LMFDB - Embedded newform 441.2.z.a.331.3

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			331.3
Character	$\chi$	$=$	441.331
Dual form			441.2.z.a.4.3

$q$-expansion

$f(q)$	$=$	$q+(-0.192530 - 2.56913i) q^{2} +(1.55341 + 0.766101i) q^{3} +(-4.58569 + 0.691182i) q^{4} +(-0.144697 - 0.633958i) q^{5} +(1.66913 - 4.13841i) q^{6} +(-1.19412 - 2.36095i) q^{7} +(1.51204 + 6.62468i) q^{8} +(1.82618 + 2.38014i) q^{9} +O(q^{10})$	\(q+(-0.192530 - 2.56913i) q^{2} +(1.55341 + 0.766101i) q^{3} +(-4.58569 + 0.691182i) q^{4} +(-0.144697 - 0.633958i) q^{5} +(1.66913 - 4.13841i) q^{6} +(-1.19412 - 2.36095i) q^{7} +(1.51204 + 6.62468i) q^{8} +(1.82618 + 2.38014i) q^{9} +(-1.60086 + 0.493800i) q^{10} +(-4.29136 - 2.06661i) q^{11} +(-7.65298 - 2.43941i) q^{12} +(-0.292340 - 3.90101i) q^{13} +(-5.83567 + 3.52241i) q^{14} +(0.260902 - 1.09565i) q^{15} +(7.86562 - 2.42622i) q^{16} +(-3.53970 - 0.533524i) q^{17} +(5.76329 - 5.14994i) q^{18} +(2.69554 - 4.66882i) q^{19} +(1.10171 + 2.80712i) q^{20} +(-0.0462435 - 4.58234i) q^{21} +(-4.48317 + 11.4229i) q^{22} +(-1.13581 - 1.42426i) q^{23} +(-2.72635 + 11.4492i) q^{24} +(4.12388 - 1.98596i) q^{25} +(-9.96590 + 1.50212i) q^{26} +(1.01338 + 5.09638i) q^{27} +(7.10773 + 10.0012i) q^{28} +(1.52934 + 3.89670i) q^{29} +(-2.86510 - 0.459345i) q^{30} +(-1.48968 + 2.58020i) q^{31} +(-2.78263 - 7.09002i) q^{32} +(-5.08302 - 6.49791i) q^{33} +(-0.689195 + 9.19667i) q^{34} +(-1.32395 + 1.09864i) q^{35} +(-10.0194 - 9.65237i) q^{36} +(-2.55648 - 6.51381i) q^{37} +(-12.5138 - 6.02631i) q^{38} +(2.53444 - 6.28383i) q^{39} +(3.98098 - 1.91714i) q^{40} +(3.97206 - 3.68553i) q^{41} +(-11.7637 + 1.00104i) q^{42} +(9.26906 + 8.60043i) q^{43} +(21.1073 + 6.51072i) q^{44} +(1.24467 - 1.50212i) q^{45} +(-3.44044 + 3.19226i) q^{46} +(0.530961 + 7.08519i) q^{47} +(14.0773 + 2.25694i) q^{48} +(-4.14814 + 5.63852i) q^{49} +(-5.89614 - 10.2124i) q^{50} +(-5.08988 - 3.54055i) q^{51} +(4.03689 + 17.6867i) q^{52} +(3.33328 - 8.49307i) q^{53} +(12.8981 - 3.58471i) q^{54} +(-0.689197 + 3.01957i) q^{55} +(13.8349 - 11.4805i) q^{56} +(7.76407 - 5.18754i) q^{57} +(9.71669 - 4.67931i) q^{58} +(2.85438 + 2.64848i) q^{59} +(-0.439122 + 5.20464i) q^{60} +(7.83228 + 1.18053i) q^{61} +(6.91568 + 3.33042i) q^{62} +(3.43870 - 7.15369i) q^{63} +(-2.84710 + 1.37109i) q^{64} +(-2.43077 + 0.749794i) q^{65} +(-15.7153 + 14.3100i) q^{66} +(0.717064 - 1.24199i) q^{67} +16.6007 q^{68} +(-0.673255 - 3.08261i) q^{69} +(3.07746 + 3.18989i) q^{70} +(-5.33059 - 6.68435i) q^{71} +(-13.0064 + 15.6967i) q^{72} +(4.76734 + 3.25032i) q^{73} +(-16.2426 + 7.82203i) q^{74} +(7.92753 + 0.0742997i) q^{75} +(-9.13393 + 23.2729i) q^{76} +(0.245260 + 12.5995i) q^{77} +(-16.6319 - 5.30148i) q^{78} +(-2.16694 - 3.75324i) q^{79} +(-2.67625 - 4.63540i) q^{80} +(-2.33014 + 8.69313i) q^{81} +(-10.2333 - 9.49515i) q^{82} +(-0.164534 + 2.19555i) q^{83} +(3.37929 + 20.9812i) q^{84} +(0.173951 + 2.32122i) q^{85} +(20.3110 - 25.4693i) q^{86} +(-0.609567 + 7.22482i) q^{87} +(7.20192 - 31.5537i) q^{88} +(-0.498638 + 6.65386i) q^{89} +(-4.09877 - 2.90850i) q^{90} +(-8.86098 + 5.34848i) q^{91} +(6.19290 + 5.74618i) q^{92} +(-4.29079 + 2.86687i) q^{93} +(18.1005 - 2.72822i) q^{94} +(-3.34987 - 1.03330i) q^{95} +(1.10910 - 13.1455i) q^{96} +(8.43105 - 14.6030i) q^{97} +(15.2847 + 9.57151i) q^{98} +(-2.91797 - 13.9880i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9}+O(q^{10}) $ 648 * q - 8 * q^2 - 13 * q^3 + 44 * q^4 + 3 * q^5 + 2 * q^6 - 7 * q^7 - 16 * q^8 - 39 * q^9	\( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9} - 22 q^{10} - 5 q^{11} + 2 q^{12} - 4 q^{13} + 52 q^{14} - 4 q^{15} + 38 q^{16} - 37 q^{17} - 16 q^{18} - 14 q^{19} - 11 q^{20} - 6 q^{21} - q^{22} - 20 q^{23} - 26 q^{24} - 97 q^{25} - 44 q^{26} + 14 q^{27} - 22 q^{28} - 53 q^{29} - 9 q^{30} + 10 q^{31} - 10 q^{32} + 2 q^{33} - 7 q^{34} - 32 q^{35} - 22 q^{36} - 39 q^{37} + 59 q^{38} - 26 q^{39} - 19 q^{40} - 17 q^{41} - 83 q^{42} - q^{43} - 31 q^{44} + 81 q^{45} + 56 q^{46} + 50 q^{47} - 23 q^{48} - 19 q^{49} - 21 q^{50} - 30 q^{51} - 9 q^{52} + 50 q^{53} + 48 q^{54} + 20 q^{55} - 239 q^{56} + 33 q^{57} + 17 q^{58} - 37 q^{59} - 152 q^{60} - 105 q^{61} - 30 q^{62} + 6 q^{63} - 88 q^{64} - 5 q^{65} - 99 q^{66} + 13 q^{67} - 290 q^{68} + 64 q^{69} + 17 q^{70} - 19 q^{71} + 11 q^{72} - 40 q^{73} - 57 q^{74} + 69 q^{75} - 41 q^{76} + 19 q^{77} + 81 q^{78} + 13 q^{79} + 163 q^{80} - 179 q^{81} - 28 q^{82} + 73 q^{83} - 341 q^{84} - 10 q^{85} + 15 q^{86} + 13 q^{87} - 13 q^{88} - 104 q^{89} + 171 q^{90} - 49 q^{91} - 91 q^{92} - 275 q^{93} - 4 q^{94} - 29 q^{95} + 231 q^{96} - 11 q^{97} - 33 q^{98} + 62 q^{99}+O(q^{100}) \) 648 * q - 8 * q^2 - 13 * q^3 + 44 * q^4 + 3 * q^5 + 2 * q^6 - 7 * q^7 - 16 * q^8 - 39 * q^9 - 22 * q^10 - 5 * q^11 + 2 * q^12 - 4 * q^13 + 52 * q^14 - 4 * q^15 + 38 * q^16 - 37 * q^17 - 16 * q^18 - 14 * q^19 - 11 * q^20 - 6 * q^21 - q^22 - 20 * q^23 - 26 * q^24 - 97 * q^25 - 44 * q^26 + 14 * q^27 - 22 * q^28 - 53 * q^29 - 9 * q^30 + 10 * q^31 - 10 * q^32 + 2 * q^33 - 7 * q^34 - 32 * q^35 - 22 * q^36 - 39 * q^37 + 59 * q^38 - 26 * q^39 - 19 * q^40 - 17 * q^41 - 83 * q^42 - q^43 - 31 * q^44 + 81 * q^45 + 56 * q^46 + 50 * q^47 - 23 * q^48 - 19 * q^49 - 21 * q^50 - 30 * q^51 - 9 * q^52 + 50 * q^53 + 48 * q^54 + 20 * q^55 - 239 * q^56 + 33 * q^57 + 17 * q^58 - 37 * q^59 - 152 * q^60 - 105 * q^61 - 30 * q^62 + 6 * q^63 - 88 * q^64 - 5 * q^65 - 99 * q^66 + 13 * q^67 - 290 * q^68 + 64 * q^69 + 17 * q^70 - 19 * q^71 + 11 * q^72 - 40 * q^73 - 57 * q^74 + 69 * q^75 - 41 * q^76 + 19 * q^77 + 81 * q^78 + 13 * q^79 + 163 * q^80 - 179 * q^81 - 28 * q^82 + 73 * q^83 - 341 * q^84 - 10 * q^85 + 15 * q^86 + 13 * q^87 - 13 * q^88 - 104 * q^89 + 171 * q^90 - 49 * q^91 - 91 * q^92 - 275 * q^93 - 4 * q^94 - 29 * q^95 + 231 * q^96 - 11 * q^97 - 33 * q^98 + 62 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.192530	−	2.56913i	−0.136139	−	1.81665i	−0.479607	−	0.877484i	$-0.659221\pi$
$2$	−0.192530	−	2.56913i	−0.136139	−	1.81665i	0.343468	−	0.939164i	$-0.388398\pi$
$3$	1.55341	+	0.766101i	0.896863	+	0.442309i
$3$	1.55341	+	0.766101i	0.896863	+	0.442309i
$4$	−4.58569	+	0.691182i	−2.29285	+	0.345591i
$5$	−0.144697	−	0.633958i	−0.0647103	−	0.283514i	0.932212	−	0.361913i	$-0.117876\pi$
$5$	−0.144697	−	0.633958i	−0.0647103	−	0.283514i	−0.996922	+	0.0783989i	$0.975019\pi$
$6$	1.66913	−	4.13841i	0.681421	−	1.68950i
$7$	−1.19412	−	2.36095i	−0.451336	−	0.892354i
$7$	−1.19412	−	2.36095i	−0.451336	−	0.892354i
$8$	1.51204	+	6.62468i	0.534587	+	2.34218i
$9$	1.82618	+	2.38014i	0.608726	+	0.793380i
$10$	−1.60086	+	0.493800i	−0.506236	+	0.156153i
$11$	−4.29136	−	2.06661i	−1.29389	−	0.623106i	−0.344970	−	0.938614i	$-0.612111\pi$
$11$	−4.29136	−	2.06661i	−1.29389	−	0.623106i	−0.948923	+	0.315507i	$0.897825\pi$
$12$	−7.65298	−	2.43941i	−2.20923	−	0.704197i
$13$	−0.292340	−	3.90101i	−0.0810805	−	1.08194i	−0.878254	−	0.478194i	$-0.841291\pi$
$13$	−0.292340	−	3.90101i	−0.0810805	−	1.08194i	0.797174	−	0.603750i	$-0.206328\pi$
$14$	−5.83567	+	3.52241i	−1.55965	+	0.941403i
$15$	0.260902	−	1.09565i	0.0673646	−	0.282896i
$16$	7.86562	−	2.42622i	1.96641	−	0.606556i
$17$	−3.53970	−	0.533524i	−0.858504	−	0.129399i	−0.294985	−	0.955502i	$-0.595315\pi$
$17$	−3.53970	−	0.533524i	−0.858504	−	0.129399i	−0.563519	+	0.826103i	$0.690553\pi$
$18$	5.76329	−	5.14994i	1.35842	−	1.21385i
$19$	2.69554	−	4.66882i	0.618400	−	1.07110i	−0.371378	−	0.928482i	$-0.621115\pi$
$19$	2.69554	−	4.66882i	0.618400	−	1.07110i	0.989778	−	0.142618i	$-0.0455522\pi$
$20$	1.10171	+	2.80712i	0.246351	+	0.627691i
$21$	−0.0462435	−	4.58234i	−0.0100912	−	0.999949i
$22$	−4.48317	+	11.4229i	−0.955816	+	2.43538i
$23$	−1.13581	−	1.42426i	−0.236833	−	0.296979i	0.649184	−	0.760631i	$-0.275110\pi$
$23$	−1.13581	−	1.42426i	−0.236833	−	0.296979i	−0.886018	+	0.463652i	$0.846539\pi$
$24$	−2.72635	+	11.4492i	−0.556514	+	2.33706i
$25$	4.12388	−	1.98596i	0.824776	−	0.397191i
$26$	−9.96590	+	1.50212i	−1.95447	+	0.294590i
$27$	1.01338	+	5.09638i	0.195025	+	0.980798i
$28$	7.10773	+	10.0012i	1.34323	+	1.89005i
$29$	1.52934	+	3.89670i	0.283992	+	0.723600i	0.999683	+	0.0251825i	$0.00801668\pi$
$29$	1.52934	+	3.89670i	0.283992	+	0.723600i	−0.715691	+	0.698417i	$0.753888\pi$
$30$	−2.86510	−	0.459345i	−0.523092	−	0.0838646i
$31$	−1.48968	+	2.58020i	−0.267555	+	0.463418i	−0.968230	−	0.250062i	$-0.919549\pi$
$31$	−1.48968	+	2.58020i	−0.267555	+	0.463418i	0.700675	+	0.713480i	$0.252882\pi$
$32$	−2.78263	−	7.09002i	−0.491904	−	1.25335i
$33$	−5.08302	−	6.49791i	−0.884840	−	1.13114i
$34$	−0.689195	+	9.19667i	−0.118196	+	1.57722i
$35$	−1.32395	+	1.09864i	−0.223789	+	0.185705i
$36$	−10.0194	−	9.65237i	−1.66990	−	1.60873i
$37$	−2.55648	−	6.51381i	−0.420283	−	1.07086i	−0.971613	−	0.236576i	$-0.923975\pi$
$37$	−2.55648	−	6.51381i	−0.420283	−	1.07086i	0.551330	−	0.834287i	$-0.314121\pi$
$38$	−12.5138	−	6.02631i	−2.03000	−	0.977597i
$39$	2.53444	−	6.28383i	0.405835	−	1.00622i
$40$	3.98098	−	1.91714i	0.629448	−	0.303126i
$41$	3.97206	−	3.68553i	0.620331	−	0.575583i	−0.306123	−	0.951992i	$-0.599032\pi$
$41$	3.97206	−	3.68553i	0.620331	−	0.575583i	0.926454	+	0.376409i	$0.122841\pi$
$42$	−11.7637	+	1.00104i	−1.81518	+	0.154464i
$43$	9.26906	+	8.60043i	1.41352	+	1.31155i	0.887291	+	0.461211i	$0.152585\pi$
$43$	9.26906	+	8.60043i	1.41352	+	1.31155i	0.526228	+	0.850343i	$0.323606\pi$
$44$	21.1073	+	6.51072i	3.18204	+	0.981529i
$45$	1.24467	−	1.50212i	0.185544	−	0.223923i
$46$	−3.44044	+	3.19226i	−0.507265	+	0.470673i
$47$	0.530961	+	7.08519i	0.0774487	+	1.03348i	0.891599	+	0.452826i	$0.149584\pi$
$47$	0.530961	+	7.08519i	0.0774487	+	1.03348i	−0.814150	+	0.580655i	$0.802797\pi$
$48$	14.0773	+	2.25694i	2.03188	+	0.325761i
$49$	−4.14814	+	5.63852i	−0.592591	+	0.805504i
$50$	−5.89614	−	10.2124i	−0.833841	−	1.44425i
$51$	−5.08988	−	3.54055i	−0.712726	−	0.495776i
$52$	4.03689	+	17.6867i	0.559815	+	2.45271i
$53$	3.33328	−	8.49307i	0.457862	−	1.16661i	−0.496521	−	0.868025i	$-0.665389\pi$
$53$	3.33328	−	8.49307i	0.457862	−	1.16661i	0.954382	−	0.298587i	$-0.0965155\pi$
$54$	12.8981	−	3.58471i	1.75521	−	0.487817i
$55$	−0.689197	+	3.01957i	−0.0929314	+	0.407159i
$56$	13.8349	−	11.4805i	1.84877	−	1.53415i
$57$	7.76407	−	5.18754i	1.02838	−	0.687107i
$58$	9.71669	−	4.67931i	1.27586	−	0.614423i
$59$	2.85438	+	2.64848i	0.371609	+	0.344803i	0.843766	−	0.536712i	$-0.180334\pi$
$59$	2.85438	+	2.64848i	0.371609	+	0.344803i	−0.472156	+	0.881515i	$0.656524\pi$
$60$	−0.439122	+	5.20464i	−0.0566904	+	0.671916i
$61$	7.83228	+	1.18053i	1.00282	+	0.151151i	0.629870	−	0.776701i	$-0.283108\pi$
$61$	7.83228	+	1.18053i	1.00282	+	0.151151i	0.372950	+	0.927851i	$0.378346\pi$
$62$	6.91568	+	3.33042i	0.878292	+	0.422963i
$63$	3.43870	−	7.15369i	0.433236	−	0.901281i
$64$	−2.84710	+	1.37109i	−0.355888	+	0.171387i
$65$	−2.43077	+	0.749794i	−0.301500	+	0.0930005i
$66$	−15.7153	+	14.3100i	−1.93442	+	1.76144i
$67$	0.717064	−	1.24199i	0.0876033	−	0.151733i	−0.818894	−	0.573944i	$-0.805413\pi$
$67$	0.717064	−	1.24199i	0.0876033	−	0.151733i	0.906498	+	0.422211i	$0.138746\pi$
$68$	16.6007			2.01314
$69$	−0.673255	−	3.08261i	−0.0810503	−	0.371103i
$70$	3.07746	+	3.18989i	0.367827	+	0.381264i
$71$	−5.33059	−	6.68435i	−0.632625	−	0.793287i	0.357434	−	0.933938i	$-0.383652\pi$
$71$	−5.33059	−	6.68435i	−0.632625	−	0.793287i	−0.990059	+	0.140651i	$0.955080\pi$
$72$	−13.0064	+	15.6967i	−1.53282	+	1.84988i
$73$	4.76734	+	3.25032i	0.557975	+	0.380421i	0.809223	−	0.587502i	$-0.199888\pi$
$73$	4.76734	+	3.25032i	0.557975	+	0.380421i	−0.251248	+	0.967923i	$0.580841\pi$
$74$	−16.2426	+	7.82203i	−1.88817	+	0.909292i
$75$	7.92753	+	0.0742997i	0.915392	+	0.00857939i
$76$	−9.13393	+	23.2729i	−1.04773	+	2.66958i
$77$	0.245260	+	12.5995i	0.0279499	+	1.43584i
$78$	−16.6319	−	5.30148i	−1.88319	−	0.600274i
$79$	−2.16694	−	3.75324i	−0.243799	−	0.422273i	0.717994	−	0.696049i	$-0.245060\pi$
$79$	−2.16694	−	3.75324i	−0.243799	−	0.422273i	−0.961793	+	0.273776i	$0.911727\pi$
$80$	−2.67625	−	4.63540i	−0.299214	−	0.518254i
$81$	−2.33014	+	8.69313i	−0.258905	+	0.965903i
$82$	−10.2333	−	9.49515i	−1.13008	−	1.04856i
$83$	−0.164534	+	2.19555i	−0.0180599	+	0.240993i	0.980867	+	0.194679i	$0.0623666\pi$
$83$	−0.164534	+	2.19555i	−0.0180599	+	0.240993i	−0.998927	+	0.0463141i	$0.985252\pi$
$84$	3.37929	+	20.9812i	0.368711	+	2.28924i
$85$	0.173951	+	2.32122i	0.0188677	+	0.251772i
$86$	20.3110	−	25.4693i	2.19020	−	2.74642i
$87$	−0.609567	+	7.22482i	−0.0653524	+	0.774582i
$88$	7.20192	−	31.5537i	0.767727	−	3.36363i
$89$	−0.498638	+	6.65386i	−0.0528555	+	0.705307i	0.906337	+	0.422555i	$0.138867\pi$
$89$	−0.498638	+	6.65386i	−0.0528555	+	0.705307i	−0.959193	+	0.282753i	$0.908752\pi$
$90$	−4.09877	−	2.90850i	−0.432048	−	0.306583i
$91$	−8.86098	+	5.34848i	−0.928883	+	0.560673i
$92$	6.19290	+	5.74618i	0.645655	+	0.599080i
$93$	−4.29079	+	2.86687i	−0.444934	+	0.297281i
$94$	18.1005	−	2.72822i	1.86693	−	0.281394i
$95$	−3.34987	−	1.03330i	−0.343689	−	0.106014i
$96$	1.10910	−	13.1455i	0.113197	−	1.34166i
$97$	8.43105	−	14.6030i	0.856043	−	1.48271i	−0.0196309	−	0.999807i	$-0.506249\pi$
$97$	8.43105	−	14.6030i	0.856043	−	1.48271i	0.875674	−	0.482903i	$-0.160418\pi$
$98$	15.2847	+	9.57151i	1.54399	+	0.966869i
$99$	−2.91797	−	13.9880i	−0.293267	−	1.40585i
$100$	−17.5382	+	11.9573i	−1.75382	+	1.19573i
$101$	−2.07854	−	9.10668i	−0.206822	−	0.906148i	−0.966666	−	0.256042i	$-0.917581\pi$
$101$	−2.07854	−	9.10668i	−0.206822	−	0.906148i	0.759843	−	0.650106i	$-0.225276\pi$
$102$	−8.11618	+	13.7582i	−0.803621	+	1.36227i
$103$	−2.33735	−	10.2406i	−0.230306	−	1.00903i	−0.949387	−	0.314109i	$-0.898294\pi$
$103$	−2.33735	−	10.2406i	−0.230306	−	1.00903i	0.719081	−	0.694926i	$-0.244563\pi$
$104$	25.4009	−	7.83514i	2.49076	−	0.768298i
$105$	−2.89832	+	0.692366i	−0.282847	+	0.0675680i
$106$	−22.4615	−	6.92847i	−2.18166	−	0.672952i
$107$	0.214273	−	2.85928i	0.0207146	−	0.276417i	−0.977222	−	0.212217i	$-0.931931\pi$
$107$	0.214273	−	2.85928i	0.0207146	−	0.276417i	0.997937	−	0.0641997i	$-0.0204495\pi$
$108$	−8.16957	−	22.6700i	−0.786118	−	2.18142i
$109$	0.888813	+	11.8604i	0.0851329	+	1.13602i	0.862189	+	0.506588i	$0.169093\pi$
$109$	0.888813	+	11.8604i	0.0851329	+	1.13602i	−0.777056	+	0.629432i	$0.783288\pi$
$110$	7.89036	+	1.18928i	0.752316	+	0.113393i
$111$	1.01896	−	12.0772i	0.0967159	−	1.14631i
$112$	−15.1207	−	15.6731i	−1.42877	−	1.48097i
$113$	−10.2234	−	6.97018i	−0.961734	−	0.655699i	−0.0227793	−	0.999741i	$-0.507252\pi$
$113$	−10.2234	−	6.97018i	−0.961734	−	0.655699i	−0.938954	+	0.344042i	$0.888204\pi$
$114$	−14.8223	−	18.9481i	−1.38823	−	1.77466i
$115$	−0.738574	+	0.926142i	−0.0688724	+	0.0863632i
$116$	−9.70642	−	16.8120i	−0.901219	−	1.56096i
$117$	8.75108	−	7.81975i	0.809038	−	0.722936i
$118$	6.25473	−	7.84319i	0.575795	−	0.722024i
$119$	2.96722	+	8.99414i	0.272005	+	0.824491i
$120$	7.65282	+	0.0717251i	0.698604	+	0.00654757i
$121$	7.28650	+	9.13699i	0.662409	+	0.830635i
$122$	1.52498	−	20.3494i	0.138065	−	1.84235i
$123$	8.99373	−	2.68215i	0.810937	−	0.241841i
$124$	5.04783	−	12.8617i	0.453308	−	1.15501i
$125$	−3.88288	−	4.86898i	−0.347295	−	0.435494i
$126$	−19.0408	−	7.45717i	−1.69629	−	0.664337i
$127$	10.0685	−	12.6255i	0.893433	−	1.12033i	−0.0986975	−	0.995117i	$-0.531468\pi$
$127$	10.0685	−	12.6255i	0.893433	−	1.12033i	0.992130	−	0.125212i	$-0.0399610\pi$
$128$	−3.54585	−	6.14160i	−0.313412	−	0.542846i
$129$	7.80988	+	20.4611i	0.687621	+	1.80150i
$130$	2.39431	+	6.10061i	0.209995	+	0.535059i
$131$	−3.27259	+	14.3381i	−0.285927	+	1.25273i	0.604132	+	0.796884i	$0.293520\pi$
$131$	−3.27259	+	14.3381i	−0.285927	+	1.25273i	−0.890059	+	0.455845i	$0.849337\pi$
$132$	27.8004	+	26.2841i	2.41971	+	2.28774i
$133$	−14.2416	−	0.788887i	−1.23491	−	0.0684051i
$134$	−3.32889	−	1.60311i	−0.287572	−	0.138488i
$135$	3.08425	−	1.37987i	0.265450	−	0.118760i
$136$	−1.81774	−	24.2561i	−0.155870	−	2.07994i
$137$	0.926250	−	4.05816i	0.0791348	−	0.346712i	−0.919824	−	0.392331i	$-0.871669\pi$
$137$	0.926250	−	4.05816i	0.0791348	−	0.346712i	0.998959	+	0.0456187i	$0.0145259\pi$
$138$	−7.79001	+	2.32317i	−0.663129	+	0.197761i
$139$	−12.9678	+	12.0323i	−1.09991	+	1.02057i	−0.100241	+	0.994963i	$0.531961\pi$
$139$	−12.9678	+	12.0323i	−1.09991	+	1.02057i	−0.999672	+	0.0256065i	$0.991848\pi$
$140$	5.31188	−	5.95314i	0.448936	−	0.503132i
$141$	−4.60317	+	11.4130i	−0.387657	+	0.961147i
$142$	−16.1467	+	14.9819i	−1.35500	+	1.25725i
$143$	−6.80732	+	17.3448i	−0.569257	+	1.45044i
$144$	20.1388	+	14.2906i	1.67823	+	1.19088i
$145$	2.24905	−	1.53338i	0.186774	−	0.127340i
$146$	7.43263	−	12.8737i	0.615129	−	1.06543i
$147$	−10.7634	+	5.58106i	−0.887754	+	0.460318i
$148$	16.2255	+	28.1033i	1.33372	+	2.31008i
$149$	8.65432	+	4.16770i	0.708990	+	0.341431i	0.753382	−	0.657583i	$-0.228421\pi$
$149$	8.65432	+	4.16770i	0.708990	+	0.341431i	−0.0443927	+	0.999014i	$0.514135\pi$
$150$	−1.33540	−	20.3811i	−0.109035	−	1.66411i
$151$	−9.00063	−	11.2864i	−0.732461	−	0.918476i	0.266510	−	0.963832i	$-0.414129\pi$
$151$	−9.00063	−	11.2864i	−0.732461	−	0.918476i	−0.998971	+	0.0453556i	$0.985558\pi$
$152$	35.0052	+	10.7977i	2.83930	+	0.875807i
$153$	−5.19427	−	9.39930i	−0.419931	−	0.759888i
$154$	32.3224	−	3.05587i	2.60461	−	0.246249i
$155$	1.85129	+	0.571048i	0.148699	+	0.0458677i
$156$	−7.27889	+	30.5675i	−0.582777	+	2.44736i
$157$	−0.996758	−	0.924856i	−0.0795500	−	0.0738116i	0.639396	−	0.768878i	$-0.279185\pi$
$157$	−0.996758	−	0.924856i	−0.0795500	−	0.0738116i	−0.718946	+	0.695066i	$0.755375\pi$
$158$	−9.22536	+	6.28975i	−0.733930	+	0.500385i
$159$	11.6845	−	10.6396i	0.926642	−	0.843775i
$160$	−4.09213	+	2.78997i	−0.323512	+	0.220566i
$161$	−2.00631	+	4.38234i	−0.158119	+	0.345376i
$162$	22.7824	+	4.31275i	1.78995	+	0.338841i
$163$	10.3825	+	9.63358i	0.813223	+	0.754560i	0.972557	−	0.232664i	$-0.0747443\pi$
$163$	10.3825	+	9.63358i	0.813223	+	0.754560i	−0.159334	+	0.987225i	$0.550935\pi$
$164$	−15.6673	+	19.6461i	−1.22341	+	1.53410i
$165$	−3.38390	+	4.16264i	−0.263437	+	0.324061i
$166$	5.67234			0.440259
$167$	−5.43277	−	0.818858i	−0.420400	−	0.0633652i	−0.0645643	−	0.997914i	$-0.520566\pi$
$167$	−5.43277	−	0.818858i	−0.420400	−	0.0633652i	−0.355836	+	0.934548i	$0.615804\pi$
$168$	30.2866	−	7.23503i	2.33666	−	0.558195i
$169$	−2.27759	+	0.343291i	−0.175199	+	0.0264070i
$170$	5.93002	−	0.893807i	0.454812	−	0.0685518i
$171$	16.0350	−	2.11032i	1.22623	−	0.161381i
$172$	−48.4495	−	33.0323i	−3.69424	−	2.51869i
$173$	−7.21598	+	18.3860i	−0.548620	+	1.39786i	0.340524	+	0.940236i	$0.389395\pi$
$173$	−7.21598	+	18.3860i	−0.548620	+	1.39786i	−0.889145	+	0.457626i	$0.848700\pi$
$174$	18.6788	+	0.175065i	1.41604	+	0.0132716i
$175$	−9.61316	−	7.36478i	−0.726686	−	0.556725i
$176$	−38.7683	−	5.84338i	−2.92227	−	0.440461i
$177$	2.40503	+	6.30093i	0.180773	+	0.473607i
$178$	17.1906			1.28849
$179$	−18.2198	−	2.74619i	−1.36181	−	0.205260i	−0.572827	−	0.819676i	$-0.694153\pi$
$179$	−18.2198	−	2.74619i	−1.36181	−	0.205260i	−0.788982	+	0.614417i	$0.789391\pi$
$180$	−4.66942	+	7.74854i	−0.348038	+	0.577542i
$181$	15.5157	−	7.47195i	1.15327	−	0.555385i	0.243255	−	0.969962i	$-0.421785\pi$
$181$	15.5157	−	7.47195i	1.15327	−	0.555385i	0.910014	+	0.414577i	$0.136070\pi$
$182$	15.4469	+	21.7352i	1.14500	+	1.61112i
$183$	11.2624	+	7.83416i	0.832537	+	0.579117i
$184$	7.71789	−	9.67793i	0.568970	−	0.713466i
$185$	−3.75956	+	2.56323i	−0.276409	+	0.188452i
$186$	8.19147	+	10.4716i	0.600628	+	0.767816i
$187$	14.0875	+	9.60472i	1.03018	+	0.702367i
$188$	−7.33198	−	32.1235i	−0.534739	−	2.34285i
$189$	10.8222	−	8.47824i	0.787197	−	0.616701i
$190$	−2.00973	+	8.80518i	−0.145801	+	0.638795i
$191$	−4.80741	+	4.46063i	−0.347852	+	0.322760i	−0.834677	−	0.550740i	$-0.814346\pi$
$191$	−4.80741	+	4.46063i	−0.347852	+	0.322760i	0.486825	+	0.873500i	$0.338155\pi$
$192$	−5.47312	−	0.0512962i	−0.394989	−	0.00370198i
$193$	2.70268	+	0.833665i	0.194543	+	0.0600085i	0.390496	−	0.920605i	$-0.372304\pi$
$193$	2.70268	+	0.833665i	0.194543	+	0.0600085i	−0.195953	+	0.980613i	$0.562780\pi$
$194$	−39.1402	−	18.8489i	−2.81010	−	1.35327i
$195$	−4.35041	−	0.697477i	−0.311539	−	0.0499474i
$196$	15.1248	−	28.7236i	1.08034	−	2.05169i
$197$	22.5704			1.60808			0.804039	−	0.594577i	$-0.202680\pi$
$197$	22.5704			1.60808			0.804039	+	0.594577i	$0.202680\pi$
$198$	−35.3753	+	10.1897i	−2.51401	+	0.724154i
$199$	0.178378	−	0.165510i	0.0126449	−	0.0117327i	−0.673825	−	0.738891i	$-0.735350\pi$
$199$	0.178378	−	0.165510i	0.0126449	−	0.0117327i	0.686470	+	0.727158i	$0.259159\pi$
$200$	19.3918	+	24.3165i	1.37121	+	1.71944i
$201$	2.06539	−	1.37998i	0.145681	−	0.0973364i
$202$	−22.9960	+	7.09334i	−1.61800	+	0.499086i
$203$	7.37368	−	8.26384i	0.517531	−	0.580008i
$204$	25.7878	+	12.7178i	1.80551	+	0.890427i
$205$	−2.91121	−	1.98483i	−0.203328	−	0.138627i
$206$	−25.8594	+	7.97656i	−1.80171	+	0.555753i
$207$	1.31575	−	5.30435i	0.0914510	−	0.368678i
$208$	−11.7641	−	29.9746i	−0.815697	−	2.07836i
$209$	−21.2162	+	14.4649i	−1.46755	+	1.00056i
$210$	2.33679	+	7.31285i	0.161254	+	0.504635i
$211$	−15.7923	−	10.7670i	−1.08719	−	0.741233i	−0.119363	−	0.992851i	$-0.538085\pi$
$211$	−15.7923	−	10.7670i	−1.08719	−	0.741233i	−0.967827	+	0.251617i	$0.919038\pi$
$212$	−9.41515	+	41.2505i	−0.646635	+	2.83309i
$213$	−3.15972	−	14.4673i	−0.216501	−	0.991285i
$214$	−7.38711			−0.504973
$215$	4.11111	−	7.12065i	0.280375	−	0.485624i
$216$	−32.2296	+	14.4192i	−2.19295	+	0.981106i
$217$	7.87059	+	0.435975i	0.534290	+	0.0295959i
$218$	30.2997	−	4.56695i	2.05216	−	0.309313i
$219$	4.91558	+	8.70135i	0.332164	+	0.587983i
$220$	1.07337	−	14.3232i	0.0723669	−	0.965669i
$221$	−1.04648	+	13.9644i	−0.0703942	+	0.939345i
$222$	−31.2239	−	0.292642i	−2.09561	−	0.0196409i
$223$	−7.89215	+	1.18955i	−0.528497	+	0.0796581i	−0.407870	−	0.913040i	$-0.633729\pi$
$223$	−7.89215	+	1.18955i	−0.528497	+	0.0796581i	−0.120627	+	0.992698i	$0.538490\pi$
$224$	−13.4164	+	15.0360i	−0.896418	+	1.00463i
$225$	12.2578	+	6.18870i	0.817186	+	0.412580i
$226$	−15.9390	+	27.6071i	−1.06024	+	1.83640i
$227$	22.2521			1.47692			0.738462	−	0.674295i	$-0.235552\pi$
$227$	22.2521			1.47692			0.738462	+	0.674295i	$0.235552\pi$
$228$	−32.0181	+	29.1548i	−2.12045	+	1.93083i
$229$	−0.523095	+	2.29183i	−0.0345671	+	0.151448i	−0.989266	−	0.146125i	$-0.953320\pi$
$229$	−0.523095	+	2.29183i	−0.0345671	+	0.151448i	0.954699	+	0.297573i	$0.0961771\pi$
$230$	2.52158	+	1.71918i	0.166268	+	0.113359i
$231$	−9.27147	+	19.7600i	−0.610018	+	1.30012i
$232$	−23.5020	+	16.0234i	−1.54298	+	1.05199i
$233$	1.67994	+	4.28043i	0.110057	+	0.280420i	0.975282	−	0.220963i	$-0.0709200\pi$
$233$	1.67994	+	4.28043i	0.110057	+	0.280420i	−0.865225	+	0.501383i	$0.832825\pi$
$234$	−21.7748	−	20.9771i	−1.42346	−	1.37132i
$235$	4.41488	−	1.36181i	0.287995	−	0.0888347i
$236$	−14.9199	−	10.1722i	−0.971203	−	0.662155i
$237$	−0.490782	−	7.49042i	−0.0318797	−	0.486555i
$238$	22.5358	−	9.35481i	1.46078	−	0.606382i
$239$	18.5874	−	5.73345i	1.20232	−	0.370866i	0.372041	−	0.928216i	$-0.378658\pi$
$239$	18.5874	−	5.73345i	1.20232	−	0.370866i	0.830277	+	0.557350i	$0.188182\pi$
$240$	−0.606135	−	9.25097i	−0.0391259	−	0.597148i
$241$	17.9170	+	22.4672i	1.15413	+	1.44724i	0.873100	+	0.487541i	$0.162106\pi$
$241$	17.9170	+	22.4672i	1.15413	+	1.44724i	0.281035	+	0.959698i	$0.409322\pi$
$242$	22.0712	−	20.4791i	1.41879	−	1.31645i
$243$	−10.2795	+	11.7189i	−0.659429	+	0.751767i
$244$	−36.7324			−2.35155
$245$	4.17481	+	1.81387i	0.266719	+	0.115884i
$246$	−8.62235	−	22.5896i	−0.549741	−	1.44026i
$247$	−19.0011	−	9.15045i	−1.20901	−	0.582229i
$248$	−19.3455	−	5.96729i	−1.22844	−	0.378923i
$249$	−1.93760	+	3.28455i	−0.122791	+	0.208150i
$250$	−11.7615	+	10.9130i	−0.743860	+	0.690201i
$251$	−1.18540	+	5.19358i	−0.0748218	+	0.327816i	−0.998462	−	0.0554457i	$-0.982342\pi$
$251$	−1.18540	+	5.19358i	−0.0748218	+	0.327816i	0.923640	+	0.383261i	$0.125199\pi$
$252$	−10.8243	+	35.1814i	−0.681868	+	2.21622i
$253$	1.93078	+	8.45930i	0.121387	+	0.531832i
$254$	−34.3749	−	23.4364i	−2.15687	−	1.47053i
$255$	−1.50807	+	3.73907i	−0.0944390	+	0.234150i
$256$	−20.3178	+	13.8524i	−1.26986	+	0.865777i
$257$	4.76465	−	5.97469i	0.297211	−	0.372691i	−0.610694	−	0.791867i	$-0.709110\pi$
$257$	4.76465	−	5.97469i	0.297211	−	0.372691i	0.907905	+	0.419176i	$0.137681\pi$
$258$	51.0634	−	24.0039i	3.17907	−	1.49442i
$259$	−12.3260	+	13.8140i	−0.765900	+	0.858361i
$260$	10.6285	−	5.11843i	0.659153	−	0.317431i
$261$	−6.48185	+	10.7561i	−0.401216	+	0.665788i
$262$	37.4666	+	5.64718i	2.31469	+	0.348884i
$263$	19.6623			1.21243			0.606215	−	0.795301i	$-0.292687\pi$
$263$	19.6623			1.21243			0.606215	+	0.795301i	$0.292687\pi$
$264$	35.3608	−	43.4985i	2.17631	−	2.67715i
$265$	−5.86656	−	0.884241i	−0.360380	−	0.0543185i
$266$	0.715186	+	36.7405i	0.0438509	+	2.25270i
$267$	−5.87211	+	9.95418i	−0.359368	+	0.609186i
$268$	−2.42979	+	6.19101i	−0.148423	+	0.378176i
$269$	−17.3694	−	11.8422i	−1.05903	−	0.722033i	−0.0970833	−	0.995276i	$-0.530951\pi$
$269$	−17.3694	−	11.8422i	−1.05903	−	0.722033i	−0.961945	+	0.273243i	$0.911904\pi$
$270$	−4.13887	−	7.65818i	−0.251884	−	0.466062i
$271$	2.02737	−	0.305577i	0.123154	−	0.0185625i	−0.0871760	−	0.996193i	$-0.527784\pi$
$271$	2.02737	−	0.305577i	0.123154	−	0.0185625i	0.210330	+	0.977630i	$0.432546\pi$
$272$	−29.1364	+	4.39161i	−1.76665	+	0.266280i
$273$	−17.8622	+	1.52000i	−1.08107	+	0.0919945i
$274$	−10.6043	−	1.59834i	−0.640628	−	0.0965591i
$275$	−21.8012			−1.31466
$276$	5.21798	+	13.6706i	0.314086	+	0.822871i
$277$	−5.31226	+	6.66137i	−0.319183	+	0.400243i	−0.915377	−	0.402598i	$-0.868107\pi$
$277$	−5.31226	+	6.66137i	−0.319183	+	0.400243i	0.596194	+	0.802840i	$0.296679\pi$
$278$	33.4093	+	30.9993i	2.00376	+	1.85921i
$279$	−8.86167	+	1.16626i	−0.530534	+	0.0698223i
$280$	−9.28004	−	7.10958i	−0.554588	−	0.424878i
$281$	2.18759	−	1.49147i	0.130500	−	0.0889737i	−0.496310	−	0.868145i	$-0.665312\pi$
$281$	2.18759	−	1.49147i	0.130500	−	0.0889737i	0.626811	+	0.779171i	$0.284360\pi$
$282$	30.2077	+	9.62879i	1.79884	+	0.573386i
$283$	3.75577	−	2.56064i	0.223257	−	0.152214i	−0.446526	−	0.894770i	$-0.647339\pi$
$283$	3.75577	−	2.56064i	0.223257	−	0.152214i	0.669784	+	0.742556i	$0.266387\pi$
$284$	29.0646	+	26.9680i	1.72466	+	1.60025i
$285$	−4.41212	−	4.17147i	−0.261351	−	0.247097i
$286$	45.8716	+	14.1495i	2.71244	+	0.836678i
$287$	−13.4445	−	4.97683i	−0.793602	−	0.293773i
$288$	11.7937	−	19.5707i	0.694948	−	1.15321i
$289$	−3.99990	−	1.23381i	−0.235288	−	0.0725768i
$290$	−4.37246	−	5.48289i	−0.256759	−	0.321966i
$291$	24.2843	−	16.2254i	1.42357	−	0.951153i
$292$	−24.1081	−	11.6099i	−1.41082	−	0.679416i
$293$	−0.732578	−	1.26886i	−0.0427977	−	0.0741278i	0.843833	−	0.536606i	$-0.180294\pi$
$293$	−0.732578	−	1.26886i	−0.0427977	−	0.0741278i	−0.886631	+	0.462478i	$0.846960\pi$
$294$	16.4107	+	26.5782i	0.957094	+	1.55007i
$295$	1.26600	−	2.19278i	0.0737096	−	0.127669i
$296$	39.2864	−	26.7850i	2.28347	−	1.55685i
$297$	6.18344	−	23.9646i	0.358800	−	1.39057i
$298$	9.04115	−	23.0365i	0.523740	−	1.33447i
$299$	−5.22401	+	4.84718i	−0.302113	+	0.280319i
$300$	−36.4045	+	5.13865i	−2.10182	+	0.296680i
$301$	9.23675	−	32.1537i	0.532398	−	1.85331i
$302$	−27.2634	+	25.2967i	−1.56883	+	1.45566i
$303$	3.74780	−	15.7388i	0.215306	−	0.904170i
$304$	9.87453	−	43.2632i	0.566343	−	2.48131i
$305$	−0.384901	−	5.13615i	−0.0220394	−	0.294095i
$306$	−23.1480	+	15.1544i	−1.32328	+	0.866318i
$307$	11.0840	+	5.33776i	0.632596	+	0.304642i	0.722566	−	0.691302i	$-0.242963\pi$
$307$	11.0840	+	5.33776i	0.632596	+	0.304642i	−0.0899697	+	0.995945i	$0.528677\pi$
$308$	−9.83320	−	57.6077i	−0.560299	−	3.28250i
$309$	4.21446	−	17.6985i	0.239752	−	1.00683i
$310$	1.11067	−	4.86615i	0.0630816	−	0.276379i
$311$	4.66834	+	11.8947i	0.264717	+	0.674489i	0.999995	−	0.00327743i	$-0.00104324\pi$
$311$	4.66834	+	11.8947i	0.264717	+	0.674489i	−0.735277	+	0.677767i	$0.762948\pi$
$312$	45.4605	+	7.28844i	2.57370	+	0.412627i
$313$	14.5230	+	25.1545i	0.820888	+	1.42182i	0.905022	+	0.425365i	$0.139854\pi$
$313$	14.5230	+	25.1545i	0.820888	+	1.42182i	−0.0841345	+	0.996454i	$0.526813\pi$
$314$	−2.18417	+	2.73886i	−0.123260	+	0.154563i
$315$	−5.03271	−	1.14487i	−0.283561	−	0.0645064i
$316$	12.5311	+	15.7135i	0.704928	+	0.883951i
$317$	3.18677	−	8.11977i	0.178987	−	0.456052i	−0.813020	−	0.582236i	$-0.802178\pi$
$317$	3.18677	−	8.11977i	0.178987	−	0.456052i	0.992007	+	0.126185i	$0.0402732\pi$
$318$	−29.5841	−	27.9706i	−1.65899	−	1.56851i
$319$	1.49000	−	19.8827i	0.0834242	−	1.11322i
$320$	1.28118	+	1.60655i	0.0716202	+	0.0898089i
$321$	2.52335	−	4.27749i	0.140840	−	0.238746i
$322$	11.6451	+	4.31073i	0.648954	+	0.240228i
$323$	−12.0323	+	15.0881i	−0.669498	+	0.839523i
$324$	4.67677	−	41.4745i	0.259821	−	2.30414i
$325$	−8.95280	−	15.5067i	−0.496612	−	0.860157i
$326$	22.7510	−	28.5288i	1.26006	−	1.58006i
$327$	−7.70556	+	19.1050i	−0.426119	+	1.05651i
$328$	30.4214	+	20.7409i	1.67974	+	1.14523i
$329$	16.0937	−	9.71416i	0.887275	−	0.535559i
$330$	11.3459	+	7.89225i	0.624569	+	0.434454i
$331$	−9.56421	−	1.44157i	−0.525696	−	0.0792360i	−0.119168	−	0.992874i	$-0.538023\pi$
$331$	−9.56421	−	1.44157i	−0.525696	−	0.0792360i	−0.406528	+	0.913638i	$0.633261\pi$
$332$	−0.763024	−	10.1819i	−0.0418764	−	0.558802i
$333$	10.8352	−	17.9802i	0.593765	−	0.985307i
$334$	−1.05778	+	14.1151i	−0.0578793	+	0.772346i
$335$	−0.891127	−	0.274876i	−0.0486875	−	0.0150181i
$336$	−11.4815	−	35.9308i	−0.626368	−	1.96018i
$337$	9.22086	−	2.84426i	0.502292	−	0.154937i	−0.0332468	−	0.999447i	$-0.510585\pi$
$337$	9.22086	−	2.84426i	0.502292	−	0.154937i	0.535539	+	0.844511i	$0.320109\pi$
$338$	1.32046	+	5.78532i	0.0718237	+	0.314680i
$339$	−10.5412	−	18.6597i	−0.572522	−	1.01346i
$340$	−2.40207	−	10.5242i	−0.130271	−	0.570753i
$341$	11.7250	−	7.99399i	0.634946	−	0.432899i
$342$	−8.50890	−	40.7896i	−0.460109	−	2.20565i
$343$	18.2656	+	3.06043i	0.986252	+	0.165248i
$344$	−42.9599	+	74.4088i	−2.31624	+	4.01185i
$345$	−1.85683	+	0.872859i	−0.0999682	+	0.0469931i
$346$	48.6253	+	14.9989i	2.61411	+	0.806347i
$347$	−29.9881	+	4.51998i	−1.60985	+	0.242645i	−0.891494	−	0.453033i	$-0.850342\pi$
$347$	−29.9881	+	4.51998i	−1.60985	+	0.242645i	−0.718353	+	0.695678i	$0.755104\pi$
$348$	−2.19838	−	33.5521i	−0.117845	−	1.79858i
$349$	−5.33370	−	4.94895i	−0.285506	−	0.264911i	0.524398	−	0.851473i	$-0.324290\pi$
$349$	−5.33370	−	4.94895i	−0.285506	−	0.264911i	−0.809904	+	0.586562i	$0.800481\pi$
$350$	−17.0703	+	26.1154i	−0.912443	+	1.39593i
$351$	19.5847	−	5.44308i	1.04536	−	0.290530i
$352$	−2.71105	+	36.1764i	−0.144499	+	1.92821i
$353$	1.56532	−	6.85813i	0.0833137	−	0.365021i	−0.916035	−	0.401098i	$-0.868629\pi$
$353$	1.56532	−	6.85813i	0.0833137	−	0.365021i	0.999349	+	0.0360763i	$0.0114859\pi$
$354$	15.7249	−	7.39195i	0.835766	−	0.392878i
$355$	−3.46628	+	4.34657i	−0.183971	+	0.230692i
$356$	−2.31243	−	30.8572i	−0.122558	−	1.63543i
$357$	−2.28110	+	16.2448i	−0.120729	+	0.859766i
$358$	−3.54746	+	47.3376i	−0.187489	+	2.50187i
$359$	−3.51217	−	3.25882i	−0.185365	−	0.171994i	0.582032	−	0.813166i	$-0.302258\pi$
$359$	−3.51217	−	3.25882i	−0.185365	−	0.171994i	−0.767397	+	0.641172i	$0.778448\pi$
$360$	11.8330	+	5.97425i	0.623656	+	0.314871i
$361$	−5.03191	−	8.71552i	−0.264837	−	0.458711i
$362$	−22.1836	−	38.4231i	−1.16594	−	2.01948i
$363$	4.31909	+	19.7757i	0.226693	+	1.03796i
$364$	36.9369	−	30.6510i	1.93602	−	1.60655i
$365$	1.37075	−	3.49260i	0.0717481	−	0.182811i
$366$	17.9586	−	30.4427i	0.938712	−	1.59127i
$367$	−24.6528	+	11.8721i	−1.28686	+	0.619721i	−0.947145	−	0.320806i	$-0.896046\pi$
$367$	−24.6528	+	11.8721i	−1.28686	+	0.619721i	−0.339719	+	0.940527i	$0.610332\pi$
$368$	−12.3894	−	8.44698i	−0.645844	−	0.440329i
$369$	16.0258	+	2.72362i	0.834268	+	0.141786i
$370$	7.30909	+	9.16530i	0.379981	+	0.476481i
$371$	−24.0320	+	2.27207i	−1.24768	+	0.117960i
$372$	17.6947	−	16.1123i	0.917427	−	0.835384i
$373$	2.48272			0.128550			0.0642751	−	0.997932i	$-0.479526\pi$
$373$	2.48272			0.128550			0.0642751	+	0.997932i	$0.479526\pi$
$374$	21.9635	−	38.0419i	1.13571	−	1.96710i
$375$	−2.30158	−	10.5382i	−0.118853	−	0.544190i
$376$	−46.1343	+	14.2305i	−2.37919	+	0.733884i
$377$	14.7540	−	7.10514i	0.759868	−	0.365933i
$378$	−23.8653	−	26.1712i	−1.22750	−	1.34610i
$379$	−24.3562	−	11.7293i	−1.25109	−	0.602494i	−0.313288	−	0.949658i	$-0.601430\pi$
$379$	−24.3562	−	11.7293i	−1.25109	−	0.602494i	−0.937804	+	0.347164i	$0.887145\pi$
$380$	16.0757	+	2.42302i	0.824664	+	0.124298i
$381$	25.3129	−	11.8991i	1.29682	−	0.609609i
$382$	12.3855	+	11.4921i	0.633697	+	0.587985i
$383$	−26.4717	+	12.7481i	−1.35264	+	0.651398i	−0.962983	−	0.269561i	$-0.913121\pi$
$383$	−26.4717	+	12.7481i	−1.35264	+	0.651398i	−0.389659	+	0.920959i	$0.627407\pi$
$384$	−0.803088	−	12.2569i	−0.0409824	−	0.625483i
$385$	7.95203	−	1.97858i	0.405273	−	0.100838i
$386$	1.62145	−	7.10403i	0.0825295	−	0.361585i
$387$	−3.54328	+	37.7676i	−0.180115	+	1.91984i
$388$	−28.5688	+	72.7922i	−1.45036	+	3.69547i
$389$	−1.65091	−	7.23312i	−0.0837046	−	0.366734i	0.915676	−	0.401917i	$-0.131656\pi$
$389$	−1.65091	−	7.23312i	−0.0837046	−	0.366734i	−0.999381	+	0.0351827i	$0.988799\pi$
$390$	−0.954327	+	11.3110i	−0.0483242	+	0.572757i
$391$	3.26055	+	5.64745i	0.164893	+	0.285604i
$392$	−43.6256	−	18.9544i	−2.20342	−	0.957342i
$393$	−16.0681	+	19.7659i	−0.810530	+	0.997058i
$394$	−4.34548	−	57.9864i	−0.218922	−	2.92131i
$395$	−2.06585	+	1.91683i	−0.103944	+	0.0964460i
$396$	23.0492	+	62.1280i	1.15826	+	3.12205i
$397$	19.9840	+	6.16424i	1.00297	+	0.309374i	0.752387	−	0.658721i	$-0.228902\pi$
$397$	19.9840	+	6.16424i	1.00297	+	0.309374i	0.250580	+	0.968096i	$0.419379\pi$
$398$	−0.459560	−	0.426409i	−0.0230357	−	0.0213740i
$399$	−21.5188	−	12.1360i	−1.07729	−	0.607560i
$400$	27.6185	−	25.6262i	1.38093	−	1.28131i
$401$	33.3745	−	16.0723i	1.66664	−	0.802614i	0.668374	−	0.743825i	$-0.266990\pi$
$401$	33.3745	−	16.0723i	1.66664	−	0.802614i	0.998270	−	0.0587889i	$-0.0187239\pi$
$402$	−3.94300	−	5.04056i	−0.196659	−	0.251400i
$403$	10.5009	+	5.05696i	0.523086	+	0.251905i
$404$	15.8259	+	40.3238i	0.787368	+	2.00618i
$405$	5.84824	+	0.219344i	0.290601	+	0.0108993i
$406$	−22.6505	−	17.3529i	−1.12413	−	0.861210i
$407$	−2.49072	+	33.2363i	−0.123460	+	1.64746i
$408$	15.7589	−	39.0723i	0.780182	−	1.93437i
$409$	−4.21689	−	10.7445i	−0.208512	−	0.531279i	0.787911	−	0.615789i	$-0.211163\pi$
$409$	−4.21689	−	10.7445i	−0.208512	−	0.531279i	−0.996423	+	0.0845099i	$0.973068\pi$
$410$	−4.53879	+	7.86142i	−0.224155	+	0.388248i
$411$	4.54781	−	5.59440i	0.224327	−	0.275951i
$412$	17.7965	+	45.3446i	0.876768	+	2.23397i
$413$	2.84443	−	9.90166i	0.139965	−	0.487229i
$414$	−13.8809	−	2.35909i	−0.682208	−	0.115943i
$415$	1.41569	−	0.213382i	0.0694937	−	0.0104745i
$416$	−26.8447	+	12.9277i	−1.31617	+	0.633835i
$417$	−29.3623	+	8.75656i	−1.43788	+	0.428810i
$418$	41.2470	+	51.7221i	2.01746	+	2.52981i
$419$	−11.3295	+	28.8670i	−0.553481	+	1.41025i	0.330982	+	0.943637i	$0.392620\pi$
$419$	−11.3295	+	28.8670i	−0.553481	+	1.41025i	−0.884463	+	0.466610i	$0.845475\pi$
$420$	12.8122	−	5.17824i	0.625174	−	0.252672i
$421$	−8.00611	−	20.3992i	−0.390194	−	0.994198i	−0.982128	−	0.188212i	$-0.939731\pi$
$421$	−8.00611	−	20.3992i	−0.390194	−	0.994198i	0.591934	−	0.805986i	$-0.298364\pi$
$422$	−24.6214	+	42.6455i	−1.19855	+	2.07595i
$423$	−15.8941	+	14.2026i	−0.772798	+	0.690553i
$424$	61.3039	+	9.24008i	2.97718	+	0.448738i
$425$	−15.6569	+	4.82950i	−0.759469	+	0.234265i
$426$	−36.5601	+	10.9031i	−1.77134	+	0.528258i
$427$	−6.56555	−	19.9013i	−0.317729	−	0.963090i
$428$	0.993691	+	13.2599i	0.0480318	+	0.640940i
$429$	−23.8624	+	21.7285i	−1.15209	+	1.04906i
$430$	−19.0854	−	9.19103i	−0.920378	−	0.443231i
$431$	17.2643	−	5.32533i	0.831593	−	0.256512i	0.150408	−	0.988624i	$-0.451941\pi$
$431$	17.2643	−	5.32533i	0.831593	−	0.256512i	0.681185	+	0.732112i	$0.261465\pi$
$432$	20.3358	+	37.6275i	0.978408	+	1.81035i
$433$	2.18934	+	9.59211i	0.105213	+	0.460968i	0.999898	+	0.0142706i	$0.00454263\pi$
$433$	2.18934	+	9.59211i	0.105213	+	0.460968i	−0.894685	+	0.446697i	$0.852600\pi$
$434$	−0.395245	−	20.3045i	−0.0189724	−	0.974646i
$435$	4.66843	−	0.658967i	0.223834	−	0.0315951i
$436$	−12.2735	−	53.7738i	−0.587794	−	2.57530i
$437$	−9.71125	+	1.46374i	−0.464552	+	0.0700200i
$438$	21.4085	−	14.3040i	1.02294	−	0.683472i
$439$	1.25368	+	16.7292i	0.0598350	+	0.798443i	0.943721	+	0.330741i	$0.107299\pi$
$439$	1.25368	+	16.7292i	0.0598350	+	0.798443i	−0.883886	+	0.467702i	$0.845082\pi$
$440$	−21.0458			−1.00332
$441$	−20.9957	+	0.423807i	−0.999796	+	0.0201813i
$442$	36.0777			1.71604
$443$	1.03120	+	13.7604i	0.0489938	+	0.653777i	0.966601	+	0.256288i	$0.0824995\pi$
$443$	1.03120	+	13.7604i	0.0489938	+	0.653777i	−0.917607	+	0.397490i	$0.869881\pi$
$444$	3.67485	+	56.0864i	0.174401	+	2.66174i
$445$	4.29041	−	0.646676i	0.203385	−	0.0306554i
$446$	4.57558	+	20.0469i	0.216660	+	0.949249i
$447$	10.2508	+	13.1042i	0.484849	+	0.619809i
$448$	6.63687	+	5.08461i	0.313563	+	0.240225i
$449$	−3.12342	−	13.6846i	−0.147403	−	0.645815i	−0.993601	−	0.112946i	$-0.963971\pi$
$449$	−3.12342	−	13.6846i	−0.147403	−	0.645815i	0.846198	−	0.532869i	$-0.178886\pi$
$450$	13.5396	−	32.6834i	0.638262	−	1.54071i
$451$	−24.6621	+	7.60724i	−1.16129	+	0.358211i
$452$	51.6989	+	24.8969i	2.43171	+	1.17105i
$453$	−5.33514	−	24.4279i	−0.250667	−	1.14772i
$454$	−4.28419	−	57.1685i	−0.201067	−	2.68305i
$455$	4.67287	+	4.84358i	0.219067	+	0.227070i
$456$	46.1054	+	43.5907i	2.15908	+	2.04132i
$457$	−11.3199	+	3.49172i	−0.529522	+	0.163336i	−0.547976	−	0.836494i	$-0.684602\pi$
$457$	−11.3199	+	3.49172i	−0.529522	+	0.163336i	0.0184543	+	0.999830i	$0.494125\pi$
$458$	5.98871	+	0.902653i	0.279834	+	0.0421782i
$459$	−0.868025	−	18.5803i	−0.0405160	−	0.867255i
$460$	2.74674	−	4.75749i	0.128067	−	0.221819i
$461$	−12.3793	−	31.5420i	−0.576563	−	1.46906i	−0.860114	−	0.510101i	$-0.829608\pi$
$461$	−12.3793	−	31.5420i	−0.576563	−	1.46906i	0.283551	−	0.958957i	$-0.408487\pi$
$462$	52.5511	+	20.0152i	2.44490	+	0.931191i
$463$	5.51724	−	14.0577i	0.256408	−	0.653317i	−0.743473	−	0.668766i	$-0.766823\pi$
$463$	5.51724	−	14.0577i	0.256408	−	0.653317i	0.999881	+	0.0154496i	$0.00491796\pi$
$464$	21.4835	+	26.9395i	0.997347	+	1.25063i
$465$	2.43834	+	2.30535i	0.113075	+	0.106908i
$466$	10.6735	−	5.14010i	0.494442	−	0.238111i
$467$	−7.50996	+	1.13194i	−0.347519	+	0.0523801i	−0.320483	−	0.947254i	$-0.603845\pi$
$467$	−7.50996	+	1.13194i	−0.347519	+	0.0523801i	−0.0270366	+	0.999634i	$0.508607\pi$
$468$	−34.7249	+	41.9075i	−1.60516	+	1.93718i
$469$	−3.78854	−	0.209858i	−0.174939	−	0.00969036i
$470$	−4.34866	−	11.0802i	−0.200589	−	0.511092i
$471$	−0.839843	−	2.20030i	−0.0386979	−	0.101385i
$472$	−13.2294	+	22.9140i	−0.608932	+	1.05470i
$473$	−22.0031	−	56.0631i	−1.01171	−	2.57778i
$474$	−19.1494	+	2.70301i	−0.879560	+	0.124153i
$475$	1.84403	−	24.6069i	0.0846099	−	1.12904i
$476$	−19.8233	−	39.1935i	−0.908601	−	1.79643i
$477$	26.3019	−	7.57618i	1.20428	−	0.346889i
$478$	−18.3086	−	46.6495i	−0.837416	−	2.13370i
$479$	24.4356	+	11.7676i	1.11649	+	0.537674i	0.898806	−	0.438346i	$-0.144435\pi$
$479$	24.4356	+	11.7676i	1.11649	+	0.537674i	0.217684	+	0.976019i	$0.430150\pi$
$480$	−8.49417	+	1.19899i	−0.387704	+	0.0547259i
$481$	−24.6630	+	11.8771i	−1.12454	+	0.541549i
$482$	54.2715	−	50.3566i	2.47200	−	2.29368i
$483$	−6.47393	+	5.27054i	−0.294574	+	0.239818i
$484$	−39.7290	−	36.8631i	−1.80586	−	1.67560i
$485$	−10.4776	−	3.23192i	−0.475765	−	0.146754i
$486$	32.0864	+	24.1531i	1.45547	+	1.09561i
$487$	−21.1320	+	19.6077i	−0.957584	+	0.888508i	−0.993839	−	0.110835i	$-0.964648\pi$
$487$	−21.1320	+	19.6077i	−0.957584	+	0.888508i	0.0362551	+	0.999343i	$0.488457\pi$
$488$	4.02211	+	53.6713i	0.182072	+	2.42959i
$489$	8.74806	+	22.9190i	0.395601	+	1.03643i
$490$	3.85628	−	11.0748i	0.174209	−	0.500310i
$491$	−11.7900	−	20.4210i	−0.532077	−	0.921585i	−0.999299	−	0.0374446i	$-0.988078\pi$
$491$	−11.7900	−	20.4210i	−0.532077	−	0.921585i	0.467221	−	0.884140i	$-0.345255\pi$
$492$	−39.3886	+	18.5158i	−1.77578	+	0.834758i
$493$	−3.33443	−	14.6091i	−0.150175	−	0.657961i
$494$	−19.8504	+	50.5780i	−0.893112	+	2.27561i
$495$	−8.44560	+	3.87389i	−0.379602	+	0.174118i
$496$	−5.45712	+	23.9092i	−0.245032	+	1.07356i
$497$	−9.41601	+	20.5672i	−0.422366	+	0.922565i
$498$	8.81148	+	4.34558i	0.394852	+	0.194730i
$499$	−28.7910	+	13.8650i	−1.28886	+	0.620684i	−0.947653	−	0.319303i	$-0.896551\pi$
$499$	−28.7910	+	13.8650i	−1.28886	+	0.620684i	−0.341210	+	0.939987i	$0.610837\pi$
$500$	21.1710	+	19.6438i	0.946797	+	0.878499i
$501$	−7.81200	−	5.43407i	−0.349015	−	0.242777i
$502$	13.5712	+	2.04553i	0.605712	+	0.0912964i
$503$	25.1960	+	12.1338i	1.12344	+	0.541018i	0.900952	−	0.433918i	$-0.142869\pi$
$503$	25.1960	+	12.1338i	1.12344	+	0.541018i	0.222484	+	0.974936i	$0.428584\pi$
$504$	52.5904	+	11.9636i	2.34256	+	0.532902i
$505$	−5.47249	+	2.63541i	−0.243523	+	0.117274i
$506$	21.3613	−	6.58909i	0.949625	−	0.292921i
$507$	−3.80103	−	1.21159i	−0.168810	−	0.0538086i
$508$	−37.4444	+	64.8556i	−1.66133	+	2.87750i
$509$	21.4741			0.951822			0.475911	−	0.879493i	$-0.342118\pi$
$509$	21.4741			0.951822			0.475911	+	0.879493i	$0.342118\pi$
$510$	9.89651	+	3.15454i	0.438225	+	0.139685i
$511$	1.98103	−	15.1367i	0.0876357	−	0.669609i
$512$	30.6572	+	38.4429i	1.35487	+	1.69895i
$513$	26.5257	+	9.00621i	1.17114	+	0.397634i
$514$	−16.2671	−	11.0907i	−0.717510	−	0.489190i
$515$	−6.15389	+	2.96356i	−0.271173	+	0.130590i
$516$	−49.9560	−	88.4300i	−2.19919	−	3.89292i
$517$	12.3638	−	31.5024i	0.543758	−	1.38547i
$518$	37.8631	+	29.0075i	1.66361	+	1.27451i
$519$	−25.2949	+	23.0329i	−1.11032	+	1.01103i
$520$	−8.64257	−	14.9694i	−0.379002	−	0.656450i
$521$	7.69446	+	13.3272i	0.337100	+	0.583875i	0.983886	−	0.178797i	$-0.0572205\pi$
$521$	7.69446	+	13.3272i	0.337100	+	0.583875i	−0.646786	+	0.762672i	$0.723887\pi$
$522$	28.8818	+	14.5818i	1.26412	+	0.638229i
$523$	−28.0248	−	26.0032i	−1.22544	−	1.13704i	−0.986109	−	0.166102i	$-0.946882\pi$
$523$	−28.0248	−	26.0032i	−1.22544	−	1.13704i	−0.239329	−	0.970938i	$-0.576928\pi$
$524$	5.09681	−	68.0122i	0.222655	−	2.97113i
$525$	−9.29103	−	18.8052i	−0.405494	−	0.820726i
$526$	−3.78557	−	50.5150i	−0.165059	−	2.20256i
$527$	6.64963	−	8.33837i	0.289662	−	0.363225i
$528$	−55.7465	−	38.7776i	−2.42605	−	1.68758i
$529$	4.37953	−	19.1880i	0.190414	−	0.834259i
$530$	−1.14224	+	15.2422i	−0.0496159	+	0.662078i
$531$	−1.09114	+	11.6304i	−0.0473515	+	0.504718i
$532$	65.8530	−	6.22597i	2.85509	−	0.269930i
$533$	−15.5385	−	14.4176i	−0.673046	−	0.624495i
$534$	26.7041	+	13.1697i	1.15560	+	0.569911i
$535$	−1.84367	+	0.277888i	−0.0797087	+	0.0120142i
$536$	9.31203	+	2.87238i	0.402218	+	0.124068i
$537$	−26.1989	−	18.2241i	−1.13057	−	0.786429i
$538$	−27.0801	+	46.9041i	−1.16751	+	2.02218i
$539$	29.4538	−	15.6244i	1.26866	−	0.672989i
$540$	−13.1897	+	8.45943i	−0.567594	+	0.364036i
$541$	−5.55963	+	3.79049i	−0.239027	+	0.162966i	−0.676909	−	0.736066i	$-0.736681\pi$
$541$	−5.55963	+	3.79049i	−0.239027	+	0.162966i	0.437882	+	0.899032i	$0.355729\pi$
$542$	−1.17539	−	5.14974i	−0.0504875	−	0.221200i
$543$	29.8265	+	0.279545i	1.27998	+	0.0119964i
$544$	6.06697	+	26.5811i	0.260119	+	1.13966i
$545$	7.39038	−	2.27963i	0.316569	−	0.0976486i
$546$	7.34408	+	45.5977i	0.314297	+	1.95140i
$547$	−21.6335	−	6.67306i	−0.924983	−	0.285319i	−0.204559	−	0.978854i	$-0.565576\pi$
$547$	−21.6335	−	6.67306i	−0.924983	−	0.285319i	−0.720423	+	0.693535i	$0.756052\pi$
$548$	−1.44257	+	19.2497i	−0.0616233	+	0.822306i
$549$	11.4933	+	20.7978i	0.490523	+	0.887627i
$550$	4.19738	+	56.0102i	0.178977	+	2.38828i
$551$	22.3154	+	3.36351i	0.950668	+	0.143290i
$552$	19.4033	−	9.12113i	0.825861	−	0.388221i
$553$	−6.27362	+	9.59786i	−0.266781	+	0.408142i
$554$	18.1367	+	12.3654i	0.770554	+	0.525354i
$555$	−7.80384	+	1.10154i	−0.331255	+	0.0467579i
$556$	51.1497	−	64.1397i	2.16923	−	2.72013i
$557$	−8.63112	−	14.9495i	−0.365712	−	0.633432i	0.623178	−	0.782080i	$-0.285841\pi$
$557$	−8.63112	−	14.9495i	−0.365712	−	0.633432i	−0.988890	+	0.148648i	$0.952508\pi$
$558$	4.70241	+	22.5422i	0.199069	+	0.954289i
$559$	30.8406	−	38.6729i	1.30442	−	1.63569i
$560$	−7.74817	+	11.8537i	−0.327420	+	0.500912i
$561$	14.5256	+	25.7126i	0.613270	+	1.08559i
$562$	−4.25296	−	5.33304i	−0.179400	−	0.224961i
$563$	−1.04553	+	13.9517i	−0.0440639	+	0.587992i	0.930849	+	0.365405i	$0.119069\pi$
$563$	−1.04553	+	13.9517i	−0.0440639	+	0.587992i	−0.974913	+	0.222588i	$0.928550\pi$
$564$	13.2203	−	55.5181i	0.556673	−	2.33773i
$565$	−2.93951	+	7.48974i	−0.123666	+	0.315096i
$566$	−7.30171	−	9.15606i	−0.306914	−	0.384858i
$567$	23.3065	−	4.87933i	0.978780	−	0.204913i
$568$	36.2216	−	45.4205i	1.51983	−	1.90580i
$569$	5.52354	+	9.56704i	0.231559	+	0.401071i	0.958267	−	0.285875i	$-0.0922841\pi$
$569$	5.52354	+	9.56704i	0.231559	+	0.401071i	−0.726708	+	0.686946i	$0.758951\pi$
$570$	−9.86759	+	12.1384i	−0.413308	+	0.508423i
$571$	13.2443	+	33.7459i	0.554256	+	1.41222i	0.883703	+	0.468048i	$0.155042\pi$
$571$	13.2443	+	33.7459i	0.554256	+	1.41222i	−0.329447	+	0.944174i	$0.606862\pi$
$572$	19.2279	−	84.2429i	0.803958	−	3.52237i
$573$	−10.8852	+	3.24623i	−0.454735	+	0.135613i
$574$	−10.1977	+	35.4987i	−0.425642	+	1.48169i
$575$	−7.51247	−	3.61782i	−0.313292	−	0.150873i
$576$	−8.46272	−	4.27265i	−0.352613	−	0.178027i
$577$	2.58502	+	34.4947i	0.107616	+	1.43603i	0.745810	+	0.666158i	$0.232063\pi$
$577$	2.58502	+	34.4947i	0.107616	+	1.43603i	−0.638194	+	0.769875i	$0.720318\pi$
$578$	−2.39971	+	10.5138i	−0.0998147	+	0.437317i
$579$	3.55970	+	3.36555i	0.147936	+	0.139867i
$580$	−9.25362	+	8.58610i	−0.384236	+	0.356519i
$581$	5.38006	−	2.23331i	0.223202	−	0.0926532i
$582$	−46.3607	−	59.2655i	−1.92171	−	2.45663i
$583$	−31.8562	+	29.5582i	−1.31935	+	1.22418i
$584$	−14.3239	+	36.4967i	−0.592727	+	1.51025i
$585$	−6.22364	−	4.41632i	−0.257316	−	0.182592i
$586$	−3.11883	+	2.12638i	−0.128838	+	0.0878400i
$587$	2.27623	−	3.94254i	0.0939499	−	0.162726i	−0.815220	−	0.579152i	$-0.803384\pi$
$587$	2.27623	−	3.94254i	0.0939499	−	0.162726i	0.909170	+	0.416425i	$0.136717\pi$
$588$	45.5003	−	33.0325i	1.87640	−	1.36224i
$589$	8.03100	+	13.9101i	0.330912	+	0.573156i
$590$	−5.87729	−	2.83035i	−0.241964	−	0.116524i
$591$	35.0612	+	17.2912i	1.44223	+	0.711266i
$592$	−35.9123	−	45.0326i	−1.47599	−	1.85083i
$593$	12.3480	+	3.80885i	0.507071	+	0.156411i	0.537727	−	0.843119i	$-0.319283\pi$
$593$	12.3480	+	3.80885i	0.507071	+	0.156411i	−0.0306555	+	0.999530i	$0.509759\pi$
$594$	−62.7588	−	11.2722i	−2.57502	−	0.462502i
$595$	5.27255	−	3.18251i	0.216154	−	0.130470i
$596$	−42.5667	−	13.1301i	−1.74360	−	0.537829i
$597$	0.403891	−	0.120450i	0.0165302	−	0.00492971i
$598$	13.4588	+	12.4879i	0.550371	+	0.510670i
$599$	−4.10884	+	2.80136i	−0.167883	+	0.114460i	−0.644347	−	0.764733i	$-0.722871\pi$
$599$	−4.10884	+	2.80136i	−0.167883	+	0.114460i	0.476464	+	0.879194i	$0.341918\pi$
$600$	11.4945	+	52.6297i	0.469262	+	2.14860i
$601$	−30.8818	+	21.0548i	−1.25969	+	0.858845i	−0.994437	−	0.105333i	$-0.966409\pi$
$601$	−30.8818	+	21.0548i	−1.25969	+	0.858845i	−0.265257	+	0.964178i	$0.585457\pi$
$602$	−84.3854	−	17.5399i	−3.43929	−	0.714871i
$603$	4.26560	−	0.561385i	0.173709	−	0.0228614i
$604$	49.0751	+	45.5350i	1.99684	+	1.85279i
$605$	4.73813	−	5.94142i	0.192632	−	0.241553i
$606$	−41.1565	−	6.59841i	−1.67187	−	0.268042i
$607$	17.6429			0.716105			0.358053	−	0.933701i	$-0.383441\pi$
$607$	17.6429			0.716105			0.358053	+	0.933701i	$0.383441\pi$
$608$	−40.6027	−	6.11987i	−1.64666	−	0.248194i
$609$	17.7853	−	7.18817i	0.720697	−	0.291279i
$610$	−13.1213	+	1.97772i	−0.531267	+	0.0800756i
$611$	27.4841	−	4.14257i	1.11189	−	0.167590i
$612$	30.3159	+	39.5121i	1.22545	+	1.59718i
$613$	−2.33985	−	1.59528i	−0.0945057	−	0.0644329i	0.515145	−	0.857103i	$-0.327738\pi$
$613$	−2.33985	−	1.59528i	−0.0945057	−	0.0644329i	−0.609651	+	0.792670i	$0.708690\pi$
$614$	11.5794	−	29.5038i	0.467307	−	1.19068i
$615$	−3.00173	−	5.31354i	−0.121042	−	0.214263i
$616$	−83.0965	+	20.6756i	−3.34805	+	0.833046i
$617$	10.0289	+	1.51161i	0.403748	+	0.0608552i	0.347777	−	0.937577i	$-0.386937\pi$
$617$	10.0289	+	1.51161i	0.403748	+	0.0608552i	0.0559708	+	0.998432i	$0.482175\pi$
$618$	−46.2811	−	7.42000i	−1.86170	−	0.298476i
$619$	−28.1497			−1.13143			−0.565716	−	0.824600i	$-0.691400\pi$
$619$	−28.1497			−1.13143			−0.565716	+	0.824600i	$0.691400\pi$
$620$	−8.88415	−	1.33907i	−0.356796	−	0.0537783i
$621$	6.10757	−	7.23184i	0.245088	−	0.290204i
$622$	29.6603	−	14.2837i	1.18927	−	0.572723i
$623$	16.3048	−	6.76827i	0.653239	−	0.271165i
$624$	4.68897	−	55.5754i	0.187709	−	2.22480i
$625$	11.7442	−	14.7267i	0.469767	−	0.589070i
$626$	61.8292	−	42.1544i	2.47119	−	1.68483i
$627$	−44.0391	+	6.21629i	−1.75875	+	0.248255i
$628$	5.21007	+	3.55216i	0.207904	+	0.141747i
$629$	5.57391	+	24.4209i	0.222246	+	0.973724i
$630$	−1.97239	+	13.1501i	−0.0785817	+	0.523912i
$631$	6.60324	−	28.9307i	0.262871	−	1.15171i	−0.655250	−	0.755412i	$-0.727437\pi$
$631$	6.60324	−	28.9307i	0.262871	−	1.15171i	0.918121	−	0.396300i	$-0.129706\pi$
$632$	21.5875	−	20.0303i	0.858706	−	0.796763i
$633$	−16.2834	−	28.8242i	−0.647206	−	1.14566i
$634$	−21.4743	−	6.62394i	−0.852852	−	0.263070i
$635$	−9.46088	−	4.55612i	−0.375444	−	0.180804i
$636$	−46.2276	+	56.8660i	−1.83305	+	2.25489i
$637$	23.2086	+	14.5335i	0.919558	+	0.575840i
$638$	−51.3681			−2.03368
$639$	6.17508	−	24.8944i	0.244283	−	0.984807i
$640$	−3.38044	+	3.13659i	−0.133624	+	0.123985i
$641$	−9.24449	−	11.5922i	−0.365135	−	0.457865i	0.564995	−	0.825094i	$-0.308878\pi$
$641$	−9.24449	−	11.5922i	−0.365135	−	0.457865i	−0.930131	+	0.367229i	$0.880307\pi$
$642$	−11.4752	−	5.65927i	−0.452891	−	0.223354i
$643$	32.4615	−	10.0130i	1.28015	−	0.394875i	0.421219	−	0.906959i	$-0.361602\pi$
$643$	32.4615	−	10.0130i	1.28015	−	0.394875i	0.858936	+	0.512084i	$0.171126\pi$
$644$	6.17132	−	21.4828i	0.243184	−	0.846539i
$645$	11.8414	−	7.91178i	0.466254	−	0.311526i
$646$	41.0798	+	28.0077i	1.61626	+	1.10195i
$647$	5.89441	−	1.81818i	0.231733	−	0.0714802i	−0.176714	−	0.984262i	$-0.556547\pi$
$647$	5.89441	−	1.81818i	0.231733	−	0.0714802i	0.408447	+	0.912782i	$0.366071\pi$
$648$	−61.1124	−	2.29208i	−2.40072	−	0.0900414i
$649$	−6.77581	−	17.2645i	−0.265974	−	0.677690i
$650$	−38.1150	+	25.9864i	−1.49499	+	1.01927i
$651$	11.8923	+	6.70691i	0.466095	+	0.262865i
$652$	−54.2696	−	37.0004i	−2.12536	−	1.44905i
$653$	2.63518	−	11.5455i	0.103123	−	0.451809i	−0.896833	−	0.442369i	$-0.854138\pi$
$653$	2.63518	−	11.5455i	0.103123	−	0.451809i	0.999955	−	0.00943994i	$-0.00300487\pi$
$654$	50.5667	+	16.1183i	1.97732	+	0.630275i
$655$	9.56330			0.373669
$656$	22.3008	−	38.6261i	0.870699	−	1.50810i
$657$	0.969803	+	17.2826i	0.0378356	+	0.674259i
$658$	−28.0555	−	39.4766i	−1.09372	−	1.53896i
$659$	48.8371	−	7.36101i	1.90242	−	0.286744i	0.910493	−	0.413524i	$-0.135702\pi$
$659$	48.8371	−	7.36101i	1.90242	−	0.286744i	0.991931	+	0.126780i	$0.0404641\pi$
$660$	12.6404	−	21.4275i	0.492027	−	0.834064i
$661$	0.766650	−	10.2302i	0.0298192	−	0.397910i	−0.962246	−	0.272183i	$-0.912255\pi$
$661$	0.766650	−	10.2302i	0.0298192	−	0.397910i	0.992065	−	0.125727i	$-0.0401264\pi$
$662$	−1.86219	+	24.8492i	−0.0723761	+	0.965792i
$663$	−12.3237	+	20.8907i	−0.478614	+	0.811328i
$664$	−14.7936	+	2.22978i	−0.574104	+	0.0865322i
$665$	1.56060	+	9.14274i	0.0605174	+	0.354540i
$666$	−48.2794	−	24.3753i	−1.87079	−	0.944523i
$667$	3.81288	−	6.60411i	0.147635	−	0.255712i
$668$	25.4790			0.985811
$669$	−13.1711	−	4.19832i	−0.509223	−	0.162316i
$670$	−0.534624	+	2.34234i	−0.0206543	+	0.0904925i
$671$	−31.1714	−	21.2523i	−1.20336	−	0.820437i
$672$	−32.3602	+	13.0788i	−1.24832	+	0.504526i
$673$	12.3871	−	8.44535i	0.477486	−	0.325545i	−0.300548	−	0.953767i	$-0.597170\pi$
$673$	12.3871	−	8.44535i	0.477486	−	0.325545i	0.778034	+	0.628222i	$0.216217\pi$
$674$	−9.08255	−	23.1420i	−0.349847	−	0.891395i
$675$	14.3002	+	19.0043i	0.550416	+	0.731476i
$676$	10.2070	−	3.14845i	0.392578	−	0.121094i
$677$	18.2335	+	12.4314i	0.700771	+	0.477778i	0.860544	−	0.509376i	$-0.170124\pi$
$677$	18.2335	+	12.4314i	0.700771	+	0.477778i	−0.159773	+	0.987154i	$0.551076\pi$
$678$	−45.9096	+	30.6744i	−1.76315	+	1.17804i
$679$	−44.5446	−	2.46746i	−1.70947	−	0.0946923i
$680$	−15.1143	+	4.66215i	−0.579607	+	0.178785i
$681$	34.5667	+	17.0474i	1.32460	+	0.653256i
$682$	−22.7950	−	28.5840i	−0.872866	−	1.09454i
$683$	−12.8637	+	11.9357i	−0.492214	+	0.456708i	−0.886801	−	0.462151i	$-0.847078\pi$
$683$	−12.8637	+	11.9357i	−0.492214	+	0.456708i	0.394588	+	0.918858i	$0.370887\pi$
$684$	−72.0729	+	20.7604i	−2.75578	+	0.793793i
$685$	−2.70673			−0.103419
$686$	4.34596	−	47.5160i	0.165930	−	1.81417i
$687$	−2.56835	+	3.15941i	−0.0979888	+	0.120539i
$688$	93.7735	+	45.1590i	3.57508	+	1.72167i
$689$	−34.1060	−	10.5203i	−1.29933	−	0.400791i
$690$	2.59998	+	4.60238i	0.0989795	+	0.175210i
$691$	12.7572	−	11.8369i	0.485306	−	0.450299i	−0.399174	−	0.916875i	$-0.630703\pi$
$691$	12.7572	−	11.8369i	0.485306	−	0.450299i	0.884481	+	0.466576i	$0.154513\pi$
$692$	20.3822	−	89.3001i	0.774814	−	3.39468i
$693$	−29.5406	+	23.5926i	−1.12215	+	0.896209i
$694$	17.3860	+	76.1731i	0.659964	+	2.89149i
$695$	9.50439	+	6.47998i	0.360522	+	0.245800i
$696$	−48.7838	+	6.88602i	−1.84914	+	0.261014i
$697$	−16.0262	+	10.9265i	−0.607036	+	0.413870i
$698$	−11.6876	+	14.6558i	−0.442382	+	0.554729i
$699$	−0.669594	+	7.93628i	−0.0253264	+	0.300178i
$700$	49.1734	+	27.1282i	1.85858	+	1.02535i
$701$	33.9658	−	16.3571i	1.28287	−	0.617798i	0.336744	−	0.941596i	$-0.390674\pi$
$701$	33.9658	−	16.3571i	1.28287	−	0.617798i	0.946126	+	0.323798i	$0.104960\pi$
$702$	−17.7546	−	49.2678i	−0.670105	−	1.85949i
$703$	−37.3029	−	5.62251i	−1.40691	−	0.212057i
$704$	15.0515			0.567273
$705$	7.90141	+	1.26679i	0.297584	+	0.0477101i
$706$	−17.9208	−	2.70112i	−0.674458	−	0.101658i
$707$	−19.0183	+	15.7818i	−0.715258	+	0.593536i
$708$	−15.3838	−	27.2318i	−0.578159	−	1.02343i
$709$	−10.3153	+	26.2829i	−0.387398	+	0.987074i	0.595571	+	0.803303i	$0.296926\pi$
$709$	−10.3153	+	26.2829i	−0.387398	+	0.987074i	−0.982969	+	0.183771i	$0.941169\pi$
$710$	11.8343	+	8.06847i	0.444132	+	0.302804i
$711$	4.97603	−	12.0117i	0.186616	−	0.450474i
$712$	−44.8336	+	6.75758i	−1.68021	+	0.253251i
$713$	5.36688	−	0.808928i	0.200991	−	0.0302946i
$714$	42.1741	+	2.73284i	1.57833	+	0.102274i
$715$	11.9808	+	1.80582i	0.448058	+	0.0675339i
$716$	85.4483			3.19335
$717$	33.2663	+	5.33340i	1.24235	+	0.199180i
$718$	−7.69612	+	9.65063i	−0.287217	+	0.360158i
$719$	−7.41770	−	6.88262i	−0.276634	−	0.256679i	0.529638	−	0.848224i	$-0.322328\pi$
$719$	−7.41770	−	6.88262i	−0.276634	−	0.256679i	−0.806272	+	0.591545i	$0.798518\pi$
$720$	6.14560	−	14.8349i	0.229033	−	0.552865i
$721$	−21.3864	+	17.7469i	−0.796471	+	0.660928i
$722$	−21.4225	+	14.6056i	−0.797262	+	0.543564i
$723$	10.6203	+	48.6270i	0.394974	+	1.80846i
$724$	−65.9855	+	44.9882i	−2.45233	+	1.67197i
$725$	14.0455	+	13.0323i	0.521637	+	0.484008i
$726$	49.9748	−	14.9037i	1.85474	−	0.553128i
$727$	38.8474	+	11.9828i	1.44077	+	0.444419i	0.914044	−	0.405615i	$-0.132943\pi$
$727$	38.8474	+	11.9828i	1.44077	+	0.444419i	0.526728	+	0.850034i	$0.323419\pi$
$728$	−48.8301	−	50.6140i	−1.80977	−	1.87588i
$729$	−24.9461	+	10.3291i	−0.923930	+	0.382561i
$730$	−9.23685	−	2.84919i	−0.341871	−	0.105453i
$731$	−28.2212	−	35.3882i	−1.04380	−	1.30888i
$732$	−57.0605	−	28.1407i	−2.10902	−	1.04011i
$733$	4.40547	+	2.12156i	0.162720	+	0.0783617i	0.513471	−	0.858107i	$-0.328359\pi$
$733$	4.40547	+	2.12156i	0.162720	+	0.0783617i	−0.350751	+	0.936469i	$0.614074\pi$
$734$	35.2475	+	61.0504i	1.30101	+	2.25341i
$735$	5.09559	+	6.01601i	0.187954	+	0.221904i
$736$	−6.93751	+	12.0161i	−0.255720	+	0.442920i
$737$	−5.64389	+	3.84794i	−0.207895	+	0.141741i
$738$	3.91189	−	41.6966i	0.143999	−	1.53487i
$739$	5.62893	−	14.3423i	0.207063	−	0.527589i	−0.789182	−	0.614159i	$-0.789495\pi$
$739$	5.62893	−	14.3423i	0.207063	−	0.527589i	0.996246	+	0.0865698i	$0.0275906\pi$
$740$	15.4685	−	14.3527i	0.568635	−	0.527616i
$741$	−22.5064	−	28.7712i	−0.826792	−	1.05694i
$742$	10.4641	+	61.3039i	0.384150	+	2.25054i
$743$	15.4585	−	14.3434i	0.567117	−	0.526207i	−0.343667	−	0.939092i	$-0.611669\pi$
$743$	15.4585	−	14.3434i	0.567117	−	0.526207i	0.910784	+	0.412884i	$0.135479\pi$
$744$	−25.4800	−	24.0902i	−0.934141	−	0.883191i
$745$	1.38989	−	6.08952i	0.0509218	−	0.223103i
$746$	−0.477996	−	6.37841i	−0.0175007	−	0.233530i
$747$	−5.52619	+	3.61786i	−0.202193	+	0.132371i
$748$	−71.2397	−	34.3072i	−2.60478	−	1.25440i
$749$	−7.00648	+	2.90845i	−0.256011	+	0.106272i
$750$	−26.6309	+	7.94198i	−0.972422	+	0.290000i
$751$	−4.65618	+	20.4000i	−0.169906	+	0.744408i	0.816129	+	0.577870i	$0.196116\pi$
$751$	−4.65618	+	20.4000i	−0.169906	+	0.744408i	−0.986035	+	0.166538i	$0.946741\pi$
$752$	21.3666	+	54.4412i	0.779160	+	1.98527i
$753$	−5.82022	+	7.15963i	−0.212101	+	0.260911i
$754$	−21.0946	−	36.5369i	−0.768220	−	1.33060i
$755$	−5.85275	+	7.33912i	−0.213004	+	0.267098i
$756$	−43.7671	+	46.3587i	−1.59179	+	1.68605i
$757$	−4.29547	−	5.38635i	−0.156122	−	0.195770i	0.697619	−	0.716469i	$-0.254243\pi$
$757$	−4.29547	−	5.38635i	−0.156122	−	0.195770i	−0.853740	+	0.520699i	$0.825671\pi$
$758$	−25.4448	+	64.8323i	−0.924198	+	2.35482i
$759$	−3.48138	+	14.6200i	−0.126366	+	0.530671i
$760$	1.78013	−	23.7542i	0.0645721	−	0.861655i
$761$	22.7892	+	28.5767i	0.826106	+	1.03590i	0.998703	+	0.0509120i	$0.0162128\pi$
$761$	22.7892	+	28.5767i	0.826106	+	1.03590i	−0.172597	+	0.984993i	$0.555216\pi$
$762$	−35.4438	−	62.7411i	−1.28399	−	2.27287i
$763$	26.9404	−	16.2612i	0.975308	−	0.588696i
$764$	18.9622	−	23.7778i	0.686028	−	0.860252i
$765$	−5.20716	+	4.65299i	−0.188265	+	0.168229i
$766$	37.8481	+	65.5549i	1.36751	+	2.36859i
$767$	9.49729	−	11.9092i	0.342927	−	0.430017i
$768$	−42.1742	+	5.95306i	−1.52183	+	0.214813i
$769$	−29.9872	−	20.4449i	−1.08136	−	0.737262i	−0.114724	−	0.993397i	$-0.536598\pi$
$769$	−29.9872	−	20.4449i	−1.08136	−	0.737262i	−0.966641	+	0.256135i	$0.917551\pi$
$770$	−6.61424	−	20.0489i	−0.238361	−	0.722511i
$771$	11.9787	−	5.63094i

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

\(f(q)\)	\(=\)	\(q+(-0.192530 - 2.56913i) q^{2} +(1.55341 + 0.766101i) q^{3} +(-4.58569 + 0.691182i) q^{4} +(-0.144697 - 0.633958i) q^{5} +(1.66913 - 4.13841i) q^{6} +(-1.19412 - 2.36095i) q^{7} +(1.51204 + 6.62468i) q^{8} +(1.82618 + 2.38014i) q^{9} +O(q^{10})\)	\(q+(-0.192530 - 2.56913i) q^{2} +(1.55341 + 0.766101i) q^{3} +(-4.58569 + 0.691182i) q^{4} +(-0.144697 - 0.633958i) q^{5} +(1.66913 - 4.13841i) q^{6} +(-1.19412 - 2.36095i) q^{7} +(1.51204 + 6.62468i) q^{8} +(1.82618 + 2.38014i) q^{9} +(-1.60086 + 0.493800i) q^{10} +(-4.29136 - 2.06661i) q^{11} +(-7.65298 - 2.43941i) q^{12} +(-0.292340 - 3.90101i) q^{13} +(-5.83567 + 3.52241i) q^{14} +(0.260902 - 1.09565i) q^{15} +(7.86562 - 2.42622i) q^{16} +(-3.53970 - 0.533524i) q^{17} +(5.76329 - 5.14994i) q^{18} +(2.69554 - 4.66882i) q^{19} +(1.10171 + 2.80712i) q^{20} +(-0.0462435 - 4.58234i) q^{21} +(-4.48317 + 11.4229i) q^{22} +(-1.13581 - 1.42426i) q^{23} +(-2.72635 + 11.4492i) q^{24} +(4.12388 - 1.98596i) q^{25} +(-9.96590 + 1.50212i) q^{26} +(1.01338 + 5.09638i) q^{27} +(7.10773 + 10.0012i) q^{28} +(1.52934 + 3.89670i) q^{29} +(-2.86510 - 0.459345i) q^{30} +(-1.48968 + 2.58020i) q^{31} +(-2.78263 - 7.09002i) q^{32} +(-5.08302 - 6.49791i) q^{33} +(-0.689195 + 9.19667i) q^{34} +(-1.32395 + 1.09864i) q^{35} +(-10.0194 - 9.65237i) q^{36} +(-2.55648 - 6.51381i) q^{37} +(-12.5138 - 6.02631i) q^{38} +(2.53444 - 6.28383i) q^{39} +(3.98098 - 1.91714i) q^{40} +(3.97206 - 3.68553i) q^{41} +(-11.7637 + 1.00104i) q^{42} +(9.26906 + 8.60043i) q^{43} +(21.1073 + 6.51072i) q^{44} +(1.24467 - 1.50212i) q^{45} +(-3.44044 + 3.19226i) q^{46} +(0.530961 + 7.08519i) q^{47} +(14.0773 + 2.25694i) q^{48} +(-4.14814 + 5.63852i) q^{49} +(-5.89614 - 10.2124i) q^{50} +(-5.08988 - 3.54055i) q^{51} +(4.03689 + 17.6867i) q^{52} +(3.33328 - 8.49307i) q^{53} +(12.8981 - 3.58471i) q^{54} +(-0.689197 + 3.01957i) q^{55} +(13.8349 - 11.4805i) q^{56} +(7.76407 - 5.18754i) q^{57} +(9.71669 - 4.67931i) q^{58} +(2.85438 + 2.64848i) q^{59} +(-0.439122 + 5.20464i) q^{60} +(7.83228 + 1.18053i) q^{61} +(6.91568 + 3.33042i) q^{62} +(3.43870 - 7.15369i) q^{63} +(-2.84710 + 1.37109i) q^{64} +(-2.43077 + 0.749794i) q^{65} +(-15.7153 + 14.3100i) q^{66} +(0.717064 - 1.24199i) q^{67} +16.6007 q^{68} +(-0.673255 - 3.08261i) q^{69} +(3.07746 + 3.18989i) q^{70} +(-5.33059 - 6.68435i) q^{71} +(-13.0064 + 15.6967i) q^{72} +(4.76734 + 3.25032i) q^{73} +(-16.2426 + 7.82203i) q^{74} +(7.92753 + 0.0742997i) q^{75} +(-9.13393 + 23.2729i) q^{76} +(0.245260 + 12.5995i) q^{77} +(-16.6319 - 5.30148i) q^{78} +(-2.16694 - 3.75324i) q^{79} +(-2.67625 - 4.63540i) q^{80} +(-2.33014 + 8.69313i) q^{81} +(-10.2333 - 9.49515i) q^{82} +(-0.164534 + 2.19555i) q^{83} +(3.37929 + 20.9812i) q^{84} +(0.173951 + 2.32122i) q^{85} +(20.3110 - 25.4693i) q^{86} +(-0.609567 + 7.22482i) q^{87} +(7.20192 - 31.5537i) q^{88} +(-0.498638 + 6.65386i) q^{89} +(-4.09877 - 2.90850i) q^{90} +(-8.86098 + 5.34848i) q^{91} +(6.19290 + 5.74618i) q^{92} +(-4.29079 + 2.86687i) q^{93} +(18.1005 - 2.72822i) q^{94} +(-3.34987 - 1.03330i) q^{95} +(1.10910 - 13.1455i) q^{96} +(8.43105 - 14.6030i) q^{97} +(15.2847 + 9.57151i) q^{98} +(-2.91797 - 13.9880i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9}+O(q^{10}) \) 648 * q - 8 * q^2 - 13 * q^3 + 44 * q^4 + 3 * q^5 + 2 * q^6 - 7 * q^7 - 16 * q^8 - 39 * q^9	\( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9} - 22 q^{10} - 5 q^{11} + 2 q^{12} - 4 q^{13} + 52 q^{14} - 4 q^{15} + 38 q^{16} - 37 q^{17} - 16 q^{18} - 14 q^{19} - 11 q^{20} - 6 q^{21} - q^{22} - 20 q^{23} - 26 q^{24} - 97 q^{25} - 44 q^{26} + 14 q^{27} - 22 q^{28} - 53 q^{29} - 9 q^{30} + 10 q^{31} - 10 q^{32} + 2 q^{33} - 7 q^{34} - 32 q^{35} - 22 q^{36} - 39 q^{37} + 59 q^{38} - 26 q^{39} - 19 q^{40} - 17 q^{41} - 83 q^{42} - q^{43} - 31 q^{44} + 81 q^{45} + 56 q^{46} + 50 q^{47} - 23 q^{48} - 19 q^{49} - 21 q^{50} - 30 q^{51} - 9 q^{52} + 50 q^{53} + 48 q^{54} + 20 q^{55} - 239 q^{56} + 33 q^{57} + 17 q^{58} - 37 q^{59} - 152 q^{60} - 105 q^{61} - 30 q^{62} + 6 q^{63} - 88 q^{64} - 5 q^{65} - 99 q^{66} + 13 q^{67} - 290 q^{68} + 64 q^{69} + 17 q^{70} - 19 q^{71} + 11 q^{72} - 40 q^{73} - 57 q^{74} + 69 q^{75} - 41 q^{76} + 19 q^{77} + 81 q^{78} + 13 q^{79} + 163 q^{80} - 179 q^{81} - 28 q^{82} + 73 q^{83} - 341 q^{84} - 10 q^{85} + 15 q^{86} + 13 q^{87} - 13 q^{88} - 104 q^{89} + 171 q^{90} - 49 q^{91} - 91 q^{92} - 275 q^{93} - 4 q^{94} - 29 q^{95} + 231 q^{96} - 11 q^{97} - 33 q^{98} + 62 q^{99}+O(q^{100}) \) 648 * q - 8 * q^2 - 13 * q^3 + 44 * q^4 + 3 * q^5 + 2 * q^6 - 7 * q^7 - 16 * q^8 - 39 * q^9 - 22 * q^10 - 5 * q^11 + 2 * q^12 - 4 * q^13 + 52 * q^14 - 4 * q^15 + 38 * q^16 - 37 * q^17 - 16 * q^18 - 14 * q^19 - 11 * q^20 - 6 * q^21 - q^22 - 20 * q^23 - 26 * q^24 - 97 * q^25 - 44 * q^26 + 14 * q^27 - 22 * q^28 - 53 * q^29 - 9 * q^30 + 10 * q^31 - 10 * q^32 + 2 * q^33 - 7 * q^34 - 32 * q^35 - 22 * q^36 - 39 * q^37 + 59 * q^38 - 26 * q^39 - 19 * q^40 - 17 * q^41 - 83 * q^42 - q^43 - 31 * q^44 + 81 * q^45 + 56 * q^46 + 50 * q^47 - 23 * q^48 - 19 * q^49 - 21 * q^50 - 30 * q^51 - 9 * q^52 + 50 * q^53 + 48 * q^54 + 20 * q^55 - 239 * q^56 + 33 * q^57 + 17 * q^58 - 37 * q^59 - 152 * q^60 - 105 * q^61 - 30 * q^62 + 6 * q^63 - 88 * q^64 - 5 * q^65 - 99 * q^66 + 13 * q^67 - 290 * q^68 + 64 * q^69 + 17 * q^70 - 19 * q^71 + 11 * q^72 - 40 * q^73 - 57 * q^74 + 69 * q^75 - 41 * q^76 + 19 * q^77 + 81 * q^78 + 13 * q^79 + 163 * q^80 - 179 * q^81 - 28 * q^82 + 73 * q^83 - 341 * q^84 - 10 * q^85 + 15 * q^86 + 13 * q^87 - 13 * q^88 - 104 * q^89 + 171 * q^90 - 49 * q^91 - 91 * q^92 - 275 * q^93 - 4 * q^94 - 29 * q^95 + 231 * q^96 - 11 * q^97 - 33 * q^98 + 62 * q^99

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