LMFDB - Embedded newform 441.2.z.a.331.11

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			331.11
Character	$\chi$	$=$	441.331
Dual form			441.2.z.a.4.11

$q$-expansion

$f(q)$	$=$	$q+(-0.132809 - 1.77221i) q^{2} +(1.41906 + 0.993117i) q^{3} +(-1.14543 + 0.172646i) q^{4} +(-0.788881 - 3.45631i) q^{5} +(1.57155 - 2.64676i) q^{6} +(2.57823 + 0.593925i) q^{7} +(-0.332830 - 1.45822i) q^{8} +(1.02744 + 2.81858i) q^{9} +O(q^{10})$	\(q+(-0.132809 - 1.77221i) q^{2} +(1.41906 + 0.993117i) q^{3} +(-1.14543 + 0.172646i) q^{4} +(-0.788881 - 3.45631i) q^{5} +(1.57155 - 2.64676i) q^{6} +(2.57823 + 0.593925i) q^{7} +(-0.332830 - 1.45822i) q^{8} +(1.02744 + 2.81858i) q^{9} +(-6.02055 + 1.85709i) q^{10} +(1.33579 + 0.643285i) q^{11} +(-1.79689 - 0.892556i) q^{12} +(-0.172992 - 2.30842i) q^{13} +(0.710149 - 4.64804i) q^{14} +(2.31306 - 5.68815i) q^{15} +(-4.75390 + 1.46638i) q^{16} +(0.421630 + 0.0635504i) q^{17} +(4.85866 - 2.19517i) q^{18} +(-2.91097 + 5.04194i) q^{19} +(1.50033 + 3.82278i) q^{20} +(3.06881 + 3.40329i) q^{21} +(0.962631 - 2.45274i) q^{22} +(1.15315 + 1.44601i) q^{23} +(0.975883 - 2.39984i) q^{24} +(-6.81893 + 3.28382i) q^{25} +(-4.06804 + 0.613158i) q^{26} +(-1.34119 + 5.02008i) q^{27} +(-3.05573 - 0.235180i) q^{28} +(-3.05029 - 7.77201i) q^{29} +(-10.3878 - 3.34379i) q^{30} +(3.82249 - 6.62074i) q^{31} +(2.13720 + 5.44550i) q^{32} +(1.25671 + 2.23946i) q^{33} +(0.0566287 - 0.755657i) q^{34} +(0.0188767 - 9.37970i) q^{35} +(-1.66348 - 3.05111i) q^{36} +(-1.11492 - 2.84076i) q^{37} +(9.32199 + 4.48923i) q^{38} +(2.04705 - 3.44758i) q^{39} +(-4.77752 + 2.30073i) q^{40} +(-1.79590 + 1.66635i) q^{41} +(5.62379 - 5.89057i) q^{42} +(8.01694 + 7.43863i) q^{43} +(-1.64112 - 0.506220i) q^{44} +(8.93136 - 5.77466i) q^{45} +(2.40948 - 2.23567i) q^{46} +(-0.218989 - 2.92221i) q^{47} +(-8.20233 - 2.64030i) q^{48} +(6.29451 + 3.06255i) q^{49} +(6.72524 + 11.6485i) q^{50} +(0.535203 + 0.508909i) q^{51} +(0.596692 + 2.61428i) q^{52} +(-3.69994 + 9.42729i) q^{53} +(9.07477 + 1.71016i) q^{54} +(1.16961 - 5.12440i) q^{55} +(0.00796409 - 3.95731i) q^{56} +(-9.13806 + 4.26386i) q^{57} +(-13.3685 + 6.43795i) q^{58} +(1.66840 + 1.54805i) q^{59} +(-1.66742 + 6.91474i) q^{60} +(-5.36407 - 0.808503i) q^{61} +(-12.2410 - 5.89496i) q^{62} +(0.974939 + 7.87715i) q^{63} +(0.402244 - 0.193711i) q^{64} +(-7.84216 + 2.41899i) q^{65} +(3.80189 - 2.52457i) q^{66} +(-2.30338 + 3.98958i) q^{67} -0.493921 q^{68} +(0.200332 + 3.19718i) q^{69} +(-16.6253 + 1.21225i) q^{70} +(9.09991 + 11.4109i) q^{71} +(3.76816 - 2.43634i) q^{72} +(4.11216 + 2.80362i) q^{73} +(-4.88636 + 2.35315i) q^{74} +(-12.9377 - 2.11207i) q^{75} +(2.46385 - 6.27778i) q^{76} +(3.06192 + 2.45190i) q^{77} +(-6.38170 - 3.16993i) q^{78} +(2.85886 + 4.95169i) q^{79} +(8.81854 + 15.2742i) q^{80} +(-6.88875 + 5.79181i) q^{81} +(3.19164 + 2.96141i) q^{82} +(-0.721157 + 9.62317i) q^{83} +(-4.10268 - 3.36843i) q^{84} +(-0.112965 - 1.50742i) q^{85} +(12.1181 - 15.1956i) q^{86} +(3.38999 - 14.0582i) q^{87} +(0.493461 - 2.16199i) q^{88} +(-0.179417 + 2.39415i) q^{89} +(-11.4201 - 15.0613i) q^{90} +(0.925016 - 6.05438i) q^{91} +(-1.57051 - 1.45722i) q^{92} +(11.9995 - 5.59902i) q^{93} +(-5.14969 + 0.776191i) q^{94} +(19.7229 + 6.08372i) q^{95} +(-2.37521 + 9.84996i) q^{96} +(-2.09625 + 3.63080i) q^{97} +(4.59151 - 11.5619i) q^{98} +(-0.440704 + 4.42597i) 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 $

$2$	−0.132809	−	1.77221i	−0.0939101	−	1.25314i	−0.822728	−	0.568435i	$-0.807549\pi$
$2$	−0.132809	−	1.77221i	−0.0939101	−	1.25314i	0.728818	−	0.684708i	$-0.240070\pi$
$3$	1.41906	+	0.993117i	0.819292	+	0.573377i
$3$	1.41906	+	0.993117i	0.819292	+	0.573377i
$4$	−1.14543	+	0.172646i	−0.572717	+	0.0863232i
$5$	−0.788881	−	3.45631i	−0.352798	−	1.54571i	−0.770688	−	0.637213i	$-0.780087\pi$
$5$	−0.788881	−	3.45631i	−0.352798	−	1.54571i	0.417889	−	0.908498i	$-0.362770\pi$
$6$	1.57155	−	2.64676i	0.641583	−	1.08054i
$7$	2.57823	+	0.593925i	0.974478	+	0.224483i
$7$	2.57823	+	0.593925i	0.974478	+	0.224483i
$8$	−0.332830	−	1.45822i	−0.117673	−	0.515560i
$9$	1.02744	+	2.81858i	0.342479	+	0.939526i
$10$	−6.02055	+	1.85709i	−1.90386	+	0.587265i
$11$	1.33579	+	0.643285i	0.402757	+	0.193958i	0.624285	−	0.781196i	$-0.285390\pi$
$11$	1.33579	+	0.643285i	0.402757	+	0.193958i	−0.221528	+	0.975154i	$0.571105\pi$
$12$	−1.79689	−	0.892556i	−0.518718	−	0.257659i
$13$	−0.172992	−	2.30842i	−0.0479794	−	0.640241i	−0.968415	−	0.249346i	$-0.919785\pi$
$13$	−0.172992	−	2.30842i	−0.0479794	−	0.640241i	0.920435	−	0.390895i	$-0.127835\pi$
$14$	0.710149	−	4.64804i	0.189795	−	1.24224i
$15$	2.31306	−	5.68815i	0.597229	−	1.46867i
$16$	−4.75390	+	1.46638i	−1.18847	+	0.366596i
$17$	0.421630	+	0.0635504i	0.102260	+	0.0154132i	0.199973	−	0.979801i	$-0.435915\pi$
$17$	0.421630	+	0.0635504i	0.102260	+	0.0154132i	−0.0977128	+	0.995215i	$0.531153\pi$
$18$	4.85866	−	2.19517i	1.14520	−	0.517405i
$19$	−2.91097	+	5.04194i	−0.667821	+	1.15670i	0.310691	+	0.950511i	$0.399440\pi$
$19$	−2.91097	+	5.04194i	−0.667821	+	1.15670i	−0.978512	+	0.206189i	$0.933894\pi$
$20$	1.50033	+	3.82278i	0.335484	+	0.854800i
$21$	3.06881	+	3.40329i	0.669669	+	0.742660i
$22$	0.962631	−	2.45274i	0.205234	−	0.522927i
$23$	1.15315	+	1.44601i	0.240449	+	0.301513i	0.887383	−	0.461032i	$-0.152521\pi$
$23$	1.15315	+	1.44601i	0.240449	+	0.301513i	−0.646935	+	0.762546i	$0.723949\pi$
$24$	0.975883	−	2.39984i	0.199201	−	0.489865i
$25$	−6.81893	+	3.28382i	−1.36379	+	0.656765i
$26$	−4.06804	+	0.613158i	−0.797807	+	0.120250i
$27$	−1.34119	+	5.02008i	−0.258112	+	0.966115i
$28$	−3.05573	−	0.235180i	−0.577478	−	0.0444449i
$29$	−3.05029	−	7.77201i	−0.566424	−	1.44323i	−0.871261	−	0.490821i	$-0.836697\pi$
$29$	−3.05029	−	7.77201i	−0.566424	−	1.44323i	0.304836	−	0.952405i	$-0.401398\pi$
$30$	−10.3878	−	3.34379i	−1.89654	−	0.610490i
$31$	3.82249	−	6.62074i	0.686539	−	1.18912i	−0.286412	−	0.958107i	$-0.592462\pi$
$31$	3.82249	−	6.62074i	0.686539	−	1.18912i	0.972951	−	0.231014i	$-0.0742042\pi$
$32$	2.13720	+	5.44550i	0.377807	+	0.962637i
$33$	1.25671	+	2.23946i	0.218765	+	0.389839i
$34$	0.0566287	−	0.755657i	0.00971174	−	0.129594i
$35$	0.0188767	−	9.37970i	0.00319074	−	1.58546i
$36$	−1.66348	−	3.05111i	−0.277246	−	0.508518i
$37$	−1.11492	−	2.84076i	−0.183291	−	0.467018i	0.809464	−	0.587169i	$-0.199758\pi$
$37$	−1.11492	−	2.84076i	−0.183291	−	0.467018i	−0.992756	+	0.120150i	$0.961662\pi$
$38$	9.32199	+	4.48923i	1.51223	+	0.728250i
$39$	2.04705	−	3.44758i	0.327790	−	0.552054i
$40$	−4.77752	+	2.30073i	−0.755392	+	0.363778i
$41$	−1.79590	+	1.66635i	−0.280473	+	0.260241i	−0.807847	−	0.589392i	$-0.799367\pi$
$41$	−1.79590	+	1.66635i	−0.280473	+	0.260241i	0.527374	+	0.849633i	$0.323177\pi$
$42$	5.62379	−	5.89057i	0.867770	−	0.908934i
$43$	8.01694	+	7.43863i	1.22257	+	1.13438i	0.986692	+	0.162598i	$0.0519875\pi$
$43$	8.01694	+	7.43863i	1.22257	+	1.13438i	0.235879	+	0.971782i	$0.424203\pi$
$44$	−1.64112	−	0.506220i	−0.247409	−	0.0763155i
$45$	8.93136	−	5.77466i	1.33141	−	0.860836i
$46$	2.40948	−	2.23567i	0.355259	−	0.329632i
$47$	−0.218989	−	2.92221i	−0.0319429	−	0.426248i	−0.990134	−	0.140121i	$-0.955251\pi$
$47$	−0.218989	−	2.92221i	−0.0319429	−	0.426248i	0.958192	−	0.286127i	$-0.0923681\pi$
$48$	−8.20233	−	2.64030i	−1.18390	−	0.381094i
$49$	6.29451	+	3.06255i	0.899215	+	0.437507i
$50$	6.72524	+	11.6485i	0.951093	+	1.64734i
$51$	0.535203	+	0.508909i	0.0749434	+	0.0712616i
$52$	0.596692	+	2.61428i	0.0827462	+	0.362535i
$53$	−3.69994	+	9.42729i	−0.508226	+	1.29494i	0.414699	+	0.909959i	$0.363887\pi$
$53$	−3.69994	+	9.42729i	−0.508226	+	1.29494i	−0.922925	+	0.384980i	$0.874208\pi$
$54$	9.07477	+	1.71016i	1.23492	+	0.232723i
$55$	1.16961	−	5.12440i	0.157710	−	0.690974i
$56$	0.00796409	−	3.95731i	0.00106425	−	0.528818i
$57$	−9.13806	+	4.26386i	−1.21037	+	0.564762i
$58$	−13.3685	+	6.43795i	−1.75537	+	0.845344i
$59$	1.66840	+	1.54805i	0.217207	+	0.201538i	0.781270	−	0.624193i	$-0.214572\pi$
$59$	1.66840	+	1.54805i	0.217207	+	0.201538i	−0.564063	+	0.825732i	$0.690763\pi$
$60$	−1.66742	+	6.91474i	−0.215263	+	0.892690i
$61$	−5.36407	−	0.808503i	−0.686798	−	0.103518i	−0.203633	−	0.979047i	$-0.565275\pi$
$61$	−5.36407	−	0.808503i	−0.686798	−	0.103518i	−0.483165	+	0.875529i	$0.660513\pi$
$62$	−12.2410	−	5.89496i	−1.55461	−	0.748661i
$63$	0.974939	+	7.87715i	0.122831	+	0.992428i
$64$	0.402244	−	0.193711i	0.0502805	−	0.0242138i
$65$	−7.84216	+	2.41899i	−0.972700	+	0.300038i
$66$	3.80189	−	2.52457i	0.467980	−	0.310754i
$67$	−2.30338	+	3.98958i	−0.281403	+	0.487405i	−0.971731	−	0.236093i	$-0.924133\pi$
$67$	−2.30338	+	3.98958i	−0.281403	+	0.487405i	0.690327	+	0.723497i	$0.257466\pi$
$68$	−0.493921			−0.0598967
$69$	0.200332	+	3.19718i	0.0241171	+	0.384895i
$70$	−16.6253	+	1.21225i	−1.98711	+	0.144892i
$71$	9.09991	+	11.4109i	1.07996	+	1.35423i	0.930847	+	0.365408i	$0.119071\pi$
$71$	9.09991	+	11.4109i	1.07996	+	1.35423i	0.149114	+	0.988820i	$0.452358\pi$
$72$	3.76816	−	2.43634i	0.444081	−	0.287125i
$73$	4.11216	+	2.80362i	0.481291	+	0.328139i	0.779543	−	0.626348i	$-0.215451\pi$
$73$	4.11216	+	2.80362i	0.481291	+	0.328139i	−0.298252	+	0.954487i	$0.596404\pi$
$74$	−4.88636	+	2.35315i	−0.568028	+	0.273548i
$75$	−12.9377	−	2.11207i	−1.49391	−	0.243881i
$76$	2.46385	−	6.27778i	0.282623	−	0.720111i
$77$	3.06192	+	2.45190i	0.348938	+	0.279419i
$78$	−6.38170	−	3.16993i	−0.722586	−	0.358924i
$79$	2.85886	+	4.95169i	0.321647	+	0.557109i	0.980828	−	0.194875i	$-0.0624302\pi$
$79$	2.85886	+	4.95169i	0.321647	+	0.557109i	−0.659181	+	0.751984i	$0.729097\pi$
$80$	8.81854	+	15.2742i	0.985943	+	1.70770i
$81$	−6.88875	+	5.79181i	−0.765417	+	0.643535i
$82$	3.19164	+	2.96141i	0.352458	+	0.327033i
$83$	−0.721157	+	9.62317i	−0.0791573	+	1.05628i	0.806284	+	0.591529i	$0.201475\pi$
$83$	−0.721157	+	9.62317i	−0.0791573	+	1.05628i	−0.885441	+	0.464752i	$0.846144\pi$
$84$	−4.10268	−	3.36843i	−0.447640	−	0.367526i
$85$	−0.112965	−	1.50742i	−0.0122528	−	0.163502i
$86$	12.1181	−	15.1956i	1.30673	−	1.63859i
$87$	3.38999	−	14.0582i	0.363445	−	1.50720i
$88$	0.493461	−	2.16199i	0.0526031	−	0.230469i
$89$	−0.179417	+	2.39415i	−0.0190182	+	0.253780i	0.979589	+	0.201013i	$0.0644232\pi$
$89$	−0.179417	+	2.39415i	−0.0190182	+	0.253780i	−0.998607	+	0.0527673i	$0.983196\pi$
$90$	−11.4201	−	15.0613i	−1.20378	−	1.58760i
$91$	0.925016	−	6.05438i	0.0969680	−	0.634671i
$92$	−1.57051	−	1.45722i	−0.163737	−	0.151925i
$93$	11.9995	−	5.59902i	1.24429	−	0.580591i
$94$	−5.14969	+	0.776191i	−0.531150	+	0.0800580i
$95$	19.7229	+	6.08372i	2.02353	+	0.624177i
$96$	−2.37521	+	9.84996i	−0.242419	+	1.00531i
$97$	−2.09625	+	3.63080i	−0.212841	+	0.368652i	−0.952603	−	0.304217i	$-0.901605\pi$
$97$	−2.09625	+	3.63080i	−0.212841	+	0.368652i	0.739761	+	0.672869i	$0.234938\pi$
$98$	4.59151	−	11.5619i	0.463813	−	1.16793i
$99$	−0.440704	+	4.42597i	−0.0442925	+	0.444827i
$100$	7.24369	−	4.93867i	0.724369	−	0.493867i
$101$	−2.88409	−	12.6360i	−0.286978	−	1.25733i	−0.888649	−	0.458588i	$-0.848355\pi$
$101$	−2.88409	−	12.6360i	−0.286978	−	1.25733i	0.601671	−	0.798744i	$-0.294502\pi$
$102$	0.830815	−	1.01608i	0.0822630	−	0.100607i
$103$	−2.92118	−	12.7985i	−0.287832	−	1.26108i	−0.887493	−	0.460821i	$-0.847555\pi$
$103$	−2.92118	−	12.7985i	−0.287832	−	1.26108i	0.599661	−	0.800254i	$-0.295302\pi$
$104$	−3.30862	+	1.02057i	−0.324437	+	0.100075i
$105$	9.34193	−	13.2916i	0.911679	−	1.29712i
$106$	17.1985	+	5.30505i	1.67047	+	0.515272i
$107$	−0.0776789	+	1.03655i	−0.00750951	+	0.100207i	−0.999699	−	0.0245320i	$-0.992190\pi$
$107$	−0.0776789	+	1.03655i	−0.00750951	+	0.100207i	0.992190	+	0.124739i	$0.0398095\pi$
$108$	0.669545	−	5.98172i	0.0644270	−	0.575591i
$109$	1.35858	+	18.1290i	0.130128	+	1.73644i	0.555583	+	0.831461i	$0.312495\pi$
$109$	1.35858	+	18.1290i	0.130128	+	1.73644i	−0.425455	+	0.904980i	$0.639886\pi$
$110$	−9.23685	−	1.39223i	−0.880700	−	0.132744i
$111$	1.23908	−	5.13844i	0.117608	−	0.487719i
$112$	−13.1275	+	0.957210i	−1.24044	+	0.0904478i
$113$	11.0537	+	7.53629i	1.03985	+	0.708955i	0.957730	−	0.287668i	$-0.0928800\pi$
$113$	11.0537	+	7.53629i	1.03985	+	0.708955i	0.0821153	+	0.996623i	$0.473832\pi$
$114$	8.77008	+	15.6283i	0.821393	+	1.46372i
$115$	4.08815	−	5.12638i	0.381222	−	0.478038i
$116$	4.83571	+	8.37570i	0.448985	+	0.777664i
$117$	6.32872	−	2.85935i	0.585091	−	0.264347i
$118$	2.52189	−	3.16235i	0.232159	−	0.291118i
$119$	1.04931	+	0.414264i	0.0961903	+	0.0379755i
$120$	−9.06446	−	1.47977i	−0.827468	−	0.135084i
$121$	−5.48786	−	6.88155i	−0.498896	−	0.625596i
$122$	−0.720442	+	9.61364i	−0.0652258	+	0.870378i
$123$	−4.20337	+	0.581107i	−0.379005	+	0.0523966i
$124$	−3.23536	+	8.24356i	−0.290544	+	0.740294i
$125$	5.67727	+	7.11907i	0.507791	+	0.636749i
$126$	13.8305	−	2.77395i	1.23212	−	0.247123i
$127$	2.60677	−	3.26878i	0.231313	−	0.290058i	−0.652606	−	0.757698i	$-0.726324\pi$
$127$	2.60677	−	3.26878i	0.231313	−	0.290058i	0.883919	+	0.467640i	$0.154896\pi$
$128$	5.45316	+	9.44515i	0.481996	+	0.834841i
$129$	3.98904	+	18.5176i	0.351216	+	1.63038i
$130$	5.32846	+	13.5767i	0.467337	+	1.19076i
$131$	1.47342	−	6.45546i	0.128733	−	0.564017i	−0.868884	−	0.495017i	$-0.835162\pi$
$131$	1.47342	−	6.45546i	0.128733	−	0.564017i	0.997617	−	0.0690000i	$-0.0219809\pi$
$132$	−1.82611	−	2.34818i	−0.158943	−	0.204383i
$133$	−10.4997	+	11.2704i	−0.910436	+	0.977265i
$134$	7.37629	+	3.55223i	0.637214	+	0.306866i
$135$	18.4090	+	0.675326i	1.58440	+	0.0581228i
$136$	−0.0476603	−	0.635982i	−0.00408683	−	0.0545350i
$137$	2.78718	−	12.2114i	0.238125	−	1.04329i	−0.704569	−	0.709635i	$-0.748860\pi$
$137$	2.78718	−	12.2114i	0.238125	−	1.04329i	0.942694	−	0.333658i	$-0.108283\pi$
$138$	5.63947	−	0.779644i	0.480064	−	0.0663677i
$139$	10.8927	−	10.1070i	0.923909	−	0.857262i	−0.0661650	−	0.997809i	$-0.521076\pi$
$139$	10.8927	−	10.1070i	0.923909	−	0.857262i	0.990074	+	0.140546i	$0.0448859\pi$
$140$	1.59775	+	10.7471i	0.135034	+	0.908294i
$141$	2.59134	−	4.36426i	0.218230	−	0.367537i
$142$	19.0140	−	17.6424i	1.59562	−	1.48052i
$143$	1.25389	−	3.19486i	0.104856	−	0.267167i
$144$	−9.01744	−	11.8926i	−0.751453	−	0.991051i
$145$	−24.4562	+	16.6739i	−2.03098	+	1.38470i
$146$	4.42248	−	7.65995i	0.366007	−	0.633942i
$147$	5.89078	+	10.5971i	0.485864	+	0.874035i
$148$	1.76751	+	3.06142i	0.145288	+	0.251647i
$149$	−13.0229	−	6.27149i	−1.06688	−	0.513781i	−0.183778	−	0.982968i	$-0.558833\pi$
$149$	−13.0229	−	6.27149i	−1.06688	−	0.513781i	−0.883099	+	0.469187i	$0.844547\pi$
$150$	−2.02480	+	23.2088i	−0.165324	+	1.89499i
$151$	2.55870	+	3.20850i	0.208224	+	0.261104i	0.874966	−	0.484184i	$-0.160883\pi$
$151$	2.55870	+	3.20850i	0.208224	+	0.261104i	−0.666743	+	0.745288i	$0.732312\pi$
$152$	8.32114	+	2.56673i	0.674933	+	0.208189i
$153$	0.254076	+	1.25369i	0.0205408	+	0.101355i
$154$	3.93863	−	5.75200i	0.317384	−	0.463509i
$155$	−25.8989	−	7.98874i	−2.08025	−	0.641671i
$156$	−1.74955	+	4.30239i	−0.140076	+	0.344467i
$157$	−17.6455	−	16.3726i	−1.40826	−	1.30668i	−0.893296	−	0.449469i	$-0.851613\pi$
$157$	−17.6455	−	16.3726i	−1.40826	−	1.30668i	−0.514969	−	0.857209i	$-0.672196\pi$
$158$	8.39576	−	5.72413i	0.667931	−	0.455388i
$159$	−14.6128	+	9.70338i	−1.15887	+	0.769528i
$160$	17.1354	−	11.6827i	1.35467	−	0.923598i
$161$	2.11427	+	4.41302i	0.166628	+	0.347795i
$162$	11.1792	+	11.4391i	0.878321	+	0.898742i
$163$	15.7554	+	14.6189i	1.23406	+	1.14504i	0.984258	+	0.176740i	$0.0565551\pi$
$163$	15.7554	+	14.6189i	1.23406	+	1.14504i	0.249799	+	0.968298i	$0.419635\pi$
$164$	1.76940	−	2.21875i	0.138167	−	0.173256i
$165$	6.74887	−	6.11025i	0.525399	−	0.475682i
$166$	17.1501			1.33110
$167$	−7.79189	−	1.17444i	−0.602954	−	0.0908808i	−0.159531	−	0.987193i	$-0.550998\pi$
$167$	−7.79189	−	1.17444i	−0.602954	−	0.0908808i	−0.443424	+	0.896312i	$0.646236\pi$
$168$	3.94137	−	5.60773i	0.304084	−	0.432646i
$169$	7.55592	−	1.13887i	0.581225	−	0.0876055i
$170$	−2.65646	+	0.400397i	−0.203741	+	0.0307091i
$171$	−17.2019	−	3.02451i	−1.31546	−	0.231290i
$172$	−10.4671	−	7.13637i	−0.798111	−	0.544143i
$173$	−2.59527	+	6.61263i	−0.197314	+	0.502749i	−0.994948	−	0.100394i	$-0.967990\pi$
$173$	−2.59527	+	6.61263i	−0.197314	+	0.502749i	0.797633	+	0.603143i	$0.206085\pi$
$174$	−25.3643	−	4.14072i	−1.92286	−	0.313907i
$175$	−19.5311	+	4.41651i	−1.47641	+	0.333857i
$176$	−7.29353	−	1.09932i	−0.549770	−	0.0828646i
$177$	0.830156	+	3.85368i	0.0623983	+	0.289660i
$178$	4.26678			0.319808
$179$	−18.8145	−	2.83584i	−1.40626	−	0.211960i	−0.598338	−	0.801244i	$-0.704172\pi$
$179$	−18.8145	−	2.83584i	−1.40626	−	0.211960i	−0.807926	+	0.589283i	$0.799410\pi$
$180$	−9.23331	+	8.15646i	−0.688210	+	0.607947i
$181$	7.07131	−	3.40536i	0.525606	−	0.253119i	−0.152212	−	0.988348i	$-0.548640\pi$
$181$	7.07131	−	3.40536i	0.525606	−	0.253119i	0.677819	+	0.735229i	$0.262926\pi$
$182$	−10.8525	−	0.835248i	−0.804440	−	0.0619127i
$183$	−6.80897	−	6.47446i	−0.503333	−	0.478606i
$184$	1.72480	−	2.16283i	0.127154	−	0.159446i
$185$	−8.93903	+	6.09453i	−0.657210	+	0.448078i
$186$	−11.5163	−	20.5220i	−0.844415	−	1.50475i
$187$	0.522329	+	0.356118i	0.0381965	+	0.0260419i
$188$	0.755347	+	3.30939i	0.0550893	+	0.241362i
$189$	−6.43944	+	12.1463i	−0.468400	+	0.883516i
$190$	8.16226	−	35.7612i	0.592152	−	2.59439i
$191$	−12.2124	+	11.3314i	−0.883655	+	0.819912i	−0.984571	−	0.174983i	$-0.944013\pi$
$191$	−12.2124	+	11.3314i	−0.883655	+	0.819912i	0.100916	+	0.994895i	$0.467823\pi$
$192$	0.763184	+	0.124590i	0.0550780	+	0.00899148i
$193$	22.6020	+	6.97178i	1.62692	+	0.501840i	0.968123	−	0.250476i	$-0.0805872\pi$
$193$	22.6020	+	6.97178i	1.62692	+	0.501840i	0.658802	+	0.752316i	$0.271063\pi$
$194$	6.71295	+	3.23279i	0.481962	+	0.232101i
$195$	−13.5308	−	4.35551i	−0.968960	−	0.311904i
$196$	−7.73868	−	2.42122i	−0.552763	−	0.172944i
$197$	−16.5925			−1.18216			−0.591082	−	0.806611i	$-0.701299\pi$
$197$	−16.5925			−1.18216			−0.591082	+	0.806611i	$0.701299\pi$
$198$	7.90229	+	0.193213i	0.561591	+	0.0137310i
$199$	13.4107	−	12.4434i	0.950663	−	0.882086i	−0.0424677	−	0.999098i	$-0.513522\pi$
$199$	13.4107	−	12.4434i	0.950663	−	0.882086i	0.993131	+	0.117012i	$0.0373315\pi$
$200$	7.05810	+	8.85057i	0.499083	+	0.625830i
$201$	−7.23075	+	3.37390i	−0.510018	+	0.237977i
$202$	−22.0107	+	6.78940i	−1.54867	+	0.477701i
$203$	−3.24835	−	21.8496i	−0.227989	−	1.53354i
$204$	−0.700901	−	0.490521i	−0.0490729	−	0.0343434i
$205$	7.17620	+	4.89265i	0.501207	+	0.341717i
$206$	−22.2937	+	6.87670i	−1.55328	+	0.479122i
$207$	−2.89089	+	4.73593i	−0.200931	+	0.329170i
$208$	4.20742	+	10.7203i	0.291732	+	0.743321i
$209$	−7.13185	+	4.86242i	−0.493321	+	0.336340i
$210$	−24.7962	−	14.7906i	−1.71110	−	1.02065i
$211$	−12.0497	−	8.21534i	−0.829534	−	0.565567i	0.0724319	−	0.997373i	$-0.476924\pi$
$211$	−12.0497	−	8.21534i	−0.829534	−	0.565567i	−0.901966	+	0.431806i	$0.857876\pi$
$212$	2.61045	−	11.4371i	0.179286	−	0.785505i
$213$	1.58089	+	25.2300i	0.108321	+	1.72873i
$214$	1.84731			0.126279
$215$	19.3858	−	33.5773i	1.32210	−	2.28995i
$216$	7.76679	+	0.284921i	0.528463	+	0.0193864i
$217$	13.7875	−	14.7995i	0.935954	−	1.00466i
$218$	31.9479	−	4.81538i	2.16379	−	0.326138i
$219$	3.05105	+	8.06234i	0.206171	+	0.544803i
$220$	−0.455003	+	6.07159i	−0.0306763	+	0.409347i
$221$	0.0737625	−	0.984292i	0.00496180	−	0.0662107i
$222$	−9.27097	−	1.51348i	−0.622226	−	0.101578i
$223$	−20.5218	+	3.09316i	−1.37424	+	0.207133i	−0.794299	−	0.607527i	$-0.792162\pi$
$223$	−20.5218	+	3.09316i	−1.37424	+	0.207133i	−0.579939	+	0.814660i	$0.696924\pi$
$224$	2.27597	+	15.3091i	0.152070	+	1.02288i
$225$	−16.2617	−	15.8458i	−1.08411	−	1.05638i
$226$	11.8879	−	20.5904i	0.790769	−	1.36965i
$227$	−14.1137			−0.936760			−0.468380	−	0.883527i	$-0.655162\pi$
$227$	−14.1137			−0.936760			−0.468380	+	0.883527i	$0.655162\pi$
$228$	9.73090	−	6.46163i	0.644445	−	0.427932i
$229$	−1.70060	+	7.45081i	−0.112379	+	0.492363i	0.887145	+	0.461491i	$0.152686\pi$
$229$	−1.70060	+	7.45081i	−0.112379	+	0.492363i	−0.999523	+	0.0308718i	$0.990172\pi$
$230$	−9.62798	−	6.56424i	−0.634850	−	0.432833i
$231$	1.91001	+	6.52022i	0.125669	+	0.428999i
$232$	−10.3181	+	7.03476i	−0.677417	+	0.461855i
$233$	−9.26266	−	23.6009i	−0.606817	−	1.54614i	−0.821950	−	0.569559i	$-0.807114\pi$
$233$	−9.26266	−	23.6009i	−0.606817	−	1.54614i	0.215134	−	0.976585i	$-0.430981\pi$
$234$	−5.90788	−	10.8361i	−0.386210	−	0.708377i
$235$	−9.92732	+	3.06217i	−0.647587	+	0.199754i
$236$	−2.17830	−	1.48514i	−0.141795	−	0.0966745i
$237$	−0.860730	+	9.86591i	−0.0559104	+	0.640860i
$238$	0.594805	−	1.91462i	0.0385555	−	0.124106i
$239$	−5.61321	+	1.73145i	−0.363088	+	0.111998i	−0.470931	−	0.882170i	$-0.656082\pi$
$239$	−5.61321	+	1.73145i	−0.363088	+	0.111998i	0.107843	+	0.994168i	$0.465606\pi$
$240$	−2.65504	+	30.4327i	−0.171382	+	1.96442i
$241$	−0.284282	−	0.356479i	−0.0183122	−	0.0229628i	0.772591	−	0.634904i	$-0.218960\pi$
$241$	−0.284282	−	0.356479i	−0.0183122	−	0.0229628i	−0.790903	+	0.611941i	$0.790389\pi$
$242$	−11.4667	+	10.6396i	−0.737110	+	0.683938i
$243$	−15.5275	+	1.37756i	−0.996088	+	0.0883708i
$244$	6.28377			0.402277
$245$	5.61950	−	24.1718i	0.359017	−	1.54428i
$246$	1.58809	+	7.37209i	0.101253	+	0.470027i
$247$	12.1425	+	5.84752i	0.772609	+	0.372069i
$248$	−10.9268	−	3.37046i	−0.693850	−	0.214024i
$249$	−10.5803	+	12.9396i	−0.670499	+	0.820015i
$250$	11.8625	−	11.0068i	0.750251	−	0.696131i
$251$	−1.56318	+	6.84872i	−0.0986667	+	0.432287i	−1.00000		0.000839737i	$-0.999733\pi$
$251$	−1.56318	+	6.84872i	−0.0986667	+	0.432287i	0.901333	+	0.433127i	$0.142590\pi$
$252$	−2.47669	−	8.85444i	−0.156017	−	0.557777i
$253$	0.610180	+	2.67337i	0.0383617	+	0.168073i
$254$	−6.13918	−	4.18562i	−0.385206	−	0.262629i
$255$	1.33674	−	2.25130i	0.0837099	−	0.140982i
$256$	16.7523	−	11.4216i	1.04702	−	0.713847i
$257$	10.0104	−	12.5526i	0.624432	−	0.783012i	−0.364529	−	0.931192i	$-0.618770\pi$
$257$	10.0104	−	12.5526i	0.624432	−	0.783012i	0.988960	+	0.148180i	$0.0473414\pi$
$258$	32.2873	−	9.52873i	2.01012	−	0.593233i
$259$	−1.18731	−	7.98630i	−0.0737758	−	0.496245i
$260$	8.56504	−	4.12471i	0.531181	−	0.255804i
$261$	18.7720	−	16.5827i	1.16196	−	1.02644i
$262$	−11.6361	−	1.75386i	−0.718883	−	0.108354i
$263$	−10.5300			−0.649308			−0.324654	−	0.945833i	$-0.605248\pi$
$263$	−10.5300			−0.649308			−0.324654	+	0.945833i	$0.605248\pi$
$264$	2.84736	−	2.57792i	0.175243	−	0.158660i
$265$	35.5025	+	5.35114i	2.18090	+	0.328718i
$266$	21.3679	+	17.1108i	1.31015	+	1.04913i
$267$	−2.63228	+	3.21925i	−0.161093	+	0.197015i
$268$	1.94959	−	4.96747i	0.119090	−	0.303437i
$269$	22.2986	+	15.2029i	1.35957	+	0.926940i	0.999981	−	0.00617064i	$-0.00196419\pi$
$269$	22.2986	+	15.2029i	1.35957	+	0.926940i	0.359590	+	0.933110i	$0.382917\pi$
$270$	−1.24806	−	32.7144i	−0.0759546	−	1.99093i
$271$	6.13721	−	0.925036i	0.372809	−	0.0561919i	0.0400344	−	0.999198i	$-0.487253\pi$
$271$	6.13721	−	0.925036i	0.372809	−	0.0561919i	0.332775	+	0.943006i	$0.392015\pi$
$272$	−2.09757	+	0.316158i	−0.127184	+	0.0191699i
$273$	7.32536	−	7.67285i	0.443351	−	0.464382i
$274$	−22.0114	−	3.31768i	−1.32976	−	0.200429i
$275$	−11.2211			−0.676659
$276$	−0.781448	−	3.62757i	−0.0470377	−	0.218354i
$277$	−9.59136	+	12.0272i	−0.576289	+	0.722643i	−0.981475	−	0.191591i	$-0.938635\pi$
$277$	−9.59136	+	12.0272i	−0.576289	+	0.722643i	0.405186	+	0.914234i	$0.367207\pi$
$278$	−19.3583	−	17.9619i	−1.16104	−	1.07728i
$279$	22.5884	+	3.97159i	1.35233	+	0.237773i
$280$	−13.6840	+	3.09432i	−0.817775	+	0.184921i
$281$	15.5467	−	10.5996i	0.927438	−	0.632316i	−0.00251437	−	0.999997i	$-0.500800\pi$
$281$	15.5467	−	10.5996i	0.927438	−	0.632316i	0.929952	+	0.367680i	$0.119848\pi$
$282$	−8.07854	−	4.01279i	−0.481070	−	0.238958i
$283$	−14.4802	+	9.87242i	−0.860757	+	0.586855i	−0.911242	−	0.411870i	$-0.864876\pi$
$283$	−14.4802	+	9.87242i	−0.860757	+	0.586855i	0.0504850	+	0.998725i	$0.483923\pi$
$284$	−12.3934	−	11.4994i	−0.735413	−	0.682364i
$285$	21.9461	+	28.2203i	1.29997	+	1.67163i
$286$	−5.82849	−	1.79785i	−0.344646	−	0.106309i
$287$	−5.61993	+	3.22961i	−0.331734	+	0.190638i
$288$	−13.1527	+	11.6188i	−0.775032	+	0.684642i
$289$	−16.0710	−	4.95725i	−0.945353	−	0.291603i
$290$	32.7978	+	41.1271i	1.92595	+	2.41507i
$291$	−6.58050	+	3.07049i	−0.385756	+	0.179995i
$292$	−5.19424	−	2.50141i	−0.303970	−	0.146384i
$293$	0.461345	+	0.799073i	0.0269520	+	0.0466823i	0.879187	−	0.476477i	$-0.158087\pi$
$293$	0.461345	+	0.799073i	0.0269520	+	0.0466823i	−0.852235	+	0.523160i	$0.824753\pi$
$294$	17.9980	−	11.8471i	1.04966	−	0.690937i
$295$	4.03437	−	6.98773i	0.234890	−	0.406841i
$296$	−3.77139	+	2.57129i	−0.219208	+	0.149453i
$297$	−5.02089	+	5.84303i	−0.291342	+	0.339047i
$298$	−9.38486	+	23.9122i	−0.543650	+	1.38520i
$299$	3.13851	−	2.91211i	0.181504	−	0.168412i
$300$	15.1839	+	0.185597i	0.876642	+	0.0107155i
$301$	16.2515	+	23.9399i	0.936721	+	1.37988i
$302$	5.34633	−	4.96067i	0.307647	−	0.285454i
$303$	8.45638	−	20.7955i	0.485806	−	1.19467i
$304$	6.44502	−	28.2375i	0.369647	−	1.61953i
$305$	1.43717	+	19.1777i	0.0822922	+	1.09811i
$306$	2.18806	−	0.616777i	0.125083	−	0.0352588i
$307$	−22.9428	−	11.0487i	−1.30941	−	0.630580i	−0.356634	−	0.934244i	$-0.616076\pi$
$307$	−22.9428	−	11.0487i	−1.30941	−	0.630580i	−0.952779	+	0.303664i	$0.901790\pi$
$308$	−3.93054	−	2.27985i	−0.223963	−	0.129907i
$309$	8.56512	−	21.0629i	0.487252	−	1.19822i
$310$	−10.7181	+	46.9592i	−0.608749	+	2.66710i
$311$	1.89190	+	4.82049i	0.107280	+	0.273345i	0.974426	−	0.224709i	$-0.0721432\pi$
$311$	1.89190	+	4.82049i	0.107280	+	0.273345i	−0.867146	+	0.498054i	$0.834048\pi$
$312$	−5.70866	−	1.83760i	−0.323189	−	0.104033i
$313$	−9.08252	−	15.7314i	−0.513375	−	0.889191i	−0.999880	−	0.0155132i	$-0.995062\pi$
$313$	−9.08252	−	15.7314i	−0.513375	−	0.889191i	0.486505	−	0.873678i	$-0.338272\pi$
$314$	−26.6723	+	33.4460i	−1.50520	+	1.88747i
$315$	26.4568	−	9.58383i	1.49067	−	0.539988i
$316$	−4.12953	−	5.17826i	−0.232304	−	0.291300i
$317$	3.07133	−	7.82562i	0.172503	−	0.439531i	−0.818309	−	0.574779i	$-0.805088\pi$
$317$	3.07133	−	7.82562i	0.172503	−	0.439531i	0.990812	+	0.135248i	$0.0431833\pi$
$318$	19.1371	+	24.6083i	1.07316	+	1.37997i
$319$	0.925055	−	12.3440i	0.0517932	−	0.691132i
$320$	−0.986847	−	1.23747i	−0.0551664	−	0.0691765i
$321$	−1.13965	+	1.39378i	−0.0636091	+	0.0777933i
$322$	7.54001	−	4.33302i	0.420188	−	0.241470i
$323$	−1.54777	+	1.94084i	−0.0861201	+	0.107991i
$324$	6.89067	−	7.82346i	0.382815	−	0.434637i
$325$	8.76007	+	15.1729i	0.485921	+	0.841640i
$326$	23.8153	−	29.8634i	1.31900	−	1.65398i
$327$	−16.0763	+	27.0752i	−0.889021	+	1.49726i
$328$	3.02765	+	2.06422i	0.167174	+	0.113977i
$329$	1.17097	−	7.66418i	0.0645576	−	0.422540i
$330$	−11.7250	−	11.1489i	−0.645438	−	0.613729i
$331$	9.61079	+	1.44859i	0.528257	+	0.0796219i	0.407755	−	0.913091i	$-0.366312\pi$
$331$	9.61079	+	1.44859i	0.528257	+	0.0796219i	0.120502	+	0.992713i	$0.461550\pi$
$332$	−0.835368	−	11.1472i	−0.0458468	−	0.611783i
$333$	6.86140	−	6.06118i	0.376002	−	0.332151i
$334$	−1.04652	+	13.9649i	−0.0572631	+	0.764123i
$335$	15.6063	+	4.81392i	0.852665	+	0.263012i
$336$	−19.5793	−	11.6789i	−1.06814	−	0.637134i
$337$	13.6223	−	4.20192i	0.742053	−	0.228893i	0.0993968	−	0.995048i	$-0.468309\pi$
$337$	13.6223	−	4.20192i	0.742053	−	0.228893i	0.642656	+	0.766155i	$0.277832\pi$
$338$	−3.02181	−	13.2394i	−0.164365	−	0.720130i
$339$	8.20140	+	21.6720i	0.445439	+	1.17706i
$340$	0.389645	+	1.70714i	0.0211314	+	0.0925829i
$341$	9.36508	−	6.38500i	0.507147	−	0.345767i
$342$	−3.07550	+	30.8871i	−0.166304	+	1.67019i
$343$	14.4097	+	11.6344i	0.778053	+	0.628199i
$344$	8.17891	−	14.1663i	0.440978	−	0.763795i
$345$	10.8924	−	3.21460i	0.586428	−	0.173068i
$346$	12.0637	+	3.72114i	0.648546	+	0.200050i
$347$	−29.2245	+	4.40488i	−1.56885	+	0.236466i	−0.875170	−	0.483816i	$-0.839250\pi$
$347$	−29.2245	+	4.40488i	−1.56885	+	0.236466i	−0.693681	+	0.720282i	$0.744012\pi$
$348$	−1.45591	+	16.6880i	−0.0780449	+	0.894571i
$349$	−13.3824	−	12.4170i	−0.716343	−	0.664669i	0.235283	−	0.971927i	$-0.424398\pi$
$349$	−13.3824	−	12.4170i	−0.716343	−	0.664669i	−0.951626	+	0.307258i	$0.900589\pi$
$350$	10.4209	+	34.0267i	0.557020	+	1.81880i
$351$	11.8205	+	2.22760i	0.630930	+	0.118900i
$352$	−0.648145	+	8.64889i	−0.0345462	+	0.460988i
$353$	2.22704	−	9.75731i	0.118533	−	0.519329i	−0.880445	−	0.474148i	$-0.842756\pi$
$353$	2.22704	−	9.75731i	0.118533	−	0.519329i	0.998979	−	0.0451813i	$-0.0143866\pi$
$354$	6.71928	−	1.98301i	0.357126	−	0.105396i
$355$	32.2610	−	40.4540i	1.71224	−	2.14708i
$356$	−0.207832	−	2.77332i	−0.0110151	−	0.146986i
$357$	1.07762	+	1.62995i	0.0570337	+	0.0862663i
$358$	−2.52696	+	33.7200i	−0.133554	+	1.78216i
$359$	−9.76156	−	9.05740i	−0.515195	−	0.478031i	0.379196	−	0.925316i	$-0.376201\pi$
$359$	−9.76156	−	9.05740i	−0.515195	−	0.478031i	−0.894392	+	0.447285i	$0.852391\pi$
$360$	−11.3934	−	11.1019i	−0.600484	−	0.585124i
$361$	−7.44745	−	12.8994i	−0.391971	−	0.678913i
$362$	−6.97415	−	12.0796i	−0.366553	−	0.634889i
$363$	−0.953380	−	15.2154i	−0.0500395	−	0.798601i
$364$	−0.0142779	+	7.09459i	−0.000748364	+	0.371858i
$365$	6.44619	−	16.4246i	0.337409	−	0.859704i
$366$	−10.5698	+	12.9268i	−0.552493	+	0.675694i
$367$	−16.5291	+	7.96000i	−0.862812	+	0.415508i	−0.812317	−	0.583216i	$-0.801794\pi$
$367$	−16.5291	+	7.96000i	−0.862812	+	0.415508i	−0.0504949	+	0.998724i	$0.516080\pi$
$368$	−7.60236	−	5.18320i	−0.396301	−	0.270193i
$369$	−6.54192	−	3.34982i	−0.340559	−	0.174385i
$370$	11.9880	+	15.0324i	0.623225	+	0.781499i
$371$	−15.1384	+	22.1082i	−0.785946	+	1.14780i
$372$	−12.7780	+	8.48498i	−0.662507	+	0.439926i
$373$	−3.05031			−0.157939			−0.0789696	−	0.996877i	$-0.525163\pi$
$373$	−3.05031			−0.157939			−0.0789696	+	0.996877i	$0.525163\pi$
$374$	0.561747	−	0.972974i	0.0290472	−	0.0503113i
$375$	0.986287	+	15.7406i	0.0509316	+	0.812839i
$376$	−4.18835	+	1.29194i	−0.215998	+	0.0666265i
$377$	−17.4134	+	8.38585i	−0.896835	+	0.431893i
$378$	22.3811	+	9.79891i	1.15116	+	0.504002i
$379$	−4.35625	−	2.09786i	−0.223765	−	0.107760i	0.318643	−	0.947875i	$-0.396773\pi$
$379$	−4.35625	−	2.09786i	−0.223765	−	0.107760i	−0.542408	+	0.840115i	$0.682487\pi$
$380$	−23.6417	−	3.56341i	−1.21279	−	0.182799i
$381$	6.94543	−	2.04976i	0.355825	−	0.105012i
$382$	21.7036	+	20.1380i	1.11045	+	1.03035i
$383$	10.1587	−	4.89217i	0.519085	−	0.249978i	−0.155948	−	0.987765i	$-0.549843\pi$
$383$	10.1587	−	4.89217i	0.519085	−	0.249978i	0.675034	+	0.737787i	$0.264129\pi$
$384$	−1.64181	+	18.8188i	−0.0837832	+	0.960344i
$385$	6.05903	−	12.5172i	0.308797	−	0.637936i
$386$	9.35373	−	40.9814i	0.476092	−	2.08590i
$387$	−12.7295	+	30.2391i	−0.647075	+	1.53714i
$388$	1.77427	−	4.52075i	0.0900747	−	0.229507i
$389$	−6.40269	−	28.0520i	−0.324629	−	1.42229i	−0.829214	−	0.558931i	$-0.811212\pi$
$389$	−6.40269	−	28.0520i	−0.324629	−	1.42229i	0.504585	−	0.863362i	$-0.331646\pi$
$390$	−5.92187	+	24.5579i	−0.299866	+	1.24354i
$391$	0.394309	+	0.682963i	0.0199410	+	0.0345389i
$392$	2.37088	−	10.1981i	0.119747	−	0.515082i
$393$	8.50189	−	7.69738i	0.428864	−	0.388282i
$394$	2.20363	+	29.4054i	0.111017	+	1.48142i
$395$	14.8593	−	13.7874i	0.747653	−	0.693720i
$396$	−0.259330	−	5.14574i	−0.0130318	−	0.258583i
$397$	20.1547	+	6.21691i	1.01154	+	0.312018i	0.755852	−	0.654743i	$-0.227223\pi$
$397$	20.1547	+	6.21691i	1.01154	+	0.312018i	0.255684	+	0.966760i	$0.417699\pi$
$398$	−23.8333	−	22.1141i	−1.19466	−	1.10848i
$399$	−26.0924	+	5.56588i	−1.30625	+	0.278643i
$400$	27.6011	−	25.6101i	1.38006	−	1.28051i
$401$	−6.13040	+	2.95224i	−0.306137	+	0.147428i	−0.580645	−	0.814157i	$-0.697200\pi$
$401$	−6.13040	+	2.95224i	−0.306137	+	0.147428i	0.274507	+	0.961585i	$0.411485\pi$
$402$	6.93958	+	12.3663i	0.346115	+	0.616777i
$403$	−15.9447	−	7.67857i	−0.794263	−	0.382497i
$404$	5.48510	+	13.9758i	0.272894	+	0.695323i
$405$	25.4527	+	19.2406i	1.26476	+	0.956075i
$406$	−38.2908	+	8.65858i	−1.90034	+	0.429718i
$407$	0.338119	−	4.51188i	0.0167599	−	0.223646i
$408$	0.563972	−	0.949826i	0.0279208	−	0.0470234i
$409$	0.189457	+	0.482729i	0.00936806	+	0.0238694i	0.935481	−	0.353376i	$-0.114966\pi$
$409$	0.189457	+	0.482729i	0.00936806	+	0.0238694i	−0.926113	+	0.377246i	$0.876871\pi$
$410$	7.71775	−	13.3675i	0.381152	−	0.660175i
$411$	16.0825	−	14.5607i	0.793293	−	0.718226i
$412$	5.55563	+	14.1555i	0.273706	+	0.697393i
$413$	3.38208	+	4.98212i	0.166421	+	0.245154i
$414$	8.77700	+	4.49430i	0.431366	+	0.220883i
$415$	33.8296	−	5.09899i	1.66063	−	0.250300i
$416$	12.2008	−	5.87559i	0.598193	−	0.288074i
$417$	25.4948	−	3.52460i	1.24849	−	0.172600i
$418$	9.56440	+	11.9934i	0.467810	+	0.586616i
$419$	0.185502	−	0.472651i	0.00906235	−	0.0230905i	−0.926271	−	0.376858i	$-0.877004\pi$
$419$	0.185502	−	0.472651i	0.00906235	−	0.0230905i	0.935333	+	0.353768i	$0.115100\pi$
$420$	−8.40582	+	16.8375i	−0.410162	+	0.821584i
$421$	7.98480	+	20.3449i	0.389155	+	0.991551i	0.982443	+	0.186561i	$0.0597342\pi$
$421$	7.98480	+	20.3449i	0.389155	+	0.991551i	−0.593288	+	0.804990i	$0.702171\pi$
$422$	−12.9590	+	22.4457i	−0.630835	+	1.09264i
$423$	8.01148	−	3.61962i	0.389531	−	0.175992i
$424$	14.9786	+	2.25765i	0.727423	+	0.109641i
$425$	−3.08375	+	0.951211i	−0.149584	+	0.0461405i
$426$	44.5030	−	6.15244i	2.15618	−	0.298087i
$427$	−13.3496	−	5.27036i	−0.646032	−	0.255050i
$428$	−0.0899811	−	1.20071i	−0.00434940	−	0.0580387i
$429$	4.95221	−	3.28842i	0.239095	−	0.158766i
$430$	−62.0806	−	29.8964i	−2.99379	−	1.44173i
$431$	20.9641	−	6.46656i	1.00980	−	0.311483i	0.254652	−	0.967033i	$-0.418039\pi$
$431$	20.9641	−	6.46656i	1.00980	−	0.311483i	0.755152	+	0.655549i	$0.227563\pi$
$432$	−0.985483	−	25.8316i	−0.0474141	−	1.24283i
$433$	2.11210	+	9.25372i	0.101501	+	0.444706i	0.999984	+	0.00569648i	$0.00181326\pi$
$433$	2.11210	+	9.25372i	0.101501	+	0.444706i	−0.898483	+	0.439009i	$0.855330\pi$
$434$	−28.0589	−	22.4688i	−1.34687	−	1.07854i
$435$	−51.2639	−	0.626614i	−2.45791	−	0.0300438i
$436$	−4.68606	−	20.5310i	−0.224422	−	0.983256i
$437$	−10.6475	+	1.60485i	−0.509337	+	0.0767703i
$438$	13.8830	−	6.47786i	0.663354	−	0.309524i
$439$	−2.48906	−	33.2141i	−0.118796	−	1.58522i	−0.664527	−	0.747264i	$-0.731367\pi$
$439$	−2.48906	−	33.2141i	−0.118796	−	1.58522i	0.545731	−	0.837960i	$-0.316252\pi$
$440$	−7.86181			−0.374797
$441$	−2.16482	+	20.8881i	−0.103087	+	0.994672i
$442$	−1.75417			−0.0834374
$443$	−0.711751	−	9.49766i	−0.0338163	−	0.451247i	−0.988252	−	0.152832i	$-0.951161\pi$
$443$	−0.711751	−	9.49766i	−0.0338163	−	0.451247i	0.954436	−	0.298416i	$-0.0964582\pi$
$444$	−0.532152	+	6.09967i	−0.0252548	+	0.289477i
$445$	8.41649	−	1.26858i	0.398980	−	0.0601365i
$446$	8.20720	+	35.9581i	0.388622	+	1.70267i
$447$	−12.2519	−	21.8329i	−0.579494	−	1.03266i
$448$	1.15213	−	0.260527i	0.0544328	−	0.0123087i
$449$	−1.41186	−	6.18578i	−0.0666299	−	0.291925i	0.930625	−	0.365975i	$-0.119265\pi$
$449$	−1.41186	−	6.18578i	−0.0666299	−	0.291925i	−0.997254	+	0.0740505i	$0.976407\pi$
$450$	−25.9223	+	30.9237i	−1.22199	+	1.45776i
$451$	−3.47090	+	1.07063i	−0.163438	+	0.0504140i
$452$	−13.9624	−	6.72394i	−0.656736	−	0.316268i
$453$	0.444511	+	7.09413i	0.0208849	+	0.333311i
$454$	1.87443	+	25.0125i	0.0879712	+	1.17389i
$455$	−21.6556	+	1.57904i	−1.01523	+	0.0740265i
$456$	9.25909	+	11.9062i	0.433597	+	0.557559i
$457$	11.0753	−	3.41629i	0.518083	−	0.159807i	−0.0246769	−	0.999695i	$-0.507856\pi$
$457$	11.0753	−	3.41629i	0.518083	−	0.159807i	0.542759	+	0.839888i	$0.317380\pi$
$458$	13.4303	+	2.02429i	0.627555	+	0.0945887i
$459$	−0.884514	+	2.03138i	−0.0412856	+	0.0948168i
$460$	−3.79766	+	6.57774i	−0.177067	+	0.306689i
$461$	0.967468	+	2.46507i	0.0450595	+	0.114810i	0.951632	−	0.307241i	$-0.0994057\pi$
$461$	0.967468	+	2.46507i	0.0450595	+	0.114810i	−0.906572	+	0.422051i	$0.861310\pi$
$462$	11.3015	−	4.25089i	0.525795	−	0.197769i
$463$	−11.2382	+	28.6344i	−0.522282	+	1.33075i	0.389859	+	0.920875i	$0.372524\pi$
$463$	−11.2382	+	28.6344i	−0.522282	+	1.33075i	−0.912141	+	0.409877i	$0.865571\pi$
$464$	25.8975	+	32.4744i	1.20226	+	1.50759i
$465$	−28.8181	−	37.0571i	−1.33641	−	1.71848i
$466$	−40.5956	+	19.5498i	−1.88055	+	0.905627i
$467$	−32.5918	+	4.91242i	−1.50817	+	0.227320i	−0.850495	−	0.525984i	$-0.823697\pi$
$467$	−32.5918	+	4.91242i	−1.50817	+	0.227320i	−0.657673	+	0.753304i	$0.728459\pi$
$468$	−6.75548	+	4.36782i	−0.312272	+	0.201903i
$469$	−8.30816	+	8.91800i	−0.383635	+	0.411795i
$470$	6.74525	+	17.1866i	0.311135	+	0.792760i
$471$	−8.78000	−	40.7577i	−0.404561	−	1.87802i
$472$	1.70211	−	2.94813i	0.0783458	−	0.135699i
$473$	5.92382	+	15.0937i	0.272378	+	0.694007i
$474$	17.5988	+	0.215115i	0.808339	+	0.00988057i
$475$	3.29283	−	43.9397i	0.151085	−	2.01609i
$476$	−1.27344	−	0.293352i	−0.0583680	−	0.0134458i
$477$	−30.3730	−	0.742628i	−1.39068	−	0.0340026i
$478$	3.81397	+	9.71785i	0.174447	+	0.444484i
$479$	4.32968	+	2.08506i	0.197828	+	0.0952690i	0.530175	−	0.847888i	$-0.322126\pi$
$479$	4.32968	+	2.08506i	0.197828	+	0.0952690i	−0.332347	+	0.943157i	$0.607840\pi$
$480$	35.9183	+	0.439040i	1.63944	+	0.0200394i
$481$	−6.36480	+	3.06513i	−0.290210	+	0.139758i
$482$	−0.594000	+	0.551152i	−0.0270560	+	0.0251043i
$483$	−1.38238	+	8.36203i	−0.0629006	+	0.380486i
$484$	7.47405	+	6.93491i	0.339730	+	0.315223i
$485$	14.2029	+	4.38101i	0.644920	+	0.198931i
$486$	4.50352	+	27.3350i	0.204284	+	1.23994i
$487$	−4.24601	+	3.93972i	−0.192405	+	0.178526i	−0.770493	−	0.637449i	$-0.779990\pi$
$487$	−4.24601	+	3.93972i	−0.192405	+	0.178526i	0.578087	+	0.815975i	$0.303799\pi$
$488$	0.606345	+	8.09111i	0.0274479	+	0.366267i
$489$	7.83952	+	36.3919i	0.354515	+	1.64570i
$490$	−43.5838	−	6.74872i	−1.96892	−	0.304876i
$491$	12.1877	+	21.1097i	0.550024	+	0.952670i	0.998272	+	0.0587604i	$0.0187148\pi$
$491$	12.1877	+	21.1097i	0.550024	+	0.952670i	−0.448248	+	0.893909i	$0.647952\pi$
$492$	4.71436	−	1.39132i	0.212540	−	0.0627254i
$493$	−0.792177	−	3.47076i	−0.0356779	−	0.156315i
$494$	8.75041	−	22.2957i	0.393699	−	1.00313i
$495$	15.6452	−	1.96835i	0.703200	−	0.0884709i
$496$	−8.46317	+	37.0795i	−0.380007	+	1.66492i
$497$	16.6844	+	34.8246i	0.748398	+	1.56210i
$498$	24.3369	+	17.0320i	1.09056	+	0.763224i
$499$	32.3282	−	15.5684i	1.44721	−	0.696938i	0.465099	−	0.885258i	$-0.346019\pi$
$499$	32.3282	−	15.5684i	1.44721	−	0.696938i	0.982108	+	0.188320i	$0.0603043\pi$
$500$	−7.73202	−	7.17427i	−0.345787	−	0.320843i
$501$	−9.89077	−	9.40485i	−0.441887	−	0.420178i
$502$	12.3450	+	1.86071i	0.550983	+	0.0830474i
$503$	−34.9332	−	16.8229i	−1.55759	−	0.750098i	−0.560639	−	0.828061i	$-0.689444\pi$
$503$	−34.9332	−	16.8229i	−1.55759	−	0.750098i	−0.996956	+	0.0779624i	$0.975159\pi$
$504$	11.1622	−	4.04343i	0.497202	−	0.180109i
$505$	−41.3989	+	19.9367i	−1.84223	+	0.887170i
$506$	4.65674	−	1.43642i	0.207018	−	0.0638564i
$507$	11.8533	+	5.88779i	0.526424	+	0.261486i
$508$	−2.42154	+	4.19422i	−0.107438	+	0.186089i
$509$	−9.76127			−0.432661			−0.216330	−	0.976320i	$-0.569409\pi$
$509$	−9.76127			−0.432661			−0.216330	+	0.976320i	$0.569409\pi$
$510$	−4.16731	−	2.06999i	−0.184531	−	0.0916608i
$511$	8.93693	+	9.67068i	0.395346	+	0.427806i
$512$	−8.86631	−	11.1180i	−0.391839	−	0.491351i
$513$	−21.4068	−	21.3755i	−0.945133	−	0.943751i
$514$	−23.5754	−	16.0734i	−1.03987	−	0.708969i
$515$	−41.9312	+	20.1930i	−1.84771	+	0.889811i
$516$	−7.76618	−	20.5220i	−0.341887	−	0.903430i
$517$	1.58729	−	4.04434i	0.0698088	−	0.177870i
$518$	−13.9957	+	3.16482i	−0.614937	+	0.139054i
$519$	−10.2499	+	6.80628i	−0.449923	+	0.298763i
$520$	6.13753	+	10.6305i	0.269148	+	0.466179i
$521$	15.0238	+	26.0219i	0.658203	+	1.14004i	0.981081	+	0.193600i	$0.0620164\pi$
$521$	15.0238	+	26.0219i	0.658203	+	1.14004i	−0.322878	+	0.946441i	$0.604650\pi$
$522$	−31.8812	−	31.0657i	−1.39540	−	1.35971i
$523$	−14.1028	−	13.0854i	−0.616670	−	0.572186i	0.308743	−	0.951145i	$-0.400092\pi$
$523$	−14.1028	−	13.0854i	−0.616670	−	0.572186i	−0.925413	+	0.378959i	$0.876282\pi$
$524$	−0.573190	+	7.64869i	−0.0250399	+	0.334134i
$525$	−32.1018	−	13.1294i	−1.40104	−	0.573014i
$526$	1.39848	+	18.6614i	0.0609765	+	0.813675i
$527$	2.03242	−	2.54858i	0.0885338	−	0.111018i
$528$	−9.25816	−	8.80333i	−0.402910	−	0.383116i
$529$	4.35681	−	19.0884i	0.189426	−	0.829931i
$530$	4.76831	−	63.6286i	0.207122	−	2.76385i
$531$	−2.64912	+	6.29302i	−0.114962	+	0.273094i
$532$	10.0809	−	14.7222i	0.437062	−	0.638288i
$533$	4.15732	+	3.85743i	0.180074	+	0.167084i
$534$	6.05479	+	4.23741i	0.262016	+	0.183371i
$535$	3.64393	−	0.549235i	0.157541	−	0.0237455i
$536$	6.58434	+	2.03100i	0.284400	+	0.0877258i
$537$	−23.8826	−	22.7093i	−1.03061	−	0.979977i
$538$	23.9814	−	41.5370i	1.03391	−	1.79079i
$539$	6.43808	+	8.14009i	0.277308	+	0.350619i
$540$	−21.2029	+	2.40471i	−0.912428	+	0.103482i
$541$	−11.0477	+	7.53221i	−0.474979	+	0.323835i	−0.777038	−	0.629454i	$-0.783279\pi$
$541$	−11.0477	+	7.53221i	−0.474979	+	0.323835i	0.302059	+	0.953289i	$0.402326\pi$
$542$	−2.45444	−	10.7536i	−0.105427	−	0.461906i
$543$	13.4165	+	2.19024i	0.575757	+	0.0939922i
$544$	0.555043	+	2.43180i	0.0237973	+	0.104263i
$545$	61.5877	−	18.9973i	2.63813	−	0.813754i
$546$	−14.5708	−	11.9631i	−0.623572	−	0.511972i
$547$	6.29189	+	1.94079i	0.269022	+	0.0829822i	0.426331	−	0.904567i	$-0.359806\pi$
$547$	6.29189	+	1.94079i	0.269022	+	0.0829822i	−0.157309	+	0.987549i	$0.550282\pi$
$548$	−1.08427	+	14.4686i	−0.0463177	+	0.618067i
$549$	−3.23241	−	15.9497i	−0.137956	−	0.680717i
$550$	1.49026	+	19.8862i	0.0635451	+	0.847950i
$551$	48.0653	+	7.24468i	2.04765	+	0.308634i
$552$	4.59553	−	1.35625i	0.195599	−	0.0577257i
$553$	4.42986	+	14.4645i	0.188377	+	0.615095i
$554$	22.5885	+	15.4006i	0.959695	+	0.654309i
$555$	−18.7376	−	0.229035i	−0.795365	−	0.00972198i
$556$	−10.7320	+	13.4575i	−0.455137	+	0.570723i
$557$	16.4886	+	28.5592i	0.698646	+	1.21009i	0.968936	+	0.247311i	$0.0795471\pi$
$557$	16.4886	+	28.5592i	0.698646	+	1.21009i	−0.270290	+	0.962779i	$0.587120\pi$
$558$	4.03855	−	40.5589i	0.170965	−	1.71700i
$559$	15.7846	−	19.7933i	0.667618	−	0.837167i
$560$	13.6645	+	44.6178i	0.577430	+	1.88545i
$561$	0.387547	+	1.02409i	0.0163623	+	0.0432369i
$562$	−20.8494	−	26.1443i	−0.879479	−	1.10283i
$563$	0.725702	−	9.68383i	0.0305847	−	0.408125i	−0.960809	−	0.277211i	$-0.910590\pi$
$563$	0.725702	−	9.68383i	0.0305847	−	0.408125i	0.991394	−	0.130914i	$-0.0417911\pi$
$564$	−2.21473	+	5.44636i	−0.0932571	+	0.229333i
$565$	17.3277	−	44.1503i	0.728983	−	1.85742i
$566$	19.4191	+	24.3508i	0.816246	+	1.02354i
$567$	−21.2007	+	10.8412i	−0.890344	+	0.455288i
$568$	13.6110	−	17.0676i	0.571104	−	0.716141i
$569$	16.4861	+	28.5547i	0.691132	+	1.19708i	0.971467	+	0.237174i	$0.0762212\pi$
$569$	16.4861	+	28.5547i	0.691132	+	1.19708i	−0.280335	+	0.959902i	$0.590445\pi$
$570$	47.0978	−	42.6410i	1.97271	−	1.78604i
$571$	−6.24328	−	15.9076i	−0.261273	−	0.665713i	0.738692	−	0.674043i	$-0.235444\pi$
$571$	−6.24328	−	15.9076i	−0.261273	−	0.665713i	−0.999965	+	0.00832962i	$0.997349\pi$
$572$	−0.884667	+	3.87598i	−0.0369898	+	0.162063i
$573$	−28.5834	+	3.95159i	−1.19409	+	0.165080i
$574$	6.46993	+	9.53079i	0.270049	+	0.397808i
$575$	−12.6117	−	6.07347i	−0.525944	−	0.253281i
$576$	0.959268	+	0.934731i	0.0399695	+	0.0389471i
$577$	−1.20808	−	16.1207i	−0.0502930	−	0.671113i	−0.964198	−	0.265184i	$-0.914567\pi$
$577$	−1.20808	−	16.1207i	−0.0502930	−	0.671113i	0.913905	−	0.405929i	$-0.133052\pi$
$578$	−6.65092	+	29.1396i	−0.276642	+	1.21205i
$579$	25.1496	+	32.3397i	1.04518	+	1.34399i
$580$	25.1342	−	23.3212i	1.04364	−	0.968359i
$581$	−7.57475	+	24.3824i	−0.314253	+	1.01155i
$582$	6.31551	+	11.2543i	0.261786	+	0.466504i
$583$	−11.0068	+	10.2128i	−0.455855	+	0.422971i
$584$	2.71966	−	6.92957i	0.112540	−	0.286748i
$585$	−14.8754	−	19.6184i	−0.615022	−	0.811120i
$586$	1.35485	−	0.923724i	0.0559685	−	0.0381587i
$587$	−5.58442	+	9.67249i	−0.230494	+	0.399227i	−0.957953	−	0.286924i	$-0.907367\pi$
$587$	−5.58442	+	9.67249i	−0.230494	+	0.399227i	0.727460	+	0.686150i	$0.240701\pi$
$588$	−8.57706	−	11.1213i	−0.353712	−	0.458633i
$589$	22.2543	+	38.5455i	0.916971	+	1.58824i
$590$	−12.9195	−	6.22172i	−0.531889	−	0.256144i
$591$	−23.5456	−	16.4783i	−0.968538	−	0.677825i
$592$	9.46584	+	11.8698i	0.389044	+	0.487845i
$593$	14.2093	+	4.38300i	0.583508	+	0.179988i	0.572435	−	0.819950i	$-0.305999\pi$
$593$	14.2093	+	4.38300i	0.583508	+	0.179988i	0.0110731	+	0.999939i	$0.496475\pi$
$594$	11.0219	+	8.12208i	0.452234	+	0.333253i
$595$	0.604043	−	3.95356i	0.0247633	−	0.162080i
$596$	15.9996	+	4.93523i	0.655369	+	0.202155i
$597$	31.3883	−	4.33936i	1.28464	−	0.177598i
$598$	−5.57769	−	5.17534i	−0.228089	−	0.211636i
$599$	−2.52754	+	1.72325i	−0.103273	+	0.0704101i	−0.613855	−	0.789419i	$-0.710382\pi$
$599$	−2.52754	+	1.72325i	−0.103273	+	0.0704101i	0.510583	+	0.859829i	$0.329430\pi$
$600$	1.22617	+	19.5690i	0.0500582	+	0.798900i
$601$	−10.4344	+	7.11407i	−0.425629	+	0.290189i	−0.757128	−	0.653267i	$-0.773398\pi$
$601$	−10.4344	+	7.11407i	−0.425629	+	0.290189i	0.331499	+	0.943456i	$0.392446\pi$
$602$	40.2683	−	31.9805i	1.64121	−	1.30343i
$603$	−13.6115	−	2.39323i	−0.554304	−	0.0974599i
$604$	−3.48475	−	3.23338i	−0.141793	−	0.131564i
$605$	−19.4555	+	24.3965i	−0.790981	+	0.991858i
$606$	−37.9771	−	12.2247i	−1.54271	−	0.496593i
$607$	13.5702			0.550798			0.275399	−	0.961330i	$-0.411190\pi$
$607$	13.5702			0.550798			0.275399	+	0.961330i	$0.411190\pi$
$608$	−33.6772	−	5.07602i	−1.36579	−	0.205860i
$609$	17.0897	−	34.2318i	0.692509	−	1.38714i
$610$	33.7961	−	5.09394i	1.36836	−	0.206248i
$611$	−6.70781	+	1.01104i	−0.271369	+	0.0409023i
$612$	−0.507472	−	1.39215i	−0.0205133	−	0.0562745i
$613$	−2.05485	−	1.40097i	−0.0829945	−	0.0565847i	0.521112	−	0.853488i	$-0.325517\pi$
$613$	−2.05485	−	1.40097i	−0.0829945	−	0.0565847i	−0.604106	+	0.796904i	$0.706470\pi$
$614$	−16.5336	+	42.1268i	−0.667240	+	1.70010i
$615$	5.32445	+	14.0697i	0.214702	+	0.567347i
$616$	2.55631	−	5.28103i	0.102997	−	0.212779i
$617$	−8.54499	−	1.28795i	−0.344008	−	0.0518509i	−0.0252341	−	0.999682i	$-0.508033\pi$
$617$	−8.54499	−	1.28795i	−0.344008	−	0.0518509i	−0.318774	+	0.947831i	$0.603271\pi$
$618$	−38.4654	−	12.3819i	−1.54730	−	0.498071i
$619$	37.9665			1.52600			0.763002	−	0.646396i	$-0.223725\pi$
$619$	37.9665			1.52600			0.763002	+	0.646396i	$0.223725\pi$
$620$	31.0446	+	4.67923i	1.24678	+	0.187922i
$621$	−8.80567	+	3.84955i	−0.353359	+	0.154477i
$622$	8.29167	−	3.99306i	0.332466	−	0.160107i
$623$	−1.88453	+	6.06611i	−0.0755019	+	0.243034i
$624$	−4.67598	+	19.3912i	−0.187189	+	0.776269i
$625$	−3.46716	+	4.34769i	−0.138687	+	0.173907i
$626$	−26.6731	+	18.1854i	−1.06607	+	0.726836i
$627$	−14.9494	−	0.182732i	−0.597023	−	0.00729760i
$628$	23.0384	+	15.7073i	0.919334	+	0.626791i
$629$	−0.289550	−	1.26860i	−0.0115451	−	0.0505825i
$630$	−20.4983	−	45.6142i	−0.816671	−	1.81731i
$631$	−4.38605	+	19.2165i	−0.174606	+	0.764998i	0.809457	+	0.587179i	$0.199761\pi$
$631$	−4.38605	+	19.2165i	−0.174606	+	0.764998i	−0.984063	+	0.177819i	$0.943096\pi$
$632$	6.26916	−	5.81693i	0.249374	−	0.231385i
$633$	−8.94038	−	23.6248i	−0.355348	−	0.939000i
$634$	−14.2766	−	4.40373i	−0.566994	−	0.174895i
$635$	−13.3544	−	6.43113i	−0.529952	−	0.255211i
$636$	15.0628	−	13.6374i	0.597278	−	0.540759i
$637$	5.98075	−	15.0602i	0.236966	−	0.596706i
$638$	−21.9990			−0.870950
$639$	−22.8130	+	37.3728i	−0.902469	+	1.47845i
$640$	28.3435	−	26.2989i	1.12038	−	1.03956i
$641$	4.07979	+	5.11589i	0.161142	+	0.202066i	0.855847	−	0.517229i	$-0.173037\pi$
$641$	4.07979	+	5.11589i	0.161142	+	0.202066i	−0.694705	+	0.719295i	$0.744465\pi$
$642$	2.62143	+	1.83459i	0.103460	+	0.0724057i
$643$	−24.6314	+	7.59777i	−0.971366	+	0.299627i	−0.739527	−	0.673127i	$-0.764951\pi$
$643$	−24.6314	+	7.59777i	−0.971366	+	0.299627i	−0.231840	+	0.972754i	$0.574474\pi$
$644$	−3.18365	−	4.68980i	−0.125453	−	0.184804i
$645$	60.8557	−	28.3956i	2.39619	−	1.11807i
$646$	3.64513	+	2.48521i	0.143416	+	0.0977793i
$647$	−6.45086	+	1.98983i	−0.253610	+	0.0782282i	−0.418953	−	0.908008i	$-0.637603\pi$
$647$	−6.45086	+	1.98983i	−0.253610	+	0.0782282i	0.165344	+	0.986236i	$0.447127\pi$
$648$	10.7385	+	8.11765i	0.421850	+	0.318892i
$649$	1.23280	+	3.14112i	0.0483917	+	0.123300i
$650$	25.7261	−	17.5398i	1.00906	−	0.687967i
$651$	34.2628	−	7.30874i	1.34287	−	0.286452i
$652$	−20.5706	−	14.0248i	−0.805609	−	0.549255i
$653$	1.46668	−	6.42593i	0.0573955	−	0.251466i	−0.938088	−	0.346396i	$-0.887405\pi$
$653$	1.46668	−	6.42593i	0.0573955	−	0.251466i	0.995484	+	0.0949296i	$0.0302626\pi$
$654$	50.1181	+	24.8948i	1.95977	+	0.973462i
$655$	−23.4745			−0.917223
$656$	6.09402	−	10.5552i	0.237932	−	0.412110i
$657$	−3.67724	+	14.4710i	−0.143463	+	0.564566i
$658$	−13.7381	−	1.05733i	−0.535566	−	0.0412191i
$659$	41.1844	−	6.20754i	1.60431	−	0.241812i	0.715006	−	0.699118i	$-0.246424\pi$
$659$	41.1844	−	6.20754i	1.60431	−	0.241812i	0.889309	+	0.457307i	$0.151186\pi$
$660$	−6.67548	+	8.16405i	−0.259843	+	0.317785i
$661$	2.25793	−	30.1300i	0.0878234	−	1.17192i	−0.762974	−	0.646429i	$-0.776262\pi$
$661$	2.25793	−	30.1300i	0.0878234	−	1.17192i	0.850798	−	0.525493i	$-0.176119\pi$
$662$	1.29082	−	17.2247i	0.0501690	−	0.669459i
$663$	1.08219	−	1.32351i	0.0420288	−	0.0514009i
$664$	14.2728	−	2.15127i	0.553891	−	0.0834856i
$665$	47.2369	+	27.3992i	1.83177	+	1.06249i
$666$	−11.6529	−	11.3549i	−0.451542	−	0.439992i
$667$	7.72093	−	13.3730i	0.298956	−	0.517806i
$668$	9.12786			0.353167
$669$	−32.1934	−	15.9912i	−1.24467	−	0.618254i
$670$	6.45862	−	28.2971i	0.249518	−	1.09321i
$671$	−6.64519	−	4.53061i	−0.256535	−	0.174902i
$672$	−11.9740	+	23.9847i	−0.461906	+	0.925231i
$673$	−26.4966	+	18.0651i	−1.02137	+	0.696357i	−0.953517	−	0.301338i	$-0.902567\pi$
$673$	−26.4966	+	18.0651i	−1.02137	+	0.696357i	−0.0678511	+	0.997695i	$0.521614\pi$
$674$	−9.25584	−	23.5835i	−0.356522	−	0.908403i
$675$	−7.33958	−	38.6358i	−0.282501	−	1.48709i
$676$	−8.45818	+	2.60900i	−0.325315	+	0.100346i
$677$	−19.6234	−	13.3790i	−0.754190	−	0.514198i	0.124133	−	0.992266i	$-0.460385\pi$
$677$	−19.6234	−	13.3790i	−0.754190	−	0.514198i	−0.878323	+	0.478068i	$0.841337\pi$
$678$	37.3182	−	17.4129i	1.43320	−	0.668737i
$679$	−7.56102	+	8.11602i	−0.290165	+	0.311464i
$680$	−2.16056	+	0.666443i	−0.0828535	+	0.0255569i
$681$	−20.0281	−	14.0166i	−0.767480	−	0.537116i
$682$	−12.5593	−	15.7489i	−0.480922	−	0.603057i
$683$	31.9614	−	29.6558i	1.22297	−	1.13475i	0.236355	−	0.971667i	$-0.424047\pi$
$683$	31.9614	−	29.6558i	1.22297	−	1.13475i	0.986613	−	0.163081i	$-0.0521432\pi$
$684$	20.2258	+	0.494527i	0.773354	+	0.0189087i
$685$	−44.4053			−1.69664
$686$	18.7049	−	27.0823i	0.714156	−	1.03401i
$687$	−9.81277	+	8.88421i	−0.374381	+	0.338954i
$688$	−49.0196	−	23.6066i	−1.86885	−	0.899993i
$689$	22.4022	+	6.91017i	0.853457	+	0.263257i
$690$	−7.14357	−	18.8767i	−0.271951	−	0.718625i
$691$	17.2937	−	16.0462i	0.657884	−	0.610427i	−0.278906	−	0.960318i	$-0.589972\pi$
$691$	17.2937	−	16.0462i	0.657884	−	0.610427i	0.936790	+	0.349891i	$0.113781\pi$
$692$	1.83106	−	8.02239i	0.0696064	−	0.304966i
$693$	−3.76493	+	11.1494i	−0.143018	+	0.423531i
$694$	11.6876	+	51.2069i	0.443657	+	1.94379i
$695$	−43.5259	−	29.6755i	−1.65103	−	1.12566i
$696$	−21.6283	−	0.264369i	−0.819819	−	0.0100209i
$697$	−0.863103	+	0.588454i	−0.0326924	+	0.0222893i
$698$	−20.2283	+	25.3655i	−0.765654	+	0.960099i
$699$	10.2942	−	42.6898i	0.389363	−	1.61468i
$700$	21.6091	−	8.43079i	0.816747	−	0.318654i
$701$	2.29032	−	1.10296i	0.0865044	−	0.0416583i	−0.390131	−	0.920759i	$-0.627570\pi$
$701$	2.29032	−	1.10296i	0.0865044	−	0.0416583i	0.476636	+	0.879101i	$0.341856\pi$
$702$	2.37791	−	21.2442i	0.0897483	−	0.801812i
$703$	17.5684	+	2.64802i	0.662606	+	0.0998718i
$704$	0.661926			0.0249473
$705$	−17.1285	−	5.51360i	−0.645097	−	0.207654i
$706$	−17.5878	−	2.65093i	−0.661925	−	0.0997691i
$707$	0.0690117	−	34.2915i	0.00259545	−	1.28966i
$708$	−1.61621	−	4.27081i	−0.0607410	−	0.160507i
$709$	11.1817	−	28.4906i	0.419939	−	1.06999i	−0.551810	−	0.833970i	$-0.686063\pi$
$709$	11.1817	−	28.4906i	0.419939	−	1.06999i	0.971749	−	0.236017i	$-0.0758420\pi$
$710$	−75.9776	−	51.8007i	−2.85139	−	1.94404i
$711$	−11.0194	+	13.1455i	−0.413261	+	0.492993i
$712$	3.55093	−	0.535216i	0.133077	−	0.0200581i
$713$	13.9815	−	2.10738i	0.523613	−	0.0789220i
$714$	2.74551	−	2.12624i	0.102748	−	0.0795726i
$715$	−12.0316	−	1.81347i	−0.449957	−	0.0678200i
$716$	22.0404			0.823689
$717$	−9.68499	−	3.11756i	−0.361692	−	0.116427i
$718$	−14.7552	+	18.5024i	−0.550660	+	0.690505i
$719$	9.67987	+	8.98160i	0.360998	+	0.334957i	0.839730	−	0.543004i	$-0.182713\pi$
$719$	9.67987	+	8.98160i	0.360998	+	0.334957i	−0.478732	+	0.877961i	$0.658904\pi$
$720$	−33.9909	+	40.5489i	−1.26677	+	1.51117i
$721$	0.0698991	−	34.7324i	0.00260318	−	1.29350i
$722$	−21.8713	+	14.9116i	−0.813965	+	0.554952i
$723$	−0.0493871	−	0.788188i	−0.00183672	−	0.0293130i
$724$	−7.51179	+	5.12145i	−0.279174	+	0.190337i
$725$	46.3216	+	42.9802i	1.72034	+	1.59624i
$726$	−26.8383	+	3.71033i	−0.996062	+	0.137703i
$727$	39.5689	+	12.2054i	1.46753	+	0.452673i	0.922583	−	0.385798i	$-0.126074\pi$
$727$	39.5689	+	12.2054i	1.46753	+	0.452673i	0.544946	+	0.838471i	$0.316550\pi$
$728$	−9.13651	+	0.666199i	−0.338622	+	0.0246910i
$729$	−23.4024	−	13.4658i	−0.866756	−	0.498732i
$730$	−29.9640	−	9.24268i	−1.10902	−	0.342087i
$731$	2.90745	+	3.64583i	0.107536	+	0.134846i
$732$	8.91701	+	6.24052i	0.329582	+	0.230656i
$733$	15.6127	+	7.51869i	0.576669	+	0.277709i	0.699400	−	0.714731i	$-0.253451\pi$
$733$	15.6127	+	7.51869i	0.576669	+	0.277709i	−0.122731	+	0.992440i	$0.539165\pi$
$734$	16.3020	+	28.2359i	0.601718	+	1.04221i
$735$	31.9798	−	28.7203i	1.17959	−	1.05936i
$736$	−5.40971	+	9.36989i	−0.199405	+	0.345379i
$737$	−5.64328	+	3.84752i	−0.207873	+	0.141725i
$738$	−5.06776	+	12.0386i	−0.186547	+	0.443145i
$739$	12.5965	−	32.0953i	0.463368	−	1.18064i	−0.488070	−	0.872805i	$-0.662299\pi$
$739$	12.5965	−	32.0953i	0.463368	−	1.18064i	0.951438	−	0.307839i	$-0.0996059\pi$
$740$	9.18687	−	8.52417i	0.337716	−	0.313355i
$741$	11.4236	+	20.3569i	0.419656	+	0.747828i
$742$	41.1909	+	23.8923i	1.51217	+	0.877113i
$743$	−25.7853	+	23.9252i	−0.945970	+	0.877732i	−0.992631	−	0.121179i	$-0.961332\pi$
$743$	−25.7853	+	23.9252i	−0.945970	+	0.877732i	0.0466610	+	0.998911i	$0.485142\pi$
$744$	−12.1584	−	15.6344i	−0.445749	−	0.573186i
$745$	−11.4027	+	49.9587i	−0.417764	+	1.83034i
$746$	0.405109	+	5.40580i	0.0148321	+	0.197920i
$747$	−27.8646	+	7.85455i	−1.01951	+	0.287383i
$748$	−0.659776	−	0.317732i	−0.0241238	−	0.0116174i
$749$	−0.815909	+	2.62633i	−0.0298127	+	0.0959642i
$750$	27.7646	−	3.83840i	1.01382	−	0.140158i
$751$	3.87337	−	16.9703i	0.141341	−	0.619257i	−0.853783	−	0.520629i	$-0.825698\pi$
$751$	3.87337	−	16.9703i	0.141341	−	0.619257i	0.995124	−	0.0986278i	$-0.0314453\pi$
$752$	5.32613	+	13.5708i	0.194224	+	0.494875i
$753$	−9.01981	+	8.16629i	−0.328700	+	0.297596i
$754$	17.1741	+	29.7465i	0.625445	+	1.08330i
$755$	9.07109	−	11.3748i	0.330131	−	0.413971i
$756$	5.27893	−	15.0246i	0.191993	−	0.546439i
$757$	−19.1184	−	23.9737i	−0.694871	−	0.871340i	0.301758	−	0.953385i	$-0.402426\pi$
$757$	−19.1184	−	23.9737i	−0.694871	−	0.871340i	−0.996629	+	0.0820444i	$0.973855\pi$
$758$	−3.13930	+	7.99880i	−0.114024	+	0.290530i
$759$	−1.78909	+	4.39964i	−0.0649400	+	0.159697i
$760$	2.30704	−	30.7853i	0.0836851	−	1.11670i
$761$	−17.9115	−	22.4603i	−0.649292	−	0.814186i	0.342839	−	0.939394i	$-0.388612\pi$
$761$	−17.9115	−	22.4603i	−0.649292	−	0.814186i	−0.992131	+	0.125208i	$0.960040\pi$
$762$	−4.55502	−	12.0366i	−0.165011	−	0.436038i
$763$	−7.26452	+	47.5475i	−0.262993	+	1.72133i
$764$	12.0321	−	15.0878i	0.435307	−	0.545857i
$765$	4.13271	−	1.86718i	0.149418	−	0.0675079i
$766$	−10.0191	−	17.3536i	−0.362006	−	0.627013i
$767$	3.28492	−	4.11916i	0.118612	−	0.148734i
$768$	35.1154	+	0.429227i	1.26712	+	0.0154884i
$769$	−36.6926	−	25.0166i	−1.32317	−	0.902121i	−0.324133	−	0.946012i	$-0.605072\pi$
$769$	−36.6926	−	25.0166i	−1.32317	−	0.902121i	−0.999036	+	0.0438903i	$0.986025\pi$
$770$	−22.9878	−	9.07549i	−0.828424	−	0.327058i
$771$	26.6716	−

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)

\(f(q)\)	\(=\)	\(q+(-0.132809 - 1.77221i) q^{2} +(1.41906 + 0.993117i) q^{3} +(-1.14543 + 0.172646i) q^{4} +(-0.788881 - 3.45631i) q^{5} +(1.57155 - 2.64676i) q^{6} +(2.57823 + 0.593925i) q^{7} +(-0.332830 - 1.45822i) q^{8} +(1.02744 + 2.81858i) q^{9} +O(q^{10})\)	\(q+(-0.132809 - 1.77221i) q^{2} +(1.41906 + 0.993117i) q^{3} +(-1.14543 + 0.172646i) q^{4} +(-0.788881 - 3.45631i) q^{5} +(1.57155 - 2.64676i) q^{6} +(2.57823 + 0.593925i) q^{7} +(-0.332830 - 1.45822i) q^{8} +(1.02744 + 2.81858i) q^{9} +(-6.02055 + 1.85709i) q^{10} +(1.33579 + 0.643285i) q^{11} +(-1.79689 - 0.892556i) q^{12} +(-0.172992 - 2.30842i) q^{13} +(0.710149 - 4.64804i) q^{14} +(2.31306 - 5.68815i) q^{15} +(-4.75390 + 1.46638i) q^{16} +(0.421630 + 0.0635504i) q^{17} +(4.85866 - 2.19517i) q^{18} +(-2.91097 + 5.04194i) q^{19} +(1.50033 + 3.82278i) q^{20} +(3.06881 + 3.40329i) q^{21} +(0.962631 - 2.45274i) q^{22} +(1.15315 + 1.44601i) q^{23} +(0.975883 - 2.39984i) q^{24} +(-6.81893 + 3.28382i) q^{25} +(-4.06804 + 0.613158i) q^{26} +(-1.34119 + 5.02008i) q^{27} +(-3.05573 - 0.235180i) q^{28} +(-3.05029 - 7.77201i) q^{29} +(-10.3878 - 3.34379i) q^{30} +(3.82249 - 6.62074i) q^{31} +(2.13720 + 5.44550i) q^{32} +(1.25671 + 2.23946i) q^{33} +(0.0566287 - 0.755657i) q^{34} +(0.0188767 - 9.37970i) q^{35} +(-1.66348 - 3.05111i) q^{36} +(-1.11492 - 2.84076i) q^{37} +(9.32199 + 4.48923i) q^{38} +(2.04705 - 3.44758i) q^{39} +(-4.77752 + 2.30073i) q^{40} +(-1.79590 + 1.66635i) q^{41} +(5.62379 - 5.89057i) q^{42} +(8.01694 + 7.43863i) q^{43} +(-1.64112 - 0.506220i) q^{44} +(8.93136 - 5.77466i) q^{45} +(2.40948 - 2.23567i) q^{46} +(-0.218989 - 2.92221i) q^{47} +(-8.20233 - 2.64030i) q^{48} +(6.29451 + 3.06255i) q^{49} +(6.72524 + 11.6485i) q^{50} +(0.535203 + 0.508909i) q^{51} +(0.596692 + 2.61428i) q^{52} +(-3.69994 + 9.42729i) q^{53} +(9.07477 + 1.71016i) q^{54} +(1.16961 - 5.12440i) q^{55} +(0.00796409 - 3.95731i) q^{56} +(-9.13806 + 4.26386i) q^{57} +(-13.3685 + 6.43795i) q^{58} +(1.66840 + 1.54805i) q^{59} +(-1.66742 + 6.91474i) q^{60} +(-5.36407 - 0.808503i) q^{61} +(-12.2410 - 5.89496i) q^{62} +(0.974939 + 7.87715i) q^{63} +(0.402244 - 0.193711i) q^{64} +(-7.84216 + 2.41899i) q^{65} +(3.80189 - 2.52457i) q^{66} +(-2.30338 + 3.98958i) q^{67} -0.493921 q^{68} +(0.200332 + 3.19718i) q^{69} +(-16.6253 + 1.21225i) q^{70} +(9.09991 + 11.4109i) q^{71} +(3.76816 - 2.43634i) q^{72} +(4.11216 + 2.80362i) q^{73} +(-4.88636 + 2.35315i) q^{74} +(-12.9377 - 2.11207i) q^{75} +(2.46385 - 6.27778i) q^{76} +(3.06192 + 2.45190i) q^{77} +(-6.38170 - 3.16993i) q^{78} +(2.85886 + 4.95169i) q^{79} +(8.81854 + 15.2742i) q^{80} +(-6.88875 + 5.79181i) q^{81} +(3.19164 + 2.96141i) q^{82} +(-0.721157 + 9.62317i) q^{83} +(-4.10268 - 3.36843i) q^{84} +(-0.112965 - 1.50742i) q^{85} +(12.1181 - 15.1956i) q^{86} +(3.38999 - 14.0582i) q^{87} +(0.493461 - 2.16199i) q^{88} +(-0.179417 + 2.39415i) q^{89} +(-11.4201 - 15.0613i) q^{90} +(0.925016 - 6.05438i) q^{91} +(-1.57051 - 1.45722i) q^{92} +(11.9995 - 5.59902i) q^{93} +(-5.14969 + 0.776191i) q^{94} +(19.7229 + 6.08372i) q^{95} +(-2.37521 + 9.84996i) q^{96} +(-2.09625 + 3.63080i) q^{97} +(4.59151 - 11.5619i) q^{98} +(-0.440704 + 4.42597i) 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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