LMFDB - Embedded newform 152.2.c.b.77.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(77,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.77"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 4 x^{12} + 4 x^{11} - 10 x^{10} + 24 x^{9} - 40 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 3x^14 - 4x^13 + 4x^12 + 4x^11 - 10x^10 + 24x^9 - 40x^8 + 48x^7 - 40x^6 + 32x^5 + 64x^4 - 128x^3 + 192x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			77.11
Root			$1.12629 - 0.855255i$ of defining polynomial
Character	$\chi$	$=$	152.77
Dual form			152.2.c.b.77.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.855255 - 1.12629i) q^{2} -1.91886i q^{3} +(-0.537077 - 1.92654i) q^{4} +1.51356i q^{5} +(-2.16120 - 1.64111i) q^{6} +0.580162 q^{7} +(-2.62919 - 1.04278i) q^{8} -0.682013 q^{9} +(1.70471 + 1.29448i) q^{10} -1.31799i q^{11} +(-3.69675 + 1.03057i) q^{12} +3.89230i q^{13} +(0.496186 - 0.653433i) q^{14} +2.90431 q^{15} +(-3.42310 + 2.06940i) q^{16} -1.20142 q^{17} +(-0.583295 + 0.768147i) q^{18} +1.00000i q^{19} +(2.91593 - 0.812898i) q^{20} -1.11325i q^{21} +(-1.48444 - 1.12722i) q^{22} +5.85527 q^{23} +(-2.00094 + 5.04503i) q^{24} +2.70913 q^{25} +(4.38387 + 3.32891i) q^{26} -4.44789i q^{27} +(-0.311591 - 1.11770i) q^{28} +1.29188i q^{29} +(2.48392 - 3.27110i) q^{30} +2.96413 q^{31} +(-0.596871 + 5.62528i) q^{32} -2.52903 q^{33} +(-1.02752 + 1.35316i) q^{34} +0.878110i q^{35} +(0.366293 + 1.31392i) q^{36} -1.18418i q^{37} +(1.12629 + 0.855255i) q^{38} +7.46877 q^{39} +(1.57830 - 3.97943i) q^{40} -9.04577 q^{41} +(-1.25384 - 0.952111i) q^{42} +8.38816i q^{43} +(-2.53915 + 0.707861i) q^{44} -1.03227i q^{45} +(5.00775 - 6.59475i) q^{46} -12.8560 q^{47} +(3.97088 + 6.56843i) q^{48} -6.66341 q^{49} +(2.31700 - 3.05128i) q^{50} +2.30536i q^{51} +(7.49866 - 2.09046i) q^{52} -3.07183i q^{53} +(-5.00963 - 3.80408i) q^{54} +1.99485 q^{55} +(-1.52535 - 0.604978i) q^{56} +1.91886 q^{57} +(1.45503 + 1.10488i) q^{58} +0.258163i q^{59} +(-1.55984 - 5.59526i) q^{60} +14.7200i q^{61} +(2.53509 - 3.33848i) q^{62} -0.395678 q^{63} +(5.82524 + 5.48330i) q^{64} -5.89123 q^{65} +(-2.16297 + 2.84843i) q^{66} -9.54884i q^{67} +(0.645257 + 2.31459i) q^{68} -11.2354i q^{69} +(0.989010 + 0.751008i) q^{70} -6.93697 q^{71} +(1.79314 + 0.711186i) q^{72} +15.2934 q^{73} +(-1.33373 - 1.01277i) q^{74} -5.19844i q^{75} +(1.92654 - 0.537077i) q^{76} -0.764646i q^{77} +(6.38770 - 8.41203i) q^{78} -13.1332 q^{79} +(-3.13216 - 5.18106i) q^{80} -10.5809 q^{81} +(-7.73645 + 10.1882i) q^{82} -3.70615i q^{83} +(-2.14471 + 0.597900i) q^{84} -1.81843i q^{85} +(9.44754 + 7.17402i) q^{86} +2.47893 q^{87} +(-1.37436 + 3.46523i) q^{88} -8.36653 q^{89} +(-1.16264 - 0.882852i) q^{90} +2.25816i q^{91} +(-3.14473 - 11.2804i) q^{92} -5.68774i q^{93} +(-10.9952 + 14.4796i) q^{94} -1.51356 q^{95} +(10.7941 + 1.14531i) q^{96} +17.0442 q^{97} +(-5.69892 + 7.50496i) q^{98} +0.898884i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 6 q^{6} - 8 q^{7} - 12 q^{8} - 24 q^{9} - 8 q^{10} + 4 q^{12} + 4 q^{14} + 2 q^{16} - 8 q^{17} + 20 q^{18} + 8 q^{20} + 20 q^{22} + 6 q^{24} - 24 q^{25} - 10 q^{26} - 14 q^{28} + 4 q^{30}+ \cdots - 48 q^{98}+O(q^{100}) $ 16 * q + 2 * q^4 + 6 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9 - 8 * q^10 + 4 * q^12 + 4 * q^14 + 2 * q^16 - 8 * q^17 + 20 * q^18 + 8 * q^20 + 20 * q^22 + 6 * q^24 - 24 * q^25 - 10 * q^26 - 14 * q^28 + 4 * q^30 + 16 * q^31 - 20 * q^32 + 8 * q^36 + 2 * q^38 + 8 * q^39 + 28 * q^40 + 16 * q^41 - 2 * q^42 - 28 * q^44 - 48 * q^46 + 24 * q^47 + 36 * q^48 + 24 * q^49 + 12 * q^50 + 8 * q^52 - 34 * q^54 + 16 * q^55 - 48 * q^56 + 38 * q^58 - 28 * q^60 - 16 * q^62 - 32 * q^63 + 14 * q^64 + 16 * q^65 - 24 * q^66 - 26 * q^68 - 32 * q^70 + 48 * q^71 - 20 * q^74 - 4 * q^76 + 56 * q^78 - 48 * q^79 + 4 * q^80 - 16 * q^81 - 12 * q^82 + 64 * q^84 + 48 * q^86 - 48 * q^87 + 40 * q^88 - 16 * q^89 + 12 * q^90 + 62 * q^92 - 36 * q^94 + 16 * q^95 - 70 * q^96 + 32 * q^97 - 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	0.855255	−	1.12629i	0.604757	−	0.796410i
$2$	0.855255	−	1.12629i	0.604757	−	0.796410i
$3$		−	1.91886i		−	1.10785i	−0.832566	−	0.553926i	$-0.813129\pi$
$3$		−	1.91886i		−	1.10785i	0.832566	−	0.553926i	$-0.186871\pi$
$4$	−0.537077	−	1.92654i	−0.268538	−	0.963269i
$5$			1.51356i			0.676885i	0.940987	+	0.338442i	$0.109900\pi$
$5$			1.51356i			0.676885i	−0.940987	+	0.338442i	$0.890100\pi$
$6$	−2.16120	−	1.64111i	−0.882305	−	0.669981i
$7$	0.580162			0.219281			0.109640	−	0.993971i	$-0.465030\pi$
$7$	0.580162			0.219281			0.109640	+	0.993971i	$0.465030\pi$
$8$	−2.62919	−	1.04278i	−0.929558	−	0.368677i
$9$	−0.682013			−0.227338
$10$	1.70471	+	1.29448i	0.539078	+	0.409351i
$11$		−	1.31799i		−	0.397388i	−0.980062	−	0.198694i	$-0.936330\pi$
$11$		−	1.31799i		−	0.397388i	0.980062	−	0.198694i	$-0.0636700\pi$
$12$	−3.69675	+	1.03057i	−1.06716	+	0.297501i
$13$			3.89230i			1.07953i	0.841816	+	0.539765i	$0.181487\pi$
$13$			3.89230i			1.07953i	−0.841816	+	0.539765i	$0.818513\pi$
$14$	0.496186	−	0.653433i	0.132611	−	0.174637i
$15$	2.90431			0.749889
$16$	−3.42310	+	2.06940i	−0.855774	+	0.517349i
$17$	−1.20142			−0.291388			−0.145694	−	0.989330i	$-0.546541\pi$
$17$	−1.20142			−0.291388			−0.145694	+	0.989330i	$0.546541\pi$
$18$	−0.583295	+	0.768147i	−0.137484	+	0.181054i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	2.91593	−	0.812898i	0.652022	−	0.181770i
$21$		−	1.11325i		−	0.242931i
$22$	−1.48444	−	1.12722i	−0.316484	−	0.240323i
$23$	5.85527			1.22091			0.610454	−	0.792052i	$-0.290987\pi$
$23$	5.85527			1.22091			0.610454	+	0.792052i	$0.290987\pi$
$24$	−2.00094	+	5.04503i	−0.408439	+	1.02981i
$25$	2.70913			0.541827
$26$	4.38387	+	3.32891i	0.859748	+	0.652853i
$27$		−	4.44789i		−	0.855996i
$28$	−0.311591	−	1.11770i	−0.0588853	−	0.211226i
$29$			1.29188i			0.239896i	0.992780	+	0.119948i	$0.0382727\pi$
$29$			1.29188i			0.239896i	−0.992780	+	0.119948i	$0.961727\pi$
$30$	2.48392	−	3.27110i	0.453500	−	0.597219i
$31$	2.96413			0.532374			0.266187	−	0.963921i	$-0.414236\pi$
$31$	2.96413			0.532374			0.266187	+	0.963921i	$0.414236\pi$
$32$	−0.596871	+	5.62528i	−0.105513	+	0.994418i
$33$	−2.52903			−0.440248
$34$	−1.02752	+	1.35316i	−0.176219	+	0.232064i
$35$			0.878110i			0.148428i
$36$	0.366293	+	1.31392i	0.0610489	+	0.218987i
$37$		−	1.18418i		−	0.194677i	−0.995251	−	0.0973387i	$-0.968967\pi$
$37$		−	1.18418i		−	0.194677i	0.995251	−	0.0973387i	$-0.0310330\pi$
$38$	1.12629	+	0.855255i	0.182709	+	0.138741i
$39$	7.46877			1.19596
$40$	1.57830	−	3.97943i	0.249552	−	0.629204i
$41$	−9.04577			−1.41271			−0.706356	−	0.707856i	$-0.749662\pi$
$41$	−9.04577			−1.41271			−0.706356	+	0.707856i	$0.749662\pi$
$42$	−1.25384	−	0.952111i	−0.193472	−	0.146914i
$43$			8.38816i			1.27918i	0.768715	+	0.639592i	$0.220896\pi$
$43$			8.38816i			1.27918i	−0.768715	+	0.639592i	$0.779104\pi$
$44$	−2.53915	+	0.707861i	−0.382792	+	0.106714i
$45$		−	1.03227i		−	0.153881i
$46$	5.00775	−	6.59475i	0.738352	−	0.972343i
$47$	−12.8560			−1.87524			−0.937620	−	0.347661i	$-0.886976\pi$
$47$	−12.8560			−1.87524			−0.937620	+	0.347661i	$0.886976\pi$
$48$	3.97088	+	6.56843i	0.573147	+	0.948072i
$49$	−6.66341			−0.951916
$50$	2.31700	−	3.05128i	0.327673	−	0.431516i
$51$			2.30536i			0.322815i
$52$	7.49866	−	2.09046i	1.03988	−	0.289895i
$53$		−	3.07183i		−	0.421949i	−0.977492	−	0.210974i	$-0.932336\pi$
$53$		−	3.07183i		−	0.421949i	0.977492	−	0.210974i	$-0.0676636\pi$
$54$	−5.00963	−	3.80408i	−0.681724	−	0.517670i
$55$	1.99485			0.268986
$56$	−1.52535	−	0.604978i	−0.203834	−	0.0808436i
$57$	1.91886			0.254159
$58$	1.45503	+	1.10488i	0.191055	+	0.145079i
$59$			0.258163i			0.0336100i	0.999859	+	0.0168050i	$0.00534945\pi$
$59$			0.258163i			0.0336100i	−0.999859	+	0.0168050i	$0.994651\pi$
$60$	−1.55984	−	5.59526i	−0.201374	−	0.722345i
$61$			14.7200i			1.88470i	0.334623	+	0.942352i	$0.391391\pi$
$61$			14.7200i			1.88470i	−0.334623	+	0.942352i	$0.608609\pi$
$62$	2.53509	−	3.33848i	0.321957	−	0.423988i
$63$	−0.395678			−0.0498507
$64$	5.82524	+	5.48330i	0.728155	+	0.685413i
$65$	−5.89123			−0.730717
$66$	−2.16297	+	2.84843i	−0.266243	+	0.350618i
$67$		−	9.54884i		−	1.16658i	−0.812265	−	0.583288i	$-0.801766\pi$
$67$		−	9.54884i		−	1.16658i	0.812265	−	0.583288i	$-0.198234\pi$
$68$	0.645257	+	2.31459i	0.0782489	+	0.280685i
$69$		−	11.2354i		−	1.35259i
$70$	0.989010	+	0.751008i	0.118209	+	0.0897627i
$71$	−6.93697			−0.823267			−0.411634	−	0.911349i	$-0.635042\pi$
$71$	−6.93697			−0.823267			−0.411634	+	0.911349i	$0.635042\pi$
$72$	1.79314	+	0.711186i	0.211323	+	0.0838141i
$73$	15.2934			1.78996			0.894978	−	0.446110i	$-0.147191\pi$
$73$	15.2934			1.78996			0.894978	+	0.446110i	$0.147191\pi$
$74$	−1.33373	−	1.01277i	−0.155043	−	0.117732i
$75$		−	5.19844i		−	0.600264i
$76$	1.92654	−	0.537077i	0.220989	−	0.0616069i
$77$		−	0.764646i		−	0.0871395i
$78$	6.38770	−	8.41203i	0.723265	−	0.952475i
$79$	−13.1332			−1.47760			−0.738798	−	0.673927i	$-0.764606\pi$
$79$	−13.1332			−1.47760			−0.738798	+	0.673927i	$0.764606\pi$
$80$	−3.13216	−	5.18106i	−0.350186	−	0.579261i
$81$	−10.5809			−1.17566
$82$	−7.73645	+	10.1882i	−0.854348	+	1.12510i
$83$		−	3.70615i		−	0.406803i	−0.979095	−	0.203402i	$-0.934800\pi$
$83$		−	3.70615i		−	0.406803i	0.979095	−	0.203402i	$-0.0651997\pi$
$84$	−2.14471	+	0.597900i	−0.234007	+	0.0652362i
$85$		−	1.81843i		−	0.197236i
$86$	9.44754	+	7.17402i	1.01875	+	0.773595i
$87$	2.47893			0.265769
$88$	−1.37436	+	3.46523i	−0.146508	+	0.369395i
$89$	−8.36653			−0.886850			−0.443425	−	0.896311i	$-0.646237\pi$
$89$	−8.36653			−0.886850			−0.443425	+	0.896311i	$0.646237\pi$
$90$	−1.16264	−	0.882852i	−0.122553	−	0.0930608i
$91$			2.25816i			0.236720i
$92$	−3.14473	−	11.2804i	−0.327861	−	1.17606i
$93$		−	5.68774i		−	0.589792i
$94$	−10.9952	+	14.4796i	−1.13406	+	1.49346i
$95$	−1.51356			−0.155288
$96$	10.7941	+	1.14531i	1.10167	+	0.116893i
$97$	17.0442			1.73057			0.865286	−	0.501278i	$-0.167137\pi$
$97$	17.0442			1.73057			0.865286	+	0.501278i	$0.167137\pi$
$98$	−5.69892	+	7.50496i	−0.575678	+	0.758116i
$99$			0.898884i			0.0903412i
$100$	−1.45501	−	5.21925i	−0.145501	−	0.521925i
$101$		−	1.97721i		−	0.196739i	−0.995150	−	0.0983697i	$-0.968637\pi$
$101$		−	1.97721i		−	0.196739i	0.995150	−	0.0983697i	$-0.0313628\pi$
$102$	2.59651	+	1.97167i	0.257093	+	0.195225i
$103$	−2.30853			−0.227466			−0.113733	−	0.993511i	$-0.536281\pi$
$103$	−2.30853			−0.227466			−0.113733	+	0.993511i	$0.536281\pi$
$104$	4.05879	−	10.2336i	0.397997	−	1.00348i
$105$	1.68497			0.164436
$106$	−3.45979	−	2.62720i	−0.336044	−	0.255176i
$107$		−	15.0396i		−	1.45393i	−0.686675	−	0.726965i	$-0.740930\pi$
$107$		−	15.0396i		−	1.45393i	0.686675	−	0.726965i	$-0.259070\pi$
$108$	−8.56902	+	2.38886i	−0.824555	+	0.229868i
$109$		−	13.4002i		−	1.28351i	−0.766911	−	0.641753i	$-0.778207\pi$
$109$		−	13.4002i		−	1.28351i	0.766911	−	0.641753i	$-0.221793\pi$
$110$	1.70611	−	2.24679i	0.162671	−	0.214223i
$111$	−2.27227			−0.215674
$112$	−1.98595	+	1.20059i	−0.187655	+	0.113445i
$113$	4.89717			0.460687			0.230343	−	0.973109i	$-0.426015\pi$
$113$	4.89717			0.460687			0.230343	+	0.973109i	$0.426015\pi$
$114$	1.64111	−	2.16120i	0.153704	−	0.202415i
$115$			8.86230i			0.826414i
$116$	2.48885	−	0.693837i	0.231084	−	0.0644212i
$117$		−	2.65460i		−	0.245418i
$118$	0.290768	+	0.220795i	0.0267673	+	0.0203259i
$119$	−0.697020			−0.0638957
$120$	−7.63596	−	3.02854i	−0.697065	−	0.276467i
$121$	9.26291			0.842083
$122$	16.5791	+	12.5894i	1.50100	+	1.13979i
$123$			17.3575i			1.56508i
$124$	−1.59197	−	5.71051i	−0.142963	−	0.512819i
$125$			11.6682i			1.04364i
$126$	−0.338405	+	0.445649i	−0.0301475	+	0.0397016i
$127$	−2.61625			−0.232155			−0.116078	−	0.993240i	$-0.537032\pi$
$127$	−2.61625			−0.232155			−0.116078	+	0.993240i	$0.537032\pi$
$128$	11.1579	−	1.87131i	0.986226	−	0.165402i
$129$	16.0957			1.41715
$130$	−5.03851	+	6.63526i	−0.441906	+	0.581951i
$131$			2.64498i			0.231093i	0.993302	+	0.115547i	$0.0368620\pi$
$131$			2.64498i			0.231093i	−0.993302	+	0.115547i	$0.963138\pi$
$132$	1.35828	+	4.87227i	0.118223	+	0.424077i
$133$			0.580162i			0.0503064i
$134$	−10.7548	−	8.16670i	−0.929073	−	0.705495i
$135$	6.73215			0.579411
$136$	3.15877	+	1.25281i	0.270862	+	0.107428i
$137$	4.88035			0.416957			0.208478	−	0.978027i	$-0.433149\pi$
$137$	4.88035			0.416957			0.208478	+	0.978027i	$0.433149\pi$
$138$	−12.6544	−	9.60916i	−1.07721	−	0.817986i
$139$			10.3334i			0.876468i	0.898861	+	0.438234i	$0.144396\pi$
$139$			10.3334i			0.876468i	−0.898861	+	0.438234i	$0.855604\pi$
$140$	1.69171	−	0.471613i	0.142976	−	0.0398585i
$141$			24.6688i			2.07749i
$142$	−5.93288	+	7.81307i	−0.497877	+	0.655659i
$143$	5.13000			0.428992
$144$	2.33460	−	1.41136i	0.194550	−	0.117613i
$145$	−1.95533			−0.162382
$146$	13.0798	−	17.2249i	1.08249	−	1.42554i
$147$			12.7861i			1.05458i
$148$	−2.28136	+	0.635994i	−0.187527	+	0.0522784i
$149$		−	8.35324i		−	0.684324i	−0.939641	−	0.342162i	$-0.888841\pi$
$149$		−	8.35324i		−	0.684324i	0.939641	−	0.342162i	$-0.111159\pi$
$150$	−5.85497	−	4.44599i	−0.478057	−	0.363014i
$151$	−5.84941			−0.476019			−0.238009	−	0.971263i	$-0.576495\pi$
$151$	−5.84941			−0.476019			−0.238009	+	0.971263i	$0.576495\pi$
$152$	1.04278	−	2.62919i	0.0845802	−	0.213255i
$153$	0.819386			0.0662434
$154$	−0.861216	−	0.653967i	−0.0693988	−	0.0526982i
$155$			4.48639i			0.360356i
$156$	−4.01130	−	14.3889i	−0.321161	−	1.15203i
$157$		−	0.361645i		−	0.0288624i	−0.999896	−	0.0144312i	$-0.995406\pi$
$157$		−	0.361645i		−	0.0288624i	0.999896	−	0.0144312i	$-0.00459375\pi$
$158$	−11.2322	+	14.7918i	−0.893587	+	1.17677i
$159$	−5.89441			−0.467457
$160$	−8.51420	−	0.903401i	−0.673107	−	0.0714201i
$161$	3.39700			0.267721
$162$	−9.04937	+	11.9172i	−0.710985	+	0.936304i
$163$			0.146029i			0.0114379i	0.999984	+	0.00571894i	$0.00182041\pi$
$163$			0.146029i			0.0114379i	−0.999984	+	0.00571894i	$0.998180\pi$
$164$	4.85828	+	17.4270i	0.379368	+	1.36082i
$165$		−	3.82784i		−	0.297997i
$166$	−4.17422	−	3.16971i	−0.323982	−	0.246017i
$167$	0.406603			0.0314639			0.0157319	−	0.999876i	$-0.494992\pi$
$167$	0.406603			0.0314639			0.0157319	+	0.999876i	$0.494992\pi$
$168$	−1.16087	+	2.92694i	−0.0895628	+	0.225818i
$169$	−2.14999			−0.165384
$170$	−2.04808	−	1.55522i	−0.157081	−	0.119280i
$171$		−	0.682013i		−	0.0521548i
$172$	16.1601	−	4.50509i	1.23220	−	0.343510i
$173$			12.6466i			0.961507i	0.876856	+	0.480753i	$0.159637\pi$
$173$			12.6466i			0.961507i	−0.876856	+	0.480753i	$0.840363\pi$
$174$	2.12012	−	2.79200i	0.160726	−	0.211661i
$175$	1.57174			0.118812
$176$	2.72744	+	4.51160i	0.205589	+	0.340075i
$177$	0.495378			0.0372349
$178$	−7.15552	+	9.42317i	−0.536329	+	0.706297i
$179$		−	5.55598i		−	0.415274i	−0.978206	−	0.207637i	$-0.933423\pi$
$179$		−	5.55598i		−	0.415274i	0.978206	−	0.207637i	$-0.0665772\pi$
$180$	−1.98870	+	0.554407i	−0.148229	+	0.0413231i
$181$		−	9.13401i		−	0.678926i	−0.940619	−	0.339463i	$-0.889755\pi$
$181$		−	9.13401i		−	0.678926i	0.940619	−	0.339463i	$-0.110245\pi$
$182$	2.54336	+	1.93131i	0.188526	+	0.143158i
$183$	28.2456			2.08797
$184$	−15.3946	−	6.10573i	−1.13490	−	0.450120i
$185$	1.79232			0.131774
$186$	−6.40607	−	4.86447i	−0.469716	−	0.356680i
$187$			1.58346i			0.115794i
$188$	6.90466	+	24.7676i	0.503574	+	1.80636i
$189$		−	2.58049i		−	0.187703i
$190$	−1.29448	+	1.70471i	−0.0939115	+	0.123673i
$191$	5.47532			0.396180			0.198090	−	0.980184i	$-0.436526\pi$
$191$	5.47532			0.396180			0.198090	+	0.980184i	$0.436526\pi$
$192$	10.5217	−	11.1778i	0.759336	−	0.806688i
$193$	16.9697			1.22151			0.610753	−	0.791821i	$-0.290867\pi$
$193$	16.9697			1.22151			0.610753	+	0.791821i	$0.290867\pi$
$194$	14.5771	−	19.1967i	1.04658	−	1.37825i
$195$			11.3044i			0.809527i
$196$	3.57876	+	12.8373i	0.255626	+	0.916951i
$197$		−	23.7727i		−	1.69374i	−0.531803	−	0.846868i	$-0.678485\pi$
$197$		−	23.7727i		−	1.69374i	0.531803	−	0.846868i	$-0.321515\pi$
$198$	1.01241	+	0.768775i	0.0719487	+	0.0546345i
$199$	−17.5747			−1.24584			−0.622918	−	0.782287i	$-0.714053\pi$
$199$	−17.5747			−1.24584			−0.622918	+	0.782287i	$0.714053\pi$
$200$	−7.12282	−	2.82502i	−0.503659	−	0.199759i
$201$	−18.3229			−1.29239
$202$	−2.22692	−	1.69102i	−0.156685	−	0.118979i
$203$			0.749498i			0.0526044i
$204$	4.44136	−	1.23816i	0.310958	−	0.0866882i
$205$		−	13.6913i		−	0.956244i
$206$	−1.97438	+	2.60008i	−0.137562	+	0.181156i
$207$	−3.99337			−0.277558
$208$	−8.05472	−	13.3237i	−0.558494	−	0.923834i
$209$	1.31799			0.0911671
$210$	1.44108	−	1.89777i	0.0994438	−	0.130959i
$211$			17.2804i			1.18963i	0.803863	+	0.594815i	$0.202775\pi$
$211$			17.2804i			1.18963i	−0.803863	+	0.594815i	$0.797225\pi$
$212$	−5.91800	+	1.64981i	−0.406450	+	0.113309i
$213$			13.3111i			0.912059i
$214$	−16.9390	−	12.8627i	−1.15792	−	0.879274i
$215$	−12.6960			−0.865860
$216$	−4.63815	+	11.6943i	−0.315586	+	0.795698i
$217$	1.71968			0.116739
$218$	−15.0926	−	11.4606i	−1.02220	−	0.776209i
$219$		−	29.3458i		−	1.98301i
$220$	−1.07139	−	3.84316i	−0.0722331	−	0.259106i
$221$		−	4.67630i		−	0.314562i
$222$	−1.94337	+	2.55924i	−0.130430	+	0.171765i
$223$	11.6027			0.776973			0.388487	−	0.921454i	$-0.372998\pi$
$223$	11.6027			0.776973			0.388487	+	0.921454i	$0.372998\pi$
$224$	−0.346282	+	3.26357i	−0.0231369	+	0.218057i
$225$	−1.84766			−0.123178
$226$	4.18833	−	5.51565i	0.278604	−	0.366896i
$227$		−	27.4484i		−	1.82182i	−0.412609	−	0.910908i	$-0.635382\pi$
$227$		−	27.4484i		−	1.82182i	0.412609	−	0.910908i	$-0.364618\pi$
$228$	−1.03057	−	3.69675i	−0.0682514	−	0.244823i
$229$		−	21.8680i		−	1.44508i	−0.691329	−	0.722540i	$-0.742975\pi$
$229$		−	21.8680i		−	1.44508i	0.691329	−	0.722540i	$-0.257025\pi$
$230$	9.98156	+	7.57953i	0.658165	+	0.499780i
$231$	−1.46725			−0.0965377
$232$	1.34714	−	3.39659i	0.0884439	−	0.222997i
$233$	−22.1975			−1.45421			−0.727103	−	0.686528i	$-0.759134\pi$
$233$	−22.1975			−1.45421			−0.727103	+	0.686528i	$0.759134\pi$
$234$	−2.98986	−	2.27036i	−0.195453	−	0.148418i
$235$		−	19.4583i		−	1.26932i
$236$	0.497361	−	0.138654i	0.0323755	−	0.00902557i
$237$			25.2007i			1.63696i
$238$	−0.596130	+	0.785049i	−0.0386414	+	0.0508872i
$239$	21.1350			1.36711			0.683555	−	0.729899i	$-0.260433\pi$
$239$	21.1350			1.36711			0.683555	+	0.729899i	$0.260433\pi$
$240$	−9.94172	+	6.01017i	−0.641735	+	0.387955i
$241$	−17.2437			−1.11076			−0.555382	−	0.831595i	$-0.687428\pi$
$241$	−17.2437			−1.11076			−0.555382	+	0.831595i	$0.687428\pi$
$242$	7.92215	−	10.4328i	0.509255	−	0.670643i
$243$			6.95957i			0.446457i
$244$	28.3587	−	7.90578i	1.81548	−	0.506116i
$245$		−	10.0855i		−	0.644338i
$246$	19.5497	+	14.8451i	1.24644	+	0.946491i
$247$	−3.89230			−0.247661
$248$	−7.79325	−	3.09092i	−0.494872	−	0.196274i
$249$	−7.11158			−0.450678
$250$	13.1419	+	9.97933i	0.831165	+	0.631148i
$251$		−	6.08851i		−	0.384303i	−0.981365	−	0.192152i	$-0.938453\pi$
$251$		−	6.08851i		−	0.384303i	0.981365	−	0.192152i	$-0.0615465\pi$
$252$	0.212509	+	0.762288i	0.0133868	+	0.0480196i
$253$		−	7.71717i		−	0.485174i
$254$	−2.23757	+	2.94667i	−0.140397	+	0.184891i
$255$	−3.48930			−0.218509
$256$	7.43518	−	14.1675i	0.464699	−	0.885469i
$257$	10.1741			0.634643			0.317322	−	0.948318i	$-0.397217\pi$
$257$	10.1741			0.634643			0.317322	+	0.948318i	$0.397217\pi$
$258$	13.7659	−	18.1285i	0.857029	−	1.12863i
$259$		−	0.687014i		−	0.0426890i
$260$	3.16404	+	11.3497i	0.196226	+	0.703877i
$261$		−	0.881077i		−	0.0545373i
$262$	2.97903	+	2.26213i	0.184045	+	0.139755i
$263$	−15.8414			−0.976822			−0.488411	−	0.872614i	$-0.662423\pi$
$263$	−15.8414			−0.976822			−0.488411	+	0.872614i	$0.662423\pi$
$264$	6.64929	+	2.63721i	0.409235	+	0.162309i
$265$	4.64940			0.285611
$266$	0.653433	+	0.496186i	0.0400645	+	0.0304231i
$267$			16.0542i			0.982500i
$268$	−18.3962	+	5.12846i	−1.12373	+	0.313271i
$269$			22.8533i			1.39339i	0.717367	+	0.696695i	$0.245347\pi$
$269$			22.8533i			1.39339i	−0.717367	+	0.696695i	$0.754653\pi$
$270$	5.75770	−	7.58238i	0.350403	−	0.461449i
$271$	12.2830			0.746142			0.373071	−	0.927803i	$-0.378305\pi$
$271$	12.2830			0.746142			0.373071	+	0.927803i	$0.378305\pi$
$272$	4.11259	−	2.48622i	0.249362	−	0.150749i
$273$	4.33309			0.262251
$274$	4.17395	−	5.49671i	0.252157	−	0.332068i
$275$		−	3.57060i		−	0.215316i
$276$	−21.6455	+	6.03429i	−1.30290	+	0.363221i
$277$			0.643776i			0.0386808i	0.999813	+	0.0193404i	$0.00615662\pi$
$277$			0.643776i			0.0386808i	−0.999813	+	0.0193404i	$0.993843\pi$
$278$	11.6385	+	8.83770i	0.698028	+	0.530050i
$279$	−2.02157			−0.121029
$280$	0.915671	−	2.30871i	0.0547218	−	0.137972i
$281$	−8.93027			−0.532735			−0.266368	−	0.963872i	$-0.585823\pi$
$281$	−8.93027			−0.532735			−0.266368	+	0.963872i	$0.585823\pi$
$282$	27.7844	+	21.0981i	1.65453	+	1.25638i
$283$			14.7397i			0.876187i	0.898929	+	0.438094i	$0.144346\pi$
$283$			14.7397i			0.876187i	−0.898929	+	0.438094i	$0.855654\pi$
$284$	3.72569	+	13.3643i	0.221079	+	0.793028i
$285$			2.90431i			0.172036i
$286$	4.38746	−	5.77789i	0.259436	−	0.341654i
$287$	−5.24801			−0.309780
$288$	0.407074	−	3.83651i	0.0239870	−	0.226069i
$289$	−15.5566			−0.915093
$290$	−1.67231	+	2.20228i	−0.0982015	+	0.129322i
$291$		−	32.7053i		−	1.91722i
$292$	−8.21373	−	29.4633i	−0.480672	−	1.72421i
$293$			23.9816i			1.40102i	0.713643	+	0.700509i	$0.247044\pi$
$293$			23.9816i			1.40102i	−0.713643	+	0.700509i	$0.752956\pi$
$294$	14.4009	+	10.9354i	0.839880	+	0.637766i
$295$	−0.390746			−0.0227501
$296$	−1.23483	+	3.11342i	−0.0717730	+	0.180964i
$297$	−5.86226			−0.340163
$298$	−9.40820	−	7.14415i	−0.545002	−	0.413850i
$299$			22.7905i			1.31801i
$300$	−10.0150	+	2.79196i	−0.578216	+	0.161194i
$301$			4.86649i			0.280500i
$302$	−5.00274	+	6.58816i	−0.287875	+	0.379106i
$303$	−3.79398			−0.217958
$304$	−2.06940	−	3.42310i	−0.118688	−	0.196328i
$305$	−22.2796			−1.27573
$306$	0.700784	−	0.922869i	0.0400612	−	0.0527569i
$307$		−	1.82132i		−	0.103948i	−0.998648	−	0.0519740i	$-0.983449\pi$
$307$		−	1.82132i		−	0.103948i	0.998648	−	0.0519740i	$-0.0165513\pi$
$308$	−1.47312	+	0.410674i	−0.0839388	+	0.0234003i
$309$			4.42974i			0.251999i
$310$	5.05300	+	3.83701i	0.286991	+	0.217928i
$311$	−4.53302			−0.257044			−0.128522	−	0.991707i	$-0.541023\pi$
$311$	−4.53302			−0.257044			−0.128522	+	0.991707i	$0.541023\pi$
$312$	−19.6368	−	7.78824i	−1.11171	−	0.440922i
$313$	12.4149			0.701730			0.350865	−	0.936426i	$-0.385888\pi$
$313$	12.4149			0.701730			0.350865	+	0.936426i	$0.385888\pi$
$314$	−0.407319	−	0.309299i	−0.0229863	−	0.0174547i
$315$		−	0.598882i		−	0.0337432i
$316$	7.05352	+	25.3015i	0.396792	+	1.42332i
$317$			23.0948i			1.29713i	0.761157	+	0.648567i	$0.224632\pi$
$317$			23.0948i			1.29713i	−0.761157	+	0.648567i	$0.775368\pi$
$318$	−5.04122	+	6.63883i	−0.282698	+	0.372287i
$319$	1.70268			0.0953317
$320$	−8.29931	+	8.81685i	−0.463945	+	0.492877i
$321$	−28.8588			−1.61074
$322$	2.90530	−	3.82602i	0.161906	−	0.213216i
$323$		−	1.20142i		−	0.0668490i
$324$	5.68275	+	20.3845i	0.315709	+	1.13247i
$325$			10.5448i			0.584918i
$326$	0.164472	+	0.124892i	0.00910924	+	0.00691714i
$327$	−25.7131			−1.42194
$328$	23.7830	+	9.43271i	1.31320	+	0.520834i
$329$	−7.45856			−0.411204
$330$	−4.31127	−	3.27378i	−0.237328	−	0.180216i
$331$		−	26.3743i		−	1.44966i	−0.688927	−	0.724831i	$-0.741918\pi$
$331$		−	26.3743i		−	1.44966i	0.688927	−	0.724831i	$-0.258082\pi$
$332$	−7.14004	+	1.99049i	−0.391861	+	0.109242i
$333$			0.807623i			0.0442575i
$334$	0.347749	−	0.457954i	0.0190280	−	0.0250581i
$335$	14.4527			0.789638
$336$	2.30375	+	3.81075i	0.125680	+	0.207894i
$337$	3.82102			0.208144			0.104072	−	0.994570i	$-0.466813\pi$
$337$	3.82102			0.208144			0.104072	+	0.994570i	$0.466813\pi$
$338$	−1.83879	+	2.42152i	−0.100017	+	0.131714i
$339$		−	9.39697i		−	0.510373i
$340$	−3.50327	+	0.976635i	−0.189991	+	0.0529655i
$341$		−	3.90669i		−	0.211559i
$342$	−0.768147	−	0.583295i	−0.0415366	−	0.0315410i
$343$	−7.92699			−0.428017
$344$	8.74697	−	22.0540i	0.471605	−	1.18907i
$345$	17.0055			0.915545
$346$	14.2438	+	10.8161i	0.765754	+	0.581478i
$347$			29.8808i			1.60408i	0.597268	+	0.802042i	$0.296253\pi$
$347$			29.8808i			1.60408i	−0.597268	+	0.802042i	$0.703747\pi$
$348$	−1.33137	−	4.77575i	−0.0713692	−	0.256007i
$349$			12.7016i			0.679902i	0.940443	+	0.339951i	$0.110411\pi$
$349$			12.7016i			0.679902i	−0.940443	+	0.339951i	$0.889589\pi$
$350$	1.34424	−	1.77024i	0.0718524	−	0.0946232i
$351$	17.3125			0.924073
$352$	7.41404	+	0.786668i	0.395170	+	0.0419296i
$353$	22.8398			1.21564			0.607820	−	0.794074i	$-0.292044\pi$
$353$	22.8398			1.21564			0.607820	+	0.794074i	$0.292044\pi$
$354$	0.423675	−	0.557942i	0.0225181	−	0.0296543i
$355$		−	10.4995i		−	0.557257i
$356$	4.49347	+	16.1184i	0.238153	+	0.854275i
$357$			1.33748i			0.0707870i
$358$	−6.25767	−	4.75178i	−0.330728	−	0.251140i
$359$	35.4003			1.86835			0.934177	−	0.356810i	$-0.116136\pi$
$359$	35.4003			1.86835			0.934177	+	0.356810i	$0.116136\pi$
$360$	−1.07642	+	2.71402i	−0.0567325	+	0.143042i
$361$	−1.00000			−0.0526316
$362$	−10.2876	−	7.81191i	−0.540703	−	0.410585i
$363$		−	17.7742i		−	0.932904i
$364$	4.35044	−	1.21281i	0.228025	−	0.0635684i
$365$			23.1475i			1.21159i
$366$	24.1572	−	31.8129i	1.26272	−	1.66288i
$367$	−17.2148			−0.898608			−0.449304	−	0.893379i	$-0.648328\pi$
$367$	−17.2148			−0.898608			−0.449304	+	0.893379i	$0.648328\pi$
$368$	−20.0432	+	12.1169i	−1.04482	+	0.631636i
$369$	6.16933			0.321163
$370$	1.53289	−	2.01868i	0.0796914	−	0.104946i
$371$		−	1.78216i		−	0.0925251i
$372$	−10.9577	+	3.05476i	−0.568128	+	0.158382i
$373$		−	20.3506i		−	1.05372i	−0.849953	−	0.526858i	$-0.823370\pi$
$373$		−	20.3506i		−	1.05372i	0.849953	−	0.526858i	$-0.176630\pi$
$374$	1.78344	+	1.35426i	0.0922196	+	0.0700273i
$375$	22.3897			1.15620
$376$	33.8008	+	13.4059i	1.74314	+	0.691358i
$377$	−5.02837			−0.258974
$378$	−2.90640	−	2.20698i	−0.149489	−	0.113515i
$379$			4.22765i			0.217160i	0.994088	+	0.108580i	$0.0346303\pi$
$379$			4.22765i			0.217160i	−0.994088	+	0.108580i	$0.965370\pi$
$380$	0.812898	+	2.91593i	0.0417008	+	0.149584i
$381$			5.02022i			0.257194i
$382$	4.68280	−	6.16682i	0.239593	−	0.315522i
$383$	9.71281			0.496301			0.248151	−	0.968721i	$-0.420177\pi$
$383$	9.71281			0.496301			0.248151	+	0.968721i	$0.420177\pi$
$384$	−3.59078	−	21.4104i	−0.183241	−	1.09259i
$385$	1.15734			0.0589834
$386$	14.5134	−	19.1129i	0.738714	−	0.972819i
$387$		−	5.72083i		−	0.290806i
$388$	−9.15403	−	32.8362i	−0.464725	−	1.66701i
$389$		−	22.3291i		−	1.13213i	−0.824361	−	0.566064i	$-0.808466\pi$
$389$		−	22.3291i		−	1.13213i	0.824361	−	0.566064i	$-0.191534\pi$
$390$	12.7321	+	9.66817i	0.644716	+	0.489567i
$391$	−7.03466			−0.355758
$392$	17.5194	+	6.94844i	0.884861	+	0.350949i
$393$	5.07534			0.256017
$394$	−26.7751	−	20.3317i	−1.34891	−	1.02430i
$395$		−	19.8778i		−	1.00016i
$396$	1.73173	−	0.482770i	0.0870229	−	0.0242601i
$397$		−	23.9210i		−	1.20056i	−0.799789	−	0.600281i	$-0.795055\pi$
$397$		−	23.9210i		−	1.20056i	0.799789	−	0.600281i	$-0.204945\pi$
$398$	−15.0308	+	19.7943i	−0.753428	+	0.992197i
$399$	1.11325			0.0557321
$400$	−9.27363	+	5.60628i	−0.463681	+	0.280314i
$401$	−16.5237			−0.825154			−0.412577	−	0.910923i	$-0.635371\pi$
$401$	−16.5237			−0.825154			−0.412577	+	0.910923i	$0.635371\pi$
$402$	−15.6707	+	20.6369i	−0.781585	+	1.02928i
$403$			11.5373i			0.574713i
$404$	−3.80916	+	1.06191i	−0.189513	+	0.0528321i
$405$		−	16.0148i		−	0.795783i
$406$	0.844155	+	0.641012i	0.0418947	+	0.0318129i
$407$	−1.56073			−0.0773625
$408$	2.40397	−	6.06122i	0.119014	−	0.300075i
$409$	16.0228			0.792278			0.396139	−	0.918191i	$-0.370350\pi$
$409$	16.0228			0.792278			0.396139	+	0.918191i	$0.370350\pi$
$410$	−15.4205	−	11.7096i	−0.761562	−	0.578295i
$411$		−	9.36470i		−	0.461926i
$412$	1.23986	+	4.44747i	0.0610834	+	0.219111i
$413$			0.149776i			0.00737002i
$414$	−3.41535	+	4.49771i	−0.167855	+	0.221050i
$415$	5.60949			0.275359
$416$	−21.8953	−	2.32320i	−1.07350	−	0.113904i
$417$	19.8283			0.970998
$418$	1.12722	−	1.48444i	0.0551339	−	0.0726064i
$419$			12.7496i			0.622858i	0.950269	+	0.311429i	$0.100808\pi$
$419$			12.7496i			0.622858i	−0.950269	+	0.311429i	$0.899192\pi$
$420$	−0.904957	−	3.24615i	−0.0441574	−	0.158396i
$421$			1.89293i			0.0922560i	0.998936	+	0.0461280i	$0.0146882\pi$
$421$			1.89293i			0.0922560i	−0.998936	+	0.0461280i	$0.985312\pi$
$422$	19.4628	+	14.7791i	0.947434	+	0.719437i
$423$	8.76796			0.426313
$424$	−3.20323	+	8.07642i	−0.155563	+	0.392225i
$425$	−3.25482			−0.157882
$426$	14.9922	+	11.3844i	0.726373	+	0.551574i
$427$			8.53999i			0.413279i
$428$	−28.9743	+	8.07740i	−1.40052	+	0.390436i
$429$		−	9.84374i		−	0.475260i
$430$	−10.8583	+	14.2994i	−0.523635	+	0.689580i
$431$	37.2166			1.79266			0.896331	−	0.443386i	$-0.146223\pi$
$431$	37.2166			1.79266			0.896331	+	0.443386i	$0.146223\pi$
$432$	9.20445	+	15.2255i	0.442849	+	0.732539i
$433$	−36.0314			−1.73156			−0.865780	−	0.500425i	$-0.833177\pi$
$433$	−36.0314			−1.73156			−0.865780	+	0.500425i	$0.833177\pi$
$434$	1.47076	−	1.93686i	0.0705988	−	0.0929723i
$435$			3.75201i			0.179895i
$436$	−25.8160	+	7.19693i	−1.23636	+	0.344671i
$437$			5.85527i			0.280095i
$438$	−33.0520	−	25.0982i	−1.57929	−	1.19924i
$439$	−18.6188			−0.888629			−0.444315	−	0.895871i	$-0.646553\pi$
$439$	−18.6188			−0.888629			−0.444315	+	0.895871i	$0.646553\pi$
$440$	−5.24484	−	2.08018i	−0.250038	−	0.0991689i
$441$	4.54453			0.216406
$442$	−5.26689	−	3.99943i	−0.250520	−	0.190233i
$443$			2.26887i			0.107797i	0.998546	+	0.0538987i	$0.0171648\pi$
$443$			2.26887i			0.107797i	−0.998546	+	0.0538987i	$0.982835\pi$
$444$	1.22038	+	4.37761i	0.0579167	+	0.207752i
$445$		−	12.6633i		−	0.600296i
$446$	9.92326	−	13.0680i	0.469880	−	0.618789i
$447$	−16.0287			−0.758130
$448$	3.37958	+	3.18120i	0.159670	+	0.150298i
$449$	0.248909			0.0117467			0.00587337	−	0.999983i	$-0.498130\pi$
$449$	0.248909			0.0117467			0.00587337	+	0.999983i	$0.498130\pi$
$450$	−1.58022	+	2.08101i	−0.0744925	+	0.0980999i
$451$			11.9222i			0.561395i
$452$	−2.63016	−	9.43458i	−0.123712	−	0.443765i
$453$			11.2242i			0.527358i
$454$	−30.9150	−	23.4754i	−1.45091	−	1.10176i
$455$	−3.41787			−0.160232
$456$	−5.04503	−	2.00094i	−0.236255	−	0.0937024i
$457$	−6.98767			−0.326869			−0.163435	−	0.986554i	$-0.552257\pi$
$457$	−6.98767			−0.326869			−0.163435	+	0.986554i	$0.552257\pi$
$458$	−24.6298	−	18.7027i	−1.15088	−	0.873922i
$459$			5.34379i			0.249427i
$460$	17.0736	−	4.75974i	0.796059	−	0.221924i
$461$		−	34.1624i		−	1.59110i	−0.605888	−	0.795550i	$-0.707182\pi$
$461$		−	34.1624i		−	1.59110i	0.605888	−	0.795550i	$-0.292818\pi$
$462$	−1.25487	+	1.65255i	−0.0583818	+	0.0768836i
$463$	34.5311			1.60480			0.802399	−	0.596788i	$-0.203556\pi$
$463$	34.5311			1.60480			0.802399	+	0.596788i	$0.203556\pi$
$464$	−2.67341	−	4.42222i	−0.124110	−	0.205296i
$465$	8.60875			0.399221
$466$	−18.9845	+	25.0009i	−0.879441	+	1.15815i
$467$			39.6496i			1.83476i	0.398008	+	0.917382i	$0.369702\pi$
$467$			39.6496i			1.83476i	−0.398008	+	0.917382i	$0.630298\pi$
$468$	−5.11418	+	1.42572i	−0.236403	+	0.0659041i
$469$		−	5.53987i		−	0.255808i
$470$	−21.9158	−	16.6418i	−1.01090	−	0.767631i
$471$	−0.693945			−0.0319753
$472$	0.269206	−	0.678759i	0.0123912	−	0.0312424i
$473$	11.0555			0.508332
$474$	28.3834	+	21.5530i	1.30369	+	0.989962i
$475$			2.70913i			0.124304i
$476$	0.374353	+	1.34284i	0.0171585	+	0.0615488i
$477$			2.09503i			0.0959247i
$478$	18.0758	−	23.8042i	0.826770	−	1.08878i
$479$	−24.8669			−1.13620			−0.568098	−	0.822961i	$-0.692321\pi$
$479$	−24.8669			−1.13620			−0.568098	+	0.822961i	$0.692321\pi$
$480$	−1.73350	+	16.3375i	−0.0791229	+	0.745703i
$481$	4.60917			0.210160
$482$	−14.7478	+	19.4215i	−0.671742	+	0.884624i
$483$		−	6.51836i		−	0.296596i
$484$	−4.97489	−	17.8453i	−0.226132	−	0.811152i
$485$			25.7974i			1.17140i
$486$	7.83852	+	5.95221i	0.355563	+	0.269998i
$487$	−39.7320			−1.80043			−0.900214	−	0.435448i	$-0.856590\pi$
$487$	−39.7320			−1.80043			−0.900214	+	0.435448i	$0.856590\pi$
$488$	15.3497	−	38.7016i	0.694847	−	1.75194i
$489$	0.280209			0.0126715
$490$	−11.3592	−	8.62566i	−0.513157	−	0.389668i
$491$		−	3.45561i		−	0.155949i	−0.996955	−	0.0779747i	$-0.975155\pi$
$491$		−	3.45561i		−	0.155949i	0.996955	−	0.0779747i	$-0.0248453\pi$
$492$	33.4400	−	9.32234i	1.50759	−	0.420283i
$493$		−	1.55209i		−	0.0699027i
$494$	−3.32891	+	4.38387i	−0.149775	+	0.197240i
$495$	−1.36052			−0.0611506
$496$	−10.1465	+	6.13397i	−0.455592	+	0.275423i
$497$	−4.02457			−0.180527
$498$	−6.08221	+	8.00973i	−0.272550	+	0.358924i
$499$			17.5837i			0.787156i	0.919291	+	0.393578i	$0.128763\pi$
$499$			17.5837i			0.787156i	−0.919291	+	0.393578i	$0.871237\pi$
$500$	22.4793	−	6.26674i	1.00531	−	0.280257i
$501$		−	0.780212i		−	0.0348573i
$502$	−6.85745	−	5.20723i	−0.306063	−	0.232410i
$503$	2.72712			0.121596			0.0607981	−	0.998150i	$-0.480635\pi$
$503$	2.72712			0.121596			0.0607981	+	0.998150i	$0.480635\pi$
$504$	1.04031	+	0.412603i	0.0463391	+	0.0183788i
$505$	2.99262			0.133170
$506$	−8.69180	−	6.60015i	−0.386398	−	0.293412i
$507$			4.12553i			0.183221i
$508$	1.40513	+	5.04031i	0.0623425	+	0.223628i
$509$		−	6.73123i		−	0.298356i	−0.988810	−	0.149178i	$-0.952337\pi$
$509$		−	6.73123i		−	0.298356i	0.988810	−	0.149178i	$-0.0476628\pi$
$510$	−2.98424	+	3.92998i	−0.132145	+	0.174022i
$511$	8.87264			0.392503
$512$	−9.59779	−	20.4910i	−0.424166	−	0.905584i
$513$	4.44789			0.196379
$514$	8.70146	−	11.4590i	0.383805	−	0.505436i
$515$		−	3.49410i		−	0.153968i
$516$	−8.64462	−	31.0090i	−0.380558	−	1.36509i
$517$			16.9441i			0.745198i
$518$	−0.773780	−	0.587572i	−0.0339979	−	0.0258164i
$519$	24.2671			1.06521
$520$	15.4891	+	6.14323i	0.679244	+	0.269398i
$521$	38.2190			1.67440			0.837202	−	0.546894i	$-0.184190\pi$
$521$	38.2190			1.67440			0.837202	+	0.546894i	$0.184190\pi$
$522$	−0.992352	−	0.753545i	−0.0434340	−	0.0329818i
$523$		−	5.37182i		−	0.234893i	−0.993079	−	0.117447i	$-0.962529\pi$
$523$		−	5.37182i		−	0.234893i	0.993079	−	0.117447i	$-0.0374709\pi$
$524$	5.09566	−	1.42056i	0.222605	−	0.0620574i
$525$		−	3.01594i		−	0.131626i
$526$	−13.5484	+	17.8421i	−0.590739	+	0.777951i
$527$	−3.56118			−0.155127
$528$	8.65711	−	5.23357i	0.376752	−	0.227762i
$529$	11.2842			0.490616
$530$	3.97643	−	5.23660i	0.172725	−	0.227463i
$531$		−	0.176071i		−	0.00764081i
$532$	1.11770	−	0.311591i	0.0484586	−	0.0135092i
$533$		−	35.2089i		−	1.52506i
$534$	18.0817	+	13.7304i	0.782473	+	0.594173i
$535$	22.7633			0.984143
$536$	−9.95729	+	25.1057i	−0.430090	+	1.08440i
$537$	−10.6611			−0.460062
$538$	25.7395	+	19.5454i	1.10971	+	0.842662i
$539$			8.78229i			0.378280i
$540$	−3.61568	−	12.9697i	−0.155594	−	0.558129i
$541$			34.3497i			1.47681i	0.674359	+	0.738404i	$0.264420\pi$
$541$			34.3497i			1.47681i	−0.674359	+	0.738404i	$0.735580\pi$
$542$	10.5051	−	13.8343i	0.451234	−	0.594235i
$543$	−17.5269			−0.752150
$544$	0.717095	−	6.75834i	0.0307452	−	0.289761i
$545$	20.2820			0.868786
$546$	3.70590	−	4.88034i	0.158598	−	0.208859i
$547$		−	2.58358i		−	0.110466i	−0.998473	−	0.0552330i	$-0.982410\pi$
$547$		−	2.58358i		−	0.110466i	0.998473	−	0.0552330i	$-0.0175902\pi$
$548$	−2.62112	−	9.40218i	−0.111969	−	0.401641i
$549$		−	10.0392i		−	0.428464i
$550$	−4.02155	−	3.05378i	−0.171480	−	0.130214i
$551$	−1.29188			−0.0550358
$552$	−11.7160	+	29.5400i	−0.498667	+	1.25731i
$553$	−7.61936			−0.324008
$554$	0.725081	+	0.550593i	0.0308057	+	0.0233924i
$555$		−	3.43921i		−	0.145986i
$556$	19.9077	−	5.54983i	0.844275	−	0.235365i
$557$		−	0.498941i		−	0.0211408i	−0.999944	−	0.0105704i	$-0.996635\pi$
$557$		−	0.498941i		−	0.0211408i	0.999944	−	0.0105704i	$-0.00336472\pi$
$558$	−1.72896	+	2.27689i	−0.0731928	+	0.0963883i
$559$	−32.6492			−1.38092
$560$	−1.81716	−	3.00586i	−0.0767890	−	0.127021i
$561$	3.03843			0.128283
$562$	−7.63766	+	10.0581i	−0.322175	+	0.424276i
$563$			32.5553i			1.37204i	0.727581	+	0.686021i	$0.240644\pi$
$563$			32.5553i			1.37204i	−0.727581	+	0.686021i	$0.759356\pi$
$564$	47.5254	−	13.2491i	2.00118	−	0.557886i
$565$			7.41216i			0.311832i
$566$	16.6013	+	12.6062i	0.697804	+	0.529880i
$567$	−6.13863			−0.257798
$568$	18.2386	+	7.23371i	0.765275	+	0.303520i
$569$	13.6834			0.573636			0.286818	−	0.957985i	$-0.407402\pi$
$569$	13.6834			0.573636			0.286818	+	0.957985i	$0.407402\pi$
$570$	3.27110	+	2.48392i	0.137011	+	0.104040i
$571$			12.2520i			0.512732i	0.966580	+	0.256366i	$0.0825253\pi$
$571$			12.2520i			0.512732i	−0.966580	+	0.256366i	$0.917475\pi$
$572$	−2.75520	−	9.88314i	−0.115201	−	0.413235i
$573$		−	10.5064i		−	0.438909i
$574$	−4.48839	+	5.91081i	−0.187342	+	0.246712i
$575$	15.8627			0.661521
$576$	−3.97289	−	3.73968i	−0.165537	−	0.155820i
$577$	14.6672			0.610605			0.305302	−	0.952255i	$-0.401242\pi$
$577$	14.6672			0.610605			0.305302	+	0.952255i	$0.401242\pi$
$578$	−13.3048	+	17.5213i	−0.553409	+	0.728789i
$579$		−	32.5624i		−	1.35325i
$580$	1.05017	+	3.76703i	0.0436057	+	0.156417i
$581$		−	2.15017i		−	0.0892040i
$582$	−36.8358	−	27.9714i	−1.52689	−	1.15945i
$583$	−4.04864			−0.167677
$584$	−40.2092	−	15.9476i	−1.66387	−	0.659915i
$585$	4.01789			0.166119
$586$	27.0103	+	20.5104i	1.11579	+	0.847275i
$587$		−	5.53206i		−	0.228333i	−0.993462	−	0.114166i	$-0.963580\pi$
$587$		−	5.53206i		−	0.228333i	0.993462	−	0.114166i	$-0.0364197\pi$
$588$	24.6330	−	6.86714i	1.01585	−	0.283196i
$589$			2.96413i			0.122135i
$590$	−0.334187	+	0.440095i	−0.0137583	+	0.0181184i
$591$	−45.6165			−1.87641
$592$	2.45053	+	4.05355i	0.100716	+	0.166600i
$593$	21.5870			0.886470			0.443235	−	0.896405i	$-0.353831\pi$
$593$	21.5870			0.886470			0.443235	+	0.896405i	$0.353831\pi$
$594$	−5.01373	+	6.60263i	−0.205716	+	0.270909i
$595$		−	1.05498i		−	0.0432500i
$596$	−16.0928	+	4.48633i	−0.659188	+	0.183767i
$597$			33.7233i			1.38020i
$598$	25.6688	+	19.4917i	1.04967	+	0.797073i
$599$	−28.3513			−1.15840			−0.579202	−	0.815184i	$-0.696636\pi$
$599$	−28.3513			−1.15840			−0.579202	+	0.815184i	$0.696636\pi$
$600$	−5.42081	+	13.6677i	−0.221303	+	0.557980i
$601$	−21.9758			−0.896410			−0.448205	−	0.893931i	$-0.647936\pi$
$601$	−21.9758			−0.896410			−0.448205	+	0.893931i	$0.647936\pi$
$602$	5.48110	+	4.16209i	0.223393	+	0.169634i
$603$			6.51243i			0.265207i
$604$	3.14158	+	11.2691i	0.127829	+	0.458534i
$605$			14.0200i			0.569993i
$606$	−3.24482	+	4.27313i	−0.131812	+	0.173584i
$607$	−7.89484			−0.320441			−0.160221	−	0.987081i	$-0.551221\pi$
$607$	−7.89484			−0.320441			−0.160221	+	0.987081i	$0.551221\pi$
$608$	−5.62528	−	0.596871i	−0.228135	−	0.0242063i
$609$	1.43818			0.0582780
$610$	−19.0548	+	25.0934i	−0.771505	+	1.01600i
$611$		−	50.0394i		−	2.02438i
$612$	−0.440073	−	1.57858i	−0.0177889	−	0.0638102i
$613$		−	29.5174i		−	1.19220i	−0.802912	−	0.596098i	$-0.796717\pi$
$613$		−	29.5174i		−	1.19220i	0.802912	−	0.596098i	$-0.203283\pi$
$614$	−2.05134	−	1.55769i	−0.0827853	−	0.0628633i
$615$	−26.2717			−1.05938
$616$	−0.797354	+	2.01040i	−0.0321263	+	0.0810012i
$617$	3.08379			0.124149			0.0620744	−	0.998072i	$-0.480228\pi$
$617$	3.08379			0.124149			0.0620744	+	0.998072i	$0.480228\pi$
$618$	4.98919	+	3.78856i	0.200695	+	0.152398i
$619$			10.9487i			0.440066i	0.975492	+	0.220033i	$0.0706164\pi$
$619$			10.9487i			0.440066i	−0.975492	+	0.220033i	$0.929384\pi$
$620$	8.64320	−	2.40954i	0.347119	−	0.0967693i
$621$		−	26.0436i		−	1.04509i
$622$	−3.87689	+	5.10551i	−0.155449	+	0.204712i
$623$	−4.85394			−0.194469
$624$	−25.5663	+	15.4558i	−1.02347	+	0.618729i
$625$	−4.11492			−0.164597
$626$	10.6179	−	13.9828i	0.424376	−	0.558865i
$627$		−	2.52903i		−	0.101000i
$628$	−0.696723	+	0.194231i	−0.0278023	+	0.00775067i
$629$			1.42270i			0.0567267i
$630$	−0.674517	−	0.512197i	−0.0268734	−	0.0204064i
$631$	−20.7432			−0.825773			−0.412886	−	0.910783i	$-0.635479\pi$
$631$	−20.7432			−0.825773			−0.412886	+	0.910783i	$0.635479\pi$
$632$	34.5295	+	13.6949i	1.37351	+	0.544756i
$633$	33.1586			1.31794
$634$	26.0116	+	19.7520i	1.03305	+	0.784451i
$635$		−	3.95986i		−	0.157142i
$636$	3.16575	+	11.3558i	0.125530	+	0.450287i
$637$		−	25.9360i		−	1.02762i
$638$	1.45622	−	1.91772i	0.0576525	−	0.0759231i
$639$	4.73110			0.187160
$640$	2.83234	+	16.8881i	0.111958	+	0.667562i
$641$	−34.5310			−1.36389			−0.681946	−	0.731403i	$-0.738866\pi$
$641$	−34.5310			−1.36389			−0.681946	+	0.731403i	$0.738866\pi$
$642$	−24.6816	+	32.5035i	−0.974106	+	1.28281i
$643$		−	21.5300i		−	0.849062i	−0.905413	−	0.424531i	$-0.860439\pi$
$643$		−	21.5300i		−	0.849062i	0.905413	−	0.424531i	$-0.139561\pi$
$644$	−1.82445	−	6.54446i	−0.0718935	−	0.257888i
$645$			24.3618i			0.959245i
$646$	−1.35316	−	1.02752i	−0.0532392	−	0.0404274i
$647$	22.7527			0.894502			0.447251	−	0.894409i	$-0.352403\pi$
$647$	22.7527			0.894502			0.447251	+	0.894409i	$0.352403\pi$
$648$	27.8191	+	11.0335i	1.09284	+	0.433437i
$649$	0.340256			0.0133562
$650$	11.8765	+	9.01846i	0.465835	+	0.353733i
$651$		−	3.29981i		−	0.129330i
$652$	0.281331	−	0.0784288i	0.0110178	−	0.00307151i
$653$			35.6805i			1.39629i	0.715958	+	0.698143i	$0.245990\pi$
$653$			35.6805i			1.39629i	−0.715958	+	0.698143i	$0.754010\pi$
$654$	−21.9912	+	28.9605i	−0.859925	+	1.13244i
$655$	−4.00334			−0.156423
$656$	30.9646	−	18.7193i	1.20896	−	0.730866i
$657$	−10.4303			−0.406924
$658$	−6.37897	+	8.40053i	−0.248678	+	0.327487i
$659$			35.8589i			1.39686i	0.715676	+	0.698432i	$0.246119\pi$
$659$			35.8589i			1.39686i	−0.715676	+	0.698432i	$0.753881\pi$
$660$	−7.37448	+	2.05584i	−0.287051	+	0.0800236i
$661$			25.4409i			0.989537i	0.869025	+	0.494769i	$0.164747\pi$
$661$			25.4409i			0.989537i	−0.869025	+	0.494769i	$0.835253\pi$
$662$	−29.7052	−	22.5567i	−1.15453	−	0.876693i
$663$	−8.97315			−0.348488
$664$	−3.86468	+	9.74416i	−0.149979	+	0.378147i
$665$	−0.878110			−0.0340516
$666$	0.909621	+	0.690724i	0.0352471	+	0.0267650i
$667$			7.56429i			0.292890i
$668$	−0.218377	−	0.783335i	−0.00844925	−	0.0303082i
$669$		−	22.2639i		−	0.860772i
$670$	12.3608	−	16.2780i	0.477539	−	0.628876i
$671$	19.4008			0.748959
$672$	6.26233	+	0.664465i	0.241574	+	0.0256323i
$673$	34.2142			1.31886			0.659431	−	0.751765i	$-0.270797\pi$
$673$	34.2142			1.31886			0.659431	+	0.751765i	$0.270797\pi$
$674$	3.26795	−	4.30359i	0.125877	−	0.165768i
$675$		−	12.0499i		−	0.463802i
$676$	1.15471	+	4.14204i	0.0444120	+	0.159309i
$677$		−	37.9103i		−	1.45701i	−0.685040	−	0.728505i	$-0.740215\pi$
$677$		−	37.9103i		−	1.45701i	0.685040	−	0.728505i	$-0.259785\pi$
$678$	−10.5837	−	8.03681i	−0.406466	−	0.308652i
$679$	9.88837			0.379481
$680$	−1.89621	+	4.78098i	−0.0727164	+	0.183342i
$681$	−52.6696			−2.01830
$682$	−4.40008	−	3.34121i	−0.168488	−	0.127942i
$683$		−	30.3542i		−	1.16147i	−0.814092	−	0.580736i	$-0.802765\pi$
$683$		−	30.3542i		−	1.16147i	0.814092	−	0.580736i	$-0.197235\pi$
$684$	−1.31392	+	0.366293i	−0.0502391	+	0.0140056i
$685$			7.38671i			0.282232i
$686$	−6.77960	+	8.92812i	−0.258846	+	0.340877i
$687$	−41.9616			−1.60094
$688$	−17.3584	−	28.7135i	−0.661785	−	1.09469i
$689$	11.9565			0.455506
$690$	14.5440	−	19.1532i	0.553682	−	0.729149i
$691$		−	3.50694i		−	0.133410i	−0.997773	−	0.0667052i	$-0.978751\pi$
$691$		−	3.50694i		−	0.133410i	0.997773	−	0.0667052i	$-0.0212487\pi$
$692$	24.3642	−	6.79222i	0.926189	−	0.258201i
$693$			0.521498i			0.0198101i
$694$	33.6545	+	25.5557i	1.27751	+	0.970081i
$695$	−15.6402			−0.593268
$696$	−6.51756	−	2.58496i	−0.247048	−	0.0979828i
$697$	10.8678			0.411647
$698$	14.3058	+	10.8631i	0.541481	+	0.411175i
$699$			42.5938i			1.61105i
$700$	−0.844143	−	3.02801i	−0.0319056	−	0.114448i
$701$		−	13.2168i		−	0.499190i	−0.968350	−	0.249595i	$-0.919703\pi$
$701$		−	13.2168i		−	0.499190i	0.968350	−	0.249595i	$-0.0802975\pi$
$702$	14.8066	−	19.4990i	0.558840	−	0.735941i
$703$	1.18418			0.0446621
$704$	7.22692	−	7.67759i	0.272375	−	0.289360i
$705$	−37.3378			−1.40622
$706$	19.5339	−	25.7244i	0.735167	−	0.968149i
$707$		−	1.14710i		−	0.0431411i
$708$	−0.266056	−	0.954365i	−0.00999901	−	0.0358672i
$709$			23.2882i			0.874605i	0.899314	+	0.437302i	$0.144066\pi$
$709$			23.2882i			0.874605i	−0.899314	+	0.437302i	$0.855934\pi$
$710$	−11.8256	−	8.97978i	−0.443805	−	0.337005i
$711$	8.95699			0.335913
$712$	21.9972	+	8.72441i	0.824379	+	0.326961i
$713$	17.3558			0.649979
$714$	1.50640	+	1.14389i	0.0563755	+	0.0428089i
$715$			7.76457i			0.290378i
$716$	−10.7038	+	2.98399i	−0.400020	+	0.111517i
$717$		−	40.5551i		−	1.51456i
$718$	30.2763	−	39.8711i	1.12990	−	1.48798i
$719$	0.192843			0.00719184			0.00359592	−	0.999994i	$-0.498855\pi$
$719$	0.192843			0.00719184			0.00359592	+	0.999994i	$0.498855\pi$
$720$	2.13617	+	3.53355i	0.0796104	+	0.131688i
$721$	−1.33932			−0.0498789
$722$	−0.855255	+	1.12629i	−0.0318293	+	0.0419163i
$723$			33.0882i			1.23056i
$724$	−17.5970	+	4.90567i	−0.653988	+	0.182318i
$725$			3.49987i			0.129982i
$726$	−20.0190	−	15.2015i	−0.742974	−	0.564180i
$727$	14.5604			0.540014			0.270007	−	0.962858i	$-0.412974\pi$
$727$	14.5604			0.540014			0.270007	+	0.962858i	$0.412974\pi$
$728$	2.35476	−	5.93713i	0.0872731	−	0.220045i
$729$	−18.3883			−0.681047
$730$	26.0709	+	19.7970i	0.964926	+	0.732720i
$731$		−	10.0777i		−	0.372739i
$732$	−15.1701	−	54.4162i	−0.560701	−	2.01128i
$733$		−	29.0856i		−	1.07430i	−0.843487	−	0.537150i	$-0.819501\pi$
$733$		−	29.0856i		−	1.07430i	0.843487	−	0.537150i	$-0.180499\pi$
$734$	−14.7231	+	19.3890i	−0.543439	+	0.715660i
$735$	−19.3526			−0.713831
$736$	−3.49484	+	32.9375i	−0.128822	+	1.21409i
$737$	−12.5853			−0.463584
$738$	5.27635	−	6.94848i	0.194225	−	0.255777i
$739$			28.8090i			1.05975i	0.848074	+	0.529877i	$0.177762\pi$
$739$			28.8090i			1.05975i	−0.848074	+	0.529877i	$0.822238\pi$
$740$	−0.962615	−	3.45298i	−0.0353864	−	0.126934i
$741$			7.46877i			0.274372i
$742$	−2.00724	−	1.52420i	−0.0736879	−	0.0559552i
$743$	42.2025			1.54826			0.774129	−	0.633027i	$-0.218188\pi$
$743$	42.2025			1.54826			0.774129	+	0.633027i	$0.218188\pi$
$744$	−5.93104	+	14.9541i	−0.217442	+	0.548245i
$745$	12.6431			0.463208
$746$	−22.9208	−	17.4050i	−0.839191	−	0.637242i
$747$			2.52764i			0.0924816i
$748$	3.05060	−	0.850440i	0.111541	−	0.0310952i
$749$		−	8.72538i		−	0.318818i
$750$	19.1489	−	25.2174i	0.699219	−	0.920808i
$751$	2.64036			0.0963483			0.0481741	−	0.998839i	$-0.484660\pi$
$751$	2.64036			0.0963483			0.0481741	+	0.998839i	$0.484660\pi$
$752$	44.0073	−	26.6042i	1.60478	−	0.970155i
$753$	−11.6830			−0.425751
$754$	−4.30054	+	5.66343i	−0.156617	+	0.206250i
$755$		−	8.85344i		−	0.322210i
$756$	−4.97142	+	1.38592i	−0.180809	+	0.0504056i
$757$			4.51764i			0.164197i	0.996624	+	0.0820983i	$0.0261621\pi$
$757$			4.51764i			0.164197i	−0.996624	+	0.0820983i	$0.973838\pi$
$758$	4.76158	+	3.61572i	0.172948	+	0.131329i
$759$	−14.8081			−0.537502
$760$	3.97943	+	1.57830i	0.144349	+	0.0572511i
$761$	−23.5124			−0.852323			−0.426162	−	0.904647i	$-0.640134\pi$
$761$	−23.5124			−0.852323			−0.426162	+	0.904647i	$0.640134\pi$
$762$	5.65424	+	4.29357i	0.204832	+	0.155540i
$763$		−	7.77428i		−	0.281448i
$764$	−2.94067	−	10.5484i	−0.106390	−	0.381628i
$765$			1.24019i			0.0448392i
$766$	8.30693	−	10.9395i	0.300142	−	0.395259i
$767$	−1.00485			−0.0362830
$768$	−27.1854	−	14.2671i	−0.980969	−	0.514818i
$769$	−29.6727			−1.07002			−0.535012	−	0.844845i	$-0.679693\pi$
$769$	−29.6727			−1.07002			−0.535012	+	0.844845i	$0.679693\pi$
$770$	0.989819	−	1.30350i	0.0356706	−	0.0469750i
$771$		−	19.5227i		−	0.703091i
$772$	−9.11403	−	32.6928i	−0.328021	−	1.17664i
$773$		−	10.1647i		−	0.365598i	−0.983150	−	0.182799i	$-0.941484\pi$
$773$		−	10.1647i		−	0.365598i	0.983150	−	0.182799i	$-0.0585158\pi$
$774$	−6.44334	−	4.89277i	−0.231601	−	0.175867i
$775$	8.03023			0.288454
$776$	−44.8123	−	17.7732i	−1.60867	−	0.638022i
$777$	−1.31828			−0.0472931
$778$	−25.1491	−	19.0970i	−0.901638	−	0.684662i
$779$		−	9.04577i		−	0.324098i
$780$	21.7784	−	6.07135i	0.779792	−	0.217389i
$781$			9.14285i			0.327157i
$782$	−6.01643	+	7.92309i	−0.215147	+	0.283329i
$783$	5.74612			0.205350
$784$	22.8095	−	13.7893i	0.814625	−	0.492473i
$785$	0.547372			0.0195365
$786$	4.34071	−	5.71633i	0.154828	−	0.203895i
$787$			18.8481i			0.671863i	0.941886	+	0.335931i	$0.109051\pi$
$787$			18.8481i			0.671863i	−0.941886	+	0.335931i	$0.890949\pi$
$788$	−45.7991	+	12.7678i	−1.63152	+	0.454833i
$789$			30.3974i			1.08217i
$790$	−22.3883	−	17.0006i	−0.796540	−	0.604855i
$791$	2.84115			0.101020
$792$	0.937334	−	2.36333i	0.0333067	−	0.0839774i
$793$	−57.2947			−2.03459
$794$	−26.9421	−	20.4586i	−0.956140	−	0.726049i
$795$		−	8.92154i		−	0.316414i
$796$	9.43896	+	33.8583i	0.334555	+	1.20008i
$797$		−	13.9098i		−	0.492709i	−0.969180	−	0.246355i	$-0.920767\pi$
$797$		−	13.9098i		−	0.492709i	0.969180	−	0.246355i	$-0.0792328\pi$
$798$	0.952111	−	1.25384i	0.0337044	−	0.0443856i
$799$	15.4455			0.546423
$800$	−1.61700	+	15.2396i	−0.0571697	+	0.538802i
$801$	5.70608			0.201614
$802$	−14.1320	+	18.6105i	−0.499018	+	0.657161i
$803$		−	20.1565i		−	0.711308i
$804$	9.84078	+	35.2997i	0.347058	+	1.24492i
$805$			5.14157i			0.181217i
$806$	12.9944	+	9.86732i	0.457707	+	0.347562i
$807$	43.8522			1.54367
$808$	−2.06178	+	5.19844i	−0.0725332	+	0.182881i
$809$	19.7630			0.694831			0.347415	−	0.937711i	$-0.387059\pi$
$809$	19.7630			0.694831			0.347415	+	0.937711i	$0.387059\pi$
$810$	−18.0374	−	13.6968i	−0.633770	−	0.481255i
$811$		−	30.1099i		−	1.05730i	−0.848839	−	0.528651i	$-0.822698\pi$
$811$		−	30.1099i		−	1.05730i	0.848839	−	0.528651i	$-0.177302\pi$
$812$	1.44394	−	0.402538i	0.0506722	−	0.0141263i
$813$		−	23.5694i		−	0.826615i
$814$	−1.33482	+	1.75784i	−0.0467855	+	0.0616123i
$815$	−0.221024			−0.00774213
$816$	−4.77071	−	7.89147i	−0.167008	−	0.276257i
$817$	−8.38816			−0.293465
$818$	13.7036	−	18.0464i	0.479135	−	0.630978i
$819$		−	1.54010i		−	0.0538153i
$820$	−26.3769	+	7.35330i	−0.921120	+	0.256788i
$821$		−	26.1788i		−	0.913645i	−0.889558	−	0.456823i	$-0.848987\pi$
$821$		−	26.1788i		−	0.913645i	0.889558	−	0.456823i	$-0.151013\pi$
$822$	−10.5474	−	8.00921i	−0.367883	−	0.279353i
$823$	41.9817			1.46339			0.731696	−	0.681631i	$-0.238729\pi$
$823$	41.9817			1.46339			0.731696	+	0.681631i	$0.238729\pi$
$824$	6.06955	+	2.40728i	0.211443	+	0.0838615i
$825$	−6.85148			−0.238538
$826$	0.168692	+	0.128097i	0.00586956	+	0.00445707i
$827$			20.6394i			0.717703i	0.933395	+	0.358851i	$0.116832\pi$
$827$			20.6394i			0.717703i	−0.933395	+	0.358851i	$0.883168\pi$
$828$	2.14475	+	7.69337i	0.0745350	+	0.267363i
$829$			36.6292i			1.27218i	0.771613	+	0.636092i	$0.219450\pi$
$829$			36.6292i			1.27218i	−0.771613	+	0.636092i	$0.780550\pi$
$830$	4.79754	−	6.31793i	0.166525	−	0.219299i
$831$	1.23531			0.0428526
$832$	−21.3426	+	22.6736i	−0.739923	+	0.786065i
$833$	8.00558			0.277377
$834$	16.9583	−	22.3325i	0.587217	−	0.773313i
$835$			0.615418i			0.0212974i
$836$	−0.707861	−	2.53915i	−0.0244819	−	0.0878184i
$837$		−	13.1841i		−	0.455710i
$838$	14.3598	+	10.9042i	0.496051	+	0.376678i
$839$	3.71855			0.128379			0.0641893	−	0.997938i	$-0.479554\pi$
$839$	3.71855			0.128379			0.0641893	+	0.997938i	$0.479554\pi$
$840$	−4.43009	−	1.75704i	−0.152853	−	0.0606237i
$841$	27.3311			0.942450
$842$	2.13200	+	1.61894i	0.0734736	+	0.0557924i
$843$			17.1359i			0.590192i
$844$	33.2913	−	9.28089i	1.14593	−	0.319461i
$845$		−	3.25414i		−	0.111946i
$846$	7.49884	−	9.87530i	0.257815	−	0.339520i
$847$	5.37399			0.184652
$848$	6.35684	+	10.5152i	0.218295	+	0.361093i
$849$	28.2835			0.970686
$850$	−2.78370	+	3.66588i	−0.0954801	+	0.125739i
$851$		−	6.93367i		−	0.237683i
$852$	25.6443	−	7.14906i	0.878558	−	0.244923i
$853$			49.7965i			1.70500i	0.522726	+	0.852501i	$0.324915\pi$
$853$			49.7965i			1.70500i	−0.522726	+	0.852501i	$0.675085\pi$
$854$	9.61854	+	7.30387i	0.329140	+	0.249933i
$855$	1.03227			0.0353028
$856$	−15.6829	+	39.5418i	−0.536030	+	1.35151i
$857$	35.6409			1.21747			0.608735	−	0.793374i	$-0.291677\pi$
$857$	35.6409			1.21747			0.608735	+	0.793374i	$0.291677\pi$
$858$	−11.0869	−	8.41891i	−0.378502	−	0.287417i
$859$		−	43.5752i		−	1.48677i	−0.668866	−	0.743383i	$-0.733220\pi$
$859$		−	43.5752i		−	1.48677i	0.668866	−	0.743383i	$-0.266780\pi$
$860$	6.81873	+	24.4593i	0.232517	+	0.834056i
$861$			10.0702i			0.343191i
$862$	31.8297	−	41.9169i	1.08412	−	1.42769i
$863$	−43.6579			−1.48613			−0.743067	−	0.669217i	$-0.766630\pi$
$863$	−43.6579			−1.48613			−0.743067	+	0.669217i	$0.766630\pi$
$864$	25.0206	+	2.65481i	0.851218	+	0.0903186i
$865$	−19.1415			−0.650829
$866$	−30.8161	+	40.5820i	−1.04717	+	1.37903i
$867$			29.8509i			1.01379i
$868$	−0.923598	−	3.31302i	−0.0313490	−	0.112451i
$869$			17.3093i			0.587179i
$870$	4.22586	+	3.20892i	0.143270	+	0.108793i
$871$	37.1669			1.25935
$872$	−13.9734	+	35.2316i	−0.473199	+	1.19309i
$873$	−11.6243			−0.393424
$874$	6.59475	+	5.00775i	0.223071	+	0.169390i
$875$			6.76947i			0.228850i
$876$	−56.5359	+	15.7610i	−1.91017	+	0.532514i
$877$		−	5.23078i		−	0.176631i	−0.996093	−	0.0883154i	$-0.971852\pi$
$877$		−	5.23078i		−	0.176631i	0.996093	−	0.0883154i	$-0.0281483\pi$
$878$	−15.9239	+	20.9703i	−0.537405	+	0.707713i
$879$	46.0172			1.55212
$880$	−6.82858	+	4.12815i	−0.230191	+	0.139160i
$881$	−22.0358			−0.742405			−0.371203	−	0.928552i	$-0.621054\pi$
$881$	−22.0358			−0.742405			−0.371203	+	0.928552i	$0.621054\pi$
$882$	3.88673	−	5.11848i	0.130873	−	0.172348i
$883$		−	56.9658i		−	1.91705i	−0.285008	−	0.958525i	$-0.591996\pi$
$883$		−	56.9658i		−	1.91705i	0.285008	−	0.958525i	$-0.408004\pi$
$884$	−9.00907	+	2.51153i	−0.303008	+	0.0844720i
$885$			0.749785i			0.0252038i
$886$	2.55542	+	1.94047i	0.0858510	+	0.0651912i
$887$	3.28694			0.110365			0.0551823	−	0.998476i	$-0.482426\pi$
$887$	3.28694			0.110365			0.0551823	+	0.998476i	$0.482426\pi$
$888$	5.97421	+	2.36946i	0.200481	+	0.0795139i
$889$	−1.51785			−0.0509071
$890$	−14.2625	−	10.8303i	−0.478082	−	0.363033i
$891$			13.9455i			0.467191i
$892$	−6.23153	−	22.3530i	−0.208647	−	0.748434i
$893$		−	12.8560i		−	0.430210i
$894$	−13.7086	+	18.0530i	−0.458484	+	0.603782i
$895$	8.40932			0.281092
$896$	6.47337	−	1.08566i	0.216260	−	0.0362695i
$897$	43.7316			1.46016
$898$	0.212881	−	0.280345i	0.00710392	−	0.00935522i
$899$			3.82929i			0.127714i
$900$	0.992337	+	3.55959i	0.0330779	+	0.118653i
$901$			3.69057i			0.122951i
$902$	13.4279	+	10.1965i	0.447101	+	0.339508i
$903$	9.33810			0.310753
$904$	−12.8756	−	5.10665i	−0.428235	−	0.169845i
$905$	13.8249			0.459555
$906$	12.6417	+	9.59955i	0.419994	+	0.318924i
$907$			0.0491571i			0.00163223i	1.00000		0.000816117i	$0.000259778\pi$
$907$			0.0491571i			0.00163223i	−1.00000		0.000816117i	$0.999740\pi$
$908$	−52.8804	+	14.7419i	−1.75490	+	0.489228i
$909$			1.34848i			0.0447263i
$910$	−2.92315	+	3.84952i	−0.0969014	+	0.127610i
$911$	32.4990			1.07674			0.538370	−	0.842708i	$-0.319040\pi$
$911$	32.4990			1.07674			0.538370	+	0.842708i	$0.319040\pi$
$912$	−6.56843	+	3.97088i	−0.217503	+	0.131489i
$913$	−4.88466			−0.161659
$914$	−5.97624	+	7.87017i	−0.197676	+	0.260322i
$915$			42.7514i			1.41332i
$916$	−42.1296	+	11.7448i	−1.39200	+	0.388059i
$917$			1.53452i			0.0506742i
$918$	6.01868	+	4.57031i	0.198646	+	0.150843i
$919$	−19.8145			−0.653619			−0.326810	−	0.945090i	$-0.605974\pi$
$919$	−19.8145			−0.653619			−0.326810	+	0.945090i	$0.605974\pi$
$920$	9.24139	−	23.3006i	0.304680	−	0.768200i
$921$	−3.49485			−0.115159
$922$	−38.4769	−	29.2175i	−1.26717	−	0.962229i
$923$		−	27.0008i		−	0.888742i
$924$	0.788024	+	2.82671i	0.0259241	+	0.0929918i
$925$		−	3.20809i		−	0.105481i
$926$	29.5329	−	38.8922i	0.970513	−	1.27808i
$927$	1.57445			0.0517116
$928$	−7.26717	−	0.771084i	−0.238557	−	0.0253121i
$929$	43.9293			1.44127			0.720637	−	0.693313i	$-0.243850\pi$
$929$	43.9293			1.44127			0.720637	+	0.693313i	$0.243850\pi$
$930$	7.36267	−	9.69598i	0.241432	−	0.317944i
$931$		−	6.66341i		−	0.218385i
$932$	11.9218	+	42.7643i	0.390510	+	1.40079i
$933$			8.69822i			0.284767i
$934$	44.6571	+	33.9105i	1.46122	+	1.10959i
$935$	−2.39666			−0.0783793
$936$	−2.76815	+	6.97943i	−0.0904798	+	0.228130i
$937$	−23.9026			−0.780863			−0.390431	−	0.920632i	$-0.627674\pi$
$937$	−23.9026			−0.780863			−0.390431	+	0.920632i	$0.627674\pi$
$938$	−6.23953	−	4.73801i	−0.203728	−	0.154701i
$939$		−	23.8224i		−	0.777413i
$940$	−37.4872	+	10.4506i	−1.22270	+	0.340862i
$941$			20.4109i			0.665375i	0.943037	+	0.332688i	$0.107955\pi$
$941$			20.4109i			0.665375i	−0.943037	+	0.332688i	$0.892045\pi$
$942$	−0.593500	+	0.781586i	−0.0193373	+	0.0254655i
$943$	−52.9654			−1.72479
$944$	−0.534242	−	0.883718i	−0.0173881	−	0.0287626i
$945$	3.90573			0.127054
$946$	9.45527	−	12.4517i	0.307417	−	0.404841i
$947$			2.72706i			0.0886176i	0.999018	+	0.0443088i	$0.0141085\pi$
$947$			2.72706i			0.0886176i	−0.999018	+	0.0443088i	$0.985891\pi$
$948$	48.5501	−	13.5347i	1.57683	−	0.439587i
$949$			59.5265i			1.93231i
$950$	3.05128	+	2.31700i	0.0989967	+	0.0751734i
$951$	44.3157			1.43703
$952$	1.83260	+	0.726835i	0.0593947	+	0.0235569i
$953$	−32.7679			−1.06146			−0.530729	−	0.847542i	$-0.678082\pi$
$953$	−32.7679			−1.06146			−0.530729	+	0.847542i	$0.678082\pi$
$954$	2.35962	+	1.79178i	0.0763954	+	0.0580111i
$955$			8.28723i			0.268168i
$956$	−11.3511	−	40.7174i	−0.367122	−	1.31690i
$957$		−	3.26720i		−	0.105613i
$958$	−21.2675	+	28.0074i	−0.687123	+	0.904879i
$959$	2.83139			0.0914305
$960$	16.9183	+	15.9252i	0.546035	+	0.513983i
$961$	−22.2139			−0.716578
$962$	3.94202	−	5.19128i	0.127096	−	0.167374i
$963$			10.2572i			0.330533i
$964$	9.26119	+	33.2206i	0.298283	+	1.06996i
$965$			25.6847i			0.826818i
$966$	−7.34159	−	5.57486i	−0.236212	−	0.179368i
$967$	36.4163			1.17107			0.585535	−	0.810647i	$-0.300885\pi$
$967$	36.4163			1.17107			0.585535	+	0.810647i	$0.300885\pi$
$968$	−24.3539	−	9.65913i	−0.782764	−	0.310456i
$969$	−2.30536			−0.0740588
$970$	29.0554	+	22.0633i	0.932914	+	0.708411i
$971$			6.40329i			0.205491i	0.994708	+	0.102746i	$0.0327628\pi$
$971$			6.40329i			0.205491i	−0.994708	+	0.102746i	$0.967237\pi$
$972$	13.4079	−	3.73782i	0.430058	−	0.119891i
$973$			5.99505i			0.192192i
$974$	−33.9810	+	44.7499i	−1.08882	+	1.43388i
$975$	20.2339			0.648003
$976$	−30.4616	−	50.3880i	−0.975051	−	1.61288i
$977$	11.6473			0.372629			0.186315	−	0.982490i	$-0.440346\pi$
$977$	11.6473			0.372629			0.186315	+	0.982490i	$0.440346\pi$
$978$	0.239650	−	0.315598i	0.00766317	−	0.0100917i
$979$			11.0270i			0.352424i
$980$	−19.4301	+	5.41668i	−0.620670	+	0.173029i
$981$			9.13910i			0.291789i
$982$	−3.89203	−	2.95543i	−0.124200	−	0.0943115i
$983$	−34.7061			−1.10695			−0.553477	−	0.832864i	$-0.686699\pi$
$983$	−34.7061			−1.10695			−0.553477	+	0.832864i	$0.686699\pi$
$984$	18.1000	−	45.6362i	0.577008	−	1.45483i
$985$	35.9815			1.14646
$986$	−1.74811	−	1.32743i	−0.0556712	−	0.0422741i
$987$			14.3119i			0.455553i
$988$	2.09046	+	7.49866i	0.0665065	+	0.238564i
$989$			49.1150i			1.56176i
$990$	−1.16359	+	1.53234i	−0.0369813	+	0.0487010i
$991$	3.30503			0.104988			0.0524939	−	0.998621i	$-0.483283\pi$
$991$	3.30503			0.104988			0.0524939	+	0.998621i	$0.483283\pi$
$992$	−1.76920	+	16.6741i	−0.0561723	+	0.529402i
$993$	−50.6085			−1.60601
$994$	−3.44203	+	4.53285i	−0.109175	+	0.143773i
$995$		−	26.6003i		−	0.843288i
$996$	3.81946	+	13.7007i	0.121024	+	0.434124i
$997$			15.9009i			0.503586i	0.967781	+	0.251793i	$0.0810203\pi$
$997$			15.9009i			0.503586i	−0.967781	+	0.251793i	$0.918980\pi$
$998$	19.8045	+	15.0386i	0.626899	+	0.476038i
$999$	−5.26708			−0.166643

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.c.b.77.11	✓	16
3.2	odd	2		1368.2.g.b.685.6		16
4.3	odd	2		608.2.c.b.305.12		16
8.3	odd	2		608.2.c.b.305.5		16
8.5	even	2	inner	152.2.c.b.77.12	yes	16
12.11	even	2		5472.2.g.b.2737.7		16
16.3	odd	4		4864.2.a.bn.1.3		8
16.5	even	4		4864.2.a.bq.1.3		8
16.11	odd	4		4864.2.a.bp.1.6		8
16.13	even	4		4864.2.a.bo.1.6		8
24.5	odd	2		1368.2.g.b.685.5		16
24.11	even	2		5472.2.g.b.2737.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.c.b.77.11	✓	16	1.1	even	1	trivial
152.2.c.b.77.12	yes	16	8.5	even	2	inner
608.2.c.b.305.5		16	8.3	odd	2
608.2.c.b.305.12		16	4.3	odd	2
1368.2.g.b.685.5		16	24.5	odd	2
1368.2.g.b.685.6		16	3.2	odd	2
4864.2.a.bn.1.3		8	16.3	odd	4
4864.2.a.bo.1.6		8	16.13	even	4
4864.2.a.bp.1.6		8	16.11	odd	4
4864.2.a.bq.1.3		8	16.5	even	4
5472.2.g.b.2737.7		16	12.11	even	2
5472.2.g.b.2737.10		16	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.855255 - 1.12629i) q^{2} -1.91886i q^{3} +(-0.537077 - 1.92654i) q^{4} +1.51356i q^{5} +(-2.16120 - 1.64111i) q^{6} +0.580162 q^{7} +(-2.62919 - 1.04278i) q^{8} -0.682013 q^{9} +(1.70471 + 1.29448i) q^{10} -1.31799i q^{11} +(-3.69675 + 1.03057i) q^{12} +3.89230i q^{13} +(0.496186 - 0.653433i) q^{14} +2.90431 q^{15} +(-3.42310 + 2.06940i) q^{16} -1.20142 q^{17} +(-0.583295 + 0.768147i) q^{18} +1.00000i q^{19} +(2.91593 - 0.812898i) q^{20} -1.11325i q^{21} +(-1.48444 - 1.12722i) q^{22} +5.85527 q^{23} +(-2.00094 + 5.04503i) q^{24} +2.70913 q^{25} +(4.38387 + 3.32891i) q^{26} -4.44789i q^{27} +(-0.311591 - 1.11770i) q^{28} +1.29188i q^{29} +(2.48392 - 3.27110i) q^{30} +2.96413 q^{31} +(-0.596871 + 5.62528i) q^{32} -2.52903 q^{33} +(-1.02752 + 1.35316i) q^{34} +0.878110i q^{35} +(0.366293 + 1.31392i) q^{36} -1.18418i q^{37} +(1.12629 + 0.855255i) q^{38} +7.46877 q^{39} +(1.57830 - 3.97943i) q^{40} -9.04577 q^{41} +(-1.25384 - 0.952111i) q^{42} +8.38816i q^{43} +(-2.53915 + 0.707861i) q^{44} -1.03227i q^{45} +(5.00775 - 6.59475i) q^{46} -12.8560 q^{47} +(3.97088 + 6.56843i) q^{48} -6.66341 q^{49} +(2.31700 - 3.05128i) q^{50} +2.30536i q^{51} +(7.49866 - 2.09046i) q^{52} -3.07183i q^{53} +(-5.00963 - 3.80408i) q^{54} +1.99485 q^{55} +(-1.52535 - 0.604978i) q^{56} +1.91886 q^{57} +(1.45503 + 1.10488i) q^{58} +0.258163i q^{59} +(-1.55984 - 5.59526i) q^{60} +14.7200i q^{61} +(2.53509 - 3.33848i) q^{62} -0.395678 q^{63} +(5.82524 + 5.48330i) q^{64} -5.89123 q^{65} +(-2.16297 + 2.84843i) q^{66} -9.54884i q^{67} +(0.645257 + 2.31459i) q^{68} -11.2354i q^{69} +(0.989010 + 0.751008i) q^{70} -6.93697 q^{71} +(1.79314 + 0.711186i) q^{72} +15.2934 q^{73} +(-1.33373 - 1.01277i) q^{74} -5.19844i q^{75} +(1.92654 - 0.537077i) q^{76} -0.764646i q^{77} +(6.38770 - 8.41203i) q^{78} -13.1332 q^{79} +(-3.13216 - 5.18106i) q^{80} -10.5809 q^{81} +(-7.73645 + 10.1882i) q^{82} -3.70615i q^{83} +(-2.14471 + 0.597900i) q^{84} -1.81843i q^{85} +(9.44754 + 7.17402i) q^{86} +2.47893 q^{87} +(-1.37436 + 3.46523i) q^{88} -8.36653 q^{89} +(-1.16264 - 0.882852i) q^{90} +2.25816i q^{91} +(-3.14473 - 11.2804i) q^{92} -5.68774i q^{93} +(-10.9952 + 14.4796i) q^{94} -1.51356 q^{95} +(10.7941 + 1.14531i) q^{96} +17.0442 q^{97} +(-5.69892 + 7.50496i) q^{98} +0.898884i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 6 q^{6} - 8 q^{7} - 12 q^{8} - 24 q^{9} - 8 q^{10} + 4 q^{12} + 4 q^{14} + 2 q^{16} - 8 q^{17} + 20 q^{18} + 8 q^{20} + 20 q^{22} + 6 q^{24} - 24 q^{25} - 10 q^{26} - 14 q^{28} + 4 q^{30}+ \cdots - 48 q^{98}+O(q^{100}) \) 16 * q + 2 * q^4 + 6 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9 - 8 * q^10 + 4 * q^12 + 4 * q^14 + 2 * q^16 - 8 * q^17 + 20 * q^18 + 8 * q^20 + 20 * q^22 + 6 * q^24 - 24 * q^25 - 10 * q^26 - 14 * q^28 + 4 * q^30 + 16 * q^31 - 20 * q^32 + 8 * q^36 + 2 * q^38 + 8 * q^39 + 28 * q^40 + 16 * q^41 - 2 * q^42 - 28 * q^44 - 48 * q^46 + 24 * q^47 + 36 * q^48 + 24 * q^49 + 12 * q^50 + 8 * q^52 - 34 * q^54 + 16 * q^55 - 48 * q^56 + 38 * q^58 - 28 * q^60 - 16 * q^62 - 32 * q^63 + 14 * q^64 + 16 * q^65 - 24 * q^66 - 26 * q^68 - 32 * q^70 + 48 * q^71 - 20 * q^74 - 4 * q^76 + 56 * q^78 - 48 * q^79 + 4 * q^80 - 16 * q^81 - 12 * q^82 + 64 * q^84 + 48 * q^86 - 48 * q^87 + 40 * q^88 - 16 * q^89 + 12 * q^90 + 62 * q^92 - 36 * q^94 + 16 * q^95 - 70 * q^96 + 32 * q^97 - 48 * q^98

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