LMFDB - Embedded newform 175.2.x.a.47.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(3,175)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("175.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([21, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			47.8
Character	$\chi$	$=$	175.47
Dual form			175.2.x.a.108.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0484513 + 0.924506i) q^{2} +(-1.02662 + 0.831339i) q^{3} +(1.13668 + 0.119470i) q^{4} +(1.84896 + 1.25752i) q^{5} +(-0.718837 - 0.989394i) q^{6} +(-0.0993238 - 2.64389i) q^{7} +(-0.455170 + 2.87383i) q^{8} +(-0.260915 + 1.22751i) q^{9} +(-1.25217 + 1.64845i) q^{10} +(0.769743 - 0.163614i) q^{11} +(-1.26626 + 0.822316i) q^{12} +(0.371838 - 0.729773i) q^{13} +(2.44910 + 0.0362743i) q^{14} +(-2.94360 + 0.246122i) q^{15} +(-0.398891 - 0.0847869i) q^{16} +(-6.94132 + 2.66452i) q^{17} +(-1.12220 - 0.300692i) q^{18} +(-0.192403 - 1.83059i) q^{19} +(1.95144 + 1.65029i) q^{20} +(2.29993 + 2.63169i) q^{21} +(0.113967 + 0.719560i) q^{22} +(4.08126 + 0.213890i) q^{23} +(-1.92184 - 3.32873i) q^{24} +(1.83730 + 4.65020i) q^{25} +(0.656664 + 0.379125i) q^{26} +(-2.55179 - 5.00818i) q^{27} +(0.202965 - 3.01712i) q^{28} +(5.50382 - 7.57536i) q^{29} +(-0.0849201 - 2.73330i) q^{30} +(1.92037 - 4.31323i) q^{31} +(-1.40844 + 5.25635i) q^{32} +(-0.654214 + 0.807887i) q^{33} +(-2.12705 - 6.54639i) q^{34} +(3.14109 - 5.01334i) q^{35} +(-0.443227 + 1.36411i) q^{36} +(-3.57509 - 5.50515i) q^{37} +(1.70171 - 0.0891829i) q^{38} +(0.224953 + 1.05832i) q^{39} +(-4.45549 + 4.74122i) q^{40} +(2.40999 - 0.783055i) q^{41} +(-2.54445 + 1.99879i) q^{42} +(1.79811 - 1.79811i) q^{43} +(0.894499 - 0.0940156i) q^{44} +(-2.02603 + 1.94151i) q^{45} +(-0.395485 + 3.76279i) q^{46} +(4.12878 - 10.7558i) q^{47} +(0.479996 - 0.244570i) q^{48} +(-6.98027 + 0.525202i) q^{49} +(-4.38815 + 1.47329i) q^{50} +(4.91096 - 8.50604i) q^{51} +(0.509847 - 0.785095i) q^{52} +(5.66273 + 6.99289i) q^{53} +(4.75373 - 2.11650i) q^{54} +(1.62897 + 0.665450i) q^{55} +(7.64330 + 0.917979i) q^{56} +(1.71936 + 1.71936i) q^{57} +(6.73680 + 5.45535i) q^{58} +(-7.62729 + 8.47097i) q^{59} +(-3.37533 - 0.0719093i) q^{60} +(-6.28292 + 5.65717i) q^{61} +(3.89456 + 1.98438i) q^{62} +(3.27131 + 0.567908i) q^{63} +(-5.56698 - 1.80882i) q^{64} +(1.60522 - 0.881728i) q^{65} +(-0.715198 - 0.643968i) q^{66} +(0.327283 + 0.852602i) q^{67} +(-8.20839 + 2.19943i) q^{68} +(-4.36771 + 3.17333i) q^{69} +(4.48267 + 3.14686i) q^{70} +(0.767293 + 0.557471i) q^{71} +(-3.40889 - 1.30855i) q^{72} +(-3.11233 - 2.02117i) q^{73} +(5.26276 - 3.03846i) q^{74} +(-5.75210 - 3.24656i) q^{75} -2.10378i q^{76} +(-0.509031 - 2.01886i) q^{77} +(-0.989324 + 0.156693i) q^{78} +(-1.98946 - 4.46840i) q^{79} +(-0.630913 - 0.658380i) q^{80} +(3.34390 + 1.48880i) q^{81} +(0.607171 + 2.26599i) q^{82} +(-5.14074 - 0.814213i) q^{83} +(2.29988 + 3.26616i) q^{84} +(-16.1849 - 3.80224i) q^{85} +(1.57524 + 1.74948i) q^{86} +(0.647369 + 12.3525i) q^{87} +(0.119835 + 2.28659i) q^{88} +(0.386903 + 0.429700i) q^{89} +(-1.69677 - 1.96715i) q^{90} +(-1.96637 - 0.910613i) q^{91} +(4.61354 + 0.730712i) q^{92} +(1.61426 + 6.02451i) q^{93} +(9.74379 + 4.33822i) q^{94} +(1.94625 - 3.62663i) q^{95} +(-2.92389 - 6.56715i) q^{96} +(10.5745 - 1.67483i) q^{97} +(-0.147349 - 6.47875i) q^{98} +0.987555i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{20}\right)$

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 $

$2$	−0.0484513	+	0.924506i	−0.0342602	+	0.653724i	0.926492	+	0.376315i	$0.122809\pi$
$2$	−0.0484513	+	0.924506i	−0.0342602	+	0.653724i	−0.960752	+	0.277409i	$0.910524\pi$
$3$	−1.02662	+	0.831339i	−0.592718	+	0.479974i	−0.878124	−	0.478433i	$-0.841205\pi$
$3$	−1.02662	+	0.831339i	−0.592718	+	0.479974i	0.285406	+	0.958407i	$0.407872\pi$
$4$	1.13668	+	0.119470i	0.568340	+	0.0597349i
$5$	1.84896	+	1.25752i	0.826880	+	0.562379i
$5$	1.84896	+	1.25752i	0.826880	+	0.562379i
$6$	−0.718837	−	0.989394i	−0.293464	−	0.403918i
$7$	−0.0993238	−	2.64389i	−0.0375409	−	0.999295i
$7$	−0.0993238	−	2.64389i	−0.0375409	−	0.999295i
$8$	−0.455170	+	2.87383i	−0.160927	+	1.01605i
$9$	−0.260915	+	1.22751i	−0.0869716	+	0.409169i
$10$	−1.25217	+	1.64845i	−0.395970	+	0.521284i
$11$	0.769743	−	0.163614i	0.232086	−	0.0493315i	−0.0904002	−	0.995906i	$-0.528815\pi$
$11$	0.769743	−	0.163614i	0.232086	−	0.0493315i	0.322487	+	0.946574i	$0.395481\pi$
$12$	−1.26626	+	0.822316i	−0.365537	+	0.237382i
$13$	0.371838	−	0.729773i	0.103129	−	0.202403i	−0.833676	−	0.552254i	$-0.813768\pi$
$13$	0.371838	−	0.729773i	0.103129	−	0.202403i	0.936805	+	0.349851i	$0.113768\pi$
$14$	2.44910	+	0.0362743i	0.654550	+	0.00969470i
$15$	−2.94360	+	0.246122i	−0.760034	+	0.0635484i
$16$	−0.398891	−	0.0847869i	−0.0997228	−	0.0211967i
$17$	−6.94132	+	2.66452i	−1.68352	+	0.646242i	−0.996744	−	0.0806290i	$-0.974307\pi$
$17$	−6.94132	+	2.66452i	−1.68352	+	0.646242i	−0.686774	+	0.726871i	$0.740974\pi$
$18$	−1.12220	−	0.300692i	−0.264504	−	0.0708737i
$19$	−0.192403	−	1.83059i	−0.0441402	−	0.419966i	−0.994171	−	0.107811i	$-0.965616\pi$
$19$	−0.192403	−	1.83059i	−0.0441402	−	0.419966i	0.950031	−	0.312155i	$-0.101051\pi$
$20$	1.95144	+	1.65029i	0.436355	+	0.369016i
$21$	2.29993	+	2.63169i	0.501887	+	0.574282i
$22$	0.113967	+	0.719560i	0.0242979	+	0.153411i
$23$	4.08126	+	0.213890i	0.851002	+	0.0445991i	0.472848	−	0.881144i	$-0.343226\pi$
$23$	4.08126	+	0.213890i	0.851002	+	0.0445991i	0.378154	+	0.925743i	$0.376559\pi$
$24$	−1.92184	−	3.32873i	−0.392294	−	0.679474i
$25$	1.83730	+	4.65020i	0.367460	+	0.930039i
$26$	0.656664	+	0.379125i	0.128782	+	0.0743525i
$27$	−2.55179	−	5.00818i	−0.491093	−	0.963824i
$28$	0.202965	−	3.01712i	0.0383569	−	0.570182i
$29$	5.50382	−	7.57536i	1.02203	−	1.40671i	0.111266	−	0.993791i	$-0.464509\pi$
$29$	5.50382	−	7.57536i	1.02203	−	1.40671i	0.910768	−	0.412919i	$-0.135491\pi$
$30$	−0.0849201	−	2.73330i	−0.0155042	−	0.499030i
$31$	1.92037	−	4.31323i	0.344909	−	0.774678i	−0.654911	−	0.755706i	$-0.727294\pi$
$31$	1.92037	−	4.31323i	0.344909	−	0.774678i	0.999820	−	0.0189722i	$-0.00603941\pi$
$32$	−1.40844	+	5.25635i	−0.248979	+	0.929201i
$33$	−0.654214	+	0.807887i	−0.113884	+	0.140635i
$34$	−2.12705	−	6.54639i	−0.364786	−	1.12270i
$35$	3.14109	−	5.01334i	0.530941	−	0.847409i
$36$	−0.443227	+	1.36411i	−0.0738712	+	0.227352i
$37$	−3.57509	−	5.50515i	−0.587740	−	0.905041i	0.412241	−	0.911075i	$-0.364746\pi$
$37$	−3.57509	−	5.50515i	−0.587740	−	0.905041i	−0.999982	+	0.00603374i	$0.998079\pi$
$38$	1.70171	−	0.0891829i	0.276054	−	0.0144674i
$39$	0.224953	+	1.05832i	0.0360213	+	0.169467i
$40$	−4.45549	+	4.74122i	−0.704474	+	0.749652i
$41$	2.40999	−	0.783055i	0.376378	−	0.122293i	−0.114718	−	0.993398i	$-0.536596\pi$
$41$	2.40999	−	0.783055i	0.376378	−	0.122293i	0.491096	+	0.871106i	$0.336596\pi$
$42$	−2.54445	+	1.99879i	−0.392617	+	0.308420i
$43$	1.79811	−	1.79811i	0.274209	−	0.274209i	−0.556583	−	0.830792i	$-0.687888\pi$
$43$	1.79811	−	1.79811i	0.274209	−	0.274209i	0.830792	+	0.556583i	$0.187888\pi$
$44$	0.894499	−	0.0940156i	0.134851	−	0.0141734i
$45$	−2.02603	+	1.94151i	−0.302023	+	0.289423i
$46$	−0.395485	+	3.76279i	−0.0583111	+	0.554793i
$47$	4.12878	−	10.7558i	0.602244	−	1.56890i	−0.205050	−	0.978751i	$-0.565736\pi$
$47$	4.12878	−	10.7558i	0.602244	−	1.56890i	0.807294	−	0.590149i	$-0.200931\pi$
$48$	0.479996	−	0.244570i	0.0692814	−	0.0353006i
$49$	−6.98027	+	0.525202i	−0.997181	+	0.0750288i
$50$	−4.38815	+	1.47329i	−0.620579	+	0.208354i
$51$	4.91096	−	8.50604i	0.687673	−	1.19108i
$52$	0.509847	−	0.785095i	0.0707030	−	0.108873i
$53$	5.66273	+	6.99289i	0.777836	+	0.960547i	0.999895	−	0.0144862i	$-0.00461127\pi$
$53$	5.66273	+	6.99289i	0.777836	+	0.960547i	−0.222060	+	0.975033i	$0.571278\pi$
$54$	4.75373	−	2.11650i	0.646900	−	0.288019i
$55$	1.62897	+	0.665450i	0.219650	+	0.0897292i
$56$	7.64330	+	0.917979i	1.02138	+	0.122670i
$57$	1.71936	+	1.71936i	0.227735	+	0.227735i
$58$	6.73680	+	5.45535i	0.884585	+	0.716323i
$59$	−7.62729	+	8.47097i	−0.992989	+	1.10283i	0.00171029	+	0.999999i	$0.499456\pi$
$59$	−7.62729	+	8.47097i	−0.992989	+	1.10283i	−0.994699	+	0.102827i	$0.967211\pi$
$60$	−3.37533	−	0.0719093i	−0.435754	−	0.00928345i
$61$	−6.28292	+	5.65717i	−0.804446	+	0.724326i	−0.964872	−	0.262722i	$-0.915380\pi$
$61$	−6.28292	+	5.65717i	−0.804446	+	0.724326i	0.160426	+	0.987048i	$0.448713\pi$
$62$	3.89456	+	1.98438i	0.494609	+	0.252016i
$63$	3.27131	+	0.567908i	0.412146	+	0.0715497i
$64$	−5.56698	−	1.80882i	−0.695872	−	0.226103i
$65$	1.60522	−	0.881728i	0.199102	−	0.109365i
$66$	−0.715198	−	0.643968i	−0.0880348	−	0.0792669i
$67$	0.327283	+	0.852602i	0.0399840	+	0.104162i	0.952119	−	0.305729i	$-0.0989001\pi$
$67$	0.327283	+	0.852602i	0.0399840	+	0.104162i	−0.912135	+	0.409891i	$0.865567\pi$
$68$	−8.20839	+	2.19943i	−0.995414	+	0.266720i
$69$	−4.36771	+	3.17333i	−0.525811	+	0.382024i
$70$	4.48267	+	3.14686i	0.535782	+	0.376121i
$71$	0.767293	+	0.557471i	0.0910610	+	0.0661597i	0.632384	−	0.774655i	$-0.282076\pi$
$71$	0.767293	+	0.557471i	0.0910610	+	0.0661597i	−0.541323	+	0.840815i	$0.682076\pi$
$72$	−3.40889	−	1.30855i	−0.401742	−	0.154214i
$73$	−3.11233	−	2.02117i	−0.364270	−	0.236560i	0.349505	−	0.936934i	$-0.386350\pi$
$73$	−3.11233	−	2.02117i	−0.364270	−	0.236560i	−0.713776	+	0.700374i	$0.753016\pi$
$74$	5.26276	−	3.03846i	0.611783	−	0.353213i
$75$	−5.75210	−	3.24656i	−0.664195	−	0.374880i
$76$		−	2.10378i		−	0.241320i
$77$	−0.509031	−	2.01886i	−0.0580094	−	0.230071i
$78$	−0.989324	+	0.156693i	−0.112019	+	0.0177420i
$79$	−1.98946	−	4.46840i	−0.223832	−	0.502735i	0.766366	−	0.642404i	$-0.222063\pi$
$79$	−1.98946	−	4.46840i	−0.223832	−	0.502735i	−0.990198	+	0.139669i	$0.955396\pi$
$80$	−0.630913	−	0.658380i	−0.0705382	−	0.0736091i
$81$	3.34390	+	1.48880i	0.371544	+	0.165422i
$82$	0.607171	+	2.26599i	0.0670509	+	0.250237i
$83$	−5.14074	−	0.814213i	−0.564269	−	0.0893715i	−0.132218	−	0.991221i	$-0.542210\pi$
$83$	−5.14074	−	0.814213i	−0.564269	−	0.0893715i	−0.432051	+	0.901849i	$0.642210\pi$
$84$	2.29988	+	3.26616i	0.250938	+	0.356367i
$85$	−16.1849	−	3.80224i	−1.75550	−	0.412410i
$86$	1.57524	+	1.74948i	0.169863	+	0.188652i
$87$	0.647369	+	12.3525i	0.0694053	+	1.32433i
$88$	0.119835	+	2.28659i	0.0127744	+	0.243751i
$89$	0.386903	+	0.429700i	0.0410117	+	0.0455481i	0.763302	−	0.646042i	$-0.223577\pi$
$89$	0.386903	+	0.429700i	0.0410117	+	0.0455481i	−0.722290	+	0.691590i	$0.756910\pi$
$90$	−1.69677	−	1.96715i	−0.178855	−	0.207356i
$91$	−1.96637	−	0.910613i	−0.206132	−	0.0954582i
$92$	4.61354	+	0.730712i	0.480994	+	0.0761820i
$93$	1.61426	+	6.02451i	0.167391	+	0.624713i
$94$	9.74379	+	4.33822i	1.00500	+	0.447453i
$95$	1.94625	−	3.62663i	0.199681	−	0.372085i
$96$	−2.92389	−	6.56715i	−0.298418	−	0.670257i
$97$	10.5745	−	1.67483i	1.07368	−	0.170054i	0.405529	−	0.914082i	$-0.367087\pi$
$97$	10.5745	−	1.67483i	1.07368	−	0.170054i	0.668148	+	0.744029i	$0.267087\pi$
$98$	−0.147349	−	6.47875i	−0.0148845	−	0.654452i
$99$			0.987555i			0.0992530i
$100$	1.53287	+	5.50529i	0.153287	+	0.550529i
$101$	−5.47339	+	3.16006i	−0.544622	+	0.314438i	−0.746950	−	0.664880i	$-0.768483\pi$
$101$	−5.47339	+	3.16006i	−0.544622	+	0.314438i	0.202328	+	0.979318i	$0.435149\pi$
$102$	7.62594	+	4.95234i	0.755081	+	0.490355i
$103$	9.24375	+	3.54834i	0.910814	+	0.349629i	0.768245	−	0.640156i	$-0.221130\pi$
$103$	9.24375	+	3.54834i	0.910814	+	0.349629i	0.142569	+	0.989785i	$0.454464\pi$
$104$	1.92800	+	1.40077i	0.189056	+	0.137357i
$105$	0.943088	+	7.75809i	0.0920360	+	0.757112i
$106$	−6.73933	+	4.89641i	−0.654582	+	0.475581i
$107$	−5.25791	+	1.40885i	−0.508302	+	0.136199i	−0.503850	−	0.863791i	$-0.668084\pi$
$107$	−5.25791	+	1.40885i	−0.508302	+	0.136199i	−0.00445150	+	0.999990i	$0.501417\pi$
$108$	−2.30225	−	5.99756i	−0.221534	−	0.577115i
$109$	−12.1845	−	10.9709i	−1.16706	−	1.05083i	−0.997869	−	0.0652420i	$-0.979218\pi$
$109$	−12.1845	−	10.9709i	−1.16706	−	1.05083i	−0.169190	−	0.985583i	$-0.554115\pi$
$110$	−0.694138	+	1.47375i	−0.0661835	+	0.140517i
$111$	8.24689	+	2.67958i	0.782760	+	0.254334i
$112$	−0.184548	+	1.06304i	−0.0174381	+	0.100448i
$113$	8.36368	+	4.26151i	0.786789	+	0.400889i	0.800739	−	0.599014i	$-0.204441\pi$
$113$	8.36368	+	4.26151i	0.786789	+	0.400889i	−0.0139501	+	0.999903i	$0.504441\pi$
$114$	−1.67287	+	1.50626i	−0.156678	+	0.141074i
$115$	7.27712	+	5.52773i	0.678595	+	0.515464i
$116$	7.16111	−	7.95322i	0.664893	−	0.738438i
$117$	0.798784	+	0.646843i	0.0738476	+	0.0598006i
$118$	−7.46191	−	7.46191i	−0.686924	−	0.686924i
$119$	7.73414	+	18.0874i	0.708987	+	1.65807i
$120$	0.632525	−	8.57143i	0.0577414	−	0.782461i
$121$	−9.48326	+	4.22222i	−0.862115	+	0.383838i
$122$	−4.92567	−	6.08270i	−0.445949	−	0.550701i
$123$	−1.82316	+	2.80742i	−0.164389	+	0.253137i
$124$	2.69815	−	4.67333i	0.242301	−	0.419678i
$125$	−2.45061	+	10.9085i	−0.219189	+	0.975682i
$126$	−0.683534	+	2.99683i	−0.0608940	+	0.266979i
$127$	2.59888	−	1.32420i	0.230613	−	0.117503i	−0.334866	−	0.942266i	$-0.608691\pi$
$127$	2.59888	−	1.32420i	0.230613	−	0.117503i	0.565480	+	0.824762i	$0.308691\pi$
$128$	−1.95833	+	5.10161i	−0.173093	+	0.450923i
$129$	−0.351133	+	3.34081i	−0.0309156	+	0.294142i
$130$	0.737388	+	1.52675i	0.0646732	+	0.133905i
$131$	−6.69495	+	0.703668i	−0.584941	+	0.0614797i	−0.392377	−	0.919805i	$-0.628347\pi$
$131$	−6.69495	+	0.703668i	−0.584941	+	0.0614797i	−0.192564	+	0.981284i	$0.561680\pi$
$132$	−0.840150	+	0.840150i	−0.0731256	+	0.0731256i
$133$	−4.82076	+	0.690511i	−0.418013	+	0.0598749i
$134$	−0.804093	+	0.261266i	−0.0694631	+	0.0225699i
$135$	1.57971	−	12.4688i	0.135959	−	1.07315i
$136$	−4.49791	−	21.1610i	−0.385693	−	1.81454i
$137$	−19.4502	+	1.01934i	−1.66175	+	0.0870884i	−0.859907	−	0.510451i	$-0.829479\pi$
$137$	−19.4502	+	1.01934i	−1.66175	+	0.0870884i	−0.801840	+	0.597539i	$0.796145\pi$
$138$	−2.72214	−	4.19173i	−0.231724	−	0.356824i
$139$	0.317252	−	0.976401i	0.0269090	−	0.0828172i	−0.936700	−	0.350133i	$-0.886137\pi$
$139$	0.317252	−	0.976401i	0.0269090	−	0.0828172i	0.963609	+	0.267315i	$0.0861365\pi$
$140$	4.16935	−	5.32330i	0.352375	−	0.449901i
$141$	4.70307	+	14.4746i	0.396070	+	1.21898i
$142$	−0.552562	+	0.682357i	−0.0463700	+	0.0572621i
$143$	0.166819	−	0.622576i	0.0139501	−	0.0520624i
$144$	0.208153	−	0.467520i	0.0173461	−	0.0389600i
$145$	19.7025	−	7.08538i	1.63620	−	0.588409i
$146$	2.01938	−	2.77944i	0.167125	−	0.230028i
$147$	6.72945	−	6.34215i	0.555036	−	0.523092i
$148$	−3.40603	−	6.68471i	−0.279974	−	0.549480i
$149$	9.86165	+	5.69362i	0.807897	+	0.466440i	0.846225	−	0.532825i	$-0.178870\pi$
$149$	9.86165	+	5.69362i	0.807897	+	0.466440i	−0.0383277	+	0.999265i	$0.512203\pi$
$150$	3.28016	−	5.16055i	0.267824	−	0.421357i
$151$	−5.54607	−	9.60607i	−0.451333	−	0.781731i	0.547136	−	0.837043i	$-0.315718\pi$
$151$	−5.54607	−	9.60607i	−0.451333	−	0.781731i	−0.998469	+	0.0553124i	$0.982385\pi$
$152$	5.34838	+	0.280297i	0.433811	+	0.0227351i
$153$	−1.45963	−	9.21574i	−0.118004	−	0.745049i
$154$	1.89111	−	0.372785i	0.152390	−	0.0300399i
$155$	8.97464	−	5.56008i	0.720861	−	0.446596i
$156$	0.129262	+	1.22985i	0.0103493	+	0.0984667i
$157$	16.1035	+	4.31493i	1.28520	+	0.344369i	0.835836	−	0.548979i	$-0.184983\pi$
$157$	16.1035	+	4.31493i	1.28520	+	0.344369i	0.449365	+	0.893348i	$0.351650\pi$
$158$	4.22746	−	1.62277i	0.336319	−	0.129101i
$159$	−11.6269	−	2.47138i	−0.922075	−	0.195993i
$160$	−9.21409	+	7.94765i	−0.728438	+	0.628317i
$161$	0.160134	−	10.8116i	0.0126203	−	0.852076i
$162$	−1.53842	+	3.01932i	−0.120870	+	0.237220i
$163$	−17.2516	+	11.2033i	−1.35125	+	0.877510i	−0.998309	−	0.0581372i	$-0.981484\pi$
$163$	−17.2516	+	11.2033i	−1.35125	+	0.877510i	−0.352938	+	0.935647i	$0.614817\pi$
$164$	2.83294	−	0.602161i	0.221216	−	0.0470209i
$165$	−2.22555	+	0.671065i	−0.173258	+	0.0522423i
$166$	1.00182	−	4.71319i	0.0777563	−	0.365815i
$167$	0.739956	−	4.67190i	0.0572595	−	0.361522i	−0.942377	−	0.334553i	$-0.891415\pi$
$167$	0.739956	−	4.67190i	0.0572595	−	0.361522i	0.999636	−	0.0269687i	$-0.00858546\pi$
$168$	−8.60990	+	5.41176i	−0.664268	+	0.417526i
$169$	7.24690	+	9.97451i	0.557454	+	0.767270i
$170$	4.29937	−	14.7788i	0.329747	−	1.13348i
$171$	2.29726	+	0.241452i	0.175676	+	0.0184643i
$172$	2.25870	−	1.82906i	0.172224	−	0.139464i
$173$	0.264149	−	5.04027i	0.0200829	−	0.383204i	−0.970035	−	0.242966i	$-0.921880\pi$
$173$	0.264149	−	5.04027i	0.0200829	−	0.383204i	0.990118	−	0.140239i	$-0.0447869\pi$
$174$	−11.4514			−0.868126
$175$	12.1121	−	5.31949i	0.915589	−	0.402116i
$176$	−0.320916			−0.0241900
$177$	0.788072	−	15.0373i	0.0592351	−	1.13027i
$178$	−0.416006	+	0.336875i	−0.0311810	+	0.0252498i
$179$	3.59011	+	0.377335i	0.268337	+	0.0282034i	0.237741	−	0.971328i	$-0.423593\pi$
$179$	3.59011	+	0.377335i	0.268337	+	0.0282034i	0.0305957	+	0.999532i	$0.490260\pi$
$180$	−2.53490	+	1.96482i	−0.188941	+	0.146449i
$181$	7.29441	+	10.0399i	0.542189	+	0.746259i	0.988927	−	0.148406i	$-0.0474142\pi$
$181$	7.29441	+	10.0399i	0.542189	+	0.746259i	−0.446737	+	0.894665i	$0.647414\pi$
$182$	0.937141	−	1.77380i	0.0694655	−	0.131483i
$183$	1.74714	−	11.0310i	0.129152	−	0.815434i
$184$	−2.47235	+	11.6315i	−0.182264	+	0.857486i
$185$	0.312631	−	14.6745i	0.0229851	−	1.07889i
$186$	−5.64791	+	1.20050i	−0.414125	+	0.0880250i
$187$	−4.90708	+	3.18670i	−0.358841	+	0.233034i
$188$	5.97810	−	11.7327i	0.435998	−	0.855694i
$189$	−12.9876	+	7.24408i	−0.944709	+	0.526930i
$190$	3.25854	+	1.97504i	0.236400	+	0.143284i
$191$	−22.6901	−	4.82293i	−1.64180	−	0.348975i	−0.707845	−	0.706367i	$-0.750333\pi$
$191$	−22.6901	−	4.82293i	−1.64180	−	0.348975i	−0.933954	+	0.357392i	$0.883666\pi$
$192$	7.21890	−	2.77108i	0.520979	−	0.199985i
$193$	14.4367	+	3.86831i	1.03918	+	0.278447i	0.737773	−	0.675049i	$-0.235877\pi$
$193$	14.4367	+	3.86831i	1.03918	+	0.278447i	0.301406	+	0.953496i	$0.402544\pi$
$194$	1.03605	+	9.85732i	0.0743838	+	0.707715i
$195$	−0.914928	+	2.23968i	−0.0655194	+	0.160387i
$196$	−7.99708	−	0.236946i	−0.571220	−	0.0169247i
$197$	−0.235850	−	1.48910i	−0.0168036	−	0.106094i	0.977861	−	0.209256i	$-0.0671040\pi$
$197$	−0.235850	−	1.48910i	−0.0168036	−	0.106094i	−0.994665	+	0.103162i	$0.967104\pi$
$198$	−0.913001	−	0.0478483i	−0.0648841	−	0.00340043i
$199$	1.75472	+	3.03927i	0.124389	+	0.215448i	0.921494	−	0.388393i	$-0.126970\pi$
$199$	1.75472	+	3.03927i	0.124389	+	0.215448i	−0.797105	+	0.603841i	$0.793636\pi$
$200$	−14.2002	+	3.16346i	−1.00410	+	0.223691i
$201$	−1.04480	−	0.603214i	−0.0736943	−	0.0425474i
$202$	−2.65630	−	5.21329i	−0.186897	−	0.366806i
$203$	−20.5751	−	13.7991i	−1.44409	−	0.968505i
$204$	6.59841	−	9.08193i	0.461981	−	0.635863i
$205$	5.44069	+	1.58277i	0.379994	+	0.110546i
$206$	−3.72834	+	8.37398i	−0.259766	+	0.583443i
$207$	−1.32741	+	4.95398i	−0.0922616	+	0.344325i
$208$	−0.210198	+	0.259573i	−0.0145746	+	0.0179982i
$209$	−0.447610	−	1.37760i	−0.0309619	−	0.0952908i
$210$	−7.21810	+	0.496001i	−0.498096	+	0.0342273i
$211$	−6.16756	+	18.9818i	−0.424593	+	1.30676i	0.478791	+	0.877929i	$0.341075\pi$
$211$	−6.16756	+	18.9818i	−0.424593	+	1.30676i	−0.903384	+	0.428833i	$0.858925\pi$
$212$	5.60127	+	8.62520i	0.384697	+	0.592381i
$213$	−1.25116	+	0.0655708i	−0.0857284	+	0.00449283i
$214$	−1.04774	−	4.92923i	−0.0716221	−	0.336955i
$215$	5.58579	−	1.06348i	0.380948	−	0.0725286i
$216$	15.5542	−	5.05385i	1.05833	−	0.343871i
$217$	−11.5944	−	4.64884i	−0.787080	−	0.315584i
$218$	10.7331	−	10.7331i	0.726934	−	0.726934i
$219$	4.87545	−	0.512430i	0.329452	−	0.0346268i
$220$	1.77212	+	0.951017i	0.119476	+	0.0641175i
$221$	−0.636549	+	6.05636i	−0.0428189	+	0.407395i
$222$	−2.87686	+	7.49447i	−0.193082	+	0.502996i
$223$	−7.80285	+	3.97575i	−0.522518	+	0.266236i	−0.695294	−	0.718725i	$-0.744726\pi$
$223$	−7.80285	+	3.97575i	−0.522518	+	0.266236i	0.172777	+	0.984961i	$0.444726\pi$
$224$	14.0371	+	3.20166i	0.937893	+	0.213920i
$225$	−6.18753	+	1.04200i	−0.412502	+	0.0694664i
$226$	−4.34502	+	7.52579i	−0.289026	+	0.500608i
$227$	−5.11458	+	7.87576i	−0.339467	+	0.522733i	−0.966637	−	0.256149i	$-0.917546\pi$
$227$	−5.11458	+	7.87576i	−0.339467	+	0.522733i	0.627171	+	0.778882i	$0.284213\pi$
$228$	1.74895	+	2.15978i	0.115827	+	0.143035i
$229$	7.85820	−	3.49870i	0.519285	−	0.231200i	−0.130321	−	0.991472i	$-0.541601\pi$
$229$	7.85820	−	3.49870i	0.519285	−	0.231200i	0.649606	+	0.760271i	$0.274934\pi$
$230$	−5.46301	+	6.45991i	−0.360220	+	0.425954i
$231$	2.20094	+	1.64942i	0.144811	+	0.108524i
$232$	19.2651	+	19.2651i	1.26482	+	1.26482i
$233$	2.16487	+	1.75308i	0.141825	+	0.114848i	0.697608	−	0.716480i	$-0.254248\pi$
$233$	2.16487	+	1.75308i	0.141825	+	0.114848i	−0.555782	+	0.831328i	$0.687581\pi$
$234$	−0.636712	+	0.707140i	−0.0416232	+	0.0462272i
$235$	21.1596	−	14.6951i	1.38030	−	0.958602i
$236$	−9.68182	+	8.71755i	−0.630233	+	0.567464i
$237$	5.75718	+	2.93343i	0.373969	+	0.190547i
$238$	−17.0967	+	6.27390i	−1.10821	+	0.406676i
$239$	−10.2364	−	3.32600i	−0.662136	−	0.215141i	−0.0413782	−	0.999144i	$-0.513175\pi$
$239$	−10.2364	−	3.32600i	−0.662136	−	0.215141i	−0.620757	+	0.784003i	$0.713175\pi$
$240$	1.19504	+	0.151403i	0.0771397	+	0.00977300i
$241$	7.84239	+	7.06132i	0.505173	+	0.454860i	0.881881	−	0.471472i	$-0.156277\pi$
$241$	7.84239	+	7.06132i	0.505173	+	0.454860i	−0.376708	+	0.926332i	$0.622944\pi$
$242$	−3.44399	−	8.97191i	−0.221388	−	0.576736i
$243$	11.6172	−	3.11283i	0.745247	−	0.199688i
$244$	−7.81753	+	5.67977i	−0.500466	+	0.363610i
$245$	−13.5667	−	7.80673i	−0.866744	−	0.498754i
$246$	−2.50714	−	1.82155i	−0.159850	−	0.116137i
$247$	−1.40746	−	0.540272i	−0.0895543	−	0.0343767i
$248$	11.5214	+	7.48208i	0.731609	+	0.475113i
$249$	5.95446	−	3.43781i	0.377349	−	0.217862i
$250$	−9.96620	−	2.79413i	−0.630318	−	0.176716i
$251$			29.0617i			1.83436i	0.398477	+	0.917178i	$0.369539\pi$
$251$			29.0617i			1.83436i	−0.398477	+	0.917178i	$0.630461\pi$
$252$	3.65058	+	1.03635i	0.229965	+	0.0652841i
$253$	3.17652	−	0.503111i	0.199706	−	0.0316303i
$254$	1.09831	+	2.46684i	0.0689140	+	0.154783i
$255$	19.7767	−	9.55170i	1.23846	−	0.598151i
$256$	−15.3164	−	6.81930i	−0.957275	−	0.426206i
$257$	4.81832	+	17.9822i	0.300559	+	1.12170i	0.936701	+	0.350129i	$0.113862\pi$
$257$	4.81832	+	17.9822i	0.300559	+	1.12170i	−0.636143	+	0.771571i	$0.719471\pi$
$258$	−3.07159	−	0.486492i	−0.191229	−	0.0302876i
$259$	−14.1999	+	9.99891i	−0.882339	+	0.621302i
$260$	1.92996	−	0.810468i	0.119691	−	0.0502631i
$261$	7.86279	+	8.73251i	0.486694	+	0.540529i
$262$	−0.326166	−	6.22362i	−0.0201506	−	0.384496i
$263$	−1.08421	−	20.6879i	−0.0668552	−	1.27567i	−0.801819	−	0.597567i	$-0.796134\pi$
$263$	−1.08421	−	20.6879i	−0.0668552	−	1.27567i	0.734964	−	0.678106i	$-0.237199\pi$
$264$	−2.02395	−	2.24783i	−0.124566	−	0.138344i
$265$	1.67648	+	20.0505i	0.102985	+	1.23169i
$266$	−0.404810	−	4.49027i	−0.0248205	−	0.275316i
$267$	−0.754428	−	0.119490i	−0.0461702	−	0.00731265i
$268$	0.270156	+	1.00824i	0.0165024	+	0.0615879i
$269$	1.17313	+	0.522309i	0.0715267	+	0.0318458i	0.442188	−	0.896922i	$-0.354202\pi$
$269$	1.17313	+	0.522309i	0.0715267	+	0.0318458i	−0.370661	+	0.928768i	$0.620869\pi$
$270$	11.4510	+	2.06458i	0.696884	+	0.125646i
$271$	5.04698	+	11.3357i	0.306582	+	0.688594i	0.999473	−	0.0324475i	$-0.0103302\pi$
$271$	5.04698	+	11.3357i	0.306582	+	0.688594i	−0.692891	+	0.721042i	$0.743664\pi$
$272$	2.99475	−	0.474322i	0.181583	−	0.0287600i
$273$	2.77574	−	0.699867i	0.167995	−	0.0423579i
$274$		−	18.0313i		−	1.08931i
$275$	2.17509	+	3.27885i	0.131163	+	0.197722i
$276$	−5.34381	+	3.08525i	−0.321660	+	0.185710i
$277$	1.03160	+	0.669930i	0.0619830	+	0.0402522i	0.575259	−	0.817972i	$-0.304901\pi$
$277$	1.03160	+	0.669930i	0.0619830	+	0.0402522i	−0.513276	+	0.858224i	$0.671568\pi$
$278$	0.887317	+	0.340609i	0.0532177	+	0.0204284i
$279$	4.79347	+	3.48266i	0.286977	+	0.208501i
$280$	12.9778	+	11.3089i	0.775570	+	0.675835i
$281$	1.42595	−	1.03602i	0.0850652	−	0.0618035i	−0.544440	−	0.838800i	$-0.683258\pi$
$281$	1.42595	−	1.03602i	0.0850652	−	0.0618035i	0.629505	+	0.776996i	$0.283258\pi$
$282$	−13.6097	+	3.64670i	−0.810445	+	0.217158i
$283$	−5.40338	−	14.0763i	−0.321198	−	0.836748i	−0.995186	−	0.0980061i	$-0.968754\pi$
$283$	−5.40338	−	14.0763i	−0.321198	−	0.836748i	0.673988	−	0.738742i	$-0.264580\pi$
$284$	0.805566	+	0.725335i	0.0478016	+	0.0430407i
$285$	1.01690	+	5.34116i	0.0602362	+	0.316383i
$286$	0.567492	+	0.184389i	0.0335565	+	0.0109032i
$287$	−2.30968	−	6.29398i	−0.136336	−	0.371522i
$288$	−6.08473	−	3.10033i	−0.358546	−	0.182689i
$289$	28.4488	−	25.6154i	1.67346	−	1.50679i
$290$	5.59587	+	18.5584i	0.328601	+	1.08978i
$291$	−9.46360	+	10.5104i	−0.554766	+	0.616130i
$292$	−3.29625	−	2.66925i	−0.192899	−	0.156206i
$293$	2.74224	+	2.74224i	0.160203	+	0.160203i	0.782657	−	0.622454i	$-0.213864\pi$
$293$	2.74224	+	2.74224i	0.160203	+	0.160203i	−0.622454	+	0.782657i	$0.713864\pi$
$294$	5.53731	+	6.52870i	0.322942	+	0.380762i
$295$	−24.7549	+	6.07102i	−1.44129	+	0.353469i
$296$	17.4482	−	7.76842i	1.01415	−	0.451530i
$297$	−2.78363	−	3.43750i	−0.161523	−	0.199464i
$298$	−5.74160	+	8.84129i	−0.332602	+	0.512162i
$299$	1.67366	−	2.89886i	0.0967902	−	0.167646i
$300$	−6.15043	−	4.37750i	−0.355095	−	0.252735i
$301$	−4.93259	−	4.57540i	−0.284310	−	0.263722i
$302$	9.14958	−	4.66195i	0.526499	−	0.268265i
$303$	2.99200	−	7.79441i	0.171886	−	0.447777i
$304$	−0.0784623	+	0.746519i	−0.00450012	+	0.0428158i
$305$	−18.7309	+	2.55899i	−1.07253	+	0.146527i
$306$	8.59073	−	0.902922i	0.491099	−	0.0516166i
$307$	19.7851	−	19.7851i	1.12920	−	1.12920i	0.138889	−	0.990308i	$-0.455647\pi$
$307$	19.7851	−	19.7851i	1.12920	−	1.12920i	0.990308	−	0.138889i	$-0.0443532\pi$
$308$	−0.337412	−	2.35562i	−0.0192258	−	0.134224i
$309$	−12.4397	+	4.04190i	−0.707669	+	0.229935i
$310$	4.70549	+	8.56651i	0.267254	+	0.486545i
$311$	−4.40295	−	20.7142i	−0.249668	−	1.17460i	−0.907045	−	0.421034i	$-0.861667\pi$
$311$	−4.40295	−	20.7142i	−0.249668	−	1.17460i	0.657377	−	0.753562i	$-0.271666\pi$
$312$	−3.14383	+	0.164761i	−0.177984	+	0.00932777i
$313$	2.61727	+	4.03024i	0.147937	+	0.227802i	0.904868	−	0.425692i	$-0.139969\pi$
$313$	2.61727	+	4.03024i	0.147937	+	0.227802i	−0.756932	+	0.653494i	$0.773302\pi$
$314$	−4.76941	+	14.6787i	−0.269153	+	0.828369i
$315$	5.33436	+	5.16376i	0.300557	+	0.290945i
$316$	−1.72754	−	5.31683i	−0.0971818	−	0.299095i
$317$	−18.7005	+	23.0932i	−1.05033	+	1.29704i	−0.0969400	+	0.995290i	$0.530905\pi$
$317$	−18.7005	+	23.0932i	−1.05033	+	1.29704i	−0.953386	+	0.301754i	$0.902428\pi$
$318$	2.84814	−	10.6294i	0.159716	−	0.596068i
$319$	2.99710	−	6.73159i	0.167805	−	0.376896i
$320$	−8.01849	−	10.3450i	−0.448247	−	0.578303i
$321$	4.22663	−	5.81746i	0.235908	−	0.324699i
$322$	9.98766	+	0.671883i	0.556591	+	0.0374426i
$323$	6.21317	+	12.1940i	0.345710	+	0.678495i
$324$	3.62308	+	2.09178i	0.201282	+	0.116210i
$325$	4.07677	+	0.388306i	0.226138	+	0.0215394i
$326$	−9.52165	−	16.4920i	−0.527355	−	0.913406i
$327$	21.6294	+	1.13355i	1.19611	+	0.0626853i
$328$	1.15341	+	7.28234i	0.0636864	+	0.402100i
$329$	−28.8473	−	9.84771i	−1.59040	−	0.542922i
$330$	−0.512573	−	2.09004i	−0.0282162	−	0.115053i
$331$	−2.40459	−	22.8781i	−0.132168	−	1.25749i	−0.836636	−	0.547759i	$-0.815481\pi$
$331$	−2.40459	−	22.8781i	−0.132168	−	1.25749i	0.704468	−	0.709735i	$-0.251185\pi$
$332$	−5.74610	−	1.53966i	−0.315358	−	0.0845000i
$333$	7.69041	−	2.95207i	0.421432	−	0.161772i
$334$	4.28334	+	0.910453i	0.234374	+	0.0498178i
$335$	−0.467028	+	1.98799i	−0.0255165	+	0.108616i
$336$	−0.694290	−	1.24476i	−0.0378766	−	0.0679073i
$337$	2.42351	−	4.75641i	0.132017	−	0.259098i	−0.815530	−	0.578715i	$-0.803554\pi$
$337$	2.42351	−	4.75641i	0.132017	−	0.259098i	0.947547	+	0.319617i	$0.103554\pi$
$338$	−9.57261	+	6.21653i	−0.520681	+	0.338134i
$339$	−12.1291	+	2.57811i	−0.658760	+	0.140024i
$340$	−17.9428	−	6.25554i	−0.973086	−	0.339254i
$341$	0.772489	−	3.63428i	0.0418326	−	0.196807i
$342$	−0.334529	+	2.11213i	−0.0180893	+	0.114211i
$343$	2.08188	+	18.4029i	0.112411	+	0.993662i
$344$	4.34902	+	5.98591i	0.234484	+	0.322739i
$345$	−12.0662	+	0.374883i	−0.649624	+	0.0201830i
$346$	4.64696	+	0.488415i	0.249822	+	0.0262573i
$347$	−13.3772	+	10.8326i	−0.718124	+	0.581525i	−0.917185	−	0.398462i	$-0.869544\pi$
$347$	−13.3772	+	10.8326i	−0.718124	+	0.581525i	0.199061	+	0.979987i	$0.436211\pi$
$348$	−0.739905	+	14.1182i	−0.0396631	+	0.756817i
$349$	−20.0775			−1.07472			−0.537362	−	0.843351i	$-0.680579\pi$
$349$	−20.0775			−1.07472			−0.537362	+	0.843351i	$0.680579\pi$
$350$	4.33105	+	11.4554i	0.231505	+	0.612319i
$351$	−4.60369			−0.245727
$352$	−0.224121	+	4.27648i	−0.0119457	+	0.227937i
$353$	−10.0129	+	8.10825i	−0.532931	+	0.431559i	−0.857637	−	0.514256i	$-0.828068\pi$
$353$	−10.0129	+	8.10825i	−0.532931	+	0.431559i	0.324706	+	0.945815i	$0.394735\pi$
$354$	13.8639	+	1.45715i	0.736858	+	0.0774469i
$355$	0.717665	+	1.99563i	0.0380897	+	0.105917i
$356$	0.388449	+	0.534654i	0.0205878	+	0.0283366i
$357$	−22.9768	−	12.1392i	−1.21606	−	0.642473i
$358$	−0.522794	+	3.30079i	−0.0276305	+	0.174452i
$359$	−1.60689	+	7.55982i	−0.0848084	+	0.398992i	−0.999992	−	0.00404548i	$-0.998712\pi$
$359$	−1.60689	+	7.55982i	−0.0848084	+	0.398992i	0.915183	+	0.403038i	$0.132046\pi$
$360$	−4.65738	−	6.70620i	−0.245465	−	0.353448i
$361$	15.2708	−	3.24590i	0.803725	−	0.170837i
$362$	−9.63536	+	6.25728i	−0.506423	+	0.328875i
$363$	6.22559	−	12.2184i	0.326759	−	0.641300i
$364$	−2.12634	−	1.27000i	−0.111451	−	0.0665660i
$365$	−3.21291	−	7.65086i	−0.168171	−	0.400465i
$366$	10.1136	+	2.14970i	0.528644	+	0.112367i
$367$	−3.08870	+	1.18564i	−0.161229	+	0.0618899i	−0.437644	−	0.899148i	$-0.644187\pi$
$367$	−3.08870	+	1.18564i	−0.161229	+	0.0618899i	0.276415	+	0.961038i	$0.410854\pi$
$368$	−1.60984	−	0.431357i	−0.0839189	−	0.0224860i
$369$	0.332402	+	3.16260i	0.0173042	+	0.164638i
$370$	13.5515	+	1.00003i	0.704511	+	0.0519891i
$371$	17.9260	−	15.6662i	0.930669	−	0.813347i
$372$	1.11515	+	7.04080i	0.0578180	+	0.365049i
$373$	−3.79343	−	0.198805i	−0.196416	−	0.0102937i	−0.0461259	−	0.998936i	$-0.514688\pi$
$373$	−3.79343	−	0.198805i	−0.196416	−	0.0102937i	−0.150290	+	0.988642i	$0.548021\pi$
$374$	−2.70837	−	4.69103i	−0.140046	−	0.242567i
$375$	−6.55279	−	13.2361i	−0.338385	−	0.683510i
$376$	29.0312	+	16.7612i	1.49717	+	0.864391i
$377$	−3.48176	−	6.83335i	−0.179320	−	0.351935i
$378$	−6.06793	−	12.3581i	−0.312101	−	0.635632i
$379$	17.8775	−	24.6063i	0.918306	−	1.26394i	−0.0459436	−	0.998944i	$-0.514629\pi$
$379$	17.8775	−	24.6063i	0.918306	−	1.26394i	0.964250	−	0.264996i	$-0.0853705\pi$
$380$	2.64554	−	3.88980i	0.135713	−	0.199543i
$381$	−1.56720	+	3.51999i	−0.0802902	+	0.180335i
$382$	5.55820	−	20.7435i	0.284382	−	1.06133i
$383$	−12.7938	+	15.7990i	−0.653732	+	0.807291i	−0.990964	−	0.134130i	$-0.957176\pi$
$383$	−12.7938	+	15.7990i	−0.653732	+	0.807291i	0.337232	+	0.941422i	$0.390509\pi$
$384$	−2.23072	−	6.86544i	−0.113836	−	0.350350i
$385$	1.59758	−	4.37291i	0.0814201	−	0.222864i
$386$	−4.27576	+	13.1594i	−0.217630	+	0.669797i
$387$	1.73804	+	2.67635i	0.0883496	+	0.136046i
$388$	12.2199	−	0.640418i	0.620372	−	0.0325123i
$389$	−2.32066	−	10.9179i	−0.117662	−	0.553558i	−0.997003	−	0.0773644i	$-0.975350\pi$
$389$	−2.32066	−	10.9179i	−0.117662	−	0.553558i	0.879341	−	0.476194i	$-0.157984\pi$
$390$	−2.02626	−	0.954372i	−0.102604	−	0.0483265i
$391$	−28.8993	+	9.38994i	−1.46150	+	0.474870i
$392$	1.66787	−	20.2992i	0.0842401	−	1.02526i
$393$	6.28817	−	6.28817i	0.317196	−	0.317196i
$394$	1.38811	−	0.145896i	0.0699317	−	0.00735012i
$395$	1.94066	−	10.7637i	0.0976453	−	0.541580i
$396$	−0.117983	+	1.12253i	−0.00592888	+	0.0564095i
$397$	4.09363	−	10.6643i	0.205453	−	0.535224i	−0.791676	−	0.610941i	$-0.790791\pi$
$397$	4.09363	−	10.6643i	0.205453	−	0.535224i	0.997129	+	0.0757170i	$0.0241246\pi$
$398$	−2.89484	+	1.47500i	−0.145105	+	0.0739348i
$399$	4.37503	−	4.71657i	0.219025	−	0.236124i
$400$	−0.338607	−	2.01070i	−0.0169304	−	0.100535i
$401$	14.5815	−	25.2559i	0.728165	−	1.26122i	−0.229493	−	0.973310i	$-0.573707\pi$
$401$	14.5815	−	25.2559i	0.728165	−	1.26122i	0.957658	−	0.287908i	$-0.0929597\pi$
$402$	0.608296	−	0.936694i	0.0303391	−	0.0467181i
$403$	−2.43361	−	3.00526i	−0.121227	−	0.149703i
$404$	−6.59902	+	2.93807i	−0.328314	+	0.146175i
$405$	4.31054	+	6.95774i	0.214193	+	0.345733i
$406$	13.7542	−	18.3532i	0.682610	−	0.910853i
$407$	−3.65262	−	3.65262i	−0.181054	−	0.181054i
$408$	22.2096	+	17.9850i	1.09954	+	0.890390i
$409$	21.5981	−	23.9872i	1.06796	−	1.18609i	0.0861370	−	0.996283i	$-0.472548\pi$
$409$	21.5981	−	23.9872i	1.06796	−	1.18609i	0.981822	−	0.189805i	$-0.0607856\pi$
$410$	−1.72689	+	4.95326i	−0.0852851	+	0.244624i
$411$	19.1206	−	17.2162i	0.943147	−	0.849214i
$412$	10.0833	+	5.13768i	0.496767	+	0.253115i
$413$	23.1538	+	19.3243i	1.13933	+	0.950888i
$414$	−4.51566	−	1.46723i	−0.221933	−	0.0721103i
$415$	−8.48113	−	7.97001i	−0.416322	−	0.391233i
$416$	3.31224	+	2.98235i	0.162396	+	0.146222i
$417$	0.486023	+	1.26613i	0.0238007	+	0.0620029i
$418$	1.29529	−	0.347072i	0.0633547	−	0.0169758i
$419$	−22.7957	+	16.5620i	−1.11364	+	0.809109i	−0.983233	−	0.182351i	$-0.941629\pi$
$419$	−22.7957	+	16.5620i	−1.11364	+	0.809109i	−0.130410	+	0.991460i	$0.541629\pi$
$420$	0.145131	+	8.93114i	0.00708167	+	0.435795i
$421$	−16.8306	−	12.2282i	−0.820274	−	0.595964i	0.0965173	−	0.995331i	$-0.469230\pi$
$421$	−16.8306	−	12.2282i	−0.820274	−	0.595964i	−0.916791	+	0.399368i	$0.869230\pi$
$422$	−17.2500	−	6.62164i	−0.839715	−	0.322337i
$423$	12.1256	+	7.87447i	0.589568	+	0.382870i
$424$	−22.6739	+	13.0908i	−1.10114	+	0.635744i
$425$	−25.1439	−	27.3830i	−1.21966	−	1.32827i
$426$		−	1.15989i		−	0.0561967i
$427$	15.5810	+	16.0494i	0.754015	+	0.776687i
$428$	−6.14488	+	0.973254i	−0.297024	+	0.0470440i
$429$	0.346312	+	0.777830i	0.0167201	+	0.0375540i
$430$	0.712553	+	5.21562i	0.0343624	+	0.251520i
$431$	2.27190	+	1.01151i	0.109434	+	0.0487229i	0.460723	−	0.887544i	$-0.347590\pi$
$431$	2.27190	+	1.01151i	0.109434	+	0.0487229i	−0.351290	+	0.936267i	$0.614257\pi$
$432$	0.593260	+	2.21408i	0.0285432	+	0.106525i
$433$	−9.13869	−	1.44743i	−0.439178	−	0.0695589i	−0.0670695	−	0.997748i	$-0.521365\pi$
$433$	−9.13869	−	1.44743i	−0.439178	−	0.0695589i	−0.372108	+	0.928189i	$0.621365\pi$
$434$	4.85964	−	10.4939i	0.233270	−	0.503722i
$435$	−14.3366	+	23.6534i	−0.687386	+	1.13410i
$436$	−12.5391	−	13.9261i	−0.600516	−	0.666940i
$437$	−0.393701	−	7.51226i	−0.0188333	−	0.359360i
$438$	0.237523	+	4.53221i	0.0113493	+	0.216557i
$439$	14.2078	+	15.7793i	0.678099	+	0.753105i	0.979731	−	0.200319i	$-0.0641980\pi$
$439$	14.2078	+	15.7793i	0.678099	+	0.753105i	−0.301632	+	0.953425i	$0.597531\pi$
$440$	−2.65385	+	4.37850i	−0.126517	+	0.208737i
$441$	1.17657	−	8.70537i	0.0560270	−	0.414541i
$442$	−5.56830	−	0.881932i	−0.264857	−	0.0419492i
$443$	−5.90047	−	22.0209i	−0.280340	−	1.04624i	−0.952178	−	0.305545i	$-0.901161\pi$
$443$	−5.90047	−	22.0209i	−0.280340	−	1.04624i	0.671838	−	0.740698i	$-0.265505\pi$
$444$	9.05395	+	4.03108i	0.429681	+	0.191306i
$445$	0.175014	+	1.28103i	0.00829645	+	0.0607269i
$446$	−3.29755	−	7.40641i	−0.156143	−	0.350704i
$447$	−14.8575	+	2.35319i	−0.702734	+	0.111302i
$448$	−4.22938	+	14.8981i	−0.199819	+	0.703870i
$449$		−	32.5816i		−	1.53762i	−0.639478	−	0.768809i	$-0.720850\pi$
$449$		−	32.5816i		−	1.53762i	0.639478	−	0.768809i	$-0.279150\pi$
$450$	−0.663538	−	5.77090i	−0.0312795	−	0.272043i
$451$	1.72696	−	0.997060i	0.0813193	−	0.0469497i
$452$	8.99770	+	5.84318i	0.423216	+	0.274840i
$453$	13.6796	+	5.25110i	0.642723	+	0.246718i
$454$	−7.03338	−	5.11005i	−0.330093	−	0.239827i
$455$	−2.49063	−	4.15643i	−0.116762	−	0.194856i
$456$	−5.72376	+	4.15856i	−0.268040	+	0.194742i
$457$	7.80380	−	2.09102i	0.365046	−	0.0978138i	−0.0716332	−	0.997431i	$-0.522821\pi$
$457$	7.80380	−	2.09102i	0.365046	−	0.0978138i	0.436679	+	0.899617i	$0.356154\pi$
$458$	2.85383	+	7.43447i	0.133351	+	0.347390i
$459$	31.0572	+	27.9641i	1.44963	+	1.30525i
$460$	7.61136	+	7.15266i	0.354881	+	0.333494i
$461$	36.2181	+	11.7680i	1.68684	+	0.548089i	0.986220	−	0.165441i	$-0.0529046\pi$
$461$	36.2181	+	11.7680i	1.68684	+	0.548089i	0.700625	+	0.713530i	$0.252905\pi$
$462$	−1.63154	+	1.95486i	−0.0759061	+	0.0909485i
$463$	32.7647	+	16.6944i	1.52270	+	0.775856i	0.997189	−	0.0749286i	$-0.0238729\pi$
$463$	32.7647	+	16.6944i	1.52270	+	0.775856i	0.525514	+	0.850785i	$0.323873\pi$
$464$	−2.83772	+	2.55509i	−0.131738	+	0.118617i
$465$	−4.59122	+	13.1690i	−0.212913	+	0.610700i
$466$	−1.72562	+	1.91650i	−0.0799378	+	0.0887799i
$467$	−16.1817	−	13.1037i	−0.748800	−	0.606366i	0.177075	−	0.984197i	$-0.443337\pi$
$467$	−16.1817	−	13.1037i	−0.748800	−	0.606366i	−0.925874	+	0.377831i	$0.876670\pi$
$468$	0.830684	+	0.830684i	0.0383984	+	0.0383984i
$469$	2.22168	−	0.949984i	0.102587	−	0.0438662i
$470$	12.5605	+	20.2742i	0.579372	+	0.935178i
$471$	−20.1193	+	8.95770i	−0.927050	+	0.412749i
$472$	−20.8724	−	25.7753i	−0.960731	−	1.18640i
$473$	1.08989	−	1.67828i	0.0501131	−	0.0771674i
$474$	−2.99091	+	5.18041i	−0.137377	+	0.237944i
$475$	8.15909	−	4.25805i	0.374365	−	0.195373i
$476$	6.63034	+	21.4836i	0.303901	+	0.984699i
$477$	−10.0613	+	5.12650i	−0.460676	+	0.234726i
$478$	3.57087	−	9.30243i	0.163328	−	0.425483i
$479$	−0.146303	+	1.39198i	−0.00668475	+	0.0636011i	−0.997356	−	0.0726744i	$-0.976847\pi$
$479$	−0.146303	+	1.39198i	−0.00668475	+	0.0636011i	0.990671	+	0.136276i	$0.0435133\pi$
$480$	2.85216	−	15.8192i	0.130183	−	0.722046i
$481$	−5.34686	+	0.561978i	−0.243796	+	0.0256240i
$482$	−6.90821	+	6.90821i	−0.314660	+	0.314660i
$483$	8.82374	+	11.2325i	0.401494	+	0.511099i
$484$	−11.2839	+	3.66635i	−0.512903	+	0.166652i
$485$	21.6579	+	10.2009i	0.983436	+	0.463199i
$486$	2.31496	+	10.8910i	0.105009	+	0.494027i
$487$	26.5638	−	1.39215i	1.20372	−	0.0630844i	0.560098	−	0.828426i	$-0.310763\pi$
$487$	26.5638	−	1.39215i	1.20372	−	0.0630844i	0.643624	+	0.765342i	$0.277430\pi$
$488$	−13.3980	−	20.6310i	−0.606497	−	0.933923i
$489$	8.39703	−	25.8434i	0.379727	−	1.16868i
$490$	7.87469	−	12.1642i	0.355742	−	0.549524i
$491$	0.0638187	+	0.196414i	0.00288010	+	0.00886403i	0.952486	−	0.304582i	$-0.0985166\pi$
$491$	0.0638187	+	0.196414i	0.00288010	+	0.00886403i	−0.949606	+	0.313446i	$0.898517\pi$
$492$	−2.40775	+	2.97333i	−0.108550	+	0.134048i
$493$	−18.0191	+	67.2481i	−0.811538	+	3.02870i
$494$	0.567678	−	1.27502i	0.0255410	−	0.0573661i
$495$	−1.24187	+	1.82595i	−0.0558178	+	0.0820703i
$496$	−1.13172	+	1.55769i	−0.0508159	+	0.0699421i
$497$	1.39768	−	2.08401i	0.0626945	−	0.0934805i
$498$	2.88977	+	5.67150i	0.129494	+	0.254146i
$499$	20.4454	+	11.8042i	0.915262	+	0.528427i	0.882120	−	0.471024i	$-0.156116\pi$
$499$	20.4454	+	11.8042i	0.915262	+	0.528427i	0.0331413	+	0.999451i	$0.489449\pi$
$500$	−4.08879	+	12.1067i	−0.182856	+	0.541426i
$501$	3.12428	+	5.41141i	0.139582	+	0.241764i
$502$	−26.8677	−	1.40808i	−1.19916	−	0.0628455i
$503$	0.515396	+	3.25409i	0.0229804	+	0.145092i	0.996511	−	0.0834657i	$-0.0265989\pi$
$503$	0.515396	+	3.25409i	0.0229804	+	0.145092i	−0.973530	+	0.228558i	$0.926599\pi$
$504$	−3.12108	+	9.14269i	−0.139024	+	0.407248i
$505$	−14.0939	−	1.04005i	−0.627170	−	0.0462817i
$506$	0.311223	+	2.96109i	0.0138355	+	0.131636i
$507$	−15.7320	−	4.21538i	−0.698682	−	0.187211i
$508$	3.11230	−	1.19470i	0.138086	−	0.0530062i
$509$	−13.6817	−	2.90814i	−0.606431	−	0.128901i	−0.105545	−	0.994414i	$-0.533659\pi$
$509$	−13.6817	−	2.90814i	−0.606431	−	0.128901i	−0.500885	+	0.865514i	$0.666992\pi$
$510$	7.87240	+	18.7464i	0.348596	+	0.830106i
$511$	−5.03461	+	8.42939i	−0.222718	+	0.372894i
$512$	2.08486	−	4.09177i	0.0921387	−	0.180832i
$513$	−8.67694	+	5.63487i	−0.383096	+	0.248786i
$514$	−16.8581	+	3.58331i	−0.743580	+	0.158053i
$515$	12.6292	+	18.1849i	0.556510	+	0.801323i
$516$	−0.798253	+	3.75548i	−0.0351411	+	0.165326i
$517$	1.41829	−	8.95476i	0.0623765	−	0.393830i
$518$	−8.55605	−	13.6123i	−0.375931	−	0.598092i
$519$	3.91899	+	5.39402i	0.172024	+	0.236771i
$520$	1.80329	+	5.01446i	0.0790796	+	0.219898i
$521$	28.2500	+	2.96919i	1.23765	+	0.130083i	0.700655	−	0.713500i	$-0.252891\pi$
$521$	28.2500	+	2.96919i	1.23765	+	0.130083i	0.536999	+	0.843583i	$0.319558\pi$
$522$	−8.45422	+	6.84609i	−0.370031	+	0.299645i
$523$	2.07809	−	39.6524i	0.0908687	−	1.73388i	−0.450225	−	0.892915i	$-0.648656\pi$
$523$	2.07809	−	39.6524i	0.0908687	−	1.73388i	0.541094	−	0.840962i	$-0.318010\pi$
$524$	−7.69409			−0.336118
$525$	−8.01220	+	15.5303i	−0.349681	+	0.677800i
$526$	19.1787			0.836229
$527$	−1.83723	+	35.0564i	−0.0800308	+	1.52708i
$528$	0.329458	−	0.266790i	0.0143378	−	0.0116105i
$529$	−6.26305	−	0.658273i	−0.272307	−	0.0286206i
$530$	−18.6181	+	0.578440i	−0.808717	+	0.0251258i
$531$	−8.40811	−	11.5728i	−0.364881	−	0.502215i
$532$	−5.56215	+	0.208955i	−0.241150	+	0.00905937i
$533$	0.324675	−	2.04992i	0.0140632	−	0.0887918i
$534$	0.147022	−	0.691684i	0.00636226	−	0.0299321i
$535$	−11.4933	−	4.00700i	−0.496900	−	0.173238i
$536$	−2.59921	+	0.552478i	−0.112269	+	0.0238634i
$537$	−3.99936	+	2.59722i	−0.172585	+	0.112078i
$538$	−0.539718	+	1.05926i	−0.0232689	+	0.0456677i
$539$	−5.28709	+	1.54634i	−0.227731	+	0.0666056i
$540$	3.28527	−	13.9844i	0.141376	−	0.601791i
$541$	1.28954	+	0.274100i	0.0554417	+	0.0117845i	0.235549	−	0.971862i	$-0.424311\pi$
$541$	1.28954	+	0.274100i	0.0554417	+	0.0117845i	−0.180107	+	0.983647i	$0.557645\pi$
$542$	−10.7244	+	4.11673i	−0.460654	+	0.176829i
$543$	−15.8351	−	4.24301i	−0.679550	−	0.182085i
$544$	−4.22927	−	40.2389i	−0.181329	−	1.72523i
$545$	−8.73243	−	35.6070i	−0.374056	−	1.52524i
$546$	0.512543	+	2.60010i	0.0219348	+	0.111274i
$547$	3.39018	+	21.4047i	0.144953	+	0.915200i	0.947766	+	0.318968i	$0.103336\pi$
$547$	3.39018	+	21.4047i	0.144953	+	0.915200i	−0.802812	+	0.596232i	$0.796664\pi$
$548$	−22.2305	−	1.16505i	−0.949639	−	0.0497685i
$549$	−5.30491	−	9.18838i	−0.226408	−	0.392150i
$550$	−3.13670	+	1.85202i	−0.133749	+	0.0789703i
$551$	−14.9263	−	8.61771i	−0.635882	−	0.367127i
$552$	−7.13156	−	13.9965i	−0.303539	−	0.595730i
$553$	−11.6164	+	5.70373i	−0.493978	+	0.242547i
$554$	−0.669337	+	0.921263i	−0.0284374	+	0.0391407i
$555$	11.8786	+	15.3250i	0.504216	+	0.650512i
$556$	0.477264	−	1.07195i	0.0202405	−	0.0454609i
$557$	−2.91942	+	10.8954i	−0.123700	+	0.461654i	−0.999790	−	0.0204931i	$-0.993476\pi$
$557$	−2.91942	+	10.8954i	−0.123700	+	0.461654i	0.876090	+	0.482147i	$0.160143\pi$
$558$	−3.45199	+	4.26285i	−0.146134	+	0.180461i
$559$	−0.643607	−	1.98082i	−0.0272217	−	0.0837797i
$560$	−1.67802	+	1.73345i	−0.0709092	+	0.0732518i
$561$	2.38847	−	7.35097i	0.100841	−	0.310358i
$562$	0.888713	+	1.36850i	0.0374881	+	0.0577266i
$563$	−4.94286	+	0.259044i	−0.208317	+	0.0109174i	−0.156209	−	0.987724i	$-0.549927\pi$
$563$	−4.94286	+	0.259044i	−0.208317	+	0.0109174i	−0.0521079	+	0.998641i	$0.516594\pi$
$564$	3.61661	+	17.0148i	0.152287	+	0.716453i
$565$	10.1052	+	18.3968i	0.425128	+	0.773960i
$566$	13.2754	−	4.31344i	0.558007	−	0.181307i
$567$	3.60409	−	8.98876i	0.151358	−	0.377493i
$568$	−1.95133	+	1.95133i	−0.0818759	+	0.0818759i
$569$	−16.8195	+	1.76780i	−0.705109	+	0.0741099i	−0.450295	−	0.892880i	$-0.648681\pi$
$569$	−16.8195	+	1.76780i	−0.705109	+	0.0741099i	−0.254814	+	0.966990i	$0.582014\pi$
$570$	−4.98720	+	0.681347i	−0.208891	+	0.0285385i
$571$	−3.00592	+	28.5994i	−0.125794	+	1.19685i	0.731434	+	0.681912i	$0.238851\pi$
$571$	−3.00592	+	28.5994i	−0.125794	+	1.19685i	−0.857228	+	0.514937i	$0.827815\pi$
$572$	0.263999	−	0.687740i	0.0110383	−	0.0287558i
$573$	27.3036	−	13.9119i	1.14062	−	0.581177i
$574$	5.93072	−	1.83036i	0.247544	−	0.0763977i
$575$	6.50388	+	19.3717i	0.271230	+	0.807854i
$576$	3.67285	−	6.36156i	0.153035	−	0.265065i
$577$	5.65186	−	8.70310i	0.235290	−	0.362315i	−0.701226	−	0.712939i	$-0.747364\pi$
$577$	5.65186	−	8.70310i	0.235290	−	0.362315i	0.936516	+	0.350624i	$0.114030\pi$
$578$	22.3032	+	27.5422i	0.927692	+	1.14560i
$579$	−18.0369	+	8.03054i	−0.749588	+	0.333738i
$580$	23.2419	−	5.69996i	0.965068	−	0.236678i
$581$	−1.64209	+	13.6724i	−0.0681253	+	0.567227i
$582$	−9.25840	−	9.25840i	−0.383773	−	0.383773i
$583$	5.50298	+	4.45623i	0.227910	+	0.184558i
$584$	7.22514	−	8.02433i	0.298978	−	0.332049i
$585$	0.663504	+	2.20047i	0.0274325	+	0.0909783i
$586$	−2.66808	+	2.40235i	−0.110217	+	0.0992401i
$587$	−4.08885	−	2.08337i	−0.168765	−	0.0859899i	0.367568	−	0.929997i	$-0.380191\pi$
$587$	−4.08885	−	2.08337i	−0.168765	−	0.0859899i	−0.536332	+	0.844007i	$0.680191\pi$
$588$	8.40693	−	6.40503i	0.346696	−	0.264139i
$589$	−8.26522	−	2.68553i	−0.340563	−	0.110655i
$590$	−4.41329	−	23.1802i	−0.181692	−	0.954315i
$591$	1.48007	+	1.33266i	0.0608820	+	0.0548184i
$592$	0.959305	+	2.49908i	0.0394272	+	0.102711i
$593$	14.8803	−	3.98715i	0.611059	−	0.163733i	0.0599990	−	0.998198i	$-0.480890\pi$
$593$	14.8803	−	3.98715i	0.611059	−	0.163733i	0.551060	+	0.834466i	$0.314224\pi$
$594$	3.31286	−	2.40693i	0.135928	−	0.0987577i
$595$	−8.44513	+	43.1687i	−0.346217	+	1.76974i
$596$	10.5293	+	7.65000i	0.431298	+	0.313356i
$597$	−4.32809	−	1.66140i	−0.177137	−	0.0679965i
$598$	2.59893	+	1.68776i	0.106278	+	0.0690177i
$599$	13.4466	−	7.76339i	0.549413	−	0.317204i	−0.199472	−	0.979903i	$-0.563923\pi$
$599$	13.4466	−	7.76339i	0.549413	−	0.317204i	0.748885	+	0.662700i	$0.230589\pi$
$600$	11.9482	−	15.0528i	0.487785	−	0.614529i
$601$		−	41.2449i		−	1.68241i	−0.540714	−	0.841207i	$-0.681846\pi$
$601$		−	41.2449i		−	1.68241i	0.540714	−	0.841207i	$-0.318154\pi$
$602$	4.46898	−	4.33853i	0.182142	−	0.176825i
$603$	−1.13197	+	0.179286i	−0.0460974	+	0.00730110i
$604$	−5.15647	−	11.5816i	−0.209814	−	0.471249i
$605$	−22.8437	−	4.11865i	−0.928728	−	0.167447i
$606$	7.06102	+	3.14377i	0.286834	+	0.127707i
$607$	2.89077	+	10.7885i	0.117333	+	0.437891i	0.999451	−	0.0331368i	$-0.0105497\pi$
$607$	2.89077	+	10.7885i	0.117333	+	0.437891i	−0.882118	+	0.471028i	$0.843883\pi$
$608$	9.89320	+	1.56693i	0.401222	+	0.0635474i
$609$	32.5944	−	2.93847i	1.32079	−	0.119073i
$610$	−1.45827	−	17.4408i	−0.0590436	−	0.706156i
$611$	−6.31408	−	7.01250i	−0.255441	−	0.283695i
$612$	−0.558129	−	10.6497i	−0.0225610	−	0.430490i
$613$	−0.162396	−	3.09870i	−0.00655911	−	0.125155i	−0.999946	−	0.0103446i	$-0.996707\pi$
$613$	−0.162396	−	3.09870i	−0.00655911	−	0.125155i	0.993387	−	0.114811i	$-0.0366262\pi$
$614$	17.3329	+	19.2501i	0.699497	+	0.776870i
$615$	−6.90133	+	2.89815i	−0.278288	+	0.116865i
$616$	6.03357	−	0.543942i	0.243099	−	0.0219161i
$617$	45.2349	+	7.16450i	1.82109	+	0.288432i	0.971153	−	0.238456i	$-0.0766413\pi$
$617$	45.2349	+	7.16450i	1.82109	+	0.288432i	0.849935	+	0.526888i	$0.176641\pi$
$618$	−3.13404	−	11.6964i	−0.126070	−	0.470498i
$619$	−16.3273	−	7.26936i	−0.656248	−	0.292180i	0.0514712	−	0.998674i	$-0.483609\pi$
$619$	−16.3273	−	7.26936i	−0.656248	−	0.292180i	−0.707719	+	0.706494i	$0.750276\pi$
$620$	10.8656	−	5.24783i	0.436371	−	0.210758i
$621$	−9.34334	−	20.9855i	−0.374935	−	0.842119i
$622$	19.3638	−	3.06692i	0.776416	−	0.122972i
$623$	1.09765	−	1.06561i	0.0439764	−	0.0426927i
$624$		−	0.441228i		−	0.0176633i
$625$	−18.2486	+	17.0876i	−0.729946	+	0.683505i
$626$	−3.85279	+	2.22441i	−0.153988	+	0.0889052i
$627$	1.60478	+	1.04216i	0.0640887	+	0.0416197i
$628$	17.7891	+	6.82858i	0.709861	+	0.272490i
$629$	39.4844	+	28.6871i	1.57435	+	1.14383i
$630$	−5.03239	+	4.68145i	−0.200495	+	0.186514i
$631$	0.0581461	−	0.0422456i	0.00231476	−	0.00168177i	−0.586627	−	0.809857i	$-0.699545\pi$
$631$	0.0581461	−	0.0422456i	0.00231476	−	0.00168177i	0.588942	+	0.808175i	$0.299545\pi$
$632$	13.7470	−	3.68350i	0.546826	−	0.146522i
$633$	−9.44859	−	24.6144i	−0.375548	−	0.978335i
$634$	−20.4438	−	18.4076i	−0.811925	−	0.731061i
$635$	6.47043	+	0.819753i	0.256771	+	0.0325309i
$636$	−12.9208	−	4.19823i	−0.512344	−	0.166471i
$637$	−2.21225	+	5.28930i	−0.0876526	+	0.209570i
$638$	6.07818	+	3.09699i	0.240637	+	0.122611i
$639$	−0.884499	+	0.796406i	−0.0349902	+	0.0315053i
$640$	−10.0362	+	6.97004i	−0.396717	+	0.275515i
$641$	−15.6503	+	17.3814i	−0.618149	+	0.686524i	−0.968192	−	0.250209i	$-0.919501\pi$
$641$	−15.6503	+	17.3814i	−0.618149	+	0.686524i	0.350042	+	0.936734i	$0.386167\pi$
$642$	5.17349	+	4.18941i	0.204181	+	0.165343i
$643$	−20.9354	−	20.9354i	−0.825611	−	0.825611i	0.161295	−	0.986906i	$-0.448433\pi$
$643$	−20.9354	−	20.9354i	−0.825611	−	0.825611i	−0.986906	+	0.161295i	$0.948433\pi$
$644$	1.47369	−	12.2702i	0.0580714	−	0.483515i
$645$	−4.85036	+	5.73547i	−0.190983	+	0.225834i
$646$	−11.5745	+	5.15330i	−0.455393	+	0.202754i
$647$	12.2729	+	15.1558i	0.482499	+	0.595837i	0.959024	−	0.283324i	$-0.0914373\pi$
$647$	12.2729	+	15.1558i	0.482499	+	0.595837i	−0.476525	+	0.879161i	$0.658104\pi$
$648$	−5.80061	+	8.93215i	−0.227869	+	0.350888i
$649$	−4.48509	+	7.76840i	−0.176055	+	0.304936i
$650$	−0.556516	+	3.75018i	−0.0218284	+	0.147094i
$651$	15.7678	−	4.86631i	0.617989	−	0.190726i
$652$	−20.9480	+	10.6735i	−0.820385	+	0.418007i
$653$	1.13219	−	2.94945i	0.0443060	−	0.115421i	−0.909642	−	0.415393i	$-0.863644\pi$
$653$	1.13219	−	2.94945i	0.0443060	−	0.115421i	0.953948	+	0.299972i	$0.0969774\pi$
$654$	−2.09594	+	19.9415i	−0.0819578	+	0.779776i
$655$	−13.2636	−	7.11796i	−0.518251	−	0.278122i
$656$	−1.02772	+	0.108018i	−0.0401257	+	0.00421738i
$657$	3.29305	−	3.29305i	0.128474	−	0.128474i
$658$	10.5020	−	26.1924i	0.409409	−	1.02108i
$659$	13.3517	−	4.33824i	0.520110	−	0.168994i	−0.0371852	−	0.999308i	$-0.511839\pi$
$659$	13.3517	−	4.33824i	0.520110	−	0.168994i	0.557295	+	0.830314i	$0.311839\pi$
$660$	−2.60991	+	0.496900i	−0.101590	+	0.0193418i
$661$	2.64972	+	12.4660i	0.103062	+	0.484870i	0.999159	+	0.0410104i	$0.0130577\pi$
$661$	2.64972	+	12.4660i	0.103062	+	0.484870i	−0.896096	+	0.443859i	$0.853609\pi$
$662$	21.2674	−	1.11458i	0.826583	−	0.0433194i
$663$	−4.38140	−	6.74676i	−0.170159	−	0.262022i
$664$	4.67982	−	14.4030i	0.181612	−	0.558945i
$665$	−9.78171	−	4.78546i	−0.379319	−	0.185572i
$666$	2.35660	+	7.25286i	0.0913163	+	0.281043i
$667$	24.0828	−	29.7398i	0.932491	−	1.15153i
$668$	1.39924	−	5.22205i	0.0541384	−	0.202047i
$669$	4.70535	−	10.5684i	0.181919	−	0.408598i
$670$	−1.81528	−	0.528091i	−0.0701305	−	0.0204019i
$671$	−3.91065	+	5.38254i	−0.150969	+	0.207791i
$672$	−17.0724	+	8.38270i	−0.658582	+	0.323369i
$673$	−14.9409	−	29.3231i	−0.575928	−	1.13032i	−0.976793	−	0.214185i	$-0.931290\pi$
$673$	−14.9409	−	29.3231i	−0.575928	−	1.13032i	0.400865	−	0.916137i	$-0.368710\pi$
$674$	4.27990	+	2.47100i	0.164856	+	0.0951795i
$675$	18.6006	−	21.0679i	0.715937	−	0.810903i
$676$	7.04576	+	12.2036i	0.270991	+	0.469370i
$677$	−5.80896	−	0.304435i	−0.223256	−	0.0117004i	−0.0596203	−	0.998221i	$-0.518989\pi$
$677$	−5.80896	−	0.304435i	−0.223256	−	0.0117004i	−0.163636	+	0.986521i	$0.552322\pi$
$678$	−1.79581	−	11.3383i	−0.0689677	−	0.435445i
$679$	−5.47837	−	27.7914i	−0.210241	−	1.06654i
$680$	18.2939	−	44.7821i	0.701538	−	1.71731i
$681$	−1.29671	−	12.3373i	−0.0496899	−	0.472768i
$682$	3.32248	+	0.890256i	0.127224	+	0.0340897i
$683$	−16.4820	+	6.32684i	−0.630666	+	0.242090i	−0.652639	−	0.757669i	$-0.726338\pi$
$683$	−16.4820	+	6.32684i	−0.630666	+	0.242090i	0.0219738	+	0.999759i	$0.493005\pi$
$684$	2.58241	+	0.548907i	0.0987408	+	0.0209880i
$685$	−37.2446	−	22.5743i	−1.42304	−	0.862519i
$686$	−17.1144	+	1.03307i	−0.653432	+	0.0394427i
$687$	−5.15877	+	10.1247i	−0.196819	+	0.386280i
$688$	−0.869707	+	0.564794i	−0.0331572	+	0.0215326i
$689$	7.20884	−	1.53229i	0.274635	−	0.0583754i
$690$	0.238044	−	11.1735i	0.00906217	−	0.425367i
$691$	−7.24591	+	34.0893i	−0.275647	+	1.29682i	0.594527	+	0.804075i	$0.297339\pi$
$691$	−7.24591	+	34.0893i	−0.275647	+	1.29682i	−0.870175	+	0.492743i	$0.835994\pi$
$692$	0.902413	−	5.69761i	0.0343046	−	0.216591i
$693$	2.61098	−	0.0980878i	0.0991831	−	0.00372605i
$694$	−9.36667	−	12.8921i	−0.355554	−	0.489378i
$695$	1.81443	−	1.40638i	0.0688251	−	0.0533469i
$696$	−35.7938	−	3.76208i	−1.35676	−	0.142601i
$697$	−14.6421	+	11.8569i	−0.554608	+	0.449113i
$698$	0.972782	−	18.5618i	0.0368203	−	0.702574i
$699$	−3.67989			−0.139186
$700$	14.4031	−	4.59953i	0.544386	−	0.173846i
$701$	−5.86630			−0.221567			−0.110783	−	0.993845i	$-0.535336\pi$
$701$	−5.86630			−0.221567			−0.110783	+	0.993845i	$0.535336\pi$
$702$	0.223055	−	4.25614i	0.00841865	−	0.160637i
$703$	−9.38980	+	7.60371i	−0.354143	+	0.286779i
$704$	−4.58109	−	0.481492i	−0.172656	−	0.0181469i
$705$	−9.50622	+	32.6770i	−0.358025	+	1.23069i
$706$	−7.01099	−	9.64980i	−0.263862	−	0.363175i
$707$	8.89848	+	14.1571i	0.334662	+	0.532434i
$708$	2.69229	−	16.9985i	0.101183	−	0.638841i
$709$	−1.95872	+	9.21505i	−0.0735612	+	0.346078i	−0.999501	−	0.0315933i	$-0.989942\pi$
$709$	−1.95872	+	9.21505i	−0.0735612	+	0.346078i	0.925940	+	0.377672i	$0.123275\pi$
$710$	−1.87974	+	0.566794i	−0.0705454	+	0.0212714i
$711$	6.00408	−	1.27621i	0.225171	−	0.0478615i
$712$	−1.41099	+	0.916309i	−0.0528792	+	0.0343401i
$713$	8.76010	−	17.1927i	0.328068	−	0.643870i
$714$	12.3360	−	20.6540i	0.461663	−	0.772957i
$715$	1.09134	−	0.941340i	0.0408138	−	0.0352041i
$716$	4.03572	+	0.857819i	0.150822	+	0.0320582i
$717$	13.2739	−	5.09536i	0.495722	−	0.190290i
$718$	−6.91124	−	1.85186i	−0.257925	−	0.0691109i
$719$	−4.40181	−	41.8805i	−0.164160	−	1.56188i	−0.697879	−	0.716216i	$-0.745873\pi$
$719$	−4.40181	−	41.8805i	−0.164160	−	1.56188i	0.533719	−	0.845662i	$-0.320794\pi$
$720$	0.972781	−	0.602669i	0.0362534	−	0.0224601i
$721$	8.46329	−	24.7919i	0.315190	−	0.923297i
$722$	2.26097	+	14.2752i	0.0841445	+	0.531267i
$723$	−13.9215	−	0.729594i	−0.517746	−	0.0271339i
$724$	7.09194	+	12.2836i	0.263570	+	0.456517i
$725$	45.3391	+	11.6756i	1.68385	+	0.433622i
$726$	10.9944	+	6.34760i	0.408039	+	0.235581i
$727$	5.76081	+	11.3062i	0.213657	+	0.419325i	0.972816	−	0.231580i	$-0.0743896\pi$
$727$	5.76081	+	11.3062i	0.213657	+	0.419325i	−0.759159	+	0.650905i	$0.774390\pi$
$728$	3.51198	−	5.23653i	0.130163	−	0.194079i
$729$	−15.7932	+	21.7374i	−0.584932	+	0.805090i
$730$	7.22894	−	2.59966i	0.267555	−	0.0962178i
$731$	−7.69016	+	17.2724i	−0.284431	+	0.638842i
$732$	3.30381	−	12.3300i	0.122112	−	0.455729i
$733$	−29.6824	+	36.6547i	−1.09634	+	1.35387i	−0.166449	+	0.986050i	$0.553230\pi$
$733$	−29.6824	+	36.6547i	−1.09634	+	1.35387i	−0.929896	+	0.367823i	$0.880103\pi$
$734$	−0.946479	−	2.91296i	−0.0349352	−	0.107519i
$735$	20.4178	−	3.26398i	0.753123	−	0.120394i
$736$	−6.87248	+	21.1513i	−0.253323	+	0.779648i
$737$	0.391422	+	0.602737i	0.0144182	+	0.0222021i
$738$	−2.93995	+	0.154076i	−0.108221	+	0.00567162i
$739$	9.32981	+	43.8933i	0.343203	+	1.61464i	0.723875	+	0.689931i	$0.242359\pi$
$739$	9.32981	+	43.8933i	0.343203	+	1.61464i	−0.380673	+	0.924710i	$0.624308\pi$
$740$	2.10853	−	16.6429i	0.0775110	−	0.611805i
$741$	1.89407	−	0.615420i	0.0695804	−	0.0226080i
$742$	13.6149	+	17.3317i	0.499820	+	0.636267i
$743$	11.1530	−	11.1530i	0.409164	−	0.409164i	−0.472283	−	0.881447i	$-0.656570\pi$
$743$	11.1530	−	11.1530i	0.409164	−	0.409164i	0.881447	+	0.472283i	$0.156570\pi$
$744$	−18.0482	+	1.89694i	−0.661680	+	0.0695453i
$745$	11.0740	+	22.9285i	0.405718	+	0.840034i
$746$	0.367593	−	3.49741i	0.0134585	−	0.128049i
$747$	2.34075	−	6.09786i	0.0856435	−	0.223109i
$748$	−5.95850	+	3.03601i	−0.217864	+	0.111007i
$749$	4.24708	+	13.7614i	0.155185	+	0.502830i
$750$	12.5544	−	5.41679i	0.458420	−	0.197793i
$751$	−21.6997	+	37.5850i	−0.791834	+	1.37150i	0.132996	+	0.991117i	$0.457540\pi$
$751$	−21.6997	+	37.5850i	−0.791834	+	1.37150i	−0.924830	+	0.380380i	$0.875793\pi$
$752$	−2.55889	+	3.94034i	−0.0933131	+	0.143689i
$753$	−24.1601	−	29.8352i	−0.880443	−	1.08726i
$754$	6.48617	−	2.88783i	0.236212	−	0.105168i
$755$	1.82535	−	24.7355i	0.0664311	−	0.900217i
$756$	−15.6282	+	6.68258i	−0.568392	+	0.243043i
$757$	−35.7542	−	35.7542i	−1.29951	−	1.29951i	−0.928716	−	0.370793i	$-0.879086\pi$
$757$	−35.7542	−	35.7542i	−1.29951	−	1.29951i	−0.370793	−	0.928716i	$-0.620914\pi$
$758$	21.8825	+	17.7201i	0.794807	+	0.643622i
$759$	−2.84282	+	3.15727i	−0.103188	+	0.114602i
$760$	9.53646	+	7.24394i	0.345924	+	0.262765i
$761$	3.28308	−	2.95609i	0.119011	−	0.107158i	−0.607476	−	0.794338i	$-0.707818\pi$
$761$	3.28308	−	2.95609i	0.119011	−	0.107158i	0.726488	+	0.687179i	$0.241151\pi$
$762$	−3.17832	−	1.61944i	−0.115138	−	0.0586660i
$763$	−27.7957	+	33.3040i	−1.00627	+	1.20569i
$764$	−25.2152	−	8.19292i	−0.912255	−	0.296409i
$765$	8.89016	−	18.8750i	0.321424	−	0.682429i
$766$	−13.9864	−	12.5934i	−0.505349	−	0.455018i
$767$	3.34577	+	8.71602i	0.120809	+	0.314717i
$768$	21.3932	−	5.73230i	0.771962	−	0.206847i
$769$	29.9959	−	21.7933i	1.08168	−	0.785888i	0.103706	−	0.994608i	$-0.466930\pi$
$769$	29.9959	−	21.7933i	1.08168	−	0.785888i	0.977975	+	0.208720i	$0.0669299\pi$
$770$	3.96538	+	1.68884i	0.142902	+	0.0608617i
$771$	−19.8959	−	14.4552i	−0.716533	−	0.520592i
$772$	15.9478	+	6.12179i	0.573974	+	0.220328i
$773$	−5.44891	−	3.53856i	−0.195984	−	0.127273i	0.442917	−	0.896563i	$-0.353944\pi$
$773$	−5.44891	−	3.53856i	−0.195984	−	0.127273i	−0.638900	+	0.769290i	$0.720610\pi$
$774$	−2.55851	+	1.47716i	−0.0919638	+	0.0530953i
$775$	23.5856	+	1.00541i	0.847221	+	0.0361154i
$776$			31.1516i			1.11828i
$777$	6.26539	−	22.0700i	0.224769	−	0.791756i
$778$	10.2061	−	1.61648i	0.365905	−	0.0579537i
$779$	−1.89714	−	4.26104i	−0.0679721	−	0.152668i
$780$	−1.30755	+	2.43649i	−0.0468180	+	0.0872403i
$781$	0.681829	+	0.303570i	0.0243978	+	0.0108626i
$782$	−7.28085	−	27.1725i	−0.260363	−	0.971687i
$783$	−51.9834	−	8.23336i	−1.85773	−	0.294236i
$784$	2.82890	+	0.382337i	0.101032	+	0.0136549i
$785$	24.3487	+	28.2286i	0.869041	+	1.00752i
$786$	5.50878	+	6.11812i	0.196492	+	0.218226i
$787$	−0.373328	−	7.12353i	−0.0133077	−	0.253926i	−0.997180	−	0.0750519i	$-0.976088\pi$
$787$	−0.373328	−	7.12353i	−0.0133077	−	0.253926i	0.983872	−	0.178874i	$-0.0572456\pi$
$788$	−0.0901835	−	1.72080i	−0.00321265	−	0.0613011i
$789$	18.3118	+	20.3373i	0.651916	+	0.724026i
$790$	9.85706	+	2.31567i	0.350698	+	0.0823877i
$791$	10.4362	−	22.5359i	0.371069	−	0.801284i
$792$	−2.83807	−	0.449506i	−0.100846	−	0.0159725i
$793$	1.79222	+	6.68866i	0.0636436	+	0.237521i
$794$	9.66083	+	4.30128i	0.342850	+	0.152647i
$795$	−18.3899	−	19.1905i	−0.652222	−	0.680618i
$796$	1.63146	+	3.66431i	0.0578255	+	0.129878i
$797$	−29.5739	+	4.68404i	−1.04756	+	0.165917i	−0.656406	−	0.754408i	$-0.727924\pi$
$797$	−29.5739	+	4.68404i	−1.04756	+	0.165917i	−0.391154	+	0.920325i	$0.627924\pi$
$798$	4.14852	+	4.27326i	0.146856	+	0.151272i
$799$			85.6610i			3.03047i
$800$	−27.0308	+	3.10800i	−0.955683	+	0.109884i
$801$	−0.628409	+	0.362812i	−0.0222037	+	0.0128193i
$802$	22.6427	+	14.7044i	0.799542	+	0.519229i
$803$	−2.72638	−	1.04656i	−0.0962120	−	0.0369323i
$804$	−1.11553	−	0.810483i	−0.0393418	−	0.0285835i
$805$	13.8919	−	19.7889i	0.489625	−	0.697467i
$806$	2.89629	−	2.10428i	0.102017	−	0.0741200i
$807$	−1.63857	+	0.439053i	−0.0576803	+	0.0154554i
$808$	−6.59016	−	17.1680i	−0.231841	−	0.603967i
$809$	−1.59024	−	1.43186i	−0.0559098	−	0.0503414i	0.640702	−	0.767790i	$-0.278643\pi$
$809$	−1.59024	−	1.43186i	−0.0559098	−	0.0503414i	−0.696612	+	0.717448i	$0.745310\pi$
$810$	−6.64132	+	3.64801i	−0.233352	+	0.128178i
$811$	11.1135	+	3.61100i	0.390248	+	0.126799i	0.497567	−	0.867425i	$-0.334227\pi$
$811$	11.1135	+	3.61100i	0.390248	+	0.126799i	−0.107319	+	0.994225i	$0.534227\pi$
$812$	−21.7387	−	18.1432i	−0.762878	−	0.636702i
$813$	−14.6051	−	7.44168i	−0.512224	−	0.260991i
$814$	3.55384	−	3.19989i	0.124562	−	0.112156i
$815$	−45.9858	−	0.979697i	−1.61081	−	0.0343173i
$816$	−2.68014	+	2.97660i	−0.0938237	+	0.104202i
$817$	−3.63756	−	2.94564i	−0.127262	−	0.103055i
$818$	21.1298	+	21.1298i	0.738786	+	0.738786i
$819$	1.63084	−	2.17614i	0.0569862	−	0.0760405i
$820$	5.99523	+	2.44910i	0.209362	+	0.0855265i
$821$	24.0040	−	10.6873i	0.837744	−	0.372988i	0.0574100	−	0.998351i	$-0.481716\pi$
$821$	24.0040	−	10.6873i	0.837744	−	0.372988i	0.780334	+	0.625363i	$0.215049\pi$
$822$	14.9901	+	18.5112i	0.522839	+	0.645653i
$823$	10.6054	−	16.3309i	0.369682	−	0.569261i	−0.604053	−	0.796944i	$-0.706448\pi$
$823$	10.6054	−	16.3309i	0.369682	−	0.569261i	0.973735	+	0.227683i	$0.0731151\pi$
$824$	−14.4048	+	24.9499i	−0.501816	+	0.869171i
$825$	−4.95882	−	1.55789i	−0.172644	−	0.0542388i
$826$	−18.9873	+	20.4696i	−0.660652	+	0.712228i
$827$	−15.3550	+	7.82374i	−0.533944	+	0.272058i	−0.700104	−	0.714041i	$-0.746863\pi$
$827$	−15.3550	+	7.82374i	−0.533944	+	0.272058i	0.166160	+	0.986099i	$0.446863\pi$
$828$	−2.10070	+	5.47250i	−0.0730042	+	0.190182i
$829$	−4.34045	+	41.2966i	−0.150750	+	1.43429i	0.613665	+	0.789567i	$0.289695\pi$
$829$	−4.34045	+	41.2966i	−0.150750	+	1.43429i	−0.764415	+	0.644725i	$0.776972\pi$
$830$	7.77925	−	7.45470i	0.270022	−	0.258756i
$831$	−1.61600	+	0.169848i	−0.0560584	+	0.00589198i
$832$	−3.39004	+	3.39004i	−0.117529	+	0.117529i
$833$	47.0529	−	22.2447i	1.63029	−	0.770733i
$834$	−1.19410	+	0.387986i	−0.0413482	+	0.0134348i
$835$	7.24314	−	7.70764i	0.250659	−	0.266734i
$836$	−0.344208	−	1.61937i	−0.0119047	−	0.0560071i
$837$	−26.5018	+	1.38890i	−0.916036	+	0.0480074i
$838$	−14.2072	−	21.8772i	−0.490781	−	0.755736i
$839$	−11.9529	+	36.7873i	−0.412660	+	1.27004i	0.501666	+	0.865061i	$0.332720\pi$
$839$	−11.9529	+	36.7873i	−0.412660	+	1.27004i	−0.914327	+	0.404977i	$0.867280\pi$
$840$	−22.7247	−	0.820976i	−0.784077	−	0.0283264i
$841$	−18.1325	−	55.8062i	−0.625260	−	1.92435i
$842$	12.1205	−	14.9675i	0.417699	−	0.515815i
$843$	−0.602629	+	2.24904i	−0.0207557	+	0.0774612i
$844$	−9.27830	+	20.8394i	−0.319372	+	0.717322i
$845$	0.856116	+	27.5556i	0.0294513	+	0.947940i
$846$	−7.86749	+	10.8287i	−0.270490	+	0.372298i
$847$	12.1050	+	24.6533i	0.415932	+	0.847098i
$848$	−1.66591	−	3.26953i	−0.0572075	−	0.112276i
$849$	17.2494	+	9.95893i	0.591997	+	0.341789i
$850$	26.5340	−	21.9189i	0.910108	−	0.751812i
$851$	−13.4134	−	23.2326i	−0.459804	−	0.796404i
$852$	−1.43001	−	0.0749435i	−0.0489913	−	0.00256752i
$853$	4.26100	+	26.9029i	0.145894	+	0.921138i	0.946677	+	0.322184i	$0.104417\pi$
$853$	4.26100	+	26.9029i	0.145894	+	0.921138i	−0.800783	+	0.598954i	$0.795583\pi$
$854$	−15.5927	+	13.6271i	−0.533572	+	0.466309i
$855$	3.94391	+	3.33528i	0.134879	+	0.114064i
$856$	−1.65556	−	15.7516i	−0.0565860	−	0.538380i
$857$	37.0493	+	9.92732i	1.26558	+	0.339111i	0.828336	−	0.560232i	$-0.189288\pi$
$857$	37.0493	+	9.92732i	1.26558	+	0.339111i	0.437244	+	0.899343i	$0.355955\pi$
$858$	−0.735888	+	0.282481i	−0.0251228	+	0.00964374i
$859$	0.881487	+	0.187366i	0.0300759	+	0.00639284i	0.222925	−	0.974836i	$-0.428439\pi$
$859$	0.881487	+	0.187366i	0.0300759	+	0.00639284i	−0.192849	+	0.981228i	$0.561773\pi$
$860$	6.47631	−	0.541501i	0.220840	−	0.0184650i
$861$	7.60358	+	4.54138i	0.259129	+	0.154770i
$862$	−1.04523	+	2.05137i	−0.0356006	+	0.0698701i
$863$	0.986845	−	0.640865i	0.0335926	−	0.0218153i	−0.527733	−	0.849410i	$-0.676958\pi$
$863$	0.986845	−	0.640865i	0.0335926	−	0.0218153i	0.561326	+	0.827595i	$0.310291\pi$
$864$	29.9188	−	6.35943i	1.01786	−	0.216352i
$865$	6.82662	−	8.98707i	0.232112	−	0.305570i
$866$	1.78094	−	8.37865i	0.0605187	−	0.284718i
$867$	−7.91096	+	49.9479i	−0.268670	+	1.69632i
$868$	−12.6237	−	6.66943i	−0.428478	−	0.226375i
$869$	−2.26247	−	3.11402i	−0.0767490	−	0.105636i
$870$	−21.1731	−	14.4003i	−0.717836	−	0.488215i
$871$	0.743903	+	0.0781873i	0.0252062	+	0.00264928i
$872$	37.0746	−	30.0225i	1.25551	−	1.01669i
$873$	−0.703169	+	13.4173i	−0.0237987	+	0.454105i
$874$	6.96421			0.235568
$875$	29.0841	+	5.39565i	0.983223	+	0.182406i
$876$	5.60304			0.189309
$877$	2.16993	−	41.4047i	0.0732732	−	1.39814i	−0.676501	−	0.736442i	$-0.736504\pi$
$877$	2.16993	−	41.4047i	0.0732732	−	1.39814i	0.749774	−	0.661694i	$-0.230162\pi$
$878$	−15.2764	+	12.3706i	−0.515555	+	0.417488i
$879$	−5.09495	−	0.535501i	−0.171849	−	0.0180620i
$880$	−0.593361	−	0.403558i	−0.0200022	−	0.0136039i
$881$	20.7423	+	28.5494i	0.698827	+	0.961852i	0.999966	+	0.00827221i	$0.00263316\pi$
$881$	20.7423	+	28.5494i	0.698827	+	0.961852i	−0.301139	+	0.953580i	$0.597367\pi$
$882$	7.99116	+	1.50953i	0.269076	+	0.0508285i
$883$	−2.01591	+	12.7280i	−0.0678407	+	0.428330i	0.930269	+	0.366877i	$0.119573\pi$
$883$	−2.01591	+	12.7280i	−0.0678407	+	0.428330i	−0.998110	+	0.0614522i	$0.980427\pi$
$884$	−1.44711	+	6.80810i	−0.0486714	+	0.228981i
$885$	20.3668	−	26.8124i	0.684622	−	0.901288i
$886$	20.6443	−	4.38808i	0.693559	−	0.147421i
$887$	38.4301	−	24.9568i	1.29036	−	0.837968i	0.297207	−	0.954813i	$-0.403945\pi$
$887$	38.4301	−	24.9568i	1.29036	−	0.837968i	0.993150	+	0.116845i	$0.0372781\pi$
$888$	−11.4544	+	22.4805i	−0.384384	+	0.754397i
$889$	−3.75915	−	6.73962i	−0.126078	−	0.226040i
$890$	−1.19280	+	0.0997335i	−0.0399829	+	0.00334307i
$891$	2.81753	+	0.598885i	0.0943909	+	0.0200634i
$892$	−9.34433	+	3.58695i	−0.312871	+	0.120100i
$893$	−20.4839	−	5.48864i	−0.685467	−	0.183670i
$894$	−1.45568	−	13.8498i	−0.0486851	−	0.463208i
$895$	6.16345	+	5.21230i	0.206022	+	0.174228i
$896$	13.6826	+	4.67088i	0.457103	+	0.156043i
$897$	0.691729	+	4.36740i	0.0230961	+	0.145823i
$898$	30.1218	+	1.57862i	1.00518	+	0.0526792i
$899$	−22.1049	−	38.2867i	−0.737238	−	1.27693i
$900$	−7.15773	+	0.445193i	−0.238591	+	0.0148398i
$901$	−57.9395	−	33.4514i	−1.93025	−	1.11443i
$902$	0.838114	+	1.64489i	0.0279062	+	0.0547689i
$903$	8.86760	+	0.596535i	0.295095	+	0.0198514i
$904$	−16.0538	+	22.0961i	−0.533940	+	0.734905i
$905$	0.861729	+	27.7362i	0.0286448	+	0.921982i
$906$	−5.51747	+	12.3924i	−0.183306	+	0.411711i
$907$	−5.09475	+	19.0139i	−0.169168	+	0.631345i	0.828303	+	0.560280i	$0.189307\pi$
$907$	−5.09475	+	19.0139i	−0.169168	+	0.631345i	−0.997472	+	0.0710652i	$0.977360\pi$
$908$	−6.75456	+	8.34119i	−0.224158	+	0.276812i
$909$	−2.45091	−	7.54313i	−0.0812916	−	0.250190i
$910$	3.96332	−	2.10121i	0.131383	−	0.0696545i
$911$	10.8138	−	33.2815i	0.358278	−	1.10267i	−0.595807	−	0.803128i	$-0.703168\pi$
$911$	10.8138	−	33.2815i	0.358278	−	1.10267i	0.954085	−	0.299537i	$-0.0968323\pi$
$912$	−0.540059	−	0.831618i	−0.0178831	−	0.0275376i
$913$	−4.09027	+	0.214362i	−0.135368	+	0.00709434i
$914$	1.55506	+	7.31597i	0.0514367	+	0.241991i
$915$	17.1020	−	18.1988i	0.565376	−	0.601634i
$916$	9.35025	−	3.03808i	0.308941	−	0.100381i
$917$	2.52539	+	17.6308i	0.0833956	+	0.582220i
$918$	−27.3577	+	27.3577i	−0.902939	+	0.902939i
$919$	−36.1268	+	3.79708i	−1.19171	+	0.125254i	−0.679547	−	0.733632i	$-0.737824\pi$
$919$	−36.1268	+	3.79708i	−1.19171	+	0.125254i	−0.512167	+	0.858886i	$0.671157\pi$
$920$	−19.1981	+	18.3972i	−0.632943	+	0.606536i
$921$	−3.86362	+	36.7599i	−0.127311	+	1.21128i
$922$	−12.6344	+	32.9137i	−0.416091	+	1.08395i
$923$	0.692136	−	0.352661i	0.0227819	−	0.0116080i
$924$	2.30471	+	2.13781i	0.0758193	+	0.0703289i
$925$	19.0315	−	26.7395i	0.625752	−	0.879188i
$926$	−17.0216	+	29.4823i	−0.559364	+	0.968847i
$927$	−6.76745	+	10.4210i	−0.222272	+	0.342269i
$928$	32.0670	+	39.5994i	1.05265	+	1.29992i
$929$	−3.00637	+	1.33852i	−0.0986357	+	0.0439154i	−0.455461	−	0.890256i	$-0.650526\pi$
$929$	−3.00637	+	1.33852i	−0.0986357	+	0.0439154i	0.356826	+	0.934171i	$0.383859\pi$
$930$	−11.9524	−	4.88267i	−0.391935	−	0.160109i
$931$	2.30445	+	12.6769i	0.0755253	+	0.415470i
$932$	2.25132	+	2.25132i	0.0737446	+	0.0737446i
$933$	21.7407	+	17.6053i	0.711758	+	0.576370i
$934$	12.8985	−	14.3252i	0.422050	−	0.468734i
$935$	−13.0803	−	0.278668i	−0.427772	−	0.00911341i
$936$	−2.22250	+	2.00115i	−0.0726447	+	0.0654096i
$937$	8.94070	+	4.55551i	0.292080	+	0.148822i	0.593891	−	0.804546i	$-0.297591\pi$
$937$	8.94070	+	4.55551i	0.292080	+	0.148822i	−0.301811	+	0.953368i	$0.597591\pi$
$938$	0.770623	+	2.09998i	0.0251617	+	0.0685668i
$939$	−6.03743	−	1.96168i	−0.197024	−	0.0640170i
$940$	25.8073	−	14.1757i	0.841742	−	0.462360i
$941$	11.2179	+	10.1007i	0.365694	+	0.329272i	0.831407	−	0.555663i	$-0.187536\pi$
$941$	11.2179	+	10.1007i	0.365694	+	0.329272i	−0.465713	+	0.884936i	$0.654202\pi$
$942$	−7.30664	−	19.0345i	−0.238063	−	0.620176i
$943$	10.0033	−	2.68038i	0.325752	−	0.0872851i
$944$	3.76069	−	2.73230i	0.122400	−	0.0889288i
$945$	−33.1231	−	2.93811i	−1.07749	−	0.0955767i
$946$	1.49877	+	1.08892i	0.0487293	+	0.0354039i
$947$	53.2064	+	20.4240i	1.72898	+	0.663692i	0.999787	−	0.0206198i	$-0.00656394\pi$
$947$	53.2064	+	20.4240i	1.72898	+	0.663692i	0.729190	+	0.684312i	$0.239897\pi$
$948$	6.19361	+	4.02218i	0.201159	+	0.130634i
$949$	−2.63228	+	1.51975i	−0.0854473	+	0.0493330i
$950$	3.54127	+	7.74944i	0.114894	+	0.251425i
$951$		−	39.2544i		−	1.27291i
$952$	−55.5006	+	13.9938i	−1.79878	+	0.453540i
$953$	−15.7565	+	2.49558i	−0.510403	+	0.0808399i	−0.406324	−	0.913729i	$-0.633190\pi$
$953$	−15.7565	+	2.49558i	−0.510403	+	0.0808399i	−0.104079	+	0.994569i	$0.533190\pi$
$954$	−4.25199	−	9.55013i	−0.137663	−	0.309197i
$955$	−35.8882	−	37.4506i	−1.16131	−	1.21187i
$956$	−11.2381	−	5.00353i	−0.363467	−	0.161826i
$957$	2.51936	+	9.40237i	0.0814392	+	0.303935i
$958$	−1.27980	−	0.202701i	−0.0413486	−	0.00654897i
$959$	4.62690	+	51.3230i	0.149410	+	1.65731i
$960$	16.8321	+	3.95428i	0.543255	+	0.127624i
$961$	5.82696	+	6.47150i	0.187966	+	0.208758i
$962$	−0.260489	−	4.97043i	−0.00839852	−	0.160253i
$963$	−0.357511	−	6.82172i	−0.0115206	−	0.219827i
$964$	8.07068	+	8.96339i	0.259939	+	0.288691i
$965$	21.8285	+	25.3068i	0.702684	+	0.814655i
$966$	−10.8121	+	7.61337i	−0.347873	+	0.244956i
$967$	30.4690	+	4.82581i	0.979817	+	0.155188i	0.625743	−	0.780030i	$-0.284796\pi$
$967$	30.4690	+	4.82581i	0.979817	+	0.155188i	0.354074	+	0.935217i	$0.384796\pi$
$968$	−7.81746	−	29.1751i	−0.251263	−	0.937725i
$969$	−16.5159	−	7.35337i	−0.530568	−	0.236224i
$970$	−10.4801	+	19.5286i	−0.336497	+	0.627027i
$971$	−1.64054	−	3.68471i	−0.0526474	−	0.118248i	0.885307	−	0.465008i	$-0.153949\pi$
$971$	−1.64054	−	3.68471i	−0.0526474	−	0.118248i	−0.937954	+	0.346760i	$0.887282\pi$
$972$	13.5770	−	2.15038i	0.435482	−	0.0689736i
$973$	−2.61300	−	0.741798i	−0.0837690	−	0.0237810i
$974$			24.6259i			0.789064i
$975$	−4.50810	+	2.99053i	−0.144375	+	0.0957737i
$976$	2.98586	−	1.72388i	0.0955749	−	0.0551802i
$977$	−20.5729	−	13.3602i	−0.658184	−	0.427430i	0.171864	−	0.985121i	$-0.445021\pi$
$977$	−20.5729	−	13.3602i	−0.658184	−	0.427430i	−0.830049	+	0.557691i	$0.811688\pi$
$978$	23.4855	+	9.01525i	0.750984	+	0.288276i
$979$	0.368121	+	0.267456i	0.0117652	+	0.00854792i
$980$	−14.4883	−	10.4946i	−0.462812	−	0.335237i
$981$	16.6460	−	12.0940i	0.531467	−	0.386133i
$982$	−0.184678	+	0.0494843i	−0.00589331	+	0.00157911i
$983$	−16.3702	−	42.6458i	−0.522128	−	1.36019i	−0.900629	−	0.434590i	$-0.856893\pi$
$983$	−16.3702	−	42.6458i	−0.522128	−	1.36019i	0.378500	−	0.925601i	$-0.376440\pi$
$984$	−7.23821	−	6.51731i	−0.230746	−	0.207764i
$985$	1.43649	−	3.04986i	0.0457703	−	0.0971767i
$986$	−61.2982	−	19.9170i	−1.95213	−	0.634286i
$987$	37.8019	−	13.8720i	1.20325	−	0.441552i
$988$	−1.53528	−	0.782265i	−0.0488438	−	0.0248872i
$989$	7.72316	−	6.95396i	0.245582	−	0.221123i
$990$	−1.62793	−	1.23658i	−0.0517390	−	0.0393012i
$991$	30.6797	−	34.0732i	0.974571	−	1.08237i	−0.0220102	−	0.999758i	$-0.507007\pi$
$991$	30.6797	−	34.0732i	0.974571	−	1.08237i	0.996582	−	0.0826135i	$-0.0263267\pi$
$992$	19.9671	+	16.1691i	0.633957	+	0.513368i
$993$	21.4880	+	21.4880i	0.681902	+	0.681902i
$994$	1.85896	+	1.39314i	0.0589625	+	0.0441876i
$995$	−0.577522	+	7.82608i	−0.0183087	+	0.248103i
$996$	7.17903	−	3.19631i	0.227476	−	0.101279i
$997$	−14.3515	−	17.7226i	−0.454517	−	0.561281i	0.497446	−	0.867495i	$-0.334271\pi$
$997$	−14.3515	−	17.7226i	−0.454517	−	0.561281i	−0.951963	+	0.306213i	$0.900938\pi$
$998$	−11.9036	+	18.3300i	−0.376802	+	0.580225i
$999$	−18.4479	+	31.9527i	−0.583665	+	1.01094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.47.8	yes	288
5.2	odd	4		875.2.bb.a.243.8		288
5.3	odd	4		875.2.bb.b.243.11		288
5.4	even	2		875.2.bb.c.257.11		288
7.3	odd	6	inner	175.2.x.a.122.8	yes	288
25.6	even	5		875.2.bb.b.607.8		288
25.8	odd	20	inner	175.2.x.a.33.8	✓	288
25.17	odd	20		875.2.bb.c.768.11		288
25.19	even	10		875.2.bb.a.607.11		288
35.3	even	12		875.2.bb.b.493.8		288
35.17	even	12		875.2.bb.a.493.11		288
35.24	odd	6		875.2.bb.c.507.11		288
175.17	even	60		875.2.bb.c.143.11		288
175.31	odd	30		875.2.bb.b.857.11		288
175.94	odd	30		875.2.bb.a.857.8		288
175.108	even	60	inner	175.2.x.a.108.8	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.8	✓	288	25.8	odd	20	inner
175.2.x.a.47.8	yes	288	1.1	even	1	trivial
175.2.x.a.108.8	yes	288	175.108	even	60	inner
175.2.x.a.122.8	yes	288	7.3	odd	6	inner
875.2.bb.a.243.8		288	5.2	odd	4
875.2.bb.a.493.11		288	35.17	even	12
875.2.bb.a.607.11		288	25.19	even	10
875.2.bb.a.857.8		288	175.94	odd	30
875.2.bb.b.243.11		288	5.3	odd	4
875.2.bb.b.493.8		288	35.3	even	12
875.2.bb.b.607.8		288	25.6	even	5
875.2.bb.b.857.11		288	175.31	odd	30
875.2.bb.c.143.11		288	175.17	even	60
875.2.bb.c.257.11		288	5.4	even	2
875.2.bb.c.507.11		288	35.24	odd	6
875.2.bb.c.768.11		288	25.17	odd	20

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0484513 + 0.924506i) q^{2} +(-1.02662 + 0.831339i) q^{3} +(1.13668 + 0.119470i) q^{4} +(1.84896 + 1.25752i) q^{5} +(-0.718837 - 0.989394i) q^{6} +(-0.0993238 - 2.64389i) q^{7} +(-0.455170 + 2.87383i) q^{8} +(-0.260915 + 1.22751i) q^{9} +(-1.25217 + 1.64845i) q^{10} +(0.769743 - 0.163614i) q^{11} +(-1.26626 + 0.822316i) q^{12} +(0.371838 - 0.729773i) q^{13} +(2.44910 + 0.0362743i) q^{14} +(-2.94360 + 0.246122i) q^{15} +(-0.398891 - 0.0847869i) q^{16} +(-6.94132 + 2.66452i) q^{17} +(-1.12220 - 0.300692i) q^{18} +(-0.192403 - 1.83059i) q^{19} +(1.95144 + 1.65029i) q^{20} +(2.29993 + 2.63169i) q^{21} +(0.113967 + 0.719560i) q^{22} +(4.08126 + 0.213890i) q^{23} +(-1.92184 - 3.32873i) q^{24} +(1.83730 + 4.65020i) q^{25} +(0.656664 + 0.379125i) q^{26} +(-2.55179 - 5.00818i) q^{27} +(0.202965 - 3.01712i) q^{28} +(5.50382 - 7.57536i) q^{29} +(-0.0849201 - 2.73330i) q^{30} +(1.92037 - 4.31323i) q^{31} +(-1.40844 + 5.25635i) q^{32} +(-0.654214 + 0.807887i) q^{33} +(-2.12705 - 6.54639i) q^{34} +(3.14109 - 5.01334i) q^{35} +(-0.443227 + 1.36411i) q^{36} +(-3.57509 - 5.50515i) q^{37} +(1.70171 - 0.0891829i) q^{38} +(0.224953 + 1.05832i) q^{39} +(-4.45549 + 4.74122i) q^{40} +(2.40999 - 0.783055i) q^{41} +(-2.54445 + 1.99879i) q^{42} +(1.79811 - 1.79811i) q^{43} +(0.894499 - 0.0940156i) q^{44} +(-2.02603 + 1.94151i) q^{45} +(-0.395485 + 3.76279i) q^{46} +(4.12878 - 10.7558i) q^{47} +(0.479996 - 0.244570i) q^{48} +(-6.98027 + 0.525202i) q^{49} +(-4.38815 + 1.47329i) q^{50} +(4.91096 - 8.50604i) q^{51} +(0.509847 - 0.785095i) q^{52} +(5.66273 + 6.99289i) q^{53} +(4.75373 - 2.11650i) q^{54} +(1.62897 + 0.665450i) q^{55} +(7.64330 + 0.917979i) q^{56} +(1.71936 + 1.71936i) q^{57} +(6.73680 + 5.45535i) q^{58} +(-7.62729 + 8.47097i) q^{59} +(-3.37533 - 0.0719093i) q^{60} +(-6.28292 + 5.65717i) q^{61} +(3.89456 + 1.98438i) q^{62} +(3.27131 + 0.567908i) q^{63} +(-5.56698 - 1.80882i) q^{64} +(1.60522 - 0.881728i) q^{65} +(-0.715198 - 0.643968i) q^{66} +(0.327283 + 0.852602i) q^{67} +(-8.20839 + 2.19943i) q^{68} +(-4.36771 + 3.17333i) q^{69} +(4.48267 + 3.14686i) q^{70} +(0.767293 + 0.557471i) q^{71} +(-3.40889 - 1.30855i) q^{72} +(-3.11233 - 2.02117i) q^{73} +(5.26276 - 3.03846i) q^{74} +(-5.75210 - 3.24656i) q^{75} -2.10378i q^{76} +(-0.509031 - 2.01886i) q^{77} +(-0.989324 + 0.156693i) q^{78} +(-1.98946 - 4.46840i) q^{79} +(-0.630913 - 0.658380i) q^{80} +(3.34390 + 1.48880i) q^{81} +(0.607171 + 2.26599i) q^{82} +(-5.14074 - 0.814213i) q^{83} +(2.29988 + 3.26616i) q^{84} +(-16.1849 - 3.80224i) q^{85} +(1.57524 + 1.74948i) q^{86} +(0.647369 + 12.3525i) q^{87} +(0.119835 + 2.28659i) q^{88} +(0.386903 + 0.429700i) q^{89} +(-1.69677 - 1.96715i) q^{90} +(-1.96637 - 0.910613i) q^{91} +(4.61354 + 0.730712i) q^{92} +(1.61426 + 6.02451i) q^{93} +(9.74379 + 4.33822i) q^{94} +(1.94625 - 3.62663i) q^{95} +(-2.92389 - 6.56715i) q^{96} +(10.5745 - 1.67483i) q^{97} +(-0.147349 - 6.47875i) q^{98} +0.987555i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more