LMFDB - Embedded newform 572.2.bs.a.15.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(15,572)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 12, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("572.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bs (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$1280$
Relative dimension:	$80$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			15.11
Character	$\chi$	$=$	572.15
Dual form			572.2.bs.a.267.11

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31882 + 0.510612i) q^{2} +(-0.0308046 - 0.144924i) q^{3} +(1.47855 - 1.34681i) q^{4} +(0.670289 - 4.23204i) q^{5} +(0.114626 + 0.175399i) q^{6} +(2.29438 - 1.48999i) q^{7} +(-1.26224 + 2.53115i) q^{8} +(2.72058 - 1.21128i) q^{9} +O(q^{10})$	\(q+(-1.31882 + 0.510612i) q^{2} +(-0.0308046 - 0.144924i) q^{3} +(1.47855 - 1.34681i) q^{4} +(0.670289 - 4.23204i) q^{5} +(0.114626 + 0.175399i) q^{6} +(2.29438 - 1.48999i) q^{7} +(-1.26224 + 2.53115i) q^{8} +(2.72058 - 1.21128i) q^{9} +(1.27694 + 5.92354i) q^{10} +(2.63401 + 2.01544i) q^{11} +(-0.240731 - 0.172790i) q^{12} +(-1.21985 + 3.39293i) q^{13} +(-2.26506 + 3.13656i) q^{14} +(-0.633974 + 0.0332252i) q^{15} +(0.372229 - 3.98264i) q^{16} +(3.32744 - 0.349728i) q^{17} +(-2.96945 + 2.98662i) q^{18} +(0.0124085 - 0.236769i) q^{19} +(-4.70868 - 7.16004i) q^{20} +(-0.286613 - 0.286613i) q^{21} +(-4.50288 - 1.31303i) q^{22} +(-2.42523 - 4.20062i) q^{23} +(0.405709 + 0.104958i) q^{24} +(-12.7056 - 4.12830i) q^{25} +(-0.123711 - 5.09752i) q^{26} +(-0.520613 - 0.716563i) q^{27} +(1.38564 - 5.29311i) q^{28} +(2.24205 - 2.49005i) q^{29} +(0.819130 - 0.367532i) q^{30} +(1.39416 + 8.80241i) q^{31} +(1.54268 + 5.44244i) q^{32} +(0.210946 - 0.443817i) q^{33} +(-4.20971 + 2.16026i) q^{34} +(-4.76779 - 10.7086i) q^{35} +(2.39116 - 5.45504i) q^{36} +(4.61665 - 0.241948i) q^{37} +(0.104532 + 0.318590i) q^{38} +(0.529295 + 0.0722682i) q^{39} +(9.86588 + 7.03847i) q^{40} +(0.348585 - 0.536773i) q^{41} +(0.524338 + 0.231642i) q^{42} +(-4.64711 + 8.04902i) q^{43} +(6.60892 - 0.567577i) q^{44} +(-3.30261 - 12.3255i) q^{45} +(5.34332 + 4.30150i) q^{46} +(-0.279313 - 0.548182i) q^{47} +(-0.588649 + 0.0687388i) q^{48} +(0.196962 - 0.442383i) q^{49} +(18.8643 - 1.04316i) q^{50} +(-0.153185 - 0.471455i) q^{51} +(2.76600 + 6.65952i) q^{52} +(-6.32952 - 4.59867i) q^{53} +(1.05248 + 0.679183i) q^{54} +(10.2950 - 9.79632i) q^{55} +(0.875325 + 7.68816i) q^{56} +(-0.0346958 + 0.00549528i) q^{57} +(-1.68541 + 4.42874i) q^{58} +(-0.346243 + 0.224853i) q^{59} +(-0.892615 + 0.902965i) q^{60} +(-0.258898 - 2.46325i) q^{61} +(-6.33326 - 10.8969i) q^{62} +(4.43726 - 6.83278i) q^{63} +(-4.81349 - 6.38986i) q^{64} +(13.5414 + 7.43670i) q^{65} +(-0.0515807 + 0.693025i) q^{66} +(-3.07969 + 11.4936i) q^{67} +(4.44878 - 4.99851i) q^{68} +(-0.534065 + 0.480874i) q^{69} +(11.7558 + 11.6882i) q^{70} +(-0.177905 + 0.219694i) q^{71} +(-0.368095 + 8.41514i) q^{72} +(-2.62559 + 5.15300i) q^{73} +(-5.96497 + 2.67640i) q^{74} +(-0.206900 + 1.96852i) q^{75} +(-0.300535 - 0.366787i) q^{76} +(9.04640 + 0.699530i) q^{77} +(-0.734944 + 0.174956i) q^{78} +(4.33496 - 5.96656i) q^{79} +(-16.6052 - 4.24481i) q^{80} +(5.89030 - 6.54184i) q^{81} +(-0.185636 + 0.885897i) q^{82} +(-16.2275 - 2.57018i) q^{83} +(-0.809785 - 0.0377601i) q^{84} +(0.750285 - 14.3163i) q^{85} +(2.01875 - 12.9880i) q^{86} +(-0.429935 - 0.248223i) q^{87} +(-8.42614 + 4.12312i) q^{88} +(2.06041 - 7.68956i) q^{89} +(10.6491 + 14.5687i) q^{90} +(2.25662 + 9.60223i) q^{91} +(-9.24326 - 2.94452i) q^{92} +(1.23274 - 0.473203i) q^{93} +(0.648271 + 0.580331i) q^{94} +(-0.993698 - 0.211217i) q^{95} +(0.741220 - 0.391225i) q^{96} +(1.81796 - 4.73596i) q^{97} +(-0.0338702 + 0.683993i) q^{98} +(9.60731 + 2.29263i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9}+O(q^{10}) $ 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9	$ 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9} - 48 q^{10} - 24 q^{13} - 40 q^{14} + 18 q^{16} - 36 q^{17} - 8 q^{18} + 18 q^{20} - 40 q^{21} - 10 q^{22} - 100 q^{24} - 44 q^{26} - 4 q^{28} - 12 q^{29} - 114 q^{30} - 92 q^{32} - 20 q^{33} + 36 q^{34} - 72 q^{36} - 24 q^{37} + 8 q^{40} + 26 q^{42} - 20 q^{44} - 80 q^{45} + 32 q^{46} + 30 q^{48} - 36 q^{49} - 78 q^{50} + 34 q^{52} - 80 q^{53} - 188 q^{54} - 48 q^{56} - 92 q^{58} + 20 q^{60} - 28 q^{61} + 42 q^{62} - 48 q^{65} + 204 q^{66} + 26 q^{68} - 36 q^{69} + 38 q^{70} - 136 q^{72} - 24 q^{73} - 6 q^{74} - 276 q^{76} - 156 q^{78} - 80 q^{80} + 60 q^{81} + 162 q^{82} - 108 q^{84} + 16 q^{85} - 88 q^{86} + 6 q^{88} - 64 q^{89} - 16 q^{92} + 64 q^{93} + 34 q^{94} + 114 q^{96} - 8 q^{97} - 24 q^{98}+O(q^{100}) $ 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9 - 48 * q^10 - 24 * q^13 - 40 * q^14 + 18 * q^16 - 36 * q^17 - 8 * q^18 + 18 * q^20 - 40 * q^21 - 10 * q^22 - 100 * q^24 - 44 * q^26 - 4 * q^28 - 12 * q^29 - 114 * q^30 - 92 * q^32 - 20 * q^33 + 36 * q^34 - 72 * q^36 - 24 * q^37 + 8 * q^40 + 26 * q^42 - 20 * q^44 - 80 * q^45 + 32 * q^46 + 30 * q^48 - 36 * q^49 - 78 * q^50 + 34 * q^52 - 80 * q^53 - 188 * q^54 - 48 * q^56 - 92 * q^58 + 20 * q^60 - 28 * q^61 + 42 * q^62 - 48 * q^65 + 204 * q^66 + 26 * q^68 - 36 * q^69 + 38 * q^70 - 136 * q^72 - 24 * q^73 - 6 * q^74 - 276 * q^76 - 156 * q^78 - 80 * q^80 + 60 * q^81 + 162 * q^82 - 108 * q^84 + 16 * q^85 - 88 * q^86 + 6 * q^88 - 64 * q^89 - 16 * q^92 + 64 * q^93 + 34 * q^94 + 114 * q^96 - 8 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.31882	+	0.510612i	−0.932544	+	0.361057i
$2$	−1.31882	+	0.510612i	−0.932544	+	0.361057i
$3$	−0.0308046	−	0.144924i	−0.0177851	−	0.0836721i	0.968360	−	0.249558i	$-0.0802852\pi$
$3$	−0.0308046	−	0.144924i	−0.0177851	−	0.0836721i	−0.986145	+	0.165885i	$0.946952\pi$
$4$	1.47855	−	1.34681i	0.739276	−	0.673403i
$5$	0.670289	−	4.23204i	0.299762	−	1.89263i	−0.132997	−	0.991116i	$-0.542460\pi$
$5$	0.670289	−	4.23204i	0.299762	−	1.89263i	0.432759	−	0.901509i	$-0.357540\pi$
$6$	0.114626	+	0.175399i	0.0467958	+	0.0716065i
$7$	2.29438	−	1.48999i	0.867194	−	0.563163i	−0.0326041	−	0.999468i	$-0.510380\pi$
$7$	2.29438	−	1.48999i	0.867194	−	0.563163i	0.899798	+	0.436306i	$0.143713\pi$
$8$	−1.26224	+	2.53115i	−0.446270	+	0.894898i
$9$	2.72058	−	1.21128i	0.906861	−	0.403760i
$10$	1.27694	+	5.92354i	0.403804	+	1.87319i
$11$	2.63401	+	2.01544i	0.794184	+	0.607677i
$11$	2.63401	+	2.01544i	0.794184	+	0.607677i
$12$	−0.240731	−	0.172790i	−0.0694931	−	0.0498803i
$13$	−1.21985	+	3.39293i	−0.338326	+	0.941029i
$13$	−1.21985	+	3.39293i	−0.338326	+	0.941029i
$14$	−2.26506	+	3.13656i	−0.605363	+	0.838280i
$15$	−0.633974	+	0.0332252i	−0.163691	+	0.00857870i
$16$	0.372229	−	3.98264i	0.0930572	−	0.995661i
$17$	3.32744	−	0.349728i	0.807024	−	0.0848216i	0.307974	−	0.951395i	$-0.400349\pi$
$17$	3.32744	−	0.349728i	0.807024	−	0.0848216i	0.499050	+	0.866573i	$0.333682\pi$
$18$	−2.96945	+	2.98662i	−0.699907	+	0.703953i
$19$	0.0124085	−	0.236769i	0.00284671	−	0.0543185i	−0.996837	−	0.0794758i	$-0.974675\pi$
$19$	0.0124085	−	0.236769i	0.00284671	−	0.0543185i	0.999684	+	0.0251574i	$0.00800868\pi$
$20$	−4.70868	−	7.16004i	−1.05289	−	1.60103i
$21$	−0.286613	−	0.286613i	−0.0625441	−	0.0625441i
$22$	−4.50288	−	1.31303i	−0.960018	−	0.279939i
$23$	−2.42523	−	4.20062i	−0.505696	−	0.875891i	−0.999978	−	0.00658946i	$-0.997902\pi$
$23$	−2.42523	−	4.20062i	−0.505696	−	0.875891i	0.494283	−	0.869301i	$-0.335431\pi$
$24$	0.405709	+	0.104958i	0.0828150	+	0.0214246i
$25$	−12.7056	−	4.12830i	−2.54112	−	0.825659i
$26$	−0.123711	−	5.09752i	−0.0242616	−	0.999706i
$27$	−0.520613	−	0.716563i	−0.100192	−	0.137903i
$28$	1.38564	−	5.29311i	0.261860	−	1.00030i
$29$	2.24205	−	2.49005i	0.416339	−	0.462391i	−0.498097	−	0.867121i	$-0.665968\pi$
$29$	2.24205	−	2.49005i	0.416339	−	0.462391i	0.914436	+	0.404730i	$0.132634\pi$
$30$	0.819130	−	0.367532i	0.149552	−	0.0671019i
$31$	1.39416	+	8.80241i	0.250399	+	1.58096i	0.717374	+	0.696688i	$0.245344\pi$
$31$	1.39416	+	8.80241i	0.250399	+	1.58096i	−0.466975	+	0.884271i	$0.654656\pi$
$32$	1.54268	+	5.44244i	0.272710	+	0.962096i
$33$	0.210946	−	0.443817i	0.0367210	−	0.0772587i
$34$	−4.20971	+	2.16026i	−0.721959	+	0.370481i
$35$	−4.76779	−	10.7086i	−0.805904	−	1.81009i
$36$	2.39116	−	5.45504i	0.398527	−	0.909173i
$37$	4.61665	−	0.241948i	0.758972	−	0.0397761i	0.331076	−	0.943604i	$-0.392588\pi$
$37$	4.61665	−	0.241948i	0.758972	−	0.0397761i	0.427896	+	0.903828i	$0.359255\pi$
$38$	0.104532	+	0.318590i	0.0169574	+	0.0516822i
$39$	0.529295	+	0.0722682i	0.0847551	+	0.0115722i
$40$	9.86588	+	7.03847i	1.55993	+	1.11288i
$41$	0.348585	−	0.536773i	0.0544398	−	0.0838299i	−0.810403	−	0.585873i	$-0.800752\pi$
$41$	0.348585	−	0.536773i	0.0544398	−	0.0838299i	0.864842	+	0.502043i	$0.167418\pi$
$42$	0.524338	+	0.231642i	0.0809071	+	0.0357431i
$43$	−4.64711	+	8.04902i	−0.708677	+	1.22746i	0.256671	+	0.966499i	$0.417374\pi$
$43$	−4.64711	+	8.04902i	−0.708677	+	1.22746i	−0.965348	+	0.260966i	$0.915959\pi$
$44$	6.60892	−	0.567577i	0.996333	−	0.0855654i
$45$	−3.30261	−	12.3255i	−0.492325	−	1.83738i
$46$	5.34332	+	4.30150i	0.787830	+	0.634221i
$47$	−0.279313	−	0.548182i	−0.0407420	−	0.0799606i	0.869738	−	0.493514i	$-0.164288\pi$
$47$	−0.279313	−	0.548182i	−0.0407420	−	0.0799606i	−0.910480	+	0.413553i	$0.864288\pi$
$48$	−0.588649	+	0.0687388i	−0.0849641	+	0.00992160i
$49$	0.196962	−	0.442383i	0.0281374	−	0.0631976i
$50$	18.8643	−	1.04316i	2.66781	−	0.147525i
$51$	−0.153185	−	0.471455i	−0.0214502	−	0.0660168i
$52$	2.76600	+	6.65952i	0.383576	+	0.923509i
$53$	−6.32952	−	4.59867i	−0.869426	−	0.631675i	0.0610066	−	0.998137i	$-0.480569\pi$
$53$	−6.32952	−	4.59867i	−0.869426	−	0.631675i	−0.930433	+	0.366462i	$0.880569\pi$
$54$	1.05248	+	0.679183i	0.143224	+	0.0924251i
$55$	10.2950	−	9.79632i	1.38817	−	1.32094i
$56$	0.875325	+	7.68816i	0.116970	+	1.02737i
$57$	−0.0346958	+	0.00549528i	−0.00459557	+	0.000727867i
$58$	−1.68541	+	4.42874i	−0.221305	+	0.581522i
$59$	−0.346243	+	0.224853i	−0.0450769	+	0.0292733i	−0.566981	−	0.823731i	$-0.691889\pi$
$59$	−0.346243	+	0.224853i	−0.0450769	+	0.0292733i	0.521904	+	0.853004i	$0.325222\pi$
$60$	−0.892615	+	0.902965i	−0.115236	+	0.116572i
$61$	−0.258898	−	2.46325i	−0.0331485	−	0.315386i	−0.998514	−	0.0544872i	$-0.982648\pi$
$61$	−0.258898	−	2.46325i	−0.0331485	−	0.315386i	0.965366	−	0.260899i	$-0.0840191\pi$
$62$	−6.33326	−	10.8969i	−0.804324	−	1.38390i
$63$	4.43726	−	6.83278i	0.559042	−	0.860849i
$64$	−4.81349	−	6.38986i	−0.601686	−	0.798733i
$65$	13.5414	+	7.43670i	1.67960	+	0.922409i
$66$	−0.0515807	+	0.693025i	−0.00634915	+	0.0853055i
$67$	−3.07969	+	11.4936i	−0.376244	+	1.40416i	0.475274	+	0.879838i	$0.342349\pi$
$67$	−3.07969	+	11.4936i	−0.376244	+	1.40416i	−0.851518	+	0.524325i	$0.824318\pi$
$68$	4.44878	−	4.99851i	0.539494	−	0.606159i
$69$	−0.534065	+	0.480874i	−0.0642938	+	0.0578904i
$70$	11.7558	+	11.6882i	1.40509	+	1.39701i
$71$	−0.177905	+	0.219694i	−0.0211134	+	0.0260729i	−0.787593	−	0.616195i	$-0.788673\pi$
$71$	−0.177905	+	0.219694i	−0.0211134	+	0.0260729i	0.766480	+	0.642268i	$0.222006\pi$
$72$	−0.368095	+	8.41514i	−0.0433804	+	0.991734i
$73$	−2.62559	+	5.15300i	−0.307301	+	0.603113i	−0.992076	−	0.125642i	$-0.959901\pi$
$73$	−2.62559	+	5.15300i	−0.307301	+	0.603113i	0.684774	+	0.728755i	$0.259901\pi$
$74$	−5.96497	+	2.67640i	−0.693414	+	0.311125i
$75$	−0.206900	+	1.96852i	−0.0238907	+	0.227305i
$76$	−0.300535	−	0.366787i	−0.0344737	−	0.0420733i
$77$	9.04640	+	0.699530i	1.03093	+	0.0797189i
$78$	−0.734944	+	0.174956i	−0.0832160	+	0.0198099i
$79$	4.33496	−	5.96656i	0.487721	−	0.671291i	−0.492245	−	0.870457i	$-0.663823\pi$
$79$	4.33496	−	5.96656i	0.487721	−	0.671291i	0.979966	+	0.199166i	$0.0638234\pi$
$80$	−16.6052	−	4.24481i	−1.85652	−	0.474584i
$81$	5.89030	−	6.54184i	0.654478	−	0.726871i
$82$	−0.185636	+	0.885897i	−0.0205001	+	0.0978309i
$83$	−16.2275	−	2.57018i	−1.78120	−	0.282114i	−0.822963	−	0.568095i	$-0.807680\pi$
$83$	−16.2275	−	2.57018i	−1.78120	−	0.282114i	−0.958235	+	0.285981i	$0.907680\pi$
$84$	−0.809785	−	0.0377601i	−0.0883548	−	0.00411996i
$85$	0.750285	−	14.3163i	0.0813799	−	1.55282i
$86$	2.01875	−	12.9880i	0.217688	−	1.40054i
$87$	−0.429935	−	0.248223i	−0.0460939	−	0.0266123i
$88$	−8.42614	+	4.12312i	−0.898230	+	0.439526i
$89$	2.06041	−	7.68956i	0.218403	−	0.815092i	−0.766538	−	0.642200i	$-0.778022\pi$
$89$	2.06041	−	7.68956i	0.218403	−	0.815092i	0.984941	−	0.172892i	$-0.0553113\pi$
$90$	10.6491	+	14.5687i	1.12251	+	1.53568i
$91$	2.25662	+	9.60223i	0.236558	+	1.00659i
$92$	−9.24326	−	2.94452i	−0.963676	−	0.306988i
$93$	1.23274	−	0.473203i	0.127829	−	0.0490689i
$94$	0.648271	+	0.580331i	0.0668640	+	0.0598566i
$95$	−0.993698	−	0.211217i	−0.101951	−	0.0216704i
$96$	0.741220	−	0.391225i	0.0756505	−	0.0399292i
$97$	1.81796	−	4.73596i	0.184586	−	0.480864i	−0.809796	−	0.586711i	$-0.800422\pi$
$97$	1.81796	−	4.73596i	0.184586	−	0.480864i	0.994382	+	0.105848i	$0.0337556\pi$
$98$	−0.0338702	+	0.683993i	−0.00342141	+	0.0690937i
$99$	9.60731	+	2.29263i	0.965571	+	0.230418i
$100$	−24.3459	+	11.0081i	−2.43459	+	1.10081i
$101$	4.73625	+	0.497800i	0.471274	+	0.0495329i	0.337189	−	0.941437i	$-0.390524\pi$
$101$	4.73625	+	0.497800i	0.471274	+	0.0495329i	0.134085	+	0.990970i	$0.457190\pi$
$102$	0.442753	+	0.543544i	0.0438391	+	0.0538189i
$103$	−3.63646	−	11.1919i	−0.358311	−	1.10277i	−0.954065	−	0.299601i	$-0.903147\pi$
$103$	−3.63646	−	11.1919i	−0.358311	−	1.10277i	0.595754	−	0.803167i	$-0.296853\pi$
$104$	−7.04828	−	7.37033i	−0.691141	−	0.722720i
$105$	−1.40507	+	1.02084i	−0.137121	+	0.0996243i
$106$	10.6956	+	2.83287i	1.03885	+	0.275152i
$107$	−1.22687	−	5.77195i	−0.118606	−	0.557995i	−0.996817	−	0.0797228i	$-0.974596\pi$
$107$	−1.22687	−	5.77195i	−0.118606	−	0.557995i	0.878212	−	0.478272i	$-0.158737\pi$
$108$	−1.73482	−	0.358310i	−0.166934	−	0.0344784i
$109$	−7.80979	+	7.80979i	−0.748043	+	0.748043i	−0.974111	−	0.226069i	$-0.927413\pi$
$109$	−7.80979	+	7.80979i	−0.748043	+	0.748043i	0.226069	+	0.974111i	$0.427413\pi$
$110$	−8.57504	+	18.1763i	−0.817598	+	1.73304i
$111$	−0.177278	−	0.661612i	−0.0168265	−	0.0627974i
$112$	−5.08006	−	9.69232i	−0.480020	−	0.915838i
$113$	9.67462	+	10.7448i	0.910111	+	1.01078i	0.999890	+	0.0148194i	$0.00471733\pi$
$113$	9.67462	+	10.7448i	0.910111	+	1.01078i	−0.0897788	+	0.995962i	$0.528616\pi$
$114$	0.0429514	−	0.0249633i	0.00402277	−	0.00233803i
$115$	−19.4028	+	7.44804i	−1.80932	+	0.694534i
$116$	−0.0386257	−	6.70128i	−0.00358630	−	0.622198i
$117$	0.791087	+	10.7083i	0.0731360	+	0.989985i
$118$	0.341818	−	0.473335i	0.0314669	−	0.0435740i
$119$	7.11333	−	5.76026i	0.652078	−	0.528042i
$120$	0.716131	−	1.64662i	0.0653735	−	0.150316i
$121$	2.87604	+	10.6174i	0.261458	+	0.965215i
$122$	1.59920	+	3.11637i	0.144785	+	0.282143i
$123$	−0.0885296	−	0.0339833i	−0.00798244	−	0.00306417i
$124$	13.9165	+	11.1371i	1.24974	+	1.00014i
$125$	−16.2613	+	31.9145i	−1.45445	+	2.85452i
$126$	−2.36303	+	11.2769i	−0.210515	+	1.00463i
$127$	−13.4014	−	5.96670i	−1.18919	−	0.529459i	−0.285800	−	0.958289i	$-0.592259\pi$
$127$	−13.4014	−	5.96670i	−1.18919	−	0.529459i	−0.903385	+	0.428830i	$0.858926\pi$
$128$	9.61084	+	5.96923i	0.849486	+	0.527610i
$129$	1.30965	+	0.425532i	0.115308	+	0.0374660i
$130$	−21.6558	−	2.89326i	−1.89934	−	0.253756i
$131$			6.28784i			0.549371i	0.961534	+	0.274685i	$0.0885737\pi$
$131$			6.28784i			0.549371i	−0.961534	+	0.274685i	$0.911426\pi$
$132$	−0.285841	−	0.940310i	−0.0248793	−	0.0818435i
$133$	−0.324313	−	0.561726i	−0.0281215	−	0.0487078i
$134$	−1.80720	−	16.7304i	−0.156118	−	1.44529i
$135$	−3.38148	+	1.72295i	−0.291032	+	0.148288i
$136$	−3.31482	+	8.86372i	−0.284244	+	0.760057i
$137$	−1.56345	+	1.93070i	−0.133574	+	0.164951i	−0.839544	−	0.543291i	$-0.817178\pi$
$137$	−1.56345	+	1.93070i	−0.133574	+	0.164951i	0.705970	+	0.708242i	$0.250511\pi$
$138$	0.458793	−	0.906884i	0.0390551	−	0.0771991i
$139$	−1.79600	+	8.44950i	−0.152334	+	0.716677i	0.833979	+	0.551796i	$0.186057\pi$
$139$	−1.79600	+	8.44950i	−0.152334	+	0.716677i	−0.986313	+	0.164881i	$0.947276\pi$
$140$	−21.4719	−	9.41198i	−1.81470	−	0.795457i
$141$	−0.0708409	+	0.0573658i	−0.00596588	+	0.00483107i
$142$	0.122445	−	0.380576i	0.0102754	−	0.0319373i
$143$	−10.0513	+	6.47848i	−0.840534	+	0.541758i
$144$	−3.81142	−	11.2860i	−0.317618	−	0.940498i
$145$	−9.03518	−	11.1575i	−0.750331	−	0.926581i
$146$	0.831481	−	8.13651i	0.0688139	−	0.673383i
$147$	−0.0701794	−	0.0149171i	−0.00578830	−	0.00123034i
$148$	6.50010	−	6.57546i	0.534305	−	0.540500i
$149$	8.25407	+	6.68401i	0.676200	+	0.547576i	0.904743	−	0.425958i	$-0.140063\pi$
$149$	8.25407	+	6.68401i	0.676200	+	0.547576i	−0.228543	+	0.973534i	$0.573396\pi$
$150$	−0.732287	−	2.70176i	−0.0597910	−	0.220598i
$151$	4.10176	+	8.05016i	0.333797	+	0.655113i	0.995511	−	0.0946430i	$-0.0301709\pi$
$151$	4.10176	+	8.05016i	0.333797	+	0.655113i	−0.661715	+	0.749756i	$0.730171\pi$
$152$	0.583636	+	0.330268i	0.0473391	+	0.0267882i
$153$	8.62897	−	4.98194i	0.697610	−	0.402766i
$154$	−12.2877	+	3.69665i	−0.990173	+	0.297884i
$155$	38.1866			3.06722
$156$	0.879921	−	0.606006i	0.0704501	−	0.0485193i
$157$	−1.34169	+	4.12929i	−0.107078	+	0.329554i	−0.990213	−	0.139567i	$-0.955429\pi$
$157$	−1.34169	+	4.12929i	−0.107078	+	0.329554i	0.883134	+	0.469120i	$0.155429\pi$
$158$	−2.67042	+	10.0823i	−0.212447	+	0.802103i
$159$	−0.471480	+	1.05896i	−0.0373908	+	0.0839812i
$160$	24.0667	−	2.88069i	1.90264	−	0.227738i
$161$	−11.8233	−	6.02427i	−0.931806	−	0.474779i
$162$	−4.42788	+	11.6351i	−0.347887	+	0.914143i
$163$	−2.98617	+	7.77925i	−0.233895	+	0.609318i	−0.999419	−	0.0340902i	$-0.989147\pi$
$163$	−2.98617	+	7.77925i	−0.233895	+	0.609318i	0.765524	+	0.643408i	$0.222480\pi$
$164$	−0.207529	−	1.26312i	−0.0162053	−	0.0986333i
$165$	−1.73686	−	1.19022i	−0.135214	−	0.0926584i
$166$	22.7134	−	4.89635i	1.76290	−	0.380030i
$167$	5.47828	+	6.76512i	0.423922	+	0.523500i	0.943701	−	0.330801i	$-0.107319\pi$
$167$	5.47828	+	6.76512i	0.423922	+	0.523500i	−0.519778	+	0.854301i	$0.673985\pi$
$168$	1.08724	−	0.363687i	0.0838822	−	0.0280591i
$169$	−10.0239	−	8.27773i	−0.771071	−	0.636749i
$170$	6.32058	+	19.2637i	0.484766	+	1.47746i
$171$	−0.253035	−	0.659179i	−0.0193501	−	0.0504087i
$172$	3.96949	+	18.1596i	0.302670	+	1.38466i
$173$	11.5430	−	10.3934i	0.877600	−	0.790195i	−0.101231	−	0.994863i	$-0.532278\pi$
$173$	11.5430	−	10.3934i	0.877600	−	0.790195i	0.978831	+	0.204668i	$0.0656115\pi$
$174$	0.693751	+	0.107831i	0.0525931	+	0.00817463i
$175$	−35.3026	+	9.45930i	−2.66862	+	0.715056i
$176$	9.00722	−	9.74013i	0.678944	−	0.734190i
$177$	0.0432525	+	0.0432525i	0.00325106	+	0.00325106i
$178$	1.20908	+	11.1932i	0.0906241	+	0.838965i
$179$	−11.5739	+	2.46010i	−0.865072	+	0.183877i	−0.619016	−	0.785379i	$-0.712468\pi$
$179$	−11.5739	+	2.46010i	−0.865072	+	0.183877i	−0.246057	+	0.969255i	$0.579135\pi$
$180$	−21.4832	−	13.7759i	−1.60126	−	1.02680i
$181$	7.32637	+	10.0839i	0.544564	+	0.749529i	0.989262	−	0.146152i	$-0.0466889\pi$
$181$	7.32637	+	10.0839i	0.544564	+	0.749529i	−0.444698	+	0.895681i	$0.646689\pi$
$182$	−7.87908	−	11.5113i	−0.584036	−	0.853276i
$183$	−0.349009	+	0.113400i	−0.0257995	+	0.00838277i
$184$	13.6937	−	0.836429i	1.00951	−	0.0616624i
$185$	2.07056	−	19.7000i	0.152230	−	1.44837i
$186$	−1.38413	+	1.25352i	−0.101489	+	0.0919124i
$187$	9.46938	+	5.78506i	0.692470	+	0.423046i
$188$	−1.15127	−	0.434336i	−0.0839653	−	0.0316772i
$189$	−2.26216	−	0.868360i	−0.164548	−	0.0631639i
$190$	1.41835	−	0.228837i	0.102898	−	0.0166016i
$191$	−0.0610301	+	0.287124i	−0.00441598	+	0.0207756i	−0.980300	−	0.197512i	$-0.936714\pi$
$191$	−0.0610301	+	0.287124i	−0.00441598	+	0.0207756i	0.975884	+	0.218288i	$0.0700471\pi$
$192$	−0.777769	+	0.894429i	−0.0561307	+	0.0645499i
$193$	7.02864	+	18.3102i	0.505933	+	1.31800i	0.914247	+	0.405158i	$0.132784\pi$
$193$	7.02864	+	18.3102i	0.505933	+	1.31800i	−0.408314	+	0.912842i	$0.633883\pi$
$194$	0.0206754	+	7.17413i	0.00148441	+	0.515073i
$195$	0.660623	−	2.19156i	0.0473082	−	0.156941i
$196$	−0.304586	−	0.919355i	−0.0217561	−	0.0656682i
$197$	−23.1347	−	6.19892i	−1.64828	−	0.441654i	−0.689147	−	0.724621i	$-0.742015\pi$
$197$	−23.1347	−	6.19892i	−1.64828	−	0.441654i	−0.959130	+	0.282967i	$0.908681\pi$
$198$	−13.8409	+	1.88205i	−0.983631	+	0.133751i
$199$	13.3762	−	23.1683i	0.948217	−	1.64236i	0.199039	−	0.979992i	$-0.436218\pi$
$199$	13.3762	−	23.1683i	0.948217	−	1.64236i	0.749178	−	0.662368i	$-0.230449\pi$
$200$	26.4869	−	26.9489i	1.87291	−	1.90558i
$201$	1.76057	+	0.0922674i	0.124181	+	0.00650804i
$202$	−6.50042	+	1.76188i	−0.457368	+	0.123965i
$203$	1.43397	−	9.05376i	0.100645	−	0.635449i
$204$	−0.861449	−	0.490760i	−0.0603135	−	0.0343600i
$205$	−2.03799	−	1.83502i	−0.142340	−	0.128163i
$206$	10.5105	+	12.9032i	0.732303	+	0.899009i
$207$	−11.6862	−	8.49051i	−0.812246	−	0.590131i
$208$	13.0588	+	6.12117i	0.905462	+	0.424427i
$209$	0.509876	−	0.598643i	0.0352689	−	0.0414090i
$210$	1.33178	−	2.06375i	0.0919013	−	0.142412i
$211$	−10.0203	−	1.05318i	−0.689829	−	0.0725039i	−0.246873	−	0.969048i	$-0.579403\pi$
$211$	−10.0203	−	1.05318i	−0.689829	−	0.0725039i	−0.442955	+	0.896544i	$0.646070\pi$
$212$	−15.5520	+	1.72527i	−1.06812	+	0.118492i
$213$	0.0373193	+	0.0190151i	0.00255708	+	0.00130290i
$214$	4.56523	+	6.98569i	0.312073	+	0.477532i
$215$	30.9489	+	25.0619i	2.11070	+	1.70921i
$216$	2.47087	−	0.413277i	0.168121	−	0.0281199i
$217$	16.3142	+	18.1188i	1.10748	+	1.22998i
$218$	6.31191	−	14.2875i	0.427496	−	0.967668i
$219$	0.827676	+	0.221775i	0.0559291	+	0.0149862i
$220$	2.02788	−	28.3497i	0.136720	−	1.91133i
$221$	−2.87238	+	11.7164i	−0.193217	+	0.788130i
$222$	0.571624	+	0.782024i	0.0383649	+	0.0524860i
$223$	21.0274	+	13.6554i	1.40810	+	0.914431i	0.999999	+	0.00149370i	$0.000475460\pi$
$223$	21.0274	+	13.6554i	1.40810	+	0.914431i	0.408101	+	0.912937i	$0.366191\pi$
$224$	11.6487	+	10.1884i	0.778310	+	0.680744i
$225$	−39.5671	+	4.15867i	−2.63781	+	0.277245i
$226$	−18.2454	−	9.23038i	−1.21367	−	0.613996i
$227$	−0.310242	−	0.477731i	−0.0205915	−	0.0317081i	0.828225	−	0.560396i	$-0.189351\pi$
$227$	−0.310242	−	0.477731i	−0.0205915	−	0.0317081i	−0.848816	+	0.528688i	$0.822684\pi$
$228$	−0.0438985	+	0.0548536i	−0.00290725	+	0.00363277i
$229$	−0.482363	−	3.04552i	−0.0318754	−	0.201253i	0.966611	−	0.256247i	$-0.0824861\pi$
$229$	−0.482363	−	3.04552i	−0.0318754	−	0.201253i	−0.998487	+	0.0549937i	$0.982486\pi$
$230$	21.7857	−	19.7299i	1.43651	−	1.30095i
$231$	−0.177292	−	1.33259i	−0.0116650	−	0.0876782i
$232$	3.47269	+	8.81803i	0.227993	+	0.578932i
$233$	−9.62260	+	13.2444i	−0.630397	+	0.867667i	−0.998058	−	0.0622927i	$-0.980159\pi$
$233$	−9.62260	+	13.2444i	−0.630397	+	0.867667i	0.367661	+	0.929960i	$0.380159\pi$
$234$	−6.51109	−	13.7184i	−0.425643	−	0.896798i
$235$	−2.50715	+	0.814623i	−0.163548	+	0.0531401i
$236$	−0.209105	+	0.798777i	−0.0136116	+	0.0519960i
$237$	−0.998237	−	0.444444i	−0.0648425	−	0.0288697i
$238$	−6.43992	+	11.2289i	−0.417438	+	0.727860i
$239$	20.0990	−	10.2410i	1.30010	−	0.662433i	0.339561	−	0.940584i	$-0.389721\pi$
$239$	20.0990	−	10.2410i	1.30010	−	0.662433i	0.960538	+	0.278151i	$0.0897214\pi$
$240$	−0.103659	+	2.53726i	−0.00669118	+	0.163779i
$241$	9.66399	−	2.58946i	0.622512	−	0.166802i	0.0662425	−	0.997804i	$-0.478899\pi$
$241$	9.66399	−	2.58946i	0.622512	−	0.166802i	0.556269	+	0.831002i	$0.312232\pi$
$242$	−9.21431	−	12.5338i	−0.592319	−	0.805704i
$243$	−3.43069	−	1.98071i	−0.220079	−	0.127063i
$244$	−3.70031	−	3.29335i	−0.236888	−	0.210835i
$245$	−1.74016	−	1.13007i	−0.111175	−	0.0721978i
$246$	0.134106		0.000386487i	0.00855032		2.46415e-5i
$247$	0.788203	+	0.330924i	0.0501522	+	0.0210562i
$248$	−24.0400	−	7.58193i	−1.52654	−	0.481453i
$249$	0.127400	+	2.43093i	0.00807363	+	0.154054i
$250$	5.14969	−	50.3926i	0.325695	−	3.18711i
$251$	−8.52090	+	3.79375i	−0.537834	+	0.239459i	−0.657632	−	0.753339i	$-0.728442\pi$
$251$	−8.52090	+	3.79375i	−0.537834	+	0.239459i	0.119798	+	0.992798i	$0.461775\pi$
$252$	−2.64171	−	16.0787i	−0.166412	−	1.01287i
$253$	2.07800	−	15.9524i	0.130643	−	1.00292i
$254$	20.7207	+	1.02606i	1.30013	+	0.0643804i
$255$	−2.09789	+	0.332274i	−0.131375	+	0.0208078i
$256$	−15.7229	−	2.96491i	−0.982681	−	0.185307i
$257$	−5.98167	−	5.38592i	−0.373127	−	0.335965i	0.461139	−	0.887328i	$-0.347441\pi$
$257$	−5.98167	−	5.38592i	−0.373127	−	0.335965i	−0.834265	+	0.551363i	$0.814108\pi$
$258$	−1.94447	+	0.107526i	−0.121058	+	0.00669425i
$259$	10.2318	−	7.43387i	0.635776	−	0.461918i
$260$	30.0374	−	7.24203i	1.86284	−	0.449132i
$261$	3.08354	−	9.49015i	0.190866	−	0.587425i
$262$	−3.21064	−	8.29250i	−0.198354	−	0.512312i
$263$	12.5185	−	7.22757i	0.771925	−	0.445671i	−0.0616361	−	0.998099i	$-0.519632\pi$
$263$	12.5185	−	7.22757i	0.771925	−	0.445671i	0.833561	+	0.552428i	$0.186298\pi$
$264$	0.857105	+	1.09414i	0.0527512	+	0.0673398i
$265$	−23.7043	+	23.7043i	−1.45615	+	1.45615i
$266$	0.714533	+	0.575216i	0.0438108	+	0.0352687i
$267$	−1.17788	−	0.0617298i	−0.0720848	−	0.00377780i
$268$	10.9261	+	21.1416i	0.667419	+	1.29143i
$269$	1.27930	+	12.1717i	0.0780003	+	0.742123i	0.961707	+	0.274081i	$0.0883737\pi$
$269$	1.27930	+	12.1717i	0.0780003	+	0.742123i	−0.883706	+	0.468042i	$0.844960\pi$
$270$	3.57980	−	3.99888i	0.217859	−	0.243364i
$271$	−1.59298	−	30.3958i	−0.0967663	−	1.84641i	−0.429109	−	0.903253i	$-0.641172\pi$
$271$	−1.59298	−	30.3958i	−0.0967663	−	1.84641i	0.332342	−	0.943159i	$-0.392161\pi$
$272$	−0.154273	−	13.3822i	−0.00935418	−	0.811415i
$273$	1.32208	−	0.622833i	0.0800161	−	0.0376956i
$274$	1.07606	−	3.34455i	0.0650074	−	0.202052i
$275$	−25.1464	−	36.4813i	−1.51638	−	2.19990i
$276$	−0.141998	+	1.43028i	−0.00854729	+	0.0860926i
$277$	−4.18316	−	9.39553i	−0.251342	−	0.564523i	0.743175	−	0.669097i	$-0.233319\pi$
$277$	−4.18316	−	9.39553i	−0.251342	−	0.564523i	−0.994517	+	0.104574i	$0.966652\pi$
$278$	−1.94582	−	12.0604i	−0.116703	−	0.723335i
$279$	14.4551	+	22.2589i	0.865406	+	1.33261i
$280$	33.1233	+	1.44888i	1.97950	+	0.0865871i
$281$	0.789716	+	0.125079i	0.0471105	+	0.00746157i	0.179945	−	0.983677i	$-0.442408\pi$
$281$	0.789716	+	0.125079i	0.0471105	+	0.00746157i	−0.132835	+	0.991138i	$0.542408\pi$
$282$	0.0641344	−	0.111827i	0.00381915	−	0.00665921i
$283$	14.7691	−	3.13926i	0.877930	−	0.186610i	0.253165	−	0.967423i	$-0.418528\pi$
$283$	14.7691	−	3.13926i	0.877930	−	0.186610i	0.624765	+	0.780813i	$0.285195\pi$
$284$	0.0328439	+	0.564432i	0.00194893	+	0.0334929i
$285$			0.150518i			0.00891589i
$286$	9.94787	−	13.6763i	0.588230	−	0.808694i
$287$		−	1.75095i		−	0.103355i
$288$	10.7893	+	12.9380i	0.635767	+	0.762378i
$289$	−5.67894	+	1.20710i	−0.334055	+	0.0710056i
$290$	17.6129	+	10.1012i	1.03426	+	0.593165i
$291$	−0.742358	−	0.117578i	−0.0435178	−	0.00689254i
$292$	3.05803	+	11.1551i	0.178958	+	0.652805i
$293$	12.6831	+	19.5302i	0.740953	+	1.14097i	0.985226	+	0.171261i	$0.0547843\pi$
$293$	12.6831	+	19.5302i	0.740953	+	1.14097i	−0.244272	+	0.969707i	$0.578549\pi$
$294$	0.100171	−	0.0161615i	0.00584207	−	0.000942559i
$295$	0.719502	+	1.61603i	0.0418910	+	0.0940888i
$296$	−5.21492	+	11.9908i	−0.303111	+	0.696954i
$297$	0.0728845	−	2.93670i	0.00422919	−	0.170404i
$298$	−14.2985	−	4.60036i	−0.828292	−	0.266492i
$299$	17.2108	−	3.10450i	0.995329	−	0.179538i
$300$	2.34530	+	3.18921i	0.135406	+	0.184129i
$301$	1.33072	+	25.3917i	0.0767015	+	1.46355i
$302$	−9.51998	−	8.52227i	−0.547813	−	0.490402i
$303$	−0.0737551	−	0.701732i	−0.00423712	−	0.0403135i
$304$	−0.938347	−	0.137551i	−0.0538179	−	0.00788908i
$305$	−10.5981	−	0.555423i	−0.606845	−	0.0318034i
$306$	−8.83618	+	10.9763i	−0.505131	+	0.627474i
$307$	−13.4644	+	13.4644i	−0.768456	+	0.768456i	−0.977835	−	0.209379i	$-0.932856\pi$
$307$	−13.4644	+	13.4644i	−0.768456	+	0.768456i	0.209379	+	0.977835i	$0.432856\pi$
$308$	14.3177	−	11.1495i	0.815827	−	0.635299i
$309$	−1.50996	+	0.871773i	−0.0858984	+	0.0495934i
$310$	−50.3611	+	19.4985i	−2.86032	+	1.10744i
$311$	0.618201	−	1.90263i	0.0350550	−	0.107888i	−0.931998	−	0.362464i	$-0.881936\pi$
$311$	0.618201	−	1.90263i	0.0350550	−	0.107888i	0.967053	+	0.254575i	$0.0819357\pi$
$312$	−0.851021	+	1.24851i	−0.0481796	+	0.0706829i
$313$	13.4185	−	9.74908i	0.758456	−	0.551051i	−0.139980	−	0.990154i	$-0.544704\pi$
$313$	13.4185	−	9.74908i	0.758456	−	0.551051i	0.898436	+	0.439104i	$0.144704\pi$
$314$	−0.339025	−	6.13086i	−0.0191323	−	0.345985i
$315$	−25.9423	−	23.3586i	−1.46169	−	1.31611i
$316$	−1.62634	−	14.6602i	−0.0914886	−	0.824702i
$317$	−21.5676	+	3.41597i	−1.21136	+	0.191860i	−0.729247	−	0.684250i	$-0.760130\pi$
$317$	−21.5676	+	3.41597i	−1.21136	+	0.191860i	−0.482110	+	0.876111i	$0.660130\pi$
$318$	0.0810774	−	1.63732i	0.00454659	−	0.0918163i
$319$	10.9241	−	2.04011i	0.611634	−	0.114224i
$320$	−30.2686	+	16.0878i	−1.69207	+	0.899336i
$321$	−0.798703	+	0.355606i	−0.0445793	+	0.0198480i
$322$	18.6688	+	1.90779i	1.04037	+	0.106317i
$323$	−0.0415161	−	0.792174i	−0.00231002	−	0.0440778i
$324$	−0.101477	−	17.6055i	−0.00563761	−	0.978085i
$325$	29.5059	−	38.0733i	1.63670	−	2.11192i
$326$	−0.0339613	−	11.7842i	−0.00188094	−	0.652665i
$327$	1.37241	+	0.891252i	0.0758943	+	0.0492863i
$328$	0.918658	+	1.55986i	0.0507244	+	0.0861288i
$329$	−1.45764	−	0.841566i	−0.0803621	−	0.0463971i
$330$	2.89834	+	0.682819i	0.159548	+	0.0375879i
$331$	−1.64196	+	0.439962i	−0.0902504	+	0.0241825i	−0.303662	−	0.952780i	$-0.598209\pi$
$331$	−1.64196	+	0.439962i	−0.0902504	+	0.0241825i	0.213411	+	0.976962i	$0.431543\pi$
$332$	−27.4547	+	18.0551i	−1.50677	+	0.990904i
$333$	12.2669	−	6.25030i	0.672222	−	0.342514i
$334$	−10.6792	−	6.12467i	−0.584339	−	0.335127i
$335$	46.5769	+	20.7374i	2.54477	+	1.13300i
$336$	−1.24816	+	1.03479i	−0.0680929	+	0.0564526i
$337$	−5.63295	+	1.83026i	−0.306846	+	0.0997005i	−0.458393	−	0.888750i	$-0.651575\pi$
$337$	−5.63295	+	1.83026i	−0.306846	+	0.0997005i	0.151546	+	0.988450i	$0.451575\pi$
$338$	17.4464	+	5.79847i	0.948960	+	0.315395i
$339$	1.25915	−	1.73308i	0.0683878	−	0.0941278i
$340$	−18.1719	−	22.1779i	−0.985511	−	1.20276i
$341$	−14.0684	+	25.9955i	−0.761849	+	1.40773i
$342$	0.670291	+	0.740133i	0.0362452	+	0.0400218i
$343$	2.78850	+	17.6059i	0.150565	+	0.950630i
$344$	−14.5075	−	21.9224i	−0.782195	−	1.18197i
$345$	1.67710	+	2.58251i	0.0902920	+	0.139038i
$346$	−9.91615	+	19.6010i	−0.533095	+	1.05376i
$347$	−5.45350	+	0.573186i	−0.292759	+	0.0307702i	−0.249770	−	0.968305i	$-0.580355\pi$
$347$	−5.45350	+	0.573186i	−0.292759	+	0.0307702i	−0.0429896	+	0.999076i	$0.513688\pi$
$348$	−0.969989	+	0.212028i	−0.0519969	+	0.0113659i
$349$	13.3074	+	8.64194i	0.712330	+	0.462592i	0.849251	−	0.527990i	$-0.177054\pi$
$349$	13.3074	+	8.64194i	0.712330	+	0.462592i	−0.136921	+	0.990582i	$0.543721\pi$
$350$	41.7276	−	30.5010i	2.23043	−	1.63035i
$351$	3.06632	−	0.892304i	0.163668	−	0.0476277i
$352$	−6.90544	+	17.4446i	−0.368061	+	0.929802i
$353$	23.2689	+	6.23488i	1.23848	+	0.331849i	0.817875	−	0.575396i	$-0.195152\pi$
$353$	23.2689	+	6.23488i	1.23848	+	0.331849i	0.420602	+	0.907245i	$0.361819\pi$
$354$	−0.0791273	−	0.0349569i	−0.00420557	−	0.00185794i
$355$	0.810507	+	0.900159i	0.0430172	+	0.0477755i
$356$	−7.30992	−	14.1444i	−0.387425	−	0.749651i
$357$	−1.05393	−	0.853453i	−0.0557797	−	0.0451695i
$358$	14.0077	−	9.15418i	0.740328	−	0.483813i
$359$	19.5212	+	9.94656i	1.03029	+	0.524959i	0.885566	−	0.464513i	$-0.153771\pi$
$359$	19.5212	+	9.94656i	1.03029	+	0.524959i	0.144724	+	0.989472i	$0.453771\pi$
$360$	35.3665	+	7.19837i	1.86398	+	0.379388i
$361$	18.8400	+	1.98016i	0.991580	+	0.104219i
$362$	−14.8111	−	9.55785i	−0.778453	−	0.502349i
$363$	1.45012	−	0.743872i	0.0761116	−	0.0390432i
$364$	16.2689	+	11.1582i	0.852721	+	0.584847i
$365$	20.0478	+	14.5656i	1.04935	+	0.762397i
$366$	0.402376	−	0.327762i	0.0210325	−	0.0171324i
$367$	12.2282	+	11.0104i	0.638309	+	0.574736i	0.923435	−	0.383754i	$-0.125369\pi$
$367$	12.2282	+	11.0104i	0.638309	+	0.574736i	−0.285127	+	0.958490i	$0.592036\pi$
$368$	−17.6323	+	8.09524i	−0.919149	+	0.421994i
$369$	0.298170	−	1.88257i	0.0155221	−	0.0980027i
$370$	7.32838	+	27.0379i	0.380984	+	1.40564i
$371$	−21.3743	−	1.12018i	−1.10970	−	0.0581568i
$372$	1.18535	−	2.35991i	0.0614576	−	0.122356i
$373$	−0.166595	+	0.288552i	−0.00862598	+	0.0149406i	−0.870306	−	0.492511i	$-0.836079\pi$
$373$	−0.166595	+	0.288552i	−0.00862598	+	0.0149406i	0.861680	+	0.507452i	$0.169412\pi$
$374$	−15.4423	−	2.79425i	−0.798502	−	0.144487i
$375$	5.12612	+	1.37354i	0.264712	+	0.0709292i
$376$	1.74010	−	0.0150449i	0.0897386	−	0.000775880i
$377$	5.71360	+	10.6446i	0.294265	+	0.548226i
$378$	3.42676	−	0.00987572i	0.176254	−	0.000507952i
$379$	−5.96665	−	15.5436i	−0.306486	−	0.798423i	−0.997164	−	0.0752608i	$-0.976021\pi$
$379$	−5.96665	−	15.5436i	−0.306486	−	0.798423i	0.690678	−	0.723163i	$-0.257312\pi$
$380$	−1.75370	+	1.02602i	−0.0899630	+	0.0526338i
$381$	−0.451895	+	2.12600i	−0.0231513	+	0.108918i
$382$	−0.0661214	−	0.409826i	−0.00338306	−	0.0209685i
$383$	−34.1654	−	13.1149i	−1.74577	−	0.670139i	−0.999992	−	0.00394443i	$-0.998744\pi$
$383$	−34.1654	−	13.1149i	−1.74577	−	0.670139i	−0.745778	−	0.666194i	$-0.767922\pi$
$384$	0.569029	−	1.57673i	0.0290381	−	0.0804619i
$385$	9.02415	−	37.8158i	0.459913	−	1.92727i
$386$	−18.6189	−	20.5589i	−0.947677	−	1.04642i
$387$	−2.89320	+	27.5270i	−0.147070	+	1.39928i
$388$	−3.69046	−	9.45080i	−0.187355	−	0.479792i
$389$	−2.07203	+	0.673243i	−0.105056	+	0.0341348i	−0.361073	−	0.932537i	$-0.617590\pi$
$389$	−2.07203	+	0.673243i	−0.105056	+	0.0341348i	0.256017	+	0.966672i	$0.417590\pi$
$390$	0.247795	+	3.22758i	0.0125476	+	0.163435i
$391$	−9.53890	−	13.1292i	−0.482403	−	0.663971i
$392$	0.871126	+	1.05693i	0.0439985	+	0.0533833i
$393$	0.911261	−	0.193694i	0.0459670	−	0.00977059i
$394$	33.6756	−	3.63760i	1.69655	−	0.183260i
$395$	−22.3450	−	22.3450i	−1.12430	−	1.12430i
$396$	17.2926	−	9.54940i	0.868987	−	0.479876i
$397$	20.3650	−	5.45678i	1.02209	−	0.273868i	0.291417	−	0.956596i	$-0.405873\pi$
$397$	20.3650	−	5.45678i	1.02209	−	0.273868i	0.730672	+	0.682728i	$0.239207\pi$
$398$	−5.81078	+	37.3848i	−0.291268	+	1.87393i
$399$	−0.0714175	+	0.0643046i	−0.00357535	+	0.00321926i
$400$	−21.1709	+	49.0652i	−1.05855	+	2.45326i
$401$	−3.31851	−	8.64500i	−0.165718	−	0.431711i	0.825424	−	0.564513i	$-0.190936\pi$
$401$	−3.31851	−	8.64500i	−0.165718	−	0.431711i	−0.991143	+	0.132802i	$0.957603\pi$
$402$	−2.36898	+	0.777282i	−0.118154	+	0.0387673i
$403$	−31.5666	−	6.00732i	−1.57244	−	0.299246i
$404$	7.67323	−	5.64278i	0.381757	−	0.280739i
$405$	−23.7371	−	29.3129i	−1.17951	−	1.45657i
$406$	2.73181	+	12.6724i	0.135577	+	0.628923i
$407$	12.6479	+	8.66726i	0.626935	+	0.429620i
$408$	1.38668	+	0.207355i	0.0686509	+	0.0102656i
$409$	2.97574	−	7.75207i	0.147141	−	0.383315i	−0.840125	−	0.542392i	$-0.817519\pi$
$409$	2.97574	−	7.75207i	0.147141	−	0.383315i	0.987266	+	0.159077i	$0.0508519\pi$
$410$	3.62472	+	1.37943i	0.179012	+	0.0681251i
$411$	0.327967	+	0.167107i	0.0161774	+	0.00824280i
$412$	−20.4500	−	11.6502i	−1.00750	−	0.573962i
$413$	−0.459385	+	1.03179i	−0.0226048	+	0.0507713i
$414$	19.7473	+	5.23032i	0.970526	+	0.257056i
$415$	−21.7542	+	66.9526i	−1.06787	+	3.28657i
$416$	−20.3476	−	1.40475i	−0.997625	−	0.0688735i
$417$	1.27986			0.0626752
$418$	−0.366759	+	1.04985i	−0.0179388	+	0.0513498i
$419$	19.9939	−	11.5435i	0.976764	−	0.563935i	0.0754722	−	0.997148i	$-0.475954\pi$
$419$	19.9939	−	11.5435i	0.976764	−	0.563935i	0.901292	+	0.433213i	$0.142620\pi$
$420$	−0.702592	+	3.40173i	−0.0342830	+	0.165988i
$421$	8.91030	+	17.4874i	0.434261	+	0.852286i	0.999623	+	0.0274432i	$0.00873652\pi$
$421$	8.91030	+	17.4874i	0.434261	+	0.852286i	−0.565362	+	0.824843i	$0.691263\pi$
$422$	13.7527	−	3.72755i	0.669473	−	0.181454i
$423$	−1.42390	−	1.15305i	−0.0692322	−	0.0560632i
$424$	19.6293	−	10.2164i	0.953284	−	0.496150i
$425$	−43.7209	−	9.29317i	−2.12078	−	0.450785i
$426$	−0.0589267	−	0.00602180i	−0.00285501	−	0.000291757i
$427$	−4.26422	−	5.26587i	−0.206360	−	0.254833i
$428$	−9.58768	−	6.88177i	−0.463438	−	0.332643i
$429$	1.24852	+	1.25712i	0.0602790	+	0.0606941i
$430$	−53.6128	−	17.2492i	−2.58544	−	0.831830i
$431$	10.0371	−	8.12792i	0.483472	−	0.391508i	−0.356365	−	0.934347i	$-0.615984\pi$
$431$	10.0371	−	8.12792i	0.483472	−	0.391508i	0.839837	+	0.542839i	$0.182651\pi$
$432$	−3.04760	+	1.80669i	−0.146628	+	0.0869245i
$433$	4.04279	−	19.0198i	0.194284	−	0.914034i	−0.767675	−	0.640840i	$-0.778586\pi$
$433$	4.04279	−	19.0198i	0.194284	−	0.914034i	0.961959	−	0.273195i	$-0.0880803\pi$
$434$	−30.7671	−	15.5651i	−1.47687	−	0.747149i
$435$	−1.33867	+	1.65312i	−0.0641844	+	0.0792611i
$436$	−1.02891	+	22.0655i	−0.0492757	+	1.05674i
$437$	−1.02467	+	0.522096i	−0.0490166	+	0.0249752i
$438$	−1.20479	+	0.130140i	−0.0575672	+	0.00621835i
$439$	3.75544	+	6.50461i	0.179237	+	0.310448i	0.941620	−	0.336679i	$-0.109304\pi$
$439$	3.75544	+	6.50461i	0.179237	+	0.310448i	−0.762382	+	0.647127i	$0.775970\pi$
$440$	11.8013	+	38.4235i	0.562603	+	1.83177i
$441$		−	1.44211i		−	0.0686721i
$442$	−2.19439	−	16.9184i	−0.104376	−	0.804728i
$443$	−11.4541	−	3.72167i	−0.544201	−	0.176822i	0.0239991	−	0.999712i	$-0.492360\pi$
$443$	−11.4541	−	3.72167i	−0.544201	−	0.176822i	−0.568200	+	0.822890i	$0.692360\pi$
$444$	−1.15318	−	0.739468i	−0.0547274	−	0.0350936i
$445$	−31.1615	−	13.8740i	−1.47719	−	0.657690i
$446$	−34.7039	−	7.27207i	−1.64328	−	0.344342i
$447$	0.714413	−	1.40211i	0.0337906	−	0.0663178i
$448$	−20.5648	−	7.48874i	−0.971595	−	0.353810i
$449$	4.41587	+	1.69509i	0.208398	+	0.0799965i	0.460328	−	0.887749i	$-0.347732\pi$
$449$	4.41587	+	1.69509i	0.208398	+	0.0799965i	−0.251930	+	0.967745i	$0.581065\pi$
$450$	50.0583	−	25.6880i	2.35977	−	1.21094i
$451$	2.00001	−	0.711317i	0.0941767	−	0.0334946i
$452$	28.7755	+	2.85684i	1.35349	+	0.134374i
$453$	1.04031	−	0.842428i	0.0488781	−	0.0395807i
$454$	0.653088	+	0.471626i	0.0306509	+	0.0221345i
$455$	42.1496	−	3.11384i	1.97600	−	0.145979i
$456$	0.0298851	−	0.0947568i	0.00139950	−	0.00443740i
$457$	−26.0139	+	9.98582i	−1.21688	+	0.467117i	−0.880246	−	0.474518i	$-0.842622\pi$
$457$	−26.0139	+	9.98582i	−1.21688	+	0.467117i	−0.336635	+	0.941635i	$0.609289\pi$
$458$	2.19122	+	3.77018i	0.102389	+	0.176169i
$459$	−1.98291	−	2.20225i	−0.0925545	−	0.102792i
$460$	−18.6570	+	37.1441i	−0.869887	+	1.73185i
$461$	2.17322	+	8.11055i	0.101217	+	0.377746i	0.997889	−	0.0649499i	$-0.0206888\pi$
$461$	2.17322	+	8.11055i	0.101217	+	0.377746i	−0.896672	+	0.442696i	$0.854022\pi$
$462$	0.914253	+	1.66692i	0.0425349	+	0.0775520i
$463$	−8.00143	+	8.00143i	−0.371858	+	0.371858i	−0.868154	−	0.496296i	$-0.834693\pi$
$463$	−8.00143	+	8.00143i	−0.371858	+	0.371858i	0.496296	+	0.868154i	$0.334693\pi$
$464$	−9.08243	−	9.85617i	−0.421641	−	0.457561i
$465$	−1.17633	−	5.53417i	−0.0545508	−	0.256641i
$466$	5.92771	−	22.3803i	0.274596	−	1.03675i
$467$	14.5136	−	10.5448i	0.671610	−	0.487953i	−0.198954	−	0.980009i	$-0.563754\pi$
$467$	14.5136	−	10.5448i	0.671610	−	0.487953i	0.870564	+	0.492056i	$0.163754\pi$
$468$	15.5917	+	14.7674i	0.720726	+	0.682622i
$469$	10.0593	+	30.9593i	0.464495	+	1.42957i
$470$	2.89051	−	2.35452i	0.133329	−	0.108606i
$471$	0.639766	+	0.0672421i	0.0294789	+	0.00309835i
$472$	−0.132094	−	1.16021i	−0.00608014	−	0.0534031i
$473$	−28.4628	+	11.8353i	−1.30872	+	0.544187i
$474$	1.54343	+	0.0764281i	0.0708921	+	0.00351046i
$475$	−1.13511	+	2.95706i	−0.0520824	+	0.135679i
$476$	2.75947	−	18.0971i	0.126480	−	0.829480i
$477$	−22.7903	−	4.84422i	−1.04349	−	0.221802i
$478$	−21.2778	+	23.7688i	−0.973223	+	1.08716i
$479$	−10.3481	+	3.97226i	−0.472816	+	0.181497i	−0.583096	−	0.812404i	$-0.698159\pi$
$479$	−10.3481	+	3.97226i	−0.472816	+	0.181497i	0.110280	+	0.993901i	$0.464825\pi$
$480$	−1.15885	−	3.39911i	−0.0528939	−	0.155147i
$481$	−4.81071	+	15.9591i	−0.219349	+	0.727672i
$482$	−11.4228	+	8.34956i	−0.520295	+	0.380312i
$483$	−0.508851	+	1.89906i	−0.0231535	+	0.0864101i
$484$	18.5519	+	11.8249i	0.843268	+	0.537493i
$485$	−18.8242	−	10.8682i	−0.854763	−	0.493498i
$486$	5.53582	+	0.860441i	0.251110	+	0.0390304i
$487$	−0.341786	+	6.52167i	−0.0154878	+	0.295525i	0.979893	+	0.199522i	$0.0639391\pi$
$487$	−0.341786	+	6.52167i	−0.0154878	+	0.295525i	−0.995381	+	0.0960027i	$0.969394\pi$
$488$	6.56165	+	2.45391i	0.297032	+	0.111083i
$489$	1.21939	+	0.193133i	0.0551428	+	0.00873375i
$490$	2.87198	+	0.601813i	0.129743	+	0.0271871i
$491$	−7.57613	+	8.41415i	−0.341906	+	0.379725i	−0.889435	−	0.457062i	$-0.848902\pi$
$491$	−7.57613	+	8.41415i	−0.341906	+	0.379725i	0.547529	+	0.836787i	$0.315569\pi$
$492$	−0.176664	+	0.0689860i	−0.00796465	+	0.00311013i
$493$	6.58946	−	9.06962i	0.296775	−	0.408475i
$494$	−1.20847	−	0.0339619i	−0.0543716	−	0.00152802i
$495$	16.1422	−	39.1218i	0.725537	−	1.75839i
$496$	35.5758	−	2.27595i	1.59740	−	0.102193i
$497$	−0.0808397	+	0.769138i	−0.00362615	+	0.0345006i
$498$	−1.40928	−	3.14090i	−0.0631513	−	0.140747i
$499$	3.87001	−	7.59533i	0.173246	−	0.340014i	−0.788014	−	0.615657i	$-0.788891\pi$
$499$	3.87001	−	7.59533i	0.173246	−	0.340014i	0.961260	+	0.275643i	$0.0888908\pi$
$500$	18.9396	+	69.0880i	0.847003	+	3.08971i
$501$	0.811674	−	1.00233i	0.0362629	−	0.0447810i
$502$	9.30036	−	9.35413i	0.415096	−	0.417495i
$503$	−24.8821	+	22.4039i	−1.10944	+	0.998942i	−0.109450	+	0.993992i	$0.534909\pi$
$503$	−24.8821	+	22.4039i	−1.10944	+	0.998942i	−0.999988	+	0.00494977i	$0.998424\pi$
$504$	11.6939	+	19.8560i	0.520889	+	0.884457i
$505$	5.28136	−	19.7103i	0.235018	−	0.877098i
$506$	5.40498	+	22.0993i	0.240281	+	0.982435i
$507$	−0.890862	+	1.70770i	−0.0395646	+	0.0758418i
$508$	−27.8507	+	9.22705i	−1.23568	+	0.409384i
$509$	18.0837	−	27.8465i	0.801548	−	1.23428i	−0.167125	−	0.985936i	$-0.553448\pi$
$509$	18.0837	−	27.8465i	0.801548	−	1.23428i	0.968673	−	0.248340i	$-0.0798850\pi$
$510$	2.59707	−	1.50942i	0.115000	−	0.0668381i
$511$	1.65382	+	15.7350i	0.0731606	+	0.696077i
$512$	22.2495	−	4.11812i	0.983299	−	0.181997i
$513$	−0.176120	+	0.114373i	−0.00777588	+	0.00504971i
$514$	10.6388	+	4.04873i	0.469259	+	0.178582i
$515$	−49.8019	+	7.88785i	−2.19453	+	0.347580i
$516$	2.50950	−	1.13468i	0.110474	−	0.0499514i
$517$	0.369113	−	2.00686i	0.0162336	−	0.0882614i
$518$	−9.69810	+	15.0284i	−0.426110	+	0.660311i
$519$	−1.86183	−	1.35270i	−0.0817255	−	0.0593770i
$520$	−35.9159	+	24.8883i	−1.57502	+	1.09143i
$521$	8.42611	+	25.9329i	0.369154	+	1.13614i	0.947338	+	0.320234i	$0.103762\pi$
$521$	8.42611	+	25.9329i	0.369154	+	1.13614i	−0.578184	+	0.815906i	$0.696238\pi$
$522$	0.779164	+	14.0903i	0.0341031	+	0.616713i
$523$	10.3472	−	23.2401i	0.452450	−	1.01622i	−0.532978	−	0.846129i	$-0.678927\pi$
$523$	10.3472	−	23.2401i	0.452450	−	1.01622i	0.985428	−	0.170091i	$-0.0544061\pi$
$524$	8.46849	+	9.29689i	0.369948	+	0.406136i
$525$	2.45837	+	4.82482i	0.107292	+	0.210572i
$526$	−12.8191	+	15.9239i	−0.558941	+	0.694316i
$527$	7.71745	+	28.8019i	0.336178	+	1.25463i
$528$	−1.68905	−	1.00532i	−0.0735063	−	0.0437511i
$529$	−0.263498	+	0.456392i	−0.0114564	+	0.0198431i
$530$	19.1580	−	43.3654i	0.832168	−	1.88367i
$531$	−0.669622	+	1.03113i	−0.0290591	+	0.0447471i
$532$	−1.23605	−	0.393755i	−0.0535895	−	0.0170714i
$533$	1.39601	+	1.83751i	0.0604680	+	0.0795912i
$534$	1.58492	−	0.520027i	0.0685862	−	0.0225038i
$535$	−25.2495	+	1.32327i	−1.09163	+	0.0572099i
$536$	−25.2047	−	22.3028i	−1.08868	−	0.963336i
$537$	0.713058	+	1.60155i	0.0307707	+	0.0691122i
$538$	−7.90219	−	15.3990i	−0.340687	−	0.663900i
$539$	1.41039	−	0.768278i	0.0607499	−	0.0330921i
$540$	−2.67922	+	7.10167i	−0.115295	+	0.305607i
$541$	−5.72275	−	36.1320i	−0.246040	−	1.55344i	−0.733132	−	0.680086i	$-0.761942\pi$
$541$	−5.72275	−	36.1320i	−0.246040	−	1.55344i	0.487092	−	0.873351i	$-0.338058\pi$
$542$	17.6213	+	39.2730i	0.756899	+	1.68692i
$543$	1.23571	−	1.37240i	0.0530296	−	0.0588953i
$544$	7.03657	+	17.5699i	0.301690	+	0.753303i
$545$	27.8165	+	38.2862i	1.19153	+	1.64000i
$546$	−1.42556	+	1.49647i	−0.0610083	+	0.0640432i
$547$	6.08094	+	1.97582i	0.260002	+	0.0844798i	0.436118	−	0.899890i	$-0.356353\pi$
$547$	6.08094	+	1.97582i	0.260002	+	0.0844798i	−0.176115	+	0.984370i	$0.556353\pi$
$548$	0.288636	+	4.96030i	0.0123299	+	0.211894i
$549$	−3.68804	−	6.38787i	−0.157402	−	0.272628i
$550$	51.7912	+	35.2721i	2.20838	+	1.50401i
$551$	−0.561746	−	0.561746i	−0.0239312	−	0.0239312i
$552$	−0.543047	−	1.95878i	−0.0231136	−	0.0833712i
$553$	1.05594	−	20.1486i	0.0449033	−	0.856806i
$554$	10.3143	+	10.2550i	0.438212	+	0.435693i
$555$	−2.91880	+	0.306778i	−0.123896	+	0.0130220i
$556$	8.72436	+	14.9119i	0.369995	+	0.632405i
$557$	−25.7487	+	1.34943i	−1.09101	+	0.0571772i	−0.589340	−	0.807885i	$-0.700612\pi$
$557$	−25.7487	+	1.34943i	−1.09101	+	0.0571772i	−0.501665	+	0.865062i	$0.667279\pi$
$558$	−30.4293	−	21.9745i	−1.28818	−	0.930255i
$559$	−21.6410	−	25.5859i	−0.915316	−	1.08217i
$560$	−44.4234	+	15.0023i	−1.87723	+	0.633965i
$561$	0.546696	−	1.55055i	0.0230815	−	0.0654643i
$562$	−1.10536	+	0.238282i	−0.0466267	+	0.0100513i
$563$	−5.18159	+	2.30699i	−0.218378	+	0.0972281i	−0.513010	−	0.858383i	$-0.671470\pi$
$563$	−5.18159	+	2.30699i	−0.218378	+	0.0972281i	0.294632	+	0.955611i	$0.404803\pi$
$564$	−0.0274813	+	0.180227i	−0.00115717	+	0.00758894i
$565$	51.9570	−	33.7413i	2.18585	−	1.41951i
$566$	−17.8747	+	11.6814i	−0.751331	+	0.491005i
$567$	3.76732	−	23.7859i	0.158213	−	0.998916i
$568$	−0.331521	−	0.727612i	−0.0139103	−	0.0305299i
$569$	−3.90787	−	18.3851i	−0.163826	−	0.770742i	−0.980947	−	0.194276i	$-0.937764\pi$
$569$	−3.90787	−	18.3851i	−0.163826	−	0.770742i	0.817121	−	0.576467i	$-0.195569\pi$
$570$	−0.0768560	−	0.198505i	−0.00321914	−	0.00831446i
$571$	23.6826			0.991088			0.495544	−	0.868583i	$-0.334969\pi$
$571$	23.6826			0.991088			0.495544	+	0.868583i	$0.334969\pi$
$572$	−6.13615	+	23.1160i	−0.256565	+	0.966527i
$573$	0.0434913			0.00181687
$574$	0.894055	+	2.30918i	0.0373171	+	0.0963833i
$575$	13.4726	+	63.3835i	0.561845	+	2.64327i
$576$	−20.8354	−	11.5537i	−0.868142	−	0.481402i
$577$	7.36608	−	46.5076i	0.306654	−	1.93614i	−0.0425596	−	0.999094i	$-0.513551\pi$
$577$	7.36608	−	46.5076i	0.306654	−	1.93614i	0.349214	−	0.937043i	$-0.386449\pi$
$578$	6.87312	−	4.49167i	0.285884	−	0.186829i
$579$	2.43709	−	1.58266i	0.101282	−	0.0657732i
$580$	−28.3860	−	4.32833i	−1.17866	−	0.179724i
$581$	−41.0616	+	18.2818i	−1.70352	+	0.758456i
$582$	1.03907	−	0.223993i	0.0430708	−	0.00928480i
$583$	−7.40372	−	24.8697i	−0.306631	−	1.03000i
$584$	−9.72892	−	13.1501i	−0.402585	−	0.544155i
$585$	45.8483	+	3.82976i	1.89559	+	0.158341i
$586$	−26.6990	−	19.2807i	−1.10293	−	0.796476i
$587$	−34.0597	+	1.78500i	−1.40580	+	0.0736746i	−0.740074	−	0.672525i	$-0.765210\pi$
$587$	−34.0597	+	1.78500i	−1.40580	+	0.0736746i	−0.665722	+	0.746200i	$0.731876\pi$
$588$	−0.123854	+	0.0724623i	−0.00510767	+	0.00298830i
$589$	2.10143	−	0.220870i	0.0865881	−	0.00910078i
$590$	−1.77405	−	1.76386i	−0.0730367	−	0.0726169i
$591$	−0.185719	+	3.54373i	−0.00763947	+	0.145770i
$592$	0.754856	−	18.4765i	0.0310244	−	0.759380i
$593$	12.3501	+	12.3501i	0.507157	+	0.507157i	0.913653	−	0.406496i	$-0.133249\pi$
$593$	12.3501	+	12.3501i	0.507157	+	0.507157i	−0.406496	+	0.913653i	$0.633249\pi$
$594$	1.40339	+	3.91018i	0.0575818	+	0.160437i
$595$	−19.6097	−	33.9649i	−0.803918	−	1.39243i
$596$	21.2061	−	1.23397i	0.868637	−	0.0505454i
$597$	−3.76971	−	1.22485i	−0.154284	−	0.0501299i
$598$	−21.1127	+	12.8823i	−0.863364	+	0.526797i
$599$	−13.8152	−	19.0150i	−0.564475	−	0.776933i	0.427412	−	0.904057i	$-0.359425\pi$
$599$	−13.8152	−	19.0150i	−0.564475	−	0.776933i	−0.991887	+	0.127124i	$0.959425\pi$
$600$	−4.72147	−	3.00845i	−0.192753	−	0.122819i
$601$	−17.7609	+	19.7255i	−0.724481	+	0.804618i	−0.987070	−	0.160290i	$-0.948757\pi$
$601$	−17.7609	+	19.7255i	−0.724481	+	0.804618i	0.262589	+	0.964908i	$0.415424\pi$
$602$	−14.7203	−	32.8074i	−0.599953	−	1.33713i
$603$	5.54338	+	34.9996i	0.225744	+	1.42529i
$604$	16.9067	+	6.37830i	0.687923	+	0.259529i
$605$	46.8609	−	5.05480i	1.90517	−	0.205507i
$606$	0.455582	+	0.887796i	0.0185068	+	0.0360642i
$607$	0.771937	+	1.73380i	0.0313320	+	0.0703727i	0.928534	−	0.371248i	$-0.121070\pi$
$607$	0.771937	+	1.73380i	0.0313320	+	0.0703727i	−0.897202	+	0.441621i	$0.854404\pi$
$608$	1.30774	−	0.297726i	0.0530359	−	0.0120744i
$609$	−1.35628	+	0.0710798i	−0.0549594	+	0.00288030i
$610$	14.2605	−	4.67901i	0.577393	−	0.189448i
$611$	2.20066	−	0.278988i	0.0890293	−	0.0112867i
$612$	6.04867	−	18.9876i	0.244503	−	0.767528i
$613$	−4.31017	+	6.63709i	−0.174086	+	0.268069i	−0.914934	−	0.403604i	$-0.867757\pi$
$613$	−4.31017	+	6.63709i	−0.174086	+	0.268069i	0.740848	+	0.671673i	$0.234424\pi$
$614$	10.8820	−	24.6322i	0.439162	−	0.994075i
$615$	−0.203159	+	0.351882i	−0.00819217	+	0.0141893i
$616$	−13.1894	+	22.0149i	−0.531415	+	0.887004i
$617$	−0.0256296	−	0.0956510i	−0.00103181	−	0.00385076i	0.965408	−	0.260744i	$-0.0839678\pi$
$617$	−0.0256296	−	0.0956510i	−0.00103181	−	0.00385076i	−0.966440	+	0.256893i	$0.917301\pi$
$618$	1.54622	−	1.92071i	0.0621979	−	0.0772623i
$619$	15.2376	+	29.9054i	0.612450	+	1.20200i	0.964018	+	0.265839i	$0.0856488\pi$
$619$	15.2376	+	29.9054i	0.612450	+	1.20200i	−0.351567	+	0.936163i	$0.614351\pi$
$620$	56.4609	−	51.4300i	2.26752	−	2.06548i
$621$	−1.74740	+	3.92473i	−0.0701209	+	0.157494i
$622$	0.156210	+	2.82488i	0.00626346	+	0.113267i
$623$	−6.72999	−	20.7128i	−0.269631	−	0.829840i
$624$	0.484837	−	2.08109i	0.0194090	−	0.0833104i
$625$	70.1237	+	50.9479i	2.80495	+	2.03791i
$626$	−12.7185	+	19.7089i	−0.508333	+	0.787725i
$627$	−0.102465	−	0.0554526i	−0.00409204	−	0.00221456i
$628$	3.57760	+	7.91237i	0.142762	+	0.315738i
$629$	15.2770	−	2.41964i	0.609135	−	0.0964775i
$630$	46.1403	+	17.5592i	1.83827	+	0.699576i
$631$	7.44519	−	4.83496i	0.296388	−	0.192477i	−0.387875	−	0.921712i	$-0.626791\pi$
$631$	7.44519	−	4.83496i	0.296388	−	0.192477i	0.684263	+	0.729235i	$0.260124\pi$
$632$	9.63052	+	18.5037i	0.383081	+	0.736038i
$633$	0.156041	+	1.48463i	0.00620209	+	0.0590089i
$634$	26.6995	−	15.5177i	1.06037	−	0.616287i
$635$	−34.2342	+	52.7160i	−1.35854	+	2.09197i
$636$	0.729108	+	2.20072i	0.0289110	+	0.0872643i
$637$	1.26071	+	1.20792i	0.0499511	+	0.0478594i
$638$	−13.3652	+	8.26853i	−0.529134	+	0.327354i
$639$	−0.217893	+	0.813189i	−0.00861972	+	0.0321692i
$640$	31.7041	−	36.6724i	1.25321	−	1.44960i
$641$	−10.7821	+	9.70822i	−0.425866	+	0.383452i	−0.854008	−	0.520260i	$-0.825835\pi$
$641$	−10.7821	+	9.70822i	−0.425866	+	0.383452i	0.428142	+	0.903712i	$0.359168\pi$
$642$	0.871766	−	0.876805i	0.0344059	−	0.0346047i
$643$	29.6053	−	36.5594i	1.16752	−	1.44176i	0.293440	−	0.955978i	$-0.405200\pi$
$643$	29.6053	−	36.5594i	1.16752	−	1.44176i	0.874078	−	0.485786i	$-0.161467\pi$
$644$	−25.5949	+	7.01648i	−1.00858	+	0.276488i
$645$	2.67871	−	5.25727i	0.105474	−	0.207005i
$646$	0.459246	+	1.02353i	0.0180688	+	0.0402704i
$647$	3.51744	−	33.4662i	0.138285	−	1.31569i	−0.676720	−	0.736240i	$-0.736599\pi$
$647$	3.51744	−	33.4662i	0.138285	−	1.31569i	0.815005	−	0.579453i	$-0.196734\pi$
$648$	9.12342	+	23.1666i	0.358402	+	0.910072i
$649$	−1.36518	−	0.105565i	−0.0535881	−	0.00414380i
$650$	−19.4723	+	65.2777i	−0.763765	+	2.56040i
$651$	2.12330	−	2.92247i	0.0832187	−	0.114541i
$652$	6.06192	+	15.5238i	0.237403	+	0.607959i
$653$	18.1807	−	20.1917i	0.711465	−	0.790162i	−0.273692	−	0.961817i	$-0.588245\pi$
$653$	18.1807	−	20.1917i	0.711465	−	0.790162i	0.985157	+	0.171655i	$0.0549115\pi$
$654$	−2.26504	−	0.474630i	−0.0885699	−	0.0185595i
$655$	26.6104	+	4.21467i	1.03975	+	0.164681i
$656$	−2.00802	−	1.58809i	−0.0784001	−	0.0620045i
$657$	−0.901387	+	17.1995i	−0.0351664	+	0.671016i
$658$	2.35207	+	0.365585i	0.0916931	+	0.0142520i
$659$	−18.0544	−	10.4237i	−0.703299	−	0.406050i	0.105276	−	0.994443i	$-0.466427\pi$
$659$	−18.0544	−	10.4237i	−0.703299	−	0.406050i	−0.808575	+	0.588393i	$0.799761\pi$
$660$	−4.17103	+	0.579411i	−0.162357	+	0.0225536i
$661$	8.51796	−	31.7894i	0.331310	−	1.23647i	−0.576504	−	0.817094i	$-0.695584\pi$
$661$	8.51796	−	31.7894i	0.331310	−	1.23647i	0.907814	−	0.419372i	$-0.137750\pi$
$662$	1.94080	−	1.41863i	0.0754312	−	0.0551368i
$663$	1.78647	+	0.0553587i	0.0693809	+	0.00214996i
$664$	26.9886	−	37.8301i	1.04736	−	1.46809i
$665$	−2.59463	+	0.995986i	−0.100615	+	0.0386227i
$666$	−12.9863	+	14.5066i	−0.503209	+	0.562120i
$667$	−15.8973	−	3.37907i	−0.615545	−	0.130838i
$668$	17.2112	+	2.62439i	0.665922	+	0.101541i
$669$	1.33125	−	3.46803i	0.0514692	−	0.134082i
$670$	−72.0152	−	3.56607i	−2.78219	−	0.137769i
$671$	4.28258	−	7.01001i	0.165327	−	0.270619i
$672$	1.11772	−	2.00203i	0.0431170	−	0.0772299i
$673$	−24.2197	−	2.54559i	−0.933600	−	0.0981253i	−0.374501	−	0.927226i	$-0.622186\pi$
$673$	−24.2197	−	2.54559i	−0.933600	−	0.0981253i	−0.559099	+	0.829101i	$0.688853\pi$
$674$	6.49428	−	5.29002i	0.250150	−	0.203764i
$675$	3.65652	+	11.2536i	0.140739	+	0.433151i
$676$	−25.9694	+	1.26123i	−0.998823	+	0.0485090i
$677$	19.5000	−	14.1676i	0.749445	−	0.544503i	−0.146210	−	0.989254i	$-0.546708\pi$
$677$	19.5000	−	14.1676i	0.749445	−	0.544503i	0.895655	+	0.444750i	$0.146708\pi$
$678$	−0.775663	+	2.92855i	−0.0297892	+	0.112470i
$679$	−2.88542	−	13.5748i	−0.110732	−	0.520954i
$680$	35.2897	+	19.9697i	1.35330	+	0.765804i
$681$	−0.0596780	+	0.0596780i	−0.00228687	+	0.00228687i
$682$	5.28008	−	41.4668i	0.202185	−	1.58785i
$683$	−10.7032	−	39.9449i	−0.409546	−	1.52845i	−0.795514	−	0.605935i	$-0.792799\pi$
$683$	−10.7032	−	39.9449i	−0.409546	−	1.52845i	0.385968	−	0.922512i	$-0.373868\pi$
$684$	−1.26191	−	0.633841i	−0.0482504	−	0.0242355i
$685$	7.12283	+	7.91071i	0.272149	+	0.302253i
$686$	−12.6673	−	21.7951i	−0.483640	−	0.832141i
$687$	−0.426511	+	0.163722i	−0.0162724	+	0.00624639i
$688$	30.3266	+	21.5038i	1.15619	+	0.819826i
$689$	23.3240	−	15.8659i	0.888574	−	0.604444i
$690$	−3.53045	−	2.54951i	−0.134402	−	0.0970580i
$691$	9.06695	−	7.34227i	0.344923	−	0.279313i	−0.441167	−	0.897425i	$-0.645435\pi$
$691$	9.06695	−	7.34227i	0.344923	−	0.279313i	0.786090	+	0.618112i	$0.212102\pi$
$692$	3.06909	−	30.9134i	0.116669	−	1.17515i
$693$	25.4588	−	9.05461i	0.967100	−	0.343956i
$694$	6.89949	−	3.54055i	0.261901	−	0.134397i
$695$	34.5548	+	13.2643i	1.31074	+	0.503145i
$696$	1.17097	−	0.774914i	0.0443856	−	0.0293730i
$697$	0.972171	−	1.90799i	0.0368236	−	0.0722704i
$698$	−21.9627	−	4.60220i	−0.831301	−	0.174196i
$699$	2.21585	+	0.986561i	0.0838112	+	0.0373152i
$700$	−39.4568	+	61.5318i	−1.49133	+	2.32568i
$701$	−39.5696	−	12.8569i	−1.49452	−	0.485600i	−0.556108	−	0.831110i	$-0.687706\pi$
$701$	−39.5696	−	12.8569i	−1.49452	−	0.485600i	−0.938415	+	0.345510i	$0.887706\pi$
$702$	−3.58829	+	2.74248i	−0.135431	+	0.103508i
$703$		−	1.09608i		−	0.0413395i
$704$	0.199575	−	26.5322i	0.00752178	−	0.999972i
$705$	0.195291	+	0.338253i	0.00735507	+	0.0127394i
$706$	−33.8710	+	3.65870i	−1.27475	+	0.137697i
$707$	11.6085	−	5.91481i	0.436582	−	0.222449i
$708$	0.122204	+	0.00569833i	0.00459270	+	0.000214156i
$709$	2.66205	−	3.28736i	0.0999753	−	0.123459i	−0.724703	−	0.689062i	$-0.758023\pi$
$709$	2.66205	−	3.28736i	0.0999753	−	0.123459i	0.824678	+	0.565602i	$0.191356\pi$
$710$	−1.52854	−	0.773290i	−0.0573651	−	0.0290210i
$711$	4.56643	−	21.4834i	0.171255	−	0.805690i
$712$	16.8627	+	14.9213i	0.631957	+	0.559200i
$713$	33.5944	−	27.2042i	1.25812	−	1.01881i
$714$	1.82572	+	0.587400i	0.0683258	+	0.0219829i
$715$	20.6799	+	46.8801i	0.773385	+	1.75322i
$716$	−13.7993	+	19.2251i	−0.515704	+	0.718478i
$717$	−2.10331	−	2.59737i	−0.0785496	−	0.0970006i
$718$	−30.8237	−	3.14992i	−1.15033	−	0.117554i
$719$	−39.6843	−	8.43517i	−1.47998	−	0.314579i	−0.604020	−	0.796969i	$-0.706435\pi$
$719$	−39.6843	−	8.43517i	−1.47998	−	0.314579i	−0.875956	+	0.482391i	$0.839769\pi$
$720$	−50.3175	+	8.56522i	−1.87522	+	0.319207i
$721$	−25.0192	−	20.2601i	−0.931763	−	0.754527i
$722$	−25.8576	+	7.00846i	−0.962320	+	0.260828i
$723$	−0.672971	−	1.32078i	−0.0250281	−	0.0491203i
$724$	24.4134	+	5.04234i	0.907318	+	0.187397i
$725$	−38.7663	+	22.3817i	−1.43974	+	0.831237i
$726$	−1.53261	+	1.72148i	−0.0568806	+	0.0638901i
$727$	−17.5087			−0.649361			−0.324680	−	0.945824i	$-0.605257\pi$
$727$	−17.5087			−0.649361			−0.324680	+	0.945824i	$0.605257\pi$
$728$	−27.1531	−	6.40849i	−1.00636	−	0.237514i
$729$	7.97938	−	24.5580i	0.295533	−	0.909556i
$730$	−33.8767	−	8.97268i	−1.25383	−	0.332094i
$731$	−12.6480	+	28.4079i	−0.467804	+	1.05070i
$732$	−0.363301	+	0.637716i	−0.0134280	+	0.0235706i
$733$	38.3312	+	19.5307i	1.41580	+	0.721384i	0.983595	−	0.180393i	$-0.0577369\pi$
$733$	38.3312	+	19.5307i	1.41580	+	0.721384i	0.432201	+	0.901777i	$0.357737\pi$
$734$	−21.7488	−	8.27675i	−0.802763	−	0.305500i
$735$	−0.110170	+	0.287003i	−0.00406369	+	0.0105863i
$736$	19.1203	−	19.6794i	0.704783	−	0.725392i
$737$	−31.2765	+	24.0673i	−1.15208	+	0.886529i
$738$	0.568031	+	2.63501i	0.0209095	+	0.0969961i
$739$	−28.5272	−	35.2281i	−1.04939	−	1.29589i	−0.953792	−	0.300468i	$-0.902857\pi$
$739$	−28.5272	−	35.2281i	−1.04939	−	1.29589i	−0.0955979	−	0.995420i	$-0.530476\pi$
$740$	−23.4707	−	31.9161i	−0.862799	−	1.17326i
$741$	0.0236786	−	0.124424i	0.000869856	−	0.00457082i
$742$	28.7607	−	9.43665i	1.05584	−	0.346430i
$743$	12.9118	+	33.6364i	0.473689	+	1.23400i	0.937475	+	0.348054i	$0.113157\pi$
$743$	12.9118	+	33.6364i	0.473689	+	1.23400i	−0.463786	+	0.885947i	$0.653509\pi$
$744$	−0.358262	+	3.71754i	−0.0131345	+	0.136292i
$745$	33.8196	−	30.4513i	1.23906	−	1.11565i
$746$	0.0723708	−	0.465612i	0.00264968	−	0.0170473i
$747$	−47.2614	+	12.6637i	−1.72920	+	0.463339i
$748$	21.7923	−	4.19991i	0.796806	−	0.153564i
$749$	−11.4150	−	11.4150i	−0.417096	−	0.417096i
$750$	−7.46175	+	0.806010i	−0.272465	+	0.0294313i
$751$	2.72281	−	0.578752i	0.0993569	−	0.0211190i	−0.157965	−	0.987445i	$-0.550493\pi$
$751$	2.72281	−	0.578752i	0.0993569	−	0.0211190i	0.257322	+	0.966326i	$0.417160\pi$
$752$	−2.28718	+	0.908354i	−0.0834050	+	0.0331243i
$753$	0.812290	+	1.11802i	0.0296015	+	0.0407430i
$754$	−12.9705	−	11.1209i	−0.472356	−	0.404998i
$755$	36.8180	−	11.9629i	1.33994	−	0.435374i
$756$	−4.51422	+	1.76277i	−0.164181	+	0.0641113i
$757$	−5.26451	+	50.0885i	−0.191342	+	1.82050i	0.304981	+	0.952358i	$0.401350\pi$
$757$	−5.26451	+	50.0885i	−0.191342	+	1.82050i	−0.496323	+	0.868138i	$0.665317\pi$
$758$	15.8057	+	17.4526i	0.574088	+	0.633906i
$759$	−2.37590	+	0.190255i	−0.0862398	+	0.00690581i
$760$	1.78891	−	2.24860i	0.0648906	−	0.0815651i
$761$	22.5735	+	8.66515i	0.818289	+	0.314112i	0.731264	−	0.682095i	$-0.238931\pi$
$761$	22.5735	+	8.66515i	0.818289	+	0.314112i	0.0870246	+	0.996206i	$0.472264\pi$
$762$	−0.489593	−	3.03454i	−0.0177361	−	0.109930i
$763$	−6.28214	+	29.5551i	−0.227429	+	1.06997i
$764$	0.296464	+	0.506723i	0.0107257	+	0.0183326i
$765$	−15.2998	−	39.8575i	−0.553167	−	1.44105i
$766$	51.7545	−	0.149153i	1.86997	−	0.00538913i
$767$	−0.340544	−	1.44906i	−0.0122963	−	0.0523226i
$768$	0.0546503	+	2.36996i	0.00197202	+	0.0855187i
$769$	−11.8377	−	3.17191i	−0.426880	−	0.114382i	0.0389814	−	0.999240i	$-0.487589\pi$
$769$	−11.8377	−	3.17191i	−0.426880	−	0.114382i	−0.465861	+	0.884858i	$0.654255\pi$
$770$	7.40803	+	54.4800i	0.266967	+	1.96332i
$771$	−0.596289	+	1.03280i	−0.0214748	+	0.0371955i
$772$	35.0525	+	17.6064i	1.26157	+	0.633669i
$773$	−38.8174	−	2.03433i	−1.39617	−	0.0731699i	−0.660658	−	0.750687i	$-0.729723\pi$
$773$	−38.8174	−	2.03433i	−1.39617	−	0.0731699i	−0.735507	+	0.677517i	$0.763056\pi$
$774$	−10.2400	−	37.7803i	−0.368069	−	1.35799i
$775$	18.6253	−	117.595i	0.669039	−	4.22415i
$776$	9.69273	+	10.5795i	0.347949	+	0.379781i
$777$	−1.39254	−	1.25385i	−0.0499570	−	0.0449815i
$778$	2.38886	−	1.94589i	0.0856448	−	0.0697634i
$779$	−0.122766	−	0.0891945i	−0.00439854	−	0.00319573i
$780$	−1.97484	−	4.13006i	−0.0707105	−	0.147880i
$781$	−0.911383	+	0.220121i	−0.0326118	+	0.00787656i
$782$	19.2840	+	12.4443i	0.689593	+	0.445007i
$783$	−2.95152	−	0.310217i	−0.105479	−	0.0110863i
$784$	−1.68854	−	0.949095i	−0.0603049	−	0.0338963i
$785$	16.5760	+	8.44590i	0.591624	+	0.301447i
$786$	−1.10288	+	0.720748i	−0.0393385	+	0.0257082i
$787$	−19.9099	−	16.1227i	−0.709712	−	0.574714i	0.205028	−	0.978756i	$-0.434271\pi$
$787$	−19.9099	−	16.1227i	−0.709712	−	0.574714i	−0.914740	+	0.404043i	$0.867605\pi$
$788$	−42.5545	+	21.9925i	−1.51594	+	0.783450i
$789$	−1.43308	−	1.59160i	−0.0510190	−	0.0566623i
$790$	40.8787	+	18.0594i	1.45440	+	0.642523i
$791$	38.2068	+	10.2375i	1.35848	+	0.364003i
$792$	−17.9298	+	21.4237i	−0.637106	+	0.761259i
$793$	8.67344	+	2.12637i	0.308003	+	0.0755097i
$794$	−24.0714	+	17.5951i	−0.854261	+	0.624426i
$795$	4.16554	+	2.70513i	0.147737	+	0.0959412i
$796$	−11.4258	−	52.2708i	−0.404976	−	1.85269i
$797$	−28.2914	+	2.97355i	−1.00213	+	0.105328i	−0.591359	−	0.806409i	$-0.701408\pi$
$797$	−28.2914	+	2.97355i	−1.00213	+	0.105328i	−0.410774	+	0.911737i	$0.634742\pi$
$798$	0.0613519	−	0.121273i	0.00217183	−	0.00429300i
$799$	−1.12111	−	1.72636i	−0.0396621	−	0.0610743i
$800$	2.86730	−	75.5181i	0.101374	−	2.66997i
$801$	−3.70870	−	23.4158i	−0.131041	−	0.827357i
$802$	8.79074	+	9.70670i	0.310412	+	0.342756i
$803$	−17.3014	+	8.28137i	−0.610552	+	0.292243i
$804$	2.72735	−	2.23472i	0.0961864	−	0.0788125i
$805$	−33.4200	+	45.9986i	−1.17790	+	1.62124i
$806$	44.6980	−	8.19573i	1.57442	−	0.288682i
$807$	1.72457	−	0.560347i	0.0607078	−	0.0197252i
$808$	−7.23830	+	11.3598i	−0.254643	+	0.399637i
$809$	−10.0352	−	4.46798i	−0.352820	−	0.157086i	0.222671	−	0.974894i	$-0.428522\pi$
$809$	−10.0352	−	4.46798i	−0.352820	−	0.157086i	−0.575491	+	0.817808i	$0.695189\pi$
$810$	46.2724	+	26.5379i	1.62585	+	0.932446i
$811$	2.93341	−	1.49465i	0.103006	−	0.0524842i	−0.401728	−	0.915759i	$-0.631590\pi$
$811$	2.93341	−	1.49465i	0.103006	−	0.0524842i	0.504734	+	0.863275i	$0.331590\pi$
$812$	−10.0735	−	15.3177i	−0.353509	−	0.537547i
$813$	−4.35602	+	1.16719i	−0.152772	+	0.0409352i
$814$	−21.1059	−	4.97234i	−0.739762	−	0.174280i
$815$	30.9205	+	17.8519i	1.08310	+	0.625326i
$816$	−1.93466	+	0.434592i	−0.0677265	+	0.0152138i
$817$	1.84809	+	1.20017i	0.0646566	+	0.0419885i
$818$	0.0338426	+	11.7430i	0.00118328	+	0.410584i
$819$	17.7703	+	23.3903i	0.620946	+	0.817322i
$820$	−5.48469	+	0.0316133i	−0.191534	+	0.00110399i
$821$	1.99469	+	38.0609i	0.0696150	+	1.32833i	0.780558	+	0.625084i	$0.214935\pi$
$821$	1.99469	+	38.0609i	0.0696150	+	1.32833i	−0.710943	+	0.703250i	$0.751731\pi$
$822$	−0.517855	−	0.0529203i	−0.0180623	−	0.00184581i
$823$	−5.93614	+	2.64294i	−0.206921	+	0.0921271i	−0.507580	−	0.861604i	$-0.669460\pi$
$823$	−5.93614	+	2.64294i	−0.206921	+	0.0921271i	0.300659	+	0.953732i	$0.402793\pi$
$824$	32.9184	+	4.92242i	1.14677	+	0.171480i
$825$	−4.51241	+	4.76812i	−0.157102	+	0.166004i
$826$	0.0789974	−	1.59531i	0.00274867	−	0.0555081i
$827$	11.5238	−	1.82519i	0.400721	−	0.0634679i	0.0471785	−	0.998886i	$-0.484977\pi$
$827$	11.5238	−	1.82519i	0.400721	−	0.0634679i	0.353542	+	0.935419i	$0.384977\pi$
$828$	−28.7137	+	3.18536i	−0.997869	+	0.110699i
$829$	−20.3973	−	18.3658i	−0.708428	−	0.637871i	0.234017	−	0.972232i	$-0.424813\pi$
$829$	−20.3973	−	18.3658i	−0.708428	−	0.637871i	−0.942445	+	0.334361i	$0.891479\pi$
$830$	−5.49697	−	99.4061i	−0.190803	−	3.45044i
$831$	−1.23278	+	0.895668i	−0.0427647	+	0.0310704i
$832$	27.5521	−	8.53714i	0.955197	−	0.295972i
$833$	0.500665	−	1.54089i	0.0173470	−	0.0533886i
$834$	−1.68791	+	0.653514i	−0.0584474	+	0.0226293i
$835$	32.3023	−	18.6497i	1.11787	−	0.645400i
$836$	−0.0523775	−	1.57183i	−0.00181151	−	0.0543629i
$837$	5.58166	−	5.58166i	0.192930	−	0.192930i
$838$	−20.4740	+	25.4328i	−0.707262	+	0.878561i
$839$	49.4028	+	2.58909i	1.70557	+	0.0893853i	0.880020	−	0.474937i	$-0.157529\pi$
$839$	49.4028	+	2.58909i	1.70557	+	0.0893853i	0.825554	+	0.564323i	$0.190863\pi$
$840$	−0.810374	−	4.84501i	−0.0279606	−	0.167169i
$841$	1.85777	+	17.6755i	0.0640609	+	0.609499i
$842$	−20.6803	−	18.5130i	−0.712692	−	0.638001i
$843$	−0.00619995	−	0.118302i	−0.000213538	−	0.00407454i
$844$	−16.2340	+	11.9383i	−0.558798	+	0.410932i
$845$	−41.7506	+	36.8732i	−1.43627	+	1.26848i
$846$	2.46662	+	0.793601i	0.0848041	+	0.0272846i
$847$	22.4185	+	20.0750i	0.770308	+	0.689786i
$848$	−20.6709	+	23.4965i	−0.709841	+	0.806872i
$849$	−0.909912	−	2.04369i	−0.0312281	−	0.0701394i
$850$	62.4051	−	10.0684i	2.14048	−	0.345344i
$851$	−12.2128	−	18.8060i	−0.418649	−	0.644662i
$852$	0.0807883	−	0.0221470i	0.00276776	−	0.000758744i
$853$	24.6985	+	3.91185i	0.845660	+	0.133939i	0.564204	−	0.825635i	$-0.309183\pi$
$853$	24.6985	+	3.91185i	0.845660	+	0.133939i	0.281455	+	0.959574i	$0.409183\pi$
$854$	8.31254	+	4.76736i	0.284449	+	0.163136i
$855$	−2.95928	+	0.629014i	−0.101205	+	0.0215118i
$856$	16.1583	+	4.18021i	0.552279	+	0.142877i
$857$		−	10.5094i		−	0.358994i	−0.983759	−	0.179497i	$-0.942553\pi$
$857$		−	10.5094i		−	0.358994i	0.983759	−	0.179497i	$-0.0574470\pi$
$858$	−2.28846	−	1.02040i	−0.0781269	−	0.0348358i
$859$			24.6645i			0.841542i	0.907167	+	0.420771i	$0.138240\pi$
$859$			24.6645i			0.841542i	−0.907167	+	0.420771i	$0.861760\pi$
$860$	79.5131	−	4.62681i	2.71137	−	0.157773i
$861$	−0.253755	+	0.0539374i	−0.00864796	+	0.00183818i
$862$	−9.08693	+	15.8443i	−0.309502	+	0.539659i
$863$	8.49526	+	1.34552i	0.289182	+	0.0458020i	0.299340	−	0.954146i	$-0.403233\pi$
$863$	8.49526	+	1.34552i	0.289182	+	0.0458020i	−0.0101580	+	0.999948i	$0.503233\pi$
$864$	3.09671	−	3.93883i	0.105352	−	0.134002i
$865$	−36.2481	−	55.8171i	−1.23247	−	1.89784i
$866$	4.38005	+	27.1479i	0.148840	+	0.922524i
$867$	0.349875	+	0.785832i	0.0118824	+	0.0266883i
$868$	48.5239	+	4.81746i	1.64701	+	0.163515i
$869$	23.4436	−	6.97916i	0.795268	−	0.236752i
$870$	0.921358	−	2.86370i	0.0312370	−	0.0970886i
$871$	−35.2401	−	24.4696i	−1.19406	−	0.829121i
$872$	−9.90994	−	29.6256i	−0.335593	−	1.00325i
$873$	−0.790657	−	15.0866i	−0.0267597	−	0.510605i
$874$	1.08476	−	1.21176i	0.0366927	−	0.0409883i
$875$	10.2427	+	97.4532i	0.346268	+	3.29452i
$876$	1.52245	−	0.786813i	0.0514388	−	0.0265839i
$877$	−32.0287	−	1.67855i	−1.08153	−	0.0566808i	−0.496768	−	0.867883i	$-0.665480\pi$
$877$	−32.0287	−	1.67855i	−1.08153	−	0.0566808i	−0.584765	+	0.811203i	$0.698813\pi$
$878$	−8.27407	−	6.66082i	−0.279236	−	0.224792i
$879$	2.43971	−	2.43971i	0.0822894	−	0.0822894i
$880$	−35.1832	−	44.6476i	−1.18602	−	1.50507i
$881$	5.88020	−	3.39494i	0.198109	−	0.114378i	−0.397664	−	0.917531i	$-0.630179\pi$
$881$	5.88020	−	3.39494i	0.198109	−	0.114378i	0.595773	+	0.803153i	$0.296846\pi$
$882$	0.736361	+	1.90188i	0.0247946	+	0.0640398i
$883$	−3.05246	+	9.39452i	−0.102724	+	0.316151i	−0.989189	−	0.146643i	$-0.953153\pi$
$883$	−3.05246	+	9.39452i	−0.102724	+	0.316151i	0.886466	+	0.462794i	$0.153153\pi$
$884$	11.5327	+	21.1918i	0.387888	+	0.712758i
$885$	0.212038	−	0.154055i	0.00712758	−	0.00517849i
$886$	17.0062	−	0.940409i	0.571334	−	0.0315937i
$887$	−19.7723	−	17.8030i	−0.663888	−	0.597767i	0.266725	−	0.963773i	$-0.414059\pi$
$887$	−19.7723	−	17.8030i	−0.663888	−	0.597767i	−0.930613	+	0.366005i	$0.880725\pi$
$888$	1.89841	+	0.386396i	0.0637065	+	0.0129666i
$889$	−39.6383	+	6.27809i	−1.32943	+	0.210560i
$890$	48.1804	+	2.38582i	1.61501	+	0.0799728i
$891$	28.6998	−	5.35976i	0.961479	−	0.179559i
$892$	49.4812	−	8.12968i	1.65675	−	0.272202i
$893$	−0.133258	+	0.0593304i	−0.00445932	+	0.00198542i
$894$	−0.226243	+	2.21392i	−0.00756671	+	0.0740445i
$895$	2.65341	+	50.6301i	0.0886937	+	1.69238i
$896$	30.9450	−	0.624354i	1.03380	−	0.0208582i
$897$	−0.980092	−	2.39864i	−0.0327243	−	0.0800882i
$898$	−6.68926	+	0.0192780i	−0.223223	+	0.000643316i
$899$	25.0442	+	16.2639i	0.835272	+	0.542432i
$900$	−52.9011	+	59.4381i	−1.76337	+	1.98127i
$901$	−22.6694	−	13.0882i	−0.755227	−	0.436031i
$902$	−2.27444	+	1.95932i	−0.0757304	+	0.0652384i
$903$	3.63888	−	0.975035i	0.121094	−	0.0324471i
$904$	−39.4083	+	10.9255i	−1.31070	+	0.363376i
$905$	47.5862	−	24.2464i	1.58182	−	0.805976i
$906$	−0.941826	+	1.64220i	−0.0312901	+	0.0545585i
$907$	45.8537	+	20.4154i	1.52255	+	0.677882i	0.986115	−	0.166062i	$-0.0531052\pi$
$907$	45.8537	+	20.4154i	1.52255	+	0.677882i	0.536432	+	0.843944i	$0.319772\pi$
$908$	−1.10212	−	0.288514i	−0.0365752	−	0.00957468i
$909$	13.4883	−	4.38262i	0.447380	−	0.145362i
$910$	−53.9976	+	25.6287i	−1.79000	+	0.849582i
$911$	−13.4628	+	18.5300i	−0.446043	+	0.613926i	−0.971542	−	0.236869i	$-0.923879\pi$
$911$	−13.4628	+	18.5300i	−0.446043	+	0.613926i	0.525498	+	0.850795i	$0.323879\pi$
$912$	0.00897095	+	0.140227i	0.000297058	+	0.00464337i
$913$	−37.5634	−	39.4753i	−1.24317	−	1.30644i
$914$	29.2087	−	26.4525i	0.966139	−	0.874970i
$915$	0.245976	+	1.55303i	0.00813172	+	0.0513417i
$916$	−4.81492	−	3.85331i	−0.159089	−	0.127317i
$917$	9.36880	+	14.4267i	0.309385	+	0.476411i
$918$	3.73959	+	1.89186i	0.123425	+	0.0624408i
$919$	−14.3703	+	1.51038i	−0.474032	+	0.0498227i	−0.338532	−	0.940955i	$-0.609930\pi$
$919$	−14.3703	+	1.51038i	−0.474032	+	0.0498227i	−0.135499	+	0.990777i	$0.543264\pi$
$920$	5.63891	−	58.5128i	0.185909	−	1.92911i
$921$	2.36609	+	1.53656i	0.0779654	+	0.0506313i
$922$	−7.00742	−	9.58666i	−0.230777	−	0.315720i
$923$	−0.528389	−	0.871612i	−0.0173921	−	0.0286895i
$924$	−2.05688	−	1.73153i	−0.0676664	−	0.0569631i
$925$	−59.6561	−	15.9848i	−1.96148	−	0.525577i
$926$	6.46679	−	14.6380i	0.212512	−	0.481036i
$927$	−23.4498	−	26.0436i	−0.770192	−	0.855385i
$928$	17.0107	+	8.36087i	0.558405	+	0.274459i
$929$	−11.1000	−	8.98859i	−0.364179	−	0.294906i	0.429713	−	0.902966i	$-0.358615\pi$
$929$	−11.1000	−	8.98859i	−0.364179	−	0.294906i	−0.793891	+	0.608060i	$0.791948\pi$
$930$	4.37717	+	6.69791i	0.143533	+	0.219633i
$931$	−0.102298	−	0.0521237i	−0.00335270	−	0.00170828i
$932$	3.61009	+	32.5422i	0.118252	+	1.06596i
$933$	−0.294781	−	0.0309827i	−0.00965069	−	0.00101433i
$934$	−13.7565	+	21.3174i	−0.450127	+	0.697527i
$935$	30.8298	−	36.1971i	1.00824	−	1.18377i
$936$	−28.1030	−	11.5141i	−0.918574	−	0.376351i
$937$	−12.3065	−	8.94120i	−0.402036	−	0.292096i	0.368334	−	0.929694i	$-0.379928\pi$
$937$	−12.3065	−	8.94120i	−0.402036	−	0.292096i	−0.770370	+	0.637597i	$0.779928\pi$
$938$	−29.0745	−	35.6932i	−0.949317	−	1.16543i
$939$	−1.82623	−	1.64435i	−0.0595968	−	0.0536612i
$940$	−2.60981	+	4.58111i	−0.0851227	+	0.149419i
$941$	−3.50221	+	22.1121i	−0.114169	+	0.720834i	0.862496	+	0.506064i	$0.168900\pi$
$941$	−3.50221	+	22.1121i	−0.114169	+	0.720834i	−0.976665	+	0.214770i	$0.931100\pi$
$942$	−0.878068	+	0.237992i	−0.0286090	+	0.00775420i
$943$	−3.10018	−	0.162474i	−0.100956	−	0.00529087i
$944$	0.766626	+	1.46266i	0.0249515	+	0.0476054i
$945$	−5.19123	+	8.99148i	−0.168871	+	0.292493i
$946$	31.4940	−	30.1420i	1.02396	−	0.980001i
$947$	47.9370	+	12.8447i	1.55774	+	0.417396i	0.931949	−	0.362591i	$-0.118108\pi$
$947$	47.9370	+	12.8447i	1.55774	+	0.417396i	0.625796	+	0.779987i	$0.284774\pi$
$948$	−2.07452	+	0.687299i	−0.0673774	+	0.0223224i
$949$	−14.2809	−	15.1943i	−0.463579	−	0.493228i
$950$	−0.0129094	−	4.47942i	−0.000418837	−	0.145332i
$951$	1.15944	+	3.02044i	0.0375974	+	0.0979446i
$952$	5.60136	+	25.2758i	0.181541	+	0.819193i
$953$	−0.461470	+	2.17104i	−0.0149485	+	0.0703270i	−0.984990	−	0.172614i	$-0.944779\pi$
$953$	−0.461470	+	2.17104i	−0.0149485	+	0.0703270i	0.970041	+	0.242941i	$0.0781121\pi$
$954$	32.5297	−	5.24834i	1.05319	−	0.169921i
$955$	1.17421	+	0.450738i	0.0379966	+	0.0145855i
$956$	15.9249	−	42.2113i	0.515047	−	1.36521i
$957$	−0.632176	−	1.52033i	−0.0204354	−	0.0491453i
$958$	11.6189	−	10.5225i	0.375391	−	0.339967i
$959$	−0.710429	+	6.75928i	−0.0229409	+	0.218269i
$960$	3.26393	+	3.89108i	0.105343	+	0.125584i
$961$	−46.0559	+	14.9645i	−1.48567	+	0.482725i
$962$	−1.80446	−	23.5035i	−0.0581783	−	0.757784i
$963$	−10.3292	−	14.2170i	−0.332855	−	0.458136i
$964$	10.8012	−	16.8442i	0.347883	−	0.542514i
$965$	82.2009	−	17.4723i	2.64614	−	0.562454i
$966$	−0.298600	−	2.76433i	−0.00960731	−	0.0889410i
$967$	−32.7019	−	32.7019i	−1.05162	−	1.05162i	−0.998593	−	0.0530291i	$-0.983112\pi$
$967$	−32.7019	−	32.7019i	−1.05162	−	1.05162i	−0.0530291	−	0.998593i	$-0.516888\pi$
$968$	−30.5044	−	6.12199i	−0.980450	−	0.196768i
$969$	−0.113527	+	0.0304193i	−0.00364700	+	0.000977210i
$970$	30.3751	+	4.72124i	0.975285	+	0.151590i
$971$	−19.7810	+	17.8109i	−0.634803	+	0.571579i	−0.922430	−	0.386163i	$-0.873800\pi$
$971$	−19.7810	+	17.8109i	−0.634803	+	0.571579i	0.287628	+	0.957742i	$0.407133\pi$
$972$	−7.74008	+	1.69189i	−0.248263	+	0.0542674i
$973$	8.46896	+	22.0624i	0.271502	+	0.707288i
$974$	−2.87929	−	8.77540i	−0.0922583	−	0.281182i
$975$	−6.42667	−	3.10330i	−0.205818	−	0.0993851i
$976$	−9.90660	+	0.114206i	−0.317103	+	0.00365563i
$977$	26.9485	+	33.2786i	0.862159	+	1.06468i	0.997270	+	0.0738469i	$0.0235276\pi$
$977$	26.9485	+	33.2786i	0.862159	+	1.06468i	−0.135111	+	0.990830i	$0.543139\pi$
$978$	−1.70677	+	0.367929i	−0.0545764	+	0.0117651i
$979$	20.9250	−	16.1018i	0.668765	−	0.514615i
$980$	−4.09491	+	0.672787i	−0.130807	+	0.0214914i
$981$	−11.7873	+	30.7070i	−0.376340	+	0.980400i
$982$	5.69516	−	14.9652i	0.181740	−	0.477558i
$983$	−42.0369	−	21.4189i	−1.34077	−	0.683155i	−0.371332	−	0.928500i	$-0.621099\pi$
$983$	−42.0369	−	21.4189i	−1.34077	−	0.683155i	−0.969436	+	0.245345i	$0.921099\pi$
$984$	0.197763	−	0.181187i	0.00630445	−	0.00577603i
$985$	−41.7410	+	93.7518i	−1.32998	+	2.98718i
$986$	−4.05924	+	15.3258i	−0.129272	+	0.488073i
$987$	−0.0770616	+	0.237171i	−0.00245290	+	0.00754924i
$988$	1.61109	−	0.572269i	0.0512556	−	0.0182063i
$989$	45.0812			1.43350
$990$	−1.31252	+	59.8368i	−0.0417147	+	1.90174i
$991$	4.72100	−	2.72567i	0.149967	−	0.0865838i	−0.423139	−	0.906065i	$-0.639072\pi$
$991$	4.72100	−	2.72567i	0.149967	−	0.0865838i	0.573106	+	0.819481i	$0.305738\pi$
$992$	−45.7558	+	21.1670i	−1.45275	+	0.672052i
$993$	0.114341	+	0.224407i	0.00362851	+	0.00712136i
$994$	−0.286118	−	1.05563i	−0.00907512	−	0.0334825i
$995$	−89.0834	−	72.1383i	−2.82413	−	2.28694i
$996$	3.46236	+	3.42268i	0.109709	+	0.108452i
$997$	8.52545	+	1.81214i	0.270004	+	0.0573910i	0.340924	−	0.940091i	$-0.389260\pi$
$997$	8.52545	+	1.81214i	0.270004	+	0.0573910i	−0.0709201	+	0.997482i	$0.522594\pi$
$998$	−1.22557	+	11.9929i	−0.0387948	+	0.379629i
$999$	−2.57686	−	3.18216i	−0.0815282	−	0.100679i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bs.a.15.11	✓	1280
4.3	odd	2	inner	572.2.bs.a.15.57	yes	1280
11.3	even	5	inner	572.2.bs.a.223.45	yes	1280
13.7	odd	12	inner	572.2.bs.a.59.25	yes	1280
44.3	odd	10	inner	572.2.bs.a.223.25	yes	1280
52.7	even	12	inner	572.2.bs.a.59.45	yes	1280
143.124	odd	60	inner	572.2.bs.a.267.57	yes	1280
572.267	even	60	inner	572.2.bs.a.267.11	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bs.a.15.11	✓	1280	1.1	even	1	trivial
572.2.bs.a.15.57	yes	1280	4.3	odd	2	inner
572.2.bs.a.59.25	yes	1280	13.7	odd	12	inner
572.2.bs.a.59.45	yes	1280	52.7	even	12	inner
572.2.bs.a.223.25	yes	1280	44.3	odd	10	inner
572.2.bs.a.223.45	yes	1280	11.3	even	5	inner
572.2.bs.a.267.11	yes	1280	572.267	even	60	inner
572.2.bs.a.267.57	yes	1280	143.124	odd	60	inner

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31882 + 0.510612i) q^{2} +(-0.0308046 - 0.144924i) q^{3} +(1.47855 - 1.34681i) q^{4} +(0.670289 - 4.23204i) q^{5} +(0.114626 + 0.175399i) q^{6} +(2.29438 - 1.48999i) q^{7} +(-1.26224 + 2.53115i) q^{8} +(2.72058 - 1.21128i) q^{9} +O(q^{10})\)	\(q+(-1.31882 + 0.510612i) q^{2} +(-0.0308046 - 0.144924i) q^{3} +(1.47855 - 1.34681i) q^{4} +(0.670289 - 4.23204i) q^{5} +(0.114626 + 0.175399i) q^{6} +(2.29438 - 1.48999i) q^{7} +(-1.26224 + 2.53115i) q^{8} +(2.72058 - 1.21128i) q^{9} +(1.27694 + 5.92354i) q^{10} +(2.63401 + 2.01544i) q^{11} +(-0.240731 - 0.172790i) q^{12} +(-1.21985 + 3.39293i) q^{13} +(-2.26506 + 3.13656i) q^{14} +(-0.633974 + 0.0332252i) q^{15} +(0.372229 - 3.98264i) q^{16} +(3.32744 - 0.349728i) q^{17} +(-2.96945 + 2.98662i) q^{18} +(0.0124085 - 0.236769i) q^{19} +(-4.70868 - 7.16004i) q^{20} +(-0.286613 - 0.286613i) q^{21} +(-4.50288 - 1.31303i) q^{22} +(-2.42523 - 4.20062i) q^{23} +(0.405709 + 0.104958i) q^{24} +(-12.7056 - 4.12830i) q^{25} +(-0.123711 - 5.09752i) q^{26} +(-0.520613 - 0.716563i) q^{27} +(1.38564 - 5.29311i) q^{28} +(2.24205 - 2.49005i) q^{29} +(0.819130 - 0.367532i) q^{30} +(1.39416 + 8.80241i) q^{31} +(1.54268 + 5.44244i) q^{32} +(0.210946 - 0.443817i) q^{33} +(-4.20971 + 2.16026i) q^{34} +(-4.76779 - 10.7086i) q^{35} +(2.39116 - 5.45504i) q^{36} +(4.61665 - 0.241948i) q^{37} +(0.104532 + 0.318590i) q^{38} +(0.529295 + 0.0722682i) q^{39} +(9.86588 + 7.03847i) q^{40} +(0.348585 - 0.536773i) q^{41} +(0.524338 + 0.231642i) q^{42} +(-4.64711 + 8.04902i) q^{43} +(6.60892 - 0.567577i) q^{44} +(-3.30261 - 12.3255i) q^{45} +(5.34332 + 4.30150i) q^{46} +(-0.279313 - 0.548182i) q^{47} +(-0.588649 + 0.0687388i) q^{48} +(0.196962 - 0.442383i) q^{49} +(18.8643 - 1.04316i) q^{50} +(-0.153185 - 0.471455i) q^{51} +(2.76600 + 6.65952i) q^{52} +(-6.32952 - 4.59867i) q^{53} +(1.05248 + 0.679183i) q^{54} +(10.2950 - 9.79632i) q^{55} +(0.875325 + 7.68816i) q^{56} +(-0.0346958 + 0.00549528i) q^{57} +(-1.68541 + 4.42874i) q^{58} +(-0.346243 + 0.224853i) q^{59} +(-0.892615 + 0.902965i) q^{60} +(-0.258898 - 2.46325i) q^{61} +(-6.33326 - 10.8969i) q^{62} +(4.43726 - 6.83278i) q^{63} +(-4.81349 - 6.38986i) q^{64} +(13.5414 + 7.43670i) q^{65} +(-0.0515807 + 0.693025i) q^{66} +(-3.07969 + 11.4936i) q^{67} +(4.44878 - 4.99851i) q^{68} +(-0.534065 + 0.480874i) q^{69} +(11.7558 + 11.6882i) q^{70} +(-0.177905 + 0.219694i) q^{71} +(-0.368095 + 8.41514i) q^{72} +(-2.62559 + 5.15300i) q^{73} +(-5.96497 + 2.67640i) q^{74} +(-0.206900 + 1.96852i) q^{75} +(-0.300535 - 0.366787i) q^{76} +(9.04640 + 0.699530i) q^{77} +(-0.734944 + 0.174956i) q^{78} +(4.33496 - 5.96656i) q^{79} +(-16.6052 - 4.24481i) q^{80} +(5.89030 - 6.54184i) q^{81} +(-0.185636 + 0.885897i) q^{82} +(-16.2275 - 2.57018i) q^{83} +(-0.809785 - 0.0377601i) q^{84} +(0.750285 - 14.3163i) q^{85} +(2.01875 - 12.9880i) q^{86} +(-0.429935 - 0.248223i) q^{87} +(-8.42614 + 4.12312i) q^{88} +(2.06041 - 7.68956i) q^{89} +(10.6491 + 14.5687i) q^{90} +(2.25662 + 9.60223i) q^{91} +(-9.24326 - 2.94452i) q^{92} +(1.23274 - 0.473203i) q^{93} +(0.648271 + 0.580331i) q^{94} +(-0.993698 - 0.211217i) q^{95} +(0.741220 - 0.391225i) q^{96} +(1.81796 - 4.73596i) q^{97} +(-0.0338702 + 0.683993i) q^{98} +(9.60731 + 2.29263i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9}+O(q^{10}) \) 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9	\( 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9} - 48 q^{10} - 24 q^{13} - 40 q^{14} + 18 q^{16} - 36 q^{17} - 8 q^{18} + 18 q^{20} - 40 q^{21} - 10 q^{22} - 100 q^{24} - 44 q^{26} - 4 q^{28} - 12 q^{29} - 114 q^{30} - 92 q^{32} - 20 q^{33} + 36 q^{34} - 72 q^{36} - 24 q^{37} + 8 q^{40} + 26 q^{42} - 20 q^{44} - 80 q^{45} + 32 q^{46} + 30 q^{48} - 36 q^{49} - 78 q^{50} + 34 q^{52} - 80 q^{53} - 188 q^{54} - 48 q^{56} - 92 q^{58} + 20 q^{60} - 28 q^{61} + 42 q^{62} - 48 q^{65} + 204 q^{66} + 26 q^{68} - 36 q^{69} + 38 q^{70} - 136 q^{72} - 24 q^{73} - 6 q^{74} - 276 q^{76} - 156 q^{78} - 80 q^{80} + 60 q^{81} + 162 q^{82} - 108 q^{84} + 16 q^{85} - 88 q^{86} + 6 q^{88} - 64 q^{89} - 16 q^{92} + 64 q^{93} + 34 q^{94} + 114 q^{96} - 8 q^{97} - 24 q^{98}+O(q^{100}) \) 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9 - 48 * q^10 - 24 * q^13 - 40 * q^14 + 18 * q^16 - 36 * q^17 - 8 * q^18 + 18 * q^20 - 40 * q^21 - 10 * q^22 - 100 * q^24 - 44 * q^26 - 4 * q^28 - 12 * q^29 - 114 * q^30 - 92 * q^32 - 20 * q^33 + 36 * q^34 - 72 * q^36 - 24 * q^37 + 8 * q^40 + 26 * q^42 - 20 * q^44 - 80 * q^45 + 32 * q^46 + 30 * q^48 - 36 * q^49 - 78 * q^50 + 34 * q^52 - 80 * q^53 - 188 * q^54 - 48 * q^56 - 92 * q^58 + 20 * q^60 - 28 * q^61 + 42 * q^62 - 48 * q^65 + 204 * q^66 + 26 * q^68 - 36 * q^69 + 38 * q^70 - 136 * q^72 - 24 * q^73 - 6 * q^74 - 276 * q^76 - 156 * q^78 - 80 * q^80 + 60 * q^81 + 162 * q^82 - 108 * q^84 + 16 * q^85 - 88 * q^86 + 6 * q^88 - 64 * q^89 - 16 * q^92 + 64 * q^93 + 34 * q^94 + 114 * q^96 - 8 * q^97 - 24 * q^98

Introduction

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