LMFDB - Embedded newform 418.2.u.b.9.9

Newspace parameters

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.u (of order $45$, degree $24$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$264$
Relative dimension:	$11$ over $\Q(\zeta_{45})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{45}]$

Embedding invariants

Embedding label			9.9
Character	$\chi$	$=$	418.9
Dual form			418.2.u.b.93.9

$q$-expansion

$f(q)$	$=$	$q+(0.990268 + 0.139173i) q^{2} +(0.530296 - 2.12690i) q^{3} +(0.961262 + 0.275637i) q^{4} +(0.0547010 - 1.56643i) q^{5} +(0.821143 - 2.03240i) q^{6} +(2.87167 - 1.27855i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-1.59366 - 0.847362i) q^{9} +O(q^{10})$	\(q+(0.990268 + 0.139173i) q^{2} +(0.530296 - 2.12690i) q^{3} +(0.961262 + 0.275637i) q^{4} +(0.0547010 - 1.56643i) q^{5} +(0.821143 - 2.03240i) q^{6} +(2.87167 - 1.27855i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-1.59366 - 0.847362i) q^{9} +(0.272174 - 1.54358i) q^{10} +(-1.49853 + 2.95879i) q^{11} +(1.09601 - 1.89834i) q^{12} +(-2.34165 + 1.46322i) q^{13} +(3.02167 - 0.866449i) q^{14} +(-3.30264 - 0.947017i) q^{15} +(0.848048 + 0.529919i) q^{16} +(-6.27809 + 3.33812i) q^{17} +(-1.46022 - 1.06091i) q^{18} +(2.16967 - 3.78055i) q^{19} +(0.484349 - 1.49067i) q^{20} +(-1.19652 - 6.78578i) q^{21} +(-1.89573 + 2.72144i) q^{22} +(-1.39052 + 0.506108i) q^{23} +(1.34954 - 1.72733i) q^{24} +(2.53710 + 0.177411i) q^{25} +(-2.52250 + 1.12309i) q^{26} +(1.75287 - 1.94675i) q^{27} +(3.11285 - 0.437482i) q^{28} +(1.22673 - 1.18464i) q^{29} +(-3.13870 - 1.39744i) q^{30} +(3.78193 + 4.20026i) q^{31} +(0.766044 + 0.642788i) q^{32} +(5.49839 + 4.75625i) q^{33} +(-6.68156 + 2.43189i) q^{34} +(-1.84568 - 4.56822i) q^{35} +(-1.29836 - 1.25381i) q^{36} +(2.62851 + 1.90972i) q^{37} +(2.67471 - 3.44179i) q^{38} +(1.87037 + 5.75639i) q^{39} +(0.687097 - 1.40876i) q^{40} +(0.410003 - 1.64443i) q^{41} +(-0.240474 - 6.88626i) q^{42} +(-11.8872 - 4.32658i) q^{43} +(-2.25603 + 2.43112i) q^{44} +(-1.41451 + 2.45000i) q^{45} +(-1.44743 + 0.307660i) q^{46} +(3.83207 + 7.85691i) q^{47} +(1.57680 - 1.52270i) q^{48} +(1.92790 - 2.14115i) q^{49} +(2.48772 + 0.528781i) q^{50} +(3.77060 + 15.1231i) q^{51} +(-2.65425 + 0.761095i) q^{52} +(0.0190311 + 0.544981i) q^{53} +(2.00674 - 1.68386i) q^{54} +(4.55277 + 2.50919i) q^{55} +3.14344 q^{56} +(-6.89028 - 6.61949i) q^{57} +(1.37966 - 1.00238i) q^{58} +(-2.51772 + 5.16209i) q^{59} +(-2.91367 - 1.82066i) q^{60} +(-4.73404 - 6.05929i) q^{61} +(3.16056 + 4.68573i) q^{62} +(-5.65986 - 0.395776i) q^{63} +(0.669131 + 0.743145i) q^{64} +(2.16395 + 3.74807i) q^{65} +(4.78294 + 5.47519i) q^{66} +(-0.957384 + 5.42960i) q^{67} +(-6.95499 + 1.47833i) q^{68} +(0.339055 + 3.22589i) q^{69} +(-1.19195 - 4.78063i) q^{70} +(-0.319354 + 9.14512i) q^{71} +(-1.11122 - 1.42230i) q^{72} +(6.81009 - 0.476208i) q^{73} +(2.33715 + 2.25696i) q^{74} +(1.72275 - 5.30209i) q^{75} +(3.12768 - 3.03605i) q^{76} +(-0.520313 + 10.4126i) q^{77} +(1.05103 + 5.96068i) q^{78} +(-2.27548 - 5.63200i) q^{79} +(0.876472 - 1.29942i) q^{80} +(-6.23893 - 9.24959i) q^{81} +(0.634874 - 1.57137i) q^{82} +(10.5529 + 2.24308i) q^{83} +(0.720249 - 6.85271i) q^{84} +(4.88552 + 10.0168i) q^{85} +(-11.1694 - 5.93886i) q^{86} +(-1.86908 - 3.23735i) q^{87} +(-2.57242 + 2.09348i) q^{88} +(-6.95620 - 5.83694i) q^{89} +(-1.74172 + 2.22930i) q^{90} +(-4.85364 + 7.19581i) q^{91} +(-1.47616 + 0.103223i) q^{92} +(10.9391 - 5.81642i) q^{93} +(2.70131 + 8.31376i) q^{94} +(-5.80329 - 3.60545i) q^{95} +(1.77338 - 1.28843i) q^{96} +(16.6004 + 2.33303i) q^{97} +(2.20713 - 1.85200i) q^{98} +(4.89530 - 3.44550i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.990268	+	0.139173i	0.700225	+	0.0984102i
$2$	0.990268	+	0.139173i	0.700225	+	0.0984102i
$3$	0.530296	−	2.12690i	0.306167	−	1.22797i	−0.598247	−	0.801312i	$-0.704136\pi$
$3$	0.530296	−	2.12690i	0.306167	−	1.22797i	0.904414	−	0.426656i	$-0.140309\pi$
$4$	0.961262	+	0.275637i	0.480631	+	0.137819i
$5$	0.0547010	−	1.56643i	0.0244630	−	0.700530i	−0.923769	−	0.382951i	$-0.874908\pi$
$5$	0.0547010	−	1.56643i	0.0244630	−	0.700530i	0.948232	−	0.317579i	$-0.102870\pi$
$6$	0.821143	−	2.03240i	0.335230	−	0.829724i
$7$	2.87167	−	1.27855i	1.08539	−	0.483247i	0.215506	−	0.976503i	$-0.430860\pi$
$7$	2.87167	−	1.27855i	1.08539	−	0.483247i	0.869884	+	0.493256i	$0.164193\pi$
$8$	0.913545	+	0.406737i	0.322987	+	0.143803i
$9$	−1.59366	−	0.847362i	−0.531219	−	0.282454i
$10$	0.272174	−	1.54358i	0.0860690	−	0.488121i
$11$	−1.49853	+	2.95879i	−0.451822	+	0.892108i
$11$	−1.49853	+	2.95879i	−0.451822	+	0.892108i
$12$	1.09601	−	1.89834i	0.316390	−	0.548004i
$13$	−2.34165	+	1.46322i	−0.649456	+	0.405825i	−0.814259	−	0.580501i	$-0.802857\pi$
$13$	−2.34165	+	1.46322i	−0.649456	+	0.405825i	0.164803	+	0.986326i	$0.447301\pi$
$14$	3.02167	−	0.866449i	0.807574	−	0.231568i
$15$	−3.30264	−	0.947017i	−0.852738	−	0.244519i
$16$	0.848048	+	0.529919i	0.212012	+	0.132480i
$17$	−6.27809	+	3.33812i	−1.52266	+	0.809612i	−0.999102	−	0.0423779i	$-0.986507\pi$
$17$	−6.27809	+	3.33812i	−1.52266	+	0.809612i	−0.523558	+	0.851990i	$0.675396\pi$
$18$	−1.46022	−	1.06091i	−0.344176	−	0.250059i
$19$	2.16967	−	3.78055i	0.497757	−	0.867317i
$19$	2.16967	−	3.78055i	0.497757	−	0.867317i
$20$	0.484349	−	1.49067i	0.108304	−	0.333325i
$21$	−1.19652	−	6.78578i	−0.261101	−	1.48078i
$22$	−1.89573	+	2.72144i	−0.404170	+	0.580213i
$23$	−1.39052	+	0.506108i	−0.289944	+	0.105531i	−0.482897	−	0.875677i	$-0.660416\pi$
$23$	−1.39052	+	0.506108i	−0.289944	+	0.105531i	0.192954	+	0.981208i	$0.438193\pi$
$24$	1.34954	−	1.72733i	0.275473	−	0.352590i
$25$	2.53710	+	0.177411i	0.507420	+	0.0354823i
$26$	−2.52250	+	1.12309i	−0.494703	+	0.220256i
$27$	1.75287	−	1.94675i	0.337339	−	0.374653i
$28$	3.11285	−	0.437482i	0.588273	−	0.0826763i
$29$	1.22673	−	1.18464i	0.227798	−	0.219982i	−0.571996	−	0.820256i	$-0.693831\pi$
$29$	1.22673	−	1.18464i	0.227798	−	0.219982i	0.799794	+	0.600274i	$0.204942\pi$
$30$	−3.13870	−	1.39744i	−0.573046	−	0.255136i
$31$	3.78193	+	4.20026i	0.679255	+	0.754389i	0.979931	−	0.199337i	$-0.0638790\pi$
$31$	3.78193	+	4.20026i	0.679255	+	0.754389i	−0.300676	+	0.953726i	$0.597212\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	5.49839	+	4.75625i	0.957147	+	0.827957i
$34$	−6.68156	+	2.43189i	−1.14588	+	0.417066i
$35$	−1.84568	−	4.56822i	−0.311977	−	0.772170i
$36$	−1.29836	−	1.25381i	−0.216393	−	0.208968i
$37$	2.62851	+	1.90972i	0.432124	+	0.313957i	0.782498	−	0.622654i	$-0.213945\pi$
$37$	2.62851	+	1.90972i	0.432124	+	0.313957i	−0.350374	+	0.936610i	$0.613945\pi$
$38$	2.67471	−	3.44179i	0.433895	−	0.558333i
$39$	1.87037	+	5.75639i	0.299498	+	0.921761i
$40$	0.687097	−	1.40876i	0.108640	−	0.222744i
$41$	0.410003	−	1.64443i	0.0640317	−	0.256817i	−0.929746	−	0.368203i	$-0.879973\pi$
$41$	0.410003	−	1.64443i	0.0640317	−	0.256817i	0.993777	+	0.111385i	$0.0355288\pi$
$42$	−0.240474	−	6.88626i	−0.0371059	−	1.06257i
$43$	−11.8872	−	4.32658i	−1.81278	−	0.659798i	−0.996637	−	0.0819482i	$-0.973886\pi$
$43$	−11.8872	−	4.32658i	−1.81278	−	0.659798i	−0.816143	−	0.577850i	$-0.803892\pi$
$44$	−2.25603	+	2.43112i	−0.340109	+	0.366505i
$45$	−1.41451	+	2.45000i	−0.210863	+	0.365225i
$46$	−1.44743	+	0.307660i	−0.213411	+	0.0453620i
$47$	3.83207	+	7.85691i	0.558965	+	1.14605i	0.971923	+	0.235298i	$0.0756065\pi$
$47$	3.83207	+	7.85691i	0.558965	+	1.14605i	−0.412959	+	0.910750i	$0.635505\pi$
$48$	1.57680	−	1.52270i	0.227592	−	0.219783i
$49$	1.92790	−	2.14115i	0.275414	−	0.305878i
$50$	2.48772	+	0.528781i	0.351817	+	0.0747809i
$51$	3.77060	+	15.1231i	0.527990	+	2.11765i
$52$	−2.65425	+	0.761095i	−0.368079	+	0.105545i
$53$	0.0190311	+	0.544981i	0.00261413	+	0.0748589i	0.999997	+	0.00255442i	$0.000813098\pi$
$53$	0.0190311	+	0.544981i	0.00261413	+	0.0748589i	−0.997383	+	0.0723044i	$0.976965\pi$
$54$	2.00674	−	1.68386i	0.273083	−	0.229144i
$55$	4.55277	+	2.50919i	0.613895	+	0.338339i
$56$	3.14344			0.420059
$57$	−6.89028	−	6.61949i	−0.912640	−	0.876773i
$58$	1.37966	−	1.00238i	0.181158	−	0.131619i
$59$	−2.51772	+	5.16209i	−0.327779	+	0.672047i	−0.997508	−	0.0705593i	$-0.977522\pi$
$59$	−2.51772	+	5.16209i	−0.327779	+	0.672047i	0.669728	+	0.742606i	$0.266411\pi$
$60$	−2.91367	−	1.82066i	−0.376153	−	0.235047i
$61$	−4.73404	−	6.05929i	−0.606131	−	0.775812i	0.382857	−	0.923808i	$-0.374940\pi$
$61$	−4.73404	−	6.05929i	−0.606131	−	0.775812i	−0.988988	+	0.147995i	$0.952718\pi$
$62$	3.16056	+	4.68573i	0.401392	+	0.595088i
$63$	−5.65986	−	0.395776i	−0.713075	−	0.0498630i
$64$	0.669131	+	0.743145i	0.0836413	+	0.0928931i
$65$	2.16395	+	3.74807i	0.268405	+	0.464891i
$66$	4.78294	+	5.47519i	0.588739	+	0.673949i
$67$	−0.957384	+	5.42960i	−0.116963	+	0.663331i	0.868796	+	0.495169i	$0.164894\pi$
$67$	−0.957384	+	5.42960i	−0.116963	+	0.663331i	−0.985760	+	0.168161i	$0.946217\pi$
$68$	−6.95499	+	1.47833i	−0.843417	+	0.179274i
$69$	0.339055	+	3.22589i	0.0408174	+	0.388352i
$70$	−1.19195	−	4.78063i	−0.142465	−	0.571395i
$71$	−0.319354	+	9.14512i	−0.0379004	+	1.08533i	0.820275	+	0.571969i	$0.193820\pi$
$71$	−0.319354	+	9.14512i	−0.0379004	+	1.08533i	−0.858175	+	0.513356i	$0.828402\pi$
$72$	−1.11122	−	1.42230i	−0.130959	−	0.167620i
$73$	6.81009	−	0.476208i	0.797060	−	0.0557359i	0.334582	−	0.942367i	$-0.391405\pi$
$73$	6.81009	−	0.476208i	0.797060	−	0.0557359i	0.462478	+	0.886631i	$0.346960\pi$
$74$	2.33715	+	2.25696i	0.271688	+	0.262366i
$75$	1.72275	−	5.30209i	0.198926	−	0.612232i
$76$	3.12768	−	3.03605i	0.358770	−	0.348259i
$77$	−0.520313	+	10.4126i	−0.0592952	+	1.18663i
$78$	1.05103	+	5.96068i	0.119006	+	0.674914i
$79$	−2.27548	−	5.63200i	−0.256011	−	0.633649i	0.743368	−	0.668882i	$-0.233227\pi$
$79$	−2.27548	−	5.63200i	−0.256011	−	0.633649i	−0.999379	+	0.0352331i	$0.988783\pi$
$80$	0.876472	−	1.29942i	0.0979925	−	0.145280i
$81$	−6.23893	−	9.24959i	−0.693214	−	1.02773i
$82$	0.634874	−	1.57137i	0.0701101	−	0.173529i
$83$	10.5529	+	2.24308i	1.15833	+	0.246210i	0.746712	−	0.665148i	$-0.231631\pi$
$83$	10.5529	+	2.24308i	1.15833	+	0.246210i	0.411615	+	0.911358i	$0.364965\pi$
$84$	0.720249	−	6.85271i	0.0785856	−	0.747692i
$85$	4.88552	+	10.0168i	0.529909	+	1.08647i
$86$	−11.1694	−	5.93886i	−1.20442	−	0.640403i
$87$	−1.86908	−	3.23735i	−0.200387	−	0.347080i
$88$	−2.57242	+	2.09348i	−0.274221	+	0.223166i
$89$	−6.95620	−	5.83694i	−0.737356	−	0.618715i	0.194770	−	0.980849i	$-0.437604\pi$
$89$	−6.95620	−	5.83694i	−0.737356	−	0.618715i	−0.932126	+	0.362134i	$0.882048\pi$
$90$	−1.74172	+	2.22930i	−0.183593	+	0.234989i
$91$	−4.85364	+	7.19581i	−0.508799	+	0.754326i
$92$	−1.47616	+	0.103223i	−0.153900	+	0.0107617i
$93$	10.9391	−	5.81642i	1.13433	−	0.603134i
$94$	2.70131	+	8.31376i	0.278618	+	0.857499i
$95$	−5.80329	−	3.60545i	−0.595405	−	0.369911i
$96$	1.77338	−	1.28843i	0.180995	−	0.131500i
$97$	16.6004	+	2.33303i	1.68551	+	0.236883i	0.915837	−	0.401551i	$-0.131529\pi$
$97$	16.6004	+	2.33303i	1.68551	+	0.236883i	0.769676	+	0.638434i	$0.220418\pi$
$98$	2.20713	−	1.85200i	0.222953	−	0.187080i
$99$	4.89530	−	3.44550i	0.491996	−	0.346285i
$100$	2.38992	+	0.869859i	0.238992	+	0.0869859i
$101$	2.89320	−	1.80787i	0.287884	−	0.179890i	−0.378288	−	0.925688i	$-0.623487\pi$
$101$	2.89320	−	1.80787i	0.287884	−	0.179890i	0.666172	+	0.745798i	$0.267932\pi$
$102$	1.62918	+	15.5007i	0.161313	+	1.53479i
$103$	0.642686	−	6.11475i	0.0633257	−	0.602504i	−0.916135	−	0.400869i	$-0.868708\pi$
$103$	0.642686	−	6.11475i	0.0633257	−	0.602504i	0.979461	−	0.201634i	$-0.0646252\pi$
$104$	−2.73435	+	0.384287i	−0.268125	+	0.0376825i
$105$	−10.6949	+	1.50307i	−1.04372	+	0.146685i
$106$	−0.0570007	+	0.542326i	−0.00553640	+	0.0526753i
$107$	1.02051	+	9.70947i	0.0986561	+	0.938650i	0.926145	+	0.377168i	$0.123102\pi$
$107$	1.02051	+	9.70947i	0.0986561	+	0.938650i	−0.827489	+	0.561482i	$0.810231\pi$
$108$	2.22156	−	1.38819i	0.213770	−	0.133578i
$109$	−14.1253	−	5.14119i	−1.35296	−	0.492436i	−0.439088	−	0.898444i	$-0.644698\pi$
$109$	−14.1253	−	5.14119i	−1.35296	−	0.492436i	−0.913870	+	0.406008i	$0.866921\pi$
$110$	4.15925	+	3.11839i	0.396569	+	0.297327i
$111$	5.45568	−	4.57786i	0.517830	−	0.434511i
$112$	3.11285	+	0.437482i	0.294136	+	0.0413382i
$113$	8.04520	−	5.84518i	0.756829	−	0.549868i	−0.141107	−	0.989994i	$-0.545066\pi$
$113$	8.04520	−	5.84518i	0.756829	−	0.549868i	0.897936	+	0.440126i	$0.145066\pi$
$114$	−5.90197	−	7.51401i	−0.552770	−	0.703752i
$115$	0.716722	+	2.20584i	0.0668347	+	0.205696i
$116$	1.50574	−	0.800616i	0.139804	−	0.0743353i
$117$	4.97166	−	0.347652i	0.459630	−	0.0321405i
$118$	−3.21164	+	4.76145i	−0.295656	+	0.438327i
$119$	−13.7607	+	17.6128i	−1.26144	+	1.61457i
$120$	−2.63193	−	2.20845i	−0.240261	−	0.201603i
$121$	−6.50885	−	8.86763i	−0.591713	−	0.806149i
$122$	−3.84467	−	6.65917i	−0.348080	−	0.602893i
$123$	−3.28012	−	1.74407i	−0.295759	−	0.157258i
$124$	2.47768	+	5.07999i	0.222502	+	0.456197i
$125$	1.23587	−	11.7585i	0.110539	−	1.05171i
$126$	−5.54969	−	1.17962i	−0.494406	−	0.105089i
$127$	−7.01465	+	17.3619i	−0.622450	+	1.54062i	0.204813	+	0.978801i	$0.434342\pi$
$127$	−7.01465	+	17.3619i	−0.622450	+	1.54062i	−0.827262	+	0.561816i	$0.810103\pi$
$128$	0.559193	+	0.829038i	0.0494261	+	0.0732773i
$129$	−15.5060	+	22.9885i	−1.36522	+	2.02403i
$130$	1.62126	+	4.01276i	0.142194	+	0.351942i
$131$	2.30975	+	13.0993i	0.201804	+	1.14449i	0.902390	+	0.430919i	$0.141811\pi$
$131$	2.30975	+	13.0993i	0.201804	+	1.14449i	−0.700587	+	0.713567i	$0.747078\pi$
$132$	3.97439	+	6.08756i	0.345926	+	0.529854i
$133$	1.39697	−	13.6305i	0.121133	−	1.18192i
$134$	−1.70372	+	5.24351i	−0.147179	+	0.452971i
$135$	−2.95358	−	2.85223i	−0.254203	−	0.245481i
$136$	−7.09305	+	0.495994i	−0.608224	+	0.0425312i
$137$	−4.58241	−	5.86522i	−0.391502	−	0.501100i	0.551367	−	0.834263i	$-0.314106\pi$
$137$	−4.58241	−	5.86522i	−0.391502	−	0.501100i	−0.942869	+	0.333163i	$0.891884\pi$
$138$	−0.113202	+	3.24168i	−0.00963640	+	0.275950i
$139$	−3.89145	−	15.6078i	−0.330069	−	1.32383i	−0.874499	−	0.485027i	$-0.838810\pi$
$139$	−3.89145	−	15.6078i	−0.330069	−	1.32383i	0.544430	−	0.838806i	$-0.316746\pi$
$140$	−0.515010	−	4.89999i	−0.0435263	−	0.414125i
$141$	18.7430	−	3.98395i	1.57845	−	0.335509i
$142$	−1.58900	+	9.01167i	−0.133346	+	0.756243i
$143$	−0.820350	−	9.12111i	−0.0686011	−	0.762746i
$144$	−0.902464	−	1.56311i	−0.0752053	−	0.130259i
$145$	−1.78856	−	1.98639i	−0.148531	−	0.164961i
$146$	6.81009	+	0.476208i	0.563607	+	0.0394112i
$147$	−3.53165	−	5.23589i	−0.291286	−	0.431849i
$148$	2.00029	+	2.56026i	0.164423	+	0.210452i
$149$	−18.6037	−	11.6249i	−1.52407	−	0.952347i	−0.994573	−	0.104037i	$-0.966824\pi$
$149$	−18.6037	−	11.6249i	−1.52407	−	0.952347i	−0.529500	−	0.848310i	$-0.677621\pi$
$150$	2.44389	−	5.01073i	0.199543	−	0.409124i
$151$	−5.64590	+	4.10199i	−0.459457	+	0.333815i	−0.793318	−	0.608807i	$-0.791648\pi$
$151$	−5.64590	+	4.10199i	−0.459457	+	0.333815i	0.333861	+	0.942622i	$0.391648\pi$
$152$	3.51978	−	2.57121i	0.285492	−	0.208553i
$153$	12.8337			1.03754
$154$	−1.96440	+	10.2389i	−0.158296	+	0.825071i
$155$	6.78630	−	5.69438i	0.545089	−	0.457384i
$156$	0.211234	+	6.04894i	0.0169122	+	0.484303i
$157$	19.8888	−	5.70302i	1.58730	−	0.455150i	0.638132	−	0.769927i	$-0.279707\pi$
$157$	19.8888	−	5.70302i	1.58730	−	0.455150i	0.949166	+	0.314776i	$0.101929\pi$
$158$	−1.46951	−	5.89387i	−0.116908	−	0.468891i
$159$	1.16921	+	0.248524i	0.0927246	+	0.0197092i
$160$	1.04879	−	1.16480i	0.0829139	−	0.0920852i
$161$	−3.34604	+	3.23123i	−0.263705	+	0.254657i
$162$	−4.89092	−	10.0279i	−0.384267	−	0.787863i
$163$	−11.3942	+	2.42191i	−0.892461	+	0.189698i	−0.631246	−	0.775582i	$-0.717456\pi$
$163$	−11.3942	+	2.42191i	−0.892461	+	0.189698i	−0.261215	+	0.965281i	$0.584123\pi$
$164$	0.847387	−	1.46772i	0.0661698	−	0.114610i
$165$	7.75111	−	8.35268i	0.603423	−	0.650256i
$166$	10.1380	+	3.68992i	0.786860	+	0.286394i
$167$	−0.178758	−	5.11897i	−0.0138327	−	0.396118i	−0.986485	−	0.163852i	$-0.947608\pi$
$167$	−0.178758	−	5.11897i	−0.0138327	−	0.396118i	0.972652	−	0.232266i	$-0.0746140\pi$
$168$	1.66695	−	6.68578i	0.128608	−	0.515819i
$169$	−2.35654	+	4.83162i	−0.181272	+	0.371663i
$170$	3.44390	+	10.5992i	0.264135	+	0.812925i
$171$	−6.66120	+	4.18639i	−0.509395	+	0.320141i
$172$	−10.2341	−	7.43553i	−0.780345	−	0.566954i
$173$	−7.15161	−	6.90623i	−0.543727	−	0.525071i	0.371274	−	0.928523i	$-0.378921\pi$
$173$	−7.15161	−	6.90623i	−0.543727	−	0.525071i	−0.915001	+	0.403452i	$0.867810\pi$
$174$	−1.40034	−	3.46597i	−0.106160	−	0.262754i
$175$	7.51255	−	2.73435i	0.567896	−	0.206697i
$176$	−2.83874	+	1.71510i	−0.213978	+	0.129280i
$177$	9.64412	+	8.09238i	0.724897	+	0.608261i
$178$	−6.07616	−	6.74825i	−0.455427	−	0.505803i
$179$	2.11434	+	0.941364i	0.158033	+	0.0703609i	0.484229	−	0.874941i	$-0.339100\pi$
$179$	2.11434	+	0.941364i	0.158033	+	0.0703609i	−0.326196	+	0.945302i	$0.605767\pi$
$180$	−2.03503	+	1.96520i	−0.151682	+	0.146478i
$181$	−4.29641	+	0.603822i	−0.319350	+	0.0448817i	−0.297027	−	0.954869i	$-0.595995\pi$
$181$	−4.29641	+	0.603822i	−0.319350	+	0.0448817i	−0.0223230	+	0.999751i	$0.507106\pi$
$182$	−5.80787	+	6.45029i	−0.430508	+	0.478127i
$183$	−15.3980	+	6.85561i	−1.13825	+	0.506781i
$184$	−1.47616	−	0.103223i	−0.108824	−	0.00760970i
$185$	3.13523	−	4.01292i	0.230507	−	0.295036i
$186$	11.6421	−	4.23738i	0.853641	−	0.310700i
$187$	−0.468911	−	23.5778i	−0.0342901	−	1.72418i
$188$	1.51796	+	8.60880i	0.110709	+	0.627861i
$189$	2.54463	−	7.83157i	0.185095	−	0.569663i
$190$	−5.24503	−	4.37802i	−0.380514	−	0.317615i
$191$	−17.1919	−	12.4907i	−1.24396	−	0.903792i	−0.246107	−	0.969243i	$-0.579152\pi$
$191$	−17.1919	−	12.4907i	−1.24396	−	0.903792i	−0.997856	+	0.0654503i	$0.979152\pi$
$192$	1.93543	−	1.02909i	0.139678	−	0.0742681i
$193$	15.8074	+	9.87757i	1.13784	+	0.711003i	0.961901	−	0.273397i	$-0.0881474\pi$
$193$	15.8074	+	9.87757i	1.13784	+	0.711003i	0.175942	+	0.984401i	$0.443703\pi$
$194$	16.1141	+	4.62065i	1.15693	+	0.331743i
$195$	9.11932	−	2.61492i	0.653048	−	0.187258i
$196$	2.44339	−	1.52680i	0.174528	−	0.109057i
$197$	−6.44641	+	11.1655i	−0.459287	+	0.795509i	−0.998923	−	0.0463893i	$-0.985229\pi$
$197$	−6.44641	+	11.1655i	−0.459287	+	0.795509i	0.539636	+	0.841898i	$0.318562\pi$
$198$	5.32718	−	2.73067i	0.378586	−	0.194060i
$199$	1.23750	−	7.01824i	0.0877244	−	0.497510i	−0.909011	−	0.416772i	$-0.863161\pi$
$199$	1.23750	−	7.01824i	0.0877244	−	0.497510i	0.996735	−	0.0807377i	$-0.0257276\pi$
$200$	2.24560	+	1.19401i	0.158788	+	0.0844289i
$201$	11.0405	+	4.91556i	0.778738	+	0.346717i
$202$	3.11665	−	1.38762i	0.219287	−	0.0976328i
$203$	2.00815	−	4.97034i	0.140944	−	0.348849i
$204$	−0.543945	+	15.5765i	−0.0380838	+	1.09058i
$205$	−2.55347	−	0.732194i	−0.178342	−	0.0511387i
$206$	1.48744	−	5.96579i	0.103635	−	0.415656i
$207$	2.64487	+	0.371712i	0.183831	+	0.0258358i
$208$	−2.76122			−0.191456
$209$	7.93452	+	12.0848i	0.548842	+	0.835926i
$210$	−10.8000			−0.745272
$211$	17.9135	+	2.51758i	1.23322	+	0.173317i	0.725509	−	0.688213i	$-0.241604\pi$
$211$	17.9135	+	2.51758i	1.23322	+	0.173317i	0.507707	+	0.861530i	$0.330493\pi$
$212$	−0.131923	+	0.529115i	−0.00906052	+	0.0363398i
$213$	19.2814	+	5.52886i	1.32114	+	0.378831i
$214$	−0.340722	+	9.75700i	−0.0232913	+	0.666975i
$215$	−7.42754	+	18.3838i	−0.506554	+	1.25377i
$216$	2.39314	−	1.06549i	0.162832	−	0.0724977i
$217$	16.2307	+	7.22638i	1.10181	+	0.490559i
$218$	−13.2723	−	7.05701i	−0.898914	−	0.477961i
$219$	2.59852	−	14.7369i	0.175591	−	0.995829i
$220$	3.68478	+	3.66690i	0.248428	+	0.247222i
$221$	9.81665	−	17.0029i	0.660339	−	1.14374i
$222$	6.03970	−	3.77403i	0.405358	−	0.253296i
$223$	−4.33983	+	1.24443i	−0.290616	+	0.0833329i	−0.417778	−	0.908549i	$-0.637191\pi$
$223$	−4.33983	+	1.24443i	−0.290616	+	0.0833329i	0.127162	+	0.991882i	$0.459413\pi$
$224$	3.02167	+	0.866449i	0.201894	+	0.0578920i
$225$	−3.89294	−	2.43258i	−0.259529	−	0.162172i
$226$	8.78040	−	4.66862i	0.584063	−	0.310552i
$227$	12.3653	+	8.98391i	0.820713	+	0.596283i	0.916917	−	0.399078i	$-0.130670\pi$
$227$	12.3653	+	8.98391i	0.820713	+	0.596283i	−0.0962033	+	0.995362i	$0.530670\pi$
$228$	−4.79878	−	8.26228i	−0.317807	−	0.547183i
$229$	1.29890	−	3.99760i	0.0858336	−	0.264169i	−0.898923	−	0.438107i	$-0.855649\pi$
$229$	1.29890	−	3.99760i	0.0858336	−	0.264169i	0.984757	+	0.173938i	$0.0556492\pi$
$230$	0.402753	+	2.28412i	0.0265567	+	0.150611i
$231$	21.8707	+	6.62842i	1.43899	+	0.436118i
$232$	1.60251	−	0.583266i	0.105210	−	0.0382933i
$233$	0.519732	−	0.665227i	0.0340488	−	0.0435805i	−0.770685	−	0.637216i	$-0.780086\pi$
$233$	0.519732	−	0.665227i	0.0340488	−	0.0435805i	0.804734	+	0.593636i	$0.202308\pi$
$234$	4.97166	+	0.347652i	0.325008	+	0.0227267i
$235$	12.5169	−	5.57290i	0.816515	−	0.363536i
$236$	−3.84305	+	4.26814i	−0.250161	+	0.277832i
$237$	−13.1854	+	1.85309i	−0.856483	+	0.120371i
$238$	−16.0780	+	15.5263i	−1.04218	+	1.00642i
$239$	−24.0154	−	10.6923i	−1.55343	−	0.691630i	−0.562596	−	0.826732i	$-0.690197\pi$
$239$	−24.0154	−	10.6923i	−1.55343	−	0.691630i	−0.990832	+	0.135102i	$0.956864\pi$
$240$	−2.29896	−	2.55325i	−0.148397	−	0.164812i
$241$	3.57373	+	2.99871i	0.230204	+	0.193164i	0.750592	−	0.660766i	$-0.229768\pi$
$241$	3.57373	+	2.99871i	0.230204	+	0.193164i	−0.520388	+	0.853930i	$0.674213\pi$
$242$	−5.21137	−	9.68719i	−0.334999	−	0.622716i
$243$	−15.5965	+	5.67668i	−1.00052	+	0.364159i
$244$	−2.88048	−	7.12944i	−0.184404	−	0.456416i
$245$	−3.24851	−	3.13705i	−0.207539	−	0.200418i
$246$	−3.00547	−	2.18360i	−0.191622	−	0.139222i
$247$	0.451175	+	12.0274i	0.0287076	+	0.765286i
$248$	1.74657	+	5.37538i	0.110907	+	0.341337i
$249$	10.3670	−	21.2554i	0.656979	−	1.34701i
$250$	2.86031	−	11.4721i	0.180902	−	0.725557i
$251$	−0.664129	−	19.0182i	−0.0419194	−	1.20042i	−0.820042	−	0.572303i	$-0.806050\pi$
$251$	−0.664129	−	19.0182i	−0.0419194	−	1.20042i	0.778123	−	0.628112i	$-0.216172\pi$
$252$	−5.33151	−	1.94051i	−0.335854	−	0.122241i
$253$	0.586264	−	4.87267i	0.0368581	−	0.306342i
$254$	−9.36269	+	16.2167i	−0.587468	+	1.01752i
$255$	23.8955	−	5.07915i	1.49640	−	0.318069i
$256$	0.438371	+	0.898794i	0.0273982	+	0.0561746i
$257$	−4.29362	+	4.14630i	−0.267829	+	0.258639i	−0.816429	−	0.577445i	$-0.804050\pi$
$257$	−4.29362	+	4.14630i	−0.267829	+	0.258639i	0.548601	+	0.836085i	$0.315161\pi$
$258$	−18.5544	+	20.6068i	−1.15515	+	1.28292i
$259$	9.98989	+	2.12342i	0.620742	+	0.131943i
$260$	1.04701	+	4.19934i	0.0649330	+	0.260432i
$261$	−2.95881	+	0.848424i	−0.183145	+	0.0525161i
$262$	0.464210	+	13.2932i	0.0286790	+	0.821258i
$263$	−5.84983	+	4.90859i	−0.360716	+	0.302677i	−0.805076	−	0.593172i	$-0.797876\pi$
$263$	−5.84983	+	4.90859i	−0.360716	+	0.302677i	0.444360	+	0.895848i	$0.353431\pi$
$264$	3.08849	+	6.58145i	0.190083	+	0.405060i
$265$	0.854717			0.0525048
$266$	3.28038	−	13.3035i	0.201133	−	0.815687i
$267$	−16.1035	+	11.6998i	−0.985515	+	0.716019i
$268$	−2.41690	+	4.95537i	−0.147635	+	0.302697i
$269$	−20.1363	−	12.5825i	−1.22773	−	0.767171i	−0.248247	−	0.968697i	$-0.579854\pi$
$269$	−20.1363	−	12.5825i	−1.22773	−	0.767171i	−0.979483	+	0.201526i	$0.935410\pi$
$270$	−2.52788	−	3.23554i	−0.153842	−	0.196908i
$271$	−2.74502	−	4.06965i	−0.166748	−	0.247214i	0.736397	−	0.676550i	$-0.236526\pi$
$271$	−2.74502	−	4.06965i	−0.166748	−	0.247214i	−0.903145	+	0.429336i	$0.858748\pi$
$272$	−7.09305	−	0.495994i	−0.430079	−	0.0300741i
$273$	12.7309	+	14.1391i	0.770511	+	0.855739i
$274$	−3.72154	−	6.44589i	−0.224826	−	0.389411i
$275$	−4.32683	+	7.24089i	−0.260918	+	0.436642i
$276$	−0.563256	+	3.19438i	−0.0339040	+	0.192279i
$277$	8.46976	−	1.80030i	0.508898	−	0.108170i	0.0536953	−	0.998557i	$-0.482900\pi$
$277$	8.46976	−	1.80030i	0.508898	−	0.108170i	0.455203	+	0.890388i	$0.349567\pi$
$278$	−1.68140	−	15.9975i	−0.100844	−	0.959464i
$279$	−2.46796	−	9.89844i	−0.147753	−	0.592604i
$280$	0.171949	−	4.92398i	0.0102759	−	0.294264i
$281$	3.30034	+	4.22424i	0.196882	+	0.251997i	0.876313	−	0.481742i	$-0.159996\pi$
$281$	3.30034	+	4.22424i	0.196882	+	0.251997i	−0.679431	+	0.733739i	$0.737773\pi$
$282$	19.1151	−	1.33665i	1.13828	−	0.0795966i
$283$	−20.7776	−	20.0647i	−1.23510	−	1.19272i	−0.973786	−	0.227466i	$-0.926956\pi$
$283$	−20.7776	−	20.0647i	−1.23510	−	1.19272i	−0.261312	−	0.965254i	$-0.584155\pi$
$284$	−2.82772	+	8.70282i	−0.167794	+	0.516418i
$285$	−10.7459	+	10.4311i	−0.636532	+	0.617883i
$286$	0.457047	−	9.14651i	0.0270257	−	0.540845i
$287$	−0.925096	−	5.24648i	−0.0546067	−	0.309690i
$288$	−0.676138	−	1.67350i	−0.0398418	−	0.0986119i
$289$	18.7650	−	27.8203i	1.10383	−	1.63649i
$290$	−1.49470	−	2.21598i	−0.0877716	−	0.130127i
$291$	13.7652	−	34.0702i	0.806933	−	1.99723i
$292$	6.67754	+	1.41935i	0.390773	+	0.0830614i
$293$	1.68052	−	15.9890i	0.0981768	−	0.934090i	−0.828945	−	0.559330i	$-0.811059\pi$
$293$	1.68052	−	15.9890i	0.0981768	−	0.934090i	0.927122	−	0.374760i	$-0.122275\pi$
$294$	−2.76859	−	5.67645i	−0.161467	−	0.331057i
$295$	7.94834	+	4.22621i	0.462770	+	0.246059i
$296$	1.62451	+	2.81373i	0.0944226	+	0.163545i
$297$	3.13332	+	8.10362i	0.181814	+	0.470219i
$298$	−16.8048	−	14.1009i	−0.973474	−	0.816842i
$299$	2.51556	−	3.21977i	0.145479	−	0.186204i
$300$	3.11747	−	4.62184i	0.179987	−	0.266842i
$301$	−39.6679	+	2.77385i	−2.28642	+	0.159882i
$302$	−6.16184	+	3.27631i	−0.354574	+	0.188530i
$303$	−2.31091	−	7.11226i	−0.132759	−	0.408589i
$304$	3.84337	−	2.05633i	0.220432	−	0.117939i
$305$	−9.75042	+	7.08410i	−0.558308	+	0.405634i
$306$	12.7088	+	1.78611i	0.726514	+	0.102105i
$307$	21.6889	−	18.1991i	1.23785	−	1.03868i	0.240161	−	0.970733i	$-0.422800\pi$
$307$	21.6889	−	18.1991i	1.23785	−	1.03868i	0.997689	−	0.0679464i	$-0.0216447\pi$
$308$	−3.37026	+	9.86583i	−0.192038	+	0.562158i
$309$	−12.6647	−	4.60956i	−0.720467	−	0.262228i
$310$	7.51276	−	4.69449i	0.426696	−	0.266629i
$311$	1.02419	+	9.74448i	0.0580763	+	0.552559i	0.984414	+	0.175865i	$0.0562723\pi$
$311$	1.02419	+	9.74448i	0.0580763	+	0.552559i	−0.926338	+	0.376693i	$0.877061\pi$
$312$	−0.632672	+	6.01947i	−0.0358180	+	0.340786i
$313$	−12.7533	+	1.79236i	−0.720857	+	0.101310i	−0.490056	−	0.871691i	$-0.663024\pi$
$313$	−12.7533	+	1.79236i	−0.720857	+	0.101310i	−0.230801	+	0.973001i	$0.574135\pi$
$314$	20.4889	−	2.87953i	1.15626	−	0.162501i
$315$	−0.929556	+	8.84413i	−0.0523745	+	0.498310i
$316$	−0.634938	−	6.04103i	−0.0357180	−	0.339835i
$317$	−18.7718	+	11.7299i	−1.05433	+	0.658818i	−0.942260	−	0.334883i	$-0.891303\pi$
$317$	−18.7718	+	11.7299i	−1.05433	+	0.658818i	−0.112069	+	0.993700i	$0.535748\pi$
$318$	1.12325	+	0.408828i	0.0629885	+	0.0229260i
$319$	1.66681	+	5.40485i	0.0933235	+	0.302613i
$320$	1.20069	−	1.00750i	0.0671205	−	0.0563208i
$321$	21.1923	+	2.97838i	1.18284	+	0.166237i
$322$	−3.76317	+	2.73411i	−0.209714	+	0.152366i
$323$	−1.00149	+	30.9772i	−0.0557242	+	1.72362i
$324$	−3.44771	−	10.6110i	−0.191539	−	0.589498i
$325$	−6.20059	+	3.29691i	−0.343947	+	0.182880i
$326$	−11.6204	+	0.812574i	−0.643592	+	0.0450043i
$327$	−18.4254	+	27.3168i	−1.01893	+	1.51062i
$328$	1.04341	−	1.33550i	0.0576125	−	0.0737407i
$329$	21.0499	+	17.6630i	1.16052	+	0.973791i
$330$	8.83815	−	7.19265i	0.486524	−	0.395942i
$331$	−9.08835	−	15.7415i	−0.499541	−	0.865230i	0.500459	−	0.865760i	$-0.333165\pi$
$331$	−9.08835	−	15.7415i	−0.499541	−	0.865230i	−1.00000		0.000530140i	$0.999831\pi$
$332$	9.52578	+	5.06495i	0.522795	+	0.277975i
$333$	−2.57071	−	5.27074i	−0.140874	−	0.288835i
$334$	0.535404	−	5.09403i	0.0292960	−	0.278733i
$335$	8.45273	+	1.79668i	0.461822	+	0.0981632i
$336$	2.58121	−	6.38872i	0.140817	−	0.348533i
$337$	−10.1079	−	14.9856i	−0.550613	−	0.816317i	0.446296	−	0.894886i	$-0.352743\pi$
$337$	−10.1079	−	14.9856i	−0.550613	−	0.816317i	−0.996909	+	0.0785681i	$0.974965\pi$
$338$	−3.00604	+	4.45663i	−0.163507	+	0.242409i
$339$	−8.16579	−	20.2110i	−0.443505	−	1.09771i
$340$	1.93526	+	10.9754i	0.104954	+	0.595224i
$341$	−18.0950	+	4.89573i	−0.979899	+	0.265119i
$342$	−7.17901	+	3.21859i	−0.388196	+	0.174041i
$343$	−4.00090	+	12.3135i	−0.216028	+	0.664867i
$344$	−9.09971	−	8.78749i	−0.490623	−	0.473790i
$345$	5.07169	−	0.354647i	0.273050	−	0.0190935i
$346$	−6.12085	−	7.83433i	−0.329059	−	0.421176i
$347$	0.221462	−	6.34183i	0.0118887	−	0.340448i	−0.978843	−	0.204613i	$-0.934406\pi$
$347$	0.221462	−	6.34183i	0.0118887	−	0.340448i	0.990732	−	0.135834i	$-0.0433715\pi$
$348$	−0.904344	−	3.62713i	−0.0484779	−	0.194434i
$349$	2.04364	+	19.4440i	0.109394	+	1.04081i	0.902194	+	0.431330i	$0.141956\pi$
$349$	2.04364	+	19.4440i	0.109394	+	1.04081i	−0.792801	+	0.609481i	$0.791378\pi$
$350$	7.81999	−	1.66219i	0.417996	−	0.0888478i
$351$	−1.25606	+	7.12344i	−0.0670433	+	0.380221i
$352$	−3.04981	+	1.30333i	−0.162555	+	0.0694677i
$353$	−2.84689	−	4.93095i	−0.151524	−	0.262448i	0.780264	−	0.625451i	$-0.215085\pi$
$353$	−2.84689	−	4.93095i	−0.151524	−	0.262448i	−0.931788	+	0.363003i	$0.881752\pi$
$354$	8.42403	+	9.35583i	0.447732	+	0.497257i
$355$	14.3077	+	1.00049i	0.759376	+	0.0531007i
$356$	−5.07785	−	7.52822i	−0.269125	−	0.398995i
$357$	30.1636	+	38.6076i	1.59642	+	2.04333i
$358$	1.96275	+	1.22646i	0.103735	+	0.0648205i
$359$	−13.6100	+	27.9045i	−0.718306	+	1.47275i	0.156198	+	0.987726i	$0.450076\pi$
$359$	−13.6100	+	27.9045i	−0.718306	+	1.47275i	−0.874503	+	0.485019i	$0.838813\pi$
$360$	−2.28873	+	1.66286i	−0.120626	+	0.0876402i
$361$	−9.58504	−	16.4051i	−0.504476	−	0.863426i
$362$	−4.33864			−0.228034
$363$	−22.3122	+	9.14120i	−1.17109	+	0.479789i
$364$	−6.64905	+	5.57922i	−0.348505	+	0.292430i
$365$	−0.373428	−	10.6936i	−0.0195461	−	0.559728i
$366$	−16.2022	+	4.64591i	−0.846904	+	0.242846i
$367$	3.03430	+	12.1699i	0.158389	+	0.635265i	0.996028	+	0.0890404i	$0.0283800\pi$
$367$	3.03430	+	12.1699i	0.158389	+	0.635265i	−0.837639	+	0.546225i	$0.816064\pi$
$368$	−1.44743	−	0.307660i	−0.0754523	−	0.0160379i
$369$	−2.04683	+	2.27324i	−0.106554	+	0.118340i
$370$	3.66321	−	3.53752i	0.190441	−	0.183907i
$371$	0.751437	+	1.54067i	0.0390127	+	0.0799878i
$372$	12.1185	−	2.57588i	0.628317	−	0.133553i
$373$	5.68720	−	9.85052i	0.294472	−	0.510040i	−0.680390	−	0.732850i	$-0.738190\pi$
$373$	5.68720	−	9.85052i	0.294472	−	0.510040i	0.974862	+	0.222810i	$0.0715229\pi$
$374$	2.81704	−	23.4136i	0.145666	−	1.21069i
$375$	−24.3538	−	8.86406i	−1.25762	−	0.457738i
$376$	0.305078	+	8.73628i	0.0157332	+	0.450539i
$377$	−1.13918	+	4.56899i	−0.0586706	+	0.235315i
$378$	3.60981	−	7.40121i	0.185669	−	0.380677i
$379$	10.3462	+	31.8422i	0.531447	+	1.63563i	0.751204	+	0.660071i	$0.229474\pi$
$379$	10.3462	+	31.8422i	0.531447	+	1.63563i	−0.219757	+	0.975555i	$0.570526\pi$
$380$	−4.58468	−	5.06538i	−0.235189	−	0.259848i
$381$	33.2072	+	24.1264i	1.70125	+	1.23603i
$382$	−15.2862	−	14.7618i	−0.782112	−	0.755277i
$383$	7.81820	+	19.3507i	0.399491	+	0.988776i	0.984125	+	0.177478i	$0.0567939\pi$
$383$	7.81820	+	19.3507i	0.399491	+	0.988776i	−0.584633	+	0.811298i	$0.698762\pi$
$384$	2.05982	−	0.749713i	0.105115	−	0.0382586i
$385$	16.2822	+	1.38462i	0.829817	+	0.0705665i
$386$	14.2789	+	11.9814i	0.726776	+	0.609838i
$387$	15.2779	+	16.9678i	0.776620	+	0.862524i
$388$	15.3142	+	6.81834i	0.777462	+	0.346149i
$389$	7.27704	−	7.02736i	0.368961	−	0.356301i	−0.486945	−	0.873432i	$-0.661889\pi$
$389$	7.27704	−	7.02736i	0.368961	−	0.356301i	0.855906	+	0.517131i	$0.173000\pi$
$390$	9.39449	−	1.32031i	0.475709	−	0.0668565i
$391$	7.04036	−	7.81912i	0.356046	−	0.395430i
$392$	2.63211	−	1.17189i	0.132941	−	0.0591893i
$393$	29.0857	+	2.03387i	1.46718	+	0.102595i
$394$	−7.93761	+	10.1597i	−0.399891	+	0.511837i
$395$	−8.94662	+	3.25630i	−0.450153	+	0.163842i
$396$	5.65537	−	1.96270i	0.284193	−	0.0986292i
$397$	−2.11483	−	11.9938i	−0.106140	−	0.601950i	−0.990759	−	0.135635i	$-0.956692\pi$
$397$	−2.11483	−	11.9938i	−0.106140	−	0.601950i	0.884619	−	0.466315i	$-0.154419\pi$
$398$	2.20221	−	6.77771i	0.110387	−	0.339736i
$399$	−28.2500	−	10.1994i	−1.41427	−	0.510610i
$400$	2.05757	+	1.49491i	0.102879	+	0.0747456i
$401$	−8.20989	+	4.36528i	−0.409982	+	0.217992i	−0.661635	−	0.749826i	$-0.730137\pi$
$401$	−8.20989	+	4.36528i	−0.409982	+	0.217992i	0.251652	+	0.967818i	$0.419026\pi$
$402$	10.2490	+	6.40426i	0.511172	+	0.319416i
$403$	−15.0019	−	4.30171i	−0.747296	−	0.214284i
$404$	3.27944	−	0.940364i	0.163158	−	0.0467849i
$405$	−14.8301	+	9.26690i	−0.736915	+	0.460476i
$406$	2.68034	−	4.64249i	0.133023	−	0.230403i
$407$	−9.58935	+	4.91543i	−0.475326	+	0.243649i
$408$	−2.70649	+	15.3492i	−0.133991	+	0.759901i
$409$	4.01572	+	2.13520i	0.198565	+	0.105579i	0.565776	−	0.824559i	$-0.308577\pi$
$409$	4.01572	+	2.13520i	0.198565	+	0.105579i	−0.367212	+	0.930137i	$0.619688\pi$
$410$	−2.42671	−	1.08044i	−0.119847	−	0.0533592i
$411$	−14.9048	+	6.63604i	−0.735199	+	0.327332i
$412$	2.30324	−	5.70072i	0.113473	−	0.280854i
$413$	−0.630071	+	18.0429i	−0.0310038	+	0.887831i
$414$	2.56740	+	0.736190i	0.126181	+	0.0361817i
$415$	4.09089	−	16.4076i	0.200814	−	0.805420i
$416$	−2.73435	−	0.384287i	−0.134062	−	0.0188412i
$417$	−35.2598			−1.72668
$418$	6.17542	+	13.0715i	0.302050	+	0.639348i
$419$	17.5666			0.858184			0.429092	−	0.903261i	$-0.358834\pi$
$419$	17.5666			0.858184			0.429092	+	0.903261i	$0.358834\pi$
$420$	−10.6949	−	1.50307i	−0.521858	−	0.0733424i
$421$	1.67852	−	6.73219i	0.0818063	−	0.328107i	−0.915423	−	0.402493i	$-0.868144\pi$
$421$	1.67852	−	6.73219i	0.0818063	−	0.328107i	0.997230	+	0.0743854i	$0.0236995\pi$
$422$	17.3888	+	4.98615i	0.846473	+	0.242722i
$423$	0.550643	−	15.7684i	0.0267732	−	0.766684i
$424$	−0.204278	+	0.505605i	−0.00992061	+	0.0245544i
$425$	−16.5204	+	7.35534i	−0.801355	+	0.356786i
$426$	18.3243	+	8.15851i	0.887815	+	0.395281i
$427$	−21.3417	−	11.3476i	−1.03280	−	0.549148i
$428$	−1.69532	+	9.61463i	−0.0819463	+	0.464741i
$429$	−19.8347	−	3.09209i	−0.957630	−	0.149287i
$430$	−9.91379	+	17.1712i	−0.478086	+	0.828068i
$431$	16.8051	−	10.5010i	0.809474	−	0.505816i	−0.0609367	−	0.998142i	$-0.519409\pi$
$431$	16.8051	−	10.5010i	0.809474	−	0.505816i	0.870411	+	0.492326i	$0.163853\pi$
$432$	2.51814	−	0.722064i	0.121154	−	0.0347403i
$433$	11.4735	+	3.28998i	0.551382	+	0.158106i	0.539749	−	0.841826i	$-0.318519\pi$
$433$	11.4735	+	3.28998i	0.551382	+	0.158106i	0.0116332	+	0.999932i	$0.496297\pi$
$434$	15.0670	+	9.41493i	0.723241	+	0.451931i
$435$	−5.17333	+	2.75071i	−0.248042	+	0.131886i
$436$	−12.1610	−	8.83548i	−0.582406	−	0.423143i
$437$	−1.10361	+	6.35502i	−0.0527929	+	0.304002i
$438$	4.62421	−	14.2319i	0.220953	−	0.680025i
$439$	2.79408	+	15.8460i	0.133354	+	0.756289i	0.975992	+	0.217808i	$0.0698906\pi$
$439$	2.79408	+	15.8460i	0.133354	+	0.756289i	−0.842638	+	0.538481i	$0.818998\pi$
$440$	3.13858	+	4.14404i	0.149626	+	0.197559i
$441$	−4.88673	+	1.77863i	−0.232702	+	0.0846965i
$442$	12.0875	−	15.4712i	0.574942	−	0.735892i
$443$	34.6708	+	2.42442i	1.64726	+	0.115188i	0.862986	−	0.505227i	$-0.168591\pi$
$443$	34.6708	+	2.42442i	1.64726	+	0.115188i	0.784274	+	0.620415i	$0.213036\pi$
$444$	6.50617	−	2.89673i	0.308769	−	0.137473i
$445$	−9.52369	+	10.5771i	−0.451466	+	0.501404i
$446$	−4.47078	+	0.628328i	−0.211698	+	0.0297522i
$447$	−34.5904	+	33.4036i	−1.63607	+	1.57994i
$448$	2.87167	+	1.27855i	0.135674	+	0.0604059i
$449$	10.0974	+	11.2142i	0.476524	+	0.529233i	0.932699	−	0.360657i	$-0.117448\pi$
$449$	10.0974	+	11.2142i	0.476524	+	0.529233i	−0.456175	+	0.889890i	$0.650781\pi$
$450$	−3.51650	−	2.95069i	−0.165769	−	0.139097i
$451$	4.25113	+	3.67734i	0.200178	+	0.173159i
$452$	9.34469	−	3.40119i	0.439537	−	0.159979i
$453$	5.73052	+	14.1835i	0.269244	+	0.666401i
$454$	10.9946	+	10.6174i	0.516004	+	0.498299i
$455$	11.0063	+	7.99651i	0.515981	+	0.374882i
$456$	−3.60220	−	8.84974i	−0.168688	−	0.414427i
$457$	7.35842	+	22.6469i	0.344212	+	1.05938i	0.962004	+	0.273035i	$0.0880275\pi$
$457$	7.35842	+	22.6469i	0.344212	+	1.05938i	−0.617792	+	0.786342i	$0.711972\pi$
$458$	1.84261	−	3.77792i	0.0860997	−	0.176531i
$459$	−4.50614	+	18.0732i	−0.210329	+	0.843583i
$460$	0.0809445	+	2.31795i	0.00377406	+	0.108075i
$461$	−3.57793	−	1.30226i	−0.166641	−	0.0606523i	0.257353	−	0.966318i	$-0.417150\pi$
$461$	−3.57793	−	1.30226i	−0.166641	−	0.0606523i	−0.423993	+	0.905665i	$0.639372\pi$
$462$	20.7353	+	9.60773i	0.964695	+	0.446992i
$463$	2.85805	−	4.95030i	0.132825	−	0.230060i	−0.791939	−	0.610600i	$-0.790928\pi$
$463$	2.85805	−	4.95030i	0.132825	−	0.230060i	0.924765	+	0.380540i	$0.124262\pi$
$464$	1.66809	−	0.354563i	0.0774391	−	0.0164602i
$465$	−8.51264	−	17.4535i	−0.394764	−	0.809387i
$466$	0.607256	−	0.586420i	0.0281306	−	0.0271654i
$467$	−5.86550	+	6.51430i	−0.271423	+	0.301446i	−0.863411	−	0.504501i	$-0.831677\pi$
$467$	−5.86550	+	6.51430i	−0.271423	+	0.301446i	0.591988	+	0.805947i	$0.298343\pi$
$468$	4.87489	+	1.03619i	0.225342	+	0.0478979i
$469$	4.19272	+	16.8161i	0.193602	+	0.776495i
$470$	13.1707	−	3.77664i	0.607520	−	0.174203i
$471$	−1.58281	−	45.3258i	−0.0729321	−	2.08850i
$472$	−4.39966	+	3.69175i	−0.202511	+	0.169927i
$473$	30.6147	−	28.6882i	1.40767	−	1.31908i
$474$	−13.3150			−0.611577
$475$	6.17539	−	9.20670i	0.283346	−	0.422432i
$476$	−18.0823	+	13.1376i	−0.828803	+	0.602161i
$477$	0.431467	−	0.884638i	0.0197555	−	0.0405048i
$478$	−22.2936	−	13.9306i	−1.01969	−	0.637170i
$479$	−2.50593	−	3.20744i	−0.114499	−	0.146552i	0.727347	−	0.686270i	$-0.240753\pi$
$479$	−2.50593	−	3.20744i	−0.114499	−	0.146552i	−0.841846	+	0.539718i	$0.818531\pi$
$480$	−1.92124	−	2.84835i	−0.0876922	−	0.130009i
$481$	−8.94939	−	0.625802i	−0.408057	−	0.0285341i
$482$	3.12161	+	3.46690i	0.142185	+	0.157913i
$483$	5.09812	+	8.83020i	0.231973	+	0.401788i
$484$	−3.81245	−	10.3182i	−0.173293	−	0.469009i
$485$	4.56259	−	25.8758i	0.207177	−	1.17496i
$486$	−16.2348	+	3.45081i	−0.736426	+	0.156532i
$487$	1.92380	+	18.3038i	0.0871758	+	0.829422i	0.947517	+	0.319704i	$0.103584\pi$
$487$	1.92380	+	18.3038i	0.0871758	+	0.829422i	−0.860342	+	0.509718i	$0.829750\pi$
$488$	−1.86022	−	7.46094i	−0.0842083	−	0.337741i
$489$	−0.891130	+	25.5186i	−0.0402983	+	1.15399i
$490$	−2.78030	−	3.55862i	−0.125601	−	0.160762i
$491$	−17.7812	+	1.24338i	−0.802453	+	0.0561130i	−0.465092	−	0.885262i	$-0.653979\pi$
$491$	−17.7812	+	1.24338i	−0.802453	+	0.0561130i	−0.337361	+	0.941375i	$0.609534\pi$
$492$	−2.67233	−	2.58064i	−0.120478	−	0.116344i
$493$	−3.74705	+	11.5322i	−0.168759	+	0.519386i
$494$	−1.22711	+	11.9732i	−0.0552102	+	0.538698i
$495$	−5.12936	−	7.85663i	−0.230548	−	0.353129i
$496$	0.981461	+	5.56614i	0.0440689	+	0.249927i
$497$	10.7754	+	26.6701i	0.483344	+	1.19632i
$498$	13.2242	−	19.6057i	0.592593	−	0.878555i
$499$	2.95413	+	4.37968i	0.132245	+	0.196061i	0.889344	−	0.457239i	$-0.151162\pi$
$499$	2.95413	+	4.37968i	0.132245	+	0.196061i	−0.757099	+	0.653300i	$0.773384\pi$
$500$	4.42907	−	10.9623i	0.198074	−	0.490251i
$501$	−10.9823	−	2.33437i	−0.490655	−	0.104292i
$502$	1.98915	−	18.9255i	0.0887801	−	0.844686i
$503$	−13.1486	−	26.9585i	−0.586265	−	1.20202i	−0.961427	−	0.275062i	$-0.911302\pi$
$503$	−13.1486	−	26.9585i	−0.586265	−	1.20202i	0.375161	−	0.926959i	$-0.377587\pi$
$504$	−5.00956	−	2.66363i	−0.223143	−	0.118648i
$505$	−2.67365	−	4.63090i	−0.118976	−	0.206072i
$506$	1.25870	−	4.74366i	0.0559562	−	0.210881i
$507$	9.02672	+	7.57432i	0.400891	+	0.336387i
$508$	−11.5285	+	14.7558i	−0.511494	+	0.654683i
$509$	8.33453	−	12.3565i	0.369422	−	0.547690i	−0.597793	−	0.801651i	$-0.703956\pi$
$509$	8.33453	−	12.3565i	0.369422	−	0.547690i	0.967215	+	0.253960i	$0.0817333\pi$
$510$	24.3698	−	1.70411i	1.07912	−	0.0754591i
$511$	18.9475	−	10.0746i	0.838188	−	0.445672i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−3.55665	−	10.8506i	−0.157030	−	0.479066i
$514$	−4.82889	+	3.50839i	−0.212993	+	0.154749i
$515$	−9.54318	−	1.34121i	−0.420523	−	0.0591006i
$516$	−21.2418	+	17.8240i	−0.935117	+	0.784656i
$517$	−28.9894	−	0.435493i	−1.27495	−	0.0191530i
$518$	9.59715	+	3.49308i	0.421675	+	0.153477i
$519$	−18.4814	+	11.5484i	−0.811241	+	0.506920i
$520$	0.452389	+	4.30419i	0.0198386	+	0.188751i
$521$	0.768166	−	7.30861i	0.0336540	−	0.320196i	−0.964724	−	0.263263i	$-0.915201\pi$
$521$	0.768166	−	7.30861i	0.0336540	−	0.320196i	0.998378	−	0.0569328i	$-0.0181321\pi$
$522$	−3.04809	+	0.428381i	−0.133411	+	0.0187497i
$523$	33.1019	−	4.65217i	1.44745	−	0.203425i	0.628729	−	0.777624i	$-0.283575\pi$
$523$	33.1019	−	4.65217i	1.44745	−	0.203425i	0.818716	+	0.574199i	$0.194686\pi$
$524$	−1.39037	+	13.2285i	−0.0607385	+	0.577888i
$525$	−1.83181	−	17.4285i	−0.0799466	−	0.760641i
$526$	−6.47604	+	4.04668i	−0.282369	+	0.176444i
$527$	−37.7642	−	13.7451i	−1.64504	−	0.598744i
$528$	2.14247	+	6.94723i	0.0932390	+	0.302339i
$529$	−15.9416	+	13.3766i	−0.693114	+	0.581592i
$530$	0.846399	+	0.118954i	0.0367652	+	0.00516701i
$531$	8.38654	−	6.09318i	0.363945	−	0.264421i
$532$	5.09994	−	12.7174i	0.221110	−	0.551371i
$533$	1.44609	+	4.45061i	0.0626371	+	0.192777i
$534$	−17.5750	+	9.34481i	−0.760546	+	0.404390i
$535$	15.2651	−	1.06744i	0.659966	−	0.0461493i
$536$	−3.08303	+	4.57078i	−0.133167	+	0.197428i
$537$	3.12342	−	3.99779i	0.134785	−	0.172517i
$538$	−18.1892	−	15.2625i	−0.784190	−	0.658014i
$539$	3.44620	+	8.91280i	0.148438	+	0.383902i
$540$	−2.05298	−	3.55586i	−0.0883461	−	0.153020i
$541$	−36.0099	−	19.1468i	−1.54819	−	0.823186i	−0.548274	−	0.836299i	$-0.684715\pi$
$541$	−36.0099	−	19.1468i	−1.54819	−	0.823186i	−0.999914	+	0.0131122i	$0.995826\pi$
$542$	−2.15192	−	4.41208i	−0.0924327	−	0.189515i
$543$	−0.994103	+	9.45826i	−0.0426610	+	0.405893i
$544$	−6.95499	−	1.47833i	−0.298193	−	0.0633828i
$545$	−8.82599	+	21.8451i	−0.378064	+	0.935741i
$546$	10.6392	+	15.7733i	0.455318	+	0.675036i
$547$	17.6792	−	26.2104i	0.755907	−	1.12068i	−0.233049	−	0.972465i	$-0.574870\pi$
$547$	17.6792	−	26.2104i	0.755907	−	1.12068i	0.988956	−	0.148213i	$-0.0473520\pi$
$548$	−2.78822	−	6.90110i	−0.119107	−	0.294800i
$549$	2.41001	+	13.6679i	0.102857	+	0.583330i
$550$	−5.29246	+	6.56824i	−0.225671	+	0.280071i
$551$	−1.81698	−	7.20799i	−0.0774060	−	0.307071i
$552$	−1.00235	+	3.08490i	−0.0426627	+	0.131302i
$553$	−13.7352	−	13.2639i	−0.584081	−	0.564040i
$554$	8.63788	−	0.604020i	0.366988	−	0.0256623i
$555$	−6.87248	−	8.79637i	−0.291721	−	0.373385i
$556$	0.561379	−	16.0758i	0.0238078	−	0.681765i
$557$	−2.66554	−	10.6909i	−0.112942	−	0.452987i	0.887019	−	0.461732i	$-0.152772\pi$
$557$	−2.66554	−	10.6909i	−0.112942	−	0.452987i	−0.999962	+	0.00874511i	$0.997216\pi$
$558$	−1.06634	−	10.1456i	−0.0451419	−	0.429497i
$559$	34.1664	−	7.26228i	1.44508	−	0.307162i
$560$	0.855562	−	4.85213i	0.0361541	−	0.205040i
$561$	−50.3963	−	11.5059i	−2.12773	−	0.485779i
$562$	2.68032	+	4.64245i	0.113063	+	0.195830i
$563$	22.2589	+	24.7210i	0.938099	+	1.04186i	0.999044	+	0.0437231i	$0.0139219\pi$
$563$	22.2589	+	24.7210i	0.938099	+	1.04186i	−0.0609450	+	0.998141i	$0.519411\pi$
$564$	19.1151	+	1.33665i	0.804889	+	0.0562833i
$565$	−8.71600	−	12.9220i	−0.366685	−	0.543633i
$566$	−17.7829	−	22.7611i	−0.747471	−	0.956719i
$567$	−29.7422	−	18.5850i	−1.24906	−	0.780497i
$568$	−4.01140	+	8.22459i	−0.168315	+	0.345096i
$569$	−18.5522	+	13.4790i	−0.777750	+	0.565069i	−0.904303	−	0.426891i	$-0.859609\pi$
$569$	−18.5522	+	13.4790i	−0.777750	+	0.565069i	0.126553	+	0.991960i	$0.459609\pi$
$570$	−12.0930	+	8.83401i	−0.506522	+	0.370016i
$571$	29.2044			1.22217			0.611083	−	0.791566i	$-0.290734\pi$
$571$	29.2044			1.22217			0.611083	+	0.791566i	$0.290734\pi$
$572$	1.72555	−	8.99389i	0.0721488	−	0.376054i
$573$	−35.6832	+	29.9418i	−1.49069	+	1.25084i
$574$	−0.185924	−	5.32417i	−0.00776033	−	0.222227i
$575$	−3.61768	+	1.03735i	−0.150868	+	0.0432607i
$576$	−0.436651	−	1.75131i	−0.0181938	−	0.0729714i
$577$	−7.44130	−	1.58170i	−0.309785	−	0.0658469i	0.0503958	−	0.998729i	$-0.483952\pi$
$577$	−7.44130	−	1.58170i	−0.309785	−	0.0658469i	−0.360181	+	0.932882i	$0.617285\pi$
$578$	22.4543	−	24.9380i	0.933974	−	1.03728i
$579$	29.3912	−	28.3828i	1.22146	−	1.17955i
$580$	−1.17175	−	2.40243i	−0.0486541	−	0.0997557i
$581$	33.1723	−	7.05098i	1.37622	−	0.292524i
$582$	18.3729	−	31.8229i	0.761583	−	1.31910i
$583$	−1.64100	−	0.760358i	−0.0679633	−	0.0314908i
$584$	6.41502	+	2.33487i	0.265455	+	0.0966178i
$585$	−0.272619	−	7.80679i	−0.0112714	−	0.322771i
$586$	3.88940	−	15.5996i	0.160670	−	0.644412i
$587$	13.9864	−	28.6764i	0.577282	−	1.18360i	−0.387822	−	0.921734i	$-0.626772\pi$
$587$	13.9864	−	28.6764i	0.577282	−	1.18360i	0.965103	−	0.261869i	$-0.0843388\pi$
$588$	−1.95164	−	6.00652i	−0.0804841	−	0.247705i
$589$	24.0848	−	5.18457i	0.992398	−	0.213627i
$590$	7.28282	+	5.29128i	0.299829	+	0.217838i
$591$	20.3294	+	19.6319i	0.836241	+	0.807548i
$592$	1.21710	+	3.01243i	0.0500226	+	0.123810i
$593$	18.5091	−	6.73675i	0.760076	−	0.276645i	0.0672369	−	0.997737i	$-0.478582\pi$
$593$	18.5091	−	6.73675i	0.760076	−	0.276645i	0.692839	+	0.721092i	$0.256359\pi$
$594$	1.97502	+	8.46083i	0.0810361	+	0.347152i
$595$	26.8366	+	22.5186i	1.10019	+	0.923172i
$596$	−14.6788	−	16.3024i	−0.601266	−	0.667773i
$597$	−14.2709	−	6.35380i	−0.584068	−	0.260044i
$598$	2.93918	−	2.83834i	0.120192	−	0.116068i
$599$	41.0820	−	5.77370i	1.67856	−	0.235907i	0.765417	−	0.643535i	$-0.222533\pi$
$599$	41.0820	−	5.77370i	1.67856	−	0.235907i	0.913148	+	0.407628i	$0.133644\pi$
$600$	3.73037	−	4.14299i	0.152292	−	0.169137i
$601$	−3.03684	+	1.35209i	−0.123875	+	0.0551528i	−0.467738	−	0.883867i	$-0.654931\pi$
$601$	−3.03684	+	1.35209i	−0.123875	+	0.0551528i	0.343863	+	0.939020i	$0.388264\pi$
$602$	−39.6679	−	2.77385i	−1.61674	−	0.113054i
$603$	6.12657	−	7.84166i	0.249493	−	0.319337i
$604$	−6.55785	+	2.38686i	−0.266835	+	0.0971200i
$605$	−14.2466	+	9.71060i	−0.579206	+	0.394792i
$606$	−1.29859	−	7.36467i	−0.0527516	−	0.299169i
$607$	−13.7055	+	42.1812i	−0.556290	+	1.71208i	0.136223	+	0.990678i	$0.456504\pi$
$607$	−13.7055	+	42.1812i	−0.556290	+	1.71208i	−0.692513	+	0.721406i	$0.743496\pi$
$608$	4.09215	−	1.50143i	0.165959	−	0.0608909i
$609$	−9.50651	−	6.90688i	−0.385223	−	0.279881i
$610$	−10.6414	+	5.65816i	−0.430860	+	0.229092i
$611$	−20.4698	−	12.7909i	−0.828118	−	0.517465i
$612$	12.3365	+	3.53745i	0.498675	+	0.142993i
$613$	43.4460	−	12.4579i	1.75477	−	0.503171i	0.764775	−	0.644298i	$-0.222850\pi$
$613$	43.4460	−	12.4579i	1.75477	−	0.503171i	0.989992	+	0.141127i	$0.0450725\pi$
$614$	24.0106	−	15.0035i	0.968991	−	0.605492i
$615$	−2.91140	+	5.04269i	−0.117399	+	0.203341i
$616$	−4.71052	+	9.30076i	−0.189792	+	0.374738i
$617$	2.51314	−	14.2528i	0.101175	−	0.573794i	−0.891504	−	0.453013i	$-0.850349\pi$
$617$	2.51314	−	14.2528i	0.101175	−	0.573794i	0.992679	−	0.120781i	$-0.0385399\pi$
$618$	−11.8999	−	6.32728i	−0.478683	−	0.254520i
$619$	−1.21843	−	0.542480i	−0.0489729	−	0.0218041i	0.382104	−	0.924119i	$-0.375200\pi$
$619$	−1.21843	−	0.542480i	−0.0489729	−	0.0218041i	−0.431077	+	0.902315i	$0.641866\pi$
$620$	8.09299	−	3.60323i	0.325022	−	0.144709i
$621$	−1.45213	+	3.59414i	−0.0582719	+	0.144228i
$622$	−0.341951	+	9.79218i	−0.0137110	+	0.392631i
$623$	−27.4388	−	7.86794i	−1.09931	−	0.315222i
$624$	−1.46426	+	5.87284i	−0.0586175	+	0.235102i
$625$	−5.75857	−	0.809314i	−0.230343	−	0.0323725i
$626$	−12.8786			−0.514733
$627$	29.9109	−	10.4674i	1.19453	−	0.418028i
$628$	20.6903			0.825633
$629$	−22.8769	−	3.21514i	−0.912161	−	0.128196i
$630$	−2.15137	+	8.62869i	−0.0857128	+	0.343775i
$631$	20.5222	+	5.88464i	0.816975	+	0.234264i	0.657999	−	0.753018i	$-0.271403\pi$
$631$	20.5222	+	5.88464i	0.816975	+	0.234264i	0.158976	+	0.987282i	$0.449181\pi$
$632$	0.211990	−	6.07061i	0.00843252	−	0.241476i
$633$	14.8541	−	36.7652i	0.590398	−	1.46129i
$634$	−20.2216	+	9.00323i	−0.803102	+	0.357564i
$635$	26.8125	+	11.9377i	1.06402	+	0.473733i
$636$	1.05542	+	0.561175i	0.0418500	+	0.0222520i
$637$	−1.38148	+	7.83476i	−0.0547362	+	0.310424i
$638$	0.898380	+	5.58422i	0.0355672	+	0.221081i
$639$	8.25817	−	14.3036i	0.326688	−	0.565840i
$640$	1.32922	−	0.830589i	0.0525420	−	0.0328319i
$641$	−10.6018	+	3.04001i	−0.418745	+	0.120073i	−0.478392	−	0.878146i	$-0.658780\pi$
$641$	−10.6018	+	3.04001i	−0.418745	+	0.120073i	0.0596469	+	0.998220i	$0.481003\pi$
$642$	20.5715	+	5.89879i	0.811893	+	0.232806i
$643$	14.7726	+	9.23095i	0.582575	+	0.364033i	0.788966	−	0.614436i	$-0.210617\pi$
$643$	14.7726	+	9.23095i	0.582575	+	0.364033i	−0.206392	+	0.978469i	$0.566172\pi$
$644$	−4.10707	+	2.18377i	−0.161841	+	0.0860524i
$645$	35.1618	+	25.5465i	1.38449	+	1.00589i
$646$	−5.30293	+	30.5364i	−0.208641	+	1.20144i
$647$	−3.51006	+	10.8029i	−0.137995	+	0.424704i	−0.996044	−	0.0888637i	$-0.971676\pi$
$647$	−3.51006	+	10.8029i	−0.137995	+	0.424704i	0.858049	+	0.513568i	$0.171676\pi$
$648$	−1.93740	−	10.9875i	−0.0761081	−	0.431631i
$649$	−11.5007	−	15.1849i	−0.451440	−	0.596060i
$650$	−6.59908	+	2.40187i	−0.258837	+	0.0942091i
$651$	23.9769	−	30.6890i	0.939729	−	1.20280i
$652$	−11.6204	−	0.812574i	−0.455088	−	0.0318229i
$653$	22.3759	−	9.96240i	0.875637	−	0.389859i	0.0808349	−	0.996728i	$-0.474241\pi$
$653$	22.3759	−	9.96240i	0.875637	−	0.389859i	0.794802	+	0.606869i	$0.207575\pi$
$654$	−22.0478	+	24.4866i	−0.862138	+	0.957502i
$655$	20.6454	−	2.90153i	0.806684	−	0.113372i
$656$	1.21912	−	1.17729i	0.0475986	−	0.0459654i
$657$	−11.2565	−	5.01170i	−0.439156	−	0.195525i
$658$	18.3868	+	20.4207i	0.716794	+	0.796080i
$659$	10.8915	+	9.13906i	0.424273	+	0.356007i	0.829786	−	0.558082i	$-0.188463\pi$
$659$	10.8915	+	9.13906i	0.424273	+	0.356007i	−0.405513	+	0.914089i	$0.632907\pi$
$660$	9.75316	−	5.89262i	0.379641	−	0.229370i
$661$	13.6246	−	4.95895i	0.529936	−	0.192881i	−0.0631739	−	0.998003i	$-0.520122\pi$
$661$	13.6246	−	4.95895i	0.529936	−	0.192881i	0.593110	+	0.805122i	$0.297900\pi$
$662$	−6.80911	−	16.8531i	−0.264644	−	0.655016i
$663$	−30.9578	−	29.8956i	−1.20230	−	1.16105i
$664$	8.72817	+	6.34139i	0.338719	+	0.246094i
$665$	−21.2749	−	2.93386i	−0.825005	−	0.113770i
$666$	−1.81215	−	5.57722i	−0.0702193	−	0.216113i
$667$	−1.10624	+	2.26813i	−0.0428337	+	0.0878222i
$668$	1.23915	−	4.96994i	0.0479440	−	0.192293i
$669$	0.345377	+	9.89030i	0.0133530	+	0.382381i
$670$	8.12041	+	2.95559i	0.313719	+	0.114184i
$671$	25.0222	−	4.92701i	0.965972	−	0.190205i
$672$	3.44523	−	5.96731i	0.132903	−	0.230194i
$673$	−25.0841	+	5.33180i	−0.966922	+	0.205526i	−0.664202	−	0.747554i	$-0.731228\pi$
$673$	−25.0841	+	5.33180i	−0.966922	+	0.205526i	−0.302721	+	0.953079i	$0.597895\pi$
$674$	−7.92395	−	16.2465i	−0.305219	−	0.625792i
$675$	4.79257	−	4.62813i	0.184466	−	0.178137i
$676$	−3.59703	+	3.99490i	−0.138347	+	0.153650i
$677$	−18.3901	−	3.90894i	−0.706790	−	0.150233i	−0.159527	−	0.987194i	$-0.550997\pi$
$677$	−18.3901	−	3.90894i	−0.706790	−	0.150233i	−0.547263	+	0.836961i	$0.684330\pi$
$678$	−5.27349	−	21.1508i	−0.202527	−	0.812291i
$679$	50.6537	−	14.5247i	1.94391	−	0.557408i
$680$	0.388945	+	11.1379i	0.0149153	+	0.427120i
$681$	25.6652	−	21.5356i	0.983492	−	0.825247i
$682$	−18.6002	+	2.32975i	−0.712240	+	0.0892109i
$683$	0.0139498			0.000533773			0.000266887	−	1.00000i	$-0.499915\pi$
$683$	0.0139498			0.000533773			0.000266887		1.00000i	$0.499915\pi$
$684$	−7.55709	+	2.18814i	−0.288952	+	0.0836657i
$685$	−9.43814	+	6.85721i	−0.360613	+	0.262001i
$686$	−5.67568	+	11.6369i	−0.216698	+	0.444297i
$687$	−7.81369	−	4.88254i	−0.298111	−	0.186280i
$688$	−7.78817	−	9.96840i	−0.296921	−	0.380042i
$689$	−0.841993	−	1.24831i	−0.0320774	−	0.0475566i
$690$	5.07169	+	0.354647i	0.193076	+	0.0135012i
$691$	−9.98325	−	11.0875i	−0.379781	−	0.421789i	0.522702	−	0.852516i	$-0.324924\pi$
$691$	−9.98325	−	11.0875i	−0.379781	−	0.421789i	−0.902483	+	0.430726i	$0.858257\pi$
$692$	−4.97095	−	8.60995i	−0.188967	−	0.327301i
$693$	9.65245	−	16.1532i	0.366666	−	0.613610i
$694$	1.10192	−	6.24929i	0.0418283	−	0.237220i
$695$	−24.6614	+	5.24194i	−0.935460	+	0.198838i
$696$	−0.390745	−	3.71769i	−0.0148111	−	0.140919i
$697$	2.91527	+	11.6925i	0.110424	+	0.442886i
$698$	−0.682322	+	19.5392i	−0.0258263	+	0.739568i
$699$	−1.13926	−	1.45819i	−0.0430908	−	0.0551537i
$700$	7.97522	−	0.557682i	0.301435	−	0.0210784i
$701$	24.3191	+	23.4847i	0.918520	+	0.887004i	0.993915	−	0.110149i	$-0.0351329\pi$
$701$	24.3191	+	23.4847i	0.918520	+	0.887004i	−0.0753952	+	0.997154i	$0.524022\pi$
$702$	−2.23522	+	6.87931i	−0.0843631	+	0.259643i
$703$	12.9228	−	5.79372i	0.487392	−	0.218514i
$704$	−3.20152	+	0.866194i	−0.120662	+	0.0326459i
$705$	−5.21532	−	29.5776i	−0.196420	−	1.11396i
$706$	−2.13292	−	5.27917i	−0.0802737	−	0.198684i
$707$	5.99687	−	8.89072i	0.225535	−	0.334370i
$708$	7.03996	+	10.4372i	0.264578	+	0.392253i
$709$	11.2133	−	27.7538i	0.421123	−	1.04232i	−0.556292	−	0.830987i	$-0.687776\pi$
$709$	11.2133	−	27.7538i	0.421123	−	1.04232i	0.977415	−	0.211330i	$-0.0677793\pi$
$710$	14.0293	+	2.98201i	0.526509	+	0.111913i
$711$	−1.14602	+	10.9036i	−0.0429790	+	0.408918i
$712$	−3.98070	−	8.16165i	−0.149183	−	0.305871i
$713$	−7.38464	−	3.92648i	−0.276557	−	0.147048i
$714$	24.4969	+	42.4298i	0.916772	+	1.58790i
$715$	−14.3325	+	0.786089i	−0.536004	+	0.0293981i
$716$	1.77296	+	1.48769i	0.0662585	+	0.0555975i
$717$	−35.4769	+	45.4083i	−1.32491	+	1.69580i
$718$	−17.3611	+	25.7388i	−0.647909	+	0.960565i
$719$	−46.3533	+	3.24134i	−1.72869	+	0.120882i	−0.899169	−	0.437601i	$-0.855828\pi$
$719$	−46.3533	+	3.24134i	−1.72869	+	0.120882i	−0.829517	+	0.558482i	$0.811384\pi$
$720$	−2.49788	+	1.32814i	−0.0930904	+	0.0494970i
$721$	−5.97243	−	18.3813i	−0.222425	−	0.684554i
$722$	−7.20861	−	17.5794i	−0.268277	−	0.654238i
$723$	8.27310	−	6.01076i	0.307680	−	0.223543i
$724$	−4.29641	−	0.603822i	−0.159675	−	0.0224409i
$725$	3.32251	−	2.78792i	0.123395	−	0.103541i
$726$	−23.3673	+	5.94698i	−0.867241	+	0.220713i
$727$	11.3647	+	4.13641i	0.421493	+	0.153411i	0.544054	−	0.839050i	$-0.316889\pi$
$727$	11.3647	+	4.13641i	0.421493	+	0.153411i	−0.122561	+	0.992461i	$0.539111\pi$
$728$	−7.36082	+	4.59955i	−0.272810	+	0.170471i
$729$	0.304272	+	2.89495i	0.0112693	+	0.107221i
$730$	1.11847	−	10.6415i	0.0413963	−	0.393859i
$731$	89.0714	−	12.5182i	3.29443	−	0.463001i
$732$	−16.6911	+	2.34579i	−0.616922	+	0.0867027i
$733$	0.203067	−	1.93205i	0.00750045	−	0.0713620i	−0.990131	−	0.140142i	$-0.955244\pi$
$733$	0.203067	−	1.93205i	0.00750045	−	0.0713620i	0.997632	+	0.0687802i	$0.0219107\pi$
$734$	1.31105	+	12.4738i	0.0483917	+	0.460416i
$735$	−8.39486	+	5.24569i	−0.309649	+	0.193490i
$736$	−1.39052	−	0.506108i	−0.0512553	−	0.0186554i
$737$	−14.6304	−	10.9691i	−0.538916	−	0.404051i
$738$	−2.34329	+	1.96625i	−0.0862576	+	0.0723787i
$739$	14.6009	+	2.05203i	0.537104	+	0.0754850i	0.402509	−	0.915416i	$-0.368138\pi$
$739$	14.6009	+	2.05203i	0.537104	+	0.0754850i	0.134594	+	0.990901i	$0.457027\pi$
$740$	4.11989	−	2.99328i	0.151450	−	0.110035i
$741$	25.8204	+	5.41849i	0.948536	+	0.199053i
$742$	0.529704	+	1.63026i	0.0194460	+	0.0598487i
$743$	34.6278	−	18.4119i	1.27037	−	0.675468i	0.309089	−	0.951033i	$-0.399976\pi$
$743$	34.6278	−	18.4119i	1.27037	−	0.675468i	0.961283	+	0.275565i	$0.0888648\pi$
$744$	12.3591	−	0.864233i	0.453107	−	0.0316843i
$745$	−19.2272	+	28.5055i	−0.704431	+	1.04436i
$746$	7.00278	−	8.96315i	0.256390	−	0.328164i
$747$	−14.9169	−	12.5168i	−0.545782	−	0.457965i
$748$	6.04817	−	22.7937i	0.221143	−	0.833419i
$749$	15.3446	+	26.5776i	0.560680	+	0.971126i
$750$	−22.8832	−	12.1672i	−0.835575	−	0.444283i
$751$	3.53787	+	7.25371i	0.129099	+	0.264692i	0.953546	−	0.301247i	$-0.0974028\pi$
$751$	3.53787	+	7.25371i	0.129099	+	0.264692i	−0.824447	+	0.565939i	$0.808514\pi$
$752$	−0.913747	+	8.69372i	−0.0333209	+	0.317027i
$753$	−40.8019	−	8.67272i	−1.48691	−	0.316052i
$754$	−1.76397	+	4.36598i	−0.0642400	+	0.159000i
$755$	6.11665	+	9.06830i	0.222608	+	0.330029i
$756$	4.60473	−	6.82679i	0.167472	−	0.248288i
$757$	8.44307	+	20.8973i	0.306869	+	0.759527i	0.999277	+	0.0380208i	$0.0121053\pi$
$757$	8.44307	+	20.8973i	0.306869	+	0.759527i	−0.692408	+	0.721506i	$0.743450\pi$
$758$	5.81390	+	32.9722i	0.211170	+	1.19761i
$759$	−10.0528	−	3.83089i	−0.364894	−	0.139052i
$760$	−3.83510	−	5.65415i	−0.139114	−	0.205097i
$761$	0.309190	−	0.951588i	0.0112081	−	0.0344950i	−0.945296	−	0.326214i	$-0.894227\pi$
$761$	0.309190	−	0.951588i	0.0112081	−	0.0344950i	0.956504	+	0.291719i	$0.0942271\pi$
$762$	29.5262	+	28.5132i	1.06962	+	1.03292i
$763$	−47.1365	+	3.29610i	−1.70646	+	0.119327i
$764$	−13.0830	−	16.7455i	−0.473328	−	0.605832i
$765$	0.702017	−	20.1031i	0.0253815	−	0.726830i
$766$	5.04901	+	20.2505i	0.182428	+	0.731680i
$767$	−1.65768	−	15.7718i	−0.0598554	−	0.569486i
$768$	2.14411	−	0.455745i	0.0773690	−	0.0164453i
$769$	5.35598	−	30.3753i	0.193142	−	1.09536i	−0.721899	−	0.691998i	$-0.756731\pi$
$769$	5.35598	−	30.3753i	0.193142	−	1.09536i	0.915041	−	0.403362i	$-0.132158\pi$
$770$	15.9310	+	3.63718i	0.574115	+	0.131075i
$771$	6.54188	+	11.3309i	0.235600

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.u (of order \(45\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.990268 + 0.139173i) q^{2} +(0.530296 - 2.12690i) q^{3} +(0.961262 + 0.275637i) q^{4} +(0.0547010 - 1.56643i) q^{5} +(0.821143 - 2.03240i) q^{6} +(2.87167 - 1.27855i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-1.59366 - 0.847362i) q^{9} +O(q^{10})\)	\(q+(0.990268 + 0.139173i) q^{2} +(0.530296 - 2.12690i) q^{3} +(0.961262 + 0.275637i) q^{4} +(0.0547010 - 1.56643i) q^{5} +(0.821143 - 2.03240i) q^{6} +(2.87167 - 1.27855i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-1.59366 - 0.847362i) q^{9} +(0.272174 - 1.54358i) q^{10} +(-1.49853 + 2.95879i) q^{11} +(1.09601 - 1.89834i) q^{12} +(-2.34165 + 1.46322i) q^{13} +(3.02167 - 0.866449i) q^{14} +(-3.30264 - 0.947017i) q^{15} +(0.848048 + 0.529919i) q^{16} +(-6.27809 + 3.33812i) q^{17} +(-1.46022 - 1.06091i) q^{18} +(2.16967 - 3.78055i) q^{19} +(0.484349 - 1.49067i) q^{20} +(-1.19652 - 6.78578i) q^{21} +(-1.89573 + 2.72144i) q^{22} +(-1.39052 + 0.506108i) q^{23} +(1.34954 - 1.72733i) q^{24} +(2.53710 + 0.177411i) q^{25} +(-2.52250 + 1.12309i) q^{26} +(1.75287 - 1.94675i) q^{27} +(3.11285 - 0.437482i) q^{28} +(1.22673 - 1.18464i) q^{29} +(-3.13870 - 1.39744i) q^{30} +(3.78193 + 4.20026i) q^{31} +(0.766044 + 0.642788i) q^{32} +(5.49839 + 4.75625i) q^{33} +(-6.68156 + 2.43189i) q^{34} +(-1.84568 - 4.56822i) q^{35} +(-1.29836 - 1.25381i) q^{36} +(2.62851 + 1.90972i) q^{37} +(2.67471 - 3.44179i) q^{38} +(1.87037 + 5.75639i) q^{39} +(0.687097 - 1.40876i) q^{40} +(0.410003 - 1.64443i) q^{41} +(-0.240474 - 6.88626i) q^{42} +(-11.8872 - 4.32658i) q^{43} +(-2.25603 + 2.43112i) q^{44} +(-1.41451 + 2.45000i) q^{45} +(-1.44743 + 0.307660i) q^{46} +(3.83207 + 7.85691i) q^{47} +(1.57680 - 1.52270i) q^{48} +(1.92790 - 2.14115i) q^{49} +(2.48772 + 0.528781i) q^{50} +(3.77060 + 15.1231i) q^{51} +(-2.65425 + 0.761095i) q^{52} +(0.0190311 + 0.544981i) q^{53} +(2.00674 - 1.68386i) q^{54} +(4.55277 + 2.50919i) q^{55} +3.14344 q^{56} +(-6.89028 - 6.61949i) q^{57} +(1.37966 - 1.00238i) q^{58} +(-2.51772 + 5.16209i) q^{59} +(-2.91367 - 1.82066i) q^{60} +(-4.73404 - 6.05929i) q^{61} +(3.16056 + 4.68573i) q^{62} +(-5.65986 - 0.395776i) q^{63} +(0.669131 + 0.743145i) q^{64} +(2.16395 + 3.74807i) q^{65} +(4.78294 + 5.47519i) q^{66} +(-0.957384 + 5.42960i) q^{67} +(-6.95499 + 1.47833i) q^{68} +(0.339055 + 3.22589i) q^{69} +(-1.19195 - 4.78063i) q^{70} +(-0.319354 + 9.14512i) q^{71} +(-1.11122 - 1.42230i) q^{72} +(6.81009 - 0.476208i) q^{73} +(2.33715 + 2.25696i) q^{74} +(1.72275 - 5.30209i) q^{75} +(3.12768 - 3.03605i) q^{76} +(-0.520313 + 10.4126i) q^{77} +(1.05103 + 5.96068i) q^{78} +(-2.27548 - 5.63200i) q^{79} +(0.876472 - 1.29942i) q^{80} +(-6.23893 - 9.24959i) q^{81} +(0.634874 - 1.57137i) q^{82} +(10.5529 + 2.24308i) q^{83} +(0.720249 - 6.85271i) q^{84} +(4.88552 + 10.0168i) q^{85} +(-11.1694 - 5.93886i) q^{86} +(-1.86908 - 3.23735i) q^{87} +(-2.57242 + 2.09348i) q^{88} +(-6.95620 - 5.83694i) q^{89} +(-1.74172 + 2.22930i) q^{90} +(-4.85364 + 7.19581i) q^{91} +(-1.47616 + 0.103223i) q^{92} +(10.9391 - 5.81642i) q^{93} +(2.70131 + 8.31376i) q^{94} +(-5.80329 - 3.60545i) q^{95} +(1.77338 - 1.28843i) q^{96} +(16.6004 + 2.33303i) q^{97} +(2.20713 - 1.85200i) q^{98} +(4.89530 - 3.44550i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Introduction

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