LMFDB - Embedded newform 276.2.e.a.91.1

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			91.1
Character	$\chi$	$=$	276.91
Dual form			276.2.e.a.91.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36293 - 0.377393i) q^{2} +1.00000i q^{3} +(1.71515 + 1.02872i) q^{4} -2.63738i q^{5} +(0.377393 - 1.36293i) q^{6} -3.76288 q^{7} +(-1.94939 - 2.04936i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.36293 - 0.377393i) q^{2} +1.00000i q^{3} +(1.71515 + 1.02872i) q^{4} -2.63738i q^{5} +(0.377393 - 1.36293i) q^{6} -3.76288 q^{7} +(-1.94939 - 2.04936i) q^{8} -1.00000 q^{9} +(-0.995329 + 3.59456i) q^{10} +0.443928 q^{11} +(-1.02872 + 1.71515i) q^{12} -3.89773 q^{13} +(5.12854 + 1.42009i) q^{14} +2.63738 q^{15} +(1.88347 + 3.52882i) q^{16} -5.41690i q^{17} +(1.36293 + 0.377393i) q^{18} -0.874510 q^{19} +(2.71313 - 4.52350i) q^{20} -3.76288i q^{21} +(-0.605043 - 0.167536i) q^{22} +(-4.40961 - 1.88557i) q^{23} +(2.04936 - 1.94939i) q^{24} -1.95578 q^{25} +(5.31232 + 1.47098i) q^{26} -1.00000i q^{27} +(-6.45391 - 3.87095i) q^{28} -5.34393 q^{29} +(-3.59456 - 0.995329i) q^{30} +0.598213i q^{31} +(-1.23528 - 5.52033i) q^{32} +0.443928i q^{33} +(-2.04430 + 7.38284i) q^{34} +9.92416i q^{35} +(-1.71515 - 1.02872i) q^{36} -8.26643i q^{37} +(1.19189 + 0.330034i) q^{38} -3.89773i q^{39} +(-5.40493 + 5.14129i) q^{40} +3.00019 q^{41} +(-1.42009 + 5.12854i) q^{42} -0.586065 q^{43} +(0.761403 + 0.456678i) q^{44} +2.63738i q^{45} +(5.29838 + 4.23405i) q^{46} +3.89063i q^{47} +(-3.52882 + 1.88347i) q^{48} +7.15930 q^{49} +(2.66558 + 0.738096i) q^{50} +5.41690 q^{51} +(-6.68518 - 4.00967i) q^{52} +3.21010i q^{53} +(-0.377393 + 1.36293i) q^{54} -1.17081i q^{55} +(7.33534 + 7.71149i) q^{56} -0.874510i q^{57} +(7.28339 + 2.01676i) q^{58} -12.1857i q^{59} +(4.52350 + 2.71313i) q^{60} +12.2477i q^{61} +(0.225762 - 0.815322i) q^{62} +3.76288 q^{63} +(-0.399731 + 7.99001i) q^{64} +10.2798i q^{65} +(0.167536 - 0.605043i) q^{66} +15.2528 q^{67} +(5.57247 - 9.29078i) q^{68} +(1.88557 - 4.40961i) q^{69} +(3.74531 - 13.5259i) q^{70} -1.61736i q^{71} +(1.94939 + 2.04936i) q^{72} +14.9948 q^{73} +(-3.11969 + 11.2665i) q^{74} -1.95578i q^{75} +(-1.49991 - 0.899626i) q^{76} -1.67045 q^{77} +(-1.47098 + 5.31232i) q^{78} -10.9038 q^{79} +(9.30683 - 4.96743i) q^{80} +1.00000 q^{81} +(-4.08905 - 1.13225i) q^{82} -11.6833 q^{83} +(3.87095 - 6.45391i) q^{84} -14.2864 q^{85} +(0.798764 + 0.221177i) q^{86} -5.34393i q^{87} +(-0.865391 - 0.909768i) q^{88} +13.2311i q^{89} +(0.995329 - 3.59456i) q^{90} +14.6667 q^{91} +(-5.62340 - 7.77028i) q^{92} -0.598213 q^{93} +(1.46830 - 5.30265i) q^{94} +2.30642i q^{95} +(5.52033 - 1.23528i) q^{96} +1.29344i q^{97} +(-9.75761 - 2.70187i) q^{98} -0.443928 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 $

$2$	−1.36293	−	0.377393i	−0.963736	−	0.266857i
$2$	−1.36293	−	0.377393i	−0.963736	−	0.266857i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.71515	+	1.02872i	0.857574	+	0.514360i
$5$		−	2.63738i		−	1.17947i	−0.807596	−	0.589736i	$-0.799232\pi$
$5$		−	2.63738i		−	1.17947i	0.807596	−	0.589736i	$-0.200768\pi$
$6$	0.377393	−	1.36293i	0.154070	−	0.556413i
$7$	−3.76288			−1.42224			−0.711118	−	0.703072i	$-0.751811\pi$
$7$	−3.76288			−1.42224			−0.711118	+	0.703072i	$0.751811\pi$
$8$	−1.94939	−	2.04936i	−0.689215	−	0.724557i
$9$	−1.00000			−0.333333
$10$	−0.995329	+	3.59456i	−0.314751	+	1.13670i
$11$	0.443928			0.133849			0.0669247	−	0.997758i	$-0.478681\pi$
$11$	0.443928			0.133849			0.0669247	+	0.997758i	$0.478681\pi$
$12$	−1.02872	+	1.71515i	−0.296966	+	0.495121i
$13$	−3.89773			−1.08103			−0.540517	−	0.841333i	$-0.681771\pi$
$13$	−3.89773			−1.08103			−0.540517	+	0.841333i	$0.681771\pi$
$14$	5.12854	+	1.42009i	1.37066	+	0.379534i
$15$	2.63738			0.680969
$16$	1.88347	+	3.52882i	0.470868	+	0.882204i
$17$		−	5.41690i		−	1.31379i	−0.753982	−	0.656895i	$-0.771869\pi$
$17$		−	5.41690i		−	1.31379i	0.753982	−	0.656895i	$-0.228131\pi$
$18$	1.36293	+	0.377393i	0.321245	+	0.0889524i
$19$	−0.874510			−0.200626			−0.100313	−	0.994956i	$-0.531984\pi$
$19$	−0.874510			−0.200626			−0.100313	+	0.994956i	$0.531984\pi$
$20$	2.71313	−	4.52350i	0.606673	−	1.01149i
$21$		−	3.76288i		−	0.821129i
$22$	−0.605043	−	0.167536i	−0.128995	−	0.0357187i
$23$	−4.40961	−	1.88557i	−0.919466	−	0.393169i
$23$	−4.40961	−	1.88557i	−0.919466	−	0.393169i
$24$	2.04936	−	1.94939i	0.418323	−	0.397918i
$25$	−1.95578			−0.391155
$26$	5.31232	+	1.47098i	1.04183	+	0.288482i
$27$		−	1.00000i		−	0.192450i
$28$	−6.45391	−	3.87095i	−1.21967	−	0.731542i
$29$	−5.34393			−0.992343			−0.496171	−	0.868225i	$-0.665261\pi$
$29$	−5.34393			−0.992343			−0.496171	+	0.868225i	$0.665261\pi$
$30$	−3.59456	−	0.995329i	−0.656274	−	0.181721i
$31$			0.598213i			0.107442i	0.998556	+	0.0537211i	$0.0171082\pi$
$31$			0.598213i			0.107442i	−0.998556	+	0.0537211i	$0.982892\pi$
$32$	−1.23528	−	5.52033i	−0.218370	−	0.975866i
$33$			0.443928i			0.0772780i
$34$	−2.04430	+	7.38284i	−0.350595	+	1.26615i
$35$			9.92416i			1.67749i
$36$	−1.71515	−	1.02872i	−0.285858	−	0.171453i
$37$		−	8.26643i		−	1.35899i	−0.733679	−	0.679496i	$-0.762198\pi$
$37$		−	8.26643i		−	1.35899i	0.733679	−	0.679496i	$-0.237802\pi$
$38$	1.19189	+	0.330034i	0.193351	+	0.0535386i
$39$		−	3.89773i		−	0.624136i
$40$	−5.40493	+	5.14129i	−0.854595	+	0.812910i
$41$	3.00019			0.468551			0.234276	−	0.972170i	$-0.424728\pi$
$41$	3.00019			0.468551			0.234276	+	0.972170i	$0.424728\pi$
$42$	−1.42009	+	5.12854i	−0.219124	+	0.791351i
$43$	−0.586065			−0.0893740			−0.0446870	−	0.999001i	$-0.514229\pi$
$43$	−0.586065			−0.0893740			−0.0446870	+	0.999001i	$0.514229\pi$
$44$	0.761403	+	0.456678i	0.114786	+	0.0688468i
$45$			2.63738i			0.393157i
$46$	5.29838	+	4.23405i	0.781203	+	0.624277i
$47$			3.89063i			0.567507i	0.958897	+	0.283753i	$0.0915797\pi$
$47$			3.89063i			0.567507i	−0.958897	+	0.283753i	$0.908420\pi$
$48$	−3.52882	+	1.88347i	−0.509341	+	0.271856i
$49$	7.15930			1.02276
$50$	2.66558	+	0.738096i	0.376970	+	0.104383i
$51$	5.41690			0.758517
$52$	−6.68518	−	4.00967i	−0.927068	−	0.556041i
$53$			3.21010i			0.440941i	0.975394	+	0.220470i	$0.0707593\pi$
$53$			3.21010i			0.440941i	−0.975394	+	0.220470i	$0.929241\pi$
$54$	−0.377393	+	1.36293i	−0.0513567	+	0.185471i
$55$		−	1.17081i		−	0.157872i
$56$	7.33534	+	7.71149i	0.980226	+	1.03049i
$57$		−	0.874510i		−	0.115832i
$58$	7.28339	+	2.01676i	0.956356	+	0.264814i
$59$		−	12.1857i		−	1.58645i	−0.608931	−	0.793223i	$-0.708401\pi$
$59$		−	12.1857i		−	1.58645i	0.608931	−	0.793223i	$-0.291599\pi$
$60$	4.52350	+	2.71313i	0.583981	+	0.350263i
$61$			12.2477i			1.56816i	0.620658	+	0.784081i	$0.286866\pi$
$61$			12.2477i			1.56816i	−0.620658	+	0.784081i	$0.713134\pi$
$62$	0.225762	−	0.815322i	0.0286718	−	0.103546i
$63$	3.76288			0.474079
$64$	−0.399731	+	7.99001i	−0.0499664	+	0.998751i
$65$			10.2798i			1.27505i
$66$	0.167536	−	0.605043i	0.0206222	−	0.0744756i
$67$	15.2528			1.86342			0.931710	−	0.363202i	$-0.118317\pi$
$67$	15.2528			1.86342			0.931710	+	0.363202i	$0.118317\pi$
$68$	5.57247	−	9.29078i	0.675761	−	1.12667i
$69$	1.88557	−	4.40961i	0.226996	−	0.530854i
$70$	3.74531	−	13.5259i	0.447650	−	1.61666i
$71$		−	1.61736i		−	0.191945i	−0.995384	−	0.0959726i	$-0.969404\pi$
$71$		−	1.61736i		−	0.191945i	0.995384	−	0.0959726i	$-0.0305961\pi$
$72$	1.94939	+	2.04936i	0.229738	+	0.241519i
$73$	14.9948			1.75501			0.877505	−	0.479568i	$-0.159206\pi$
$73$	14.9948			1.75501			0.877505	+	0.479568i	$0.159206\pi$
$74$	−3.11969	+	11.2665i	−0.362657	+	1.30971i
$75$		−	1.95578i		−	0.225833i
$76$	−1.49991	−	0.899626i	−0.172052	−	0.103194i
$77$	−1.67045			−0.190366
$78$	−1.47098	+	5.31232i	−0.166555	+	0.601502i
$79$	−10.9038			−1.22677			−0.613387	−	0.789782i	$-0.710193\pi$
$79$	−10.9038			−1.22677			−0.613387	+	0.789782i	$0.710193\pi$
$80$	9.30683	−	4.96743i	1.04054	−	0.555375i
$81$	1.00000			0.111111
$82$	−4.08905	−	1.13225i	−0.451560	−	0.125036i
$83$	−11.6833			−1.28241			−0.641205	−	0.767370i	$-0.721565\pi$
$83$	−11.6833			−1.28241			−0.641205	+	0.767370i	$0.721565\pi$
$84$	3.87095	−	6.45391i	0.422356	−	0.704179i
$85$	−14.2864			−1.54958
$86$	0.798764	+	0.221177i	0.0861330	+	0.0238501i
$87$		−	5.34393i		−	0.572929i
$88$	−0.865391	−	0.909768i	−0.0922510	−	0.0969816i
$89$			13.2311i			1.40249i	0.712918	+	0.701247i	$0.247373\pi$
$89$			13.2311i			1.40249i	−0.712918	+	0.701247i	$0.752627\pi$
$90$	0.995329	−	3.59456i	0.104917	−	0.378900i
$91$	14.6667			1.53749
$92$	−5.62340	−	7.77028i	−0.586280	−	0.810108i
$93$	−0.598213			−0.0620318
$94$	1.46830	−	5.30265i	0.151443	−	0.546927i
$95$			2.30642i			0.236633i
$96$	5.52033	−	1.23528i	0.563417	−	0.126076i
$97$			1.29344i			0.131329i	0.997842	+	0.0656646i	$0.0209167\pi$
$97$			1.29344i			0.131329i	−0.997842	+	0.0656646i	$0.979083\pi$
$98$	−9.75761	−	2.70187i	−0.985667	−	0.272930i
$99$	−0.443928			−0.0446165
$100$	−3.35445	−	2.01195i	−0.335445	−	0.201195i
$101$	13.3947			1.33282			0.666410	−	0.745586i	$-0.267830\pi$
$101$	13.3947			1.33282			0.666410	+	0.745586i	$0.267830\pi$
$102$	−7.38284	−	2.04430i	−0.731011	−	0.202416i
$103$	4.33560			0.427200			0.213600	−	0.976921i	$-0.431481\pi$
$103$	4.33560			0.427200			0.213600	+	0.976921i	$0.431481\pi$
$104$	7.59820	+	7.98783i	0.745065	+	0.783271i
$105$	−9.92416			−0.968498
$106$	1.21147	−	4.37514i	0.117668	−	0.424951i
$107$	−18.8035			−1.81780			−0.908901	−	0.417012i	$-0.863077\pi$
$107$	−18.8035			−1.81780			−0.908901	+	0.417012i	$0.863077\pi$
$108$	1.02872	−	1.71515i	0.0989886	−	0.165040i
$109$		−	1.41395i		−	0.135432i	−0.997705	−	0.0677159i	$-0.978429\pi$
$109$		−	1.41395i		−	0.135432i	0.997705	−	0.0677159i	$-0.0215711\pi$
$110$	−0.441855	+	1.59573i	−0.0421292	+	0.152147i
$111$	8.26643			0.784614
$112$	−7.08728	−	13.2785i	−0.669685	−	1.25470i
$113$			7.50077i			0.705613i	0.935696	+	0.352807i	$0.114773\pi$
$113$			7.50077i			0.705613i	−0.935696	+	0.352807i	$0.885227\pi$
$114$	−0.330034	+	1.19189i	−0.0309105	+	0.111631i
$115$	−4.97297	+	11.6298i	−0.463732	+	1.08449i
$116$	−9.16563	−	5.49741i	−0.851008	−	0.510421i
$117$	3.89773			0.360345
$118$	−4.59881	+	16.6083i	−0.423355	+	1.52892i
$119$			20.3832i			1.86852i
$120$	−5.14129	−	5.40493i	−0.469334	−	0.493401i
$121$	−10.8029			−0.982084
$122$	4.62222	−	16.6928i	0.418476	−	1.51130i
$123$			3.00019i			0.270518i
$124$	−0.615394	+	1.02602i	−0.0552640	+	0.0921397i
$125$		−	8.02878i		−	0.718116i
$126$	−5.12854	−	1.42009i	−0.456887	−	0.126511i
$127$			14.2562i			1.26503i	0.774547	+	0.632516i	$0.217978\pi$
$127$			14.2562i			1.26503i	−0.774547	+	0.632516i	$0.782022\pi$
$128$	3.56018	−	10.7390i	0.314678	−	0.949198i
$129$		−	0.586065i		−	0.0516001i
$130$	3.87952	−	14.0106i	0.340257	−	1.22881i
$131$		−	9.62271i		−	0.840740i	−0.907353	−	0.420370i	$-0.861900\pi$
$131$		−	9.62271i		−	0.840740i	0.907353	−	0.420370i	$-0.138100\pi$
$132$	−0.456678	+	0.761403i	−0.0397487	+	0.0662716i
$133$	3.29068			0.285338
$134$	−20.7884	−	5.75629i	−1.79585	−	0.497267i
$135$	−2.63738			−0.226990
$136$	−11.1012	+	10.5597i	−0.951916	+	0.905484i
$137$			0.547723i			0.0467951i	0.999726	+	0.0233976i	$0.00744836\pi$
$137$			0.547723i			0.0467951i	−0.999726	+	0.0233976i	$0.992552\pi$
$138$	−4.23405	+	5.29838i	−0.360427	+	0.451028i
$139$		−	14.0406i		−	1.19091i	−0.803389	−	0.595455i	$-0.796972\pi$
$139$		−	14.0406i		−	1.19091i	0.803389	−	0.595455i	$-0.203028\pi$
$140$	−10.2092	+	17.0214i	−0.862833	+	1.43857i
$141$	−3.89063			−0.327650
$142$	−0.610380	+	2.20434i	−0.0512220	+	0.184984i
$143$	−1.73031			−0.144696
$144$	−1.88347	−	3.52882i	−0.156956	−	0.294068i
$145$			14.0940i			1.17044i
$146$	−20.4369	−	5.65894i	−1.69137	−	0.468337i
$147$			7.15930i			0.590489i
$148$	8.50384	−	14.1781i	0.699011	−	1.16544i
$149$		−	17.8061i		−	1.45873i	−0.684125	−	0.729365i	$-0.739816\pi$
$149$		−	17.8061i		−	1.45873i	0.684125	−	0.729365i	$-0.260184\pi$
$150$	−0.738096	+	2.66558i	−0.0602653	+	0.217644i
$151$		−	23.1344i		−	1.88265i	−0.337502	−	0.941325i	$-0.609582\pi$
$151$		−	23.1344i		−	1.88265i	0.337502	−	0.941325i	$-0.390418\pi$
$152$	1.70476	+	1.79218i	0.138275	+	0.145365i
$153$			5.41690i			0.437930i
$154$	2.27670	+	0.630417i	0.183462	+	0.0508004i
$155$	1.57772			0.126725
$156$	4.00967	−	6.68518i	0.321030	−	0.535243i
$157$		−	16.2745i		−	1.29884i	−0.760428	−	0.649422i	$-0.775011\pi$
$157$		−	16.2745i		−	1.29884i	0.760428	−	0.649422i	$-0.224989\pi$
$158$	14.8611	+	4.11502i	1.18229	+	0.327374i
$159$	−3.21010			−0.254577
$160$	−14.5592	+	3.25792i	−1.15101	+	0.257561i
$161$	16.5928	+	7.09519i	1.30770	+	0.559179i
$162$	−1.36293	−	0.377393i	−0.107082	−	0.0296508i
$163$		−	24.0378i		−	1.88279i	−0.337308	−	0.941394i	$-0.609516\pi$
$163$		−	24.0378i		−	1.88279i	0.337308	−	0.941394i	$-0.390484\pi$
$164$	5.14577	+	3.08636i	0.401817	+	0.241004i
$165$	1.17081			0.0911473
$166$	15.9235	+	4.40920i	1.23590	+	0.342220i
$167$			12.2209i			0.945684i	0.881147	+	0.472842i	$0.156772\pi$
$167$			12.2209i			0.945684i	−0.881147	+	0.472842i	$0.843228\pi$
$168$	−7.71149	+	7.33534i	−0.594955	+	0.565934i
$169$	2.19227			0.168636
$170$	19.4714	+	5.39160i	1.49339	+	0.413517i
$171$	0.874510			0.0668754
$172$	−1.00519	−	0.602896i	−0.0766449	−	0.0459704i
$173$	12.3773			0.941026			0.470513	−	0.882393i	$-0.344069\pi$
$173$	12.3773			0.941026			0.470513	+	0.882393i	$0.344069\pi$
$174$	−2.01676	+	7.28339i	−0.152890	+	0.552153i
$175$	7.35936			0.556315
$176$	0.836126	+	1.56654i	0.0630253	+	0.118082i
$177$	12.1857			0.915935
$178$	4.99333	−	18.0331i	0.374266	−	1.35163i
$179$		−	5.33092i		−	0.398451i	−0.979954	−	0.199226i	$-0.936157\pi$
$179$		−	5.33092i		−	0.398451i	0.979954	−	0.199226i	$-0.0638427\pi$
$180$	−2.71313	+	4.52350i	−0.202224	+	0.337162i
$181$		−	10.2332i		−	0.760625i	−0.924858	−	0.380312i	$-0.875816\pi$
$181$		−	10.2332i		−	0.760625i	0.924858	−	0.380312i	$-0.124184\pi$
$182$	−19.9897	−	5.53511i	−1.48173	−	0.410290i
$183$	−12.2477			−0.905379
$184$	4.73185	+	12.7126i	0.348836	+	0.937184i
$185$	−21.8017			−1.60289
$186$	0.815322	+	0.225762i	0.0597823	+	0.0165536i
$187$		−	2.40471i		−	0.175850i
$188$	−4.00237	+	6.67301i	−0.291903	+	0.486679i
$189$			3.76288i			0.273710i
$190$	0.870425	−	3.14348i	0.0631473	−	0.228052i
$191$	18.0753			1.30788			0.653941	−	0.756546i	$-0.273114\pi$
$191$	18.0753			1.30788			0.653941	+	0.756546i	$0.273114\pi$
$192$	−7.99001	−	0.399731i	−0.576629	−	0.0288481i
$193$	−0.0704641			−0.00507212			−0.00253606	−	0.999997i	$-0.500807\pi$
$193$	−0.0704641			−0.00507212			−0.00253606	+	0.999997i	$0.500807\pi$
$194$	0.488137	−	1.76287i	0.0350462	−	0.126567i
$195$	−10.2798			−0.736151
$196$	12.2793	+	7.36491i	0.877090	+	0.526065i
$197$	−16.3762			−1.16676			−0.583379	−	0.812200i	$-0.698270\pi$
$197$	−16.3762			−1.16676			−0.583379	+	0.812200i	$0.698270\pi$
$198$	0.605043	+	0.167536i	0.0429985	+	0.0119062i
$199$	0.218434			0.0154844			0.00774218	−	0.999970i	$-0.497536\pi$
$199$	0.218434			0.0154844			0.00774218	+	0.999970i	$0.497536\pi$
$200$	3.81258	+	4.00808i	0.269590	+	0.283414i
$201$			15.2528i			1.07585i
$202$	−18.2560	−	5.05506i	−1.28449	−	0.355673i
$203$	20.1086			1.41135
$204$	9.29078	+	5.57247i	0.650485	+	0.390151i
$205$		−	7.91265i		−	0.552643i
$206$	−5.90912	−	1.63623i	−0.411708	−	0.114001i
$207$	4.40961	+	1.88557i	0.306489	+	0.131056i
$208$	−7.34125	−	13.7544i	−0.509024	−	0.953693i
$209$	−0.388220			−0.0268537
$210$	13.5259	+	3.74531i	0.933377	+	0.258451i
$211$			10.1413i			0.698157i	0.937094	+	0.349078i	$0.113505\pi$
$211$			10.1413i			0.698157i	−0.937094	+	0.349078i	$0.886495\pi$
$212$	−3.30229	+	5.50580i	−0.226802	+	0.378140i
$213$	1.61736			0.110820
$214$	25.6278	+	7.09631i	1.75188	+	0.485094i
$215$			1.54568i			0.105414i
$216$	−2.04936	+	1.94939i	−0.139441	+	0.132639i
$217$		−	2.25101i		−	0.152808i
$218$	−0.533615	+	1.92711i	−0.0361409	+	0.130520i
$219$			14.9948i			1.01326i
$220$	1.20443	−	2.00811i	0.0812029	−	0.135387i
$221$			21.1136i			1.42025i
$222$	−11.2665	−	3.11969i	−0.756161	−	0.209380i
$223$			16.1279i			1.08001i	0.841663	+	0.540003i	$0.181577\pi$
$223$			16.1279i			1.08001i	−0.841663	+	0.540003i	$0.818423\pi$
$224$	4.64823	+	20.7724i	0.310573	+	1.38791i
$225$	1.95578			0.130385
$226$	2.83074	−	10.2230i	0.188298	−	0.680025i
$227$	−7.08184			−0.470038			−0.235019	−	0.971991i	$-0.575515\pi$
$227$	−7.08184			−0.470038			−0.235019	+	0.971991i	$0.575515\pi$
$228$	0.899626	−	1.49991i	0.0595792	−	0.0993343i
$229$		−	3.37854i		−	0.223260i	−0.993750	−	0.111630i	$-0.964393\pi$
$229$		−	3.37854i		−	0.223260i	0.993750	−	0.111630i	$-0.0356072\pi$
$230$	11.1668	−	13.9738i	0.736318	−	0.921407i
$231$		−	1.67045i		−	0.109908i
$232$	10.4174	+	10.9516i	0.683937	+	0.719009i
$233$	−13.6186			−0.892181			−0.446091	−	0.894988i	$-0.647184\pi$
$233$	−13.6186			−0.892181			−0.446091	+	0.894988i	$0.647184\pi$
$234$	−5.31232	−	1.47098i	−0.347277	−	0.0961607i
$235$	10.2611			0.669359
$236$	12.5357	−	20.9003i	0.816005	−	1.36050i
$237$		−	10.9038i		−	0.708278i
$238$	7.69246	−	27.7808i	0.498628	−	1.80076i
$239$		−	24.4272i		−	1.58006i	−0.613066	−	0.790032i	$-0.710064\pi$
$239$		−	24.4272i		−	1.58006i	0.613066	−	0.790032i	$-0.289936\pi$
$240$	4.96743	+	9.30683i	0.320646	+	0.600753i
$241$			18.5960i			1.19787i	0.800797	+	0.598936i	$0.204410\pi$
$241$			18.5960i			1.19787i	−0.800797	+	0.598936i	$0.795590\pi$
$242$	14.7236	+	4.07695i	0.946470	+	0.262076i
$243$			1.00000i			0.0641500i
$244$	−12.5995	+	21.0067i	−0.806600	+	1.34482i
$245$		−	18.8818i		−	1.20631i
$246$	1.13225	−	4.08905i	0.0721897	−	0.260708i
$247$	3.40860			0.216884
$248$	1.22595	−	1.16615i	0.0778481	−	0.0740508i
$249$		−	11.6833i		−	0.740400i
$250$	−3.03001	+	10.9427i	−0.191634	+	0.692074i
$251$	−11.0122			−0.695081			−0.347541	−	0.937665i	$-0.612983\pi$
$251$	−11.0122			−0.695081			−0.347541	+	0.937665i	$0.612983\pi$
$252$	6.45391	+	3.87095i	0.406558	+	0.243847i
$253$	−1.95755	−	0.837058i	−0.123070	−	0.0526254i
$254$	5.38019	−	19.4302i	0.337583	−	1.21916i
$255$		−	14.2864i		−	0.894650i
$256$	−8.90508	+	13.2928i	−0.556567	+	0.830802i
$257$	−1.80376			−0.112516			−0.0562579	−	0.998416i	$-0.517917\pi$
$257$	−1.80376			−0.112516			−0.0562579	+	0.998416i	$0.517917\pi$
$258$	−0.221177	+	0.798764i	−0.0137699	+	0.0497289i
$259$			31.1056i			1.93281i
$260$	−10.5750	+	17.6314i	−0.655835	+	1.09345i
$261$	5.34393			0.330781
$262$	−3.63155	+	13.1151i	−0.224358	+	0.810252i
$263$	12.9884			0.800899			0.400450	−	0.916319i	$-0.368854\pi$
$263$	12.9884			0.800899			0.400450	+	0.916319i	$0.368854\pi$
$264$	0.909768	−	0.865391i	0.0559923	−	0.0532611i
$265$	8.46625			0.520078
$266$	−4.48496	−	1.24188i	−0.274991	−	0.0761445i
$267$	−13.2311			−0.809731
$268$	26.1607	+	15.6908i	1.59802	+	0.958469i
$269$	−3.59883			−0.219425			−0.109712	−	0.993963i	$-0.534993\pi$
$269$	−3.59883			−0.219425			−0.109712	+	0.993963i	$0.534993\pi$
$270$	3.59456	+	0.995329i	0.218758	+	0.0605738i
$271$		−	17.7331i		−	1.07721i	−0.842560	−	0.538603i	$-0.818952\pi$
$271$		−	17.7331i		−	1.07721i	0.842560	−	0.538603i	$-0.181048\pi$
$272$	19.1152	−	10.2026i	1.15903	−	0.618621i
$273$			14.6667i			0.887668i
$274$	0.206707	−	0.746507i	0.0124876	−	0.0450982i
$275$	−0.868224			−0.0523559
$276$	7.77028	−	5.62340i	0.467716	−	0.338489i
$277$	−4.19147			−0.251841			−0.125920	−	0.992040i	$-0.540188\pi$
$277$	−4.19147			−0.251841			−0.125920	+	0.992040i	$0.540188\pi$
$278$	−5.29883	+	19.1364i	−0.317803	+	1.14772i
$279$		−	0.598213i		−	0.0358141i
$280$	20.3381	−	19.3461i	1.21544	−	1.15615i
$281$		−	15.5993i		−	0.930574i	−0.885160	−	0.465287i	$-0.845951\pi$
$281$		−	15.5993i		−	0.930574i	0.885160	−	0.465287i	$-0.154049\pi$
$282$	5.30265	+	1.46830i	0.315768	+	0.0874359i
$283$	−13.8442			−0.822952			−0.411476	−	0.911421i	$-0.634987\pi$
$283$	−13.8442			−0.822952			−0.411476	+	0.911421i	$0.634987\pi$
$284$	1.66381	−	2.77401i	0.0987289	−	0.164607i
$285$	−2.30642			−0.136620
$286$	2.35829	+	0.653007i	0.139449	+	0.0386131i
$287$	−11.2894			−0.666391
$288$	1.23528	+	5.52033i	0.0727898	+	0.325289i
$289$	−12.3428			−0.726046
$290$	5.31897	−	19.2091i	0.312341	−	1.12800i
$291$	−1.29344			−0.0758230
$292$	25.7183	+	15.4255i	1.50505	+	0.902707i
$293$		−	7.35396i		−	0.429623i	−0.976656	−	0.214811i	$-0.931086\pi$
$293$		−	7.35396i		−	0.429623i	0.976656	−	0.214811i	$-0.0689137\pi$
$294$	2.70187	−	9.75761i	0.157576	−	0.569075i
$295$	−32.1384			−1.87117
$296$	−16.9409	+	16.1145i	−0.984667	+	0.936637i
$297$		−	0.443928i		−	0.0257593i
$298$	−6.71989	+	24.2684i	−0.389272	+	1.40583i
$299$	17.1874	+	7.34944i	0.993975	+	0.425029i
$300$	2.01195	−	3.35445i	0.116160	−	0.193669i
$301$	2.20529			0.127111
$302$	−8.73076	+	31.5305i	−0.502399	+	1.81438i
$303$			13.3947i			0.769504i
$304$	−1.64711	−	3.08598i	−0.0944684	−	0.176993i
$305$	32.3020			1.84960
$306$	2.04430	−	7.38284i	0.116865	−	0.422049i
$307$		−	6.72809i		−	0.383993i	−0.981396	−	0.191996i	$-0.938504\pi$
$307$		−	6.72809i		−	0.383993i	0.981396	−	0.191996i	$-0.0614961\pi$
$308$	−2.86507	−	1.71843i	−0.163253	−	0.0979164i
$309$			4.33560i			0.246644i
$310$	−2.15031	−	0.595419i	−0.122130	−	0.0338175i
$311$			2.75954i			0.156479i	0.996935	+	0.0782396i	$0.0249299\pi$
$311$			2.75954i			0.156479i	−0.996935	+	0.0782396i	$0.975070\pi$
$312$	−7.98783	+	7.59820i	−0.452222	+	0.430163i
$313$			1.14544i			0.0647439i	0.999476	+	0.0323719i	$0.0103061\pi$
$313$			1.14544i			0.0647439i	−0.999476	+	0.0323719i	$0.989694\pi$
$314$	−6.14187	+	22.1809i	−0.346606	+	1.25174i
$315$		−	9.92416i		−	0.559163i
$316$	−18.7016	−	11.2170i	−1.05205	−	0.631003i
$317$	−25.3550			−1.42408			−0.712038	−	0.702141i	$-0.752228\pi$
$317$	−25.3550			−1.42408			−0.712038	+	0.702141i	$0.752228\pi$
$318$	4.37514	+	1.21147i	0.245345	+	0.0679358i
$319$	−2.37232			−0.132824
$320$	21.0727	+	1.05424i	1.17800	+	0.0589340i
$321$		−	18.8035i		−	1.04951i
$322$	−19.9372	−	15.9323i	−1.11106	−	0.887870i
$323$			4.73713i			0.263581i
$324$	1.71515	+	1.02872i	0.0952860	+	0.0571511i
$325$	7.62308			0.422852
$326$	−9.07172	+	32.7619i	−0.502436	+	1.81451i
$327$	1.41395			0.0781915
$328$	−5.84855	−	6.14846i	−0.322932	−	0.339492i
$329$		−	14.6400i		−	0.807129i
$330$	−1.59573	−	0.441855i	−0.0878419	−	0.0243233i
$331$			22.6100i			1.24276i	0.783509	+	0.621380i	$0.213428\pi$
$331$			22.6100i			1.24276i	−0.783509	+	0.621380i	$0.786572\pi$
$332$	−20.0386	−	12.0189i	−1.09976	−	0.659620i
$333$			8.26643i			0.452997i
$334$	4.61209	−	16.6563i	0.252363	−	0.911389i
$335$		−	40.2273i		−	2.19785i
$336$	13.2785	−	7.08728i	0.724403	−	0.386643i
$337$		−	20.9510i		−	1.14128i	−0.821202	−	0.570638i	$-0.806696\pi$
$337$		−	20.9510i		−	1.14128i	0.821202	−	0.570638i	$-0.193304\pi$
$338$	−2.98790	−	0.827346i	−0.162520	−	0.0450017i
$339$	−7.50077			−0.407386
$340$	−24.5033	−	14.6967i	−1.32888	−	0.797042i
$341$			0.265564i			0.0143811i
$342$	−1.19189	−	0.330034i	−0.0644503	−	0.0178462i
$343$	−0.599411			−0.0323652
$344$	1.14247	+	1.20106i	0.0615979	+	0.0647566i
$345$	−11.6298	−	4.97297i	−0.626128	−	0.267736i
$346$	−16.8693	−	4.67109i	−0.906900	−	0.251120i
$347$			5.06673i			0.271996i	0.990709	+	0.135998i	$0.0434241\pi$
$347$			5.06673i			0.271996i	−0.990709	+	0.135998i	$0.956576\pi$
$348$	5.49741	−	9.16563i	0.294692	−	0.491329i
$349$	24.6005			1.31683			0.658416	−	0.752654i	$-0.271227\pi$
$349$	24.6005			1.31683			0.658416	+	0.752654i	$0.271227\pi$
$350$	−10.0303	−	2.77737i	−0.536141	−	0.148457i
$351$			3.89773i			0.208045i
$352$	−0.548378	−	2.45063i	−0.0292286	−	0.130619i
$353$	−1.34090			−0.0713690			−0.0356845	−	0.999363i	$-0.511361\pi$
$353$	−1.34090			−0.0713690			−0.0356845	+	0.999363i	$0.511361\pi$
$354$	−16.6083	−	4.59881i	−0.882720	−	0.244424i
$355$	−4.26559			−0.226394
$356$	−13.6111	+	22.6933i	−0.721387	+	1.20274i
$357$	−20.3832			−1.07879
$358$	−2.01185	+	7.26566i	−0.106330	+	0.384002i
$359$	12.1085			0.639064			0.319532	−	0.947576i	$-0.396474\pi$
$359$	12.1085			0.639064			0.319532	+	0.947576i	$0.396474\pi$
$360$	5.40493	−	5.14129i	0.284865	−	0.270970i
$361$	−18.2352			−0.959749
$362$	−3.86192	+	13.9471i	−0.202978	+	0.733042i
$363$		−	10.8029i		−	0.567007i
$364$	25.1556	+	15.0879i	1.31851	+	0.790822i
$365$		−	39.5470i		−	2.06999i
$366$	16.6928	+	4.62222i	0.872547	+	0.241607i
$367$	−21.2655			−1.11005			−0.555024	−	0.831834i	$-0.687291\pi$
$367$	−21.2655			−1.11005			−0.555024	+	0.831834i	$0.687291\pi$
$368$	−1.65153	−	19.1121i	−0.0860918	−	0.996287i
$369$	−3.00019			−0.156184
$370$	29.7142	+	8.22782i	1.54477	+	0.427744i
$371$		−	12.0792i		−	0.627122i
$372$	−1.02602	−	0.615394i	−0.0531969	−	0.0319067i
$373$			10.5684i			0.547213i	0.961842	+	0.273606i	$0.0882165\pi$
$373$			10.5684i			0.547213i	−0.961842	+	0.273606i	$0.911783\pi$
$374$	−0.907523	+	3.27745i	−0.0469269	+	0.169473i
$375$	8.02878			0.414604
$376$	7.97330	−	7.58437i	0.411191	−	0.391134i
$377$	20.8292			1.07276
$378$	1.42009	−	5.12854i	0.0730414	−	0.263784i
$379$	17.7038			0.909383			0.454691	−	0.890649i	$-0.349750\pi$
$379$	17.7038			0.909383			0.454691	+	0.890649i	$0.349750\pi$
$380$	−2.37266	+	3.95585i	−0.121715	+	0.202931i
$381$	−14.2562			−0.730367
$382$	−24.6353	−	6.82149i	−1.26045	−	0.349018i
$383$	37.1701			1.89930			0.949652	−	0.313307i	$-0.101437\pi$
$383$	37.1701			1.89930			0.949652	+	0.313307i	$0.101437\pi$
$384$	10.7390	+	3.56018i	0.548020	+	0.181680i
$385$			4.40561i			0.224531i
$386$	0.0960376	+	0.0265927i	0.00488818	+	0.00135353i
$387$	0.586065			0.0297913
$388$	−1.33059	+	2.21845i	−0.0675505	+	0.112625i
$389$		−	12.8197i		−	0.649987i	−0.945716	−	0.324993i	$-0.894638\pi$
$389$		−	12.8197i		−	0.649987i	0.945716	−	0.324993i	$-0.105362\pi$
$390$	14.0106	+	3.87952i	0.709455	+	0.196447i
$391$	−10.2139	+	23.8864i	−0.516541	+	1.20799i
$392$	−13.9563	−	14.6720i	−0.704899	−	0.741046i
$393$	9.62271			0.485402
$394$	22.3196	+	6.18027i	1.12445	+	0.311358i
$395$			28.7575i			1.44695i
$396$	−0.761403	−	0.456678i	−0.0382619	−	0.0229489i
$397$	−9.42657			−0.473106			−0.236553	−	0.971619i	$-0.576018\pi$
$397$	−9.42657			−0.473106			−0.236553	+	0.971619i	$0.576018\pi$
$398$	−0.297710	−	0.0824354i	−0.0149228	−	0.00413211i
$399$			3.29068i			0.164740i
$400$	−3.68364	−	6.90157i	−0.184182	−	0.345079i
$401$			15.9154i			0.794778i	0.917650	+	0.397389i	$0.130084\pi$
$401$			15.9154i			0.794778i	−0.917650	+	0.397389i	$0.869916\pi$
$402$	5.75629	−	20.7884i	0.287097	−	1.03683i
$403$		−	2.33167i		−	0.116149i
$404$	22.9738	+	13.7794i	1.14299	+	0.685549i
$405$		−	2.63738i		−	0.131052i
$406$	−27.4066	−	7.58884i	−1.36016	−	0.376628i
$407$		−	3.66970i		−	0.181900i
$408$	−10.5597	−	11.1012i	−0.522781	−	0.549589i
$409$	−7.65459			−0.378495			−0.189247	−	0.981929i	$-0.560605\pi$
$409$	−7.65459			−0.378495			−0.189247	+	0.981929i	$0.560605\pi$
$410$	−2.98618	+	10.7844i	−0.147477	+	0.532602i
$411$	−0.547723			−0.0270172
$412$	7.43620	+	4.46012i	0.366355	+	0.219734i
$413$			45.8535i			2.25630i
$414$	−5.29838	−	4.23405i	−0.260401	−	0.208092i
$415$			30.8133i			1.51257i
$416$	4.81480	+	21.5167i	0.236065	+	1.05495i
$417$	14.0406			0.687572
$418$	0.529116	+	0.146511i	0.0258799	+	0.00716611i
$419$	14.8784			0.726856			0.363428	−	0.931622i	$-0.381606\pi$
$419$	14.8784			0.726856			0.363428	+	0.931622i	$0.381606\pi$
$420$	−17.0214	−	10.2092i	−0.830559	−	0.498157i
$421$		−	27.5405i		−	1.34224i	−0.741347	−	0.671122i	$-0.765813\pi$
$421$		−	27.5405i		−	1.34224i	0.741347	−	0.671122i	$-0.234187\pi$
$422$	3.82726	−	13.8219i	0.186308	−	0.672839i
$423$		−	3.89063i		−	0.189169i
$424$	6.57864	−	6.25774i	0.319487	−	0.303903i
$425$			10.5942i			0.513896i
$426$	−2.20434	−	0.610380i	−0.106801	−	0.0295730i
$427$		−	46.0868i		−	2.23030i
$428$	−32.2508	−	19.3435i	−1.55890	−	0.935005i
$429$		−	1.73031i		−	0.0835402i
$430$	0.583327	−	2.10665i	0.0281305	−	0.101591i
$431$	3.16378			0.152394			0.0761969	−	0.997093i	$-0.475722\pi$
$431$	3.16378			0.152394			0.0761969	+	0.997093i	$0.475722\pi$
$432$	3.52882	−	1.88347i	0.169780	−	0.0906185i
$433$			25.1258i			1.20747i	0.797186	+	0.603734i	$0.206321\pi$
$433$			25.1258i			1.20747i	−0.797186	+	0.603734i	$0.793679\pi$
$434$	−0.849515	+	3.06796i	−0.0407780	+	0.147267i
$435$	−14.0940			−0.675754
$436$	1.45456	−	2.42513i	0.0696607	−	0.116143i
$437$	3.85624	+	1.64895i	0.184469	+	0.0788800i
$438$	5.65894	−	20.4369i	0.270395	−	0.976511i
$439$			5.17548i			0.247012i	0.992344	+	0.123506i	$0.0394139\pi$
$439$			5.17548i			0.247012i	−0.992344	+	0.123506i	$0.960586\pi$
$440$	−2.39940	+	2.28236i	−0.114387	+	0.108807i
$441$	−7.15930			−0.340919
$442$	7.96812	−	28.7763i	0.379005	−	1.36875i
$443$			8.90381i			0.423033i	0.977374	+	0.211516i	$0.0678402\pi$
$443$			8.90381i			0.423033i	−0.977374	+	0.211516i	$0.932160\pi$
$444$	14.1781	+	8.50384i	0.672865	+	0.403574i
$445$	34.8955			1.65420
$446$	6.08657	−	21.9812i	0.288208	−	1.04084i
$447$	17.8061			0.842198
$448$	1.50414	−	30.0655i	0.0710640	−	1.42046i
$449$	−6.09398			−0.287593			−0.143796	−	0.989607i	$-0.545931\pi$
$449$	−6.09398			−0.287593			−0.143796	+	0.989607i	$0.545931\pi$
$450$	−2.66558	−	0.738096i	−0.125657	−	0.0347942i
$451$	1.33187			0.0627153
$452$	−7.71619	+	12.8649i	−0.362939	+	0.605116i
$453$	23.1344			1.08695
$454$	9.65204	+	2.67264i	0.452993	+	0.125433i
$455$		−	38.6816i		−	1.81342i
$456$	−1.79218	+	1.70476i	−0.0839267	+	0.0798329i
$457$			6.46875i			0.302595i	0.988488	+	0.151298i	$0.0483452\pi$
$457$			6.46875i			0.302595i	−0.988488	+	0.151298i	$0.951655\pi$
$458$	−1.27504	+	4.60471i	−0.0595787	+	0.215164i
$459$	−5.41690			−0.252839
$460$	−20.4932	+	14.8311i	−0.955500	+	0.691502i
$461$	−16.0481			−0.747434			−0.373717	−	0.927543i	$-0.621917\pi$
$461$	−16.0481			−0.747434			−0.373717	+	0.927543i	$0.621917\pi$
$462$	−0.630417	+	2.27670i	−0.0293296	+	0.105922i
$463$			1.86102i			0.0864888i	0.999065	+	0.0432444i	$0.0137694\pi$
$463$			1.86102i			0.0864888i	−0.999065	+	0.0432444i	$0.986231\pi$
$464$	−10.0651	−	18.8577i	−0.467262	−	0.875448i
$465$			1.57772i			0.0731648i
$466$	18.5611	+	5.13955i	0.859827	+	0.238085i
$467$	−25.3051			−1.17098			−0.585491	−	0.810679i	$-0.699098\pi$
$467$	−25.3051			−1.17098			−0.585491	+	0.810679i	$0.699098\pi$
$468$	6.68518	+	4.00967i	0.309023	+	0.185347i
$469$	−57.3943			−2.65022
$470$	−13.9851	−	3.87246i	−0.645085	−	0.178623i
$471$	16.2745			0.749888
$472$	−24.9729	+	23.7548i	−1.14947	+	1.09340i
$473$	−0.260171			−0.0119627
$474$	−4.11502	+	14.8611i	−0.189009	+	0.682593i
$475$	1.71034			0.0784760
$476$	−20.9686	+	34.9601i	−0.961092	+	1.60240i
$477$		−	3.21010i		−	0.146980i
$478$	−9.21866	+	33.2925i	−0.421651	+	1.52276i
$479$	3.31118			0.151291			0.0756457	−	0.997135i	$-0.475898\pi$
$479$	3.31118			0.151291			0.0756457	+	0.997135i	$0.475898\pi$
$480$	−3.25792	−	14.5592i	−0.148703	−	0.664534i
$481$			32.2203i			1.46912i
$482$	7.01800	−	25.3450i	0.319661	−	1.15443i
$483$	−7.09519	+	16.5928i	−0.322842	+	0.755000i
$484$	−18.5286	−	11.1132i	−0.842210	−	0.505145i
$485$	3.41130			0.154899
$486$	0.377393	−	1.36293i	0.0171189	−	0.0618237i
$487$		−	22.6258i		−	1.02527i	−0.858605	−	0.512637i	$-0.828669\pi$
$487$		−	22.6258i		−	1.02527i	0.858605	−	0.512637i	$-0.171331\pi$
$488$	25.1000	−	23.8757i	1.13622	−	1.08080i
$489$	24.0378			1.08703
$490$	−7.12586	+	25.7345i	−0.321913	+	1.16257i
$491$			25.1776i			1.13625i	0.822942	+	0.568125i	$0.192331\pi$
$491$			25.1776i			1.13625i	−0.822942	+	0.568125i	$0.807669\pi$
$492$	−3.08636	+	5.14577i	−0.139144	+	0.231989i
$493$			28.9475i			1.30373i
$494$	−4.64568	−	1.28638i	−0.209019	−	0.0578771i
$495$			1.17081i			0.0526239i
$496$	−2.11098	+	1.12672i	−0.0947860	+	0.0505911i
$497$			6.08593i			0.272991i
$498$	−4.40920	+	15.9235i	−0.197581	+	0.713550i
$499$		−	33.4253i		−	1.49632i	−0.663516	−	0.748162i	$-0.730937\pi$
$499$		−	33.4253i		−	1.49632i	0.663516	−	0.748162i	$-0.269063\pi$
$500$	8.25936	−	13.7705i	0.369370	−	0.615838i
$501$	−12.2209			−0.545991
$502$	15.0088	+	4.15591i	0.669875	+	0.185488i
$503$	1.88385			0.0839966			0.0419983	−	0.999118i	$-0.486628\pi$
$503$	1.88385			0.0839966			0.0419983	+	0.999118i	$0.486628\pi$
$504$	−7.33534	−	7.71149i	−0.326742	−	0.343497i
$505$		−	35.3268i		−	1.57202i
$506$	2.35210	+	1.87962i	0.104564	+	0.0835591i
$507$			2.19227i			0.0973620i
$508$	−14.6656	+	24.4515i	−0.650682	+	1.08486i
$509$	−10.9621			−0.485886			−0.242943	−	0.970041i	$-0.578113\pi$
$509$	−10.9621			−0.485886			−0.242943	+	0.970041i	$0.578113\pi$
$510$	−5.39160	+	19.4714i	−0.238744	+	0.862207i
$511$	−56.4237			−2.49604
$512$	17.1536	−	14.7565i	0.758090	−	0.652150i
$513$			0.874510i			0.0386106i
$514$	2.45840	+	0.680729i	0.108435	+	0.0300256i
$515$		−	11.4346i		−	0.503870i
$516$	0.602896	−	1.00519i	0.0265410	−	0.0442509i
$517$			1.72716i			0.0759605i
$518$	11.7390	−	42.3947i	0.515784	−	1.86272i
$519$			12.3773i			0.543301i
$520$	21.0670	−	20.0393i	0.923847	−	0.878783i
$521$		−	16.8720i		−	0.739174i	−0.929196	−	0.369587i	$-0.879499\pi$
$521$		−	16.8720i		−	0.739174i	0.929196	−	0.369587i	$-0.120501\pi$
$522$	−7.28339	−	2.01676i	−0.318785	−	0.0882713i
$523$	−11.4507			−0.500705			−0.250353	−	0.968155i	$-0.580547\pi$
$523$	−11.4507			−0.500705			−0.250353	+	0.968155i	$0.580547\pi$
$524$	9.89908	−	16.5044i	0.432443	−	0.720997i
$525$			7.35936i			0.321189i
$526$	−17.7023	−	4.90173i	−0.771855	−	0.213726i
$527$	3.24046			0.141157
$528$	−1.56654	+	0.836126i	−0.0681749	+	0.0363877i
$529$	15.8892	+	16.6293i	0.690837	+	0.723011i
$530$	−11.5389	−	3.19511i	−0.501218	−	0.138787i
$531$			12.1857i			0.528815i
$532$	5.64400	+	3.38519i	0.244699	+	0.146766i
$533$	−11.6939			−0.506520
$534$	18.0331	+	4.99333i	0.780367	+	0.216083i
$535$			49.5920i			2.14405i
$536$	−29.7336	−	31.2583i	−1.28430	−	1.35015i
$537$	5.33092			0.230046
$538$	4.90495	+	1.35818i	0.211468	+	0.0585551i
$539$	3.17821			0.136895
$540$	−4.52350	−	2.71313i	−0.194660	−	0.116754i
$541$	29.3626			1.26240			0.631198	−	0.775622i	$-0.282563\pi$
$541$	29.3626			1.26240			0.631198	+	0.775622i	$0.282563\pi$
$542$	−6.69233	+	24.1689i	−0.287460	+	1.03814i
$543$	10.2332			0.439147
$544$	−29.9031	+	6.69141i	−1.28208	+	0.286892i
$545$	−3.72912			−0.159738
$546$	5.53511	−	19.9897i	0.236881	−	0.855478i
$547$		−	16.9183i		−	0.723375i	−0.932299	−	0.361687i	$-0.882201\pi$
$547$		−	16.9183i		−	0.723375i	0.932299	−	0.361687i	$-0.117799\pi$
$548$	−0.563454	+	0.939426i	−0.0240695	+	0.0401303i
$549$		−	12.2477i		−	0.522721i
$550$	1.18333	+	0.327662i	0.0504572	+	0.0139715i
$551$	4.67332			0.199090
$552$	−12.7126	+	4.73185i	−0.541083	+	0.201401i
$553$	41.0298			1.74476
$554$	5.71267	+	1.58183i	0.242708	+	0.0672056i
$555$		−	21.8017i		−	0.925431i
$556$	14.4439	−	24.0817i	0.612556	−	1.02129i
$557$			25.7916i			1.09282i	0.837516	+	0.546412i	$0.184007\pi$
$557$			25.7916i			1.09282i	−0.837516	+	0.546412i	$0.815993\pi$
$558$	−0.225762	+	0.815322i	−0.00955725	+	0.0345153i
$559$	2.28432			0.0966164
$560$	−35.0205	+	18.6919i	−1.47989	+	0.789875i
$561$	2.40471			0.101527
$562$	−5.88705	+	21.2607i	−0.248330	+	0.896827i
$563$	10.3819			0.437544			0.218772	−	0.975776i	$-0.429795\pi$
$563$	10.3819			0.437544			0.218772	+	0.975776i	$0.429795\pi$
$564$	−6.67301	−	4.00237i	−0.280985	−	0.168530i
$565$	19.7824			0.832251
$566$	18.8687	+	5.22471i	0.793109	+	0.219611i
$567$	−3.76288			−0.158026
$568$	−3.31455	+	3.15287i	−0.139075	+	0.132291i
$569$		−	10.9488i		−	0.458999i	−0.973309	−	0.229499i	$-0.926291\pi$
$569$		−	10.9488i		−	0.458999i	0.973309	−	0.229499i	$-0.0737088\pi$
$570$	3.14348	+	0.870425i	0.131666	+	0.0364581i
$571$	2.07053			0.0866489			0.0433245	−	0.999061i	$-0.486205\pi$
$571$	2.07053			0.0866489			0.0433245	+	0.999061i	$0.486205\pi$
$572$	−2.96774	−	1.78001i	−0.124087	−	0.0744258i
$573$			18.0753i			0.755106i
$574$	15.3866	+	4.26053i	0.642225	+	0.177831i
$575$	8.62420	+	3.68775i	0.359654	+	0.153790i
$576$	0.399731	−	7.99001i	0.0166555	−	0.332917i
$577$	0.754391			0.0314057			0.0157029	−	0.999877i	$-0.495001\pi$
$577$	0.754391			0.0314057			0.0157029	+	0.999877i	$0.495001\pi$
$578$	16.8223	+	4.65808i	0.699716	+	0.193751i
$579$		−	0.0704641i		−	0.00292839i
$580$	−14.4988	+	24.1733i	−0.602028	+	1.00374i
$581$	43.9629			1.82389
$582$	1.76287	+	0.488137i	0.0730733	+	0.0202339i
$583$			1.42505i			0.0590197i
$584$	−29.2308	−	30.7297i	−1.20958	−	1.27161i
$585$		−	10.2798i		−	0.425017i
$586$	−2.77533	+	10.0229i	−0.114648	+	0.414043i
$587$			8.98386i			0.370803i	0.982663	+	0.185402i	$0.0593586\pi$
$587$			8.98386i			0.370803i	−0.982663	+	0.185402i	$0.940641\pi$
$588$	−7.36491	+	12.2793i	−0.303724	+	0.506388i
$589$		−	0.523143i		−	0.0215557i
$590$	43.8023	+	12.1288i	1.80331	+	0.499335i
$591$		−	16.3762i		−	0.673628i
$592$	29.1707	−	15.5696i	1.19891	−	0.639905i
$593$	10.0225			0.411575			0.205787	−	0.978597i	$-0.434024\pi$
$593$	10.0225			0.411575			0.205787	+	0.978597i	$0.434024\pi$
$594$	−0.167536	+	0.605043i	−0.00687407	+	0.0248252i
$595$	53.7581			2.20387
$596$	18.3174	−	30.5400i	0.750312	−	1.25097i
$597$			0.218434i			0.00893990i
$598$	−20.6516	−	16.5032i	−0.844507	−	0.674865i
$599$			42.5653i			1.73917i	0.493781	+	0.869586i	$0.335614\pi$
$599$			42.5653i			1.73917i	−0.493781	+	0.869586i	$0.664386\pi$
$600$	−4.00808	+	3.81258i	−0.163629	+	0.155648i
$601$	26.9032			1.09741			0.548703	−	0.836017i	$-0.315122\pi$
$601$	26.9032			1.09741			0.548703	+	0.836017i	$0.315122\pi$
$602$	−3.00566	−	0.832263i	−0.122501	−	0.0339205i
$603$	−15.2528			−0.621140
$604$	23.7988	−	39.6789i	0.968360	−	1.61451i
$605$			28.4914i			1.15834i
$606$	5.05506	−	18.2560i	0.205348	−	0.741598i
$607$		−	4.29457i		−	0.174311i	−0.996195	−	0.0871557i	$-0.972222\pi$
$607$		−	4.29457i		−	0.174311i	0.996195	−	0.0871557i	$-0.0277778\pi$
$608$	1.08027	+	4.82759i	0.0438107	+	0.195784i
$609$			20.1086i			0.814841i
$610$	−44.0253	−	12.1905i	−1.78253	−	0.493581i
$611$		−	15.1646i		−	0.613495i
$612$	−5.57247	+	9.29078i	−0.225254	+	0.375558i
$613$			43.1668i			1.74349i	0.489958	+	0.871746i	$0.337012\pi$
$613$			43.1668i			1.74349i	−0.489958	+	0.871746i	$0.662988\pi$
$614$	−2.53914	+	9.16991i	−0.102471	+	0.370067i
$615$	7.91265			0.319069
$616$	3.25637	+	3.42335i	0.131203	+	0.137931i
$617$			12.4584i			0.501555i	0.968045	+	0.250777i	$0.0806862\pi$
$617$			12.4584i			0.501555i	−0.968045	+	0.250777i	$0.919314\pi$
$618$	1.63623	−	5.90912i	0.0658187	−	0.237700i
$619$	−22.8503			−0.918430			−0.459215	−	0.888325i	$-0.651869\pi$
$619$	−22.8503			−0.918430			−0.459215	+	0.888325i	$0.651869\pi$
$620$	2.70602	+	1.62303i	0.108676	+	0.0651824i
$621$	−1.88557	+	4.40961i	−0.0756654	+	0.176951i
$622$	1.04143	−	3.76106i	0.0417576	−	0.150805i
$623$		−	49.7871i		−	1.99468i
$624$	13.7544	−	7.34125i	0.550615	−	0.293885i
$625$	−30.9538			−1.23815
$626$	0.432280	−	1.56115i	0.0172774	−	0.0623960i
$627$		−	0.388220i		−	0.0155040i
$628$	16.7419	−	27.9131i	0.668073	−	1.11385i
$629$	−44.7784			−1.78543
$630$	−3.74531	+	13.5259i	−0.149217	+	0.538885i
$631$	21.4492			0.853877			0.426939	−	0.904281i	$-0.359592\pi$
$631$	21.4492			0.853877			0.426939	+	0.904281i	$0.359592\pi$
$632$	21.2558	+	22.3458i	0.845511	+	0.888868i
$633$	−10.1413			−0.403081
$634$	34.5570	+	9.56879i	1.37243	+	0.380025i
$635$	37.5990			1.49207
$636$	−5.50580	−	3.30229i	−0.218319	−	0.130944i
$637$	−27.9050			−1.10564
$638$	3.23330	+	0.895298i	0.128008	+	0.0354452i
$639$			1.61736i			0.0639817i
$640$	−28.3227	−	9.38955i	−1.11955	−	0.371154i
$641$		−	8.45936i		−	0.334125i	−0.985946	−	0.167062i	$-0.946572\pi$
$641$		−	8.45936i		−	0.334125i	0.985946	−	0.167062i	$-0.0534281\pi$
$642$	−7.09631	+	25.6278i	−0.280069	+	1.01145i
$643$	33.3589			1.31555			0.657773	−	0.753216i	$-0.271498\pi$
$643$	33.3589			1.31555			0.657773	+	0.753216i	$0.271498\pi$
$644$	21.1602	+	29.2387i	0.833829	+	1.15217i
$645$	−1.54568			−0.0608609
$646$	1.78776	−	6.45637i	0.0703385	−	0.254022i
$647$			10.1383i			0.398580i	0.979941	+	0.199290i	$0.0638635\pi$
$647$			10.1383i			0.398580i	−0.979941	+	0.199290i	$0.936136\pi$
$648$	−1.94939	−	2.04936i	−0.0765794	−	0.0805064i
$649$		−	5.40959i		−	0.212345i
$650$	−10.3897	−	2.87690i	−0.407518	−	0.112841i
$651$	2.25101			0.0882239
$652$	24.7282	−	41.2285i	0.968431	−	1.61463i
$653$	28.2360			1.10496			0.552480	−	0.833526i	$-0.313681\pi$
$653$	28.2360			1.10496			0.552480	+	0.833526i	$0.313681\pi$
$654$	−1.92711	−	0.533615i	−0.0753560	−	0.0208660i
$655$	−25.3788			−0.991630
$656$	5.65077	+	10.5871i	0.220626	+	0.413358i
$657$	−14.9948			−0.585003
$658$	−5.52504	+	19.9533i	−0.215388	+	0.777859i
$659$	−2.19610			−0.0855478			−0.0427739	−	0.999085i	$-0.513620\pi$
$659$	−2.19610			−0.0855478			−0.0427739	+	0.999085i	$0.513620\pi$
$660$	2.00811	+	1.20443i	0.0781655	+	0.0468825i
$661$			30.6073i			1.19049i	0.803546	+	0.595243i	$0.202944\pi$
$661$			30.6073i			1.19049i	−0.803546	+	0.595243i	$0.797056\pi$
$662$	8.53288	−	30.8159i	0.331640	−	1.19769i
$663$	−21.1136			−0.819984
$664$	22.7754	+	23.9433i	0.883856	+	0.929179i
$665$		−	8.67877i		−	0.336548i
$666$	3.11969	−	11.2665i	0.120886	−	0.436570i
$667$	23.5646	+	10.0764i	0.912426	+	0.390158i
$668$	−12.5719	+	20.9607i	−0.486422	+	0.810994i
$669$	−16.1279			−0.623542
$670$	−15.1815	+	54.8270i	−0.586513	+	2.11815i
$671$			5.43712i			0.209898i
$672$	−20.7724	+	4.64823i	−0.801312	+	0.179309i
$673$	−28.2666			−1.08960			−0.544799	−	0.838567i	$-0.683394\pi$
$673$	−28.2666			−1.08960			−0.544799	+	0.838567i	$0.683394\pi$
$674$	−7.90678	+	28.5548i	−0.304558	+	1.09989i
$675$			1.95578i			0.0752778i
$676$	3.76006	+	2.25523i	0.144618	+	0.0867395i
$677$			9.48783i			0.364647i	0.983239	+	0.182323i	$0.0583618\pi$
$677$			9.48783i			0.364647i	−0.983239	+	0.182323i	$0.941638\pi$
$678$	10.2230	+	2.83074i	0.392613	+	0.108714i
$679$		−	4.86708i		−	0.186781i
$680$	27.8498	+	29.2780i	1.06799	+	1.12276i
$681$		−	7.08184i		−	0.271377i
$682$	0.100222	−	0.361944i	0.00383770	−	0.0138596i
$683$		−	15.6468i		−	0.598709i	−0.954142	−	0.299354i	$-0.903229\pi$
$683$		−	15.6468i		−	0.598709i	0.954142	−	0.299354i	$-0.0967713\pi$
$684$	1.49991	+	0.899626i	0.0573507	+	0.0343981i
$685$	1.44455			0.0551936
$686$	0.816955	+	0.226214i	0.0311915	+	0.00863688i
$687$	3.37854			0.128899
$688$	−1.10384	−	2.06811i	−0.0420833	−	0.0788461i
$689$		−	12.5121i		−	0.476672i
$690$	13.9738	+	11.1668i	0.531975	+	0.425113i
$691$			6.15202i			0.234034i	0.993130	+	0.117017i	$0.0373332\pi$
$691$			6.15202i			0.234034i	−0.993130	+	0.117017i	$0.962667\pi$
$692$	21.2288	+	12.7327i	0.807000	+	0.484026i
$693$	1.67045			0.0634552
$694$	1.91215	−	6.90558i	0.0725841	−	0.262132i
$695$	−37.0305			−1.40465
$696$	−10.9516	+	10.4174i	−0.415120	+	0.394871i
$697$		−	16.2517i		−	0.615578i
$698$	−33.5287	−	9.28405i	−1.26908	−	0.351406i
$699$		−	13.6186i		−	0.515101i
$700$	12.6224	+	7.57072i	0.477081	+	0.286146i
$701$		−	22.5282i		−	0.850880i	−0.904987	−	0.425440i	$-0.860119\pi$
$701$		−	22.5282i		−	0.850880i	0.904987	−	0.425440i	$-0.139881\pi$
$702$	1.47098	−	5.31232i	0.0555184	−	0.200501i
$703$			7.22907i			0.272650i
$704$	−0.177452	+	3.54699i	−0.00668797	+	0.133682i
$705$			10.2611i			0.386454i
$706$	1.82755	+	0.506047i	0.0687808	+	0.0190453i
$707$	−50.4026			−1.89558
$708$	20.9003	+	12.5357i	0.785483	+	0.471120i
$709$		−	27.8820i		−	1.04713i	−0.851985	−	0.523565i	$-0.824602\pi$
$709$		−	27.8820i		−	1.04713i	0.851985	−	0.523565i	$-0.175398\pi$
$710$	5.81370	+	1.60980i	0.218184	+	0.0604149i
$711$	10.9038			0.408925
$712$	27.1153	−	25.7926i	1.01619	−	0.966620i
$713$	1.12797	−	2.63788i	0.0422430	−	0.0987896i
$714$	27.7808	+	7.69246i	1.03967	+	0.287883i
$715$			4.56349i			0.170665i
$716$	5.48402	−	9.14331i	0.204947	−	0.341702i
$717$	24.4272			0.912250
$718$	−16.5031	−	4.56968i	−0.615889	−	0.170539i
$719$			3.48406i			0.129934i	0.997887	+	0.0649668i	$0.0206942\pi$
$719$			3.48406i			0.129934i	−0.997887	+	0.0649668i	$0.979306\pi$
$720$	−9.30683	+	4.96743i	−0.346845	+	0.185125i
$721$	−16.3144			−0.607579
$722$	24.8533	+	6.88185i	0.924945	+	0.256116i
$723$	−18.5960			−0.691592
$724$	10.5271	−	17.5514i	0.391235	−	0.652292i
$725$	10.4515			0.388160
$726$	−4.07695	+	14.7236i	−0.151310	+	0.546445i
$727$	37.4694			1.38966			0.694832	−	0.719172i	$-0.255479\pi$
$727$	37.4694			1.38966			0.694832	+	0.719172i	$0.255479\pi$
$728$	−28.5911	−	30.0573i	−1.05966	−	1.11400i
$729$	−1.00000			−0.0370370
$730$	−14.9248	+	53.8998i	−0.552391	+	1.99492i
$731$			3.17465i			0.117419i
$732$	−21.0067	−	12.5995i	−0.776430	−	0.465691i
$733$			21.7887i			0.804784i	0.915467	+	0.402392i	$0.131821\pi$
$733$			21.7887i			0.804784i	−0.915467	+	0.402392i	$0.868179\pi$
$734$	28.9833	+	8.02544i	1.06979	+	0.296224i
$735$	18.8818			0.696465
$736$	−4.96186	+	26.6717i	−0.182897	+	0.983132i
$737$	6.77113			0.249418
$738$	4.08905	+	1.13225i	0.150520	+	0.0416788i
$739$		−	38.4986i		−	1.41619i	−0.706116	−	0.708096i	$-0.749554\pi$
$739$		−	38.4986i		−	1.41619i	0.706116	−	0.708096i	$-0.250446\pi$
$740$	−37.3932	−	22.4279i	−1.37460	−	0.824464i
$741$			3.40860i			0.125218i
$742$	−4.55862	+	16.4631i	−0.167352	+	0.604380i
$743$	16.0420			0.588524			0.294262	−	0.955725i	$-0.404926\pi$
$743$	16.0420			0.588524			0.294262	+	0.955725i	$0.404926\pi$
$744$	1.16615	+	1.22595i	0.0427532	+	0.0449456i
$745$	−46.9613			−1.72053
$746$	3.98845	−	14.4040i	0.146028	−	0.527369i
$747$	11.6833			0.427470
$748$	2.47378	−	4.12444i	0.0904502	−	0.150805i
$749$	70.7554			2.58534
$750$	−10.9427	−	3.03001i	−0.399569	−	0.110640i
$751$	−14.1886			−0.517751			−0.258876	−	0.965911i	$-0.583352\pi$
$751$	−14.1886			−0.517751			−0.258876	+	0.965911i	$0.583352\pi$
$752$	−13.7293	+	7.32789i	−0.500657	+	0.267221i
$753$		−	11.0122i		−	0.401305i
$754$	−28.3887	−	7.86079i	−1.03385	−	0.286273i
$755$	−61.0142			−2.22053
$756$	−3.87095	+	6.45391i	−0.140785	+	0.234726i
$757$		−	44.8913i		−	1.63160i	−0.578333	−	0.815801i	$-0.696297\pi$
$757$		−	44.8913i		−	1.63160i	0.578333	−	0.815801i	$-0.303703\pi$
$758$	−24.1290	−	6.68129i	−0.876405	−	0.242675i
$759$	0.837058	−	1.95755i	0.0303833	−	0.0710545i
$760$	4.72667	−	4.49611i	0.171454	−	0.163091i
$761$	−29.9876			−1.08705			−0.543525	−	0.839393i	$-0.682911\pi$
$761$	−29.9876			−1.08705			−0.543525	+	0.839393i	$0.682911\pi$
$762$	19.4302	+	5.38019i	0.703881	+	0.194904i
$763$			5.32052i			0.192616i
$764$	31.0018	+	18.5944i	1.12161	+	0.672722i
$765$	14.2864			0.516527
$766$	−50.6602	−	14.0277i	−1.83043	−	0.506843i
$767$			47.4966i			1.71500i
$768$	−13.2928	−	8.90508i	−0.479664	−	0.321334i
$769$		−	48.7531i		−	1.75808i	−0.476746	−	0.879041i	$-0.658184\pi$
$769$		−	48.7531i		−	1.75808i	0.476746	−	0.879041i	$-0.341816\pi$
$770$	1.66265	−	6.00454i	0.0599177	−	0.216388i
$771$		−	1.80376i		−	0.0649610i
$772$	−0.120856	−	0.0724878i	−0.00434972	−	0.00260889i
$773$		−	20.1101i		−	0.723310i	−0.932312	−	0.361655i	$-0.882212\pi$
$773$		−	20.1101i		−	0.723310i	0.932312	−	0.361655i	$-0.117788\pi$
$774$	−0.798764	−	0.221177i	−0.0287110	−	0.00795004i
$775$		−	1.16997i		−	0.0420266i
$776$	2.65073	−	2.52143i	0.0951556	−	0.0905140i
$777$	−31.1056			−1.11591
$778$	−4.83808	+	17.4724i	−0.173454	+	0.626416i
$779$	−2.62370			−0.0940037
$780$	−17.6314	−	10.5750i	−0.631304	−	0.378646i
$781$		−	0.717991i		−	0.0256917i
$782$	22.9354	−	28.7008i	0.820170	−	1.02634i
$783$			5.34393i			0.190976i
$784$	13.4843	+	25.2638i	0.481583	+	0.902280i
$785$	−42.9220			−1.53195
$786$	−13.1151	−	3.63155i	−0.467799	−	0.129533i
$787$	37.2635			1.32830			0.664151	−	0.747599i	$-0.268793\pi$
$787$	37.2635			1.32830			0.664151	+	0.747599i	$0.268793\pi$
$788$	−28.0877	−	16.8465i	−1.00058	−	0.600133i
$789$			12.9884i			0.462399i
$790$	10.8529	−	39.1944i	0.386128	−	1.39447i
$791$		−	28.2245i		−	1.00355i
$792$	0.865391	+	0.909768i	0.0307503	+	0.0323272i
$793$		−	47.7383i		−	1.69524i
$794$	12.8477	+	3.55752i	0.455949	+	0.126252i
$795$			8.46625i			0.300267i
$796$	0.374646	+	0.224707i	0.0132790	+	0.00796454i
$797$			10.1031i			0.357872i	0.983861	+	0.178936i	$0.0572655\pi$
$797$			10.1031i			0.357872i	−0.983861	+	0.178936i	$0.942735\pi$
$798$	1.24188	−	4.48496i	0.0439621	−	0.158766i
$799$	21.0752			0.745585
$800$	2.41594	+	10.7965i	0.0854164	+	0.381715i
$801$		−	13.2311i		−	0.467498i
$802$	6.00637	−	21.6916i	0.212092	−	0.765956i
$803$	6.65662			0.234907
$804$	−15.6908	+	26.1607i	−0.553372	+	0.922618i
$805$	18.7127	−	43.7616i	0.659536	−	1.54239i
$806$	−0.879957	+	3.17790i	−0.0309952	+	0.111937i
$807$		−	3.59883i		−	0.126685i
$808$	−26.1115	−	27.4505i	−0.918599	−	0.965704i
$809$	−11.5458			−0.405930			−0.202965	−	0.979186i	$-0.565058\pi$
$809$	−11.5458			−0.405930			−0.202965	+	0.979186i	$0.565058\pi$
$810$	−0.995329	+	3.59456i	−0.0349723	+	0.126300i
$811$			19.6062i			0.688466i	0.938884	+	0.344233i	$0.111861\pi$
$811$			19.6062i			0.688466i	−0.938884	+	0.344233i	$0.888139\pi$
$812$	34.4892	+	20.6861i	1.21033	+	0.725940i
$813$	17.7331			0.621925
$814$	−1.38492	+	5.00154i	−0.0485414	+	0.175304i
$815$	−63.3969			−2.22070
$816$	10.2026	+	19.1152i	0.357161	+	0.669167i
$817$	0.512519			0.0179308
$818$	10.4327	+	2.88879i	0.364769	+	0.101004i
$819$	−14.6667			−0.512496
$820$	8.13990	−	13.5714i	0.284258	−	0.473933i
$821$	−29.5246			−1.03041			−0.515207	−	0.857066i	$-0.672285\pi$
$821$	−29.5246			−1.03041			−0.515207	+	0.857066i	$0.672285\pi$
$822$	0.746507	+	0.206707i	0.0260374	+	0.00720973i
$823$			0.192280i			0.00670247i	0.999994	+	0.00335124i	$0.00106673\pi$
$823$			0.192280i			0.00670247i	−0.999994	+	0.00335124i	$0.998933\pi$
$824$	−8.45179	−	8.88520i	−0.294432	−	0.309531i
$825$		−	0.868224i		−	0.0302277i
$826$	17.3048	−	62.4950i	0.602111	−	2.17448i
$827$	−19.9788			−0.694730			−0.347365	−	0.937730i	$-0.612923\pi$
$827$	−19.9788			−0.694730			−0.347365	+	0.937730i	$0.612923\pi$
$828$	5.62340	+	7.77028i	0.195427	+	0.270036i
$829$	48.6264			1.68887			0.844433	−	0.535661i	$-0.179938\pi$
$829$	48.6264			1.68887			0.844433	+	0.535661i	$0.179938\pi$
$830$	11.6287	−	41.9964i	0.403640	−	1.45772i
$831$		−	4.19147i		−	0.145400i
$832$	1.55804	−	31.1429i	0.0540154	−	1.07968i
$833$		−	38.7812i		−	1.34369i
$834$	−19.1364	−	5.29883i	−0.662638	−	0.183484i
$835$	32.2312			1.11541
$836$	−0.665854	−	0.399369i	−0.0230291	−	0.0138125i
$837$	0.598213			0.0206773
$838$	−20.2782	−	5.61499i	−0.700497	−	0.193967i
$839$	−41.6351			−1.43740			−0.718701	−	0.695319i	$-0.755263\pi$
$839$	−41.6351			−1.43740			−0.718701	+	0.695319i	$0.755263\pi$
$840$	19.3461	+	20.3381i	0.667503	+	0.701733i
$841$	−0.442430			−0.0152562
$842$	−10.3936	+	37.5358i	−0.358188	+	1.29357i
$843$	15.5993			0.537267
$844$	−10.4326	+	17.3939i	−0.359104	+	0.598721i
$845$		−	5.78184i		−	0.198901i
$846$	−1.46830	+	5.30265i	−0.0504811	+	0.182309i
$847$	40.6502			1.39676
$848$	−11.3278	+	6.04613i	−0.389000	+	0.207625i
$849$		−	13.8442i		−	0.475132i
$850$	3.99819	−	14.4392i	0.137137	−	0.495260i
$851$	−15.5869	+	36.4517i	−0.534313	+	1.24955i
$852$	2.77401	+	1.66381i	0.0950361	+	0.0570012i
$853$	−51.2775			−1.75571			−0.877854	−	0.478928i	$-0.841025\pi$
$853$	−51.2775			−1.75571			−0.877854	+	0.478928i	$0.841025\pi$
$854$	−17.3929	+	62.8131i	−0.595171	+	2.14942i
$855$		−	2.30642i		−	0.0788777i
$856$	36.6554	+	38.5351i	1.25286	+	1.31710i
$857$	23.4840			0.802199			0.401099	−	0.916035i	$-0.368628\pi$
$857$	23.4840			0.802199			0.401099	+	0.916035i	$0.368628\pi$
$858$	−0.653007	+	2.35829i	−0.0222933	+	0.0805107i
$859$		−	3.41554i		−	0.116537i	−0.998301	−	0.0582684i	$-0.981442\pi$
$859$		−	3.41554i		−	0.116537i	0.998301	−	0.0582684i	$-0.0185579\pi$
$860$	−1.59007	+	2.65106i	−0.0542208	+	0.0904005i
$861$		−	11.2894i		−	0.384741i
$862$	−4.31200	−	1.19399i	−0.146867	−	0.0406674i
$863$		−	11.9996i		−	0.408471i	−0.978922	−	0.204236i	$-0.934529\pi$
$863$		−	11.9996i		−	0.408471i	0.978922	−	0.204236i	$-0.0654709\pi$
$864$	−5.52033	+	1.23528i	−0.187806	+	0.0420252i
$865$		−	32.6435i		−	1.10991i
$866$	9.48229	−	34.2446i	0.322221	−	1.16368i
$867$		−	12.3428i		−	0.419183i
$868$	2.31566	−	3.86081i	0.0785985	−	0.131045i
$869$	−4.84051			−0.164203
$870$	19.2091	+	5.31897i	0.651249	+	0.180330i
$871$	−59.4511			−2.01442
$872$	−2.89769	+	2.75634i	−0.0981280	+	0.0933415i
$873$		−	1.29344i		−	0.0437764i
$874$	−4.63348	−	3.70272i	−0.156730	−	0.125246i
$875$			30.2114i			1.02133i
$876$	−15.4255	+	25.7183i	−0.521178	+	0.868942i
$877$	6.90835			0.233279			0.116639	−	0.993174i	$-0.462788\pi$
$877$	6.90835			0.233279			0.116639	+	0.993174i	$0.462788\pi$
$878$	1.95319	−	7.05381i	0.0659170	−	0.238055i
$879$	7.35396			0.248043
$880$	4.13156	−	2.20518i	0.139275	−	0.0743367i
$881$			45.9651i			1.54860i	0.632816	+	0.774302i	$0.281899\pi$
$881$			45.9651i			1.54860i	−0.632816	+	0.774302i	$0.718101\pi$
$882$	9.75761	+	2.70187i	0.328556	+	0.0909767i
$883$			3.13486i			0.105497i	0.998608	+	0.0527483i	$0.0167981\pi$
$883$			3.13486i			0.105497i	−0.998608	+	0.0527483i	$0.983202\pi$
$884$	−21.7200	+	36.2129i	−0.730521	+	1.21797i
$885$		−	32.1384i		−	1.08032i
$886$	3.36024	−	12.1353i	0.112889	−	0.407692i
$887$			36.0841i			1.21159i	0.795622	+	0.605793i	$0.207144\pi$
$887$			36.0841i			1.21159i	−0.795622	+	0.605793i	$0.792856\pi$
$888$	−16.1145	−	16.9409i	−0.540768	−	0.568498i
$889$		−	53.6444i		−	1.79918i
$890$	−47.5600	−	13.1693i	−1.59422	−	0.441436i
$891$	0.443928			0.0148722
$892$	−16.5911	+	27.6618i	−0.555512	+	0.926186i
$893$		−	3.40240i		−	0.113857i
$894$	−24.2684	−	6.71989i	−0.811656	−	0.224747i
$895$	−14.0597			−0.469962
$896$	−13.3965	+	40.4094i	−0.447547	+	1.34998i
$897$	−7.34944	+	17.1874i	−0.245391	+	0.573872i
$898$	8.30566	+	2.29983i	0.277163	+	0.0767462i
$899$		−	3.19681i		−	0.106620i
$900$	3.35445	+	2.01195i	0.111815	+	0.0670648i
$901$	17.3888			0.579304
$902$	−1.81524	−	0.502639i	−0.0604410	−	0.0167360i
$903$			2.20529i			0.0733876i
$904$	15.3718	−	14.6220i	0.511257	−	0.486319i
$905$	−26.9887			−0.897136
$906$	−31.5305	−	8.73076i	−1.04753	−	0.290060i
$907$	15.9472			0.529518			0.264759	−	0.964315i	$-0.414708\pi$
$907$	15.9472			0.529518			0.264759	+	0.964315i	$0.414708\pi$
$908$	−12.1464	−	7.28523i	−0.403093	−	0.241769i
$909$	−13.3947			−0.444273
$910$	−14.5982	+	52.7203i	−0.483925	+	1.74766i
$911$	−38.4869			−1.27513			−0.637563	−	0.770398i	$-0.720058\pi$
$911$	−38.4869			−1.27513			−0.637563	+	0.770398i	$0.720058\pi$
$912$	3.08598	−	1.64711i	0.102187	−	0.0545414i
$913$	−5.18655			−0.171650
$914$	2.44126	−	8.81644i	0.0807498	−	0.291622i
$915$			32.3020i			1.06787i
$916$	3.47557	−	5.79470i	0.114836	−	0.191462i
$917$			36.2092i			1.19573i
$918$	7.38284	+	2.04430i	0.243670	+	0.0674720i
$919$	−15.0013			−0.494846			−0.247423	−	0.968908i	$-0.579584\pi$
$919$	−15.0013			−0.494846			−0.247423	+	0.968908i	$0.579584\pi$
$920$	33.5279	−	12.4797i	1.10538	−	0.411443i
$921$	6.72809			0.221698
$922$	21.8724	+	6.05644i	0.720329	+	0.199458i
$923$			6.30402i			0.207499i
$924$	1.71843	−	2.86507i	0.0565321	−	0.0942539i
$925$			16.1673i			0.531577i
$926$	0.702335	−	2.53643i	0.0230802	−	0.0833523i
$927$	−4.33560			−0.142400
$928$	6.60127	+	29.5003i	0.216697	+	0.968394i
$929$	−15.7205			−0.515772			−0.257886	−	0.966175i	$-0.583026\pi$
$929$	−15.7205			−0.515772			−0.257886	+	0.966175i	$0.583026\pi$
$930$	0.595419	−	2.15031i	0.0195246	−	0.0705116i
$931$	−6.26087			−0.205192
$932$	−23.3578	−	14.0097i	−0.765112	−	0.458902i
$933$	−2.75954			−0.0903433
$934$	34.4891	+	9.54999i	1.12852	+	0.312485i
$935$	−6.34214			−0.207410
$936$	−7.59820	−	7.98783i	−0.248355	−	0.261090i
$937$		−	1.61758i		−	0.0528441i	−0.999651	−	0.0264220i	$-0.991589\pi$
$937$		−	1.61758i		−	0.0528441i	0.999651	−	0.0264220i	$-0.00841137\pi$
$938$	78.2244	+	21.6602i	2.55412	+	0.707232i
$939$	−1.14544			−0.0373799
$940$	17.5993	+	10.5558i	0.574025	+	0.344291i
$941$			46.9526i			1.53061i	0.643667	+	0.765305i	$0.277412\pi$
$941$			46.9526i			1.53061i	−0.643667	+	0.765305i	$0.722588\pi$
$942$	−22.1809	−	6.14187i	−0.722694	−	0.200113i
$943$	−13.2297	−	5.65707i	−0.430817	−	0.184220i
$944$	43.0012	−	22.9515i	1.39957	−	0.747006i
$945$	9.92416			0.322833
$946$	0.354594	+	0.0981866i	0.0115288	+	0.00319232i
$947$		−	7.94250i		−	0.258097i	−0.991638	−	0.129048i	$-0.958808\pi$
$947$		−	7.94250i		−	0.258097i	0.991638	−	0.129048i	$-0.0411922\pi$
$948$	11.2170	−	18.7016i	0.364310	−	0.607401i
$949$	−58.4457			−1.89723
$950$	−2.33108	−	0.645473i	−0.0756302	−	0.0209419i
$951$		−	25.3550i		−	0.822191i
$952$	41.7724	−	39.7348i	1.35385	−	1.28781i
$953$		−	50.7392i		−	1.64361i	−0.569772	−	0.821803i	$-0.692969\pi$
$953$		−	50.7392i		−	1.64361i	0.569772	−	0.821803i	$-0.307031\pi$
$954$	−1.21147	+	4.37514i	−0.0392228	+	0.141650i
$955$		−	47.6714i		−	1.54261i
$956$	25.1287	−	41.8963i	0.812721	−	1.35502i
$957$		−	2.37232i		−	0.0766862i
$958$	−4.51290	−	1.24962i	−0.145805	−	0.0403732i
$959$		−	2.06102i		−	0.0665537i
$960$	−1.05424	+	21.0727i	−0.0340256	+	0.680118i
$961$	30.6421			0.988456
$962$	12.1597	−	43.9139i	0.392045	−	1.41584i
$963$	18.8035			0.605934
$964$	−19.1301	+	31.8949i	−0.616138	+	1.02726i
$965$			0.185841i			0.00598242i
$966$	15.9323	−	19.9372i	0.512612	−	0.641468i
$967$		−	4.98236i		−	0.160222i	−0.996786	−	0.0801110i	$-0.974473\pi$
$967$		−	4.98236i		−	0.160222i	0.996786	−	0.0801110i	$-0.0255275\pi$
$968$	21.0592	+	22.1391i	0.676867	+	0.711576i
$969$	−4.73713			−0.152179
$970$	−4.64936	−	1.28740i	−0.149282	−	0.0413360i
$971$	25.0545			0.804038			0.402019	−	0.915631i	$-0.368309\pi$
$971$	25.0545			0.804038			0.402019	+	0.915631i	$0.368309\pi$
$972$	−1.02872	+	1.71515i	−0.0329962	+	0.0550134i
$973$			52.8332i			1.69376i
$974$	−8.53884	+	30.8374i	−0.273602	+	0.988094i
$975$			7.62308i			0.244134i
$976$	−43.2200	+	23.0683i	−1.38344	+	0.738397i
$977$			31.9225i			1.02129i	0.859791	+	0.510645i	$0.170594\pi$
$977$			31.9225i			1.02129i	−0.859791	+	0.510645i	$0.829406\pi$
$978$	−32.7619	−	9.07172i	−1.04761	−	0.290081i
$979$			5.87366i			0.187723i
$980$	19.4241	−	32.3851i	0.620479	−	1.03450i
$981$			1.41395i			0.0451439i
$982$	9.50186	−	34.3153i	0.303216	−	1.09504i
$983$	26.8959			0.857847			0.428924	−	0.903341i	$-0.358893\pi$
$983$	26.8959			0.857847			0.428924	+	0.903341i	$0.358893\pi$
$984$	6.14846	−	5.84855i	0.196006	−	0.186445i
$985$			43.1903i			1.37616i
$986$	10.9246	−	39.4534i	0.347910	−	1.25645i
$987$	14.6400			0.465996
$988$	5.84626	+	3.50649i	0.185994	+	0.111556i
$989$	2.58431	+	1.10507i	0.0821764	+	0.0351391i
$990$	0.441855	−	1.59573i	0.0140431	−	0.0507155i
$991$		−	57.1447i		−	1.81526i	−0.419769	−	0.907631i	$-0.637889\pi$
$991$		−	57.1447i		−	1.81526i	0.419769	−	0.907631i	$-0.362111\pi$
$992$	3.30234	−	0.738964i	0.104849	−	0.0234621i
$993$	−22.6100			−0.717508
$994$	2.29679	−	8.29469i	0.0728498	−	0.263092i
$995$		−	0.576093i		−	0.0182634i
$996$	12.0189	−	20.0386i	0.380832	−	0.634948i
$997$	12.7009			0.402242			0.201121	−	0.979566i	$-0.435542\pi$
$997$	12.7009			0.402242			0.201121	+	0.979566i	$0.435542\pi$
$998$	−12.6145	+	45.5564i	−0.399305	+	1.44206i
$999$	−8.26643			−0.261538

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.e.a.91.1	✓	24
3.2	odd	2		828.2.e.f.91.24		24
4.3	odd	2	inner	276.2.e.a.91.3	yes	24
8.3	odd	2		4416.2.i.d.1471.7		24
8.5	even	2		4416.2.i.d.1471.6		24
12.11	even	2		828.2.e.f.91.22		24
23.22	odd	2	inner	276.2.e.a.91.2	yes	24
69.68	even	2		828.2.e.f.91.23		24
92.91	even	2	inner	276.2.e.a.91.4	yes	24
184.45	odd	2		4416.2.i.d.1471.5		24
184.91	even	2		4416.2.i.d.1471.8		24
276.275	odd	2		828.2.e.f.91.21		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.e.a.91.1	✓	24	1.1	even	1	trivial
276.2.e.a.91.2	yes	24	23.22	odd	2	inner
276.2.e.a.91.3	yes	24	4.3	odd	2	inner
276.2.e.a.91.4	yes	24	92.91	even	2	inner
828.2.e.f.91.21		24	276.275	odd	2
828.2.e.f.91.22		24	12.11	even	2
828.2.e.f.91.23		24	69.68	even	2
828.2.e.f.91.24		24	3.2	odd	2
4416.2.i.d.1471.5		24	184.45	odd	2
4416.2.i.d.1471.6		24	8.5	even	2
4416.2.i.d.1471.7		24	8.3	odd	2
4416.2.i.d.1471.8		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)

\(f(q)\)	\(=\)	\(q+(-1.36293 - 0.377393i) q^{2} +1.00000i q^{3} +(1.71515 + 1.02872i) q^{4} -2.63738i q^{5} +(0.377393 - 1.36293i) q^{6} -3.76288 q^{7} +(-1.94939 - 2.04936i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.36293 - 0.377393i) q^{2} +1.00000i q^{3} +(1.71515 + 1.02872i) q^{4} -2.63738i q^{5} +(0.377393 - 1.36293i) q^{6} -3.76288 q^{7} +(-1.94939 - 2.04936i) q^{8} -1.00000 q^{9} +(-0.995329 + 3.59456i) q^{10} +0.443928 q^{11} +(-1.02872 + 1.71515i) q^{12} -3.89773 q^{13} +(5.12854 + 1.42009i) q^{14} +2.63738 q^{15} +(1.88347 + 3.52882i) q^{16} -5.41690i q^{17} +(1.36293 + 0.377393i) q^{18} -0.874510 q^{19} +(2.71313 - 4.52350i) q^{20} -3.76288i q^{21} +(-0.605043 - 0.167536i) q^{22} +(-4.40961 - 1.88557i) q^{23} +(2.04936 - 1.94939i) q^{24} -1.95578 q^{25} +(5.31232 + 1.47098i) q^{26} -1.00000i q^{27} +(-6.45391 - 3.87095i) q^{28} -5.34393 q^{29} +(-3.59456 - 0.995329i) q^{30} +0.598213i q^{31} +(-1.23528 - 5.52033i) q^{32} +0.443928i q^{33} +(-2.04430 + 7.38284i) q^{34} +9.92416i q^{35} +(-1.71515 - 1.02872i) q^{36} -8.26643i q^{37} +(1.19189 + 0.330034i) q^{38} -3.89773i q^{39} +(-5.40493 + 5.14129i) q^{40} +3.00019 q^{41} +(-1.42009 + 5.12854i) q^{42} -0.586065 q^{43} +(0.761403 + 0.456678i) q^{44} +2.63738i q^{45} +(5.29838 + 4.23405i) q^{46} +3.89063i q^{47} +(-3.52882 + 1.88347i) q^{48} +7.15930 q^{49} +(2.66558 + 0.738096i) q^{50} +5.41690 q^{51} +(-6.68518 - 4.00967i) q^{52} +3.21010i q^{53} +(-0.377393 + 1.36293i) q^{54} -1.17081i q^{55} +(7.33534 + 7.71149i) q^{56} -0.874510i q^{57} +(7.28339 + 2.01676i) q^{58} -12.1857i q^{59} +(4.52350 + 2.71313i) q^{60} +12.2477i q^{61} +(0.225762 - 0.815322i) q^{62} +3.76288 q^{63} +(-0.399731 + 7.99001i) q^{64} +10.2798i q^{65} +(0.167536 - 0.605043i) q^{66} +15.2528 q^{67} +(5.57247 - 9.29078i) q^{68} +(1.88557 - 4.40961i) q^{69} +(3.74531 - 13.5259i) q^{70} -1.61736i q^{71} +(1.94939 + 2.04936i) q^{72} +14.9948 q^{73} +(-3.11969 + 11.2665i) q^{74} -1.95578i q^{75} +(-1.49991 - 0.899626i) q^{76} -1.67045 q^{77} +(-1.47098 + 5.31232i) q^{78} -10.9038 q^{79} +(9.30683 - 4.96743i) q^{80} +1.00000 q^{81} +(-4.08905 - 1.13225i) q^{82} -11.6833 q^{83} +(3.87095 - 6.45391i) q^{84} -14.2864 q^{85} +(0.798764 + 0.221177i) q^{86} -5.34393i q^{87} +(-0.865391 - 0.909768i) q^{88} +13.2311i q^{89} +(0.995329 - 3.59456i) q^{90} +14.6667 q^{91} +(-5.62340 - 7.77028i) q^{92} -0.598213 q^{93} +(1.46830 - 5.30265i) q^{94} +2.30642i q^{95} +(5.52033 - 1.23528i) q^{96} +1.29344i q^{97} +(-9.75761 - 2.70187i) q^{98} -0.443928 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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