LMFDB - Embedded newform 441.2.z.a.4.3

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			4.3
Character	$\chi$	$=$	441.4
Dual form			441.2.z.a.331.3

$q$-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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{3}\right)$

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	0.343468	+	0.939164i	$0.388398\pi$
$2$	−0.192530	+	2.56913i	−0.136139	+	1.81665i	−0.479607	+	0.877484i	$0.659221\pi$
$3$	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	−0.996922	−	0.0783989i	$-0.975019\pi$
$5$	−0.144697	+	0.633958i	−0.0647103	+	0.283514i	0.932212	+	0.361913i	$0.117876\pi$
$6$	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	−0.948923	−	0.315507i	$-0.897825\pi$
$11$	−4.29136	+	2.06661i	−1.29389	+	0.623106i	−0.344970	+	0.938614i	$0.612111\pi$
$12$	−7.65298	+	2.43941i	−2.20923	+	0.704197i
$13$	−0.292340	+	3.90101i	−0.0810805	+	1.08194i	0.797174	+	0.603750i	$0.206328\pi$
$13$	−0.292340	+	3.90101i	−0.0810805	+	1.08194i	−0.878254	+	0.478194i	$0.841291\pi$
$14$	−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	−0.563519	−	0.826103i	$-0.690553\pi$
$17$	−3.53970	+	0.533524i	−0.858504	+	0.129399i	−0.294985	+	0.955502i	$0.595315\pi$
$18$	5.76329	+	5.14994i	1.35842	+	1.21385i
$19$	2.69554	+	4.66882i	0.618400	+	1.07110i	0.989778	+	0.142618i	$0.0455522\pi$
$19$	2.69554	+	4.66882i	0.618400	+	1.07110i	−0.371378	+	0.928482i	$0.621115\pi$
$20$	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	−0.886018	−	0.463652i	$-0.846539\pi$
$23$	−1.13581	+	1.42426i	−0.236833	+	0.296979i	0.649184	+	0.760631i	$0.275110\pi$
$24$	−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	−0.715691	−	0.698417i	$-0.753888\pi$
$29$	1.52934	−	3.89670i	0.283992	−	0.723600i	0.999683	−	0.0251825i	$-0.00801668\pi$
$30$	−2.86510	+	0.459345i	−0.523092	+	0.0838646i
$31$	−1.48968	−	2.58020i	−0.267555	−	0.463418i	0.700675	−	0.713480i	$-0.252882\pi$
$31$	−1.48968	−	2.58020i	−0.267555	−	0.463418i	−0.968230	+	0.250062i	$0.919549\pi$
$32$	−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	0.551330	+	0.834287i	$0.314121\pi$
$37$	−2.55648	+	6.51381i	−0.420283	+	1.07086i	−0.971613	+	0.236576i	$0.923975\pi$
$38$	−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	0.926454	−	0.376409i	$-0.122841\pi$
$41$	3.97206	+	3.68553i	0.620331	+	0.575583i	−0.306123	+	0.951992i	$0.599032\pi$
$42$	−11.7637	−	1.00104i	−1.81518	−	0.154464i
$43$	9.26906	−	8.60043i	1.41352	−	1.31155i	0.526228	−	0.850343i	$-0.323606\pi$
$43$	9.26906	−	8.60043i	1.41352	−	1.31155i	0.887291	−	0.461211i	$-0.152585\pi$
$44$	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	−0.814150	−	0.580655i	$-0.802797\pi$
$47$	0.530961	−	7.08519i	0.0774487	−	1.03348i	0.891599	−	0.452826i	$-0.149584\pi$
$48$	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	0.954382	+	0.298587i	$0.0965155\pi$
$53$	3.33328	+	8.49307i	0.457862	+	1.16661i	−0.496521	+	0.868025i	$0.665389\pi$
$54$	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	−0.472156	−	0.881515i	$-0.656524\pi$
$59$	2.85438	−	2.64848i	0.371609	−	0.344803i	0.843766	+	0.536712i	$0.180334\pi$
$60$	−0.439122	−	5.20464i	−0.0566904	−	0.671916i
$61$	7.83228	−	1.18053i	1.00282	−	0.151151i	0.372950	−	0.927851i	$-0.378346\pi$
$61$	7.83228	−	1.18053i	1.00282	−	0.151151i	0.629870	+	0.776701i	$0.283108\pi$
$62$	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	0.906498	−	0.422211i	$-0.138746\pi$
$67$	0.717064	+	1.24199i	0.0876033	+	0.151733i	−0.818894	+	0.573944i	$0.805413\pi$
$68$	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	−0.990059	−	0.140651i	$-0.955080\pi$
$71$	−5.33059	+	6.68435i	−0.632625	+	0.793287i	0.357434	+	0.933938i	$0.383652\pi$
$72$	−13.0064	−	15.6967i	−1.53282	−	1.84988i
$73$	4.76734	−	3.25032i	0.557975	−	0.380421i	−0.251248	−	0.967923i	$-0.580841\pi$
$73$	4.76734	−	3.25032i	0.557975	−	0.380421i	0.809223	+	0.587502i	$0.199888\pi$
$74$	−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	−0.961793	−	0.273776i	$-0.911727\pi$
$79$	−2.16694	+	3.75324i	−0.243799	+	0.422273i	0.717994	+	0.696049i	$0.245060\pi$
$80$	−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	−0.998927	−	0.0463141i	$-0.985252\pi$
$83$	−0.164534	−	2.19555i	−0.0180599	−	0.240993i	0.980867	−	0.194679i	$-0.0623666\pi$
$84$	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	−0.959193	−	0.282753i	$-0.908752\pi$
$89$	−0.498638	−	6.65386i	−0.0528555	−	0.705307i	0.906337	−	0.422555i	$-0.138867\pi$
$90$	−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	0.875674	+	0.482903i	$0.160418\pi$
$97$	8.43105	+	14.6030i	0.856043	+	1.48271i	−0.0196309	+	0.999807i	$0.506249\pi$
$98$	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	0.759843	+	0.650106i	$0.225276\pi$
$101$	−2.07854	+	9.10668i	−0.206822	+	0.906148i	−0.966666	+	0.256042i	$0.917581\pi$
$102$	−8.11618	−	13.7582i	−0.803621	−	1.36227i
$103$	−2.33735	+	10.2406i	−0.230306	+	1.00903i	0.719081	+	0.694926i	$0.244563\pi$
$103$	−2.33735	+	10.2406i	−0.230306	+	1.00903i	−0.949387	+	0.314109i	$0.898294\pi$
$104$	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	0.997937	+	0.0641997i	$0.0204495\pi$
$107$	0.214273	+	2.85928i	0.0207146	+	0.276417i	−0.977222	+	0.212217i	$0.931931\pi$
$108$	−8.16957	+	22.6700i	−0.786118	+	2.18142i
$109$	0.888813	−	11.8604i	0.0851329	−	1.13602i	−0.777056	−	0.629432i	$-0.783288\pi$
$109$	0.888813	−	11.8604i	0.0851329	−	1.13602i	0.862189	−	0.506588i	$-0.169093\pi$
$110$	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	−0.938954	−	0.344042i	$-0.888204\pi$
$113$	−10.2234	+	6.97018i	−0.961734	+	0.655699i	−0.0227793	+	0.999741i	$0.507252\pi$
$114$	−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	0.992130	+	0.125212i	$0.0399610\pi$
$127$	10.0685	+	12.6255i	0.893433	+	1.12033i	−0.0986975	+	0.995117i	$0.531468\pi$
$128$	−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	−0.890059	−	0.455845i	$-0.849337\pi$
$131$	−3.27259	−	14.3381i	−0.285927	−	1.25273i	0.604132	−	0.796884i	$-0.293520\pi$
$132$	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	0.998959	−	0.0456187i	$-0.0145259\pi$
$137$	0.926250	+	4.05816i	0.0791348	+	0.346712i	−0.919824	+	0.392331i	$0.871669\pi$
$138$	−7.79001	−	2.32317i	−0.663129	−	0.197761i
$139$	−12.9678	−	12.0323i	−1.09991	−	1.02057i	−0.999672	−	0.0256065i	$-0.991848\pi$
$139$	−12.9678	−	12.0323i	−1.09991	−	1.02057i	−0.100241	−	0.994963i	$-0.531961\pi$
$140$	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	−0.0443927	−	0.999014i	$-0.514135\pi$
$149$	8.65432	−	4.16770i	0.708990	−	0.341431i	0.753382	+	0.657583i	$0.228421\pi$
$150$	−1.33540	+	20.3811i	−0.109035	+	1.66411i
$151$	−9.00063	+	11.2864i	−0.732461	+	0.918476i	−0.998971	−	0.0453556i	$-0.985558\pi$
$151$	−9.00063	+	11.2864i	−0.732461	+	0.918476i	0.266510	+	0.963832i	$0.414129\pi$
$152$	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	−0.718946	−	0.695066i	$-0.755375\pi$
$157$	−0.996758	+	0.924856i	−0.0795500	+	0.0738116i	0.639396	+	0.768878i	$0.279185\pi$
$158$	−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	−0.159334	−	0.987225i	$-0.550935\pi$
$163$	10.3825	−	9.63358i	0.813223	−	0.754560i	0.972557	+	0.232664i	$0.0747443\pi$
$164$	−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	−0.355836	−	0.934548i	$-0.615804\pi$
$167$	−5.43277	+	0.818858i	−0.420400	+	0.0633652i	−0.0645643	+	0.997914i	$0.520566\pi$
$168$	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	−0.889145	−	0.457626i	$-0.848700\pi$
$173$	−7.21598	−	18.3860i	−0.548620	−	1.39786i	0.340524	−	0.940236i	$-0.389395\pi$
$174$	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	−0.788982	−	0.614417i	$-0.789391\pi$
$179$	−18.2198	+	2.74619i	−1.36181	+	0.205260i	−0.572827	+	0.819676i	$0.694153\pi$
$180$	−4.66942	−	7.74854i	−0.348038	−	0.577542i
$181$	15.5157	+	7.47195i	1.15327	+	0.555385i	0.910014	−	0.414577i	$-0.136070\pi$
$181$	15.5157	+	7.47195i	1.15327	+	0.555385i	0.243255	+	0.969962i	$0.421785\pi$
$182$	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	0.486825	−	0.873500i	$-0.338155\pi$
$191$	−4.80741	−	4.46063i	−0.347852	−	0.322760i	−0.834677	+	0.550740i	$0.814346\pi$
$192$	−5.47312	+	0.0512962i	−0.394989	+	0.00370198i
$193$	2.70268	−	0.833665i	0.194543	−	0.0600085i	−0.195953	−	0.980613i	$-0.562780\pi$
$193$	2.70268	−	0.833665i	0.194543	−	0.0600085i	0.390496	+	0.920605i	$0.372304\pi$
$194$	−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	0.686470	−	0.727158i	$-0.259159\pi$
$199$	0.178378	+	0.165510i	0.0126449	+	0.0117327i	−0.673825	+	0.738891i	$0.735350\pi$
$200$	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	−0.967827	−	0.251617i	$-0.919038\pi$
$211$	−15.7923	+	10.7670i	−1.08719	+	0.741233i	−0.119363	+	0.992851i	$0.538085\pi$
$212$	−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	−0.120627	−	0.992698i	$-0.538490\pi$
$223$	−7.89215	−	1.18955i	−0.528497	−	0.0796581i	−0.407870	+	0.913040i	$0.633729\pi$
$224$	−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	0.954699	−	0.297573i	$-0.0961771\pi$
$229$	−0.523095	−	2.29183i	−0.0345671	−	0.151448i	−0.989266	+	0.146125i	$0.953320\pi$
$230$	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	−0.865225	−	0.501383i	$-0.832825\pi$
$233$	1.67994	−	4.28043i	0.110057	−	0.280420i	0.975282	+	0.220963i	$0.0709200\pi$
$234$	−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	0.830277	−	0.557350i	$-0.188182\pi$
$239$	18.5874	+	5.73345i	1.20232	+	0.370866i	0.372041	+	0.928216i	$0.378658\pi$
$240$	−0.606135	+	9.25097i	−0.0391259	+	0.597148i
$241$	17.9170	−	22.4672i	1.15413	−	1.44724i	0.281035	−	0.959698i	$-0.409322\pi$
$241$	17.9170	−	22.4672i	1.15413	−	1.44724i	0.873100	−	0.487541i	$-0.162106\pi$
$242$	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	0.923640	−	0.383261i	$-0.125199\pi$
$251$	−1.18540	−	5.19358i	−0.0748218	−	0.327816i	−0.998462	+	0.0554457i	$0.982342\pi$
$252$	−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	0.907905	−	0.419176i	$-0.137681\pi$
$257$	4.76465	+	5.97469i	0.297211	+	0.372691i	−0.610694	+	0.791867i	$0.709110\pi$
$258$	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	−0.961945	−	0.273243i	$-0.911904\pi$
$269$	−17.3694	+	11.8422i	−1.05903	+	0.722033i	−0.0970833	+	0.995276i	$0.530951\pi$
$270$	−4.13887	+	7.65818i	−0.251884	+	0.466062i
$271$	2.02737	+	0.305577i	0.123154	+	0.0185625i	0.210330	−	0.977630i	$-0.432546\pi$
$271$	2.02737	+	0.305577i	0.123154	+	0.0185625i	−0.0871760	+	0.996193i	$0.527784\pi$
$272$	−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	0.596194	−	0.802840i	$-0.296679\pi$
$277$	−5.31226	−	6.66137i	−0.319183	−	0.400243i	−0.915377	+	0.402598i	$0.868107\pi$
$278$	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	0.626811	−	0.779171i	$-0.284360\pi$
$281$	2.18759	+	1.49147i	0.130500	+	0.0889737i	−0.496310	+	0.868145i	$0.665312\pi$
$282$	30.2077	−	9.62879i	1.79884	−	0.573386i
$283$	3.75577	+	2.56064i	0.223257	+	0.152214i	0.669784	−	0.742556i	$-0.266387\pi$
$283$	3.75577	+	2.56064i	0.223257	+	0.152214i	−0.446526	+	0.894770i	$0.647339\pi$
$284$	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	−0.886631	−	0.462478i	$-0.846960\pi$
$293$	−0.732578	+	1.26886i	−0.0427977	+	0.0741278i	0.843833	+	0.536606i	$0.180294\pi$
$294$	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	−0.0899697	−	0.995945i	$-0.528677\pi$
$307$	11.0840	−	5.33776i	0.632596	−	0.304642i	0.722566	+	0.691302i	$0.242963\pi$
$308$	−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	−0.735277	−	0.677767i	$-0.762948\pi$
$311$	4.66834	−	11.8947i	0.264717	−	0.674489i	0.999995	+	0.00327743i	$0.00104324\pi$
$312$	45.4605	−	7.28844i	2.57370	−	0.412627i
$313$	14.5230	−	25.1545i	0.820888	−	1.42182i	−0.0841345	−	0.996454i	$-0.526813\pi$
$313$	14.5230	−	25.1545i	0.820888	−	1.42182i	0.905022	−	0.425365i	$-0.139854\pi$
$314$	−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	0.992007	−	0.126185i	$-0.0402732\pi$
$317$	3.18677	+	8.11977i	0.178987	+	0.456052i	−0.813020	+	0.582236i	$0.802178\pi$
$318$	−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	−0.406528	−	0.913638i	$-0.633261\pi$
$331$	−9.56421	+	1.44157i	−0.525696	+	0.0792360i	−0.119168	+	0.992874i	$0.538023\pi$
$332$	−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	0.535539	−	0.844511i	$-0.320109\pi$
$337$	9.22086	+	2.84426i	0.502292	+	0.154937i	−0.0332468	+	0.999447i	$0.510585\pi$
$338$	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	−0.718353	−	0.695678i	$-0.755104\pi$
$347$	−29.9881	−	4.51998i	−1.60985	−	0.242645i	−0.891494	+	0.453033i	$0.850342\pi$
$348$	−2.19838	+	33.5521i	−0.117845	+	1.79858i
$349$	−5.33370	+	4.94895i	−0.285506	+	0.264911i	−0.809904	−	0.586562i	$-0.800481\pi$
$349$	−5.33370	+	4.94895i	−0.285506	+	0.264911i	0.524398	+	0.851473i	$0.324290\pi$
$350$	−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	0.999349	−	0.0360763i	$-0.0114859\pi$
$353$	1.56532	+	6.85813i	0.0833137	+	0.365021i	−0.916035	+	0.401098i	$0.868629\pi$
$354$	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	−0.767397	−	0.641172i	$-0.778448\pi$
$359$	−3.51217	+	3.25882i	−0.185365	+	0.171994i	0.582032	+	0.813166i	$0.302258\pi$
$360$	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	−0.339719	−	0.940527i	$-0.610332\pi$
$367$	−24.6528	−	11.8721i	−1.28686	−	0.619721i	−0.947145	+	0.320806i	$0.896046\pi$
$368$	−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	−0.937804	−	0.347164i	$-0.887145\pi$
$379$	−24.3562	+	11.7293i	−1.25109	+	0.602494i	−0.313288	+	0.949658i	$0.601430\pi$
$380$	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	−0.389659	−	0.920959i	$-0.627407\pi$
$383$	−26.4717	−	12.7481i	−1.35264	−	0.651398i	−0.962983	+	0.269561i	$0.913121\pi$
$384$	−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	−0.999381	−	0.0351827i	$-0.988799\pi$
$389$	−1.65091	+	7.23312i	−0.0837046	+	0.366734i	0.915676	+	0.401917i	$0.131656\pi$
$390$	−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	0.250580	−	0.968096i	$-0.419379\pi$
$397$	19.9840	−	6.16424i	1.00297	−	0.309374i	0.752387	+	0.658721i	$0.228902\pi$
$398$	−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	0.998270	+	0.0587889i	$0.0187239\pi$
$401$	33.3745	+	16.0723i	1.66664	+	0.802614i	0.668374	+	0.743825i	$0.266990\pi$
$402$	−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	−0.996423	−	0.0845099i	$-0.973068\pi$
$409$	−4.21689	+	10.7445i	−0.208512	+	0.531279i	0.787911	+	0.615789i	$0.211163\pi$
$410$	−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	−0.884463	−	0.466610i	$-0.845475\pi$
$419$	−11.3295	−	28.8670i	−0.553481	−	1.41025i	0.330982	−	0.943637i	$-0.392620\pi$
$420$	12.8122	+	5.17824i	0.625174	+	0.252672i
$421$	−8.00611	+	20.3992i	−0.390194	+	0.994198i	0.591934	+	0.805986i	$0.298364\pi$
$421$	−8.00611	+	20.3992i	−0.390194	+	0.994198i	−0.982128	+	0.188212i	$0.939731\pi$
$422$	−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	0.681185	−	0.732112i	$-0.261465\pi$
$431$	17.2643	+	5.32533i	0.831593	+	0.256512i	0.150408	+	0.988624i	$0.451941\pi$
$432$	20.3358	−	37.6275i	0.978408	−	1.81035i
$433$	2.18934	−	9.59211i	0.105213	−	0.460968i	−0.894685	−	0.446697i	$-0.852600\pi$
$433$	2.18934	−	9.59211i	0.105213	−	0.460968i	0.999898	−	0.0142706i	$-0.00454263\pi$
$434$	−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	−0.883886	−	0.467702i	$-0.845082\pi$
$439$	1.25368	−	16.7292i	0.0598350	−	0.798443i	0.943721	−	0.330741i	$-0.107299\pi$
$440$	−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	−0.917607	−	0.397490i	$-0.869881\pi$
$443$	1.03120	−	13.7604i	0.0489938	−	0.653777i	0.966601	−	0.256288i	$-0.0824995\pi$
$444$	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	0.846198	+	0.532869i	$0.178886\pi$
$449$	−3.12342	+	13.6846i	−0.147403	+	0.645815i	−0.993601	+	0.112946i	$0.963971\pi$
$450$	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	0.0184543	−	0.999830i	$-0.494125\pi$
$457$	−11.3199	−	3.49172i	−0.529522	−	0.163336i	−0.547976	+	0.836494i	$0.684602\pi$
$458$	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	0.283551	+	0.958957i	$0.408487\pi$
$461$	−12.3793	+	31.5420i	−0.576563	+	1.46906i	−0.860114	+	0.510101i	$0.829608\pi$
$462$	52.5511	−	20.0152i	2.44490	−	0.931191i
$463$	5.51724	+	14.0577i	0.256408	+	0.653317i	0.999881	−	0.0154496i	$-0.00491796\pi$
$463$	5.51724	+	14.0577i	0.256408	+	0.653317i	−0.743473	+	0.668766i	$0.766823\pi$
$464$	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	−0.0270366	−	0.999634i	$-0.508607\pi$
$467$	−7.50996	−	1.13194i	−0.347519	−	0.0523801i	−0.320483	+	0.947254i	$0.603845\pi$
$468$	−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	0.217684	−	0.976019i	$-0.430150\pi$
$479$	24.4356	−	11.7676i	1.11649	−	0.537674i	0.898806	+	0.438346i	$0.144435\pi$
$480$	−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	0.0362551	−	0.999343i	$-0.488457\pi$
$487$	−21.1320	−	19.6077i	−0.957584	−	0.888508i	−0.993839	+	0.110835i	$0.964648\pi$
$488$	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	0.467221	+	0.884140i	$0.345255\pi$
$491$	−11.7900	+	20.4210i	−0.532077	+	0.921585i	−0.999299	+	0.0374446i	$0.988078\pi$
$492$	−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	−0.341210	−	0.939987i	$-0.610837\pi$
$499$	−28.7910	−	13.8650i	−1.28886	−	0.620684i	−0.947653	+	0.319303i	$0.896551\pi$
$500$	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	0.222484	−	0.974936i	$-0.428584\pi$
$503$	25.1960	−	12.1338i	1.12344	−	0.541018i	0.900952	+	0.433918i	$0.142869\pi$
$504$	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	−0.646786	−	0.762672i	$-0.723887\pi$
$521$	7.69446	−	13.3272i	0.337100	−	0.583875i	0.983886	+	0.178797i	$0.0572205\pi$
$522$	28.8818	−	14.5818i	1.26412	−	0.638229i
$523$	−28.0248	+	26.0032i	−1.22544	+	1.13704i	−0.239329	+	0.970938i	$0.576928\pi$
$523$	−28.0248	+	26.0032i	−1.22544	+	1.13704i	−0.986109	+	0.166102i	$0.946882\pi$
$524$	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	0.437882	−	0.899032i	$-0.355729\pi$
$541$	−5.55963	−	3.79049i	−0.239027	−	0.162966i	−0.676909	+	0.736066i	$0.736681\pi$
$542$	−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	−0.720423	−	0.693535i	$-0.756052\pi$
$547$	−21.6335	+	6.67306i	−0.924983	+	0.285319i	−0.204559	+	0.978854i	$0.565576\pi$
$548$	−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	−0.988890	−	0.148648i	$-0.952508\pi$
$557$	−8.63112	+	14.9495i	−0.365712	+	0.633432i	0.623178	+	0.782080i	$0.285841\pi$
$558$	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	−0.974913	−	0.222588i	$-0.928550\pi$
$563$	−1.04553	−	13.9517i	−0.0440639	−	0.587992i	0.930849	−	0.365405i	$-0.119069\pi$
$564$	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	−0.726708	−	0.686946i	$-0.758951\pi$
$569$	5.52354	−	9.56704i	0.231559	−	0.401071i	0.958267	+	0.285875i	$0.0922841\pi$
$570$	−9.86759	−	12.1384i	−0.413308	−	0.508423i
$571$	13.2443	−	33.7459i	0.554256	−	1.41222i	−0.329447	−	0.944174i	$-0.606862\pi$
$571$	13.2443	−	33.7459i	0.554256	−	1.41222i	0.883703	−	0.468048i	$-0.155042\pi$
$572$	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	−0.638194	−	0.769875i	$-0.720318\pi$
$577$	2.58502	−	34.4947i	0.107616	−	1.43603i	0.745810	−	0.666158i	$-0.232063\pi$
$578$	−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	0.909170	−	0.416425i	$-0.136717\pi$
$587$	2.27623	+	3.94254i	0.0939499	+	0.162726i	−0.815220	+	0.579152i	$0.803384\pi$
$588$	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	−0.0306555	−	0.999530i	$-0.509759\pi$
$593$	12.3480	−	3.80885i	0.507071	−	0.156411i	0.537727	+	0.843119i	$0.319283\pi$
$594$	−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	0.476464	−	0.879194i	$-0.341918\pi$
$599$	−4.10884	−	2.80136i	−0.167883	−	0.114460i	−0.644347	+	0.764733i	$0.722871\pi$
$600$	11.4945	−	52.6297i	0.469262	−	2.14860i
$601$	−30.8818	−	21.0548i	−1.25969	−	0.858845i	−0.265257	−	0.964178i	$-0.585457\pi$
$601$	−30.8818	−	21.0548i	−1.25969	−	0.858845i	−0.994437	+	0.105333i	$0.966409\pi$
$602$	−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	−0.609651	−	0.792670i	$-0.708690\pi$
$613$	−2.33985	+	1.59528i	−0.0945057	+	0.0644329i	0.515145	+	0.857103i	$0.327738\pi$
$614$	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	0.0559708	−	0.998432i	$-0.482175\pi$
$617$	10.0289	−	1.51161i	0.403748	−	0.0608552i	0.347777	+	0.937577i	$0.386937\pi$
$618$	−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	0.918121	+	0.396300i	$0.129706\pi$
$631$	6.60324	+	28.9307i	0.262871	+	1.15171i	−0.655250	+	0.755412i	$0.727437\pi$
$632$	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	−0.930131	−	0.367229i	$-0.880307\pi$
$641$	−9.24449	+	11.5922i	−0.365135	+	0.457865i	0.564995	+	0.825094i	$0.308878\pi$
$642$	−11.4752	+	5.65927i	−0.452891	+	0.223354i
$643$	32.4615	+	10.0130i	1.28015	+	0.394875i	0.858936	−	0.512084i	$-0.171126\pi$
$643$	32.4615	+	10.0130i	1.28015	+	0.394875i	0.421219	+	0.906959i	$0.361602\pi$
$644$	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	0.408447	−	0.912782i	$-0.366071\pi$
$647$	5.89441	+	1.81818i	0.231733	+	0.0714802i	−0.176714	+	0.984262i	$0.556547\pi$
$648$	−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	0.999955	+	0.00943994i	$0.00300487\pi$
$653$	2.63518	+	11.5455i	0.103123	+	0.451809i	−0.896833	+	0.442369i	$0.854138\pi$
$654$	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	0.991931	−	0.126780i	$-0.0404641\pi$
$659$	48.8371	+	7.36101i	1.90242	+	0.286744i	0.910493	+	0.413524i	$0.135702\pi$
$660$	12.6404	+	21.4275i	0.492027	+	0.834064i
$661$	0.766650	+	10.2302i	0.0298192	+	0.397910i	0.992065	+	0.125727i	$0.0401264\pi$
$661$	0.766650	+	10.2302i	0.0298192	+	0.397910i	−0.962246	+	0.272183i	$0.912255\pi$
$662$	−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	0.778034	−	0.628222i	$-0.216217\pi$
$673$	12.3871	+	8.44535i	0.477486	+	0.325545i	−0.300548	+	0.953767i	$0.597170\pi$
$674$	−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	−0.159773	−	0.987154i	$-0.551076\pi$
$677$	18.2335	−	12.4314i	0.700771	−	0.477778i	0.860544	+	0.509376i	$0.170124\pi$
$678$	−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	0.394588	−	0.918858i	$-0.370887\pi$
$683$	−12.8637	−	11.9357i	−0.492214	−	0.456708i	−0.886801	+	0.462151i	$0.847078\pi$
$684$	−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	0.884481	−	0.466576i	$-0.154513\pi$
$691$	12.7572	+	11.8369i	0.485306	+	0.450299i	−0.399174	+	0.916875i	$0.630703\pi$
$692$	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	0.946126	−	0.323798i	$-0.104960\pi$
$701$	33.9658	+	16.3571i	1.28287	+	0.617798i	0.336744	+	0.941596i	$0.390674\pi$
$702$	−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	−0.982969	−	0.183771i	$-0.941169\pi$
$709$	−10.3153	−	26.2829i	−0.387398	−	0.987074i	0.595571	−	0.803303i	$-0.296926\pi$
$710$	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	−0.806272	−	0.591545i	$-0.798518\pi$
$719$	−7.41770	+	6.88262i	−0.276634	+	0.256679i	0.529638	+	0.848224i	$0.322328\pi$
$720$	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	0.526728	−	0.850034i	$-0.323419\pi$
$727$	38.8474	−	11.9828i	1.44077	−	0.444419i	0.914044	+	0.405615i	$0.132943\pi$
$728$	−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	−0.350751	−	0.936469i	$-0.614074\pi$
$733$	4.40547	−	2.12156i	0.162720	−	0.0783617i	0.513471	+	0.858107i	$0.328359\pi$
$734$	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	0.996246	−	0.0865698i	$-0.0275906\pi$
$739$	5.62893	+	14.3423i	0.207063	+	0.527589i	−0.789182	+	0.614159i	$0.789495\pi$
$740$	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	0.910784	−	0.412884i	$-0.135479\pi$
$743$	15.4585	+	14.3434i	0.567117	+	0.526207i	−0.343667	+	0.939092i	$0.611669\pi$
$744$	−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	−0.986035	−	0.166538i	$-0.946741\pi$
$751$	−4.65618	−	20.4000i	−0.169906	−	0.744408i	0.816129	−	0.577870i	$-0.196116\pi$
$752$	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	−0.853740	−	0.520699i	$-0.825671\pi$
$757$	−4.29547	+	5.38635i	−0.156122	+	0.195770i	0.697619	+	0.716469i	$0.254243\pi$
$758$	−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	−0.172597	−	0.984993i	$-0.555216\pi$
$761$	22.7892	−	28.5767i	0.826106	−	1.03590i	0.998703	−	0.0509120i	$-0.0162128\pi$
$762$	−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	−0.966641	−	0.256135i	$-0.917551\pi$
$769$	−29.9872	+	20.4449i	−1.08136	+	0.737262i	−0.114724	+	0.993397i	$0.536598\pi$
$770$	−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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