LMFDB - Embedded newform 864.2.w.a.107.7

Newspace parameters

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.w (of order $8$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			107.7
Character	$\chi$	$=$	864.107
Dual form			864.2.w.a.323.7

$q$-expansion

$f(q)$	$=$	$q+(-1.07850 - 0.914792i) q^{2} +(0.326309 + 1.97320i) q^{4} +(1.10881 + 0.459283i) q^{5} +(2.29035 - 2.29035i) q^{7} +(1.45315 - 2.42660i) q^{8} +O(q^{10})$	\(q+(-1.07850 - 0.914792i) q^{2} +(0.326309 + 1.97320i) q^{4} +(1.10881 + 0.459283i) q^{5} +(2.29035 - 2.29035i) q^{7} +(1.45315 - 2.42660i) q^{8} +(-0.775695 - 1.50966i) q^{10} +(-4.23612 - 1.75466i) q^{11} +(-0.644097 - 1.55499i) q^{13} +(-4.56533 + 0.374940i) q^{14} +(-3.78704 + 1.28775i) q^{16} -5.75819 q^{17} +(4.00625 - 1.65944i) q^{19} +(-0.544443 + 2.33777i) q^{20} +(2.96349 + 5.76757i) q^{22} +(4.82067 - 4.82067i) q^{23} +(-2.51702 - 2.51702i) q^{25} +(-0.727835 + 2.26626i) q^{26} +(5.26669 + 3.77196i) q^{28} +(-1.52718 - 3.68694i) q^{29} +10.9561i q^{31} +(5.26234 + 2.07553i) q^{32} +(6.21019 + 5.26755i) q^{34} +(3.59147 - 1.48764i) q^{35} +(1.67353 - 4.04025i) q^{37} +(-5.83877 - 1.87518i) q^{38} +(2.72575 - 2.02322i) q^{40} +(-2.75672 - 2.75672i) q^{41} +(3.26736 - 7.88810i) q^{43} +(2.08001 - 8.93129i) q^{44} +(-9.60899 + 0.789163i) q^{46} +3.05588i q^{47} -3.49141i q^{49} +(0.412047 + 5.01715i) q^{50} +(2.85813 - 1.77834i) q^{52} +(3.81361 - 9.20688i) q^{53} +(-3.89116 - 3.89116i) q^{55} +(-2.22954 - 8.88597i) q^{56} +(-1.72573 + 5.37340i) q^{58} +(-2.49029 + 6.01210i) q^{59} +(4.36611 - 1.80850i) q^{61} +(10.0225 - 11.8161i) q^{62} +(-3.77673 - 7.05240i) q^{64} -2.02000i q^{65} +(-4.89651 - 11.8212i) q^{67} +(-1.87895 - 11.3621i) q^{68} +(-5.23427 - 1.68104i) q^{70} +(0.814206 + 0.814206i) q^{71} +(-6.13068 + 6.13068i) q^{73} +(-5.50089 + 2.82647i) q^{74} +(4.58169 + 7.36364i) q^{76} +(-13.7210 + 5.68342i) q^{77} -7.99746 q^{79} +(-4.79054 - 0.311461i) q^{80} +(0.451287 + 5.49495i) q^{82} +(4.51997 + 10.9122i) q^{83} +(-6.38472 - 2.64464i) q^{85} +(-10.7398 + 5.51834i) q^{86} +(-10.4136 + 7.72958i) q^{88} +(6.05533 - 6.05533i) q^{89} +(-5.03667 - 2.08626i) q^{91} +(11.0852 + 7.93912i) q^{92} +(2.79550 - 3.29576i) q^{94} +5.20430 q^{95} +11.5086 q^{97} +(-3.19392 + 3.76548i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) $ 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$-1$

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 $

$2$	−1.07850	−	0.914792i	−0.762612	−	0.646856i
$2$	−1.07850	−	0.914792i	−0.762612	−	0.646856i
$3$		0			0
$3$		0			0
$4$	0.326309	+	1.97320i	0.163155	+	0.986601i
$5$	1.10881	+	0.459283i	0.495873	+	0.205397i	0.616582	−	0.787291i	$-0.288517\pi$
$5$	1.10881	+	0.459283i	0.495873	+	0.205397i	−0.120709	+	0.992688i	$0.538517\pi$
$6$		0			0
$7$	2.29035	−	2.29035i	0.865671	−	0.865671i	−0.126319	−	0.991990i	$-0.540316\pi$
$7$	2.29035	−	2.29035i	0.865671	−	0.865671i	0.991990	+	0.126319i	$0.0403161\pi$
$8$	1.45315	−	2.42660i	0.513765	−	0.857931i
$9$		0			0
$10$	−0.775695	−	1.50966i	−0.245296	−	0.477397i
$11$	−4.23612	−	1.75466i	−1.27724	−	0.529050i	−0.362082	−	0.932146i	$-0.617934\pi$
$11$	−4.23612	−	1.75466i	−1.27724	−	0.529050i	−0.915158	+	0.403096i	$0.867934\pi$
$12$		0			0
$13$	−0.644097	−	1.55499i	−0.178640	−	0.431276i	0.809041	−	0.587752i	$-0.199987\pi$
$13$	−0.644097	−	1.55499i	−0.178640	−	0.431276i	−0.987682	+	0.156476i	$0.949987\pi$
$14$	−4.56533	+	0.374940i	−1.22014	+	0.100207i
$15$		0			0
$16$	−3.78704	+	1.28775i	−0.946761	+	0.321937i
$17$	−5.75819			−1.39657			−0.698284	−	0.715821i	$-0.746053\pi$
$17$	−5.75819			−1.39657			−0.698284	+	0.715821i	$0.746053\pi$
$18$		0			0
$19$	4.00625	−	1.65944i	0.919096	−	0.380702i	0.127564	−	0.991830i	$-0.459284\pi$
$19$	4.00625	−	1.65944i	0.919096	−	0.380702i	0.791531	+	0.611128i	$0.209284\pi$
$20$	−0.544443	+	2.33777i	−0.121741	+	0.522740i
$21$		0			0
$22$	2.96349	+	5.76757i	0.631819	+	1.22965i
$23$	4.82067	−	4.82067i	1.00518	−	1.00518i	0.00519281	−	0.999987i	$-0.498347\pi$
$23$	4.82067	−	4.82067i	1.00518	−	1.00518i	0.999987	−	0.00519281i	$-0.00165293\pi$
$24$		0			0
$25$	−2.51702	−	2.51702i	−0.503405	−	0.503405i
$26$	−0.727835	+	2.26626i	−0.142740	+	0.444451i
$27$		0			0
$28$	5.26669	+	3.77196i	0.995310	+	0.712833i
$29$	−1.52718	−	3.68694i	−0.283590	−	0.684647i	0.716324	−	0.697768i	$-0.245823\pi$
$29$	−1.52718	−	3.68694i	−0.283590	−	0.684647i	−0.999914	+	0.0131208i	$0.995823\pi$
$30$		0			0
$31$			10.9561i			1.96777i	0.178802	+	0.983885i	$0.442778\pi$
$31$			10.9561i			1.96777i	−0.178802	+	0.983885i	$0.557222\pi$
$32$	5.26234	+	2.07553i	0.930258	+	0.366905i
$33$		0			0
$34$	6.21019	+	5.26755i	1.06504	+	0.903378i
$35$	3.59147	−	1.48764i	0.607070	−	0.251457i
$36$		0			0
$37$	1.67353	−	4.04025i	0.275126	−	0.664213i	−0.724561	−	0.689210i	$-0.757958\pi$
$37$	1.67353	−	4.04025i	0.275126	−	0.664213i	0.999688	+	0.0249970i	$0.00795762\pi$
$38$	−5.83877	−	1.87518i	−0.947173	−	0.304195i
$39$		0			0
$40$	2.72575	−	2.02322i	0.430979	−	0.319899i
$41$	−2.75672	−	2.75672i	−0.430528	−	0.430528i	0.458280	−	0.888808i	$-0.348466\pi$
$41$	−2.75672	−	2.75672i	−0.430528	−	0.430528i	−0.888808	+	0.458280i	$0.848466\pi$
$42$		0			0
$43$	3.26736	−	7.88810i	0.498268	−	1.20292i	−0.452148	−	0.891943i	$-0.649342\pi$
$43$	3.26736	−	7.88810i	0.498268	−	1.20292i	0.950416	−	0.310982i	$-0.100658\pi$
$44$	2.08001	−	8.93129i	0.313573	−	1.34644i
$45$		0			0
$46$	−9.60899	+	0.789163i	−1.41677	+	0.116356i
$47$			3.05588i			0.445746i	0.974847	+	0.222873i	$0.0715436\pi$
$47$			3.05588i			0.445746i	−0.974847	+	0.222873i	$0.928456\pi$
$48$		0			0
$49$		−	3.49141i		−	0.498773i
$50$	0.412047	+	5.01715i	0.0582722	+	0.709533i
$51$		0			0
$52$	2.85813	−	1.77834i	0.396351	−	0.246611i
$53$	3.81361	−	9.20688i	0.523840	−	1.26466i	−0.411661	−	0.911337i	$-0.635051\pi$
$53$	3.81361	−	9.20688i	0.523840	−	1.26466i	0.935501	−	0.353325i	$-0.114949\pi$
$54$		0			0
$55$	−3.89116	−	3.89116i	−0.524683	−	0.524683i
$56$	−2.22954	−	8.88597i	−0.297935	−	1.18744i
$57$		0			0
$58$	−1.72573	+	5.37340i	−0.226599	+	0.705562i
$59$	−2.49029	+	6.01210i	−0.324208	+	0.782708i	0.674792	+	0.738008i	$0.264233\pi$
$59$	−2.49029	+	6.01210i	−0.324208	+	0.782708i	−0.999000	+	0.0447004i	$0.985767\pi$
$60$		0			0
$61$	4.36611	−	1.80850i	0.559023	−	0.231555i	−0.0852381	−	0.996361i	$-0.527165\pi$
$61$	4.36611	−	1.80850i	0.559023	−	0.231555i	0.644261	+	0.764806i	$0.277165\pi$
$62$	10.0225	−	11.8161i	1.27286	−	1.50065i
$63$		0			0
$64$	−3.77673	−	7.05240i	−0.472092	−	0.881549i
$65$		−	2.02000i		−	0.250550i
$66$		0			0
$67$	−4.89651	−	11.8212i	−0.598204	−	1.44419i	−0.875410	−	0.483381i	$-0.839409\pi$
$67$	−4.89651	−	11.8212i	−0.598204	−	1.44419i	0.277207	−	0.960810i	$-0.410591\pi$
$68$	−1.87895	−	11.3621i	−0.227857	−	1.37785i
$69$		0			0
$70$	−5.23427	−	1.68104i	−0.625615	−	0.200923i
$71$	0.814206	+	0.814206i	0.0966285	+	0.0966285i	0.753769	−	0.657140i	$-0.228234\pi$
$71$	0.814206	+	0.814206i	0.0966285	+	0.0966285i	−0.657140	+	0.753769i	$0.728234\pi$
$72$		0			0
$73$	−6.13068	+	6.13068i	−0.717541	+	0.717541i	−0.968101	−	0.250560i	$-0.919385\pi$
$73$	−6.13068	+	6.13068i	−0.717541	+	0.717541i	0.250560	+	0.968101i	$0.419385\pi$
$74$	−5.50089	+	2.82647i	−0.639465	+	0.328570i
$75$		0			0
$76$	4.58169	+	7.36364i	0.525555	+	0.844667i
$77$	−13.7210	+	5.68342i	−1.56365	+	0.647686i
$78$		0			0
$79$	−7.99746			−0.899785			−0.449892	−	0.893083i	$-0.648538\pi$
$79$	−7.99746			−0.899785			−0.449892	+	0.893083i	$0.648538\pi$
$80$	−4.79054	−	0.311461i	−0.535598	−	0.0348223i
$81$		0			0
$82$	0.451287	+	5.49495i	0.0498363	+	0.606816i
$83$	4.51997	+	10.9122i	0.496131	+	1.19777i	0.951551	+	0.307490i	$0.0994891\pi$
$83$	4.51997	+	10.9122i	0.496131	+	1.19777i	−0.455420	+	0.890277i	$0.650511\pi$
$84$		0			0
$85$	−6.38472	−	2.64464i	−0.692520	−	0.286851i
$86$	−10.7398	+	5.51834i	−1.15810	+	0.595058i
$87$		0			0
$88$	−10.4136	+	7.72958i	−1.11009	+	0.823976i
$89$	6.05533	−	6.05533i	0.641864	−	0.641864i	−0.309150	−	0.951013i	$-0.600044\pi$
$89$	6.05533	−	6.05533i	0.641864	−	0.641864i	0.951013	+	0.309150i	$0.100044\pi$
$90$		0			0
$91$	−5.03667	−	2.08626i	−0.527987	−	0.218699i
$92$	11.0852	+	7.93912i	1.15571	+	0.827711i
$93$		0			0
$94$	2.79550	−	3.29576i	0.288334	−	0.339932i
$95$	5.20430			0.533950
$96$		0			0
$97$	11.5086			1.16852			0.584262	−	0.811565i	$-0.301384\pi$
$97$	11.5086			1.16852			0.584262	+	0.811565i	$0.301384\pi$
$98$	−3.19392	+	3.76548i	−0.322634	+	0.380371i
$99$		0			0
$100$	4.14526	−	5.78792i	0.414526	−	0.578792i
$101$	0.407683	+	0.168868i	0.0405660	+	0.0168030i	0.402874	−	0.915255i	$-0.368011\pi$
$101$	0.407683	+	0.168868i	0.0405660	+	0.0168030i	−0.362308	+	0.932058i	$0.618011\pi$
$102$		0			0
$103$	−1.14131	+	1.14131i	−0.112456	+	0.112456i	−0.761096	−	0.648639i	$-0.775338\pi$
$103$	−1.14131	+	1.14131i	−0.112456	+	0.112456i	0.648639	+	0.761096i	$0.275338\pi$
$104$	−4.70929	−	0.696661i	−0.461784	−	0.0683132i
$105$		0			0
$106$	−12.5354	+	6.44092i	−1.21754	+	0.625598i
$107$	8.61819	+	3.56977i	0.833152	+	0.345103i	0.758150	−	0.652081i	$-0.226104\pi$
$107$	8.61819	+	3.56977i	0.833152	+	0.345103i	0.0750020	+	0.997183i	$0.476104\pi$
$108$		0			0
$109$	−3.95363	−	9.54490i	−0.378689	−	0.914236i	−0.992212	−	0.124559i	$-0.960248\pi$
$109$	−3.95363	−	9.54490i	−0.378689	−	0.914236i	0.613523	−	0.789677i	$-0.289752\pi$
$110$	0.636998	+	7.75620i	0.0607353	+	0.739524i
$111$		0			0
$112$	−5.72427	+	11.6231i	−0.540892	+	1.09828i
$113$	−9.49602			−0.893310			−0.446655	−	0.894706i	$-0.647385\pi$
$113$	−9.49602			−0.893310			−0.446655	+	0.894706i	$0.647385\pi$
$114$		0			0
$115$	7.55924	−	3.13114i	0.704903	−	0.291980i
$116$	6.77674	−	4.21652i	0.629204	−	0.391494i
$117$		0			0
$118$	8.18559	−	4.20592i	0.753545	−	0.387187i
$119$	−13.1883	+	13.1883i	−1.20897	+	1.20897i
$120$		0			0
$121$	7.08774	+	7.08774i	0.644340	+	0.644340i
$122$	−6.36324	−	2.04362i	−0.576100	−	0.185021i
$123$		0			0
$124$	−21.6185	+	3.57507i	−1.94140	+	0.321051i
$125$	−3.93128	−	9.49095i	−0.351624	−	0.848896i
$126$		0			0
$127$		−	17.3638i		−	1.54079i	−0.637568	−	0.770394i	$-0.720059\pi$
$127$		−	17.3638i		−	1.54079i	0.637568	−	0.770394i	$-0.279941\pi$
$128$	−2.37828	+	11.0609i	−0.210213	+	0.977656i
$129$		0			0
$130$	−1.84788	+	2.17857i	−0.162070	+	0.191073i
$131$	12.9137	−	5.34903i	1.12827	−	0.467347i	0.261081	−	0.965317i	$-0.415921\pi$
$131$	12.9137	−	5.34903i	1.12827	−	0.467347i	0.867194	+	0.497970i	$0.165921\pi$
$132$		0			0
$133$	5.37500	−	12.9764i	0.466072	−	1.12520i
$134$	−5.53309	+	17.2284i	−0.477986	+	1.48831i
$135$		0			0
$136$	−8.36750	+	13.9728i	−0.717507	+	1.19816i
$137$	−1.43528	−	1.43528i	−0.122624	−	0.122624i	0.643132	−	0.765756i	$-0.277635\pi$
$137$	−1.43528	−	1.43528i	−0.122624	−	0.122624i	−0.765756	+	0.643132i	$0.777635\pi$
$138$		0			0
$139$	1.00602	−	2.42876i	0.0853298	−	0.206004i	−0.875455	−	0.483300i	$-0.839438\pi$
$139$	1.00602	−	2.42876i	0.0853298	−	0.206004i	0.960785	+	0.277295i	$0.0894381\pi$
$140$	4.10734	+	6.60127i	0.347133	+	0.557909i
$141$		0			0
$142$	−0.133289	−	1.62295i	−0.0111853	−	0.136195i
$143$			7.71729i			0.645352i
$144$		0			0
$145$		−	4.78951i		−	0.397747i
$146$	12.2202	−	1.00362i	1.01135	−	0.0830599i
$147$		0			0
$148$	8.51832	+	1.98383i	0.700201	+	0.163070i
$149$	−2.21125	+	5.33842i	−0.181152	+	0.437341i	−0.988205	−	0.153140i	$-0.951062\pi$
$149$	−2.21125	+	5.33842i	−0.181152	+	0.437341i	0.807052	+	0.590480i	$0.201062\pi$
$150$		0			0
$151$	7.88070	+	7.88070i	0.641322	+	0.641322i	0.950880	−	0.309558i	$-0.100181\pi$
$151$	7.88070	+	7.88070i	0.641322	+	0.641322i	−0.309558	+	0.950880i	$0.600181\pi$
$152$	1.79487	−	12.1329i	0.145583	−	0.984112i
$153$		0			0
$154$	19.9972	+	6.42231i	1.61142	+	0.517525i
$155$	−5.03194	+	12.1482i	−0.404175	+	0.975765i
$156$		0			0
$157$	−12.8602	+	5.32685i	−1.02635	+	0.425129i	−0.831394	−	0.555683i	$-0.812457\pi$
$157$	−12.8602	+	5.32685i	−1.02635	+	0.425129i	−0.194957	+	0.980812i	$0.562457\pi$
$158$	8.62523	+	7.31602i	0.686187	+	0.582031i
$159$		0			0
$160$	4.88166	+	4.71826i	0.385929	+	0.373011i
$161$		−	22.0821i		−	1.74031i
$162$		0			0
$163$	2.99107	+	7.22108i	0.234278	+	0.565598i	0.996672	−	0.0815153i	$-0.0259759\pi$
$163$	2.99107	+	7.22108i	0.234278	+	0.565598i	−0.762394	+	0.647114i	$0.775976\pi$
$164$	4.54003	−	6.33912i	0.354517	−	0.495002i
$165$		0			0
$166$	5.10760	−	15.9036i	0.396427	−	1.23436i
$167$	10.0758	+	10.0758i	0.779690	+	0.779690i	0.979778	−	0.200088i	$-0.0641227\pi$
$167$	10.0758	+	10.0758i	0.779690	+	0.779690i	−0.200088	+	0.979778i	$0.564123\pi$
$168$		0			0
$169$	7.18926	−	7.18926i	0.553020	−	0.553020i
$170$	4.46661	+	8.69293i	0.342573	+	0.666717i
$171$		0			0
$172$	16.6310	+	3.87320i	1.26810	+	0.295328i
$173$	7.96435	−	3.29894i	0.605518	−	0.250814i	−0.0587927	−	0.998270i	$-0.518725\pi$
$173$	7.96435	−	3.29894i	0.605518	−	0.250814i	0.664311	+	0.747456i	$0.268725\pi$
$174$		0			0
$175$	−11.5297			−0.871566
$176$	18.3019	+	1.18992i	1.37956	+	0.0896932i
$177$		0			0
$178$	−12.0700	+	0.991282i	−0.904687	+	0.0742997i
$179$	2.93955	+	7.09670i	0.219712	+	0.530432i	0.994850	−	0.101360i	$-0.0323195\pi$
$179$	2.93955	+	7.09670i	0.219712	+	0.530432i	−0.775138	+	0.631793i	$0.782319\pi$
$180$		0			0
$181$	−8.77358	−	3.63414i	−0.652135	−	0.270123i	0.0319896	−	0.999488i	$-0.489816\pi$
$181$	−8.77358	−	3.63414i	−0.652135	−	0.270123i	−0.684125	+	0.729365i	$0.739816\pi$
$182$	3.52354	+	6.85754i	0.261182	+	0.508314i
$183$		0			0
$184$	−4.69268	−	18.7030i	−0.345949	−	1.37880i
$185$	3.71123	−	3.71123i	0.272855	−	0.272855i
$186$		0			0
$187$	24.3924	+	10.1037i	1.78375	+	0.738854i
$188$	−6.02987	+	0.997164i	−0.439774	+	0.0727256i
$189$		0			0
$190$	−5.61282	−	4.76086i	−0.407197	−	0.345389i
$191$	11.3188			0.819002			0.409501	−	0.912310i	$-0.365703\pi$
$191$	11.3188			0.819002			0.409501	+	0.912310i	$0.365703\pi$
$192$		0			0
$193$	−1.00738			−0.0725131			−0.0362565	−	0.999343i	$-0.511543\pi$
$193$	−1.00738			−0.0725131			−0.0362565	+	0.999343i	$0.511543\pi$
$194$	−12.4120	−	10.5280i	−0.891131	−	0.755867i
$195$		0			0
$196$	6.88926	−	1.13928i	0.492090	−	0.0813772i
$197$	4.85159	+	2.00959i	0.345661	+	0.143178i	0.548758	−	0.835981i	$-0.315101\pi$
$197$	4.85159	+	2.00959i	0.345661	+	0.143178i	−0.203097	+	0.979159i	$0.565101\pi$
$198$		0			0
$199$	−11.9610	+	11.9610i	−0.847891	+	0.847891i	−0.989870	−	0.141979i	$-0.954653\pi$
$199$	−11.9610	+	11.9610i	−0.847891	+	0.847891i	0.141979	+	0.989870i	$0.454653\pi$
$200$	−9.76540	+	2.45020i	−0.690518	+	0.173255i
$201$		0			0
$202$	−0.285206	−	0.555069i	−0.0200670	−	0.0390545i
$203$	−11.9422	−	4.94660i	−0.838175	−	0.347184i
$204$		0			0
$205$	−1.79056	−	4.32279i	−0.125058	−	0.301917i
$206$	2.27496	−	0.186837i	0.158504	−	0.0130175i
$207$		0			0
$208$	4.44166	+	5.05937i	0.307973	+	0.350804i
$209$	−19.8827			−1.37532
$210$		0			0
$211$	9.78520	−	4.05316i	0.673641	−	0.279031i	−0.0195249	−	0.999809i	$-0.506215\pi$
$211$	9.78520	−	4.05316i	0.673641	−	0.279031i	0.693166	+	0.720778i	$0.256215\pi$
$212$	19.4114	+	4.52074i	1.33318	+	0.310485i
$213$		0			0
$214$	−6.02909	−	11.7338i	−0.412140	−	0.802109i
$215$	7.24574	−	7.24574i	0.494155	−	0.494155i
$216$		0			0
$217$	25.0933	+	25.0933i	1.70344	+	1.70344i
$218$	−4.46763	+	13.9109i	−0.302586	+	0.942164i
$219$		0			0
$220$	6.40831	−	8.94775i	0.432048	−	0.603257i
$221$	3.70884	+	8.95392i	0.249483	+	0.602306i
$222$		0			0
$223$			11.6867i			0.782596i	0.920264	+	0.391298i	$0.127974\pi$
$223$			11.6867i			0.782596i	−0.920264	+	0.391298i	$0.872026\pi$
$224$	16.8063	−	7.29891i	1.12292	−	0.487679i
$225$		0			0
$226$	10.2414	+	8.68688i	0.681249	+	0.577843i
$227$	27.4221	−	11.3586i	1.82007	−	0.753897i	0.844029	−	0.536297i	$-0.180177\pi$
$227$	27.4221	−	11.3586i	1.82007	−	0.753897i	0.976038	−	0.217600i	$-0.0698227\pi$
$228$		0			0
$229$	−4.97093	+	12.0009i	−0.328488	+	0.793040i	0.670217	+	0.742165i	$0.266201\pi$
$229$	−4.97093	+	12.0009i	−0.328488	+	0.793040i	−0.998705	+	0.0508750i	$0.983799\pi$
$230$	−11.0170	−	3.53821i	−0.726437	−	0.233303i
$231$		0			0
$232$	−11.1659	−	1.65181i	−0.733079	−	0.108447i
$233$	15.1524	+	15.1524i	0.992666	+	0.992666i	0.999973	−	0.00730690i	$-0.00232588\pi$
$233$	15.1524	+	15.1524i	0.992666	+	0.992666i	−0.00730690	+	0.999973i	$0.502326\pi$
$234$		0			0
$235$	−1.40351	+	3.38838i	−0.0915552	+	0.221034i
$236$	−12.6757	−	2.95204i	−0.825117	−	0.192162i
$237$		0			0
$238$	26.2881	−	2.15898i	1.70400	−	0.139946i
$239$		−	23.6477i		−	1.52964i	−0.644241	−	0.764822i	$-0.722827\pi$
$239$		−	23.6477i		−	1.52964i	0.644241	−	0.764822i	$-0.277173\pi$
$240$		0			0
$241$			15.2836i			0.984506i	0.870452	+	0.492253i	$0.163826\pi$
$241$			15.2836i			0.984506i	−0.870452	+	0.492253i	$0.836174\pi$
$242$	−1.16029	−	14.1279i	−0.0745863	−	0.908177i
$243$		0			0
$244$	4.99324	+	8.02508i	0.319659	+	0.513753i
$245$	1.60354	−	3.87130i	0.102447	−	0.247328i
$246$		0			0
$247$	−5.16082	−	5.16082i	−0.328375	−	0.328375i
$248$	26.5860	+	15.9208i	1.68821	+	1.01097i
$249$		0			0
$250$	−4.44238	+	13.8323i	−0.280961	+	0.874829i
$251$	−4.23813	+	10.2317i	−0.267508	+	0.645822i	−0.999365	−	0.0356366i	$-0.988654\pi$
$251$	−4.23813	+	10.2317i	−0.267508	+	0.645822i	0.731857	+	0.681459i	$0.238654\pi$
$252$		0			0
$253$	−28.8796	+	11.9623i	−1.81564	+	0.752065i
$254$	−15.8843	+	18.7268i	−0.996668	+	1.17502i
$255$		0			0
$256$	12.6834	−	9.75352i	0.792713	−	0.609595i
$257$			24.2953i			1.51550i	0.652544	+	0.757751i	$0.273702\pi$
$257$			24.2953i			1.51550i	−0.652544	+	0.757751i	$0.726298\pi$
$258$		0			0
$259$	−5.42063	−	13.0866i	−0.336822	−	0.813159i
$260$	3.98587	−	0.659146i	0.247193	−	0.0408785i
$261$		0			0
$262$	−18.8206	−	6.04444i	−1.16274	−	0.373427i
$263$	17.0847	+	17.0847i	1.05349	+	1.05349i	0.998486	+	0.0550047i	$0.0175174\pi$
$263$	17.0847	+	17.0847i	1.05349	+	1.05349i	0.0550047	+	0.998486i	$0.482483\pi$
$264$		0			0
$265$	8.45712	−	8.45712i	0.519517	−	0.519517i
$266$	−17.6676	+	9.07800i	−1.08327	+	0.556608i
$267$		0			0
$268$	21.7279	−	13.5192i	1.32724	−	0.825814i
$269$	−27.5091	+	11.3947i	−1.67726	+	0.694745i	−0.999190	−	0.0402507i	$-0.987184\pi$
$269$	−27.5091	+	11.3947i	−1.67726	+	0.694745i	−0.678072	+	0.734995i	$0.737184\pi$
$270$		0			0
$271$	−1.03250			−0.0627197			−0.0313598	−	0.999508i	$-0.509984\pi$
$271$	−1.03250			−0.0627197			−0.0313598	+	0.999508i	$0.509984\pi$
$272$	21.8065	−	7.41510i	1.32222	−	0.449607i
$273$		0			0
$274$	0.234960	+	2.86092i	0.0141945	+	0.172835i
$275$	6.24590	+	15.0789i	0.376642	+	0.909294i
$276$		0			0
$277$	6.98129	+	2.89174i	0.419465	+	0.173748i	0.582425	−	0.812885i	$-0.302104\pi$
$277$	6.98129	+	2.89174i	0.419465	+	0.173748i	−0.162960	+	0.986633i	$0.552104\pi$
$278$	−3.30680	+	1.69910i	−0.198329	+	0.101905i
$279$		0			0
$280$	1.60904	−	10.8768i	0.0961586	−	0.650014i
$281$	−5.66031	+	5.66031i	−0.337666	+	0.337666i	−0.855488	−	0.517822i	$-0.826743\pi$
$281$	−5.66031	+	5.66031i	−0.337666	+	0.337666i	0.517822	+	0.855488i	$0.326743\pi$
$282$		0			0
$283$	−8.97137	−	3.71606i	−0.533292	−	0.220897i	0.0997521	−	0.995012i	$-0.468195\pi$
$283$	−8.97137	−	3.71606i	−0.533292	−	0.220897i	−0.633045	+	0.774115i	$0.718195\pi$
$284$	−1.34091	+	1.87228i	−0.0795683	+	0.111099i
$285$		0			0
$286$	7.05972	−	8.32307i	0.417450	−	0.492154i
$287$	−12.6277			−0.745391
$288$		0			0
$289$	16.1568			0.950401
$290$	−4.38141	+	5.16547i	−0.257285	+	0.303327i
$291$		0			0
$292$	−14.0976	−	10.0966i	−0.824997	−	0.590856i
$293$	−12.4522	−	5.15788i	−0.727467	−	0.301327i	−0.0119561	−	0.999929i	$-0.503806\pi$
$293$	−12.4522	−	5.15788i	−0.727467	−	0.301327i	−0.715510	+	0.698602i	$0.753806\pi$
$294$		0			0
$295$	−5.52250	+	5.52250i	−0.321533	+	0.321533i
$296$	−7.37218	−	9.93205i	−0.428499	−	0.577289i
$297$		0			0
$298$	7.26837	−	3.73464i	0.421045	−	0.216342i
$299$	−10.6011	−	4.39110i	−0.613075	−	0.253944i
$300$		0			0
$301$	−10.5831	−	25.5499i	−0.610001	−	1.47267i
$302$	−1.29010	−	15.7085i	−0.0742370	−	0.903923i
$303$		0			0
$304$	−13.0349	+	11.4434i	−0.747602	+	0.656325i
$305$	5.67178			0.324765
$306$		0			0
$307$	−15.2016	+	6.29670i	−0.867600	+	0.359372i	−0.771675	−	0.636017i	$-0.780581\pi$
$307$	−15.2016	+	6.29670i	−0.867600	+	0.359372i	−0.0959250	+	0.995389i	$0.530581\pi$
$308$	−15.6918	−	25.2197i	−0.894125	−	1.43703i
$309$		0			0
$310$	16.5400	−	8.49858i	0.939408	−	0.482687i
$311$	−14.4880	+	14.4880i	−0.821542	+	0.821542i	−0.986329	−	0.164787i	$-0.947306\pi$
$311$	−14.4880	+	14.4880i	−0.821542	+	0.821542i	0.164787	+	0.986329i	$0.447306\pi$
$312$		0			0
$313$	7.88864	+	7.88864i	0.445893	+	0.445893i	0.893986	−	0.448094i	$-0.147897\pi$
$313$	7.88864	+	7.88864i	0.445893	+	0.445893i	−0.448094	+	0.893986i	$0.647897\pi$
$314$	18.7426	+	6.01938i	1.05771	+	0.339693i
$315$		0			0
$316$	−2.60965	−	15.7806i	−0.146804	−	0.887728i
$317$	2.14940	+	5.18912i	0.120722	+	0.291450i	0.972676	−	0.232168i	$-0.0745819\pi$
$317$	2.14940	+	5.18912i	0.120722	+	0.291450i	−0.851953	+	0.523618i	$0.824582\pi$
$318$		0			0
$319$			18.2980i			1.02449i
$320$	−0.948623	−	9.55433i	−0.0530297	−	0.534103i
$321$		0			0
$322$	−20.2005	+	23.8154i	−1.12573	+	1.32718i
$323$	−23.0687	+	9.55539i	−1.28358	+	0.531676i
$324$		0			0
$325$	−2.29273	+	5.53515i	−0.127178	+	0.307035i
$326$	3.37993	−	10.5241i	0.187197	−	0.582877i
$327$		0			0
$328$	−10.6954	+	2.68353i	−0.590554	+	0.148173i
$329$	6.99905	+	6.99905i	0.385870	+	0.385870i
$330$		0			0
$331$	4.79808	−	11.5836i	0.263726	−	0.636692i	−0.735437	−	0.677593i	$-0.763023\pi$
$331$	4.79808	−	11.5836i	0.263726	−	0.636692i	0.999163	+	0.0409015i	$0.0130230\pi$
$332$	−20.0570	+	12.4796i	−1.10077	+	0.684905i
$333$		0			0
$334$	−1.64945	−	20.0840i	−0.0902540	−	1.09895i
$335$		−	15.3563i		−	0.839005i
$336$		0			0
$337$			34.5409i			1.88156i	0.339011	+	0.940782i	$0.389907\pi$
$337$			34.5409i			1.88156i	−0.339011	+	0.940782i	$0.610093\pi$
$338$	−14.3303	+	1.17691i	−0.779464	+	0.0640155i
$339$		0			0
$340$	3.13501	−	13.4613i	0.170020	−	0.730042i
$341$	19.2242	−	46.4113i	1.04105	−	2.51331i
$342$		0			0
$343$	8.03590	+	8.03590i	0.433898	+	0.433898i
$344$	−14.3933	−	19.3911i	−0.776034	−	1.04550i
$345$		0			0
$346$	−11.6074	−	3.72783i	−0.624016	−	0.200409i
$347$	13.4976	−	32.5861i	0.724590	−	1.74932i	0.0647598	−	0.997901i	$-0.479372\pi$
$347$	13.4976	−	32.5861i	0.724590	−	1.74932i	0.659830	−	0.751415i	$-0.270628\pi$
$348$		0			0
$349$	19.4574	−	8.05954i	1.04153	−	0.431417i	0.204671	−	0.978831i	$-0.434388\pi$
$349$	19.4574	−	8.05954i	1.04153	−	0.431417i	0.836862	+	0.547414i	$0.184388\pi$
$350$	12.4348	+	10.5473i	0.664667	+	0.563778i
$351$		0			0
$352$	−18.6501	−	18.0258i	−0.994052	−	0.960779i
$353$		−	28.8838i		−	1.53733i	−0.639653	−	0.768664i	$-0.720922\pi$
$353$		−	28.8838i		−	1.53733i	0.639653	−	0.768664i	$-0.279078\pi$
$354$		0			0
$355$	0.528846	+	1.27675i	0.0280682	+	0.0677627i
$356$	13.9243	+	9.97248i	0.737986	+	0.528540i
$357$		0			0
$358$	3.32171	−	10.3428i	0.175558	−	0.546636i
$359$	21.9015	+	21.9015i	1.15592	+	1.15592i	0.985345	+	0.170574i	$0.0545623\pi$
$359$	21.9015	+	21.9015i	1.15592	+	1.15592i	0.170574	+	0.985345i	$0.445438\pi$
$360$		0			0
$361$	−0.138774	+	0.138774i	−0.00730389	+	0.00730389i
$362$	6.13780	+	11.9454i	0.322595	+	0.627837i
$363$		0			0
$364$	2.47309	−	10.6191i	0.129625	−	0.556594i
$365$	−9.61344	+	3.98202i	−0.503191	+	0.208428i
$366$		0			0
$367$	4.27993			0.223411			0.111705	−	0.993741i	$-0.464369\pi$
$367$	4.27993			0.223411			0.111705	+	0.993741i	$0.464369\pi$
$368$	−12.0483	+	24.4639i	−0.628060	+	1.27527i
$369$		0			0
$370$	−7.39756	+	0.607544i	−0.384581	+	0.0315847i
$371$	−12.3525	−	29.8215i	−0.641308	−	1.54825i
$372$		0			0
$373$	−1.63995	−	0.679288i	−0.0849132	−	0.0351722i	0.339823	−	0.940490i	$-0.389633\pi$
$373$	−1.63995	−	0.679288i	−0.0849132	−	0.0351722i	−0.424736	+	0.905317i	$0.639633\pi$
$374$	−17.0644	−	33.2108i	−0.882378	−	1.71729i
$375$		0			0
$376$	7.41539	+	4.44065i	0.382420	+	0.229009i
$377$	−4.74949	+	4.74949i	−0.244611	+	0.244611i
$378$		0			0
$379$	24.5928	+	10.1867i	1.26325	+	0.523254i	0.910904	−	0.412618i	$-0.135385\pi$
$379$	24.5928	+	10.1867i	1.26325	+	0.523254i	0.352342	+	0.935871i	$0.385385\pi$
$380$	1.69821	+	10.2691i	0.0871165	+	0.526795i
$381$		0			0
$382$	−12.2073	−	10.3544i	−0.624581	−	0.529777i
$383$	−8.94049			−0.456838			−0.228419	−	0.973563i	$-0.573356\pi$
$383$	−8.94049			−0.456838			−0.228419	+	0.973563i	$0.573356\pi$
$384$		0			0
$385$	−17.8242			−0.908406
$386$	1.08646	+	0.921547i	0.0552994	+	0.0469055i
$387$		0			0
$388$	3.75537	+	22.7088i	0.190650	+	1.15287i
$389$	−26.3896	−	10.9309i	−1.33801	−	0.554221i	−0.405079	−	0.914282i	$-0.632756\pi$
$389$	−26.3896	−	10.9309i	−1.33801	−	0.554221i	−0.932929	+	0.360061i	$0.882756\pi$
$390$		0			0
$391$	−27.7584	+	27.7584i	−1.40380	+	1.40380i
$392$	−8.47225	−	5.07353i	−0.427913	−	0.256252i
$393$		0			0
$394$	−3.39406	−	6.60553i	−0.170990	−	0.332782i
$395$	−8.86763	−	3.67309i	−0.446179	−	0.184813i
$396$		0			0
$397$	−5.22517	−	12.6147i	−0.262244	−	0.633113i	0.736833	−	0.676075i	$-0.236320\pi$
$397$	−5.22517	−	12.6147i	−0.262244	−	0.633113i	−0.999077	+	0.0429622i	$0.986320\pi$
$398$	23.8417	−	1.95806i	1.19507	−	0.0981486i
$399$		0			0
$400$	12.7734	+	6.29079i	0.638669	+	0.314539i
$401$	5.30249			0.264794			0.132397	−	0.991197i	$-0.457733\pi$
$401$	5.30249			0.264794			0.132397	+	0.991197i	$0.457733\pi$
$402$		0			0
$403$	17.0366	−	7.05678i	0.848652	−	0.351523i
$404$	−0.200180	+	0.859544i	−0.00995931	+	0.0427639i
$405$		0			0
$406$	8.35446	+	16.2595i	0.414625	+	0.806945i
$407$	−14.1785	+	14.1785i	−0.702804	+	0.702804i
$408$		0			0
$409$	−22.2095	−	22.2095i	−1.09819	−	1.09819i	−0.994622	−	0.103568i	$-0.966974\pi$
$409$	−22.2095	−	22.2095i	−1.09819	−	1.09819i	−0.103568	−	0.994622i	$-0.533026\pi$
$410$	−2.02334	+	6.30010i	−0.0999259	+	0.311140i
$411$		0			0
$412$	−2.62445	−	1.87961i	−0.129297	−	0.0926018i
$413$	8.06617	+	19.4735i	0.396910	+	0.958226i
$414$		0			0
$415$			14.1754i			0.695844i
$416$	−0.162034	−	9.51971i	−0.00794438	−	0.466742i
$417$		0			0
$418$	21.4434	+	18.1885i	1.04883	+	0.889631i
$419$	19.3284	−	8.00610i	0.944256	−	0.391124i	0.143187	−	0.989696i	$-0.454265\pi$
$419$	19.3284	−	8.00610i	0.944256	−	0.391124i	0.801069	+	0.598572i	$0.204265\pi$
$420$		0			0
$421$	−8.19769	+	19.7910i	−0.399531	+	0.964554i	0.588246	+	0.808682i	$0.299819\pi$
$421$	−8.19769	+	19.7910i	−0.399531	+	0.964554i	−0.987777	+	0.155872i	$0.950181\pi$
$422$	−14.2611	−	4.58011i	−0.694220	−	0.222956i
$423$		0			0
$424$	−16.7996	−	22.6330i	−0.815862	−	1.09916i
$425$	14.4935	+	14.4935i	0.703039	+	0.703039i
$426$		0			0
$427$	5.85782	−	14.1420i	0.283480	−	0.684380i
$428$	−4.23168	+	18.1703i	−0.204546	+	0.878293i
$429$		0			0
$430$	−14.4428	+	1.18616i	−0.696496	+	0.0572015i
$431$		−	4.03116i		−	0.194174i	−0.995276	−	0.0970871i	$-0.969047\pi$
$431$		−	4.03116i		−	0.194174i	0.995276	−	0.0970871i	$-0.0309526\pi$
$432$		0			0
$433$			19.5320i			0.938650i	0.883025	+	0.469325i	$0.155503\pi$
$433$			19.5320i			0.938650i	−0.883025	+	0.469325i	$0.844497\pi$
$434$	−4.10787	−	50.0181i	−0.197184	−	2.40095i
$435$		0			0
$436$	17.5439	−	10.9159i	0.840201	−	0.522776i
$437$	11.3132	−	27.3124i	0.541182	−	1.30653i
$438$		0			0
$439$	−2.79500	−	2.79500i	−0.133398	−	0.133398i	0.637255	−	0.770653i	$-0.280070\pi$
$439$	−2.79500	−	2.79500i	−0.133398	−	0.133398i	−0.770653	+	0.637255i	$0.780070\pi$
$440$	−15.0967	+	3.78784i	−0.719706	+	0.180578i
$441$		0			0
$442$	4.19101	−	13.0496i	0.199346	−	0.620706i
$443$	−7.32465	+	17.6833i	−0.348005	+	0.840157i	0.648851	+	0.760916i	$0.275250\pi$
$443$	−7.32465	+	17.6833i	−0.348005	+	0.840157i	−0.996855	+	0.0792418i	$0.974750\pi$
$444$		0			0
$445$	9.49530	−	3.93308i	0.450120	−	0.186446i
$446$	10.6909	−	12.6040i	0.506227	−	0.596817i
$447$		0			0
$448$	−24.8025	−	7.50241i	−1.17181	−	0.354456i
$449$		−	32.9730i		−	1.55609i	−0.628208	−	0.778045i	$-0.716211\pi$
$449$		−	32.9730i		−	1.55609i	0.628208	−	0.778045i	$-0.283789\pi$
$450$		0			0
$451$	6.84071	+	16.5149i	0.322117	+	0.777658i
$452$	−3.09864	−	18.7375i	−0.145748	−	0.881340i
$453$		0			0
$454$	−39.9654	−	12.8353i	−1.87567	−	0.602391i
$455$	−4.62651	−	4.62651i	−0.216894	−	0.216894i
$456$		0			0
$457$	−16.3157	+	16.3157i	−0.763214	+	0.763214i	−0.976902	−	0.213688i	$-0.931452\pi$
$457$	−16.3157	+	16.3157i	−0.763214	+	0.763214i	0.213688	+	0.976902i	$0.431452\pi$
$458$	16.3394	−	8.39554i	0.763492	−	0.392298i
$459$		0			0
$460$	8.64502	+	13.8942i	0.403076	+	0.647819i
$461$	12.1576	−	5.03583i	0.566234	−	0.234542i	−0.0811549	−	0.996702i	$-0.525861\pi$
$461$	12.1576	−	5.03583i	0.566234	−	0.234542i	0.647389	+	0.762160i	$0.275861\pi$
$462$		0			0
$463$	−7.60945			−0.353641			−0.176821	−	0.984243i	$-0.556581\pi$
$463$	−7.60945			−0.353641			−0.176821	+	0.984243i	$0.556581\pi$
$464$	10.5313	+	11.9960i	0.488905	+	0.556899i
$465$		0			0
$466$	−2.48051	−	30.2031i	−0.114907	−	1.39913i
$467$	1.94882	+	4.70488i	0.0901809	+	0.217716i	0.962534	−	0.271160i	$-0.0874072\pi$
$467$	1.94882	+	4.70488i	0.0901809	+	0.217716i	−0.872353	+	0.488876i	$0.837407\pi$
$468$		0			0
$469$	−38.2894	−	15.8600i	−1.76804	−	0.732347i
$470$	4.61335	−	2.37043i	0.212798	−	0.109340i
$471$		0			0
$472$	10.9702	+	14.7794i	0.504943	+	0.680276i
$473$	−27.6819	+	27.6819i	−1.27281	+	1.27281i
$474$		0			0
$475$	−14.2607	−	5.90696i	−0.654324	−	0.271030i
$476$	−30.3266	−	21.7197i	−1.39002	−	0.995520i
$477$		0			0
$478$	−21.6328	+	25.5040i	−0.989460	+	1.16653i
$479$	8.04063			0.367386			0.183693	−	0.982984i	$-0.441195\pi$
$479$	8.04063			0.367386			0.183693	+	0.982984i	$0.441195\pi$
$480$		0			0
$481$	−7.36045			−0.335608
$482$	13.9814	−	16.4834i	0.636833	−	0.750796i
$483$		0			0
$484$	−11.6727	+	16.2983i	−0.530579	+	0.740833i
$485$	12.7608	+	5.28571i	0.579440	+	0.240012i
$486$		0			0
$487$	13.0819	−	13.0819i	0.592796	−	0.592796i	−0.345590	−	0.938386i	$-0.612321\pi$
$487$	13.0819	−	13.0819i	0.592796	−	0.592796i	0.938386	+	0.345590i	$0.112321\pi$
$488$	1.95609	−	13.2228i	0.0885481	−	0.598568i
$489$		0			0
$490$	−5.27085	+	2.70827i	−0.238113	+	0.122347i
$491$	−1.59917	−	0.662398i	−0.0721696	−	0.0298936i	0.346307	−	0.938121i	$-0.387436\pi$
$491$	−1.59917	−	0.662398i	−0.0721696	−	0.0298936i	−0.418476	+	0.908228i	$0.637436\pi$
$492$		0			0
$493$	8.79380	+	21.2301i	0.396053	+	0.956156i
$494$	0.844847	+	10.2870i	0.0380115	+	0.462834i
$495$		0			0
$496$	−14.1087	−	41.4912i	−0.633498	−	1.86301i
$497$	3.72963			0.167297
$498$		0			0
$499$	13.5962	−	5.63174i	0.608651	−	0.252111i	−0.0570007	−	0.998374i	$-0.518154\pi$
$499$	13.5962	−	5.63174i	0.608651	−	0.252111i	0.665652	+	0.746263i	$0.268154\pi$
$500$	17.4447	−	10.8542i	0.780152	−	0.485414i
$501$		0			0
$502$	13.9307	−	7.15790i	0.621759	−	0.319472i
$503$	−25.4762	+	25.4762i	−1.13593	+	1.13593i	−0.146752	+	0.989173i	$0.546882\pi$
$503$	−25.4762	+	25.4762i	−1.13593	+	1.13593i	−0.989173	+	0.146752i	$0.953118\pi$
$504$		0			0
$505$	0.374484	+	0.374484i	0.0166643	+	0.0166643i
$506$	42.0896	+	13.5175i	1.87111	+	0.600927i
$507$		0			0
$508$	34.2623	−	5.66597i	1.52014	−	0.251387i
$509$	5.65965	+	13.6636i	0.250860	+	0.605629i	0.998274	−	0.0587294i	$-0.0187049\pi$
$509$	5.65965	+	13.6636i	0.250860	+	0.605629i	−0.747414	+	0.664358i	$0.768705\pi$
$510$		0			0
$511$			28.0828i			1.24231i
$512$	−22.6015	−	1.08355i	−0.998853	−	0.0478868i
$513$		0			0
$514$	22.2252	−	26.2024i	0.980311	−	1.15574i
$515$	−1.78967	+	0.741307i	−0.0788624	+	0.0326659i
$516$		0			0
$517$	5.36204	−	12.9451i	0.235822	−	0.569325i
$518$	−6.12535	+	19.0726i	−0.269133	+	0.838000i
$519$		0			0
$520$	−4.90173	−	2.93536i	−0.214955	−	0.128724i
$521$	−6.11420	−	6.11420i	−0.267868	−	0.267868i	0.560373	−	0.828241i	$-0.310658\pi$
$521$	−6.11420	−	6.11420i	−0.267868	−	0.267868i	−0.828241	+	0.560373i	$0.810658\pi$
$522$		0			0
$523$	−3.45240	+	8.33482i	−0.150963	+	0.364456i	−0.981211	−	0.192937i	$-0.938199\pi$
$523$	−3.45240	+	8.33482i	−0.150963	+	0.364456i	0.830248	+	0.557394i	$0.188199\pi$
$524$	14.7686	+	23.7359i	0.645168	+	1.03691i
$525$		0			0
$526$	−2.79684	−	34.0548i	−0.121948	−	1.48486i
$527$		−	63.0872i		−	2.74812i
$528$		0			0
$529$		−	23.4777i		−	1.02077i
$530$	−16.8575	+	1.38446i	−0.732242	+	0.0601373i
$531$		0			0
$532$	27.3590	+	6.37164i	1.18616	+	0.276246i
$533$	−2.51107	+	6.06227i	−0.108767	+	0.262586i
$534$		0			0
$535$	7.91637	+	7.91637i	0.342254	+	0.342254i
$536$	−35.8006	−	5.29611i	−1.54635	−	0.228757i
$537$		0			0
$538$	40.0923	+	12.8761i	1.72850	+	0.555126i
$539$	−6.12624	+	14.7901i	−0.263876	+	0.637053i
$540$		0			0
$541$	8.67432	−	3.59302i	0.372938	−	0.154476i	−0.188339	−	0.982104i	$-0.560310\pi$
$541$	8.67432	−	3.59302i	0.372938	−	0.154476i	0.561277	+	0.827628i	$0.310310\pi$
$542$	1.11354	+	0.944520i	0.0478308	+	0.0405706i
$543$		0			0
$544$	−30.3016	−	11.9513i	−1.29917	−	0.512408i
$545$		−	12.3993i		−	0.531127i
$546$		0			0
$547$	−8.99937	−	21.7264i	−0.384785	−	0.928954i	−0.991026	−	0.133673i	$-0.957323\pi$
$547$	−8.99937	−	21.7264i	−0.384785	−	0.928954i	0.606240	−	0.795282i	$-0.292677\pi$
$548$	2.36374	−	3.30043i	0.100974	−	0.140988i
$549$		0			0
$550$	7.05792	−	21.9763i	0.300951	−	0.937072i
$551$	−12.2365	−	12.2365i	−0.521293	−	0.521293i
$552$		0			0
$553$	−18.3170	+	18.3170i	−0.778918	+	0.778918i
$554$	−4.88395	−	9.50517i	−0.207499	−	0.403836i
$555$		0			0
$556$	5.12070	+	1.19256i	0.217166	+	0.0505759i
$557$	−12.0218	+	4.97960i	−0.509380	+	0.210992i	−0.622545	−	0.782584i	$-0.713901\pi$
$557$	−12.0218	+	4.97960i	−0.509380	+	0.210992i	0.113165	+	0.993576i	$0.463901\pi$
$558$		0			0
$559$	−14.3704			−0.607803
$560$	−11.6854	+	10.2587i	−0.493797	+	0.433507i
$561$		0			0
$562$	11.2826	−	0.926616i	0.475929	−	0.0390869i
$563$	−3.87198	−	9.34780i	−0.163185	−	0.393963i	0.821044	−	0.570865i	$-0.193392\pi$
$563$	−3.87198	−	9.34780i	−0.163185	−	0.393963i	−0.984228	+	0.176903i	$0.943392\pi$
$564$		0			0
$565$	−10.5292	−	4.36135i	−0.442969	−	0.183484i
$566$	6.27616	+	12.2147i	0.263807	+	0.513422i
$567$		0			0
$568$	3.15891	−	0.792589i	0.132545	−	0.0332563i
$569$	27.9604	−	27.9604i	1.17216	−	1.17216i	0.190469	−	0.981693i	$-0.438999\pi$
$569$	27.9604	−	27.9604i	1.17216	−	1.17216i	0.981693	−	0.190469i	$-0.0610008\pi$
$570$		0			0
$571$	−1.06863	−	0.442642i	−0.0447209	−	0.0185240i	0.360211	−	0.932871i	$-0.382705\pi$
$571$	−1.06863	−	0.442642i	−0.0447209	−	0.0185240i	−0.404932	+	0.914347i	$0.632705\pi$
$572$	−15.2278	+	2.51822i	−0.636705	+	0.105292i
$573$		0			0
$574$	13.6190	+	11.5518i	0.568445	+	0.482161i
$575$	−24.2675			−1.01202
$576$		0			0
$577$	39.9542			1.66332			0.831658	−	0.555288i	$-0.187392\pi$
$577$	39.9542			1.66332			0.831658	+	0.555288i	$0.187392\pi$
$578$	−17.4251	−	14.7801i	−0.724787	−	0.614772i
$579$		0			0
$580$	9.45066	−	1.56286i	0.392417	−	0.0648943i
$581$	35.3450	+	14.6404i	1.46636	+	0.607386i
$582$		0			0
$583$	−32.3099	+	32.3099i	−1.33814	+	1.33814i
$584$	5.96790	+	23.7854i	0.246954	+	0.984248i
$585$		0			0
$586$	8.71129	+	16.9540i	0.359860	+	0.700361i
$587$	−6.65416	−	2.75624i	−0.274646	−	0.113762i	0.241109	−	0.970498i	$-0.422489\pi$
$587$	−6.65416	−	2.75624i	−0.274646	−	0.113762i	−0.515756	+	0.856736i	$0.672489\pi$
$588$		0			0
$589$	18.1810	+	43.8927i	0.749134	+	1.80857i
$590$	11.0079	−	0.904056i	0.453190	−	0.0372194i
$591$		0			0
$592$	−1.13490	+	17.4557i	−0.0466439	+	0.717425i
$593$	−30.4542			−1.25060			−0.625302	−	0.780383i	$-0.715024\pi$
$593$	−30.4542			−1.25060			−0.625302	+	0.780383i	$0.715024\pi$
$594$		0			0
$595$	−20.6804	+	8.56610i	−0.847814	+	0.351176i
$596$	−11.2553	−	2.62126i	−0.461036	−	0.107371i
$597$		0			0
$598$	7.41626	+	14.4336i	0.303273	+	0.590232i
$599$	27.7991	−	27.7991i	1.13584	−	1.13584i	0.146654	−	0.989188i	$-0.453150\pi$
$599$	27.7991	−	27.7991i	1.13584	−	1.13584i	0.989188	−	0.146654i	$-0.0468502\pi$
$600$		0			0
$601$	10.9042	+	10.9042i	0.444792	+	0.444792i	0.893619	−	0.448827i	$-0.148158\pi$
$601$	10.9042	+	10.9042i	0.444792	+	0.444792i	−0.448827	+	0.893619i	$0.648158\pi$
$602$	−11.9590	+	37.2369i	−0.487413	+	1.51766i
$603$		0			0
$604$	−12.9787	+	18.1217i	−0.528094	+	0.737363i
$605$	4.60365	+	11.1142i	0.187165	+	0.451857i
$606$		0			0
$607$		−	12.2609i		−	0.497654i	−0.968548	−	0.248827i	$-0.919955\pi$
$607$		−	12.2609i		−	0.497654i	0.968548	−	0.248827i	$-0.0800451\pi$
$608$	24.5264	−	0.417462i	0.994678	−	0.0169303i
$609$		0			0
$610$	−6.11700	−	5.18850i	−0.247670	−	0.210076i
$611$	4.75186	−	1.96829i	0.192240	−	0.0796283i
$612$		0			0
$613$	12.0970	−	29.2047i	0.488593	−	1.17957i	−0.466835	−	0.884344i	$-0.654606\pi$
$613$	12.0970	−	29.2047i	0.488593	−	1.17957i	0.955428	−	0.295224i	$-0.0953942\pi$
$614$	22.1550	+	7.11532i	0.894104	+	0.287151i
$615$		0			0
$616$	−6.14724	+	41.5542i	−0.247679	+	1.67426i
$617$	20.3519	+	20.3519i	0.819336	+	0.819336i	0.986012	−	0.166676i	$-0.0533033\pi$
$617$	20.3519	+	20.3519i	0.819336	+	0.819336i	−0.166676	+	0.986012i	$0.553303\pi$
$618$		0			0
$619$	17.1759	−	41.4663i	0.690358	−	1.66667i	−0.0537006	−	0.998557i	$-0.517102\pi$
$619$	17.1759	−	41.4663i	0.690358	−	1.66667i	0.744059	−	0.668114i	$-0.232898\pi$
$620$	−25.6127	−	5.96496i	−1.02863	−	0.239559i
$621$		0			0
$622$	28.8789	−	2.37175i	1.15794	−	0.0950986i
$623$		−	27.7377i		−	1.11129i
$624$		0			0
$625$			5.46885i			0.218754i
$626$	−1.29140	−	15.7243i	−0.0516148	−	0.628471i
$627$		0			0
$628$	−14.7073	−	23.6375i	−0.586886	−	0.943237i
$629$	−9.63649	+	23.2646i	−0.384232	+	0.927619i
$630$		0			0
$631$	−12.5561	−	12.5561i	−0.499851	−	0.499851i	0.411540	−	0.911392i	$-0.364991\pi$
$631$	−12.5561	−	12.5561i	−0.499851	−	0.499851i	−0.911392	+	0.411540i	$0.864991\pi$
$632$	−11.6215	+	19.4066i	−0.462278	+	0.771953i
$633$		0			0
$634$	2.42884	−	7.56270i	0.0964617	−	0.300353i
$635$	7.97489	−	19.2531i	0.316474	−	0.764036i
$636$		0			0
$637$	−5.42910	+	2.24881i	−0.215109	+	0.0891010i
$638$	16.7389	−	19.7343i	0.662699	−	0.781290i
$639$		0			0
$640$	−7.71714	+	11.1721i	−0.305047	+	0.441616i
$641$		−	23.6971i		−	0.935980i	−0.883734	−	0.467990i	$-0.844978\pi$
$641$		−	23.6971i		−	0.935980i	0.883734	−	0.467990i	$-0.155022\pi$
$642$		0			0
$643$	14.2539	+	34.4119i	0.562118	+	1.35707i	0.908069	+	0.418820i	$0.137556\pi$
$643$	14.2539	+	34.4119i	0.562118	+	1.35707i	−0.345952	+	0.938252i	$0.612444\pi$
$644$	43.5723	−	7.20558i	1.71699	−	0.283940i
$645$		0			0
$646$	33.6207	+	10.7977i	1.32279	+	0.424828i
$647$	−9.10926	−	9.10926i	−0.358122	−	0.358122i	0.504998	−	0.863120i	$-0.331493\pi$
$647$	−9.10926	−	9.10926i	−0.358122	−	0.358122i	−0.863120	+	0.504998i	$0.831493\pi$
$648$		0			0
$649$	21.0984	−	21.0984i	0.828183	−	0.828183i
$650$	7.53621	−	3.87226i	0.295595	−	0.151883i
$651$		0			0
$652$	−13.2726	+	8.25828i	−0.519796	+	0.323419i
$653$	−45.0078	+	18.6428i	−1.76129	+	0.729551i	−0.764951	+	0.644089i	$0.777237\pi$
$653$	−45.0078	+	18.6428i	−1.76129	+	0.729551i	−0.996341	+	0.0854621i	$0.972763\pi$
$654$		0			0
$655$	16.7755			0.655473
$656$	13.9898	+	6.88987i	0.546210	+	0.269004i
$657$		0			0
$658$	−1.14577	−	13.9511i	−0.0446668	−	0.543871i
$659$	7.19109	+	17.3608i	0.280125	+	0.676281i	0.999838	−	0.0179900i	$-0.00572670\pi$
$659$	7.19109	+	17.3608i	0.280125	+	0.676281i	−0.719713	+	0.694271i	$0.755727\pi$
$660$		0			0
$661$	33.0166	+	13.6759i	1.28420	+	0.531931i	0.917250	−	0.398312i	$-0.130404\pi$
$661$	33.0166	+	13.6759i	1.28420	+	0.531931i	0.366945	+	0.930243i	$0.380404\pi$
$662$	−15.7713	+	8.10362i	−0.612969	+	0.314956i
$663$		0			0
$664$	33.0476	+	4.88884i	1.28250	+	0.189724i
$665$	11.9197	−	11.9197i	0.462225	−	0.462225i
$666$		0			0
$667$	−25.1355	−	10.4115i	−0.973252	−	0.403134i
$668$	−16.5938	+	23.1695i	−0.642033	+	0.896453i
$669$		0			0
$670$	−14.0478	+	16.5617i	−0.542715	+	0.639836i
$671$	−21.6687			−0.836510
$672$		0			0
$673$	24.2342			0.934159			0.467080	−	0.884215i	$-0.345306\pi$
$673$	24.2342			0.934159			0.467080	+	0.884215i	$0.345306\pi$
$674$	31.5978	−	37.2523i	1.21710	−	1.43490i
$675$		0			0
$676$	16.5318	+	11.8399i	0.635838	+	0.455382i
$677$	13.5836	+	5.62649i	0.522058	+	0.216244i	0.628121	−	0.778116i	$-0.283824\pi$
$677$	13.5836	+	5.62649i	0.522058	+	0.216244i	−0.106062	+	0.994359i	$0.533824\pi$
$678$		0			0
$679$	26.3588	−	26.3588i	1.01156	−	1.01156i
$680$	−15.6954	+	11.6501i	−0.601891	+	0.446761i
$681$		0			0
$682$	−63.1900	+	32.4683i	−2.41967	+	1.24328i
$683$	−36.2049	−	14.9966i	−1.38534	−	0.573828i	−0.439438	−	0.898273i	$-0.644822\pi$
$683$	−36.2049	−	14.9966i	−1.38534	−	0.573828i	−0.945905	+	0.324445i	$0.894822\pi$
$684$		0			0
$685$	−0.932246	−	2.25064i	−0.0356193	−	0.0859926i
$686$	−1.31551	−	16.0179i	−0.0502263	−	0.611565i
$687$		0			0
$688$	−2.21575	+	34.0801i	−0.0844745	+	1.29929i
$689$	−16.7729			−0.638997
$690$		0			0
$691$	27.6470	−	11.4518i	1.05174	−	0.435645i	0.211228	−	0.977437i	$-0.432254\pi$
$691$	27.6470	−	11.4518i	1.05174	−	0.435645i	0.840513	+	0.541792i	$0.182254\pi$
$692$	9.10832	+	14.6388i	0.346246	+	0.556483i
$693$		0			0
$694$	−44.3667	+	22.7965i	−1.68414	+	0.865344i
$695$	2.23097	−	2.23097i	0.0846256	−	0.0846256i
$696$		0			0
$697$	15.8738	+	15.8738i	0.601261	+	0.601261i
$698$	−28.3576	−	9.10734i	−1.07335	−	0.344718i
$699$		0			0
$700$	−3.76226	−	22.7505i	−0.142200	−	0.859887i
$701$	12.3452	+	29.8040i	0.466272	+	1.12568i	0.965778	+	0.259369i	$0.0835147\pi$
$701$	12.3452	+	29.8040i	0.466272	+	1.12568i	−0.499506	+	0.866310i	$0.666485\pi$
$702$		0			0
$703$		−	18.9634i		−	0.715217i
$704$	3.62416	+	36.5017i	0.136590	+	1.37571i
$705$		0			0
$706$	−26.4227	+	31.1510i	−0.994430	+	1.17239i
$707$	1.32050	−	0.546971i	0.0496627	−	0.0205710i
$708$		0			0
$709$	6.65689	−	16.0712i	0.250005	−	0.603565i	−0.748199	−	0.663474i	$-0.769081\pi$
$709$	6.65689	−	16.0712i	0.250005	−	0.603565i	0.998204	+	0.0599095i	$0.0190812\pi$
$710$	0.597600	−	1.86075i	0.0224275	−	0.0698328i
$711$		0			0
$712$	−5.89456	−	23.4931i	−0.220908	−	0.880442i
$713$	52.8157	+	52.8157i	1.97796	+	1.97796i
$714$		0			0
$715$	−3.54442	+	8.55698i	−0.132554	+	0.320013i
$716$	−13.0440	+	8.11604i	−0.487478	+	0.303311i
$717$		0			0
$718$	−3.58537	−	43.6561i	−0.133805	−	1.62923i
$719$		−	9.06929i		−	0.338228i	−0.985597	−	0.169114i	$-0.945909\pi$
$719$		−	9.06929i		−	0.338228i	0.985597	−	0.169114i	$-0.0540905\pi$
$720$		0			0
$721$			5.22799i			0.194701i
$722$	0.276616	−	0.0227178i	0.0102946	−	0.000845470i
$723$		0			0
$724$	4.30798	−	18.4979i	0.160105	−	0.687469i
$725$	−5.43616	+	13.1241i	−0.201894	+	0.487415i
$726$		0			0
$727$	4.93965	+	4.93965i	0.183201	+	0.183201i	0.792749	−	0.609548i	$-0.208649\pi$
$727$	4.93965	+	4.93965i	0.183201	+	0.183201i	−0.609548	+	0.792749i	$0.708649\pi$
$728$	−12.3815	+	9.19033i	−0.458890	+	0.340616i
$729$		0			0
$730$	14.0108	+	4.49971i	0.518562	+	0.166542i
$731$	−18.8141	+	45.4212i	−0.695864	+	1.67997i
$732$		0			0
$733$	18.9279	−	7.84021i	0.699119	−	0.289585i	−0.00467439	−	0.999989i	$-0.501488\pi$
$733$	18.9279	−	7.84021i	0.699119	−	0.289585i	0.703794	+	0.710404i	$0.251488\pi$
$734$	−4.61589	−	3.91525i	−0.170376	−	0.144515i
$735$		0			0
$736$	35.3734	−	15.3626i	1.30388	−	0.566271i
$737$			58.6678i			2.16106i
$738$		0			0
$739$	−8.94853	−	21.6037i	−0.329177	−	0.794704i	−0.998654	−	0.0518708i	$-0.983482\pi$
$739$	−8.94853	−	21.6037i	−0.329177	−	0.794704i	0.669477	−	0.742833i	$-0.266518\pi$
$740$	8.53402	+	6.11200i	0.313717	+	0.224682i
$741$		0			0
$742$	−13.9584	+	43.4623i	−0.512429	+	1.59555i
$743$	34.2959	+	34.2959i	1.25819	+	1.25819i	0.951955	+	0.306239i	$0.0990708\pi$
$743$	34.2959	+	34.2959i	1.25819	+	1.25819i	0.306239	+	0.951955i	$0.400929\pi$
$744$		0			0
$745$	−4.90369	+	4.90369i	−0.179657	+	0.179657i
$746$	1.14727	+	2.23282i	0.0420045	+	0.0817494i
$747$		0			0
$748$	−11.9771	+	51.4281i	−0.437926	+	1.88040i
$749$	27.9147	−	11.5626i	1.01998	−	0.422490i
$750$		0			0
$751$	−8.46502			−0.308893			−0.154446	−	0.988001i	$-0.549359\pi$
$751$	−8.46502			−0.308893			−0.154446	+	0.988001i	$0.549359\pi$
$752$	−3.93521	−	11.5728i	−0.143502	−	0.422015i
$753$		0			0
$754$	9.46711	−	0.777511i	0.344772	−	0.0283153i
$755$	5.11870	+	12.3576i	0.186289	+	0.449740i
$756$		0			0
$757$	−38.2928	−	15.8614i	−1.39178	−	0.576493i	−0.444173	−	0.895941i	$-0.646502\pi$
$757$	−38.2928	−	15.8614i	−1.39178	−	0.576493i	−0.947604	+	0.319449i	$0.896502\pi$
$758$	−17.2045	−	33.4836i	−0.624897	−	1.21618i
$759$		0			0
$760$	7.56261	−	12.6287i	0.274325	−	0.458092i
$761$	0.833887	−	0.833887i	0.0302284	−	0.0302284i	−0.691831	−	0.722059i	$-0.743196\pi$
$761$	0.833887	−	0.833887i	0.0302284	−	0.0302284i	0.722059	+	0.691831i	$0.243196\pi$
$762$		0			0
$763$	−30.9164	−	12.8060i	−1.11925	−	0.463608i
$764$	3.69344	+	22.3343i	0.133624	+	0.808028i
$765$		0			0
$766$	9.64229	+	8.17870i	0.348390	+	0.295508i
$767$	10.9527			0.395480
$768$		0			0
$769$	−32.1393			−1.15897			−0.579486	−	0.814982i	$-0.696747\pi$
$769$	−32.1393			−1.15897			−0.579486	+	0.814982i	$0.696747\pi$
$770$	19.2234	+	16.3055i	0.692762	+	0.587608i
$771$		0			0
$772$	−0.328719	−	1.98777i	−0.0118309	−	0.0715415i
$773$	28.3337	+	11.7362i	1.01909	+	0.422122i	0.828764	−	0.559598i	$-0.189045\pi$
$773$	28.3337	+	11.7362i	1.01909	+	0.422122i	0.190329	+	0.981720i	$0.439045\pi$
$774$		0			0
$775$	27.5767	−	27.5767i	0.990585	−	0.990585i
$776$	16.7237	−	27.9268i	0.600347	−	1.00251i
$777$		0			0
$778$	18.4616	+	35.9300i	0.661880	+	1.28815i
$779$	−15.6187	−	6.46949i	−0.559599	−	0.231794i
$780$		0			0
$781$	−2.02042	−	4.87773i	−0.0722964	−	0.174539i
$782$	55.3304	−	4.54415i	1.97861	−	0.162499i
$783$		0			0
$784$	4.49606	+	13.2221i	0.160574	+	0.472219i
$785$	−16.7059			−0.596261
$786$		0			0
$787$	17.1011	−	7.08351i	0.609588	−	0.252500i	−0.0564642	−	0.998405i	$-0.517983\pi$
$787$	17.1011	−	7.08351i	0.609588	−	0.252500i	0.666052	+	0.745905i	$0.267983\pi$
$788$	−2.38221	+	10.2289i	−0.0848628	+	0.364390i

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07850 - 0.914792i) q^{2} +(0.326309 + 1.97320i) q^{4} +(1.10881 + 0.459283i) q^{5} +(2.29035 - 2.29035i) q^{7} +(1.45315 - 2.42660i) q^{8} +O(q^{10})\)	\(q+(-1.07850 - 0.914792i) q^{2} +(0.326309 + 1.97320i) q^{4} +(1.10881 + 0.459283i) q^{5} +(2.29035 - 2.29035i) q^{7} +(1.45315 - 2.42660i) q^{8} +(-0.775695 - 1.50966i) q^{10} +(-4.23612 - 1.75466i) q^{11} +(-0.644097 - 1.55499i) q^{13} +(-4.56533 + 0.374940i) q^{14} +(-3.78704 + 1.28775i) q^{16} -5.75819 q^{17} +(4.00625 - 1.65944i) q^{19} +(-0.544443 + 2.33777i) q^{20} +(2.96349 + 5.76757i) q^{22} +(4.82067 - 4.82067i) q^{23} +(-2.51702 - 2.51702i) q^{25} +(-0.727835 + 2.26626i) q^{26} +(5.26669 + 3.77196i) q^{28} +(-1.52718 - 3.68694i) q^{29} +10.9561i q^{31} +(5.26234 + 2.07553i) q^{32} +(6.21019 + 5.26755i) q^{34} +(3.59147 - 1.48764i) q^{35} +(1.67353 - 4.04025i) q^{37} +(-5.83877 - 1.87518i) q^{38} +(2.72575 - 2.02322i) q^{40} +(-2.75672 - 2.75672i) q^{41} +(3.26736 - 7.88810i) q^{43} +(2.08001 - 8.93129i) q^{44} +(-9.60899 + 0.789163i) q^{46} +3.05588i q^{47} -3.49141i q^{49} +(0.412047 + 5.01715i) q^{50} +(2.85813 - 1.77834i) q^{52} +(3.81361 - 9.20688i) q^{53} +(-3.89116 - 3.89116i) q^{55} +(-2.22954 - 8.88597i) q^{56} +(-1.72573 + 5.37340i) q^{58} +(-2.49029 + 6.01210i) q^{59} +(4.36611 - 1.80850i) q^{61} +(10.0225 - 11.8161i) q^{62} +(-3.77673 - 7.05240i) q^{64} -2.02000i q^{65} +(-4.89651 - 11.8212i) q^{67} +(-1.87895 - 11.3621i) q^{68} +(-5.23427 - 1.68104i) q^{70} +(0.814206 + 0.814206i) q^{71} +(-6.13068 + 6.13068i) q^{73} +(-5.50089 + 2.82647i) q^{74} +(4.58169 + 7.36364i) q^{76} +(-13.7210 + 5.68342i) q^{77} -7.99746 q^{79} +(-4.79054 - 0.311461i) q^{80} +(0.451287 + 5.49495i) q^{82} +(4.51997 + 10.9122i) q^{83} +(-6.38472 - 2.64464i) q^{85} +(-10.7398 + 5.51834i) q^{86} +(-10.4136 + 7.72958i) q^{88} +(6.05533 - 6.05533i) q^{89} +(-5.03667 - 2.08626i) q^{91} +(11.0852 + 7.93912i) q^{92} +(2.79550 - 3.29576i) q^{94} +5.20430 q^{95} +11.5086 q^{97} +(-3.19392 + 3.76548i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) \) 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

Introduction

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