259859i	0.00379516	+	0.00101691i	0.260716	−	0.965416i	$-0.416041\pi$
$653$	0.0969809	+	0.0259859i	0.00379516	+	0.00101691i	−0.256921	+	0.966432i	$0.582708\pi$
$654$		0			0
$655$	−1.04206	−	0.601635i	−0.0407167	−	0.0235078i
$656$	−11.0291	+	1.70012i	−0.430613	+	0.0663787i
$657$		0			0
$658$	0.441579	−	0.476708i	0.0172145	−	0.0185840i
$659$	−18.4436	+	4.94194i	−0.718459	+	0.192511i	−0.599484	−	0.800387i	$-0.704628\pi$
$659$	−18.4436	+	4.94194i	−0.718459	+	0.192511i	−0.118975	+	0.992897i	$0.537961\pi$
$660$		0			0
$661$	26.6109	+	7.13036i	1.03504	+	0.277339i	0.736058	−	0.676919i	$-0.236685\pi$
$661$	26.6109	+	7.13036i	1.03504	+	0.277339i	0.298985	+	0.954258i	$0.403352\pi$
$662$	14.8092	+	23.5250i	0.575575	+	0.914325i
$663$		0			0
$664$	3.54694	+	1.53693i	0.137648	+	0.0596444i
$665$	−0.197324			−0.00765189
$666$		0			0
$667$	27.8876	+	27.8876i	1.07981	+	1.07981i
$668$	7.95255	−	16.5845i	0.307693	−	0.641675i
$669$		0			0
$670$	−3.76362	−	0.855711i	−0.145401	−	0.0330590i
$671$	−12.1947	−	21.1218i	−0.470769	−	0.815396i
$672$		0			0
$673$	21.3890	−	37.0468i	0.824484	−	1.42805i	−0.0778289	−	0.996967i	$-0.524799\pi$
$673$	21.3890	−	37.0468i	0.824484	−	1.42805i	0.902313	−	0.431082i	$-0.141868\pi$
$674$	9.59139	−	10.3544i	0.369446	−	0.398837i
$675$		0			0
$676$	−20.4307	+	1.56544i	−0.785795	+	0.0602093i
$677$	−7.49190	+	2.00745i	−0.287937	+	0.0771525i	−0.399897	−	0.916560i	$-0.630954\pi$
$677$	−7.49190	+	2.00745i	−0.287937	+	0.0771525i	0.111960	+	0.993713i	$0.464287\pi$
$678$		0			0
$679$	−3.45654	−	5.98690i	−0.132650	−	0.229756i
$680$	−3.41253	−	4.59961i	−0.130865	−	0.176387i
$681$		0			0
$682$	−5.53433	+	10.4927i	−0.211921	+	0.401786i
$683$	31.9083	−	31.9083i	1.22094	−	1.22094i	0.253637	−	0.967299i	$-0.418373\pi$
$683$	31.9083	−	31.9083i	1.22094	−	1.22094i	0.967299	−	0.253637i	$-0.0816269\pi$
$684$		0			0
$685$	0.168341	+	0.168341i	0.00643198	+	0.00643198i
$686$	4.20236	+	13.5834i	0.160447	+	0.518616i
$687$		0			0
$688$	−3.18854	+	29.1761i	−0.121562	+	1.11233i
$689$	−5.45840	+	3.15141i	−0.207948	+	0.120059i
$690$		0			0
$691$	−7.81032	−	29.1485i	−0.297118	−	1.10886i	−0.939520	−	0.342493i	$-0.888729\pi$
$691$	−7.81032	−	29.1485i	−0.297118	−	1.10886i	0.642402	−	0.766368i	$-0.277938\pi$
$692$	12.0569	+	10.3408i	0.458335	+	0.393097i
$693$		0			0
$694$	−0.378387	−	9.89117i	−0.0143634	−	0.375464i
$695$	4.76578	+	2.75152i	0.180776	+	0.104371i
$696$		0			0
$697$	16.2968	−	9.40898i	0.617286	−	0.356390i
$698$	−15.2277	−	24.1898i	−0.576378	−	0.915599i
$699$		0			0
$700$	3.17607	−	6.62351i	0.120044	−	0.250345i
$701$	−6.92803	+	6.92803i	−0.261668	+	0.261668i	−0.825732	−	0.564063i	$-0.809237\pi$
$701$	−6.92803	+	6.92803i	−0.261668	+	0.261668i	0.564063	+	0.825732i	$0.309237\pi$
$702$		0			0
$703$		−	8.37625i		−	0.315916i
$704$	−16.3381	+	8.74012i	−0.615765	+	0.329406i
$705$		0			0
$706$	−3.03277	+	13.3389i	−0.114140	+	0.502015i
$707$	3.05773	−	11.4116i	0.114998	−	0.429178i
$708$		0			0
$709$	3.97247	+	14.8255i	0.149189	+	0.556782i	0.999533	+	0.0305546i	$0.00972734\pi$
$709$	3.97247	+	14.8255i	0.149189	+	0.556782i	−0.850344	+	0.526228i	$0.823606\pi$
$710$	−0.259090	−	6.77271i	−0.00972347	−	0.254175i
$711$		0			0
$712$	34.9764	+	27.7494i	1.31079	+	1.03995i
$713$	−12.6753	+	21.9543i	−0.474695	+	0.822195i
$714$		0			0
$715$	0.298680	−	1.11469i	0.0111700	−	0.0416871i
$716$	22.2246	+	4.16662i	0.830571	+	0.155714i
$717$		0			0
$718$	−1.14420	+	0.353988i	−0.0427013	+	0.0132107i
$719$	−6.93438			−0.258609			−0.129304	−	0.991605i	$-0.541274\pi$
$719$	−6.93438			−0.258609			−0.129304	+	0.991605i	$0.541274\pi$
$720$		0			0
$721$	8.43787			0.314243
$722$	24.6265	−	7.61884i	0.916504	−	0.283544i
$723$		0			0
$724$	−7.57137	+	40.3854i	−0.281388	+	1.50091i
$725$	−7.16001	+	26.7215i	−0.265916	+	0.992412i
$726$		0			0
$727$	−7.03023	+	12.1767i	−0.260737	+	0.451610i	−0.966438	−	0.256900i	$-0.917299\pi$
$727$	−7.03023	+	12.1767i	−0.260737	+	0.451610i	0.705701	+	0.708510i	$0.250632\pi$
$728$	−0.401936	−	3.48858i	−0.0148967	−	0.129295i
$729$		0			0
$730$	0.132720	+	3.46934i	0.00491217	+	0.128406i
$731$	−12.8096	−	47.8061i	−0.473780	−	1.76817i
$732$		0			0
$733$	−0.0626936	+	0.233976i	−0.00231564	+	0.00864209i	−0.967074	−	0.254495i	$-0.918091\pi$
$733$	−0.0626936	+	0.233976i	−0.00231564	+	0.00864209i	0.964758	+	0.263138i	$0.0847573\pi$
$734$	5.64642	−	24.8343i	0.208413	−	0.916651i
$735$		0			0
$736$	−35.6028	+	17.3292i	−1.31234	+	0.638763i
$737$		−	21.0565i		−	0.775627i
$738$		0			0
$739$	−6.77417	+	6.77417i	−0.249192	+	0.249192i	−0.820639	−	0.571447i	$-0.806382\pi$
$739$	−6.77417	+	6.77417i	−0.249192	+	0.249192i	0.571447	+	0.820639i	$0.306382\pi$
$740$	−5.16069	−	2.47463i	−0.189711	−	0.0909693i
$741$		0			0
$742$	2.14020	+	3.39979i	0.0785692	+	0.124810i
$743$	5.26562	−	3.04011i	0.193177	−	0.111531i	−0.400292	−	0.916388i	$-0.631091\pi$
$743$	5.26562	−	3.04011i	0.193177	−	0.111531i	0.593469	+	0.804857i	$0.297758\pi$
$744$		0			0
$745$	3.39524	+	1.96024i	0.124392	+	0.0718178i
$746$	1.04709	+	27.3713i	0.0383367	+	1.00214i
$747$		0			0
$748$	20.3413	−	23.7171i	0.743751	−	0.867185i
$749$	−2.57365	−	9.60501i	−0.0940393	−	0.350959i
$750$		0			0
$751$	21.6001	−	12.4708i	0.788199	−	0.455067i	−0.0511293	−	0.998692i	$-0.516282\pi$
$751$	21.6001	−	12.4708i	0.788199	−	0.455067i	0.839328	+	0.543625i	$0.182949\pi$
$752$	−1.53831	−	1.91579i	−0.0560962	−	0.0698617i
$753$		0			0
$754$	3.90875	+	12.6343i	0.142348	+	0.460115i
$755$	4.01206	+	4.01206i	0.146014	+	0.146014i
$756$		0			0
$757$	27.5078	−	27.5078i	0.999789	−	0.999789i	−0.000211103	−	1.00000i	$-0.500067\pi$
$757$	27.5078	−	27.5078i	0.999789	−	0.999789i	1.00000		0.000211103i	$6.71963e-5\pi$
$758$	6.67064	−	12.6471i	0.242289	−	0.459362i
$759$		0			0
$760$	−0.109349	+	0.738042i	−0.00396649	+	0.0267716i
$761$	−3.41665	−	5.91781i	−0.123854	−	0.214521i	0.797431	−	0.603411i	$-0.206192\pi$
$761$	−3.41665	−	5.91781i	−0.123854	−	0.214521i	−0.921284	+	0.388890i	$0.872859\pi$
$762$		0			0
$763$	−0.546823	+	0.146521i	−0.0197963	+	0.00530440i
$764$	3.12873	+	40.8333i	0.113194	+	1.47730i
$765$		0			0
$766$	7.32143	−	7.90387i	0.264534	−	0.285579i
$767$	−0.00723364	+	0.0125290i	−0.000261192	+	0.000452397i
$768$		0			0
$769$	−1.16390	−	2.01594i	−0.0419714	−	0.0726966i	0.844277	−	0.535908i	$-0.180031\pi$
$769$	−1.16390	−	2.01594i	−0.0419714	−	0.0726966i	−0.886248	+	0.463211i	$0.846697\pi$
$770$	−0.717250	−	0.163077i	−0.0258479	−	0.00587687i
$771$		0			0
$772$	8.56018	+	4.10474i	0.308088	+	0.147733i
$773$	4.66783	+	4.66783i	0.167890	+	0.167890i	0.786051	−	0.618161i	$-0.212122\pi$
$773$	4.66783	+	4.66783i	0.167890	+	0.167890i	−0.618161	+	0.786051i	$0.712122\pi$
$774$		0			0
$775$	−17.7820			−0.638749
$776$	−24.3080	+	9.61065i	−0.872607	+	0.345002i
$777$		0			0
$778$	−1.21517	−	1.93034i	−0.0435659	−	0.0692062i
$779$	−2.36790	−	0.634477i	−0.0848389	−	0.0227325i
$780$		0			0
$781$	35.7158	−	9.57001i	1.27801	−	0.342442i
$782$	45.3748	−	48.9846i	1.62260	−	1.75168i
$783$		0			0
$784$	25.4610	−	3.92479i	0.909321	−	0.140171i
$785$	2.47661	+	1.42987i	0.0883942	+	0.0510344i
$786$		0			0
$787$	−28.3785	−	7.60400i	−1.01158	−	0.271053i	−0.285293	−	0.958440i	$-0.592091\pi$
$787$	−28.3785	−	7.60400i	−1.01158	−	0.271053i	−0.726291	+	0.687387i	$0.758758\pi$
$788$	18.4948	+	3.46737i	0.658850	+	0.123520i
$789$		0			0
$790$	3.32591	+	1.75424i	0.118331	+	0.0624130i
$791$		−	3.05151i		−	0.108499i
$792$		0			0
$793$		−	17.4774i		−	0.620640i
$794$	−19.4979	+	36.9667i	−0.691955	+	1.31190i
$795$		0			0
$796$	−37.6996	+	25.7956i	−1.33623	+	0.914302i
$797$	−48.4997	−	12.9954i	−1.71795	−	0.460322i	−0.740596	−	0.671951i	$-0.765457\pi$
$797$	−48.4997	−	12.9954i	−1.71795	−	0.460322i	−0.977350	+	0.211629i	$0.932123\pi$
$798$		0			0
$799$	3.58808	+	2.07158i	0.126937	+	0.0732871i
$800$	−23.0136	−	15.5498i	−0.813653	−	0.549769i
$801$		0			0
$802$	−19.9609	−	18.4900i	−0.704846	−	0.652905i
$803$	−18.2955	+	4.90227i	−0.645634	+	0.172997i
$804$		0			0
$805$	−1.51831	−	0.406831i	−0.0535135	−	0.0143389i
$806$	−7.19411	+	4.52876i	−0.253402	+	0.159519i
$807$		0			0
$808$	−40.9879	−	17.7605i	−1.44195	−	0.624814i
$809$	−54.3452			−1.91068			−0.955338	−	0.295515i	$-0.904509\pi$
$809$	−54.3452			−1.91068			−0.955338	+	0.295515i	$0.904509\pi$
$810$		0			0
$811$	−22.9318	−	22.9318i	−0.805245	−	0.805245i	0.178665	−	0.983910i	$-0.442822\pi$
$811$	−22.9318	−	22.9318i	−0.805245	−	0.805245i	−0.983910	+	0.178665i	$0.942822\pi$
$812$	7.95185	−	2.79741i	0.279055	−	0.0981699i
$813$		0			0
$814$	6.92248	−	30.4467i	0.242633	−	1.06716i
$815$	−1.32664	−	2.29781i	−0.0464701	−	0.0804886i
$816$		0			0
$817$	−3.22372	+	5.58364i	−0.112784	+	0.195347i
$818$	−5.61914	−	5.20506i	−0.196469	−	0.181991i
$819$		0			0
$820$	−1.09047	+	1.27144i	−0.0380808	+	0.0444007i
$821$	42.0690	−	11.2724i	1.46822	−	0.393408i	0.565899	−	0.824475i	$-0.308529\pi$
$821$	42.0690	−	11.2724i	1.46822	−	0.393408i	0.902320	+	0.431067i	$0.141863\pi$
$822$		0			0
$823$	−2.52571	−	4.37465i	−0.0880406	−	0.152491i	0.818642	−	0.574304i	$-0.194727\pi$
$823$	−2.52571	−	4.37465i	−0.0880406	−	0.152491i	−0.906683	+	0.421813i	$0.861394\pi$
$824$	4.67592	−	31.5598i	0.162893	−	1.09944i
$825$		0			0
$826$	0.00815629	+	0.00430200i	0.000283794	+	0.000149686i
$827$	27.8757	−	27.8757i	0.969334	−	0.969334i	−0.0302095	−	0.999544i	$-0.509617\pi$
$827$	27.8757	−	27.8757i	0.969334	−	0.969334i	0.999544	+	0.0302095i	$0.00961743\pi$
$828$		0			0
$829$	3.00281	+	3.00281i	0.104292	+	0.104292i	0.757327	−	0.653035i	$-0.226505\pi$
$829$	3.00281	+	3.00281i	0.104292	+	0.104292i	−0.653035	+	0.757327i	$0.726505\pi$
$830$	0.554306	−	0.171489i	0.0192402	−	0.00595246i
$831$		0			0
$832$	−13.2709	−	0.429880i	−0.460086	−	0.0149034i
$833$	−37.6217	+	21.7209i	−1.30352	+	0.752585i
$834$		0			0
$835$	−0.714531	−	2.66667i	−0.0247274	−	0.0922838i
$836$	−4.05846	+	0.310968i	−0.140365	+	0.0107550i
$837$		0			0
$838$	9.51950	−	0.364168i	0.328846	−	0.0125800i
$839$	−6.29143	−	3.63236i	−0.217204	−	0.125403i	0.387451	−	0.921890i	$-0.373356\pi$
$839$	−6.29143	−	3.63236i	−0.217204	−	0.125403i	−0.604655	+	0.796487i	$0.706689\pi$
$840$		0			0
$841$	−2.37837	+	1.37315i	−0.0820126	+	0.0473500i
$842$	23.5688	−	14.8368i	0.812234	−	0.511309i
$843$		0			0
$844$	−28.9308	+	10.1777i	−0.995839	+	0.350330i
$845$	−2.17480	+	2.17480i	−0.0748154	+	0.0748154i
$846$		0			0
$847$			4.21567i			0.144852i
$848$	13.9021	−	6.12088i	0.477401	−	0.210192i
$849$		0			0
$850$	45.6704	+	10.3838i	1.56648	+	0.356161i
$851$	17.2697	−	64.4513i	0.591997	−	2.20936i
$852$		0			0
$853$	7.07889	+	26.4188i	0.242377	+	0.904562i	0.974684	+	0.223587i	$0.0717768\pi$
$853$	7.07889	+	26.4188i	0.242377	+	0.904562i	−0.732307	+	0.680974i	$0.761557\pi$
$854$	−11.1317	+	0.425845i	−0.380921	+	0.0145721i
$855$		0			0
$856$	−37.3514	+	4.30344i	−1.27665	+	0.147088i
$857$	3.27792	−	5.67752i	0.111971	−	0.193940i	−0.804594	−	0.593826i	$-0.797617\pi$
$857$	3.27792	−	5.67752i	0.111971	−	0.193940i	0.916565	+	0.399886i	$0.130950\pi$
$858$		0			0
$859$	8.89601	−	33.2003i	0.303528	−	1.13278i	−0.630677	−	0.776045i	$-0.717223\pi$
$859$	8.89601	−	33.2003i	0.303528	−	1.13278i	0.934205	−	0.356736i	$-0.116110\pi$
$860$	2.48774	+	3.63576i	0.0848312	+	0.123978i
$861$		0			0
$862$	9.60384	+	31.0427i	0.327108	+	1.05732i
$863$	−39.5164			−1.34515			−0.672576	−	0.740028i	$-0.734812\pi$
$863$	−39.5164			−1.34515			−0.672576	+	0.740028i	$0.734812\pi$
$864$		0			0
$865$	2.38418			0.0810646
$866$	3.92429	+	12.6845i	0.133353	+	0.431038i
$867$		0			0
$868$	3.05976	+	4.47175i	0.103855	+	0.151781i
$869$	−5.30936	+	19.8148i	−0.180108	+	0.672171i
$870$		0			0
$871$	7.54456	−	13.0676i	0.255638	−	0.442777i
$872$	0.244999	+	2.12645i	0.00829671	+	0.0720108i
$873$		0			0
$874$	−8.69196	+	0.332511i	−0.294010	+	0.0112473i
$875$	−0.575974	−	2.14957i	−0.0194715	−	0.0726686i
$876$		0			0
$877$	12.4013	−	46.2823i	0.418763	−	1.56284i	−0.358415	−	0.933562i	$-0.616683\pi$
$877$	12.4013	−	46.2823i	0.418763	−	1.56284i	0.777178	−	0.629281i	$-0.216651\pi$
$878$	7.29741	+	1.65917i	0.246276	+	0.0559942i
$879$		0			0
$880$	−1.00742	+	2.59233i	−0.0339601	+	0.0873874i
$881$			23.6718i			0.797522i	0.917055	+	0.398761i	$0.130560\pi$
$881$			23.6718i			0.797522i	−0.917055	+	0.398761i	$0.869440\pi$
$882$		0			0
$883$	−7.40173	+	7.40173i	−0.249088	+	0.249088i	−0.820596	−	0.571508i	$-0.806359\pi$
$883$	−7.40173	+	7.40173i	−0.249088	+	0.249088i	0.571508	+	0.820596i	$0.306359\pi$
$884$	21.1215	−	7.43043i	0.710394	−	0.249912i
$885$		0			0
$886$	−25.7652	+	16.2194i	−0.865600	+	0.544903i
$887$	19.6764	−	11.3602i	0.660669	−	0.381438i	−0.131863	−	0.991268i	$-0.542096\pi$
$887$	19.6764	−	11.3602i	0.660669	−	0.381438i	0.792532	+	0.609830i	$0.208762\pi$
$888$		0			0
$889$	−1.15825	−	0.668713i	−0.0388463	−	0.0224279i
$890$	6.69665	−	0.256180i	0.224472	−	0.00858718i
$891$		0			0
$892$	−14.7362	+	1.12912i	−0.493403	+	0.0378056i
$893$	−0.139693	−	0.521341i	−0.00467465	−	0.0174460i
$894$		0			0
$895$	2.93931	−	1.69701i	0.0982504	−	0.0567249i
$896$	0.0495516	+	8.46303i	0.00165540	+	0.282730i
$897$		0			0
$898$	−30.9606	+	9.57846i	−1.03317	+	0.319637i
$899$	−14.4292	−	14.4292i	−0.481240	−	0.481240i
$900$		0			0
$901$	−18.1123	+	18.1123i	−0.603409	+	0.603409i
$902$	−8.08270	−	4.26318i	−0.269124	−	0.141949i
$903$		0			0
$904$	−11.4134	−	1.69102i	−0.379606	−	0.0562425i
$905$	3.08372	+	5.34117i	0.102506	+	0.177546i
$906$		0			0
$907$	28.8653	−	7.73443i	0.958456	−	0.256818i	0.254509	−	0.967070i	$-0.418086\pi$
$907$	28.8653	−	7.73443i	0.958456	−	0.256818i	0.703947	+	0.710253i	$0.251419\pi$
$908$	−27.7845	+	32.3957i	−0.922062	+	1.07509i
$909$		0			0
$910$	−0.386691	−	0.358195i	−0.0128187	−	0.0118741i
$911$	−2.23081	+	3.86388i	−0.0739100	+	0.128016i	−0.900612	−	0.434625i	$-0.856881\pi$
$911$	−2.23081	+	3.86388i	−0.0739100	+	0.128016i	0.826702	+	0.562640i	$0.190214\pi$
$912$		0			0
$913$	1.58272	+	2.74135i	0.0523804	+	0.0907255i
$914$	−0.970230	+	4.26731i	−0.0320924	+	0.141150i
$915$		0			0
$916$	34.7629	−	12.2294i	1.14860	−	0.404070i
$917$	−2.12015	−	2.12015i	−0.0700134	−	0.0700134i
$918$		0			0
$919$	−43.4889			−1.43457			−0.717283	−	0.696782i	$-0.754615\pi$
$919$	−43.4889			−1.43457			−0.717283	+	0.696782i	$0.754615\pi$
$920$	−2.36304	+	5.45344i	−0.0779071	+	0.179794i
$921$		0			0
$922$	−1.90033	+	1.19627i	−0.0625839	+	0.0393971i
$923$	25.5939	+	6.85787i	0.842435	+	0.225730i
$924$		0			0
$925$	45.2089	−	12.1137i	1.48646	−	0.398295i
$926$	−0.118782	−	0.110029i	−0.00390343	−	0.00361578i
$927$		0			0
$928$	−6.05646	−	31.2922i	−0.198813	−	1.02722i
$929$	−33.8981	−	19.5711i	−1.11216	−	0.642107i	−0.172774	−	0.984962i	$-0.555273\pi$
$929$	−33.8981	−	19.5711i	−1.11216	−	0.642107i	−0.939389	+	0.342854i	$0.888606\pi$
$930$		0			0
$931$	5.46638	+	1.46471i	0.179153	+	0.0480040i
$932$	−23.6445	+	16.1786i	−0.774503	+	0.529947i
$933$		0			0
$934$	0.303579	−	0.575564i	0.00993340	−	0.0188330i
$935$		−	4.68992i		−	0.153377i
$936$		0			0
$937$		−	34.6928i		−	1.13336i	−0.823936	−	0.566682i	$-0.808227\pi$
$937$		−	34.6928i		−	1.13336i	0.823936	−	0.566682i	$-0.191773\pi$
$938$	−8.50686	−	4.48691i	−0.277759	−	0.146503i
$939$		0			0
$940$	−0.362474	−	0.0679559i	−0.0118226	−	0.00221648i
$941$	23.5900	+	6.32091i	0.769011	+	0.206056i	0.621934	−	0.783069i	$-0.286347\pi$
$941$	23.5900	+	6.32091i	0.769011	+	0.206056i	0.147076	+	0.989125i	$0.453014\pi$
$942$		0			0
$943$	−16.9118	−	9.76401i	−0.550723	−	0.317960i
$944$	0.0206105	−	0.0281226i	0.000670814	−	0.000915314i
$945$		0			0
$946$	−16.3324	+	17.6317i	−0.531012	+	0.573256i
$947$	−51.8344	+	13.8890i	−1.68439	+	0.451331i	−0.968933	−	0.247325i	$-0.920449\pi$
$947$	−51.8344	+	13.8890i	−1.68439	+	0.451331i	−0.715458	+	0.698656i	$0.753782\pi$
$948$		0			0
$949$	−13.1106	−	3.51297i	−0.425587	−	0.114036i
$950$	−3.25044	−	5.16345i	−0.105458	−	0.167525i
$951$		0			0
$952$	−5.24725	−	13.2718i	−0.170064	−	0.430140i
$953$	40.6369			1.31636			0.658180	−	0.752861i	$-0.271327\pi$
$953$	40.6369			1.31636			0.658180	+	0.752861i	$0.271327\pi$
$954$		0			0
$955$	4.34661	+	4.34661i	0.140653	+	0.140653i
$956$	−41.4495	−	19.8757i	−1.34057	−	0.642825i
$957$		0			0
$958$	25.3163	+	5.75600i	0.817931	+	0.185968i
$959$	0.296615	+	0.513752i	0.00957819	+	0.0165899i
$960$		0			0
$961$	−8.94172	+	15.4875i	−0.288443	+	0.499597i
$962$	15.2051	−	16.4147i	0.490233	−	0.529232i
$963$		0			0
$964$	3.13952	+	40.9740i	0.101117	+	1.31969i
$965$	1.37641	−	0.368808i	0.0443082	−	0.0118724i
$966$		0			0
$967$	−2.97787	−	5.15783i	−0.0957620	−	0.165865i	0.814164	−	0.580634i	$-0.197195\pi$
$967$	−2.97787	−	5.15783i	−0.0957620	−	0.165865i	−0.909926	+	0.414770i	$0.863862\pi$
$968$	15.7677	+	2.33615i	0.506793	+	0.0750866i
$969$		0			0
$970$	−1.83040	+	3.47032i	−0.0587707	+	0.111425i
$971$	17.0165	−	17.0165i	0.546085	−	0.546085i	−0.379221	−	0.925306i	$-0.623808\pi$
$971$	17.0165	−	17.0165i	0.546085	−	0.546085i	0.925306	+	0.379221i	$0.123808\pi$
$972$		0			0
$973$	9.69630	+	9.69630i	0.310849	+	0.310849i
$974$	10.3947	+	33.5991i	0.333069	+	1.07658i
$975$		0			0
$976$	−4.57598	+	41.8716i	−0.146474	+	1.34028i
$977$	10.2439	−	5.91431i	0.327731	−	0.189215i	−0.327102	−	0.944989i	$-0.606072\pi$
$977$	10.2439	−	5.91431i	0.327731	−	0.189215i	0.654833	+	0.755773i	$0.272739\pi$
$978$		0			0
$979$	9.46254	+	35.3147i	0.302424	+	1.12866i
$980$	2.51738	−	2.93516i	0.0804147	−	0.0937603i
$981$		0			0
$982$	0.0112498	+	0.294074i	0.000358996	+	0.00938428i
$983$	−38.2947	−	22.1094i	−1.22141	−	0.705181i	−0.256192	−	0.966626i	$-0.582468\pi$
$983$	−38.2947	−	22.1094i	−1.22141	−	0.705181i	−0.965218	+	0.261445i	$0.915801\pi$
$984$		0			0
$985$	2.44603	−	1.41222i	0.0779370	−	0.0449970i
$986$	28.6332	+	45.4850i	0.911868	+	1.44854i
$987$		0			0
$988$	−2.63008	−	1.26116i	−0.0836739	−	0.0401229i
$989$	−36.3170	+	36.3170i	−1.15481	+	1.15481i
$990$		0			0
$991$		−	21.3026i		−	0.676701i	−0.941020	−	0.338350i	$-0.890131\pi$
$991$		−	21.3026i		−	0.676701i	0.941020	−	0.338350i	$-0.109869\pi$
$992$	18.4211	−	8.96623i	0.584870	−	0.284678i
$993$		0			0
$994$	3.74433	−	16.4685i	0.118763	−	0.522348i
$995$	−1.77461	+	6.62295i	−0.0562590	+	0.209962i
$996$		0			0
$997$	7.81197	+	29.1547i	0.247408	+	0.923338i	0.972158	+	0.234326i	$0.0752884\pi$
$997$	7.81197	+	29.1547i	0.247408	+	0.923338i	−0.724750	+	0.689012i	$0.758045\pi$
$998$	−1.91632	−	50.0934i	−0.0606601	−	1.58568i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.v.a.35.8		88
3.2	odd	2		144.2.u.a.83.15	yes	88
4.3	odd	2		1728.2.z.a.1007.11		88
9.4	even	3		144.2.u.a.131.21	yes	88
9.5	odd	6	inner	432.2.v.a.179.2		88
12.11	even	2		576.2.y.a.47.2		88
16.5	even	4		1728.2.z.a.143.11		88
16.11	odd	4	inner	432.2.v.a.251.2		88
36.23	even	6		1728.2.z.a.1583.11		88
36.31	odd	6		576.2.y.a.239.12		88
48.5	odd	4		576.2.y.a.335.12		88
48.11	even	4		144.2.u.a.11.21	✓	88
144.5	odd	12		1728.2.z.a.719.11		88
144.59	even	12	inner	432.2.v.a.395.8		88
144.85	even	12		576.2.y.a.527.2		88
144.139	odd	12		144.2.u.a.59.15	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.21	✓	88	48.11	even	4
144.2.u.a.59.15	yes	88	144.139	odd	12
144.2.u.a.83.15	yes	88	3.2	odd	2
144.2.u.a.131.21	yes	88	9.4	even	3
432.2.v.a.35.8		88	1.1	even	1	trivial
432.2.v.a.179.2		88	9.5	odd	6	inner
432.2.v.a.251.2		88	16.11	odd	4	inner
432.2.v.a.395.8		88	144.59	even	12	inner
576.2.y.a.47.2		88	12.11	even	2
576.2.y.a.239.12		88	36.31	odd	6
576.2.y.a.335.12		88	48.5	odd	4
576.2.y.a.527.2		88	144.85	even	12
1728.2.z.a.143.11		88	16.5	even	4
1728.2.z.a.719.11		88	144.5	odd	12
1728.2.z.a.1007.11		88	4.3	odd	2
1728.2.z.a.1583.11		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)

\(f(q)\)	\(=\)	\(q+(-0.417977 - 1.35103i) q^{2} +(-1.65059 + 1.12940i) q^{4} +(-0.0776974 + 0.289971i) q^{5} +(-0.374023 + 0.647827i) q^{7} +(2.21577 + 1.75794i) q^{8} +O(q^{10})\)	\(q+(-0.417977 - 1.35103i) q^{2} +(-1.65059 + 1.12940i) q^{4} +(-0.0776974 + 0.289971i) q^{5} +(-0.374023 + 0.647827i) q^{7} +(2.21577 + 1.75794i) q^{8} +(0.424236 - 0.0162292i) q^{10} +(0.599457 + 2.23720i) q^{11} +(-0.429571 + 1.60318i) q^{13} +(1.03157 + 0.234541i) q^{14} +(1.44890 - 3.72836i) q^{16} +6.74518i q^{17} +(0.621335 - 0.621335i) q^{19} +(-0.199247 - 0.566375i) q^{20} +(2.77198 - 1.74499i) q^{22} +(6.06191 - 3.49985i) q^{23} +(4.25208 + 2.45494i) q^{25} +(2.34550 - 0.0897272i) q^{26} +(-0.114299 - 1.49172i) q^{28} +(1.45829 + 5.44240i) q^{29} +(-3.13647 + 1.81084i) q^{31} +(-5.64276 - 0.399142i) q^{32} +(9.11297 - 2.81933i) q^{34} +(-0.158790 - 0.158790i) q^{35} +(6.74053 - 6.74053i) q^{37} +(-1.09915 - 0.579742i) q^{38} +(-0.681911 + 0.505921i) q^{40} +(-1.39492 - 2.41607i) q^{41} +(-7.08744 + 1.89907i) q^{43} +(-3.51616 - 3.01568i) q^{44} +(-7.26216 - 6.72700i) q^{46} +(0.307120 - 0.531947i) q^{47} +(3.22021 + 5.57757i) q^{49} +(1.53944 - 6.77082i) q^{50} +(-1.10159 - 3.13135i) q^{52} +(2.68523 + 2.68523i) q^{53} -0.695300 q^{55} +(-1.96759 + 0.777926i) q^{56} +(6.74334 - 4.24499i) q^{58} +(0.00841962 + 0.00225603i) q^{59} +(-10.1714 + 2.72542i) q^{61} +(3.75748 + 3.48059i) q^{62} +(1.81929 + 7.79039i) q^{64} +(-0.431499 - 0.249126i) q^{65} +(-8.78151 - 2.35300i) q^{67} +(-7.61803 - 11.1335i) q^{68} +(-0.148160 + 0.280902i) q^{70} -15.9645i q^{71} +8.17785i q^{73} +(-11.9241 - 6.28930i) q^{74} +(-0.323832 + 1.72731i) q^{76} +(-1.67353 - 0.448421i) q^{77} +(7.67035 + 4.42848i) q^{79} +(0.968541 + 0.709822i) q^{80} +(-2.68115 + 2.89445i) q^{82} +(1.32013 - 0.353727i) q^{83} +(-1.95590 - 0.524083i) q^{85} +(5.52810 + 8.78161i) q^{86} +(-2.60461 + 6.01094i) q^{88} +15.7852 q^{89} +(-0.877914 - 0.877914i) q^{91} +(-6.05300 + 12.6232i) q^{92} +(-0.847048 - 0.192588i) q^{94} +(0.131893 + 0.228445i) q^{95} +(-4.62075 + 8.00338i) q^{97} +(6.18952 - 6.68192i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7}+O(q^{10}) \) 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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