LMFDB - Embedded newform 441.2.bb.c.415.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(37,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([0, 32])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			415.4
Character	$\chi$	$=$	441.415
Dual form			441.2.bb.c.424.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.206956 - 2.76163i) q^{2} +(-5.60611 - 0.844986i) q^{4} +(0.116448 + 0.108048i) q^{5} +(-1.85394 + 1.88756i) q^{7} +(-2.26127 + 9.90726i) q^{8} +(0.322487 - 0.299224i) q^{10} +(-1.22138 - 0.832720i) q^{11} +(-4.48658 + 2.16062i) q^{13} +(4.82907 + 5.51055i) q^{14} +(16.0571 + 4.95296i) q^{16} +(0.262423 - 0.668642i) q^{17} +(-2.79266 + 4.83703i) q^{19} +(-0.561520 - 0.704124i) q^{20} +(-2.55244 + 3.20065i) q^{22} +(-1.20493 - 3.07011i) q^{23} +(-0.371765 - 4.96086i) q^{25} +(5.03832 + 12.8374i) q^{26} +(11.9884 - 9.01534i) q^{28} +(-2.33749 - 2.93113i) q^{29} +(0.368945 + 0.639031i) q^{31} +(9.57613 - 24.3996i) q^{32} +(-1.79223 - 0.863094i) q^{34} +(-0.419834 + 0.0194881i) q^{35} +(-3.44919 + 0.519882i) q^{37} +(12.7801 + 8.71335i) q^{38} +(-1.33377 + 0.909352i) q^{40} +(-0.880638 + 3.85833i) q^{41} +(1.46276 + 6.40876i) q^{43} +(6.14353 + 5.70037i) q^{44} +(-8.72787 + 2.69219i) q^{46} +(0.771974 - 10.3013i) q^{47} +(-0.125788 - 6.99887i) q^{49} -13.7770 q^{50} +(26.9780 - 8.32160i) q^{52} +(-10.7834 - 1.62534i) q^{53} +(-0.0522529 - 0.228935i) q^{55} +(-14.5083 - 22.6358i) q^{56} +(-8.57844 + 5.84868i) q^{58} +(-9.45312 + 8.77121i) q^{59} +(3.56105 - 0.536742i) q^{61} +(1.84112 - 0.886639i) q^{62} +(-35.1217 - 16.9137i) q^{64} +(-0.755902 - 0.233165i) q^{65} +(3.13450 + 5.42912i) q^{67} +(-2.03616 + 3.52674i) q^{68} +(-0.0330681 + 1.16346i) q^{70} +(-0.474231 + 0.594667i) q^{71} +(0.0447067 + 0.596570i) q^{73} +(0.721892 + 9.63298i) q^{74} +(19.7432 - 24.7572i) q^{76} +(3.83617 - 0.761608i) q^{77} +(0.0318244 - 0.0551215i) q^{79} +(1.33466 + 2.31169i) q^{80} +(10.4730 + 3.23050i) q^{82} +(7.67321 + 3.69522i) q^{83} +(0.102804 - 0.0495076i) q^{85} +(18.0014 - 2.71327i) q^{86} +(11.0118 - 10.2175i) q^{88} +(-0.703926 + 0.479929i) q^{89} +(4.23955 - 12.4744i) q^{91} +(4.16077 + 18.2295i) q^{92} +(-28.2886 - 4.26382i) q^{94} +(-0.847828 + 0.261520i) q^{95} -10.8136 q^{97} +(-19.3543 - 1.10108i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32}+ \cdots - 119 q^{98}+O(q^{100}) $ 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{19}{21}\right)$	$1$

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 $

$2$	0.206956	−	2.76163i	0.146340	−	1.95277i	−0.129536	−	0.991575i	$-0.541349\pi$
$2$	0.206956	−	2.76163i	0.146340	−	1.95277i	0.275876	−	0.961193i	$-0.411032\pi$
$3$		0			0
$3$		0			0
$4$	−5.60611	−	0.844986i	−2.80306	−	0.422493i
$5$	0.116448	+	0.108048i	0.0520769	+	0.0483203i	0.705782	−	0.708429i	$-0.250596\pi$
$5$	0.116448	+	0.108048i	0.0520769	+	0.0483203i	−0.653705	+	0.756749i	$0.726786\pi$
$6$		0			0
$7$	−1.85394	+	1.88756i	−0.700725	+	0.713432i
$7$	−1.85394	+	1.88756i	−0.700725	+	0.713432i
$8$	−2.26127	+	9.90726i	−0.799479	+	3.50275i
$9$		0			0
$10$	0.322487	−	0.299224i	0.101979	−	0.0946230i
$11$	−1.22138	−	0.832720i	−0.368259	−	0.251074i	0.365025	−	0.930998i	$-0.381061\pi$
$11$	−1.22138	−	0.832720i	−0.368259	−	0.251074i	−0.733283	+	0.679923i	$0.762013\pi$
$12$		0			0
$13$	−4.48658	+	2.16062i	−1.24435	+	0.599249i	−0.935992	−	0.352020i	$-0.885495\pi$
$13$	−4.48658	+	2.16062i	−1.24435	+	0.599249i	−0.308361	+	0.951269i	$0.599781\pi$
$14$	4.82907	+	5.51055i	1.29062	+	1.47276i
$15$		0			0
$16$	16.0571	+	4.95296i	4.01428	+	1.23824i
$17$	0.262423	−	0.668642i	0.0636468	−	0.162169i	−0.895512	−	0.445037i	$-0.853190\pi$
$17$	0.262423	−	0.668642i	0.0636468	−	0.162169i	0.959159	+	0.282868i	$0.0912857\pi$
$18$		0			0
$19$	−2.79266	+	4.83703i	−0.640680	+	1.10969i	0.344601	+	0.938749i	$0.388014\pi$
$19$	−2.79266	+	4.83703i	−0.640680	+	1.10969i	−0.985281	+	0.170941i	$0.945319\pi$
$20$	−0.561520	−	0.704124i	−0.125560	−	0.157447i
$21$		0			0
$22$	−2.55244	+	3.20065i	−0.544181	+	0.682381i
$23$	−1.20493	−	3.07011i	−0.251245	−	0.640162i	0.748491	−	0.663145i	$-0.230779\pi$
$23$	−1.20493	−	3.07011i	−0.251245	−	0.640162i	−0.999736	+	0.0229833i	$0.992684\pi$
$24$		0			0
$25$	−0.371765	−	4.96086i	−0.0743529	−	0.992171i
$26$	5.03832	+	12.8374i	0.988096	+	2.51763i
$27$		0			0
$28$	11.9884	−	9.01534i	2.26559	−	1.70374i
$29$	−2.33749	−	2.93113i	−0.434062	−	0.544296i	0.515906	−	0.856645i	$-0.327456\pi$
$29$	−2.33749	−	2.93113i	−0.434062	−	0.544296i	−0.949967	+	0.312349i	$0.898884\pi$
$30$		0			0
$31$	0.368945	+	0.639031i	0.0662645	+	0.114773i	0.897254	−	0.441514i	$-0.145559\pi$
$31$	0.368945	+	0.639031i	0.0662645	+	0.114773i	−0.830990	+	0.556288i	$0.812225\pi$
$32$	9.57613	−	24.3996i	1.69284	−	4.31328i
$33$		0			0
$34$	−1.79223	−	0.863094i	−0.307365	−	0.148019i
$35$	−0.419834	+	0.0194881i	−0.0709649	+	0.00329409i
$36$		0			0
$37$	−3.44919	+	0.519882i	−0.567043	+	0.0854680i	−0.426306	−	0.904579i	$-0.640185\pi$
$37$	−3.44919	+	0.519882i	−0.567043	+	0.0854680i	−0.140737	+	0.990047i	$0.544947\pi$
$38$	12.7801	+	8.71335i	2.07321	+	1.41349i
$39$		0			0
$40$	−1.33377	+	0.909352i	−0.210888	+	0.143781i
$41$	−0.880638	+	3.85833i	−0.137533	+	0.602570i	0.858440	+	0.512914i	$0.171434\pi$
$41$	−0.880638	+	3.85833i	−0.137533	+	0.602570i	−0.995973	+	0.0896560i	$0.971423\pi$
$42$		0			0
$43$	1.46276	+	6.40876i	0.223069	+	0.977327i	0.955153	+	0.296113i	$0.0956905\pi$
$43$	1.46276	+	6.40876i	0.223069	+	0.977327i	−0.732084	+	0.681214i	$0.761452\pi$
$44$	6.14353	+	5.70037i	0.926173	+	0.859363i
$45$		0			0
$46$	−8.72787	+	2.69219i	−1.28685	+	0.396942i
$47$	0.771974	−	10.3013i	0.112604	−	1.50260i	−0.599416	−	0.800437i	$-0.704601\pi$
$47$	0.771974	−	10.3013i	0.112604	−	1.50260i	0.712020	−	0.702159i	$-0.247780\pi$
$48$		0			0
$49$	−0.125788	−	6.99887i	−0.0179697	−	0.999839i
$50$	−13.7770			−1.94836
$51$		0			0
$52$	26.9780	−	8.32160i	3.74117	−	1.15400i
$53$	−10.7834	−	1.62534i	−1.48122	−	0.223258i	−0.641853	−	0.766828i	$-0.721834\pi$
$53$	−10.7834	−	1.62534i	−1.48122	−	0.223258i	−0.839364	+	0.543570i	$0.817072\pi$
$54$		0			0
$55$	−0.0522529	−	0.228935i	−0.00704578	−	0.0308696i
$56$	−14.5083	−	22.6358i	−1.93876	−	3.02483i
$57$		0			0
$58$	−8.57844	+	5.84868i	−1.12640	+	0.767970i
$59$	−9.45312	+	8.77121i	−1.23069	+	1.14191i	−0.245693	+	0.969348i	$0.579016\pi$
$59$	−9.45312	+	8.77121i	−1.23069	+	1.14191i	−0.984998	+	0.172567i	$0.944794\pi$
$60$		0			0
$61$	3.56105	−	0.536742i	0.455946	−	0.0687228i	0.0829458	−	0.996554i	$-0.473567\pi$
$61$	3.56105	−	0.536742i	0.455946	−	0.0687228i	0.373000	+	0.927831i	$0.378329\pi$
$62$	1.84112	−	0.886639i	0.233823	−	0.112603i
$63$		0			0
$64$	−35.1217	−	16.9137i	−4.39021	−	2.11422i
$65$	−0.755902	−	0.233165i	−0.0937581	−	0.0289205i
$66$		0			0
$67$	3.13450	+	5.42912i	0.382940	+	0.663272i	0.991481	−	0.130250i	$-0.0415782\pi$
$67$	3.13450	+	5.42912i	0.382940	+	0.663272i	−0.608541	+	0.793523i	$0.708245\pi$
$68$	−2.03616	+	3.52674i	−0.246921	+	0.427680i
$69$		0			0
$70$	−0.0330681	+	1.16346i	−0.00395239	+	0.139060i
$71$	−0.474231	+	0.594667i	−0.0562809	+	0.0705740i	−0.809175	−	0.587567i	$-0.800086\pi$
$71$	−0.474231	+	0.594667i	−0.0562809	+	0.0705740i	0.752894	+	0.658141i	$0.228657\pi$
$72$		0			0
$73$	0.0447067	+	0.596570i	0.00523253	+	0.0698232i	0.999209	−	0.0397727i	$-0.0126634\pi$
$73$	0.0447067	+	0.596570i	0.00523253	+	0.0698232i	−0.993976	+	0.109596i	$0.965044\pi$
$74$	0.721892	+	9.63298i	0.0839183	+	1.11981i
$75$		0			0
$76$	19.7432	−	24.7572i	2.26470	−	2.83984i
$77$	3.83617	−	0.761608i	0.437172	−	0.0867933i
$78$		0			0
$79$	0.0318244	−	0.0551215i	0.00358053	−	0.00620166i	−0.864230	−	0.503098i	$-0.832194\pi$
$79$	0.0318244	−	0.0551215i	0.00358053	−	0.00620166i	0.867810	+	0.496896i	$0.165527\pi$
$80$	1.33466	+	2.31169i	0.149219	+	0.258455i
$81$		0			0
$82$	10.4730	+	3.23050i	1.15655	+	0.356749i
$83$	7.67321	+	3.69522i	0.842244	+	0.405603i	0.804693	−	0.593691i	$-0.202330\pi$
$83$	7.67321	+	3.69522i	0.842244	+	0.405603i	0.0375512	+	0.999295i	$0.488044\pi$
$84$		0			0
$85$	0.102804	−	0.0495076i	0.0111506	−	0.00536986i
$86$	18.0014	−	2.71327i	1.94114	−	0.292579i
$87$		0			0
$88$	11.0118	−	10.2175i	1.17387	−	1.08919i
$89$	−0.703926	+	0.479929i	−0.0746160	+	0.0508724i	−0.600054	−	0.799960i	$-0.704854\pi$
$89$	−0.703926	+	0.479929i	−0.0746160	+	0.0508724i	0.525437	+	0.850832i	$0.323902\pi$
$90$		0			0
$91$	4.23955	−	12.4744i	0.444426	−	1.30767i
$92$	4.16077	+	18.2295i	0.433790	+	1.90056i
$93$		0			0
$94$	−28.2886	−	4.26382i	−2.91774	−	0.439779i
$95$	−0.847828	+	0.261520i	−0.0869853	+	0.0268314i
$96$		0			0
$97$	−10.8136			−1.09796			−0.548978	−	0.835837i	$-0.684983\pi$
$97$	−10.8136			−1.09796			−0.548978	+	0.835837i	$0.684983\pi$
$98$	−19.3543	−	1.10108i	−1.95508	−	0.111225i
$99$		0			0
$100$	−2.10770	+	28.1253i	−0.210770	+	2.81253i
$101$	11.6947	−	3.60735i	1.16367	−	0.358945i	0.348018	−	0.937488i	$-0.386855\pi$
$101$	11.6947	−	3.60735i	1.16367	−	0.358945i	0.815652	+	0.578543i	$0.196378\pi$
$102$		0			0
$103$	3.78643	+	3.51329i	0.373088	+	0.346175i	0.844325	−	0.535832i	$-0.180002\pi$
$103$	3.78643	+	3.51329i	0.373088	+	0.346175i	−0.471237	+	0.882007i	$0.656192\pi$
$104$	−11.2605	−	49.3355i	−1.10418	−	4.83774i
$105$		0			0
$106$	−6.72028	+	29.4435i	−0.652731	+	2.85980i
$107$	−3.17320	+	2.16345i	−0.306765	+	0.209149i	−0.706911	−	0.707303i	$-0.749912\pi$
$107$	−3.17320	+	2.16345i	−0.306765	+	0.209149i	0.400146	+	0.916451i	$0.368959\pi$
$108$		0			0
$109$	2.08946	+	1.42457i	0.200134	+	0.136449i	0.659240	−	0.751932i	$-0.270878\pi$
$109$	2.08946	+	1.42457i	0.200134	+	0.136449i	−0.459106	+	0.888381i	$0.651830\pi$
$110$	−0.643048	+	0.0969238i	−0.0613122	+	0.00924133i
$111$		0			0
$112$	−39.1180	+	21.1263i	−3.69630	+	1.99625i
$113$	−2.75985	−	1.32907i	−0.259625	−	0.125029i	0.299544	−	0.954082i	$-0.403165\pi$
$113$	−2.75985	−	1.32907i	−0.259625	−	0.125029i	−0.559169	+	0.829054i	$0.688880\pi$
$114$		0			0
$115$	0.191407	−	0.487696i	0.0178488	−	0.0454779i
$116$	10.6275	+	18.4074i	0.986739	+	1.70908i
$117$		0			0
$118$	22.2665	+	27.9213i	2.04979	+	2.57036i
$119$	0.775587	+	1.73496i	0.0710980	+	0.159044i
$120$		0			0
$121$	−3.22042	−	8.20548i	−0.292765	−	0.745953i
$122$	−0.745304	−	9.94539i	−0.0674767	−	0.900414i
$123$		0			0
$124$	−1.52838	−	3.89424i	−0.137252	−	0.349713i
$125$	0.987934	−	1.23883i	0.0883635	−	0.110804i
$126$		0			0
$127$	−5.24676	−	6.57923i	−0.465575	−	0.583813i	0.492506	−	0.870309i	$-0.336081\pi$
$127$	−5.24676	−	6.57923i	−0.465575	−	0.583813i	−0.958081	+	0.286496i	$0.907509\pi$
$128$	−27.7666	+	48.0932i	−2.45425	+	4.25088i
$129$		0			0
$130$	−0.800353	+	2.03927i	−0.0701956	+	0.178856i
$131$	3.77801	+	1.16536i	0.330086	+	0.101818i	0.455369	−	0.890303i	$-0.349507\pi$
$131$	3.77801	+	1.16536i	0.330086	+	0.101818i	−0.125282	+	0.992121i	$0.539984\pi$
$132$		0			0
$133$	−3.95276	−	14.2389i	−0.342748	−	1.23467i
$134$	15.6419	−	7.53275i	1.35126	−	0.650731i
$135$		0			0
$136$	6.03100	+	4.11187i	0.517154	+	0.352590i
$137$	−10.2139	+	9.47709i	−0.872630	+	0.809683i	−0.982885	−	0.184221i	$-0.941024\pi$
$137$	−10.2139	+	9.47709i	−0.872630	+	0.809683i	0.110255	+	0.993903i	$0.464833\pi$
$138$		0			0
$139$	−4.36479	+	19.1234i	−0.370217	+	1.62203i	0.355949	+	0.934505i	$0.384158\pi$
$139$	−4.36479	+	19.1234i	−0.370217	+	1.62203i	−0.726165	+	0.687520i	$0.758699\pi$
$140$	2.37010	+	0.245501i	0.200310	+	0.0207486i
$141$		0			0
$142$	1.54411	+	1.43272i	0.129578	+	0.120231i
$143$	7.27899	+	1.09713i	0.608700	+	0.0917468i
$144$		0			0
$145$	0.0445054	−	0.593883i	0.00369597	−	0.0493193i
$146$	1.65676			0.137114
$147$		0			0
$148$	19.7758			1.62556
$149$	0.213722	−	2.85193i	0.0175088	−	0.233639i	−0.981583	−	0.191035i	$-0.938816\pi$
$149$	0.213722	−	2.85193i	0.0175088	−	0.233639i	0.999092	−	0.0426039i	$-0.0135653\pi$
$150$		0			0
$151$	−5.21225	−	0.785621i	−0.424167	−	0.0639329i	−0.0665097	−	0.997786i	$-0.521186\pi$
$151$	−5.21225	−	0.785621i	−0.424167	−	0.0639329i	−0.357657	+	0.933853i	$0.616424\pi$
$152$	−41.6068	−	38.6054i	−3.37475	−	3.13131i
$153$		0			0
$154$	−1.30936	−	10.7517i	−0.105511	−	0.866398i
$155$	−0.0260830	+	0.114277i	−0.00209504	+	0.00917897i
$156$		0			0
$157$	11.5645	−	10.7303i	0.922951	−	0.856373i	−0.0670048	−	0.997753i	$-0.521344\pi$
$157$	11.5645	−	10.7303i	0.922951	−	0.856373i	0.989955	+	0.141380i	$0.0451538\pi$
$158$	−0.145639	−	0.0992950i	−0.0115864	−	0.00789949i
$159$		0			0
$160$	3.75143	−	1.80660i	0.296577	−	0.142824i
$161$	8.02889	+	3.41743i	0.632765	+	0.269331i
$162$		0			0
$163$	−14.9512	−	4.61184i	−1.17107	−	0.361227i	−0.352599	−	0.935775i	$-0.614702\pi$
$163$	−14.9512	−	4.61184i	−1.17107	−	0.361227i	−0.818471	+	0.574547i	$0.805178\pi$
$164$	8.19719	−	20.8861i	0.640093	−	1.63093i
$165$		0			0
$166$	11.7929	−	20.4258i	0.915303	−	1.58535i
$167$	6.32373	+	7.92971i	0.489345	+	0.613619i	0.963789	−	0.266667i	$-0.0859223\pi$
$167$	6.32373	+	7.92971i	0.489345	+	0.613619i	−0.474444	+	0.880286i	$0.657351\pi$
$168$		0			0
$169$	7.35574	−	9.22381i	0.565826	−	0.709524i
$170$	−0.115446	−	0.294152i	−0.00885430	−	0.0225604i
$171$		0			0
$172$	−2.78508	−	37.1643i	−0.212360	−	2.83375i
$173$	−8.99650	−	22.9227i	−0.683991	−	1.74278i	−0.669417	−	0.742887i	$-0.733456\pi$
$173$	−8.99650	−	22.9227i	−0.683991	−	1.74278i	−0.0145746	−	0.999894i	$-0.504639\pi$
$174$		0			0
$175$	10.0532	+	8.49542i	0.759947	+	0.642193i
$176$	−15.4873	−	19.4205i	−1.16740	−	1.46387i
$177$		0			0
$178$	1.17970	+	2.04331i	0.0884226	+	0.153152i
$179$	6.51764	−	16.6067i	0.487151	−	1.24124i	−0.450223	−	0.892916i	$-0.648655\pi$
$179$	6.51764	−	16.6067i	0.487151	−	1.24124i	0.937374	−	0.348325i	$-0.113249\pi$
$180$		0			0
$181$	0.380366	+	0.183174i	0.0282724	+	0.0136153i	0.447967	−	0.894050i	$-0.352148\pi$
$181$	0.380366	+	0.183174i	0.0282724	+	0.0136153i	−0.419694	+	0.907666i	$0.637863\pi$
$182$	−33.5722	−	14.2897i	−2.48854	−	1.05922i
$183$		0			0
$184$	33.1410	−	4.99521i	2.44319	−	0.368252i
$185$	−0.457822	−	0.312138i	−0.0336597	−	0.0229488i
$186$		0			0
$187$	−0.877308	+	0.598138i	−0.0641551	+	0.0437402i
$188$	−13.0322	+	57.0978i	−0.950472	+	4.16429i
$189$		0			0
$190$	0.546760	+	2.39551i	0.0396661	+	0.173789i
$191$	−7.21918	−	6.69842i	−0.522361	−	0.484681i	0.374355	−	0.927285i	$-0.377864\pi$
$191$	−7.21918	−	6.69842i	−0.522361	−	0.484681i	−0.896717	+	0.442605i	$0.854054\pi$
$192$		0			0
$193$	−6.56280	+	2.02436i	−0.472401	+	0.145716i	−0.521809	−	0.853062i	$-0.674743\pi$
$193$	−6.56280	+	2.02436i	−0.472401	+	0.145716i	0.0494082	+	0.998779i	$0.484266\pi$
$194$	−2.23794	+	29.8632i	−0.160675	+	2.14405i
$195$		0			0
$196$	−5.20876	+	39.3428i	−0.372054	+	2.81020i
$197$	13.9994			0.997417			0.498709	−	0.866770i	$-0.333808\pi$
$197$	13.9994			0.997417			0.498709	+	0.866770i	$0.333808\pi$
$198$		0			0
$199$	16.7080	−	5.15374i	1.18440	−	0.365339i	0.360872	−	0.932615i	$-0.382479\pi$
$199$	16.7080	−	5.15374i	1.18440	−	0.365339i	0.823528	+	0.567276i	$0.192003\pi$
$200$	49.9892	+	7.53465i	3.53477	+	0.532780i
$201$		0			0
$202$	−7.54188	−	33.0431i	−0.530645	−	2.32491i
$203$	9.86627	+	1.02197i	0.692476	+	0.0717284i
$204$		0			0
$205$	−0.519431	+	0.354142i	−0.0362787	+	0.0247344i
$206$	10.4860	−	9.72962i	0.730597	−	0.677895i
$207$		0			0
$208$	−82.7430	+	12.4715i	−5.73719	+	0.864743i
$209$	7.43877	−	3.58232i	0.514551	−	0.247795i
$210$		0			0
$211$	20.3687	+	9.80905i	1.40224	+	0.675283i	0.973614	−	0.228199i	$-0.0732838\pi$
$211$	20.3687	+	9.80905i	1.40224	+	0.675283i	0.428625	+	0.903482i	$0.358998\pi$
$212$	59.0797	+	18.2237i	4.05761	+	1.25161i
$213$		0			0
$214$	5.31795	+	9.21095i	0.363527	+	0.629648i
$215$	−0.522117	+	0.904332i	−0.0356081	+	0.0616750i
$216$		0			0
$217$	−1.89022	−	0.488321i	−0.128316	−	0.0331494i
$218$	4.36656	−	5.47550i	0.295741	−	0.370847i
$219$		0			0
$220$	0.0994890	+	1.32759i	0.00670754	+	0.0895060i
$221$	0.267303	+	3.56691i	0.0179808	+	0.239936i
$222$		0			0
$223$	−0.940902	+	1.17985i	−0.0630075	+	0.0790089i	−0.812337	−	0.583189i	$-0.801805\pi$
$223$	−0.940902	+	1.17985i	−0.0630075	+	0.0790089i	0.749329	+	0.662198i	$0.230376\pi$
$224$	28.3022	+	63.3110i	1.89102	+	4.23015i
$225$		0			0
$226$	−4.24157	+	7.34662i	−0.282145	+	0.488690i
$227$	0.927526	+	1.60652i	0.0615620	+	0.106629i	0.895164	−	0.445737i	$-0.147058\pi$
$227$	0.927526	+	1.60652i	0.0615620	+	0.106629i	−0.833602	+	0.552366i	$0.813725\pi$
$228$		0			0
$229$	14.3472	+	4.42553i	0.948091	+	0.292447i	0.729974	−	0.683475i	$-0.239532\pi$
$229$	14.3472	+	4.42553i	0.948091	+	0.292447i	0.218117	+	0.975923i	$0.430008\pi$
$230$	−1.30722	−	0.629526i	−0.0861958	−	0.0415097i
$231$		0			0
$232$	34.3251	−	16.5301i	2.25356	−	1.08525i
$233$	−14.6739	+	2.21173i	−0.961318	+	0.144895i	−0.610908	−	0.791701i	$-0.709196\pi$
$233$	−14.6739	+	2.21173i	−0.961318	+	0.144895i	−0.350409	+	0.936597i	$0.613958\pi$
$234$		0			0
$235$	1.20292	−	1.11615i	0.0784700	−	0.0728095i
$236$	60.4068	−	41.1847i	3.93215	−	2.68089i
$237$		0			0
$238$	4.95184	−	1.78283i	0.320980	−	0.115563i
$239$	1.62551	+	7.12184i	0.105146	+	0.460673i	0.999900	+	0.0141153i	$0.00449320\pi$
$239$	1.62551	+	7.12184i	0.105146	+	0.460673i	−0.894755	+	0.446558i	$0.852650\pi$
$240$		0			0
$241$	−5.69057	−	0.857715i	−0.366562	−	0.0552503i	−0.0368211	−	0.999322i	$-0.511723\pi$
$241$	−5.69057	−	0.857715i	−0.366562	−	0.0552503i	−0.329741	+	0.944072i	$0.606961\pi$
$242$	−23.3270	+	7.19543i	−1.49952	+	0.462540i
$243$		0			0
$244$	−20.4172			−1.30708
$245$	0.741563	−	0.828593i	0.0473767	−	0.0529368i
$246$		0			0
$247$	2.07850	−	27.7356i	0.132252	−	1.76477i
$248$	−7.16534	+	2.21021i	−0.454999	+	0.140349i
$249$		0			0
$250$	−3.21673	−	2.98469i	−0.203444	−	0.188768i
$251$	0.655661	+	2.87264i	0.0413849	+	0.181319i	0.991396	−	0.130897i	$-0.0417857\pi$
$251$	0.655661	+	2.87264i	0.0413849	+	0.181319i	−0.950011	+	0.312216i	$0.898929\pi$
$252$		0			0
$253$	−1.08487	+	4.75312i	−0.0682051	+	0.298826i
$254$	−19.2553	+	13.1280i	−1.20818	+	0.823725i
$255$		0			0
$256$	62.6521	+	42.7154i	3.91575	+	2.66972i
$257$	−8.90974	+	1.34293i	−0.555774	+	0.0837695i	−0.420923	−	0.907096i	$-0.638294\pi$
$257$	−8.90974	+	1.34293i	−0.555774	+	0.0837695i	−0.134851	+	0.990866i	$0.543056\pi$
$258$		0			0
$259$	5.41329	−	7.47440i	0.336366	−	0.464436i
$260$	4.04065	+	1.94587i	0.250590	+	0.120678i
$261$		0			0
$262$	4.00018	−	10.1923i	0.247132	−	0.629682i
$263$	−7.66738	−	13.2803i	−0.472791	−	0.818898i	0.526724	−	0.850036i	$-0.323420\pi$
$263$	−7.66738	−	13.2803i	−0.472791	−	0.818898i	−0.999515	+	0.0311383i	$0.990087\pi$
$264$		0			0
$265$	−1.08009	−	1.35439i	−0.0663494	−	0.0831995i
$266$	−40.1406	+	7.96925i	−2.46118	+	0.488626i
$267$		0			0
$268$	−12.9848	−	33.0849i	−0.793176	−	2.02098i
$269$	−0.714185	−	9.53014i	−0.0435447	−	0.581063i	−0.975715	−	0.219043i	$-0.929706\pi$
$269$	−0.714185	−	9.53014i	−0.0435447	−	0.581063i	0.932170	−	0.362020i	$-0.117913\pi$
$270$		0			0
$271$	−5.98378	−	15.2464i	−0.363489	−	0.926154i	−0.989263	−	0.146149i	$-0.953312\pi$
$271$	−5.98378	−	15.2464i	−0.363489	−	0.926154i	0.625774	−	0.780004i	$-0.284783\pi$
$272$	7.52550	−	9.43668i	0.456301	−	0.572183i
$273$		0			0
$274$	24.0584	+	30.1683i	1.45342	+	1.82253i
$275$	−3.67694	+	6.36864i	−0.221728	+	0.384044i
$276$		0			0
$277$	−7.23614	+	18.4374i	−0.434778	+	1.10780i	0.530758	+	0.847524i	$0.321907\pi$
$277$	−7.23614	+	18.4374i	−0.434778	+	1.10780i	−0.965535	+	0.260272i	$0.916188\pi$
$278$	51.9085	+	16.0116i	3.11326	+	0.960314i
$279$		0			0
$280$	0.756283	−	4.20347i	0.0451966	−	0.251206i
$281$	−1.83386	+	0.883140i	−0.109399	+	0.0526837i	−0.487783	−	0.872965i	$-0.662194\pi$
$281$	−1.83386	+	0.883140i	−0.109399	+	0.0526837i	0.378384	+	0.925649i	$0.376480\pi$
$282$		0			0
$283$	19.8825	+	13.5557i	1.18189	+	0.805802i	0.984648	−	0.174552i	$-0.0558476\pi$
$283$	19.8825	+	13.5557i	1.18189	+	0.805802i	0.197247	+	0.980354i	$0.436800\pi$
$284$	3.16108	−	2.93305i	0.187575	−	0.174045i
$285$		0			0
$286$	4.53630	−	19.8748i	0.268237	−	1.17522i
$287$	−5.65018	−	8.81538i	−0.333520	−	0.520356i
$288$		0			0
$289$	12.0837	+	11.2120i	0.710804	+	0.659530i
$290$	−1.63088	−	0.245815i	−0.0957683	−	0.0144347i
$291$		0			0
$292$	0.253462	−	3.38222i	0.0148327	−	0.197929i
$293$	−26.0006			−1.51897			−0.759487	−	0.650523i	$-0.774550\pi$
$293$	−26.0006			−1.51897			−0.759487	+	0.650523i	$0.774550\pi$
$294$		0			0
$295$	−2.04850			−0.119268
$296$	2.64894	−	35.3476i	0.153966	−	2.05454i
$297$		0			0
$298$	−7.83173	−	1.18044i	−0.453680	−	0.0683813i
$299$	12.0394	+	11.1709i	0.696254	+	0.646029i
$300$		0			0
$301$	−14.8088	−	9.12043i	−0.853566	−	0.525693i
$302$	−3.24830	+	14.2317i	−0.186919	+	0.818944i
$303$		0			0
$304$	−68.7996	+	63.8367i	−3.94593	+	3.66129i
$305$	0.472670	+	0.322261i	0.0270650	+	0.0184526i
$306$		0			0
$307$	−5.79149	+	2.78904i	−0.330538	+	0.159179i	−0.591791	−	0.806092i	$-0.701579\pi$
$307$	−5.79149	+	2.78904i	−0.330538	+	0.159179i	0.261253	+	0.965270i	$0.415864\pi$
$308$	−22.1496	+	1.02815i	−1.26209	+	0.0585843i
$309$		0			0
$310$	0.310194	+	0.0956821i	0.0176178	+	0.00543438i
$311$	−11.4931	+	29.2840i	−0.651715	+	1.66054i	0.0950645	+	0.995471i	$0.469694\pi$
$311$	−11.4931	+	29.2840i	−0.651715	+	1.66054i	−0.746779	+	0.665072i	$0.768401\pi$
$312$		0			0
$313$	9.77989	−	16.9393i	0.552792	−	0.957464i	−0.445280	−	0.895392i	$-0.646896\pi$
$313$	9.77989	−	16.9393i	0.552792	−	0.957464i	0.998072	−	0.0620724i	$-0.0197710\pi$
$314$	−27.2399	−	34.1577i	−1.53723	−	1.92763i
$315$		0			0
$316$	−0.224988	+	0.282126i	−0.0126566	+	0.0158708i
$317$	−9.40932	−	23.9746i	−0.528480	−	1.34655i	−0.907070	−	0.420981i	$-0.861686\pi$
$317$	−9.40932	−	23.9746i	−0.528480	−	1.34655i	0.378589	−	0.925565i	$-0.376409\pi$
$318$		0			0
$319$	0.414153	+	5.52648i	0.0231881	+	0.309424i
$320$	−2.26235	−	5.76438i	−0.126469	−	0.322239i
$321$		0			0
$322$	11.0993	−	21.4656i	0.618540	−	1.19623i
$323$	2.50138	+	3.13664i	0.139181	+	0.174527i
$324$		0			0
$325$	12.3865	+	21.4540i	0.687079	+	1.19006i
$326$	−15.8304	+	40.3353i	−0.876767	+	2.23397i
$327$		0			0
$328$	−36.2341	−	17.4494i	−2.00069	−	0.963484i
$329$	18.0131	+	20.5551i	0.993095	+	1.13324i
$330$		0			0
$331$	−13.0158	+	1.96182i	−0.715415	+	0.107831i	−0.496656	−	0.867948i	$-0.665439\pi$
$331$	−13.0158	+	1.96182i	−0.715415	+	0.107831i	−0.218759	+	0.975779i	$0.570201\pi$
$332$	−39.8945	−	27.1996i	−2.18949	−	1.49277i
$333$		0			0
$334$	23.2077	−	15.8227i	1.26987	−	0.865780i
$335$	−0.221598	+	0.970883i	−0.0121072	+	0.0530450i
$336$		0			0
$337$	−3.06582	−	13.4322i	−0.167006	−	0.731700i	−0.987183	−	0.159591i	$-0.948982\pi$
$337$	−3.06582	−	13.4322i	−0.167006	−	0.731700i	0.820177	−	0.572109i	$-0.193875\pi$
$338$	−23.9504	−	22.2228i	−1.30273	−	1.20876i
$339$		0			0
$340$	−0.618162	+	0.190678i	−0.0335245	+	0.0103410i
$341$	0.0815137	−	1.08773i	0.00441422	−	0.0589036i
$342$		0			0
$343$	13.4440	+	12.7381i	0.725908	+	0.687791i
$344$	−66.8010			−3.60167
$345$		0			0
$346$	−65.1659	+	20.1010i	−3.50334	+	1.08064i
$347$	14.4821	+	2.18282i	0.777439	+	0.117180i	0.525763	−	0.850631i	$-0.323780\pi$
$347$	14.4821	+	2.18282i	0.777439	+	0.117180i	0.251677	+	0.967811i	$0.419018\pi$
$348$		0			0
$349$	4.39555	+	19.2582i	0.235289	+	1.03087i	0.945179	+	0.326554i	$0.105887\pi$
$349$	4.39555	+	19.2582i	0.235289	+	1.03087i	−0.709890	+	0.704313i	$0.751255\pi$
$350$	25.5418	−	26.0049i	1.36526	−	1.39002i
$351$		0			0
$352$	−32.0141	+	21.8268i	−1.70636	+	1.16337i
$353$	−7.02774	+	6.52079i	−0.374049	+	0.347067i	−0.844688	−	0.535259i	$-0.820214\pi$
$353$	−7.02774	+	6.52079i	−0.374049	+	0.347067i	0.470639	+	0.882326i	$0.344023\pi$
$354$		0			0
$355$	−0.119475	+	0.0180080i	−0.00634109	+	0.000955766i
$356$	4.35182	−	2.09573i	0.230646	−	0.111073i
$357$		0			0
$358$	−44.5126	−	21.4362i	−2.35257	−	1.13294i
$359$	15.4279	+	4.75887i	0.814252	+	0.251164i	0.673790	−	0.738922i	$-0.264665\pi$
$359$	15.4279	+	4.75887i	0.814252	+	0.251164i	0.140462	+	0.990086i	$0.455141\pi$
$360$		0			0
$361$	−6.09789	−	10.5619i	−0.320942	−	0.555888i
$362$	0.584579	−	1.01252i	0.0307248	−	0.0532169i
$363$		0			0
$364$	−34.3081	+	66.3504i	−1.79823	+	3.47771i
$365$	−0.0592519	+	0.0742996i	−0.00310139	+	0.00388902i
$366$		0			0
$367$	1.44595	+	19.2948i	0.0754777	+	1.00718i	0.898443	+	0.439089i	$0.144699\pi$
$367$	1.44595	+	19.2948i	0.0754777	+	1.00718i	−0.822966	+	0.568091i	$0.807682\pi$
$368$	−4.14154	−	55.2650i	−0.215893	−	2.88089i
$369$		0			0
$370$	−0.956758	+	1.19974i	−0.0497395	+	0.0623713i
$371$	23.0598	−	17.3411i	1.19720	−	0.900305i
$372$		0			0
$373$	−4.78444	+	8.28690i	−0.247729	+	0.429079i	−0.962895	−	0.269875i	$-0.913018\pi$
$373$	−4.78444	+	8.28690i	−0.247729	+	0.429079i	0.715166	+	0.698954i	$0.246351\pi$
$374$	1.47027	+	2.54659i	0.0760260	+	0.131681i
$375$		0			0
$376$	100.312	+	30.9421i	5.17319	+	1.59572i
$377$	16.8204	+	8.10028i	0.866295	+	0.417186i
$378$		0			0
$379$	−19.8820	+	9.57467i	−1.02127	+	0.491818i	−0.868104	−	0.496383i	$-0.834661\pi$
$379$	−19.8820	+	9.57467i	−1.02127	+	0.491818i	−0.153166	+	0.988200i	$0.548947\pi$
$380$	4.97400	−	0.749710i	0.255161	−	0.0384593i
$381$		0			0
$382$	−19.9926	+	18.5504i	−1.02291	+	0.949123i
$383$	−2.22696	+	1.51832i	−0.113792	+	0.0775824i	−0.618879	−	0.785486i	$-0.712413\pi$
$383$	−2.22696	+	1.51832i	−0.113792	+	0.0775824i	0.505087	+	0.863069i	$0.331461\pi$
$384$		0			0
$385$	0.529003	+	0.325802i	0.0269605	+	0.0166044i
$386$	4.23232	+	18.5430i	0.215419	+	0.943814i
$387$		0			0
$388$	60.6223	+	9.13734i	3.07763	+	0.463878i
$389$	24.0751	−	7.42619i	1.22066	−	0.376523i	0.383529	−	0.923529i	$-0.374709\pi$
$389$	24.0751	−	7.42619i	1.22066	−	0.376523i	0.837129	+	0.547006i	$0.184232\pi$
$390$		0			0
$391$	−2.36900			−0.119806
$392$	69.6241	+	14.5801i	3.51655	+	0.736406i
$393$		0			0
$394$	2.89726	−	38.6612i	0.145962	−	1.94772i
$395$	0.00966162	−	0.00298022i	0.000486129	−	0.000149951i
$396$		0			0
$397$	−6.55527	−	6.08240i	−0.329000	−	0.305267i	0.498326	−	0.866990i	$-0.333948\pi$
$397$	−6.55527	−	6.08240i	−0.329000	−	0.305267i	−0.827326	+	0.561723i	$0.810139\pi$
$398$	−10.7749	−	47.2080i	−0.540098	−	2.36632i
$399$		0			0
$400$	18.6015	−	81.4983i	0.930073	−	4.07492i
$401$	−31.2139	+	21.2813i	−1.55875	+	1.06274i	−0.592349	+	0.805681i	$0.701800\pi$
$401$	−31.2139	+	21.2813i	−1.55875	+	1.06274i	−0.966397	+	0.257054i	$0.917248\pi$
$402$		0			0
$403$	−3.03601	−	2.06991i	−0.151234	−	0.103110i
$404$	−68.6102	+	10.3413i	−3.41349	+	0.514500i
$405$		0			0
$406$	4.86419	−	27.0355i	0.241406	−	1.34175i
$407$	4.64567	+	2.23724i	0.230277	+	0.110896i
$408$		0			0
$409$	−2.52891	+	6.44357i	−0.125047	+	0.318614i	−0.979664	−	0.200644i	$-0.935696\pi$
$409$	−2.52891	+	6.44357i	−0.125047	+	0.318614i	0.854617	+	0.519258i	$0.173792\pi$
$410$	0.870511	+	1.50777i	0.0429915	+	0.0744634i
$411$		0			0
$412$	−18.2585	−	22.8954i	−0.899530	−	1.12797i
$413$	0.969330	−	34.1047i	0.0476976	−	1.67818i
$414$		0			0
$415$	0.494267	+	1.25937i	0.0242626	+	0.0618201i
$416$	9.75423	+	130.161i	0.478240	+	6.38167i
$417$		0			0
$418$	−8.35356	−	21.2845i	−0.408586	−	1.04106i
$419$	−21.7028	+	27.2144i	−1.06025	+	1.32951i	−0.118592	+	0.992943i	$0.537838\pi$
$419$	−21.7028	+	27.2144i	−1.06025	+	1.32951i	−0.941659	+	0.336569i	$0.890733\pi$
$420$		0			0
$421$	5.44856	+	6.83228i	0.265547	+	0.332985i	0.896672	−	0.442696i	$-0.145978\pi$
$421$	5.44856	+	6.83228i	0.265547	+	0.332985i	−0.631125	+	0.775681i	$0.717406\pi$
$422$	31.3044	−	54.2208i	1.52387	−	2.63943i
$423$		0			0
$424$	40.4869	−	103.159i	1.96622	−	5.00984i
$425$	−3.41460	−	1.05326i	−0.165632	−	0.0510908i
$426$		0			0
$427$	−5.58885	+	7.71680i	−0.270464	+	0.373442i
$428$	19.6174	−	9.44725i	0.948244	−	0.456650i
$429$		0			0
$430$	2.38938	+	1.62905i	0.115226	+	0.0785598i
$431$	−1.36907	+	1.27031i	−0.0659456	+	0.0611886i	−0.712457	−	0.701716i	$-0.752418\pi$
$431$	−1.36907	+	1.27031i	−0.0659456	+	0.0611886i	0.646512	+	0.762904i	$0.276227\pi$
$432$		0			0
$433$	−7.94869	+	34.8255i	−0.381990	+	1.67361i	0.309250	+	0.950981i	$0.399922\pi$
$433$	−7.94869	+	34.8255i	−0.381990	+	1.67361i	−0.691240	+	0.722625i	$0.742935\pi$
$434$	−1.73975	+	5.11902i	−0.0835109	+	0.245721i
$435$		0			0
$436$	−10.5100	−	9.75187i	−0.503338	−	0.467030i
$437$	18.2152	+	2.74549i	0.871349	+	0.131335i
$438$		0			0
$439$	−0.406215	+	5.42056i	−0.0193876	+	0.258709i	0.979085	+	0.203453i	$0.0652165\pi$
$439$	−0.406215	+	5.42056i	−0.0193876	+	0.258709i	−0.998472	+	0.0552558i	$0.982403\pi$
$440$	2.38628			0.113761
$441$		0			0
$442$	9.90582			0.471172
$443$	−2.30793	+	30.7971i	−0.109653	+	1.46322i	0.622791	+	0.782388i	$0.285999\pi$
$443$	−2.30793	+	30.7971i	−0.109653	+	1.46322i	−0.732444	+	0.680828i	$0.761620\pi$
$444$		0			0
$445$	−0.133826	−	0.0201710i	−0.00634394	−	0.000956196i
$446$	3.06360	+	2.84260i	0.145065	+	0.134601i
$447$		0			0
$448$	97.0394	−	34.9374i	4.58468	−	1.65064i
$449$	−1.41120	+	6.18287i	−0.0665986	+	0.291788i	−0.997249	−	0.0741215i	$-0.976385\pi$
$449$	−1.41120	+	6.18287i	−0.0665986	+	0.291788i	0.930651	+	0.365909i	$0.119242\pi$
$450$		0			0
$451$	4.28850	−	3.97914i	0.201937	−	0.187371i
$452$	14.3490	+	9.78296i	0.674919	+	0.460152i
$453$		0			0
$454$	4.62858	−	2.22901i	0.217230	−	0.104612i
$455$	1.84151	−	0.994538i	0.0863314	−	0.0466246i
$456$		0			0
$457$	−25.9268	−	7.99736i	−1.21281	−	0.374101i	−0.378603	−	0.925559i	$-0.623595\pi$
$457$	−25.9268	−	7.99736i	−1.21281	−	0.374101i	−0.834202	+	0.551458i	$0.814072\pi$
$458$	15.1909	−	38.7058i	0.709825	−	1.80861i
$459$		0			0
$460$	−1.48514	+	2.57235i	−0.0692452	+	0.119936i
$461$	−2.03252	−	2.54870i	−0.0946641	−	0.118705i	0.732243	−	0.681043i	$-0.238473\pi$
$461$	−2.03252	−	2.54870i	−0.0946641	−	0.118705i	−0.826907	+	0.562338i	$0.809902\pi$
$462$		0			0
$463$	−18.4772	+	23.1697i	−0.858709	+	1.07679i	0.137561	+	0.990493i	$0.456074\pi$
$463$	−18.4772	+	23.1697i	−0.858709	+	1.07679i	−0.996270	+	0.0862933i	$0.972498\pi$
$464$	−23.0156	−	58.6429i	−1.06847	−	2.72243i
$465$		0			0
$466$	3.07114	+	40.9816i	0.142268	+	1.89843i
$467$	12.6796	+	32.3070i	0.586740	+	1.49499i	0.848147	+	0.529760i	$0.177718\pi$
$467$	12.6796	+	32.3070i	0.586740	+	1.49499i	−0.261408	+	0.965228i	$0.584187\pi$
$468$		0			0
$469$	−16.0590	−	4.14870i	−0.741535	−	0.191569i
$470$	−2.83344	−	3.55302i	−0.130697	−	0.163889i
$471$		0			0
$472$	−65.5227	−	113.489i	−3.01592	−	5.22373i
$473$	3.55013	−	9.04557i	0.163235	−	0.415916i
$474$		0			0
$475$	25.0340	+	12.0557i	1.14864	+	0.553155i
$476$	−2.88201	−	10.3818i	−0.132097	−	0.475847i
$477$		0			0
$478$	20.0043	−	3.01516i	0.914975	−	0.137910i
$479$	18.7408	+	12.7773i	0.856289	+	0.583808i	0.909934	−	0.414752i	$-0.136132\pi$
$479$	18.7408	+	12.7773i	0.856289	+	0.583808i	−0.0536456	+	0.998560i	$0.517084\pi$
$480$		0			0
$481$	14.3518	−	9.78489i	0.654386	−	0.446153i
$482$	−3.54639	+	15.5377i	−0.161534	+	0.707725i
$483$		0			0
$484$	11.1205	+	48.7221i	0.505477	+	2.21464i
$485$	−1.25922	−	1.16838i	−0.0571782	−	0.0530536i
$486$		0			0
$487$	−29.2489	+	9.02210i	−1.32540	+	0.408830i	−0.875054	−	0.484026i	$-0.839174\pi$
$487$	−29.2489	+	9.02210i	−1.32540	+	0.408830i	−0.450342	+	0.892856i	$0.648698\pi$
$488$	−2.73485	+	36.4940i	−0.123801	+	1.65201i
$489$		0			0
$490$	−2.13480	−	2.21941i	−0.0964403	−	0.100263i
$491$	7.93412			0.358062			0.179031	−	0.983843i	$-0.442704\pi$
$491$	7.93412			0.358062			0.179031	+	0.983843i	$0.442704\pi$
$492$		0			0
$493$	−2.57328	+	0.793753i	−0.115895	+	0.0357488i
$494$	−76.1653	−	11.4801i	−3.42684	−	0.516513i
$495$		0			0
$496$	2.75909	+	12.0884i	0.123887	+	0.542784i
$497$	−0.243274	−	1.99762i	−0.0109123	−	0.0896055i
$498$		0			0
$499$	27.8754	−	19.0052i	1.24788	−	0.850788i	0.254656	−	0.967032i	$-0.418038\pi$
$499$	27.8754	−	19.0052i	1.24788	−	0.850788i	0.993221	+	0.116244i	$0.0370855\pi$
$500$	−6.58526	+	6.11023i	−0.294502	+	0.273258i
$501$		0			0
$502$	8.06886	−	1.21618i	0.360131	−	0.0542810i
$503$	−18.3233	+	8.82406i	−0.816997	+	0.393445i	−0.795223	−	0.606318i	$-0.792646\pi$
$503$	−18.3233	+	8.82406i	−0.816997	+	0.393445i	−0.0217749	+	0.999763i	$0.506932\pi$
$504$		0			0
$505$	1.75159	+	0.843521i	0.0779447	+	0.0375362i
$506$	12.9019	+	3.97969i	0.573557	+	0.176919i
$507$		0			0
$508$	23.8546	+	41.3174i	1.05838	+	1.83316i
$509$	10.0193	−	17.3539i	0.444097	−	0.769199i	−0.553892	−	0.832589i	$-0.686858\pi$
$509$	10.0193	−	17.3539i	0.444097	−	0.769199i	0.997989	+	0.0633901i	$0.0201912\pi$
$510$		0			0
$511$	−1.20895	−	1.02162i	−0.0534807	−	0.0451938i
$512$	61.6817	−	77.3464i	2.72597	−	3.41826i
$513$		0			0
$514$	1.86475	+	24.8833i	0.0822505	+	1.09756i
$515$	0.0613177	+	0.818228i	0.00270198	+	0.0360555i
$516$		0			0
$517$	−9.52095	+	11.9389i	−0.418731	+	0.525072i
$518$	−19.5212	−	16.4964i	−0.857713	−	0.724810i
$519$		0			0
$520$	4.01932	−	6.96167i	0.176259	−	0.305289i
$521$	−18.7782	−	32.5248i	−0.822687	−	1.42494i	−0.903674	−	0.428221i	$-0.859141\pi$
$521$	−18.7782	−	32.5248i	−0.822687	−	1.42494i	0.0809869	−	0.996715i	$-0.474193\pi$
$522$		0			0
$523$	−30.8956	−	9.53003i	−1.35097	−	0.416719i	−0.466998	−	0.884258i	$-0.654665\pi$
$523$	−30.8956	−	9.53003i	−1.35097	−	0.416719i	−0.883972	+	0.467539i	$0.845141\pi$
$524$	−20.1952	−	9.72552i	−0.882233	−	0.424861i
$525$		0			0
$526$	−38.2621	+	18.4260i	−1.66831	+	0.803414i
$527$	0.524103	−	0.0789958i	0.0228303	−	0.00344111i
$528$		0			0
$529$	8.88648	−	8.24545i	0.386369	−	0.358498i
$530$	−3.96386	+	2.70251i	−0.172179	+	0.117390i
$531$		0			0
$532$	10.1280	+	83.1649i	0.439103	+	3.60566i
$533$	−4.38534	−	19.2134i	−0.189950	−	0.832226i
$534$		0			0
$535$	−0.603268	−	0.0909280i	−0.0260815	−	0.00393116i
$536$	−60.8756	+	18.7776i	−2.62943	+	0.811071i
$537$		0			0
$538$	−26.4665			−1.14105
$539$	−5.67446	+	8.65299i	−0.244416	+	0.372711i
$540$		0			0
$541$	1.49211	−	19.9108i	0.0641506	−	0.856030i	−0.868601	−	0.495512i	$-0.834981\pi$
$541$	1.49211	−	19.9108i	0.0641506	−	0.856030i	0.932752	−	0.360519i	$-0.117400\pi$
$542$	−43.3433	+	13.3697i	−1.86176	+	0.574276i
$543$		0			0
$544$	−13.8016	−	12.8060i	−0.591739	−	0.549053i
$545$	0.0893913	+	0.391649i	0.00382910	+	0.0167764i
$546$		0			0
$547$	3.83205	−	16.7893i	0.163846	−	0.717858i	−0.824528	−	0.565821i	$-0.808559\pi$
$547$	3.83205	−	16.7893i	0.163846	−	0.717858i	0.988375	−	0.152037i	$-0.0485834\pi$
$548$	65.2682	−	44.4991i	2.78812	−	1.90091i
$549$		0			0
$550$	16.8269	+	11.4724i	0.717501	+	0.489184i
$551$	20.7058	−	3.12089i	0.882095	−	0.132954i
$552$		0			0
$553$	0.0450447	+	0.162263i	0.00191549	+	0.00690012i
$554$	49.4197	+	23.7993i	2.09964	+	1.01113i
$555$		0			0
$556$	40.6285	−	103.520i	1.72303	−	4.39022i
$557$	3.01437	+	5.22104i	0.127723	+	0.221222i	0.922794	−	0.385294i	$-0.125900\pi$
$557$	3.01437	+	5.22104i	0.127723	+	0.221222i	−0.795071	+	0.606516i	$0.792567\pi$
$558$		0			0
$559$	−20.4097	−	25.5930i	−0.863238	−	1.08247i
$560$	−6.83784	−	1.76650i	−0.288951	−	0.0746482i
$561$		0			0
$562$	2.05938	+	5.24721i	0.0868697	+	0.221340i
$563$	0.713440	+	9.52019i	0.0300679	+	0.401228i	0.991850	+	0.127412i	$0.0406670\pi$
$563$	0.713440	+	9.52019i	0.0300679	+	0.401228i	−0.961782	+	0.273816i	$0.911714\pi$
$564$		0			0
$565$	−0.177775	−	0.452962i	−0.00747903	−	0.0190563i
$566$	41.5506	−	52.1028i	1.74650	−	2.19005i
$567$		0			0
$568$	−4.81916	−	6.04303i	−0.202207	−	0.253560i
$569$	9.26009	−	16.0389i	0.388203	−	0.672387i	−0.604005	−	0.796981i	$-0.706429\pi$
$569$	9.26009	−	16.0389i	0.388203	−	0.672387i	0.992208	+	0.124593i	$0.0397626\pi$
$570$		0			0
$571$	−0.0465428	+	0.118589i	−0.00194776	+	0.00496280i	−0.931844	−	0.362858i	$-0.881801\pi$
$571$	−0.0465428	+	0.118589i	−0.00194776	+	0.00496280i	0.929897	+	0.367821i	$0.119896\pi$
$572$	−39.8798	−	12.3013i	−1.66746	−	0.514343i
$573$		0			0
$574$	−25.5142	+	13.7793i	−1.06494	+	0.575138i
$575$	−14.7824	+	7.11883i	−0.616469	+	0.296876i
$576$		0			0
$577$	−7.07883	−	4.82626i	−0.294695	−	0.200920i	0.406942	−	0.913454i	$-0.366595\pi$
$577$	−7.07883	−	4.82626i	−0.294695	−	0.200920i	−0.701638	+	0.712534i	$0.747547\pi$
$578$	33.4642	−	31.0502i	1.39193	−	1.29152i
$579$		0			0
$580$	−0.751325	+	3.29177i	−0.0311971	+	0.136683i
$581$	−21.2007	+	7.63293i	−0.879552	+	0.316667i
$582$		0			0
$583$	11.8172	+	10.9647i	0.489417	+	0.454112i
$584$	−6.01147	−	0.906083i	−0.248756	−	0.0374940i
$585$		0			0
$586$	−5.38098	+	71.8042i	−0.222286	+	2.96620i
$587$	−37.2781			−1.53863			−0.769317	−	0.638868i	$-0.779403\pi$
$587$	−37.2781			−1.53863			−0.769317	+	0.638868i	$0.779403\pi$
$588$		0			0
$589$	−4.12135			−0.169817
$590$	−0.423949	+	5.65720i	−0.0174537	+	0.232903i
$591$		0			0
$592$	−57.9590	−	8.73591i	−2.38210	−	0.359044i
$593$	−15.2016	−	14.1050i	−0.624255	−	0.579224i	0.303307	−	0.952893i	$-0.401909\pi$
$593$	−15.2016	−	14.1050i	−0.624255	−	0.579224i	−0.927562	+	0.373669i	$0.878100\pi$
$594$		0			0
$595$	−0.0971434	+	0.285833i	−0.00398249	+	0.0117180i
$596$	−3.60799	+	15.8076i	−0.147789	+	0.647506i
$597$		0			0
$598$	33.3415	−	30.9364i	1.36343	−	1.26508i
$599$	9.05227	+	6.17173i	0.369866	+	0.252170i	0.733961	−	0.679191i	$-0.237669\pi$
$599$	9.05227	+	6.17173i	0.369866	+	0.252170i	−0.364095	+	0.931362i	$0.618622\pi$
$600$		0			0
$601$	34.4798	−	16.6046i	1.40646	−	0.677315i	0.431999	−	0.901874i	$-0.357809\pi$
$601$	34.4798	−	16.6046i	1.40646	−	0.677315i	0.974460	+	0.224559i	$0.0720942\pi$
$602$	−28.2520	+	39.0090i	−1.15147	+	1.58989i
$603$		0			0
$604$	28.5566	+	8.80856i	1.16195	+	0.358415i
$605$	0.511573	−	1.30347i	0.0207984	−	0.0529935i
$606$		0			0
$607$	3.50859	−	6.07705i	0.142409	−	0.246660i	−0.785994	−	0.618234i	$-0.787848\pi$
$607$	3.50859	−	6.07705i	0.142409	−	0.246660i	0.928403	+	0.371574i	$0.121182\pi$
$608$	91.2786	+	114.460i	3.70184	+	4.64196i
$609$		0			0
$610$	0.987787	−	1.23865i	0.0399943	−	0.0501513i
$611$	18.7937	+	47.8855i	0.760310	+	1.93724i
$612$		0			0
$613$	−2.56850	−	34.2742i	−0.103741	−	1.38432i	−0.769734	−	0.638365i	$-0.779611\pi$
$613$	−2.56850	−	34.2742i	−0.103741	−	1.38432i	0.665993	−	0.745958i	$-0.268008\pi$
$614$	6.50371	+	16.5712i	0.262468	+	0.668758i
$615$		0			0
$616$	−1.12916	+	39.7282i	−0.0454952	+	1.60069i
$617$	21.5991	+	27.0844i	0.869548	+	1.09038i	0.995157	+	0.0982984i	$0.0313400\pi$
$617$	21.5991	+	27.0844i	0.869548	+	1.09038i	−0.125609	+	0.992080i	$0.540089\pi$
$618$		0			0
$619$	7.97891	+	13.8199i	0.320699	+	0.555468i	0.980633	−	0.195857i	$-0.0627487\pi$
$619$	7.97891	+	13.8199i	0.320699	+	0.555468i	−0.659933	+	0.751324i	$0.729415\pi$
$620$	0.242787	−	0.618612i	0.00975057	−	0.0248440i
$621$		0			0
$622$	78.4930	+	37.8002i	3.14728	+	1.51565i
$623$	0.399144	−	2.21847i	0.0159913	−	0.0888810i
$624$		0			0
$625$	−24.3471	+	3.66974i	−0.973885	+	0.146789i
$626$	−44.7560	−	30.5141i	−1.78881	−	1.21959i
$627$		0			0
$628$	−73.8991	+	50.3836i	−2.94890	+	2.01052i
$629$	−0.557531	+	2.44270i	−0.0222302	+	0.0973969i
$630$		0			0
$631$	−1.01937	−	4.46616i	−0.0405805	−	0.177795i	0.950576	−	0.310491i	$-0.100494\pi$
$631$	−1.01937	−	4.46616i	−0.0405805	−	0.177795i	−0.991157	+	0.132696i	$0.957636\pi$
$632$	0.474140	+	0.439937i	0.0188603	+	0.0174998i
$633$		0			0
$634$	−68.1562	+	21.0234i	−2.70683	+	0.834946i
$635$	0.0998972	−	1.33304i	0.00396430	−	0.0528999i
$636$		0			0
$637$	15.6863	+	31.1292i	0.621513	+	1.23338i
$638$	15.3478			0.607626
$639$		0			0
$640$	−8.42971	+	2.60022i	−0.333213	+	0.102783i
$641$	−0.955720	−	0.144052i	−0.0377487	−	0.00568970i	0.130141	−	0.991496i	$-0.458457\pi$
$641$	−0.955720	−	0.144052i	−0.0377487	−	0.00568970i	−0.167889	+	0.985806i	$0.553695\pi$
$642$		0			0
$643$	−7.16570	−	31.3950i	−0.282588	−	1.23810i	−0.894463	−	0.447143i	$-0.852442\pi$
$643$	−7.16570	−	31.3950i	−0.282588	−	1.23810i	0.611875	−	0.790954i	$-0.290416\pi$
$644$	−42.1232	−	25.9428i	−1.65989	−	1.02229i
$645$		0			0
$646$	9.17990	−	6.25875i	0.361179	−	0.246247i
$647$	−4.50360	+	4.17873i	−0.177055	+	0.164283i	−0.763722	−	0.645545i	$-0.776630\pi$
$647$	−4.50360	+	4.17873i	−0.177055	+	0.164283i	0.586667	+	0.809828i	$0.300440\pi$
$648$		0			0
$649$	18.8498	−	2.84114i	0.739918	−	0.111525i
$650$	61.8116	−	29.7669i	2.42445	−	1.16755i
$651$		0			0
$652$	79.9213	+	38.4881i	3.12996	+	1.50731i
$653$	−21.1621	−	6.52765i	−0.828137	−	0.255447i	−0.148423	−	0.988924i	$-0.547420\pi$
$653$	−21.1621	−	6.52765i	−0.828137	−	0.255447i	−0.679714	+	0.733477i	$0.737896\pi$
$654$		0			0
$655$	0.314026	+	0.543908i	0.0122700	+	0.0212523i
$656$	−33.2506	+	57.5918i	−1.29822	+	2.24858i
$657$		0			0
$658$	60.4936	−	45.4916i	2.35829	−	1.77345i
$659$	12.7464	−	15.9834i	0.496528	−	0.622627i	−0.468914	−	0.883244i	$-0.655355\pi$
$659$	12.7464	−	15.9834i	0.496528	−	0.622627i	0.965442	+	0.260617i	$0.0839260\pi$
$660$		0			0
$661$	2.01235	+	26.8529i	0.0782712	+	1.04446i	0.888661	+	0.458565i	$0.151636\pi$
$661$	2.01235	+	26.8529i	0.0782712	+	1.04446i	−0.810390	+	0.585891i	$0.800745\pi$
$662$	2.72413	+	36.3509i	0.105876	+	1.41282i
$663$		0			0
$664$	−53.9607	+	67.6646i	−2.09408	+	2.62590i
$665$	1.07819	−	2.08517i	0.0418104	−	0.0808595i
$666$		0			0
$667$	−6.18236	+	10.7082i	−0.239382	+	0.414621i
$668$	−28.7511	−	49.7983i	−1.11241	−	1.92675i
$669$		0			0
$670$	2.63536	+	0.812901i	0.101813	+	0.0314051i
$671$	−4.79634	−	2.30979i	−0.185161	−	0.0891686i
$672$		0			0
$673$	25.2078	−	12.1395i	0.971691	−	0.467942i	0.120451	−	0.992719i	$-0.461566\pi$
$673$	25.2078	−	12.1395i	0.971691	−	0.467942i	0.851239	+	0.524778i	$0.175852\pi$
$674$	−37.7294	+	5.68679i	−1.45328	+	0.219047i
$675$		0			0
$676$	−49.0311	+	45.4942i	−1.88581	+	1.74978i
$677$	−26.7394	+	18.2306i	−1.02768	+	0.700660i	−0.954973	−	0.296694i	$-0.904116\pi$
$677$	−26.7394	+	18.2306i	−1.02768	+	0.700660i	−0.0727063	+	0.997353i	$0.523164\pi$
$678$		0			0
$679$	20.0478	−	20.4114i	0.769365	−	0.783316i
$680$	0.258018	+	1.13045i	0.00989455	+	0.0433509i
$681$		0			0
$682$	−2.98703	−	0.450222i	−0.114379	−	0.0172399i
$683$	−2.58965	+	0.798802i	−0.0990903	+	0.0305653i	−0.343904	−	0.939005i	$-0.611749\pi$
$683$	−2.58965	+	0.798802i	−0.0990903	+	0.0305653i	0.244814	+	0.969570i	$0.421273\pi$
$684$		0			0
$685$	−2.21336			−0.0845681
$686$	37.9602	−	34.4912i	1.44933	−	1.31688i
$687$		0			0
$688$	−8.25469	+	110.151i	−0.314707	+	4.19947i
$689$	51.8924	−	16.0067i	1.97694	−	0.609807i
$690$		0			0
$691$	−2.29213	−	2.12679i	−0.0871968	−	0.0809068i	0.635370	−	0.772208i	$-0.280847\pi$
$691$	−2.29213	−	2.12679i	−0.0871968	−	0.0809068i	−0.722567	+	0.691301i	$0.757038\pi$
$692$	31.0660	+	136.109i	1.18095	+	5.17410i
$693$		0			0
$694$	9.02531	−	39.5424i	0.342596	−	1.50101i
$695$	−2.57451	+	1.75527i	−0.0976566	+	0.0665811i
$696$		0			0
$697$	2.34874	+	1.60134i	0.0889649	+	0.0606552i
$698$	54.0937	−	8.15331i	2.04748	−	0.308607i
$699$		0			0
$700$	−49.1806	−	56.1210i	−1.85885	−	2.12118i
$701$	−25.1584	−	12.1157i	−0.950220	−	0.457602i	−0.106457	−	0.994317i	$-0.533951\pi$
$701$	−25.1584	−	12.1157i	−0.950220	−	0.457602i	−0.843763	+	0.536715i	$0.819665\pi$
$702$		0			0
$703$	7.11773	−	18.1357i	0.268450	−	0.684000i
$704$	28.8124	+	49.9046i	1.08591	+	1.88085i
$705$		0			0
$706$	16.5536	+	20.7575i	0.623002	+	0.781220i
$707$	−14.8723	+	28.7624i	−0.559330	+	1.08172i
$708$		0			0
$709$	14.5618	+	37.1029i	0.546880	+	1.39343i	0.890786	+	0.454423i	$0.150155\pi$
$709$	14.5618	+	37.1029i	0.546880	+	1.39343i	−0.343906	+	0.939004i	$0.611750\pi$
$710$	0.0250054	+	0.333674i	0.000938436	+	0.0125226i
$711$		0			0
$712$	−3.16302	−	8.05923i	−0.118539	−	0.302032i
$713$	1.51734	−	1.90269i	0.0568250	−	0.0712562i
$714$		0			0
$715$	0.729079	+	0.914236i	0.0272660	+	0.0341905i
$716$	−50.5710	+	87.5916i	−1.88993	+	3.27345i
$717$		0			0
$718$	16.3351	−	41.6212i	0.609622	−	1.55329i
$719$	−41.0406	−	12.6593i	−1.53056	−	0.472114i	−0.588762	−	0.808306i	$-0.700385\pi$
$719$	−41.0406	−	12.6593i	−1.53056	−	0.472114i	−0.941793	+	0.336193i	$0.890861\pi$
$720$		0			0
$721$	−13.6514	+	0.633677i	−0.508404	+	0.0235994i
$722$	−30.4300	+	14.6543i	−1.13249	+	0.545376i
$723$		0			0
$724$	−1.97759	−	1.34830i	−0.0734967	−	0.0501092i
$725$	−13.6719	+	12.6857i	−0.507761	+	0.471134i
$726$		0			0
$727$	0.0236792	−	0.103745i	0.000878213	−	0.00384770i	−0.974487	−	0.224444i	$-0.927943\pi$
$727$	0.0236792	−	0.103745i	0.000878213	−	0.00384770i	0.975365	+	0.220597i	$0.0708004\pi$
$728$	114.000	+	70.2103i	4.22513	+	2.60217i
$729$		0			0
$730$	0.192926	+	0.179009i	0.00714049	+	0.00662541i
$731$	4.66903	+	0.703743i	0.172690	+	0.0260289i
$732$		0			0
$733$	−0.0587855	+	0.784438i	−0.00217129	+	0.0289739i	−0.998184	−	0.0602353i	$-0.980815\pi$
$733$	−0.0587855	+	0.784438i	−0.00217129	+	0.0289739i	0.996013	+	0.0892092i	$0.0284340\pi$
$734$	53.5844			1.97783
$735$		0			0
$736$	−86.4479			−3.18651
$737$	0.692528	−	9.24115i	0.0255096	−	0.340402i
$738$		0			0
$739$	12.5382	+	1.88984i	0.461227	+	0.0695187i	0.375546	−	0.926804i	$-0.377455\pi$
$739$	12.5382	+	1.88984i	0.461227	+	0.0695187i	0.0856810	+	0.996323i	$0.472693\pi$
$740$	2.30285	+	2.13673i	0.0846544	+	0.0785478i
$741$		0			0
$742$	−43.1174	−	67.2715i	−1.58289	−	2.46961i
$743$	8.81831	−	38.6356i	0.323513	−	1.41740i	−0.507742	−	0.861509i	$-0.669520\pi$
$743$	8.81831	−	38.6356i	0.323513	−	1.41740i	0.831255	−	0.555892i	$-0.187623\pi$
$744$		0			0
$745$	0.333031	−	0.309008i	0.0122013	−	0.0113212i
$746$	21.8952	+	14.9279i	0.801640	+	0.546549i
$747$		0			0
$748$	5.42371	−	2.61192i	0.198310	−	0.0955012i
$749$	1.79928	−	10.0005i	0.0657444	−	0.365412i
$750$		0			0
$751$	−15.5823	−	4.80651i	−0.568607	−	0.175392i	−0.00289640	−	0.999996i	$-0.500922\pi$
$751$	−15.5823	−	4.80651i	−0.568607	−	0.175392i	−0.565711	+	0.824604i	$0.691398\pi$
$752$	63.4175	−	161.585i	2.31260	−	5.89240i
$753$		0			0
$754$	25.8511	−	44.7754i	0.941441	−	1.63062i
$755$	−0.522070	−	0.654655i	−0.0190001	−	0.0238253i
$756$		0			0
$757$	2.42579	−	3.04185i	0.0881669	−	0.110558i	−0.735791	−	0.677208i	$-0.763190\pi$
$757$	2.42579	−	3.04185i	0.0881669	−	0.110558i	0.823958	+	0.566651i	$0.191761\pi$
$758$	22.3270	+	56.8883i	0.810954	+	2.06628i
$759$		0			0
$760$	−0.673784	−	8.99102i	−0.0244407	−	0.326139i
$761$	−12.2832	−	31.2970i	−0.445264	−	1.13451i	−0.960701	−	0.277586i	$-0.910466\pi$
$761$	−12.2832	−	31.2970i	−0.445264	−	1.13451i	0.515437	−	0.856928i	$-0.327630\pi$
$762$		0			0
$763$	−6.56271	+	1.30292i	−0.237586	+	0.0471687i
$764$	34.8115	+	43.6522i	1.25943	+	1.57928i
$765$		0			0
$766$	3.73215	+	6.46427i	0.134848	+	0.233564i
$767$	23.4609	−	59.7774i	0.847123	−	2.15844i
$768$		0			0
$769$	16.1710	+	7.78754i	0.583141	+	0.280826i	0.702106	−	0.712072i	$-0.252243\pi$
$769$	16.1710	+	7.78754i	0.583141	+	0.280826i	−0.118965	+	0.992898i	$0.537958\pi$
$770$	1.00922	−	1.39348i	0.0363699	−	0.0502177i
$771$		0			0
$772$	38.5024	−	5.80330i	1.38573	−	0.208865i
$773$	39.1048	+	26.6612i	1.40650	+	0.958936i	0.998953	+	0.0457515i	$0.0145682\pi$
$773$	39.1048	+	26.6612i	1.40650	+	0.958936i	0.407547	+	0.913184i	$0.366384\pi$
$774$		0			0
$775$	3.03298	−	2.06785i	0.108948	−	0.0742794i
$776$	24.4525	−	107.133i	0.877792	−	3.84586i
$777$		0			0
$778$	−15.5259	−	68.0235i	−0.556631	−	2.43876i
$779$	−16.2035	−	15.0347i	−0.580551	−	0.538673i
$780$		0			0
$781$	1.07440	−	0.331410i	0.0384452	−	0.0118588i
$782$	−0.490279	+	6.54231i	−0.0175323	+	0.233953i
$783$		0			0
$784$	32.6453	−	113.005i	1.16590	−	4.03588i
$785$	2.50605			0.0894447
$786$		0			0
$787$	8.74001	−	2.69594i	0.311548	−	0.0960997i	−0.135038	−	0.990840i	$-0.543116\pi$
$787$	8.74001	−	2.69594i	0.311548	−	0.0960997i	0.446586	+	0.894741i	$0.352640\pi$
$788$	−78.4823	−	11.8293i	−2.79582	−	0.421402i
$789$		0			0
$790$	−0.00623073	−	0.0272986i	−0.000221679	−	0.000971241i
$791$	7.62531	−	2.74536i	0.271125	−	0.0976138i
$792$		0			0
$793$	−14.8172	+	10.1022i	−0.526176	+	0.358741i
$794$	−18.1540	+	16.8444i	−0.644261	+	0.597787i
$795$		0			0
$796$	−98.0219	+	14.7744i	−3.47429	+	0.523666i
$797$	7.37350	−	3.55089i	0.261183	−	0.125779i	−0.298710	−	0.954344i	$-0.596556\pi$
$797$	7.37350	−	3.55089i	0.261183	−	0.125779i	0.559893	+	0.828565i	$0.310842\pi$
$798$		0			0
$799$	−6.68528	−	3.21946i	−0.236508	−	0.113896i
$800$	−124.603	−	38.4349i	−4.40538	−	1.35888i
$801$		0			0
$802$	52.3111	+	90.6055i	1.84717	+	3.19939i
$803$	0.442172	−	0.765864i	0.0156039	−	0.0270268i
$804$		0			0
$805$	0.565700	+	1.26545i	0.0199383	+	0.0446014i
$806$	−6.34466	+	7.95595i	−0.223481	+	0.280236i
$807$		0			0
$808$	9.29402	+	124.020i	0.326963	+	4.36301i
$809$	0.0625196	+	0.834265i	0.00219807	+	0.0293312i	0.998195	−	0.0600564i	$-0.0191281\pi$
$809$	0.0625196	+	0.834265i	0.00219807	+	0.0293312i	−0.995997	+	0.0893876i	$0.971509\pi$
$810$		0			0
$811$	18.1407	−	22.7477i	0.637005	−	0.798779i	−0.353620	−	0.935389i	$-0.615049\pi$
$811$	18.1407	−	22.7477i	0.637005	−	0.798779i	0.990625	+	0.136610i	$0.0436207\pi$
$812$	−54.4479	−	14.0661i	−1.91075	−	0.493625i
$813$		0			0
$814$	7.13987	−	12.3666i	0.250252	−	0.433450i
$815$	−1.24274	−	2.15248i	−0.0435311	−	0.0753981i
$816$		0			0
$817$	−35.0844	−	10.8221i	−1.22745	−	0.378617i
$818$	17.2714	+	8.31746i	0.603880	+	0.290813i
$819$		0			0
$820$	3.21124	−	1.54645i	0.112141	−	0.0540044i
$821$	−31.4921	+	4.74666i	−1.09908	+	0.165660i	−0.673447	−	0.739236i	$-0.735187\pi$
$821$	−31.4921	+	4.74666i	−1.09908	+	0.165660i	−0.425634	+	0.904896i	$0.639949\pi$
$822$		0			0
$823$	24.3761	−	22.6178i	0.849699	−	0.788405i	−0.129442	−	0.991587i	$-0.541319\pi$
$823$	24.3761	−	22.6178i	0.849699	−	0.788405i	0.979141	+	0.203182i	$0.0651282\pi$
$824$	−43.3692	+	29.5686i	−1.51084	+	1.03007i
$825$		0			0
$826$	−93.9839	−	9.73509i	−3.27012	−	0.338727i
$827$	−7.79416	−	34.1485i	−0.271030	−	1.18746i	−0.908800	−	0.417232i	$-0.863000\pi$
$827$	−7.79416	−	34.1485i	−0.271030	−	1.18746i	0.637770	−	0.770227i	$-0.279857\pi$
$828$		0			0
$829$	−41.6779	−	6.28194i	−1.44753	−	0.218181i	−0.622215	−	0.782847i	$-0.713767\pi$
$829$	−41.6779	−	6.28194i	−1.44753	−	0.218181i	−0.825319	+	0.564666i	$0.809005\pi$
$830$	3.58021	−	1.10435i	0.124271	−	0.0383325i
$831$		0			0
$832$	194.121			6.72992
$833$	−4.71275	−	1.75255i	−0.163287	−	0.0607224i
$834$		0			0
$835$	−0.120402	+	1.60666i	−0.00416670	+	0.0556007i
$836$	−44.7296	+	13.7973i	−1.54701	+	0.477188i
$837$		0			0
$838$	70.6647	+	65.5673i	2.44107	+	2.26498i
$839$	−0.399501	−	1.75033i	−0.0137923	−	0.0604281i	0.967563	−	0.252628i	$-0.0812949\pi$
$839$	−0.399501	−	1.75033i	−0.0137923	−	0.0604281i	−0.981356	+	0.192200i	$0.938438\pi$
$840$		0			0
$841$	3.32549	−	14.5699i	0.114672	−	0.502411i
$842$	19.9959	−	13.6329i	0.689103	−	0.469822i
$843$		0			0
$844$	−105.901	−	72.2019i	−3.64526	−	2.48529i
$845$	1.85317	−	0.279320i	0.0637509	−	0.00960891i
$846$		0			0
$847$	21.4588	+	9.13377i	0.737334	+	0.313840i
$848$	−165.100	−	79.5081i	−5.66957	−	2.73032i
$849$		0			0
$850$	−3.61539	+	9.21187i	−0.124007	+	0.315965i
$851$	5.75212	+	9.96297i	0.197180	+	0.341526i
$852$		0			0
$853$	−14.1630	−	17.7599i	−0.484933	−	0.608086i	0.477824	−	0.878456i	$-0.341426\pi$
$853$	−14.1630	−	17.7599i	−0.484933	−	0.608086i	−0.962757	+	0.270369i	$0.912854\pi$
$854$	20.1543	+	17.0314i	0.689666	+	0.582802i
$855$		0			0
$856$	−14.2584	−	36.3299i	−0.487343	−	1.24173i
$857$	−1.60926	−	21.4740i	−0.0549711	−	0.733538i	−0.954791	−	0.297277i	$-0.903921\pi$
$857$	−1.60926	−	21.4740i	−0.0549711	−	0.733538i	0.899820	−	0.436261i	$-0.143698\pi$
$858$		0			0
$859$	8.12797	+	20.7097i	0.277323	+	0.706607i	0.999883	+	0.0152989i	$0.00486999\pi$
$859$	8.12797	+	20.7097i	0.277323	+	0.706607i	−0.722560	+	0.691308i	$0.757035\pi$
$860$	3.69119	−	4.62861i	0.125869	−	0.157834i
$861$		0			0
$862$	3.22479	+	4.04375i	0.109837	+	0.137731i
$863$	27.4119	−	47.4788i	0.933113	−	1.61620i	0.155148	−	0.987891i	$-0.450415\pi$
$863$	27.4119	−	47.4788i	0.933113	−	1.61620i	0.777965	−	0.628307i	$-0.216252\pi$
$864$		0			0
$865$	1.42912	−	3.64134i	0.0485916	−	0.123809i
$866$	94.5301	+	29.1587i	3.21226	+	0.990852i
$867$		0			0
$868$	10.1841	+	4.33479i	0.345672	+	0.147132i
$869$	−0.0847703	+	0.0408232i	−0.00287564	+	0.00138483i
$870$		0			0
$871$	−25.7935	−	17.5857i	−0.873978	−	0.595868i
$872$	−18.8384	+	17.4795i	−0.637950	+	0.591931i
$873$		0			0
$874$	11.3518	−	49.7353i	0.383979	−	1.68232i
$875$	0.506796	+	4.16151i	0.0171328	+	0.140685i
$876$		0			0
$877$	40.3652	+	37.4535i	1.36304	+	1.26471i	0.932037	+	0.362362i	$0.118030\pi$
$877$	40.3652	+	37.4535i	1.36304	+	1.26471i	0.431000	+	0.902352i	$0.358161\pi$
$878$	14.8855	+	2.24363i	0.502362	+	0.0757188i
$879$		0			0
$880$	0.294875	−	3.93484i	0.00994024	−	0.132643i
$881$	37.6398			1.26812			0.634058	−	0.773286i	$-0.281388\pi$
$881$	37.6398			1.26812			0.634058	+	0.773286i	$0.281388\pi$
$882$		0			0
$883$	−22.5780			−0.759809			−0.379905	−	0.925026i	$-0.624043\pi$
$883$	−22.5780			−0.759809			−0.379905	+	0.925026i	$0.624043\pi$
$884$	1.51546	−	20.2224i	0.0509704	−	0.680152i
$885$		0			0
$886$	84.5727	+	12.7473i	2.84127	+	0.428253i
$887$	9.19397	+	8.53076i	0.308703	+	0.286435i	0.819276	−	0.573400i	$-0.194376\pi$
$887$	9.19397	+	8.53076i	0.308703	+	0.286435i	−0.510572	+	0.859835i	$0.670566\pi$
$888$		0			0
$889$	22.1459	+	2.29393i	0.742750	+	0.0769359i
$890$	−0.0834008	+	0.365403i	−0.00279560	+	0.0122483i
$891$		0			0
$892$	6.27176	−	5.81935i	0.209994	−	0.194846i
$893$	47.6717	+	32.5020i	1.59527	+	1.08764i
$894$		0			0
$895$	2.55327	−	1.22959i	0.0853465	−	0.0411007i
$896$	−39.3012	−	141.573i	−1.31296	−	4.72963i
$897$		0			0
$898$	16.7827	+	5.17679i	0.560047	+	0.172752i
$899$	1.01067	−	2.57516i	0.0337079	−	0.0858863i
$900$		0			0
$901$	−3.91658	+	6.78372i	−0.130480	+	0.225999i
$902$	−10.1014	−	12.6668i	−0.336340	−	0.421757i
$903$		0			0
$904$	19.4082	−	24.3371i	0.645508	−	0.809441i
$905$	0.0245011	+	0.0624278i	0.000814445	+	0.00207517i
$906$		0			0
$907$	−0.269698	−	3.59887i	−0.00895518	−	0.119499i	0.990935	−	0.134345i	$-0.0428931\pi$
$907$	−0.269698	−	3.59887i	−0.00895518	−	0.119499i	−0.999890	+	0.0148465i	$0.995274\pi$
$908$	−3.84233	−	9.79009i	−0.127512	−	0.324896i
$909$		0			0
$910$	−2.36543	−	5.29140i	−0.0784134	−	0.175408i
$911$	−17.7004	−	22.1956i	−0.586440	−	0.735373i	0.396756	−	0.917924i	$-0.370136\pi$
$911$	−17.7004	−	22.1956i	−0.586440	−	0.735373i	−0.983196	+	0.182551i	$0.941564\pi$
$912$		0			0
$913$	−6.29478	−	10.9029i	−0.208327	−	0.360833i
$914$	−27.4515	+	69.9452i	−0.908014	+	2.31358i
$915$		0			0
$916$	−76.6927	−	36.9332i	−2.53400	−	1.22031i
$917$	−9.20391	+	4.97072i	−0.303940	+	0.164148i
$918$		0			0
$919$	−38.5354	+	5.80828i	−1.27117	+	0.191597i	−0.749759	−	0.661711i	$-0.769831\pi$
$919$	−38.5354	+	5.80828i	−1.27117	+	0.191597i	−0.521407	+	0.853308i	$0.674593\pi$
$920$	4.39891	+	2.99913i	0.145028	+	0.0988783i
$921$		0			0
$922$	−7.45922	+	5.08561i	−0.245656	+	0.167486i
$923$	0.842824	−	3.69265i	0.0277419	−	0.121545i
$924$		0			0
$925$	3.86135	+	16.9177i	0.126960	+	0.556249i
$926$	60.1622	+	55.8223i	1.97705	+	1.83444i
$927$		0			0
$928$	−93.9024	+	28.9651i	−3.08250	+	0.950825i
$929$	0.357723	−	4.77348i	0.0117365	−	0.156613i	−0.988256	−	0.152806i	$-0.951169\pi$
$929$	0.357723	−	4.77348i	0.0117365	−	0.156613i	0.999993	−	0.00380713i	$-0.00121185\pi$
$930$		0			0
$931$	34.2050	+	18.9370i	1.12102	+	0.620636i
$932$	84.1323			2.75585
$933$		0			0
$934$	91.8441	−	28.3301i	3.00523	−	0.926991i
$935$	−0.166788	−	0.0251392i	−0.00545454	−	0.000822140i
$936$		0			0
$937$	2.04967	+	8.98021i	0.0669599	+	0.293371i	0.997310	−	0.0733026i	$-0.0233539\pi$
$937$	2.04967	+	8.98021i	0.0669599	+	0.293371i	−0.930350	+	0.366673i	$0.880497\pi$
$938$	−14.7807	+	43.4904i	−0.482607	+	1.42001i
$939$		0			0
$940$	−7.68685	+	5.24081i	−0.250717	+	0.170936i
$941$	−18.6257	+	17.2821i	−0.607180	+	0.563381i	−0.922691	−	0.385541i	$-0.874015\pi$
$941$	−18.6257	+	17.2821i	−0.607180	+	0.563381i	0.315511	+	0.948922i	$0.397824\pi$
$942$		0			0
$943$	12.9066	−	1.94536i	0.420296	−	0.0633495i
$944$	−195.233	+	94.0193i	−6.35430	+	3.06007i
$945$		0			0
$946$	−24.2458	−	11.6762i	−0.788300	−	0.379625i
$947$	29.2549	+	9.02394i	0.950656	+	0.293239i	0.731030	−	0.682345i	$-0.239040\pi$
$947$	29.2549	+	9.02394i	0.950656	+	0.293239i	0.219626	+	0.975584i	$0.429516\pi$
$948$		0			0
$949$	−1.48954	−	2.57996i	−0.0483526	−	0.0837492i
$950$	38.4744	−	66.6397i	1.24828	−	2.16208i
$951$		0			0
$952$	−18.9426	+	3.76073i	−0.613932	+	0.121886i
$953$	−24.2399	+	30.3958i	−0.785207	+	0.984618i	0.214762	+	0.976666i	$0.431102\pi$
$953$	−24.2399	+	30.3958i	−0.785207	+	0.984618i	−0.999968	+	0.00795142i	$0.997469\pi$
$954$		0			0
$955$	−0.116908	−	1.56003i	−0.00378306	−	0.0504814i
$956$	−3.09496	−	41.2994i	−0.100098	−	1.33572i
$957$		0			0
$958$	39.1646	−	49.1108i	1.26535	−	1.58670i
$959$	1.04734	−	36.8493i	0.0338203	−	1.18993i
$960$		0			0
$961$	15.2278	−	26.3753i	0.491218	−	0.850815i
$962$	−24.0521	−	41.6594i	−0.775470	−	1.34315i
$963$		0			0
$964$	31.1772	+	9.61690i	1.00415	+	0.309739i
$965$	−0.982950	−	0.473364i	−0.0316423	−	0.0152381i
$966$		0			0
$967$	2.40379	−	1.15760i	0.0773005	−	0.0372260i	−0.394834	−	0.918752i	$-0.629198\pi$
$967$	2.40379	−	1.15760i	0.0773005	−	0.0372260i	0.472135	+	0.881526i	$0.343484\pi$
$968$	88.5761	−	13.3507i	2.84694	−	0.429108i
$969$		0			0
$970$	−3.48725	+	3.23569i	−0.111969	+	0.103892i
$971$	34.8274	−	23.7449i	1.11766	−	0.762010i	0.143904	−	0.989592i	$-0.454034\pi$
$971$	34.8274	−	23.7449i	1.11766	−	0.762010i	0.973759	+	0.227582i	$0.0730819\pi$
$972$		0			0
$973$	−28.0045	−	43.6925i	−0.897784	−	1.40072i
$974$	18.8625	+	82.6419i	0.604393	+	2.64802i
$975$		0			0
$976$	59.8387	+	9.01923i	1.91539	+	0.288698i
$977$	3.60479	−	1.11193i	0.115327	−	0.0355738i	−0.236554	−	0.971618i	$-0.576018\pi$
$977$	3.60479	−	1.11193i	0.115327	−	0.0355738i	0.351882	+	0.936044i	$0.385542\pi$
$978$		0			0
$979$	1.25940			0.0402507
$980$	−4.85744	+	4.01857i	−0.155165	+	0.128369i
$981$		0			0
$982$	1.64201	−	21.9111i	0.0523987	−	0.699212i
$983$	−57.6292	+	17.7763i	−1.83809	+	0.566975i	−0.838324	+	0.545172i	$0.816464\pi$
$983$	−57.6292	+	17.7763i	−1.83809	+	0.566975i	−0.999762	+	0.0218029i	$0.993059\pi$
$984$		0			0
$985$	1.63020	+	1.51260i	0.0519424	+	0.0481955i
$986$	1.65950	+	7.27073i	0.0528492	+	0.231547i
$987$		0			0
$988$	−35.0885	+	153.733i	−1.11631	+	4.89089i
$989$	17.9131	−	12.2129i	0.569603	−	0.388348i
$990$		0			0
$991$	22.3240	+	15.2202i	0.709145	+	0.483487i	0.863384	−	0.504547i	$-0.168340\pi$
$991$	22.3240	+	15.2202i	0.709145	+	0.483487i	−0.154239	+	0.988034i	$0.549293\pi$
$992$	19.1252	−	2.88266i	0.607225	−	0.0915244i
$993$		0			0
$994$	−5.56703	+	0.258414i	−0.176576	+	0.00819639i
$995$	2.50246	+	1.20512i	0.0793332	+	0.0382049i
$996$		0			0
$997$	16.1618	−	41.1795i	0.511848	−	1.30417i	−0.408389	−	0.912808i	$-0.633909\pi$
$997$	16.1618	−	41.1795i	0.511848	−	1.30417i	0.920238	−	0.391360i	$-0.127995\pi$
$998$	−46.7163	−	80.9149i	−1.47878	−	2.56132i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.c.415.4		48
3.2	odd	2		147.2.m.a.121.1	✓	48
49.32	even	21	inner	441.2.bb.c.424.4		48
147.32	odd	42		147.2.m.a.130.1	yes	48
147.89	even	42		7203.2.a.k.1.1		24
147.107	odd	42		7203.2.a.i.1.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.a.121.1	✓	48	3.2	odd	2
147.2.m.a.130.1	yes	48	147.32	odd	42
441.2.bb.c.415.4		48	1.1	even	1	trivial
441.2.bb.c.424.4		48	49.32	even	21	inner
7203.2.a.i.1.1		24	147.107	odd	42
7203.2.a.k.1.1		24	147.89	even	42

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.206956 - 2.76163i) q^{2} +(-5.60611 - 0.844986i) q^{4} +(0.116448 + 0.108048i) q^{5} +(-1.85394 + 1.88756i) q^{7} +(-2.26127 + 9.90726i) q^{8} +(0.322487 - 0.299224i) q^{10} +(-1.22138 - 0.832720i) q^{11} +(-4.48658 + 2.16062i) q^{13} +(4.82907 + 5.51055i) q^{14} +(16.0571 + 4.95296i) q^{16} +(0.262423 - 0.668642i) q^{17} +(-2.79266 + 4.83703i) q^{19} +(-0.561520 - 0.704124i) q^{20} +(-2.55244 + 3.20065i) q^{22} +(-1.20493 - 3.07011i) q^{23} +(-0.371765 - 4.96086i) q^{25} +(5.03832 + 12.8374i) q^{26} +(11.9884 - 9.01534i) q^{28} +(-2.33749 - 2.93113i) q^{29} +(0.368945 + 0.639031i) q^{31} +(9.57613 - 24.3996i) q^{32} +(-1.79223 - 0.863094i) q^{34} +(-0.419834 + 0.0194881i) q^{35} +(-3.44919 + 0.519882i) q^{37} +(12.7801 + 8.71335i) q^{38} +(-1.33377 + 0.909352i) q^{40} +(-0.880638 + 3.85833i) q^{41} +(1.46276 + 6.40876i) q^{43} +(6.14353 + 5.70037i) q^{44} +(-8.72787 + 2.69219i) q^{46} +(0.771974 - 10.3013i) q^{47} +(-0.125788 - 6.99887i) q^{49} -13.7770 q^{50} +(26.9780 - 8.32160i) q^{52} +(-10.7834 - 1.62534i) q^{53} +(-0.0522529 - 0.228935i) q^{55} +(-14.5083 - 22.6358i) q^{56} +(-8.57844 + 5.84868i) q^{58} +(-9.45312 + 8.77121i) q^{59} +(3.56105 - 0.536742i) q^{61} +(1.84112 - 0.886639i) q^{62} +(-35.1217 - 16.9137i) q^{64} +(-0.755902 - 0.233165i) q^{65} +(3.13450 + 5.42912i) q^{67} +(-2.03616 + 3.52674i) q^{68} +(-0.0330681 + 1.16346i) q^{70} +(-0.474231 + 0.594667i) q^{71} +(0.0447067 + 0.596570i) q^{73} +(0.721892 + 9.63298i) q^{74} +(19.7432 - 24.7572i) q^{76} +(3.83617 - 0.761608i) q^{77} +(0.0318244 - 0.0551215i) q^{79} +(1.33466 + 2.31169i) q^{80} +(10.4730 + 3.23050i) q^{82} +(7.67321 + 3.69522i) q^{83} +(0.102804 - 0.0495076i) q^{85} +(18.0014 - 2.71327i) q^{86} +(11.0118 - 10.2175i) q^{88} +(-0.703926 + 0.479929i) q^{89} +(4.23955 - 12.4744i) q^{91} +(4.16077 + 18.2295i) q^{92} +(-28.2886 - 4.26382i) q^{94} +(-0.847828 + 0.261520i) q^{95} -10.8136 q^{97} +(-19.3543 - 1.10108i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32}+ \cdots - 119 q^{98}+O(q^{100}) \) 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Introduction

L-functions

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