LMFDB - Embedded newform 225.2.q.a.106.11

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			106.11
Character	$\chi$	$=$	225.106
Dual form			225.2.q.a.121.11

$q$-expansion

$f(q)$	$=$	$q+(-0.750960 - 0.159622i) q^{2} +(-1.69865 - 0.338529i) q^{3} +(-1.28863 - 0.573734i) q^{4} +(-0.934384 - 2.03148i) q^{5} +(1.22158 + 0.525362i) q^{6} +(-1.54115 + 2.66935i) q^{7} +(2.11835 + 1.53907i) q^{8} +(2.77080 + 1.15008i) q^{9} +O(q^{10})$	\(q+(-0.750960 - 0.159622i) q^{2} +(-1.69865 - 0.338529i) q^{3} +(-1.28863 - 0.573734i) q^{4} +(-0.934384 - 2.03148i) q^{5} +(1.22158 + 0.525362i) q^{6} +(-1.54115 + 2.66935i) q^{7} +(2.11835 + 1.53907i) q^{8} +(2.77080 + 1.15008i) q^{9} +(0.377417 + 1.67471i) q^{10} +(2.10386 + 0.447190i) q^{11} +(1.99470 + 1.41081i) q^{12} +(-1.99041 + 0.423076i) q^{13} +(1.58343 - 1.75858i) q^{14} +(0.899473 + 3.76709i) q^{15} +(0.542593 + 0.602611i) q^{16} +(6.22843 + 4.52522i) q^{17} +(-1.89718 - 1.30594i) q^{18} +(-2.68599 - 1.95149i) q^{19} +(0.0385425 + 3.15392i) q^{20} +(3.52153 - 4.01256i) q^{21} +(-1.50854 - 0.671643i) q^{22} +(-3.89453 + 4.32531i) q^{23} +(-3.07731 - 3.33147i) q^{24} +(-3.25385 + 3.79637i) q^{25} +1.56225 q^{26} +(-4.31727 - 2.89157i) q^{27} +(3.51747 - 2.55559i) q^{28} +(-0.382713 - 3.64127i) q^{29} +(-0.0741604 - 2.97251i) q^{30} +(-0.995438 + 9.47096i) q^{31} +(-2.92971 - 5.07440i) q^{32} +(-3.42233 - 1.47183i) q^{33} +(-3.95498 - 4.39245i) q^{34} +(6.86278 + 0.636623i) q^{35} +(-2.91069 - 3.07173i) q^{36} +(-1.42994 + 4.40091i) q^{37} +(1.70557 + 1.89423i) q^{38} +(3.52423 - 0.0448436i) q^{39} +(1.14725 - 5.74149i) q^{40} +(8.46629 - 1.79957i) q^{41} +(-3.28502 + 2.45117i) q^{42} +(0.735688 - 1.27425i) q^{43} +(-2.45453 - 1.78332i) q^{44} +(-0.252620 - 6.70345i) q^{45} +(3.61505 - 2.62649i) q^{46} +(-0.121577 - 1.15673i) q^{47} +(-0.717673 - 1.20731i) q^{48} +(-1.25030 - 2.16559i) q^{49} +(3.04950 - 2.33154i) q^{50} +(-9.04798 - 9.79524i) q^{51} +(2.80764 + 0.596782i) q^{52} +(-5.64868 + 4.10401i) q^{53} +(2.78054 + 2.86059i) q^{54} +(-1.05736 - 4.69181i) q^{55} +(-7.37304 + 3.28269i) q^{56} +(3.90191 + 4.22417i) q^{57} +(-0.293823 + 2.79554i) q^{58} +(-0.193316 + 0.0410905i) q^{59} +(1.00222 - 5.37043i) q^{60} +(-0.235109 - 0.0499739i) q^{61} +(2.25930 - 6.95342i) q^{62} +(-7.34019 + 5.62379i) q^{63} +(0.888950 + 2.73591i) q^{64} +(2.71928 + 3.64818i) q^{65} +(2.33510 + 1.65157i) q^{66} +(-1.30455 + 12.4120i) q^{67} +(-5.42985 - 9.40478i) q^{68} +(8.07966 - 6.02876i) q^{69} +(-5.05206 - 1.57353i) q^{70} +(-5.29885 + 3.84984i) q^{71} +(4.09947 + 6.70074i) q^{72} +(-2.49299 - 7.67263i) q^{73} +(1.77631 - 3.07666i) q^{74} +(6.81232 - 5.34717i) q^{75} +(2.34161 + 4.05579i) q^{76} +(-4.43608 + 4.92677i) q^{77} +(-2.65372 - 0.528868i) q^{78} +(1.18352 + 11.2604i) q^{79} +(0.717204 - 1.66534i) q^{80} +(6.35463 + 6.37328i) q^{81} -6.64510 q^{82} +(-5.53451 + 2.46412i) q^{83} +(-6.84008 + 3.15028i) q^{84} +(3.37316 - 16.8812i) q^{85} +(-0.755870 + 0.839479i) q^{86} +(-0.582580 + 6.31478i) q^{87} +(3.76846 + 4.18530i) q^{88} +(-0.671050 - 2.06528i) q^{89} +(-0.880307 + 5.07435i) q^{90} +(1.93819 - 5.96515i) q^{91} +(7.50018 - 3.33929i) q^{92} +(4.89709 - 15.7508i) q^{93} +(-0.0933394 + 0.888065i) q^{94} +(-1.45467 + 7.27999i) q^{95} +(3.25870 + 9.61140i) q^{96} +(-1.64971 - 15.6960i) q^{97} +(0.593254 + 1.82585i) q^{98} +(5.31507 + 3.65868i) 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 $

$2$	−0.750960	−	0.159622i	−0.531009	−	0.112869i	−0.0653986	−	0.997859i	$-0.520832\pi$
$2$	−0.750960	−	0.159622i	−0.531009	−	0.112869i	−0.465611	+	0.884990i	$0.654165\pi$
$3$	−1.69865	−	0.338529i	−0.980714	−	0.195450i
$3$	−1.69865	−	0.338529i	−0.980714	−	0.195450i
$4$	−1.28863	−	0.573734i	−0.644314	−	0.286867i
$5$	−0.934384	−	2.03148i	−0.417869	−	0.908507i
$5$	−0.934384	−	2.03148i	−0.417869	−	0.908507i
$6$	1.22158	+	0.525362i	0.498708	+	0.214478i
$7$	−1.54115	+	2.66935i	−0.582501	+	1.00892i	0.412681	+	0.910876i	$0.364592\pi$
$7$	−1.54115	+	2.66935i	−0.582501	+	1.00892i	−0.995182	+	0.0980456i	$0.968741\pi$
$8$	2.11835	+	1.53907i	0.748951	+	0.544145i
$9$	2.77080	+	1.15008i	0.923599	+	0.383360i
$10$	0.377417	+	1.67471i	0.119350	+	0.529590i
$11$	2.10386	+	0.447190i	0.634338	+	0.134833i	0.513847	−	0.857882i	$-0.328220\pi$
$11$	2.10386	+	0.447190i	0.634338	+	0.134833i	0.120491	+	0.992714i	$0.461553\pi$
$12$	1.99470	+	1.41081i	0.575820	+	0.407266i
$13$	−1.99041	+	0.423076i	−0.552042	+	0.117340i	−0.475483	−	0.879725i	$-0.657727\pi$
$13$	−1.99041	+	0.423076i	−0.552042	+	0.117340i	−0.0765588	+	0.997065i	$0.524393\pi$
$14$	1.58343	−	1.75858i	0.423190	−	0.470000i
$15$	0.899473	+	3.76709i	0.232243	+	0.972658i
$16$	0.542593	+	0.602611i	0.135648	+	0.150653i
$17$	6.22843	+	4.52522i	1.51062	+	1.09753i	0.965903	+	0.258903i	$0.0833609\pi$
$17$	6.22843	+	4.52522i	1.51062	+	1.09753i	0.544712	+	0.838623i	$0.316639\pi$
$18$	−1.89718	−	1.30594i	−0.447170	−	0.307814i
$19$	−2.68599	−	1.95149i	−0.616209	−	0.447702i	0.235386	−	0.971902i	$-0.424364\pi$
$19$	−2.68599	−	1.95149i	−0.616209	−	0.447702i	−0.851595	+	0.524200i	$0.824364\pi$
$20$	0.0385425	+	3.15392i	0.00861836	+	0.705237i
$21$	3.52153	−	4.01256i	0.768460	−	0.875613i
$22$	−1.50854	−	0.671643i	−0.321621	−	0.143195i
$23$	−3.89453	+	4.32531i	−0.812065	+	0.901890i	−0.996721	−	0.0809136i	$-0.974216\pi$
$23$	−3.89453	+	4.32531i	−0.812065	+	0.901890i	0.184656	+	0.982803i	$0.440883\pi$
$24$	−3.07731	−	3.33147i	−0.628154	−	0.680032i
$25$	−3.25385	+	3.79637i	−0.650770	+	0.759275i
$26$	1.56225			0.306383
$27$	−4.31727	−	2.89157i	−0.830859	−	0.556484i
$28$	3.51747	−	2.55559i	0.664740	−	0.482962i
$29$	−0.382713	−	3.64127i	−0.0710679	−	0.676166i	−0.970827	−	0.239780i	$-0.922925\pi$
$29$	−0.382713	−	3.64127i	−0.0710679	−	0.676166i	0.899759	−	0.436386i	$-0.143742\pi$
$30$	−0.0741604	−	2.97251i	−0.0135398	−	0.542703i
$31$	−0.995438	+	9.47096i	−0.178786	+	1.70103i	0.426063	+	0.904694i	$0.359900\pi$
$31$	−0.995438	+	9.47096i	−0.178786	+	1.70103i	−0.604849	+	0.796341i	$0.706766\pi$
$32$	−2.92971	−	5.07440i	−0.517904	−	0.897035i
$33$	−3.42233	−	1.47183i	−0.595751	−	0.256213i
$34$	−3.95498	−	4.39245i	−0.678273	−	0.753299i
$35$	6.86278	+	0.636623i	1.16002	+	0.107609i
$36$	−2.91069	−	3.07173i	−0.485114	−	0.511955i
$37$	−1.42994	+	4.40091i	−0.235081	+	0.723505i	0.762029	+	0.647542i	$0.224203\pi$
$37$	−1.42994	+	4.40091i	−0.235081	+	0.723505i	−0.997111	+	0.0759630i	$0.975797\pi$
$38$	1.70557	+	1.89423i	0.276681	+	0.307285i
$39$	3.52423	−	0.0448436i	0.564329	−	0.00718073i
$40$	1.14725	−	5.74149i	0.181396	−	0.907809i
$41$	8.46629	−	1.79957i	1.32221	−	0.281045i	0.507872	−	0.861432i	$-0.330432\pi$
$41$	8.46629	−	1.79957i	1.32221	−	0.281045i	0.814341	+	0.580387i	$0.197099\pi$
$42$	−3.28502	+	2.45117i	−0.506889	+	0.378223i
$43$	0.735688	−	1.27425i	0.112191	−	0.194321i	−0.804462	−	0.594004i	$-0.797546\pi$
$43$	0.735688	−	1.27425i	0.112191	−	0.194321i	0.916654	+	0.399683i	$0.130880\pi$
$44$	−2.45453	−	1.78332i	−0.370034	−	0.268845i
$45$	−0.252620	−	6.70345i	−0.0376584	−	0.999291i
$46$	3.61505	−	2.62649i	0.533010	−	0.387254i
$47$	−0.121577	−	1.15673i	−0.0177339	−	0.168727i	0.982070	−	0.188515i	$-0.0603674\pi$
$47$	−0.121577	−	1.15673i	−0.0177339	−	0.168727i	−0.999804	+	0.0197884i	$0.993701\pi$
$48$	−0.717673	−	1.20731i	−0.103587	−	0.174260i
$49$	−1.25030	−	2.16559i	−0.178615	−	0.309370i
$50$	3.04950	−	2.33154i	0.431264	−	0.329730i
$51$	−9.04798	−	9.79524i	−1.26697	−	1.37161i
$52$	2.80764	+	0.596782i	0.389349	+	0.0827588i
$53$	−5.64868	+	4.10401i	−0.775906	+	0.563729i	−0.903747	−	0.428066i	$-0.859195\pi$
$53$	−5.64868	+	4.10401i	−0.775906	+	0.563729i	0.127842	+	0.991795i	$0.459195\pi$
$54$	2.78054	+	2.86059i	0.378384	+	0.389276i
$55$	−1.05736	−	4.69181i	−0.142574	−	0.632643i
$56$	−7.37304	+	3.28269i	−0.985264	+	0.438668i
$57$	3.90191	+	4.22417i	0.516821	+	0.559505i
$58$	−0.293823	+	2.79554i	−0.0385808	+	0.367072i
$59$	−0.193316	+	0.0410905i	−0.0251676	+	0.00534953i	−0.220478	−	0.975392i	$-0.570762\pi$
$59$	−0.193316	+	0.0410905i	−0.0251676	+	0.00534953i	0.195311	+	0.980741i	$0.437428\pi$
$60$	1.00222	−	5.37043i	0.129386	−	0.693320i
$61$	−0.235109	−	0.0499739i	−0.0301026	−	0.00639851i	0.192836	−	0.981231i	$-0.438232\pi$
$61$	−0.235109	−	0.0499739i	−0.0301026	−	0.00639851i	−0.222938	+	0.974833i	$0.571565\pi$
$62$	2.25930	−	6.95342i	0.286932	−	0.883085i
$63$	−7.34019	+	5.62379i	−0.924777	+	0.708531i
$64$	0.888950	+	2.73591i	0.111119	+	0.341988i
$65$	2.71928	+	3.64818i	0.337286	+	0.452501i
$66$	2.33510	+	1.65157i	0.287431	+	0.203294i
$67$	−1.30455	+	12.4120i	−0.159377	+	1.51637i	0.563920	+	0.825829i	$0.309293\pi$
$67$	−1.30455	+	12.4120i	−0.159377	+	1.51637i	−0.723297	+	0.690537i	$0.757374\pi$
$68$	−5.42985	−	9.40478i	−0.658467	−	1.14050i
$69$	8.07966	−	6.02876i	0.972677	−	0.725778i
$70$	−5.05206	−	1.57353i	−0.603836	−	0.188072i
$71$	−5.29885	+	3.84984i	−0.628858	+	0.456892i	−0.856004	−	0.516969i	$-0.827060\pi$
$71$	−5.29885	+	3.84984i	−0.628858	+	0.456892i	0.227146	+	0.973861i	$0.427060\pi$
$72$	4.09947	+	6.70074i	0.483127	+	0.789690i
$73$	−2.49299	−	7.67263i	−0.291782	−	0.898013i	−0.984283	−	0.176597i	$-0.943491\pi$
$73$	−2.49299	−	7.67263i	−0.291782	−	0.898013i	0.692501	−	0.721417i	$-0.256509\pi$
$74$	1.77631	−	3.07666i	0.206492	−	0.357655i
$75$	6.81232	−	5.34717i	0.786619	−	0.617438i
$76$	2.34161	+	4.05579i	0.268601	+	0.465231i
$77$	−4.43608	+	4.92677i	−0.505538	+	0.561457i
$78$	−2.65372	−	0.528868i	−0.300474	−	0.0598825i
$79$	1.18352	+	11.2604i	0.133156	+	1.26689i	0.833272	+	0.552864i	$0.186465\pi$
$79$	1.18352	+	11.2604i	0.133156	+	1.26689i	−0.700116	+	0.714029i	$0.746868\pi$
$80$	0.717204	−	1.66534i	0.0801858	−	0.186191i
$81$	6.35463	+	6.37328i	0.706070	+	0.708142i
$82$	−6.64510			−0.733829
$83$	−5.53451	+	2.46412i	−0.607491	+	0.270472i	−0.687341	−	0.726334i	$-0.741222\pi$
$83$	−5.53451	+	2.46412i	−0.607491	+	0.270472i	0.0798505	+	0.996807i	$0.474556\pi$
$84$	−6.84008	+	3.15028i	−0.746314	+	0.343724i
$85$	3.37316	−	16.8812i	0.365870	−	1.83103i
$86$	−0.755870	+	0.839479i	−0.0815076	+	0.0905234i
$87$	−0.582580	+	6.31478i	−0.0624591	+	0.677016i
$88$	3.76846	+	4.18530i	0.401720	+	0.446155i
$89$	−0.671050	−	2.06528i	−0.0711312	−	0.218919i	0.909171	−	0.416423i	$-0.136716\pi$
$89$	−0.671050	−	2.06528i	−0.0711312	−	0.218919i	−0.980302	+	0.197504i	$0.936716\pi$
$90$	−0.880307	+	5.07435i	−0.0927925	+	0.534883i
$91$	1.93819	−	5.96515i	0.203178	−	0.625317i
$92$	7.50018	−	3.33929i	0.781948	−	0.348145i
$93$	4.89709	−	15.7508i	0.507804	−	1.63328i
$94$	−0.0933394	+	0.888065i	−0.00962723	+	0.0915969i
$95$	−1.45467	+	7.27999i	−0.149245	+	0.746911i
$96$	3.25870	+	9.61140i	0.332590	+	0.980959i
$97$	−1.64971	−	15.6960i	−0.167503	−	1.59368i	−0.678828	−	0.734297i	$-0.737512\pi$
$97$	−1.64971	−	15.6960i	−0.167503	−	1.59368i	0.511325	−	0.859387i	$-0.329155\pi$
$98$	0.593254	+	1.82585i	0.0599277	+	0.184438i
$99$	5.31507	+	3.65868i	0.534184	+	0.367711i
$100$	6.37112	−	3.02527i	0.637112	−	0.302527i
$101$	−3.00231	+	5.20015i	−0.298741	+	0.517434i	−0.975848	−	0.218450i	$-0.929900\pi$
$101$	−3.00231	+	5.20015i	−0.298741	+	0.517434i	0.677107	+	0.735884i	$0.263233\pi$
$102$	5.23114	+	8.80009i	0.517960	+	0.871339i
$103$	12.6259	+	5.62140i	1.24406	+	0.553893i	0.919916	−	0.392114i	$-0.128256\pi$
$103$	12.6259	+	5.62140i	1.24406	+	0.553893i	0.324147	+	0.946007i	$0.394923\pi$
$104$	−4.86755	−	2.16717i	−0.477302	−	0.212509i
$105$	−11.4419	−	3.40464i	−1.11662	−	0.332259i
$106$	4.89702	−	2.18030i	0.475641	−	0.211769i
$107$	8.62739			0.834041			0.417021	−	0.908897i	$-0.363074\pi$
$107$	8.62739			0.834041			0.417021	+	0.908897i	$0.363074\pi$
$108$	3.90436	+	6.20313i	0.375697	+	0.596896i
$109$	−5.90681	+	18.1793i	−0.565770	+	1.74126i	0.0998844	+	0.994999i	$0.468153\pi$
$109$	−5.90681	+	18.1793i	−0.565770	+	1.74126i	−0.665654	+	0.746261i	$0.731847\pi$
$110$	0.0451199	+	3.69214i	0.00430201	+	0.352032i
$111$	3.91880	−	6.99151i	0.371956	−	0.663605i
$112$	−2.44480	+	0.519659i	−0.231012	+	0.0491031i
$113$	3.05589	−	0.649550i	0.287474	−	0.0611045i	−0.0619175	−	0.998081i	$-0.519722\pi$
$113$	3.05589	−	0.649550i	0.287474	−	0.0611045i	0.349392	+	0.936977i	$0.386388\pi$
$114$	−2.25591	−	3.79501i	−0.211286	−	0.355436i
$115$	12.4258	+	3.87017i	1.15871	+	0.360895i
$116$	−1.59595	+	4.91182i	−0.148180	+	0.456051i
$117$	−6.00161	−	1.11688i	−0.554849	−	0.103256i
$118$	0.151731			0.0139680
$119$	−21.6784	+	9.65183i	−1.98725	+	0.884782i
$120$	−3.89242	+	9.36438i	−0.355328	+	0.854847i
$121$	−5.82275	−	2.59245i	−0.529341	−	0.235678i
$122$	0.168581	+	0.0750569i	0.0152626	+	0.00679533i
$123$	−14.9904	+	0.190744i	−1.35164	+	0.0171988i
$124$	6.71656	−	11.6334i	0.603165	−	1.04471i
$125$	10.7526	+	3.06287i	0.961743	+	0.273952i
$126$	6.40987	−	3.05159i	0.571037	−	0.271857i
$127$	−0.645138	−	1.98553i	−0.0572468	−	0.176187i	0.918344	−	0.395782i	$-0.129526\pi$
$127$	−0.645138	−	1.98553i	−0.0572468	−	0.176187i	−0.975591	+	0.219595i	$0.929526\pi$
$128$	0.994094	+	9.45817i	0.0878663	+	0.835992i
$129$	−1.68104	+	1.91545i	−0.148008	+	0.168646i
$130$	−1.45975	−	3.17369i	−0.128028	−	0.278351i
$131$	0.0987788	−	0.939817i	0.00863034	−	0.0821122i	−0.989359	−	0.145495i	$-0.953522\pi$
$131$	0.0987788	−	0.939817i	0.00863034	−	0.0821122i	0.997989	+	0.0633832i	$0.0201890\pi$
$132$	3.56567	+	3.86015i	0.310352	+	0.335983i
$133$	9.34873	−	4.16232i	0.810638	−	0.360919i
$134$	2.96089	−	9.11268i	0.255782	−	0.787216i
$135$	−1.84020	+	11.4723i	−0.158379	+	0.987378i
$136$	6.22937	+	19.1720i	0.534164	+	1.64399i
$137$	−4.39938	−	4.88600i	−0.375864	−	0.417439i	0.525300	−	0.850917i	$-0.323953\pi$
$137$	−4.39938	−	4.88600i	−0.375864	−	0.417439i	−0.901164	+	0.433478i	$0.857286\pi$
$138$	−7.02983	+	3.23767i	−0.598419	+	0.275609i
$139$	3.98464	−	4.42539i	0.337972	−	0.375356i	−0.550070	−	0.835119i	$-0.685399\pi$
$139$	3.98464	−	4.42539i	0.337972	−	0.375356i	0.888042	+	0.459762i	$0.152065\pi$
$140$	−8.47832	−	4.75778i	−0.716549	−	0.402106i
$141$	−0.185070	+	2.00603i	−0.0155857	+	0.168938i
$142$	4.59375	−	2.04527i	0.385499	−	0.171635i
$143$	−4.37675			−0.366002
$144$	0.810365	+	2.29374i	0.0675304	+	0.191145i
$145$	−7.03957	+	4.17982i	−0.584605	+	0.347115i
$146$	0.647418	+	6.15978i	0.0535807	+	0.509787i
$147$	1.39071	+	4.10183i	0.114704	+	0.338313i
$148$	4.36762	−	4.85073i	0.359016	−	0.398728i
$149$	−0.502162	−	0.869771i	−0.0411387	−	0.0712544i	0.844723	−	0.535204i	$-0.179765\pi$
$149$	−0.502162	−	0.869771i	−0.0411387	−	0.0712544i	−0.885862	+	0.463950i	$0.846432\pi$
$150$	−5.96931	+	2.92812i	−0.487392	+	0.239080i
$151$	−2.55785	+	4.43032i	−0.208155	+	0.360534i	−0.951133	−	0.308781i	$-0.900079\pi$
$151$	−2.55785	+	4.43032i	−0.208155	+	0.360534i	0.742979	+	0.669315i	$0.233412\pi$
$152$	−2.68640	−	8.26788i	−0.217896	−	0.670614i
$153$	12.0533	+	19.7016i	0.974455	+	1.59278i
$154$	4.11774	−	2.99171i	0.331817	−	0.241079i
$155$	20.1702	−	6.82730i	1.62011	−	0.548382i
$156$	−4.56716	−	1.96419i	−0.365665	−	0.157261i
$157$	−9.66548	−	16.7411i	−0.771390	−	1.33609i	−0.936801	−	0.349861i	$-0.886229\pi$
$157$	−9.66548	−	16.7411i	−0.771390	−	1.33609i	0.165412	−	0.986225i	$-0.447105\pi$
$158$	0.908629	−	8.64502i	0.0722866	−	0.687761i
$159$	10.9844	−	5.05901i	0.871122	−	0.401206i
$160$	−7.57109	+	10.6931i	−0.598547	+	0.845363i
$161$	−5.54373	−	17.0618i	−0.436907	−	1.34466i
$162$	−3.75476	−	5.80042i	−0.295002	−	0.455724i
$163$	2.96080	−	9.11239i	0.231907	−	0.713738i	−0.765609	−	0.643306i	$-0.777562\pi$
$163$	2.96080	−	9.11239i	0.231907	−	0.713738i	0.997517	−	0.0704316i	$-0.0224377\pi$
$164$	−11.9424	−	2.53843i	−0.932543	−	0.198218i
$165$	0.207765	+	8.32766i	0.0161745	+	0.648308i
$166$	4.54952	−	0.967031i	0.353111	−	0.0750561i
$167$	1.55155	−	14.7620i	0.120063	−	1.14232i	−0.754124	−	0.656732i	$-0.771938\pi$
$167$	1.55155	−	14.7620i	0.120063	−	1.14232i	0.874187	−	0.485589i	$-0.161395\pi$
$168$	13.6355	−	3.08014i	1.05200	−	0.237638i
$169$	−8.09333	+	3.60338i	−0.622564	+	0.277183i
$170$	−5.22772	+	12.1387i	−0.400948	+	0.930997i
$171$	−5.19797	−	8.49628i	−0.397499	−	0.649727i
$172$	−1.67911	+	1.21994i	−0.128031	+	0.0930199i
$173$	4.38960	+	0.933037i	0.333735	+	0.0709375i	0.371731	−	0.928340i	$-0.378764\pi$
$173$	4.38960	+	0.933037i	0.333735	+	0.0709375i	−0.0379966	+	0.999278i	$0.512098\pi$
$174$	1.44547	−	4.64916i	0.109581	−	0.352452i
$175$	−5.11919	−	14.5365i	−0.386974	−	1.09885i
$176$	0.872060	+	1.51045i	0.0657340	+	0.113855i
$177$	0.342285	−	0.00435536i	0.0257277	−	0.000327369i
$178$	0.174269	+	1.65806i	0.0130620	+	0.124277i
$179$	−0.751808	+	0.546221i	−0.0561928	+	0.0408265i	−0.615527	−	0.788116i	$-0.711057\pi$
$179$	−0.751808	+	0.546221i	−0.0561928	+	0.0408265i	0.559334	+	0.828942i	$0.311057\pi$
$180$	−3.52046	+	8.78319i	−0.262400	+	0.654660i
$181$	0.784552	+	0.570010i	0.0583153	+	0.0423685i	0.616561	−	0.787307i	$-0.288525\pi$
$181$	0.784552	+	0.570010i	0.0583153	+	0.0423685i	−0.558246	+	0.829676i	$0.688525\pi$
$182$	−2.40767	+	4.17021i	−0.178469	+	0.309117i
$183$	0.382449	+	0.164479i	0.0282715	+	0.0121586i
$184$	−14.9070	+	3.16857i	−1.09896	+	0.233590i
$185$	10.2765	−	1.20724i	0.755543	−	0.0887579i
$186$	−6.19169	+	11.0466i	−0.453997	+	0.809973i
$187$	11.0801	+	12.3057i	0.810258	+	0.899883i
$188$	−0.506988	+	1.56035i	−0.0369759	+	0.113800i
$189$	14.3722	−	7.06796i	1.04542	−	0.514119i
$190$	2.25444	−	5.23479i	0.163554	−	0.379771i
$191$	−9.36301	−	10.3987i	−0.677483	−	0.752421i	0.302140	−	0.953263i	$-0.402299\pi$
$191$	−9.36301	−	10.3987i	−0.677483	−	0.752421i	−0.979624	+	0.200842i	$0.935632\pi$
$192$	−0.583829	−	4.94827i	−0.0421342	−	0.357111i
$193$	3.40138	+	5.89137i	0.244837	+	0.424070i	0.962086	−	0.272747i	$-0.0879323\pi$
$193$	3.40138	+	5.89137i	0.244837	+	0.424070i	−0.717249	+	0.696817i	$0.754599\pi$
$194$	−1.26655	+	12.0504i	−0.0909327	+	0.865167i
$195$	−3.38409	−	7.11752i	−0.242340	−	0.509696i
$196$	0.368704	+	3.50798i	0.0263360	+	0.250570i
$197$	6.91644	−	5.02509i	0.492776	−	0.358023i	−0.313475	−	0.949596i	$-0.601493\pi$
$197$	6.91644	−	5.02509i	0.492776	−	0.358023i	0.806251	+	0.591574i	$0.201493\pi$
$198$	−3.40740	−	3.59592i	−0.242153	−	0.255551i
$199$	12.3769			0.877375			0.438688	−	0.898640i	$-0.355444\pi$
$199$	12.3769			0.877375			0.438688	+	0.898640i	$0.355444\pi$
$200$	−12.7357	+	3.03414i	−0.900551	+	0.214546i
$201$	6.41779	−	20.6420i	0.452676	−	1.45597i
$202$	3.08467	−	3.42588i	0.217037	−	0.241044i
$203$	10.3097	+	4.59015i	0.723596	+	0.322166i
$204$	6.03961	+	17.8136i	0.422857	+	1.24720i
$205$	−11.5666	−	15.5177i	−0.807844	−	1.08380i
$206$	−8.58423	−	6.23680i	−0.598091	−	0.434539i
$207$	−15.7654	+	7.50554i	−1.09577	+	0.521671i
$208$	−1.33494	−	0.969888i	−0.0925612	−	0.0672496i
$209$	−4.77827	−	5.30681i	−0.330520	−	0.367079i
$210$	8.04897	+	4.38313i	0.555432	+	0.302465i
$211$	−7.27264	+	8.07708i	−0.500669	+	0.556049i	−0.939513	−	0.342514i	$-0.888722\pi$
$211$	−7.27264	+	8.07708i	−0.500669	+	0.556049i	0.438844	+	0.898563i	$0.355388\pi$
$212$	9.63366	−	2.04770i	0.661642	−	0.140636i
$213$	10.3042	−	4.74571i	0.706029	−	0.325170i
$214$	−6.47883	−	1.37712i	−0.442883	−	0.0941378i
$215$	−3.27603	−	0.303900i	−0.223424	−	0.0207258i
$216$	−4.69515	−	12.7700i	−0.319465	−	0.868886i
$217$	−23.7472	−	17.2534i	−1.61207	−	1.17123i
$218$	7.33758	−	12.7091i	0.496964	−	0.860767i
$219$	1.63730	+	13.8770i	0.110639	+	0.937723i
$220$	−1.32931	+	6.65264i	−0.0896221	+	0.448521i
$221$	−14.3117	−	6.37196i	−0.962706	−	0.428624i
$222$	−4.05886	+	4.62483i	−0.272413	+	0.310398i
$223$	−20.1097	−	4.27444i	−1.34664	−	0.286238i	−0.522510	−	0.852633i	$-0.675004\pi$
$223$	−20.1097	−	4.27444i	−1.34664	−	0.286238i	−0.824134	+	0.566395i	$0.808338\pi$
$224$	18.0605			1.20672
$225$	−13.3819	+	6.77679i	−0.892126	+	0.451786i
$226$	−2.39854			−0.159548
$227$	−17.9839	−	3.82260i	−1.19363	−	0.253715i	−0.432091	−	0.901830i	$-0.642224\pi$
$227$	−17.9839	−	3.82260i	−1.19363	−	0.253715i	−0.761542	+	0.648115i	$0.775557\pi$
$228$	−2.60457	−	7.68205i	−0.172492	−	0.508756i
$229$	11.3448	+	5.05103i	0.749685	+	0.333781i	0.745763	−	0.666211i	$-0.232085\pi$
$229$	11.3448	+	5.05103i	0.749685	+	0.333781i	0.00392172	+	0.999992i	$0.498752\pi$
$230$	−8.71351	−	4.88976i	−0.574552	−	0.322421i
$231$	9.20318	−	6.86709i	0.605525	−	0.451821i
$232$	4.79346	−	8.30251i	0.314706	−	0.545087i
$233$	4.65048	+	3.37877i	0.304663	+	0.221351i	0.729603	−	0.683871i	$-0.239705\pi$
$233$	4.65048	+	3.37877i	0.304663	+	0.221351i	−0.424940	+	0.905221i	$0.639705\pi$
$234$	4.32869	+	1.79672i	0.282975	+	0.117455i
$235$	−2.23628	+	1.32781i	−0.145879	+	0.0866170i
$236$	0.272687	+	0.0579614i	0.0177504	+	0.00377297i
$237$	1.80159	−	19.5281i	0.117026	−	1.26848i
$238$	17.8202	−	3.78781i	1.15511	−	0.245527i
$239$	14.1539	−	15.7195i	0.915540	−	1.01681i	−0.0842522	−	0.996444i	$-0.526850\pi$
$239$	14.1539	−	15.7195i	0.915540	−	1.01681i	0.999793	−	0.0203661i	$-0.00648318\pi$
$240$	−1.78204	+	2.58603i	−0.115030	+	0.166927i
$241$	5.77768	+	6.41676i	0.372173	+	0.413340i	0.899915	−	0.436065i	$-0.143628\pi$
$241$	5.77768	+	6.41676i	0.372173	+	0.413340i	−0.527743	+	0.849404i	$0.676961\pi$
$242$	3.95884	+	2.87627i	0.254484	+	0.184893i
$243$	−8.63673	−	12.9772i	−0.554046	−	0.832486i
$244$	0.274296	+	0.199288i	0.0175600	+	0.0127581i
$245$	−3.23109	+	4.56346i	−0.206427	+	0.291549i
$246$	11.2877	+	2.24956i	0.719676	+	0.143426i
$247$	6.17186	+	2.74789i	0.392706	+	0.174844i
$248$	−16.6852	+	18.5308i	−1.05951	+	1.17671i
$249$	10.2353	−	2.31208i	0.648638	−	0.146522i
$250$	−7.58589	−	4.01645i	−0.479774	−	0.254022i
$251$	−6.58070			−0.415370			−0.207685	−	0.978196i	$-0.566593\pi$
$251$	−6.58070			−0.415370			−0.207685	+	0.978196i	$0.566593\pi$
$252$	12.6853	−	3.03565i	0.799102	−	0.191228i
$253$	−10.1278	+	7.35826i	−0.636728	+	0.462610i
$254$	0.167540	+	1.59403i	0.0105124	+	0.100019i
$255$	−11.4446	+	27.5333i	−0.716688	+	1.72420i
$256$	1.36460	−	12.9833i	0.0852873	−	0.811455i
$257$	5.84297	+	10.1203i	0.364474	+	0.631288i	0.988692	−	0.149963i	$-0.0479153\pi$
$257$	5.84297	+	10.1203i	0.364474	+	0.631288i	−0.624217	+	0.781251i	$0.714582\pi$
$258$	1.56814	−	1.17009i	0.0976284	−	0.0728469i
$259$	−9.54383	−	10.5995i	−0.593025	−	0.658621i
$260$	−1.41106	−	6.26129i	−0.0875103	−	0.388309i
$261$	3.12733	−	10.5294i	0.193577	−	0.651751i
$262$	−0.224194	+	0.689998i	−0.0138508	+	0.0426282i
$263$	13.0953	+	14.5438i	0.807492	+	0.896811i	0.996365	−	0.0851910i	$-0.0271500\pi$
$263$	13.0953	+	14.5438i	0.807492	+	0.896811i	−0.188873	+	0.982002i	$0.560483\pi$
$264$	−4.98444	−	8.38508i	−0.306771	−	0.516066i
$265$	13.6153	+	7.64048i	0.836379	+	0.469351i
$266$	−7.68493	+	1.63348i	−0.471193	+	0.100155i
$267$	0.440720	+	3.73535i	0.0269716	+	0.228600i
$268$	8.80227	−	15.2460i	0.537684	−	0.931297i
$269$	−3.43410	−	2.49502i	−0.209381	−	0.152124i	0.478153	−	0.878277i	$-0.341307\pi$
$269$	−3.43410	−	2.49502i	−0.209381	−	0.152124i	−0.687534	+	0.726153i	$0.741307\pi$
$270$	3.21314	−	8.32151i	0.195546	−	0.506431i
$271$	11.4304	−	8.30468i	0.694348	−	0.504473i	−0.183739	−	0.982975i	$-0.558820\pi$
$271$	11.4304	−	8.30468i	0.694348	−	0.504473i	0.878087	+	0.478502i	$0.158820\pi$
$272$	0.652558	+	6.20867i	0.0395671	+	0.376456i
$273$	−5.31168	+	9.47654i	−0.321477	+	0.573546i
$274$	2.52385	+	4.37143i	0.152471	+	0.264088i
$275$	−8.54335	+	6.53196i	−0.515183	+	0.393892i
$276$	−13.8706	+	3.13325i	−0.834912	+	0.188600i
$277$	12.7809	+	2.71665i	0.767927	+	0.163228i	0.575187	−	0.818022i	$-0.304929\pi$
$277$	12.7809	+	2.71665i	0.767927	+	0.163228i	0.192740	+	0.981250i	$0.438263\pi$
$278$	−3.69869	+	2.68726i	−0.221833	+	0.161171i
$279$	−13.6505	+	25.0973i	−0.817235	+	1.50253i
$280$	13.5580	+	11.9109i	0.810245	+	0.711813i
$281$	14.9151	−	6.64062i	0.889759	−	0.396146i	0.0896305	−	0.995975i	$-0.471431\pi$
$281$	14.9151	−	6.64062i	0.889759	−	0.396146i	0.800128	+	0.599829i	$0.204765\pi$
$282$	0.459186	−	1.47691i	0.0273441	−	0.0879487i
$283$	0.500115	−	4.75828i	0.0297288	−	0.282850i	−0.969551	−	0.244891i	$-0.921248\pi$
$283$	0.500115	−	4.75828i	0.0297288	−	0.282850i	0.999279	−	0.0379590i	$-0.0120856\pi$
$284$	9.03704	−	1.92088i	0.536250	−	0.113983i
$285$	4.93544	−	11.8737i	0.292351	−	0.703336i
$286$	3.28677	+	0.698624i	0.194351	+	0.0413105i
$287$	−8.24417	+	25.3729i	−0.486638	+	1.49772i
$288$	−2.28165	−	17.4295i	−0.134448	−	1.02704i
$289$	13.0624	+	40.2020i	0.768377	+	2.36482i
$290$	5.95363	−	2.01521i	0.349609	−	0.118337i
$291$	−2.51126	+	27.2204i	−0.147212	+	1.59569i
$292$	−1.18952	+	11.3175i	−0.0696111	+	0.662305i
$293$	14.9796	+	25.9455i	0.875119	+	1.51575i	0.856636	+	0.515922i	$0.172551\pi$
$293$	14.9796	+	25.9455i	0.875119	+	1.51575i	0.0184836	+	0.999829i	$0.494116\pi$
$294$	−0.389627	−	3.30230i	−0.0227235	−	0.192594i
$295$	0.264106	+	0.354323i	0.0153768	+	0.0206295i
$296$	−9.80245	+	7.12190i	−0.569756	+	0.413952i
$297$	−7.78985	−	8.01411i	−0.452013	−	0.465026i
$298$	0.238270	+	0.733319i	0.0138026	+	0.0424800i
$299$	5.92179	−	10.2568i	0.342466	−	0.593168i
$300$	−11.8464	+	2.98206i	−0.683953	+	0.172169i
$301$	2.26762	+	3.92763i	0.130703	+	0.226385i
$302$	2.62802	−	2.91871i	0.151225	−	0.167953i
$303$	6.86026	−	7.81685i	0.394112	−	0.449066i
$304$	−0.281414	−	2.67747i	−0.0161402	−	0.153564i
$305$	0.118161	+	0.524315i	0.00676587	+	0.0300222i
$306$	−5.90677	−	16.7191i	−0.337668	−	0.955769i
$307$	−15.7491			−0.898850			−0.449425	−	0.893318i	$-0.648371\pi$
$307$	−15.7491			−0.898850			−0.449425	+	0.893318i	$0.648371\pi$
$308$	8.54311	−	3.80364i	0.486789	−	0.216732i
$309$	−19.5439	−	13.8230i	−1.11181	−	0.786362i
$310$	−16.2368	+	1.90743i	−0.922189	+	0.108335i
$311$	−3.78422	+	4.20281i	−0.214584	+	0.238319i	−0.840821	−	0.541313i	$-0.817927\pi$
$311$	−3.78422	+	4.20281i	−0.214584	+	0.238319i	0.626237	+	0.779632i	$0.284594\pi$
$312$	7.53459	+	5.32906i	0.426562	+	0.301699i
$313$	−1.17569	−	1.30574i	−0.0664539	−	0.0738045i	0.709001	−	0.705207i	$-0.249146\pi$
$313$	−1.17569	−	1.30574i	−0.0664539	−	0.0738045i	−0.775455	+	0.631403i	$0.782479\pi$
$314$	4.58615	+	14.1147i	0.258812	+	0.796540i
$315$	18.2832	+	9.65670i	1.03014	+	0.544093i
$316$	4.93536	−	15.1895i	0.277636	−	0.854475i
$317$	19.5170	−	8.68952i	1.09618	−	0.488052i	0.222690	−	0.974889i	$-0.428516\pi$
$317$	19.5170	−	8.68952i	1.09618	−	0.488052i	0.873493	+	0.486837i	$0.161849\pi$
$318$	−9.05640	+	2.04577i	−0.507858	+	0.114721i
$319$	0.823162	−	7.83187i	0.0460882	−	0.438500i
$320$	4.72733	−	4.36228i	0.264266	−	0.243859i
$321$	−14.6549	−	2.92062i	−0.817956	−	0.163013i
$322$	1.43968	+	13.6977i	0.0802304	+	0.763341i
$323$	−7.89860	−	24.3094i	−0.439490	−	1.35261i
$324$	−4.53219	−	11.8587i	−0.251788	−	0.658814i
$325$	4.87036	−	8.93298i	0.270159	−	0.495513i
$326$	−3.67797	+	6.37044i	−0.203704	+	0.352826i
$327$	16.1878	−	28.8805i	0.895186	−	1.59710i
$328$	20.7043	+	9.21814i	1.14320	+	0.508986i
$329$	3.27509	+	1.45817i	0.180562	+	0.0803913i
$330$	1.17325	−	6.28691i	0.0645854	−	0.346083i
$331$	−17.7867	+	7.91914i	−0.977644	+	0.435275i	−0.832433	−	0.554126i	$-0.813053\pi$
$331$	−17.7867	+	7.91914i	−0.977644	+	0.435275i	−0.145211	+	0.989401i	$0.546386\pi$
$332$	8.54567			0.469005
$333$	−9.02348	+	10.5495i	−0.494484	+	0.578108i
$334$	−3.52150	+	10.8381i	−0.192688	+	0.593032i
$335$	26.4337	−	8.94740i	1.44423	−	0.488849i
$336$	4.32877	−	0.0550809i	0.236154	−	0.00300491i
$337$	−28.0885	+	5.97039i	−1.53008	+	0.325228i	−0.894591	−	0.446886i	$-0.852533\pi$
$337$	−28.0885	+	5.97039i	−1.53008	+	0.325228i	−0.635485	+	0.772113i	$0.719200\pi$
$338$	6.65295	−	1.41413i	0.361873	−	0.0769184i
$339$	−5.41077	+	0.0688486i	−0.293873	+	0.00373934i
$340$	−14.0321	+	19.8183i	−0.760997	+	1.07480i
$341$	−6.32958	+	19.4804i	−0.342766	+	1.05492i
$342$	2.54728	+	7.21008i	0.137741	+	0.389876i
$343$	−13.8685			−0.748829
$344$	3.51961	−	1.56703i	0.189765	−	0.0844887i
$345$	−19.7968	−	10.7805i	−1.06583	−	0.580404i
$346$	−3.14748	−	1.40135i	−0.169210	−	0.0753369i
$347$	−7.39283	−	3.29150i	−0.396868	−	0.176697i	0.198591	−	0.980082i	$-0.436363\pi$
$347$	−7.39283	−	3.29150i	−0.396868	−	0.176697i	−0.595459	+	0.803385i	$0.703030\pi$
$348$	4.37374	−	7.80316i	0.234457	−	0.418293i
$349$	−8.94831	+	15.4989i	−0.478992	+	0.829639i	−0.999710	−	0.0240902i	$-0.992331\pi$
$349$	−8.94831	+	15.4989i	−0.478992	+	0.829639i	0.520718	+	0.853729i	$0.325664\pi$
$350$	1.52397	+	11.7334i	0.0814597	+	0.627179i
$351$	9.81651	+	3.92890i	0.523966	+	0.209709i
$352$	−3.89448	−	11.9860i	−0.207576	−	0.638854i
$353$	1.58045	+	15.0370i	0.0841188	+	0.800337i	0.952520	+	0.304475i	$0.0984811\pi$
$353$	1.58045	+	15.0370i	0.0841188	+	0.800337i	−0.868401	+	0.495862i	$0.834852\pi$
$354$	−0.257738	−	0.0513654i	−0.0136986	−	0.00273004i
$355$	12.7721	+	7.16730i	0.677870	+	0.380401i
$356$	−0.320188	+	3.04638i	−0.0169699	+	0.161458i
$357$	40.0913	−	9.05630i	2.12186	−	0.479310i
$358$	0.651767	−	0.290185i	0.0344470	−	0.0153368i
$359$	−5.02999	+	15.4807i	−0.265473	+	0.817042i	0.726111	+	0.687577i	$0.241326\pi$
$359$	−5.02999	+	15.4807i	−0.265473	+	0.817042i	−0.991584	+	0.129464i	$0.958674\pi$
$360$	9.78196	−	14.5891i	0.515555	−	0.768911i
$361$	−2.46507	−	7.58672i	−0.129741	−	0.399301i
$362$	−0.498182	−	0.553287i	−0.0261838	−	0.0290801i
$363$	9.01316	+	6.37483i	0.473068	+	0.334592i
$364$	−5.92002	+	6.57485i	−0.310293	+	0.344616i
$365$	−13.2574	+	12.2337i	−0.693925	+	0.640339i
$366$	−0.260950	−	0.184564i	−0.0136401	−	0.00964734i
$367$	11.3366	−	5.04737i	0.591764	−	0.263470i	−0.0889303	−	0.996038i	$-0.528345\pi$
$367$	11.3366	−	5.04737i	0.591764	−	0.263470i	0.680694	+	0.732568i	$0.261678\pi$
$368$	−4.71962			−0.246027
$369$	25.5280	+	4.75069i	1.32894	+	0.247311i
$370$	−7.90994	−	0.733762i	−0.411218	−	0.0381465i
$371$	−2.24957	−	21.4032i	−0.116792	−	1.11120i
$372$	−15.3473	+	17.4873i	−0.795721	+	0.906676i
$373$	−21.0233	+	23.3487i	−1.08854	+	1.20895i	−0.111983	+	0.993710i	$0.535720\pi$
$373$	−21.0233	+	23.3487i	−1.08854	+	1.20895i	−0.976561	+	0.215240i	$0.930947\pi$
$374$	−6.35647	−	11.0097i	−0.328685	−	0.569300i
$375$	−17.2280	−	8.84281i	−0.889651	−	0.456641i
$376$	1.52275	−	2.63748i	0.0785299	−	0.136018i
$377$	2.30229	+	7.08571i	0.118574	+	0.364933i
$378$	−11.9212	+	3.01365i	−0.613158	+	0.155005i
$379$	18.1814	−	13.2096i	0.933915	−	0.678529i	−0.0130329	−	0.999915i	$-0.504149\pi$
$379$	18.1814	−	13.2096i	0.933915	−	0.678529i	0.946948	+	0.321386i	$0.104149\pi$
$380$	6.05130	−	8.54661i	0.310425	−	0.438432i
$381$	0.423702	+	3.59111i	0.0217069	+	0.183978i
$382$	5.37139	+	9.30353i	0.274824	+	0.476010i
$383$	2.04712	−	19.4770i	0.104603	−	0.995230i	−0.808775	−	0.588118i	$-0.799869\pi$
$383$	2.04712	−	19.4770i	0.104603	−	0.995230i	0.913378	−	0.407112i	$-0.133464\pi$
$384$	1.51325	−	16.4026i	0.0772226	−	0.837043i
$385$	14.1536	+	4.40833i	0.721337	+	0.224669i
$386$	−1.61391	−	4.96712i	−0.0821461	−	0.252820i
$387$	3.50393	−	2.68459i	0.178115	−	0.136465i
$388$	−6.87945	+	21.1728i	−0.349251	+	1.07488i
$389$	27.8479	+	5.91925i	1.41194	+	0.300118i	0.849880	−	0.526976i	$-0.176674\pi$
$389$	27.8479	+	5.91925i	1.41194	+	0.300118i	0.562064	+	0.827094i	$0.310008\pi$
$390$	1.40521	+	5.88515i	0.0711554	+	0.298006i
$391$	−43.8297	+	9.31630i	−2.21657	+	0.471145i
$392$	0.684417	−	6.51179i	0.0345683	−	0.328895i
$393$	−0.485945	+	1.56298i	−0.0245127	+	0.0788418i
$394$	−5.99608	+	2.66963i	−0.302078	+	0.134494i
$395$	21.7694	−	12.9258i	1.09534	−	0.650369i
$396$	−4.75004	−	7.76412i	−0.238698	−	0.390162i
$397$	26.7333	−	19.4229i	1.34171	−	0.974807i	0.342327	−	0.939581i	$-0.388785\pi$
$397$	26.7333	−	19.4229i	1.34171	−	0.974807i	0.999379	−	0.0352262i	$-0.0112152\pi$
$398$	−9.29456	−	1.97562i	−0.465894	−	0.0990289i
$399$	−17.2893	+	3.90550i	−0.865545	+	0.195520i
$400$	−4.05325	+	0.0990806i	−0.202663	+	0.00495403i
$401$	7.60381	+	13.1702i	0.379716	+	0.657688i	0.991021	−	0.133707i	$-0.0426883\pi$
$401$	7.60381	+	13.1702i	0.379716	+	0.657688i	−0.611305	+	0.791395i	$0.709355\pi$
$402$	−8.11441	+	14.4769i	−0.404710	+	0.722041i
$403$	−2.02560	−	19.2723i	−0.100902	−	0.960020i
$404$	6.85237	−	4.97854i	0.340918	−	0.247691i
$405$	7.00954	−	18.8644i	0.348307	−	0.937381i
$406$	−7.00945	−	5.09267i	−0.347873	−	0.252745i
$407$	−4.97644	+	8.61945i	−0.246673	+	0.427250i
$408$	−4.09121	−	34.6753i	−0.202545	−	1.71668i
$409$	6.63574	−	1.41047i	0.328116	−	0.0697432i	−0.0409084	−	0.999163i	$-0.513025\pi$
$409$	6.63574	−	1.41047i	0.328116	−	0.0697432i	0.369024	+	0.929420i	$0.379692\pi$
$410$	6.20908	+	13.4994i	0.306645	+	0.666689i
$411$	5.81893	+	9.78891i	0.287027	+	0.482851i
$412$	−13.0449	−	14.4878i	−0.642674	−	0.713762i
$413$	0.188244	−	0.579355i	0.00926287	−	0.0285082i
$414$	13.0372	−	3.11986i	0.640745	−	0.153333i
$415$	10.1772	+	8.94082i	0.499578	+	0.438888i
$416$	7.97818	+	8.86067i	0.391163	+	0.434430i
$417$	−8.26661	+	6.16825i	−0.404817	+	0.302061i
$418$	2.74121	+	4.74792i	0.134077	+	0.232228i
$419$	−2.96511	+	28.2111i	−0.144855	+	1.37820i	0.644659	+	0.764470i	$0.276999\pi$
$419$	−2.96511	+	28.2111i	−0.144855	+	1.37820i	−0.789514	+	0.613733i	$0.789667\pi$
$420$	12.7910	+	10.9519i	0.624138	+	0.534400i
$421$	1.15103	+	10.9513i	0.0560976	+	0.533733i	0.986097	+	0.166171i	$0.0531405\pi$
$421$	1.15103	+	10.9513i	0.0560976	+	0.533733i	−0.929999	+	0.367561i	$0.880193\pi$
$422$	6.75074	−	4.90470i	0.328621	−	0.238757i
$423$	0.993467	−	3.34489i	0.0483040	−	0.162634i
$424$	−18.2823			−0.887866
$425$	−37.4458	+	8.92105i	−1.81639	+	0.432734i
$426$	−8.49553	+	1.91907i	−0.411610	+	0.0929793i
$427$	0.495737	−	0.550572i	0.0239904	−	0.0266440i
$428$	−11.1175	−	4.94983i	−0.537385	−	0.239259i
$429$	7.43455	+	1.48166i	0.358944	+	0.0715350i
$430$	2.41166	+	0.751142i	0.116301	+	0.0362233i
$431$	2.54049	+	1.84577i	0.122371	+	0.0889077i	0.647287	−	0.762246i	$-0.275903\pi$
$431$	2.54049	+	1.84577i	0.122371	+	0.0889077i	−0.524916	+	0.851154i	$0.675903\pi$
$432$	−0.600027	−	4.17058i	−0.0288688	−	0.200657i
$433$	5.14241	+	3.73618i	0.247129	+	0.179549i	0.704453	−	0.709750i	$-0.251192\pi$
$433$	5.14241	+	3.73618i	0.247129	+	0.179549i	−0.457325	+	0.889300i	$0.651192\pi$
$434$	15.0792	+	16.7472i	0.723826	+	0.803890i
$435$	13.3727	−	4.71693i	0.641173	−	0.226160i
$436$	18.0418	−	20.0374i	0.864044	−	0.959618i
$437$	18.9015	−	4.01763i	0.904179	−	0.192189i
$438$	0.985525	−	10.6824i	0.0470902	−	0.510427i
$439$	−8.69090	−	1.84731i	−0.414794	−	0.0881671i	−0.00421247	−	0.999991i	$-0.501341\pi$
$439$	−8.69090	−	1.84731i	−0.414794	−	0.0881671i	−0.410581	+	0.911824i	$0.634674\pi$
$440$	4.98118	−	11.5663i	0.237469	−	0.551400i
$441$	−0.973735	−	7.43836i	−0.0463683	−	0.354207i
$442$	9.73039	+	7.06954i	0.462827	+	0.336264i
$443$	11.9049	−	20.6199i	0.565618	−	0.979679i	−0.431374	−	0.902173i	$-0.641971\pi$
$443$	11.9049	−	20.6199i	0.565618	−	0.979679i	0.996992	−	0.0775061i	$-0.0246957\pi$
$444$	−9.06115	+	6.76111i	−0.430023	+	0.320868i
$445$	−3.56856	+	3.29299i	−0.169166	+	0.156103i
$446$	14.4193	+	6.41988i	0.682773	+	0.303990i
$447$	0.558554	+	1.64743i	0.0264187	+	0.0779207i
$448$	−8.67311	−	1.84353i	−0.409766	−	0.0870985i
$449$	−38.5889			−1.82112			−0.910561	−	0.413375i	$-0.864350\pi$
$449$	−38.5889			−1.82112			−0.910561	+	0.413375i	$0.864350\pi$
$450$	11.1310	−	2.95306i	0.524720	−	0.139209i
$451$	18.6167			0.876624
$452$	−4.31058	−	0.916242i	−0.202753	−	0.0430964i
$453$	5.84466	−	6.65964i	0.274606	−	0.312897i
$454$	12.8950	+	5.74124i	0.605194	+	0.269450i
$455$	−13.9291	+	1.63633i	−0.653007	+	0.0767124i
$456$	1.76432	+	14.9536i	0.0826220	+	0.700267i
$457$	−11.3704	+	19.6941i	−0.531884	+	0.921250i	0.467423	+	0.884034i	$0.345182\pi$
$457$	−11.3704	+	19.6941i	−0.531884	+	0.921250i	−0.999307	+	0.0372166i	$0.988151\pi$
$458$	−7.71324	−	5.60399i	−0.360416	−	0.261857i
$459$	−13.8048	−	37.5465i	−0.644352	−	1.75252i
$460$	−13.7918	−	12.1163i	−0.643045	−	0.564926i
$461$	−1.18583	−	0.252056i	−0.0552297	−	0.0117394i	0.180214	−	0.983627i	$-0.442321\pi$
$461$	−1.18583	−	0.252056i	−0.0552297	−	0.0117394i	−0.235444	+	0.971888i	$0.575654\pi$
$462$	−8.00736	+	3.68789i	−0.372536	+	0.171576i
$463$	10.9272	−	2.32264i	0.507828	−	0.107942i	0.0531294	−	0.998588i	$-0.483080\pi$
$463$	10.9272	−	2.32264i	0.507828	−	0.107942i	0.454698	+	0.890646i	$0.349747\pi$
$464$	1.98661	−	2.20635i	0.0922261	−	0.102427i
$465$	−36.5733	+	4.76897i	−1.69605	+	0.221156i
$466$	−2.95300	−	3.27964i	−0.136795	−	0.151926i
$467$	−28.0248	−	20.3612i	−1.29683	−	0.942204i	−0.296913	−	0.954905i	$-0.595957\pi$
$467$	−28.0248	−	20.3612i	−1.29683	−	0.942204i	−0.999919	+	0.0127009i	$0.995957\pi$
$468$	7.09305	+	4.88257i	0.327876	+	0.225697i
$469$	−31.1215	−	22.6111i	−1.43706	−	1.04408i
$470$	1.89131	−	0.640177i	0.0872394	−	0.0295292i
$471$	10.7509	+	31.7093i	0.495375	+	1.46109i
$472$	−0.472752	−	0.210483i	−0.0217602	−	0.00968826i
$473$	2.11762	−	2.35185i	0.0973681	−	0.108138i
$474$	−4.47003	+	14.3772i	−0.205315	+	0.660369i
$475$	16.1484	−	3.84718i	0.740939	−	0.176521i
$476$	33.4729			1.53423
$477$	−20.3713	+	4.87493i	−0.932737	+	0.223208i
$478$	−13.1382	+	9.54546i	−0.600927	+	0.436599i
$479$	−4.32087	−	41.1104i	−0.197426	−	1.87838i	−0.425815	−	0.904810i	$-0.640013\pi$
$479$	−4.32087	−	41.1104i	−0.197426	−	1.87838i	0.228390	−	0.973570i	$-0.426654\pi$
$480$	16.4805	−	15.6007i	0.752229	−	0.712073i
$481$	0.984260	−	9.36461i	0.0448784	−	0.426990i
$482$	−3.31455	−	5.74097i	−0.150974	−	0.261494i
$483$	3.64091	+	30.8587i	0.165667	+	1.40412i
$484$	6.01598	+	6.68142i	0.273453	+	0.303701i
$485$	−30.3446	+	18.0174i	−1.37788	+	0.818129i
$486$	4.41441	+	11.1239i	0.200242	+	0.504593i
$487$	−1.47545	+	4.54096i	−0.0668589	+	0.205771i	−0.978905	−	0.204318i	$-0.934502\pi$
$487$	−1.47545	+	4.54096i	−0.0668589	+	0.205771i	0.912046	+	0.410089i	$0.134502\pi$
$488$	−0.421130	−	0.467712i	−0.0190637	−	0.0211723i
$489$	−8.11415	+	14.4764i	−0.366934	+	0.654646i
$490$	3.15485	−	2.91123i	0.142522	−	0.131516i
$491$	35.2447	−	7.49150i	1.59057	−	0.338087i	0.674242	−	0.738510i	$-0.264470\pi$
$491$	35.2447	−	7.49150i	1.59057	−	0.338087i	0.916330	+	0.400424i	$0.131137\pi$
$492$	19.4265	+	8.35473i	0.875816	+	0.376660i
$493$	14.0938	−	24.4112i	0.634754	−	1.09943i
$494$	−4.19620	−	3.04872i	−0.188796	−	0.137168i
$495$	2.46623	−	14.2161i	0.110849	−	0.638966i
$496$	−6.24742	+	4.53902i	−0.280518	+	0.203808i
$497$	−2.11025	−	20.0777i	−0.0946578	−	0.900608i
$498$	−8.05539	+	0.102500i	−0.360971	+	0.00459312i
$499$	4.85852	+	8.41520i	0.217497	+	0.376716i	0.954042	−	0.299673i	$-0.0968774\pi$
$499$	4.85852	+	8.41520i	0.217497	+	0.376716i	−0.736545	+	0.676388i	$0.763544\pi$
$500$	−12.0989	−	10.1161i	−0.541077	−	0.452404i
$501$	−7.63291	+	24.5502i	−0.341013	+	1.09682i
$502$	4.94185	+	1.05042i	0.220565	+	0.0468826i
$503$	−2.45420	+	1.78308i	−0.109427	+	0.0795036i	−0.641153	−	0.767413i	$-0.721544\pi$
$503$	−2.45420	+	1.78308i	−0.109427	+	0.0795036i	0.531726	+	0.846917i	$0.321544\pi$
$504$	−24.2046	+	0.616075i	−1.07816	+	0.0274422i
$505$	13.3693	+	1.24020i	0.594928	+	0.0551882i
$506$	8.78010	−	3.90915i	0.390323	−	0.173783i
$507$	14.9676	−	3.38105i	0.664733	−	0.150158i
$508$	−0.307824	+	2.92875i	−0.0136575	+	0.129942i
$509$	11.0397	−	2.34655i	0.489325	−	0.104009i	0.0433596	−	0.999060i	$-0.486194\pi$
$509$	11.0397	−	2.34655i	0.489325	−	0.104009i	0.445965	+	0.895050i	$0.352861\pi$
$510$	12.9893	−	18.8496i	0.575178	−	0.834676i
$511$	24.3230	+	5.17002i	1.07599	+	0.228708i
$512$	2.78050	−	8.55750i	0.122882	−	0.378192i
$513$	5.95328	+	16.1918i	0.262844	+	0.714887i
$514$	−2.77242	−	8.53262i	−0.122286	−	0.376358i
$515$	−0.377636	−	30.9018i	−0.0166406	−	1.36169i
$516$	3.26520	−	1.50383i	0.143742	−	0.0662023i
$517$	0.261496	−	2.48797i	0.0115006	−	0.109421i
$518$	5.47513	+	9.48321i	0.240563	+	0.416668i
$519$	−7.14051	−	3.07090i	−0.313434	−	0.134798i
$520$	0.145587	+	11.9133i	0.00638441	+	0.522433i
$521$	23.1526	−	16.8213i	1.01433	−	0.736956i	0.0492197	−	0.998788i	$-0.484327\pi$
$521$	23.1526	−	16.8213i	1.01433	−	0.736956i	0.965114	+	0.261832i	$0.0843266\pi$
$522$	−4.02922	+	7.40794i	−0.176354	+	0.324237i
$523$	2.37046	+	7.29554i	0.103653	+	0.319012i	0.989412	−	0.145134i	$-0.0463614\pi$
$523$	2.37046	+	7.29554i	0.103653	+	0.319012i	−0.885759	+	0.464146i	$0.846361\pi$
$524$	−0.666495	+	1.15440i	−0.0291160	+	0.0504303i
$525$	3.77467	+	26.4253i	0.164740	+	1.15330i
$526$	−7.51256	−	13.0121i	−0.327563	−	0.567356i
$527$	−49.0581	+	54.4846i	−2.13701	+	2.37339i
$528$	−0.969990	−	2.86094i	−0.0422134	−	0.124506i
$529$	−1.13682	−	10.8161i	−0.0494268	−	0.470264i
$530$	−9.00494	−	7.91099i	−0.391149	−	0.343631i
$531$	−0.582896	−	0.108475i	−0.0252955	−	0.00470742i
$532$	−14.4351			−0.625841
$533$	−16.0901	+	7.16377i	−0.696939	+	0.310297i
$534$	0.265279	−	2.87545i	0.0114797	−	0.124433i
$535$	−8.06130	−	17.5264i	−0.348520	−	0.757732i
$536$	−21.8665	+	24.2852i	−0.944488	+	1.04896i
$537$	1.46197	−	0.673327i	0.0630886	−	0.0290562i
$538$	2.18062	+	2.42182i	0.0940130	+	0.104412i
$539$	−1.66204	−	5.11522i	−0.0715890	−	0.220328i
$540$	8.95338	−	13.7277i	0.385292	−	0.590748i
$541$	12.1397	−	37.3621i	0.521926	−	1.60632i	−0.248390	−	0.968660i	$-0.579902\pi$
$541$	12.1397	−	37.3621i	0.521926	−	1.60632i	0.770316	−	0.637662i	$-0.220098\pi$
$542$	−9.90939	+	4.41195i	−0.425645	+	0.189509i
$543$	−1.13971	−	1.23384i	−0.0489097	−	0.0529491i
$544$	4.71530	−	44.8631i	0.202167	−	1.92349i
$545$	42.4501	−	4.98686i	1.81836	−	0.213614i
$546$	5.50152	−	6.26865i	0.235443	−	0.268273i
$547$	0.0902248	+	0.858432i	0.00385773	+	0.0367039i	0.996281	−	0.0861587i	$-0.0274592\pi$
$547$	0.0902248	+	0.858432i	0.00385773	+	0.0367039i	−0.992424	+	0.122863i	$0.960793\pi$
$548$	2.86589	+	8.82032i	0.122425	+	0.376785i
$549$	−0.593965	−	0.408862i	−0.0253498	−	0.0174498i
$550$	7.45836	−	3.54154i	0.318025	−	0.151012i
$551$	−6.07792	+	10.5273i	−0.258928	+	0.448477i
$552$	26.3943	−	0.335851i	1.12342	−	0.0142948i
$553$	−31.8820	−	14.1948i	−1.35576	−	0.603623i
$554$	−9.16428	−	4.08020i	−0.389353	−	0.173351i
$555$	−17.8648	−	1.42822i	−0.758319	−	0.0606245i
$556$	−7.67371	+	3.41656i	−0.325438	+	0.144894i
$557$	−17.9941			−0.762437			−0.381218	−	0.924485i	$-0.624495\pi$
$557$	−17.9941			−0.762437			−0.381218	+	0.924485i	$0.624495\pi$
$558$	14.2571	−	16.6681i	0.603550	−	0.705618i
$559$	−0.925221	+	2.84754i	−0.0391327	+	0.120438i
$560$	3.34006	+	4.48101i	0.141143	+	0.189357i
$561$	−14.6554	−	24.6540i	−0.618750	−	1.04089i
$562$	−12.2606	+	2.60607i	−0.517183	+	0.109931i
$563$	−10.6898	+	2.27219i	−0.450521	+	0.0957612i	−0.427584	−	0.903976i	$-0.640635\pi$
$563$	−10.6898	+	2.27219i	−0.450521	+	0.0957612i	−0.0229373	+	0.999737i	$0.507302\pi$
$564$	1.38942	−	2.47885i	0.0585050	−	0.104378i
$565$	−4.17493	−	5.60107i	−0.175641	−	0.235639i
$566$	−1.13509	+	3.49345i	−0.0477114	+	0.146841i
$567$	−26.8060	+	7.14057i	−1.12575	+	0.299876i
$568$	−17.1500			−0.719599
$569$	−3.23472	+	1.44019i	−0.135606	+	0.0603759i	−0.473418	−	0.880838i	$-0.656980\pi$
$569$	−3.23472	+	1.44019i	−0.135606	+	0.0603759i	0.337812	+	0.941214i	$0.390313\pi$
$570$	−5.60162	+	8.12886i	−0.234626	+	0.340480i
$571$	21.9586	+	9.77660i	0.918939	+	0.409138i	0.811018	−	0.585022i	$-0.198914\pi$
$571$	21.9586	+	9.77660i	0.918939	+	0.409138i	0.107921	+	0.994159i	$0.465581\pi$
$572$	5.64001	+	2.51109i	0.235821	+	0.104994i
$573$	12.3842	+	20.8333i	0.517357	+	0.870324i
$574$	10.2411	−	17.7381i	0.427456	−	0.740375i
$575$	−3.74828	−	28.8590i	−0.156314	−	1.20350i
$576$	−0.683413	+	8.60300i	−0.0284755	+	0.358459i
$577$	0.345780	+	1.06420i	0.0143950	+	0.0443033i	0.957996	−	0.286782i	$-0.0925854\pi$
$577$	0.345780	+	1.06420i	0.0143950	+	0.0443033i	−0.943601	+	0.331085i	$0.892585\pi$
$578$	−3.39225	−	32.2751i	−0.141099	−	1.34247i
$579$	−3.78335	−	11.1588i	−0.157231	−	0.463744i
$580$	11.4695	−	1.34739i	0.476245	−	0.0559472i
$581$	1.95191	−	18.5711i	0.0809787	−	0.770461i
$582$	6.23081	−	20.0406i	0.258275	−	0.830708i
$583$	−13.7193	+	6.10823i	−0.568196	+	0.252977i
$584$	6.52771	−	20.0902i	0.270119	−	0.831340i
$585$	3.33888	+	13.2358i	0.138046	+	0.547231i
$586$	−7.10765	−	21.8751i	−0.293614	−	0.903652i
$587$	19.5420	+	21.7036i	0.806587	+	0.895805i	0.996292	−	0.0860359i	$-0.0274200\pi$
$587$	19.5420	+	21.7036i	0.806587	+	0.895805i	−0.189705	+	0.981841i	$0.560753\pi$
$588$	0.561255	−	6.08364i	0.0231458	−	0.250885i
$589$	21.1562	−	23.4963i	0.871725	−	0.968149i
$590$	−0.141775	−	0.308240i	−0.00583680	−	0.0126900i
$591$	−13.4497	+	6.19443i	−0.553247	+	0.254805i
$592$	−3.42792	+	1.52621i	−0.140886	+	0.0627267i
$593$	11.3423			0.465772			0.232886	−	0.972504i	$-0.425183\pi$
$593$	11.3423			0.465772			0.232886	+	0.972504i	$0.425183\pi$
$594$	4.57065	+	7.26171i	0.187536	+	0.297951i
$595$	39.8635	+	35.0207i	1.63424	+	1.43571i
$596$	0.148083	+	1.40892i	0.00606573	+	0.0577116i
$597$	−21.0240	−	4.18993i	−0.860454	−	0.171483i
$598$	−6.08424	+	6.75724i	−0.248803	+	0.276324i
$599$	−14.7936	−	25.6233i	−0.604450	−	1.04694i	−0.992138	−	0.125148i	$-0.960060\pi$
$599$	−14.7936	−	25.6233i	−0.604450	−	1.04694i	0.387688	−	0.921791i	$-0.373274\pi$
$600$	22.6606	−	0.842535i	0.925115	−	0.0343964i
$601$	3.62053	−	6.27094i	0.147684	−	0.255797i	−0.782687	−	0.622416i	$-0.786151\pi$
$601$	3.62053	−	6.27094i	0.147684	−	0.255797i	0.930371	+	0.366619i	$0.119485\pi$
$602$	−1.07596	−	3.31145i	−0.0438527	−	0.134965i
$603$	−17.8894	+	32.8908i	−0.728515	+	1.33942i
$604$	5.83794	−	4.24151i	0.237542	−	0.172585i
$605$	0.174157	+	14.2512i	0.00708047	+	0.579392i
$606$	−6.39952	+	4.77510i	−0.259963	+	0.193975i
$607$	3.82155	+	6.61912i	0.155112	+	0.268662i	0.933100	−	0.359618i	$-0.117093\pi$
$607$	3.82155	+	6.61912i	0.155112	+	0.268662i	−0.777988	+	0.628279i	$0.783760\pi$
$608$	−2.03346	+	19.3471i	−0.0824677	+	0.784627i
$609$	−15.9586	−	11.2872i	−0.646673	−	0.457379i
$610$	−0.00504219	−	0.412601i	−0.000204152	−	0.0167057i
$611$	0.731374	+	2.25094i	0.0295882	+	0.0910632i
$612$	−4.22877	−	32.3035i	−0.170938	−	1.30579i
$613$	−13.8744	+	42.7010i	−0.560381	+	1.72468i	0.120910	+	0.992664i	$0.461419\pi$
$613$	−13.8744	+	42.7010i	−0.560381	+	1.72468i	−0.681291	+	0.732013i	$0.738581\pi$
$614$	11.8270	+	2.51390i	0.477298	+	0.101453i
$615$	14.3943	+	30.2746i	0.580435	+	1.22079i
$616$	−16.9798	+	3.60918i	−0.684137	+	0.145418i
$617$	−1.39059	+	13.2306i	−0.0559832	+	0.532645i	0.930208	+	0.367033i	$0.119626\pi$
$617$	−1.39059	+	13.2306i	−0.0559832	+	0.532645i	−0.986191	+	0.165612i	$0.947040\pi$
$618$	12.4702	+	13.5001i	0.501626	+	0.543055i
$619$	14.9640	−	6.66238i	0.601452	−	0.267784i	−0.0833411	−	0.996521i	$-0.526559\pi$
$619$	14.9640	−	6.66238i	0.601452	−	0.267784i	0.684793	+	0.728737i	$0.259892\pi$
$620$	−29.9090	−	2.77449i	−1.20117	−	0.111426i
$621$	29.3207	−	7.41221i	1.17660	−	0.297442i
$622$	3.51266	−	2.55210i	0.140845	−	0.102330i
$623$	6.54716	+	1.39164i	0.262306	+	0.0557549i
$624$	1.93925	+	2.09941i	0.0776321	+	0.0840437i
$625$	−3.82490	−	24.7057i	−0.152996	−	0.988227i
$626$	0.674473	+	1.16822i	0.0269573	+	0.0466915i
$627$	6.32008	+	10.6320i	0.252400	+	0.424600i
$628$	2.85027	+	27.1185i	0.113738	+	1.08215i
$629$	−28.8214	+	20.9399i	−1.14918	+	0.834930i
$630$	−12.1885	−	10.1702i	−0.485603	−	0.405190i
$631$	5.16265	+	3.75089i	0.205522	+	0.149320i	0.685785	−	0.727804i	$-0.259459\pi$
$631$	5.16265	+	3.75089i	0.205522	+	0.149320i	−0.480263	+	0.877124i	$0.659459\pi$
$632$	−14.8235	+	25.6750i	−0.589646	+	1.02130i
$633$	15.0880	−	11.2581i	0.599693	−	0.447470i
$634$	−16.0435	+	3.41016i	−0.637170	+	0.135435i
$635$	−3.43077	+	3.16584i	−0.136146	+	0.125632i
$636$	−17.0574	+	0.217044i	−0.676369	+	0.00860637i
$637$	3.40483	+	3.78145i	0.134904	+	0.149826i
$638$	−1.86830	+	5.75003i	−0.0739666	+	0.227646i
$639$	−19.1097	+	4.57302i	−0.755967	+	0.180906i
$640$	18.2853	−	10.8571i	0.722788	−	0.429163i
$641$	−17.9521	−	19.9378i	−0.709065	−	0.787496i	0.275727	−	0.961236i	$-0.411081\pi$
$641$	−17.9521	−	19.9378i	−0.709065	−	0.787496i	−0.984792	+	0.173740i	$0.944415\pi$
$642$	10.5390	+	4.53250i	0.415943	+	0.178884i
$643$	−11.0055	−	19.0621i	−0.434016	−	0.751738i	0.563199	−	0.826321i	$-0.309571\pi$
$643$	−11.0055	−	19.0621i	−0.434016	−	0.751738i	−0.997215	+	0.0745838i	$0.976237\pi$
$644$	−2.64516	+	25.1670i	−0.104234	+	0.991719i
$645$	5.46194	+	1.62525i	0.215064	+	0.0639941i
$646$	2.05123	+	19.5162i	0.0807047	+	0.767853i
$647$	−17.8461	+	12.9660i	−0.701604	+	0.509745i	−0.880454	−	0.474131i	$-0.842762\pi$
$647$	−17.8461	+	12.9660i	−0.701604	+	0.509745i	0.178850	+	0.983876i	$0.442762\pi$
$648$	3.65241	+	23.2811i	0.143480	+	0.914568i
$649$	−0.425085			−0.0166860
$650$	−5.08334	+	5.93090i	−0.199385	+	0.232629i
$651$	34.4974	+	37.3465i	1.35206	+	1.46372i
$652$	−9.04346	+	10.0438i	−0.354169	+	0.393345i
$653$	7.28940	+	3.24545i	0.285256	+	0.127004i	0.544377	−	0.838841i	$-0.316766\pi$
$653$	7.28940	+	3.24545i	0.285256	+	0.127004i	−0.259121	+	0.965845i	$0.583433\pi$
$654$	−16.7663	+	19.1042i	−0.655616	+	0.747034i
$655$	−2.00152	+	0.677483i	−0.0782059	+	0.0264715i
$656$	5.67819	+	4.12545i	0.221696	+	0.161072i
$657$	1.91658	−	24.1264i	0.0747728	−	0.941262i
$658$	−2.22671	−	1.61780i	−0.0868062	−	0.0630684i
$659$	20.9084	+	23.2211i	0.814474	+	0.904565i	0.996902	−	0.0786543i	$-0.0250623\pi$
$659$	20.9084	+	23.2211i	0.814474	+	0.904565i	−0.182428	+	0.983219i	$0.558396\pi$
$660$	4.51014	−	10.8505i	0.175557	−	0.422354i
$661$	−19.4729	+	21.6268i	−0.757407	+	0.841186i	−0.991375	−	0.131058i	$-0.958162\pi$
$661$	−19.4729	+	21.6268i	−0.757407	+	0.841186i	0.233967	+	0.972244i	$0.424829\pi$
$662$	14.6212	−	3.10782i	0.568267	−	0.120789i
$663$	22.1534	+	15.6686i	0.860365	+	0.608518i
$664$	−15.5165	−	3.29813i	−0.602157	−	0.127992i
$665$	−17.1910	−	15.1026i	−0.666639	−	0.585653i
$666$	8.46020	−	6.48190i	0.327826	−	0.251169i
$667$	17.2401	+	12.5257i	0.667539	+	0.484996i
$668$	−10.4689	+	18.1326i	−0.405053	+	0.701572i
$669$	32.7122	+	14.0685i	1.26473	+	0.543918i
$670$	−21.2789	+	2.49975i	−0.822075	+	0.0965737i
$671$	−0.472289	−	0.210276i	−0.0182325	−	0.00811763i
$672$	−30.6784	−	6.11399i	−1.18344	−	0.235852i
$673$	35.7329	+	7.59526i	1.37740	+	0.292776i	0.836342	−	0.548209i	$-0.184690\pi$
$673$	35.7329	+	7.59526i	1.37740	+	0.292776i	0.541059	+	0.840984i	$0.318023\pi$
$674$	22.0463			0.849193
$675$	25.0252	−	6.98121i	0.963222	−	0.268707i
$676$	12.4967			0.480642
$677$	28.3570	+	6.02747i	1.08985	+	0.231654i	0.717584	−	0.696472i	$-0.245248\pi$
$677$	28.3570	+	6.02747i	1.08985	+	0.231654i	0.372264	+	0.928127i	$0.378581\pi$
$678$	4.07426	+	0.811973i	0.156471	+	0.0311836i
$679$	44.4406	+	19.7862i	1.70547	+	0.759325i
$680$	33.1270	−	30.5689i	1.27036	−	1.17226i
$681$	29.2542	+	12.5813i	1.12102	+	0.482116i
$682$	7.86276	−	13.6187i	0.301081	−	0.521487i
$683$	14.2219	+	10.3328i	0.544186	+	0.395374i	0.825637	−	0.564201i	$-0.190816\pi$
$683$	14.2219	+	10.3328i	0.544186	+	0.395374i	−0.281451	+	0.959576i	$0.590816\pi$
$684$	1.82364	+	13.9308i	0.0697287	+	0.532657i
$685$	−5.81513	+	13.5027i	−0.222185	+	0.515910i
$686$	10.4147	+	2.21371i	0.397635	+	0.0845199i
$687$	−17.5609	−	12.4204i	−0.669989	−	0.473869i
$688$	1.16706	−	0.248065i	0.0444936	−	0.00945741i
$689$	9.50691	−	10.5585i	0.362184	−	0.402247i
$690$	13.1458	+	11.2557i	0.500454	+	0.428499i
$691$	29.6400	+	32.9185i	1.12756	+	1.25228i	0.964045	+	0.265738i	$0.0856155\pi$
$691$	29.6400	+	32.9185i	1.12756	+	1.25228i	0.163512	+	0.986541i	$0.447718\pi$
$692$	−5.12124	−	3.72080i	−0.194680	−	0.141444i
$693$	−17.9577	+	8.54922i	−0.682155	+	0.324758i
$694$	5.02633	+	3.65184i	0.190797	+	0.138622i
$695$	−12.7133	−	3.95971i	−0.482242	−	0.150200i
$696$	−10.9530	+	12.4803i	−0.415173	+	0.473065i
$697$	60.8751	+	27.1033i	2.30581	+	1.02661i
$698$	9.19379	−	10.2107i	0.347990	−	0.386482i
$699$	−6.75571	−	7.31366i	−0.255524	−	0.276628i
$700$	−1.74335	+	21.6692i	−0.0658923	+	0.819018i
$701$	−42.4529			−1.60343			−0.801713	−	0.597710i	$-0.796078\pi$
$701$	−42.4529			−1.60343			−0.801713	+	0.597710i	$0.796078\pi$
$702$	−6.74467	−	4.51737i	−0.254561	−	0.170497i
$703$	12.4291	−	9.03029i	0.468774	−	0.340584i
$704$	0.646759	+	6.15350i	0.0243756	+	0.231919i
$705$	4.24815	−	1.49844i	0.159995	−	0.0564345i
$706$	1.21337	−	11.5444i	0.0456658	−	0.434481i
$707$	−9.25403	−	16.0285i	−0.348034	−	0.602812i
$708$	−0.443577	−	0.190768i	−0.0166707	−	0.00716951i
$709$	−22.3975	−	24.8749i	−0.841156	−	0.934198i	0.157421	−	0.987532i	$-0.449682\pi$
$709$	−22.3975	−	24.8749i	−0.841156	−	0.934198i	−0.998577	+	0.0533336i	$0.983015\pi$
$710$	−8.44725	−	7.42105i	−0.317020	−	0.278507i
$711$	−9.67108	+	32.5614i	−0.362694	+	1.22115i
$712$	1.75710	−	5.40779i	0.0658500	−	0.202665i
$713$	−37.0881	−	41.1905i	−1.38896	−	1.54260i
$714$	−31.5525	+	0.401486i	−1.18082	+	0.0150252i
$715$	4.08957	+	8.89130i	0.152941	+	0.332516i
$716$	1.28219	−	0.272537i	0.0479176	−	0.0101852i
$717$	−29.3640	+	21.9104i	−1.09662	+	0.818258i
$718$	6.24838	−	10.8225i	0.233188	−	0.403893i
$719$	2.88089	+	2.09309i	0.107439	+	0.0780592i	0.640208	−	0.768202i	$-0.278848\pi$
$719$	2.88089	+	2.09309i	0.107439	+	0.0780592i	−0.532768	+	0.846261i	$0.678848\pi$
$720$	3.90250	−	3.78948i	0.145438	−	0.141225i
$721$	−34.4639	+	25.0395i	−1.28350	+	0.932519i
$722$	0.640169	+	6.09081i	0.0238246	+	0.226676i
$723$	−7.64197	−	12.8557i	−0.284208	−	0.478109i
$724$	−0.683962	−	1.18466i	−0.0254192	−	0.0440274i
$725$	15.0689	+	10.3952i	0.559645	+	0.386069i
$726$	−5.75097	−	6.22594i	−0.213439	−	0.231066i
$727$	33.7243	+	7.16832i	1.25076	+	0.265858i	0.785248	−	0.619181i	$-0.212535\pi$
$727$	33.7243	+	7.16832i	1.25076	+	0.265858i	0.465516	+	0.885039i	$0.345869\pi$
$728$	13.2866	−	9.65327i	0.492433	−	0.357774i
$729$	10.2776	+	24.9674i	0.380652	+	0.924718i
$730$	11.9085	−	7.07082i	0.440755	−	0.261703i
$731$	10.3484	−	4.60742i	0.382751	−	0.170412i
$732$	−0.398468	−	0.431377i	−0.0147278	−	0.0159441i
$733$	1.40464	−	13.3643i	0.0518816	−	0.493621i	−0.937469	−	0.348069i	$-0.886838\pi$
$733$	1.40464	−	13.3643i	0.0518816	−	0.493621i	0.989351	−	0.145552i	$-0.0464958\pi$
$734$	−9.31898	+	1.98081i	−0.343970	+	0.0731131i
$735$	7.03335	−	6.65789i	0.259429	−	0.245580i
$736$	33.3582	+	7.09050i	1.22960	+	0.261359i
$737$	−8.29511	+	25.5297i	−0.305554	+	0.940400i
$738$	−18.4122	−	7.64240i	−0.677763	−	0.281321i
$739$	4.06977	+	12.5255i	0.149709	+	0.460756i	0.997586	−	0.0694356i	$-0.0221199\pi$
$739$	4.06977	+	12.5255i	0.149709	+	0.460756i	−0.847878	+	0.530192i	$0.822120\pi$
$740$	−13.9352	−	4.34030i	−0.512269	−	0.159552i
$741$	−9.55357	−	6.75705i	−0.350959	−	0.248226i
$742$	−1.72708	+	16.4321i	−0.0634031	+	0.603240i
$743$	−21.7820	−	37.7276i	−0.799106	−	1.38409i	−0.920199	−	0.391451i	$-0.871973\pi$
$743$	−21.7820	−	37.7276i	−0.799106	−	1.38409i	0.121093	−	0.992641i	$-0.461360\pi$
$744$	34.6154	−	25.8288i	1.26906	−	0.946931i
$745$	−1.29771	+	1.83283i	−0.0475445	+	0.0671499i
$746$	19.5146	−	14.1782i	0.714480	−	0.519100i
$747$	−18.1689	+	0.462451i	−0.664766	+	0.0169202i
$748$	−7.21794	−	22.2145i	−0.263914	−	0.812244i
$749$	−13.2961	+	23.0296i	−0.485830	+	0.841482i
$750$	11.5261	+	9.39056i	0.420872	+	0.342895i
$751$	−15.6168	−	27.0491i	−0.569864	−	0.987034i	−0.996579	−	0.0826477i	$-0.973662\pi$
$751$	−15.6168	−	27.0491i	−0.569864	−	0.987034i	0.426714	−	0.904386i	$-0.359671\pi$
$752$	0.631092	−	0.700898i	0.0230135	−	0.0255591i
$753$	11.1783	+	2.22775i	0.407359	+	0.0811839i
$754$	−0.597895	−	5.68859i	−0.0217740	−	0.207166i
$755$	11.3901	+	1.05660i	0.414529	+	0.0384536i
$756$	−22.5756	+	0.862151i	−0.821065	+	0.0313561i
$757$	35.2792			1.28224			0.641122	−	0.767439i	$-0.278469\pi$
$757$	35.2792			1.28224			0.641122	+	0.767439i	$0.278469\pi$
$758$	−15.7620	+	7.01771i	−0.572503	+	0.254895i
$759$	19.6945	−	9.07054i	0.714865	−	0.329240i
$760$	−14.2859	+	13.1827i	−0.518205	+	0.478189i
$761$	10.3514	−	11.4964i	0.375238	−	0.416744i	−0.525715	−	0.850661i	$-0.676202\pi$
$761$	10.3514	−	11.4964i	0.375238	−	0.416744i	0.900953	+	0.433917i	$0.142869\pi$
$762$	0.255035	−	2.76442i	0.00923895	−	0.100144i
$763$	−39.4237	−	43.7844i	−1.42723	−	1.58510i
$764$	6.09936	+	18.7719i	0.220667	+	0.679144i
$765$	28.7611	−	42.8951i	1.03986	−	1.55087i
$766$	−4.64626	+	14.2997i	−0.167876	+	0.516670i
$767$	0.367394	−	0.163574i	0.0132658	−	0.00590633i
$768$	−6.71318	+	21.5920i	−0.242241	+	0.779136i
$769$	3.71413	−	35.3376i	0.133935	−	1.27431i	−0.696648	−	0.717413i	$-0.745326\pi$
$769$	3.71413	−	35.3376i	0.133935	−	1.27431i	0.830583	−	0.556894i	$-0.188007\pi$
$770$	−9.92516	−	5.56971i	−0.357678	−	0.200718i
$771$	−6.49912

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)

\(f(q)\)	\(=\)	\(q+(-0.750960 - 0.159622i) q^{2} +(-1.69865 - 0.338529i) q^{3} +(-1.28863 - 0.573734i) q^{4} +(-0.934384 - 2.03148i) q^{5} +(1.22158 + 0.525362i) q^{6} +(-1.54115 + 2.66935i) q^{7} +(2.11835 + 1.53907i) q^{8} +(2.77080 + 1.15008i) q^{9} +O(q^{10})\)	\(q+(-0.750960 - 0.159622i) q^{2} +(-1.69865 - 0.338529i) q^{3} +(-1.28863 - 0.573734i) q^{4} +(-0.934384 - 2.03148i) q^{5} +(1.22158 + 0.525362i) q^{6} +(-1.54115 + 2.66935i) q^{7} +(2.11835 + 1.53907i) q^{8} +(2.77080 + 1.15008i) q^{9} +(0.377417 + 1.67471i) q^{10} +(2.10386 + 0.447190i) q^{11} +(1.99470 + 1.41081i) q^{12} +(-1.99041 + 0.423076i) q^{13} +(1.58343 - 1.75858i) q^{14} +(0.899473 + 3.76709i) q^{15} +(0.542593 + 0.602611i) q^{16} +(6.22843 + 4.52522i) q^{17} +(-1.89718 - 1.30594i) q^{18} +(-2.68599 - 1.95149i) q^{19} +(0.0385425 + 3.15392i) q^{20} +(3.52153 - 4.01256i) q^{21} +(-1.50854 - 0.671643i) q^{22} +(-3.89453 + 4.32531i) q^{23} +(-3.07731 - 3.33147i) q^{24} +(-3.25385 + 3.79637i) q^{25} +1.56225 q^{26} +(-4.31727 - 2.89157i) q^{27} +(3.51747 - 2.55559i) q^{28} +(-0.382713 - 3.64127i) q^{29} +(-0.0741604 - 2.97251i) q^{30} +(-0.995438 + 9.47096i) q^{31} +(-2.92971 - 5.07440i) q^{32} +(-3.42233 - 1.47183i) q^{33} +(-3.95498 - 4.39245i) q^{34} +(6.86278 + 0.636623i) q^{35} +(-2.91069 - 3.07173i) q^{36} +(-1.42994 + 4.40091i) q^{37} +(1.70557 + 1.89423i) q^{38} +(3.52423 - 0.0448436i) q^{39} +(1.14725 - 5.74149i) q^{40} +(8.46629 - 1.79957i) q^{41} +(-3.28502 + 2.45117i) q^{42} +(0.735688 - 1.27425i) q^{43} +(-2.45453 - 1.78332i) q^{44} +(-0.252620 - 6.70345i) q^{45} +(3.61505 - 2.62649i) q^{46} +(-0.121577 - 1.15673i) q^{47} +(-0.717673 - 1.20731i) q^{48} +(-1.25030 - 2.16559i) q^{49} +(3.04950 - 2.33154i) q^{50} +(-9.04798 - 9.79524i) q^{51} +(2.80764 + 0.596782i) q^{52} +(-5.64868 + 4.10401i) q^{53} +(2.78054 + 2.86059i) q^{54} +(-1.05736 - 4.69181i) q^{55} +(-7.37304 + 3.28269i) q^{56} +(3.90191 + 4.22417i) q^{57} +(-0.293823 + 2.79554i) q^{58} +(-0.193316 + 0.0410905i) q^{59} +(1.00222 - 5.37043i) q^{60} +(-0.235109 - 0.0499739i) q^{61} +(2.25930 - 6.95342i) q^{62} +(-7.34019 + 5.62379i) q^{63} +(0.888950 + 2.73591i) q^{64} +(2.71928 + 3.64818i) q^{65} +(2.33510 + 1.65157i) q^{66} +(-1.30455 + 12.4120i) q^{67} +(-5.42985 - 9.40478i) q^{68} +(8.07966 - 6.02876i) q^{69} +(-5.05206 - 1.57353i) q^{70} +(-5.29885 + 3.84984i) q^{71} +(4.09947 + 6.70074i) q^{72} +(-2.49299 - 7.67263i) q^{73} +(1.77631 - 3.07666i) q^{74} +(6.81232 - 5.34717i) q^{75} +(2.34161 + 4.05579i) q^{76} +(-4.43608 + 4.92677i) q^{77} +(-2.65372 - 0.528868i) q^{78} +(1.18352 + 11.2604i) q^{79} +(0.717204 - 1.66534i) q^{80} +(6.35463 + 6.37328i) q^{81} -6.64510 q^{82} +(-5.53451 + 2.46412i) q^{83} +(-6.84008 + 3.15028i) q^{84} +(3.37316 - 16.8812i) q^{85} +(-0.755870 + 0.839479i) q^{86} +(-0.582580 + 6.31478i) q^{87} +(3.76846 + 4.18530i) q^{88} +(-0.671050 - 2.06528i) q^{89} +(-0.880307 + 5.07435i) q^{90} +(1.93819 - 5.96515i) q^{91} +(7.50018 - 3.33929i) q^{92} +(4.89709 - 15.7508i) q^{93} +(-0.0933394 + 0.888065i) q^{94} +(-1.45467 + 7.27999i) q^{95} +(3.25870 + 9.61140i) q^{96} +(-1.64971 - 15.6960i) q^{97} +(0.593254 + 1.82585i) q^{98} +(5.31507 + 3.65868i) 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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