LMFDB - Embedded newform 450.2.h.e.91.2

Newspace parameters

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.h (of order $5$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.58140625.2
Defining polynomial:	$x^{8} - 3 x^{7} + 4 x^{6} - 7 x^{5} + 11 x^{4} + 5 x^{3} - 10 x^{2} - 25 x + 25$
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.2
Root			$-0.357358 - 1.86824i$ of defining polynomial
Character	$\chi$	$=$	450.91
Dual form			450.2.h.e.361.2

$q$-expansion

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(2.02373 + 0.951057i) q^{5} +3.77447 q^{7} +(-0.309017 + 0.951057i) q^{8} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(2.02373 + 0.951057i) q^{5} +3.77447 q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.07822 + 1.95894i) q^{10} +(-3.05361 - 2.21858i) q^{11} +(-2.56969 + 1.86699i) q^{13} +(3.05361 + 2.21858i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.430307 - 1.32435i) q^{17} +(1.20945 - 3.72230i) q^{19} +(-0.279141 + 2.21858i) q^{20} +(-1.16637 - 3.58973i) q^{22} +(0.720859 + 0.523735i) q^{23} +(3.19098 + 3.84937i) q^{25} -3.17632 q^{26} +(1.16637 + 3.58973i) q^{28} +(-0.0152089 - 0.0468081i) q^{29} +(-1.72466 + 5.30795i) q^{31} -1.00000 q^{32} +(1.12656 - 0.818492i) q^{34} +(7.63851 + 3.58973i) q^{35} +(-5.70152 + 4.14240i) q^{37} +(3.16637 - 2.30051i) q^{38} +(-1.52988 + 1.63079i) q^{40} +(-1.20477 + 0.875319i) q^{41} +2.69767 q^{43} +(1.16637 - 3.58973i) q^{44} +(0.275344 + 0.847421i) q^{46} +(-1.16637 - 3.58973i) q^{47} +7.24660 q^{49} +(0.318958 + 4.98982i) q^{50} +(-2.56969 - 1.86699i) q^{52} +(-3.58963 - 11.0477i) q^{53} +(-4.06969 - 7.39396i) q^{55} +(-1.16637 + 3.58973i) q^{56} +(0.0152089 - 0.0468081i) q^{58} +(-0.558282 + 0.405615i) q^{59} +(-8.38168 - 6.08965i) q^{61} +(-4.51521 + 3.28049i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(-6.97599 + 1.33437i) q^{65} +(4.73519 - 14.5734i) q^{67} +1.39250 q^{68} +(4.06969 + 7.39396i) q^{70} +(2.06969 + 6.36986i) q^{71} +(-4.18158 - 3.03810i) q^{73} -7.04746 q^{74} +3.91385 q^{76} +(-11.5257 - 8.37394i) q^{77} +(-0.558282 - 1.71821i) q^{79} +(-2.19625 + 0.420099i) q^{80} -1.48918 q^{82} +(3.08023 - 9.47997i) q^{83} +(2.13035 - 2.27088i) q^{85} +(2.18246 + 1.58565i) q^{86} +(3.05361 - 2.21858i) q^{88} +(11.7390 + 8.52891i) q^{89} +(-9.69922 + 7.04690i) q^{91} +(-0.275344 + 0.847421i) q^{92} +(1.16637 - 3.58973i) q^{94} +(5.98771 - 6.38268i) q^{95} +(-0.0278640 - 0.0857567i) q^{97} +(5.86263 + 4.25945i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8q + 2q^{2} - 2q^{4} + 4q^{7} + 2q^{8} + O(q^{10}) $	$ 8q + 2q^{2} - 2q^{4} + 4q^{7} + 2q^{8} - q^{11} - 13q^{13} + q^{14} - 2q^{16} + 11q^{17} + 20q^{19} - 5q^{20} + q^{22} + 3q^{23} + 30q^{25} - 22q^{26} - q^{28} + 15q^{29} - 9q^{31} - 8q^{32} - q^{34} + 15q^{35} - 6q^{37} + 15q^{38} - 5q^{40} + 9q^{41} + 12q^{43} - q^{44} + 7q^{46} + q^{47} - 4q^{49} + 5q^{50} - 13q^{52} - 7q^{53} - 25q^{55} + q^{56} - 15q^{58} - 10q^{59} + 6q^{61} - 21q^{62} - 2q^{64} + 10q^{65} - 11q^{67} - 24q^{68} + 25q^{70} + 9q^{71} - 8q^{73} - 24q^{74} - 10q^{76} - 33q^{77} - 10q^{79} + 26q^{82} - 27q^{83} + 5q^{85} + 23q^{86} + q^{88} + 15q^{89} + q^{91} - 7q^{92} - q^{94} + 30q^{95} - 36q^{97} + 19q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	2.02373	+	0.951057i	0.905040	+	0.425325i
$5$	2.02373	+	0.951057i	0.905040	+	0.425325i
$6$		0			0
$7$	3.77447			1.42661			0.713307	−	0.700851i	$-0.247196\pi$
$7$	3.77447			1.42661			0.713307	+	0.700851i	$0.247196\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$		0			0
$10$	1.07822	+	1.95894i	0.340962	+	0.619471i
$11$	−3.05361	−	2.21858i	−0.920698	−	0.668926i	0.0230000	−	0.999735i	$-0.492678\pi$
$11$	−3.05361	−	2.21858i	−0.920698	−	0.668926i	−0.943698	+	0.330810i	$0.892678\pi$
$12$		0			0
$13$	−2.56969	+	1.86699i	−0.712705	+	0.517810i	−0.884045	−	0.467402i	$-0.845190\pi$
$13$	−2.56969	+	1.86699i	−0.712705	+	0.517810i	0.171340	+	0.985212i	$0.445190\pi$
$14$	3.05361	+	2.21858i	0.816111	+	0.592939i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.430307	−	1.32435i	0.104365	−	0.321201i	−0.885216	−	0.465180i	$-0.845990\pi$
$17$	0.430307	−	1.32435i	0.104365	−	0.321201i	0.989581	+	0.143979i	$0.0459896\pi$
$18$		0			0
$19$	1.20945	−	3.72230i	0.277466	−	0.853953i	−0.711090	−	0.703101i	$-0.751798\pi$
$19$	1.20945	−	3.72230i	0.277466	−	0.853953i	0.988556	−	0.150852i	$-0.0482018\pi$
$20$	−0.279141	+	2.21858i	−0.0624178	+	0.496089i
$21$		0			0
$22$	−1.16637	−	3.58973i	−0.248672	−	0.765333i
$23$	0.720859	+	0.523735i	0.150310	+	0.109206i	0.660398	−	0.750916i	$-0.270387\pi$
$23$	0.720859	+	0.523735i	0.150310	+	0.109206i	−0.510089	+	0.860122i	$0.670387\pi$
$24$		0			0
$25$	3.19098	+	3.84937i	0.638197	+	0.769873i
$26$	−3.17632			−0.622927
$27$		0			0
$28$	1.16637	+	3.58973i	0.220424	+	0.678396i
$29$	−0.0152089	−	0.0468081i	−0.00282422	−	0.00869205i	0.949634	−	0.313360i	$-0.101455\pi$
$29$	−0.0152089	−	0.0468081i	−0.00282422	−	0.00869205i	−0.952459	+	0.304668i	$0.901455\pi$
$30$		0			0
$31$	−1.72466	+	5.30795i	−0.309757	+	0.953335i	0.668102	+	0.744070i	$0.267107\pi$
$31$	−1.72466	+	5.30795i	−0.309757	+	0.953335i	−0.977859	+	0.209265i	$0.932893\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	1.12656	−	0.818492i	0.193203	−	0.140370i
$35$	7.63851	+	3.58973i	1.29114	+	0.606775i
$36$		0			0
$37$	−5.70152	+	4.14240i	−0.937324	+	0.681006i	−0.947775	−	0.318940i	$-0.896673\pi$
$37$	−5.70152	+	4.14240i	−0.937324	+	0.681006i	0.0104512	+	0.999945i	$0.496673\pi$
$38$	3.16637	−	2.30051i	0.513654	−	0.373191i
$39$		0			0
$40$	−1.52988	+	1.63079i	−0.241895	+	0.257851i
$41$	−1.20477	+	0.875319i	−0.188154	+	0.136702i	−0.677875	−	0.735178i	$-0.737099\pi$
$41$	−1.20477	+	0.875319i	−0.188154	+	0.136702i	0.489721	+	0.871879i	$0.337099\pi$
$42$		0			0
$43$	2.69767			0.411391			0.205695	−	0.978616i	$-0.434054\pi$
$43$	2.69767			0.411391			0.205695	+	0.978616i	$0.434054\pi$
$44$	1.16637	−	3.58973i	0.175838	−	0.541172i
$45$		0			0
$46$	0.275344	+	0.847421i	0.0405972	+	0.124945i
$47$	−1.16637	−	3.58973i	−0.170133	−	0.523616i	0.829245	−	0.558886i	$-0.188771\pi$
$47$	−1.16637	−	3.58973i	−0.170133	−	0.523616i	−0.999378	+	0.0352696i	$0.988771\pi$
$48$		0			0
$49$	7.24660			1.03523
$50$	0.318958	+	4.98982i	0.0451075	+	0.705667i
$51$		0			0
$52$	−2.56969	−	1.86699i	−0.356352	−	0.258905i
$53$	−3.58963	−	11.0477i	−0.493073	−	1.51752i	−0.819938	−	0.572453i	$-0.805992\pi$
$53$	−3.58963	−	11.0477i	−0.493073	−	1.51752i	0.326864	−	0.945071i	$-0.394008\pi$
$54$		0			0
$55$	−4.06969	−	7.39396i	−0.548757	−	0.997001i
$56$	−1.16637	+	3.58973i	−0.155863	+	0.479698i
$57$		0			0
$58$	0.0152089	−	0.0468081i	0.00199702	−	0.00614620i
$59$	−0.558282	+	0.405615i	−0.0726821	+	0.0528066i	−0.623533	−	0.781797i	$-0.714303\pi$
$59$	−0.558282	+	0.405615i	−0.0726821	+	0.0528066i	0.550851	+	0.834604i	$0.314303\pi$
$60$		0			0
$61$	−8.38168	−	6.08965i	−1.07316	−	0.779700i	−0.0966862	−	0.995315i	$-0.530824\pi$
$61$	−8.38168	−	6.08965i	−1.07316	−	0.779700i	−0.976478	+	0.215615i	$0.930824\pi$
$62$	−4.51521	+	3.28049i	−0.573432	+	0.416623i
$63$		0			0
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−6.97599	+	1.33437i	−0.865265	+	0.165508i
$66$		0			0
$67$	4.73519	−	14.5734i	0.578496	−	1.78043i	−0.0454589	−	0.998966i	$-0.514475\pi$
$67$	4.73519	−	14.5734i	0.578496	−	1.78043i	0.623955	−	0.781461i	$-0.285525\pi$
$68$	1.39250			0.168866
$69$		0			0
$70$	4.06969	+	7.39396i	0.486421	+	0.883747i
$71$	2.06969	+	6.36986i	0.245627	+	0.755963i	0.995533	+	0.0944182i	$0.0300991\pi$
$71$	2.06969	+	6.36986i	0.245627	+	0.755963i	−0.749905	+	0.661545i	$0.769901\pi$
$72$		0			0
$73$	−4.18158	−	3.03810i	−0.489417	−	0.355582i	0.315543	−	0.948911i	$-0.397813\pi$
$73$	−4.18158	−	3.03810i	−0.489417	−	0.355582i	−0.804960	+	0.593329i	$0.797813\pi$
$74$	−7.04746			−0.819251
$75$		0			0
$76$	3.91385			0.448950
$77$	−11.5257	−	8.37394i	−1.31348	−	0.954299i
$78$		0			0
$79$	−0.558282	−	1.71821i	−0.0628116	−	0.193314i	0.914726	−	0.404074i	$-0.132406\pi$
$79$	−0.558282	−	1.71821i	−0.0628116	−	0.193314i	−0.977538	+	0.210760i	$0.932406\pi$
$80$	−2.19625	+	0.420099i	−0.245548	+	0.0469685i
$81$		0			0
$82$	−1.48918			−0.164453
$83$	3.08023	−	9.47997i	0.338099	−	1.04056i	−0.627076	−	0.778958i	$-0.715749\pi$
$83$	3.08023	−	9.47997i	0.338099	−	1.04056i	0.965175	−	0.261604i	$-0.0842514\pi$
$84$		0			0
$85$	2.13035	−	2.27088i	0.231069	−	0.246311i
$86$	2.18246	+	1.58565i	0.235341	+	0.170985i
$87$		0			0
$88$	3.05361	−	2.21858i	0.325516	−	0.236501i
$89$	11.7390	+	8.52891i	1.24434	+	0.904063i	0.997879	−	0.0650909i	$-0.0207337\pi$
$89$	11.7390	+	8.52891i	1.24434	+	0.904063i	0.246457	+	0.969154i	$0.420734\pi$
$90$		0			0
$91$	−9.69922	+	7.04690i	−1.01675	+	0.738716i
$92$	−0.275344	+	0.847421i	−0.0287066	+	0.0883497i
$93$		0			0
$94$	1.16637	−	3.58973i	0.120302	−	0.370253i
$95$	5.98771	−	6.38268i	0.614326	−	0.654849i
$96$		0			0
$97$	−0.0278640	−	0.0857567i	−0.00282917	−	0.00870727i	0.949632	−	0.313367i	$-0.101457\pi$
$97$	−0.0278640	−	0.0857567i	−0.00282917	−	0.00870727i	−0.952461	+	0.304660i	$0.901457\pi$
$98$	5.86263	+	4.25945i	0.592215	+	0.430269i
$99$		0			0
$100$	−2.67490	+	4.22433i	−0.267490	+	0.422433i
$101$	−16.3785			−1.62972			−0.814859	−	0.579659i	$-0.803186\pi$
$101$	−16.3785			−1.62972			−0.814859	+	0.579659i	$0.803186\pi$
$102$		0			0
$103$	−0.375822	−	1.15666i	−0.0370308	−	0.113969i	0.930832	−	0.365446i	$-0.119084\pi$
$103$	−0.375822	−	1.15666i	−0.0370308	−	0.113969i	−0.967863	+	0.251477i	$0.919084\pi$
$104$	−0.981536	−	3.02086i	−0.0962475	−	0.296219i
$105$		0			0
$106$	3.58963	−	11.0477i	0.348656	−	1.07305i
$107$	10.8125			1.04528			0.522641	−	0.852553i	$-0.324947\pi$
$107$	10.8125			1.04528			0.522641	+	0.852553i	$0.324947\pi$
$108$		0			0
$109$	−9.23519	+	6.70976i	−0.884571	+	0.642678i	−0.934457	−	0.356077i	$-0.884114\pi$
$109$	−9.23519	+	6.70976i	−0.884571	+	0.642678i	0.0498859	+	0.998755i	$0.484114\pi$
$110$	1.05361	−	8.37394i	0.100458	−	0.798424i
$111$		0			0
$112$	−3.05361	+	2.21858i	−0.288539	+	0.209636i
$113$	−8.43232	+	6.12644i	−0.793246	+	0.576327i	−0.908925	−	0.416960i	$-0.863096\pi$
$113$	−8.43232	+	6.12644i	−0.793246	+	0.576327i	0.115679	+	0.993287i	$0.463096\pi$
$114$		0			0
$115$	0.960724	+	1.74548i	0.0895880	+	0.162767i
$116$	0.0398173	−	0.0289290i	0.00369695	−	0.00268599i
$117$		0			0
$118$	−0.690074			−0.0635265
$119$	1.62418	−	4.99871i	0.148888	−	0.458231i
$120$		0			0
$121$	1.00326	+	3.08770i	0.0912051	+	0.280700i
$122$	−3.20152	−	9.85326i	−0.289852	−	0.892072i
$123$		0			0
$124$	−5.58111			−0.501198
$125$	2.79673	+	10.8249i	0.250147	+	0.968208i
$126$		0			0
$127$	2.87115	+	2.08601i	0.254773	+	0.185104i	0.707840	−	0.706373i	$-0.249670\pi$
$127$	2.87115	+	2.08601i	0.254773	+	0.185104i	−0.453066	+	0.891477i	$0.649670\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$		0			0
$130$	−6.42801	−	3.02086i	−0.563774	−	0.264947i
$131$	−1.25252	+	3.85486i	−0.109433	+	0.336801i	−0.990745	−	0.135734i	$-0.956661\pi$
$131$	−1.25252	+	3.85486i	−0.109433	+	0.336801i	0.881312	+	0.472535i	$0.156661\pi$
$132$		0			0
$133$	4.56502	−	14.0497i	0.395837	−	1.21826i
$134$	12.3969	−	9.00687i	1.07093	−	0.778075i
$135$		0			0
$136$	1.12656	+	0.818492i	0.0966015	+	0.0701851i
$137$	−2.88636	+	2.09706i	−0.246598	+	0.179164i	−0.704218	−	0.709984i	$-0.748702\pi$
$137$	−2.88636	+	2.09706i	−0.246598	+	0.179164i	0.457620	+	0.889148i	$0.348702\pi$
$138$		0			0
$139$	8.04650	+	5.84613i	0.682495	+	0.495862i	0.874185	−	0.485594i	$-0.161397\pi$
$139$	8.04650	+	5.84613i	0.682495	+	0.495862i	−0.191689	+	0.981456i	$0.561397\pi$
$140$	−1.05361	+	8.37394i	−0.0890461	+	0.707727i
$141$		0			0
$142$	−2.06969	+	6.36986i	−0.173685	+	0.534547i
$143$	11.9889			1.00256
$144$		0			0
$145$	0.0137385	−	0.109192i	0.00114092	−	0.00906786i
$146$	−1.59722	−	4.91575i	−0.132187	−	0.406830i
$147$		0			0
$148$	−5.70152	−	4.14240i	−0.468662	−	0.340503i
$149$	19.5103			1.59834			0.799171	−	0.601104i	$-0.205272\pi$
$149$	19.5103			1.59834			0.799171	+	0.601104i	$0.205272\pi$
$150$		0			0
$151$	−18.4324			−1.50001			−0.750003	−	0.661435i	$-0.769948\pi$
$151$	−18.4324			−1.50001			−0.750003	+	0.661435i	$0.769948\pi$
$152$	3.16637	+	2.30051i	0.256827	+	0.186596i
$153$		0			0
$154$	−4.40244	−	13.5493i	−0.354759	−	1.09184i
$155$	−8.53840	+	9.10162i	−0.685821	+	0.731059i
$156$		0			0
$157$	10.1564			0.810572			0.405286	−	0.914190i	$-0.367172\pi$
$157$	10.1564			0.810572			0.405286	+	0.914190i	$0.367172\pi$
$158$	0.558282	−	1.71821i	0.0444145	−	0.136694i
$159$		0			0
$160$	−2.02373	−	0.951057i	−0.159990	−	0.0751876i
$161$	2.72086	+	1.97682i	0.214434	+	0.155795i
$162$		0			0
$163$	15.0481	−	10.9331i	1.17865	−	0.856343i	0.186636	−	0.982429i	$-0.440242\pi$
$163$	15.0481	−	10.9331i	1.17865	−	0.856343i	0.992019	+	0.126086i	$0.0402416\pi$
$164$	−1.20477	−	0.875319i	−0.0940770	−	0.0683510i
$165$		0			0
$166$	8.06414	−	5.85894i	0.625899	−	0.454742i
$167$	−0.671048	+	2.06527i	−0.0519273	+	0.159816i	−0.973657	−	0.228016i	$-0.926776\pi$
$167$	−0.671048	+	2.06527i	−0.0519273	+	0.159816i	0.921730	+	0.387832i	$0.126776\pi$
$168$		0			0
$169$	−0.899554	+	2.76854i	−0.0691965	+	0.212965i
$170$	3.05828	−	0.584988i	0.234560	−	0.0448666i
$171$		0			0
$172$	0.833625	+	2.56564i	0.0635633	+	0.195628i
$173$	−5.17306	−	3.75845i	−0.393300	−	0.285750i	0.373506	−	0.927628i	$-0.378155\pi$
$173$	−5.17306	−	3.75845i	−0.393300	−	0.285750i	−0.766807	+	0.641878i	$0.778155\pi$
$174$		0			0
$175$	12.0443	+	14.5293i	0.910461	+	1.09831i
$176$	3.77447			0.284511
$177$		0			0
$178$	4.48391	+	13.8001i	0.336084	+	1.03436i
$179$	−2.47630	−	7.62127i	−0.185087	−	0.569640i	0.814862	−	0.579654i	$-0.196812\pi$
$179$	−2.47630	−	7.62127i	−0.185087	−	0.569640i	−0.999950	+	0.0100140i	$0.996812\pi$
$180$		0			0
$181$	−3.35682	+	10.3312i	−0.249510	+	0.767913i	0.745352	+	0.666671i	$0.232282\pi$
$181$	−3.35682	+	10.3312i	−0.249510	+	0.767913i	−0.994862	+	0.101242i	$0.967718\pi$
$182$	−11.9889			−0.888676
$183$		0			0
$184$	−0.720859	+	0.523735i	−0.0531424	+	0.0386102i
$185$	−15.4780	+	2.96063i	−1.13797	+	0.217670i
$186$		0			0
$187$	−4.25215	+	3.08937i	−0.310948	+	0.225917i
$188$	3.05361	−	2.21858i	0.222707	−	0.161806i
$189$		0			0
$190$	8.59580	−	1.64421i	0.623605	−	0.119283i
$191$	−6.62243	+	4.81147i	−0.479182	+	0.348146i	−0.801009	−	0.598652i	$-0.795703\pi$
$191$	−6.62243	+	4.81147i	−0.479182	+	0.348146i	0.321827	+	0.946798i	$0.395703\pi$
$192$		0			0
$193$	−17.5576			−1.26382			−0.631912	−	0.775040i	$-0.717730\pi$
$193$	−17.5576			−1.26382			−0.631912	+	0.775040i	$0.717730\pi$
$194$	0.0278640	−	0.0857567i	0.00200052	−	0.00615697i
$195$		0			0
$196$	2.23932	+	6.89193i	0.159952	+	0.492281i
$197$	−1.47012	−	4.52458i	−0.104742	−	0.322363i	0.884928	−	0.465728i	$-0.154208\pi$
$197$	−1.47012	−	4.52458i	−0.104742	−	0.322363i	−0.989670	+	0.143365i	$0.954208\pi$
$198$		0			0
$199$	14.5320			1.03015			0.515073	−	0.857146i	$-0.327765\pi$
$199$	14.5320			1.03015			0.515073	+	0.857146i	$0.327765\pi$
$200$	−4.64703	+	1.84529i	−0.328595	+	0.130481i
$201$		0			0
$202$	−13.2505	−	9.62702i	−0.932299	−	0.677355i
$203$	−0.0574054	−	0.176676i	−0.00402907	−	0.0124002i
$204$		0			0
$205$	−3.27062	+	0.625604i	−0.228430	+	0.0436941i
$206$	0.375822	−	1.15666i	0.0261848	−	0.0805884i
$207$		0			0
$208$	0.981536	−	3.02086i	0.0680572	−	0.209459i
$209$	−11.9514	+	8.68318i	−0.826694	+	0.600628i
$210$		0			0
$211$	11.4362	+	8.30886i	0.787298	+	0.572006i	0.907160	−	0.420785i	$-0.138245\pi$
$211$	11.4362	+	8.30886i	0.787298	+	0.572006i	−0.119862	+	0.992791i	$0.538245\pi$
$212$	9.39777	−	6.82788i	0.645441	−	0.468941i
$213$		0			0
$214$	8.74748	+	6.35542i	0.597965	+	0.434447i
$215$	5.45936	+	2.56564i	0.372325	+	0.174975i
$216$		0			0
$217$	−6.50966	+	20.0347i	−0.441904	+	1.36004i
$218$	−11.4153			−0.773143
$219$		0			0
$220$	5.77447	−	6.15537i	0.389315	−	0.414995i
$221$	1.36679	+	4.20655i	0.0919402	+	0.282963i
$222$		0			0
$223$	−3.73139	−	2.71102i	−0.249873	−	0.181543i	0.455798	−	0.890083i	$-0.349354\pi$
$223$	−3.73139	−	2.71102i	−0.249873	−	0.181543i	−0.705670	+	0.708540i	$0.749354\pi$
$224$	−3.77447			−0.252192
$225$		0			0
$226$	−10.4229			−0.693322
$227$	−5.08578	−	3.69503i	−0.337555	−	0.245248i	0.406075	−	0.913840i	$-0.366897\pi$
$227$	−5.08578	−	3.69503i	−0.337555	−	0.245248i	−0.743630	+	0.668592i	$0.766897\pi$
$228$		0			0
$229$	5.48103	+	16.8689i	0.362196	+	1.11473i	0.951718	+	0.306973i	$0.0993163\pi$
$229$	5.48103	+	16.8689i	0.362196	+	1.11473i	−0.589522	+	0.807753i	$0.700684\pi$
$230$	−0.248723	+	1.97682i	−0.0164003	+	0.130348i
$231$		0			0
$232$	0.0492169			0.00323125
$233$	−0.792338	+	2.43856i	−0.0519078	+	0.159756i	−0.973650	−	0.228047i	$-0.926766\pi$
$233$	−0.792338	+	2.43856i	−0.0519078	+	0.159756i	0.921742	+	0.387803i	$0.126766\pi$
$234$		0			0
$235$	1.05361	−	8.37394i	0.0687298	−	0.546256i
$236$	−0.558282	−	0.405615i	−0.0363410	−	0.0264033i
$237$		0			0
$238$	4.25215	−	3.08937i	0.275626	−	0.200254i
$239$	7.63851	+	5.54970i	0.494094	+	0.358980i	0.806757	−	0.590884i	$-0.201221\pi$
$239$	7.63851	+	5.54970i	0.494094	+	0.358980i	−0.312662	+	0.949864i	$0.601221\pi$
$240$		0			0
$241$	23.8131	−	17.3012i	1.53394	−	1.11447i	0.579940	−	0.814659i	$-0.303076\pi$
$241$	23.8131	−	17.3012i	1.53394	−	1.11447i	0.953998	−	0.299812i	$-0.0969240\pi$
$242$	−1.00326	+	3.08770i	−0.0644917	+	0.198485i
$243$		0			0
$244$	3.20152	−	9.85326i	0.204956	−	0.630790i
$245$	14.6652	+	6.89193i	0.936924	+	0.440309i
$246$		0			0
$247$	3.84159	+	11.8232i	0.244434	+	0.752292i
$248$	−4.51521	−	3.28049i	−0.286716	−	0.208311i
$249$		0			0
$250$	−4.10011	+	10.4014i	−0.259314	+	0.657842i
$251$	6.00759			0.379196			0.189598	−	0.981862i	$-0.439282\pi$
$251$	6.00759			0.379196			0.189598	+	0.981862i	$0.439282\pi$
$252$		0			0
$253$	−1.03928	−	3.19856i	−0.0653387	−	0.201092i
$254$	1.09668	+	3.37524i	0.0688119	+	0.211781i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	13.6286			0.850127			0.425063	−	0.905164i	$-0.360252\pi$
$257$	13.6286			0.850127			0.425063	+	0.905164i	$0.360252\pi$
$258$		0			0
$259$	−21.5202	+	15.6353i	−1.33720	+	0.971533i
$260$	−3.42476	−	6.22221i	−0.212394	−	0.385885i
$261$		0			0
$262$	−3.27914	+	2.38244i	−0.202586	+	0.147187i
$263$	−7.41298	+	5.38584i	−0.457104	+	0.332105i	−0.792394	−	0.610010i	$-0.791166\pi$
$263$	−7.41298	+	5.38584i	−0.457104	+	0.332105i	0.335290	+	0.942115i	$0.391166\pi$
$264$		0			0
$265$	3.24258	−	25.7716i	0.199190	−	1.58314i
$266$	11.9514	−	8.68318i	0.732786	−	0.532400i
$267$		0			0
$268$	15.3234			0.936026
$269$	−8.68419	+	26.7272i	−0.529484	+	1.62959i	0.225790	+	0.974176i	$0.427504\pi$
$269$	−8.68419	+	26.7272i	−0.529484	+	1.62959i	−0.755274	+	0.655409i	$0.772496\pi$
$270$		0			0
$271$	−2.81162	−	8.65329i	−0.170794	−	0.525650i	0.828623	−	0.559808i	$-0.189125\pi$
$271$	−2.81162	−	8.65329i	−0.170794	−	0.525650i	−0.999416	+	0.0341581i	$0.989125\pi$
$272$	0.430307	+	1.32435i	0.0260912	+	0.0803004i
$273$		0			0
$274$	−3.56773			−0.215535
$275$	−1.20390	−	18.8339i	−0.0725977	−	1.13573i
$276$		0			0
$277$	−15.2006	−	11.0439i	−0.913318	−	0.663564i	0.0285338	−	0.999593i	$-0.490916\pi$
$277$	−15.2006	−	11.0439i	−0.913318	−	0.663564i	−0.941852	+	0.336028i	$0.890916\pi$
$278$	3.07349	+	9.45923i	0.184336	+	0.567327i
$279$		0			0
$280$	−5.77447	+	6.15537i	−0.345090	+	0.367854i
$281$	−2.43554	+	7.49583i	−0.145292	+	0.447164i	−0.997048	−	0.0767748i	$-0.975538\pi$
$281$	−2.43554	+	7.49583i	−0.145292	+	0.447164i	0.851756	+	0.523938i	$0.175538\pi$
$282$		0			0
$283$	−5.65496	+	17.4042i	−0.336153	+	1.03457i	0.629999	+	0.776596i	$0.283055\pi$
$283$	−5.65496	+	17.4042i	−0.336153	+	1.03457i	−0.966151	+	0.257975i	$0.916945\pi$
$284$	−5.41853	+	3.93679i	−0.321530	+	0.233606i
$285$		0			0
$286$	9.69922	+	7.04690i	0.573527	+	0.416692i
$287$	−4.54738	+	3.30386i	−0.268423	+	0.195021i
$288$		0			0
$289$	12.1846	+	8.85260i	0.716739	+	0.520741i
$290$	0.0752958	−	0.0802625i	0.00442152	−	0.00471318i
$291$		0			0
$292$	1.59722	−	4.91575i	0.0934704	−	0.287672i
$293$	29.4990			1.72335			0.861675	−	0.507461i	$-0.169416\pi$
$293$	29.4990			1.72335			0.861675	+	0.507461i	$0.169416\pi$
$294$		0			0
$295$	−1.51558	+	0.289899i	−0.0882402	+	0.0168786i
$296$	−2.17779	−	6.70254i	−0.126581	−	0.389577i
$297$		0			0
$298$	15.7841	+	11.4678i	0.914350	+	0.664314i
$299$	−2.83020			−0.163674
$300$		0			0
$301$	10.1823			0.586896
$302$	−14.9121	−	10.8343i	−0.858095	−	0.623443i
$303$		0			0
$304$	1.20945	+	3.72230i	0.0693666	+	0.213488i
$305$	−11.1707	−	20.2953i	−0.639631	−	1.16210i
$306$		0			0
$307$	13.9131			0.794064			0.397032	−	0.917805i	$-0.370040\pi$
$307$	13.9131			0.794064			0.397032	+	0.917805i	$0.370040\pi$
$308$	4.40244	−	13.5493i	0.250852	−	0.772044i
$309$		0			0
$310$	−12.2575	+	2.34462i	−0.696180	+	0.133165i
$311$	21.0050	+	15.2610i	1.19108	+	0.865373i	0.993378	−	0.114889i	$-0.0366512\pi$
$311$	21.0050	+	15.2610i	1.19108	+	0.865373i	0.197705	+	0.980262i	$0.436651\pi$
$312$		0			0
$313$	−7.66454	+	5.56861i	−0.433225	+	0.314757i	−0.782937	−	0.622101i	$-0.786279\pi$
$313$	−7.66454	+	5.56861i	−0.433225	+	0.314757i	0.349712	+	0.936857i	$0.386279\pi$
$314$	8.21673	+	5.96980i	0.463697	+	0.336895i
$315$		0			0
$316$	1.46160	−	1.06192i	0.0822215	−	0.0597374i
$317$	−7.57321	+	23.3079i	−0.425354	+	1.30910i	0.477301	+	0.878740i	$0.341615\pi$
$317$	−7.57321	+	23.3079i	−0.425354	+	1.30910i	−0.902655	+	0.430365i	$0.858385\pi$
$318$		0			0
$319$	−0.0574054	+	0.176676i	−0.00321408	+	0.00989194i
$320$	−1.07822	−	1.95894i	−0.0602741	−	0.109508i
$321$		0			0
$322$	1.03928	+	3.19856i	0.0579166	+	0.178249i
$323$	−4.40918	−	3.20346i	−0.245333	−	0.178245i
$324$		0			0
$325$	−15.3866	−	3.93416i	−0.853494	−	0.218228i
$326$	18.6004			1.03018
$327$		0			0
$328$	−0.460183	−	1.41630i	−0.0254093	−	0.0782019i
$329$	−4.40244	−	13.5493i	−0.242715	−	0.746998i
$330$		0			0
$331$	−3.06247	+	9.42530i	−0.168328	+	0.518061i	−0.999266	−	0.0383039i	$-0.987804\pi$
$331$	−3.06247	+	9.42530i	−0.168328	+	0.518061i	0.830938	+	0.556365i	$0.187804\pi$
$332$	9.96783			0.547056
$333$		0			0
$334$	−1.75683	+	1.27641i	−0.0961293	+	0.0698420i
$335$	23.4429	−	24.9893i	1.28082	−	1.36531i
$336$		0			0
$337$	8.03812	−	5.84003i	0.437864	−	0.318127i	−0.346922	−	0.937894i	$-0.612773\pi$
$337$	8.03812	−	5.84003i	0.437864	−	0.318127i	0.784786	+	0.619767i	$0.212773\pi$
$338$	−2.35506	+	1.71105i	−0.128099	+	0.0930690i
$339$		0			0
$340$	2.81805	+	1.32435i	0.152830	+	0.0718228i
$341$	17.0425	−	12.3821i	0.922904	−	0.670529i
$342$		0			0
$343$	0.930796			0.0502583
$344$	−0.833625	+	2.56564i	−0.0449461	+	0.138330i
$345$		0			0
$346$	−1.97593	−	6.08130i	−0.106227	−	0.326933i
$347$	6.06757	+	18.6741i	0.325724	+	1.00248i	0.971113	+	0.238622i	$0.0766956\pi$
$347$	6.06757	+	18.6741i	0.325724	+	1.00248i	−0.645388	+	0.763855i	$0.723304\pi$
$348$		0			0
$349$	1.48432			0.0794538			0.0397269	−	0.999211i	$-0.487351\pi$
$349$	1.48432			0.0794538			0.0397269	+	0.999211i	$0.487351\pi$
$350$	1.20390	+	18.8339i	0.0643510	+	1.00671i
$351$		0			0
$352$	3.05361	+	2.21858i	0.162758	+	0.118251i
$353$	−3.17632	−	9.77569i	−0.169058	−	0.520308i	0.830254	−	0.557385i	$-0.188195\pi$
$353$	−3.17632	−	9.77569i	−0.169058	−	0.520308i	−0.999312	+	0.0370772i	$0.988195\pi$
$354$		0			0
$355$	−1.86959	+	14.8593i	−0.0992277	+	0.788649i
$356$	−4.48391	+	13.8001i	−0.237647	+	0.731402i
$357$		0			0
$358$	2.47630	−	7.62127i	0.130877	−	0.402797i
$359$	−8.39154	+	6.09681i	−0.442889	+	0.321777i	−0.786782	−	0.617231i	$-0.788254\pi$
$359$	−8.39154	+	6.09681i	−0.442889	+	0.321777i	0.343893	+	0.939009i	$0.388254\pi$
$360$		0			0
$361$	2.97859	+	2.16408i	0.156768	+	0.113899i
$362$	−8.78826	+	6.38504i	−0.461901	+	0.335590i
$363$		0			0
$364$	−9.69922	−	7.04690i	−0.508377	−	0.369358i
$365$	−5.57300	−	10.1252i	−0.291704	−	0.529978i
$366$		0			0
$367$	8.05741	−	24.7981i	0.420593	−	1.29445i	−0.486558	−	0.873648i	$-0.661748\pi$
$367$	8.05741	−	24.7981i	0.420593	−	1.29445i	0.907151	−	0.420804i	$-0.138252\pi$
$368$	−0.891031			−0.0464482
$369$		0			0
$370$	−14.2622	−	6.70254i	−0.741455	−	0.348448i
$371$	−13.5489	−	41.6993i	−0.703426	−	2.16492i
$372$		0			0
$373$	−7.65001	−	5.55806i	−0.396102	−	0.287785i	0.371849	−	0.928293i	$-0.378724\pi$
$373$	−7.65001	−	5.55806i	−0.396102	−	0.287785i	−0.767952	+	0.640508i	$0.778724\pi$
$374$	−5.25595			−0.271779
$375$		0			0
$376$	3.77447			0.194653
$377$	0.126472	+	0.0918876i	0.00651366	+	0.00473245i
$378$		0			0
$379$	−10.9163	−	33.5968i	−0.560731	−	1.72575i	−0.680307	−	0.732927i	$-0.738154\pi$
$379$	−10.9163	−	33.5968i	−0.560731	−	1.72575i	0.119576	−	0.992825i	$-0.461846\pi$
$380$	7.92059	+	3.72230i	0.406318	+	0.190950i
$381$		0			0
$382$	−8.18577			−0.418820
$383$	−9.21407	+	28.3580i	−0.470817	+	1.44902i	0.380700	+	0.924698i	$0.375683\pi$
$383$	−9.21407	+	28.3580i	−0.470817	+	1.44902i	−0.851517	+	0.524327i	$0.824317\pi$
$384$		0			0
$385$	−15.3609	−	27.9083i	−0.782865	−	1.42234i
$386$	−14.2044	−	10.3201i	−0.722985	−	0.525280i
$387$		0			0
$388$	0.0729490	−	0.0530006i	0.00370343	−	0.00269070i
$389$	−17.2942	−	12.5649i	−0.876848	−	0.637068i	0.0555675	−	0.998455i	$-0.482303\pi$
$389$	−17.2942	−	12.5649i	−0.876848	−	0.637068i	−0.932416	+	0.361387i	$0.882303\pi$
$390$		0			0
$391$	1.00380	−	0.729301i	0.0507642	−	0.0368824i
$392$	−2.23932	+	6.89193i	−0.113103	+	0.348095i
$393$		0			0
$394$	1.47012	−	4.52458i	0.0740638	−	0.227945i
$395$	0.504306	−	4.00816i	0.0253744	−	0.201673i
$396$		0			0
$397$	6.49555	+	19.9913i	0.326002	+	1.00333i	0.970986	+	0.239136i	$0.0768642\pi$
$397$	6.49555	+	19.9913i	0.326002	+	1.00333i	−0.644984	+	0.764196i	$0.723136\pi$
$398$	11.7566	+	8.54169i	0.589307	+	0.428156i
$399$		0			0
$400$	−4.84416	−	1.23859i	−0.242208	−	0.0619295i
$401$	−16.7820			−0.838053			−0.419026	−	0.907974i	$-0.637629\pi$
$401$	−16.7820			−0.838053			−0.419026	+	0.907974i	$0.637629\pi$
$402$		0			0
$403$	−5.47805	−	16.8597i	−0.272881	−	0.839842i
$404$	−5.06122	−	15.5768i	−0.251805	−	0.774977i
$405$		0			0
$406$	0.0574054	−	0.176676i	0.00284898	−	0.00876826i
$407$	26.6004			1.31853
$408$		0			0
$409$	−29.4165	+	21.3723i	−1.45455	+	1.05679i	−0.469809	+	0.882768i	$0.655677\pi$
$409$	−29.4165	+	21.3723i	−1.45455	+	1.05679i	−0.984741	+	0.174025i	$0.944323\pi$
$410$	−3.01371	−	1.41630i	−0.148836	−	0.0699459i
$411$		0			0
$412$	0.983915	−	0.714856i	0.0484740	−	0.0352184i
$413$	−2.10722	+	1.53098i	−0.103689	+	0.0753347i
$414$		0			0
$415$	15.2495	−	16.2554i	0.748571	−	0.797948i
$416$	2.56969	−	1.86699i	0.125990	−	0.0915368i
$417$		0			0
$418$	−14.7727			−0.722557
$419$	10.6731	−	32.8484i	0.521415	−	1.60475i	−0.249884	−	0.968276i	$-0.580392\pi$
$419$	10.6731	−	32.8484i	0.521415	−	1.60475i	0.771298	−	0.636474i	$-0.219608\pi$
$420$		0			0
$421$	3.00798	+	9.25762i	0.146600	+	0.451189i	0.997213	−	0.0746033i	$-0.0237691\pi$
$421$	3.00798	+	9.25762i	0.146600	+	0.451189i	−0.850613	+	0.525792i	$0.823769\pi$
$422$	4.36823	+	13.4440i	0.212642	+	0.654445i
$423$		0			0
$424$	11.6163			0.564136
$425$	6.47100	−	2.56956i	0.313890	−	0.124642i
$426$		0			0
$427$	−31.6364	−	22.9852i	−1.53099	−	1.11233i
$428$	3.34124	+	10.2833i	0.161505	+	0.497061i
$429$		0			0
$430$	2.90867	+	5.28457i	0.140269	+	0.254845i
$431$	0.956560	−	2.94399i	0.0460759	−	0.141807i	−0.925372	−	0.379061i	$-0.876247\pi$
$431$	0.956560	−	2.94399i	0.0460759	−	0.141807i	0.971448	+	0.237254i	$0.0762472\pi$
$432$		0			0
$433$	−5.63542	+	17.3440i	−0.270821	+	0.833501i	0.719474	+	0.694519i	$0.244383\pi$
$433$	−5.63542	+	17.3440i	−0.270821	+	0.833501i	−0.990295	+	0.138981i	$0.955617\pi$
$434$	−17.0425	+	12.3821i	−0.818067	+	0.594360i
$435$		0			0
$436$	−9.23519	−	6.70976i	−0.442285	−	0.321339i
$437$	2.82134	−	2.04982i	0.134963	−	0.0980563i
$438$		0			0
$439$	21.4595	+	15.5912i	1.02421	+	0.744129i	0.967141	−	0.254242i	$-0.0818259\pi$
$439$	21.4595	+	15.5912i	1.02421	+	0.744129i	0.0570645	+	0.998370i	$0.481826\pi$
$440$	8.28968	−	1.58565i	0.395195	−	0.0755929i
$441$		0			0
$442$	−1.36679	+	4.20655i	−0.0650115	+	0.200085i
$443$	−35.5267			−1.68793			−0.843963	−	0.536401i	$-0.819783\pi$
$443$	−35.5267			−1.68793			−0.843963	+	0.536401i	$0.819783\pi$
$444$		0			0
$445$	15.6452	+	28.4247i	0.741653	+	1.34746i
$446$	−1.42527	−	4.38652i	−0.0674883	−	0.207708i
$447$		0			0
$448$	−3.05361	−	2.21858i	−0.144269	−	0.104818i
$449$	−16.1841			−0.763776			−0.381888	−	0.924209i	$-0.624726\pi$
$449$	−16.1841			−0.763776			−0.381888	+	0.924209i	$0.624726\pi$
$450$		0			0
$451$	5.62087			0.264676
$452$	−8.43232	−	6.12644i	−0.396623	−	0.288163i
$453$		0			0
$454$	−1.94259	−	5.97869i	−0.0911705	−	0.280594i
$455$	−26.3306	+	5.03652i	−1.23440	+	0.236116i
$456$		0			0
$457$	23.7205			1.10960			0.554799	−	0.831984i	$-0.312795\pi$
$457$	23.7205			1.10960			0.554799	+	0.831984i	$0.312795\pi$
$458$	−5.48103	+	16.8689i	−0.256112	+	0.788230i
$459$		0			0
$460$	−1.36317	+	1.45309i	−0.0635580	+	0.0677504i
$461$	−6.36936	−	4.62761i	−0.296651	−	0.215529i	0.429497	−	0.903068i	$-0.358691\pi$
$461$	−6.36936	−	4.62761i	−0.296651	−	0.215529i	−0.726147	+	0.687539i	$0.758691\pi$
$462$		0			0
$463$	−12.4775	+	9.06543i	−0.579878	+	0.421306i	−0.838680	−	0.544624i	$-0.816672\pi$
$463$	−12.4775	+	9.06543i	−0.579878	+	0.421306i	0.258802	+	0.965930i	$0.416672\pi$
$464$	0.0398173	+	0.0289290i	0.00184847	+	0.00134299i
$465$		0			0
$466$	−2.07437	+	1.50712i	−0.0960932	+	0.0698158i
$467$	5.26481	−	16.2034i	0.243626	−	0.749805i	−0.752233	−	0.658897i	$-0.771023\pi$
$467$	5.26481	−	16.2034i	0.243626	−	0.749805i	0.995859	−	0.0909075i	$-0.0289768\pi$
$468$		0			0
$469$	17.8728	−	55.0069i	0.825290	−	2.53998i
$470$	5.77447	−	6.15537i	0.266356	−	0.283926i
$471$		0			0
$472$	−0.213245	−	0.656300i	−0.00981538	−	0.0302086i
$473$	−8.23762	−	5.98498i	−0.378766	−	0.275190i
$474$		0			0
$475$	18.1878	−	7.22218i	0.834514	−	0.331376i
$476$	5.25595			0.240906
$477$		0			0
$478$	2.91765	+	8.97961i	0.133450	+	0.410718i
$479$	7.75544	+	23.8688i	0.354355	+	1.09059i	0.956382	+	0.292118i	$0.0943598\pi$
$479$	7.75544	+	23.8688i	0.354355	+	1.09059i	−0.602027	+	0.798476i	$0.705640\pi$
$480$		0			0
$481$	6.91734	−	21.2894i	0.315403	−	0.970712i
$482$	29.4346			1.34071
$483$		0			0
$484$	−2.62656	+	1.90831i	−0.119389	+	0.0867412i
$485$	0.0251701	−	0.200049i	0.00114292	−	0.00908375i
$486$		0			0
$487$	11.0735	−	8.04536i	0.501788	−	0.364570i	−0.307912	−	0.951415i	$-0.599630\pi$
$487$	11.0735	−	8.04536i	0.501788	−	0.364570i	0.809699	+	0.586845i	$0.199630\pi$
$488$	8.38168	−	6.08965i	0.379421	−	0.275665i
$489$		0			0
$490$	7.81341	+	14.1957i	0.352974	+	0.641295i
$491$	−2.08733	+	1.51654i	−0.0942001	+	0.0684403i	−0.633888	−	0.773425i	$-0.718542\pi$
$491$	−2.08733	+	1.51654i	−0.0942001	+	0.0684403i	0.539688	+	0.841865i	$0.318542\pi$
$492$		0			0
$493$	−0.0685347			−0.00308665
$494$	−3.84159	+	11.8232i	−0.172841	+	0.531950i
$495$		0			0
$496$	−1.72466	−	5.30795i	−0.0774394	−	0.238334i
$497$	7.81199	+	24.0428i	0.350416	+	1.07847i
$498$		0			0
$499$	−39.0539			−1.74829			−0.874146	−	0.485664i	$-0.838578\pi$
$499$	−39.0539			−1.74829			−0.874146	+	0.485664i	$0.838578\pi$
$500$	−9.43085	+	6.00492i	−0.421760	+	0.268548i
$501$		0			0
$502$	4.86025	+	3.53118i	0.216923	+	0.157604i
$503$	−3.69387	−	11.3686i	−0.164702	−	0.506899i	0.834313	−	0.551292i	$-0.185865\pi$
$503$	−3.69387	−	11.3686i	−0.164702	−	0.506899i	−0.999014	+	0.0443923i	$0.985865\pi$
$504$		0			0
$505$	−33.1456	−	15.5768i	−1.47496	−	0.693160i
$506$	1.03928	−	3.19856i	0.0462014	−	0.142193i
$507$		0			0
$508$	−1.09668	+	3.37524i	−0.0486574	+	0.149752i
$509$	−3.94254	+	2.86442i	−0.174750	+	0.126963i	−0.671722	−	0.740803i	$-0.734445\pi$
$509$	−3.94254	+	2.86442i	−0.174750	+	0.126963i	0.496972	+	0.867767i	$0.334445\pi$
$510$		0			0
$511$	−15.7832	−	11.4672i	−0.698210	−	0.507279i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$		0			0
$514$	11.0257	+	8.01067i	0.486325	+	0.353336i
$515$	0.339487	−	2.69820i	0.0149596	−	0.118897i
$516$		0			0
$517$	−4.40244	+	13.5493i	−0.193619	+	0.595899i
$518$	−26.6004			−1.16876
$519$		0			0
$520$	0.886640	−	7.04690i	0.0388817	−	0.309027i
$521$	2.70131	+	8.31378i	0.118347	+	0.364233i	0.992630	−	0.121182i	$-0.0386684\pi$
$521$	2.70131	+	8.31378i	0.118347	+	0.364233i	−0.874284	+	0.485415i	$0.838668\pi$
$522$		0			0
$523$	17.0534	+	12.3900i	0.745694	+	0.541778i	0.894489	−	0.447090i	$-0.147540\pi$
$523$	17.0534	+	12.3900i	0.745694	+	0.541778i	−0.148795	+	0.988868i	$0.547540\pi$
$524$	−4.05324			−0.177067
$525$		0			0
$526$	−9.16294			−0.399523
$527$	6.28743	+	4.56809i	0.273885	+	0.198989i
$528$		0			0
$529$	−6.86205	−	21.1192i	−0.298350	−	0.918227i
$530$	17.7715	−	18.9437i	0.771943	−	0.822863i
$531$		0			0
$532$	14.7727			0.640478
$533$	1.46169	−	4.49861i	0.0633126	−	0.194856i
$534$		0			0
$535$	21.8816	+	10.2833i	0.946022	+	0.444585i
$536$	12.3969	+	9.00687i	0.535464	+	0.389038i
$537$		0			0
$538$	−22.7355	+	16.5183i	−0.980197	+	0.712155i
$539$	−22.1283	−	16.0771i	−0.953133	−	0.692492i
$540$		0			0
$541$	−26.5406	+	19.2829i	−1.14107	+	0.829036i	−0.987268	−	0.159066i	$-0.949152\pi$
$541$	−26.5406	+	19.2829i	−1.14107	+	0.829036i	−0.153802	+	0.988102i	$0.549152\pi$
$542$	2.81162	−	8.65329i	0.120770	−	0.371690i
$543$		0			0
$544$	−0.430307	+	1.32435i	−0.0184492	+	0.0567809i
$545$	−25.0709	+	4.79557i	−1.07392	+	0.205419i
$546$		0			0
$547$	−1.69044	−	5.20264i	−0.0722781	−	0.222449i	0.908391	−	0.418121i	$-0.137311\pi$
$547$	−1.69044	−	5.20264i	−0.0722781	−	0.222449i	−0.980669	+	0.195672i	$0.937311\pi$
$548$	−2.88636	−	2.09706i	−0.123299	−	0.0895820i
$549$		0			0
$550$	10.0963	−	15.9446i	0.430508	−	0.679879i
$551$	−0.192628			−0.00820623
$552$		0			0
$553$	−2.10722	−	6.48535i	−0.0896080	−	0.275785i
$554$	−5.80613	−	17.8694i	−0.246679	−	0.759199i
$555$		0			0
$556$	−3.07349	+	9.45923i	−0.130345	+	0.401161i
$557$	5.19840			0.220263			0.110132	−	0.993917i	$-0.464873\pi$
$557$	5.19840			0.220263			0.110132	+	0.993917i	$0.464873\pi$
$558$		0			0
$559$	−6.93218	+	5.03652i	−0.293200	+	0.213022i
$560$	−8.28968	+	1.58565i	−0.350303	+	0.0670059i
$561$		0			0
$562$	−6.37633	+	4.63268i	−0.268969	+	0.195418i
$563$	−4.05741	+	2.94788i	−0.170999	+	0.124238i	−0.669993	−	0.742367i	$-0.733703\pi$
$563$	−4.05741	+	2.94788i	−0.170999	+	0.124238i	0.498994	+	0.866605i	$0.333703\pi$
$564$		0			0
$565$	−22.8913	+	4.37866i	−0.963046	+	0.184212i
$566$	−14.8049	+	10.7564i	−0.622296	+	0.452124i
$567$		0			0
$568$	−6.69767			−0.281028
$569$	12.9303	−	39.7952i	0.542064	−	1.66830i	−0.185805	−	0.982587i	$-0.559489\pi$
$569$	12.9303	−	39.7952i	0.542064	−	1.66830i	0.727869	−	0.685716i	$-0.240511\pi$
$570$		0			0
$571$	−13.7723	−	42.3869i	−0.576355	−	1.77384i	−0.631519	−	0.775360i	$-0.717568\pi$
$571$	−13.7723	−	42.3869i	−0.576355	−	1.77384i	0.0551642	−	0.998477i	$-0.482432\pi$
$572$	3.70477	+	11.4021i	0.154904	+	0.476747i
$573$		0			0
$574$	−5.62087			−0.234611
$575$	0.284202	+	4.44608i	0.0118520	+	0.185414i
$576$		0			0
$577$	20.3401	+	14.7779i	0.846769	+	0.615213i	0.924253	−	0.381780i	$-0.124689\pi$
$577$	20.3401	+	14.7779i	0.846769	+	0.615213i	−0.0774845	+	0.996994i	$0.524689\pi$
$578$	4.65409	+	14.3238i	0.193584	+	0.595792i
$579$		0			0
$580$	0.108093	−	0.0206760i	0.00448831	−	0.000858524i
$581$	11.6262	−	35.7818i	0.482337	−	1.48448i
$582$		0			0
$583$	−13.5489	+	41.6993i	−0.561140	+	1.72701i
$584$	4.18158	−	3.03810i	0.173035	−	0.125717i
$585$		0			0
$586$	23.8652	+	17.3391i	0.985861	+	0.716270i
$587$	17.2770	−	12.5525i	0.713099	−	0.518097i	−0.171073	−	0.985258i	$-0.554723\pi$
$587$	17.2770	−	12.5525i	0.713099	−	0.518097i	0.884172	+	0.467162i	$0.154723\pi$
$588$		0			0
$589$	17.6719	+	12.8394i	0.728157	+	0.529037i
$590$	−1.39653	−	0.656300i	−0.0574940	−	0.0270194i
$591$		0			0
$592$	2.17779	−	6.70254i	0.0895065	−	0.275473i
$593$	33.4430			1.37334			0.686669	−	0.726970i	$-0.259072\pi$
$593$	33.4430			1.37334			0.686669	+	0.726970i	$0.259072\pi$
$594$		0			0
$595$	8.04095	−	8.57136i	0.329647	−	0.351391i
$596$	6.02900	+	18.5554i	0.246957	+	0.760057i
$597$		0			0
$598$	−2.28968	−	1.66355i	−0.0936318	−	0.0680275i
$599$	−26.3174			−1.07530			−0.537650	−	0.843168i	$-0.680688\pi$
$599$	−26.3174			−1.07530			−0.537650	+	0.843168i	$0.680688\pi$
$600$		0			0
$601$	20.9964			0.856462			0.428231	−	0.903669i	$-0.359137\pi$
$601$	20.9964			0.856462			0.428231	+	0.903669i	$0.359137\pi$
$602$	8.23762	+	5.98498i	0.335740	+	0.243930i
$603$		0			0
$604$	−5.69592	−	17.5302i	−0.231764	−	0.713295i
$605$	−0.906260	+	7.20284i	−0.0368447	+	0.292837i
$606$		0			0
$607$	9.32822			0.378621			0.189310	−	0.981917i	$-0.439375\pi$
$607$	9.32822			0.378621			0.189310	+	0.981917i	$0.439375\pi$
$608$	−1.20945	+	3.72230i	−0.0490496	+	0.150959i
$609$		0			0
$610$	2.89199	−	22.9852i	0.117093	−	0.930643i
$611$	9.69922	+	7.04690i	0.392389	+	0.285087i
$612$		0			0
$613$	25.9724	−	18.8700i	1.04902	−	0.762154i	0.0769902	−	0.997032i	$-0.475469\pi$
$613$	25.9724	−	18.8700i	1.04902	−	0.762154i	0.972025	+	0.234878i	$0.0754690\pi$
$614$	11.2560	+	8.17793i	0.454253	+	0.330034i
$615$		0			0
$616$	11.5257	−	8.37394i	0.464385	−	0.337396i
$617$	9.86557	−	30.3631i	0.397173	−	1.22237i	−0.530084	−	0.847945i	$-0.677840\pi$
$617$	9.86557	−	30.3631i	0.397173	−	1.22237i	0.927257	−	0.374427i	$-0.122160\pi$
$618$		0			0
$619$	−1.40420	+	4.32167i	−0.0564394	+	0.173703i	−0.975302	−	0.220875i	$-0.929109\pi$
$619$	−1.40420	+	4.32167i	−0.0564394	+	0.173703i	0.918863	+	0.394577i	$0.129109\pi$
$620$	−11.2947	−	5.30795i	−0.453605	−	0.213172i
$621$		0			0
$622$	8.02319	+	24.6928i	0.321701	+	0.990093i
$623$	44.3086	+	32.1921i	1.77519	+	1.28975i
$624$		0			0
$625$	−4.63525	+	24.5665i	−0.185410	+	0.982661i
$626$	−9.47389			−0.378653
$627$		0			0
$628$	3.13851	+	9.65934i	0.125240	+	0.385450i
$629$	3.03257	+	9.33329i	0.120916	+	0.372143i
$630$		0			0
$631$	−8.31756	+	25.5988i	−0.331117	+	1.01907i	0.637486	+	0.770462i	$0.279974\pi$
$631$	−8.31756	+	25.5988i	−0.331117	+	1.01907i	−0.968603	+	0.248611i	$0.920026\pi$
$632$	1.80664			0.0718642
$633$		0			0
$634$	−19.8269	+	14.4051i	−0.787427	+	0.572100i
$635$	3.82652	+	6.95215i	0.151851	+	0.275888i
$636$		0			0
$637$	−18.6215	+	13.5293i	−0.737813	+	0.536052i
$638$	−0.150289	+	0.109192i	−0.00595001	+	0.00432293i
$639$		0			0
$640$	0.279141	−	2.21858i	0.0110340	−	0.0876969i
$641$	28.9303	−	21.0191i	1.14268	−	0.830205i	0.155189	−	0.987885i	$-0.450401\pi$
$641$	28.9303	−	21.0191i	1.14268	−	0.830205i	0.987490	+	0.157679i	$0.0504013\pi$
$642$		0			0
$643$	28.2255			1.11311			0.556553	−	0.830812i	$-0.312124\pi$
$643$	28.2255			1.11311			0.556553	+	0.830812i	$0.312124\pi$
$644$	−1.03928	+	3.19856i	−0.0409532	+	0.126041i
$645$		0			0
$646$	−1.68416	−	5.18330i	−0.0662623	−	0.203934i
$647$	−0.394848	−	1.21522i	−0.0155231	−	0.0477751i	0.942995	−	0.332807i	$-0.107996\pi$
$647$	−0.394848	−	1.21522i	−0.0155231	−	0.0477751i	−0.958518	+	0.285032i	$0.907996\pi$
$648$		0			0
$649$	2.60466			0.102242
$650$	−10.1356	−	12.2268i	−0.397550	−	0.479575i
$651$		0			0
$652$	15.0481	+	10.9331i	0.589327	+	0.428171i
$653$	8.47040	+	26.0692i	0.331472	+	1.02017i	0.968434	+	0.249272i	$0.0801912\pi$
$653$	8.47040	+	26.0692i	0.331472	+	1.02017i	−0.636961	+	0.770896i	$0.719809\pi$
$654$		0			0
$655$	−6.20096	+	6.60999i	−0.242291	+	0.258274i
$656$	0.460183	−	1.41630i	0.0179671	−	0.0552971i
$657$		0			0
$658$	4.40244	−	13.5493i	0.171625	−	0.528208i
$659$	−33.3535	+	24.2327i	−1.29927	+	0.943972i	−0.999948	−	0.0101814i	$-0.996759\pi$
$659$	−33.3535	+	24.2327i	−1.29927	+	0.943972i	−0.299318	+	0.954153i	$0.596759\pi$
$660$		0			0
$661$	21.4653	+	15.5955i	0.834904	+	0.606593i	0.920942	−	0.389699i	$-0.127421\pi$
$661$	21.4653	+	15.5955i	0.834904	+	0.606593i	−0.0860388	+	0.996292i	$0.527421\pi$
$662$	−8.01764	+	5.82516i	−0.311614	+	0.226401i
$663$		0			0
$664$	8.06414	+	5.85894i	0.312949	+	0.227371i
$665$	22.6004	−	24.0912i	0.876407	−	0.934217i
$666$		0			0
$667$	0.0135516	−	0.0417075i	0.000524719	−	0.00161492i
$668$	−2.17156			−0.0840201
$669$		0			0
$670$	33.6540	−	6.43735i	1.30017	−	0.248696i
$671$	12.0840	+	37.1908i	0.466499	+	1.43574i
$672$		0			0
$673$	6.42142	+	4.66543i	0.247527	+	0.179839i	0.704630	−	0.709575i	$-0.251113\pi$
$673$	6.42142	+	4.66543i	0.247527	+	0.179839i	−0.457103	+	0.889414i	$0.651113\pi$
$674$	9.93566			0.382707
$675$		0			0
$676$	−2.91102			−0.111962
$677$	23.8667	+	17.3402i	0.917271	+	0.666436i	0.942843	−	0.333237i	$-0.108141\pi$
$677$	23.8667	+	17.3402i	0.917271	+	0.666436i	−0.0255722	+	0.999673i	$0.508141\pi$
$678$		0			0
$679$	−0.105172	−	0.323686i	−0.00403613	−	0.0124219i
$680$	1.50142	+	2.72783i	0.0575768	+	0.104607i
$681$		0			0
$682$	21.0657			0.806647
$683$	−11.6650	+	35.9012i	−0.446349	+	1.37372i	0.434648	+	0.900600i	$0.356873\pi$
$683$	−11.6650	+	35.9012i	−0.446349	+	1.37372i	−0.880997	+	0.473121i	$0.843127\pi$
$684$		0			0
$685$	−7.83564	+	1.49880i	−0.299384	+	0.0572663i
$686$	0.753030	+	0.547108i	0.0287508	+	0.0208887i
$687$		0			0
$688$	−2.18246	+	1.58565i	−0.0832055	+	0.0604523i
$689$	29.8503	+	21.6875i	1.13721	+	0.826228i
$690$		0			0
$691$	−14.2843	+	10.3782i	−0.543401	+	0.394804i	−0.825347	−	0.564626i	$-0.809020\pi$
$691$	−14.2843	+	10.3782i	−0.543401	+	0.394804i	0.281945	+	0.959430i	$0.409020\pi$
$692$	1.97593	−	6.08130i	0.0751137	−	0.231176i
$693$		0			0
$694$	−6.06757	+	18.6741i	−0.230322	+	0.708858i
$695$	10.7240	+	19.4837i	0.406783	+	0.739058i
$696$		0			0
$697$	0.640805	+	1.97219i	0.0242722	+	0.0747022i
$698$	1.20084	+	0.872461i	0.0454524	+	0.0330231i
$699$		0			0
$700$	−10.0963	+	15.9446i	−0.381605	+	0.602648i
$701$	16.8372			0.635931			0.317965	−	0.948102i	$-0.397000\pi$
$701$	16.8372			0.635931			0.317965	+	0.948102i	$0.397000\pi$
$702$		0			0
$703$	8.52354	+	26.2328i	0.321471	+	0.989387i
$704$	1.16637	+	3.58973i	0.0439594	+	0.135293i
$705$		0			0
$706$	3.17632	−	9.77569i	0.119542	−	0.367913i
$707$	−61.8200			−2.32498
$708$		0			0
$709$	23.1615	−	16.8278i	0.869849	−	0.631982i	−0.0606978	−	0.998156i	$-0.519333\pi$
$709$	23.1615	−	16.8278i	0.869849	−	0.631982i	0.930546	+	0.366174i	$0.119333\pi$
$710$	−10.2466	+	10.9225i	−0.384548	+	0.409914i
$711$		0			0
$712$	−11.7390	+	8.52891i	−0.439939	+	0.319635i
$713$	−4.02319	+	2.92302i	−0.150670	+	0.109468i
$714$		0			0
$715$	24.2623	+	11.4021i	0.907359	+	0.426415i
$716$	6.48304	−	4.71020i	0.242283	−	0.176029i
$717$		0			0
$718$	−10.3725			−0.387099
$719$	2.54857	−	7.84368i	0.0950455	−	0.292520i	−0.892220	−	0.451601i	$-0.850853\pi$
$719$	2.54857	−	7.84368i	0.0950455	−	0.292520i	0.987266	+	0.159081i	$0.0508531\pi$
$720$		0			0
$721$	−1.41853	−	4.36578i	−0.0528287	−	0.162590i
$722$	1.13772	+	3.50155i	0.0423416	+	0.130314i
$723$		0			0
$724$	−10.8629			−0.403716
$725$	0.131650	−	0.207908i	0.00488937	−	0.00772152i
$726$		0			0
$727$	1.71013	+	1.24248i	0.0634251	+	0.0460810i	0.619046	−	0.785355i	$-0.287519\pi$
$727$	1.71013	+	1.24248i	0.0634251	+	0.0460810i	−0.555621	+	0.831436i	$0.687519\pi$
$728$	−3.70477	−	11.4021i	−0.137308	−	0.422591i
$729$		0			0
$730$	1.44280	−	11.4672i	0.0534005	−	0.424420i
$731$	1.16082	−	3.57265i	0.0429346	−	0.132139i
$732$		0			0
$733$	13.9537	−	42.9451i	0.515393	−	1.58622i	−0.267174	−	0.963648i	$-0.586090\pi$
$733$	13.9537	−	42.9451i	0.515393	−	1.58622i	0.782567	−	0.622567i	$-0.213910\pi$
$734$	21.0946	−	15.3261i	0.778614	−	0.565697i
$735$		0			0
$736$	−0.720859	−	0.523735i	−0.0265712	−	0.0193051i
$737$	−46.7917	+	33.9961i	−1.72359	+	1.25226i
$738$		0			0
$739$	−24.2478	−	17.6171i	−0.891969	−	0.648054i	0.0444213	−	0.999013i	$-0.485856\pi$
$739$	−24.2478	−	17.6171i	−0.891969	−	0.648054i	−0.936391	+	0.350959i	$0.885856\pi$
$740$	−7.59869	−	13.8056i	−0.279334	−	0.507503i
$741$		0			0
$742$	13.5489	−	41.6993i	0.497397	−	1.53083i
$743$	−17.6562			−0.647741			−0.323871	−	0.946101i	$-0.604984\pi$
$743$	−17.6562			−0.647741			−0.323871	+	0.946101i	$0.604984\pi$
$744$		0			0
$745$	39.4835	+	18.5554i	1.44656	+	0.679816i
$746$	−2.92204	−	8.99312i	−0.106984	−	0.329262i
$747$		0			0
$748$	−4.25215	−	3.08937i	−0.155474	−	0.112959i
$749$	40.8113			1.49121
$750$		0			0
$751$	30.1342			1.09961			0.549806	−	0.835293i	$-0.314702\pi$
$751$	30.1342			1.09961			0.549806	+	0.835293i	$0.314702\pi$
$752$	3.05361	+	2.21858i	0.111354	+	0.0809031i
$753$		0			0
$754$	0.0483082	+	0.148677i	0.00175928	+	0.00541451i
$755$	−37.3022	−	17.5302i	−1.35757	−	0.637990i
$756$		0			0
$757$	−4.90706			−0.178350			−0.0891750	−	0.996016i	$-0.528423\pi$
$757$	−4.90706			−0.178350			−0.0891750	+	0.996016i	$0.528423\pi$
$758$	10.9163	−	33.5968i	0.396497	−	1.22029i
$759$		0			0
$760$	4.21998	+	7.66701i	0.153075	+	0.278112i
$761$	10.7466	+	7.80786i	0.389564	+	0.283035i	0.765277	−	0.643701i	$-0.222602\pi$
$761$	10.7466	+	7.80786i	0.389564	+	0.283035i	−0.375713	+	0.926736i	$0.622602\pi$
$762$		0			0
$763$	−34.8579	+	25.3258i	−1.26194	+	0.916854i
$764$	−6.62243	−	4.81147i	−0.239591	−	0.174073i
$765$		0			0
$766$	−24.1227	+	17.5262i	−0.871590	+	0.633247i
$767$	0.677332	−	2.08461i	0.0244571	−	0.0752711i
$768$		0			0
$769$	−8.83716	+	27.1980i	−0.318676	+	0.980784i	0.655539	+	0.755162i	$0.272442\pi$
$769$	−8.83716	+	27.1980i	−0.318676	+	0.980784i	−0.974215	+	0.225623i	$0.927558\pi$
$770$	3.97681	−	31.6072i	0.143314	−	1.13904i
$771$		0			0
$772$	−5.42560	−	16.6983i	−0.195272	−	0.600984i
$773$	−36.4564	−	26.4871i	−1.31124	−	0.952675i	−0.999997	−	0.00234562i	$-0.999253\pi$
$773$	−36.4564	−	26.4871i	−1.31124	−	0.952675i	−0.311247	−	0.950329i	$-0.600747\pi$
$774$		0			0
$775$	−25.9356	+	10.2987i	−0.931634	+	0.369941i
$776$	0.0901699			0.00323691
$777$		0			0
$778$	−6.60578	−	20.3305i	−0.236829	−	0.728884i
$779$	1.80109	+	5.54318i	0.0645307	+	0.198605i
$780$		0			0
$781$	7.81199	−	24.0428i	0.279535	−	0.860320i
$782$	1.24076			0.0443695
$783$		0			0
$784$	−5.86263	+	4.25945i	−0.209379	+	0.152123i
$785$	20.5539	+	9.65934i	0.733600	+	0.344757i
$786$		0			0
$787$	−20.8458	+	15.1454i	−0.743074	+	0.539875i	−0.893672	−	0.448720i	$-0.851880\pi$
$787$	−20.8458	+	15.1454i	−0.743074	+	0.539875i	0.150598	+	0.988595i	$0.451880\pi$
$788$	3.84883	−

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(2.02373 + 0.951057i) q^{5} +3.77447 q^{7} +(-0.309017 + 0.951057i) q^{8} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(2.02373 + 0.951057i) q^{5} +3.77447 q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.07822 + 1.95894i) q^{10} +(-3.05361 - 2.21858i) q^{11} +(-2.56969 + 1.86699i) q^{13} +(3.05361 + 2.21858i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.430307 - 1.32435i) q^{17} +(1.20945 - 3.72230i) q^{19} +(-0.279141 + 2.21858i) q^{20} +(-1.16637 - 3.58973i) q^{22} +(0.720859 + 0.523735i) q^{23} +(3.19098 + 3.84937i) q^{25} -3.17632 q^{26} +(1.16637 + 3.58973i) q^{28} +(-0.0152089 - 0.0468081i) q^{29} +(-1.72466 + 5.30795i) q^{31} -1.00000 q^{32} +(1.12656 - 0.818492i) q^{34} +(7.63851 + 3.58973i) q^{35} +(-5.70152 + 4.14240i) q^{37} +(3.16637 - 2.30051i) q^{38} +(-1.52988 + 1.63079i) q^{40} +(-1.20477 + 0.875319i) q^{41} +2.69767 q^{43} +(1.16637 - 3.58973i) q^{44} +(0.275344 + 0.847421i) q^{46} +(-1.16637 - 3.58973i) q^{47} +7.24660 q^{49} +(0.318958 + 4.98982i) q^{50} +(-2.56969 - 1.86699i) q^{52} +(-3.58963 - 11.0477i) q^{53} +(-4.06969 - 7.39396i) q^{55} +(-1.16637 + 3.58973i) q^{56} +(0.0152089 - 0.0468081i) q^{58} +(-0.558282 + 0.405615i) q^{59} +(-8.38168 - 6.08965i) q^{61} +(-4.51521 + 3.28049i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(-6.97599 + 1.33437i) q^{65} +(4.73519 - 14.5734i) q^{67} +1.39250 q^{68} +(4.06969 + 7.39396i) q^{70} +(2.06969 + 6.36986i) q^{71} +(-4.18158 - 3.03810i) q^{73} -7.04746 q^{74} +3.91385 q^{76} +(-11.5257 - 8.37394i) q^{77} +(-0.558282 - 1.71821i) q^{79} +(-2.19625 + 0.420099i) q^{80} -1.48918 q^{82} +(3.08023 - 9.47997i) q^{83} +(2.13035 - 2.27088i) q^{85} +(2.18246 + 1.58565i) q^{86} +(3.05361 - 2.21858i) q^{88} +(11.7390 + 8.52891i) q^{89} +(-9.69922 + 7.04690i) q^{91} +(-0.275344 + 0.847421i) q^{92} +(1.16637 - 3.58973i) q^{94} +(5.98771 - 6.38268i) q^{95} +(-0.0278640 - 0.0857567i) q^{97} +(5.86263 + 4.25945i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8q + 2q^{2} - 2q^{4} + 4q^{7} + 2q^{8} + O(q^{10}) \)	\( 8q + 2q^{2} - 2q^{4} + 4q^{7} + 2q^{8} - q^{11} - 13q^{13} + q^{14} - 2q^{16} + 11q^{17} + 20q^{19} - 5q^{20} + q^{22} + 3q^{23} + 30q^{25} - 22q^{26} - q^{28} + 15q^{29} - 9q^{31} - 8q^{32} - q^{34} + 15q^{35} - 6q^{37} + 15q^{38} - 5q^{40} + 9q^{41} + 12q^{43} - q^{44} + 7q^{46} + q^{47} - 4q^{49} + 5q^{50} - 13q^{52} - 7q^{53} - 25q^{55} + q^{56} - 15q^{58} - 10q^{59} + 6q^{61} - 21q^{62} - 2q^{64} + 10q^{65} - 11q^{67} - 24q^{68} + 25q^{70} + 9q^{71} - 8q^{73} - 24q^{74} - 10q^{76} - 33q^{77} - 10q^{79} + 26q^{82} - 27q^{83} + 5q^{85} + 23q^{86} + q^{88} + 15q^{89} + q^{91} - 7q^{92} - q^{94} + 30q^{95} - 36q^{97} + 19q^{98} + O(q^{100}) \)

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