LMFDB - Embedded newform 225.2.q.a.106.1

Newspace parameters

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			106.1
Character	$\chi$	$=$	225.106
Dual form			225.2.q.a.121.1

$q$-expansion

$f(q)$	$=$	$q+(-2.59352 - 0.551270i) q^{2} +(0.494958 - 1.65982i) q^{3} +(4.59535 + 2.04598i) q^{4} +(-0.527975 - 2.17284i) q^{5} +(-2.19869 + 4.03193i) q^{6} +(1.02644 - 1.77785i) q^{7} +(-6.50010 - 4.72260i) q^{8} +(-2.51003 - 1.64309i) q^{9} +O(q^{10})$	\(q+(-2.59352 - 0.551270i) q^{2} +(0.494958 - 1.65982i) q^{3} +(4.59535 + 2.04598i) q^{4} +(-0.527975 - 2.17284i) q^{5} +(-2.19869 + 4.03193i) q^{6} +(1.02644 - 1.77785i) q^{7} +(-6.50010 - 4.72260i) q^{8} +(-2.51003 - 1.64309i) q^{9} +(0.171493 + 5.92636i) q^{10} +(5.61416 + 1.19333i) q^{11} +(5.67048 - 6.61480i) q^{12} +(2.04279 - 0.434208i) q^{13} +(-3.64218 + 4.04505i) q^{14} +(-3.86786 - 0.199118i) q^{15} +(7.52292 + 8.35505i) q^{16} +(-0.0247468 - 0.0179796i) q^{17} +(5.60404 + 5.64508i) q^{18} +(-5.30003 - 3.85070i) q^{19} +(2.01936 - 11.0652i) q^{20} +(-2.44288 - 2.58368i) q^{21} +(-13.9026 - 6.18983i) q^{22} +(-2.69572 + 2.99390i) q^{23} +(-11.0560 + 8.45153i) q^{24} +(-4.44248 + 2.29441i) q^{25} -5.53738 q^{26} +(-3.96959 + 3.35296i) q^{27} +(8.35433 - 6.06978i) q^{28} +(-0.343074 - 3.26413i) q^{29} +(9.92161 + 2.64865i) q^{30} +(-0.336018 + 3.19700i) q^{31} +(-6.87040 - 11.8999i) q^{32} +(4.75948 - 8.72787i) q^{33} +(0.0542697 + 0.0602726i) q^{34} +(-4.40493 - 1.29164i) q^{35} +(-8.17277 - 12.6860i) q^{36} +(1.37908 - 4.24438i) q^{37} +(11.6230 + 12.9086i) q^{38} +(0.290384 - 3.60558i) q^{39} +(-6.82956 + 16.6171i) q^{40} +(-1.88764 + 0.401231i) q^{41} +(4.91135 + 8.04751i) q^{42} +(0.309512 - 0.536091i) q^{43} +(23.3575 + 16.9702i) q^{44} +(-2.24493 + 6.32142i) q^{45} +(8.64184 - 6.27867i) q^{46} +(0.271227 + 2.58056i) q^{47} +(17.5915 - 8.35134i) q^{48} +(1.39282 + 2.41244i) q^{49} +(12.7865 - 3.50160i) q^{50} +(-0.0420916 + 0.0321762i) q^{51} +(10.2757 + 2.18417i) q^{52} +(-2.83942 + 2.06296i) q^{53} +(12.1436 - 6.50765i) q^{54} +(-0.371228 - 12.8287i) q^{55} +(-15.0681 + 6.70874i) q^{56} +(-9.01477 + 6.89118i) q^{57} +(-0.909647 + 8.65471i) q^{58} +(7.94668 - 1.68912i) q^{59} +(-17.3668 - 8.82860i) q^{60} +(8.06706 + 1.71471i) q^{61} +(2.63388 - 8.10625i) q^{62} +(-5.49758 + 2.77594i) q^{63} +(4.31002 + 13.2649i) q^{64} +(-2.02201 - 4.20940i) q^{65} +(-17.1552 + 20.0121i) q^{66} +(0.0735643 - 0.699918i) q^{67} +(-0.0769343 - 0.133254i) q^{68} +(3.63508 + 5.95627i) q^{69} +(10.7122 + 5.77819i) q^{70} +(3.81216 - 2.76970i) q^{71} +(8.55584 + 22.5341i) q^{72} +(2.55263 + 7.85620i) q^{73} +(-5.91647 + 10.2476i) q^{74} +(1.60948 + 8.50938i) q^{75} +(-16.4770 - 28.5391i) q^{76} +(7.88418 - 8.75627i) q^{77} +(-2.74077 + 9.19107i) q^{78} +(-1.25546 - 11.9449i) q^{79} +(14.1823 - 20.7574i) q^{80} +(3.60054 + 8.24840i) q^{81} +5.11682 q^{82} +(12.0272 - 5.35485i) q^{83} +(-5.93973 - 16.8710i) q^{84} +(-0.0260011 + 0.0632637i) q^{85} +(-1.09826 + 1.21974i) q^{86} +(-5.58769 - 1.04616i) q^{87} +(-30.8570 - 34.2701i) q^{88} +(1.99904 + 6.15242i) q^{89} +(9.30707 - 15.1572i) q^{90} +(1.32485 - 4.07747i) q^{91} +(-18.5132 + 8.24263i) q^{92} +(5.14015 + 2.14011i) q^{93} +(0.719149 - 6.84224i) q^{94} +(-5.56867 + 13.5492i) q^{95} +(-23.1523 + 5.51372i) q^{96} +(1.06825 + 10.1637i) q^{97} +(-2.28241 - 7.02454i) q^{98} +(-12.1310 - 12.2198i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.59352	−	0.551270i	−1.83390	−	0.389806i	−0.844560	−	0.535462i	$-0.820138\pi$
$2$	−2.59352	−	0.551270i	−1.83390	−	0.389806i	−0.989335	+	0.145655i	$0.953471\pi$
$3$	0.494958	−	1.65982i	0.285764	−	0.958300i
$3$	0.494958	−	1.65982i	0.285764	−	0.958300i
$4$	4.59535	+	2.04598i	2.29768	+	1.02299i
$5$	−0.527975	−	2.17284i	−0.236118	−	0.971724i
$5$	−0.527975	−	2.17284i	−0.236118	−	0.971724i
$6$	−2.19869	+	4.03193i	−0.897612	+	1.64603i
$7$	1.02644	−	1.77785i	0.387959	−	0.671966i	−0.604215	−	0.796821i	$-0.706513\pi$
$7$	1.02644	−	1.77785i	0.387959	−	0.671966i	0.992175	+	0.124855i	$0.0398467\pi$
$8$	−6.50010	−	4.72260i	−2.29813	−	1.66969i
$9$	−2.51003	−	1.64309i	−0.836678	−	0.547695i
$10$	0.171493	+	5.92636i	0.0542308	+	1.87408i
$11$	5.61416	+	1.19333i	1.69273	+	0.359801i	0.950592	−	0.310443i	$-0.100477\pi$
$11$	5.61416	+	1.19333i	1.69273	+	0.359801i	0.742140	+	0.670244i	$0.233811\pi$
$12$	5.67048	−	6.61480i	1.63693	−	1.90953i
$13$	2.04279	−	0.434208i	0.566568	−	0.120428i	0.0842823	−	0.996442i	$-0.473140\pi$
$13$	2.04279	−	0.434208i	0.566568	−	0.120428i	0.482285	+	0.876014i	$0.339807\pi$
$14$	−3.64218	+	4.04505i	−0.973413	+	1.08109i
$15$	−3.86786	−	0.199118i	−0.998678	−	0.0514120i
$16$	7.52292	+	8.35505i	1.88073	+	2.08876i
$17$	−0.0247468	−	0.0179796i	−0.00600198	−	0.00436070i	0.584780	−	0.811192i	$-0.301181\pi$
$17$	−0.0247468	−	0.0179796i	−0.00600198	−	0.00436070i	−0.590782	+	0.806831i	$0.701181\pi$
$18$	5.60404	+	5.64508i	1.32088	+	1.33056i
$19$	−5.30003	−	3.85070i	−1.21591	−	0.883410i	−0.220156	−	0.975465i	$-0.570657\pi$
$19$	−5.30003	−	3.85070i	−1.21591	−	0.883410i	−0.995754	+	0.0920546i	$0.970657\pi$
$20$	2.01936	−	11.0652i	0.451544	−	2.47425i
$21$	−2.44288	−	2.58368i	−0.533080	−	0.563805i
$22$	−13.9026	−	6.18983i	−2.96404	−	1.31968i
$23$	−2.69572	+	2.99390i	−0.562096	+	0.624271i	−0.955463	−	0.295111i	$-0.904644\pi$
$23$	−2.69572	+	2.99390i	−0.562096	+	0.624271i	0.393367	+	0.919382i	$0.371310\pi$
$24$	−11.0560	+	8.45153i	−2.25679	+	1.72516i
$25$	−4.44248	+	2.29441i	−0.888497	+	0.458883i
$26$	−5.53738			−1.08597
$27$	−3.96959	+	3.35296i	−0.763949	+	0.645277i
$28$	8.35433	−	6.06978i	1.57882	−	1.14708i
$29$	−0.343074	−	3.26413i	−0.0637072	−	0.606134i	−0.979073	−	0.203510i	$-0.934765\pi$
$29$	−0.343074	−	3.26413i	−0.0637072	−	0.606134i	0.915366	−	0.402624i	$-0.131902\pi$
$30$	9.92161	+	2.64865i	1.81143	+	0.483575i
$31$	−0.336018	+	3.19700i	−0.0603507	+	0.574198i	0.922005	+	0.387177i	$0.126550\pi$
$31$	−0.336018	+	3.19700i	−0.0603507	+	0.574198i	−0.982356	+	0.187021i	$0.940117\pi$
$32$	−6.87040	−	11.8999i	−1.21453	−	2.10362i
$33$	4.75948	−	8.72787i	0.828519	−	1.51933i
$34$	0.0542697	+	0.0602726i	0.00930718	+	0.0103367i
$35$	−4.40493	−	1.29164i	−0.744569	−	0.218327i
$36$	−8.17277	−	12.6860i	−1.36213	−	2.11434i
$37$	1.37908	−	4.24438i	0.226720	−	0.697771i	−0.771393	−	0.636359i	$-0.780440\pi$
$37$	1.37908	−	4.24438i	0.226720	−	0.697771i	0.998112	−	0.0614120i	$-0.0195604\pi$
$38$	11.6230	+	12.9086i	1.88549	+	2.09405i
$39$	0.290384	−	3.60558i	0.0464987	−	0.577356i
$40$	−6.82956	+	16.6171i	−1.07985	+	2.62739i
$41$	−1.88764	+	0.401231i	−0.294800	+	0.0626617i	−0.352938	−	0.935647i	$-0.614817\pi$
$41$	−1.88764	+	0.401231i	−0.294800	+	0.0626617i	0.0581374	+	0.998309i	$0.481484\pi$
$42$	4.91135	+	8.04751i	0.757838	+	1.24176i
$43$	0.309512	−	0.536091i	0.0472002	−	0.0817531i	−0.841460	−	0.540319i	$-0.818303\pi$
$43$	0.309512	−	0.536091i	0.0472002	−	0.0817531i	0.888660	+	0.458566i	$0.151637\pi$
$44$	23.3575	+	16.9702i	3.52128	+	2.55836i
$45$	−2.24493	+	6.32142i	−0.334654	+	0.942341i
$46$	8.64184	−	6.27867i	1.27417	−	0.925739i
$47$	0.271227	+	2.58056i	0.0395626	+	0.376413i	0.996332	+	0.0855668i	$0.0272701\pi$
$47$	0.271227	+	2.58056i	0.0395626	+	0.376413i	−0.956770	+	0.290846i	$0.906063\pi$
$48$	17.5915	−	8.35134i	2.53911	−	1.20541i
$49$	1.39282	+	2.41244i	0.198975	+	0.344635i
$50$	12.7865	−	3.50160i	1.80829	−	0.495201i
$51$	−0.0420916	+	0.0321762i	−0.00589400	+	0.00450557i
$52$	10.2757	+	2.18417i	1.42499	+	0.302890i
$53$	−2.83942	+	2.06296i	−0.390024	+	0.283369i	−0.765465	−	0.643477i	$-0.777491\pi$
$53$	−2.83942	+	2.06296i	−0.390024	+	0.283369i	0.375441	+	0.926846i	$0.377491\pi$
$54$	12.1436	−	6.50765i	1.65253	−	0.885579i
$55$	−0.371228	−	12.8287i	−0.0500564	−	1.72983i
$56$	−15.0681	+	6.70874i	−2.01356	+	0.896493i
$57$	−9.01477	+	6.89118i	−1.19404	+	0.912760i
$58$	−0.909647	+	8.65471i	−0.119442	+	1.13642i
$59$	7.94668	−	1.68912i	1.03457	−	0.219904i	0.340826	−	0.940127i	$-0.389293\pi$
$59$	7.94668	−	1.68912i	1.03457	−	0.219904i	0.693744	+	0.720222i	$0.255960\pi$
$60$	−17.3668	−	8.82860i	−2.24204	−	1.13977i
$61$	8.06706	+	1.71471i	1.03288	+	0.219546i	0.693011	−	0.720927i	$-0.256284\pi$
$61$	8.06706	+	1.71471i	1.03288	+	0.219546i	0.339870	+	0.940472i	$0.389617\pi$
$62$	2.63388	−	8.10625i	0.334503	−	1.02949i
$63$	−5.49758	+	2.77594i	−0.692629	+	0.349735i
$64$	4.31002	+	13.2649i	0.538753	+	1.65811i
$65$	−2.02201	−	4.20940i	−0.250799	−	0.522112i
$66$	−17.1552	+	20.0121i	−2.11166	+	2.46332i
$67$	0.0735643	−	0.699918i	0.00898731	−	0.0855086i	−0.989109	−	0.147186i	$-0.952978\pi$
$67$	0.0735643	−	0.699918i	0.00898731	−	0.0855086i	0.998096	+	0.0616775i	$0.0196450\pi$
$68$	−0.0769343	−	0.133254i	−0.00932966	−	0.0161594i
$69$	3.63508	+	5.95627i	0.437612	+	0.717051i
$70$	10.7122	+	5.77819i	1.28036	+	0.690626i
$71$	3.81216	−	2.76970i	0.452421	−	0.328703i	−0.338130	−	0.941099i	$-0.609794\pi$
$71$	3.81216	−	2.76970i	0.452421	−	0.328703i	0.790551	+	0.612397i	$0.209794\pi$
$72$	8.55584	+	22.5341i	1.00831	+	2.65567i
$73$	2.55263	+	7.85620i	0.298763	+	0.919499i	0.981931	+	0.189237i	$0.0606016\pi$
$73$	2.55263	+	7.85620i	0.298763	+	0.919499i	−0.683168	+	0.730261i	$0.739398\pi$
$74$	−5.91647	+	10.2476i	−0.687776	+	1.19126i
$75$	1.60948	+	8.50938i	0.185847	+	0.982579i
$76$	−16.4770	−	28.5391i	−1.89005	−	3.27366i
$77$	7.88418	−	8.75627i	0.898486	−	0.997870i
$78$	−2.74077	+	9.19107i	−0.310331	+	1.04068i
$79$	−1.25546	−	11.9449i	−0.141251	−	1.34391i	−0.803804	−	0.594894i	$-0.797194\pi$
$79$	−1.25546	−	11.9449i	−0.141251	−	1.34391i	0.662554	−	0.749015i	$-0.269473\pi$
$80$	14.1823	−	20.7574i	1.58563	−	2.32075i
$81$	3.60054	+	8.24840i	0.400060	+	0.916489i
$82$	5.11682			0.565058
$83$	12.0272	−	5.35485i	1.32015	−	0.587771i	0.378890	−	0.925442i	$-0.376306\pi$
$83$	12.0272	−	5.35485i	1.32015	−	0.587771i	0.941264	+	0.337671i	$0.109639\pi$
$84$	−5.93973	−	16.8710i	−0.648077	−	1.84078i
$85$	−0.0260011	+	0.0632637i	−0.00282022	+	0.00686191i
$86$	−1.09826	+	1.21974i	−0.118428	+	0.131528i
$87$	−5.58769	−	1.04616i	−0.599063	−	0.112161i
$88$	−30.8570	−	34.2701i	−3.28936	−	3.65321i
$89$	1.99904	+	6.15242i	0.211898	+	0.652155i	0.999359	+	0.0357910i	$0.0113951\pi$
$89$	1.99904	+	6.15242i	0.211898	+	0.652155i	−0.787461	+	0.616364i	$0.788605\pi$
$90$	9.30707	−	15.1572i	0.981051	−	1.59770i
$91$	1.32485	−	4.07747i	0.138882	−	0.427435i
$92$	−18.5132	+	8.24263i	−1.93014	+	0.859353i
$93$	5.14015	+	2.14011i	0.533008	+	0.221919i
$94$	0.719149	−	6.84224i	0.0741745	−	0.705724i
$95$	−5.56867	+	13.5492i	−0.571333	+	1.39012i
$96$	−23.1523	+	5.51372i	−2.36297	+	0.562742i
$97$	1.06825	+	10.1637i	0.108464	+	1.03196i	0.904430	+	0.426623i	$0.140297\pi$
$97$	1.06825	+	10.1637i	0.108464	+	1.03196i	−0.795966	+	0.605342i	$0.793036\pi$
$98$	−2.28241	−	7.02454i	−0.230558	−	0.709585i
$99$	−12.1310	−	12.2198i	−1.21921	−	1.22814i
$100$	−25.1091	+	1.45440i	−2.51091	+	0.145440i
$101$	−1.06922	+	1.85194i	−0.106391	+	0.184275i	−0.914306	−	0.405025i	$-0.867263\pi$
$101$	−1.06922	+	1.85194i	−0.106391	+	0.184275i	0.807915	+	0.589300i	$0.200596\pi$
$102$	0.126903	−	0.0602458i	0.0125653	−	0.00596522i
$103$	−1.10330	−	0.491221i	−0.108711	−	0.0484014i	0.351660	−	0.936128i	$-0.385617\pi$
$103$	−1.10330	−	0.491221i	−0.108711	−	0.0484014i	−0.460372	+	0.887726i	$0.652284\pi$
$104$	−15.3289	−	6.82487i	−1.50312	−	0.669234i
$105$	−4.32415	+	6.67211i	−0.421994	+	0.651131i
$106$	8.50133	−	3.78504i	0.825722	−	0.367635i
$107$	−11.1600			−1.07887			−0.539437	−	0.842026i	$-0.681363\pi$
$107$	−11.1600			−1.07887			−0.539437	+	0.842026i	$0.681363\pi$
$108$	−25.1018	+	7.28631i	−2.41542	+	0.701125i
$109$	2.86190	−	8.80802i	0.274120	−	0.843655i	−0.715331	−	0.698786i	$-0.753724\pi$
$109$	2.86190	−	8.80802i	0.274120	−	0.843655i	0.989451	−	0.144869i	$-0.0462761\pi$
$110$	−6.10930	+	33.4762i	−0.582499	+	3.19183i
$111$	−6.36233	−	4.38982i	−0.603886	−	0.416663i
$112$	22.5759	−	4.79866i	2.13322	−	0.453431i
$113$	8.55043	−	1.81745i	0.804357	−	0.170971i	0.212654	−	0.977128i	$-0.431789\pi$
$113$	8.55043	−	1.81745i	0.804357	−	0.170971i	0.591703	+	0.806156i	$0.298456\pi$
$114$	27.1789	−	12.9029i	2.54553	−	1.20846i
$115$	7.92854	+	4.27667i	0.739340	+	0.398801i
$116$	5.10181	−	15.7018i	0.473691	−	1.45787i
$117$	−5.84091	−	2.26660i	−0.539992	−	0.209547i
$118$	−21.5410			−1.98301
$119$	−0.0573663	+	0.0255411i	−0.00525876	+	0.00234135i
$120$	24.2011	+	19.5606i	2.20925	+	1.78563i
$121$	20.0457	+	8.92494i	1.82234	+	0.811358i
$122$	−19.9768	−	8.89425i	−1.80862	−	0.805248i
$123$	−0.268330	+	3.33175i	−0.0241945	+	0.300413i
$124$	−8.08513	+	14.0039i	−0.726066	+	1.25758i
$125$	7.33092	+	8.44142i	0.655698	+	0.755024i
$126$	15.7884	−	4.16880i	1.40654	−	0.371387i
$127$	−0.411180	−	1.26548i	−0.0364863	−	0.112293i	0.931155	−	0.364625i	$-0.118803\pi$
$127$	−0.411180	−	1.26548i	−0.0364863	−	0.112293i	−0.967641	+	0.252331i	$0.918803\pi$
$128$	−0.992989	−	9.44766i	−0.0877687	−	0.835063i
$129$	−0.736621	−	0.779078i	−0.0648559	−	0.0685940i
$130$	2.92360	+	12.0318i	0.256417	+	1.05526i
$131$	1.77837	−	16.9200i	0.155377	−	1.47831i	−0.587686	−	0.809089i	$-0.699961\pi$
$131$	1.77837	−	16.9200i	0.155377	−	1.47831i	0.743062	−	0.669222i	$-0.233373\pi$
$132$	39.7286	−	30.3698i	3.45793	−	2.64335i
$133$	−12.2862	+	5.47015i	−1.06534	+	0.474322i
$134$	−0.576634	+	1.77470i	−0.0498136	+	0.153310i
$135$	9.38130	+	6.85502i	0.807413	+	0.589986i
$136$	0.0759462	+	0.233738i	0.00651233	+	0.0200429i
$137$	3.32795	+	3.69607i	0.284326	+	0.315776i	0.868342	−	0.495966i	$-0.165186\pi$
$137$	3.32795	+	3.69607i	0.284326	+	0.315776i	−0.584016	+	0.811742i	$0.698519\pi$
$138$	−6.14414	−	17.4516i	−0.523024	−	1.48558i
$139$	−8.86185	+	9.84208i	−0.751652	+	0.834794i	−0.990679	−	0.136219i	$-0.956505\pi$
$139$	−8.86185	+	9.84208i	−0.751652	+	0.834794i	0.239027	+	0.971013i	$0.423172\pi$
$140$	−17.5995	−	14.9479i	−1.48743	−	1.26333i
$141$	4.41752	+	0.827076i	0.372022	+	0.0696524i
$142$	−11.4138	+	5.08174i	−0.957822	+	0.426450i
$143$	11.9867			1.00238
$144$	−5.15473	−	33.3323i	−0.429561	−	2.77769i
$145$	−6.91131	+	2.46883i	−0.573953	+	0.205025i
$146$	−2.28942	−	21.7824i	−0.189474	−	1.80272i
$147$	4.69362	−	1.11779i	0.387123	−	0.0921935i
$148$	15.0213	−	16.6828i	1.23474	−	1.37132i
$149$	7.12203	+	12.3357i	0.583459	+	1.01058i	0.995066	+	0.0992193i	$0.0316345\pi$
$149$	7.12203	+	12.3357i	0.583459	+	1.01058i	−0.411606	+	0.911362i	$0.635032\pi$
$150$	0.516735	−	22.9565i	0.0421913	−	1.87439i
$151$	9.46978	−	16.4021i	0.770640	−	1.33479i	−0.166573	−	0.986029i	$-0.553270\pi$
$151$	9.46978	−	16.4021i	0.770640	−	1.33479i	0.937213	−	0.348758i	$-0.113397\pi$
$152$	16.2654	+	50.0598i	1.31930	+	4.06038i
$153$	0.0325733	+	0.0857905i	0.00263340	+	0.00693575i
$154$	−25.2748	+	18.3632i	−2.03670	+	1.47975i
$155$	7.12399	−	0.957823i	0.572212	−	0.0769342i
$156$	8.71138	−	15.9748i	0.697469	−	1.27901i
$157$	4.74777	+	8.22338i	0.378913	+	0.656297i	0.990904	−	0.134567i	$-0.0429645\pi$
$157$	4.74777	+	8.22338i	0.378913	+	0.656297i	−0.611991	+	0.790865i	$0.709631\pi$
$158$	−3.32881	+	31.6715i	−0.264826	+	2.51965i
$159$	2.01876	+	5.73401i	0.160098	+	0.454737i
$160$	−22.2292	+	21.2111i	−1.75737	+	1.67689i
$161$	2.55571	+	7.86566i	0.201418	+	0.619901i
$162$	−4.79099	−	23.3773i	−0.376415	−	1.83669i
$163$	−2.92027	+	8.98768i	−0.228733	+	0.703969i	0.769158	+	0.639059i	$0.220676\pi$
$163$	−2.92027	+	8.98768i	−0.228733	+	0.703969i	−0.997891	+	0.0649101i	$0.979324\pi$
$164$	−9.49529	−	2.01829i	−0.741458	−	0.157602i
$165$	−21.4772	−	5.73350i	−1.67200	−	0.446352i
$166$	−34.1447	+	7.25768i	−2.65014	+	0.563305i
$167$	1.55302	−	14.7760i	0.120176	−	1.14340i	−0.753689	−	0.657231i	$-0.771727\pi$
$167$	1.55302	−	14.7760i	0.120176	−	1.14340i	0.873865	−	0.486169i	$-0.161606\pi$
$168$	3.67727	+	28.3309i	0.283708	+	2.18578i
$169$	−7.89164	+	3.51359i	−0.607050	+	0.270276i
$170$	0.102310	−	0.149742i	0.00784680	−	0.0114847i
$171$	6.97623	+	18.3738i	0.533486	+	1.40508i
$172$	2.51915	−	1.83027i	0.192083	−	0.139557i
$173$	−6.49513	−	1.38058i	−0.493815	−	0.104964i	−0.0457288	−	0.998954i	$-0.514561\pi$
$173$	−6.49513	−	1.38058i	−0.493815	−	0.104964i	−0.448086	+	0.893990i	$0.647894\pi$
$174$	13.9151	+	5.79357i	1.05490	+	0.439209i
$175$	−0.480830	+	10.2532i	−0.0363473	+	0.775067i
$176$	32.2646	+	55.8839i	2.43203	+	4.21241i
$177$	1.12963	−	14.0261i	0.0849080	−	1.05427i
$178$	−1.79291	−	17.0584i	−0.134385	−	1.27858i
$179$	−3.95088	+	2.87048i	−0.295303	+	0.214550i	−0.725564	−	0.688154i	$-0.758421\pi$
$179$	−3.95088	+	2.87048i	−0.295303	+	0.214550i	0.430262	+	0.902704i	$0.358421\pi$
$180$	−23.2497	+	24.4561i	−1.73293	+	1.82285i
$181$	8.58407	+	6.23669i	0.638049	+	0.463570i	0.859179	−	0.511675i	$-0.170975\pi$
$181$	8.58407	+	6.23669i	0.638049	+	0.463570i	−0.221131	+	0.975244i	$0.570975\pi$
$182$	−5.68381	+	9.84464i	−0.421312	+	0.729734i
$183$	6.83896	−	12.5412i	0.505551	−	0.927072i
$184$	31.6614	−	6.72984i	2.33411	−	0.496130i
$185$	−9.95048	−	0.755600i	−0.731574	−	0.0555528i
$186$	−12.1513	−	8.38402i	−0.890976	−	0.614747i
$187$	−0.117477	−	0.130471i	−0.00859077	−	0.00954101i
$188$	−4.03339	+	12.4135i	−0.294165	+	0.905347i
$189$	1.88650	+	10.4990i	0.137223	+	0.763688i
$190$	21.9117	−	32.0703i	1.58964	−	2.32662i
$191$	−15.9877	−	17.7561i	−1.15683	−	1.28479i	−0.952038	−	0.305981i	$-0.901016\pi$
$191$	−15.9877	−	17.7561i	−1.15683	−	1.28479i	−0.204790	−	0.978806i	$-0.565651\pi$
$192$	24.1507	−	0.588326i	1.74292	−	0.0424588i
$193$	−12.8260	−	22.2154i	−0.923239	−	1.59910i	−0.794369	−	0.607435i	$-0.792198\pi$
$193$	−12.8260	−	22.2154i	−0.923239	−	1.59910i	−0.128870	−	0.991662i	$-0.541135\pi$
$194$	2.83241	−	26.9486i	0.203355	−	1.93479i
$195$	−7.98768	+	1.27270i	−0.572010	+	0.0911400i
$196$	1.46470	+	13.9357i	0.104622	+	0.995409i
$197$	12.4362	−	9.03540i	0.886039	−	0.643745i	−0.0488029	−	0.998808i	$-0.515541\pi$
$197$	12.4362	−	9.03540i	0.886039	−	0.643745i	0.934842	+	0.355063i	$0.115541\pi$
$198$	24.7255	+	38.3798i	1.75717	+	2.72753i
$199$	−3.19201			−0.226275			−0.113138	−	0.993579i	$-0.536090\pi$
$199$	−3.19201			−0.226275			−0.113138	+	0.993579i	$0.536090\pi$
$200$	39.7122	+	6.06615i	2.80807	+	0.428941i
$201$	−1.12533	−	0.468533i	−0.0793746	−	0.0330478i
$202$	3.79395	−	4.21361i	0.266942	−	0.296469i
$203$	−6.15529	−	2.74051i	−0.432017	−	0.192346i
$204$	−0.259258	+	0.0617423i	−0.0181517	+	0.00432283i
$205$	1.86844	+	3.88971i	0.130497	+	0.271669i
$206$	2.59063	+	1.88221i	0.180498	+	0.131140i
$207$	11.6856	−	3.08549i	0.812204	−	0.214457i
$208$	18.9956	+	13.8011i	1.31711	+	0.956934i
$209$	−25.1601	−	27.9431i	−1.74036	−	1.93286i
$210$	14.8929	−	14.9205i	1.02771	−	1.02961i
$211$	−17.7962	+	19.7647i	−1.22514	+	1.36065i	−0.313540	+	0.949575i	$0.601515\pi$
$211$	−17.7962	+	19.7647i	−1.22514	+	1.36065i	−0.911599	+	0.411080i	$0.865152\pi$
$212$	−17.2689	+	3.67062i	−1.18603	+	0.252099i
$213$	−2.71035	−	7.69840i	−0.185710	−	0.527486i
$214$	28.9436	+	6.15215i	1.97854	+	0.420552i
$215$	−1.32826	−	0.389478i	−0.0905863	−	0.0265622i
$216$	41.6374	−	3.04777i	2.83307	−	0.207374i
$217$	5.33890	+	3.87893i	0.362428	+	0.263319i
$218$	−12.2780	+	21.2661i	−0.831570	+	1.44032i
$219$	14.3034	−	0.348439i	0.966531	−	0.0235453i
$220$	24.5414	−	59.7121i	1.65458	−	4.02579i
$221$	−0.0583594	−	0.0259833i	−0.00392568	−	0.00174782i
$222$	14.0809	+	14.8924i	0.945045	+	0.999515i
$223$	16.7193	+	3.55379i	1.11960	+	0.237979i	0.730298	−	0.683129i	$-0.239381\pi$
$223$	16.7193	+	3.55379i	1.11960	+	0.237979i	0.389306	+	0.921108i	$0.372715\pi$
$224$	−28.2083			−1.88475
$225$	14.9207	+	1.54032i	0.994714	+	0.102688i
$226$	−23.1776			−1.54175
$227$	12.0554	+	2.56245i	0.800145	+	0.170076i	0.589798	−	0.807551i	$-0.299207\pi$
$227$	12.0554	+	2.56245i	0.800145	+	0.170076i	0.210347	+	0.977627i	$0.432541\pi$
$228$	−55.5253	+	13.2234i	−3.67725	+	0.875739i
$229$	18.7663	+	8.35530i	1.24011	+	0.552134i	0.918757	−	0.394824i	$-0.129195\pi$
$229$	18.7663	+	8.35530i	1.24011	+	0.552134i	0.321356	+	0.946958i	$0.395861\pi$
$230$	−18.2052	−	15.4624i	−1.20042	−	1.01956i
$231$	−10.6315	−	17.4203i	−0.699504	−	1.14617i
$232$	−13.1852	+	22.8374i	−0.865648	+	1.49935i
$233$	−6.68678	−	4.85823i	−0.438065	−	0.318273i	0.346800	−	0.937939i	$-0.387268\pi$
$233$	−6.68678	−	4.85823i	−0.438065	−	0.318273i	−0.784866	+	0.619666i	$0.787268\pi$
$234$	13.8990	+	9.09838i	0.908606	+	0.594780i
$235$	5.46394	−	1.95181i	0.356428	−	0.127322i
$236$	39.9737	+	8.49667i	2.60207	+	0.553086i
$237$	−20.4479	−	3.82838i	−1.32823	−	0.248680i
$238$	0.162861	−	0.0346171i	0.0105567	−	0.00224389i
$239$	−12.0829	+	13.4195i	−0.781580	+	0.868032i	−0.994026	−	0.109141i	$-0.965190\pi$
$239$	−12.0829	+	13.4195i	−0.781580	+	0.868032i	0.212447	+	0.977173i	$0.431857\pi$
$240$	−27.4340	−	33.8141i	−1.77086	−	2.18269i
$241$	8.67315	+	9.63251i	0.558687	+	0.620484i	0.954631	−	0.297790i	$-0.0962495\pi$
$241$	8.67315	+	9.63251i	0.558687	+	0.620484i	−0.395945	+	0.918274i	$0.629583\pi$
$242$	−47.0690	−	34.1976i	−3.02571	−	2.19831i
$243$	15.4730	−	1.89366i	0.992594	−	0.121478i
$244$	33.5627	+	24.3848i	2.14863	+	1.56107i
$245$	4.50648	−	4.30010i	0.287908	−	0.274723i
$246$	2.53261	−	8.49303i	0.161473	−	0.541496i
$247$	−12.4988	−	5.56484i	−0.795282	−	0.354082i
$248$	17.2823	−	19.1939i	1.09743	−	1.21882i
$249$	−2.93516	−	22.6134i	−0.186008	−	1.43307i
$250$	−14.3594	−	25.9343i	−0.908167	−	1.64023i
$251$	−8.02701			−0.506661			−0.253330	−	0.967380i	$-0.581526\pi$
$251$	−8.02701			−0.506661			−0.253330	+	0.967380i	$0.581526\pi$
$252$	−30.9428	+	1.50847i	−1.94921	+	0.0950247i
$253$	−18.7069	+	13.5914i	−1.17609	+	0.854481i
$254$	0.368782	+	3.50872i	0.0231394	+	0.220157i
$255$	0.0921372	+	0.0744702i	0.00576985	+	0.00466350i
$256$	0.282957	−	2.69215i	0.0176848	−	0.168260i
$257$	6.92454	+	11.9937i	0.431941	+	0.748144i	0.997040	−	0.0768792i	$-0.0244956\pi$
$257$	6.92454	+	11.9937i	0.431941	+	0.748144i	−0.565100	+	0.825023i	$0.691162\pi$
$258$	1.48096	+	2.42663i	0.0922005	+	0.151075i
$259$	−6.13033	−	6.80842i	−0.380920	−	0.423055i
$260$	−0.679467	−	23.4807i	−0.0421388	−	1.45621i
$261$	−4.50212	+	8.75678i	−0.278674	+	0.542031i
$262$	−13.9397	+	42.9021i	−0.861200	+	2.65050i
$263$	−10.4760	−	11.6348i	−0.645979	−	0.717432i	0.327846	−	0.944731i	$-0.393677\pi$
$263$	−10.4760	−	11.6348i	−0.645979	−	0.717432i	−0.973825	+	0.227299i	$0.927011\pi$
$264$	−72.1553	+	34.2549i	−4.44085	+	2.10824i
$265$	5.98162	+	5.08042i	0.367448	+	0.312087i
$266$	34.8799	−	7.41395i	2.13862	−	0.454579i
$267$	11.2014	−	0.272873i	0.685513	−	0.0166996i
$268$	1.77007	−	3.06586i	0.108124	−	0.187277i
$269$	−5.63335	−	4.09287i	−0.343472	−	0.249547i	0.402654	−	0.915352i	$-0.368088\pi$
$269$	−5.63335	−	4.09287i	−0.343472	−	0.249547i	−0.746125	+	0.665806i	$0.768088\pi$
$270$	−20.5516	−	22.9502i	−1.25073	−	1.39671i
$271$	14.6785	−	10.6646i	0.891658	−	0.647828i	−0.0446517	−	0.999003i	$-0.514218\pi$
$271$	14.6785	−	10.6646i	0.891658	−	0.647828i	0.936310	+	0.351175i	$0.114218\pi$
$272$	−0.0359478	−	0.342020i	−0.00217965	−	0.0207380i
$273$	−6.11214	−	4.21719i	−0.369923	−	0.255236i
$274$	−6.59358	−	11.4204i	−0.398333	−	0.689933i
$275$	−27.6788	+	7.57987i	−1.66909	+	0.457083i
$276$	4.51805	+	34.8085i	0.271954	+	2.09522i
$277$	15.3604	+	3.26495i	0.922916	+	0.196172i	0.644779	−	0.764369i	$-0.276950\pi$
$277$	15.3604	+	3.26495i	0.922916	+	0.196172i	0.278138	+	0.960541i	$0.410283\pi$
$278$	28.4090	−	20.6404i	1.70386	−	1.23793i
$279$	6.09636	−	7.47247i	0.364980	−	0.447365i
$280$	22.5326	+	29.1985i	1.34658	+	1.74494i
$281$	−17.6073	+	7.83927i	−1.05036	+	0.467651i	−0.857988	−	0.513670i	$-0.828286\pi$
$281$	−17.6073	+	7.83927i	−1.05036	+	0.467651i	−0.192375	+	0.981322i	$0.561619\pi$
$282$	−11.0010	−	4.58028i	−0.655099	−	0.272752i
$283$	−0.661298	+	6.29183i	−0.0393101	+	0.374010i	0.957127	+	0.289669i	$0.0935453\pi$
$283$	−0.661298	+	6.29183i	−0.0393101	+	0.374010i	−0.996437	+	0.0843413i	$0.973121\pi$
$284$	23.1850	−	4.92812i	1.37578	−	0.292430i
$285$	19.7330	+	15.9493i	1.16888	+	0.944754i
$286$	−31.0877	−	6.60790i	−1.83825	−	0.390733i
$287$	−1.22423	+	3.76779i	−0.0722640	+	0.222406i
$288$	−2.30758	+	41.1578i	−0.135976	+	2.42525i
$289$	−5.25300	−	16.1671i	−0.309000	−	0.951004i
$290$	19.2856	−	2.59296i	1.13249	−	0.152264i
$291$	17.3986	+	3.25749i	1.01993	+	0.190957i
$292$	−4.34340	+	41.3247i	−0.254178	+	2.41834i
$293$	11.3054	+	19.5815i	0.660467	+	1.14396i	0.980493	+	0.196554i	$0.0629752\pi$
$293$	11.3054	+	19.5815i	0.660467	+	1.14396i	−0.320026	+	0.947409i	$0.603691\pi$
$294$	−12.7892	+	0.311553i	−0.745881	+	0.0181702i
$295$	−7.86584	−	16.3751i	−0.457967	−	0.953393i
$296$	−29.0086	+	21.0760i	−1.68609	+	1.22502i
$297$	−26.2871	+	14.0870i	−1.52533	+	0.817412i
$298$	−11.6708	−	35.9191i	−0.676072	−	2.08074i
$299$	−4.20681	+	7.28640i	−0.243286	+	0.421384i
$300$	−10.0139	+	42.3966i	−0.578153	+	2.44777i
$301$	−0.635394	−	1.10053i	−0.0366235	−	0.0634338i
$302$	−33.6021	+	37.3189i	−1.93358	+	2.14746i
$303$	2.54468	+	2.69134i	0.146188	+	0.154614i
$304$	−7.69894	−	73.2505i	−0.441564	−	4.20121i
$305$	−0.533423	−	18.4338i	−0.0305437	−	1.05551i
$306$	−0.0371858	−	0.240456i	−0.00212577	−	0.0137460i
$307$	1.98814			0.113469			0.0567346	−	0.998389i	$-0.481931\pi$
$307$	1.98814			0.113469			0.0567346	+	0.998389i	$0.481931\pi$
$308$	54.1458	−	24.1072i	3.08524	−	1.37364i
$309$	−1.36143	+	1.58815i	−0.0774489	+	0.0903468i
$310$	−19.0042	−	1.44310i	−1.07937	−	0.0819628i
$311$	5.89093	−	6.54254i	0.334044	−	0.370993i	−0.552600	−	0.833447i	$-0.686364\pi$
$311$	5.89093	−	6.54254i	0.334044	−	0.370993i	0.886644	+	0.462454i	$0.153031\pi$
$312$	−18.9152	+	22.0653i	−1.07086	+	1.24920i
$313$	21.9681	+	24.3980i	1.24171	+	1.37906i	0.898009	+	0.439977i	$0.145013\pi$
$313$	21.9681	+	24.3980i	1.24171	+	1.37906i	0.343699	+	0.939080i	$0.388320\pi$
$314$	−7.78014	−	23.9448i	−0.439059	−	1.35128i
$315$	8.93426	+	10.4797i	0.503388	+	0.590466i
$316$	18.6698	−	57.4598i	1.05026	−	3.23237i
$317$	14.2770	−	6.35653i	0.801876	−	0.357018i	0.0354668	−	0.999371i	$-0.488708\pi$
$317$	14.2770	−	6.35653i	0.801876	−	0.357018i	0.766409	+	0.642353i	$0.222042\pi$
$318$	−2.07470	−	15.9841i	−0.116343	−	0.896347i
$319$	1.96910	−	18.7347i	0.110249	−	1.04894i
$320$	26.5469	−	16.3685i	1.48402	−	0.915029i
$321$	−5.52371	+	18.5236i	−0.308303	+	1.03389i
$322$	−2.29218	−	21.8086i	−0.127738	−	1.21535i
$323$	0.0619248	+	0.190585i	0.00344559	+	0.0106044i
$324$	−0.330319	+	45.2710i	−0.0183511	+	2.51505i
$325$	−8.07880	+	6.61596i	−0.448131	+	0.366988i
$326$	12.5284	−	21.6999i	0.693885	−	1.20184i
$327$	−13.2032	−	9.10984i	−0.730141	−	0.503776i
$328$	14.1647	+	6.30653i	0.782115	+	0.348220i
$329$	4.86625	+	2.16660i	0.268285	+	0.119448i
$330$	52.5408	+	26.7097i	2.89227	+	1.47032i
$331$	−19.7512	+	8.79380i	−1.08562	+	0.483351i	−0.869963	−	0.493117i	$-0.835857\pi$
$331$	−19.7512	+	8.79380i	−1.08562	+	0.483351i	−0.215662	+	0.976468i	$0.569191\pi$
$332$	66.2251			3.63457
$333$	−10.4354	+	8.38758i	−0.571857	+	0.459637i
$334$	−12.1733	+	37.4657i	−0.666095	+	2.05003i
$335$	−1.55965	+	0.209696i	−0.0852128	+	0.0114569i
$336$	3.20919	−	39.8472i	0.175076	−	2.17384i
$337$	−13.9270	+	2.96027i	−0.758651	+	0.161256i	−0.570967	−	0.820973i	$-0.693431\pi$
$337$	−13.9270	+	2.96027i	−0.758651	+	0.161256i	−0.187684	+	0.982229i	$0.560098\pi$
$338$	22.4041	−	4.76213i	1.21862	−	0.259026i
$339$	1.21545	−	15.0918i	0.0660143	−	0.819673i
$340$	−0.248921	+	0.237521i	−0.0134996	+	0.0128814i
$341$	−5.70153	+	17.5475i	−0.308755	+	0.950250i
$342$	−7.96409	−	51.4985i	−0.430648	−	2.78472i
$343$	20.0888			1.08470
$344$	−4.54360	+	2.02294i	−0.244974	+	0.109070i
$345$	11.0228	−	11.0432i	0.593448	−	0.594547i
$346$	16.0842	+	7.16113i	0.864690	+	0.384985i
$347$	17.3445	+	7.72226i	0.931100	+	0.414553i	0.815509	−	0.578744i	$-0.196457\pi$
$347$	17.3445	+	7.72226i	0.931100	+	0.414553i	0.115591	+	0.993297i	$0.463124\pi$
$348$	−23.5370	−	16.2398i	−1.26171	−	0.870545i
$349$	−1.26140	+	2.18481i	−0.0675211	+	0.116950i	−0.897810	−	0.440384i	$-0.854842\pi$
$349$	−1.26140	+	2.18481i	−0.0675211	+	0.116950i	0.830288	+	0.557334i	$0.188176\pi$
$350$	6.89930	−	26.3267i	0.368783	−	1.40722i
$351$	−6.65316	+	8.57301i	−0.355119	+	0.457594i
$352$	−24.3711	−	75.0065i	−1.29898	−	3.99786i
$353$	−0.463649	−	4.41132i	−0.0246775	−	0.234791i	−0.999908	−	0.0135978i	$-0.995672\pi$
$353$	−0.463649	−	4.41132i	−0.0246775	−	0.234791i	0.975230	−	0.221193i	$-0.0709951\pi$
$354$	−10.6619	+	35.7543i	−0.566673	+	1.90032i
$355$	−8.03085	−	6.82090i	−0.426233	−	0.362016i
$356$	−3.40144	+	32.3625i	−0.180276	+	1.71521i
$357$	0.0139999	+	0.107860i	0.000740954	+	0.00570855i
$358$	11.8291	−	5.26665i	0.625187	−	0.278351i
$359$	−10.5484	+	32.4646i	−0.556722	+	1.71341i	0.134630	+	0.990896i	$0.457015\pi$
$359$	−10.5484	+	32.4646i	−0.556722	+	1.71341i	−0.691352	+	0.722518i	$0.742985\pi$
$360$	44.4457	−	30.4879i	2.34250	−	1.60685i
$361$	7.39111	+	22.7475i	0.389006	+	1.19724i
$362$	−18.8248	−	20.9071i	−0.989412	−	1.09885i
$363$	24.7356	−	28.8550i	1.29828	−	1.51449i
$364$	14.4306	−	16.0268i	0.756368	−	0.840032i
$365$	15.7226	−	9.69435i	0.822956	−	0.507425i
$366$	−24.6506	+	28.7557i	−1.28851	+	1.50309i
$367$	9.93344	−	4.42265i	0.518521	−	0.230861i	−0.130753	−	0.991415i	$-0.541739\pi$
$367$	9.93344	−	4.42265i	0.518521	−	0.230861i	0.649274	+	0.760554i	$0.275073\pi$
$368$	−45.2939			−2.36111
$369$	5.39730	+	2.09445i	0.280972	+	0.109033i
$370$	25.3902	+	7.44506i	1.31997	+	0.387050i
$371$	0.753133	+	7.16558i	0.0391007	+	0.372018i
$372$	19.2422	+	20.3512i	0.997659	+	1.05516i
$373$	−16.2843	+	18.0855i	−0.843168	+	0.936433i	−0.998678	−	0.0514011i	$-0.983631\pi$
$373$	−16.2843	+	18.0855i	−0.843168	+	0.936433i	0.155510	+	0.987834i	$0.450298\pi$
$374$	0.232754	+	0.403141i	0.0120354	+	0.0208459i
$375$	17.6398	−	7.98990i	0.910914	−	0.412597i
$376$	10.4239	−	18.0548i	0.537573	−	0.931104i
$377$	−2.11814	−	6.51896i	−0.109090	−	0.335744i
$378$	0.895084	−	28.2693i	0.0460382	−	1.45401i
$379$	−4.12810	+	2.99924i	−0.212046	+	0.154061i	−0.688739	−	0.725009i	$-0.741835\pi$
$379$	−4.12810	+	2.99924i	−0.212046	+	0.154061i	0.476693	+	0.879070i	$0.341835\pi$
$380$	−53.3114	+	50.8699i	−2.73482	+	2.60957i
$381$	−2.30399	+	0.0561268i	−0.118037	+	0.00287546i
$382$	31.6759	+	54.8643i	1.62068	+	2.80710i
$383$	2.14547	−	20.4128i	0.109628	−	1.04304i	−0.791997	−	0.610525i	$-0.790958\pi$
$383$	2.14547	−	20.4128i	0.109628	−	1.04304i	0.901625	−	0.432518i	$-0.142375\pi$
$384$	−16.1729	−	3.02800i	−0.825322	−	0.154522i
$385$	−23.1886	−	12.5080i	−1.18180	−	0.637466i
$386$	21.0179	+	64.6866i	1.06979	+	3.29246i
$387$	−1.65773	+	0.837051i	−0.0842671	+	0.0425497i
$388$	−15.8857	+	48.8913i	−0.806476	+	2.48208i
$389$	11.6762	+	2.48186i	0.592008	+	0.125835i	0.494167	−	0.869367i	$-0.335473\pi$
$389$	11.6762	+	2.48186i	0.592008	+	0.125835i	0.0978410	+	0.995202i	$0.468806\pi$
$390$	21.4178	+	1.10259i	1.08453	+	0.0558319i
$391$	0.120540	−	0.0256215i	0.00609595	−	0.00129573i
$392$	2.33950	−	22.2589i	0.118163	−	1.12424i
$393$	−27.2041	−	11.3265i	−1.37226	−	0.571346i
$394$	−37.2343	+	16.5778i	−1.87584	+	0.835177i
$395$	−25.2916	+	9.03455i	−1.27256	+	0.454577i
$396$	−30.7446	−	80.9742i	−1.54498	−	4.06911i
$397$	−11.3426	+	8.24087i	−0.569268	+	0.413597i	−0.834839	−	0.550494i	$-0.814439\pi$
$397$	−11.3426	+	8.24087i	−0.569268	+	0.413597i	0.265571	+	0.964091i	$0.414439\pi$
$398$	8.27853	+	1.75966i	0.414965	+	0.0882036i
$399$	2.99836	+	23.1004i	0.150106	+	1.15646i
$400$	−52.5904	−	19.8565i	−2.62952	−	0.992825i
$401$	−0.970609	−	1.68114i	−0.0484699	−	0.0839523i	0.840773	−	0.541388i	$-0.182101\pi$
$401$	−0.970609	−	1.68114i	−0.0484699	−	0.0839523i	−0.889242	+	0.457436i	$0.848768\pi$
$402$	2.66028	+	1.83551i	0.132682	+	0.0915469i
$403$	0.701749	+	6.67670i	0.0349566	+	0.332590i
$404$	−8.70247	+	6.32271i	−0.432964	+	0.314567i
$405$	16.0215	−	12.1784i	0.796113	−	0.605148i
$406$	14.4531	+	10.5008i	0.717296	+	0.521146i
$407$	12.8073	−	22.1829i	0.634835	−	1.09957i
$408$	0.425555	−	0.0103668i	0.0210681	−	0.000513233i
$409$	−10.7137	+	2.27726i	−0.529757	+	0.112603i	−0.465022	−	0.885299i	$-0.653953\pi$
$409$	−10.7137	+	2.27726i	−0.529757	+	0.112603i	−0.0647348	+	0.997903i	$0.520620\pi$
$410$	−2.70156	−	11.1180i	−0.133420	−	0.549081i
$411$	7.78202	−	3.69442i	0.383859	−	0.182232i
$412$	−4.06502	−	4.51467i	−0.200269	−	0.222422i
$413$	5.15382	−	15.8618i	0.253603	−	0.780509i
$414$	−32.0077	+	1.56038i	−1.57309	+	0.0766887i
$415$	−17.9853	−	23.3059i	−0.882863	−	1.14404i
$416$	−19.2018	−	21.3258i	−0.941446	−	1.04558i
$417$	11.9499	+	19.5805i	0.585188	+	0.958862i
$418$	49.8489	+	86.3409i	2.43819	+	4.22307i
$419$	−1.73963	+	16.5515i	−0.0849865	+	0.808593i	0.866142	+	0.499798i	$0.166592\pi$
$419$	−1.73963	+	16.5515i	−0.0849865	+	0.808593i	−0.951129	+	0.308795i	$0.900074\pi$
$420$	−33.5220	+	21.8136i	−1.63571	+	1.06439i
$421$	−0.804767	−	7.65685i	−0.0392220	−	0.373172i	−0.996473	−	0.0839137i	$-0.973258\pi$
$421$	−0.804767	−	7.65685i	−0.0392220	−	0.373172i	0.957251	−	0.289258i	$-0.0934087\pi$
$422$	57.0504	−	41.4495i	2.77717	−	2.01773i
$423$	3.55928	−	6.92294i	0.173058	−	0.336605i
$424$	28.1990			1.36946
$425$	0.151190	+	0.0230947i	0.00733379	+	0.00112026i
$426$	2.78546	+	21.4601i	0.134956	+	1.03975i
$427$	11.3289	−	12.5820i	0.548243	−	0.608886i
$428$	−51.2840	−	22.8331i	−2.47890	−	1.10368i
$429$	5.93290	−	19.8958i	0.286443	−	0.960578i
$430$	3.23015	+	1.74235i	0.155772	+	0.0840234i
$431$	−26.1475	−	18.9973i	−1.25948	−	0.915066i	−0.260748	−	0.965407i	$-0.583969\pi$
$431$	−26.1475	−	18.9973i	−1.25948	−	0.915066i	−0.998732	+	0.0503406i	$0.983969\pi$
$432$	−57.8771	−	7.94211i	−2.78461	−	0.382115i
$433$	−25.4573	−	18.4958i	−1.22340	−	0.888852i	−0.227022	−	0.973890i	$-0.572899\pi$
$433$	−25.4573	−	18.4958i	−1.22340	−	0.888852i	−0.996378	+	0.0850377i	$0.972899\pi$
$434$	−11.7082	−	13.0033i	−0.562011	−	0.624177i
$435$	0.677016	+	12.6935i	0.0324604	+	0.608608i
$436$	31.1725	−	34.6206i	1.49289	−	1.65802i
$437$	25.8160	−	5.48736i	1.23495	−	0.262496i
$438$	−37.2881	−	6.98132i	−1.78170	−	0.333580i
$439$	17.7158	+	3.76561i	0.845530	+	0.179723i	0.610254	−	0.792206i	$-0.291067\pi$
$439$	17.7158	+	3.76561i	0.845530	+	0.179723i	0.235276	+	0.971929i	$0.424401\pi$
$440$	−58.1719	+	85.1411i	−2.77324	+	4.05894i
$441$	0.467812	−	8.34384i	0.0222767	−	0.397326i
$442$	0.137032	+	0.0995598i	0.00651797	+	0.00473558i
$443$	−19.3559	+	33.5254i	−0.919626	+	1.59284i	−0.119642	+	0.992817i	$0.538175\pi$
$443$	−19.3559	+	33.5254i	−0.919626	+	1.59284i	−0.799984	+	0.600022i	$0.795159\pi$
$444$	−20.2557	−	33.1900i	−0.961292	−	1.57513i
$445$	12.3128	−	7.59193i	0.583682	−	0.359892i
$446$	−41.4026	−	18.4336i	−1.96047	−	0.872858i
$447$	24.0002	−	5.71566i	1.13517	−	0.270342i
$448$	28.0070	+	5.95308i	1.32321	+	0.281256i
$449$	−4.76841			−0.225035			−0.112518	−	0.993650i	$-0.535891\pi$
$449$	−4.76841			−0.225035			−0.112518	+	0.993650i	$0.535891\pi$
$450$	−37.8480	−	12.2202i	−1.78417	−	0.576065i
$451$	−11.0763			−0.521564
$452$	43.0107	+	9.14221i	2.02305	+	0.430014i
$453$	−22.5375	−	23.8365i	−1.05891	−	1.11994i
$454$	−29.8533	−	13.2915i	−1.40109	−	0.623803i
$455$	−9.55918	−	0.725886i	−0.448141	−	0.0340301i
$456$	91.1411	−	2.22026i	4.26807	−	0.103973i
$457$	2.37786	−	4.11857i	0.111232	−	0.192659i	−0.805035	−	0.593227i	$-0.797854\pi$
$457$	2.37786	−	4.11857i	0.111232	−	0.192659i	0.916267	+	0.400568i	$0.131187\pi$
$458$	−44.0648	−	32.0149i	−2.05901	−	1.49596i
$459$	0.158520	−	0.0116033i	0.00739906	−	0.000541595i
$460$	27.6845	+	35.8744i	1.29079	+	1.67265i
$461$	−8.66085	−	1.84092i	−0.403376	−	0.0857402i	0.00175591	−	0.999998i	$-0.499441\pi$
$461$	−8.66085	−	1.84092i	−0.403376	−	0.0857402i	−0.405132	+	0.914258i	$0.632774\pi$
$462$	17.9698	+	51.0408i	0.836030	+	2.37463i
$463$	−1.51448	+	0.321912i	−0.0703838	+	0.0149605i	−0.242969	−	0.970034i	$-0.578121\pi$
$463$	−1.51448	+	0.321912i	−0.0703838	+	0.0149605i	0.172585	+	0.984995i	$0.444788\pi$
$464$	24.6911	−	27.4222i	1.14625	−	1.27304i
$465$	1.93625	−	12.2986i	0.0897916	−	0.570336i
$466$	14.6641	+	16.2861i	0.679301	+	0.754440i
$467$	27.9575	+	20.3123i	1.29372	+	0.939942i	0.999873	−	0.0159111i	$-0.00506487\pi$
$467$	27.9575	+	20.3123i	1.29372	+	0.939942i	0.293846	+	0.955853i	$0.405065\pi$
$468$	−22.2036	−	22.3662i	−1.02636	−	1.03388i
$469$	−1.16884	−	0.849213i	−0.0539721	−	0.0392130i
$470$	−15.2468	+	2.04994i	−0.703283	+	0.0945567i
$471$	15.9993	−	3.81024i	0.737210	−	0.175567i
$472$	−59.6312	−	26.5495i	−2.74475	−	1.22204i
$473$	2.37738	−	2.64035i	0.109312	−	0.121403i
$474$	50.9215	+	21.2013i	2.33890	+	0.973807i
$475$	32.3804	+	4.94619i	1.48571	+	0.226947i
$476$	−0.315875			−0.0144781
$477$	10.5167	−	0.512689i	0.481524	−	0.0234744i
$478$	38.7350	−	28.1427i	1.77170	−	1.28722i
$479$	2.55709	+	24.3290i	0.116836	+	1.11162i	0.883129	+	0.469131i	$0.155433\pi$
$479$	2.55709	+	24.3290i	0.116836	+	1.11162i	−0.766293	+	0.642492i	$0.777901\pi$
$480$	24.2043	+	47.3951i	1.10477	+	2.16328i
$481$	0.974229	−	9.26917i	0.0444210	−	0.422638i
$482$	−17.1839	−	29.7633i	−0.782704	−	1.35568i
$483$	14.3206	−	0.348859i	0.651609	−	0.0158736i
$484$	73.8570	+	82.0265i	3.35714	+	3.72848i
$485$	21.5200	−	7.68730i	0.977175	−	0.349062i
$486$	−41.1735	−	3.61855i	−1.86767	−	0.164141i
$487$	1.67643	−	5.15952i	0.0759663	−	0.233800i	−0.905862	−	0.423574i	$-0.860775\pi$
$487$	1.67643	−	5.15952i	0.0759663	−	0.233800i	0.981828	+	0.189774i	$0.0607754\pi$
$488$	−44.3388	−	49.2432i	−2.00712	−	2.22914i
$489$	13.4726	+	9.29566i	0.609250	+	0.420364i
$490$	−14.0582	+	8.66810i	−0.635083	+	0.391585i
$491$	−21.5355	+	4.57751i	−0.971883	+	0.206580i	−0.666381	−	0.745611i	$-0.732158\pi$
$491$	−21.5355	+	4.57751i	−0.971883	+	0.206580i	−0.305502	+	0.952191i	$0.598824\pi$
$492$	−8.04977	+	14.7616i	−0.362912	+	0.665502i
$493$	−0.0501978	+	0.0869451i	−0.00226080	+	0.00391581i
$494$	29.3482	+	21.3227i	1.32044	+	0.959356i
$495$	−20.1469	+	32.8105i	−0.905535	+	1.47472i
$496$	−29.2390	+	21.2433i	−1.31287	+	0.953854i
$497$	−1.01115	−	9.62041i	−0.0453561	−	0.431534i
$498$	−4.85370	+	60.2664i	−0.217499	+	2.70060i
$499$	−20.3177	−	35.1912i	−0.909544	−	1.57538i	−0.814699	−	0.579884i	$-0.803098\pi$
$499$	−20.3177	−	35.1912i	−0.909544	−	1.57538i	−0.0948451	−	0.995492i	$-0.530236\pi$
$500$	16.4172	+	53.7902i	0.734198	+	2.40557i
$501$	−23.7569	−	9.89122i	−1.06138	−	0.441907i
$502$	20.8182	+	4.42505i	0.929162	+	0.197500i
$503$	32.8363	−	23.8569i	1.46410	−	1.06373i	0.481825	−	0.876268i	$-0.339974\pi$
$503$	32.8363	−	23.8569i	1.46410	−	1.06373i	0.982272	−	0.187461i	$-0.0600258\pi$
$504$	48.8444	+	7.91896i	2.17570	+	0.352739i
$505$	4.58849	+	1.34546i	0.204185	+	0.0598723i
$506$	56.0092	−	24.9369i	2.48991	−	1.10858i
$507$	1.92591	+	14.8378i	0.0855326	+	0.658971i
$508$	0.699637	−	6.65660i	0.0310414	−	0.295339i
$509$	43.4149	−	9.22813i	1.92433	−	0.409030i	0.924737	−	0.380606i	$-0.124284\pi$
$509$	43.4149	−	9.22813i	1.92433	−	0.409030i	0.999596	−	0.0284240i	$-0.00904887\pi$
$510$	−0.197906	−	0.243932i	−0.00876344	−	0.0108015i
$511$	16.5873	+	3.52574i	0.733779	+	0.155970i
$512$	−8.08909	+	24.8957i	−0.357491	+	1.10024i
$513$	33.9502	−	2.48508i	1.49894	−	0.109719i
$514$	−11.3472	−	34.9231i	−0.500503	−	1.54039i
$515$	−0.484830	+	2.65665i	−0.0213642	+	0.117066i
$516$	−1.79105	−	5.08725i	−0.0788468	−	0.223954i
$517$	−1.55673	+	14.8113i	−0.0684650	+	0.651401i
$518$	12.1459	+	21.0372i	0.533658	+	0.924323i
$519$	−5.50633	+	10.0974i	−0.241701	+	0.443228i
$520$	−6.73608	+	36.9107i	−0.295397	+	1.61864i
$521$	−7.98161	+	5.79898i	−0.349681	+	0.254058i	−0.748735	−	0.662869i	$-0.769338\pi$
$521$	−7.98161	+	5.79898i	−0.349681	+	0.254058i	0.399054	+	0.916927i	$0.369338\pi$
$522$	16.5037	−	20.2290i	0.722346	−	0.885399i
$523$	−2.46257	−	7.57903i	−0.107681	−	0.331408i	0.882669	−	0.469994i	$-0.155744\pi$
$523$	−2.46257	−	7.57903i	−0.107681	−	0.331408i	−0.990350	+	0.138587i	$0.955744\pi$
$524$	42.7904	−	74.1151i	1.86931	−	3.23773i
$525$	16.7805	+	5.87298i	0.732360	+	0.256318i
$526$	20.7558	+	35.9502i	0.904998	+	1.56750i
$527$	0.0657962	−	0.0730741i	0.00286613	−	0.00318316i
$528$	108.727	−	25.8934i	4.73174	−	1.12687i
$529$	0.707623	+	6.73259i	0.0307662	+	0.292721i
$530$	−12.7128	−	16.4736i	−0.552208	−	0.715569i
$531$	−22.7218	−	8.81732i	−0.986042	−	0.382639i
$532$	−67.6511			−2.93305
$533$	−3.68184	+	1.63926i	−0.159478	+	0.0710042i
$534$	−29.2014	−	5.46728i	−1.26367	−	0.236592i
$535$	5.89218	+	24.2488i	0.254741	+	1.04837i
$536$	−3.78360	+	4.20212i	−0.163427	+	0.181504i
$537$	2.80898	+	7.97853i	0.121216	+	0.344299i
$538$	12.3539	+	13.7204i	0.532616	+	0.591530i
$539$	4.94071	+	15.2059i	0.212811	+	0.654966i
$540$	29.0851	+	50.6952i	1.25162	+	2.18157i
$541$	−3.72498	+	11.4643i	−0.160149	+	0.492889i	−0.998646	−	0.0520177i	$-0.983435\pi$
$541$	−3.72498	+	11.4643i	−0.160149	+	0.492889i	0.838497	+	0.544906i	$0.183435\pi$
$542$	−43.9481	+	19.5670i	−1.88773	+	0.840474i
$543$	14.6006	−	11.1611i	0.626570	−	0.478971i
$544$	−0.0439348	+	0.418011i	−0.00188369	+	0.0179221i
$545$	−20.6494	−	1.56804i	−0.884525	−	0.0671673i
$546$	13.5271	+	14.3068i	0.578908	+	0.612275i
$547$	−0.130795	−	1.24443i	−0.00559239	−	0.0532080i	0.991370	−	0.131095i	$-0.0418493\pi$
$547$	−0.130795	−	1.24443i	−0.00559239	−	0.0532080i	−0.996962	+	0.0778871i	$0.975183\pi$
$548$	7.73103	+	23.7937i	0.330253	+	1.01642i
$549$	−17.4312	−	17.5588i	−0.743945	−	0.749393i
$550$	75.9640	−	4.40007i	3.23912	−	0.187620i
$551$	−10.7509	+	18.6211i	−0.458003	+	0.793284i
$552$	4.50070	−	55.8834i	0.191562	−	2.37855i
$553$	−22.5250	−	10.0288i	−0.957860	−	0.426467i
$554$	−38.0376	−	16.9354i	−1.61606	−	0.719518i
$555$	−6.17923	+	16.1421i	−0.262294	+	0.685192i
$556$	−60.8600	+	27.0966i	−2.58104	+	1.14915i
$557$	−44.8687			−1.90115			−0.950574	−	0.310498i	$-0.899504\pi$
$557$	−44.8687			−1.90115			−0.950574	+	0.310498i	$0.899504\pi$
$558$	−19.9304	+	16.0193i	−0.843720	+	0.678150i
$559$	0.399493	−	1.22951i	0.0168967	−	0.0520028i
$560$	−22.3463	−	46.5203i	−0.944302	−	1.96584i
$561$	−0.274706	+	0.130413i	−0.0115981	+	0.00550606i
$562$	49.9864	−	10.6249i	2.10855	−	0.448186i
$563$	−38.3393	+	8.14927i	−1.61581	+	0.343451i	−0.925112	−	0.379693i	$-0.876029\pi$
$563$	−38.3393	+	8.14927i	−1.61581	+	0.343451i	−0.690697	+	0.723144i	$0.742696\pi$
$564$	18.6079	+	12.8389i	0.783533	+	0.540614i
$565$	−8.46345	−	17.6192i	−0.356060	−	0.741244i
$566$	5.18358	−	15.9534i	0.217882	−	0.670573i
$567$	18.3602	+	2.06528i	0.771056	+	0.0867338i
$568$	−37.8596			−1.58855
$569$	−23.6982	+	10.5511i	−0.993480	+	0.442326i	−0.838093	−	0.545528i	$-0.816329\pi$
$569$	−23.6982	+	10.5511i	−0.993480	+	0.442326i	−0.155387	+	0.987854i	$0.549663\pi$
$570$	−42.3856	−	52.2430i	−1.77534	−	2.18822i
$571$	9.92558	+	4.41915i	0.415373	+	0.184936i	0.603773	−	0.797157i	$-0.293663\pi$
$571$	9.92558	+	4.41915i	0.415373	+	0.184936i	−0.188400	+	0.982092i	$0.560330\pi$
$572$	55.0831	+	24.5246i	2.30314	+	1.02542i
$573$	−37.3852	+	17.7482i	−1.56179	+	0.741442i
$574$	5.25213	−	9.09696i	0.219220	−	0.379700i
$575$	5.10644	−	19.4854i	0.212953	−	0.812599i
$576$	10.9770	−	40.3771i	0.457376	−	1.68238i
$577$	−1.77776	−	5.47137i	−0.0740090	−	0.227776i	0.907208	−	0.420681i	$-0.138209\pi$
$577$	−1.77776	−	5.47137i	−0.0740090	−	0.227776i	−0.981217	+	0.192905i	$0.938209\pi$
$578$	4.71134	+	44.8254i	0.195966	+	1.86449i
$579$	−43.2219	+	10.2933i	−1.79624	+	0.427776i
$580$	−36.8111	−	2.79529i	−1.52850	−	0.116068i
$581$	2.82510	−	26.8790i	0.117205	−	1.11513i
$582$	−43.3280	−	18.0397i	−1.79600	−	0.747770i
$583$	−18.4027	+	8.19342i	−0.762163	+	0.339337i
$584$	20.5093	−	63.1211i	0.848680	−	2.61197i
$585$	−1.84110	+	13.8881i	−0.0761202	+	0.574201i
$586$	−18.5260	−	57.0173i	−0.765304	−	2.35536i
$587$	4.62878	+	5.14078i	0.191050	+	0.212183i	0.831058	−	0.556186i	$-0.187736\pi$
$587$	4.62878	+	5.14078i	0.191050	+	0.212183i	−0.640008	+	0.768368i	$0.721069\pi$
$588$	23.8558	+	4.46644i	0.983797	+	0.184193i
$589$	14.0916	−	15.6503i	0.580634	−	0.644859i
$590$	11.3731	+	46.8052i	0.468224	+	1.92694i
$591$	−8.84180	−	25.1140i	−0.363703	−	1.03305i
$592$	45.8367	−	20.4078i	1.88388	−	0.838756i
$593$	18.6586			0.766219			0.383109	−	0.923703i	$-0.374853\pi$
$593$	18.6586			0.766219			0.383109	+	0.923703i	$0.374853\pi$
$594$	75.9418	−	22.0437i	3.11593	−	0.904463i
$595$	0.0857849	+	0.111163i	0.00351684	+	0.00455723i
$596$	7.48957	+	71.2585i	0.306785	+	2.91886i
$597$	−1.57991	+	5.29817i	−0.0646613	+	0.216840i
$598$	14.9272	−	16.5783i	0.610419	−	0.677939i
$599$	−3.61776	−	6.26614i	−0.147818	−	0.256027i	0.782603	−	0.622521i	$-0.213892\pi$
$599$	−3.61776	−	6.26614i	−0.147818	−	0.256027i	−0.930421	+	0.366494i	$0.880558\pi$
$600$	29.7246	−	62.9127i	1.21350	−	2.56840i
$601$	3.28224	−	5.68501i	0.133886	−	0.231897i	−0.791286	−	0.611447i	$-0.790588\pi$
$601$	3.28224	−	5.68501i	0.133886	−	0.231897i	0.925171	+	0.379550i	$0.123921\pi$
$602$	1.04122	+	3.20453i	0.0424368	+	0.130607i
$603$	−1.33467	+	1.63595i	−0.0543521	+	0.0666208i
$604$	77.0755	−	55.9986i	3.13616	−	2.27855i
$605$	8.80883	−	48.2684i	0.358130	−	1.96239i
$606$	−5.11601	−	8.38285i	−0.207824	−	0.340530i
$607$	−8.23189	−	14.2580i	−0.334122	−	0.578716i	0.649194	−	0.760623i	$-0.275106\pi$
$607$	−8.23189	−	14.2580i	−0.334122	−	0.578716i	−0.983316	+	0.181907i	$0.941773\pi$
$608$	−9.40952	+	89.5256i	−0.381606	+	3.63074i
$609$	−7.59538	+	8.86027i	−0.307780	+	0.359036i
$610$	−8.77853	+	48.1024i	−0.355432	+	1.94761i
$611$	1.67456	+	5.15376i	0.0677454	+	0.208499i
$612$	−0.0258401	+	0.460882i	−0.00104453	+	0.0186301i
$613$	5.27406	−	16.2319i	0.213017	−	0.655599i	−0.786271	−	0.617881i	$-0.787991\pi$
$613$	5.27406	−	16.2319i	0.213017	−	0.655599i	0.999288	−	0.0377179i	$-0.0120088\pi$
$614$	−5.15628	−	1.09600i	−0.208090	−	0.0442310i
$615$	7.38103	−	1.17604i	0.297632	−	0.0474226i
$616$	−92.6003	+	19.6828i	−3.73097	+	0.793042i
$617$	0.234760	−	2.23359i	0.00945108	−	0.0899210i	−0.988780	−	0.149382i	$-0.952272\pi$
$617$	0.234760	−	2.23359i	0.00945108	−	0.0899210i	0.998231	+	0.0594611i	$0.0189382\pi$
$618$	4.40639	−	3.36839i	0.177251	−	0.135496i
$619$	−9.53950	+	4.24726i	−0.383425	+	0.170712i	−0.589392	−	0.807847i	$-0.700633\pi$
$619$	−9.53950	+	4.24726i	−0.383425	+	0.170712i	0.205967	+	0.978559i	$0.433966\pi$
$620$	34.6969	+	10.1740i	1.39346	+	0.408599i
$621$	0.662487	−	20.9232i	0.0265847	−	0.839619i
$622$	−18.8849	+	13.7207i	−0.757217	+	0.550150i
$623$	12.9900	+	2.76111i	0.520434	+	0.110622i
$624$	32.3094	−	24.6984i	1.29341	−	0.988726i
$625$	14.4713	−	20.3858i	0.578853	−	0.815432i
$626$	−43.5247	−	75.3870i	−1.73960	−	3.01307i
$627$	−58.8338	+	27.9306i	−2.34959	+	1.11544i
$628$	4.99279	+	47.5032i	0.199234	+	1.89558i
$629$	−0.110440	+	0.0802394i	−0.00440353	+	0.00319936i
$630$	−17.3940	−	32.1046i	−0.692994	−	1.27908i
$631$	3.19101	+	2.31840i	0.127032	+	0.0922941i	0.649487	−	0.760373i	$-0.274984\pi$
$631$	3.19101	+	2.31840i	0.127032	+	0.0922941i	−0.522455	+	0.852667i	$0.674984\pi$
$632$	−48.2504	+	83.5722i	−1.91930	+	3.32432i
$633$	23.9975	+	39.3212i	0.953815	+	1.56288i
$634$	−40.5318	+	8.61531i	−1.60972	+	0.342158i
$635$	−2.53260	+	1.56157i	−0.100503	+	0.0619691i
$636$	−2.45479	+	30.4801i	−0.0973388	+	1.20862i
$637$	3.89275	+	4.32333i	0.154236	+	0.171297i
$638$	−15.4348	+	47.5034i	−0.611070	+	1.88068i
$639$	−14.1195	+	0.688330i	−0.558559	+	0.0272299i
$640$	−20.0040	+	7.14574i	−0.790727	+	0.282460i
$641$	8.84259	+	9.82070i	0.349261	+	0.387894i	0.892021	−	0.451994i	$-0.149287\pi$
$641$	8.84259	+	9.82070i	0.349261	+	0.387894i	−0.542760	+	0.839888i	$0.682620\pi$
$642$	24.5373	−	44.9962i	0.968411	−	1.77586i
$643$	−7.49326	−	12.9787i	−0.295505	−	0.511831i	0.679597	−	0.733586i	$-0.262155\pi$
$643$	−7.49326	−	12.9787i	−0.295505	−	0.511831i	−0.975102	+	0.221755i	$0.928821\pi$
$644$	−4.34863	+	41.3744i	−0.171360	+	1.63038i
$645$	−1.30390	+	2.01190i	−0.0513408	+	0.0792183i
$646$	−0.0555395	−	0.528423i	−0.00218517	−	0.0207905i
$647$	−40.6013	+	29.4986i	−1.59620	+	1.15971i	−0.701867	+	0.712308i	$0.747650\pi$
$647$	−40.6013	+	29.4986i	−1.59620	+	1.15971i	−0.894334	+	0.447400i	$0.852350\pi$
$648$	15.5500	−	70.6193i	0.610861	−	2.77419i
$649$	46.6296			1.83037
$650$	24.5997	−	12.7050i	0.964880	−	0.498332i
$651$	9.08088	−	6.94172i	0.355908	−	0.272068i
$652$	−31.8083	+	35.3267i	−1.24571	+	1.38350i
$653$	6.42228	+	2.85938i	0.251323	+	0.111896i	0.528532	−	0.848913i	$-0.322743\pi$
$653$	6.42228	+	2.85938i	0.251323	+	0.111896i	−0.277209	+	0.960810i	$0.589409\pi$
$654$	29.2209	+	30.9051i	1.14263	+	1.20849i
$655$	−37.7035	+	5.06925i	−1.47320	+	0.198072i
$656$	−17.5529	−	12.7529i	−0.685325	−	0.497918i
$657$	6.50121	−	23.9135i	0.253636	−	0.932955i
$658$	−11.4263	−	8.30172i	−0.445445	−	0.323635i
$659$	23.7000	+	26.3215i	0.923221	+	1.02534i	0.999601	+	0.0282619i	$0.00899723\pi$
$659$	23.7000	+	26.3215i	0.923221	+	1.02534i	−0.0763797	+	0.997079i	$0.524336\pi$
$660$	−86.9646	−	70.2894i	−3.38509	−	2.73601i
$661$	−3.44767	+	3.82903i	−0.134099	+	0.148932i	−0.806454	−	0.591297i	$-0.798616\pi$
$661$	−3.44767	+	3.82903i	−0.134099	+	0.148932i	0.672355	+	0.740229i	$0.265283\pi$
$662$	56.0729	−	11.9187i	2.17933	−	0.463232i
$663$	−0.0720131	+	0.0840057i	−0.00279676	+	0.00326251i
$664$	−103.467	−	21.9925i	−4.01528	−	0.853475i
$665$	18.3726	+	23.8078i	0.712457	+	0.923226i
$666$	31.6883	−	16.0006i	1.22790	−	0.620012i
$667$	10.6973	+	7.77205i	0.414201	+	0.300935i
$668$	37.3681	−	64.7234i	1.44581	−	2.50422i
$669$	14.1740	−	25.9920i	0.547998	−	1.00491i
$670$	4.16058	+	0.315938i	0.160737	+	0.0122058i
$671$	43.2436	+	19.2533i	1.66940	+	0.743264i
$672$	−13.9619	+	46.8209i	−0.538593	+	1.80616i
$673$	−19.2634	−	4.09455i	−0.742548	−	0.157833i	−0.178922	−	0.983863i	$-0.557261\pi$
$673$	−19.2634	−	4.09455i	−0.742548	−	0.157833i	−0.563626	+	0.826030i	$0.690594\pi$
$674$	37.7518			1.45414
$675$	9.94178	−	24.0034i	0.382659	−	0.923890i
$676$	−43.4536			−1.67129
$677$	8.61159	+	1.83045i	0.330970	+	0.0703499i	0.370400	−	0.928872i	$-0.379221\pi$
$677$	8.61159	+	1.83045i	0.330970	+	0.0703499i	−0.0394295	+	0.999222i	$0.512554\pi$
$678$	−11.4719	+	38.4708i	−0.440577	+	1.47746i
$679$	19.1660	+	8.53326i	0.735524	+	0.327476i
$680$	0.467779	−	0.288427i	0.0179385	−	0.0110607i
$681$	10.2201	−	18.7415i	0.391636	−	0.718177i
$682$	24.4604	−	42.3667i	0.936638	−	1.62230i
$683$	−22.8601	−	16.6088i	−0.874716	−	0.635519i	0.0571320	−	0.998367i	$-0.481804\pi$
$683$	−22.8601	−	16.6088i	−0.874716	−	0.635519i	−0.931848	+	0.362848i	$0.881804\pi$
$684$	−5.53419	+	98.7072i	−0.211605	+	3.77417i
$685$	6.27389	−	9.18255i	0.239713	−	0.350847i
$686$	−52.1008	−	11.0744i	−1.98922	−	0.422821i
$687$	23.1569	−	27.0133i	0.883489	−	1.03062i
$688$	6.80750	−	1.44698i	0.259534	−	0.0551656i
$689$	−4.90458	+	5.44708i	−0.186849	+	0.207517i
$690$	−34.6756	+	22.5643i	−1.32008	+	0.859007i
$691$	−33.8032	−	37.5422i	−1.28593	−	1.42817i	−0.848743	−	0.528805i	$-0.822640\pi$
$691$	−33.8032	−	37.5422i	−1.28593	−	1.42817i	−0.437190	−	0.899369i	$-0.644026\pi$
$692$	−27.0227	−	19.6332i	−1.02725	−	0.746341i
$693$	−34.1769	+	9.02416i	−1.29827	+	0.342799i
$694$	−40.7262	−	29.5893i	−1.54594	−	1.12319i
$695$	26.0641	+	14.0590i	0.988668	+	0.533289i
$696$	31.3799	+	33.1886i	1.18945	+	1.25801i
$697$	0.0539271	+	0.0240099i	0.00204263	+	0.000909439i
$698$	4.47588	−	4.97097i	0.169415	−	0.188154i
$699$	−11.3735	+	8.69426i	−0.430184	+	0.328847i
$700$	−23.1874	+	46.1332i	−0.876401	+	1.74367i
$701$	30.7464			1.16128			0.580638	−	0.814162i	$-0.302803\pi$
$701$	30.7464			1.16128			0.580638	+	0.814162i	$0.302803\pi$
$702$	21.9811	−	18.5666i	0.829624	−	0.700751i
$703$	−23.6530	+	17.1849i	−0.892089	+	0.648140i
$704$	8.36782	+	79.6144i	0.315374	+	3.00058i
$705$	−0.535235	−	10.0352i	−0.0201581	−	0.377949i
$706$	−1.22935	+	11.6964i	−0.0462670	+	0.440201i
$707$	2.19498	+	3.80182i	0.0825509	+	0.142982i
$708$	33.8883	−	62.1438i	1.27360	−	2.33551i
$709$	−17.7193	−	19.6793i	−0.665463	−	0.739072i	0.312022	−	0.950075i	$-0.398994\pi$
$709$	−17.7193	−	19.6793i	−0.665463	−	0.739072i	−0.977485	+	0.211003i	$0.932327\pi$
$710$	17.0680	+	22.1173i	0.640551	+	0.830047i
$711$	−16.4753	+	32.0450i	−0.617871	+	1.20178i
$712$	16.0614	−	49.4320i	0.601927	−	1.85254i
$713$	−8.66569	−	9.62422i	−0.324533	−	0.360430i
$714$	0.0231508	−	0.287454i	0.000866397	−	0.0107577i
$715$	−6.32868	−	26.0452i	−0.236679	−	0.974035i
$716$	−24.0286	+	5.10744i	−0.897992	+	0.190874i
$717$	16.2934	+	26.6976i	0.608488	+	0.997040i
$718$	45.2541	−	78.3825i	1.68887	−	2.92521i
$719$	2.59090	+	1.88240i	0.0966244	+	0.0702017i	0.635048	−	0.772472i	$-0.280980\pi$
$719$	2.59090	+	1.88240i	0.0966244	+	0.0702017i	−0.538424	+	0.842674i	$0.680980\pi$
$720$	−69.7042	+	28.7990i	−2.59772	+	1.07328i
$721$	−2.00579	+	1.45730i	−0.0746997	+	0.0542725i
$722$	−6.62899	−	63.0706i	−0.246705	−	2.34724i
$723$	20.2811	−	9.62822i	0.754263	−	0.358077i
$724$	26.6867	+	46.2227i	0.991802	+	1.71785i
$725$	9.01337	+	13.7137i	0.334748	+	0.509314i
$726$	−80.0592	+	61.1999i	−2.97128	+	2.27134i
$727$	−40.1628	−	8.53687i	−1.48956	−	0.316615i	−0.609996	−	0.792404i	$-0.708829\pi$
$727$	−40.1628	−	8.53687i	−1.48956	−	0.316615i	−0.879559	+	0.475789i	$0.842162\pi$
$728$	−27.8679	+	20.2472i	−1.03285	+	0.750411i
$729$	4.51534	−	26.6198i	0.167235	−	0.985917i
$730$	−46.1209	+	16.4751i	−1.70701	+	0.609772i
$731$	−0.0172981	+	0.00770163i	−0.000639795	+	0.000284855i
$732$	57.0865	−	43.6388i	2.10998	−	1.61294i
$733$	4.35613	−	41.4458i	0.160897	−	1.53084i	−0.554538	−	0.832158i	$-0.687105\pi$
$733$	4.35613	−	41.4458i	0.160897	−	1.53084i	0.715436	−	0.698679i	$-0.246228\pi$
$734$	−28.2006	+	5.99423i	−1.04090	+	0.221251i
$735$	−4.90689	−	9.60833i	−0.180993	−	0.354409i
$736$	54.1477	+	11.5095i	1.99591	+	0.424244i
$737$	1.24823	−	3.84166i	0.0459792	−	0.141509i
$738$	−12.8434	−	8.40737i	−0.472772	−	0.309480i
$739$	7.60793	+	23.4148i	0.279862	+	0.861327i	0.987892	+	0.155144i	$0.0495842\pi$
$739$	7.60793	+	23.4148i	0.279862	+	0.861327i	−0.708030	+	0.706183i	$0.750416\pi$
$740$	−44.1800	−	23.8308i	−1.62409	−	0.876036i
$741$	−15.4231	+	17.9915i	−0.566580	+	0.660935i
$742$	1.99690	−	18.9993i	0.0733086	−	0.697484i
$743$	−1.29297	−	2.23949i	−0.0474346	−	0.0821591i	0.841333	−	0.540517i	$-0.181771\pi$
$743$	−1.29297	−	2.23949i	−0.0474346	−	0.0821591i	−0.888768	+	0.458358i	$0.848438\pi$
$744$	−23.3046	−	38.1858i	−0.854387	−	1.39996i
$745$	23.0433	−	21.9880i	0.844241	−	0.805578i
$746$	52.2036	−	37.9281i	1.91131	−	1.38865i
$747$	−38.9871	−	6.32084i	−1.42646	−	0.231267i
$748$	−0.272906	−	0.839918i	−0.00997843	−	0.0307104i
$749$	−11.4551	+	19.8408i	−0.418559	+	0.724966i
$750$	−50.1537	+	10.9977i	−1.83135	+	0.401579i
$751$	−1.67267	−	2.89715i	−0.0610367	−	0.105719i	0.833892	−	0.551927i	$-0.186107\pi$
$751$	−1.67267	−	2.89715i	−0.0610367	−	0.105719i	−0.894929	+	0.446208i	$0.852774\pi$
$752$	−19.5203	+	21.6795i	−0.711831	+	0.790569i
$753$	−3.97303	+	13.3234i	−0.144785	+	0.485533i
$754$	1.89973	+	18.0747i	0.0691841	+	0.658243i
$755$	−40.6391	−	11.9164i	−1.47901	−	0.433683i
$756$	−12.8116	+	52.1063i	−0.465953	+	1.89509i
$757$	−12.7280			−0.462606			−0.231303	−	0.972882i	$-0.574299\pi$
$757$	−12.7280			−0.462606			−0.231303	+	0.972882i	$0.574299\pi$
$758$	12.3597	−	5.50289i	0.448925	−	0.199874i
$759$	13.3001	+	37.7773i	0.482765	+	1.37123i
$760$	100.184	−	61.7725i	3.63406	−	2.24072i
$761$	−14.9541	+	16.6083i	−0.542087	+	0.602049i	−0.950491	−	0.310753i	$-0.899419\pi$
$761$	−14.9541	+	16.6083i	−0.542087	+	0.602049i	0.408404	+	0.912801i	$0.366086\pi$
$762$	6.00639	+	1.12456i	0.217589	+	0.0407384i
$763$	−12.7218	−	14.1290i	−0.460560	−	0.511503i
$764$	−37.1403	−	114.306i	−1.34369	−	4.13545i
$765$	0.169211	−	0.116072i	0.00611785	−	0.00419659i
$766$	−16.8172	+	51.7582i	−0.607632	+	1.87010i
$767$	15.4999	−	6.90102i	0.559671	−	0.249181i
$768$	−4.32845	−	1.80216i	−0.156189	−	0.0650298i
$769$	−3.71745	+	35.3692i	−0.134055	+	1.27545i	0.696113	+	0.717932i	$0.254911\pi$
$769$	−3.71745	+	35.3692i	−0.134055	+	1.27545i	−0.830168	+	0.557514i	$0.811755\pi$
$770$	53.2449	+	45.2229i	1.91881	+	1.62972i
$771$	23.3347	− </

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.59352 - 0.551270i) q^{2} +(0.494958 - 1.65982i) q^{3} +(4.59535 + 2.04598i) q^{4} +(-0.527975 - 2.17284i) q^{5} +(-2.19869 + 4.03193i) q^{6} +(1.02644 - 1.77785i) q^{7} +(-6.50010 - 4.72260i) q^{8} +(-2.51003 - 1.64309i) q^{9} +O(q^{10})\)	\(q+(-2.59352 - 0.551270i) q^{2} +(0.494958 - 1.65982i) q^{3} +(4.59535 + 2.04598i) q^{4} +(-0.527975 - 2.17284i) q^{5} +(-2.19869 + 4.03193i) q^{6} +(1.02644 - 1.77785i) q^{7} +(-6.50010 - 4.72260i) q^{8} +(-2.51003 - 1.64309i) q^{9} +(0.171493 + 5.92636i) q^{10} +(5.61416 + 1.19333i) q^{11} +(5.67048 - 6.61480i) q^{12} +(2.04279 - 0.434208i) q^{13} +(-3.64218 + 4.04505i) q^{14} +(-3.86786 - 0.199118i) q^{15} +(7.52292 + 8.35505i) q^{16} +(-0.0247468 - 0.0179796i) q^{17} +(5.60404 + 5.64508i) q^{18} +(-5.30003 - 3.85070i) q^{19} +(2.01936 - 11.0652i) q^{20} +(-2.44288 - 2.58368i) q^{21} +(-13.9026 - 6.18983i) q^{22} +(-2.69572 + 2.99390i) q^{23} +(-11.0560 + 8.45153i) q^{24} +(-4.44248 + 2.29441i) q^{25} -5.53738 q^{26} +(-3.96959 + 3.35296i) q^{27} +(8.35433 - 6.06978i) q^{28} +(-0.343074 - 3.26413i) q^{29} +(9.92161 + 2.64865i) q^{30} +(-0.336018 + 3.19700i) q^{31} +(-6.87040 - 11.8999i) q^{32} +(4.75948 - 8.72787i) q^{33} +(0.0542697 + 0.0602726i) q^{34} +(-4.40493 - 1.29164i) q^{35} +(-8.17277 - 12.6860i) q^{36} +(1.37908 - 4.24438i) q^{37} +(11.6230 + 12.9086i) q^{38} +(0.290384 - 3.60558i) q^{39} +(-6.82956 + 16.6171i) q^{40} +(-1.88764 + 0.401231i) q^{41} +(4.91135 + 8.04751i) q^{42} +(0.309512 - 0.536091i) q^{43} +(23.3575 + 16.9702i) q^{44} +(-2.24493 + 6.32142i) q^{45} +(8.64184 - 6.27867i) q^{46} +(0.271227 + 2.58056i) q^{47} +(17.5915 - 8.35134i) q^{48} +(1.39282 + 2.41244i) q^{49} +(12.7865 - 3.50160i) q^{50} +(-0.0420916 + 0.0321762i) q^{51} +(10.2757 + 2.18417i) q^{52} +(-2.83942 + 2.06296i) q^{53} +(12.1436 - 6.50765i) q^{54} +(-0.371228 - 12.8287i) q^{55} +(-15.0681 + 6.70874i) q^{56} +(-9.01477 + 6.89118i) q^{57} +(-0.909647 + 8.65471i) q^{58} +(7.94668 - 1.68912i) q^{59} +(-17.3668 - 8.82860i) q^{60} +(8.06706 + 1.71471i) q^{61} +(2.63388 - 8.10625i) q^{62} +(-5.49758 + 2.77594i) q^{63} +(4.31002 + 13.2649i) q^{64} +(-2.02201 - 4.20940i) q^{65} +(-17.1552 + 20.0121i) q^{66} +(0.0735643 - 0.699918i) q^{67} +(-0.0769343 - 0.133254i) q^{68} +(3.63508 + 5.95627i) q^{69} +(10.7122 + 5.77819i) q^{70} +(3.81216 - 2.76970i) q^{71} +(8.55584 + 22.5341i) q^{72} +(2.55263 + 7.85620i) q^{73} +(-5.91647 + 10.2476i) q^{74} +(1.60948 + 8.50938i) q^{75} +(-16.4770 - 28.5391i) q^{76} +(7.88418 - 8.75627i) q^{77} +(-2.74077 + 9.19107i) q^{78} +(-1.25546 - 11.9449i) q^{79} +(14.1823 - 20.7574i) q^{80} +(3.60054 + 8.24840i) q^{81} +5.11682 q^{82} +(12.0272 - 5.35485i) q^{83} +(-5.93973 - 16.8710i) q^{84} +(-0.0260011 + 0.0632637i) q^{85} +(-1.09826 + 1.21974i) q^{86} +(-5.58769 - 1.04616i) q^{87} +(-30.8570 - 34.2701i) q^{88} +(1.99904 + 6.15242i) q^{89} +(9.30707 - 15.1572i) q^{90} +(1.32485 - 4.07747i) q^{91} +(-18.5132 + 8.24263i) q^{92} +(5.14015 + 2.14011i) q^{93} +(0.719149 - 6.84224i) q^{94} +(-5.56867 + 13.5492i) q^{95} +(-23.1523 + 5.51372i) q^{96} +(1.06825 + 10.1637i) q^{97} +(-2.28241 - 7.02454i) q^{98} +(-12.1310 - 12.2198i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

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