LMFDB - Embedded newform 276.2.e.a.91.5

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			91.5
Character	$\chi$	$=$	276.91
Dual form			276.2.e.a.91.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.588134 - 1.28612i) q^{2} -1.00000i q^{3} +(-1.30820 + 1.51282i) q^{4} -2.28672i q^{5} +(-1.28612 + 0.588134i) q^{6} -3.41490 q^{7} +(2.71506 + 0.792755i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.588134 - 1.28612i) q^{2} -1.00000i q^{3} +(-1.30820 + 1.51282i) q^{4} -2.28672i q^{5} +(-1.28612 + 0.588134i) q^{6} -3.41490 q^{7} +(2.71506 + 0.792755i) q^{8} -1.00000 q^{9} +(-2.94099 + 1.34490i) q^{10} -1.67149 q^{11} +(1.51282 + 1.30820i) q^{12} +0.215808 q^{13} +(2.00842 + 4.39196i) q^{14} -2.28672 q^{15} +(-0.577241 - 3.95813i) q^{16} -0.222714i q^{17} +(0.588134 + 1.28612i) q^{18} -7.32186 q^{19} +(3.45939 + 2.99148i) q^{20} +3.41490i q^{21} +(0.983061 + 2.14974i) q^{22} +(4.75380 - 0.633562i) q^{23} +(0.792755 - 2.71506i) q^{24} -0.229084 q^{25} +(-0.126924 - 0.277554i) q^{26} +1.00000i q^{27} +(4.46736 - 5.16612i) q^{28} -6.15775 q^{29} +(1.34490 + 2.94099i) q^{30} -3.33926i q^{31} +(-4.75113 + 3.07031i) q^{32} +1.67149i q^{33} +(-0.286437 + 0.130986i) q^{34} +7.80892i q^{35} +(1.30820 - 1.51282i) q^{36} -1.86514i q^{37} +(4.30623 + 9.41677i) q^{38} -0.215808i q^{39} +(1.81281 - 6.20857i) q^{40} +8.94190 q^{41} +(4.39196 - 2.00842i) q^{42} -2.67923 q^{43} +(2.18664 - 2.52866i) q^{44} +2.28672i q^{45} +(-3.61070 - 5.74132i) q^{46} -6.03026i q^{47} +(-3.95813 + 0.577241i) q^{48} +4.66154 q^{49} +(0.134732 + 0.294628i) q^{50} -0.222714 q^{51} +(-0.282319 + 0.326478i) q^{52} -11.0574i q^{53} +(1.28612 - 0.588134i) q^{54} +3.82223i q^{55} +(-9.27165 - 2.70718i) q^{56} +7.32186i q^{57} +(3.62158 + 7.91959i) q^{58} -3.93157i q^{59} +(2.99148 - 3.45939i) q^{60} -9.89882i q^{61} +(-4.29468 + 1.96393i) q^{62} +3.41490 q^{63} +(6.74308 + 4.30475i) q^{64} -0.493492i q^{65} +(2.14974 - 0.983061i) q^{66} +1.94227 q^{67} +(0.336926 + 0.291354i) q^{68} +(-0.633562 - 4.75380i) q^{69} +(10.0432 - 4.59269i) q^{70} -8.94968i q^{71} +(-2.71506 - 0.792755i) q^{72} -14.6311 q^{73} +(-2.39879 + 1.09695i) q^{74} +0.229084i q^{75} +(9.57843 - 11.0766i) q^{76} +5.70798 q^{77} +(-0.277554 + 0.126924i) q^{78} +4.15186 q^{79} +(-9.05113 + 1.31999i) q^{80} +1.00000 q^{81} +(-5.25903 - 11.5003i) q^{82} +15.1113 q^{83} +(-5.16612 - 4.46736i) q^{84} -0.509285 q^{85} +(1.57575 + 3.44581i) q^{86} +6.15775i q^{87} +(-4.53820 - 1.32508i) q^{88} -11.2497i q^{89} +(2.94099 - 1.34490i) q^{90} -0.736962 q^{91} +(-5.26044 + 8.02046i) q^{92} -3.33926 q^{93} +(-7.75562 + 3.54660i) q^{94} +16.7430i q^{95} +(3.07031 + 4.75113i) q^{96} +16.3374i q^{97} +(-2.74161 - 5.99529i) q^{98} +1.67149 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 $

$2$	−0.588134	−	1.28612i	−0.415873	−	0.909422i
$2$	−0.588134	−	1.28612i	−0.415873	−	0.909422i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.30820	+	1.51282i	−0.654099	+	0.756409i
$5$		−	2.28672i		−	1.02265i	−0.859387	−	0.511326i	$-0.829155\pi$
$5$		−	2.28672i		−	1.02265i	0.859387	−	0.511326i	$-0.170845\pi$
$6$	−1.28612	+	0.588134i	−0.525055	+	0.240105i
$7$	−3.41490			−1.29071			−0.645355	−	0.763882i	$-0.723291\pi$
$7$	−3.41490			−1.29071			−0.645355	+	0.763882i	$0.723291\pi$
$8$	2.71506	+	0.792755i	0.959918	+	0.280281i
$9$	−1.00000			−0.333333
$10$	−2.94099	+	1.34490i	−0.930023	+	0.425294i
$11$	−1.67149			−0.503974			−0.251987	−	0.967731i	$-0.581084\pi$
$11$	−1.67149			−0.503974			−0.251987	+	0.967731i	$0.581084\pi$
$12$	1.51282	+	1.30820i	0.436713	+	0.377644i
$13$	0.215808			0.0598543			0.0299272	−	0.999552i	$-0.490472\pi$
$13$	0.215808			0.0598543			0.0299272	+	0.999552i	$0.490472\pi$
$14$	2.00842	+	4.39196i	0.536772	+	1.17380i
$15$	−2.28672			−0.590428
$16$	−0.577241	−	3.95813i	−0.144310	−	0.989533i
$17$		−	0.222714i		−	0.0540161i	−0.999635	−	0.0270081i	$-0.991402\pi$
$17$		−	0.222714i		−	0.0540161i	0.999635	−	0.0270081i	$-0.00859798\pi$
$18$	0.588134	+	1.28612i	0.138624	+	0.303141i
$19$	−7.32186			−1.67975			−0.839875	−	0.542780i	$-0.817372\pi$
$19$	−7.32186			−1.67975			−0.839875	+	0.542780i	$0.817372\pi$
$20$	3.45939	+	2.99148i	0.773543	+	0.668915i
$21$			3.41490i			0.745192i
$22$	0.983061	+	2.14974i	0.209589	+	0.458325i
$23$	4.75380	−	0.633562i	0.991235	−	0.132107i
$23$	4.75380	−	0.633562i	0.991235	−	0.132107i
$24$	0.792755	−	2.71506i	0.161821	−	0.554209i
$25$	−0.229084			−0.0458167
$26$	−0.126924	−	0.277554i	−0.0248918	−	0.0544329i
$27$			1.00000i			0.192450i
$28$	4.46736	−	5.16612i	0.844252	−	0.976306i
$29$	−6.15775			−1.14346			−0.571732	−	0.820440i	$-0.693728\pi$
$29$	−6.15775			−1.14346			−0.571732	+	0.820440i	$0.693728\pi$
$30$	1.34490	+	2.94099i	0.245543	+	0.536949i
$31$		−	3.33926i		−	0.599749i	−0.953979	−	0.299874i	$-0.903055\pi$
$31$		−	3.33926i		−	0.599749i	0.953979	−	0.299874i	$-0.0969448\pi$
$32$	−4.75113	+	3.07031i	−0.839888	+	0.542759i
$33$			1.67149i			0.290969i
$34$	−0.286437	+	0.130986i	−0.0491235	+	0.0224639i
$35$			7.80892i			1.31995i
$36$	1.30820	−	1.51282i	0.218033	−	0.252136i
$37$		−	1.86514i		−	0.306628i	−0.988178	−	0.153314i	$-0.951005\pi$
$37$		−	1.86514i		−	0.306628i	0.988178	−	0.153314i	$-0.0489945\pi$
$38$	4.30623	+	9.41677i	0.698563	+	1.52760i
$39$		−	0.215808i		−	0.0345569i
$40$	1.81281	−	6.20857i	0.286630	−	0.981662i
$41$	8.94190			1.39649			0.698245	−	0.715859i	$-0.253965\pi$
$41$	8.94190			1.39649			0.698245	+	0.715859i	$0.253965\pi$
$42$	4.39196	−	2.00842i	0.677695	−	0.309906i
$43$	−2.67923			−0.408579			−0.204290	−	0.978911i	$-0.565488\pi$
$43$	−2.67923			−0.408579			−0.204290	+	0.978911i	$0.565488\pi$
$44$	2.18664	−	2.52866i	0.329649	−	0.381210i
$45$			2.28672i			0.340884i
$46$	−3.61070	−	5.74132i	−0.532369	−	0.846512i
$47$		−	6.03026i		−	0.879603i	−0.898095	−	0.439802i	$-0.855049\pi$
$47$		−	6.03026i		−	0.879603i	0.898095	−	0.439802i	$-0.144951\pi$
$48$	−3.95813	+	0.577241i	−0.571307	+	0.0833175i
$49$	4.66154			0.665934
$50$	0.134732	+	0.294628i	0.0190539	+	0.0416667i
$51$	−0.222714			−0.0311862
$52$	−0.282319	+	0.326478i	−0.0391506	+	0.0452744i
$53$		−	11.0574i		−	1.51884i	−0.650598	−	0.759422i	$-0.725482\pi$
$53$		−	11.0574i		−	1.51884i	0.650598	−	0.759422i	$-0.274518\pi$
$54$	1.28612	−	0.588134i	0.175018	−	0.0800349i
$55$			3.82223i			0.515390i
$56$	−9.27165	−	2.70718i	−1.23898	−	0.361762i
$57$			7.32186i			0.969804i
$58$	3.62158	+	7.91959i	0.475537	+	1.03989i
$59$		−	3.93157i		−	0.511847i	−0.966697	−	0.255923i	$-0.917621\pi$
$59$		−	3.93157i		−	0.511847i	0.966697	−	0.255923i	$-0.0823795\pi$
$60$	2.99148	−	3.45939i	0.386198	−	0.446605i
$61$		−	9.89882i		−	1.26741i	−0.773573	−	0.633707i	$-0.781533\pi$
$61$		−	9.89882i		−	1.26741i	0.773573	−	0.633707i	$-0.218467\pi$
$62$	−4.29468	+	1.96393i	−0.545425	+	0.249420i
$63$	3.41490			0.430237
$64$	6.74308	+	4.30475i	0.842885	+	0.538094i
$65$		−	0.493492i		−	0.0612101i
$66$	2.14974	−	0.983061i	0.264614	−	0.121006i
$67$	1.94227			0.237286			0.118643	−	0.992937i	$-0.462146\pi$
$67$	1.94227			0.237286			0.118643	+	0.992937i	$0.462146\pi$
$68$	0.336926	+	0.291354i	0.0408583	+	0.0353319i
$69$	−0.633562	−	4.75380i	−0.0762719	−	0.572290i
$70$	10.0432	−	4.59269i	1.20039	−	0.548931i
$71$		−	8.94968i		−	1.06213i	−0.847331	−	0.531066i	$-0.821792\pi$
$71$		−	8.94968i		−	1.06213i	0.847331	−	0.531066i	$-0.178208\pi$
$72$	−2.71506	−	0.792755i	−0.319973	−	0.0934271i
$73$	−14.6311			−1.71244			−0.856221	−	0.516610i	$-0.827194\pi$
$73$	−14.6311			−1.71244			−0.856221	+	0.516610i	$0.827194\pi$
$74$	−2.39879	+	1.09695i	−0.278854	+	0.127518i
$75$			0.229084i			0.0264523i
$76$	9.57843	−	11.0766i	1.09872	−	1.27058i
$77$	5.70798			0.650484
$78$	−0.277554	+	0.126924i	−0.0314268	+	0.0143713i
$79$	4.15186			0.467121			0.233560	−	0.972342i	$-0.424962\pi$
$79$	4.15186			0.467121			0.233560	+	0.972342i	$0.424962\pi$
$80$	−9.05113	+	1.31999i	−1.01195	+	0.147579i
$81$	1.00000			0.111111
$82$	−5.25903	−	11.5003i	−0.580763	−	1.27000i
$83$	15.1113			1.65868			0.829342	−	0.558741i	$-0.188715\pi$
$83$	15.1113			1.65868			0.829342	+	0.558741i	$0.188715\pi$
$84$	−5.16612	−	4.46736i	−0.563670	−	0.487429i
$85$	−0.509285			−0.0552397
$86$	1.57575	+	3.44581i	0.169917	+	0.371571i
$87$			6.15775i			0.660180i
$88$	−4.53820	−	1.32508i	−0.483773	−	0.141254i
$89$		−	11.2497i		−	1.19247i	−0.802811	−	0.596233i	$-0.796663\pi$
$89$		−	11.2497i		−	1.19247i	0.802811	−	0.596233i	$-0.203337\pi$
$90$	2.94099	−	1.34490i	0.310008	−	0.141765i
$91$	−0.736962			−0.0772546
$92$	−5.26044	+	8.02046i	−0.548439	+	0.836191i
$93$	−3.33926			−0.346265
$94$	−7.75562	+	3.54660i	−0.799931	+	0.365804i
$95$			16.7430i			1.71780i
$96$	3.07031	+	4.75113i	0.313362	+	0.484910i
$97$			16.3374i			1.65881i	0.558647	+	0.829406i	$0.311321\pi$
$97$			16.3374i			1.65881i	−0.558647	+	0.829406i	$0.688679\pi$
$98$	−2.74161	−	5.99529i	−0.276944	−	0.605616i
$99$	1.67149			0.167991
$100$	0.299686	−	0.346562i	0.0299686	−	0.0346562i
$101$	−2.59985			−0.258695			−0.129348	−	0.991599i	$-0.541288\pi$
$101$	−2.59985			−0.258695			−0.129348	+	0.991599i	$0.541288\pi$
$102$	0.130986	+	0.286437i	0.0129695	+	0.0283615i
$103$	16.7590			1.65131			0.825655	−	0.564175i	$-0.190806\pi$
$103$	16.7590			1.65131			0.825655	+	0.564175i	$0.190806\pi$
$104$	0.585931	+	0.171083i	0.0574552	+	0.0167761i
$105$	7.80892			0.762072
$106$	−14.2211	+	6.50320i	−1.38127	+	0.631647i
$107$	−4.71288			−0.455611			−0.227806	−	0.973707i	$-0.573155\pi$
$107$	−4.71288			−0.455611			−0.227806	+	0.973707i	$0.573155\pi$
$108$	−1.51282	−	1.30820i	−0.145571	−	0.125881i
$109$			10.3442i			0.990799i	0.868665	+	0.495399i	$0.164978\pi$
$109$			10.3442i			0.990799i	−0.868665	+	0.495399i	$0.835022\pi$
$110$	4.91584	−	2.24798i	0.468707	−	0.214337i
$111$	−1.86514			−0.177032
$112$	1.97122	+	13.5166i	0.186263	+	1.27720i
$113$			15.1580i			1.42594i	0.701194	+	0.712971i	$0.252651\pi$
$113$			15.1580i			1.42594i	−0.701194	+	0.712971i	$0.747349\pi$
$114$	9.41677	−	4.30623i	0.881961	−	0.403316i
$115$	−1.44878	−	10.8706i	−0.135099	−	1.01369i
$116$	8.05555	−	9.31555i	0.747939	−	0.864927i
$117$	−0.215808			−0.0199514
$118$	−5.05646	+	2.31229i	−0.465485	+	0.212863i
$119$			0.760547i			0.0697192i
$120$	−6.20857	−	1.81281i	−0.566763	−	0.165486i
$121$	−8.20611			−0.746010
$122$	−12.7310	+	5.82183i	−1.15261	+	0.527084i
$123$		−	8.94190i		−	0.806264i
$124$	5.05169	+	4.36841i	0.453656	+	0.392295i
$125$		−	10.9097i		−	0.975797i
$126$	−2.00842	−	4.39196i	−0.178924	−	0.391267i
$127$			19.6957i			1.74771i	0.486189	+	0.873853i	$0.338387\pi$
$127$			19.6957i			1.74771i	−0.486189	+	0.873853i	$0.661613\pi$
$128$	1.57059	−	11.2042i	0.138822	−	0.990317i
$129$			2.67923i			0.235893i
$130$	−0.634689	+	0.290239i	−0.0556659	+	0.0254557i
$131$			15.1167i			1.32075i	0.750936	+	0.660375i	$0.229602\pi$
$131$			15.1167i			1.32075i	−0.750936	+	0.660375i	$0.770398\pi$
$132$	−2.52866	−	2.18664i	−0.220092	−	0.190323i
$133$	25.0034			2.16807
$134$	−1.14231	−	2.49799i	−0.0986809	−	0.215793i
$135$	2.28672			0.196809
$136$	0.176558	−	0.604682i	0.0151397	−	0.0518511i
$137$			8.64369i			0.738480i	0.929334	+	0.369240i	$0.120382\pi$
$137$			8.64369i			0.738480i	−0.929334	+	0.369240i	$0.879618\pi$
$138$	−5.74132	+	3.61070i	−0.488734	+	0.307364i
$139$		−	12.0852i		−	1.02506i	−0.858670	−	0.512528i	$-0.828709\pi$
$139$		−	12.0852i		−	1.02506i	0.858670	−	0.512528i	$-0.171291\pi$
$140$	−11.8135	−	10.2156i	−0.998421	−	0.863376i
$141$	−6.03026			−0.507839
$142$	−11.5103	+	5.26361i	−0.965927	+	0.441712i
$143$	−0.360721			−0.0301650
$144$	0.577241	+	3.95813i	0.0481034	+	0.329844i
$145$			14.0810i			1.16937i
$146$	8.60505	+	18.8173i	0.712159	+	1.55733i
$147$		−	4.66154i		−	0.384477i
$148$	2.82162	+	2.43997i	0.231936	+	0.200565i
$149$		−	6.26416i		−	0.513180i	−0.966520	−	0.256590i	$-0.917401\pi$
$149$		−	6.26416i		−	0.513180i	0.966520	−	0.256590i	$-0.0825990\pi$
$150$	0.294628	−	0.134732i	0.0240563	−	0.0110008i
$151$		−	7.96308i		−	0.648026i	−0.946053	−	0.324013i	$-0.894968\pi$
$151$		−	7.96308i		−	0.648026i	0.946053	−	0.324013i	$-0.105032\pi$
$152$	−19.8793	−	5.80444i	−1.61242	−	0.470802i
$153$			0.222714i			0.0180054i
$154$	−3.35705	−	7.34113i	−0.270519	−	0.591565i
$155$	−7.63595			−0.613334
$156$	0.326478	+	0.282319i	0.0261392	+	0.0226036i
$157$			14.6161i			1.16649i	0.812296	+	0.583245i	$0.198217\pi$
$157$			14.6161i			1.16649i	−0.812296	+	0.583245i	$0.801783\pi$
$158$	−2.44185	−	5.33978i	−0.194263	−	0.424810i
$159$	−11.0574			−0.876905
$160$	7.02094	+	10.8645i	0.555054	+	0.858913i
$161$	−16.2337	+	2.16355i	−1.27940	+	0.170512i
$162$	−0.588134	−	1.28612i	−0.0462082	−	0.101047i
$163$			6.24865i			0.489432i	0.969595	+	0.244716i	$0.0786947\pi$
$163$			6.24865i			0.489432i	−0.969595	+	0.244716i	$0.921305\pi$
$164$	−11.6978	+	13.5275i	−0.913442	+	1.05632i
$165$	3.82223			0.297560
$166$	−8.88749	−	19.4350i	−0.689803	−	1.50844i
$167$		−	20.4559i		−	1.58293i	−0.611216	−	0.791463i	$-0.709320\pi$
$167$		−	20.4559i		−	1.58293i	0.611216	−	0.791463i	$-0.290680\pi$
$168$	−2.70718	+	9.27165i	−0.208863	+	0.715323i
$169$	−12.9534			−0.996417
$170$	0.299528	+	0.655000i	0.0229727	+	0.0502362i
$171$	7.32186			0.559916
$172$	3.50496	−	4.05319i	0.267251	−	0.309053i
$173$	−12.6233			−0.959733			−0.479867	−	0.877341i	$-0.659315\pi$
$173$	−12.6233			−0.959733			−0.479867	+	0.877341i	$0.659315\pi$
$174$	7.91959	−	3.62158i	0.600382	−	0.274551i
$175$	0.782297			0.0591361
$176$	0.964853	+	6.61598i	0.0727285	+	0.498698i
$177$	−3.93157			−0.295515
$178$	−14.4685	+	6.61634i	−1.08446	+	0.495915i
$179$		−	10.9656i		−	0.819609i	−0.912173	−	0.409805i	$-0.865597\pi$
$179$		−	10.9656i		−	0.819609i	0.912173	−	0.409805i	$-0.134403\pi$
$180$	−3.45939	−	2.99148i	−0.257848	−	0.222972i
$181$			0.836647i			0.0621875i	0.999516	+	0.0310937i	$0.00989904\pi$
$181$			0.836647i			0.0621875i	−0.999516	+	0.0310937i	$0.990101\pi$
$182$	0.433432	+	0.947820i	0.0321281	+	0.0702571i
$183$	−9.89882			−0.731741
$184$	13.4091	+	2.04844i	0.988532	+	0.151013i
$185$	−4.26506			−0.313573
$186$	1.96393	+	4.29468i	0.144002	+	0.314901i
$187$			0.372265i			0.0272227i
$188$	9.12268	+	7.88876i	0.665340	+	0.575347i
$189$		−	3.41490i		−	0.248397i
$190$	21.5335	−	9.84714i	1.56220	−	0.714387i
$191$	−2.31708			−0.167658			−0.0838289	−	0.996480i	$-0.526715\pi$
$191$	−2.31708			−0.167658			−0.0838289	+	0.996480i	$0.526715\pi$
$192$	4.30475	−	6.74308i	0.310669	−	0.486640i
$193$	17.7641			1.27869			0.639344	−	0.768921i	$-0.279206\pi$
$193$	17.7641			1.27869			0.639344	+	0.768921i	$0.279206\pi$
$194$	21.0118	−	9.60858i	1.50856	−	0.689856i
$195$	−0.493492			−0.0353397
$196$	−6.09821	+	7.05206i	−0.435587	+	0.503719i
$197$	22.6018			1.61031			0.805157	−	0.593061i	$-0.202081\pi$
$197$	22.6018			1.61031			0.805157	+	0.593061i	$0.202081\pi$
$198$	−0.983061	−	2.14974i	−0.0698631	−	0.152775i
$199$	8.34906			0.591849			0.295925	−	0.955211i	$-0.404372\pi$
$199$	8.34906			0.591849			0.295925	+	0.955211i	$0.404372\pi$
$200$	−0.621975	−	0.181607i	−0.0439803	−	0.0128416i
$201$		−	1.94227i		−	0.136997i
$202$	1.52906	+	3.34372i	0.107584	+	0.235263i
$203$	21.0281			1.47588
$204$	0.291354	−	0.336926i	0.0203989	−	0.0235896i
$205$		−	20.4476i		−	1.42812i
$206$	−9.85652	−	21.5540i	−0.686736	−	1.50174i
$207$	−4.75380	+	0.633562i	−0.330412	+	0.0440356i
$208$	−0.124573	−	0.854196i	−0.00863759	−	0.0592278i
$209$	12.2384			0.846550
$210$	−4.59269	−	10.0432i	−0.316926	−	0.693046i
$211$			13.6444i			0.939318i	0.882848	+	0.469659i	$0.155623\pi$
$211$			13.6444i			0.939318i	−0.882848	+	0.469659i	$0.844377\pi$
$212$	16.7278	+	14.4652i	1.14887	+	0.993474i
$213$	−8.94968			−0.613222
$214$	2.77180	+	6.06132i	0.189477	+	0.414343i
$215$			6.12665i			0.417834i
$216$	−0.792755	+	2.71506i	−0.0539402	+	0.184736i
$217$			11.4032i			0.774102i
$218$	13.3039	−	6.08380i	0.901055	−	0.412047i
$219$			14.6311i			0.988679i
$220$	−5.78234	−	5.00023i	−0.389846	−	0.337116i
$221$		−	0.0480635i		−	0.00323310i
$222$	1.09695	+	2.39879i	0.0736227	+	0.160996i
$223$			11.6016i			0.776904i	0.921469	+	0.388452i	$0.126990\pi$
$223$			11.6016i			0.776904i	−0.921469	+	0.388452i	$0.873010\pi$
$224$	16.2246	−	10.4848i	1.08405	−	0.700545i
$225$	0.229084			0.0152722
$226$	19.4949	−	8.91491i	1.29678	−	0.593011i
$227$	−8.50129			−0.564251			−0.282125	−	0.959378i	$-0.591039\pi$
$227$	−8.50129			−0.564251			−0.282125	+	0.959378i	$0.591039\pi$
$228$	−11.0766	−	9.57843i	−0.733569	−	0.634347i
$229$		−	24.5691i		−	1.62357i	−0.583955	−	0.811786i	$-0.698495\pi$
$229$		−	24.5691i		−	1.62357i	0.583955	−	0.811786i	$-0.301505\pi$
$230$	−13.1288	+	8.25667i	−0.865687	+	0.544429i
$231$		−	5.70798i		−	0.375557i
$232$	−16.7186	−	4.88159i	−1.09763	−	0.320492i
$233$	1.51528			0.0992694			0.0496347	−	0.998767i	$-0.484194\pi$
$233$	1.51528			0.0992694			0.0496347	+	0.998767i	$0.484194\pi$
$234$	0.126924	+	0.277554i	0.00829728	+	0.0181443i
$235$	−13.7895			−0.899528
$236$	5.94775	+	5.14327i	0.387166	+	0.334798i
$237$		−	4.15186i		−	0.269692i
$238$	0.978153	−	0.447303i	0.0634042	−	0.0289944i
$239$		−	0.931528i		−	0.0602555i	−0.999546	−	0.0301278i	$-0.990409\pi$
$239$		−	0.931528i		−	0.0602555i	0.999546	−	0.0301278i	$-0.00959141\pi$
$240$	1.31999	+	9.05113i	0.0852048	+	0.584248i
$241$		−	8.72544i		−	0.562055i	−0.959700	−	0.281027i	$-0.909325\pi$
$241$		−	8.72544i		−	0.562055i	0.959700	−	0.281027i	$-0.0906752\pi$
$242$	4.82629	+	10.5540i	0.310246	+	0.678439i
$243$		−	1.00000i		−	0.0641500i
$244$	14.9751	+	12.9496i	0.958683	+	0.829013i
$245$		−	10.6596i		−	0.681019i
$246$	−11.5003	+	5.25903i	−0.733234	+	0.335304i
$247$	−1.58011			−0.100540
$248$	2.64722	−	9.06628i	0.168098	−	0.575710i
$249$		−	15.1113i		−	0.957642i
$250$	−14.0312	+	6.41639i	−0.887412	+	0.405808i
$251$	−3.46463			−0.218685			−0.109343	−	0.994004i	$-0.534875\pi$
$251$	−3.46463			−0.218685			−0.109343	+	0.994004i	$0.534875\pi$
$252$	−4.46736	+	5.16612i	−0.281417	+	0.325435i
$253$	−7.94594	+	1.05899i	−0.499557	+	0.0665783i
$254$	25.3309	−	11.5837i	1.58940	−	0.726825i
$255$			0.509285i			0.0318927i
$256$	−15.3336	+	4.56959i	−0.958349	+	0.285599i
$257$	−2.26338			−0.141186			−0.0705928	−	0.997505i	$-0.522489\pi$
$257$	−2.26338			−0.141186			−0.0705928	+	0.997505i	$0.522489\pi$
$258$	3.44581	−	1.57575i	0.214527	−	0.0981017i
$259$			6.36928i			0.395768i
$260$	0.746564	+	0.645585i	0.0462999	+	0.0400375i
$261$	6.15775			0.381155
$262$	19.4418	−	8.89062i	1.20112	−	0.549265i
$263$	1.20387			0.0742340			0.0371170	−	0.999311i	$-0.488183\pi$
$263$	1.20387			0.0742340			0.0371170	+	0.999311i	$0.488183\pi$
$264$	−1.32508	+	4.53820i	−0.0815533	+	0.279307i
$265$	−25.2851			−1.55325
$266$	−14.7054	−	32.1573i	−0.901643	−	1.97169i
$267$	−11.2497			−0.688471
$268$	−2.54087	+	2.93830i	−0.155208	+	0.179485i
$269$	16.0520			0.978710			0.489355	−	0.872085i	$-0.337232\pi$
$269$	16.0520			0.978710			0.489355	+	0.872085i	$0.337232\pi$
$270$	−1.34490	−	2.94099i	−0.0818478	−	0.178983i
$271$		−	19.4504i		−	1.18152i	−0.806846	−	0.590762i	$-0.798827\pi$
$271$		−	19.4504i		−	1.18152i	0.806846	−	0.590762i	$-0.201173\pi$
$272$	−0.881532	+	0.128560i	−0.0534507	+	0.00779508i
$273$			0.736962i			0.0446030i
$274$	11.1168	−	5.08365i	0.671590	−	0.307114i
$275$	0.382911			0.0230904
$276$	8.02046	+	5.26044i	0.482775	+	0.316641i
$277$	−10.4753			−0.629402			−0.314701	−	0.949191i	$-0.601904\pi$
$277$	−10.4753			−0.629402			−0.314701	+	0.949191i	$0.601904\pi$
$278$	−15.5430	+	7.10774i	−0.932209	+	0.426294i
$279$			3.33926i			0.199916i
$280$	−6.19056	+	21.2017i	−0.369957	+	1.26704i
$281$			5.01591i			0.299224i	0.988745	+	0.149612i	$0.0478025\pi$
$281$			5.01591i			0.299224i	−0.988745	+	0.149612i	$0.952198\pi$
$282$	3.54660	+	7.75562i	0.211197	+	0.461840i
$283$	5.75726			0.342234			0.171117	−	0.985251i	$-0.445262\pi$
$283$	5.75726			0.342234			0.171117	+	0.985251i	$0.445262\pi$
$284$	13.5392	+	11.7079i	0.803406	+	0.694739i
$285$	16.7430			0.991771
$286$	0.212152	+	0.463930i	0.0125448	+	0.0274327i
$287$	−30.5357			−1.80246
$288$	4.75113	−	3.07031i	0.279963	−	0.180920i
$289$	16.9504			0.997082
$290$	18.1099	−	8.28153i	1.06345	−	0.486308i
$291$	16.3374			0.957715
$292$	19.1404	−	22.1342i	1.12011	−	1.29531i
$293$		−	1.86241i		−	0.108803i	−0.998519	−	0.0544017i	$-0.982675\pi$
$293$		−	1.86241i		−	0.108803i	0.998519	−	0.0544017i	$-0.0173252\pi$
$294$	−5.99529	+	2.74161i	−0.349652	+	0.159894i
$295$	−8.99039			−0.523441
$296$	1.47860	−	5.06397i	0.0859420	−	0.294337i
$297$		−	1.67149i		−	0.0969898i
$298$	−8.05644	+	3.68416i	−0.466697	+	0.213418i
$299$	1.02591	−	0.136728i	0.0593297	−	0.00790716i
$300$	−0.346562	−	0.299686i	−0.0200088	−	0.0173024i
$301$	9.14931			0.527357
$302$	−10.2415	+	4.68336i	−0.589330	+	0.269497i
$303$			2.59985i			0.149358i
$304$	4.22647	+	28.9809i	0.242405	+	1.66217i
$305$	−22.6358			−1.29612
$306$	0.286437	−	0.130986i	0.0163745	−	0.00748796i
$307$		−	29.6535i		−	1.69242i	−0.532852	−	0.846208i	$-0.678880\pi$
$307$		−	29.6535i		−	1.69242i	0.532852	−	0.846208i	$-0.321120\pi$
$308$	−7.46716	+	8.63513i	−0.425481	+	0.492032i
$309$		−	16.7590i		−	0.953385i
$310$	4.49096	+	9.82073i	0.255069	+	0.557780i
$311$		−	1.49246i		−	0.0846297i	−0.999104	−	0.0423149i	$-0.986527\pi$
$311$		−	1.49246i		−	0.0846297i	0.999104	−	0.0423149i	$-0.0134733\pi$
$312$	0.171083	−	0.585931i	0.00968566	−	0.0331718i
$313$		−	26.6881i		−	1.50850i	−0.656586	−	0.754252i	$-0.728000\pi$
$313$		−	26.6881i		−	1.50850i	0.656586	−	0.754252i	$-0.272000\pi$
$314$	18.7980	−	8.59621i	1.06083	−	0.485112i
$315$		−	7.80892i		−	0.439983i
$316$	−5.43145	+	6.28101i	−0.305543	+	0.353335i
$317$	−10.1157			−0.568155			−0.284077	−	0.958801i	$-0.591687\pi$
$317$	−10.1157			−0.568155			−0.284077	+	0.958801i	$0.591687\pi$
$318$	6.50320	+	14.2211i	0.364682	+	0.797477i
$319$	10.2926			0.576276
$320$	9.84376	−	15.4195i	0.550283	−	0.861978i
$321$			4.71288i			0.263047i
$322$	12.3302	+	19.6060i	0.687135	+	1.09260i
$323$			1.63068i			0.0907336i
$324$	−1.30820	+	1.51282i	−0.0726776	+	0.0840455i
$325$	−0.0494380			−0.00274233
$326$	8.03650	−	3.67504i	0.445101	−	0.203542i
$327$	10.3442			0.572038
$328$	24.2778	+	7.08874i	1.34052	+	0.391410i
$329$			20.5927i			1.13531i
$330$	−2.24798	−	4.91584i	−0.123747	−	0.270608i
$331$			7.15217i			0.393119i	0.980492	+	0.196559i	$0.0629769\pi$
$331$			7.15217i			0.393119i	−0.980492	+	0.196559i	$0.937023\pi$
$332$	−19.7686	+	22.8607i	−1.08494	+	1.25464i
$333$			1.86514i			0.102209i
$334$	−26.3087	+	12.0308i	−1.43955	+	0.658297i
$335$		−	4.44142i		−	0.242661i
$336$	13.5166	−	1.97122i	0.737392	−	0.107539i
$337$			24.7318i			1.34723i	0.739084	+	0.673613i	$0.235259\pi$
$337$			24.7318i			1.34723i	−0.739084	+	0.673613i	$0.764741\pi$
$338$	7.61835	+	16.6596i	0.414384	+	0.906164i
$339$	15.1580			0.823267
$340$	0.666245	−	0.770456i	0.0361322	−	0.0417838i
$341$			5.58155i			0.302258i
$342$	−4.30623	−	9.41677i	−0.232854	−	0.509201i
$343$	7.98561			0.431182
$344$	−7.27427	−	2.12398i	−0.392202	−	0.114517i
$345$	−10.8706	+	1.44878i	−0.585253	+	0.0779996i
$346$	7.42420	+	16.2351i	0.399128	+	0.872803i
$347$		−	2.97378i		−	0.159641i	−0.996809	−	0.0798205i	$-0.974565\pi$
$347$		−	2.97378i		−	0.159641i	0.996809	−	0.0798205i	$-0.0254347\pi$
$348$	−9.31555	−	8.05555i	−0.499366	−	0.431823i
$349$	−26.6834			−1.42833			−0.714164	−	0.699978i	$-0.753193\pi$
$349$	−26.6834			−1.42833			−0.714164	+	0.699978i	$0.753193\pi$
$350$	−0.460095	−	1.00613i	−0.0245931	−	0.0537797i
$351$			0.215808i			0.0115190i
$352$	7.94147	−	5.13200i	0.423282	−	0.273536i
$353$	13.4160			0.714059			0.357030	−	0.934093i	$-0.383790\pi$
$353$	13.4160			0.714059			0.357030	+	0.934093i	$0.383790\pi$
$354$	2.31229	+	5.05646i	0.122897	+	0.268748i
$355$	−20.4654			−1.08619
$356$	17.0188	+	14.7168i	0.901993	+	0.779991i
$357$	0.760547			0.0402524
$358$	−14.1031	+	6.44925i	−0.745371	+	0.340854i
$359$	−31.0658			−1.63959			−0.819796	−	0.572656i	$-0.805913\pi$
$359$	−31.0658			−1.63959			−0.819796	+	0.572656i	$0.805913\pi$
$360$	−1.81281	+	6.20857i	−0.0955434	+	0.327221i
$361$	34.6096			1.82156
$362$	1.07603	−	0.492060i	0.0565547	−	0.0258621i
$363$			8.20611i			0.430709i
$364$	0.964092	−	1.11489i	0.0505321	−	0.0584361i
$365$			33.4572i			1.75123i
$366$	5.82183	+	12.7310i	0.304312	+	0.665462i
$367$	12.2462			0.639249			0.319625	−	0.947544i	$-0.396443\pi$
$367$	12.2462			0.639249			0.319625	+	0.947544i	$0.396443\pi$
$368$	−5.25181	−	18.4504i	−0.273769	−	0.961795i
$369$	−8.94190			−0.465497
$370$	2.50842	+	5.48537i	0.130407	+	0.285171i
$371$			37.7598i			1.96039i
$372$	4.36841	−	5.05169i	0.226492	−	0.261918i
$373$		−	26.3387i		−	1.36377i	−0.731461	−	0.681884i	$-0.761161\pi$
$373$		−	26.3387i		−	1.36377i	0.731461	−	0.681884i	$-0.238839\pi$
$374$	0.478777	−	0.218942i	0.0247569	−	0.0113212i
$375$	−10.9097			−0.563377
$376$	4.78052	−	16.3725i	0.246536	−	0.844347i
$377$	−1.32889			−0.0684413
$378$	−4.39196	+	2.00842i	−0.225898	+	0.103302i
$379$	−27.3785			−1.40634			−0.703169	−	0.711023i	$-0.748232\pi$
$379$	−27.3785			−1.40634			−0.703169	+	0.711023i	$0.748232\pi$
$380$	−25.3292	−	21.9032i	−1.29936	−	1.12361i
$381$	19.6957			1.00904
$382$	1.36275	+	2.98003i	0.0697244	+	0.152472i
$383$	−7.27236			−0.371600			−0.185800	−	0.982588i	$-0.559488\pi$
$383$	−7.27236			−0.371600			−0.185800	+	0.982588i	$0.559488\pi$
$384$	−11.2042	−	1.57059i	−0.571760	−	0.0801487i
$385$		−	13.0525i		−	0.665219i
$386$	−10.4477	−	22.8467i	−0.531772	−	1.16287i
$387$	2.67923			0.136193
$388$	−24.7155	−	21.3725i	−1.25474	−	1.08503i
$389$			2.95190i			0.149668i	0.997196	+	0.0748338i	$0.0238426\pi$
$389$			2.95190i			0.149668i	−0.997196	+	0.0748338i	$0.976157\pi$
$390$	0.290239	+	0.634689i	0.0146968	+	0.0321387i
$391$	−0.141103	−	1.05874i	−0.00713590	−	0.0535427i
$392$	12.6563	+	3.69546i	0.639242	+	0.186649i
$393$	15.1167			0.762535
$394$	−13.2929	−	29.0686i	−0.669687	−	1.46446i
$395$		−	9.49414i		−	0.477702i
$396$	−2.18664	+	2.52866i	−0.109883	+	0.127070i
$397$	−6.45977			−0.324206			−0.162103	−	0.986774i	$-0.551828\pi$
$397$	−6.45977			−0.324206			−0.162103	+	0.986774i	$0.551828\pi$
$398$	−4.91036	−	10.7379i	−0.246134	−	0.538241i
$399$		−	25.0034i		−	1.25174i
$400$	0.132236	+	0.906742i	0.00661182	+	0.0453371i
$401$			26.1702i			1.30688i	0.756979	+	0.653439i	$0.226674\pi$
$401$			26.1702i			1.30688i	−0.756979	+	0.653439i	$0.773326\pi$
$402$	−2.49799	+	1.14231i	−0.124588	+	0.0569735i
$403$		−	0.720639i		−	0.0358976i
$404$	3.40112	−	3.93311i	0.169212	−	0.195679i
$405$		−	2.28672i		−	0.113628i
$406$	−12.3673	−	27.0446i	−0.613780	−	1.34220i
$407$			3.11757i			0.154532i
$408$	−0.604682	−	0.176558i	−0.0299362	−	0.00874092i
$409$	31.4425			1.55473			0.777366	−	0.629048i	$-0.216555\pi$
$409$	31.4425			1.55473			0.777366	+	0.629048i	$0.216555\pi$
$410$	−26.2980	+	12.0259i	−1.29877	+	0.593918i
$411$	8.64369			0.426362
$412$	−21.9240	+	25.3533i	−1.08012	+	1.24907i
$413$			13.4259i			0.660646i
$414$	3.61070	+	5.74132i	0.177456	+	0.282171i
$415$		−	34.5554i		−	1.69626i
$416$	−1.02533	+	0.662597i	−0.0502710	+	0.0324865i
$417$	−12.0852			−0.591817
$418$	−7.19783	−	15.7401i	−0.352057	−	0.769871i
$419$	−8.80834			−0.430316			−0.215158	−	0.976579i	$-0.569027\pi$
$419$	−8.80834			−0.430316			−0.215158	+	0.976579i	$0.569027\pi$
$420$	−10.2156	+	11.8135i	−0.498470	+	0.576438i
$421$		−	20.1534i		−	0.982218i	−0.871098	−	0.491109i	$-0.836592\pi$
$421$		−	20.1534i		−	0.982218i	0.871098	−	0.491109i	$-0.163408\pi$
$422$	17.5483	−	8.02472i	0.854237	−	0.390637i
$423$			6.03026i			0.293201i
$424$	8.76578	−	30.0214i	0.425704	−	1.45797i
$425$			0.0510202i			0.00247484i
$426$	5.26361	+	11.5103i	0.255023	+	0.557678i
$427$			33.8035i			1.63586i
$428$	6.16537	−	7.12973i	0.298015	−	0.344629i
$429$			0.360721i			0.0174158i
$430$	7.87959	−	3.60329i	0.379988	−	0.173766i
$431$	−23.3895			−1.12663			−0.563317	−	0.826241i	$-0.690475\pi$
$431$	−23.3895			−1.12663			−0.563317	+	0.826241i	$0.690475\pi$
$432$	3.95813	−	0.577241i	0.190436	−	0.0277725i
$433$			13.5765i			0.652444i	0.945293	+	0.326222i	$0.105776\pi$
$433$			13.5765i			0.652444i	−0.945293	+	0.326222i	$0.894224\pi$
$434$	14.6659	−	6.70663i	0.703986	−	0.321929i
$435$	14.0810			0.675134
$436$	−15.6490	−	13.5323i	−0.749450	−	0.648080i
$437$	−34.8066	+	4.63885i	−1.66503	+	0.221906i
$438$	18.8173	−	8.60505i	0.899127	−	0.411165i
$439$			41.3682i			1.97440i	0.159500	+	0.987198i	$0.449012\pi$
$439$			41.3682i			1.97440i	−0.159500	+	0.987198i	$0.550988\pi$
$440$	−3.03010	+	10.3776i	−0.144454	+	0.494732i
$441$	−4.66154			−0.221978
$442$	−0.0618153	+	0.0282678i	−0.00294025	+	0.00134456i
$443$		−	14.5889i		−	0.693138i	−0.938024	−	0.346569i	$-0.887347\pi$
$443$		−	14.5889i		−	0.693138i	0.938024	−	0.346569i	$-0.112653\pi$
$444$	2.43997	−	2.82162i	0.115796	−	0.133908i
$445$	−25.7249			−1.21948
$446$	14.9211	−	6.82332i	0.706534	−	0.323094i
$447$	−6.26416			−0.296285
$448$	−23.0269	−	14.7003i	−1.08792	−	0.694524i
$449$	−26.5707			−1.25395			−0.626975	−	0.779040i	$-0.715707\pi$
$449$	−26.5707			−1.25395			−0.626975	+	0.779040i	$0.715707\pi$
$450$	−0.134732	−	0.294628i	−0.00635132	−	0.0138889i
$451$	−14.9463			−0.703794
$452$	−22.9312	−	19.8296i	−1.07860	−	0.932706i
$453$	−7.96308			−0.374138
$454$	4.99990	+	10.9337i	0.234657	+	0.513142i
$455$			1.68523i			0.0790046i
$456$	−5.80444	+	19.8793i	−0.271818	+	0.930932i
$457$		−	25.5083i		−	1.19323i	−0.802529	−	0.596613i	$-0.796513\pi$
$457$		−	25.5083i		−	1.19323i	0.802529	−	0.596613i	$-0.203487\pi$
$458$	−31.5988	+	14.4499i	−1.47651	+	0.675201i
$459$	0.222714			0.0103954
$460$	18.3405	+	12.0292i	0.855132	+	0.560862i
$461$	4.44751			0.207141			0.103570	−	0.994622i	$-0.466973\pi$
$461$	4.44751			0.207141			0.103570	+	0.994622i	$0.466973\pi$
$462$	−7.34113	+	3.35705i	−0.341540	+	0.156184i
$463$		−	26.1370i		−	1.21469i	−0.794438	−	0.607345i	$-0.792234\pi$
$463$		−	26.1370i		−	1.21469i	0.794438	−	0.607345i	$-0.207766\pi$
$464$	3.55450	+	24.3732i	0.165014	+	1.13150i
$465$			7.63595i			0.354109i
$466$	−0.891188	−	1.94883i	−0.0412835	−	0.0902778i
$467$	36.8413			1.70481			0.852407	−	0.522879i	$-0.175142\pi$
$467$	36.8413			1.70481			0.852407	+	0.522879i	$0.175142\pi$
$468$	0.282319	−	0.326478i	0.0130502	−	0.0150915i
$469$	−6.63266			−0.306268
$470$	8.11007	+	17.7349i	0.374090	+	0.818051i
$471$	14.6161			0.673474
$472$	3.11677	−	10.6744i	0.143461	−	0.491331i
$473$	4.47831			0.205913
$474$	−5.33978	+	2.44185i	−0.245264	+	0.112158i
$475$	1.67732			0.0769606
$476$	−1.15057	−	0.994945i	−0.0527363	−	0.0456032i
$477$			11.0574i			0.506281i
$478$	−1.19805	+	0.547863i	−0.0547977	+	0.0250587i
$479$	3.16502			0.144613			0.0723067	−	0.997382i	$-0.476964\pi$
$479$	3.16502			0.144613			0.0723067	+	0.997382i	$0.476964\pi$
$480$	10.8645	−	7.02094i	0.495894	−	0.320460i
$481$		−	0.402513i		−	0.0183530i
$482$	−11.2219	+	5.13173i	−0.511145	+	0.233744i
$483$	2.16355	+	16.2337i	0.0984449	+	0.738661i
$484$	10.7352	−	12.4144i	0.487964	−	0.564289i
$485$	37.3590			1.69639
$486$	−1.28612	+	0.588134i	−0.0583395	+	0.0266783i
$487$			7.18055i			0.325382i	0.986677	+	0.162691i	$0.0520173\pi$
$487$			7.18055i			0.325382i	−0.986677	+	0.162691i	$0.947983\pi$
$488$	7.84734	−	26.8759i	0.355232	−	1.21661i
$489$	6.24865			0.282574
$490$	−13.7095	+	6.26929i	−0.619334	+	0.283218i
$491$		−	6.31534i		−	0.285007i	−0.989794	−	0.142504i	$-0.954485\pi$
$491$		−	6.31534i		−	0.285007i	0.989794	−	0.142504i	$-0.0455152\pi$
$492$	13.5275	+	11.6978i	0.609865	+	0.527376i
$493$			1.37142i			0.0617655i
$494$	0.929319	+	2.03221i	0.0418120	+	0.0914336i
$495$		−	3.82223i		−	0.171797i
$496$	−13.2172	+	1.92756i	−0.593471	+	0.0865498i
$497$			30.5623i			1.37090i
$498$	−19.4350	+	8.88749i	−0.870901	+	0.398258i
$499$			15.5187i			0.694713i	0.937733	+	0.347356i	$0.112921\pi$
$499$			15.5187i			0.694713i	−0.937733	+	0.347356i	$0.887079\pi$
$500$	16.5045	+	14.2721i	0.738102	+	0.638268i
$501$	−20.4559			−0.913903
$502$	2.03766	+	4.45592i	0.0909454	+	0.198877i
$503$	25.7887			1.14986			0.574931	−	0.818202i	$-0.305029\pi$
$503$	25.7887			1.14986			0.574931	+	0.818202i	$0.305029\pi$
$504$	9.27165	+	2.70718i	0.412992	+	0.120587i
$505$			5.94513i			0.264555i
$506$	6.03526	+	9.59658i	0.268300	+	0.426620i
$507$			12.9534i			0.575282i
$508$	−29.7960	−	25.7658i	−1.32198	−	1.14317i
$509$	15.2413			0.675560			0.337780	−	0.941225i	$-0.390324\pi$
$509$	15.2413			0.675560			0.337780	+	0.941225i	$0.390324\pi$
$510$	0.655000	−	0.299528i	0.0290039	−	0.0132633i
$511$	49.9638			2.21027
$512$	14.8952	+	17.0333i	0.658282	+	0.752771i
$513$		−	7.32186i		−	0.323268i
$514$	1.33117	+	2.91097i	0.0587154	+	0.128397i
$515$		−	38.3231i		−	1.68872i
$516$	−4.05319	−	3.50496i	−0.178432	−	0.154297i
$517$			10.0795i			0.443297i
$518$	8.19164	−	3.74599i	0.359920	−	0.164589i
$519$			12.6233i			0.554102i
$520$	0.391218	−	1.33986i	0.0171561	−	0.0587567i
$521$			16.0695i			0.704017i	0.935997	+	0.352008i	$0.114501\pi$
$521$			16.0695i			0.704017i	−0.935997	+	0.352008i	$0.885499\pi$
$522$	−3.62158	−	7.91959i	−0.158512	−	0.346631i
$523$	23.1547			1.01248			0.506242	−	0.862391i	$-0.331034\pi$
$523$	23.1547			1.01248			0.506242	+	0.862391i	$0.331034\pi$
$524$	−22.8688	−	19.7756i	−0.999027	−	0.863900i
$525$		−	0.782297i		−	0.0341422i
$526$	−0.708039	−	1.54832i	−0.0308720	−	0.0675101i
$527$	−0.743701			−0.0323961
$528$	6.61598	−	0.964853i	0.287924	−	0.0419898i
$529$	22.1972	−	6.02365i	0.965096	−	0.261898i
$530$	14.8710	+	32.5196i	0.645955	+	1.41256i
$531$			3.93157i			0.170616i
$532$	−32.7094	+	37.8256i	−1.41813	+	1.63995i
$533$	1.92973			0.0835860
$534$	6.61634	+	14.4685i	0.286317	+	0.626111i
$535$			10.7770i			0.465932i
$536$	5.27337	+	1.53974i	0.227775	+	0.0665068i
$537$	−10.9656			−0.473202
$538$	−9.44074	−	20.6448i	−0.407019	−	0.890061i
$539$	−7.79172			−0.335613
$540$	−2.99148	+	3.45939i	−0.128733	+	0.148868i
$541$	−4.33392			−0.186330			−0.0931650	−	0.995651i	$-0.529698\pi$
$541$	−4.33392			−0.186330			−0.0931650	+	0.995651i	$0.529698\pi$
$542$	−25.0154	+	11.4394i	−1.07451	+	0.491365i
$543$	0.836647			0.0359040
$544$	0.683802	+	1.05814i	0.0293178	+	0.0453675i
$545$	23.6544			1.01324
$546$	0.947820	−	0.433432i	0.0405630	−	0.0185492i
$547$		−	38.0780i		−	1.62810i	−0.580797	−	0.814049i	$-0.697259\pi$
$547$		−	38.0780i		−	1.62810i	0.580797	−	0.814049i	$-0.302741\pi$
$548$	−13.0763	−	11.3076i	−0.558593	−	0.483039i
$549$			9.89882i			0.422471i
$550$	−0.225203	−	0.492469i	−0.00960269	−	0.0209989i
$551$	45.0861			1.92073
$552$	2.04844	−	13.4091i	0.0871875	−	0.570729i
$553$	−14.1782			−0.602918
$554$	6.16090	+	13.4725i	0.261751	+	0.572392i
$555$			4.26506i			0.181042i
$556$	18.2828	+	15.8099i	0.775362	+	0.670488i
$557$		−	27.4879i		−	1.16470i	−0.812938	−	0.582350i	$-0.802133\pi$
$557$		−	27.4879i		−	1.16470i	0.812938	−	0.582350i	$-0.197867\pi$
$558$	4.29468	−	1.96393i	0.181808	−	0.0831399i
$559$	−0.578199			−0.0244552
$560$	30.9087	−	4.50762i	1.30613	−	0.190482i
$561$	0.372265			0.0157170
$562$	6.45105	−	2.95003i	0.272121	−	0.124439i
$563$	36.8387			1.55257			0.776284	−	0.630384i	$-0.217102\pi$
$563$	36.8387			1.55257			0.776284	+	0.630384i	$0.217102\pi$
$564$	7.88876	−	9.12268i	0.332177	−	0.384134i
$565$	34.6620			1.45824
$566$	−3.38604	−	7.40452i	−0.142326	−	0.311235i
$567$	−3.41490			−0.143412
$568$	7.09491	−	24.2989i	0.297696	−	1.01956i
$569$		−	29.8461i		−	1.25121i	−0.780139	−	0.625606i	$-0.784852\pi$
$569$		−	29.8461i		−	1.25121i	0.780139	−	0.625606i	$-0.215148\pi$
$570$	−9.84714	−	21.5335i	−0.412451	−	0.901939i
$571$	−4.27041			−0.178711			−0.0893555	−	0.996000i	$-0.528481\pi$
$571$	−4.27041			−0.178711			−0.0893555	+	0.996000i	$0.528481\pi$
$572$	0.471894	−	0.545706i	0.0197309	−	0.0228171i
$573$			2.31708i			0.0967973i
$574$	17.9591	+	39.2725i	0.749597	+	1.63920i
$575$	−1.08902	+	0.145139i	−0.0454151	+	0.00605270i
$576$	−6.74308	−	4.30475i	−0.280962	−	0.179365i
$577$	−5.65262			−0.235322			−0.117661	−	0.993054i	$-0.537540\pi$
$577$	−5.65262			−0.235322			−0.117661	+	0.993054i	$0.537540\pi$
$578$	−9.96910	−	21.8002i	−0.414660	−	0.906769i
$579$		−	17.7641i		−	0.738250i
$580$	−21.3021	−	18.4208i	−0.884520	−	0.764881i
$581$	−51.6037			−2.14088
$582$	−9.60858	−	21.0118i	−0.398288	−	0.870968i
$583$			18.4823i			0.765458i
$584$	−39.7243	−	11.5989i	−1.64380	−	0.479965i
$585$			0.493492i			0.0204034i
$586$	−2.39528	+	1.09535i	−0.0989483	+	0.0452484i
$587$		−	18.3560i		−	0.757632i	−0.925472	−	0.378816i	$-0.876331\pi$
$587$		−	18.3560i		−	0.757632i	0.925472	−	0.378816i	$-0.123669\pi$
$588$	7.05206	+	6.09821i	0.290822	+	0.251486i
$589$			24.4496i			1.00743i
$590$	5.28755	+	11.5627i	0.217685	+	0.476029i
$591$		−	22.6018i		−	0.929716i
$592$	−7.38248	+	1.07664i	−0.303418	+	0.0442495i
$593$	6.20287			0.254721			0.127361	−	0.991856i	$-0.459349\pi$
$593$	6.20287			0.254721			0.127361	+	0.991856i	$0.459349\pi$
$594$	−2.14974	+	0.983061i	−0.0882047	+	0.0403355i
$595$	1.73916			0.0712985
$596$	9.47654	+	8.19475i	0.388174	+	0.335670i
$597$		−	8.34906i		−	0.341704i
$598$	−0.779219	−	1.23902i	−0.0318646	−	0.0506674i
$599$			10.1258i			0.413730i	0.978370	+	0.206865i	$0.0663260\pi$
$599$			10.1258i			0.413730i	−0.978370	+	0.206865i	$0.933674\pi$
$600$	−0.181607	+	0.621975i	−0.00741408	+	0.0253920i
$601$	25.2858			1.03143			0.515714	−	0.856761i	$-0.327527\pi$
$601$	25.2858			1.03143			0.515714	+	0.856761i	$0.327527\pi$
$602$	−5.38102	−	11.7671i	−0.219314	−	0.479591i
$603$	−1.94227			−0.0790953
$604$	12.0467	+	10.4173i	0.490173	+	0.423873i
$605$			18.7651i			0.762909i
$606$	3.34372	−	1.52906i	0.135829	−	0.0621139i
$607$			23.2916i			0.945379i	0.881229	+	0.472689i	$0.156717\pi$
$607$			23.2916i			0.945379i	−0.881229	+	0.472689i	$0.843283\pi$
$608$	34.7871	−	22.4804i	1.41080	−	0.911699i
$609$		−	21.0281i		−	0.852101i
$610$	13.3129	+	29.1123i	0.539023	+	1.17872i
$611$		−	1.30138i		−	0.0526481i
$612$	−0.336926	−	0.291354i	−0.0136194	−	0.0117773i
$613$			34.8237i			1.40652i	0.710934	+	0.703259i	$0.248272\pi$
$613$			34.8237i			1.40652i	−0.710934	+	0.703259i	$0.751728\pi$
$614$	−38.1379	+	17.4403i	−1.53912	+	0.703831i
$615$	−20.4476			−0.824527
$616$	15.4975	+	4.52503i	0.624412	+	0.182319i
$617$		−	38.6296i		−	1.55517i	−0.628778	−	0.777585i	$-0.716444\pi$
$617$		−	38.6296i		−	1.55517i	0.628778	−	0.777585i	$-0.283556\pi$
$618$	−21.5540	+	9.85652i	−0.867029	+	0.396487i
$619$	1.81828			0.0730829			0.0365414	−	0.999332i	$-0.488366\pi$
$619$	1.81828			0.0730829			0.0365414	+	0.999332i	$0.488366\pi$
$620$	9.98933	−	11.5518i	0.401181	−	0.463932i
$621$	0.633562	+	4.75380i	0.0254240	+	0.190763i
$622$	−1.91948	+	0.877767i	−0.0769642	+	0.0351952i
$623$			38.4166i			1.53913i
$624$	−0.854196	+	0.124573i	−0.0341952	+	0.00498691i
$625$	−26.0929			−1.04372
$626$	−34.3241	+	15.6962i	−1.37187	+	0.627346i
$627$		−	12.2384i		−	0.488756i
$628$	−22.1115	−	19.1207i	−0.882344	−	0.763000i
$629$	−0.415394			−0.0165628
$630$	−10.0432	+	4.59269i	−0.400130	+	0.182977i
$631$	−9.23992			−0.367835			−0.183918	−	0.982942i	$-0.558878\pi$
$631$	−9.23992			−0.367835			−0.183918	+	0.982942i	$0.558878\pi$
$632$	11.2725	+	3.29141i	0.448398	+	0.130925i
$633$	13.6444			0.542316
$634$	5.94939	+	13.0100i	0.236281	+	0.516693i
$635$	45.0384			1.78730
$636$	14.4652	−	16.7278i	0.573582	−	0.663299i
$637$	1.00600			0.0398590
$638$	−6.05344	−	13.2375i	−0.239658	−	0.524079i
$639$			8.94968i			0.354044i
$640$	−25.6208	−	3.59149i	−1.01275	−	0.141966i
$641$		−	1.91640i		−	0.0756931i	−0.999284	−	0.0378465i	$-0.987950\pi$
$641$		−	1.91640i		−	0.0756931i	0.999284	−	0.0378465i	$-0.0120498\pi$
$642$	6.06132	−	2.77180i	0.239221	−	0.109394i
$643$	−25.7633			−1.01601			−0.508003	−	0.861355i	$-0.669616\pi$
$643$	−25.7633			−1.01601			−0.508003	+	0.861355i	$0.669616\pi$
$644$	17.9639	−	27.3891i	0.707876	−	1.07928i
$645$	6.12665			0.241237
$646$	2.09725	−	0.959059i	0.0825151	−	0.0377337i
$647$			44.3852i			1.74496i	0.488649	+	0.872481i	$0.337490\pi$
$647$			44.3852i			1.74496i	−0.488649	+	0.872481i	$0.662510\pi$
$648$	2.71506	+	0.792755i	0.106658	+	0.0311424i
$649$			6.57158i			0.257957i
$650$	0.0290762	+	0.0635831i	0.00114046	+	0.00249393i
$651$	11.4032			0.446928
$652$	−9.45307	−	8.17447i	−0.370211	−	0.320137i
$653$	−1.40588			−0.0550162			−0.0275081	−	0.999622i	$-0.508757\pi$
$653$	−1.40588			−0.0550162			−0.0275081	+	0.999622i	$0.508757\pi$
$654$	−6.08380	−	13.3039i	−0.237895	−	0.520224i
$655$	34.5676			1.35067
$656$	−5.16163	−	35.3932i	−0.201528	−	1.38187i
$657$	14.6311			0.570814
$658$	26.4847	−	12.1113i	1.03248	−	0.472147i
$659$	−23.4125			−0.912020			−0.456010	−	0.889975i	$-0.650722\pi$
$659$	−23.4125			−0.912020			−0.456010	+	0.889975i	$0.650722\pi$
$660$	−5.00023	+	5.78234i	−0.194634	+	0.225077i
$661$		−	16.2832i		−	0.633343i	−0.948535	−	0.316671i	$-0.897435\pi$
$661$		−	16.2832i		−	0.633343i	0.948535	−	0.316671i	$-0.102565\pi$
$662$	9.19854	−	4.20643i	0.357511	−	0.163488i
$663$	−0.0480635			−0.00186663
$664$	41.0281	+	11.9796i	1.59220	+	0.464898i
$665$		−	57.1758i		−	2.21718i
$666$	2.39879	−	1.09695i	0.0929513	−	0.0425061i
$667$	−29.2727	+	3.90131i	−1.13344	+	0.151059i
$668$	30.9461	+	26.7604i	1.19734	+	1.03539i
$669$	11.6016			0.448546
$670$	−5.71219	+	2.61215i	−0.220681	+	0.100916i
$671$			16.5458i			0.638743i
$672$	−10.4848	−	16.2246i	−0.404460	−	0.625878i
$673$	−30.6829			−1.18274			−0.591369	−	0.806401i	$-0.701412\pi$
$673$	−30.6829			−1.18274			−0.591369	+	0.806401i	$0.701412\pi$
$674$	31.8080	−	14.5456i	1.22520	−	0.560276i
$675$		−	0.229084i		−	0.00881743i
$676$	16.9456	−	19.5962i	0.651755	−	0.753699i
$677$		−	27.1779i		−	1.04453i	−0.852783	−	0.522265i	$-0.825087\pi$
$677$		−	27.1779i		−	1.04453i	0.852783	−	0.522265i	$-0.174913\pi$
$678$	−8.91491	−	19.4949i	−0.342375	−	0.748698i
$679$		−	55.7906i		−	2.14105i
$680$	−1.38274	−	0.403738i	−0.0530256	−	0.0154827i
$681$			8.50129i			0.325770i
$682$	7.17852	−	3.28270i	0.274880	−	0.125701i
$683$			7.03091i			0.269030i	0.990912	+	0.134515i	$0.0429477\pi$
$683$			7.03091i			0.269030i	−0.990912	+	0.134515i	$0.957052\pi$
$684$	−9.57843	+	11.0766i	−0.366241	+	0.423526i
$685$	19.7657			0.755208
$686$	−4.69661	−	10.2704i	−0.179317	−	0.392127i
$687$	−24.5691			−0.937370
$688$	1.54656	+	10.6047i	0.0589621	+	0.404302i
$689$		−	2.38626i		−	0.0909094i
$690$	8.25667	+	13.1288i	0.314326	+	0.499805i
$691$		−	14.4883i		−	0.551161i	−0.961278	−	0.275581i	$-0.911130\pi$
$691$		−	14.4883i		−	0.551161i	0.961278	−	0.275581i	$-0.0888701\pi$
$692$	16.5138	−	19.0968i	0.627760	−	0.725951i
$693$	−5.70798			−0.216828
$694$	−3.82463	+	1.74898i	−0.145181	+	0.0663904i
$695$	−27.6355			−1.04828
$696$	−4.88159	+	16.7186i	−0.185036	+	0.633718i
$697$		−	1.99149i		−	0.0754330i
$698$	15.6934	+	34.3180i	0.594004	+	1.29895i
$699$		−	1.51528i		−	0.0573132i
$700$	−1.02340	+	1.18347i	−0.0386808	+	0.0447311i
$701$			30.6833i			1.15889i	0.815011	+	0.579446i	$0.196731\pi$
$701$			30.6833i			1.15889i	−0.815011	+	0.579446i	$0.803269\pi$
$702$	0.277554	−	0.126924i	0.0104756	−	0.00479043i
$703$			13.6563i			0.515057i
$704$	−11.2710	−	7.19536i	−0.424792	−	0.271185i
$705$			13.7895i			0.519343i
$706$	−7.89038	−	17.2545i	−0.296958	−	0.649381i
$707$	8.87824			0.333901
$708$	5.14327	−	5.94775i	0.193296	−	0.223530i
$709$		−	40.3842i		−	1.51666i	−0.651872	−	0.758329i	$-0.726016\pi$
$709$		−	40.3842i		−	1.51666i	0.651872	−	0.758329i	$-0.273984\pi$
$710$	12.0364	+	26.3209i	0.451718	+	0.987806i
$711$	−4.15186			−0.155707
$712$	8.91827	−	30.5436i	0.334226	−	1.14467i
$713$	−2.11563	−	15.8742i	−0.0792309	−	0.594492i
$714$	−0.447303	−	0.978153i	−0.0167399	−	0.0366064i
$715$			0.824868i			0.0308483i
$716$	16.5890	+	14.3452i	0.619960	+	0.536105i
$717$	−0.931528			−0.0347885
$718$	18.2709	+	39.9543i	0.681862	+	1.49108i
$719$		−	10.1289i		−	0.377743i	−0.982002	−	0.188871i	$-0.939517\pi$
$719$		−	10.1289i		−	0.377743i	0.982002	−	0.188871i	$-0.0604829\pi$
$720$	9.05113	−	1.31999i	0.337316	−	0.0491930i
$721$	−57.2302			−2.13136
$722$	−20.3551	−	44.5120i	−0.757537	−	1.65657i
$723$	−8.72544			−0.324503
$724$	−1.26570	−	1.09450i	−0.0470392	−	0.0406767i
$725$	1.41064			0.0523898
$726$	10.5540	−	4.82629i	0.391697	−	0.179121i
$727$	19.6637			0.729287			0.364643	−	0.931147i	$-0.381191\pi$
$727$	19.6637			0.729287			0.364643	+	0.931147i	$0.381191\pi$
$728$	−2.00089	−	0.584231i	−0.0741581	−	0.0216530i
$729$	−1.00000			−0.0370370
$730$	43.0299	−	19.6773i	1.59261	−	0.728291i
$731$			0.596703i			0.0220699i
$732$	12.9496	−	14.9751i	0.478631	−	0.553496i
$733$			43.7893i			1.61740i	0.588225	+	0.808698i	$0.299827\pi$
$733$			43.7893i			1.61740i	−0.588225	+	0.808698i	$0.700173\pi$
$734$	−7.20243	−	15.7501i	−0.265847	−	0.581347i
$735$	−10.6596			−0.393186
$736$	−20.6407	+	17.6058i	−0.760825	+	0.648957i
$737$	−3.24649			−0.119586
$738$	5.25903	+	11.5003i	0.193588	+	0.423333i
$739$		−	5.01539i		−	0.184494i	−0.995736	−	0.0922471i	$-0.970595\pi$
$739$		−	5.01539i		−	0.184494i	0.995736	−	0.0922471i	$-0.0294050\pi$
$740$	5.57954	−	6.45226i	0.205108	−	0.237190i
$741$			1.58011i			0.0580470i
$742$	48.5635	−	22.2078i	1.78282	−	0.815274i
$743$	−25.6622			−0.941456			−0.470728	−	0.882278i	$-0.656009\pi$
$743$	−25.6622			−0.941456			−0.470728	+	0.882278i	$0.656009\pi$
$744$	−9.06628	−	2.64722i	−0.332386	−	0.0970517i
$745$	−14.3244			−0.524804
$746$	−33.8747	+	15.4907i	−1.24024	+	0.567155i
$747$	−15.1113			−0.552895
$748$	−0.563169	−	0.486996i	−0.0205915	−	0.0178063i
$749$	16.0940			0.588062
$750$	6.41639	+	14.0312i	0.234293	+	0.512348i
$751$	−2.55682			−0.0932995			−0.0466498	−	0.998911i	$-0.514854\pi$
$751$	−2.55682			−0.0932995			−0.0466498	+	0.998911i	$0.514854\pi$
$752$	−23.8685	+	3.48091i	−0.870396	+	0.126936i
$753$			3.46463i			0.126258i
$754$	0.781565	+	1.70911i	0.0284629	+	0.0622421i
$755$	−18.2093			−0.662705
$756$	5.16612	+	4.46736i	0.187890	+	0.162476i
$757$			38.7648i			1.40893i	0.709738	+	0.704465i	$0.248813\pi$
$757$			38.7648i			1.40893i	−0.709738	+	0.704465i	$0.751187\pi$
$758$	16.1022	+	35.2119i	0.584859	+	1.27896i
$759$	1.05899	+	7.94594i	0.0384390	+	0.288419i
$760$	−13.2731	+	45.4583i	−0.481467	+	1.64895i
$761$	8.24722			0.298961			0.149481	−	0.988765i	$-0.452240\pi$
$761$	8.24722			0.298961			0.149481	+	0.988765i	$0.452240\pi$
$762$	−11.5837	−	25.3309i	−0.419633	−	0.917643i
$763$		−	35.3246i		−	1.27883i
$764$	3.03119	−	3.50532i	0.109665	−	0.126818i
$765$	0.509285			0.0184132
$766$	4.27712	+	9.35311i	0.154539	+	0.337942i
$767$		−	0.848463i		−	0.0306362i
$768$	4.56959	+	15.3336i	0.164891	+	0.553303i
$769$		−	3.32777i		−	0.120003i	−0.998198	−	0.0600013i	$-0.980890\pi$
$769$		−	3.32777i		−	0.120003i	0.998198	−	0.0600013i	$-0.0191105\pi$
$770$	−16.7871	+	7.67664i	−0.604965	+	0.276647i
$771$			2.26338i			0.0815136i
$772$	−23.2389	+	26.8738i	−0.836387	+	0.967211i
$773$		−	7.05843i		−	0.253874i	−0.991911	−	0.126937i	$-0.959485\pi$
$773$		−	7.05843i		−	0.253874i	0.991911	−	0.126937i	$-0.0405146\pi$
$774$	−1.57575	−	3.44581i	−0.0566391	−	0.123857i
$775$			0.764969i			0.0274785i
$776$	−12.9516	+	44.3570i	−0.464934	+	1.59232i
$777$	6.36928			0.228496
$778$	3.79650	−	1.73612i	0.136111	−	0.0622427i
$779$	−65.4713			−2.34575
$780$	0.645585	−	0.746564i	0.0231156	−	0.0267313i
$781$			14.9593i			0.535287i
$782$	−1.27867	+	0.804155i	−0.0457253	+	0.0287565i
$783$		−	6.15775i		−	0.220060i
$784$	−2.69083	−	18.4510i	−0.0961011	−	0.658964i
$785$	33.4229			1.19291
$786$	−8.89062	−	19.4418i	−0.317118	−	0.693466i
$787$	−36.6452			−1.30626			−0.653130	−	0.757246i	$-0.726545\pi$
$787$	−36.6452			−1.30626			−0.653130	+	0.757246i	$0.726545\pi$
$788$	−29.5677	+	34.1925i	−1.05330	+	1.21806i
$789$		−	1.20387i		−	0.0428590i
$790$	−12.2106	+	5.58383i	−0.434433	+	0.198664i
$791$		−	51.7629i		−	1.84048i
$792$	4.53820	+	1.32508i	0.161258	+	0.0470848i
$793$		−	2.13624i		−	0.0758602i
$794$	3.79921	+	8.30802i	0.134829	+	0.294841i
$795$			25.2851i			0.896769i
$796$	−10.9222	+	12.6306i	−0.387128	+	0.447680i
$797$		−	37.8542i		−	1.34086i	−0.741971	−	0.670432i	$-0.766109\pi$
$797$		−	37.8542i		−	1.34086i	0.741971	−	0.670432i	$-0.233891\pi$
$798$	−32.1573	+	14.7054i	−1.13836	+	0.520564i
$799$	−1.34302			−0.0475128
$800$	1.08840	−	0.703357i	0.0384809	−	0.0248674i
$801$			11.2497i			0.397489i
$802$	33.6580	−	15.3916i	1.18850	−	0.543496i
$803$	24.4558			0.863026
$804$	2.93830	+	2.54087i	0.103626	+	0.0896096i
$805$	4.94743	+	37.1220i	0.174374	+	1.30838i
$806$	−0.926826	+	0.423832i	−0.0326461	+	0.0149288i
$807$		−	16.0520i		−	0.565058i
$808$	−7.05875	−	2.06105i	−0.248326	−	0.0725074i
$809$	−16.8995			−0.594153			−0.297077	−	0.954854i	$-0.596012\pi$
$809$	−16.8995			−0.594153			−0.297077	+	0.954854i	$0.596012\pi$
$810$	−2.94099	+	1.34490i	−0.103336	+	0.0472549i
$811$			33.7625i			1.18556i	0.805364	+	0.592781i	$0.201970\pi$
$811$			33.7625i			1.18556i	−0.805364	+	0.592781i	$0.798030\pi$
$812$	−27.5089	+	31.8117i	−0.965372	+	1.11637i
$813$	−19.4504			−0.682154
$814$	4.00956	−	1.83355i	0.140535	−	0.0642659i
$815$	14.2889			0.500519
$816$	0.128560	+	0.881532i	0.00450049	+	0.0308598i
$817$	19.6170			0.686310
$818$	−18.4924	−	40.4388i	−0.646572	−	1.41391i
$819$	0.736962			0.0257515
$820$	30.9335	+	26.7495i	1.08025	+	0.934133i
$821$	6.08599			0.212403			0.106201	−	0.994345i	$-0.466131\pi$
$821$	6.08599			0.212403			0.106201	+	0.994345i	$0.466131\pi$
$822$	−5.08365	−	11.1168i	−0.177313	−	0.387743i
$823$			9.97406i			0.347674i	0.984774	+	0.173837i	$0.0556166\pi$
$823$			9.97406i			0.347674i	−0.984774	+	0.173837i	$0.944383\pi$
$824$	45.5016	+	13.2858i	1.58512	+	0.462832i
$825$		−	0.382911i		−	0.0133313i
$826$	17.2673	−	7.89623i	0.600806	−	0.274745i
$827$	−20.5116			−0.713258			−0.356629	−	0.934246i	$-0.616074\pi$
$827$	−20.5116			−0.713258			−0.356629	+	0.934246i	$0.616074\pi$
$828$	5.26044	−	8.02046i	0.182813	−	0.278730i
$829$	−7.44995			−0.258748			−0.129374	−	0.991596i	$-0.541297\pi$
$829$	−7.44995			−0.258748			−0.129374	+	0.991596i	$0.541297\pi$
$830$	−44.4423	+	20.3232i	−1.54261	+	0.705428i
$831$			10.4753i			0.363385i
$832$	1.45521	+	0.929000i	0.0504503	+	0.0322073i
$833$		−	1.03819i		−	0.0359712i
$834$	7.10774	+	15.5430i	0.246121	+	0.538211i
$835$	−46.7770			−1.61878
$836$	−16.0103	+	18.5145i	−0.553727	+	0.640338i
$837$	3.33926			0.115422
$838$	5.18049	+	11.3286i	0.178957	+	0.391339i
$839$	−14.4632			−0.499324			−0.249662	−	0.968333i	$-0.580319\pi$
$839$	−14.4632			−0.499324			−0.249662	+	0.968333i	$0.580319\pi$
$840$	21.2017	+	6.19056i	0.731527	+	0.213595i
$841$	8.91784			0.307512
$842$	−25.9197	+	11.8529i	−0.893252	+	0.408479i
$843$	5.01591			0.172757
$844$	−20.6415	−	17.8495i	−0.710509	−	0.614407i
$845$			29.6208i			1.01899i
$846$	7.75562	−	3.54660i	0.266644	−	0.121935i
$847$	28.0231			0.962884
$848$	−43.7664	+	6.38275i	−1.50295	+	0.219185i
$849$		−	5.75726i		−	0.197589i
$850$	0.0656179	−	0.0300067i	0.00225068	−	0.00102922i
$851$	−1.18168	−	8.86651i	−0.0405076	−	0.303940i
$852$	11.7079	−	13.5392i	0.401108	−	0.463847i
$853$	2.97482			0.101856			0.0509279	−	0.998702i	$-0.483782\pi$
$853$	2.97482			0.101856			0.0509279	+	0.998702i	$0.483782\pi$
$854$	43.4752	−	19.8810i	1.48769	−	0.680312i
$855$		−	16.7430i		−	0.572600i
$856$	−12.7957	−	3.73616i	−0.437349	−	0.127699i
$857$	36.9443			1.26199			0.630997	−	0.775786i	$-0.282646\pi$
$857$	36.9443			1.26199			0.630997	+	0.775786i	$0.282646\pi$
$858$	0.463930	−	0.212152i	0.0158383	−	0.00724276i
$859$			16.5018i			0.563034i	0.959556	+	0.281517i	$0.0908376\pi$
$859$			16.5018i			0.563034i	−0.959556	+	0.281517i	$0.909162\pi$
$860$	−9.26851	−	8.01487i	−0.316054	−	0.273305i
$861$			30.5357i			1.04065i
$862$	13.7562	+	30.0817i	0.468537	+	1.02459i
$863$		−	45.7125i		−	1.55607i	−0.628219	−	0.778037i	$-0.716216\pi$
$863$		−	45.7125i		−	1.55607i	0.628219	−	0.778037i	$-0.283784\pi$
$864$	−3.07031	−	4.75113i	−0.104454	−	0.161637i
$865$			28.8660i			0.981473i
$866$	17.4610	−	7.98479i	0.593347	−	0.271334i
$867$		−	16.9504i		−	0.575666i
$868$	−17.2510	−	14.9177i	−0.585538	−	0.506339i
$869$	−6.93980			−0.235417
$870$	−8.28153	−	18.1099i	−0.280770	−	0.613982i
$871$	0.419157			0.0142026
$872$	−8.20046	+	28.0852i	−0.277702	+	0.951086i
$873$		−	16.3374i		−	0.552937i
$874$	26.4371	+	42.0372i	0.894247	+	1.42193i
$875$			37.2557i			1.25947i
$876$	−22.1342	−	19.1404i	−0.747846	−	0.646693i
$877$	45.1046			1.52307			0.761537	−	0.648121i	$-0.224445\pi$
$877$	45.1046			1.52307			0.761537	+	0.648121i	$0.224445\pi$
$878$	53.2044	−	24.3300i	1.79556	−	0.821099i
$879$	−1.86241			−0.0628177
$880$	15.1289	−	2.20635i	0.509995	−	0.0743760i
$881$		−	43.8083i		−	1.47594i	−0.674833	−	0.737970i	$-0.735784\pi$
$881$		−	43.8083i		−	1.47594i	0.674833	−	0.737970i	$-0.264216\pi$
$882$	2.74161	+	5.99529i	0.0923148	+	0.201872i
$883$			17.2830i			0.581618i	0.956781	+	0.290809i	$0.0939244\pi$
$883$			17.2830i			0.581618i	−0.956781	+	0.290809i	$0.906076\pi$
$884$	0.0727113	+	0.0628765i	0.00244555	+	0.00211477i
$885$			8.99039i			0.302209i
$886$	−18.7630	+	8.58021i	−0.630355	+	0.288258i
$887$		−	23.4906i		−	0.788737i	−0.918952	−	0.394368i	$-0.870963\pi$
$887$		−	23.4906i		−	0.788737i	0.918952	−	0.394368i	$-0.129037\pi$
$888$	−5.06397	−	1.47860i	−0.169936	−	0.0496186i
$889$		−	67.2587i		−	2.25578i
$890$	15.1297	+	33.0853i	0.507149	+	1.10902i
$891$	−1.67149			−0.0559971
$892$	−17.5512	−	15.1772i	−0.587657	−	0.508172i
$893$			44.1527i			1.47751i
$894$	3.68416	+	8.05644i	0.123217	+	0.269448i
$895$	−25.0753			−0.838175
$896$	−5.36340	+	38.2611i	−0.179179	+	1.27821i
$897$	−0.136728	−	1.02591i	−0.00456520	−	0.0342540i
$898$	15.6271	+	34.1731i	0.521484	+	1.14037i
$899$			20.5623i			0.685792i
$900$	−0.299686	+	0.346562i	−0.00998955	+	0.0115521i
$901$	−2.46263			−0.0820421
$902$	8.79043	+	19.2227i	0.292689	+	0.640046i
$903$		−	9.14931i		−	0.304470i
$904$	−12.0166	+	41.1547i	−0.399665	+	1.36879i
$905$	1.91318			0.0635961
$906$	4.68336	+	10.2415i	0.155594	+	0.340250i
$907$	48.6715			1.61611			0.808056	−	0.589106i	$-0.200520\pi$
$907$	48.6715			1.61611			0.808056	+	0.589106i	$0.200520\pi$
$908$	11.1214	−	12.8609i	0.369075	−	0.426804i
$909$	2.59985			0.0862317
$910$	2.16740	−	0.991138i	0.0718485	−	0.0328559i
$911$	−41.6954			−1.38143			−0.690716	−	0.723126i	$-0.742704\pi$
$911$	−41.6954			−1.38143			−0.690716	+	0.723126i	$0.742704\pi$
$912$	28.9809	−	4.22647i	0.959652	−	0.139953i
$913$	−25.2585			−0.835933
$914$	−32.8066	+	15.0023i	−1.08515	+	0.496231i
$915$			22.6358i			0.748317i
$916$	37.1686	+	32.1412i	1.22809	+	1.06198i
$917$		−	51.6219i		−	1.70471i
$918$	−0.130986	−	0.286437i	−0.00432318	−	0.00945382i
$919$	−17.1500			−0.565725			−0.282862	−	0.959160i	$-0.591284\pi$
$919$	−17.1500			−0.565725			−0.282862	+	0.959160i	$0.591284\pi$
$920$	4.68421	−	30.6628i	0.154434	−	1.01092i
$921$	−29.6535			−0.977117
$922$	−2.61573	−	5.72001i	−0.0861444	−	0.188379i
$923$		−	1.93141i		−	0.0635732i
$924$	8.63513	+	7.46716i	0.284075	+	0.245651i
$925$			0.427273i			0.0140487i
$926$	−33.6153	+	15.3721i	−1.10467	+	0.505158i
$927$	−16.7590			−0.550437
$928$	29.2562	−	18.9062i	0.960383	−	0.620626i
$929$	−50.4355			−1.65474			−0.827368	−	0.561660i	$-0.810163\pi$
$929$	−50.4355			−1.65474			−0.827368	+	0.561660i	$0.810163\pi$
$930$	9.82073	−	4.49096i	0.322034	−	0.147264i
$931$	−34.1311			−1.11860
$932$	−1.98229	+	2.29235i	−0.0649320	+	0.0750883i
$933$	−1.49246			−0.0488610
$934$	−21.6676	−	47.3823i	−0.708987	−	1.55040i
$935$	0.851265			0.0278394
$936$	−0.585931	−	0.171083i	−0.0191517	−	0.00559202i
$937$			34.3371i			1.12174i	0.827902	+	0.560872i	$0.189534\pi$
$937$			34.3371i			1.12174i	−0.827902	+	0.560872i	$0.810466\pi$
$938$	3.90089	+	8.53038i	0.127369	+	0.278527i
$939$	−26.6881			−0.870935
$940$	18.0394	−	20.8610i	0.588380	−	0.680411i
$941$			21.1847i			0.690600i	0.938492	+	0.345300i	$0.112223\pi$
$941$			21.1847i			0.690600i	−0.938492	+	0.345300i	$0.887777\pi$
$942$	−8.59621	−	18.7980i	−0.280080	−	0.612472i
$943$	42.5080	−	5.66524i	1.38425	−	0.184486i
$944$	−15.5617	+	2.26946i	−0.506489	+	0.0738647i
$945$	−7.80892			−0.254024
$946$	−2.63385	−	5.75964i	−0.0856338	−	0.187262i
$947$		−	1.66910i		−	0.0542384i	−0.999632	−	0.0271192i	$-0.991367\pi$
$947$		−	1.66910i		−	0.0542384i	0.999632	−	0.0271192i	$-0.00863336\pi$
$948$	6.28101	+	5.43145i	0.203998	+	0.176405i
$949$	−3.15751			−0.102497
$950$	−0.986487	−	2.15723i	−0.0320059	−	0.0699897i
$951$			10.1157i			0.328024i
$952$	−0.602928	+	2.06493i	−0.0195410	+	0.0669247i
$953$		−	2.48553i		−	0.0805144i	−0.999189	−	0.0402572i	$-0.987182\pi$
$953$		−	2.48553i		−	0.0805144i	0.999189	−	0.0402572i	$-0.0128177\pi$
$954$	14.2211	−	6.50320i	0.460424	−	0.210549i
$955$			5.29850i			0.171456i
$956$	1.40923	+	1.21862i	0.0455778	+	0.0394130i
$957$		−	10.2926i		−	0.332713i
$958$	−1.86145	−	4.07058i	−0.0601409	−	0.131515i
$959$		−	29.5173i		−	0.953164i
$960$	−15.4195	−	9.84376i	−0.497663	−	0.317706i
$961$	19.8493			0.640301
$962$	−0.517678	+	0.236731i	−0.0166906	+	0.00763252i
$963$	4.71288			0.151870
$964$	13.2000	+	11.4146i	0.425144	+	0.367639i
$965$		−	40.6215i		−	1.30765i
$966$	19.6060	−	12.3302i	0.630814	−	0.396717i
$967$		−	34.4514i		−	1.10788i	−0.832556	−	0.553941i	$-0.813123\pi$
$967$		−	34.4514i		−	1.10788i	0.832556	−	0.553941i	$-0.186877\pi$
$968$	−22.2801	−	6.50544i	−0.716109	−	0.209093i
$969$	1.63068			0.0523850
$970$	−21.9721	−	48.0481i	−0.705482	−	1.54273i
$971$	42.1631			1.35308			0.676539	−	0.736407i	$-0.263479\pi$
$971$	42.1631			1.35308			0.676539	+	0.736407i	$0.263479\pi$
$972$	1.51282	+	1.30820i	0.0485237	+	0.0419604i
$973$			41.2699i			1.32305i
$974$	9.23503	−	4.22313i	0.295910	−	0.135318i
$975$			0.0494380i			0.00158328i
$976$	−39.1808	+	5.71400i	−1.25415	+	0.182901i
$977$		−	56.9040i		−	1.82052i	−0.414037	−	0.910260i	$-0.635882\pi$
$977$		−	56.9040i		−	1.82052i	0.414037	−	0.910260i	$-0.364118\pi$
$978$	−3.67504	−	8.03650i	−0.117515	−	0.256979i
$979$			18.8038i			0.600972i
$980$	16.1261	+	13.9449i	0.515129	+	0.445453i
$981$		−	10.3442i		−	0.330266i
$982$	−8.12226	+	3.71426i	−0.259192	+	0.118527i
$983$	28.7573			0.917215			0.458608	−	0.888639i	$-0.348348\pi$
$983$	28.7573			0.917215			0.458608	+	0.888639i	$0.348348\pi$
$984$	7.08874	−	24.2778i	0.225981	−	0.773947i
$985$		−	51.6841i		−	1.64679i
$986$	1.76380	−	0.806577i	0.0561710	−	0.0256867i
$987$	20.5927			0.655473
$988$	2.06710	−	2.39043i	0.0657632	−	0.0760496i
$989$	−12.7365	+	1.69746i	−0.404998	+	0.0539760i
$990$	−4.91584	+	2.24798i	−0.156236	+	0.0714456i
$991$			46.2858i			1.47032i	0.677895	+	0.735159i	$0.262892\pi$
$991$			46.2858i			1.47032i	−0.677895	+	0.735159i	$0.737108\pi$
$992$	10.2526	+	15.8652i	0.325519	+	0.503722i
$993$	7.15217			0.226967
$994$	39.3067	−	17.9747i	1.24673	−	0.570123i
$995$		−	19.0920i		−	0.605256i
$996$	22.8607	+	19.7686i	0.724369	+	0.626392i
$997$	−8.77812			−0.278006			−0.139003	−	0.990292i	$-0.544390\pi$
$997$	−8.77812			−0.278006			−0.139003	+	0.990292i	$0.544390\pi$
$998$	19.9589	−	9.12708i	0.631787	−	0.288913i
$999$	1.86514			0.0590105

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.e.a.91.5	✓	24
3.2	odd	2		828.2.e.f.91.20		24
4.3	odd	2	inner	276.2.e.a.91.7	yes	24
8.3	odd	2		4416.2.i.d.1471.14		24
8.5	even	2		4416.2.i.d.1471.15		24
12.11	even	2		828.2.e.f.91.18		24
23.22	odd	2	inner	276.2.e.a.91.6	yes	24
69.68	even	2		828.2.e.f.91.19		24
92.91	even	2	inner	276.2.e.a.91.8	yes	24
184.45	odd	2		4416.2.i.d.1471.16		24
184.91	even	2		4416.2.i.d.1471.13		24
276.275	odd	2		828.2.e.f.91.17		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.e.a.91.5	✓	24	1.1	even	1	trivial
276.2.e.a.91.6	yes	24	23.22	odd	2	inner
276.2.e.a.91.7	yes	24	4.3	odd	2	inner
276.2.e.a.91.8	yes	24	92.91	even	2	inner
828.2.e.f.91.17		24	276.275	odd	2
828.2.e.f.91.18		24	12.11	even	2
828.2.e.f.91.19		24	69.68	even	2
828.2.e.f.91.20		24	3.2	odd	2
4416.2.i.d.1471.13		24	184.91	even	2
4416.2.i.d.1471.14		24	8.3	odd	2
4416.2.i.d.1471.15		24	8.5	even	2
4416.2.i.d.1471.16		24	184.45	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.588134 - 1.28612i) q^{2} -1.00000i q^{3} +(-1.30820 + 1.51282i) q^{4} -2.28672i q^{5} +(-1.28612 + 0.588134i) q^{6} -3.41490 q^{7} +(2.71506 + 0.792755i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.588134 - 1.28612i) q^{2} -1.00000i q^{3} +(-1.30820 + 1.51282i) q^{4} -2.28672i q^{5} +(-1.28612 + 0.588134i) q^{6} -3.41490 q^{7} +(2.71506 + 0.792755i) q^{8} -1.00000 q^{9} +(-2.94099 + 1.34490i) q^{10} -1.67149 q^{11} +(1.51282 + 1.30820i) q^{12} +0.215808 q^{13} +(2.00842 + 4.39196i) q^{14} -2.28672 q^{15} +(-0.577241 - 3.95813i) q^{16} -0.222714i q^{17} +(0.588134 + 1.28612i) q^{18} -7.32186 q^{19} +(3.45939 + 2.99148i) q^{20} +3.41490i q^{21} +(0.983061 + 2.14974i) q^{22} +(4.75380 - 0.633562i) q^{23} +(0.792755 - 2.71506i) q^{24} -0.229084 q^{25} +(-0.126924 - 0.277554i) q^{26} +1.00000i q^{27} +(4.46736 - 5.16612i) q^{28} -6.15775 q^{29} +(1.34490 + 2.94099i) q^{30} -3.33926i q^{31} +(-4.75113 + 3.07031i) q^{32} +1.67149i q^{33} +(-0.286437 + 0.130986i) q^{34} +7.80892i q^{35} +(1.30820 - 1.51282i) q^{36} -1.86514i q^{37} +(4.30623 + 9.41677i) q^{38} -0.215808i q^{39} +(1.81281 - 6.20857i) q^{40} +8.94190 q^{41} +(4.39196 - 2.00842i) q^{42} -2.67923 q^{43} +(2.18664 - 2.52866i) q^{44} +2.28672i q^{45} +(-3.61070 - 5.74132i) q^{46} -6.03026i q^{47} +(-3.95813 + 0.577241i) q^{48} +4.66154 q^{49} +(0.134732 + 0.294628i) q^{50} -0.222714 q^{51} +(-0.282319 + 0.326478i) q^{52} -11.0574i q^{53} +(1.28612 - 0.588134i) q^{54} +3.82223i q^{55} +(-9.27165 - 2.70718i) q^{56} +7.32186i q^{57} +(3.62158 + 7.91959i) q^{58} -3.93157i q^{59} +(2.99148 - 3.45939i) q^{60} -9.89882i q^{61} +(-4.29468 + 1.96393i) q^{62} +3.41490 q^{63} +(6.74308 + 4.30475i) q^{64} -0.493492i q^{65} +(2.14974 - 0.983061i) q^{66} +1.94227 q^{67} +(0.336926 + 0.291354i) q^{68} +(-0.633562 - 4.75380i) q^{69} +(10.0432 - 4.59269i) q^{70} -8.94968i q^{71} +(-2.71506 - 0.792755i) q^{72} -14.6311 q^{73} +(-2.39879 + 1.09695i) q^{74} +0.229084i q^{75} +(9.57843 - 11.0766i) q^{76} +5.70798 q^{77} +(-0.277554 + 0.126924i) q^{78} +4.15186 q^{79} +(-9.05113 + 1.31999i) q^{80} +1.00000 q^{81} +(-5.25903 - 11.5003i) q^{82} +15.1113 q^{83} +(-5.16612 - 4.46736i) q^{84} -0.509285 q^{85} +(1.57575 + 3.44581i) q^{86} +6.15775i q^{87} +(-4.53820 - 1.32508i) q^{88} -11.2497i q^{89} +(2.94099 - 1.34490i) q^{90} -0.736962 q^{91} +(-5.26044 + 8.02046i) q^{92} -3.33926 q^{93} +(-7.75562 + 3.54660i) q^{94} +16.7430i q^{95} +(3.07031 + 4.75113i) q^{96} +16.3374i q^{97} +(-2.74161 - 5.99529i) q^{98} +1.67149 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

Introduction

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