LMFDB - Embedded newform 52.2.l.b.19.2

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			19.2
Root			$1.41121 + 0.0921725i$ of defining polynomial
Character	$\chi$	$=$	52.19
Dual form			52.2.l.b.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.785427 - 1.17605i) q^{2} +(1.81380 + 1.04720i) q^{3} +(-0.766209 + 1.84741i) q^{4} +(0.894007 - 0.894007i) q^{5} +(-0.193046 - 2.95563i) q^{6} +(-4.37156 - 1.17136i) q^{7} +(2.77446 - 0.549903i) q^{8} +(0.693255 + 1.20075i) q^{9} +O(q^{10})$	\(q+(-0.785427 - 1.17605i) q^{2} +(1.81380 + 1.04720i) q^{3} +(-0.766209 + 1.84741i) q^{4} +(0.894007 - 0.894007i) q^{5} +(-0.193046 - 2.95563i) q^{6} +(-4.37156 - 1.17136i) q^{7} +(2.77446 - 0.549903i) q^{8} +(0.693255 + 1.20075i) q^{9} +(-1.75358 - 0.349224i) 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} +(-2.82585 - 2.83100i) q^{16} +(-0.0484649 + 0.0279812i) q^{17} +(0.867649 - 1.75841i) q^{18} +(0.576896 - 2.15300i) q^{19} +(0.966601 + 2.33659i) q^{20} +(-6.70250 - 6.70250i) q^{21} +(1.45859 - 1.66244i) q^{22} +(0.528908 - 0.916096i) q^{23} +(5.60818 + 1.90799i) q^{24} +3.40150i q^{25} +(5.09864 + 0.0620559i) q^{26} -3.37929i q^{27} +(5.51350 - 7.17856i) q^{28} +(3.67452 - 6.36446i) q^{29} +(-2.81494 - 2.46977i) q^{30} +(4.52800 + 4.52800i) q^{31} +(-1.10992 + 5.54690i) q^{32} +(-0.847713 + 3.16371i) q^{33} +(0.0709732 + 0.0350202i) q^{34} +(-4.95540 + 2.86100i) q^{35} +(-2.74946 + 0.360699i) 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} +(-2.61818 + 13.1468i) q^{42} +(-1.04025 - 1.80177i) q^{43} +(-3.10074 - 0.409658i) q^{44} +(1.69325 + 0.453706i) q^{45} +(-1.49280 + 0.0975016i) q^{46} +(5.38281 - 5.38281i) q^{47} +(-2.16091 - 8.09411i) q^{48} +(11.6763 + 6.74130i) q^{49} +(4.00035 - 2.67163i) q^{50} -0.117208 q^{51} +(-3.93163 - 6.04502i) q^{52} -4.40150 q^{53} +(-3.97423 + 2.65419i) q^{54} +(1.71230 + 0.988596i) q^{55} +(-12.7728 - 0.845942i) q^{56} +(3.30100 - 3.30100i) q^{57} +(-10.3710 + 0.677380i) q^{58} +(8.67757 + 2.32515i) q^{59} +(-0.693654 + 5.25034i) q^{60} +(1.00750 + 1.74504i) q^{61} +(1.76876 - 8.88159i) 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} +(-0.0145586 - 0.110974i) q^{68} +(1.91867 - 1.10774i) q^{69} +(7.25680 + 3.58071i) q^{70} +(-1.76582 + 6.59011i) q^{71} +(2.58370 + 2.95021i) q^{72} +(-5.45504 - 5.45504i) q^{73} +(2.05365 + 1.80183i) q^{74} +(-3.56205 + 6.16966i) q^{75} +(3.53546 + 2.71541i) q^{76} -7.07759i q^{77} +(9.18295 + 5.45185i) q^{78} +8.87422i q^{79} +(-5.05726 - 0.00460805i) q^{80} +(5.61856 - 9.73163i) q^{81} +(1.44840 - 1.65082i) q^{82} +(-6.96160 - 6.96160i) q^{83} +(17.5178 - 7.24676i) q^{84} +(-0.0183126 + 0.0683434i) q^{85} +(-1.30194 + 2.63855i) q^{86} +(13.3297 - 7.69592i) q^{87} +(1.95363 + 3.96840i) 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} +(-10.5583 - 2.10267i) q^{94} +(-1.40905 - 2.44055i) q^{95} +(-7.82188 + 8.89868i) q^{96} +(-0.440720 - 0.118091i) q^{97} +(-1.24273 - 19.0267i) 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 $\left(\mathbb{Z}/52\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.785427	−	1.17605i	−0.555381	−	0.831596i
$2$	−0.785427	−	1.17605i	−0.555381	−	0.831596i
$3$	1.81380	+	1.04720i	1.04720	+	0.604601i	0.921864	−	0.387513i	$-0.126666\pi$
$3$	1.81380	+	1.04720i	1.04720	+	0.604601i	0.125336	+	0.992114i	$0.459999\pi$
$4$	−0.766209	+	1.84741i	−0.383104	+	0.923705i
$5$	0.894007	−	0.894007i	0.399812	−	0.399812i	−0.478355	−	0.878167i	$-0.658767\pi$
$5$	0.894007	−	0.894007i	0.399812	−	0.399812i	0.878167	+	0.478355i	$0.158767\pi$
$6$	−0.193046	−	2.95563i	−0.0788107	−	1.20663i
$7$	−4.37156	−	1.17136i	−1.65229	−	0.442731i	−0.692040	−	0.721859i	$-0.743288\pi$
$7$	−4.37156	−	1.17136i	−1.65229	−	0.442731i	−0.960254	+	0.279128i	$0.909955\pi$
$8$	2.77446	−	0.549903i	0.980918	−	0.194420i
$9$	0.693255	+	1.20075i	0.231085	+	0.400251i
$10$	−1.75358	−	0.349224i	−0.554530	−	0.110434i
$11$	0.404752	+	1.51056i	0.122037	+	0.455450i	0.999717	−	0.0237985i	$-0.00757602\pi$
$11$	0.404752	+	1.51056i	0.122037	+	0.455450i	−0.877679	+	0.479248i	$0.840909\pi$
$12$	−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
$16$	−2.82585	−	2.83100i	−0.706462	−	0.707751i
$17$	−0.0484649	+	0.0279812i	−0.0117545	+	0.00678645i	−0.505866	−	0.862612i	$-0.668827\pi$
$17$	−0.0484649	+	0.0279812i	−0.0117545	+	0.00678645i	0.494111	+	0.869399i	$0.335494\pi$
$18$	0.867649	−	1.75841i	0.204507	−	0.414461i
$19$	0.576896	−	2.15300i	0.132349	−	0.493933i	−0.867646	−	0.497183i	$-0.834368\pi$
$19$	0.576896	−	2.15300i	0.132349	−	0.493933i	0.999995	+	0.00324996i	$0.00103450\pi$
$20$	0.966601	+	2.33659i	0.216139	+	0.522478i
$21$	−6.70250	−	6.70250i	−1.46261	−	1.46261i
$22$	1.45859	−	1.66244i	0.310973	−	0.354434i
$23$	0.528908	−	0.916096i	0.110285	−	0.191019i	−0.805600	−	0.592460i	$-0.798157\pi$
$23$	0.528908	−	0.916096i	0.110285	−	0.191019i	0.915885	+	0.401440i	$0.131490\pi$
$24$	5.60818	+	1.90799i	1.14476	+	0.389468i
$25$			3.40150i			0.680301i
$26$	5.09864	+	0.0620559i	0.999926	+	0.0121702i
$27$		−	3.37929i		−	0.650346i
$28$	5.51350	−	7.17856i	1.04195	−	1.35662i
$29$	3.67452	−	6.36446i	0.682342	−	1.18185i	−0.291923	−	0.956442i	$-0.594295\pi$
$29$	3.67452	−	6.36446i	0.682342	−	1.18185i	0.974264	−	0.225409i	$-0.0723717\pi$
$30$	−2.81494	−	2.46977i	−0.513935	−	0.450916i
$31$	4.52800	+	4.52800i	0.813253	+	0.813253i	0.985120	−	0.171867i	$-0.0549801\pi$
$31$	4.52800	+	4.52800i	0.813253	+	0.813253i	−0.171867	+	0.985120i	$0.554980\pi$
$32$	−1.10992	+	5.54690i	−0.196207	+	0.980562i
$33$	−0.847713	+	3.16371i	−0.147568	+	0.550731i
$34$	0.0709732	+	0.0350202i	0.0121718	+	0.00600591i
$35$	−4.95540	+	2.86100i	−0.837616	+	0.483598i
$36$	−2.74946	+	0.360699i	−0.458243	+	0.0601165i
$37$	−1.86603	+	0.500000i	−0.306773	+	0.0821995i	−0.408921	−	0.912570i	$-0.634095\pi$
$37$	−1.86603	+	0.500000i	−0.306773	+	0.0821995i	0.102149	+	0.994769i	$0.467428\pi$
$38$	−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	0.990183	−	0.139779i	$-0.0446391\pi$
$41$	0.401924	+	1.50000i	0.0627700	+	0.234261i	−0.927413	+	0.374039i	$0.877972\pi$
$42$	−2.61818	+	13.1468i	−0.403994	+	2.02860i
$43$	−1.04025	−	1.80177i	−0.158637	−	0.274767i	0.775740	−	0.631052i	$-0.217377\pi$
$43$	−1.04025	−	1.80177i	−0.158637	−	0.274767i	−0.934377	+	0.356285i	$0.884043\pi$
$44$	−3.10074	−	0.409658i	−0.467454	−	0.0617582i
$45$	1.69325	+	0.453706i	0.252415	+	0.0676345i
$46$	−1.49280	+	0.0975016i	−0.220101	+	0.0143758i
$47$	5.38281	−	5.38281i	0.785163	−	0.785163i	−0.195534	−	0.980697i	$-0.562644\pi$
$47$	5.38281	−	5.38281i	0.785163	−	0.785163i	0.980697	+	0.195534i	$0.0626440\pi$
$48$	−2.16091	−	8.09411i	−0.311900	−	1.16828i
$49$	11.6763	+	6.74130i	1.66804	+	0.963043i
$50$	4.00035	−	2.67163i	0.565736	−	0.377826i
$51$	−0.117208			−0.0164124
$52$	−3.93163	−	6.04502i	−0.545219	−	0.838294i
$53$	−4.40150			−0.604593			−0.302297	−	0.953214i	$-0.597753\pi$
$53$	−4.40150			−0.604593			−0.302297	+	0.953214i	$0.597753\pi$
$54$	−3.97423	+	2.65419i	−0.540825	+	0.361189i
$55$	1.71230	+	0.988596i	0.230886	+	0.133302i
$56$	−12.7728	−	0.845942i	−1.70684	−	0.113044i
$57$	3.30100	−	3.30100i	0.437228	−	0.437228i
$58$	−10.3710	+	0.677380i	−1.36178	+	0.0889444i
$59$	8.67757	+	2.32515i	1.12972	+	0.302708i	0.774812	−	0.632192i	$-0.217845\pi$
$59$	8.67757	+	2.32515i	1.12972	+	0.302708i	0.354911	+	0.934900i	$0.384511\pi$
$60$	−0.693654	+	5.25034i	−0.0895504	+	0.677816i
$61$	1.00750	+	1.74504i	0.128997	+	0.223429i	0.923288	−	0.384108i	$-0.125491\pi$
$61$	1.00750	+	1.74504i	0.128997	+	0.223429i	−0.794291	+	0.607537i	$0.792158\pi$
$62$	1.76876	−	8.88159i	0.224633	−	1.12796i
$63$	−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	$-0.772736\pi$
$67$	−8.86360	+	2.37500i	−1.08286	+	0.290152i	−0.327094	+	0.944992i	$0.606069\pi$
$68$	−0.0145586	−	0.110974i	−0.00176549	−	0.0134576i
$69$	1.91867	−	1.10774i	0.230981	−	0.133357i
$70$	7.25680	+	3.58071i	0.867354	+	0.427977i
$71$	−1.76582	+	6.59011i	−0.209564	+	0.782103i	0.778446	+	0.627712i	$0.216008\pi$
$71$	−1.76582	+	6.59011i	−0.209564	+	0.782103i	−0.988010	+	0.154391i	$0.950658\pi$
$72$	2.58370	+	2.95021i	0.304492	+	0.347686i
$73$	−5.45504	−	5.45504i	−0.638464	−	0.638464i	0.311713	−	0.950176i	$-0.399097\pi$
$73$	−5.45504	−	5.45504i	−0.638464	−	0.638464i	−0.950176	+	0.311713i	$0.899097\pi$
$74$	2.05365	+	1.80183i	0.238732	+	0.209459i
$75$	−3.56205	+	6.16966i	−0.411311	+	0.712411i
$76$	3.53546	+	2.71541i	0.405545	+	0.311479i
$77$		−	7.07759i		−	0.806567i
$78$	9.18295	+	5.45185i	1.03976	+	0.617301i
$79$			8.87422i			0.998428i	0.866479	+	0.499214i	$0.166378\pi$
$79$			8.87422i			0.998428i	−0.866479	+	0.499214i	$0.833622\pi$
$80$	−5.05726	−	0.00460805i	−0.565419	−	0.000515196i
$81$	5.61856	−	9.73163i	0.624284	−	1.08129i
$82$	1.44840	−	1.65082i	0.159949	−	0.182303i
$83$	−6.96160	−	6.96160i	−0.764135	−	0.764135i	0.212932	−	0.977067i	$-0.431699\pi$
$83$	−6.96160	−	6.96160i	−0.764135	−	0.764135i	−0.977067	+	0.212932i	$0.931699\pi$
$84$	17.5178	−	7.24676i	1.91135	−	0.790686i
$85$	−0.0183126	+	0.0683434i	−0.00198628	+	0.00741288i
$86$	−1.30194	+	2.63855i	−0.140391	+	0.284522i
$87$	13.3297	−	7.69592i	1.42910	−	0.825089i
$88$	1.95363	+	3.96840i	0.208257	+	0.423032i
$89$	−15.3098	+	4.10226i	−1.62284	+	0.434838i	−0.951834	−	0.306615i	$-0.900804\pi$
$89$	−15.3098	+	4.10226i	−1.62284	+	0.434838i	−0.671005	+	0.741453i	$0.734137\pi$
$90$	−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
$94$	−10.5583	−	2.10267i	−1.08900	−	0.216874i
$95$	−1.40905	−	2.44055i	−0.144566	−	0.250395i
$96$	−7.82188	+	8.89868i	−0.798317	+	0.908218i
$97$	−0.440720	−	0.118091i	−0.0447483	−	0.0119903i	0.236375	−	0.971662i	$-0.424040\pi$
$97$	−0.440720	−	0.118091i	−0.0447483	−	0.0119903i	−0.281124	+	0.959672i	$0.590707\pi$
$98$	−1.24273	−	19.0267i	−0.125534	−	1.92199i
$99$	−1.53321	+	1.53321i	−0.154093	+	0.154093i
$100$	−6.28397	−	2.60626i	−0.628397	−	0.260626i
$101$	−9.58352	−	5.53305i	−0.953596	−	0.550559i	−0.0594000	−	0.998234i	$-0.518919\pi$
$101$	−9.58352	−	5.53305i	−0.953596	−	0.550559i	−0.894196	+	0.447675i	$0.852252\pi$
$102$	0.0920582	+	0.137843i	0.00911512	+	0.0136485i
$103$	−3.85469			−0.379813			−0.189907	−	0.981802i	$-0.560819\pi$
$103$	−3.85469			−0.379813			−0.189907	+	0.981802i	$0.560819\pi$
$104$	−4.02127	+	9.37174i	−0.394318	+	0.918974i
$105$	−11.9842			−1.16953
$106$	3.45706	+	5.17641i	0.335779	+	0.502777i
$107$	0.254277	+	0.146807i	0.0245819	+	0.0141924i	0.512241	−	0.858842i	$-0.328816\pi$
$107$	0.254277	+	0.146807i	0.0245819	+	0.0141924i	−0.487659	+	0.873034i	$0.662149\pi$
$108$	6.24294	+	2.58924i	0.600727	+	0.249150i
$109$	−1.15289	+	1.15289i	−0.110427	+	0.110427i	−0.760161	−	0.649734i	$-0.774880\pi$
$109$	−1.15289	+	1.15289i	−0.110427	+	0.110427i	0.649734	+	0.760161i	$0.274880\pi$
$110$	−0.182243	−	2.79023i	−0.0173762	−	0.266038i
$111$	−3.90820	−	1.04720i	−0.370950	−	0.0993958i
$112$	9.03725	+	15.6860i	0.853940	+	1.48218i
$113$	4.56853	+	7.91292i	0.429771	+	0.744385i	0.996853	−	0.0792763i	$-0.0252609\pi$
$113$	4.56853	+	7.91292i	0.429771	+	0.744385i	−0.567082	+	0.823662i	$0.691928\pi$
$114$	−6.47485	−	1.28946i	−0.606425	−	0.120769i
$115$	−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
$120$	6.71951	−	3.30799i	0.613404	−	0.301976i
$121$	7.40832	−	4.27720i	0.673484	−	0.388836i
$122$	1.26094	−	2.55547i	0.114160	−	0.231362i
$123$	−0.841789	+	3.14160i	−0.0759016	+	0.283268i
$124$	−11.8345	+	4.89568i	−1.06277	+	0.439645i
$125$	7.51100	+	7.51100i	0.671804	+	0.671804i
$126$	−5.85270	+	6.67066i	−0.521400	+	0.594270i
$127$	−4.71771	+	8.17131i	−0.418629	+	0.725086i	−0.995802	−	0.0915355i	$-0.970822\pi$
$127$	−4.71771	+	8.17131i	−0.418629	+	0.725086i	0.577173	+	0.816622i	$0.304156\pi$
$128$	−9.39697	−	6.30055i	−0.830583	−	0.556895i
$129$		−	4.35741i		−	0.383648i
$130$	4.61370	−	4.50274i	0.404648	−	0.394917i
$131$		−	9.03673i		−	0.789543i	−0.918779	−	0.394771i	$-0.870824\pi$
$131$		−	9.03673i		−	0.789543i	0.918779	−	0.394771i	$-0.129176\pi$
$132$	−5.19514	−	3.99013i	−0.452179	−	0.347297i
$133$	−5.04387	+	8.73623i	−0.437359	+	0.757527i
$134$	9.75484	+	8.55870i	0.842690	+	0.739359i
$135$	−3.02111	−	3.02111i	−0.260016	−	0.260016i
$136$	−0.119077	+	0.104284i	−0.0102108	+	0.00894226i
$137$	2.42949	−	9.06696i	0.207565	−	0.774643i	−0.781087	−	0.624422i	$-0.785335\pi$
$137$	2.42949	−	9.06696i	0.207565	−	0.774643i	0.988652	−	0.150221i	$-0.0479986\pi$
$138$	−2.80974	−	1.38641i	−0.239181	−	0.118019i
$139$	−8.97386	+	5.18106i	−0.761153	+	0.439452i	−0.829710	−	0.558195i	$-0.811494\pi$
$139$	−8.97386	+	5.18106i	−0.761153	+	0.439452i	0.0685564	+	0.997647i	$0.478161\pi$
$140$	−1.48857	−	11.3468i	−0.125807	−	0.958978i
$141$	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
$146$	−2.13089	+	10.7000i	−0.176354	+	0.885535i
$147$	14.1190	+	24.4548i	1.16451	+	2.01700i
$148$	0.506060	−	3.83042i	0.0415978	−	0.314858i
$149$	10.0965	+	2.70535i	0.827138	+	0.221631i	0.647465	−	0.762095i	$-0.275829\pi$
$149$	10.0965	+	2.70535i	0.827138	+	0.221631i	0.179673	+	0.983726i	$0.442496\pi$
$150$	10.0536	−	0.656647i	0.820872	−	0.0536150i
$151$	3.84960	−	3.84960i	0.313276	−	0.313276i	−0.532901	−	0.846177i	$-0.678898\pi$
$151$	3.84960	−	3.84960i	0.313276	−	0.313276i	0.846177	+	0.532901i	$0.178898\pi$
$152$	0.416629	−	6.29065i	0.0337930	−	0.510239i
$153$	−0.0671971	−	0.0387963i	−0.00543256	−	0.00313649i
$154$	−8.32363	+	5.55893i	−0.670738	+	0.447952i
$155$	8.09612			0.650296
$156$	−0.800859	−	15.0817i	−0.0641200	−	1.20750i
$157$	8.76868			0.699817			0.349908	−	0.936784i	$-0.386213\pi$
$157$	8.76868			0.699817			0.349908	+	0.936784i	$0.386213\pi$
$158$	10.4366	−	6.97005i	0.830289	−	0.554508i
$159$	−7.98346	−	4.60925i	−0.633130	−	0.365538i
$160$	3.96669	+	5.95124i	0.313595	+	0.470487i
$161$	−3.38523	+	3.38523i	−0.266793	+	0.266793i
$162$	−15.8579	+	1.03575i	−1.24591	+	0.0813765i
$163$	8.48845	+	2.27447i	0.664867	+	0.178151i	0.575441	−	0.817843i	$-0.304830\pi$
$163$	8.48845	+	2.27447i	0.664867	+	0.178151i	0.0894254	+	0.995994i	$0.471497\pi$
$164$	−3.07907	−	0.406795i	−0.240435	−	0.0317653i
$165$	2.07051	+	3.58624i	0.161189	+	0.279188i
$166$	−2.71939	+	13.6550i	−0.211066	+	1.05984i
$167$	2.25084	+	8.40025i	0.174175	+	0.650031i	0.996691	+	0.0812880i	$0.0259033\pi$
$167$	2.25084	+	8.40025i	0.174175	+	0.650031i	−0.822515	+	0.568743i	$0.807430\pi$
$168$	−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
$172$	4.12566	−	0.541241i	0.314578	−	0.0412692i
$173$	5.44621	−	3.14437i	0.414068	−	0.239062i	−0.278468	−	0.960445i	$-0.589827\pi$
$173$	5.44621	−	3.14437i	0.414068	−	0.239062i	0.692536	+	0.721383i	$0.256493\pi$
$174$	−19.5203	−	9.63190i	−1.47983	−	0.730192i
$175$	3.98437	−	14.8699i	0.301190	−	1.12406i
$176$	3.13262	−	5.41446i	0.236130	−	0.408130i
$177$	13.3045	+	13.3045i	1.00003	+	1.00003i
$178$	16.8492	+	14.7832i	1.26290	+	1.10805i
$179$	12.0998	−	20.9574i	0.904379	−	1.56643i	0.0826294	−	0.996580i	$-0.473668\pi$
$179$	12.0998	−	20.9574i	0.904379	−	1.56643i	0.821749	−	0.569849i	$-0.192998\pi$
$180$	−2.13557	+	2.78050i	−0.159176	+	0.207246i
$181$		−	5.03261i		−	0.374071i	−0.982353	−	0.187035i	$-0.940112\pi$
$181$		−	5.03261i		−	0.374071i	0.982353	−	0.187035i	$-0.0598879\pi$
$182$	−22.2163	−	6.24360i	−1.64678	−	0.462807i
$183$			4.22020i			0.311967i
$184$	0.963669	−	2.83252i	0.0710426	−	0.208816i
$185$	−1.22124	+	2.11524i	−0.0897870	+	0.155516i
$186$	12.5090	−	14.2572i	0.917203	−	1.04539i
$187$	−0.0618835	−	0.0618835i	−0.00452537	−	0.00452537i
$188$	5.81990	+	14.0686i	0.424460	+	1.02606i
$189$	−3.95836	+	14.7728i	−0.287928	+	1.07456i
$190$	−1.76351	+	3.57399i	−0.127939	+	0.259285i
$191$	−16.5728	+	9.56832i	−1.19917	+	0.692340i	−0.960370	−	0.278730i	$-0.910087\pi$
$191$	−16.5728	+	9.56832i	−1.19917	+	0.692340i	−0.238798	+	0.971069i	$0.576753\pi$
$192$	16.6088	+	2.20969i	1.19864	+	0.159471i
$193$	−9.21820	+	2.47001i	−0.663541	+	0.177795i	−0.574843	−	0.818263i	$-0.694937\pi$
$193$	−9.21820	+	2.47001i	−0.663541	+	0.177795i	−0.0886973	+	0.996059i	$0.528270\pi$
$194$	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	0.975071	−	0.221893i	$-0.0712237\pi$
$197$	0.276336	+	1.03130i	0.0196881	+	0.0734770i	−0.955383	+	0.295370i	$0.904557\pi$
$198$	3.00736	+	0.598913i	0.213724	+	0.0425629i
$199$	−5.66340	−	9.80930i	−0.401468	−	0.695363i	0.592435	−	0.805618i	$-0.298167\pi$
$199$	−5.66340	−	9.80930i	−0.401468	−	0.695363i	−0.993903	+	0.110255i	$0.964833\pi$
$200$	1.87050	+	9.43732i	0.132264	+	0.667320i
$201$	−18.5639	−	4.97419i	−1.30940	−	0.350852i
$202$	1.01999	+	15.6166i	0.0717663	+	1.09878i
$203$	−23.5184	+	23.5184i	−1.65067	+	1.65067i
$204$	0.0898056	−	0.216531i	0.00628765	−	0.0151602i
$205$	1.70033	+	0.981687i	0.118756	+	0.0685640i
$206$	3.02757	+	4.53332i	0.210941	+	0.315851i
$207$	1.46667			0.101941
$208$	14.1801	−	2.63159i	0.983212	−	0.182468i
$209$	3.48573			0.241113
$210$	9.41269	+	14.0940i	0.649537	+	0.972581i
$211$	−4.65089	−	2.68519i	−0.320180	−	0.184856i	0.331293	−	0.943528i	$-0.392515\pi$
$211$	−4.65089	−	2.68519i	−0.320180	−	0.184856i	−0.651473	+	0.758672i	$0.725849\pi$
$212$	3.37247	−	8.13138i	0.231622	−	0.558466i
$213$	−10.1040	+	10.1040i	−0.692315	+	0.692315i
$214$	−0.0270631	−	0.414350i	−0.00185000	−	0.0283244i
$215$	−2.54079	−	0.680801i	−0.173280	−	0.0464303i
$216$	−1.85828	−	9.37570i	−0.126440	−	0.637936i
$217$	−14.4905	−	25.0983i	−0.983680	−	1.70378i
$218$	2.26138	+	0.450351i	0.153160	+	0.0305016i
$219$	−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	$-0.453848\pi$
$223$	11.4144	−	3.05848i	0.764366	−	0.204811i	0.619881	+	0.784696i	$0.287181\pi$
$224$	11.3495	−	22.9485i	0.758317	−	1.53331i
$225$	−4.08436	+	2.35811i	−0.272291	+	0.157207i
$226$	5.71778	−	11.5879i	0.380341	−	0.770813i
$227$	0.454601	−	1.69660i	0.0301730	−	0.112607i	−0.949197	−	0.314682i	$-0.898102\pi$
$227$	0.454601	−	1.69660i	0.0301730	−	0.112607i	0.979370	+	0.202075i	$0.0647686\pi$
$228$	3.56905	+	8.62755i	0.236366	+	0.571374i
$229$	−7.04097	−	7.04097i	−0.465280	−	0.465280i	0.435101	−	0.900382i	$-0.356713\pi$
$229$	−7.04097	−	7.04097i	−0.465280	−	0.465280i	−0.900382	+	0.435101i	$0.856713\pi$
$230$	−1.24740	+	1.42174i	−0.0822514	+	0.0937466i
$231$	7.41165	−	12.8374i	0.487651	−	0.844636i
$232$	6.69497	−	19.6785i	0.439546	−	1.29196i
$233$			21.3205i			1.39675i	0.715731	+	0.698376i	$0.246094\pi$
$233$			21.3205i			1.39675i	−0.715731	+	0.698376i	$0.753906\pi$
$234$	3.46014	+	6.16523i	0.226197	+	0.403033i
$235$		−	9.62453i		−	0.627835i
$236$	−10.9443	+	14.2495i	−0.712415	+	0.927562i
$237$	−9.29308	+	16.0961i	−0.603651	+	1.04555i
$238$	−0.269242	−	0.236228i	−0.0174524	−	0.0153124i
$239$	15.1574	+	15.1574i	0.980452	+	0.980452i	0.999813	−	0.0193606i	$-0.00616305\pi$
$239$	15.1574	+	15.1574i	0.980452	+	0.980452i	−0.0193606	+	0.999813i	$0.506163\pi$
$240$	−9.16805	−	5.30432i	−0.591795	−	0.342393i
$241$	5.19414	−	19.3848i	0.334584	−	1.24869i	−0.569735	−	0.821828i	$-0.692954\pi$
$241$	5.19414	−	19.3848i	0.334584	−	1.24869i	0.904319	−	0.426857i	$-0.140379\pi$
$242$	−10.8489	−	5.35317i	−0.697395	−	0.344115i
$243$	11.6023	−	6.69857i	0.744285	−	0.429713i
$244$	−3.99575	+	0.524199i	−0.255802	+	0.0335584i
$245$	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
$250$	2.93400	−	14.7327i	0.185563	−	0.931777i
$251$	−7.30873	−	12.6591i	−0.461323	−	0.799035i	0.537704	−	0.843134i	$-0.319292\pi$
$251$	−7.30873	−	12.6591i	−0.461323	−	0.799035i	−0.999027	+	0.0440987i	$0.985958\pi$
$252$	12.4419	+	1.64378i	0.783768	+	0.103548i
$253$	1.59789	+	0.428153i	0.100459	+	0.0269178i
$254$	13.3153	−	0.869686i	0.835477	−	0.0545690i
$255$	−0.104785	+	0.104785i	−0.00656186	+	0.00656186i
$256$	−0.0291576	+	16.0000i	−0.00182235	+	0.999998i
$257$	−12.1456	−	7.01228i	−0.757624	−	0.437414i	0.0708183	−	0.997489i	$-0.477439\pi$
$257$	−12.1456	−	7.01228i	−0.757624	−	0.437414i	−0.828442	+	0.560075i	$0.810772\pi$
$258$	−5.12455	+	3.42242i	−0.319040	+	0.213071i
$259$	8.74312			0.543271
$260$	−8.91919	−	1.88939i	−0.553145	−	0.117175i
$261$	10.1895			0.630715
$262$	−10.6277	+	7.09769i	−0.656581	+	0.438497i
$263$	25.6857	+	14.8297i	1.58385	+	0.914436i	0.994290	+	0.106711i	$0.0340320\pi$
$263$	25.6857	+	14.8297i	1.58385	+	0.914436i	0.589560	+	0.807725i	$0.299301\pi$
$264$	−0.612210	+	9.24373i	−0.0376789	+	0.568912i
$265$	−3.93497	+	3.93497i	−0.241724	+	0.241724i
$266$	14.2359	−	0.929812i	0.872857	−	0.0570104i
$267$	−32.0649	−	8.59176i	−1.96234	−	0.525807i
$268$	2.40378	−	18.1945i	0.146834	−	1.11140i
$269$	−0.890973	−	1.54321i	−0.0543236	−	0.0940912i	0.837585	−	0.546307i	$-0.183967\pi$
$269$	−0.890973	−	1.54321i	−0.0543236	−	0.0940912i	−0.891908	+	0.452216i	$0.850634\pi$
$270$	−1.18013	+	5.92586i	−0.0718204	+	0.360636i
$271$	5.43955	+	20.3007i	0.330429	+	1.23318i	0.908740	+	0.417362i	$0.137045\pi$
$271$	5.43955	+	20.3007i	0.330429	+	1.23318i	−0.578311	+	0.815816i	$0.696288\pi$
$272$	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
$276$	0.576357	+	4.39333i	0.0346926	+	0.264448i
$277$	−13.5377	+	7.81599i	−0.813402	+	0.469618i	−0.848136	−	0.529779i	$-0.822275\pi$
$277$	−13.5377	+	7.81599i	−0.813402	+	0.469618i	0.0347342	+	0.999397i	$0.488942\pi$
$278$	13.1415	+	6.48441i	0.788177	+	0.388909i
$279$	−2.29795	+	8.57606i	−0.137575	+	0.513435i
$280$	−12.1753	+	10.6627i	−0.727612	+	0.637219i
$281$	17.0835	+	17.0835i	1.01912	+	1.01912i	0.999814	+	0.0193039i	$0.00614502\pi$
$281$	17.0835	+	17.0835i	1.01912	+	1.01912i	0.0193039	+	0.999814i	$0.493855\pi$
$282$	−16.9487	−	14.8705i	−1.00928	−	0.885523i
$283$	−9.43908	+	16.3490i	−0.561095	+	0.971845i	0.436306	+	0.899798i	$0.356287\pi$
$283$	−9.43908	+	16.3490i	−0.561095	+	0.971845i	−0.997401	+	0.0720471i	$0.977047\pi$
$284$	−10.8217	−	8.31159i	−0.642147	−	0.493202i
$285$		−	5.90223i		−	0.349618i
$286$	1.96995	+	7.72690i	0.116485	+	0.456901i
$287$		−	7.02813i		−	0.414858i
$288$	−7.42990	+	2.51268i	−0.437811	+	0.148061i
$289$	−8.49843	+	14.7197i	−0.499908	+	0.865866i
$290$	−8.66618	+	9.87734i	−0.508896	+	0.580018i
$291$	−0.675715	−	0.675715i	−0.0396111	−	0.0396111i
$292$	14.2574	−	5.89800i	0.834351	−	0.345154i
$293$	−0.0178432	+	0.0665919i	−0.00104241	+	0.00389034i	−0.966445	−	0.256873i	$-0.917308\pi$
$293$	−0.0178432	+	0.0665919i	−0.00104241	+	0.00389034i	0.965403	+	0.260764i	$0.0839743\pi$
$294$	17.6707	−	35.8121i	1.03058	−	2.08861i
$295$	9.83650	−	5.67910i	0.572703	−	0.330650i
$296$	−4.90225	+	2.41336i	−0.284938	+	0.140274i
$297$	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
$302$	−7.55092	−	1.50376i	−0.434506	−	0.0865316i
$303$	−11.5884	−	20.0717i	−0.665737	−	1.15309i
$304$	−7.72538	+	4.45087i	−0.443081	+	0.255275i
$305$	2.46078	+	0.659365i	0.140904	+	0.0377551i
$306$	0.00715190	+	0.109499i	0.000408847	+	0.00625965i
$307$	6.80614	−	6.80614i	0.388447	−	0.388447i	−0.485686	−	0.874133i	$-0.661430\pi$
$307$	6.80614	−	6.80614i	0.388447	−	0.388447i	0.874133	+	0.485686i	$0.161430\pi$
$308$	13.0752	+	5.42291i	0.745030	+	0.308999i
$309$	−6.99164	−	4.03663i	−0.397740	−	0.229636i
$310$	−6.35891	−	9.52148i	−0.361162	−	0.540784i
$311$	−26.1979			−1.48555			−0.742775	−	0.669542i	$-0.766491\pi$
$311$	−26.1979			−1.48555			−0.742775	+	0.669542i	$0.766491\pi$
$312$	−17.1079	+	12.7874i	−0.968542	+	0.723945i
$313$	24.8487			1.40453			0.702265	−	0.711915i	$-0.252172\pi$
$313$	24.8487			1.40453			0.702265	+	0.711915i	$0.252172\pi$
$314$	−6.88716	−	10.3124i	−0.388665	−	0.581965i
$315$	−6.87071	−	3.96681i	−0.387121	−	0.223504i
$316$	−16.3943	−	6.79950i	−0.922253	−	0.382502i
$317$	24.2717	−	24.2717i	1.36323	−	1.36323i	0.493472	−	0.869762i	$-0.335727\pi$
$317$	24.2717	−	24.2717i	1.36323	−	1.36323i	0.869762	−	0.493472i	$-0.164273\pi$
$318$	0.849693	+	13.0092i	0.0476484	+	0.729521i
$319$	11.1011	+	2.97454i	0.621545	+	0.166542i
$320$	3.88343	−	9.33931i	0.217090	−	0.522083i
$321$	0.307472	+	0.532557i	0.0171614	+	0.0297245i
$322$	6.64006	+	1.32236i	0.370036	+	0.0736924i
$323$	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
$328$	1.93997	+	3.94067i	0.107117	+	0.217587i
$329$	−29.8364	+	17.2261i	−1.64494	+	0.949704i
$330$	2.59137	−	5.25177i	0.142650	−	0.289100i
$331$	−4.93784	+	18.4283i	−0.271408	+	1.01291i	0.686802	+	0.726844i	$0.259014\pi$
$331$	−4.93784	+	18.4283i	−0.271408	+	1.01291i	−0.958210	+	0.286065i	$0.907653\pi$
$332$	18.1950	−	7.52689i	0.998578	−	0.413092i
$333$	−1.89401	−	1.89401i	−0.103791	−	0.103791i
$334$	8.11128	−	9.24489i	0.443830	−	0.505858i
$335$	−5.80086	+	10.0474i	−0.316935	+	0.548947i
$336$	−0.0345472	+	37.9151i	−0.00188471	+	2.06844i
$337$			28.8443i			1.57125i	0.618702	+	0.785626i	$0.287659\pi$
$337$			28.8443i			1.57125i	−0.618702	+	0.785626i	$0.712341\pi$
$338$	−10.5796	+	15.0357i	−0.575456	+	0.817833i
$339$			19.1366i			1.03936i
$340$	−0.112227	−	0.0861961i	−0.00608637	−	0.00467464i
$341$	−5.00708	+	8.67251i	−0.271148	+	0.469643i
$342$	−3.28532	−	2.88247i	−0.177650	−	0.155866i
$343$	−20.7456	−	20.7456i	−1.12016	−	1.12016i
$344$	−3.87693	−	4.42689i	−0.209030	−	0.238682i
$345$	0.724973	−	2.70564i	0.0390312	−	0.145667i
$346$	−7.97555	−	3.93537i	−0.428768	−	0.211567i
$347$	23.8280	−	13.7571i	1.27916	−	0.738521i	0.302463	−	0.953161i	$-0.402191\pi$
$347$	23.8280	−	13.7571i	1.27916	−	0.738521i	0.976693	+	0.214640i	$0.0688578\pi$
$348$	4.00417	+	30.5221i	0.214646	+	1.63616i
$349$	22.2539	−	5.96291i	1.19122	−	0.319187i	0.391853	−	0.920028i	$-0.371834\pi$
$349$	22.2539	−	5.96291i	1.19122	−	0.319187i	0.799369	+	0.600841i	$0.205167\pi$
$350$	−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	−0.959190	−	0.282761i	$-0.908750\pi$
$353$	−5.07073	−	18.9242i	−0.269888	−	1.00723i	0.689303	−	0.724473i	$-0.257917\pi$
$354$	5.19710	−	26.0965i	0.276223	−	1.38702i
$355$	4.31295	+	7.47026i	0.228908	+	0.396480i
$356$	4.15197	−	31.4267i	0.220054	−	1.66561i
$357$	0.512381	+	0.137292i	0.0271181	+	0.00726627i
$358$	−34.1505	+	2.23053i	−1.80491	+	0.117887i
$359$	10.7783	−	10.7783i	0.568858	−	0.568858i	−0.362951	−	0.931808i	$-0.618231\pi$
$359$	10.7783	−	10.7783i	0.568858	−	0.568858i	0.931808	+	0.362951i	$0.118231\pi$
$360$	4.94735	+	0.327662i	0.260748	+	0.0172693i
$361$	12.1519	+	7.01588i	0.639572	+	0.369257i
$362$	−5.91862	+	3.95275i	−0.311076	+	0.207752i
$363$	17.9163			0.940363
$364$	10.1065	+	31.0315i	0.529724	+	1.62649i
$365$	−9.75368			−0.510531
$366$	4.96319	−	3.31466i	0.259430	−	0.173260i
$367$	−29.3207	−	16.9283i	−1.53053	−	0.883651i	−0.999337	−	0.0363994i	$-0.988411\pi$
$367$	−29.3207	−	16.9283i	−1.53053	−	0.883651i	−0.531191	−	0.847252i	$-0.678256\pi$
$368$	−4.08808	+	1.09141i	−0.213106	+	0.0568935i
$369$	−1.52249	+	1.52249i	−0.0792578	+	0.0792578i
$370$	3.44683	−	0.225129i	0.179192	−	0.0117039i
$371$	19.2414	+	5.15573i	0.998965	+	0.267672i
$372$	−26.5921	−	3.51325i	−1.37874	−	0.182153i
$373$	−5.98260	−	10.3622i	−0.309767	−	0.536533i	0.668544	−	0.743673i	$-0.266918\pi$
$373$	−5.98260	−	10.3622i	−0.309767	−	0.536533i	−0.978311	+	0.207140i	$0.933584\pi$
$374$	−0.0241734	+	0.121383i	−0.00124998	+	0.00627659i
$375$	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	$-0.449043\pi$
$379$	15.4002	−	4.12647i	0.791055	−	0.211963i	0.631653	+	0.775251i	$0.282377\pi$
$380$	5.58832	−	0.733126i	0.286675	−	0.0376086i
$381$	−17.1140	+	9.88076i	−0.876776	+	0.506207i
$382$	24.2696	+	11.9753i	1.24174	+	0.612711i
$383$	6.06022	−	22.6171i	0.309663	−	1.15568i	−0.619194	−	0.785238i	$-0.712540\pi$
$383$	6.06022	−	22.6171i	0.309663	−	1.15568i	0.928857	−	0.370439i	$-0.120793\pi$
$384$	−10.4463	−	21.2685i	−0.533086	−	1.08535i
$385$	−6.32741	−	6.32741i	−0.322475	−	0.322475i
$386$	10.1451	+	8.90110i	0.516372	+	0.453054i
$387$	1.44232	−	2.49817i	0.0733172	−	0.126989i
$388$	0.555845	−	0.723709i	0.0282188	−	0.0367407i
$389$		−	39.2161i		−	1.98834i	−0.107845	−	0.994168i	$-0.534395\pi$
$389$		−	39.2161i		−	1.98834i	0.107845	−	0.994168i	$-0.465605\pi$
$390$	13.0836	−	3.33562i	0.662514	−	0.168906i
$391$			0.0591980i			0.00299377i
$392$	36.1024	+	12.2826i	1.82345	+	0.620366i
$393$	9.46326	−	16.3909i	0.477358	−	0.826809i
$394$	0.995822	−	1.13500i	0.0501688	−	0.0571803i
$395$	7.93361	+	7.93361i	0.399183	+	0.399183i
$396$	−1.65771	−	4.00722i	−0.0833028	−	0.201370i
$397$	−2.81223	+	10.4954i	−0.141142	+	0.526749i	0.858755	+	0.512387i	$0.171239\pi$
$397$	−2.81223	+	10.4954i	−0.141142	+	0.526749i	−0.999897	+	0.0143624i	$0.995428\pi$
$398$	−7.08808	+	14.3650i	−0.355293	+	0.720050i
$399$	−18.2972	+	10.5639i	−0.916004	+	0.528855i
$400$	9.62967	−	9.61214i	0.481483	−	0.480607i
$401$	−1.48858	+	0.398864i	−0.0743361	+	0.0199183i	−0.295795	−	0.955251i	$-0.595585\pi$
$401$	−1.48858	+	0.398864i	−0.0743361	+	0.0199183i	0.221459	+	0.975170i	$0.428918\pi$
$402$	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
$406$	46.1310	+	9.18695i	2.28944	+	0.455941i
$407$	−1.51056	−	2.61636i	−0.0748755	−	0.129688i
$408$	−0.325188	+	0.0644529i	−0.0160992	+	0.00319090i
$409$	−0.657171	−	0.176088i	−0.0324950	−	0.00870701i	0.242535	−	0.970143i	$-0.422021\pi$
$409$	−0.657171	−	0.176088i	−0.0324950	−	0.00870701i	−0.275030	+	0.961436i	$0.588688\pi$
$410$	−0.180969	−	2.77073i	−0.00893743	−	0.136836i
$411$	13.9015	−	13.9015i	0.685712	−	0.685712i
$412$	2.95349	−	7.12118i	0.145508	−	0.350836i
$413$	−35.2109	−	20.3290i	−1.73262	−	1.00033i
$414$	−1.15196	−	1.72489i	−0.0566159	−	0.0847735i
$415$	−12.4474			−0.611020
$416$	−14.2323	−	14.6096i	−0.697796	−	0.716296i
$417$	−21.7024			−1.06277
$418$	−2.73779	−	4.09941i	−0.133910	−	0.200509i
$419$	−20.8664	−	12.0472i	−1.01939	−	0.588546i	−0.105463	−	0.994423i	$-0.533633\pi$
$419$	−20.8664	−	12.0472i	−1.01939	−	0.588546i	−0.913927	+	0.405878i	$0.866966\pi$
$420$	9.18237	−	22.1397i	0.448054	−	1.08031i
$421$	−15.8266	+	15.8266i	−0.771339	+	0.771339i	−0.978341	−	0.207002i	$-0.933629\pi$
$421$	−15.8266	+	15.8266i	−0.771339	+	0.771339i	0.207002	+	0.978341i	$0.433629\pi$
$422$	0.495002	+	7.57872i	0.0240963	+	0.368926i
$423$	10.1951	+	2.73176i	0.495701	+	0.132823i
$424$	−12.2118	+	2.42040i	−0.593056	+	0.117545i
$425$	−0.0951783	−	0.164854i	−0.00461683	−	0.00799658i
$426$	19.8188	+	3.94690i	0.960225	+	0.191228i
$427$	−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	$-0.647402\pi$
$431$	−8.01815	+	2.14846i	−0.386221	+	0.103487i	0.0604836	+	0.998169i	$0.480736\pi$
$432$	−9.56679	+	9.54938i	−0.460283	+	0.459445i
$433$	21.0862	−	12.1741i	1.01334	−	0.585050i	0.101170	−	0.994869i	$-0.467742\pi$
$433$	21.0862	−	12.1741i	1.01334	−	0.585050i	0.912167	+	0.409819i	$0.134408\pi$
$434$	−18.1357	+	36.7545i	−0.870543	+	1.76427i
$435$	5.03666	−	18.7971i	0.241489	−	0.901250i
$436$	−1.24651	−	3.01322i	−0.0596970	−	0.144307i
$437$	−1.66723	−	1.66723i	−0.0797545	−	0.0797545i
$438$	−15.0700	+	17.1762i	−0.720073	+	0.820708i
$439$	−0.506851	+	0.877892i	−0.0241907	+	0.0418995i	−0.877867	−	0.478904i	$-0.841034\pi$
$439$	−0.506851	+	0.877892i	−0.0241907	+	0.0418995i	0.853677	+	0.520803i	$0.174368\pi$
$440$	5.29433	+	1.80122i	0.252397	+	0.0858697i
$441$			18.6937i			0.890178i
$442$	−0.248842	+	0.139659i	−0.0118362	+	0.00664289i
$443$			39.1335i			1.85929i	0.368460	+	0.929644i	$0.379885\pi$
$443$			39.1335i			1.85929i	−0.368460	+	0.929644i	$0.620115\pi$
$444$	4.92911	−	6.41768i	0.233925	−	0.304570i
$445$	−10.0196	+	17.3545i	−0.474977	+	0.822684i
$446$	−12.5621	−	11.0218i	−0.594834	−	0.521895i
$447$	15.4800	+	15.4800i	0.732181	+	0.732181i
$448$	−35.9028	+	4.67679i	−1.69625	+	0.220957i
$449$	−6.54345	+	24.4205i	−0.308804	+	1.15247i	0.620817	+	0.783956i	$0.286801\pi$
$449$	−6.54345	+	24.4205i	−0.308804	+	1.15247i	−0.929621	+	0.368517i	$0.879865\pi$
$450$	5.98123	+	2.95131i	0.281958	+	0.139126i
$451$	−2.10315	+	1.21426i	−0.0990337	+	0.0571771i
$452$	−18.1189	+	2.37700i	−0.852240	+	0.111805i
$453$	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	0.944758	+	0.327768i	$0.106296\pi$
$457$	6.20927	+	23.1733i	0.290458	+	1.08400i	−0.654301	+	0.756235i	$0.727037\pi$
$458$	−2.75040	+	13.8107i	−0.128518	+	0.645333i
$459$	0.0945569	+	0.163777i	0.00441354	+	0.00764447i
$460$	2.65179	+	0.350343i	0.123640	+	0.0163348i
$461$	−4.85332	−	1.30044i	−0.226042	−	0.0605677i	0.144020	−	0.989575i	$-0.453997\pi$
$461$	−4.85332	−	1.30044i	−0.226042	−	0.0605677i	−0.370062	+	0.929007i	$0.620664\pi$
$462$	−20.9187	+	1.36630i	−0.973228	+	0.0635661i
$463$	1.18158	−	1.18158i	0.0549128	−	0.0549128i	−0.679117	−	0.734030i	$-0.737637\pi$
$463$	1.18158	−	1.18158i	0.0549128	−	0.0549128i	0.734030	+	0.679117i	$0.237637\pi$
$464$	−28.4014	+	7.58242i	−1.31850	+	0.352005i
$465$	14.6848	+	8.47826i	0.680990	+	0.393170i
$466$	25.0741	−	16.7457i	1.16153	−	0.775730i
$467$	−24.9759			−1.15575			−0.577873	−	0.816127i	$-0.696117\pi$
$467$	−24.9759			−1.15575			−0.577873	+	0.816127i	$0.696117\pi$
$468$	4.53295	−	8.91165i	0.209536	−	0.411941i
$469$	41.5297			1.91766
$470$	−11.3190	+	7.55936i	−0.522105	+	0.348687i
$471$	15.9047	+	9.18256i	0.732848	+	0.423110i
$472$	25.3541	+	1.67920i	1.16702	+	0.0772914i
$473$	2.30063	−	2.30063i	0.105783	−	0.105783i
$474$	26.2289	−	1.71313i	1.20473	−	0.0786868i
$475$	7.32345	+	1.96231i	0.336023	+	0.0900371i
$476$	−0.0663464	+	0.502183i	−0.00304098	+	0.0230175i
$477$	−3.05136	−	5.28512i	−0.139712	−	0.241989i
$478$	5.92090	−	29.7310i	0.270816	−	1.35986i
$479$	−8.10477	−	30.2474i	−0.370317	−	1.38204i	−0.860069	−	0.510178i	$-0.829579\pi$
$479$	−8.10477	−	30.2474i	−0.370317	−	1.38204i	0.489752	−	0.871862i	$-0.337087\pi$
$480$	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
$484$	2.22542	+	16.9634i	0.101155	+	0.771065i
$485$	−0.499580	+	0.288433i	−0.0226848	+	0.0130971i
$486$	−16.9906	−	8.38365i	−0.770710	−	0.380290i
$487$	−4.40472	+	16.4386i	−0.199597	+	0.744906i	0.791432	+	0.611258i	$0.209336\pi$
$487$	−4.40472	+	16.4386i	−0.199597	+	0.744906i	−0.991029	+	0.133649i	$0.957331\pi$
$488$	3.75486	+	4.28750i	0.169974	+	0.194086i
$489$	13.0146	+	13.0146i	0.588538	+	0.588538i
$490$	−18.1210	−	15.8990i	−0.818625	−	0.718245i
$491$	5.60847	−	9.71415i	0.253107	−	0.438393i	−0.711273	−	0.702916i	$-0.751881\pi$
$491$	5.60847	−	9.71415i	0.253107	−	0.438393i	0.964380	+	0.264523i	$0.0852143\pi$
$492$	−5.15884	−	3.96225i	−0.232578	−	0.178632i
$493$			0.411271i			0.0185227i
$494$	3.07499	−	10.9416i	0.138350	−	0.492286i
$495$			2.74139i			0.123217i
$496$	0.0233390	−	25.6142i	0.00104795	−	1.15011i
$497$	15.4387	−	26.7407i	0.692522	−	1.19948i
$498$	−19.2320	+	21.9198i	−0.861807	+	0.982251i
$499$	−6.87805	−	6.87805i	−0.307904	−	0.307904i	0.536192	−	0.844096i	$-0.319862\pi$
$499$	−6.87805	−	6.87805i	−0.307904	−	0.307904i	−0.844096	+	0.536192i	$0.819862\pi$
$500$	−19.6309	+	8.12091i	−0.877920	+	0.363178i
$501$	−4.71416	+	17.5935i	−0.210613	+	0.786019i
$502$	−9.14731	+	18.5383i	−0.408264	+	0.827403i
$503$	−6.53009	+	3.77015i	−0.291162	+	0.168103i	−0.638466	−	0.769650i	$-0.720431\pi$
$503$	−6.53009	+	3.77015i	−0.291162	+	0.168103i	0.347304	+	0.937753i	$0.387097\pi$
$504$	−7.83906	−	15.9235i	−0.349179	−	0.709287i
$505$	−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	0.887028	−	0.461716i	$-0.152766\pi$
$509$	−2.52725	−	9.43184i	−0.112019	−	0.418059i	−0.999047	+	0.0436566i	$0.986099\pi$
$510$	0.205533	+	0.0409317i	0.00910116	+	0.00181249i
$511$	17.4572	+	30.2368i	0.772262	+	1.33760i
$512$	18.8397	−	12.5325i	0.832607	−	0.553864i
$513$	−7.27563	−	1.94950i	−0.321227	−	0.0860725i
$514$	1.29268	+	19.7916i	0.0570177	+	0.872968i
$515$	−3.44611	+	3.44611i	−0.151854	+	0.151854i
$516$	8.04991	+	3.33868i	0.354378	+	0.146977i
$517$	10.3097	+	5.95233i	0.453421	+	0.261783i
$518$	−6.86708	−	10.2824i	−0.301722	−	0.451782i
$519$	13.1711			0.578149
$520$	4.78336	+	11.9734i	0.209764	+	0.525070i
$521$	−19.5755			−0.857619			−0.428809	−	0.903395i	$-0.641067\pi$
$521$	−19.5755			−0.857619			−0.428809	+	0.903395i	$0.641067\pi$
$522$	−8.00312	−	11.9834i	−0.350287	−	0.524500i
$523$	31.0210	+	17.9100i	1.35645	+	0.783148i	0.989144	−	0.146951i	$-0.0469459\pi$
$523$	31.0210	+	17.9100i	1.35645	+	0.783148i	0.367309	+	0.930099i	$0.380279\pi$
$524$	16.6945	+	6.92402i	0.729305	+	0.302477i
$525$	22.7986	−	22.7986i	0.995012	−	0.995012i
$526$	−2.73377	−	41.8554i	−0.119198	−	1.82498i
$527$	−0.346148	−	0.0927502i	−0.0150785	−	0.00404026i
$528$	11.3520	−	6.54028i	0.494031	−	0.284629i
$529$	10.9405	+	18.9495i	0.475674	+	0.823892i
$530$	7.71838	+	1.53711i	0.335265	+	0.0667677i
$531$	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
$536$	−23.2857	+	11.4634i	−1.00579	+	0.495145i
$537$	43.8932	−	25.3417i	1.89413	−	1.09358i
$538$	−1.11511	+	2.25991i	−0.0480756	+	0.0974317i
$539$	−5.45711	+	20.3662i	−0.235054	+	0.877235i
$540$	7.89603	−	3.26643i	0.339791	−	0.140565i
$541$	−12.3423	−	12.3423i	−0.530636	−	0.530636i	0.390126	−	0.920762i	$-0.372432\pi$
$541$	−12.3423	−	12.3423i	−0.530636	−	0.530636i	−0.920762	+	0.390126i	$0.872432\pi$
$542$	19.6023	−	22.3419i	0.841992	−	0.959667i
$543$	5.27014	−	9.12816i	0.226164	−	0.391727i
$544$	−0.101417	−	0.299887i	−0.00434822	−	0.0128575i
$545$			2.06139i			0.0883001i
$546$	−33.7577	−	34.5896i	−1.44470	−	1.48030i
$547$		−	5.49854i		−	0.235101i	−0.993067	−	0.117550i	$-0.962496\pi$
$547$		−	5.49854i		−	0.235101i	0.993067	−	0.117550i	$-0.0375041\pi$
$548$	14.8889	+	11.4354i	0.636023	+	0.488498i
$549$	−1.39690	+	2.41951i	−0.0596184	+	0.103262i
$550$	5.65480	+	4.96141i	0.241122	+	0.211555i
$551$	−11.5829	−	11.5829i	−0.493448	−	0.493448i
$552$	4.71411	−	4.12847i	0.200646	−	0.175719i
$553$	10.3949	−	38.7942i	0.442035	−	1.64970i
$554$	19.8249	+	9.78218i	0.842280	+	0.415605i
$555$	−4.43016	+	2.55776i	−0.188050	+	0.108571i
$556$	−2.69570	−	20.5482i	−0.114323	−	0.871437i
$557$	−3.31443	+	0.888098i	−0.140437	+	0.0376299i	−0.328353	−	0.944555i	$-0.606493\pi$
$557$	−3.31443	+	0.888098i	−0.140437	+	0.0376299i	0.187916	+	0.982185i	$0.439827\pi$
$558$	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
$562$	6.67329	−	33.5090i	0.281496	−	1.41349i
$563$	−4.66786	−	8.08497i	−0.196727	−	0.340741i	0.750738	−	0.660600i	$-0.229698\pi$
$563$	−4.66786	−	8.08497i	−0.196727	−	0.340741i	−0.947465	+	0.319859i	$0.896365\pi$
$564$	−4.17649	+	31.6123i	−0.175862	+	1.33112i
$565$	11.1585	+	2.98991i	0.469442	+	0.125787i
$566$	26.6410	−	1.74005i	1.11980	−	0.0731397i
$567$	−35.9611	+	35.9611i	−1.51022	+	1.51022i
$568$	−1.27526	+	19.2550i	−0.0535085	+	0.807922i
$569$	29.5605	+	17.0668i	1.23924	+	0.715477i	0.968939	−	0.247299i	$-0.0795430\pi$
$569$	29.5605	+	17.0668i	1.23924	+	0.715477i	0.270302	+	0.962775i	$0.412876\pi$
$570$	−6.94135	+	4.63577i	−0.290741	+	0.194171i
$571$	−30.2446			−1.26570			−0.632848	−	0.774276i	$-0.718114\pi$
$571$	−30.2446			−1.26570			−0.632848	+	0.774276i	$0.718114\pi$
$572$	7.54001	−	8.38568i	0.315264	−	0.350623i
$573$	−40.0798			−1.67436
$574$	−8.26547	+	5.52009i	−0.344994	+	0.230404i
$575$	3.11610	+	1.79908i	0.129951	+	0.0750270i
$576$	8.79070	+	6.76445i	0.366279	+	0.281852i
$577$	−24.5041	+	24.5041i	−1.02012	+	1.02012i	−0.0203254	+	0.999793i	$0.506470\pi$
$577$	−24.5041	+	24.5041i	−1.02012	+	1.02012i	−0.999793	+	0.0203254i	$0.993530\pi$
$578$	23.9861	−	1.56664i	0.997690	−	0.0651638i
$579$	−19.3066	−	5.17319i	−0.802355	−	0.214990i
$580$	18.4229	+	2.43397i	0.764971	+	0.101065i
$581$	22.2785	+	38.5875i	0.924269	+	1.60088i
$582$	−0.263953	+	1.32540i	−0.0109412	+	0.0549397i
$583$	−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	$-0.357561\pi$
$587$	30.4837	−	8.16808i	1.25820	−	0.337133i	0.825498	+	0.564405i	$0.190895\pi$
$588$	−55.9961	+	7.34607i	−2.30924	+	0.302947i
$589$	12.3610	−	7.13662i	0.509325	−	0.294059i
$590$	−14.4048	−	7.10774i	−0.593036	−	0.292621i
$591$	−0.578757	+	2.15995i	−0.0238069	+	0.0888485i
$592$	6.68861	+	3.86980i	0.274900	+	0.159048i
$593$	−11.3864	−	11.3864i	−0.467582	−	0.467582i	0.433548	−	0.901130i	$-0.357261\pi$
$593$	−11.3864	−	11.3864i	−0.467582	−	0.467582i	−0.901130	+	0.433548i	$0.857261\pi$
$594$	−5.61788	−	4.92901i	−0.230504	−	0.202240i
$595$	0.160109	−	0.277317i	0.00656382	−	0.0113689i
$596$	−12.7339	+	16.5795i	−0.521602	+	0.679124i
$597$		−	23.7229i		−	0.970912i
$598$	2.75356	−	4.63802i	0.112602	−	0.189663i
$599$		−	37.4177i		−	1.52885i	−0.644715	−	0.764423i	$-0.723024\pi$
$599$		−	37.4177i		−	1.52885i	0.644715	−	0.764423i	$-0.276976\pi$
$600$	−6.49005	+	19.0762i	−0.264955	+	0.778784i
$601$	6.94234	−	12.0245i	0.283184	−	0.490489i	−0.688983	−	0.724777i	$-0.741943\pi$
$601$	6.94234	−	12.0245i	0.283184	−	0.490489i	0.972167	+	0.234288i	$0.0752760\pi$
$602$	8.78217	−	10.0095i	0.357935	−	0.407959i
$603$	−8.99652	−	8.99652i	−0.366366	−	0.366366i
$604$	4.16219	+	10.0614i	0.169357	+	0.409392i
$605$	2.79925	−	10.4469i	0.113806	−	0.424728i
$606$	−14.5036	+	29.3935i	−0.589168	+	1.19403i
$607$	17.4664	−	10.0842i	0.708938	−	0.409306i	−0.101730	−	0.994812i	$-0.532438\pi$
$607$	17.4664	−	10.0842i	0.708938	−	0.409306i	0.810668	+	0.585506i	$0.199104\pi$
$608$	11.3022	+	5.58963i	0.458364	+	0.226690i
$609$	−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	0.882337	+	0.470619i	$0.155969\pi$
$613$	8.75275	+	32.6657i	0.353520	+	1.31935i	−0.528817	+	0.848736i	$0.677364\pi$
$614$	−13.3501	−	2.65867i	−0.538767	−	0.107295i
$615$	2.05605	+	3.56118i	0.0829078	+	0.143600i
$616$	−3.89199	−	19.6365i	−0.156813	−	0.791176i
$617$	−17.6816	−	4.73777i	−0.711834	−	0.190735i	−0.115309	−	0.993330i	$-0.536786\pi$
$617$	−17.6816	−	4.73777i	−0.711834	−	0.190735i	−0.596525	+	0.802594i	$0.703453\pi$
$618$	0.744132	+	11.3930i	0.0299334	+	0.458295i
$619$	5.55216	−	5.55216i	0.223160	−	0.223160i	−0.586668	−	0.809828i	$-0.699561\pi$
$619$	5.55216	−	5.55216i	0.223160	−	0.223160i	0.809828	+	0.586668i	$0.199561\pi$
$620$	−6.20332	+	14.9569i	−0.249131	+	0.600682i
$621$	−3.09576	−	1.78734i	−0.124228	−	0.0717233i
$622$	20.5766	+	30.8102i	0.825046	+	1.23538i
$623$	71.7330			2.87392
$624$	28.4757	+	10.0762i	1.13994	+	0.403371i
$625$	−3.57775			−0.143110
$626$	−19.5168	−	29.2234i	−0.780050	−	1.16800i
$627$	6.32243	+	3.65026i	0.252494	+	0.145777i
$628$	−6.71863	+	16.1993i	−0.268103	+	0.646424i
$629$	0.0764462	−	0.0764462i	0.00304811	−	0.00304811i
$630$	0.731261	+	11.1960i	0.0291341	+	0.446058i
$631$	−22.8754	−	6.12944i	−0.910655	−	0.244009i	−0.227069	−	0.973879i	$-0.572914\pi$
$631$	−22.8754	−	6.12944i	−0.910655	−	0.244009i	−0.683587	+	0.729869i	$0.739581\pi$
$632$	4.87996	+	24.6211i	0.194114	+	0.979376i
$633$	−5.62386	−	9.74082i	−0.223528	−	0.387163i
$634$	−47.6085	−	9.48119i	−1.89077	−	0.376546i
$635$	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
$640$	−14.0337	+	2.76822i	−0.554730	+	0.109423i
$641$	−8.61576	+	4.97431i	−0.340302	+	0.196473i	−0.660406	−	0.750909i	$-0.729616\pi$
$641$	−8.61576	+	4.97431i	−0.340302	+	0.196473i	0.320104	+	0.947383i	$0.396282\pi$
$642$	0.384820	−	0.779889i	0.0151876	−	0.0307798i
$643$	6.27341	−	23.4127i	0.247399	−	0.923306i	−0.724763	−	0.688998i	$-0.758051\pi$
$643$	6.27341	−	23.4127i	0.247399	−	0.923306i	0.972162	−	0.234308i	$-0.0752823\pi$
$644$	−3.66011	−	8.84769i	−0.144229	−	0.348648i
$645$	−3.89555	−	3.89555i	−0.153387	−	0.153387i
$646$	0.116343	−	0.132602i	0.00457744	−	0.00521717i
$647$	−8.08819	+	14.0092i	−0.317980	+	0.550757i	−0.980066	−	0.198670i	$-0.936338\pi$
$647$	−8.08819	+	14.0092i	−0.317980	+	0.550757i	0.662087	+	0.749427i	$0.269671\pi$
$648$	10.2370	−	30.0896i	0.402147	−	1.18203i
$649$			14.0491i			0.551474i
$650$	−0.211083	+	17.3431i	−0.00827937	+	0.680250i
$651$		−	60.6979i		−	2.37894i
$652$	−10.7058	+	13.9389i	−0.419272	+	0.545891i
$653$	9.72518	−	16.8445i	0.380576	−	0.659177i	−0.610569	−	0.791963i	$-0.709059\pi$
$653$	9.72518	−	16.8445i	0.380576	−	0.659177i	0.991145	+	0.132787i	$0.0423925\pi$
$654$	3.63009	+	3.18496i	0.141948	+	0.124542i
$655$	−8.07890	−	8.07890i	−0.315669	−	0.315669i
$656$	3.11073	−	5.37662i	0.121454	−	0.209922i
$657$	2.76842	−	10.3319i	0.108006	−	0.403085i
$658$	43.6931	+	21.5594i	1.70334	+	0.840475i
$659$	−29.2584	+	16.8924i	−1.13975	+	0.658033i	−0.946368	−	0.323091i	$-0.895278\pi$
$659$	−29.2584	+	16.8924i	−1.13975	+	0.658033i	−0.193379	+	0.981124i	$0.561945\pi$
$660$	−8.21170	+	1.07728i	−0.319640	+	0.0419332i
$661$	−8.51422	+	2.28138i	−0.331165	+	0.0887353i	−0.420570	−	0.907260i	$-0.638170\pi$
$661$	−8.51422	+	2.28138i	−0.331165	+	0.0887353i	0.0894055	+	0.995995i	$0.471503\pi$
$662$	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
$666$	−0.739851	+	3.71506i	−0.0286686	+	0.143956i
$667$	−3.88697	−	6.73243i	−0.150504	−	0.260681i
$668$	−17.2433	−	2.27812i	−0.667164	−	0.0881430i
$669$	23.9063	+	6.40568i	0.924272	+	0.247658i
$670$	16.3724	−	1.06936i	0.632522	−	0.0413130i
$671$	−2.22819	+	2.22819i	−0.0860183	+	0.0860183i
$672$	44.6173	−	29.7389i	1.72115	−	1.14720i
$673$	−17.6598	−	10.1959i	−0.680734	−	0.393022i	0.119398	−	0.992847i	$-0.461904\pi$
$673$	−17.6598	−	10.1959i	−0.680734	−	0.393022i	−0.800131	+	0.599825i	$0.795237\pi$
$674$	33.9225	−	22.6551i	1.30665	−	0.872643i
$675$	11.4947			0.442431
$676$	25.9923	+	0.632801i	0.999704	+	0.0243385i
$677$	−1.01359			−0.0389554			−0.0194777	−	0.999810i	$-0.506200\pi$
$677$	−1.01359			−0.0389554			−0.0194777	+	0.999810i	$0.506200\pi$
$678$	22.5057	−	15.0304i	0.864328	−	0.577241i
$679$	1.78831	+	1.03248i	0.0686289	+	0.0396229i
$680$	−0.0132252	+	0.199686i	−0.000507162	+	0.00765761i
$681$	2.60123	−	2.60123i	0.0996794	−	0.0996794i
$682$	14.1320	−	0.923030i	0.541144	−	0.0353446i
$683$	−24.3916	−	6.53572i	−0.933320	−	0.250082i	−0.240050	−	0.970761i	$-0.577164\pi$
$683$	−24.3916	−	6.53572i	−0.933320	−	0.250082i	−0.693270	+	0.720678i	$0.743831\pi$
$684$	−0.809565	+	6.12768i	−0.0309545	+	0.234298i
$685$	−5.93395	−	10.2779i	−0.226725	−	0.392698i
$686$	−8.10382	+	40.6922i	−0.309405	+	1.55363i
$687$	−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	$-0.822663\pi$
$691$	−34.6849	+	9.29380i	−1.31948	+	0.353553i	−0.470695	+	0.882296i	$0.655997\pi$
$692$	1.63601	+	12.4706i	0.0621917	+	0.474062i
$693$	8.49843	−	4.90657i	0.322829	−	0.186385i
$694$	−34.8943	−	17.2179i	−1.32457	−	0.653581i
$695$	−3.39079	+	12.6546i	−0.128620	+	0.480016i
$696$	32.7507	−	28.6820i	1.24141	−	1.08719i
$697$	−0.0614511	−	0.0614511i	−0.00232763	−	0.00232763i
$698$	−24.4915	−	21.4883i	−0.927017	−	0.813345i
$699$	−22.3268	+	38.6712i	−0.844478	+	1.46268i
$700$	24.4179	+	18.7542i	0.922910	+	0.708842i
$701$		−	16.0203i		−	0.605077i	−0.953137	−	0.302539i	$-0.902166\pi$
$701$		−	16.0203i		−	0.605077i	0.953137	−	0.302539i	$-0.0978342\pi$
$702$	0.209705	−	17.2298i	0.00791481	−	0.650297i
$703$			4.30601i			0.162404i
$704$	7.60248	+	9.93584i	0.286529	+	0.374471i
$705$	10.0788	−	17.4570i	0.379590	−	0.657469i
$706$	−18.2732	+	20.8270i	−0.687722	+	0.783836i
$707$	35.4138	+	35.4138i	1.33187	+	1.33187i
$708$	−34.7729	+	14.3848i	−1.30685	+	0.540616i
$709$	6.09039	−	22.7296i	0.228729	−	0.853630i	−0.752147	−	0.658996i	$-0.770981\pi$
$709$	6.09039	−	22.7296i	0.228729	−	0.853630i	0.980876	−	0.194634i	$-0.0623519\pi$
$710$	5.39792	−	10.9396i	0.202580	−	0.410556i
$711$	−10.6557	+	6.15209i	−0.399621	+	0.230722i
$712$	−40.2206	+	19.8004i	−1.50733	+	0.742053i
$713$	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
$718$	−21.1415	−	4.21031i	−0.788993	−	0.157127i
$719$	23.4982	+	40.7001i	0.876334	+	1.51786i	0.855334	+	0.518076i	$0.173352\pi$
$719$	23.4982	+	40.7001i	0.876334	+	1.51786i	0.0210001	+	0.999779i	$0.493315\pi$
$720$	−3.50044	−	6.07571i	−0.130454	−	0.226428i
$721$	16.8510	+	4.51521i	0.627563	+	0.168155i
$722$	−1.29334	−	19.8017i	−0.0481333	−	0.736944i
$723$	29.7209	−	29.7209i	1.10533	−	1.10533i
$724$	9.29729	+	3.85603i	0.345531	+	0.143308i
$725$	21.6487	+	12.4989i	0.804014	+	0.464198i
$726$	−14.0720	−	21.0706i	−0.522260	−	0.782002i
$727$	20.0985			0.745412			0.372706	−	0.927950i	$-0.378430\pi$
$727$	20.0985			0.745412			0.372706	+	0.927950i	$0.378430\pi$
$728$	28.5568	−	36.2588i	1.05839	−	1.34384i
$729$	−5.65241			−0.209348
$730$	7.66081	+	11.4709i	0.283539	+	0.424556i
$731$	0.100831	+	0.0582151i	0.00372939	+	0.00215316i
$732$	−7.79645	−	3.23356i	−0.288165	−	0.119516i
$733$	−13.3827	+	13.3827i	−0.494300	+	0.494300i	−0.909658	−	0.415358i	$-0.863656\pi$
$733$	−13.3827	+	13.3827i	−0.494300	+	0.494300i	0.415358	+	0.909658i	$0.363656\pi$
$734$	3.12065	+	47.7787i	0.115185	+	1.76354i
$735$	34.4852	+	9.24028i	1.27201	+	0.340833i
$736$	4.49445	+	3.95059i	0.165668	+	0.145621i
$737$	−7.17513	−	12.4277i	−0.264299	−	0.457780i
$738$	2.98634	+	0.594727i	0.109929	+	0.0218922i
$739$	0.588495	+	2.19629i	0.0216481	+	0.0807920i	0.975905	−	0.218197i	$-0.0700174\pi$
$739$	0.588495	+	2.19629i	0.0216481	+	0.0807920i	−0.954257	+	0.298989i	$0.903351\pi$
$740$	−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	$-0.677292\pi$
$743$	−15.3189	+	4.10470i	−0.561998	+	0.150587i	−0.0333737	+	0.999443i	$0.510625\pi$
$744$	16.7544	+	34.0332i	0.614247	+	1.24772i
$745$	11.4449	−	6.60774i	0.419311	−	0.242089i
$746$	−7.48758	+	15.1746i	−0.274140	+	0.555581i
$747$	3.53299	−	13.1853i	0.129266	−	0.482425i
$748$	0.161740	−	0.0669086i	0.00591380	−	0.00244642i
$749$	−0.939623	−	0.939623i	−0.0343331	−	0.0343331i
$750$	20.7498	−	23.6497i	0.757675	−	0.863565i
$751$	15.5912	−	27.0047i	0.568930	−	0.985416i	−0.427742	−	0.903901i	$-0.640691\pi$
$751$	15.5912	−	27.0047i	0.568930	−	0.985416i	0.996672	−	0.0815150i	$-0.0259759\pi$
$752$	−30.4497	−	0.0277450i	−1.11039	−	0.00101176i
$753$		−	30.6148i		−	1.11567i
$754$	19.1300	−	32.2221i	0.696674	−	1.17346i
$755$		−	6.88313i		−	0.250503i
$756$	−24.2585	−	18.6317i	−0.882272	−	0.677630i
$757$	6.38361	−	11.0567i	0.232016	−	0.401864i	−0.726385	−	0.687288i	$-0.758801\pi$
$757$	6.38361	−	11.0567i	0.232016	−	0.401864i	0.958401	+	0.285424i	$0.0921344\pi$
$758$	−16.9487	−	14.8704i	−0.615604	−	0.540119i
$759$	2.44990	+	2.44990i	0.0889256	+	0.0889256i
$760$	−5.25141	−	5.99635i	−0.190489	−	0.217511i
$761$	−2.86736	+	10.7011i	−0.103942	+	0.387915i	−0.998223	−	0.0595898i	$-0.981021\pi$
$761$	−2.86736	+	10.7011i	−0.103942	+	0.387915i	0.894281	+	0.447505i	$0.147687\pi$
$762$	25.0621	+	12.3664i	0.907904	+	0.447986i
$763$	6.39038	−	3.68949i	0.231347	−	0.133568i
$764$	−4.97838	−	37.9481i	−0.180111	−	1.37292i
$765$	−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	−0.904944	−	0.425530i	$-0.860088\pi$
$769$	−9.26223	−	34.5671i	−0.334004	−	1.24652i	0.570940	−	0.820992i	$-0.306579\pi$
$770$	−2.47166	+	12.4111i	−0.0890725	+	0.447265i
$771$	−14.6865	−	25.4378i	−0.528922	−	0.916120i
$772$	2.49994	−	18.9223i	0.0899750	−	0.681030i
$773$	47.3258	+	12.6809i	1.70219	+	0.456100i	0.973489	−	0.228733i	$-0.0734582\pi$
$773$	47.3258	+	12.6809i	1.70219	+	0.456100i	0.728700	+	0.684833i	$0.240125\pi$
$774$	−4.07082	+	0.265884i	−0.146323	+	0.00955701i
$775$	−15.4020	+	15.4020i	−0.553256	+	0.553256i
$776$	−1.28770	−	0.0852839i	−0.0462256	−	0.00306151i
$777$	15.8583	+	9.15579i	0.568913	+	0.328462i
$778$	−46.1203	+	30.8014i	−1.65349	+	1.10428i
$779$	3.46137			0.124017
$780$	−14.1991	−	12.7672i	−0.508409	−	0.457137i
$781$	−10.6695			−0.381783
$782$	0.0696201	−	0.0464957i	0.00248961	−	0.00166268i
$783$	−21.5074	−	12.4173i	−0.768611	−	0.443758i
$784$	−13.9107	−	52.1055i	−0.496812	−	1.86091i
$785$	7.83925	−	7.83925i	0.279795	−	0.279795i
$786$	−26.7092	+	1.74451i	−0.952687	+	0.0622245i
$787$	35.2028	+	9.43257i	1.25485	+	0.336235i	0.824206	−	0.566290i	$-0.191622\pi$
$787$	35.2028	+	9.43257i	1.25485	+	0.336235i	0.430639	+	0.902524i	$0.358288\pi$
$788$	−2.11696	−	0.279685i	−0.0754137	−	0.00996335i
$789$	31.0592	+	53.7962i	1.10574	+	1.91519i
$790$	3.09909	−	15.5616i	0.110261	−	0.553658i
$791$	−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
$796$	22.4611	−	2.94666i	0.796114	−	0.104441i
$797$	17.1575	−	9.90590i	0.607750	−	0.350885i	−0.164334	−	0.986405i	$-0.552548\pi$
$797$	17.1575	−	9.90590i	0.607750	−	0.350885i	0.772084	+	0.635520i	$0.219214\pi$
$798$	26.7948	+	13.2213i	0.948525	+	0.468029i
$799$	−0.110260	+	0.411495i	−0.00390071	+	0.0145576i
$800$	−18.8678	−	3.77538i	−0.667077	−	0.133480i
$801$	−15.5394	−	15.5394i	−0.549058	−	0.549058i
$802$	1.63826	+	1.43737i	0.0578488	+	0.0507554i
$803$	6.03220	−	10.4481i	0.212872	−	0.368705i
$804$	23.4132	−	30.4839i	0.825720	−	1.07509i
$805$			6.05283i			0.213334i
$806$	22.8057	+	23.3676i	0.803295	+	0.823090i
$807$		−	3.73211i		−	0.131376i
$808$	−29.6317	−	10.0812i	−1.04244	−	0.354655i
$809$	−6.74791	+	11.6877i	−0.237244	+	0.410918i	−0.959922	−	0.280266i	$-0.909577\pi$
$809$	−6.74791	+	11.6877i	−0.237244	+	0.410918i	0.722679	+	0.691184i	$0.242911\pi$
$810$	−13.2511	+	15.1030i	−0.465596	+	0.530667i
$811$	11.4250	+	11.4250i	0.401187	+	0.401187i	0.878651	−	0.477464i	$-0.158444\pi$
$811$	11.4250	+	11.4250i	0.401187	+	0.401187i	−0.477464	+	0.878651i	$0.658444\pi$
$812$	−25.4282	−	61.4682i	−0.892354	−	2.15711i
$813$	−11.3926	+	42.5177i	−0.399555	+	1.49116i
$814$	−1.89055	+	3.83146i	−0.0662637	+	0.134292i
$815$	9.62213	−	5.55534i	0.337048	−	0.194595i
$816$	0.331212	+	0.331816i	0.0115947	+	0.0116159i
$817$	−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	0.934081	+	0.357061i	$0.116221\pi$
$821$	8.70120	+	32.4733i	0.303674	+	1.13333i	−0.630407	+	0.776265i	$0.717112\pi$
$822$	−27.2676	−	5.43032i	−0.951067	−	0.189404i
$823$	9.30064	+	16.1092i	0.324200	+	0.561531i	0.981350	−	0.192229i	$-0.0615716\pi$
$823$	9.30064	+	16.1092i	0.324200	+	0.561531i	−0.657150	+	0.753760i	$0.728238\pi$
$824$	−10.6947	+	2.11970i	−0.372566	+	0.0738433i
$825$	−10.7614	−	2.88350i	−0.374663	−	0.100391i
$826$	3.74756	+	57.3769i	0.130394	+	1.99640i
$827$	1.07171	−	1.07171i	0.0372671	−	0.0372671i	−0.688228	−	0.725495i	$-0.741611\pi$
$827$	1.07171	−	1.07171i	0.0372671	−	0.0372671i	0.725495	+	0.688228i	$0.241611\pi$
$828$	−1.12378	+	2.70954i	−0.0390539	+	0.0941632i
$829$	26.0238	+	15.0248i	0.903844	+	0.521835i	0.878445	−	0.477843i	$-0.158581\pi$
$829$	26.0238	+	15.0248i	0.903844	+	0.521835i	0.0253987	+	0.999677i	$0.491914\pi$
$830$	9.77655	+	14.6389i	0.339349	+	0.508122i
$831$	−32.7396			−1.13573
$832$	−6.00328	+	28.2128i	−0.208126	+	0.978102i
$833$	−0.754520			−0.0261426
$834$	17.0457	+	25.5232i	0.590244	+	0.883798i
$835$	9.52214	+	5.49761i	0.329527	+	0.190253i
$836$	−2.67080	+	6.43958i	−0.0923715	+	0.222717i
$837$	15.3014	−	15.3014i	0.528895	−	0.528895i
$838$	2.22085	+	34.0023i	0.0767179	+	1.17459i
$839$	−36.0525	−	9.66025i	−1.24467	−	0.333509i	−0.424396	−	0.905477i	$-0.639514\pi$
$839$	−36.0525	−	9.66025i	−1.24467	−	0.333509i	−0.820276	+	0.571968i	$0.806180\pi$
$840$	−33.2495	+	6.59013i	−1.14722	+	0.227381i
$841$	−12.5042	−	21.6580i	−0.431180	−	0.746826i
$842$	31.0435	+	6.18229i	1.06983	+	0.213056i
$843$	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
$848$	12.4380	+	12.4607i	0.427122	+	0.427901i
$849$	−34.2413	+	19.7692i	−1.17516	+	0.678478i
$850$	−0.119121	+	0.241415i	−0.00408583	+	0.00828048i
$851$	−0.528908	+	1.97391i	−0.0181307	+	0.0676648i
$852$	−10.9245	−	26.4080i	−0.374266	−	0.904724i
$853$	−36.7666	−	36.7666i	−1.25887	−	1.25887i	−0.951635	−	0.307230i	$-0.900598\pi$
$853$	−36.7666	−	36.7666i	−1.25887	−	1.25887i	−0.307230	−	0.951635i	$-0.599402\pi$
$854$	−8.50565	+	9.69438i	−0.291057	+	0.331735i
$855$	1.95366	−	3.38384i	0.0668138	−	0.115725i
$856$	0.786210	+	0.267482i	0.0268721	+	0.00914233i
$857$			23.1948i			0.792319i	0.918182	+	0.396160i	$0.129657\pi$
$857$			23.1948i			0.792319i	−0.918182	+	0.396160i	$0.870343\pi$
$858$	−4.51851	+	16.0780i	−0.154259	+	0.548894i
$859$			53.8518i			1.83740i	0.394956	+	0.918700i	$0.370760\pi$
$859$			53.8518i			1.83740i	−0.394956	+	0.918700i	$0.629240\pi$
$860$	3.20449	−	4.17224i	0.109272	−	0.142272i
$861$	7.35986	−	12.7477i	0.250823	−	0.434439i
$862$	8.82437	+	7.74232i	0.300559	+	0.263705i
$863$	−23.1715	−	23.1715i	−0.788766	−	0.788766i	0.192526	−	0.981292i	$-0.438332\pi$
$863$	−23.1715	−	23.1715i	−0.788766	−	0.788766i	−0.981292	+	0.192526i	$0.938332\pi$
$864$	18.7446	+	3.75073i	0.637704	+	0.127603i
$865$	2.05786	−	7.68003i	0.0699693	−	0.261129i
$866$	−30.8791	−	15.2366i	−1.04931	−	0.517761i
$867$	−30.8290	+	17.7991i	−1.04701	+	0.604490i
$868$	57.4696	−	7.53939i	1.95065	−	0.255903i
$869$	−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
$874$	−0.651267	+	3.27025i	−0.0220294	+	0.110618i
$875$	−24.0367	−	41.6328i	−0.812590	−	1.40745i
$876$	32.0365	+	4.23253i	1.08241	+	0.143004i
$877$	−34.6168	−	9.27555i	−1.16893	−	0.313213i	−0.378401	−	0.925642i	$-0.623526\pi$
$877$	−34.6168	−	9.27555i	−1.16893	−	0.313213i	−0.790526	+	0.612429i	$0.790193\pi$
$878$	1.43054	−	0.0934355i	0.0482785	−	0.00315330i
$879$	−0.102099	+	0.102099i	−0.00344372	+	0.00344372i
$880$	−2.03998	−	7.64114i	−0.0687676	−	0.257583i
$881$	1.42362	+	0.821926i	0.0479629	+	0.0276914i	0.523790	−	0.851848i	$-0.324518\pi$
$881$	1.42362	+	0.821926i	0.0479629	+	0.0276914i	−0.475827	+	0.879539i	$0.657851\pi$
$882$	21.9849	−	14.6826i	0.740269	−	0.494388i
$883$	−15.1271			−0.509067			−0.254534	−	0.967064i	$-0.581922\pi$
$883$	−15.1271			−0.509067			−0.254534	+	0.967064i	$0.581922\pi$
$884$	0.359694	+	0.182960i	0.0120978	+	0.00615360i
$885$	23.7886			0.799646
$886$	46.0231	−	30.7365i	1.54618	−	1.03261i
$887$	3.23210	+	1.86605i	0.108523	+	0.0626559i	0.553279	−	0.832996i	$-0.313376\pi$
$887$	3.23210	+	1.86605i	0.108523	+	0.0626559i	−0.444756	+	0.895652i	$0.646710\pi$
$888$	−11.4190	−	0.756278i	−0.383196	−	0.0253790i
$889$	30.1952	−	30.1952i	1.01272	−	1.01272i
$890$	28.2796	−	1.84707i	0.947934	−	0.0619140i
$891$	16.9743	+	4.54825i	0.568660	+	0.152372i
$892$	−3.09555	+	23.4305i	−0.103647	+	0.784512i
$893$	−8.48388	−	14.6945i	−0.283902	−	0.491733i
$894$	6.04693	−	30.3638i	0.202240	−	1.01552i
$895$	−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
$900$	−1.22692	−	9.35230i	−0.0408973	−	0.311743i
$901$	0.213319	−	0.123160i	0.00710668	−	0.00410304i
$902$	3.07991	+	1.51971i	0.102550	+	0.0506009i
$903$	−5.10407	+	19.0487i	−0.169853	+	0.633899i
$904$	17.0265	+	19.4418i	0.566294	+	0.646625i
$905$	−4.49918	−	4.49918i	−0.149558	−	0.149558i
$906$	−12.1211	−	10.6348i	−0.402698	−	0.353319i
$907$	22.0895	−	38.2602i	0.733471	−	1.27041i	−0.221921	−	0.975065i	$-0.571233\pi$
$907$	22.0895	−	38.2602i	0.733471	−	1.27041i	0.955391	−	0.295344i	$-0.0954341\pi$
$908$	2.78599	+	2.13978i	0.0924563	+	0.0710111i
$909$		−	15.3432i		−	0.508903i
$910$	−25.4434	+	14.2797i	−0.843439	+	0.473368i
$911$			23.3467i			0.773510i	0.922182	+	0.386755i	$0.126404\pi$
$911$			23.3467i			0.773510i	−0.922182	+	0.386755i	$0.873596\pi$
$912$	−18.6733	−	0.0170146i	−0.618334	−	0.000563410i
$913$	7.69816	−	13.3336i	0.254772	−	0.441278i
$914$	22.3762	−	25.5034i	0.740138	−	0.843578i
$915$	3.77289	+	3.77289i	0.124728	+	0.124728i
$916$	18.4024	−	7.61271i	0.608033	−	0.251531i
$917$	−10.5852	+	39.5046i	−0.349555	+	1.30456i
$918$	0.118344	−	0.239839i	0.00390592	−	0.00791587i
$919$	36.7181	−	21.1992i	1.21122	−	0.699297i	0.248193	−	0.968710i	$-0.420163\pi$
$919$	36.7181	−	21.1992i	1.21122	−	0.699297i	0.963025	+	0.269413i	$0.0868298\pi$
$920$	−1.67076	−	3.39381i	−0.0550834	−	0.111891i
$921$	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
$926$	−2.31765	−	0.461559i	−0.0761628	−	0.0151678i
$927$	−2.67228	−	4.62852i	−0.0877691	−	0.152021i
$928$	31.2246	+	27.4462i	1.02500	+	0.900966i
$929$	−50.7606	−	13.6013i	−1.66540	−	0.446243i	−0.701537	−	0.712633i	$-0.747503\pi$
$929$	−50.7606	−	13.6013i	−1.66540	−	0.446243i	−0.963865	+	0.266390i	$0.914169\pi$
$930$	−1.56292	−	23.9291i	−0.0512503	−	0.784668i
$931$	21.2500	−	21.2500i	0.696442	−	0.696442i
$932$	−39.3877	−	16.3360i	−1.29019	−	0.535102i
$933$	−47.5179	−	27.4345i	−1.55567	−	0.898165i
$934$	19.6167	+	29.3730i	0.641879	+	0.961113i
$935$	−0.110649			−0.00361860
$936$	−14.0409	+	1.66845i	−0.458941	+	0.0545351i
$937$	−36.4769			−1.19165			−0.595824	−	0.803115i	$-0.703175\pi$
$937$	−36.4769			−1.19165			−0.595824	+	0.803115i	$0.703175\pi$
$938$	−32.6186	−	48.8412i	−1.06503	−	1.59472i
$939$	45.0706	+	26.0215i	1.47082	+	0.849181i
$940$	17.7805	+	7.37440i	0.579934	+	0.240526i
$941$	−15.2238	+	15.2238i	−0.496283	+	0.496283i	−0.910279	−	0.413996i	$-0.864133\pi$
$941$	−15.2238	+	15.2238i	−0.496283	+	0.496283i	0.413996	+	0.910279i	$0.364133\pi$
$942$	−1.69276	−	25.9170i	−0.0551531	−	0.844420i
$943$	1.58672	+	0.425162i	0.0516709	+	0.0138452i
$944$	−17.9390	−	31.1367i	−0.583864	−	1.01341i
$945$	9.66817	+	16.7458i	0.314506	+	0.544740i
$946$	−4.51264	−	0.898689i	−0.146719	−	0.0292189i
$947$	4.47717	+	16.7090i	0.145488	+	0.542970i	0.999733	+	0.0230991i	$0.00735331\pi$
$947$	4.47717	+	16.7090i	0.145488	+	0.542970i	−0.854245	+	0.519871i	$0.825980\pi$
$948$	−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
$952$	0.642705	−	0.316401i	0.0208302	−	0.0102546i
$953$	13.3736	−	7.72124i	0.433213	−	0.250115i	−0.267502	−	0.963557i	$-0.586198\pi$
$953$	13.3736	−	7.72124i	0.433213	−	0.250115i	0.700714	+	0.713442i	$0.252865\pi$
$954$	−3.81896	+	7.73964i	−0.123643	+	0.250580i
$955$	−6.26207	+	23.3704i	−0.202636	+	0.756247i
$956$	−39.6157	+	16.3882i	−1.28126	+	0.530033i
$957$	17.0203	+	17.0203i	0.550190	+	0.550190i
$958$	−29.2069	+	33.2888i	−0.943633	+	1.07551i
$959$	−21.2413	+	36.7910i	−0.685917	+	1.18804i
$960$	16.8239	−	12.8729i	0.542989	−	0.415472i
$961$			10.0056i			0.322760i
$962$	−9.54522	+	2.43352i	−0.307750	+	0.0784599i
$963$			0.407098i			0.0131186i
$964$	31.8319	+	24.4485i	1.02524	+	0.787434i
$965$	−6.03293	+	10.4493i	−0.194207	+	0.336376i
$966$	10.6590	+	9.35197i	0.342947	+	0.300895i
$967$	9.02312	+	9.02312i	0.290164	+	0.290164i	0.837145	−	0.546981i	$-0.184223\pi$
$967$	9.02312	+	9.02312i	0.290164	+	0.290164i	−0.546981	+	0.837145i	$0.684223\pi$
$968$	18.2020	−	15.9408i	0.585035	−	0.512355i
$969$	−0.0676167	+	0.252349i	−0.00217216	+	0.00810661i
$970$	0.731597	+	0.360991i	0.0234902	+	0.0115907i
$971$	23.2558	−	13.4267i	0.746314	−	0.430884i	−0.0780468	−	0.996950i	$-0.524868\pi$
$971$	23.2558	−	13.4267i	0.746314	−	0.430884i	0.824360	+	0.566065i	$0.191535\pi$
$972$	3.48525	+	26.5666i	0.111789	+	0.852125i
$973$	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	−0.967181	−	0.254087i	$-0.918225\pi$
$977$	−8.02121	−	29.9356i	−0.256621	−	0.957724i	0.710560	−	0.703637i	$-0.248442\pi$
$978$	5.08384	−	25.5278i	0.162563	−	0.816289i
$979$	−12.3934	−	21.4660i	−0.396094	−	0.686055i
$980$	−4.46537	+	33.7988i	−0.142641	+	1.07966i
$981$	−2.18359	−	0.585090i	−0.0697165	−	0.0186805i
$982$	−15.8294	+	1.03389i	−0.505137	+	0.0329929i
$983$	15.4374	−	15.4374i	0.492377	−	0.492377i	−0.416677	−	0.909055i	$-0.636805\pi$
$983$	15.4374	−	15.4374i	0.492377	−	0.492377i	0.909055	+	0.416677i	$0.136805\pi$
$984$	−0.607932	+	9.17913i	−0.0193802	+	0.292620i
$985$	1.16903	+	0.674942i	0.0372485	+	0.0215054i
$986$	0.483677	−	0.323023i	0.0154034	−	0.0102872i
$987$	−72.1565			−2.29677
$988$	−15.2831	+	4.97747i	−0.486220	+	0.158354i
$989$	−2.20079			−0.0699811
$990$	3.22403	−	2.15317i	0.102466	−	0.0684321i
$991$	−11.3554	−	6.55602i	−0.360715	−	0.208259i	0.308679	−	0.951166i	$-0.400113\pi$
$991$	−11.3554	−	6.55602i	−0.360715	−	0.208259i	−0.669394	+	0.742907i	$0.733446\pi$
$992$	−30.1421	+	20.0907i	−0.957011	+	0.637879i
$993$	−28.2543	+	28.2543i	−0.896624	+	0.896624i
$994$	−43.5745	+	2.84605i	−1.38210	+	0.0902714i
$995$	−13.8327	−	3.70646i	−0.438526	−	0.117503i
$996$	40.8842	+	5.40146i	1.29547	+	0.171152i
$997$	−6.93112	−	12.0050i	−0.219511	−	0.380204i	0.735148	−	0.677907i	$-0.237113\pi$
$997$	−6.93112	−	12.0050i	−0.219511	−	0.380204i	−0.954658	+	0.297703i	$0.903779\pi$
$998$	−2.68675	+	13.4912i	−0.0850477	+	0.427055i
$999$	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.19.2	yes	16
3.2	odd	2		468.2.cb.f.19.3		16
4.3	odd	2	inner	52.2.l.b.19.3	yes	16
8.3	odd	2		832.2.bu.n.383.4		16
8.5	even	2		832.2.bu.n.383.1		16
12.11	even	2		468.2.cb.f.19.2		16
13.2	odd	12		676.2.l.k.427.2		16
13.3	even	3		676.2.l.m.587.4		16
13.4	even	6		676.2.f.i.239.5		16
13.5	odd	4		676.2.l.i.319.2		16
13.6	odd	12		676.2.f.i.99.7		16
13.7	odd	12		676.2.f.h.99.2		16
13.8	odd	4		676.2.l.m.319.3		16
13.9	even	3		676.2.f.h.239.4		16
13.10	even	6		676.2.l.i.587.1		16
13.11	odd	12	inner	52.2.l.b.11.3	yes	16
13.12	even	2		676.2.l.k.19.3		16
39.11	even	12		468.2.cb.f.271.2		16
52.3	odd	6		676.2.l.m.587.3		16
52.7	even	12		676.2.f.h.99.4		16
52.11	even	12	inner	52.2.l.b.11.2	✓	16
52.15	even	12		676.2.l.k.427.3		16
52.19	even	12		676.2.f.i.99.5		16
52.23	odd	6		676.2.l.i.587.2		16
52.31	even	4		676.2.l.i.319.1		16
52.35	odd	6		676.2.f.h.239.2		16
52.43	odd	6		676.2.f.i.239.7		16
52.47	even	4		676.2.l.m.319.4		16
52.51	odd	2		676.2.l.k.19.2		16
104.11	even	12		832.2.bu.n.63.1		16
104.37	odd	12		832.2.bu.n.63.4		16
156.11	odd	12		468.2.cb.f.271.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.l.b.11.2	✓	16	52.11	even	12	inner
52.2.l.b.11.3	yes	16	13.11	odd	12	inner
52.2.l.b.19.2	yes	16	1.1	even	1	trivial
52.2.l.b.19.3	yes	16	4.3	odd	2	inner
468.2.cb.f.19.2		16	12.11	even	2
468.2.cb.f.19.3		16	3.2	odd	2
468.2.cb.f.271.2		16	39.11	even	12
468.2.cb.f.271.3		16	156.11	odd	12
676.2.f.h.99.2		16	13.7	odd	12
676.2.f.h.99.4		16	52.7	even	12
676.2.f.h.239.2		16	52.35	odd	6
676.2.f.h.239.4		16	13.9	even	3
676.2.f.i.99.5		16	52.19	even	12
676.2.f.i.99.7		16	13.6	odd	12
676.2.f.i.239.5		16	13.4	even	6
676.2.f.i.239.7		16	52.43	odd	6
676.2.l.i.319.1		16	52.31	even	4
676.2.l.i.319.2		16	13.5	odd	4
676.2.l.i.587.1		16	13.10	even	6
676.2.l.i.587.2		16	52.23	odd	6
676.2.l.k.19.2		16	52.51	odd	2
676.2.l.k.19.3		16	13.12	even	2
676.2.l.k.427.2		16	13.2	odd	12
676.2.l.k.427.3		16	52.15	even	12
676.2.l.m.319.3		16	13.8	odd	4
676.2.l.m.319.4		16	52.47	even	4
676.2.l.m.587.3		16	52.3	odd	6
676.2.l.m.587.4		16	13.3	even	3
832.2.bu.n.63.1		16	104.11	even	12
832.2.bu.n.63.4		16	104.37	odd	12
832.2.bu.n.383.1		16	8.5	even	2
832.2.bu.n.383.4		16	8.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.785427 - 1.17605i) q^{2} +(1.81380 + 1.04720i) q^{3} +(-0.766209 + 1.84741i) q^{4} +(0.894007 - 0.894007i) q^{5} +(-0.193046 - 2.95563i) q^{6} +(-4.37156 - 1.17136i) q^{7} +(2.77446 - 0.549903i) q^{8} +(0.693255 + 1.20075i) q^{9} +O(q^{10})\)	\(q+(-0.785427 - 1.17605i) q^{2} +(1.81380 + 1.04720i) q^{3} +(-0.766209 + 1.84741i) q^{4} +(0.894007 - 0.894007i) q^{5} +(-0.193046 - 2.95563i) q^{6} +(-4.37156 - 1.17136i) q^{7} +(2.77446 - 0.549903i) q^{8} +(0.693255 + 1.20075i) q^{9} +(-1.75358 - 0.349224i) 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} +(-2.82585 - 2.83100i) q^{16} +(-0.0484649 + 0.0279812i) q^{17} +(0.867649 - 1.75841i) q^{18} +(0.576896 - 2.15300i) q^{19} +(0.966601 + 2.33659i) q^{20} +(-6.70250 - 6.70250i) q^{21} +(1.45859 - 1.66244i) q^{22} +(0.528908 - 0.916096i) q^{23} +(5.60818 + 1.90799i) q^{24} +3.40150i q^{25} +(5.09864 + 0.0620559i) q^{26} -3.37929i q^{27} +(5.51350 - 7.17856i) q^{28} +(3.67452 - 6.36446i) q^{29} +(-2.81494 - 2.46977i) q^{30} +(4.52800 + 4.52800i) q^{31} +(-1.10992 + 5.54690i) q^{32} +(-0.847713 + 3.16371i) q^{33} +(0.0709732 + 0.0350202i) q^{34} +(-4.95540 + 2.86100i) q^{35} +(-2.74946 + 0.360699i) 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} +(-2.61818 + 13.1468i) q^{42} +(-1.04025 - 1.80177i) q^{43} +(-3.10074 - 0.409658i) q^{44} +(1.69325 + 0.453706i) q^{45} +(-1.49280 + 0.0975016i) q^{46} +(5.38281 - 5.38281i) q^{47} +(-2.16091 - 8.09411i) q^{48} +(11.6763 + 6.74130i) q^{49} +(4.00035 - 2.67163i) q^{50} -0.117208 q^{51} +(-3.93163 - 6.04502i) q^{52} -4.40150 q^{53} +(-3.97423 + 2.65419i) q^{54} +(1.71230 + 0.988596i) q^{55} +(-12.7728 - 0.845942i) q^{56} +(3.30100 - 3.30100i) q^{57} +(-10.3710 + 0.677380i) q^{58} +(8.67757 + 2.32515i) q^{59} +(-0.693654 + 5.25034i) q^{60} +(1.00750 + 1.74504i) q^{61} +(1.76876 - 8.88159i) 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} +(-0.0145586 - 0.110974i) q^{68} +(1.91867 - 1.10774i) q^{69} +(7.25680 + 3.58071i) q^{70} +(-1.76582 + 6.59011i) q^{71} +(2.58370 + 2.95021i) q^{72} +(-5.45504 - 5.45504i) q^{73} +(2.05365 + 1.80183i) q^{74} +(-3.56205 + 6.16966i) q^{75} +(3.53546 + 2.71541i) q^{76} -7.07759i q^{77} +(9.18295 + 5.45185i) q^{78} +8.87422i q^{79} +(-5.05726 - 0.00460805i) q^{80} +(5.61856 - 9.73163i) q^{81} +(1.44840 - 1.65082i) q^{82} +(-6.96160 - 6.96160i) q^{83} +(17.5178 - 7.24676i) q^{84} +(-0.0183126 + 0.0683434i) q^{85} +(-1.30194 + 2.63855i) q^{86} +(13.3297 - 7.69592i) q^{87} +(1.95363 + 3.96840i) 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} +(-10.5583 - 2.10267i) q^{94} +(-1.40905 - 2.44055i) q^{95} +(-7.82188 + 8.89868i) q^{96} +(-0.440720 - 0.118091i) q^{97} +(-1.24273 - 19.0267i) 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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