LMFDB - Embedded newform 287.2.f.a.50.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(50,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("287.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.f (of order $4$, degree $2$, 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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			50.9
Character	$\chi$	$=$	287.50
Dual form			287.2.f.a.155.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.447748i q^{2} +(1.09022 + 1.09022i) q^{3} +1.79952 q^{4} -1.12660i q^{5} +(0.488146 - 0.488146i) q^{6} +(0.707107 + 0.707107i) q^{7} -1.70123i q^{8} -0.622822i q^{9} +O(q^{10})$	\(q-0.447748i q^{2} +(1.09022 + 1.09022i) q^{3} +1.79952 q^{4} -1.12660i q^{5} +(0.488146 - 0.488146i) q^{6} +(0.707107 + 0.707107i) q^{7} -1.70123i q^{8} -0.622822i q^{9} -0.504431 q^{10} +(-1.42082 - 1.42082i) q^{11} +(1.96188 + 1.96188i) q^{12} +(1.34520 + 1.34520i) q^{13} +(0.316606 - 0.316606i) q^{14} +(1.22824 - 1.22824i) q^{15} +2.83732 q^{16} +(-2.21038 + 2.21038i) q^{17} -0.278868 q^{18} +(-3.80056 + 3.80056i) q^{19} -2.02733i q^{20} +1.54181i q^{21} +(-0.636172 + 0.636172i) q^{22} -8.28194 q^{23} +(1.85472 - 1.85472i) q^{24} +3.73078 q^{25} +(0.602310 - 0.602310i) q^{26} +(3.94969 - 3.94969i) q^{27} +(1.27245 + 1.27245i) q^{28} +(6.32744 + 6.32744i) q^{29} +(-0.549943 - 0.549943i) q^{30} +2.36754 q^{31} -4.67286i q^{32} -3.09803i q^{33} +(0.989692 + 0.989692i) q^{34} +(0.796624 - 0.796624i) q^{35} -1.12078i q^{36} -10.7271 q^{37} +(1.70169 + 1.70169i) q^{38} +2.93313i q^{39} -1.91660 q^{40} +(-6.15222 + 1.77487i) q^{41} +0.690343 q^{42} -6.75096i q^{43} +(-2.55680 - 2.55680i) q^{44} -0.701669 q^{45} +3.70823i q^{46} +(5.77065 - 5.77065i) q^{47} +(3.09331 + 3.09331i) q^{48} +1.00000i q^{49} -1.67045i q^{50} -4.81961 q^{51} +(2.42071 + 2.42071i) q^{52} +(-1.80005 - 1.80005i) q^{53} +(-1.76847 - 1.76847i) q^{54} +(-1.60069 + 1.60069i) q^{55} +(1.20295 - 1.20295i) q^{56} -8.28693 q^{57} +(2.83310 - 2.83310i) q^{58} -4.13994 q^{59} +(2.21025 - 2.21025i) q^{60} +13.6091i q^{61} -1.06006i q^{62} +(0.440402 - 0.440402i) q^{63} +3.58237 q^{64} +(1.51549 - 1.51549i) q^{65} -1.38714 q^{66} +(-2.59555 + 2.59555i) q^{67} +(-3.97762 + 3.97762i) q^{68} +(-9.02917 - 9.02917i) q^{69} +(-0.356687 - 0.356687i) q^{70} +(-6.09378 - 6.09378i) q^{71} -1.05956 q^{72} +2.91486i q^{73} +4.80305i q^{74} +(4.06739 + 4.06739i) q^{75} +(-6.83919 + 6.83919i) q^{76} -2.00935i q^{77} +1.31331 q^{78} +(-8.34492 - 8.34492i) q^{79} -3.19651i q^{80} +6.74362 q^{81} +(0.794695 + 2.75465i) q^{82} -5.43799 q^{83} +2.77452i q^{84} +(2.49020 + 2.49020i) q^{85} -3.02273 q^{86} +13.7967i q^{87} +(-2.41715 + 2.41715i) q^{88} +(9.82079 + 9.82079i) q^{89} +0.314171i q^{90} +1.90240i q^{91} -14.9035 q^{92} +(2.58115 + 2.58115i) q^{93} +(-2.58380 - 2.58380i) q^{94} +(4.28170 + 4.28170i) q^{95} +(5.09447 - 5.09447i) q^{96} +(-8.27386 + 8.27386i) q^{97} +0.447748 q^{98} +(-0.884921 + 0.884921i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6}+O(q^{10}) $ 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6	$ 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6} - 32 q^{10} - 8 q^{11} + 16 q^{12} + 16 q^{13} - 8 q^{15} + 28 q^{16} + 20 q^{17} - 12 q^{18} - 20 q^{19} + 4 q^{22} + 16 q^{23} - 12 q^{24} - 40 q^{25} - 20 q^{26} - 20 q^{27} - 12 q^{29} + 4 q^{30} + 32 q^{34} + 4 q^{35} - 16 q^{38} + 64 q^{40} + 16 q^{41} + 32 q^{42} + 8 q^{44} + 72 q^{45} - 24 q^{47} - 40 q^{48} - 64 q^{51} - 96 q^{52} + 8 q^{53} + 52 q^{54} - 8 q^{55} - 88 q^{57} - 36 q^{58} + 48 q^{59} + 52 q^{60} - 8 q^{63} - 84 q^{64} - 44 q^{65} + 56 q^{66} + 40 q^{67} - 60 q^{68} + 28 q^{69} - 8 q^{70} + 20 q^{71} + 80 q^{72} - 20 q^{75} - 4 q^{76} + 12 q^{78} - 12 q^{79} + 16 q^{81} - 52 q^{82} + 40 q^{83} + 8 q^{85} + 80 q^{86} + 96 q^{88} - 8 q^{89} - 20 q^{92} - 64 q^{93} + 52 q^{94} + 68 q^{96} - 60 q^{97} - 4 q^{98} - 36 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6 - 32 * q^10 - 8 * q^11 + 16 * q^12 + 16 * q^13 - 8 * q^15 + 28 * q^16 + 20 * q^17 - 12 * q^18 - 20 * q^19 + 4 * q^22 + 16 * q^23 - 12 * q^24 - 40 * q^25 - 20 * q^26 - 20 * q^27 - 12 * q^29 + 4 * q^30 + 32 * q^34 + 4 * q^35 - 16 * q^38 + 64 * q^40 + 16 * q^41 + 32 * q^42 + 8 * q^44 + 72 * q^45 - 24 * q^47 - 40 * q^48 - 64 * q^51 - 96 * q^52 + 8 * q^53 + 52 * q^54 - 8 * q^55 - 88 * q^57 - 36 * q^58 + 48 * q^59 + 52 * q^60 - 8 * q^63 - 84 * q^64 - 44 * q^65 + 56 * q^66 + 40 * q^67 - 60 * q^68 + 28 * q^69 - 8 * q^70 + 20 * q^71 + 80 * q^72 - 20 * q^75 - 4 * q^76 + 12 * q^78 - 12 * q^79 + 16 * q^81 - 52 * q^82 + 40 * q^83 + 8 * q^85 + 80 * q^86 + 96 * q^88 - 8 * q^89 - 20 * q^92 - 64 * q^93 + 52 * q^94 + 68 * q^96 - 60 * q^97 - 4 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	0.447748i		−	0.316606i	−0.987391	−	0.158303i	$-0.949398\pi$
$2$		−	0.447748i		−	0.316606i	0.987391	−	0.158303i	$-0.0506023\pi$
$3$	1.09022	+	1.09022i	0.629441	+	0.629441i	0.947927	−	0.318486i	$-0.103174\pi$
$3$	1.09022	+	1.09022i	0.629441	+	0.629441i	−0.318486	+	0.947927i	$0.603174\pi$
$4$	1.79952			0.899761
$5$		−	1.12660i		−	0.503829i	−0.967749	−	0.251914i	$-0.918940\pi$
$5$		−	1.12660i		−	0.503829i	0.967749	−	0.251914i	$-0.0810602\pi$
$6$	0.488146	−	0.488146i	0.199285	−	0.199285i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		−	1.70123i		−	0.601475i
$9$		−	0.622822i		−	0.207607i
$10$	−0.504431			−0.159515
$11$	−1.42082	−	1.42082i	−0.428395	−	0.428395i	0.459687	−	0.888081i	$-0.347962\pi$
$11$	−1.42082	−	1.42082i	−0.428395	−	0.428395i	−0.888081	+	0.459687i	$0.847962\pi$
$12$	1.96188	+	1.96188i	0.566346	+	0.566346i
$13$	1.34520	+	1.34520i	0.373091	+	0.373091i	0.868602	−	0.495511i	$-0.165019\pi$
$13$	1.34520	+	1.34520i	0.373091	+	0.373091i	−0.495511	+	0.868602i	$0.665019\pi$
$14$	0.316606	−	0.316606i	0.0846165	−	0.0846165i
$15$	1.22824	−	1.22824i	0.317131	−	0.317131i
$16$	2.83732			0.709330
$17$	−2.21038	+	2.21038i	−0.536095	+	0.536095i	−0.922380	−	0.386285i	$-0.873758\pi$
$17$	−2.21038	+	2.21038i	−0.536095	+	0.536095i	0.386285	+	0.922380i	$0.373758\pi$
$18$	−0.278868			−0.0657298
$19$	−3.80056	+	3.80056i	−0.871908	+	0.871908i	−0.992680	−	0.120772i	$-0.961463\pi$
$19$	−3.80056	+	3.80056i	−0.871908	+	0.871908i	0.120772	+	0.992680i	$0.461463\pi$
$20$		−	2.02733i		−	0.453325i
$21$			1.54181i			0.336450i
$22$	−0.636172	+	0.636172i	−0.135632	+	0.135632i
$23$	−8.28194			−1.72690			−0.863452	−	0.504431i	$-0.831702\pi$
$23$	−8.28194			−1.72690			−0.863452	+	0.504431i	$0.831702\pi$
$24$	1.85472	−	1.85472i	0.378593	−	0.378593i
$25$	3.73078			0.746156
$26$	0.602310	−	0.602310i	0.118123	−	0.118123i
$27$	3.94969	−	3.94969i	0.760118	−	0.760118i
$28$	1.27245	+	1.27245i	0.240471	+	0.240471i
$29$	6.32744	+	6.32744i	1.17498	+	1.17498i	0.981008	+	0.193969i	$0.0621360\pi$
$29$	6.32744	+	6.32744i	1.17498	+	1.17498i	0.193969	+	0.981008i	$0.437864\pi$
$30$	−0.549943	−	0.549943i	−0.100405	−	0.100405i
$31$	2.36754			0.425223			0.212612	−	0.977137i	$-0.431803\pi$
$31$	2.36754			0.425223			0.212612	+	0.977137i	$0.431803\pi$
$32$		−	4.67286i		−	0.826054i
$33$		−	3.09803i		−	0.539298i
$34$	0.989692	+	0.989692i	0.169731	+	0.169731i
$35$	0.796624	−	0.796624i	0.134654	−	0.134654i
$36$		−	1.12078i		−	0.186797i
$37$	−10.7271			−1.76353			−0.881764	−	0.471690i	$-0.843644\pi$
$37$	−10.7271			−1.76353			−0.881764	+	0.471690i	$0.843644\pi$
$38$	1.70169	+	1.70169i	0.276051	+	0.276051i
$39$			2.93313i			0.469677i
$40$	−1.91660			−0.303041
$41$	−6.15222	+	1.77487i	−0.960816	+	0.277188i
$41$	−6.15222	+	1.77487i	−0.960816	+	0.277188i
$42$	0.690343			0.106522
$43$		−	6.75096i		−	1.02951i	−0.857337	−	0.514756i	$-0.827883\pi$
$43$		−	6.75096i		−	1.02951i	0.857337	−	0.514756i	$-0.172117\pi$
$44$	−2.55680	−	2.55680i	−0.385453	−	0.385453i
$45$	−0.701669			−0.104599
$46$			3.70823i			0.546748i
$47$	5.77065	−	5.77065i	0.841736	−	0.841736i	−0.147348	−	0.989085i	$-0.547074\pi$
$47$	5.77065	−	5.77065i	0.841736	−	0.841736i	0.989085	+	0.147348i	$0.0470739\pi$
$48$	3.09331	+	3.09331i	0.446482	+	0.446482i
$49$			1.00000i			0.142857i
$50$		−	1.67045i		−	0.236238i
$51$	−4.81961			−0.674880
$52$	2.42071	+	2.42071i	0.335692	+	0.335692i
$53$	−1.80005	−	1.80005i	−0.247256	−	0.247256i	0.572588	−	0.819843i	$-0.305940\pi$
$53$	−1.80005	−	1.80005i	−0.247256	−	0.247256i	−0.819843	+	0.572588i	$0.805940\pi$
$54$	−1.76847	−	1.76847i	−0.240658	−	0.240658i
$55$	−1.60069	+	1.60069i	−0.215838	+	0.215838i
$56$	1.20295	−	1.20295i	0.160751	−	0.160751i
$57$	−8.28693			−1.09763
$58$	2.83310	−	2.83310i	0.372004	−	0.372004i
$59$	−4.13994			−0.538974			−0.269487	−	0.963004i	$-0.586854\pi$
$59$	−4.13994			−0.538974			−0.269487	+	0.963004i	$0.586854\pi$
$60$	2.21025	−	2.21025i	0.285342	−	0.285342i
$61$			13.6091i			1.74246i	0.490874	+	0.871230i	$0.336677\pi$
$61$			13.6091i			1.74246i	−0.490874	+	0.871230i	$0.663323\pi$
$62$		−	1.06006i		−	0.134628i
$63$	0.440402	−	0.440402i	0.0554854	−	0.0554854i
$64$	3.58237			0.447797
$65$	1.51549	−	1.51549i	0.187974	−	0.187974i
$66$	−1.38714			−0.170745
$67$	−2.59555	+	2.59555i	−0.317097	+	0.317097i	−0.847651	−	0.530554i	$-0.821984\pi$
$67$	−2.59555	+	2.59555i	−0.317097	+	0.317097i	0.530554	+	0.847651i	$0.321984\pi$
$68$	−3.97762	+	3.97762i	−0.482357	+	0.482357i
$69$	−9.02917	−	9.02917i	−1.08698	−	1.08698i
$70$	−0.356687	−	0.356687i	−0.0426322	−	0.0426322i
$71$	−6.09378	−	6.09378i	−0.723199	−	0.723199i	0.246056	−	0.969256i	$-0.420865\pi$
$71$	−6.09378	−	6.09378i	−0.723199	−	0.723199i	−0.969256	+	0.246056i	$0.920865\pi$
$72$	−1.05956			−0.124871
$73$			2.91486i			0.341159i	0.985344	+	0.170579i	$0.0545639\pi$
$73$			2.91486i			0.341159i	−0.985344	+	0.170579i	$0.945436\pi$
$74$			4.80305i			0.558344i
$75$	4.06739	+	4.06739i	0.469662	+	0.469662i
$76$	−6.83919	+	6.83919i	−0.784509	+	0.784509i
$77$		−	2.00935i		−	0.228987i
$78$	1.31331			0.148703
$79$	−8.34492	−	8.34492i	−0.938877	−	0.938877i	0.0593599	−	0.998237i	$-0.481094\pi$
$79$	−8.34492	−	8.34492i	−0.938877	−	0.938877i	−0.998237	+	0.0593599i	$0.981094\pi$
$80$		−	3.19651i		−	0.357381i
$81$	6.74362			0.749292
$82$	0.794695	+	2.75465i	0.0877594	+	0.304200i
$83$	−5.43799			−0.596897			−0.298448	−	0.954426i	$-0.596469\pi$
$83$	−5.43799			−0.596897			−0.298448	+	0.954426i	$0.596469\pi$
$84$			2.77452i			0.302725i
$85$	2.49020	+	2.49020i	0.270100	+	0.270100i
$86$	−3.02273			−0.325949
$87$			13.7967i			1.47916i
$88$	−2.41715	+	2.41715i	−0.257669	+	0.257669i
$89$	9.82079	+	9.82079i	1.04100	+	1.04100i	0.999123	+	0.0418786i	$0.0133343\pi$
$89$	9.82079	+	9.82079i	1.04100	+	1.04100i	0.0418786	+	0.999123i	$0.486666\pi$
$90$			0.314171i			0.0331166i
$91$			1.90240i			0.199425i
$92$	−14.9035			−1.55380
$93$	2.58115	+	2.58115i	0.267653	+	0.267653i
$94$	−2.58380	−	2.58380i	−0.266499	−	0.266499i
$95$	4.28170	+	4.28170i	0.439293	+	0.439293i
$96$	5.09447	−	5.09447i	0.519952	−	0.519952i
$97$	−8.27386	+	8.27386i	−0.840083	+	0.840083i	−0.988869	−	0.148786i	$-0.952463\pi$
$97$	−8.27386	+	8.27386i	−0.840083	+	0.840083i	0.148786	+	0.988869i	$0.452463\pi$
$98$	0.447748			0.0452294
$99$	−0.884921	+	0.884921i	−0.0889379	+	0.0889379i
$100$	6.71362			0.671362
$101$	8.85292	−	8.85292i	0.880898	−	0.880898i	−0.112728	−	0.993626i	$-0.535959\pi$
$101$	8.85292	−	8.85292i	0.880898	−	0.880898i	0.993626	+	0.112728i	$0.0359587\pi$
$102$			2.15797i			0.213671i
$103$		−	8.91085i		−	0.878012i	−0.898484	−	0.439006i	$-0.855331\pi$
$103$		−	8.91085i		−	0.878012i	0.898484	−	0.439006i	$-0.144669\pi$
$104$	2.28849	−	2.28849i	0.224405	−	0.224405i
$105$	1.73700			0.169514
$106$	−0.805968	+	0.805968i	−0.0782826	+	0.0782826i
$107$	−1.25186			−0.121022			−0.0605108	−	0.998168i	$-0.519273\pi$
$107$	−1.25186			−0.121022			−0.0605108	+	0.998168i	$0.519273\pi$
$108$	7.10755	−	7.10755i	0.683924	−	0.683924i
$109$	9.96117	−	9.96117i	0.954107	−	0.954107i	−0.0448852	−	0.998992i	$-0.514292\pi$
$109$	9.96117	−	9.96117i	0.954107	−	0.954107i	0.998992	+	0.0448852i	$0.0142922\pi$
$110$	0.716708	+	0.716708i	0.0683355	+	0.0683355i
$111$	−11.6950	−	11.6950i	−1.11004	−	1.11004i
$112$	2.00629	+	2.00629i	0.189576	+	0.189576i
$113$	6.53061			0.614348			0.307174	−	0.951653i	$-0.400617\pi$
$113$	6.53061			0.614348			0.307174	+	0.951653i	$0.400617\pi$
$114$			3.71046i			0.347516i
$115$			9.33040i			0.870064i
$116$	11.3864	+	11.3864i	1.05720	+	1.05720i
$117$	0.837819	−	0.837819i	0.0774564	−	0.0774564i
$118$			1.85365i			0.170642i
$119$	−3.12594			−0.286555
$120$	−2.08952	−	2.08952i	−0.190746	−	0.190746i
$121$		−	6.96252i		−	0.632956i
$122$	6.09343			0.551673
$123$	−8.64231	−	4.77229i	−0.779251	−	0.430303i
$124$	4.26044			0.382599
$125$		−	9.83606i		−	0.879764i
$126$	−0.197189	−	0.197189i	−0.0175670	−	0.0175670i
$127$	8.71171			0.773040			0.386520	−	0.922281i	$-0.373677\pi$
$127$	8.71171			0.773040			0.386520	+	0.922281i	$0.373677\pi$
$128$		−	10.9497i		−	0.967829i
$129$	7.36006	−	7.36006i	0.648017	−	0.648017i
$130$	−0.678560	−	0.678560i	−0.0595137	−	0.0595137i
$131$		−	2.06917i		−	0.180784i	−0.995906	−	0.0903922i	$-0.971188\pi$
$131$		−	2.06917i		−	0.180784i	0.995906	−	0.0903922i	$-0.0288121\pi$
$132$		−	5.57498i		−	0.485239i
$133$	−5.37480			−0.466055
$134$	1.16215	+	1.16215i	0.100395	+	0.100395i
$135$	−4.44970	−	4.44970i	−0.382969	−	0.382969i
$136$	3.76036	+	3.76036i	0.322448	+	0.322448i
$137$	−11.0263	+	11.0263i	−0.942038	+	0.942038i	−0.998410	−	0.0563718i	$-0.982047\pi$
$137$	−11.0263	+	11.0263i	−0.942038	+	0.942038i	0.0563718	+	0.998410i	$0.482047\pi$
$138$	−4.04280	+	4.04280i	−0.344146	+	0.344146i
$139$	17.0980			1.45023			0.725116	−	0.688627i	$-0.241786\pi$
$139$	17.0980			1.45023			0.725116	+	0.688627i	$0.241786\pi$
$140$	1.43354	−	1.43354i	0.121156	−	0.121156i
$141$	12.5826			1.05965
$142$	−2.72848	+	2.72848i	−0.228969	+	0.228969i
$143$		−	3.82258i		−	0.319660i
$144$		−	1.76715i		−	0.147262i
$145$	7.12847	−	7.12847i	0.591987	−	0.591987i
$146$	1.30512			0.108013
$147$	−1.09022	+	1.09022i	−0.0899202	+	0.0899202i
$148$	−19.3037			−1.58675
$149$	12.3462	−	12.3462i	1.01144	−	1.01144i	0.0115090	−	0.999934i	$-0.496336\pi$
$149$	12.3462	−	12.3462i	1.01144	−	1.01144i	0.999934	−	0.0115090i	$-0.00366352\pi$
$150$	1.82117	−	1.82117i	0.148698	−	0.148698i
$151$	8.85634	+	8.85634i	0.720718	+	0.720718i	0.968752	−	0.248033i	$-0.0797842\pi$
$151$	8.85634	+	8.85634i	0.720718	+	0.720718i	−0.248033	+	0.968752i	$0.579784\pi$
$152$	6.46563	+	6.46563i	0.524431	+	0.524431i
$153$	1.37667	+	1.37667i	0.111297	+	0.111297i
$154$	−0.899683			−0.0724985
$155$		−	2.66726i		−	0.214240i
$156$			5.27824i			0.422597i
$157$	10.0620	+	10.0620i	0.803038	+	0.803038i	0.983569	−	0.180531i	$-0.0577818\pi$
$157$	10.0620	+	10.0620i	0.803038	+	0.803038i	−0.180531	+	0.983569i	$0.557782\pi$
$158$	−3.73642	+	3.73642i	−0.297254	+	0.297254i
$159$		−	3.92491i		−	0.311266i
$160$	−5.26443			−0.416190
$161$	−5.85622	−	5.85622i	−0.461535	−	0.461535i
$162$		−	3.01945i		−	0.237230i
$163$	−0.515330			−0.0403637			−0.0201819	−	0.999796i	$-0.506425\pi$
$163$	−0.515330			−0.0403637			−0.0201819	+	0.999796i	$0.506425\pi$
$164$	−11.0711	+	3.19392i	−0.864504	+	0.249403i
$165$	−3.49023			−0.271714
$166$			2.43485i			0.188981i
$167$	5.45682	+	5.45682i	0.422261	+	0.422261i	0.885982	−	0.463720i	$-0.153486\pi$
$167$	5.45682	+	5.45682i	0.422261	+	0.422261i	−0.463720	+	0.885982i	$0.653486\pi$
$168$	2.62297			0.202367
$169$		−	9.38089i		−	0.721607i
$170$	1.11498	−	1.11498i	0.0855153	−	0.0855153i
$171$	2.36707	+	2.36707i	0.181015	+	0.181015i
$172$		−	12.1485i		−	0.926314i
$173$		−	1.67864i		−	0.127624i	−0.997962	−	0.0638122i	$-0.979674\pi$
$173$		−	1.67864i		−	0.127624i	0.997962	−	0.0638122i	$-0.0203259\pi$
$174$	6.17743			0.468310
$175$	2.63806	+	2.63806i	0.199419	+	0.199419i
$176$	−4.03133	−	4.03133i	−0.303873	−	0.303873i
$177$	−4.51346	−	4.51346i	−0.339252	−	0.339252i
$178$	4.39724	−	4.39724i	0.329587	−	0.329587i
$179$	4.31353	−	4.31353i	0.322408	−	0.322408i	−0.527282	−	0.849690i	$-0.676789\pi$
$179$	4.31353	−	4.31353i	0.322408	−	0.322408i	0.849690	+	0.527282i	$0.176789\pi$
$180$	−1.26267			−0.0941138
$181$	−7.50490	+	7.50490i	−0.557835	+	0.557835i	−0.928691	−	0.370856i	$-0.879064\pi$
$181$	−7.50490	+	7.50490i	−0.557835	+	0.557835i	0.370856	+	0.928691i	$0.379064\pi$
$182$	0.851795			0.0631393
$183$	−14.8369	+	14.8369i	−1.09678	+	1.09678i
$184$			14.0895i			1.03869i
$185$			12.0851i			0.888517i
$186$	1.15571	−	1.15571i	0.0847405	−	0.0847405i
$187$	6.28111			0.459320
$188$	10.3844	−	10.3844i	0.757361	−	0.757361i
$189$	5.58570			0.406300
$190$	1.91712	−	1.91712i	0.139083	−	0.139083i
$191$	−4.28311	+	4.28311i	−0.309915	+	0.309915i	−0.844876	−	0.534962i	$-0.820326\pi$
$191$	−4.28311	+	4.28311i	−0.309915	+	0.309915i	0.534962	+	0.844876i	$0.320326\pi$
$192$	3.90559	+	3.90559i	0.281862	+	0.281862i
$193$	2.12022	+	2.12022i	0.152616	+	0.152616i	0.779286	−	0.626669i	$-0.215582\pi$
$193$	2.12022	+	2.12022i	0.152616	+	0.152616i	−0.626669	+	0.779286i	$0.715582\pi$
$194$	3.70461	+	3.70461i	0.265975	+	0.265975i
$195$	3.30446			0.236637
$196$			1.79952i			0.128537i
$197$			8.17739i			0.582615i	0.956630	+	0.291307i	$0.0940902\pi$
$197$			8.17739i			0.582615i	−0.956630	+	0.291307i	$0.905910\pi$
$198$	0.396222	+	0.396222i	0.0281583	+	0.0281583i
$199$	9.43935	−	9.43935i	0.669138	−	0.669138i	−0.288379	−	0.957516i	$-0.593116\pi$
$199$	9.43935	−	9.43935i	0.669138	−	0.669138i	0.957516	+	0.288379i	$0.0931162\pi$
$200$		−	6.34692i		−	0.448795i
$201$	−5.65946			−0.399187
$202$	−3.96388	−	3.96388i	−0.278898	−	0.278898i
$203$			8.94835i			0.628051i
$204$	−8.67299			−0.607231
$205$	1.99956	+	6.93107i	0.139655	+	0.484087i
$206$	−3.98982			−0.277984
$207$			5.15818i			0.358518i
$208$	3.81676	+	3.81676i	0.264644	+	0.264644i
$209$	10.7999			0.747042
$210$		−	0.777737i		−	0.0536690i
$211$	−11.3156	+	11.3156i	−0.778996	+	0.778996i	−0.979660	−	0.200664i	$-0.935690\pi$
$211$	−11.3156	+	11.3156i	−0.778996	+	0.778996i	0.200664	+	0.979660i	$0.435690\pi$
$212$	−3.23922	−	3.23922i	−0.222471	−	0.222471i
$213$		−	13.2872i		−	0.910423i
$214$			0.560517i			0.0383162i
$215$	−7.60560			−0.518698
$216$	−6.71933	−	6.71933i	−0.457192	−	0.457192i
$217$	1.67411	+	1.67411i	0.113646	+	0.113646i
$218$	−4.46010	−	4.46010i	−0.302076	−	0.302076i
$219$	−3.17785	+	3.17785i	−0.214739	+	0.214739i
$220$	−2.88048	+	2.88048i	−0.194202	+	0.194202i
$221$	−5.94678			−0.400024
$222$	−5.23641	+	5.23641i	−0.351445	+	0.351445i
$223$	−11.2518			−0.753474			−0.376737	−	0.926320i	$-0.622954\pi$
$223$	−11.2518			−0.753474			−0.376737	+	0.926320i	$0.622954\pi$
$224$	3.30421	−	3.30421i	0.220772	−	0.220772i
$225$		−	2.32361i		−	0.154908i
$226$		−	2.92407i		−	0.194506i
$227$	−4.74022	+	4.74022i	−0.314619	+	0.314619i	−0.846696	−	0.532077i	$-0.821412\pi$
$227$	−4.74022	+	4.74022i	−0.314619	+	0.314619i	0.532077	+	0.846696i	$0.321412\pi$
$228$	−14.9125			−0.987604
$229$	14.0812	−	14.0812i	0.930510	−	0.930510i	−0.0672279	−	0.997738i	$-0.521415\pi$
$229$	14.0812	−	14.0812i	0.930510	−	0.930510i	0.997738	+	0.0672279i	$0.0214155\pi$
$230$	4.17767			0.275467
$231$	2.19064	−	2.19064i	0.144134	−	0.144134i
$232$	10.7644	−	10.7644i	0.706719	−	0.706719i
$233$	10.5719	+	10.5719i	0.692591	+	0.692591i	0.962801	−	0.270210i	$-0.0870931\pi$
$233$	10.5719	+	10.5719i	0.692591	+	0.692591i	−0.270210	+	0.962801i	$0.587093\pi$
$234$	−0.375132	−	0.375132i	−0.0245232	−	0.0245232i
$235$	−6.50119	−	6.50119i	−0.424091	−	0.424091i
$236$	−7.44991			−0.484948
$237$		−	18.1957i		−	1.18194i
$238$			1.39964i			0.0907249i
$239$	17.2689	+	17.2689i	1.11703	+	1.11703i	0.992175	+	0.124855i	$0.0398467\pi$
$239$	17.2689	+	17.2689i	1.11703	+	1.11703i	0.124855	+	0.992175i	$0.460153\pi$
$240$	3.48492	−	3.48492i	0.224950	−	0.224950i
$241$			7.03370i			0.453081i	0.974002	+	0.226540i	$0.0727415\pi$
$241$			7.03370i			0.453081i	−0.974002	+	0.226540i	$0.927258\pi$
$242$	−3.11746			−0.200398
$243$	−4.49700	−	4.49700i	−0.288483	−	0.288483i
$244$			24.4898i			1.56780i
$245$	1.12660			0.0719756
$246$	−2.13679	+	3.86958i	−0.136237	+	0.246715i
$247$	−10.2250			−0.650602
$248$		−	4.02773i		−	0.255761i
$249$	−5.92863	−	5.92863i	−0.375712	−	0.375712i
$250$	−4.40408			−0.278539
$251$			12.6967i			0.801411i	0.916207	+	0.400705i	$0.131235\pi$
$251$			12.6967i			0.801411i	−0.916207	+	0.400705i	$0.868765\pi$
$252$	0.792513	−	0.792513i	0.0499236	−	0.0499236i
$253$	11.7672	+	11.7672i	0.739796	+	0.739796i
$254$		−	3.90066i		−	0.244749i
$255$			5.42975i			0.340024i
$256$	2.26202			0.141376
$257$	−12.8871	−	12.8871i	−0.803876	−	0.803876i	0.179823	−	0.983699i	$-0.442448\pi$
$257$	−12.8871	−	12.8871i	−0.803876	−	0.803876i	−0.983699	+	0.179823i	$0.942448\pi$
$258$	−3.29545	−	3.29545i	−0.205166	−	0.205166i
$259$	−7.58522	−	7.58522i	−0.471323	−	0.471323i
$260$	2.72716	−	2.72716i	0.169132	−	0.169132i
$261$	3.94087	−	3.94087i	0.243934	−	0.243934i
$262$	−0.926468			−0.0572374
$263$	−1.07067	+	1.07067i	−0.0660204	+	0.0660204i	−0.739346	−	0.673326i	$-0.764865\pi$
$263$	−1.07067	+	1.07067i	−0.0660204	+	0.0660204i	0.673326	+	0.739346i	$0.264865\pi$
$264$	−5.27047			−0.324375
$265$	−2.02793	+	2.02793i	−0.124575	+	0.124575i
$266$			2.40656i			0.147556i
$267$			21.4137i			1.31050i
$268$	−4.67074	+	4.67074i	−0.285311	+	0.285311i
$269$	7.49312			0.456864			0.228432	−	0.973560i	$-0.426640\pi$
$269$	7.49312			0.456864			0.228432	+	0.973560i	$0.426640\pi$
$270$	−1.99235	+	1.99235i	−0.121250	+	0.121250i
$271$	−19.8610			−1.20647			−0.603236	−	0.797563i	$-0.706122\pi$
$271$	−19.8610			−1.20647			−0.603236	+	0.797563i	$0.706122\pi$
$272$	−6.27154	+	6.27154i	−0.380268	+	0.380268i
$273$	−2.07404	+	2.07404i	−0.125527	+	0.125527i
$274$	4.93700	+	4.93700i	0.298255	+	0.298255i
$275$	−5.30078	−	5.30078i	−0.319649	−	0.319649i
$276$	−16.2482	−	16.2482i	−0.978026	−	0.978026i
$277$	20.6345			1.23980			0.619902	−	0.784679i	$-0.287172\pi$
$277$	20.6345			1.23980			0.619902	+	0.784679i	$0.287172\pi$
$278$		−	7.65560i		−	0.459152i
$279$		−	1.47456i		−	0.0882795i
$280$	−1.35524	−	1.35524i	−0.0809911	−	0.0809911i
$281$	0.134861	−	0.134861i	0.00804516	−	0.00804516i	−0.703073	−	0.711118i	$-0.748189\pi$
$281$	0.134861	−	0.134861i	0.00804516	−	0.00804516i	0.711118	+	0.703073i	$0.248189\pi$
$282$		−	5.63384i		−	0.335491i
$283$	−23.3706			−1.38924			−0.694620	−	0.719377i	$-0.744427\pi$
$283$	−23.3706			−1.38924			−0.694620	+	0.719377i	$0.744427\pi$
$284$	−10.9659	−	10.9659i	−0.650706	−	0.650706i
$285$			9.33602i			0.553018i
$286$	−1.71155			−0.101206
$287$	−5.60530	−	3.09525i	−0.330870	−	0.182707i
$288$	−2.91036			−0.171495
$289$			7.22848i			0.425205i
$290$	−3.19176	−	3.19176i	−0.187427	−	0.187427i
$291$	−18.0407			−1.05757
$292$			5.24535i			0.306961i
$293$	10.8042	−	10.8042i	0.631186	−	0.631186i	−0.317180	−	0.948365i	$-0.602736\pi$
$293$	10.8042	−	10.8042i	0.631186	−	0.631186i	0.948365	+	0.317180i	$0.102736\pi$
$294$	0.488146	+	0.488146i	0.0284693	+	0.0284693i
$295$			4.66404i			0.271551i
$296$			18.2493i			1.06072i
$297$	−11.2236			−0.651261
$298$	−5.52801	−	5.52801i	−0.320229	−	0.320229i
$299$	−11.1408	−	11.1408i	−0.644292	−	0.644292i
$300$	7.31935	+	7.31935i	0.422583	+	0.422583i
$301$	4.77365	−	4.77365i	0.275148	−	0.275148i
$302$	3.96541	−	3.96541i	0.228184	−	0.228184i
$303$	19.3033			1.10895
$304$	−10.7834	+	10.7834i	−0.618471	+	0.618471i
$305$	15.3319			0.877902
$306$	0.616402	−	0.616402i	0.0352374	−	0.0352374i
$307$			4.20442i			0.239959i	0.992776	+	0.119979i	$0.0382828\pi$
$307$			4.20442i			0.239959i	−0.992776	+	0.119979i	$0.961717\pi$
$308$		−	3.61587i		−	0.206033i
$309$	9.71482	−	9.71482i	0.552657	−	0.552657i
$310$	−1.19426			−0.0678296
$311$	4.43227	−	4.43227i	0.251331	−	0.251331i	−0.570185	−	0.821516i	$-0.693129\pi$
$311$	4.43227	−	4.43227i	0.251331	−	0.251331i	0.821516	+	0.570185i	$0.193129\pi$
$312$	4.98993			0.282499
$313$	8.95036	−	8.95036i	0.505904	−	0.505904i	−0.407362	−	0.913267i	$-0.633551\pi$
$313$	8.95036	−	8.95036i	0.505904	−	0.505904i	0.913267	+	0.407362i	$0.133551\pi$
$314$	4.50526	−	4.50526i	0.254247	−	0.254247i
$315$	−0.496155	−	0.496155i	−0.0279552	−	0.0279552i
$316$	−15.0169	−	15.0169i	−0.844764	−	0.844764i
$317$	−7.34767	−	7.34767i	−0.412686	−	0.412686i	0.469987	−	0.882673i	$-0.344259\pi$
$317$	−7.34767	−	7.34767i	−0.412686	−	0.412686i	−0.882673	+	0.469987i	$0.844259\pi$
$318$	−1.75737			−0.0985486
$319$		−	17.9804i		−	1.00671i
$320$		−	4.03589i		−	0.225613i
$321$	−1.36481	−	1.36481i	−0.0761760	−	0.0761760i
$322$	−2.62211	+	2.62211i	−0.146125	+	0.146125i
$323$		−	16.8013i		−	0.934851i
$324$	12.1353			0.674183
$325$	5.01864	+	5.01864i	0.278384	+	0.278384i
$326$			0.230738i			0.0127794i
$327$	21.7198			1.20111
$328$	3.01946	+	10.4663i	0.166722	+	0.577907i
$329$	8.16094			0.449927
$330$			1.56275i			0.0860263i
$331$	−5.82764	−	5.82764i	−0.320316	−	0.320316i	0.528572	−	0.848888i	$-0.322728\pi$
$331$	−5.82764	−	5.82764i	−0.320316	−	0.320316i	−0.848888	+	0.528572i	$0.822728\pi$
$332$	−9.78578			−0.537064
$333$			6.68110i			0.366122i
$334$	2.44328	−	2.44328i	0.133690	−	0.133690i
$335$	2.92413	+	2.92413i	0.159762	+	0.159762i
$336$			4.37461i			0.238654i
$337$		−	16.5585i		−	0.901997i	−0.892525	−	0.450999i	$-0.851068\pi$
$337$		−	16.5585i		−	0.901997i	0.892525	−	0.450999i	$-0.148932\pi$
$338$	−4.20028			−0.228465
$339$	7.11982	+	7.11982i	0.386696	+	0.386696i
$340$	4.48117	+	4.48117i	0.243025	+	0.243025i
$341$	−3.36386	−	3.36386i	−0.182163	−	0.182163i
$342$	1.05985	−	1.05985i	0.0573103	−	0.0573103i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−11.4849			−0.619226
$345$	−10.1722	+	10.1722i	−0.547654	+	0.547654i
$346$	−0.751607			−0.0404066
$347$	−5.77456	+	5.77456i	−0.309995	+	0.309995i	−0.844907	−	0.534913i	$-0.820345\pi$
$347$	−5.77456	+	5.77456i	−0.309995	+	0.309995i	0.534913	+	0.844907i	$0.320345\pi$
$348$			24.8274i			1.33089i
$349$			15.7084i			0.840853i	0.907327	+	0.420427i	$0.138120\pi$
$349$			15.7084i			0.840853i	−0.907327	+	0.420427i	$0.861880\pi$
$350$	1.18119	−	1.18119i	0.0631371	−	0.0631371i
$351$	10.6262			0.567186
$352$	−6.63932	+	6.63932i	−0.353877	+	0.353877i
$353$	−23.1400			−1.23162			−0.615809	−	0.787895i	$-0.711171\pi$
$353$	−23.1400			−1.23162			−0.615809	+	0.787895i	$0.711171\pi$
$354$	−2.02089	+	2.02089i	−0.107409	+	0.107409i
$355$	−6.86523	+	6.86523i	−0.364369	+	0.364369i
$356$	17.6727	+	17.6727i	0.936652	+	0.936652i
$357$	−3.40798	−	3.40798i	−0.180369	−	0.180369i
$358$	−1.93137	−	1.93137i	−0.102076	−	0.102076i
$359$	20.8873			1.10239			0.551196	−	0.834376i	$-0.314172\pi$
$359$	20.8873			1.10239			0.551196	+	0.834376i	$0.314172\pi$
$360$			1.19370i			0.0629135i
$361$		−	9.88852i		−	0.520448i
$362$	3.36031	+	3.36031i	0.176614	+	0.176614i
$363$	7.59071	−	7.59071i	0.398409	−	0.398409i
$364$			3.42340i			0.179435i
$365$	3.28387			0.171886
$366$	6.64321	+	6.64321i	0.347246	+	0.347246i
$367$		−	31.3123i		−	1.63449i	−0.576291	−	0.817244i	$-0.695501\pi$
$367$		−	31.3123i		−	1.63449i	0.576291	−	0.817244i	$-0.304499\pi$
$368$	−23.4985			−1.22494
$369$	1.10543	+	3.83174i	0.0575463	+	0.199473i
$370$	5.41110			0.281310
$371$		−	2.54565i		−	0.132164i
$372$	4.64484	+	4.64484i	0.240824	+	0.240824i
$373$	23.2504			1.20386			0.601931	−	0.798548i	$-0.294398\pi$
$373$	23.2504			1.20386			0.601931	+	0.798548i	$0.294398\pi$
$374$		−	2.81236i		−	0.145423i
$375$	10.7235	−	10.7235i	0.553760	−	0.553760i
$376$	−9.81721	−	9.81721i	−0.506284	−	0.506284i
$377$			17.0233i			0.876746i
$378$		−	2.50099i		−	0.128637i
$379$	12.7622			0.655552			0.327776	−	0.944756i	$-0.393701\pi$
$379$	12.7622			0.655552			0.327776	+	0.944756i	$0.393701\pi$
$380$	7.70500	+	7.70500i	0.395258	+	0.395258i
$381$	9.49772	+	9.49772i	0.486583	+	0.486583i
$382$	1.91775	+	1.91775i	0.0981208	+	0.0981208i
$383$	−15.9793	+	15.9793i	−0.816503	+	0.816503i	−0.985599	−	0.169097i	$-0.945915\pi$
$383$	−15.9793	+	15.9793i	−0.816503	+	0.816503i	0.169097	+	0.985599i	$0.445915\pi$
$384$	11.9377	−	11.9377i	0.609191	−	0.609191i
$385$	−2.26372			−0.115370
$386$	0.949323	−	0.949323i	0.0483193	−	0.0483193i
$387$	−4.20465			−0.213734
$388$	−14.8890	+	14.8890i	−0.755874	+	0.755874i
$389$			19.0593i			0.966347i	0.875525	+	0.483174i	$0.160516\pi$
$389$			19.0593i			0.966347i	−0.875525	+	0.483174i	$0.839484\pi$
$390$		−	1.47957i		−	0.0749207i
$391$	18.3062	−	18.3062i	0.925784	−	0.925784i
$392$	1.70123			0.0859251
$393$	2.25586	−	2.25586i	0.113793	−	0.113793i
$394$	3.66141			0.184459
$395$	−9.40135	+	9.40135i	−0.473033	+	0.473033i
$396$	−1.59243	+	1.59243i	−0.0800228	+	0.0800228i
$397$	−3.56448	−	3.56448i	−0.178896	−	0.178896i	0.611978	−	0.790875i	$-0.290374\pi$
$397$	−3.56448	−	3.56448i	−0.178896	−	0.178896i	−0.790875	+	0.611978i	$0.790374\pi$
$398$	−4.22645	−	4.22645i	−0.211853	−	0.211853i
$399$	−5.85974	−	5.85974i	−0.293354	−	0.293354i
$400$	10.5854			0.529271
$401$		−	6.91340i		−	0.345239i	−0.984989	−	0.172619i	$-0.944777\pi$
$401$		−	6.91340i		−	0.345239i	0.984989	−	0.172619i	$-0.0552230\pi$
$402$			2.53401i			0.126385i
$403$	3.18481	+	3.18481i	0.158647	+	0.158647i
$404$	15.9310	−	15.9310i	0.792598	−	0.792598i
$405$		−	7.59734i		−	0.377515i
$406$	4.00661			0.198845
$407$	15.2414	+	15.2414i	0.755486	+	0.755486i
$408$			8.19926i			0.405924i
$409$	−20.6903			−1.02307			−0.511536	−	0.859262i	$-0.670923\pi$
$409$	−20.6903			−1.02307			−0.511536	+	0.859262i	$0.670923\pi$
$410$	3.10337	−	0.895301i	0.153265	−	0.0442157i
$411$	−24.0422			−1.18592
$412$		−	16.0353i		−	0.790001i
$413$	−2.92738	−	2.92738i	−0.144047	−	0.144047i
$414$	2.30957			0.113509
$415$			6.12642i			0.300734i
$416$	6.28593	−	6.28593i	0.308193	−	0.308193i
$417$	18.6406	+	18.6406i	0.912836	+	0.912836i
$418$		−	4.83562i		−	0.236518i
$419$			12.2112i			0.596559i	0.954479	+	0.298279i	$0.0964127\pi$
$419$			12.2112i			0.596559i	−0.954479	+	0.298279i	$0.903587\pi$
$420$	3.12576			0.152522
$421$	12.4711	+	12.4711i	0.607803	+	0.607803i	0.942371	−	0.334569i	$-0.108591\pi$
$421$	12.4711	+	12.4711i	0.607803	+	0.607803i	−0.334569	+	0.942371i	$0.608591\pi$
$422$	5.06653	+	5.06653i	0.246635	+	0.246635i
$423$	−3.59409	−	3.59409i	−0.174751	−	0.174751i
$424$	−3.06229	+	3.06229i	−0.148718	+	0.148718i
$425$	−8.24643	+	8.24643i	−0.400010	+	0.400010i
$426$	−5.94931			−0.288245
$427$	−9.62305	+	9.62305i	−0.465692	+	0.465692i
$428$	−2.25275			−0.108891
$429$	4.16747	−	4.16747i	0.201207	−	0.201207i
$430$			3.40539i			0.164223i
$431$		−	24.1017i		−	1.16094i	−0.814283	−	0.580468i	$-0.802870\pi$
$431$		−	24.1017i		−	1.16094i	0.814283	−	0.580468i	$-0.197130\pi$
$432$	11.2065	−	11.2065i	0.539174	−	0.539174i
$433$	−25.1406			−1.20818			−0.604090	−	0.796916i	$-0.706463\pi$
$433$	−25.1406			−1.20818			−0.604090	+	0.796916i	$0.706463\pi$
$434$	0.749578	−	0.749578i	0.0359809	−	0.0359809i
$435$	15.5433			0.745242
$436$	17.9253	−	17.9253i	0.858468	−	0.858468i
$437$	31.4760	−	31.4760i	1.50570	−	1.50570i
$438$	1.42288	+	1.42288i	0.0679878	+	0.0679878i
$439$	−23.5159	−	23.5159i	−1.12235	−	1.12235i	−0.991387	−	0.130967i	$-0.958192\pi$
$439$	−23.5159	−	23.5159i	−1.12235	−	1.12235i	−0.130967	−	0.991387i	$-0.541808\pi$
$440$	2.72315	+	2.72315i	0.129821	+	0.129821i
$441$	0.622822			0.0296582
$442$			2.66266i			0.126650i
$443$			22.0949i			1.04976i	0.851176	+	0.524881i	$0.175890\pi$
$443$			22.0949i			1.04976i	−0.851176	+	0.524881i	$0.824110\pi$
$444$	−21.0454	−	21.0454i	−0.998768	−	0.998768i
$445$	11.0641	−	11.0641i	0.524487	−	0.524487i
$446$			5.03796i			0.238554i
$447$	26.9203			1.27329
$448$	2.53312	+	2.53312i	0.119679	+	0.119679i
$449$			0.283994i			0.0134025i	0.999978	+	0.00670126i	$0.00213309\pi$
$449$			0.283994i			0.0134025i	−0.999978	+	0.00670126i	$0.997867\pi$
$450$	−1.04039			−0.0490447
$451$	11.2630	+	6.21945i	0.530354	+	0.292862i
$452$	11.7520			0.552766
$453$			19.3108i			0.907300i
$454$	2.12242	+	2.12242i	0.0996103	+	0.0996103i
$455$	2.14323			0.100476
$456$			14.0980i			0.660198i
$457$	25.5706	−	25.5706i	1.19614	−	1.19614i	0.220833	−	0.975312i	$-0.429123\pi$
$457$	25.5706	−	25.5706i	1.19614	−	1.19614i	0.975312	−	0.220833i	$-0.0708775\pi$
$458$	−6.30482	−	6.30482i	−0.294605	−	0.294605i
$459$			17.4606i			0.814990i
$460$			16.7903i			0.782850i
$461$	−34.8796			−1.62451			−0.812253	−	0.583306i	$-0.801759\pi$
$461$	−34.8796			−1.62451			−0.812253	+	0.583306i	$0.801759\pi$
$462$	−0.980856	−	0.980856i	−0.0456335	−	0.0456335i
$463$	−13.8973	−	13.8973i	−0.645862	−	0.645862i	0.306128	−	0.951990i	$-0.400966\pi$
$463$	−13.8973	−	13.8973i	−0.645862	−	0.645862i	−0.951990	+	0.306128i	$0.900966\pi$
$464$	17.9530	+	17.9530i	0.833446	+	0.833446i
$465$	2.90792	−	2.90792i	0.134851	−	0.134851i
$466$	4.73357	−	4.73357i	0.219279	−	0.219279i
$467$	12.0235			0.556379			0.278190	−	0.960526i	$-0.410266\pi$
$467$	12.0235			0.556379			0.278190	+	0.960526i	$0.410266\pi$
$468$	1.50767	−	1.50767i	0.0696922	−	0.0696922i
$469$	−3.67066			−0.169495
$470$	−2.91090	+	2.91090i	−0.134270	+	0.134270i
$471$			21.9397i			1.01093i
$472$			7.04298i			0.324180i
$473$	−9.59192	+	9.59192i	−0.441037	+	0.441037i
$474$	−8.14708			−0.374208
$475$	−14.1791	+	14.1791i	−0.650580	+	0.650580i
$476$	−5.62520			−0.257831
$477$	−1.12111	+	1.12111i	−0.0513321	+	0.0513321i
$478$	7.73211	−	7.73211i	0.353658	−	0.353658i
$479$	−1.12552	−	1.12552i	−0.0514262	−	0.0514262i	0.680926	−	0.732352i	$-0.261578\pi$
$479$	−1.12552	−	1.12552i	−0.0514262	−	0.0514262i	−0.732352	+	0.680926i	$0.761578\pi$
$480$	−5.73941	−	5.73941i	−0.261967	−	0.261967i
$481$	−14.4301	−	14.4301i	−0.657956	−	0.657956i
$482$	3.14933			0.143448
$483$		−	12.7692i		−	0.581018i
$484$		−	12.5292i		−	0.569509i
$485$	9.32130	+	9.32130i	0.423258	+	0.423258i
$486$	−2.01353	+	2.01353i	−0.0913354	+	0.0913354i
$487$		−	19.0612i		−	0.863747i	−0.901934	−	0.431873i	$-0.857853\pi$
$487$		−	19.0612i		−	0.863747i	0.901934	−	0.431873i	$-0.142147\pi$
$488$	23.1521			1.04805
$489$	−0.561825	−	0.561825i	−0.0254066	−	0.0254066i
$490$		−	0.504431i		−	0.0227879i
$491$	18.4717			0.833617			0.416808	−	0.908994i	$-0.363149\pi$
$491$	18.4717			0.833617			0.416808	+	0.908994i	$0.363149\pi$
$492$	−15.5520	−	8.58785i	−0.701139	−	0.387170i
$493$	−27.9720			−1.25980
$494$			4.57823i			0.205984i
$495$	0.996948	+	0.996948i	0.0448095	+	0.0448095i
$496$	6.71748			0.301624
$497$		−	8.61791i		−	0.386566i
$498$	−2.65453	+	2.65453i	−0.118952	+	0.118952i
$499$	8.28781	+	8.28781i	0.371013	+	0.371013i	0.867846	−	0.496833i	$-0.165504\pi$
$499$	8.28781	+	8.28781i	0.371013	+	0.371013i	−0.496833	+	0.867846i	$0.665504\pi$
$500$		−	17.7002i		−	0.791577i
$501$			11.8983i			0.531578i
$502$	5.68494			0.253731
$503$	24.6393	+	24.6393i	1.09861	+	1.09861i	0.994573	+	0.104037i	$0.0331760\pi$
$503$	24.6393	+	24.6393i	1.09861	+	1.09861i	0.104037	+	0.994573i	$0.466824\pi$
$504$	−0.749225	−	0.749225i	−0.0333731	−	0.0333731i
$505$	−9.97366	−	9.97366i	−0.443822	−	0.443822i
$506$	5.26874	−	5.26874i	0.234224	−	0.234224i
$507$	10.2273	−	10.2273i	0.454209	−	0.454209i
$508$	15.6769			0.695551
$509$	30.6038	−	30.6038i	1.35649	−	1.35649i	0.478281	−	0.878207i	$-0.341260\pi$
$509$	30.6038	−	30.6038i	1.35649	−	1.35649i	0.878207	−	0.478281i	$-0.158740\pi$
$510$	2.43116			0.107654
$511$	−2.06112	+	2.06112i	−0.0911785	+	0.0911785i
$512$		−	22.9123i		−	1.01259i
$513$			30.0221i			1.32551i
$514$	−5.77019	+	5.77019i	−0.254512	+	0.254512i
$515$	−10.0389			−0.442368
$516$	13.2446	−	13.2446i	0.583060	−	0.583060i
$517$	−16.3982			−0.721190
$518$	−3.39627	+	3.39627i	−0.149224	+	0.149224i
$519$	1.83009	−	1.83009i	0.0803320	−	0.0803320i
$520$	−2.57820	−	2.57820i	−0.113062	−	0.113062i
$521$	−8.63588	−	8.63588i	−0.378345	−	0.378345i	0.492160	−	0.870505i	$-0.336207\pi$
$521$	−8.63588	−	8.63588i	−0.378345	−	0.378345i	−0.870505	+	0.492160i	$0.836207\pi$
$522$	−1.76452	−	1.76452i	−0.0772309	−	0.0772309i
$523$	−0.410397			−0.0179454			−0.00897271	−	0.999960i	$-0.502856\pi$
$523$	−0.410397			−0.0179454			−0.00897271	+	0.999960i	$0.502856\pi$
$524$		−	3.72352i		−	0.162663i
$525$			5.75216i			0.251045i
$526$	0.479391	+	0.479391i	0.0209025	+	0.0209025i
$527$	−5.23316	+	5.23316i	−0.227960	+	0.227960i
$528$		−	8.79011i		−	0.382541i
$529$	45.5905			1.98220
$530$	0.908001	+	0.908001i	0.0394410	+	0.0394410i
$531$			2.57845i			0.111895i
$532$	−9.67207			−0.419338
$533$	−10.6635	−	5.88840i	−0.461888	−	0.255055i
$534$	9.58796			0.414912
$535$			1.41034i			0.0609742i
$536$	4.41562	+	4.41562i	0.190726	+	0.190726i
$537$	9.40542			0.405874
$538$		−	3.35503i		−	0.144646i
$539$	1.42082	−	1.42082i	0.0611992	−	0.0611992i
$540$	−8.00734	−	8.00734i	−0.344581	−	0.344581i
$541$		−	24.0316i		−	1.03320i	−0.856228	−	0.516599i	$-0.827198\pi$
$541$		−	24.0316i		−	1.03320i	0.856228	−	0.516599i	$-0.172802\pi$
$542$			8.89274i			0.381976i
$543$	−16.3641			−0.702249
$544$	10.3288	+	10.3288i	0.442843	+	0.442843i
$545$	−11.2222	−	11.2222i	−0.480707	−	0.480707i
$546$	0.928648	+	0.928648i	0.0397425	+	0.0397425i
$547$	−7.94944	+	7.94944i	−0.339893	+	0.339893i	−0.856327	−	0.516434i	$-0.827259\pi$
$547$	−7.94944	+	7.94944i	−0.339893	+	0.339893i	0.516434	+	0.856327i	$0.327259\pi$
$548$	−19.8420	+	19.8420i	−0.847609	+	0.847609i
$549$	8.47602			0.361748
$550$	−2.37342	+	2.37342i	−0.101203	+	0.101203i
$551$	−48.0956			−2.04894
$552$	−15.3607	+	15.3607i	−0.653795	+	0.653795i
$553$		−	11.8015i		−	0.501851i
$554$		−	9.23905i		−	0.392530i
$555$	−13.1755	+	13.1755i	−0.559269	+	0.559269i
$556$	30.7682			1.30486
$557$	−25.9164	+	25.9164i	−1.09811	+	1.09811i	−0.103483	+	0.994631i	$0.532999\pi$
$557$	−25.9164	+	25.9164i	−1.09811	+	1.09811i	−0.994631	+	0.103483i	$0.967001\pi$
$558$	−0.660231			−0.0279498
$559$	9.08137	−	9.08137i	0.384101	−	0.384101i
$560$	2.26028	−	2.26028i	0.0955141	−	0.0955141i
$561$	6.84782	+	6.84782i	0.289115	+	0.289115i
$562$	−0.0603840	−	0.0603840i	−0.00254714	−	0.00254714i
$563$	19.6196	+	19.6196i	0.826868	+	0.826868i	0.987082	−	0.160214i	$-0.0512186\pi$
$563$	19.6196	+	19.6196i	0.826868	+	0.826868i	−0.160214	+	0.987082i	$0.551219\pi$
$564$	22.6427			0.953429
$565$		−	7.35735i		−	0.309526i
$566$			10.4642i			0.439842i
$567$	4.76846	+	4.76846i	0.200257	+	0.200257i
$568$	−10.3669	+	10.3669i	−0.434987	+	0.434987i
$569$			16.5469i			0.693681i	0.937924	+	0.346840i	$0.112745\pi$
$569$			16.5469i			0.693681i	−0.937924	+	0.346840i	$0.887255\pi$
$570$	4.18019			0.175089
$571$	−26.7943	−	26.7943i	−1.12131	−	1.12131i	−0.991545	−	0.129761i	$-0.958579\pi$
$571$	−26.7943	−	26.7943i	−1.12131	−	1.12131i	−0.129761	−	0.991545i	$-0.541421\pi$
$572$		−	6.87881i		−	0.287618i
$573$	−9.33909			−0.390146
$574$	−1.38590	+	2.50976i	−0.0578462	+	0.104756i
$575$	−30.8981			−1.28854
$576$		−	2.23118i		−	0.0929659i
$577$	−24.6524	−	24.6524i	−1.02629	−	1.02629i	−0.999645	−	0.0266498i	$-0.991516\pi$
$577$	−24.6524	−	24.6524i	−1.02629	−	1.02629i	−0.0266498	−	0.999645i	$-0.508484\pi$
$578$	3.23654			0.134622
$579$			4.62302i			0.192126i
$580$	12.8278	−	12.8278i	0.532647	−	0.532647i
$581$	−3.84524	−	3.84524i	−0.159527	−	0.159527i
$582$			8.07771i			0.334832i
$583$			5.11510i			0.211846i
$584$	4.95885			0.205199
$585$	−0.943884	−	0.943884i	−0.0390248	−	0.0390248i
$586$	−4.83755	−	4.83755i	−0.199837	−	0.199837i
$587$	−26.2143	−	26.2143i	−1.08198	−	1.08198i	−0.996325	−	0.0856530i	$-0.972702\pi$
$587$	−26.2143	−	26.2143i	−1.08198	−	1.08198i	−0.0856530	−	0.996325i	$-0.527298\pi$
$588$	−1.96188	+	1.96188i	−0.0809066	+	0.0809066i
$589$	−8.99799	+	8.99799i	−0.370756	+	0.370756i
$590$	2.08831			0.0859746
$591$	−8.91518	+	8.91518i	−0.366722	+	0.366722i
$592$	−30.4363			−1.25092
$593$	−32.0968	+	32.0968i	−1.31806	+	1.31806i	−0.402746	+	0.915312i	$0.631944\pi$
$593$	−32.0968	+	32.0968i	−1.31806	+	1.31806i	−0.915312	+	0.402746i	$0.868056\pi$
$594$			5.02536i			0.206193i
$595$			3.52167i			0.144375i
$596$	22.2173	−	22.2173i	0.910056	−	0.910056i
$597$	20.5820			0.842366
$598$	−4.98830	+	4.98830i	−0.203987	+	0.203987i
$599$	−33.2181			−1.35726			−0.678628	−	0.734482i	$-0.737425\pi$
$599$	−33.2181			−1.35726			−0.678628	+	0.734482i	$0.737425\pi$
$600$	6.91956	−	6.91956i	0.282490	−	0.282490i
$601$	−15.5705	+	15.5705i	−0.635136	+	0.635136i	−0.949352	−	0.314216i	$-0.898258\pi$
$601$	−15.5705	+	15.5705i	−0.635136	+	0.635136i	0.314216	+	0.949352i	$0.398258\pi$
$602$	−2.13739	−	2.13739i	−0.0871136	−	0.0871136i
$603$	1.61657	+	1.61657i	0.0658316	+	0.0658316i
$604$	15.9372	+	15.9372i	0.648474	+	0.648474i
$605$	−7.84394			−0.318902
$606$		−	8.64304i		−	0.351099i
$607$		−	20.3461i		−	0.825823i	−0.910771	−	0.412911i	$-0.864512\pi$
$607$		−	20.3461i		−	0.825823i	0.910771	−	0.412911i	$-0.135488\pi$
$608$	17.7595	+	17.7595i	0.720243	+	0.720243i
$609$	−9.75571	+	9.75571i	−0.395321	+	0.395321i
$610$		−	6.86483i		−	0.277949i
$611$	15.5253			0.628088
$612$	2.47735	+	2.47735i	0.100141	+	0.100141i
$613$		−	31.2708i		−	1.26301i	−0.775370	−	0.631507i	$-0.782437\pi$
$613$		−	31.2708i		−	1.26301i	0.775370	−	0.631507i	$-0.217563\pi$
$614$	1.88252			0.0759724
$615$	−5.37645	+	9.73639i	−0.216799	+	0.392609i
$616$	−3.41836			−0.137730
$617$			38.1367i			1.53533i	0.640854	+	0.767663i	$0.278580\pi$
$617$			38.1367i			1.53533i	−0.640854	+	0.767663i	$0.721420\pi$
$618$	−4.34980	−	4.34980i	−0.174974	−	0.174974i
$619$	38.0207			1.52818			0.764090	−	0.645110i	$-0.223188\pi$
$619$	38.0207			1.52818			0.764090	+	0.645110i	$0.223188\pi$
$620$		−	4.79980i		−	0.192765i
$621$	−32.7111	+	32.7111i	−1.31265	+	1.31265i
$622$	−1.98454	−	1.98454i	−0.0795729	−	0.0795729i
$623$			13.8887i			0.556439i
$624$			8.32224i			0.333156i
$625$	7.57264			0.302906
$626$	−4.00751	−	4.00751i	−0.160172	−	0.160172i
$627$	11.7743	+	11.7743i	0.470219	+	0.470219i
$628$	18.1068	+	18.1068i	0.722542	+	0.722542i
$629$	23.7110	−	23.7110i	0.945418	−	0.945418i
$630$	−0.222153	+	0.222153i	−0.00885077	+	0.00885077i
$631$	−27.5831			−1.09807			−0.549033	−	0.835801i	$-0.685004\pi$
$631$	−27.5831			−1.09807			−0.549033	+	0.835801i	$0.685004\pi$
$632$	−14.1966	+	14.1966i	−0.564711	+	0.564711i
$633$	−24.6730			−0.980664
$634$	−3.28991	+	3.28991i	−0.130659	+	0.130659i
$635$		−	9.81458i		−	0.389480i
$636$		−	7.06296i		−	0.280065i
$637$	−1.34520	+	1.34520i	−0.0532987	+	0.0532987i
$638$	−8.05068			−0.318729
$639$	−3.79535	+	3.79535i	−0.150142	+	0.150142i
$640$	−12.3359			−0.487620
$641$	−13.4247	+	13.4247i	−0.530242	+	0.530242i	−0.920644	−	0.390402i	$-0.872336\pi$
$641$	−13.4247	+	13.4247i	−0.530242	+	0.530242i	0.390402	+	0.920644i	$0.372336\pi$
$642$	−0.611090	+	0.611090i	−0.0241178	+	0.0241178i
$643$	−2.86874	−	2.86874i	−0.113132	−	0.113132i	0.648275	−	0.761407i	$-0.275491\pi$
$643$	−2.86874	−	2.86874i	−0.113132	−	0.113132i	−0.761407	+	0.648275i	$0.775491\pi$
$644$	−10.5384	−	10.5384i	−0.415271	−	0.415271i
$645$	−8.29181	−	8.29181i	−0.326490	−	0.326490i
$646$	−7.52277			−0.295979
$647$			14.8133i			0.582371i	0.956667	+	0.291186i	$0.0940497\pi$
$647$			14.8133i			0.582371i	−0.956667	+	0.291186i	$0.905950\pi$
$648$		−	11.4725i		−	0.450681i
$649$	5.88212	+	5.88212i	0.230894	+	0.230894i
$650$	2.24709	−	2.24709i	0.0881380	−	0.0881380i
$651$			3.65030i			0.143067i
$652$	−0.927347			−0.0363177
$653$	8.04444	+	8.04444i	0.314803	+	0.314803i	0.846767	−	0.531964i	$-0.178546\pi$
$653$	8.04444	+	8.04444i	0.314803	+	0.314803i	−0.531964	+	0.846767i	$0.678546\pi$
$654$		−	9.72501i		−	0.380278i
$655$	−2.33112			−0.0910844
$656$	−17.4558	+	5.03588i	−0.681535	+	0.196618i
$657$	1.81544			0.0708271
$658$		−	3.65405i		−	0.142450i
$659$	2.01551	+	2.01551i	0.0785129	+	0.0785129i	0.745273	−	0.666760i	$-0.232319\pi$
$659$	2.01551	+	2.01551i	0.0785129	+	0.0785129i	−0.666760	+	0.745273i	$0.732319\pi$
$660$	−6.28075			−0.244478
$661$		−	10.4338i		−	0.405829i	−0.979197	−	0.202914i	$-0.934959\pi$
$661$		−	10.4338i		−	0.405829i	0.979197	−	0.202914i	$-0.0650413\pi$
$662$	−2.60932	+	2.60932i	−0.101414	+	0.101414i
$663$	−6.48333	−	6.48333i	−0.251792	−	0.251792i
$664$			9.25127i			0.359019i
$665$			6.05523i			0.234812i
$666$	2.99145			0.115916
$667$	−52.4035	−	52.4035i	−2.02907	−	2.02907i
$668$	9.81967	+	9.81967i	0.379934	+	0.379934i
$669$	−12.2669	−	12.2669i	−0.474267	−	0.474267i
$670$	1.30928	−	1.30928i	0.0505817	−	0.0505817i
$671$	19.3361	−	19.3361i	0.746461	−	0.746461i
$672$	7.20467			0.277926
$673$	−29.1357	+	29.1357i	−1.12310	+	1.12310i	−0.131828	+	0.991273i	$0.542085\pi$
$673$	−29.1357	+	29.1357i	−1.12310	+	1.12310i	−0.991273	+	0.131828i	$0.957915\pi$
$674$	−7.41403			−0.285578
$675$	14.7354	−	14.7354i	0.567167	−	0.567167i
$676$		−	16.8811i		−	0.649273i
$677$			42.9464i			1.65056i	0.564722	+	0.825282i	$0.308984\pi$
$677$			42.9464i			1.65056i	−0.564722	+	0.825282i	$0.691016\pi$
$678$	3.18789	−	3.18789i	0.122430	−	0.122430i
$679$	−11.7010			−0.449043
$680$	4.23640	−	4.23640i	0.162459	−	0.162459i
$681$	−10.3358			−0.396069
$682$	−1.50616	+	1.50616i	−0.0576740	+	0.0576740i
$683$	−9.07699	+	9.07699i	−0.347321	+	0.347321i	−0.859111	−	0.511790i	$-0.828983\pi$
$683$	−9.07699	+	9.07699i	−0.347321	+	0.347321i	0.511790	+	0.859111i	$0.328983\pi$
$684$	4.25960	+	4.25960i	0.162870	+	0.162870i
$685$	12.4222	+	12.4222i	0.474626	+	0.474626i
$686$	0.316606	+	0.316606i	0.0120881	+	0.0120881i
$687$	30.7033			1.17140
$688$		−	19.1546i		−	0.730263i
$689$		−	4.84284i		−	0.184498i
$690$	4.55460	+	4.55460i	0.173391	+	0.173391i
$691$	12.2221	−	12.2221i	0.464952	−	0.464952i	−0.435322	−	0.900275i	$-0.643366\pi$
$691$	12.2221	−	12.2221i	0.464952	−	0.464952i	0.900275	+	0.435322i	$0.143366\pi$
$692$		−	3.02074i		−	0.114831i
$693$	−1.25147			−0.0475393
$694$	2.58555	+	2.58555i	0.0981462	+	0.0981462i
$695$		−	19.2625i		−	0.730669i
$696$	23.4713			0.889677
$697$	9.67559	−	17.5218i	0.366489	−	0.663687i
$698$	7.03343			0.266219
$699$			23.0516i			0.871891i
$700$	4.74725	+	4.74725i	0.179429	+	0.179429i
$701$	31.2771			1.18132			0.590660	−	0.806920i	$-0.298867\pi$
$701$	31.2771			1.18132			0.590660	+	0.806920i	$0.298867\pi$
$702$		−	4.75788i		−	0.179574i
$703$	40.7691	−	40.7691i	1.53764	−	1.53764i
$704$	−5.08992	−	5.08992i	−0.191834	−	0.191834i
$705$		−	14.1755i		−	0.533881i
$706$			10.3609i			0.389938i
$707$	12.5199			0.470860
$708$	−8.12207	−	8.12207i	−0.305246	−	0.305246i
$709$	7.47414	+	7.47414i	0.280697	+	0.280697i	0.833387	−	0.552690i	$-0.186399\pi$
$709$	7.47414	+	7.47414i	0.280697	+	0.280697i	−0.552690	+	0.833387i	$0.686399\pi$
$710$	3.07390	+	3.07390i	0.115361	+	0.115361i
$711$	−5.19740	+	5.19740i	−0.194918	+	0.194918i
$712$	16.7074	−	16.7074i	0.626137	−	0.626137i
$713$	−19.6078			−0.734320
$714$	−1.52592	+	1.52592i	−0.0571060	+	0.0571060i
$715$	−4.30650			−0.161054
$716$	7.76228	−	7.76228i	0.290090	−	0.290090i
$717$			37.6539i			1.40621i
$718$		−	9.35227i		−	0.349024i
$719$	−9.01589	+	9.01589i	−0.336236	+	0.336236i	−0.854949	−	0.518713i	$-0.826411\pi$
$719$	−9.01589	+	9.01589i	−0.336236	+	0.336236i	0.518713	+	0.854949i	$0.326411\pi$
$720$	−1.99086			−0.0741950
$721$	6.30092	−	6.30092i	0.234659	−	0.234659i
$722$	−4.42757			−0.164777
$723$	−7.66831	+	7.66831i	−0.285188	+	0.285188i
$724$	−13.5052	+	13.5052i	−0.501918	+	0.501918i
$725$	23.6063	+	23.6063i	0.876716	+	0.876716i
$726$	−3.39873	−	3.39873i	−0.126139	−	0.126139i
$727$	−10.0972	−	10.0972i	−0.374484	−	0.374484i	0.494623	−	0.869107i	$-0.335306\pi$
$727$	−10.0972	−	10.0972i	−0.374484	−	0.374484i	−0.869107	+	0.494623i	$0.835306\pi$
$728$	3.23641			0.119949
$729$		−	30.0364i		−	1.11246i
$730$		−	1.47035i		−	0.0544200i
$731$	14.9221	+	14.9221i	0.551915	+	0.551915i
$732$	−26.6994	+	26.6994i	−0.986837	+	0.986837i
$733$		−	48.3708i		−	1.78662i	−0.449444	−	0.893308i	$-0.648378\pi$
$733$		−	48.3708i		−	1.78662i	0.449444	−	0.893308i	$-0.351622\pi$
$734$	−14.0200			−0.517489
$735$	1.22824	+	1.22824i	0.0453044	+	0.0453044i
$736$			38.7004i			1.42652i
$737$	7.37563			0.271685
$738$	1.71566	−	0.494954i	0.0631542	−	0.0182195i
$739$	20.9855			0.771963			0.385982	−	0.922506i	$-0.373863\pi$
$739$	20.9855			0.771963			0.385982	+	0.922506i	$0.373863\pi$
$740$			21.7475i			0.799453i
$741$	−11.1476	−	11.1476i	−0.409516	−	0.409516i
$742$	−1.13981			−0.0418438
$743$		−	3.87455i		−	0.142144i	−0.997471	−	0.0710718i	$-0.977358\pi$
$743$		−	3.87455i		−	0.142144i	0.997471	−	0.0710718i	$-0.0226419\pi$
$744$	4.39113	−	4.39113i	0.160987	−	0.160987i
$745$	−13.9092	−	13.9092i	−0.509594	−	0.509594i
$746$		−	10.4104i		−	0.381150i
$747$			3.38690i			0.123920i
$748$	11.3030			0.413278
$749$	−0.885197	−	0.885197i	−0.0323444	−	0.0323444i
$750$	−4.80144	−	4.80144i	−0.175324	−	0.175324i
$751$	7.43651	+	7.43651i	0.271362	+	0.271362i	0.829648	−	0.558286i	$-0.188541\pi$
$751$	7.43651	+	7.43651i	0.271362	+	0.271362i	−0.558286	+	0.829648i	$0.688541\pi$
$752$	16.3732	−	16.3732i	0.597069	−	0.597069i
$753$	−13.8423	+	13.8423i	−0.504441	+	0.504441i
$754$	7.62216			0.277583
$755$	9.97751	−	9.97751i	0.363119	−	0.363119i
$756$	10.0516			0.365573
$757$	20.3909	−	20.3909i	0.741119	−	0.741119i	−0.231674	−	0.972793i	$-0.574420\pi$
$757$	20.3909	−	20.3909i	0.741119	−	0.741119i	0.972793	+	0.231674i	$0.0744204\pi$
$758$		−	5.71427i		−	0.207552i
$759$			25.6577i			0.931317i
$760$	7.28415	−	7.28415i	0.264224	−	0.264224i
$761$	−27.3033			−0.989743			−0.494872	−	0.868966i	$-0.664785\pi$
$761$	−27.3033			−0.989743			−0.494872	+	0.868966i	$0.664785\pi$
$762$	4.25259	−	4.25259i	0.154055	−	0.154055i
$763$	14.0872			0.509992
$764$	−7.70754	+	7.70754i	−0.278849	+	0.278849i
$765$	1.55095	−	1.55095i	0.0560748	−	0.0560748i
$766$	7.15469	+	7.15469i	0.258510	+	0.258510i
$767$	−5.56904	−	5.56904i	−0.201086	−	0.201086i
$768$	2.46611	+	2.46611i	0.0889880	+	0.0889880i
$769$	−25.3983			−0.915884			−0.457942	−	0.888982i	$-0.651413\pi$
$769$	−25.3983			−0.915884			−0.457942	+	0.888982i	$0.651413\pi$
$770$			1.01358i			0.0365268i
$771$		−	28.0997i		−	1.01199i
$772$	3.81537	+	3.81537i	0.137318	+	0.137318i
$773$	9.78592	−	9.78592i	0.351975	−	0.351975i	−0.508869	−	0.860844i	$-0.669936\pi$
$773$	9.78592	−	9.78592i	0.351975	−	0.351975i	0.860844	+	0.508869i	$0.169936\pi$
$774$			1.88262i			0.0676695i
$775$	8.83279			0.317283
$776$	14.0757	+	14.0757i	0.505290	+	0.505290i
$777$		−	16.5392i		−	0.593340i
$778$	8.53379			0.305951
$779$	16.6364	−	30.1274i	0.596060	−	1.07943i
$780$	5.94644			0.212917
$781$			17.3164i			0.619629i
$782$	−8.19657	−	8.19657i	−0.293109	−	0.293109i
$783$	49.9828			1.78624
$784$			2.83732i			0.101333i
$785$	11.3358	−	11.3358i	0.404594	−	0.404594i
$786$	−1.01006	−	1.01006i	−0.0360276	−	0.0360276i
$787$			29.2462i			1.04251i	0.853400	+	0.521257i	$0.174537\pi$
$787$			29.2462i			1.04251i	−0.853400	+	0.521257i	$0.825463\pi$
$788$			14.7154i			0.524214i
$789$	−2.33454			−0.0831120
$790$	4.20944	+	4.20944i	0.149765	+	0.149765i
$791$	4.61784	+	4.61784i	0.164191	+	0.164191i
$792$	1.50545	+	1.50545i	0.0534940	+	0.0534940i
$793$	−18.3069	+	18.3069i	−0.650096	+	0.650096i
$794$	−1.59599	+	1.59599i	−0.0566396	+	0.0566396i
$795$	−4.42179			−0.156825
$796$	16.9863	−	16.9863i	0.602064	−	0.602064i
$797$	7.77678			0.275468			0.137734	−	0.990469i	$-0.456018\pi$
$797$	7.77678			0.275468			0.137734	+	0.990469i	$0.456018\pi$
$798$	−2.62369	+	2.62369i	−0.0928776	+	0.0928776i
$799$			25.5106i			0.902501i
$800$		−	17.4334i		−	0.616365i
$801$	6.11661	−	6.11661i	0.216120	−	0.216120i
$802$	−3.09546			−0.109305
$803$	4.14150	−	4.14150i	0.146151	−	0.146151i
$804$	−10.1843			−0.359173
$805$	−6.59759	+	6.59759i	−0.232534	+	0.232534i
$806$	1.42600	−	1.42600i	0.0502285	−	0.0502285i
$807$	8.16918	+	8.16918i	0.287569	+	0.287569i
$808$	−15.0608	−	15.0608i	−0.529839	−	0.529839i
$809$	−26.8886	−	26.8886i	−0.945353	−	0.945353i	0.0532289	−	0.998582i	$-0.483049\pi$
$809$	−26.8886	−	26.8886i	−0.945353	−	0.945353i	−0.998582	+	0.0532289i	$0.983049\pi$
$810$	−3.40170			−0.119523
$811$			13.7461i			0.482689i	0.970439	+	0.241345i	$0.0775884\pi$
$811$			13.7461i			0.482689i	−0.970439	+	0.241345i	$0.922412\pi$
$812$			16.1028i			0.565096i
$813$	−21.6530	−	21.6530i	−0.759403	−	0.759403i
$814$	6.82429	−	6.82429i	0.239191	−	0.239191i
$815$			0.580568i			0.0203364i
$816$	−13.6748			−0.478713
$817$	25.6574	+	25.6574i	0.897639	+	0.897639i
$818$			9.26407i			0.323910i
$819$	1.18486			0.0414022
$820$	3.59825	+	12.4726i	0.125656	+	0.435562i
$821$	6.22802			0.217359			0.108680	−	0.994077i	$-0.465338\pi$
$821$	6.22802			0.217359			0.108680	+	0.994077i	$0.465338\pi$
$822$			10.7649i			0.375468i
$823$	−5.14856	−	5.14856i	−0.179468	−	0.179468i	0.611656	−	0.791124i	$-0.290504\pi$
$823$	−5.14856	−	5.14856i	−0.179468	−	0.179468i	−0.791124	+	0.611656i	$0.790504\pi$
$824$	−15.1594			−0.528103
$825$		−	11.5581i		−	0.402401i
$826$	−1.31073	+	1.31073i	−0.0456061	+	0.0456061i
$827$	−0.456773	−	0.456773i	−0.0158836	−	0.0158836i	0.699120	−	0.715004i	$-0.253575\pi$
$827$	−0.456773	−	0.456773i	−0.0158836	−	0.0158836i	−0.715004	+	0.699120i	$0.753575\pi$
$828$			9.28225i			0.322581i
$829$			47.2498i			1.64105i	0.571607	+	0.820527i	$0.306320\pi$
$829$			47.2498i			1.64105i	−0.571607	+	0.820527i	$0.693680\pi$
$830$	2.74309			0.0952142
$831$	22.4962	+	22.4962i	0.780384	+	0.780384i
$832$	4.81900	+	4.81900i	0.167069	+	0.167069i
$833$	−2.21038	−	2.21038i	−0.0765850	−	0.0765850i
$834$	8.34632	−	8.34632i	0.289009	−	0.289009i
$835$	6.14763	−	6.14763i	0.212748	−	0.212748i
$836$	19.4346			0.672159
$837$	9.35106	−	9.35106i	0.323220	−	0.323220i
$838$	5.46757			0.188874
$839$	−13.0253	+	13.0253i	−0.449684	+	0.449684i	−0.895250	−	0.445565i	$-0.853003\pi$
$839$	−13.0253	+	13.0253i	−0.449684	+	0.449684i	0.445565	+	0.895250i	$0.353003\pi$
$840$		−	2.95503i		−	0.101958i
$841$			51.0730i			1.76114i
$842$	5.58390	−	5.58390i	0.192434	−	0.192434i
$843$	0.294058			0.0101279
$844$	−20.3626	+	20.3626i	−0.700910	+	0.700910i
$845$	−10.5685			−0.363566
$846$	−1.60925	+	1.60925i	−0.0553271	+	0.0553271i
$847$	4.92324	−	4.92324i	0.169165	−	0.169165i
$848$	−5.10731	−	5.10731i	−0.175386	−	0.175386i
$849$	−25.4792	−	25.4792i	−0.874445	−	0.874445i
$850$	3.69232	+	3.69232i	0.126646	+	0.126646i
$851$	88.8414			3.04544
$852$		−	23.9106i		−	0.819162i
$853$			23.0542i			0.789361i	0.918818	+	0.394681i	$0.129145\pi$
$853$			23.0542i			0.789361i	−0.918818	+	0.394681i	$0.870855\pi$
$854$	4.30871	+	4.30871i	0.147441	+	0.147441i
$855$	2.66674	−	2.66674i	0.0912004	−	0.0912004i
$856$			2.12970i			0.0727916i
$857$	−29.7212			−1.01526			−0.507628	−	0.861576i	$-0.669478\pi$
$857$	−29.7212			−1.01526			−0.507628	+	0.861576i	$0.669478\pi$
$858$	−1.86598	−	1.86598i	−0.0637034	−	0.0637034i
$859$			8.11334i			0.276823i	0.990375	+	0.138412i	$0.0441997\pi$
$859$			8.11334i			0.276823i	−0.990375	+	0.138412i	$0.955800\pi$
$860$	−13.6864			−0.466704
$861$	−2.73651	−	9.48556i	−0.0932601	−	0.323267i
$862$	−10.7915			−0.367559
$863$		−	35.5761i		−	1.21103i	−0.795836	−	0.605513i	$-0.792968\pi$
$863$		−	35.5761i		−	1.21103i	0.795836	−	0.605513i	$-0.207032\pi$
$864$	−18.4564	−	18.4564i	−0.627898	−	0.627898i
$865$	−1.89114			−0.0643008
$866$			11.2567i			0.382517i
$867$	−7.88067	+	7.88067i	−0.267642	+	0.267642i
$868$	3.01259	+	3.01259i	0.102254	+	0.102254i
$869$			23.7133i			0.804419i
$870$		−	6.95947i		−	0.235948i
$871$	−6.98305			−0.236612
$872$	−16.9462	−	16.9462i	−0.573872	−	0.573872i
$873$	5.15315	+	5.15315i	0.174408	+	0.174408i
$874$	−14.0933	−	14.0933i	−0.476714	−	0.476714i
$875$	6.95515	−	6.95515i	0.235127	−	0.235127i
$876$	−5.71861	+	5.71861i	−0.193214	+	0.193214i
$877$	−11.7972			−0.398364			−0.199182	−	0.979963i	$-0.563828\pi$
$877$	−11.7972			−0.398364			−0.199182	+	0.979963i	$0.563828\pi$
$878$	−10.5292	+	10.5292i	−0.355344	+	0.355344i
$879$	23.5579			0.794589
$880$	−4.54168	+	4.54168i	−0.153100	+	0.153100i
$881$		−	36.0172i		−	1.21345i	−0.794911	−	0.606726i	$-0.792483\pi$
$881$		−	36.0172i		−	1.21345i	0.794911	−	0.606726i	$-0.207517\pi$
$882$		−	0.278868i		−	0.00938997i
$883$	40.7261	−	40.7261i	1.37054	−	1.37054i	0.510906	−	0.859636i	$-0.329310\pi$
$883$	40.7261	−	40.7261i	1.37054	−	1.37054i	0.859636	−	0.510906i	$-0.170690\pi$
$884$	−10.7014			−0.359926
$885$	−5.08485	+	5.08485i	−0.170925	+	0.170925i
$886$	9.89297			0.332361
$887$	13.7832	−	13.7832i	0.462793	−	0.462793i	−0.436777	−	0.899570i	$-0.643880\pi$
$887$	13.7832	−	13.7832i	0.462793	−	0.462793i	0.899570	+	0.436777i	$0.143880\pi$
$888$	−19.8958	+	19.8958i	−0.667661	+	0.667661i
$889$	6.16011	+	6.16011i	0.206604	+	0.206604i
$890$	−4.95391	−	4.95391i	−0.166056	−	0.166056i
$891$	−9.58150	−	9.58150i	−0.320992	−	0.320992i
$892$	−20.2478			−0.677946
$893$			43.8634i			1.46783i
$894$		−	12.0535i		−	0.403130i
$895$	−4.85960	−	4.85960i	−0.162439	−	0.162439i
$896$	7.74263	−	7.74263i	0.258663	−	0.258663i
$897$		−	24.2920i		−	0.811088i
$898$	0.127158			0.00424332
$899$	14.9805	+	14.9805i	0.499627	+	0.499627i
$900$		−	4.18139i		−	0.139380i
$901$	7.95756			0.265105
$902$	2.78475	−	5.04299i	0.0927219	−	0.167913i
$903$	10.4087			0.346380
$904$		−	11.1101i		−	0.369515i
$905$	8.45499	+	8.45499i	0.281053	+	0.281053i
$906$	8.64637			0.287256
$907$		−	34.3009i		−	1.13894i	−0.822011	−	0.569472i	$-0.807148\pi$
$907$		−	34.3009i		−	1.13894i	0.822011	−	0.569472i	$-0.192852\pi$
$908$	−8.53012	+	8.53012i	−0.283082	+	0.283082i
$909$	−5.51380	−	5.51380i	−0.182881	−	0.182881i
$910$		−	0.959629i		−	0.0318114i
$911$			30.4444i			1.00867i	0.863509	+	0.504334i	$0.168262\pi$
$911$			30.4444i			1.00867i	−0.863509	+	0.504334i	$0.831738\pi$
$912$	−23.5127			−0.778582
$913$	7.72643	+	7.72643i	0.255707	+	0.255707i
$914$	−11.4492	−	11.4492i	−0.378706	−	0.378706i
$915$	16.7152	+	16.7152i	0.552588	+	0.552588i
$916$	25.3394	−	25.3394i	0.837236	−	0.837236i
$917$	1.46313	−	1.46313i	0.0483167	−	0.0483167i
$918$	7.81795			0.258031
$919$	1.54570	−	1.54570i	0.0509880	−	0.0509880i	−0.681153	−	0.732141i	$-0.738521\pi$
$919$	1.54570	−	1.54570i	0.0509880	−	0.0509880i	0.732141	+	0.681153i	$0.238521\pi$
$920$	15.8732			0.523322
$921$	−4.58376	+	4.58376i	−0.151040	+	0.151040i
$922$			15.6173i			0.514328i
$923$		−	16.3947i		−	0.539638i
$924$	3.94210	−	3.94210i	0.129686	−	0.129686i
$925$	−40.0206			−1.31587
$926$	−6.22249	+	6.22249i	−0.204484	+	0.204484i
$927$	−5.54988			−0.182282
$928$	29.5673	−	29.5673i	0.970593	−	0.970593i
$929$	24.4947	−	24.4947i	0.803645	−	0.803645i	−0.180018	−	0.983663i	$-0.557616\pi$
$929$	24.4947	−	24.4947i	0.803645	−	0.803645i	0.983663	+	0.180018i	$0.0576156\pi$
$930$	−1.30201	−	1.30201i	−0.0426947	−	0.0426947i
$931$	−3.80056	−	3.80056i	−0.124558	−	0.124558i
$932$	19.0244	+	19.0244i	0.623167	+	0.623167i
$933$	9.66434			0.316396
$934$		−	5.38348i		−	0.176153i
$935$		−	7.07627i		−	0.231419i
$936$	−1.42532	−	1.42532i	−0.0465881	−	0.0465881i
$937$	−5.18689	+	5.18689i	−0.169448	+	0.169448i	−0.786737	−	0.617288i	$-0.788231\pi$
$937$	−5.18689	+	5.18689i	−0.169448	+	0.169448i	0.617288	+	0.786737i	$0.288231\pi$
$938$			1.64353i			0.0536632i
$939$	19.5158			0.636874
$940$	−11.6990	−	11.6990i	−0.381580	−	0.381580i
$941$		−	9.70556i		−	0.316392i	−0.987408	−	0.158196i	$-0.949432\pi$
$941$		−	9.70556i		−	0.316392i	0.987408	−	0.158196i	$-0.0505678\pi$
$942$	9.82349			0.320066
$943$	50.9523	−	14.6994i	1.65924	−	0.478677i
$944$	−11.7463			−0.382310
$945$		−	6.29283i		−	0.204706i
$946$	4.29477	+	4.29477i	0.139635	+	0.139635i
$947$	−48.2220			−1.56701			−0.783503	−	0.621388i	$-0.786569\pi$
$947$	−48.2220			−1.56701			−0.783503	+	0.621388i	$0.786569\pi$
$948$		−	32.7435i		−	1.06346i
$949$	−3.92106	+	3.92106i	−0.127283	+	0.127283i
$950$	6.34865	+	6.34865i	0.205977	+	0.205977i
$951$		−	16.0212i		−	0.519524i
$952$			5.31795i			0.172356i
$953$	6.64250			0.215172			0.107586	−	0.994196i	$-0.465688\pi$
$953$	6.64250			0.215172			0.107586	+	0.994196i	$0.465688\pi$
$954$	0.501975	+	0.501975i	0.0162520	+	0.0162520i
$955$	4.82533	+	4.82533i	0.156144	+	0.156144i
$956$	31.0757	+	31.0757i	1.00506	+	1.00506i
$957$	19.6026	−	19.6026i	0.633663	−	0.633663i
$958$	−0.503948	+	0.503948i	−0.0162818	+	0.0162818i
$959$	−15.5935			−0.503541
$960$	4.40002	−	4.40002i	0.142010	−	0.142010i
$961$	−25.3947			−0.819185
$962$	−6.46106	+	6.46106i	−0.208313	+	0.208313i
$963$			0.779685i			0.0251250i
$964$			12.6573i			0.407664i
$965$	2.38863	−	2.38863i	0.0768926	−	0.0768926i
$966$	−5.71738			−0.183954
$967$	1.10945	−	1.10945i	0.0356776	−	0.0356776i	−0.689043	−	0.724721i	$-0.741969\pi$
$967$	1.10945	−	1.10945i	0.0356776	−	0.0356776i	0.724721	+	0.689043i	$0.241969\pi$
$968$	−11.8448			−0.380708
$969$	18.3172	−	18.3172i	0.588434	−	0.588434i
$970$	4.17360	−	4.17360i	0.134006	−	0.134006i
$971$	−23.2880	−	23.2880i	−0.747348	−	0.747348i	0.226632	−	0.973980i	$-0.427228\pi$
$971$	−23.2880	−	23.2880i	−0.747348	−	0.747348i	−0.973980	+	0.226632i	$0.927228\pi$
$972$	−8.09245	−	8.09245i	−0.259566	−	0.259566i
$973$	12.0901	+	12.0901i	0.387591	+	0.387591i
$974$	−8.53464			−0.273467
$975$			10.9429i			0.350453i
$976$			38.6132i			1.23598i
$977$	14.7617	+	14.7617i	0.472268	+	0.472268i	0.902648	−	0.430380i	$-0.141620\pi$
$977$	14.7617	+	14.7617i	0.472268	+	0.472268i	−0.430380	+	0.902648i	$0.641620\pi$
$978$	−0.251556	+	0.251556i	−0.00804388	+	0.00804388i
$979$		−	27.9072i		−	0.891919i
$980$	2.02733			0.0647608
$981$	−6.20404	−	6.20404i	−0.198080	−	0.198080i
$982$		−	8.27068i		−	0.263928i
$983$	10.4649			0.333779			0.166890	−	0.985976i	$-0.446628\pi$
$983$	10.4649			0.333779			0.166890	+	0.985976i	$0.446628\pi$
$984$	−8.11877	+	14.7026i	−0.258817	+	0.468700i
$985$	9.21261			0.293538
$986$			12.5244i			0.398859i
$987$	8.89725	+	8.89725i	0.283203	+	0.283203i
$988$	−18.4001			−0.585386
$989$			55.9110i			1.77787i
$990$	0.446382	−	0.446382i	0.0141870	−	0.0141870i
$991$	34.1271	+	34.1271i	1.08408	+	1.08408i	0.996124	+	0.0879582i	$0.0280342\pi$
$991$	34.1271	+	34.1271i	1.08408	+	1.08408i	0.0879582	+	0.996124i	$0.471966\pi$
$992$		−	11.0632i		−	0.351257i
$993$		−	12.7069i		−	0.403240i
$994$	−3.85866			−0.122389
$995$	−10.6343	−	10.6343i	−0.337131	−	0.337131i
$996$	−10.6687	−	10.6687i	−0.338050	−	0.338050i
$997$	4.53772	+	4.53772i	0.143711	+	0.143711i	0.775302	−	0.631591i	$-0.217598\pi$
$997$	4.53772	+	4.53772i	0.143711	+	0.143711i	−0.631591	+	0.775302i	$0.717598\pi$
$998$	3.71085	−	3.71085i	0.117465	−	0.117465i
$999$	−42.3688	+	42.3688i	−1.34049	+	1.34049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.f.a.50.9	✓	40
41.32	even	4	inner	287.2.f.a.155.12	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.f.a.50.9	✓	40	1.1	even	1	trivial
287.2.f.a.155.12	yes	40	41.32	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.447748i q^{2} +(1.09022 + 1.09022i) q^{3} +1.79952 q^{4} -1.12660i q^{5} +(0.488146 - 0.488146i) q^{6} +(0.707107 + 0.707107i) q^{7} -1.70123i q^{8} -0.622822i q^{9} +O(q^{10})\)	\(q-0.447748i q^{2} +(1.09022 + 1.09022i) q^{3} +1.79952 q^{4} -1.12660i q^{5} +(0.488146 - 0.488146i) q^{6} +(0.707107 + 0.707107i) q^{7} -1.70123i q^{8} -0.622822i q^{9} -0.504431 q^{10} +(-1.42082 - 1.42082i) q^{11} +(1.96188 + 1.96188i) q^{12} +(1.34520 + 1.34520i) q^{13} +(0.316606 - 0.316606i) q^{14} +(1.22824 - 1.22824i) q^{15} +2.83732 q^{16} +(-2.21038 + 2.21038i) q^{17} -0.278868 q^{18} +(-3.80056 + 3.80056i) q^{19} -2.02733i q^{20} +1.54181i q^{21} +(-0.636172 + 0.636172i) q^{22} -8.28194 q^{23} +(1.85472 - 1.85472i) q^{24} +3.73078 q^{25} +(0.602310 - 0.602310i) q^{26} +(3.94969 - 3.94969i) q^{27} +(1.27245 + 1.27245i) q^{28} +(6.32744 + 6.32744i) q^{29} +(-0.549943 - 0.549943i) q^{30} +2.36754 q^{31} -4.67286i q^{32} -3.09803i q^{33} +(0.989692 + 0.989692i) q^{34} +(0.796624 - 0.796624i) q^{35} -1.12078i q^{36} -10.7271 q^{37} +(1.70169 + 1.70169i) q^{38} +2.93313i q^{39} -1.91660 q^{40} +(-6.15222 + 1.77487i) q^{41} +0.690343 q^{42} -6.75096i q^{43} +(-2.55680 - 2.55680i) q^{44} -0.701669 q^{45} +3.70823i q^{46} +(5.77065 - 5.77065i) q^{47} +(3.09331 + 3.09331i) q^{48} +1.00000i q^{49} -1.67045i q^{50} -4.81961 q^{51} +(2.42071 + 2.42071i) q^{52} +(-1.80005 - 1.80005i) q^{53} +(-1.76847 - 1.76847i) q^{54} +(-1.60069 + 1.60069i) q^{55} +(1.20295 - 1.20295i) q^{56} -8.28693 q^{57} +(2.83310 - 2.83310i) q^{58} -4.13994 q^{59} +(2.21025 - 2.21025i) q^{60} +13.6091i q^{61} -1.06006i q^{62} +(0.440402 - 0.440402i) q^{63} +3.58237 q^{64} +(1.51549 - 1.51549i) q^{65} -1.38714 q^{66} +(-2.59555 + 2.59555i) q^{67} +(-3.97762 + 3.97762i) q^{68} +(-9.02917 - 9.02917i) q^{69} +(-0.356687 - 0.356687i) q^{70} +(-6.09378 - 6.09378i) q^{71} -1.05956 q^{72} +2.91486i q^{73} +4.80305i q^{74} +(4.06739 + 4.06739i) q^{75} +(-6.83919 + 6.83919i) q^{76} -2.00935i q^{77} +1.31331 q^{78} +(-8.34492 - 8.34492i) q^{79} -3.19651i q^{80} +6.74362 q^{81} +(0.794695 + 2.75465i) q^{82} -5.43799 q^{83} +2.77452i q^{84} +(2.49020 + 2.49020i) q^{85} -3.02273 q^{86} +13.7967i q^{87} +(-2.41715 + 2.41715i) q^{88} +(9.82079 + 9.82079i) q^{89} +0.314171i q^{90} +1.90240i q^{91} -14.9035 q^{92} +(2.58115 + 2.58115i) q^{93} +(-2.58380 - 2.58380i) q^{94} +(4.28170 + 4.28170i) q^{95} +(5.09447 - 5.09447i) q^{96} +(-8.27386 + 8.27386i) q^{97} +0.447748 q^{98} +(-0.884921 + 0.884921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6}+O(q^{10}) \) 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6	\( 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6} - 32 q^{10} - 8 q^{11} + 16 q^{12} + 16 q^{13} - 8 q^{15} + 28 q^{16} + 20 q^{17} - 12 q^{18} - 20 q^{19} + 4 q^{22} + 16 q^{23} - 12 q^{24} - 40 q^{25} - 20 q^{26} - 20 q^{27} - 12 q^{29} + 4 q^{30} + 32 q^{34} + 4 q^{35} - 16 q^{38} + 64 q^{40} + 16 q^{41} + 32 q^{42} + 8 q^{44} + 72 q^{45} - 24 q^{47} - 40 q^{48} - 64 q^{51} - 96 q^{52} + 8 q^{53} + 52 q^{54} - 8 q^{55} - 88 q^{57} - 36 q^{58} + 48 q^{59} + 52 q^{60} - 8 q^{63} - 84 q^{64} - 44 q^{65} + 56 q^{66} + 40 q^{67} - 60 q^{68} + 28 q^{69} - 8 q^{70} + 20 q^{71} + 80 q^{72} - 20 q^{75} - 4 q^{76} + 12 q^{78} - 12 q^{79} + 16 q^{81} - 52 q^{82} + 40 q^{83} + 8 q^{85} + 80 q^{86} + 96 q^{88} - 8 q^{89} - 20 q^{92} - 64 q^{93} + 52 q^{94} + 68 q^{96} - 60 q^{97} - 4 q^{98} - 36 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6 - 32 * q^10 - 8 * q^11 + 16 * q^12 + 16 * q^13 - 8 * q^15 + 28 * q^16 + 20 * q^17 - 12 * q^18 - 20 * q^19 + 4 * q^22 + 16 * q^23 - 12 * q^24 - 40 * q^25 - 20 * q^26 - 20 * q^27 - 12 * q^29 + 4 * q^30 + 32 * q^34 + 4 * q^35 - 16 * q^38 + 64 * q^40 + 16 * q^41 + 32 * q^42 + 8 * q^44 + 72 * q^45 - 24 * q^47 - 40 * q^48 - 64 * q^51 - 96 * q^52 + 8 * q^53 + 52 * q^54 - 8 * q^55 - 88 * q^57 - 36 * q^58 + 48 * q^59 + 52 * q^60 - 8 * q^63 - 84 * q^64 - 44 * q^65 + 56 * q^66 + 40 * q^67 - 60 * q^68 + 28 * q^69 - 8 * q^70 + 20 * q^71 + 80 * q^72 - 20 * q^75 - 4 * q^76 + 12 * q^78 - 12 * q^79 + 16 * q^81 - 52 * q^82 + 40 * q^83 + 8 * q^85 + 80 * q^86 + 96 * q^88 - 8 * q^89 - 20 * q^92 - 64 * q^93 + 52 * q^94 + 68 * q^96 - 60 * q^97 - 4 * q^98 - 36 * q^99

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