LMFDB - Embedded newform 648.2.t.a.37.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(37,648)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("648.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.t (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			37.8
Character	$\chi$	$=$	648.37
Dual form			648.2.t.a.613.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.12116 - 0.861977i) q^{2} +(0.513991 + 1.93283i) q^{4} +(1.15428 + 3.17134i) q^{5} +(0.593321 + 3.36489i) q^{7} +(1.08978 - 2.61005i) q^{8} +(1.43950 - 4.55054i) q^{10} +(0.197048 - 0.541384i) q^{11} +(4.30199 - 5.12691i) q^{13} +(2.23525 - 4.28400i) q^{14} +(-3.47163 + 1.98691i) q^{16} +(-1.15893 + 2.00733i) q^{17} +(-0.353289 + 0.203971i) q^{19} +(-5.53637 + 3.86106i) q^{20} +(-0.687582 + 0.437127i) q^{22} +(-1.15186 + 6.53250i) q^{23} +(-4.89486 + 4.10727i) q^{25} +(-9.24249 + 2.03986i) q^{26} +(-6.19878 + 2.87631i) q^{28} +(2.24644 + 2.67721i) q^{29} +(-0.382945 + 2.17179i) q^{31} +(5.60491 + 0.764819i) q^{32} +(3.02962 - 1.25156i) q^{34} +(-9.98637 + 5.76564i) q^{35} +(-1.05249 - 0.607656i) q^{37} +(0.571912 + 0.0758426i) q^{38} +(9.53529 + 0.443366i) q^{40} +(-5.09057 - 4.27150i) q^{41} +(0.442145 - 1.21478i) q^{43} +(1.14768 + 0.102592i) q^{44} +(6.92227 - 6.33109i) q^{46} +(0.547022 + 3.10232i) q^{47} +(-4.39261 + 1.59878i) q^{49} +(9.02828 - 0.385648i) q^{50} +(12.1206 + 5.67980i) q^{52} -9.35460i q^{53} +1.94436 q^{55} +(9.42913 + 2.11841i) q^{56} +(-0.210928 - 4.93796i) q^{58} +(3.00302 + 8.25072i) q^{59} +(-4.67459 + 0.824257i) q^{61} +(2.30137 - 2.10483i) q^{62} +(-5.62474 - 5.68879i) q^{64} +(21.2249 + 7.72523i) q^{65} +(-9.67062 + 11.5250i) q^{67} +(-4.47550 - 1.20826i) q^{68} +(16.1662 + 2.14383i) q^{70} +(3.92323 - 6.79524i) q^{71} +(0.641809 + 1.11165i) q^{73} +(0.656224 + 1.58850i) q^{74} +(-0.575829 - 0.578006i) q^{76} +(1.93861 + 0.341829i) q^{77} +(3.84081 - 3.22282i) q^{79} +(-10.3084 - 8.71628i) q^{80} +(2.02541 + 9.17698i) q^{82} +(-6.67152 - 7.95081i) q^{83} +(-7.70366 - 1.35836i) q^{85} +(-1.54283 + 0.980846i) q^{86} +(-1.19830 - 1.10430i) q^{88} +(2.86501 + 4.96234i) q^{89} +(19.8040 + 11.4338i) q^{91} +(-13.2182 + 1.13131i) q^{92} +(2.06083 - 3.94971i) q^{94} +(-1.05466 - 0.884962i) q^{95} +(10.5548 + 3.84165i) q^{97} +(6.30293 + 1.99385i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	−1.12116	−	0.861977i	−0.792779	−	0.609510i
$2$	−1.12116	−	0.861977i	−0.792779	−	0.609510i
$3$		0			0
$3$		0			0
$4$	0.513991	+	1.93283i	0.256996	+	0.966413i
$5$	1.15428	+	3.17134i	0.516208	+	1.41827i	0.874667	+	0.484723i	$0.161080\pi$
$5$	1.15428	+	3.17134i	0.516208	+	1.41827i	−0.358460	+	0.933545i	$0.616698\pi$
$6$		0			0
$7$	0.593321	+	3.36489i	0.224254	+	1.27181i	0.864106	+	0.503311i	$0.167885\pi$
$7$	0.593321	+	3.36489i	0.224254	+	1.27181i	−0.639851	+	0.768499i	$0.721004\pi$
$8$	1.08978	−	2.61005i	0.385297	−	0.922793i
$9$		0			0
$10$	1.43950	−	4.55054i	0.455210	−	1.43901i
$11$	0.197048	−	0.541384i	0.0594121	−	0.163233i	−0.906435	−	0.422344i	$-0.861207\pi$
$11$	0.197048	−	0.541384i	0.0594121	−	0.163233i	0.965848	+	0.259111i	$0.0834295\pi$
$12$		0			0
$13$	4.30199	−	5.12691i	1.19316	−	1.42195i	0.311379	−	0.950286i	$-0.399209\pi$
$13$	4.30199	−	5.12691i	1.19316	−	1.42195i	0.881779	−	0.471664i	$-0.156346\pi$
$14$	2.23525	−	4.28400i	0.597396	−	1.14495i
$15$		0			0
$16$	−3.47163	+	1.98691i	−0.867906	+	0.496728i
$17$	−1.15893	+	2.00733i	−0.281082	+	0.486849i	−0.971652	−	0.236417i	$-0.924027\pi$
$17$	−1.15893	+	2.00733i	−0.281082	+	0.486849i	0.690569	+	0.723266i	$0.257360\pi$
$18$		0			0
$19$	−0.353289	+	0.203971i	−0.0810500	+	0.0467943i	−0.539977	−	0.841680i	$-0.681567\pi$
$19$	−0.353289	+	0.203971i	−0.0810500	+	0.0467943i	0.458927	+	0.888474i	$0.348234\pi$
$20$	−5.53637	+	3.86106i	−1.23797	+	0.863358i
$21$		0			0
$22$	−0.687582	+	0.437127i	−0.146593	+	0.0931957i
$23$	−1.15186	+	6.53250i	−0.240178	+	1.36212i	0.591250	+	0.806488i	$0.298635\pi$
$23$	−1.15186	+	6.53250i	−0.240178	+	1.36212i	−0.831429	+	0.555631i	$0.812477\pi$
$24$		0			0
$25$	−4.89486	+	4.10727i	−0.978971	+	0.821454i
$26$	−9.24249	+	2.03986i	−1.81260	+	0.400050i
$27$		0			0
$28$	−6.19878	+	2.87631i	−1.17146	+	0.543572i
$29$	2.24644	+	2.67721i	0.417154	+	0.497145i	0.933171	−	0.359434i	$-0.117030\pi$
$29$	2.24644	+	2.67721i	0.417154	+	0.497145i	−0.516016	+	0.856579i	$0.672586\pi$
$30$		0			0
$31$	−0.382945	+	2.17179i	−0.0687790	+	0.390065i	0.930913	+	0.365241i	$0.119014\pi$
$31$	−0.382945	+	2.17179i	−0.0687790	+	0.390065i	−0.999692	+	0.0248236i	$0.992098\pi$
$32$	5.60491	+	0.764819i	0.990818	+	0.135202i
$33$		0			0
$34$	3.02962	−	1.25156i	0.519575	−	0.214641i
$35$	−9.98637	+	5.76564i	−1.68801	+	0.974570i
$36$		0			0
$37$	−1.05249	−	0.607656i	−0.173028	−	0.0998980i	0.410985	−	0.911642i	$-0.365185\pi$
$37$	−1.05249	−	0.607656i	−0.173028	−	0.0998980i	−0.584013	+	0.811744i	$0.698518\pi$
$38$	0.571912	+	0.0758426i	0.0927763	+	0.0123033i
$39$		0			0
$40$	9.53529	+	0.443366i	1.50766	+	0.0701023i
$41$	−5.09057	−	4.27150i	−0.795014	−	0.667096i	0.151967	−	0.988386i	$-0.451439\pi$
$41$	−5.09057	−	4.27150i	−0.795014	−	0.667096i	−0.946981	+	0.321290i	$0.895884\pi$
$42$		0			0
$43$	0.442145	−	1.21478i	0.0674265	−	0.185253i	−0.901403	−	0.432981i	$-0.857462\pi$
$43$	0.442145	−	1.21478i	0.0674265	−	0.185253i	0.968830	+	0.247728i	$0.0796840\pi$
$44$	1.14768	+	0.102592i	0.173020	+	0.0154663i
$45$		0			0
$46$	6.92227	−	6.33109i	1.02063	−	0.933468i
$47$	0.547022	+	3.10232i	0.0797914	+	0.452520i	0.998359	+	0.0572567i	$0.0182354\pi$
$47$	0.547022	+	3.10232i	0.0797914	+	0.452520i	−0.918568	+	0.395263i	$0.870654\pi$
$48$		0			0
$49$	−4.39261	+	1.59878i	−0.627516	+	0.228397i
$50$	9.02828	−	0.385648i	1.27679	−	0.0545389i
$51$		0			0
$52$	12.1206	+	5.67980i	1.68083	+	0.787647i
$53$		−	9.35460i		−	1.28495i	−0.766305	−	0.642477i	$-0.777907\pi$
$53$		−	9.35460i		−	1.28495i	0.766305	−	0.642477i	$-0.222093\pi$
$54$		0			0
$55$	1.94436			0.262178
$56$	9.42913	+	2.11841i	1.26002	+	0.283084i
$57$		0			0
$58$	−0.210928	−	4.93796i	−0.0276962	−	0.648385i
$59$	3.00302	+	8.25072i	0.390959	+	1.07415i	0.966564	+	0.256424i	$0.0825444\pi$
$59$	3.00302	+	8.25072i	0.390959	+	1.07415i	−0.575605	+	0.817728i	$0.695233\pi$
$60$		0			0
$61$	−4.67459	+	0.824257i	−0.598520	+	0.105535i	−0.464697	−	0.885470i	$-0.653837\pi$
$61$	−4.67459	+	0.824257i	−0.598520	+	0.105535i	−0.133824	+	0.991005i	$0.542726\pi$
$62$	2.30137	−	2.10483i	0.292275	−	0.267314i
$63$		0			0
$64$	−5.62474	−	5.68879i	−0.703092	−	0.711099i
$65$	21.2249	+	7.72523i	2.63262	+	0.958196i
$66$		0			0
$67$	−9.67062	+	11.5250i	−1.18145	+	1.40800i	−0.288723	+	0.957413i	$0.593231\pi$
$67$	−9.67062	+	11.5250i	−1.18145	+	1.40800i	−0.892731	+	0.450589i	$0.851214\pi$
$68$	−4.47550	−	1.20826i	−0.542734	−	0.146523i
$69$		0			0
$70$	16.1662	+	2.14383i	1.93222	+	0.256237i
$71$	3.92323	−	6.79524i	0.465602	−	0.806446i	−0.533627	−	0.845720i	$-0.679171\pi$
$71$	3.92323	−	6.79524i	0.465602	−	0.806446i	0.999228	+	0.0392740i	$0.0125045\pi$
$72$		0			0
$73$	0.641809	+	1.11165i	0.0751180	+	0.130108i	0.901138	−	0.433533i	$-0.142733\pi$
$73$	0.641809	+	1.11165i	0.0751180	+	0.130108i	−0.826020	+	0.563641i	$0.809400\pi$
$74$	0.656224	+	1.58850i	0.0762844	+	0.184660i
$75$		0			0
$76$	−0.575829	−	0.578006i	−0.0660521	−	0.0663019i
$77$	1.93861	+	0.341829i	0.220925	+	0.0389551i
$78$		0			0
$79$	3.84081	−	3.22282i	0.432125	−	0.362596i	−0.400628	−	0.916241i	$-0.631208\pi$
$79$	3.84081	−	3.22282i	0.432125	−	0.362596i	0.832753	+	0.553645i	$0.186764\pi$
$80$	−10.3084	−	8.71628i	−1.15251	−	0.974510i
$81$		0			0
$82$	2.02541	+	9.17698i	0.223669	+	1.01343i
$83$	−6.67152	−	7.95081i	−0.732295	−	0.872715i	0.263468	−	0.964668i	$-0.415134\pi$
$83$	−6.67152	−	7.95081i	−0.732295	−	0.872715i	−0.995763	+	0.0919529i	$0.970689\pi$
$84$		0			0
$85$	−7.70366	−	1.35836i	−0.835580	−	0.147335i
$86$	−1.54283	+	0.980846i	−0.166368	+	0.105767i
$87$		0			0
$88$	−1.19830	−	1.10430i	−0.127739	−	0.117718i
$89$	2.86501	+	4.96234i	0.303690	+	0.526007i	0.976969	−	0.213382i	$-0.0684478\pi$
$89$	2.86501	+	4.96234i	0.303690	+	0.526007i	−0.673278	+	0.739389i	$0.735114\pi$
$90$		0			0
$91$	19.8040	+	11.4338i	2.07602	+	1.19859i
$92$	−13.2182	+	1.13131i	−1.37809	+	0.117947i
$93$		0			0
$94$	2.06083	−	3.94971i	0.212558	−	0.407381i
$95$	−1.05466	−	0.884962i	−0.108205	−	0.0907952i
$96$		0			0
$97$	10.5548	+	3.84165i	1.07168	+	0.390061i	0.816806	−	0.576913i	$-0.195743\pi$
$97$	10.5548	+	3.84165i	1.07168	+	0.390061i	0.254877	+	0.966974i	$0.417965\pi$
$98$	6.30293	+	1.99385i	0.636692	+	0.201409i
$99$		0			0
$100$	−10.4546	−	7.34980i	−1.04546	−	0.734980i
$101$	12.2411	−	2.15844i	1.21804	−	0.214773i	0.472557	−	0.881300i	$-0.343331\pi$
$101$	12.2411	−	2.15844i	1.21804	−	0.214773i	0.745481	+	0.666527i	$0.232220\pi$
$102$		0			0
$103$	−14.8537	+	5.40632i	−1.46358	+	0.532701i	−0.946350	−	0.323144i	$-0.895260\pi$
$103$	−14.8537	+	5.40632i	−1.46358	+	0.532701i	−0.517233	+	0.855844i	$0.673038\pi$
$104$	−8.69326	−	16.8156i	−0.852444	−	1.64891i
$105$		0			0
$106$	−8.06345	+	10.4880i	−0.783192	+	1.01868i
$107$		−	2.44491i		−	0.236359i	−0.992992	−	0.118179i	$-0.962294\pi$
$107$		−	2.44491i		−	0.236359i	0.992992	−	0.118179i	$-0.0377058\pi$
$108$		0			0
$109$		−	16.2522i		−	1.55668i	−0.627843	−	0.778340i	$-0.716062\pi$
$109$		−	16.2522i		−	1.55668i	0.627843	−	0.778340i	$-0.283938\pi$
$110$	−2.17994	−	1.67600i	−0.207849	−	0.159800i
$111$		0			0
$112$	−8.74553	−	10.5028i	−0.826375	−	0.992418i
$113$	11.4376	−	4.16294i	1.07596	−	0.391617i	0.257556	−	0.966263i	$-0.417083\pi$
$113$	11.4376	−	4.16294i	1.07596	−	0.391617i	0.818402	+	0.574646i	$0.194860\pi$
$114$		0			0
$115$	−22.0464	+	3.88737i	−2.05583	+	0.362499i
$116$	−4.01992	+	5.71804i	−0.373240	+	0.530907i
$117$		0			0
$118$	3.74507	−	11.8389i	0.344762	−	1.08986i
$119$	−7.44207	−	2.70869i	−0.682213	−	0.248305i
$120$		0			0
$121$	8.17222	+	6.85731i	0.742929	+	0.623392i
$122$	5.95145	+	3.10527i	0.538819	+	0.281138i
$123$		0			0
$124$	−4.39452	+	0.376115i	−0.394639	+	0.0337762i
$125$	−4.06195	−	2.34517i	−0.363312	−	0.209758i
$126$		0			0
$127$	−4.79341	−	8.30243i	−0.425346	−	0.736722i	0.571106	−	0.820876i	$-0.306514\pi$
$127$	−4.79341	−	8.30243i	−0.425346	−	0.736722i	−0.996453	+	0.0841546i	$0.973181\pi$
$128$	1.40262	+	11.2264i	0.123975	+	0.992285i
$129$		0			0
$130$	−17.1375	−	26.9566i	−1.50306	−	2.36425i
$131$	−0.406480	−	0.0716734i	−0.0355143	−	0.00626213i	0.155863	−	0.987779i	$-0.450184\pi$
$131$	−0.406480	−	0.0716734i	−0.0355143	−	0.00626213i	−0.191377	+	0.981517i	$0.561295\pi$
$132$		0			0
$133$	−0.895956	−	1.06776i	−0.0776892	−	0.0925864i
$134$	20.7766	−	4.58549i	1.79482	−	0.396126i
$135$		0			0
$136$	3.97625	+	5.21243i	0.340960	+	0.446962i
$137$	−12.0727	+	10.1302i	−1.03144	+	0.865480i	−0.991021	−	0.133703i	$-0.957313\pi$
$137$	−12.0727	+	10.1302i	−1.03144	+	0.865480i	−0.0404177	+	0.999183i	$0.512869\pi$
$138$		0			0
$139$	2.17442	+	0.383409i	0.184432	+	0.0325204i	0.265101	−	0.964221i	$-0.414595\pi$
$139$	2.17442	+	0.383409i	0.184432	+	0.0325204i	−0.0806691	+	0.996741i	$0.525706\pi$
$140$	−16.2769	−	16.3384i	−1.37565	−	1.38085i
$141$		0			0
$142$	−10.2559	+	4.23680i	−0.860656	+	0.355544i
$143$	−1.92793	−	3.33928i	−0.161222	−	0.279244i
$144$		0			0
$145$	−5.89733	+	10.2145i	−0.489747	+	0.848267i
$146$	0.238644	−	1.79955i	0.0197503	−	0.148932i
$147$		0			0
$148$	0.633521	−	2.34661i	0.0520751	−	0.192890i
$149$	4.40044	−	5.24424i	0.360498	−	0.429625i	−0.555060	−	0.831810i	$-0.687305\pi$
$149$	4.40044	−	5.24424i	0.360498	−	0.429625i	0.915558	+	0.402186i	$0.131749\pi$
$150$		0			0
$151$	11.0866	+	4.03519i	0.902213	+	0.328379i	0.751139	−	0.660144i	$-0.229505\pi$
$151$	11.0866	+	4.03519i	0.902213	+	0.328379i	0.151074	+	0.988522i	$0.451727\pi$
$152$	0.147367	+	1.14439i	0.0119531	+	0.0928221i
$153$		0			0
$154$	−1.87884	−	2.05428i	−0.151401	−	0.165539i
$155$	−7.32952	+	1.29239i	−0.588721	+	0.103807i
$156$		0			0
$157$	4.12184	+	11.3247i	0.328959	+	0.903808i	0.988376	+	0.152030i	$0.0485810\pi$
$157$	4.12184	+	11.3247i	0.328959	+	0.903808i	−0.659417	+	0.751778i	$0.729197\pi$
$158$	−7.08416	+	0.302604i	−0.563585	+	0.0240739i
$159$		0			0
$160$	4.04411	+	18.6579i	0.319715	+	1.47504i
$161$	−22.6646			−1.78622
$162$		0			0
$163$		−	13.3972i		−	1.04935i	−0.851303	−	0.524675i	$-0.824187\pi$
$163$		−	13.3972i		−	1.04935i	0.851303	−	0.524675i	$-0.175813\pi$
$164$	5.63955	−	12.0347i	0.440375	−	0.939752i
$165$		0			0
$166$	0.626417	+	14.6648i	0.0486194	+	1.13821i
$167$	6.36473	−	2.31657i	0.492517	−	0.179262i	−0.0838081	−	0.996482i	$-0.526708\pi$
$167$	6.36473	−	2.31657i	0.492517	−	0.179262i	0.576325	+	0.817220i	$0.304486\pi$
$168$		0			0
$169$	−5.52068	−	31.3093i	−0.424668	−	2.40841i
$170$	7.46615	+	8.16332i	0.572627	+	0.626098i
$171$		0			0
$172$	2.57522	+	0.230201i	0.196359	+	0.0175526i
$173$	−0.576454	+	1.58380i	−0.0438270	+	0.120414i	−0.959675	−	0.281111i	$-0.909297\pi$
$173$	−0.576454	+	1.58380i	−0.0438270	+	0.120414i	0.915848	+	0.401524i	$0.131519\pi$
$174$		0			0
$175$	−16.7247	−	14.0337i	−1.26427	−	1.06085i
$176$	0.391606	+	2.27100i	0.0295184	+	0.171183i
$177$		0			0
$178$	1.06530	−	8.03314i	0.0798473	−	0.602110i
$179$	−10.3190	−	5.95768i	−0.771279	−	0.445298i	0.0620517	−	0.998073i	$-0.480236\pi$
$179$	−10.3190	−	5.95768i	−0.771279	−	0.445298i	−0.833331	+	0.552775i	$0.813569\pi$
$180$		0			0
$181$	14.3027	−	8.25769i	1.06311	−	0.613789i	0.136822	−	0.990596i	$-0.456311\pi$
$181$	14.3027	−	8.25769i	1.06311	−	0.613789i	0.926292	+	0.376806i	$0.122978\pi$
$182$	−12.3477	−	29.8897i	−0.915271	−	2.21557i
$183$		0			0
$184$	15.7949	+	10.1254i	1.16441	+	0.746456i
$185$	0.712223	−	4.03922i	0.0523636	−	0.296969i
$186$		0			0
$187$	0.858372	+	1.02297i	0.0627703	+	0.0748068i
$188$	−5.71507	+	2.65186i	−0.416815	+	0.193407i
$189$		0			0
$190$	0.419620	+	1.90127i	0.0304424	+	0.137933i
$191$	10.1267	−	8.49734i	0.732745	−	0.614846i	−0.198134	−	0.980175i	$-0.563488\pi$
$191$	10.1267	−	8.49734i	0.732745	−	0.614846i	0.930878	+	0.365329i	$0.119044\pi$
$192$		0			0
$193$	−0.0307325	+	0.174293i	−0.00221218	+	0.0125459i	−0.985894	−	0.167372i	$-0.946472\pi$
$193$	−0.0307325	+	0.174293i	−0.00221218	+	0.0125459i	0.983682	+	0.179918i	$0.0575831\pi$
$194$	−8.52224	−	13.4051i	−0.611861	−	0.962433i
$195$		0			0
$196$	−5.34793	−	7.66839i	−0.381995	−	0.547742i
$197$	0.841221	−	0.485679i	0.0599345	−	0.0346032i	−0.469733	−	0.882808i	$-0.655650\pi$
$197$	0.841221	−	0.485679i	0.0599345	−	0.0346032i	0.529668	+	0.848205i	$0.322317\pi$
$198$		0			0
$199$	2.04926	−	3.54942i	0.145268	−	0.251612i	−0.784205	−	0.620502i	$-0.786929\pi$
$199$	2.04926	−	3.54942i	0.145268	−	0.251612i	0.929473	+	0.368890i	$0.120262\pi$
$200$	5.38585	+	17.2519i	0.380837	+	1.21989i
$201$		0			0
$202$	−15.5848	−	8.13161i	−1.09654	−	0.572138i
$203$	−7.67565	+	9.14748i	−0.538725	+	0.642027i
$204$		0			0
$205$	7.67047	−	21.0745i	0.535729	−	1.47190i
$206$	21.3135	+	6.74225i	1.48498	+	0.469755i
$207$		0			0
$208$	−4.74818	+	26.3464i	−0.329227	+	1.82679i
$209$	0.0408121	+	0.231457i	0.00282303	+	0.0160102i
$210$		0			0
$211$	1.28341	+	3.52613i	0.0883534	+	0.242749i	0.975998	−	0.217781i	$-0.0698817\pi$
$211$	1.28341	+	3.52613i	0.0883534	+	0.242749i	−0.887644	+	0.460530i	$0.847660\pi$
$212$	18.0808	−	4.80819i	1.24180	−	0.330228i
$213$		0			0
$214$	−2.10746	+	2.74114i	−0.144063	+	0.187380i
$215$	4.36285			0.297544
$216$		0			0
$217$	−7.53504			−0.511512
$218$	−14.0090	+	18.2213i	−0.948812	+	1.23410i
$219$		0			0
$220$	0.999386	+	3.75811i	0.0673786	+	0.253372i
$221$	5.30569	+	14.5773i	0.356899	+	0.980572i
$222$		0			0
$223$	0.680991	+	3.86209i	0.0456025	+	0.258625i	0.999082	−	0.0428323i	$-0.0136381\pi$
$223$	0.680991	+	3.86209i	0.0456025	+	0.258625i	−0.953480	+	0.301457i	$0.902527\pi$
$224$	0.751980	+	19.3137i	0.0502437	+	1.29045i
$225$		0			0
$226$	−16.4117	−	5.19162i	−1.09169	−	0.345342i
$227$	4.04735	−	11.1200i	0.268632	−	0.738061i	−0.729882	−	0.683573i	$-0.760425\pi$
$227$	4.04735	−	11.1200i	0.268632	−	0.738061i	0.998514	−	0.0544879i	$-0.0173526\pi$
$228$		0			0
$229$	−6.81207	+	8.11831i	−0.450154	+	0.536473i	−0.942624	−	0.333857i	$-0.891650\pi$
$229$	−6.81207	+	8.11831i	−0.450154	+	0.536473i	0.492470	+	0.870330i	$0.336094\pi$
$230$	28.0683	+	14.6451i	1.85077	+	0.965669i
$231$		0			0
$232$	9.43579	−	2.94575i	0.619490	−	0.193398i
$233$	0.565006	−	0.978619i	0.0370148	−	0.0641115i	−0.846925	−	0.531713i	$-0.821548\pi$
$233$	0.565006	−	0.978619i	0.0370148	−	0.0641115i	0.883939	+	0.467602i	$0.154882\pi$
$234$		0			0
$235$	−9.20711	+	5.31572i	−0.600605	+	0.346760i
$236$	−14.4037	+	10.0451i	−0.937599	+	0.653881i
$237$		0			0
$238$	6.00890	+	9.45176i	0.389499	+	0.612667i
$239$	−1.00787	+	5.71591i	−0.0651936	+	0.369731i	0.934704	+	0.355427i	$0.115665\pi$
$239$	−1.00787	+	5.71591i	−0.0651936	+	0.369731i	−0.999898	+	0.0143045i	$0.995447\pi$
$240$		0			0
$241$	22.5974	−	18.9615i	1.45563	−	1.22142i	0.527286	−	0.849688i	$-0.323210\pi$
$241$	22.5974	−	18.9615i	1.45563	−	1.22142i	0.928342	−	0.371728i	$-0.121235\pi$
$242$	−3.25151	−	14.7324i	−0.209015	−	0.947034i
$243$		0			0
$244$	−3.99585	−	8.61151i	−0.255808	−	0.551295i
$245$	−10.1406	−	12.0851i	−0.647857	−	0.772086i
$246$		0			0
$247$	−0.474102	+	2.68876i	−0.0301664	+	0.171082i
$248$	5.25115	+	3.36629i	0.333449	+	0.213760i
$249$		0			0
$250$	2.53261	+	6.13061i	0.160176	+	0.387734i
$251$	5.20730	−	3.00644i	0.328682	−	0.189765i	−0.326574	−	0.945172i	$-0.605894\pi$
$251$	5.20730	−	3.00644i	0.328682	−	0.189765i	0.655256	+	0.755407i	$0.272561\pi$
$252$		0			0
$253$	3.30962	+	1.91081i	0.208074	+	0.120132i
$254$	−1.78233	+	13.4401i	−0.111833	+	0.843310i
$255$		0			0
$256$	8.10437	−	13.7956i	0.506523	−	0.862226i
$257$	−19.8936	−	16.6927i	−1.24093	−	1.04126i	−0.997451	−	0.0713589i	$-0.977266\pi$
$257$	−19.8936	−	16.6927i	−1.24093	−	1.04126i	−0.243480	−	0.969906i	$-0.578289\pi$
$258$		0			0
$259$	1.42023	−	3.90205i	0.0882489	−	0.242462i
$260$	−4.02210	+	44.9947i	−0.249440	+	2.79045i
$261$		0			0
$262$	0.393948	+	0.430734i	0.0243382	+	0.0266108i
$263$	2.41565	+	13.6998i	0.148956	+	0.844769i	0.964106	+	0.265519i	$0.0855433\pi$
$263$	2.41565	+	13.6998i	0.148956	+	0.844769i	−0.815150	+	0.579250i	$0.803346\pi$
$264$		0			0
$265$	29.6667	−	10.7978i	1.82241	−	0.663303i
$266$	0.0841249	+	1.96942i	0.00515803	+	0.120753i
$267$		0			0
$268$	−27.2464	−	12.7679i	−1.66434	−	0.779921i
$269$		−	3.89404i		−	0.237424i	−0.992929	−	0.118712i	$-0.962123\pi$
$269$		−	3.89404i		−	0.237424i	0.992929	−	0.118712i	$-0.0378765\pi$
$270$		0			0
$271$	27.1005			1.64624			0.823119	−	0.567869i	$-0.192232\pi$
$271$	27.1005			1.64624			0.823119	+	0.567869i	$0.192232\pi$
$272$	0.0349931	−	9.27139i	0.00212177	−	0.562161i
$273$		0			0
$274$	22.2674	−	0.951165i	1.34522	−	0.0574620i
$275$	1.25909	+	3.45933i	0.0759261	+	0.208605i
$276$		0			0
$277$	−7.05421	+	1.24385i	−0.423847	+	0.0747356i	−0.381503	−	0.924368i	$-0.624593\pi$
$277$	−7.05421	+	1.24385i	−0.423847	+	0.0747356i	−0.0423435	+	0.999103i	$0.513482\pi$
$278$	−2.10738	−	2.30417i	−0.126392	−	0.138195i
$279$		0			0
$280$	4.16561	+	32.3483i	0.248943	+	1.93318i
$281$	0.728892	+	0.265295i	0.0434820	+	0.0158262i	0.363670	−	0.931528i	$-0.381524\pi$
$281$	0.728892	+	0.265295i	0.0434820	+	0.0158262i	−0.320188	+	0.947354i	$0.603746\pi$
$282$		0			0
$283$	0.982704	−	1.17114i	0.0584157	−	0.0696171i	−0.736045	−	0.676932i	$-0.763309\pi$
$283$	0.982704	−	1.17114i	0.0584157	−	0.0696171i	0.794461	+	0.607315i	$0.207753\pi$
$284$	15.1505	+	4.09023i	0.899017	+	0.242710i
$285$		0			0
$286$	−0.716862	+	5.40569i	−0.0423889	+	0.319645i
$287$	11.3528	−	19.6636i	0.670134	−	1.16071i
$288$		0			0
$289$	5.81375	+	10.0697i	0.341985	+	0.592336i
$290$	15.4165	−	6.36868i	0.905288	−	0.373982i
$291$		0			0
$292$	−1.81873	+	1.81188i	−0.106433	+	0.106032i
$293$	15.6621	+	2.76164i	0.914987	+	0.161337i	0.611267	−	0.791424i	$-0.290660\pi$
$293$	15.6621	+	2.76164i	0.914987	+	0.161337i	0.303720	+	0.952761i	$0.401771\pi$
$294$		0			0
$295$	−22.6996	+	19.0472i	−1.32162	+	1.10897i
$296$	−2.73300	+	2.08484i	−0.158853	+	0.121179i
$297$		0			0
$298$	−9.45399	+	2.08654i	−0.547655	+	0.120870i
$299$	28.5363	+	34.0082i	1.65029	+	1.96674i
$300$		0			0
$301$	4.34995	+	0.767013i	0.250727	+	0.0442099i
$302$	−8.95158	−	14.0805i	−0.515105	−	0.810240i
$303$		0			0
$304$	0.821214	−	1.41007i	0.0470998	−	0.0808729i
$305$	−8.00977	−	13.8733i	−0.458638	−	0.794385i
$306$		0			0
$307$	0.370582	+	0.213955i	0.0211502	+	0.0122111i	0.510538	−	0.859855i	$-0.329446\pi$
$307$	0.370582	+	0.213955i	0.0211502	+	0.0122111i	−0.489388	+	0.872066i	$0.662780\pi$
$308$	0.335733	+	3.92269i	0.0191302	+	0.223516i
$309$		0			0
$310$	9.33156	+	4.86890i	0.529997	+	0.276535i
$311$	−8.46179	−	7.10028i	−0.479824	−	0.402620i	0.370539	−	0.928817i	$-0.379173\pi$
$311$	−8.46179	−	7.10028i	−0.479824	−	0.402620i	−0.850363	+	0.526197i	$0.823617\pi$
$312$		0			0
$313$	−26.1193	−	9.50664i	−1.47635	−	0.537347i	−0.526533	−	0.850155i	$-0.676508\pi$
$313$	−26.1193	−	9.50664i	−1.47635	−	0.537347i	−0.949817	+	0.312807i	$0.898731\pi$
$314$	5.14037	−	16.2497i	0.290088	−	0.917023i
$315$		0			0
$316$	8.20330	+	5.76711i	0.461472	+	0.324425i
$317$	3.46040	−	0.610163i	0.194356	−	0.0342701i	−0.0756229	−	0.997136i	$-0.524095\pi$
$317$	3.46040	−	0.610163i	0.194356	−	0.0342701i	0.269979	+	0.962866i	$0.412983\pi$
$318$		0			0
$319$	1.89205	−	0.688651i	0.105935	−	0.0385571i
$320$	11.5486	−	24.4044i	0.645587	−	1.36425i
$321$		0			0
$322$	25.4106	+	19.5363i	1.41607	+	1.08872i
$323$		−	0.945557i		−	0.0526122i
$324$		0			0
$325$			42.7649i			2.37217i
$326$	−11.5481	+	15.0204i	−0.639589	+	0.831902i
$327$		0			0
$328$	−16.6965	+	8.63165i	−0.921908	+	0.476603i
$329$	−10.1144	+	3.68134i	−0.557625	+	0.202959i
$330$		0			0
$331$	17.1533	−	3.02459i	0.942832	−	0.166247i	0.318956	−	0.947770i	$-0.396668\pi$
$331$	17.1533	−	3.02459i	0.942832	−	0.166247i	0.623876	+	0.781523i	$0.285557\pi$
$332$	11.9384	−	16.9815i	0.655206	−	0.931983i
$333$		0			0
$334$	−9.13270	−	2.88901i	−0.499719	−	0.158079i
$335$	−47.7123	−	17.3659i	−2.60680	−	0.948798i
$336$		0			0
$337$	−2.18023	−	1.82943i	−0.118765	−	0.0996554i	0.581471	−	0.813567i	$-0.302477\pi$
$337$	−2.18023	−	1.82943i	−0.118765	−	0.0996554i	−0.700236	+	0.713912i	$0.746922\pi$
$338$	−20.7984	+	39.8614i	−1.13128	+	2.16818i
$339$		0			0
$340$	−1.33414	−	15.5880i	−0.0723538	−	0.845379i
$341$	1.10031	+	0.635266i	0.0595853	+	0.0344016i
$342$		0			0
$343$	3.97285	+	6.88117i	0.214514	+	0.371548i
$344$	−2.68880	−	2.47787i	−0.144971	−	0.133598i
$345$		0			0
$346$	2.01149	−	1.27879i	0.108138	−	0.0687484i
$347$	−25.7859	−	4.54675i	−1.38426	−	0.244082i	−0.568599	−	0.822615i	$-0.692514\pi$
$347$	−25.7859	−	4.54675i	−1.38426	−	0.244082i	−0.815659	+	0.578533i	$0.803626\pi$
$348$		0			0
$349$	−3.27963	−	3.90851i	−0.175555	−	0.209218i	0.671091	−	0.741375i	$-0.265826\pi$
$349$	−3.27963	−	3.90851i	−0.175555	−	0.209218i	−0.846646	+	0.532157i	$0.821382\pi$
$350$	6.65433	+	30.1504i	0.355689	+	1.61160i
$351$		0			0
$352$	1.51850	−	2.88371i	0.0809361	−	0.153702i
$353$	11.4022	−	9.56754i	0.606875	−	0.509229i	−0.286772	−	0.957999i	$-0.592582\pi$
$353$	11.4022	−	9.56754i	0.606875	−	0.509229i	0.893647	+	0.448770i	$0.148138\pi$
$354$		0			0
$355$	26.0785	+	4.59835i	1.38410	+	0.244055i
$356$	−8.11875	+	8.08816i	−0.430293	+	0.428672i
$357$		0			0
$358$	6.43386	+	15.5743i	0.340040	+	0.823125i
$359$	7.74329	+	13.4118i	0.408675	+	0.707846i	0.994742	−	0.102417i	$-0.0326575\pi$
$359$	7.74329	+	13.4118i	0.408675	+	0.707846i	−0.586066	+	0.810263i	$0.699324\pi$
$360$		0			0
$361$	−9.41679	+	16.3104i	−0.495621	+	0.858440i
$362$	−23.1536	−	3.07045i	−1.21693	−	0.161380i
$363$		0			0
$364$	−11.9205	+	44.1545i	−0.624805	+	2.31432i
$365$	−2.78459	+	3.31854i	−0.145752	+	0.173700i
$366$		0			0
$367$	24.0744	+	8.76237i	1.25667	+	0.457392i	0.882652	−	0.470027i	$-0.155756\pi$
$367$	24.0744	+	8.76237i	1.25667	+	0.457392i	0.374023	+	0.927419i	$0.377978\pi$
$368$	−8.98068	−	24.9670i	−0.468150	−	1.30150i
$369$		0			0
$370$	−4.28022	+	3.91468i	−0.222518	+	0.203515i
$371$	31.4772	−	5.55028i	1.63422	−	0.288156i
$372$		0			0
$373$	4.86012	+	13.3531i	0.251648	+	0.691396i	0.999617	+	0.0276634i	$0.00880666\pi$
$373$	4.86012	+	13.3531i	0.251648	+	0.691396i	−0.747970	+	0.663733i	$0.768971\pi$
$374$	−0.0805960	−	1.88680i	−0.00416752	−	0.0975644i
$375$		0			0
$376$	8.69335	+	1.95310i	0.448325	+	0.100724i
$377$	23.3900			1.20465
$378$		0			0
$379$		−	1.93137i		−	0.0992080i	−0.998769	−	0.0496040i	$-0.984204\pi$
$379$		−	1.93137i		−	0.0992080i	0.998769	−	0.0496040i	$-0.0157959\pi$
$380$	1.16839	−	2.49333i	0.0599373	−	0.127905i
$381$		0			0
$382$	−18.6782	+	0.797850i	−0.955659	+	0.0408216i
$383$	−12.4377	+	4.52695i	−0.635537	+	0.231317i	−0.639639	−	0.768675i	$-0.720916\pi$
$383$	−12.4377	+	4.52695i	−0.635537	+	0.231317i	0.00410258	+	0.999992i	$0.498694\pi$
$384$		0			0
$385$	1.15363	+	6.54257i	0.0587945	+	0.333440i
$386$	0.184692	−	0.168919i	0.00940060	−	0.00859776i
$387$		0			0
$388$	−2.00014	+	22.3753i	−0.101542	+	1.13593i
$389$	8.22522	−	22.5986i	0.417035	−	1.14579i	−0.536339	−	0.844003i	$-0.680193\pi$
$389$	8.22522	−	22.5986i	0.417035	−	1.14579i	0.953374	−	0.301792i	$-0.0975848\pi$
$390$		0			0
$391$	−11.7780	−	9.88288i	−0.595637	−	0.499799i
$392$	−0.614104	+	13.2073i	−0.0310169	+	0.667068i
$393$		0			0
$394$	−1.36179	−	0.180590i	−0.0686058	−	0.00909799i
$395$	14.6540	+	8.46051i	0.737325	+	0.425695i
$396$		0			0
$397$	28.6833	−	16.5603i	1.43957	−	0.831137i	0.441752	−	0.897137i	$-0.354357\pi$
$397$	28.6833	−	16.5603i	1.43957	−	0.831137i	0.997820	+	0.0659997i	$0.0210236\pi$
$398$	−5.35707	+	2.21305i	−0.268525	+	0.110930i
$399$		0			0
$400$	8.83232	−	23.9846i	0.441616	−	1.19923i
$401$	−1.94567	+	11.0344i	−0.0971620	+	0.551033i	0.896901	+	0.442231i	$0.145813\pi$
$401$	−1.94567	+	11.0344i	−0.0971620	+	0.551033i	−0.994063	+	0.108802i	$0.965298\pi$
$402$		0			0
$403$	9.48715	+	11.3063i	0.472588	+	0.563209i
$404$	10.4637	+	22.5505i	0.520590	+	1.12193i
$405$		0			0
$406$	16.4905	−	3.63954i	0.818412	−	0.180627i
$407$	−0.536366	+	0.450065i	−0.0265867	+	0.0223089i
$408$		0			0
$409$	1.95004	−	11.0592i	0.0964233	−	0.546844i	−0.897879	−	0.440243i	$-0.854892\pi$
$409$	1.95004	−	11.0592i	0.0964233	−	0.546844i	0.994302	−	0.106601i	$-0.0339966\pi$
$410$	−26.7655	+	17.0160i	−1.32185	+	0.840362i
$411$		0			0
$412$	−18.0842	−	25.9309i	−0.890943	−	1.27752i
$413$	−25.9810	+	15.0001i	−1.27844	+	0.738109i
$414$		0			0
$415$	17.5140	−	30.3351i	0.859728	−	1.48909i
$416$	28.0334	−	25.4457i	1.37445	−	1.24758i
$417$		0			0
$418$	0.153754	−	0.294679i	0.00752035	−	0.0144132i
$419$	8.95678	−	10.6743i	0.437567	−	0.521472i	−0.501522	−	0.865145i	$-0.667226\pi$
$419$	8.95678	−	10.6743i	0.437567	−	0.521472i	0.939090	+	0.343672i	$0.111671\pi$
$420$		0			0
$421$	4.06687	−	11.1736i	0.198207	−	0.544570i	−0.800276	−	0.599632i	$-0.795314\pi$
$421$	4.06687	−	11.1736i	0.198207	−	0.544570i	0.998483	+	0.0550623i	$0.0175358\pi$
$422$	1.60054	−	5.05962i	0.0779132	−	0.246298i
$423$		0			0
$424$	−24.4160	−	10.1945i	−1.18575	−	0.495089i
$425$	−2.57184	−	14.5856i	−0.124753	−	0.707507i
$426$		0			0
$427$	−5.54707	−	15.2404i	−0.268442	−	0.737537i
$428$	4.72559	−	1.25666i	0.228420	−	0.0607432i
$429$		0			0
$430$	−4.89145	−	3.76068i	−0.235887	−	0.181356i
$431$	28.2506			1.36079			0.680393	−	0.732848i	$-0.261809\pi$
$431$	28.2506			1.36079			0.680393	+	0.732848i	$0.261809\pi$
$432$		0			0
$433$	−27.8524			−1.33850			−0.669251	−	0.743036i	$-0.733385\pi$
$433$	−27.8524			−1.33850			−0.669251	+	0.743036i	$0.733385\pi$
$434$	8.44798	+	6.49503i	0.405516	+	0.311772i
$435$		0			0
$436$	31.4127	−	8.35350i	1.50440	−	0.400060i
$437$	−0.925505	−	2.54280i	−0.0442729	−	0.121639i
$438$		0			0
$439$	−2.13242	−	12.0935i	−0.101775	−	0.577193i	−0.992460	−	0.122572i	$-0.960886\pi$
$439$	−2.13242	−	12.0935i	−0.101775	−	0.577193i	0.890685	−	0.454621i	$-0.150225\pi$
$440$	2.11894	−	5.07489i	0.101016	−	0.241936i
$441$		0			0
$442$	6.61674	−	20.9168i	0.314726	−	0.994910i
$443$	7.22670	−	19.8552i	0.343351	−	0.943348i	−0.641064	−	0.767487i	$-0.721507\pi$
$443$	7.22670	−	19.8552i	0.343351	−	0.943348i	0.984415	−	0.175861i	$-0.0562710\pi$
$444$		0			0
$445$	−12.4303	+	14.8138i	−0.589252	+	0.702243i
$446$	2.56554	−	4.91701i	0.121482	−	0.232827i
$447$		0			0
$448$	15.8049	−	22.3019i	0.746710	−	1.05367i
$449$	−13.8708	+	24.0249i	−0.654604	+	1.13381i	0.327389	+	0.944890i	$0.393831\pi$
$449$	−13.8708	+	24.0249i	−0.654604	+	1.13381i	−0.981993	+	0.188917i	$0.939502\pi$
$450$		0			0
$451$	−3.31561	+	1.91427i	−0.156126	+	0.0901393i
$452$	13.9251	+	19.9671i	0.654980	+	0.939176i
$453$		0			0
$454$	−14.1229	+	8.97856i	−0.662821	+	0.421385i
$455$	−13.4014	+	76.0030i	−0.628266	+	3.56307i
$456$		0			0
$457$	−26.0906	+	21.8926i	−1.22047	+	1.02409i	−0.221668	+	0.975122i	$0.571150\pi$
$457$	−26.0906	+	21.8926i	−1.22047	+	1.02409i	−0.998800	+	0.0489720i	$0.984405\pi$
$458$	14.6352	−	3.23006i	0.683858	−	0.150931i
$459$		0			0
$460$	−18.8452	−	40.6137i	−0.878664	−	1.89362i
$461$	8.93591	+	10.6494i	0.416187	+	0.495992i	0.932884	−	0.360176i	$-0.117283\pi$
$461$	8.93591	+	10.6494i	0.416187	+	0.495992i	−0.516698	+	0.856168i	$0.672839\pi$
$462$		0			0
$463$	3.22751	−	18.3041i	0.149995	−	0.850665i	−0.813224	−	0.581950i	$-0.802290\pi$
$463$	3.22751	−	18.3041i	0.149995	−	0.850665i	0.963220	−	0.268715i	$-0.0865991\pi$
$464$	−13.1182	−	4.83078i	−0.608996	−	0.224263i
$465$		0			0
$466$	−1.47701	+	0.610165i	−0.0684211	+	0.0282653i
$467$	8.34116	−	4.81577i	0.385983	−	0.222847i	−0.294435	−	0.955671i	$-0.595132\pi$
$467$	8.34116	−	4.81577i	0.385983	−	0.222847i	0.680418	+	0.732824i	$0.261798\pi$
$468$		0			0
$469$	−44.5181	−	25.7026i	−2.05566	−	1.18683i
$470$	14.9047	+	1.97654i	0.687500	+	0.0911712i
$471$		0			0
$472$	24.8074	+	1.15348i	1.14186	+	0.0530933i
$473$	−0.570541	−	0.478741i	−0.0262335	−	0.0220125i
$474$		0			0
$475$	0.891532	−	2.44946i	0.0409063	−	0.112389i
$476$	1.41027	−	15.7765i	0.0646395	−	0.723113i
$477$		0			0
$478$	6.05696	−	5.53968i	0.277039	−	0.253379i
$479$	−5.05443	−	28.6651i	−0.230943	−	1.30974i	−0.850992	−	0.525179i	$-0.823998\pi$
$479$	−5.05443	−	28.6651i	−0.230943	−	1.30974i	0.620049	−	0.784563i	$-0.287113\pi$
$480$		0			0
$481$	−7.64321	+	2.78190i	−0.348500	+	0.126844i
$482$	−41.6796	+	1.78037i	−1.89846	+	0.0810937i
$483$		0			0
$484$	−9.05352	+	19.3201i	−0.411524	+	0.878185i
$485$			37.9074i			1.72129i
$486$		0			0
$487$	−13.1429			−0.595563			−0.297782	−	0.954634i	$-0.596247\pi$
$487$	−13.1429			−0.595563			−0.297782	+	0.954634i	$0.596247\pi$
$488$	−2.94295	+	13.0992i	−0.133221	+	0.592973i
$489$		0			0
$490$	0.952140	+	22.2902i	0.0430133	+	1.00697i
$491$	−4.01945	−	11.0433i	−0.181395	−	0.498379i	0.815352	−	0.578965i	$-0.196543\pi$
$491$	−4.01945	−	11.0433i	−0.181395	−	0.498379i	−0.996748	+	0.0805856i	$0.974321\pi$
$492$		0			0
$493$	−7.97752	+	1.40665i	−0.359289	+	0.0633524i
$494$	2.84920	−	2.60587i	0.128191	−	0.117243i
$495$		0			0
$496$	−2.98571	−	8.30052i	−0.134062	−	0.372704i
$497$	25.1930	+	9.16949i	1.13006	+	0.411308i
$498$		0			0
$499$	23.2598	−	27.7199i	1.04125	−	1.24091i	0.0713387	−	0.997452i	$-0.477273\pi$
$499$	23.2598	−	27.7199i	1.04125	−	1.24091i	0.969911	−	0.243461i	$-0.0782827\pi$
$500$	2.44499	−	9.05643i	0.109343	−	0.405016i
$501$		0			0
$502$	−8.42969	−	1.11788i	−0.376236	−	0.0498936i
$503$	−1.18773	+	2.05720i	−0.0529581	+	0.0917261i	−0.891289	−	0.453435i	$-0.850198\pi$
$503$	−1.18773	+	2.05720i	−0.0529581	+	0.0917261i	0.838331	+	0.545161i	$0.183532\pi$
$504$		0			0
$505$	20.9748	+	36.3294i	0.933366	+	1.61664i
$506$	−2.06353	−	4.99514i	−0.0917352	−	0.222061i
$507$		0			0
$508$	13.5834	−	13.5322i	0.602665	−	0.600394i
$509$	−40.5051	−	7.14215i	−1.79536	−	0.316570i	−0.826269	−	0.563276i	$-0.809541\pi$
$509$	−40.5051	−	7.14215i	−1.79536	−	0.316570i	−0.969090	+	0.246706i	$0.920652\pi$
$510$		0			0
$511$	−3.35977	+	2.81918i	−0.148627	+	0.124713i
$512$	−20.9778	+	8.48130i	−0.927096	+	0.374824i
$513$		0			0
$514$	7.91515	+	35.8631i	0.349123	+	1.58185i
$515$	−34.2906	−	40.8660i	−1.51103	−	1.80077i
$516$		0			0
$517$	1.78734	+	0.315155i	0.0786069	+	0.0138605i
$518$	−4.95578	+	3.15061i	−0.217745	+	0.138430i
$519$		0			0
$520$	43.2938	−	46.9792i	1.89856	−	2.06017i
$521$	5.21530	+	9.03316i	0.228486	+	0.395750i	0.957360	−	0.288899i	$-0.0932890\pi$
$521$	5.21530	+	9.03316i	0.228486	+	0.395750i	−0.728873	+	0.684649i	$0.759956\pi$
$522$		0			0
$523$	−14.6626	−	8.46543i	−0.641149	−	0.370167i	0.143908	−	0.989591i	$-0.454033\pi$
$523$	−14.6626	−	8.46543i	−0.641149	−	0.370167i	−0.785057	+	0.619424i	$0.787366\pi$
$524$	−0.0703951	−	0.822494i	−0.00307523	−	0.0359308i
$525$		0			0
$526$	9.10062	−	17.4419i	0.396806	−	0.760504i
$527$	−3.91569	−	3.28565i	−0.170570	−	0.143125i
$528$		0			0
$529$	−19.7338	−	7.18252i	−0.857992	−	0.312283i
$530$	−42.5685	−	13.4660i	−1.84906	−	0.584924i
$531$		0			0
$532$	1.60328	−	2.28054i	0.0695109	−	0.0988741i
$533$	−43.7992	+	7.72298i	−1.89715	+	0.334519i
$534$		0			0
$535$	7.75366	−	2.82210i	0.335220	−	0.122010i
$536$	19.5419	+	37.8006i	0.844083	+	1.63274i
$537$		0			0
$538$	−3.35658	+	4.36584i	−0.144712	+	0.188225i
$539$			2.69313i			0.116001i
$540$		0			0
$541$			29.4745i			1.26721i	0.773658	+	0.633603i	$0.218425\pi$
$541$			29.4745i			1.26721i	−0.773658	+	0.633603i	$0.781575\pi$
$542$	−30.3839	−	23.3600i	−1.30510	−	1.00340i
$543$		0			0
$544$	−8.03096	+	10.3645i	−0.344325	+	0.444376i
$545$	51.5414	−	18.7595i	2.20779	−	0.803570i
$546$		0			0
$547$	−31.4846	+	5.55158i	−1.34618	+	0.237369i	−0.799850	−	0.600199i	$-0.795088\pi$
$547$	−31.4846	+	5.55158i	−1.34618	+	0.237369i	−0.546333	+	0.837568i	$0.683977\pi$
$548$	−25.7851	−	18.1276i	−1.10149	−	0.774371i
$549$		0			0
$550$	1.57022	−	4.96376i	0.0669543	−	0.211655i
$551$	−1.33972	−	0.487617i	−0.0570739	−	0.0207732i
$552$		0			0
$553$	13.1233	+	11.0117i	0.558059	+	0.468267i
$554$	8.98106	+	4.68602i	0.381569	+	0.199090i
$555$		0			0
$556$	0.376572	+	4.39985i	0.0159702	+	0.186595i
$557$	−7.19468	−	4.15385i	−0.304849	−	0.176004i	0.339770	−	0.940508i	$-0.389651\pi$
$557$	−7.19468	−	4.15385i	−0.304849	−	0.176004i	−0.644619	+	0.764504i	$0.722984\pi$
$558$		0			0
$559$	−4.32598	−	7.49282i	−0.182970	−	0.316913i
$560$	23.2131	−	39.8582i	0.980934	−	1.68432i
$561$		0			0
$562$	−0.588525	−	0.925725i	−0.0248254	−	0.0390494i
$563$	6.57453	+	1.15927i	0.277083	+	0.0488573i	0.310463	−	0.950585i	$-0.399516\pi$
$563$	6.57453	+	1.15927i	0.277083	+	0.0488573i	−0.0333796	+	0.999443i	$0.510627\pi$
$564$		0			0
$565$	26.4043	+	31.4674i	1.11084	+	1.32384i
$566$	−2.11126	+	0.465966i	−0.0887430	+	0.0195860i
$567$		0			0
$568$	−13.4604	−	17.6452i	−0.564787	−	0.740375i
$569$	24.2709	−	20.3657i	1.01749	−	0.853775i	0.0281798	−	0.999603i	$-0.491029\pi$
$569$	24.2709	−	20.3657i	1.01749	−	0.853775i	0.989310	+	0.145827i	$0.0465844\pi$
$570$		0			0
$571$	−32.6020	−	5.74861i	−1.36435	−	0.240572i	−0.556936	−	0.830555i	$-0.688023\pi$
$571$	−32.6020	−	5.74861i	−1.36435	−	0.240572i	−0.807416	+	0.589983i	$0.799134\pi$
$572$	5.46329	−	5.44271i	0.228432	−	0.227571i
$573$		0			0
$574$	−29.6778	+	12.2602i	−1.23873	+	0.511729i
$575$	−21.1926	−	36.7066i	−0.883791	−	1.53077i
$576$		0			0
$577$	15.0611	−	26.0866i	0.627001	−	1.08600i	−0.361149	−	0.932508i	$-0.617615\pi$
$577$	15.0611	−	26.0866i	0.627001	−	1.08600i	0.988150	−	0.153490i	$-0.0490512\pi$
$578$	2.16172	−	16.3011i	0.0899159	−	0.678035i
$579$		0			0
$580$	−22.7740	−	6.14836i	−0.945638	−	0.255297i
$581$	22.7953	−	27.1663i	0.945707	−	1.12705i
$582$		0			0
$583$	−5.06443	−	1.84330i	−0.209747	−	0.0763418i
$584$	3.60089	−	0.463700i	0.149006	−	0.0191880i
$585$		0			0
$586$	−15.1792	−	16.5966i	−0.627046	−	0.685598i
$587$	−15.0318	+	2.65051i	−0.620427	+	0.109398i	−0.475022	−	0.879974i	$-0.657560\pi$
$587$	−15.0318	+	2.65051i	−0.620427	+	0.109398i	−0.145406	+	0.989372i	$0.546449\pi$
$588$		0			0
$589$	−0.307693	−	0.845379i	−0.0126783	−	0.0348332i
$590$	41.8681	−	1.78842i	1.72368	−	0.0736281i
$591$		0			0
$592$	4.86121	+	0.0183477i	0.199795	+	0.000754087i
$593$	−27.1813			−1.11620			−0.558101	−	0.829773i	$-0.688470\pi$
$593$	−27.1813			−1.11620			−0.558101	+	0.829773i	$0.688470\pi$
$594$		0			0
$595$		−	26.7279i		−	1.09574i
$596$	12.3980	+	5.80978i	0.507841	+	0.237978i
$597$		0			0
$598$	−2.67939	−	62.7262i	−0.109568	−	2.56506i
$599$	39.7660	−	14.4737i	1.62480	−	0.591378i	0.640509	−	0.767951i	$-0.278723\pi$
$599$	39.7660	−	14.4737i	1.62480	−	0.591378i	0.984288	+	0.176573i	$0.0565012\pi$
$600$		0			0
$601$	−0.648834	−	3.67972i	−0.0264665	−	0.150099i	0.968711	−	0.248193i	$-0.0798366\pi$
$601$	−0.648834	−	3.67972i	−0.0264665	−	0.150099i	−0.995177	+	0.0980937i	$0.968726\pi$
$602$	−4.21583	−	4.60950i	−0.171824	−	0.187869i
$603$		0			0
$604$	−2.10090	+	23.5025i	−0.0854844	+	0.956302i
$605$	−12.3139	+	33.8321i	−0.500631	+	1.37547i
$606$		0			0
$607$	35.5497	+	29.8298i	1.44292	+	1.21075i	0.937550	+	0.347850i	$0.113088\pi$
$607$	35.5497	+	29.8298i	1.44292	+	1.21075i	0.505370	+	0.862903i	$0.331356\pi$
$608$	−2.13616	+	0.873040i	−0.0866325	+	0.0354065i
$609$		0			0
$610$	−2.97827	+	22.4584i	−0.120587	+	0.909315i
$611$	18.2586	+	10.5416i	0.738664	+	0.426468i
$612$		0			0
$613$	−21.9670	+	12.6827i	−0.887239	+	0.512248i	−0.873038	−	0.487652i	$-0.837854\pi$
$613$	−21.9670	+	12.6827i	−0.887239	+	0.512248i	−0.0142005	+	0.999899i	$0.504520\pi$
$614$	−0.231056	−	0.559311i	−0.00932466	−	0.0225719i
$615$		0			0
$616$	3.00486	−	4.68735i	0.121069	−	0.188859i
$617$	−1.23909	+	7.02722i	−0.0498838	+	0.282905i	−0.999538	−	0.0303950i	$-0.990323\pi$
$617$	−1.23909	+	7.02722i	−0.0498838	+	0.282905i	0.949654	+	0.313300i	$0.101435\pi$
$618$		0			0
$619$	−17.2889	−	20.6041i	−0.694900	−	0.828149i	0.297039	−	0.954865i	$-0.404001\pi$
$619$	−17.2889	−	20.6041i	−0.694900	−	0.828149i	−0.991939	+	0.126716i	$0.959556\pi$
$620$	−6.26528	−	13.5024i	−0.251620	−	0.542269i
$621$		0			0
$622$	3.36672	+	15.2544i	0.134993	+	0.611646i
$623$	−14.9979	+	12.5847i	−0.600877	+	0.504196i
$624$		0			0
$625$	−2.79914	+	15.8747i	−0.111966	+	0.634989i
$626$	21.0893	+	33.1727i	0.842900	+	1.32585i
$627$		0			0
$628$	−19.7700	+	13.7876i	−0.788910	+	0.550185i
$629$	2.43953	−	1.40846i	0.0972705	−	0.0561592i
$630$		0			0
$631$	−11.7466	+	20.3457i	−0.467624	+	0.809949i	−0.999316	−	0.0369893i	$-0.988223\pi$
$631$	−11.7466	+	20.3457i	−0.467624	+	0.809949i	0.531691	+	0.846938i	$0.321557\pi$
$632$	−4.22608	−	13.5369i	−0.168104	−	0.538469i
$633$		0			0
$634$	−4.40561	−	2.29870i	−0.174969	−	0.0912930i
$635$	20.7970	−	24.7848i	0.825302	−	0.983557i
$636$		0			0
$637$	−10.7002	+	29.3985i	−0.423956	+	1.16481i
$638$	−2.71489	−	0.858820i	−0.107484	−	0.0340010i
$639$		0			0
$640$	−33.9839	+	17.4066i	−1.34333	+	0.688055i
$641$	7.57282	+	42.9476i	0.299108	+	1.69633i	0.650019	+	0.759918i	$0.274761\pi$
$641$	7.57282	+	42.9476i	0.299108	+	1.69633i	−0.350911	+	0.936409i	$0.614128\pi$
$642$		0			0
$643$	−0.120739	−	0.331727i	−0.00476148	−	0.0130820i	0.937289	−	0.348553i	$-0.113327\pi$
$643$	−0.120739	−	0.331727i	−0.00476148	−	0.0130820i	−0.942051	+	0.335471i	$0.891105\pi$
$644$	−11.6494	−	43.8066i	−0.459050	−	1.72622i
$645$		0			0
$646$	−0.815048	+	1.06012i	−0.0320676	+	0.0417098i
$647$	26.0967			1.02597			0.512984	−	0.858398i	$-0.328540\pi$
$647$	26.0967			1.02597			0.512984	+	0.858398i	$0.328540\pi$
$648$		0			0
$649$	5.05855			0.198565
$650$	36.8624	−	47.9463i	1.44586	−	1.88061i
$651$		0			0
$652$	25.8944	−	6.88605i	1.01410	−	0.269678i
$653$	−0.281991	−	0.774764i	−0.0110352	−	0.0303189i	0.934053	−	0.357135i	$-0.116246\pi$
$653$	−0.281991	−	0.774764i	−0.0110352	−	0.0303189i	−0.945088	+	0.326816i	$0.894024\pi$
$654$		0			0
$655$	−0.241889	−	1.37182i	−0.00945137	−	0.0536014i
$656$	26.1597	+	4.71453i	1.02136	+	0.184071i
$657$		0			0
$658$	14.5131	+	4.59101i	0.565779	+	0.178976i
$659$	−14.2971	+	39.2809i	−0.556935	+	1.53017i	0.267123	+	0.963662i	$0.413927\pi$
$659$	−14.2971	+	39.2809i	−0.556935	+	1.53017i	−0.824058	+	0.566505i	$0.808295\pi$
$660$		0			0
$661$	1.06741	−	1.27208i	0.0415173	−	0.0494784i	−0.744886	−	0.667192i	$-0.767496\pi$
$661$	1.06741	−	1.27208i	0.0415173	−	0.0494784i	0.786404	+	0.617713i	$0.211941\pi$
$662$	−21.8387	−	11.3947i	−0.848786	−	0.442868i
$663$		0			0
$664$	−28.0226	+	8.74835i	−1.08749	+	0.339502i
$665$	2.35205	−	4.07387i	0.0912086	−	0.157978i
$666$		0			0
$667$	−20.0764	+	11.5911i	−0.777362	+	0.448810i
$668$	7.74894	+	11.1112i	0.299816	+	0.429905i
$669$		0			0
$670$	38.5241	+	60.5968i	1.48831	+	2.34106i
$671$	−0.474878	+	2.69317i	−0.0183325	+	0.103969i
$672$		0			0
$673$	−4.23311	+	3.55200i	−0.163175	+	0.136920i	−0.720719	−	0.693227i	$-0.756188\pi$
$673$	−4.23311	+	3.55200i	−0.163175	+	0.136920i	0.557544	+	0.830147i	$0.311744\pi$
$674$	0.867456	+	3.93039i	0.0334132	+	0.151393i
$675$		0			0
$676$	57.6779	−	26.7632i	2.21838	−	1.02936i
$677$	2.08429	+	2.48396i	0.0801056	+	0.0954662i	0.804609	−	0.593805i	$-0.202375\pi$
$677$	2.08429	+	2.48396i	0.0801056	+	0.0954662i	−0.724503	+	0.689272i	$0.757931\pi$
$678$		0			0
$679$	−6.66432	+	37.7952i	−0.255753	+	1.45045i
$680$	−11.9407	+	18.6266i	−0.457906	+	0.714299i
$681$		0			0
$682$	−0.686041	−	1.66068i	−0.0262699	−	0.0635907i
$683$	22.4547	−	12.9642i	0.859206	−	0.496063i	−0.00454025	−	0.999990i	$-0.501445\pi$
$683$	22.4547	−	12.9642i	0.859206	−	0.496063i	0.863746	+	0.503927i	$0.168112\pi$
$684$		0			0
$685$	−46.0615	−	26.5936i	−1.75992	−	1.01609i
$686$	1.47722	−	11.1394i	0.0564006	−	0.425304i
$687$		0			0
$688$	0.878705	+	5.09578i	0.0335003	+	0.194275i
$689$	−47.9602	−	40.2434i	−1.82714	−	1.53315i
$690$		0			0
$691$	10.2247	−	28.0920i	0.388964	−	1.06867i	−0.578504	−	0.815679i	$-0.696363\pi$
$691$	10.2247	−	28.0920i	0.388964	−	1.06867i	0.967469	−	0.252991i	$-0.0814145\pi$
$692$	−3.35749	−	0.300128i	−0.127633	−	0.0114092i
$693$		0			0
$694$	24.9909	+	27.3245i	0.948640	+	1.03722i
$695$	1.29396	+	7.33841i	0.0490827	+	0.278362i
$696$		0			0
$697$	14.4739	−	5.26808i	0.548240	−	0.199543i
$698$	0.307938	+	7.20902i	0.0116556	+	0.272866i
$699$		0			0
$700$	18.5284	−	39.5392i	0.700306	−	1.49444i
$701$		−	24.6223i		−	0.929973i	−0.885318	−	0.464987i	$-0.846059\pi$
$701$		−	24.6223i		−	0.929973i	0.885318	−	0.464987i	$-0.153941\pi$
$702$		0			0
$703$	0.495778			0.0186986
$704$	−4.18816	+	1.92418i	−0.157847	+	0.0725203i
$705$		0			0
$706$	−21.0306	+	0.898336i	−0.791498	+	0.0338093i
$707$	14.5258	+	39.9094i	0.546300	+	1.50095i
$708$		0			0
$709$	26.4148	−	4.65765i	0.992030	−	0.174922i	0.346001	−	0.938234i	$-0.387540\pi$
$709$	26.4148	−	4.65765i	0.992030	−	0.174922i	0.646029	+	0.763313i	$0.276428\pi$
$710$	−25.2745	−	27.6346i	−0.948535	−	1.03711i
$711$		0			0
$712$	16.0742	−	2.06994i	0.602407	−	0.0775742i
$713$	−13.7461	−	5.00317i	−0.514796	−	0.187370i
$714$		0			0
$715$	8.36463	−	9.96858i	0.312819	−	0.372804i
$716$	6.21128	−	23.0070i	0.232126	−	0.859813i
$717$		0			0
$718$	2.87919	−	21.7113i	0.107450	−	0.810257i
$719$	−9.26666	+	16.0503i	−0.345588	+	0.598576i	−0.985460	−	0.169905i	$-0.945654\pi$
$719$	−9.26666	+	16.0503i	−0.345588	+	0.598576i	0.639872	+	0.768481i	$0.278987\pi$
$720$		0			0
$721$	−27.0047	−	46.7736i	−1.00571	−	1.74194i
$722$	24.6169	−	10.1694i	0.916145	−	0.378467i
$723$		0			0
$724$	23.3122	+	23.4003i	0.866390	+	0.869666i
$725$	−21.9920	−	3.87779i	−0.816764	−	0.144017i
$726$		0			0
$727$	4.82234	−	4.04643i	0.178851	−	0.150074i	−0.548967	−	0.835844i	$-0.684979\pi$
$727$	4.82234	−	4.04643i	0.178851	−	0.150074i	0.727818	+	0.685770i	$0.240534\pi$
$728$	51.4249	−	39.2290i	1.90593	−	1.45392i
$729$		0			0
$730$	5.98247	−	1.32036i	0.221421	−	0.0488687i
$731$	1.92605	+	2.29538i	0.0712377	+	0.0848978i
$732$		0			0
$733$	22.4113	+	3.95172i	0.827781	+	0.145960i	0.571458	−	0.820631i	$-0.306378\pi$
$733$	22.4113	+	3.95172i	0.827781	+	0.145960i	0.256323	+	0.966591i	$0.417489\pi$
$734$	−19.4383	−	30.5756i	−0.717480	−	1.12857i
$735$		0			0
$736$	−11.4522	+	35.7331i	−0.422135	+	1.31714i
$737$	4.33388	+	7.50649i	0.159640	+	0.276505i
$738$		0			0
$739$	37.2940	+	21.5317i	1.37188	+	0.792056i	0.991165	−	0.132636i	$-0.0423440\pi$
$739$	37.2940	+	21.5317i	1.37188	+	0.792056i	0.380717	+	0.924692i	$0.375677\pi$
$740$	8.17317	−	0.699520i	0.300452	−	0.0257149i
$741$		0			0
$742$	−40.0752	−	20.9099i	−1.47121	−	0.767626i
$743$	27.0616	+	22.7074i	0.992794	+	0.833053i	0.985970	−	0.166924i	$-0.0533834\pi$
$743$	27.0616	+	22.7074i	0.992794	+	0.833053i	0.00682406	+	0.999977i	$0.497828\pi$
$744$		0			0
$745$	21.7106	+	7.90201i	0.795415	+	0.289507i
$746$	6.06108	−	19.1602i	0.221912	−	0.701506i
$747$		0			0
$748$	−1.53602	+	2.18488i	−0.0561625	+	0.0798871i
$749$	8.22687	−	1.45062i	0.300603	−	0.0530045i
$750$		0			0
$751$	−23.5008	+	8.55359i	−0.857557	+	0.312125i	−0.733117	−	0.680102i	$-0.761935\pi$
$751$	−23.5008	+	8.55359i	−0.857557	+	0.312125i	−0.124439	+	0.992227i	$0.539713\pi$
$752$	−8.06309	−	9.68320i	−0.294031	−	0.353110i
$753$		0			0
$754$	−26.2239	−	20.1616i	−0.955017	−	0.734243i
$755$			39.8171i			1.44909i
$756$		0			0
$757$			31.3025i			1.13771i	0.822439	+	0.568853i	$0.192613\pi$
$757$			31.3025i			1.13771i	−0.822439	+	0.568853i	$0.807387\pi$
$758$	−1.66480	+	2.16538i	−0.0604682	+	0.0786500i
$759$		0			0
$760$	−3.45915	+	1.78829i	−0.125476	+	0.0648681i
$761$	2.59308	−	0.943805i	0.0939992	−	0.0342129i	−0.294592	−	0.955623i	$-0.595184\pi$
$761$	2.59308	−	0.943805i	0.0939992	−	0.0342129i	0.388592	+	0.921410i	$0.372962\pi$
$762$		0			0
$763$	54.6869	−	9.64278i	1.97980	−	0.349092i
$764$	21.6289	+	15.2056i	0.782507	+	0.550121i
$765$		0			0
$766$	17.8468	+	5.64558i	0.644830	+	0.203983i
$767$	55.2197	+	20.0983i	1.99387	+	0.725708i
$768$		0			0
$769$	3.61913	+	3.03681i	0.130509	+	0.109510i	0.705706	−	0.708505i	$-0.250630\pi$
$769$	3.61913	+	3.03681i	0.130509	+	0.109510i	−0.575197	+	0.818015i	$0.695074\pi$
$770$	4.34614	−	8.32966i	0.156624	−	0.300180i
$771$		0			0
$772$	−0.352674	+	0.0301844i	−0.0126930	+	0.00108636i
$773$	−17.3435	−	10.0133i	−0.623803	−	0.360153i	0.154545	−	0.987986i	$-0.450609\pi$
$773$	−17.3435	−	10.0133i	−0.623803	−	0.360153i	−0.778348	+	0.627833i	$0.783942\pi$
$774$		0			0
$775$	−7.04567	−	12.2035i	−0.253088	−	0.438361i
$776$	21.5294	−	23.3621i	0.772861	−	0.838651i
$777$		0			0
$778$	−28.7012	+	18.2467i	−1.02899	+	0.654175i
$779$	2.66971	+	0.470742i	0.0956522	+	0.0168661i
$780$		0			0
$781$	−2.90577	−	3.46296i	−0.103977	−	0.123914i
$782$	4.68614	+	21.2326i	0.167576	+	0.759276i
$783$		0			0
$784$	12.0729	−	14.2781i	0.431174	−	0.509932i
$785$	−31.1567	+	26.1436i	−1.11203	+	0.933105i
$786$		0			0
$787$	−41.5062	−	7.31867i	−1.47954	−	0.260882i	−0.625144	−	0.780510i	$-0.714960\pi$
$787$	−41.5062	−	7.31867i	−1.47954	−	0.260882i	−0.854393	+	0.519627i	$0.826071\pi$
$788$	1.37111	+	1.37630i	0.0488439	+	0.0490286i
$789$		0			0
$790$	−9.13673	−	22.1170i	−0.325070	−	0.786888i
$791$	20.7940	+	36.0163i	0.739350	+	1.28059i
$792$		0			0
$793$	−15.8842	+	27.5122i	−0.564063	+	0.976986i
$794$	−46.4331	−	6.15761i	−1.64785	−	0.218525i
$795$		0			0
$796$	7.91372	+	2.13649i	0.280494	+	0.0757258i
$797$	−32.1711	+	38.3400i	−1.13956	+	1.35807i	−0.215189	+	0.976572i	$0.569037\pi$
$797$	−32.1711	+	38.3400i	−1.13956	+	1.35807i	−0.924369	+	0.381500i	$0.875408\pi$
$798$		0			0
$799$	−6.86134	−	2.49732i	−0.242737	−	0.0883489i
$800$	−30.5766	+	19.2772i	−1.08104	+	0.681553i
$801$		0			0
$802$	11.6928	−	10.6942i	0.412888	−	0.377626i
$803$	0.728294	−	0.128418i	0.0257009	−	0.00453177i
$804$		0			0
$805$	−26.1611	−	71.8771i	−0.922059	−	2.53334i
$806$	−0.890787	−	20.8539i	−0.0313766	−	0.734547i
$807$		0			0
$808$	7.70655	−	34.3022i	0.271116	−	1.20675i
$809$	−7.89082			−0.277426			−0.138713	−	0.990333i	$-0.544297\pi$
$809$	−7.89082			−0.277426			−0.138713	+	0.990333i	$0.544297\pi$
$810$		0			0
$811$		−	16.9433i		−	0.594960i	−0.954728	−	0.297480i	$-0.903854\pi$
$811$		−	16.9433i		−	0.594960i	0.954728	−	0.297480i	$-0.0961461\pi$
$812$	−21.6257	−	10.1340i	−0.758913	−	0.355632i
$813$		0			0
$814$	0.989297	−	0.0422584i	0.0346748	−	0.00148116i
$815$	42.4871	−	15.4641i	1.48826	−	0.541682i
$816$		0			0
$817$	0.0915762	+	0.519355i	0.00320385	+	0.0181699i
$818$	−11.7191	+	10.7183i	−0.409749	+	0.374755i
$819$		0			0
$820$	44.6758	+	3.99359i	1.56015	+	0.139462i
$821$	−16.2209	+	44.5665i	−0.566112	+	1.55538i	0.244410	+	0.969672i	$0.421406\pi$
$821$	−16.2209	+	44.5665i	−0.566112	+	1.55538i	−0.810522	+	0.585708i	$0.800816\pi$
$822$		0			0
$823$	−3.65996	−	3.07107i	−0.127578	−	0.107051i	0.576766	−	0.816909i	$-0.304314\pi$
$823$	−3.65996	−	3.07107i	−0.127578	−	0.107051i	−0.704344	+	0.709858i	$0.748759\pi$
$824$	−2.07661	+	44.6608i	−0.0723422	+	1.55583i
$825$		0			0
$826$	42.0586	+	5.57750i	1.46341	+	0.194066i
$827$	−25.0451	−	14.4598i	−0.870903	−	0.502816i	−0.00325451	−	0.999995i	$-0.501036\pi$
$827$	−25.0451	−	14.4598i	−0.870903	−	0.502816i	−0.867648	+	0.497179i	$0.834369\pi$
$828$		0			0
$829$	17.1833	−	9.92077i	0.596800	−	0.344563i	−0.170982	−	0.985274i	$-0.554694\pi$
$829$	17.1833	−	9.92077i	0.596800	−	0.344563i	0.767782	+	0.640711i	$0.221361\pi$
$830$	−45.7841	+	18.9138i	−1.58919	+	0.656508i
$831$		0			0
$832$	−53.3635	+	4.36442i	−1.85005	+	0.151309i
$833$	1.88146	−	10.6703i	0.0651888	−	0.369704i
$834$		0			0
$835$	14.6933	+	17.5108i	0.508482	+	0.605986i
$836$	−0.426389	+	0.197850i	−0.0147470	+	0.00684278i
$837$		0			0
$838$	−19.2429	+	4.24701i	−0.664737	+	0.146711i
$839$	−26.2638	+	22.0379i	−0.906725	+	0.760833i	−0.971493	−	0.237067i	$-0.923814\pi$
$839$	−26.2638	+	22.0379i	−0.906725	+	0.760833i	0.0647677	+	0.997900i	$0.479369\pi$
$840$		0			0
$841$	2.91487	−	16.5310i	0.100513	−	0.570036i
$842$	−14.1910	+	9.02187i	−0.489055	+	0.310914i
$843$		0			0
$844$	−6.15574	+	4.29300i	−0.211889	+	0.147771i
$845$	92.9203	−	53.6476i	3.19656	−	1.84553i
$846$		0			0
$847$	−18.2253	+	31.5672i	−0.626230	+	1.08466i
$848$	18.5868	+	32.4757i	0.638272	+	1.11522i
$849$		0			0
$850$	−9.68904	+	18.5697i	−0.332331	+	0.636935i
$851$	5.18183	−	6.17546i	0.177631	−	0.211692i
$852$		0			0
$853$	−11.5939	+	31.8539i	−0.396967	+	1.09066i	0.566787	+	0.823865i	$0.308186\pi$
$853$	−11.5939	+	31.8539i	−0.396967	+	1.09066i	−0.963754	+	0.266793i	$0.914036\pi$
$854$	−6.91777	+	21.8684i	−0.236721	+	0.748321i
$855$		0			0
$856$	−6.38135	−	2.66443i	−0.218110	−	0.0910683i
$857$	−0.670084	−	3.80024i	−0.0228896	−	0.129814i	0.971222	−	0.238177i	$-0.0765500\pi$
$857$	−0.670084	−	3.80024i	−0.0228896	−	0.129814i	−0.994111	+	0.108364i	$0.965439\pi$
$858$		0			0
$859$	7.37600	+	20.2654i	0.251666	+	0.691446i	0.999617	+	0.0276917i	$0.00881567\pi$
$859$	7.37600	+	20.2654i	0.251666	+	0.691446i	−0.747951	+	0.663754i	$0.768962\pi$
$860$	2.24247	+	8.43263i	0.0764676	+	0.287550i
$861$		0			0
$862$	−31.6734	−	24.3514i	−1.07880	−	0.829412i
$863$	−30.2497			−1.02971			−0.514857	−	0.857276i	$-0.672155\pi$
$863$	−30.2497			−1.02971			−0.514857	+	0.857276i	$0.672155\pi$
$864$		0			0
$865$	−5.68815			−0.193403
$866$	31.2270	+	24.0082i	1.06114	+	0.815830i
$867$		0			0
$868$	−3.87295	−	14.5639i	−0.131456	−	0.494332i
$869$	−0.987962	−	2.71440i	−0.0335143	−	0.0920799i
$870$		0			0
$871$	17.4847	+	99.1608i	0.592447	+	3.35994i
$872$	−42.4191	−	17.7114i	−1.43649	−	0.599784i
$873$		0			0
$874$	−1.15420	+	3.64865i	−0.0390414	+	0.123417i
$875$	5.48119	−	15.0594i	0.185298	−	0.509102i
$876$		0			0
$877$	10.0265	−	11.9491i	0.338571	−	0.403493i	−0.569715	−	0.821842i	$-0.692947\pi$
$877$	10.0265	−	11.9491i	0.338571	−	0.403493i	0.908286	+	0.418349i	$0.137391\pi$
$878$	−8.03357	+	15.3969i	−0.271120	+	0.519619i
$879$		0			0
$880$	−6.75010	+	3.86328i	−0.227546	+	0.130231i
$881$	−18.2832	+	31.6674i	−0.615977	+	1.06690i	0.374235	+	0.927334i	$0.377905\pi$
$881$	−18.2832	+	31.6674i	−0.615977	+	1.06690i	−0.990212	+	0.139569i	$0.955428\pi$
$882$		0			0
$883$	−26.1355	+	15.0893i	−0.879529	+	0.507796i	−0.870503	−	0.492163i	$-0.836206\pi$
$883$	−26.1355	+	15.0893i	−0.879529	+	0.507796i	−0.00902592	+	0.999959i	$0.502873\pi$
$884$	−25.4482	+	17.7476i	−0.855916	+	0.596915i
$885$		0			0
$886$	−25.2170	+	16.0316i	−0.847181	+	0.538591i
$887$	7.16882	−	40.6564i	0.240705	−	1.36511i	−0.589553	−	0.807730i	$-0.700696\pi$
$887$	7.16882	−	40.6564i	0.240705	−	1.36511i	0.830258	−	0.557379i	$-0.188193\pi$
$888$		0			0
$889$	25.0927	−	21.0553i	0.841584	−	0.706172i
$890$	26.7055	−	5.89404i	0.895171	−	0.197569i
$891$		0			0
$892$	−7.11472	+	3.30132i	−0.238219	+	0.110536i
$893$	−0.826041	−	0.984438i	−0.0276424	−	0.0329430i
$894$		0			0
$895$	6.98289	−	39.6019i	0.233412	−	1.32375i
$896$	−36.9435	+	11.3805i	−1.23420	+	0.380197i
$897$		0			0
$898$	36.2603	−	14.9794i	1.21002	−	0.499870i
$899$	−6.67459	+	3.85358i	−0.222610	+	0.128524i
$900$		0			0
$901$	18.7778	+	10.8414i	0.625578	+	0.361178i
$902$	5.36737	+	0.711781i	0.178714	+	0.0236997i
$903$		0			0
$904$	1.59902	−	34.3894i	0.0531826	−	1.14378i
$905$	42.6973	+	35.8273i	1.41931	+	1.19094i
$906$		0			0
$907$	−13.9229	+	38.2529i	−0.462303	+	1.27017i	0.461446	+	0.887168i	$0.347331\pi$
$907$	−13.9229	+	38.2529i	−0.462303	+	1.27017i	−0.923749	+	0.382999i	$0.874891\pi$
$908$	23.5733	+	2.10723i	0.782308	+	0.0699310i
$909$		0			0
$910$	80.5379	−	73.6597i	2.66980	−	2.44179i
$911$	−7.42318	−	42.0989i	−0.245941	−	1.39480i	−0.818298	−	0.574795i	$-0.805082\pi$
$911$	−7.42318	−	42.0989i	−0.245941	−	1.39480i	0.572357	−	0.820005i	$-0.306029\pi$
$912$		0			0
$913$	−5.61905	+	2.04517i	−0.185963	+	0.0676852i
$914$	48.1227	−	2.05559i	1.59176	−	0.0679928i
$915$		0			0
$916$	−19.1926	−	8.99380i	−0.634142	−	0.297163i
$917$		−	1.41029i		−	0.0465717i
$918$		0			0
$919$	−4.00742			−0.132193			−0.0660963	−	0.997813i	$-0.521054\pi$
$919$	−4.00742			−0.132193			−0.0660963	+	0.997813i	$0.521054\pi$
$920$	−13.8796	+	61.7785i	−0.457595	+	2.03678i
$921$		0			0
$922$	−0.839029	−	19.6422i	−0.0276319	−	0.646882i
$923$	−17.9609	−	49.3471i	−0.591189	−	1.62428i
$924$		0			0
$925$	7.64760	−	1.34848i	0.251452	−	0.0443377i
$926$	−19.3963	+	17.7398i	−0.637402	+	0.582966i
$927$		0			0
$928$	10.5435	+	16.7236i	0.346109	+	0.548980i
$929$	−46.5451	−	16.9410i	−1.52710	−	0.555818i	−0.564188	−	0.825646i	$-0.690811\pi$
$929$	−46.5451	−	16.9410i	−1.52710	−	0.555818i	−0.962908	+	0.269829i	$0.913033\pi$
$930$		0			0
$931$	1.22576	−	1.46080i	0.0401725	−	0.0478758i
$932$	2.18191	+	0.589056i	0.0714708	+	0.0192952i
$933$		0			0
$934$	−13.5028	−	1.79065i	−0.441826	−	0.0585917i
$935$	−2.25339	+	3.90298i	−0.0736936	+	0.127641i
$936$		0			0
$937$	4.84280	+	8.38798i	0.158207	+	0.274023i	0.934222	−	0.356691i	$-0.116095\pi$
$937$	4.84280	+	8.38798i	0.158207	+	0.274023i	−0.776015	+	0.630715i	$0.782762\pi$
$938$	27.7569	+	67.1902i	0.906293	+	2.19384i
$939$		0			0
$940$	−15.0067	−	15.0635i	−0.489466	−	0.491317i
$941$	−5.10500	−	0.900150i	−0.166418	−	0.0293440i	0.0898181	−	0.995958i	$-0.471371\pi$
$941$	−5.10500	−	0.900150i	−0.166418	−	0.0293440i	−0.256236	+	0.966614i	$0.582483\pi$
$942$		0			0
$943$	33.7672	−	28.3340i	1.09961	−	0.922682i
$944$	−26.8188	−	22.6767i	−0.872877	−	0.738063i
$945$		0			0
$946$	0.227003	+	1.02854i	0.00738051	+	0.0334406i
$947$	19.6357	+	23.4009i	0.638075	+	0.760428i	0.984065	−	0.177811i	$-0.0569014\pi$
$947$	19.6357	+	23.4009i	0.638075	+	0.760428i	−0.345990	+	0.938238i	$0.612457\pi$
$948$		0			0
$949$	8.46036	+	1.49179i	0.274635	+	0.0484256i
$950$	−3.11093	+	1.97776i	−0.100932	+	0.0641669i
$951$		0			0
$952$	−15.1801	+	16.4723i	−0.491989	+	0.533870i
$953$	−8.71927	−	15.1022i	−0.282445	−	0.489209i	0.689542	−	0.724246i	$-0.257812\pi$
$953$	−8.71927	−	15.1022i	−0.282445	−	0.489209i	−0.971986	+	0.235037i	$0.924479\pi$
$954$		0			0
$955$	38.6370	+	22.3071i	1.25027	+	0.721841i
$956$	−11.5659	+	0.989894i	−0.374068	+	0.0320155i
$957$		0			0
$958$	−19.0418	+	36.4949i	−0.615214	+	1.17910i
$959$	−41.2500	−	34.6128i	−1.33203	−	1.11771i
$960$		0			0
$961$	24.5605	+	8.93927i	0.792273	+	0.288364i
$962$	10.9672	+	3.46932i	0.353596	+	0.111855i
$963$		0			0
$964$	48.2641	+	33.9308i	1.55448	+	1.09284i
$965$	−0.588217	+	0.103718i	−0.0189354	+	0.00333882i
$966$		0			0
$967$	−46.2859	+	16.8467i	−1.48845	+	0.541752i	−0.953042	−	0.302839i	$-0.902065\pi$
$967$	−46.2859	+	16.8467i	−1.48845	+	0.541752i	−0.535411	+	0.844592i	$0.679843\pi$
$968$	26.8039	−	13.8569i	0.861510	−	0.445378i
$969$		0			0
$970$	32.6753	−	42.5002i	1.04914	−	1.36460i
$971$		−	13.2201i		−	0.424253i	−0.977242	−	0.212126i	$-0.931961\pi$
$971$		−	13.2201i		−	0.424253i	0.977242	−	0.212126i	$-0.0680388\pi$
$972$		0			0
$973$			7.54418i			0.241855i
$974$	14.7353	+	11.3289i	0.472150	+	0.363002i
$975$		0			0
$976$	14.5907	−	12.1495i	0.467037	−	0.388896i
$977$	22.1311	−	8.05506i	0.708037	−	0.257704i	0.0371983	−	0.999308i	$-0.488157\pi$
$977$	22.1311	−	8.05506i	0.708037	−	0.257704i	0.670838	+	0.741604i	$0.265934\pi$
$978$		0			0
$979$	3.25108	−	0.573253i	0.103905	−	0.0183212i
$980$	18.1461	−	25.8116i	0.579657	−	0.824520i
$981$		0			0
$982$	−5.01267	+	15.8460i	−0.159961	+	0.505667i
$983$	44.1620	+	16.0737i	1.40855	+	0.512670i	0.930704	−	0.365773i	$-0.119195\pi$
$983$	44.1620	+	16.0737i	1.40855	+	0.512670i	0.477846	+	0.878444i	$0.341418\pi$
$984$		0			0
$985$	2.51126	+	2.10719i	0.0800153	+	0.0671408i
$986$	10.1566	+	5.29936i	0.323451	+	0.168766i
$987$		0			0
$988$	−5.44060	+	0.465646i	−0.173088	+	0.0148142i
$989$	7.42628	+	4.28756i	0.236142	+	0.136337i
$990$		0			0
$991$	−10.5119	−	18.2072i	−0.333922	−	0.578370i	0.649355	−	0.760486i	$-0.275039\pi$
$991$	−10.5119	−	18.2072i	−0.333922	−	0.578370i	−0.983277	+	0.182115i	$0.941706\pi$
$992$	−3.80740	+	11.8798i	−0.120885	+	0.377184i
$993$		0			0
$994$	−20.3414	−	31.9962i	−0.645190	−	1.01486i
$995$	13.6219	+	2.40190i	0.431842	+	0.0761454i
$996$		0			0
$997$	−1.15413	−	1.37543i	−0.0365515	−	0.0435604i	0.747459	−	0.664308i	$-0.231274\pi$
$997$	−1.15413	−	1.37543i	−0.0365515	−	0.0435604i	−0.784011	+	0.620748i	$0.786829\pi$
$998$	−49.9718	+	11.0290i	−1.58183	+	0.349117i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.t.a.37.8		204
3.2	odd	2		216.2.t.a.157.27	yes	204
8.5	even	2	inner	648.2.t.a.37.23		204
12.11	even	2		864.2.bf.a.49.13		204
24.5	odd	2		216.2.t.a.157.12	✓	204
24.11	even	2		864.2.bf.a.49.22		204
27.11	odd	18		216.2.t.a.205.12	yes	204
27.16	even	9	inner	648.2.t.a.613.23		204
108.11	even	18		864.2.bf.a.529.22		204
216.11	even	18		864.2.bf.a.529.13		204
216.173	odd	18		216.2.t.a.205.27	yes	204
216.205	even	18	inner	648.2.t.a.613.8		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.12	✓	204	24.5	odd	2
216.2.t.a.157.27	yes	204	3.2	odd	2
216.2.t.a.205.12	yes	204	27.11	odd	18
216.2.t.a.205.27	yes	204	216.173	odd	18
648.2.t.a.37.8		204	1.1	even	1	trivial
648.2.t.a.37.23		204	8.5	even	2	inner
648.2.t.a.613.8		204	216.205	even	18	inner
648.2.t.a.613.23		204	27.16	even	9	inner
864.2.bf.a.49.13		204	12.11	even	2
864.2.bf.a.49.22		204	24.11	even	2
864.2.bf.a.529.13		204	216.11	even	18
864.2.bf.a.529.22		204	108.11	even	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.12116 - 0.861977i) q^{2} +(0.513991 + 1.93283i) q^{4} +(1.15428 + 3.17134i) q^{5} +(0.593321 + 3.36489i) q^{7} +(1.08978 - 2.61005i) q^{8} +(1.43950 - 4.55054i) q^{10} +(0.197048 - 0.541384i) q^{11} +(4.30199 - 5.12691i) q^{13} +(2.23525 - 4.28400i) q^{14} +(-3.47163 + 1.98691i) q^{16} +(-1.15893 + 2.00733i) q^{17} +(-0.353289 + 0.203971i) q^{19} +(-5.53637 + 3.86106i) q^{20} +(-0.687582 + 0.437127i) q^{22} +(-1.15186 + 6.53250i) q^{23} +(-4.89486 + 4.10727i) q^{25} +(-9.24249 + 2.03986i) q^{26} +(-6.19878 + 2.87631i) q^{28} +(2.24644 + 2.67721i) q^{29} +(-0.382945 + 2.17179i) q^{31} +(5.60491 + 0.764819i) q^{32} +(3.02962 - 1.25156i) q^{34} +(-9.98637 + 5.76564i) q^{35} +(-1.05249 - 0.607656i) q^{37} +(0.571912 + 0.0758426i) q^{38} +(9.53529 + 0.443366i) q^{40} +(-5.09057 - 4.27150i) q^{41} +(0.442145 - 1.21478i) q^{43} +(1.14768 + 0.102592i) q^{44} +(6.92227 - 6.33109i) q^{46} +(0.547022 + 3.10232i) q^{47} +(-4.39261 + 1.59878i) q^{49} +(9.02828 - 0.385648i) q^{50} +(12.1206 + 5.67980i) q^{52} -9.35460i q^{53} +1.94436 q^{55} +(9.42913 + 2.11841i) q^{56} +(-0.210928 - 4.93796i) q^{58} +(3.00302 + 8.25072i) q^{59} +(-4.67459 + 0.824257i) q^{61} +(2.30137 - 2.10483i) q^{62} +(-5.62474 - 5.68879i) q^{64} +(21.2249 + 7.72523i) q^{65} +(-9.67062 + 11.5250i) q^{67} +(-4.47550 - 1.20826i) q^{68} +(16.1662 + 2.14383i) q^{70} +(3.92323 - 6.79524i) q^{71} +(0.641809 + 1.11165i) q^{73} +(0.656224 + 1.58850i) q^{74} +(-0.575829 - 0.578006i) q^{76} +(1.93861 + 0.341829i) q^{77} +(3.84081 - 3.22282i) q^{79} +(-10.3084 - 8.71628i) q^{80} +(2.02541 + 9.17698i) q^{82} +(-6.67152 - 7.95081i) q^{83} +(-7.70366 - 1.35836i) q^{85} +(-1.54283 + 0.980846i) q^{86} +(-1.19830 - 1.10430i) q^{88} +(2.86501 + 4.96234i) q^{89} +(19.8040 + 11.4338i) q^{91} +(-13.2182 + 1.13131i) q^{92} +(2.06083 - 3.94971i) q^{94} +(-1.05466 - 0.884962i) q^{95} +(10.5548 + 3.84165i) q^{97} +(6.30293 + 1.99385i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

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Database

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