LMFDB - Embedded newform 507.2.t.b.127.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			127.9
Character	$\chi$	$=$	507.127
Dual form			507.2.t.b.4.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.805348 - 0.0324544i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(-1.34598 + 0.108659i) q^{4} +(3.20699 - 1.21625i) q^{5} +(-0.255235 - 0.764522i) q^{6} +(-0.483860 + 1.13566i) q^{7} +(-2.68071 + 0.325497i) q^{8} +(-0.845190 + 0.534466i) q^{9} +O(q^{10})$	\(q+(0.805348 - 0.0324544i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(-1.34598 + 0.108659i) q^{4} +(3.20699 - 1.21625i) q^{5} +(-0.255235 - 0.764522i) q^{6} +(-0.483860 + 1.13566i) q^{7} +(-2.68071 + 0.325497i) q^{8} +(-0.845190 + 0.534466i) q^{9} +(2.54327 - 1.08359i) q^{10} +(2.77501 - 4.38834i) q^{11} +(0.478845 + 1.26261i) q^{12} +(3.01421 - 1.97851i) q^{13} +(-0.352819 + 0.930306i) q^{14} +(-2.06047 - 2.74199i) q^{15} +(0.517408 - 0.0840871i) q^{16} +(-5.08545 - 2.16671i) q^{17} +(-0.663327 + 0.457861i) q^{18} +(4.80489 + 2.77410i) q^{19} +(-4.18439 + 1.98552i) q^{20} +(1.22544 + 0.148796i) q^{21} +(2.09243 - 3.62420i) q^{22} +(-1.90116 - 3.29291i) q^{23} +(1.05847 + 2.48431i) q^{24} +(5.06296 - 4.48540i) q^{25} +(2.36328 - 1.69122i) q^{26} +(0.748511 + 0.663123i) q^{27} +(0.527867 - 1.58116i) q^{28} +(-0.131184 - 3.25530i) q^{29} +(-1.74839 - 2.14139i) q^{30} +(-2.50702 + 2.82984i) q^{31} +(5.70561 - 1.16481i) q^{32} +(-4.98713 - 1.44454i) q^{33} +(-4.16587 - 1.57991i) q^{34} +(-0.170485 + 4.23055i) q^{35} +(1.07954 - 0.811219i) q^{36} +(-8.92640 - 1.82234i) q^{37} +(3.95964 + 2.07818i) q^{38} +(-2.73900 - 2.34475i) q^{39} +(-8.20112 + 4.30428i) q^{40} +(3.60284 - 1.04357i) q^{41} +(0.991737 + 0.0800612i) q^{42} +(0.0693153 + 0.339529i) q^{43} +(-3.25829 + 6.20815i) q^{44} +(-2.06047 + 2.74199i) q^{45} +(-1.63797 - 2.59024i) q^{46} +(7.76987 + 5.36316i) q^{47} +(-0.224719 - 0.473586i) q^{48} +(3.79346 + 3.94941i) q^{49} +(3.93188 - 3.77662i) q^{50} +(-0.666300 + 5.48748i) q^{51} +(-3.84210 + 2.99056i) q^{52} +(-0.910009 - 7.49460i) q^{53} +(0.624333 + 0.509752i) q^{54} +(3.56213 - 17.4485i) q^{55} +(0.927434 - 3.20187i) q^{56} +(1.32777 - 5.38699i) q^{57} +(-0.211298 - 2.61739i) q^{58} +(-1.35922 + 8.36361i) q^{59} +(3.07130 + 3.46678i) q^{60} +(6.36764 + 4.78497i) q^{61} +(-1.92718 + 2.36037i) q^{62} +(-0.198018 - 1.21846i) q^{63} +(3.53927 - 0.872352i) q^{64} +(7.26019 - 10.0111i) q^{65} +(-4.06326 - 1.00150i) q^{66} +(-0.716692 + 8.87782i) q^{67} +(7.08035 + 2.36377i) q^{68} +(-2.63396 + 2.74225i) q^{69} +3.41260i q^{70} +(6.04540 + 5.80668i) q^{71} +(2.09174 - 1.70785i) q^{72} +(-0.437205 - 0.833024i) q^{73} +(-7.24801 - 1.17792i) q^{74} +(-5.71691 - 3.61515i) q^{75} +(-6.76873 - 3.21180i) q^{76} +(3.64094 + 5.27482i) q^{77} +(-2.28195 - 1.79945i) q^{78} +(-5.43313 + 7.87125i) q^{79} +(1.55705 - 0.898965i) q^{80} +(0.428693 - 0.903450i) q^{81} +(2.86767 - 0.957368i) q^{82} +(3.25337 + 13.1995i) q^{83} +(-1.66559 - 0.0671210i) q^{84} +(-18.9442 - 0.763426i) q^{85} +(0.0668422 + 0.271189i) q^{86} +(-3.09028 + 1.03169i) q^{87} +(-6.01062 + 12.6671i) q^{88} +(-9.38692 + 5.41954i) q^{89} +(-1.57041 + 2.27513i) q^{90} +(0.788462 + 4.38045i) q^{91} +(2.91673 + 4.22562i) q^{92} +(3.41560 + 1.62072i) q^{93} +(6.43151 + 4.06704i) q^{94} +(18.7832 + 3.05257i) q^{95} +(-2.70622 - 5.15627i) q^{96} +(1.58439 - 1.29362i) q^{97} +(3.18324 + 3.05754i) q^{98} +5.19213i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{77}{78}\right)$

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 $

$2$	0.805348	−	0.0324544i	0.569467	−	0.0229487i	0.246137	−	0.969235i	$-0.420839\pi$
$2$	0.805348	−	0.0324544i	0.569467	−	0.0229487i	0.323330	+	0.946286i	$0.395198\pi$
$3$	−0.278217	−	0.960518i	−0.160629	−	0.554555i
$3$	−0.278217	−	0.960518i	−0.160629	−	0.554555i
$4$	−1.34598	+	0.108659i	−0.672991	+	0.0543295i
$5$	3.20699	−	1.21625i	1.43421	−	0.543924i	0.489550	−	0.871975i	$-0.337161\pi$
$5$	3.20699	−	1.21625i	1.43421	−	0.543924i	0.944660	+	0.328051i	$0.106392\pi$
$6$	−0.255235	−	0.764522i	−0.104199	−	0.312115i
$7$	−0.483860	+	1.13566i	−0.182882	+	0.429240i	−0.986036	−	0.166532i	$-0.946743\pi$
$7$	−0.483860	+	1.13566i	−0.182882	+	0.429240i	0.803154	+	0.595771i	$0.203154\pi$
$8$	−2.68071	+	0.325497i	−0.947774	+	0.115081i
$9$	−0.845190	+	0.534466i	−0.281730	+	0.178155i
$10$	2.54327	−	1.08359i	0.804253	−	0.342660i
$11$	2.77501	−	4.38834i	0.836699	−	1.32313i	−0.107651	−	0.994189i	$-0.534333\pi$
$11$	2.77501	−	4.38834i	0.836699	−	1.32313i	0.944349	−	0.328944i	$-0.106693\pi$
$12$	0.478845	+	1.26261i	0.138231	+	0.364484i
$13$	3.01421	−	1.97851i	0.835993	−	0.548741i
$13$	3.01421	−	1.97851i	0.835993	−	0.548741i
$14$	−0.352819	+	0.930306i	−0.0942948	+	0.248635i
$15$	−2.06047	−	2.74199i	−0.532011	−	0.707979i
$16$	0.517408	−	0.0840871i	0.129352	−	0.0210218i
$17$	−5.08545	−	2.16671i	−1.23340	−	0.525503i	−0.325841	−	0.945425i	$-0.605647\pi$
$17$	−5.08545	−	2.16671i	−1.23340	−	0.525503i	−0.907561	+	0.419921i	$0.862058\pi$
$18$	−0.663327	+	0.457861i	−0.156348	+	0.107919i
$19$	4.80489	+	2.77410i	1.10232	+	0.636423i	0.936829	−	0.349789i	$-0.113747\pi$
$19$	4.80489	+	2.77410i	1.10232	+	0.636423i	0.165488	+	0.986212i	$0.447080\pi$
$20$	−4.18439	+	1.98552i	−0.935659	+	0.443976i
$21$	1.22544	+	0.148796i	0.267413	+	0.0324699i
$22$	2.09243	−	3.62420i	0.446108	−	0.772682i
$23$	−1.90116	−	3.29291i	−0.396420	−	0.686619i	0.596862	−	0.802344i	$-0.296414\pi$
$23$	−1.90116	−	3.29291i	−0.396420	−	0.686619i	−0.993281	+	0.115725i	$0.963081\pi$
$24$	1.05847	+	2.48431i	0.216058	+	0.507108i
$25$	5.06296	−	4.48540i	1.01259	−	0.897079i
$26$	2.36328	−	1.69122i	0.463478	−	0.331675i
$27$	0.748511	+	0.663123i	0.144051	+	0.127618i
$28$	0.527867	−	1.58116i	0.0997576	−	0.298810i
$29$	−0.131184	−	3.25530i	−0.0243603	−	0.604494i	−0.964559	−	0.263868i	$-0.915002\pi$
$29$	−0.131184	−	3.25530i	−0.0243603	−	0.604494i	0.940199	−	0.340627i	$-0.110639\pi$
$30$	−1.74839	−	2.14139i	−0.319210	−	0.390962i
$31$	−2.50702	+	2.82984i	−0.450273	+	0.508253i	−0.929188	−	0.369608i	$-0.879492\pi$
$31$	−2.50702	+	2.82984i	−0.450273	+	0.508253i	0.478914	+	0.877862i	$0.341030\pi$
$32$	5.70561	−	1.16481i	1.00862	−	0.205911i
$33$	−4.98713	−	1.44454i	−0.868148	−	0.251462i
$34$	−4.16587	−	1.57991i	−0.714441	−	0.270952i
$35$	−0.170485	+	4.23055i	−0.0288173	+	0.715094i
$36$	1.07954	−	0.811219i	0.179923	−	0.135203i
$37$	−8.92640	−	1.82234i	−1.46749	−	0.299591i	−0.601188	−	0.799108i	$-0.705306\pi$
$37$	−8.92640	−	1.82234i	−1.46749	−	0.299591i	−0.866304	+	0.499517i	$0.833511\pi$
$38$	3.95964	+	2.07818i	0.642339	+	0.337125i
$39$	−2.73900	−	2.34475i	−0.438592	−	0.375461i
$40$	−8.20112	+	4.30428i	−1.29671	+	0.680566i
$41$	3.60284	−	1.04357i	0.562668	−	0.162979i	0.0153183	−	0.999883i	$-0.495124\pi$
$41$	3.60284	−	1.04357i	0.562668	−	0.162979i	0.547350	+	0.836904i	$0.315637\pi$
$42$	0.991737	+	0.0800612i	0.153028	+	0.0123537i
$43$	0.0693153	+	0.339529i	0.0105705	+	0.0517777i	0.984734	−	0.174067i	$-0.0556909\pi$
$43$	0.0693153	+	0.339529i	0.0105705	+	0.0517777i	−0.974163	+	0.225845i	$0.927486\pi$
$44$	−3.25829	+	6.20815i	−0.491206	+	0.935914i
$45$	−2.06047	+	2.74199i	−0.307157	+	0.408752i
$46$	−1.63797	−	2.59024i	−0.241505	−	0.381910i
$47$	7.76987	+	5.36316i	1.13335	+	0.782297i	0.978623	−	0.205660i	$-0.0659342\pi$
$47$	7.76987	+	5.36316i	1.13335	+	0.782297i	0.154729	+	0.987957i	$0.450550\pi$
$48$	−0.224719	−	0.473586i	−0.0324354	−	0.0683562i
$49$	3.79346	+	3.94941i	0.541923	+	0.564202i
$50$	3.93188	−	3.77662i	0.556052	−	0.534095i
$51$	−0.666300	+	5.48748i	−0.0933007	+	0.768401i
$52$	−3.84210	+	2.99056i	−0.532803	+	0.414717i
$53$	−0.910009	−	7.49460i	−0.124999	−	1.02946i	−0.911336	−	0.411664i	$-0.864948\pi$
$53$	−0.910009	−	7.49460i	−0.124999	−	1.02946i	0.786336	−	0.617799i	$-0.211975\pi$
$54$	0.624333	+	0.509752i	0.0849610	+	0.0693685i
$55$	3.56213	−	17.4485i	0.480317	−	2.35275i
$56$	0.927434	−	3.20187i	0.123934	−	0.427868i
$57$	1.32777	−	5.38699i	0.175868	−	0.713524i
$58$	−0.211298	−	2.61739i	−0.0277448	−	0.343681i
$59$	−1.35922	+	8.36361i	−0.176955	+	1.08885i	0.734851	+	0.678229i	$0.237252\pi$
$59$	−1.35922	+	8.36361i	−0.176955	+	1.08885i	−0.911806	+	0.410621i	$0.865312\pi$
$60$	3.07130	+	3.46678i	0.396503	+	0.447559i
$61$	6.36764	+	4.78497i	0.815293	+	0.612653i	0.924420	−	0.381375i	$-0.124549\pi$
$61$	6.36764	+	4.78497i	0.815293	+	0.612653i	−0.109128	+	0.994028i	$0.534806\pi$
$62$	−1.92718	+	2.36037i	−0.244752	+	0.299767i
$63$	−0.198018	−	1.21846i	−0.0249480	−	0.153511i
$64$	3.53927	−	0.872352i	0.442409	−	0.109044i
$65$	7.26019	−	10.0111i	0.900516	−	1.24173i
$66$	−4.06326	−	1.00150i	−0.500153	−	0.123277i
$67$	−0.716692	+	8.87782i	−0.0875578	+	1.08460i	0.792545	+	0.609814i	$0.208756\pi$
$67$	−0.716692	+	8.87782i	−0.0875578	+	1.08460i	−0.880102	+	0.474784i	$0.842526\pi$
$68$	7.08035	+	2.36377i	0.858619	+	0.286649i
$69$	−2.63396	+	2.74225i	−0.317092	+	0.330128i
$70$			3.41260i			0.407884i
$71$	6.04540	+	5.80668i	0.717456	+	0.689126i	0.959680	−	0.281094i	$-0.0906973\pi$
$71$	6.04540	+	5.80668i	0.717456	+	0.689126i	−0.242224	+	0.970220i	$0.577877\pi$
$72$	2.09174	−	1.70785i	0.246514	−	0.201272i
$73$	−0.437205	−	0.833024i	−0.0511710	−	0.0974981i	0.858528	−	0.512767i	$-0.171380\pi$
$73$	−0.437205	−	0.833024i	−0.0511710	−	0.0974981i	−0.909699	+	0.415269i	$0.863687\pi$
$74$	−7.24801	−	1.17792i	−0.842564	−	0.136930i
$75$	−5.71691	−	3.61515i	−0.660132	−	0.417442i
$76$	−6.76873	−	3.21180i	−0.776426	−	0.368419i
$77$	3.64094	+	5.27482i	0.414924	+	0.601121i
$78$	−2.28195	−	1.79945i	−0.258380	−	0.203747i
$79$	−5.43313	+	7.87125i	−0.611275	+	0.885585i	−0.999350	−	0.0360429i	$-0.988525\pi$
$79$	−5.43313	+	7.87125i	−0.611275	+	0.885585i	0.388075	+	0.921628i	$0.373140\pi$
$80$	1.55705	−	0.898965i	0.174084	−	0.100507i
$81$	0.428693	−	0.903450i	0.0476325	−	0.100383i
$82$	2.86767	−	0.957368i	0.316681	−	0.105724i
$83$	3.25337	+	13.1995i	0.357104	+	1.44883i	0.825044	+	0.565068i	$0.191150\pi$
$83$	3.25337	+	13.1995i	0.357104	+	1.44883i	−0.467940	+	0.883760i	$0.655004\pi$
$84$	−1.66559	−	0.0671210i	−0.181731	−	0.00732350i
$85$	−18.9442	−	0.763426i	−2.05479	−	0.0828052i
$86$	0.0668422	+	0.271189i	0.00720778	+	0.0292431i
$87$	−3.09028	+	1.03169i	−0.331313	+	0.110608i
$88$	−6.01062	+	12.6671i	−0.640734	+	1.35032i
$89$	−9.38692	+	5.41954i	−0.995012	+	0.574470i	−0.906769	−	0.421629i	$-0.861459\pi$
$89$	−9.38692	+	5.41954i	−0.995012	+	0.574470i	−0.0882430	+	0.996099i	$0.528125\pi$
$90$	−1.57041	+	2.27513i	−0.165535	+	0.239820i
$91$	0.788462	+	4.38045i	0.0826533	+	0.459196i
$92$	2.91673	+	4.22562i	0.304091	+	0.440551i
$93$	3.41560	+	1.62072i	0.354182	+	0.168061i
$94$	6.43151	+	4.06704i	0.663360	+	0.419483i
$95$	18.7832	+	3.05257i	1.92712	+	0.313187i
$96$	−2.70622	−	5.15627i	−0.276203	−	0.526260i
$97$	1.58439	−	1.29362i	0.160871	−	0.131347i	−0.548591	−	0.836091i	$-0.684836\pi$
$97$	1.58439	−	1.29362i	0.160871	−	0.131347i	0.709462	+	0.704744i	$0.248938\pi$
$98$	3.18324	+	3.05754i	0.321555	+	0.308858i
$99$			5.19213i			0.521829i
$100$	−6.32728	+	6.58740i	−0.632728	+	0.658740i
$101$	−1.67315	−	0.558580i	−0.166485	−	0.0555808i	0.232204	−	0.972667i	$-0.425406\pi$
$101$	−1.67315	−	0.558580i	−0.166485	−	0.0555808i	−0.398689	+	0.917086i	$0.630535\pi$
$102$	−0.358511	+	4.44095i	−0.0354979	+	0.439720i
$103$	−18.1193	−	4.46600i	−1.78534	−	0.440048i	−0.798537	−	0.601946i	$-0.794392\pi$
$103$	−18.1193	−	4.46600i	−1.78534	−	0.440048i	−0.986807	+	0.161898i	$0.948238\pi$
$104$	−7.43623	+	6.28493i	−0.729182	+	0.616288i
$105$	4.11095	−	1.01326i	0.401188	−	0.0988839i
$106$	−0.976107	−	6.00623i	−0.0948079	−	0.583377i
$107$	−8.27597	+	10.1362i	−0.800068	+	0.979905i	0.199932	+	0.979810i	$0.435928\pi$
$107$	−8.27597	+	10.1362i	−0.800068	+	0.979905i	−1.00000		9.56991e-5i	$0.999970\pi$
$108$	−1.07954	−	0.811219i	−0.103878	−	0.0780596i
$109$	8.91470	+	10.0626i	0.853874	+	0.963824i	0.999675	−	0.0254899i	$-0.00811457\pi$
$109$	8.91470	+	10.0626i	0.853874	+	0.963824i	−0.145802	+	0.989314i	$0.546576\pi$
$110$	2.30247	−	14.1677i	0.219532	−	1.35084i
$111$	0.733092	+	9.08098i	0.0695821	+	0.861928i
$112$	−0.154859	+	0.628287i	−0.0146328	+	0.0593676i
$113$	4.82549	−	16.6595i	0.453944	−	1.56720i	−0.328517	−	0.944498i	$-0.606549\pi$
$113$	4.82549	−	16.6595i	0.453944	−	1.56720i	0.782461	−	0.622699i	$-0.213964\pi$
$114$	0.894488	−	4.38149i	0.0837765	−	0.410364i
$115$	−10.1020	−	8.24804i	−0.942017	−	0.769133i
$116$	0.530289	+	4.36732i	0.0492361	+	0.405496i
$117$	−1.49014	+	3.28321i	−0.137763	+	0.303533i
$118$	−0.823208	+	6.77973i	−0.0757825	+	0.624125i
$119$	4.92129	−	4.72696i	0.451134	−	0.433320i
$120$	6.41603	+	6.67980i	0.585701	+	0.609779i
$121$	−6.84116	−	14.4174i	−0.621924	−	1.31068i
$122$	5.28346	+	3.64691i	0.478342	+	0.330176i
$123$	−2.00474	−	3.17025i	−0.180762	−	0.285852i
$124$	3.06691	−	4.08132i	0.275417	−	0.366513i
$125$	2.81180	−	5.35743i	0.251495	−	0.479183i
$126$	−0.199018	−	0.974855i	−0.0177299	−	0.0868470i
$127$	9.75963	+	0.787879i	0.866027	+	0.0699129i	0.505491	−	0.862832i	$-0.331312\pi$
$127$	9.75963	+	0.787879i	0.866027	+	0.0699129i	0.360537	+	0.932745i	$0.382594\pi$
$128$	−8.36473	+	2.42287i	−0.739345	+	0.214154i
$129$	0.306839	−	0.161042i	0.0270157	−	0.0141789i
$130$	5.52208	−	8.29805i	0.484318	−	0.727788i
$131$	−10.2990	−	5.40532i	−0.899826	−	0.472265i	−0.0496518	−	0.998767i	$-0.515811\pi$
$131$	−10.2990	−	5.40532i	−0.899826	−	0.472265i	−0.850174	+	0.526501i	$0.823503\pi$
$132$	6.86955	+	1.40243i	0.597918	+	0.122066i
$133$	−5.47534	+	4.11445i	−0.474772	+	0.356768i
$134$	−0.289062	+	7.17299i	−0.0249711	+	0.619652i
$135$	3.20699	+	1.21625i	0.276014	+	0.104678i
$136$	14.3379	+	4.15301i	1.22946	+	0.356118i
$137$	11.9953	−	2.44886i	1.02483	−	0.209220i	0.341924	−	0.939728i	$-0.388921\pi$
$137$	11.9953	−	2.44886i	1.02483	−	0.209220i	0.682905	+	0.730507i	$0.260716\pi$
$138$	−2.03226	+	2.29395i	−0.172997	+	0.195274i
$139$	−7.94595	−	9.73202i	−0.673966	−	0.825459i	0.318507	−	0.947921i	$-0.396819\pi$
$139$	−7.94595	−	9.73202i	−0.673966	−	0.825459i	−0.992473	+	0.122462i	$0.960921\pi$
$140$	−0.230217	−	5.71277i	−0.0194569	−	0.482817i
$141$	2.98969	−	8.95523i	0.251778	−	0.754166i
$142$	5.05710	+	4.48020i	0.424383	+	0.375970i
$143$	−0.317884	−	18.7178i	−0.0265828	−	1.56526i
$144$	−0.392367	+	0.347607i	−0.0326972	+	0.0289672i
$145$	−4.37997	−	10.2802i	−0.363737	−	0.853722i
$146$	−0.379138	−	0.656686i	−0.0313776	−	0.0543477i
$147$	2.73808	−	4.74249i	0.225833	−	0.391154i
$148$	12.2128	+	1.48290i	1.00389	+	0.121894i
$149$	7.81141	−	3.70656i	0.639936	−	0.303653i	−0.0809386	−	0.996719i	$-0.525792\pi$
$149$	7.81141	−	3.70656i	0.639936	−	0.303653i	0.720874	+	0.693066i	$0.243740\pi$
$150$	−4.72143	−	2.72592i	−0.385503	−	0.222570i
$151$	−5.24758	+	3.62214i	−0.427042	+	0.294766i	−0.762134	−	0.647420i	$-0.775848\pi$
$151$	−5.24758	+	3.62214i	−0.427042	+	0.294766i	0.335092	+	0.942186i	$0.391233\pi$
$152$	−13.7835	−	5.87259i	−1.11799	−	0.476330i
$153$	5.45620	−	0.886718i	0.441107	−	0.0716869i
$154$	3.10342	+	4.12990i	0.250081	+	0.332797i
$155$	−4.59818	+	12.1244i	−0.369335	+	0.973856i
$156$	3.94143	+	2.85838i	0.315567	+	0.228853i
$157$	4.54493	+	11.9840i	0.362725	+	0.956427i	0.984834	+	0.173497i	$0.0555067\pi$
$157$	4.54493	+	11.9840i	0.362725	+	0.956427i	−0.622109	+	0.782930i	$0.713724\pi$
$158$	−4.12011	+	6.51543i	−0.327778	+	0.518339i
$159$	−6.94552	+	2.95921i	−0.550815	+	0.234681i
$160$	16.8811	−	10.6750i	1.33457	−	0.843932i
$161$	4.65953	−	0.565769i	0.367222	−	0.0445888i
$162$	0.315926	−	0.741505i	0.0248215	−	0.0582581i
$163$	1.38214	+	4.14002i	0.108258	+	0.324271i	0.988705	−	0.149872i	$-0.0478861\pi$
$163$	1.38214	+	4.14002i	0.108258	+	0.324271i	−0.880448	+	0.474143i	$0.842758\pi$
$164$	−4.73596	+	1.79611i	−0.369816	+	0.140253i
$165$	−17.7506	+	1.43298i	−1.38188	+	0.111557i
$166$	3.04848	+	10.5246i	0.236608	+	0.816865i
$167$	21.9907	−	0.886194i	1.70169	−	0.0685758i	0.829734	−	0.558160i	$-0.188492\pi$
$167$	21.9907	−	0.886194i	1.70169	−	0.0685758i	0.871956	+	0.489584i	$0.162851\pi$
$168$	−3.33348			−0.257184
$169$	5.17098	−	11.9273i	0.397768	−	0.917486i
$170$	−15.2815			−1.17204
$171$	−5.54371	+	0.223404i	−0.423938	+	0.0170841i
$172$	−0.130190	−	0.449468i	−0.00992690	−	0.0342716i
$173$	−0.106451	+	0.00859362i	−0.00809332	+	0.000653361i	−0.0845126	−	0.996422i	$-0.526933\pi$
$173$	−0.106451	+	0.00859362i	−0.00809332	+	0.000653361i	0.0764192	+	0.997076i	$0.475651\pi$
$174$	−2.45527	+	0.931160i	−0.186133	+	0.0705911i
$175$	2.64412	+	7.92012i	0.199877	+	0.598705i
$176$	1.06681	−	2.50390i	0.0804141	−	0.188739i
$177$	8.41156	−	1.02135i	0.632251	−	0.0767692i
$178$	−7.38385	+	4.66926i	−0.553443	+	0.349976i
$179$	−1.30689	+	0.556813i	−0.0976815	+	0.0416182i	−0.440255	−	0.897873i	$-0.645112\pi$
$179$	−1.30689	+	0.556813i	−0.0976815	+	0.0416182i	0.342573	+	0.939491i	$0.388702\pi$
$180$	2.47542	−	3.91456i	0.184507	−	0.291774i
$181$	−3.49265	−	9.20936i	−0.259607	−	0.684526i	−0.999925	−	0.0122696i	$-0.996094\pi$
$181$	−3.49265	−	9.20936i	−0.259607	−	0.684526i	0.740318	−	0.672257i	$-0.234675\pi$
$182$	0.777151	+	3.50220i	0.0576063	+	0.259600i
$183$	2.82446	−	7.44749i	0.208790	−	0.550535i
$184$	6.16829	+	8.20851i	0.454733	+	0.605139i
$185$	−30.8433	+	5.01253i	−2.26765	+	0.368528i
$186$	2.80335	+	1.19440i	0.205552	+	0.0875773i
$187$	−23.6204	+	16.3040i	−1.72730	+	1.19227i
$188$	−11.0409	−	6.37445i	−0.805238	−	0.464904i
$189$	−1.11526	+	0.529196i	−0.0811230	+	0.0384934i
$190$	15.2261	+	1.84879i	1.10462	+	0.134125i
$191$	−7.12161	+	12.3350i	−0.515302	+	0.892529i	0.484540	+	0.874769i	$0.338987\pi$
$191$	−7.12161	+	12.3350i	−0.515302	+	0.892529i	−0.999842	+	0.0177601i	$0.994346\pi$
$192$	−1.82260	−	3.15683i	−0.131535	−	0.227825i
$193$	−7.90786	−	18.5604i	−0.569220	−	1.33601i	−0.917170	−	0.398496i	$-0.869532\pi$
$193$	−7.90786	−	18.5604i	−0.569220	−	1.33601i	0.347950	−	0.937513i	$-0.386878\pi$
$194$	1.23401	−	1.09323i	0.0885965	−	0.0784896i
$195$	−11.6358	−	4.18828i	−0.833254	−	0.299929i
$196$	−5.53507	−	4.90365i	−0.395362	−	0.350261i
$197$	−0.834376	+	2.49926i	−0.0594468	+	0.178065i	−0.974072	−	0.226237i	$-0.927357\pi$
$197$	−0.834376	+	2.49926i	−0.0594468	+	0.178065i	0.914625	+	0.404302i	$0.132486\pi$
$198$	0.168508	+	4.18147i	0.0119753	+	0.297164i
$199$	2.44892	+	2.99939i	0.173600	+	0.212621i	0.854075	−	0.520150i	$-0.174124\pi$
$199$	2.44892	+	2.99939i	0.173600	+	0.212621i	−0.680475	+	0.732771i	$0.738227\pi$
$200$	−12.1123	+	13.6720i	−0.856472	+	0.966758i
$201$	8.72670	−	1.78157i	0.615534	−	0.125662i
$202$	−1.36560	−	0.395551i	−0.0960832	−	0.0278308i
$203$	3.76040	+	1.42613i	0.263928	+	0.100095i
$204$	0.300565	−	7.45845i	0.0210438	−	0.522196i
$205$	10.2850	−	7.72868i	0.718336	−	0.539795i
$206$	−14.7373	−	3.00863i	−1.02679	−	0.209621i
$207$	3.36679	+	1.76703i	0.234008	+	0.122817i
$208$	1.39321	−	1.27716i	0.0966019	−	0.0885548i
$209$	25.5073	−	13.3873i	1.76438	−	0.926018i
$210$	3.27786	−	0.949445i	0.226194	−	0.0655179i
$211$	7.59534	+	0.613159i	0.522885	+	0.0422116i	0.339092	−	0.940753i	$-0.389880\pi$
$211$	7.59534	+	0.613159i	0.522885	+	0.0422116i	0.183793	+	0.982965i	$0.441162\pi$
$212$	2.03921	+	9.98872i	0.140054	+	0.686028i
$213$	3.89549	−	7.42223i	0.266914	−	0.508563i
$214$	−6.33607	+	8.43178i	−0.433125	+	0.576385i
$215$	0.635246	+	1.00456i	0.0433234	+	0.0685105i
$216$	−2.22238	−	1.53400i	−0.151214	−	0.104376i
$217$	−2.00069	−	4.21637i	−0.135816	−	0.286226i
$218$	7.50602	+	7.81459i	0.508371	+	0.529271i
$219$	−0.678497	+	0.651705i	−0.0458486	+	0.0440382i
$220$	−2.89863	+	23.8724i	−0.195426	+	1.60948i
$221$	−19.6155	+	3.53070i	−1.31948	+	0.237501i
$222$	0.885113	+	7.28956i	0.0594049	+	0.489243i
$223$	−9.79428	−	7.99679i	−0.655874	−	0.535504i	0.245034	−	0.969514i	$-0.421201\pi$
$223$	−9.79428	−	7.99679i	−0.655874	−	0.535504i	−0.900908	+	0.434010i	$0.857098\pi$
$224$	−1.43789	+	7.04325i	−0.0960731	+	0.470597i
$225$	−1.88188	+	6.49699i	−0.125458	+	0.433133i
$226$	3.34553	−	13.5733i	0.222541	−	0.902885i
$227$	−0.484078	−	5.99638i	−0.0321294	−	0.397994i	−0.992756	−	0.120150i	$-0.961662\pi$
$227$	−0.484078	−	5.99638i	−0.0321294	−	0.397994i	0.960626	−	0.277843i	$-0.0896196\pi$
$228$	−1.20181	+	7.39506i	−0.0795921	+	0.489750i
$229$	6.88388	+	7.77029i	0.454899	+	0.513475i	0.930553	−	0.366157i	$-0.119327\pi$
$229$	6.88388	+	7.77029i	0.454899	+	0.513475i	−0.475653	+	0.879633i	$0.657788\pi$
$230$	−8.40332	−	6.31469i	−0.554099	−	0.416378i
$231$	4.05358	−	4.96474i	0.266706	−	0.326656i
$232$	1.41126	+	8.68382i	0.0926536	+	0.570120i
$233$	14.7445	−	3.63420i	0.965945	−	0.238084i	0.275365	−	0.961340i	$-0.411201\pi$
$233$	14.7445	−	3.63420i	0.965945	−	0.238084i	0.690580	+	0.723256i	$0.257355\pi$
$234$	−1.09352	+	2.69249i	−0.0714859	+	0.176014i
$235$	31.4408	+	7.74947i	2.05097	+	0.505520i
$236$	0.920704	−	11.4050i	0.0599327	−	0.742400i
$237$	9.07207	+	3.02870i	0.589294	+	0.196735i
$238$	3.80994	−	3.96657i	0.246962	−	0.257114i
$239$		−	19.3611i		−	1.25237i	−0.779675	−	0.626184i	$-0.784616\pi$
$239$		−	19.3611i		−	1.25237i	0.779675	−	0.626184i	$-0.215384\pi$
$240$	−1.29667	−	1.24547i	−0.0836998	−	0.0803947i
$241$	−16.0008	+	13.0642i	−1.03070	+	0.841540i	−0.987515	−	0.157527i	$-0.949648\pi$
$241$	−16.0008	+	13.0642i	−1.03070	+	0.841540i	−0.0431847	+	0.999067i	$0.513750\pi$
$242$	−5.97742	−	11.3890i	−0.384243	−	0.732115i
$243$	−0.987050	−	0.160411i	−0.0633193	−	0.0102904i
$244$	−9.09066	−	5.74858i	−0.581970	−	0.368015i
$245$	16.9691	+	8.05193i	1.08411	+	0.514419i
$246$	−1.71741	−	2.48809i	−0.109498	−	0.158635i
$247$	19.9716	−	1.14479i	1.27076	−	0.0728410i
$248$	5.79947	−	8.40199i	0.368267	−	0.533527i
$249$	11.7732	−	6.79724i	0.746094	−	0.430758i
$250$	2.09060	−	4.40585i	0.132221	−	0.278651i
$251$	21.3336	−	7.12221i	1.34657	−	0.449550i	0.450225	−	0.892915i	$-0.351344\pi$
$251$	21.3336	−	7.12221i	1.34657	−	0.449550i	0.896341	+	0.443365i	$0.146215\pi$
$252$	0.398926	+	1.61850i	0.0251299	+	0.101956i
$253$	−19.7261	−	0.794936i	−1.24017	−	0.0499772i
$254$	7.88547	+	0.317774i	0.494778	+	0.0199389i
$255$	4.53733	+	18.4087i	0.284139	+	1.15280i
$256$	−13.5731	+	4.53136i	−0.848318	+	0.283210i
$257$	−8.69496	+	18.3242i	−0.542377	+	1.14303i	0.428519	+	0.903533i	$0.359035\pi$
$257$	−8.69496	+	18.3242i	−0.542377	+	1.14303i	−0.970896	+	0.239502i	$0.923016\pi$
$258$	0.241886	−	0.139653i	0.0150591	−	0.00869440i
$259$	6.38869	−	9.25562i	0.396974	−	0.575116i
$260$	−8.68429	+	14.2637i	−0.538577	+	0.884595i
$261$	1.85072	+	2.68124i	0.114557	+	0.165964i
$262$	−8.46969	−	4.01892i	−0.523259	−	0.248290i
$263$	4.15652	+	2.62842i	0.256302	+	0.162076i	0.656438	−	0.754380i	$-0.272063\pi$
$263$	4.15652	+	2.62842i	0.256302	+	0.162076i	−0.400135	+	0.916456i	$0.631037\pi$
$264$	13.8392	+	2.24910i	0.851746	+	0.138422i
$265$	−12.0337	−	22.9283i	−0.739225	−	1.40847i
$266$	−4.27602	+	3.49126i	−0.262180	+	0.214063i
$267$	7.81717	+	7.50850i	0.478403	+	0.459512i
$268$		−	12.0273i		−	0.734682i
$269$	10.8898	−	11.3374i	0.663960	−	0.691256i	−0.301008	−	0.953622i	$-0.597323\pi$
$269$	10.8898	−	11.3374i	0.663960	−	0.691256i	0.964969	+	0.262366i	$0.0845026\pi$
$270$	2.62222	+	0.875424i	0.159583	+	0.0532766i
$271$	0.399918	−	4.95387i	0.0242933	−	0.300926i	−0.973189	−	0.230008i	$-0.926125\pi$
$271$	0.399918	−	4.95387i	0.0242933	−	0.300926i	0.997482	−	0.0709185i	$-0.0225930\pi$
$272$	−2.81344	−	0.693452i	−0.170590	−	0.0420467i
$273$	3.98814	−	1.97605i	0.241373	−	0.119596i
$274$	9.58093	−	2.36149i	0.578805	−	0.142663i
$275$	−5.63361	−	34.6650i	−0.339720	−	2.09038i
$276$	3.24730	−	3.97722i	0.195464	−	0.239400i
$277$	−16.6637	−	12.5219i	−1.00122	−	0.752370i	−0.0322357	−	0.999480i	$-0.510263\pi$
$277$	−16.6637	−	12.5219i	−1.00122	−	0.752370i	−0.968987	+	0.247110i	$0.920519\pi$
$278$	−6.71510	−	7.57978i	−0.402745	−	0.454605i
$279$	0.606454	−	3.73166i	0.0363075	−	0.223409i
$280$	−0.920010	−	11.3964i	−0.0549811	−	0.681063i
$281$	−0.799529	+	3.24382i	−0.0476959	+	0.193510i	−0.989957	−	0.141369i	$-0.954849\pi$
$281$	−0.799529	+	3.24382i	−0.0476959	+	0.193510i	0.942261	+	0.334879i	$0.108696\pi$
$282$	2.11711	−	7.30910i	0.126072	−	0.435251i
$283$	1.16522	−	5.70760i	0.0692649	−	0.339282i	−0.930361	−	0.366646i	$-0.880506\pi$
$283$	1.16522	−	5.70760i	0.0692649	−	0.339282i	0.999626	+	0.0273638i	$0.00871126\pi$
$284$	−8.76794	−	7.15880i	−0.520282	−	0.424797i
$285$	−2.29377	−	18.8909i	−0.135871	−	1.11900i
$286$	−0.863482	−	15.0640i	−0.0510588	−	0.890754i
$287$	−0.558122	+	4.59655i	−0.0329449	+	0.271326i
$288$	−4.19978	+	4.03394i	−0.247474	+	0.237702i
$289$	9.39082	+	9.77688i	0.552401	+	0.575111i
$290$	−3.86104	−	8.13697i	−0.226728	−	0.477819i
$291$	−1.68335	−	1.16193i	−0.0986797	−	0.0681137i
$292$	0.678986	+	1.07373i	0.0397346	+	0.0628353i
$293$	−16.3181	+	21.7154i	−0.953313	+	1.26863i	0.00991672	+	0.999951i	$0.496843\pi$
$293$	−16.3181	+	21.7154i	−0.953313	+	1.26863i	−0.963230	+	0.268679i	$0.913413\pi$
$294$	2.05119	−	3.90822i	0.119628	−	0.227932i
$295$	5.81325	+	28.4752i	0.338460	+	1.65789i
$296$	24.5223	+	1.97964i	1.42533	+	0.115064i
$297$	4.98713	−	1.44454i	0.289383	−	0.0838208i
$298$	6.17061	−	3.23859i	0.357454	−	0.187606i
$299$	−12.2456	−	6.16406i	−0.708180	−	0.356477i
$300$	8.08768	+	4.24474i	0.466942	+	0.245070i
$301$	−0.419129	−	0.0855658i	−0.0241582	−	0.00493193i
$302$	−4.10857	+	3.08739i	−0.236422	+	0.177659i
$303$	−0.0710263	+	1.76250i	−0.00408036	+	0.101253i
$304$	2.71936	+	1.03132i	0.155966	+	0.0591500i
$305$	26.2407	+	7.60070i	1.50254	+	0.435215i
$306$	4.36536	−	0.891195i	0.249551	−	0.0509462i
$307$	17.6061	−	19.8732i	1.00483	−	1.13422i	0.0138948	−	0.999903i	$-0.495577\pi$
$307$	17.6061	−	19.8732i	1.00483	−	1.13422i	0.990938	−	0.134319i	$-0.0428845\pi$
$308$	−5.47380	−	6.70419i	−0.311899	−	0.382007i
$309$	0.751424	+	18.6464i	0.0427470	+	1.06076i
$310$	−3.30965	+	9.91361i	−0.187975	+	0.563055i
$311$	9.12536	+	8.08436i	0.517452	+	0.458422i	0.880975	−	0.473163i	$-0.156888\pi$
$311$	9.12536	+	8.08436i	0.517452	+	0.458422i	−0.363523	+	0.931585i	$0.618426\pi$
$312$	8.10568	+	5.39406i	0.458894	+	0.305378i
$313$	−14.0361	+	12.4349i	−0.793366	+	0.702861i	−0.959025	−	0.283322i	$-0.908563\pi$
$313$	−14.0361	+	12.4349i	−0.793366	+	0.702861i	0.165659	+	0.986183i	$0.447025\pi$
$314$	4.04919	+	9.50379i	0.228509	+	0.536330i
$315$	−2.11699	−	3.66674i	−0.119279	−	0.206597i
$316$	6.45762	−	11.1849i	0.363269	−	0.629201i
$317$	−31.8210	−	3.86377i	−1.78724	−	0.217011i	−0.841127	−	0.540837i	$-0.818108\pi$
$317$	−31.8210	−	3.86377i	−1.78724	−	0.217011i	−0.946117	+	0.323826i	$0.895031\pi$
$318$	−5.49752	+	2.60861i	−0.308286	+	0.146283i
$319$	−14.6494	−	8.45783i	−0.820209	−	0.473548i
$320$	10.2894	−	7.10227i	0.575196	−	0.397029i
$321$	12.0385	+	5.12914i	0.671926	+	0.286281i
$322$	3.73418	−	0.606863i	0.208098	−	0.0338192i
$323$	−18.4243	−	24.5183i	−1.02516	−	1.36424i
$324$	−0.478845	+	1.26261i	−0.0266025	+	0.0701450i
$325$	6.38645	−	23.5371i	0.354257	−	1.30560i
$326$	1.24747	+	3.28930i	0.0690908	+	0.182177i
$327$	7.18510	−	11.3623i	0.397337	−	0.628338i
$328$	−9.31847	+	3.97023i	−0.514526	+	0.219219i
$329$	−9.85026	+	6.22893i	−0.543062	+	0.343412i
$330$	−14.2489	+	1.73013i	−0.784377	+	0.0952406i
$331$	−2.69147	+	6.31710i	−0.147936	+	0.347219i	−0.977418	−	0.211314i	$-0.932226\pi$
$331$	−2.69147	+	6.31710i	−0.147936	+	0.347219i	0.829482	+	0.558534i	$0.188636\pi$
$332$	−5.81322	−	17.4127i	−0.319042	−	0.955647i
$333$	8.51849	−	3.23064i	0.466810	−	0.177038i
$334$	17.6814	−	1.42739i	0.967483	−	0.0781033i
$335$	8.49923	+	29.3427i	0.464363	+	1.60317i
$336$	0.646566	−	0.0260557i	0.0352731	−	0.00142146i
$337$	−19.7371			−1.07515			−0.537575	−	0.843216i	$-0.680659\pi$
$337$	−19.7371			−1.07515			−0.537575	+	0.843216i	$0.680659\pi$
$338$	3.77734	−	9.77347i	0.205460	−	0.531607i
$339$	−17.3443			−0.942014
$340$	25.5815	−	1.03090i	1.38735	−	0.0559085i
$341$	5.46126	+	18.8545i	0.295744	+	1.02103i
$342$	−4.45737	+	0.359836i	−0.241027	+	0.0194577i
$343$	−14.4003	+	5.46130i	−0.777541	+	0.294883i
$344$	−0.296330	−	0.887616i	−0.0159770	−	0.0478571i
$345$	−5.11183	+	11.9979i	−0.275212	+	0.645946i
$346$	−0.0854513	+	0.0103757i	−0.00459389	+	0.000557799i
$347$	−19.5609	+	12.3695i	−1.05008	+	0.664032i	−0.943872	−	0.330311i	$-0.892846\pi$
$347$	−19.5609	+	12.3695i	−1.05008	+	0.664032i	−0.106211	+	0.994344i	$0.533872\pi$
$348$	4.04736	−	1.72442i	0.216961	−	0.0924385i
$349$	13.8630	−	21.9225i	0.742067	−	1.17348i	−0.237308	−	0.971434i	$-0.576265\pi$
$349$	13.8630	−	21.9225i	0.742067	−	1.17348i	0.979375	−	0.202050i	$-0.0647604\pi$
$350$	2.38648	+	6.29264i	0.127563	+	0.336356i
$351$	3.56817	+	0.517856i	0.190455	+	0.0276411i
$352$	10.7216	−	28.2705i	0.571463	−	1.50682i
$353$	−13.1197	−	17.4591i	−0.698291	−	0.929256i	0.301416	−	0.953493i	$-0.402541\pi$
$353$	−13.1197	−	17.4591i	−0.698291	−	0.929256i	−0.999706	+	0.0242368i	$0.992284\pi$
$354$	6.74109	−	1.09553i	0.358285	−	0.0582269i
$355$	26.4499	+	11.2693i	1.40382	+	0.598110i
$356$	12.0457	−	8.31458i	0.638423	−	0.440672i
$357$	−5.90952	−	3.41186i	−0.312765	−	0.180575i
$358$	−1.03443	+	0.490843i	−0.0546713	+	0.0259419i
$359$	15.1951	+	1.84502i	0.801969	+	0.0973766i	0.511250	−	0.859432i	$-0.329183\pi$
$359$	15.1951	+	1.84502i	0.801969	+	0.0973766i	0.290719	+	0.956809i	$0.406106\pi$
$360$	4.63101	−	8.02115i	0.244076	−	0.422752i
$361$	5.89131	+	10.2040i	0.310069	+	0.537055i
$362$	−3.11168	−	7.30339i	−0.163546	−	0.383858i
$363$	−11.9449	+	10.5822i	−0.626944	+	0.555424i
$364$	−1.53723	−	5.81034i	−0.0805728	−	0.304544i
$365$	−2.41528	−	2.13975i	−0.126421	−	0.112000i
$366$	2.03297	−	6.08949i	0.106265	−	0.318303i
$367$	0.00437954	+	0.108677i	0.000228610	+	0.00567290i	0.999299	−	0.0374293i	$-0.0119169\pi$
$367$	0.00437954	+	0.108677i	0.000228610	+	0.00567290i	−0.999071	+	0.0431022i	$0.986276\pi$
$368$	−1.26057	−	1.54392i	−0.0657117	−	0.0804822i
$369$	−2.48733	+	2.80761i	−0.129485	+	0.146158i
$370$	−24.6769	+	5.03783i	−1.28289	+	0.261904i
$371$	8.95165	+	2.59288i	0.464746	+	0.134615i
$372$	−4.77345	−	1.81033i	−0.247492	−	0.0938612i
$373$	−0.795867	+	19.7492i	−0.0412084	+	1.02258i	0.837861	+	0.545883i	$0.183806\pi$
$373$	−0.795867	+	19.7492i	−0.0412084	+	1.02258i	−0.879070	+	0.476693i	$0.841835\pi$
$374$	−18.4935	+	13.8970i	−0.956277	+	0.718596i
$375$	−5.92820	−	1.21025i	−0.306131	−	0.0624971i
$376$	−22.5745	−	11.8480i	−1.16419	−	0.611013i
$377$	−6.83607	−	9.55263i	−0.352076	−	0.491985i
$378$	−0.880996	+	0.462382i	−0.0453135	+	0.0237824i
$379$	−7.98378	+	2.31253i	−0.410099	+	0.118787i	−0.476853	−	0.878983i	$-0.658223\pi$
$379$	−7.98378	+	2.31253i	−0.410099	+	0.118787i	0.0667545	+	0.997769i	$0.478736\pi$
$380$	−25.6136	−	2.06774i	−1.31395	−	0.106073i
$381$	−1.95853	−	9.59350i	−0.100338	−	0.491490i
$382$	−5.33505	+	10.1651i	−0.272965	+	0.520092i
$383$	13.6972	−	18.2277i	0.699895	−	0.931391i	−0.299849	−	0.953987i	$-0.596936\pi$
$383$	13.6972	−	18.2277i	0.699895	−	0.931391i	0.999745	+	0.0225951i	$0.00719286\pi$
$384$	4.65443	+	7.36039i	0.237520	+	0.375608i
$385$	18.0920	+	12.4880i	0.922052	+	0.636447i
$386$	−6.97095	−	14.6910i	−0.354812	−	0.747750i
$387$	−0.240051	−	0.249920i	−0.0122025	−	0.0127041i
$388$	−1.99200	+	1.91335i	−0.101129	+	0.0971354i
$389$	0.540248	−	4.44934i	0.0273916	−	0.225590i	−0.972584	−	0.232551i	$-0.925293\pi$
$389$	0.540248	−	4.44934i	0.0273916	−	0.225590i	0.999976	+	0.00696082i	$0.00221572\pi$
$390$	−9.50677	−	2.99539i	−0.481394	−	0.151677i
$391$	2.53349	+	20.8652i	0.128124	+	1.05520i
$392$	−11.4547	−	9.35247i	−0.578549	−	0.472371i
$393$	−2.32655	+	11.3962i	−0.117359	+	0.574863i
$394$	−0.590851	+	2.03985i	−0.0297666	+	0.102766i
$395$	−7.85058	+	31.8511i	−0.395006	+	1.60260i
$396$	−0.564171	−	6.98851i	−0.0283507	−	0.351186i
$397$	1.34758	−	8.29198i	0.0676330	−	0.416163i	−0.931052	−	0.364888i	$-0.881107\pi$
$397$	1.34758	−	8.29198i	0.0676330	−	0.416163i	0.998685	−	0.0512750i	$-0.0163285\pi$
$398$	2.06958	+	2.33607i	0.103739	+	0.117097i
$399$	5.47534	+	4.11445i	0.274110	+	0.205980i
$400$	2.24246	−	2.74651i	0.112123	−	0.137326i
$401$	−1.27861	−	7.86759i	−0.0638506	−	0.392889i	−0.999230	−	0.0392420i	$-0.987506\pi$
$401$	−1.27861	−	7.86759i	−0.0638506	−	0.392889i	0.935379	−	0.353647i	$-0.115058\pi$
$402$	6.97021	−	1.71800i	0.347643	−	0.0856862i
$403$	−1.95782	+	13.4899i	−0.0975259	+	0.671979i
$404$	2.31273	+	0.570036i	0.115063	+	0.0283604i
$405$	0.275990	−	3.41875i	0.0137141	−	0.169879i
$406$	3.07471	+	1.02649i	0.152595	+	0.0509438i
$407$	−32.7679	+	34.1150i	−1.62425	+	1.69102i
$408$		−	14.9272i		−	0.739007i
$409$	23.1694	+	22.2545i	1.14565	+	1.10042i	0.993705	+	0.112028i	$0.0357347\pi$
$409$	23.1694	+	22.2545i	1.14565	+	1.10042i	0.151950	+	0.988388i	$0.451445\pi$
$410$	8.03218	−	6.55808i	0.396681	−	0.323880i
$411$	−5.68948	−	10.8404i	−0.280642	−	0.534718i
$412$	24.8735	+	4.04233i	1.22543	+	0.199151i
$413$	−8.84056	−	5.59043i	−0.435015	−	0.275087i
$414$	2.76879	+	1.31381i	0.136078	+	0.0645700i
$415$	26.4874	+	38.3736i	1.30021	+	1.88369i
$416$	14.8934	−	14.7996i	0.730207	−	0.725611i
$417$	−7.13708	+	10.3398i	−0.349504	+	0.506344i
$418$	20.1078	−	11.6093i	0.983505	−	0.567827i
$419$	−0.945039	+	1.99163i	−0.0461682	+	0.0972973i	−0.925224	−	0.379422i	$-0.876123\pi$
$419$	−0.945039	+	1.99163i	−0.0461682	+	0.0972973i	0.879056	+	0.476719i	$0.158174\pi$
$420$	−5.42317	+	1.81052i	−0.264624	+	0.0883443i
$421$	2.50477	+	10.1623i	0.122075	+	0.495278i	0.999868	+	0.0162380i	$0.00516893\pi$
$421$	2.50477	+	10.1623i	0.122075	+	0.495278i	−0.877793	+	0.479040i	$0.840985\pi$
$422$	6.13679	+	0.247304i	0.298734	+	0.0120386i
$423$	−9.43344	−	0.380155i	−0.458670	−	0.0184838i
$424$	4.87894	+	19.7946i	0.236942	+	0.961312i
$425$	−35.4660	+	11.8403i	−1.72035	+	0.574338i
$426$	2.89634	−	6.10391i	0.140328	−	0.295735i
$427$	−8.51515	+	4.91623i	−0.412077	+	0.237913i
$428$	10.0379	−	14.5424i	0.485201	−	0.702935i
$429$	−17.8903	+	5.51295i	−0.863753	+	0.266168i
$430$	0.544197	+	0.788405i	0.0262435	+	0.0380203i
$431$	−22.4395	−	10.6477i	−1.08087	−	0.512879i	−0.196901	−	0.980423i	$-0.563088\pi$
$431$	−22.4395	−	10.6477i	−1.08087	−	0.512879i	−0.883970	+	0.467544i	$0.845139\pi$
$432$	0.443046	+	0.280165i	0.0213161	+	0.0134795i
$433$	26.7111	+	4.34098i	1.28366	+	0.208614i	0.763696	−	0.645576i	$-0.223383\pi$
$433$	26.7111	+	4.34098i	1.28366	+	0.208614i	0.519960	+	0.854191i	$0.325947\pi$
$434$	−1.74809	−	3.33071i	−0.0839111	−	0.159879i
$435$	−8.65570	+	7.06716i	−0.415009	+	0.338845i
$436$	−13.0924	−	12.5754i	−0.627013	−	0.602254i
$437$		−	21.0961i		−	1.00916i
$438$	−0.525276	+	0.546870i	−0.0250986	+	0.0261305i
$439$	−21.4103	−	7.14780i	−1.02186	−	0.341146i	−0.244126	−	0.969744i	$-0.578501\pi$
$439$	−21.4103	−	7.14780i	−1.02186	−	0.341146i	−0.777731	+	0.628598i	$0.783629\pi$
$440$	−3.86961	+	47.9337i	−0.184476	+	2.28515i
$441$	−5.31703	−	1.31053i	−0.253192	−	0.0624061i
$442$	−15.6827	+	3.48005i	−0.745950	+	0.165529i
$443$	24.7095	−	6.09034i	1.17398	−	0.289361i	0.396361	−	0.918095i	$-0.370273\pi$
$443$	24.7095	−	6.09034i	1.17398	−	0.289361i	0.777620	+	0.628734i	$0.216427\pi$
$444$	−1.97346	−	12.1432i	−0.0936562	−	0.576290i
$445$	−23.5122	+	28.7973i	−1.11459	+	1.36512i
$446$	−8.14734	−	6.12233i	−0.385788	−	0.289901i
$447$	−5.73349	−	6.47177i	−0.271185	−	0.306104i
$448$	−0.721816	+	4.44151i	−0.0341026	+	0.209842i
$449$	0.360040	+	4.45990i	0.0169914	+	0.210476i	0.999682	+	0.0252210i	$0.00802895\pi$
$449$	0.360040	+	4.45990i	0.0169914	+	0.210476i	−0.982691	+	0.185255i	$0.940689\pi$
$450$	−1.30471	+	5.29342i	−0.0615046	+	0.249534i
$451$	5.41837	−	18.7064i	0.255141	−	0.880849i
$452$	−4.68482	+	22.9478i	−0.220355	+	1.07937i
$453$	4.93910	+	4.03265i	0.232059	+	0.189470i
$454$	−0.584460	−	4.81346i	−0.0274301	−	0.225907i
$455$	7.85632	+	13.0891i	0.368310	+	0.613626i
$456$	−1.80592	+	14.8731i	−0.0845702	+	0.696498i
$457$	4.42722	−	4.25240i	0.207097	−	0.198919i	−0.581999	−	0.813190i	$-0.697729\pi$
$457$	4.42722	−	4.25240i	0.207097	−	0.198919i	0.789095	+	0.614271i	$0.210550\pi$
$458$	5.79610	+	6.03438i	0.270834	+	0.281968i
$459$	−2.36972	−	4.99408i	−0.110609	−	0.233104i
$460$	14.4933	+	10.0040i	0.675756	+	0.466441i
$461$	1.70325	+	2.69347i	0.0793282	+	0.125448i	0.882524	−	0.470268i	$-0.155843\pi$
$461$	1.70325	+	2.69347i	0.0793282	+	0.125448i	−0.803195	+	0.595716i	$0.796868\pi$
$462$	3.10342	−	4.12990i	0.144384	−	0.192140i
$463$	2.50369	−	4.77039i	0.116356	−	0.221699i	−0.820312	−	0.571917i	$-0.806200\pi$
$463$	2.50369	−	4.77039i	0.116356	−	0.221699i	0.936668	+	0.350218i	$0.113892\pi$
$464$	−0.341605	−	1.67329i	−0.0158586	−	0.0776805i
$465$	12.9250	+	1.04341i	0.599383	+	0.0483872i
$466$	11.7565	−	3.40532i	0.544610	−	0.157748i
$467$	2.75395	−	1.44538i	0.127438	−	0.0668844i	−0.399800	−	0.916603i	$-0.630920\pi$
$467$	2.75395	−	1.44538i	0.127438	−	0.0668844i	0.527237	+	0.849718i	$0.323228\pi$
$468$	1.64895	−	4.58106i	0.0762226	−	0.211760i
$469$	−9.73542	−	5.10954i	−0.449540	−	0.235937i
$470$	25.5723	+	5.22063i	1.17956	+	0.240810i
$471$	10.2464	−	7.69965i	0.472128	−	0.354781i
$472$	0.921340	−	22.8628i	0.0424081	−	1.05235i
$473$	1.68232	+	0.638019i	0.0773531	+	0.0293361i
$474$	7.40447	+	2.14473i	0.340099	+	0.0985108i
$475$	36.7699	−	7.50664i	1.68712	−	0.344428i
$476$	−6.11034	+	6.89715i	−0.280067	+	0.316130i
$477$	4.77474	+	5.84799i	0.218620	+	0.267761i
$478$	−0.628355	−	15.5925i	−0.0287403	−	0.713183i
$479$	−6.63533	+	19.8752i	−0.303176	+	0.908123i	0.681208	+	0.732090i	$0.261455\pi$
$479$	−6.63533	+	19.8752i	−0.303176	+	0.908123i	−0.984384	+	0.176033i	$0.943673\pi$
$480$	−14.9501	−	13.2447i	−0.682378	−	0.604534i
$481$	−30.5116	+	12.1681i	−1.39121	+	0.554817i
$482$	−12.4622	+	11.0405i	−0.567637	+	0.502883i
$483$	−1.83979	−	4.31815i	−0.0837135	−	0.196483i
$484$	10.7747	+	18.6623i	0.489757	+	0.848285i
$485$	3.50777	−	6.07564i	0.159280	−	0.275881i
$486$	−0.800125	−	0.0971528i	−0.0362944	−	0.00440694i
$487$	31.5272	−	14.9598i	1.42863	−	0.677895i	0.451843	−	0.892097i	$-0.350767\pi$
$487$	31.5272	−	14.9598i	1.42863	−	0.677895i	0.976789	+	0.214203i	$0.0687153\pi$
$488$	−18.6273	−	10.7545i	−0.843217	−	0.486832i
$489$	3.59203	−	2.47940i	0.162437	−	0.112122i
$490$	13.9273	+	5.93388i	0.629173	+	0.268066i
$491$	−8.10365	+	1.31697i	−0.365712	+	0.0594341i	−0.340491	−	0.940248i	$-0.610593\pi$
$491$	−8.10365	+	1.31697i	−0.365712	+	0.0594341i	−0.0252216	+	0.999682i	$0.508029\pi$
$492$	3.04282	+	4.04926i	0.137181	+	0.182555i
$493$	−6.38615	+	16.8389i	−0.287618	+	0.758386i
$494$	16.0469	−	1.57012i	0.721985	−	0.0706429i
$495$	6.31493	+	16.6511i	0.283835	+	0.748411i
$496$	−1.05920	+	1.67499i	−0.0475594	+	0.0752092i
$497$	−9.51955	+	4.05590i	−0.427010	+	0.181932i
$498$	9.26090	−	5.85624i	0.414991	−	0.262424i
$499$	−15.5946	+	1.89353i	−0.698112	+	0.0847662i	−0.461896	−	0.886934i	$-0.652831\pi$
$499$	−15.5946	+	1.89353i	−0.698112	+	0.0847662i	−0.236217	+	0.971700i	$0.575907\pi$
$500$	−3.20249	+	7.51653i	−0.143220	+	0.336150i
$501$	−6.96940	−	20.8759i	−0.311370	−	0.932666i
$502$	16.9499	−	6.42823i	0.756509	−	0.286906i
$503$	14.7283	−	1.18899i	0.656701	−	0.0530144i	0.252375	−	0.967629i	$-0.418788\pi$
$503$	14.7283	−	1.18899i	0.656701	−	0.0530144i	0.404326	+	0.914615i	$0.367506\pi$
$504$	0.927434	+	3.20187i	0.0413112	+	0.142623i
$505$	−6.04516	+	0.243612i	−0.269006	+	0.0108406i
$506$	−15.9122			−0.707384
$507$	−12.8951	−	1.64843i	−0.572690	−	0.0732094i
$508$	−13.2219			−0.586627
$509$	30.8866	−	1.24469i	1.36903	−	0.0551699i	0.655180	−	0.755473i	$-0.272593\pi$
$509$	30.8866	−	1.24469i	1.36903	−	0.0551699i	0.713846	+	0.700303i	$0.246952\pi$
$510$	4.25157	+	14.6781i	0.188263	+	0.649959i
$511$	1.15758	−	0.0934495i	0.0512083	−	0.00413396i
$512$	5.50129	−	2.08636i	0.243125	−	0.0922052i
$513$	1.75694	+	5.26268i	0.0775708	+	0.232353i
$514$	−6.40777	+	15.0396i	−0.282634	+	0.663367i
$515$	−63.5401	+	7.71516i	−2.79991	+	0.339971i
$516$	−0.395501	+	0.250100i	−0.0174110	+	0.0110100i
$517$	45.0968	−	19.2140i	1.98336	−	0.845029i
$518$	4.84474	−	7.66134i	0.212865	−	0.336620i
$519$	0.0378709	+	0.0998573i	0.00166235	+	0.00438325i
$520$	−16.2039	+	29.2000i	−0.710586	+	1.28051i
$521$	0.536824	−	1.41549i	0.0235187	−	0.0620137i	−0.922743	−	0.385417i	$-0.874058\pi$
$521$	0.536824	−	1.41549i	0.0235187	−	0.0620137i	0.946261	+	0.323403i	$0.104827\pi$
$522$	1.57749	+	2.09926i	0.0690451	+	0.0918823i
$523$	17.1774	−	2.79161i	0.751117	−	0.122068i	0.227212	−	0.973845i	$-0.427039\pi$
$523$	17.1774	−	2.79161i	0.751117	−	0.122068i	0.523905	+	0.851777i	$0.324475\pi$
$524$	14.4496	+	6.15639i	0.631233	+	0.268943i
$525$	6.87178	−	4.74324i	0.299909	−	0.207012i
$526$	3.43275	+	1.98190i	0.149675	+	0.0864149i
$527$	18.8807	−	8.95901i	0.822457	−	0.390260i
$528$	−2.70185	−	0.328064i	−0.117583	−	0.0142772i
$529$	4.27117	−	7.39788i	0.185703	−	0.321647i
$530$	−10.4354	−	18.0747i	−0.453287	−	0.785116i
$531$	−3.32127	−	7.79530i	−0.144131	−	0.338287i
$532$	6.92264	−	6.13292i	0.300134	−	0.265896i
$533$	8.79500	−	10.2738i	0.380954	−	0.445008i
$534$	6.53923	+	5.79325i	0.282980	+	0.250699i
$535$	−14.2128	+	42.5724i	−0.614471	+	1.84057i
$536$	−0.968461	−	24.0321i	−0.0418312	−	1.03803i
$537$	0.898429	+	1.10038i	0.0387701	+	0.0474847i
$538$	8.40210	−	9.48401i	0.362240	−	0.408885i
$539$	27.8583	−	5.68731i	1.19994	−	0.244970i
$540$	−4.44871	−	1.28858i	−0.191442	−	0.0554518i
$541$	−19.2641	−	7.30592i	−0.828230	−	0.314106i	−0.0961857	−	0.995363i	$-0.530664\pi$
$541$	−19.2641	−	7.30592i	−0.828230	−	0.314106i	−0.732044	+	0.681257i	$0.761434\pi$
$542$	0.161298	−	4.00257i	0.00692834	−	0.171925i
$543$	−7.87404	+	5.91696i	−0.337907	+	0.253921i
$544$	−31.5394	−	6.43881i	−1.35224	−	0.276062i
$545$	40.8280	+	21.4282i	1.74888	+	0.917883i
$546$	3.14771	−	1.72084i	0.134710	−	0.0736452i
$547$	−23.2191	+	12.1863i	−0.992777	+	0.521050i	−0.881219	−	0.472708i	$-0.843276\pi$
$547$	−23.2191	+	12.1863i	−0.992777	+	0.521050i	−0.111558	+	0.993758i	$0.535584\pi$
$548$	−15.8794	+	4.59952i	−0.678334	+	0.196482i
$549$	−7.93927	−	0.640924i	−0.338840	−	0.0273540i
$550$	−5.66206	−	27.7346i	−0.241431	−	1.18261i
$551$	8.40022	−	16.0053i	0.357861	−	0.681848i
$552$	6.16829	−	8.20851i	0.262540	−	0.349377i
$553$	−6.31020	−	9.97878i	−0.268337	−	0.424341i
$554$	−13.8265	−	9.54371i	−0.587430	−	0.405473i
$555$	13.3958	+	28.2310i	0.568619	+	1.19834i
$556$	11.7526	+	12.2357i	0.498420	+	0.518910i
$557$	−9.40994	+	9.03837i	−0.398712	+	0.382968i	−0.865089	−	0.501618i	$-0.832738\pi$
$557$	−9.40994	+	9.03837i	−0.398712	+	0.382968i	0.466377	+	0.884586i	$0.345559\pi$
$558$	0.367298	−	3.02497i	0.0155490	−	0.128057i
$559$	0.880693	+	0.886272i	0.0372494	+	0.0374853i
$560$	0.267524	+	2.20326i	0.0113050	+	0.0931047i
$561$	22.2319	+	18.1518i	0.938631	+	0.766369i
$562$	−0.538623	+	2.63835i	−0.0227205	+	0.111292i
$563$	−9.28043	+	32.0398i	−0.391123	+	1.35031i	0.487635	+	0.873048i	$0.337860\pi$
$563$	−9.28043	+	32.0398i	−0.391123	+	1.35031i	−0.878758	+	0.477267i	$0.841627\pi$
$564$	−3.05101	+	12.3784i	−0.128471	+	0.521226i
$565$	−4.78686	−	59.2960i	−0.201385	−	2.49460i
$566$	0.753167	−	4.63443i	0.0316580	−	0.194799i
$567$	0.818587	+	0.923993i	0.0343774	+	0.0388041i
$568$	−18.0960	−	13.5983i	−0.759291	−	0.570570i
$569$	−18.2709	+	22.3778i	−0.765955	+	0.938125i	−0.999414	−	0.0342420i	$-0.989098\pi$
$569$	−18.2709	+	22.3778i	−0.765955	+	0.938125i	0.233458	+	0.972367i	$0.424996\pi$
$570$	−2.46038	−	15.1393i	−0.103054	−	0.634117i
$571$	−17.7602	+	4.37750i	−0.743241	+	0.183193i	−0.592714	−	0.805413i	$-0.701943\pi$
$571$	−17.7602	+	4.37750i	−0.743241	+	0.183193i	−0.150528	+	0.988606i	$0.548097\pi$
$572$	2.46172	+	25.1593i	0.102930	+	1.05196i
$573$	13.8293	+	3.40863i	0.577729	+	0.142397i
$574$	−0.300304	+	3.71993i	−0.0125345	+	0.155267i
$575$	−24.3955	−	8.14442i	−1.01736	−	0.339646i
$576$	−2.52512	+	2.62892i	−0.105213	+	0.109539i
$577$			2.22146i			0.0924807i	0.998930	+	0.0462404i	$0.0147240\pi$
$577$			2.22146i			0.0924807i	−0.998930	+	0.0462404i	$0.985276\pi$
$578$	7.88019	+	7.56902i	0.327773	+	0.314830i
$579$	−15.6275	+	12.7595i	−0.649458	+	0.530266i
$580$	7.01239	+	13.3610i	0.291174	+	0.554785i
$581$	−16.5643	−	2.69196i	−0.687202	−	0.111681i
$582$	−1.39339	−	0.881128i	−0.0577580	−	0.0365239i
$583$	−35.4141	−	16.8042i	−1.46670	−	0.695959i
$584$	1.44317	+	2.09079i	0.0597186	+	0.0865174i
$585$	−0.785644	+	12.3416i	−0.0324824	+	0.510263i
$586$	−12.4370	+	18.0181i	−0.513767	+	0.744320i
$587$	−11.3065	+	6.52782i	−0.466670	+	0.269432i	−0.714845	−	0.699283i	$-0.753503\pi$
$587$	−11.3065	+	6.52782i	−0.466670	+	0.269432i	0.248175	+	0.968715i	$0.420169\pi$
$588$	−3.17009	+	6.68082i	−0.130732	+	0.275512i
$589$	−19.8962	+	6.64232i	−0.819808	+	0.273692i
$590$	5.60583	+	22.7438i	0.230788	+	0.936346i
$591$	2.63272	+	0.106095i	0.108296	+	0.00436417i
$592$	−4.77183	−	0.192298i	−0.196121	−	0.00790341i
$593$	0.861297	+	3.49442i	0.0353692	+	0.143499i	0.985972	−	0.166912i	$-0.0533796\pi$
$593$	0.861297	+	3.49442i	0.0353692	+	0.143499i	−0.950603	+	0.310411i	$0.899533\pi$
$594$	3.96950	−	1.32521i	0.162870	−	0.0543741i
$595$	10.0334	−	21.1448i	0.411327	−	0.866854i
$596$	−10.1113	+	5.83774i	−0.414174	+	0.239123i
$597$	2.19963	−	3.18672i	0.0900249	−	0.130424i
$598$	−10.0620	−	4.56679i	−0.411466	−	0.186750i
$599$	26.2877	+	38.0844i	1.07409	+	1.55609i	0.805283	+	0.592891i	$0.202014\pi$
$599$	26.2877	+	38.0844i	1.07409	+	1.55609i	0.268806	+	0.963194i	$0.413371\pi$
$600$	16.5021	+	7.83034i	0.673695	+	0.319672i
$601$	−17.1436	−	10.8409i	−0.699300	−	0.442211i	0.136936	−	0.990580i	$-0.456274\pi$
$601$	−17.1436	−	10.8409i	−0.699300	−	0.442211i	−0.836236	+	0.548369i	$0.815249\pi$
$602$	−0.340322	−	0.0553077i	−0.0138705	−	0.00225417i
$603$	−4.13915	−	7.88649i	−0.168559	−	0.321163i
$604$	6.66957	−	5.44553i	0.271381	−	0.221576i
$605$	−39.4747	−	37.9160i	−1.60488	−	1.54151i
$606$			1.42173i			0.0577539i
$607$	5.17312	−	5.38579i	0.209971	−	0.218603i	−0.607886	−	0.794024i	$-0.707982\pi$
$607$	5.17312	−	5.38579i	0.209971	−	0.218603i	0.817857	+	0.575421i	$0.195162\pi$
$608$	30.6461	+	10.2312i	1.24287	+	0.414929i
$609$	0.323616	−	4.00870i	0.0131136	−	0.162441i
$610$	21.3796	+	5.26959i	0.865633	+	0.213359i
$611$	34.0311	+	0.792915i	1.37675	+	0.0320779i
$612$	−7.24760	+	1.78637i	−0.292967	+	0.0722098i
$613$	2.71173	+	16.6859i	0.109526	+	0.673938i	0.982513	+	0.186195i	$0.0596157\pi$
$613$	2.71173	+	16.6859i	0.109526	+	0.673938i	−0.872987	+	0.487743i	$0.837820\pi$
$614$	13.5341	−	16.5762i	0.546190	−	0.668962i
$615$	−10.2850	−	7.72868i	−0.414732	−	0.311651i
$616$	−11.4772	−	12.9551i	−0.462431	−	0.521977i
$617$	−4.64778	+	28.5990i	−0.187113	+	1.15135i	0.708233	+	0.705979i	$0.249493\pi$
$617$	−4.64778	+	28.5990i	−0.187113	+	1.15135i	−0.895346	+	0.445372i	$0.853071\pi$
$618$	1.21032	+	14.9925i	0.0486861	+	0.603085i
$619$	−9.19664	+	37.3122i	−0.369644	+	1.49970i	0.431984	+	0.901881i	$0.357814\pi$
$619$	−9.19664	+	37.3122i	−0.369644	+	1.49970i	−0.801628	+	0.597823i	$0.796032\pi$
$620$	4.87165	−	16.8189i	0.195650	−	0.675462i
$621$	0.760563	−	3.72548i	0.0305203	−	0.149498i
$622$	7.61147	+	6.21457i	0.305192	+	0.249182i
$623$	−1.61281	−	13.2827i	−0.0646158	−	0.532159i
$624$	−1.61435	−	0.982879i	−0.0646256	−	0.0393467i
$625$	−1.57516	+	12.9726i	−0.0630063	+	0.518904i
$626$	−10.9004	+	10.4699i	−0.435666	+	0.418463i
$627$	−19.9553	−	20.7757i	−0.796939	−	0.829701i
$628$	−7.41956	−	15.6364i	−0.296073	−	0.623960i
$629$	41.4463	+	28.6083i	1.65257	+	1.14069i
$630$	−1.82392	−	2.88430i	−0.0726666	−	0.114913i
$631$	−20.0882	+	26.7325i	−0.799697	+	1.06420i	0.196789	+	0.980446i	$0.436949\pi$
$631$	−20.0882	+	26.7325i	−0.799697	+	1.06420i	−0.996486	+	0.0837576i	$0.973308\pi$
$632$	12.0026	−	22.8690i	0.477437	−	0.909680i
$633$	−1.52421	−	7.46605i	−0.0605817	−	0.296749i
$634$	−25.7524	−	2.07895i	−1.02276	−	0.0825655i
$635$	32.2573	−	9.34344i	1.28009	−	0.370783i
$636$	9.02700	−	4.73773i	0.357944	−	0.187863i
$637$	19.2483	+	4.39897i	0.762645	+	0.174293i
$638$	−12.0724	−	6.33606i	−0.477949	−	0.250847i
$639$	−8.21298	−	1.67669i	−0.324901	−	0.0663289i
$640$	−23.8788	+	17.9437i	−0.943892	+	0.709289i
$641$	0.197007	−	4.88868i	0.00778132	−	0.193091i	−0.990623	−	0.136623i	$-0.956375\pi$
$641$	0.197007	−	4.88868i	0.00778132	−	0.193091i	0.998404	−	0.0564682i	$-0.0179839\pi$
$642$	9.86168	+	3.74004i	0.389210	+	0.147608i
$643$	4.29474	+	1.24399i	0.169368	+	0.0490580i	0.361818	−	0.932249i	$-0.382156\pi$
$643$	4.29474	+	1.24399i	0.169368	+	0.0490580i	−0.192450	+	0.981307i	$0.561643\pi$
$644$	−6.21016	+	1.26781i	−0.244715	+	0.0499589i
$645$	0.788163	−	0.889652i	0.0310339	−	0.0350300i
$646$	−15.6337	−	19.1478i	−0.615101	−	0.753362i
$647$	−0.872097	−	21.6409i	−0.0342857	−	0.850790i	−0.921254	−	0.388961i	$-0.872834\pi$
$647$	−0.872097	−	21.6409i	−0.0342857	−	0.850790i	0.886969	−	0.461830i	$-0.152807\pi$
$648$	−0.855129	+	2.56143i	−0.0335927	+	0.100622i
$649$	32.9305	+	29.1739i	1.29263	+	1.14517i
$650$	4.37944	−	19.1628i	0.171776	−	0.751627i
$651$	−3.49327	+	3.09477i	−0.136912	+	0.121293i
$652$	−2.31019	−	5.42221i	−0.0904739	−	0.212350i
$653$	7.08879	+	12.2781i	0.277406	+	0.480481i	0.970739	−	0.240136i	$-0.0771921\pi$
$653$	7.08879	+	12.2781i	0.277406	+	0.480481i	−0.693334	+	0.720617i	$0.743859\pi$
$654$	5.41775	−	9.38382i	0.211851	−	0.366936i
$655$	−39.6030	−	4.80867i	−1.54742	−	0.187890i
$656$	1.77639	−	0.842906i	0.0693562	−	0.0329099i
$657$	0.814744	+	0.470393i	0.0317862	+	0.0183518i
$658$	−7.73073	+	5.33614i	−0.301375	+	0.208024i
$659$	−16.3686	−	6.97403i	−0.637632	−	0.271669i	0.0488617	−	0.998806i	$-0.484441\pi$
$659$	−16.3686	−	6.97403i	−0.637632	−	0.271669i	−0.686493	+	0.727136i	$0.740851\pi$
$660$	23.7363	−	3.85752i	0.923934	−	0.150154i
$661$	29.7856	+	39.6375i	1.15853	+	1.54172i	0.791121	+	0.611660i	$0.209498\pi$
$661$	29.7856	+	39.6375i	1.15853	+	1.54172i	0.367406	+	0.930060i	$0.380246\pi$
$662$	−1.96255	+	5.17482i	−0.0762766	+	0.201125i
$663$	8.84867	+	17.8587i	0.343654	+	0.693575i
$664$	−13.0177	−	34.3249i	−0.505186	−	1.33207i
$665$	−12.5552	+	19.8544i	−0.486868	+	0.769920i
$666$	6.75550	−	2.87825i	0.261770	−	0.111530i
$667$	−10.4700	+	6.62083i	−0.405401	+	0.256360i
$668$	−29.5028	+	3.58228i	−1.14150	+	0.138603i
$669$	−4.95612	+	11.6324i	−0.191615	+	0.449736i
$670$	7.79714	+	23.3553i	0.301230	+	0.902294i
$671$	38.6683	−	14.6650i	1.49277	−	0.566135i
$672$	7.16522	−	0.578436i	0.276404	−	0.0223137i
$673$	−9.28751	−	32.0642i	−0.358007	−	1.23598i	−0.914314	−	0.405007i	$-0.867269\pi$
$673$	−9.28751	−	32.0642i	−0.358007	−	1.23598i	0.556307	−	0.830977i	$-0.312218\pi$
$674$	−15.8953	+	0.640557i	−0.612263	+	0.0246733i
$675$	6.76405			0.260348
$676$	−5.66404	+	16.6158i	−0.217848	+	0.639071i
$677$	4.58739			0.176308			0.0881539	−	0.996107i	$-0.471903\pi$
$677$	4.58739			0.176308			0.0881539	+	0.996107i	$0.471903\pi$
$678$	−13.9682	+	0.562900i	−0.536446	+	0.0216180i
$679$	0.702487	+	2.42527i	0.0269590	+	0.0930732i
$680$	51.0324	−	4.11976i	1.95700	−	0.157986i
$681$	−5.62495	+	2.13326i	−0.215549	+	0.0817468i
$682$	5.01013	+	15.0072i	0.191848	+	0.574654i
$683$	18.9305	−	44.4316i	0.724357	−	1.70013i	0.0103932	−	0.999946i	$-0.496692\pi$
$683$	18.9305	−	44.4316i	0.724357	−	1.70013i	0.713964	−	0.700183i	$-0.246898\pi$
$684$	7.43746	−	0.903071i	0.284378	−	0.0345298i
$685$	35.4904	−	22.4428i	1.35602	−	0.857495i
$686$	−11.4200	+	4.86560i	−0.436017	+	0.185770i
$687$	5.54829	−	8.77392i	0.211681	−	0.334746i
$688$	0.0644143	+	0.169847i	0.00245577	+	0.00647534i
$689$	−17.5711	−	20.7899i	−0.669406	−	0.792031i
$690$	−3.72742	+	9.82840i	−0.141900	+	0.374161i
$691$	24.9079	+	33.1464i	0.947543	+	1.26095i	0.965310	+	0.261108i	$0.0840879\pi$
$691$	24.9079	+	33.1464i	0.947543	+	1.26095i	−0.0177669	+	0.999842i	$0.505656\pi$
$692$	0.142347	−	0.0231337i	0.00541124	−	0.000879412i
$693$	−5.89650	−	2.51226i	−0.223990	−	0.0954330i
$694$	−15.3519	+	10.5966i	−0.582749	+	0.402243i
$695$	−37.3191	−	21.5462i	−1.41560	−	0.817295i
$696$	7.94833	−	3.77153i	0.301281	−	0.142959i
$697$	−20.5831	−	2.49925i	−0.779642	−	0.0946657i
$698$	10.4530	−	18.1052i	0.395653	−	0.685291i
$699$	−7.59289	−	13.1513i	−0.287190	−	0.497427i
$700$	−4.41954	−	10.3730i	−0.167043	−	0.392064i
$701$	5.41919	−	4.80098i	0.204680	−	0.181331i	−0.554555	−	0.832147i	$-0.687112\pi$
$701$	5.41919	−	4.80098i	0.204680	−	0.181331i	0.759235	+	0.650816i	$0.225573\pi$
$702$	2.89042	+	0.301252i	0.109092	+	0.0113700i
$703$	−37.8350	−	33.5189i	−1.42697	−	1.26419i
$704$	5.99336	−	17.9523i	0.225883	−	0.676603i
$705$	−1.30388	−	32.3555i	−0.0491071	−	1.21858i
$706$	−11.1325	−	13.6349i	−0.418979	−	0.513156i
$707$	1.44393	−	1.62986i	0.0543046	−	0.0612972i
$708$	−11.2108	+	2.28871i	−0.421329	+	0.0860149i
$709$	35.4457	+	10.2670i	1.33119	+	0.385584i	0.866185	−	0.499723i	$-0.166565\pi$
$709$	35.4457	+	10.2670i	1.33119	+	0.385584i	0.465006	+	0.885307i	$0.346052\pi$
$710$	21.6671	+	8.21726i	0.813153	+	0.308388i
$711$	0.385115	−	9.55653i	0.0144429	−	0.358398i
$712$	23.3996	−	17.5836i	0.876935	−	0.658974i
$713$	14.0846	+	2.87540i	0.527474	+	0.107685i
$714$	−4.86995	−	2.55595i	−0.182253	−	0.0956540i
$715$	−23.7850	−	59.6411i	−0.889507	−	2.23045i
$716$	1.69855	−	0.891466i	0.0634777	−	0.0333157i
$717$	−18.5967	+	5.38661i	−0.694508	+	0.201167i
$718$	12.2973	+	0.992737i	0.458930	+	0.0370486i
$719$	−1.71224	−	8.38712i	−0.0638559	−	0.312787i	0.935300	−	0.353855i	$-0.115129\pi$
$719$	−1.71224	−	8.38712i	−0.0638559	−	0.312787i	−0.999156	+	0.0410676i	$0.986924\pi$
$720$	−0.835540	+	1.59199i	−0.0311387	+	0.0593299i
$721$	13.8391	−	18.4164i	0.515393	−	0.685864i
$722$	5.07572	+	8.02661i	0.188899	+	0.298719i
$723$	17.0001	+	11.7343i	0.632241	+	0.436404i
$724$	5.70172	+	12.0161i	0.211903	+	0.446576i
$725$	−15.2655	−	15.8931i	−0.566946	−	0.590254i
$726$	−9.27635	+	8.91005i	−0.344278	+	0.330683i
$727$	−2.45189	+	20.1931i	−0.0909356	+	0.748922i	0.873907	+	0.486093i	$0.161579\pi$
$727$	−2.45189	+	20.1931i	−0.0909356	+	0.748922i	−0.964842	+	0.262829i	$0.915345\pi$
$728$	−3.53946	−	11.4861i	−0.131181	−	0.425702i
$729$	0.120537	+	0.992709i	0.00446432	+	0.0367670i
$730$	−2.01458	−	1.64486i	−0.0745631	−	0.0608789i
$731$	0.383160	−	1.87684i	0.0141717	−	0.0694175i
$732$	−2.99244	+	10.3311i	−0.110604	+	0.381848i
$733$	12.9383	−	52.4927i	0.477887	−	1.93886i	0.184809	−	0.982774i	$-0.440833\pi$
$733$	12.9383	−	52.4927i	0.477887	−	1.93886i	0.293078	−	0.956089i	$-0.405320\pi$
$734$	0.00705411	+	0.0873809i	0.000260372	+	0.00322529i
$735$	3.01293	−	18.5393i	0.111134	−	0.683832i
$736$	−14.6829	−	16.5736i	−0.541219	−	0.610910i
$737$	36.9700	+	27.7812i	1.36181	+	1.02333i
$738$	−1.91204	+	2.34183i	−0.0703833	+	0.0862039i
$739$	−1.08899	−	6.70080i	−0.0400590	−	0.246493i	0.959296	−	0.282402i	$-0.0911313\pi$
$739$	−1.08899	−	6.70080i	−0.0400590	−	0.246493i	−0.999355	+	0.0359094i	$0.988567\pi$
$740$	40.9699	−	10.0982i	1.50608	−	0.371216i
$741$	−6.65603	−	18.8646i	−0.244515	−	0.693007i
$742$	7.29334	+	1.79765i	0.267747	+	0.0659937i
$743$	3.81201	−	47.2202i	0.139849	−	1.73234i	−0.423304	−	0.905988i	$-0.639130\pi$
$743$	3.81201	−	47.2202i	0.139849	−	1.73234i	0.563153	−	0.826352i	$-0.309588\pi$
$744$	−9.68378	−	3.23292i	−0.355024	−	0.118525i
$745$	20.5430	−	21.3875i	0.752638	−	0.783579i
$746$			15.9308i			0.583269i
$747$	−9.80437	−	9.41723i	−0.358723	−	0.344558i
$748$	30.0211	−	24.5115i	1.09768	−	0.896228i
$749$	−7.50691	−	14.3032i	−0.274296	−	0.522628i
$750$	−4.81354	−	0.782277i	−0.175766	−	0.0285647i
$751$	−21.8539	−	13.8195i	−0.797459	−	0.504282i	0.0725226	−	0.997367i	$-0.476895\pi$
$751$	−21.8539	−	13.8195i	−0.797459	−	0.504282i	−0.869982	+	0.493084i	$0.835869\pi$
$752$	4.47117	+	2.12160i	0.163047	+	0.0773667i
$753$	−12.7764	−	18.5098i	−0.465598	−	0.674535i
$754$	−5.81544	−	7.47133i	−0.211786	−	0.272090i
$755$	−12.4235	+	17.9985i	−0.452137	+	0.655034i
$756$	1.44361	−	0.833471i	0.0525038	−	0.0303131i
$757$	3.37976	−	7.12269i	0.122839	−	0.258879i	−0.832710	−	0.553709i	$-0.813212\pi$
$757$	3.37976	−	7.12269i	0.122839	−	0.258879i	0.955550	+	0.294831i	$0.0952632\pi$
$758$	−6.35467	+	2.12150i	−0.230812	+	0.0770563i
$759$	4.72461	+	19.1685i	0.171492	+	0.695772i
$760$	−51.3460	−	2.06917i	−1.86251	−	0.0750568i
$761$	−28.5622	−	1.15102i	−1.03538	−	0.0417243i	−0.483249	−	0.875483i	$-0.660544\pi$
$761$	−28.5622	−	1.15102i	−1.03538	−	0.0417243i	−0.552129	+	0.833758i	$0.686185\pi$
$762$	−1.88865	−	7.66255i	−0.0684185	−	0.277585i
$763$	−15.7412	+	5.25518i	−0.569870	+	0.190250i
$764$	8.24526	−	17.3765i	0.298303	−	0.628660i
$765$	16.4195	−	9.47980i	0.593648	−	0.342743i
$766$	10.4395	−	15.1242i	0.377193	−	0.546459i
$767$	12.4505	+	27.8989i	0.449562	+	1.00737i
$768$	8.12873	+	11.7765i	0.293320	+	0.424948i
$769$	−44.0437	−	20.8990i	−1.58826	−	0.753637i	−0.589715	−	0.807612i	$-0.700760\pi$
$769$	−44.0437	−	20.8990i	−1.58826	−	0.753637i	−0.998542	+	0.0539743i	$0.982811\pi$
$770$	14.9756	+	9.47001i	0.539684	+	0.341276i
$771$	20.0198	+	3.25354i	0.720997	+	0.117173i
$772$	12.6606	+	24.1227i	0.455665	+	0.868197i
$773$	40.1869	−	32.8116i	1.44542	−	1.18015i	0.495120	−	0.868824i	$-0.335124\pi$
$773$	40.1869	−	32.8116i	1.44542	−	1.18015i	0.950303	−	0.311327i	$-0.100773\pi$
$774$	−0.201436	−	0.193482i	−0.00724046	−	0.00695456i
$775$			25.5723i			0.918584i
$776$	−3.82623	+	3.98353i	−0.137354	+	0.143000i
$777$	−10.6676	−	3.56138i	−0.382699	−	0.127764i
$778$	0.290687	−	3.60080i	0.0104216	−	0.129095i
$779$	20.2062	+	4.98038i	0.723963	+	0.178441i
$780$	16.1166	+	4.37302i	0.577068	+	0.156579i
$781$	42.2577	−	10.4156i	1.51210	−	0.372699i
$782$	2.71751	+	16.7215i	0.0971779	+	0.597960i
$783$	2.06047	−	2.52362i	0.0736353	−	0.0901868i
$784$	2.29486	+	1.72448i	0.0819595	+	0.0615885i
$785$	29.1511	+	32.9048i	1.04045	+	1.17442i
$786$	−1.50383	+	9.25343i	−0.0536398	+	0.330059i
$787$	−2.20980	−	27.3733i	−0.0787708	−	0.975752i	−0.908582	−	0.417707i	$-0.862834\pi$
$787$	−2.20980	−	27.3733i	−0.0787708	−	0.975752i	0.829811	−	0.558045i	$-0.188448\pi$
$788$	0.851488	−	3.45462i	0.0303330	−	0.123066i
$789$	1.36823	−	4.72369i	0.0487104	−	0.168168i
$790$	−5.28875	+	25.9060i	−0.188165	+	0.921694i
$791$	16.5847	+	13.5410i	0.589685	+	0.481463i
$792$	−1.69002	−	13.9186i	−0.0600523	−	0.494575i
$793$	28.6605	+	1.82448i	1.01777	+	0.0647890i
$794$	0.816158	−	6.72167i	0.0289644	−	0.238543i
$795$	−18.6751	+	17.9376i	−0.662336	+	0.636183i
$796$	−3.62212	−	3.77102i	−0.128383	−	0.133660i
$797$	−16.9395	−	35.6992i	−0.600028	−	1.26453i	−0.945353	−	0.326049i	$-0.894283\pi$
$797$	−16.9395	−	35.6992i	−0.600028	−	1.26453i	0.345325	−	0.938483i	$-0.387769\pi$
$798$	4.54309	+	3.13587i	0.160823	+	0.111008i
$799$	−27.8929	−	44.1091i	−0.986779	−	1.56047i
$800$	23.6627	−	31.4893i	0.836602	−	1.11332i
$801$	5.03717	−	9.59753i	0.177980	−	0.339112i
$802$	−1.28506	−	6.29465i	−0.0453771	−	0.222272i
$803$	−4.86884	−	0.393053i	−0.171818	−	0.0138706i
$804$	−11.5524	+	3.34619i	−0.407422	+	0.118011i
$805$	14.2549	−	7.48157i	0.502421	−	0.263691i
$806$	−1.13892	+	10.9276i	−0.0401167	+	0.384908i
$807$	−13.9195	−	7.30554i	−0.489991	−	0.257167i
$808$	4.66705	+	0.952785i	0.164186	+	0.0335189i
$809$	9.39884	−	7.06277i	0.330445	−	0.248314i	−0.422550	−	0.906340i	$-0.638865\pi$
$809$	9.39884	−	7.06277i	0.330445	−	0.248314i	0.752995	+	0.658026i	$0.228608\pi$
$810$	0.111315	−	2.76224i	0.00391120	−	0.0970554i
$811$	−11.5400	−	4.37654i	−0.405223	−	0.153681i	0.143568	−	0.989640i	$-0.454143\pi$
$811$	−11.5400	−	4.37654i	−0.405223	−	0.153681i	−0.548791	+	0.835960i	$0.684912\pi$
$812$	−5.21639	−	1.51095i	−0.183059	−	0.0530238i
$813$	−4.86954	+	0.994125i	−0.170782	+	0.0348655i
$814$	−25.2824	+	28.5379i	−0.886148	+	1.00025i
$815$	9.46781	+	11.5960i	0.331643	+	0.406189i
$816$	0.116676	+	2.89529i	0.00408449	+	0.101356i
$817$	−0.608836	+	1.82369i	−0.0213005	+	0.0638027i
$818$	19.3817	+	17.1707i	0.677666	+	0.600360i
$819$	−3.00760	−	3.28091i	−0.105094	−	0.114644i
$820$	−13.0036	+	11.5202i	−0.454107	+	0.402304i
$821$	−1.12141	−	2.63205i	−0.0391376	−	0.0918592i	0.899263	−	0.437407i	$-0.144103\pi$
$821$	−1.12141	−	2.63205i	−0.0391376	−	0.0918592i	−0.938401	+	0.345548i	$0.887693\pi$
$822$	−4.93383	−	8.54565i	−0.172087	−	0.298064i
$823$	−20.6207	+	35.7160i	−0.718791	+	1.24498i	0.242688	+	0.970104i	$0.421971\pi$
$823$	−20.6207	+	35.7160i	−0.718791	+	1.24498i	−0.961479	+	0.274878i	$0.911363\pi$
$824$	50.0261	+	6.07427i	1.74274	+	0.211607i
$825$	−31.7290	+	15.0556i	−1.10466	+	0.524169i
$826$	−7.30116	−	4.21533i	−0.254040	−	0.146670i
$827$	20.1564	−	13.9130i	0.700906	−	0.483801i	−0.163533	−	0.986538i	$-0.552289\pi$
$827$	20.1564	−	13.9130i	0.700906	−	0.483801i	0.864439	+	0.502737i	$0.167674\pi$
$828$	−4.72364	−	2.01256i	−0.164158	−	0.0699412i
$829$	24.5865	−	3.99569i	0.853924	−	0.138776i	0.282335	−	0.959316i	$-0.408891\pi$
$829$	24.5865	−	3.99569i	0.853924	−	0.138776i	0.571590	+	0.820540i	$0.306327\pi$
$830$	22.5770	+	30.0445i	0.783658	+	1.04286i
$831$	−7.39142	+	19.4896i	−0.256406	+	0.676086i
$832$	8.94217	−	9.63195i	0.310014	−	0.333928i
$833$	−10.7342	−	28.3038i	−0.371919	−	0.980670i
$834$	−5.41226	+	8.55880i	−0.187411	+	0.296367i
$835$	69.4461	−	29.5882i	2.40328	−	1.02394i
$836$	−32.8778	+	20.7906i	−1.13710	+	0.719059i
$837$	−3.75306	+	0.455703i	−0.129725	+	0.0157514i
$838$	−0.696448	+	1.63462i	−0.0240584	+	0.0564671i
$839$	0.854656	+	2.56001i	0.0295060	+	0.0883813i	0.962260	−	0.272134i	$-0.0877292\pi$
$839$	0.854656	+	2.56001i	0.0295060	+	0.0883813i	−0.932753	+	0.360515i	$0.882601\pi$
$840$	−10.6905	+	4.05435i	−0.368856	+	0.139888i
$841$	18.3262	−	1.47944i	0.631937	−	0.0510152i
$842$	2.34702	+	8.10286i	0.0808837	+	0.279243i
$843$	3.33819	−	0.134524i	0.114973	−	0.00463327i
$844$	−10.2898			−0.354190
$845$	2.07667	−	44.5400i	0.0714395	−	1.53222i
$846$	−7.60954			−0.261621
$847$	19.6835	−	0.793218i	0.676333	−	0.0272553i
$848$	−1.10105	−	3.80125i	−0.0378100	−	0.130535i
$849$	−5.80644	+	0.468744i	−0.199277	+	0.0160873i
$850$	−28.1782	+	10.6866i	−0.966504	+	0.366546i
$851$	10.9697	+	32.8584i	0.376038	+	1.12637i
$852$	−4.43677	+	10.4135i	−0.152001	+	0.356760i
$853$	−43.5886	+	5.29262i	−1.49245	+	0.181216i	−0.825717	−	0.564084i	$-0.809229\pi$
$853$	−43.5886	+	5.29262i	−1.49245	+	0.181216i	−0.666729	+	0.745300i	$0.732306\pi$
$854$	−6.69811	+	4.23563i	−0.229205	+	0.144940i
$855$	−17.5069	+	7.45899i	−0.598723	+	0.255092i
$856$	18.8861	−	29.8661i	0.645515	−	1.02080i
$857$	−1.96103	−	5.17082i	−0.0669877	−	0.176632i	0.897342	−	0.441336i	$-0.145495\pi$
$857$	−1.96103	−	5.17082i	−0.0669877	−	0.176632i	−0.964330	+	0.264704i	$0.914726\pi$
$858$	−14.2290	+	5.02046i	−0.485771	+	0.171396i
$859$	−9.06569	+	23.9043i	−0.309317	+	0.815603i	0.686741	+	0.726902i	$0.259041\pi$
$859$	−9.06569	+	23.9043i	−0.309317	+	0.815603i	−0.996058	+	0.0887005i	$0.971729\pi$
$860$	−0.964184	−	1.28310i	−0.0328784	−	0.0437532i
$861$	4.57034	−	0.742753i	0.155757	−	0.0253130i
$862$	−18.4171	−	7.84681i	−0.627290	−	0.267263i
$863$	10.2268	−	7.05908i	0.348126	−	0.240294i	−0.381151	−	0.924513i	$-0.624472\pi$
$863$	10.2268	−	7.05908i	0.348126	−	0.240294i	0.729277	+	0.684219i	$0.239857\pi$
$864$	5.04312	+	2.91165i	0.171571	+	0.0990563i
$865$	−0.330935	+	0.157031i	−0.0112521	+	0.00533921i
$866$	21.6527	+	2.62911i	0.735787	+	0.0893407i
$867$	6.77818	−	11.7402i	0.230199	−	0.398717i
$868$	3.15104	+	5.45776i	0.106953	+	0.185248i
$869$	19.4647	+	45.6852i	0.660293	+	1.54977i
$870$	−6.74149	+	5.97244i	−0.228558	+	0.202485i
$871$	15.4046	+	28.1776i	0.521965	+	0.954763i
$872$	−27.1731	−	24.0732i	−0.920196	−	0.815223i
$873$	−0.647720	+	1.94016i	−0.0219220	+	0.0656644i
$874$	−0.684661	−	16.9897i	−0.0231590	−	0.574685i
$875$	4.72371	+	5.78550i	0.159691	+	0.195585i
$876$	0.842431	−	0.950908i	0.0284631	−	0.0321282i
$877$	35.4223	−	7.23152i	1.19613	−	0.244191i	0.439624	−	0.898182i	$-0.355112\pi$
$877$	35.4223	−	7.23152i	1.19613	−	0.244191i	0.756502	+	0.653991i	$0.226907\pi$
$878$	−17.4747	−	5.06161i	−0.589743	−	0.170821i
$879$	25.3980	+	9.63221i	0.856655	+	0.324886i
$880$	0.375886	−	9.32751i	0.0126711	−	0.314430i
$881$	12.8573	−	9.66160i	0.433172	−	0.325508i	−0.361689	−	0.932299i	$-0.617800\pi$
$881$	12.8573	−	9.66160i	0.433172	−	0.325508i	0.794861	+	0.606791i	$0.207543\pi$
$882$	−4.32459	−	0.882871i	−0.145616	−	0.0297278i
$883$	−35.2947	−	18.5241i	−1.18776	−	0.623385i	−0.249185	−	0.968456i	$-0.580163\pi$
$883$	−35.2947	−	18.5241i	−1.18776	−	0.623385i	−0.938577	+	0.345071i	$0.887855\pi$
$884$	26.0184	−	6.88365i	0.875095	−	0.231522i
$885$	25.7336	−	13.5060i	0.865024	−	0.454000i
$886$	19.7021	−	5.70677i	0.661904	−	0.191723i
$887$	−54.8013	−	4.42402i	−1.84005	−	0.148544i	−0.889064	−	0.457782i	$-0.848644\pi$
$887$	−54.8013	−	4.42402i	−1.84005	−	0.148544i	−0.950985	+	0.309238i	$0.899926\pi$
$888$	−4.92104	−	24.1048i	−0.165139	−	0.808905i
$889$	−5.61706	+	10.7024i	−0.188390	+	0.358947i
$890$	−18.0009	+	23.9549i	−0.603393	+	0.802970i
$891$	−2.77501	−	4.38834i	−0.0929665	−	0.147015i
$892$	14.0519	+	9.69929i	0.470491	+	0.324756i
$893$	22.4554	+	47.3238i	0.751442	+	1.58363i
$894$	−4.82749	−	5.02595i	−0.161456	−	0.168093i
$895$	−3.51396	+	3.37520i	−0.117459	+	0.112821i
$896$	1.29580	−	10.6718i	0.0432895	−	0.356521i
$897$	−2.51376	+	13.4770i	−0.0839321	+	0.449985i
$898$	0.434701	+	3.58009i	0.0145062	+	0.119469i
$899$	9.54085	+	7.78986i	0.318205	+	0.259806i
$900$	1.82702	−	8.94932i	0.0609006	−	0.298311i
$901$	−11.6108	+	40.0851i	−0.386812	+	1.33543i
$902$	3.75657	−	15.2410i	0.125080	−	0.507470i
$903$	0.0344215	+	0.426387i	0.00114548	+	0.0141893i
$904$	−7.51311	+	46.2300i	−0.249882	+	1.53759i
$905$	−22.4018	−	25.2864i	−0.744660	−	0.840548i
$906$	4.10857	+	3.08739i	0.136498	+	0.102572i
$907$	1.89177	−	2.31700i	0.0628153	−	0.0769348i	−0.742242	−	0.670132i	$-0.766237\pi$
$907$	1.89177	−	2.31700i	0.0628153	−	0.0769348i	0.805057	+	0.593198i	$0.202135\pi$
$908$	1.30312	+	8.01842i	0.0432455	+	0.266101i
$909$	1.71267	−	0.422136i	0.0568058	−	0.0140014i
$910$	6.75187	+	10.2863i	0.223822	+	0.340988i
$911$	−2.48456	−	0.612388i	−0.0823170	−	0.0202893i	0.197942	−	0.980214i	$-0.436574\pi$
$911$	−2.48456	−	0.612388i	−0.0823170	−	0.0202893i	−0.280259	+	0.959924i	$0.590420\pi$
$912$	0.234025	−	2.89892i	0.00774935	−	0.0959929i
$913$	66.9518	+	22.3518i	2.21578	+	0.739736i
$914$	3.42744	−	3.56835i	0.113370	−	0.118030i
$915$		−	27.3193i		−	0.903148i
$916$	−10.1099	−	9.71068i	−0.334040	−	0.320850i
$917$	11.1219	−	9.08074i	0.367277	−	0.299872i
$918$	−2.07053	−	3.94506i	−0.0683376	−	0.130206i
$919$	−22.6198	−	3.67607i	−0.746158	−	0.121262i	−0.224568	−	0.974459i	$-0.572097\pi$
$919$	−22.6198	−	3.67607i	−0.746158	−	0.121262i	−0.521590	+	0.853196i	$0.674661\pi$
$920$	29.7653	+	18.8224i	0.981331	+	0.620556i
$921$	−23.9869	−	11.3819i	−0.790394	−	0.375047i
$922$	1.45912	+	2.11391i	0.0480537	+	0.0696178i
$923$	29.7107	+	5.54170i	0.977940	+	0.182407i
$924$	−4.91659	+	7.12291i	−0.161744	+	0.234327i
$925$	−53.3680	+	30.8120i	−1.75473	+	1.01309i
$926$	1.86152	−	3.92308i	0.0611735	−	0.128920i
$927$	17.7011	−	5.90951i	0.581382	−	0.194094i
$928$	−4.54029	−	18.4207i	−0.149042	−	0.604689i
$929$	−7.66770	−	0.308998i	−0.251569	−	0.0101379i	−0.0858389	−	0.996309i	$-0.527357\pi$
$929$	−7.66770	−	0.308998i	−0.251569	−	0.0101379i	−0.165730	+	0.986171i	$0.552998\pi$
$930$	10.4430	+	0.420838i	0.342439	+	0.0137998i
$931$	7.27109	+	29.5000i	0.238300	+	0.966822i
$932$	−19.4510	+	6.49369i	−0.637137	+	0.212708i
$933$	5.22634	−	11.0143i	0.171103	−	0.360591i
$934$	2.17098	−	1.25342i	0.0710366	−	0.0410130i
$935$	−55.9207	+	81.0151i	−1.82880	+	2.64948i
$936$	2.92595	−	9.28637i	0.0956376	−	0.303535i
$937$	−14.1157	−	20.4502i	−0.461141	−	0.668077i	0.521574	−	0.853206i	$-0.325345\pi$
$937$	−14.1157	−	20.4502i	−0.461141	−	0.668077i	−0.982714	+	0.185129i	$0.940730\pi$
$938$	−8.00623	−	3.79900i	−0.261413	−	0.124042i
$939$	15.8490	+	10.0223i	0.517213	+	0.327066i
$940$	−43.1609	−	7.01432i	−1.40775	−	0.228782i
$941$	−17.9382	−	34.1783i	−0.584767	−	1.11418i	−0.980630	−	0.195871i	$-0.937247\pi$
$941$	−17.9382	−	34.1783i	−0.584767	−	1.11418i	0.395862	−	0.918310i	$-0.370446\pi$
$942$	8.00201	−	6.53344i	0.260719	−	0.212871i
$943$	−10.2860	−	9.87981i	−0.334957	−	0.321731i
$944$			4.44170i			0.144565i
$945$	−2.93298	+	3.05356i	−0.0954100	+	0.0993323i
$946$	1.37556	+	0.459229i	0.0447233	+	0.0149308i
$947$	−3.49360	+	43.2760i	−0.113527	+	1.40628i	0.649720	+	0.760173i	$0.274886\pi$
$947$	−3.49360	+	43.2760i	−0.113527	+	1.40628i	−0.763247	+	0.646107i	$0.776396\pi$
$948$	−12.5399	−	3.09082i	−0.407278	−	0.100385i
$949$	−2.96598	−	1.64590i	−0.0962797	−	0.0534281i
$950$	29.3690	−	7.23880i	0.952855	−	0.234858i
$951$	5.14193	+	31.6396i	0.166739	+	1.02598i
$952$	−11.6539	+	14.2735i	−0.377706	+	0.462606i
$953$	−12.8261	−	9.63817i	−0.415477	−	0.312211i	0.372367	−	0.928086i	$-0.378546\pi$
$953$	−12.8261	−	9.63817i	−0.415477	−	0.312211i	−0.787844	+	0.615875i	$0.788803\pi$
$954$	4.03512	+	4.55471i	0.130642	+	0.147464i
$955$	−7.83649	+	48.2199i	−0.253583	+	1.56036i
$956$	2.10376	+	26.0598i	0.0680405	+	0.842833i
$957$	−4.04818	+	16.4241i	−0.130859	+	0.530917i
$958$	−4.69871	+	16.2218i	−0.151808	+	0.524104i
$959$	−3.02298	+	14.8075i	−0.0976171	+	0.478160i
$960$	−9.68455	−	7.90719i	−0.312568	−	0.255204i
$961$	2.01380	+	16.5851i	0.0649611	+	0.535003i
$962$	−24.1776	+	10.7898i	−0.779516	+	0.347876i
$963$	1.57730	−	12.9903i	0.0508279	−	0.418605i
$964$	20.1172	−	19.3228i	0.647931	−	0.622346i
$965$	−47.9346	−	49.9052i	−1.54307	−	1.60650i
$966$	−1.62182	−	3.41791i	−0.0521811	−	0.109969i
$967$	−30.5023	−	21.0542i	−0.980888	−	0.677058i	−0.0342690	−	0.999413i	$-0.510910\pi$
$967$	−30.5023	−	21.0542i	−0.980888	−	0.677058i	−0.946619	+	0.322355i	$0.895526\pi$
$968$	23.0320	+	36.4222i	0.740276	+	1.17065i
$969$	−18.4243	+	24.5183i	−0.591875	+	0.787642i
$970$	2.62780	−	5.00685i	0.0843735	−	0.160760i
$971$	−4.70164	−	23.0302i	−0.150883	−	0.739073i	−0.982873	−	0.184283i	$-0.941004\pi$
$971$	−4.70164	−	23.0302i	−0.150883	−	0.739073i	0.831990	−	0.554790i	$-0.187201\pi$
$972$	1.34598	+	0.108659i	0.0431724	+	0.00348524i
$973$	14.8970	−	4.31497i	0.477576	−	0.138332i
$974$	24.9048	−	13.0711i	0.798003	−	0.418824i
$975$	−24.3846	+	0.414123i	−0.780933	+	0.0132626i
$976$	3.69702	+	1.94035i	0.118339	+	0.0621090i
$977$	−49.7538	−	10.1573i	−1.59177	−	0.324961i	−0.679220	−	0.733935i	$-0.737682\pi$
$977$	−49.7538	−	10.1573i	−1.59177	−	0.324961i	−0.912546	+	0.408974i	$0.865887\pi$
$978$	2.81236	−	2.11335i	0.0899295	−	0.0675776i
$979$	−2.26608	+	56.2323i	−0.0724243	+	1.79719i
$980$	−23.7150	−	8.99391i	−0.757548	−	0.287300i
$981$	−12.9127	−	3.74022i	−0.412272	−	0.119416i
$982$	−6.48352	+	1.32362i	−0.206897	+	0.0422384i
$983$	0.288992	−	0.326204i	0.00921741	−	0.0104043i	−0.743884	−	0.668309i	$-0.767018\pi$
$983$	0.288992	−	0.326204i	0.00921741	−	0.0104043i	0.753101	+	0.657904i	$0.228557\pi$
$984$	6.40604	+	7.84597i	0.204217	+	0.250120i
$985$	0.363893	+	9.02991i	0.0115946	+	0.287717i
$986$	−4.59658	+	13.7684i	−0.146385	+	0.438476i
$987$	8.72351	+	7.72836i	0.277672	+	0.245996i
$988$	−26.7570	+	3.71095i	−0.851253	+	0.118061i
$989$	0.986258	−	0.873749i	0.0313612	−	0.0277836i
$990$	5.62612	+	13.2050i	0.178810	+	0.419682i
$991$	−11.9704	−	20.7333i	−0.380251	−	0.658614i	0.610847	−	0.791749i	$-0.290829\pi$
$991$	−11.9704	−	20.7333i	−0.380251	−	0.658614i	−0.991098	+	0.133135i	$0.957496\pi$
$992$	−11.0078	+	19.0661i	−0.349499	+	0.605351i
$993$	6.81650	+	0.827673i	0.216315	+	0.0262654i
$994$	−7.53492	+	3.57536i	−0.238993	+	0.113404i
$995$	11.5017	+	6.64050i	0.364628	+	0.210518i
$996$	−15.1079	+	10.4282i	−0.478712	+	0.330431i
$997$	9.86421	+	4.20275i	0.312403	+	0.133102i	0.542477	−	0.840071i	$-0.317487\pi$
$997$	9.86421	+	4.20275i	0.312403	+	0.133102i	−0.230074	+	0.973173i	$0.573897\pi$
$998$	−12.4977	+	2.03107i	−0.395607	+	0.0642923i
$999$	−5.47308	−	7.28334i	−0.173160	−	0.230435i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.b.127.9	yes	360
169.4	even	78	inner	507.2.t.b.4.9	✓	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.b.4.9	✓	360	169.4	even	78	inner
507.2.t.b.127.9	yes	360	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.805348 - 0.0324544i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(-1.34598 + 0.108659i) q^{4} +(3.20699 - 1.21625i) q^{5} +(-0.255235 - 0.764522i) q^{6} +(-0.483860 + 1.13566i) q^{7} +(-2.68071 + 0.325497i) q^{8} +(-0.845190 + 0.534466i) q^{9} +O(q^{10})\)	\(q+(0.805348 - 0.0324544i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(-1.34598 + 0.108659i) q^{4} +(3.20699 - 1.21625i) q^{5} +(-0.255235 - 0.764522i) q^{6} +(-0.483860 + 1.13566i) q^{7} +(-2.68071 + 0.325497i) q^{8} +(-0.845190 + 0.534466i) q^{9} +(2.54327 - 1.08359i) q^{10} +(2.77501 - 4.38834i) q^{11} +(0.478845 + 1.26261i) q^{12} +(3.01421 - 1.97851i) q^{13} +(-0.352819 + 0.930306i) q^{14} +(-2.06047 - 2.74199i) q^{15} +(0.517408 - 0.0840871i) q^{16} +(-5.08545 - 2.16671i) q^{17} +(-0.663327 + 0.457861i) q^{18} +(4.80489 + 2.77410i) q^{19} +(-4.18439 + 1.98552i) q^{20} +(1.22544 + 0.148796i) q^{21} +(2.09243 - 3.62420i) q^{22} +(-1.90116 - 3.29291i) q^{23} +(1.05847 + 2.48431i) q^{24} +(5.06296 - 4.48540i) q^{25} +(2.36328 - 1.69122i) q^{26} +(0.748511 + 0.663123i) q^{27} +(0.527867 - 1.58116i) q^{28} +(-0.131184 - 3.25530i) q^{29} +(-1.74839 - 2.14139i) q^{30} +(-2.50702 + 2.82984i) q^{31} +(5.70561 - 1.16481i) q^{32} +(-4.98713 - 1.44454i) q^{33} +(-4.16587 - 1.57991i) q^{34} +(-0.170485 + 4.23055i) q^{35} +(1.07954 - 0.811219i) q^{36} +(-8.92640 - 1.82234i) q^{37} +(3.95964 + 2.07818i) q^{38} +(-2.73900 - 2.34475i) q^{39} +(-8.20112 + 4.30428i) q^{40} +(3.60284 - 1.04357i) q^{41} +(0.991737 + 0.0800612i) q^{42} +(0.0693153 + 0.339529i) q^{43} +(-3.25829 + 6.20815i) q^{44} +(-2.06047 + 2.74199i) q^{45} +(-1.63797 - 2.59024i) q^{46} +(7.76987 + 5.36316i) q^{47} +(-0.224719 - 0.473586i) q^{48} +(3.79346 + 3.94941i) q^{49} +(3.93188 - 3.77662i) q^{50} +(-0.666300 + 5.48748i) q^{51} +(-3.84210 + 2.99056i) q^{52} +(-0.910009 - 7.49460i) q^{53} +(0.624333 + 0.509752i) q^{54} +(3.56213 - 17.4485i) q^{55} +(0.927434 - 3.20187i) q^{56} +(1.32777 - 5.38699i) q^{57} +(-0.211298 - 2.61739i) q^{58} +(-1.35922 + 8.36361i) q^{59} +(3.07130 + 3.46678i) q^{60} +(6.36764 + 4.78497i) q^{61} +(-1.92718 + 2.36037i) q^{62} +(-0.198018 - 1.21846i) q^{63} +(3.53927 - 0.872352i) q^{64} +(7.26019 - 10.0111i) q^{65} +(-4.06326 - 1.00150i) q^{66} +(-0.716692 + 8.87782i) q^{67} +(7.08035 + 2.36377i) q^{68} +(-2.63396 + 2.74225i) q^{69} +3.41260i q^{70} +(6.04540 + 5.80668i) q^{71} +(2.09174 - 1.70785i) q^{72} +(-0.437205 - 0.833024i) q^{73} +(-7.24801 - 1.17792i) q^{74} +(-5.71691 - 3.61515i) q^{75} +(-6.76873 - 3.21180i) q^{76} +(3.64094 + 5.27482i) q^{77} +(-2.28195 - 1.79945i) q^{78} +(-5.43313 + 7.87125i) q^{79} +(1.55705 - 0.898965i) q^{80} +(0.428693 - 0.903450i) q^{81} +(2.86767 - 0.957368i) q^{82} +(3.25337 + 13.1995i) q^{83} +(-1.66559 - 0.0671210i) q^{84} +(-18.9442 - 0.763426i) q^{85} +(0.0668422 + 0.271189i) q^{86} +(-3.09028 + 1.03169i) q^{87} +(-6.01062 + 12.6671i) q^{88} +(-9.38692 + 5.41954i) q^{89} +(-1.57041 + 2.27513i) q^{90} +(0.788462 + 4.38045i) q^{91} +(2.91673 + 4.22562i) q^{92} +(3.41560 + 1.62072i) q^{93} +(6.43151 + 4.06704i) q^{94} +(18.7832 + 3.05257i) q^{95} +(-2.70622 - 5.15627i) q^{96} +(1.58439 - 1.29362i) q^{97} +(3.18324 + 3.05754i) q^{98} +5.19213i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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