LMFDB - Embedded newform 819.2.et.b.271.6

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			271.6
Character	$\chi$	$=$	819.271
Dual form			819.2.et.b.136.6

$q$-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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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	0.963562	−	0.267487i	$-0.0861932\pi$
$2$	0.984398	+	0.984398i	0.696075	+	0.696075i	−0.267487	+	0.963562i	$0.586193\pi$
$3$		0			0
$3$		0			0
$4$		−	0.0619199i		−	0.0309600i
$5$	0.172312	+	0.643078i	0.0770604	+	0.287593i	0.993693	−	0.112138i	$-0.0357700\pi$
$5$	0.172312	+	0.643078i	0.0770604	+	0.287593i	−0.916632	+	0.399732i	$0.869103\pi$
$6$		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	0.851544	+	0.524283i	$0.175667\pi$
$11$	1.24780	+	4.65687i	0.376227	+	1.40410i	−0.475317	+	0.879815i	$0.657667\pi$
$12$		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	0.612760	−	0.790269i	$-0.290059\pi$
$19$	3.26172	+	0.873976i	0.748290	+	0.200504i	0.135531	+	0.990773i	$0.456726\pi$
$20$	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	$0.258217\pi$
$23$			6.95512i			1.45024i	−0.688621	+	0.725122i	$0.741783\pi$
$24$		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	0.990318	−	0.138817i	$-0.0443301\pi$
$29$	2.01911	+	3.49720i	0.374940	+	0.649414i	−0.615378	+	0.788232i	$0.710997\pi$
$30$		0			0
$31$	−4.10087	−	1.09883i	−0.736539	−	0.197355i	−0.129000	−	0.991645i	$-0.541177\pi$
$31$	−4.10087	−	1.09883i	−0.736539	−	0.197355i	−0.607539	+	0.794290i	$0.707843\pi$
$32$	−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	−0.875566	−	0.483099i	$-0.839511\pi$
$37$	−2.38729	+	2.38729i	−0.392467	+	0.392467i	0.483099	+	0.875566i	$0.339511\pi$
$38$	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	−0.0402801	−	0.999188i	$-0.512825\pi$
$41$	−3.68025	−	0.986119i	−0.574758	−	0.154006i	−0.534478	+	0.845182i	$0.679492\pi$
$42$		0			0
$43$	3.42191	+	1.97564i	0.521836	+	0.301282i	0.737686	−	0.675144i	$-0.235919\pi$
$43$	3.42191	+	1.97564i	0.521836	+	0.301282i	−0.215849	+	0.976427i	$0.569252\pi$
$44$	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	0.526201	−	0.850360i	$-0.323616\pi$
$47$	9.64648	−	2.58477i	1.40708	−	0.377027i	0.880883	+	0.473333i	$0.156949\pi$
$48$		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	0.674384	−	0.738380i	$-0.264409\pi$
$53$	−2.20051	−	3.81140i	−0.302264	−	0.523537i	−0.976648	+	0.214844i	$0.931076\pi$
$54$		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	0.366358	−	0.930474i	$-0.380605\pi$
$59$	−4.33306	−	4.33306i	−0.564117	−	0.564117i	−0.930474	+	0.366358i	$0.880605\pi$
$60$		0			0
$61$	4.21802	−	2.43528i	0.540062	−	0.311805i	−0.205042	−	0.978753i	$-0.565733\pi$
$61$	4.21802	−	2.43528i	0.540062	−	0.311805i	0.745104	+	0.666948i	$0.232400\pi$
$62$	−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	−0.764409	−	0.644731i	$-0.776969\pi$
$67$	−9.03697	+	2.42145i	−1.10404	+	0.295827i	−0.339633	+	0.940558i	$0.610303\pi$
$68$			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	−0.443617	−	0.896216i	$-0.646305\pi$
$71$	−3.19935	+	0.857263i	−0.379693	+	0.101738i	0.0639244	+	0.997955i	$0.479638\pi$
$72$		0			0
$73$	−0.0301918	+	0.112678i	−0.00353369	+	0.0131879i	−0.967670	−	0.252219i	$-0.918840\pi$
$73$	−0.0301918	+	0.112678i	−0.00353369	+	0.0131879i	0.964136	+	0.265407i	$0.0855063\pi$
$74$	−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	−0.854852	−	0.518872i	$-0.826352\pi$
$79$	0.194920	−	0.337611i	0.0219302	−	0.0379842i	0.876782	+	0.480888i	$0.159686\pi$
$80$	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	−0.321741	+	0.946828i	$0.604268\pi$
$83$	−11.5572	+	11.5572i	−1.26857	+	1.26857i	−0.946828	+	0.321741i	$0.895732\pi$
$84$		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	0.244742	−	0.969588i	$-0.421297\pi$
$89$	−6.83819	−	6.83819i	−0.724847	−	0.724847i	−0.969588	+	0.244742i	$0.921297\pi$
$90$		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	−0.645163	−	0.764045i	$-0.723210\pi$
$97$	−4.61378	−	17.2188i	−0.468458	−	1.74831i	0.176705	−	0.984264i	$-0.443456\pi$
$98$	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	−0.443413	−	0.896317i	$-0.646233\pi$
$101$	5.57293	−	9.65259i	0.554527	−	0.960469i	0.997940	−	0.0641517i	$-0.0204342\pi$
$102$		0			0
$103$	3.73616	−	6.47122i	0.368135	−	0.637628i	−0.621139	−	0.783700i	$-0.713330\pi$
$103$	3.73616	−	6.47122i	0.368135	−	0.637628i	0.989274	+	0.146072i	$0.0466632\pi$
$104$	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	0.846814	+	0.531890i	$0.178518\pi$
$109$	−1.59208	+	5.94172i	−0.152493	+	0.569113i	−0.999307	+	0.0372233i	$0.988149\pi$
$110$	−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	−0.838743	−	0.544528i	$-0.816709\pi$
$113$	0.554932	−	0.961171i	0.0522036	−	0.0904194i	0.890946	+	0.454109i	$0.150042\pi$
$114$		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	0.531840	−	0.846845i	$-0.321501\pi$
$127$	17.2552	−	9.96228i	1.53115	−	0.884009i	0.999309	−	0.0371647i	$-0.0118326\pi$
$128$	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	0.182426	−	0.983220i	$-0.441605\pi$
$131$	−6.61385	−	3.81851i	−0.577855	−	0.333625i	−0.760280	+	0.649595i	$0.774938\pi$
$132$		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	−0.982387	−	0.186859i	$-0.940169\pi$
$137$	−9.31142	+	9.31142i	−0.795528	+	0.795528i	0.186859	+	0.982387i	$0.440169\pi$
$138$		0			0
$139$	−14.9082	−	8.60724i	−1.26449	−	0.730056i	−0.290554	−	0.956859i	$-0.593839\pi$
$139$	−14.9082	−	8.60724i	−1.26449	−	0.730056i	−0.973941	+	0.226802i	$0.927173\pi$
$140$	−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	−0.994275	−	0.106854i	$-0.965922\pi$
$149$	−0.973843	+	3.63443i	−0.0797804	+	0.297744i	0.914494	+	0.404599i	$0.132589\pi$
$150$		0			0
$151$	7.30304	+	1.95684i	0.594313	+	0.159246i	0.543424	−	0.839459i	$-0.317128\pi$
$151$	7.30304	+	1.95684i	0.594313	+	0.159246i	0.0508895	+	0.998704i	$0.483794\pi$
$152$	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	−0.760207	+	0.649681i	$0.774903\pi$
$157$	−21.3379	+	12.3194i	−1.70295	+	0.983199i	−0.942744	+	0.333518i	$0.891764\pi$
$158$	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	0.936065	−	0.351828i	$-0.114440\pi$
$163$	20.0547	+	5.37364i	1.57081	+	0.420896i	0.634742	+	0.772724i	$0.281107\pi$
$164$	−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	−0.534676	−	0.845057i	$-0.679566\pi$
$167$	4.53457	−	16.9233i	0.350896	−	1.30956i	0.885571	−	0.464503i	$-0.153767\pi$
$168$		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	0.731272	−	0.682086i	$-0.238927\pi$
$173$	−2.96030	−	5.12740i	−0.225068	−	0.389829i	−0.956340	+	0.292257i	$0.905594\pi$
$174$		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	0.372992	−	0.927835i	$-0.378332\pi$
$179$	−3.26505	−	1.88508i	−0.244041	−	0.140897i	−0.617033	+	0.786938i	$0.711665\pi$
$180$		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	0.651167	−	0.758935i	$-0.274280\pi$
$191$	−4.58382	−	7.93941i	−0.331674	−	0.574476i	−0.982840	+	0.184459i	$0.940947\pi$
$192$		0			0
$193$	−6.57695	−	24.5455i	−0.473419	−	1.76682i	−0.627345	−	0.778742i	$-0.715858\pi$
$193$	−6.57695	−	24.5455i	−0.473419	−	1.76682i	0.153926	−	0.988082i	$-0.450808\pi$
$194$	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	−0.951422	−	0.307889i	$-0.900377\pi$
$197$	0.371638	−	1.38697i	0.0264781	−	0.0988175i	0.977900	+	0.209071i	$0.0670441\pi$
$198$		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	0.922821	+	0.385229i	$0.125878\pi$
$211$	11.5485	+	20.0025i	0.795029	+	1.37703i	−0.127792	+	0.991801i	$0.540789\pi$
$212$	−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	0.137029	−	0.990567i	$-0.456245\pi$
$223$	−3.57776	−	0.958657i	−0.239584	−	0.0641964i	−0.376613	+	0.926371i	$0.622911\pi$
$224$	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	−0.141493	+	0.989939i	$0.545190\pi$
$227$	−17.0467	+	17.0467i	−1.13143	+	1.13143i	−0.989939	+	0.141493i	$0.954810\pi$
$228$		0			0
$229$	18.0095	−	4.82564i	1.19010	−	0.318887i	0.391176	−	0.920316i	$-0.372068\pi$
$229$	18.0095	−	4.82564i	1.19010	−	0.318887i	0.798926	+	0.601429i	$0.205402\pi$
$230$	−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	0.622779	−	0.782398i	$-0.286003\pi$
$233$	3.91672	+	2.26132i	0.256593	+	0.148144i	−0.366187	+	0.930541i	$0.619337\pi$
$234$		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	0.968998	−	0.247067i	$-0.0794668\pi$
$239$	11.1608	+	11.1608i	0.721931	+	0.721931i	−0.247067	+	0.968998i	$0.579467\pi$
$240$		0			0
$241$	−5.35165	−	5.35165i	−0.344730	−	0.344730i	0.513412	−	0.858142i	$-0.328381\pi$
$241$	−5.35165	−	5.35165i	−0.344730	−	0.344730i	−0.858142	+	0.513412i	$0.828381\pi$
$242$	−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	−0.307767	−	0.951462i	$-0.599582\pi$
$251$	10.6165	−	18.3883i	0.670106	−	1.16066i	0.977874	−	0.209197i	$-0.0670849\pi$
$252$		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	−0.861300	−	0.508096i	$-0.830350\pi$
$263$	0.152018	−	0.263302i	0.00937381	−	0.0162359i	0.870674	+	0.491860i	$0.163683\pi$
$264$		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	$-0.815821\pi$
$269$		−	17.9385i		−	1.09373i	0.837221	−	0.546865i	$-0.184179\pi$
$270$		0			0
$271$	−9.18147	−	9.18147i	−0.557734	−	0.557734i	0.370927	−	0.928662i	$-0.379040\pi$
$271$	−9.18147	−	9.18147i	−0.557734	−	0.557734i	−0.928662	+	0.370927i	$0.879040\pi$
$272$	−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	$-0.940238\pi$
$277$		−	6.21287i		−	0.373295i	0.982427	−	0.186648i	$-0.0597623\pi$
$278$	−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	−0.756779	−	0.653671i	$-0.773228\pi$
$281$	−1.72841	+	1.72841i	−0.103108	+	0.103108i	0.653671	+	0.756779i	$0.273228\pi$
$282$		0			0
$283$	−9.00809	+	15.6025i	−0.535475	+	0.927471i	0.463665	+	0.886011i	$0.346534\pi$
$283$	−9.00809	+	15.6025i	−0.535475	+	0.927471i	−0.999140	+	0.0414599i	$0.986799\pi$
$284$	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	−0.384532	−	0.923111i	$-0.625637\pi$
$293$	−4.38187	+	1.17412i	−0.255992	+	0.0685927i	0.128541	+	0.991704i	$0.458971\pi$
$294$		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	0.954973	−	0.296691i	$-0.0958832\pi$
$307$	11.5340	+	11.5340i	0.658282	+	0.658282i	−0.296691	+	0.954973i	$0.595883\pi$
$308$	−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	0.670247	−	0.742138i	$-0.266188\pi$
$311$	−5.42435	−	9.39525i	−0.307587	−	0.532756i	−0.977834	+	0.209382i	$0.932855\pi$
$312$		0			0
$313$	−6.22407	−	3.59347i	−0.351805	−	0.203115i	0.313675	−	0.949530i	$-0.398440\pi$
$313$	−6.22407	−	3.59347i	−0.351805	−	0.203115i	−0.665480	+	0.746416i	$0.731773\pi$
$314$	−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	−0.506367	−	0.862318i	$-0.669012\pi$
$317$	−9.14677	+	2.45087i	−0.513734	+	0.137655i	−0.00736711	+	0.999973i	$0.502345\pi$
$318$		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	−0.910788	−	0.412875i	$-0.864525\pi$
$331$	1.53579	−	5.73166i	0.0844148	−	0.315040i	0.995203	+	0.0978341i	$0.0311915\pi$
$332$	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	$0.143961\pi$
$337$			16.0448i			0.874014i	−0.899458	+	0.437007i	$0.856039\pi$
$338$	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	0.793592	+	0.608450i	$0.208208\pi$
$349$	−3.69715	+	13.7979i	−0.197904	+	0.738587i	−0.991496	+	0.130137i	$0.958458\pi$
$350$	−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	0.926465	−	0.376381i	$-0.122832\pi$
$353$	−1.20372	−	4.49235i	−0.0640677	−	0.239104i	−0.990533	+	0.137277i	$0.956165\pi$
$354$		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	−0.971711	−	0.236171i	$-0.924107\pi$
$359$	−4.70405	−	17.5557i	−0.248270	−	0.926557i	0.723441	−	0.690386i	$-0.242559\pi$
$360$		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	0.793218	−	0.608937i	$-0.208404\pi$
$367$	12.6911	+	7.32723i	0.662472	+	0.382478i	−0.130746	+	0.991416i	$0.541737\pi$
$368$			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	0.930569	−	0.366115i	$-0.119312\pi$
$373$	2.86259	+	4.95816i	0.148220	+	0.256724i	−0.782350	+	0.622839i	$0.785979\pi$
$374$	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	−0.972821	−	0.231559i	$-0.925617\pi$
$379$	−0.283332	+	1.05741i	−0.0145538	+	0.0543156i	0.958267	+	0.285875i	$0.0922840\pi$
$380$	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	0.271381	−	0.962472i	$-0.412520\pi$
$383$	0.492561	+	0.131981i	0.0251687	+	0.00674393i	−0.246213	+	0.969216i	$0.579186\pi$
$384$		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	0.0249566	−	0.999689i	$-0.492055\pi$
$389$	17.8137	−	10.2847i	0.903191	−	0.521457i	0.878234	+	0.478231i	$0.158722\pi$
$390$		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	0.455874	+	0.890045i	$0.349327\pi$
$397$	−7.65009	+	28.5505i	−0.383947	+	1.43291i	−0.839820	+	0.542864i	$0.817340\pi$
$398$	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	−0.580653	−	0.814151i	$-0.697203\pi$
$401$	4.67580	−	4.67580i	0.233499	−	0.233499i	0.814151	+	0.580653i	$0.197203\pi$
$402$		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	−0.664090	−	0.747653i	$-0.731181\pi$
$409$	1.68995	−	1.68995i	0.0835625	−	0.0835625i	0.747653	+	0.664090i	$0.231181\pi$
$410$	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	−0.786093	−	0.618108i	$-0.787899\pi$
$419$	−13.1791	+	7.60897i	−0.643842	+	0.371722i	0.142251	+	0.989831i	$0.454566\pi$
$420$		0			0
$421$	−15.0076	−	15.0076i	−0.731425	−	0.731425i	0.239477	−	0.970902i	$-0.423024\pi$
$421$	−15.0076	−	15.0076i	−0.731425	−	0.731425i	−0.970902	+	0.239477i	$0.923024\pi$
$422$	−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	−0.877536	−	0.479511i	$-0.840814\pi$
$431$	−29.0180	+	7.77536i	−1.39775	+	0.374526i	−0.520213	+	0.854037i	$0.674147\pi$
$432$		0			0
$433$	−7.75396	+	13.4302i	−0.372631	+	0.645417i	−0.989969	−	0.141281i	$-0.954878\pi$
$433$	−7.75396	+	13.4302i	−0.372631	+	0.645417i	0.617338	+	0.786698i	$0.288211\pi$
$434$	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	−0.975310	−	0.220839i	$-0.929120\pi$
$443$	−6.23855	+	10.8055i	−0.296403	+	0.513384i	0.678908	+	0.734224i	$0.262454\pi$
$444$		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	0.895932	+	0.444191i	$0.146509\pi$
$449$	7.24956	+	27.0557i	0.342128	+	1.27684i	−0.553804	+	0.832647i	$0.686824\pi$
$450$		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	0.352978	−	0.935631i	$-0.385169\pi$
$457$	−12.4557	−	12.4557i	−0.582653	−	0.582653i	−0.935631	+	0.352978i	$0.885169\pi$
$458$	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	0.925757	−	0.378118i	$-0.123429\pi$
$461$	−1.39627	−	5.21097i	−0.0650310	−	0.242699i	−0.990788	+	0.135419i	$0.956762\pi$
$462$		0			0
$463$	−19.4789	+	19.4789i	−0.905259	+	0.905259i	−0.995885	−	0.0906259i	$-0.971113\pi$
$463$	−19.4789	+	19.4789i	−0.905259	+	0.905259i	0.0906259	+	0.995885i	$0.471113\pi$
$464$	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	−0.955423	−	0.295239i	$-0.904601\pi$
$467$	−4.79805	+	8.31047i	−0.222027	+	0.384563i	0.733396	+	0.679802i	$0.237934\pi$
$468$		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	0.499927	−	0.866068i	$-0.333360\pi$
$479$	29.8944	−	8.01018i	1.36591	−	0.365994i	0.865983	+	0.500073i	$0.166694\pi$
$480$		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	0.791055	−	0.611745i	$-0.209532\pi$
$487$	3.95701	+	3.95701i	0.179309	+	0.179309i	−0.611745	+	0.791055i	$0.709532\pi$
$488$	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	−0.745915	−	0.666041i	$-0.767987\pi$
$491$	−12.0113	+	6.93474i	−0.542063	+	0.312960i	0.203851	+	0.979002i	$0.434654\pi$
$492$		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	−0.0556630	−	0.998450i	$-0.517727\pi$
$499$	8.83159	−	2.36642i	0.395356	−	0.105935i	0.451019	+	0.892514i	$0.351061\pi$
$500$	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	0.970434	−	0.241369i	$-0.0775963\pi$
$503$	27.9587	+	16.1420i	1.24662	+	0.719736i	0.276185	+	0.961104i	$0.410930\pi$
$504$		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	−0.492063	−	0.870559i	$-0.663757\pi$
$509$	8.53926	−	8.53926i	0.378496	−	0.378496i	0.870559	+	0.492063i	$0.163757\pi$
$510$		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	−0.706376	−	0.707837i	$-0.749671\pi$
$521$	−10.1929	+	5.88486i	−0.446558	+	0.257821i	0.259817	+	0.965658i	$0.416338\pi$
$522$		0			0
$523$		−	15.3301i		−	0.670337i	−0.942158	−	0.335168i	$-0.891207\pi$
$523$		−	15.3301i		−	0.670337i	0.942158	−	0.335168i	$-0.108793\pi$
$524$	−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	−0.997747	−	0.0670818i	$-0.978631\pi$
$541$	−3.88929	−	14.5150i	−0.167214	−	0.624050i	0.830534	−	0.556968i	$-0.188036\pi$
$542$		−	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	0.950915	−	0.309453i	$-0.100146\pi$
$557$	−0.644961	−	2.40703i	−0.0273279	−	0.101989i	−0.978243	+	0.207464i	$0.933479\pi$
$558$		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	$-0.613897\pi$
$569$		−	44.6858i		−	1.87333i	0.350230	−	0.936664i	$-0.386103\pi$
$570$		0			0
$571$	23.8503	−	13.7700i	0.998103	−	0.576255i	0.0904162	−	0.995904i	$-0.471180\pi$
$571$	23.8503	−	13.7700i	0.998103	−	0.576255i	0.907686	+	0.419649i	$0.137847\pi$
$572$	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	0.608974	−	0.793190i	$-0.291582\pi$
$577$	17.7698	+	4.76139i	0.739765	+	0.198219i	0.130791	+	0.991410i	$0.458248\pi$
$578$	−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	0.649927	−	0.759997i	$-0.274800\pi$
$587$	20.1767	+	5.40633i	0.832781	+	0.223143i	0.182855	+	0.983140i	$0.441466\pi$
$588$		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	−0.430182	−	0.902742i	$-0.641550\pi$
$593$	−8.55614	+	2.29261i	−0.351358	+	0.0941462i	0.0788231	+	0.996889i	$0.474884\pi$
$594$		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	−0.952001	−	0.306096i	$-0.900977\pi$
$599$	−18.1377	−	31.4154i	−0.741087	−	1.28360i	0.210914	−	0.977505i	$-0.432356\pi$
$600$		0			0
$601$	30.7163	−	17.7340i	1.25294	−	0.723387i	0.281250	−	0.959635i	$-0.409251\pi$
$601$	30.7163	−	17.7340i	1.25294	−	0.723387i	0.971693	+	0.236248i	$0.0759177\pi$
$602$	−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	−0.878398	−	0.477930i	$-0.841387\pi$
$607$	−22.2647	+	12.8545i	−0.903697	+	0.521749i	−0.0252989	+	0.999680i	$0.508054\pi$
$608$	−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	0.789352	−	0.613941i	$-0.210417\pi$
$613$	44.0688	−	11.8082i	1.77992	−	0.476928i	0.990569	+	0.137013i	$0.0437501\pi$
$614$			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	−0.889769	−	0.456411i	$-0.849135\pi$
$617$	−35.5733	+	9.53183i	−1.43213	+	0.383737i	−0.542357	+	0.840148i	$0.682468\pi$
$618$		0			0
$619$	−1.37524	+	5.13248i	−0.0552757	+	0.206292i	−0.988041	−	0.154193i	$-0.950722\pi$
$619$	−1.37524	+	5.13248i	−0.0552757	+	0.206292i	0.932765	+	0.360485i	$0.117389\pi$
$620$	−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	−0.999939	−	0.0110350i	$-0.996487\pi$
$631$	−3.50380	−	13.0763i	−0.139484	−	0.520561i	0.860455	−	0.509526i	$-0.170179\pi$
$632$	−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	$-0.860981\pi$
$641$		−	21.4184i		−	0.845978i	0.906135	−	0.422989i	$-0.139019\pi$
$642$		0			0
$643$	−3.68080	−	13.7369i	−0.145157	−	0.541732i	−0.999748	−	0.0224315i	$-0.992859\pi$
$643$	−3.68080	−	13.7369i	−0.145157	−	0.541732i	0.854592	−	0.519300i	$-0.173807\pi$
$644$	−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	−0.994193	−	0.107608i	$-0.965681\pi$
$647$	−10.2738	+	17.7948i	−0.403906	+	0.699585i	0.590288	+	0.807193i	$0.299014\pi$
$648$		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	−0.717848	−	0.696200i	$-0.754873\pi$
$659$	6.26381	−	10.8492i	0.244003	−	0.422626i	0.961851	+	0.273574i	$0.0882059\pi$
$660$		0			0
$661$	22.2227	−	5.95454i	0.864361	−	0.231605i	0.200713	−	0.979650i	$-0.435674\pi$
$661$	22.2227	−	5.95454i	0.864361	−	0.231605i	0.663648	+	0.748045i	$0.269007\pi$
$662$	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	−0.714229	−	0.699912i	$-0.753223\pi$
$673$	−12.0684	+	6.96769i	−0.465202	+	0.268585i	0.249027	+	0.968497i	$0.419889\pi$
$674$	−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	−0.912657	−	0.408727i	$-0.865973\pi$
$677$	−44.8299	−	25.8826i	−1.72295	−	0.994747i	−0.810296	−	0.586020i	$-0.800694\pi$
$678$		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	−0.206348	−	0.978479i	$-0.566158\pi$
$683$	20.1791	−	20.1791i	0.772131	−	0.772131i	0.978479	+	0.206348i	$0.0661578\pi$
$684$		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	−0.912667	−	0.408704i	$-0.865981\pi$
$691$	−13.2476	+	13.2476i	−0.503963	+	0.503963i	0.408704	+	0.912667i	$0.365981\pi$
$692$	−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	$0.124116\pi$
$701$			20.1282i			0.760231i	−0.924939	+	0.380115i	$0.875884\pi$
$702$		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	0.336132	−	0.941815i	$-0.390881\pi$
$709$	4.16243	+	1.11532i	0.156323	+	0.0418867i	−0.179809	+	0.983702i	$0.557548\pi$
$710$	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	0.993711	+	0.111973i	$0.0357171\pi$
$719$	15.9230	+	27.5794i	0.593827	+	1.02854i	−0.399884	+	0.916566i	$0.630950\pi$
$720$		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	0.999041	+	0.0437858i	$0.0139419\pi$
$733$	4.21647	+	15.7361i	0.155739	+	0.581226i	−0.843302	+	0.537440i	$0.819391\pi$
$734$	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	0.975664	+	0.219273i	$0.0703684\pi$
$739$	6.53382	+	24.3845i	0.240350	+	0.897000i	−0.735313	+	0.677727i	$0.762965\pi$
$740$	−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	−0.994289	−	0.106721i	$-0.965965\pi$
$743$	−2.17652	+	8.12290i	−0.0798489	+	0.298000i	0.914440	+	0.404721i	$0.132631\pi$
$744$		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	$-0.785660\pi$
$751$		−	34.1800i		−	1.24725i	0.781725	−	0.623623i	$-0.214340\pi$
$752$	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	0.716249	−	0.697845i	$-0.245857\pi$
$757$	−6.77459	−	11.7339i	−0.246227	−	0.426477i	−0.962476	+	0.271368i	$0.912524\pi$
$758$	−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	−0.806544	−	0.591174i	$-0.798665\pi$
$761$	5.17326	−	19.3069i	0.187531	−	0.699873i	0.994075	−	0.108700i	$-0.0346686\pi$
$762$		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	0.761184	−	0.648536i	$-0.224619\pi$
$769$	30.3963	+	8.14467i	1.09612	+	0.293704i	0.334936	+	0.942241i	$0.391285\pi$
$770$	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	−0.0257585	−	0.999668i	$-0.508200\pi$
$773$	27.0775	−	27.0775i	0.973910	−	0.973910i	0.999668	+	0.0257585i	$0.00820008\pi$
$774$		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	0.369618	−	0.929184i	$-0.379489\pi$
$787$	−15.6978	−	15.6978i	−0.559566	−	0.559566i	−0.929184	+	0.369618i	$0.879489\pi$
$788$	−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	0.457647	+	0.889134i	$0.348692\pi$
$797$	−15.2784	+	26.4630i	−0.541189	+	0.937367i	−0.998836	+	0.0482334i	$0.984641\pi$
$798$		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	−0.528750	−	0.848778i	$-0.677339\pi$
$809$	13.3877	−	23.1882i	0.470688	−	0.815255i	0.999438	+	0.0335223i	$0.0106725\pi$
$810$		0			0
$811$	−7.94016	+	7.94016i	−0.278817	+	0.278817i	−0.832637	−	0.553820i	$-0.813170\pi$
$811$	−7.94016	+	7.94016i	−0.278817	+	0.278817i	0.553820	+	0.832637i	$0.313170\pi$
$812$	−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	0.584536	−	0.811368i	$-0.301277\pi$
$821$	−6.49943	−	6.49943i	−0.226832	−	0.226832i	−0.811368	+	0.584536i	$0.801277\pi$
$822$		0			0
$823$		−	34.6382i		−	1.20741i	−0.797208	−	0.603705i	$-0.793690\pi$
$823$		−	34.6382i		−	1.20741i	0.797208	−	0.603705i	$-0.206310\pi$
$824$	−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	−0.303482	−	0.952837i	$-0.598149\pi$
$827$	18.6739	−	18.6739i	0.649355	−	0.649355i	0.952837	+	0.303482i	$0.0981492\pi$
$828$		0			0
$829$	16.3278	−	28.2806i	0.567089	−	0.982228i	−0.429763	−	0.902942i	$-0.641403\pi$
$829$	16.3278	−	28.2806i	0.567089	−	0.982228i	0.996852	−	0.0792856i	$-0.0252639\pi$
$830$	−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	0.479058	−	0.877783i	$-0.340978\pi$
$839$	38.6060	−	10.3444i	1.33283	−	0.357130i	0.853768	+	0.520654i	$0.174312\pi$
$840$		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	0.961890	−	0.273436i	$-0.0881603\pi$
$853$	20.1071	+	20.1071i	0.688454	+	0.688454i	−0.273436	+	0.961890i	$0.588160\pi$
$854$	−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	0.729470	−	0.684013i	$-0.239767\pi$
$857$	−6.66400	−	11.5424i	−0.227638	−	0.394280i	−0.957108	+	0.289733i	$0.906434\pi$
$858$		0			0
$859$	−11.1463	−	6.43532i	−0.380307	−	0.219570i	0.297645	−	0.954677i	$-0.403799\pi$
$859$	−11.1463	−	6.43532i	−0.380307	−	0.219570i	−0.677952	+	0.735106i	$0.737132\pi$
$860$	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	−0.496573	−	0.867995i	$-0.665408\pi$
$863$	−14.4716	+	3.87766i	−0.492620	+	0.131997i	0.00395268	+	0.999992i	$0.498742\pi$
$864$		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	−0.835630	−	0.549292i	$-0.814897\pi$
$877$	4.81802	−	17.9811i	0.162693	−	0.607178i	0.998323	−	0.0578858i	$-0.0184359\pi$
$878$	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	0.927762	−	0.373173i	$-0.121730\pi$
$881$	4.17631	+	7.23358i	0.140703	+	0.243705i	−0.787058	+	0.616879i	$0.788397\pi$
$882$		0			0
$883$			44.6713i			1.50331i	0.659557	+	0.751655i	$0.270744\pi$
$883$			44.6713i			1.50331i	−0.659557	+	0.751655i	$0.729256\pi$
$884$	−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	$-0.989617\pi$
$887$		−	1.94254i		−	0.0652241i	0.999468	−	0.0326121i	$-0.0103826\pi$
$888$		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	−0.497633	−	0.867388i	$-0.665797\pi$
$907$	−45.1033	−	26.0404i	−1.49763	−	0.864656i	−0.999996	+	0.00273135i	$0.999131\pi$
$908$	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	0.798022	−	0.602628i	$-0.205880\pi$
$919$	−3.72510	−	6.45206i	−0.122880	−	0.212834i	−0.920902	+	0.389794i	$0.872546\pi$
$920$	−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	0.0139191	−	0.999903i	$-0.495569\pi$
$929$	−14.4466	−	3.87096i	−0.473978	−	0.127002i	−0.487897	+	0.872901i	$0.662236\pi$
$930$		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	$-0.995719\pi$
$937$		−	0.823290i		−	0.0268957i	0.999910	−	0.0134479i	$-0.00428071\pi$
$938$	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	0.629231	−	0.777218i	$-0.283370\pi$
$941$	24.0974	+	6.45688i	0.785553	+	0.210488i	0.156321	+	0.987706i	$0.450036\pi$
$942$		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	−0.834485	−	0.551030i	$-0.814235\pi$
$947$	−8.72288	+	8.72288i	−0.283455	+	0.283455i	0.551030	+	0.834485i	$0.314235\pi$
$948$		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	0.761249	−	0.648460i	$-0.224586\pi$
$953$	17.9140	+	10.3426i	0.580291	+	0.335031i	−0.180958	+	0.983491i	$0.557920\pi$
$954$		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	0.802395	−	0.596793i	$-0.203559\pi$
$967$	6.39351	+	6.39351i	0.205601	+	0.205601i	−0.596793	+	0.802395i	$0.703559\pi$
$968$	−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	−0.720420	−	0.693538i	$-0.756051\pi$
$971$	−14.9575	+	8.63569i	−0.480008	+	0.277133i	0.240412	+	0.970671i	$0.422717\pi$
$972$		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	−0.965686	−	0.259714i	$-0.916372\pi$
$977$	−52.2660	+	14.0046i	−1.67214	+	0.448048i	−0.706452	+	0.707761i	$0.749705\pi$
$978$		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	0.619159	+	0.785266i	$0.287474\pi$
$983$	−9.70939	+	36.2359i	−0.309681	+	1.15575i	−0.928840	+	0.370481i	$0.879193\pi$
$984$		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	0.444425	+	0.895816i	$0.353408\pi$
$991$	−17.4270	+	30.1845i	−0.553587	+	0.958841i	−0.998012	+	0.0630250i	$0.979925\pi$
$992$	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	$-0.922505\pi$
$997$		−	15.2231i		−	0.482119i	0.970510	−	0.241060i	$-0.0774949\pi$
$998$	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.271.6		28
3.2	odd	2		91.2.ba.a.89.2	yes	28
7.3	odd	6		819.2.gh.b.388.2		28
13.6	odd	12		819.2.gh.b.19.2		28
21.2	odd	6		637.2.bd.b.440.2		28
21.5	even	6		637.2.bd.a.440.2		28
21.11	odd	6		637.2.x.a.570.6		28
21.17	even	6		91.2.w.a.24.6	yes	28
21.20	even	2		637.2.bb.a.362.2		28
39.32	even	12		91.2.w.a.19.6	✓	28
91.45	even	12	inner	819.2.et.b.136.6		28
273.32	even	12		637.2.bb.a.227.2		28
273.110	odd	12		637.2.bd.b.97.2		28
273.149	even	12		637.2.bd.a.97.2		28
273.188	odd	12		637.2.x.a.19.6		28
273.227	odd	12		91.2.ba.a.45.2	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.6	✓	28	39.32	even	12
91.2.w.a.24.6	yes	28	21.17	even	6
91.2.ba.a.45.2	yes	28	273.227	odd	12
91.2.ba.a.89.2	yes	28	3.2	odd	2
637.2.x.a.19.6		28	273.188	odd	12
637.2.x.a.570.6		28	21.11	odd	6
637.2.bb.a.227.2		28	273.32	even	12
637.2.bb.a.362.2		28	21.20	even	2
637.2.bd.a.97.2		28	273.149	even	12
637.2.bd.a.440.2		28	21.5	even	6
637.2.bd.b.97.2		28	273.110	odd	12
637.2.bd.b.440.2		28	21.2	odd	6
819.2.et.b.136.6		28	91.45	even	12	inner
819.2.et.b.271.6		28	1.1	even	1	trivial
819.2.gh.b.19.2		28	13.6	odd	12
819.2.gh.b.388.2		28	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
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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