LMFDB - Embedded newform 392.2.z.a.37.17

Newspace parameters

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.z (of order $42$, degree $12$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			37.17
Character	$\chi$	$=$	392.37
Dual form			392.2.z.a.53.17

$q$-expansion

$f(q)$	$=$	$q+(-0.767597 - 1.18777i) q^{2} +(-1.83996 - 1.98301i) q^{3} +(-0.821590 + 1.82346i) q^{4} +(-0.819891 + 2.65802i) q^{5} +(-0.943005 + 3.70760i) q^{6} +(2.51957 - 0.807328i) q^{7} +(2.79649 - 0.423820i) q^{8} +(-0.322667 + 4.30570i) q^{9} +O(q^{10})$	\(q+(-0.767597 - 1.18777i) q^{2} +(-1.83996 - 1.98301i) q^{3} +(-0.821590 + 1.82346i) q^{4} +(-0.819891 + 2.65802i) q^{5} +(-0.943005 + 3.70760i) q^{6} +(2.51957 - 0.807328i) q^{7} +(2.79649 - 0.423820i) q^{8} +(-0.322667 + 4.30570i) q^{9} +(3.78646 - 1.06645i) q^{10} +(0.808795 - 0.0606108i) q^{11} +(5.12762 - 1.72587i) q^{12} +(0.864213 - 1.79456i) q^{13} +(-2.89293 - 2.37296i) q^{14} +(6.77944 - 3.26480i) q^{15} +(-2.64998 - 2.99626i) q^{16} +(-2.72664 - 0.410975i) q^{17} +(5.36185 - 2.92179i) q^{18} +(5.29583 + 3.05755i) q^{19} +(-4.17317 - 3.67884i) q^{20} +(-6.23684 - 3.51087i) q^{21} +(-0.692821 - 0.914137i) q^{22} +(5.21964 - 0.786734i) q^{23} +(-5.98588 - 4.76565i) q^{24} +(-2.26166 - 1.54197i) q^{25} +(-2.79488 + 0.351011i) q^{26} +(2.78703 - 2.22258i) q^{27} +(-0.597923 + 5.25761i) q^{28} +(-1.35645 - 1.08173i) q^{29} +(-9.08171 - 5.54635i) q^{30} +(-4.70362 - 8.14691i) q^{31} +(-1.52475 + 5.44749i) q^{32} +(-1.60834 - 1.49232i) q^{33} +(1.60482 + 3.55408i) q^{34} +(0.0801256 + 7.35898i) q^{35} +(-7.58615 - 4.12589i) q^{36} +(10.2554 - 4.02494i) q^{37} +(-0.433402 - 8.63719i) q^{38} +(-5.14873 + 1.58817i) q^{39} +(-1.16630 + 7.78062i) q^{40} +(0.479000 + 2.09864i) q^{41} +(0.617285 + 10.1029i) q^{42} +(-1.35673 - 0.309665i) q^{43} +(-0.553977 + 1.52460i) q^{44} +(-11.1801 - 4.38786i) q^{45} +(-4.94104 - 5.59583i) q^{46} +(4.15496 - 2.83281i) q^{47} +(-1.06575 + 10.7679i) q^{48} +(5.69644 - 4.06824i) q^{49} +(-0.0954648 + 3.86994i) q^{50} +(4.20194 + 6.16312i) q^{51} +(2.56226 + 3.05024i) q^{52} +(2.81358 + 1.10425i) q^{53} +(-4.77924 - 1.60430i) q^{54} +(-0.502019 + 2.19949i) q^{55} +(6.70379 - 3.32553i) q^{56} +(-3.68098 - 16.1274i) q^{57} +(-0.243641 + 2.44148i) q^{58} +(-2.78489 - 9.02838i) q^{59} +(0.383310 + 15.0443i) q^{60} +(-6.37127 + 2.50054i) q^{61} +(-6.06616 + 11.8404i) q^{62} +(2.66313 + 11.1090i) q^{63} +(7.64075 - 2.37042i) q^{64} +(4.06141 + 3.76843i) q^{65} +(-0.537977 + 3.05584i) q^{66} +(13.1478 - 7.59089i) q^{67} +(2.98957 - 4.63425i) q^{68} +(-11.1640 - 8.90301i) q^{69} +(8.67927 - 5.74390i) q^{70} +(8.16537 + 10.2391i) q^{71} +(0.922504 + 12.1776i) q^{72} +(9.40747 + 6.41390i) q^{73} +(-12.6527 - 9.09149i) q^{74} +(1.10362 + 7.32205i) q^{75} +(-9.92631 + 7.14466i) q^{76} +(1.98888 - 0.805677i) q^{77} +(5.83854 + 4.89643i) q^{78} +(5.74880 - 9.95721i) q^{79} +(10.1368 - 4.58709i) q^{80} +(3.27320 + 0.493356i) q^{81} +(2.12502 - 2.17985i) q^{82} +(2.46351 + 5.11554i) q^{83} +(11.5260 - 8.48812i) q^{84} +(3.32792 - 6.91051i) q^{85} +(0.673611 + 1.84918i) q^{86} +(0.350731 + 4.68018i) q^{87} +(2.23610 - 0.512282i) q^{88} +(-0.395591 + 5.27880i) q^{89} +(3.37003 + 16.6475i) q^{90} +(0.728646 - 5.21921i) q^{91} +(-2.85383 + 10.1641i) q^{92} +(-7.50090 + 24.3173i) q^{93} +(-6.55406 - 2.76068i) q^{94} +(-12.4690 + 11.5696i) q^{95} +(13.6079 - 6.99957i) q^{96} +5.90936 q^{97} +(-9.20470 - 3.64329i) q^{98} +3.50199i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{16}{21}\right)$

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 $

$2$	−0.767597	−	1.18777i	−0.542773	−	0.839879i
$2$	−0.767597	−	1.18777i	−0.542773	−	0.839879i
$3$	−1.83996	−	1.98301i	−1.06230	−	1.14489i	−0.989051	−	0.147576i	$-0.952853\pi$
$3$	−1.83996	−	1.98301i	−1.06230	−	1.14489i	−0.0732512	−	0.997314i	$-0.523337\pi$
$4$	−0.821590	+	1.82346i	−0.410795	+	0.911728i
$5$	−0.819891	+	2.65802i	−0.366666	+	1.18870i	0.564909	+	0.825153i	$0.308911\pi$
$5$	−0.819891	+	2.65802i	−0.366666	+	1.18870i	−0.931575	+	0.363549i	$0.881565\pi$
$6$	−0.943005	+	3.70760i	−0.384980	+	1.51362i
$7$	2.51957	−	0.807328i	0.952307	−	0.305141i
$7$	2.51957	−	0.807328i	0.952307	−	0.305141i
$8$	2.79649	−	0.423820i	0.988710	−	0.149843i
$9$	−0.322667	+	4.30570i	−0.107556	+	1.43523i
$10$	3.78646	−	1.06645i	1.19738	−	0.337240i
$11$	0.808795	−	0.0606108i	0.243861	−	0.0182749i	0.0477611	−	0.998859i	$-0.484791\pi$
$11$	0.808795	−	0.0606108i	0.243861	−	0.0182749i	0.196100	+	0.980584i	$0.437172\pi$
$12$	5.12762	−	1.72587i	1.48022	−	0.498216i
$13$	0.864213	−	1.79456i	0.239689	−	0.497720i	−0.746073	−	0.665864i	$-0.768063\pi$
$13$	0.864213	−	1.79456i	0.239689	−	0.497720i	0.985762	+	0.168144i	$0.0537773\pi$
$14$	−2.89293	−	2.37296i	−0.773169	−	0.634201i
$15$	6.77944	−	3.26480i	1.75044	−	0.842969i
$16$	−2.64998	−	2.99626i	−0.662495	−	0.749066i
$17$	−2.72664	−	0.410975i	−0.661307	−	0.0996760i	−0.190191	−	0.981747i	$-0.560911\pi$
$17$	−2.72664	−	0.410975i	−0.661307	−	0.0996760i	−0.471116	+	0.882071i	$0.656149\pi$
$18$	5.36185	−	2.92179i	1.26380	−	0.688671i
$19$	5.29583	+	3.05755i	1.21495	+	0.701450i	0.963833	−	0.266507i	$-0.0858696\pi$
$19$	5.29583	+	3.05755i	1.21495	+	0.701450i	0.251114	+	0.967957i	$0.419203\pi$
$20$	−4.17317	−	3.67884i	−0.933149	−	0.822613i
$21$	−6.23684	−	3.51087i	−1.36099	−	0.766134i
$22$	−0.692821	−	0.914137i	−0.147710	−	0.194895i
$23$	5.21964	−	0.786734i	1.08837	−	0.164045i	0.419743	−	0.907643i	$-0.362120\pi$
$23$	5.21964	−	0.786734i	1.08837	−	0.164045i	0.668627	+	0.743598i	$0.266882\pi$
$24$	−5.98588	−	4.76565i	−1.22186	−	0.972785i
$25$	−2.26166	−	1.54197i	−0.452331	−	0.308394i
$26$	−2.79488	+	0.351011i	−0.548122	+	0.0688389i
$27$	2.78703	−	2.22258i	0.536365	−	0.427737i
$28$	−0.597923	+	5.25761i	−0.112997	+	0.993595i
$29$	−1.35645	−	1.08173i	−0.251886	−	0.200872i	0.489404	−	0.872057i	$-0.337214\pi$
$29$	−1.35645	−	1.08173i	−0.251886	−	0.200872i	−0.741290	+	0.671185i	$0.765786\pi$
$30$	−9.08171	−	5.54635i	−1.65809	−	1.01262i
$31$	−4.70362	−	8.14691i	−0.844795	−	1.46323i	−0.885799	−	0.464070i	$-0.846389\pi$
$31$	−4.70362	−	8.14691i	−0.844795	−	1.46323i	0.0410034	−	0.999159i	$-0.486945\pi$
$32$	−1.52475	+	5.44749i	−0.269541	+	0.962989i
$33$	−1.60834	−	1.49232i	−0.279977	−	0.259780i
$34$	1.60482	+	3.55408i	0.275224	+	0.609520i
$35$	0.0801256	+	7.35898i	0.0135437	+	1.24390i
$36$	−7.58615	−	4.12589i	−1.26436	−	0.687648i
$37$	10.2554	−	4.02494i	1.68597	−	0.661696i	0.688024	−	0.725688i	$-0.258478\pi$
$37$	10.2554	−	4.02494i	1.68597	−	0.661696i	0.997950	+	0.0639917i	$0.0203831\pi$
$38$	−0.433402	−	8.63719i	−0.0703071	−	1.40114i
$39$	−5.14873	+	1.58817i	−0.824457	+	0.254311i
$40$	−1.16630	+	7.78062i	−0.184408	+	1.23022i
$41$	0.479000	+	2.09864i	0.0748073	+	0.327752i	0.998460	−	0.0554788i	$-0.0176685\pi$
$41$	0.479000	+	2.09864i	0.0748073	+	0.327752i	−0.923653	+	0.383231i	$0.874811\pi$
$42$	0.617285	+	10.1029i	0.0952492	+	1.55890i
$43$	−1.35673	−	0.309665i	−0.206899	−	0.0472234i	0.117815	−	0.993036i	$-0.462411\pi$
$43$	−1.35673	−	0.309665i	−0.206899	−	0.0472234i	−0.324714	+	0.945812i	$0.605268\pi$
$44$	−0.553977	+	1.52460i	−0.0835152	+	0.229842i
$45$	−11.1801	−	4.38786i	−1.66663	−	0.654103i
$46$	−4.94104	−	5.59583i	−0.728516	−	0.825060i
$47$	4.15496	−	2.83281i	0.606064	−	0.413207i	−0.221033	−	0.975266i	$-0.570943\pi$
$47$	4.15496	−	2.83281i	0.606064	−	0.413207i	0.827097	+	0.562059i	$0.189991\pi$
$48$	−1.06575	+	10.7679i	−0.153828	+	1.55422i
$49$	5.69644	−	4.06824i	0.813777	−	0.581177i
$50$	−0.0954648	+	3.86994i	−0.0135008	+	0.547292i
$51$	4.20194	+	6.16312i	0.588390	+	0.863009i
$52$	2.56226	+	3.05024i	0.355322	+	0.422992i
$53$	2.81358	+	1.10425i	0.386474	+	0.151680i	0.550620	−	0.834756i	$-0.314391\pi$
$53$	2.81358	+	1.10425i	0.386474	+	0.151680i	−0.164145	+	0.986436i	$0.552487\pi$
$54$	−4.77924	−	1.60430i	−0.650372	−	0.218318i
$55$	−0.502019	+	2.19949i	−0.0676922	+	0.296579i
$56$	6.70379	−	3.32553i	0.895832	−	0.444393i
$57$	−3.68098	−	16.1274i	−0.487558	−	2.13613i
$58$	−0.243641	+	2.44148i	−0.0319916	+	0.320581i
$59$	−2.78489	−	9.02838i	−0.362561	−	1.17540i	−0.934760	−	0.355280i	$-0.884386\pi$
$59$	−2.78489	−	9.02838i	−0.362561	−	1.17540i	0.572199	−	0.820115i	$-0.306091\pi$
$60$	0.383310	+	15.0443i	0.0494851	+	1.94222i
$61$	−6.37127	+	2.50054i	−0.815757	+	0.320161i	−0.736281	−	0.676676i	$-0.763420\pi$
$61$	−6.37127	+	2.50054i	−0.815757	+	0.320161i	−0.0794760	+	0.996837i	$0.525325\pi$
$62$	−6.06616	+	11.8404i	−0.770403	+	1.50373i
$63$	2.66313	+	11.1090i	0.335523	+	1.39960i
$64$	7.64075	−	2.37042i	0.955094	−	0.296303i
$65$	4.06141	+	3.76843i	0.503755	+	0.467417i
$66$	−0.537977	+	3.05584i	−0.0662204	+	0.376148i
$67$	13.1478	−	7.59089i	1.60626	−	0.927374i	0.616062	−	0.787698i	$-0.288727\pi$
$67$	13.1478	−	7.59089i	1.60626	−	0.927374i	0.990197	−	0.139677i	$-0.0446063\pi$
$68$	2.98957	−	4.63425i	0.362539	−	0.561986i
$69$	−11.1640	−	8.90301i	−1.34399	−	1.07180i
$70$	8.67927	−	5.74390i	1.03737	−	0.686528i
$71$	8.16537	+	10.2391i	0.969051	+	1.21515i	0.976574	+	0.215180i	$0.0690338\pi$
$71$	8.16537	+	10.2391i	0.969051	+	1.21515i	−0.00752318	+	0.999972i	$0.502395\pi$
$72$	0.922504	+	12.1776i	0.108718	+	1.43514i
$73$	9.40747	+	6.41390i	1.10106	+	0.750690i	0.970584	−	0.240761i	$-0.0773970\pi$
$73$	9.40747	+	6.41390i	1.10106	+	0.750690i	0.130476	+	0.991451i	$0.458349\pi$
$74$	−12.6527	−	9.09149i	−1.47085	−	1.05686i
$75$	1.10362	+	7.32205i	0.127435	+	0.845477i
$76$	−9.92631	+	7.14466i	−1.13863	+	0.819549i
$77$	1.98888	−	0.805677i	0.226654	−	0.0918154i
$78$	5.83854	+	4.89643i	0.661084	+	0.554411i
$79$	5.74880	−	9.95721i	0.646790	−	1.12027i	−0.337095	−	0.941471i	$-0.609444\pi$
$79$	5.74880	−	9.95721i	0.646790	−	1.12027i	0.983885	−	0.178803i	$-0.0572224\pi$
$80$	10.1368	−	4.58709i	1.13333	−	0.512852i
$81$	3.27320	+	0.493356i	0.363689	+	0.0548173i
$82$	2.12502	−	2.17985i	0.234669	−	0.240724i
$83$	2.46351	+	5.11554i	0.270406	+	0.561503i	0.991312	−	0.131529i	$-0.0419886\pi$
$83$	2.46351	+	5.11554i	0.270406	+	0.561503i	−0.720907	+	0.693032i	$0.756274\pi$
$84$	11.5260	−	8.48812i	1.25759	−	0.926129i
$85$	3.32792	−	6.91051i	0.360964	−	0.749550i
$86$	0.673611	+	1.84918i	0.0726374	+	0.199402i
$87$	0.350731	+	4.68018i	0.0376023	+	0.501768i
$88$	2.23610	−	0.512282i	0.238369	−	0.0546094i
$89$	−0.395591	+	5.27880i	−0.0419326	+	0.559551i	0.936186	+	0.351504i	$0.114330\pi$
$89$	−0.395591	+	5.27880i	−0.0419326	+	0.559551i	−0.978119	+	0.208047i	$0.933289\pi$
$90$	3.37003	+	16.6475i	0.355233	+	1.75480i
$91$	0.728646	−	5.21921i	0.0763828	−	0.547122i
$92$	−2.85383	+	10.1641i	−0.297532	+	1.05969i
$93$	−7.50090	+	24.3173i	−0.777807	+	2.52159i
$94$	−6.55406	−	2.76068i	−0.675999	−	0.284743i
$95$	−12.4690	+	11.5696i	−1.27930	+	1.18701i
$96$	13.6079	−	6.99957i	1.38885	−	0.714391i
$97$	5.90936			0.600005			0.300002	−	0.953938i	$-0.403013\pi$
$97$	5.90936			0.600005			0.300002	+	0.953938i	$0.403013\pi$
$98$	−9.20470	−	3.64329i	−0.929815	−	0.368028i
$99$			3.50199i			0.351963i
$100$	4.66987	−	2.85716i	0.466987	−	0.285716i
$101$	−4.11974	−	4.44003i	−0.409930	−	0.441799i	0.494012	−	0.869455i	$-0.335530\pi$
$101$	−4.11974	−	4.44003i	−0.409930	−	0.441799i	−0.903942	+	0.427656i	$0.859339\pi$
$102$	4.09496	−	9.72173i	0.405462	−	0.962595i
$103$	−7.42944	−	2.29168i	−0.732044	−	0.225806i	−0.0937474	−	0.995596i	$-0.529885\pi$
$103$	−7.42944	−	2.29168i	−0.732044	−	0.225806i	−0.638297	+	0.769790i	$0.720361\pi$
$104$	1.65620	−	5.38473i	0.162403	−	0.528017i
$105$	14.4455	−	13.6991i	1.40973	−	1.33690i
$106$	−0.848102	−	4.18950i	−0.0823750	−	0.406920i
$107$	1.05601	+	0.0791370i	0.102088	+	0.00765047i	0.125676	−	0.992071i	$-0.459890\pi$
$107$	1.05601	+	0.0791370i	0.102088	+	0.00765047i	−0.0235879	+	0.999722i	$0.507509\pi$
$108$	1.76299	+	6.90808i	0.169643	+	0.664731i
$109$	−4.31368	+	0.323266i	−0.413176	+	0.0309632i	−0.279697	−	0.960088i	$-0.590234\pi$
$109$	−4.31368	+	0.323266i	−0.413176	+	0.0309632i	−0.133479	+	0.991052i	$0.542615\pi$
$110$	2.99783	−	1.09204i	0.285832	−	0.104122i
$111$	−26.8510	−	12.9308i	−2.54858	−	1.22733i
$112$	−9.09577	−	5.40989i	−0.859470	−	0.511186i
$113$	−13.7715	+	6.63200i	−1.29551	+	0.623886i	−0.949330	−	0.314281i	$-0.898237\pi$
$113$	−13.7715	+	6.63200i	−1.29551	+	0.623886i	−0.346183	+	0.938167i	$0.612522\pi$
$114$	−16.3302	+	16.7515i	−1.52946	+	1.56892i
$115$	−2.18838	+	14.5189i	−0.204067	+	1.35390i
$116$	3.08693	−	1.58468i	0.286614	−	0.147134i
$117$	7.44796	+	4.30008i	0.688564	+	0.397543i
$118$	−8.58596	+	10.2380i	−0.790402	+	0.942481i
$119$	−7.20174	+	1.16581i	−0.660183	+	0.106870i
$120$	17.5750	−	12.0033i	1.60437	−	1.09574i
$121$	−10.2267	+	1.54142i	−0.929697	+	0.140129i
$122$	7.86063	+	5.64819i	0.711668	+	0.511363i
$123$	3.28027	−	4.81127i	0.295772	−	0.433818i
$124$	18.7200	−	1.88343i	1.68110	−	0.169137i
$125$	−4.92081	+	3.92421i	−0.440130	+	0.350992i
$126$	11.1507	−	11.6904i	0.993384	−	1.04146i
$127$	−5.27250	+	6.61150i	−0.467858	+	0.586676i	−0.958645	−	0.284604i	$-0.908138\pi$
$127$	−5.27250	+	6.61150i	−0.467858	+	0.586676i	0.490787	+	0.871280i	$0.336709\pi$
$128$	−8.68053	−	7.25592i	−0.767258	−	0.641339i
$129$	1.88226	+	3.26017i	0.165724	+	0.287042i
$130$	1.35851	−	7.71665i	0.119149	−	0.676795i
$131$	−14.6035	+	15.7388i	−1.27591	+	1.37511i	−0.383722	+	0.923449i	$0.625358\pi$
$131$	−14.6035	+	15.7388i	−1.27591	+	1.37511i	−0.892191	+	0.451658i	$0.850833\pi$
$132$	4.04259	−	1.70666i	0.351862	−	0.148546i
$133$	15.8117	+	3.42823i	1.37104	+	0.297265i
$134$	−19.1084	−	9.78981i	−1.65072	−	0.845710i
$135$	3.62261	+	9.23027i	0.311785	+	0.794415i
$136$	−7.79921	+	0.00631655i	−0.668777	+	0.000541639i
$137$	−12.4658	+	3.84518i	−1.06502	+	0.328516i	−0.777256	−	0.629184i	$-0.783389\pi$
$137$	−12.4658	+	3.84518i	−1.06502	+	0.328516i	−0.287767	+	0.957700i	$0.592913\pi$
$138$	−2.00525	+	20.0942i	−0.170698	+	1.71053i
$139$	12.1524	−	2.77371i	1.03075	−	0.235263i	0.326490	−	0.945201i	$-0.394134\pi$
$139$	12.1524	−	2.77371i	1.03075	−	0.235263i	0.704264	+	0.709938i	$0.251277\pi$
$140$	−13.4846	−	5.89996i	−1.13966	−	0.498638i
$141$	−13.2624	−	3.02707i	−1.11690	−	0.254925i
$142$	5.89391	−	17.5580i	0.494606	−	1.47344i
$143$	0.590202	−	1.50381i	0.0493551	−	0.125755i
$144$	13.7561	−	10.4432i	1.14634	−	0.870268i
$145$	3.98739	−	2.71856i	0.331135	−	0.225764i
$146$	0.397090	−	16.0972i	0.0328634	−	1.33221i
$147$	−18.5486	−	3.81068i	−1.52986	−	0.314300i
$148$	−1.08642	+	22.0071i	−0.0893029	+	1.80897i
$149$	6.40175	+	9.38964i	0.524452	+	0.769229i	0.993486	−	0.113950i	$-0.0363505\pi$
$149$	6.40175	+	9.38964i	0.524452	+	0.769229i	−0.469035	+	0.883180i	$0.655398\pi$
$150$	7.84976	−	6.93123i	0.640930	−	0.565932i
$151$	3.90261	−	9.94370i	0.317590	−	0.809207i	−0.679550	−	0.733629i	$-0.737825\pi$
$151$	3.90261	−	9.94370i	0.317590	−	0.809207i	0.997140	−	0.0755773i	$-0.0240800\pi$
$152$	16.1056	+	6.30594i	1.30634	+	0.511479i
$153$	2.64933	−	11.6075i	0.214186	−	0.938408i
$154$	−2.48362	−	1.74390i	−0.200136	−	0.140527i
$155$	25.5111	−	5.82274i	2.04910	−	0.467694i
$156$	1.33418	−	10.6933i	0.106820	−	0.856150i
$157$	2.01272	+	6.52507i	0.160632	+	0.520757i	0.999730	−	0.0232231i	$-0.00739282\pi$
$157$	2.01272	+	6.52507i	0.160632	+	0.520757i	−0.839098	+	0.543980i	$0.816917\pi$
$158$	−16.2396	+	0.814881i	−1.29196	+	0.0648285i
$159$	−2.98714	−	7.61111i	−0.236896	−	0.603600i
$160$	−13.2294	−	8.51917i	−1.04588	−	0.673499i
$161$	12.5161	−	6.19619i	0.986405	−	0.488328i
$162$	−1.92651	−	4.26650i	−0.151361	−	0.335208i
$163$	−3.82009	+	4.11708i	−0.299212	+	0.322474i	−0.864706	−	0.502278i	$-0.832495\pi$
$163$	−3.82009	+	4.11708i	−0.299212	+	0.322474i	0.565494	+	0.824753i	$0.308686\pi$
$164$	−4.22031	−	0.850783i	−0.329551	−	0.0664350i
$165$	5.28530	−	3.05147i	0.411460	−	0.237556i
$166$	4.18509	−	6.85276i	0.324826	−	0.531877i
$167$	10.5918	−	13.2817i	0.819619	−	1.02777i	−0.179413	−	0.983774i	$-0.557420\pi$
$167$	10.5918	−	13.2817i	0.819619	−	1.02777i	0.999032	−	0.0439954i	$-0.0140087\pi$
$168$	−18.9293	−	7.17481i	−1.46042	−	0.553549i
$169$	5.63180	+	7.06205i	0.433215	+	0.543235i
$170$	−10.7626	+	1.35168i	−0.825453	+	0.103669i
$171$	−14.8737	+	21.8157i	−1.13742	+	1.66829i
$172$	1.67933	−	2.21952i	0.128048	−	0.169237i
$173$	−1.77635	−	11.7853i	−0.135053	−	0.896018i	−0.949045	−	0.315142i	$-0.897948\pi$
$173$	−1.77635	−	11.7853i	−0.135053	−	0.896018i	0.813992	−	0.580877i	$-0.197290\pi$
$174$	5.28975	−	4.00908i	0.401015	−	0.303927i
$175$	−6.94327	−	2.05920i	−0.524862	−	0.155661i
$176$	−2.32490	−	2.26275i	−0.175246	−	0.170561i
$177$	−12.7793	+	22.1343i	−0.960548	+	1.66372i
$178$	6.57365	−	3.58212i	0.492716	−	0.268491i
$179$	2.29785	−	15.2453i	0.171750	−	1.13948i	−0.722321	−	0.691558i	$-0.756925\pi$
$179$	2.29785	−	15.2453i	0.171750	−	1.13948i	0.894070	−	0.447926i	$-0.147837\pi$
$180$	17.1865	−	16.7814i	1.28101	−	1.25081i
$181$	2.82702	+	5.87037i	0.210131	+	0.436341i	0.979220	−	0.202800i	$-0.0650042\pi$
$181$	2.82702	+	5.87037i	0.210131	+	0.436341i	−0.769089	+	0.639141i	$0.779290\pi$
$182$	−6.75852	+	3.14079i	−0.500975	+	0.232811i
$183$	16.6815	+	8.03337i	1.23313	+	0.593844i
$184$	14.2632	−	4.41228i	1.05150	−	0.325278i
$185$	2.29008	+	30.5590i	0.168370	+	2.24674i
$186$	34.6410	−	9.75656i	2.54000	−	0.715386i
$187$	−2.23020	−	0.167131i	−0.163089	−	0.0122218i
$188$	1.75182	+	9.90380i	0.127765	+	0.722309i
$189$	5.22776	−	7.85000i	0.380264	−	0.571004i
$190$	23.3132	+	5.92956i	1.69132	+	0.430176i
$191$	7.24760	+	2.23559i	0.524418	+	0.161761i	0.545650	−	0.838013i	$-0.316283\pi$
$191$	7.24760	+	2.23559i	0.524418	+	0.161761i	−0.0212323	+	0.999775i	$0.506759\pi$
$192$	−18.7592	−	10.7902i	−1.35383	−	0.778714i
$193$	−1.75887	+	1.63200i	−0.126606	+	0.117474i	−0.740935	−	0.671577i	$-0.765617\pi$
$193$	−1.75887	+	1.63200i	−0.126606	+	0.117474i	0.614329	+	0.789050i	$0.289427\pi$
$194$	−4.53601	−	7.01896i	−0.325666	−	0.503932i
$195$		−	14.9876i		−	1.07328i
$196$	2.73811	+	13.7296i	0.195579	+	0.980688i
$197$		−	16.5908i		−	1.18204i	−0.806655	−	0.591022i	$-0.798724\pi$
$197$		−	16.5908i		−	1.18204i	0.806655	−	0.591022i	$-0.201276\pi$
$198$	4.15955	−	2.68811i	0.295606	−	0.191036i
$199$	−18.6304	+	17.2865i	−1.32067	+	1.22541i	−0.364990	+	0.931011i	$0.618928\pi$
$199$	−18.6304	+	17.2865i	−1.32067	+	1.22541i	−0.955684	+	0.294395i	$0.904882\pi$
$200$	−6.97823	−	3.35358i	−0.493435	−	0.237134i
$201$	−39.2442	−	12.1052i	−2.76807	−	0.853837i
$202$	−2.11142	+	8.30145i	−0.148559	+	0.584088i
$203$	−4.29097	−	1.63039i	−0.301167	−	0.114431i
$204$	−14.6904	+	2.59850i	−1.02854	+	0.181932i
$205$	−5.97095	−	0.447461i	−0.417029	−	0.0312520i
$206$	2.98083	+	10.5835i	0.207684	+	0.737390i
$207$	1.70323	+	22.7280i	0.118383	+	1.57971i
$208$	−7.66711	+	2.16613i	−0.531619	+	0.150194i
$209$	4.46857	+	2.15195i	0.309097	+	0.148853i
$210$	−27.3597	−	6.64248i	−1.88800	−	0.458375i
$211$	8.55578	+	17.7663i	0.589004	+	1.22308i	0.956139	+	0.292912i	$0.0946244\pi$
$211$	8.55578	+	17.7663i	0.589004	+	1.22308i	−0.367135	+	0.930168i	$0.619661\pi$
$212$	−4.32515	+	4.22319i	−0.297053	+	0.290050i
$213$	5.28014	−	35.0314i	0.361789	−	2.40031i
$214$	−0.716594	−	1.31504i	−0.0489853	−	0.0898944i
$215$	1.93546	−	3.35232i	0.131998	−	0.228626i
$216$	6.85194	−	7.39665i	0.466216	−	0.503278i
$217$	−18.4283	−	16.7293i	−1.25100	−	1.13566i
$218$	3.69513	+	4.87552i	0.250266	+	0.330212i
$219$	−4.59056	−	30.4564i	−0.310201	−	2.05805i
$220$	−3.59822	−	2.72249i	−0.242592	−	0.183550i
$221$	−3.09391	+	4.53794i	−0.208119	+	0.305255i
$222$	5.25199	+	41.8184i	0.352490	+	2.80667i
$223$	−14.6906	−	18.4214i	−0.983753	−	1.23359i	−0.972320	−	0.233652i	$-0.924932\pi$
$223$	−14.6906	−	18.4214i	−0.983753	−	1.23359i	−0.0114324	−	0.999935i	$-0.503639\pi$
$224$	0.556194	+	14.9563i	0.0371622	+	0.999309i
$225$	7.36902	−	9.24046i	0.491268	−	0.616031i
$226$	18.4482	+	11.2666i	1.22716	+	0.749446i
$227$	15.1043	−	8.72048i	1.00251	−	0.578799i	0.0935190	−	0.995617i	$-0.470188\pi$
$227$	15.1043	−	8.72048i	1.00251	−	0.578799i	0.908990	+	0.416819i	$0.136855\pi$
$228$	32.4319	+	6.53803i	2.14786	+	0.432992i
$229$	8.91524	−	9.60835i	0.589136	−	0.634937i	−0.366173	−	0.930547i	$-0.619332\pi$
$229$	8.91524	−	9.60835i	0.589136	−	0.634937i	0.955309	+	0.295609i	$0.0955227\pi$
$230$	18.9249	−	8.54541i	1.24787	−	0.563467i
$231$	−5.25713	−	2.46155i	−0.345894	−	0.161958i
$232$	−4.25175	−	2.45016i	−0.279141	−	0.160861i
$233$	8.66794	+	22.0856i	0.567856	+	1.44687i	0.869731	+	0.493526i	$0.164292\pi$
$233$	8.66794	+	22.0856i	0.567856	+	1.44687i	−0.301875	+	0.953347i	$0.597613\pi$
$234$	−0.609528	−	12.1472i	−0.0398461	−	0.794086i
$235$	4.12304	+	13.3666i	0.268958	+	0.871939i
$236$	18.7509	+	2.33951i	1.22058	+	0.152289i
$237$	−30.3228	+	6.92098i	−1.96968	+	0.449566i
$238$	6.91275	+	7.65913i	0.448087	+	0.496468i
$239$	1.07752	−	4.72093i	0.0696991	−	0.305372i	−0.928048	−	0.372461i	$-0.878514\pi$
$239$	1.07752	−	4.72093i	0.0696991	−	0.305372i	0.997747	+	0.0670893i	$0.0213712\pi$
$240$	−27.7476	−	11.6613i	−1.79110	−	0.752735i
$241$	0.438215	−	1.11655i	0.0282279	−	0.0719235i	−0.916065	−	0.401030i	$-0.868652\pi$
$241$	0.438215	−	1.11655i	0.0282279	−	0.0719235i	0.944293	+	0.329107i	$0.106748\pi$
$242$	9.68081	+	10.9637i	0.622306	+	0.704775i
$243$	−11.0685	−	16.2345i	−0.710046	−	1.04145i
$244$	0.674948	−	13.6721i	0.0432091	−	0.875269i
$245$	6.14300	+	18.4768i	0.392462	+	1.18044i
$246$	−8.23260	−	0.203084i	−0.524891	−	0.0129482i
$247$	10.0637	−	6.86129i	0.640336	−	0.436574i
$248$	−16.6065	−	20.7893i	−1.05451	−	1.32012i
$249$	5.61138	−	14.2976i	0.355607	−	0.906071i
$250$	8.43825	+	2.83257i	0.533682	+	0.179147i
$251$	−22.9264	−	5.23279i	−1.44710	−	0.330291i	−0.574411	−	0.818567i	$-0.694769\pi$
$251$	−22.9264	−	5.23279i	−1.44710	−	0.330291i	−0.872689	+	0.488276i	$0.837626\pi$
$252$	−22.4448	−	4.27094i	−1.41389	−	0.269044i
$253$	4.17393	−	0.952673i	0.262413	−	0.0598941i
$254$	11.9001	+	1.18754i	0.746678	+	0.0745128i
$255$	−19.8268	+	6.11577i	−1.24160	+	0.382984i
$256$	−1.95521	+	15.8801i	−0.122200	+	0.992505i
$257$	−0.783922	−	1.99740i	−0.0488997	−	0.124594i	0.904337	−	0.426819i	$-0.140366\pi$
$257$	−0.783922	−	1.99740i	−0.0488997	−	0.124594i	−0.953237	+	0.302225i	$0.902271\pi$
$258$	2.42751	−	4.73819i	0.151130	−	0.294987i
$259$	22.5897	−	18.4206i	1.40365	−	1.14460i
$260$	−10.2084	+	4.30969i	−0.633097	+	0.267275i
$261$	5.09528	−	5.49140i	0.315390	−	0.339909i
$262$	29.9037	+	5.26450i	1.84746	+	0.325242i
$263$	−3.12733	−	5.41669i	−0.192839	−	0.334008i	0.753351	−	0.657619i	$-0.228436\pi$
$263$	−3.12733	−	5.41669i	−0.192839	−	0.334008i	−0.946190	+	0.323611i	$0.895103\pi$
$264$	−5.13020	−	3.49163i	−0.315742	−	0.214895i
$265$	−5.24194	+	6.57318i	−0.322010	+	0.403787i
$266$	−8.06504	−	21.4121i	−0.494499	−	1.31286i
$267$	11.1958	−	8.92832i	0.685169	−	0.546404i
$268$	3.03954	+	30.2110i	0.185670	+	1.84543i
$269$	−3.37323	+	4.94761i	−0.205669	+	0.301661i	−0.915190	−	0.403024i	$-0.867959\pi$
$269$	−3.37323	+	4.94761i	−0.205669	+	0.301661i	0.709520	+	0.704685i	$0.248912\pi$
$270$	8.18272	−	11.3880i	0.497984	−	0.693049i
$271$	7.19029	−	1.08376i	0.436779	−	0.0658338i	0.0730276	−	0.997330i	$-0.476734\pi$
$271$	7.19029	−	1.08376i	0.436779	−	0.0658338i	0.363751	+	0.931496i	$0.381496\pi$
$272$	5.99415	+	9.25881i	0.363449	+	0.561398i
$273$	−11.6904	+	8.15823i	−0.707535	+	0.493759i
$274$	14.1359	+	11.8549i	0.853980	+	0.716182i
$275$	−1.92268	−	1.11006i	−0.115942	−	0.0669390i
$276$	25.4065	−	13.0425i	1.52929	−	0.785065i
$277$	1.28276	−	8.51057i	0.0770737	−	0.511350i	−0.916668	−	0.399649i	$-0.869132\pi$
$277$	1.28276	−	8.51057i	0.0770737	−	0.511350i	0.993742	−	0.111701i	$-0.0356299\pi$
$278$	−12.6227	−	12.3052i	−0.757058	−	0.738015i
$279$	36.5958	−	17.6236i	2.19094	−	1.05510i
$280$	3.34296	+	20.5454i	0.199780	+	1.22782i
$281$	−10.6772	−	5.14187i	−0.636948	−	0.306738i	0.0873991	−	0.996173i	$-0.472144\pi$
$281$	−10.6772	−	5.14187i	−0.636948	−	0.306738i	−0.724347	+	0.689435i	$0.757859\pi$
$282$	6.58476	+	18.0763i	0.392117	+	1.07643i
$283$	−20.8176	+	1.56006i	−1.23748	+	0.0927361i	−0.677344	−	0.735667i	$-0.736869\pi$
$283$	−20.8176	+	1.56006i	−1.23748	+	0.0927361i	−0.560133	+	0.828403i	$0.689250\pi$
$284$	−25.3790	+	6.47689i	−1.50597	+	0.384333i
$285$	45.8851	+	3.43861i	2.71800	+	0.203686i
$286$	−2.23921	+	0.453296i	−0.132408	+	0.0268040i
$287$	2.90116	+	4.90095i	0.171250	+	0.289294i
$288$	−22.9632	−	8.32285i	−1.35312	−	0.490429i
$289$	−8.97908	−	2.76968i	−0.528181	−	0.162922i
$290$	−6.28973	−	2.64935i	−0.369346	−	0.155575i
$291$	−10.8730	−	11.7183i	−0.637386	−	0.686939i
$292$	−19.4245	+	11.8845i	−1.13674	+	0.695488i
$293$			22.3587i			1.30621i	0.757268	+	0.653104i	$0.226534\pi$
$293$			22.3587i			1.30621i	−0.757268	+	0.653104i	$0.773466\pi$
$294$	9.71162	+	24.9565i	0.566393	+	1.45549i
$295$	26.2809			1.53013
$296$	26.9733	−	15.6022i	1.56779	−	0.906857i
$297$	2.11943	−	1.96654i	0.122982	−	0.114110i
$298$	6.23876	−	14.8113i	0.361402	−	0.857993i
$299$	3.09904	−	10.0468i	0.179222	−	0.581024i
$300$	−14.2581	−	4.00331i	−0.823195	−	0.231131i
$301$	−3.66837	+	0.315105i	−0.211441	+	0.0181624i
$302$	−14.8065	+	2.99735i	−0.852015	+	0.172478i
$303$	−1.22444	+	16.3390i	−0.0703420	+	0.938648i
$304$	−4.87262	−	23.9702i	−0.279464	−	1.37478i
$305$	−1.42274	−	18.9851i	−0.0814658	−	1.08709i
$306$	−15.8206	+	5.76307i	−0.904404	+	0.329453i
$307$	−9.34870	+	19.4128i	−0.533558	+	1.10795i	0.443755	+	0.896148i	$0.353646\pi$
$307$	−9.34870	+	19.4128i	−0.533558	+	1.10795i	−0.977314	+	0.211797i	$0.932068\pi$
$308$	−0.164929	+	4.28857i	−0.00939772	+	0.244364i
$309$	9.12546	+	18.9492i	0.519130	+	1.07798i
$310$	−26.4983	−	25.8318i	−1.50500	−	1.46715i
$311$	9.74297	+	1.46852i	0.552473	+	0.0832719i	0.419345	−	0.907827i	$-0.362260\pi$
$311$	9.74297	+	1.46852i	0.552473	+	0.0832719i	0.133128	+	0.991099i	$0.457498\pi$
$312$	−13.7253	+	6.62345i	−0.777042	+	0.374979i
$313$	−3.50554	+	6.07177i	−0.198145	+	0.343197i	−0.947927	−	0.318488i	$-0.896825\pi$
$313$	−3.50554	+	6.07177i	−0.198145	+	0.343197i	0.749782	+	0.661685i	$0.230158\pi$
$314$	6.20532	−	7.39927i	0.350186	−	0.417565i
$315$	−31.7114	−	2.02951i	−1.78673	−	0.114350i
$316$	13.4334	+	18.6634i	0.755686	+	1.04990i
$317$	−1.19971	−	7.95957i	−0.0673826	−	0.447054i	−0.996926	−	0.0783427i	$-0.975037\pi$
$317$	−1.19971	−	7.95957i	−0.0673826	−	0.447054i	0.929544	−	0.368711i	$-0.120201\pi$
$318$	−6.74732	+	9.39030i	−0.378371	+	0.526582i
$319$	−1.16265	−	0.792682i	−0.0650960	−	0.0443817i
$320$	0.0360449	+	22.2528i	0.00201497	+	1.24397i
$321$	−1.78609	−	2.23968i	−0.0996897	−	0.125007i
$322$	−16.9669	−	10.1100i	−0.945531	−	0.563410i
$323$	−13.1832	−	10.5133i	−0.733536	−	0.584975i
$324$	−3.58884	+	5.56320i	−0.199380	+	0.309067i
$325$	−4.72171	+	2.72608i	−0.261913	+	0.151216i
$326$	7.82242	+	1.37713i	0.433244	+	0.0762720i
$327$	8.57804	+	7.95926i	0.474367	+	0.440148i
$328$	2.22897	+	5.66581i	0.123074	+	0.312842i
$329$	8.18171	−	10.4919i	0.451072	−	0.578435i
$330$	−7.68141	−	3.93541i	−0.422848	−	0.216637i
$331$	−27.4985	+	10.7924i	−1.51146	+	0.593203i	−0.969039	−	0.246907i	$-0.920586\pi$
$331$	−27.4985	+	10.7924i	−1.51146	+	0.593203i	−0.542417	+	0.840110i	$0.682491\pi$
$332$	−11.3520	+	0.289233i	−0.623019	+	0.0158737i
$333$	14.0211	+	45.4553i	0.768351	+	2.49093i
$334$	−23.9058	−	2.38562i	−1.30807	−	0.130535i
$335$	9.39697	+	41.1708i	0.513411	+	2.24940i
$336$	6.00803	+	27.9910i	0.327765	+	1.52703i
$337$	−3.47609	+	15.2297i	−0.189354	+	0.829616i	0.787603	+	0.616183i	$0.211322\pi$
$337$	−3.47609	+	15.2297i	−0.189354	+	0.829616i	−0.976958	+	0.213433i	$0.931535\pi$
$338$	4.06514	−	12.1101i	0.221114	−	0.658702i
$339$	38.4903	+	15.1063i	2.09051	+	0.820463i
$340$	9.86681	+	11.7459i	0.535103	+	0.637012i
$341$	−4.29806	−	6.30409i	−0.232753	−	0.341386i
$342$	37.3290	+	0.920843i	2.01852	+	0.0497935i
$343$	11.0682	−	14.8491i	0.597625	−	0.801776i
$344$	−3.92533	−	0.290966i	−0.211639	−	0.0156878i
$345$	32.8177	−	22.3747i	1.76684	−	1.20461i
$346$	−12.6347	+	11.1562i	−0.679244	+	0.599763i
$347$	−7.91679	−	3.10711i	−0.424995	−	0.166798i	0.143197	−	0.989694i	$-0.454262\pi$
$347$	−7.91679	−	3.10711i	−0.424995	−	0.166798i	−0.568192	+	0.822896i	$0.692357\pi$
$348$	−8.82226	−	3.20565i	−0.472923	−	0.171841i
$349$	30.9397	+	7.06178i	1.65616	+	0.378008i	0.945525	−	0.325550i	$-0.105549\pi$
$349$	30.9397	+	7.06178i	1.65616	+	0.378008i	0.710638	+	0.703558i	$0.248407\pi$
$350$	2.88378	+	9.82764i	0.154145	+	0.525309i
$351$	−1.57996	−	6.92227i	−0.0843322	−	0.369484i
$352$	−0.903037	+	4.49832i	−0.0481320	+	0.239761i
$353$	19.8388	−	6.11947i	1.05591	−	0.325706i	0.282275	−	0.959333i	$-0.408911\pi$
$353$	19.8388	−	6.11947i	1.05591	−	0.325706i	0.773639	+	0.633627i	$0.218435\pi$
$354$	36.0998	−	1.81143i	1.91868	−	0.0962767i
$355$	−33.9103	+	13.3088i	−1.79977	+	0.706359i
$356$	−9.30064	−	5.05835i	−0.492933	−	0.268092i
$357$	15.5627	+	12.1360i	0.823668	+	0.642308i
$358$	−19.8717	+	8.97290i	−1.05025	+	0.474233i
$359$	−16.7821	−	15.5715i	−0.885726	−	0.821833i	0.0991542	−	0.995072i	$-0.468386\pi$
$359$	−16.7821	−	15.5715i	−0.885726	−	0.821833i	−0.984880	+	0.173239i	$0.944577\pi$
$360$	−33.1247	−	7.53227i	−1.74582	−	0.396986i
$361$	9.19723	+	15.9301i	0.484065	+	0.838425i
$362$	4.80263	−	7.86393i	0.252421	−	0.413319i
$363$	21.8733	+	17.4434i	1.14805	+	0.915540i
$364$	8.91835	+	5.61670i	0.467448	+	0.294395i
$365$	−24.7614	+	19.7465i	−1.29607	+	1.03358i
$366$	−3.26286	−	25.9801i	−0.170552	−	1.35800i
$367$	7.47334	+	5.09523i	0.390105	+	0.265969i	0.742451	−	0.669901i	$-0.233663\pi$
$367$	7.47334	+	5.09523i	0.390105	+	0.265969i	−0.352346	+	0.935870i	$0.614616\pi$
$368$	−16.1892	−	13.5546i	−0.843920	−	0.706582i
$369$	−9.19065	+	1.38527i	−0.478446	+	0.0721142i
$370$	34.5392	−	26.1771i	1.79561	−	1.36088i
$371$	7.98049	+	0.510745i	0.414326	+	0.0265166i
$372$	−38.1789	−	33.6564i	−1.97948	−	1.74500i
$373$	−4.46989	−	2.58069i	−0.231442	−	0.133623i	0.379795	−	0.925071i	$-0.375995\pi$
$373$	−4.46989	−	2.58069i	−0.231442	−	0.133623i	−0.611237	+	0.791447i	$0.709328\pi$
$374$	1.51338	+	2.77725i	0.0782552	+	0.143608i
$375$	16.8358	+	2.53759i	0.869398	+	0.131041i
$376$	10.4187	−	9.68288i	0.537305	−	0.499357i
$377$	−3.11348	+	1.49937i	−0.160352	+	0.0772216i
$378$	−13.3368	−	0.183734i	−0.685971	−	0.00945027i
$379$	−4.76123	+	9.88679i	−0.244568	+	0.507850i	−0.986730	−	0.162370i	$-0.948086\pi$
$379$	−4.76123	+	9.88679i	−0.244568	+	0.507850i	0.742162	+	0.670220i	$0.233800\pi$
$380$	−10.8522	−	32.2422i	−0.556705	−	1.65399i
$381$	22.8118	−	1.70951i	1.16869	−	0.0875809i
$382$	−2.90787	−	10.3245i	−0.148780	−	0.528248i
$383$	0.327563	−	4.37102i	0.0167377	−	0.223349i	−0.982562	−	0.185934i	$-0.940469\pi$
$383$	0.327563	−	4.37102i	0.0167377	−	0.223349i	0.999300	−	0.0374143i	$-0.0119121\pi$
$384$	1.58330	+	30.5642i	0.0807975	+	1.55972i
$385$	0.510839	+	5.94706i	0.0260348	+	0.303090i
$386$	3.28854	+	0.836420i	0.167382	+	0.0425727i
$387$	1.77109	−	5.74174i	0.0900298	−	0.291869i
$388$	−4.85507	+	10.7755i	−0.246479	+	0.547041i
$389$	−1.97643	−	2.13008i	−0.100209	−	0.107999i	0.680956	−	0.732324i	$-0.261565\pi$
$389$	−1.97643	−	2.13008i	−0.100209	−	0.107999i	−0.781165	+	0.624325i	$0.785374\pi$
$390$	−17.8018	+	11.5044i	−0.901427	+	0.582548i
$391$	−14.5554			−0.736098
$392$	14.2059	−	13.7911i	0.717504	−	0.696554i
$393$	58.0800			2.92975
$394$	−19.7060	+	12.7350i	−0.992775	+	0.641582i
$395$	21.7531	+	23.4442i	1.09452	+	1.17961i
$396$	−6.38571	−	2.87720i	−0.320894	−	0.144584i
$397$	5.94231	−	19.2645i	0.298236	−	0.966857i	−0.675149	−	0.737681i	$-0.735921\pi$
$397$	5.94231	−	19.2645i	0.298236	−	0.966857i	0.973385	−	0.229176i	$-0.0736031\pi$
$398$	34.8330	+	8.85956i	1.74602	+	0.444089i
$399$	−22.2946	−	37.6624i	−1.11613	−	1.88548i
$400$	1.37319	+	10.8627i	0.0686595	+	0.543136i
$401$	0.683884	−	9.12579i	0.0341515	−	0.455720i	−0.953746	−	0.300613i	$-0.902809\pi$
$401$	0.683884	−	9.12579i	0.0341515	−	0.455720i	0.987898	−	0.155107i	$-0.0495723\pi$
$402$	15.7455	+	55.9050i	0.785315	+	2.78829i
$403$	−18.6850	+	1.40025i	−0.930767	+	0.0697513i
$404$	11.4809	−	3.86429i	0.571198	−	0.192255i
$405$	−3.99502	+	8.29573i	−0.198514	+	0.412218i
$406$	1.35720	+	6.34816i	0.0673569	+	0.315054i
$407$	8.05055	−	3.87694i	0.399051	−	0.192173i
$408$	14.3628	+	15.4543i	0.711063	+	0.765100i
$409$	−7.19319	−	1.08420i	−0.355680	−	0.0536102i	−0.0312282	−	0.999512i	$-0.509942\pi$
$409$	−7.19319	−	1.08420i	−0.355680	−	0.0536102i	−0.324452	+	0.945902i	$0.605180\pi$
$410$	4.05180	+	7.43557i	0.200104	+	0.367217i
$411$	30.5616	+	17.6447i	1.50749	+	0.870351i
$412$	10.2827	−	11.6644i	0.506593	−	0.574665i
$413$	−14.3056	−	20.4993i	−0.703932	−	1.00870i
$414$	25.6883	−	19.4690i	1.26251	−	0.956850i
$415$	−15.6170	+	2.35389i	−0.766609	+	0.115548i
$416$	8.45811	+	7.44404i	0.414693	+	0.364974i
$417$	−27.8602	−	18.9948i	−1.36432	−	0.930179i
$418$	−0.874041	−	6.95945i	−0.0427507	−	0.340398i
$419$	4.95314	−	3.95000i	0.241977	−	0.192970i	−0.494991	−	0.868898i	$-0.664829\pi$
$419$	4.95314	−	3.95000i	0.241977	−	0.192970i	0.736967	+	0.675928i	$0.236257\pi$
$420$	13.1115	+	37.5958i	0.639775	+	1.83449i
$421$	−5.88017	−	4.68928i	−0.286582	−	0.228541i	0.469638	−	0.882859i	$-0.344384\pi$
$421$	−5.88017	−	4.68928i	−0.286582	−	0.228541i	−0.756220	+	0.654318i	$0.772956\pi$
$422$	14.5348	−	23.7996i	0.707544	−	1.15855i
$423$	10.8565	+	18.8041i	0.527863	+	0.914285i
$424$	8.33615	+	1.89557i	0.404839	+	0.0920570i
$425$	5.53301	+	5.13388i	0.268390	+	0.249030i
$426$	−45.6623	+	20.6184i	−2.21234	+	0.998967i
$427$	−14.0341	+	11.4440i	−0.679157	+	0.553813i
$428$	−1.01191	+	1.86057i	−0.0489125	+	0.0899340i
$429$	−4.06801	+	1.59658i	−0.196405	+	0.0770835i
$430$	−5.46744	+	0.274348i	−0.263663	+	0.0132302i
$431$	−24.8921	+	7.67819i	−1.19901	+	0.369845i	−0.829035	−	0.559196i	$-0.811110\pi$
$431$	−24.8921	+	7.67819i	−1.19901	+	0.369845i	−0.369974	+	0.929042i	$0.620634\pi$
$432$	−14.0450	−	2.46088i	−0.675742	−	0.118399i
$433$	0.261931	+	1.14760i	0.0125876	+	0.0551500i	0.980832	−	0.194857i	$-0.0624243\pi$
$433$	0.261931	+	1.14760i	0.0125876	+	0.0551500i	−0.968244	+	0.250007i	$0.919567\pi$
$434$	−5.72505	+	34.7300i	−0.274811	+	1.66709i
$435$	−12.7276	−	2.90499i	−0.610240	−	0.139283i
$436$	2.95461	−	8.13139i	0.141500	−	0.389423i
$437$	30.0478	+	11.7929i	1.43738	+	0.564131i
$438$	−32.6515	+	28.8308i	−1.56015	+	1.37759i
$439$	−14.0191	+	9.55804i	−0.669094	+	0.456180i	−0.849624	−	0.527389i	$-0.823171\pi$
$439$	−14.0191	+	9.55804i	−0.669094	+	0.456180i	0.180530	+	0.983569i	$0.442219\pi$
$440$	−0.471705	+	6.36362i	−0.0224877	+	0.303374i
$441$	15.6785	+	25.8398i	0.746597	+	1.23047i
$442$	7.76490	+	0.191547i	0.369339	+	0.00911096i
$443$	−10.6820	−	15.6676i	−0.507518	−	0.744392i	0.483900	−	0.875123i	$-0.339220\pi$
$443$	−10.6820	−	15.6676i	−0.507518	−	0.744392i	−0.991418	+	0.130731i	$0.958267\pi$
$444$	45.6391	−	38.3378i	2.16594	−	1.81943i
$445$	−13.7068	−	5.37953i	−0.649765	−	0.255014i
$446$	−10.6039	+	31.5892i	−0.502110	+	1.49579i
$447$	6.84075	−	29.9713i	0.323556	−	1.41759i
$448$	17.3377	−	12.1410i	0.819129	−	0.573610i
$449$	0.527129	+	2.30950i	0.0248768	+	0.108992i	0.985842	−	0.167677i	$-0.0536265\pi$
$449$	0.527129	+	2.30950i	0.0248768	+	0.108992i	−0.960965	+	0.276669i	$0.910769\pi$
$450$	−16.6320	−	1.65975i	−0.784039	−	0.0782411i
$451$	0.514613	+	1.66834i	0.0242322	+	0.0785588i
$452$	−0.778642	−	30.5605i	−0.0366242	−	1.43744i
$453$	−26.8991	+	10.5571i	−1.26383	+	0.496016i
$454$	−21.9519	−	11.2466i	−1.03026	−	0.527830i
$455$	13.2754	+	6.21594i	0.622358	+	0.291408i
$456$	−17.1290	−	43.5402i	−0.802138	−	2.03896i
$457$	11.7462	+	10.8989i	0.549466	+	0.509830i	0.905331	−	0.424708i	$-0.139623\pi$
$457$	11.7462	+	10.8989i	0.549466	+	0.509830i	−0.355865	+	0.934538i	$0.615814\pi$
$458$	−18.2558	−	3.21391i	−0.853038	−	0.150176i
$459$	−8.51266	+	4.91479i	−0.397337	+	0.229403i
$460$	−24.6767	−	15.9190i	−1.15056	−	0.742228i
$461$	−6.84059	−	5.45519i	−0.318598	−	0.254073i	0.451112	−	0.892467i	$-0.351028\pi$
$461$	−6.84059	−	5.45519i	−0.318598	−	0.254073i	−0.769710	+	0.638394i	$0.779599\pi$
$462$	1.11160	+	8.13373i	0.0517163	+	0.378415i
$463$	−14.1698	−	17.7684i	−0.658526	−	0.825766i	0.334656	−	0.942341i	$-0.391380\pi$
$463$	−14.1698	−	17.7684i	−0.658526	−	0.825766i	−0.993182	+	0.116575i	$0.962809\pi$
$464$	0.353407	+	6.93083i	0.0164065	+	0.321756i
$465$	−58.4860	−	39.8751i	−2.71222	−	1.84916i
$466$	19.5791	−	27.2483i	0.906982	−	1.26225i
$467$	−1.69232	−	11.2278i	−0.0783113	−	0.519561i	−0.993252	−	0.115974i	$-0.963001\pi$
$467$	−1.69232	−	11.2278i	−0.0783113	−	0.519561i	0.914941	−	0.403588i	$-0.132237\pi$
$468$	−13.9602	+	10.0481i	−0.645309	+	0.464475i
$469$	26.9984	−	29.7403i	1.24667	−	1.37328i
$470$	12.7116	−	15.1574i	0.586341	−	0.699157i
$471$	9.23593	−	15.9971i	0.425569	−	0.737108i
$472$	−11.6143	−	24.0675i	−0.534593	−	1.10780i
$473$	−1.11609	−	0.168223i	−0.0513177	−	0.00773489i
$474$	31.4962	+	30.7039i	1.44667	+	1.41028i
$475$	−7.26270	−	15.0812i	−0.333235	−	0.691971i
$476$	3.79107	−	14.0899i	0.173763	−	0.645809i
$477$	−5.66240	+	11.7581i	−0.259264	+	0.538367i
$478$	−6.43447	+	2.34392i	−0.294306	+	0.107209i
$479$	−2.14746	−	28.6558i	−0.0981198	−	1.30932i	−0.801282	−	0.598287i	$-0.795848\pi$
$479$	−2.14746	−	28.6558i	−0.0981198	−	1.30932i	0.703162	−	0.711030i	$-0.251771\pi$
$480$	7.44802	+	41.9089i	0.339954	+	1.91287i
$481$	1.63985	−	21.8823i	0.0747707	−	0.997745i
$482$	−1.66258	+	0.336565i	−0.0757284	+	0.0153301i
$483$	−35.3162	−	13.4187i	−1.60694	−	0.610572i
$484$	5.59141	−	19.9143i	0.254155	−	0.905195i
$485$	−4.84503	+	15.7072i	−0.220001	+	0.713227i
$486$	−10.7867	+	25.6084i	−0.489295	+	1.16162i
$487$	−4.54669	+	4.21871i	−0.206030	+	0.191168i	−0.776438	−	0.630194i	$-0.782976\pi$
$487$	−4.54669	+	4.21871i	−0.206030	+	0.191168i	0.570408	+	0.821361i	$0.306785\pi$
$488$	−16.7574	+	9.69301i	−0.758573	+	0.438782i
$489$	15.1930			0.687051
$490$	17.2308	−	21.4792i	0.778407	−	0.970330i
$491$			17.0046i			0.767408i	0.923456	+	0.383704i	$0.125352\pi$
$491$			17.0046i			0.767408i	−0.923456	+	0.383704i	$0.874648\pi$
$492$	6.07810	+	9.93431i	0.274022	+	0.447873i
$493$	3.25397	+	3.50695i	0.146552	+	0.157945i
$494$	−15.8745	−	6.68661i	−0.714226	−	0.300845i
$495$	−9.30835	−	2.87124i	−0.418379	−	0.129053i
$496$	−11.9458	+	35.6825i	−0.536382	+	1.60219i
$497$	28.8395	+	19.2058i	1.29363	+	0.861500i
$498$	−21.2895	+	4.30974i	−0.954004	+	0.193124i
$499$	−37.1877	−	2.78683i	−1.66475	−	0.124756i	−0.791221	−	0.611531i	$-0.790554\pi$
$499$	−37.1877	−	2.78683i	−1.66475	−	0.124756i	−0.873527	+	0.486775i	$0.838173\pi$
$500$	−3.11274	−	12.1970i	−0.139206	−	0.545465i
$501$	−45.8262	+	3.43420i	−2.04736	+	0.153429i
$502$	11.3829	+	31.2479i	0.508042	+	1.39466i
$503$	−8.41718	−	4.05350i	−0.375304	−	0.180737i	0.236717	−	0.971579i	$-0.423929\pi$
$503$	−8.41718	−	4.05350i	−0.375304	−	0.180737i	−0.612020	+	0.790842i	$0.709643\pi$
$504$	12.1556	+	29.9375i	0.541455	+	1.33352i
$505$	15.1794	−	7.31002i	0.675475	−	0.325292i
$506$	−4.33546	−	4.22640i	−0.192734	−	0.187886i
$507$	3.64181	−	24.1618i	0.161738	−	1.07306i
$508$	−7.72395	−	15.0461i	−0.342695	−	0.667563i
$509$	14.9894	+	8.65416i	0.664395	+	0.383589i	0.793950	−	0.607984i	$-0.208021\pi$
$509$	14.9894	+	8.65416i	0.664395	+	0.383589i	−0.129554	+	0.991572i	$0.541355\pi$
$510$	22.4831	+	18.8552i	0.995570	+	0.834924i
$511$	28.8809	+	8.56534i	1.27761	+	0.378908i
$512$	20.3627	−	9.86717i	0.899912	−	0.436072i
$513$	21.5553	−	3.24894i	0.951691	−	0.143444i
$514$	−1.77072	+	2.46432i	−0.0781029	+	0.108696i
$515$	12.1827	−	17.8687i	0.536832	−	0.787388i
$516$	−7.49123	+	0.753696i	−0.329783	+	0.0331796i
$517$	3.18882	−	2.54300i	0.140244	−	0.111841i
$518$	−39.2192	−	12.6917i	−1.72319	−	0.557643i
$519$	−20.1019	+	25.2070i	−0.882375	+	1.10646i
$520$	12.9548	+	8.81710i	0.568107	+	0.386655i
$521$	21.1911	+	36.7040i	0.928398	+	1.60803i	0.786002	+	0.618223i	$0.212147\pi$
$521$	21.1911	+	36.7040i	0.928398	+	1.60803i	0.142396	+	0.989810i	$0.454519\pi$
$522$	−10.4336	−	1.83683i	−0.456668	−	0.0803958i
$523$	0.829462	−	0.893947i	0.0362698	−	0.0390896i	−0.714656	−	0.699476i	$-0.753417\pi$
$523$	0.829462	−	0.893947i	0.0362698	−	0.0390896i	0.750926	+	0.660386i	$0.229607\pi$
$524$	−16.7010	−	39.5597i	−0.729585	−	1.72817i
$525$	8.69194	+	17.5574i	0.379348	+	0.766268i
$526$	−4.03325	+	7.87238i	−0.175858	+	0.343252i
$527$	9.47690	+	24.1468i	0.412820	+	1.05185i
$528$	−0.209321	+	8.77366i	−0.00910954	+	0.381824i
$529$	4.64749	−	1.43356i	0.202065	−	0.0623287i
$530$	11.8311	+	1.18066i	0.513911	+	0.0512844i
$531$	39.7721	−	9.07771i	1.72596	−	0.393939i
$532$	−19.2419	+	26.0153i	−0.834243	+	1.12790i
$533$	4.18008	+	0.954076i	0.181059	+	0.0413256i
$534$	−19.1986	−	6.44462i	−0.830805	−	0.278886i
$535$	−1.07616	+	2.74201i	−0.0465265	+	0.118548i
$536$	33.5506	−	26.8002i	1.44916	−	1.15759i
$537$	−34.4594	+	23.4940i	−1.48703	+	1.01384i
$538$	8.46590	+	0.208839i	0.364991	+	0.00900371i
$539$	4.36068	−	3.63564i	0.187828	−	0.156598i
$540$	−19.8073	−	0.977820i	−0.852370	−	0.0420787i
$541$	0.588537	+	0.863225i	0.0253032	+	0.0371129i	0.838682	−	0.544622i	$-0.183327\pi$
$541$	0.588537	+	0.863225i	0.0253032	+	0.0371129i	−0.813379	+	0.581734i	$0.802374\pi$
$542$	−6.80650	−	7.70851i	−0.292364	−	0.331109i
$543$	6.43937	−	16.4073i	0.276340	−	0.704103i
$544$	6.39623	−	14.2267i	0.274236	−	0.609965i
$545$	2.67750	−	11.7309i	0.114691	−	0.502496i
$546$	18.6636	+	7.62326i	0.798729	+	0.326246i
$547$	21.6910	−	4.95084i	0.927442	−	0.211683i	0.267984	−	0.963423i	$-0.413643\pi$
$547$	21.6910	−	4.95084i	0.927442	−	0.211683i	0.659459	+	0.751741i	$0.270786\pi$
$548$	3.23024	−	25.8900i	0.137989	−	1.10596i
$549$	−8.71076	−	28.2396i	−0.371766	−	1.20524i
$550$	0.157349	+	3.13577i	0.00670937	+	0.133710i
$551$	−3.87607	−	9.87606i	−0.165126	−	0.420734i
$552$	−34.9934	−	20.1657i	−1.48942	−	0.858308i
$553$	6.44575	−	29.7290i	0.274101	−	1.26421i
$554$	−11.0932	+	5.00906i	−0.471306	+	0.212815i
$555$	56.3851	−	60.7687i	2.39341	−	2.57949i
$556$	−4.92656	+	24.4382i	−0.208933	+	1.03641i
$557$	−0.573251	+	0.330967i	−0.0242894	+	0.0140235i	−0.512096	−	0.858928i	$-0.671131\pi$
$557$	−0.573251	+	0.330967i	−0.0242894	+	0.0140235i	0.487806	+	0.872952i	$0.337797\pi$
$558$	−49.0236	−	29.9396i	−2.07534	−	1.26744i
$559$	−1.72821	+	2.16711i	−0.0730956	+	0.0916590i
$560$	21.8371	−	19.7412i	0.922787	−	0.834220i
$561$	3.77206	+	4.73002i	0.159257	+	0.199702i
$562$	2.08843	+	16.6289i	0.0880953	+	0.701449i
$563$	3.42774	−	5.02757i	0.144462	−	0.211887i	−0.747187	−	0.664613i	$-0.768596\pi$
$563$	3.42774	−	5.02757i	0.144462	−	0.211887i	0.891649	+	0.452727i	$0.149549\pi$
$564$	16.4160	−	21.6965i	0.691239	−	0.913586i
$565$	−6.33688	−	42.0424i	−0.266594	−	1.76874i
$566$	17.8325	+	23.5290i	0.749556	+	0.988997i
$567$	8.64535	−	1.39951i	0.363071	−	0.0587737i
$568$	27.1739	+	25.1728i	1.14019	+	1.05623i
$569$	13.1185	−	22.7219i	0.549956	−	0.952552i	−0.448320	−	0.893873i	$-0.647978\pi$
$569$	13.1185	−	22.7219i	0.549956	−	0.952552i	0.998277	−	0.0586796i	$-0.0186890\pi$
$570$	−31.1370	−	57.1403i	−1.30418	−	2.39334i
$571$	−0.754857	+	5.00815i	−0.0315898	+	0.209584i	−0.999057	−	0.0434107i	$-0.986178\pi$
$571$	−0.754857	+	5.00815i	−0.0315898	+	0.209584i	0.967468	+	0.252995i	$0.0814157\pi$
$572$	2.25723	+	2.31172i	0.0943794	+	0.0966579i
$573$	−8.90211	−	18.4854i	−0.371891	−	0.772240i
$574$	3.59427	−	7.20786i	0.150022	−	0.300850i
$575$	−13.0181	−	6.26921i	−0.542894	−	0.261444i
$576$	7.74089	+	33.6636i	0.322537	+	1.40265i
$577$	−0.139926	−	1.86719i	−0.00582521	−	0.0777321i	0.993534	−	0.113539i	$-0.0362188\pi$
$577$	−0.139926	−	1.86719i	−0.00582521	−	0.0777321i	−0.999359	+	0.0358073i	$0.988600\pi$
$578$	3.60257	+	12.7911i	0.149847	+	0.532038i
$579$	6.47252	+	0.485048i	0.268989	+	0.0201579i
$580$	1.68117	+	9.50438i	0.0698068	+	0.394648i
$581$	10.3369	+	10.9001i	0.428847	+	0.452212i
$582$	−5.57256	+	21.9095i	−0.230990	+	0.908179i
$583$	2.34254	+	0.722577i	0.0970180	+	0.0299261i
$584$	29.0263	+	13.9494i	1.20112	+	0.577229i
$585$	−17.5362	+	16.2712i	−0.725033	+	0.672733i
$586$	26.5569	−	17.1625i	1.09706	−	0.708974i
$587$		−	3.46259i		−	0.142916i	−0.997444	−	0.0714582i	$-0.977235\pi$
$587$		−	3.46259i		−	0.142916i	0.997444	−	0.0714582i	$-0.0227653\pi$
$588$	22.1879	−	30.6917i	0.915015	−	1.26570i
$589$		−	57.5262i		−	2.37033i
$590$	−20.1732	−	31.2157i	−0.830516	−	1.28513i
$591$	−32.8996	+	30.5264i	−1.35331	+	1.25569i
$592$	−39.2364	−	20.0618i	−1.61260	−	0.824536i
$593$	41.3555	+	12.7565i	1.69827	+	0.523847i	0.984326	−	0.176358i	$-0.0564316\pi$
$593$	41.3555	+	12.7565i	1.69827	+	0.523847i	0.713943	+	0.700204i	$0.246908\pi$
$594$	−3.96266	−	1.00788i	−0.162590	−	0.0413538i
$595$	2.80588	−	20.0982i	0.115030	−	0.823947i
$596$	−22.3812	+	3.95887i	−0.916770	+	0.162162i
$597$	68.5584	+	5.13774i	2.80591	+	0.210274i
$598$	−14.3121	+	4.03098i	−0.585267	+	0.164839i
$599$	2.02913	+	27.0769i	0.0829081	+	1.10633i	0.871167	+	0.490987i	$0.163364\pi$
$599$	2.02913	+	27.0769i	0.0829081	+	1.10633i	−0.788259	+	0.615344i	$0.789017\pi$
$600$	6.18950	+	20.0083i	0.252685	+	0.816836i
$601$	−18.4502	−	8.88516i	−0.752601	−	0.362433i	0.0179275	−	0.999839i	$-0.494293\pi$
$601$	−18.4502	−	8.88516i	−0.752601	−	0.362433i	−0.770528	+	0.637406i	$0.780007\pi$
$602$	3.19010	+	4.11530i	0.130019	+	0.167727i
$603$	28.4417	+	59.0598i	1.15823	+	2.40510i
$604$	14.9255	+	15.2859i	0.607312	+	0.621974i
$605$	4.28762	−	28.4465i	0.174316	−	1.15651i
$606$	20.3468	−	11.0874i	0.826531	−	0.450394i
$607$	−5.51859	+	9.55848i	−0.223993	+	0.387967i	−0.956017	−	0.293312i	$-0.905243\pi$
$607$	−5.51859	+	9.55848i	−0.223993	+	0.387967i	0.732024	+	0.681279i	$0.238576\pi$
$608$	−24.7308	+	24.1870i	−1.00297	+	0.980911i
$609$	4.66213	+	11.5089i	0.188919	+	0.466363i
$610$	−21.4579	+	16.2628i	−0.868803	+	0.658462i
$611$	−1.49286	−	9.90446i	−0.0603946	−	0.400692i
$612$	18.9890	+	14.3675i	0.767587	+	0.580772i
$613$	−19.9492	+	29.2601i	−0.805740	+	1.18180i	0.174629	+	0.984634i	$0.444127\pi$
$613$	−19.9492	+	29.2601i	−0.805740	+	1.18180i	−0.980369	+	0.197169i	$0.936825\pi$
$614$	30.2339	−	3.79709i	1.22014	−	0.153238i
$615$	10.0990	+	12.6637i	0.407231	+	0.510651i
$616$	5.22043	−	3.09600i	0.210337	−	0.124741i
$617$	−4.44574	+	5.57478i	−0.178979	+	0.224432i	−0.863226	−	0.504818i	$-0.831560\pi$
$617$	−4.44574	+	5.57478i	−0.178979	+	0.224432i	0.684247	+	0.729250i	$0.260131\pi$
$618$	15.5026	−	25.3843i	0.623607	−	1.02111i
$619$	−32.9826	+	19.0425i	−1.32568	+	0.765382i	−0.984628	−	0.174662i	$-0.944117\pi$
$619$	−32.9826	+	19.0425i	−1.32568	+	0.765382i	−0.341052	+	0.940044i	$0.610783\pi$
$620$	−10.3422	+	51.3023i	−0.415351	+	2.06035i
$621$	12.7987	−	13.7937i	0.513595	−	0.553524i
$622$	−5.73441	−	12.6996i	−0.229929	−	0.509208i
$623$	3.26500	+	13.6197i	0.130810	+	0.545660i
$624$	18.4026	+	11.2183i	0.736695	+	0.449093i
$625$	−11.3963	−	29.0374i	−0.455853	−	1.16150i
$626$	9.90271	−	0.496904i	0.395792	−	0.0198603i
$627$	−3.95466	−	12.8207i	−0.157934	−	0.512009i
$628$	−13.5518	−	1.69083i	−0.540776	−	0.0674714i
$629$	−29.6169	+	6.75986i	−1.18090	+	0.269533i
$630$	21.9310	+	39.2237i	0.873752	+	1.56271i
$631$	−0.840793	+	3.68375i	−0.0334714	+	0.146648i	−0.988902	−	0.148567i	$-0.952534\pi$
$631$	−0.840793	+	3.68375i	−0.0334714	+	0.146648i	0.955431	+	0.295215i	$0.0953912\pi$
$632$	11.8564	−	30.2817i	0.471623	−	1.20454i
$633$	19.4883	−	49.6554i	0.774591	−	1.97363i
$634$	−8.53324	+	7.53473i	−0.338898	+	0.299242i
$635$	−13.2506	−	19.4351i	−0.525835	−	0.771259i
$636$	16.3327	+	0.806292i	0.647635	+	0.0319716i
$637$	−2.37774	−	13.7384i	−0.0942096	−	0.544335i
$638$	−0.0490757	+	1.98942i	−0.00194292	+	0.0787620i
$639$	−46.7209	+	31.8538i	−1.84825	+	1.26012i
$640$	26.4035	−	17.1240i	1.04369	−	0.676884i
$641$	−16.2232	+	41.3359i	−0.640776	+	1.63267i	0.126962	+	0.991908i	$0.459477\pi$
$641$	−16.2232	+	41.3359i	−0.640776	+	1.63267i	−0.767739	+	0.640763i	$0.778618\pi$
$642$	−1.28923	+	3.84064i	−0.0508819	+	0.151578i
$643$	41.6887	+	9.51517i	1.64404	+	0.375242i	0.941662	−	0.336560i	$-0.109264\pi$
$643$	41.6887	+	9.51517i	1.64404	+	0.375242i	0.702380	+	0.711802i	$0.252121\pi$
$644$	1.01540	+	27.9132i	0.0400123	+	1.09994i
$645$	−10.2089	+	2.33010i	−0.401973	+	0.0917478i
$646$	−2.36794	+	23.7286i	−0.0931652	+	0.933590i
$647$	38.3736	−	11.8367i	1.50862	−	0.465348i	0.573359	−	0.819304i	$-0.305640\pi$
$647$	38.3736	−	11.8367i	1.50862	−	0.465348i	0.935262	+	0.353956i	$0.115164\pi$
$648$	9.36258	−	0.00758271i	0.367797	−	0.000297877i
$649$	−2.79962	−	7.13332i	−0.109895	−	0.280007i
$650$	6.86232	+	3.51577i	0.269162	+	0.137900i
$651$	0.733041	+	67.3248i	0.0287302	+	2.63867i
$652$	−4.36876	−	10.3483i	−0.171094	−	0.405271i
$653$	0.296297	−	0.319332i	0.0115950	−	0.0124964i	−0.727228	−	0.686396i	$-0.759192\pi$
$653$	0.296297	−	0.319332i	0.0115950	−	0.0124964i	0.738823	+	0.673900i	$0.235382\pi$
$654$	2.86928	−	16.2982i	0.112198	−	0.637311i
$655$	−29.8608	−	51.7205i	−1.16676	−	2.02089i
$656$	5.01873	−	6.99656i	0.195949	−	0.273170i
$657$	−30.6518	+	38.4361i	−1.19584	+	1.49954i
$658$	−18.7422	−	1.66445i	−0.730646	−	0.0648871i
$659$	−25.6134	+	20.4260i	−0.997758	+	0.795685i	−0.978942	−	0.204138i	$-0.934561\pi$
$659$	−25.6134	+	20.4260i	−0.997758	+	0.795685i	−0.0188154	+	0.999823i	$0.505989\pi$
$660$	1.22187	+	12.1446i	0.0475612	+	0.472726i
$661$	−7.55402	+	11.0797i	−0.293817	+	0.430951i	−0.944556	−	0.328351i	$-0.893507\pi$
$661$	−7.55402	+	11.0797i	−0.293817	+	0.430951i	0.650739	+	0.759302i	$0.274459\pi$
$662$	33.9266	+	24.3777i	1.31860	+	0.947466i
$663$	14.6914	−	2.21438i	0.570568	−	0.0859993i
$664$	9.05727	+	13.2615i	0.351490	+	0.514645i
$665$	−22.0761	+	39.2169i	−0.856076	+	1.52077i
$666$	43.2278	−	51.5452i	1.67504	−	1.99733i
$667$	−7.93119	−	4.57907i	−0.307097	−	0.177302i
$668$	15.5165	+	30.2258i	0.600351	+	1.16947i
$669$	−9.49965	+	63.0261i	−0.367278	+	2.43673i
$670$	41.6883	−	42.7640i	1.61056	−	1.65212i
$671$	−5.00149	+	2.40859i	−0.193080	+	0.0929827i
$672$	28.6350	−	28.6219i	1.10462	−	1.10411i
$673$	−1.05199	−	0.506611i	−0.0405512	−	0.0195284i	0.413498	−	0.910505i	$-0.364307\pi$
$673$	−1.05199	−	0.506611i	−0.0405512	−	0.0195284i	−0.454049	+	0.890976i	$0.650021\pi$
$674$	20.7576	−	7.56151i	0.799554	−	0.291258i
$675$	−9.73047	+	0.729198i	−0.374526	+	0.0280669i
$676$	−17.5044	+	4.46723i	−0.673245	+	0.171816i
$677$	5.89701	+	0.441920i	0.226641	+	0.0169844i	0.187566	−	0.982252i	$-0.439940\pi$
$677$	5.89701	+	0.441920i	0.226641	+	0.0169844i	0.0390743	+	0.999236i	$0.487559\pi$
$678$	−11.6022	−	57.3132i	−0.445580	−	2.20110i
$679$	14.8890	−	4.77080i	0.571389	−	0.183086i
$680$	6.37771	−	20.7356i	0.244574	−	0.795175i
$681$	−45.0841	−	13.9066i	−1.72763	−	0.532902i
$682$	−4.18863	+	9.94410i	−0.160391	+	0.380779i
$683$	14.8189	+	15.9710i	0.567031	+	0.611114i	0.949849	−	0.312710i	$-0.101237\pi$
$683$	14.8189	+	15.9710i	0.567031	+	0.611114i	−0.382817	+	0.923824i	$0.625046\pi$
$684$	−27.5599	−	45.0450i	−1.05378	−	1.72234i
$685$		−	36.2869i		−	1.38645i
$686$	−26.1332	−	1.74830i	−0.997770	−	0.0667504i
$687$	−35.4571			−1.35277
$688$	2.66747	+	4.88572i	0.101696	+	0.186266i
$689$	4.41316	−	4.09482i	0.168128	−	0.156000i
$690$	−51.7667	−	21.8051i	−1.97073	−	0.830104i
$691$	−7.10221	+	23.0248i	−0.270181	+	0.875905i	0.714214	+	0.699928i	$0.246785\pi$
$691$	−7.10221	+	23.0248i	−0.270181	+	0.875905i	−0.984394	+	0.175977i	$0.943692\pi$
$692$	22.9494	+	6.44358i	0.872404	+	0.244948i
$693$	2.82725	+	8.82349i	0.107398	+	0.335177i
$694$	2.38637	+	11.7883i	0.0905855	+	0.447479i
$695$	−2.59107	+	34.5755i	−0.0982851	+	1.31152i
$696$	2.96437	+	12.9394i	0.112364	+	0.490468i
$697$	−0.443574	−	5.91908i	−0.0168016	−	0.224201i
$698$	−15.3614	−	42.1698i	−0.581439	−	1.59615i
$699$	27.8471	−	57.8251i	1.05327	−	2.18715i
$700$	9.45938	−	10.9689i	0.357531	−	0.414587i
$701$	−10.8186	−	22.4651i	−0.408613	−	0.848493i	−0.999140	−	0.0414752i	$-0.986794\pi$
$701$	−10.8186	−	22.4651i	−0.408613	−	0.848493i	0.590527	−	0.807018i	$-0.298920\pi$
$702$	−7.00928	+	7.19015i	−0.264548	+	0.271375i
$703$	66.6172	+	10.0409i	2.51252	+	0.378701i
$704$	6.03613	−	2.38030i	0.227495	−	0.0897109i
$705$	18.9198	−	32.7700i	0.712559	−	1.23419i
$706$	−22.4967	−	18.8667i	−0.846676	−	0.710056i
$707$	−13.9645	−	7.86096i	−0.525190	−	0.295642i
$708$	−29.8616	−	41.4877i	−1.12227	−	1.55920i
$709$	−1.63672	−	10.8589i	−0.0614683	−	0.407815i	−0.998313	−	0.0580686i	$-0.981506\pi$
$709$	−1.63672	−	10.8589i	−0.0614683	−	0.407815i	0.936844	−	0.349747i	$-0.113732\pi$
$710$	41.8373	+	30.0618i	1.57012	+	1.12820i
$711$	41.0178	+	27.9654i	1.53829	+	1.04879i
$712$	1.13099	+	14.9298i	0.0423857	+	0.559517i
$713$	−30.9607	−	38.8234i	−1.15949	−	1.45395i
$714$	2.46890	−	27.8005i	0.0923964	−	1.04041i
$715$	3.51325	+	2.80173i	0.131388	+	0.104779i
$716$	25.9112	+	16.7154i	0.968346	+	0.624683i
$717$	−11.3442	+	6.54959i	−0.423658	+	0.244599i
$718$	−5.61347	+	31.8859i	−0.209493	+	1.18997i
$719$	−16.9132	−	15.6932i	−0.630757	−	0.585257i	0.298627	−	0.954370i	$-0.403471\pi$
$719$	−16.9132	−	15.6932i	−0.630757	−	0.585257i	−0.929385	+	0.369113i	$0.879662\pi$
$720$	16.4798	+	45.1262i	0.614166	+	1.68175i
$721$	−20.5691	+	0.223959i	−0.766034	+	0.00834068i
$722$	11.8615	−	23.1521i	0.441438	−	0.861630i
$723$	−3.02043	+	1.18543i	−0.112331	+	0.0440867i
$724$	−13.0270	+	0.331911i	−0.484145	+	0.0123354i
$725$	1.39982	+	4.53810i	0.0519879	+	0.168541i
$726$	3.92882	−	39.3699i	0.145812	−	1.46115i
$727$	7.70913	+	33.7759i	0.285916	+	1.25268i	0.890074	+	0.455815i	$0.150652\pi$
$727$	7.70913	+	33.7759i	0.285916	+	1.25268i	−0.604158	+	0.796864i	$0.706491\pi$
$728$	−0.174352	−	14.9043i	−0.00646193	−	0.552390i
$729$	−9.61779	+	42.1383i	−0.356215	+	1.56068i
$730$	42.4611	+	14.2534i	1.57155	+	0.527542i
$731$	3.57205	+	1.40192i	0.132117	+	0.0518521i
$732$	−28.3538	+	23.8178i	−1.04799	+	0.880330i
$733$	−9.01867	−	13.2280i	−0.333112	−	0.488586i	0.622742	−	0.782427i	$-0.286019\pi$
$733$	−9.01867	−	13.2280i	−0.333112	−	0.488586i	−0.955854	+	0.293841i	$0.905066\pi$
$734$	0.315451	−	12.7877i	0.0116435	−	0.472002i
$735$	25.3367	−	46.1781i	0.934557	−	1.70331i
$736$	−3.67294	+	29.6335i	−0.135386	+	1.09230i
$737$	10.1738	−	6.93637i	0.374756	−	0.255505i
$738$	8.70009	+	9.85304i	0.320255	+	0.362695i
$739$	−20.7300	−	8.13594i	−0.762566	−	0.299285i	−0.0479948	−	0.998848i	$-0.515283\pi$
$739$	−20.7300	−	8.13594i	−0.762566	−	0.299285i	−0.714572	+	0.699562i	$0.753378\pi$
$740$	−57.6045	−	20.9311i	−2.11758	−	0.769443i
$741$	−32.1227	−	7.33181i	−1.18006	−	0.269341i
$742$	−5.51915	−	9.87102i	−0.202614	−	0.362377i
$743$	−8.58355	−	37.6070i	−0.314900	−	1.37967i	−0.846373	−	0.532591i	$-0.821218\pi$
$743$	−8.58355	−	37.6070i	−0.314900	−	1.37967i	0.531473	−	0.847075i	$-0.321639\pi$
$744$	−10.6700	+	71.1822i	−0.391183	+	2.60967i
$745$	−30.2066	+	9.31750i	−1.10668	+	0.341367i
$746$	0.365808	+	7.29013i	0.0133932	+	0.266911i
$747$	−22.8209	+	8.95652i	−0.834971	+	0.327702i
$748$	2.13707	−	3.92936i	0.0781389	−	0.143672i
$749$	2.72458	−	0.653156i	0.0995540	−	0.0238658i
$750$	−9.90906	−	21.9449i	−0.361828	−	0.801315i
$751$	−20.2248	−	18.7659i	−0.738015	−	0.684778i	0.218704	−	0.975791i	$-0.429817\pi$
$751$	−20.2248	−	18.7659i	−0.738015	−	0.684778i	−0.956719	+	0.291014i	$0.906008\pi$
$752$	−19.4984	−	4.94249i	−0.711034	−	0.180234i
$753$	31.8070	+	55.0913i	1.15911	+	2.00764i
$754$	4.17081	+	2.54718i	0.151892	+	0.0927629i
$755$	23.2308	+	18.5260i	0.845457	+	0.674229i
$756$	10.0191	+	15.9821i	0.364390	+	0.581262i
$757$	−28.3110	+	22.5773i	−1.02898	+	0.820585i	−0.983958	−	0.178401i	$-0.942908\pi$
$757$	−28.3110	+	22.5773i	−1.02898	+	0.820585i	−0.0450233	+	0.998986i	$0.514336\pi$
$758$	15.3979	−	1.93383i	0.559278	−	0.0702399i
$759$	−9.56903	−	6.52406i	−0.347334	−	0.236808i
$760$	−29.9662	+	37.6389i	−1.08699	+	1.36531i
$761$	37.0390	−	5.58274i	1.34266	−	0.202374i	0.561903	−	0.827203i	$-0.310070\pi$
$761$	37.0390	−	5.58274i	1.34266	−	0.202374i	0.780761	+	0.624829i	$0.214831\pi$
$762$	−19.5408	−	25.7830i	−0.707888	−	0.934018i
$763$	−10.6076	+	4.29705i	−0.384022	+	0.155564i
$764$	−10.0310	+	11.3789i	−0.362911	+	0.411676i
$765$	28.6807	+	16.5588i	1.03695	+	0.598686i
$766$	−5.44320	+	2.96611i	−0.196671	+	0.107170i
$767$	−18.6087	−	2.80481i	−0.671920	−	0.101276i
$768$	35.0878	−	25.3416i	1.26612	−	0.914434i
$769$	9.87339	−	4.75478i	0.356044	−	0.171462i	−0.247308	−	0.968937i	$-0.579546\pi$
$769$	9.87339	−	4.75478i	0.356044	−	0.171462i	0.603351	+	0.797475i	$0.293832\pi$
$770$	6.67161	−	5.17170i	0.240428	−	0.186375i
$771$	−2.51847	+	5.22966i	−0.0907006	+	0.188342i

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.z (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.767597 - 1.18777i) q^{2} +(-1.83996 - 1.98301i) q^{3} +(-0.821590 + 1.82346i) q^{4} +(-0.819891 + 2.65802i) q^{5} +(-0.943005 + 3.70760i) q^{6} +(2.51957 - 0.807328i) q^{7} +(2.79649 - 0.423820i) q^{8} +(-0.322667 + 4.30570i) q^{9} +O(q^{10})\)	\(q+(-0.767597 - 1.18777i) q^{2} +(-1.83996 - 1.98301i) q^{3} +(-0.821590 + 1.82346i) q^{4} +(-0.819891 + 2.65802i) q^{5} +(-0.943005 + 3.70760i) q^{6} +(2.51957 - 0.807328i) q^{7} +(2.79649 - 0.423820i) q^{8} +(-0.322667 + 4.30570i) q^{9} +(3.78646 - 1.06645i) q^{10} +(0.808795 - 0.0606108i) q^{11} +(5.12762 - 1.72587i) q^{12} +(0.864213 - 1.79456i) q^{13} +(-2.89293 - 2.37296i) q^{14} +(6.77944 - 3.26480i) q^{15} +(-2.64998 - 2.99626i) q^{16} +(-2.72664 - 0.410975i) q^{17} +(5.36185 - 2.92179i) q^{18} +(5.29583 + 3.05755i) q^{19} +(-4.17317 - 3.67884i) q^{20} +(-6.23684 - 3.51087i) q^{21} +(-0.692821 - 0.914137i) q^{22} +(5.21964 - 0.786734i) q^{23} +(-5.98588 - 4.76565i) q^{24} +(-2.26166 - 1.54197i) q^{25} +(-2.79488 + 0.351011i) q^{26} +(2.78703 - 2.22258i) q^{27} +(-0.597923 + 5.25761i) q^{28} +(-1.35645 - 1.08173i) q^{29} +(-9.08171 - 5.54635i) q^{30} +(-4.70362 - 8.14691i) q^{31} +(-1.52475 + 5.44749i) q^{32} +(-1.60834 - 1.49232i) q^{33} +(1.60482 + 3.55408i) q^{34} +(0.0801256 + 7.35898i) q^{35} +(-7.58615 - 4.12589i) q^{36} +(10.2554 - 4.02494i) q^{37} +(-0.433402 - 8.63719i) q^{38} +(-5.14873 + 1.58817i) q^{39} +(-1.16630 + 7.78062i) q^{40} +(0.479000 + 2.09864i) q^{41} +(0.617285 + 10.1029i) q^{42} +(-1.35673 - 0.309665i) q^{43} +(-0.553977 + 1.52460i) q^{44} +(-11.1801 - 4.38786i) q^{45} +(-4.94104 - 5.59583i) q^{46} +(4.15496 - 2.83281i) q^{47} +(-1.06575 + 10.7679i) q^{48} +(5.69644 - 4.06824i) q^{49} +(-0.0954648 + 3.86994i) q^{50} +(4.20194 + 6.16312i) q^{51} +(2.56226 + 3.05024i) q^{52} +(2.81358 + 1.10425i) q^{53} +(-4.77924 - 1.60430i) q^{54} +(-0.502019 + 2.19949i) q^{55} +(6.70379 - 3.32553i) q^{56} +(-3.68098 - 16.1274i) q^{57} +(-0.243641 + 2.44148i) q^{58} +(-2.78489 - 9.02838i) q^{59} +(0.383310 + 15.0443i) q^{60} +(-6.37127 + 2.50054i) q^{61} +(-6.06616 + 11.8404i) q^{62} +(2.66313 + 11.1090i) q^{63} +(7.64075 - 2.37042i) q^{64} +(4.06141 + 3.76843i) q^{65} +(-0.537977 + 3.05584i) q^{66} +(13.1478 - 7.59089i) q^{67} +(2.98957 - 4.63425i) q^{68} +(-11.1640 - 8.90301i) q^{69} +(8.67927 - 5.74390i) q^{70} +(8.16537 + 10.2391i) q^{71} +(0.922504 + 12.1776i) q^{72} +(9.40747 + 6.41390i) q^{73} +(-12.6527 - 9.09149i) q^{74} +(1.10362 + 7.32205i) q^{75} +(-9.92631 + 7.14466i) q^{76} +(1.98888 - 0.805677i) q^{77} +(5.83854 + 4.89643i) q^{78} +(5.74880 - 9.95721i) q^{79} +(10.1368 - 4.58709i) q^{80} +(3.27320 + 0.493356i) q^{81} +(2.12502 - 2.17985i) q^{82} +(2.46351 + 5.11554i) q^{83} +(11.5260 - 8.48812i) q^{84} +(3.32792 - 6.91051i) q^{85} +(0.673611 + 1.84918i) q^{86} +(0.350731 + 4.68018i) q^{87} +(2.23610 - 0.512282i) q^{88} +(-0.395591 + 5.27880i) q^{89} +(3.37003 + 16.6475i) q^{90} +(0.728646 - 5.21921i) q^{91} +(-2.85383 + 10.1641i) q^{92} +(-7.50090 + 24.3173i) q^{93} +(-6.55406 - 2.76068i) q^{94} +(-12.4690 + 11.5696i) q^{95} +(13.6079 - 6.99957i) q^{96} +5.90936 q^{97} +(-9.20470 - 3.64329i) q^{98} +3.50199i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

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