LMFDB - Embedded newform 276.2.e.a.91.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(91,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("276.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.e (of order $2$, degree $1$, 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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.19
Character	$\chi$	$=$	276.91
Dual form			276.2.e.a.91.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11292 + 0.872582i) q^{2} +1.00000i q^{3} +(0.477201 + 1.94224i) q^{4} -0.970352i q^{5} +(-0.872582 + 1.11292i) q^{6} +4.31859 q^{7} +(-1.16367 + 2.57796i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(1.11292 + 0.872582i) q^{2} +1.00000i q^{3} +(0.477201 + 1.94224i) q^{4} -0.970352i q^{5} +(-0.872582 + 1.11292i) q^{6} +4.31859 q^{7} +(-1.16367 + 2.57796i) q^{8} -1.00000 q^{9} +(0.846712 - 1.07993i) q^{10} -3.90252 q^{11} +(-1.94224 + 0.477201i) q^{12} +1.84266 q^{13} +(4.80627 + 3.76833i) q^{14} +0.970352 q^{15} +(-3.54456 + 1.85367i) q^{16} -0.465311i q^{17} +(-1.11292 - 0.872582i) q^{18} -6.89951 q^{19} +(1.88465 - 0.463053i) q^{20} +4.31859i q^{21} +(-4.34321 - 3.40527i) q^{22} +(1.65482 - 4.50129i) q^{23} +(-2.57796 - 1.16367i) q^{24} +4.05842 q^{25} +(2.05075 + 1.60788i) q^{26} -1.00000i q^{27} +(2.06084 + 8.38772i) q^{28} +1.41075 q^{29} +(1.07993 + 0.846712i) q^{30} +2.44938i q^{31} +(-5.56231 - 1.02992i) q^{32} -3.90252i q^{33} +(0.406022 - 0.517856i) q^{34} -4.19056i q^{35} +(-0.477201 - 1.94224i) q^{36} -11.3060i q^{37} +(-7.67864 - 6.02039i) q^{38} +1.84266i q^{39} +(2.50153 + 1.12917i) q^{40} -2.17712 q^{41} +(-3.76833 + 4.80627i) q^{42} +5.37792 q^{43} +(-1.86229 - 7.57962i) q^{44} +0.970352i q^{45} +(5.76943 - 3.56563i) q^{46} -8.65255i q^{47} +(-1.85367 - 3.54456i) q^{48} +11.6502 q^{49} +(4.51671 + 3.54130i) q^{50} +0.465311 q^{51} +(0.879322 + 3.57889i) q^{52} +10.2970i q^{53} +(0.872582 - 1.11292i) q^{54} +3.78682i q^{55} +(-5.02542 + 11.1332i) q^{56} -6.89951i q^{57} +(1.57006 + 1.23100i) q^{58} -8.30235i q^{59} +(0.463053 + 1.88465i) q^{60} +7.91911i q^{61} +(-2.13729 + 2.72598i) q^{62} -4.31859 q^{63} +(-5.29174 - 5.99979i) q^{64} -1.78803i q^{65} +(3.40527 - 4.34321i) q^{66} +2.57980 q^{67} +(0.903743 - 0.222047i) q^{68} +(4.50129 + 1.65482i) q^{69} +(3.65660 - 4.66377i) q^{70} +6.53127i q^{71} +(1.16367 - 2.57796i) q^{72} -1.48003 q^{73} +(9.86537 - 12.5827i) q^{74} +4.05842i q^{75} +(-3.29246 - 13.4005i) q^{76} -16.8534 q^{77} +(-1.60788 + 2.05075i) q^{78} -12.2763 q^{79} +(1.79872 + 3.43947i) q^{80} +1.00000 q^{81} +(-2.42297 - 1.89972i) q^{82} -10.1607 q^{83} +(-8.38772 + 2.06084i) q^{84} -0.451515 q^{85} +(5.98521 + 4.69267i) q^{86} +1.41075i q^{87} +(4.54125 - 10.0605i) q^{88} +4.10556i q^{89} +(-0.846712 + 1.07993i) q^{90} +7.95772 q^{91} +(9.53224 + 1.06602i) q^{92} -2.44938 q^{93} +(7.55006 - 9.62964i) q^{94} +6.69496i q^{95} +(1.02992 - 5.56231i) q^{96} +5.32755i q^{97} +(12.9658 + 10.1658i) q^{98} +3.90252 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 4 q^{6} + 4 q^{8} - 24 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 4 * q^6 + 4 * q^8 - 24 * q^9	$ 24 q + 4 q^{2} + 4 q^{6} + 4 q^{8} - 24 q^{9} + 8 q^{16} - 4 q^{18} - 4 q^{24} - 24 q^{25} + 40 q^{26} - 32 q^{29} - 36 q^{32} + 16 q^{41} - 32 q^{48} + 40 q^{49} - 12 q^{50} - 40 q^{52} - 4 q^{54} + 24 q^{58} - 40 q^{62} + 48 q^{64} + 16 q^{69} + 72 q^{70} - 4 q^{72} + 16 q^{77} + 24 q^{81} - 40 q^{82} - 64 q^{85} + 44 q^{92} + 16 q^{93} + 72 q^{94} + 44 q^{96} - 52 q^{98}+O(q^{100}) $ 24 * q + 4 * q^2 + 4 * q^6 + 4 * q^8 - 24 * q^9 + 8 * q^16 - 4 * q^18 - 4 * q^24 - 24 * q^25 + 40 * q^26 - 32 * q^29 - 36 * q^32 + 16 * q^41 - 32 * q^48 + 40 * q^49 - 12 * q^50 - 40 * q^52 - 4 * q^54 + 24 * q^58 - 40 * q^62 + 48 * q^64 + 16 * q^69 + 72 * q^70 - 4 * q^72 + 16 * q^77 + 24 * q^81 - 40 * q^82 - 64 * q^85 + 44 * q^92 + 16 * q^93 + 72 * q^94 + 44 * q^96 - 52 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	1.11292	+	0.872582i	0.786956	+	0.617009i
$2$	1.11292	+	0.872582i	0.786956	+	0.617009i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.477201	+	1.94224i	0.238601	+	0.971118i
$5$		−	0.970352i		−	0.433955i	−0.976177	−	0.216977i	$-0.930380\pi$
$5$		−	0.970352i		−	0.433955i	0.976177	−	0.216977i	$-0.0696198\pi$
$6$	−0.872582	+	1.11292i	−0.356230	+	0.454349i
$7$	4.31859			1.63227			0.816137	−	0.577858i	$-0.196111\pi$
$7$	4.31859			1.63227			0.816137	+	0.577858i	$0.196111\pi$
$8$	−1.16367	+	2.57796i	−0.411420	+	0.911446i
$9$	−1.00000			−0.333333
$10$	0.846712	−	1.07993i	0.267754	−	0.341503i
$11$	−3.90252			−1.17665			−0.588327	−	0.808623i	$-0.700213\pi$
$11$	−3.90252			−1.17665			−0.588327	+	0.808623i	$0.700213\pi$
$12$	−1.94224	+	0.477201i	−0.560675	+	0.137756i
$13$	1.84266			0.511063			0.255532	−	0.966801i	$-0.417750\pi$
$13$	1.84266			0.511063			0.255532	+	0.966801i	$0.417750\pi$
$14$	4.80627	+	3.76833i	1.28453	+	1.00713i
$15$	0.970352			0.250544
$16$	−3.54456	+	1.85367i	−0.886139	+	0.463419i
$17$		−	0.465311i		−	0.112854i	−0.998407	−	0.0564272i	$-0.982029\pi$
$17$		−	0.465311i		−	0.112854i	0.998407	−	0.0564272i	$-0.0179709\pi$
$18$	−1.11292	−	0.872582i	−0.262319	−	0.205670i
$19$	−6.89951			−1.58286			−0.791429	−	0.611262i	$-0.790662\pi$
$19$	−6.89951			−1.58286			−0.791429	+	0.611262i	$0.790662\pi$
$20$	1.88465	−	0.463053i	0.421421	−	0.103542i
$21$			4.31859i			0.942394i
$22$	−4.34321	−	3.40527i	−0.925976	−	0.726006i
$23$	1.65482	−	4.50129i	0.345053	−	0.938583i
$23$	1.65482	−	4.50129i	0.345053	−	0.938583i
$24$	−2.57796	−	1.16367i	−0.526224	−	0.237533i
$25$	4.05842			0.811683
$26$	2.05075	+	1.60788i	0.402184	+	0.315330i
$27$		−	1.00000i		−	0.192450i
$28$	2.06084	+	8.38772i	0.389462	+	1.58513i
$29$	1.41075			0.261970			0.130985	−	0.991384i	$-0.458186\pi$
$29$	1.41075			0.261970			0.130985	+	0.991384i	$0.458186\pi$
$30$	1.07993	+	0.846712i	0.197167	+	0.154588i
$31$			2.44938i			0.439922i	0.975509	+	0.219961i	$0.0705931\pi$
$31$			2.44938i			0.439922i	−0.975509	+	0.219961i	$0.929407\pi$
$32$	−5.56231	−	1.02992i	−0.983286	−	0.182065i
$33$		−	3.90252i		−	0.679342i
$34$	0.406022	−	0.517856i	0.0696322	−	0.0888115i
$35$		−	4.19056i		−	0.708333i
$36$	−0.477201	−	1.94224i	−0.0795336	−	0.323706i
$37$		−	11.3060i		−	1.85869i	−0.369215	−	0.929344i	$-0.620373\pi$
$37$		−	11.3060i		−	1.85869i	0.369215	−	0.929344i	$-0.379627\pi$
$38$	−7.67864	−	6.02039i	−1.24564	−	0.976637i
$39$			1.84266i			0.295062i
$40$	2.50153	+	1.12917i	0.395526	+	0.178538i
$41$	−2.17712			−0.340009			−0.170005	−	0.985443i	$-0.554378\pi$
$41$	−2.17712			−0.340009			−0.170005	+	0.985443i	$0.554378\pi$
$42$	−3.76833	+	4.80627i	−0.581465	+	0.741623i
$43$	5.37792			0.820125			0.410062	−	0.912058i	$-0.365507\pi$
$43$	5.37792			0.820125			0.410062	+	0.912058i	$0.365507\pi$
$44$	−1.86229	−	7.57962i	−0.280751	−	1.14267i
$45$			0.970352i			0.144652i
$46$	5.76943	−	3.56563i	0.850656	−	0.525723i
$47$		−	8.65255i		−	1.26210i	−0.775740	−	0.631052i	$-0.782623\pi$
$47$		−	8.65255i		−	1.26210i	0.775740	−	0.631052i	$-0.217377\pi$
$48$	−1.85367	−	3.54456i	−0.267555	−	0.511613i
$49$	11.6502			1.66432
$50$	4.51671	+	3.54130i	0.638759	+	0.500816i
$51$	0.465311			0.0651566
$52$	0.879322	+	3.57889i	0.121940	+	0.496303i
$53$			10.2970i			1.41440i	0.707013	+	0.707201i	$0.250042\pi$
$53$			10.2970i			1.41440i	−0.707013	+	0.707201i	$0.749958\pi$
$54$	0.872582	−	1.11292i	0.118743	−	0.151450i
$55$			3.78682i			0.510615i
$56$	−5.02542	+	11.1332i	−0.671550	+	1.48773i
$57$		−	6.89951i		−	0.913863i
$58$	1.57006	+	1.23100i	0.206159	+	0.161638i
$59$		−	8.30235i		−	1.08087i	−0.841385	−	0.540437i	$-0.818259\pi$
$59$		−	8.30235i		−	1.08087i	0.841385	−	0.540437i	$-0.181741\pi$
$60$	0.463053	+	1.88465i	0.0597799	+	0.243308i
$61$			7.91911i			1.01394i	0.861964	+	0.506969i	$0.169234\pi$
$61$			7.91911i			1.01394i	−0.861964	+	0.506969i	$0.830766\pi$
$62$	−2.13729	+	2.72598i	−0.271436	+	0.346200i
$63$	−4.31859			−0.544091
$64$	−5.29174	−	5.99979i	−0.661468	−	0.749974i
$65$		−	1.78803i		−	0.221778i
$66$	3.40527	−	4.34321i	0.419160	−	0.534613i
$67$	2.57980			0.315173			0.157586	−	0.987505i	$-0.449629\pi$
$67$	2.57980			0.315173			0.157586	+	0.987505i	$0.449629\pi$
$68$	0.903743	−	0.222047i	0.109595	−	0.0269272i
$69$	4.50129	+	1.65482i	0.541891	+	0.199216i
$70$	3.65660	−	4.66377i	0.437048	−	0.557427i
$71$			6.53127i			0.775119i	0.921845	+	0.387560i	$0.126682\pi$
$71$			6.53127i			0.775119i	−0.921845	+	0.387560i	$0.873318\pi$
$72$	1.16367	−	2.57796i	0.137140	−	0.303815i
$73$	−1.48003			−0.173224			−0.0866122	−	0.996242i	$-0.527604\pi$
$73$	−1.48003			−0.173224			−0.0866122	+	0.996242i	$0.527604\pi$
$74$	9.86537	−	12.5827i	1.14683	−	1.46271i
$75$			4.05842i			0.468626i
$76$	−3.29246	−	13.4005i	−0.377671	−	1.53714i
$77$	−16.8534			−1.92062
$78$	−1.60788	+	2.05075i	−0.182056	+	0.232201i
$79$	−12.2763			−1.38119			−0.690596	−	0.723240i	$-0.742652\pi$
$79$	−12.2763			−1.38119			−0.690596	+	0.723240i	$0.742652\pi$
$80$	1.79872	+	3.43947i	0.201103	+	0.384544i
$81$	1.00000			0.111111
$82$	−2.42297	−	1.89972i	−0.267572	−	0.209789i
$83$	−10.1607			−1.11528			−0.557641	−	0.830082i	$-0.688293\pi$
$83$	−10.1607			−1.11528			−0.557641	+	0.830082i	$0.688293\pi$
$84$	−8.38772	+	2.06084i	−0.915176	+	0.224856i
$85$	−0.451515			−0.0489737
$86$	5.98521	+	4.69267i	0.645402	+	0.506024i
$87$			1.41075i			0.151249i
$88$	4.54125	−	10.0605i	0.484099	−	1.07246i
$89$			4.10556i			0.435188i	0.976039	+	0.217594i	$0.0698209\pi$
$89$			4.10556i			0.435188i	−0.976039	+	0.217594i	$0.930179\pi$
$90$	−0.846712	+	1.07993i	−0.0892513	+	0.113834i
$91$	7.95772			0.834195
$92$	9.53224	+	1.06602i	0.993805	+	0.111141i
$93$	−2.44938			−0.253989
$94$	7.55006	−	9.62964i	0.778729	−	0.993221i
$95$			6.69496i			0.686888i
$96$	1.02992	−	5.56231i	0.105116	−	0.567701i
$97$			5.32755i			0.540931i	0.962730	+	0.270465i	$0.0871776\pi$
$97$			5.32755i			0.540931i	−0.962730	+	0.270465i	$0.912822\pi$
$98$	12.9658	+	10.1658i	1.30975	+	1.02690i
$99$	3.90252			0.392218
$100$	1.93668	+	7.88240i	0.193668	+	0.788240i
$101$	−18.4465			−1.83550			−0.917750	−	0.397159i	$-0.869996\pi$
$101$	−18.4465			−1.83550			−0.917750	+	0.397159i	$0.869996\pi$
$102$	0.517856	+	0.406022i	0.0512754	+	0.0402022i
$103$	5.00805			0.493458			0.246729	−	0.969085i	$-0.420644\pi$
$103$	5.00805			0.493458			0.246729	+	0.969085i	$0.420644\pi$
$104$	−2.14425	+	4.75031i	−0.210261	+	0.465807i
$105$	4.19056			0.408956
$106$	−8.98497	+	11.4598i	−0.872698	+	1.11307i
$107$	11.6091			1.12229			0.561146	−	0.827717i	$-0.310360\pi$
$107$	11.6091			1.12229			0.561146	+	0.827717i	$0.310360\pi$
$108$	1.94224	−	0.477201i	0.186892	−	0.0459187i
$109$		−	6.98849i		−	0.669376i	−0.942329	−	0.334688i	$-0.891369\pi$
$109$		−	6.98849i		−	0.669376i	0.942329	−	0.334688i	$-0.108631\pi$
$110$	−3.30431	+	4.21445i	−0.315054	+	0.401832i
$111$	11.3060			1.07311
$112$	−15.3075	+	8.00527i	−1.44642	+	0.756426i
$113$		−	6.30662i		−	0.593277i	−0.954990	−	0.296639i	$-0.904134\pi$
$113$		−	6.30662i		−	0.593277i	0.954990	−	0.296639i	$-0.0958657\pi$
$114$	6.02039	−	7.67864i	0.563861	−	0.719170i
$115$	−4.36783	−	1.60575i	−0.407303	−	0.149737i
$116$	0.673213	+	2.74001i	0.0625063	+	0.254404i
$117$	−1.84266			−0.170354
$118$	7.24448	−	9.23988i	0.666908	−	0.850600i
$119$		−	2.00949i		−	0.184209i
$120$	−1.12917	+	2.50153i	−0.103079	+	0.228357i
$121$	4.22969			0.384517
$122$	−6.91007	+	8.81337i	−0.625609	+	0.797925i
$123$		−	2.17712i		−	0.196304i
$124$	−4.75728	+	1.16885i	−0.427216	+	0.104966i
$125$		−	8.78985i		−	0.786189i
$126$	−4.80627	−	3.76833i	−0.428176	−	0.335709i
$127$			13.1900i			1.17042i	0.810881	+	0.585211i	$0.198988\pi$
$127$			13.1900i			1.17042i	−0.810881	+	0.585211i	$0.801012\pi$
$128$	−0.653999	−	11.2948i	−0.0578059	−	0.998328i
$129$			5.37792i			0.473499i
$130$	1.56021	−	1.98995i	0.136839	−	0.174530i
$131$			10.4156i			0.910019i	0.890487	+	0.455009i	$0.150364\pi$
$131$			10.4156i			0.910019i	−0.890487	+	0.455009i	$0.849636\pi$
$132$	7.57962	−	1.86229i	0.659721	−	0.162091i
$133$	−29.7962			−2.58366
$134$	2.87112	+	2.25109i	0.248027	+	0.194464i
$135$	−0.970352			−0.0835146
$136$	1.19955	+	0.541469i	0.102861	+	0.0464306i
$137$			11.6572i			0.995942i	0.867194	+	0.497971i	$0.165921\pi$
$137$			11.6572i			0.995942i	−0.867194	+	0.497971i	$0.834079\pi$
$138$	3.56563	+	5.76943i	0.303527	+	0.491126i
$139$		−	19.2719i		−	1.63462i	−0.576198	−	0.817310i	$-0.695464\pi$
$139$		−	19.2719i		−	1.63462i	0.576198	−	0.817310i	$-0.304536\pi$
$140$	8.13905	−	1.99974i	0.687875	−	0.169009i
$141$	8.65255			0.728676
$142$	−5.69907	+	7.26881i	−0.478255	+	0.609985i
$143$	−7.19104			−0.601345
$144$	3.54456	−	1.85367i	0.295380	−	0.154473i
$145$		−	1.36893i		−	0.113683i
$146$	−1.64716	−	1.29145i	−0.136320	−	0.106881i
$147$			11.6502i			0.960895i
$148$	21.9588	−	5.39522i	1.80500	−	0.443484i
$149$			15.4488i			1.26562i	0.774308	+	0.632810i	$0.218098\pi$
$149$			15.4488i			1.26562i	−0.774308	+	0.632810i	$0.781902\pi$
$150$	−3.54130	+	4.51671i	−0.289146	+	0.368788i
$151$			16.7532i			1.36336i	0.731651	+	0.681679i	$0.238750\pi$
$151$			16.7532i			1.36336i	−0.731651	+	0.681679i	$0.761250\pi$
$152$	8.02876	−	17.7867i	0.651219	−	1.44269i
$153$			0.465311i			0.0376182i
$154$	−18.7566	−	14.7060i	−1.51145	−	1.18504i
$155$	2.37676			0.190906
$156$	−3.57889	+	0.879322i	−0.286540	+	0.0704021i
$157$			18.2689i			1.45801i	0.684506	+	0.729007i	$0.260018\pi$
$157$			18.2689i			1.45801i	−0.684506	+	0.729007i	$0.739982\pi$
$158$	−13.6626	−	10.7121i	−1.08694	−	0.852208i
$159$	−10.2970			−0.816605
$160$	−0.999383	+	5.39740i	−0.0790081	+	0.426702i
$161$	7.14648	−	19.4392i	0.563221	−	1.53203i
$162$	1.11292	+	0.872582i	0.0874396	+	0.0685565i
$163$			12.4694i			0.976675i	0.872655	+	0.488338i	$0.162396\pi$
$163$			12.4694i			0.976675i	−0.872655	+	0.488338i	$0.837604\pi$
$164$	−1.03893	−	4.22848i	−0.0811264	−	0.330189i
$165$	−3.78682			−0.294804
$166$	−11.3081	−	8.86604i	−0.877678	−	0.688138i
$167$		−	5.96626i		−	0.461683i	−0.972991	−	0.230841i	$-0.925852\pi$
$167$		−	5.96626i		−	0.461683i	0.972991	−	0.230841i	$-0.0741479\pi$
$168$	−11.1332	−	5.02542i	−0.858941	−	0.387720i
$169$	−9.60459			−0.738814
$170$	−0.502503	−	0.393984i	−0.0385402	−	0.0302172i
$171$	6.89951			0.527619
$172$	2.56635	+	10.4452i	0.195682	+	0.796438i
$173$	9.22836			0.701620			0.350810	−	0.936447i	$-0.385906\pi$
$173$	9.22836			0.701620			0.350810	+	0.936447i	$0.385906\pi$
$174$	−1.23100	+	1.57006i	−0.0933217	+	0.119026i
$175$	17.5266			1.32489
$176$	13.8327	−	7.23401i	1.04268	−	0.545284i
$177$	8.30235			0.624043
$178$	−3.58244	+	4.56918i	−0.268515	+	0.342474i
$179$			12.1701i			0.909633i	0.890585	+	0.454817i	$0.150295\pi$
$179$			12.1701i			0.909633i	−0.890585	+	0.454817i	$0.849705\pi$
$180$	−1.88465	+	0.463053i	−0.140474	+	0.0345140i
$181$		−	3.67886i		−	0.273447i	−0.990609	−	0.136724i	$-0.956343\pi$
$181$		−	3.67886i		−	0.273447i	0.990609	−	0.136724i	$-0.0436572\pi$
$182$	8.85634	+	6.94376i	0.656475	+	0.514706i
$183$	−7.91911			−0.585397
$184$	9.67847	+	9.50406i	0.713506	+	0.700649i
$185$	−10.9708			−0.806586
$186$	−2.72598	−	2.13729i	−0.199878	−	0.156714i
$187$			1.81589i			0.132791i
$188$	16.8053	−	4.12901i	1.22565	−	0.301139i
$189$		−	4.31859i		−	0.314131i
$190$	−5.84190	+	7.45098i	−0.423816	+	0.540551i
$191$	−4.75578			−0.344116			−0.172058	−	0.985087i	$-0.555042\pi$
$191$	−4.75578			−0.344116			−0.172058	+	0.985087i	$0.555042\pi$
$192$	5.99979	−	5.29174i	0.432998	−	0.381898i
$193$	−2.88765			−0.207857			−0.103929	−	0.994585i	$-0.533141\pi$
$193$	−2.88765			−0.207857			−0.103929	+	0.994585i	$0.533141\pi$
$194$	−4.64873	+	5.92916i	−0.333759	+	0.425689i
$195$	1.78803			0.128044
$196$	5.55951	+	22.6275i	0.397108	+	1.61625i
$197$	9.81861			0.699547			0.349774	−	0.936834i	$-0.386258\pi$
$197$	9.81861			0.699547			0.349774	+	0.936834i	$0.386258\pi$
$198$	4.34321	+	3.40527i	0.308659	+	0.242002i
$199$	0.931744			0.0660496			0.0330248	−	0.999455i	$-0.489486\pi$
$199$	0.931744			0.0660496			0.0330248	+	0.999455i	$0.489486\pi$
$200$	−4.72266	+	10.4624i	−0.333943	+	0.739805i
$201$			2.57980i			0.181965i
$202$	−20.5296	−	16.0961i	−1.44446	−	1.13252i
$203$	6.09247			0.427607
$204$	0.222047	+	0.903743i	0.0155464	+	0.0632747i
$205$			2.11257i			0.147549i
$206$	5.57358	+	4.36994i	0.388330	+	0.304468i
$207$	−1.65482	+	4.50129i	−0.115018	+	0.312861i
$208$	−6.53143	+	3.41570i	−0.452873	+	0.236836i
$209$	26.9255			1.86248
$210$	4.66377	+	3.65660i	0.321831	+	0.252330i
$211$			5.42105i			0.373201i	0.982436	+	0.186600i	$0.0597469\pi$
$211$			5.42105i			0.373201i	−0.982436	+	0.186600i	$0.940253\pi$
$212$	−19.9992	+	4.91374i	−1.37355	+	0.337477i
$213$	−6.53127			−0.447515
$214$	12.9200	+	10.1299i	0.883195	+	0.692464i
$215$		−	5.21847i		−	0.355897i
$216$	2.57796	+	1.16367i	0.175408	+	0.0791778i
$217$			10.5779i			0.718074i
$218$	6.09803	−	7.77766i	0.413011	−	0.526769i
$219$		−	1.48003i		−	0.100011i
$220$	−7.35490	+	1.80708i	−0.495867	+	0.121833i
$221$		−	0.857412i		−	0.0576758i
$222$	12.5827	+	9.86537i	0.844494	+	0.662121i
$223$		−	19.2322i		−	1.28788i	−0.765075	−	0.643942i	$-0.777298\pi$
$223$		−	19.2322i		−	1.28788i	0.765075	−	0.643942i	$-0.222702\pi$
$224$	−24.0213	−	4.44779i	−1.60499	−	0.297181i
$225$	−4.05842			−0.270561
$226$	5.50305	−	7.01880i	0.366057	−	0.466883i
$227$	4.73466			0.314250			0.157125	−	0.987579i	$-0.449777\pi$
$227$	4.73466			0.314250			0.157125	+	0.987579i	$0.449777\pi$
$228$	13.4005	−	3.29246i	0.887469	−	0.218048i
$229$		−	15.8899i		−	1.05003i	−0.851092	−	0.525016i	$-0.824059\pi$
$229$		−	15.8899i		−	1.05003i	0.851092	−	0.525016i	$-0.175941\pi$
$230$	−3.45992	−	5.59838i	−0.228140	−	0.369146i
$231$		−	16.8534i		−	1.10887i
$232$	−1.64165	+	3.63686i	−0.107780	+	0.238772i
$233$	21.9190			1.43596			0.717981	−	0.696063i	$-0.245067\pi$
$233$	21.9190			1.43596			0.717981	+	0.696063i	$0.245067\pi$
$234$	−2.05075	−	1.60788i	−0.134061	−	0.105110i
$235$	−8.39602			−0.547696
$236$	16.1251	−	3.96189i	1.04966	−	0.257897i
$237$		−	12.2763i		−	0.797432i
$238$	1.75344	−	2.23641i	0.113659	−	0.144965i
$239$		−	13.2261i		−	0.855522i	−0.903892	−	0.427761i	$-0.859302\pi$
$239$		−	13.2261i		−	0.855522i	0.903892	−	0.427761i	$-0.140698\pi$
$240$	−3.43947	+	1.79872i	−0.222017	+	0.116107i
$241$		−	22.5247i		−	1.45094i	−0.688252	−	0.725472i	$-0.741622\pi$
$241$		−	22.5247i		−	1.45094i	0.688252	−	0.725472i	$-0.258378\pi$
$242$	4.70732	+	3.69075i	0.302598	+	0.237250i
$243$			1.00000i			0.0641500i
$244$	−15.3808	+	3.77901i	−0.984653	+	0.241926i
$245$		−	11.3048i		−	0.722239i
$246$	1.89972	−	2.42297i	0.121122	−	0.154483i
$247$	−12.7135			−0.808940
$248$	−6.31441	−	2.85028i	−0.400965	−	0.180993i
$249$		−	10.1607i		−	0.643908i
$250$	7.66987	−	9.78244i	0.485085	−	0.618696i
$251$	−6.58687			−0.415760			−0.207880	−	0.978154i	$-0.566656\pi$
$251$	−6.58687			−0.415760			−0.207880	+	0.978154i	$0.566656\pi$
$252$	−2.06084	−	8.38772i	−0.129821	−	0.528377i
$253$	−6.45796	+	17.5664i	−0.406008	+	1.10439i
$254$	−11.5094	+	14.6795i	−0.722161	+	0.921072i
$255$		−	0.451515i		−	0.0282750i
$256$	9.12778	−	13.1409i	0.570486	−	0.821307i
$257$	7.07589			0.441382			0.220691	−	0.975344i	$-0.429169\pi$
$257$	7.07589			0.441382			0.220691	+	0.975344i	$0.429169\pi$
$258$	−4.69267	+	5.98521i	−0.292153	+	0.372623i
$259$		−	48.8258i		−	3.03389i
$260$	3.47278	−	0.853252i	0.215373	−	0.0529164i
$261$	−1.41075			−0.0873234
$262$	−9.08850	+	11.5918i	−0.561489	+	0.716145i
$263$	27.8622			1.71806			0.859030	−	0.511925i	$-0.171068\pi$
$263$	27.8622			1.71806			0.859030	+	0.511925i	$0.171068\pi$
$264$	10.0605	+	4.54125i	0.619184	+	0.279495i
$265$	9.99171			0.613786
$266$	−33.1609	−	25.9996i	−2.03323	−	1.59414i
$267$	−4.10556			−0.251256
$268$	1.23108	+	5.01058i	0.0752004	+	0.306070i
$269$	6.40697			0.390640			0.195320	−	0.980740i	$-0.437425\pi$
$269$	6.40697			0.390640			0.195320	+	0.980740i	$0.437425\pi$
$270$	−1.07993	−	0.846712i	−0.0657224	−	0.0515292i
$271$			3.79581i			0.230579i	0.993332	+	0.115290i	$0.0367796\pi$
$271$			3.79581i			0.230579i	−0.993332	+	0.115290i	$0.963220\pi$
$272$	0.862535	+	1.64932i	0.0522989	+	0.100005i
$273$			7.95772i			0.481623i
$274$	−10.1719	+	12.9736i	−0.614505	+	0.783763i
$275$	−15.8381			−0.955071
$276$	−1.06602	+	9.53224i	−0.0641670	+	0.573773i
$277$	−31.4992			−1.89260			−0.946302	−	0.323285i	$-0.895213\pi$
$277$	−31.4992			−1.89260			−0.946302	+	0.323285i	$0.895213\pi$
$278$	16.8163	−	21.4481i	1.00857	−	1.28637i
$279$		−	2.44938i		−	0.146641i
$280$	10.8031	+	4.87643i	0.645607	+	0.291422i
$281$			5.61716i			0.335092i	0.985864	+	0.167546i	$0.0535843\pi$
$281$			5.61716i			0.335092i	−0.985864	+	0.167546i	$0.946416\pi$
$282$	9.62964	+	7.55006i	0.573436	+	0.449600i
$283$	−28.1538			−1.67357			−0.836784	−	0.547533i	$-0.815567\pi$
$283$	−28.1538			−1.67357			−0.836784	+	0.547533i	$0.815567\pi$
$284$	−12.6853	+	3.11673i	−0.752732	+	0.184944i
$285$	−6.69496			−0.396575
$286$	−8.00308	−	6.27477i	−0.473232	−	0.371035i
$287$	−9.40210			−0.554988
$288$	5.56231	+	1.02992i	0.327762	+	0.0606885i
$289$	16.7835			0.987264
$290$	1.19450	−	1.52351i	0.0701435	−	0.0894638i
$291$	−5.32755			−0.312307
$292$	−0.706272	−	2.87457i	−0.0413315	−	0.168221i
$293$			15.0358i			0.878402i	0.898389	+	0.439201i	$0.144738\pi$
$293$			15.0358i			0.878402i	−0.898389	+	0.439201i	$0.855262\pi$
$294$	−10.1658	+	12.9658i	−0.592881	+	0.756183i
$295$	−8.05620			−0.469050
$296$	29.1463	+	13.1564i	1.69409	+	0.764701i
$297$			3.90252i			0.226447i
$298$	−13.4804	+	17.1934i	−0.780898	+	0.995987i
$299$	3.04927	−	8.29436i	0.176344	−	0.479675i
$300$	−7.88240	+	1.93668i	−0.455091	+	0.111814i
$301$	23.2250			1.33867
$302$	−14.6186	+	18.6451i	−0.841204	+	1.07290i
$303$		−	18.4465i		−	1.05973i
$304$	24.4557	−	12.7895i	1.40263	−	0.733526i
$305$	7.68433			0.440003
$306$	−0.406022	+	0.517856i	−0.0232107	+	0.0296038i
$307$		−	8.80462i		−	0.502506i	−0.967921	−	0.251253i	$-0.919157\pi$
$307$		−	8.80462i		−	0.502506i	0.967921	−	0.251253i	$-0.0808426\pi$
$308$	−8.04247	−	32.7333i	−0.458262	−	1.86515i
$309$			5.00805i			0.284898i
$310$	2.64516	+	2.07392i	0.150235	+	0.117791i
$311$		−	12.1343i		−	0.688073i	−0.938956	−	0.344037i	$-0.888206\pi$
$311$		−	12.1343i		−	0.688073i	0.938956	−	0.344037i	$-0.111794\pi$
$312$	−4.75031	−	2.14425i	−0.268934	−	0.121395i
$313$			18.6533i			1.05435i	0.849758	+	0.527173i	$0.176748\pi$
$313$			18.6533i			1.05435i	−0.849758	+	0.527173i	$0.823252\pi$
$314$	−15.9411	+	20.3319i	−0.899608	+	1.14739i
$315$			4.19056i			0.236111i
$316$	−5.85827	−	23.8435i	−0.329553	−	1.34130i
$317$	−0.822029			−0.0461697			−0.0230849	−	0.999734i	$-0.507349\pi$
$317$	−0.822029			−0.0461697			−0.0230849	+	0.999734i	$0.507349\pi$
$318$	−11.4598	−	8.98497i	−0.642632	−	0.503852i
$319$	−5.50550			−0.308249
$320$	−5.82191	+	5.13485i	−0.325455	+	0.287047i
$321$			11.6091i			0.647956i
$322$	24.9158	−	15.3985i	1.38850	−	0.858125i
$323$			3.21042i			0.178633i
$324$	0.477201	+	1.94224i	0.0265112	+	0.107902i
$325$	7.47830			0.414821
$326$	−10.8805	+	13.8774i	−0.602617	+	0.768601i
$327$	6.98849			0.386464
$328$	2.53345	−	5.61253i	0.139887	−	0.309900i
$329$		−	37.3668i		−	2.06010i
$330$	−4.21445	−	3.30431i	−0.231998	−	0.181896i
$331$		−	10.3513i		−	0.568960i	−0.958682	−	0.284480i	$-0.908179\pi$
$331$		−	10.3513i		−	0.568960i	0.958682	−	0.284480i	$-0.0918209\pi$
$332$	−4.84870	−	19.7345i	−0.266107	−	1.08307i
$333$			11.3060i			0.619563i
$334$	5.20605	−	6.63999i	0.284862	−	0.363324i
$335$		−	2.50331i		−	0.136771i
$336$	−8.00527	−	15.3075i	−0.436723	−	0.835093i
$337$		−	21.0886i		−	1.14877i	−0.818586	−	0.574383i	$-0.805242\pi$
$337$		−	21.0886i		−	1.14877i	0.818586	−	0.574383i	$-0.194758\pi$
$338$	−10.6892	−	8.38079i	−0.581415	−	0.455855i
$339$	6.30662			0.342529
$340$	−0.215464	−	0.876949i	−0.0116852	−	0.0475593i
$341$		−	9.55878i		−	0.517637i
$342$	7.67864	+	6.02039i	0.415213	+	0.325546i
$343$	20.0825			1.08435
$344$	−6.25812	+	13.8640i	−0.337415	+	0.747499i
$345$	1.60575	−	4.36783i	0.0864509	−	0.235156i
$346$	10.2705	+	8.05250i	0.552144	+	0.432905i
$347$			27.2876i			1.46488i	0.680833	+	0.732438i	$0.261618\pi$
$347$			27.2876i			1.46488i	−0.680833	+	0.732438i	$0.738382\pi$
$348$	−2.74001	+	0.673213i	−0.146880	+	0.0360880i
$349$	14.6029			0.781674			0.390837	−	0.920460i	$-0.372186\pi$
$349$	14.6029			0.781674			0.390837	+	0.920460i	$0.372186\pi$
$350$	19.5058	+	15.2934i	1.04263	+	0.817468i
$351$		−	1.84266i		−	0.0983542i
$352$	21.7070	+	4.01928i	1.15699	+	0.214228i
$353$	−31.7068			−1.68758			−0.843792	−	0.536671i	$-0.819682\pi$
$353$	−31.7068			−1.68758			−0.843792	+	0.536671i	$0.819682\pi$
$354$	9.23988	+	7.24448i	0.491094	+	0.385040i
$355$	6.33763			0.336367
$356$	−7.97396	+	1.95918i	−0.422619	+	0.103836i
$357$	2.00949			0.106353
$358$	−10.6194	+	13.5444i	−0.561252	+	0.715842i
$359$	−0.349815			−0.0184625			−0.00923126	−	0.999957i	$-0.502938\pi$
$359$	−0.349815			−0.0184625			−0.00923126	+	0.999957i	$0.502938\pi$
$360$	−2.50153	−	1.12917i	−0.131842	−	0.0595125i
$361$	28.6033			1.50544
$362$	3.21010	−	4.09429i	0.168719	−	0.215191i
$363$			4.22969i			0.222001i
$364$	3.79743	+	15.4558i	0.199040	+	0.810102i
$365$			1.43615i			0.0751715i
$366$	−8.81337	−	6.91007i	−0.460682	−	0.361195i
$367$	18.4010			0.960525			0.480262	−	0.877125i	$-0.340541\pi$
$367$	18.4010			0.960525			0.480262	+	0.877125i	$0.340541\pi$
$368$	2.47833	+	19.0226i	0.129192	+	0.991620i
$369$	2.17712			0.113336
$370$	−12.2096	−	9.57289i	−0.634748	−	0.497671i
$371$			44.4685i			2.30869i
$372$	−1.16885	−	4.75728i	−0.0606020	−	0.246653i
$373$		−	13.9803i		−	0.723873i	−0.932203	−	0.361937i	$-0.882116\pi$
$373$		−	13.9803i		−	0.723873i	0.932203	−	0.361937i	$-0.117884\pi$
$374$	−1.58451	+	2.02094i	−0.0819331	+	0.104501i
$375$	8.78985			0.453906
$376$	22.3059	+	10.0687i	1.15034	+	0.519255i
$377$	2.59954			0.133883
$378$	3.76833	−	4.80627i	0.193822	−	0.247208i
$379$	5.77175			0.296475			0.148237	−	0.988952i	$-0.452640\pi$
$379$	5.77175			0.296475			0.148237	+	0.988952i	$0.452640\pi$
$380$	−13.0032	+	3.19484i	−0.667050	+	0.163892i
$381$	−13.1900			−0.675744
$382$	−5.29282	−	4.14980i	−0.270804	−	0.212322i
$383$	−25.0817			−1.28161			−0.640806	−	0.767702i	$-0.721400\pi$
$383$	−25.0817			−1.28161			−0.640806	+	0.767702i	$0.721400\pi$
$384$	11.2948	−	0.653999i	0.576385	−	0.0333742i
$385$			16.3537i			0.833464i
$386$	−3.21373	−	2.51971i	−0.163575	−	0.128250i
$387$	−5.37792			−0.273375
$388$	−10.3474	+	2.54232i	−0.525308	+	0.129066i
$389$			5.11212i			0.259195i	0.991567	+	0.129597i	$0.0413685\pi$
$389$			5.11212i			0.259195i	−0.991567	+	0.129597i	$0.958631\pi$
$390$	1.98995	+	1.56021i	0.100765	+	0.0790041i
$391$	−2.09450	−	0.770004i	−0.105923	−	0.0389408i
$392$	−13.5570	+	30.0338i	−0.684734	+	1.51694i
$393$	−10.4156			−0.525400
$394$	10.9274	+	8.56755i	0.550513	+	0.431627i
$395$			11.9123i			0.599375i
$396$	1.86229	+	7.57962i	0.0935836	+	0.380890i
$397$	−10.0824			−0.506022			−0.253011	−	0.967463i	$-0.581421\pi$
$397$	−10.0824			−0.506022			−0.253011	+	0.967463i	$0.581421\pi$
$398$	1.03696	+	0.813023i	0.0519782	+	0.0407532i
$399$		−	29.7962i		−	1.49168i
$400$	−14.3853	+	7.52298i	−0.719265	+	0.376149i
$401$			19.0551i			0.951566i	0.879563	+	0.475783i	$0.157835\pi$
$401$			19.0551i			0.951566i	−0.879563	+	0.475783i	$0.842165\pi$
$402$	−2.25109	+	2.87112i	−0.112274	+	0.143199i
$403$			4.51339i			0.224828i
$404$	−8.80272	−	35.8275i	−0.437952	−	1.78249i
$405$		−	0.970352i		−	0.0482172i
$406$	6.78046	+	5.31618i	0.336508	+	0.263837i
$407$			44.1218i			2.18703i
$408$	−0.541469	+	1.19955i	−0.0268067	+	0.0593867i
$409$	−21.9642			−1.08606			−0.543031	−	0.839713i	$-0.682723\pi$
$409$	−21.9642			−1.08606			−0.543031	+	0.839713i	$0.682723\pi$
$410$	−1.84339	+	2.35114i	−0.0910388	+	0.116114i
$411$	−11.6572			−0.575007
$412$	2.38985	+	9.72682i	0.117739	+	0.479206i
$413$		−	35.8544i		−	1.76428i
$414$	−5.76943	+	3.56563i	−0.283552	+	0.175241i
$415$			9.85946i			0.483982i
$416$	−10.2495	−	1.89779i	−0.502522	−	0.0930469i
$417$	19.2719			0.943748
$418$	29.9661	+	23.4947i	1.46569	+	1.14916i
$419$	34.1016			1.66597			0.832985	−	0.553296i	$-0.186630\pi$
$419$	34.1016			1.66597			0.832985	+	0.553296i	$0.186630\pi$
$420$	1.99974	+	8.13905i	0.0975773	+	0.397145i
$421$			33.6148i			1.63828i	0.573591	+	0.819142i	$0.305550\pi$
$421$			33.6148i			1.63828i	−0.573591	+	0.819142i	$0.694450\pi$
$422$	−4.73031	+	6.03322i	−0.230268	+	0.293693i
$423$			8.65255i			0.420701i
$424$	−26.5452	−	11.9823i	−1.28915	−	0.581913i
$425$		−	1.88843i		−	0.0916021i
$426$	−7.26881	−	5.69907i	−0.352175	−	0.276121i
$427$			34.1994i			1.65503i
$428$	5.53987	+	22.5476i	0.267780	+	1.08988i
$429$		−	7.19104i		−	0.347187i
$430$	4.55355	−	5.80777i	0.219591	−	0.280075i
$431$	35.2100			1.69600			0.848002	−	0.529993i	$-0.177805\pi$
$431$	35.2100			1.69600			0.848002	+	0.529993i	$0.177805\pi$
$432$	1.85367	+	3.54456i	0.0891850	+	0.170538i
$433$		−	18.4252i		−	0.885457i	−0.896656	−	0.442728i	$-0.854011\pi$
$433$		−	18.4252i		−	0.885457i	0.896656	−	0.442728i	$-0.145989\pi$
$434$	−9.23008	+	11.7724i	−0.443058	+	0.565093i
$435$	1.36893			0.0656351
$436$	13.5733	−	3.33492i	0.650043	−	0.159713i
$437$	−11.4174	+	31.0567i	−0.546170	+	1.48564i
$438$	1.29145	−	1.64716i	0.0617077	−	0.0787044i
$439$			10.2140i			0.487486i	0.969840	+	0.243743i	$0.0783753\pi$
$439$			10.2140i			0.487486i	−0.969840	+	0.243743i	$0.921625\pi$
$440$	−9.76227	−	4.40661i	−0.465398	−	0.210077i
$441$	−11.6502			−0.554773
$442$	0.748162	−	0.954235i	0.0355864	−	0.0453883i
$443$		−	21.2576i		−	1.00998i	−0.863125	−	0.504990i	$-0.831496\pi$
$443$		−	21.2576i		−	1.00998i	0.863125	−	0.504990i	$-0.168504\pi$
$444$	5.39522	+	21.9588i	0.256046	+	1.04212i
$445$	3.98384			0.188852
$446$	16.7817	−	21.4040i	0.794635	−	1.01351i
$447$	−15.4488			−0.730705
$448$	−22.8529	−	25.9106i	−1.07970	−	1.22416i
$449$	21.0150			0.991757			0.495879	−	0.868392i	$-0.334846\pi$
$449$	21.0150			0.991757			0.495879	+	0.868392i	$0.334846\pi$
$450$	−4.51671	−	3.54130i	−0.212920	−	0.166939i
$451$	8.49627			0.400074
$452$	12.2489	−	3.00953i	0.576142	−	0.141556i
$453$	−16.7532			−0.787136
$454$	5.26932	+	4.13138i	0.247301	+	0.193895i
$455$		−	7.72179i		−	0.362003i
$456$	17.7867	+	8.02876i	0.832937	+	0.375981i
$457$		−	28.7829i		−	1.34641i	−0.739458	−	0.673203i	$-0.764918\pi$
$457$		−	28.7829i		−	1.34641i	0.739458	−	0.673203i	$-0.235082\pi$
$458$	13.8652	−	17.6842i	0.647879	−	0.826329i
$459$	−0.465311			−0.0217189
$460$	1.03442	−	9.24963i	0.0482299	−	0.431266i
$461$	−17.7275			−0.825653			−0.412827	−	0.910810i	$-0.635458\pi$
$461$	−17.7275			−0.825653			−0.412827	+	0.910810i	$0.635458\pi$
$462$	14.7060	−	18.7566i	0.684184	−	0.872634i
$463$			31.8121i			1.47844i	0.673466	+	0.739218i	$0.264805\pi$
$463$			31.8121i			1.47844i	−0.673466	+	0.739218i	$0.735195\pi$
$464$	−5.00050	+	2.61508i	−0.232142	+	0.121402i
$465$			2.37676i			0.110220i
$466$	24.3942	+	19.1261i	1.13004	+	0.886000i
$467$	22.8162			1.05581			0.527903	−	0.849304i	$-0.322978\pi$
$467$	22.8162			1.05581			0.527903	+	0.849304i	$0.322978\pi$
$468$	−0.879322	−	3.57889i	−0.0406467	−	0.165434i
$469$	11.1411			0.514448
$470$	−9.34414	−	7.32622i	−0.431013	−	0.337933i
$471$	−18.2689			−0.841785
$472$	21.4031	+	9.66120i	0.985158	+	0.444693i
$473$	−20.9874			−0.965004
$474$	10.7121	−	13.6626i	0.492022	−	0.627544i
$475$	−28.0011			−1.28478
$476$	3.90290	−	0.958930i	0.178889	−	0.0439525i
$477$		−	10.2970i		−	0.471467i
$478$	11.5408	−	14.7196i	0.527865	−	0.673259i
$479$	−17.0079			−0.777112			−0.388556	−	0.921425i	$-0.627026\pi$
$479$	−17.0079			−0.777112			−0.388556	+	0.921425i	$0.627026\pi$
$480$	−5.39740	−	0.999383i	−0.246356	−	0.0456154i
$481$		−	20.8331i		−	0.949907i
$482$	19.6547	−	25.0683i	0.895245	−	1.14183i
$483$	19.4392	+	7.14648i	0.884515	+	0.325176i
$484$	2.01841	+	8.21505i	0.0917460	+	0.373411i
$485$	5.16960			0.234740
$486$	−0.872582	+	1.11292i	−0.0395811	+	0.0504833i
$487$			11.2862i			0.511428i	0.966752	+	0.255714i	$0.0823105\pi$
$487$			11.2862i			0.511428i	−0.966752	+	0.255714i	$0.917689\pi$
$488$	−20.4151	−	9.21524i	−0.924150	−	0.417154i
$489$	−12.4694			−0.563884
$490$	9.86439	−	12.5814i	0.445628	−	0.568371i
$491$			13.5158i			0.609959i	0.952359	+	0.304979i	$0.0986496\pi$
$491$			13.5158i			0.609959i	−0.952359	+	0.304979i	$0.901350\pi$
$492$	4.22848	−	1.03893i	0.190635	−	0.0468384i
$493$		−	0.656439i		−	0.0295645i
$494$	−14.1492	−	11.0936i	−0.636601	−	0.499123i
$495$		−	3.78682i		−	0.170205i
$496$	−4.54036	−	8.68198i	−0.203868	−	0.389832i
$497$			28.2059i			1.26521i
$498$	8.86604	−	11.3081i	0.397297	−	0.506728i
$499$		−	38.2829i		−	1.71378i	−0.515503	−	0.856888i	$-0.672395\pi$
$499$		−	38.2829i		−	1.71378i	0.515503	−	0.856888i	$-0.327605\pi$
$500$	17.0720	−	4.19453i	0.763482	−	0.187585i
$501$	5.96626			0.266553
$502$	−7.33069	−	5.74759i	−0.327185	−	0.256527i
$503$	−20.5418			−0.915912			−0.457956	−	0.888975i	$-0.651418\pi$
$503$	−20.5418			−0.915912			−0.457956	+	0.888975i	$0.651418\pi$
$504$	5.02542	−	11.1332i	0.223850	−	0.495910i
$505$			17.8996i			0.796524i
$506$	−22.5153	+	13.9150i	−1.00093	+	0.618595i
$507$		−	9.60459i		−	0.426555i
$508$	−25.6181	+	6.29428i	−1.13662	+	0.279264i
$509$	20.9755			0.929723			0.464861	−	0.885383i	$-0.346104\pi$
$509$	20.9755			0.929723			0.464861	+	0.885383i	$0.346104\pi$
$510$	0.393984	−	0.502503i	0.0174459	−	0.0222512i
$511$	−6.39165			−0.282750
$512$	21.6251	−	6.66011i	0.955701	−	0.294338i
$513$			6.89951i			0.304621i
$514$	7.87493	+	6.17429i	0.347348	+	0.272336i
$515$		−	4.85957i		−	0.214138i
$516$	−10.4452	+	2.56635i	−0.459823	+	0.112977i
$517$			33.7668i			1.48506i
$518$	42.6045	−	54.3394i	1.87194	−	2.38754i
$519$			9.22836i			0.405080i
$520$	4.60948	+	2.08068i	0.202139	+	0.0912440i
$521$			38.6543i			1.69348i	0.532011	+	0.846738i	$0.321437\pi$
$521$			38.6543i			1.69348i	−0.532011	+	0.846738i	$0.678563\pi$
$522$	−1.57006	−	1.23100i	−0.0687197	−	0.0538793i
$523$	18.6282			0.814554			0.407277	−	0.913305i	$-0.366478\pi$
$523$	18.6282			0.814554			0.407277	+	0.913305i	$0.366478\pi$
$524$	−20.2296	+	4.97036i	−0.883735	+	0.217131i
$525$			17.5266i			0.764926i
$526$	31.0086	+	24.3121i	1.35204	+	1.06006i
$527$	1.13972			0.0496472
$528$	7.23401	+	13.8327i	0.314820	+	0.601992i
$529$	−17.5232	−	14.8976i	−0.761877	−	0.647722i
$530$	11.1200	+	8.71859i	0.483023	+	0.378711i
$531$			8.30235i			0.360291i
$532$	−14.2188	−	57.8712i	−0.616462	−	2.50904i
$533$	−4.01170			−0.173766
$534$	−4.56918	−	3.58244i	−0.197728	−	0.155027i
$535$		−	11.2649i		−	0.487024i
$536$	−3.00204	+	6.65062i	−0.129668	+	0.287263i
$537$	−12.1701			−0.525177
$538$	7.13048	+	5.59061i	0.307417	+	0.241028i
$539$	−45.4653			−1.95833
$540$	−0.463053	−	1.88465i	−0.0199266	−	0.0811025i
$541$	4.27843			0.183944			0.0919721	−	0.995762i	$-0.470683\pi$
$541$	4.27843			0.183944			0.0919721	+	0.995762i	$0.470683\pi$
$542$	−3.31216	+	4.22445i	−0.142269	+	0.181456i
$543$	3.67886			0.157875
$544$	−0.479232	+	2.58820i	−0.0205469	+	0.110968i
$545$	−6.78129			−0.290479
$546$	−6.94376	+	8.85634i	−0.297166	+	0.379016i
$547$		−	6.36365i		−	0.272090i	−0.990703	−	0.136045i	$-0.956561\pi$
$547$		−	6.36365i		−	0.272090i	0.990703	−	0.136045i	$-0.0434392\pi$
$548$	−22.6410	+	5.56283i	−0.967177	+	0.237632i
$549$		−	7.91911i		−	0.337979i
$550$	−17.6266	−	13.8200i	−0.751599	−	0.589287i
$551$	−9.73351			−0.414662
$552$	−9.50406	+	9.67847i	−0.404520	+	0.411943i
$553$	−53.0164			−2.25449
$554$	−35.0562	−	27.4856i	−1.48940	−	1.16775i
$555$		−	10.9708i		−	0.465683i
$556$	37.4305	−	9.19657i	1.58741	−	0.390021i
$557$		−	0.386337i		−	0.0163696i	−0.999967	−	0.00818482i	$-0.997395\pi$
$557$		−	0.386337i		−	0.0163696i	0.999967	−	0.00818482i	$-0.00260534\pi$
$558$	2.13729	−	2.72598i	0.0904786	−	0.115400i
$559$	9.90970			0.419136
$560$	7.76793	+	14.8537i	0.328255	+	0.627682i
$561$	−1.81589			−0.0766668
$562$	−4.90144	+	6.25148i	−0.206755	+	0.263703i
$563$	40.8503			1.72163			0.860816	−	0.508915i	$-0.169953\pi$
$563$	40.8503			1.72163			0.860816	+	0.508915i	$0.169953\pi$
$564$	4.12901	+	16.8053i	0.173863	+	0.707630i
$565$	−6.11965			−0.257455
$566$	−31.3330	−	24.5665i	−1.31703	−	1.03261i
$567$	4.31859			0.181364
$568$	−16.8373	−	7.60025i	−0.706479	−	0.318899i
$569$		−	25.9526i		−	1.08799i	−0.839089	−	0.543994i	$-0.816911\pi$
$569$		−	25.9526i		−	1.08799i	0.839089	−	0.543994i	$-0.183089\pi$
$570$	−7.45098	−	5.84190i	−0.312087	−	0.244690i
$571$	7.93263			0.331970			0.165985	−	0.986128i	$-0.446920\pi$
$571$	7.93263			0.331970			0.165985	+	0.986128i	$0.446920\pi$
$572$	−3.43157	−	13.9667i	−0.143481	−	0.583977i
$573$		−	4.75578i		−	0.198675i
$574$	−10.4638	−	8.20410i	−0.436752	−	0.342433i
$575$	6.71593	−	18.2681i	0.280074	−	0.761832i
$576$	5.29174	+	5.99979i	0.220489	+	0.249991i
$577$	14.6432			0.609606			0.304803	−	0.952415i	$-0.401409\pi$
$577$	14.6432			0.609606			0.304803	+	0.952415i	$0.401409\pi$
$578$	18.6788	+	14.6450i	0.776934	+	0.609150i
$579$		−	2.88765i		−	0.120007i
$580$	2.65878	−	0.653254i	0.110400	−	0.0271249i
$581$	−43.8799			−1.82045
$582$	−5.92916	−	4.64873i	−0.245772	−	0.192696i
$583$		−	40.1843i		−	1.66426i
$584$	1.72227	−	3.81546i	0.0712679	−	0.157885i
$585$			1.78803i			0.0739261i
$586$	−13.1200	+	16.7337i	−0.541982	+	0.691264i
$587$		−	41.3242i		−	1.70563i	−0.522212	−	0.852816i	$-0.674893\pi$
$587$		−	41.3242i		−	1.70563i	0.522212	−	0.852816i	$-0.325107\pi$
$588$	−22.6275	+	5.55951i	−0.933143	+	0.229270i
$589$		−	16.8996i		−	0.696334i
$590$	−8.96594	−	7.02970i	−0.369122	−	0.289408i
$591$			9.81861i			0.403884i
$592$	20.9576	+	40.0746i	0.861351	+	1.64706i
$593$	26.2292			1.07710			0.538552	−	0.842592i	$-0.318971\pi$
$593$	26.2292			1.07710			0.538552	+	0.842592i	$0.318971\pi$
$594$	−3.40527	+	4.34321i	−0.139720	+	0.178204i
$595$	−1.94991			−0.0799386
$596$	−30.0053	+	7.37221i	−1.22907	+	0.301978i
$597$			0.931744i			0.0381338i
$598$	10.6311	−	6.57026i	0.434739	−	0.268678i
$599$		−	4.73989i		−	0.193667i	−0.995301	−	0.0968333i	$-0.969129\pi$
$599$		−	4.73989i		−	0.193667i	0.995301	−	0.0968333i	$-0.0308714\pi$
$600$	−10.4624	−	4.72266i	−0.427127	−	0.192802i
$601$	−19.0914			−0.778756			−0.389378	−	0.921078i	$-0.627310\pi$
$601$	−19.0914			−0.778756			−0.389378	+	0.921078i	$0.627310\pi$
$602$	25.8477	+	20.2657i	1.05347	+	0.825970i
$603$	−2.57980			−0.105058
$604$	−32.5387	+	7.99467i	−1.32398	+	0.325298i
$605$		−	4.10428i		−	0.166863i
$606$	16.0961	−	20.5296i	0.653860	−	0.833958i
$607$			9.93980i			0.403444i	0.979443	+	0.201722i	$0.0646538\pi$
$607$			9.93980i			0.403444i	−0.979443	+	0.201722i	$0.935346\pi$
$608$	38.3772	+	7.10593i	1.55640	+	0.288184i
$609$			6.09247i			0.246879i
$610$	8.55207	+	6.70520i	0.346263	+	0.271486i
$611$		−	15.9437i		−	0.645015i
$612$	−0.903743	+	0.222047i	−0.0365317	+	0.00897572i
$613$		−	9.80580i		−	0.396053i	−0.980197	−	0.198026i	$-0.936547\pi$
$613$		−	9.80580i		−	0.396053i	0.980197	−	0.198026i	$-0.0634532\pi$
$614$	7.68275	−	9.79887i	0.310051	−	0.395450i
$615$	−2.11257			−0.0851872
$616$	19.6118	−	43.4474i	0.790183	−	1.75054i
$617$		−	18.9909i		−	0.764546i	−0.924049	−	0.382273i	$-0.875141\pi$
$617$		−	18.9909i		−	0.764546i	0.924049	−	0.382273i	$-0.124859\pi$
$618$	−4.36994	+	5.57358i	−0.175785	+	0.224202i
$619$	−17.5989			−0.707360			−0.353680	−	0.935366i	$-0.615070\pi$
$619$	−17.5989			−0.707360			−0.353680	+	0.935366i	$0.615070\pi$
$620$	1.13420	+	4.61624i	0.0455504	+	0.185393i
$621$	−4.50129	−	1.65482i	−0.180630	−	0.0664055i
$622$	10.5882	−	13.5046i	0.424547	−	0.541484i
$623$			17.7302i			0.710347i
$624$	−3.41570	−	6.53143i	−0.136737	−	0.261467i
$625$	11.7628			0.470513
$626$	−16.2765	+	20.7597i	−0.650541	+	0.829724i
$627$			26.9255i			1.07530i
$628$	−35.4825	+	8.71793i	−1.41590	+	0.347883i
$629$	−5.26078			−0.209761
$630$	−3.65660	+	4.66377i	−0.145683	+	0.185809i
$631$	0.929499			0.0370028			0.0185014	−	0.999829i	$-0.494110\pi$
$631$	0.929499			0.0370028			0.0185014	+	0.999829i	$0.494110\pi$
$632$	14.2856	−	31.6478i	0.568250	−	1.25888i
$633$	−5.42105			−0.215467
$634$	−0.914856	−	0.717288i	−0.0363336	−	0.0284871i
$635$	12.7989			0.507910
$636$	−4.91374	−	19.9992i	−0.194842	−	0.793020i
$637$	21.4675			0.850573
$638$	−6.12720	−	4.80400i	−0.242578	−	0.190192i
$639$		−	6.53127i		−	0.258373i
$640$	−10.9599	+	0.634609i	−0.433229	+	0.0250851i
$641$		−	19.5919i		−	0.773833i	−0.922115	−	0.386917i	$-0.873540\pi$
$641$		−	19.5919i		−	0.773833i	0.922115	−	0.386917i	$-0.126460\pi$
$642$	−10.1299	+	12.9200i	−0.399794	+	0.509913i
$643$	−16.3569			−0.645052			−0.322526	−	0.946561i	$-0.604532\pi$
$643$	−16.3569			−0.645052			−0.322526	+	0.946561i	$0.604532\pi$
$644$	41.1659	+	4.60372i	1.62216	+	0.181412i
$645$	5.21847			0.205477
$646$	−2.80135	+	3.57295i	−0.110218	+	0.140576i
$647$			15.9654i			0.627666i	0.949478	+	0.313833i	$0.101613\pi$
$647$			15.9654i			0.627666i	−0.949478	+	0.313833i	$0.898387\pi$
$648$	−1.16367	+	2.57796i	−0.0457133	+	0.101272i
$649$			32.4001i			1.27182i
$650$	8.32278	+	6.52543i	0.326446	+	0.255948i
$651$	−10.5779			−0.414580
$652$	−24.2184	+	5.95039i	−0.948466	+	0.233035i
$653$	36.1940			1.41638			0.708190	−	0.706022i	$-0.249512\pi$
$653$	36.1940			1.41638			0.708190	+	0.706022i	$0.249512\pi$
$654$	7.77766	+	6.09803i	0.304130	+	0.238452i
$655$	10.1068			0.394907
$656$	7.71693	−	4.03568i	0.301296	−	0.157567i
$657$	1.48003			0.0577415
$658$	32.6056	−	41.5865i	1.27110	−	1.62121i
$659$	16.6792			0.649731			0.324865	−	0.945760i	$-0.394681\pi$
$659$	16.6792			0.649731			0.324865	+	0.945760i	$0.394681\pi$
$660$	−1.80708	−	7.35490i	−0.0703404	−	0.286289i
$661$			0.212547i			0.00826711i	0.999991	+	0.00413355i	$0.00131575\pi$
$661$			0.212547i			0.00826711i	−0.999991	+	0.00413355i	$0.998684\pi$
$662$	9.03237	−	11.5202i	0.351053	−	0.447746i
$663$	0.857412			0.0332991
$664$	11.8237	−	26.1939i	0.458849	−	1.01652i
$665$			28.9128i			1.12119i
$666$	−9.86537	+	12.5827i	−0.382275	+	0.487569i
$667$	2.33454	−	6.35020i	0.0903936	−	0.245881i
$668$	11.5879	−	2.84711i	0.448348	−	0.110158i
$669$	19.2322			0.743560
$670$	2.18435	−	2.78600i	0.0843887	−	0.107633i
$671$		−	30.9045i		−	1.19306i
$672$	4.44779	−	24.0213i	0.171577	−	0.926643i
$673$	−13.1013			−0.505016			−0.252508	−	0.967595i	$-0.581255\pi$
$673$	−13.1013			−0.505016			−0.252508	+	0.967595i	$0.581255\pi$
$674$	18.4015	−	23.4700i	0.708799	−	0.904029i
$675$		−	4.05842i		−	0.156209i
$676$	−4.58332	−	18.6544i	−0.176282	−	0.717476i
$677$		−	26.4689i		−	1.01728i	−0.860979	−	0.508641i	$-0.830148\pi$
$677$		−	26.4689i		−	1.01728i	0.860979	−	0.508641i	$-0.169852\pi$
$678$	7.01880	+	5.50305i	0.269555	+	0.211343i
$679$			23.0075i			0.882948i
$680$	0.525415	−	1.16399i	0.0201488	−	0.0446369i
$681$			4.73466i			0.181433i
$682$	8.34082	−	10.6382i	0.319386	−	0.407358i
$683$			37.9967i			1.45390i	0.686688	+	0.726952i	$0.259064\pi$
$683$			37.9967i			1.45390i	−0.686688	+	0.726952i	$0.740936\pi$
$684$	3.29246	+	13.4005i	0.125890	+	0.512380i
$685$	11.3116			0.432194
$686$	22.3503	+	17.5236i	0.853338	+	0.669054i
$687$	15.8899			0.606236
$688$	−19.0623	+	9.96891i	−0.726745	+	0.380061i
$689$			18.9739i			0.722848i
$690$	5.59838	−	3.45992i	0.213127	−	0.131717i
$691$		−	22.3477i		−	0.850146i	−0.905159	−	0.425073i	$-0.860248\pi$
$691$		−	22.3477i		−	0.850146i	0.905159	−	0.425073i	$-0.139752\pi$
$692$	4.40379	+	17.9237i	0.167407	+	0.681355i
$693$	16.8534			0.640208
$694$	−23.8107	+	30.3691i	−0.903842	+	1.15279i
$695$	−18.7005			−0.709351
$696$	−3.63686	−	1.64165i	−0.137855	−	0.0622267i
$697$			1.01304i			0.0383716i
$698$	16.2519	+	12.7422i	0.615143	+	0.482300i
$699$			21.9190i			0.829053i
$700$	8.36374	+	34.0409i	0.316120	+	1.28662i
$701$		−	28.4890i		−	1.07601i	−0.842941	−	0.538006i	$-0.819178\pi$
$701$		−	28.4890i		−	1.07601i	0.842941	−	0.538006i	$-0.180822\pi$
$702$	1.60788	−	2.05075i	0.0606854	−	0.0774004i
$703$			78.0056i			2.94204i
$704$	20.6511	+	23.4143i	0.778319	+	0.882460i
$705$		−	8.39602i		−	0.316212i
$706$	−35.2873	−	27.6668i	−1.32805	−	1.04125i
$707$	−79.6631			−2.99604
$708$	3.96189	+	16.1251i	0.148897	+	0.606019i
$709$			4.28903i			0.161078i	0.996751	+	0.0805390i	$0.0256641\pi$
$709$			4.28903i			0.161078i	−0.996751	+	0.0805390i	$0.974336\pi$
$710$	7.05331	+	5.53011i	0.264706	+	0.207541i
$711$	12.2763			0.460398
$712$	−10.5840	−	4.77752i	−0.396651	−	0.179045i
$713$	11.0254	+	4.05328i	0.412904	+	0.151796i
$714$	2.23641	+	1.75344i	0.0836955	+	0.0656210i
$715$			6.97784i			0.260957i
$716$	−23.6371	+	5.80757i	−0.883361	+	0.217039i
$717$	13.2261			0.493936
$718$	−0.389317	−	0.305242i	−0.0145292	−	0.0113915i
$719$		−	10.8502i		−	0.404643i	−0.979319	−	0.202321i	$-0.935151\pi$
$719$		−	10.8502i		−	0.404643i	0.979319	−	0.202321i	$-0.0648486\pi$
$720$	−1.79872	−	3.43947i	−0.0670342	−	0.128181i
$721$	21.6277			0.805459
$722$	31.8333	+	24.9587i	1.18471	+	0.928868i
$723$	22.5247			0.837703
$724$	7.14520	−	1.75555i	0.265549	−	0.0652447i
$725$	5.72542			0.212637
$726$	−3.69075	+	4.70732i	−0.136976	+	0.174705i
$727$	−42.9919			−1.59448			−0.797241	−	0.603661i	$-0.793708\pi$
$727$	−42.9919			−1.59448			−0.797241	+	0.603661i	$0.793708\pi$
$728$	−9.26016	+	20.5147i	−0.343204	+	0.760324i
$729$	−1.00000			−0.0370370
$730$	−1.25316	+	1.59833i	−0.0463815	+	0.0591567i
$731$		−	2.50240i		−	0.0925547i
$732$	−3.77901	−	15.3808i	−0.139676	−	0.568490i
$733$			42.4143i			1.56661i	0.621638	+	0.783305i	$0.286468\pi$
$733$			42.4143i			1.56661i	−0.621638	+	0.783305i	$0.713532\pi$
$734$	20.4789	+	16.0564i	0.755891	+	0.592652i
$735$	11.3048			0.416985
$736$	−13.8405	+	23.3332i	−0.510169	+	0.860074i
$737$	−10.0677			−0.370850
$738$	2.42297	+	1.89972i	0.0891908	+	0.0699295i
$739$		−	12.4060i		−	0.456361i	−0.973619	−	0.228181i	$-0.926722\pi$
$739$		−	12.4060i		−	0.456361i	0.973619	−	0.228181i	$-0.0732776\pi$
$740$	−5.23526	−	21.3078i	−0.192452	−	0.783290i
$741$		−	12.7135i		−	0.467042i
$742$	−38.8024	+	49.4901i	−1.42448	+	1.81684i
$743$	−15.6040			−0.572456			−0.286228	−	0.958162i	$-0.592401\pi$
$743$	−15.6040			−0.572456			−0.286228	+	0.958162i	$0.592401\pi$
$744$	2.85028	−	6.31441i	0.104496	−	0.231497i
$745$	14.9908			0.549221
$746$	12.1990	−	15.5590i	0.446636	−	0.569657i
$747$	10.1607			0.371760
$748$	−3.52688	+	0.866543i	−0.128955	+	0.0316840i
$749$	50.1349			1.83189
$750$	9.78244	+	7.66987i	0.357204	+	0.280064i
$751$	51.1891			1.86792			0.933958	−	0.357384i	$-0.116331\pi$
$751$	51.1891			1.86792			0.933958	+	0.357384i	$0.116331\pi$
$752$	16.0390	+	30.6695i	0.584883	+	1.11840i
$753$		−	6.58687i		−	0.240039i
$754$	2.89310	+	2.26832i	0.105360	+	0.0826072i
$755$	16.2565			0.591636
$756$	8.38772	−	2.06084i	0.305059	−	0.0749520i
$757$		−	16.8739i		−	0.613291i	−0.951824	−	0.306646i	$-0.900793\pi$
$757$		−	16.8739i		−	0.613291i	0.951824	−	0.306646i	$-0.0992067\pi$
$758$	6.42352	+	5.03632i	0.233313	+	0.182928i
$759$	−17.5664	−	6.45796i	−0.637619	−	0.234409i
$760$	−17.2593	−	7.79073i	−0.626062	−	0.282599i
$761$	−41.4611			−1.50297			−0.751483	−	0.659753i	$-0.770661\pi$
$761$	−41.4611			−1.50297			−0.751483	+	0.659753i	$0.770661\pi$
$762$	−14.6795	−	11.5094i	−0.531781	−	0.416940i
$763$		−	30.1804i		−	1.09260i
$764$	−2.26946	−	9.23684i	−0.0821063	−	0.334177i
$765$	0.451515			0.0163246
$766$	−27.9140	−	21.8858i	−1.00857	−	0.790766i
$767$		−	15.2984i		−	0.552395i
$768$	13.1409	+	9.12778i	0.474182	+	0.329370i
$769$		−	1.77883i		−	0.0641461i	−0.999486	−	0.0320731i	$-0.989789\pi$
$769$		−	1.77883i		−	0.0641461i	0.999486	−	0.0320731i	$-0.0102109\pi$
$770$	−14.2700	+	18.2005i	−0.514254	+	0.655900i
$771$			7.07589i			0.254832i
$772$	−1.37799	−	5.60849i	−0.0495949	−	0.201854i
$773$		−	42.8728i		−	1.54203i	−0.636819	−	0.771014i	$-0.719750\pi$
$773$		−	42.8728i		−	1.54203i	0.636819	−	0.771014i	$-0.280250\pi$
$774$	−5.98521	−	4.69267i	−0.215134	−	0.168675i
$775$			9.94062i			0.357078i
$776$	−13.7342	−	6.19952i	−0.493029	−	0.222550i
$777$	48.8258			1.75162
$778$	−4.46075	+	5.68941i	−0.159925	+	0.203975i
$779$	15.0211			0.538186
$780$	0.853252	+	3.47278i	0.0305513	+	0.124346i
$781$		−	25.4884i		−	0.912048i
$782$	−1.65913	−	2.68458i	−0.0593302	−	0.0960003i
$783$		−	1.41075i		−	0.0504162i
$784$	−41.2949	+	21.5958i	−1.47482	+	0.771277i
$785$	17.7272			0.632712
$786$	−11.5918	−	9.08850i	−0.413467	−	0.324176i
$787$	14.3265			0.510685			0.255343	−	0.966851i	$-0.417812\pi$
$787$	14.3265			0.510685			0.255343	+	0.966851i	$0.417812\pi$
$788$	4.68546	+	19.0701i	0.166912	+	0.679343i
$789$			27.8622i			0.991922i
$790$	−10.3945	+	13.2575i	−0.369820	+	0.471682i
$791$		−	27.2357i		−	0.968391i
$792$	−4.54125	+	10.0605i	−0.161366	+	0.357486i
$793$			14.5923i			0.518186i
$794$	−11.2210	−	8.79773i	−0.398217	−	0.312220i
$795$			9.99171i			0.354370i
$796$	0.444630	+	1.80967i	0.0157595	+	0.0641420i
$797$			1.25470i			0.0444439i	0.999753	+	0.0222220i	$0.00707405\pi$
$797$			1.25470i			0.0444439i	−0.999753	+	0.0222220i	$0.992926\pi$
$798$	25.9996	−	33.1609i	0.920377	−	1.17388i
$799$	−4.02613			−0.142434
$800$	−22.5742	−	4.17983i	−0.798117	−	0.147779i
$801$		−	4.10556i		−	0.145063i
$802$	−16.6271	+	21.2069i	−0.587125	+	0.748841i
$803$	5.77585			0.203825
$804$	−5.01058	+	1.23108i	−0.176710	+	0.0434170i
$805$	−18.8629	−	6.93460i	−0.664830	−	0.244412i
$806$	−3.93831	+	5.02306i	−0.138721	+	0.176930i
$807$			6.40697i			0.225536i
$808$	21.4657	−	47.5544i	0.755161	−	1.67296i
$809$	−43.0379			−1.51313			−0.756566	−	0.653917i	$-0.773124\pi$
$809$	−43.0379			−1.51313			−0.756566	+	0.653917i	$0.773124\pi$
$810$	0.846712	−	1.07993i	0.0297504	−	0.0379448i
$811$		−	4.45785i		−	0.156536i	−0.996932	−	0.0782682i	$-0.975061\pi$
$811$		−	4.45785i		−	0.156536i	0.996932	−	0.0782682i	$-0.0249390\pi$
$812$	2.90733	+	11.8330i	0.102027	+	0.415257i
$813$	−3.79581			−0.133125
$814$	−38.4998	+	49.1042i	−1.34942	+	1.72110i
$815$	12.0997			0.423833
$816$	−1.64932	+	0.862535i	−0.0577378	+	0.0301948i
$817$	−37.1050			−1.29814
$818$	−24.4445	−	19.1656i	−0.854683	−	0.670109i
$819$	−7.95772			−0.278065
$820$	−4.10312	+	1.00812i	−0.143287	+	0.0352052i
$821$	−21.0960			−0.736254			−0.368127	−	0.929775i	$-0.620001\pi$
$821$	−21.0960			−0.736254			−0.368127	+	0.929775i	$0.620001\pi$
$822$	−12.9736	−	10.1719i	−0.452506	−	0.354785i
$823$			10.4657i			0.364812i	0.983223	+	0.182406i	$0.0583885\pi$
$823$			10.4657i			0.364812i	−0.983223	+	0.182406i	$0.941611\pi$
$824$	−5.82772	+	12.9106i	−0.203018	+	0.449760i
$825$		−	15.8381i		−	0.551411i
$826$	31.2859	−	39.9033i	1.08858	−	1.38841i
$827$	48.9407			1.70183			0.850917	−	0.525301i	$-0.176047\pi$
$827$	48.9407			1.70183			0.850917	+	0.525301i	$0.176047\pi$
$828$	−9.53224	−	1.06602i	−0.331268	−	0.0370468i
$829$	13.7469			0.477451			0.238726	−	0.971087i	$-0.423270\pi$
$829$	13.7469			0.477451			0.238726	+	0.971087i	$0.423270\pi$
$830$	−8.60318	+	10.9728i	−0.298621	+	0.380872i
$831$		−	31.4992i		−	1.09270i
$832$	−9.75090	−	11.0556i	−0.338052	−	0.383284i
$833$		−	5.42098i		−	0.187826i
$834$	21.4481	+	16.8163i	0.742689	+	0.582301i
$835$	−5.78937			−0.200349
$836$	12.8489	+	52.2957i	0.444388	+	1.80868i
$837$	2.44938			0.0846631
$838$	37.9525	+	29.7564i	1.31105	+	1.02792i
$839$	−7.02013			−0.242362			−0.121181	−	0.992630i	$-0.538668\pi$
$839$	−7.02013			−0.242362			−0.121181	+	0.992630i	$0.538668\pi$
$840$	−4.87643	+	10.8031i	−0.168253	+	0.372742i
$841$	−27.0098			−0.931372
$842$	−29.3316	+	37.4107i	−1.01084	+	1.28926i
$843$	−5.61716			−0.193465
$844$	−10.5290	+	2.58693i	−0.362422	+	0.0890459i
$845$			9.31983i			0.320612i
$846$	−7.55006	+	9.62964i	−0.259576	+	0.331074i
$847$	18.2663			0.627637
$848$	−19.0873	−	36.4983i	−0.655460	−	1.25336i
$849$		−	28.1538i		−	0.966235i
$850$	1.64781	−	2.10167i	0.0565193	−	0.0720868i
$851$	−50.8914	−	18.7093i	−1.74453	−	0.641346i
$852$	−3.11673	−	12.6853i	−0.106777	−	0.434590i
$853$	26.2493			0.898759			0.449379	−	0.893341i	$-0.351645\pi$
$853$	26.2493			0.898759			0.449379	+	0.893341i	$0.351645\pi$
$854$	−29.8418	+	38.0613i	−1.02116	+	1.30243i
$855$		−	6.69496i		−	0.228963i
$856$	−13.5092	+	29.9277i	−0.461733	+	1.02291i
$857$	−41.7873			−1.42743			−0.713713	−	0.700438i	$-0.752988\pi$
$857$	−41.7873			−1.42743			−0.713713	+	0.700438i	$0.752988\pi$
$858$	6.27477	−	8.00308i	0.214217	−	0.273221i
$859$		−	21.8496i		−	0.745500i	−0.927932	−	0.372750i	$-0.878415\pi$
$859$		−	21.8496i		−	0.745500i	0.927932	−	0.372750i	$-0.121585\pi$
$860$	10.1355	−	2.49026i	0.345618	−	0.0849172i
$861$		−	9.40210i		−	0.320423i
$862$	39.1860	+	30.7236i	1.33468	+	1.04645i
$863$		−	26.9168i		−	0.916259i	−0.888885	−	0.458130i	$-0.848520\pi$
$863$		−	26.9168i		−	0.916259i	0.888885	−	0.458130i	$-0.151480\pi$
$864$	−1.02992	+	5.56231i	−0.0350385	+	0.189234i
$865$		−	8.95476i		−	0.304471i
$866$	16.0775	−	20.5058i	0.546335	−	0.696816i
$867$			16.7835i			0.569997i
$868$	−20.5448	+	5.04778i	−0.697334	+	0.171333i
$869$	47.9086			1.62519
$870$	1.52351	+	1.19450i	0.0516519	+	0.0404974i
$871$	4.75371			0.161073
$872$	18.0160	+	8.13230i	0.610100	+	0.275394i
$873$		−	5.32755i		−	0.180310i
$874$	−39.8062	+	24.6011i	−1.34647	+	0.832145i
$875$		−	37.9598i		−	1.28328i
$876$	2.87457	−	0.706272i	0.0971226	−	0.0238627i
$877$	−18.1085			−0.611481			−0.305741	−	0.952115i	$-0.598904\pi$
$877$	−18.1085			−0.611481			−0.305741	+	0.952115i	$0.598904\pi$
$878$	−8.91252	+	11.3674i	−0.300783	+	0.383630i
$879$	−15.0358			−0.507146
$880$	−7.01954	−	13.4226i	−0.236629	−	0.452476i
$881$			43.3246i			1.45964i	0.683638	+	0.729822i	$0.260397\pi$
$881$			43.3246i			1.45964i	−0.683638	+	0.729822i	$0.739603\pi$
$882$	−12.9658	−	10.1658i	−0.436582	−	0.342300i
$883$			2.94208i			0.0990090i	0.998774	+	0.0495045i	$0.0157642\pi$
$883$			2.94208i			0.0990090i	−0.998774	+	0.0495045i	$0.984236\pi$
$884$	1.66530	−	0.409158i	0.0560100	−	0.0137615i
$885$		−	8.05620i		−	0.270806i
$886$	18.5490	−	23.6581i	0.623167	−	0.794811i
$887$			6.42544i			0.215745i	0.994165	+	0.107873i	$0.0344039\pi$
$887$			6.42544i			0.215745i	−0.994165	+	0.107873i	$0.965596\pi$
$888$	−13.1564	+	29.1463i	−0.441500	+	0.978085i
$889$			56.9622i			1.91045i
$890$	4.43371	+	3.47622i	0.148618	+	0.116523i
$891$	−3.90252			−0.130739
$892$	37.3535	−	9.17763i	1.25069	−	0.307290i
$893$			59.6984i			1.99773i
$894$	−17.1934	−	13.4804i	−0.575033	−	0.450852i
$895$	11.8092			0.394740
$896$	−2.82435	−	48.7776i	−0.0943550	−	1.62954i
$897$	8.29436	+	3.04927i	0.276941	+	0.101812i
$898$	23.3881	+	18.3373i	0.780470	+	0.611923i
$899$			3.45548i			0.115247i
$900$	−1.93668	−	7.88240i	−0.0645561	−	0.262747i
$901$	4.79130			0.159622
$902$	9.45570	+	7.41369i	0.314840	+	0.246849i
$903$			23.2250i			0.772881i
$904$	16.2582	+	7.33883i	0.540740	+	0.244086i
$905$	−3.56979			−0.118664
$906$	−18.6451	−	14.6186i	−0.619441	−	0.485669i
$907$	30.9016			1.02607			0.513036	−	0.858367i	$-0.328521\pi$
$907$	30.9016			1.02607			0.513036	+	0.858367i	$0.328521\pi$
$908$	2.25939	+	9.19583i	0.0749804	+	0.305174i
$909$	18.4465			0.611833
$910$	6.73789	−	8.59377i	0.223359	−	0.284881i
$911$	−4.99389			−0.165455			−0.0827275	−	0.996572i	$-0.526363\pi$
$911$	−4.99389			−0.165455			−0.0827275	+	0.996572i	$0.526363\pi$
$912$	12.7895	+	24.4557i	0.423501	+	0.809810i
$913$	39.6524			1.31230
$914$	25.1154	−	32.0332i	0.830744	−	1.05956i
$915$			7.68433i			0.254036i
$916$	30.8619	−	7.58266i	1.01970	−	0.250538i
$917$			44.9809i			1.48540i
$918$	−0.517856	−	0.406022i	−0.0170918	−	0.0134007i
$919$	−19.7919			−0.652874			−0.326437	−	0.945219i	$-0.605848\pi$
$919$	−19.7919			−0.652874			−0.326437	+	0.945219i	$0.605848\pi$
$920$	9.22229	−	9.39153i	0.304050	−	0.309629i
$921$	8.80462			0.290122
$922$	−19.7294	−	15.4687i	−0.649753	−	0.509435i
$923$			12.0349i			0.396135i
$924$	32.7333	−	8.04247i	1.07685	−	0.264578i
$925$		−	45.8843i		−	1.50867i
$926$	−27.7587	+	35.4045i	−0.912208	+	1.16346i
$927$	−5.00805			−0.164486
$928$	−7.84704	−	1.45296i	−0.257592	−	0.0476957i
$929$	5.57300			0.182844			0.0914222	−	0.995812i	$-0.470859\pi$
$929$	5.57300			0.182844			0.0914222	+	0.995812i	$0.470859\pi$
$930$	−2.07392	+	2.64516i	−0.0680066	+	0.0867382i
$931$	−80.3810			−2.63438
$932$	10.4598	+	42.5719i	0.342621	+	1.39449i
$933$	12.1343			0.397259
$934$	25.3927	+	19.9090i	0.830874	+	0.651442i
$935$	1.76205			0.0576252
$936$	2.14425	−	4.75031i	0.0700872	−	0.155269i
$937$		−	50.2612i		−	1.64196i	−0.570955	−	0.820981i	$-0.693427\pi$
$937$		−	50.2612i		−	1.64196i	0.570955	−	0.820981i	$-0.306573\pi$
$938$	12.3992	+	9.72153i	0.404848	+	0.317419i
$939$	−18.6533			−0.608727
$940$	−4.00659	−	16.3071i	−0.130681	−	0.531877i
$941$			7.71181i			0.251398i	0.992068	+	0.125699i	$0.0401173\pi$
$941$			7.71181i			0.251398i	−0.992068	+	0.125699i	$0.959883\pi$
$942$	−20.3319	−	15.9411i	−0.662448	−	0.519389i
$943$	−3.60274	+	9.79985i	−0.117321	+	0.319127i
$944$	15.3899	+	29.4281i	0.500897	+	0.957805i
$945$	−4.19056			−0.136319
$946$	−23.3574	−	18.3133i	−0.759416	−	0.595416i
$947$		−	22.9326i		−	0.745208i	−0.927990	−	0.372604i	$-0.878465\pi$
$947$		−	22.9326i		−	0.745208i	0.927990	−	0.372604i	$-0.121535\pi$
$948$	23.8435	−	5.85827i	0.774400	−	0.190268i
$949$	−2.72720			−0.0885286
$950$	−31.1631	−	24.4333i	−1.01106	−	0.792720i
$951$		−	0.822029i		−	0.0266561i
$952$	5.18038	+	2.33838i	0.167897	+	0.0757874i
$953$			16.2716i			0.527088i	0.964647	+	0.263544i	$0.0848915\pi$
$953$			16.2716i			0.527088i	−0.964647	+	0.263544i	$0.915109\pi$
$954$	8.98497	−	11.4598i	0.290899	−	0.371024i
$955$			4.61478i			0.149331i
$956$	25.6881	−	6.31149i	0.830813	−	0.204128i
$957$		−	5.50550i		−	0.177967i
$958$	−18.9285	−	14.8408i	−0.611553	−	0.479485i
$959$			50.3427i			1.62565i
$960$	−5.13485	−	5.82191i	−0.165727	−	0.187901i
$961$	25.0005			0.806468
$962$	18.1786	−	23.1856i	0.586101	−	0.747535i
$963$	−11.6091			−0.374098
$964$	43.7483	−	10.7488i	1.40904	−	0.346196i
$965$			2.80203i			0.0902007i
$966$	15.3985	+	24.9158i	0.495439	+	0.801653i
$967$			6.40555i			0.205989i	0.994682	+	0.102994i	$0.0328423\pi$
$967$			6.40555i			0.205989i	−0.994682	+	0.102994i	$0.967158\pi$
$968$	−4.92196	+	10.9040i	−0.158198	+	0.350466i
$969$	−3.21042			−0.103134
$970$	5.75338	+	4.51090i	0.184730	+	0.144836i
$971$	−18.9658			−0.608643			−0.304321	−	0.952569i	$-0.598430\pi$
$971$	−18.9658			−0.608643			−0.304321	+	0.952569i	$0.598430\pi$
$972$	−1.94224	+	0.477201i	−0.0622972	+	0.0153062i
$973$		−	83.2274i		−	2.66815i
$974$	−9.84816	+	12.5607i	−0.315555	+	0.402471i
$975$			7.47830i			0.239497i
$976$	−14.6795	−	28.0697i	−0.469878	−	0.898490i
$977$		−	45.8814i		−	1.46788i	−0.679216	−	0.733938i	$-0.737680\pi$
$977$		−	45.8814i		−	1.46788i	0.679216	−	0.733938i	$-0.262320\pi$
$978$	−13.8774	−	10.8805i	−0.443752	−	0.347921i
$979$		−	16.0220i		−	0.512066i
$980$	21.9567	−	5.39468i	0.701379	−	0.172327i
$981$			6.98849i			0.223125i
$982$	−11.7936	+	15.0420i	−0.376350	+	0.480011i
$983$	36.6503			1.16896			0.584482	−	0.811407i	$-0.301298\pi$
$983$	36.6503			1.16896			0.584482	+	0.811407i	$0.301298\pi$
$984$	5.61253	+	2.53345i	0.178921	+	0.0807635i
$985$		−	9.52751i		−	0.303572i
$986$	0.572797	−	0.730567i	0.0182416	−	0.0232660i
$987$	37.3668			1.18940
$988$	−6.06690	−	24.6926i	−0.193014	−	0.785576i
$989$	8.89946	−	24.2075i	0.282986	−	0.769755i
$990$	3.30431	−	4.21445i	0.105018	−	0.133944i
$991$		−	3.83227i		−	0.121736i	−0.998146	−	0.0608681i	$-0.980613\pi$
$991$		−	3.83227i		−	0.121736i	0.998146	−	0.0608681i	$-0.0193869\pi$
$992$	2.52266	−	13.6242i	0.0800946	−	0.432570i
$993$	10.3513			0.328489
$994$	−24.6120	+	31.3910i	−0.780644	+	0.995663i
$995$		−	0.904120i		−	0.0286625i
$996$	19.7345	−	4.84870i	0.625311	−	0.153637i
$997$	13.6128			0.431122			0.215561	−	0.976490i	$-0.430842\pi$
$997$	13.6128			0.431122			0.215561	+	0.976490i	$0.430842\pi$
$998$	33.4049	−	42.6059i	1.05741	−	1.34867i
$999$	−11.3060			−0.357705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.e.a.91.19	yes	24
3.2	odd	2		828.2.e.f.91.6		24
4.3	odd	2	inner	276.2.e.a.91.17	✓	24
8.3	odd	2		4416.2.i.d.1471.3		24
8.5	even	2		4416.2.i.d.1471.2		24
12.11	even	2		828.2.e.f.91.8		24
23.22	odd	2	inner	276.2.e.a.91.20	yes	24
69.68	even	2		828.2.e.f.91.5		24
92.91	even	2	inner	276.2.e.a.91.18	yes	24
184.45	odd	2		4416.2.i.d.1471.1		24
184.91	even	2		4416.2.i.d.1471.4		24
276.275	odd	2		828.2.e.f.91.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.e.a.91.17	✓	24	4.3	odd	2	inner
276.2.e.a.91.18	yes	24	92.91	even	2	inner
276.2.e.a.91.19	yes	24	1.1	even	1	trivial
276.2.e.a.91.20	yes	24	23.22	odd	2	inner
828.2.e.f.91.5		24	69.68	even	2
828.2.e.f.91.6		24	3.2	odd	2
828.2.e.f.91.7		24	276.275	odd	2
828.2.e.f.91.8		24	12.11	even	2
4416.2.i.d.1471.1		24	184.45	odd	2
4416.2.i.d.1471.2		24	8.5	even	2
4416.2.i.d.1471.3		24	8.3	odd	2
4416.2.i.d.1471.4		24	184.91	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11292 + 0.872582i) q^{2} +1.00000i q^{3} +(0.477201 + 1.94224i) q^{4} -0.970352i q^{5} +(-0.872582 + 1.11292i) q^{6} +4.31859 q^{7} +(-1.16367 + 2.57796i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(1.11292 + 0.872582i) q^{2} +1.00000i q^{3} +(0.477201 + 1.94224i) q^{4} -0.970352i q^{5} +(-0.872582 + 1.11292i) q^{6} +4.31859 q^{7} +(-1.16367 + 2.57796i) q^{8} -1.00000 q^{9} +(0.846712 - 1.07993i) q^{10} -3.90252 q^{11} +(-1.94224 + 0.477201i) q^{12} +1.84266 q^{13} +(4.80627 + 3.76833i) q^{14} +0.970352 q^{15} +(-3.54456 + 1.85367i) q^{16} -0.465311i q^{17} +(-1.11292 - 0.872582i) q^{18} -6.89951 q^{19} +(1.88465 - 0.463053i) q^{20} +4.31859i q^{21} +(-4.34321 - 3.40527i) q^{22} +(1.65482 - 4.50129i) q^{23} +(-2.57796 - 1.16367i) q^{24} +4.05842 q^{25} +(2.05075 + 1.60788i) q^{26} -1.00000i q^{27} +(2.06084 + 8.38772i) q^{28} +1.41075 q^{29} +(1.07993 + 0.846712i) q^{30} +2.44938i q^{31} +(-5.56231 - 1.02992i) q^{32} -3.90252i q^{33} +(0.406022 - 0.517856i) q^{34} -4.19056i q^{35} +(-0.477201 - 1.94224i) q^{36} -11.3060i q^{37} +(-7.67864 - 6.02039i) q^{38} +1.84266i q^{39} +(2.50153 + 1.12917i) q^{40} -2.17712 q^{41} +(-3.76833 + 4.80627i) q^{42} +5.37792 q^{43} +(-1.86229 - 7.57962i) q^{44} +0.970352i q^{45} +(5.76943 - 3.56563i) q^{46} -8.65255i q^{47} +(-1.85367 - 3.54456i) q^{48} +11.6502 q^{49} +(4.51671 + 3.54130i) q^{50} +0.465311 q^{51} +(0.879322 + 3.57889i) q^{52} +10.2970i q^{53} +(0.872582 - 1.11292i) q^{54} +3.78682i q^{55} +(-5.02542 + 11.1332i) q^{56} -6.89951i q^{57} +(1.57006 + 1.23100i) q^{58} -8.30235i q^{59} +(0.463053 + 1.88465i) q^{60} +7.91911i q^{61} +(-2.13729 + 2.72598i) q^{62} -4.31859 q^{63} +(-5.29174 - 5.99979i) q^{64} -1.78803i q^{65} +(3.40527 - 4.34321i) q^{66} +2.57980 q^{67} +(0.903743 - 0.222047i) q^{68} +(4.50129 + 1.65482i) q^{69} +(3.65660 - 4.66377i) q^{70} +6.53127i q^{71} +(1.16367 - 2.57796i) q^{72} -1.48003 q^{73} +(9.86537 - 12.5827i) q^{74} +4.05842i q^{75} +(-3.29246 - 13.4005i) q^{76} -16.8534 q^{77} +(-1.60788 + 2.05075i) q^{78} -12.2763 q^{79} +(1.79872 + 3.43947i) q^{80} +1.00000 q^{81} +(-2.42297 - 1.89972i) q^{82} -10.1607 q^{83} +(-8.38772 + 2.06084i) q^{84} -0.451515 q^{85} +(5.98521 + 4.69267i) q^{86} +1.41075i q^{87} +(4.54125 - 10.0605i) q^{88} +4.10556i q^{89} +(-0.846712 + 1.07993i) q^{90} +7.95772 q^{91} +(9.53224 + 1.06602i) q^{92} -2.44938 q^{93} +(7.55006 - 9.62964i) q^{94} +6.69496i q^{95} +(1.02992 - 5.56231i) q^{96} +5.32755i q^{97} +(12.9658 + 10.1658i) q^{98} +3.90252 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 4 q^{6} + 4 q^{8} - 24 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 4 * q^6 + 4 * q^8 - 24 * q^9	\( 24 q + 4 q^{2} + 4 q^{6} + 4 q^{8} - 24 q^{9} + 8 q^{16} - 4 q^{18} - 4 q^{24} - 24 q^{25} + 40 q^{26} - 32 q^{29} - 36 q^{32} + 16 q^{41} - 32 q^{48} + 40 q^{49} - 12 q^{50} - 40 q^{52} - 4 q^{54} + 24 q^{58} - 40 q^{62} + 48 q^{64} + 16 q^{69} + 72 q^{70} - 4 q^{72} + 16 q^{77} + 24 q^{81} - 40 q^{82} - 64 q^{85} + 44 q^{92} + 16 q^{93} + 72 q^{94} + 44 q^{96} - 52 q^{98}+O(q^{100}) \) 24 * q + 4 * q^2 + 4 * q^6 + 4 * q^8 - 24 * q^9 + 8 * q^16 - 4 * q^18 - 4 * q^24 - 24 * q^25 + 40 * q^26 - 32 * q^29 - 36 * q^32 + 16 * q^41 - 32 * q^48 + 40 * q^49 - 12 * q^50 - 40 * q^52 - 4 * q^54 + 24 * q^58 - 40 * q^62 + 48 * q^64 + 16 * q^69 + 72 * q^70 - 4 * q^72 + 16 * q^77 + 24 * q^81 - 40 * q^82 - 64 * q^85 + 44 * q^92 + 16 * q^93 + 72 * q^94 + 44 * q^96 - 52 * q^98

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