LMFDB - Embedded newform 819.2.et.b.136.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			136.6
Character	$\chi$	$=$	819.136
Dual form			819.2.et.b.271.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984398 - 0.984398i) q^{2} +0.0619199i q^{4} +(0.172312 - 0.643078i) q^{5} +(-2.46519 - 0.960657i) q^{7} +(2.02975 + 2.02975i) q^{8} +O(q^{10})$	\(q+(0.984398 - 0.984398i) q^{2} +0.0619199i q^{4} +(0.172312 - 0.643078i) q^{5} +(-2.46519 - 0.960657i) q^{7} +(2.02975 + 2.02975i) q^{8} +(-0.463421 - 0.802669i) q^{10} +(1.24780 - 4.65687i) q^{11} +(3.60544 - 0.0282257i) q^{13} +(-3.37239 + 1.48106i) q^{14} +3.87233 q^{16} -0.467904 q^{17} +(3.26172 - 0.873976i) q^{19} +(0.0398194 + 0.0106696i) q^{20} +(-3.35587 - 5.81255i) q^{22} -6.95512i q^{23} +(3.94627 + 2.27838i) q^{25} +(3.52140 - 3.57698i) q^{26} +(0.0594838 - 0.152644i) q^{28} +(2.01911 - 3.49720i) q^{29} +(-4.10087 + 1.09883i) q^{31} +(-0.247590 + 0.247590i) q^{32} +(-0.460604 + 0.460604i) q^{34} +(-1.04256 + 1.41977i) q^{35} +(-2.38729 - 2.38729i) q^{37} +(2.35049 - 4.07117i) q^{38} +(1.65504 - 0.955538i) q^{40} +(-3.68025 + 0.986119i) q^{41} +(3.42191 - 1.97564i) q^{43} +(0.288353 + 0.0772639i) q^{44} +(-6.84661 - 6.84661i) q^{46} +(9.64648 + 2.58477i) q^{47} +(5.15428 + 4.73639i) q^{49} +(6.12753 - 1.64187i) q^{50} +(0.00174773 + 0.223249i) q^{52} +(-2.20051 + 3.81140i) q^{53} +(-2.77972 - 1.60487i) q^{55} +(-3.05382 - 6.95360i) q^{56} +(-1.45503 - 5.43025i) q^{58} +(-4.33306 + 4.33306i) q^{59} +(4.21802 + 2.43528i) q^{61} +(-2.95521 + 5.11858i) q^{62} +8.23211i q^{64} +(0.603111 - 2.32344i) q^{65} +(-9.03697 - 2.42145i) q^{67} -0.0289726i q^{68} +(0.371330 + 2.42392i) q^{70} +(-3.19935 - 0.857263i) q^{71} +(-0.0301918 - 0.112678i) q^{73} -4.70008 q^{74} +(0.0541165 + 0.201966i) q^{76} +(-7.54972 + 10.2813i) q^{77} +(0.194920 + 0.337611i) q^{79} +(0.667250 - 2.49021i) q^{80} +(-2.65209 + 4.59356i) q^{82} +(-11.5572 - 11.5572i) q^{83} +(-0.0806256 + 0.300899i) q^{85} +(1.42371 - 5.31334i) q^{86} +(11.9850 - 6.91955i) q^{88} +(-6.83819 + 6.83819i) q^{89} +(-8.91519 - 3.39401i) q^{91} +0.430661 q^{92} +(12.0404 - 6.95154i) q^{94} -2.24814i q^{95} +(-4.61378 + 17.2188i) q^{97} +(9.73636 - 0.411364i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8}+O(q^{10}) $ 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8	$ 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8} - 6 q^{10} - 2 q^{11} + 20 q^{14} + 4 q^{16} + 12 q^{17} + 14 q^{19} - 36 q^{20} - 8 q^{22} - 24 q^{26} + 2 q^{28} + 8 q^{29} - 4 q^{31} - 10 q^{32} - 12 q^{34} + 20 q^{35} - 10 q^{37} + 48 q^{40} + 18 q^{41} + 48 q^{43} + 6 q^{44} + 24 q^{46} + 6 q^{47} - 50 q^{49} - 10 q^{50} - 26 q^{52} - 12 q^{53} + 6 q^{55} - 54 q^{56} - 46 q^{58} - 42 q^{59} + 30 q^{61} - 36 q^{62} - 28 q^{65} - 10 q^{67} - 88 q^{70} + 42 q^{71} + 40 q^{73} - 12 q^{74} - 52 q^{76} + 4 q^{79} - 30 q^{80} - 54 q^{82} - 66 q^{83} - 54 q^{85} + 18 q^{86} - 6 q^{88} + 26 q^{91} + 156 q^{92} - 18 q^{94} - 62 q^{97} + 56 q^{98}+O(q^{100}) $ 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8 - 6 * q^10 - 2 * q^11 + 20 * q^14 + 4 * q^16 + 12 * q^17 + 14 * q^19 - 36 * q^20 - 8 * q^22 - 24 * q^26 + 2 * q^28 + 8 * q^29 - 4 * q^31 - 10 * q^32 - 12 * q^34 + 20 * q^35 - 10 * q^37 + 48 * q^40 + 18 * q^41 + 48 * q^43 + 6 * q^44 + 24 * q^46 + 6 * q^47 - 50 * q^49 - 10 * q^50 - 26 * q^52 - 12 * q^53 + 6 * q^55 - 54 * q^56 - 46 * q^58 - 42 * q^59 + 30 * q^61 - 36 * q^62 - 28 * q^65 - 10 * q^67 - 88 * q^70 + 42 * q^71 + 40 * q^73 - 12 * q^74 - 52 * q^76 + 4 * q^79 - 30 * q^80 - 54 * q^82 - 66 * q^83 - 54 * q^85 + 18 * q^86 - 6 * q^88 + 26 * q^91 + 156 * q^92 - 18 * q^94 - 62 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.984398	−	0.984398i	0.696075	−	0.696075i	−0.267487	−	0.963562i	$-0.586193\pi$
$2$	0.984398	−	0.984398i	0.696075	−	0.696075i	0.963562	+	0.267487i	$0.0861932\pi$
$3$		0			0
$3$		0			0
$4$			0.0619199i			0.0309600i
$5$	0.172312	−	0.643078i	0.0770604	−	0.287593i	−0.916632	−	0.399732i	$-0.869103\pi$
$5$	0.172312	−	0.643078i	0.0770604	−	0.287593i	0.993693	+	0.112138i	$0.0357700\pi$
$6$		0			0
$7$	−2.46519	−	0.960657i	−0.931752	−	0.363094i
$7$	−2.46519	−	0.960657i	−0.931752	−	0.363094i
$8$	2.02975	+	2.02975i	0.717625	+	0.717625i
$9$		0			0
$10$	−0.463421	−	0.802669i	−0.146547	−	0.253826i
$11$	1.24780	−	4.65687i	0.376227	−	1.40410i	−0.475317	−	0.879815i	$-0.657667\pi$
$11$	1.24780	−	4.65687i	0.376227	−	1.40410i	0.851544	−	0.524283i	$-0.175667\pi$
$12$		0			0
$13$	3.60544	−	0.0282257i	0.999969	−	0.00782840i
$13$	3.60544	−	0.0282257i	0.999969	−	0.00782840i
$14$	−3.37239	+	1.48106i	−0.901310	+	0.395829i
$15$		0			0
$16$	3.87233			0.968082
$17$	−0.467904			−0.113483			−0.0567417	−	0.998389i	$-0.518071\pi$
$17$	−0.467904			−0.113483			−0.0567417	+	0.998389i	$0.518071\pi$
$18$		0			0
$19$	3.26172	−	0.873976i	0.748290	−	0.200504i	0.135531	−	0.990773i	$-0.456726\pi$
$19$	3.26172	−	0.873976i	0.748290	−	0.200504i	0.612760	+	0.790269i	$0.290059\pi$
$20$	0.0398194	+	0.0106696i	0.00890388	+	0.00238579i
$21$		0			0
$22$	−3.35587	−	5.81255i	−0.715475	−	1.23924i
$23$		−	6.95512i		−	1.45024i	−0.688621	−	0.725122i	$-0.741783\pi$
$23$		−	6.95512i		−	1.45024i	0.688621	−	0.725122i	$-0.258217\pi$
$24$		0			0
$25$	3.94627	+	2.27838i	0.789254	+	0.455676i
$26$	3.52140	−	3.57698i	0.690604	−	0.701503i
$27$		0			0
$28$	0.0594838	−	0.152644i	0.0112414	−	0.0288470i
$29$	2.01911	−	3.49720i	0.374940	−	0.649414i	−0.615378	−	0.788232i	$-0.710997\pi$
$29$	2.01911	−	3.49720i	0.374940	−	0.649414i	0.990318	+	0.138817i	$0.0443301\pi$
$30$		0			0
$31$	−4.10087	+	1.09883i	−0.736539	+	0.197355i	−0.607539	−	0.794290i	$-0.707843\pi$
$31$	−4.10087	+	1.09883i	−0.736539	+	0.197355i	−0.129000	+	0.991645i	$0.541177\pi$
$32$	−0.247590	+	0.247590i	−0.0437681	+	0.0437681i
$33$		0			0
$34$	−0.460604	+	0.460604i	−0.0789929	+	0.0789929i
$35$	−1.04256	+	1.41977i	−0.176225	+	0.239986i
$36$		0			0
$37$	−2.38729	−	2.38729i	−0.392467	−	0.392467i	0.483099	−	0.875566i	$-0.339511\pi$
$37$	−2.38729	−	2.38729i	−0.392467	−	0.392467i	−0.875566	+	0.483099i	$0.839511\pi$
$38$	2.35049	−	4.07117i	0.381300	−	0.660432i
$39$		0			0
$40$	1.65504	−	0.955538i	0.261685	−	0.151084i
$41$	−3.68025	+	0.986119i	−0.574758	+	0.154006i	−0.534478	−	0.845182i	$-0.679492\pi$
$41$	−3.68025	+	0.986119i	−0.574758	+	0.154006i	−0.0402801	+	0.999188i	$0.512825\pi$
$42$		0			0
$43$	3.42191	−	1.97564i	0.521836	−	0.301282i	−0.215849	−	0.976427i	$-0.569252\pi$
$43$	3.42191	−	1.97564i	0.521836	−	0.301282i	0.737686	+	0.675144i	$0.235919\pi$
$44$	0.288353	+	0.0772639i	0.0434708	+	0.0116480i
$45$		0			0
$46$	−6.84661	−	6.84661i	−1.00948	−	1.00948i
$47$	9.64648	+	2.58477i	1.40708	+	0.377027i	0.880883	−	0.473333i	$-0.156949\pi$
$47$	9.64648	+	2.58477i	1.40708	+	0.377027i	0.526201	+	0.850360i	$0.323616\pi$
$48$		0			0
$49$	5.15428	+	4.73639i	0.736325	+	0.676628i
$50$	6.12753	−	1.64187i	0.866564	−	0.232195i
$51$		0			0
$52$	0.00174773	+	0.223249i	0.000242367	+	0.0309590i
$53$	−2.20051	+	3.81140i	−0.302264	+	0.523537i	−0.976648	−	0.214844i	$-0.931076\pi$
$53$	−2.20051	+	3.81140i	−0.302264	+	0.523537i	0.674384	+	0.738380i	$0.264409\pi$
$54$		0			0
$55$	−2.77972	−	1.60487i	−0.374817	−	0.216401i
$56$	−3.05382	−	6.95360i	−0.408084	−	0.929214i
$57$		0			0
$58$	−1.45503	−	5.43025i	−0.191055	−	0.713027i
$59$	−4.33306	+	4.33306i	−0.564117	+	0.564117i	−0.930474	−	0.366358i	$-0.880605\pi$
$59$	−4.33306	+	4.33306i	−0.564117	+	0.564117i	0.366358	+	0.930474i	$0.380605\pi$
$60$		0			0
$61$	4.21802	+	2.43528i	0.540062	+	0.311805i	0.745104	−	0.666948i	$-0.232400\pi$
$61$	4.21802	+	2.43528i	0.540062	+	0.311805i	−0.205042	+	0.978753i	$0.565733\pi$
$62$	−2.95521	+	5.11858i	−0.375312	+	0.650060i
$63$		0			0
$64$			8.23211i			1.02901i
$65$	0.603111	−	2.32344i	0.0748067	−	0.288188i
$66$		0			0
$67$	−9.03697	−	2.42145i	−1.10404	−	0.295827i	−0.339633	−	0.940558i	$-0.610303\pi$
$67$	−9.03697	−	2.42145i	−1.10404	−	0.295827i	−0.764409	+	0.644731i	$0.776969\pi$
$68$		−	0.0289726i		−	0.00351344i
$69$		0			0
$70$	0.371330	+	2.42392i	0.0443824	+	0.289714i
$71$	−3.19935	−	0.857263i	−0.379693	−	0.101738i	0.0639244	−	0.997955i	$-0.479638\pi$
$71$	−3.19935	−	0.857263i	−0.379693	−	0.101738i	−0.443617	+	0.896216i	$0.646305\pi$
$72$		0			0
$73$	−0.0301918	−	0.112678i	−0.00353369	−	0.0131879i	0.964136	−	0.265407i	$-0.0855063\pi$
$73$	−0.0301918	−	0.112678i	−0.00353369	−	0.0131879i	−0.967670	+	0.252219i	$0.918840\pi$
$74$	−4.70008			−0.546373
$75$		0			0
$76$	0.0541165	+	0.201966i	0.00620759	+	0.0231670i
$77$	−7.54972	+	10.2813i	−0.860370	+	1.17167i
$78$		0			0
$79$	0.194920	+	0.337611i	0.0219302	+	0.0379842i	0.876782	−	0.480888i	$-0.159686\pi$
$79$	0.194920	+	0.337611i	0.0219302	+	0.0379842i	−0.854852	+	0.518872i	$0.826352\pi$
$80$	0.667250	−	2.49021i	0.0746008	−	0.278414i
$81$		0			0
$82$	−2.65209	+	4.59356i	−0.292875	+	0.507274i
$83$	−11.5572	−	11.5572i	−1.26857	−	1.26857i	−0.946828	−	0.321741i	$-0.895732\pi$
$83$	−11.5572	−	11.5572i	−1.26857	−	1.26857i	−0.321741	−	0.946828i	$-0.604268\pi$
$84$		0			0
$85$	−0.0806256	+	0.300899i	−0.00874507	+	0.0326371i
$86$	1.42371	−	5.31334i	0.153522	−	0.572952i
$87$		0			0
$88$	11.9850	−	6.91955i	1.27761	−	0.737626i
$89$	−6.83819	+	6.83819i	−0.724847	+	0.724847i	−0.969588	−	0.244742i	$-0.921297\pi$
$89$	−6.83819	+	6.83819i	−0.724847	+	0.724847i	0.244742	+	0.969588i	$0.421297\pi$
$90$		0			0
$91$	−8.91519	−	3.39401i	−0.934566	−	0.355789i
$92$	0.430661			0.0448995
$93$		0			0
$94$	12.0404	−	6.95154i	1.24187	−	0.716997i
$95$		−	2.24814i		−	0.230654i
$96$		0			0
$97$	−4.61378	+	17.2188i	−0.468458	+	1.74831i	0.176705	+	0.984264i	$0.443456\pi$
$97$	−4.61378	+	17.2188i	−0.468458	+	1.74831i	−0.645163	+	0.764045i	$0.723210\pi$
$98$	9.73636	−	0.411364i	0.983521	−	0.0415540i
$99$		0			0
$100$	−0.141077	+	0.244353i	−0.0141077	+	0.0244353i
$101$	5.57293	+	9.65259i	0.554527	+	0.960469i	0.997940	+	0.0641517i	$0.0204342\pi$
$101$	5.57293	+	9.65259i	0.554527	+	0.960469i	−0.443413	+	0.896317i	$0.646233\pi$
$102$		0			0
$103$	3.73616	+	6.47122i	0.368135	+	0.637628i	0.989274	−	0.146072i	$-0.0466632\pi$
$103$	3.73616	+	6.47122i	0.368135	+	0.637628i	−0.621139	+	0.783700i	$0.713330\pi$
$104$	7.37544	+	7.26085i	0.723221	+	0.711985i
$105$		0			0
$106$	1.58576	+	5.91812i	0.154022	+	0.574819i
$107$	4.15105			0.401297			0.200649	−	0.979663i	$-0.435695\pi$
$107$	4.15105			0.401297			0.200649	+	0.979663i	$0.435695\pi$
$108$		0			0
$109$	−1.59208	−	5.94172i	−0.152493	−	0.569113i	−0.999307	−	0.0372233i	$-0.988149\pi$
$109$	−1.59208	−	5.94172i	−0.152493	−	0.569113i	0.846814	−	0.531890i	$-0.178518\pi$
$110$	−4.31618	+	1.15652i	−0.411532	+	0.110270i
$111$		0			0
$112$	−9.54600	−	3.71998i	−0.902012	−	0.351505i
$113$	0.554932	+	0.961171i	0.0522036	+	0.0904194i	0.890946	−	0.454109i	$-0.150042\pi$
$113$	0.554932	+	0.961171i	0.0522036	+	0.0904194i	−0.838743	+	0.544528i	$0.816709\pi$
$114$		0			0
$115$	−4.47269	−	1.19845i	−0.417080	−	0.111756i
$116$	0.216547	+	0.125023i	0.0201058	+	0.0116081i
$117$		0			0
$118$			8.53092i			0.785335i
$119$	1.15347	+	0.449495i	0.105738	+	0.0412051i
$120$		0			0
$121$	−10.6031	−	6.12170i	−0.963918	−	0.556519i
$122$	6.54950	−	1.75493i	0.592963	−	0.158884i
$123$		0			0
$124$	−0.0680392	−	0.253926i	−0.00611010	−	0.0228032i
$125$	4.49900	−	4.49900i	0.402403	−	0.402403i
$126$		0			0
$127$	17.2552	+	9.96228i	1.53115	+	0.884009i	0.999309	+	0.0371647i	$0.0118326\pi$
$127$	17.2552	+	9.96228i	1.53115	+	0.884009i	0.531840	+	0.846845i	$0.321501\pi$
$128$	7.60849	+	7.60849i	0.672502	+	0.672502i
$129$		0			0
$130$	−1.69349	−	2.88090i	−0.148529	−	0.252671i
$131$	−6.61385	+	3.81851i	−0.577855	+	0.333625i	−0.760280	−	0.649595i	$-0.774938\pi$
$131$	−6.61385	+	3.81851i	−0.577855	+	0.333625i	0.182426	+	0.983220i	$0.441605\pi$
$132$		0			0
$133$	−8.88034	−	0.978883i	−0.770023	−	0.0848799i
$134$	−11.2797	+	6.51231i	−0.974414	+	0.562578i
$135$		0			0
$136$	−0.949728	−	0.949728i	−0.0814385	−	0.0814385i
$137$	−9.31142	−	9.31142i	−0.795528	−	0.795528i	0.186859	−	0.982387i	$-0.440169\pi$
$137$	−9.31142	−	9.31142i	−0.795528	−	0.795528i	−0.982387	+	0.186859i	$0.940169\pi$
$138$		0			0
$139$	−14.9082	+	8.60724i	−1.26449	+	0.730056i	−0.973941	−	0.226802i	$-0.927173\pi$
$139$	−14.9082	+	8.60724i	−1.26449	+	0.730056i	−0.290554	+	0.956859i	$0.593839\pi$
$140$	−0.0879123	−	0.0645552i	−0.00742995	−	0.00545591i
$141$		0			0
$142$	−3.99332	+	2.30555i	−0.335112	+	0.193477i
$143$	4.36744	−	16.8253i	0.365223	−	1.40700i
$144$		0			0
$145$	−1.90106	−	1.90106i	−0.157874	−	0.157874i
$146$	−0.140640	−	0.0811987i	−0.0116395	−	0.00672006i
$147$		0			0
$148$	0.147821	−	0.147821i	0.0121508	−	0.0121508i
$149$	−0.973843	−	3.63443i	−0.0797804	−	0.297744i	0.914494	−	0.404599i	$-0.132589\pi$
$149$	−0.973843	−	3.63443i	−0.0797804	−	0.297744i	−0.994275	+	0.106854i	$0.965922\pi$
$150$		0			0
$151$	7.30304	−	1.95684i	0.594313	−	0.159246i	0.0508895	−	0.998704i	$-0.483794\pi$
$151$	7.30304	−	1.95684i	0.594313	−	0.159246i	0.543424	+	0.839459i	$0.317128\pi$
$152$	8.39443	+	4.84653i	0.680879	+	0.393105i
$153$		0			0
$154$	2.68899	+	17.5528i	0.216685	+	1.41445i
$155$			2.82653i			0.227032i
$156$		0			0
$157$	−21.3379	−	12.3194i	−1.70295	−	0.983199i	−0.942744	−	0.333518i	$-0.891764\pi$
$157$	−21.3379	−	12.3194i	−1.70295	−	0.983199i	−0.760207	−	0.649681i	$-0.774903\pi$
$158$	0.524222	+	0.140465i	0.0417049	+	0.0111748i
$159$		0			0
$160$	0.116557	+	0.201882i	0.00921463	+	0.0159602i
$161$	−6.68149	+	17.1457i	−0.526575	+	1.35127i
$162$		0			0
$163$	20.0547	−	5.37364i	1.57081	−	0.420896i	0.634742	−	0.772724i	$-0.281107\pi$
$163$	20.0547	−	5.37364i	1.57081	−	0.420896i	0.936065	+	0.351828i	$0.114440\pi$
$164$	−0.0610604	−	0.227881i	−0.00476802	−	0.0177945i
$165$		0			0
$166$	−22.7538			−1.76604
$167$	4.53457	+	16.9233i	0.350896	+	1.30956i	0.885571	+	0.464503i	$0.153767\pi$
$167$	4.53457	+	16.9233i	0.350896	+	1.30956i	−0.534676	+	0.845057i	$0.679566\pi$
$168$		0			0
$169$	12.9984	−	0.203532i	0.999877	−	0.0156563i
$170$	0.216837	+	0.375572i	0.0166306	+	0.0288051i
$171$		0			0
$172$	0.122332	+	0.211884i	0.00932769	+	0.0161560i
$173$	−2.96030	+	5.12740i	−0.225068	+	0.389829i	−0.956340	−	0.292257i	$-0.905594\pi$
$173$	−2.96030	+	5.12740i	−0.225068	+	0.389829i	0.731272	+	0.682086i	$0.238927\pi$
$174$		0			0
$175$	−7.53954	−	9.40764i	−0.569936	−	0.711150i
$176$	4.83190	−	18.0329i	0.364218	−	1.35928i
$177$		0			0
$178$			13.4630i			1.00910i
$179$	−3.26505	+	1.88508i	−0.244041	+	0.140897i	−0.617033	−	0.786938i	$-0.711665\pi$
$179$	−3.26505	+	1.88508i	−0.244041	+	0.140897i	0.372992	+	0.927835i	$0.378332\pi$
$180$		0			0
$181$	5.68899			0.422859			0.211430	−	0.977393i	$-0.432188\pi$
$181$	5.68899			0.422859			0.211430	+	0.977393i	$0.432188\pi$
$182$	−12.1172	+	5.43505i	−0.898184	+	0.402872i
$183$		0			0
$184$	14.1172	−	14.1172i	1.04073	−	1.04073i
$185$	−1.94657	+	1.12385i	−0.143115	+	0.0826273i
$186$		0			0
$187$	−0.583852	+	2.17896i	−0.0426955	+	0.159342i
$188$	−0.160049	+	0.597309i	−0.0116727	+	0.0435633i
$189$		0			0
$190$	−2.21307	−	2.21307i	−0.160553	−	0.160553i
$191$	−4.58382	+	7.93941i	−0.331674	+	0.574476i	−0.982840	−	0.184459i	$-0.940947\pi$
$191$	−4.58382	+	7.93941i	−0.331674	+	0.574476i	0.651167	+	0.758935i	$0.274280\pi$
$192$		0			0
$193$	−6.57695	+	24.5455i	−0.473419	+	1.76682i	0.153926	+	0.988082i	$0.450808\pi$
$193$	−6.57695	+	24.5455i	−0.473419	+	1.76682i	−0.627345	+	0.778742i	$0.715858\pi$
$194$	12.4084	+	21.4920i	0.890872	+	1.54304i
$195$		0			0
$196$	−0.293277	+	0.319152i	−0.0209484	+	0.0227966i
$197$	0.371638	+	1.38697i	0.0264781	+	0.0988175i	0.977900	−	0.209071i	$-0.0670441\pi$
$197$	0.371638	+	1.38697i	0.0264781	+	0.0988175i	−0.951422	+	0.307889i	$0.900377\pi$
$198$		0			0
$199$	11.0158			0.780892			0.390446	−	0.920626i	$-0.372321\pi$
$199$	11.0158			0.780892			0.390446	+	0.920626i	$0.372321\pi$
$200$	3.38540	+	12.6345i	0.239384	+	0.893393i
$201$		0			0
$202$	14.9880	+	4.01602i	1.05455	+	0.282566i
$203$	−8.33710	+	6.68158i	−0.585149	+	0.468955i
$204$		0			0
$205$			2.53661i			0.177164i
$206$	10.0481	+	2.69239i	0.700086	+	0.187588i
$207$		0			0
$208$	13.9614	−	0.109299i	0.968052	−	0.00757853i
$209$		−	16.2800i		−	1.12611i
$210$		0			0
$211$	11.5485	−	20.0025i	0.795029	−	1.37703i	−0.127792	−	0.991801i	$-0.540789\pi$
$211$	11.5485	−	20.0025i	0.795029	−	1.37703i	0.922821	−	0.385229i	$-0.125878\pi$
$212$	−0.236002	−	0.136256i	−0.0162087	−	0.00935808i
$213$		0			0
$214$	4.08629	−	4.08629i	0.279333	−	0.279333i
$215$	−0.680855	−	2.54098i	−0.0464339	−	0.173294i
$216$		0			0
$217$	11.1650	+	1.23072i	0.757930	+	0.0835469i
$218$	−7.41625	−	4.28178i	−0.502292	−	0.289998i
$219$		0			0
$220$	0.0993735	−	0.172120i	0.00669976	−	0.0116043i
$221$	−1.68700	+	0.0132069i	−0.113480	+	0.000888393i
$222$		0			0
$223$	−3.57776	+	0.958657i	−0.239584	+	0.0641964i	−0.376613	−	0.926371i	$-0.622911\pi$
$223$	−3.57776	+	0.958657i	−0.239584	+	0.0641964i	0.137029	+	0.990567i	$0.456245\pi$
$224$	0.848203	−	0.372506i	0.0566730	−	0.0248891i
$225$		0			0
$226$	1.49245	+	0.399901i	0.0992763	+	0.0266010i
$227$	−17.0467	−	17.0467i	−1.13143	−	1.13143i	−0.989939	−	0.141493i	$-0.954810\pi$
$227$	−17.0467	−	17.0467i	−1.13143	−	1.13143i	−0.141493	−	0.989939i	$-0.545190\pi$
$228$		0			0
$229$	18.0095	+	4.82564i	1.19010	+	0.318887i	0.798926	−	0.601429i	$-0.205402\pi$
$229$	18.0095	+	4.82564i	1.19010	+	0.318887i	0.391176	+	0.920316i	$0.372068\pi$
$230$	−5.58266	+	3.22315i	−0.368110	+	0.212528i
$231$		0			0
$232$	11.1967	−	3.00016i	0.735102	−	0.196970i
$233$	3.91672	−	2.26132i	0.256593	−	0.148144i	−0.366187	−	0.930541i	$-0.619337\pi$
$233$	3.91672	−	2.26132i	0.256593	−	0.148144i	0.622779	+	0.782398i	$0.286003\pi$
$234$		0			0
$235$	3.32442	−	5.75806i	0.216861	−	0.375614i
$236$	−0.268303	−	0.268303i	−0.0174650	−	0.0174650i
$237$		0			0
$238$	1.57796	−	0.692991i	0.102284	−	0.0449200i
$239$	11.1608	−	11.1608i	0.721931	−	0.721931i	−0.247067	−	0.968998i	$-0.579467\pi$
$239$	11.1608	−	11.1608i	0.721931	−	0.721931i	0.968998	+	0.247067i	$0.0794668\pi$
$240$		0			0
$241$	−5.35165	+	5.35165i	−0.344730	+	0.344730i	−0.858142	−	0.513412i	$-0.828381\pi$
$241$	−5.35165	+	5.35165i	−0.344730	+	0.344730i	0.513412	+	0.858142i	$0.328381\pi$
$242$	−16.4639	+	4.41148i	−1.05834	+	0.283581i
$243$		0			0
$244$	−0.150792	+	0.261180i	−0.00965348	+	0.0167203i
$245$	3.93402	−	2.49847i	0.251335	−	0.159621i
$246$		0			0
$247$	11.7353	−	3.24313i	0.746698	−	0.206356i
$248$	−10.5541	−	6.09341i	−0.670186	−	0.386932i
$249$		0			0
$250$		−	8.85761i		−	0.560205i
$251$	10.6165	+	18.3883i	0.670106	+	1.16066i	0.977874	+	0.209197i	$0.0670849\pi$
$251$	10.6165	+	18.3883i	0.670106	+	1.16066i	−0.307767	+	0.951462i	$0.599582\pi$
$252$		0			0
$253$	−32.3891	−	8.67863i	−2.03628	−	0.545621i
$254$	26.7928	−	7.17911i	1.68113	−	0.450458i
$255$		0			0
$256$	−1.48464			−0.0927899
$257$	25.2410			1.57449			0.787245	−	0.616640i	$-0.211506\pi$
$257$	25.2410			1.57449			0.787245	+	0.616640i	$0.211506\pi$
$258$		0			0
$259$	3.59174	+	8.17846i	0.223180	+	0.508185i
$260$	0.143868	+	0.0373446i	0.00892229	+	0.00231601i
$261$		0			0
$262$	−2.75173	+	10.2696i	−0.170002	+	0.634458i
$263$	0.152018	+	0.263302i	0.00937381	+	0.0162359i	0.870674	−	0.491860i	$-0.163683\pi$
$263$	0.152018	+	0.263302i	0.00937381	+	0.0162359i	−0.861300	+	0.508096i	$0.830350\pi$
$264$		0			0
$265$	2.07186	+	2.07186i	0.127273	+	0.127273i
$266$	−9.70540	+	7.77818i	−0.595076	+	0.476911i
$267$		0			0
$268$	0.149936	−	0.559569i	0.00915880	−	0.0341811i
$269$			17.9385i			1.09373i	0.837221	+	0.546865i	$0.184179\pi$
$269$			17.9385i			1.09373i	−0.837221	+	0.546865i	$0.815821\pi$
$270$		0			0
$271$	−9.18147	+	9.18147i	−0.557734	+	0.557734i	−0.928662	−	0.370927i	$-0.879040\pi$
$271$	−9.18147	+	9.18147i	−0.557734	+	0.557734i	0.370927	+	0.928662i	$0.379040\pi$
$272$	−1.81188			−0.109861
$273$		0			0
$274$	−18.3323			−1.10749
$275$	15.5343	−	15.5343i	0.936752	−	0.936752i
$276$		0			0
$277$			6.21287i			0.373295i	0.982427	+	0.186648i	$0.0597623\pi$
$277$			6.21287i			0.373295i	−0.982427	+	0.186648i	$0.940238\pi$
$278$	−6.20263	+	23.1485i	−0.372009	+	1.38836i
$279$		0			0
$280$	−4.99792	+	0.765652i	−0.298683	+	0.0457565i
$281$	−1.72841	−	1.72841i	−0.103108	−	0.103108i	0.653671	−	0.756779i	$-0.273228\pi$
$281$	−1.72841	−	1.72841i	−0.103108	−	0.103108i	−0.756779	+	0.653671i	$0.773228\pi$
$282$		0			0
$283$	−9.00809	−	15.6025i	−0.535475	−	0.927471i	−0.999140	−	0.0414599i	$-0.986799\pi$
$283$	−9.00809	−	15.6025i	−0.535475	−	0.927471i	0.463665	−	0.886011i	$-0.346534\pi$
$284$	0.0530817	−	0.198103i	0.00314982	−	0.0117553i
$285$		0			0
$286$	−12.2635	−	20.8621i	−0.725154	−	1.23360i
$287$	10.0198	+	1.10449i	0.591451	+	0.0651958i
$288$		0			0
$289$	−16.7811			−0.987122
$290$	−3.74280			−0.219785
$291$		0			0
$292$	0.00697698	−	0.00186948i	0.000408297	−	0.000109403i
$293$	−4.38187	−	1.17412i	−0.255992	−	0.0685927i	0.128541	−	0.991704i	$-0.458971\pi$
$293$	−4.38187	−	1.17412i	−0.255992	−	0.0685927i	−0.384532	+	0.923111i	$0.625637\pi$
$294$		0			0
$295$	2.03986	+	3.53314i	0.118765	+	0.205707i
$296$		−	9.69119i		−	0.563289i
$297$		0			0
$298$	−4.53638	−	2.61908i	−0.262785	−	0.151719i
$299$	−0.196313	−	25.0763i	−0.0113531	−	1.45020i
$300$		0			0
$301$	−10.3336	+	1.58304i	−0.595616	+	0.0912449i
$302$	5.26279	−	9.11542i	0.302839	−	0.524533i
$303$		0			0
$304$	12.6305	−	3.38432i	0.724406	−	0.194104i
$305$	2.29289	−	2.29289i	0.131291	−	0.131291i
$306$		0			0
$307$	11.5340	−	11.5340i	0.658282	−	0.658282i	−0.296691	−	0.954973i	$-0.595883\pi$
$307$	11.5340	−	11.5340i	0.658282	−	0.658282i	0.954973	+	0.296691i	$0.0958832\pi$
$308$	−0.636619	−	0.467478i	−0.0362747	−	0.0266370i
$309$		0			0
$310$	2.78243	+	2.78243i	0.158031	+	0.158031i
$311$	−5.42435	+	9.39525i	−0.307587	+	0.532756i	−0.977834	−	0.209382i	$-0.932855\pi$
$311$	−5.42435	+	9.39525i	−0.307587	+	0.532756i	0.670247	+	0.742138i	$0.266188\pi$
$312$		0			0
$313$	−6.22407	+	3.59347i	−0.351805	+	0.203115i	−0.665480	−	0.746416i	$-0.731773\pi$
$313$	−6.22407	+	3.59347i	−0.351805	+	0.203115i	0.313675	+	0.949530i	$0.398440\pi$
$314$	−33.1322	+	8.87776i	−1.86976	+	0.501001i
$315$		0			0
$316$	−0.0209048	+	0.0120694i	−0.00117599	+	0.000678958i
$317$	−9.14677	−	2.45087i	−0.513734	−	0.137655i	−0.00736711	−	0.999973i	$-0.502345\pi$
$317$	−9.14677	−	2.45087i	−0.513734	−	0.137655i	−0.506367	+	0.862318i	$0.669012\pi$
$318$		0			0
$319$	−13.7666	−	13.7666i	−0.770779	−	0.770779i
$320$	5.29389	+	1.41849i	0.295937	+	0.0792962i
$321$		0			0
$322$	10.3009	+	23.4554i	0.574048	+	1.30712i
$323$	−1.52617	+	0.408937i	−0.0849185	+	0.0227538i
$324$		0			0
$325$	14.2923	+	8.10318i	0.792797	+	0.449483i
$326$	14.4520	−	25.0316i	0.800423	−	1.38637i
$327$		0			0
$328$	−9.47156	−	5.46841i	−0.522979	−	0.301942i
$329$	−21.2973	−	15.6389i	−1.17416	−	0.862200i
$330$		0			0
$331$	1.53579	+	5.73166i	0.0844148	+	0.315040i	0.995203	−	0.0978341i	$-0.0311915\pi$
$331$	1.53579	+	5.73166i	0.0844148	+	0.315040i	−0.910788	+	0.412875i	$0.864525\pi$
$332$	0.715621	−	0.715621i	0.0392748	−	0.0392748i
$333$		0			0
$334$	21.1230	+	12.1954i	1.15580	+	0.667302i
$335$	−3.11436	+	5.39424i	−0.170156	+	0.294719i
$336$		0			0
$337$		−	16.0448i		−	0.874014i	−0.899458	−	0.437007i	$-0.856039\pi$
$337$		−	16.0448i		−	0.874014i	0.899458	−	0.437007i	$-0.143961\pi$
$338$	12.5953	−	12.9960i	0.685091	−	0.706887i
$339$		0			0
$340$	−0.0186316	−	0.00499233i	−0.00101044	−	0.000270747i
$341$			20.4683i			1.10842i
$342$		0			0
$343$	−8.15620	−	16.6276i	−0.440393	−	0.897805i
$344$	10.9557	+	2.93557i	0.590691	+	0.158275i
$345$		0			0
$346$	2.13328	+	7.96152i	0.114686	+	0.428014i
$347$	−22.9374			−1.23135			−0.615673	−	0.788002i	$-0.711116\pi$
$347$	−22.9374			−1.23135			−0.615673	+	0.788002i	$0.711116\pi$
$348$		0			0
$349$	−3.69715	−	13.7979i	−0.197904	−	0.738587i	−0.991496	−	0.130137i	$-0.958458\pi$
$349$	−3.69715	−	13.7979i	−0.197904	−	0.738587i	0.793592	−	0.608450i	$-0.208208\pi$
$350$	−16.6828	−	1.83895i	−0.891732	−	0.0982959i
$351$		0			0
$352$	0.844049	+	1.46194i	0.0449880	+	0.0779214i
$353$	−1.20372	+	4.49235i	−0.0640677	+	0.239104i	−0.990533	−	0.137277i	$-0.956165\pi$
$353$	−1.20372	+	4.49235i	−0.0640677	+	0.239104i	0.926465	+	0.376381i	$0.122832\pi$
$354$		0			0
$355$	−1.10257	+	1.90972i	−0.0585186	+	0.101357i
$356$	−0.423420	−	0.423420i	−0.0224412	−	0.0224412i
$357$		0			0
$358$	−1.35844	+	5.06977i	−0.0717959	+	0.267946i
$359$	−4.70405	+	17.5557i	−0.248270	+	0.926557i	0.723441	+	0.690386i	$0.242559\pi$
$359$	−4.70405	+	17.5557i	−0.248270	+	0.926557i	−0.971711	+	0.236171i	$0.924107\pi$
$360$		0			0
$361$	−6.57949	+	3.79867i	−0.346289	+	0.199930i
$362$	5.60023	−	5.60023i	0.294342	−	0.294342i
$363$		0			0
$364$	0.210157	−	0.552028i	0.0110152	−	0.0289341i
$365$	−0.0776629			−0.00406506
$366$		0			0
$367$	12.6911	−	7.32723i	0.662472	−	0.382478i	−0.130746	−	0.991416i	$-0.541737\pi$
$367$	12.6911	−	7.32723i	0.662472	−	0.382478i	0.793218	+	0.608937i	$0.208404\pi$
$368$		−	26.9325i		−	1.40395i
$369$		0			0
$370$	−0.809882	+	3.02252i	−0.0421038	+	0.157133i
$371$	9.08613	−	7.28188i	0.471728	−	0.378056i
$372$		0			0
$373$	2.86259	−	4.95816i	0.148220	−	0.256724i	−0.782350	−	0.622839i	$-0.785979\pi$
$373$	2.86259	−	4.95816i	0.148220	−	0.256724i	0.930569	+	0.366115i	$0.119312\pi$
$374$	1.57023	+	2.71971i	0.0811945	+	0.140633i
$375$		0			0
$376$	14.3335	+	24.8264i	0.739195	+	1.28032i
$377$	7.18108	−	12.6660i	0.369844	−	0.652330i
$378$		0			0
$379$	−0.283332	−	1.05741i	−0.0145538	−	0.0543156i	0.958267	−	0.285875i	$-0.0922840\pi$
$379$	−0.283332	−	1.05741i	−0.0145538	−	0.0543156i	−0.972821	+	0.231559i	$0.925617\pi$
$380$	0.139205			0.00714105
$381$		0			0
$382$	3.30324	+	12.3278i	0.169008	+	0.630747i
$383$	0.492561	−	0.131981i	0.0251687	−	0.00674393i	−0.246213	−	0.969216i	$-0.579186\pi$
$383$	0.492561	−	0.131981i	0.0251687	−	0.00674393i	0.271381	+	0.962472i	$0.412520\pi$
$384$		0			0
$385$	5.31079	+	6.62666i	0.270663	+	0.337726i
$386$	17.6882	+	30.6369i	0.900306	+	1.55938i
$387$		0			0
$388$	−1.06619	−	0.285685i	−0.0541276	−	0.0145034i
$389$	17.8137	+	10.2847i	0.903191	+	0.521457i	0.878234	−	0.478231i	$-0.158722\pi$
$389$	17.8137	+	10.2847i	0.903191	+	0.521457i	0.0249566	+	0.999689i	$0.492055\pi$
$390$		0			0
$391$			3.25433i			0.164578i
$392$	0.848200	+	20.0756i	0.0428406	+	1.01397i
$393$		0			0
$394$	1.73117	+	0.999492i	0.0872151	+	0.0503537i
$395$	0.250697	−	0.0671742i	0.0126140	−	0.00337990i
$396$		0			0
$397$	−7.65009	−	28.5505i	−0.383947	−	1.43291i	−0.839820	−	0.542864i	$-0.817340\pi$
$397$	−7.65009	−	28.5505i	−0.383947	−	1.43291i	0.455874	−	0.890045i	$-0.349327\pi$
$398$	10.8440	−	10.8440i	0.543559	−	0.543559i
$399$		0			0
$400$	15.2812	+	8.82263i	0.764062	+	0.441131i
$401$	4.67580	+	4.67580i	0.233499	+	0.233499i	0.814151	−	0.580653i	$-0.197203\pi$
$401$	4.67580	+	4.67580i	0.233499	+	0.233499i	−0.580653	+	0.814151i	$0.697203\pi$
$402$		0			0
$403$	−14.7544	+	4.07750i	−0.734971	+	0.203115i
$404$	−0.597688	+	0.345075i	−0.0297361	+	0.0171681i
$405$		0			0
$406$	−1.62969	+	14.7844i	−0.0808799	+	0.733736i
$407$	−14.0961	+	8.13841i	−0.698719	+	0.403406i
$408$		0			0
$409$	1.68995	+	1.68995i	0.0835625	+	0.0835625i	0.747653	−	0.664090i	$-0.231181\pi$
$409$	1.68995	+	1.68995i	0.0835625	+	0.0835625i	−0.664090	+	0.747653i	$0.731181\pi$
$410$	2.49703	+	2.49703i	0.123320	+	0.123320i
$411$		0			0
$412$	−0.400697	+	0.231343i	−0.0197409	+	0.0113974i
$413$	14.8444	−	6.51922i	0.730444	−	0.320790i
$414$		0			0
$415$	−9.42364	+	5.44074i	−0.462588	+	0.267076i
$416$	−0.885682	+	0.899659i	−0.0434241	+	0.0441094i
$417$		0			0
$418$	−16.0260	−	16.0260i	−0.783855	−	0.783855i
$419$	−13.1791	−	7.60897i	−0.643842	−	0.371722i	0.142251	−	0.989831i	$-0.454566\pi$
$419$	−13.1791	−	7.60897i	−0.643842	−	0.371722i	−0.786093	+	0.618108i	$0.787899\pi$
$420$		0			0
$421$	−15.0076	+	15.0076i	−0.731425	+	0.731425i	−0.970902	−	0.239477i	$-0.923024\pi$
$421$	−15.0076	+	15.0076i	−0.731425	+	0.731425i	0.239477	+	0.970902i	$0.423024\pi$
$422$	−8.32216	−	31.0587i	−0.405116	−	1.51192i
$423$		0			0
$424$	−12.2027	+	3.26970i	−0.592615	+	0.158791i
$425$	−1.84647	−	1.06606i	−0.0895671	−	0.0517116i
$426$		0			0
$427$	−8.05874	−	10.0555i	−0.389990	−	0.486619i
$428$			0.257033i			0.0124241i
$429$		0			0
$430$	−3.17157	−	1.83111i	−0.152947	−	0.0883039i
$431$	−29.0180	−	7.77536i	−1.39775	−	0.374526i	−0.520213	−	0.854037i	$-0.674147\pi$
$431$	−29.0180	−	7.77536i	−1.39775	−	0.374526i	−0.877536	+	0.479511i	$0.840814\pi$
$432$		0			0
$433$	−7.75396	−	13.4302i	−0.372631	−	0.645417i	0.617338	−	0.786698i	$-0.288211\pi$
$433$	−7.75396	−	13.4302i	−0.372631	−	0.645417i	−0.989969	+	0.141281i	$0.954878\pi$
$434$	12.2023	−	9.77930i	0.585731	−	0.469421i
$435$		0			0
$436$	0.367911	−	0.0985813i	0.0176197	−	0.00472119i
$437$	−6.07861	−	22.6857i	−0.290779	−	1.08520i
$438$		0			0
$439$	14.4339			0.688894			0.344447	−	0.938806i	$-0.388067\pi$
$439$	14.4339			0.688894			0.344447	+	0.938806i	$0.388067\pi$
$440$	−2.38465	−	8.89962i	−0.113684	−	0.424273i
$441$		0			0
$442$	−1.64768	+	1.67368i	−0.0783721	+	0.0796088i
$443$	−6.23855	−	10.8055i	−0.296403	−	0.513384i	0.678908	−	0.734224i	$-0.262454\pi$
$443$	−6.23855	−	10.8055i	−0.296403	−	0.513384i	−0.975310	+	0.220839i	$0.929120\pi$
$444$		0			0
$445$	3.21919	+	5.57580i	0.152604	+	0.264318i
$446$	−2.57824	+	4.46564i	−0.122083	+	0.211454i
$447$		0			0
$448$	7.90823	−	20.2937i	0.373629	−	0.958786i
$449$	7.24956	−	27.0557i	0.342128	−	1.27684i	−0.553804	−	0.832647i	$-0.686824\pi$
$449$	7.24956	−	27.0557i	0.342128	−	1.27684i	0.895932	−	0.444191i	$-0.146509\pi$
$450$		0			0
$451$			18.3689i			0.864958i
$452$	−0.0595156	+	0.0343614i	−0.00279938	+	0.00161622i
$453$		0			0
$454$	−33.5616			−1.57512
$455$	−3.71881	+	5.14834i	−0.174341	+	0.241358i
$456$		0			0
$457$	−12.4557	+	12.4557i	−0.582653	+	0.582653i	−0.935631	−	0.352978i	$-0.885169\pi$
$457$	−12.4557	+	12.4557i	−0.582653	+	0.582653i	0.352978	+	0.935631i	$0.385169\pi$
$458$	22.4789	−	12.9782i	1.05037	−	0.606431i
$459$		0			0
$460$	0.0742082	−	0.276949i	0.00345997	−	0.0129128i
$461$	−1.39627	+	5.21097i	−0.0650310	+	0.242699i	−0.990788	−	0.135419i	$-0.956762\pi$
$461$	−1.39627	+	5.21097i	−0.0650310	+	0.242699i	0.925757	+	0.378118i	$0.123429\pi$
$462$		0			0
$463$	−19.4789	−	19.4789i	−0.905259	−	0.905259i	0.0906259	−	0.995885i	$-0.471113\pi$
$463$	−19.4789	−	19.4789i	−0.905259	−	0.905259i	−0.995885	+	0.0906259i	$0.971113\pi$
$464$	7.81866	−	13.5423i	0.362972	−	0.628686i
$465$		0			0
$466$	1.62957	−	6.08165i	0.0754885	−	0.281727i
$467$	−4.79805	−	8.31047i	−0.222027	−	0.384563i	0.733396	−	0.679802i	$-0.237934\pi$
$467$	−4.79805	−	8.31047i	−0.222027	−	0.384563i	−0.955423	+	0.295239i	$0.904601\pi$
$468$		0			0
$469$	19.9516	+	14.6508i	0.921281	+	0.676509i
$470$	−2.39567	−	8.94077i	−0.110504	−	0.412407i
$471$		0			0
$472$	−17.5901			−0.809649
$473$	−4.93042	−	18.4006i	−0.226701	−	0.846060i
$474$		0			0
$475$	14.8629	+	3.98250i	0.681956	+	0.182729i
$476$	−0.0278327	+	0.0714227i	−0.00127571	+	0.00327366i
$477$		0			0
$478$		−	21.9733i		−	1.00504i
$479$	29.8944	+	8.01018i	1.36591	+	0.365994i	0.865983	−	0.500073i	$-0.166694\pi$
$479$	29.8944	+	8.01018i	1.36591	+	0.365994i	0.499927	+	0.866068i	$0.333360\pi$
$480$		0			0
$481$	−8.67460	−	8.53984i	−0.395528	−	0.389383i
$482$			10.5363i			0.479916i
$483$		0			0
$484$	0.379055	−	0.656543i	0.0172298	−	0.0298429i
$485$	10.2781	+	5.93404i	0.466703	+	0.269451i
$486$		0			0
$487$	3.95701	−	3.95701i	0.179309	−	0.179309i	−0.611745	−	0.791055i	$-0.709532\pi$
$487$	3.95701	−	3.95701i	0.179309	−	0.179309i	0.791055	+	0.611745i	$0.209532\pi$
$488$	3.61853	+	13.5045i	0.163803	+	0.611322i
$489$		0			0
$490$	1.41316	−	6.33213i	0.0638399	−	0.286056i
$491$	−12.0113	−	6.93474i	−0.542063	−	0.312960i	0.203851	−	0.979002i	$-0.434654\pi$
$491$	−12.0113	−	6.93474i	−0.542063	−	0.312960i	−0.745915	+	0.666041i	$0.767987\pi$
$492$		0			0
$493$	−0.944750	+	1.63635i	−0.0425494	+	0.0736977i
$494$	8.35965	−	14.7447i	0.376119	−	0.663396i
$495$		0			0
$496$	−15.8799	+	4.25501i	−0.713030	+	0.191056i
$497$	7.06345	+	5.18679i	0.316839	+	0.232659i
$498$		0			0
$499$	8.83159	+	2.36642i	0.395356	+	0.105935i	0.451019	−	0.892514i	$-0.351061\pi$
$499$	8.83159	+	2.36642i	0.395356	+	0.105935i	−0.0556630	+	0.998450i	$0.517727\pi$
$500$	0.278578	+	0.278578i	0.0124584	+	0.0124584i
$501$		0			0
$502$	28.5522	+	7.65055i	1.27435	+	0.341461i
$503$	27.9587	−	16.1420i	1.24662	−	0.719736i	0.276185	−	0.961104i	$-0.410930\pi$
$503$	27.9587	−	16.1420i	1.24662	−	0.719736i	0.970434	+	0.241369i	$0.0775963\pi$
$504$		0			0
$505$	7.16766	−	1.92057i	0.318957	−	0.0854642i
$506$	−40.4270	+	23.3405i	−1.79720	+	1.03761i
$507$		0			0
$508$	−0.616864	+	1.06844i	−0.0273689	+	0.0474043i
$509$	8.53926	+	8.53926i	0.378496	+	0.378496i	0.870559	−	0.492063i	$-0.163757\pi$
$509$	8.53926	+	8.53926i	0.378496	+	0.378496i	−0.492063	+	0.870559i	$0.663757\pi$
$510$		0			0
$511$	−0.0338159	+	0.306775i	−0.00149593	+	0.0135709i
$512$	−16.6785	+	16.6785i	−0.737091	+	0.737091i
$513$		0			0
$514$	24.8472	−	24.8472i	1.09596	−	1.09596i
$515$	4.80529	−	1.28757i	0.211746	−	0.0567372i
$516$		0			0
$517$	24.0738	−	41.6971i	1.05877	−	1.83384i
$518$	11.5866	+	4.51516i	0.509085	+	0.198385i
$519$		0			0
$520$	5.94018	−	3.49185i	0.260494	−	0.153128i
$521$	−10.1929	−	5.88486i	−0.446558	−	0.257821i	0.259817	−	0.965658i	$-0.416338\pi$
$521$	−10.1929	−	5.88486i	−0.446558	−	0.257821i	−0.706376	+	0.707837i	$0.749671\pi$
$522$		0			0
$523$			15.3301i			0.670337i	0.942158	+	0.335168i	$0.108793\pi$
$523$			15.3301i			0.670337i	−0.942158	+	0.335168i	$0.891207\pi$
$524$	−0.236442	−	0.409529i	−0.0103290	−	0.0178904i
$525$		0			0
$526$	0.408840	+	0.109548i	0.0178263	+	0.00477654i
$527$	1.91881	−	0.514145i	0.0835849	−	0.0223965i
$528$		0			0
$529$	−25.3737			−1.10321
$530$	4.07906			0.177183
$531$		0			0
$532$	0.0606124	−	0.549870i	0.00262788	−	0.0238399i
$533$	−13.2411	+	3.65927i	−0.573535	+	0.158501i
$534$		0			0
$535$	0.715277	−	2.66945i	0.0309241	−	0.115410i
$536$	−13.4279	−	23.2577i	−0.579995	−	1.00458i
$537$		0			0
$538$	17.6586	+	17.6586i	0.761318	+	0.761318i
$539$	28.4883	−	18.0927i	1.22708	−	0.779307i
$540$		0			0
$541$	−3.88929	+	14.5150i	−0.167214	+	0.624050i	0.830534	+	0.556968i	$0.188036\pi$
$541$	−3.88929	+	14.5150i	−0.167214	+	0.624050i	−0.997747	+	0.0670818i	$0.978631\pi$
$542$			18.0764i			0.776450i
$543$		0			0
$544$	0.115848	−	0.115848i	0.00496695	−	0.00496695i
$545$	−4.09532			−0.175424
$546$		0			0
$547$	20.0277			0.856322			0.428161	−	0.903702i	$-0.359162\pi$
$547$	20.0277			0.856322			0.428161	+	0.903702i	$0.359162\pi$
$548$	0.576562	−	0.576562i	0.0246295	−	0.0246295i
$549$		0			0
$550$		−	30.5838i		−	1.30410i
$551$	3.52931	−	13.1716i	0.150354	−	0.561127i
$552$		0			0
$553$	−0.156185	−	1.01952i	−0.00664167	−	0.0433546i
$554$	6.11594	+	6.11594i	0.259841	+	0.259841i
$555$		0			0
$556$	−0.532959	−	0.923113i	−0.0226025	−	0.0391487i
$557$	−0.644961	+	2.40703i	−0.0273279	+	0.101989i	−0.978243	−	0.207464i	$-0.933479\pi$
$557$	−0.644961	+	2.40703i	−0.0273279	+	0.101989i	0.950915	+	0.309453i	$0.100146\pi$
$558$		0			0
$559$	12.2817	−	7.21964i	0.519462	−	0.305358i
$560$	−4.03713	+	5.49783i	−0.170600	+	0.232326i
$561$		0			0
$562$	−3.40288			−0.143542
$563$	−19.7161			−0.830933			−0.415467	−	0.909608i	$-0.636382\pi$
$563$	−19.7161			−0.830933			−0.415467	+	0.909608i	$0.636382\pi$
$564$		0			0
$565$	0.713730	−	0.191243i	0.0300268	−	0.00804567i
$566$	−24.2266	−	6.49150i	−1.01832	−	0.272858i
$567$		0			0
$568$	−4.75385	−	8.23391i	−0.199467	−	0.345487i
$569$			44.6858i			1.87333i	0.350230	+	0.936664i	$0.386103\pi$
$569$			44.6858i			1.87333i	−0.350230	+	0.936664i	$0.613897\pi$
$570$		0			0
$571$	23.8503	+	13.7700i	0.998103	+	0.576255i	0.907686	−	0.419649i	$-0.137847\pi$
$571$	23.8503	+	13.7700i	0.998103	+	0.576255i	0.0904162	+	0.995904i	$0.471180\pi$
$572$	1.04182	+	0.270431i	0.0435607	+	0.0113073i
$573$		0			0
$574$	10.9507	−	8.77623i	0.457075	−	0.366313i
$575$	15.8464	−	27.4468i	0.660841	−	1.14461i
$576$		0			0
$577$	17.7698	−	4.76139i	0.739765	−	0.198219i	0.130791	−	0.991410i	$-0.458248\pi$
$577$	17.7698	−	4.76139i	0.739765	−	0.198219i	0.608974	+	0.793190i	$0.291582\pi$
$578$	−16.5193	+	16.5193i	−0.687110	+	0.687110i
$579$		0			0
$580$	0.117713	−	0.117713i	0.00488778	−	0.00488778i
$581$	17.3882	+	39.5932i	0.721382	+	1.64260i
$582$		0			0
$583$	15.0034	+	15.0034i	0.621377	+	0.621377i
$584$	0.167425	−	0.289989i	0.00692811	−	0.0119998i
$585$		0			0
$586$	−5.46930	+	3.15770i	−0.225935	+	0.130444i
$587$	20.1767	−	5.40633i	0.832781	−	0.223143i	0.182855	−	0.983140i	$-0.441466\pi$
$587$	20.1767	−	5.40633i	0.832781	−	0.223143i	0.649927	+	0.759997i	$0.274800\pi$
$588$		0			0
$589$	−12.4156	+	7.16813i	−0.511574	+	0.295358i
$590$	5.48605	+	1.46998i	0.225857	+	0.0605182i
$591$		0			0
$592$	−9.24435	−	9.24435i	−0.379940	−	0.379940i
$593$	−8.55614	−	2.29261i	−0.351358	−	0.0941462i	0.0788231	−	0.996889i	$-0.474884\pi$
$593$	−8.55614	−	2.29261i	−0.351358	−	0.0941462i	−0.430182	+	0.902742i	$0.641550\pi$
$594$		0			0
$595$	0.487817	−	0.664318i	0.0199986	−	0.0272344i
$596$	0.225044	−	0.0603003i	0.00921815	−	0.00247000i
$597$		0			0
$598$	−24.8783	−	24.4918i	−1.01735	−	1.00154i
$599$	−18.1377	+	31.4154i	−0.741087	+	1.28360i	0.210914	+	0.977505i	$0.432356\pi$
$599$	−18.1377	+	31.4154i	−0.741087	+	1.28360i	−0.952001	+	0.306096i	$0.900977\pi$
$600$		0			0
$601$	30.7163	+	17.7340i	1.25294	+	0.723387i	0.971693	−	0.236248i	$-0.0759177\pi$
$601$	30.7163	+	17.7340i	1.25294	+	0.723387i	0.281250	+	0.959635i	$0.409251\pi$
$602$	−8.61399	+	11.7307i	−0.351080	+	0.478107i
$603$		0			0
$604$	0.121168	+	0.452204i	0.00493024	+	0.0183999i
$605$	−5.76378	+	5.76378i	−0.234331	+	0.234331i
$606$		0			0
$607$	−22.2647	−	12.8545i	−0.903697	−	0.521749i	−0.0252989	−	0.999680i	$-0.508054\pi$
$607$	−22.2647	−	12.8545i	−0.903697	−	0.521749i	−0.878398	+	0.477930i	$0.841387\pi$
$608$	−0.591182	+	1.02396i	−0.0239756	+	0.0415269i
$609$		0			0
$610$		−	4.51424i		−	0.182776i
$611$	34.8528	+	9.04695i	1.40999	+	0.366000i
$612$		0			0
$613$	44.0688	+	11.8082i	1.77992	+	0.476928i	0.990569	−	0.137013i	$-0.0437501\pi$
$613$	44.0688	+	11.8082i	1.77992	+	0.476928i	0.789352	+	0.613941i	$0.210417\pi$
$614$		−	22.7082i		−	0.916427i
$615$		0			0
$616$	−36.1926	+	5.54449i	−1.45824	+	0.223394i
$617$	−35.5733	−	9.53183i	−1.43213	−	0.383737i	−0.542357	−	0.840148i	$-0.682468\pi$
$617$	−35.5733	−	9.53183i	−1.43213	−	0.383737i	−0.889769	+	0.456411i	$0.849135\pi$
$618$		0			0
$619$	−1.37524	−	5.13248i	−0.0552757	−	0.206292i	0.932765	−	0.360485i	$-0.117389\pi$
$619$	−1.37524	−	5.13248i	−0.0552757	−	0.206292i	−0.988041	+	0.154193i	$0.950722\pi$
$620$	−0.175018			−0.00702890
$621$		0			0
$622$	3.90895	+	14.5884i	0.156734	+	0.584941i
$623$	23.4266	−	10.2883i	0.938565	−	0.412190i
$624$		0			0
$625$	9.27392	+	16.0629i	0.370957	+	0.642516i
$626$	−2.58956	+	9.66437i	−0.103500	+	0.386266i
$627$		0			0
$628$	0.762819	−	1.32124i	0.0304398	−	0.0527233i
$629$	1.11702	+	1.11702i	0.0445385	+	0.0445385i
$630$		0			0
$631$	−3.50380	+	13.0763i	−0.139484	+	0.520561i	0.860455	+	0.509526i	$0.170179\pi$
$631$	−3.50380	+	13.0763i	−0.139484	+	0.520561i	−0.999939	+	0.0110350i	$0.996487\pi$
$632$	−0.289627	+	1.08090i	−0.0115208	+	0.0429961i
$633$		0			0
$634$	−11.4167	+	6.59143i	−0.453415	+	0.261779i
$635$	9.37981	−	9.37981i	0.372226	−	0.372226i
$636$		0			0
$637$	18.7171	+	16.9313i	0.741600	+	0.670843i
$638$	−27.1035			−1.07304
$639$		0			0
$640$	6.20389	−	3.58182i	0.245230	−	0.141584i
$641$			21.4184i			0.845978i	0.906135	+	0.422989i	$0.139019\pi$
$641$			21.4184i			0.845978i	−0.906135	+	0.422989i	$0.860981\pi$
$642$		0			0
$643$	−3.68080	+	13.7369i	−0.145157	+	0.541732i	0.854592	+	0.519300i	$0.173807\pi$
$643$	−3.68080	+	13.7369i	−0.145157	+	0.541732i	−0.999748	+	0.0224315i	$0.992859\pi$
$644$	−1.06166	−	0.413717i	−0.0418352	−	0.0163027i
$645$		0			0
$646$	−1.09980	+	1.90492i	−0.0432712	+	0.0749480i
$647$	−10.2738	−	17.7948i	−0.403906	−	0.699585i	0.590288	−	0.807193i	$-0.299014\pi$
$647$	−10.2738	−	17.7948i	−0.403906	−	0.699585i	−0.994193	+	0.107608i	$0.965681\pi$
$648$		0			0
$649$	14.7717	+	25.5853i	0.579839	+	1.00431i
$650$	22.0461	−	6.09261i	0.864720	−	0.238972i
$651$		0			0
$652$	0.332736	+	1.24179i	0.0130309	+	0.0486321i
$653$	43.6957			1.70994			0.854972	−	0.518675i	$-0.173574\pi$
$653$	43.6957			1.70994			0.854972	+	0.518675i	$0.173574\pi$
$654$		0			0
$655$	1.31595	+	4.91120i	0.0514185	+	0.191896i
$656$	−14.2511	+	3.81857i	−0.556413	+	0.149090i
$657$		0			0
$658$	−36.3599	+	5.57012i	−1.41746	+	0.217146i
$659$	6.26381	+	10.8492i	0.244003	+	0.422626i	0.961851	−	0.273574i	$-0.0882059\pi$
$659$	6.26381	+	10.8492i	0.244003	+	0.422626i	−0.717848	+	0.696200i	$0.754873\pi$
$660$		0			0
$661$	22.2227	+	5.95454i	0.864361	+	0.231605i	0.663648	−	0.748045i	$-0.269007\pi$
$661$	22.2227	+	5.95454i	0.864361	+	0.231605i	0.200713	+	0.979650i	$0.435674\pi$
$662$	7.15407	+	4.13040i	0.278051	+	0.160533i
$663$		0			0
$664$		−	46.9165i		−	1.82071i
$665$	−2.15969	+	5.54208i	−0.0837492	+	0.214913i
$666$		0			0
$667$	−24.3235	−	14.0432i	−0.941809	−	0.543754i
$668$	−1.04789	+	0.280780i	−0.0405439	+	0.0108637i
$669$		0			0
$670$	2.24430	+	8.37585i	0.0867050	+	0.323587i
$671$	16.6040	−	16.6040i	0.640991	−	0.640991i
$672$		0			0
$673$	−12.0684	−	6.96769i	−0.465202	−	0.268585i	0.249027	−	0.968497i	$-0.419889\pi$
$673$	−12.0684	−	6.96769i	−0.465202	−	0.268585i	−0.714229	+	0.699912i	$0.753223\pi$
$674$	−15.7944	−	15.7944i	−0.608379	−	0.608379i
$675$		0			0
$676$	0.0126027	+	0.804860i	0.000484719	+	0.0309562i
$677$	−44.8299	+	25.8826i	−1.72295	+	0.994747i	−0.810296	+	0.586020i	$0.800694\pi$
$677$	−44.8299	+	25.8826i	−1.72295	+	0.994747i	−0.912657	+	0.408727i	$0.865973\pi$
$678$		0			0
$679$	27.9152	−	38.0154i	1.07129	−	1.45890i
$680$	−0.774399	+	0.447100i	−0.0296969	+	0.0171455i
$681$		0			0
$682$	20.1490	+	20.1490i	0.771545	+	0.771545i
$683$	20.1791	+	20.1791i	0.772131	+	0.772131i	0.978479	−	0.206348i	$-0.0661578\pi$
$683$	20.1791	+	20.1791i	0.772131	+	0.772131i	−0.206348	+	0.978479i	$0.566158\pi$
$684$		0			0
$685$	−7.59245	+	4.38350i	−0.290092	+	0.167485i
$686$	−24.3971	−	8.33921i	−0.931486	−	0.318393i
$687$		0			0
$688$	13.2508	−	7.65033i	0.505180	−	0.291666i
$689$	−7.82625	+	13.8039i	−0.298156	+	0.525887i
$690$		0			0
$691$	−13.2476	−	13.2476i	−0.503963	−	0.503963i	0.408704	−	0.912667i	$-0.365981\pi$
$691$	−13.2476	−	13.2476i	−0.503963	−	0.503963i	−0.912667	+	0.408704i	$0.865981\pi$
$692$	−0.317488	−	0.183302i	−0.0120691	−	0.00696809i
$693$		0			0
$694$	−22.5796	+	22.5796i	−0.857108	+	0.857108i
$695$	2.96627	+	11.0703i	0.112517	+	0.419919i
$696$		0			0
$697$	1.72200	−	0.461409i	0.0652254	−	0.0174771i
$698$	−17.2221	−	9.94320i	−0.651867	−	0.376356i
$699$		0			0
$700$	0.582520	−	0.466848i	0.0220172	−	0.0176452i
$701$		−	20.1282i		−	0.760231i	−0.924939	−	0.380115i	$-0.875884\pi$
$701$		−	20.1282i		−	0.760231i	0.924939	−	0.380115i	$-0.124116\pi$
$702$		0			0
$703$	−9.87309	−	5.70023i	−0.372371	−	0.214988i
$704$	38.3358	+	10.2720i	1.44484	+	0.387142i
$705$		0			0
$706$	3.23732	+	5.60721i	0.121838	+	0.211030i
$707$	−4.46547	−	29.1491i	−0.167941	−	1.09626i
$708$		0			0
$709$	4.16243	−	1.11532i	0.156323	−	0.0418867i	−0.179809	−	0.983702i	$-0.557548\pi$
$709$	4.16243	−	1.11532i	0.156323	−	0.0418867i	0.336132	+	0.941815i	$0.390881\pi$
$710$	0.794548	+	2.96529i	0.0298189	+	0.111285i
$711$		0			0
$712$	−27.7596			−1.04034
$713$	7.64247	+	28.5221i	0.286213	+	1.06816i
$714$		0			0
$715$	−10.0674	−	5.70781i	−0.376500	−	0.213460i
$716$	−0.116724	−	0.202172i	−0.00436217	−	0.00755550i
$717$		0			0
$718$	12.6512	+	21.9125i	0.472138	+	0.817767i
$719$	15.9230	−	27.5794i	0.593827	−	1.02854i	−0.399884	−	0.916566i	$-0.630950\pi$
$719$	15.9230	−	27.5794i	0.593827	−	1.02854i	0.993711	−	0.111973i	$-0.0357171\pi$
$720$		0			0
$721$	−2.99371	−	19.5419i	−0.111491	−	0.727779i
$722$	−2.73743	+	10.2162i	−0.101877	+	0.380209i
$723$		0			0
$724$			0.352262i			0.0130917i
$725$	15.9359	−	9.20060i	0.591845	−	0.341702i
$726$		0			0
$727$	−49.3169			−1.82906			−0.914531	−	0.404516i	$-0.867440\pi$
$727$	−49.3169			−1.82906			−0.914531	+	0.404516i	$0.867440\pi$
$728$	−11.2066	−	24.9846i	−0.415345	−	0.925991i
$729$		0			0
$730$	−0.0764512	+	0.0764512i	−0.00282959	+	0.00282959i
$731$	−1.60112	+	0.924410i	−0.0592197	+	0.0341905i
$732$		0			0
$733$	4.21647	−	15.7361i	0.155739	−	0.581226i	−0.843302	−	0.537440i	$-0.819391\pi$
$733$	4.21647	−	15.7361i	0.155739	−	0.581226i	0.999041	−	0.0437858i	$-0.0139419\pi$
$734$	5.28022	−	19.7061i	0.194896	−	0.727364i
$735$		0			0
$736$	1.72202	+	1.72202i	0.0634744	+	0.0634744i
$737$	−22.5527	+	39.0625i	−0.830741	+	1.43888i
$738$		0			0
$739$	6.53382	−	24.3845i	0.240350	−	0.897000i	−0.735313	−	0.677727i	$-0.762965\pi$
$739$	6.53382	−	24.3845i	0.240350	−	0.897000i	0.975664	−	0.219273i	$-0.0703684\pi$
$740$	−0.0695889	−	0.120532i	−0.00255814	−	0.00443083i
$741$		0			0
$742$	1.77610	−	16.1126i	0.0652027	−	0.591513i
$743$	−2.17652	−	8.12290i	−0.0798489	−	0.298000i	0.914440	−	0.404721i	$-0.132631\pi$
$743$	−2.17652	−	8.12290i	−0.0798489	−	0.298000i	−0.994289	+	0.106721i	$0.965965\pi$
$744$		0			0
$745$	−2.50503			−0.0917772
$746$	−2.06287	−	7.69874i	−0.0755270	−	0.281871i
$747$		0			0
$748$	−0.134921	−	0.0361521i	−0.00493321	−	0.00132185i
$749$	−10.2331	−	3.98773i	−0.373910	−	0.145709i
$750$		0			0
$751$			34.1800i			1.24725i	0.781725	+	0.623623i	$0.214340\pi$
$751$			34.1800i			1.24725i	−0.781725	+	0.623623i	$0.785660\pi$
$752$	37.3543	+	10.0091i	1.36217	+	0.364993i
$753$		0			0
$754$	−5.39930	−	19.5374i	−0.196631	−	0.711509i
$755$		−	5.03362i		−	0.183192i
$756$		0			0
$757$	−6.77459	+	11.7339i	−0.246227	+	0.426477i	−0.962476	−	0.271368i	$-0.912524\pi$
$757$	−6.77459	+	11.7339i	−0.246227	+	0.426477i	0.716249	+	0.697845i	$0.245857\pi$
$758$	−1.31983	−	0.762002i	−0.0479382	−	0.0276771i
$759$		0			0
$760$	4.56316	−	4.56316i	0.165523	−	0.165523i
$761$	5.17326	+	19.3069i	0.187531	+	0.699873i	0.994075	+	0.108700i	$0.0346686\pi$
$761$	5.17326	+	19.3069i	0.187531	+	0.699873i	−0.806544	+	0.591174i	$0.798665\pi$
$762$		0			0
$763$	−1.78318	+	16.1769i	−0.0645555	+	0.585642i
$764$	−0.491608	−	0.283830i	−0.0177857	−	0.0102686i
$765$		0			0
$766$	0.354954	−	0.614799i	0.0128250	−	0.0222136i
$767$	−15.5003	+	15.7449i	−0.559683	+	0.568515i
$768$		0			0
$769$	30.3963	−	8.14467i	1.09612	−	0.293704i	0.334936	−	0.942241i	$-0.391285\pi$
$769$	30.3963	−	8.14467i	1.09612	−	0.293704i	0.761184	+	0.648536i	$0.224619\pi$
$770$	11.7512	+	1.29534i	0.423484	+	0.0466808i
$771$		0			0
$772$	−1.51986	−	0.407244i	−0.0547008	−	0.0146570i
$773$	27.0775	+	27.0775i	0.973910	+	0.973910i	0.999668	−	0.0257585i	$-0.00820008\pi$
$773$	27.0775	+	27.0775i	0.973910	+	0.973910i	−0.0257585	+	0.999668i	$0.508200\pi$
$774$		0			0
$775$	−18.6867	−	5.00708i	−0.671246	−	0.179860i
$776$	−44.3148	+	25.5852i	−1.59081	+	0.918453i
$777$		0			0
$778$	27.6601	−	7.41149i	0.991661	−	0.265715i
$779$	−11.1421	+	6.43289i	−0.399207	+	0.230482i
$780$		0			0
$781$	−7.98432	+	13.8292i	−0.285701	+	0.494849i
$782$	3.20356	+	3.20356i	0.114559	+	0.114559i
$783$		0			0
$784$	19.9590	+	18.3409i	0.712823	+	0.655031i
$785$	−11.5992	+	11.5992i	−0.413992	+	0.413992i
$786$		0			0
$787$	−15.6978	+	15.6978i	−0.559566	+	0.559566i	−0.929184	−	0.369618i	$-0.879489\pi$
$787$	−15.6978	+	15.6978i	−0.559566	+	0.559566i	0.369618	+	0.929184i	$0.379489\pi$
$788$	−0.0858811	+	0.0230118i	−0.00305939	+	0.000819760i
$789$		0			0
$790$	0.180660	−	0.312912i	0.00642759	−	0.0111329i
$791$	−0.444656	−	2.90256i	−0.0158101	−	0.103203i
$792$		0			0
$793$	15.2766	+	8.66119i	0.542487	+	0.307568i
$794$	−35.6358	−	20.5743i	−1.26467	−	0.730156i
$795$		0			0
$796$			0.682100i			0.0241764i
$797$	−15.2784	−	26.4630i	−0.541189	−	0.937367i	−0.998836	−	0.0482334i	$-0.984641\pi$
$797$	−15.2784	−	26.4630i	−0.541189	−	0.937367i	0.457647	−	0.889134i	$-0.348692\pi$
$798$		0			0
$799$	−4.51362	−	1.20942i	−0.159681	−	0.0427863i
$800$	−1.54116	+	0.412952i	−0.0544882	+	0.0146001i
$801$		0			0
$802$	9.20571			0.325065
$803$	−0.562397			−0.0198466
$804$		0			0
$805$	9.87471	+	7.25113i	0.348038	+	0.255569i
$806$	−10.5104	+	18.5381i	−0.370212	+	0.652978i
$807$		0			0
$808$	−8.28071	+	30.9040i	−0.291314	+	1.08720i
$809$	13.3877	+	23.1882i	0.470688	+	0.815255i	0.999438	−	0.0335223i	$-0.0106725\pi$
$809$	13.3877	+	23.1882i	0.470688	+	0.815255i	−0.528750	+	0.848778i	$0.677339\pi$
$810$		0			0
$811$	−7.94016	−	7.94016i	−0.278817	−	0.278817i	0.553820	−	0.832637i	$-0.313170\pi$
$811$	−7.94016	−	7.94016i	−0.278817	−	0.278817i	−0.832637	+	0.553820i	$0.813170\pi$
$812$	−0.413723	−	0.516232i	−0.0145188	−	0.0181162i
$813$		0			0
$814$	−5.86478	+	21.8876i	−0.205560	+	0.767161i
$815$		−	13.8227i		−	0.484188i
$816$		0			0
$817$	9.43466	−	9.43466i	0.330077	−	0.330077i
$818$	3.32716			0.116331
$819$		0			0
$820$	−0.157067			−0.00548500
$821$	−6.49943	+	6.49943i	−0.226832	+	0.226832i	−0.811368	−	0.584536i	$-0.801277\pi$
$821$	−6.49943	+	6.49943i	−0.226832	+	0.226832i	0.584536	+	0.811368i	$0.301277\pi$
$822$		0			0
$823$			34.6382i			1.20741i	0.797208	+	0.603705i	$0.206310\pi$
$823$			34.6382i			1.20741i	−0.797208	+	0.603705i	$0.793690\pi$
$824$	−5.55149	+	20.7184i	−0.193395	+	0.721761i
$825$		0			0
$826$	8.19528	−	21.0303i	0.285150	−	0.731737i
$827$	18.6739	+	18.6739i	0.649355	+	0.649355i	0.952837	−	0.303482i	$-0.0981492\pi$
$827$	18.6739	+	18.6739i	0.649355	+	0.649355i	−0.303482	+	0.952837i	$0.598149\pi$
$828$		0			0
$829$	16.3278	+	28.2806i	0.567089	+	0.982228i	0.996852	+	0.0792856i	$0.0252639\pi$
$829$	16.3278	+	28.2806i	0.567089	+	0.982228i	−0.429763	+	0.902942i	$0.641403\pi$
$830$	−3.92076	+	14.6325i	−0.136092	+	0.507901i
$831$		0			0
$832$	0.232357	+	29.6804i	0.00805552	+	1.02898i
$833$	−2.41171	−	2.21618i	−0.0835606	−	0.0767860i
$834$		0			0
$835$	11.6643			0.403661
$836$	1.00805			0.0348643
$837$		0			0
$838$	−20.4638	+	5.48325i	−0.706909	+	0.189416i
$839$	38.6060	+	10.3444i	1.33283	+	0.357130i	0.853768	−	0.520654i	$-0.174312\pi$
$839$	38.6060	+	10.3444i	1.33283	+	0.357130i	0.479058	+	0.877783i	$0.340978\pi$
$840$		0			0
$841$	6.34638	+	10.9922i	0.218841	+	0.379043i
$842$			29.5469i			1.01825i
$843$		0			0
$844$	1.23855	+	0.715080i	0.0426328	+	0.0246141i
$845$	2.10890	−	8.39407i	0.0725483	−	0.288765i
$846$		0			0
$847$	20.2578	+	25.2771i	0.696065	+	0.868531i
$848$	−8.52111	+	14.7590i	−0.292616	+	0.506826i
$849$		0			0
$850$	−2.86710	+	0.768236i	−0.0983406	+	0.0263503i
$851$	−16.6039	+	16.6039i	−0.569173	+	0.569173i
$852$		0			0
$853$	20.1071	−	20.1071i	0.688454	−	0.688454i	−0.273436	−	0.961890i	$-0.588160\pi$
$853$	20.1071	−	20.1071i	0.688454	−	0.688454i	0.961890	+	0.273436i	$0.0881603\pi$
$854$	−17.8316	−	1.96558i	−0.610185	−	0.0672609i
$855$		0			0
$856$	8.42560	+	8.42560i	0.287981	+	0.287981i
$857$	−6.66400	+	11.5424i	−0.227638	+	0.394280i	−0.957108	−	0.289733i	$-0.906434\pi$
$857$	−6.66400	+	11.5424i	−0.227638	+	0.394280i	0.729470	+	0.684013i	$0.239767\pi$
$858$		0			0
$859$	−11.1463	+	6.43532i	−0.380307	+	0.219570i	−0.677952	−	0.735106i	$-0.737132\pi$
$859$	−11.1463	+	6.43532i	−0.380307	+	0.219570i	0.297645	+	0.954677i	$0.403799\pi$
$860$	0.157338	−	0.0421585i	0.00536517	−	0.00143759i
$861$		0			0
$862$	−36.2193	+	20.9112i	−1.23364	+	0.712240i
$863$	−14.4716	−	3.87766i	−0.492620	−	0.131997i	0.00395268	−	0.999992i	$-0.498742\pi$
$863$	−14.4716	−	3.87766i	−0.492620	−	0.131997i	−0.496573	+	0.867995i	$0.665408\pi$
$864$		0			0
$865$	2.78722	+	2.78722i	0.0947683	+	0.0947683i
$866$	−20.8537	−	5.58773i	−0.708638	−	0.189879i
$867$		0			0
$868$	−0.0762063	+	0.691337i	−0.00258661	+	0.0234655i
$869$	1.81543	−	0.486443i	0.0615842	−	0.0165014i
$870$		0			0
$871$	−32.6506	−	8.47532i	−1.10632	−	0.287175i
$872$	8.82868	−	15.2917i	0.298977	−	0.517843i
$873$		0			0
$874$	−28.3155	−	16.3480i	−0.957787	−	0.552978i
$875$	−15.4129	+	6.76887i	−0.521050	+	0.228830i
$876$		0			0
$877$	4.81802	+	17.9811i	0.162693	+	0.607178i	0.998323	+	0.0578858i	$0.0184359\pi$
$877$	4.81802	+	17.9811i	0.162693	+	0.607178i	−0.835630	+	0.549292i	$0.814897\pi$
$878$	14.2087	−	14.2087i	0.479521	−	0.479521i
$879$		0			0
$880$	−10.7640	−	6.21458i	−0.362853	−	0.209494i
$881$	4.17631	−	7.23358i	0.140703	−	0.243705i	−0.787058	−	0.616879i	$-0.788397\pi$
$881$	4.17631	−	7.23358i	0.140703	−	0.243705i	0.927762	+	0.373173i	$0.121730\pi$
$882$		0			0
$883$		−	44.6713i		−	1.50331i	−0.659557	−	0.751655i	$-0.729256\pi$
$883$		−	44.6713i		−	1.50331i	0.659557	−	0.751655i	$-0.270744\pi$
$884$	−0.000817771	−	0.104459i	−2.75046e−5	−	0.00351333i
$885$		0			0
$886$	−16.7781	−	4.49569i	−0.563672	−	0.151036i
$887$			1.94254i			0.0652241i	0.999468	+	0.0326121i	$0.0103826\pi$
$887$			1.94254i			0.0652241i	−0.999468	+	0.0326121i	$0.989617\pi$
$888$		0			0
$889$	−32.9669	−	41.1352i	−1.10567	−	1.37963i
$890$	8.65777	+	2.31984i	0.290209	+	0.0777613i
$891$		0			0
$892$	−0.0593600	−	0.221534i	−0.00198752	−	0.00741752i
$893$	33.7232			1.12850
$894$		0			0
$895$	0.649644	+	2.42450i	0.0217152	+	0.0810422i
$896$	−11.4472	−	26.0655i	−0.382424	−	0.870787i
$897$		0			0
$898$	−19.4972	−	33.7701i	−0.650628	−	1.12692i
$899$	−4.43730	+	16.5602i	−0.147992	+	0.552315i
$900$		0			0
$901$	1.02963	−	1.78337i	0.0343019	−	0.0594127i
$902$	18.0823	+	18.0823i	0.602075	+	0.602075i
$903$		0			0
$904$	−0.824563	+	3.07731i	−0.0274246	+	0.102350i
$905$	0.980283	−	3.65847i	0.0325857	−	0.121612i
$906$		0			0
$907$	−45.1033	+	26.0404i	−1.49763	+	0.864656i	−0.999996	−	0.00273135i	$-0.999131\pi$
$907$	−45.1033	+	26.0404i	−1.49763	+	0.864656i	−0.497633	+	0.867388i	$0.665797\pi$
$908$	1.05553	−	1.05553i	0.0350291	−	0.0350291i
$909$		0			0
$910$	1.40722	+	8.72881i	0.0466490	+	0.289357i
$911$	48.8065			1.61703			0.808516	−	0.588474i	$-0.200271\pi$
$911$	48.8065			1.61703			0.808516	+	0.588474i	$0.200271\pi$
$912$		0			0
$913$	−68.2415	+	39.3992i	−2.25846	+	1.30392i
$914$			24.5227i			0.811140i
$915$		0			0
$916$	−0.298803	+	1.11515i	−0.00987273	+	0.0368455i
$917$	19.9726	−	3.05969i	0.659555	−	0.101040i
$918$		0			0
$919$	−3.72510	+	6.45206i	−0.122880	+	0.212834i	−0.920902	−	0.389794i	$-0.872546\pi$
$919$	−3.72510	+	6.45206i	−0.122880	+	0.212834i	0.798022	+	0.602628i	$0.205880\pi$
$920$	−6.64588	−	11.5110i	−0.219108	−	0.379507i
$921$		0			0
$922$	3.75518	+	6.50415i	0.123670	+	0.214203i
$923$	−11.5593	−	3.00051i	−0.380478	−	0.0987629i
$924$		0			0
$925$	−3.98173	−	14.8600i	−0.130918	−	0.488594i
$926$	−38.3499			−1.26026
$927$		0			0
$928$	0.365960	+	1.36578i	0.0120132	+	0.0448340i
$929$	−14.4466	+	3.87096i	−0.473978	+	0.127002i	−0.487897	−	0.872901i	$-0.662236\pi$
$929$	−14.4466	+	3.87096i	−0.473978	+	0.127002i	0.0139191	+	0.999903i	$0.495569\pi$
$930$		0			0
$931$	20.9513	+	10.9441i	0.686652	+	0.358678i
$932$	0.140021	+	0.242523i	0.00458653	+	0.00794410i
$933$		0			0
$934$	−12.9040	−	3.45762i	−0.422232	−	0.113137i
$935$	1.30064	+	0.750925i	0.0425355	+	0.0245579i
$936$		0			0
$937$			0.823290i			0.0268957i	0.999910	+	0.0134479i	$0.00428071\pi$
$937$			0.823290i			0.0268957i	−0.999910	+	0.0134479i	$0.995719\pi$
$938$	34.0625	−	5.21818i	1.11218	−	0.170380i
$939$		0			0
$940$	0.356538	+	0.205848i	0.0116290	+	0.00671401i
$941$	24.0974	−	6.45688i	0.785553	−	0.210488i	0.156321	−	0.987706i	$-0.450036\pi$
$941$	24.0974	−	6.45688i	0.785553	−	0.210488i	0.629231	+	0.777218i	$0.283370\pi$
$942$		0			0
$943$	6.85858	+	25.5966i	0.223346	+	0.833539i
$944$	−16.7790	+	16.7790i	−0.546111	+	0.546111i
$945$		0			0
$946$	−22.9670	−	13.2600i	−0.746722	−	0.431120i
$947$	−8.72288	−	8.72288i	−0.283455	−	0.283455i	0.551030	−	0.834485i	$-0.314235\pi$
$947$	−8.72288	−	8.72288i	−0.283455	−	0.283455i	−0.834485	+	0.551030i	$0.814235\pi$
$948$		0			0
$949$	−0.112035	−	0.405400i	−0.00363682	−	0.0131598i
$950$	18.5514	−	10.7106i	0.601886	−	0.347499i
$951$		0			0
$952$	1.42889	+	3.25362i	0.0463107	+	0.105450i
$953$	17.9140	−	10.3426i	0.580291	−	0.335031i	−0.180958	−	0.983491i	$-0.557920\pi$
$953$	17.9140	−	10.3426i	0.580291	−	0.335031i	0.761249	+	0.648460i	$0.224586\pi$
$954$		0			0
$955$	4.31581	+	4.31581i	0.139656	+	0.139656i
$956$	0.691075	+	0.691075i	0.0223510	+	0.0223510i
$957$		0			0
$958$	37.3132	−	21.5428i	1.20553	−	0.696016i
$959$	14.0093	+	31.8995i	0.452384	+	1.03009i
$960$		0			0
$961$	−11.2370	+	6.48771i	−0.362485	+	0.209281i
$962$	−16.9459	+	0.132663i	−0.546357	+	0.00427723i
$963$		0			0
$964$	−0.331374	−	0.331374i	−0.0106728	−	0.0106728i
$965$	14.6514	+	8.45899i	0.471645	+	0.272304i
$966$		0			0
$967$	6.39351	−	6.39351i	0.205601	−	0.205601i	−0.596793	−	0.802395i	$-0.703559\pi$
$967$	6.39351	−	6.39351i	0.205601	−	0.205601i	0.802395	+	0.596793i	$0.203559\pi$
$968$	−9.09612	−	33.9472i	−0.292360	−	1.09110i
$969$		0			0
$970$	15.9592	−	4.27624i	0.512418	−	0.137302i
$971$	−14.9575	−	8.63569i	−0.480008	−	0.277133i	0.240412	−	0.970671i	$-0.422717\pi$
$971$	−14.9575	−	8.63569i	−0.480008	−	0.277133i	−0.720420	+	0.693538i	$0.756051\pi$
$972$		0			0
$973$	45.0200	−	6.89680i	1.44327	−	0.221101i
$974$		−	7.79056i		−	0.249626i
$975$		0			0
$976$	16.3336	+	9.43018i	0.522824	+	0.301853i
$977$	−52.2660	−	14.0046i	−1.67214	−	0.448048i	−0.706452	−	0.707761i	$-0.749705\pi$
$977$	−52.2660	−	14.0046i	−1.67214	−	0.448048i	−0.965686	+	0.259714i	$0.916372\pi$
$978$		0			0
$979$	23.3118	+	40.3773i	0.745049	+	1.29046i
$980$	0.154705	+	0.243594i	0.00494186	+	0.00778133i
$981$		0			0
$982$	−18.6505	+	4.99738i	−0.595161	+	0.159473i
$983$	−9.70939	−	36.2359i	−0.309681	−	1.15575i	−0.928840	−	0.370481i	$-0.879193\pi$
$983$	−9.70939	−	36.2359i	−0.309681	−	1.15575i	0.619159	−	0.785266i	$-0.287474\pi$
$984$		0			0
$985$	0.955968			0.0304597
$986$	0.680815	+	2.54083i	0.0216816	+	0.0809167i
$987$		0			0
$988$	0.200815	+	0.726648i	0.00638876	+	0.0231177i
$989$	−13.7408	−	23.7998i	−0.436933	−	0.756790i
$990$		0			0
$991$	−17.4270	−	30.1845i	−0.553587	−	0.958841i	−0.998012	−	0.0630250i	$-0.979925\pi$
$991$	−17.4270	−	30.1845i	−0.553587	−	0.958841i	0.444425	−	0.895816i	$-0.353408\pi$
$992$	0.743276	−	1.28739i	0.0235990	−	0.0408748i
$993$		0			0
$994$	12.0591	−	1.84739i	0.382492	−	0.0585955i
$995$	1.89816	−	7.08404i	0.0601758	−	0.224579i
$996$		0			0
$997$			15.2231i			0.482119i	0.970510	+	0.241060i	$0.0774949\pi$
$997$			15.2231i			0.482119i	−0.970510	+	0.241060i	$0.922505\pi$
$998$	11.0233	−	6.36431i	0.348936	−	0.201459i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.b.136.6		28
3.2	odd	2		91.2.ba.a.45.2	yes	28
7.5	odd	6		819.2.gh.b.19.2		28
13.11	odd	12		819.2.gh.b.388.2		28
21.2	odd	6		637.2.x.a.19.6		28
21.5	even	6		91.2.w.a.19.6	✓	28
21.11	odd	6		637.2.bd.b.97.2		28
21.17	even	6		637.2.bd.a.97.2		28
21.20	even	2		637.2.bb.a.227.2		28
39.11	even	12		91.2.w.a.24.6	yes	28
91.89	even	12	inner	819.2.et.b.271.6		28
273.11	even	12		637.2.bd.a.440.2		28
273.89	odd	12		91.2.ba.a.89.2	yes	28
273.128	even	12		637.2.bb.a.362.2		28
273.167	odd	12		637.2.x.a.570.6		28
273.206	odd	12		637.2.bd.b.440.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.6	✓	28	21.5	even	6
91.2.w.a.24.6	yes	28	39.11	even	12
91.2.ba.a.45.2	yes	28	3.2	odd	2
91.2.ba.a.89.2	yes	28	273.89	odd	12
637.2.x.a.19.6		28	21.2	odd	6
637.2.x.a.570.6		28	273.167	odd	12
637.2.bb.a.227.2		28	21.20	even	2
637.2.bb.a.362.2		28	273.128	even	12
637.2.bd.a.97.2		28	21.17	even	6
637.2.bd.a.440.2		28	273.11	even	12
637.2.bd.b.97.2		28	21.11	odd	6
637.2.bd.b.440.2		28	273.206	odd	12
819.2.et.b.136.6		28	1.1	even	1	trivial
819.2.et.b.271.6		28	91.89	even	12	inner
819.2.gh.b.19.2		28	7.5	odd	6
819.2.gh.b.388.2		28	13.11	odd	12

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984398 - 0.984398i) q^{2} +0.0619199i q^{4} +(0.172312 - 0.643078i) q^{5} +(-2.46519 - 0.960657i) q^{7} +(2.02975 + 2.02975i) q^{8} +O(q^{10})\)	\(q+(0.984398 - 0.984398i) q^{2} +0.0619199i q^{4} +(0.172312 - 0.643078i) q^{5} +(-2.46519 - 0.960657i) q^{7} +(2.02975 + 2.02975i) q^{8} +(-0.463421 - 0.802669i) q^{10} +(1.24780 - 4.65687i) q^{11} +(3.60544 - 0.0282257i) q^{13} +(-3.37239 + 1.48106i) q^{14} +3.87233 q^{16} -0.467904 q^{17} +(3.26172 - 0.873976i) q^{19} +(0.0398194 + 0.0106696i) q^{20} +(-3.35587 - 5.81255i) q^{22} -6.95512i q^{23} +(3.94627 + 2.27838i) q^{25} +(3.52140 - 3.57698i) q^{26} +(0.0594838 - 0.152644i) q^{28} +(2.01911 - 3.49720i) q^{29} +(-4.10087 + 1.09883i) q^{31} +(-0.247590 + 0.247590i) q^{32} +(-0.460604 + 0.460604i) q^{34} +(-1.04256 + 1.41977i) q^{35} +(-2.38729 - 2.38729i) q^{37} +(2.35049 - 4.07117i) q^{38} +(1.65504 - 0.955538i) q^{40} +(-3.68025 + 0.986119i) q^{41} +(3.42191 - 1.97564i) q^{43} +(0.288353 + 0.0772639i) q^{44} +(-6.84661 - 6.84661i) q^{46} +(9.64648 + 2.58477i) q^{47} +(5.15428 + 4.73639i) q^{49} +(6.12753 - 1.64187i) q^{50} +(0.00174773 + 0.223249i) q^{52} +(-2.20051 + 3.81140i) q^{53} +(-2.77972 - 1.60487i) q^{55} +(-3.05382 - 6.95360i) q^{56} +(-1.45503 - 5.43025i) q^{58} +(-4.33306 + 4.33306i) q^{59} +(4.21802 + 2.43528i) q^{61} +(-2.95521 + 5.11858i) q^{62} +8.23211i q^{64} +(0.603111 - 2.32344i) q^{65} +(-9.03697 - 2.42145i) q^{67} -0.0289726i q^{68} +(0.371330 + 2.42392i) q^{70} +(-3.19935 - 0.857263i) q^{71} +(-0.0301918 - 0.112678i) q^{73} -4.70008 q^{74} +(0.0541165 + 0.201966i) q^{76} +(-7.54972 + 10.2813i) q^{77} +(0.194920 + 0.337611i) q^{79} +(0.667250 - 2.49021i) q^{80} +(-2.65209 + 4.59356i) q^{82} +(-11.5572 - 11.5572i) q^{83} +(-0.0806256 + 0.300899i) q^{85} +(1.42371 - 5.31334i) q^{86} +(11.9850 - 6.91955i) q^{88} +(-6.83819 + 6.83819i) q^{89} +(-8.91519 - 3.39401i) q^{91} +0.430661 q^{92} +(12.0404 - 6.95154i) q^{94} -2.24814i q^{95} +(-4.61378 + 17.2188i) q^{97} +(9.73636 - 0.411364i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8}+O(q^{10}) \) 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8	\( 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8} - 6 q^{10} - 2 q^{11} + 20 q^{14} + 4 q^{16} + 12 q^{17} + 14 q^{19} - 36 q^{20} - 8 q^{22} - 24 q^{26} + 2 q^{28} + 8 q^{29} - 4 q^{31} - 10 q^{32} - 12 q^{34} + 20 q^{35} - 10 q^{37} + 48 q^{40} + 18 q^{41} + 48 q^{43} + 6 q^{44} + 24 q^{46} + 6 q^{47} - 50 q^{49} - 10 q^{50} - 26 q^{52} - 12 q^{53} + 6 q^{55} - 54 q^{56} - 46 q^{58} - 42 q^{59} + 30 q^{61} - 36 q^{62} - 28 q^{65} - 10 q^{67} - 88 q^{70} + 42 q^{71} + 40 q^{73} - 12 q^{74} - 52 q^{76} + 4 q^{79} - 30 q^{80} - 54 q^{82} - 66 q^{83} - 54 q^{85} + 18 q^{86} - 6 q^{88} + 26 q^{91} + 156 q^{92} - 18 q^{94} - 62 q^{97} + 56 q^{98}+O(q^{100}) \) 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8 - 6 * q^10 - 2 * q^11 + 20 * q^14 + 4 * q^16 + 12 * q^17 + 14 * q^19 - 36 * q^20 - 8 * q^22 - 24 * q^26 + 2 * q^28 + 8 * q^29 - 4 * q^31 - 10 * q^32 - 12 * q^34 + 20 * q^35 - 10 * q^37 + 48 * q^40 + 18 * q^41 + 48 * q^43 + 6 * q^44 + 24 * q^46 + 6 * q^47 - 50 * q^49 - 10 * q^50 - 26 * q^52 - 12 * q^53 + 6 * q^55 - 54 * q^56 - 46 * q^58 - 42 * q^59 + 30 * q^61 - 36 * q^62 - 28 * q^65 - 10 * q^67 - 88 * q^70 + 42 * q^71 + 40 * q^73 - 12 * q^74 - 52 * q^76 + 4 * q^79 - 30 * q^80 - 54 * q^82 - 66 * q^83 - 54 * q^85 + 18 * q^86 - 6 * q^88 + 26 * q^91 + 156 * q^92 - 18 * q^94 - 62 * q^97 + 56 * q^98

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