LMFDB - Embedded newform 52.2.l.b.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [52,2,Mod(7,52)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(52, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 11]))

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

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

chi := DirichletCharacter("52.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 52 = 2^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	52.l (of order $12$, degree $4$, 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:	$0.415222090511$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.102930383934669717504.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 5 x^{14} - 2 x^{13} + 5 x^{12} - 8 x^{11} - 12 x^{10} + 32 x^{9} - 36 x^{8} + \cdots + 256 $ x^16 - 4x^15 + 5x^14 - 2x^13 + 5x^12 - 8x^11 - 12x^10 + 32x^9 - 36x^8 + 64x^7 - 48x^6 - 64x^5 + 80x^4 - 64x^3 + 320x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.3
Root			$1.17605 + 0.785427i$ of defining polynomial
Character	$\chi$	$=$	52.11
Dual form			52.2.l.b.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0921725 + 1.41121i) q^{2} +(-1.81380 + 1.04720i) q^{3} +(-1.98301 + 0.260149i) q^{4} +(0.894007 + 0.894007i) q^{5} +(-1.64500 - 2.46313i) q^{6} +(4.37156 - 1.17136i) q^{7} +(-0.549903 - 2.77446i) q^{8} +(0.693255 - 1.20075i) q^{9} +O(q^{10})$	\(q+(0.0921725 + 1.41121i) q^{2} +(-1.81380 + 1.04720i) q^{3} +(-1.98301 + 0.260149i) q^{4} +(0.894007 + 0.894007i) q^{5} +(-1.64500 - 2.46313i) q^{6} +(4.37156 - 1.17136i) q^{7} +(-0.549903 - 2.77446i) q^{8} +(0.693255 - 1.20075i) q^{9} +(-1.17923 + 1.34403i) q^{10} +(-0.404752 + 1.51056i) q^{11} +(3.32436 - 2.54846i) q^{12} +(-2.03880 - 2.97377i) q^{13} +(2.05596 + 6.06121i) q^{14} +(-2.55776 - 0.685349i) q^{15} +(3.86465 - 1.03176i) q^{16} +(-0.0484649 - 0.0279812i) q^{17} +(1.75841 + 0.867649i) q^{18} +(-0.576896 - 2.15300i) q^{19} +(-2.00540 - 1.54025i) q^{20} +(-6.70250 + 6.70250i) q^{21} +(-2.16901 - 0.431957i) q^{22} +(-0.528908 - 0.916096i) q^{23} +(3.90283 + 4.45646i) q^{24} -3.40150i q^{25} +(4.00868 - 3.15126i) q^{26} -3.37929i q^{27} +(-8.36411 + 3.46006i) q^{28} +(3.67452 + 6.36446i) q^{29} +(0.731414 - 3.67269i) q^{30} +(-4.52800 + 4.52800i) q^{31} +(1.81223 + 5.35871i) q^{32} +(-0.847713 - 3.16371i) q^{33} +(0.0350202 - 0.0709732i) q^{34} +(4.95540 + 2.86100i) q^{35} +(-1.06236 + 2.56145i) q^{36} +(-1.86603 - 0.500000i) q^{37} +(2.98516 - 1.01257i) q^{38} +(6.81211 + 3.25881i) q^{39} +(1.98877 - 2.97200i) q^{40} +(0.401924 - 1.50000i) q^{41} +(-10.0764 - 8.84083i) q^{42} +(1.04025 - 1.80177i) q^{43} +(0.409658 - 3.10074i) q^{44} +(1.69325 - 0.453706i) q^{45} +(1.24405 - 0.830838i) q^{46} +(-5.38281 - 5.38281i) q^{47} +(-5.92925 + 5.91846i) q^{48} +(11.6763 - 6.74130i) q^{49} +(4.80023 - 0.313525i) q^{50} +0.117208 q^{51} +(4.81657 + 5.36662i) q^{52} -4.40150 q^{53} +(4.76888 - 0.311478i) q^{54} +(-1.71230 + 0.988596i) q^{55} +(-5.65381 - 11.4846i) q^{56} +(3.30100 + 3.30100i) q^{57} +(-8.64288 + 5.77214i) q^{58} +(-8.67757 + 2.32515i) q^{59} +(5.25034 + 0.693654i) q^{60} +(1.00750 - 1.74504i) q^{61} +(-6.80730 - 5.97259i) q^{62} +(1.62410 - 6.06121i) q^{63} +(-7.39521 + 3.05136i) q^{64} +(0.835873 - 4.48127i) q^{65} +(4.38651 - 1.48790i) q^{66} +(8.86360 + 2.37500i) q^{67} +(0.103386 + 0.0428789i) q^{68} +(1.91867 + 1.10774i) q^{69} +(-3.58071 + 7.25680i) q^{70} +(1.76582 + 6.59011i) q^{71} +(-3.71266 - 1.26311i) q^{72} +(-5.45504 + 5.45504i) q^{73} +(0.533607 - 2.67943i) q^{74} +(3.56205 + 6.16966i) q^{75} +(1.70409 + 4.11935i) q^{76} +7.07759i q^{77} +(-3.97096 + 9.91366i) q^{78} +8.87422i q^{79} +(4.37741 + 2.53262i) q^{80} +(5.61856 + 9.73163i) q^{81} +(2.15386 + 0.428939i) q^{82} +(6.96160 - 6.96160i) q^{83} +(11.5475 - 15.0348i) q^{84} +(-0.0183126 - 0.0683434i) q^{85} +(2.63855 + 1.30194i) q^{86} +(-13.3297 - 7.69592i) q^{87} +(4.41355 + 0.292308i) q^{88} +(-15.3098 - 4.10226i) q^{89} +(0.796345 + 2.34771i) q^{90} +(-12.3961 - 10.6119i) q^{91} +(1.28715 + 1.67903i) q^{92} +(3.47118 - 12.9546i) q^{93} +(7.10010 - 8.09240i) q^{94} +(1.40905 - 2.44055i) q^{95} +(-8.89868 - 7.82188i) q^{96} +(-0.440720 + 0.118091i) q^{97} +(10.5896 + 15.8563i) q^{98} +(1.53321 + 1.53321i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 6 q^{4} - 12 q^{5} - 14 q^{6} + 10 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 - 6 * q^4 - 12 * q^5 - 14 * q^6 + 10 * q^8 + 4 * q^9	$ 16 q - 2 q^{2} - 6 q^{4} - 12 q^{5} - 14 q^{6} + 10 q^{8} + 4 q^{9} - 12 q^{13} + 8 q^{14} - 2 q^{16} + 12 q^{17} - 6 q^{18} + 2 q^{20} - 28 q^{21} + 10 q^{24} + 16 q^{26} + 12 q^{28} - 8 q^{29} + 42 q^{30} + 28 q^{32} - 20 q^{33} + 14 q^{34} - 6 q^{36} - 16 q^{37} - 40 q^{40} + 48 q^{41} - 28 q^{42} - 8 q^{44} + 20 q^{45} - 46 q^{46} - 10 q^{48} + 60 q^{49} + 10 q^{50} - 32 q^{52} - 32 q^{53} - 16 q^{54} - 60 q^{56} + 12 q^{57} - 48 q^{58} - 24 q^{60} + 4 q^{61} - 18 q^{62} - 8 q^{65} + 56 q^{66} + 16 q^{68} - 12 q^{69} + 28 q^{70} + 56 q^{72} + 20 q^{73} + 4 q^{74} + 22 q^{76} + 68 q^{78} + 44 q^{80} + 48 q^{81} + 84 q^{84} + 20 q^{85} + 16 q^{86} + 36 q^{88} - 52 q^{89} - 12 q^{92} - 92 q^{93} - 38 q^{94} - 72 q^{96} - 28 q^{97} - 2 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 6 * q^4 - 12 * q^5 - 14 * q^6 + 10 * q^8 + 4 * q^9 - 12 * q^13 + 8 * q^14 - 2 * q^16 + 12 * q^17 - 6 * q^18 + 2 * q^20 - 28 * q^21 + 10 * q^24 + 16 * q^26 + 12 * q^28 - 8 * q^29 + 42 * q^30 + 28 * q^32 - 20 * q^33 + 14 * q^34 - 6 * q^36 - 16 * q^37 - 40 * q^40 + 48 * q^41 - 28 * q^42 - 8 * q^44 + 20 * q^45 - 46 * q^46 - 10 * q^48 + 60 * q^49 + 10 * q^50 - 32 * q^52 - 32 * q^53 - 16 * q^54 - 60 * q^56 + 12 * q^57 - 48 * q^58 - 24 * q^60 + 4 * q^61 - 18 * q^62 - 8 * q^65 + 56 * q^66 + 16 * q^68 - 12 * q^69 + 28 * q^70 + 56 * q^72 + 20 * q^73 + 4 * q^74 + 22 * q^76 + 68 * q^78 + 44 * q^80 + 48 * q^81 + 84 * q^84 + 20 * q^85 + 16 * q^86 + 36 * q^88 - 52 * q^89 - 12 * q^92 - 92 * q^93 - 38 * q^94 - 72 * q^96 - 28 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/52\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.0921725	+	1.41121i	0.0651758	+	0.997874i
$2$	0.0921725	+	1.41121i	0.0651758	+	0.997874i
$3$	−1.81380	+	1.04720i	−1.04720	+	0.604601i	−0.921864	−	0.387513i	$-0.873334\pi$
$3$	−1.81380	+	1.04720i	−1.04720	+	0.604601i	−0.125336	+	0.992114i	$0.540001\pi$
$4$	−1.98301	+	0.260149i	−0.991504	+	0.130074i
$5$	0.894007	+	0.894007i	0.399812	+	0.399812i	0.878167	−	0.478355i	$-0.158767\pi$
$5$	0.894007	+	0.894007i	0.399812	+	0.399812i	−0.478355	+	0.878167i	$0.658767\pi$
$6$	−1.64500	−	2.46313i	−0.671568	−	1.00557i
$7$	4.37156	−	1.17136i	1.65229	−	0.442731i	0.692040	−	0.721859i	$-0.256712\pi$
$7$	4.37156	−	1.17136i	1.65229	−	0.442731i	0.960254	+	0.279128i	$0.0900455\pi$
$8$	−0.549903	−	2.77446i	−0.194420	−	0.980918i
$9$	0.693255	−	1.20075i	0.231085	−	0.400251i
$10$	−1.17923	+	1.34403i	−0.372904	+	0.425020i
$11$	−0.404752	+	1.51056i	−0.122037	+	0.455450i	−0.999717	−	0.0237985i	$-0.992424\pi$
$11$	−0.404752	+	1.51056i	−0.122037	+	0.455450i	0.877679	+	0.479248i	$0.159091\pi$
$12$	3.32436	−	2.54846i	0.959660	−	0.735678i
$13$	−2.03880	−	2.97377i	−0.565460	−	0.824775i
$13$	−2.03880	−	2.97377i	−0.565460	−	0.824775i
$14$	2.05596	+	6.06121i	0.549479	+	1.61993i
$15$	−2.55776	−	0.685349i	−0.660410	−	0.176956i
$16$	3.86465	−	1.03176i	0.966161	−	0.257939i
$17$	−0.0484649	−	0.0279812i	−0.0117545	−	0.00678645i	0.494111	−	0.869399i	$-0.335494\pi$
$17$	−0.0484649	−	0.0279812i	−0.0117545	−	0.00678645i	−0.505866	+	0.862612i	$0.668827\pi$
$18$	1.75841	+	0.867649i	0.414461	+	0.204507i
$19$	−0.576896	−	2.15300i	−0.132349	−	0.493933i	0.867646	−	0.497183i	$-0.165632\pi$
$19$	−0.576896	−	2.15300i	−0.132349	−	0.493933i	−0.999995	+	0.00324996i	$0.998966\pi$
$20$	−2.00540	−	1.54025i	−0.448421	−	0.344410i
$21$	−6.70250	+	6.70250i	−1.46261	+	1.46261i
$22$	−2.16901	−	0.431957i	−0.462435	−	0.0920936i
$23$	−0.528908	−	0.916096i	−0.110285	−	0.191019i	0.805600	−	0.592460i	$-0.201843\pi$
$23$	−0.528908	−	0.916096i	−0.110285	−	0.191019i	−0.915885	+	0.401440i	$0.868510\pi$
$24$	3.90283	+	4.45646i	0.796661	+	0.909671i
$25$		−	3.40150i		−	0.680301i
$26$	4.00868	−	3.15126i	0.786168	−	0.618013i
$27$		−	3.37929i		−	0.650346i
$28$	−8.36411	+	3.46006i	−1.58067	+	0.653891i
$29$	3.67452	+	6.36446i	0.682342	+	1.18185i	0.974264	+	0.225409i	$0.0723717\pi$
$29$	3.67452	+	6.36446i	0.682342	+	1.18185i	−0.291923	+	0.956442i	$0.594295\pi$
$30$	0.731414	−	3.67269i	0.133537	−	0.670539i
$31$	−4.52800	+	4.52800i	−0.813253	+	0.813253i	−0.985120	−	0.171867i	$-0.945020\pi$
$31$	−4.52800	+	4.52800i	−0.813253	+	0.813253i	0.171867	+	0.985120i	$0.445020\pi$
$32$	1.81223	+	5.35871i	0.320361	+	0.947296i
$33$	−0.847713	−	3.16371i	−0.147568	−	0.550731i
$34$	0.0350202	−	0.0709732i	0.00600591	−	0.0121718i
$35$	4.95540	+	2.86100i	0.837616	+	0.483598i
$36$	−1.06236	+	2.56145i	−0.177059	+	0.426909i
$37$	−1.86603	−	0.500000i	−0.306773	−	0.0821995i	0.102149	−	0.994769i	$-0.467428\pi$
$37$	−1.86603	−	0.500000i	−0.306773	−	0.0821995i	−0.408921	+	0.912570i	$0.634095\pi$
$38$	2.98516	−	1.01257i	0.484257	−	0.164260i
$39$	6.81211	+	3.25881i	1.09081	+	0.521827i
$40$	1.98877	−	2.97200i	0.314451	−	0.469914i
$41$	0.401924	−	1.50000i	0.0627700	−	0.234261i	−0.927413	−	0.374039i	$-0.877972\pi$
$41$	0.401924	−	1.50000i	0.0627700	−	0.234261i	0.990183	+	0.139779i	$0.0446391\pi$
$42$	−10.0764	−	8.84083i	−1.55482	−	1.36417i
$43$	1.04025	−	1.80177i	0.158637	−	0.274767i	−0.775740	−	0.631052i	$-0.782623\pi$
$43$	1.04025	−	1.80177i	0.158637	−	0.274767i	0.934377	+	0.356285i	$0.115957\pi$
$44$	0.409658	−	3.10074i	0.0617582	−	0.467454i
$45$	1.69325	−	0.453706i	0.252415	−	0.0676345i
$46$	1.24405	−	0.830838i	0.183425	−	0.122500i
$47$	−5.38281	−	5.38281i	−0.785163	−	0.785163i	0.195534	−	0.980697i	$-0.437356\pi$
$47$	−5.38281	−	5.38281i	−0.785163	−	0.785163i	−0.980697	+	0.195534i	$0.937356\pi$
$48$	−5.92925	+	5.91846i	−0.855814	+	0.854256i
$49$	11.6763	−	6.74130i	1.66804	−	0.963043i
$50$	4.80023	−	0.313525i	0.678854	−	0.0443392i
$51$	0.117208			0.0164124
$52$	4.81657	+	5.36662i	0.667939	+	0.744216i
$53$	−4.40150			−0.604593			−0.302297	−	0.953214i	$-0.597753\pi$
$53$	−4.40150			−0.604593			−0.302297	+	0.953214i	$0.597753\pi$
$54$	4.76888	−	0.311478i	0.648963	−	0.0423868i
$55$	−1.71230	+	0.988596i	−0.230886	+	0.133302i
$56$	−5.65381	−	11.4846i	−0.755522	−	1.53469i
$57$	3.30100	+	3.30100i	0.437228	+	0.437228i
$58$	−8.64288	+	5.77214i	−1.13487	+	0.757919i
$59$	−8.67757	+	2.32515i	−1.12972	+	0.302708i	−0.774812	−	0.632192i	$-0.782155\pi$
$59$	−8.67757	+	2.32515i	−1.12972	+	0.302708i	−0.354911	+	0.934900i	$0.615489\pi$
$60$	5.25034	+	0.693654i	0.677816	+	0.0895504i
$61$	1.00750	−	1.74504i	0.128997	−	0.223429i	−0.794291	−	0.607537i	$-0.792158\pi$
$61$	1.00750	−	1.74504i	0.128997	−	0.223429i	0.923288	+	0.384108i	$0.125491\pi$
$62$	−6.80730	−	5.97259i	−0.864528	−	0.758519i
$63$	1.62410	−	6.06121i	0.204617	−	0.763640i
$64$	−7.39521	+	3.05136i	−0.924402	+	0.381420i
$65$	0.835873	−	4.48127i	0.103677	−	0.555833i
$66$	4.38651	−	1.48790i	0.539942	−	0.183148i
$67$	8.86360	+	2.37500i	1.08286	+	0.290152i	0.755768	−	0.654840i	$-0.227264\pi$
$67$	8.86360	+	2.37500i	1.08286	+	0.290152i	0.327094	+	0.944992i	$0.393931\pi$
$68$	0.103386	+	0.0428789i	0.0125374	+	0.00519984i
$69$	1.91867	+	1.10774i	0.230981	+	0.133357i
$70$	−3.58071	+	7.25680i	−0.427977	+	0.867354i
$71$	1.76582	+	6.59011i	0.209564	+	0.782103i	0.988010	+	0.154391i	$0.0493416\pi$
$71$	1.76582	+	6.59011i	0.209564	+	0.782103i	−0.778446	+	0.627712i	$0.783992\pi$
$72$	−3.71266	−	1.26311i	−0.437541	−	0.148859i
$73$	−5.45504	+	5.45504i	−0.638464	+	0.638464i	−0.950176	−	0.311713i	$-0.899097\pi$
$73$	−5.45504	+	5.45504i	−0.638464	+	0.638464i	0.311713	+	0.950176i	$0.399097\pi$
$74$	0.533607	−	2.67943i	0.0620306	−	0.311478i
$75$	3.56205	+	6.16966i	0.411311	+	0.712411i
$76$	1.70409	+	4.11935i	0.195473	+	0.472521i
$77$			7.07759i			0.806567i
$78$	−3.97096	+	9.91366i	−0.449623	+	1.12250i
$79$			8.87422i			0.998428i	0.866479	+	0.499214i	$0.166378\pi$
$79$			8.87422i			0.998428i	−0.866479	+	0.499214i	$0.833622\pi$
$80$	4.37741	+	2.53262i	0.489410	+	0.283156i
$81$	5.61856	+	9.73163i	0.624284	+	1.08129i
$82$	2.15386	+	0.428939i	0.237854	+	0.0473684i
$83$	6.96160	−	6.96160i	0.764135	−	0.764135i	−0.212932	−	0.977067i	$-0.568301\pi$
$83$	6.96160	−	6.96160i	0.764135	−	0.764135i	0.977067	+	0.212932i	$0.0683014\pi$
$84$	11.5475	−	15.0348i	1.25993	−	1.64043i
$85$	−0.0183126	−	0.0683434i	−0.00198628	−	0.00741288i
$86$	2.63855	+	1.30194i	0.284522	+	0.140391i
$87$	−13.3297	−	7.69592i	−1.42910	−	0.825089i
$88$	4.41355	+	0.292308i	0.470486	+	0.0311602i
$89$	−15.3098	−	4.10226i	−1.62284	−	0.434838i	−0.671005	−	0.741453i	$-0.734137\pi$
$89$	−15.3098	−	4.10226i	−1.62284	−	0.434838i	−0.951834	+	0.306615i	$0.900804\pi$
$90$	0.796345	+	2.34771i	0.0839421	+	0.247471i
$91$	−12.3961	−	10.6119i	−1.29946	−	1.11242i
$92$	1.28715	+	1.67903i	0.134195	+	0.175051i
$93$	3.47118	−	12.9546i	0.359945	−	1.34333i
$94$	7.10010	−	8.09240i	0.732320	−	0.834667i
$95$	1.40905	−	2.44055i	0.144566	−	0.250395i
$96$	−8.89868	−	7.82188i	−0.908218	−	0.798317i
$97$	−0.440720	+	0.118091i	−0.0447483	+	0.0119903i	−0.281124	−	0.959672i	$-0.590707\pi$
$97$	−0.440720	+	0.118091i	−0.0447483	+	0.0119903i	0.236375	+	0.971662i	$0.424040\pi$
$98$	10.5896	+	15.8563i	1.06971	+	1.60173i
$99$	1.53321	+	1.53321i	0.154093	+	0.154093i
$100$	0.884898	+	6.74521i	0.0884898	+	0.674521i
$101$	−9.58352	+	5.53305i	−0.953596	+	0.550559i	−0.894196	−	0.447675i	$-0.852252\pi$
$101$	−9.58352	+	5.53305i	−0.953596	+	0.550559i	−0.0594000	+	0.998234i	$0.518919\pi$
$102$	0.0108033	+	0.165404i	0.00106969	+	0.0163775i
$103$	3.85469			0.379813			0.189907	−	0.981802i	$-0.439181\pi$
$103$	3.85469			0.379813			0.189907	+	0.981802i	$0.439181\pi$
$104$	−7.12946	+	7.29184i	−0.699101	+	0.715023i
$105$	−11.9842			−1.16953
$106$	−0.405698	−	6.21143i	−0.0394049	−	0.603308i
$107$	−0.254277	+	0.146807i	−0.0245819	+	0.0141924i	−0.512241	−	0.858842i	$-0.671184\pi$
$107$	−0.254277	+	0.146807i	−0.0245819	+	0.0141924i	0.487659	+	0.873034i	$0.337851\pi$
$108$	0.879120	+	6.70117i	0.0845934	+	0.644820i
$109$	−1.15289	−	1.15289i	−0.110427	−	0.110427i	0.649734	−	0.760161i	$-0.274880\pi$
$109$	−1.15289	−	1.15289i	−0.110427	−	0.110427i	−0.760161	+	0.649734i	$0.774880\pi$
$110$	−1.55294	−	2.32529i	−0.148067	−	0.221707i
$111$	3.90820	−	1.04720i	0.370950	−	0.0993958i
$112$	15.6860	−	9.03725i	1.48218	−	0.853940i
$113$	4.56853	−	7.91292i	0.429771	−	0.744385i	−0.567082	−	0.823662i	$-0.691928\pi$
$113$	4.56853	−	7.91292i	0.429771	−	0.744385i	0.996853	+	0.0792763i	$0.0252609\pi$
$114$	−4.35413	+	4.96265i	−0.407802	+	0.464795i
$115$	0.346148	−	1.29184i	0.0322785	−	0.120465i
$116$	−8.94232	−	11.6649i	−0.830273	−	1.08305i
$117$	−4.98417	+	0.386509i	−0.460786	+	0.0357328i
$118$	−4.08110	−	12.0315i	−0.375695	−	1.10759i
$119$	−0.244643	−	0.0655520i	−0.0224264	−	0.00600914i
$120$	−0.494952	+	7.47326i	−0.0451828	+	0.682212i
$121$	7.40832	+	4.27720i	0.673484	+	0.388836i
$122$	2.55547	+	1.26094i	0.231362	+	0.114160i
$123$	0.841789	+	3.14160i	0.0759016	+	0.283268i
$124$	7.80111	−	10.1570i	0.700560	−	0.912127i
$125$	7.51100	−	7.51100i	0.671804	−	0.671804i
$126$	8.70331	+	1.73326i	0.775353	+	0.154411i
$127$	4.71771	+	8.17131i	0.418629	+	0.725086i	0.995802	−	0.0915355i	$-0.0291775\pi$
$127$	4.71771	+	8.17131i	0.418629	+	0.725086i	−0.577173	+	0.816622i	$0.695844\pi$
$128$	−4.98774	−	10.1549i	−0.440858	−	0.897577i
$129$			4.35741i			0.383648i
$130$	6.40104	+	0.766540i	0.561408	+	0.0672300i
$131$		−	9.03673i		−	0.789543i	−0.918779	−	0.394771i	$-0.870824\pi$
$131$		−	9.03673i		−	0.789543i	0.918779	−	0.394771i	$-0.129176\pi$
$132$	2.50406	+	6.05313i	0.217950	+	0.526857i
$133$	−5.04387	−	8.73623i	−0.437359	−	0.757527i
$134$	−2.53463	+	12.7273i	−0.218959	+	1.09947i
$135$	3.02111	−	3.02111i	0.260016	−	0.260016i
$136$	−0.0509817	+	0.149851i	−0.00437165	+	0.0128496i
$137$	2.42949	+	9.06696i	0.207565	+	0.774643i	0.988652	+	0.150221i	$0.0479986\pi$
$137$	2.42949	+	9.06696i	0.207565	+	0.774643i	−0.781087	+	0.624422i	$0.785335\pi$
$138$	−1.38641	+	2.80974i	−0.118019	+	0.239181i
$139$	8.97386	+	5.18106i	0.761153	+	0.439452i	0.829710	−	0.558195i	$-0.188506\pi$
$139$	8.97386	+	5.18106i	0.761153	+	0.439452i	−0.0685564	+	0.997647i	$0.521839\pi$
$140$	−10.5709	−	4.38425i	−0.893403	−	0.370537i
$141$	15.4002	+	4.12648i	1.29693	+	0.347512i
$142$	−9.13725	+	3.09936i	−0.766781	+	0.260092i
$143$	5.31725	−	1.87608i	0.444651	−	0.156885i
$144$	1.44030	−	5.35575i	0.120025	−	0.446312i
$145$	−2.40482	+	8.97492i	−0.199710	+	0.745326i
$146$	−8.20099	−	7.19538i	−0.678719	−	0.595494i
$147$	−14.1190	+	24.4548i	−1.16451	+	2.01700i
$148$	3.83042	+	0.506060i	0.314858	+	0.0415978i
$149$	10.0965	−	2.70535i	0.827138	−	0.221631i	0.179673	−	0.983726i	$-0.442496\pi$
$149$	10.0965	−	2.70535i	0.827138	−	0.221631i	0.647465	+	0.762095i	$0.275829\pi$
$150$	−8.37834	+	5.59547i	−0.684089	+	0.456868i
$151$	−3.84960	−	3.84960i	−0.313276	−	0.313276i	0.532901	−	0.846177i	$-0.321102\pi$
$151$	−3.84960	−	3.84960i	−0.313276	−	0.313276i	−0.846177	+	0.532901i	$0.821102\pi$
$152$	−5.65618	+	2.78451i	−0.458777	+	0.225854i
$153$	−0.0671971	+	0.0387963i	−0.00543256	+	0.00313649i
$154$	−9.98795	+	0.652360i	−0.804852	+	0.0525686i
$155$	−8.09612			−0.650296
$156$	−14.3562	−	4.69008i	−1.14942	−	0.375507i
$157$	8.76868			0.699817			0.349908	−	0.936784i	$-0.386213\pi$
$157$	8.76868			0.699817			0.349908	+	0.936784i	$0.386213\pi$
$158$	−12.5234	+	0.817959i	−0.996305	+	0.0650734i
$159$	7.98346	−	4.60925i	0.633130	−	0.365538i
$160$	−3.17058	+	6.41087i	−0.250656	+	0.506824i
$161$	−3.38523	−	3.38523i	−0.266793	−	0.266793i
$162$	−13.2155	+	8.82594i	−1.03831	+	0.693431i
$163$	−8.48845	+	2.27447i	−0.664867	+	0.178151i	−0.575441	−	0.817843i	$-0.695170\pi$
$163$	−8.48845	+	2.27447i	−0.664867	+	0.178151i	−0.0894254	+	0.995994i	$0.528503\pi$
$164$	−0.406795	+	3.07907i	−0.0317653	+	0.240435i
$165$	2.07051	−	3.58624i	0.161189	−	0.279188i
$166$	10.4659	+	9.18259i	0.812313	+	0.712707i
$167$	−2.25084	+	8.40025i	−0.174175	+	0.650031i	0.822515	+	0.568743i	$0.192570\pi$
$167$	−2.25084	+	8.40025i	−0.174175	+	0.650031i	−0.996691	+	0.0812880i	$0.974097\pi$
$168$	22.2815	+	14.9101i	1.71906	+	1.15034i
$169$	−4.68662	+	12.1258i	−0.360509	+	0.932756i
$170$	0.0947588	−	0.0321422i	0.00726766	−	0.00246519i
$171$	−2.98516	−	0.799871i	−0.228281	−	0.0611677i
$172$	−1.59410	+	3.84354i	−0.121549	+	0.293067i
$173$	5.44621	+	3.14437i	0.414068	+	0.239062i	0.692536	−	0.721383i	$-0.256493\pi$
$173$	5.44621	+	3.14437i	0.414068	+	0.239062i	−0.278468	+	0.960445i	$0.589827\pi$
$174$	9.63190	−	19.5203i	0.730192	−	1.47983i
$175$	−3.98437	−	14.8699i	−0.301190	−	1.12406i
$176$	−0.00569973	+	6.25537i	−0.000429633	+	0.471516i
$177$	13.3045	−	13.3045i	1.00003	−	1.00003i
$178$	4.37799	−	21.9834i	0.328144	−	1.64773i
$179$	−12.0998	−	20.9574i	−0.904379	−	1.56643i	−0.821749	−	0.569849i	$-0.807002\pi$
$179$	−12.0998	−	20.9574i	−0.904379	−	1.56643i	−0.0826294	−	0.996580i	$-0.526332\pi$
$180$	−3.23971	+	1.34020i	−0.241473	+	0.0998927i
$181$			5.03261i			0.374071i	0.982353	+	0.187035i	$0.0598879\pi$
$181$			5.03261i			0.374071i	−0.982353	+	0.187035i	$0.940112\pi$
$182$	13.8329	−	18.4715i	1.02537	−	1.36920i
$183$			4.22020i			0.311967i
$184$	−2.25082	+	1.97120i	−0.165933	+	0.145319i
$185$	−1.22124	−	2.11524i	−0.0897870	−	0.155516i
$186$	18.6016	+	3.70449i	1.36393	+	0.271627i
$187$	0.0618835	−	0.0618835i	0.00452537	−	0.00452537i
$188$	12.0745	+	9.27382i	0.880622	+	0.676363i
$189$	−3.95836	−	14.7728i	−0.287928	−	1.07456i
$190$	3.57399	+	1.76351i	0.259285	+	0.127939i
$191$	16.5728	+	9.56832i	1.19917	+	0.692340i	0.960370	−	0.278730i	$-0.0899133\pi$
$191$	16.5728	+	9.56832i	1.19917	+	0.692340i	0.238798	+	0.971069i	$0.423247\pi$
$192$	10.2181	−	13.2788i	0.737426	−	0.958318i
$193$	−9.21820	−	2.47001i	−0.663541	−	0.177795i	−0.0886973	−	0.996059i	$-0.528270\pi$
$193$	−9.21820	−	2.47001i	−0.663541	−	0.177795i	−0.574843	+	0.818263i	$0.694937\pi$
$194$	−0.207272	−	0.611062i	−0.0148813	−	0.0438717i
$195$	3.17667	+	9.00346i	0.227486	+	0.644751i
$196$	−21.4004	+	16.4056i	−1.52860	+	1.17183i
$197$	0.276336	−	1.03130i	0.0196881	−	0.0734770i	−0.955383	−	0.295370i	$-0.904557\pi$
$197$	0.276336	−	1.03130i	0.0196881	−	0.0734770i	0.975071	+	0.221893i	$0.0712237\pi$
$198$	−2.02235	+	2.30499i	−0.143722	+	0.163809i
$199$	5.66340	−	9.80930i	0.401468	−	0.695363i	−0.592435	−	0.805618i	$-0.701833\pi$
$199$	5.66340	−	9.80930i	0.401468	−	0.695363i	0.993903	+	0.110255i	$0.0351668\pi$
$200$	−9.43732	+	1.87050i	−0.667320	+	0.132264i
$201$	−18.5639	+	4.97419i	−1.30940	+	0.350852i
$202$	−8.69162	−	13.0143i	−0.611540	−	0.915686i
$203$	23.5184	+	23.5184i	1.65067	+	1.65067i
$204$	−0.232424	+	0.0304915i	−0.0162729	+	0.00213483i
$205$	1.70033	−	0.981687i	0.118756	−	0.0685640i
$206$	0.355296	+	5.43976i	0.0247547	+	0.379006i
$207$	−1.46667			−0.101941
$208$	−10.9474	−	9.38903i	−0.759067	−	0.651012i
$209$	3.48573			0.241113
$210$	−1.10461	−	16.9121i	−0.0762254	−	1.16705i
$211$	4.65089	−	2.68519i	0.320180	−	0.184856i	−0.331293	−	0.943528i	$-0.607485\pi$
$211$	4.65089	−	2.68519i	0.320180	−	0.184856i	0.651473	+	0.758672i	$0.274151\pi$
$212$	8.72822	−	1.14505i	0.599457	−	0.0786421i
$213$	−10.1040	−	10.1040i	−0.692315	−	0.692315i
$214$	−0.230612	−	0.345306i	−0.0157643	−	0.0236046i
$215$	2.54079	−	0.680801i	0.173280	−	0.0464303i
$216$	−9.37570	+	1.85828i	−0.637936	+	0.126440i
$217$	−14.4905	+	25.0983i	−0.983680	+	1.70378i
$218$	1.52070	−	1.73323i	0.102995	−	0.117389i
$219$	4.18185	−	15.6069i	0.282583	−	1.05462i
$220$	3.13832	−	2.40585i	0.211585	−	0.162202i
$221$	0.0156003	+	0.201172i	0.00104939	+	0.0135323i
$222$	1.83804	+	5.41876i	0.123361	+	0.363683i
$223$	−11.4144	−	3.05848i	−0.764366	−	0.204811i	−0.144485	−	0.989507i	$-0.546152\pi$
$223$	−11.4144	−	3.05848i	−0.764366	−	0.204811i	−0.619881	+	0.784696i	$0.712819\pi$
$224$	14.1992	+	21.3032i	0.948727	+	1.42338i
$225$	−4.08436	−	2.35811i	−0.272291	−	0.157207i
$226$	11.5879	+	5.71778i	0.770813	+	0.380341i
$227$	−0.454601	−	1.69660i	−0.0301730	−	0.112607i	0.949197	−	0.314682i	$-0.101898\pi$
$227$	−0.454601	−	1.69660i	−0.0301730	−	0.112607i	−0.979370	+	0.202075i	$0.935231\pi$
$228$	−7.40466	−	5.68716i	−0.490386	−	0.376641i
$229$	−7.04097	+	7.04097i	−0.465280	+	0.465280i	−0.900382	−	0.435101i	$-0.856713\pi$
$229$	−7.04097	+	7.04097i	−0.465280	+	0.465280i	0.435101	+	0.900382i	$0.356713\pi$
$230$	1.85496	+	0.369414i	0.122313	+	0.0243585i
$231$	−7.41165	−	12.8374i	−0.487651	−	0.844636i
$232$	15.6373	−	13.6946i	1.02664	−	0.899097i
$233$		−	21.3205i		−	1.39675i	−0.715731	−	0.698376i	$-0.753906\pi$
$233$		−	21.3205i		−	1.39675i	0.715731	−	0.698376i	$-0.246094\pi$
$234$	−1.00485	−	6.99806i	−0.0656889	−	0.457478i
$235$		−	9.62453i		−	0.627835i
$236$	16.6028	−	6.86825i	1.08075	−	0.447085i
$237$	−9.29308	−	16.0961i	−0.603651	−	1.04555i
$238$	0.0699580	−	0.351284i	0.00453470	−	0.0227704i
$239$	−15.1574	+	15.1574i	−0.980452	+	0.980452i	−0.999813	−	0.0193606i	$-0.993837\pi$
$239$	−15.1574	+	15.1574i	−0.980452	+	0.980452i	0.0193606	+	0.999813i	$0.493837\pi$
$240$	−10.5919	−	0.00965110i	−0.683706	−	0.000622976i
$241$	5.19414	+	19.3848i	0.334584	+	1.24869i	0.904319	+	0.426857i	$0.140379\pi$
$241$	5.19414	+	19.3848i	0.334584	+	1.24869i	−0.569735	+	0.821828i	$0.692954\pi$
$242$	−5.35317	+	10.8489i	−0.344115	+	0.697395i
$243$	−11.6023	−	6.69857i	−0.744285	−	0.429713i
$244$	−1.54391	+	3.72252i	−0.0988385	+	0.238310i
$245$	16.4654	+	4.41190i	1.05194	+	0.281866i
$246$	−4.35586	+	1.47751i	−0.277719	+	0.0942024i
$247$	−5.22637	+	6.10509i	−0.332546	+	0.388458i
$248$	15.0527	+	10.0728i	0.955847	+	0.639622i
$249$	−5.33679	+	19.9172i	−0.338205	+	1.26220i
$250$	11.2919	+	9.90727i	0.714161	+	0.626591i
$251$	7.30873	−	12.6591i	0.461323	−	0.799035i	−0.537704	−	0.843134i	$-0.680708\pi$
$251$	7.30873	−	12.6591i	0.461323	−	0.799035i	0.999027	+	0.0440987i	$0.0140416\pi$
$252$	−1.64378	+	12.4419i	−0.103548	+	0.783768i
$253$	1.59789	−	0.428153i	0.100459	−	0.0269178i
$254$	−11.0966	+	7.41083i	−0.696260	+	0.464997i
$255$	0.104785	+	0.104785i	0.00656186	+	0.00656186i
$256$	13.8710	−	7.97474i	0.866935	−	0.498421i
$257$	−12.1456	+	7.01228i	−0.757624	+	0.437414i	−0.828442	−	0.560075i	$-0.810772\pi$
$257$	−12.1456	+	7.01228i	−0.757624	+	0.437414i	0.0708183	+	0.997489i	$0.477439\pi$
$258$	−6.14920	+	0.401633i	−0.382832	+	0.0250046i
$259$	−8.74312			−0.543271
$260$	−0.491746	+	9.10384i	−0.0304968	+	0.564596i
$261$	10.1895			0.630715
$262$	12.7527	−	0.832938i	0.787864	−	0.0514591i
$263$	−25.6857	+	14.8297i	−1.58385	+	0.914436i	−0.589560	+	0.807725i	$0.700699\pi$
$263$	−25.6857	+	14.8297i	−1.58385	+	0.914436i	−0.994290	+	0.106711i	$0.965968\pi$
$264$	−8.31141	+	4.09167i	−0.511532	+	0.251825i
$265$	−3.93497	−	3.93497i	−0.241724	−	0.241724i
$266$	11.8637	−	7.92318i	0.727411	−	0.485801i
$267$	32.0649	−	8.59176i	1.96234	−	0.525807i
$268$	−18.1945	−	2.40378i	−1.11140	−	0.146834i
$269$	−0.890973	+	1.54321i	−0.0543236	+	0.0940912i	−0.891908	−	0.452216i	$-0.850634\pi$
$269$	−0.890973	+	1.54321i	−0.0543236	+	0.0940912i	0.837585	+	0.546307i	$0.183967\pi$
$270$	4.54188	+	3.98495i	0.276410	+	0.242516i
$271$	−5.43955	+	20.3007i	−0.330429	+	1.23318i	0.578311	+	0.815816i	$0.303712\pi$
$271$	−5.43955	+	20.3007i	−0.330429	+	1.23318i	−0.908740	+	0.417362i	$0.862955\pi$
$272$	−0.216170	−	0.0581336i	−0.0131072	−	0.00352487i
$273$	33.5967	+	6.26667i	2.03337	+	0.379276i
$274$	−12.5714	+	4.26423i	−0.759468	+	0.257612i
$275$	5.13816	+	1.37677i	0.309843	+	0.0830221i
$276$	−4.09292	−	1.69753i	−0.246365	−	0.102179i
$277$	−13.5377	−	7.81599i	−0.813402	−	0.469618i	0.0347342	−	0.999397i	$-0.488942\pi$
$277$	−13.5377	−	7.81599i	−0.813402	−	0.469618i	−0.848136	+	0.529779i	$0.822275\pi$
$278$	−6.48441	+	13.1415i	−0.388909	+	0.788177i
$279$	2.29795	+	8.57606i	0.137575	+	0.513435i
$280$	5.21274	−	15.3218i	0.311521	−	0.915654i
$281$	17.0835	−	17.0835i	1.01912	−	1.01912i	0.0193039	−	0.999814i	$-0.493855\pi$
$281$	17.0835	−	17.0835i	1.01912	−	1.01912i	0.999814	−	0.0193039i	$-0.00614502\pi$
$282$	−4.40383	+	22.1132i	−0.262245	+	1.31682i
$283$	9.43908	+	16.3490i	0.561095	+	0.971845i	0.997401	+	0.0720471i	$0.0229532\pi$
$283$	9.43908	+	16.3490i	0.561095	+	0.971845i	−0.436306	+	0.899798i	$0.643713\pi$
$284$	−5.21604	−	12.6089i	−0.309515	−	0.748199i
$285$			5.90223i			0.349618i
$286$	3.13763	+	7.33082i	0.185532	+	0.433481i
$287$		−	7.02813i		−	0.414858i
$288$	7.69083	+	1.53891i	0.453186	+	0.0906811i
$289$	−8.49843	−	14.7197i	−0.499908	−	0.865866i
$290$	−12.8871	−	2.56646i	−0.756758	−	0.150708i
$291$	0.675715	−	0.675715i	0.0396111	−	0.0396111i
$292$	9.39826	−	12.2365i	0.549992	−	0.716088i
$293$	−0.0178432	−	0.0665919i	−0.00104241	−	0.00389034i	0.965403	−	0.260764i	$-0.0839743\pi$
$293$	−0.0178432	−	0.0665919i	−0.00104241	−	0.00389034i	−0.966445	+	0.256873i	$0.917308\pi$
$294$	−35.8121	−	17.6707i	−2.08861	−	1.03058i
$295$	−9.83650	−	5.67910i	−0.572703	−	0.330650i
$296$	−0.361095	+	5.45216i	−0.0209882	+	0.316900i
$297$	5.10461	+	1.36778i	0.296200	+	0.0793665i
$298$	4.74843	+	13.9989i	0.275069	+	0.810935i
$299$	−1.64592	+	3.44058i	−0.0951862	+	0.198974i
$300$	−8.66861	−	11.3078i	−0.500483	−	0.652857i
$301$	2.43701	−	9.09504i	0.140467	−	0.524230i
$302$	5.07775	−	5.78741i	0.292192	−	0.333028i
$303$	11.5884	−	20.0717i	0.665737	−	1.15309i
$304$	−4.45087	−	7.72538i	−0.255275	−	0.443081i
$305$	2.46078	−	0.659365i	0.140904	−	0.0377551i
$306$	−0.0609433	−	0.0912530i	−0.00348389	−	0.00521659i
$307$	−6.80614	−	6.80614i	−0.388447	−	0.388447i	0.485686	−	0.874133i	$-0.338570\pi$
$307$	−6.80614	−	6.80614i	−0.388447	−	0.388447i	−0.874133	+	0.485686i	$0.838570\pi$
$308$	−1.84123	−	14.0349i	−0.104914	−	0.799714i
$309$	−6.99164	+	4.03663i	−0.397740	+	0.229636i
$310$	−0.746240	−	11.4253i	−0.0423836	−	0.648914i
$311$	26.1979			1.48555			0.742775	−	0.669542i	$-0.233509\pi$
$311$	26.1979			1.48555			0.742775	+	0.669542i	$0.233509\pi$
$312$	5.29542	−	20.6919i	0.299794	−	1.17145i
$313$	24.8487			1.40453			0.702265	−	0.711915i	$-0.252172\pi$
$313$	24.8487			1.40453			0.702265	+	0.711915i	$0.252172\pi$
$314$	0.808231	+	12.3744i	0.0456111	+	0.698329i
$315$	6.87071	−	3.96681i	0.387121	−	0.223504i
$316$	−2.30862	−	17.5977i	−0.129870	−	0.989945i
$317$	24.2717	+	24.2717i	1.36323	+	1.36323i	0.869762	+	0.493472i	$0.164273\pi$
$317$	24.2717	+	24.2717i	1.36323	+	1.36323i	0.493472	+	0.869762i	$0.335727\pi$
$318$	7.24047	+	10.8415i	0.406025	+	0.607959i
$319$	−11.1011	+	2.97454i	−0.621545	+	0.166542i
$320$	−9.33931	−	3.88343i	−0.522083	−	0.217090i
$321$	0.307472	−	0.532557i	0.0171614	−	0.0297245i
$322$	4.46523	−	5.08928i	0.248838	−	0.283614i
$323$	−0.0322845	+	0.120487i	−0.00179636	+	0.00670410i
$324$	−13.6733	−	17.8362i	−0.759629	−	0.990902i
$325$	−10.1153	+	6.93497i	−0.561095	+	0.384683i
$326$	−3.99215	−	11.7693i	−0.221105	−	0.651842i
$327$	3.29843	+	0.883811i	0.182404	+	0.0488749i
$328$	−4.38270	−	0.290266i	−0.241994	−	0.0160272i
$329$	−29.8364	−	17.2261i	−1.64494	−	0.949704i
$330$	5.25177	+	2.59137i	0.289100	+	0.142650i
$331$	4.93784	+	18.4283i	0.271408	+	1.01291i	0.958210	+	0.286065i	$0.0923472\pi$
$331$	4.93784	+	18.4283i	0.271408	+	1.01291i	−0.686802	+	0.726844i	$0.740986\pi$
$332$	−11.9939	+	15.6160i	−0.658248	+	0.857037i
$333$	−1.89401	+	1.89401i	−0.103791	+	0.103791i
$334$	−12.0620	−	2.40213i	−0.660001	−	0.131439i
$335$	5.80086	+	10.0474i	0.316935	+	0.548947i
$336$	−18.9875	+	32.8181i	−1.03585	+	1.79038i
$337$		−	28.8443i		−	1.57125i	−0.618702	−	0.785626i	$-0.712341\pi$
$337$		−	28.8443i		−	1.57125i	0.618702	−	0.785626i	$-0.287659\pi$
$338$	−17.5440	−	5.49612i	−0.954269	−	0.298950i
$339$			19.1366i			1.03936i
$340$	0.0540934	+	0.130762i	0.00293363	+	0.00709154i
$341$	−5.00708	−	8.67251i	−0.271148	−	0.469643i
$342$	0.853633	−	4.28640i	0.0461592	−	0.231782i
$343$	20.7456	−	20.7456i	1.12016	−	1.12016i
$344$	−5.57097	−	1.89533i	−0.300366	−	0.102190i
$345$	0.724973	+	2.70564i	0.0390312	+	0.145667i
$346$	−3.93537	+	7.97555i	−0.211567	+	0.428768i
$347$	−23.8280	−	13.7571i	−1.27916	−	0.738521i	−0.302463	−	0.953161i	$-0.597809\pi$
$347$	−23.8280	−	13.7571i	−1.27916	−	0.738521i	−0.976693	+	0.214640i	$0.931142\pi$
$348$	28.4350	+	11.7934i	1.52428	+	0.632190i
$349$	22.2539	+	5.96291i	1.19122	+	0.319187i	0.799369	−	0.600841i	$-0.205167\pi$
$349$	22.2539	+	5.96291i	1.19122	+	0.319187i	0.391853	+	0.920028i	$0.371834\pi$
$350$	20.6172	−	6.99337i	1.10204	−	0.373811i
$351$	−10.0492	+	6.88969i	−0.536389	+	0.367745i
$352$	−8.82814	+	0.568530i	−0.470542	+	0.0303027i
$353$	−5.07073	+	18.9242i	−0.269888	+	1.00723i	0.689303	+	0.724473i	$0.257917\pi$
$353$	−5.07073	+	18.9242i	−0.269888	+	1.00723i	−0.959190	+	0.282761i	$0.908750\pi$
$354$	20.0017	+	17.5491i	1.06308	+	0.932724i
$355$	−4.31295	+	7.47026i	−0.228908	+	0.396480i
$356$	31.4267	+	4.15197i	1.66561	+	0.220054i
$357$	0.512381	−	0.137292i	0.0271181	−	0.00726627i
$358$	28.4600	−	19.0070i	1.50416	−	1.00455i
$359$	−10.7783	−	10.7783i	−0.568858	−	0.568858i	0.362951	−	0.931808i	$-0.381769\pi$
$359$	−10.7783	−	10.7783i	−0.568858	−	0.568858i	−0.931808	+	0.362951i	$0.881769\pi$
$360$	−2.18991	−	4.44837i	−0.115419	−	0.234449i
$361$	12.1519	−	7.01588i	0.639572	−	0.369257i
$362$	−7.10205	+	0.463868i	−0.373275	+	0.0243804i
$363$	−17.9163			−0.940363
$364$	27.3422	+	17.8186i	1.43312	+	0.933947i
$365$	−9.75368			−0.510531
$366$	−5.95558	+	0.388987i	−0.311303	+	0.0203327i
$367$	29.3207	−	16.9283i	1.53053	−	0.883651i	0.531191	−	0.847252i	$-0.321744\pi$
$367$	29.3207	−	16.9283i	1.53053	−	0.883651i	0.999337	−	0.0363994i	$-0.0115889\pi$
$368$	−2.98923	−	2.99468i	−0.155824	−	0.156109i
$369$	−1.52249	−	1.52249i	−0.0792578	−	0.0792578i
$370$	2.87248	−	1.91838i	0.149333	−	0.0997320i
$371$	−19.2414	+	5.15573i	−0.998965	+	0.267672i
$372$	−3.51325	+	26.5921i	−0.182153	+	1.37874i
$373$	−5.98260	+	10.3622i	−0.309767	+	0.536533i	−0.978311	−	0.207140i	$-0.933584\pi$
$373$	−5.98260	+	10.3622i	−0.309767	+	0.536533i	0.668544	+	0.743673i	$0.266918\pi$
$374$	0.0930344	+	0.0816265i	0.00481070	+	0.00422081i
$375$	−5.75796	+	21.4890i	−0.297340	+	1.10969i
$376$	−11.9743	+	17.8944i	−0.617529	+	0.922832i
$377$	11.4348	−	23.9030i	0.588924	−	1.23107i
$378$	20.4826	−	6.94770i	1.05351	−	0.357351i
$379$	−15.4002	−	4.12647i	−0.791055	−	0.211963i	−0.159402	−	0.987214i	$-0.550957\pi$
$379$	−15.4002	−	4.12647i	−0.791055	−	0.211963i	−0.631653	+	0.775251i	$0.717623\pi$
$380$	−2.15925	+	5.20619i	−0.110767	+	0.267072i
$381$	−17.1140	−	9.88076i	−0.876776	−	0.506207i
$382$	−11.9753	+	24.2696i	−0.612711	+	1.24174i
$383$	−6.06022	−	22.6171i	−0.309663	−	1.15568i	−0.928857	−	0.370439i	$-0.879207\pi$
$383$	−6.06022	−	22.6171i	−0.309663	−	1.15568i	0.619194	−	0.785238i	$-0.287460\pi$
$384$	19.6810	+	13.1959i	1.00434	+	0.673399i
$385$	−6.32741	+	6.32741i	−0.322475	+	0.322475i
$386$	2.63603	−	13.2365i	0.134170	−	0.673718i
$387$	−1.44232	−	2.49817i	−0.0733172	−	0.126989i
$388$	0.843230	−	0.348827i	0.0428085	−	0.0177090i
$389$			39.2161i			1.98834i	0.107845	+	0.994168i	$0.465605\pi$
$389$			39.2161i			1.98834i	−0.107845	+	0.994168i	$0.534395\pi$
$390$	−12.4129	+	5.31281i	−0.628554	+	0.269025i
$391$			0.0591980i			0.00299377i
$392$	−25.1243	−	28.6882i	−1.26897	−	1.44898i
$393$	9.46326	+	16.3909i	0.477358	+	0.826809i
$394$	1.48085	+	0.294909i	0.0746040	+	0.0148573i
$395$	−7.93361	+	7.93361i	−0.399183	+	0.399183i
$396$	−3.43922	−	2.64150i	−0.172828	−	0.132740i
$397$	−2.81223	−	10.4954i	−0.141142	−	0.526749i	−0.999897	−	0.0143624i	$-0.995428\pi$
$397$	−2.81223	−	10.4954i	−0.141142	−	0.526749i	0.858755	−	0.512387i	$-0.171239\pi$
$398$	14.3650	+	7.08808i	0.720050	+	0.355293i
$399$	18.2972	+	10.5639i	0.916004	+	0.528855i
$400$	−3.50952	−	13.1456i	−0.175476	−	0.657280i
$401$	−1.48858	−	0.398864i	−0.0743361	−	0.0199183i	0.221459	−	0.975170i	$-0.428918\pi$
$401$	−1.48858	−	0.398864i	−0.0743361	−	0.0199183i	−0.295795	+	0.955251i	$0.595585\pi$
$402$	−8.73069	−	25.7391i	−0.435447	−	1.28375i
$403$	22.6969	+	4.23356i	1.13061	+	0.210889i
$404$	17.5648	−	13.4652i	0.873881	−	0.669920i
$405$	−3.67711	+	13.7232i	−0.182717	+	0.681910i
$406$	−31.0216	+	35.3571i	−1.53958	+	1.75474i
$407$	1.51056	−	2.61636i	0.0748755	−	0.129688i
$408$	−0.0644529	−	0.325188i	−0.00319090	−	0.0160992i
$409$	−0.657171	+	0.176088i	−0.0324950	+	0.00870701i	−0.275030	−	0.961436i	$-0.588688\pi$
$409$	−0.657171	+	0.176088i	−0.0324950	+	0.00870701i	0.242535	+	0.970143i	$0.422021\pi$
$410$	1.54209	+	2.30904i	0.0761583	+	0.114035i
$411$	−13.9015	−	13.9015i	−0.685712	−	0.685712i
$412$	−7.64387	+	1.00279i	−0.376587	+	0.0494040i
$413$	−35.2109	+	20.3290i	−1.73262	+	1.00033i
$414$	−0.135187	−	2.06978i	−0.00664407	−	0.101724i
$415$	12.4474			0.611020
$416$	12.2408	−	16.3145i	0.600155	−	0.799884i
$417$	−21.7024			−1.06277
$418$	0.321289	+	4.91909i	0.0157147	+	0.240600i
$419$	20.8664	−	12.0472i	1.01939	−	0.588546i	0.105463	−	0.994423i	$-0.466367\pi$
$419$	20.8664	−	12.0472i	1.01939	−	0.588546i	0.913927	+	0.405878i	$0.133034\pi$
$420$	23.7647	−	3.11767i	1.15960	−	0.152127i
$421$	−15.8266	−	15.8266i	−0.771339	−	0.771339i	0.207002	−	0.978341i	$-0.433629\pi$
$421$	−15.8266	−	15.8266i	−0.771339	−	0.771339i	−0.978341	+	0.207002i	$0.933629\pi$
$422$	4.21804	+	6.31586i	0.205331	+	0.307451i
$423$	−10.1951	+	2.73176i	−0.495701	+	0.132823i
$424$	2.42040	+	12.2118i	0.117545	+	0.593056i
$425$	−0.0951783	+	0.164854i	−0.00461683	+	0.00799658i
$426$	13.3275	−	15.1902i	0.645721	−	0.735965i
$427$	2.36028	−	8.80867i	0.114222	−	0.426281i
$428$	0.466042	−	0.357269i	0.0225270	−	0.0172693i
$429$	−7.67983	+	8.97106i	−0.370785	+	0.433127i
$430$	1.19494	+	3.52282i	0.0576252	+	0.169886i
$431$	8.01815	+	2.14846i	0.386221	+	0.103487i	0.446704	−	0.894682i	$-0.352598\pi$
$431$	8.01815	+	2.14846i	0.386221	+	0.103487i	−0.0604836	+	0.998169i	$0.519264\pi$
$432$	−3.48660	−	13.0598i	−0.167749	−	0.628339i
$433$	21.0862	+	12.1741i	1.01334	+	0.585050i	0.912167	−	0.409819i	$-0.134408\pi$
$433$	21.0862	+	12.1741i	1.01334	+	0.585050i	0.101170	+	0.994869i	$0.467742\pi$
$434$	−36.7545	−	18.1357i	−1.76427	−	0.870543i
$435$	−5.03666	−	18.7971i	−0.241489	−	0.901250i
$436$	2.58612	+	1.98627i	0.123853	+	0.0951252i
$437$	−1.66723	+	1.66723i	−0.0797545	+	0.0797545i
$438$	22.4100	+	4.46293i	1.07079	+	0.213247i
$439$	0.506851	+	0.877892i	0.0241907	+	0.0418995i	0.877867	−	0.478904i	$-0.158966\pi$
$439$	0.506851	+	0.877892i	0.0241907	+	0.0418995i	−0.853677	+	0.520803i	$0.825632\pi$
$440$	3.68441	+	4.20706i	0.175648	+	0.200564i
$441$		−	18.6937i		−	0.890178i
$442$	−0.282457	+	0.0405578i	−0.0134351	+	0.00192914i
$443$			39.1335i			1.85929i	0.368460	+	0.929644i	$0.379885\pi$
$443$			39.1335i			1.85929i	−0.368460	+	0.929644i	$0.620115\pi$
$444$	−7.47757	+	3.09332i	−0.354870	+	0.146803i
$445$	−10.0196	−	17.3545i	−0.474977	−	0.822684i
$446$	3.26406	−	16.3900i	0.154558	−	0.776089i
$447$	−15.4800	+	15.4800i	−0.732181	+	0.732181i
$448$	−28.7544	+	22.0016i	−1.35852	+	1.03948i
$449$	−6.54345	−	24.4205i	−0.308804	−	1.15247i	−0.929621	−	0.368517i	$-0.879865\pi$
$449$	−6.54345	−	24.4205i	−0.308804	−	1.15247i	0.620817	−	0.783956i	$-0.286801\pi$
$450$	2.95131	−	5.98123i	0.139126	−	0.281958i
$451$	2.10315	+	1.21426i	0.0990337	+	0.0571771i
$452$	−7.00089	+	16.8799i	−0.329294	+	0.793963i
$453$	11.0137	+	2.95112i	0.517469	+	0.138656i
$454$	2.35234	−	0.797916i	0.110401	−	0.0374480i
$455$	−1.59509	−	20.5692i	−0.0747790	−	0.964300i
$456$	7.34325	−	10.9737i	0.343879	−	0.513891i
$457$	6.20927	−	23.1733i	0.290458	−	1.08400i	−0.654301	−	0.756235i	$-0.727037\pi$
$457$	6.20927	−	23.1733i	0.290458	−	1.08400i	0.944758	−	0.327768i	$-0.106296\pi$
$458$	−10.5852	−	9.28728i	−0.494616	−	0.433966i
$459$	−0.0945569	+	0.163777i	−0.00441354	+	0.00764447i
$460$	−0.350343	+	2.65179i	−0.0163348	+	0.123640i
$461$	−4.85332	+	1.30044i	−0.226042	+	0.0605677i	−0.370062	−	0.929007i	$-0.620664\pi$
$461$	−4.85332	+	1.30044i	−0.226042	+	0.0605677i	0.144020	+	0.989575i	$0.453997\pi$
$462$	17.4330	−	11.6426i	0.811057	−	0.541664i
$463$	−1.18158	−	1.18158i	−0.0549128	−	0.0549128i	0.679117	−	0.734030i	$-0.262363\pi$
$463$	−1.18158	−	1.18158i	−0.0549128	−	0.0549128i	−0.734030	+	0.679117i	$0.762363\pi$
$464$	20.7673	+	20.8052i	0.964097	+	0.965856i
$465$	14.6848	−	8.47826i	0.680990	−	0.393170i
$466$	30.0876	−	1.96517i	1.39378	−	0.0910345i
$467$	24.9759			1.15575			0.577873	−	0.816127i	$-0.303883\pi$
$467$	24.9759			1.15575			0.577873	+	0.816127i	$0.303883\pi$
$468$	9.78309	−	2.06308i	0.452224	−	0.0953657i
$469$	41.5297			1.91766
$470$	13.5822	−	0.887117i	0.626500	−	0.0409197i
$471$	−15.9047	+	9.18256i	−0.732848	+	0.423110i
$472$	11.2228	+	22.7969i	0.516573	+	1.04931i
$473$	2.30063	+	2.30063i	0.105783	+	0.105783i
$474$	21.8583	−	14.5981i	1.00399	−	0.670512i
$475$	−7.32345	+	1.96231i	−0.336023	+	0.0900371i
$476$	0.502183	+	0.0663464i	0.0230175	+	0.00304098i
$477$	−3.05136	+	5.28512i	−0.139712	+	0.241989i
$478$	−22.7873	−	19.9932i	−1.04227	−	0.914466i
$479$	8.10477	−	30.2474i	0.370317	−	1.38204i	−0.489752	−	0.871862i	$-0.662913\pi$
$479$	8.10477	−	30.2474i	0.370317	−	1.38204i	0.860069	−	0.510178i	$-0.170421\pi$
$480$	−0.962665	−	14.9483i	−0.0439395	−	0.682293i
$481$	2.31756	+	6.56853i	0.105672	+	0.299499i
$482$	−26.8772	+	9.11676i	−1.22422	+	0.415257i
$483$	9.68514	+	2.59513i	0.440689	+	0.118082i
$484$	−15.8035	−	6.55445i	−0.718340	−	0.297930i
$485$	−0.499580	−	0.288433i	−0.0226848	−	0.0130971i
$486$	8.38365	−	16.9906i	0.380290	−	0.770710i
$487$	4.40472	+	16.4386i	0.199597	+	0.744906i	0.991029	+	0.133649i	$0.0426694\pi$
$487$	4.40472	+	16.4386i	0.199597	+	0.744906i	−0.791432	+	0.611258i	$0.790664\pi$
$488$	−5.39555	−	1.83566i	−0.244245	−	0.0830963i
$489$	13.0146	−	13.0146i	0.588538	−	0.588538i
$490$	−4.70844	+	23.6428i	−0.212706	+	1.06807i
$491$	−5.60847	−	9.71415i	−0.253107	−	0.438393i	0.711273	−	0.702916i	$-0.248119\pi$
$491$	−5.60847	−	9.71415i	−0.253107	−	0.438393i	−0.964380	+	0.264523i	$0.914786\pi$
$492$	−2.48656	−	6.01083i	−0.112103	−	0.270989i
$493$		−	0.411271i		−	0.0185227i
$494$	−9.09727	−	6.81276i	−0.409306	−	0.306521i
$495$			2.74139i			0.123217i
$496$	−12.8273	+	22.1709i	−0.575964	+	0.995503i
$497$	15.4387	+	26.7407i	0.692522	+	1.19948i
$498$	−28.5991	−	5.69549i	−1.28156	−	0.255221i
$499$	6.87805	−	6.87805i	0.307904	−	0.307904i	−0.536192	−	0.844096i	$-0.680138\pi$
$499$	6.87805	−	6.87805i	0.307904	−	0.307904i	0.844096	+	0.536192i	$0.180138\pi$
$500$	−12.9404	+	16.8484i	−0.578712	+	0.753481i
$501$	−4.71416	−	17.5935i	−0.210613	−	0.786019i
$502$	18.5383	+	9.14731i	0.827403	+	0.408264i
$503$	6.53009	+	3.77015i	0.291162	+	0.168103i	0.638466	−	0.769650i	$-0.279569\pi$
$503$	6.53009	+	3.77015i	0.291162	+	0.168103i	−0.347304	+	0.937753i	$0.612903\pi$
$504$	−17.7096	−	1.17291i	−0.788850	−	0.0522454i
$505$	−13.5143	−	3.62115i	−0.601379	−	0.161139i
$506$	0.751495	+	2.21549i	0.0334080	+	0.0984905i
$507$	−4.19755	−	26.9017i	−0.186420	−	1.19475i
$508$	−11.4810	−	14.9765i	−0.509387	−	0.664473i
$509$	−2.52725	+	9.43184i	−0.112019	+	0.418059i	−0.999047	−	0.0436566i	$-0.986099\pi$
$509$	−2.52725	+	9.43184i	−0.112019	+	0.418059i	0.887028	+	0.461716i	$0.152766\pi$
$510$	−0.138214	+	0.157531i	−0.00612024	+	0.00697559i
$511$	−17.4572	+	30.2368i	−0.772262	+	1.33760i
$512$	12.5325	+	18.8397i	0.553864	+	0.832607i
$513$	−7.27563	+	1.94950i	−0.321227	+	0.0860725i
$514$	−11.0153	−	16.4937i	−0.485863	−	0.727504i
$515$	3.44611	+	3.44611i	0.151854	+	0.151854i
$516$	−1.13357	−	8.64077i	−0.0499028	−	0.380389i
$517$	10.3097	−	5.95233i	0.453421	−	0.261783i
$518$	−0.805875	−	12.3383i	−0.0354081	−	0.542116i
$519$	−13.1711			−0.578149
$520$	−12.8927	+	0.145169i	−0.565384	+	0.00636608i
$521$	−19.5755			−0.857619			−0.428809	−	0.903395i	$-0.641067\pi$
$521$	−19.5755			−0.857619			−0.428809	+	0.903395i	$0.641067\pi$
$522$	0.939194	+	14.3795i	0.0411074	+	0.629374i
$523$	−31.0210	+	17.9100i	−1.35645	+	0.783148i	−0.989144	−	0.146951i	$-0.953054\pi$
$523$	−31.0210	+	17.9100i	−1.35645	+	0.783148i	−0.367309	+	0.930099i	$0.619721\pi$
$524$	2.35090	+	17.9199i	0.102699	+	0.782835i
$525$	22.7986	+	22.7986i	0.995012	+	0.995012i
$526$	−23.2952	−	34.8810i	−1.01572	−	1.52088i
$527$	0.346148	−	0.0927502i	0.0150785	−	0.00404026i
$528$	−6.54028	−	11.3520i	−0.284629	−	0.494031i
$529$	10.9405	−	18.9495i	0.475674	−	0.823892i
$530$	5.19037	−	5.91576i	0.225455	−	0.256964i
$531$	−3.22384	+	12.0315i	−0.139903	+	0.522124i
$532$	12.2747	+	16.0119i	0.532178	+	0.694202i
$533$	−5.28010	+	1.86297i	−0.228706	+	0.0806940i
$534$	15.0803	+	44.4583i	0.652587	+	1.92390i
$535$	−0.358572	−	0.0960790i	−0.0155024	−	0.00415386i
$536$	1.71520	−	25.8977i	0.0740853	−	1.11861i
$537$	43.8932	+	25.3417i	1.89413	+	1.09358i
$538$	−2.25991	−	1.11511i	−0.0974317	−	0.0480756i
$539$	5.45711	+	20.3662i	0.235054	+	0.877235i
$540$	−5.20495	+	6.77683i	−0.223985	+	0.291628i
$541$	−12.3423	+	12.3423i	−0.530636	+	0.530636i	−0.920762	−	0.390126i	$-0.872432\pi$
$541$	−12.3423	+	12.3423i	−0.530636	+	0.530636i	0.390126	+	0.920762i	$0.372432\pi$
$542$	−29.1498	−	5.80516i	−1.25209	−	0.249353i
$543$	−5.27014	−	9.12816i	−0.226164	−	0.391727i
$544$	0.0621137	−	0.310418i	0.00266310	−	0.0133091i
$545$		−	2.06139i		−	0.0883001i
$546$	−5.74687	+	47.9896i	−0.245943	+	2.05376i
$547$		−	5.49854i		−	0.235101i	−0.993067	−	0.117550i	$-0.962496\pi$
$547$		−	5.49854i		−	0.235101i	0.993067	−	0.117550i	$-0.0375041\pi$
$548$	−7.17645	−	17.3478i	−0.306563	−	0.741063i
$549$	−1.39690	−	2.41951i	−0.0596184	−	0.103262i
$550$	−1.46930	+	7.37791i	−0.0626514	+	0.314595i
$551$	11.5829	−	11.5829i	0.493448	−	0.493448i
$552$	2.01831	−	5.93242i	0.0859049	−	0.252501i
$553$	10.3949	+	38.7942i	0.442035	+	1.64970i
$554$	9.78218	−	19.8249i	0.415605	−	0.842280i
$555$	4.43016	+	2.55776i	0.188050	+	0.108571i
$556$	−19.1431	−	7.93955i	−0.811848	−	0.336712i
$557$	−3.31443	−	0.888098i	−0.140437	−	0.0376299i	0.187916	−	0.982185i	$-0.439827\pi$
$557$	−3.31443	−	0.888098i	−0.140437	−	0.0376299i	−0.328353	+	0.944555i	$0.606493\pi$
$558$	−11.8908	+	4.03336i	−0.503377	+	0.170746i
$559$	−7.47891	+	0.579970i	−0.316324	+	0.0245301i
$560$	22.1027	+	5.94400i	0.934011	+	0.251180i
$561$	−0.0474401	+	0.177049i	−0.00200292	+	0.00747501i
$562$	25.6830	+	22.5338i	1.08337	+	0.950529i
$563$	4.66786	−	8.08497i	0.196727	−	0.340741i	−0.750738	−	0.660600i	$-0.770302\pi$
$563$	4.66786	−	8.08497i	0.196727	−	0.340741i	0.947465	+	0.319859i	$0.103635\pi$
$564$	−31.6123	−	4.17649i	−1.33112	−	0.175862i
$565$	11.1585	−	2.98991i	0.469442	−	0.125787i
$566$	−22.2018	+	14.8274i	−0.933209	+	0.623243i
$567$	35.9611	+	35.9611i	1.51022	+	1.51022i
$568$	17.3130	−	8.52310i	0.726435	−	0.357621i
$569$	29.5605	−	17.0668i	1.23924	−	0.715477i	0.270302	−	0.962775i	$-0.412876\pi$
$569$	29.5605	−	17.0668i	1.23924	−	0.715477i	0.968939	+	0.247299i	$0.0795430\pi$
$570$	−8.32927	+	0.544024i	−0.348875	+	0.0227866i
$571$	30.2446			1.26570			0.632848	−	0.774276i	$-0.281886\pi$
$571$	30.2446			1.26570			0.632848	+	0.774276i	$0.281886\pi$
$572$	−10.0561	+	5.10355i	−0.420467	+	0.213390i
$573$	−40.0798			−1.67436
$574$	9.91815	−	0.647801i	0.413976	−	0.0270387i
$575$	−3.11610	+	1.79908i	−0.129951	+	0.0750270i
$576$	−1.46284	+	10.9952i	−0.0609515	+	0.458133i
$577$	−24.5041	−	24.5041i	−1.02012	−	1.02012i	−0.999793	−	0.0203254i	$-0.993530\pi$
$577$	−24.5041	−	24.5041i	−1.02012	−	1.02012i	−0.0203254	−	0.999793i	$-0.506470\pi$
$578$	19.9892	−	13.3498i	0.831443	−	0.555279i
$579$	19.3066	−	5.17319i	0.802355	−	0.214990i
$580$	2.43397	−	18.4229i	0.101065	−	0.764971i
$581$	22.2785	−	38.5875i	0.924269	−	1.60088i
$582$	1.01586	+	0.891291i	0.0421086	+	0.0369452i
$583$	1.78152	−	6.64872i	0.0737830	−	0.275362i
$584$	18.1345	+	12.1350i	0.750411	+	0.502151i
$585$	−4.80142	−	4.11034i	−0.198514	−	0.169941i
$586$	0.0923302	−	0.0313184i	0.00381413	−	0.00129375i
$587$	−30.4837	−	8.16808i	−1.25820	−	0.337133i	−0.432699	−	0.901538i	$-0.642439\pi$
$587$	−30.4837	−	8.16808i	−1.25820	−	0.337133i	−0.825498	+	0.564405i	$0.809105\pi$
$588$	21.6362	−	52.1671i	0.892260	−	2.15133i
$589$	12.3610	+	7.13662i	0.509325	+	0.294059i
$590$	7.10774	−	14.4048i	0.292621	−	0.593036i
$591$	0.578757	+	2.15995i	0.0238069	+	0.0888485i
$592$	−7.72740	−	0.00704101i	−0.317594	−	0.000289384i
$593$	−11.3864	+	11.3864i	−0.467582	+	0.467582i	−0.901130	−	0.433548i	$-0.857261\pi$
$593$	−11.3864	+	11.3864i	−0.467582	+	0.467582i	0.433548	+	0.901130i	$0.357261\pi$
$594$	−1.45971	+	7.32974i	−0.0598927	+	0.300743i
$595$	−0.160109	−	0.277317i	−0.00656382	−	0.0113689i
$596$	−19.3177	+	7.99133i	−0.791283	+	0.327338i
$597$			23.7229i			0.970912i
$598$	−5.00708	−	2.00561i	−0.204755	−	0.0820155i
$599$		−	37.4177i		−	1.52885i	−0.644715	−	0.764423i	$-0.723024\pi$
$599$		−	37.4177i		−	1.52885i	0.644715	−	0.764423i	$-0.276976\pi$
$600$	15.1587	−	13.2755i	0.618850	−	0.541969i
$601$	6.94234	+	12.0245i	0.283184	+	0.490489i	0.972167	−	0.234288i	$-0.0752760\pi$
$601$	6.94234	+	12.0245i	0.283184	+	0.490489i	−0.688983	+	0.724777i	$0.741943\pi$
$602$	13.0596	+	2.60081i	0.532270	+	0.106001i
$603$	8.99652	−	8.99652i	0.366366	−	0.366366i
$604$	8.63526	+	6.63232i	0.351364	+	0.269865i
$605$	2.79925	+	10.4469i	0.113806	+	0.424728i
$606$	29.3935	+	14.5036i	1.19403	+	0.589168i
$607$	−17.4664	−	10.0842i	−0.708938	−	0.409306i	0.101730	−	0.994812i	$-0.467562\pi$
$607$	−17.4664	−	10.0842i	−0.708938	−	0.409306i	−0.810668	+	0.585506i	$0.800896\pi$
$608$	10.4919	−	6.99316i	0.425501	−	0.283610i
$609$	−67.2863	−	18.0293i	−2.72658	−	0.730585i
$610$	1.15732	+	3.41190i	0.0468584	+	0.138144i
$611$	−5.03278	+	26.9817i	−0.203605	+	1.09156i
$612$	0.123160	−	0.0944146i	0.00497843	−	0.00381648i
$613$	8.75275	−	32.6657i	0.353520	−	1.31935i	−0.528817	−	0.848736i	$-0.677364\pi$
$613$	8.75275	−	32.6657i	0.353520	−	1.31935i	0.882337	−	0.470619i	$-0.155969\pi$
$614$	8.97753	−	10.2322i	0.362304	−	0.412938i
$615$	−2.05605	+	3.56118i	−0.0829078	+	0.143600i
$616$	19.6365	−	3.89199i	0.791176	−	0.156813i
$617$	−17.6816	+	4.73777i	−0.711834	+	0.190735i	−0.596525	−	0.802594i	$-0.703453\pi$
$617$	−17.6816	+	4.73777i	−0.711834	+	0.190735i	−0.115309	+	0.993330i	$0.536786\pi$
$618$	−6.34095	−	9.49458i	−0.255070	−	0.381928i
$619$	−5.55216	−	5.55216i	−0.223160	−	0.223160i	0.586668	−	0.809828i	$-0.300439\pi$
$619$	−5.55216	−	5.55216i	−0.223160	−	0.223160i	−0.809828	+	0.586668i	$0.800439\pi$
$620$	16.0547	−	2.10620i	0.644771	−	0.0845869i
$621$	−3.09576	+	1.78734i	−0.124228	+	0.0717233i
$622$	2.41473	+	36.9707i	0.0968219	+	1.48239i
$623$	−71.7330			−2.87392
$624$	29.6887	+	5.56571i	1.18850	+	0.222807i
$625$	−3.57775			−0.143110
$626$	2.29037	+	35.0666i	0.0915415	+	1.40154i
$627$	−6.32243	+	3.65026i	−0.252494	+	0.145777i
$628$	−17.3884	+	2.28116i	−0.693871	+	0.0910283i
$629$	0.0764462	+	0.0764462i	0.00304811	+	0.00304811i
$630$	6.23127	+	9.33036i	0.248260	+	0.371731i
$631$	22.8754	−	6.12944i	0.910655	−	0.244009i	0.227069	−	0.973879i	$-0.427086\pi$
$631$	22.8754	−	6.12944i	0.910655	−	0.244009i	0.683587	+	0.729869i	$0.260419\pi$
$632$	24.6211	−	4.87996i	0.979376	−	0.194114i
$633$	−5.62386	+	9.74082i	−0.223528	+	0.387163i
$634$	−32.0152	+	36.4896i	−1.27149	+	1.44919i
$635$	−3.08754	+	11.5229i	−0.122525	+	0.457271i
$636$	−14.6322	+	11.2171i	−0.580204	+	0.444786i
$637$	−43.8526	−	20.9784i	−1.73750	−	0.831195i
$638$	−5.22091	−	15.3918i	−0.206698	−	0.609369i
$639$	9.13725	+	2.44832i	0.361464	+	0.0968540i
$640$	4.61950	−	13.5376i	0.182602	−	0.535122i
$641$	−8.61576	−	4.97431i	−0.340302	−	0.196473i	0.320104	−	0.947383i	$-0.396282\pi$
$641$	−8.61576	−	4.97431i	−0.340302	−	0.196473i	−0.660406	+	0.750909i	$0.729616\pi$
$642$	0.779889	+	0.384820i	0.0307798	+	0.0151876i
$643$	−6.27341	−	23.4127i	−0.247399	−	0.923306i	−0.972162	−	0.234308i	$-0.924718\pi$
$643$	−6.27341	−	23.4127i	−0.247399	−	0.923306i	0.724763	−	0.688998i	$-0.241949\pi$
$644$	7.59360	+	5.83227i	0.299230	+	0.229824i
$645$	−3.89555	+	3.89555i	−0.153387	+	0.153387i
$646$	−0.173008	−	0.0344545i	−0.00680693	−	0.00135559i
$647$	8.08819	+	14.0092i	0.317980	+	0.550757i	0.980066	−	0.198670i	$-0.0636623\pi$
$647$	8.08819	+	14.0092i	0.317980	+	0.550757i	−0.662087	+	0.749427i	$0.730329\pi$
$648$	23.9103	−	20.9399i	0.939286	−	0.822597i
$649$		−	14.0491i		−	0.551474i
$650$	−10.7190	−	13.6356i	−0.420435	−	0.534830i
$651$		−	60.6979i		−	2.37894i
$652$	16.2410	−	6.71856i	0.636045	−	0.263119i
$653$	9.72518	+	16.8445i	0.380576	+	0.659177i	0.991145	−	0.132787i	$-0.0423925\pi$
$653$	9.72518	+	16.8445i	0.380576	+	0.659177i	−0.610569	+	0.791963i	$0.709059\pi$
$654$	−0.943216	+	4.73623i	−0.0368827	+	0.185201i
$655$	8.07890	−	8.07890i	0.315669	−	0.315669i
$656$	0.00565990	−	6.21165i	0.000220982	−	0.242524i
$657$	2.76842	+	10.3319i	0.108006	+	0.403085i
$658$	21.5594	−	43.6931i	0.840475	−	1.70334i
$659$	29.2584	+	16.8924i	1.13975	+	0.658033i	0.946368	−	0.323091i	$-0.104722\pi$
$659$	29.2584	+	16.8924i	1.13975	+	0.658033i	0.193379	+	0.981124i	$0.438055\pi$
$660$	−3.17289	+	7.65018i	−0.123505	+	0.297783i
$661$	−8.51422	−	2.28138i	−0.331165	−	0.0887353i	0.0894055	−	0.995995i	$-0.471503\pi$
$661$	−8.51422	−	2.28138i	−0.331165	−	0.0887353i	−0.420570	+	0.907260i	$0.638170\pi$
$662$	−25.5510	+	8.66689i	−0.993066	+	0.336848i
$663$	−0.238963	−	0.348549i	−0.00928055	−	0.0135365i
$664$	−23.1429	−	15.4864i	−0.898117	−	0.600991i
$665$	3.30100	−	12.3195i	0.128007	−	0.477730i
$666$	−2.84741	−	2.49826i	−0.110335	−	0.0968056i
$667$	3.88697	−	6.73243i	0.150504	−	0.260681i
$668$	2.27812	−	17.2433i	0.0881430	−	0.667164i
$669$	23.9063	−	6.40568i	0.924272	−	0.247658i
$670$	−13.6443	+	9.11230i	−0.527124	+	0.352039i
$671$	2.22819	+	2.22819i	0.0860183	+	0.0860183i
$672$	−48.0633	−	23.7703i	−1.85408	−	0.916959i
$673$	−17.6598	+	10.1959i	−0.680734	+	0.393022i	−0.800131	−	0.599825i	$-0.795237\pi$
$673$	−17.6598	+	10.1959i	−0.680734	+	0.393022i	0.119398	+	0.992847i	$0.461904\pi$
$674$	40.7053	−	2.65866i	1.56791	−	0.102408i
$675$	−11.4947			−0.442431
$676$	6.13909	−	25.2648i	0.236119	−	0.971724i
$677$	−1.01359			−0.0389554			−0.0194777	−	0.999810i	$-0.506200\pi$
$677$	−1.01359			−0.0389554			−0.0194777	+	0.999810i	$0.506200\pi$
$678$	−27.0058	+	1.76387i	−1.03715	+	0.0677412i
$679$	−1.78831	+	1.03248i	−0.0686289	+	0.0396229i
$680$	−0.179546	+	0.0883896i	−0.00688526	+	0.00338959i
$681$	2.60123	+	2.60123i	0.0996794	+	0.0996794i
$682$	11.7772	−	7.86539i	0.450972	−	0.301181i
$683$	24.3916	−	6.53572i	0.933320	−	0.250082i	0.240050	−	0.970761i	$-0.422836\pi$
$683$	24.3916	−	6.53572i	0.933320	−	0.250082i	0.693270	+	0.720678i	$0.256169\pi$
$684$	6.12768	+	0.809565i	0.234298	+	0.0309545i
$685$	−5.93395	+	10.2779i	−0.226725	+	0.392698i
$686$	31.1886	+	27.3642i	1.19078	+	1.04477i
$687$	5.39763	−	20.1442i	0.205932	−	0.768550i
$688$	2.16122	−	8.03648i	0.0823957	−	0.306388i
$689$	8.97377	+	13.0891i	0.341873	+	0.498654i
$690$	−3.75139	+	1.27247i	−0.142813	+	0.0484422i
$691$	34.6849	+	9.29380i	1.31948	+	0.353553i	0.848782	−	0.528743i	$-0.177337\pi$
$691$	34.6849	+	9.29380i	1.31948	+	0.353553i	0.470695	+	0.882296i	$0.344003\pi$
$692$	−11.6179	−	4.81849i	−0.441646	−	0.183171i
$693$	8.49843	+	4.90657i	0.322829	+	0.186385i
$694$	17.2179	−	34.8943i	0.653581	−	1.32457i
$695$	3.39079	+	12.6546i	0.128620	+	0.480016i
$696$	−14.0219	+	41.2147i	−0.531500	+	1.56224i
$697$	−0.0614511	+	0.0614511i	−0.00232763	+	0.00232763i
$698$	−6.36370	+	31.9544i	−0.240869	+	1.20949i
$699$	22.3268	+	38.6712i	0.844478	+	1.46268i
$700$	11.7694	+	28.4506i	0.444842	+	1.07533i
$701$			16.0203i			0.605077i	0.953137	+	0.302539i	$0.0978342\pi$
$701$			16.0203i			0.605077i	−0.953137	+	0.302539i	$0.902166\pi$
$702$	−10.6490	−	13.5465i	−0.401922	−	0.511281i
$703$			4.30601i			0.162404i
$704$	−1.61602	−	12.4059i	−0.0609062	−	0.467566i
$705$	10.0788	+	17.4570i	0.379590	+	0.657469i
$706$	−27.1734	−	5.41155i	−1.02268	−	0.203666i
$707$	−35.4138	+	35.4138i	−1.33187	+	1.33187i
$708$	−22.9218	+	29.8441i	−0.861454	+	1.12161i
$709$	6.09039	+	22.7296i	0.228729	+	0.853630i	0.980876	+	0.194634i	$0.0623519\pi$
$709$	6.09039	+	22.7296i	0.228729	+	0.853630i	−0.752147	+	0.658996i	$0.770981\pi$
$710$	−10.9396	−	5.39792i	−0.410556	−	0.202580i
$711$	10.6557	+	6.15209i	0.399621	+	0.230722i
$712$	−2.96261	+	44.7323i	−0.111029	+	1.67641i
$713$	6.54298	+	1.75319i	0.245036	+	0.0656573i
$714$	0.240975	+	0.710421i	0.00901826	+	0.0265868i
$715$	6.43088	+	3.07644i	0.240501	+	0.115052i
$716$	29.4460	+	38.4110i	1.10045	+	1.43549i
$717$	11.6197	−	43.3654i	0.433947	−	1.61951i
$718$	14.2170	−	16.2039i	0.530573	−	0.604724i
$719$	−23.4982	+	40.7001i	−0.876334	+	1.51786i	−0.0210001	+	0.999779i	$0.506685\pi$
$719$	−23.4982	+	40.7001i	−0.876334	+	1.51786i	−0.855334	+	0.518076i	$0.826648\pi$
$720$	6.07571	−	3.50044i	0.226428	−	0.130454i
$721$	16.8510	−	4.51521i	0.627563	−	0.168155i
$722$	11.0209	+	16.5021i	0.410157	+	0.614145i
$723$	−29.7209	−	29.7209i	−1.10533	−	1.10533i
$724$	−1.30923	−	9.97970i	−0.0486571	−	0.370893i
$725$	21.6487	−	12.4989i	0.804014	−	0.464198i
$726$	−1.65139	−	25.2836i	−0.0612889	−	0.938364i
$727$	−20.0985			−0.745412			−0.372706	−	0.927950i	$-0.621570\pi$
$727$	−20.0985			−0.745412			−0.372706	+	0.927950i	$0.621570\pi$
$728$	−22.6255	+	40.2278i	−0.838557	+	1.49094i
$729$	−5.65241			−0.209348
$730$	−0.899021	−	13.7645i	−0.0332743	−	0.509445i
$731$	−0.100831	+	0.0582151i	−0.00372939	+	0.00215316i
$732$	−1.09788	−	8.36870i	−0.0405789	−	0.309316i
$733$	−13.3827	−	13.3827i	−0.494300	−	0.494300i	0.415358	−	0.909658i	$-0.363656\pi$
$733$	−13.3827	−	13.3827i	−0.494300	−	0.494300i	−0.909658	+	0.415358i	$0.863656\pi$
$734$	26.5919	+	39.8173i	0.981526	+	1.46968i
$735$	−34.4852	+	9.24028i	−1.27201	+	0.340833i
$736$	3.95059	−	4.49445i	0.145621	−	0.165668i
$737$	−7.17513	+	12.4277i	−0.264299	+	0.457780i
$738$	2.00822	−	2.28888i	0.0739236	−	0.0842550i
$739$	−0.588495	+	2.19629i	−0.0216481	+	0.0807920i	−0.975905	−	0.218197i	$-0.929983\pi$
$739$	−0.588495	+	2.19629i	−0.0216481	+	0.0807920i	0.954257	+	0.298989i	$0.0966493\pi$
$740$	2.97200	+	3.87684i	0.109253	+	0.142515i
$741$	3.08635	−	16.5465i	0.113380	−	0.607850i
$742$	−9.04933	−	26.6784i	−0.332211	−	0.979396i
$743$	15.3189	+	4.10470i	0.561998	+	0.150587i	0.528624	−	0.848856i	$-0.322708\pi$
$743$	15.3189	+	4.10470i	0.561998	+	0.150587i	0.0333737	+	0.999443i	$0.489375\pi$
$744$	−37.8508	−	2.50685i	−1.38768	−	0.0919057i
$745$	11.4449	+	6.60774i	0.419311	+	0.242089i
$746$	−15.1746	−	7.48758i	−0.555581	−	0.274140i
$747$	−3.53299	−	13.1853i	−0.129266	−	0.482425i
$748$	−0.106617	+	0.138815i	−0.00389829	+	0.00507556i
$749$	−0.939623	+	0.939623i	−0.0343331	+	0.0343331i
$750$	−30.8561	−	6.14497i	−1.12671	−	0.224383i
$751$	−15.5912	−	27.0047i	−0.568930	−	0.985416i	−0.996672	−	0.0815150i	$-0.974024\pi$
$751$	−15.5912	−	27.0047i	−0.568930	−	0.985416i	0.427742	−	0.903901i	$-0.359309\pi$
$752$	−26.3564	−	15.2489i	−0.961118	−	0.556070i
$753$			30.6148i			1.11567i
$754$	34.7861	+	13.9337i	1.26683	+	0.507436i
$755$		−	6.88313i		−	0.250503i
$756$	11.6926	+	28.2648i	0.425255	+	1.02798i
$757$	6.38361	+	11.0567i	0.232016	+	0.401864i	0.958401	−	0.285424i	$-0.0921344\pi$
$757$	6.38361	+	11.0567i	0.232016	+	0.401864i	−0.726385	+	0.687288i	$0.758801\pi$
$758$	4.40383	−	22.1132i	0.159954	−	0.803188i
$759$	−2.44990	+	2.44990i	−0.0889256	+	0.0889256i
$760$	−7.54603	−	2.56729i	−0.273723	−	0.0931252i
$761$	−2.86736	−	10.7011i	−0.103942	−	0.387915i	0.894281	−	0.447505i	$-0.147687\pi$
$761$	−2.86736	−	10.7011i	−0.103942	−	0.387915i	−0.998223	+	0.0595898i	$0.981021\pi$
$762$	12.3664	−	25.0621i	0.447986	−	0.907904i
$763$	−6.39038	−	3.68949i	−0.231347	−	0.133568i
$764$	−35.3532	−	14.6627i	−1.27904	−	0.530477i
$765$	−0.0947588	−	0.0253905i	−0.00342601	−	0.000917997i
$766$	31.3588	−	10.6369i	1.13304	−	0.384327i
$767$	24.6062	+	21.0646i	0.888480	+	0.760598i
$768$	−16.8081	+	28.9903i	−0.606508	+	1.04610i
$769$	−9.26223	+	34.5671i	−0.334004	+	1.24652i	0.570940	+	0.820992i	$0.306579\pi$
$769$	−9.26223	+	34.5671i	−0.334004	+	1.24652i	−0.904944	+	0.425530i	$0.860088\pi$
$770$	−9.51250	−	8.34608i	−0.342807	−	0.300772i
$771$	14.6865	−	25.4378i	0.528922	−	0.916120i
$772$	18.9223	+	2.49994i	0.681030	+	0.0899750i
$773$	47.3258	−	12.6809i	1.70219	−	0.456100i	0.728700	−	0.684833i	$-0.240125\pi$
$773$	47.3258	−	12.6809i	1.70219	−	0.456100i	0.973489	+	0.228733i	$0.0734582\pi$
$774$	3.39249	−	2.26567i	0.121941	−	0.0814379i
$775$	15.4020	+	15.4020i	0.553256	+	0.553256i
$776$	0.569990	+	1.15782i	0.0204615	+	0.0415633i
$777$	15.8583	−	9.15579i	0.568913	−	0.328462i
$778$	−55.3420	+	3.61465i	−1.98411	+	0.129591i
$779$	−3.46137			−0.124017
$780$	−8.64161	−	17.0275i	−0.309419	−	0.609684i
$781$	−10.6695			−0.381783
$782$	−0.0835407	+	0.00545643i	−0.00298741	+	0.000195122i
$783$	21.5074	−	12.4173i	0.768611	−	0.443758i
$784$	38.1693	−	38.0998i	1.36319	−	1.36071i
$785$	7.83925	+	7.83925i	0.279795	+	0.279795i
$786$	−22.2586	+	14.8654i	−0.793939	+	0.530231i
$787$	−35.2028	+	9.43257i	−1.25485	+	0.336235i	−0.824206	−	0.566290i	$-0.808378\pi$
$787$	−35.2028	+	9.43257i	−1.25485	+	0.336235i	−0.430639	+	0.902524i	$0.641712\pi$
$788$	−0.279685	+	2.11696i	−0.00996335	+	0.0754137i
$789$	31.0592	−	53.7962i	1.10574	−	1.91519i
$790$	−11.9272	−	10.4647i	−0.424352	−	0.372318i
$791$	10.7027	−	39.9432i	0.380546	−	1.42022i
$792$	3.41070	−	5.09693i	0.121194	−	0.181112i
$793$	−7.24342	+	0.561708i	−0.257221	+	0.0199469i
$794$	14.5520	−	4.93603i	0.516430	−	0.175173i
$795$	11.2580	+	3.01656i	0.399279	+	0.106987i
$796$	−8.67869	+	20.9253i	−0.307608	+	0.741676i
$797$	17.1575	+	9.90590i	0.607750	+	0.350885i	0.772084	−	0.635520i	$-0.219214\pi$
$797$	17.1575	+	9.90590i	0.607750	+	0.350885i	−0.164334	+	0.986405i	$0.552548\pi$
$798$	−13.2213	+	26.7948i	−0.468029	+	0.948525i
$799$	0.110260	+	0.411495i	0.00390071	+	0.0145576i
$800$	18.2277	−	6.16432i	0.644446	−	0.217942i
$801$	−15.5394	+	15.5394i	−0.549058	+	0.549058i
$802$	0.425673	−	2.13746i	0.0150310	−	0.0754763i
$803$	−6.03220	−	10.4481i	−0.212872	−	0.368705i
$804$	35.5184	−	14.6932i	1.25264	−	0.518191i
$805$		−	6.05283i		−	0.213334i
$806$	−3.88240	+	32.4202i	−0.136752	+	1.14195i
$807$		−	3.73211i		−	0.131376i
$808$	20.6212	+	23.5464i	0.725452	+	0.828360i
$809$	−6.74791	−	11.6877i	−0.237244	−	0.410918i	0.722679	−	0.691184i	$-0.242911\pi$
$809$	−6.74791	−	11.6877i	−0.237244	−	0.410918i	−0.959922	+	0.280266i	$0.909577\pi$
$810$	−19.7052	−	3.92427i	−0.692369	−	0.137885i
$811$	−11.4250	+	11.4250i	−0.401187	+	0.401187i	−0.878651	−	0.477464i	$-0.841556\pi$
$811$	−11.4250	+	11.4250i	−0.401187	+	0.401187i	0.477464	+	0.878651i	$0.341556\pi$
$812$	−52.7556	−	40.5190i	−1.85136	−	1.42194i
$813$	−11.3926	−	42.5177i	−0.399555	−	1.49116i
$814$	3.83146	+	1.89055i	0.134292	+	0.0662637i
$815$	−9.62213	−	5.55534i	−0.337048	−	0.194595i
$816$	0.452967	−	0.120930i	0.0158570	−	0.00423339i
$817$	−4.47933	−	1.20023i	−0.156712	−	0.0419908i
$818$	−0.309070	−	0.911173i	−0.0108064	−	0.0318584i
$819$	−21.3358	+	7.52788i	−0.745534	+	0.263045i
$820$	−3.11639	+	2.38903i	−0.108829	+	0.0834287i
$821$	8.70120	−	32.4733i	0.303674	−	1.13333i	−0.630407	−	0.776265i	$-0.717112\pi$
$821$	8.70120	−	32.4733i	0.303674	−	1.13333i	0.934081	−	0.357061i	$-0.116221\pi$
$822$	18.3366	−	20.8993i	0.639562	−	0.728946i
$823$	−9.30064	+	16.1092i	−0.324200	+	0.561531i	−0.981350	−	0.192229i	$-0.938428\pi$
$823$	−9.30064	+	16.1092i	−0.324200	+	0.561531i	0.657150	+	0.753760i	$0.271762\pi$
$824$	−2.11970	−	10.6947i	−0.0738433	−	0.372566i
$825$	−10.7614	+	2.88350i	−0.374663	+	0.100391i
$826$	−31.9339	−	47.8161i	−1.11112	−	1.66373i
$827$	−1.07171	−	1.07171i	−0.0372671	−	0.0372671i	0.688228	−	0.725495i	$-0.258389\pi$
$827$	−1.07171	−	1.07171i	−0.0372671	−	0.0372671i	−0.725495	+	0.688228i	$0.758389\pi$
$828$	2.90842	−	0.381553i	0.101075	−	0.0132599i
$829$	26.0238	−	15.0248i	0.903844	−	0.521835i	0.0253987	−	0.999677i	$-0.491914\pi$
$829$	26.0238	−	15.0248i	0.903844	−	0.521835i	0.878445	+	0.477843i	$0.158581\pi$
$830$	1.14731	+	17.5659i	0.0398238	+	0.609721i
$831$	32.7396			1.13573
$832$	24.1514	+	15.7706i	0.837299	+	0.546746i
$833$	−0.754520			−0.0261426
$834$	−2.00037	−	30.6266i	−0.0692671	−	1.06051i
$835$	−9.52214	+	5.49761i	−0.329527	+	0.190253i
$836$	−6.91224	+	0.906810i	−0.239065	+	0.0313627i
$837$	15.3014	+	15.3014i	0.528895	+	0.528895i
$838$	18.9244	+	28.3364i	0.653734	+	0.978864i
$839$	36.0525	−	9.66025i	1.24467	−	0.333509i	0.424396	−	0.905477i	$-0.360486\pi$
$839$	36.0525	−	9.66025i	1.24467	−	0.333509i	0.820276	+	0.571968i	$0.193820\pi$
$840$	6.59013	+	33.2495i	0.227381	+	1.14722i
$841$	−12.5042	+	21.6580i	−0.431180	+	0.746826i
$842$	20.8758	−	23.7933i	0.719426	−	0.819972i
$843$	−13.0963	+	48.8760i	−0.451060	+	1.68338i
$844$	−8.52420	+	6.53468i	−0.293415	+	0.224933i
$845$	−15.0304	+	6.65070i	−0.517063	+	0.228791i
$846$	−4.79478	−	14.1356i	−0.164848	−	0.485990i
$847$	37.3960	+	10.0202i	1.28494	+	0.344300i
$848$	−17.0103	+	4.54128i	−0.584134	+	0.155948i
$849$	−34.2413	−	19.7692i	−1.17516	−	0.678478i
$850$	−0.241415	−	0.119121i	−0.00828048	−	0.00408583i
$851$	0.528908	+	1.97391i	0.0181307	+	0.0676648i
$852$	22.6649	+	17.4078i	0.776486	+	0.596381i
$853$	−36.7666	+	36.7666i	−1.25887	+	1.25887i	−0.307230	+	0.951635i	$0.599402\pi$
$853$	−36.7666	+	36.7666i	−1.25887	+	1.25887i	−0.951635	+	0.307230i	$0.900598\pi$
$854$	12.6484	+	2.51892i	0.432820	+	0.0861957i
$855$	−1.95366	−	3.38384i	−0.0668138	−	0.115725i
$856$	0.547137	+	0.624751i	0.0187008	+	0.0213535i
$857$		−	23.1948i		−	0.792319i	−0.918182	−	0.396160i	$-0.870343\pi$
$857$		−	23.1948i		−	0.792319i	0.918182	−	0.396160i	$-0.129657\pi$
$858$	−13.3679	−	10.0109i	−0.456372	−	0.341768i
$859$			53.8518i			1.83740i	0.394956	+	0.918700i	$0.370760\pi$
$859$			53.8518i			1.83740i	−0.394956	+	0.918700i	$0.629240\pi$
$860$	−4.86129	+	2.01102i	−0.165769	+	0.0685751i
$861$	7.35986	+	12.7477i	0.250823	+	0.434439i
$862$	−2.29286	+	11.5133i	−0.0780952	+	0.392144i
$863$	23.1715	−	23.1715i	0.788766	−	0.788766i	−0.192526	−	0.981292i	$-0.561668\pi$
$863$	23.1715	−	23.1715i	0.788766	−	0.788766i	0.981292	+	0.192526i	$0.0616680\pi$
$864$	18.1087	−	6.12407i	0.616069	−	0.208345i
$865$	2.05786	+	7.68003i	0.0699693	+	0.261129i
$866$	−15.2366	+	30.8791i	−0.517761	+	1.04931i
$867$	30.8290	+	17.7991i	1.04701	+	0.604490i
$868$	22.2055	−	53.5399i	0.753704	−	1.81726i
$869$	−13.4050	−	3.59186i	−0.454734	−	0.121846i
$870$	26.0623	−	8.84034i	0.883595	−	0.299715i
$871$	−11.0084	−	31.2005i	−0.373005	−	1.05719i
$872$	−2.56467	+	3.83263i	−0.0868507	+	0.129789i
$873$	−0.163734	+	0.611062i	−0.00554154	+	0.0206813i
$874$	−2.50648	−	2.19914i	−0.0847830	−	0.0743869i
$875$	24.0367	−	41.6328i	0.812590	−	1.40745i
$876$	−4.23253	+	32.0365i	−0.143004	+	1.08241i
$877$	−34.6168	+	9.27555i	−1.16893	+	0.313213i	−0.790526	−	0.612429i	$-0.790193\pi$
$877$	−34.6168	+	9.27555i	−1.16893	+	0.313213i	−0.378401	+	0.925642i	$0.623526\pi$
$878$	−1.19217	+	0.796189i	−0.0402338	+	0.0268701i
$879$	0.102099	+	0.102099i	0.00344372	+	0.00344372i
$880$	−5.59744	+	5.58724i	−0.188690	+	0.188346i
$881$	1.42362	−	0.821926i	0.0479629	−	0.0276914i	−0.475827	−	0.879539i	$-0.657851\pi$
$881$	1.42362	−	0.821926i	0.0479629	−	0.0276914i	0.523790	+	0.851848i	$0.324518\pi$
$882$	26.3807	−	1.72305i	0.888286	−	0.0580181i
$883$	15.1271			0.509067			0.254534	−	0.967064i	$-0.418078\pi$
$883$	15.1271			0.509067			0.254534	+	0.967064i	$0.418078\pi$
$884$	−0.0832702	−	0.394867i	−0.00280068	−	0.0132808i
$885$	23.7886			0.799646
$886$	−55.2254	+	3.60703i	−1.85533	+	0.121181i
$887$	−3.23210	+	1.86605i	−0.108523	+	0.0626559i	−0.553279	−	0.832996i	$-0.686624\pi$
$887$	−3.23210	+	1.86605i	−0.108523	+	0.0626559i	0.444756	+	0.895652i	$0.353290\pi$
$888$	−5.05454	−	10.2673i	−0.169619	−	0.344547i
$889$	30.1952	+	30.1952i	1.01272	+	1.01272i
$890$	23.5673	−	15.7394i	0.789978	−	0.527586i
$891$	−16.9743	+	4.54825i	−0.568660	+	0.152372i
$892$	23.4305	+	3.09555i	0.784512	+	0.103647i
$893$	−8.48388	+	14.6945i	−0.283902	+	0.491733i
$894$	−23.2724	−	20.4187i	−0.778344	−	0.682903i
$895$	7.91879	−	29.5533i	0.264696	−	0.987859i
$896$	−33.6992	−	38.5504i	−1.12581	−	1.28788i
$897$	−0.617599	−	7.96415i	−0.0206210	−	0.265915i
$898$	33.8592	−	11.4851i	1.12990	−	0.383261i
$899$	−45.4565	−	12.1800i	−1.51606	−	0.406227i
$900$	8.71279	+	3.61361i	0.290426	+	0.120454i
$901$	0.213319	+	0.123160i	0.00710668	+	0.00410304i
$902$	−1.51971	+	3.07991i	−0.0506009	+	0.102550i
$903$	5.10407	+	19.0487i	0.169853	+	0.633899i
$904$	−24.4663	−	8.32384i	−0.813737	−	0.276847i
$905$	−4.49918	+	4.49918i	−0.149558	+	0.149558i
$906$	−3.14947	+	15.8146i	−0.104634	+	0.525406i
$907$	−22.0895	−	38.2602i	−0.733471	−	1.27041i	−0.955391	−	0.295344i	$-0.904566\pi$
$907$	−22.0895	−	38.2602i	−0.733471	−	1.27041i	0.221921	−	0.975065i	$-0.428767\pi$
$908$	1.34285	+	3.24610i	0.0445639	+	0.107726i
$909$			15.3432i			0.508903i
$910$	28.8804	−	4.14692i	0.957376	−	0.137469i
$911$			23.3467i			0.773510i	0.922182	+	0.386755i	$0.126404\pi$
$911$			23.3467i			0.773510i	−0.922182	+	0.386755i	$0.873596\pi$
$912$	16.1630	+	9.35137i	0.535211	+	0.309655i
$913$	7.69816	+	13.3336i	0.254772	+	0.441278i
$914$	33.2747	+	6.62663i	1.10063	+	0.219189i
$915$	−3.77289	+	3.77289i	−0.124728	+	0.124728i
$916$	12.1306	−	15.7940i	0.400806	−	0.521848i
$917$	−10.5852	−	39.5046i	−0.349555	−	1.30456i
$918$	−0.239839	−	0.118344i	−0.00791587	−	0.00390592i
$919$	−36.7181	−	21.1992i	−1.21122	−	0.699297i	−0.248193	−	0.968710i	$-0.579837\pi$
$919$	−36.7181	−	21.1992i	−1.21122	−	0.699297i	−0.963025	+	0.269413i	$0.913170\pi$
$920$	−3.77451	−	0.249985i	−0.124442	−	0.00824176i
$921$	19.4724	+	5.21761i	0.641637	+	0.171926i
$922$	−2.28254	−	6.72918i	−0.0751714	−	0.221614i
$923$	15.9973	−	18.6870i	0.526559	−	0.615091i
$924$	18.0370	+	23.5285i	0.593374	+	0.774029i
$925$	−1.70075	+	6.34729i	−0.0559204	+	0.208698i
$926$	1.55855	−	1.77637i	0.0512171	−	0.0583751i
$927$	2.67228	−	4.62852i	0.0877691	−	0.152021i
$928$	−27.4462	+	31.2246i	−0.900966	+	1.02500i
$929$	−50.7606	+	13.6013i	−1.66540	+	0.446243i	−0.963865	−	0.266390i	$-0.914169\pi$
$929$	−50.7606	+	13.6013i	−1.66540	+	0.446243i	−0.701537	+	0.712633i	$0.747503\pi$
$930$	13.3181	+	19.9418i	0.436718	+	0.653917i
$931$	−21.2500	−	21.2500i	−0.696442	−	0.696442i
$932$	5.54651	+	42.2787i	0.181682	+	1.38489i
$933$	−47.5179	+	27.4345i	−1.55567	+	0.898165i
$934$	2.30209	+	35.2461i	0.0753266	+	1.15329i
$935$	0.110649			0.00361860
$936$	3.81316	+	13.6158i	0.124637	+	0.445047i
$937$	−36.4769			−1.19165			−0.595824	−	0.803115i	$-0.703175\pi$
$937$	−36.4769			−1.19165			−0.595824	+	0.803115i	$0.703175\pi$
$938$	3.82790	+	58.6070i	0.124985	+	1.91359i
$939$	−45.0706	+	26.0215i	−1.47082	+	0.849181i
$940$	2.50381	+	19.0855i	0.0816653	+	0.622501i
$941$	−15.2238	−	15.2238i	−0.496283	−	0.496283i	0.413996	−	0.910279i	$-0.364133\pi$
$941$	−15.2238	−	15.2238i	−0.496283	−	0.496283i	−0.910279	+	0.413996i	$0.864133\pi$
$942$	−14.4245	−	21.5984i	−0.469974	−	0.703713i
$943$	−1.58672	+	0.425162i	−0.0516709	+	0.0138452i
$944$	−31.1367	+	17.9390i	−1.01341	+	0.583864i
$945$	9.66817	−	16.7458i	0.314506	−	0.544740i
$946$	−3.03461	+	3.45872i	−0.0986636	+	0.112453i
$947$	−4.47717	+	16.7090i	−0.145488	+	0.542970i	0.854245	+	0.519871i	$0.174020\pi$
$947$	−4.47717	+	16.7090i	−0.145488	+	0.542970i	−0.999733	+	0.0230991i	$0.992647\pi$
$948$	22.6156	+	29.5011i	0.734522	+	0.958151i
$949$	27.3437	+	5.10032i	0.887615	+	0.165563i
$950$	−3.44425	−	10.1540i	−0.111746	−	0.329440i
$951$	−69.4414	−	18.6068i	−2.25179	−	0.603365i
$952$	−0.0473410	+	0.714799i	−0.00153433	+	0.0231668i
$953$	13.3736	+	7.72124i	0.433213	+	0.250115i	0.700714	−	0.713442i	$-0.252865\pi$
$953$	13.3736	+	7.72124i	0.433213	+	0.250115i	−0.267502	+	0.963557i	$0.586198\pi$
$954$	−7.73964	−	3.81896i	−0.250580	−	0.123643i
$955$	6.26207	+	23.3704i	0.202636	+	0.756247i
$956$	26.1141	−	34.0005i	0.844590	−	1.09965i
$957$	17.0203	−	17.0203i	0.550190	−	0.550190i
$958$	43.4324	+	8.64953i	1.40324	+	0.279454i
$959$	21.2413	+	36.7910i	0.685917	+	1.18804i
$960$	21.0064	−	2.73634i	0.677979	−	0.0883150i
$961$		−	10.0056i		−	0.322760i
$962$	−9.05594	+	3.87599i	−0.291975	+	0.124967i
$963$			0.407098i			0.0131186i
$964$	−15.3430	−	37.0890i	−0.494164	−	1.19456i
$965$	−6.03293	−	10.4493i	−0.194207	−	0.336376i
$966$	−2.76956	+	13.9069i	−0.0891090	+	0.447448i
$967$	−9.02312	+	9.02312i	−0.290164	+	0.290164i	−0.837145	−	0.546981i	$-0.815777\pi$
$967$	−9.02312	+	9.02312i	−0.290164	+	0.290164i	0.546981	+	0.837145i	$0.315777\pi$
$968$	7.79304	−	22.9061i	0.250478	−	0.736230i
$969$	−0.0676167	−	0.252349i	−0.00217216	−	0.00810661i
$970$	0.360991	−	0.731597i	0.0115907	−	0.0234902i
$971$	−23.2558	−	13.4267i	−0.746314	−	0.430884i	0.0780468	−	0.996950i	$-0.475132\pi$
$971$	−23.2558	−	13.4267i	−0.746314	−	0.430884i	−0.824360	+	0.566065i	$0.808465\pi$
$972$	24.7500	+	10.2650i	0.793857	+	0.329250i
$973$	45.2986	+	12.1377i	1.45221	+	0.389118i
$974$	−22.7923	+	7.73116i	−0.730313	+	0.247722i
$975$	11.0848	−	23.1714i	0.354999	−	0.742079i
$976$	2.09317	−	7.78344i	0.0670007	−	0.249142i
$977$	−8.02121	+	29.9356i	−0.256621	+	0.957724i	0.710560	+	0.703637i	$0.248442\pi$
$977$	−8.02121	+	29.9356i	−0.256621	+	0.957724i	−0.967181	+	0.254087i	$0.918225\pi$
$978$	19.5658	+	17.1666i	0.625646	+	0.548929i
$979$	12.3934	−	21.4660i	0.396094	−	0.686055i
$980$	−33.7988	−	4.46537i	−1.07966	−	0.142641i
$981$	−2.18359	+	0.585090i	−0.0697165	+	0.0186805i
$982$	13.1917	−	8.81008i	0.420965	−	0.281141i
$983$	−15.4374	−	15.4374i	−0.492377	−	0.492377i	0.416677	−	0.909055i	$-0.363195\pi$
$983$	−15.4374	−	15.4374i	−0.492377	−	0.492377i	−0.909055	+	0.416677i	$0.863195\pi$
$984$	8.25333	−	4.06308i	0.263106	−	0.129526i
$985$	1.16903	−	0.674942i	0.0372485	−	0.0215054i
$986$	0.580388	−	0.0379079i	0.0184833	−	0.00120723i
$987$	72.1565			2.29677
$988$	8.77569	−	13.4661i	0.279192	−	0.428413i
$989$	−2.20079			−0.0699811
$990$	−3.86867	+	0.252681i	−0.122955	+	0.00803074i
$991$	11.3554	−	6.55602i	0.360715	−	0.208259i	−0.308679	−	0.951166i	$-0.599887\pi$
$991$	11.3554	−	6.55602i	0.360715	−	0.208259i	0.669394	+	0.742907i	$0.266554\pi$
$992$	−32.4700	−	16.0585i	−1.03092	−	0.509856i
$993$	−28.2543	−	28.2543i	−0.896624	−	0.896624i
$994$	−36.3136	+	24.2520i	−1.15180	+	0.769227i
$995$	13.8327	−	3.70646i	0.438526	−	0.117503i
$996$	5.40146	−	40.8842i	0.171152	−	1.29547i
$997$	−6.93112	+	12.0050i	−0.219511	+	0.380204i	−0.954658	−	0.297703i	$-0.903779\pi$
$997$	−6.93112	+	12.0050i	−0.219511	+	0.380204i	0.735148	+	0.677907i	$0.237113\pi$
$998$	10.3403	+	9.07238i	0.327317	+	0.287181i
$999$	−1.68965	+	6.30585i	−0.0534581	+	0.199508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	52.2.l.b.11.3	yes	16
3.2	odd	2		468.2.cb.f.271.2		16
4.3	odd	2	inner	52.2.l.b.11.2	✓	16
8.3	odd	2		832.2.bu.n.63.1		16
8.5	even	2		832.2.bu.n.63.4		16
12.11	even	2		468.2.cb.f.271.3		16
13.2	odd	12		676.2.f.h.239.4		16
13.3	even	3		676.2.f.h.99.2		16
13.4	even	6		676.2.l.i.319.2		16
13.5	odd	4		676.2.l.m.587.4		16
13.6	odd	12	inner	52.2.l.b.19.2	yes	16
13.7	odd	12		676.2.l.k.19.3		16
13.8	odd	4		676.2.l.i.587.1		16
13.9	even	3		676.2.l.m.319.3		16
13.10	even	6		676.2.f.i.99.7		16
13.11	odd	12		676.2.f.i.239.5		16
13.12	even	2		676.2.l.k.427.2		16
39.32	even	12		468.2.cb.f.19.3		16
52.3	odd	6		676.2.f.h.99.4		16
52.7	even	12		676.2.l.k.19.2		16
52.11	even	12		676.2.f.i.239.7		16
52.15	even	12		676.2.f.h.239.2		16
52.19	even	12	inner	52.2.l.b.19.3	yes	16
52.23	odd	6		676.2.f.i.99.5		16
52.31	even	4		676.2.l.m.587.3		16
52.35	odd	6		676.2.l.m.319.4		16
52.43	odd	6		676.2.l.i.319.1		16
52.47	even	4		676.2.l.i.587.2		16
52.51	odd	2		676.2.l.k.427.3		16
104.19	even	12		832.2.bu.n.383.4		16
104.45	odd	12		832.2.bu.n.383.1		16
156.71	odd	12		468.2.cb.f.19.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.l.b.11.2	✓	16	4.3	odd	2	inner
52.2.l.b.11.3	yes	16	1.1	even	1	trivial
52.2.l.b.19.2	yes	16	13.6	odd	12	inner
52.2.l.b.19.3	yes	16	52.19	even	12	inner
468.2.cb.f.19.2		16	156.71	odd	12
468.2.cb.f.19.3		16	39.32	even	12
468.2.cb.f.271.2		16	3.2	odd	2
468.2.cb.f.271.3		16	12.11	even	2
676.2.f.h.99.2		16	13.3	even	3
676.2.f.h.99.4		16	52.3	odd	6
676.2.f.h.239.2		16	52.15	even	12
676.2.f.h.239.4		16	13.2	odd	12
676.2.f.i.99.5		16	52.23	odd	6
676.2.f.i.99.7		16	13.10	even	6
676.2.f.i.239.5		16	13.11	odd	12
676.2.f.i.239.7		16	52.11	even	12
676.2.l.i.319.1		16	52.43	odd	6
676.2.l.i.319.2		16	13.4	even	6
676.2.l.i.587.1		16	13.8	odd	4
676.2.l.i.587.2		16	52.47	even	4
676.2.l.k.19.2		16	52.7	even	12
676.2.l.k.19.3		16	13.7	odd	12
676.2.l.k.427.2		16	13.12	even	2
676.2.l.k.427.3		16	52.51	odd	2
676.2.l.m.319.3		16	13.9	even	3
676.2.l.m.319.4		16	52.35	odd	6
676.2.l.m.587.3		16	52.31	even	4
676.2.l.m.587.4		16	13.5	odd	4
832.2.bu.n.63.1		16	8.3	odd	2
832.2.bu.n.63.4		16	8.5	even	2
832.2.bu.n.383.1		16	104.45	odd	12
832.2.bu.n.383.4		16	104.19	even	12

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:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	52.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0921725 + 1.41121i) q^{2} +(-1.81380 + 1.04720i) q^{3} +(-1.98301 + 0.260149i) q^{4} +(0.894007 + 0.894007i) q^{5} +(-1.64500 - 2.46313i) q^{6} +(4.37156 - 1.17136i) q^{7} +(-0.549903 - 2.77446i) q^{8} +(0.693255 - 1.20075i) q^{9} +O(q^{10})\)	\(q+(0.0921725 + 1.41121i) q^{2} +(-1.81380 + 1.04720i) q^{3} +(-1.98301 + 0.260149i) q^{4} +(0.894007 + 0.894007i) q^{5} +(-1.64500 - 2.46313i) q^{6} +(4.37156 - 1.17136i) q^{7} +(-0.549903 - 2.77446i) q^{8} +(0.693255 - 1.20075i) q^{9} +(-1.17923 + 1.34403i) q^{10} +(-0.404752 + 1.51056i) q^{11} +(3.32436 - 2.54846i) q^{12} +(-2.03880 - 2.97377i) q^{13} +(2.05596 + 6.06121i) q^{14} +(-2.55776 - 0.685349i) q^{15} +(3.86465 - 1.03176i) q^{16} +(-0.0484649 - 0.0279812i) q^{17} +(1.75841 + 0.867649i) q^{18} +(-0.576896 - 2.15300i) q^{19} +(-2.00540 - 1.54025i) q^{20} +(-6.70250 + 6.70250i) q^{21} +(-2.16901 - 0.431957i) q^{22} +(-0.528908 - 0.916096i) q^{23} +(3.90283 + 4.45646i) q^{24} -3.40150i q^{25} +(4.00868 - 3.15126i) q^{26} -3.37929i q^{27} +(-8.36411 + 3.46006i) q^{28} +(3.67452 + 6.36446i) q^{29} +(0.731414 - 3.67269i) q^{30} +(-4.52800 + 4.52800i) q^{31} +(1.81223 + 5.35871i) q^{32} +(-0.847713 - 3.16371i) q^{33} +(0.0350202 - 0.0709732i) q^{34} +(4.95540 + 2.86100i) q^{35} +(-1.06236 + 2.56145i) q^{36} +(-1.86603 - 0.500000i) q^{37} +(2.98516 - 1.01257i) q^{38} +(6.81211 + 3.25881i) q^{39} +(1.98877 - 2.97200i) q^{40} +(0.401924 - 1.50000i) q^{41} +(-10.0764 - 8.84083i) q^{42} +(1.04025 - 1.80177i) q^{43} +(0.409658 - 3.10074i) q^{44} +(1.69325 - 0.453706i) q^{45} +(1.24405 - 0.830838i) q^{46} +(-5.38281 - 5.38281i) q^{47} +(-5.92925 + 5.91846i) q^{48} +(11.6763 - 6.74130i) q^{49} +(4.80023 - 0.313525i) q^{50} +0.117208 q^{51} +(4.81657 + 5.36662i) q^{52} -4.40150 q^{53} +(4.76888 - 0.311478i) q^{54} +(-1.71230 + 0.988596i) q^{55} +(-5.65381 - 11.4846i) q^{56} +(3.30100 + 3.30100i) q^{57} +(-8.64288 + 5.77214i) q^{58} +(-8.67757 + 2.32515i) q^{59} +(5.25034 + 0.693654i) q^{60} +(1.00750 - 1.74504i) q^{61} +(-6.80730 - 5.97259i) q^{62} +(1.62410 - 6.06121i) q^{63} +(-7.39521 + 3.05136i) q^{64} +(0.835873 - 4.48127i) q^{65} +(4.38651 - 1.48790i) q^{66} +(8.86360 + 2.37500i) q^{67} +(0.103386 + 0.0428789i) q^{68} +(1.91867 + 1.10774i) q^{69} +(-3.58071 + 7.25680i) q^{70} +(1.76582 + 6.59011i) q^{71} +(-3.71266 - 1.26311i) q^{72} +(-5.45504 + 5.45504i) q^{73} +(0.533607 - 2.67943i) q^{74} +(3.56205 + 6.16966i) q^{75} +(1.70409 + 4.11935i) q^{76} +7.07759i q^{77} +(-3.97096 + 9.91366i) q^{78} +8.87422i q^{79} +(4.37741 + 2.53262i) q^{80} +(5.61856 + 9.73163i) q^{81} +(2.15386 + 0.428939i) q^{82} +(6.96160 - 6.96160i) q^{83} +(11.5475 - 15.0348i) q^{84} +(-0.0183126 - 0.0683434i) q^{85} +(2.63855 + 1.30194i) q^{86} +(-13.3297 - 7.69592i) q^{87} +(4.41355 + 0.292308i) q^{88} +(-15.3098 - 4.10226i) q^{89} +(0.796345 + 2.34771i) q^{90} +(-12.3961 - 10.6119i) q^{91} +(1.28715 + 1.67903i) q^{92} +(3.47118 - 12.9546i) q^{93} +(7.10010 - 8.09240i) q^{94} +(1.40905 - 2.44055i) q^{95} +(-8.89868 - 7.82188i) q^{96} +(-0.440720 + 0.118091i) q^{97} +(10.5896 + 15.8563i) q^{98} +(1.53321 + 1.53321i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 6 q^{4} - 12 q^{5} - 14 q^{6} + 10 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 - 6 * q^4 - 12 * q^5 - 14 * q^6 + 10 * q^8 + 4 * q^9	\( 16 q - 2 q^{2} - 6 q^{4} - 12 q^{5} - 14 q^{6} + 10 q^{8} + 4 q^{9} - 12 q^{13} + 8 q^{14} - 2 q^{16} + 12 q^{17} - 6 q^{18} + 2 q^{20} - 28 q^{21} + 10 q^{24} + 16 q^{26} + 12 q^{28} - 8 q^{29} + 42 q^{30} + 28 q^{32} - 20 q^{33} + 14 q^{34} - 6 q^{36} - 16 q^{37} - 40 q^{40} + 48 q^{41} - 28 q^{42} - 8 q^{44} + 20 q^{45} - 46 q^{46} - 10 q^{48} + 60 q^{49} + 10 q^{50} - 32 q^{52} - 32 q^{53} - 16 q^{54} - 60 q^{56} + 12 q^{57} - 48 q^{58} - 24 q^{60} + 4 q^{61} - 18 q^{62} - 8 q^{65} + 56 q^{66} + 16 q^{68} - 12 q^{69} + 28 q^{70} + 56 q^{72} + 20 q^{73} + 4 q^{74} + 22 q^{76} + 68 q^{78} + 44 q^{80} + 48 q^{81} + 84 q^{84} + 20 q^{85} + 16 q^{86} + 36 q^{88} - 52 q^{89} - 12 q^{92} - 92 q^{93} - 38 q^{94} - 72 q^{96} - 28 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 6 * q^4 - 12 * q^5 - 14 * q^6 + 10 * q^8 + 4 * q^9 - 12 * q^13 + 8 * q^14 - 2 * q^16 + 12 * q^17 - 6 * q^18 + 2 * q^20 - 28 * q^21 + 10 * q^24 + 16 * q^26 + 12 * q^28 - 8 * q^29 + 42 * q^30 + 28 * q^32 - 20 * q^33 + 14 * q^34 - 6 * q^36 - 16 * q^37 - 40 * q^40 + 48 * q^41 - 28 * q^42 - 8 * q^44 + 20 * q^45 - 46 * q^46 - 10 * q^48 + 60 * q^49 + 10 * q^50 - 32 * q^52 - 32 * q^53 - 16 * q^54 - 60 * q^56 + 12 * q^57 - 48 * q^58 - 24 * q^60 + 4 * q^61 - 18 * q^62 - 8 * q^65 + 56 * q^66 + 16 * q^68 - 12 * q^69 + 28 * q^70 + 56 * q^72 + 20 * q^73 + 4 * q^74 + 22 * q^76 + 68 * q^78 + 44 * q^80 + 48 * q^81 + 84 * q^84 + 20 * q^85 + 16 * q^86 + 36 * q^88 - 52 * q^89 - 12 * q^92 - 92 * q^93 - 38 * q^94 - 72 * q^96 - 28 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

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